LMFDB - Embedded newform 72.7.m.a.65.2

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			65.2
Character	$\chi$	$=$	72.65
Dual form			72.7.m.a.41.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-26.5258 - 5.03801i) q^{3} +(-212.009 + 122.404i) q^{5} +(-198.515 + 343.838i) q^{7} +(678.237 + 267.274i) q^{9} +O(q^{10})$	\(q+(-26.5258 - 5.03801i) q^{3} +(-212.009 + 122.404i) q^{5} +(-198.515 + 343.838i) q^{7} +(678.237 + 267.274i) q^{9} +(426.493 + 246.236i) q^{11} +(-1436.82 - 2488.64i) q^{13} +(6240.39 - 2178.75i) q^{15} +928.923i q^{17} -10042.5 q^{19} +(6998.02 - 8120.46i) q^{21} +(-1335.86 + 771.260i) q^{23} +(22152.8 - 38369.8i) q^{25} +(-16644.3 - 10506.6i) q^{27} +(29249.3 + 16887.1i) q^{29} +(7234.19 + 12530.0i) q^{31} +(-10072.5 - 8680.27i) q^{33} -97195.8i q^{35} +31633.1 q^{37} +(25574.9 + 73251.9i) q^{39} +(27990.9 - 16160.6i) q^{41} +(-17558.4 + 30412.0i) q^{43} +(-176508. + 26354.0i) q^{45} +(65811.0 + 37996.0i) q^{47} +(-19991.8 - 34626.8i) q^{49} +(4679.92 - 24640.4i) q^{51} -89863.6i q^{53} -120561. q^{55} +(266385. + 50594.1i) q^{57} +(-181648. + 104874. i) q^{59} +(109571. - 189783. i) q^{61} +(-226539. + 180146. i) q^{63} +(609237. + 351743. i) q^{65} +(-245898. - 425909. i) q^{67} +(39320.4 - 13728.2i) q^{69} +695612. i q^{71} -674709. q^{73} +(-780928. + 906184. i) q^{75} +(-169330. + 97762.8i) q^{77} +(-46129.2 + 79898.1i) q^{79} +(388570. + 362551. i) q^{81} +(280324. + 161845. i) q^{83} +(-113704. - 196940. i) q^{85} +(-690783. - 595301. i) q^{87} -741890. i q^{89} +1.14092e6 q^{91} +(-128767. - 368814. i) q^{93} +(2.12910e6 - 1.22924e6i) q^{95} +(517838. - 896922. i) q^{97} +(223451. + 280997. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) $ 36 * q + 10 * q^3 + 74 * q^9	$ 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) $ 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−26.5258	−	5.03801i	−0.982437	−	0.186593i
$3$	−26.5258	−	5.03801i	−0.982437	−	0.186593i
$4$		0			0
$5$	−212.009	+	122.404i	−1.69607	+	0.979229i	−0.746659	+	0.665207i	$0.768343\pi$
$5$	−212.009	+	122.404i	−1.69607	+	0.979229i	−0.949416	+	0.314023i	$0.898323\pi$
$6$		0			0
$7$	−198.515	+	343.838i	−0.578761	+	1.00244i	0.416861	+	0.908970i	$0.363130\pi$
$7$	−198.515	+	343.838i	−0.578761	+	1.00244i	−0.995622	+	0.0934725i	$0.970203\pi$
$8$		0			0
$9$	678.237	+	267.274i	0.930366	+	0.366632i
$10$		0			0
$11$	426.493	+	246.236i	0.320430	+	0.185000i	0.651584	−	0.758576i	$-0.274105\pi$
$11$	426.493	+	246.236i	0.320430	+	0.185000i	−0.331154	+	0.943577i	$0.607438\pi$
$12$		0			0
$13$	−1436.82	−	2488.64i	−0.653990	−	1.13274i	−0.982146	−	0.188121i	$-0.939760\pi$
$13$	−1436.82	−	2488.64i	−0.653990	−	1.13274i	0.328156	−	0.944624i	$-0.393573\pi$
$14$		0			0
$15$	6240.39	−	2178.75i	1.84900	−	0.645556i
$16$		0			0
$17$			928.923i			0.189075i	0.995521	+	0.0945373i	$0.0301372\pi$
$17$			928.923i			0.189075i	−0.995521	+	0.0945373i	$0.969863\pi$
$18$		0			0
$19$	−10042.5			−1.46413			−0.732066	−	0.681233i	$-0.761444\pi$
$19$	−10042.5			−1.46413			−0.732066	+	0.681233i	$0.761444\pi$
$20$		0			0
$21$	6998.02	−	8120.46i	0.755645	−	0.876844i
$22$		0			0
$23$	−1335.86	+	771.260i	−0.109794	+	0.0633895i	−0.553891	−	0.832589i	$-0.686858\pi$
$23$	−1335.86	+	771.260i	−0.109794	+	0.0633895i	0.444097	+	0.895978i	$0.353524\pi$
$24$		0			0
$25$	22152.8	−	38369.8i	1.41778	−	2.45567i
$26$		0			0
$27$	−16644.3	−	10506.6i	−0.845616	−	0.533792i
$28$		0			0
$29$	29249.3	+	16887.1i	1.19928	+	0.692405i	0.960395	−	0.278642i	$-0.0898844\pi$
$29$	29249.3	+	16887.1i	1.19928	+	0.692405i	0.238886	+	0.971048i	$0.423218\pi$
$30$		0			0
$31$	7234.19	+	12530.0i	0.242831	+	0.420596i	0.961520	−	0.274736i	$-0.0885905\pi$
$31$	7234.19	+	12530.0i	0.242831	+	0.420596i	−0.718688	+	0.695332i	$0.755257\pi$
$32$		0			0
$33$	−10072.5	−	8680.27i	−0.280283	−	0.241541i
$34$		0			0
$35$		−	97195.8i		−	2.26696i
$36$		0			0
$37$	31633.1			0.624506			0.312253	−	0.949999i	$-0.398916\pi$
$37$	31633.1			0.624506			0.312253	+	0.949999i	$0.398916\pi$
$38$		0			0
$39$	25574.9	+	73251.9i	0.431143	+	1.23488i
$40$		0			0
$41$	27990.9	−	16160.6i	0.406130	−	0.234479i	−0.282995	−	0.959121i	$-0.591328\pi$
$41$	27990.9	−	16160.6i	0.406130	−	0.234479i	0.689126	+	0.724642i	$0.257995\pi$
$42$		0			0
$43$	−17558.4	+	30412.0i	−0.220841	+	0.382507i	−0.955064	−	0.296401i	$-0.904213\pi$
$43$	−17558.4	+	30412.0i	−0.220841	+	0.382507i	0.734223	+	0.678909i	$0.237547\pi$
$44$		0			0
$45$	−176508.	+	26354.0i	−1.93699	+	0.289207i
$46$		0			0
$47$	65811.0	+	37996.0i	0.633877	+	0.365969i	0.782252	−	0.622962i	$-0.214071\pi$
$47$	65811.0	+	37996.0i	0.633877	+	0.365969i	−0.148375	+	0.988931i	$0.547404\pi$
$48$		0			0
$49$	−19991.8	−	34626.8i	−0.169927	−	0.294323i
$50$		0			0
$51$	4679.92	−	24640.4i	0.0352800	−	0.185754i
$52$		0			0
$53$		−	89863.6i		−	0.603610i	−0.953370	−	0.301805i	$-0.902411\pi$
$53$		−	89863.6i		−	0.603610i	0.953370	−	0.301805i	$-0.0975891\pi$
$54$		0			0
$55$	−120561.			−0.724631
$56$		0			0
$57$	266385.	+	50594.1i	1.43842	+	0.273197i
$58$		0			0
$59$	−181648.	+	104874.i	−0.884451	+	0.510638i	−0.872123	−	0.489286i	$-0.837257\pi$
$59$	−181648.	+	104874.i	−0.884451	+	0.510638i	−0.0123276	+	0.999924i	$0.503924\pi$
$60$		0			0
$61$	109571.	−	189783.i	0.482732	−	0.836117i	−0.517071	−	0.855942i	$-0.672978\pi$
$61$	109571.	−	189783.i	0.482732	−	0.836117i	0.999803	+	0.0198256i	$0.00631110\pi$
$62$		0			0
$63$	−226539.	+	180146.i	−0.905986	+	0.720447i
$64$		0			0
$65$	609237.	+	351743.i	2.21843	+	1.28081i
$66$		0			0
$67$	−245898.	−	425909.i	−0.817582	−	1.41609i	−0.907459	−	0.420141i	$-0.861981\pi$
$67$	−245898.	−	425909.i	−0.817582	−	1.41609i	0.0898771	−	0.995953i	$-0.471353\pi$
$68$		0			0
$69$	39320.4	−	13728.2i	0.119694	−	0.0417895i
$70$		0			0
$71$			695612.i			1.94353i	0.235943	+	0.971767i	$0.424182\pi$
$71$			695612.i			1.94353i	−0.235943	+	0.971767i	$0.575818\pi$
$72$		0			0
$73$	−674709.			−1.73439			−0.867197	−	0.497965i	$-0.834081\pi$
$73$	−674709.			−1.73439			−0.867197	+	0.497965i	$0.834081\pi$
$74$		0			0
$75$	−780928.	+	906184.i	−1.85109	+	2.14799i
$76$		0			0
$77$	−169330.	+	97762.8i	−0.370905	+	0.214142i
$78$		0			0
$79$	−46129.2	+	79898.1i	−0.0935609	+	0.162052i	−0.909007	−	0.416781i	$-0.863158\pi$
$79$	−46129.2	+	79898.1i	−0.0935609	+	0.162052i	0.815446	+	0.578833i	$0.196492\pi$
$80$		0			0
$81$	388570.	+	362551.i	0.731163	+	0.682203i
$82$		0			0
$83$	280324.	+	161845.i	0.490259	+	0.283051i	0.724682	−	0.689084i	$-0.241987\pi$
$83$	280324.	+	161845.i	0.490259	+	0.283051i	−0.234423	+	0.972135i	$0.575320\pi$
$84$		0			0
$85$	−113704.	−	196940.i	−0.185147	−	0.320685i
$86$		0			0
$87$	−690783.	−	595301.i	−1.04902	−	0.904022i
$88$		0			0
$89$		−	741890.i		−	1.05237i	−0.850369	−	0.526186i	$-0.823621\pi$
$89$		−	741890.i		−	1.05237i	0.850369	−	0.526186i	$-0.176379\pi$
$90$		0			0
$91$	1.14092e6			1.51402
$92$		0			0
$93$	−128767.	−	368814.i	−0.160086	−	0.458520i
$94$		0			0
$95$	2.12910e6	−	1.22924e6i	2.48328	−	1.43372i
$96$		0			0
$97$	517838.	−	896922.i	0.567387	−	0.982742i	−0.429437	−	0.903097i	$-0.641288\pi$
$97$	517838.	−	896922.i	0.567387	−	0.982742i	0.996823	−	0.0796453i	$-0.0253788\pi$
$98$		0			0
$99$	223451.	+	280997.i	0.230290	+	0.289598i
$100$		0			0
$101$	−222543.	−	128485.i	−0.215998	−	0.124707i	0.388098	−	0.921618i	$-0.373132\pi$
$101$	−222543.	−	128485.i	−0.215998	−	0.124707i	−0.604096	+	0.796912i	$0.706466\pi$
$102$		0			0
$103$	−377603.	−	654027.i	−0.345560	−	0.598527i	0.639896	−	0.768462i	$-0.278978\pi$
$103$	−377603.	−	654027.i	−0.345560	−	0.598527i	−0.985455	+	0.169935i	$0.945644\pi$
$104$		0			0
$105$	−489673.	+	2.57820e6i	−0.422998	+	2.22714i
$106$		0			0
$107$		−	1.64484e6i		−	1.34268i	−0.741152	−	0.671338i	$-0.765720\pi$
$107$		−	1.64484e6i		−	1.34268i	0.741152	−	0.671338i	$-0.234280\pi$
$108$		0			0
$109$	−1.04558e6			−0.807379			−0.403689	−	0.914896i	$-0.632272\pi$
$109$	−1.04558e6			−0.807379			−0.403689	+	0.914896i	$0.632272\pi$
$110$		0			0
$111$	−839094.	−	159368.i	−0.613538	−	0.116528i
$112$		0			0
$113$	1.36714e6	−	789321.i	0.947500	−	0.547039i	0.0551963	−	0.998476i	$-0.482422\pi$
$113$	1.36714e6	−	789321.i	0.947500	−	0.547039i	0.892303	+	0.451436i	$0.149088\pi$
$114$		0			0
$115$	188810.	−	327029.i	0.124146	−	0.215027i
$116$		0			0
$117$	−309353.	−	2.07191e6i	−0.193151	−	1.29364i
$118$		0			0
$119$	−319399.	−	184405.i	−0.189536	−	0.109429i
$120$		0			0
$121$	−764517.	−	1.32418e6i	−0.431550	−	0.747466i
$122$		0			0
$123$	−823898.	+	287653.i	−0.442750	+	0.154580i
$124$		0			0
$125$			7.02122e6i			3.59487i
$126$		0			0
$127$	997767.			0.487100			0.243550	−	0.969888i	$-0.421688\pi$
$127$	997767.			0.487100			0.243550	+	0.969888i	$0.421688\pi$
$128$		0			0
$129$	618966.	−	718244.i	0.288335	−	0.334582i
$130$		0			0
$131$	846508.	−	488731.i	0.376545	−	0.217398i	−0.299769	−	0.954012i	$-0.596910\pi$
$131$	846508.	−	488731.i	0.376545	−	0.217398i	0.676314	+	0.736613i	$0.263576\pi$
$132$		0			0
$133$	1.99358e6	−	3.45299e6i	0.847382	−	1.46771i
$134$		0			0
$135$	4.81479e6	+	190187.i	1.95693	+	0.0772999i
$136$		0			0
$137$	788183.	+	455058.i	0.306525	+	0.176972i	0.645370	−	0.763870i	$-0.276703\pi$
$137$	788183.	+	455058.i	0.306525	+	0.176972i	−0.338846	+	0.940842i	$0.610036\pi$
$138$		0			0
$139$	618879.	+	1.07193e6i	0.230442	+	0.399137i	0.957938	−	0.286975i	$-0.0926496\pi$
$139$	618879.	+	1.07193e6i	0.230442	+	0.399137i	−0.727496	+	0.686111i	$0.759316\pi$
$140$		0			0
$141$	−1.55427e6	−	1.33943e6i	−0.554457	−	0.477818i
$142$		0			0
$143$		−	1.41518e6i		−	0.483954i
$144$		0			0
$145$	−8.26816e6			−2.71209
$146$		0			0
$147$	355848.	+	1.01922e6i	0.112024	+	0.320861i
$148$		0			0
$149$	−2.91293e6	+	1.68178e6i	−0.880585	+	0.508406i	−0.870851	−	0.491547i	$-0.836432\pi$
$149$	−2.91293e6	+	1.68178e6i	−0.880585	+	0.508406i	−0.00973378	+	0.999953i	$0.503098\pi$
$150$		0			0
$151$	−136502.	+	236428.i	−0.0396467	+	0.0686701i	−0.885168	−	0.465272i	$-0.845957\pi$
$151$	−136502.	+	236428.i	−0.0396467	+	0.0686701i	0.845521	+	0.533942i	$0.179290\pi$
$152$		0			0
$153$	−248277.	+	630030.i	−0.0693207	+	0.175909i
$154$		0			0
$155$	−3.06743e6	−	1.77098e6i	−0.823721	−	0.475575i
$156$		0			0
$157$	2.96625e6	+	5.13770e6i	0.766495	+	1.32761i	0.939453	+	0.342679i	$0.111334\pi$
$157$	2.96625e6	+	5.13770e6i	0.766495	+	1.32761i	−0.172958	+	0.984929i	$0.555332\pi$
$158$		0			0
$159$	−452733.	+	2.38370e6i	−0.112629	+	0.593009i
$160$		0			0
$161$		−	612427.i		−	0.146749i
$162$		0			0
$163$	−1.11655e6			−0.257819			−0.128910	−	0.991656i	$-0.541148\pi$
$163$	−1.11655e6			−0.257819			−0.128910	+	0.991656i	$0.541148\pi$
$164$		0			0
$165$	3.19797e6	+	607385.i	0.711905	+	0.135211i
$166$		0			0
$167$	−1.26903e6	+	732673.i	−0.272472	+	0.157312i	−0.630010	−	0.776587i	$-0.716949\pi$
$167$	−1.26903e6	+	732673.i	−0.272472	+	0.157312i	0.357539	+	0.933898i	$0.383616\pi$
$168$		0			0
$169$	−1.71548e6	+	2.97130e6i	−0.355407	+	0.615583i
$170$		0			0
$171$	−6.81119e6	−	2.68410e6i	−1.36218	−	0.536797i
$172$		0			0
$173$	−3.85053e6	−	2.22310e6i	−0.743673	−	0.429360i	0.0797303	−	0.996816i	$-0.474594\pi$
$173$	−3.85053e6	−	2.22310e6i	−0.743673	−	0.429360i	−0.823403	+	0.567457i	$0.807927\pi$
$174$		0			0
$175$	8.79532e6	+	1.52339e7i	1.64111	+	2.84249i
$176$		0			0
$177$	5.34671e6	−	1.86673e6i	0.964199	−	0.336638i
$178$		0			0
$179$		−	9.09049e6i		−	1.58500i	−0.609874	−	0.792498i	$-0.708780\pi$
$179$		−	9.09049e6i		−	1.58500i	0.609874	−	0.792498i	$-0.291220\pi$
$180$		0			0
$181$	4.84434e6			0.816957			0.408479	−	0.912768i	$-0.366059\pi$
$181$	4.84434e6			0.816957			0.408479	+	0.912768i	$0.366059\pi$
$182$		0			0
$183$	−3.86259e6	+	4.48212e6i	−0.630268	+	0.731358i
$184$		0			0
$185$	−6.70651e6	+	3.87201e6i	−1.05921	+	0.611535i
$186$		0			0
$187$	−228734.	+	396179.i	−0.0349789	+	0.0605852i
$188$		0			0
$189$	6.91671e6	−	3.63720e6i	1.02451	−	0.538743i
$190$		0			0
$191$	7.26283e6	+	4.19320e6i	1.04233	+	0.601790i	0.920493	−	0.390760i	$-0.127788\pi$
$191$	7.26283e6	+	4.19320e6i	1.04233	+	0.601790i	0.121839	+	0.992550i	$0.461121\pi$
$192$		0			0
$193$	−2.38712e6	−	4.13461e6i	−0.332049	−	0.575126i	0.650865	−	0.759194i	$-0.274407\pi$
$193$	−2.38712e6	−	4.13461e6i	−0.332049	−	0.575126i	−0.982913	+	0.184068i	$0.941073\pi$
$194$		0			0
$195$	−1.43884e7	−	1.23996e7i	−1.94048	−	1.67226i
$196$		0			0
$197$			830671.i			0.108650i	0.998523	+	0.0543251i	$0.0173007\pi$
$197$			830671.i			0.108650i	−0.998523	+	0.0543251i	$0.982699\pi$
$198$		0			0
$199$	7.45481e6			0.945970			0.472985	−	0.881071i	$-0.343177\pi$
$199$	7.45481e6			0.945970			0.472985	+	0.881071i	$0.343177\pi$
$200$		0			0
$201$	4.37692e6	+	1.25364e7i	0.538990	+	1.54378i
$202$		0			0
$203$	−1.16128e7	+	6.70467e6i	−1.38819	+	0.801474i
$204$		0			0
$205$	−3.95622e6	+	6.85238e6i	−0.459218	+	0.795389i
$206$		0			0
$207$	−1.11217e6	+	166056.i	−0.125389	+	0.0187216i
$208$		0			0
$209$	−4.28305e6	−	2.47282e6i	−0.469152	−	0.270865i
$210$		0			0
$211$	1.25156e6	+	2.16776e6i	0.133230	+	0.230762i	0.924920	−	0.380162i	$-0.124132\pi$
$211$	1.25156e6	+	2.16776e6i	0.133230	+	0.230762i	−0.791690	+	0.610923i	$0.790798\pi$
$212$		0			0
$213$	3.50450e6	−	1.84517e7i	0.362649	−	1.90940i
$214$		0			0
$215$		−	8.59684e6i		−	0.865015i
$216$		0			0
$217$	−5.74438e6			−0.562165
$218$		0			0
$219$	1.78972e7	+	3.39919e6i	1.70393	+	0.323626i
$220$		0			0
$221$	2.31176e6	−	1.33469e6i	0.214173	−	0.123653i
$222$		0			0
$223$	7.70194e6	−	1.33401e7i	0.694521	−	1.20295i	−0.275821	−	0.961209i	$-0.588950\pi$
$223$	7.70194e6	−	1.33401e7i	0.694521	−	1.20295i	0.970342	−	0.241736i	$-0.0777169\pi$
$224$		0			0
$225$	2.52801e7	−	2.01029e7i	2.21938	−	1.76487i
$226$		0			0
$227$	−5.81586e6	−	3.35779e6i	−0.497206	−	0.287062i	0.230353	−	0.973107i	$-0.426012\pi$
$227$	−5.81586e6	−	3.35779e6i	−0.497206	−	0.287062i	−0.727559	+	0.686045i	$0.759345\pi$
$228$		0			0
$229$	−2.67688e6	−	4.63649e6i	−0.222906	−	0.386085i	0.732783	−	0.680463i	$-0.238221\pi$
$229$	−2.67688e6	−	4.63649e6i	−0.222906	−	0.386085i	−0.955689	+	0.294377i	$0.904888\pi$
$230$		0			0
$231$	4.98415e6	−	1.74015e6i	0.404348	−	0.141173i
$232$		0			0
$233$			419244.i			0.0331436i	0.999863	+	0.0165718i	$0.00527520\pi$
$233$			419244.i			0.0331436i	−0.999863	+	0.0165718i	$0.994725\pi$
$234$		0			0
$235$	−1.86034e7			−1.43347
$236$		0			0
$237$	1.62614e6	−	1.88696e6i	0.122156	−	0.141748i
$238$		0			0
$239$	−1.20461e6	+	695480.i	−0.0882372	+	0.0509438i	−0.543469	−	0.839429i	$-0.682890\pi$
$239$	−1.20461e6	+	695480.i	−0.0882372	+	0.0509438i	0.455232	+	0.890373i	$0.349556\pi$
$240$		0			0
$241$	1.16135e7	−	2.01152e7i	0.829686	−	1.43706i	−0.0685995	−	0.997644i	$-0.521853\pi$
$241$	1.16135e7	−	2.01152e7i	0.829686	−	1.43706i	0.898285	−	0.439413i	$-0.144814\pi$
$242$		0			0
$243$	−8.48059e6	−	1.15746e7i	−0.591027	−	0.806652i
$244$		0			0
$245$	8.47689e6	+	4.89414e6i	0.576419	+	0.332796i
$246$		0			0
$247$	1.44292e7	+	2.49921e7i	0.957529	+	1.65849i
$248$		0			0
$249$	−6.62044e6	−	5.70534e6i	−0.428833	−	0.369559i
$250$		0			0
$251$			2.47268e6i			0.156368i	0.996939	+	0.0781838i	$0.0249121\pi$
$251$			2.47268e6i			0.156368i	−0.996939	+	0.0781838i	$0.975088\pi$
$252$		0			0
$253$	−759647.			−0.0469084
$254$		0			0
$255$	2.02389e6	+	5.79684e6i	0.122058	+	0.349600i
$256$		0			0
$257$	−1.96517e6	+	1.13459e6i	−0.115771	+	0.0668404i	−0.556767	−	0.830668i	$-0.687959\pi$
$257$	−1.96517e6	+	1.13459e6i	−0.115771	+	0.0668404i	0.440996	+	0.897509i	$0.354625\pi$
$258$		0			0
$259$	−6.27964e6	+	1.08767e7i	−0.361439	+	0.626031i
$260$		0			0
$261$	1.53245e7	+	1.92710e7i	0.861913	+	1.08388i
$262$		0			0
$263$	−2.43586e7	−	1.40635e7i	−1.33902	−	0.773082i	−0.352355	−	0.935866i	$-0.614619\pi$
$263$	−2.43586e7	−	1.40635e7i	−1.33902	−	0.773082i	−0.986662	+	0.162785i	$0.947952\pi$
$264$		0			0
$265$	1.09996e7	+	1.90519e7i	0.591072	+	1.02377i
$266$		0			0
$267$	−3.73765e6	+	1.96792e7i	−0.196365	+	1.03389i
$268$		0			0
$269$		−	676848.i		−	0.0347724i	−0.999849	−	0.0173862i	$-0.994466\pi$
$269$		−	676848.i		−	0.0347724i	0.999849	−	0.0173862i	$-0.00553447\pi$
$270$		0			0
$271$	−3.12938e7			−1.57235			−0.786177	−	0.618001i	$-0.787943\pi$
$271$	−3.12938e7			−1.57235			−0.786177	+	0.618001i	$0.787943\pi$
$272$		0			0
$273$	−3.02638e7	−	5.74795e6i	−1.48742	−	0.282504i
$274$		0			0
$275$	1.88960e7	−	1.09096e7i	0.908599	−	0.524580i
$276$		0			0
$277$	1.07007e6	−	1.85342e6i	0.0503470	−	0.0872035i	−0.839754	−	0.542968i	$-0.817301\pi$
$277$	1.07007e6	−	1.85342e6i	0.0503470	−	0.0872035i	0.890101	+	0.455764i	$0.150634\pi$
$278$		0			0
$279$	1.55755e6	+	1.04318e7i	0.0717183	+	0.480338i
$280$		0			0
$281$	1.14787e7	+	6.62721e6i	0.517335	+	0.298684i	0.735844	−	0.677151i	$-0.236786\pi$
$281$	1.14787e7	+	6.62721e6i	0.517335	+	0.298684i	−0.218508	+	0.975835i	$0.570119\pi$
$282$		0			0
$283$	4.68162e6	+	8.10881e6i	0.206556	+	0.357765i	0.950627	−	0.310335i	$-0.100441\pi$
$283$	4.68162e6	+	8.10881e6i	0.206556	+	0.357765i	−0.744072	+	0.668100i	$0.767108\pi$
$284$		0			0
$285$	−6.26690e7	+	2.18801e7i	−2.70719	+	0.945180i
$286$		0			0
$287$			1.28324e7i			0.542830i
$288$		0			0
$289$	2.32747e7			0.964251
$290$		0			0
$291$	−1.82548e7	+	2.11827e7i	−0.740794	+	0.859612i
$292$		0			0
$293$	2.55674e7	−	1.47614e7i	1.01645	−	0.586845i	0.103373	−	0.994643i	$-0.467036\pi$
$293$	2.55674e7	−	1.47614e7i	1.01645	−	0.586845i	0.913072	+	0.407797i	$0.133703\pi$
$294$		0			0
$295$	2.56740e7	−	4.44687e7i	1.00006	−	1.73216i
$296$		0			0
$297$	−4.51154e6	−	8.57941e6i	−0.172209	−	0.327482i
$298$		0			0
$299$	3.83878e6	+	2.21632e6i	0.143608	+	0.0829123i
$300$		0			0
$301$	−6.97120e6	−	1.20745e7i	−0.255628	−	0.442760i
$302$		0			0
$303$	5.25583e6	+	4.52935e6i	0.188935	+	0.162820i
$304$		0			0
$305$			5.36476e7i			1.89082i
$306$		0			0
$307$	112293.			0.00388096			0.00194048	−	0.999998i	$-0.499382\pi$
$307$	112293.			0.00388096			0.00194048	+	0.999998i	$0.499382\pi$
$308$		0			0
$309$	6.72122e6	+	1.92510e7i	0.227810	+	0.652494i
$310$		0			0
$311$	2.66674e7	−	1.53964e7i	0.886542	−	0.511845i	0.0137323	−	0.999906i	$-0.495629\pi$
$311$	2.66674e7	−	1.53964e7i	0.886542	−	0.511845i	0.872810	+	0.488060i	$0.162295\pi$
$312$		0			0
$313$	5.43624e6	−	9.41584e6i	0.177282	−	0.307062i	−0.763666	−	0.645611i	$-0.776603\pi$
$313$	5.43624e6	−	9.41584e6i	0.177282	−	0.307062i	0.940949	+	0.338549i	$0.109936\pi$
$314$		0			0
$315$	2.59779e7	−	6.59218e7i	0.831138	−	2.10910i
$316$		0			0
$317$	−3.27264e7	−	1.88946e7i	−1.02736	−	0.593144i	−0.111130	−	0.993806i	$-0.535447\pi$
$317$	−3.27264e7	−	1.88946e7i	−1.02736	−	0.593144i	−0.916226	+	0.400662i	$0.868780\pi$
$318$		0			0
$319$	8.31640e6	+	1.44044e7i	0.256191	+	0.443735i
$320$		0			0
$321$	−8.28669e6	+	4.36306e7i	−0.250534	+	1.31909i
$322$		0			0
$323$		−	9.32870e6i		−	0.276830i
$324$		0			0
$325$	−1.27318e8			−3.70886
$326$		0			0
$327$	2.77348e7	+	5.26763e6i	0.793199	+	0.150651i
$328$		0			0
$329$	−2.61289e7	+	1.50855e7i	−0.733726	+	0.423617i
$330$		0			0
$331$	8.14358e6	−	1.41051e7i	0.224560	−	0.388948i	−0.731628	−	0.681704i	$-0.761239\pi$
$331$	8.14358e6	−	1.41051e7i	0.224560	−	0.388948i	0.956187	+	0.292756i	$0.0945723\pi$
$332$		0			0
$333$	2.14547e7	+	8.45472e6i	0.581019	+	0.228964i
$334$		0			0
$335$	1.04266e8	+	6.01977e7i	2.77336	+	1.60120i
$336$		0			0
$337$	4.22163e6	+	7.31208e6i	0.110304	+	0.191052i	0.915893	−	0.401423i	$-0.131484\pi$
$337$	4.22163e6	+	7.31208e6i	0.110304	+	0.191052i	−0.805589	+	0.592475i	$0.798151\pi$
$338$		0			0
$339$	−4.02412e7	+	1.40497e7i	−1.03293	+	0.360635i
$340$		0			0
$341$			7.12526e6i			0.179696i
$342$		0			0
$343$	−3.08355e7			−0.764132
$344$		0			0
$345$	−6.65592e6	+	7.72348e6i	−0.162088	+	0.188086i
$346$		0			0
$347$	−4.39381e7	+	2.53677e7i	−1.05161	+	0.607145i	−0.923099	−	0.384563i	$-0.874352\pi$
$347$	−4.39381e7	+	2.53677e7i	−1.05161	+	0.607145i	−0.128508	+	0.991708i	$0.541019\pi$
$348$		0			0
$349$	5.17983e6	−	8.97174e6i	0.121854	−	0.211057i	−0.798645	−	0.601803i	$-0.794449\pi$
$349$	5.17983e6	−	8.97174e6i	0.121854	−	0.211057i	0.920499	+	0.390745i	$0.127783\pi$
$350$		0			0
$351$	−2.23248e6	+	5.65177e7i	−0.0516257	+	1.30696i
$352$		0			0
$353$	−3.69105e7	−	2.13103e7i	−0.839124	−	0.484469i	0.0178422	−	0.999841i	$-0.494320\pi$
$353$	−3.69105e7	−	2.13103e7i	−0.839124	−	0.484469i	−0.856966	+	0.515372i	$0.827654\pi$
$354$		0			0
$355$	−8.51455e7	−	1.47476e8i	−1.90317	−	3.29638i
$356$		0			0
$357$	7.54328e6	+	6.50063e6i	0.165789	+	0.142873i
$358$		0			0
$359$			3.23891e7i			0.700027i	0.936745	+	0.350014i	$0.113823\pi$
$359$			3.23891e7i			0.700027i	−0.936745	+	0.350014i	$0.886177\pi$
$360$		0			0
$361$	5.38057e7			1.14368
$362$		0			0
$363$	1.36082e7	+	3.89766e7i	0.284499	+	0.814863i
$364$		0			0
$365$	1.43045e8	−	8.25868e7i	2.94166	−	1.69837i
$366$		0			0
$367$	6.73073e6	−	1.16580e7i	0.136165	−	0.235844i	−0.789877	−	0.613265i	$-0.789856\pi$
$367$	6.73073e6	−	1.16580e7i	0.136165	−	0.235844i	0.926042	+	0.377421i	$0.123189\pi$
$368$		0			0
$369$	2.33038e7	−	3.47943e6i	0.463817	−	0.0692516i
$370$		0			0
$371$	3.08985e7	+	1.78393e7i	0.605084	+	0.349345i
$372$		0			0
$373$	3.25880e7	+	5.64441e7i	0.627959	+	1.08766i	0.987961	+	0.154705i	$0.0494428\pi$
$373$	3.25880e7	+	5.64441e7i	0.627959	+	1.08766i	−0.360002	+	0.932952i	$0.617224\pi$
$374$		0			0
$375$	3.53730e7	−	1.86244e8i	0.670776	−	3.53173i
$376$		0			0
$377$		−	9.70545e7i		−	1.81131i
$378$		0			0
$379$	7.50377e7			1.37836			0.689179	−	0.724591i	$-0.257971\pi$
$379$	7.50377e7			1.37836			0.689179	+	0.724591i	$0.257971\pi$
$380$		0			0
$381$	−2.64666e7	−	5.02676e6i	−0.478545	−	0.0908893i
$382$		0			0
$383$	−3.69467e7	+	2.13312e7i	−0.657627	+	0.379681i	−0.791372	−	0.611335i	$-0.790633\pi$
$383$	−3.69467e7	+	2.13312e7i	−0.657627	+	0.379681i	0.133745	+	0.991016i	$0.457300\pi$
$384$		0			0
$385$	2.39331e7	−	4.14533e7i	0.419388	−	0.726401i
$386$		0			0
$387$	−2.00371e7	+	1.59336e7i	−0.345702	+	0.274905i
$388$		0			0
$389$	2.41289e7	+	1.39308e7i	0.409910	+	0.236662i	0.690751	−	0.723093i	$-0.257280\pi$
$389$	2.41289e7	+	1.39308e7i	0.409910	+	0.236662i	−0.280841	+	0.959754i	$0.590613\pi$
$390$		0			0
$391$	−716442.	−	1.24091e6i	−0.0119853	−	0.0207592i
$392$		0			0
$393$	−2.49165e7	+	8.69928e6i	−0.410497	+	0.143320i
$394$		0			0
$395$		−	2.25855e7i		−	0.366470i
$396$		0			0
$397$	8.40155e7			1.34273			0.671363	−	0.741128i	$-0.265709\pi$
$397$	8.40155e7			1.34273			0.671363	+	0.741128i	$0.265709\pi$
$398$		0			0
$399$	−7.02776e7	+	8.15496e7i	−1.10636	+	1.28382i
$400$		0			0
$401$	−3.94167e7	+	2.27572e7i	−0.611289	+	0.352928i	−0.773470	−	0.633833i	$-0.781481\pi$
$401$	−3.94167e7	+	2.27572e7i	−0.611289	+	0.352928i	0.162181	+	0.986761i	$0.448147\pi$
$402$		0			0
$403$	2.07884e7	−	3.60066e7i	0.317619	−	0.550132i
$404$		0			0
$405$	−1.26758e8	−	2.93018e7i	−1.90814	−	0.441092i
$406$		0			0
$407$	1.34913e7	+	7.78920e6i	0.200111	+	0.115534i
$408$		0			0
$409$	1.18969e6	+	2.06060e6i	0.0173886	+	0.0301179i	0.874589	−	0.484865i	$-0.161131\pi$
$409$	1.18969e6	+	2.06060e6i	0.0173886	+	0.0301179i	−0.857200	+	0.514983i	$0.827798\pi$
$410$		0			0
$411$	−1.86146e7	−	1.60416e7i	−0.268120	−	0.231059i
$412$		0			0
$413$		−	8.32765e7i		−	1.18215i
$414$		0			0
$415$	−7.92417e7			−1.10869
$416$		0			0
$417$	−1.10159e7	−	3.15517e7i	−0.151918	−	0.435126i
$418$		0			0
$419$	−1.59401e7	+	9.20302e6i	−0.216695	+	0.125109i	−0.604419	−	0.796667i	$-0.706595\pi$
$419$	−1.59401e7	+	9.20302e6i	−0.216695	+	0.125109i	0.387724	+	0.921776i	$0.373261\pi$
$420$		0			0
$421$	−2.50661e7	+	4.34158e7i	−0.335924	+	0.581838i	−0.983662	−	0.180026i	$-0.942382\pi$
$421$	−2.50661e7	+	4.34158e7i	−0.335924	+	0.581838i	0.647738	+	0.761863i	$0.275715\pi$
$422$		0			0
$423$	3.44801e7	+	4.33599e7i	0.455562	+	0.572884i
$424$		0			0
$425$	3.56426e7	+	2.05783e7i	0.464304	+	0.268066i
$426$		0			0
$427$	4.35030e7	+	7.53493e7i	0.558773	+	0.967823i
$428$		0			0
$429$	−7.12970e6	+	3.75388e7i	−0.0903024	+	0.475454i
$430$		0			0
$431$		−	1.09231e8i		−	1.36431i	−0.731207	−	0.682156i	$-0.761042\pi$
$431$		−	1.09231e8i		−	1.36431i	0.731207	−	0.682156i	$-0.238958\pi$
$432$		0			0
$433$	−1.14550e8			−1.41101			−0.705507	−	0.708703i	$-0.749281\pi$
$433$	−1.14550e8			−1.41101			−0.705507	+	0.708703i	$0.749281\pi$
$434$		0			0
$435$	2.19320e8	+	4.16550e7i	2.66446	+	0.506057i
$436$		0			0
$437$	1.34154e7	−	7.74537e6i	0.160753	−	0.0928107i
$438$		0			0
$439$	−4.79743e7	+	8.30940e7i	−0.567042	+	0.982146i	0.429814	+	0.902917i	$0.358579\pi$
$439$	−4.79743e7	+	8.30940e7i	−0.567042	+	0.982146i	−0.996856	+	0.0792284i	$0.974754\pi$
$440$		0			0
$441$	−4.30432e6	−	2.88285e7i	−0.0501867	−	0.336129i
$442$		0			0
$443$	−3.95905e7	−	2.28576e7i	−0.455386	−	0.262917i	0.254716	−	0.967016i	$-0.418018\pi$
$443$	−3.95905e7	−	2.28576e7i	−0.455386	−	0.262917i	−0.710102	+	0.704099i	$0.751351\pi$
$444$		0			0
$445$	9.08101e7	+	1.57288e8i	1.03051	+	1.78490i
$446$		0			0
$447$	8.57407e7	−	2.99352e7i	0.959985	−	0.335166i
$448$		0			0
$449$			9.51568e7i			1.05124i	0.850720	+	0.525619i	$0.176166\pi$
$449$			9.51568e7i			1.05124i	−0.850720	+	0.525619i	$0.823834\pi$
$450$		0			0
$451$	1.59172e7			0.173515
$452$		0			0
$453$	4.81194e6	−	5.58374e6i	0.0517637	−	0.0600663i
$454$		0			0
$455$	−2.41885e8	+	1.39653e8i	−2.56788	+	1.48257i
$456$		0			0
$457$	5.08965e7	−	8.81554e7i	0.533261	−	0.923634i	−0.465985	−	0.884793i	$-0.654300\pi$
$457$	5.08965e7	−	8.81554e7i	0.533261	−	0.923634i	0.999245	−	0.0388417i	$-0.0123668\pi$
$458$		0			0
$459$	9.75986e6	−	1.54612e7i	0.100927	−	0.159884i
$460$		0			0
$461$	−7.14873e7	−	4.12732e7i	−0.729669	−	0.421275i	0.0886318	−	0.996064i	$-0.471751\pi$
$461$	−7.14873e7	−	4.12732e7i	−0.729669	−	0.421275i	−0.818301	+	0.574790i	$0.805084\pi$
$462$		0			0
$463$	−6.80171e7	−	1.17809e8i	−0.685291	−	1.18696i	−0.973345	−	0.229345i	$-0.926342\pi$
$463$	−6.80171e7	−	1.17809e8i	−0.685291	−	1.18696i	0.288054	−	0.957614i	$-0.406992\pi$
$464$		0			0
$465$	7.24439e7	+	6.24305e7i	0.720515	+	0.620923i
$466$		0			0
$467$			1.23685e8i			1.21441i	0.794544	+	0.607207i	$0.207710\pi$
$467$			1.23685e8i			1.21441i	−0.794544	+	0.607207i	$0.792290\pi$
$468$		0			0
$469$	1.95258e8			1.89274
$470$		0			0
$471$	−5.27985e7	−	1.51226e8i	−0.505311	−	1.44731i
$472$		0			0
$473$	−1.49770e7	+	8.64700e6i	−0.141528	+	0.0817113i
$474$		0			0
$475$	−2.22469e8	+	3.85328e8i	−2.07582	+	3.59542i
$476$		0			0
$477$	2.40182e7	−	6.09488e7i	0.221302	−	0.561578i
$478$		0			0
$479$	1.21775e6	+	703071.i	0.0110803	+	0.00639724i	0.505530	−	0.862809i	$-0.331297\pi$
$479$	1.21775e6	+	703071.i	0.0110803	+	0.00639724i	−0.494450	+	0.869206i	$0.664630\pi$
$480$		0			0
$481$	−4.54510e7	−	7.87234e7i	−0.408421	−	0.707406i
$482$		0			0
$483$	−3.08541e6	+	1.62451e7i	−0.0273824	+	0.144172i
$484$		0			0
$485$			2.53541e8i			2.22241i
$486$		0			0
$487$	−1.61712e8			−1.40008			−0.700042	−	0.714102i	$-0.746835\pi$
$487$	−1.61712e8			−1.40008			−0.700042	+	0.714102i	$0.746835\pi$
$488$		0			0
$489$	2.96174e7	+	5.62518e6i	0.253291	+	0.0481072i
$490$		0			0
$491$	−4.57736e7	+	2.64274e7i	−0.386697	+	0.223259i	−0.680728	−	0.732536i	$-0.738336\pi$
$491$	−4.57736e7	+	2.64274e7i	−0.386697	+	0.223259i	0.294031	+	0.955796i	$0.405003\pi$
$492$		0			0
$493$	−1.56868e7	+	2.71703e7i	−0.130916	+	0.226754i
$494$		0			0
$495$	−8.17686e7	−	3.22227e7i	−0.674173	−	0.265673i
$496$		0			0
$497$	−2.39178e8	−	1.38089e8i	−1.94828	−	1.12484i
$498$		0			0
$499$	−1.12276e7	−	1.94468e7i	−0.0903620	−	0.156511i	0.817302	−	0.576210i	$-0.195469\pi$
$499$	−1.12276e7	−	1.94468e7i	−0.0903620	−	0.156511i	−0.907663	+	0.419699i	$0.862136\pi$
$500$		0			0
$501$	3.73532e7	−	1.30414e7i	0.297039	−	0.103707i
$502$		0			0
$503$		−	1.38515e8i		−	1.08841i	−0.838953	−	0.544204i	$-0.816832\pi$
$503$		−	1.38515e8i		−	1.08841i	0.838953	−	0.544204i	$-0.183168\pi$
$504$		0			0
$505$	6.29083e7			0.488466
$506$		0			0
$507$	6.04739e7	−	7.01735e7i	0.464028	−	0.538455i
$508$		0			0
$509$	8.81616e7	−	5.09001e7i	0.668538	−	0.385981i	−0.126984	−	0.991905i	$-0.540530\pi$
$509$	8.81616e7	−	5.09001e7i	0.668538	−	0.385981i	0.795522	+	0.605924i	$0.207196\pi$
$510$		0			0
$511$	1.33940e8	−	2.31990e8i	1.00380	−	1.73863i
$512$		0			0
$513$	1.67150e8	+	1.05513e8i	1.23809	+	0.781543i
$514$		0			0
$515$	1.60111e8	+	9.24399e7i	1.17219	+	0.676765i
$516$		0			0
$517$	1.87119e7	+	3.24100e7i	0.135409	+	0.234535i
$518$		0			0
$519$	9.09384e7	+	7.83686e7i	0.650497	+	0.560583i
$520$		0			0
$521$		−	8.07944e7i		−	0.571305i	−0.958333	−	0.285653i	$-0.907790\pi$
$521$		−	8.07944e7i		−	0.571305i	0.958333	−	0.285653i	$-0.0922103\pi$
$522$		0			0
$523$	2.78945e8			1.94990			0.974951	−	0.222418i	$-0.0713951\pi$
$523$	2.78945e8			1.94990			0.974951	+	0.222418i	$0.0713951\pi$
$524$		0			0
$525$	−1.56554e8	−	4.48404e8i	−1.08190	−	3.09878i
$526$		0			0
$527$	−1.16394e7	+	6.72001e6i	−0.0795241	+	0.0459133i
$528$		0			0
$529$	−7.28283e7	+	1.26142e8i	−0.491964	+	0.852106i
$530$		0			0
$531$	−1.51230e8	+	2.25799e7i	−1.01008	+	0.150813i
$532$		0			0
$533$	−8.04356e7	−	4.64395e7i	−0.531211	−	0.306695i
$534$		0			0
$535$	2.01334e8	+	3.48720e8i	1.31479	+	2.27728i
$536$		0			0
$537$	−4.57980e7	+	2.41133e8i	−0.295749	+	1.55716i
$538$		0			0
$539$		−	1.96908e7i		−	0.125747i
$540$		0			0
$541$	−6.31693e7			−0.398946			−0.199473	−	0.979903i	$-0.563923\pi$
$541$	−6.31693e7			−0.398946			−0.199473	+	0.979903i	$0.563923\pi$
$542$		0			0
$543$	−1.28500e8	−	2.44058e7i	−0.802609	−	0.152438i
$544$		0			0
$545$	2.21673e8	−	1.27983e8i	1.36937	−	0.790609i
$546$		0			0
$547$	1.00037e8	−	1.73270e8i	0.611223	−	1.05867i	−0.379812	−	0.925064i	$-0.624011\pi$
$547$	1.00037e8	−	1.73270e8i	0.611223	−	1.05867i	0.991035	−	0.133605i	$-0.0426555\pi$
$548$		0			0
$549$	1.25039e8	−	9.94321e7i	0.755665	−	0.600910i
$550$		0			0
$551$	−2.93735e8	−	1.69588e8i	−1.75591	−	1.01377i
$552$		0			0
$553$	−1.83147e7	−	3.17219e7i	−0.108299	−	0.187579i
$554$		0			0
$555$	1.97403e8	−	6.89207e7i	1.15471	−	0.403154i
$556$		0			0
$557$		−	7.17289e7i		−	0.415077i	−0.978227	−	0.207538i	$-0.933455\pi$
$557$		−	7.17289e7i		−	0.415077i	0.978227	−	0.207538i	$-0.0665452\pi$
$558$		0			0
$559$	1.00913e8			0.577711
$560$		0			0
$561$	8.06331e6	−	9.35660e6i	0.0456693	−	0.0529943i
$562$		0			0
$563$	1.66950e8	−	9.63886e7i	0.935537	−	0.540133i	0.0469787	−	0.998896i	$-0.485041\pi$
$563$	1.66950e8	−	9.63886e7i	0.935537	−	0.540133i	0.888559	+	0.458763i	$0.151707\pi$
$564$		0			0
$565$	−1.93232e8	+	3.34687e8i	−1.07135	+	1.85564i
$566$		0			0
$567$	−2.01796e8	+	6.16333e7i	−1.10704	+	0.338116i
$568$		0			0
$569$	−2.44576e8	−	1.41206e8i	−1.32763	−	0.766508i	−0.342698	−	0.939445i	$-0.611341\pi$
$569$	−2.44576e8	−	1.41206e8i	−1.32763	−	0.766508i	−0.984933	+	0.172937i	$0.944674\pi$
$570$		0			0
$571$	−7.00764e7	−	1.21376e8i	−0.376412	−	0.651965i	0.614125	−	0.789209i	$-0.289509\pi$
$571$	−7.00764e7	−	1.21376e8i	−0.376412	−	0.651965i	−0.990537	+	0.137244i	$0.956176\pi$
$572$		0			0
$573$	−1.71527e8	−	1.47818e8i	−0.911736	−	0.785713i
$574$		0			0
$575$			6.83423e7i			0.359490i
$576$		0			0
$577$	1.44701e8			0.753260			0.376630	−	0.926364i	$-0.377083\pi$
$577$	1.44701e8			0.753260			0.376630	+	0.926364i	$0.377083\pi$
$578$		0			0
$579$	4.24900e7	+	1.21700e8i	0.218903	+	0.626983i
$580$		0			0
$581$	−1.11297e8	+	6.42573e7i	−0.567485	+	0.327638i
$582$		0			0
$583$	2.21276e7	−	3.83261e7i	0.111668	−	0.193415i
$584$		0			0
$585$	3.19195e8	+	4.01399e8i	1.59437	+	2.00497i
$586$		0			0
$587$	6.44176e7	+	3.71915e7i	0.318486	+	0.183878i	0.650718	−	0.759320i	$-0.274468\pi$
$587$	6.44176e7	+	3.71915e7i	0.318486	+	0.183878i	−0.332231	+	0.943198i	$0.607802\pi$
$588$		0			0
$589$	−7.26493e7	−	1.25832e8i	−0.355537	−	0.615809i
$590$		0			0
$591$	4.18492e6	−	2.20342e7i	0.0202733	−	0.106742i
$592$		0			0
$593$			1.48313e8i			0.711239i	0.934631	+	0.355620i	$0.115730\pi$
$593$			1.48313e8i			0.711239i	−0.934631	+	0.355620i	$0.884270\pi$
$594$		0			0
$595$	9.02874e7			0.428624
$596$		0			0
$597$	−1.97745e8	−	3.75574e7i	−0.929356	−	0.176511i
$598$		0			0
$599$	2.30279e8	−	1.32952e8i	1.07145	−	0.618605i	0.142876	−	0.989741i	$-0.454365\pi$
$599$	2.30279e8	−	1.32952e8i	1.07145	−	0.618605i	0.928579	+	0.371136i	$0.121032\pi$
$600$		0			0
$601$	−1.01761e8	+	1.76255e8i	−0.468768	+	0.811931i	−0.999363	−	0.0356953i	$-0.988635\pi$
$601$	−1.01761e8	+	1.76255e8i	−0.468768	+	0.811931i	0.530594	+	0.847626i	$0.321969\pi$
$602$		0			0
$603$	−5.29429e7	−	3.54589e8i	−0.241466	−	1.61724i
$604$		0			0
$605$	3.24169e8	+	1.87159e8i	1.46388	+	0.845172i
$606$		0			0
$607$	−2.04661e8	−	3.54483e8i	−0.915101	−	1.58500i	−0.806754	−	0.590888i	$-0.798778\pi$
$607$	−2.04661e8	−	3.54483e8i	−0.915101	−	1.58500i	−0.108347	−	0.994113i	$-0.534556\pi$
$608$		0			0
$609$	3.41818e8	−	1.19341e8i	1.51336	−	0.528371i
$610$		0			0
$611$		−	2.18373e8i		−	0.957361i
$612$		0			0
$613$	1.14639e8			0.497680			0.248840	−	0.968545i	$-0.419951\pi$
$613$	1.14639e8			0.497680			0.248840	+	0.968545i	$0.419951\pi$
$614$		0			0
$615$	1.39464e8	−	1.61833e8i	0.599567	−	0.695733i
$616$		0			0
$617$	−1.12410e8	+	6.48997e7i	−0.478572	+	0.276304i	−0.719821	−	0.694159i	$-0.755776\pi$
$617$	−1.12410e8	+	6.48997e7i	−0.478572	+	0.276304i	0.241249	+	0.970463i	$0.422443\pi$
$618$		0			0
$619$	2.36361e6	−	4.09390e6i	0.00996563	−	0.0172610i	−0.861000	−	0.508606i	$-0.830161\pi$
$619$	2.36361e6	−	4.09390e6i	0.00996563	−	0.0172610i	0.870965	+	0.491345i	$0.163494\pi$
$620$		0			0
$621$	3.03378e7	+	1.19836e6i	0.126680	+	0.00500394i
$622$		0			0
$623$	2.55090e8	+	1.47276e8i	1.05494	+	0.609072i
$624$		0			0
$625$	−5.13286e8	−	8.89037e8i	−2.10242	−	3.64150i
$626$		0			0
$627$	1.01153e8	+	8.71715e7i	0.410371	+	0.353649i
$628$		0			0
$629$			2.93847e7i			0.118078i
$630$		0			0
$631$	1.82528e8			0.726511			0.363256	−	0.931690i	$-0.381665\pi$
$631$	1.82528e8			0.726511			0.363256	+	0.931690i	$0.381665\pi$
$632$		0			0
$633$	−2.22773e7	−	6.38069e7i	−0.0878319	−	0.251569i
$634$		0			0
$635$	−2.11536e8	+	1.22130e8i	−0.826158	+	0.476982i
$636$		0			0
$637$	−5.74491e7	+	9.95047e7i	−0.222262	+	0.384969i
$638$		0			0
$639$	−1.85919e8	+	4.71790e8i	−0.712561	+	1.80820i
$640$		0			0
$641$	2.05472e8	+	1.18630e8i	0.780152	+	0.450421i	0.836484	−	0.547991i	$-0.184607\pi$
$641$	2.05472e8	+	1.18630e8i	0.780152	+	0.450421i	−0.0563319	+	0.998412i	$0.517940\pi$
$642$		0			0
$643$	1.76840e7	+	3.06296e7i	0.0665194	+	0.115215i	0.897367	−	0.441285i	$-0.145477\pi$
$643$	1.76840e7	+	3.06296e7i	0.0665194	+	0.115215i	−0.830848	+	0.556500i	$0.812144\pi$
$644$		0			0
$645$	−4.33109e7	+	2.28038e8i	−0.161406	+	0.849823i
$646$		0			0
$647$		−	1.23059e8i		−	0.454359i	−0.973853	−	0.227180i	$-0.927050\pi$
$647$		−	1.23059e8i		−	0.454359i	0.973853	−	0.227180i	$-0.0729505\pi$
$648$		0			0
$649$	−1.03295e8			−0.377873
$650$		0			0
$651$	1.52374e8	+	2.89402e7i	0.552292	+	0.104896i
$652$		0			0
$653$	−3.20266e8	+	1.84905e8i	−1.15019	+	0.664064i	−0.948934	−	0.315474i	$-0.897837\pi$
$653$	−3.20266e8	+	1.84905e8i	−1.15019	+	0.664064i	−0.201259	+	0.979538i	$0.564503\pi$
$654$		0			0
$655$	−1.19645e8	+	2.07231e8i	−0.425766	+	0.737448i
$656$		0			0
$657$	−4.57613e8	−	1.80332e8i	−1.61362	−	0.635884i
$658$		0			0
$659$	4.13407e8	+	2.38681e8i	1.44451	+	0.833990i	0.998146	−	0.0608596i	$-0.0193842\pi$
$659$	4.13407e8	+	2.38681e8i	1.44451	+	0.833990i	0.446367	+	0.894850i	$0.352718\pi$
$660$		0			0
$661$	−2.57597e7	−	4.46170e7i	−0.0891940	−	0.154489i	0.817977	−	0.575251i	$-0.195096\pi$
$661$	−2.57597e7	−	4.46170e7i	−0.0891940	−	0.154489i	−0.907171	+	0.420763i	$0.861762\pi$
$662$		0			0
$663$	−6.80454e7	+	2.37572e7i	−0.233484	+	0.0815181i
$664$		0			0
$665$			9.76087e8i			3.31913i
$666$		0			0
$667$	−5.20973e7			−0.175565
$668$		0			0
$669$	−2.71508e8	+	3.15056e8i	−0.906784	+	1.05223i
$670$		0			0
$671$	9.34625e7	−	5.39606e7i	0.309364	−	0.178611i
$672$		0			0
$673$	2.85435e8	−	4.94388e8i	0.936402	−	1.62190i	0.164288	−	0.986412i	$-0.447467\pi$
$673$	2.85435e8	−	4.94388e8i	0.936402	−	1.62190i	0.772114	−	0.635484i	$-0.219199\pi$
$674$		0			0
$675$	−7.71854e8	+	4.05885e8i	−2.50971	+	1.31975i
$676$		0			0
$677$	2.16888e8	+	1.25221e8i	0.698989	+	0.403561i	0.806971	−	0.590592i	$-0.201106\pi$
$677$	2.16888e8	+	1.25221e8i	0.698989	+	0.403561i	−0.107982	+	0.994153i	$0.534439\pi$
$678$		0			0
$679$	2.05597e8	+	3.56105e8i	0.656762	+	1.13754i
$680$		0			0
$681$	1.37354e8	+	1.18368e8i	0.434910	+	0.374796i
$682$		0			0
$683$		−	5.02526e8i		−	1.57723i	−0.614884	−	0.788617i	$-0.710797\pi$
$683$		−	5.02526e8i		−	1.57723i	0.614884	−	0.788617i	$-0.289203\pi$
$684$		0			0
$685$	−2.22803e8			−0.693185
$686$		0			0
$687$	4.76477e7	+	1.36473e8i	0.146951	+	0.420897i
$688$		0			0
$689$	−2.23638e8	+	1.29117e8i	−0.683735	+	0.394755i
$690$		0			0
$691$	−1.47776e8	+	2.55956e8i	−0.447889	+	0.775766i	−0.998248	−	0.0591614i	$-0.981157\pi$
$691$	−1.47776e8	+	2.55956e8i	−0.447889	+	0.775766i	0.550359	+	0.834928i	$0.314491\pi$
$692$		0			0
$693$	−1.40976e8	+	2.10487e7i	−0.423588	+	0.0632450i
$694$		0			0
$695$	−2.62416e8	−	1.51506e8i	−0.781693	−	0.451310i
$696$		0			0
$697$	1.50119e7	+	2.60014e7i	0.0443341	+	0.0767889i
$698$		0			0
$699$	2.11215e6	−	1.11208e7i	0.00618435	−	0.0325615i
$700$		0			0
$701$		−	4.14000e8i		−	1.20184i	−0.799309	−	0.600920i	$-0.794801\pi$
$701$		−	4.14000e8i		−	1.20184i	0.799309	−	0.600920i	$-0.205199\pi$
$702$		0			0
$703$	−3.17675e8			−0.914360
$704$		0			0
$705$	4.93470e8	+	9.37240e7i	1.40829	+	0.267475i
$706$		0			0
$707$	8.83563e7	−	5.10125e7i	0.250022	−	0.144351i
$708$		0			0
$709$	−6.48784e7	+	1.12373e8i	−0.182038	+	0.315299i	−0.942574	−	0.333996i	$-0.891603\pi$
$709$	−6.48784e7	+	1.12373e8i	−0.182038	+	0.315299i	0.760537	+	0.649295i	$0.224936\pi$
$710$		0			0
$711$	−5.26412e7	+	4.18607e7i	−0.146459	+	0.116466i
$712$		0			0
$713$	−1.93278e7	−	1.11589e7i	−0.0533228	−	0.0307859i
$714$		0			0
$715$	1.73223e8	+	3.00032e8i	0.473902	+	0.820822i
$716$		0			0
$717$	3.54570e7	−	1.23794e7i	0.0961933	−	0.0335846i
$718$		0			0
$719$		−	4.96356e8i		−	1.33539i	−0.744437	−	0.667693i	$-0.767282\pi$
$719$		−	4.96356e8i		−	1.33539i	0.744437	−	0.667693i	$-0.232718\pi$
$720$		0			0
$721$	2.99839e8			0.799985
$722$		0			0
$723$	−4.09399e8	+	4.75064e8i	−1.08326	+	1.25701i
$724$		0			0
$725$	1.29591e9	−	7.48192e8i	3.40063	−	1.96336i
$726$		0			0
$727$	−7.45235e7	+	1.29079e8i	−0.193950	+	0.335932i	−0.946556	−	0.322540i	$-0.895463\pi$
$727$	−7.45235e7	+	1.29079e8i	−0.193950	+	0.335932i	0.752606	+	0.658471i	$0.228797\pi$
$728$		0			0
$729$	1.66642e8	+	3.49750e8i	0.430132	+	0.902766i
$730$		0			0
$731$	−2.82504e7	−	1.63104e7i	−0.0723224	−	0.0417554i
$732$		0			0
$733$	−6.92416e7	−	1.19930e8i	−0.175815	−	0.304520i	0.764628	−	0.644472i	$-0.222923\pi$
$733$	−6.92416e7	−	1.19930e8i	−0.175815	−	0.304520i	−0.940443	+	0.339952i	$0.889589\pi$
$734$		0			0
$735$	−2.00200e8	−	1.72528e8i	−0.504198	−	0.434507i
$736$		0			0
$737$		−	2.42196e8i		−	0.605012i
$738$		0			0
$739$	3.03625e7			0.0752324			0.0376162	−	0.999292i	$-0.488024\pi$
$739$	3.03625e7			0.0752324			0.0376162	+	0.999292i	$0.488024\pi$
$740$		0			0
$741$	−2.56836e8	−	7.35631e8i	−0.631250	−	1.80803i
$742$		0			0
$743$	−3.19868e8	+	1.84676e8i	−0.779839	+	0.450240i	−0.836373	−	0.548160i	$-0.815328\pi$
$743$	−3.19868e8	+	1.84676e8i	−0.779839	+	0.450240i	0.0565343	+	0.998401i	$0.481995\pi$
$744$		0			0
$745$	4.11712e8	−	7.13107e8i	0.995692	−	1.72459i
$746$		0			0
$747$	1.46869e8	+	1.84693e8i	0.352345	+	0.443086i
$748$		0			0
$749$	5.65557e8	+	3.26524e8i	1.34596	+	0.777088i
$750$		0			0
$751$	−3.48938e8	−	6.04378e8i	−0.823813	−	1.42689i	−0.902823	−	0.430011i	$-0.858510\pi$
$751$	−3.48938e8	−	6.04378e8i	−0.823813	−	1.42689i	0.0790108	−	0.996874i	$-0.474824\pi$
$752$		0			0
$753$	1.24574e7	−	6.55898e7i	0.0291771	−	0.153621i
$754$		0			0
$755$		−	6.68332e7i		−	0.155293i
$756$		0			0
$757$	−1.53374e8			−0.353560			−0.176780	−	0.984250i	$-0.556568\pi$
$757$	−1.53374e8			−0.353560			−0.176780	+	0.984250i	$0.556568\pi$
$758$		0			0
$759$	2.01503e7	+	3.82711e6i	0.0460845	+	0.00875276i
$760$		0			0
$761$	−5.34064e8	+	3.08342e8i	−1.21182	+	0.699646i	−0.963156	−	0.268943i	$-0.913326\pi$
$761$	−5.34064e8	+	3.08342e8i	−1.21182	+	0.699646i	−0.248667	+	0.968589i	$0.579992\pi$
$762$		0			0
$763$	2.07563e8	−	3.59510e8i	0.467279	−	0.809351i
$764$		0			0
$765$	−2.44809e7	−	1.63962e8i	−0.0546817	−	0.366235i
$766$		0			0
$767$	5.21989e8	+	3.01370e8i	1.15684	+	0.667905i
$768$		0			0
$769$	1.37844e8	+	2.38753e8i	0.303116	+	0.525012i	0.976840	−	0.213971i	$-0.0686397\pi$
$769$	1.37844e8	+	2.38753e8i	0.303116	+	0.525012i	−0.673724	+	0.738983i	$0.735306\pi$
$770$		0			0
$771$	5.78437e7	−	2.01954e7i	0.126210	−	0.0440645i
$772$		0			0
$773$			2.23151e8i			0.483125i	0.970385	+	0.241563i	$0.0776600\pi$
$773$			2.23151e8i			0.483125i	−0.970385	+	0.241563i	$0.922340\pi$
$774$		0			0
$775$	6.41031e8			1.37713
$776$		0			0
$777$	2.21369e8	−	2.56875e8i	0.471905	−	0.547595i
$778$		0			0
$779$	−2.81098e8	+	1.62292e8i	−0.594629	+	0.343309i
$780$		0			0
$781$	−1.71284e8	+	2.96673e8i	−0.359555	+	0.622767i
$782$		0			0
$783$	−3.09406e8	−	5.88384e8i	−0.644530	−	1.22568i
$784$		0			0
$785$	−1.25775e9	−	7.26160e8i	−2.60007	−	1.50115i
$786$		0			0
$787$	−1.14119e8	−	1.97660e8i	−0.234117	−	0.405503i	0.724898	−	0.688856i	$-0.241887\pi$
$787$	−1.14119e8	−	1.97660e8i	−0.234117	−	0.405503i	−0.959016	+	0.283353i	$0.908553\pi$
$788$		0			0
$789$	5.75281e8	+	4.95764e8i	1.17125	+	1.00936i
$790$		0			0
$791$			6.26768e8i			1.26642i
$792$		0			0
$793$	−6.29734e8			−1.26281
$794$		0			0
$795$	−1.95790e8	−	5.60784e8i	−0.389664	−	1.11608i
$796$		0			0
$797$	6.08500e8	−	3.51318e8i	1.20195	−	0.693945i	0.240960	−	0.970535i	$-0.422538\pi$
$797$	6.08500e8	−	3.51318e8i	1.20195	−	0.693945i	0.960988	+	0.276590i	$0.0892045\pi$
$798$		0			0
$799$	−3.52954e7	+	6.11334e7i	−0.0691954	+	0.119850i
$800$		0			0
$801$	1.98288e8	−	5.03177e8i	0.385833	−	0.979092i
$802$		0			0
$803$	−2.87758e8	−	1.66137e8i	−0.555752	−	0.320864i
$804$		0			0
$805$	7.49632e7	+	1.29840e8i	0.143701	+	0.248898i
$806$		0			0
$807$	−3.40996e6	+	1.79539e7i	−0.00648827	+	0.0341617i
$808$		0			0
$809$			9.86181e8i			1.86256i	0.364300	+	0.931282i	$0.381308\pi$
$809$			9.86181e8i			1.86256i	−0.364300	+	0.931282i	$0.618692\pi$
$810$		0			0
$811$	2.83806e8			0.532059			0.266029	−	0.963965i	$-0.414288\pi$
$811$	2.83806e8			0.532059			0.266029	+	0.963965i	$0.414288\pi$
$812$		0			0
$813$	8.30093e8	+	1.57658e8i	1.54474	+	0.293390i
$814$		0			0
$815$	2.36719e8	−	1.36670e8i	0.437280	−	0.252464i
$816$		0			0
$817$	1.76330e8	−	3.05412e8i	0.323340	−	0.560042i
$818$		0			0
$819$	7.73813e8	+	3.04938e8i	1.40859	+	0.555086i
$820$		0			0
$821$	−2.91498e8	−	1.68297e8i	−0.526752	−	0.304121i	0.212941	−	0.977065i	$-0.431696\pi$
$821$	−2.91498e8	−	1.68297e8i	−0.526752	−	0.304121i	−0.739693	+	0.672945i	$0.765029\pi$
$822$		0			0
$823$	−3.88238e8	−	6.72449e8i	−0.696465	−	1.20631i	−0.969684	−	0.244360i	$-0.921422\pi$
$823$	−3.88238e8	−	6.72449e8i	−0.696465	−	1.20631i	0.273220	−	0.961952i	$-0.411911\pi$
$824$		0			0
$825$	−5.56195e8	+	1.94188e8i	−0.990524	+	0.345829i
$826$		0			0
$827$			5.97073e8i			1.05563i	0.849360	+	0.527814i	$0.176988\pi$
$827$			5.97073e8i			1.05563i	−0.849360	+	0.527814i	$0.823012\pi$
$828$		0			0
$829$	−6.82475e8			−1.19791			−0.598953	−	0.800784i	$-0.704416\pi$
$829$	−6.82475e8			−1.19791			−0.598953	+	0.800784i	$0.704416\pi$
$830$		0			0
$831$	−3.77220e7	+	4.37724e7i	−0.0657343	+	0.0762776i
$832$		0			0
$833$	3.21656e7	−	1.85708e7i	0.0556490	−	0.0321290i
$834$		0			0
$835$	1.79364e8	−	3.10667e8i	0.308088	−	0.533624i
$836$		0			0
$837$	1.12403e7	−	2.84559e8i	0.0191690	−	0.485284i
$838$		0			0
$839$	8.26569e8	+	4.77220e8i	1.39957	+	0.808039i	0.994347	−	0.106180i	$-0.0338621\pi$
$839$	8.26569e8	+	4.77220e8i	1.39957	+	0.808039i	0.405219	+	0.914220i	$0.367195\pi$
$840$		0			0
$841$	2.72935e8	+	4.72737e8i	0.458850	+	0.794752i
$842$		0			0
$843$	−2.71093e8	−	2.33622e8i	−0.452517	−	0.389969i
$844$		0			0
$845$		−	8.39924e8i		−	1.39210i
$846$		0			0
$847$	6.07072e8			0.999056
$848$		0			0
$849$	−8.33316e7	−	2.38679e8i	−0.136172	−	0.390023i
$850$		0			0
$851$	−4.22575e7	+	2.43974e7i	−0.0685669	+	0.0395871i
$852$		0			0
$853$	−4.60467e8	+	7.97551e8i	−0.741910	+	1.28503i	0.209715	+	0.977763i	$0.432746\pi$
$853$	−4.60467e8	+	7.97551e8i	−0.741910	+	1.28503i	−0.951625	+	0.307263i	$0.900587\pi$
$854$		0			0
$855$	1.77258e9	−	2.64660e8i	2.83601	−	0.423438i
$856$		0			0
$857$	−1.72620e7	−	9.96623e6i	−0.0274252	−	0.0158339i	0.486225	−	0.873834i	$-0.338374\pi$
$857$	−1.72620e7	−	9.96623e6i	−0.0274252	−	0.0158339i	−0.513650	+	0.858000i	$0.671707\pi$
$858$		0			0
$859$	2.32987e7	+	4.03545e7i	0.0367580	+	0.0636667i	0.883819	−	0.467829i	$-0.154964\pi$
$859$	2.32987e7	+	4.03545e7i	0.0367580	+	0.0636667i	−0.847061	+	0.531495i	$0.821630\pi$
$860$		0			0
$861$	6.46499e7	−	3.40391e8i	0.101288	−	0.533296i
$862$		0			0
$863$		−	4.40004e8i		−	0.684580i	−0.939594	−	0.342290i	$-0.888797\pi$
$863$		−	4.40004e8i		−	0.684580i	0.939594	−	0.342290i	$-0.111203\pi$
$864$		0			0
$865$	1.08846e9			1.68177
$866$		0			0
$867$	−6.17379e8	−	1.17258e8i	−0.947316	−	0.179922i
$868$		0			0
$869$	−3.93475e7	+	2.27173e7i	−0.0599595	+	0.0346176i
$870$		0			0
$871$	−7.06622e8	+	1.22390e9i	−1.06938	+	1.85222i
$872$		0			0
$873$	5.90942e8	−	4.69921e8i	0.888182	−	0.706288i
$874$		0			0
$875$	−2.41416e9	−	1.39382e9i	−3.60365	−	2.08057i
$876$		0			0
$877$	4.57956e8	+	7.93202e8i	0.678929	+	1.17594i	0.975304	+	0.220868i	$0.0708891\pi$
$877$	4.57956e8	+	7.93202e8i	0.678929	+	1.17594i	−0.296374	+	0.955072i	$0.595778\pi$
$878$		0			0
$879$	−7.52565e8	+	2.62748e8i	−1.10810	+	0.386877i
$880$		0			0
$881$		−	6.43981e8i		−	0.941772i	−0.882194	−	0.470886i	$-0.843934\pi$
$881$		−	6.43981e8i		−	0.941772i	0.882194	−	0.470886i	$-0.156066\pi$
$882$		0			0
$883$	−1.22590e9			−1.78063			−0.890317	−	0.455341i	$-0.849517\pi$
$883$	−1.22590e9			−1.78063			−0.890317	+	0.455341i	$0.849517\pi$
$884$		0			0
$885$	−9.05057e8	+	1.05022e9i	−1.30571	+	1.51513i
$886$		0			0
$887$	−7.70366e8	+	4.44771e8i	−1.10389	+	0.637332i	−0.937240	−	0.348684i	$-0.886629\pi$
$887$	−7.70366e8	+	4.44771e8i	−1.10389	+	0.637332i	−0.166651	+	0.986016i	$0.553295\pi$
$888$		0			0
$889$	−1.98072e8	+	3.43070e8i	−0.281914	+	0.488290i
$890$		0			0
$891$	7.64492e7	+	2.50305e8i	0.108079	+	0.353864i
$892$		0			0
$893$	−6.60906e8	−	3.81574e8i	−0.928080	−	0.535827i
$894$		0			0
$895$	1.11271e9	+	1.92727e9i	1.55207	+	2.68827i
$896$		0			0
$897$	−9.06609e7	−	7.81295e7i	−0.125615	−	0.108252i
$898$		0			0
$899$			4.88657e8i			0.672551i
$900$		0			0
$901$	8.34764e7			0.114127
$902$		0			0
$903$	1.24085e8	+	3.55406e8i	0.168522	+	0.482683i
$904$		0			0
$905$	−1.02705e9	+	5.92965e8i	−1.38562	+	0.799988i
$906$		0			0
$907$	6.62269e7	−	1.14708e8i	0.0887590	−	0.153735i	−0.818228	−	0.574894i	$-0.805043\pi$
$907$	6.62269e7	−	1.14708e8i	0.0887590	−	0.153735i	0.906987	+	0.421159i	$0.138377\pi$
$908$		0			0
$909$	−1.16596e8	−	1.46624e8i	−0.155236	−	0.195215i
$910$		0			0
$911$	4.08901e8	+	2.36079e8i	0.540832	+	0.312250i	0.745416	−	0.666599i	$-0.232251\pi$
$911$	4.08901e8	+	2.36079e8i	0.540832	+	0.312250i	−0.204584	+	0.978849i	$0.565584\pi$
$912$		0			0
$913$	7.97040e7	+	1.38051e8i	0.104729	+	0.181396i
$914$		0			0
$915$	2.70277e8	−	1.42305e9i	0.352814	−	1.85761i
$916$		0			0
$917$			3.88082e8i			0.503286i
$918$		0			0
$919$	7.13214e8			0.918911			0.459456	−	0.888201i	$-0.348045\pi$
$919$	7.13214e8			0.918911			0.459456	+	0.888201i	$0.348045\pi$
$920$		0			0
$921$	−2.97867e6	−	565735.i	−0.00381280	−	0.000724159i
$922$		0			0
$923$	1.73113e9	−	9.99467e8i	2.20153	−	1.27105i
$924$		0			0
$925$	7.00762e8	−	1.21376e9i	0.885412	−	1.53358i
$926$		0			0
$927$	−8.12994e7	−	5.44509e8i	−0.102058	−	0.683543i
$928$		0			0
$929$	2.94877e8	+	1.70247e8i	0.367784	+	0.212340i	0.672490	−	0.740106i	$-0.265225\pi$
$929$	2.94877e8	+	1.70247e8i	0.367784	+	0.212340i	−0.304706	+	0.952447i	$0.598558\pi$
$930$		0			0
$931$	2.00767e8	+	3.47739e8i	0.248796	+	0.430928i
$932$		0			0
$933$	−7.84941e8	+	2.74052e8i	−0.966479	+	0.337434i
$934$		0			0
$935$		−	1.11991e8i		−	0.137009i
$936$		0			0
$937$	1.23380e8			0.149978			0.0749890	−	0.997184i	$-0.476108\pi$
$937$	1.23380e8			0.149978			0.0749890	+	0.997184i	$0.476108\pi$
$938$		0			0
$939$	−1.91638e8	+	2.22375e8i	−0.231464	+	0.268589i
$940$		0			0
$941$	−5.34908e8	+	3.08829e8i	−0.641964	+	0.370638i	−0.785371	−	0.619026i	$-0.787528\pi$
$941$	−5.34908e8	+	3.08829e8i	−0.641964	+	0.370638i	0.143407	+	0.989664i	$0.454194\pi$
$942$		0			0
$943$	−2.49280e7	+	4.31765e7i	−0.0297271	+	0.0514888i
$944$		0			0
$945$	−1.02120e9	+	1.61775e9i	−1.21008	+	1.91697i
$946$		0			0
$947$	−1.09339e8	−	6.31271e7i	−0.128744	−	0.0743303i	0.434245	−	0.900795i	$-0.357015\pi$
$947$	−1.09339e8	−	6.31271e7i	−0.128744	−	0.0743303i	−0.562989	+	0.826465i	$0.690349\pi$
$948$		0			0
$949$	9.69433e8	+	1.67911e9i	1.13428	+	1.96463i
$950$		0			0
$951$	7.72904e8	+	6.66071e8i	0.898636	+	0.774424i
$952$		0			0
$953$		−	7.72478e8i		−	0.892499i	−0.894909	−	0.446249i	$-0.852759\pi$
$953$		−	7.72478e8i		−	0.892499i	0.894909	−	0.446249i	$-0.147241\pi$
$954$		0			0
$955$	−2.05305e9			−2.35716
$956$		0			0
$957$	−1.48030e8	−	4.23987e8i	−0.168893	−	0.483745i
$958$		0			0
$959$	−3.12932e8	+	1.80671e8i	−0.354809	+	0.204849i
$960$		0			0
$961$	3.39085e8	−	5.87312e8i	0.382066	−	0.661757i
$962$		0			0
$963$	4.39622e8	−	1.11559e9i	0.492267	−	1.24918i
$964$		0			0
$965$	1.01218e9	+	5.84384e8i	1.12636	+	0.650304i
$966$		0			0
$967$	−3.11472e8	−	5.39486e8i	−0.344461	−	0.596624i	0.640795	−	0.767712i	$-0.278605\pi$
$967$	−3.11472e8	−	5.39486e8i	−0.344461	−	0.596624i	−0.985256	+	0.171088i	$0.945272\pi$
$968$		0			0
$969$	−4.69981e7	+	2.47451e8i	−0.0516545	+	0.271968i
$970$		0			0
$971$			1.15549e9i			1.26214i	0.775727	+	0.631069i	$0.217384\pi$
$971$			1.15549e9i			1.26214i	−0.775727	+	0.631069i	$0.782616\pi$
$972$		0			0
$973$	−4.91426e8			−0.533482
$974$		0			0
$975$	3.37722e9	+	6.41430e8i	3.64372	+	0.692046i
$976$		0			0
$977$	−1.03371e9	+	5.96814e8i	−1.10845	+	0.639963i	−0.938427	−	0.345477i	$-0.887717\pi$
$977$	−1.03371e9	+	5.96814e8i	−1.10845	+	0.639963i	−0.170022	+	0.985440i	$0.554384\pi$
$978$		0			0
$979$	1.82680e8	−	3.16411e8i	0.194689	−	0.337212i
$980$		0			0
$981$	−7.09150e8	−	2.79457e8i	−0.751158	−	0.296011i
$982$		0			0
$983$	−5.52448e8	−	3.18956e8i	−0.581609	−	0.335792i	0.180164	−	0.983637i	$-0.442337\pi$
$983$	−5.52448e8	−	3.18956e8i	−0.581609	−	0.335792i	−0.761772	+	0.647845i	$0.775671\pi$
$984$		0			0
$985$	−1.01677e8	−	1.76110e8i	−0.106393	−	0.184279i
$986$		0			0
$987$	7.69092e8	−	2.68518e8i	0.799883	−	0.279269i
$988$		0			0
$989$		−	5.41683e7i		−	0.0559960i
$990$		0			0
$991$	−6.25970e8			−0.643180			−0.321590	−	0.946879i	$-0.604217\pi$
$991$	−6.25970e8			−0.643180			−0.321590	+	0.946879i	$0.604217\pi$
$992$		0			0
$993$	−2.87077e8	+	3.33122e8i	−0.293191	+	0.340216i
$994$		0			0
$995$	−1.58049e9	+	9.12496e8i	−1.60444	+	0.926321i
$996$		0			0
$997$	−9.12186e8	+	1.57995e9i	−0.920445	+	1.59426i	−0.121717	+	0.992565i	$0.538840\pi$
$997$	−9.12186e8	+	1.57995e9i	−0.920445	+	1.59426i	−0.798728	+	0.601693i	$0.794493\pi$
$998$		0			0
$999$	−5.26509e8	−	3.32357e8i	−0.528092	−	0.333356i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.m.a.65.2	yes	36
3.2	odd	2		216.7.m.a.89.18		36
4.3	odd	2		144.7.q.d.65.17		36
9.2	odd	6		648.7.e.c.161.36		36
9.4	even	3		216.7.m.a.17.18		36
9.5	odd	6	inner	72.7.m.a.41.2	✓	36
9.7	even	3		648.7.e.c.161.1		36
12.11	even	2		432.7.q.d.305.18		36
36.23	even	6		144.7.q.d.113.17		36
36.31	odd	6		432.7.q.d.17.18		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.7.m.a.41.2	✓	36	9.5	odd	6	inner
72.7.m.a.65.2	yes	36	1.1	even	1	trivial
144.7.q.d.65.17		36	4.3	odd	2
144.7.q.d.113.17		36	36.23	even	6
216.7.m.a.17.18		36	9.4	even	3
216.7.m.a.89.18		36	3.2	odd	2
432.7.q.d.17.18		36	36.31	odd	6
432.7.q.d.305.18		36	12.11	even	2
648.7.e.c.161.1		36	9.7	even	3
648.7.e.c.161.36		36	9.2	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)

\(f(q)\)	\(=\)	\(q+(-26.5258 - 5.03801i) q^{3} +(-212.009 + 122.404i) q^{5} +(-198.515 + 343.838i) q^{7} +(678.237 + 267.274i) q^{9} +O(q^{10})\)	\(q+(-26.5258 - 5.03801i) q^{3} +(-212.009 + 122.404i) q^{5} +(-198.515 + 343.838i) q^{7} +(678.237 + 267.274i) q^{9} +(426.493 + 246.236i) q^{11} +(-1436.82 - 2488.64i) q^{13} +(6240.39 - 2178.75i) q^{15} +928.923i q^{17} -10042.5 q^{19} +(6998.02 - 8120.46i) q^{21} +(-1335.86 + 771.260i) q^{23} +(22152.8 - 38369.8i) q^{25} +(-16644.3 - 10506.6i) q^{27} +(29249.3 + 16887.1i) q^{29} +(7234.19 + 12530.0i) q^{31} +(-10072.5 - 8680.27i) q^{33} -97195.8i q^{35} +31633.1 q^{37} +(25574.9 + 73251.9i) q^{39} +(27990.9 - 16160.6i) q^{41} +(-17558.4 + 30412.0i) q^{43} +(-176508. + 26354.0i) q^{45} +(65811.0 + 37996.0i) q^{47} +(-19991.8 - 34626.8i) q^{49} +(4679.92 - 24640.4i) q^{51} -89863.6i q^{53} -120561. q^{55} +(266385. + 50594.1i) q^{57} +(-181648. + 104874. i) q^{59} +(109571. - 189783. i) q^{61} +(-226539. + 180146. i) q^{63} +(609237. + 351743. i) q^{65} +(-245898. - 425909. i) q^{67} +(39320.4 - 13728.2i) q^{69} +695612. i q^{71} -674709. q^{73} +(-780928. + 906184. i) q^{75} +(-169330. + 97762.8i) q^{77} +(-46129.2 + 79898.1i) q^{79} +(388570. + 362551. i) q^{81} +(280324. + 161845. i) q^{83} +(-113704. - 196940. i) q^{85} +(-690783. - 595301. i) q^{87} -741890. i q^{89} +1.14092e6 q^{91} +(-128767. - 368814. i) q^{93} +(2.12910e6 - 1.22924e6i) q^{95} +(517838. - 896922. i) q^{97} +(223451. + 280997. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 10 q^{3} + 74 q^{9}+O(q^{10}) \) 36 * q + 10 * q^3 + 74 * q^9	\( 36 q + 10 q^{3} + 74 q^{9} + 1350 q^{11} + 7912 q^{15} + 9540 q^{19} + 3828 q^{21} + 30888 q^{23} + 56250 q^{25} + 11392 q^{27} + 38556 q^{29} + 27720 q^{31} + 33514 q^{33} + 134068 q^{39} + 179226 q^{41} + 15930 q^{43} - 185620 q^{45} + 187596 q^{47} - 198774 q^{49} - 158098 q^{51} - 197064 q^{55} - 244990 q^{57} - 408618 q^{59} + 17136 q^{61} - 417048 q^{63} - 125712 q^{65} + 27090 q^{67} - 848504 q^{69} - 534060 q^{73} - 1405714 q^{75} + 48168 q^{77} + 172620 q^{79} + 349010 q^{81} + 1801980 q^{83} - 791568 q^{85} + 28500 q^{87} + 538560 q^{91} - 1116448 q^{93} + 1832652 q^{95} + 770706 q^{97} - 614260 q^{99}+O(q^{100}) \) 36 * q + 10 * q^3 + 74 * q^9 + 1350 * q^11 + 7912 * q^15 + 9540 * q^19 + 3828 * q^21 + 30888 * q^23 + 56250 * q^25 + 11392 * q^27 + 38556 * q^29 + 27720 * q^31 + 33514 * q^33 + 134068 * q^39 + 179226 * q^41 + 15930 * q^43 - 185620 * q^45 + 187596 * q^47 - 198774 * q^49 - 158098 * q^51 - 197064 * q^55 - 244990 * q^57 - 408618 * q^59 + 17136 * q^61 - 417048 * q^63 - 125712 * q^65 + 27090 * q^67 - 848504 * q^69 - 534060 * q^73 - 1405714 * q^75 + 48168 * q^77 + 172620 * q^79 + 349010 * q^81 + 1801980 * q^83 - 791568 * q^85 + 28500 * q^87 + 538560 * q^91 - 1116448 * q^93 + 1832652 * q^95 + 770706 * q^97 - 614260 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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