LMFDB - Embedded newform 144.7.q.d.65.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,7,Mod(65,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("144.65");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	144.q (of order $6$, degree $2$, not 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:	$33.1277880413$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.6
Character	$\chi$	$=$	144.65
Dual form			144.7.q.d.113.6

$q$-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 $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$1$

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	−0.907478	−	0.420100i	$-0.861995\pi$
$5$	−124.675	+	71.9811i	−0.997400	+	0.575849i	−0.0899218	+	0.995949i	$0.528662\pi$
$6$		0			0
$7$	−53.2895	+	92.3001i	−0.155363	+	0.269097i	−0.933191	−	0.359380i	$-0.882988\pi$
$7$	−53.2895	+	92.3001i	−0.155363	+	0.269097i	0.777828	+	0.628477i	$0.216321\pi$
$8$		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	$-0.0611358\pi$
$11$	1739.76	+	1004.45i	1.30711	+	0.754659i	0.325495	+	0.945544i	$0.394469\pi$
$12$		0			0
$13$	48.1438	+	83.3874i	0.0219134	+	0.0379551i	0.876774	−	0.480902i	$-0.159691\pi$
$13$	48.1438	+	83.3874i	0.0219134	+	0.0379551i	−0.854861	+	0.518858i	$0.826358\pi$
$14$		0			0
$15$	3591.13	+	1487.41i	1.06404	+	0.440713i
$16$		0			0
$17$		−	4372.29i		−	0.889942i	−0.895545	−	0.444971i	$-0.853214\pi$
$17$		−	4372.29i		−	0.889942i	0.895545	−	0.444971i	$-0.146786\pi$
$18$		0			0
$19$	−2326.88			−0.339245			−0.169623	−	0.985509i	$-0.554255\pi$
$19$	−2326.88			−0.339245			−0.169623	+	0.985509i	$0.554255\pi$
$20$		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	$-0.646192\pi$
$23$	1354.63	−	782.094i	0.111336	−	0.0642799i	0.554634	+	0.832094i	$0.312858\pi$
$24$		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	−0.225858	−	0.974160i	$-0.572519\pi$
$29$	−28838.4	−	16649.9i	−1.18243	−	0.682679i	−0.956577	+	0.291481i	$0.905852\pi$
$30$		0			0
$31$	15212.2	+	26348.4i	0.510632	+	0.884441i	0.999924	+	0.0123209i	$0.00392198\pi$
$31$	15212.2	+	26348.4i	0.510632	+	0.884441i	−0.489292	+	0.872120i	$0.662745\pi$
$32$		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	−0.954190	−	0.299203i	$-0.903279\pi$
$41$	−80787.0	+	46642.4i	−1.17217	+	0.676751i	−0.217978	+	0.975954i	$0.569946\pi$
$42$		0			0
$43$	33877.9	−	58678.2i	0.426099	−	0.738026i	−0.570423	−	0.821351i	$-0.693221\pi$
$43$	33877.9	−	58678.2i	0.426099	−	0.738026i	0.996522	+	0.0833254i	$0.0265541\pi$
$44$		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	$-0.620254\pi$
$47$	−141018.	−	81416.9i	−1.35826	−	0.784190i	−0.989389	+	0.145292i	$0.953588\pi$
$48$		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	$-0.824240\pi$
$53$		−	156182.i		−	1.04906i	0.851391	−	0.524532i	$-0.175760\pi$
$54$		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	0.564807	−	0.825223i	$-0.308951\pi$
$59$	320776.	−	185200.i	1.56187	−	0.901749i	0.997068	−	0.0765256i	$-0.0243827\pi$
$60$		0			0
$61$	134449.	−	232872.i	0.592336	−	1.02596i	−0.401581	−	0.915823i	$-0.631539\pi$
$61$	134449.	−	232872.i	0.592336	−	1.02596i	0.993917	−	0.110132i	$-0.0351274\pi$
$62$		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	−0.845183	−	0.534477i	$-0.820509\pi$
$67$	−266314.	−	461270.i	−0.885462	−	1.53367i	−0.0402793	−	0.999188i	$-0.512825\pi$
$68$		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	$-0.713114\pi$
$79$	181815.	−	314913.i	0.368764	−	0.638718i	0.989373	+	0.145403i	$0.0464478\pi$
$80$		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	$-0.268970\pi$
$83$	198892.	+	114830.i	0.347843	+	0.200827i	−0.315892	+	0.948795i	$0.602304\pi$
$84$		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	$0.198162\pi$
$89$			822140.i			1.16621i	−0.812398	+	0.583104i	$0.801838\pi$
$90$		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	−0.588948	−	0.808171i	$-0.700458\pi$
$97$	370018.	−	640891.i	0.405423	−	0.702213i	0.994371	+	0.105958i	$0.0337910\pi$
$98$		0			0
$99$	−1.03551e6	+	1.03559e6i	−1.06720	+	1.06729i
$100$		0			0
$101$	−1.44645e6	−	835106.i	−1.40391	−	0.810545i	−0.409115	−	0.912483i	$-0.634162\pi$
$101$	−1.44645e6	−	835106.i	−1.40391	−	0.810545i	−0.994791	+	0.101938i	$0.967496\pi$
$102$		0			0
$103$	107611.	+	186388.i	0.0984795	+	0.170571i	0.911055	−	0.412284i	$-0.135269\pi$
$103$	107611.	+	186388.i	0.0984795	+	0.170571i	−0.812576	+	0.582855i	$0.801935\pi$
$104$		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	−0.761069	−	0.648671i	$-0.775325\pi$
$113$	−836647.	+	483038.i	−0.579838	+	0.334770i	0.181231	+	0.983441i	$0.441992\pi$
$114$		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	$-0.408401\pi$
$127$	1.16272e6			0.567626			0.283813	+	0.958880i	$0.408401\pi$
$128$		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	$-0.630840\pi$
$131$	437330.	−	252492.i	0.194534	−	0.112314i	0.594103	+	0.804389i	$0.297507\pi$
$132$		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	0.241065	−	0.970509i	$-0.422503\pi$
$137$	−1.23139e6	−	710942.i	−0.478887	−	0.276486i	−0.719953	+	0.694023i	$0.755837\pi$
$138$		0			0
$139$	1.40705e6	+	2.43709e6i	0.523921	+	0.907458i	0.999612	+	0.0278457i	$0.00886470\pi$
$139$	1.40705e6	+	2.43709e6i	0.523921	+	0.907458i	−0.475691	+	0.879612i	$0.657802\pi$
$140$		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	−0.341378	−	0.939926i	$-0.610894\pi$
$149$	998781.	−	576646.i	0.301933	−	0.174321i	0.643311	+	0.765605i	$0.277560\pi$
$150$		0			0
$151$	−785975.	+	1.36135e6i	−0.228285	+	0.395402i	−0.957300	−	0.289096i	$-0.906645\pi$
$151$	−785975.	+	1.36135e6i	−0.228285	+	0.395402i	0.729015	+	0.684498i	$0.239979\pi$
$152$		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	0.845221	+	0.534417i	$0.179469\pi$
$157$	3.42652e6	+	5.93490e6i	0.885429	+	1.53361i	0.0402080	+	0.999191i	$0.487198\pi$
$158$		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	$-0.186006\pi$
$163$	7.22428e6			1.66814			0.834069	+	0.551660i	$0.186006\pi$
$164$		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	$-0.868998\pi$
$167$	−4.78931e6	+	2.76511e6i	−1.02831	+	0.593694i	−0.111809	+	0.993730i	$0.535665\pi$
$168$		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	0.655804	−	0.754931i	$-0.272330\pi$
$173$	1.70821e6	+	986236.i	0.329916	+	0.190477i	−0.325888	+	0.945408i	$0.605663\pi$
$174$		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	$-0.565248\pi$
$191$	−8.03548e6	−	4.63929e6i	−1.15322	−	0.665811i	−0.949670	+	0.313253i	$0.898581\pi$
$192$		0			0
$193$	−4.84018e6	−	8.38344e6i	−0.673271	−	1.16614i	−0.976971	−	0.213372i	$-0.931555\pi$
$193$	−4.84018e6	−	8.38344e6i	−0.673271	−	1.16614i	0.303700	−	0.952768i	$-0.401778\pi$
$194$		0			0
$195$	48859.7	+	371065.i	0.00658942	+	0.0500433i
$196$		0			0
$197$		−	1.09301e7i		−	1.42963i	−0.699313	−	0.714816i	$-0.746511\pi$
$197$		−	1.09301e7i		−	1.42963i	0.699313	−	0.714816i	$-0.253489\pi$
$198$		0			0
$199$	9.81142e6			1.24501			0.622505	−	0.782616i	$-0.286115\pi$
$199$	9.81142e6			1.24501			0.622505	+	0.782616i	$0.286115\pi$
$200$		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	$-0.316067\pi$
$211$	−4.24898e6	−	7.35946e6i	−0.452312	−	0.783427i	−0.998529	+	0.0542165i	$0.982734\pi$
$212$		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	0.0386755	+	0.999252i	$0.487686\pi$
$223$	−9.38221e6	+	1.62505e7i	−0.846040	+	1.46538i	−0.884715	+	0.466132i	$0.845647\pi$
$224$		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	$-0.379596\pi$
$227$	−2.93422e6	−	1.69407e6i	−0.250851	−	0.144829i	−0.620154	+	0.784480i	$0.712930\pi$
$228$		0			0
$229$	−1.78200e6	−	3.08652e6i	−0.148389	−	0.257018i	0.782243	−	0.622973i	$-0.214076\pi$
$229$	−1.78200e6	−	3.08652e6i	−0.148389	−	0.257018i	−0.930632	+	0.365956i	$0.880742\pi$
$230$		0			0
$231$	5.34089e6	+	2.21213e6i	0.433289	+	0.179463i
$232$		0			0
$233$		−	1.98835e7i		−	1.57190i	−0.618291	−	0.785949i	$-0.712175\pi$
$233$		−	1.98835e7i		−	1.57190i	0.618291	−	0.785949i	$-0.287825\pi$
$234$		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	$-0.691236\pi$
$239$	−1.82336e6	+	1.05272e6i	−0.133561	+	0.0771113i	0.431731	+	0.902002i	$0.357903\pi$
$240$		0			0
$241$	−1.31473e6	+	2.27719e6i	−0.0939262	+	0.162685i	−0.909160	−	0.416447i	$-0.863275\pi$
$241$	−1.31473e6	+	2.27719e6i	−0.0939262	+	0.162685i	0.815234	+	0.579132i	$0.196608\pi$
$242$		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	−0.358693	−	0.933456i	$-0.616777\pi$
$257$	4.58920e6	−	2.64958e6i	0.270357	−	0.156091i	0.629050	+	0.777365i	$0.283444\pi$
$258$		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	$-0.503520\pi$
$263$	−1.60550e7	−	9.26938e6i	−0.882560	−	0.509546i	−0.871502	+	0.490393i	$0.836853\pi$
$264$		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	$0.264613\pi$
$269$			2.87621e7i			1.47762i	−0.673912	+	0.738811i	$0.735387\pi$
$270$		0			0
$271$	2.12312e7			1.06676			0.533380	−	0.845875i	$-0.320921\pi$
$271$	2.12312e7			1.06676			0.533380	+	0.845875i	$0.320921\pi$
$272$		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	−0.804979	−	0.593303i	$-0.797824\pi$
$277$	2.36611e6	−	4.09821e6i	0.111326	−	0.192821i	0.916305	+	0.400481i	$0.131157\pi$
$278$		0			0
$279$	−2.14235e7	+	5.74139e6i	−0.986454	+	0.264365i
$280$		0			0
$281$	−5.99752e6	−	3.46267e6i	−0.270304	−	0.156060i	0.358722	−	0.933445i	$-0.383213\pi$
$281$	−5.99752e6	−	3.46267e6i	−0.270304	−	0.156060i	−0.629026	+	0.777384i	$0.716546\pi$
$282$		0			0
$283$	−9.09878e6	−	1.57595e7i	−0.401443	−	0.695320i	0.592457	−	0.805602i	$-0.298158\pi$
$283$	−9.09878e6	−	1.57595e7i	−0.401443	−	0.695320i	−0.993900	+	0.110282i	$0.964825\pi$
$284$		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	−0.428198	−	0.903685i	$-0.640851\pi$
$293$	3.52950e6	−	2.03776e6i	0.140317	−	0.0810120i	0.568515	+	0.822673i	$0.307518\pi$
$294$		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	$-0.750371\pi$
$307$	−4.09672e7			−1.41586			−0.707931	+	0.706282i	$0.750371\pi$
$308$		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	$-0.698055\pi$
$311$	−5.12927e6	+	2.96139e6i	−0.170520	+	0.0984496i	0.412311	+	0.911043i	$0.364722\pi$
$312$		0			0
$313$	−1.50612e7	+	2.60868e7i	−0.491164	+	0.850721i	−0.999948	−	0.0101728i	$-0.996762\pi$
$313$	−1.50612e7	+	2.60868e7i	−0.491164	+	0.850721i	0.508784	+	0.860894i	$0.330095\pi$
$314$		0			0
$315$	1.08043e7	+	2.89451e6i	0.345673	+	0.0926068i
$316$		0			0
$317$	1.20152e6	+	693697.i	0.0377183	+	0.0217767i	0.518741	−	0.854932i	$-0.326401\pi$
$317$	1.20152e6	+	693697.i	0.0377183	+	0.0217767i	−0.481022	+	0.876708i	$0.659734\pi$
$318$		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	$-0.812591\pi$
$331$	2.36146e6	−	4.09016e6i	0.0651172	−	0.112786i	0.896746	+	0.442546i	$0.145925\pi$
$332$		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	0.915354	+	0.402651i	$0.131911\pi$
$337$	3.08625e7	+	5.34554e7i	0.806383	+	1.39670i	−0.108971	+	0.994045i	$0.534756\pi$
$338$		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	$-0.396545\pi$
$347$	5.43027e7	−	3.13517e7i	1.29967	−	0.750365i	0.980347	+	0.197282i	$0.0632113\pi$
$348$		0			0
$349$	3.44844e7	−	5.97287e7i	0.811233	−	1.40510i	−0.100768	−	0.994910i	$-0.532130\pi$
$349$	3.44844e7	−	5.97287e7i	0.811233	−	1.40510i	0.912001	−	0.410188i	$-0.134537\pi$
$350$		0			0
$351$	1.50366e6	+	1.15364e6i	0.0347719	+	0.0266778i
$352$		0			0
$353$	−1.84347e7	−	1.06433e7i	−0.419095	−	0.241965i	0.275595	−	0.961274i	$-0.411125\pi$
$353$	−1.84347e7	−	1.06433e7i	−0.419095	−	0.241965i	−0.694690	+	0.719309i	$0.744458\pi$
$354$		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	$-0.790438\pi$
$367$	6.64119e6	−	1.15029e7i	0.134353	−	0.232706i	0.925350	+	0.379114i	$0.123771\pi$
$368$		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	0.843085	−	0.537780i	$-0.180737\pi$
$373$	−2.29319e6	−	3.97192e6i	−0.0441889	−	0.0765374i	−0.887274	+	0.461243i	$0.847404\pi$
$374$		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	$-0.542760\pi$
$379$	−1.45824e7			−0.267863			−0.133931	+	0.990991i	$0.542760\pi$
$380$		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	$-0.443670\pi$
$383$	6.27308e7	−	3.62176e7i	1.11657	−	0.644650i	0.940522	+	0.339732i	$0.110337\pi$
$384$		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	0.985049	−	0.172276i	$-0.0551121\pi$
$389$	7.81934e7	+	4.51450e7i	1.32838	+	0.766939i	0.343329	+	0.939215i	$0.388445\pi$
$390$		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	0.111364	−	0.993780i	$-0.464478\pi$
$401$	6.62663e7	−	3.82589e7i	1.02768	−	0.593334i	0.916320	+	0.400446i	$0.131145\pi$
$402$		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	0.920524	−	0.390686i	$-0.127762\pi$
$409$	8.34137e6	+	1.44477e7i	0.121918	+	0.211168i	−0.798606	+	0.601854i	$0.794429\pi$
$410$		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	$-0.675723\pi$
$419$	−3.62457e6	+	2.09265e6i	−0.0492736	+	0.0284481i	0.475161	+	0.879899i	$0.342390\pi$
$420$		0			0
$421$	−4.24928e7	+	7.35996e7i	−0.569467	+	0.986346i	0.427151	+	0.904180i	$0.359517\pi$
$421$	−4.24928e7	+	7.35996e7i	−0.569467	+	0.986346i	−0.996619	+	0.0821661i	$0.973816\pi$
$422$		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	$-0.809714\pi$
$439$	6.27209e6	−	1.08636e7i	0.0741343	−	0.128404i	0.900709	+	0.434422i	$0.143047\pi$
$440$		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	$-0.400960\pi$
$443$	−3.17519e7	−	1.83319e7i	−0.365223	−	0.210861i	−0.671369	+	0.741123i	$0.734294\pi$
$444$		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	$-0.903478\pi$
$449$		−	5.40589e7i		−	0.597212i	0.954376	−	0.298606i	$-0.0965216\pi$
$450$		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	−0.712911	−	0.701255i	$-0.752624\pi$
$457$	2.39420e7	−	4.14688e7i	0.250849	−	0.434483i	0.963760	+	0.266772i	$0.0859569\pi$
$458$		0			0
$459$	−3.29388e7	−	7.95067e7i	−0.340619	−	0.822178i
$460$		0			0
$461$	−1.07133e8	−	6.18534e7i	−1.09351	−	0.631337i	−0.158999	−	0.987279i	$-0.550827\pi$
$461$	−1.07133e8	−	6.18534e7i	−1.09351	−	0.631337i	−0.934508	+	0.355942i	$0.884160\pi$
$462$		0			0
$463$	−2.61569e7	−	4.53052e7i	−0.263538	−	0.456462i	0.703641	−	0.710555i	$-0.251556\pi$
$463$	−2.61569e7	−	4.53052e7i	−0.263538	−	0.456462i	−0.967180	+	0.254093i	$0.918223\pi$
$464$		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	$-0.498505\pi$
$479$	−9.44028e7	−	5.45035e7i	−0.858971	−	0.495927i	−0.863668	+	0.504062i	$0.831838\pi$
$480$		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	$-0.217597\pi$
$487$	1.79097e8			1.55061			0.775303	+	0.631590i	$0.217597\pi$
$488$		0			0
$489$	−1.18746e8	−	1.54745e8i	−1.01553	−	1.32340i
$490$		0			0
$491$	−1.99035e8	+	1.14913e8i	−1.68146	+	0.970790i	−0.720762	+	0.693183i	$0.756208\pi$
$491$	−1.99035e8	+	1.14913e8i	−1.68146	+	0.970790i	−0.960695	+	0.277607i	$0.910459\pi$
$492$		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	$-0.165491\pi$
$499$	458787.	+	794643.i	0.00369241	+	0.00639544i	−0.864173	+	0.503194i	$0.832158\pi$
$500$		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	0.316927	−	0.948450i	$-0.397349\pi$
$509$	1.71008e8	−	9.87317e7i	1.29677	−	0.748692i	0.979845	+	0.199758i	$0.0640156\pi$
$510$		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	$0.0611200\pi$
$521$			5.39765e7i			0.381673i	−0.981622	+	0.190836i	$0.938880\pi$
$522$		0			0
$523$	1.09281e8			0.763909			0.381954	−	0.924181i	$-0.375251\pi$
$523$	1.09281e8			0.763909			0.381954	+	0.924181i	$0.375251\pi$
$524$		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	$-0.712542\pi$
$547$	6.06280e7	−	1.05011e8i	0.370434	−	0.641611i	0.989632	+	0.143624i	$0.0458756\pi$
$548$		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	$0.0551160\pi$
$557$			5.95457e7i			0.344576i	−0.985047	+	0.172288i	$0.944884\pi$
$558$		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	$-0.375997\pi$
$563$	2.44627e8	−	1.41236e8i	1.37082	−	0.791442i	0.991031	+	0.133632i	$0.0426639\pi$
$564$		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	0.537624	−	0.843185i	$-0.319322\pi$
$569$	1.40407e7	+	8.10640e6i	0.0762170	+	0.0440039i	−0.461407	+	0.887188i	$0.652655\pi$
$570$		0			0
$571$	1.40346e8	+	2.43086e8i	0.753860	+	1.30572i	0.945939	+	0.324345i	$0.105144\pi$
$571$	1.40346e8	+	2.43086e8i	0.753860	+	1.30572i	−0.192079	+	0.981380i	$0.561523\pi$
$572$		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	$-0.374120\pi$
$587$	−4.47664e7	−	2.58459e7i	−0.221329	−	0.127784i	−0.606565	+	0.795034i	$0.707453\pi$
$588$		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	$-0.962951\pi$
$593$		−	4.84333e7i		−	0.232263i	0.993234	−	0.116132i	$-0.0370494\pi$
$594$		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	$-0.669692\pi$
$599$	−3.53845e6	+	2.04292e6i	−0.0164639	+	0.00950543i	0.491745	+	0.870739i	$0.336359\pi$
$600$		0			0
$601$	−3.90601e7	+	6.76540e7i	−0.179932	+	0.311652i	−0.941857	−	0.336013i	$-0.890921\pi$
$601$	−3.90601e7	+	6.76540e7i	−0.179932	+	0.311652i	0.761925	+	0.647666i	$0.224255\pi$
$602$		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	$-0.268574\pi$
$607$	−7.03843e7	−	1.21909e8i	−0.314709	−	0.545093i	−0.979376	+	0.202048i	$0.935240\pi$
$608$		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	0.0585887	−	0.998282i	$-0.481340\pi$
$617$	2.23709e8	−	1.29159e8i	0.952421	−	0.549880i	0.893832	+	0.448402i	$0.148007\pi$
$618$		0			0
$619$	−9.28102e7	+	1.60752e8i	−0.391312	+	0.677773i	−0.992623	−	0.121242i	$-0.961312\pi$
$619$	−9.28102e7	+	1.60752e8i	−0.391312	+	0.677773i	0.601310	+	0.799015i	$0.294645\pi$
$620$		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	$-0.578931\pi$
$631$	−1.23326e8			−0.490871			−0.245435	+	0.969413i	$0.578931\pi$
$632$		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	−0.0789374	−	0.996880i	$-0.525153\pi$
$641$	−2.58563e8	−	1.49281e8i	−0.981729	−	0.566802i	−0.902792	+	0.430078i	$0.858486\pi$
$642$		0			0
$643$	3.66786e7	+	6.35293e7i	0.137969	+	0.238969i	0.926728	−	0.375734i	$-0.122609\pi$
$643$	3.66786e7	+	6.35293e7i	0.137969	+	0.238969i	−0.788759	+	0.614703i	$0.789276\pi$
$644$		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	−0.587319	+	0.809356i	$0.699817\pi$
$653$	−4.40473e8	+	2.54307e8i	−1.58190	+	0.913311i	−0.994582	+	0.103955i	$0.966850\pi$
$654$		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	$-0.525845\pi$
$659$	−2.81850e8	−	1.62726e8i	−0.984830	−	0.568592i	−0.903725	+	0.428114i	$0.859178\pi$
$660$		0			0
$661$	5.06288e7	+	8.76917e7i	0.175305	+	0.303637i	0.940267	−	0.340439i	$-0.110576\pi$
$661$	5.06288e7	+	8.76917e7i	0.175305	+	0.303637i	−0.764962	+	0.644075i	$0.777242\pi$
$662$		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	0.402962	+	0.915217i	$0.367981\pi$
$673$	−1.80186e8	+	3.12091e8i	−0.591120	+	1.02385i	−0.994082	+	0.108633i	$0.965353\pi$
$674$		0			0
$675$	1.30966e7	−	9.95279e7i	0.0425839	−	0.323619i
$676$		0			0
$677$	−1.21214e8	−	6.99830e7i	−0.390649	−	0.225542i	0.291792	−	0.956482i	$-0.405748\pi$
$677$	−1.21214e8	−	6.99830e7i	−0.390649	−	0.225542i	−0.682441	+	0.730940i	$0.739082\pi$
$678$		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	$-0.678548\pi$
$691$	1.54192e8	−	2.67069e8i	0.467335	−	0.809447i	0.999303	+	0.0373166i	$0.0118810\pi$
$692$		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	$0.0853882\pi$
$701$			1.82604e8i			0.530099i	−0.964235	+	0.265049i	$0.914612\pi$
$702$		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	−0.537248	−	0.843424i	$-0.680536\pi$
$709$	1.64587e8	−	2.85073e8i	0.461803	−	0.799865i	0.999051	+	0.0435587i	$0.0138695\pi$
$710$		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	−0.422875	−	0.906188i	$-0.638979\pi$
$727$	2.20302e8	−	3.81574e8i	0.573344	−	0.993061i	0.996219	−	0.0868730i	$-0.0276874\pi$
$728$		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	−0.998823	−	0.0485091i	$-0.984553\pi$
$733$	−2.13230e8	−	3.69324e8i	−0.541422	−	0.937770i	0.457401	−	0.889260i	$-0.348780\pi$
$734$		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	$-0.628199\pi$
$739$	−3.16367e8			−0.783895			−0.391947	+	0.919988i	$0.628199\pi$
$740$		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	$-0.578353\pi$
$743$	1.94589e8	−	1.12346e8i	0.474409	−	0.273900i	0.718084	+	0.695957i	$0.245020\pi$
$744$		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	$-0.295798\pi$
$751$	−1.67156e8	−	2.89522e8i	−0.394641	−	0.683538i	−0.993055	+	0.117649i	$0.962464\pi$
$752$		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	−0.207376	−	0.978261i	$-0.566492\pi$
$761$	2.36281e8	−	1.36417e8i	0.536135	−	0.309538i	0.743511	+	0.668724i	$0.233159\pi$
$762$		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	−0.994315	−	0.106483i	$-0.966041\pi$
$769$	−2.68022e8	−	4.64227e8i	−0.589374	−	1.02083i	0.404940	−	0.914343i	$-0.367292\pi$
$770$		0			0
$771$	−1.32187e8	−	5.47504e7i	−0.288421	−	0.119460i
$772$		0			0
$773$			6.46060e8i			1.39873i	0.714764	+	0.699366i	$0.246534\pi$
$773$			6.46060e8i			1.39873i	−0.714764	+	0.699366i	$0.753466\pi$
$774$		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	$-0.194997\pi$
$787$	−4.33267e7	−	7.50441e7i	−0.0888857	−	0.153954i	−0.907040	+	0.421044i	$0.861664\pi$
$788$		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	−0.740535	−	0.672018i	$-0.765428\pi$
$797$	−2.67720e8	+	1.54568e8i	−0.528818	+	0.305313i	0.211717	+	0.977331i	$0.432095\pi$
$798$		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	$-0.765888\pi$
$809$		−	7.10498e8i		−	1.34189i	0.741507	−	0.670945i	$-0.234112\pi$
$810$		0			0
$811$	3.80207e8			0.712784			0.356392	−	0.934337i	$-0.384007\pi$
$811$	3.80207e8			0.712784			0.356392	+	0.934337i	$0.384007\pi$
$812$		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	0.529547	−	0.848281i	$-0.322362\pi$
$821$	3.30301e7	+	1.90700e7i	0.0596872	+	0.0344604i	−0.469859	+	0.882741i	$0.655695\pi$
$822$		0			0
$823$	3.47622e8	+	6.02100e8i	0.623603	+	1.08011i	0.988809	+	0.149185i	$0.0476651\pi$
$823$	3.47622e8	+	6.02100e8i	0.623603	+	1.08011i	−0.365206	+	0.930927i	$0.619002\pi$
$824$		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	$-0.416272\pi$
$839$	−2.63528e8	−	1.52148e8i	−0.446212	−	0.257621i	−0.706229	+	0.707983i	$0.749605\pi$
$840$		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	−0.434863	−	0.900497i	$-0.643203\pi$
$853$	3.49067e8	−	6.04602e8i	0.562421	−	0.974142i	0.997284	−	0.0736458i	$-0.0234634\pi$
$854$		0			0
$855$	6.32145e7	+	2.35879e8i	0.101139	+	0.377391i
$856$		0			0
$857$	7.22145e8	+	4.16931e8i	1.14731	+	0.662402i	0.948231	−	0.317581i	$-0.102871\pi$
$857$	7.22145e8	+	4.16931e8i	1.14731	+	0.662402i	0.199082	+	0.979983i	$0.436204\pi$
$858$		0			0
$859$	−2.45038e8	−	4.24419e8i	−0.386594	−	0.669600i	0.605395	−	0.795925i	$-0.293015\pi$
$859$	−2.45038e8	−	4.24419e8i	−0.386594	−	0.669600i	−0.991989	+	0.126325i	$0.959682\pi$
$860$		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	0.844840	−	0.535019i	$-0.179695\pi$
$877$	−2.76013e7	−	4.78069e7i	−0.0409196	−	0.0708748i	−0.885760	+	0.464144i	$0.846362\pi$
$878$		0			0
$879$	−1.01663e8	−	4.21078e7i	−0.149692	−	0.0620006i
$880$		0			0
$881$			8.32288e8i			1.21715i	0.793495	+	0.608577i	$0.208259\pi$
$881$			8.32288e8i			1.21715i	−0.793495	+	0.608577i	$0.791741\pi$
$882$		0			0
$883$	8.04504e8			1.16855			0.584273	−	0.811557i	$-0.301380\pi$
$883$	8.04504e8			1.16855			0.584273	+	0.811557i	$0.301380\pi$
$884$		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	$-0.817264\pi$
$887$	−5.50775e8	+	3.17990e8i	−0.789230	+	0.455662i	0.0504616	+	0.998726i	$0.483931\pi$
$888$		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	0.405215	+	0.914222i	$0.367197\pi$
$907$	−4.39576e8	+	7.61369e8i	−0.589132	+	1.02041i	−0.994346	+	0.106185i	$0.966137\pi$
$908$		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	$-0.320549\pi$
$911$	5.25800e7	+	3.03571e7i	0.0695449	+	0.0401518i	−0.464824	+	0.885403i	$0.653883\pi$
$912$		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	$-0.817557\pi$
$919$	−1.30423e9			−1.68038			−0.840190	+	0.542292i	$0.817557\pi$
$920$		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	0.880758	−	0.473566i	$-0.157034\pi$
$929$	7.30422e8	+	4.21709e8i	0.911017	+	0.525976i	0.0302588	+	0.999542i	$0.490367\pi$
$930$		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	−0.985021	−	0.172437i	$-0.944836\pi$
$941$	−1.10670e9	+	6.38955e8i	−1.32820	+	0.766835i	−0.343176	+	0.939271i	$0.611503\pi$
$942$		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	$-0.405010\pi$
$947$	−3.28443e8	−	1.89627e8i	−0.386732	−	0.223280i	−0.680743	+	0.732522i	$0.738343\pi$
$948$		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	$-0.849104\pi$
$953$		−	7.90215e8i		−	0.912992i	0.889726	−	0.456496i	$-0.150896\pi$
$954$		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	$-0.0444180\pi$
$967$	3.38801e8	+	5.86820e8i	0.374684	+	0.648971i	−0.615596	+	0.788062i	$0.711085\pi$
$968$		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	−0.915027	−	0.403394i	$-0.867831\pi$
$977$	−9.54202e8	+	5.50909e8i	−1.02319	+	0.590739i	−0.108164	+	0.994133i	$0.534497\pi$
$978$		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	$-0.261334\pi$
$983$	3.68969e8	+	2.13024e8i	0.388445	+	0.224269i	−0.293041	+	0.956100i	$0.594667\pi$
$984$		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	$-0.558824\pi$
$991$	−3.57667e8			−0.367500			−0.183750	+	0.982973i	$0.558824\pi$
$992$		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	0.403991	+	0.914763i	$0.367623\pi$
$997$	−5.84916e8	+	1.01310e9i	−0.590212	+	1.02228i	−0.994204	+	0.107515i	$0.965711\pi$
$998$		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	144.7.q.d.65.6		36
3.2	odd	2		432.7.q.d.305.16		36
4.3	odd	2		72.7.m.a.65.13	yes	36
9.4	even	3		432.7.q.d.17.16		36
9.5	odd	6	inner	144.7.q.d.113.6		36
12.11	even	2		216.7.m.a.89.16		36
36.7	odd	6		648.7.e.c.161.7		36
36.11	even	6		648.7.e.c.161.30		36
36.23	even	6		72.7.m.a.41.13	✓	36
36.31	odd	6		216.7.m.a.17.16		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.13	✓	36	36.23	even	6
72.7.m.a.65.13	yes	36	4.3	odd	2
144.7.q.d.65.6		36	1.1	even	1	trivial
144.7.q.d.113.6		36	9.5	odd	6	inner
216.7.m.a.17.16		36	36.31	odd	6
216.7.m.a.89.16		36	12.11	even	2
432.7.q.d.17.16		36	9.4	even	3
432.7.q.d.305.16		36	3.2	odd	2
648.7.e.c.161.7		36	36.7	odd	6
648.7.e.c.161.30		36	36.11	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	144.q (of order \(6\), degree \(2\), not 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

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Representations

Groups

Database

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