LMFDB - Embedded newform 98.8.c.a.67.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,8,Mod(67,98)] 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("98.67"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-8,-66,-64,-400,1056,0,1024,-2169] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$30.6137324974$
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:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.8.c.a.79.1

$q$-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} +(-33.0000 + 57.1577i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-200.000 - 346.410i) q^{5} +528.000 q^{6} +512.000 q^{8} +(-1084.50 - 1878.41i) q^{9} +(-1600.00 + 2771.28i) q^{10} +(-20.0000 + 34.6410i) q^{11} +(-2112.00 - 3658.09i) q^{12} +4452.00 q^{13} +26400.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(18251.0 - 31611.7i) q^{17} +(-8676.00 + 15027.3i) q^{18} +(-23111.0 - 40029.4i) q^{19} +25600.0 q^{20} +320.000 q^{22} +(52600.0 + 91105.9i) q^{23} +(-16896.0 + 29264.7i) q^{24} +(-40937.5 + 70905.8i) q^{25} +(-17808.0 - 30844.4i) q^{26} -1188.00 q^{27} -126334. q^{29} +(-105600. - 182905. i) q^{30} +(-85482.0 + 148059. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-1320.00 - 2286.31i) q^{33} -292016. q^{34} +138816. q^{36} +(-10477.0 - 18146.7i) q^{37} +(-184888. + 320235. i) q^{38} +(-146916. + 254466. i) q^{39} +(-102400. - 177362. i) q^{40} -318486. q^{41} +77744.0 q^{43} +(-1280.00 - 2217.03i) q^{44} +(-433800. + 751364. i) q^{45} +(420800. - 728847. i) q^{46} +(351858. + 609436. i) q^{47} +270336. q^{48} +655000. q^{50} +(1.20457e6 + 2.08637e6i) q^{51} +(-142464. + 246755. i) q^{52} +(-801639. + 1.38848e6i) q^{53} +(4752.00 + 8230.71i) q^{54} +16000.0 q^{55} +3.05065e6 q^{57} +(505336. + 875268. i) q^{58} +(-585947. + 1.01489e6i) q^{59} +(-844800. + 1.46324e6i) q^{60} +(-1.03444e6 - 1.79170e6i) q^{61} +1.36771e6 q^{62} +262144. q^{64} +(-890400. - 1.54222e6i) q^{65} +(-10560.0 + 18290.5i) q^{66} +(497134. - 861061. i) q^{67} +(1.16806e6 + 2.02315e6i) q^{68} -6.94320e6 q^{69} +33280.0 q^{71} +(-555264. - 961745. i) q^{72} +(-1.48573e6 + 2.57335e6i) q^{73} +(-83816.0 + 145174. i) q^{74} +(-2.70188e6 - 4.67978e6i) q^{75} +2.95821e6 q^{76} +2.35066e6 q^{78} +(1.18808e6 + 2.05782e6i) q^{79} +(-819200. + 1.41890e6i) q^{80} +(2.41101e6 - 4.17598e6i) q^{81} +(1.27394e6 + 2.20654e6i) q^{82} +2.12236e6 q^{83} -1.46008e7 q^{85} +(-310976. - 538626. i) q^{86} +(4.16902e6 - 7.22096e6i) q^{87} +(-10240.0 + 17736.2i) q^{88} +(3.46017e6 + 5.99320e6i) q^{89} +6.94080e6 q^{90} -6.73280e6 q^{92} +(-5.64181e6 - 9.77191e6i) q^{93} +(2.81486e6 - 4.87549e6i) q^{94} +(-9.24440e6 + 1.60118e7i) q^{95} +(-1.08134e6 - 1.87294e6i) q^{96} -4.95271e6 q^{97} +86760.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8 q^{2} - 66 q^{3} - 64 q^{4} - 400 q^{5} + 1056 q^{6} + 1024 q^{8} - 2169 q^{9} - 3200 q^{10} - 40 q^{11} - 4224 q^{12} + 8904 q^{13} + 52800 q^{15} - 4096 q^{16} + 36502 q^{17} - 17352 q^{18} - 46222 q^{19}+ \cdots + 173520 q^{99}+O(q^{100}) $ 2 * q - 8 * q^2 - 66 * q^3 - 64 * q^4 - 400 * q^5 + 1056 * q^6 + 1024 * q^8 - 2169 * q^9 - 3200 * q^10 - 40 * q^11 - 4224 * q^12 + 8904 * q^13 + 52800 * q^15 - 4096 * q^16 + 36502 * q^17 - 17352 * q^18 - 46222 * q^19 + 51200 * q^20 + 640 * q^22 + 105200 * q^23 - 33792 * q^24 - 81875 * q^25 - 35616 * q^26 - 2376 * q^27 - 252668 * q^29 - 211200 * q^30 - 170964 * q^31 - 32768 * q^32 - 2640 * q^33 - 584032 * q^34 + 277632 * q^36 - 20954 * q^37 - 369776 * q^38 - 293832 * q^39 - 204800 * q^40 - 636972 * q^41 + 155488 * q^43 - 2560 * q^44 - 867600 * q^45 + 841600 * q^46 + 703716 * q^47 + 540672 * q^48 + 1310000 * q^50 + 2409132 * q^51 - 284928 * q^52 - 1603278 * q^53 + 9504 * q^54 + 32000 * q^55 + 6101304 * q^57 + 1010672 * q^58 - 1171894 * q^59 - 1689600 * q^60 - 2068872 * q^61 + 2735424 * q^62 + 524288 * q^64 - 1780800 * q^65 - 21120 * q^66 + 994268 * q^67 + 2336128 * q^68 - 13886400 * q^69 + 66560 * q^71 - 1110528 * q^72 - 2971454 * q^73 - 167632 * q^74 - 5403750 * q^75 + 5916416 * q^76 + 4701312 * q^78 + 2376168 * q^79 - 1638400 * q^80 + 4822011 * q^81 + 2547888 * q^82 + 4244716 * q^83 - 29201600 * q^85 - 621952 * q^86 + 8338044 * q^87 - 20480 * q^88 + 6920346 * q^89 + 13881600 * q^90 - 13465600 * q^92 - 11283624 * q^93 + 5629728 * q^94 - 18488800 * q^95 - 2162688 * q^96 - 9905420 * q^97 + 173520 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

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

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
$3$	−33.0000	+	57.1577i	−0.705650	+	1.22222i	0.260806	+	0.965391i	$0.416012\pi$
$3$	−33.0000	+	57.1577i	−0.705650	+	1.22222i	−0.966456	+	0.256831i	$0.917322\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−200.000	−	346.410i	−0.715542	−	1.23935i	−0.962750	−	0.270392i	$-0.912847\pi$
$5$	−200.000	−	346.410i	−0.715542	−	1.23935i	0.247208	−	0.968962i	$-0.420487\pi$
$6$	528.000			0.997940
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	−1084.50	−	1878.41i	−0.495885	−	0.858898i
$10$	−1600.00	+	2771.28i	−0.505964	+	0.876356i
$11$	−20.0000	+	34.6410i	−0.00453060	+	0.00784723i	−0.868282	−	0.496071i	$-0.834775\pi$
$11$	−20.0000	+	34.6410i	−0.00453060	+	0.00784723i	0.863751	+	0.503918i	$0.168109\pi$
$12$	−2112.00	−	3658.09i	−0.352825	−	0.611111i
$13$	4452.00			0.562022			0.281011	−	0.959705i	$-0.409330\pi$
$13$	4452.00			0.562022			0.281011	+	0.959705i	$0.409330\pi$
$14$		0			0
$15$	26400.0			2.01969
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	18251.0	−	31611.7i	0.900981	−	1.56054i	0.0747571	−	0.997202i	$-0.476182\pi$
$17$	18251.0	−	31611.7i	0.900981	−	1.56054i	0.826224	−	0.563342i	$-0.190485\pi$
$18$	−8676.00	+	15027.3i	−0.350643	+	0.607332i
$19$	−23111.0	−	40029.4i	−0.773003	−	1.33888i	−0.935910	−	0.352239i	$-0.885420\pi$
$19$	−23111.0	−	40029.4i	−0.773003	−	1.33888i	0.162907	−	0.986641i	$-0.447913\pi$
$20$	25600.0			0.715542
$21$		0			0
$22$	320.000			0.00640723
$23$	52600.0	+	91105.9i	0.901443	+	1.56135i	0.825622	+	0.564224i	$0.190824\pi$
$23$	52600.0	+	91105.9i	0.901443	+	1.56135i	0.0758212	+	0.997121i	$0.475842\pi$
$24$	−16896.0	+	29264.7i	−0.249485	+	0.432121i
$25$	−40937.5	+	70905.8i	−0.524000	+	0.907595i
$26$	−17808.0	−	30844.4i	−0.198705	−	0.344167i
$27$	−1188.00			−0.0116156
$28$		0			0
$29$	−126334.			−0.961894			−0.480947	−	0.876750i	$-0.659707\pi$
$29$	−126334.			−0.961894			−0.480947	+	0.876750i	$0.659707\pi$
$30$	−105600.	−	182905.i	−0.714068	−	1.23680i
$31$	−85482.0	+	148059.i	−0.515358	+	0.892626i	0.484483	+	0.874800i	$0.339008\pi$
$31$	−85482.0	+	148059.i	−0.515358	+	0.892626i	−0.999841	+	0.0178252i	$0.994326\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$	−1320.00	−	2286.31i	−0.00639404	−	0.0110748i
$34$	−292016.			−1.27418
$35$		0			0
$36$	138816.			0.495885
$37$	−10477.0	−	18146.7i	−0.0340041	−	0.0588968i	0.848523	−	0.529159i	$-0.177493\pi$
$37$	−10477.0	−	18146.7i	−0.0340041	−	0.0588968i	−0.882527	+	0.470262i	$0.844159\pi$
$38$	−184888.	+	320235.i	−0.546596	+	0.946731i
$39$	−146916.	+	254466.i	−0.396591	+	0.686916i
$40$	−102400.	−	177362.i	−0.252982	−	0.438178i
$41$	−318486.			−0.721684			−0.360842	−	0.932627i	$-0.617511\pi$
$41$	−318486.			−0.721684			−0.360842	+	0.932627i	$0.617511\pi$
$42$		0			0
$43$	77744.0			0.149117			0.0745585	−	0.997217i	$-0.476245\pi$
$43$	77744.0			0.149117			0.0745585	+	0.997217i	$0.476245\pi$
$44$	−1280.00	−	2217.03i	−0.00226530	−	0.00392361i
$45$	−433800.	+	751364.i	−0.709653	+	1.22915i
$46$	420800.	−	728847.i	0.637417	−	1.10404i
$47$	351858.	+	609436.i	0.494339	+	0.856220i	0.999979	−	0.00652440i	$-0.00207680\pi$
$47$	351858.	+	609436.i	0.494339	+	0.856220i	−0.505640	+	0.862745i	$0.668743\pi$
$48$	270336.			0.352825
$49$		0			0
$50$	655000.			0.741048
$51$	1.20457e6	+	2.08637e6i	1.27155	+	2.20240i
$52$	−142464.	+	246755.i	−0.140506	+	0.243363i
$53$	−801639.	+	1.38848e6i	−0.739628	+	1.28107i	0.213035	+	0.977045i	$0.431665\pi$
$53$	−801639.	+	1.38848e6i	−0.739628	+	1.28107i	−0.952663	+	0.304029i	$0.901668\pi$
$54$	4752.00	+	8230.71i	0.00410675	+	0.00711310i
$55$	16000.0			0.0129673
$56$		0			0
$57$	3.05065e6			2.18188
$58$	505336.	+	875268.i	0.340081	+	0.589037i
$59$	−585947.	+	1.01489e6i	−0.371429	+	0.643335i	−0.989786	−	0.142563i	$-0.954466\pi$
$59$	−585947.	+	1.01489e6i	−0.371429	+	0.643335i	0.618356	+	0.785898i	$0.287799\pi$
$60$	−844800.	+	1.46324e6i	−0.504922	+	0.874551i
$61$	−1.03444e6	−	1.79170e6i	−0.583511	−	1.01067i	−0.995059	−	0.0992830i	$-0.968345\pi$
$61$	−1.03444e6	−	1.79170e6i	−0.583511	−	1.01067i	0.411548	−	0.911388i	$-0.364988\pi$
$62$	1.36771e6			0.728826
$63$		0			0
$64$	262144.			0.125000
$65$	−890400.	−	1.54222e6i	−0.402150	−	0.696545i
$66$	−10560.0	+	18290.5i	−0.00452127	+	0.00783106i
$67$	497134.	−	861061.i	0.201935	−	0.349762i	−0.747217	−	0.664580i	$-0.768610\pi$
$67$	497134.	−	861061.i	0.201935	−	0.349762i	0.949152	+	0.314819i	$0.101944\pi$
$68$	1.16806e6	+	2.02315e6i	0.450490	+	0.780272i
$69$	−6.94320e6			−2.54441
$70$		0			0
$71$	33280.0			0.0110352			0.00551759	−	0.999985i	$-0.498244\pi$
$71$	33280.0			0.0110352			0.00551759	+	0.999985i	$0.498244\pi$
$72$	−555264.	−	961745.i	−0.175322	−	0.303666i
$73$	−1.48573e6	+	2.57335e6i	−0.447002	+	0.774229i	−0.998189	−	0.0601519i	$-0.980841\pi$
$73$	−1.48573e6	+	2.57335e6i	−0.447002	+	0.774229i	0.551188	+	0.834381i	$0.314175\pi$
$74$	−83816.0	+	145174.i	−0.0240445	+	0.0416463i
$75$	−2.70188e6	−	4.67978e6i	−0.739522	−	1.28089i
$76$	2.95821e6			0.773003
$77$		0			0
$78$	2.35066e6			0.560865
$79$	1.18808e6	+	2.05782e6i	0.271114	+	0.469584i	0.969147	−	0.246482i	$-0.0792745\pi$
$79$	1.18808e6	+	2.05782e6i	0.271114	+	0.469584i	−0.698033	+	0.716065i	$0.745941\pi$
$80$	−819200.	+	1.41890e6i	−0.178885	+	0.309839i
$81$	2.41101e6	−	4.17598e6i	0.504081	−	0.873095i
$82$	1.27394e6	+	2.20654e6i	0.255154	+	0.441939i
$83$	2.12236e6			0.407423			0.203711	−	0.979031i	$-0.434700\pi$
$83$	2.12236e6			0.407423			0.203711	+	0.979031i	$0.434700\pi$
$84$		0			0
$85$	−1.46008e7			−2.57876
$86$	−310976.	−	538626.i	−0.0527208	−	0.0913152i
$87$	4.16902e6	−	7.22096e6i	0.678761	−	1.17565i
$88$	−10240.0	+	17736.2i	−0.00160181	+	0.00277441i
$89$	3.46017e6	+	5.99320e6i	0.520275	+	0.901142i	0.999722	+	0.0235717i	$0.00750381\pi$
$89$	3.46017e6	+	5.99320e6i	0.520275	+	0.901142i	−0.479447	+	0.877571i	$0.659163\pi$
$90$	6.94080e6			1.00360
$91$		0			0
$92$	−6.73280e6			−0.901443
$93$	−5.64181e6	−	9.77191e6i	−0.727325	−	1.25976i
$94$	2.81486e6	−	4.87549e6i	0.349551	−	0.605439i
$95$	−9.24440e6	+	1.60118e7i	−1.10623	+	1.91605i
$96$	−1.08134e6	−	1.87294e6i	−0.124743	−	0.216060i
$97$	−4.95271e6			−0.550988			−0.275494	−	0.961303i	$-0.588841\pi$
$97$	−4.95271e6			−0.550988			−0.275494	+	0.961303i	$0.588841\pi$
$98$		0			0
$99$	86760.0			0.00898662
$100$	−2.62000e6	−	4.53797e6i	−0.262000	−	0.453797i
$101$	1.61500e6	−	2.79726e6i	0.155972	−	0.270152i	−0.777440	−	0.628957i	$-0.783482\pi$
$101$	1.61500e6	−	2.79726e6i	0.155972	−	0.270152i	0.933413	+	0.358805i	$0.116816\pi$
$102$	9.63653e6	−	1.66910e7i	0.899125	−	1.55733i
$103$	−899546.	−	1.55806e6i	−0.0811135	−	0.140493i	0.822615	−	0.568599i	$-0.192514\pi$
$103$	−899546.	−	1.55806e6i	−0.0811135	−	0.140493i	−0.903728	+	0.428106i	$0.859181\pi$
$104$	2.27942e6			0.198705
$105$		0			0
$106$	1.28262e7			1.04599
$107$	7.82144e6	+	1.35471e7i	0.617225	+	1.06906i	0.989990	+	0.141139i	$0.0450764\pi$
$107$	7.82144e6	+	1.35471e7i	0.617225	+	1.06906i	−0.372765	+	0.927926i	$0.621590\pi$
$108$	38016.0	−	65845.6i	0.00290391	−	0.00502972i
$109$	3.15945e6	−	5.47233e6i	0.233679	−	0.404743i	−0.725209	−	0.688529i	$-0.758257\pi$
$109$	3.15945e6	−	5.47233e6i	0.233679	−	0.404743i	0.958888	+	0.283785i	$0.0915903\pi$
$110$	−64000.0	−	110851.i	−0.00458464	−	0.00794084i
$111$	1.38296e6			0.0959799
$112$		0			0
$113$	−1.02288e7			−0.666881			−0.333441	−	0.942771i	$-0.608210\pi$
$113$	−1.02288e7			−0.666881			−0.333441	+	0.942771i	$0.608210\pi$
$114$	−1.22026e7	−	2.11355e7i	−0.771411	−	1.33612i
$115$	2.10400e7	−	3.64423e7i	1.29004	−	2.23442i
$116$	4.04269e6	−	7.00214e6i	0.240474	−	0.416512i
$117$	−4.82819e6	−	8.36268e6i	−0.278698	−	0.482719i
$118$	9.37515e6			0.525281
$119$		0			0
$120$	1.35168e7			0.714068
$121$	9.74279e6	+	1.68750e7i	0.499959	+	0.865954i
$122$	−8.27549e6	+	1.43336e7i	−0.412605	+	0.714652i
$123$	1.05100e7	−	1.82039e7i	0.509256	−	0.882058i
$124$	−5.47085e6	−	9.47579e6i	−0.257679	−	0.446313i
$125$	1.50000e6			0.0686920
$126$		0			0
$127$	6.00725e6			0.260233			0.130117	−	0.991499i	$-0.458465\pi$
$127$	6.00725e6			0.260233			0.130117	+	0.991499i	$0.458465\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$	−2.56555e6	+	4.44367e6i	−0.105224	+	0.182254i
$130$	−7.12320e6	+	1.23377e7i	−0.284363	+	0.492532i
$131$	1.03198e7	+	1.78744e7i	0.401072	+	0.694677i	0.993856	−	0.110685i	$-0.0353045\pi$
$131$	1.03198e7	+	1.78744e7i	0.401072	+	0.694677i	−0.592784	+	0.805362i	$0.701971\pi$
$132$	168960.			0.00639404
$133$		0			0
$134$	−7.95414e6			−0.285579
$135$	237600.	+	411535.i	0.00831148	+	0.0143959i
$136$	9.34451e6	−	1.61852e7i	0.318545	−	0.551736i
$137$	−2.38099e6	+	4.12400e6i	−0.0791109	+	0.137024i	−0.902867	−	0.429921i	$-0.858541\pi$
$137$	−2.38099e6	+	4.12400e6i	−0.0791109	+	0.137024i	0.823756	+	0.566945i	$0.191875\pi$
$138$	2.77728e7	+	4.81039e7i	0.899586	+	1.55813i
$139$	5.05723e6			0.159721			0.0798604	−	0.996806i	$-0.474553\pi$
$139$	5.05723e6			0.159721			0.0798604	+	0.996806i	$0.474553\pi$
$140$		0			0
$141$	−4.64453e7			−1.39532
$142$	−133120.	−	230571.i	−0.00390152	−	0.00675764i
$143$	−89040.0	+	154222.i	−0.00254630	+	0.00441032i
$144$	−4.44211e6	+	7.69396e6i	−0.123971	+	0.214724i
$145$	2.52668e7	+	4.37634e7i	0.688275	+	1.19213i
$146$	2.37716e7			0.632156
$147$		0			0
$148$	1.34106e6			0.0340041
$149$	1.36368e7	+	2.36197e7i	0.337723	+	0.584954i	0.984004	−	0.178146i	$-0.0570098\pi$
$149$	1.36368e7	+	2.36197e7i	0.337723	+	0.584954i	−0.646281	+	0.763100i	$0.723676\pi$
$150$	−2.16150e7	+	3.74383e7i	−0.522921	+	0.905725i
$151$	−3.24460e6	+	5.61982e6i	−0.0766906	+	0.132832i	−0.901820	−	0.432111i	$-0.857769\pi$
$151$	−3.24460e6	+	5.61982e6i	−0.0766906	+	0.132832i	0.825130	+	0.564944i	$0.191102\pi$
$152$	−1.18328e7	−	2.04951e7i	−0.273298	−	0.473366i
$153$	−7.91728e7			−1.78713
$154$		0			0
$155$	6.83856e7			1.47504
$156$	−9.40262e6	−	1.62858e7i	−0.198296	−	0.343458i
$157$	−3.15405e7	+	5.46298e7i	−0.650459	+	1.12663i	0.332553	+	0.943085i	$0.392090\pi$
$157$	−3.15405e7	+	5.46298e7i	−0.650459	+	1.12663i	−0.983012	+	0.183543i	$0.941243\pi$
$158$	9.50467e6	−	1.64626e7i	0.191707	−	0.332046i
$159$	−5.29082e7	−	9.16396e7i	−1.04384	−	1.80798i
$160$	1.31072e7			0.252982
$161$		0			0
$162$	−3.85761e7			−0.712879
$163$	−4.16136e7	−	7.20768e7i	−0.752624	−	1.30358i	−0.946547	−	0.322567i	$-0.895454\pi$
$163$	−4.16136e7	−	7.20768e7i	−0.752624	−	1.30358i	0.193923	−	0.981017i	$-0.437879\pi$
$164$	1.01916e7	−	1.76523e7i	0.180421	−	0.312498i
$165$	−528000.	+	914523.i	−0.00915040	+	0.0158490i
$166$	−8.48943e6	−	1.47041e7i	−0.144046	−	0.249494i
$167$	−3.06916e7			−0.509931			−0.254965	−	0.966950i	$-0.582064\pi$
$167$	−3.06916e7			−0.509931			−0.254965	+	0.966950i	$0.582064\pi$
$168$		0			0
$169$	−4.29282e7			−0.684131
$170$	5.84032e7	+	1.01157e8i	0.911728	+	1.57916i
$171$	−5.01278e7	+	8.68238e7i	−0.766641	+	1.32786i
$172$	−2.48781e6	+	4.30901e6i	−0.0372793	+	0.0645696i
$173$	−2.63669e7	−	4.56688e7i	−0.387167	−	0.670592i	0.604900	−	0.796301i	$-0.293213\pi$
$173$	−2.63669e7	−	4.56688e7i	−0.387167	−	0.670592i	−0.992067	+	0.125709i	$0.959880\pi$
$174$	−6.67044e7			−0.959913
$175$		0			0
$176$	163840.			0.00226530
$177$	−3.86725e7	−	6.69827e7i	−0.524199	−	0.907939i
$178$	2.76814e7	−	4.79456e7i	0.367890	−	0.637204i
$179$	−4.21369e7	+	7.29833e7i	−0.549133	+	0.951126i	0.449202	+	0.893430i	$0.351708\pi$
$179$	−4.21369e7	+	7.29833e7i	−0.549133	+	0.951126i	−0.998334	+	0.0576952i	$0.981625\pi$
$180$	−2.77632e7	−	4.80873e7i	−0.354826	−	0.614577i
$181$	1.03956e8			1.30309			0.651547	−	0.758608i	$-0.274120\pi$
$181$	1.03956e8			1.30309			0.651547	+	0.758608i	$0.274120\pi$
$182$		0			0
$183$	1.36546e8			1.64702
$184$	2.69312e7	+	4.66462e7i	0.318708	+	0.552019i
$185$	−4.19080e6	+	7.25868e6i	−0.0486627	+	0.0842862i
$186$	−4.51345e7	+	7.81752e7i	−0.514296	+	0.890787i
$187$	730040.	+	1.26447e6i	0.00816396	+	0.0141404i
$188$	−4.50378e7			−0.494339
$189$		0			0
$190$	1.47910e8			1.56445
$191$	6.23876e7	+	1.08059e8i	0.647861	+	1.12213i	0.983633	+	0.180185i	$0.0576695\pi$
$191$	6.23876e7	+	1.08059e8i	0.647861	+	1.12213i	−0.335772	+	0.941943i	$0.608997\pi$
$192$	−8.65075e6	+	1.49835e7i	−0.0882063	+	0.152778i
$193$	−7.37944e7	+	1.27816e8i	−0.738878	+	1.27977i	0.214123	+	0.976807i	$0.431311\pi$
$193$	−7.37944e7	+	1.27816e8i	−0.738878	+	1.27977i	−0.953001	+	0.302968i	$0.902023\pi$
$194$	1.98108e7	+	3.43134e7i	0.194804	+	0.337410i
$195$	1.17533e8			1.13511
$196$		0			0
$197$	1.55812e8			1.45200			0.726002	−	0.687692i	$-0.241376\pi$
$197$	1.55812e8			1.45200			0.726002	+	0.687692i	$0.241376\pi$
$198$	−347040.	−	601091.i	−0.00317725	−	0.00550316i
$199$	−6.65963e6	+	1.15348e7i	−0.0599052	+	0.103759i	−0.894423	−	0.447223i	$-0.852413\pi$
$199$	−6.65963e6	+	1.15348e7i	−0.0599052	+	0.103759i	0.834517	+	0.550981i	$0.185746\pi$
$200$	−2.09600e7	+	3.63038e7i	−0.185262	+	0.320883i
$201$	3.28108e7	+	5.68300e7i	0.284991	+	0.493619i
$202$	−2.58400e7			−0.220578
$203$		0			0
$204$	−1.54184e8			−1.27155
$205$	6.36972e7	+	1.10327e8i	0.516395	+	0.894422i
$206$	−7.19637e6	+	1.24645e7i	−0.0573559	+	0.0993433i
$207$	1.14089e8	−	1.97609e8i	0.894024	−	1.54849i
$208$	−9.11770e6	−	1.57923e7i	−0.0702528	−	0.121681i
$209$	1.84888e6			0.0140087
$210$		0			0
$211$	−2.04940e8			−1.50189			−0.750945	−	0.660365i	$-0.770402\pi$
$211$	−2.04940e8			−1.50189			−0.750945	+	0.660365i	$0.770402\pi$
$212$	−5.13049e7	−	8.88627e7i	−0.369814	−	0.640537i
$213$	−1.09824e6	+	1.90221e6i	−0.00778697	+	0.0134874i
$214$	6.25715e7	−	1.08377e8i	0.436444	−	0.755943i
$215$	−1.55488e7	−	2.69313e7i	−0.106699	−	0.184809i
$216$	−608256.			−0.00410675
$217$		0			0
$218$	−5.05512e7			−0.330471
$219$	−9.80580e7	−	1.69841e8i	−0.630854	−	1.09267i
$220$	−512000.	+	886810.i	−0.00324183	+	0.00561502i
$221$	8.12535e7	−	1.40735e8i	0.506371	−	0.877060i
$222$	−5.53186e6	−	9.58146e6i	−0.0339340	−	0.0587755i
$223$	6.84858e7			0.413555			0.206778	−	0.978388i	$-0.433702\pi$
$223$	6.84858e7			0.413555			0.206778	+	0.978388i	$0.433702\pi$
$224$		0			0
$225$	1.77587e8			1.03937
$226$	4.09150e7	+	7.08669e7i	0.235778	+	0.408380i
$227$	−9.68133e6	+	1.67686e7i	−0.0549344	+	0.0951492i	−0.892185	−	0.451670i	$-0.850828\pi$
$227$	−9.68133e6	+	1.67686e7i	−0.0549344	+	0.0951492i	0.837250	+	0.546820i	$0.184162\pi$
$228$	−9.76209e7	+	1.69084e8i	−0.545470	+	0.944781i
$229$	1.54078e8	+	2.66872e8i	0.847847	+	1.46851i	0.883126	+	0.469137i	$0.155435\pi$
$229$	1.54078e8	+	2.66872e8i	0.847847	+	1.46851i	−0.0352785	+	0.999378i	$0.511232\pi$
$230$	−3.36640e8			−1.82439
$231$		0			0
$232$	−6.46830e7			−0.340081
$233$	−1.77899e7	−	3.08129e7i	−0.0921355	−	0.159583i	0.816274	−	0.577665i	$-0.196036\pi$
$233$	−1.77899e7	−	3.08129e7i	−0.0921355	−	0.159583i	−0.908409	+	0.418082i	$0.862703\pi$
$234$	−3.86256e7	+	6.69014e7i	−0.197069	+	0.341334i
$235$	1.40743e8	−	2.43774e8i	0.707440	−	1.22532i
$236$	−3.75006e7	−	6.49530e7i	−0.185715	−	0.321667i
$237$	−1.56827e8			−0.765247
$238$		0			0
$239$	−2.30056e8			−1.09004			−0.545018	−	0.838424i	$-0.683477\pi$
$239$	−2.30056e8			−1.09004			−0.545018	+	0.838424i	$0.683477\pi$
$240$	−5.40672e7	−	9.36471e7i	−0.252461	−	0.437276i
$241$	2.51747e6	−	4.36039e6i	0.0115853	−	0.0200662i	−0.860175	−	0.510000i	$-0.829646\pi$
$241$	2.51747e6	−	4.36039e6i	0.0115853	−	0.0200662i	0.871760	+	0.489933i	$0.162979\pi$
$242$	7.79423e7	−	1.35000e8i	0.353524	−	0.612322i
$243$	1.57827e8	+	2.73365e8i	0.705603	+	1.22214i
$244$	1.32408e8			0.583511
$245$		0			0
$246$	−1.68161e8			−0.720197
$247$	−1.02890e8	−	1.78211e8i	−0.434445	−	0.752480i
$248$	−4.37668e7	+	7.58063e7i	−0.182206	+	0.315591i
$249$	−7.00378e7	+	1.21309e8i	−0.287498	+	0.497961i
$250$	−6.00000e6	−	1.03923e7i	−0.0242863	−	0.0420651i
$251$	1.03283e8			0.412258			0.206129	−	0.978525i	$-0.433913\pi$
$251$	1.03283e8			0.412258			0.206129	+	0.978525i	$0.433913\pi$
$252$		0			0
$253$	−4.20800e6			−0.0163363
$254$	−2.40290e7	−	4.16194e7i	−0.0920063	−	0.159360i
$255$	4.81826e8	−	8.34548e8i	1.81970	−	3.15181i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.16141e8	−	2.01162e8i	−0.426796	−	0.739232i	0.569790	−	0.821790i	$-0.307024\pi$
$257$	−1.16141e8	−	2.01162e8i	−0.426796	−	0.739232i	−0.996586	+	0.0825580i	$0.973691\pi$
$258$	4.10488e7			0.148810
$259$		0			0
$260$	1.13971e8			0.402150
$261$	1.37009e8	+	2.37307e8i	0.476989	+	0.826169i
$262$	8.25585e7	−	1.42995e8i	0.283601	−	0.491211i
$263$	−2.08374e8	+	3.60915e8i	−0.706317	+	1.22338i	0.259898	+	0.965636i	$0.416311\pi$
$263$	−2.08374e8	+	3.60915e8i	−0.706317	+	1.22338i	−0.966214	+	0.257740i	$0.917022\pi$
$264$	−675840.	−	1.17059e6i	−0.00226063	−	0.00391553i
$265$	6.41311e8			2.11694
$266$		0			0
$267$	−4.56743e8			−1.46853
$268$	3.18166e7	+	5.51079e7i	0.100968	+	0.174881i
$269$	−1.57339e8	+	2.72520e8i	−0.492838	+	0.853621i	−0.999966	−	0.00825013i	$-0.997374\pi$
$269$	−1.57339e8	+	2.72520e8i	−0.492838	+	0.853621i	0.507128	+	0.861871i	$0.330707\pi$
$270$	1.90080e6	−	3.29228e6i	0.00587710	−	0.0101794i
$271$	9.60685e7	+	1.66395e8i	0.293216	+	0.507866i	0.974568	−	0.224090i	$-0.0719410\pi$
$271$	9.60685e7	+	1.66395e8i	0.293216	+	0.507866i	−0.681352	+	0.731956i	$0.738608\pi$
$272$	−1.49512e8			−0.450490
$273$		0			0
$274$	3.80959e7			0.111880
$275$	−1.63750e6	−	2.83623e6i	−0.00474807	−	0.00822389i
$276$	2.22182e8	−	3.84831e8i	0.636104	−	1.10176i
$277$	2.20197e8	−	3.81392e8i	0.622489	−	1.07818i	−0.366532	−	0.930406i	$-0.619455\pi$
$277$	2.20197e8	−	3.81392e8i	0.622489	−	1.07818i	0.989021	−	0.147777i	$-0.0472118\pi$
$278$	−2.02289e7	−	3.50375e7i	−0.0564698	−	0.0978086i
$279$	3.70821e8			1.02223
$280$		0			0
$281$	3.59235e8			0.965842			0.482921	−	0.875664i	$-0.339576\pi$
$281$	3.59235e8			0.965842			0.482921	+	0.875664i	$0.339576\pi$
$282$	1.85781e8	+	3.21782e8i	0.493321	+	0.854457i
$283$	−4.05734e7	+	7.02751e7i	−0.106411	+	0.184310i	−0.914314	−	0.405006i	$-0.867269\pi$
$283$	−4.05734e7	+	7.02751e7i	−0.106411	+	0.184310i	0.807903	+	0.589316i	$0.200603\pi$
$284$	−1.06496e6	+	1.84456e6i	−0.00275879	+	0.00477837i
$285$	−6.10130e8	−	1.05678e9i	−1.56123	−	2.70412i
$286$	1.42464e6			0.00360101
$287$		0			0
$288$	7.10738e7			0.175322
$289$	−4.61029e8	−	7.98525e8i	−1.12353	−	1.94601i
$290$	2.02134e8	−	3.50107e8i	0.486684	−	0.842962i
$291$	1.63439e8	−	2.83085e8i	0.388805	−	0.673429i
$292$	−9.50865e7	−	1.64695e8i	−0.223501	−	0.387115i
$293$	−2.53416e8			−0.588569			−0.294285	−	0.955718i	$-0.595081\pi$
$293$	−2.53416e8			−0.588569			−0.294285	+	0.955718i	$0.595081\pi$
$294$		0			0
$295$	4.68758e8			1.06309
$296$	−5.36422e6	−	9.29111e6i	−0.0120223	−	0.0208232i
$297$	23760.0	−	41153.5i	5.26258e−5	−	9.11506e-5i
$298$	1.09095e8	−	1.88957e8i	0.238807	−	0.413625i
$299$	2.34175e8	+	4.05603e8i	0.506631	+	0.877511i
$300$	3.45840e8			0.739522
$301$		0			0
$302$	5.19137e7			0.108457
$303$	1.06590e8	+	1.84619e8i	0.220124	+	0.381266i
$304$	−9.46627e7	+	1.63961e8i	−0.193251	+	0.334720i
$305$	−4.13774e8	+	7.16678e8i	−0.835053	+	1.44635i
$306$	3.16691e8	+	5.48526e8i	0.631846	+	1.09439i
$307$	−8.72706e8			−1.72141			−0.860703	−	0.509107i	$-0.829976\pi$
$307$	−8.72706e8			−1.72141			−0.860703	+	0.509107i	$0.829976\pi$
$308$		0			0
$309$	1.18740e8			0.228951
$310$	−2.73542e8	−	4.73789e8i	−0.521505	−	0.903274i
$311$	−3.35806e8	+	5.81633e8i	−0.633033	+	1.09645i	0.353895	+	0.935285i	$0.384857\pi$
$311$	−3.35806e8	+	5.81633e8i	−0.633033	+	1.09645i	−0.986928	+	0.161161i	$0.948476\pi$
$312$	−7.52210e7	+	1.30287e8i	−0.140216	+	0.242861i
$313$	−9.61082e7	−	1.66464e8i	−0.177156	−	0.306843i	0.763749	−	0.645513i	$-0.223356\pi$
$313$	−9.61082e7	−	1.66464e8i	−0.177156	−	0.306843i	−0.940905	+	0.338670i	$0.890023\pi$
$314$	5.04648e8			0.919888
$315$		0			0
$316$	−1.52075e8			−0.271114
$317$	6.69186e7	+	1.15906e8i	0.117988	+	0.204362i	0.918970	−	0.394326i	$-0.129022\pi$
$317$	6.69186e7	+	1.15906e8i	0.117988	+	0.204362i	−0.800982	+	0.598688i	$0.795689\pi$
$318$	−4.23265e8	+	7.33117e8i	−0.738104	+	1.27843i
$319$	2.52668e6	−	4.37634e6i	0.00435796	−	0.00754820i
$320$	−5.24288e7	−	9.08093e7i	−0.0894427	−	0.154919i
$321$	−1.03243e9			−1.74218
$322$		0			0
$323$	−1.68720e9			−2.78584
$324$	1.54304e8	+	2.67263e8i	0.252041	+	0.436547i
$325$	−1.82254e8	+	3.15673e8i	−0.294500	+	0.510088i
$326$	−3.32908e8	+	5.76614e8i	−0.532186	+	0.921773i
$327$	2.08524e8	+	3.61174e8i	0.329791	+	0.571214i
$328$	−1.63065e8			−0.255154
$329$		0			0
$330$	8.44800e6			0.0129406
$331$	−2.12649e8	−	3.68319e8i	−0.322304	−	0.558247i	0.658659	−	0.752441i	$-0.271124\pi$
$331$	−2.12649e8	−	3.68319e8i	−0.322304	−	0.558247i	−0.980963	+	0.194195i	$0.937791\pi$
$332$	−6.79155e7	+	1.17633e8i	−0.101856	+	0.176419i
$333$	−2.27246e7	+	3.93602e7i	−0.0337242	+	0.0584120i
$334$	1.22766e8	+	2.12637e8i	0.180288	+	0.312268i
$335$	−3.97707e8			−0.577972
$336$		0			0
$337$	1.07703e9			1.53293			0.766463	−	0.642288i	$-0.222015\pi$
$337$	1.07703e9			1.53293			0.766463	+	0.642288i	$0.222015\pi$
$338$	1.71713e8	+	2.97415e8i	0.241877	+	0.418943i
$339$	3.37549e8	−	5.84652e8i	0.470585	−	0.815077i
$340$	4.67226e8	−	8.09258e8i	0.644689	−	1.11663i
$341$	−3.41928e6	−	5.92237e6i	−0.00466976	−	0.00808826i
$342$	8.02044e8			1.08419
$343$		0			0
$344$	3.98049e7			0.0527208
$345$	1.38864e9	+	2.40520e9i	1.82063	+	3.15343i
$346$	−2.10935e8	+	3.65351e8i	−0.273768	+	0.474180i
$347$	3.61882e8	−	6.26798e8i	0.464958	−	0.805331i	−0.534242	−	0.845332i	$-0.679403\pi$
$347$	3.61882e8	−	6.26798e8i	0.464958	−	0.805331i	0.999200	+	0.0400010i	$0.0127361\pi$
$348$	2.66817e8	+	4.62141e8i	0.339380	+	0.587824i
$349$	4.48132e8			0.564310			0.282155	−	0.959369i	$-0.408951\pi$
$349$	4.48132e8			0.564310			0.282155	+	0.959369i	$0.408951\pi$
$350$		0			0
$351$	−5.28898e6			−0.00652825
$352$	−655360.	−	1.13512e6i	−0.000800904	−	0.00138721i
$353$	−7.49728e8	+	1.29857e9i	−0.907177	+	1.57128i	−0.0892088	+	0.996013i	$0.528434\pi$
$353$	−7.49728e8	+	1.29857e9i	−0.907177	+	1.57128i	−0.817968	+	0.575264i	$0.804899\pi$
$354$	−3.09380e8	+	5.35862e8i	−0.370664	+	0.642010i
$355$	−6.65600e6	−	1.15285e7i	−0.00789613	−	0.0136765i
$356$	−4.42902e8			−0.520275
$357$		0			0
$358$	6.74191e8			0.776591
$359$	1.28445e8	+	2.22473e8i	0.146516	+	0.253774i	0.929938	−	0.367717i	$-0.119861\pi$
$359$	1.28445e8	+	2.22473e8i	0.146516	+	0.253774i	−0.783421	+	0.621491i	$0.786527\pi$
$360$	−2.22106e8	+	3.84698e8i	−0.250900	+	0.434572i
$361$	−6.21301e8	+	1.07612e9i	−0.695067	+	1.20389i
$362$	−4.15825e8	−	7.20230e8i	−0.460713	−	0.797979i
$363$	−1.28605e9			−1.41118
$364$		0			0
$365$	1.18858e9			1.27939
$366$	−5.46182e8	−	9.46015e8i	−0.582309	−	1.00859i
$367$	3.25212e8	−	5.63284e8i	0.343428	−	0.594835i	−0.641639	−	0.767007i	$-0.721745\pi$
$367$	3.25212e8	−	5.63284e8i	0.343428	−	0.594835i	0.985067	+	0.172172i	$0.0550786\pi$
$368$	2.15450e8	−	3.73170e8i	0.225361	−	0.390336i
$369$	3.45398e8	+	5.98247e8i	0.357872	+	0.619852i
$370$	6.70528e7			0.0688194
$371$		0			0
$372$	7.22152e8			0.727325
$373$	2.33064e8	+	4.03678e8i	0.232538	+	0.402768i	0.958554	−	0.284910i	$-0.0919637\pi$
$373$	2.33064e8	+	4.03678e8i	0.232538	+	0.402768i	−0.726016	+	0.687677i	$0.758630\pi$
$374$	5.84032e6	−	1.01157e7i	0.00577279	−	0.00999877i
$375$	−4.95000e7	+	8.57365e7i	−0.0484725	+	0.0839569i
$376$	1.80151e8	+	3.12031e8i	0.174775	+	0.302720i
$377$	−5.62439e8			−0.540606
$378$		0			0
$379$	2.85860e8			0.269721			0.134861	−	0.990865i	$-0.456941\pi$
$379$	2.85860e8			0.269721			0.134861	+	0.990865i	$0.456941\pi$
$380$	−5.91642e8	−	1.02475e9i	−0.553116	−	0.958025i
$381$	−1.98239e8	+	3.43360e8i	−0.183634	+	0.318063i
$382$	4.99101e8	−	8.64468e8i	0.458107	−	0.793464i
$383$	−8.25375e8	−	1.42959e9i	−0.750681	−	1.30022i	−0.947493	−	0.319777i	$-0.896392\pi$
$383$	−8.25375e8	−	1.42959e9i	−0.750681	−	1.30022i	0.196812	−	0.980441i	$-0.436941\pi$
$384$	1.38412e8			0.124743
$385$		0			0
$386$	1.18071e9			1.04493
$387$	−8.43134e7	−	1.46035e8i	−0.0739449	−	0.128076i
$388$	1.58487e8	−	2.74507e8i	0.137747	−	0.238585i
$389$	−7.56521e8	+	1.31033e9i	−0.651624	+	1.12865i	0.331104	+	0.943594i	$0.392579\pi$
$389$	−7.56521e8	+	1.31033e9i	−0.651624	+	1.12865i	−0.982729	+	0.185052i	$0.940754\pi$
$390$	−4.70131e8	−	8.14291e8i	−0.401322	−	0.695110i
$391$	3.84001e9			3.24873
$392$		0			0
$393$	−1.36221e9			−1.13207
$394$	−6.23246e8	−	1.07949e9i	−0.513361	−	0.889167i
$395$	4.75234e8	−	8.23129e8i	0.387987	−	0.672013i
$396$	−2.77632e6	+	4.80873e6i	−0.00224665	+	0.00389132i
$397$	−4.31897e8	−	7.48068e8i	−0.346428	−	0.600032i	0.639184	−	0.769054i	$-0.279272\pi$
$397$	−4.31897e8	−	7.48068e8i	−0.346428	−	0.600032i	−0.985612	+	0.169022i	$0.945939\pi$
$398$	1.06554e8			0.0847187
$399$		0			0
$400$	3.35360e8			0.262000
$401$	−5.70209e7	−	9.87630e7i	−0.0441599	−	0.0764873i	0.843101	−	0.537756i	$-0.180728\pi$
$401$	−5.70209e7	−	9.87630e7i	−0.0441599	−	0.0764873i	−0.887261	+	0.461269i	$0.847394\pi$
$402$	2.62487e8	−	4.54640e8i	0.201519	−	0.349041i
$403$	−3.80566e8	+	6.59159e8i	−0.289642	+	0.501675i
$404$	1.03360e8	+	1.79025e8i	0.0779862	+	0.135076i
$405$	−1.92880e9			−1.44277
$406$		0			0
$407$	838160.			0.000616235
$408$	6.16738e8	+	1.06822e9i	0.449562	+	0.778665i
$409$	−5.91639e8	+	1.02475e9i	−0.427588	+	0.740604i	−0.996658	−	0.0816850i	$-0.973970\pi$
$409$	−5.91639e8	+	1.02475e9i	−0.427588	+	0.740604i	0.569070	+	0.822289i	$0.307303\pi$
$410$	5.09578e8	−	8.82614e8i	0.365146	−	0.632452i
$411$	−1.57146e8	−	2.72184e8i	−0.111649	−	0.193382i
$412$	1.15142e8			0.0811135
$413$		0			0
$414$	−1.82543e9			−1.26434
$415$	−4.24472e8	−	7.35206e8i	−0.291528	−	0.504941i
$416$	−7.29416e7	+	1.26339e8i	−0.0496762	+	0.0860417i
$417$	−1.66889e8	+	2.89060e8i	−0.112707	+	0.195214i
$418$	−7.39552e6	−	1.28094e7i	−0.00495281	−	0.00857852i
$419$	−2.27959e8			−0.151394			−0.0756970	−	0.997131i	$-0.524118\pi$
$419$	−2.27959e8			−0.151394			−0.0756970	+	0.997131i	$0.524118\pi$
$420$		0			0
$421$	−3.90700e7			−0.0255186			−0.0127593	−	0.999919i	$-0.504062\pi$
$421$	−3.90700e7			−0.0255186			−0.0127593	+	0.999919i	$0.504062\pi$
$422$	8.19760e8	+	1.41987e9i	0.530998	+	0.919716i
$423$	7.63180e8	−	1.32187e9i	0.490270	−	0.849173i
$424$	−4.10439e8	+	7.10901e8i	−0.261498	+	0.452928i
$425$	1.49430e9	+	2.58820e9i	0.944228	+	1.63545i
$426$	1.75718e7			0.0110124
$427$		0			0
$428$	−1.00114e9			−0.617225
$429$	−5.87664e6	−	1.01786e7i	−0.00359359	−	0.00622428i
$430$	−1.24390e8	+	2.15450e8i	−0.0754479	+	0.130680i
$431$	1.29310e9	−	2.23972e9i	0.777968	−	1.34748i	−0.155143	−	0.987892i	$-0.549584\pi$
$431$	1.29310e9	−	2.23972e9i	0.777968	−	1.34748i	0.933111	−	0.359588i	$-0.117083\pi$
$432$	2.43302e6	+	4.21412e6i	0.00145196	+	0.00251486i
$433$	1.78893e9			1.05897			0.529486	−	0.848318i	$-0.322385\pi$
$433$	1.78893e9			1.05897			0.529486	+	0.848318i	$0.322385\pi$
$434$		0			0
$435$	−3.33522e9			−1.94273
$436$	2.02205e8	+	3.50229e8i	0.116839	+	0.202372i
$437$	2.43128e9	−	4.21110e9i	1.39364	−	2.41385i
$438$	−7.84464e8	+	1.35873e9i	−0.446081	+	0.772635i
$439$	−2.29452e8	−	3.97423e8i	−0.129440	−	0.224196i	0.794020	−	0.607892i	$-0.207984\pi$
$439$	−2.29452e8	−	3.97423e8i	−0.129440	−	0.224196i	−0.923460	+	0.383696i	$0.874651\pi$
$440$	8.19200e6			0.00458464
$441$		0			0
$442$	−1.30006e9			−0.716117
$443$	−6.92294e8	−	1.19909e9i	−0.378336	−	0.655297i	0.612484	−	0.790483i	$-0.290170\pi$
$443$	−6.92294e8	−	1.19909e9i	−0.378336	−	0.655297i	−0.990820	+	0.135186i	$0.956837\pi$
$444$	−4.42548e7	+	7.66516e7i	−0.0239950	+	0.0415605i
$445$	1.38407e9	−	2.39728e9i	0.744557	−	1.28961i
$446$	−2.73943e8	−	4.74484e8i	−0.146214	−	0.253250i
$447$	−1.80006e9			−0.953259
$448$		0			0
$449$	−2.73611e9			−1.42650			−0.713248	−	0.700911i	$-0.752777\pi$
$449$	−2.73611e9			−1.42650			−0.713248	+	0.700911i	$0.752777\pi$
$450$	−7.10348e8	−	1.23036e9i	−0.367474	−	0.636484i
$451$	6.36972e6	−	1.10327e7i	0.00326966	−	0.00566322i
$452$	3.27320e8	−	5.66936e8i	0.166720	−	0.288768i
$453$	−2.14144e8	−	3.70908e8i	−0.108234	−	0.187466i
$454$	1.54901e8			0.0776890
$455$		0			0
$456$	1.56193e9			0.771411
$457$	−1.21527e9	−	2.10490e9i	−0.595614	−	1.03163i	−0.993460	−	0.114181i	$-0.963576\pi$
$457$	−1.21527e9	−	2.10490e9i	−0.595614	−	1.03163i	0.397846	−	0.917452i	$-0.369758\pi$
$458$	1.23263e9	−	2.13497e9i	0.599518	−	1.03840i
$459$	−2.16822e7	+	3.75547e7i	−0.0104655	+	0.0181267i
$460$	1.34656e9	+	2.33231e9i	0.645020	+	1.11721i
$461$	−3.94884e9			−1.87723			−0.938613	−	0.344971i	$-0.887889\pi$
$461$	−3.94884e9			−1.87723			−0.938613	+	0.344971i	$0.887889\pi$
$462$		0			0
$463$	2.57453e9			1.20549			0.602746	−	0.797933i	$-0.294073\pi$
$463$	2.57453e9			1.20549			0.602746	+	0.797933i	$0.294073\pi$
$464$	2.58732e8	+	4.48137e8i	0.120237	+	0.208256i
$465$	−2.25672e9	+	3.90876e9i	−1.04086	+	1.80283i
$466$	−1.42319e8	+	2.46504e8i	−0.0651496	+	0.112842i
$467$	1.49241e8	+	2.58493e8i	0.0678078	+	0.117446i	0.897936	−	0.440126i	$-0.145066\pi$
$467$	1.49241e8	+	2.58493e8i	0.0678078	+	0.117446i	−0.830128	+	0.557572i	$0.811733\pi$
$468$	6.18009e8			0.278698
$469$		0			0
$470$	−2.25189e9			−1.00047
$471$	−2.08167e9	−	3.60557e9i	−0.917993	−	1.59001i
$472$	−3.00005e8	+	5.19624e8i	−0.131320	+	0.227453i
$473$	−1.55488e6	+	2.69313e6i	−0.000675589	+	0.00117016i
$474$	6.27308e8	+	1.08653e9i	0.270556	+	0.468616i
$475$	3.78443e9			1.62021
$476$		0			0
$477$	3.47751e9			1.46708
$478$	9.20224e8	+	1.59388e9i	0.385386	+	0.667508i
$479$	1.31000e9	−	2.26899e9i	0.544625	−	0.943318i	−0.454006	−	0.890999i	$-0.650005\pi$
$479$	1.31000e9	−	2.26899e9i	0.544625	−	0.943318i	0.998630	−	0.0523188i	$-0.0166612\pi$
$480$	−4.32538e8	+	7.49177e8i	−0.178517	+	0.309200i
$481$	−4.66436e7	−	8.07891e7i	−0.0191110	−	0.0331013i
$482$	−4.02796e7			−0.0163840
$483$		0			0
$484$	−1.24708e9			−0.499959
$485$	9.90542e8	+	1.71567e9i	0.394255	+	0.682869i
$486$	1.26262e9	−	2.18692e9i	0.498936	−	0.864183i
$487$	2.08331e9	−	3.60840e9i	0.817339	−	1.41567i	−0.0902966	−	0.995915i	$-0.528781\pi$
$487$	2.08331e9	−	3.60840e9i	0.817339	−	1.41567i	0.907636	−	0.419758i	$-0.137885\pi$
$488$	−5.29631e8	−	9.17348e8i	−0.206302	−	0.357326i
$489$	5.49299e9			2.12436
$490$		0			0
$491$	2.41300e9			0.919967			0.459983	−	0.887928i	$-0.347855\pi$
$491$	2.41300e9			0.919967			0.459983	+	0.887928i	$0.347855\pi$
$492$	6.72642e8	+	1.16505e9i	0.254628	+	0.441029i
$493$	−2.30572e9	+	3.99363e9i	−0.866648	+	1.50108i
$494$	−8.23121e8	+	1.42569e9i	−0.307199	+	0.532084i
$495$	−1.73520e7	−	3.00545e7i	−0.00643030	−	0.0111376i
$496$	7.00269e8			0.257679
$497$		0			0
$498$	1.12061e9			0.406584
$499$	5.20459e8	+	9.01462e8i	0.187515	+	0.324785i	0.944421	−	0.328739i	$-0.106623\pi$
$499$	5.20459e8	+	9.01462e8i	0.187515	+	0.324785i	−0.756906	+	0.653523i	$0.773290\pi$
$500$	−4.80000e7	+	8.31384e7i	−0.0171730	+	0.0297445i
$501$	1.01282e9	−	1.75426e9i	0.359833	−	0.623249i
$502$	−4.13130e8	−	7.15563e8i	−0.145755	−	0.252455i
$503$	1.17273e9			0.410876			0.205438	−	0.978670i	$-0.434138\pi$
$503$	1.17273e9			0.410876			0.205438	+	0.978670i	$0.434138\pi$
$504$		0			0
$505$	−1.29200e9			−0.446419
$506$	1.68320e7	+	2.91539e7i	0.00577576	+	0.0100039i
$507$	1.41663e9	−	2.45368e9i	0.482757	−	0.836160i
$508$	−1.92232e8	+	3.32955e8i	−0.0650583	+	0.112684i
$509$	−4.06909e7	−	7.04787e7i	−0.0136768	−	0.0236889i	0.859106	−	0.511798i	$-0.171020\pi$
$509$	−4.06909e7	−	7.04787e7i	−0.0136768	−	0.0236889i	−0.872783	+	0.488109i	$0.837687\pi$
$510$	−7.70922e9			−2.57345
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	2.74559e7	+	4.75550e7i	0.00897893	+	0.0155520i
$514$	−9.29129e8	+	1.60930e9i	−0.301790	+	0.522716i
$515$	−3.59818e8	+	6.23224e8i	−0.116080	+	0.201057i
$516$	−1.64195e8	−	2.84395e8i	−0.0526122	−	0.0911271i
$517$	−2.81486e7			−0.00895861
$518$		0			0
$519$	3.48043e9			1.09282
$520$	−4.55885e8	−	7.89616e8i	−0.142182	−	0.246266i
$521$	−1.38729e9	+	2.40286e9i	−0.429770	+	0.744383i	−0.996853	−	0.0792777i	$-0.974739\pi$
$521$	−1.38729e9	+	2.40286e9i	−0.429770	+	0.744383i	0.567083	+	0.823661i	$0.308072\pi$
$522$	1.09607e9	−	1.89846e9i	0.337282	−	0.584189i
$523$	2.49607e9	+	4.32331e9i	0.762957	+	1.32148i	0.941320	+	0.337515i	$0.109586\pi$
$523$	2.49607e9	+	4.32331e9i	0.762957	+	1.32148i	−0.178363	+	0.983965i	$0.557080\pi$
$524$	−1.32094e9			−0.401072
$525$		0			0
$526$	3.33399e9			0.998883
$527$	3.12026e9	+	5.40446e9i	0.928655	+	1.60848i
$528$	−5.40672e6	+	9.36471e6i	−0.00159851	+	0.00276870i
$529$	−3.83111e9	+	6.63567e9i	−1.12520	+	1.94890i
$530$	−2.56524e9	−	4.44313e9i	−0.748451	−	1.29635i
$531$	2.54184e9			0.736745
$532$		0			0
$533$	−1.41790e9			−0.405602
$534$	1.82697e9	+	3.16441e9i	0.519203	+	0.899286i
$535$	3.12858e9	−	5.41885e9i	0.883300	−	1.52992i
$536$	2.54533e8	−	4.40863e8i	0.0713948	−	0.123659i
$537$	−2.78104e9	−	4.81690e9i	−0.774991	−	1.34232i
$538$	2.51743e9			0.696978
$539$		0			0
$540$	−3.04128e7			−0.00831148
$541$	−8.15476e8	−	1.41245e9i	−0.221422	−	0.383514i	0.733818	−	0.679346i	$-0.237736\pi$
$541$	−8.15476e8	−	1.41245e9i	−0.221422	−	0.383514i	−0.955240	+	0.295832i	$0.904403\pi$
$542$	7.68548e8	−	1.33116e9i	0.207335	−	0.359115i
$543$	−3.43056e9	+	5.94190e9i	−0.919529	+	1.59267i
$544$	5.98049e8	+	1.03585e9i	0.159272	+	0.275868i
$545$	−2.52756e9			−0.668827
$546$		0			0
$547$	2.00950e9			0.524967			0.262484	−	0.964936i	$-0.415458\pi$
$547$	2.00950e9			0.524967			0.262484	+	0.964936i	$0.415458\pi$
$548$	−1.52384e8	−	2.63936e8i	−0.0395554	−	0.0685120i
$549$	−2.24369e9	+	3.88619e9i	−0.578709	+	1.00235i
$550$	−1.31000e7	+	2.26899e7i	−0.00335739	+	0.00581517i
$551$	2.91971e9	+	5.05708e9i	0.743547	+	1.28786i
$552$	−3.55492e9			−0.899586
$553$		0			0
$554$	−3.52315e9			−0.880332
$555$	−2.76593e8	−	4.79073e8i	−0.0686777	−	0.118953i
$556$	−1.61831e8	+	2.80300e8i	−0.0399302	+	0.0691611i
$557$	2.23979e9	−	3.87944e9i	0.549180	−	0.951208i	−0.449151	−	0.893456i	$-0.648273\pi$
$557$	2.23979e9	−	3.87944e9i	0.549180	−	0.951208i	0.998331	−	0.0577518i	$-0.0183932\pi$
$558$	−1.48328e9	−	2.56912e9i	−0.361414	−	0.625987i
$559$	3.46116e8			0.0838071
$560$		0			0
$561$	−9.63653e7			−0.0230436
$562$	−1.43694e9	−	2.48885e9i	−0.341477	−	0.591455i
$563$	−7.53652e8	+	1.30536e9i	−0.177988	+	0.308285i	−0.941191	−	0.337874i	$-0.890292\pi$
$563$	−7.53652e8	+	1.30536e9i	−0.177988	+	0.308285i	0.763203	+	0.646159i	$0.223626\pi$
$564$	1.48625e9	−	2.57426e9i	0.348831	−	0.604192i
$565$	2.04575e9	+	3.54335e9i	0.477181	+	0.826502i
$566$	6.49174e8			0.150489
$567$		0			0
$568$	1.70394e7			0.00390152
$569$	−1.16544e9	−	2.01860e9i	−0.265214	−	0.459364i	0.702406	−	0.711777i	$-0.252109\pi$
$569$	−1.16544e9	−	2.01860e9i	−0.265214	−	0.459364i	−0.967620	+	0.252413i	$0.918776\pi$
$570$	−4.88104e9	+	8.45421e9i	−1.10395	+	1.91210i
$571$	1.45551e9	−	2.52101e9i	0.327181	−	0.566694i	−0.654770	−	0.755828i	$-0.727235\pi$
$571$	1.45551e9	−	2.52101e9i	0.327181	−	0.566694i	0.981951	+	0.189134i	$0.0605680\pi$
$572$	−5.69856e6	−	9.87020e6i	−0.00127315	−	0.00220516i
$573$	−8.23517e9			−1.82865
$574$		0			0
$575$	−8.61325e9			−1.88942
$576$	−2.84295e8	−	4.92414e8i	−0.0619856	−	0.107362i
$577$	−4.32403e9	+	7.48943e9i	−0.937072	+	1.62306i	−0.166175	+	0.986096i	$0.553142\pi$
$577$	−4.32403e9	+	7.48943e9i	−0.937072	+	1.62306i	−0.770897	+	0.636960i	$0.780192\pi$
$578$	−3.68823e9	+	6.38820e9i	−0.794457	+	1.37604i
$579$	−4.87043e9	−	8.43583e9i	−1.04278	−	1.80615i
$580$	−3.23415e9			−0.688275
$581$		0			0
$582$	−2.61503e9			−0.549853
$583$	−3.20656e7	−	5.55392e7i	−0.00670191	−	0.0116081i
$584$	−7.60692e8	+	1.31756e9i	−0.158039	+	0.273731i
$585$	−1.93128e9	+	3.34507e9i	−0.398840	+	0.690812i
$586$	1.01366e9	+	1.75572e9i	0.208091	+	0.360424i
$587$	6.33513e9			1.29277			0.646387	−	0.763010i	$-0.276279\pi$
$587$	6.33513e9			1.29277			0.646387	+	0.763010i	$0.276279\pi$
$588$		0			0
$589$	7.90230e9			1.59349
$590$	−1.87503e9	−	3.24765e9i	−0.375860	−	0.651009i
$591$	−5.14178e9	+	8.90583e9i	−1.02461	+	1.77467i
$592$	−4.29138e7	+	7.43289e7i	−0.00850102	+	0.0147242i
$593$	−8.50810e8	−	1.47365e9i	−0.167549	−	0.290203i	0.770009	−	0.638033i	$-0.220252\pi$
$593$	−8.50810e8	−	1.47365e9i	−0.167549	−	0.290203i	−0.937557	+	0.347830i	$0.886919\pi$
$594$	−380160.			−7.44241e−5
$595$		0			0
$596$	−1.74551e9			−0.337723
$597$	−4.39536e8	−	7.61298e8i	−0.0845442	−	0.146435i
$598$	1.87340e9	−	3.24483e9i	0.358242	−	0.620494i
$599$	−1.50989e9	+	2.61520e9i	−0.287045	+	0.497177i	−0.973103	−	0.230370i	$-0.926006\pi$
$599$	−1.50989e9	+	2.61520e9i	−0.287045	+	0.497177i	0.686058	+	0.727547i	$0.259340\pi$
$600$	−1.38336e9	−	2.39605e9i	−0.261460	−	0.452863i
$601$	5.92708e9			1.11373			0.556865	−	0.830603i	$-0.312004\pi$
$601$	5.92708e9			1.11373			0.556865	+	0.830603i	$0.312004\pi$
$602$		0			0
$603$	−2.15657e9			−0.400546
$604$	−2.07655e8	−	3.59668e8i	−0.0383453	−	0.0664160i
$605$	3.89711e9	−	6.75000e9i	0.715483	−	1.23925i
$606$	8.52720e8	−	1.47695e9i	0.155651	−	0.269596i
$607$	−7.28246e8	−	1.26136e9i	−0.132165	−	0.228917i	0.792346	−	0.610072i	$-0.208860\pi$
$607$	−7.28246e8	−	1.26136e9i	−0.132165	−	0.228917i	−0.924511	+	0.381155i	$0.875526\pi$
$608$	1.51460e9			0.273298
$609$		0			0
$610$	6.62039e9			1.18094
$611$	1.56647e9	+	2.71321e9i	0.277829	+	0.481215i
$612$	2.53353e9	−	4.38820e9i	0.446783	−	0.773850i
$613$	3.35804e9	−	5.81629e9i	0.588808	−	1.01985i	−0.405581	−	0.914059i	$-0.632931\pi$
$613$	3.35804e9	−	5.81629e9i	0.588808	−	1.01985i	0.994389	−	0.105786i	$-0.0337359\pi$
$614$	3.49082e9	+	6.04628e9i	0.608609	+	1.05414i
$615$	−8.40803e9			−1.45758
$616$		0			0
$617$	7.02027e9			1.20325			0.601625	−	0.798779i	$-0.294520\pi$
$617$	7.02027e9			1.20325			0.601625	+	0.798779i	$0.294520\pi$
$618$	−4.74960e8	−	8.22655e8i	−0.0809464	−	0.140203i
$619$	2.57176e9	−	4.45442e9i	0.435826	−	0.754872i	−0.561537	−	0.827452i	$-0.689790\pi$
$619$	2.57176e9	−	4.45442e9i	0.435826	−	0.754872i	0.997363	+	0.0725793i	$0.0231230\pi$
$620$	−2.18834e9	+	3.79031e9i	−0.368760	+	0.638711i
$621$	−6.24888e7	−	1.08234e8i	−0.0104708	−	0.0181360i
$622$	5.37289e9			0.895245
$623$		0			0
$624$	1.20354e9			0.198296
$625$	2.89824e9	+	5.01990e9i	0.474848	+	0.822461i
$626$	−7.68866e8	+	1.33171e9i	−0.125268	+	0.216971i
$627$	−6.10130e7	+	1.05678e8i	−0.00988522	+	0.0171217i
$628$	−2.01859e9	−	3.49631e9i	−0.325230	−	0.563314i
$629$	−7.64863e8			−0.122548
$630$		0			0
$631$	−4.41574e9			−0.699681			−0.349841	−	0.936809i	$-0.613764\pi$
$631$	−4.41574e9			−0.699681			−0.349841	+	0.936809i	$0.613764\pi$
$632$	6.08299e8	+	1.05360e9i	0.0958534	+	0.166023i
$633$	6.76302e9	−	1.17139e10i	1.05981	−	1.83564i
$634$	5.35349e8	−	9.27251e8i	0.0834304	−	0.144506i
$635$	−1.20145e9	−	2.08097e9i	−0.186208	−	0.322521i
$636$	6.77225e9			1.04384
$637$		0			0
$638$	−4.04269e7			−0.00616308
$639$	−3.60922e7	−	6.25135e7i	−0.00547217	−	0.00947808i
$640$	−4.19430e8	+	7.26475e8i	−0.0632456	+	0.109545i
$641$	−3.47088e8	+	6.01174e8i	−0.0520519	+	0.0901565i	−0.890877	−	0.454244i	$-0.849909\pi$
$641$	−3.47088e8	+	6.01174e8i	−0.0520519	+	0.0901565i	0.838825	+	0.544400i	$0.183243\pi$
$642$	4.12972e9	+	7.15288e9i	0.615954	+	1.06686i
$643$	−9.50809e9			−1.41044			−0.705220	−	0.708988i	$-0.749152\pi$
$643$	−9.50809e9			−1.41044			−0.705220	+	0.708988i	$0.749152\pi$
$644$		0			0
$645$	2.05244e9			0.301170
$646$	6.74878e9	+	1.16892e10i	0.984944	+	1.70597i
$647$	−3.86608e9	+	6.69624e9i	−0.561184	+	0.971999i	0.436209	+	0.899845i	$0.356321\pi$
$647$	−3.86608e9	+	6.69624e9i	−0.561184	+	0.971999i	−0.997393	+	0.0721541i	$0.977013\pi$
$648$	1.23443e9	−	2.13810e9i	0.178220	−	0.308686i
$649$	−2.34379e7	−	4.05956e7i	−0.00336560	−	0.00582938i
$650$	2.91606e9			0.416485
$651$		0			0
$652$	5.32654e9			0.752624
$653$	2.53161e9	+	4.38487e9i	0.355795	+	0.616255i	0.987254	−	0.159154i	$-0.0508768\pi$
$653$	2.53161e9	+	4.38487e9i	0.355795	+	0.616255i	−0.631459	+	0.775410i	$0.717543\pi$
$654$	1.66819e9	−	2.88939e9i	0.233197	−	0.403909i
$655$	4.12792e9	−	7.14977e9i	0.573967	−	0.994140i
$656$	6.52259e8	+	1.12975e9i	0.0902105	+	0.156249i
$657$	6.44508e9			0.886645
$658$		0			0
$659$	8.08113e9			1.09995			0.549975	−	0.835181i	$-0.314637\pi$
$659$	8.08113e9			1.09995			0.549975	+	0.835181i	$0.314637\pi$
$660$	−3.37920e7	−	5.85295e7i	−0.00457520	−	0.00792448i
$661$	3.15045e9	−	5.45673e9i	0.424294	−	0.734899i	−0.572060	−	0.820212i	$-0.693856\pi$
$661$	3.15045e9	−	5.45673e9i	0.424294	−	0.734899i	0.996354	+	0.0853128i	$0.0271889\pi$
$662$	−1.70119e9	+	2.94655e9i	−0.227903	+	0.394740i
$663$	5.36273e9	+	9.28852e9i	0.714642	+	1.23780i
$664$	1.08665e9			0.144046
$665$		0			0
$666$	3.63594e8			0.0476932
$667$	−6.64517e9	−	1.15098e10i	−0.867093	−	1.50185i
$668$	9.82130e8	−	1.70110e9i	0.127483	−	0.220807i
$669$	−2.26003e9	+	3.91449e9i	−0.291825	+	0.505457i
$670$	1.59083e9	+	2.75540e9i	0.204344	+	0.353934i
$671$	8.27549e7			0.0105746
$672$		0			0
$673$	−9.62624e9			−1.21732			−0.608659	−	0.793432i	$-0.708292\pi$
$673$	−9.62624e9			−1.21732			−0.608659	+	0.793432i	$0.708292\pi$
$674$	−4.30810e9	−	7.46185e9i	−0.541971	−	0.938722i
$675$	4.86338e7	−	8.42361e7i	0.00608660	−	0.0105423i
$676$	1.37370e9	−	2.37932e9i	0.171033	−	0.296237i
$677$	−4.72714e9	−	8.18765e9i	−0.585516	−	1.01414i	−0.994811	−	0.101741i	$-0.967559\pi$
$677$	−4.72714e9	−	8.18765e9i	−0.585516	−	1.01414i	0.409295	−	0.912402i	$-0.365775\pi$
$678$	−5.40079e9			−0.665508
$679$		0			0
$680$	−7.47561e9			−0.911728
$681$	−6.38968e8	−	1.10672e9i	−0.0775290	−	0.134284i
$682$	−2.73542e7	+	4.73789e7i	−0.00330202	+	0.00571926i
$683$	−1.24440e8	+	2.15536e8i	−0.0149447	+	0.0258849i	−0.873401	−	0.487002i	$-0.838091\pi$
$683$	−1.24440e8	+	2.15536e8i	−0.0149447	+	0.0258849i	0.858456	+	0.512887i	$0.171424\pi$
$684$	−3.20818e9	−	5.55672e9i	−0.383320	−	0.663930i
$685$	1.90479e9			0.226429
$686$		0			0
$687$	−2.03383e10			−2.39313
$688$	−1.59220e8	−	2.75777e8i	−0.0186396	−	0.0322848i
$689$	−3.56890e9	+	6.18151e9i	−0.415687	+	0.719991i
$690$	1.11091e10	−	1.92416e10i	1.28738	−	2.22981i
$691$	−1.73206e9	−	3.00001e9i	−0.199705	−	0.345900i	0.748728	−	0.662878i	$-0.230665\pi$
$691$	−1.73206e9	−	3.00001e9i	−0.199705	−	0.345900i	−0.948433	+	0.316978i	$0.897332\pi$
$692$	3.37497e9			0.387167
$693$		0			0
$694$	−5.79011e9			−0.657550
$695$	−1.01145e9	−	1.75188e9i	−0.114287	−	0.197951i
$696$	2.13454e9	−	3.69713e9i	0.239978	−	0.415654i
$697$	−5.81269e9	+	1.00679e10i	−0.650223	+	1.12622i
$698$	−1.79253e9	−	3.10475e9i	−0.199514	−	0.345568i
$699$	2.34826e9			0.260062
$700$		0			0
$701$	5.56322e9			0.609976			0.304988	−	0.952356i	$-0.401347\pi$
$701$	5.56322e9			0.609976			0.304988	+	0.952356i	$0.401347\pi$
$702$	2.11559e7	+	3.66431e7i	0.00230808	+	0.00399772i
$703$	−4.84268e8	+	8.38777e8i	−0.0525705	+	0.0910548i
$704$	−5.24288e6	+	9.08093e6i	−0.000566325	+	0.000980903i
$705$	9.28905e9	+	1.60891e10i	0.998411	+	1.72930i
$706$	1.19956e10			1.28294
$707$		0			0
$708$	4.95008e9			0.524199
$709$	−4.11848e9	−	7.13342e9i	−0.433986	−	0.751685i	0.563227	−	0.826303i	$-0.309560\pi$
$709$	−4.11848e9	−	7.13342e9i	−0.433986	−	0.751685i	−0.997212	+	0.0746172i	$0.976227\pi$
$710$	−5.32480e7	+	9.22282e7i	−0.00558340	+	0.00967074i
$711$	2.57695e9	−	4.46342e9i	0.268883	−	0.465719i
$712$	1.77161e9	+	3.06852e9i	0.183945	+	0.318602i
$713$	−1.79854e10			−1.85826
$714$		0			0
$715$	7.12320e7			0.00728793
$716$	−2.69676e9	−	4.67093e9i	−0.274566	−	0.475563i
$717$	7.59185e9	−	1.31495e10i	0.769185	−	1.33227i
$718$	1.02756e9	−	1.77979e9i	0.103603	−	0.179445i
$719$	2.92606e9	+	5.06808e9i	0.293584	+	0.508502i	0.974654	−	0.223716i	$-0.0718187\pi$
$719$	2.92606e9	+	5.06808e9i	0.293584	+	0.508502i	−0.681071	+	0.732218i	$0.738485\pi$
$720$	3.55369e9			0.354826
$721$		0			0
$722$	9.94081e9			0.982973
$723$	1.66153e8	+	2.87786e8i	0.0163503	+	0.0283195i
$724$	−3.32660e9	+	5.76184e9i	−0.325774	+	0.564256i
$725$	5.17180e9	−	8.95782e9i	0.504033	−	0.873010i
$726$	5.14419e9	+	8.91000e9i	0.498929	+	0.864171i
$727$	−1.51706e10			−1.46431			−0.732154	−	0.681139i	$-0.761485\pi$
$727$	−1.51706e10			−1.46431			−0.732154	+	0.681139i	$0.761485\pi$
$728$		0			0
$729$	−1.02875e10			−0.983472
$730$	−4.75433e9	−	8.23473e9i	−0.452334	−	0.783465i
$731$	1.41891e9	−	2.45762e9i	0.134352	−	0.232704i
$732$	−4.36946e9	+	7.56812e9i	−0.411755	+	0.713180i
$733$	−7.79846e9	−	1.35073e10i	−0.731383	−	1.26679i	−0.956292	−	0.292413i	$-0.905542\pi$
$733$	−7.79846e9	−	1.35073e10i	−0.731383	−	1.26679i	0.224909	−	0.974380i	$-0.427791\pi$
$734$	−5.20339e9			−0.485680
$735$		0			0
$736$	−3.44719e9			−0.318708
$737$	1.98854e7	+	3.44425e7i	0.00182977	+	0.00316926i
$738$	2.76318e9	−	4.78598e9i	0.253054	−	0.438302i
$739$	3.47786e9	−	6.02384e9i	0.316998	−	0.549057i	−0.662862	−	0.748742i	$-0.730658\pi$
$739$	3.47786e9	−	6.02384e9i	0.316998	−	0.549057i	0.979860	+	0.199684i	$0.0639917\pi$
$740$	−2.68211e8	−	4.64555e8i	−0.0243313	−	0.0421431i
$741$	1.35815e10			1.22626
$742$		0			0
$743$	−1.17803e10			−1.05365			−0.526824	−	0.849975i	$-0.676617\pi$
$743$	−1.17803e10			−1.05365			−0.526824	+	0.849975i	$0.676617\pi$
$744$	−2.88861e9	−	5.00322e9i	−0.257148	−	0.445394i
$745$	5.45473e9	−	9.44787e9i	0.483310	−	0.837118i
$746$	1.86451e9	−	3.22943e9i	0.164429	−	0.284800i
$747$	−2.30170e9	−	3.98666e9i	−0.202035	−	0.349934i
$748$	−9.34451e7			−0.00816396
$749$		0			0
$750$	7.92000e8			0.0685505
$751$	3.48100e9	+	6.02927e9i	0.299892	+	0.519428i	0.976111	−	0.217273i	$-0.0697161\pi$
$751$	3.48100e9	+	6.02927e9i	0.299892	+	0.519428i	−0.676219	+	0.736700i	$0.736383\pi$
$752$	1.44121e9	−	2.49625e9i	0.123585	−	0.214055i
$753$	−3.40833e9	+	5.90339e9i	−0.290910	+	0.503871i
$754$	2.24976e9	+	3.89669e9i	0.191133	+	0.331052i
$755$	2.59568e9			0.219501
$756$		0			0
$757$	−2.07114e10			−1.73530			−0.867648	−	0.497179i	$-0.834369\pi$
$757$	−2.07114e10			−1.73530			−0.867648	+	0.497179i	$0.834369\pi$
$758$	−1.14344e9	−	1.98049e9i	−0.0953609	−	0.165170i
$759$	1.38864e8	−	2.40520e8i	0.0115277	−	0.0199666i
$760$	−4.73313e9	+	8.19803e9i	−0.391112	+	0.677426i
$761$	8.26962e9	+	1.43234e10i	0.680204	+	1.17815i	0.974918	+	0.222563i	$0.0714422\pi$
$761$	8.26962e9	+	1.43234e10i	0.680204	+	1.17815i	−0.294714	+	0.955585i	$0.595224\pi$
$762$	3.17183e9			0.259697
$763$		0			0
$764$	−7.98562e9			−0.647861
$765$	1.58346e10	+	2.74263e10i	1.27877	+	2.21489i
$766$	−6.60300e9	+	1.14367e10i	−0.530812	+	0.919393i
$767$	−2.60864e9	+	4.51829e9i	−0.208752	+	0.361568i
$768$	−5.53648e8	−	9.58947e8i	−0.0441031	−	0.0763889i
$769$	2.33650e10			1.85278			0.926391	−	0.376562i	$-0.122894\pi$
$769$	2.33650e10			1.85278			0.926391	+	0.376562i	$0.122894\pi$
$770$		0			0
$771$	1.53306e10			1.20467
$772$	−4.72284e9	−	8.18020e9i	−0.369439	−	0.639887i
$773$	3.54631e9	−	6.14240e9i	0.276152	−	0.478310i	−0.694273	−	0.719712i	$-0.744274\pi$
$773$	3.54631e9	−	6.14240e9i	0.276152	−	0.478310i	0.970425	+	0.241402i	$0.0776072\pi$
$774$	−6.74507e8	+	1.16828e9i	−0.0522869	+	0.0905636i
$775$	−6.99884e9	−	1.21223e10i	−0.540095	−	0.935472i
$776$	−2.53579e9			−0.194804
$777$		0			0
$778$	1.21043e10			0.921536
$779$	7.36053e9	+	1.27488e10i	0.557864	+	0.966248i
$780$	−3.76105e9	+	6.51433e9i	−0.283777	+	0.491517i
$781$	−665600.	+	1.15285e6i	−4.99959e−5	+	8.65955e-5i
$782$	−1.53600e10	−	2.66044e10i	−1.14860	−	1.98943i
$783$	1.50085e8			0.0111730
$784$		0			0
$785$	2.52324e10			1.86172
$786$	5.44886e9	+	9.43770e9i	0.400246	+	0.693246i
$787$	−6.15149e9	+	1.06547e10i	−0.449851	+	0.779165i	−0.998376	−	0.0569690i	$-0.981856\pi$
$787$	−6.15149e9	+	1.06547e10i	−0.449851	+	0.779165i	0.548525	+	0.836134i	$0.315190\pi$
$788$	−4.98597e9	+	8.63595e9i	−0.363001	+	0.628736i
$789$	−1.37527e10	−	2.38204e10i	−0.996825	−	1.72655i
$790$	−7.60374e9			−0.548697
$791$		0			0
$792$	4.44211e7			0.00317725
$793$	−4.60531e9	−	7.97663e9i	−0.327946	−	0.568020i
$794$	−3.45518e9	+	5.98454e9i	−0.244962	+	0.424287i
$795$	−2.11633e10	+	3.66559e10i	−1.49382	+	2.58737i
$796$	−4.26216e8	−	7.38228e8i	−0.0299526	−	0.0518794i
$797$	3.66650e9			0.256535			0.128268	−	0.991740i	$-0.459058\pi$
$797$	3.66650e9			0.256535			0.128268	+	0.991740i	$0.459058\pi$
$798$		0			0
$799$	2.56870e10			1.78156
$800$	−1.34144e9	−	2.32344e9i	−0.0926310	−	0.160442i
$801$	7.50512e9	−	1.29992e10i	0.515993	−	0.893726i
$802$	−4.56167e8	+	7.90104e8i	−0.0312258	+	0.0540847i
$803$	−5.94291e7	−	1.02934e8i	−0.00405037	−	0.00701545i
$804$	−4.19979e9			−0.284991
$805$		0			0
$806$	6.08905e9			0.409616
$807$	−1.03844e10	−	1.79863e10i	−0.695543	−	1.20472i
$808$	8.26880e8	−	1.43220e9i	0.0551446	−	0.0955132i
$809$	1.48305e10	−	2.56871e10i	0.984770	−	1.70567i	0.341817	−	0.939767i	$-0.388958\pi$
$809$	1.48305e10	−	2.56871e10i	0.984770	−	1.70567i	0.642953	−	0.765905i	$-0.277709\pi$
$810$	7.71522e9	+	1.33631e10i	0.510094	+	0.883510i
$811$	−2.51278e10			−1.65417			−0.827087	−	0.562073i	$-0.810004\pi$
$811$	−2.51278e10			−1.65417			−0.827087	+	0.562073i	$0.810004\pi$
$812$		0			0
$813$	−1.26810e10			−0.827633
$814$	−3.35264e6	−	5.80694e6i	−0.000217872	−	0.000377365i
$815$	−1.66454e10	+	2.88307e10i	−1.07707	+	1.86554i
$816$	4.93390e9	−	8.54577e9i	0.317889	−	0.550599i
$817$	−1.79674e9	−	3.11205e9i	−0.115268	−	0.199650i
$818$	9.46623e9			0.604700
$819$		0			0
$820$	−8.15324e9			−0.516395
$821$	−2.28886e9	−	3.96442e9i	−0.144350	−	0.250022i	0.784780	−	0.619774i	$-0.212776\pi$
$821$	−2.28886e9	−	3.96442e9i	−0.144350	−	0.250022i	−0.929130	+	0.369752i	$0.879443\pi$
$822$	−1.25716e9	+	2.17747e9i	−0.0789479	+	0.136742i
$823$	−9.65663e8	+	1.67258e9i	−0.0603846	+	0.104589i	−0.894637	−	0.446793i	$-0.852566\pi$
$823$	−9.65663e8	+	1.67258e9i	−0.0603846	+	0.104589i	0.834253	+	0.551382i	$0.185899\pi$
$824$	−4.60568e8	−	7.97726e8i	−0.0286779	−	0.0496717i
$825$	2.16150e8			0.0134019
$826$		0			0
$827$	1.58094e10			0.971958			0.485979	−	0.873971i	$-0.338463\pi$
$827$	1.58094e10			0.971958			0.485979	+	0.873971i	$0.338463\pi$
$828$	7.30172e9	+	1.26470e10i	0.447012	+	0.774247i
$829$	−1.23268e9	+	2.13506e9i	−0.0751465	+	0.130158i	−0.901150	−	0.433507i	$-0.857276\pi$
$829$	−1.23268e9	+	2.13506e9i	−0.0751465	+	0.130158i	0.826003	+	0.563665i	$0.190609\pi$
$830$	−3.39577e9	+	5.88165e9i	−0.206141	+	0.357047i
$831$	1.45330e10	+	2.51719e10i	0.878519	+	1.52164i
$832$	1.16707e9			0.0702528
$833$		0			0
$834$	2.67022e9			0.159392
$835$	6.13831e9	+	1.06319e10i	0.364877	+	0.631985i
$836$	−5.91642e7	+	1.02475e8i	−0.00350217	+	0.00606593i
$837$	1.01553e8	−	1.75894e8i	0.00598621	−	0.0103684i
$838$	9.11838e8	+	1.57935e9i	0.0535259	+	0.0927095i
$839$	−2.51861e10			−1.47229			−0.736147	−	0.676822i	$-0.763357\pi$
$839$	−2.51861e10			−1.47229			−0.736147	+	0.676822i	$0.763357\pi$
$840$		0			0
$841$	−1.28960e9			−0.0747598
$842$	1.56280e8	+	2.70685e8i	0.00902218	+	0.0156269i
$843$	−1.18547e10	+	2.05330e10i	−0.681547	+	1.18047i
$844$	6.55808e9	−	1.13589e10i	0.375472	−	0.650337i
$845$	8.58564e9	+	1.48708e10i	0.489524	+	0.847881i
$846$	−1.22109e10			−0.693347
$847$		0			0
$848$	6.56703e9			0.369814
$849$	−2.67784e9	−	4.63816e9i	−0.150179	−	0.260117i
$850$	1.19544e10	−	2.07056e10i	0.667670	−	1.15644i
$851$	1.10218e9	−	1.90903e9i	0.0613055	−	0.106184i
$852$	−7.02874e7	−	1.21741e8i	−0.00389349	−	0.00674372i
$853$	−1.07306e10			−0.591972			−0.295986	−	0.955192i	$-0.595648\pi$
$853$	−1.07306e10			−0.591972			−0.295986	+	0.955192i	$0.595648\pi$
$854$		0			0
$855$	4.01022e10			2.19425
$856$	4.00458e9	+	6.93613e9i	0.218222	+	0.377971i
$857$	−1.39666e10	+	2.41908e10i	−0.757979	+	1.31286i	0.185901	+	0.982569i	$0.440480\pi$
$857$	−1.39666e10	+	2.41908e10i	−0.757979	+	1.31286i	−0.943880	+	0.330290i	$0.892854\pi$
$858$	−4.70131e7	+	8.14291e7i	−0.00254105	+	0.00440123i
$859$	−9.74913e9	−	1.68860e10i	−0.524795	−	0.908972i	−0.999583	−	0.0288717i	$-0.990809\pi$
$859$	−9.74913e9	−	1.68860e10i	−0.524795	−	0.908972i	0.474788	−	0.880100i	$-0.342525\pi$
$860$	1.99025e9			0.106699
$861$		0			0
$862$	−2.06896e10			−1.10021
$863$	8.17753e9	+	1.41639e10i	0.433096	+	0.750145i	0.997138	−	0.0756013i	$-0.0240876\pi$
$863$	8.17753e9	+	1.41639e10i	0.433096	+	0.750145i	−0.564042	+	0.825746i	$0.690754\pi$
$864$	1.94642e7	−	3.37130e7i	0.00102669	−	0.00177827i
$865$	−1.05468e10	+	1.82675e10i	−0.554068	+	0.959674i
$866$	−7.15571e9	−	1.23940e10i	−0.374403	−	0.648486i
$867$	6.08558e10			3.17128
$868$		0			0
$869$	−9.50467e7			−0.00491324
$870$	1.33409e10	+	2.31071e10i	0.686858	+	1.18967i
$871$	2.21324e9	−	3.83345e9i	0.113492	−	0.196574i
$872$	1.61764e9	−	2.80183e9i	0.0826178	−	0.143098i
$873$	5.37121e9	+	9.30322e9i	0.273226	+	0.473242i
$874$	−3.89004e10			−1.97090
$875$		0			0
$876$	1.25514e10			0.630854
$877$	−1.34437e10	−	2.32851e10i	−0.673007	−	1.16568i	−0.977047	−	0.213023i	$-0.931669\pi$
$877$	−1.34437e10	−	2.32851e10i	−0.673007	−	1.16568i	0.304040	−	0.952659i	$-0.401664\pi$
$878$	−1.83562e9	+	3.17939e9i	−0.0915276	+	0.158530i
$879$	8.36273e9	−	1.44847e10i	0.415324	−	0.719362i
$880$	−3.27680e7	−	5.67558e7i	−0.00162092	−	0.00280751i
$881$	−1.08918e10			−0.536644			−0.268322	−	0.963329i	$-0.586469\pi$
$881$	−1.08918e10			−0.536644			−0.268322	+	0.963329i	$0.586469\pi$
$882$		0			0
$883$	−3.99542e10			−1.95299			−0.976495	−	0.215542i	$-0.930848\pi$
$883$	−3.99542e10			−1.95299			−0.976495	+	0.215542i	$0.930848\pi$
$884$	5.20022e9	+	9.00705e9i	0.253186	+	0.438530i
$885$	−1.54690e10	+	2.67931e10i	−0.750172	+	1.29934i
$886$	−5.53835e9	+	9.59271e9i	−0.267524	+	0.463365i
$887$	6.51528e9	+	1.12848e10i	0.313473	+	0.542951i	0.979112	−	0.203323i	$-0.0651741\pi$
$887$	6.51528e9	+	1.12848e10i	0.313473	+	0.542951i	−0.665639	+	0.746274i	$0.731841\pi$
$888$	7.08078e8			0.0339340
$889$		0			0
$890$	−2.21451e10			−1.05296
$891$	9.64402e7	+	1.67039e8i	0.00456758	+	0.00791128i
$892$	−2.19155e9	+	3.79587e9i	−0.103389	+	0.179075i
$893$	1.62636e10	−	2.81693e10i	0.764251	−	1.32372i
$894$	7.20024e9	+	1.24712e10i	0.337028	+	0.583749i
$895$	3.37095e10			1.57171
$896$		0			0
$897$	−3.09111e10			−1.43002
$898$	1.09444e10	+	1.89563e10i	0.504343	+	0.873547i
$899$	1.07993e10	−	1.87049e10i	0.495719	−	0.858611i
$900$	−5.68278e9	+	9.84286e9i	−0.259844	+	0.450062i
$901$	2.92614e10	+	5.06823e10i	1.33278	+	2.30844i
$902$	−1.01916e8			−0.00462400
$903$		0			0
$904$	−5.23713e9			−0.235778
$905$	−2.07913e10	−	3.60115e10i	−0.932418	−	1.61500i
$906$	−1.71315e9	+	2.96726e9i	−0.0765327	+	0.132558i
$907$	−2.02007e10	+	3.49887e10i	−0.898962	+	1.55705i	−0.0701394	+	0.997537i	$0.522344\pi$
$907$	−2.02007e10	+	3.49887e10i	−0.898962	+	1.55705i	−0.828823	+	0.559511i	$0.810989\pi$
$908$	−6.19605e8	−	1.07319e9i	−0.0274672	−	0.0475746i
$909$	−7.00587e9			−0.309377
$910$		0			0
$911$	1.98919e10			0.871690			0.435845	−	0.900022i	$-0.356450\pi$
$911$	1.98919e10			0.871690			0.435845	+	0.900022i	$0.356450\pi$
$912$	−6.24774e9	−	1.08214e10i	−0.272735	−	0.472391i
$913$	−4.24472e7	+	7.35206e7i	−0.00184587	+	0.00319714i
$914$	−9.72213e9	+	1.68392e10i	−0.421163	+	0.729475i
$915$	−2.73091e10	−	4.73008e10i	−1.17851	−	2.04124i
$916$	−1.97220e10			−0.847847
$917$		0			0
$918$	3.46915e8			0.0148004
$919$	2.05495e10	+	3.55928e10i	0.873368	+	1.51272i	0.858491	+	0.512828i	$0.171402\pi$
$919$	2.05495e10	+	3.55928e10i	0.873368	+	1.51272i	0.0148764	+	0.999889i	$0.495265\pi$
$920$	1.07725e10	−	1.86585e10i	0.456098	−	0.789985i
$921$	2.87993e10	−	4.98818e10i	1.21471	−	2.10394i
$922$	1.57954e10	+	2.73584e10i	0.663700	+	1.14956i
$923$	1.48163e8			0.00620201
$924$		0			0
$925$	1.71561e9			0.0712725
$926$	−1.02981e10	−	1.78369e10i	−0.426206	−	0.738210i
$927$	−1.95112e9	+	3.37943e9i	−0.0804459	+	0.139336i
$928$	2.06986e9	−	3.58510e9i	0.0850202	−	0.147259i
$929$	−9.51870e9	−	1.64869e10i	−0.389513	−	0.674657i	0.602871	−	0.797839i	$-0.294023\pi$
$929$	−9.51870e9	−	1.64869e10i	−0.389513	−	0.674657i	−0.992384	+	0.123182i	$0.960690\pi$
$930$	3.61076e10			1.47200
$931$		0			0
$932$	2.27710e9			0.0921355
$933$	−2.21632e10	−	3.83877e10i	−0.893401	−	1.54742i
$934$	1.19393e9	−	2.06795e9i	0.0479473	−	0.0830472i
$935$	2.92016e8	−	5.05787e8i	0.0116833	−	0.0202361i
$936$	−2.47204e9	−	4.28169e9i	−0.0985347	−	0.170667i
$937$	−3.93830e10			−1.56394			−0.781971	−	0.623315i	$-0.785786\pi$
$937$	−3.93830e10			−1.56394			−0.781971	+	0.623315i	$0.785786\pi$
$938$		0			0
$939$	1.26863e10			0.500040
$940$	9.00756e9	+	1.56016e10i	0.353720	+	0.612661i
$941$	−7.95932e9	+	1.37859e10i	−0.311395	+	0.539352i	−0.978665	−	0.205464i	$-0.934130\pi$
$941$	−7.95932e9	+	1.37859e10i	−0.311395	+	0.539352i	0.667269	+	0.744816i	$0.267463\pi$
$942$	−1.66534e10	+	2.88445e10i	−0.649119	+	1.12431i
$943$	−1.67524e10	−	2.90159e10i	−0.650557	−	1.12680i
$944$	4.80008e9			0.185715
$945$		0			0
$946$	2.48781e7			0.000955428
$947$	−1.78619e9	−	3.09376e9i	−0.0683442	−	0.118376i	0.829828	−	0.558019i	$-0.188438\pi$
$947$	−1.78619e9	−	3.09376e9i	−0.0683442	−	0.118376i	−0.898173	+	0.439643i	$0.855105\pi$
$948$	5.01847e9	−	8.69224e9i	0.191312	−	0.331362i
$949$	−6.61446e9	+	1.14566e10i	−0.251225	+	0.435134i
$950$	−1.51377e10	−	2.62193e10i	−0.572832	−	0.992174i
$951$	−8.83326e9			−0.333034
$952$		0			0
$953$	4.05101e9			0.151614			0.0758068	−	0.997123i	$-0.475847\pi$
$953$	4.05101e9			0.151614			0.0758068	+	0.997123i	$0.475847\pi$
$954$	−1.39100e10	−	2.40929e10i	−0.518691	−	0.898400i
$955$	2.49551e10	−	4.32234e10i	0.927143	−	1.60586i
$956$	7.36180e9	−	1.27510e10i	0.272509	−	0.472000i
$957$	1.66761e8	+	2.88838e8i	0.00615039	+	0.0106528i
$958$	−2.09600e10			−0.770216
$959$		0			0
$960$	6.92060e9			0.252461
$961$	−8.58038e8	−	1.48616e9i	−0.0311871	−	0.0540176i
$962$	−3.73149e8	+	6.46313e8i	−0.0135135	+	0.0234061i
$963$	1.69647e10	−	2.93837e10i	0.612145	−	1.06027i
$964$	1.61118e8	+	2.79065e8i	0.00579263	+	0.0100331i
$965$	5.90355e10			2.11479
$966$		0			0
$967$	2.55791e10			0.909689			0.454844	−	0.890571i	$-0.349695\pi$
$967$	2.55791e10			0.909689			0.454844	+	0.890571i	$0.349695\pi$
$968$	4.98831e9	+	8.64000e9i	0.176762	+	0.306161i
$969$	5.56774e10	−	9.64362e10i	1.96583	−	3.40492i
$970$	7.92434e9	−	1.37254e10i	0.278780	−	0.482861i
$971$	2.05161e10	+	3.55350e10i	0.719165	+	1.24563i	0.961331	+	0.275395i	$0.0888087\pi$
$971$	2.05161e10	+	3.55350e10i	0.719165	+	1.24563i	−0.242166	+	0.970235i	$0.577858\pi$
$972$	−2.02019e10			−0.705603
$973$		0			0
$974$	−3.33330e10			−1.15589
$975$	−1.20287e10	−	2.08344e10i	−0.415627	−	0.719888i
$976$	−4.23705e9	+	7.33879e9i	−0.145878	+	0.252668i
$977$	−2.43638e10	+	4.21994e10i	−0.835824	+	1.44769i	0.0575338	+	0.998344i	$0.481676\pi$
$977$	−2.43638e10	+	4.21994e10i	−0.835824	+	1.44769i	−0.893358	+	0.449346i	$0.851657\pi$
$978$	−2.19720e10	−	3.80565e10i	−0.751074	−	1.30090i
$979$	−2.76814e8			−0.00942863
$980$		0			0
$981$	−1.37057e10			−0.463511
$982$	−9.65200e9	−	1.67178e10i	−0.325257	−	0.563362i
$983$	−3.47381e9	+	6.01681e9i	−0.116646	+	0.202036i	−0.918436	−	0.395569i	$-0.870548\pi$
$983$	−3.47381e9	+	6.01681e9i	−0.116646	+	0.202036i	0.801791	+	0.597605i	$0.203881\pi$
$984$	5.38114e9	−	9.32041e9i	0.180049	−	0.311855i
$985$	−3.11623e10	−	5.39747e10i	−1.03897	−	1.79955i
$986$	3.68915e10			1.22563
$987$		0			0
$988$	1.31699e10			0.434445
$989$	4.08933e9	+	7.08293e9i	0.134421	+	0.232823i
$990$	−1.38816e8	+	2.40436e8i	−0.00454691	+	0.00787548i
$991$	9.17823e9	−	1.58972e10i	0.299572	−	0.518874i	−0.676466	−	0.736474i	$-0.736490\pi$
$991$	9.17823e9	−	1.58972e10i	0.299572	−	0.518874i	0.976038	+	0.217600i	$0.0698228\pi$
$992$	−2.80107e9	−	4.85160e9i	−0.0911032	−	0.157795i
$993$	2.80697e10			0.909735
$994$		0			0
$995$	5.32770e9			0.171459
$996$	−4.48242e9	−	7.76378e9i	−0.143749	−	0.248981i
$997$	1.72477e10	−	2.98739e10i	0.551185	−	0.954681i	−0.447004	−	0.894532i	$-0.647509\pi$
$997$	1.72477e10	−	2.98739e10i	0.551185	−	0.954681i	0.998189	−	0.0601492i	$-0.0191576\pi$
$998$	4.16368e9	−	7.21170e9i	0.132593	−	0.229657i
$999$	1.24467e7	+	2.15583e7i	0.000394979	+	0.000684124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.a.67.1		2
7.2	even	3	inner	98.8.c.a.79.1		2
7.3	odd	6		14.8.a.b.1.1	✓	1
7.4	even	3		98.8.a.c.1.1		1
7.5	odd	6		98.8.c.b.79.1		2
7.6	odd	2		98.8.c.b.67.1		2
21.17	even	6		126.8.a.c.1.1		1
28.3	even	6		112.8.a.d.1.1		1
35.3	even	12		350.8.c.b.99.1		2
35.17	even	12		350.8.c.b.99.2		2
35.24	odd	6		350.8.a.d.1.1		1
56.3	even	6		448.8.a.b.1.1		1
56.45	odd	6		448.8.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.a.b.1.1	✓	1	7.3	odd	6
98.8.a.c.1.1		1	7.4	even	3
98.8.c.a.67.1		2	1.1	even	1	trivial
98.8.c.a.79.1		2	7.2	even	3	inner
98.8.c.b.67.1		2	7.6	odd	2
98.8.c.b.79.1		2	7.5	odd	6
112.8.a.d.1.1		1	28.3	even	6
126.8.a.c.1.1		1	21.17	even	6
350.8.a.d.1.1		1	35.24	odd	6
350.8.c.b.99.1		2	35.3	even	12
350.8.c.b.99.2		2	35.17	even	12
448.8.a.b.1.1		1	56.3	even	6
448.8.a.i.1.1		1	56.45	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-33.0000 + 57.1577i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-200.000 - 346.410i) q^{5} +528.000 q^{6} +512.000 q^{8} +(-1084.50 - 1878.41i) q^{9} +(-1600.00 + 2771.28i) q^{10} +(-20.0000 + 34.6410i) q^{11} +(-2112.00 - 3658.09i) q^{12} +4452.00 q^{13} +26400.0 q^{15} +(-2048.00 - 3547.24i) q^{16} +(18251.0 - 31611.7i) q^{17} +(-8676.00 + 15027.3i) q^{18} +(-23111.0 - 40029.4i) q^{19} +25600.0 q^{20} +320.000 q^{22} +(52600.0 + 91105.9i) q^{23} +(-16896.0 + 29264.7i) q^{24} +(-40937.5 + 70905.8i) q^{25} +(-17808.0 - 30844.4i) q^{26} -1188.00 q^{27} -126334. q^{29} +(-105600. - 182905. i) q^{30} +(-85482.0 + 148059. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +(-1320.00 - 2286.31i) q^{33} -292016. q^{34} +138816. q^{36} +(-10477.0 - 18146.7i) q^{37} +(-184888. + 320235. i) q^{38} +(-146916. + 254466. i) q^{39} +(-102400. - 177362. i) q^{40} -318486. q^{41} +77744.0 q^{43} +(-1280.00 - 2217.03i) q^{44} +(-433800. + 751364. i) q^{45} +(420800. - 728847. i) q^{46} +(351858. + 609436. i) q^{47} +270336. q^{48} +655000. q^{50} +(1.20457e6 + 2.08637e6i) q^{51} +(-142464. + 246755. i) q^{52} +(-801639. + 1.38848e6i) q^{53} +(4752.00 + 8230.71i) q^{54} +16000.0 q^{55} +3.05065e6 q^{57} +(505336. + 875268. i) q^{58} +(-585947. + 1.01489e6i) q^{59} +(-844800. + 1.46324e6i) q^{60} +(-1.03444e6 - 1.79170e6i) q^{61} +1.36771e6 q^{62} +262144. q^{64} +(-890400. - 1.54222e6i) q^{65} +(-10560.0 + 18290.5i) q^{66} +(497134. - 861061. i) q^{67} +(1.16806e6 + 2.02315e6i) q^{68} -6.94320e6 q^{69} +33280.0 q^{71} +(-555264. - 961745. i) q^{72} +(-1.48573e6 + 2.57335e6i) q^{73} +(-83816.0 + 145174. i) q^{74} +(-2.70188e6 - 4.67978e6i) q^{75} +2.95821e6 q^{76} +2.35066e6 q^{78} +(1.18808e6 + 2.05782e6i) q^{79} +(-819200. + 1.41890e6i) q^{80} +(2.41101e6 - 4.17598e6i) q^{81} +(1.27394e6 + 2.20654e6i) q^{82} +2.12236e6 q^{83} -1.46008e7 q^{85} +(-310976. - 538626. i) q^{86} +(4.16902e6 - 7.22096e6i) q^{87} +(-10240.0 + 17736.2i) q^{88} +(3.46017e6 + 5.99320e6i) q^{89} +6.94080e6 q^{90} -6.73280e6 q^{92} +(-5.64181e6 - 9.77191e6i) q^{93} +(2.81486e6 - 4.87549e6i) q^{94} +(-9.24440e6 + 1.60118e7i) q^{95} +(-1.08134e6 - 1.87294e6i) q^{96} -4.95271e6 q^{97} +86760.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8 q^{2} - 66 q^{3} - 64 q^{4} - 400 q^{5} + 1056 q^{6} + 1024 q^{8} - 2169 q^{9} - 3200 q^{10} - 40 q^{11} - 4224 q^{12} + 8904 q^{13} + 52800 q^{15} - 4096 q^{16} + 36502 q^{17} - 17352 q^{18} - 46222 q^{19}+ \cdots + 173520 q^{99}+O(q^{100}) \) 2 * q - 8 * q^2 - 66 * q^3 - 64 * q^4 - 400 * q^5 + 1056 * q^6 + 1024 * q^8 - 2169 * q^9 - 3200 * q^10 - 40 * q^11 - 4224 * q^12 + 8904 * q^13 + 52800 * q^15 - 4096 * q^16 + 36502 * q^17 - 17352 * q^18 - 46222 * q^19 + 51200 * q^20 + 640 * q^22 + 105200 * q^23 - 33792 * q^24 - 81875 * q^25 - 35616 * q^26 - 2376 * q^27 - 252668 * q^29 - 211200 * q^30 - 170964 * q^31 - 32768 * q^32 - 2640 * q^33 - 584032 * q^34 + 277632 * q^36 - 20954 * q^37 - 369776 * q^38 - 293832 * q^39 - 204800 * q^40 - 636972 * q^41 + 155488 * q^43 - 2560 * q^44 - 867600 * q^45 + 841600 * q^46 + 703716 * q^47 + 540672 * q^48 + 1310000 * q^50 + 2409132 * q^51 - 284928 * q^52 - 1603278 * q^53 + 9504 * q^54 + 32000 * q^55 + 6101304 * q^57 + 1010672 * q^58 - 1171894 * q^59 - 1689600 * q^60 - 2068872 * q^61 + 2735424 * q^62 + 524288 * q^64 - 1780800 * q^65 - 21120 * q^66 + 994268 * q^67 + 2336128 * q^68 - 13886400 * q^69 + 66560 * q^71 - 1110528 * q^72 - 2971454 * q^73 - 167632 * q^74 - 5403750 * q^75 + 5916416 * q^76 + 4701312 * q^78 + 2376168 * q^79 - 1638400 * q^80 + 4822011 * q^81 + 2547888 * q^82 + 4244716 * q^83 - 29201600 * q^85 - 621952 * q^86 + 8338044 * q^87 - 20480 * q^88 + 6920346 * q^89 + 13881600 * q^90 - 13465600 * q^92 - 11283624 * q^93 + 5629728 * q^94 - 18488800 * q^95 - 2162688 * q^96 - 9905420 * q^97 + 173520 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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