Properties

Label 84.12.k.b.5.5
Level $84$
Weight $12$
Character 84.5
Analytic conductor $64.541$
Analytic rank $0$
Dimension $56$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [84,12,Mod(5,84)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(84, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 3, 5]))
 
N = Newforms(chi, 12, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.5");
 
S:= CuspForms(chi, 12);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.k (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(56\)
Relative dimension: \(28\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 84.5
Dual form 84.12.k.b.17.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-377.843 - 185.422i) q^{3} +(2528.83 - 4380.06i) q^{5} +(-41471.0 + 16046.3i) q^{7} +(108384. + 140121. i) q^{9} +O(q^{10})\) \(q+(-377.843 - 185.422i) q^{3} +(2528.83 - 4380.06i) q^{5} +(-41471.0 + 16046.3i) q^{7} +(108384. + 140121. i) q^{9} +(-456316. + 263454. i) q^{11} -2.07826e6i q^{13} +(-1.76766e6 + 1.18607e6i) q^{15} +(3.35427e6 + 5.80977e6i) q^{17} +(1.56480e7 + 9.03437e6i) q^{19} +(1.86449e7 + 1.62667e6i) q^{21} +(-3.17125e7 - 1.83092e7i) q^{23} +(1.16241e7 + 2.01336e7i) q^{25} +(-1.49707e7 - 7.30407e7i) q^{27} +1.82965e8i q^{29} +(-1.05444e8 + 6.08780e7i) q^{31} +(2.21266e8 - 1.49333e7i) q^{33} +(-3.45895e7 + 2.22224e8i) q^{35} +(2.41836e7 - 4.18872e7i) q^{37} +(-3.85356e8 + 7.85257e8i) q^{39} -6.29202e7 q^{41} -1.04363e9 q^{43} +(8.87823e8 - 1.20387e8i) q^{45} +(1.32425e9 - 2.29366e9i) q^{47} +(1.46236e9 - 1.33091e9i) q^{49} +(-1.90129e8 - 2.81714e9i) q^{51} +(2.42170e9 - 1.39817e9i) q^{53} +2.66492e9i q^{55} +(-4.23731e9 - 6.31506e9i) q^{57} +(1.18937e9 + 2.06005e9i) q^{59} +(3.69101e9 + 2.13101e9i) q^{61} +(-6.74322e9 - 4.07180e9i) q^{63} +(-9.10290e9 - 5.25556e9i) q^{65} +(-2.51703e9 - 4.35962e9i) q^{67} +(8.58742e9 + 1.27982e10i) q^{69} -1.63164e10i q^{71} +(1.87306e10 - 1.08141e10i) q^{73} +(-6.58888e8 - 9.76272e9i) q^{75} +(1.46964e10 - 1.82479e10i) q^{77} +(1.31030e10 - 2.26950e10i) q^{79} +(-7.88678e9 + 3.03738e10i) q^{81} -5.02431e10 q^{83} +3.39295e10 q^{85} +(3.39259e10 - 6.91323e10i) q^{87} +(-1.52449e10 + 2.64050e10i) q^{89} +(3.33483e10 + 8.61876e10i) q^{91} +(5.11294e10 - 3.45073e9i) q^{93} +(7.91420e10 - 4.56927e10i) q^{95} -1.24537e11i q^{97} +(-8.63730e10 - 3.53852e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 56 q - 729 q^{3} - 27194 q^{7} - 172347 q^{9} - 4853058 q^{15} + 28700520 q^{19} - 11325429 q^{21} - 316601194 q^{25} - 1368416388 q^{31} + 40874949 q^{33} - 87435712 q^{37} + 1177474410 q^{39} - 3055078348 q^{43} + 4109921793 q^{45} - 742582522 q^{49} - 694793715 q^{51} + 14605100370 q^{57} + 72584834058 q^{61} - 7310837811 q^{63} + 6131679148 q^{67} - 74402605464 q^{73} - 161115157854 q^{75} + 52181713528 q^{79} + 44948282337 q^{81} + 4658488716 q^{85} + 243101263104 q^{87} - 85311757146 q^{91} - 256628211777 q^{93} + 157345775874 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{5}{6}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −377.843 185.422i −0.897728 0.440550i
\(4\) 0 0
\(5\) 2528.83 4380.06i 0.361896 0.626823i −0.626377 0.779520i \(-0.715463\pi\)
0.988273 + 0.152698i \(0.0487962\pi\)
\(6\) 0 0
\(7\) −41471.0 + 16046.3i −0.932621 + 0.360856i
\(8\) 0 0
\(9\) 108384. + 140121.i 0.611832 + 0.790988i
\(10\) 0 0
\(11\) −456316. + 263454.i −0.854292 + 0.493225i −0.862097 0.506744i \(-0.830849\pi\)
0.00780495 + 0.999970i \(0.497516\pi\)
\(12\) 0 0
\(13\) 2.07826e6i 1.55243i −0.630469 0.776214i \(-0.717137\pi\)
0.630469 0.776214i \(-0.282863\pi\)
\(14\) 0 0
\(15\) −1.76766e6 + 1.18607e6i −0.601031 + 0.403283i
\(16\) 0 0
\(17\) 3.35427e6 + 5.80977e6i 0.572967 + 0.992407i 0.996259 + 0.0864144i \(0.0275409\pi\)
−0.423293 + 0.905993i \(0.639126\pi\)
\(18\) 0 0
\(19\) 1.56480e7 + 9.03437e6i 1.44982 + 0.837053i 0.998470 0.0552953i \(-0.0176100\pi\)
0.451348 + 0.892348i \(0.350943\pi\)
\(20\) 0 0
\(21\) 1.86449e7 + 1.62667e6i 0.996216 + 0.0869149i
\(22\) 0 0
\(23\) −3.17125e7 1.83092e7i −1.02737 0.593153i −0.111140 0.993805i \(-0.535450\pi\)
−0.916230 + 0.400652i \(0.868784\pi\)
\(24\) 0 0
\(25\) 1.16241e7 + 2.01336e7i 0.238062 + 0.412336i
\(26\) 0 0
\(27\) −1.49707e7 7.30407e7i −0.200790 0.979634i
\(28\) 0 0
\(29\) 1.82965e8i 1.65646i 0.560391 + 0.828228i \(0.310651\pi\)
−0.560391 + 0.828228i \(0.689349\pi\)
\(30\) 0 0
\(31\) −1.05444e8 + 6.08780e7i −0.661503 + 0.381919i −0.792849 0.609418i \(-0.791403\pi\)
0.131346 + 0.991337i \(0.458070\pi\)
\(32\) 0 0
\(33\) 2.21266e8 1.49333e7i 0.984212 0.0664246i
\(34\) 0 0
\(35\) −3.45895e7 + 2.22224e8i −0.111319 + 0.715181i
\(36\) 0 0
\(37\) 2.41836e7 4.18872e7i 0.0573338 0.0993051i −0.835934 0.548830i \(-0.815073\pi\)
0.893268 + 0.449525i \(0.148407\pi\)
\(38\) 0 0
\(39\) −3.85356e8 + 7.85257e8i −0.683922 + 1.39366i
\(40\) 0 0
\(41\) −6.29202e7 −0.0848162 −0.0424081 0.999100i \(-0.513503\pi\)
−0.0424081 + 0.999100i \(0.513503\pi\)
\(42\) 0 0
\(43\) −1.04363e9 −1.08260 −0.541301 0.840829i \(-0.682068\pi\)
−0.541301 + 0.840829i \(0.682068\pi\)
\(44\) 0 0
\(45\) 8.87823e8 1.20387e8i 0.717229 0.0972548i
\(46\) 0 0
\(47\) 1.32425e9 2.29366e9i 0.842230 1.45879i −0.0457747 0.998952i \(-0.514576\pi\)
0.888005 0.459834i \(-0.152091\pi\)
\(48\) 0 0
\(49\) 1.46236e9 1.33091e9i 0.739565 0.673085i
\(50\) 0 0
\(51\) −1.90129e8 2.81714e9i −0.0771637 1.14333i
\(52\) 0 0
\(53\) 2.42170e9 1.39817e9i 0.795433 0.459243i −0.0464390 0.998921i \(-0.514787\pi\)
0.841872 + 0.539678i \(0.181454\pi\)
\(54\) 0 0
\(55\) 2.66492e9i 0.713986i
\(56\) 0 0
\(57\) −4.23731e9 6.31506e9i −0.932779 1.39016i
\(58\) 0 0
\(59\) 1.18937e9 + 2.06005e9i 0.216587 + 0.375139i 0.953762 0.300562i \(-0.0971743\pi\)
−0.737176 + 0.675701i \(0.763841\pi\)
\(60\) 0 0
\(61\) 3.69101e9 + 2.13101e9i 0.559540 + 0.323051i 0.752961 0.658065i \(-0.228625\pi\)
−0.193421 + 0.981116i \(0.561958\pi\)
\(62\) 0 0
\(63\) −6.74322e9 4.07180e9i −0.856041 0.516908i
\(64\) 0 0
\(65\) −9.10290e9 5.25556e9i −0.973097 0.561818i
\(66\) 0 0
\(67\) −2.51703e9 4.35962e9i −0.227760 0.394491i 0.729384 0.684104i \(-0.239807\pi\)
−0.957144 + 0.289613i \(0.906473\pi\)
\(68\) 0 0
\(69\) 8.58742e9 + 1.27982e10i 0.660986 + 0.985097i
\(70\) 0 0
\(71\) 1.63164e10i 1.07326i −0.843818 0.536629i \(-0.819697\pi\)
0.843818 0.536629i \(-0.180303\pi\)
\(72\) 0 0
\(73\) 1.87306e10 1.08141e10i 1.05749 0.610541i 0.132751 0.991149i \(-0.457619\pi\)
0.924736 + 0.380609i \(0.124286\pi\)
\(74\) 0 0
\(75\) −6.58888e8 9.76272e9i −0.0320608 0.475044i
\(76\) 0 0
\(77\) 1.46964e10 1.82479e10i 0.618747 0.768269i
\(78\) 0 0
\(79\) 1.31030e10 2.26950e10i 0.479094 0.829815i −0.520619 0.853789i \(-0.674299\pi\)
0.999713 + 0.0239743i \(0.00763198\pi\)
\(80\) 0 0
\(81\) −7.88678e9 + 3.03738e10i −0.251323 + 0.967903i
\(82\) 0 0
\(83\) −5.02431e10 −1.40006 −0.700031 0.714113i \(-0.746830\pi\)
−0.700031 + 0.714113i \(0.746830\pi\)
\(84\) 0 0
\(85\) 3.39295e10 0.829418
\(86\) 0 0
\(87\) 3.39259e10 6.91323e10i 0.729751 1.48705i
\(88\) 0 0
\(89\) −1.52449e10 + 2.64050e10i −0.289388 + 0.501234i −0.973664 0.227989i \(-0.926785\pi\)
0.684276 + 0.729223i \(0.260118\pi\)
\(90\) 0 0
\(91\) 3.33483e10 + 8.61876e10i 0.560204 + 1.44783i
\(92\) 0 0
\(93\) 5.11294e10 3.45073e9i 0.762104 0.0514346i
\(94\) 0 0
\(95\) 7.91420e10 4.56927e10i 1.04937 0.605852i
\(96\) 0 0
\(97\) 1.24537e11i 1.47249i −0.676714 0.736246i \(-0.736597\pi\)
0.676714 0.736246i \(-0.263403\pi\)
\(98\) 0 0
\(99\) −8.63730e10 3.53852e10i −0.912818 0.373963i
\(100\) 0 0
\(101\) −8.08856e10 1.40098e11i −0.765780 1.32637i −0.939833 0.341633i \(-0.889020\pi\)
0.174054 0.984736i \(-0.444313\pi\)
\(102\) 0 0
\(103\) 9.55052e10 + 5.51399e10i 0.811750 + 0.468664i 0.847563 0.530694i \(-0.178069\pi\)
−0.0358133 + 0.999358i \(0.511402\pi\)
\(104\) 0 0
\(105\) 5.42746e10 7.75520e10i 0.415007 0.592996i
\(106\) 0 0
\(107\) −1.09178e11 6.30340e10i −0.752532 0.434475i 0.0740760 0.997253i \(-0.476399\pi\)
−0.826608 + 0.562778i \(0.809733\pi\)
\(108\) 0 0
\(109\) −4.16744e10 7.21822e10i −0.259432 0.449350i 0.706658 0.707556i \(-0.250202\pi\)
−0.966090 + 0.258206i \(0.916869\pi\)
\(110\) 0 0
\(111\) −1.69044e10 + 1.13426e10i −0.0952190 + 0.0638906i
\(112\) 0 0
\(113\) 3.11618e11i 1.59107i −0.605905 0.795537i \(-0.707189\pi\)
0.605905 0.795537i \(-0.292811\pi\)
\(114\) 0 0
\(115\) −1.60391e11 + 9.26016e10i −0.743603 + 0.429319i
\(116\) 0 0
\(117\) 2.91208e11 2.25251e11i 1.22795 0.949826i
\(118\) 0 0
\(119\) −2.32330e11 1.87114e11i −0.892478 0.718782i
\(120\) 0 0
\(121\) −3.83951e9 + 6.65023e9i −0.0134572 + 0.0233086i
\(122\) 0 0
\(123\) 2.37740e10 + 1.16668e10i 0.0761419 + 0.0373658i
\(124\) 0 0
\(125\) 3.64537e11 1.06841
\(126\) 0 0
\(127\) 6.70824e11 1.80172 0.900862 0.434106i \(-0.142936\pi\)
0.900862 + 0.434106i \(0.142936\pi\)
\(128\) 0 0
\(129\) 3.94328e11 + 1.93512e11i 0.971882 + 0.476940i
\(130\) 0 0
\(131\) −3.25093e11 + 5.63077e11i −0.736233 + 1.27519i 0.217947 + 0.975961i \(0.430064\pi\)
−0.954180 + 0.299233i \(0.903269\pi\)
\(132\) 0 0
\(133\) −7.93905e11 1.23573e11i −1.65419 0.257477i
\(134\) 0 0
\(135\) −3.57780e11 1.19135e11i −0.686722 0.228666i
\(136\) 0 0
\(137\) 1.20519e11 6.95818e10i 0.213350 0.123178i −0.389517 0.921019i \(-0.627358\pi\)
0.602867 + 0.797841i \(0.294025\pi\)
\(138\) 0 0
\(139\) 9.47003e11i 1.54800i −0.633188 0.773998i \(-0.718254\pi\)
0.633188 0.773998i \(-0.281746\pi\)
\(140\) 0 0
\(141\) −9.25654e11 + 6.21101e11i −1.39876 + 0.938549i
\(142\) 0 0
\(143\) 5.47527e11 + 9.48344e11i 0.765697 + 1.32623i
\(144\) 0 0
\(145\) 8.01399e11 + 4.62688e11i 1.03830 + 0.599465i
\(146\) 0 0
\(147\) −7.99324e11 + 2.31721e11i −0.960456 + 0.278432i
\(148\) 0 0
\(149\) 3.15654e11 + 1.82243e11i 0.352116 + 0.203294i 0.665617 0.746294i \(-0.268168\pi\)
−0.313501 + 0.949588i \(0.601502\pi\)
\(150\) 0 0
\(151\) 3.52012e11 + 6.09703e11i 0.364909 + 0.632041i 0.988762 0.149501i \(-0.0477668\pi\)
−0.623853 + 0.781542i \(0.714433\pi\)
\(152\) 0 0
\(153\) −4.50521e11 + 1.09969e12i −0.434423 + 1.06040i
\(154\) 0 0
\(155\) 6.15800e11i 0.552860i
\(156\) 0 0
\(157\) 9.68725e11 5.59294e11i 0.810499 0.467942i −0.0366302 0.999329i \(-0.511662\pi\)
0.847129 + 0.531387i \(0.178329\pi\)
\(158\) 0 0
\(159\) −1.17428e12 + 7.92521e10i −0.916402 + 0.0618481i
\(160\) 0 0
\(161\) 1.60894e12 + 2.50435e11i 1.17219 + 0.182453i
\(162\) 0 0
\(163\) −6.28553e11 + 1.08869e12i −0.427868 + 0.741090i −0.996684 0.0813755i \(-0.974069\pi\)
0.568815 + 0.822465i \(0.307402\pi\)
\(164\) 0 0
\(165\) 4.94135e11 1.00692e12i 0.314546 0.640965i
\(166\) 0 0
\(167\) −1.33942e12 −0.797951 −0.398975 0.916962i \(-0.630634\pi\)
−0.398975 + 0.916962i \(0.630634\pi\)
\(168\) 0 0
\(169\) −2.52701e12 −1.41003
\(170\) 0 0
\(171\) 4.30089e11 + 3.17179e12i 0.224947 + 1.65892i
\(172\) 0 0
\(173\) −8.61920e11 + 1.49289e12i −0.422876 + 0.732444i −0.996219 0.0868719i \(-0.972313\pi\)
0.573343 + 0.819315i \(0.305646\pi\)
\(174\) 0 0
\(175\) −8.05134e11 6.48437e11i −0.370816 0.298647i
\(176\) 0 0
\(177\) −6.74168e10 9.98913e11i −0.0291686 0.432190i
\(178\) 0 0
\(179\) 3.88058e11 2.24046e11i 0.157836 0.0911265i −0.419002 0.907985i \(-0.637620\pi\)
0.576838 + 0.816859i \(0.304287\pi\)
\(180\) 0 0
\(181\) 3.81573e11i 0.145998i −0.997332 0.0729989i \(-0.976743\pi\)
0.997332 0.0729989i \(-0.0232569\pi\)
\(182\) 0 0
\(183\) −9.99488e11 1.48958e12i −0.359995 0.536517i
\(184\) 0 0
\(185\) −1.22312e11 2.11851e11i −0.0414978 0.0718763i
\(186\) 0 0
\(187\) −3.06122e12 1.76740e12i −0.978961 0.565204i
\(188\) 0 0
\(189\) 1.79288e12 + 2.78885e12i 0.540768 + 0.841172i
\(190\) 0 0
\(191\) 4.74749e12 + 2.74097e12i 1.35139 + 0.780226i 0.988444 0.151584i \(-0.0484375\pi\)
0.362946 + 0.931810i \(0.381771\pi\)
\(192\) 0 0
\(193\) −7.42187e11 1.28550e12i −0.199502 0.345548i 0.748865 0.662723i \(-0.230599\pi\)
−0.948367 + 0.317175i \(0.897266\pi\)
\(194\) 0 0
\(195\) 2.46497e12 + 3.67366e12i 0.626068 + 0.933057i
\(196\) 0 0
\(197\) 3.36944e12i 0.809084i 0.914519 + 0.404542i \(0.132569\pi\)
−0.914519 + 0.404542i \(0.867431\pi\)
\(198\) 0 0
\(199\) 3.04647e12 1.75888e12i 0.691998 0.399525i −0.112362 0.993667i \(-0.535842\pi\)
0.804360 + 0.594142i \(0.202508\pi\)
\(200\) 0 0
\(201\) 1.42672e11 + 2.11397e12i 0.0306733 + 0.454485i
\(202\) 0 0
\(203\) −2.93591e12 7.58776e12i −0.597743 1.54485i
\(204\) 0 0
\(205\) −1.59114e11 + 2.75594e11i −0.0306947 + 0.0531647i
\(206\) 0 0
\(207\) −8.71626e11 6.42802e12i −0.159402 1.17555i
\(208\) 0 0
\(209\) −9.52057e12 −1.65142
\(210\) 0 0
\(211\) 8.92926e12 1.46981 0.734907 0.678168i \(-0.237226\pi\)
0.734907 + 0.678168i \(0.237226\pi\)
\(212\) 0 0
\(213\) −3.02543e12 + 6.16506e12i −0.472823 + 0.963494i
\(214\) 0 0
\(215\) −2.63915e12 + 4.57114e12i −0.391789 + 0.678599i
\(216\) 0 0
\(217\) 3.39600e12 4.21665e12i 0.479114 0.594894i
\(218\) 0 0
\(219\) −9.08239e12 + 6.12972e11i −1.21831 + 0.0822239i
\(220\) 0 0
\(221\) 1.20742e13 6.97105e12i 1.54064 0.889490i
\(222\) 0 0
\(223\) 7.14685e12i 0.867836i 0.900952 + 0.433918i \(0.142869\pi\)
−0.900952 + 0.433918i \(0.857131\pi\)
\(224\) 0 0
\(225\) −1.56127e12 + 3.81095e12i −0.180499 + 0.440585i
\(226\) 0 0
\(227\) 4.59923e12 + 7.96609e12i 0.506457 + 0.877209i 0.999972 + 0.00747206i \(0.00237845\pi\)
−0.493515 + 0.869737i \(0.664288\pi\)
\(228\) 0 0
\(229\) 8.73020e12 + 5.04038e12i 0.916071 + 0.528894i 0.882379 0.470539i \(-0.155940\pi\)
0.0336912 + 0.999432i \(0.489274\pi\)
\(230\) 0 0
\(231\) −8.93651e12 + 4.16980e12i −0.893927 + 0.417108i
\(232\) 0 0
\(233\) −1.21726e13 7.02786e12i −1.16125 0.670449i −0.209648 0.977777i \(-0.567232\pi\)
−0.951604 + 0.307328i \(0.900565\pi\)
\(234\) 0 0
\(235\) −6.69758e12 1.16006e13i −0.609600 1.05586i
\(236\) 0 0
\(237\) −9.15903e12 + 6.14558e12i −0.795671 + 0.533884i
\(238\) 0 0
\(239\) 1.09354e12i 0.0907083i 0.998971 + 0.0453542i \(0.0144416\pi\)
−0.998971 + 0.0453542i \(0.985558\pi\)
\(240\) 0 0
\(241\) 1.69008e13 9.75768e12i 1.33910 0.773131i 0.352427 0.935839i \(-0.385356\pi\)
0.986674 + 0.162708i \(0.0520230\pi\)
\(242\) 0 0
\(243\) 8.61195e12 1.00142e13i 0.652029 0.758194i
\(244\) 0 0
\(245\) −2.13140e12 9.77086e12i −0.154259 0.707163i
\(246\) 0 0
\(247\) 1.87758e13 3.25206e13i 1.29946 2.25074i
\(248\) 0 0
\(249\) 1.89840e13 + 9.31619e12i 1.25688 + 0.616797i
\(250\) 0 0
\(251\) −9.20006e12 −0.582888 −0.291444 0.956588i \(-0.594136\pi\)
−0.291444 + 0.956588i \(0.594136\pi\)
\(252\) 0 0
\(253\) 1.92946e13 1.17023
\(254\) 0 0
\(255\) −1.28200e13 6.29128e12i −0.744592 0.365400i
\(256\) 0 0
\(257\) 1.09065e13 1.88906e13i 0.606809 1.05102i −0.384954 0.922936i \(-0.625783\pi\)
0.991763 0.128088i \(-0.0408841\pi\)
\(258\) 0 0
\(259\) −3.30785e11 + 2.12516e12i −0.0176359 + 0.113303i
\(260\) 0 0
\(261\) −2.56373e13 + 1.98306e13i −1.31024 + 1.01347i
\(262\) 0 0
\(263\) 1.44069e13 8.31780e12i 0.706013 0.407617i −0.103570 0.994622i \(-0.533027\pi\)
0.809583 + 0.587005i \(0.199693\pi\)
\(264\) 0 0
\(265\) 1.41429e13i 0.664793i
\(266\) 0 0
\(267\) 1.06563e13 7.15020e12i 0.480610 0.322483i
\(268\) 0 0
\(269\) −4.62345e12 8.00806e12i −0.200138 0.346649i 0.748435 0.663208i \(-0.230806\pi\)
−0.948573 + 0.316559i \(0.897472\pi\)
\(270\) 0 0
\(271\) −9.19663e12 5.30968e12i −0.382206 0.220667i 0.296572 0.955011i \(-0.404157\pi\)
−0.678778 + 0.734344i \(0.737490\pi\)
\(272\) 0 0
\(273\) 3.38065e12 3.87489e13i 0.134929 1.54655i
\(274\) 0 0
\(275\) −1.06086e13 6.12486e12i −0.406749 0.234837i
\(276\) 0 0
\(277\) 4.05927e12 + 7.03086e12i 0.149558 + 0.259042i 0.931064 0.364856i \(-0.118882\pi\)
−0.781506 + 0.623897i \(0.785548\pi\)
\(278\) 0 0
\(279\) −1.99587e13 8.17669e12i −0.706822 0.289571i
\(280\) 0 0
\(281\) 2.55205e13i 0.868970i −0.900679 0.434485i \(-0.856930\pi\)
0.900679 0.434485i \(-0.143070\pi\)
\(282\) 0 0
\(283\) 7.15629e12 4.13169e12i 0.234349 0.135301i −0.378228 0.925713i \(-0.623466\pi\)
0.612577 + 0.790411i \(0.290133\pi\)
\(284\) 0 0
\(285\) −3.83757e13 + 2.58998e12i −1.20895 + 0.0815925i
\(286\) 0 0
\(287\) 2.60936e12 1.00963e12i 0.0791014 0.0306065i
\(288\) 0 0
\(289\) −5.36635e12 + 9.29479e12i −0.156582 + 0.271207i
\(290\) 0 0
\(291\) −2.30919e13 + 4.70554e13i −0.648706 + 1.32190i
\(292\) 0 0
\(293\) 3.18412e13 0.861424 0.430712 0.902489i \(-0.358262\pi\)
0.430712 + 0.902489i \(0.358262\pi\)
\(294\) 0 0
\(295\) 1.20309e13 0.313527
\(296\) 0 0
\(297\) 2.60742e13 + 2.93855e13i 0.654714 + 0.737859i
\(298\) 0 0
\(299\) −3.80513e13 + 6.59068e13i −0.920827 + 1.59492i
\(300\) 0 0
\(301\) 4.32803e13 1.67463e13i 1.00966 0.390664i
\(302\) 0 0
\(303\) 4.58482e12 + 6.79331e13i 0.103131 + 1.52808i
\(304\) 0 0
\(305\) 1.86679e13 1.07779e13i 0.404991 0.233822i
\(306\) 0 0
\(307\) 2.39021e12i 0.0500236i 0.999687 + 0.0250118i \(0.00796233\pi\)
−0.999687 + 0.0250118i \(0.992038\pi\)
\(308\) 0 0
\(309\) −2.58618e13 3.85430e13i −0.522261 0.778349i
\(310\) 0 0
\(311\) −1.15843e13 2.00646e13i −0.225781 0.391064i 0.730773 0.682621i \(-0.239160\pi\)
−0.956553 + 0.291557i \(0.905827\pi\)
\(312\) 0 0
\(313\) 2.97553e13 + 1.71793e13i 0.559849 + 0.323229i 0.753085 0.657923i \(-0.228565\pi\)
−0.193236 + 0.981152i \(0.561898\pi\)
\(314\) 0 0
\(315\) −3.48872e13 + 1.92388e13i −0.633808 + 0.349518i
\(316\) 0 0
\(317\) 1.46252e13 + 8.44384e12i 0.256611 + 0.148154i 0.622788 0.782391i \(-0.286000\pi\)
−0.366177 + 0.930545i \(0.619333\pi\)
\(318\) 0 0
\(319\) −4.82030e13 8.34901e13i −0.817007 1.41510i
\(320\) 0 0
\(321\) 2.95643e13 + 4.40611e13i 0.484162 + 0.721568i
\(322\) 0 0
\(323\) 1.21215e14i 1.91841i
\(324\) 0 0
\(325\) 4.18429e13 2.41580e13i 0.640122 0.369575i
\(326\) 0 0
\(327\) 2.36222e12 + 3.50009e13i 0.0349388 + 0.517687i
\(328\) 0 0
\(329\) −1.81132e13 + 1.16370e14i −0.259070 + 1.66442i
\(330\) 0 0
\(331\) 5.99104e13 1.03768e14i 0.828797 1.43552i −0.0701849 0.997534i \(-0.522359\pi\)
0.898982 0.437985i \(-0.144308\pi\)
\(332\) 0 0
\(333\) 8.49039e12 1.15128e12i 0.113628 0.0154077i
\(334\) 0 0
\(335\) −2.54605e13 −0.329701
\(336\) 0 0
\(337\) −7.40574e13 −0.928120 −0.464060 0.885804i \(-0.653608\pi\)
−0.464060 + 0.885804i \(0.653608\pi\)
\(338\) 0 0
\(339\) −5.77808e13 + 1.17743e14i −0.700947 + 1.42835i
\(340\) 0 0
\(341\) 3.20772e13 5.55593e13i 0.376744 0.652540i
\(342\) 0 0
\(343\) −3.92895e13 + 7.86596e13i −0.446847 + 0.894610i
\(344\) 0 0
\(345\) 7.77729e13 5.24891e12i 0.856690 0.0578181i
\(346\) 0 0
\(347\) −1.26636e12 + 7.31136e11i −0.0135128 + 0.00780164i −0.506741 0.862098i \(-0.669150\pi\)
0.493228 + 0.869900i \(0.335817\pi\)
\(348\) 0 0
\(349\) 1.95539e13i 0.202159i −0.994878 0.101080i \(-0.967770\pi\)
0.994878 0.101080i \(-0.0322297\pi\)
\(350\) 0 0
\(351\) −1.51798e14 + 3.11130e13i −1.52081 + 0.311712i
\(352\) 0 0
\(353\) 4.60785e12 + 7.98102e12i 0.0447442 + 0.0774993i 0.887530 0.460750i \(-0.152419\pi\)
−0.842786 + 0.538249i \(0.819086\pi\)
\(354\) 0 0
\(355\) −7.14669e13 4.12614e13i −0.672742 0.388408i
\(356\) 0 0
\(357\) 5.30894e13 + 1.13779e14i 0.484543 + 1.03845i
\(358\) 0 0
\(359\) −9.73063e13 5.61798e13i −0.861235 0.497234i 0.00319073 0.999995i \(-0.498984\pi\)
−0.864426 + 0.502761i \(0.832318\pi\)
\(360\) 0 0
\(361\) 1.04994e14 + 1.81856e14i 0.901315 + 1.56112i
\(362\) 0 0
\(363\) 2.68383e12 1.80081e12i 0.0223496 0.0149962i
\(364\) 0 0
\(365\) 1.09388e14i 0.883809i
\(366\) 0 0
\(367\) −1.90508e13 + 1.09990e13i −0.149365 + 0.0862361i −0.572820 0.819681i \(-0.694151\pi\)
0.423455 + 0.905917i \(0.360817\pi\)
\(368\) 0 0
\(369\) −6.81956e12 8.81645e12i −0.0518933 0.0670886i
\(370\) 0 0
\(371\) −7.79950e13 + 9.68428e13i −0.576116 + 0.715337i
\(372\) 0 0
\(373\) 1.16570e13 2.01905e13i 0.0835964 0.144793i −0.821196 0.570646i \(-0.806693\pi\)
0.904792 + 0.425853i \(0.140026\pi\)
\(374\) 0 0
\(375\) −1.37738e14 6.75933e13i −0.959140 0.470687i
\(376\) 0 0
\(377\) 3.80250e14 2.57153
\(378\) 0 0
\(379\) 4.29279e12 0.0281984 0.0140992 0.999901i \(-0.495512\pi\)
0.0140992 + 0.999901i \(0.495512\pi\)
\(380\) 0 0
\(381\) −2.53466e14 1.24386e14i −1.61746 0.793749i
\(382\) 0 0
\(383\) −5.48745e13 + 9.50455e13i −0.340234 + 0.589302i −0.984476 0.175519i \(-0.943840\pi\)
0.644242 + 0.764822i \(0.277173\pi\)
\(384\) 0 0
\(385\) −4.27620e13 1.10517e14i −0.257646 0.665878i
\(386\) 0 0
\(387\) −1.13113e14 1.46234e14i −0.662371 0.856325i
\(388\) 0 0
\(389\) 3.36280e13 1.94151e13i 0.191416 0.110514i −0.401229 0.915978i \(-0.631417\pi\)
0.592645 + 0.805464i \(0.298084\pi\)
\(390\) 0 0
\(391\) 2.45656e14i 1.35943i
\(392\) 0 0
\(393\) 2.27241e14 1.52476e14i 1.22272 0.820430i
\(394\) 0 0
\(395\) −6.62703e13 1.14783e14i −0.346765 0.600614i
\(396\) 0 0
\(397\) −4.33485e13 2.50273e13i −0.220611 0.127370i 0.385622 0.922657i \(-0.373987\pi\)
−0.606233 + 0.795287i \(0.707320\pi\)
\(398\) 0 0
\(399\) 2.77059e14 + 1.93899e14i 1.37158 + 0.959896i
\(400\) 0 0
\(401\) 1.97545e14 + 1.14053e14i 0.951420 + 0.549303i 0.893522 0.449020i \(-0.148227\pi\)
0.0578982 + 0.998322i \(0.481560\pi\)
\(402\) 0 0
\(403\) 1.26520e14 + 2.19140e14i 0.592902 + 1.02694i
\(404\) 0 0
\(405\) 1.13095e14 + 1.11355e14i 0.515751 + 0.507815i
\(406\) 0 0
\(407\) 2.54851e13i 0.113114i
\(408\) 0 0
\(409\) −1.73107e12 + 9.99435e11i −0.00747889 + 0.00431794i −0.503735 0.863858i \(-0.668041\pi\)
0.496256 + 0.868176i \(0.334708\pi\)
\(410\) 0 0
\(411\) −5.84394e13 + 3.94408e12i −0.245796 + 0.0165888i
\(412\) 0 0
\(413\) −8.23806e13 6.63475e13i −0.337365 0.271706i
\(414\) 0 0
\(415\) −1.27056e14 + 2.20068e14i −0.506677 + 0.877590i
\(416\) 0 0
\(417\) −1.75595e14 + 3.57819e14i −0.681969 + 1.38968i
\(418\) 0 0
\(419\) −8.63464e13 −0.326638 −0.163319 0.986573i \(-0.552220\pi\)
−0.163319 + 0.986573i \(0.552220\pi\)
\(420\) 0 0
\(421\) 2.54049e14 0.936194 0.468097 0.883677i \(-0.344940\pi\)
0.468097 + 0.883677i \(0.344940\pi\)
\(422\) 0 0
\(423\) 4.64918e14 6.30420e13i 1.66918 0.226338i
\(424\) 0 0
\(425\) −7.79811e13 + 1.35067e14i −0.272804 + 0.472510i
\(426\) 0 0
\(427\) −1.87265e14 2.91481e13i −0.638414 0.0993702i
\(428\) 0 0
\(429\) −3.10353e13 4.59849e14i −0.103120 1.52792i
\(430\) 0 0
\(431\) −7.58473e13 + 4.37905e13i −0.245649 + 0.141826i −0.617770 0.786359i \(-0.711964\pi\)
0.372121 + 0.928184i \(0.378631\pi\)
\(432\) 0 0
\(433\) 2.31081e13i 0.0729594i −0.999334 0.0364797i \(-0.988386\pi\)
0.999334 0.0364797i \(-0.0116144\pi\)
\(434\) 0 0
\(435\) −2.17011e14 3.23421e14i −0.668021 0.995581i
\(436\) 0 0
\(437\) −3.30824e14 5.73004e14i −0.993000 1.71993i
\(438\) 0 0
\(439\) −9.33538e13 5.38979e13i −0.273261 0.157767i 0.357108 0.934063i \(-0.383763\pi\)
−0.630369 + 0.776296i \(0.717096\pi\)
\(440\) 0 0
\(441\) 3.44985e14 + 6.06582e13i 0.984892 + 0.173172i
\(442\) 0 0
\(443\) −1.17079e14 6.75957e13i −0.326031 0.188234i 0.328047 0.944662i \(-0.393610\pi\)
−0.654078 + 0.756427i \(0.726943\pi\)
\(444\) 0 0
\(445\) 7.71035e13 + 1.33547e14i 0.209457 + 0.362790i
\(446\) 0 0
\(447\) −8.54758e13 1.27388e14i −0.226544 0.337628i
\(448\) 0 0
\(449\) 3.46184e14i 0.895266i −0.894217 0.447633i \(-0.852267\pi\)
0.894217 0.447633i \(-0.147733\pi\)
\(450\) 0 0
\(451\) 2.87115e13 1.65766e13i 0.0724578 0.0418335i
\(452\) 0 0
\(453\) −1.99530e13 2.95643e14i −0.0491437 0.728161i
\(454\) 0 0
\(455\) 4.61838e14 + 7.18859e13i 1.11027 + 0.172815i
\(456\) 0 0
\(457\) −1.58574e13 + 2.74658e13i −0.0372128 + 0.0644545i −0.884032 0.467426i \(-0.845181\pi\)
0.846819 + 0.531881i \(0.178515\pi\)
\(458\) 0 0
\(459\) 3.74134e14 3.31975e14i 0.857151 0.760563i
\(460\) 0 0
\(461\) −4.58396e14 −1.02538 −0.512692 0.858573i \(-0.671352\pi\)
−0.512692 + 0.858573i \(0.671352\pi\)
\(462\) 0 0
\(463\) 5.80655e14 1.26830 0.634151 0.773210i \(-0.281350\pi\)
0.634151 + 0.773210i \(0.281350\pi\)
\(464\) 0 0
\(465\) 1.14183e14 2.32676e14i 0.243562 0.496318i
\(466\) 0 0
\(467\) 8.58928e13 1.48771e14i 0.178943 0.309938i −0.762576 0.646899i \(-0.776066\pi\)
0.941519 + 0.336961i \(0.109399\pi\)
\(468\) 0 0
\(469\) 1.74339e14 + 1.40409e14i 0.354768 + 0.285722i
\(470\) 0 0
\(471\) −4.69732e14 + 3.17023e13i −0.933759 + 0.0630196i
\(472\) 0 0
\(473\) 4.76224e14 2.74948e14i 0.924858 0.533967i
\(474\) 0 0
\(475\) 4.20067e14i 0.797083i
\(476\) 0 0
\(477\) 4.58387e14 + 1.87792e14i 0.849927 + 0.348198i
\(478\) 0 0
\(479\) −3.77979e14 6.54679e14i −0.684893 1.18627i −0.973470 0.228813i \(-0.926516\pi\)
0.288578 0.957457i \(-0.406818\pi\)
\(480\) 0 0
\(481\) −8.70525e13 5.02598e13i −0.154164 0.0890067i
\(482\) 0 0
\(483\) −5.61492e14 3.92959e14i −0.971929 0.680202i
\(484\) 0 0
\(485\) −5.45478e14 3.14932e14i −0.922991 0.532889i
\(486\) 0 0
\(487\) −1.70058e14 2.94549e14i −0.281312 0.487246i 0.690396 0.723431i \(-0.257436\pi\)
−0.971708 + 0.236185i \(0.924103\pi\)
\(488\) 0 0
\(489\) 4.39361e14 2.94805e14i 0.710597 0.476800i
\(490\) 0 0
\(491\) 3.84858e14i 0.608628i 0.952572 + 0.304314i \(0.0984272\pi\)
−0.952572 + 0.304314i \(0.901573\pi\)
\(492\) 0 0
\(493\) −1.06299e15 + 6.13716e14i −1.64388 + 0.949094i
\(494\) 0 0
\(495\) −3.73412e14 + 2.88835e14i −0.564754 + 0.436839i
\(496\) 0 0
\(497\) 2.61818e14 + 6.76659e14i 0.387292 + 1.00094i
\(498\) 0 0
\(499\) 4.54888e14 7.87890e14i 0.658191 1.14002i −0.322893 0.946436i \(-0.604655\pi\)
0.981084 0.193585i \(-0.0620114\pi\)
\(500\) 0 0
\(501\) 5.06091e14 + 2.48358e14i 0.716343 + 0.351537i
\(502\) 0 0
\(503\) 8.36732e14 1.15868 0.579338 0.815087i \(-0.303311\pi\)
0.579338 + 0.815087i \(0.303311\pi\)
\(504\) 0 0
\(505\) −8.18183e14 −1.10853
\(506\) 0 0
\(507\) 9.54813e14 + 4.68563e14i 1.26583 + 0.621190i
\(508\) 0 0
\(509\) −3.82102e14 + 6.61820e14i −0.495715 + 0.858603i −0.999988 0.00494131i \(-0.998427\pi\)
0.504273 + 0.863544i \(0.331760\pi\)
\(510\) 0 0
\(511\) −6.03250e14 + 7.49027e14i −0.765918 + 0.951004i
\(512\) 0 0
\(513\) 4.25615e14 1.27819e15i 0.528897 1.58836i
\(514\) 0 0
\(515\) 4.83032e14 2.78879e14i 0.587538 0.339215i
\(516\) 0 0
\(517\) 1.39551e15i 1.66164i
\(518\) 0 0
\(519\) 6.02486e14 4.04259e14i 0.702306 0.471237i
\(520\) 0 0
\(521\) 3.18221e14 + 5.51176e14i 0.363180 + 0.629046i 0.988482 0.151336i \(-0.0483576\pi\)
−0.625302 + 0.780383i \(0.715024\pi\)
\(522\) 0 0
\(523\) −1.07555e15 6.20972e14i −1.20191 0.693925i −0.240933 0.970542i \(-0.577453\pi\)
−0.960980 + 0.276617i \(0.910787\pi\)
\(524\) 0 0
\(525\) 1.83980e14 + 3.94297e14i 0.201323 + 0.431467i
\(526\) 0 0
\(527\) −7.07375e14 4.08403e14i −0.758039 0.437654i
\(528\) 0 0
\(529\) 1.94049e14 + 3.36103e14i 0.203660 + 0.352749i
\(530\) 0 0
\(531\) −1.59748e14 + 3.89933e14i −0.164216 + 0.400839i
\(532\) 0 0
\(533\) 1.30765e14i 0.131671i
\(534\) 0 0
\(535\) −5.52185e14 + 3.18804e14i −0.544677 + 0.314469i
\(536\) 0 0
\(537\) −1.88168e14 + 1.26995e13i −0.181839 + 0.0122724i
\(538\) 0 0
\(539\) −3.16666e14 + 9.92581e14i −0.299822 + 0.939783i
\(540\) 0 0
\(541\) 1.54401e14 2.67431e14i 0.143241 0.248100i −0.785475 0.618894i \(-0.787581\pi\)
0.928715 + 0.370794i \(0.120914\pi\)
\(542\) 0 0
\(543\) −7.07522e13 + 1.44175e14i −0.0643192 + 0.131066i
\(544\) 0 0
\(545\) −4.21549e14 −0.375550
\(546\) 0 0
\(547\) −7.43428e14 −0.649096 −0.324548 0.945869i \(-0.605212\pi\)
−0.324548 + 0.945869i \(0.605212\pi\)
\(548\) 0 0
\(549\) 1.01448e14 + 7.48156e14i 0.0868156 + 0.640242i
\(550\) 0 0
\(551\) −1.65298e15 + 2.86304e15i −1.38654 + 2.40156i
\(552\) 0 0
\(553\) −1.79223e14 + 1.15144e15i −0.147369 + 0.946787i
\(554\) 0 0
\(555\) 6.93298e12 + 1.02726e14i 0.00558867 + 0.0828072i
\(556\) 0 0
\(557\) 1.60735e15 9.28006e14i 1.27030 0.733411i 0.295259 0.955417i \(-0.404594\pi\)
0.975045 + 0.222006i \(0.0712606\pi\)
\(558\) 0 0
\(559\) 2.16893e15i 1.68066i
\(560\) 0 0
\(561\) 8.28947e14 + 1.23542e15i 0.629841 + 0.938680i
\(562\) 0 0
\(563\) 9.25039e14 + 1.60221e15i 0.689229 + 1.19378i 0.972087 + 0.234619i \(0.0753841\pi\)
−0.282858 + 0.959162i \(0.591283\pi\)
\(564\) 0 0
\(565\) −1.36490e15 7.88027e14i −0.997321 0.575804i
\(566\) 0 0
\(567\) −1.60314e14 1.38619e15i −0.114885 0.993379i
\(568\) 0 0
\(569\) 7.92264e14 + 4.57414e14i 0.556868 + 0.321508i 0.751888 0.659291i \(-0.229144\pi\)
−0.195019 + 0.980799i \(0.562477\pi\)
\(570\) 0 0
\(571\) −2.35338e13 4.07618e13i −0.0162253 0.0281031i 0.857799 0.513986i \(-0.171832\pi\)
−0.874024 + 0.485883i \(0.838498\pi\)
\(572\) 0 0
\(573\) −1.28557e15 1.91595e15i −0.869454 1.29579i
\(574\) 0 0
\(575\) 8.51315e14i 0.564829i
\(576\) 0 0
\(577\) 1.95406e15 1.12818e15i 1.27195 0.734363i 0.296599 0.955002i \(-0.404148\pi\)
0.975355 + 0.220639i \(0.0708143\pi\)
\(578\) 0 0
\(579\) 4.20691e13 + 6.23337e14i 0.0268678 + 0.398099i
\(580\) 0 0
\(581\) 2.08363e15 8.06214e14i 1.30573 0.505221i
\(582\) 0 0
\(583\) −7.36708e14 + 1.27602e15i −0.453021 + 0.784655i
\(584\) 0 0
\(585\) −2.50196e14 1.84513e15i −0.150981 1.11345i
\(586\) 0 0
\(587\) 4.92840e14 0.291875 0.145937 0.989294i \(-0.453380\pi\)
0.145937 + 0.989294i \(0.453380\pi\)
\(588\) 0 0
\(589\) −2.19998e15 −1.27875
\(590\) 0 0
\(591\) 6.24769e14 1.27312e15i 0.356442 0.726337i
\(592\) 0 0
\(593\) −1.58000e15 + 2.73664e15i −0.884821 + 1.53256i −0.0389032 + 0.999243i \(0.512386\pi\)
−0.845918 + 0.533313i \(0.820947\pi\)
\(594\) 0 0
\(595\) −1.40709e15 + 5.44441e14i −0.773533 + 0.299301i
\(596\) 0 0
\(597\) −1.47722e15 + 9.96980e13i −0.797237 + 0.0538056i
\(598\) 0 0
\(599\) 2.85300e15 1.64718e15i 1.51166 0.872758i 0.511754 0.859132i \(-0.328996\pi\)
0.999907 0.0136257i \(-0.00433731\pi\)
\(600\) 0 0
\(601\) 2.34878e15i 1.22189i −0.791673 0.610945i \(-0.790790\pi\)
0.791673 0.610945i \(-0.209210\pi\)
\(602\) 0 0
\(603\) 3.38069e14 8.25203e14i 0.172687 0.421517i
\(604\) 0 0
\(605\) 1.94189e13 + 3.36345e13i 0.00974025 + 0.0168706i
\(606\) 0 0
\(607\) 4.32839e14 + 2.49900e14i 0.213201 + 0.123092i 0.602798 0.797894i \(-0.294052\pi\)
−0.389597 + 0.920985i \(0.627386\pi\)
\(608\) 0 0
\(609\) −2.97625e14 + 3.41137e15i −0.143971 + 1.65019i
\(610\) 0 0
\(611\) −4.76683e15 2.75213e15i −2.26466 1.30750i
\(612\) 0 0
\(613\) 1.24578e15 + 2.15776e15i 0.581312 + 1.00686i 0.995324 + 0.0965904i \(0.0307937\pi\)
−0.414012 + 0.910271i \(0.635873\pi\)
\(614\) 0 0
\(615\) 1.11222e14 7.46281e13i 0.0509772 0.0342050i
\(616\) 0 0
\(617\) 2.42597e15i 1.09224i −0.837708 0.546118i \(-0.816105\pi\)
0.837708 0.546118i \(-0.183895\pi\)
\(618\) 0 0
\(619\) 2.68654e15 1.55107e15i 1.18821 0.686015i 0.230313 0.973117i \(-0.426025\pi\)
0.957900 + 0.287101i \(0.0926916\pi\)
\(620\) 0 0
\(621\) −8.62559e14 + 2.59040e15i −0.374787 + 1.12555i
\(622\) 0 0
\(623\) 2.08521e14 1.33967e15i 0.0890156 0.571889i
\(624\) 0 0
\(625\) 3.54267e14 6.13608e14i 0.148590 0.257366i
\(626\) 0 0
\(627\) 3.59728e15 + 1.76532e15i 1.48253 + 0.727534i
\(628\) 0 0
\(629\) 3.24473e14 0.131402
\(630\) 0 0
\(631\) 2.43683e15 0.969759 0.484880 0.874581i \(-0.338863\pi\)
0.484880 + 0.874581i \(0.338863\pi\)
\(632\) 0 0
\(633\) −3.37386e15 1.65568e15i −1.31949 0.647526i
\(634\) 0 0
\(635\) 1.69640e15 2.93825e15i 0.652037 1.12936i
\(636\) 0 0
\(637\) −2.76598e15 3.03917e15i −1.04492 1.14812i
\(638\) 0 0
\(639\) 2.28628e15 1.76844e15i 0.848934 0.656654i
\(640\) 0 0
\(641\) −1.38245e15 + 7.98158e14i −0.504580 + 0.291320i −0.730603 0.682802i \(-0.760761\pi\)
0.226023 + 0.974122i \(0.427428\pi\)
\(642\) 0 0
\(643\) 2.81384e14i 0.100958i 0.998725 + 0.0504789i \(0.0160748\pi\)
−0.998725 + 0.0504789i \(0.983925\pi\)
\(644\) 0 0
\(645\) 1.84478e15 1.23782e15i 0.650677 0.436595i
\(646\) 0 0
\(647\) 2.45457e15 + 4.25143e15i 0.851140 + 1.47422i 0.880180 + 0.474640i \(0.157422\pi\)
−0.0290395 + 0.999578i \(0.509245\pi\)
\(648\) 0 0
\(649\) −1.08546e15 6.26690e14i −0.370056 0.213652i
\(650\) 0 0
\(651\) −2.06502e15 + 9.63541e14i −0.692194 + 0.322979i
\(652\) 0 0
\(653\) −4.36912e15 2.52251e15i −1.44003 0.831401i −0.442179 0.896927i \(-0.645794\pi\)
−0.997851 + 0.0655255i \(0.979128\pi\)
\(654\) 0 0
\(655\) 1.64421e15 + 2.84785e15i 0.532880 + 0.922975i
\(656\) 0 0
\(657\) 3.54538e15 + 1.45247e15i 1.12993 + 0.462911i
\(658\) 0 0
\(659\) 5.76865e14i 0.180803i −0.995905 0.0904013i \(-0.971185\pi\)
0.995905 0.0904013i \(-0.0288150\pi\)
\(660\) 0 0
\(661\) −1.65926e15 + 9.57974e14i −0.511453 + 0.295288i −0.733431 0.679764i \(-0.762082\pi\)
0.221977 + 0.975052i \(0.428749\pi\)
\(662\) 0 0
\(663\) −5.85475e15 + 3.95138e14i −1.77494 + 0.119791i
\(664\) 0 0
\(665\) −2.54890e15 + 3.16485e15i −0.760036 + 0.943702i
\(666\) 0 0
\(667\) 3.34995e15 5.80229e15i 0.982531 1.70179i
\(668\) 0 0
\(669\) 1.32518e15 2.70039e15i 0.382325 0.779081i
\(670\) 0 0
\(671\) −2.24569e15 −0.637347
\(672\) 0 0
\(673\) 4.69954e15 1.31212 0.656058 0.754710i \(-0.272223\pi\)
0.656058 + 0.754710i \(0.272223\pi\)
\(674\) 0 0
\(675\) 1.29655e15 1.15045e15i 0.356138 0.316007i
\(676\) 0 0
\(677\) −2.85106e15 + 4.93819e15i −0.770494 + 1.33453i 0.166799 + 0.985991i \(0.446657\pi\)
−0.937293 + 0.348544i \(0.886676\pi\)
\(678\) 0 0
\(679\) 1.99835e15 + 5.16467e15i 0.531358 + 1.37328i
\(680\) 0 0
\(681\) −2.60697e14 3.86273e15i −0.0682066 1.01062i
\(682\) 0 0
\(683\) 4.57744e15 2.64279e15i 1.17844 0.680375i 0.222790 0.974866i \(-0.428484\pi\)
0.955654 + 0.294491i \(0.0951502\pi\)
\(684\) 0 0
\(685\) 7.03841e14i 0.178310i
\(686\) 0 0
\(687\) −2.36405e15 3.52325e15i −0.589379 0.878377i
\(688\) 0 0
\(689\) −2.90576e15 5.03293e15i −0.712942 1.23485i
\(690\) 0 0
\(691\) 2.22946e15 + 1.28718e15i 0.538356 + 0.310820i 0.744412 0.667720i \(-0.232730\pi\)
−0.206056 + 0.978540i \(0.566063\pi\)
\(692\) 0 0
\(693\) 4.14978e15 + 8.14983e13i 0.986261 + 0.0193694i
\(694\) 0 0
\(695\) −4.14793e15 2.39481e15i −0.970319 0.560214i
\(696\) 0 0
\(697\) −2.11052e14 3.65552e14i −0.0485969 0.0841723i
\(698\) 0 0
\(699\) 3.29622e15 + 4.91250e15i 0.747122 + 1.11347i
\(700\) 0 0
\(701\) 4.70196e15i 1.04913i −0.851370 0.524566i \(-0.824228\pi\)
0.851370 0.524566i \(-0.175772\pi\)
\(702\) 0 0
\(703\) 7.56848e14 4.36966e14i 0.166247 0.0959829i
\(704\) 0 0
\(705\) 3.79637e14 + 5.62507e15i 0.0820972 + 1.21643i
\(706\) 0 0
\(707\) 5.60246e15 + 4.51209e15i 1.19281 + 0.960664i
\(708\) 0 0
\(709\) 2.64468e15 4.58071e15i 0.554394 0.960238i −0.443557 0.896246i \(-0.646284\pi\)
0.997950 0.0639916i \(-0.0203831\pi\)
\(710\) 0 0
\(711\) 4.60020e15 6.23778e14i 0.949499 0.128750i
\(712\) 0 0
\(713\) 4.45851e15 0.906145
\(714\) 0 0
\(715\) 5.53840e15 1.10841
\(716\) 0 0
\(717\) 2.02767e14 4.13188e14i 0.0399615 0.0814314i
\(718\) 0 0
\(719\) 4.80696e15 8.32590e15i 0.932957 1.61593i 0.154719 0.987959i \(-0.450553\pi\)
0.778238 0.627970i \(-0.216114\pi\)
\(720\) 0 0
\(721\) −4.84549e15 7.54208e14i −0.926176 0.144161i
\(722\) 0 0
\(723\) −8.19515e15 + 5.53092e14i −1.54275 + 0.104121i
\(724\) 0 0
\(725\) −3.68375e15 + 2.12682e15i −0.683017 + 0.394340i
\(726\) 0 0
\(727\) 7.14214e15i 1.30433i −0.758075 0.652167i \(-0.773860\pi\)
0.758075 0.652167i \(-0.226140\pi\)
\(728\) 0 0
\(729\) −5.11082e15 + 2.18694e15i −0.919367 + 0.393401i
\(730\) 0 0
\(731\) −3.50061e15 6.06323e15i −0.620295 1.07438i
\(732\) 0 0
\(733\) −5.60636e15 3.23684e15i −0.978610 0.565001i −0.0767595 0.997050i \(-0.524457\pi\)
−0.901850 + 0.432049i \(0.857791\pi\)
\(734\) 0 0
\(735\) −1.00640e15 + 4.08706e15i −0.173058 + 0.702799i
\(736\) 0 0
\(737\) 2.29712e15 + 1.32624e15i 0.389146 + 0.224674i
\(738\) 0 0
\(739\) −2.41104e15 4.17604e15i −0.402401 0.696979i 0.591614 0.806221i \(-0.298491\pi\)
−0.994015 + 0.109242i \(0.965158\pi\)
\(740\) 0 0
\(741\) −1.31243e16 + 8.80624e15i −2.15813 + 1.44807i
\(742\) 0 0
\(743\) 3.11657e15i 0.504938i 0.967605 + 0.252469i \(0.0812426\pi\)
−0.967605 + 0.252469i \(0.918757\pi\)
\(744\) 0 0
\(745\) 1.59647e15 9.21720e14i 0.254859 0.147143i
\(746\) 0 0
\(747\) −5.44556e15 7.04012e15i −0.856603 1.10743i
\(748\) 0 0
\(749\) 5.53919e15 + 8.62184e14i 0.858611 + 0.133644i
\(750\) 0 0
\(751\) 3.44104e14 5.96006e14i 0.0525618 0.0910398i −0.838547 0.544829i \(-0.816595\pi\)
0.891109 + 0.453789i \(0.149928\pi\)
\(752\) 0 0
\(753\) 3.47618e15 + 1.70590e15i 0.523275 + 0.256791i
\(754\) 0 0
\(755\) 3.56071e15 0.528236
\(756\) 0 0
\(757\) −1.38072e15 −0.201874 −0.100937 0.994893i \(-0.532184\pi\)
−0.100937 + 0.994893i \(0.532184\pi\)
\(758\) 0 0
\(759\) −7.29032e15 3.57764e15i −1.05055 0.515545i
\(760\) 0 0
\(761\) −6.84283e15 + 1.18521e16i −0.971897 + 1.68338i −0.282082 + 0.959390i \(0.591025\pi\)
−0.689816 + 0.723985i \(0.742308\pi\)
\(762\) 0 0
\(763\) 2.88653e15 + 2.32475e15i 0.404103 + 0.325455i
\(764\) 0 0
\(765\) 3.67742e15 + 4.75424e15i 0.507464 + 0.656059i
\(766\) 0 0
\(767\) 4.28133e15 2.47182e15i 0.582376 0.336235i
\(768\) 0 0
\(769\) 4.76967e15i 0.639577i 0.947489 + 0.319789i \(0.103612\pi\)
−0.947489 + 0.319789i \(0.896388\pi\)
\(770\) 0 0
\(771\) −7.62367e15 + 5.11537e15i −1.00778 + 0.676205i
\(772\) 0 0
\(773\) 2.51065e15 + 4.34858e15i 0.327190 + 0.566709i 0.981953 0.189125i \(-0.0605651\pi\)
−0.654763 + 0.755834i \(0.727232\pi\)
\(774\) 0 0
\(775\) −2.45139e15 1.41531e15i −0.314958 0.181841i
\(776\) 0 0
\(777\) 5.19036e14 7.41643e14i 0.0657480 0.0939462i
\(778\) 0 0
\(779\) −9.84574e14 5.68444e14i −0.122968 0.0709957i
\(780\) 0 0
\(781\) 4.29863e15 + 7.44545e15i 0.529358 + 0.916876i
\(782\) 0 0
\(783\) 1.33639e16 2.73912e15i 1.62272 0.332599i
\(784\) 0 0
\(785\) 5.65743e15i 0.677385i
\(786\) 0 0
\(787\) 1.48661e15 8.58292e14i 0.175523 0.101338i −0.409664 0.912236i \(-0.634354\pi\)
0.585188 + 0.810898i \(0.301021\pi\)
\(788\) 0 0
\(789\) −6.98584e15 + 4.71476e14i −0.813383 + 0.0548954i
\(790\) 0 0
\(791\) 5.00030e15 + 1.29231e16i 0.574150 + 1.48387i
\(792\) 0 0
\(793\) 4.42879e15 7.67088e15i 0.501513 0.868646i
\(794\) 0 0
\(795\) −2.62241e15 + 5.34381e15i −0.292874 + 0.596804i
\(796\) 0 0
\(797\) 2.09272e15 0.230511 0.115255 0.993336i \(-0.463231\pi\)
0.115255 + 0.993336i \(0.463231\pi\)
\(798\) 0 0
\(799\) 1.77675e16 1.93028
\(800\) 0 0
\(801\) −5.35220e15 + 7.25748e14i −0.573527 + 0.0777691i
\(802\) 0 0
\(803\) −5.69804e15 + 9.86930e15i −0.602268 + 1.04316i
\(804\) 0 0
\(805\) 5.16565e15 6.41395e15i 0.538577 0.668726i
\(806\) 0 0
\(807\) 2.62070e14 + 3.88308e15i 0.0269534 + 0.399367i
\(808\) 0 0
\(809\) −1.63793e16 + 9.45661e15i −1.66180 + 0.959442i −0.689948 + 0.723859i \(0.742367\pi\)
−0.971854 + 0.235584i \(0.924300\pi\)
\(810\) 0 0
\(811\) 1.88710e15i 0.188878i 0.995531 + 0.0944388i \(0.0301057\pi\)
−0.995531 + 0.0944388i \(0.969894\pi\)
\(812\) 0 0
\(813\) 2.49035e15 + 3.71148e15i 0.245902 + 0.366479i
\(814\) 0 0
\(815\) 3.17900e15 + 5.50620e15i 0.309688 + 0.536395i
\(816\) 0 0
\(817\) −1.63307e16 9.42851e15i −1.56958 0.906195i
\(818\) 0 0
\(819\) −8.46227e15 + 1.40142e16i −0.802463 + 1.32894i
\(820\) 0 0
\(821\) 1.28090e15 + 7.39526e14i 0.119847 + 0.0691937i 0.558725 0.829353i \(-0.311291\pi\)
−0.438878 + 0.898547i \(0.644624\pi\)
\(822\) 0 0
\(823\) 1.50919e15 + 2.61399e15i 0.139330 + 0.241326i 0.927243 0.374460i \(-0.122172\pi\)
−0.787913 + 0.615786i \(0.788839\pi\)
\(824\) 0 0
\(825\) 2.87269e15 + 4.28130e15i 0.261693 + 0.390013i
\(826\) 0 0
\(827\) 1.29098e16i 1.16049i −0.814443 0.580243i \(-0.802958\pi\)
0.814443 0.580243i \(-0.197042\pi\)
\(828\) 0 0
\(829\) −2.65564e14 + 1.53323e14i −0.0235569 + 0.0136006i −0.511732 0.859145i \(-0.670996\pi\)
0.488175 + 0.872746i \(0.337663\pi\)
\(830\) 0 0
\(831\) −2.30090e14 3.40924e15i −0.0201415 0.298437i
\(832\) 0 0
\(833\) 1.26374e16 + 4.03176e15i 1.09172 + 0.348295i
\(834\) 0 0
\(835\) −3.38716e15 + 5.86673e15i −0.288775 + 0.500174i
\(836\) 0 0
\(837\) 6.02514e15 + 6.79030e15i 0.506964 + 0.571346i
\(838\) 0 0
\(839\) 9.78378e15 0.812486 0.406243 0.913765i \(-0.366839\pi\)
0.406243 + 0.913765i \(0.366839\pi\)
\(840\) 0 0
\(841\) −2.12758e16 −1.74385
\(842\) 0 0
\(843\) −4.73207e15 + 9.64276e15i −0.382825 + 0.780099i
\(844\) 0 0
\(845\) −6.39036e15 + 1.10684e16i −0.510286 + 0.883841i
\(846\) 0 0
\(847\) 5.25171e13 3.37401e14i 0.00413944 0.0265943i
\(848\) 0 0
\(849\) −3.47006e15 + 2.34195e14i −0.269988 + 0.0182216i
\(850\) 0 0
\(851\) −1.53384e15 + 8.85564e14i −0.117806 + 0.0680154i
\(852\) 0 0
\(853\) 1.21089e16i 0.918087i −0.888414 0.459044i \(-0.848192\pi\)
0.888414 0.459044i \(-0.151808\pi\)
\(854\) 0 0
\(855\) 1.49803e16 + 6.13710e15i 1.12126 + 0.459356i
\(856\) 0 0
\(857\) −5.76637e15 9.98764e15i −0.426096 0.738021i 0.570426 0.821349i \(-0.306778\pi\)
−0.996522 + 0.0833285i \(0.973445\pi\)
\(858\) 0 0
\(859\) 9.25897e15 + 5.34567e15i 0.675461 + 0.389978i 0.798143 0.602469i \(-0.205816\pi\)
−0.122682 + 0.992446i \(0.539149\pi\)
\(860\) 0 0
\(861\) −1.17314e15 1.02351e14i −0.0844953 0.00737179i
\(862\) 0 0
\(863\) −1.50838e16 8.70865e15i −1.07264 0.619286i −0.143735 0.989616i \(-0.545911\pi\)
−0.928900 + 0.370330i \(0.879245\pi\)
\(864\) 0 0
\(865\) 4.35929e15 + 7.55052e15i 0.306075 + 0.530137i
\(866\) 0 0
\(867\) 3.75110e15 2.51693e15i 0.260048 0.174489i
\(868\) 0 0
\(869\) 1.38081e16i 0.945205i
\(870\) 0 0
\(871\) −9.06043e15 + 5.23104e15i −0.612419 + 0.353580i
\(872\) 0 0
\(873\) 1.74502e16 1.34978e16i 1.16472 0.900918i
\(874\) 0 0
\(875\) −1.51177e16 + 5.84946e15i −0.996420 + 0.385542i
\(876\) 0 0
\(877\) 6.44792e15 1.11681e16i 0.419683 0.726913i −0.576224 0.817292i \(-0.695474\pi\)
0.995907 + 0.0903788i \(0.0288078\pi\)
\(878\) 0 0
\(879\) −1.20310e16 5.90406e15i −0.773325 0.379500i
\(880\) 0 0
\(881\) 4.53304e15 0.287754 0.143877 0.989596i \(-0.454043\pi\)
0.143877 + 0.989596i \(0.454043\pi\)
\(882\) 0 0
\(883\) −1.27808e16 −0.801264 −0.400632 0.916239i \(-0.631209\pi\)
−0.400632 + 0.916239i \(0.631209\pi\)
\(884\) 0 0
\(885\) −4.54578e15 2.23079e15i −0.281462 0.138124i
\(886\) 0 0
\(887\) 6.11265e15 1.05874e16i 0.373809 0.647456i −0.616339 0.787481i \(-0.711385\pi\)
0.990148 + 0.140025i \(0.0447182\pi\)
\(888\) 0 0
\(889\) −2.78198e16 + 1.07642e16i −1.68033 + 0.650164i
\(890\) 0 0
\(891\) −4.40325e15 1.59379e16i −0.262691 0.950831i
\(892\) 0 0
\(893\) 4.14436e16 2.39275e16i 2.44216 1.40998i
\(894\) 0 0
\(895\) 2.26629e15i 0.131913i
\(896\) 0 0
\(897\) 2.65980e16 1.78469e16i 1.52929 1.02613i
\(898\) 0 0
\(899\) −1.11386e16 1.92926e16i −0.632632 1.09575i
\(900\) 0 0
\(901\) 1.62461e16 + 9.37969e15i 0.911513 + 0.526262i
\(902\) 0 0
\(903\) −1.94583e16 1.69764e15i −1.07851 0.0940942i
\(904\) 0 0
\(905\) −1.67131e15 9.64933e14i −0.0915146 0.0528360i
\(906\) 0 0
\(907\) 5.28559e15 + 9.15491e15i 0.285926 + 0.495238i 0.972833 0.231507i \(-0.0743656\pi\)
−0.686908 + 0.726745i \(0.741032\pi\)
\(908\) 0 0
\(909\) 1.08640e16 2.65182e16i 0.580613 1.41724i
\(910\) 0 0
\(911\) 4.63984e15i 0.244992i 0.992469 + 0.122496i \(0.0390899\pi\)
−0.992469 + 0.122496i \(0.960910\pi\)
\(912\) 0 0
\(913\) 2.29268e16 1.32368e16i 1.19606 0.690546i
\(914\) 0 0
\(915\) −9.05198e15 + 6.10920e14i −0.466582 + 0.0314897i
\(916\) 0 0
\(917\) 4.44665e15 2.85679e16i 0.226465 1.45495i
\(918\) 0 0
\(919\) 4.88230e15 8.45640e15i 0.245691 0.425550i −0.716635 0.697449i \(-0.754318\pi\)
0.962326 + 0.271899i \(0.0876518\pi\)
\(920\) 0 0
\(921\) 4.43198e14 9.03125e14i 0.0220379 0.0449076i
\(922\) 0 0
\(923\) −3.39098e16 −1.66616
\(924\) 0 0
\(925\) 1.12445e15 0.0545961
\(926\) 0 0
\(927\) 2.62499e15 + 1.93586e16i 0.125947 + 0.928828i
\(928\) 0 0
\(929\) 1.10412e16 1.91239e16i 0.523517 0.906757i −0.476109 0.879386i \(-0.657953\pi\)
0.999625 0.0273709i \(-0.00871352\pi\)
\(930\) 0 0
\(931\) 3.49069e16 7.61452e15i 1.63564 0.356796i
\(932\) 0 0
\(933\) 6.56629e14 + 9.72925e15i 0.0304068 + 0.450537i
\(934\) 0 0
\(935\) −1.54826e16 + 8.93887e15i −0.708565 + 0.409090i
\(936\) 0 0
\(937\) 3.35109e16i 1.51572i 0.652418 + 0.757859i \(0.273755\pi\)
−0.652418 + 0.757859i \(0.726245\pi\)
\(938\) 0 0
\(939\) −8.05744e15 1.20084e16i −0.360194 0.536813i
\(940\) 0 0
\(941\) 8.69651e14 + 1.50628e15i 0.0384239 + 0.0665522i 0.884598 0.466355i \(-0.154433\pi\)
−0.846174 + 0.532907i \(0.821100\pi\)
\(942\) 0 0
\(943\) 1.99536e15 + 1.15202e15i 0.0871377 + 0.0503090i
\(944\) 0 0
\(945\) 1.67492e16 8.00403e14i 0.722967 0.0345489i
\(946\) 0 0
\(947\) 1.40621e16 + 8.11878e15i 0.599966 + 0.346390i 0.769028 0.639215i \(-0.220741\pi\)
−0.169062 + 0.985605i \(0.554074\pi\)
\(948\) 0 0
\(949\) −2.24745e16 3.89270e16i −0.947821 1.64167i
\(950\) 0 0
\(951\) −3.96035e15 5.90228e15i −0.165097 0.246052i
\(952\) 0 0
\(953\) 1.58666e16i 0.653842i −0.945052 0.326921i \(-0.893989\pi\)
0.945052 0.326921i \(-0.106011\pi\)
\(954\) 0 0
\(955\) 2.40112e16 1.38629e16i 0.978126 0.564721i
\(956\) 0 0
\(957\) 2.73228e15 + 4.04841e16i 0.110030 + 1.63030i
\(958\) 0 0
\(959\) −3.88152e15 + 4.81951e15i −0.154525 + 0.191867i
\(960\) 0 0
\(961\) −5.29197e15 + 9.16596e15i −0.208276 + 0.360744i
\(962\) 0 0
\(963\) −3.00079e15 2.21301e16i −0.116759 0.861069i
\(964\) 0 0
\(965\) −7.50744e15 −0.288796
\(966\) 0 0
\(967\) −3.19955e16 −1.21687 −0.608433 0.793605i \(-0.708202\pi\)
−0.608433 + 0.793605i \(0.708202\pi\)
\(968\) 0 0
\(969\) 2.24759e16 4.58003e16i 0.845156 1.72221i
\(970\) 0 0
\(971\) −1.64085e16 + 2.84204e16i −0.610048 + 1.05663i 0.381184 + 0.924499i \(0.375516\pi\)
−0.991232 + 0.132135i \(0.957817\pi\)
\(972\) 0 0
\(973\) 1.51959e16 + 3.92732e16i 0.558605 + 1.44369i
\(974\) 0 0
\(975\) −2.02895e16 + 1.36934e15i −0.737472 + 0.0497721i
\(976\) 0 0
\(977\) −1.62593e16 + 9.38730e15i −0.584361 + 0.337381i −0.762865 0.646558i \(-0.776208\pi\)
0.178504 + 0.983939i \(0.442874\pi\)
\(978\) 0 0
\(979\) 1.60654e16i 0.570934i
\(980\) 0 0
\(981\) 5.59740e15 1.36629e16i 0.196701 0.480134i
\(982\) 0 0
\(983\) 1.42416e16 + 2.46671e16i 0.494895 + 0.857183i 0.999983 0.00588469i \(-0.00187317\pi\)
−0.505088 + 0.863068i \(0.668540\pi\)
\(984\) 0 0
\(985\) 1.47583e16 + 8.52073e15i 0.507152 + 0.292804i
\(986\) 0 0
\(987\) 2.84215e16 4.06110e16i 0.965833 1.38006i
\(988\) 0 0
\(989\) 3.30960e16 + 1.91080e16i 1.11223 + 0.642148i
\(990\) 0 0
\(991\) 1.73725e16 + 3.00900e16i 0.577373 + 1.00004i 0.995779 + 0.0917800i \(0.0292556\pi\)
−0.418406 + 0.908260i \(0.637411\pi\)
\(992\) 0 0
\(993\) −4.18776e16 + 2.80993e16i −1.37645 + 0.923580i
\(994\) 0 0
\(995\) 1.77916e16i 0.578346i
\(996\) 0 0
\(997\) −4.29010e16 + 2.47689e16i −1.37925 + 0.796313i −0.992070 0.125689i \(-0.959886\pi\)
−0.387185 + 0.922002i \(0.626552\pi\)
\(998\) 0 0
\(999\) −3.42151e15 1.13930e15i −0.108795 0.0362268i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 84.12.k.b.5.5 56
3.2 odd 2 inner 84.12.k.b.5.14 yes 56
7.3 odd 6 inner 84.12.k.b.17.14 yes 56
21.17 even 6 inner 84.12.k.b.17.5 yes 56
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.12.k.b.5.5 56 1.1 even 1 trivial
84.12.k.b.5.14 yes 56 3.2 odd 2 inner
84.12.k.b.17.5 yes 56 21.17 even 6 inner
84.12.k.b.17.14 yes 56 7.3 odd 6 inner