LMFDB - Embedded newform 81.8.e.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,8,Mod(10,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("81.10");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	81.e (of order $9$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$25.3031870642$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	81.37
Dual form			81.8.e.a.46.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(14.1817 - 11.8998i) q^{2} +(37.2867 - 211.463i) q^{4} +(47.2604 - 17.2014i) q^{5} +(-206.697 - 1172.23i) q^{7} +(-802.766 - 1390.43i) q^{8} +O(q^{10})$	\(q+(14.1817 - 11.8998i) q^{2} +(37.2867 - 211.463i) q^{4} +(47.2604 - 17.2014i) q^{5} +(-206.697 - 1172.23i) q^{7} +(-802.766 - 1390.43i) q^{8} +(465.538 - 806.335i) q^{10} +(-3140.49 - 1143.04i) q^{11} +(1674.59 + 1405.15i) q^{13} +(-16880.7 - 14164.6i) q^{14} +(-2103.14 - 765.481i) q^{16} +(-1028.25 + 1780.98i) q^{17} +(-20475.8 - 35465.2i) q^{19} +(-1875.28 - 10635.2i) q^{20} +(-58139.3 + 21161.0i) q^{22} +(7712.48 - 43739.6i) q^{23} +(-57909.6 + 48591.9i) q^{25} +40469.5 q^{26} -255591. q^{28} +(-187740. + 157532. i) q^{29} +(45015.1 - 255293. i) q^{31} +(154179. - 56116.7i) q^{32} +(6611.07 + 37493.3i) q^{34} +(-29932.6 - 51844.8i) q^{35} +(112089. - 194144. i) q^{37} +(-712411. - 259296. i) q^{38} +(-61856.4 - 51903.7i) q^{40} +(199081. + 167049. i) q^{41} +(884528. + 321942. i) q^{43} +(-358810. + 621477. i) q^{44} +(-411118. - 712078. i) q^{46} +(147817. + 838311. i) q^{47} +(-557533. + 202925. i) q^{49} +(-243019. + 1.37823e6i) q^{50} +(359577. - 301721. i) q^{52} +498422. q^{53} -168083. q^{55} +(-1.46398e6 + 1.22843e6i) q^{56} +(-787854. + 4.46814e6i) q^{58} +(1.82549e6 - 664426. i) q^{59} +(-447017. - 2.53516e6i) q^{61} +(-2.39956e6 - 4.15615e6i) q^{62} +(1.66198e6 - 2.87863e6i) q^{64} +(103312. + 37602.6i) q^{65} +(-791577. - 664212. i) q^{67} +(338272. + 283844. i) q^{68} +(-1.04144e6 - 379053. i) q^{70} +(2.07039e6 - 3.58601e6i) q^{71} +(-689373. - 1.19403e6i) q^{73} +(-720671. - 4.08713e6i) q^{74} +(-8.26306e6 + 3.00751e6i) q^{76} +(-690787. + 3.91765e6i) q^{77} +(1.73621e6 - 1.45686e6i) q^{79} -112563. q^{80} +4.81115e6 q^{82} +(-439916. + 369134. i) q^{83} +(-17960.2 + 101857. i) q^{85} +(1.63751e7 - 5.96006e6i) q^{86} +(931752. + 5.28423e6i) q^{88} +(3.14525e6 + 5.44773e6i) q^{89} +(1.30103e6 - 2.25345e6i) q^{91} +(-8.96175e6 - 3.26181e6i) q^{92} +(1.20720e7 + 1.01297e7i) q^{94} +(-1.57775e6 - 1.32389e6i) q^{95} +(4.46485e6 + 1.62507e6i) q^{97} +(-5.49196e6 + 9.51236e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8}+O(q^{10}) $ 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8	\( 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8} - 3 q^{10} - 9399 q^{11} - 6 q^{13} - 16647 q^{14} + 378 q^{16} + 58959 q^{17} - 3 q^{19} - 240243 q^{20} + 105762 q^{22} + 144084 q^{23} - 107997 q^{25} - 443202 q^{26} - 12 q^{28} - 107886 q^{29} + 297975 q^{31} + 639576 q^{32} - 265806 q^{34} + 450672 q^{35} - 3 q^{37} + 145596 q^{38} + 283521 q^{40} - 227085 q^{41} - 1080969 q^{43} + 1205115 q^{44} - 3 q^{46} + 5184339 q^{47} + 976008 q^{49} - 2324559 q^{50} - 3366135 q^{52} - 5631750 q^{53} - 12 q^{55} - 5254923 q^{56} + 3884295 q^{58} + 12534492 q^{59} + 3865440 q^{61} + 9923646 q^{62} - 10223619 q^{64} - 17158395 q^{65} + 5567061 q^{67} - 19858455 q^{68} - 1020993 q^{70} + 18563877 q^{71} + 3770934 q^{73} + 36278085 q^{74} - 1156998 q^{76} - 8471751 q^{77} + 16415526 q^{79} - 101080590 q^{80} - 12 q^{82} - 3147699 q^{83} - 7672131 q^{85} + 70854834 q^{86} - 34323078 q^{88} + 54647613 q^{89} + 3315066 q^{91} - 73858515 q^{92} + 22126539 q^{94} - 32541447 q^{95} + 41250117 q^{97} + 88493274 q^{98}+O(q^{100}) \) 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8 - 3 * q^10 - 9399 * q^11 - 6 * q^13 - 16647 * q^14 + 378 * q^16 + 58959 * q^17 - 3 * q^19 - 240243 * q^20 + 105762 * q^22 + 144084 * q^23 - 107997 * q^25 - 443202 * q^26 - 12 * q^28 - 107886 * q^29 + 297975 * q^31 + 639576 * q^32 - 265806 * q^34 + 450672 * q^35 - 3 * q^37 + 145596 * q^38 + 283521 * q^40 - 227085 * q^41 - 1080969 * q^43 + 1205115 * q^44 - 3 * q^46 + 5184339 * q^47 + 976008 * q^49 - 2324559 * q^50 - 3366135 * q^52 - 5631750 * q^53 - 12 * q^55 - 5254923 * q^56 + 3884295 * q^58 + 12534492 * q^59 + 3865440 * q^61 + 9923646 * q^62 - 10223619 * q^64 - 17158395 * q^65 + 5567061 * q^67 - 19858455 * q^68 - 1020993 * q^70 + 18563877 * q^71 + 3770934 * q^73 + 36278085 * q^74 - 1156998 * q^76 - 8471751 * q^77 + 16415526 * q^79 - 101080590 * q^80 - 12 * q^82 - 3147699 * q^83 - 7672131 * q^85 + 70854834 * q^86 - 34323078 * q^88 + 54647613 * q^89 + 3315066 * q^91 - 73858515 * q^92 + 22126539 * q^94 - 32541447 * q^95 + 41250117 * q^97 + 88493274 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	14.1817	−	11.8998i	1.25349	−	1.05181i	0.257150	−	0.966372i	$-0.417217\pi$
$2$	14.1817	−	11.8998i	1.25349	−	1.05181i	0.996344	−	0.0854343i	$-0.0272278\pi$
$3$		0			0
$3$		0			0
$4$	37.2867	−	211.463i	0.291302	−	1.65206i
$5$	47.2604	−	17.2014i	0.169084	−	0.0615415i	−0.256091	−	0.966653i	$-0.582435\pi$
$5$	47.2604	−	17.2014i	0.169084	−	0.0615415i	0.425175	+	0.905111i	$0.360213\pi$
$6$		0			0
$7$	−206.697	−	1172.23i	−0.227767	−	1.29173i	−0.857325	−	0.514776i	$-0.827875\pi$
$7$	−206.697	−	1172.23i	−0.227767	−	1.29173i	0.629558	−	0.776953i	$-0.283236\pi$
$8$	−802.766	−	1390.43i	−0.554337	−	0.960140i
$9$		0			0
$10$	465.538	−	806.335i	0.147216	−	0.254985i
$11$	−3140.49	−	1143.04i	−0.711414	−	0.258934i	−0.0391378	−	0.999234i	$-0.512461\pi$
$11$	−3140.49	−	1143.04i	−0.711414	−	0.258934i	−0.672276	+	0.740300i	$0.734683\pi$
$12$		0			0
$13$	1674.59	+	1405.15i	0.211401	+	0.177387i	0.742340	−	0.670024i	$-0.233716\pi$
$13$	1674.59	+	1405.15i	0.211401	+	0.177387i	−0.530939	+	0.847410i	$0.678161\pi$
$14$	−16880.7	−	14164.6i	−1.64415	−	1.37961i
$15$		0			0
$16$	−2103.14	−	765.481i	−0.128366	−	0.0467212i
$17$	−1028.25	+	1780.98i	−0.0507607	+	0.0879201i	−0.890289	−	0.455395i	$-0.849498\pi$
$17$	−1028.25	+	1780.98i	−0.0507607	+	0.0879201i	0.839529	+	0.543315i	$0.182831\pi$
$18$		0			0
$19$	−20475.8	−	35465.2i	−0.684864	−	1.18622i	−0.973480	−	0.228774i	$-0.926528\pi$
$19$	−20475.8	−	35465.2i	−0.684864	−	1.18622i	0.288616	−	0.957445i	$-0.406805\pi$
$20$	−1875.28	−	10635.2i	−0.0524155	−	0.297263i
$21$		0			0
$22$	−58139.3	+	21161.0i	−1.16410	+	0.423698i
$23$	7712.48	−	43739.6i	0.132174	−	0.749597i	−0.844612	−	0.535379i	$-0.820169\pi$
$23$	7712.48	−	43739.6i	0.132174	−	0.749597i	0.976786	−	0.214218i	$-0.0687202\pi$
$24$		0			0
$25$	−57909.6	+	48591.9i	−0.741242	+	0.621976i
$26$	40469.5			0.451566
$27$		0			0
$28$	−255591.			−2.20036
$29$	−187740.	+	157532.i	−1.42943	+	1.19944i	−0.483383	+	0.875409i	$0.660592\pi$
$29$	−187740.	+	157532.i	−1.42943	+	1.19944i	−0.946048	+	0.324026i	$0.894963\pi$
$30$		0			0
$31$	45015.1	−	255293.i	0.271389	−	1.53912i	−0.478815	−	0.877916i	$-0.658933\pi$
$31$	45015.1	−	255293.i	0.271389	−	1.53912i	0.750203	−	0.661207i	$-0.229956\pi$
$32$	154179.	−	56116.7i	0.831766	−	0.302738i
$33$		0			0
$34$	6611.07	+	37493.3i	0.0288467	+	0.163598i
$35$	−29932.6	−	51844.8i	−0.118007	−	0.204394i
$36$		0			0
$37$	112089.	−	194144.i	0.363796	−	0.630113i	−0.624786	−	0.780796i	$-0.714814\pi$
$37$	112089.	−	194144.i	0.363796	−	0.630113i	0.988582	+	0.150683i	$0.0481472\pi$
$38$	−712411.	−	259296.i	−2.10614	−	0.766574i
$39$		0			0
$40$	−61856.4	−	51903.7i	−0.152818	−	0.128230i
$41$	199081.	+	167049.i	0.451114	+	0.378530i	0.839849	−	0.542820i	$-0.182643\pi$
$41$	199081.	+	167049.i	0.451114	+	0.378530i	−0.388735	+	0.921350i	$0.627088\pi$
$42$		0			0
$43$	884528.	+	321942.i	1.69657	+	0.617501i	0.995428	−	0.0955188i	$-0.0304510\pi$
$43$	884528.	+	321942.i	1.69657	+	0.617501i	0.701144	+	0.713020i	$0.252673\pi$
$44$	−358810.	+	621477.i	−0.635009	+	1.09987i
$45$		0			0
$46$	−411118.	−	712078.i	−0.622751	−	1.07864i
$47$	147817.	+	838311.i	0.207674	+	1.17778i	0.893176	+	0.449706i	$0.148471\pi$
$47$	147817.	+	838311.i	0.207674	+	1.17778i	−0.685503	+	0.728070i	$0.740418\pi$
$48$		0			0
$49$	−557533.	+	202925.i	−0.676993	+	0.246405i
$50$	−243019.	+	1.37823e6i	−0.274944	+	1.55929i
$51$		0			0
$52$	359577.	−	301721.i	0.354634	−	0.297573i
$53$	498422.			0.459866			0.229933	−	0.973206i	$-0.426149\pi$
$53$	498422.			0.459866			0.229933	+	0.973206i	$0.426149\pi$
$54$		0			0
$55$	−168083.			−0.136224
$56$	−1.46398e6	+	1.22843e6i	−1.11398	+	0.934741i
$57$		0			0
$58$	−787854.	+	4.46814e6i	−0.530210	+	3.00697i
$59$	1.82549e6	−	664426.i	1.15717	−	0.421177i	0.309087	−	0.951034i	$-0.399977\pi$
$59$	1.82549e6	−	664426.i	1.15717	−	0.421177i	0.848087	+	0.529857i	$0.177755\pi$
$60$		0			0
$61$	−447017.	−	2.53516e6i	−0.252156	−	1.43005i	−0.803268	−	0.595618i	$-0.796907\pi$
$61$	−447017.	−	2.53516e6i	−0.252156	−	1.43005i	0.551111	−	0.834432i	$-0.314204\pi$
$62$	−2.39956e6	−	4.15615e6i	−1.27867	−	2.21473i
$63$		0			0
$64$	1.66198e6	−	2.87863e6i	0.792493	−	1.37264i
$65$	103312.	+	37602.6i	0.0466612	+	0.0169833i
$66$		0			0
$67$	−791577.	−	664212.i	−0.321537	−	0.269802i	0.467704	−	0.883885i	$-0.345081\pi$
$67$	−791577.	−	664212.i	−0.321537	−	0.269802i	−0.789241	+	0.614083i	$0.789526\pi$
$68$	338272.	+	283844.i	0.130462	+	0.109471i
$69$		0			0
$70$	−1.04144e6	−	379053.i	−0.362903	−	0.132086i
$71$	2.07039e6	−	3.58601e6i	0.686510	−	1.18907i	−0.286449	−	0.958095i	$-0.592475\pi$
$71$	2.07039e6	−	3.58601e6i	0.686510	−	1.18907i	0.972960	−	0.230975i	$-0.0741916\pi$
$72$		0			0
$73$	−689373.	−	1.19403e6i	−0.207407	−	0.359240i	0.743490	−	0.668747i	$-0.233169\pi$
$73$	−689373.	−	1.19403e6i	−0.207407	−	0.359240i	−0.950897	+	0.309507i	$0.899836\pi$
$74$	−720671.	−	4.08713e6i	−0.206741	−	1.17249i
$75$		0			0
$76$	−8.26306e6	+	3.00751e6i	−2.15920	+	0.785885i
$77$	−690787.	+	3.91765e6i	−0.172436	+	0.977931i
$78$		0			0
$79$	1.73621e6	−	1.45686e6i	0.396195	−	0.332447i	−0.422826	−	0.906211i	$-0.638962\pi$
$79$	1.73621e6	−	1.45686e6i	0.396195	−	0.332447i	0.819021	+	0.573764i	$0.194517\pi$
$80$	−112563.			−0.0245798
$81$		0			0
$82$	4.81115e6			0.963609
$83$	−439916.	+	369134.i	−0.0844494	+	0.0708615i	−0.684035	−	0.729449i	$-0.739777\pi$
$83$	−439916.	+	369134.i	−0.0844494	+	0.0708615i	0.599586	+	0.800311i	$0.295332\pi$
$84$		0			0
$85$	−17960.2	+	101857.i	−0.00317208	+	0.0179898i
$86$	1.63751e7	−	5.96006e6i	2.77613	−	1.01043i
$87$		0			0
$88$	931752.	+	5.28423e6i	0.145751	+	0.826594i
$89$	3.14525e6	+	5.44773e6i	0.472923	+	0.819126i	0.999520	−	0.0309891i	$-0.00986572\pi$
$89$	3.14525e6	+	5.44773e6i	0.472923	+	0.819126i	−0.526597	+	0.850115i	$0.676532\pi$
$90$		0			0
$91$	1.30103e6	−	2.25345e6i	0.180985	−	0.313476i
$92$	−8.96175e6	−	3.26181e6i	−1.19987	−	0.436718i
$93$		0			0
$94$	1.20720e7	+	1.01297e7i	1.49911	+	1.25790i
$95$	−1.57775e6	−	1.32389e6i	−0.188801	−	0.158423i
$96$		0			0
$97$	4.46485e6	+	1.62507e6i	0.496713	+	0.180789i	0.578215	−	0.815884i	$-0.303749\pi$
$97$	4.46485e6	+	1.62507e6i	0.496713	+	0.180789i	−0.0815021	+	0.996673i	$0.525972\pi$
$98$	−5.49196e6	+	9.51236e6i	−0.589436	+	1.02093i
$99$		0			0
$100$	8.11614e6	+	1.40576e7i	0.811614	+	1.40576i
$101$	676026.	+	3.83393e6i	0.0652888	+	0.370271i	0.999894	+	0.0145833i	$0.00464219\pi$
$101$	676026.	+	3.83393e6i	0.0652888	+	0.370271i	−0.934605	+	0.355688i	$0.884247\pi$
$102$		0			0
$103$	1.03720e7	−	3.77511e6i	0.935263	−	0.340408i	0.170969	−	0.985276i	$-0.445310\pi$
$103$	1.03720e7	−	3.77511e6i	0.935263	−	0.340408i	0.764294	+	0.644869i	$0.223088\pi$
$104$	609458.	−	3.45641e6i	0.0531285	−	0.301307i
$105$		0			0
$106$	7.06845e6	−	5.93113e6i	0.576439	−	0.483690i
$107$	3.83305e6			0.302483			0.151241	−	0.988497i	$-0.451673\pi$
$107$	3.83305e6			0.302483			0.151241	+	0.988497i	$0.451673\pi$
$108$		0			0
$109$	−1.02204e7			−0.755915			−0.377958	−	0.925823i	$-0.623374\pi$
$109$	−1.02204e7			−0.755915			−0.377958	+	0.925823i	$0.623374\pi$
$110$	−2.38369e6	+	2.00015e6i	−0.170756	+	0.143281i
$111$		0			0
$112$	−462611.	+	2.62360e6i	−0.0311138	+	0.176455i
$113$	2.02044e7	−	7.35382e6i	1.31726	−	0.479444i	0.414683	−	0.909966i	$-0.363893\pi$
$113$	2.02044e7	−	7.35382e6i	1.31726	−	0.479444i	0.902580	+	0.430522i	$0.141670\pi$
$114$		0			0
$115$	−387887.	−	2.19982e6i	−0.0237828	−	0.134879i
$116$	2.63121e7	+	4.55739e7i	1.56514	+	2.71090i
$117$		0			0
$118$	1.79820e7	−	3.11457e7i	1.00751	−	1.74506i
$119$	2.30026e6	+	837227.i	0.125130	+	0.0455438i
$120$		0			0
$121$	−6.37193e6	−	5.34669e6i	−0.326981	−	0.274370i
$122$	−3.65074e7	−	3.06334e7i	−1.82021	−	1.52734i
$123$		0			0
$124$	−5.23066e7	−	1.90381e7i	−2.46366	−	0.896699i
$125$	−3.86557e6	+	6.69536e6i	−0.177023	+	0.306612i
$126$		0			0
$127$	1.92667e7	+	3.33708e7i	0.834629	+	1.44562i	0.894332	+	0.447403i	$0.147651\pi$
$127$	1.92667e7	+	3.33708e7i	0.834629	+	1.44562i	−0.0597037	+	0.998216i	$0.519016\pi$
$128$	−7.03873e6	−	3.99186e7i	−0.296660	−	1.68244i
$129$		0			0
$130$	1.91261e6	−	696131.i	0.0763526	−	0.0277901i
$131$	−12664.1	+	71821.7i	−0.000492181	+	0.00279130i	−0.985053	−	0.172252i	$-0.944896\pi$
$131$	−12664.1	+	71821.7i	−0.000492181	+	0.00279130i	0.984561	+	0.175044i	$0.0560067\pi$
$132$		0			0
$133$	−3.73412e7	+	3.13330e7i	−1.37628	+	1.15484i
$134$	−1.91299e7			−0.686824
$135$		0			0
$136$	3.30178e6			0.112554
$137$	−2.92600e6	+	2.45520e6i	−0.0972192	+	0.0815766i	−0.690102	−	0.723712i	$-0.742434\pi$
$137$	−2.92600e6	+	2.45520e6i	−0.0972192	+	0.0815766i	0.592883	+	0.805289i	$0.297990\pi$
$138$		0			0
$139$	−2.81452e6	+	1.59619e7i	−0.0888900	+	0.504120i	0.907559	+	0.419924i	$0.137943\pi$
$139$	−2.81452e6	+	1.59619e7i	−0.0888900	+	0.504120i	−0.996449	+	0.0841959i	$0.973168\pi$
$140$	−1.20794e7	+	4.39652e6i	−0.372045	+	0.135413i
$141$		0			0
$142$	−1.33114e7	−	7.54928e7i	−0.390135	−	2.21257i
$143$	−3.65289e6	−	6.32698e6i	−0.104462	−	0.180934i
$144$		0			0
$145$	−6.16288e6	+	1.06744e7i	−0.167879	+	0.290775i
$146$	−2.39852e7	−	8.72989e6i	−0.637835	−	0.232153i
$147$		0			0
$148$	−3.68749e7	−	3.09417e7i	−0.935007	−	0.784564i
$149$	2.80040e7	+	2.34982e7i	0.693536	+	0.581946i	0.919926	−	0.392091i	$-0.128248\pi$
$149$	2.80040e7	+	2.34982e7i	0.693536	+	0.581946i	−0.226391	+	0.974037i	$0.572693\pi$
$150$		0			0
$151$	−6.02173e7	−	2.19173e7i	−1.42332	−	0.518045i	−0.488309	−	0.872671i	$-0.662386\pi$
$151$	−6.02173e7	−	2.19173e7i	−1.42332	−	0.518045i	−0.935008	+	0.354625i	$0.884608\pi$
$152$	−3.28746e7	+	5.69405e7i	−0.759291	+	1.31513i
$153$		0			0
$154$	3.68228e7	+	6.37790e7i	0.812446	+	1.40720i
$155$	−2.26396e6	−	1.28396e7i	−0.0488325	−	0.276943i
$156$		0			0
$157$	−1.54374e7	+	5.61877e6i	−0.318366	+	0.115876i	−0.496260	−	0.868174i	$-0.665294\pi$
$157$	−1.54374e7	+	5.61877e6i	−0.318366	+	0.115876i	0.177894	+	0.984050i	$0.443072\pi$
$158$	7.28606e6	−	4.13213e7i	0.146958	−	0.833440i
$159$		0			0
$160$	6.32129e6	−	5.30419e6i	0.122007	−	0.102376i
$161$	−5.28673e7			−0.998381
$162$		0			0
$163$	−3.94658e7			−0.713780			−0.356890	−	0.934146i	$-0.616163\pi$
$163$	−3.94658e7			−0.713780			−0.356890	+	0.934146i	$0.616163\pi$
$164$	4.27477e7	−	3.58696e7i	0.756763	−	0.634999i
$165$		0			0
$166$	−1.84612e6	+	1.04699e7i	−0.0313243	+	0.177649i
$167$	−7.06208e7	+	2.57039e7i	−1.17334	+	0.427062i	−0.853846	−	0.520526i	$-0.825736\pi$
$167$	−7.06208e7	+	2.57039e7i	−1.17334	+	0.427062i	−0.319496	+	0.947587i	$0.603514\pi$
$168$		0			0
$169$	−1.00664e7	−	5.70891e7i	−0.160424	−	0.909808i
$170$	957378.	+	1.65823e6i	0.0149456	+	0.0258865i
$171$		0			0
$172$	1.01060e8	−	1.75041e8i	1.51436	−	2.62295i
$173$	3.19643e7	+	1.16340e7i	0.469357	+	0.170832i	0.565861	−	0.824501i	$-0.308544\pi$
$173$	3.19643e7	+	1.16340e7i	0.469357	+	0.170832i	−0.0965040	+	0.995333i	$0.530766\pi$
$174$		0			0
$175$	6.89308e7	+	5.78398e7i	0.972255	+	0.815819i
$176$	5.72991e6	+	4.80796e6i	0.0792233	+	0.0664763i
$177$		0			0
$178$	1.09432e8	+	3.98300e7i	1.45437	+	0.529346i
$179$	−3.46740e7	+	6.00572e7i	−0.451875	+	0.782671i	−0.998503	−	0.0547050i	$-0.982578\pi$
$179$	−3.46740e7	+	6.00572e7i	−0.451875	+	0.782671i	0.546627	+	0.837376i	$0.315911\pi$
$180$		0			0
$181$	4.64009e7	+	8.03687e7i	0.581636	+	1.00742i	0.995286	+	0.0969870i	$0.0309205\pi$
$181$	4.64009e7	+	8.03687e7i	0.581636	+	1.00742i	−0.413650	+	0.910436i	$0.635746\pi$
$182$	−8.36491e6	−	4.74398e7i	−0.102852	−	0.583301i
$183$		0			0
$184$	−6.70083e7	+	2.43890e7i	−0.792987	+	0.288624i
$185$	1.95783e6	−	1.11034e7i	0.0227339	−	0.128931i
$186$		0			0
$187$	5.26494e6	−	4.41781e6i	0.0588773	−	0.0494039i
$188$	1.82784e8			2.00625
$189$		0			0
$190$	−3.81291e7			−0.403291
$191$	−1.31521e8	+	1.10360e8i	−1.36578	+	1.14602i	−0.391626	+	0.920125i	$0.628087\pi$
$191$	−1.31521e8	+	1.10360e8i	−1.36578	+	1.14602i	−0.974151	+	0.225898i	$0.927468\pi$
$192$		0			0
$193$	−4.50117e6	+	2.55274e7i	−0.0450687	+	0.255597i	−0.999015	−	0.0443812i	$-0.985868\pi$
$193$	−4.50117e6	+	2.55274e7i	−0.0450687	+	0.255597i	0.953946	+	0.299978i	$0.0969795\pi$
$194$	8.26570e7	−	3.00847e7i	0.812781	−	0.295828i
$195$		0			0
$196$	2.21227e7	+	1.25464e8i	0.209866	+	1.19021i
$197$	−2.26705e7	−	3.92664e7i	−0.211266	−	0.365923i	0.740845	−	0.671676i	$-0.234425\pi$
$197$	−2.26705e7	−	3.92664e7i	−0.211266	−	0.365923i	−0.952111	+	0.305753i	$0.901092\pi$
$198$		0			0
$199$	−2.12501e7	+	3.68063e7i	−0.191150	+	0.331082i	−0.945632	−	0.325239i	$-0.894555\pi$
$199$	−2.12501e7	+	3.68063e7i	−0.191150	+	0.331082i	0.754481	+	0.656321i	$0.227888\pi$
$200$	1.14052e8	+	4.15114e7i	1.00808	+	0.366912i
$201$		0			0
$202$	5.52103e7	+	4.63269e7i	0.471292	+	0.395461i
$203$	2.23470e8	+	1.87514e8i	1.87492	+	1.57325i
$204$		0			0
$205$	1.22821e7	+	4.47033e6i	0.0995715	+	0.0362411i
$206$	1.02169e8	−	1.76963e8i	0.814303	−	1.41041i
$207$		0			0
$208$	−2.44629e6	−	4.23709e6i	−0.0188489	−	0.0326472i
$209$	2.37658e7	+	1.34783e8i	0.180070	+	1.02123i
$210$		0			0
$211$	7.07489e7	−	2.57505e7i	0.518479	−	0.188711i	−0.0695078	−	0.997581i	$-0.522143\pi$
$211$	7.07489e7	−	2.57505e7i	0.518479	−	0.188711i	0.587987	+	0.808870i	$0.299921\pi$
$212$	1.85845e7	−	1.05398e8i	0.133960	−	0.759725i
$213$		0			0
$214$	5.43589e7	−	4.56126e7i	0.379160	−	0.318153i
$215$	4.73410e7			0.324865
$216$		0			0
$217$	−3.08568e8			−2.04994
$218$	−1.44942e8	+	1.21620e8i	−0.947535	+	0.795076i
$219$		0			0
$220$	−6.26724e6	+	3.55433e7i	−0.0396823	+	0.225049i
$221$	−4.22444e6	+	1.53757e6i	−0.0263267	+	0.00958213i
$222$		0			0
$223$	4.18338e7	+	2.37251e8i	0.252615	+	1.43265i	0.802120	+	0.597163i	$0.203705\pi$
$223$	4.18338e7	+	2.37251e8i	0.252615	+	1.43265i	−0.549505	+	0.835491i	$0.685184\pi$
$224$	−9.76502e7	−	1.69135e8i	−0.580504	−	1.00546i
$225$		0			0
$226$	1.99023e8	−	3.44719e8i	1.14690	−	1.98649i
$227$	−2.75187e8	−	1.00160e8i	−1.56148	−	0.568333i	−0.590407	−	0.807106i	$-0.701033\pi$
$227$	−2.75187e8	−	1.00160e8i	−1.56148	−	0.568333i	−0.971076	+	0.238772i	$0.923255\pi$
$228$		0			0
$229$	−1.09950e8	−	9.22590e7i	−0.605022	−	0.507673i	0.288034	−	0.957620i	$-0.406998\pi$
$229$	−1.09950e8	−	9.22590e7i	−0.605022	−	0.507673i	−0.893055	+	0.449947i	$0.851443\pi$
$230$	−3.16783e7	−	2.65813e7i	−0.171678	−	0.144055i
$231$		0			0
$232$	3.69749e8	+	1.34578e8i	1.94401	+	0.707563i
$233$	1.06805e8	−	1.84992e8i	0.553153	−	0.958090i	−0.444891	−	0.895585i	$-0.646758\pi$
$233$	1.06805e8	−	1.84992e8i	0.553153	−	0.958090i	0.998045	−	0.0625052i	$-0.0199090\pi$
$234$		0			0
$235$	2.14060e7	+	3.70763e7i	0.107596	+	0.186363i
$236$	−7.24349e7	−	4.10799e8i	−0.358720	−	2.03440i
$237$		0			0
$238$	4.25844e7	−	1.54995e7i	0.204753	−	0.0745241i
$239$	6.20528e7	−	3.51919e8i	0.294014	−	1.66744i	−0.377167	−	0.926145i	$-0.623102\pi$
$239$	6.20528e7	−	3.51919e8i	0.294014	−	1.66744i	0.671181	−	0.741293i	$-0.265787\pi$
$240$		0			0
$241$	1.88815e8	−	1.58434e8i	0.868913	−	0.729105i	−0.0949556	−	0.995482i	$-0.530271\pi$
$241$	1.88815e8	−	1.58434e8i	0.868913	−	0.729105i	0.963869	+	0.266377i	$0.0858265\pi$
$242$	−1.53989e8			−0.698452
$243$		0			0
$244$	−5.52761e8			−2.43598
$245$	−2.28586e7	+	1.91807e7i	−0.0993045	+	0.0833263i
$246$		0			0
$247$	1.55452e7	−	8.81613e7i	0.0656383	−	0.372253i
$248$	−3.91104e8	+	1.42350e8i	−1.62821	+	0.592622i
$249$		0			0
$250$	2.48535e7	+	1.40951e8i	0.100600	+	0.570529i
$251$	−7.73485e7	−	1.33972e8i	−0.308741	−	0.534755i	0.669346	−	0.742950i	$-0.266574\pi$
$251$	−7.73485e7	−	1.33972e8i	−0.308741	−	0.534755i	−0.978087	+	0.208196i	$0.933241\pi$
$252$		0			0
$253$	−7.42173e7	+	1.28548e8i	−0.288126	+	0.499050i
$254$	6.70340e8	+	2.43984e8i	2.56671	+	0.934207i
$255$		0			0
$256$	−2.48919e8	−	2.08868e8i	−0.927295	−	0.778093i
$257$	2.24855e8	+	1.88676e8i	0.826299	+	0.693347i	0.954438	−	0.298409i	$-0.0964560\pi$
$257$	2.24855e8	+	1.88676e8i	0.826299	+	0.693347i	−0.128139	+	0.991756i	$0.540900\pi$
$258$		0			0
$259$	−2.50751e8	−	9.12659e7i	−0.896795	−	0.326407i
$260$	1.18037e7	−	2.04447e7i	0.0416498	−	0.0721396i
$261$		0			0
$262$	675068.	+	1.16925e6i	0.00231896	+	0.00401655i
$263$	4.70753e7	+	2.66977e8i	0.159569	+	0.904960i	0.954489	+	0.298246i	$0.0964015\pi$
$263$	4.70753e7	+	2.66977e8i	0.159569	+	0.904960i	−0.794920	+	0.606714i	$0.792487\pi$
$264$		0			0
$265$	2.35556e7	−	8.57354e6i	0.0777560	−	0.0283009i
$266$	−1.56703e8	+	8.88708e8i	−0.510496	+	2.89517i
$267$		0			0
$268$	−1.69972e8	+	1.42623e8i	−0.539392	+	0.452604i
$269$	−2.38529e8			−0.747152			−0.373576	−	0.927600i	$-0.621868\pi$
$269$	−2.38529e8			−0.747152			−0.373576	+	0.927600i	$0.621868\pi$
$270$		0			0
$271$	6.88069e7			0.210010			0.105005	−	0.994472i	$-0.466514\pi$
$271$	6.88069e7			0.210010			0.105005	+	0.994472i	$0.466514\pi$
$272$	3.52586e6	−	2.95855e6i	0.0106237	−	0.00891430i
$273$		0			0
$274$	−1.22790e7	+	6.96377e7i	−0.0360609	+	0.204511i
$275$	2.37407e8	−	8.64090e7i	0.688381	−	0.250550i
$276$		0			0
$277$	−5.19556e7	−	2.94655e8i	−0.146877	−	0.832979i	−0.965841	−	0.259135i	$-0.916563\pi$
$277$	−5.19556e7	−	2.94655e8i	−0.146877	−	0.832979i	0.818964	−	0.573844i	$-0.194548\pi$
$278$	1.50030e8	+	2.59859e8i	0.418813	+	0.725406i
$279$		0			0
$280$	−4.80578e7	+	8.32385e7i	−0.130831	+	0.226606i
$281$	3.84334e8	+	1.39886e8i	1.03332	+	0.376099i	0.802345	−	0.596860i	$-0.203585\pi$
$281$	3.84334e8	+	1.39886e8i	1.03332	+	0.376099i	0.230978	+	0.972959i	$0.425807\pi$
$282$		0			0
$283$	3.65980e8	+	3.07094e8i	0.959854	+	0.805413i	0.980929	−	0.194365i	$-0.0622646\pi$
$283$	3.65980e8	+	3.07094e8i	0.959854	+	0.805413i	−0.0210756	+	0.999778i	$0.506709\pi$
$284$	−6.81112e8	−	5.71521e8i	−1.76443	−	1.48053i
$285$		0			0
$286$	−1.27094e8	−	4.62584e7i	−0.321250	−	0.116926i
$287$	1.54671e8	−	2.67898e8i	0.386209	−	0.668934i
$288$		0			0
$289$	2.03055e8	+	3.51701e8i	0.494847	+	0.857100i
$290$	3.96239e7	+	2.24718e8i	0.0954035	+	0.541060i
$291$		0			0
$292$	−2.78198e8	+	1.01256e8i	−0.653903	+	0.238001i
$293$	−9.32682e7	+	5.28950e8i	−0.216619	+	1.22851i	0.661455	+	0.749984i	$0.269939\pi$
$293$	−9.32682e7	+	5.28950e8i	−0.216619	+	1.22851i	−0.878075	+	0.478524i	$0.841172\pi$
$294$		0			0
$295$	7.48446e7	−	6.28020e7i	0.169740	−	0.142428i
$296$	−3.59926e8			−0.806662
$297$		0			0
$298$	6.76768e8			1.48144
$299$	7.43760e7	−	6.24089e7i	0.160910	−	0.135020i
$300$		0			0
$301$	1.94562e8	−	1.10342e9i	0.411222	−	2.33216i
$302$	−1.11479e9	+	4.05752e8i	−2.32900	+	0.847688i
$303$		0			0
$304$	1.59157e7	+	9.02622e7i	0.0324913	+	0.184267i
$305$	−6.47345e7	−	1.12123e8i	−0.130643	−	0.226280i
$306$		0			0
$307$	−1.10256e8	+	1.90969e8i	−0.217480	+	0.376686i	−0.954037	−	0.299689i	$-0.903117\pi$
$307$	−1.10256e8	+	1.90969e8i	−0.217480	+	0.376686i	0.736557	+	0.676375i	$0.236450\pi$
$308$	8.02681e8	+	2.92152e8i	1.56537	+	0.569746i
$309$		0			0
$310$	−1.84896e8	−	1.55146e8i	−0.352501	−	0.295784i
$311$	−3.56570e8	−	2.99197e8i	−0.672176	−	0.564023i	0.241533	−	0.970393i	$-0.422350\pi$
$311$	−3.56570e8	−	2.99197e8i	−0.672176	−	0.564023i	−0.913709	+	0.406370i	$0.866794\pi$
$312$		0			0
$313$	2.18007e7	+	7.93481e6i	0.0401851	+	0.0146262i	0.362035	−	0.932165i	$-0.382082\pi$
$313$	2.18007e7	+	7.93481e6i	0.0401851	+	0.0146262i	−0.321849	+	0.946791i	$0.604304\pi$
$314$	−1.52066e8	+	2.63386e8i	−0.277191	+	0.480108i
$315$		0			0
$316$	−2.43334e8	−	4.21467e8i	−0.433808	−	0.751378i
$317$	−1.68192e8	−	9.53866e8i	−0.296551	−	1.68182i	−0.660832	−	0.750534i	$-0.729797\pi$
$317$	−1.68192e8	−	9.53866e8i	−0.296551	−	1.68182i	0.364282	−	0.931289i	$-0.381315\pi$
$318$		0			0
$319$	7.69660e8	−	2.80133e8i	1.32749	−	0.483167i
$320$	2.90294e7	−	1.64634e8i	0.0495236	−	0.280862i
$321$		0			0
$322$	−7.49745e8	+	6.29111e8i	−1.25146	+	1.05010i
$323$	8.42171e7			0.139057
$324$		0			0
$325$	−1.65254e8			−0.267030
$326$	−5.59691e8	+	4.69636e8i	−0.894719	+	0.750758i
$327$		0			0
$328$	7.24545e7	−	4.10910e8i	0.113372	−	0.642966i
$329$	9.52144e8	−	3.46552e8i	1.47407	−	0.536516i
$330$		0			0
$331$	−1.15778e8	−	6.56611e8i	−0.175480	−	0.995199i	−0.937588	−	0.347749i	$-0.886946\pi$
$331$	−1.15778e8	−	6.56611e8i	−0.175480	−	0.995199i	0.762107	−	0.647451i	$-0.224165\pi$
$332$	6.16551e7	+	1.06790e8i	0.0924668	+	0.160157i
$333$		0			0
$334$	−6.95648e8	+	1.20490e9i	−1.02159	+	1.76945i
$335$	−4.88356e7	−	1.77747e7i	−0.0709708	−	0.0258313i
$336$		0			0
$337$	−1.34974e7	−	1.13256e7i	−0.0192107	−	0.0161197i	0.633132	−	0.774044i	$-0.281769\pi$
$337$	−1.34974e7	−	1.13256e7i	−0.0192107	−	0.0161197i	−0.652342	+	0.757924i	$0.726214\pi$
$338$	−8.22108e8	−	6.89831e8i	−1.15803	−	0.971704i
$339$		0			0
$340$	2.08694e7	+	7.59583e6i	0.0287961	+	0.0104809i
$341$	−4.33181e8	+	7.50291e8i	−0.591601	+	1.02468i
$342$		0			0
$343$	−1.37023e8	−	2.37331e8i	−0.183343	−	0.317559i
$344$	−2.62431e8	−	1.48832e9i	−0.347585	−	1.97125i
$345$		0			0
$346$	5.91749e8	−	2.15379e8i	0.768018	−	0.279536i
$347$	7.41102e7	−	4.20300e8i	0.0952193	−	0.540016i	−0.899461	−	0.437002i	$-0.856040\pi$
$347$	7.41102e7	−	4.20300e8i	0.0952193	−	0.540016i	0.994680	−	0.103014i	$-0.0328486\pi$
$348$		0			0
$349$	−3.59447e8	+	3.01612e8i	−0.452633	+	0.379804i	−0.840412	−	0.541948i	$-0.817687\pi$
$349$	−3.59447e8	+	3.01612e8i	−0.452633	+	0.379804i	0.387779	+	0.921752i	$0.373242\pi$
$350$	1.66584e9			2.07680
$351$		0			0
$352$	−5.48342e8			−0.670119
$353$	−2.23701e8	+	1.87708e8i	−0.270681	+	0.227128i	−0.768016	−	0.640430i	$-0.778756\pi$
$353$	−2.23701e8	+	1.87708e8i	−0.270681	+	0.227128i	0.497336	+	0.867558i	$0.334312\pi$
$354$		0			0
$355$	3.61629e7	−	2.05090e8i	0.0429006	−	0.243302i
$356$	1.26927e9	−	4.61977e8i	1.49100	−	0.542681i
$357$		0			0
$358$	2.22935e8	+	1.26433e9i	0.256795	+	1.45636i
$359$	1.53978e8	+	2.66698e8i	0.175642	+	0.304221i	0.940383	−	0.340116i	$-0.110466\pi$
$359$	1.53978e8	+	2.66698e8i	0.175642	+	0.304221i	−0.764741	+	0.644338i	$0.777133\pi$
$360$		0			0
$361$	−3.91584e8	+	6.78244e8i	−0.438077	+	0.758771i
$362$	1.61442e9	+	5.87599e8i	1.78869	+	0.651030i
$363$		0			0
$364$	−4.28011e8	−	3.59144e8i	−0.465158	−	0.390314i
$365$	−5.31190e7	−	4.45721e7i	−0.0571775	−	0.0479776i
$366$		0			0
$367$	6.68263e8	+	2.43228e8i	0.705693	+	0.256851i	0.669840	−	0.742506i	$-0.266363\pi$
$367$	6.68263e8	+	2.43228e8i	0.705693	+	0.256851i	0.0358536	+	0.999357i	$0.488585\pi$
$368$	−4.97023e7	+	8.60869e7i	−0.0519887	+	0.0900471i
$369$		0			0
$370$	−1.04363e8	−	1.80763e8i	−0.107113	−	0.185525i
$371$	−1.03022e8	−	5.84267e8i	−0.104742	−	0.594022i
$372$		0			0
$373$	−1.18186e7	+	4.30162e6i	−0.0117919	+	0.00429191i	−0.347909	−	0.937528i	$-0.613108\pi$
$373$	−1.18186e7	+	4.30162e6i	−0.0117919	+	0.00429191i	0.336117	+	0.941820i	$0.390886\pi$
$374$	2.20944e7	−	1.25304e8i	0.0218390	−	0.123855i
$375$		0			0
$376$	1.04695e9	−	8.78497e8i	1.01571	−	0.852281i
$377$	−5.35744e8			−0.514947
$378$		0			0
$379$	9.83693e8			0.928159			0.464080	−	0.885794i	$-0.346385\pi$
$379$	9.83693e8			0.928159			0.464080	+	0.885794i	$0.346385\pi$
$380$	−3.38782e8	+	2.84272e8i	−0.316722	+	0.265761i
$381$		0			0
$382$	−5.51932e8	+	3.13016e9i	−0.506599	+	2.87306i
$383$	6.50767e8	−	2.36860e8i	0.591875	−	0.215425i	−0.0286789	−	0.999589i	$-0.509130\pi$
$383$	6.50767e8	−	2.36860e8i	0.591875	−	0.215425i	0.620554	+	0.784164i	$0.286908\pi$
$384$		0			0
$385$	3.47421e7	+	1.97032e8i	0.0310273	+	0.175964i
$386$	2.39938e8	+	4.15584e8i	0.212345	+	0.367793i
$387$		0			0
$388$	5.10122e8	−	8.83557e8i	0.443367	−	0.767933i
$389$	−1.37784e9	−	5.01491e8i	−1.18679	−	0.431956i	−0.328195	−	0.944610i	$-0.606440\pi$
$389$	−1.37784e9	−	5.01491e8i	−1.18679	−	0.431956i	−0.858595	+	0.512654i	$0.828662\pi$
$390$		0			0
$391$	6.99691e7	+	5.87111e7i	0.0591954	+	0.0496708i
$392$	7.29722e8	+	6.12309e8i	0.611866	+	0.513416i
$393$		0			0
$394$	−7.88768e8	−	2.87088e8i	−0.649700	−	0.236471i
$395$	5.69942e7	−	9.87169e7i	0.0465309	−	0.0805938i
$396$		0			0
$397$	−7.45945e8	−	1.29202e9i	−0.598329	−	1.03634i	−0.993068	−	0.117543i	$-0.962498\pi$
$397$	−7.45945e8	−	1.29202e9i	−0.598329	−	1.03634i	0.394738	−	0.918794i	$-0.370835\pi$
$398$	1.36626e8	+	7.74846e8i	0.108628	+	0.616063i
$399$		0			0
$400$	1.58988e8	−	5.78669e7i	0.124209	−	0.0452085i
$401$	−1.40559e8	+	7.97150e8i	−0.108856	+	0.617355i	0.880753	+	0.473575i	$0.157037\pi$
$401$	−1.40559e8	+	7.97150e8i	−0.108856	+	0.617355i	−0.989610	+	0.143780i	$0.954074\pi$
$402$		0			0
$403$	4.34107e8	−	3.64259e8i	0.330392	−	0.277231i
$404$	8.35942e8			0.630727
$405$		0			0
$406$	5.40055e9			4.00495
$407$	−5.73930e8	+	4.81584e8i	−0.421967	+	0.354072i
$408$		0			0
$409$	7.48926e7	−	4.24737e8i	0.0541262	−	0.306965i	−0.945711	−	0.325009i	$-0.894633\pi$
$409$	7.48926e7	−	4.24737e8i	0.0541262	−	0.306965i	0.999837	+	0.0180439i	$0.00574385\pi$
$410$	2.27377e8	−	8.27585e7i	0.162931	−	0.0593019i
$411$		0			0
$412$	−4.11559e8	−	2.33406e9i	−0.289929	−	1.64427i
$413$	−1.15619e9	−	2.00257e9i	−0.807611	−	1.39882i
$414$		0			0
$415$	−1.44410e7	+	2.50126e7i	−0.00991812	+	0.0171787i
$416$	3.37040e8	+	1.22672e8i	0.229538	+	0.0835449i
$417$		0			0
$418$	1.94093e9	+	1.62863e9i	1.29985	+	1.09070i
$419$	1.69317e9	+	1.42073e9i	1.12448	+	0.943548i	0.998822	−	0.0485263i	$-0.0154525\pi$
$419$	1.69317e9	+	1.42073e9i	1.12448	+	0.943548i	0.125655	+	0.992074i	$0.459897\pi$
$420$		0			0
$421$	6.48906e8	+	2.36182e8i	0.423833	+	0.154262i	0.545126	−	0.838354i	$-0.316482\pi$
$421$	6.48906e8	+	2.36182e8i	0.423833	+	0.154262i	−0.121293	+	0.992617i	$0.538704\pi$
$422$	6.96911e8	−	1.20708e9i	0.451423	−	0.781887i
$423$		0			0
$424$	−4.00116e8	−	6.93021e8i	−0.254921	−	0.441536i
$425$	−2.69957e7	−	1.53100e8i	−0.0170582	−	0.0967420i
$426$		0			0
$427$	−2.87941e9	+	1.04802e9i	−1.78980	+	0.651435i
$428$	1.42921e8	−	8.10548e8i	0.0881139	−	0.499719i
$429$		0			0
$430$	6.71374e8	−	5.63350e8i	0.407216	−	0.341695i
$431$	−1.16727e9			−0.702264			−0.351132	−	0.936326i	$-0.614203\pi$
$431$	−1.16727e9			−0.702264			−0.351132	+	0.936326i	$0.614203\pi$
$432$		0			0
$433$	5.23670e8			0.309992			0.154996	−	0.987915i	$-0.450464\pi$
$433$	5.23670e8			0.309992			0.154996	+	0.987915i	$0.450464\pi$
$434$	−4.37601e9	+	3.67190e9i	−2.56959	+	2.15614i
$435$		0			0
$436$	−3.81083e8	+	2.16123e9i	−0.220200	+	1.24881i
$437$	−1.70915e9	+	6.22081e8i	−0.979707	+	0.356584i
$438$		0			0
$439$	4.29222e8	+	2.43424e9i	0.242134	+	1.37321i	0.827055	+	0.562122i	$0.190015\pi$
$439$	4.29222e8	+	2.43424e9i	0.242134	+	1.37321i	−0.584920	+	0.811091i	$0.698874\pi$
$440$	1.34931e8	+	2.33707e8i	0.0755140	+	0.130794i
$441$		0			0
$442$	−4.16128e7	+	7.20754e7i	−0.0229218	+	0.0397017i
$443$	8.39832e8	+	3.05674e8i	0.458965	+	0.167050i	0.561147	−	0.827716i	$-0.310360\pi$
$443$	8.39832e8	+	3.05674e8i	0.458965	+	0.167050i	−0.102182	+	0.994766i	$0.532582\pi$
$444$		0			0
$445$	2.42354e8	+	2.03359e8i	0.130374	+	0.109397i
$446$	3.41652e9	+	2.86680e9i	1.82352	+	1.53012i
$447$		0			0
$448$	−3.71796e9	−	1.35323e9i	−1.95358	−	0.711045i
$449$	−8.18668e8	+	1.41798e9i	−0.426821	+	0.739276i	−0.996589	−	0.0825302i	$-0.973700\pi$
$449$	−8.18668e8	+	1.41798e9i	−0.426821	+	0.739276i	0.569768	+	0.821806i	$0.307033\pi$
$450$		0			0
$451$	−4.34267e8	−	7.52173e8i	−0.222915	−	0.386100i
$452$	−8.01705e8	−	4.54669e9i	−0.408348	−	2.31585i
$453$		0			0
$454$	−5.09449e9	+	1.85424e9i	−2.55508	+	0.929975i
$455$	2.27248e7	−	1.28879e8i	0.0113099	−	0.0641418i
$456$		0			0
$457$	9.60141e8	−	8.05654e8i	0.470575	−	0.394859i	−0.376430	−	0.926445i	$-0.622848\pi$
$457$	9.60141e8	−	8.05654e8i	0.470575	−	0.394859i	0.847004	+	0.531586i	$0.178404\pi$
$458$	−2.65714e9			−1.29236
$459$		0			0
$460$	−4.79644e8			−0.229756
$461$	1.64915e9	−	1.38380e9i	0.783983	−	0.657840i	−0.160265	−	0.987074i	$-0.551235\pi$
$461$	1.64915e9	−	1.38380e9i	0.783983	−	0.657840i	0.944248	+	0.329234i	$0.106791\pi$
$462$		0			0
$463$	3.32458e6	−	1.88547e7i	0.00155670	−	0.00882846i	−0.984020	−	0.178061i	$-0.943018\pi$
$463$	3.32458e6	−	1.88547e7i	0.00155670	−	0.00882846i	0.985576	+	0.169232i	$0.0541288\pi$
$464$	5.15431e8	−	1.87602e8i	0.239529	−	0.0871813i
$465$		0			0
$466$	−6.86696e8	−	3.89445e9i	−0.314350	−	1.78277i
$467$	1.54789e9	+	2.68103e9i	0.703285	+	1.21812i	0.967307	+	0.253608i	$0.0816174\pi$
$467$	1.54789e9	+	2.68103e9i	0.703285	+	1.21812i	−0.264022	+	0.964517i	$0.585049\pi$
$468$		0			0
$469$	−6.14996e8	+	1.06520e9i	−0.275275	+	0.476791i
$470$	7.44774e8	+	2.71076e8i	0.330889	+	0.120434i
$471$		0			0
$472$	−2.38928e9	−	2.00485e9i	−1.04585	−	0.877575i
$473$	−2.40986e9	−	2.02211e9i	−1.04707	−	0.878599i
$474$		0			0
$475$	2.90907e9	+	1.05881e9i	1.24545	+	0.453307i
$476$	2.62812e8	−	4.55203e8i	0.111692	−	0.193456i
$477$		0			0
$478$	−3.30776e9	−	5.72921e9i	−1.38528	−	2.39937i
$479$	−4.81517e8	−	2.73082e9i	−0.200188	−	1.13532i	−0.904835	−	0.425763i	$-0.860006\pi$
$479$	−4.81517e8	−	2.73082e9i	−0.200188	−	1.13532i	0.704647	−	0.709558i	$-0.251105\pi$
$480$		0			0
$481$	4.60505e8	−	1.67610e8i	0.188680	−	0.0686740i
$482$	7.92365e8	−	4.49373e9i	0.322300	−	1.82786i
$483$		0			0
$484$	−1.36822e9	+	1.14807e9i	−0.548524	+	0.460266i
$485$	2.38964e8			0.0951122
$486$		0			0
$487$	−3.05782e9			−1.19967			−0.599833	−	0.800125i	$-0.704766\pi$
$487$	−3.05782e9			−1.19967			−0.599833	+	0.800125i	$0.704766\pi$
$488$	−3.16612e9	+	2.65669e9i	−1.23327	+	1.03484i
$489$		0			0
$490$	−9.59267e7	+	5.44027e8i	−0.0368344	+	0.208898i
$491$	1.71642e9	−	6.24724e8i	0.654391	−	0.238179i	0.00657824	−	0.999978i	$-0.497906\pi$
$491$	1.71642e9	−	6.24724e8i	0.654391	−	0.238179i	0.647813	+	0.761799i	$0.275684\pi$
$492$		0			0
$493$	−8.75187e7	−	4.96343e8i	−0.0328955	−	0.186560i
$494$	−8.28647e8	−	1.43526e9i	−0.309261	−	0.535656i
$495$		0			0
$496$	−2.90095e8	+	5.02459e8i	−0.106747	+	0.184891i
$497$	−4.63159e9	−	1.68576e9i	−1.69232	−	0.615954i
$498$		0			0
$499$	−1.40467e9	−	1.17866e9i	−0.506083	−	0.424654i	0.353665	−	0.935372i	$-0.384935\pi$
$499$	−1.40467e9	−	1.17866e9i	−0.506083	−	0.424654i	−0.859748	+	0.510718i	$0.829380\pi$
$500$	1.27169e9	+	1.06707e9i	0.454973	+	0.381768i
$501$		0			0
$502$	−2.69117e9	−	9.79505e8i	−0.949463	−	0.345576i
$503$	−1.79570e8	+	3.11025e8i	−0.0629139	+	0.108970i	−0.895767	−	0.444524i	$-0.853373\pi$
$503$	−1.79570e8	+	3.11025e8i	−0.0629139	+	0.108970i	0.832853	+	0.553494i	$0.186706\pi$
$504$		0			0
$505$	9.78982e7	+	1.69565e8i	0.0338263	+	0.0585889i
$506$	4.77176e8	+	2.70620e9i	0.163739	+	0.928609i
$507$		0			0
$508$	7.77509e9	−	2.82990e9i	2.63137	−	0.957741i
$509$	4.68255e8	−	2.65561e9i	0.157388	−	0.892589i	−0.799183	−	0.601088i	$-0.794734\pi$
$509$	4.68255e8	−	2.65561e9i	0.157388	−	0.892589i	0.956570	−	0.291501i	$-0.0941547\pi$
$510$		0			0
$511$	−1.25719e9	+	1.05491e9i	−0.416800	+	0.349737i
$512$	−8.27168e8			−0.272363
$513$		0			0
$514$	5.43403e9			1.76503
$515$	4.25249e8	−	3.56827e8i	0.137189	−	0.115115i
$516$		0			0
$517$	4.94009e8	−	2.80167e9i	0.157224	−	0.891661i
$518$	−4.64211e9	+	1.68959e9i	−1.46744	+	0.534106i
$519$		0			0
$520$	−3.06518e7	−	1.73835e8i	−0.00955969	−	0.0542157i
$521$	3.15466e9	+	5.46404e9i	0.977285	+	1.69271i	0.672180	+	0.740388i	$0.265358\pi$
$521$	3.15466e9	+	5.46404e9i	0.977285	+	1.69271i	0.305105	+	0.952319i	$0.401308\pi$
$522$		0			0
$523$	−1.80285e9	+	3.12262e9i	−0.551065	+	0.954473i	0.447133	+	0.894468i	$0.352445\pi$
$523$	−1.80285e9	+	3.12262e9i	−0.551065	+	0.954473i	−0.998198	+	0.0600054i	$0.980888\pi$
$524$	1.47154e7	+	5.35598e6i	0.00446801	+	0.00162622i
$525$		0			0
$526$	3.84459e9	+	3.22599e9i	1.15186	+	0.966525i
$527$	4.08386e8	+	3.42676e8i	0.121544	+	0.101987i
$528$		0			0
$529$	1.34581e9	+	4.89837e8i	0.395267	+	0.143865i
$530$	2.32034e8	−	4.01895e8i	0.0676996	−	0.117259i
$531$		0			0
$532$	5.23345e9	+	9.06460e9i	1.50694	+	2.61010i
$533$	9.86509e7	+	5.59477e8i	0.0282199	+	0.160043i
$534$		0			0
$535$	1.81151e8	−	6.59337e7i	0.0511450	−	0.0186153i
$536$	−2.88090e8	+	1.63384e9i	−0.0808075	+	0.458282i
$537$		0			0
$538$	−3.38274e9	+	2.83846e9i	−0.936550	+	0.785859i
$539$	1.98288e9			0.545425
$540$		0			0
$541$	3.62830e6			0.000985173			0.000492586	−	1.00000i	$-0.499843\pi$
$541$	3.62830e6			0.000985173			0.000492586		1.00000i	$0.499843\pi$
$542$	9.75796e8	−	8.18790e8i	0.263246	−	0.220890i
$543$		0			0
$544$	−5.85921e7	+	3.32292e8i	−0.0156043	+	0.0884961i
$545$	−4.83018e8	+	1.75804e8i	−0.127813	+	0.0465202i
$546$		0			0
$547$	9.86282e8	+	5.59349e9i	0.257659	+	1.46126i	0.789153	+	0.614196i	$0.210520\pi$
$547$	9.86282e8	+	5.59349e9i	0.257659	+	1.46126i	−0.531494	+	0.847062i	$0.678369\pi$
$548$	4.10084e8	+	7.10287e8i	0.106449	+	0.184375i
$549$		0			0
$550$	2.33857e9	−	4.05052e9i	0.599351	−	1.03811i
$551$	9.43104e9	+	3.43262e9i	2.40176	+	0.874168i
$552$		0			0
$553$	−2.06665e9	−	1.73412e9i	−0.519671	−	0.436056i
$554$	−4.24315e9	−	3.56043e9i	−1.06024	−	0.889648i
$555$		0			0
$556$	3.27042e9	+	1.19033e9i	0.806940	+	0.293702i
$557$	−1.62844e9	+	2.82053e9i	−0.399280	+	0.691573i	−0.993637	−	0.112628i	$-0.964073\pi$
$557$	−1.62844e9	+	2.82053e9i	−0.399280	+	0.691573i	0.594357	+	0.804201i	$0.297407\pi$
$558$		0			0
$559$	1.02885e9	+	1.78202e9i	0.249120	+	0.431489i
$560$	2.32663e7	+	1.31950e8i	0.00559847	+	0.0317505i
$561$		0			0
$562$	7.11511e9	−	2.58969e9i	1.69085	−	0.615418i
$563$	−3.81550e8	+	2.16388e9i	−0.0901099	+	0.511039i	0.906027	+	0.423221i	$0.139100\pi$
$563$	−3.81550e8	+	2.16388e9i	−0.0901099	+	0.511039i	−0.996137	+	0.0878180i	$0.972011\pi$
$564$		0			0
$565$	8.28375e8	−	6.95089e8i	0.193222	−	0.162133i
$566$	8.84457e9			2.05031
$567$		0			0
$568$	−6.64814e9			−1.52223
$569$	2.27584e9	−	1.90966e9i	0.517903	−	0.434573i	−0.345997	−	0.938236i	$-0.612459\pi$
$569$	2.27584e9	−	1.90966e9i	0.517903	−	0.434573i	0.863900	+	0.503663i	$0.168015\pi$
$570$		0			0
$571$	8.76218e8	−	4.96928e9i	0.196964	−	1.11704i	−0.712631	−	0.701539i	$-0.752497\pi$
$571$	8.76218e8	−	4.96928e9i	0.196964	−	1.11704i	0.909595	−	0.415497i	$-0.136392\pi$
$572$	−1.47413e9	+	5.36539e8i	−0.329343	+	0.119871i
$573$		0			0
$574$	−9.94449e8	−	5.63980e9i	−0.219478	−	1.24472i
$575$	1.67877e9	+	2.90771e9i	0.368258	+	0.637842i
$576$		0			0
$577$	3.68812e9	−	6.38801e9i	0.799262	−	1.38436i	−0.120835	−	0.992673i	$-0.538557\pi$
$577$	3.68812e9	−	6.38801e9i	0.799262	−	1.38436i	0.920097	−	0.391691i	$-0.128110\pi$
$578$	7.06484e9	+	2.57139e9i	1.52179	+	0.553886i
$579$		0			0
$580$	2.02745e9	+	1.70124e9i	0.431472	+	0.362048i
$581$	5.23640e8	+	4.39386e8i	0.110769	+	0.0929459i
$582$		0			0
$583$	−1.56529e9	−	5.69718e8i	−0.327155	−	0.119075i
$584$	−1.10681e9	+	1.91705e9i	−0.229947	+	0.398280i
$585$		0			0
$586$	4.97172e9	+	8.61127e9i	1.02062	+	1.76777i
$587$	−1.12601e9	−	6.38590e9i	−0.229778	−	1.30313i	−0.853338	−	0.521359i	$-0.825425\pi$
$587$	−1.12601e9	−	6.38590e9i	−0.229778	−	1.30313i	0.623560	−	0.781775i	$-0.285686\pi$
$588$		0			0
$589$	−9.97575e9	+	3.63087e9i	−2.01160	+	0.732163i
$590$	3.14087e8	−	1.78127e9i	0.0629604	−	0.357066i
$591$		0			0
$592$	−3.84353e8	+	3.22510e8i	−0.0761385	+	0.0638878i
$593$	−5.91503e9			−1.16484			−0.582419	−	0.812889i	$-0.697894\pi$
$593$	−5.91503e9			−1.16484			−0.582419	+	0.812889i	$0.697894\pi$
$594$		0			0
$595$	1.23113e8			0.0239604
$596$	6.01318e9	−	5.04565e9i	1.16343	−	0.976238i
$597$		0			0
$598$	3.12120e8	−	1.77012e9i	0.0596854	−	0.338493i
$599$	1.98184e9	−	7.21331e8i	0.376769	−	0.137133i	−0.146692	−	0.989182i	$-0.546863\pi$
$599$	1.98184e9	−	7.21331e8i	0.376769	−	0.137133i	0.523461	+	0.852050i	$0.324641\pi$
$600$		0			0
$601$	4.78158e8	+	2.71177e9i	0.0898486	+	0.509556i	0.996205	+	0.0870418i	$0.0277414\pi$
$601$	4.78158e8	+	2.71177e9i	0.0898486	+	0.509556i	−0.906356	+	0.422515i	$0.861148\pi$
$602$	−1.03713e10	−	1.79636e10i	−1.93751	−	3.35587i
$603$		0			0
$604$	−6.88000e9	+	1.19165e10i	−1.27046	+	2.20049i
$605$	−3.93110e8	−	1.43081e8i	−0.0721723	−	0.0262686i
$606$		0			0
$607$	5.39694e9	+	4.52857e9i	0.979461	+	0.821866i	0.984008	−	0.178124i	$-0.0570028\pi$
$607$	5.39694e9	+	4.52857e9i	0.979461	+	0.821866i	−0.00454665	+	0.999990i	$0.501447\pi$
$608$	−5.14714e9	−	4.31896e9i	−0.928760	−	0.779322i
$609$		0			0
$610$	−2.25229e9	−	8.19767e8i	−0.401763	−	0.146230i
$611$	−9.30419e8	+	1.61153e9i	−0.165019	+	0.285822i
$612$		0			0
$613$	−2.34098e9	−	4.05469e9i	−0.410474	−	0.710962i	0.584468	−	0.811417i	$-0.301303\pi$
$613$	−2.34098e9	−	4.05469e9i	−0.410474	−	0.710962i	−0.994942	+	0.100455i	$0.967970\pi$
$614$	7.08886e8	+	4.02029e9i	0.123591	+	0.700920i
$615$		0			0
$616$	6.00176e9	−	2.18446e9i	1.03454	−	0.376541i
$617$	−1.17457e9	+	6.66132e9i	−0.201317	+	1.14173i	0.701814	+	0.712361i	$0.252374\pi$
$617$	−1.17457e9	+	6.66132e9i	−0.201317	+	1.14173i	−0.903131	+	0.429366i	$0.858737\pi$
$618$		0			0
$619$	6.24146e9	−	5.23721e9i	1.05772	−	0.887529i	0.0638320	−	0.997961i	$-0.479668\pi$
$619$	6.24146e9	−	5.23721e9i	1.05772	−	0.887529i	0.993884	+	0.110432i	$0.0352234\pi$
$620$	−2.79951e9			−0.471750
$621$		0			0
$622$	−8.61715e9			−1.43581
$623$	5.73591e9	−	4.81300e9i	0.950372	−	0.797457i
$624$		0			0
$625$	9.58030e8	−	5.43326e9i	0.156964	−	0.890185i
$626$	4.03593e8	−	1.46896e8i	0.0657557	−	0.0239331i
$627$		0			0
$628$	6.12552e8	+	3.47395e9i	0.0986925	+	0.559713i
$629$	2.30511e8	+	3.99257e8i	0.0369330	+	0.0639699i
$630$		0			0
$631$	2.10448e9	−	3.64507e9i	0.333459	−	0.577568i	−0.649729	−	0.760166i	$-0.725117\pi$
$631$	2.10448e9	−	3.64507e9i	0.333459	−	0.577568i	0.983188	+	0.182598i	$0.0584508\pi$
$632$	−3.41943e9	−	1.24457e9i	−0.538821	−	0.196115i
$633$		0			0
$634$	−1.37361e10	−	1.15259e10i	−2.14067	−	1.79624i
$635$	1.48457e9	+	1.24571e9i	0.230088	+	0.193067i
$636$		0			0
$637$	−1.21878e9	−	4.43600e8i	−0.186826	−	0.0679991i
$638$	7.58152e9	−	1.31316e10i	1.15580	−	2.00191i
$639$		0			0
$640$	−1.01931e9	−	1.76549e9i	−0.153701	−	0.266217i
$641$	7.05592e8	+	4.00161e9i	0.105816	+	0.600111i	0.990891	+	0.134664i	$0.0429955\pi$
$641$	7.05592e8	+	4.00161e9i	0.105816	+	0.600111i	−0.885075	+	0.465448i	$0.845893\pi$
$642$		0			0
$643$	−4.77448e9	+	1.73777e9i	−0.708251	+	0.257782i	−0.670930	−	0.741521i	$-0.734105\pi$
$643$	−4.77448e9	+	1.73777e9i	−0.708251	+	0.257782i	−0.0373215	+	0.999303i	$0.511883\pi$
$644$	−1.97124e9	+	1.11795e10i	−0.290830	+	1.64938i
$645$		0			0
$646$	1.19434e9	−	1.00217e9i	0.174307	−	0.146261i
$647$	2.78642e9			0.404466			0.202233	−	0.979337i	$-0.435180\pi$
$647$	2.78642e9			0.404466			0.202233	+	0.979337i	$0.435180\pi$
$648$		0			0
$649$	−6.49241e9			−0.932286
$650$	−2.34357e9	+	1.96649e9i	−0.334720	+	0.280863i
$651$		0			0
$652$	−1.47155e9	+	8.34556e9i	−0.207926	+	1.17920i
$653$	6.62932e8	−	2.41287e8i	0.0931692	−	0.0339108i	−0.295015	−	0.955493i	$-0.595325\pi$
$653$	6.62932e8	−	2.41287e8i	0.0931692	−	0.0339108i	0.388184	+	0.921582i	$0.373102\pi$
$654$		0			0
$655$	636922.	+	3.61216e6i	8.85608e−5	+	0.000502254i
$656$	−2.90823e8	−	5.03720e8i	−0.0402221	−	0.0696668i
$657$		0			0
$658$	9.37907e9	−	1.62450e10i	1.28342	−	2.22295i
$659$	−5.41298e9	−	1.97016e9i	−0.736779	−	0.268166i	−0.0537478	−	0.998555i	$-0.517117\pi$
$659$	−5.41298e9	−	1.97016e9i	−0.736779	−	0.268166i	−0.683032	+	0.730389i	$0.739339\pi$
$660$		0			0
$661$	4.47424e9	+	3.75434e9i	0.602580	+	0.505625i	0.892274	−	0.451495i	$-0.149109\pi$
$661$	4.47424e9	+	3.75434e9i	0.602580	+	0.505625i	−0.289694	+	0.957119i	$0.593553\pi$
$662$	−9.45548e9	−	7.93409e9i	−1.26672	−	1.06290i
$663$		0			0
$664$	8.66405e8	+	3.15346e8i	0.114850	+	0.0418021i
$665$	−1.22579e9	+	2.12313e9i	−0.161637	+	0.279963i
$666$		0			0
$667$	5.44247e9	+	9.42663e9i	0.710159	+	1.23003i
$668$	2.80221e9	+	1.58921e10i	0.363733	+	2.06283i
$669$		0			0
$670$	−9.04086e8	+	3.29060e8i	−0.116131	+	0.0422682i
$671$	−1.49395e9	+	8.47260e9i	−0.190900	+	1.08265i
$672$		0			0
$673$	−1.03174e10	+	8.65730e9i	−1.30472	+	1.09479i	−0.315407	+	0.948956i	$0.602141\pi$
$673$	−1.03174e10	+	8.65730e9i	−1.30472	+	1.09479i	−0.989310	+	0.145831i	$0.953414\pi$
$674$	−3.26188e8			−0.0410354
$675$		0			0
$676$	−1.24476e10			−1.54979
$677$	−6.29972e9	+	5.28609e9i	−0.780299	+	0.654749i	−0.943324	−	0.331873i	$-0.892319\pi$
$677$	−6.29972e9	+	5.28609e9i	−0.780299	+	0.654749i	0.163025	+	0.986622i	$0.447875\pi$
$678$		0			0
$679$	9.82096e8	−	5.56974e9i	0.120395	−	0.682796i
$680$	1.56043e8	−	5.67951e7i	0.0190311	−	0.00692675i
$681$		0			0
$682$	2.78511e9	+	1.57951e10i	0.336199	+	1.90668i
$683$	−9.33371e8	−	1.61665e9i	−0.112094	−	0.194152i	0.804520	−	0.593925i	$-0.202422\pi$
$683$	−9.33371e8	−	1.61665e9i	−0.112094	−	0.194152i	−0.916614	+	0.399773i	$0.869089\pi$
$684$		0			0
$685$	−9.60510e7	+	1.66365e8i	−0.0114179	+	0.0197763i
$686$	−4.76741e9	−	1.73519e9i	−0.563829	−	0.205217i
$687$		0			0
$688$	−1.61385e9	−	1.35418e9i	−0.188931	−	0.158532i
$689$	8.34653e8	+	7.00357e8i	0.0972162	+	0.0815741i
$690$		0			0
$691$	1.38344e10	+	5.03531e9i	1.59510	+	0.580568i	0.978416	−	0.206645i	$-0.0662544\pi$
$691$	1.38344e10	+	5.03531e9i	1.59510	+	0.580568i	0.616682	+	0.787213i	$0.288477\pi$
$692$	3.65201e9	−	6.32547e9i	0.418949	−	0.725640i
$693$		0			0
$694$	−3.95049e9	−	6.84245e9i	−0.448635	−	0.777058i
$695$	1.41552e8	+	8.02781e8i	0.0159944	+	0.0907090i
$696$		0			0
$697$	−5.02216e8	+	1.82792e8i	−0.0561792	+	0.0204476i
$698$	−1.50843e9	+	8.55472e9i	−0.167892	+	0.952164i
$699$		0			0
$700$	1.48012e10	−	1.24197e10i	1.63100	−	1.36857i
$701$	−1.40848e9			−0.154432			−0.0772159	−	0.997014i	$-0.524603\pi$
$701$	−1.40848e9			−0.154432			−0.0772159	+	0.997014i	$0.524603\pi$
$702$		0			0
$703$	−9.18048e9			−0.996602
$704$	−8.50982e9	+	7.14059e9i	−0.919213	+	0.771312i
$705$		0			0
$706$	−9.38767e8	+	5.32401e9i	−0.100402	+	0.569407i
$707$	4.35454e9	−	1.58492e9i	0.463419	−	0.168671i
$708$		0			0
$709$	−1.09213e9	−	6.19380e9i	−0.115084	−	0.652672i	−0.986709	−	0.162499i	$-0.948045\pi$
$709$	−1.09213e9	−	6.19380e9i	−0.115084	−	0.652672i	0.871625	−	0.490173i	$-0.163067\pi$
$710$	−1.92768e9	−	3.33885e9i	−0.202130	−	0.350100i
$711$		0			0
$712$	5.04980e9	−	8.74650e9i	0.524317	−	0.908144i
$713$	−1.08193e10	−	3.93789e9i	−1.11785	−	0.406865i
$714$		0			0
$715$	−2.81470e8	−	2.36181e8i	−0.0287979	−	0.0241643i
$716$	1.14070e10	+	9.57161e9i	1.16138	+	0.974517i
$717$		0			0
$718$	5.35733e9	+	1.94991e9i	0.540148	+	0.196598i
$719$	1.11352e8	−	1.92867e8i	0.0111724	−	0.0193512i	−0.860385	−	0.509644i	$-0.829777\pi$
$719$	1.11352e8	−	1.92867e8i	0.0111724	−	0.0193512i	0.871558	+	0.490293i	$0.163110\pi$
$720$		0			0
$721$	−6.56918e9	−	1.13782e10i	−0.652736	−	1.13057i
$722$	2.51767e9	+	1.42784e10i	0.248954	+	1.41189i
$723$		0			0
$724$	1.87252e10	−	6.81540e9i	1.83375	−	0.667431i
$725$	3.21713e9	−	1.82453e10i	0.313535	−	1.77814i
$726$		0			0
$727$	2.88247e9	−	2.41868e9i	0.278224	−	0.233458i	−0.492988	−	0.870036i	$-0.664095\pi$
$727$	2.88247e9	−	2.41868e9i	0.278224	−	0.233458i	0.771212	+	0.636578i	$0.219651\pi$
$728$	−4.17770e9			−0.401307
$729$		0			0
$730$	−1.28372e9			−0.122135
$731$	−1.48289e9	+	1.24429e9i	−0.140410	+	0.117818i
$732$		0			0
$733$	−9.63011e8	+	5.46151e9i	−0.0903166	+	0.512211i	0.905766	+	0.423779i	$0.139297\pi$
$733$	−9.63011e8	+	5.46151e9i	−0.0903166	+	0.512211i	−0.996082	+	0.0884318i	$0.971814\pi$
$734$	1.23714e10	−	4.50284e9i	1.15474	−	0.420291i
$735$		0			0
$736$	−1.26542e9	−	7.17655e9i	−0.116994	−	0.663503i
$737$	1.72671e9	+	2.99076e9i	0.158885	+	0.275198i
$738$		0			0
$739$	−6.47103e9	+	1.12082e10i	−0.589818	+	1.02159i	0.404438	+	0.914565i	$0.367467\pi$
$739$	−6.47103e9	+	1.12082e10i	−0.589818	+	1.02159i	−0.994256	+	0.107029i	$0.965866\pi$
$740$	−2.27496e9	−	8.28019e8i	−0.206378	−	0.0751155i
$741$		0			0
$742$	−8.41370e9	−	7.05993e9i	−0.756090	−	0.634435i
$743$	1.16093e9	+	9.74136e8i	0.103835	+	0.0871282i	0.693227	−	0.720719i	$-0.256188\pi$
$743$	1.16093e9	+	9.74136e8i	0.103835	+	0.0871282i	−0.589392	+	0.807847i	$0.700633\pi$
$744$		0			0
$745$	1.72768e9	+	6.28825e8i	0.153080	+	0.0557164i
$746$	−1.16419e8	+	2.01643e8i	−0.0102669	+	0.0177827i
$747$		0			0
$748$	−7.37892e8	−	1.27807e9i	−0.0644670	−	0.111660i
$749$	−7.92277e8	−	4.49323e9i	−0.0688955	−	0.390726i
$750$		0			0
$751$	−6.92256e9	+	2.51960e9i	−0.596385	+	0.217066i	−0.622535	−	0.782592i	$-0.713897\pi$
$751$	−6.92256e9	+	2.51960e9i	−0.596385	+	0.217066i	0.0261503	+	0.999658i	$0.491675\pi$
$752$	3.30831e8	−	1.87624e9i	0.0283690	−	0.160889i
$753$		0			0
$754$	−7.59774e9	+	6.37526e9i	−0.645482	+	0.541624i
$755$	−3.22290e9			−0.272542
$756$		0			0
$757$	−8.90887e9			−0.746427			−0.373213	−	0.927746i	$-0.621744\pi$
$757$	−8.90887e9			−0.746427			−0.373213	+	0.927746i	$0.621744\pi$
$758$	1.39504e10	−	1.17058e10i	1.16344	−	0.976243i
$759$		0			0
$760$	−5.74212e8	+	3.25652e9i	−0.0474488	+	0.269095i
$761$	−1.14537e10	+	4.16880e9i	−0.942105	+	0.342898i	−0.766997	−	0.641651i	$-0.778250\pi$
$761$	−1.14537e10	+	4.16880e9i	−0.942105	+	0.342898i	−0.175108	+	0.984549i	$0.556028\pi$
$762$		0			0
$763$	2.11251e9	+	1.19806e10i	0.172172	+	0.976437i
$764$	1.84330e10	+	3.19269e10i	1.49544	+	2.59018i
$765$		0			0
$766$	6.41037e9	−	1.11031e10i	0.515326	−	0.892571i
$767$	3.99057e9	+	1.45245e9i	0.319339	+	0.116230i
$768$		0			0
$769$	4.55056e9	+	3.81837e9i	0.360846	+	0.302786i	0.805128	−	0.593101i	$-0.202097\pi$
$769$	4.55056e9	+	3.81837e9i	0.360846	+	0.302786i	−0.444282	+	0.895887i	$0.646541\pi$
$770$	2.83735e9	+	2.38082e9i	0.223973	+	0.187935i
$771$		0			0
$772$	5.23027e9	+	1.90366e9i	0.409132	+	0.148912i
$773$	2.73305e9	−	4.73377e9i	0.212823	−	0.368620i	−0.739774	−	0.672856i	$-0.765068\pi$
$773$	2.73305e9	−	4.73377e9i	0.212823	−	0.368620i	0.952597	+	0.304235i	$0.0984009\pi$
$774$		0			0
$775$	9.79838e9	+	1.69713e10i	0.756133	+	1.30966i
$776$	−1.32468e9	−	7.51261e9i	−0.101764	−	0.577132i
$777$		0			0
$778$	−2.55077e10	+	9.28403e9i	−1.94197	+	0.706818i
$779$	1.84807e9	−	1.04809e10i	0.140067	−	0.794361i
$780$		0			0
$781$	−1.06010e10	+	8.89528e9i	−0.796283	+	0.668161i
$782$	1.69093e9			0.126445
$783$		0			0
$784$	1.32790e9			0.0984149
$785$	−6.32929e8	+	5.31091e8i	−0.0466994	+	0.0391854i
$786$		0			0
$787$	1.58652e9	−	8.99761e9i	0.116020	−	0.657985i	−0.870219	−	0.492664i	$-0.836023\pi$
$787$	1.58652e9	−	8.99761e9i	0.116020	−	0.657985i	0.986240	−	0.165320i	$-0.0528658\pi$
$788$	−9.14870e9	+	3.32985e9i	−0.666067	+	0.242428i
$789$		0			0
$790$	−3.66441e8	−	2.07819e9i	−0.0264429	−	0.149965i
$791$	−1.27966e10	−	2.21643e10i	−0.919341	−	1.59234i
$792$		0			0
$793$	2.81371e9	−	4.87349e9i	0.200365	−	0.347043i
$794$	−2.59535e10	−	9.44630e9i	−1.84003	−	0.669715i
$795$		0			0
$796$	6.99082e9	+	5.86600e9i	0.491284	+	0.412236i
$797$	1.28943e10	+	1.08196e10i	0.902182	+	0.757020i	0.970616	−	0.240635i	$-0.0773558\pi$
$797$	1.28943e10	+	1.08196e10i	0.902182	+	0.757020i	−0.0684338	+	0.997656i	$0.521800\pi$
$798$		0			0
$799$	−1.64501e9	−	5.98734e8i	−0.114092	−	0.0415260i
$800$	−6.20164e9	+	1.07416e10i	−0.428244	+	0.741741i
$801$		0			0
$802$	7.49259e9	+	1.29775e10i	0.512887	+	0.888346i
$803$	8.00139e8	+	4.53782e9i	0.0545332	+	0.309273i
$804$		0			0
$805$	−2.49853e9	+	9.09390e8i	−0.168810	+	0.0614419i
$806$	1.82174e9	−	1.03316e10i	0.122550	−	0.695016i
$807$		0			0
$808$	4.78813e9	−	4.01772e9i	0.319320	−	0.267941i
$809$	−1.70637e10			−1.13306			−0.566532	−	0.824040i	$-0.691715\pi$
$809$	−1.70637e10			−1.13306			−0.566532	+	0.824040i	$0.691715\pi$
$810$		0			0
$811$	2.76727e10			1.82171			0.910854	−	0.412729i	$-0.135424\pi$
$811$	2.76727e10			1.82171			0.910854	+	0.412729i	$0.135424\pi$
$812$	4.79847e10	−	4.02639e10i	3.14526	−	2.63918i
$813$		0			0
$814$	−2.40851e9	+	1.36593e10i	−0.156517	+	0.887655i
$815$	−1.86517e9	+	6.78866e8i	−0.120689	+	0.0439271i
$816$		0			0
$817$	−6.69372e9	−	3.79620e10i	−0.429428	−	2.43541i
$818$	−3.99220e9	−	6.91469e9i	−0.255021	−	0.441709i
$819$		0			0
$820$	1.40327e9	−	2.43053e9i	0.0888776	−	0.153941i
$821$	−2.43417e9	−	8.85964e8i	−0.153514	−	0.0558747i	0.264120	−	0.964490i	$-0.414918\pi$
$821$	−2.43417e9	−	8.85964e8i	−0.153514	−	0.0558747i	−0.417634	+	0.908615i	$0.637141\pi$
$822$		0			0
$823$	2.00925e10	+	1.68596e10i	1.25642	+	1.05426i	0.996054	+	0.0887539i	$0.0282885\pi$
$823$	2.00925e10	+	1.68596e10i	1.25642	+	1.05426i	0.260368	+	0.965509i	$0.416156\pi$
$824$	−1.35753e10	−	1.13911e10i	−0.845290	−	0.709283i
$825$		0			0
$826$	−4.02269e10	−	1.46414e10i	−2.48363	−	0.903966i
$827$	1.28605e10	−	2.22750e10i	0.790656	−	1.36946i	−0.134905	−	0.990859i	$-0.543073\pi$
$827$	1.28605e10	−	2.22750e10i	0.790656	−	1.36946i	0.925561	−	0.378598i	$-0.123594\pi$
$828$		0			0
$829$	1.04933e10	+	1.81750e10i	0.639693	+	1.10798i	0.985500	+	0.169676i	$0.0542720\pi$
$829$	1.04933e10	+	1.81750e10i	0.639693	+	1.10798i	−0.345807	+	0.938306i	$0.612395\pi$
$830$	9.28477e7	+	5.26565e8i	0.00563635	+	0.0319653i
$831$		0			0
$832$	6.82804e9	−	2.48520e9i	0.411022	−	0.149600i
$833$	2.11877e8	−	1.20161e9i	0.0127006	−	0.0720289i
$834$		0			0
$835$	−2.89542e9	+	2.42955e9i	−0.172111	+	0.144419i
$836$	2.93877e10			1.73958
$837$		0			0
$838$	4.09184e10			2.40195
$839$	−1.50403e10	+	1.26203e10i	−0.879202	+	0.737738i	−0.966015	−	0.258486i	$-0.916776\pi$
$839$	−1.50403e10	+	1.26203e10i	−0.879202	+	0.737738i	0.0868127	+	0.996225i	$0.472332\pi$
$840$		0			0
$841$	7.43436e9	−	4.21623e10i	0.430980	−	2.44421i
$842$	1.20131e10	−	4.37241e9i	0.693526	−	0.252423i
$843$		0			0
$844$	−2.80729e9	−	1.59209e10i	−0.160727	−	0.911528i
$845$	−1.45775e9	−	2.52490e9i	−0.0831161	−	0.143961i
$846$		0			0
$847$	−4.95051e9	+	8.57454e9i	−0.279936	+	0.484863i
$848$	−1.04825e9	−	3.81532e8i	−0.0590310	−	0.0214855i
$849$		0			0
$850$	−2.20471e9	−	1.84997e9i	−0.123136	−	0.103324i
$851$	−7.62731e9	−	6.40008e9i	−0.424246	−	0.355985i
$852$		0			0
$853$	−1.17545e10	−	4.27827e9i	−0.648457	−	0.236019i	−0.00321183	−	0.999995i	$-0.501022\pi$
$853$	−1.17545e10	−	4.27827e9i	−0.648457	−	0.236019i	−0.645245	+	0.763976i	$0.723245\pi$
$854$	−2.83635e10	+	4.91271e10i	−1.55832	+	2.69910i
$855$		0			0
$856$	−3.07704e9	−	5.32959e9i	−0.167677	−	0.290426i
$857$	3.27540e9	+	1.85757e10i	0.177759	+	1.00812i	0.934911	+	0.354883i	$0.115479\pi$
$857$	3.27540e9	+	1.85757e10i	0.177759	+	1.00812i	−0.757152	+	0.653239i	$0.773410\pi$
$858$		0			0
$859$	9.36714e8	−	3.40936e8i	0.0504232	−	0.0183526i	−0.316685	−	0.948531i	$-0.602570\pi$
$859$	9.36714e8	−	3.40936e8i	0.0504232	−	0.0183526i	0.367109	+	0.930178i	$0.380348\pi$
$860$	1.76519e9	−	1.00109e10i	0.0946338	−	0.536695i
$861$		0			0
$862$	−1.65538e10	+	1.38903e10i	−0.880283	+	0.738645i
$863$	7.17408e9			0.379952			0.189976	−	0.981789i	$-0.439159\pi$
$863$	7.17408e9			0.379952			0.189976	+	0.981789i	$0.439159\pi$
$864$		0			0
$865$	1.71077e9			0.0898740
$866$	7.42651e9	−	6.23158e9i	0.388573	−	0.326051i
$867$		0			0
$868$	−1.15055e10	+	6.52507e10i	−0.597152	+	3.38662i
$869$	−7.11781e9	+	2.59067e9i	−0.367940	+	0.133919i
$870$		0			0
$871$	−3.92251e8	−	2.22457e9i	−0.0201141	−	0.114073i
$872$	8.20455e9	+	1.42107e10i	0.419032	+	0.725784i
$873$		0			0
$874$	−1.68360e10	+	2.91608e10i	−0.852999	+	1.47744i
$875$	8.64754e9	+	3.14745e9i	0.436379	+	0.158829i
$876$		0			0
$877$	6.00544e9	+	5.03916e9i	0.300640	+	0.252267i	0.780610	−	0.625018i	$-0.214908\pi$
$877$	6.00544e9	+	5.03916e9i	0.300640	+	0.252267i	−0.479971	+	0.877284i	$0.659353\pi$
$878$	3.50541e10	+	2.94139e10i	1.74787	+	1.46663i
$879$		0			0
$880$	3.53501e8	+	1.28664e8i	0.0174865	+	0.00636455i
$881$	2.14294e9	−	3.71168e9i	0.105583	−	0.182875i	−0.808393	−	0.588643i	$-0.799662\pi$
$881$	2.14294e9	−	3.71168e9i	0.105583	−	0.182875i	0.913976	+	0.405768i	$0.132996\pi$
$882$		0			0
$883$	−1.78123e10	−	3.08518e10i	−0.870678	−	1.50806i	−0.861296	−	0.508103i	$-0.830347\pi$
$883$	−1.78123e10	−	3.08518e10i	−0.870678	−	1.50806i	−0.00938227	−	0.999956i	$-0.502987\pi$
$884$	1.67624e8	+	9.50645e8i	0.00816120	+	0.0462845i
$885$		0			0
$886$	1.55477e10	−	5.65889e9i	0.751013	−	0.273347i
$887$	4.53735e9	−	2.57326e10i	0.218308	−	1.23809i	−0.656765	−	0.754095i	$-0.728076\pi$
$887$	4.53735e9	−	2.57326e10i	0.218308	−	1.23809i	0.875073	−	0.483991i	$-0.160813\pi$
$888$		0			0
$889$	3.51361e10	−	2.94827e10i	1.67725	−	1.40738i
$890$	5.85693e9			0.278487
$891$		0			0
$892$	5.17297e10			2.44041
$893$	2.67042e10	−	2.24075e10i	1.25487	−	1.05296i
$894$		0			0
$895$	−6.05642e8	+	3.43477e9i	−0.0282381	+	0.160146i
$896$	−4.53391e10	+	1.65021e10i	−2.10569	+	0.766409i
$897$		0			0
$898$	5.26358e9	+	2.98513e10i	0.242557	+	1.37561i
$899$	3.17658e10	+	5.50200e10i	1.45815	+	2.52558i
$900$		0			0
$901$	−5.12502e8	+	8.87680e8i	−0.0233431	+	0.0404315i
$902$	−1.51094e10	−	5.49936e9i	−0.685525	−	0.249511i
$903$		0			0
$904$	−2.64444e10	−	2.21895e10i	−1.19054	−	0.998983i
$905$	3.57538e9	+	3.00010e9i	0.160344	+	0.134544i
$906$		0			0
$907$	−3.16294e10	−	1.15121e10i	−1.40755	−	0.512307i	−0.477142	−	0.878826i	$-0.658327\pi$
$907$	−3.16294e10	−	1.15121e10i	−1.40755	−	0.512307i	−0.930411	+	0.366518i	$0.880550\pi$
$908$	−3.14409e10	+	5.44573e10i	−1.39378	+	2.41410i
$909$		0			0
$910$	−1.21136e9	−	2.09813e9i	−0.0532878	−	0.0922972i
$911$	−1.67880e9	−	9.52096e9i	−0.0735674	−	0.417221i	−0.999243	−	0.0389032i	$-0.987614\pi$
$911$	−1.67880e9	−	9.52096e9i	−0.0735674	−	0.417221i	0.925676	−	0.378318i	$-0.123498\pi$
$912$		0			0
$913$	1.80349e9	−	6.56416e8i	0.0784269	−	0.0285451i
$914$	4.02925e9	−	2.28510e10i	0.174547	−	0.989906i
$915$		0			0
$916$	−2.36090e10	+	1.98103e10i	−1.01495	+	0.851643i
$917$	8.68095e7			0.00371770
$918$		0			0
$919$	8.28632e9			0.352174			0.176087	−	0.984375i	$-0.443656\pi$
$919$	8.28632e9			0.352174			0.176087	+	0.984375i	$0.443656\pi$
$920$	−2.74731e9	+	2.30527e9i	−0.116319	+	0.0976033i
$921$		0			0
$922$	6.92069e9	−	3.92492e10i	0.290798	−	1.64920i
$923$	8.50593e9	−	3.09591e9i	0.356054	−	0.129593i
$924$		0			0
$925$	2.94280e9	+	1.66894e10i	0.122254	+	0.693339i
$926$	−1.77219e8	−	3.06952e8i	−0.00733452	−	0.0127038i
$927$		0			0
$928$	−2.01054e10	+	3.48236e10i	−0.825837	+	1.43039i
$929$	−2.42743e10	−	8.83511e9i	−0.993325	−	0.361541i	−0.206318	−	0.978485i	$-0.566148\pi$
$929$	−2.42743e10	−	8.83511e9i	−0.993325	−	0.361541i	−0.787007	+	0.616944i	$0.788370\pi$
$930$		0			0
$931$	1.86127e10	+	1.56179e10i	0.755938	+	0.634308i
$932$	−3.51365e10	−	2.94830e10i	−1.42168	−	1.19293i
$933$		0			0
$934$	5.38554e10	+	1.96018e10i	2.16279	+	0.787193i
$935$	1.72831e8	−	2.99352e8i	0.00691482	−	0.0119768i
$936$		0			0
$937$	−6.55436e9	−	1.13525e10i	−0.260281	−	0.450819i	0.706036	−	0.708176i	$-0.250482\pi$
$937$	−6.55436e9	−	1.13525e10i	−0.260281	−	0.450819i	−0.966316	+	0.257357i	$0.917148\pi$
$938$	3.95408e9	+	2.24247e10i	0.156436	+	0.887191i
$939$		0			0
$940$	8.63842e9	−	3.14413e9i	0.339224	−	0.123468i
$941$	−4.29320e9	+	2.43479e10i	−0.167964	+	0.952573i	0.777991	+	0.628276i	$0.216239\pi$
$941$	−4.29320e9	+	2.43479e10i	−0.167964	+	0.952573i	−0.945955	+	0.324297i	$0.894872\pi$
$942$		0			0
$943$	8.84207e9	−	7.41938e9i	0.343370	−	0.288122i
$944$	−4.34788e9			−0.168219
$945$		0			0
$946$	−5.82385e10			−2.23661
$947$	−2.37020e10	+	1.98883e10i	−0.906901	+	0.760980i	−0.971527	−	0.236930i	$-0.923859\pi$
$947$	−2.37020e10	+	1.98883e10i	−0.906901	+	0.760980i	0.0646262	+	0.997910i	$0.479414\pi$
$948$		0			0
$949$	5.23371e8	−	2.96818e9i	0.0198782	−	0.112735i
$950$	5.38551e10	−	1.96017e10i	2.03795	−	0.741755i
$951$		0			0
$952$	−6.82466e8	−	3.87045e9i	−0.0256361	−	0.145389i
$953$	−2.41145e10	−	4.17676e10i	−0.902514	−	1.56320i	−0.824220	−	0.566270i	$-0.808386\pi$
$953$	−2.41145e10	−	4.17676e10i	−0.902514	−	1.56320i	−0.0782942	−	0.996930i	$-0.524947\pi$
$954$		0			0
$955$	−4.31742e9	+	7.47799e9i	−0.160403	+	0.277826i
$956$	−7.21041e10	−	2.62438e10i	−2.66905	−	0.971456i
$957$		0			0
$958$	−3.93250e10	−	3.29976e10i	−1.44507	−	1.21256i
$959$	3.48287e9	+	2.92247e9i	0.127518	+	0.107000i
$960$		0			0
$961$	−3.72949e10	−	1.35742e10i	−1.35556	−	0.493382i
$962$	4.53620e9	−	7.85692e9i	0.164278	−	0.284538i
$963$		0			0
$964$	−2.64628e10	−	4.58349e10i	−0.951406	−	1.64788i
$965$	2.26380e8	+	1.28386e9i	0.00810946	+	0.0459910i
$966$		0			0
$967$	4.12916e10	−	1.50289e10i	1.46848	−	0.534484i	0.520795	−	0.853682i	$-0.325636\pi$
$967$	4.12916e10	−	1.50289e10i	1.46848	−	0.534484i	0.947688	+	0.319198i	$0.103414\pi$
$968$	−2.31903e9	+	1.31519e10i	−0.0821755	+	0.466041i
$969$		0			0
$970$	3.38890e9	−	2.84363e9i	0.119223	−	0.100040i
$971$	−6.06510e9			−0.212604			−0.106302	−	0.994334i	$-0.533901\pi$
$971$	−6.06510e9			−0.212604			−0.106302	+	0.994334i	$0.533901\pi$
$972$		0			0
$973$	1.92929e10			0.671432
$974$	−4.33649e10	+	3.63875e10i	−1.50377	+	1.26182i
$975$		0			0
$976$	−1.00048e9	+	5.67398e9i	−0.0344455	+	0.195350i
$977$	3.18719e10	−	1.16004e10i	1.09340	−	0.397964i	0.268518	−	0.963275i	$-0.413466\pi$
$977$	3.18719e10	−	1.16004e10i	1.09340	−	0.397964i	0.824878	+	0.565311i	$0.191244\pi$
$978$		0			0
$979$	−3.65062e9	−	2.07037e10i	−0.124345	−	0.705193i
$980$	3.20368e9	+	5.54894e9i	0.108732	+	0.188330i
$981$		0			0
$982$	1.69075e10	−	2.92847e10i	0.569757	−	0.986848i
$983$	3.63368e10	+	1.32255e10i	1.22014	+	0.444095i	0.870210	−	0.492681i	$-0.163983\pi$
$983$	3.63368e10	+	1.32255e10i	1.22014	+	0.444095i	0.349930	+	0.936776i	$0.386205\pi$
$984$		0			0
$985$	−1.74685e9	−	1.46578e9i	−0.0582410	−	0.0488700i
$986$	−7.14756e9	−	5.99752e9i	−0.237459	−	0.199252i
$987$		0			0
$988$	−1.80632e10	−	6.57448e9i	−0.595863	−	0.216876i
$989$	2.09035e10	−	3.62060e10i	0.687120	−	1.19013i
$990$		0			0
$991$	−7.09471e9	−	1.22884e10i	−0.231567	−	0.401086i	0.726702	−	0.686953i	$-0.241052\pi$
$991$	−7.09471e9	−	1.22884e10i	−0.231567	−	0.401086i	−0.958269	+	0.285866i	$0.907719\pi$
$992$	−7.38581e9	−	4.18870e10i	−0.240219	−	1.36235i
$993$		0			0
$994$	−8.57439e10	+	3.12082e10i	−2.76918	+	1.00790i
$995$	−3.71170e8	+	2.10501e9i	−0.0119452	+	0.0677444i
$996$		0			0
$997$	−9.27985e9	+	7.78672e9i	−0.296557	+	0.248841i	−0.778909	−	0.627136i	$-0.784227\pi$
$997$	−9.27985e9	+	7.78672e9i	−0.296557	+	0.248841i	0.482353	+	0.875977i	$0.339782\pi$
$998$	−3.39464e10			−1.08103
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.8.e.a.37.19		120
3.2	odd	2		27.8.e.a.22.2	yes	120
27.11	odd	18		27.8.e.a.16.2	✓	120
27.16	even	9	inner	81.8.e.a.46.19		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.8.e.a.16.2	✓	120	27.11	odd	18
27.8.e.a.22.2	yes	120	3.2	odd	2
81.8.e.a.37.19		120	1.1	even	1	trivial
81.8.e.a.46.19		120	27.16	even	9	inner

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(14.1817 - 11.8998i) q^{2} +(37.2867 - 211.463i) q^{4} +(47.2604 - 17.2014i) q^{5} +(-206.697 - 1172.23i) q^{7} +(-802.766 - 1390.43i) q^{8} +O(q^{10})\)	\(q+(14.1817 - 11.8998i) q^{2} +(37.2867 - 211.463i) q^{4} +(47.2604 - 17.2014i) q^{5} +(-206.697 - 1172.23i) q^{7} +(-802.766 - 1390.43i) q^{8} +(465.538 - 806.335i) q^{10} +(-3140.49 - 1143.04i) q^{11} +(1674.59 + 1405.15i) q^{13} +(-16880.7 - 14164.6i) q^{14} +(-2103.14 - 765.481i) q^{16} +(-1028.25 + 1780.98i) q^{17} +(-20475.8 - 35465.2i) q^{19} +(-1875.28 - 10635.2i) q^{20} +(-58139.3 + 21161.0i) q^{22} +(7712.48 - 43739.6i) q^{23} +(-57909.6 + 48591.9i) q^{25} +40469.5 q^{26} -255591. q^{28} +(-187740. + 157532. i) q^{29} +(45015.1 - 255293. i) q^{31} +(154179. - 56116.7i) q^{32} +(6611.07 + 37493.3i) q^{34} +(-29932.6 - 51844.8i) q^{35} +(112089. - 194144. i) q^{37} +(-712411. - 259296. i) q^{38} +(-61856.4 - 51903.7i) q^{40} +(199081. + 167049. i) q^{41} +(884528. + 321942. i) q^{43} +(-358810. + 621477. i) q^{44} +(-411118. - 712078. i) q^{46} +(147817. + 838311. i) q^{47} +(-557533. + 202925. i) q^{49} +(-243019. + 1.37823e6i) q^{50} +(359577. - 301721. i) q^{52} +498422. q^{53} -168083. q^{55} +(-1.46398e6 + 1.22843e6i) q^{56} +(-787854. + 4.46814e6i) q^{58} +(1.82549e6 - 664426. i) q^{59} +(-447017. - 2.53516e6i) q^{61} +(-2.39956e6 - 4.15615e6i) q^{62} +(1.66198e6 - 2.87863e6i) q^{64} +(103312. + 37602.6i) q^{65} +(-791577. - 664212. i) q^{67} +(338272. + 283844. i) q^{68} +(-1.04144e6 - 379053. i) q^{70} +(2.07039e6 - 3.58601e6i) q^{71} +(-689373. - 1.19403e6i) q^{73} +(-720671. - 4.08713e6i) q^{74} +(-8.26306e6 + 3.00751e6i) q^{76} +(-690787. + 3.91765e6i) q^{77} +(1.73621e6 - 1.45686e6i) q^{79} -112563. q^{80} +4.81115e6 q^{82} +(-439916. + 369134. i) q^{83} +(-17960.2 + 101857. i) q^{85} +(1.63751e7 - 5.96006e6i) q^{86} +(931752. + 5.28423e6i) q^{88} +(3.14525e6 + 5.44773e6i) q^{89} +(1.30103e6 - 2.25345e6i) q^{91} +(-8.96175e6 - 3.26181e6i) q^{92} +(1.20720e7 + 1.01297e7i) q^{94} +(-1.57775e6 - 1.32389e6i) q^{95} +(4.46485e6 + 1.62507e6i) q^{97} +(-5.49196e6 + 9.51236e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8}+O(q^{10}) \) 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8	\( 120 q + 6 q^{2} - 6 q^{4} + 219 q^{5} - 6 q^{7} + 4611 q^{8} - 3 q^{10} - 9399 q^{11} - 6 q^{13} - 16647 q^{14} + 378 q^{16} + 58959 q^{17} - 3 q^{19} - 240243 q^{20} + 105762 q^{22} + 144084 q^{23} - 107997 q^{25} - 443202 q^{26} - 12 q^{28} - 107886 q^{29} + 297975 q^{31} + 639576 q^{32} - 265806 q^{34} + 450672 q^{35} - 3 q^{37} + 145596 q^{38} + 283521 q^{40} - 227085 q^{41} - 1080969 q^{43} + 1205115 q^{44} - 3 q^{46} + 5184339 q^{47} + 976008 q^{49} - 2324559 q^{50} - 3366135 q^{52} - 5631750 q^{53} - 12 q^{55} - 5254923 q^{56} + 3884295 q^{58} + 12534492 q^{59} + 3865440 q^{61} + 9923646 q^{62} - 10223619 q^{64} - 17158395 q^{65} + 5567061 q^{67} - 19858455 q^{68} - 1020993 q^{70} + 18563877 q^{71} + 3770934 q^{73} + 36278085 q^{74} - 1156998 q^{76} - 8471751 q^{77} + 16415526 q^{79} - 101080590 q^{80} - 12 q^{82} - 3147699 q^{83} - 7672131 q^{85} + 70854834 q^{86} - 34323078 q^{88} + 54647613 q^{89} + 3315066 q^{91} - 73858515 q^{92} + 22126539 q^{94} - 32541447 q^{95} + 41250117 q^{97} + 88493274 q^{98}+O(q^{100}) \) 120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8 - 3 * q^10 - 9399 * q^11 - 6 * q^13 - 16647 * q^14 + 378 * q^16 + 58959 * q^17 - 3 * q^19 - 240243 * q^20 + 105762 * q^22 + 144084 * q^23 - 107997 * q^25 - 443202 * q^26 - 12 * q^28 - 107886 * q^29 + 297975 * q^31 + 639576 * q^32 - 265806 * q^34 + 450672 * q^35 - 3 * q^37 + 145596 * q^38 + 283521 * q^40 - 227085 * q^41 - 1080969 * q^43 + 1205115 * q^44 - 3 * q^46 + 5184339 * q^47 + 976008 * q^49 - 2324559 * q^50 - 3366135 * q^52 - 5631750 * q^53 - 12 * q^55 - 5254923 * q^56 + 3884295 * q^58 + 12534492 * q^59 + 3865440 * q^61 + 9923646 * q^62 - 10223619 * q^64 - 17158395 * q^65 + 5567061 * q^67 - 19858455 * q^68 - 1020993 * q^70 + 18563877 * q^71 + 3770934 * q^73 + 36278085 * q^74 - 1156998 * q^76 - 8471751 * q^77 + 16415526 * q^79 - 101080590 * q^80 - 12 * q^82 - 3147699 * q^83 - 7672131 * q^85 + 70854834 * q^86 - 34323078 * q^88 + 54647613 * q^89 + 3315066 * q^91 - 73858515 * q^92 + 22126539 * q^94 - 32541447 * q^95 + 41250117 * q^97 + 88493274 * q^98

Introduction

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