LMFDB - Embedded newform 72.7.m.a.41.13

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			41.13
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(16.4370 - 21.4202i) q^{3} +(-124.675 - 71.9811i) q^{5} +(53.2895 + 92.3001i) q^{7} +(-188.649 - 704.168i) q^{9} +O(q^{10})$	\(q+(16.4370 - 21.4202i) q^{3} +(-124.675 - 71.9811i) q^{5} +(53.2895 + 92.3001i) q^{7} +(-188.649 - 704.168i) q^{9} +(-1739.76 + 1004.45i) q^{11} +(48.1438 - 83.3874i) q^{13} +(-3591.13 + 1487.41i) q^{15} +4372.29i q^{17} +2326.88 q^{19} +(2853.01 + 375.668i) q^{21} +(-1354.63 - 782.094i) q^{23} +(2550.06 + 4416.84i) q^{25} +(-18184.2 - 7533.53i) q^{27} +(-28838.4 + 16649.9i) q^{29} +(-15212.2 + 26348.4i) q^{31} +(-7080.94 + 53776.1i) q^{33} -15343.4i q^{35} -41378.1 q^{37} +(-994.835 - 2401.89i) q^{39} +(-80787.0 - 46642.4i) q^{41} +(-33877.9 - 58678.2i) q^{43} +(-27167.0 + 101371. i) q^{45} +(141018. - 81416.9i) q^{47} +(53145.0 - 92049.8i) q^{49} +(93655.2 + 71867.4i) q^{51} +156182. i q^{53} +289206. q^{55} +(38247.0 - 49842.3i) q^{57} +(-320776. - 185200. i) q^{59} +(134449. + 232872. i) q^{61} +(54941.8 - 54937.1i) q^{63} +(-12004.6 + 6930.88i) q^{65} +(266314. - 461270. i) q^{67} +(-39018.6 + 16161.1i) q^{69} -279389. i q^{71} +506606. q^{73} +(136525. + 17976.8i) q^{75} +(-185422. - 107053. i) q^{77} +(-181815. - 314913. i) q^{79} +(-460264. + 265681. i) q^{81} +(-198892. + 114830. i) q^{83} +(314722. - 545115. i) q^{85} +(-117374. + 891398. i) q^{87} -822140. i q^{89} +10262.2 q^{91} +(314343. + 758938. i) q^{93} +(-290104. - 167492. i) q^{95} +(370018. + 640891. i) q^{97} +(1.03551e6 + 1.03559e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	16.4370	−	21.4202i	0.608778	−	0.793340i
$3$	16.4370	−	21.4202i	0.608778	−	0.793340i
$4$		0			0
$5$	−124.675	−	71.9811i	−0.997400	−	0.575849i	−0.0899218	−	0.995949i	$-0.528662\pi$
$5$	−124.675	−	71.9811i	−0.997400	−	0.575849i	−0.907478	+	0.420100i	$0.861995\pi$
$6$		0			0
$7$	53.2895	+	92.3001i	0.155363	+	0.269097i	0.933191	−	0.359380i	$-0.117012\pi$
$7$	53.2895	+	92.3001i	0.155363	+	0.269097i	−0.777828	+	0.628477i	$0.783679\pi$
$8$		0			0
$9$	−188.649	−	704.168i	−0.258777	−	0.965937i
$10$		0			0
$11$	−1739.76	+	1004.45i	−1.30711	+	0.754659i	−0.981612	−	0.190885i	$-0.938864\pi$
$11$	−1739.76	+	1004.45i	−1.30711	+	0.754659i	−0.325495	+	0.945544i	$0.605531\pi$
$12$		0			0
$13$	48.1438	−	83.3874i	0.0219134	−	0.0379551i	−0.854861	−	0.518858i	$-0.826358\pi$
$13$	48.1438	−	83.3874i	0.0219134	−	0.0379551i	0.876774	+	0.480902i	$0.159691\pi$
$14$		0			0
$15$	−3591.13	+	1487.41i	−1.06404	+	0.440713i
$16$		0			0
$17$			4372.29i			0.889942i	0.895545	+	0.444971i	$0.146786\pi$
$17$			4372.29i			0.889942i	−0.895545	+	0.444971i	$0.853214\pi$
$18$		0			0
$19$	2326.88			0.339245			0.169623	−	0.985509i	$-0.445745\pi$
$19$	2326.88			0.339245			0.169623	+	0.985509i	$0.445745\pi$
$20$		0			0
$21$	2853.01	+	375.668i	0.308067	+	0.0405645i
$22$		0			0
$23$	−1354.63	−	782.094i	−0.111336	−	0.0642799i	0.443298	−	0.896374i	$-0.353808\pi$
$23$	−1354.63	−	782.094i	−0.111336	−	0.0642799i	−0.554634	+	0.832094i	$0.687142\pi$
$24$		0			0
$25$	2550.06	+	4416.84i	0.163204	+	0.282678i
$26$		0			0
$27$	−18184.2	−	7533.53i	−0.923855	−	0.382743i
$28$		0			0
$29$	−28838.4	+	16649.9i	−1.18243	+	0.682679i	−0.956577	−	0.291481i	$-0.905852\pi$
$29$	−28838.4	+	16649.9i	−1.18243	+	0.682679i	−0.225858	+	0.974160i	$0.572519\pi$
$30$		0			0
$31$	−15212.2	+	26348.4i	−0.510632	+	0.884441i	0.489292	+	0.872120i	$0.337255\pi$
$31$	−15212.2	+	26348.4i	−0.510632	+	0.884441i	−0.999924	+	0.0123209i	$0.996078\pi$
$32$		0			0
$33$	−7080.94	+	53776.1i	−0.197038	+	1.49640i
$34$		0			0
$35$		−	15343.4i		−	0.357863i
$36$		0			0
$37$	−41378.1			−0.816894			−0.408447	−	0.912782i	$-0.633929\pi$
$37$	−41378.1			−0.816894			−0.408447	+	0.912782i	$0.633929\pi$
$38$		0			0
$39$	−994.835	−	2401.89i	−0.0167709	−	0.0404911i
$40$		0			0
$41$	−80787.0	−	46642.4i	−1.17217	−	0.676751i	−0.217978	−	0.975954i	$-0.569946\pi$
$41$	−80787.0	−	46642.4i	−1.17217	−	0.676751i	−0.954190	+	0.299203i	$0.903279\pi$
$42$		0			0
$43$	−33877.9	−	58678.2i	−0.426099	−	0.738026i	0.570423	−	0.821351i	$-0.306779\pi$
$43$	−33877.9	−	58678.2i	−0.426099	−	0.738026i	−0.996522	+	0.0833254i	$0.973446\pi$
$44$		0			0
$45$	−27167.0	+	101371.i	−0.298129	+	1.11244i
$46$		0			0
$47$	141018.	−	81416.9i	1.35826	−	0.784190i	0.368868	−	0.929482i	$-0.379746\pi$
$47$	141018.	−	81416.9i	1.35826	−	0.784190i	0.989389	+	0.145292i	$0.0464123\pi$
$48$		0			0
$49$	53145.0	−	92049.8i	0.451725	−	0.782410i
$50$		0			0
$51$	93655.2	+	71867.4i	0.706027	+	0.541778i
$52$		0			0
$53$			156182.i			1.04906i	0.851391	+	0.524532i	$0.175760\pi$
$53$			156182.i			1.04906i	−0.851391	+	0.524532i	$0.824240\pi$
$54$		0			0
$55$	289206.			1.73828
$56$		0			0
$57$	38247.0	−	49842.3i	0.206525	−	0.269137i
$58$		0			0
$59$	−320776.	−	185200.i	−1.56187	−	0.901749i	−0.997068	−	0.0765256i	$-0.975617\pi$
$59$	−320776.	−	185200.i	−1.56187	−	0.901749i	−0.564807	−	0.825223i	$-0.691049\pi$
$60$		0			0
$61$	134449.	+	232872.i	0.592336	+	1.02596i	0.993917	+	0.110132i	$0.0351274\pi$
$61$	134449.	+	232872.i	0.592336	+	1.02596i	−0.401581	+	0.915823i	$0.631539\pi$
$62$		0			0
$63$	54941.8	−	54937.1i	0.219726	−	0.219707i
$64$		0			0
$65$	−12004.6	+	6930.88i	−0.0437129	+	0.0252376i
$66$		0			0
$67$	266314.	−	461270.i	0.885462	−	1.53367i	0.0402793	−	0.999188i	$-0.487175\pi$
$67$	266314.	−	461270.i	0.885462	−	1.53367i	0.845183	−	0.534477i	$-0.179491\pi$
$68$		0			0
$69$	−39018.6	+	16161.1i	−0.118775	+	0.0491952i
$70$		0			0
$71$		−	279389.i		−	0.780612i	−0.920685	−	0.390306i	$-0.872369\pi$
$71$		−	279389.i		−	0.780612i	0.920685	−	0.390306i	$-0.127631\pi$
$72$		0			0
$73$	506606.			1.30227			0.651136	−	0.758961i	$-0.274293\pi$
$73$	506606.			1.30227			0.651136	+	0.758961i	$0.274293\pi$
$74$		0			0
$75$	136525.	+	17976.8i	0.323615	+	0.0426118i
$76$		0			0
$77$	−185422.	−	107053.i	−0.406152	−	0.234492i
$78$		0			0
$79$	−181815.	−	314913.i	−0.368764	−	0.638718i	0.620609	−	0.784120i	$-0.286886\pi$
$79$	−181815.	−	314913.i	−0.368764	−	0.638718i	−0.989373	+	0.145403i	$0.953552\pi$
$80$		0			0
$81$	−460264.	+	265681.i	−0.866068	+	0.499925i
$82$		0			0
$83$	−198892.	+	114830.i	−0.347843	+	0.200827i	−0.663735	−	0.747968i	$-0.731030\pi$
$83$	−198892.	+	114830.i	−0.347843	+	0.200827i	0.315892	+	0.948795i	$0.397696\pi$
$84$		0			0
$85$	314722.	−	545115.i	0.512472	−	0.887628i
$86$		0			0
$87$	−117374.	+	891398.i	−0.178244	+	1.35367i
$88$		0			0
$89$		−	822140.i		−	1.16621i	−0.812398	−	0.583104i	$-0.801838\pi$
$89$		−	822140.i		−	1.16621i	0.812398	−	0.583104i	$-0.198162\pi$
$90$		0			0
$91$	10262.2			0.0136181
$92$		0			0
$93$	314343.	+	758938.i	0.390801	+	0.943534i
$94$		0			0
$95$	−290104.	−	167492.i	−0.338363	−	0.195354i
$96$		0			0
$97$	370018.	+	640891.i	0.405423	+	0.702213i	0.994371	−	0.105958i	$-0.0337910\pi$
$97$	370018.	+	640891.i	0.405423	+	0.702213i	−0.588948	+	0.808171i	$0.700458\pi$
$98$		0			0
$99$	1.03551e6	+	1.03559e6i	1.06720	+	1.06729i
$100$		0			0
$101$	−1.44645e6	+	835106.i	−1.40391	+	0.810545i	−0.994791	−	0.101938i	$-0.967496\pi$
$101$	−1.44645e6	+	835106.i	−1.40391	+	0.810545i	−0.409115	+	0.912483i	$0.634162\pi$
$102$		0			0
$103$	−107611.	+	186388.i	−0.0984795	+	0.170571i	−0.911055	−	0.412284i	$-0.864731\pi$
$103$	−107611.	+	186388.i	−0.0984795	+	0.170571i	0.812576	+	0.582855i	$0.198065\pi$
$104$		0			0
$105$	−328658.	−	252199.i	−0.283907	−	0.217859i
$106$		0			0
$107$		−	1.19727e6i		−	0.977330i	−0.872472	−	0.488665i	$-0.837484\pi$
$107$		−	1.19727e6i		−	0.977330i	0.872472	−	0.488665i	$-0.162516\pi$
$108$		0			0
$109$	−268991.			−0.207710			−0.103855	−	0.994592i	$-0.533118\pi$
$109$	−268991.			−0.207710			−0.103855	+	0.994592i	$0.533118\pi$
$110$		0			0
$111$	−680133.	+	886327.i	−0.497307	+	0.648075i
$112$		0			0
$113$	−836647.	−	483038.i	−0.579838	−	0.334770i	0.181231	−	0.983441i	$-0.441992\pi$
$113$	−836647.	−	483038.i	−0.579838	−	0.334770i	−0.761069	+	0.648671i	$0.775325\pi$
$114$		0			0
$115$	112592.	+	195015.i	0.0740311	+	0.128226i
$116$		0			0
$117$	−67801.0	−	18170.4i	−0.0423330	−	0.0113450i
$118$		0			0
$119$	−403563.	+	232997.i	−0.239481	+	0.138264i
$120$		0			0
$121$	1.13206e6	−	1.96079e6i	0.639019	−	1.10681i
$122$		0			0
$123$	−2.32698e6	+	963810.i	−1.25048	+	0.517936i
$124$		0			0
$125$			1.51518e6i			0.775774i
$126$		0			0
$127$	−1.16272e6			−0.567626			−0.283813	−	0.958880i	$-0.591599\pi$
$127$	−1.16272e6			−0.567626			−0.283813	+	0.958880i	$0.591599\pi$
$128$		0			0
$129$	−1.81375e6	−	238824.i	−0.844905	−	0.111252i
$130$		0			0
$131$	−437330.	−	252492.i	−0.194534	−	0.112314i	0.399569	−	0.916703i	$-0.369160\pi$
$131$	−437330.	−	252492.i	−0.194534	−	0.112314i	−0.594103	+	0.804389i	$0.702493\pi$
$132$		0			0
$133$	123998.	+	214772.i	0.0527062	+	0.0912898i
$134$		0			0
$135$	1.72485e6	+	2.24816e6i	0.701050	+	0.913749i
$136$		0			0
$137$	−1.23139e6	+	710942.i	−0.478887	+	0.276486i	−0.719953	−	0.694023i	$-0.755837\pi$
$137$	−1.23139e6	+	710942.i	−0.478887	+	0.276486i	0.241065	+	0.970509i	$0.422503\pi$
$138$		0			0
$139$	−1.40705e6	+	2.43709e6i	−0.523921	+	0.907458i	0.475691	+	0.879612i	$0.342198\pi$
$139$	−1.40705e6	+	2.43709e6i	−0.523921	+	0.907458i	−0.999612	+	0.0278457i	$0.991135\pi$
$140$		0			0
$141$	573954.	−	4.35889e6i	0.204748	−	1.55496i
$142$		0			0
$143$			193432.i			0.0661486i
$144$		0			0
$145$	4.79390e6			1.57248
$146$		0			0
$147$	−1.09818e6	−	2.65140e6i	−0.345717	−	0.834686i
$148$		0			0
$149$	998781.	+	576646.i	0.301933	+	0.174321i	0.643311	−	0.765605i	$-0.277560\pi$
$149$	998781.	+	576646.i	0.301933	+	0.174321i	−0.341378	+	0.939926i	$0.610894\pi$
$150$		0			0
$151$	785975.	+	1.36135e6i	0.228285	+	0.395402i	0.957300	−	0.289096i	$-0.0933547\pi$
$151$	785975.	+	1.36135e6i	0.228285	+	0.395402i	−0.729015	+	0.684498i	$0.760021\pi$
$152$		0			0
$153$	3.07882e6	−	824827.i	0.859628	−	0.230297i
$154$		0			0
$155$	3.79317e6	−	2.18999e6i	1.01861	−	0.588094i
$156$		0			0
$157$	3.42652e6	−	5.93490e6i	0.885429	−	1.53361i	0.0402080	−	0.999191i	$-0.487198\pi$
$157$	3.42652e6	−	5.93490e6i	0.885429	−	1.53361i	0.845221	−	0.534417i	$-0.179469\pi$
$158$		0			0
$159$	3.34544e6	+	2.56716e6i	0.832265	+	0.638648i
$160$		0			0
$161$		−	166710.i		−	0.0399469i
$162$		0			0
$163$	−7.22428e6			−1.66814			−0.834069	−	0.551660i	$-0.813994\pi$
$163$	−7.22428e6			−1.66814			−0.834069	+	0.551660i	$0.813994\pi$
$164$		0			0
$165$	4.75368e6	−	6.19485e6i	1.05823	−	1.37905i
$166$		0			0
$167$	4.78931e6	+	2.76511e6i	1.02831	+	0.593694i	0.916500	−	0.400035i	$-0.131002\pi$
$167$	4.78931e6	+	2.76511e6i	1.02831	+	0.593694i	0.111809	+	0.993730i	$0.464335\pi$
$168$		0			0
$169$	2.40877e6	+	4.17211e6i	0.499040	+	0.864362i
$170$		0			0
$171$	−438964.	−	1.63852e6i	−0.0877890	−	0.327690i
$172$		0			0
$173$	1.70821e6	−	986236.i	0.329916	−	0.190477i	−0.325888	−	0.945408i	$-0.605663\pi$
$173$	1.70821e6	−	986236.i	0.329916	−	0.190477i	0.655804	+	0.754931i	$0.272330\pi$
$174$		0			0
$175$	−271783.	+	470743.i	−0.0507118	+	0.0878354i
$176$		0			0
$177$	−9.23963e6	+	3.82695e6i	−1.66623	+	0.690133i
$178$		0			0
$179$		−	5.13469e6i		−	0.895271i	−0.894216	−	0.447636i	$-0.852266\pi$
$179$		−	5.13469e6i		−	0.895271i	0.894216	−	0.447636i	$-0.147734\pi$
$180$		0			0
$181$	−9.46001e6			−1.59535			−0.797675	−	0.603088i	$-0.793937\pi$
$181$	−9.46001e6			−1.59535			−0.797675	+	0.603088i	$0.793937\pi$
$182$		0			0
$183$	7.19811e6	+	947807.i	1.17453	+	0.154656i
$184$		0			0
$185$	5.15881e6	+	2.97844e6i	0.814769	+	0.470407i
$186$		0			0
$187$	−4.39175e6	−	7.60673e6i	−0.671603	−	1.16325i
$188$		0			0
$189$	−273683.	−	2.07987e6i	−0.0405380	−	0.308070i
$190$		0			0
$191$	8.03548e6	−	4.63929e6i	1.15322	−	0.665811i	0.203549	−	0.979065i	$-0.434752\pi$
$191$	8.03548e6	−	4.63929e6i	1.15322	−	0.665811i	0.949670	+	0.313253i	$0.101419\pi$
$192$		0			0
$193$	−4.84018e6	+	8.38344e6i	−0.673271	+	1.16614i	0.303700	+	0.952768i	$0.401778\pi$
$193$	−4.84018e6	+	8.38344e6i	−0.673271	+	1.16614i	−0.976971	+	0.213372i	$0.931555\pi$
$194$		0			0
$195$	−48859.7	+	371065.i	−0.00658942	+	0.0500433i
$196$		0			0
$197$			1.09301e7i			1.42963i	0.699313	+	0.714816i	$0.253489\pi$
$197$			1.09301e7i			1.42963i	−0.699313	+	0.714816i	$0.746511\pi$
$198$		0			0
$199$	−9.81142e6			−1.24501			−0.622505	−	0.782616i	$-0.713885\pi$
$199$	−9.81142e6			−1.24501			−0.622505	+	0.782616i	$0.713885\pi$
$200$		0			0
$201$	−5.50307e6	−	1.32864e7i	−0.677668	−	1.63614i
$202$		0			0
$203$	−3.07357e6	−	1.77453e6i	−0.367413	−	0.212126i
$204$		0			0
$205$	6.71474e6	+	1.16303e7i	0.779413	+	1.34998i
$206$		0			0
$207$	−295177.	+	1.10143e6i	−0.0332791	+	0.124178i
$208$		0			0
$209$	−4.04822e6	+	2.33724e6i	−0.443430	+	0.256014i
$210$		0			0
$211$	4.24898e6	−	7.35946e6i	0.452312	−	0.783427i	−0.546217	−	0.837643i	$-0.683933\pi$
$211$	4.24898e6	−	7.35946e6i	0.452312	−	0.783427i	0.998529	+	0.0542165i	$0.0172661\pi$
$212$		0			0
$213$	−5.98457e6	−	4.59233e6i	−0.619291	−	0.475220i
$214$		0			0
$215$			9.75427e6i			0.981475i
$216$		0			0
$217$	−3.24261e6			−0.317333
$218$		0			0
$219$	8.32709e6	−	1.08516e7i	0.792795	−	1.03315i
$220$		0			0
$221$	364594.	+	210498.i	0.0337779	+	0.0195017i
$222$		0			0
$223$	9.38221e6	+	1.62505e7i	0.846040	+	1.46538i	0.884715	+	0.466132i	$0.154353\pi$
$223$	9.38221e6	+	1.62505e7i	0.846040	+	1.46538i	−0.0386755	+	0.999252i	$0.512314\pi$
$224$		0			0
$225$	2.62913e6	−	2.62891e6i	0.230815	−	0.230796i
$226$		0			0
$227$	2.93422e6	−	1.69407e6i	0.250851	−	0.144829i	−0.369303	−	0.929309i	$-0.620404\pi$
$227$	2.93422e6	−	1.69407e6i	0.250851	−	0.144829i	0.620154	+	0.784480i	$0.287070\pi$
$228$		0			0
$229$	−1.78200e6	+	3.08652e6i	−0.148389	+	0.257018i	−0.930632	−	0.365956i	$-0.880742\pi$
$229$	−1.78200e6	+	3.08652e6i	−0.148389	+	0.257018i	0.782243	+	0.622973i	$0.214076\pi$
$230$		0			0
$231$	−5.34089e6	+	2.21213e6i	−0.433289	+	0.179463i
$232$		0			0
$233$			1.98835e7i			1.57190i	0.618291	+	0.785949i	$0.287825\pi$
$233$			1.98835e7i			1.57190i	−0.618291	+	0.785949i	$0.712175\pi$
$234$		0			0
$235$	−2.34419e7			−1.80630
$236$		0			0
$237$	−9.73398e6	−	1.28172e6i	−0.731216	−	0.0962824i
$238$		0			0
$239$	1.82336e6	+	1.05272e6i	0.133561	+	0.0771113i	0.565292	−	0.824891i	$-0.308764\pi$
$239$	1.82336e6	+	1.05272e6i	0.133561	+	0.0771113i	−0.431731	+	0.902002i	$0.642097\pi$
$240$		0			0
$241$	−1.31473e6	−	2.27719e6i	−0.0939262	−	0.162685i	0.815234	−	0.579132i	$-0.196608\pi$
$241$	−1.31473e6	−	2.27719e6i	−0.0939262	−	0.162685i	−0.909160	+	0.416447i	$0.863275\pi$
$242$		0			0
$243$	−1.87444e6	+	1.42259e7i	−0.130633	+	0.991431i
$244$		0			0
$245$	−1.32517e7	+	7.65087e6i	−0.901100	+	0.520250i
$246$		0			0
$247$	112025.	−	194033.i	0.00743402	−	0.0128761i
$248$		0			0
$249$	−809505.	+	6.14778e6i	−0.0524350	+	0.398217i
$250$		0			0
$251$		−	6.87341e6i		−	0.434661i	−0.976098	−	0.217331i	$-0.930265\pi$
$251$		−	6.87341e6i		−	0.434661i	0.976098	−	0.217331i	$-0.0697350\pi$
$252$		0			0
$253$	3.14230e6			0.194038
$254$		0			0
$255$	−6.50337e6	−	1.57015e7i	−0.392209	−	0.946934i
$256$		0			0
$257$	4.58920e6	+	2.64958e6i	0.270357	+	0.156091i	0.629050	−	0.777365i	$-0.283444\pi$
$257$	4.58920e6	+	2.64958e6i	0.270357	+	0.156091i	−0.358693	+	0.933456i	$0.616777\pi$
$258$		0			0
$259$	−2.20502e6	−	3.81921e6i	−0.126915	−	0.219823i
$260$		0			0
$261$	1.71646e7	+	1.71661e7i	0.965412	+	0.965495i
$262$		0			0
$263$	1.60550e7	−	9.26938e6i	0.882560	−	0.509546i	0.0110583	−	0.999939i	$-0.496480\pi$
$263$	1.60550e7	−	9.26938e6i	0.882560	−	0.509546i	0.871502	+	0.490393i	$0.163147\pi$
$264$		0			0
$265$	1.12421e7	−	1.94719e7i	0.604102	−	1.04634i
$266$		0			0
$267$	−1.76104e7	−	1.35135e7i	−0.925199	−	0.709962i
$268$		0			0
$269$		−	2.87621e7i		−	1.47762i	−0.673912	−	0.738811i	$-0.735387\pi$
$269$		−	2.87621e7i		−	1.47762i	0.673912	−	0.738811i	$-0.264613\pi$
$270$		0			0
$271$	−2.12312e7			−1.06676			−0.533380	−	0.845875i	$-0.679079\pi$
$271$	−2.12312e7			−1.06676			−0.533380	+	0.845875i	$0.679079\pi$
$272$		0			0
$273$	168680.	−	219819.i	0.00829043	−	0.0108038i
$274$		0			0
$275$	−8.87300e6	−	5.12283e6i	−0.426651	−	0.246327i
$276$		0			0
$277$	2.36611e6	+	4.09821e6i	0.111326	+	0.192821i	0.916305	−	0.400481i	$-0.131157\pi$
$277$	2.36611e6	+	4.09821e6i	0.111326	+	0.192821i	−0.804979	+	0.593303i	$0.797824\pi$
$278$		0			0
$279$	2.14235e7	+	5.74139e6i	0.986454	+	0.264365i
$280$		0			0
$281$	−5.99752e6	+	3.46267e6i	−0.270304	+	0.156060i	−0.629026	−	0.777384i	$-0.716546\pi$
$281$	−5.99752e6	+	3.46267e6i	−0.270304	+	0.156060i	0.358722	+	0.933445i	$0.383213\pi$
$282$		0			0
$283$	9.09878e6	−	1.57595e7i	0.401443	−	0.695320i	−0.592457	−	0.805602i	$-0.701842\pi$
$283$	9.09878e6	−	1.57595e7i	0.401443	−	0.695320i	0.993900	+	0.110282i	$0.0351755\pi$
$284$		0			0
$285$	−8.35615e6	+	3.46102e6i	−0.360970	+	0.149510i
$286$		0			0
$287$		−	9.94220e6i		−	0.420568i
$288$		0			0
$289$	5.02068e6			0.208003
$290$		0			0
$291$	1.98100e7	+	2.60847e6i	0.803906	+	0.105854i
$292$		0			0
$293$	3.52950e6	+	2.03776e6i	0.140317	+	0.0810120i	0.568515	−	0.822673i	$-0.307518\pi$
$293$	3.52950e6	+	2.03776e6i	0.140317	+	0.0810120i	−0.428198	+	0.903685i	$0.640851\pi$
$294$		0			0
$295$	2.66618e7	+	4.61797e7i	1.03854	+	1.79881i
$296$		0			0
$297$	3.92033e7	−	5.15863e6i	1.49642	−	0.196909i
$298$		0			0
$299$	−130434.	+	75305.9i	−0.00487951	+	0.00281718i
$300$		0			0
$301$	3.61067e6	−	6.25387e6i	0.132400	−	0.229324i
$302$		0			0
$303$	−5.88713e6	+	4.47098e7i	−0.211629	+	1.60722i
$304$		0			0
$305$		−	3.87111e7i		−	1.36438i
$306$		0			0
$307$	4.09672e7			1.41586			0.707931	−	0.706282i	$-0.249629\pi$
$307$	4.09672e7			1.41586			0.707931	+	0.706282i	$0.249629\pi$
$308$		0			0
$309$	2.22366e6	+	5.36871e6i	0.0753690	+	0.181968i
$310$		0			0
$311$	5.12927e6	+	2.96139e6i	0.170520	+	0.0984496i	0.582831	−	0.812593i	$-0.301945\pi$
$311$	5.12927e6	+	2.96139e6i	0.170520	+	0.0984496i	−0.412311	+	0.911043i	$0.635278\pi$
$312$		0			0
$313$	−1.50612e7	−	2.60868e7i	−0.491164	−	0.850721i	0.508784	−	0.860894i	$-0.330095\pi$
$313$	−1.50612e7	−	2.60868e7i	−0.491164	−	0.850721i	−0.999948	+	0.0101728i	$0.996762\pi$
$314$		0			0
$315$	−1.08043e7	+	2.89451e6i	−0.345673	+	0.0926068i
$316$		0			0
$317$	1.20152e6	−	693697.i	0.0377183	−	0.0217767i	−0.481022	−	0.876708i	$-0.659734\pi$
$317$	1.20152e6	−	693697.i	0.0377183	−	0.0217767i	0.518741	+	0.854932i	$0.326401\pi$
$318$		0			0
$319$	3.34479e7	−	5.79335e7i	1.03038	−	1.78467i
$320$		0			0
$321$	−2.56458e7	−	1.96796e7i	−0.775355	−	0.594977i
$322$		0			0
$323$			1.01738e7i			0.301909i
$324$		0			0
$325$	491079.			0.0143054
$326$		0			0
$327$	−4.42141e6	+	5.76183e6i	−0.126450	+	0.164785i
$328$		0			0
$329$	1.50296e7	+	8.67734e6i	0.422046	+	0.243668i
$330$		0			0
$331$	−2.36146e6	−	4.09016e6i	−0.0651172	−	0.112786i	0.831629	−	0.555332i	$-0.187409\pi$
$331$	−2.36146e6	−	4.09016e6i	−0.0651172	−	0.112786i	−0.896746	+	0.442546i	$0.854075\pi$
$332$		0			0
$333$	7.80593e6	+	2.91371e7i	0.211394	+	0.789068i
$334$		0			0
$335$	−6.64054e7	+	3.83392e7i	−1.76632	+	1.01979i
$336$		0			0
$337$	3.08625e7	−	5.34554e7i	0.806383	−	1.39670i	−0.108971	−	0.994045i	$-0.534756\pi$
$337$	3.08625e7	−	5.34554e7i	0.806383	−	1.39670i	0.915354	−	0.402651i	$-0.131911\pi$
$338$		0			0
$339$	−2.40988e7	+	9.98142e6i	−0.618579	+	0.256208i
$340$		0			0
$341$		−	6.11198e7i		−	1.54141i
$342$		0			0
$343$	2.38672e7			0.591451
$344$		0			0
$345$	6.02794e6	+	793725.i	0.146795	+	0.0193291i
$346$		0			0
$347$	−5.43027e7	−	3.13517e7i	−1.29967	−	0.750365i	−0.319323	−	0.947646i	$-0.603455\pi$
$347$	−5.43027e7	−	3.13517e7i	−1.29967	−	0.750365i	−0.980347	+	0.197282i	$0.936789\pi$
$348$		0			0
$349$	3.44844e7	+	5.97287e7i	0.811233	+	1.40510i	0.912001	+	0.410188i	$0.134537\pi$
$349$	3.44844e7	+	5.97287e7i	0.811233	+	1.40510i	−0.100768	+	0.994910i	$0.532130\pi$
$350$		0			0
$351$	−1.50366e6	+	1.15364e6i	−0.0347719	+	0.0266778i
$352$		0			0
$353$	−1.84347e7	+	1.06433e7i	−0.419095	+	0.241965i	−0.694690	−	0.719309i	$-0.744458\pi$
$353$	−1.84347e7	+	1.06433e7i	−0.419095	+	0.241965i	0.275595	+	0.961274i	$0.411125\pi$
$354$		0			0
$355$	−2.01108e7	+	3.48329e7i	−0.449514	+	0.778582i
$356$		0			0
$357$	−1.64253e6	+	1.24742e7i	−0.0361001	+	0.274162i
$358$		0			0
$359$			8.45699e7i			1.82782i	0.405921	+	0.913908i	$0.366951\pi$
$359$			8.45699e7i			1.82782i	−0.405921	+	0.913908i	$0.633049\pi$
$360$		0			0
$361$	−4.16315e7			−0.884913
$362$		0			0
$363$	−2.33927e7	−	5.64785e7i	−0.489059	−	1.18076i
$364$		0			0
$365$	−6.31611e7	−	3.64661e7i	−1.29889	−	0.749912i
$366$		0			0
$367$	−6.64119e6	−	1.15029e7i	−0.134353	−	0.232706i	0.790997	−	0.611820i	$-0.209562\pi$
$367$	−6.64119e6	−	1.15029e7i	−0.134353	−	0.232706i	−0.925350	+	0.379114i	$0.876229\pi$
$368$		0			0
$369$	−1.76037e7	+	6.56866e7i	−0.350368	+	1.30737i
$370$		0			0
$371$	−1.44156e7	+	8.32284e6i	−0.282300	+	0.162986i
$372$		0			0
$373$	−2.29319e6	+	3.97192e6i	−0.0441889	+	0.0765374i	−0.887274	−	0.461243i	$-0.847404\pi$
$373$	−2.29319e6	+	3.97192e6i	−0.0441889	+	0.0765374i	0.843085	+	0.537780i	$0.180737\pi$
$374$		0			0
$375$	3.24555e7	+	2.49051e7i	0.615453	+	0.472275i
$376$		0			0
$377$			3.20635e6i			0.0598393i
$378$		0			0
$379$	1.45824e7			0.267863			0.133931	−	0.990991i	$-0.457240\pi$
$379$	1.45824e7			0.267863			0.133931	+	0.990991i	$0.457240\pi$
$380$		0			0
$381$	−1.91116e7	+	2.49056e7i	−0.345558	+	0.450321i
$382$		0			0
$383$	−6.27308e7	−	3.62176e7i	−1.11657	−	0.644650i	−0.176044	−	0.984382i	$-0.556330\pi$
$383$	−6.27308e7	−	3.62176e7i	−1.11657	−	0.644650i	−0.940522	+	0.339732i	$0.889663\pi$
$384$		0			0
$385$	1.54116e7	+	2.66938e7i	0.270064	+	0.467765i
$386$		0			0
$387$	−3.49283e7	+	3.49253e7i	−0.602621	+	0.602569i
$388$		0			0
$389$	7.81934e7	−	4.51450e7i	1.32838	−	0.766939i	0.343329	−	0.939215i	$-0.388445\pi$
$389$	7.81934e7	−	4.51450e7i	1.32838	−	0.766939i	0.985049	+	0.172276i	$0.0551121\pi$
$390$		0			0
$391$	3.41954e6	−	5.92281e6i	0.0572054	−	0.0990827i
$392$		0			0
$393$	−1.25968e7	+	5.21746e6i	−0.207531	+	0.0859570i
$394$		0			0
$395$			5.23490e7i			0.849409i
$396$		0			0
$397$	−7.64278e7			−1.22146			−0.610731	−	0.791838i	$-0.709124\pi$
$397$	−7.64278e7			−1.22146			−0.610731	+	0.791838i	$0.709124\pi$
$398$		0			0
$399$	6.63862e6	+	874136.i	0.104510	+	0.0137613i
$400$		0			0
$401$	6.62663e7	+	3.82589e7i	1.02768	+	0.593334i	0.916320	−	0.400446i	$-0.131145\pi$
$401$	6.62663e7	+	3.82589e7i	1.02768	+	0.593334i	0.111364	+	0.993780i	$0.464478\pi$
$402$		0			0
$403$	1.46475e6	+	2.53702e6i	0.0223794	+	0.0387622i
$404$		0			0
$405$	7.65074e7	+	6582.02i	1.15170	+	9.90819e-5i
$406$		0			0
$407$	7.19880e7	−	4.15623e7i	1.06777	−	0.616476i
$408$		0			0
$409$	8.34137e6	−	1.44477e7i	0.121918	−	0.211168i	−0.798606	−	0.601854i	$-0.794429\pi$
$409$	8.34137e6	−	1.44477e7i	0.121918	−	0.211168i	0.920524	+	0.390686i	$0.127762\pi$
$410$		0			0
$411$	−5.01184e6	+	3.80623e7i	−0.0721890	+	0.548239i
$412$		0			0
$413$		−	3.94769e7i		−	0.560394i
$414$		0			0
$415$	3.30625e7			0.462585
$416$		0			0
$417$	2.90751e7	+	7.01978e7i	0.400971	+	0.968089i
$418$		0			0
$419$	3.62457e6	+	2.09265e6i	0.0492736	+	0.0284481i	0.524434	−	0.851451i	$-0.324277\pi$
$419$	3.62457e6	+	2.09265e6i	0.0492736	+	0.0284481i	−0.475161	+	0.879899i	$0.657610\pi$
$420$		0			0
$421$	−4.24928e7	−	7.35996e7i	−0.569467	−	0.986346i	−0.996619	−	0.0821661i	$-0.973816\pi$
$421$	−4.24928e7	−	7.35996e7i	−0.569467	−	0.986346i	0.427151	−	0.904180i	$-0.359517\pi$
$422$		0			0
$423$	−8.39341e7	−	8.39413e7i	−1.10896	−	1.10906i
$424$		0			0
$425$	−1.93117e7	+	1.11496e7i	−0.251567	+	0.145242i
$426$		0			0
$427$	−1.43294e7	+	2.48193e7i	−0.184054	+	0.318791i
$428$		0			0
$429$	4.14335e6	+	3.17945e6i	0.0524783	+	0.0402698i
$430$		0			0
$431$		−	8.01870e6i		−	0.100155i	−0.998745	−	0.0500774i	$-0.984053\pi$
$431$		−	8.01870e6i		−	0.100155i	0.998745	−	0.0500774i	$-0.0159468\pi$
$432$		0			0
$433$	−1.34153e8			−1.65248			−0.826242	−	0.563316i	$-0.809526\pi$
$433$	−1.34153e8			−1.65248			−0.826242	+	0.563316i	$0.809526\pi$
$434$		0			0
$435$	7.87975e7	−	1.02686e8i	0.957292	−	1.24751i
$436$		0			0
$437$	−3.15206e6	−	1.81984e6i	−0.0377702	−	0.0218067i
$438$		0			0
$439$	−6.27209e6	−	1.08636e7i	−0.0741343	−	0.128404i	0.826575	−	0.562826i	$-0.190286\pi$
$439$	−6.27209e6	−	1.08636e7i	−0.0741343	−	0.128404i	−0.900709	+	0.434422i	$0.856953\pi$
$440$		0			0
$441$	−7.48442e7	−	2.00579e7i	−0.872655	−	0.233867i
$442$		0			0
$443$	3.17519e7	−	1.83319e7i	0.365223	−	0.210861i	−0.306147	−	0.951984i	$-0.599040\pi$
$443$	3.17519e7	−	1.83319e7i	0.365223	−	0.210861i	0.671369	+	0.741123i	$0.265706\pi$
$444$		0			0
$445$	−5.91786e7	+	1.02500e8i	−0.671559	+	1.16317i
$446$		0			0
$447$	2.87688e7	−	1.19157e7i	0.322107	−	0.133413i
$448$		0			0
$449$			5.40589e7i			0.597212i	0.954376	+	0.298606i	$0.0965216\pi$
$449$			5.40589e7i			0.597212i	−0.954376	+	0.298606i	$0.903478\pi$
$450$		0			0
$451$	1.87400e8			2.04286
$452$		0			0
$453$	4.20794e7	+	5.54078e6i	0.452663	+	0.0596042i
$454$		0			0
$455$	−1.27944e6	−	738687.i	−0.0135827	−	0.00784199i
$456$		0			0
$457$	2.39420e7	+	4.14688e7i	0.250849	+	0.434483i	0.963760	−	0.266772i	$-0.0859569\pi$
$457$	2.39420e7	+	4.14688e7i	0.250849	+	0.434483i	−0.712911	+	0.701255i	$0.752624\pi$
$458$		0			0
$459$	3.29388e7	−	7.95067e7i	0.340619	−	0.822178i
$460$		0			0
$461$	−1.07133e8	+	6.18534e7i	−1.09351	+	0.631337i	−0.934508	−	0.355942i	$-0.884160\pi$
$461$	−1.07133e8	+	6.18534e7i	−1.09351	+	0.631337i	−0.158999	+	0.987279i	$0.550827\pi$
$462$		0			0
$463$	2.61569e7	−	4.53052e7i	0.263538	−	0.456462i	−0.703641	−	0.710555i	$-0.748444\pi$
$463$	2.61569e7	−	4.53052e7i	0.263538	−	0.456462i	0.967180	+	0.254093i	$0.0817771\pi$
$464$		0			0
$465$	1.54385e7	−	1.17247e8i	0.153548	−	1.16612i
$466$		0			0
$467$			6.71249e7i			0.659072i	0.944143	+	0.329536i	$0.106892\pi$
$467$			6.71249e7i			0.659072i	−0.944143	+	0.329536i	$0.893108\pi$
$468$		0			0
$469$	5.67670e7			0.550272
$470$		0			0
$471$	−7.08049e7	−	1.70949e8i	−0.677643	−	1.63607i
$472$		0			0
$473$	1.17879e8	+	6.80573e7i	1.11391	+	0.643119i
$474$		0			0
$475$	5.93370e6	+	1.02775e7i	0.0553662	+	0.0958971i
$476$		0			0
$477$	1.09978e8	−	2.94635e7i	1.01333	−	0.271474i
$478$		0			0
$479$	9.44028e7	−	5.45035e7i	0.858971	−	0.495927i	−0.00469653	−	0.999989i	$-0.501495\pi$
$479$	9.44028e7	−	5.45035e7i	0.858971	−	0.495927i	0.863668	+	0.504062i	$0.168162\pi$
$480$		0			0
$481$	−1.99210e6	+	3.45041e6i	−0.0179009	+	0.0310053i
$482$		0			0
$483$	−3.57095e6	−	2.74021e6i	−0.0316915	−	0.0243188i
$484$		0			0
$485$		−	1.06537e8i		−	0.933849i
$486$		0			0
$487$	−1.79097e8			−1.55061			−0.775303	−	0.631590i	$-0.782403\pi$
$487$	−1.79097e8			−1.55061			−0.775303	+	0.631590i	$0.782403\pi$
$488$		0			0
$489$	−1.18746e8	+	1.54745e8i	−1.01553	+	1.32340i
$490$		0			0
$491$	1.99035e8	+	1.14913e8i	1.68146	+	0.970790i	0.960695	+	0.277607i	$0.0895413\pi$
$491$	1.99035e8	+	1.14913e8i	1.68146	+	0.970790i	0.720762	+	0.693183i	$0.243792\pi$
$492$		0			0
$493$	−7.27980e7	−	1.26090e8i	−0.607545	−	1.05230i
$494$		0			0
$495$	−5.45584e7	−	2.03650e8i	−0.449827	−	1.67907i
$496$		0			0
$497$	2.57877e7	−	1.48885e7i	0.210060	−	0.121278i
$498$		0			0
$499$	−458787.	+	794643.i	−0.00369241	+	0.00639544i	−0.867866	−	0.496799i	$-0.834509\pi$
$499$	−458787.	+	794643.i	−0.00369241	+	0.00639544i	0.864173	+	0.503194i	$0.167842\pi$
$500$		0			0
$501$	1.37951e8	−	5.71378e7i	1.09701	−	0.454371i
$502$		0			0
$503$			1.59072e6i			0.0124994i	0.999980	+	0.00624970i	$0.00198935\pi$
$503$			1.59072e6i			0.0124994i	−0.999980	+	0.00624970i	$0.998011\pi$
$504$		0			0
$505$	2.40447e8			1.86701
$506$		0			0
$507$	1.28960e8	+	1.69808e7i	0.989538	+	0.130297i
$508$		0			0
$509$	1.71008e8	+	9.87317e7i	1.29677	+	0.748692i	0.979845	−	0.199758i	$-0.0640156\pi$
$509$	1.71008e8	+	9.87317e7i	1.29677	+	0.748692i	0.316927	+	0.948450i	$0.397349\pi$
$510$		0			0
$511$	2.69968e7	+	4.67598e7i	0.202325	+	0.350437i
$512$		0			0
$513$	−4.23126e7	−	1.75296e7i	−0.313413	−	0.129844i
$514$		0			0
$515$	2.68328e7	−	1.54919e7i	0.196447	−	0.113419i
$516$		0			0
$517$	−1.63559e8	+	2.83292e8i	−1.18359	+	2.05004i
$518$		0			0
$519$	6.95253e6	−	5.28010e7i	0.0497326	−	0.377694i
$520$		0			0
$521$		−	5.39765e7i		−	0.381673i	−0.981622	−	0.190836i	$-0.938880\pi$
$521$		−	5.39765e7i		−	0.381673i	0.981622	−	0.190836i	$-0.0611200\pi$
$522$		0			0
$523$	−1.09281e8			−0.763909			−0.381954	−	0.924181i	$-0.624749\pi$
$523$	−1.09281e8			−0.763909			−0.381954	+	0.924181i	$0.624749\pi$
$524$		0			0
$525$	5.61609e6	+	1.35593e7i	0.0388111	+	0.0937040i
$526$		0			0
$527$	−1.15203e8	−	6.65123e7i	−0.787102	−	0.454433i
$528$		0			0
$529$	−7.27946e7	−	1.26084e8i	−0.491736	−	0.851712i
$530$		0			0
$531$	−6.98980e7	+	2.60818e8i	−0.466854	+	1.74202i
$532$		0			0
$533$	−7.77878e6	+	4.49108e6i	−0.0513724	+	0.0296599i
$534$		0			0
$535$	−8.61809e7	+	1.49270e8i	−0.562794	+	0.974788i
$536$		0			0
$537$	−1.09986e8	−	8.43989e7i	−0.710255	−	0.545022i
$538$		0			0
$539$			2.13526e8i			1.36359i
$540$		0			0
$541$	−2.57746e8			−1.62780			−0.813900	−	0.581005i	$-0.802660\pi$
$541$	−2.57746e8			−1.62780			−0.813900	+	0.581005i	$0.802660\pi$
$542$		0			0
$543$	−1.55494e8	+	2.02635e8i	−0.971214	+	1.26565i
$544$		0			0
$545$	3.35364e7	+	1.93623e7i	0.207170	+	0.119610i
$546$		0			0
$547$	−6.06280e7	−	1.05011e8i	−0.370434	−	0.641611i	0.619198	−	0.785235i	$-0.287458\pi$
$547$	−6.06280e7	−	1.05011e8i	−0.370434	−	0.641611i	−0.989632	+	0.143624i	$0.954124\pi$
$548$		0			0
$549$	1.38618e8	−	1.38606e8i	0.837725	−	0.837653i
$550$		0			0
$551$	−6.71036e7	+	3.87423e7i	−0.401135	+	0.231596i
$552$		0			0
$553$	1.93777e7	−	3.35631e7i	0.114585	−	0.198466i
$554$		0			0
$555$	1.48594e8	−	6.15460e7i	0.869207	−	0.360015i
$556$		0			0
$557$		−	5.95457e7i		−	0.344576i	−0.985047	−	0.172288i	$-0.944884\pi$
$557$		−	5.95457e7i		−	0.344576i	0.985047	−	0.172288i	$-0.0551160\pi$
$558$		0			0
$559$	−6.52403e6			−0.0373492
$560$		0			0
$561$	−2.35125e8	−	3.09599e7i	−1.33171	−	0.175352i
$562$		0			0
$563$	−2.44627e8	−	1.41236e8i	−1.37082	−	0.791442i	−0.379787	−	0.925074i	$-0.624003\pi$
$563$	−2.44627e8	−	1.41236e8i	−1.37082	−	0.791442i	−0.991031	+	0.133632i	$0.957336\pi$
$564$		0			0
$565$	6.95393e7	+	1.20446e8i	0.385554	+	0.667799i
$566$		0			0
$567$	−4.90496e7	−	2.83245e7i	−0.269083	−	0.155386i
$568$		0			0
$569$	1.40407e7	−	8.10640e6i	0.0762170	−	0.0440039i	−0.461407	−	0.887188i	$-0.652655\pi$
$569$	1.40407e7	−	8.10640e6i	0.0762170	−	0.0440039i	0.537624	+	0.843185i	$0.319322\pi$
$570$		0			0
$571$	−1.40346e8	+	2.43086e8i	−0.753860	+	1.30572i	0.192079	+	0.981380i	$0.438477\pi$
$571$	−1.40346e8	+	2.43086e8i	−0.753860	+	1.30572i	−0.945939	+	0.324345i	$0.894856\pi$
$572$		0			0
$573$	3.27050e7	−	2.48378e8i	0.173840	−	1.32023i
$574$		0			0
$575$		−	7.97756e6i		−	0.0419630i
$576$		0			0
$577$	1.67978e8			0.874429			0.437214	−	0.899357i	$-0.355965\pi$
$577$	1.67978e8			0.874429			0.437214	+	0.899357i	$0.355965\pi$
$578$		0			0
$579$	1.00017e8	+	2.41476e8i	0.515273	+	1.24405i
$580$		0			0
$581$	−2.11977e7	−	1.22385e7i	−0.108084	−	0.0624023i
$582$		0			0
$583$	−1.56877e8	−	2.71718e8i	−0.791685	−	1.37124i
$584$		0			0
$585$	7.14517e6	+	7.14578e6i	0.0356899	+	0.0356929i
$586$		0			0
$587$	4.47664e7	−	2.58459e7i	0.221329	−	0.127784i	−0.385237	−	0.922818i	$-0.625880\pi$
$587$	4.47664e7	−	2.58459e7i	0.221329	−	0.127784i	0.606565	+	0.795034i	$0.292547\pi$
$588$		0			0
$589$	−3.53971e7	+	6.13096e7i	−0.173230	+	0.300042i
$590$		0			0
$591$	2.34124e8	+	1.79658e8i	1.13418	+	0.870329i
$592$		0			0
$593$			4.84333e7i			0.232263i	0.993234	+	0.116132i	$0.0370494\pi$
$593$			4.84333e7i			0.232263i	−0.993234	+	0.116132i	$0.962951\pi$
$594$		0			0
$595$	6.70856e7			0.318477
$596$		0			0
$597$	−1.61271e8	+	2.10162e8i	−0.757935	+	0.987716i
$598$		0			0
$599$	3.53845e6	+	2.04292e6i	0.0164639	+	0.00950543i	0.508209	−	0.861234i	$-0.330308\pi$
$599$	3.53845e6	+	2.04292e6i	0.0164639	+	0.00950543i	−0.491745	+	0.870739i	$0.663641\pi$
$600$		0			0
$601$	−3.90601e7	−	6.76540e7i	−0.179932	−	0.311652i	0.761925	−	0.647666i	$-0.224255\pi$
$601$	−3.90601e7	−	6.76540e7i	−0.179932	−	0.311652i	−0.941857	+	0.336013i	$0.890921\pi$
$602$		0			0
$603$	−3.75051e8	−	1.00512e8i	−1.71056	−	0.458423i
$604$		0			0
$605$	−2.82279e8	+	1.62974e8i	−1.27472	+	0.735957i
$606$		0			0
$607$	7.03843e7	−	1.21909e8i	0.314709	−	0.545093i	−0.664666	−	0.747140i	$-0.731426\pi$
$607$	7.03843e7	−	1.21909e8i	0.314709	−	0.545093i	0.979376	+	0.202048i	$0.0647596\pi$
$608$		0			0
$609$	−8.85310e7	+	3.66685e7i	−0.391962	+	0.162346i
$610$		0			0
$611$		−	1.56789e7i		−	0.0687371i
$612$		0			0
$613$	2.44586e8			1.06182			0.530910	−	0.847428i	$-0.321850\pi$
$613$	2.44586e8			1.06182			0.530910	+	0.847428i	$0.321850\pi$
$614$		0			0
$615$	3.59493e8	+	4.73360e7i	1.54549	+	0.203501i
$616$		0			0
$617$	2.23709e8	+	1.29159e8i	0.952421	+	0.549880i	0.893832	−	0.448402i	$-0.148007\pi$
$617$	2.23709e8	+	1.29159e8i	0.952421	+	0.549880i	0.0585887	+	0.998282i	$0.481340\pi$
$618$		0			0
$619$	9.28102e7	+	1.60752e8i	0.391312	+	0.677773i	0.992623	−	0.121242i	$-0.0386878\pi$
$619$	9.28102e7	+	1.60752e8i	0.391312	+	0.677773i	−0.601310	+	0.799015i	$0.705355\pi$
$620$		0			0
$621$	1.87409e7	+	2.44269e7i	0.0782557	+	0.101998i
$622$		0			0
$623$	7.58836e7	−	4.38114e7i	0.313822	−	0.181185i
$624$		0			0
$625$	1.48909e8	−	2.57919e8i	0.609933	−	1.05643i
$626$		0			0
$627$	−1.64765e7	+	1.25131e8i	−0.0668441	+	0.507647i
$628$		0			0
$629$		−	1.80917e8i		−	0.726988i
$630$		0			0
$631$	1.23326e8			0.490871			0.245435	−	0.969413i	$-0.421069\pi$
$631$	1.23326e8			0.490871			0.245435	+	0.969413i	$0.421069\pi$
$632$		0			0
$633$	−8.78003e7	−	2.11982e8i	−0.346166	−	0.835771i
$634$		0			0
$635$	1.44961e8	+	8.36936e7i	0.566150	+	0.326867i
$636$		0			0
$637$	−5.11720e6	−	8.86324e6i	−0.0197977	−	0.0342905i
$638$		0			0
$639$	−1.96737e8	+	5.27065e7i	−0.754022	+	0.202005i
$640$		0			0
$641$	−2.58563e8	+	1.49281e8i	−0.981729	+	0.566802i	−0.902792	−	0.430078i	$-0.858486\pi$
$641$	−2.58563e8	+	1.49281e8i	−0.981729	+	0.566802i	−0.0789374	+	0.996880i	$0.525153\pi$
$642$		0			0
$643$	−3.66786e7	+	6.35293e7i	−0.137969	+	0.238969i	−0.926728	−	0.375734i	$-0.877391\pi$
$643$	−3.66786e7	+	6.35293e7i	−0.137969	+	0.238969i	0.788759	+	0.614703i	$0.210724\pi$
$644$		0			0
$645$	2.08938e8	+	1.60331e8i	0.778644	+	0.597501i
$646$		0			0
$647$			1.17069e7i			0.0432245i	0.999766	+	0.0216123i	$0.00687993\pi$
$647$			1.17069e7i			0.0432245i	−0.999766	+	0.0216123i	$0.993120\pi$
$648$		0			0
$649$	7.44098e8			2.72205
$650$		0			0
$651$	−5.32989e7	+	6.94574e7i	−0.193186	+	0.251753i
$652$		0			0
$653$	−4.40473e8	−	2.54307e8i	−1.58190	−	0.913311i	−0.994582	−	0.103955i	$-0.966850\pi$
$653$	−4.40473e8	−	2.54307e8i	−1.58190	−	0.913311i	−0.587319	−	0.809356i	$-0.699817\pi$
$654$		0			0
$655$	3.63494e7	+	6.29590e7i	0.129352	+	0.224044i
$656$		0			0
$657$	−9.55706e7	−	3.56736e8i	−0.336999	−	1.25791i
$658$		0			0
$659$	2.81850e8	−	1.62726e8i	0.984830	−	0.568592i	0.0811048	−	0.996706i	$-0.474155\pi$
$659$	2.81850e8	−	1.62726e8i	0.984830	−	0.568592i	0.903725	+	0.428114i	$0.140822\pi$
$660$		0			0
$661$	5.06288e7	−	8.76917e7i	0.175305	−	0.303637i	−0.764962	−	0.644075i	$-0.777242\pi$
$661$	5.06288e7	−	8.76917e7i	0.175305	−	0.303637i	0.940267	+	0.340439i	$0.110576\pi$
$662$		0			0
$663$	1.05018e7	−	4.34970e6i	0.0360347	−	0.0149252i
$664$		0			0
$665$		−	3.57022e7i		−	0.121403i
$666$		0			0
$667$	5.20870e7			0.175530
$668$		0			0
$669$	5.02304e8	+	6.61405e7i	1.67760	+	0.220897i
$670$		0			0
$671$	−4.67818e8	−	2.70095e8i	−1.54849	−	0.894022i
$672$		0			0
$673$	−1.80186e8	−	3.12091e8i	−0.591120	−	1.02385i	−0.994082	−	0.108633i	$-0.965353\pi$
$673$	−1.80186e8	−	3.12091e8i	−0.591120	−	1.02385i	0.402962	−	0.915217i	$-0.367981\pi$
$674$		0			0
$675$	−1.30966e7	−	9.95279e7i	−0.0425839	−	0.323619i
$676$		0			0
$677$	−1.21214e8	+	6.99830e7i	−0.390649	+	0.225542i	−0.682441	−	0.730940i	$-0.739082\pi$
$677$	−1.21214e8	+	6.99830e7i	−0.390649	+	0.225542i	0.291792	+	0.956482i	$0.405748\pi$
$678$		0			0
$679$	−3.94362e7	+	6.83055e7i	−0.125975	+	0.218196i
$680$		0			0
$681$	1.19425e7	−	9.06971e7i	0.0378141	−	0.287179i
$682$		0			0
$683$		−	3.34089e8i		−	1.04858i	−0.851541	−	0.524288i	$-0.824331\pi$
$683$		−	3.34089e8i		−	1.04858i	0.851541	−	0.524288i	$-0.175669\pi$
$684$		0			0
$685$	2.04698e8			0.636856
$686$		0			0
$687$	3.68231e7	+	8.89041e7i	0.113566	+	0.274190i
$688$		0			0
$689$	1.30236e7	+	7.51917e6i	0.0398174	+	0.0229886i
$690$		0			0
$691$	−1.54192e8	−	2.67069e8i	−0.467335	−	0.809447i	0.531969	−	0.846764i	$-0.321452\pi$
$691$	−1.54192e8	−	2.67069e8i	−0.467335	−	0.809447i	−0.999303	+	0.0373166i	$0.988119\pi$
$692$		0			0
$693$	−4.04040e7	+	1.50764e8i	−0.121402	+	0.452999i
$694$		0			0
$695$	3.50848e8	−	2.02562e8i	1.04512	−	0.603399i
$696$		0			0
$697$	2.03934e8	−	3.53224e8i	0.602270	−	1.04316i
$698$		0			0
$699$	4.25908e8	+	3.26825e8i	1.24705	+	0.956938i
$700$		0			0
$701$		−	1.82604e8i		−	0.530099i	−0.964235	−	0.265049i	$-0.914612\pi$
$701$		−	1.82604e8i		−	0.530099i	0.964235	−	0.265049i	$-0.0853882\pi$
$702$		0			0
$703$	−9.62820e7			−0.277127
$704$		0			0
$705$	−3.85315e8	+	5.02130e8i	−1.09964	+	1.43301i
$706$		0			0
$707$	−1.54161e8	−	8.90047e7i	−0.436230	−	0.251858i
$708$		0			0
$709$	1.64587e8	+	2.85073e8i	0.461803	+	0.799865i	0.999051	−	0.0435587i	$-0.0138695\pi$
$709$	1.64587e8	+	2.85073e8i	0.461803	+	0.799865i	−0.537248	+	0.843424i	$0.680536\pi$
$710$		0			0
$711$	−1.87452e8	+	1.87436e8i	−0.521533	+	0.521488i
$712$		0			0
$713$	4.12138e7	−	2.37948e7i	0.113704	−	0.0656468i
$714$		0			0
$715$	1.39235e7	−	2.41161e7i	0.0380916	−	0.0659766i
$716$		0			0
$717$	5.25200e7	−	2.17532e7i	0.142484	−	0.0590154i
$718$		0			0
$719$		−	1.01542e7i		−	0.0273188i	−0.999907	−	0.0136594i	$-0.995652\pi$
$719$		−	1.01542e7i		−	0.0273188i	0.999907	−	0.0136594i	$-0.00434805\pi$
$720$		0			0
$721$	−2.29382e7			−0.0612003
$722$		0			0
$723$	−7.03880e7	−	9.26830e6i	−0.186245	−	0.0245237i
$724$		0			0
$725$	−1.47080e8	−	8.49164e7i	−0.385956	−	0.222832i
$726$		0			0
$727$	−2.20302e8	−	3.81574e8i	−0.573344	−	0.993061i	−0.996219	−	0.0868730i	$-0.972313\pi$
$727$	−2.20302e8	−	3.81574e8i	−0.573344	−	0.993061i	0.422875	−	0.906188i	$-0.361021\pi$
$728$		0			0
$729$	2.73912e8	+	2.73983e8i	0.707016	+	0.707198i
$730$		0			0
$731$	2.56558e8	−	1.48124e8i	0.656800	−	0.379204i
$732$		0			0
$733$	−2.13230e8	+	3.69324e8i	−0.541422	+	0.937770i	0.457401	+	0.889260i	$0.348780\pi$
$733$	−2.13230e8	+	3.69324e8i	−0.541422	+	0.937770i	−0.998823	+	0.0485091i	$0.984553\pi$
$734$		0			0
$735$	−5.39353e7	+	4.09611e8i	−0.135835	+	1.03160i
$736$		0			0
$737$			1.07000e9i			2.67289i
$738$		0			0
$739$	3.16367e8			0.783895			0.391947	−	0.919988i	$-0.371801\pi$
$739$	3.16367e8			0.783895			0.391947	+	0.919988i	$0.371801\pi$
$740$		0			0
$741$	−2.31486e6	−	5.58892e6i	−0.00568946	−	0.0137364i
$742$		0			0
$743$	−1.94589e8	−	1.12346e8i	−0.474409	−	0.273900i	0.243675	−	0.969857i	$-0.421647\pi$
$743$	−1.94589e8	−	1.12346e8i	−0.474409	−	0.273900i	−0.718084	+	0.695957i	$0.754980\pi$
$744$		0			0
$745$	−8.30153e7	−	1.43787e8i	−0.200766	−	0.347736i
$746$		0			0
$747$	1.18381e8	+	1.18391e8i	0.284001	+	0.284025i
$748$		0			0
$749$	1.10508e8	−	6.38020e7i	0.262996	−	0.151841i
$750$		0			0
$751$	1.67156e8	−	2.89522e8i	0.394641	−	0.683538i	−0.598415	−	0.801187i	$-0.704202\pi$
$751$	1.67156e8	−	2.89522e8i	0.394641	−	0.683538i	0.993055	+	0.117649i	$0.0375358\pi$
$752$		0			0
$753$	−1.47230e8	−	1.12978e8i	−0.344834	−	0.264613i
$754$		0			0
$755$		−	2.26302e8i		−	0.525832i
$756$		0			0
$757$	3.61999e7			0.0834488			0.0417244	−	0.999129i	$-0.486715\pi$
$757$	3.61999e7			0.0834488			0.0417244	+	0.999129i	$0.486715\pi$
$758$		0			0
$759$	5.16500e7	−	6.73086e7i	0.118126	−	0.153938i
$760$		0			0
$761$	2.36281e8	+	1.36417e8i	0.536135	+	0.309538i	0.743511	−	0.668724i	$-0.233159\pi$
$761$	2.36281e8	+	1.36417e8i	0.536135	+	0.309538i	−0.207376	+	0.978261i	$0.566492\pi$
$762$		0			0
$763$	−1.43344e7	−	2.48279e7i	−0.0322705	−	0.0558941i
$764$		0			0
$765$	−4.43224e8	−	1.18782e8i	−0.990009	−	0.265318i
$766$		0			0
$767$	−3.08867e7	+	1.78325e7i	−0.0684520	+	0.0395208i
$768$		0			0
$769$	−2.68022e8	+	4.64227e8i	−0.589374	+	1.02083i	0.404940	+	0.914343i	$0.367292\pi$
$769$	−2.68022e8	+	4.64227e8i	−0.589374	+	1.02083i	−0.994315	+	0.106483i	$0.966041\pi$
$770$		0			0
$771$	1.32187e8	−	5.47504e7i	0.288421	−	0.119460i
$772$		0			0
$773$		−	6.46060e8i		−	1.39873i	−0.714764	−	0.699366i	$-0.753466\pi$
$773$		−	6.46060e8i		−	1.39873i	0.714764	−	0.699366i	$-0.246534\pi$
$774$		0			0
$775$	−1.55169e8			−0.333349
$776$		0			0
$777$	−1.18052e8	−	1.55444e7i	−0.251658	−	0.0331369i
$778$		0			0
$779$	−1.87982e8	−	1.08531e8i	−0.397652	−	0.229585i
$780$		0			0
$781$	2.80633e8	+	4.86070e8i	0.589095	+	1.02034i
$782$		0			0
$783$	6.49837e8	−	8.55099e7i	1.35369	−	0.178128i
$784$		0			0
$785$	−8.54401e8	+	4.93289e8i	−1.76625	+	1.01975i
$786$		0			0
$787$	4.33267e7	−	7.50441e7i	0.0888857	−	0.153954i	−0.818155	−	0.574998i	$-0.805003\pi$
$787$	4.33267e7	−	7.50441e7i	0.0888857	−	0.153954i	0.907040	+	0.421044i	$0.138336\pi$
$788$		0			0
$789$	6.53451e7	−	4.96263e8i	0.133040	−	1.01037i
$790$		0			0
$791$		−	1.02964e8i		−	0.208043i
$792$		0			0
$793$	2.58915e7			0.0519204
$794$		0			0
$795$	−2.32305e8	−	5.60869e8i	−0.462336	−	1.11625i
$796$		0			0
$797$	−2.67720e8	−	1.54568e8i	−0.528818	−	0.305313i	0.211717	−	0.977331i	$-0.432095\pi$
$797$	−2.67720e8	−	1.54568e8i	−0.528818	−	0.305313i	−0.740535	+	0.672018i	$0.765428\pi$
$798$		0			0
$799$	3.55978e8	+	6.16572e8i	0.697884	+	1.20877i
$800$		0			0
$801$	−5.78925e8	+	1.55096e8i	−1.12648	+	0.301788i
$802$		0			0
$803$	−8.81373e8	+	5.08861e8i	−1.70221	+	0.982771i
$804$		0			0
$805$	−1.19999e7	+	2.07845e7i	−0.0230034	+	0.0398430i
$806$		0			0
$807$	−6.16089e8	−	4.72763e8i	−1.17226	−	0.899545i
$808$		0			0
$809$			7.10498e8i			1.34189i	0.741507	+	0.670945i	$0.234112\pi$
$809$			7.10498e8i			1.34189i	−0.741507	+	0.670945i	$0.765888\pi$
$810$		0			0
$811$	−3.80207e8			−0.712784			−0.356392	−	0.934337i	$-0.615993\pi$
$811$	−3.80207e8			−0.712784			−0.356392	+	0.934337i	$0.615993\pi$
$812$		0			0
$813$	−3.48978e8	+	4.54777e8i	−0.649421	+	0.846304i
$814$		0			0
$815$	9.00687e8	+	5.20012e8i	1.66380	+	0.960595i
$816$		0			0
$817$	−7.88299e7	−	1.36537e8i	−0.144552	−	0.250372i
$818$		0			0
$819$	−1.93596e6	−	7.22634e6i	−0.00352407	−	0.0131543i
$820$		0			0
$821$	3.30301e7	−	1.90700e7i	0.0596872	−	0.0344604i	−0.469859	−	0.882741i	$-0.655695\pi$
$821$	3.30301e7	−	1.90700e7i	0.0596872	−	0.0344604i	0.529547	+	0.848281i	$0.322362\pi$
$822$		0			0
$823$	−3.47622e8	+	6.02100e8i	−0.623603	+	1.08011i	0.365206	+	0.930927i	$0.380998\pi$
$823$	−3.47622e8	+	6.02100e8i	−0.623603	+	1.08011i	−0.988809	+	0.149185i	$0.952335\pi$
$824$		0			0
$825$	−2.55578e8	+	1.05857e8i	−0.455157	+	0.188521i
$826$		0			0
$827$			4.10947e8i			0.726556i	0.931681	+	0.363278i	$0.118342\pi$
$827$			4.10947e8i			0.726556i	−0.931681	+	0.363278i	$0.881658\pi$
$828$		0			0
$829$	−1.04443e9			−1.83322			−0.916611	−	0.399780i	$-0.869087\pi$
$829$	−1.04443e9			−1.83322			−0.916611	+	0.399780i	$0.869087\pi$
$830$		0			0
$831$	1.26676e8	+	1.66800e7i	0.220746	+	0.0290665i
$832$		0			0
$833$	4.02468e8	+	2.32365e8i	0.696300	+	0.402009i
$834$		0			0
$835$	−3.98071e8	−	6.89480e8i	−0.683757	−	1.18430i
$836$		0			0
$837$	4.75119e8	−	3.64523e8i	0.810264	−	0.621654i
$838$		0			0
$839$	2.63528e8	−	1.52148e8i	0.446212	−	0.257621i	−0.260017	−	0.965604i	$-0.583728\pi$
$839$	2.63528e8	−	1.52148e8i	0.446212	−	0.257621i	0.706229	+	0.707983i	$0.250395\pi$
$840$		0			0
$841$	2.57024e8	−	4.45179e8i	0.432101	−	0.748422i
$842$		0			0
$843$	−2.44103e7	+	1.85384e8i	−0.0407466	+	0.309449i
$844$		0			0
$845$		−	6.93544e8i		−	1.14949i
$846$		0			0
$847$	2.41308e8			0.397120
$848$		0			0
$849$	−1.88016e8	−	4.53938e8i	−0.307235	−	0.741776i
$850$		0			0
$851$	5.60519e7	+	3.23616e7i	0.0909497	+	0.0525099i
$852$		0			0
$853$	3.49067e8	+	6.04602e8i	0.562421	+	0.974142i	0.997284	+	0.0736458i	$0.0234634\pi$
$853$	3.49067e8	+	6.04602e8i	0.562421	+	0.974142i	−0.434863	+	0.900497i	$0.643203\pi$
$854$		0			0
$855$	−6.32145e7	+	2.35879e8i	−0.101139	+	0.377391i
$856$		0			0
$857$	7.22145e8	−	4.16931e8i	1.14731	−	0.662402i	0.199082	−	0.979983i	$-0.436204\pi$
$857$	7.22145e8	−	4.16931e8i	1.14731	−	0.662402i	0.948231	+	0.317581i	$0.102871\pi$
$858$		0			0
$859$	2.45038e8	−	4.24419e8i	0.386594	−	0.669600i	−0.605395	−	0.795925i	$-0.706985\pi$
$859$	2.45038e8	−	4.24419e8i	0.386594	−	0.669600i	0.991989	+	0.126325i	$0.0403183\pi$
$860$		0			0
$861$	−2.12964e8	−	1.63420e8i	−0.333654	−	0.256033i
$862$		0			0
$863$			5.57427e8i			0.867272i	0.901088	+	0.433636i	$0.142770\pi$
$863$			5.57427e8i			0.867272i	−0.901088	+	0.433636i	$0.857230\pi$
$864$		0			0
$865$	−2.83961e8			−0.438744
$866$		0			0
$867$	8.25249e7	−	1.07544e8i	0.126627	−	0.165017i
$868$		0			0
$869$	6.32629e8	+	3.65248e8i	0.964028	+	0.556582i
$870$		0			0
$871$	−2.56427e7	−	4.44145e7i	−0.0388070	−	0.0672157i
$872$		0			0
$873$	3.81491e8	−	3.81458e8i	0.573379	−	0.573330i
$874$		0			0
$875$	−1.39852e8	+	8.07434e7i	−0.208758	+	0.120527i
$876$		0			0
$877$	−2.76013e7	+	4.78069e7i	−0.0409196	+	0.0708748i	−0.885760	−	0.464144i	$-0.846362\pi$
$877$	−2.76013e7	+	4.78069e7i	−0.0409196	+	0.0708748i	0.844840	+	0.535019i	$0.179695\pi$
$878$		0			0
$879$	1.01663e8	−	4.21078e7i	0.149692	−	0.0620006i
$880$		0			0
$881$		−	8.32288e8i		−	1.21715i	−0.793495	−	0.608577i	$-0.791741\pi$
$881$		−	8.32288e8i		−	1.21715i	0.793495	−	0.608577i	$-0.208259\pi$
$882$		0			0
$883$	−8.04504e8			−1.16855			−0.584273	−	0.811557i	$-0.698620\pi$
$883$	−8.04504e8			−1.16855			−0.584273	+	0.811557i	$0.698620\pi$
$884$		0			0
$885$	1.42742e9	+	1.87954e8i	2.05931	+	0.271158i
$886$		0			0
$887$	5.50775e8	+	3.17990e8i	0.789230	+	0.455662i	0.839691	−	0.543064i	$-0.182736\pi$
$887$	5.50775e8	+	3.17990e8i	0.789230	+	0.455662i	−0.0504616	+	0.998726i	$0.516069\pi$
$888$		0			0
$889$	−6.19605e7	−	1.07319e8i	−0.0881881	−	0.152746i
$890$		0			0
$891$	5.33886e8	−	9.24534e8i	0.754771	−	1.30704i
$892$		0			0
$893$	3.28133e8	−	1.89448e8i	0.460782	−	0.266033i
$894$		0			0
$895$	−3.69600e8	+	6.40167e8i	−0.515541	+	0.892943i
$896$		0			0
$897$	−530874.	+	4.03172e6i	−0.000735553	+	0.00558615i
$898$		0			0
$899$		−	1.01313e9i		−	1.39439i
$900$		0			0
$901$	−6.82870e8			−0.933607
$902$		0			0
$903$	−7.46103e7	−	1.80136e8i	−0.101329	−	0.244646i
$904$		0			0
$905$	1.17943e9	+	6.80942e8i	1.59120	+	0.918680i
$906$		0			0
$907$	4.39576e8	+	7.61369e8i	0.589132	+	1.02041i	0.994346	+	0.106185i	$0.0338635\pi$
$907$	4.39576e8	+	7.61369e8i	0.589132	+	1.02041i	−0.405215	+	0.914222i	$0.632803\pi$
$908$		0			0
$909$	8.60925e8	+	8.60999e8i	1.14623	+	1.14633i
$910$		0			0
$911$	−5.25800e7	+	3.03571e7i	−0.0695449	+	0.0401518i	−0.534369	−	0.845251i	$-0.679451\pi$
$911$	−5.25800e7	+	3.03571e7i	−0.0695449	+	0.0401518i	0.464824	+	0.885403i	$0.346117\pi$
$912$		0			0
$913$	2.30683e8	−	3.99555e8i	0.303112	−	0.525006i
$914$		0			0
$915$	−8.29200e8	−	6.36296e8i	−1.08242	−	0.830607i
$916$		0			0
$917$		−	5.38208e7i		−	0.0697978i
$918$		0			0
$919$	1.30423e9			1.68038			0.840190	−	0.542292i	$-0.182443\pi$
$919$	1.30423e9			1.68038			0.840190	+	0.542292i	$0.182443\pi$
$920$		0			0
$921$	6.73378e8	−	8.77524e8i	0.861946	−	1.12326i
$922$		0			0
$923$	−2.32976e7	−	1.34509e7i	−0.0296282	−	0.0171059i
$924$		0			0
$925$	−1.05517e8	−	1.82761e8i	−0.133320	−	0.230918i
$926$		0			0
$927$	1.51549e8	+	4.06145e7i	0.190246	+	0.0509849i
$928$		0			0
$929$	7.30422e8	−	4.21709e8i	0.911017	−	0.525976i	0.0302588	−	0.999542i	$-0.490367\pi$
$929$	7.30422e8	−	4.21709e8i	0.911017	−	0.525976i	0.880758	+	0.473566i	$0.157034\pi$
$930$		0			0
$931$	1.23662e8	−	2.14189e8i	0.153245	−	0.265429i
$932$		0			0
$933$	1.47743e8	−	6.11936e7i	0.181913	−	0.0753462i
$934$		0			0
$935$			1.26449e9i			1.54697i
$936$		0			0
$937$	−1.31817e9			−1.60233			−0.801165	−	0.598443i	$-0.795786\pi$
$937$	−1.31817e9			−1.60233			−0.801165	+	0.598443i	$0.795786\pi$
$938$		0			0
$939$	−8.06345e8	−	1.06175e8i	−0.973922	−	0.128241i
$940$		0			0
$941$	−1.10670e9	−	6.38955e8i	−1.32820	−	0.766835i	−0.343176	−	0.939271i	$-0.611503\pi$
$941$	−1.10670e9	−	6.38955e8i	−1.32820	−	0.766835i	−0.985021	+	0.172437i	$0.944836\pi$
$942$		0			0
$943$	7.29574e7	+	1.26366e8i	0.0870030	+	0.150694i
$944$		0			0
$945$	−1.15590e8	+	2.79007e8i	−0.136969	+	0.330613i
$946$		0			0
$947$	3.28443e8	−	1.89627e8i	0.386732	−	0.223280i	−0.294011	−	0.955802i	$-0.594990\pi$
$947$	3.28443e8	−	1.89627e8i	0.386732	−	0.223280i	0.680743	+	0.732522i	$0.261657\pi$
$948$		0			0
$949$	2.43899e7	−	4.22446e7i	0.0285372	−	0.0494279i
$950$		0			0
$951$	4.89026e6	−	3.71390e7i	0.00568578	−	0.0431806i
$952$		0			0
$953$			7.90215e8i			0.912992i	0.889726	+	0.456496i	$0.150896\pi$
$953$			7.90215e8i			0.912992i	−0.889726	+	0.456496i	$0.849104\pi$
$954$		0			0
$955$	−1.33576e9			−1.53363
$956$		0			0
$957$	−6.91162e8	−	1.66871e9i	−0.788577	−	1.90391i
$958$		0			0
$959$	−1.31240e8	−	7.57715e7i	−0.148803	−	0.0859113i
$960$		0			0
$961$	−1.90731e7	−	3.30355e7i	−0.0214907	−	0.0372230i
$962$		0			0
$963$	−8.43080e8	+	2.25864e8i	−0.944039	+	0.252911i
$964$		0			0
$965$	1.20690e9	−	6.96804e8i	1.34304	−	0.775405i
$966$		0			0
$967$	−3.38801e8	+	5.86820e8i	−0.374684	+	0.648971i	−0.990280	−	0.139091i	$-0.955582\pi$
$967$	−3.38801e8	+	5.86820e8i	−0.374684	+	0.648971i	0.615596	+	0.788062i	$0.288915\pi$
$968$		0			0
$969$	2.17925e8	+	1.67227e8i	0.239516	+	0.183796i
$970$		0			0
$971$			6.48713e8i			0.708590i	0.935134	+	0.354295i	$0.115279\pi$
$971$			6.48713e8i			0.708590i	−0.935134	+	0.354295i	$0.884721\pi$
$972$		0			0
$973$	−2.99925e8			−0.325592
$974$		0			0
$975$	8.07187e6	−	1.05190e7i	0.00870884	−	0.0113491i
$976$		0			0
$977$	−9.54202e8	−	5.50909e8i	−1.02319	−	0.590739i	−0.108164	−	0.994133i	$-0.534497\pi$
$977$	−9.54202e8	−	5.50909e8i	−1.02319	−	0.590739i	−0.915027	+	0.403394i	$0.867831\pi$
$978$		0			0
$979$	8.25799e8	+	1.43033e9i	0.880088	+	1.52436i
$980$		0			0
$981$	5.07448e7	+	1.89415e8i	0.0537507	+	0.200635i
$982$		0			0
$983$	−3.68969e8	+	2.13024e8i	−0.388445	+	0.224269i	−0.681486	−	0.731831i	$-0.738666\pi$
$983$	−3.68969e8	+	2.13024e8i	−0.388445	+	0.224269i	0.293041	+	0.956100i	$0.405333\pi$
$984$		0			0
$985$	7.86758e8	−	1.36271e9i	0.823252	−	1.42591i
$986$		0			0
$987$	4.32912e8	−	1.79307e8i	0.450244	−	0.186486i
$988$		0			0
$989$			1.05983e8i			0.109559i
$990$		0			0
$991$	3.57667e8			0.367500			0.183750	−	0.982973i	$-0.441176\pi$
$991$	3.57667e8			0.367500			0.183750	+	0.982973i	$0.441176\pi$
$992$		0			0
$993$	−1.26427e8	−	1.66472e7i	−0.129120	−	0.0170018i
$994$		0			0
$995$	1.22324e9	+	7.06237e8i	1.24177	+	0.716937i
$996$		0			0
$997$	−5.84916e8	−	1.01310e9i	−0.590212	−	1.02228i	−0.994204	−	0.107515i	$-0.965711\pi$
$997$	−5.84916e8	−	1.01310e9i	−0.590212	−	1.02228i	0.403991	−	0.914763i	$-0.367623\pi$
$998$		0			0
$999$	7.52429e8	+	3.11723e8i	0.754691	+	0.312660i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.13	✓	36
3.2	odd	2		216.7.m.a.17.16		36
4.3	odd	2		144.7.q.d.113.6		36
9.2	odd	6	inner	72.7.m.a.65.13	yes	36
9.4	even	3		648.7.e.c.161.30		36
9.5	odd	6		648.7.e.c.161.7		36
9.7	even	3		216.7.m.a.89.16		36
12.11	even	2		432.7.q.d.17.16		36
36.7	odd	6		432.7.q.d.305.16		36
36.11	even	6		144.7.q.d.65.6		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.13	✓	36	1.1	even	1	trivial
72.7.m.a.65.13	yes	36	9.2	odd	6	inner
144.7.q.d.65.6		36	36.11	even	6
144.7.q.d.113.6		36	4.3	odd	2
216.7.m.a.17.16		36	3.2	odd	2
216.7.m.a.89.16		36	9.7	even	3
432.7.q.d.17.16		36	12.11	even	2
432.7.q.d.305.16		36	36.7	odd	6
648.7.e.c.161.7		36	9.5	odd	6
648.7.e.c.161.30		36	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(16.4370 - 21.4202i) q^{3} +(-124.675 - 71.9811i) q^{5} +(53.2895 + 92.3001i) q^{7} +(-188.649 - 704.168i) q^{9} +O(q^{10})\)	\(q+(16.4370 - 21.4202i) q^{3} +(-124.675 - 71.9811i) q^{5} +(53.2895 + 92.3001i) q^{7} +(-188.649 - 704.168i) q^{9} +(-1739.76 + 1004.45i) q^{11} +(48.1438 - 83.3874i) q^{13} +(-3591.13 + 1487.41i) q^{15} +4372.29i q^{17} +2326.88 q^{19} +(2853.01 + 375.668i) q^{21} +(-1354.63 - 782.094i) q^{23} +(2550.06 + 4416.84i) q^{25} +(-18184.2 - 7533.53i) q^{27} +(-28838.4 + 16649.9i) q^{29} +(-15212.2 + 26348.4i) q^{31} +(-7080.94 + 53776.1i) q^{33} -15343.4i q^{35} -41378.1 q^{37} +(-994.835 - 2401.89i) q^{39} +(-80787.0 - 46642.4i) q^{41} +(-33877.9 - 58678.2i) q^{43} +(-27167.0 + 101371. i) q^{45} +(141018. - 81416.9i) q^{47} +(53145.0 - 92049.8i) q^{49} +(93655.2 + 71867.4i) q^{51} +156182. i q^{53} +289206. q^{55} +(38247.0 - 49842.3i) q^{57} +(-320776. - 185200. i) q^{59} +(134449. + 232872. i) q^{61} +(54941.8 - 54937.1i) q^{63} +(-12004.6 + 6930.88i) q^{65} +(266314. - 461270. i) q^{67} +(-39018.6 + 16161.1i) q^{69} -279389. i q^{71} +506606. q^{73} +(136525. + 17976.8i) q^{75} +(-185422. - 107053. i) q^{77} +(-181815. - 314913. i) q^{79} +(-460264. + 265681. i) q^{81} +(-198892. + 114830. i) q^{83} +(314722. - 545115. i) q^{85} +(-117374. + 891398. i) q^{87} -822140. i q^{89} +10262.2 q^{91} +(314343. + 758938. i) q^{93} +(-290104. - 167492. i) q^{95} +(370018. + 640891. i) q^{97} +(1.03551e6 + 1.03559e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 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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