Properties

Label 84.9.p.b.65.16
Level $84$
Weight $9$
Character 84.65
Analytic conductor $34.220$
Analytic rank $0$
Dimension $40$
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] = [84,9,Mod(53,84)]
 
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, 4]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("84.53");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.p (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: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(40\)
Relative dimension: \(20\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 65.16
Character \(\chi\) \(=\) 84.65
Dual form 84.9.p.b.53.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(58.8129 - 55.6960i) q^{3} +(-726.008 - 419.161i) q^{5} +(-1188.37 - 2086.29i) q^{7} +(356.917 - 6551.28i) q^{9} +O(q^{10})\) \(q+(58.8129 - 55.6960i) q^{3} +(-726.008 - 419.161i) q^{5} +(-1188.37 - 2086.29i) q^{7} +(356.917 - 6551.28i) q^{9} +(11852.6 - 6843.09i) q^{11} -4288.33 q^{13} +(-66044.2 + 15783.7i) q^{15} +(-20828.2 + 12025.2i) q^{17} +(-66484.9 + 115155. i) q^{19} +(-186089. - 56513.3i) q^{21} +(-31316.3 - 18080.5i) q^{23} +(156079. + 270338. i) q^{25} +(-343889. - 405179. i) q^{27} +1.12585e6i q^{29} +(-148437. - 257101. i) q^{31} +(315952. - 1.06260e6i) q^{33} +(-11726.0 + 2.01278e6i) q^{35} +(1.66179e6 - 2.87830e6i) q^{37} +(-252209. + 238843. i) q^{39} +3.70409e6i q^{41} -1.75904e6 q^{43} +(-3.00517e6 + 4.60668e6i) q^{45} +(-2.29987e6 - 1.32783e6i) q^{47} +(-2.94037e6 + 4.95854e6i) q^{49} +(-555213. + 1.86728e6i) q^{51} +(-4.36123e6 + 2.51796e6i) q^{53} -1.14734e7 q^{55} +(2.50351e6 + 1.04756e7i) q^{57} +(-1.72091e7 + 9.93569e6i) q^{59} +(6.29128e6 - 1.08968e7i) q^{61} +(-1.40920e7 + 7.04069e6i) q^{63} +(3.11336e6 + 1.79750e6i) q^{65} +(-1.30656e7 - 2.26303e7i) q^{67} +(-2.84881e6 + 680826. i) q^{69} +1.53174e6i q^{71} +(2.43157e7 + 4.21161e7i) q^{73} +(2.42362e7 + 7.20634e6i) q^{75} +(-2.83619e7 - 1.65958e7i) q^{77} +(2.10421e7 - 3.64460e7i) q^{79} +(-4.27919e7 - 4.67654e6i) q^{81} +1.42941e7i q^{83} +2.01619e7 q^{85} +(6.27053e7 + 6.62145e7i) q^{87} +(3.35488e7 + 1.93694e7i) q^{89} +(5.09611e6 + 8.94668e6i) q^{91} +(-2.30495e7 - 6.85350e6i) q^{93} +(9.65372e7 - 5.57358e7i) q^{95} -9.15468e7 q^{97} +(-4.06007e7 - 8.00921e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 40 q + 81 q^{3} - 34 q^{7} + 4771 q^{9} - 55464 q^{13} + 68482 q^{15} + 311690 q^{19} - 172343 q^{21} + 1766792 q^{25} - 3451932 q^{27} + 31596 q^{31} + 1874885 q^{33} - 1853482 q^{37} + 11217526 q^{39} - 13372600 q^{43} - 527785 q^{45} - 12653462 q^{49} - 1103461 q^{51} + 71577224 q^{55} - 17195214 q^{57} - 21761970 q^{61} + 21945045 q^{63} - 26337350 q^{67} - 5588722 q^{69} + 41115682 q^{73} - 17971730 q^{75} - 120916932 q^{79} - 24550133 q^{81} + 139250060 q^{85} - 16321046 q^{87} + 345074940 q^{91} + 25774675 q^{93} - 707216948 q^{97} - 94510994 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 \(a_p\))
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
\(3\) 58.8129 55.6960i 0.726085 0.687605i
\(4\) 0 0
\(5\) −726.008 419.161i −1.16161 0.670658i −0.209923 0.977718i \(-0.567321\pi\)
−0.951690 + 0.307060i \(0.900655\pi\)
\(6\) 0 0
\(7\) −1188.37 2086.29i −0.494946 0.868924i
\(8\) 0 0
\(9\) 356.917 6551.28i 0.0543999 0.998519i
\(10\) 0 0
\(11\) 11852.6 6843.09i 0.809547 0.467392i −0.0372513 0.999306i \(-0.511860\pi\)
0.846799 + 0.531914i \(0.178527\pi\)
\(12\) 0 0
\(13\) −4288.33 −0.150146 −0.0750732 0.997178i \(-0.523919\pi\)
−0.0750732 + 0.997178i \(0.523919\pi\)
\(14\) 0 0
\(15\) −66044.2 + 15783.7i −1.30458 + 0.311776i
\(16\) 0 0
\(17\) −20828.2 + 12025.2i −0.249377 + 0.143978i −0.619479 0.785013i \(-0.712656\pi\)
0.370102 + 0.928991i \(0.379323\pi\)
\(18\) 0 0
\(19\) −66484.9 + 115155.i −0.510163 + 0.883628i 0.489768 + 0.871853i \(0.337081\pi\)
−0.999931 + 0.0117749i \(0.996252\pi\)
\(20\) 0 0
\(21\) −186089. 56513.3i −0.956849 0.290585i
\(22\) 0 0
\(23\) −31316.3 18080.5i −0.111907 0.0646097i 0.443002 0.896521i \(-0.353914\pi\)
−0.554909 + 0.831911i \(0.687247\pi\)
\(24\) 0 0
\(25\) 156079. + 270338.i 0.399563 + 0.692064i
\(26\) 0 0
\(27\) −343889. 405179.i −0.647087 0.762416i
\(28\) 0 0
\(29\) 1.12585e6i 1.59180i 0.605428 + 0.795900i \(0.293002\pi\)
−0.605428 + 0.795900i \(0.706998\pi\)
\(30\) 0 0
\(31\) −148437. 257101.i −0.160730 0.278392i 0.774401 0.632695i \(-0.218051\pi\)
−0.935131 + 0.354303i \(0.884718\pi\)
\(32\) 0 0
\(33\) 315952. 1.06260e6i 0.266419 0.896015i
\(34\) 0 0
\(35\) −11726.0 + 2.01278e6i −0.00781406 + 1.34129i
\(36\) 0 0
\(37\) 1.66179e6 2.87830e6i 0.886684 1.53578i 0.0429137 0.999079i \(-0.486336\pi\)
0.843771 0.536704i \(-0.180331\pi\)
\(38\) 0 0
\(39\) −252209. + 238843.i −0.109019 + 0.103241i
\(40\) 0 0
\(41\) 3.70409e6i 1.31083i 0.755270 + 0.655414i \(0.227506\pi\)
−0.755270 + 0.655414i \(0.772494\pi\)
\(42\) 0 0
\(43\) −1.75904e6 −0.514518 −0.257259 0.966342i \(-0.582819\pi\)
−0.257259 + 0.966342i \(0.582819\pi\)
\(44\) 0 0
\(45\) −3.00517e6 + 4.60668e6i −0.732856 + 1.12341i
\(46\) 0 0
\(47\) −2.29987e6 1.32783e6i −0.471316 0.272114i 0.245474 0.969403i \(-0.421056\pi\)
−0.716791 + 0.697289i \(0.754390\pi\)
\(48\) 0 0
\(49\) −2.94037e6 + 4.95854e6i −0.510056 + 0.860141i
\(50\) 0 0
\(51\) −555213. + 1.86728e6i −0.0820690 + 0.276013i
\(52\) 0 0
\(53\) −4.36123e6 + 2.51796e6i −0.552721 + 0.319113i −0.750219 0.661190i \(-0.770052\pi\)
0.197498 + 0.980303i \(0.436718\pi\)
\(54\) 0 0
\(55\) −1.14734e7 −1.25384
\(56\) 0 0
\(57\) 2.50351e6 + 1.04756e7i 0.237165 + 0.992379i
\(58\) 0 0
\(59\) −1.72091e7 + 9.93569e6i −1.42020 + 0.819955i −0.996316 0.0857601i \(-0.972668\pi\)
−0.423887 + 0.905715i \(0.639335\pi\)
\(60\) 0 0
\(61\) 6.29128e6 1.08968e7i 0.454381 0.787010i −0.544272 0.838909i \(-0.683194\pi\)
0.998652 + 0.0518987i \(0.0165273\pi\)
\(62\) 0 0
\(63\) −1.40920e7 + 7.04069e6i −0.894562 + 0.446944i
\(64\) 0 0
\(65\) 3.11336e6 + 1.79750e6i 0.174412 + 0.100697i
\(66\) 0 0
\(67\) −1.30656e7 2.26303e7i −0.648383 1.12303i −0.983509 0.180858i \(-0.942112\pi\)
0.335127 0.942173i \(-0.391221\pi\)
\(68\) 0 0
\(69\) −2.84881e6 + 680826.i −0.125680 + 0.0300358i
\(70\) 0 0
\(71\) 1.53174e6i 0.0602770i 0.999546 + 0.0301385i \(0.00959483\pi\)
−0.999546 + 0.0301385i \(0.990405\pi\)
\(72\) 0 0
\(73\) 2.43157e7 + 4.21161e7i 0.856240 + 1.48305i 0.875490 + 0.483237i \(0.160539\pi\)
−0.0192491 + 0.999815i \(0.506128\pi\)
\(74\) 0 0
\(75\) 2.42362e7 + 7.20634e6i 0.765983 + 0.227756i
\(76\) 0 0
\(77\) −2.83619e7 1.65958e7i −0.806811 0.472101i
\(78\) 0 0
\(79\) 2.10421e7 3.64460e7i 0.540233 0.935711i −0.458658 0.888613i \(-0.651670\pi\)
0.998890 0.0470974i \(-0.0149971\pi\)
\(80\) 0 0
\(81\) −4.27919e7 4.67654e6i −0.994081 0.108639i
\(82\) 0 0
\(83\) 1.42941e7i 0.301193i 0.988595 + 0.150597i \(0.0481195\pi\)
−0.988595 + 0.150597i \(0.951881\pi\)
\(84\) 0 0
\(85\) 2.01619e7 0.386239
\(86\) 0 0
\(87\) 6.27053e7 + 6.62145e7i 1.09453 + 1.15578i
\(88\) 0 0
\(89\) 3.35488e7 + 1.93694e7i 0.534709 + 0.308714i 0.742932 0.669367i \(-0.233435\pi\)
−0.208223 + 0.978081i \(0.566768\pi\)
\(90\) 0 0
\(91\) 5.09611e6 + 8.94668e6i 0.0743144 + 0.130466i
\(92\) 0 0
\(93\) −2.30495e7 6.85350e6i −0.308127 0.0916179i
\(94\) 0 0
\(95\) 9.65372e7 5.57358e7i 1.18522 0.684289i
\(96\) 0 0
\(97\) −9.15468e7 −1.03409 −0.517043 0.855960i \(-0.672967\pi\)
−0.517043 + 0.855960i \(0.672967\pi\)
\(98\) 0 0
\(99\) −4.06007e7 8.00921e7i −0.422661 0.833775i
\(100\) 0 0
\(101\) 1.56504e7 9.03574e6i 0.150397 0.0868317i −0.422913 0.906170i \(-0.638992\pi\)
0.573310 + 0.819339i \(0.305659\pi\)
\(102\) 0 0
\(103\) 8.21411e7 1.42273e8i 0.729813 1.26407i −0.227149 0.973860i \(-0.572940\pi\)
0.956962 0.290213i \(-0.0937263\pi\)
\(104\) 0 0
\(105\) 1.11414e8 + 1.19030e8i 0.916605 + 0.979266i
\(106\) 0 0
\(107\) 4.09176e7 + 2.36238e7i 0.312158 + 0.180225i 0.647892 0.761732i \(-0.275651\pi\)
−0.335734 + 0.941957i \(0.608984\pi\)
\(108\) 0 0
\(109\) −6.56157e7 1.13650e8i −0.464838 0.805123i 0.534356 0.845259i \(-0.320554\pi\)
−0.999194 + 0.0401362i \(0.987221\pi\)
\(110\) 0 0
\(111\) −6.25752e7 2.61836e8i −0.412203 1.72480i
\(112\) 0 0
\(113\) 2.75240e8i 1.68810i −0.536265 0.844049i \(-0.680165\pi\)
0.536265 0.844049i \(-0.319835\pi\)
\(114\) 0 0
\(115\) 1.51572e7 + 2.62531e7i 0.0866620 + 0.150103i
\(116\) 0 0
\(117\) −1.53058e6 + 2.80941e7i −0.00816794 + 0.149924i
\(118\) 0 0
\(119\) 4.98394e7 + 2.91633e7i 0.248534 + 0.145428i
\(120\) 0 0
\(121\) −1.35236e7 + 2.34236e7i −0.0630887 + 0.109273i
\(122\) 0 0
\(123\) 2.06303e8 + 2.17848e8i 0.901331 + 0.951773i
\(124\) 0 0
\(125\) 6.57799e7i 0.269434i
\(126\) 0 0
\(127\) −3.06495e8 −1.17817 −0.589085 0.808071i \(-0.700512\pi\)
−0.589085 + 0.808071i \(0.700512\pi\)
\(128\) 0 0
\(129\) −1.03454e8 + 9.79712e7i −0.373584 + 0.353785i
\(130\) 0 0
\(131\) 2.53627e7 + 1.46432e7i 0.0861212 + 0.0497221i 0.542442 0.840093i \(-0.317500\pi\)
−0.456321 + 0.889815i \(0.650833\pi\)
\(132\) 0 0
\(133\) 3.19255e8 + 1.85991e6i 1.02031 + 0.00594408i
\(134\) 0 0
\(135\) 7.98308e7 + 4.38308e8i 0.240345 + 1.31961i
\(136\) 0 0
\(137\) 3.15124e8 1.81937e8i 0.894539 0.516462i 0.0191146 0.999817i \(-0.493915\pi\)
0.875424 + 0.483355i \(0.160582\pi\)
\(138\) 0 0
\(139\) 5.44570e8 1.45880 0.729398 0.684089i \(-0.239800\pi\)
0.729398 + 0.684089i \(0.239800\pi\)
\(140\) 0 0
\(141\) −2.09217e8 + 5.00000e7i −0.529323 + 0.126501i
\(142\) 0 0
\(143\) −5.08278e7 + 2.93454e7i −0.121551 + 0.0701773i
\(144\) 0 0
\(145\) 4.71912e8 8.17376e8i 1.06755 1.84906i
\(146\) 0 0
\(147\) 1.03239e8 + 4.55393e8i 0.221093 + 0.975253i
\(148\) 0 0
\(149\) −8.04115e8 4.64256e8i −1.63145 0.941916i −0.983647 0.180106i \(-0.942356\pi\)
−0.647800 0.761811i \(-0.724311\pi\)
\(150\) 0 0
\(151\) −2.34121e8 4.05510e8i −0.450332 0.779998i 0.548074 0.836430i \(-0.315361\pi\)
−0.998406 + 0.0564316i \(0.982028\pi\)
\(152\) 0 0
\(153\) 7.13463e7 + 1.40743e8i 0.130198 + 0.256840i
\(154\) 0 0
\(155\) 2.48876e8i 0.431178i
\(156\) 0 0
\(157\) −4.57530e8 7.92466e8i −0.753046 1.30431i −0.946340 0.323173i \(-0.895250\pi\)
0.193294 0.981141i \(-0.438083\pi\)
\(158\) 0 0
\(159\) −1.16257e8 + 3.90991e8i −0.181899 + 0.611757i
\(160\) 0 0
\(161\) −505798. + 8.68209e7i −0.000752790 + 0.129217i
\(162\) 0 0
\(163\) −2.22372e8 + 3.85159e8i −0.315014 + 0.545620i −0.979440 0.201734i \(-0.935342\pi\)
0.664427 + 0.747353i \(0.268676\pi\)
\(164\) 0 0
\(165\) −6.74786e8 + 6.39024e8i −0.910396 + 0.862147i
\(166\) 0 0
\(167\) 8.98625e8i 1.15535i 0.816268 + 0.577674i \(0.196039\pi\)
−0.816268 + 0.577674i \(0.803961\pi\)
\(168\) 0 0
\(169\) −7.97341e8 −0.977456
\(170\) 0 0
\(171\) 7.30685e8 + 4.76663e8i 0.854566 + 0.557476i
\(172\) 0 0
\(173\) 2.38451e8 + 1.37670e8i 0.266204 + 0.153693i 0.627161 0.778889i \(-0.284217\pi\)
−0.360957 + 0.932582i \(0.617550\pi\)
\(174\) 0 0
\(175\) 3.78522e8 6.46886e8i 0.403588 0.689725i
\(176\) 0 0
\(177\) −4.58740e8 + 1.54283e9i −0.467384 + 1.57190i
\(178\) 0 0
\(179\) −6.90561e8 + 3.98695e8i −0.672651 + 0.388355i −0.797080 0.603873i \(-0.793623\pi\)
0.124429 + 0.992228i \(0.460290\pi\)
\(180\) 0 0
\(181\) −6.51285e8 −0.606816 −0.303408 0.952861i \(-0.598124\pi\)
−0.303408 + 0.952861i \(0.598124\pi\)
\(182\) 0 0
\(183\) −2.36900e8 9.91273e8i −0.211233 0.883871i
\(184\) 0 0
\(185\) −2.41295e9 + 1.39311e9i −2.05997 + 1.18932i
\(186\) 0 0
\(187\) −1.64579e8 + 2.85058e8i −0.134588 + 0.233114i
\(188\) 0 0
\(189\) −4.36653e8 + 1.19895e9i −0.342207 + 0.939624i
\(190\) 0 0
\(191\) 9.93412e8 + 5.73547e8i 0.746442 + 0.430959i 0.824407 0.565998i \(-0.191509\pi\)
−0.0779648 + 0.996956i \(0.524842\pi\)
\(192\) 0 0
\(193\) −3.83109e8 6.63564e8i −0.276117 0.478248i 0.694299 0.719686i \(-0.255714\pi\)
−0.970416 + 0.241438i \(0.922381\pi\)
\(194\) 0 0
\(195\) 2.83220e8 6.76855e7i 0.195878 0.0468120i
\(196\) 0 0
\(197\) 3.70739e8i 0.246152i −0.992397 0.123076i \(-0.960724\pi\)
0.992397 0.123076i \(-0.0392759\pi\)
\(198\) 0 0
\(199\) −8.89835e8 1.54124e9i −0.567410 0.982784i −0.996821 0.0796742i \(-0.974612\pi\)
0.429411 0.903109i \(-0.358721\pi\)
\(200\) 0 0
\(201\) −2.02885e9 6.03253e8i −1.24298 0.369586i
\(202\) 0 0
\(203\) 2.34884e9 1.33792e9i 1.38315 0.787855i
\(204\) 0 0
\(205\) 1.55261e9 2.68920e9i 0.879117 1.52267i
\(206\) 0 0
\(207\) −1.29628e8 + 1.98709e8i −0.0706018 + 0.108227i
\(208\) 0 0
\(209\) 1.81985e9i 0.953785i
\(210\) 0 0
\(211\) 3.53555e9 1.78372 0.891862 0.452307i \(-0.149399\pi\)
0.891862 + 0.452307i \(0.149399\pi\)
\(212\) 0 0
\(213\) 8.53117e7 + 9.00861e7i 0.0414467 + 0.0437662i
\(214\) 0 0
\(215\) 1.27707e9 + 7.37319e8i 0.597671 + 0.345066i
\(216\) 0 0
\(217\) −3.59988e8 + 6.15213e8i −0.162349 + 0.277451i
\(218\) 0 0
\(219\) 3.77577e9 + 1.12268e9i 1.64146 + 0.488067i
\(220\) 0 0
\(221\) 8.93182e7 5.15679e7i 0.0374430 0.0216177i
\(222\) 0 0
\(223\) −1.83868e9 −0.743510 −0.371755 0.928331i \(-0.621244\pi\)
−0.371755 + 0.928331i \(0.621244\pi\)
\(224\) 0 0
\(225\) 1.82677e9 9.26033e8i 0.712775 0.361323i
\(226\) 0 0
\(227\) 1.39182e9 8.03568e8i 0.524179 0.302635i −0.214464 0.976732i \(-0.568800\pi\)
0.738643 + 0.674097i \(0.235467\pi\)
\(228\) 0 0
\(229\) 4.11805e8 7.13267e8i 0.149744 0.259364i −0.781389 0.624045i \(-0.785488\pi\)
0.931133 + 0.364680i \(0.118822\pi\)
\(230\) 0 0
\(231\) −2.59236e9 + 6.03595e8i −0.910432 + 0.211981i
\(232\) 0 0
\(233\) −3.56617e9 2.05893e9i −1.20998 0.698582i −0.247224 0.968958i \(-0.579518\pi\)
−0.962755 + 0.270377i \(0.912852\pi\)
\(234\) 0 0
\(235\) 1.11315e9 + 1.92803e9i 0.364991 + 0.632184i
\(236\) 0 0
\(237\) −7.92348e8 3.31546e9i −0.251144 1.05087i
\(238\) 0 0
\(239\) 2.95475e9i 0.905584i −0.891616 0.452792i \(-0.850428\pi\)
0.891616 0.452792i \(-0.149572\pi\)
\(240\) 0 0
\(241\) 2.43372e9 + 4.21532e9i 0.721442 + 1.24958i 0.960422 + 0.278550i \(0.0898539\pi\)
−0.238979 + 0.971025i \(0.576813\pi\)
\(242\) 0 0
\(243\) −2.77718e9 + 2.10830e9i −0.796488 + 0.604654i
\(244\) 0 0
\(245\) 4.21316e9 2.36745e9i 1.16935 0.657078i
\(246\) 0 0
\(247\) 2.85109e8 4.93824e8i 0.0765991 0.132674i
\(248\) 0 0
\(249\) 7.96125e8 + 8.40679e8i 0.207102 + 0.218692i
\(250\) 0 0
\(251\) 2.63362e9i 0.663526i −0.943363 0.331763i \(-0.892357\pi\)
0.943363 0.331763i \(-0.107643\pi\)
\(252\) 0 0
\(253\) −4.94905e8 −0.120792
\(254\) 0 0
\(255\) 1.18578e9 1.12294e9i 0.280442 0.265580i
\(256\) 0 0
\(257\) −6.46260e9 3.73119e9i −1.48141 0.855292i −0.481631 0.876374i \(-0.659956\pi\)
−0.999778 + 0.0210818i \(0.993289\pi\)
\(258\) 0 0
\(259\) −7.97978e9 4.64883e7i −1.77334 0.0103311i
\(260\) 0 0
\(261\) 7.37576e9 + 4.01835e8i 1.58944 + 0.0865937i
\(262\) 0 0
\(263\) 7.11969e9 4.11056e9i 1.48812 0.859167i 0.488213 0.872725i \(-0.337649\pi\)
0.999908 + 0.0135574i \(0.00431560\pi\)
\(264\) 0 0
\(265\) 4.22172e9 0.856063
\(266\) 0 0
\(267\) 3.05190e9 7.29362e8i 0.600517 0.143515i
\(268\) 0 0
\(269\) −5.18973e9 + 2.99629e9i −0.991141 + 0.572236i −0.905615 0.424100i \(-0.860590\pi\)
−0.0855260 + 0.996336i \(0.527257\pi\)
\(270\) 0 0
\(271\) −2.24850e9 + 3.89452e9i −0.416885 + 0.722065i −0.995624 0.0934470i \(-0.970211\pi\)
0.578740 + 0.815512i \(0.303545\pi\)
\(272\) 0 0
\(273\) 7.98011e8 + 2.42348e8i 0.143667 + 0.0436303i
\(274\) 0 0
\(275\) 3.69989e9 + 2.13613e9i 0.646931 + 0.373506i
\(276\) 0 0
\(277\) −2.19189e9 3.79646e9i −0.372305 0.644852i 0.617614 0.786481i \(-0.288099\pi\)
−0.989920 + 0.141629i \(0.954766\pi\)
\(278\) 0 0
\(279\) −1.73732e9 + 8.80691e8i −0.286724 + 0.145347i
\(280\) 0 0
\(281\) 4.89493e9i 0.785093i −0.919732 0.392547i \(-0.871594\pi\)
0.919732 0.392547i \(-0.128406\pi\)
\(282\) 0 0
\(283\) −2.71265e9 4.69845e9i −0.422910 0.732502i 0.573312 0.819337i \(-0.305658\pi\)
−0.996223 + 0.0868347i \(0.972325\pi\)
\(284\) 0 0
\(285\) 2.57338e9 8.65472e9i 0.390053 1.31182i
\(286\) 0 0
\(287\) 7.72778e9 4.40181e9i 1.13901 0.648789i
\(288\) 0 0
\(289\) −3.19867e9 + 5.54026e9i −0.458541 + 0.794216i
\(290\) 0 0
\(291\) −5.38413e9 + 5.09879e9i −0.750834 + 0.711042i
\(292\) 0 0
\(293\) 1.26502e10i 1.71643i 0.513287 + 0.858217i \(0.328428\pi\)
−0.513287 + 0.858217i \(0.671572\pi\)
\(294\) 0 0
\(295\) 1.66586e10 2.19964
\(296\) 0 0
\(297\) −6.84865e9 2.44916e9i −0.880195 0.314768i
\(298\) 0 0
\(299\) 1.34295e8 + 7.75350e7i 0.0168025 + 0.00970092i
\(300\) 0 0
\(301\) 2.09038e9 + 3.66985e9i 0.254659 + 0.447077i
\(302\) 0 0
\(303\) 4.17189e8 1.40308e9i 0.0494951 0.166461i
\(304\) 0 0
\(305\) −9.13504e9 + 5.27412e9i −1.05563 + 0.609468i
\(306\) 0 0
\(307\) −2.92066e9 −0.328797 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(308\) 0 0
\(309\) −3.09305e9 1.29424e10i −0.339276 1.41965i
\(310\) 0 0
\(311\) −1.47356e10 + 8.50759e9i −1.57516 + 0.909421i −0.579643 + 0.814871i \(0.696808\pi\)
−0.995520 + 0.0945502i \(0.969859\pi\)
\(312\) 0 0
\(313\) −5.43531e9 + 9.41424e9i −0.566301 + 0.980862i 0.430627 + 0.902530i \(0.358293\pi\)
−0.996927 + 0.0783315i \(0.975041\pi\)
\(314\) 0 0
\(315\) 1.31821e10 + 7.95216e8i 1.33888 + 0.0807686i
\(316\) 0 0
\(317\) 1.19740e10 + 6.91320e9i 1.18578 + 0.684608i 0.957344 0.288952i \(-0.0933069\pi\)
0.228432 + 0.973560i \(0.426640\pi\)
\(318\) 0 0
\(319\) 7.70429e9 + 1.33442e10i 0.743995 + 1.28864i
\(320\) 0 0
\(321\) 3.72223e9 8.89561e8i 0.350577 0.0837830i
\(322\) 0 0
\(323\) 3.19797e9i 0.293808i
\(324\) 0 0
\(325\) −6.69320e8 1.15930e9i −0.0599930 0.103911i
\(326\) 0 0
\(327\) −1.01889e10 3.02954e9i −0.891119 0.264963i
\(328\) 0 0
\(329\) −3.71459e7 + 6.37614e9i −0.00317050 + 0.544220i
\(330\) 0 0
\(331\) −3.57896e9 + 6.19894e9i −0.298157 + 0.516423i −0.975714 0.219047i \(-0.929705\pi\)
0.677558 + 0.735470i \(0.263038\pi\)
\(332\) 0 0
\(333\) −1.82635e10 1.19142e10i −1.48527 0.968918i
\(334\) 0 0
\(335\) 2.19064e10i 1.73937i
\(336\) 0 0
\(337\) −2.08762e10 −1.61857 −0.809287 0.587414i \(-0.800146\pi\)
−0.809287 + 0.587414i \(0.800146\pi\)
\(338\) 0 0
\(339\) −1.53298e10 1.61877e10i −1.16074 1.22570i
\(340\) 0 0
\(341\) −3.51873e9 2.03154e9i −0.260237 0.150248i
\(342\) 0 0
\(343\) 1.38392e10 + 2.41893e8i 0.999847 + 0.0174762i
\(344\) 0 0
\(345\) 2.35363e9 + 6.99825e8i 0.166136 + 0.0493984i
\(346\) 0 0
\(347\) −1.19483e10 + 6.89837e9i −0.824118 + 0.475805i −0.851834 0.523811i \(-0.824510\pi\)
0.0277165 + 0.999616i \(0.491176\pi\)
\(348\) 0 0
\(349\) −6.40544e9 −0.431765 −0.215882 0.976419i \(-0.569263\pi\)
−0.215882 + 0.976419i \(0.569263\pi\)
\(350\) 0 0
\(351\) 1.47471e9 + 1.73754e9i 0.0971579 + 0.114474i
\(352\) 0 0
\(353\) −1.02481e9 + 5.91677e8i −0.0660003 + 0.0381053i −0.532637 0.846344i \(-0.678799\pi\)
0.466637 + 0.884449i \(0.345466\pi\)
\(354\) 0 0
\(355\) 6.42046e8 1.11206e9i 0.0404252 0.0700185i
\(356\) 0 0
\(357\) 4.55548e9 1.06068e9i 0.280454 0.0652997i
\(358\) 0 0
\(359\) −2.06909e9 1.19459e9i −0.124567 0.0719186i 0.436422 0.899742i \(-0.356246\pi\)
−0.560989 + 0.827824i \(0.689579\pi\)
\(360\) 0 0
\(361\) −3.48706e8 6.03976e8i −0.0205320 0.0355624i
\(362\) 0 0
\(363\) 5.09236e8 + 2.13082e9i 0.0293287 + 0.122721i
\(364\) 0 0
\(365\) 4.07688e10i 2.29698i
\(366\) 0 0
\(367\) −8.76690e8 1.51847e9i −0.0483261 0.0837033i 0.840850 0.541267i \(-0.182055\pi\)
−0.889177 + 0.457564i \(0.848722\pi\)
\(368\) 0 0
\(369\) 2.42665e10 + 1.32205e9i 1.30889 + 0.0713089i
\(370\) 0 0
\(371\) 1.04359e10 + 6.10652e9i 0.550852 + 0.322328i
\(372\) 0 0
\(373\) −1.46590e10 + 2.53901e10i −0.757302 + 1.31169i 0.186920 + 0.982375i \(0.440150\pi\)
−0.944222 + 0.329310i \(0.893184\pi\)
\(374\) 0 0
\(375\) 3.66368e9 + 3.86871e9i 0.185264 + 0.195632i
\(376\) 0 0
\(377\) 4.82802e9i 0.239003i
\(378\) 0 0
\(379\) −6.47809e9 −0.313972 −0.156986 0.987601i \(-0.550178\pi\)
−0.156986 + 0.987601i \(0.550178\pi\)
\(380\) 0 0
\(381\) −1.80258e10 + 1.70705e10i −0.855452 + 0.810115i
\(382\) 0 0
\(383\) −2.27121e10 1.31128e10i −1.05551 0.609398i −0.131322 0.991340i \(-0.541922\pi\)
−0.924186 + 0.381942i \(0.875255\pi\)
\(384\) 0 0
\(385\) 1.36346e10 + 2.39369e10i 0.620584 + 1.08949i
\(386\) 0 0
\(387\) −6.27831e8 + 1.15239e10i −0.0279897 + 0.513756i
\(388\) 0 0
\(389\) 2.16168e10 1.24804e10i 0.944044 0.545044i 0.0528181 0.998604i \(-0.483180\pi\)
0.891226 + 0.453560i \(0.149846\pi\)
\(390\) 0 0
\(391\) 8.69682e8 0.0372094
\(392\) 0 0
\(393\) 2.30722e9 5.51393e8i 0.0967205 0.0231148i
\(394\) 0 0
\(395\) −3.05535e10 + 1.76401e10i −1.25508 + 0.724622i
\(396\) 0 0
\(397\) 1.61597e10 2.79894e10i 0.650535 1.12676i −0.332459 0.943118i \(-0.607878\pi\)
0.982993 0.183641i \(-0.0587884\pi\)
\(398\) 0 0
\(399\) 1.88799e10 1.76718e10i 0.744918 0.697253i
\(400\) 0 0
\(401\) 3.13160e10 + 1.80803e10i 1.21112 + 0.699242i 0.963004 0.269487i \(-0.0868542\pi\)
0.248119 + 0.968730i \(0.420188\pi\)
\(402\) 0 0
\(403\) 6.36548e8 + 1.10253e9i 0.0241330 + 0.0417996i
\(404\) 0 0
\(405\) 2.91071e10 + 2.13319e10i 1.08188 + 0.792884i
\(406\) 0 0
\(407\) 4.54871e10i 1.65772i
\(408\) 0 0
\(409\) 6.85527e9 + 1.18737e10i 0.244980 + 0.424319i 0.962126 0.272605i \(-0.0878851\pi\)
−0.717146 + 0.696923i \(0.754552\pi\)
\(410\) 0 0
\(411\) 8.40021e9 2.82514e10i 0.294390 0.990085i
\(412\) 0 0
\(413\) 4.11794e10 + 2.40959e10i 1.41540 + 0.828214i
\(414\) 0 0
\(415\) 5.99154e9 1.03777e10i 0.201998 0.349870i
\(416\) 0 0
\(417\) 3.20278e10 3.03304e10i 1.05921 1.00308i
\(418\) 0 0
\(419\) 4.32974e10i 1.40477i −0.711797 0.702386i \(-0.752118\pi\)
0.711797 0.702386i \(-0.247882\pi\)
\(420\) 0 0
\(421\) 1.86814e10 0.594677 0.297338 0.954772i \(-0.403901\pi\)
0.297338 + 0.954772i \(0.403901\pi\)
\(422\) 0 0
\(423\) −9.51987e9 + 1.45932e10i −0.297351 + 0.455815i
\(424\) 0 0
\(425\) −6.50170e9 3.75376e9i −0.199284 0.115056i
\(426\) 0 0
\(427\) −3.02102e10 1.75998e8i −0.908746 0.00529414i
\(428\) 0 0
\(429\) −1.35491e9 + 4.55680e9i −0.0400019 + 0.134533i
\(430\) 0 0
\(431\) −1.77405e10 + 1.02425e10i −0.514112 + 0.296822i −0.734522 0.678585i \(-0.762594\pi\)
0.220411 + 0.975407i \(0.429260\pi\)
\(432\) 0 0
\(433\) 1.27553e9 0.0362859 0.0181430 0.999835i \(-0.494225\pi\)
0.0181430 + 0.999835i \(0.494225\pi\)
\(434\) 0 0
\(435\) −1.77700e10 7.43559e10i −0.496285 2.07663i
\(436\) 0 0
\(437\) 4.16412e9 2.40416e9i 0.114182 0.0659230i
\(438\) 0 0
\(439\) 1.41474e10 2.45041e10i 0.380908 0.659751i −0.610285 0.792182i \(-0.708945\pi\)
0.991192 + 0.132431i \(0.0422782\pi\)
\(440\) 0 0
\(441\) 3.14353e10 + 2.10330e10i 0.831120 + 0.556093i
\(442\) 0 0
\(443\) 4.36607e10 + 2.52075e10i 1.13364 + 0.654508i 0.944848 0.327509i \(-0.106209\pi\)
0.188793 + 0.982017i \(0.439543\pi\)
\(444\) 0 0
\(445\) −1.62378e10 2.81247e10i −0.414083 0.717213i
\(446\) 0 0
\(447\) −7.31495e10 + 1.74817e10i −1.83224 + 0.437879i
\(448\) 0 0
\(449\) 6.43076e10i 1.58226i −0.611650 0.791128i \(-0.709494\pi\)
0.611650 0.791128i \(-0.290506\pi\)
\(450\) 0 0
\(451\) 2.53474e10 + 4.39030e10i 0.612671 + 1.06118i
\(452\) 0 0
\(453\) −3.63546e10 1.08096e10i −0.863310 0.256695i
\(454\) 0 0
\(455\) 5.02848e7 8.63146e9i 0.00117325 0.201390i
\(456\) 0 0
\(457\) 1.16839e10 2.02372e10i 0.267870 0.463965i −0.700441 0.713710i \(-0.747013\pi\)
0.968312 + 0.249745i \(0.0803468\pi\)
\(458\) 0 0
\(459\) 1.20349e10 + 4.30383e9i 0.271139 + 0.0969626i
\(460\) 0 0
\(461\) 7.53854e9i 0.166911i 0.996512 + 0.0834553i \(0.0265956\pi\)
−0.996512 + 0.0834553i \(0.973404\pi\)
\(462\) 0 0
\(463\) 3.19399e10 0.695041 0.347520 0.937672i \(-0.387024\pi\)
0.347520 + 0.937672i \(0.387024\pi\)
\(464\) 0 0
\(465\) 1.38614e10 + 1.46372e10i 0.296480 + 0.313072i
\(466\) 0 0
\(467\) 1.57779e10 + 9.10936e9i 0.331727 + 0.191523i 0.656608 0.754232i \(-0.271991\pi\)
−0.324881 + 0.945755i \(0.605324\pi\)
\(468\) 0 0
\(469\) −3.16866e10 + 5.41518e10i −0.654914 + 1.11924i
\(470\) 0 0
\(471\) −7.10459e10 2.11246e10i −1.44363 0.429245i
\(472\) 0 0
\(473\) −2.08491e10 + 1.20372e10i −0.416527 + 0.240482i
\(474\) 0 0
\(475\) −4.15077e10 −0.815369
\(476\) 0 0
\(477\) 1.49393e10 + 2.94704e10i 0.288573 + 0.569262i
\(478\) 0 0
\(479\) −4.99587e10 + 2.88436e10i −0.949005 + 0.547909i −0.892772 0.450509i \(-0.851242\pi\)
−0.0562336 + 0.998418i \(0.517909\pi\)
\(480\) 0 0
\(481\) −7.12630e9 + 1.23431e10i −0.133132 + 0.230592i
\(482\) 0 0
\(483\) 4.80583e9 + 5.13436e9i 0.0883038 + 0.0943404i
\(484\) 0 0
\(485\) 6.64637e10 + 3.83729e10i 1.20121 + 0.693517i
\(486\) 0 0
\(487\) −2.63352e10 4.56138e10i −0.468188 0.810925i 0.531151 0.847277i \(-0.321760\pi\)
−0.999339 + 0.0363521i \(0.988426\pi\)
\(488\) 0 0
\(489\) 8.37349e9 + 3.50376e10i 0.146444 + 0.612771i
\(490\) 0 0
\(491\) 4.95042e10i 0.851758i 0.904780 + 0.425879i \(0.140035\pi\)
−0.904780 + 0.425879i \(0.859965\pi\)
\(492\) 0 0
\(493\) −1.35385e10 2.34494e10i −0.229184 0.396958i
\(494\) 0 0
\(495\) −4.09507e9 + 7.51657e10i −0.0682088 + 1.25198i
\(496\) 0 0
\(497\) 3.19565e9 1.82027e9i 0.0523761 0.0298339i
\(498\) 0 0
\(499\) 3.65446e10 6.32970e10i 0.589414 1.02090i −0.404895 0.914363i \(-0.632692\pi\)
0.994309 0.106532i \(-0.0339747\pi\)
\(500\) 0 0
\(501\) 5.00498e10 + 5.28507e10i 0.794422 + 0.838881i
\(502\) 0 0
\(503\) 5.81734e10i 0.908766i −0.890806 0.454383i \(-0.849860\pi\)
0.890806 0.454383i \(-0.150140\pi\)
\(504\) 0 0
\(505\) −1.51497e10 −0.232937
\(506\) 0 0
\(507\) −4.68939e10 + 4.44087e10i −0.709717 + 0.672103i
\(508\) 0 0
\(509\) −2.67878e9 1.54660e9i −0.0399086 0.0230412i 0.479913 0.877316i \(-0.340668\pi\)
−0.519822 + 0.854275i \(0.674002\pi\)
\(510\) 0 0
\(511\) 5.89702e10 1.00779e11i 0.864866 1.47804i
\(512\) 0 0
\(513\) 6.95219e10 1.26623e10i 1.00381 0.182828i
\(514\) 0 0
\(515\) −1.19270e11 + 6.88607e10i −1.69552 + 0.978909i
\(516\) 0 0
\(517\) −3.63459e10 −0.508737
\(518\) 0 0
\(519\) 2.16917e10 5.18400e9i 0.298967 0.0714490i
\(520\) 0 0
\(521\) −2.52830e10 + 1.45971e10i −0.343145 + 0.198115i −0.661662 0.749803i \(-0.730148\pi\)
0.318517 + 0.947917i \(0.396815\pi\)
\(522\) 0 0
\(523\) 6.17406e10 1.06938e11i 0.825210 1.42931i −0.0765488 0.997066i \(-0.524390\pi\)
0.901759 0.432240i \(-0.142277\pi\)
\(524\) 0 0
\(525\) −1.37670e10 5.91274e10i −0.181218 0.778308i
\(526\) 0 0
\(527\) 6.18336e9 + 3.56996e9i 0.0801645 + 0.0462830i
\(528\) 0 0
\(529\) −3.85017e10 6.66869e10i −0.491651 0.851565i
\(530\) 0 0
\(531\) 5.89493e10 + 1.16288e11i 0.741482 + 1.46271i
\(532\) 0 0
\(533\) 1.58844e10i 0.196816i
\(534\) 0 0
\(535\) −1.98043e10 3.43021e10i −0.241738 0.418703i
\(536\) 0 0
\(537\) −1.84082e10 + 6.19099e10i −0.221367 + 0.744497i
\(538\) 0 0
\(539\) −9.19253e8 + 7.88928e10i −0.0108913 + 0.934721i
\(540\) 0 0
\(541\) 1.85709e10 3.21657e10i 0.216792 0.375495i −0.737033 0.675856i \(-0.763774\pi\)
0.953825 + 0.300362i \(0.0971073\pi\)
\(542\) 0 0
\(543\) −3.83040e10 + 3.62739e10i −0.440600 + 0.417249i
\(544\) 0 0
\(545\) 1.10014e11i 1.24699i
\(546\) 0 0
\(547\) 8.32028e10 0.929370 0.464685 0.885476i \(-0.346168\pi\)
0.464685 + 0.885476i \(0.346168\pi\)
\(548\) 0 0
\(549\) −6.91427e10 4.51052e10i −0.761127 0.496521i
\(550\) 0 0
\(551\) −1.29647e11 7.48520e10i −1.40656 0.812077i
\(552\) 0 0
\(553\) −1.01042e11 5.88650e8i −1.08045 0.00629443i
\(554\) 0 0
\(555\) −6.43215e10 + 2.16324e11i −0.677929 + 2.27999i
\(556\) 0 0
\(557\) −8.57873e9 + 4.95293e9i −0.0891256 + 0.0514567i −0.543900 0.839150i \(-0.683053\pi\)
0.454775 + 0.890606i \(0.349720\pi\)
\(558\) 0 0
\(559\) 7.54333e9 0.0772531
\(560\) 0 0
\(561\) 6.19726e9 + 2.59315e10i 0.0625674 + 0.261804i
\(562\) 0 0
\(563\) 8.62703e10 4.98082e10i 0.858672 0.495755i −0.00489502 0.999988i \(-0.501558\pi\)
0.863568 + 0.504233i \(0.168225\pi\)
\(564\) 0 0
\(565\) −1.15370e11 + 1.99827e11i −1.13214 + 1.96092i
\(566\) 0 0
\(567\) 4.10959e10 + 9.48336e10i 0.397618 + 0.917551i
\(568\) 0 0
\(569\) −6.89683e10 3.98189e10i −0.657962 0.379874i 0.133538 0.991044i \(-0.457366\pi\)
−0.791500 + 0.611169i \(0.790699\pi\)
\(570\) 0 0
\(571\) 7.14946e10 + 1.23832e11i 0.672556 + 1.16490i 0.977177 + 0.212428i \(0.0681371\pi\)
−0.304620 + 0.952474i \(0.598530\pi\)
\(572\) 0 0
\(573\) 9.03697e10 2.15971e10i 0.838310 0.200344i
\(574\) 0 0
\(575\) 1.12879e10i 0.103263i
\(576\) 0 0
\(577\) −1.00892e11 1.74750e11i −0.910235 1.57657i −0.813732 0.581240i \(-0.802568\pi\)
−0.0965021 0.995333i \(-0.530765\pi\)
\(578\) 0 0
\(579\) −5.94896e10 1.76885e10i −0.529330 0.157390i
\(580\) 0 0
\(581\) 2.98216e10 1.69867e10i 0.261714 0.149075i
\(582\) 0 0
\(583\) −3.44612e10 + 5.96886e10i −0.298302 + 0.516675i
\(584\) 0 0
\(585\) 1.28872e10 1.97550e10i 0.110036 0.168676i
\(586\) 0 0
\(587\) 2.93750e10i 0.247415i −0.992319 0.123707i \(-0.960522\pi\)
0.992319 0.123707i \(-0.0394784\pi\)
\(588\) 0 0
\(589\) 3.94754e10 0.327993
\(590\) 0 0
\(591\) −2.06487e10 2.18043e10i −0.169255 0.178728i
\(592\) 0 0
\(593\) −4.24481e10 2.45074e10i −0.343273 0.198189i 0.318445 0.947941i \(-0.396839\pi\)
−0.661718 + 0.749752i \(0.730173\pi\)
\(594\) 0 0
\(595\) −2.39597e10 4.20635e10i −0.191168 0.335612i
\(596\) 0 0
\(597\) −1.38175e11 4.10846e10i −1.08775 0.323431i
\(598\) 0 0
\(599\) 1.62609e11 9.38821e10i 1.26310 0.729248i 0.289423 0.957201i \(-0.406537\pi\)
0.973672 + 0.227953i \(0.0732033\pi\)
\(600\) 0 0
\(601\) 1.40135e11 1.07411 0.537053 0.843548i \(-0.319537\pi\)
0.537053 + 0.843548i \(0.319537\pi\)
\(602\) 0 0
\(603\) −1.52921e11 + 7.75195e10i −1.15664 + 0.586330i
\(604\) 0 0
\(605\) 1.96365e10 1.13371e10i 0.146569 0.0846218i
\(606\) 0 0
\(607\) 7.63717e10 1.32280e11i 0.562572 0.974403i −0.434699 0.900576i \(-0.643145\pi\)
0.997271 0.0738270i \(-0.0235213\pi\)
\(608\) 0 0
\(609\) 6.36255e10 2.09508e11i 0.462554 1.52311i
\(610\) 0 0
\(611\) 9.86262e9 + 5.69418e9i 0.0707664 + 0.0408570i
\(612\) 0 0
\(613\) 2.80686e10 + 4.86162e10i 0.198783 + 0.344302i 0.948134 0.317871i \(-0.102968\pi\)
−0.749351 + 0.662173i \(0.769635\pi\)
\(614\) 0 0
\(615\) −5.84640e10 2.44634e11i −0.408684 1.71008i
\(616\) 0 0
\(617\) 4.29400e10i 0.296293i 0.988965 + 0.148147i \(0.0473308\pi\)
−0.988965 + 0.148147i \(0.952669\pi\)
\(618\) 0 0
\(619\) 5.43304e9 + 9.41031e9i 0.0370067 + 0.0640975i 0.883936 0.467609i \(-0.154884\pi\)
−0.846929 + 0.531706i \(0.821551\pi\)
\(620\) 0 0
\(621\) 3.44349e9 + 1.89064e10i 0.0231544 + 0.127128i
\(622\) 0 0
\(623\) 5.41857e8 9.30104e10i 0.00359693 0.617418i
\(624\) 0 0
\(625\) 8.85409e10 1.53357e11i 0.580262 1.00504i
\(626\) 0 0
\(627\) 1.01358e11 + 1.07031e11i 0.655827 + 0.692529i
\(628\) 0 0
\(629\) 7.99331e10i 0.510651i
\(630\) 0 0
\(631\) −3.12531e10 −0.197140 −0.0985701 0.995130i \(-0.531427\pi\)
−0.0985701 + 0.995130i \(0.531427\pi\)
\(632\) 0 0
\(633\) 2.07936e11 1.96916e11i 1.29514 1.22650i
\(634\) 0 0
\(635\) 2.22518e11 + 1.28471e11i 1.36858 + 0.790149i
\(636\) 0 0
\(637\) 1.26093e10 2.12639e10i 0.0765831 0.129147i
\(638\) 0 0
\(639\) 1.00349e10 + 5.46705e8i 0.0601877 + 0.00327906i
\(640\) 0 0
\(641\) −1.01252e9 + 5.84579e8i −0.00599752 + 0.00346267i −0.502996 0.864289i \(-0.667769\pi\)
0.496998 + 0.867752i \(0.334436\pi\)
\(642\) 0 0
\(643\) 3.03236e10 0.177393 0.0886966 0.996059i \(-0.471730\pi\)
0.0886966 + 0.996059i \(0.471730\pi\)
\(644\) 0 0
\(645\) 1.16174e11 2.77640e10i 0.671229 0.160414i
\(646\) 0 0
\(647\) 1.76301e11 1.01788e11i 1.00609 0.580868i 0.0960476 0.995377i \(-0.469380\pi\)
0.910045 + 0.414509i \(0.136047\pi\)
\(648\) 0 0
\(649\) −1.35982e11 + 2.35527e11i −0.766481 + 1.32758i
\(650\) 0 0
\(651\) 1.30929e10 + 5.62323e10i 0.0728975 + 0.313085i
\(652\) 0 0
\(653\) 6.23592e10 + 3.60031e10i 0.342964 + 0.198010i 0.661582 0.749873i \(-0.269885\pi\)
−0.318618 + 0.947883i \(0.603219\pi\)
\(654\) 0 0
\(655\) −1.22757e10 2.12621e10i −0.0666930 0.115516i
\(656\) 0 0
\(657\) 2.84593e11 1.44267e11i 1.52744 0.774295i
\(658\) 0 0
\(659\) 2.86928e11i 1.52136i 0.649128 + 0.760679i \(0.275134\pi\)
−0.649128 + 0.760679i \(0.724866\pi\)
\(660\) 0 0
\(661\) 1.11955e11 + 1.93912e11i 0.586460 + 1.01578i 0.994692 + 0.102900i \(0.0328123\pi\)
−0.408232 + 0.912878i \(0.633854\pi\)
\(662\) 0 0
\(663\) 2.38094e9 8.00752e9i 0.0123224 0.0414423i
\(664\) 0 0
\(665\) −2.31002e11 1.35170e11i −1.18122 0.691182i
\(666\) 0 0
\(667\) 2.03559e10 3.52574e10i 0.102846 0.178134i
\(668\) 0 0
\(669\) −1.08138e11 + 1.02407e11i −0.539852 + 0.511241i
\(670\) 0 0
\(671\) 1.72207e11i 0.849496i
\(672\) 0 0
\(673\) −5.41750e10 −0.264082 −0.132041 0.991244i \(-0.542153\pi\)
−0.132041 + 0.991244i \(0.542153\pi\)
\(674\) 0 0
\(675\) 5.58611e10 1.56206e11i 0.269088 0.752459i
\(676\) 0 0
\(677\) −9.84930e10 5.68650e10i −0.468868 0.270701i 0.246898 0.969042i \(-0.420589\pi\)
−0.715766 + 0.698340i \(0.753922\pi\)
\(678\) 0 0
\(679\) 1.08791e11 + 1.90993e11i 0.511817 + 0.898541i
\(680\) 0 0
\(681\) 3.71015e10 1.24779e11i 0.172506 0.580167i
\(682\) 0 0
\(683\) 3.73633e11 2.15717e11i 1.71697 0.991291i 0.792639 0.609691i \(-0.208707\pi\)
0.924328 0.381600i \(-0.124627\pi\)
\(684\) 0 0
\(685\) −3.05044e11 −1.38548
\(686\) 0 0
\(687\) −1.55067e10 6.48852e10i −0.0696131 0.291285i
\(688\) 0 0
\(689\) 1.87024e10 1.07978e10i 0.0829890 0.0479137i
\(690\) 0 0
\(691\) 6.06267e10 1.05009e11i 0.265921 0.460588i −0.701884 0.712291i \(-0.747657\pi\)
0.967804 + 0.251704i \(0.0809908\pi\)
\(692\) 0 0
\(693\) −1.18846e11 + 1.79883e11i −0.515292 + 0.779934i
\(694\) 0 0
\(695\) −3.95363e11 2.28263e11i −1.69456 0.978353i
\(696\) 0 0
\(697\) −4.45422e10 7.71494e10i −0.188730 0.326890i
\(698\) 0 0
\(699\) −3.24410e11 + 7.75296e10i −1.35890 + 0.324757i
\(700\) 0 0
\(701\) 1.58865e11i 0.657895i −0.944348 0.328947i \(-0.893306\pi\)
0.944348 0.328947i \(-0.106694\pi\)
\(702\) 0 0
\(703\) 2.20968e11 + 3.82728e11i 0.904707 + 1.56700i
\(704\) 0 0
\(705\) 1.72851e11 + 5.13953e10i 0.699707 + 0.208049i
\(706\) 0 0
\(707\) −3.74495e10 2.19134e10i −0.149889 0.0877064i
\(708\) 0 0
\(709\) −6.06898e10 + 1.05118e11i −0.240177 + 0.415998i −0.960764 0.277365i \(-0.910539\pi\)
0.720588 + 0.693364i \(0.243872\pi\)
\(710\) 0 0
\(711\) −2.31258e11 1.50861e11i −0.904936 0.590335i
\(712\) 0 0
\(713\) 1.07353e10i 0.0415388i
\(714\) 0 0
\(715\) 4.92019e10 0.188260
\(716\) 0 0
\(717\) −1.64567e11 1.73777e11i −0.622684 0.657531i
\(718\) 0 0
\(719\) 3.18390e11 + 1.83822e11i 1.19136 + 0.687832i 0.958615 0.284705i \(-0.0918957\pi\)
0.232746 + 0.972538i \(0.425229\pi\)
\(720\) 0 0
\(721\) −3.94435e11 2.29789e9i −1.45960 0.00850330i
\(722\) 0 0
\(723\) 3.77910e11 + 1.12367e11i 1.38304 + 0.411231i
\(724\) 0 0
\(725\) −3.04359e11 + 1.75722e11i −1.10163 + 0.636025i
\(726\) 0 0
\(727\) −1.43071e11 −0.512168 −0.256084 0.966654i \(-0.582432\pi\)
−0.256084 + 0.966654i \(0.582432\pi\)
\(728\) 0 0
\(729\) −4.59105e10 + 2.78673e11i −0.162556 + 0.986699i
\(730\) 0 0
\(731\) 3.66375e10 2.11527e10i 0.128309 0.0740791i
\(732\) 0 0
\(733\) 5.43153e10 9.40769e10i 0.188151 0.325887i −0.756483 0.654014i \(-0.773084\pi\)
0.944634 + 0.328127i \(0.106417\pi\)
\(734\) 0 0
\(735\) 1.15931e11 3.73893e11i 0.397237 1.28114i
\(736\) 0 0
\(737\) −3.09723e11 1.78819e11i −1.04979 0.606098i
\(738\) 0 0
\(739\) −7.57046e10 1.31124e11i −0.253831 0.439648i 0.710746 0.703448i \(-0.248357\pi\)
−0.964577 + 0.263800i \(0.915024\pi\)
\(740\) 0 0
\(741\) −1.07359e10 4.49227e10i −0.0356094 0.149002i
\(742\) 0 0
\(743\) 3.17021e11i 1.04024i 0.854094 + 0.520119i \(0.174112\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(744\) 0 0
\(745\) 3.89196e11 + 6.74107e11i 1.26341 + 2.18828i
\(746\) 0 0
\(747\) 9.36449e10 + 5.10183e9i 0.300747 + 0.0163849i
\(748\) 0 0
\(749\) 6.60872e8 1.13439e11i 0.00209986 0.360443i
\(750\) 0 0
\(751\) 8.57533e10 1.48529e11i 0.269582 0.466930i −0.699172 0.714954i \(-0.746448\pi\)
0.968754 + 0.248024i \(0.0797811\pi\)
\(752\) 0 0
\(753\) −1.46682e11 1.54891e11i −0.456244 0.481777i
\(754\) 0 0
\(755\) 3.92538e11i 1.20807i
\(756\) 0 0
\(757\) −3.69046e10 −0.112382 −0.0561911 0.998420i \(-0.517896\pi\)
−0.0561911 + 0.998420i \(0.517896\pi\)
\(758\) 0 0
\(759\) −2.91068e10 + 2.75642e10i −0.0877056 + 0.0830574i
\(760\) 0 0
\(761\) 4.32044e10 + 2.49441e10i 0.128822 + 0.0743754i 0.563026 0.826439i \(-0.309637\pi\)
−0.434204 + 0.900814i \(0.642970\pi\)
\(762\) 0 0
\(763\) −1.59130e11 + 2.71951e11i −0.469521 + 0.802402i
\(764\) 0 0
\(765\) 7.19614e9 1.32086e11i 0.0210113 0.385667i
\(766\) 0 0
\(767\) 7.37984e10 4.26075e10i 0.213238 0.123113i
\(768\) 0 0
\(769\) −4.96051e10 −0.141847 −0.0709236 0.997482i \(-0.522595\pi\)
−0.0709236 + 0.997482i \(0.522595\pi\)
\(770\) 0 0
\(771\) −5.87897e11 + 1.40499e11i −1.66373 + 0.397609i
\(772\) 0 0
\(773\) −2.63590e11 + 1.52184e11i −0.738262 + 0.426236i −0.821437 0.570299i \(-0.806827\pi\)
0.0831749 + 0.996535i \(0.473494\pi\)
\(774\) 0 0
\(775\) 4.63360e10 8.02563e10i 0.128443 0.222471i
\(776\) 0 0
\(777\) −4.71903e11 + 4.41707e11i −1.29470 + 1.21185i
\(778\) 0 0
\(779\) −4.26545e11 2.46266e11i −1.15828 0.668736i
\(780\) 0 0
\(781\) 1.04818e10 + 1.81551e10i 0.0281730 + 0.0487971i
\(782\) 0 0
\(783\) 4.56171e11 3.87167e11i 1.21361 1.03003i
\(784\) 0 0
\(785\) 7.67116e11i 2.02014i
\(786\) 0 0
\(787\) 2.54476e11 + 4.40765e11i 0.663358 + 1.14897i 0.979728 + 0.200334i \(0.0642026\pi\)
−0.316370 + 0.948636i \(0.602464\pi\)
\(788\) 0 0
\(789\) 1.89788e11 6.38292e11i 0.489736 1.64707i
\(790\) 0 0
\(791\) −5.74229e11 + 3.27086e11i −1.46683 + 0.835518i
\(792\) 0 0
\(793\) −2.69791e10 + 4.67292e10i −0.0682236 + 0.118167i
\(794\) 0 0
\(795\) 2.48292e11 2.35133e11i 0.621575 0.588633i
\(796\) 0 0
\(797\) 1.31085e11i 0.324876i −0.986719 0.162438i \(-0.948064\pi\)
0.986719 0.162438i \(-0.0519358\pi\)
\(798\) 0 0
\(799\) 6.38696e10 0.156714
\(800\) 0 0
\(801\) 1.38869e11 2.12875e11i 0.337345 0.517123i
\(802\) 0 0
\(803\) 5.76408e11 + 3.32789e11i 1.38633 + 0.800401i
\(804\) 0 0
\(805\) 3.67591e10 6.28207e10i 0.0875350 0.149596i
\(806\) 0 0
\(807\) −1.38342e11 + 4.65268e11i −0.326181 + 1.09701i
\(808\) 0 0
\(809\) 3.16264e11 1.82595e11i 0.738339 0.426280i −0.0831258 0.996539i \(-0.526490\pi\)
0.821465 + 0.570259i \(0.193157\pi\)
\(810\) 0 0
\(811\) −2.53712e11 −0.586487 −0.293244 0.956038i \(-0.594735\pi\)
−0.293244 + 0.956038i \(0.594735\pi\)
\(812\) 0 0
\(813\) 8.46681e10 + 3.54280e11i 0.193802 + 0.810933i
\(814\) 0 0
\(815\) 3.22888e11 1.86419e11i 0.731848 0.422533i
\(816\) 0 0
\(817\) 1.16949e11 2.02562e11i 0.262488 0.454643i
\(818\) 0 0
\(819\) 6.04312e10 3.01928e10i 0.134315 0.0671071i
\(820\) 0 0
\(821\) −9.29739e10 5.36785e10i −0.204639 0.118148i 0.394179 0.919034i \(-0.371029\pi\)
−0.598817 + 0.800886i \(0.704363\pi\)
\(822\) 0 0
\(823\) 9.17659e10 + 1.58943e11i 0.200024 + 0.346452i 0.948536 0.316670i \(-0.102565\pi\)
−0.748512 + 0.663121i \(0.769231\pi\)
\(824\) 0 0
\(825\) 3.36575e11 8.04368e10i 0.726551 0.173636i
\(826\) 0 0
\(827\) 8.71283e11i 1.86267i 0.364157 + 0.931337i \(0.381357\pi\)
−0.364157 + 0.931337i \(0.618643\pi\)
\(828\) 0 0
\(829\) −1.08452e11 1.87845e11i −0.229625 0.397723i 0.728072 0.685501i \(-0.240417\pi\)
−0.957697 + 0.287778i \(0.907083\pi\)
\(830\) 0 0
\(831\) −3.40359e11 1.01202e11i −0.713728 0.212219i
\(832\) 0 0
\(833\) 1.61538e9 1.38636e11i 0.00335501 0.287936i
\(834\) 0 0
\(835\) 3.76668e11 6.52409e11i 0.774842 1.34207i
\(836\) 0 0
\(837\) −5.31260e10 + 1.48558e11i −0.108244 + 0.302687i
\(838\) 0 0
\(839\) 4.64214e11i 0.936852i −0.883503 0.468426i \(-0.844821\pi\)
0.883503 0.468426i \(-0.155179\pi\)
\(840\) 0 0
\(841\) −7.67291e11 −1.53383
\(842\) 0 0
\(843\) −2.72628e11 2.87885e11i −0.539834 0.570045i
\(844\) 0 0
\(845\) 5.78876e11 + 3.34214e11i 1.13543 + 0.655538i
\(846\) 0 0
\(847\) 6.49393e10 + 3.78321e8i 0.126175 + 0.000735067i
\(848\) 0 0
\(849\) −4.21224e11 1.25246e11i −0.810741 0.241064i
\(850\) 0 0
\(851\) −1.04082e11 + 6.00918e10i −0.198453 + 0.114577i
\(852\) 0 0
\(853\) −4.67940e11 −0.883882 −0.441941 0.897044i \(-0.645710\pi\)
−0.441941 + 0.897044i \(0.645710\pi\)
\(854\) 0 0
\(855\) −3.30685e11 6.52336e11i −0.618800 1.22069i
\(856\) 0 0
\(857\) 4.80557e11 2.77449e11i 0.890884 0.514352i 0.0166525 0.999861i \(-0.494699\pi\)
0.874232 + 0.485509i \(0.161366\pi\)
\(858\) 0 0
\(859\) −2.15341e11 + 3.72981e11i −0.395506 + 0.685037i −0.993166 0.116713i \(-0.962764\pi\)
0.597660 + 0.801750i \(0.296097\pi\)
\(860\) 0 0
\(861\) 2.09330e11 6.89290e11i 0.380907 1.25426i
\(862\) 0 0
\(863\) −5.39592e11 3.11533e11i −0.972797 0.561644i −0.0727089 0.997353i \(-0.523164\pi\)
−0.900088 + 0.435709i \(0.856498\pi\)
\(864\) 0 0
\(865\) −1.15412e11 1.99899e11i −0.206151 0.357064i
\(866\) 0 0
\(867\) 1.20447e11 + 5.03992e11i 0.213167 + 0.891963i
\(868\) 0 0
\(869\) 5.75972e11i 1.01000i
\(870\) 0 0
\(871\) 5.60298e10 + 9.70464e10i 0.0973523 + 0.168619i
\(872\) 0 0
\(873\) −3.26747e10 + 5.99749e11i −0.0562541 + 1.03255i
\(874\) 0 0
\(875\) 1.37236e11 7.81706e10i 0.234118 0.133356i
\(876\) 0 0
\(877\) −1.84222e11 + 3.19082e11i −0.311418 + 0.539392i −0.978670 0.205441i \(-0.934137\pi\)
0.667252 + 0.744832i \(0.267471\pi\)
\(878\) 0 0
\(879\) 7.04565e11 + 7.43995e11i 1.18023 + 1.24628i
\(880\) 0 0
\(881\) 7.03606e11i 1.16795i −0.811770 0.583977i \(-0.801496\pi\)
0.811770 0.583977i \(-0.198504\pi\)
\(882\) 0 0
\(883\) 5.02291e10 0.0826252 0.0413126 0.999146i \(-0.486846\pi\)
0.0413126 + 0.999146i \(0.486846\pi\)
\(884\) 0 0
\(885\) 9.79742e11 9.27818e11i 1.59712 1.51248i
\(886\) 0 0
\(887\) −9.99354e11 5.76977e11i −1.61445 0.932104i −0.988321 0.152385i \(-0.951305\pi\)
−0.626130 0.779719i \(-0.715362\pi\)
\(888\) 0 0
\(889\) 3.64228e11 + 6.39435e11i 0.583131 + 1.02374i
\(890\) 0 0
\(891\) −5.39197e11 + 2.37400e11i −0.855533 + 0.376678i
\(892\) 0 0
\(893\) 3.05814e11 1.76562e11i 0.480896 0.277645i
\(894\) 0 0
\(895\) 6.68470e11 1.04181
\(896\) 0 0
\(897\) 1.22166e10 2.91961e9i 0.0188704 0.00450977i
\(898\) 0 0
\(899\) 2.89457e11 1.67118e11i 0.443144 0.255850i
\(900\) 0 0
\(901\) 6.05577e10 1.04889e11i 0.0918904 0.159159i
\(902\) 0 0
\(903\) 3.27337e11 + 9.94089e10i 0.492316 + 0.149511i
\(904\) 0 0
\(905\) 4.72838e11 + 2.72993e11i 0.704885 + 0.406966i
\(906\) 0 0
\(907\) 6.66818e10 + 1.15496e11i 0.0985322 + 0.170663i 0.911077 0.412236i \(-0.135252\pi\)
−0.812545 + 0.582898i \(0.801919\pi\)
\(908\) 0 0
\(909\) −5.36098e10 1.05755e11i −0.0785216 0.154898i
\(910\) 0 0
\(911\) 1.47755e11i 0.214520i −0.994231 0.107260i \(-0.965792\pi\)
0.994231 0.107260i \(-0.0342078\pi\)
\(912\) 0 0
\(913\) 9.78160e10 + 1.69422e11i 0.140775 + 0.243830i
\(914\) 0 0
\(915\) −2.43511e11 + 8.18972e11i −0.347404 + 1.16838i
\(916\) 0 0
\(917\) 4.09640e8 7.03152e10i 0.000579329 0.0994425i
\(918\) 0 0
\(919\) 3.80288e11 6.58679e11i 0.533152 0.923446i −0.466098 0.884733i \(-0.654341\pi\)
0.999250 0.0387135i \(-0.0123260\pi\)
\(920\) 0 0
\(921\) −1.71773e11 + 1.62669e11i −0.238735 + 0.226082i
\(922\) 0 0
\(923\) 6.56861e9i 0.00905037i
\(924\) 0 0
\(925\) 1.03748e12 1.41715
\(926\) 0 0
\(927\) −9.02750e11 5.88909e11i −1.22250 0.797498i
\(928\) 0 0
\(929\) 2.97498e11 + 1.71761e11i 0.399413 + 0.230601i 0.686230 0.727384i \(-0.259264\pi\)
−0.286818 + 0.957985i \(0.592597\pi\)
\(930\) 0 0
\(931\) −3.75512e11 6.68268e11i −0.499833 0.889512i
\(932\) 0 0
\(933\) −3.92804e11 + 1.32107e12i −0.518381 + 1.74341i
\(934\) 0 0
\(935\) 2.38971e11 1.37970e11i 0.312679 0.180525i
\(936\) 0 0
\(937\) −2.22618e11 −0.288803 −0.144401 0.989519i \(-0.546126\pi\)
−0.144401 + 0.989519i \(0.546126\pi\)
\(938\) 0 0
\(939\) 2.04669e11 + 8.56404e11i 0.263262 + 1.10158i
\(940\) 0 0
\(941\) 1.53177e11 8.84367e10i 0.195360 0.112791i −0.399130 0.916895i \(-0.630688\pi\)
0.594489 + 0.804104i \(0.297354\pi\)
\(942\) 0 0
\(943\) 6.69716e10 1.15998e11i 0.0846923 0.146691i
\(944\) 0 0
\(945\) 8.19567e11 6.87420e11i 1.02768 0.861976i
\(946\) 0 0
\(947\) 5.66637e11 + 3.27148e11i 0.704539 + 0.406766i 0.809036 0.587759i \(-0.199990\pi\)
−0.104497 + 0.994525i \(0.533323\pi\)
\(948\) 0 0
\(949\) −1.04274e11 1.80608e11i −0.128561 0.222675i
\(950\) 0 0
\(951\) 1.08926e12 2.60319e11i 1.33171 0.318261i
\(952\) 0 0
\(953\) 1.08868e12i 1.31987i −0.751324 0.659934i \(-0.770584\pi\)
0.751324 0.659934i \(-0.229416\pi\)
\(954\) 0 0
\(955\) −4.80817e11 8.32800e11i −0.578051 1.00121i
\(956\) 0 0
\(957\) 1.19633e12 + 3.55715e11i 1.42628 + 0.424086i
\(958\) 0 0
\(959\) −7.54055e11 4.41231e11i −0.891515 0.521665i
\(960\) 0 0
\(961\) 3.82378e11 6.62299e11i 0.448332 0.776534i
\(962\) 0 0
\(963\) 1.69370e11 2.59631e11i 0.196939 0.301892i
\(964\) 0 0
\(965\) 6.42337e11i 0.740720i
\(966\) 0 0
\(967\) 1.11340e12 1.27334 0.636669 0.771137i \(-0.280312\pi\)
0.636669 + 0.771137i \(0.280312\pi\)
\(968\) 0 0
\(969\) −1.78114e11 1.88082e11i −0.202024 0.213330i
\(970\) 0 0
\(971\) −8.01034e11 4.62477e11i −0.901102 0.520252i −0.0235447 0.999723i \(-0.507495\pi\)
−0.877558 + 0.479471i \(0.840829\pi\)
\(972\) 0 0
\(973\) −6.47149e11 1.13613e12i −0.722026 1.26758i
\(974\) 0 0
\(975\) −1.03933e11 3.09032e10i −0.115010 0.0341967i
\(976\) 0 0
\(977\) −1.22820e12 + 7.09101e11i −1.34800 + 0.778269i −0.987966 0.154669i \(-0.950569\pi\)
−0.360036 + 0.932939i \(0.617235\pi\)
\(978\) 0 0
\(979\) 5.30187e11 0.577163
\(980\) 0 0
\(981\) −7.67971e11 + 3.89304e11i −0.829218 + 0.420351i
\(982\) 0 0
\(983\) 1.42369e12 8.21970e11i 1.52476 0.880322i 0.525194 0.850983i \(-0.323993\pi\)
0.999569 0.0293398i \(-0.00934049\pi\)
\(984\) 0 0
\(985\) −1.55399e11 + 2.69160e11i −0.165084 + 0.285934i
\(986\) 0 0
\(987\) 3.52941e11 + 3.77068e11i 0.371906 + 0.397330i
\(988\) 0 0
\(989\) 5.50864e10 + 3.18042e10i 0.0575784 + 0.0332429i
\(990\) 0 0
\(991\) −7.61463e11 1.31889e12i −0.789504 1.36746i −0.926271 0.376857i \(-0.877005\pi\)
0.136768 0.990603i \(-0.456329\pi\)
\(992\) 0 0
\(993\) 1.34767e11 + 5.63911e11i 0.138607 + 0.579981i
\(994\) 0 0
\(995\) 1.49194e12i 1.52215i
\(996\) 0 0
\(997\) 7.56987e11 + 1.31114e12i 0.766140 + 1.32699i 0.939642 + 0.342159i \(0.111158\pi\)
−0.173502 + 0.984833i \(0.555508\pi\)
\(998\) 0 0
\(999\) −1.73770e12 + 3.16494e11i −1.74467 + 0.317763i
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 84.9.p.b.65.16 yes 40
3.2 odd 2 inner 84.9.p.b.65.2 yes 40
7.4 even 3 inner 84.9.p.b.53.2 40
21.11 odd 6 inner 84.9.p.b.53.16 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.9.p.b.53.2 40 7.4 even 3 inner
84.9.p.b.53.16 yes 40 21.11 odd 6 inner
84.9.p.b.65.2 yes 40 3.2 odd 2 inner
84.9.p.b.65.16 yes 40 1.1 even 1 trivial