LMFDB - Embedded newform 162.8.c.j.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,8,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,8,0,-64,-105] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$50.6063741284$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.8.c.j.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-52.5000 - 90.9327i) q^{5} +(468.500 - 811.466i) q^{7} -512.000 q^{8} -840.000 q^{10} +(-2971.50 + 5146.79i) q^{11} +(-34.0000 - 58.8897i) q^{13} +(-3748.00 - 6491.73i) q^{14} +(-2048.00 + 3547.24i) q^{16} -5400.00 q^{17} -48382.0 q^{19} +(-3360.00 + 5819.69i) q^{20} +(23772.0 + 41174.3i) q^{22} +(321.000 + 555.988i) q^{23} +(33550.0 - 58110.3i) q^{25} -544.000 q^{26} -59968.0 q^{28} +(62967.0 - 109062. i) q^{29} +(80637.5 + 139668. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-21600.0 + 37412.3i) q^{34} -98385.0 q^{35} -414286. q^{37} +(-193528. + 335200. i) q^{38} +(26880.0 + 46557.5i) q^{40} +(313737. + 543408. i) q^{41} +(-285295. + 494145. i) q^{43} +380352. q^{44} +5136.00 q^{46} +(-269349. + 466526. i) q^{47} +(-27213.0 - 47134.3i) q^{49} +(-268400. - 464882. i) q^{50} +(-2176.00 + 3768.94i) q^{52} +356283. q^{53} +624015. q^{55} +(-239872. + 415470. i) q^{56} +(-503736. - 872496. i) q^{58} +(1.45541e6 + 2.52085e6i) q^{59} +(-1.34208e6 + 2.32456e6i) q^{61} +1.29020e6 q^{62} +262144. q^{64} +(-3570.00 + 6183.42i) q^{65} +(-1.34054e6 - 2.32188e6i) q^{67} +(172800. + 299298. i) q^{68} +(-393540. + 681631. i) q^{70} -3.70548e6 q^{71} -153151. q^{73} +(-1.65714e6 + 2.87026e6i) q^{74} +(1.54822e6 + 2.68160e6i) q^{76} +(2.78430e6 + 4.82254e6i) q^{77} +(3.78964e6 - 6.56386e6i) q^{79} +430080. q^{80} +5.01979e6 q^{82} +(-4.67300e6 + 8.09387e6i) q^{83} +(283500. + 491036. i) q^{85} +(2.28236e6 + 3.95316e6i) q^{86} +(1.52141e6 - 2.63516e6i) q^{88} +4.03360e6 q^{89} -63716.0 q^{91} +(20544.0 - 35583.3i) q^{92} +(2.15479e6 + 3.73221e6i) q^{94} +(2.54006e6 + 4.39950e6i) q^{95} +(2.87705e6 - 4.98319e6i) q^{97} -435408. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8 q^{2} - 64 q^{4} - 105 q^{5} + 937 q^{7} - 1024 q^{8} - 1680 q^{10} - 5943 q^{11} - 68 q^{13} - 7496 q^{14} - 4096 q^{16} - 10800 q^{17} - 96764 q^{19} - 6720 q^{20} + 47544 q^{22} + 642 q^{23}+ \cdots - 870816 q^{98}+O(q^{100}) $ 2 * q + 8 * q^2 - 64 * q^4 - 105 * q^5 + 937 * q^7 - 1024 * q^8 - 1680 * q^10 - 5943 * q^11 - 68 * q^13 - 7496 * q^14 - 4096 * q^16 - 10800 * q^17 - 96764 * q^19 - 6720 * q^20 + 47544 * q^22 + 642 * q^23 + 67100 * q^25 - 1088 * q^26 - 119936 * q^28 + 125934 * q^29 + 161275 * q^31 + 32768 * q^32 - 43200 * q^34 - 196770 * q^35 - 828572 * q^37 - 387056 * q^38 + 53760 * q^40 + 627474 * q^41 - 570590 * q^43 + 760704 * q^44 + 10272 * q^46 - 538698 * q^47 - 54426 * q^49 - 536800 * q^50 - 4352 * q^52 + 712566 * q^53 + 1248030 * q^55 - 479744 * q^56 - 1007472 * q^58 + 2910828 * q^59 - 2684168 * q^61 + 2580400 * q^62 + 524288 * q^64 - 7140 * q^65 - 2681078 * q^67 + 345600 * q^68 - 787080 * q^70 - 7410960 * q^71 - 306302 * q^73 - 3314288 * q^74 + 3096448 * q^76 + 5568591 * q^77 + 7579288 * q^79 + 860160 * q^80 + 10039584 * q^82 - 9345999 * q^83 + 567000 * q^85 + 4564720 * q^86 + 3042816 * q^88 + 8067204 * q^89 - 127432 * q^91 + 41088 * q^92 + 4309584 * q^94 + 5080110 * q^95 + 5754097 * q^97 - 870816 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−52.5000	−	90.9327i	−0.187830	−	0.325331i	0.756697	−	0.653766i	$-0.226812\pi$
$5$	−52.5000	−	90.9327i	−0.187830	−	0.325331i	−0.944526	+	0.328436i	$0.893479\pi$
$6$		0			0
$7$	468.500	−	811.466i	0.516258	−	0.894184i	−0.483564	−	0.875309i	$-0.660658\pi$
$7$	468.500	−	811.466i	0.516258	−	0.894184i	0.999822	−	0.0188755i	$-0.00600862\pi$
$8$	−512.000			−0.353553
$9$		0			0
$10$	−840.000			−0.265631
$11$	−2971.50	+	5146.79i	−0.673134	+	1.16590i	0.303877	+	0.952711i	$0.401719\pi$
$11$	−2971.50	+	5146.79i	−0.673134	+	1.16590i	−0.977011	+	0.213190i	$0.931615\pi$
$12$		0			0
$13$	−34.0000	−	58.8897i	−0.00429217	−	0.00743426i	0.863871	−	0.503713i	$-0.168033\pi$
$13$	−34.0000	−	58.8897i	−0.00429217	−	0.00743426i	−0.868164	+	0.496278i	$0.834700\pi$
$14$	−3748.00	−	6491.73i	−0.365049	−	0.632284i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−5400.00			−0.266577			−0.133288	−	0.991077i	$-0.542554\pi$
$17$	−5400.00			−0.266577			−0.133288	+	0.991077i	$0.542554\pi$
$18$		0			0
$19$	−48382.0			−1.61825			−0.809126	−	0.587635i	$-0.800059\pi$
$19$	−48382.0			−1.61825			−0.809126	+	0.587635i	$0.800059\pi$
$20$	−3360.00	+	5819.69i	−0.0939149	+	0.162665i
$21$		0			0
$22$	23772.0	+	41174.3i	0.475977	+	0.824417i
$23$	321.000	+	555.988i	0.00550120	+	0.00952836i	0.868763	−	0.495228i	$-0.164916\pi$
$23$	321.000	+	555.988i	0.00550120	+	0.00952836i	−0.863262	+	0.504757i	$0.831582\pi$
$24$		0			0
$25$	33550.0	−	58110.3i	0.429440	−	0.743812i
$26$	−544.000			−0.00607005
$27$		0			0
$28$	−59968.0			−0.516258
$29$	62967.0	−	109062.i	0.479424	−	0.830387i	−0.520297	−	0.853985i	$-0.674179\pi$
$29$	62967.0	−	109062.i	0.479424	−	0.830387i	0.999722	+	0.0235980i	$0.00751219\pi$
$30$		0			0
$31$	80637.5	+	139668.i	0.486151	+	0.842038i	0.999873	−	0.0159184i	$-0.00506719\pi$
$31$	80637.5	+	139668.i	0.486151	+	0.842038i	−0.513722	+	0.857956i	$0.671734\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$		0			0
$34$	−21600.0	+	37412.3i	−0.0942492	+	0.163244i
$35$	−98385.0			−0.387874
$36$		0			0
$37$	−414286.			−1.34460			−0.672302	−	0.740277i	$-0.734694\pi$
$37$	−414286.			−1.34460			−0.672302	+	0.740277i	$0.734694\pi$
$38$	−193528.	+	335200.i	−0.572139	+	0.990973i
$39$		0			0
$40$	26880.0	+	46557.5i	0.0664078	+	0.115022i
$41$	313737.	+	543408.i	0.710922	+	1.23135i	0.964511	+	0.264042i	$0.0850557\pi$
$41$	313737.	+	543408.i	0.710922	+	1.23135i	−0.253589	+	0.967312i	$0.581611\pi$
$42$		0			0
$43$	−285295.	+	494145.i	−0.547211	+	0.947797i	0.451254	+	0.892396i	$0.350977\pi$
$43$	−285295.	+	494145.i	−0.547211	+	0.947797i	−0.998464	+	0.0554009i	$0.982356\pi$
$44$	380352.			0.673134
$45$		0			0
$46$	5136.00			0.00777987
$47$	−269349.	+	466526.i	−0.378419	+	0.655441i	−0.990832	−	0.135097i	$-0.956865\pi$
$47$	−269349.	+	466526.i	−0.378419	+	0.655441i	0.612413	+	0.790538i	$0.290199\pi$
$48$		0			0
$49$	−27213.0	−	47134.3i	−0.0330438	−	0.0572336i
$50$	−268400.	−	464882.i	−0.303660	−	0.525954i
$51$		0			0
$52$	−2176.00	+	3768.94i	−0.00214609	+	0.00371713i
$53$	356283.			0.328723			0.164361	−	0.986400i	$-0.447444\pi$
$53$	356283.			0.328723			0.164361	+	0.986400i	$0.447444\pi$
$54$		0			0
$55$	624015.			0.505738
$56$	−239872.	+	415470.i	−0.182525	+	0.316142i
$57$		0			0
$58$	−503736.	−	872496.i	−0.339004	−	0.587172i
$59$	1.45541e6	+	2.52085e6i	0.922581	+	1.59796i	0.795406	+	0.606077i	$0.207258\pi$
$59$	1.45541e6	+	2.52085e6i	0.922581	+	1.59796i	0.127175	+	0.991880i	$0.459409\pi$
$60$		0			0
$61$	−1.34208e6	+	2.32456e6i	−0.757051	+	1.31125i	0.187297	+	0.982303i	$0.440027\pi$
$61$	−1.34208e6	+	2.32456e6i	−0.757051	+	1.31125i	−0.944348	+	0.328948i	$0.893306\pi$
$62$	1.29020e6			0.687521
$63$		0			0
$64$	262144.			0.125000
$65$	−3570.00	+	6183.42i	−0.00161240	+	0.00279275i
$66$		0			0
$67$	−1.34054e6	−	2.32188e6i	−0.544525	−	0.943145i	−0.998637	−	0.0521999i	$-0.983377\pi$
$67$	−1.34054e6	−	2.32188e6i	−0.544525	−	0.943145i	0.454112	−	0.890945i	$-0.349957\pi$
$68$	172800.	+	299298.i	0.0666442	+	0.115431i
$69$		0			0
$70$	−393540.	+	681631.i	−0.137134	+	0.237523i
$71$	−3.70548e6			−1.22868			−0.614342	−	0.789040i	$-0.710578\pi$
$71$	−3.70548e6			−1.22868			−0.614342	+	0.789040i	$0.710578\pi$
$72$		0			0
$73$	−153151.			−0.0460776			−0.0230388	−	0.999735i	$-0.507334\pi$
$73$	−153151.			−0.0460776			−0.0230388	+	0.999735i	$0.507334\pi$
$74$	−1.65714e6	+	2.87026e6i	−0.475389	+	0.823398i
$75$		0			0
$76$	1.54822e6	+	2.68160e6i	0.404563	+	0.700724i
$77$	2.78430e6	+	4.82254e6i	0.695021	+	1.20381i
$78$		0			0
$79$	3.78964e6	−	6.56386e6i	0.864776	−	1.49784i	−0.00249356	−	0.999997i	$-0.500794\pi$
$79$	3.78964e6	−	6.56386e6i	0.864776	−	1.49784i	0.867269	−	0.497839i	$-0.165873\pi$
$80$	430080.			0.0939149
$81$		0			0
$82$	5.01979e6			1.00540
$83$	−4.67300e6	+	8.09387e6i	−0.897062	+	1.55376i	−0.0658301	+	0.997831i	$0.520970\pi$
$83$	−4.67300e6	+	8.09387e6i	−0.897062	+	1.55376i	−0.831232	+	0.555926i	$0.812364\pi$
$84$		0			0
$85$	283500.	+	491036.i	0.0500711	+	0.0867256i
$86$	2.28236e6	+	3.95316e6i	0.386936	+	0.670193i
$87$		0			0
$88$	1.52141e6	−	2.63516e6i	0.237989	−	0.412209i
$89$	4.03360e6			0.606496			0.303248	−	0.952912i	$-0.401929\pi$
$89$	4.03360e6			0.606496			0.303248	+	0.952912i	$0.401929\pi$
$90$		0			0
$91$	−63716.0			−0.00886347
$92$	20544.0	−	35583.3i	0.00275060	−	0.00476418i
$93$		0			0
$94$	2.15479e6	+	3.73221e6i	0.267583	+	0.463467i
$95$	2.54006e6	+	4.39950e6i	0.303956	+	0.526467i
$96$		0			0
$97$	2.87705e6	−	4.98319e6i	0.320071	−	0.554379i	−0.660432	−	0.750886i	$-0.729627\pi$
$97$	2.87705e6	−	4.98319e6i	0.320071	−	0.554379i	0.980502	+	0.196507i	$0.0629599\pi$
$98$	−435408.			−0.0467310
$99$		0			0
$100$	−4.29440e6			−0.429440
$101$	−4.43961e6	+	7.68963e6i	−0.428766	+	0.742644i	−0.996764	−	0.0803857i	$-0.974385\pi$
$101$	−4.43961e6	+	7.68963e6i	−0.428766	+	0.742644i	0.567998	+	0.823030i	$0.307718\pi$
$102$		0			0
$103$	1.32783e6	+	2.29986e6i	0.119732	+	0.207382i	0.919662	−	0.392712i	$-0.128463\pi$
$103$	1.32783e6	+	2.29986e6i	0.119732	+	0.207382i	−0.799929	+	0.600094i	$0.795130\pi$
$104$	17408.0	+	30151.5i	0.00151751	+	0.00262841i
$105$		0			0
$106$	1.42513e6	−	2.46840e6i	0.116221	−	0.201301i
$107$	2.11234e7			1.66694			0.833471	−	0.552564i	$-0.186350\pi$
$107$	2.11234e7			1.66694			0.833471	+	0.552564i	$0.186350\pi$
$108$		0			0
$109$	−1.84213e7			−1.36247			−0.681237	−	0.732063i	$-0.738558\pi$
$109$	−1.84213e7			−1.36247			−0.681237	+	0.732063i	$0.738558\pi$
$110$	2.49606e6	−	4.32330e6i	0.178805	−	0.309700i
$111$		0			0
$112$	1.91898e6	+	3.32376e6i	0.129064	+	0.223546i
$113$	9.31424e6	+	1.61327e7i	0.607258	+	1.05180i	0.991690	+	0.128648i	$0.0410637\pi$
$113$	9.31424e6	+	1.61327e7i	0.607258	+	1.05180i	−0.384433	+	0.923153i	$0.625603\pi$
$114$		0			0
$115$	33705.0	−	58378.8i	0.00206658	−	0.00357942i
$116$	−8.05978e6			−0.479424
$117$		0			0
$118$	2.32866e7			1.30473
$119$	−2.52990e6	+	4.38192e6i	−0.137622	+	0.238369i
$120$		0			0
$121$	−7.91604e6	−	1.37110e7i	−0.406218	−	0.703590i
$122$	1.07367e7	+	1.85965e7i	0.535316	+	0.927195i
$123$		0			0
$124$	5.16080e6	−	8.93877e6i	0.243075	−	0.421019i
$125$	−1.52486e7			−0.698306
$126$		0			0
$127$	−2.58380e6			−0.111930			−0.0559649	−	0.998433i	$-0.517823\pi$
$127$	−2.58380e6			−0.111930			−0.0559649	+	0.998433i	$0.517823\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$		0			0
$130$	28560.0	+	49467.4i	0.00114014	+	0.00197477i
$131$	−2.09642e7	−	3.63110e7i	−0.814757	−	1.41120i	−0.909503	−	0.415698i	$-0.863537\pi$
$131$	−2.09642e7	−	3.63110e7i	−0.814757	−	1.41120i	0.0947460	−	0.995501i	$-0.469796\pi$
$132$		0			0
$133$	−2.26670e7	+	3.92603e7i	−0.835435	+	1.44702i
$134$	−2.14486e7			−0.770074
$135$		0			0
$136$	2.76480e6			0.0942492
$137$	−633309.	+	1.09692e6i	−0.0210423	+	0.0364464i	−0.876355	−	0.481666i	$-0.840032\pi$
$137$	−633309.	+	1.09692e6i	−0.0210423	+	0.0364464i	0.855312	+	0.518112i	$0.173365\pi$
$138$		0			0
$139$	−1.15281e7	−	1.99672e7i	−0.364086	−	0.630616i	0.624543	−	0.780991i	$-0.285285\pi$
$139$	−1.15281e7	−	1.99672e7i	−0.364086	−	0.630616i	−0.988629	+	0.150374i	$0.951952\pi$
$140$	3.14832e6	+	5.45305e6i	0.0969685	+	0.167954i
$141$		0			0
$142$	−1.48219e7	+	2.56723e7i	−0.434405	+	0.752412i
$143$	404124.			0.0115568
$144$		0			0
$145$	−1.32231e7			−0.360200
$146$	−612604.	+	1.06106e6i	−0.0162909	+	0.0282167i
$147$		0			0
$148$	1.32572e7	+	2.29621e7i	0.336151	+	0.582230i
$149$	−1.19133e7	−	2.06345e7i	−0.295040	−	0.511024i	0.679954	−	0.733255i	$-0.262000\pi$
$149$	−1.19133e7	−	2.06345e7i	−0.295040	−	0.511024i	−0.974994	+	0.222230i	$0.928666\pi$
$150$		0			0
$151$	−2.25247e7	+	3.90139e7i	−0.532401	+	0.922146i	0.466883	+	0.884319i	$0.345377\pi$
$151$	−2.25247e7	+	3.90139e7i	−0.532401	+	0.922146i	−0.999284	+	0.0378270i	$0.987956\pi$
$152$	2.47716e7			0.572139
$153$		0			0
$154$	4.45487e7			0.982908
$155$	8.46694e6	−	1.46652e7i	0.182627	−	0.316320i
$156$		0			0
$157$	−1.76288e7	−	3.05339e7i	−0.363558	−	0.629700i	0.624986	−	0.780636i	$-0.285105\pi$
$157$	−1.76288e7	−	3.05339e7i	−0.363558	−	0.629700i	−0.988544	+	0.150936i	$0.951771\pi$
$158$	−3.03172e7	−	5.25108e7i	−0.611489	−	1.05913i
$159$		0			0
$160$	1.72032e6	−	2.97968e6i	0.0332039	−	0.0575109i
$161$	601554.			0.0113601
$162$		0			0
$163$	−6.55009e7			−1.18465			−0.592326	−	0.805699i	$-0.701790\pi$
$163$	−6.55009e7			−1.18465			−0.592326	+	0.805699i	$0.701790\pi$
$164$	2.00792e7	−	3.47781e7i	0.355461	−	0.615677i
$165$		0			0
$166$	3.73840e7	+	6.47510e7i	0.634319	+	1.09867i
$167$	−2.64045e7	−	4.57339e7i	−0.438703	−	0.759855i	0.558887	−	0.829244i	$-0.311228\pi$
$167$	−2.64045e7	−	4.57339e7i	−0.438703	−	0.759855i	−0.997590	+	0.0693886i	$0.977895\pi$
$168$		0			0
$169$	3.13719e7	−	5.43378e7i	0.499963	−	0.865962i
$170$	4.53600e6			0.0708112
$171$		0			0
$172$	3.65178e7			0.547211
$173$	5.53665e7	−	9.58976e7i	0.812991	−	1.40814i	−0.0977712	−	0.995209i	$-0.531171\pi$
$173$	5.53665e7	−	9.58976e7i	0.812991	−	1.40814i	0.910762	−	0.412932i	$-0.135495\pi$
$174$		0			0
$175$	−3.14364e7	−	5.44494e7i	−0.443403	−	0.767997i
$176$	−1.21713e7	−	2.10812e7i	−0.168283	−	0.291475i
$177$		0			0
$178$	1.61344e7	−	2.79456e7i	0.214429	−	0.371402i
$179$	−1.19427e7			−0.155639			−0.0778195	−	0.996967i	$-0.524796\pi$
$179$	−1.19427e7			−0.155639			−0.0778195	+	0.996967i	$0.524796\pi$
$180$		0			0
$181$	−7.95226e7			−0.996817			−0.498408	−	0.866942i	$-0.666082\pi$
$181$	−7.95226e7			−0.996817			−0.498408	+	0.866942i	$0.666082\pi$
$182$	−254864.	+	441437.i	−0.00313371	+	0.00542774i
$183$		0			0
$184$	−164352.	−	284666.i	−0.00194497	−	0.00336878i
$185$	2.17500e7	+	3.76721e7i	0.252556	+	0.437441i
$186$		0			0
$187$	1.60461e7	−	2.77927e7i	0.179442	−	0.310802i
$188$	3.44767e7			0.378419
$189$		0			0
$190$	4.06409e7			0.429858
$191$	3.01157e6	−	5.21620e6i	0.0312735	−	0.0541673i	−0.849965	−	0.526839i	$-0.823377\pi$
$191$	3.01157e6	−	5.21620e6i	0.0312735	−	0.0541673i	0.881239	+	0.472672i	$0.156710\pi$
$192$		0			0
$193$	2.92925e7	+	5.07361e7i	0.293296	+	0.508003i	0.974587	−	0.224009i	$-0.0719147\pi$
$193$	2.92925e7	+	5.07361e7i	0.293296	+	0.508003i	−0.681291	+	0.732012i	$0.738581\pi$
$194$	−2.30164e7	−	3.98656e7i	−0.226324	−	0.392005i
$195$		0			0
$196$	−1.74163e6	+	3.01660e6i	−0.0165219	+	0.0286168i
$197$	−1.68414e8			−1.56945			−0.784725	−	0.619844i	$-0.787196\pi$
$197$	−1.68414e8			−1.56945			−0.784725	+	0.619844i	$0.787196\pi$
$198$		0			0
$199$	−1.01669e8			−0.914543			−0.457271	−	0.889327i	$-0.651173\pi$
$199$	−1.01669e8			−0.914543			−0.457271	+	0.889327i	$0.651173\pi$
$200$	−1.71776e7	+	2.97525e7i	−0.151830	+	0.262977i
$201$		0			0
$202$	3.55169e7	+	6.15171e7i	0.303183	+	0.525129i
$203$	−5.90001e7	−	1.02191e8i	−0.495013	−	0.857387i
$204$		0			0
$205$	3.29424e7	−	5.70579e7i	0.267065	−	0.462570i
$206$	2.12452e7			0.169327
$207$		0			0
$208$	278528.			0.00214609
$209$	1.43767e8	−	2.49012e8i	1.08930	−	1.88672i
$210$		0			0
$211$	4.31910e7	+	7.48090e7i	0.316523	+	0.548233i	0.979760	−	0.200176i	$-0.0641513\pi$
$211$	4.31910e7	+	7.48090e7i	0.316523	+	0.548233i	−0.663237	+	0.748409i	$0.730818\pi$
$212$	−1.14011e7	−	1.97472e7i	−0.0821806	−	0.142341i
$213$		0			0
$214$	8.44935e7	−	1.46347e8i	0.589353	−	1.02079i
$215$	5.99120e7			0.411130
$216$		0			0
$217$	1.51115e8			1.00392
$218$	−7.36854e7	+	1.27627e8i	−0.481708	+	0.834342i
$219$		0			0
$220$	−1.99685e7	−	3.45864e7i	−0.126435	−	0.218991i
$221$	183600.	+	318005.i	0.00114419	+	0.00198180i
$222$		0			0
$223$	−2.08087e7	+	3.60416e7i	−0.125654	+	0.217639i	−0.921988	−	0.387217i	$-0.873436\pi$
$223$	−2.08087e7	+	3.60416e7i	−0.125654	+	0.217639i	0.796334	+	0.604857i	$0.206770\pi$
$224$	3.07036e7			0.182525
$225$		0			0
$226$	1.49028e8			0.858792
$227$	−1.04658e8	+	1.81272e8i	−0.593855	+	1.02859i	0.399852	+	0.916580i	$0.369061\pi$
$227$	−1.04658e8	+	1.81272e8i	−0.593855	+	1.02859i	−0.993707	+	0.112007i	$0.964272\pi$
$228$		0			0
$229$	−1.66459e8	−	2.88316e8i	−0.915976	−	1.58652i	−0.805466	−	0.592642i	$-0.798085\pi$
$229$	−1.66459e8	−	2.88316e8i	−0.915976	−	1.58652i	−0.110510	−	0.993875i	$-0.535248\pi$
$230$	−269640.	−	467030.i	−0.00146129	−	0.00253103i
$231$		0			0
$232$	−3.22391e7	+	5.58398e7i	−0.169502	+	0.293586i
$233$	7.95428e7			0.411960			0.205980	−	0.978556i	$-0.433962\pi$
$233$	7.95428e7			0.411960			0.205980	+	0.978556i	$0.433962\pi$
$234$		0			0
$235$	5.65633e7			0.284313
$236$	9.31465e7	−	1.61334e8i	0.461291	−	0.798979i
$237$		0			0
$238$	2.02392e7	+	3.50553e7i	0.0973137	+	0.168552i
$239$	−7.34502e7	−	1.27220e8i	−0.348017	−	0.602783i	0.637880	−	0.770136i	$-0.279812\pi$
$239$	−7.34502e7	−	1.27220e8i	−0.348017	−	0.602783i	−0.985897	+	0.167352i	$0.946478\pi$
$240$		0			0
$241$	1.51528e7	−	2.62454e7i	0.0697320	−	0.120779i	−0.829051	−	0.559173i	$-0.811119\pi$
$241$	1.51528e7	−	2.62454e7i	0.0697320	−	0.120779i	0.898783	+	0.438393i	$0.144452\pi$
$242$	−1.26657e8			−0.574479
$243$		0			0
$244$	1.71787e8			0.757051
$245$	−2.85736e6	+	4.94910e6i	−0.0124132	+	0.0215003i
$246$		0			0
$247$	1.64499e6	+	2.84920e6i	0.00694582	+	0.0120305i
$248$	−4.12864e7	−	7.15101e7i	−0.171880	−	0.297705i
$249$		0			0
$250$	−6.09945e7	+	1.05646e8i	−0.246888	+	0.427623i
$251$	1.47027e8			0.586866			0.293433	−	0.955980i	$-0.405202\pi$
$251$	1.47027e8			0.586866			0.293433	+	0.955980i	$0.405202\pi$
$252$		0			0
$253$	−3.81541e6			−0.0148122
$254$	−1.03352e7	+	1.79011e7i	−0.0395732	+	0.0685427i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.83888e8	+	3.18503e8i	0.675752	+	1.17044i	0.976248	+	0.216654i	$0.0695144\pi$
$257$	1.83888e8	+	3.18503e8i	0.675752	+	1.17044i	−0.300496	+	0.953783i	$0.597152\pi$
$258$		0			0
$259$	−1.94093e8	+	3.36179e8i	−0.694162	+	1.20232i
$260$	456960.			0.00161240
$261$		0			0
$262$	−3.35427e8			−1.15224
$263$	−1.62928e8	+	2.82200e8i	−0.552270	+	0.956559i	0.445840	+	0.895112i	$0.352905\pi$
$263$	−1.62928e8	+	2.82200e8i	−0.552270	+	0.956559i	−0.998110	+	0.0614470i	$0.980428\pi$
$264$		0			0
$265$	−1.87049e7	−	3.23978e7i	−0.0617439	−	0.106944i
$266$	1.81336e8	+	3.14083e8i	0.590742	+	1.02319i
$267$		0			0
$268$	−8.57945e7	+	1.48600e8i	−0.272262	+	0.471572i
$269$	−3.39029e8			−1.06195			−0.530976	−	0.847387i	$-0.678174\pi$
$269$	−3.39029e8			−1.06195			−0.530976	+	0.847387i	$0.678174\pi$
$270$		0			0
$271$	−2.50778e6			−0.00765416			−0.00382708	−	0.999993i	$-0.501218\pi$
$271$	−2.50778e6			−0.00765416			−0.00382708	+	0.999993i	$0.501218\pi$
$272$	1.10592e7	−	1.91551e7i	0.0333221	−	0.0577156i
$273$		0			0
$274$	5.06647e6	+	8.77539e6i	0.0148792	+	0.0257715i
$275$	1.99388e8	+	3.45350e8i	0.578141	+	1.00137i
$276$		0			0
$277$	2.64293e7	−	4.57768e7i	0.0747146	−	0.129410i	−0.826248	−	0.563307i	$-0.809529\pi$
$277$	2.64293e7	−	4.57768e7i	0.0747146	−	0.129410i	0.900962	+	0.433898i	$0.142862\pi$
$278$	−1.84449e8			−0.514896
$279$		0			0
$280$	5.03731e7			0.137134
$281$	−2.69776e8	+	4.67266e8i	−0.725322	+	1.25630i	0.233519	+	0.972352i	$0.424976\pi$
$281$	−2.69776e8	+	4.67266e8i	−0.725322	+	1.25630i	−0.958841	+	0.283943i	$0.908357\pi$
$282$		0			0
$283$	−3.29283e7	−	5.70334e7i	−0.0863607	−	0.149581i	0.819609	−	0.572923i	$-0.194190\pi$
$283$	−3.29283e7	−	5.70334e7i	−0.0863607	−	0.149581i	−0.905970	+	0.423341i	$0.860857\pi$
$284$	1.18575e8	+	2.05379e8i	0.307171	+	0.532036i
$285$		0			0
$286$	1.61650e6	−	2.79985e6i	0.00408595	−	0.00707708i
$287$	5.87943e8			1.46808
$288$		0			0
$289$	−3.81179e8			−0.928937
$290$	−5.28923e7	+	9.16121e7i	−0.127350	+	0.220577i
$291$		0			0
$292$	4.90083e6	+	8.48849e6i	0.0115194	+	0.0199522i
$293$	1.76292e7	+	3.05346e7i	0.0409444	+	0.0709179i	0.885771	−	0.464122i	$-0.153630\pi$
$293$	1.76292e7	+	3.05346e7i	0.0409444	+	0.0709179i	−0.844827	+	0.535040i	$0.820297\pi$
$294$		0			0
$295$	1.52818e8	−	2.64689e8i	0.346576	−	0.600288i
$296$	2.12114e8			0.475389
$297$		0			0
$298$	−1.90613e8			−0.417249
$299$	21828.0	−	37807.2i	4.72242e−5	−	8.17947e-5i
$300$		0			0
$301$	2.67321e8	+	4.63014e8i	0.565003	+	0.978614i
$302$	1.80197e8	+	3.12111e8i	0.376465	+	0.652056i
$303$		0			0
$304$	9.90863e7	−	1.71623e8i	0.202282	−	0.350362i
$305$	2.81838e8			0.568787
$306$		0			0
$307$	1.14259e8			0.225376			0.112688	−	0.993630i	$-0.464054\pi$
$307$	1.14259e8			0.225376			0.112688	+	0.993630i	$0.464054\pi$
$308$	1.78195e8	−	3.08643e8i	0.347510	−	0.601906i
$309$		0			0
$310$	−6.77355e7	−	1.17321e8i	−0.129137	−	0.223672i
$311$	−7.77314e7	−	1.34635e8i	−0.146533	−	0.253802i	0.783411	−	0.621504i	$-0.213478\pi$
$311$	−7.77314e7	−	1.34635e8i	−0.146533	−	0.253802i	−0.929944	+	0.367702i	$0.880145\pi$
$312$		0			0
$313$	−1.91150e8	+	3.31081e8i	−0.352345	+	0.610280i	−0.986660	−	0.162795i	$-0.947949\pi$
$313$	−1.91150e8	+	3.31081e8i	−0.352345	+	0.610280i	0.634315	+	0.773075i	$0.281282\pi$
$314$	−2.82060e8			−0.514148
$315$		0			0
$316$	−4.85074e8			−0.864776
$317$	−2.22443e8	+	3.85283e8i	−0.392204	+	0.679317i	−0.992740	−	0.120281i	$-0.961621\pi$
$317$	−2.22443e8	+	3.85283e8i	−0.392204	+	0.679317i	0.600536	+	0.799598i	$0.294954\pi$
$318$		0			0
$319$	3.74213e8	+	6.48156e8i	0.645433	+	1.11792i
$320$	−1.37626e7	−	2.38375e7i	−0.0234787	−	0.0406663i
$321$		0			0
$322$	2.40622e6	−	4.16769e6i	0.00401642	−	0.00695664i
$323$	2.61263e8			0.431389
$324$		0			0
$325$	−4.56280e6			−0.00737292
$326$	−2.62004e8	+	4.53804e8i	−0.418838	+	0.725448i
$327$		0			0
$328$	−1.60633e8	−	2.78225e8i	−0.251349	−	0.435349i
$329$	2.52380e8	+	4.37135e8i	0.390723	+	0.676753i
$330$		0			0
$331$	2.75444e8	−	4.77083e8i	0.417480	−	0.723096i	−0.578205	−	0.815891i	$-0.696247\pi$
$331$	2.75444e8	−	4.77083e8i	0.417480	−	0.723096i	0.995685	+	0.0927950i	$0.0295801\pi$
$332$	5.98144e8			0.897062
$333$		0			0
$334$	−4.22472e8			−0.620419
$335$	−1.40757e8	+	2.43798e8i	−0.204556	+	0.354301i
$336$		0			0
$337$	2.48397e8	+	4.30236e8i	0.353542	+	0.612353i	0.986867	−	0.161533i	$-0.0516438\pi$
$337$	2.48397e8	+	4.30236e8i	0.353542	+	0.612353i	−0.633325	+	0.773886i	$0.718310\pi$
$338$	−2.50976e8	−	4.34702e8i	−0.353527	−	0.612327i
$339$		0			0
$340$	1.81440e7	−	3.14263e7i	0.0250355	−	0.0433628i
$341$	−9.58457e8			−1.30898
$342$		0			0
$343$	7.20663e8			0.964279
$344$	1.46071e8	−	2.53002e8i	0.193468	−	0.335097i
$345$		0			0
$346$	−4.42932e8	−	7.67180e8i	−0.574871	−	0.995706i
$347$	1.25581e8	+	2.17512e8i	0.161350	+	0.279467i	0.935353	−	0.353715i	$-0.115082\pi$
$347$	1.25581e8	+	2.17512e8i	0.161350	+	0.279467i	−0.774003	+	0.633182i	$0.781748\pi$
$348$		0			0
$349$	2.41457e8	−	4.18216e8i	0.304054	−	0.526637i	−0.672996	−	0.739646i	$-0.734993\pi$
$349$	2.41457e8	−	4.18216e8i	0.304054	−	0.526637i	0.977050	+	0.213009i	$0.0683263\pi$
$350$	−5.02982e8			−0.627067
$351$		0			0
$352$	−1.94740e8			−0.237989
$353$	2.43467e8	−	4.21698e8i	0.294598	−	0.510258i	−0.680294	−	0.732940i	$-0.738148\pi$
$353$	2.43467e8	−	4.21698e8i	0.294598	−	0.510258i	0.974891	+	0.222682i	$0.0714811\pi$
$354$		0			0
$355$	1.94538e8	+	3.36949e8i	0.230783	+	0.399729i
$356$	−1.29075e8	−	2.23565e8i	−0.151624	−	0.262621i
$357$		0			0
$358$	−4.77710e7	+	8.27417e7i	−0.0550267	+	0.0953090i
$359$	−4.59969e8			−0.524684			−0.262342	−	0.964975i	$-0.584495\pi$
$359$	−4.59969e8			−0.524684			−0.262342	+	0.964975i	$0.584495\pi$
$360$		0			0
$361$	1.44695e9			1.61874
$362$	−3.18090e8	+	5.50949e8i	−0.352428	+	0.610423i
$363$		0			0
$364$	2.03891e6	+	3.53150e6i	0.00221587	+	0.00383799i
$365$	8.04043e6	+	1.39264e7i	0.00865474	+	0.0149905i
$366$		0			0
$367$	−3.26252e8	+	5.65084e8i	−0.344526	+	0.596736i	−0.985267	−	0.171021i	$-0.945294\pi$
$367$	−3.26252e8	+	5.65084e8i	−0.344526	+	0.596736i	0.640742	+	0.767756i	$0.278627\pi$
$368$	−2.62963e6			−0.00275060
$369$		0			0
$370$	3.48000e8			0.357169
$371$	1.66919e8	−	2.89111e8i	0.169706	−	0.293939i
$372$		0			0
$373$	−9.58955e8	−	1.66096e9i	−0.956791	−	1.65721i	−0.730214	−	0.683218i	$-0.760580\pi$
$373$	−9.58955e8	−	1.66096e9i	−0.956791	−	1.65721i	−0.226577	−	0.973993i	$-0.572754\pi$
$374$	−1.28369e8	−	2.22341e8i	−0.126885	−	0.219771i
$375$		0			0
$376$	1.37907e8	−	2.38861e8i	0.133791	−	0.231733i
$377$	−8.56351e6			−0.00823109
$378$		0			0
$379$	1.43151e9			1.35070			0.675348	−	0.737499i	$-0.263993\pi$
$379$	1.43151e9			1.35070			0.675348	+	0.737499i	$0.263993\pi$
$380$	1.62564e8	−	2.81568e8i	0.151978	−	0.263233i
$381$		0			0
$382$	−2.40926e7	−	4.17296e7i	−0.0221137	−	0.0383021i
$383$	6.99297e7	+	1.21122e8i	0.0636013	+	0.110161i	0.896073	−	0.443907i	$-0.146408\pi$
$383$	6.99297e7	+	1.21122e8i	0.0636013	+	0.110161i	−0.832471	+	0.554068i	$0.813075\pi$
$384$		0			0
$385$	2.92351e8	−	5.06367e8i	0.261091	−	0.452223i
$386$	4.68680e8			0.414783
$387$		0			0
$388$	−3.68262e8			−0.320071
$389$	8.87960e8	−	1.53799e9i	0.764838	−	1.32474i	−0.175494	−	0.984481i	$-0.556152\pi$
$389$	8.87960e8	−	1.53799e9i	0.764838	−	1.32474i	0.940332	−	0.340258i	$-0.110515\pi$
$390$		0			0
$391$	−1.73340e6	−	3.00234e6i	−0.00146649	−	0.00254004i
$392$	1.39331e7	+	2.41328e7i	0.0116828	+	0.0202351i
$393$		0			0
$394$	−6.73658e8	+	1.16681e9i	−0.554884	+	0.961088i
$395$	−7.95825e8			−0.649722
$396$		0			0
$397$	−1.05301e9			−0.844630			−0.422315	−	0.906449i	$-0.638782\pi$
$397$	−1.05301e9			−0.844630			−0.422315	+	0.906449i	$0.638782\pi$
$398$	−4.06677e8	+	7.04385e8i	−0.323340	+	0.560041i
$399$		0			0
$400$	1.37421e8	+	2.38020e8i	0.107360	+	0.185953i
$401$	−1.16506e9	−	2.01794e9i	−0.902284	−	1.56280i	−0.824522	−	0.565830i	$-0.808556\pi$
$401$	−1.16506e9	−	2.01794e9i	−0.902284	−	1.56280i	−0.0777620	−	0.996972i	$-0.524777\pi$
$402$		0			0
$403$	5.48335e6	−	9.49744e6i	0.00417329	−	0.00722835i
$404$	5.68270e8			0.428766
$405$		0			0
$406$	−9.44001e8			−0.700054
$407$	1.23105e9	−	2.13224e9i	0.905098	−	1.56768i
$408$		0			0
$409$	7.52109e7	+	1.30269e8i	0.0543562	+	0.0941478i	0.891923	−	0.452187i	$-0.149356\pi$
$409$	7.52109e7	+	1.30269e8i	0.0543562	+	0.0941478i	−0.837567	+	0.546335i	$0.816023\pi$
$410$	−2.63539e8	−	4.56463e8i	−0.188843	−	0.327086i
$411$		0			0
$412$	8.49809e7	−	1.47191e8i	0.0598661	−	0.103691i
$413$	2.72745e9			1.90516
$414$		0			0
$415$	9.81330e8			0.673980
$416$	1.11411e6	−	1.92970e6i	0.000758756	−	0.00131420i
$417$		0			0
$418$	−1.15014e9	−	1.99210e9i	−0.770251	−	1.33411i
$419$	−4.55716e8	−	7.89324e8i	−0.302653	−	0.524211i	0.674083	−	0.738656i	$-0.264539\pi$
$419$	−4.55716e8	−	7.89324e8i	−0.302653	−	0.524211i	−0.976736	+	0.214445i	$0.931206\pi$
$420$		0			0
$421$	3.76741e8	−	6.52535e8i	0.246068	−	0.426203i	−0.716363	−	0.697728i	$-0.754195\pi$
$421$	3.76741e8	−	6.52535e8i	0.246068	−	0.426203i	0.962431	+	0.271525i	$0.0875279\pi$
$422$	6.91056e8			0.447631
$423$		0			0
$424$	−1.82417e8			−0.116221
$425$	−1.81170e8	+	3.13796e8i	−0.114479	+	0.198283i
$426$		0			0
$427$	1.25753e9	+	2.17811e9i	0.781667	+	1.35389i
$428$	−6.75948e8	−	1.17078e9i	−0.416735	−	0.721807i
$429$		0			0
$430$	2.39648e8	−	4.15082e8i	0.145356	−	0.251764i
$431$	−2.72892e9			−1.64180			−0.820900	−	0.571072i	$-0.806528\pi$
$431$	−2.72892e9			−1.64180			−0.820900	+	0.571072i	$0.806528\pi$
$432$		0			0
$433$	1.84699e9			1.09335			0.546673	−	0.837346i	$-0.315894\pi$
$433$	1.84699e9			1.09335			0.546673	+	0.837346i	$0.315894\pi$
$434$	6.04459e8	−	1.04695e9i	0.354938	−	0.614771i
$435$		0			0
$436$	5.89483e8	+	1.02101e9i	0.340619	+	0.589969i
$437$	−1.55306e7	−	2.68998e7i	−0.00890233	−	0.0154193i
$438$		0			0
$439$	−7.50330e8	+	1.29961e9i	−0.423279	+	0.733140i	−0.996258	−	0.0864296i	$-0.972454\pi$
$439$	−7.50330e8	+	1.29961e9i	−0.423279	+	0.733140i	0.572979	+	0.819570i	$0.305788\pi$
$440$	−3.19496e8			−0.178805
$441$		0			0
$442$	2.93760e6			0.00161813
$443$	−6.58449e8	+	1.14047e9i	−0.359840	+	0.623261i	−0.987934	−	0.154876i	$-0.950502\pi$
$443$	−6.58449e8	+	1.14047e9i	−0.359840	+	0.623261i	0.628094	+	0.778138i	$0.283835\pi$
$444$		0			0
$445$	−2.11764e8	−	3.66786e8i	−0.113918	−	0.197312i
$446$	1.66469e8	+	2.88333e8i	0.0888509	+	0.153894i
$447$		0			0
$448$	1.22814e8	−	2.12721e8i	0.0645322	−	0.111773i
$449$	2.71216e8			0.141401			0.0707006	−	0.997498i	$-0.477477\pi$
$449$	2.71216e8			0.141401			0.0707006	+	0.997498i	$0.477477\pi$
$450$		0			0
$451$	−3.72908e9			−1.91418
$452$	5.96111e8	−	1.03250e9i	0.303629	−	0.525900i
$453$		0			0
$454$	8.37261e8	+	1.45018e9i	0.419919	+	0.727321i
$455$	3.34509e6	+	5.79387e6i	0.00166482	+	0.00288356i
$456$		0			0
$457$	1.07531e9	−	1.86249e9i	0.527018	−	0.912822i	−0.472486	−	0.881338i	$-0.656643\pi$
$457$	1.07531e9	−	1.86249e9i	0.527018	−	0.912822i	0.999504	−	0.0314843i	$-0.0100234\pi$
$458$	−2.66335e9			−1.29539
$459$		0			0
$460$	−4.31424e6			−0.00206658
$461$	−4.92094e8	+	8.52332e8i	−0.233935	+	0.405187i	−0.958963	−	0.283533i	$-0.908494\pi$
$461$	−4.92094e8	+	8.52332e8i	−0.233935	+	0.405187i	0.725028	+	0.688720i	$0.241827\pi$
$462$		0			0
$463$	1.28374e9	+	2.22351e9i	0.601096	+	1.04113i	0.992655	+	0.120976i	$0.0386025\pi$
$463$	1.28374e9	+	2.22351e9i	0.601096	+	1.04113i	−0.391559	+	0.920153i	$0.628064\pi$
$464$	2.57913e8	+	4.46718e8i	0.119856	+	0.207597i
$465$		0			0
$466$	3.18171e8	−	5.51089e8i	0.145650	−	0.252273i
$467$	−6.97867e8			−0.317076			−0.158538	−	0.987353i	$-0.550678\pi$
$467$	−6.97867e8			−0.317076			−0.158538	+	0.987353i	$0.550678\pi$
$468$		0			0
$469$	−2.51217e9			−1.12446
$470$	2.26253e8	−	3.91882e8i	0.100520	−	0.174106i
$471$		0			0
$472$	−7.45172e8	−	1.29068e9i	−0.326182	−	0.564963i
$473$	−1.69551e9	−	2.93671e9i	−0.736692	−	1.27599i
$474$		0			0
$475$	−1.62322e9	+	2.81149e9i	−0.694942	+	1.20368i
$476$	3.23827e8			0.137622
$477$		0			0
$478$	−1.17520e9			−0.492171
$479$	1.53533e9	−	2.65927e9i	0.638304	−	1.10557i	−0.347501	−	0.937680i	$-0.612970\pi$
$479$	1.53533e9	−	2.65927e9i	0.638304	−	1.10557i	0.985805	−	0.167895i	$-0.0536970\pi$
$480$		0			0
$481$	1.40857e7	+	2.43972e7i	0.00577127	+	0.00999613i
$482$	−1.21222e8	−	2.09963e8i	−0.0493080	−	0.0854039i
$483$		0			0
$484$	−5.06626e8	+	8.77503e8i	−0.203109	+	0.351795i
$485$	−6.04180e8			−0.240475
$486$		0			0
$487$	−1.74254e9			−0.683646			−0.341823	−	0.939764i	$-0.611044\pi$
$487$	−1.74254e9			−0.683646			−0.341823	+	0.939764i	$0.611044\pi$
$488$	6.87147e8	−	1.19017e9i	0.267658	−	0.463597i
$489$		0			0
$490$	2.28589e7	+	3.95928e7i	0.00877747	+	0.0152030i
$491$	5.05269e8	+	8.75152e8i	0.192636	+	0.333655i	0.946123	−	0.323807i	$-0.104963\pi$
$491$	5.05269e8	+	8.75152e8i	0.192636	+	0.333655i	−0.753487	+	0.657463i	$0.771630\pi$
$492$		0			0
$493$	−3.40022e8	+	5.88935e8i	−0.127803	+	0.221362i
$494$	2.63198e7			0.00982287
$495$		0			0
$496$	−6.60582e8			−0.243075
$497$	−1.73602e9	+	3.00687e9i	−0.634318	+	1.09867i
$498$		0			0
$499$	−7.80436e8	−	1.35176e9i	−0.281181	−	0.487019i	0.690495	−	0.723337i	$-0.257393\pi$
$499$	−7.80436e8	−	1.35176e9i	−0.281181	−	0.487019i	−0.971676	+	0.236318i	$0.924059\pi$
$500$	4.87956e8	+	8.45165e8i	0.174576	+	0.302375i
$501$		0			0
$502$	5.88108e8	−	1.01863e9i	0.207488	−	0.359380i
$503$	1.63663e9			0.573407			0.286704	−	0.958019i	$-0.407441\pi$
$503$	1.63663e9			0.573407			0.286704	+	0.958019i	$0.407441\pi$
$504$		0			0
$505$	9.32318e8			0.322140
$506$	−1.52616e7	+	2.64339e7i	−0.00523690	+	0.00907057i
$507$		0			0
$508$	8.26816e7	+	1.43209e8i	0.0279824	+	0.0484670i
$509$	2.64263e8	+	4.57717e8i	0.0888227	+	0.153845i	0.907014	−	0.421101i	$-0.138356\pi$
$509$	2.64263e8	+	4.57717e8i	0.0888227	+	0.153845i	−0.818191	+	0.574946i	$0.805023\pi$
$510$		0			0
$511$	−7.17512e7	+	1.24277e8i	−0.0237879	+	0.0412019i
$512$	−1.34218e8			−0.0441942
$513$		0			0
$514$	2.94221e9			0.955658
$515$	1.39422e8	−	2.41486e8i	0.0449785	−	0.0779051i
$516$		0			0
$517$	−1.60074e9	−	2.77256e9i	−0.509453	−	0.882399i
$518$	1.55274e9	+	2.68943e9i	0.490846	+	0.850171i
$519$		0			0
$520$	1.82784e6	−	3.16591e6i	0.000570068	−	0.000987386i
$521$	4.50707e9			1.39625			0.698124	−	0.715977i	$-0.254018\pi$
$521$	4.50707e9			1.39625			0.698124	+	0.715977i	$0.254018\pi$
$522$		0			0
$523$	3.60454e9			1.10178			0.550888	−	0.834579i	$-0.314289\pi$
$523$	3.60454e9			1.10178			0.550888	+	0.834579i	$0.314289\pi$
$524$	−1.34171e9	+	2.32390e9i	−0.407378	+	0.705600i
$525$		0			0
$526$	1.30343e9	+	2.25760e9i	0.390514	+	0.676390i
$527$	−4.35443e8	−	7.54209e8i	−0.129597	−	0.224468i
$528$		0			0
$529$	1.70221e9	−	2.94831e9i	0.499939	−	0.865921i
$530$	−2.99278e8			−0.0873190
$531$		0			0
$532$	2.90137e9			0.835435
$533$	2.13341e7	−	3.69518e7i	0.00610280	−	0.0105704i
$534$		0			0
$535$	−1.10898e9	−	1.92081e9i	−0.313101	−	0.542307i
$536$	6.86356e8	+	1.18880e9i	0.192519	+	0.333452i
$537$		0			0
$538$	−1.35612e9	+	2.34887e9i	−0.375456	+	0.650310i
$539$	3.23454e8			0.0889716
$540$		0			0
$541$	−2.24714e9			−0.610154			−0.305077	−	0.952328i	$-0.598682\pi$
$541$	−2.24714e9			−0.610154			−0.305077	+	0.952328i	$0.598682\pi$
$542$	−1.00311e7	+	1.73744e7i	−0.00270616	+	0.00468720i
$543$		0			0
$544$	−8.84736e7	−	1.53241e8i	−0.0235623	−	0.0408111i
$545$	9.67120e8	+	1.67510e9i	0.255913	+	0.443255i
$546$		0			0
$547$	−2.13370e9	+	3.69568e9i	−0.557415	+	0.965470i	0.440297	+	0.897852i	$0.354873\pi$
$547$	−2.13370e9	+	3.69568e9i	−0.557415	+	0.965470i	−0.997711	+	0.0676181i	$0.978460\pi$
$548$	8.10636e7			0.0210423
$549$		0			0
$550$	3.19020e9			0.817615
$551$	−3.04647e9	+	5.27664e9i	−0.775829	+	1.34378i
$552$		0			0
$553$	−3.55090e9	−	6.15033e9i	−0.892894	−	1.54654i
$554$	−2.11434e8	−	3.66214e8i	−0.0528312	−	0.0915064i
$555$		0			0
$556$	−7.37796e8	+	1.27790e9i	−0.182043	+	0.315308i
$557$	7.18311e8			0.176124			0.0880622	−	0.996115i	$-0.471933\pi$
$557$	7.18311e8			0.176124			0.0880622	+	0.996115i	$0.471933\pi$
$558$		0			0
$559$	3.88001e7			0.00939489
$560$	2.01492e8	−	3.48995e8i	0.0484843	−	0.0839772i
$561$		0			0
$562$	2.15821e9	+	3.73812e9i	0.512880	+	0.888335i
$563$	2.85577e9	+	4.94635e9i	0.674442	+	1.16817i	0.976632	+	0.214920i	$0.0689489\pi$
$563$	2.85577e9	+	4.94635e9i	0.674442	+	1.16817i	−0.302190	+	0.953248i	$0.597718\pi$
$564$		0			0
$565$	9.77995e8	−	1.69394e9i	0.228122	−	0.395119i
$566$	−5.26852e8			−0.122133
$567$		0			0
$568$	1.89721e9			0.434405
$569$	−3.18000e9	+	5.50793e9i	−0.723660	+	1.25342i	0.235863	+	0.971786i	$0.424208\pi$
$569$	−3.18000e9	+	5.50793e9i	−0.723660	+	1.25342i	−0.959523	+	0.281629i	$0.909125\pi$
$570$		0			0
$571$	2.37475e9	+	4.11319e9i	0.533816	+	0.924597i	0.999220	+	0.0394982i	$0.0125760\pi$
$571$	2.37475e9	+	4.11319e9i	0.533816	+	0.924597i	−0.465403	+	0.885099i	$0.654091\pi$
$572$	−1.29320e7	−	2.23988e7i	−0.00288921	−	0.00500425i
$573$		0			0
$574$	2.35177e9	−	4.07339e9i	0.519043	−	0.899010i
$575$	4.30782e7			0.00944975
$576$		0			0
$577$	−8.95938e8			−0.194161			−0.0970807	−	0.995277i	$-0.530950\pi$
$577$	−8.95938e8			−0.194161			−0.0970807	+	0.995277i	$0.530950\pi$
$578$	−1.52471e9	+	2.64088e9i	−0.328429	+	0.568855i
$579$		0			0
$580$	4.23138e8	+	7.32897e8i	0.0900501	+	0.155971i
$581$	4.37860e9	+	7.58396e9i	0.926230	+	1.60428i
$582$		0			0
$583$	−1.05869e9	+	1.83371e9i	−0.221274	+	0.383258i
$584$	7.84133e7			0.0162909
$585$		0			0
$586$	2.82067e8			0.0579042
$587$	3.21382e9	−	5.56650e9i	0.655826	−	1.13592i	−0.325861	−	0.945418i	$-0.605654\pi$
$587$	3.21382e9	−	5.56650e9i	0.655826	−	1.13592i	0.981686	−	0.190505i	$-0.0610127\pi$
$588$		0			0
$589$	−3.90140e9	−	6.75743e9i	−0.786715	−	1.36263i
$590$	−1.22255e9	−	2.11751e9i	−0.245066	−	0.424467i
$591$		0			0
$592$	8.48458e8	−	1.46957e9i	0.168075	−	0.291115i
$593$	−6.89741e9			−1.35830			−0.679148	−	0.734001i	$-0.737651\pi$
$593$	−6.89741e9			−1.35830			−0.679148	+	0.734001i	$0.737651\pi$
$594$		0			0
$595$	5.31279e8			0.103398
$596$	−7.62452e8	+	1.32061e9i	−0.147520	+	0.255512i
$597$		0			0
$598$	−174624.	−	302458.i	−3.33926e−5	−	5.78376e-5i
$599$	4.25282e9	+	7.36610e9i	0.808506	+	1.40037i	0.913899	+	0.405942i	$0.133057\pi$
$599$	4.25282e9	+	7.36610e9i	0.808506	+	1.40037i	−0.105393	+	0.994431i	$0.533610\pi$
$600$		0			0
$601$	3.51840e9	−	6.09404e9i	0.661126	−	1.14510i	−0.319194	−	0.947689i	$-0.603412\pi$
$601$	3.51840e9	−	6.09404e9i	0.661126	−	1.14510i	0.980320	−	0.197415i	$-0.0632545\pi$
$602$	4.27714e9			0.799035
$603$		0			0
$604$	2.88316e9			0.532401
$605$	−8.31184e8	+	1.43965e9i	−0.152600	+	0.264310i
$606$		0			0
$607$	4.58441e9	+	7.94042e9i	0.831999	+	1.44106i	0.896451	+	0.443143i	$0.146137\pi$
$607$	4.58441e9	+	7.94042e9i	0.831999	+	1.44106i	−0.0644524	+	0.997921i	$0.520530\pi$
$608$	−7.92691e8	−	1.37298e9i	−0.143035	−	0.247743i
$609$		0			0
$610$	1.12735e9	−	1.95263e9i	0.201097	−	0.348309i
$611$	3.66315e7			0.00649696
$612$		0			0
$613$	1.89814e9			0.332826			0.166413	−	0.986056i	$-0.446781\pi$
$613$	1.89814e9			0.332826			0.166413	+	0.986056i	$0.446781\pi$
$614$	4.57038e8	−	7.91613e8i	0.0796825	−	0.138014i
$615$		0			0
$616$	−1.42556e9	−	2.46914e9i	−0.245727	−	0.425612i
$617$	−5.04005e9	−	8.72962e9i	−0.863847	−	1.49623i	−0.868188	−	0.496236i	$-0.834715\pi$
$617$	−5.04005e9	−	8.72962e9i	−0.863847	−	1.49623i	0.00434118	−	0.999991i	$-0.498618\pi$
$618$		0			0
$619$	1.03899e9	−	1.79957e9i	0.176073	−	0.304967i	−0.764459	−	0.644672i	$-0.776994\pi$
$619$	1.03899e9	−	1.79957e9i	0.176073	−	0.304967i	0.940532	+	0.339705i	$0.110327\pi$
$620$	−1.08377e9			−0.182627
$621$		0			0
$622$	−1.24370e9			−0.207229
$623$	1.88974e9	−	3.27313e9i	0.313108	−	0.542319i
$624$		0			0
$625$	−1.82054e9	−	3.15327e9i	−0.298277	−	0.516632i
$626$	1.52920e9	+	2.64865e9i	0.249146	+	0.431533i
$627$		0			0
$628$	−1.12824e9	+	1.95417e9i	−0.181779	+	0.314850i
$629$	2.23714e9			0.358440
$630$		0			0
$631$	−8.91619e9			−1.41279			−0.706393	−	0.707820i	$-0.749679\pi$
$631$	−8.91619e9			−1.41279			−0.706393	+	0.707820i	$0.749679\pi$
$632$	−1.94030e9	+	3.36069e9i	−0.305744	+	0.529565i
$633$		0			0
$634$	1.77955e9	+	3.08227e9i	0.277330	+	0.480350i
$635$	1.35649e8	+	2.34952e8i	0.0210237	+	0.0364142i
$636$		0			0
$637$	−1.85048e6	+	3.20513e6i	−0.000283659	+	0.000491313i
$638$	5.98741e9			0.912780
$639$		0			0
$640$	−2.20201e8			−0.0332039
$641$	9.39525e8	−	1.62730e9i	0.140898	−	0.244043i	−0.786937	−	0.617033i	$-0.788334\pi$
$641$	9.39525e8	−	1.62730e9i	0.140898	−	0.244043i	0.927835	+	0.372991i	$0.121668\pi$
$642$		0			0
$643$	1.15260e9	+	1.99636e9i	0.170978	+	0.296143i	0.938762	−	0.344566i	$-0.111974\pi$
$643$	1.15260e9	+	1.99636e9i	0.170978	+	0.296143i	−0.767784	+	0.640709i	$0.778641\pi$
$644$	−1.92497e7	−	3.33415e7i	−0.00284004	−	0.00491909i
$645$		0			0
$646$	1.04505e9	−	1.81008e9i	0.152519	−	0.264171i
$647$	−5.73867e9			−0.833002			−0.416501	−	0.909135i	$-0.636744\pi$
$647$	−5.73867e9			−0.833002			−0.416501	+	0.909135i	$0.636744\pi$
$648$		0			0
$649$	−1.72991e10			−2.48408
$650$	−1.82512e7	+	3.16120e7i	−0.00260672	+	0.00451497i
$651$		0			0
$652$	2.09603e9	+	3.63043e9i	0.296163	+	0.512969i
$653$	3.68438e9	+	6.38153e9i	0.517807	+	0.896868i	0.999786	+	0.0206853i	$0.00658480\pi$
$653$	3.68438e9	+	6.38153e9i	0.517807	+	0.896868i	−0.481979	+	0.876183i	$0.660082\pi$
$654$		0			0
$655$	−2.20124e9	+	3.81265e9i	−0.306071	+	0.530130i
$656$	−2.57013e9			−0.355461
$657$		0			0
$658$	4.03808e9			0.552566
$659$	−6.22699e9	+	1.07855e10i	−0.847577	+	1.46805i	0.0357868	+	0.999359i	$0.488606\pi$
$659$	−6.22699e9	+	1.07855e10i	−0.847577	+	1.46805i	−0.883364	+	0.468687i	$0.844727\pi$
$660$		0			0
$661$	2.76604e9	+	4.79091e9i	0.372523	+	0.645228i	0.989953	−	0.141398i	$-0.0451596\pi$
$661$	2.76604e9	+	4.79091e9i	0.372523	+	0.645228i	−0.617430	+	0.786626i	$0.711826\pi$
$662$	−2.20355e9	−	3.81667e9i	−0.295203	−	0.511306i
$663$		0			0
$664$	2.39258e9	−	4.14406e9i	0.317159	−	0.549336i
$665$	4.76006e9			0.627678
$666$		0			0
$667$	8.08496e7			0.0105496
$668$	−1.68989e9	+	2.92697e9i	−0.219351	+	0.379928i
$669$		0			0
$670$	1.12605e9	+	1.95038e9i	0.144643	+	0.250529i
$671$	−7.97601e9	−	1.38148e10i	−1.01919	−	1.76529i
$672$		0			0
$673$	−5.58942e9	+	9.68116e9i	−0.706829	+	1.22426i	0.259199	+	0.965824i	$0.416541\pi$
$673$	−5.58942e9	+	9.68116e9i	−0.706829	+	1.22426i	−0.966028	+	0.258439i	$0.916792\pi$
$674$	3.97435e9			0.499984
$675$		0			0
$676$	−4.01561e9			−0.499963
$677$	8.00186e9	−	1.38596e10i	0.991130	−	1.71669i	0.380476	−	0.924791i	$-0.375760\pi$
$677$	8.00186e9	−	1.38596e10i	0.991130	−	1.71669i	0.610654	−	0.791898i	$-0.290907\pi$
$678$		0			0
$679$	−2.69579e9	−	4.66925e9i	−0.330478	−	0.572405i
$680$	−1.45152e8	−	2.51411e8i	−0.0177028	−	0.0306621i
$681$		0			0
$682$	−3.83383e9	+	6.64039e9i	−0.462794	+	0.801582i
$683$	9.70052e8			0.116499			0.0582496	−	0.998302i	$-0.481448\pi$
$683$	9.70052e8			0.116499			0.0582496	+	0.998302i	$0.481448\pi$
$684$		0			0
$685$	1.32995e8			0.0158095
$686$	2.88265e9	−	4.99290e9i	0.340924	−	0.590498i
$687$		0			0
$688$	−1.16857e9	−	2.02402e9i	−0.136803	−	0.236949i
$689$	−1.21136e7	−	2.09814e7i	−0.00141093	−	0.00244381i
$690$		0			0
$691$	−1.04881e8	+	1.81659e8i	−0.0120927	+	0.0209451i	−0.872008	−	0.489491i	$-0.837183\pi$
$691$	−1.04881e8	+	1.81659e8i	−0.0120927	+	0.0209451i	0.859916	+	0.510436i	$0.170516\pi$
$692$	−7.08691e9			−0.812991
$693$		0			0
$694$	2.00929e9			0.228184
$695$	−1.21045e9	+	2.09655e9i	−0.136773	+	0.236897i
$696$		0			0
$697$	−1.69418e9	−	2.93441e9i	−0.189516	−	0.328251i
$698$	−1.93166e9	−	3.34573e9i	−0.214999	−	0.372389i
$699$		0			0
$700$	−2.01193e9	+	3.48476e9i	−0.221702	+	0.383999i
$701$	−1.65792e10			−1.81782			−0.908910	−	0.416993i	$-0.863084\pi$
$701$	−1.65792e10			−1.81782			−0.908910	+	0.416993i	$0.863084\pi$
$702$		0			0
$703$	2.00440e10			2.17591
$704$	−7.78961e8	+	1.34920e9i	−0.0841417	+	0.145738i
$705$		0			0
$706$	−1.94774e9	−	3.37358e9i	−0.208312	−	0.360807i
$707$	4.15992e9	+	7.20519e9i	0.442707	+	0.766791i
$708$		0			0
$709$	4.89451e9	−	8.47753e9i	0.515759	−	0.893321i	−0.484073	−	0.875027i	$-0.660843\pi$
$709$	4.89451e9	−	8.47753e9i	0.515759	−	0.893321i	0.999833	−	0.0182937i	$-0.00582340\pi$
$710$	3.11260e9			0.326377
$711$		0			0
$712$	−2.06520e9			−0.214429
$713$	−5.17693e7	+	8.96670e7i	−0.00534883	+	0.00926444i
$714$		0			0
$715$	−2.12165e7	−	3.67481e7i	−0.00217071	−	0.00375979i
$716$	3.82168e8	+	6.61934e8i	0.0389097	+	0.0673936i
$717$		0			0
$718$	−1.83987e9	+	3.18676e9i	−0.185504	+	0.321302i
$719$	1.08605e10			1.08968			0.544838	−	0.838541i	$-0.316591\pi$
$719$	1.08605e10			1.08968			0.544838	+	0.838541i	$0.316591\pi$
$720$		0			0
$721$	2.48835e9			0.247251
$722$	5.78778e9	−	1.00247e10i	0.572311	−	0.991272i
$723$		0			0
$724$	2.54472e9	+	4.40759e9i	0.249204	+	0.431634i
$725$	−4.22509e9	−	7.31806e9i	−0.411768	−	0.713203i
$726$		0			0
$727$	−4.00529e9	+	6.93737e9i	−0.386602	+	0.669614i	−0.991990	−	0.126317i	$-0.959685\pi$
$727$	−4.00529e9	+	6.93737e9i	−0.386602	+	0.669614i	0.605388	+	0.795930i	$0.293018\pi$
$728$	3.26226e7			0.00313371
$729$		0			0
$730$	1.28647e8			0.0122397
$731$	1.54059e9	−	2.66839e9i	0.145874	−	0.252661i
$732$		0			0
$733$	−8.35865e9	−	1.44776e10i	−0.783921	−	1.35779i	−0.929641	−	0.368466i	$-0.879883\pi$
$733$	−8.35865e9	−	1.44776e10i	−0.783921	−	1.35779i	0.145720	−	0.989326i	$-0.453450\pi$
$734$	2.61001e9	+	4.52068e9i	0.243616	+	0.421956i
$735$		0			0
$736$	−1.05185e7	+	1.82186e7i	−0.000972484	+	0.00168439i
$737$	1.59336e10			1.46615
$738$		0			0
$739$	−9.35702e9			−0.852869			−0.426434	−	0.904519i	$-0.640230\pi$
$739$	−9.35702e9			−0.852869			−0.426434	+	0.904519i	$0.640230\pi$
$740$	1.39200e9	−	2.41102e9i	0.126278	−	0.218720i
$741$		0			0
$742$	−1.33535e9	−	2.31289e9i	−0.120000	−	0.207846i
$743$	−7.91592e9	−	1.37108e10i	−0.708012	−	1.22631i	−0.965594	−	0.260056i	$-0.916259\pi$
$743$	−7.91592e9	−	1.37108e10i	−0.708012	−	1.22631i	0.257582	−	0.966256i	$-0.417074\pi$
$744$		0			0
$745$	−1.25090e9	+	2.16662e9i	−0.110835	+	0.191971i
$746$	−1.53433e10			−1.35311
$747$		0			0
$748$	−2.05390e9			−0.179442
$749$	9.89631e9	−	1.71409e10i	0.860571	−	1.49055i
$750$		0			0
$751$	7.52700e9	+	1.30371e10i	0.648458	+	1.12316i	0.983491	+	0.180956i	$0.0579192\pi$
$751$	7.52700e9	+	1.30371e10i	0.648458	+	1.12316i	−0.335033	+	0.942206i	$0.608748\pi$
$752$	−1.10325e9	−	1.91089e9i	−0.0946047	−	0.163860i
$753$		0			0
$754$	−3.42540e7	+	5.93298e7i	−0.00291013	+	0.00504049i
$755$	4.73018e9			0.400003
$756$		0			0
$757$	6.81448e9			0.570949			0.285474	−	0.958386i	$-0.407849\pi$
$757$	6.81448e9			0.570949			0.285474	+	0.958386i	$0.407849\pi$
$758$	5.72605e9	−	9.91781e9i	0.477543	−	0.827129i
$759$		0			0
$760$	−1.30051e9	−	2.25255e9i	−0.107465	−	0.186134i
$761$	−1.71134e9	−	2.96413e9i	−0.140764	−	0.243810i	0.787021	−	0.616927i	$-0.211622\pi$
$761$	−1.71134e9	−	2.96413e9i	−0.140764	−	0.243810i	−0.927784	+	0.373117i	$0.878289\pi$
$762$		0			0
$763$	−8.63040e9	+	1.49483e10i	−0.703388	+	1.21830i
$764$	−3.85481e8			−0.0312735
$765$		0			0
$766$	1.11887e9			0.0899458
$767$	9.89682e7	−	1.71418e8i	0.00791975	−	0.0137174i
$768$		0			0
$769$	−4.81185e9	−	8.33437e9i	−0.381566	−	0.660892i	0.609720	−	0.792617i	$-0.291282\pi$
$769$	−4.81185e9	−	8.33437e9i	−0.381566	−	0.660892i	−0.991286	+	0.131725i	$0.957949\pi$
$770$	−2.33881e9	−	4.05093e9i	−0.184619	−	0.319770i
$771$		0			0
$772$	1.87472e9	−	3.24711e9i	0.146648	−	0.254001i
$773$	−2.46796e10			−1.92181			−0.960905	−	0.276880i	$-0.910700\pi$
$773$	−2.46796e10			−1.92181			−0.960905	+	0.276880i	$0.910700\pi$
$774$		0			0
$775$	1.08216e10			0.835091
$776$	−1.47305e9	+	2.55140e9i	−0.113162	+	0.196003i
$777$		0			0
$778$	−7.10368e9	−	1.23039e10i	−0.540822	−	0.936732i
$779$	−1.51792e10	−	2.62912e10i	−1.15045	−	1.99264i
$780$		0			0
$781$	1.10108e10	−	1.90713e10i	0.827069	−	1.43253i
$782$	−2.77344e7			−0.00207393
$783$		0			0
$784$	2.22929e8			0.0165219
$785$	−1.85102e9	+	3.20606e9i	−0.136574	+	0.236553i
$786$		0			0
$787$	1.23130e10	+	2.13268e10i	0.900436	+	1.55960i	0.826929	+	0.562307i	$0.190086\pi$
$787$	1.23130e10	+	2.13268e10i	0.900436	+	1.55960i	0.0735075	+	0.997295i	$0.476581\pi$
$788$	5.38926e9	+	9.33448e9i	0.392363	+	0.679592i
$789$		0			0
$790$	−3.18330e9	+	5.51364e9i	−0.229712	+	0.397872i
$791$	1.74549e10			1.25401
$792$		0			0
$793$	1.82523e8			0.0129976
$794$	−4.21205e9	+	7.29548e9i	−0.298622	+	0.517228i
$795$		0			0
$796$	3.25342e9	+	5.63508e9i	0.228636	+	0.396009i
$797$	−2.23164e9	−	3.86532e9i	−0.156142	−	0.270446i	0.777332	−	0.629091i	$-0.216573\pi$
$797$	−2.23164e9	−	3.86532e9i	−0.156142	−	0.270446i	−0.933474	+	0.358644i	$0.883239\pi$
$798$		0			0
$799$	1.45448e9	−	2.51924e9i	0.100878	−	0.174725i
$800$	2.19873e9			0.151830
$801$		0			0
$802$	−1.86410e10			−1.27602
$803$	4.55088e8	−	7.88236e8i	0.0310164	−	0.0537220i
$804$		0			0
$805$	−3.15816e7	−	5.47009e7i	−0.00213377	−	0.00369580i
$806$	−4.38668e7	−	7.59795e7i	−0.00295096	−	0.00511121i
$807$		0			0
$808$	2.27308e9	−	3.93709e9i	0.151592	−	0.262564i
$809$	−2.56496e9			−0.170318			−0.0851590	−	0.996367i	$-0.527140\pi$
$809$	−2.56496e9			−0.170318			−0.0851590	+	0.996367i	$0.527140\pi$
$810$		0			0
$811$	3.95820e9			0.260570			0.130285	−	0.991477i	$-0.458411\pi$
$811$	3.95820e9			0.260570			0.130285	+	0.991477i	$0.458411\pi$
$812$	−3.77601e9	+	6.54023e9i	−0.247506	+	0.428694i
$813$		0			0
$814$	−9.84841e9	−	1.70579e10i	−0.640001	−	1.10851i
$815$	3.43880e9	+	5.95617e9i	0.222513	+	0.385403i
$816$		0			0
$817$	1.38031e10	−	2.39077e10i	0.885525	−	1.53377i
$818$	1.20337e9			0.0768713
$819$		0			0
$820$	−4.21663e9			−0.267065
$821$	−7.92551e9	+	1.37274e10i	−0.499835	+	0.865739i	−1.00000		0.000191070i	$-0.999939\pi$
$821$	−7.92551e9	+	1.37274e10i	−0.499835	+	0.865739i	0.500165	+	0.865930i	$0.333273\pi$
$822$		0			0
$823$	7.87267e9	+	1.36359e10i	0.492292	+	0.852674i	0.999961	−	0.00887803i	$-0.00282600\pi$
$823$	7.87267e9	+	1.36359e10i	0.492292	+	0.852674i	−0.507669	+	0.861552i	$0.669493\pi$
$824$	−6.79847e8	−	1.17753e9i	−0.0423317	−	0.0733207i
$825$		0			0
$826$	1.09098e10	−	1.88963e10i	0.673575	−	1.16667i
$827$	−2.15640e9			−0.132574			−0.0662872	−	0.997801i	$-0.521115\pi$
$827$	−2.15640e9			−0.132574			−0.0662872	+	0.997801i	$0.521115\pi$
$828$		0			0
$829$	2.95703e10			1.80267			0.901333	−	0.433126i	$-0.142589\pi$
$829$	2.95703e10			1.80267			0.901333	+	0.433126i	$0.142589\pi$
$830$	3.92532e9	−	6.79885e9i	0.238288	−	0.412726i
$831$		0			0
$832$	−8.91290e6	−	1.54376e7i	−0.000536522	−	0.000929283i
$833$	1.46950e8	+	2.54525e8i	0.00880872	+	0.0152571i
$834$		0			0
$835$	−2.77247e9	+	4.80206e9i	−0.164803	+	0.285447i
$836$	−1.84022e10			−1.08930
$837$		0			0
$838$	−7.29146e9			−0.428016
$839$	1.55991e9	−	2.70184e9i	0.0911869	−	0.157940i	−0.816824	−	0.576887i	$-0.804267\pi$
$839$	1.55991e9	−	2.70184e9i	0.0911869	−	0.157940i	0.908011	+	0.418947i	$0.137601\pi$
$840$		0			0
$841$	6.95252e8	+	1.20421e9i	0.0403048	+	0.0698099i
$842$	−3.01393e9	−	5.22028e9i	−0.173997	−	0.301371i
$843$		0			0
$844$	2.76422e9	−	4.78778e9i	0.158261	−	0.274117i
$845$	−6.58811e9			−0.375632
$846$		0			0
$847$	−1.48347e10			−0.838852
$848$	−7.29668e8	+	1.26382e9i	−0.0410903	+	0.0711705i
$849$		0			0
$850$	1.44936e9	+	2.51037e9i	0.0809487	+	0.140207i
$851$	−1.32986e8	−	2.30338e8i	−0.00739694	−	0.0128119i
$852$		0			0
$853$	7.19709e9	−	1.24657e10i	0.397041	−	0.687695i	−0.596319	−	0.802748i	$-0.703370\pi$
$853$	7.19709e9	−	1.24657e10i	0.397041	−	0.687695i	0.993359	+	0.115053i	$0.0367038\pi$
$854$	2.01205e10			1.10544
$855$		0			0
$856$	−1.08152e10			−0.589353
$857$	−2.36600e9	+	4.09804e9i	−0.128405	+	0.222404i	−0.923059	−	0.384659i	$-0.874319\pi$
$857$	−2.36600e9	+	4.09804e9i	−0.128405	+	0.222404i	0.794654	+	0.607063i	$0.207652\pi$
$858$		0			0
$859$	2.41867e9	+	4.18926e9i	0.130197	+	0.225508i	0.923752	−	0.382990i	$-0.125106\pi$
$859$	2.41867e9	+	4.18926e9i	0.130197	+	0.225508i	−0.793555	+	0.608498i	$0.791772\pi$
$860$	−1.91718e9	−	3.32066e9i	−0.102782	−	0.178024i
$861$		0			0
$862$	−1.09157e10	+	1.89065e10i	−0.580464	+	1.00539i
$863$	−1.90890e10			−1.01099			−0.505493	−	0.862831i	$-0.668689\pi$
$863$	−1.90890e10			−1.01099			−0.505493	+	0.862831i	$0.668689\pi$
$864$		0			0
$865$	−1.16270e10			−0.610815
$866$	7.38797e9	−	1.27963e10i	0.386556	−	0.669535i
$867$		0			0
$868$	−4.83567e9	−	8.37563e9i	−0.250979	−	0.434709i
$869$	2.25219e10	+	3.90090e10i	1.16422	+	2.01649i
$870$		0			0
$871$	−9.11567e7	+	1.57888e8i	−0.00467439	+	0.00809628i
$872$	9.43173e9			0.481708
$873$		0			0
$874$	−2.48490e8			−0.0125898
$875$	−7.14398e9	+	1.23737e10i	−0.360506	+	0.624414i
$876$		0			0
$877$	1.68182e10	+	2.91299e10i	0.841938	+	1.45828i	0.888254	+	0.459352i	$0.151918\pi$
$877$	1.68182e10	+	2.91299e10i	0.841938	+	1.45828i	−0.0463168	+	0.998927i	$0.514748\pi$
$878$	6.00264e9	+	1.03969e10i	0.299303	+	0.518408i
$879$		0			0
$880$	−1.27798e9	+	2.21353e9i	−0.0632173	+	0.109495i
$881$	2.81256e10			1.38575			0.692876	−	0.721057i	$-0.256343\pi$
$881$	2.81256e10			1.38575			0.692876	+	0.721057i	$0.256343\pi$
$882$		0			0
$883$	1.99944e10			0.977341			0.488671	−	0.872468i	$-0.337482\pi$
$883$	1.99944e10			0.977341			0.488671	+	0.872468i	$0.337482\pi$
$884$	1.17504e7	−	2.03523e7i	0.000572097	−	0.000990901i
$885$		0			0
$886$	5.26760e9	+	9.12374e9i	0.254445	+	0.440712i
$887$	1.61338e10	+	2.79446e10i	0.776255	+	1.34451i	0.934087	+	0.357047i	$0.116216\pi$
$887$	1.61338e10	+	2.79446e10i	0.776255	+	1.34451i	−0.157832	+	0.987466i	$0.550450\pi$
$888$		0			0
$889$	−1.21051e9	+	2.09666e9i	−0.0577846	+	0.100086i
$890$	−3.38823e9			−0.161104
$891$		0			0
$892$	2.66351e9			0.125654
$893$	1.30316e10	−	2.25715e10i	0.612377	−	1.06067i
$894$		0			0
$895$	6.26994e8	+	1.08599e9i	0.0292336	+	0.0506341i
$896$	−9.82516e8	−	1.70177e9i	−0.0456312	−	0.0790355i
$897$		0			0
$898$	1.08486e9	−	1.87904e9i	0.0499929	−	0.0865902i
$899$	2.03100e10			0.932290
$900$		0			0
$901$	−1.92393e9			−0.0876299
$902$	−1.49163e10	+	2.58358e10i	−0.676766	+	1.17219i
$903$		0			0
$904$	−4.76889e9	−	8.25996e9i	−0.214698	−	0.371868i
$905$	4.17494e9	+	7.23120e9i	0.187232	+	0.324295i
$906$		0			0
$907$	−5.76161e9	+	9.97941e9i	−0.256400	+	0.444098i	−0.965275	−	0.261236i	$-0.915870\pi$
$907$	−5.76161e9	+	9.97941e9i	−0.256400	+	0.444098i	0.708875	+	0.705335i	$0.249203\pi$
$908$	1.33962e10			0.593855
$909$		0			0
$910$	5.35214e7			0.00235441
$911$	2.94854e9	−	5.10703e9i	0.129209	−	0.223797i	−0.794161	−	0.607707i	$-0.792089\pi$
$911$	2.94854e9	−	5.10703e9i	0.129209	−	0.223797i	0.923370	+	0.383910i	$0.125423\pi$
$912$		0			0
$913$	−2.77716e10	−	4.81019e10i	−1.20769	−	2.09177i
$914$	−8.60245e9	−	1.48999e10i	−0.372658	−	0.645463i
$915$		0			0
$916$	−1.06534e10	+	1.84522e10i	−0.457988	+	0.793258i
$917$	−3.92868e10			−1.68250
$918$		0			0
$919$	4.37679e9			0.186017			0.0930083	−	0.995665i	$-0.470352\pi$
$919$	4.37679e9			0.186017			0.0930083	+	0.995665i	$0.470352\pi$
$920$	−1.72570e7	+	2.98899e7i	−0.000730646	+	0.00126552i
$921$		0			0
$922$	3.93675e9	+	6.81866e9i	0.165417	+	0.286511i
$923$	1.25986e8	+	2.18215e8i	0.00527372	+	0.00913436i
$924$		0			0
$925$	−1.38993e10	+	2.40743e10i	−0.577427	+	1.00013i
$926$	2.05399e10			0.850078
$927$		0			0
$928$	4.12661e9			0.169502
$929$	−1.51512e10	+	2.62426e10i	−0.620000	+	1.07387i	0.369485	+	0.929237i	$0.379534\pi$
$929$	−1.51512e10	+	2.62426e10i	−0.620000	+	1.07387i	−0.989485	+	0.144635i	$0.953799\pi$
$930$		0			0
$931$	1.31662e9	+	2.28045e9i	0.0534732	+	0.0926183i
$932$	−2.54537e9	−	4.40871e9i	−0.102990	−	0.178384i
$933$		0			0
$934$	−2.79147e9	+	4.83496e9i	−0.112103	+	0.194169i
$935$	−3.36968e9			−0.134818
$936$		0			0
$937$	2.61397e10			1.03804			0.519018	−	0.854763i	$-0.326298\pi$
$937$	2.61397e10			1.03804			0.519018	+	0.854763i	$0.326298\pi$
$938$	−1.00487e10	+	1.74048e10i	−0.397557	+	0.688588i
$939$		0			0
$940$	−1.81003e9	−	3.13506e9i	−0.0710783	−	0.123111i
$941$	1.21220e10	+	2.09959e10i	0.474253	+	0.821429i	0.999565	−	0.0294797i	$-0.00938504\pi$
$941$	1.21220e10	+	2.09959e10i	0.474253	+	0.821429i	−0.525313	+	0.850909i	$0.676052\pi$
$942$		0			0
$943$	−2.01419e8	+	3.48868e8i	−0.00782186	+	0.0135479i
$944$	−1.19228e10			−0.461291
$945$		0			0
$946$	−2.71281e10			−1.04184
$947$	−1.28877e10	+	2.23222e10i	−0.493119	+	0.854106i	−0.999969	−	0.00792781i	$-0.997476\pi$
$947$	−1.28877e10	+	2.23222e10i	−0.493119	+	0.854106i	0.506850	+	0.862034i	$0.330810\pi$
$948$		0			0
$949$	5.20713e6	+	9.01902e6i	0.000197773	+	0.000342553i
$950$	1.29857e10	+	2.24919e10i	0.491398	+	0.851127i
$951$		0			0
$952$	1.29531e9	−	2.24354e9i	0.0486569	−	0.0842761i
$953$	2.22288e10			0.831937			0.415968	−	0.909379i	$-0.363443\pi$
$953$	2.22288e10			0.831937			0.415968	+	0.909379i	$0.363443\pi$
$954$		0			0
$955$	−6.32431e8			−0.0234964
$956$	−4.70082e9	+	8.14205e9i	−0.174009	+	0.301392i
$957$		0			0
$958$	−1.22826e10	−	2.12742e10i	−0.451349	−	0.781759i
$959$	5.93411e8	+	1.02782e9i	0.0217265	+	0.0376314i
$960$		0			0
$961$	7.51494e8	−	1.30163e9i	0.0273145	−	0.0473102i
$962$	2.25372e8			0.00816181
$963$		0			0
$964$	−1.93955e9			−0.0697320
$965$	3.07571e9	−	5.32729e9i	0.110179	−	0.190836i
$966$		0			0
$967$	1.54705e9	+	2.67957e9i	0.0550189	+	0.0952956i	0.892223	−	0.451595i	$-0.149145\pi$
$967$	1.54705e9	+	2.67957e9i	0.0550189	+	0.0952956i	−0.837204	+	0.546890i	$0.815811\pi$
$968$	4.05301e9	+	7.02002e9i	0.143620	+	0.248757i
$969$		0			0
$970$	−2.41672e9	+	4.18588e9i	−0.0850208	+	0.147260i
$971$	−1.62621e10			−0.570044			−0.285022	−	0.958521i	$-0.592001\pi$
$971$	−1.62621e10			−0.570044			−0.285022	+	0.958521i	$0.592001\pi$
$972$		0			0
$973$	−2.16036e10			−0.751850
$974$	−6.97016e9	+	1.20727e10i	−0.241705	+	0.418646i
$975$		0			0
$976$	−5.49718e9	−	9.52139e9i	−0.189263	−	0.327813i
$977$	−2.21128e9	−	3.83005e9i	−0.0758601	−	0.131393i	0.825600	−	0.564256i	$-0.190837\pi$
$977$	−2.21128e9	−	3.83005e9i	−0.0758601	−	0.131393i	−0.901460	+	0.432863i	$0.857504\pi$
$978$		0			0
$979$	−1.19858e10	+	2.07601e10i	−0.408253	+	0.707115i
$980$	3.65743e8			0.0124132
$981$		0			0
$982$	8.08431e9			0.272428
$983$	−1.86923e10	+	3.23761e10i	−0.627663	+	1.08714i	0.360357	+	0.932815i	$0.382655\pi$
$983$	−1.86923e10	+	3.23761e10i	−0.627663	+	1.08714i	−0.988019	+	0.154329i	$0.950678\pi$
$984$		0			0
$985$	8.84176e9	+	1.53144e10i	0.294789	+	0.510590i
$986$	2.72017e9	+	4.71148e9i	0.0903707	+	0.156527i
$987$		0			0
$988$	1.05279e8	−	1.82349e8i	0.00347291	−	0.00601525i
$989$	−3.66319e8			−0.0120413
$990$		0			0
$991$	−1.24473e10			−0.406273			−0.203136	−	0.979150i	$-0.565113\pi$
$991$	−1.24473e10			−0.406273			−0.203136	+	0.979150i	$0.565113\pi$
$992$	−2.64233e9	+	4.57665e9i	−0.0859402	+	0.148853i
$993$		0			0
$994$	1.38881e10	+	2.40550e10i	0.448530	+	0.776877i
$995$	5.33764e9	+	9.24506e9i	0.171778	+	0.297529i
$996$		0			0
$997$	−1.42168e10	+	2.46241e10i	−0.454326	+	0.786915i	−0.998649	−	0.0519600i	$-0.983453\pi$
$997$	−1.42168e10	+	2.46241e10i	−0.454326	+	0.786915i	0.544323	+	0.838876i	$0.316786\pi$
$998$	−1.24870e10			−0.397650
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.8.c.j.55.1		2
3.2	odd	2		162.8.c.c.55.1		2
9.2	odd	6		54.8.a.e.1.1	yes	1
9.4	even	3	inner	162.8.c.j.109.1		2
9.5	odd	6		162.8.c.c.109.1		2
9.7	even	3		54.8.a.b.1.1	✓	1
36.7	odd	6		432.8.a.f.1.1		1
36.11	even	6		432.8.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.8.a.b.1.1	✓	1	9.7	even	3
54.8.a.e.1.1	yes	1	9.2	odd	6
162.8.c.c.55.1		2	3.2	odd	2
162.8.c.c.109.1		2	9.5	odd	6
162.8.c.j.55.1		2	1.1	even	1	trivial
162.8.c.j.109.1		2	9.4	even	3	inner
432.8.a.c.1.1		1	36.11	even	6
432.8.a.f.1.1		1	36.7	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-52.5000 - 90.9327i) q^{5} +(468.500 - 811.466i) q^{7} -512.000 q^{8} -840.000 q^{10} +(-2971.50 + 5146.79i) q^{11} +(-34.0000 - 58.8897i) q^{13} +(-3748.00 - 6491.73i) q^{14} +(-2048.00 + 3547.24i) q^{16} -5400.00 q^{17} -48382.0 q^{19} +(-3360.00 + 5819.69i) q^{20} +(23772.0 + 41174.3i) q^{22} +(321.000 + 555.988i) q^{23} +(33550.0 - 58110.3i) q^{25} -544.000 q^{26} -59968.0 q^{28} +(62967.0 - 109062. i) q^{29} +(80637.5 + 139668. i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-21600.0 + 37412.3i) q^{34} -98385.0 q^{35} -414286. q^{37} +(-193528. + 335200. i) q^{38} +(26880.0 + 46557.5i) q^{40} +(313737. + 543408. i) q^{41} +(-285295. + 494145. i) q^{43} +380352. q^{44} +5136.00 q^{46} +(-269349. + 466526. i) q^{47} +(-27213.0 - 47134.3i) q^{49} +(-268400. - 464882. i) q^{50} +(-2176.00 + 3768.94i) q^{52} +356283. q^{53} +624015. q^{55} +(-239872. + 415470. i) q^{56} +(-503736. - 872496. i) q^{58} +(1.45541e6 + 2.52085e6i) q^{59} +(-1.34208e6 + 2.32456e6i) q^{61} +1.29020e6 q^{62} +262144. q^{64} +(-3570.00 + 6183.42i) q^{65} +(-1.34054e6 - 2.32188e6i) q^{67} +(172800. + 299298. i) q^{68} +(-393540. + 681631. i) q^{70} -3.70548e6 q^{71} -153151. q^{73} +(-1.65714e6 + 2.87026e6i) q^{74} +(1.54822e6 + 2.68160e6i) q^{76} +(2.78430e6 + 4.82254e6i) q^{77} +(3.78964e6 - 6.56386e6i) q^{79} +430080. q^{80} +5.01979e6 q^{82} +(-4.67300e6 + 8.09387e6i) q^{83} +(283500. + 491036. i) q^{85} +(2.28236e6 + 3.95316e6i) q^{86} +(1.52141e6 - 2.63516e6i) q^{88} +4.03360e6 q^{89} -63716.0 q^{91} +(20544.0 - 35583.3i) q^{92} +(2.15479e6 + 3.73221e6i) q^{94} +(2.54006e6 + 4.39950e6i) q^{95} +(2.87705e6 - 4.98319e6i) q^{97} -435408. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8 q^{2} - 64 q^{4} - 105 q^{5} + 937 q^{7} - 1024 q^{8} - 1680 q^{10} - 5943 q^{11} - 68 q^{13} - 7496 q^{14} - 4096 q^{16} - 10800 q^{17} - 96764 q^{19} - 6720 q^{20} + 47544 q^{22} + 642 q^{23}+ \cdots - 870816 q^{98}+O(q^{100}) \) 2 * q + 8 * q^2 - 64 * q^4 - 105 * q^5 + 937 * q^7 - 1024 * q^8 - 1680 * q^10 - 5943 * q^11 - 68 * q^13 - 7496 * q^14 - 4096 * q^16 - 10800 * q^17 - 96764 * q^19 - 6720 * q^20 + 47544 * q^22 + 642 * q^23 + 67100 * q^25 - 1088 * q^26 - 119936 * q^28 + 125934 * q^29 + 161275 * q^31 + 32768 * q^32 - 43200 * q^34 - 196770 * q^35 - 828572 * q^37 - 387056 * q^38 + 53760 * q^40 + 627474 * q^41 - 570590 * q^43 + 760704 * q^44 + 10272 * q^46 - 538698 * q^47 - 54426 * q^49 - 536800 * q^50 - 4352 * q^52 + 712566 * q^53 + 1248030 * q^55 - 479744 * q^56 - 1007472 * q^58 + 2910828 * q^59 - 2684168 * q^61 + 2580400 * q^62 + 524288 * q^64 - 7140 * q^65 - 2681078 * q^67 + 345600 * q^68 - 787080 * q^70 - 7410960 * q^71 - 306302 * q^73 - 3314288 * q^74 + 3096448 * q^76 + 5568591 * q^77 + 7579288 * q^79 + 860160 * q^80 + 10039584 * q^82 - 9345999 * q^83 + 567000 * q^85 + 4564720 * q^86 + 3042816 * q^88 + 8067204 * q^89 - 127432 * q^91 + 41088 * q^92 + 4309584 * q^94 + 5080110 * q^95 + 5754097 * q^97 - 870816 * q^98

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