LMFDB - Embedded newform 72.7.m.a.41.1

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			41.1
Character	$\chi$	$=$	72.41
Dual form			72.7.m.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.9340 - 1.88607i) q^{3} +(43.3462 + 25.0260i) q^{5} +(47.2533 + 81.8451i) q^{7} +(721.885 + 101.599i) q^{9} +O(q^{10})$	\(q+(-26.9340 - 1.88607i) q^{3} +(43.3462 + 25.0260i) q^{5} +(47.2533 + 81.8451i) q^{7} +(721.885 + 101.599i) q^{9} +(-300.659 + 173.586i) q^{11} +(130.240 - 225.583i) q^{13} +(-1120.29 - 755.805i) q^{15} -1803.83i q^{17} -8109.62 q^{19} +(-1118.36 - 2293.54i) q^{21} +(-17630.4 - 10178.9i) q^{23} +(-6559.90 - 11362.1i) q^{25} +(-19251.7 - 4098.00i) q^{27} +(-6412.04 + 3701.99i) q^{29} +(4894.49 - 8477.50i) q^{31} +(8425.36 - 4108.30i) q^{33} +4730.24i q^{35} -2221.66 q^{37} +(-3933.36 + 5830.21i) q^{39} +(-11705.7 - 6758.30i) q^{41} +(-32780.2 - 56777.0i) q^{43} +(28748.4 + 22469.8i) q^{45} +(-80870.1 + 46690.4i) q^{47} +(54358.8 - 94152.1i) q^{49} +(-3402.15 + 48584.4i) q^{51} +84671.5i q^{53} -17376.6 q^{55} +(218425. + 15295.3i) q^{57} +(-108395. - 62582.1i) q^{59} +(25533.1 + 44224.6i) q^{61} +(25796.1 + 63883.7i) q^{63} +(11290.8 - 6518.77i) q^{65} +(99125.3 - 171690. i) q^{67} +(455660. + 307412. i) q^{69} +397626. i q^{71} +522867. q^{73} +(155255. + 318399. i) q^{75} +(-28414.3 - 16405.0i) q^{77} +(-273140. - 473092. i) q^{79} +(510796. + 146686. i) q^{81} +(-642501. + 370948. i) q^{83} +(45142.5 - 78189.2i) q^{85} +(179684. - 87616.0i) q^{87} -267951. i q^{89} +24617.1 q^{91} +(-147817. + 219102. i) q^{93} +(-351522. - 202951. i) q^{95} +(-702146. - 1.21615e6i) q^{97} +(-234677. + 94762.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−26.9340	−	1.88607i	−0.997557	−	0.0698545i
$3$	−26.9340	−	1.88607i	−0.997557	−	0.0698545i
$4$		0			0
$5$	43.3462	+	25.0260i	0.346770	+	0.200208i	0.663262	−	0.748388i	$-0.269172\pi$
$5$	43.3462	+	25.0260i	0.346770	+	0.200208i	−0.316492	+	0.948595i	$0.602505\pi$
$6$		0			0
$7$	47.2533	+	81.8451i	0.137765	+	0.238616i	0.926650	−	0.375925i	$-0.122675\pi$
$7$	47.2533	+	81.8451i	0.137765	+	0.238616i	−0.788885	+	0.614540i	$0.789342\pi$
$8$		0			0
$9$	721.885	+	101.599i	0.990241	+	0.139368i
$10$		0			0
$11$	−300.659	+	173.586i	−0.225890	+	0.130417i	−0.608674	−	0.793420i	$-0.708298\pi$
$11$	−300.659	+	173.586i	−0.225890	+	0.130417i	0.382785	+	0.923838i	$0.374965\pi$
$12$		0			0
$13$	130.240	−	225.583i	0.0592809	−	0.102678i	−0.834862	−	0.550459i	$-0.814453\pi$
$13$	130.240	−	225.583i	0.0592809	−	0.102678i	0.894143	+	0.447782i	$0.147786\pi$
$14$		0			0
$15$	−1120.29	−	755.805i	−0.331937	−	0.223942i
$16$		0			0
$17$		−	1803.83i		−	0.367154i	−0.983005	−	0.183577i	$-0.941232\pi$
$17$		−	1803.83i		−	0.367154i	0.983005	−	0.183577i	$-0.0587677\pi$
$18$		0			0
$19$	−8109.62			−1.18233			−0.591167	−	0.806550i	$-0.701332\pi$
$19$	−8109.62			−1.18233			−0.591167	+	0.806550i	$0.701332\pi$
$20$		0			0
$21$	−1118.36	−	2293.54i	−0.120760	−	0.247656i
$22$		0			0
$23$	−17630.4	−	10178.9i	−1.44904	−	0.836601i	−0.450611	−	0.892720i	$-0.648794\pi$
$23$	−17630.4	−	10178.9i	−1.44904	−	0.836601i	−0.998424	+	0.0561191i	$0.982127\pi$
$24$		0			0
$25$	−6559.90	−	11362.1i	−0.419834	−	0.727173i
$26$		0			0
$27$	−19251.7	−	4098.00i	−0.978086	−	0.208200i
$28$		0			0
$29$	−6412.04	+	3701.99i	−0.262907	+	0.151789i	−0.625660	−	0.780096i	$-0.715170\pi$
$29$	−6412.04	+	3701.99i	−0.262907	+	0.151789i	0.362753	+	0.931885i	$0.381837\pi$
$30$		0			0
$31$	4894.49	−	8477.50i	0.164294	−	0.284566i	−0.772110	−	0.635489i	$-0.780799\pi$
$31$	4894.49	−	8477.50i	0.164294	−	0.284566i	0.936404	+	0.350923i	$0.114132\pi$
$32$		0			0
$33$	8425.36	−	4108.30i	0.234448	−	0.114319i
$34$		0			0
$35$			4730.24i			0.110326i
$36$		0			0
$37$	−2221.66			−0.0438603			−0.0219302	−	0.999760i	$-0.506981\pi$
$37$	−2221.66			−0.0438603			−0.0219302	+	0.999760i	$0.506981\pi$
$38$		0			0
$39$	−3933.36	+	5830.21i	−0.0663086	+	0.0982857i
$40$		0			0
$41$	−11705.7	−	6758.30i	−0.169843	−	0.0980586i	0.412669	−	0.910881i	$-0.364597\pi$
$41$	−11705.7	−	6758.30i	−0.169843	−	0.0980586i	−0.582512	+	0.812822i	$0.697930\pi$
$42$		0			0
$43$	−32780.2	−	56777.0i	−0.412294	−	0.714114i	0.582846	−	0.812582i	$-0.301939\pi$
$43$	−32780.2	−	56777.0i	−0.412294	−	0.714114i	−0.995140	+	0.0984685i	$0.968606\pi$
$44$		0			0
$45$	28748.4	+	22469.8i	0.315483	+	0.246582i
$46$		0			0
$47$	−80870.1	+	46690.4i	−0.778923	+	0.449711i	−0.836048	−	0.548656i	$-0.815140\pi$
$47$	−80870.1	+	46690.4i	−0.778923	+	0.449711i	0.0571255	+	0.998367i	$0.481806\pi$
$48$		0			0
$49$	54358.8	−	94152.1i	0.462042	−	0.800280i
$50$		0			0
$51$	−3402.15	+	48584.4i	−0.0256474	+	0.366257i
$52$		0			0
$53$			84671.5i			0.568734i	0.958715	+	0.284367i	$0.0917835\pi$
$53$			84671.5i			0.568734i	−0.958715	+	0.284367i	$0.908217\pi$
$54$		0			0
$55$	−17376.6			−0.104442
$56$		0			0
$57$	218425.	+	15295.3i	1.17944	+	0.0825913i
$58$		0			0
$59$	−108395.	−	62582.1i	−0.527782	−	0.304715i	0.212331	−	0.977198i	$-0.431895\pi$
$59$	−108395.	−	62582.1i	−0.527782	−	0.304715i	−0.740113	+	0.672483i	$0.765228\pi$
$60$		0			0
$61$	25533.1	+	44224.6i	0.112490	+	0.194838i	0.916774	−	0.399407i	$-0.130784\pi$
$61$	25533.1	+	44224.6i	0.112490	+	0.194838i	−0.804284	+	0.594246i	$0.797451\pi$
$62$		0			0
$63$	25796.1	+	63883.7i	0.103165	+	0.255487i
$64$		0			0
$65$	11290.8	−	6518.77i	0.0411137	−	0.0237370i
$66$		0			0
$67$	99125.3	−	171690.i	0.329579	−	0.570848i	−0.652849	−	0.757488i	$-0.726426\pi$
$67$	99125.3	−	171690.i	0.329579	−	0.570848i	0.982428	+	0.186640i	$0.0597597\pi$
$68$		0			0
$69$	455660.	+	307412.i	1.38706	+	0.935779i
$70$		0			0
$71$			397626.i			1.11096i	0.831529	+	0.555481i	$0.187466\pi$
$71$			397626.i			1.11096i	−0.831529	+	0.555481i	$0.812534\pi$
$72$		0			0
$73$	522867.			1.34407			0.672036	−	0.740518i	$-0.265420\pi$
$73$	522867.			1.34407			0.672036	+	0.740518i	$0.265420\pi$
$74$		0			0
$75$	155255.	+	318399.i	0.368012	+	0.754724i
$76$		0			0
$77$	−28414.3	−	16405.0i	−0.0622392	−	0.0359338i
$78$		0			0
$79$	−273140.	−	473092.i	−0.553992	−	0.959542i	−0.997981	−	0.0635100i	$-0.979771\pi$
$79$	−273140.	−	473092.i	−0.553992	−	0.959542i	0.443989	−	0.896032i	$-0.353563\pi$
$80$		0			0
$81$	510796.	+	146686.i	0.961153	+	0.276015i
$82$		0			0
$83$	−642501.	+	370948.i	−1.12367	+	0.648752i	−0.942336	−	0.334669i	$-0.891375\pi$
$83$	−642501.	+	370948.i	−1.12367	+	0.648752i	−0.181336	+	0.983421i	$0.558042\pi$
$84$		0			0
$85$	45142.5	−	78189.2i	0.0735071	−	0.127318i
$86$		0			0
$87$	179684.	−	87616.0i	0.272868	−	0.133053i
$88$		0			0
$89$		−	267951.i		−	0.380089i	−0.981776	−	0.190044i	$-0.939137\pi$
$89$		−	267951.i		−	0.380089i	0.981776	−	0.190044i	$-0.0608632\pi$
$90$		0			0
$91$	24617.1			0.0326673
$92$		0			0
$93$	−147817.	+	219102.i	−0.183771	+	0.272394i
$94$		0			0
$95$	−351522.	−	202951.i	−0.409998	−	0.236712i
$96$		0			0
$97$	−702146.	−	1.21615e6i	−0.769329	−	1.33252i	−0.937927	−	0.346832i	$-0.887258\pi$
$97$	−702146.	−	1.21615e6i	−0.769329	−	1.33252i	0.168599	−	0.985685i	$-0.446076\pi$
$98$		0			0
$99$	−234677.	+	94762.2i	−0.241861	+	0.0976629i
$100$		0			0
$101$	−1.37646e6	+	794700.i	−1.33598	+	0.771328i	−0.986208	−	0.165508i	$-0.947074\pi$
$101$	−1.37646e6	+	794700.i	−1.33598	+	0.771328i	−0.349770	+	0.936836i	$0.613740\pi$
$102$		0			0
$103$	958725.	−	1.66056e6i	0.877369	−	1.51965i	0.0231519	−	0.999732i	$-0.492630\pi$
$103$	958725.	−	1.66056e6i	0.877369	−	1.51965i	0.854217	−	0.519916i	$-0.174037\pi$
$104$		0			0
$105$	8921.57	−	127404.i	0.00770679	−	0.110057i
$106$		0			0
$107$			929634.i			0.758858i	0.925221	+	0.379429i	$0.123880\pi$
$107$			929634.i			0.758858i	−0.925221	+	0.379429i	$0.876120\pi$
$108$		0			0
$109$	−1.30847e6			−1.01038			−0.505190	−	0.863008i	$-0.668578\pi$
$109$	−1.30847e6			−1.01038			−0.505190	+	0.863008i	$0.668578\pi$
$110$		0			0
$111$	59838.2	+	4190.21i	0.0437532	+	0.00306384i
$112$		0			0
$113$	−2.09554e6	−	1.20986e6i	−1.45231	−	0.838494i	−0.453701	−	0.891154i	$-0.649897\pi$
$113$	−2.09554e6	−	1.20986e6i	−1.45231	−	0.838494i	−0.998612	+	0.0526605i	$0.983230\pi$
$114$		0			0
$115$	−509475.	−	882436.i	−0.334988	−	0.580216i
$116$		0			0
$117$	116937.	−	149613.i	0.0730123	−	0.0934136i
$118$		0			0
$119$	147635.	−	85236.9i	0.0876087	−	0.0505809i
$120$		0			0
$121$	−825517.	+	1.42984e6i	−0.465983	+	0.807106i
$122$		0			0
$123$	302536.	+	204106.i	0.162578	+	0.109683i
$124$		0			0
$125$		−	1.43873e6i		−	0.736631i
$126$		0			0
$127$	2.56556e6			1.25248			0.626239	−	0.779631i	$-0.284593\pi$
$127$	2.56556e6			1.25248			0.626239	+	0.779631i	$0.284593\pi$
$128$		0			0
$129$	775819.	+	1.59106e6i	0.361403	+	0.741170i
$130$		0			0
$131$	1.95681e6	+	1.12976e6i	0.870430	+	0.502543i	0.867491	−	0.497453i	$-0.165731\pi$
$131$	1.95681e6	+	1.12976e6i	0.870430	+	0.502543i	0.00293907	+	0.999996i	$0.499064\pi$
$132$		0			0
$133$	−383206.	−	663733.i	−0.162884	−	0.282123i
$134$		0			0
$135$	−731931.	−	659425.i	−0.297488	−	0.268018i
$136$		0			0
$137$	−885360.	+	511163.i	−0.344317	+	0.198791i	−0.662179	−	0.749345i	$-0.730368\pi$
$137$	−885360.	+	511163.i	−0.344317	+	0.198791i	0.317862	+	0.948137i	$0.397035\pi$
$138$		0			0
$139$	80418.9	−	139290.i	0.0299443	−	0.0518650i	−0.850665	−	0.525708i	$-0.823800\pi$
$139$	80418.9	−	139290.i	0.0299443	−	0.0518650i	0.880609	+	0.473843i	$0.157134\pi$
$140$		0			0
$141$	2.26622e6	−	1.10503e6i	0.808435	−	0.394201i
$142$		0			0
$143$			90431.2i			0.0309250i
$144$		0			0
$145$	−370584.			−0.121558
$146$		0			0
$147$	−1.64168e6	+	2.43337e6i	−0.516816	+	0.766049i
$148$		0			0
$149$	−283066.	−	163428.i	−0.0855716	−	0.0494048i	0.456604	−	0.889670i	$-0.349066\pi$
$149$	−283066.	−	163428.i	−0.0855716	−	0.0494048i	−0.542175	+	0.840265i	$0.682399\pi$
$150$		0			0
$151$	−102248.	−	177099.i	−0.0296977	−	0.0514380i	0.850795	−	0.525498i	$-0.176121\pi$
$151$	−102248.	−	177099.i	−0.0296977	−	0.0514380i	−0.880492	+	0.474060i	$0.842788\pi$
$152$		0			0
$153$	183267.	−	1.30216e6i	0.0511695	−	0.363571i
$154$		0			0
$155$	424315.	−	244978.i	0.113945	−	0.0657859i
$156$		0			0
$157$	−2.94115e6	+	5.09422e6i	−0.760008	+	1.31637i	0.182838	+	0.983143i	$0.441472\pi$
$157$	−2.94115e6	+	5.09422e6i	−0.760008	+	1.31637i	−0.942846	+	0.333229i	$0.891862\pi$
$158$		0			0
$159$	159697.	−	2.28055e6i	0.0397287	−	0.567345i
$160$		0			0
$161$		−	1.92395e6i		−	0.461016i
$162$		0			0
$163$	3.72674e6			0.860530			0.430265	−	0.902703i	$-0.358420\pi$
$163$	3.72674e6			0.860530			0.430265	+	0.902703i	$0.358420\pi$
$164$		0			0
$165$	468022.	+	32773.5i	0.104187	+	0.00729577i
$166$		0			0
$167$	5.86777e6	+	3.38776e6i	1.25986	+	0.727382i	0.973048	−	0.230603i	$-0.0740700\pi$
$167$	5.86777e6	+	3.38776e6i	1.25986	+	0.727382i	0.286816	+	0.957986i	$0.407403\pi$
$168$		0			0
$169$	2.37948e6	+	4.12138e6i	0.492972	+	0.853852i
$170$		0			0
$171$	−5.85422e6	−	823931.i	−1.17079	−	0.164779i
$172$		0			0
$173$	6.64433e6	−	3.83610e6i	1.28325	−	0.740887i	0.305812	−	0.952092i	$-0.401072\pi$
$173$	6.64433e6	−	3.83610e6i	1.28325	−	0.740887i	0.977442	+	0.211205i	$0.0677387\pi$
$174$		0			0
$175$	619954.	−	1.07379e6i	0.115677	−	0.200358i
$176$		0			0
$177$	2.80149e6	+	1.89003e6i	0.505207	+	0.340839i
$178$		0			0
$179$			7.94400e6i			1.38510i	0.721372	+	0.692548i	$0.243512\pi$
$179$			7.94400e6i			1.38510i	−0.721372	+	0.692548i	$0.756488\pi$
$180$		0			0
$181$	2.19228e6			0.369710			0.184855	−	0.982766i	$-0.440818\pi$
$181$	2.19228e6			0.369710			0.184855	+	0.982766i	$0.440818\pi$
$182$		0			0
$183$	−604299.	−	1.23931e6i	−0.0986049	−	0.202220i
$184$		0			0
$185$	−96300.5	−	55599.1i	−0.0152094	−	0.00878117i
$186$		0			0
$187$	313118.	+	542337.i	0.0478833	+	0.0829363i
$188$		0			0
$189$	−574303.	−	1.76930e6i	−0.0850660	−	0.262069i
$190$		0			0
$191$	7.86024e6	−	4.53811e6i	1.12807	−	0.651291i	0.184620	−	0.982810i	$-0.440894\pi$
$191$	7.86024e6	−	4.53811e6i	1.12807	−	0.651291i	0.943449	+	0.331519i	$0.107561\pi$
$192$		0			0
$193$	−6.06203e6	+	1.04997e7i	−0.843230	+	1.46052i	0.0439189	+	0.999035i	$0.486016\pi$
$193$	−6.06203e6	+	1.04997e7i	−0.843230	+	1.46052i	−0.887149	+	0.461483i	$0.847318\pi$
$194$		0			0
$195$	−316403.	+	154282.i	−0.0426714	+	0.0208070i
$196$		0			0
$197$		−	7.23520e6i		−	0.946350i	−0.880968	−	0.473175i	$-0.843108\pi$
$197$		−	7.23520e6i		−	0.946350i	0.880968	−	0.473175i	$-0.156892\pi$
$198$		0			0
$199$	6.79293e6			0.861981			0.430991	−	0.902356i	$-0.358164\pi$
$199$	6.79293e6			0.861981			0.430991	+	0.902356i	$0.358164\pi$
$200$		0			0
$201$	−2.99366e6	+	4.43735e6i	−0.368651	+	0.546431i
$202$		0			0
$203$	−605980.	−	349863.i	−0.0724386	−	0.0418224i
$204$		0			0
$205$	−338266.	−	585894.i	−0.0392642	−	0.0680076i
$206$		0			0
$207$	−1.16930e7	−	9.13925e6i	−1.31830	−	1.03039i
$208$		0			0
$209$	2.43823e6	−	1.40771e6i	0.267077	−	0.154197i
$210$		0			0
$211$	−7.92009e6	+	1.37180e7i	−0.843107	+	1.46030i	0.0441472	+	0.999025i	$0.485943\pi$
$211$	−7.92009e6	+	1.37180e7i	−0.843107	+	1.46030i	−0.887255	+	0.461280i	$0.847390\pi$
$212$		0			0
$213$	749951.	−	1.07097e7i	0.0776058	−	1.10825i
$214$		0			0
$215$		−	3.28143e6i		−	0.330178i
$216$		0			0
$217$	925122.			0.0905357
$218$		0			0
$219$	−1.40829e7	−	986165.i	−1.34079	−	0.0938896i
$220$		0			0
$221$	−406912.	−	234931.i	−0.0376985	−	0.0217652i
$222$		0			0
$223$	−1.01499e7	−	1.75802e7i	−0.915267	−	1.58529i	−0.806509	−	0.591221i	$-0.798646\pi$
$223$	−1.01499e7	−	1.75802e7i	−0.915267	−	1.58529i	−0.108758	−	0.994068i	$-0.534687\pi$
$224$		0			0
$225$	−3.58112e6	−	8.86860e6i	−0.314392	−	0.778588i
$226$		0			0
$227$	−6.08023e6	+	3.51042e6i	−0.519808	+	0.300111i	−0.736856	−	0.676050i	$-0.763690\pi$
$227$	−6.08023e6	+	3.51042e6i	−0.519808	+	0.300111i	0.217048	+	0.976161i	$0.430357\pi$
$228$		0			0
$229$	−5.68083e6	+	9.83948e6i	−0.473048	+	0.819343i	−0.999524	−	0.0308468i	$-0.990180\pi$
$229$	−5.68083e6	+	9.83948e6i	−0.473048	+	0.819343i	0.526476	+	0.850190i	$0.323513\pi$
$230$		0			0
$231$	734370.	+	495444.i	0.0595770	+	0.0401937i
$232$		0			0
$233$		−	1.66215e7i		−	1.31402i	−0.753882	−	0.657010i	$-0.771821\pi$
$233$		−	1.66215e7i		−	1.31402i	0.753882	−	0.657010i	$-0.228179\pi$
$234$		0			0
$235$	−4.67389e6			−0.360143
$236$		0			0
$237$	6.46447e6	+	1.32574e7i	0.485610	+	0.995897i
$238$		0			0
$239$	−7.25205e6	−	4.18697e6i	−0.531211	−	0.306695i	0.210299	−	0.977637i	$-0.432556\pi$
$239$	−7.25205e6	−	4.18697e6i	−0.531211	−	0.306695i	−0.741509	+	0.670943i	$0.765890\pi$
$240$		0			0
$241$	1.17661e6	+	2.03795e6i	0.0840587	+	0.145594i	0.904990	−	0.425433i	$-0.139878\pi$
$241$	1.17661e6	+	2.03795e6i	0.0840587	+	0.145594i	−0.820931	+	0.571027i	$0.806545\pi$
$242$		0			0
$243$	−1.34811e7	−	4.91424e6i	−0.939524	−	0.342482i
$244$		0			0
$245$	4.71249e6	−	2.72076e6i	0.320444	−	0.185009i
$246$		0			0
$247$	−1.05620e6	+	1.82939e6i	−0.0700898	+	0.121399i
$248$		0			0
$249$	1.80048e7	−	8.77933e6i	1.16624	−	0.568674i
$250$		0			0
$251$			1.16696e7i			0.737960i	0.929437	+	0.368980i	$0.120293\pi$
$251$			1.16696e7i			0.737960i	−0.929437	+	0.368980i	$0.879707\pi$
$252$		0			0
$253$	7.06766e6			0.436429
$254$		0			0
$255$	−1.36334e6	+	2.02081e6i	−0.0822213	+	0.121872i
$256$		0			0
$257$	9.36599e6	+	5.40746e6i	0.551765	+	0.318562i	0.749834	−	0.661626i	$-0.230133\pi$
$257$	9.36599e6	+	5.40746e6i	0.551765	+	0.318562i	−0.198068	+	0.980188i	$0.563467\pi$
$258$		0			0
$259$	−104981.	−	181832.i	−0.00604241	−	0.0104658i
$260$		0			0
$261$	−5.00487e6	+	2.02096e6i	−0.281496	+	0.113667i
$262$		0			0
$263$	9.43770e6	−	5.44886e6i	0.518799	−	0.299529i	−0.217644	−	0.976028i	$-0.569837\pi$
$263$	9.43770e6	−	5.44886e6i	0.518799	−	0.299529i	0.736443	+	0.676499i	$0.236504\pi$
$264$		0			0
$265$	−2.11899e6	+	3.67019e6i	−0.113865	+	0.197220i
$266$		0			0
$267$	−505375.	+	7.21700e6i	−0.0265509	+	0.379160i
$268$		0			0
$269$			1.14678e7i			0.589148i	0.955629	+	0.294574i	$0.0951777\pi$
$269$			1.14678e7i			0.589148i	−0.955629	+	0.294574i	$0.904822\pi$
$270$		0			0
$271$	2.28328e7			1.14723			0.573616	−	0.819124i	$-0.305540\pi$
$271$	2.28328e7			1.14723			0.573616	+	0.819124i	$0.305540\pi$
$272$		0			0
$273$	−663038.	−	46429.7i	−0.0325875	−	0.00228196i
$274$		0			0
$275$	3.94459e6	+	2.27741e6i	0.189672	+	0.109507i
$276$		0			0
$277$	−8.00512e6	−	1.38653e7i	−0.376642	−	0.652363i	0.613930	−	0.789361i	$-0.289588\pi$
$277$	−8.00512e6	−	1.38653e7i	−0.376642	−	0.652363i	−0.990571	+	0.136998i	$0.956255\pi$
$278$		0			0
$279$	4.39456e6	−	5.62251e6i	0.202350	−	0.258891i
$280$		0			0
$281$	−1.98103e7	+	1.14375e7i	−0.892839	+	0.515481i	−0.874870	−	0.484358i	$-0.839053\pi$
$281$	−1.98103e7	+	1.14375e7i	−0.892839	+	0.515481i	−0.0179688	+	0.999839i	$0.505720\pi$
$282$		0			0
$283$	−129170.	+	223729.i	−0.00569904	+	0.00987103i	−0.868861	−	0.495056i	$-0.835147\pi$
$283$	−129170.	+	223729.i	−0.00569904	+	0.00987103i	0.863162	+	0.504927i	$0.168481\pi$
$284$		0			0
$285$	9.08512e6	+	6.12929e6i	0.392461	+	0.264774i
$286$		0			0
$287$		−	1.27741e6i		−	0.0540361i
$288$		0			0
$289$	2.08838e7			0.865198
$290$		0			0
$291$	1.66179e7	+	3.40802e7i	0.674367	+	1.38300i
$292$		0			0
$293$	2.70256e6	+	1.56032e6i	0.107441	+	0.0620313i	0.552758	−	0.833342i	$-0.313575\pi$
$293$	2.70256e6	+	1.56032e6i	0.107441	+	0.0620313i	−0.445316	+	0.895373i	$0.646909\pi$
$294$		0			0
$295$	−3.13235e6	−	5.42540e6i	−0.122013	−	0.211332i
$296$		0			0
$297$	6.49954e6	−	2.10971e6i	0.248092	−	0.0805292i
$298$		0			0
$299$	−4.59238e6	+	2.65141e6i	−0.171800	+	0.0991890i
$300$		0			0
$301$	3.09795e6	−	5.36581e6i	0.113599	−	0.196759i
$302$		0			0
$303$	3.85725e7	−	1.88084e7i	1.38660	−	0.676119i
$304$		0			0
$305$			2.55596e6i			0.0900855i
$306$		0			0
$307$	2.13914e7			0.739304			0.369652	−	0.929170i	$-0.379477\pi$
$307$	2.13914e7			0.739304			0.369652	+	0.929170i	$0.379477\pi$
$308$		0			0
$309$	−2.89543e7	+	4.29174e7i	−0.981380	+	1.45465i
$310$		0			0
$311$	−608086.	−	351079.i	−0.0202155	−	0.0116714i	0.489858	−	0.871802i	$-0.337049\pi$
$311$	−608086.	−	351079.i	−0.0202155	−	0.0116714i	−0.510074	+	0.860131i	$0.670382\pi$
$312$		0			0
$313$	−1.97544e7	−	3.42157e7i	−0.644216	−	1.11582i	−0.984482	−	0.175486i	$-0.943850\pi$
$313$	−1.97544e7	−	3.42157e7i	−0.644216	−	1.11582i	0.340266	−	0.940329i	$-0.389483\pi$
$314$		0			0
$315$	−480588.	+	3.41469e6i	−0.0153759	+	0.109250i
$316$		0			0
$317$	−3.11347e7	+	1.79756e7i	−0.977388	+	0.564295i	−0.901481	−	0.432820i	$-0.857519\pi$
$317$	−3.11347e7	+	1.79756e7i	−0.977388	+	0.564295i	−0.0759076	+	0.997115i	$0.524185\pi$
$318$		0			0
$319$	1.28522e6	−	2.22607e6i	0.0395919	−	0.0685752i
$320$		0			0
$321$	1.75336e6	−	2.50388e7i	0.0530097	−	0.757005i
$322$		0			0
$323$			1.46284e7i			0.434099i
$324$		0			0
$325$	−3.41745e6			−0.0995525
$326$		0			0
$327$	3.52424e7	+	2.46787e6i	1.00791	+	0.0705796i
$328$		0			0
$329$	−7.64276e6	−	4.41255e6i	−0.214616	−	0.123909i
$330$		0			0
$331$	−5.56272e6	−	9.63492e6i	−0.153392	−	0.265683i	0.779080	−	0.626924i	$-0.215686\pi$
$331$	−5.56272e6	−	9.63492e6i	−0.153392	−	0.265683i	−0.932472	+	0.361241i	$0.882353\pi$
$332$		0			0
$333$	−1.60378e6	−	225718.i	−0.0434323	−	0.00611272i
$334$		0			0
$335$	8.59342e6	−	4.96141e6i	0.228576	−	0.131969i
$336$		0			0
$337$	−270186.	+	467976.i	−0.00705949	+	0.0122274i	−0.869534	−	0.493874i	$-0.835580\pi$
$337$	−270186.	+	467976.i	−0.00705949	+	0.0122274i	0.862474	+	0.506101i	$0.168914\pi$
$338$		0			0
$339$	5.41594e7	+	3.65388e7i	1.39019	+	0.937896i
$340$		0			0
$341$			3.39845e6i			0.0857072i
$342$		0			0
$343$	2.13931e7			0.530142
$344$		0			0
$345$	1.20579e7	+	2.47285e7i	0.293639	+	0.602199i
$346$		0			0
$347$	−4.64762e7	−	2.68330e7i	−1.11235	−	0.642216i	−0.172914	−	0.984937i	$-0.555318\pi$
$347$	−4.64762e7	−	2.68330e7i	−1.11235	−	0.642216i	−0.939437	+	0.342721i	$0.888651\pi$
$348$		0			0
$349$	−2.10601e7	−	3.64772e7i	−0.495433	−	0.858116i	0.504553	−	0.863381i	$-0.331657\pi$
$349$	−2.10601e7	−	3.64772e7i	−0.495433	−	0.858116i	−0.999986	+	0.00526522i	$0.998324\pi$
$350$		0			0
$351$	−3.43178e6	+	3.80912e6i	−0.0793593	+	0.0880852i
$352$		0			0
$353$	−4.62869e7	+	2.67237e7i	−1.05229	+	0.607537i	−0.923288	−	0.384108i	$-0.874509\pi$
$353$	−4.62869e7	+	2.67237e7i	−1.05229	+	0.607537i	−0.128997	+	0.991645i	$0.541176\pi$
$354$		0			0
$355$	−9.95097e6	+	1.72356e7i	−0.222423	+	0.385248i
$356$		0			0
$357$	−4.13716e6	+	2.01732e6i	−0.0909280	+	0.0443375i
$358$		0			0
$359$			8.43724e6i			0.182355i	0.995835	+	0.0911773i	$0.0290630\pi$
$359$			8.43724e6i			0.182355i	−0.995835	+	0.0911773i	$0.970937\pi$
$360$		0			0
$361$	1.87201e7			0.397911
$362$		0			0
$363$	2.49313e7	−	3.69543e7i	0.521224	−	0.772583i
$364$		0			0
$365$	2.26643e7	+	1.30852e7i	0.466084	+	0.269094i
$366$		0			0
$367$	−2.56716e7	−	4.44645e7i	−0.519344	−	0.899530i	−0.999747	−	0.0224823i	$-0.992843\pi$
$367$	−2.56716e7	−	4.44645e7i	−0.519344	−	0.899530i	0.480403	−	0.877048i	$-0.340490\pi$
$368$		0			0
$369$	−7.76355e6	−	6.06801e6i	−0.154519	−	0.120772i
$370$		0			0
$371$	−6.92995e6	+	4.00101e6i	−0.135709	+	0.0783516i
$372$		0			0
$373$	4.03014e7	−	6.98042e7i	0.776594	−	1.34510i	−0.157300	−	0.987551i	$-0.550279\pi$
$373$	4.03014e7	−	6.98042e7i	0.776594	−	1.34510i	0.933894	−	0.357550i	$-0.116388\pi$
$374$		0			0
$375$	−2.71355e6	+	3.87509e7i	−0.0514570	+	0.734832i
$376$		0			0
$377$			1.92859e6i			0.0359928i
$378$		0			0
$379$	−6.25088e7			−1.14822			−0.574108	−	0.818780i	$-0.694651\pi$
$379$	−6.25088e7			−1.14822			−0.574108	+	0.818780i	$0.694651\pi$
$380$		0			0
$381$	−6.91008e7	−	4.83882e6i	−1.24942	−	0.0874913i
$382$		0			0
$383$	−7.76855e7	−	4.48517e7i	−1.38275	−	0.798331i	−0.390266	−	0.920702i	$-0.627617\pi$
$383$	−7.76855e7	−	4.48517e7i	−1.38275	−	0.798331i	−0.992484	+	0.122371i	$0.960950\pi$
$384$		0			0
$385$	−821101.	−	1.42219e6i	−0.0143885	−	0.0249215i
$386$		0			0
$387$	−1.78951e7	−	4.43170e7i	−0.308746	−	0.764605i
$388$		0			0
$389$	−5.57627e6	+	3.21946e6i	−0.0947316	+	0.0546933i	−0.546617	−	0.837382i	$-0.684085\pi$
$389$	−5.57627e6	+	3.21946e6i	−0.0947316	+	0.0546933i	0.451886	+	0.892076i	$0.350751\pi$
$390$		0			0
$391$	−1.83610e7	+	3.18022e7i	−0.307162	+	0.532019i
$392$		0			0
$393$	−5.05739e7	−	3.41198e7i	−0.833199	−	0.562119i
$394$		0			0
$395$		−	2.73423e7i		−	0.443654i
$396$		0			0
$397$	2.83276e7			0.452729			0.226365	−	0.974043i	$-0.427316\pi$
$397$	2.83276e7			0.452729			0.226365	+	0.974043i	$0.427316\pi$
$398$		0			0
$399$	9.06945e6	+	1.85998e7i	0.142778	+	0.292812i
$400$		0			0
$401$	1.26754e7	+	7.31814e6i	0.196575	+	0.113493i	0.595057	−	0.803684i	$-0.297129\pi$
$401$	1.26754e7	+	7.31814e6i	0.196575	+	0.113493i	−0.398482	+	0.917176i	$0.630463\pi$
$402$		0			0
$403$	−1.27492e6	−	2.20822e6i	−0.0194790	−	0.0337386i
$404$		0			0
$405$	1.84701e7	+	1.91414e7i	0.278039	+	0.288144i
$406$		0			0
$407$	667961.	−	385647.i	0.00990759	−	0.00572015i
$408$		0			0
$409$	−1.24499e7	+	2.15639e7i	−0.181969	+	0.315179i	−0.942551	−	0.334063i	$-0.891580\pi$
$409$	−1.24499e7	+	2.15639e7i	−0.181969	+	0.315179i	0.760582	+	0.649242i	$0.224914\pi$
$410$		0			0
$411$	2.48104e7	−	1.20978e7i	0.357362	−	0.174254i
$412$		0			0
$413$		−	1.18288e7i		−	0.167916i
$414$		0			0
$415$	−3.71333e7			−0.519541
$416$		0			0
$417$	−2.42872e6	+	3.59996e6i	−0.0334941	+	0.0496466i
$418$		0			0
$419$	−2.36861e7	−	1.36752e7i	−0.321996	−	0.185905i	0.330286	−	0.943881i	$-0.392855\pi$
$419$	−2.36861e7	−	1.36752e7i	−0.321996	−	0.185905i	−0.652282	+	0.757976i	$0.726188\pi$
$420$		0			0
$421$	−3.65424e7	−	6.32932e7i	−0.489723	−	0.848225i	0.510207	−	0.860051i	$-0.329569\pi$
$421$	−3.65424e7	−	6.32932e7i	−0.489723	−	0.848225i	−0.999930	+	0.0118268i	$0.996235\pi$
$422$		0			0
$423$	−6.31227e7	+	2.54888e7i	−0.833996	+	0.336766i
$424$		0			0
$425$	−2.04953e7	+	1.18329e7i	−0.266985	+	0.154144i
$426$		0			0
$427$	−2.41305e6	+	4.17952e6i	−0.0309943	+	0.0536837i
$428$		0			0
$429$	170560.	−	2.43568e6i	0.00216025	−	0.0308495i
$430$		0			0
$431$			1.66388e7i			0.207822i	0.994587	+	0.103911i	$0.0331357\pi$
$431$			1.66388e7i			0.207822i	−0.994587	+	0.103911i	$0.966864\pi$
$432$		0			0
$433$	6.90956e7			0.851111			0.425556	−	0.904932i	$-0.360079\pi$
$433$	6.90956e7			0.851111			0.425556	+	0.904932i	$0.360079\pi$
$434$		0			0
$435$	9.98131e6	+	698947.i	0.121261	+	0.00849135i
$436$		0			0
$437$	1.42976e8	+	8.25472e7i	1.71324	+	0.989141i
$438$		0			0
$439$	6.42802e7	+	1.11337e8i	0.759772	+	1.31596i	0.942966	+	0.332888i	$0.108023\pi$
$439$	6.42802e7	+	1.11337e8i	0.759772	+	1.31596i	−0.183194	+	0.983077i	$0.558644\pi$
$440$		0			0
$441$	4.88066e7	−	6.24442e7i	0.569066	−	0.728076i
$442$		0			0
$443$	1.19805e8	−	6.91694e7i	1.37805	−	0.795615i	0.386121	−	0.922448i	$-0.373815\pi$
$443$	1.19805e8	−	6.91694e7i	1.37805	−	0.795615i	0.991924	+	0.126833i	$0.0404813\pi$
$444$		0			0
$445$	6.70572e6	−	1.16147e7i	0.0760967	−	0.131803i
$446$		0			0
$447$	7.31589e6	+	4.93567e6i	0.0819114	+	0.0552617i
$448$		0			0
$449$			8.72014e7i			0.963351i	0.876350	+	0.481676i	$0.159972\pi$
$449$			8.72014e7i			0.963351i	−0.876350	+	0.481676i	$0.840028\pi$
$450$		0			0
$451$	4.69257e6			0.0511542
$452$		0			0
$453$	2.41993e6	+	4.96283e6i	0.0260320	+	0.0533869i
$454$		0			0
$455$	1.06706e6	+	616067.i	0.0113280	+	0.00654024i
$456$		0			0
$457$	8.32538e7	+	1.44200e8i	0.872279	+	1.51083i	0.859634	+	0.510911i	$0.170692\pi$
$457$	8.32538e7	+	1.44200e8i	0.872279	+	1.51083i	0.0126451	+	0.999920i	$0.495975\pi$
$458$		0			0
$459$	−7.39210e6	+	3.47267e7i	−0.0764416	+	0.359108i
$460$		0			0
$461$	1.20062e8	−	6.93180e7i	1.22547	−	0.707527i	0.259393	−	0.965772i	$-0.416477\pi$
$461$	1.20062e8	−	6.93180e7i	1.22547	−	0.707527i	0.966079	+	0.258245i	$0.0831441\pi$
$462$		0			0
$463$	−6.29492e7	+	1.09031e8i	−0.634230	+	1.09852i	0.352447	+	0.935832i	$0.385350\pi$
$463$	−6.29492e7	+	1.09031e8i	−0.634230	+	1.09852i	−0.986678	+	0.162688i	$0.947984\pi$
$464$		0			0
$465$	−1.18906e7	+	5.79797e6i	−0.118262	+	0.0576656i
$466$		0			0
$467$		−	4.47224e7i		−	0.439111i	−0.975600	−	0.219556i	$-0.929539\pi$
$467$		−	4.47224e7i		−	0.439111i	0.975600	−	0.219556i	$-0.0704607\pi$
$468$		0			0
$469$	1.87360e7			0.181618
$470$		0			0
$471$	8.88251e7	−	1.31661e8i	0.850106	−	1.26007i
$472$		0			0
$473$	1.97113e7	+	1.13804e7i	0.186266	+	0.107541i
$474$		0			0
$475$	5.31983e7	+	9.21422e7i	0.496383	+	0.859761i
$476$		0			0
$477$	−8.60255e6	+	6.11231e7i	−0.0792633	+	0.563184i
$478$		0			0
$479$	1.77174e7	−	1.02292e7i	0.161211	−	0.0930750i	−0.417224	−	0.908804i	$-0.636997\pi$
$479$	1.77174e7	−	1.02292e7i	0.161211	−	0.0930750i	0.578435	+	0.815729i	$0.303664\pi$
$480$		0			0
$481$	−289349.	+	501167.i	−0.00260008	+	0.00450347i
$482$		0			0
$483$	−3.62871e6	+	5.18198e7i	−0.0322041	+	0.459890i
$484$		0			0
$485$		−	7.02875e7i		−	0.616102i
$486$		0			0
$487$	−1.25702e8			−1.08831			−0.544157	−	0.838984i	$-0.683150\pi$
$487$	−1.25702e8			−1.08831			−0.544157	+	0.838984i	$0.683150\pi$
$488$		0			0
$489$	−1.00376e8	−	7.02890e6i	−0.858428	−	0.0601120i
$490$		0			0
$491$	−4.83092e7	−	2.78913e7i	−0.408118	−	0.235627i	0.281863	−	0.959455i	$-0.409048\pi$
$491$	−4.83092e7	−	2.78913e7i	−0.408118	−	0.235627i	−0.689981	+	0.723828i	$0.742381\pi$
$492$		0			0
$493$	6.67776e6	+	1.15662e7i	0.0557301	+	0.0965274i
$494$		0			0
$495$	−1.25439e7	−	1.76545e6i	−0.103423	−	0.0145559i
$496$		0			0
$497$	−3.25437e7	+	1.87891e7i	−0.265093	+	0.153051i
$498$		0			0
$499$	1.76192e7	−	3.05173e7i	0.141803	−	0.245610i	−0.786373	−	0.617752i	$-0.788043\pi$
$499$	1.76192e7	−	3.05173e7i	0.141803	−	0.245610i	0.928176	+	0.372143i	$0.121377\pi$
$500$		0			0
$501$	−1.51653e8	−	1.02313e8i	−1.20597	−	0.813613i
$502$		0			0
$503$			3.06848e7i			0.241113i	0.992706	+	0.120556i	$0.0384678\pi$
$503$			3.06848e7i			0.241113i	−0.992706	+	0.120556i	$0.961532\pi$
$504$		0			0
$505$	−7.95525e7			−0.617703
$506$		0			0
$507$	−5.63158e7	−	1.15493e8i	−0.432122	−	0.886202i
$508$		0			0
$509$	2.16470e8	+	1.24979e8i	1.64151	+	0.947727i	0.980297	+	0.197529i	$0.0632917\pi$
$509$	2.16470e8	+	1.24979e8i	1.64151	+	0.947727i	0.661214	+	0.750198i	$0.270042\pi$
$510$		0			0
$511$	2.47072e7	+	4.27941e7i	0.185166	+	0.320716i
$512$		0			0
$513$	1.56124e8	+	3.32333e7i	1.15642	+	0.246162i
$514$		0			0
$515$	8.31142e7	−	4.79860e7i	0.608490	−	0.351312i
$516$		0			0
$517$	1.62095e7	−	2.80758e7i	0.117300	−	0.203170i
$518$		0			0
$519$	−1.86194e8	+	9.07901e7i	−1.33187	+	0.649436i
$520$		0			0
$521$		−	2.33057e8i		−	1.64797i	−0.566612	−	0.823985i	$-0.691746\pi$
$521$		−	2.33057e8i		−	1.64797i	0.566612	−	0.823985i	$-0.308254\pi$
$522$		0			0
$523$	−1.09330e6			−0.00764248			−0.00382124	−	0.999993i	$-0.501216\pi$
$523$	−1.09330e6			−0.00764248			−0.00382124	+	0.999993i	$0.501216\pi$
$524$		0			0
$525$	−1.87231e7	+	2.77523e7i	−0.129390	+	0.191788i
$526$		0			0
$527$	−1.52920e7	−	8.82881e6i	−0.104479	−	0.0603213i
$528$		0			0
$529$	1.33203e8	+	2.30715e8i	0.899803	+	1.55850i
$530$		0			0
$531$	−7.18908e7	−	5.61900e7i	−0.480164	−	0.375297i
$532$		0			0
$533$	−3.04911e6	+	1.76040e6i	−0.0201368	+	0.0116260i
$534$		0			0
$535$	−2.32650e7	+	4.02961e7i	−0.151929	+	0.263149i
$536$		0			0
$537$	1.49830e7	−	2.13964e8i	0.0967553	−	1.38171i
$538$		0			0
$539$			3.77436e7i			0.241033i
$540$		0			0
$541$	−1.55394e8			−0.981393			−0.490696	−	0.871331i	$-0.663258\pi$
$541$	−1.55394e8			−0.981393			−0.490696	+	0.871331i	$0.663258\pi$
$542$		0			0
$543$	−5.90471e7	−	4.13481e6i	−0.368807	−	0.0258259i
$544$		0			0
$545$	−5.67173e7	−	3.27457e7i	−0.350369	−	0.202286i
$546$		0			0
$547$	−1.99007e7	−	3.44690e7i	−0.121592	−	0.210604i	0.798804	−	0.601592i	$-0.205467\pi$
$547$	−1.99007e7	−	3.44690e7i	−0.121592	−	0.210604i	−0.920396	+	0.390988i	$0.872133\pi$
$548$		0			0
$549$	1.39388e7	+	3.45193e7i	0.0842380	+	0.208614i
$550$		0			0
$551$	5.19992e7	−	3.00217e7i	0.310843	−	0.179466i
$552$		0			0
$553$	2.58135e7	−	4.47103e7i	0.152641	−	0.264382i
$554$		0			0
$555$	2.48890e6	+	1.67914e6i	0.0145589	+	0.00982217i
$556$		0			0
$557$		−	3.89082e7i		−	0.225152i	−0.993643	−	0.112576i	$-0.964090\pi$
$557$		−	3.89082e7i		−	0.225152i	0.993643	−	0.112576i	$-0.0359101\pi$
$558$		0			0
$559$	−1.70772e7			−0.0977646
$560$		0			0
$561$	−7.41066e6	−	1.51979e7i	−0.0419728	−	0.0860785i
$562$		0			0
$563$	1.59732e7	+	9.22215e6i	0.0895092	+	0.0516782i	0.544086	−	0.839029i	$-0.316876\pi$
$563$	1.59732e7	+	9.22215e6i	0.0895092	+	0.0516782i	−0.454577	+	0.890707i	$0.650210\pi$
$564$		0			0
$565$	−6.05558e7	−	1.04886e8i	−0.335746	−	0.581529i
$566$		0			0
$567$	1.21313e7	+	4.87376e7i	0.0665515	+	0.267371i
$568$		0			0
$569$	−2.42858e8	+	1.40214e8i	−1.31830	+	0.761124i	−0.983456	−	0.181148i	$-0.942019\pi$
$569$	−2.42858e8	+	1.40214e8i	−1.31830	+	0.761124i	−0.334849	+	0.942272i	$0.608685\pi$
$570$		0			0
$571$	1.05713e8	−	1.83100e8i	0.567831	−	0.983512i	−0.428949	−	0.903329i	$-0.641116\pi$
$571$	1.05713e8	−	1.83100e8i	0.567831	−	0.983512i	0.996780	−	0.0801837i	$-0.0255507\pi$
$572$		0			0
$573$	−2.20267e8	+	1.07405e8i	−1.17081	+	0.570899i
$574$		0			0
$575$			2.67091e8i			1.40493i
$576$		0			0
$577$	−7.16438e7			−0.372950			−0.186475	−	0.982460i	$-0.559706\pi$
$577$	−7.16438e7			−0.372950			−0.186475	+	0.982460i	$0.559706\pi$
$578$		0			0
$579$	1.83078e8	−	2.71367e8i	0.943194	−	1.39805i
$580$		0			0
$581$	−6.07206e7	−	3.50570e7i	−0.309605	−	0.178750i
$582$		0			0
$583$	−1.46977e7	−	2.54572e7i	−0.0741729	−	0.128471i
$584$		0			0
$585$	8.81300e6	−	3.55867e6i	0.0440206	−	0.0177754i
$586$		0			0
$587$	1.51958e8	−	8.77328e7i	0.751292	−	0.433758i	−0.0748689	−	0.997193i	$-0.523854\pi$
$587$	1.51958e8	−	8.77328e7i	0.751292	−	0.433758i	0.826160	+	0.563435i	$0.190520\pi$
$588$		0			0
$589$	−3.96924e7	+	6.87493e7i	−0.194250	+	0.336451i
$590$		0			0
$591$	−1.36461e7	+	1.94873e8i	−0.0661069	+	0.944039i
$592$		0			0
$593$		−	2.53177e8i		−	1.21412i	−0.794657	−	0.607058i	$-0.792349\pi$
$593$		−	2.53177e8i		−	1.21412i	0.794657	−	0.607058i	$-0.207651\pi$
$594$		0			0
$595$	8.53254e6			0.0405067
$596$		0			0
$597$	−1.82961e8	−	1.28120e7i	−0.859876	−	0.0602133i
$598$		0			0
$599$	−4.13187e7	−	2.38554e7i	−0.192250	−	0.110996i	0.400785	−	0.916172i	$-0.368737\pi$
$599$	−4.13187e7	−	2.38554e7i	−0.192250	−	0.110996i	−0.593035	+	0.805176i	$0.702071\pi$
$600$		0			0
$601$	8.17398e6	+	1.41577e7i	0.0376539	+	0.0652185i	0.884238	−	0.467036i	$-0.154678\pi$
$601$	8.17398e6	+	1.41577e7i	0.0376539	+	0.0652185i	−0.846584	+	0.532255i	$0.821345\pi$
$602$		0			0
$603$	8.90007e7	−	1.13869e8i	0.405921	−	0.519344i
$604$		0			0
$605$	−7.15661e7	+	4.13187e7i	−0.323178	+	0.186587i
$606$		0			0
$607$	1.08834e8	−	1.88506e8i	0.486628	−	0.842865i	−0.513253	−	0.858237i	$-0.671560\pi$
$607$	1.08834e8	−	1.88506e8i	0.486628	−	0.842865i	0.999882	+	0.0153720i	$0.00489326\pi$
$608$		0			0
$609$	1.56616e7	+	1.05661e7i	0.0693401	+	0.0467804i
$610$		0			0
$611$			2.43239e7i			0.106637i
$612$		0			0
$613$	−4.18390e8			−1.81635			−0.908175	−	0.418591i	$-0.862524\pi$
$613$	−4.18390e8			−1.81635			−0.908175	+	0.418591i	$0.862524\pi$
$614$		0			0
$615$	8.00583e6	+	1.64185e7i	0.0344176	+	0.0705842i
$616$		0			0
$617$	−3.24865e8	−	1.87561e8i	−1.38308	−	0.798522i	−0.390557	−	0.920579i	$-0.627718\pi$
$617$	−3.24865e8	−	1.87561e8i	−1.38308	−	0.798522i	−0.992523	+	0.122057i	$0.961051\pi$
$618$		0			0
$619$	4.64086e7	+	8.03821e7i	0.195671	+	0.338913i	0.947120	−	0.320879i	$-0.103978\pi$
$619$	4.64086e7	+	8.03821e7i	0.195671	+	0.338913i	−0.751449	+	0.659791i	$0.770645\pi$
$620$		0			0
$621$	2.97702e8	+	2.68211e8i	1.24310	+	1.11996i
$622$		0			0
$623$	2.19305e7	−	1.26616e7i	0.0906950	−	0.0523628i
$624$		0			0
$625$	−6.64928e7	+	1.15169e8i	−0.272355	+	0.471732i
$626$		0			0
$627$	−6.83265e7	+	3.33167e7i	−0.277196	+	0.135164i
$628$		0			0
$629$			4.00749e6i			0.0161035i
$630$		0			0
$631$	9.70867e7			0.386431			0.193215	−	0.981156i	$-0.438108\pi$
$631$	9.70867e7			0.386431			0.193215	+	0.981156i	$0.438108\pi$
$632$		0			0
$633$	2.39193e8	−	3.54543e8i	0.943057	−	1.39784i
$634$		0			0
$635$	1.11207e8	+	6.42055e7i	0.434322	+	0.250756i
$636$		0			0
$637$	−1.41594e7	−	2.45248e7i	−0.0547805	−	0.0948826i
$638$		0			0
$639$	−4.03984e7	+	2.87040e8i	−0.154832	+	1.10012i
$640$		0			0
$641$	−2.45683e8	+	1.41845e8i	−0.932829	+	0.538569i	−0.887705	−	0.460413i	$-0.847701\pi$
$641$	−2.45683e8	+	1.41845e8i	−0.932829	+	0.538569i	−0.0451235	+	0.998981i	$0.514368\pi$
$642$		0			0
$643$	2.44419e8	−	4.23345e8i	0.919393	−	1.59244i	0.119054	−	0.992888i	$-0.462014\pi$
$643$	2.44419e8	−	4.23345e8i	0.919393	−	1.59244i	0.800339	−	0.599548i	$-0.204653\pi$
$644$		0			0
$645$	−6.18901e6	+	8.83821e7i	−0.0230644	+	0.329371i
$646$		0			0
$647$			2.40018e8i			0.886198i	0.896473	+	0.443099i	$0.146121\pi$
$647$			2.40018e8i			0.886198i	−0.896473	+	0.443099i	$0.853879\pi$
$648$		0			0
$649$	4.34534e7			0.158961
$650$		0			0
$651$	−2.49173e7	−	1.74485e6i	−0.0903146	−	0.00632433i
$652$		0			0
$653$	1.47195e8	+	8.49829e7i	0.528631	+	0.305205i	0.740459	−	0.672102i	$-0.234608\pi$
$653$	1.47195e8	+	8.49829e7i	0.528631	+	0.305205i	−0.211828	+	0.977307i	$0.567942\pi$
$654$		0			0
$655$	5.65468e7	+	9.79419e7i	0.201226	+	0.348534i
$656$		0			0
$657$	3.77450e8	+	5.31228e7i	1.33095	+	0.187320i
$658$		0			0
$659$	−2.21696e8	+	1.27996e8i	−0.774641	+	0.447239i	−0.834528	−	0.550966i	$-0.814259\pi$
$659$	−2.21696e8	+	1.27996e8i	−0.774641	+	0.447239i	0.0598865	+	0.998205i	$0.480926\pi$
$660$		0			0
$661$	1.91639e8	−	3.31929e8i	0.663560	−	1.14932i	−0.316113	−	0.948721i	$-0.602378\pi$
$661$	1.91639e8	−	3.31929e8i	0.663560	−	1.14932i	0.979674	−	0.200599i	$-0.0642887\pi$
$662$		0			0
$663$	1.05167e7	+	7.09511e6i	0.0360860	+	0.0243455i
$664$		0			0
$665$		−	3.83604e7i		−	0.130442i
$666$		0			0
$667$	1.50729e8			0.507949
$668$		0			0
$669$	2.40221e8	+	4.92649e8i	0.802292	+	1.64535i
$670$		0			0
$671$	−1.53535e7	−	8.86435e6i	−0.0508206	−	0.0293413i
$672$		0			0
$673$	1.91879e8	+	3.32345e8i	0.629481	+	1.09029i	0.987656	+	0.156639i	$0.0500658\pi$
$673$	1.91879e8	+	3.32345e8i	0.629481	+	1.09029i	−0.358175	+	0.933655i	$0.616601\pi$
$674$		0			0
$675$	7.97272e7	+	2.45622e8i	0.259236	+	0.798648i
$676$		0			0
$677$	1.99077e8	−	1.14937e8i	0.641588	−	0.370421i	−0.143638	−	0.989630i	$-0.545880\pi$
$677$	1.99077e8	−	1.14937e8i	0.641588	−	0.370421i	0.785226	+	0.619210i	$0.212547\pi$
$678$		0			0
$679$	6.63574e7	−	1.14934e8i	0.211973	−	0.367148i
$680$		0			0
$681$	1.70386e8	−	8.30822e7i	0.539502	−	0.263067i
$682$		0			0
$683$			3.14317e8i			0.986521i	0.869882	+	0.493260i	$0.164195\pi$
$683$			3.14317e8i			0.986521i	−0.869882	+	0.493260i	$0.835805\pi$
$684$		0			0
$685$	−5.11694e7			−0.159198
$686$		0			0
$687$	1.71566e8	−	2.54303e8i	0.529127	−	0.784297i
$688$		0			0
$689$	1.91004e7	+	1.10276e7i	0.0583963	+	0.0337151i
$690$		0			0
$691$	−1.00073e8	−	1.73332e8i	−0.303308	−	0.525344i	0.673575	−	0.739119i	$-0.264758\pi$
$691$	−1.00073e8	−	1.73332e8i	−0.303308	−	0.525344i	−0.976883	+	0.213774i	$0.931424\pi$
$692$		0			0
$693$	−1.88451e7	−	1.47294e7i	−0.0566238	−	0.0442573i
$694$		0			0
$695$	6.97172e6	−	4.02512e6i	0.0207676	−	0.0119902i
$696$		0			0
$697$	−1.21908e7	+	2.11151e7i	−0.0360026	+	0.0623584i
$698$		0			0
$699$	−3.13493e7	+	4.47684e8i	−0.0917903	+	1.31081i
$700$		0			0
$701$			4.95298e7i			0.143785i	0.997412	+	0.0718924i	$0.0229038\pi$
$701$			4.95298e7i			0.143785i	−0.997412	+	0.0718924i	$0.977096\pi$
$702$		0			0
$703$	1.80168e7			0.0518575
$704$		0			0
$705$	1.25887e8	+	8.81529e6i	0.359263	+	0.0251576i
$706$		0			0
$707$	−1.30085e8	−	7.51044e7i	−0.368101	−	0.212523i
$708$		0			0
$709$	−6.60462e7	−	1.14395e8i	−0.185314	−	0.320974i	0.758368	−	0.651827i	$-0.225997\pi$
$709$	−6.60462e7	−	1.14395e8i	−0.185314	−	0.320974i	−0.943682	+	0.330853i	$0.892664\pi$
$710$		0			0
$711$	−1.49110e8	−	3.69269e8i	−0.414856	−	1.02739i
$712$		0			0
$713$	−1.72584e8	+	9.96412e7i	−0.476136	+	0.274897i
$714$		0			0
$715$	−2.26313e6	+	3.91985e6i	−0.00619143	+	0.0107239i
$716$		0			0
$717$	1.87430e8	+	1.26450e8i	0.508489	+	0.343053i
$718$		0			0
$719$			3.37217e8i			0.907240i	0.891195	+	0.453620i	$0.149868\pi$
$719$			3.37217e8i			0.907240i	−0.891195	+	0.453620i	$0.850132\pi$
$720$		0			0
$721$	1.81212e8			0.483482
$722$		0			0
$723$	−2.78472e7	−	5.71095e7i	−0.0736829	−	0.151110i
$724$		0			0
$725$	8.41247e7	+	4.85694e7i	0.220754	+	0.127453i
$726$		0			0
$727$	−1.63490e8	−	2.83173e8i	−0.425488	−	0.736968i	0.570978	−	0.820966i	$-0.306564\pi$
$727$	−1.63490e8	−	2.83173e8i	−0.425488	−	0.736968i	−0.996466	+	0.0839982i	$0.973231\pi$
$728$		0			0
$729$	3.53833e8	+	1.57787e8i	0.913305	+	0.407275i
$730$		0			0
$731$	−1.02416e8	+	5.91299e7i	−0.262190	+	0.151375i
$732$		0			0
$733$	2.58064e8	−	4.46979e8i	0.655262	−	1.13495i	−0.326566	−	0.945174i	$-0.605892\pi$
$733$	2.58064e8	−	4.46979e8i	0.655262	−	1.13495i	0.981828	−	0.189773i	$-0.0607751\pi$
$734$		0			0
$735$	−1.32058e8	+	6.43930e7i	−0.332585	+	0.162172i
$736$		0			0
$737$			6.88269e7i			0.171932i
$738$		0			0
$739$	−2.84520e8			−0.704984			−0.352492	−	0.935815i	$-0.614666\pi$
$739$	−2.84520e8			−0.704984			−0.352492	+	0.935815i	$0.614666\pi$
$740$		0			0
$741$	3.18981e7	−	4.72808e7i	0.0783988	−	0.116206i
$742$		0			0
$743$	−3.73704e8	−	2.15758e8i	−0.911090	−	0.526018i	−0.0303086	−	0.999541i	$-0.509649\pi$
$743$	−3.73704e8	−	2.15758e8i	−0.911090	−	0.526018i	−0.880782	+	0.473522i	$0.842982\pi$
$744$		0			0
$745$	−8.17991e6	−	1.41680e7i	−0.0197824	−	0.0342642i
$746$		0			0
$747$	−5.01500e8	+	2.02504e8i	−1.20312	+	0.485817i
$748$		0			0
$749$	−7.60860e7	+	4.39283e7i	−0.181075	+	0.104544i
$750$		0			0
$751$	1.97300e8	−	3.41733e8i	0.465808	−	0.806803i	−0.533430	−	0.845844i	$-0.679097\pi$
$751$	1.97300e8	−	3.41733e8i	0.465808	−	0.806803i	0.999238	+	0.0390416i	$0.0124305\pi$
$752$		0			0
$753$	2.20096e7	−	3.14308e8i	0.0515499	−	0.736158i
$754$		0			0
$755$		−	1.02354e7i		−	0.0237829i
$756$		0			0
$757$	−3.23281e8			−0.745234			−0.372617	−	0.927985i	$-0.621539\pi$
$757$	−3.23281e8			−0.745234			−0.372617	+	0.927985i	$0.621539\pi$
$758$		0			0
$759$	−1.90361e8	−	1.33301e7i	−0.435363	−	0.0304866i
$760$		0			0
$761$	−4.43296e8	−	2.55937e8i	−1.00586	−	0.580736i	−0.0958862	−	0.995392i	$-0.530568\pi$
$761$	−4.43296e8	−	2.55937e8i	−1.00586	−	0.580736i	−0.909978	+	0.414656i	$0.863902\pi$
$762$		0			0
$763$	−6.18296e7	−	1.07092e8i	−0.139195	−	0.241092i
$764$		0			0
$765$	4.05317e7	−	5.18572e7i	0.0905338	−	0.115831i
$766$		0			0
$767$	−2.82349e7	+	1.63014e7i	−0.0625748	+	0.0361276i
$768$		0			0
$769$	−3.69190e8	+	6.39456e8i	−0.811841	+	1.40615i	0.0997330	+	0.995014i	$0.468201\pi$
$769$	−3.69190e8	+	6.39456e8i	−0.811841	+	1.40615i	−0.911574	+	0.411136i	$0.865132\pi$
$770$		0			0
$771$	−2.42065e8	−	1.63310e8i	−0.528165	−	0.356327i
$772$		0			0
$773$		−	7.92930e8i		−	1.71671i	−0.513058	−	0.858354i	$-0.671487\pi$
$773$		−	7.92930e8i		−	1.71671i	0.513058	−	0.858354i	$-0.328513\pi$
$774$		0			0
$775$	−1.28429e8			−0.275905
$776$		0			0
$777$	2.48460e6	+	5.09547e6i	0.00529656	+	0.0108623i
$778$		0			0
$779$	9.49289e7	+	5.48072e7i	0.200810	+	0.115938i
$780$		0			0
$781$	−6.90221e7	−	1.19550e8i	−0.144889	−	0.250955i
$782$		0			0
$783$	1.38613e8	−	4.49930e7i	0.288748	−	0.0937258i
$784$		0			0
$785$	−2.54976e8	+	1.47210e8i	−0.527096	+	0.304319i
$786$		0			0
$787$	−8.20011e7	+	1.42030e8i	−0.168227	+	0.291378i	−0.937797	−	0.347185i	$-0.887137\pi$
$787$	−8.20011e7	+	1.42030e8i	−0.168227	+	0.291378i	0.769570	+	0.638563i	$0.220471\pi$
$788$		0			0
$789$	−2.64473e8	+	1.28960e8i	−0.538455	+	0.262557i
$790$		0			0
$791$		−	2.28679e8i		−	0.462059i
$792$		0			0
$793$	1.33017e7			0.0266740
$794$		0			0
$795$	6.39951e7	−	9.48565e7i	0.127364	−	0.188784i
$796$		0			0
$797$	5.09610e8	+	2.94223e8i	1.00661	+	0.581169i	0.910198	−	0.414173i	$-0.135929\pi$
$797$	5.09610e8	+	2.94223e8i	1.00661	+	0.581169i	0.0964151	+	0.995341i	$0.469262\pi$
$798$		0			0
$799$	8.42214e7	+	1.45876e8i	0.165113	+	0.285985i
$800$		0			0
$801$	2.72236e7	−	1.93430e8i	0.0529721	−	0.376379i
$802$		0			0
$803$	−1.57205e8	+	9.07621e7i	−0.303612	+	0.175290i
$804$		0			0
$805$	4.81487e7	−	8.33961e7i	0.0922991	−	0.159867i
$806$		0			0
$807$	2.16292e7	−	3.08875e8i	0.0411546	−	0.587708i
$808$		0			0
$809$		−	9.90263e7i		−	0.187027i	−0.995618	−	0.0935136i	$-0.970190\pi$
$809$		−	9.90263e7i		−	0.187027i	0.995618	−	0.0935136i	$-0.0298099\pi$
$810$		0			0
$811$	−3.01452e8			−0.565140			−0.282570	−	0.959247i	$-0.591187\pi$
$811$	−3.01452e8			−0.565140			−0.282570	+	0.959247i	$0.591187\pi$
$812$		0			0
$813$	−6.14980e8	−	4.30643e7i	−1.14443	−	0.0801394i
$814$		0			0
$815$	1.61540e8	+	9.32652e7i	0.298406	+	0.172285i
$816$		0			0
$817$	2.65835e8	+	4.60440e8i	0.487469	+	0.844320i
$818$		0			0
$819$	1.77707e7	+	2.50108e6i	0.0323485	+	0.00455277i
$820$		0			0
$821$	4.93466e8	−	2.84903e8i	0.891718	−	0.514834i	0.0172139	−	0.999852i	$-0.494520\pi$
$821$	4.93466e8	−	2.84903e8i	0.891718	−	0.514834i	0.874504	+	0.485018i	$0.161187\pi$
$822$		0			0
$823$	8.72089e7	−	1.51050e8i	0.156445	−	0.270970i	−0.777139	−	0.629329i	$-0.783330\pi$
$823$	8.72089e7	−	1.51050e8i	0.156445	−	0.270970i	0.933584	+	0.358358i	$0.116663\pi$
$824$		0			0
$825$	−1.01948e8	−	6.87796e7i	−0.181559	−	0.122489i
$826$		0			0
$827$		−	1.40108e7i		−	0.0247712i	−0.999923	−	0.0123856i	$-0.996057\pi$
$827$		−	1.40108e7i		−	0.0247712i	0.999923	−	0.0123856i	$-0.00394256\pi$
$828$		0			0
$829$	5.93224e8			1.04125			0.520625	−	0.853785i	$-0.325699\pi$
$829$	5.93224e8			1.04125			0.520625	+	0.853785i	$0.325699\pi$
$830$		0			0
$831$	1.89459e8	+	3.88546e8i	0.330151	+	0.677079i
$832$		0			0
$833$	−1.69834e8	−	9.80539e7i	−0.293826	−	0.169641i
$834$		0			0
$835$	1.69564e8	+	2.93693e8i	0.291255	+	0.504469i
$836$		0			0
$837$	−1.28968e8	+	1.43148e8i	−0.219940	+	0.244124i
$838$		0			0
$839$	2.54203e8	−	1.46764e8i	0.430423	−	0.248505i	−0.269104	−	0.963111i	$-0.586727\pi$
$839$	2.54203e8	−	1.46764e8i	0.430423	−	0.248505i	0.699527	+	0.714606i	$0.253394\pi$
$840$		0			0
$841$	−2.70002e8	+	4.67658e8i	−0.453920	+	0.786212i
$842$		0			0
$843$	5.55145e8	−	2.70695e8i	0.926666	−	0.451853i
$844$		0			0
$845$			2.38195e8i			0.394787i
$846$		0			0
$847$	−1.56034e8			−0.256784
$848$		0			0
$849$	3.90104e6	−	5.78230e6i	0.00637466	−	0.00944882i
$850$		0			0
$851$	3.91687e7	+	2.26141e7i	0.0635552	+	0.0366936i
$852$		0			0
$853$	−4.82580e8	−	8.35853e8i	−0.777539	−	1.34674i	−0.933356	−	0.358951i	$-0.883134\pi$
$853$	−4.82580e8	−	8.35853e8i	−0.777539	−	1.34674i	0.155817	−	0.987786i	$-0.450199\pi$
$854$		0			0
$855$	−2.33139e8	−	1.82222e8i	−0.373006	−	0.291542i
$856$		0			0
$857$	2.68736e8	−	1.55155e8i	0.426957	−	0.246504i	−0.271093	−	0.962553i	$-0.587385\pi$
$857$	2.68736e8	−	1.55155e8i	0.426957	−	0.246504i	0.698049	+	0.716050i	$0.254052\pi$
$858$		0			0
$859$	−6.20030e8	+	1.07392e9i	−0.978213	+	1.69431i	−0.309317	+	0.950959i	$0.600100\pi$
$859$	−6.20030e8	+	1.07392e9i	−0.978213	+	1.69431i	−0.668896	+	0.743356i	$0.733233\pi$
$860$		0			0
$861$	−2.40928e6	+	3.44058e7i	−0.00377467	+	0.0539041i
$862$		0			0
$863$		−	9.05111e8i		−	1.40822i	−0.710092	−	0.704109i	$-0.751347\pi$
$863$		−	9.05111e8i		−	1.40822i	0.710092	−	0.704109i	$-0.248653\pi$
$864$		0			0
$865$	3.84009e8			0.593325
$866$		0			0
$867$	−5.62484e8	−	3.93883e7i	−0.863084	−	0.0604380i
$868$		0			0
$869$	1.64244e8	+	9.48262e7i	0.250282	+	0.144500i
$870$		0			0
$871$	−2.58202e7	−	4.47219e7i	−0.0390755	−	0.0676808i
$872$		0			0
$873$	−3.83309e8	−	9.49260e8i	−0.576111	−	1.42673i
$874$		0			0
$875$	1.17753e8	−	6.79849e7i	0.175772	−	0.101482i
$876$		0			0
$877$	−2.85356e8	+	4.94252e8i	−0.423047	+	0.732739i	−0.996236	−	0.0866842i	$-0.972373\pi$
$877$	−2.85356e8	+	4.94252e8i	−0.423047	+	0.732739i	0.573189	+	0.819423i	$0.305706\pi$
$878$		0			0
$879$	−6.98479e7	−	4.71230e7i	−0.102846	−	0.0693851i
$880$		0			0
$881$			9.25463e8i			1.35342i	0.736252	+	0.676708i	$0.236594\pi$
$881$			9.25463e8i			1.35342i	−0.736252	+	0.676708i	$0.763406\pi$
$882$		0			0
$883$	4.36852e8			0.634530			0.317265	−	0.948337i	$-0.397236\pi$
$883$	4.36852e8			0.634530			0.317265	+	0.948337i	$0.397236\pi$
$884$		0			0
$885$	7.41343e7	+	1.52036e8i	0.106952	+	0.219339i
$886$		0			0
$887$	5.96419e8	+	3.44343e8i	0.854635	+	0.493424i	0.862212	−	0.506547i	$-0.169078\pi$
$887$	5.96419e8	+	3.44343e8i	0.854635	+	0.493424i	−0.00757687	+	0.999971i	$0.502412\pi$
$888$		0			0
$889$	1.21231e8	+	2.09978e8i	0.172547	+	0.298861i
$890$		0			0
$891$	−1.79038e8	+	4.45644e7i	−0.253112	+	0.0630021i
$892$		0			0
$893$	6.55826e8	−	3.78641e8i	0.920946	−	0.531709i
$894$		0			0
$895$	−1.98806e8	+	3.44342e8i	−0.277307	+	0.480310i
$896$		0			0
$897$	1.28692e8	−	6.27516e7i	0.178309	−	0.0869456i
$898$		0			0
$899$			7.24774e7i			0.0997524i
$900$		0			0
$901$	1.52733e8			0.208813
$902$		0			0
$903$	−9.35606e7	+	1.38680e8i	−0.127066	+	0.188343i
$904$		0			0
$905$	9.50272e7	+	5.48640e7i	0.128204	+	0.0740188i
$906$		0			0
$907$	2.05077e8	+	3.55204e8i	0.274850	+	0.476054i	0.970097	−	0.242717i	$-0.0780385\pi$
$907$	2.05077e8	+	3.55204e8i	0.274850	+	0.476054i	−0.695247	+	0.718771i	$0.744705\pi$
$908$		0			0
$909$	−1.07439e9	+	4.33835e8i	−1.43044	+	0.577608i
$910$		0			0
$911$	6.60969e8	−	3.81611e8i	0.874231	−	0.504738i	0.00547907	−	0.999985i	$-0.498256\pi$
$911$	6.60969e8	−	3.81611e8i	0.874231	−	0.504738i	0.868752	+	0.495247i	$0.164923\pi$
$912$		0			0
$913$	1.28782e8	−	2.23058e8i	0.169217	−	0.293093i
$914$		0			0
$915$	4.82073e6	−	6.88424e7i	0.00629288	−	0.0898654i
$916$		0			0
$917$			2.13540e8i			0.276931i
$918$		0			0
$919$	1.18843e9			1.53118			0.765591	−	0.643328i	$-0.222447\pi$
$919$	1.18843e9			1.53118			0.765591	+	0.643328i	$0.222447\pi$
$920$		0			0
$921$	−5.76156e8	−	4.03457e7i	−0.737498	−	0.0516438i
$922$		0			0
$923$	8.96974e7	+	5.17868e7i	0.114071	+	0.0658589i
$924$		0			0
$925$	1.45739e7	+	2.52427e7i	0.0184140	+	0.0318941i
$926$		0			0
$927$	8.60801e8	−	1.10133e9i	1.08060	−	1.38254i
$928$		0			0
$929$	−1.35033e8	+	7.79611e7i	−0.168419	+	0.0972368i	−0.581840	−	0.813303i	$-0.697667\pi$
$929$	−1.35033e8	+	7.79611e7i	−0.168419	+	0.0972368i	0.413421	+	0.910540i	$0.364334\pi$
$930$		0			0
$931$	−4.40829e8	+	7.63538e8i	−0.546287	+	0.946197i
$932$		0			0
$933$	1.57161e7	+	1.06029e7i	0.0193508	+	0.0130550i
$934$		0			0
$935$			3.13444e7i			0.0383464i
$936$		0			0
$937$	−1.52193e8			−0.185001			−0.0925006	−	0.995713i	$-0.529486\pi$
$937$	−1.52193e8			−0.185001			−0.0925006	+	0.995713i	$0.529486\pi$
$938$		0			0
$939$	4.67534e8	+	9.58825e8i	0.564698	+	1.15809i
$940$		0			0
$941$	1.13663e9	+	6.56236e8i	1.36412	+	0.787574i	0.990169	−	0.139875i	$-0.0446700\pi$
$941$	1.13663e9	+	6.56236e8i	1.36412	+	0.787574i	0.373949	+	0.927449i	$0.378003\pi$
$942$		0			0
$943$	1.37584e8	+	2.38303e8i	0.164072	+	0.284181i
$944$		0			0
$945$	1.93845e7	−	9.10650e7i	0.0229699	−	0.107909i
$946$		0			0
$947$	9.56281e7	−	5.52109e7i	0.112599	−	0.0650092i	−0.442643	−	0.896698i	$-0.645959\pi$
$947$	9.56281e7	−	5.52109e7i	0.112599	−	0.0650092i	0.555242	+	0.831689i	$0.312626\pi$
$948$		0			0
$949$	6.80983e7	−	1.17950e8i	0.0796778	−	0.138006i
$950$		0			0
$951$	8.72487e8	−	4.25434e8i	1.01442	−	0.494642i
$952$		0			0
$953$		−	7.90824e8i		−	0.913694i	−0.889545	−	0.456847i	$-0.848979\pi$
$953$		−	7.90824e8i		−	0.913694i	0.889545	−	0.456847i	$-0.151021\pi$
$954$		0			0
$955$	4.54282e8			0.521574
$956$		0			0
$957$	−3.88148e7	+	5.75331e7i	−0.0442855	+	0.0656421i
$958$		0			0
$959$	−8.36724e7	−	4.83083e7i	−0.0948695	−	0.0547729i
$960$		0			0
$961$	3.95840e8	+	6.85615e8i	0.446015	+	0.772520i
$962$		0			0
$963$	−9.44500e7	+	6.71089e8i	−0.105760	+	0.751452i
$964$		0			0
$965$	−5.25532e8	+	3.03416e8i	−0.584814	+	0.337642i
$966$		0			0
$967$	−4.72480e8	+	8.18359e8i	−0.522521	+	0.905033i	0.477136	+	0.878830i	$0.341675\pi$
$967$	−4.72480e8	+	8.18359e8i	−0.522521	+	0.905033i	−0.999657	+	0.0262032i	$0.991658\pi$
$968$		0			0
$969$	2.75902e7	−	3.94001e8i	0.0303238	−	0.433038i
$970$		0			0
$971$		−	1.03020e9i		−	1.12529i	−0.826698	−	0.562646i	$-0.809783\pi$
$971$		−	1.03020e9i		−	1.12529i	0.826698	−	0.562646i	$-0.190217\pi$
$972$		0			0
$973$	1.52002e7			0.0165011
$974$		0			0
$975$	9.20458e7	+	6.44556e6i	0.0993093	+	0.00695420i
$976$		0			0
$977$	1.90278e8	+	1.09857e8i	0.204035	+	0.117800i	0.598536	−	0.801096i	$-0.295749\pi$
$977$	1.90278e8	+	1.09857e8i	0.204035	+	0.117800i	−0.394501	+	0.918896i	$0.629083\pi$
$978$		0			0
$979$	4.65124e7	+	8.05618e7i	0.0495702	+	0.0858580i
$980$		0			0
$981$	−9.44566e8	−	1.32940e8i	−1.00052	−	0.140814i
$982$		0			0
$983$	1.04462e9	−	6.03114e8i	1.09976	−	0.634949i	0.163605	−	0.986526i	$-0.447688\pi$
$983$	1.04462e9	−	6.03114e8i	1.09976	−	0.634949i	0.936159	+	0.351577i	$0.114354\pi$
$984$		0			0
$985$	1.81068e8	−	3.13619e8i	0.189467	−	0.328166i
$986$		0			0
$987$	1.97528e8	+	1.33263e8i	0.205436	+	0.138598i
$988$		0			0
$989$			1.33467e9i			1.37970i
$990$		0			0
$991$	−6.18670e8			−0.635680			−0.317840	−	0.948144i	$-0.602957\pi$
$991$	−6.18670e8			−0.635680			−0.317840	+	0.948144i	$0.602957\pi$
$992$		0			0
$993$	1.31655e8	+	2.69999e8i	0.134458	+	0.275749i
$994$		0			0
$995$	2.94448e8	+	1.70000e8i	0.298909	+	0.172575i
$996$		0			0
$997$	−6.71321e8	−	1.16276e9i	−0.677400	−	1.17329i	−0.975761	−	0.218838i	$-0.929773\pi$
$997$	−6.71321e8	−	1.16276e9i	−0.677400	−	1.17329i	0.298361	−	0.954453i	$-0.403560\pi$
$998$		0			0
$999$	4.27706e7	+	9.10436e6i	0.0428992	+	0.00913173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.41.1	✓	36
3.2	odd	2		216.7.m.a.17.8		36
4.3	odd	2		144.7.q.d.113.18		36
9.2	odd	6	inner	72.7.m.a.65.1	yes	36
9.4	even	3		648.7.e.c.161.15		36
9.5	odd	6		648.7.e.c.161.22		36
9.7	even	3		216.7.m.a.89.8		36
12.11	even	2		432.7.q.d.17.8		36
36.7	odd	6		432.7.q.d.305.8		36
36.11	even	6		144.7.q.d.65.18		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.1	✓	36	1.1	even	1	trivial
72.7.m.a.65.1	yes	36	9.2	odd	6	inner
144.7.q.d.65.18		36	36.11	even	6
144.7.q.d.113.18		36	4.3	odd	2
216.7.m.a.17.8		36	3.2	odd	2
216.7.m.a.89.8		36	9.7	even	3
432.7.q.d.17.8		36	12.11	even	2
432.7.q.d.305.8		36	36.7	odd	6
648.7.e.c.161.15		36	9.4	even	3
648.7.e.c.161.22		36	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-26.9340 - 1.88607i) q^{3} +(43.3462 + 25.0260i) q^{5} +(47.2533 + 81.8451i) q^{7} +(721.885 + 101.599i) q^{9} +O(q^{10})\)	\(q+(-26.9340 - 1.88607i) q^{3} +(43.3462 + 25.0260i) q^{5} +(47.2533 + 81.8451i) q^{7} +(721.885 + 101.599i) q^{9} +(-300.659 + 173.586i) q^{11} +(130.240 - 225.583i) q^{13} +(-1120.29 - 755.805i) q^{15} -1803.83i q^{17} -8109.62 q^{19} +(-1118.36 - 2293.54i) q^{21} +(-17630.4 - 10178.9i) q^{23} +(-6559.90 - 11362.1i) q^{25} +(-19251.7 - 4098.00i) q^{27} +(-6412.04 + 3701.99i) q^{29} +(4894.49 - 8477.50i) q^{31} +(8425.36 - 4108.30i) q^{33} +4730.24i q^{35} -2221.66 q^{37} +(-3933.36 + 5830.21i) q^{39} +(-11705.7 - 6758.30i) q^{41} +(-32780.2 - 56777.0i) q^{43} +(28748.4 + 22469.8i) q^{45} +(-80870.1 + 46690.4i) q^{47} +(54358.8 - 94152.1i) q^{49} +(-3402.15 + 48584.4i) q^{51} +84671.5i q^{53} -17376.6 q^{55} +(218425. + 15295.3i) q^{57} +(-108395. - 62582.1i) q^{59} +(25533.1 + 44224.6i) q^{61} +(25796.1 + 63883.7i) q^{63} +(11290.8 - 6518.77i) q^{65} +(99125.3 - 171690. i) q^{67} +(455660. + 307412. i) q^{69} +397626. i q^{71} +522867. q^{73} +(155255. + 318399. i) q^{75} +(-28414.3 - 16405.0i) q^{77} +(-273140. - 473092. i) q^{79} +(510796. + 146686. i) q^{81} +(-642501. + 370948. i) q^{83} +(45142.5 - 78189.2i) q^{85} +(179684. - 87616.0i) q^{87} -267951. i q^{89} +24617.1 q^{91} +(-147817. + 219102. i) q^{93} +(-351522. - 202951. i) q^{95} +(-702146. - 1.21615e6i) q^{97} +(-234677. + 94762.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 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

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