LMFDB - Embedded newform 72.7.m.a.41.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,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, 7, names="a")

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

chi := DirichletCharacter("72.41");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
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:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.18
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(26.9914 - 0.680128i) q^{3} +(158.588 + 91.5607i) q^{5} +(99.1040 + 171.653i) q^{7} +(728.075 - 36.7153i) q^{9} +O(q^{10})$	\(q+(26.9914 - 0.680128i) q^{3} +(158.588 + 91.5607i) q^{5} +(99.1040 + 171.653i) q^{7} +(728.075 - 36.7153i) q^{9} +(-759.234 + 438.344i) q^{11} +(-1074.15 + 1860.48i) q^{13} +(4342.79 + 2363.49i) q^{15} -5777.45i q^{17} -2650.82 q^{19} +(2791.71 + 4565.76i) q^{21} +(8158.04 + 4710.04i) q^{23} +(8954.23 + 15509.2i) q^{25} +(19626.8 - 1486.18i) q^{27} +(-8037.81 + 4640.63i) q^{29} +(3182.61 - 5512.44i) q^{31} +(-20194.7 + 12347.9i) q^{33} +36296.1i q^{35} +97410.1 q^{37} +(-27727.4 + 50947.5i) q^{39} +(92695.0 + 53517.5i) q^{41} +(-50935.0 - 88221.9i) q^{43} +(118825. + 60840.5i) q^{45} +(-145714. + 84127.8i) q^{47} +(39181.3 - 67864.0i) q^{49} +(-3929.40 - 155942. i) q^{51} -116314. i q^{53} -160540. q^{55} +(-71549.5 + 1802.90i) q^{57} +(-307446. - 177504. i) q^{59} +(-112775. - 195332. i) q^{61} +(78457.4 + 121338. i) q^{63} +(-340693. + 196699. i) q^{65} +(104218. - 180510. i) q^{67} +(223400. + 121582. i) q^{69} -504622. i q^{71} -83724.5 q^{73} +(252236. + 412525. i) q^{75} +(-150486. - 86883.3i) q^{77} +(31420.8 + 54422.4i) q^{79} +(528745. - 53462.9i) q^{81} +(-421194. + 243176. i) q^{83} +(528987. - 916233. i) q^{85} +(-213796. + 130724. i) q^{87} +1.22749e6i q^{89} -425809. q^{91} +(82154.0 - 150953. i) q^{93} +(-420388. - 242711. i) q^{95} +(-598663. - 1.03691e6i) q^{97} +(-536685. + 347023. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * 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
$3$	26.9914	−	0.680128i	0.999683	−	0.0251899i
$3$	26.9914	−	0.680128i	0.999683	−	0.0251899i
$4$		0			0
$5$	158.588	+	91.5607i	1.26870	+	0.732486i	0.974742	−	0.223332i	$-0.0716934\pi$
$5$	158.588	+	91.5607i	1.26870	+	0.732486i	0.293960	+	0.955818i	$0.405027\pi$
$6$		0			0
$7$	99.1040	+	171.653i	0.288933	+	0.500447i	0.973555	−	0.228451i	$-0.0733662\pi$
$7$	99.1040	+	171.653i	0.288933	+	0.500447i	−0.684622	+	0.728898i	$0.740033\pi$
$8$		0			0
$9$	728.075	−	36.7153i	0.998731	−	0.0503639i
$10$		0			0
$11$	−759.234	+	438.344i	−0.570424	+	0.329334i	−0.757318	−	0.653046i	$-0.773491\pi$
$11$	−759.234	+	438.344i	−0.570424	+	0.329334i	0.186895	+	0.982380i	$0.440158\pi$
$12$		0			0
$13$	−1074.15	+	1860.48i	−0.488915	+	0.846826i	−0.999919	−	0.0127529i	$-0.995941\pi$
$13$	−1074.15	+	1860.48i	−0.488915	+	0.846826i	0.511004	+	0.859579i	$0.329274\pi$
$14$		0			0
$15$	4342.79	+	2363.49i	1.28675	+	0.700295i
$16$		0			0
$17$		−	5777.45i		−	1.17595i	−0.808879	−	0.587976i	$-0.799925\pi$
$17$		−	5777.45i		−	1.17595i	0.808879	−	0.587976i	$-0.200075\pi$
$18$		0			0
$19$	−2650.82			−0.386474			−0.193237	−	0.981152i	$-0.561899\pi$
$19$	−2650.82			−0.386474			−0.193237	+	0.981152i	$0.561899\pi$
$20$		0			0
$21$	2791.71	+	4565.76i	0.301448	+	0.493010i
$22$		0			0
$23$	8158.04	+	4710.04i	0.670505	+	0.387116i	0.796268	−	0.604944i	$-0.206805\pi$
$23$	8158.04	+	4710.04i	0.670505	+	0.387116i	−0.125763	+	0.992060i	$0.540138\pi$
$24$		0			0
$25$	8954.23	+	15509.2i	0.573071	+	0.992588i
$26$		0			0
$27$	19626.8	−	1486.18i	0.997145	−	0.0755058i
$28$		0			0
$29$	−8037.81	+	4640.63i	−0.329567	+	0.190276i	−0.655649	−	0.755066i	$-0.727605\pi$
$29$	−8037.81	+	4640.63i	−0.329567	+	0.190276i	0.326082	+	0.945342i	$0.394272\pi$
$30$		0			0
$31$	3182.61	−	5512.44i	0.106831	−	0.185037i	−0.807654	−	0.589657i	$-0.799263\pi$
$31$	3182.61	−	5512.44i	0.106831	−	0.185037i	0.914485	+	0.404620i	$0.132596\pi$
$32$		0			0
$33$	−20194.7	+	12347.9i	−0.561947	+	0.343599i
$34$		0			0
$35$			36296.1i			0.846557i
$36$		0			0
$37$	97410.1			1.92309			0.961543	−	0.274654i	$-0.0885632\pi$
$37$	97410.1			1.92309			0.961543	+	0.274654i	$0.0885632\pi$
$38$		0			0
$39$	−27727.4	+	50947.5i	−0.467428	+	0.858873i
$40$		0			0
$41$	92695.0	+	53517.5i	1.34495	+	0.776505i	0.987529	−	0.157440i	$-0.0503240\pi$
$41$	92695.0	+	53517.5i	1.34495	+	0.776505i	0.357418	+	0.933945i	$0.383657\pi$
$42$		0			0
$43$	−50935.0	−	88221.9i	−0.640635	−	1.10961i	−0.985291	−	0.170883i	$-0.945338\pi$
$43$	−50935.0	−	88221.9i	−0.640635	−	1.10961i	0.344656	−	0.938729i	$-0.387995\pi$
$44$		0			0
$45$	118825.	+	60840.5i	1.30398	+	0.667659i
$46$		0			0
$47$	−145714.	+	84127.8i	−1.40348	+	0.810301i	−0.994748	−	0.102353i	$-0.967363\pi$
$47$	−145714.	+	84127.8i	−1.40348	+	0.810301i	−0.408734	+	0.912654i	$0.634029\pi$
$48$		0			0
$49$	39181.3	−	67864.0i	0.333035	−	0.576834i
$50$		0			0
$51$	−3929.40	−	155942.i	−0.0296221	−	1.17558i
$52$		0			0
$53$		−	116314.i		−	0.781276i	−0.920544	−	0.390638i	$-0.872254\pi$
$53$		−	116314.i		−	0.781276i	0.920544	−	0.390638i	$-0.127746\pi$
$54$		0			0
$55$	−160540.			−0.964930
$56$		0			0
$57$	−71549.5	+	1802.90i	−0.386351	+	0.00973524i
$58$		0			0
$59$	−307446.	−	177504.i	−1.49697	−	0.864275i	−0.496974	−	0.867765i	$-0.665556\pi$
$59$	−307446.	−	177504.i	−1.49697	−	0.864275i	−0.999994	+	0.00349063i	$0.998889\pi$
$60$		0			0
$61$	−112775.	−	195332.i	−0.496847	−	0.860564i	0.503146	−	0.864201i	$-0.332176\pi$
$61$	−112775.	−	195332.i	−0.496847	−	0.860564i	−0.999993	+	0.00363701i	$0.998842\pi$
$62$		0			0
$63$	78457.4	+	121338.i	0.313771	+	0.485260i
$64$		0			0
$65$	−340693.	+	196699.i	−1.24058	+	0.716247i
$66$		0			0
$67$	104218.	−	180510.i	0.346511	−	0.600174i	−0.639116	−	0.769110i	$-0.720700\pi$
$67$	104218.	−	180510.i	0.346511	−	0.600174i	0.985627	+	0.168936i	$0.0540331\pi$
$68$		0			0
$69$	223400.	+	121582.i	0.680044	+	0.370103i
$70$		0			0
$71$		−	504622.i		−	1.40991i	−0.709253	−	0.704954i	$-0.750967\pi$
$71$		−	504622.i		−	1.40991i	0.709253	−	0.704954i	$-0.249033\pi$
$72$		0			0
$73$	−83724.5			−0.215221			−0.107610	−	0.994193i	$-0.534320\pi$
$73$	−83724.5			−0.215221			−0.107610	+	0.994193i	$0.534320\pi$
$74$		0			0
$75$	252236.	+	412525.i	0.597892	+	0.977837i
$76$		0			0
$77$	−150486.	−	86883.3i	−0.329628	−	0.190311i
$78$		0			0
$79$	31420.8	+	54422.4i	0.0637289	+	0.110382i	0.896129	−	0.443793i	$-0.146367\pi$
$79$	31420.8	+	54422.4i	0.0637289	+	0.110382i	−0.832401	+	0.554174i	$0.813034\pi$
$80$		0			0
$81$	528745.	−	53462.9i	0.994927	−	0.100600i
$82$		0			0
$83$	−421194.	+	243176.i	−0.736627	+	0.425292i	−0.820842	−	0.571156i	$-0.806495\pi$
$83$	−421194.	+	243176.i	−0.736627	+	0.425292i	0.0842144	+	0.996448i	$0.473162\pi$
$84$		0			0
$85$	528987.	−	916233.i	0.861367	−	1.49193i
$86$		0			0
$87$	−213796.	+	130724.i	−0.324670	+	0.198517i
$88$		0			0
$89$			1.22749e6i			1.74120i	0.491991	+	0.870600i	$0.336269\pi$
$89$			1.22749e6i			1.74120i	−0.491991	+	0.870600i	$0.663731\pi$
$90$		0			0
$91$	−425809.			−0.565055
$92$		0			0
$93$	82154.0	−	150953.i	0.102136	−	0.187669i
$94$		0			0
$95$	−420388.	−	242711.i	−0.490320	−	0.283086i
$96$		0			0
$97$	−598663.	−	1.03691e6i	−0.655945	−	1.13613i	−0.981656	−	0.190660i	$-0.938937\pi$
$97$	−598663.	−	1.03691e6i	−0.655945	−	1.13613i	0.325711	−	0.945469i	$-0.394396\pi$
$98$		0			0
$99$	−536685.	+	347023.i	−0.553113	+	0.357645i
$100$		0			0
$101$	−754493.	+	435607.i	−0.732303	+	0.422796i	−0.819264	−	0.573416i	$-0.805618\pi$
$101$	−754493.	+	435607.i	−0.732303	+	0.422796i	0.0869609	+	0.996212i	$0.472284\pi$
$102$		0			0
$103$	882865.	−	1.52917e6i	0.807947	−	1.39940i	−0.106337	−	0.994330i	$-0.533912\pi$
$103$	882865.	−	1.52917e6i	0.807947	−	1.39940i	0.914284	−	0.405074i	$-0.132754\pi$
$104$		0			0
$105$	24686.0	+	979685.i	0.0213247	+	0.846289i
$106$		0			0
$107$			1.44072e6i			1.17605i	0.808841	+	0.588027i	$0.200095\pi$
$107$			1.44072e6i			1.17605i	−0.808841	+	0.588027i	$0.799905\pi$
$108$		0			0
$109$	2.41497e6			1.86480			0.932399	−	0.361431i	$-0.117712\pi$
$109$	2.41497e6			1.86480			0.932399	+	0.361431i	$0.117712\pi$
$110$		0			0
$111$	2.62924e6	−	66251.3i	1.92248	−	0.0484424i
$112$		0			0
$113$	224801.	+	129789.i	0.155798	+	0.0899501i	0.575872	−	0.817540i	$-0.304663\pi$
$113$	224801.	+	129789.i	0.155798	+	0.0899501i	−0.420074	+	0.907490i	$0.637996\pi$
$114$		0			0
$115$	862510.	+	1.49391e6i	0.567114	+	0.982271i
$116$		0			0
$117$	−713751.	+	1.39400e6i	−0.445645	+	0.870375i
$118$		0			0
$119$	991717.	−	572568.i	0.588501	−	0.339771i
$120$		0			0
$121$	−501490.	+	868606.i	−0.283078	+	0.490306i
$122$		0			0
$123$	2.53837e6	+	1.38147e6i	1.36408	+	0.742380i
$124$		0			0
$125$			418151.i			0.214093i
$126$		0			0
$127$	−2.12837e6			−1.03905			−0.519525	−	0.854455i	$-0.673891\pi$
$127$	−2.12837e6			−1.03905			−0.519525	+	0.854455i	$0.673891\pi$
$128$		0			0
$129$	−1.43481e6	−	2.34659e6i	−0.668383	−	1.09312i
$130$		0			0
$131$	−1.87964e6	−	1.08521e6i	−0.836103	−	0.482724i	0.0198347	−	0.999803i	$-0.493686\pi$
$131$	−1.87964e6	−	1.08521e6i	−0.836103	−	0.482724i	−0.855938	+	0.517079i	$0.827019\pi$
$132$		0			0
$133$	−262707.	−	455022.i	−0.111665	−	0.193409i
$134$		0			0
$135$	3.24865e6	+	1.56135e6i	1.32039	+	0.634600i
$136$		0			0
$137$	1.15769e6	−	668392.i	0.450226	−	0.259938i	−0.257700	−	0.966225i	$-0.582965\pi$
$137$	1.15769e6	−	668392.i	0.450226	−	0.259938i	0.707926	+	0.706287i	$0.249631\pi$
$138$		0			0
$139$	−836231.	+	1.44840e6i	−0.311374	+	0.539315i	−0.978660	−	0.205486i	$-0.934122\pi$
$139$	−836231.	+	1.44840e6i	−0.311374	+	0.539315i	0.667286	+	0.744801i	$0.267456\pi$
$140$		0			0
$141$	−3.87580e6	+	2.36983e6i	−1.38262	+	0.845397i
$142$		0			0
$143$		−	1.88338e6i		−	0.644066i
$144$		0			0
$145$	−1.69960e6			−0.557497
$146$		0			0
$147$	1.01140e6	−	1.85839e6i	0.318399	−	0.585040i
$148$		0			0
$149$	−2.82032e6	−	1.62831e6i	−0.852588	−	0.492242i	0.00893551	−	0.999960i	$-0.497156\pi$
$149$	−2.82032e6	−	1.62831e6i	−0.852588	−	0.492242i	−0.861523	+	0.507718i	$0.830489\pi$
$150$		0			0
$151$	945927.	+	1.63839e6i	0.274743	+	0.475869i	0.970070	−	0.242824i	$-0.0780738\pi$
$151$	945927.	+	1.63839e6i	0.274743	+	0.475869i	−0.695327	+	0.718693i	$0.744741\pi$
$152$		0			0
$153$	−212120.	−	4.20641e6i	−0.0592254	−	1.17446i
$154$		0			0
$155$	1.00945e6	−	582804.i	0.271074	−	0.156505i
$156$		0			0
$157$	2.86613e6	−	4.96428e6i	0.740622	−	1.28280i	−0.211590	−	0.977358i	$-0.567864\pi$
$157$	2.86613e6	−	4.96428e6i	0.740622	−	1.28280i	0.952212	−	0.305437i	$-0.0988025\pi$
$158$		0			0
$159$	−79108.4	−	3.13948e6i	−0.0196803	−	0.781028i
$160$		0			0
$161$			1.86714e6i			0.447403i
$162$		0			0
$163$	−4.05001e6			−0.935175			−0.467587	−	0.883947i	$-0.654877\pi$
$163$	−4.05001e6			−0.935175			−0.467587	+	0.883947i	$0.654877\pi$
$164$		0			0
$165$	−4.33321e6	+	109188.i	−0.964624	+	0.0243065i
$166$		0			0
$167$	1.24508e6	+	718847.i	0.267330	+	0.154343i	0.627674	−	0.778477i	$-0.284007\pi$
$167$	1.24508e6	+	718847.i	0.267330	+	0.154343i	−0.360344	+	0.932820i	$0.617341\pi$
$168$		0			0
$169$	105824.	+	183293.i	0.0219243	+	0.0379739i
$170$		0			0
$171$	−1.93000e6	+	97325.6i	−0.385983	+	0.0194643i
$172$		0			0
$173$	−2.15519e6	+	1.24430e6i	−0.416243	+	0.240318i	−0.693469	−	0.720487i	$-0.743918\pi$
$173$	−2.15519e6	+	1.24430e6i	−0.416243	+	0.240318i	0.277226	+	0.960805i	$0.410585\pi$
$174$		0			0
$175$	−1.77480e6	+	3.07404e6i	−0.331158	+	0.573583i
$176$		0			0
$177$	−8.41913e6	−	4.58198e6i	−1.51826	−	0.826292i
$178$		0			0
$179$		−	7.42678e6i		−	1.29492i	−0.762101	−	0.647458i	$-0.775832\pi$
$179$		−	7.42678e6i		−	1.29492i	0.762101	−	0.647458i	$-0.224168\pi$
$180$		0			0
$181$	−4.39649e6			−0.741430			−0.370715	−	0.928747i	$-0.620887\pi$
$181$	−4.39649e6			−0.741430			−0.370715	+	0.928747i	$0.620887\pi$
$182$		0			0
$183$	−3.17680e6	−	5.19558e6i	−0.518367	−	0.847776i
$184$		0			0
$185$	1.54481e7	+	8.91894e6i	2.43982	+	1.40863i
$186$		0			0
$187$	2.53251e6	+	4.38643e6i	0.387281	+	0.670790i
$188$		0			0
$189$	2.20020e6	+	3.22172e6i	0.325895	+	0.477202i
$190$		0			0
$191$	4.15768e6	−	2.40044e6i	0.596693	−	0.344501i	−0.171046	−	0.985263i	$-0.554715\pi$
$191$	4.15768e6	−	2.40044e6i	0.596693	−	0.344501i	0.767740	+	0.640762i	$0.221381\pi$
$192$		0			0
$193$	3.29608e6	−	5.70898e6i	0.458486	−	0.794121i	−0.540395	−	0.841411i	$-0.681725\pi$
$193$	3.29608e6	−	5.70898e6i	0.458486	−	0.794121i	0.998881	+	0.0472902i	$0.0150585\pi$
$194$		0			0
$195$	−9.06201e6	+	5.54091e6i	−1.22214	+	0.747269i
$196$		0			0
$197$			2.39406e6i			0.313138i	0.987667	+	0.156569i	$0.0500433\pi$
$197$			2.39406e6i			0.313138i	−0.987667	+	0.156569i	$0.949957\pi$
$198$		0			0
$199$	573407.			0.0727619			0.0363809	−	0.999338i	$-0.488417\pi$
$199$	573407.			0.0727619			0.0363809	+	0.999338i	$0.488417\pi$
$200$		0			0
$201$	2.69021e6	−	4.94311e6i	0.331283	−	0.608712i
$202$		0			0
$203$	−1.59316e6	−	919811.i	−0.190446	−	0.109954i
$204$		0			0
$205$	9.80020e6	+	1.69744e7i	1.13756	+	1.97031i
$206$		0			0
$207$	6.11259e6	+	3.12974e6i	0.689151	+	0.352856i
$208$		0			0
$209$	2.01259e6	−	1.16197e6i	0.220454	−	0.127279i
$210$		0			0
$211$	−7.97149e6	+	1.38070e7i	−0.848579	+	1.46978i	0.0338972	+	0.999425i	$0.489208\pi$
$211$	−7.97149e6	+	1.38070e7i	−0.848579	+	1.46978i	−0.882476	+	0.470357i	$0.844125\pi$
$212$		0			0
$213$	−343207.	−	1.36205e7i	−0.0355155	−	1.40946i
$214$		0			0
$215$		−	1.86546e7i		−	1.87702i
$216$		0			0
$217$	1.26164e6			0.123468
$218$		0			0
$219$	−2.25984e6	+	56943.3i	−0.215152	+	0.00542139i
$220$		0			0
$221$	1.07488e7	+	6.20582e6i	0.995825	+	0.574940i
$222$		0			0
$223$	5.01011e6	+	8.67777e6i	0.451786	+	0.782516i	0.998497	−	0.0548049i	$-0.0174537\pi$
$223$	5.01011e6	+	8.67777e6i	0.451786	+	0.782516i	−0.546711	+	0.837321i	$0.684120\pi$
$224$		0			0
$225$	7.08877e6	+	1.09631e7i	0.622334	+	0.962466i
$226$		0			0
$227$	−340619.	+	196656.i	−0.0291200	+	0.0168124i	−0.514489	−	0.857497i	$-0.672018\pi$
$227$	−340619.	+	196656.i	−0.0291200	+	0.0168124i	0.485369	+	0.874309i	$0.338685\pi$
$228$		0			0
$229$	2.51815e6	−	4.36156e6i	0.209689	−	0.363192i	−0.741928	−	0.670480i	$-0.766088\pi$
$229$	2.51815e6	−	4.36156e6i	0.209689	−	0.363192i	0.951616	+	0.307288i	$0.0994216\pi$
$230$		0			0
$231$	−4.12093e6	−	2.24275e6i	−0.334318	−	0.181947i
$232$		0			0
$233$			1.08218e6i			0.0855522i	0.999085	+	0.0427761i	$0.0136202\pi$
$233$			1.08218e6i			0.0855522i	−0.999085	+	0.0427761i	$0.986380\pi$
$234$		0			0
$235$	−3.08112e7			−2.37413
$236$		0			0
$237$	885107.	+	1.44757e6i	0.0664891	+	0.108741i
$238$		0			0
$239$	−2.04795e6	−	1.18238e6i	−0.150012	−	0.0866094i	0.423115	−	0.906076i	$-0.360937\pi$
$239$	−2.04795e6	−	1.18238e6i	−0.150012	−	0.0866094i	−0.573127	+	0.819466i	$0.694270\pi$
$240$		0			0
$241$	4.56342e6	+	7.90408e6i	0.326017	+	0.564677i	0.981718	−	0.190343i	$-0.0609601\pi$
$241$	4.56342e6	+	7.90408e6i	0.326017	+	0.564677i	−0.655701	+	0.755021i	$0.727627\pi$
$242$		0			0
$243$	1.42352e7	−	1.80265e6i	0.992077	−	0.125630i
$244$		0			0
$245$	1.24273e7	−	7.17493e6i	0.845046	−	0.487887i
$246$		0			0
$247$	2.84737e6	−	4.93179e6i	0.188953	−	0.327276i
$248$		0			0
$249$	−1.12032e7	+	6.85015e6i	−0.725681	+	0.443713i
$250$		0			0
$251$			2.49527e7i			1.57796i	0.614419	+	0.788980i	$0.289391\pi$
$251$			2.49527e7i			1.57796i	−0.614419	+	0.788980i	$0.710609\pi$
$252$		0			0
$253$	−8.25847e6			−0.509962
$254$		0			0
$255$	1.36550e7	−	2.50902e7i	0.823512	−	1.51316i
$256$		0			0
$257$	−2.99803e6	−	1.73091e6i	−0.176618	−	0.101971i	0.409084	−	0.912497i	$-0.365848\pi$
$257$	−2.99803e6	−	1.73091e6i	−0.176618	−	0.101971i	−0.585703	+	0.810526i	$0.699181\pi$
$258$		0			0
$259$	9.65373e6	+	1.67208e7i	0.555643	+	0.962402i
$260$		0			0
$261$	−5.68175e6	+	3.67384e6i	−0.319566	+	0.206632i
$262$		0			0
$263$	1.19794e7	−	6.91629e6i	0.658516	−	0.380194i	−0.133195	−	0.991090i	$-0.542524\pi$
$263$	1.19794e7	−	6.91629e6i	0.658516	−	0.380194i	0.791711	+	0.610895i	$0.209190\pi$
$264$		0			0
$265$	1.06498e7	−	1.84460e7i	0.572274	−	0.991207i
$266$		0			0
$267$	834852.	+	3.31318e7i	0.0438607	+	1.74065i
$268$		0			0
$269$			3.90919e6i			0.200831i	0.994946	+	0.100415i	$0.0320172\pi$
$269$			3.90919e6i			0.200831i	−0.994946	+	0.100415i	$0.967983\pi$
$270$		0			0
$271$	2.33711e7			1.17428			0.587139	−	0.809486i	$-0.300254\pi$
$271$	2.33711e7			1.17428			0.587139	+	0.809486i	$0.300254\pi$
$272$		0			0
$273$	−1.14932e7	+	289605.i	−0.564875	+	0.0142337i
$274$		0			0
$275$	−1.35967e7	−	7.85006e6i	−0.653786	−	0.377464i
$276$		0			0
$277$	2.98882e6	+	5.17679e6i	0.140624	+	0.243568i	0.927732	−	0.373247i	$-0.121756\pi$
$277$	2.98882e6	+	5.17679e6i	0.140624	+	0.243568i	−0.787108	+	0.616816i	$0.788422\pi$
$278$		0			0
$279$	2.11479e6	−	4.13032e6i	0.0973764	−	0.190183i
$280$		0			0
$281$	−1.70261e7	+	9.83001e6i	−0.767353	+	0.443032i	−0.831930	−	0.554881i	$-0.812764\pi$
$281$	−1.70261e7	+	9.83001e6i	−0.767353	+	0.443032i	0.0645762	+	0.997913i	$0.479430\pi$
$282$		0			0
$283$	1.61814e7	−	2.80270e7i	0.713931	−	1.23657i	−0.249439	−	0.968390i	$-0.580246\pi$
$283$	1.61814e7	−	2.80270e7i	0.713931	−	1.23657i	0.963370	−	0.268175i	$-0.0864204\pi$
$284$		0			0
$285$	−1.15120e7	−	6.26521e6i	−0.497295	−	0.270645i
$286$		0			0
$287$			2.12152e7i			0.897432i
$288$		0			0
$289$	−9.24133e6			−0.382861
$290$		0			0
$291$	−1.68640e7	−	2.75806e7i	−0.684356	−	1.11925i
$292$		0			0
$293$	−1.08984e7	−	6.29219e6i	−0.433271	−	0.250149i	0.267468	−	0.963567i	$-0.413813\pi$
$293$	−1.08984e7	−	6.29219e6i	−0.433271	−	0.250149i	−0.700739	+	0.713418i	$0.747146\pi$
$294$		0			0
$295$	−3.25048e7	−	5.62999e7i	−1.26614	−	2.19302i
$296$		0			0
$297$	−1.42499e7	+	9.73165e6i	−0.543928	+	0.371464i
$298$		0			0
$299$	−1.75258e7	+	1.01186e7i	−0.655640	+	0.378534i
$300$		0			0
$301$	1.00957e7	−	1.74863e7i	0.370201	−	0.641207i
$302$		0			0
$303$	−2.00686e7	+	1.22708e7i	−0.721421	+	0.441108i
$304$		0			0
$305$		−	4.13030e7i		−	1.45573i
$306$		0			0
$307$	−3.09143e7			−1.06843			−0.534214	−	0.845350i	$-0.679392\pi$
$307$	−3.09143e7			−1.06843			−0.534214	+	0.845350i	$0.679392\pi$
$308$		0			0
$309$	2.27898e7	−	4.18749e7i	0.772439	−	1.41931i
$310$		0			0
$311$	−2.51018e7	−	1.44925e7i	−0.834494	−	0.481795i	0.0208947	−	0.999782i	$-0.493349\pi$
$311$	−2.51018e7	−	1.44925e7i	−0.834494	−	0.481795i	−0.855389	+	0.517986i	$0.826682\pi$
$312$		0			0
$313$	233930.	+	405178.i	0.00762873	+	0.0132134i	0.869815	−	0.493379i	$-0.164238\pi$
$313$	233930.	+	405178.i	0.00762873	+	0.0132134i	−0.862186	+	0.506592i	$0.830905\pi$
$314$		0			0
$315$	1.33262e6	+	2.64263e7i	0.0426359	+	0.845483i
$316$		0			0
$317$	−3.03504e7	+	1.75228e7i	−0.952767	+	0.550080i	−0.893939	−	0.448188i	$-0.852070\pi$
$317$	−3.03504e7	+	1.75228e7i	−0.952767	+	0.550080i	−0.0588276	+	0.998268i	$0.518736\pi$
$318$		0			0
$319$	4.06839e6	−	7.04665e6i	0.125329	−	0.217075i
$320$		0			0
$321$	979872.	+	3.88870e7i	0.0296247	+	1.17568i
$322$		0			0
$323$			1.53150e7i			0.454474i
$324$		0			0
$325$	−3.84726e7			−1.12073
$326$		0			0
$327$	6.51834e7	−	1.64249e6i	1.86421	−	0.0469741i
$328$		0			0
$329$	−2.88816e7	−	1.66748e7i	−0.811024	−	0.468245i
$330$		0			0
$331$	2.09831e7	+	3.63438e7i	0.578609	+	1.00218i	0.995639	+	0.0932879i	$0.0297377\pi$
$331$	2.09831e7	+	3.63438e7i	0.578609	+	1.00218i	−0.417030	+	0.908893i	$0.636929\pi$
$332$		0			0
$333$	7.09218e7	−	3.57644e6i	1.92065	−	0.0968541i
$334$		0			0
$335$	3.30553e7	−	1.90845e7i	0.879238	−	0.507628i
$336$		0			0
$337$	3.56345e6	−	6.17207e6i	0.0931066	−	0.161265i	−0.815710	−	0.578461i	$-0.803654\pi$
$337$	3.56345e6	−	6.17207e6i	0.0931066	−	0.161265i	0.908817	+	0.417195i	$0.136987\pi$
$338$		0			0
$339$	6.15597e6	+	3.35029e6i	0.158015	+	0.0859970i
$340$		0			0
$341$			5.58030e6i			0.140733i
$342$		0			0
$343$	3.88511e7			0.962766
$344$		0			0
$345$	2.42964e7	+	3.97362e7i	0.591678	+	0.967674i
$346$		0			0
$347$	−4.99596e6	−	2.88442e6i	−0.119572	−	0.0690351i	0.439021	−	0.898477i	$-0.355325\pi$
$347$	−4.99596e6	−	2.88442e6i	−0.119572	−	0.0690351i	−0.558593	+	0.829442i	$0.688659\pi$
$348$		0			0
$349$	−1.59084e7	−	2.75542e7i	−0.374240	−	0.648203i	0.615973	−	0.787767i	$-0.288763\pi$
$349$	−1.59084e7	−	2.75542e7i	−0.374240	−	0.648203i	−0.990213	+	0.139564i	$0.955430\pi$
$350$		0			0
$351$	−1.83171e7	+	3.81116e7i	−0.423579	+	0.881324i
$352$		0			0
$353$	−4.70363e7	+	2.71564e7i	−1.06932	+	0.617373i	−0.927996	−	0.372590i	$-0.878470\pi$
$353$	−4.70363e7	+	2.71564e7i	−1.06932	+	0.617373i	−0.141326	+	0.989963i	$0.545137\pi$
$354$		0			0
$355$	4.62035e7	−	8.00269e7i	1.03274	−	1.78875i
$356$		0			0
$357$	2.63785e7	−	1.61289e7i	0.579755	−	0.354488i
$358$		0			0
$359$			5.92104e7i			1.27972i	0.768492	+	0.639859i	$0.221007\pi$
$359$			5.92104e7i			1.27972i	−0.768492	+	0.639859i	$0.778993\pi$
$360$		0			0
$361$	−4.00190e7			−0.850638
$362$		0			0
$363$	−1.29452e7	+	2.37860e7i	−0.270637	+	0.497281i
$364$		0			0
$365$	−1.32777e7	−	7.66587e6i	−0.273051	−	0.157646i
$366$		0			0
$367$	3.34799e7	+	5.79889e7i	0.677308	+	1.17313i	0.975789	+	0.218716i	$0.0701868\pi$
$367$	3.34799e7	+	5.79889e7i	0.677308	+	1.17313i	−0.298481	+	0.954416i	$0.596480\pi$
$368$		0			0
$369$	6.94538e7	+	3.55614e7i	1.38235	+	0.707783i
$370$		0			0
$371$	1.99657e7	−	1.15272e7i	0.390987	−	0.225736i
$372$		0			0
$373$	−3.73788e7	+	6.47420e7i	−0.720276	+	1.24756i	0.240612	+	0.970621i	$0.422652\pi$
$373$	−3.73788e7	+	6.47420e7i	−0.720276	+	1.24756i	−0.960889	+	0.276934i	$0.910682\pi$
$374$		0			0
$375$	284396.	+	1.12865e7i	0.00539299	+	0.214025i
$376$		0			0
$377$		−	1.99389e7i		−	0.372115i
$378$		0			0
$379$	5.30043e7			0.973629			0.486815	−	0.873505i	$-0.338159\pi$
$379$	5.30043e7			0.973629			0.486815	+	0.873505i	$0.338159\pi$
$380$		0			0
$381$	−5.74478e7	+	1.44757e6i	−1.03872	+	0.0261736i
$382$		0			0
$383$	3.68632e7	+	2.12830e7i	0.656141	+	0.378823i	0.790805	−	0.612068i	$-0.209662\pi$
$383$	3.68632e7	+	2.12830e7i	0.656141	+	0.378823i	−0.134664	+	0.990891i	$0.542996\pi$
$384$		0			0
$385$	−1.59102e7	−	2.75573e7i	−0.278800	−	0.482896i
$386$		0			0
$387$	−4.03235e7	−	6.23621e7i	−0.695706	−	1.07594i
$388$		0			0
$389$	−3.33237e7	+	1.92395e7i	−0.566116	+	0.326847i	−0.755596	−	0.655037i	$-0.772653\pi$
$389$	−3.33237e7	+	1.92395e7i	−0.566116	+	0.326847i	0.189481	+	0.981884i	$0.439319\pi$
$390$		0			0
$391$	2.72120e7	−	4.71326e7i	0.455230	−	0.788481i
$392$		0			0
$393$	−5.14721e7	−	2.80129e7i	−0.847998	−	0.461510i
$394$		0			0
$395$			1.15076e7i			0.186722i
$396$		0			0
$397$	2.19717e7			0.351149			0.175575	−	0.984466i	$-0.443822\pi$
$397$	2.19717e7			0.351149			0.175575	+	0.984466i	$0.443822\pi$
$398$		0			0
$399$	−7.40032e6	−	1.21030e7i	−0.116502	−	0.190535i
$400$		0			0
$401$	7.94451e7	+	4.58677e7i	1.23207	+	0.711334i	0.967460	−	0.253023i	$-0.0814247\pi$
$401$	7.94451e7	+	4.58677e7i	1.23207	+	0.711334i	0.264606	+	0.964357i	$0.414758\pi$
$402$		0			0
$403$	6.83717e6	+	1.18423e7i	0.104463	+	0.180935i
$404$		0			0
$405$	8.87476e7	+	3.99337e7i	1.33595	+	0.601138i
$406$		0			0
$407$	−7.39570e7	+	4.26991e7i	−1.09697	+	0.633338i
$408$		0			0
$409$	4.96652e7	−	8.60227e7i	0.725910	−	1.25731i	−0.232689	−	0.972551i	$-0.574752\pi$
$409$	4.96652e7	−	8.60227e7i	0.725910	−	1.25731i	0.958598	−	0.284761i	$-0.0919143\pi$
$410$		0			0
$411$	3.07931e7	−	1.88282e7i	0.443535	−	0.271197i
$412$		0			0
$413$		−	7.03654e7i		−	0.998870i
$414$		0			0
$415$	−8.90616e7			−1.24608
$416$		0			0
$417$	−2.15860e7	+	3.96630e7i	−0.297690	+	0.546988i
$418$		0			0
$419$	6.66530e7	+	3.84821e7i	0.906103	+	0.523139i	0.879175	−	0.476498i	$-0.158094\pi$
$419$	6.66530e7	+	3.84821e7i	0.906103	+	0.523139i	0.0269278	+	0.999637i	$0.491428\pi$
$420$		0			0
$421$	5.97731e7	+	1.03530e8i	0.801050	+	1.38746i	0.918926	+	0.394431i	$0.129058\pi$
$421$	5.97731e7	+	1.03530e8i	0.801050	+	1.38746i	−0.117876	+	0.993028i	$0.537608\pi$
$422$		0			0
$423$	−1.03002e8	+	6.66013e7i	−1.36089	+	0.879957i
$424$		0			0
$425$	8.96035e7	−	5.17326e7i	1.16723	−	0.673903i
$426$		0			0
$427$	2.23529e7	−	3.87163e7i	0.287111	−	0.497291i
$428$		0			0
$429$	−1.28094e6	−	5.08352e7i	−0.0162240	−	0.643861i
$430$		0			0
$431$			1.04141e7i			0.130073i	0.997883	+	0.0650366i	$0.0207164\pi$
$431$			1.04141e7i			0.130073i	−0.997883	+	0.0650366i	$0.979284\pi$
$432$		0			0
$433$	7.71824e7			0.950725			0.475362	−	0.879790i	$-0.342317\pi$
$433$	7.71824e7			0.950725			0.475362	+	0.879790i	$0.342317\pi$
$434$		0			0
$435$	−4.58746e7	+	1.15594e6i	−0.557320	+	0.0140433i
$436$		0			0
$437$	−2.16255e7	−	1.24855e7i	−0.259133	−	0.149610i
$438$		0			0
$439$	−5.58328e7	−	9.67052e7i	−0.659927	−	1.14303i	−0.980634	−	0.195848i	$-0.937254\pi$
$439$	−5.58328e7	−	9.67052e7i	−0.659927	−	1.14303i	0.320707	−	0.947178i	$-0.396079\pi$
$440$		0			0
$441$	2.60353e7	−	5.08486e7i	0.303561	−	0.592875i
$442$		0			0
$443$	−5.70510e7	+	3.29384e7i	−0.656224	+	0.378871i	−0.790837	−	0.612027i	$-0.790354\pi$
$443$	−5.70510e7	+	3.29384e7i	−0.656224	+	0.378871i	0.134613	+	0.990898i	$0.457021\pi$
$444$		0			0
$445$	−1.12390e8	+	1.94665e8i	−1.27540	+	2.20907i
$446$		0			0
$447$	−7.72318e7	−	4.20323e7i	−0.864717	−	0.470609i
$448$		0			0
$449$		−	8.73745e7i		−	0.965263i	−0.875823	−	0.482632i	$-0.839681\pi$
$449$		−	8.73745e7i		−	0.965263i	0.875823	−	0.482632i	$-0.160319\pi$
$450$		0			0
$451$	−9.38363e7			−1.02292
$452$		0			0
$453$	2.66462e7	+	4.35792e7i	0.286643	+	0.468797i
$454$		0			0
$455$	−6.75281e7	−	3.89874e7i	−0.716886	−	0.413895i
$456$		0			0
$457$	−2.34936e7	−	4.06922e7i	−0.246151	−	0.426346i	0.716304	−	0.697789i	$-0.245833\pi$
$457$	−2.34936e7	−	4.06922e7i	−0.246151	−	0.426346i	−0.962455	+	0.271443i	$0.912499\pi$
$458$		0			0
$459$	−8.58634e6	−	1.13393e8i	−0.0887912	−	1.17259i
$460$		0			0
$461$	−1.02795e7	+	5.93490e6i	−0.104923	+	0.0605774i	−0.551543	−	0.834146i	$-0.685961\pi$
$461$	−1.02795e7	+	5.93490e6i	−0.104923	+	0.0605774i	0.446620	+	0.894724i	$0.352628\pi$
$462$		0			0
$463$	−6.16667e7	+	1.06810e8i	−0.621309	+	1.07614i	0.367933	+	0.929852i	$0.380066\pi$
$463$	−6.16667e7	+	1.06810e8i	−0.621309	+	1.07614i	−0.989242	+	0.146287i	$0.953268\pi$
$464$		0			0
$465$	2.68500e7	−	1.64173e7i	0.267046	−	0.163283i
$466$		0			0
$467$			2.69246e7i			0.264362i	0.991226	+	0.132181i	$0.0421980\pi$
$467$			2.69246e7i			0.264362i	−0.991226	+	0.132181i	$0.957802\pi$
$468$		0			0
$469$	4.13135e7			0.400474
$470$		0			0
$471$	7.39846e7	−	1.35942e8i	0.708074	−	1.30104i
$472$		0			0
$473$	7.73431e7	+	4.46540e7i	0.730866	+	0.421966i
$474$		0			0
$475$	−2.37361e7	−	4.11121e7i	−0.221477	−	0.383609i
$476$		0			0
$477$	−4.27050e6	−	8.46853e7i	−0.0393481	−	0.780285i
$478$		0			0
$479$	1.50969e8	−	8.71619e7i	1.37367	−	0.793086i	0.382278	−	0.924047i	$-0.375140\pi$
$479$	1.50969e8	−	8.71619e7i	1.37367	−	0.793086i	0.991387	+	0.130961i	$0.0418064\pi$
$480$		0			0
$481$	−1.04633e8	+	1.81229e8i	−0.940226	+	1.62852i
$482$		0			0
$483$	1.26989e6	+	5.03967e7i	0.0112700	+	0.447261i
$484$		0			0
$485$		−	2.19256e8i		−	1.92188i
$486$		0			0
$487$	1.04748e8			0.906901			0.453451	−	0.891281i	$-0.350193\pi$
$487$	1.04748e8			0.906901			0.453451	+	0.891281i	$0.350193\pi$
$488$		0			0
$489$	−1.09315e8	+	2.75452e6i	−0.934878	+	0.0235570i
$490$		0			0
$491$	−9.24621e7	−	5.33830e7i	−0.781123	−	0.450982i	0.0557051	−	0.998447i	$-0.482259\pi$
$491$	−9.24621e7	−	5.33830e7i	−0.781123	−	0.450982i	−0.836828	+	0.547466i	$0.815593\pi$
$492$		0			0
$493$	2.68110e7	+	4.64380e7i	0.223755	+	0.387555i
$494$		0			0
$495$	−1.16885e8	+	5.89428e6i	−0.963706	+	0.0485976i
$496$		0			0
$497$	8.66200e7	−	5.00101e7i	0.705584	−	0.407369i
$498$		0			0
$499$	−3.01640e7	+	5.22455e7i	−0.242765	+	0.420482i	−0.961501	−	0.274802i	$-0.911388\pi$
$499$	−3.01640e7	+	5.22455e7i	−0.242765	+	0.420482i	0.718736	+	0.695283i	$0.244721\pi$
$500$		0			0
$501$	3.40954e7	+	1.85559e7i	0.271133	+	0.147560i
$502$		0			0
$503$			1.26548e8i			0.994377i	0.867643	+	0.497188i	$0.165634\pi$
$503$			1.26548e8i			0.994377i	−0.867643	+	0.497188i	$0.834366\pi$
$504$		0			0
$505$	−1.59538e8			−1.23877
$506$		0			0
$507$	2.98101e6	+	4.87536e6i	0.0228739	+	0.0374096i
$508$		0			0
$509$	−9.13440e7	−	5.27375e7i	−0.692670	−	0.399913i	0.111941	−	0.993715i	$-0.464293\pi$
$509$	−9.13440e7	−	5.27375e7i	−0.692670	−	0.399913i	−0.804612	+	0.593801i	$0.797626\pi$
$510$		0			0
$511$	−8.29743e6	−	1.43716e7i	−0.0621843	−	0.107706i
$512$		0			0
$513$	−5.20272e7	+	3.93960e6i	−0.385370	+	0.0291810i
$514$		0			0
$515$	2.80023e8	−	1.61672e8i	2.05009	−	1.18362i
$516$		0			0
$517$	7.37538e7	−	1.27745e8i	0.533719	−	0.924429i
$518$		0			0
$519$	−5.73253e7	+	3.50512e7i	−0.410057	+	0.250727i
$520$		0			0
$521$			4.96312e7i			0.350947i	0.984484	+	0.175473i	$0.0561456\pi$
$521$			4.96312e7i			0.350947i	−0.984484	+	0.175473i	$0.943854\pi$
$522$		0			0
$523$	5.88066e7			0.411075			0.205538	−	0.978649i	$-0.434106\pi$
$523$	5.88066e7			0.411075			0.205538	+	0.978649i	$0.434106\pi$
$524$		0			0
$525$	−4.58137e7	+	8.41800e7i	−0.316605	+	0.581743i
$526$		0			0
$527$	−3.18478e7	−	1.83873e7i	−0.217594	−	0.125628i
$528$		0			0
$529$	−2.96489e7	−	5.13534e7i	−0.200282	−	0.346899i
$530$		0			0
$531$	−2.30361e8	−	1.17948e8i	−1.53860	−	0.787785i
$532$		0			0
$533$	−1.99136e8	+	1.14971e8i	−1.31513	+	0.759290i
$534$		0			0
$535$	−1.31913e8	+	2.28480e8i	−0.861443	+	1.49206i
$536$		0			0
$537$	−5.05116e6	−	2.00460e8i	−0.0326188	−	1.29451i
$538$		0			0
$539$			6.86995e7i			0.438720i
$540$		0			0
$541$	2.86869e8			1.81172			0.905860	−	0.423576i	$-0.139225\pi$
$541$	2.86869e8			1.81172			0.905860	+	0.423576i	$0.139225\pi$
$542$		0			0
$543$	−1.18668e8	+	2.99018e6i	−0.741195	+	0.0186766i
$544$		0			0
$545$	3.82984e8	+	2.21116e8i	2.36587	+	1.36594i
$546$		0			0
$547$	7.73272e7	+	1.33935e8i	0.472466	+	0.818334i	0.999504	−	0.0315073i	$-0.0100308\pi$
$547$	7.73272e7	+	1.33935e8i	0.472466	+	0.818334i	−0.527038	+	0.849842i	$0.676697\pi$
$548$		0			0
$549$	−8.92802e7	−	1.38076e8i	−0.539558	−	0.834449i
$550$		0			0
$551$	2.13068e7	−	1.23015e7i	0.127369	−	0.0735365i
$552$		0			0
$553$	−6.22786e6	+	1.07870e7i	−0.0368267	+	0.0637858i
$554$		0			0
$555$	4.23031e8	+	2.30228e8i	2.47453	+	1.34673i
$556$		0			0
$557$			2.20227e8i			1.27440i	0.770700	+	0.637199i	$0.219907\pi$
$557$			2.20227e8i			1.27440i	−0.770700	+	0.637199i	$0.780093\pi$
$558$		0			0
$559$	2.18846e8			1.25286
$560$		0			0
$561$	7.13394e7	+	1.16674e8i	0.404055	+	0.660822i
$562$		0			0
$563$	8.07565e7	+	4.66248e7i	0.452535	+	0.261271i	0.708900	−	0.705309i	$-0.249192\pi$
$563$	8.07565e7	+	4.66248e7i	0.452535	+	0.261271i	−0.256365	+	0.966580i	$0.582525\pi$
$564$		0			0
$565$	2.37671e7	+	4.11658e7i	0.131774	+	0.228240i
$566$		0			0
$567$	6.15778e7	+	8.54624e7i	0.337812	+	0.468841i
$568$		0			0
$569$	9.00890e7	−	5.20129e7i	0.489030	−	0.282341i	−0.235142	−	0.971961i	$-0.575556\pi$
$569$	9.00890e7	−	5.20129e7i	0.489030	−	0.282341i	0.724172	+	0.689620i	$0.242222\pi$
$570$		0			0
$571$	8.77953e7	−	1.52066e8i	0.471588	−	0.816814i	−0.527884	−	0.849317i	$-0.677014\pi$
$571$	8.77953e7	−	1.52066e8i	0.471588	−	0.816814i	0.999472	+	0.0325024i	$0.0103476\pi$
$572$		0			0
$573$	1.10589e8	−	6.76190e7i	0.587826	−	0.359422i
$574$		0			0
$575$			1.68699e8i			0.887380i
$576$		0			0
$577$	−2.31295e8			−1.20403			−0.602016	−	0.798484i	$-0.705636\pi$
$577$	−2.31295e8			−1.20403			−0.602016	+	0.798484i	$0.705636\pi$
$578$		0			0
$579$	8.50832e7	−	1.56335e8i	0.438337	−	0.805418i
$580$		0			0
$581$	−8.34840e7	−	4.81995e7i	−0.425672	−	0.245762i
$582$		0			0
$583$	5.09855e7	+	8.83095e7i	0.257301	+	0.445658i
$584$		0			0
$585$	−2.40828e8	+	1.55720e8i	−1.20293	+	0.777818i
$586$		0			0
$587$	2.24539e8	−	1.29637e8i	1.11014	−	0.640938i	0.171272	−	0.985224i	$-0.445212\pi$
$587$	2.24539e8	−	1.29637e8i	1.11014	−	0.640938i	0.938865	+	0.344286i	$0.111879\pi$
$588$		0			0
$589$	−8.43653e6	+	1.46125e7i	−0.0412874	+	0.0715119i
$590$		0			0
$591$	1.62826e6	+	6.46190e7i	0.00788792	+	0.313039i
$592$		0			0
$593$			2.31522e8i			1.11027i	0.831760	+	0.555135i	$0.187333\pi$
$593$			2.31522e8i			1.11027i	−0.831760	+	0.555135i	$0.812667\pi$
$594$		0			0
$595$	2.09699e8			0.995510
$596$		0			0
$597$	1.54771e7	−	389990.i	0.0727388	−	0.00183287i
$598$		0			0
$599$	−2.26435e8	−	1.30732e8i	−1.05357	−	0.608277i	−0.129921	−	0.991524i	$-0.541473\pi$
$599$	−2.26435e8	−	1.30732e8i	−1.05357	−	0.608277i	−0.923646	+	0.383247i	$0.874806\pi$
$600$		0			0
$601$	−1.95499e8	−	3.38615e8i	−0.900580	−	1.55985i	−0.826743	−	0.562579i	$-0.809809\pi$
$601$	−1.95499e8	−	3.38615e8i	−0.900580	−	1.55985i	−0.0738365	−	0.997270i	$-0.523524\pi$
$602$		0			0
$603$	6.92508e7	−	1.35251e8i	0.315844	−	0.616864i
$604$		0			0
$605$	−1.59060e8	+	9.18336e7i	−0.718284	+	0.414701i
$606$		0			0
$607$	−1.92686e8	+	3.33742e8i	−0.861556	+	1.49226i	0.00887013	+	0.999961i	$0.497177\pi$
$607$	−1.92686e8	+	3.33742e8i	−0.861556	+	1.49226i	−0.870426	+	0.492299i	$0.836157\pi$
$608$		0			0
$609$	−4.36272e7	−	2.37435e7i	−0.193155	−	0.105122i
$610$		0			0
$611$		−	3.61462e8i		−	1.58467i
$612$		0			0
$613$	−3.45866e7			−0.150151			−0.0750753	−	0.997178i	$-0.523920\pi$
$613$	−3.45866e7			−0.150151			−0.0750753	+	0.997178i	$0.523920\pi$
$614$		0			0
$615$	2.76066e8	+	4.51499e8i	1.18683	+	1.94103i
$616$		0			0
$617$	−2.54502e7	−	1.46937e7i	−0.108352	−	0.0625568i	0.444845	−	0.895608i	$-0.353259\pi$
$617$	−2.54502e7	−	1.46937e7i	−0.108352	−	0.0625568i	−0.553197	+	0.833051i	$0.686592\pi$
$618$		0			0
$619$	−1.95742e8	−	3.39036e8i	−0.825302	−	1.42947i	−0.901688	−	0.432387i	$-0.857672\pi$
$619$	−1.95742e8	−	3.39036e8i	−0.825302	−	1.42947i	0.0763862	−	0.997078i	$-0.475662\pi$
$620$		0			0
$621$	1.67116e8	+	8.03188e7i	0.697821	+	0.335384i
$622$		0			0
$623$	−2.10703e8	+	1.21649e8i	−0.871378	+	0.503090i
$624$		0			0
$625$	1.01624e8	−	1.76017e8i	0.416251	−	0.720967i
$626$		0			0
$627$	5.35325e7	−	3.27321e7i	0.217178	−	0.132792i
$628$		0			0
$629$		−	5.62782e8i		−	2.26146i
$630$		0			0
$631$	−3.43149e7			−0.136583			−0.0682913	−	0.997665i	$-0.521755\pi$
$631$	−3.43149e7			−0.136583			−0.0682913	+	0.997665i	$0.521755\pi$
$632$		0			0
$633$	−2.05771e8	+	3.78093e8i	−0.811286	+	1.49069i
$634$		0			0
$635$	−3.37534e8	−	1.94875e8i	−1.31825	−	0.761090i
$636$		0			0
$637$	8.41729e7	+	1.45792e8i	0.325652	+	0.564046i
$638$		0			0
$639$	−1.85273e7	−	3.67402e8i	−0.0710085	−	1.40812i
$640$		0			0
$641$	−3.36825e8	+	1.94466e8i	−1.27888	+	0.738362i	−0.976642	−	0.214871i	$-0.931067\pi$
$641$	−3.36825e8	+	1.94466e8i	−1.27888	+	0.738362i	−0.302237	+	0.953233i	$0.597734\pi$
$642$		0			0
$643$	−1.90459e8	+	3.29885e8i	−0.716422	+	1.24088i	0.245987	+	0.969273i	$0.420888\pi$
$643$	−1.90459e8	+	3.29885e8i	−0.716422	+	1.24088i	−0.962409	+	0.271605i	$0.912445\pi$
$644$		0			0
$645$	−1.26875e7	−	5.03513e8i	−0.0472821	−	1.87643i
$646$		0			0
$647$			2.98723e7i			0.110295i	0.998478	+	0.0551474i	$0.0175629\pi$
$647$			2.98723e7i			0.110295i	−0.998478	+	0.0551474i	$0.982437\pi$
$648$		0			0
$649$	3.11231e8			1.13854
$650$		0			0
$651$	3.40534e7	−	858075.i	0.123429	−	0.00311016i
$652$		0			0
$653$	2.42142e7	+	1.39801e7i	0.0869623	+	0.0502077i	0.542851	−	0.839829i	$-0.317345\pi$
$653$	2.42142e7	+	1.39801e7i	0.0869623	+	0.0502077i	−0.455888	+	0.890037i	$0.650678\pi$
$654$		0			0
$655$	−1.98725e8	−	3.44202e8i	−0.707177	−	1.22487i
$656$		0			0
$657$	−6.09577e7	+	3.07397e6i	−0.214947	+	0.0108393i
$658$		0			0
$659$	−1.74085e7	+	1.00508e7i	−0.0608282	+	0.0351192i	−0.530106	−	0.847932i	$-0.677848\pi$
$659$	−1.74085e7	+	1.00508e7i	−0.0608282	+	0.0351192i	0.469277	+	0.883051i	$0.344514\pi$
$660$		0			0
$661$	5.83864e7	−	1.01128e8i	0.202165	−	0.350161i	−0.747060	−	0.664756i	$-0.768535\pi$
$661$	5.83864e7	−	1.01128e8i	0.202165	−	0.350161i	0.949226	+	0.314595i	$0.101869\pi$
$662$		0			0
$663$	2.94346e8	+	1.60194e8i	1.00999	+	0.549673i
$664$		0			0
$665$		−	9.62146e7i		−	0.327172i
$666$		0			0
$667$	−8.74304e7			−0.294635
$668$		0			0
$669$	1.41132e8	+	2.30818e8i	0.471354	+	0.770888i
$670$		0			0
$671$	1.71245e8	+	9.88683e7i	0.566826	+	0.327257i
$672$		0			0
$673$	−1.57856e8	−	2.73414e8i	−0.517863	−	0.896965i	−0.999785	−	0.0207508i	$-0.993394\pi$
$673$	−1.57856e8	−	2.73414e8i	−0.517863	−	0.896965i	0.481922	−	0.876214i	$-0.339939\pi$
$674$		0			0
$675$	1.98792e8	+	2.91088e8i	0.646381	+	0.946484i
$676$		0			0
$677$	−3.26299e8	+	1.88389e8i	−1.05160	+	0.607141i	−0.923097	−	0.384568i	$-0.874350\pi$
$677$	−3.26299e8	+	1.88389e8i	−1.05160	+	0.607141i	−0.128502	+	0.991709i	$0.541017\pi$
$678$		0			0
$679$	1.18660e8	−	2.05525e8i	0.379048	−	0.656531i
$680$		0			0
$681$	−9.06004e6	+	5.53970e6i	−0.0286872	+	0.0175406i
$682$		0			0
$683$			2.52914e8i			0.793800i	0.917862	+	0.396900i	$0.129914\pi$
$683$			2.52914e8i			0.793800i	−0.917862	+	0.396900i	$0.870086\pi$
$684$		0			0
$685$	2.44794e8			0.761604
$686$		0			0
$687$	6.50021e7	−	1.19438e8i	0.200473	−	0.368358i
$688$		0			0
$689$	2.16399e8	+	1.24938e8i	0.661605	+	0.381978i
$690$		0			0
$691$	−4.60547e7	−	7.97690e7i	−0.139585	−	0.241769i	0.787754	−	0.615989i	$-0.211244\pi$
$691$	−4.60547e7	−	7.97690e7i	−0.139585	−	0.241769i	−0.927340	+	0.374221i	$0.877910\pi$
$692$		0			0
$693$	−1.12755e8	−	5.77324e7i	−0.338795	−	0.173468i
$694$		0			0
$695$	−2.65232e8	+	1.53132e8i	−0.790081	+	0.456154i
$696$		0			0
$697$	3.09195e8	−	5.35541e8i	0.913132	−	1.58159i
$698$		0			0
$699$	736020.	+	2.92096e7i	0.00215505	+	0.0855251i
$700$		0			0
$701$			3.19671e8i			0.928001i	0.885835	+	0.464001i	$0.153586\pi$
$701$			3.19671e8i			0.928001i	−0.885835	+	0.464001i	$0.846414\pi$
$702$		0			0
$703$	−2.58217e8			−0.743222
$704$		0			0
$705$	−8.31639e8	+	2.09556e7i	−2.37338	+	0.0598043i
$706$		0			0
$707$	−1.49547e8	−	8.63407e7i	−0.423173	−	0.244319i
$708$		0			0
$709$	−1.01451e7	−	1.75718e7i	−0.0284653	−	0.0493034i	0.851442	−	0.524449i	$-0.175729\pi$
$709$	−1.01451e7	−	1.75718e7i	−0.0284653	−	0.0493034i	−0.879907	+	0.475146i	$0.842395\pi$
$710$		0			0
$711$	2.48748e7	+	3.84700e7i	0.0692072	+	0.107032i
$712$		0			0
$713$	5.19276e7	−	2.99804e7i	0.143262	−	0.0827122i
$714$		0			0
$715$	1.72444e8	−	2.98681e8i	0.471769	−	0.817128i
$716$		0			0
$717$	−5.60813e7	−	3.05214e7i	−0.152146	−	0.0828031i
$718$		0			0
$719$		−	5.55247e8i		−	1.49382i	−0.664923	−	0.746912i	$-0.731536\pi$
$719$		−	5.55247e8i		−	1.49382i	0.664923	−	0.746912i	$-0.268464\pi$
$720$		0			0
$721$	3.49982e8			0.933770
$722$		0			0
$723$	1.28549e8	+	2.10239e8i	0.340137	+	0.556286i
$724$		0			0
$725$	−1.43945e8	−	8.31066e7i	−0.377731	−	0.218083i
$726$		0			0
$727$	−2.21130e8	−	3.83009e8i	−0.575500	−	0.996795i	−0.995987	−	0.0894964i	$-0.971474\pi$
$727$	−2.21130e8	−	3.83009e8i	−0.575500	−	0.996795i	0.420487	−	0.907298i	$-0.361859\pi$
$728$		0			0
$729$	3.83003e8	−	5.83380e7i	0.988598	−	0.150581i
$730$		0			0
$731$	−5.09698e8	+	2.94274e8i	−1.30485	+	0.753355i
$732$		0			0
$733$	−2.86889e8	+	4.96907e8i	−0.728455	+	1.26172i	0.229082	+	0.973407i	$0.426428\pi$
$733$	−2.86889e8	+	4.96907e8i	−0.728455	+	1.26172i	−0.957536	+	0.288313i	$0.906906\pi$
$734$		0			0
$735$	3.30552e8	−	2.02114e8i	0.832488	−	0.509019i
$736$		0			0
$737$			1.82733e8i			0.456471i
$738$		0			0
$739$	3.88736e7			0.0963211			0.0481605	−	0.998840i	$-0.484664\pi$
$739$	3.88736e7			0.0963211			0.0481605	+	0.998840i	$0.484664\pi$
$740$		0			0
$741$	7.35004e7	−	1.35053e8i	0.180649	−	0.331932i
$742$		0			0
$743$	−2.16715e8	−	1.25120e8i	−0.528350	−	0.305043i	0.211994	−	0.977271i	$-0.432004\pi$
$743$	−2.16715e8	−	1.25120e8i	−0.528350	−	0.305043i	−0.740344	+	0.672228i	$0.765337\pi$
$744$		0			0
$745$	−2.98179e8	−	5.16460e8i	−0.721120	−	1.24902i
$746$		0			0
$747$	−2.97732e8	+	1.92515e8i	−0.714273	+	0.461852i
$748$		0			0
$749$	−2.47304e8	+	1.42781e8i	−0.588553	+	0.339801i
$750$		0			0
$751$	1.13893e7	−	1.97269e7i	0.0268893	−	0.0465736i	−0.852268	−	0.523106i	$-0.824773\pi$
$751$	1.13893e7	−	1.97269e7i	0.0268893	−	0.0465736i	0.879157	+	0.476532i	$0.158107\pi$
$752$		0			0
$753$	1.69710e7	+	6.73509e8i	0.0397487	+	1.57746i
$754$		0			0
$755$			3.46439e8i			0.804982i
$756$		0			0
$757$	6.87959e7			0.158590			0.0792949	−	0.996851i	$-0.474733\pi$
$757$	6.87959e7			0.158590			0.0792949	+	0.996851i	$0.474733\pi$
$758$		0			0
$759$	−2.22908e8	+	5.61682e6i	−0.509801	+	0.0128459i
$760$		0			0
$761$	5.03600e8	+	2.90754e8i	1.14270	+	0.659738i	0.947098	−	0.320945i	$-0.104001\pi$
$761$	5.03600e8	+	2.90754e8i	1.14270	+	0.659738i	0.195602	+	0.980683i	$0.437334\pi$
$762$		0			0
$763$	2.39333e8	+	4.14537e8i	0.538802	+	0.933232i
$764$		0			0
$765$	3.51503e8	−	6.86508e8i	0.785135	−	1.53342i
$766$		0			0
$767$	6.60483e8	−	3.81330e8i	1.46378	−	0.845114i
$768$		0			0
$769$	2.00530e8	−	3.47327e8i	0.440960	−	0.763766i	−0.556801	−	0.830646i	$-0.687971\pi$
$769$	2.00530e8	−	3.47327e8i	0.440960	−	0.763766i	0.997761	+	0.0668804i	$0.0213046\pi$
$770$		0			0
$771$	−8.20982e7	−	4.46807e7i	−0.179131	−	0.0974893i
$772$		0			0
$773$			3.08680e8i			0.668297i	0.942520	+	0.334149i	$0.108449\pi$
$773$			3.08680e8i			0.668297i	−0.942520	+	0.334149i	$0.891551\pi$
$774$		0			0
$775$	1.13991e8			0.244887
$776$		0			0
$777$	2.71940e8	+	4.44751e8i	0.579710	+	0.948100i
$778$		0			0
$779$	−2.45718e8	−	1.41865e8i	−0.519786	−	0.300099i
$780$		0			0
$781$	2.21198e8	+	3.83126e8i	0.464331	+	0.804245i
$782$		0			0
$783$	−1.50860e8	+	1.03026e8i	−0.314259	+	0.214617i
$784$		0			0
$785$	9.09066e8	−	5.24850e8i	1.87926	−	1.08499i
$786$		0			0
$787$	−4.44768e8	+	7.70361e8i	−0.912451	+	1.58041i	−0.101861	+	0.994799i	$0.532480\pi$
$787$	−4.44768e8	+	7.70361e8i	−0.912451	+	1.58041i	−0.810591	+	0.585613i	$0.800854\pi$
$788$		0			0
$789$	3.18636e8	−	1.94828e8i	0.648730	−	0.396662i
$790$		0			0
$791$			5.14504e7i			0.103958i
$792$		0			0
$793$	4.84547e8			0.971664
$794$		0			0
$795$	2.74908e8	−	5.05127e8i	0.547124	−	1.00531i
$796$		0			0
$797$	3.69735e8	+	2.13466e8i	0.730323	+	0.421652i	0.818540	−	0.574449i	$-0.194784\pi$
$797$	3.69735e8	+	2.13466e8i	0.730323	+	0.421652i	−0.0882171	+	0.996101i	$0.528117\pi$
$798$		0			0
$799$	4.86044e8	+	8.41853e8i	0.952874	+	1.65043i
$800$		0			0
$801$	4.50677e7	+	8.93706e8i	0.0876936	+	1.73899i
$802$		0			0
$803$	6.35664e7	−	3.67001e7i	0.122767	−	0.0708795i
$804$		0			0
$805$	−1.70956e8	+	2.96105e8i	−0.327716	+	0.567621i
$806$		0			0
$807$	2.65875e6	+	1.05515e8i	0.00505891	+	0.200767i
$808$		0			0
$809$		−	1.00833e8i		−	0.190439i	−0.995456	−	0.0952197i	$-0.969645\pi$
$809$		−	1.00833e8i		−	0.190439i	0.995456	−	0.0952197i	$-0.0303554\pi$
$810$		0			0
$811$	−6.60774e8			−1.23877			−0.619384	−	0.785088i	$-0.712618\pi$
$811$	−6.60774e8			−1.23877			−0.619384	+	0.785088i	$0.712618\pi$
$812$		0			0
$813$	6.30819e8	−	1.58953e7i	1.17391	−	0.0295800i
$814$		0			0
$815$	−6.42282e8	−	3.70821e8i	−1.18646	−	0.685002i
$816$		0			0
$817$	1.35020e8	+	2.33861e8i	0.247588	+	0.428836i
$818$		0			0
$819$	−3.10021e8	+	1.56337e7i	−0.564338	+	0.0284583i
$820$		0			0
$821$	−3.96490e8	+	2.28914e8i	−0.716478	+	0.413659i	−0.813455	−	0.581628i	$-0.802416\pi$
$821$	−3.96490e8	+	2.28914e8i	−0.716478	+	0.413659i	0.0969772	+	0.995287i	$0.469083\pi$
$822$		0			0
$823$	1.21895e8	−	2.11128e8i	0.218668	−	0.378744i	−0.735733	−	0.677272i	$-0.763162\pi$
$823$	1.21895e8	−	2.11128e8i	0.218668	−	0.378744i	0.954401	+	0.298527i	$0.0964954\pi$
$824$		0			0
$825$	−3.72334e8	−	2.02637e8i	−0.663087	−	0.360875i
$826$		0			0
$827$		−	3.58110e8i		−	0.633141i	−0.948569	−	0.316570i	$-0.897469\pi$
$827$		−	3.58110e8i		−	0.633141i	0.948569	−	0.316570i	$-0.102531\pi$
$828$		0			0
$829$	−2.46113e8			−0.431988			−0.215994	−	0.976395i	$-0.569299\pi$
$829$	−2.46113e8			−0.431988			−0.215994	+	0.976395i	$0.569299\pi$
$830$		0			0
$831$	8.41934e7	+	1.37696e8i	0.146715	+	0.239949i
$832$		0			0
$833$	−3.92081e8	−	2.26368e8i	−0.678329	−	0.391633i
$834$		0			0
$835$	1.31636e8	+	2.28001e8i	0.226108	+	0.391631i
$836$		0			0
$837$	5.42720e7	−	1.12922e8i	0.0925548	−	0.192575i
$838$		0			0
$839$	7.03483e8	−	4.06156e8i	1.19115	−	0.687713i	0.232585	−	0.972576i	$-0.425281\pi$
$839$	7.03483e8	−	4.06156e8i	1.19115	−	0.687713i	0.958568	+	0.284863i	$0.0919481\pi$
$840$		0			0
$841$	−2.54341e8	+	4.40531e8i	−0.427590	+	0.740608i
$842$		0			0
$843$	−4.52872e8	+	2.76906e8i	−0.755950	+	0.462221i
$844$		0			0
$845$			3.87574e7i			0.0642368i
$846$		0			0
$847$	−1.98799e8			−0.327162
$848$		0			0
$849$	4.17697e8	−	7.67494e8i	0.682556	−	1.25416i
$850$		0			0
$851$	7.94675e8	+	4.58806e8i	1.28944	+	0.744458i
$852$		0			0
$853$	−1.36163e8	−	2.35842e8i	−0.219388	−	0.379992i	0.735233	−	0.677815i	$-0.237073\pi$
$853$	−1.36163e8	−	2.35842e8i	−0.219388	−	0.379992i	−0.954621	+	0.297823i	$0.903739\pi$
$854$		0			0
$855$	−3.14985e8	−	1.61277e8i	−0.503955	−	0.258033i
$856$		0			0
$857$	3.46008e8	−	1.99768e8i	0.549723	−	0.317383i	−0.199287	−	0.979941i	$-0.563863\pi$
$857$	3.46008e8	−	1.99768e8i	0.549723	−	0.317383i	0.749010	+	0.662558i	$0.230529\pi$
$858$		0			0
$859$	2.23255e8	−	3.86689e8i	0.352226	−	0.610074i	−0.634413	−	0.772994i	$-0.718758\pi$
$859$	2.23255e8	−	3.86689e8i	0.352226	−	0.610074i	0.986639	+	0.162921i	$0.0520915\pi$
$860$		0			0
$861$	1.44291e7	+	5.72629e8i	0.0226062	+	0.897147i
$862$		0			0
$863$			2.49116e8i			0.387588i	0.981042	+	0.193794i	$0.0620793\pi$
$863$			2.49116e8i			0.387588i	−0.981042	+	0.193794i	$0.937921\pi$
$864$		0			0
$865$	−4.55715e8			−0.704118
$866$		0			0
$867$	−2.49437e8	+	6.28529e6i	−0.382739	+	0.00964423i
$868$		0			0
$869$	−4.77115e7	−	2.75462e7i	−0.0727049	−	0.0419762i
$870$		0			0
$871$	2.23890e8	+	3.87789e8i	0.338829	+	0.586868i
$872$		0			0
$873$	−4.73942e8	−	7.32971e8i	−0.712332	−	1.10165i
$874$		0			0
$875$	−7.17769e7	+	4.14404e7i	−0.107142	+	0.0618586i
$876$		0			0
$877$	−4.02127e8	+	6.96504e8i	−0.596162	+	1.03258i	0.397220	+	0.917723i	$0.369975\pi$
$877$	−4.02127e8	+	6.96504e8i	−0.596162	+	1.03258i	−0.993382	+	0.114859i	$0.963358\pi$
$878$		0			0
$879$	−2.98443e8	−	1.62423e8i	−0.439435	−	0.239156i
$880$		0			0
$881$			6.17231e7i			0.0902651i	0.998981	+	0.0451325i	$0.0143710\pi$
$881$			6.17231e7i			0.0902651i	−0.998981	+	0.0451325i	$0.985629\pi$
$882$		0			0
$883$	3.32125e8			0.482413			0.241207	−	0.970474i	$-0.422457\pi$
$883$	3.32125e8			0.482413			0.241207	+	0.970474i	$0.422457\pi$
$884$		0			0
$885$	−9.15641e8	−	1.49751e9i	−1.32098	−	2.16043i
$886$		0			0
$887$	7.70758e8	+	4.44998e8i	1.10445	+	0.637657i	0.937387	−	0.348289i	$-0.113237\pi$
$887$	7.70758e8	+	4.44998e8i	1.10445	+	0.637657i	0.167066	+	0.985946i	$0.446571\pi$
$888$		0			0
$889$	−2.10930e8	−	3.65342e8i	−0.300216	−	0.519989i
$890$		0			0
$891$	−3.78006e8	+	2.72363e8i	−0.534399	+	0.385048i
$892$		0			0
$893$	3.86261e8	−	2.23008e8i	0.542409	−	0.313160i
$894$		0			0
$895$	6.80002e8	−	1.17780e9i	0.948508	−	1.64286i
$896$		0			0
$897$	−4.66166e8	+	2.85034e8i	−0.645897	+	0.394929i
$898$		0			0
$899$			5.90773e7i			0.0813095i
$900$		0			0
$901$	−6.71998e8			−0.918742
$902$		0			0
$903$	2.60605e8	−	4.78847e8i	0.353932	−	0.650329i
$904$		0			0
$905$	−6.97230e8	−	4.02546e8i	−0.940655	−	0.543087i
$906$		0			0
$907$	−2.60588e8	−	4.51352e8i	−0.349247	−	0.604913i	0.636869	−	0.770972i	$-0.280229\pi$
$907$	−2.60588e8	−	4.51352e8i	−0.349247	−	0.604913i	−0.986116	+	0.166059i	$0.946896\pi$
$908$		0			0
$909$	−5.33334e8	+	3.44856e8i	−0.710080	+	0.459141i
$910$		0			0
$911$	4.98271e8	−	2.87677e8i	0.659038	−	0.380496i	−0.132872	−	0.991133i	$-0.542420\pi$
$911$	4.98271e8	−	2.87677e8i	0.659038	−	0.380496i	0.791910	+	0.610637i	$0.209087\pi$
$912$		0			0
$913$	2.13190e8	−	3.69256e8i	0.280126	−	0.485193i
$914$		0			0
$915$	−2.80913e7	−	1.11483e9i	−0.0366698	−	1.45527i
$916$		0			0
$917$		−	4.30194e8i		−	0.557900i
$918$		0			0
$919$	−7.03958e8			−0.906985			−0.453493	−	0.891260i	$-0.649822\pi$
$919$	−7.03958e8			−0.906985			−0.453493	+	0.891260i	$0.649822\pi$
$920$		0			0
$921$	−8.34423e8	+	2.10257e7i	−1.06809	+	0.0269136i
$922$		0			0
$923$	9.38837e8	+	5.42038e8i	1.19395	+	0.689326i
$924$		0			0
$925$	8.72232e8	+	1.51075e9i	1.10206	+	1.90883i
$926$		0			0
$927$	5.86648e8	−	1.14576e9i	0.736442	−	1.43832i
$928$		0			0
$929$	−1.69928e8	+	9.81081e7i	−0.211943	+	0.122365i	−0.602214	−	0.798335i	$-0.705715\pi$
$929$	−1.69928e8	+	9.81081e7i	−0.211943	+	0.122365i	0.390271	+	0.920700i	$0.372381\pi$
$930$		0			0
$931$	−1.03863e8	+	1.79895e8i	−0.128709	+	0.222931i
$932$		0			0
$933$	−6.87390e8	−	3.74101e8i	−0.846366	−	0.460622i
$934$		0			0
$935$			9.27513e8i			1.13471i
$936$		0			0
$937$	−1.34881e9			−1.63958			−0.819791	−	0.572663i	$-0.805911\pi$
$937$	−1.34881e9			−1.63958			−0.819791	+	0.572663i	$0.805911\pi$
$938$		0			0
$939$	6.58967e6	+	1.07772e7i	0.00795915	+	0.0130170i
$940$		0			0
$941$	−1.34854e9	−	7.78582e8i	−1.61844	−	0.934405i	−0.987325	−	0.158714i	$-0.949265\pi$
$941$	−1.34854e9	−	7.78582e8i	−1.61844	−	0.934405i	−0.631113	−	0.775691i	$-0.717402\pi$
$942$		0			0
$943$	5.04140e8	+	8.73195e8i	0.601195	+	1.04130i
$944$		0			0
$945$	5.39427e7	+	7.12378e8i	0.0639200	+	0.844141i
$946$		0			0
$947$	−1.35078e9	+	7.79873e8i	−1.59050	+	0.918278i	−0.597284	+	0.802030i	$0.703753\pi$
$947$	−1.35078e9	+	7.79873e8i	−1.59050	+	0.918278i	−0.993220	+	0.116248i	$0.962913\pi$
$948$		0			0
$949$	8.99323e7	−	1.55767e8i	0.105225	−	0.182254i
$950$		0			0
$951$	−8.07283e8	+	4.93608e8i	−0.938608	+	0.573906i
$952$		0			0
$953$		−	1.60545e9i		−	1.85489i	−0.373960	−	0.927445i	$-0.622000\pi$
$953$		−	1.60545e9i		−	1.85489i	0.373960	−	0.927445i	$-0.378000\pi$
$954$		0			0
$955$	8.79144e8			1.00937
$956$		0			0
$957$	1.05019e8	−	1.92966e8i	0.119821	−	0.220164i
$958$		0			0
$959$	2.29463e8	+	1.32481e8i	0.260170	+	0.150209i
$960$		0			0
$961$	4.23494e8	+	7.33513e8i	0.477174	+	0.826490i
$962$		0			0
$963$	5.28963e7	+	1.04895e9i	0.0592307	+	1.17456i
$964$		0			0
$965$	1.04544e9	−	6.03583e8i	1.16336	−	0.671669i
$966$		0			0
$967$	3.52026e8	−	6.09728e8i	0.389310	−	0.674305i	−0.603047	−	0.797706i	$-0.706047\pi$
$967$	3.52026e8	−	6.09728e8i	0.389310	−	0.674305i	0.992357	+	0.123401i	$0.0393801\pi$
$968$		0			0
$969$	1.04162e7	+	4.13373e8i	0.0114482	+	0.454330i
$970$		0			0
$971$		−	3.88547e8i		−	0.424410i	−0.977225	−	0.212205i	$-0.931936\pi$
$971$		−	3.88547e8i		−	0.424410i	0.977225	−	0.212205i	$-0.0680644\pi$
$972$		0			0
$973$	−3.31496e8			−0.359865
$974$		0			0
$975$	−1.03843e9	+	2.61663e7i	−1.12038	+	0.0282311i
$976$		0			0
$977$	1.39867e9	+	8.07522e8i	1.49979	+	0.865906i	1.00000		0.000239097i	$-7.61070e-5\pi$
$977$	1.39867e9	+	8.07522e8i	1.49979	+	0.865906i	0.499793	+	0.866145i	$0.333409\pi$
$978$		0			0
$979$	−5.38064e8	−	9.31954e8i	−0.573437	−	0.993222i
$980$		0			0
$981$	1.75828e9	−	8.86662e7i	1.86243	−	0.0939184i
$982$		0			0
$983$	6.42229e8	−	3.70791e8i	0.676128	−	0.390363i	−0.122266	−	0.992497i	$-0.539016\pi$
$983$	6.42229e8	−	3.70791e8i	0.676128	−	0.390363i	0.798395	+	0.602134i	$0.205683\pi$
$984$		0			0
$985$	−2.19201e8	+	3.79668e8i	−0.229369	+	0.397279i
$986$		0			0
$987$	−7.90897e8	−	4.30434e8i	−0.822562	−	0.447667i
$988$		0			0
$989$		−	9.59623e8i		−	0.992001i
$990$		0			0
$991$	3.10728e6			0.00319271			0.00159635	−	0.999999i	$-0.499492\pi$
$991$	3.10728e6			0.00319271			0.00159635	+	0.999999i	$0.499492\pi$
$992$		0			0
$993$	5.91082e8	+	9.66699e8i	0.603671	+	0.987287i
$994$		0			0
$995$	9.09354e7	+	5.25016e7i	0.0923132	+	0.0532970i
$996$		0			0
$997$	6.12144e8	+	1.06026e9i	0.617686	+	1.06986i	0.989907	+	0.141720i	$0.0452632\pi$
$997$	6.12144e8	+	1.06026e9i	0.617686	+	1.06986i	−0.372220	+	0.928144i	$0.621403\pi$
$998$		0			0
$999$	1.91185e9	−	1.44769e8i	1.91760	−	0.145204i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.18	✓	36
3.2	odd	2		216.7.m.a.17.2		36
4.3	odd	2		144.7.q.d.113.1		36
9.2	odd	6	inner	72.7.m.a.65.18	yes	36
9.4	even	3		648.7.e.c.161.4		36
9.5	odd	6		648.7.e.c.161.33		36
9.7	even	3		216.7.m.a.89.2		36
12.11	even	2		432.7.q.d.17.2		36
36.7	odd	6		432.7.q.d.305.2		36
36.11	even	6		144.7.q.d.65.1		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.18	✓	36	1.1	even	1	trivial
72.7.m.a.65.18	yes	36	9.2	odd	6	inner
144.7.q.d.65.1		36	36.11	even	6
144.7.q.d.113.1		36	4.3	odd	2
216.7.m.a.17.2		36	3.2	odd	2
216.7.m.a.89.2		36	9.7	even	3
432.7.q.d.17.2		36	12.11	even	2
432.7.q.d.305.2		36	36.7	odd	6
648.7.e.c.161.4		36	9.4	even	3
648.7.e.c.161.33		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(26.9914 - 0.680128i) q^{3} +(158.588 + 91.5607i) q^{5} +(99.1040 + 171.653i) q^{7} +(728.075 - 36.7153i) q^{9} +O(q^{10})\)	\(q+(26.9914 - 0.680128i) q^{3} +(158.588 + 91.5607i) q^{5} +(99.1040 + 171.653i) q^{7} +(728.075 - 36.7153i) q^{9} +(-759.234 + 438.344i) q^{11} +(-1074.15 + 1860.48i) q^{13} +(4342.79 + 2363.49i) q^{15} -5777.45i q^{17} -2650.82 q^{19} +(2791.71 + 4565.76i) q^{21} +(8158.04 + 4710.04i) q^{23} +(8954.23 + 15509.2i) q^{25} +(19626.8 - 1486.18i) q^{27} +(-8037.81 + 4640.63i) q^{29} +(3182.61 - 5512.44i) q^{31} +(-20194.7 + 12347.9i) q^{33} +36296.1i q^{35} +97410.1 q^{37} +(-27727.4 + 50947.5i) q^{39} +(92695.0 + 53517.5i) q^{41} +(-50935.0 - 88221.9i) q^{43} +(118825. + 60840.5i) q^{45} +(-145714. + 84127.8i) q^{47} +(39181.3 - 67864.0i) q^{49} +(-3929.40 - 155942. i) q^{51} -116314. i q^{53} -160540. q^{55} +(-71549.5 + 1802.90i) q^{57} +(-307446. - 177504. i) q^{59} +(-112775. - 195332. i) q^{61} +(78457.4 + 121338. i) q^{63} +(-340693. + 196699. i) q^{65} +(104218. - 180510. i) q^{67} +(223400. + 121582. i) q^{69} -504622. i q^{71} -83724.5 q^{73} +(252236. + 412525. i) q^{75} +(-150486. - 86883.3i) q^{77} +(31420.8 + 54422.4i) q^{79} +(528745. - 53462.9i) q^{81} +(-421194. + 243176. i) q^{83} +(528987. - 916233. i) q^{85} +(-213796. + 130724. i) q^{87} +1.22749e6i q^{89} -425809. q^{91} +(82154.0 - 150953. i) q^{93} +(-420388. - 242711. i) q^{95} +(-598663. - 1.03691e6i) q^{97} +(-536685. + 347023. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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