Properties

Label 84.9.m.b.61.1
Level $84$
Weight $9$
Character 84.61
Analytic conductor $34.220$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 84.m (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(34.2198032451\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 61.1
Root \(44.6586 + 77.3509i\) of defining polynomial
Character \(\chi\) \(=\) 84.61
Dual form 84.9.m.b.73.1

$q$-expansion

\(f(q)\) \(=\) \(q+(40.5000 - 23.3827i) q^{3} +(-939.615 - 542.487i) q^{5} +(1451.57 + 1912.52i) q^{7} +(1093.50 - 1894.00i) q^{9} +O(q^{10})\) \(q+(40.5000 - 23.3827i) q^{3} +(-939.615 - 542.487i) q^{5} +(1451.57 + 1912.52i) q^{7} +(1093.50 - 1894.00i) q^{9} +(-8435.48 - 14610.7i) q^{11} -9958.41i q^{13} -50739.2 q^{15} +(-91736.7 + 52964.2i) q^{17} +(147650. + 85245.9i) q^{19} +(103509. + 43515.5i) q^{21} +(-105694. + 183067. i) q^{23} +(393272. + 681166. i) q^{25} -102276. i q^{27} -567529. q^{29} +(549248. - 317108. i) q^{31} +(-683274. - 394488. i) q^{33} +(-326400. - 2.58449e6i) q^{35} +(-1.07740e6 + 1.86611e6i) q^{37} +(-232854. - 403316. i) q^{39} +5.45428e6i q^{41} +5.56726e6 q^{43} +(-2.05494e6 + 1.18642e6i) q^{45} +(2.76739e6 + 1.59775e6i) q^{47} +(-1.55068e6 + 5.55233e6i) q^{49} +(-2.47689e6 + 4.29010e6i) q^{51} +(4.38272e6 + 7.59109e6i) q^{53} +1.83046e7i q^{55} +7.97311e6 q^{57} +(-8.08566e6 + 4.66826e6i) q^{59} +(-2.13748e7 - 1.23407e7i) q^{61} +(5.20961e6 - 657931. i) q^{63} +(-5.40231e6 + 9.35707e6i) q^{65} +(-6.91779e6 - 1.19820e7i) q^{67} +9.88562e6i q^{69} +1.19189e7 q^{71} +(-1.83300e7 + 1.05828e7i) q^{73} +(3.18550e7 + 1.83915e7i) q^{75} +(1.56985e7 - 3.73415e7i) q^{77} +(-8.61190e6 + 1.49162e7i) q^{79} +(-2.39148e6 - 4.14217e6i) q^{81} +6.82663e7i q^{83} +1.14930e8 q^{85} +(-2.29849e7 + 1.32703e7i) q^{87} +(-7.87155e7 - 4.54464e7i) q^{89} +(1.90457e7 - 1.44553e7i) q^{91} +(1.48297e7 - 2.56858e7i) q^{93} +(-9.24895e7 - 1.60197e8i) q^{95} +3.95376e7i q^{97} -3.68968e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 486 q^{3} + 285 q^{5} + 198 q^{7} + 13122 q^{9} - 17919 q^{11} + 15390 q^{15} - 205782 q^{17} + 74313 q^{19} - 39609 q^{21} - 62832 q^{23} + 878679 q^{25} - 575454 q^{29} + 1442952 q^{31} - 1451439 q^{33} - 3989514 q^{35} - 2058621 q^{37} - 930933 q^{39} + 7721322 q^{43} + 623295 q^{45} + 12088194 q^{47} - 16964694 q^{49} - 5556114 q^{51} - 5506743 q^{53} + 4012902 q^{57} + 7511901 q^{59} - 37215576 q^{61} - 3641355 q^{63} + 5047122 q^{65} - 36824553 q^{67} - 30011556 q^{71} + 95080185 q^{73} + 71172999 q^{75} - 38333727 q^{77} + 8514456 q^{79} - 28697814 q^{81} + 20121540 q^{85} - 23305887 q^{87} + 83038554 q^{89} - 198538635 q^{91} + 38959704 q^{93} - 221605224 q^{95} - 78377706 q^{99}+O(q^{100}) \) 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
\(3\) 40.5000 23.3827i 0.500000 0.288675i
\(4\) 0 0
\(5\) −939.615 542.487i −1.50338 0.867979i −0.999992 0.00392070i \(-0.998752\pi\)
−0.503392 0.864058i \(-0.667915\pi\)
\(6\) 0 0
\(7\) 1451.57 + 1912.52i 0.604570 + 0.796552i
\(8\) 0 0
\(9\) 1093.50 1894.00i 0.166667 0.288675i
\(10\) 0 0
\(11\) −8435.48 14610.7i −0.576155 0.997929i −0.995915 0.0902942i \(-0.971219\pi\)
0.419760 0.907635i \(-0.362114\pi\)
\(12\) 0 0
\(13\) 9958.41i 0.348672i −0.984686 0.174336i \(-0.944222\pi\)
0.984686 0.174336i \(-0.0557778\pi\)
\(14\) 0 0
\(15\) −50739.2 −1.00226
\(16\) 0 0
\(17\) −91736.7 + 52964.2i −1.09837 + 0.634142i −0.935792 0.352554i \(-0.885313\pi\)
−0.162575 + 0.986696i \(0.551980\pi\)
\(18\) 0 0
\(19\) 147650. + 85245.9i 1.13297 + 0.654122i 0.944681 0.327991i \(-0.106372\pi\)
0.188292 + 0.982113i \(0.439705\pi\)
\(20\) 0 0
\(21\) 103509. + 43515.5i 0.532230 + 0.223752i
\(22\) 0 0
\(23\) −105694. + 183067.i −0.377692 + 0.654183i −0.990726 0.135874i \(-0.956616\pi\)
0.613034 + 0.790057i \(0.289949\pi\)
\(24\) 0 0
\(25\) 393272. + 681166.i 1.00678 + 1.74379i
\(26\) 0 0
\(27\) 102276.i 0.192450i
\(28\) 0 0
\(29\) −567529. −0.802409 −0.401205 0.915989i \(-0.631408\pi\)
−0.401205 + 0.915989i \(0.631408\pi\)
\(30\) 0 0
\(31\) 549248. 317108.i 0.594732 0.343369i −0.172234 0.985056i \(-0.555099\pi\)
0.766967 + 0.641687i \(0.221765\pi\)
\(32\) 0 0
\(33\) −683274. 394488.i −0.576155 0.332643i
\(34\) 0 0
\(35\) −326400. 2.58449e6i −0.217510 1.72228i
\(36\) 0 0
\(37\) −1.07740e6 + 1.86611e6i −0.574870 + 0.995703i 0.421186 + 0.906974i \(0.361614\pi\)
−0.996056 + 0.0887291i \(0.971719\pi\)
\(38\) 0 0
\(39\) −232854. 403316.i −0.100653 0.174336i
\(40\) 0 0
\(41\) 5.45428e6i 1.93020i 0.261884 + 0.965099i \(0.415656\pi\)
−0.261884 + 0.965099i \(0.584344\pi\)
\(42\) 0 0
\(43\) 5.56726e6 1.62842 0.814212 0.580568i \(-0.197169\pi\)
0.814212 + 0.580568i \(0.197169\pi\)
\(44\) 0 0
\(45\) −2.05494e6 + 1.18642e6i −0.501128 + 0.289326i
\(46\) 0 0
\(47\) 2.76739e6 + 1.59775e6i 0.567125 + 0.327430i 0.756000 0.654572i \(-0.227151\pi\)
−0.188876 + 0.982001i \(0.560484\pi\)
\(48\) 0 0
\(49\) −1.55068e6 + 5.55233e6i −0.268991 + 0.963143i
\(50\) 0 0
\(51\) −2.47689e6 + 4.29010e6i −0.366122 + 0.634142i
\(52\) 0 0
\(53\) 4.38272e6 + 7.59109e6i 0.555443 + 0.962056i 0.997869 + 0.0652510i \(0.0207848\pi\)
−0.442425 + 0.896805i \(0.645882\pi\)
\(54\) 0 0
\(55\) 1.83046e7i 2.00036i
\(56\) 0 0
\(57\) 7.97311e6 0.755315
\(58\) 0 0
\(59\) −8.08566e6 + 4.66826e6i −0.667279 + 0.385254i −0.795045 0.606551i \(-0.792553\pi\)
0.127766 + 0.991804i \(0.459219\pi\)
\(60\) 0 0
\(61\) −2.13748e7 1.23407e7i −1.54377 0.891296i −0.998596 0.0529726i \(-0.983130\pi\)
−0.545174 0.838323i \(-0.683536\pi\)
\(62\) 0 0
\(63\) 5.20961e6 657931.i 0.330706 0.0417655i
\(64\) 0 0
\(65\) −5.40231e6 + 9.35707e6i −0.302640 + 0.524187i
\(66\) 0 0
\(67\) −6.91779e6 1.19820e7i −0.343295 0.594605i 0.641747 0.766916i \(-0.278210\pi\)
−0.985043 + 0.172311i \(0.944877\pi\)
\(68\) 0 0
\(69\) 9.88562e6i 0.436122i
\(70\) 0 0
\(71\) 1.19189e7 0.469031 0.234515 0.972112i \(-0.424650\pi\)
0.234515 + 0.972112i \(0.424650\pi\)
\(72\) 0 0
\(73\) −1.83300e7 + 1.05828e7i −0.645463 + 0.372658i −0.786716 0.617315i \(-0.788220\pi\)
0.141253 + 0.989974i \(0.454887\pi\)
\(74\) 0 0
\(75\) 3.18550e7 + 1.83915e7i 1.00678 + 0.581262i
\(76\) 0 0
\(77\) 1.56985e7 3.73415e7i 0.446577 1.06226i
\(78\) 0 0
\(79\) −8.61190e6 + 1.49162e7i −0.221101 + 0.382958i −0.955143 0.296147i \(-0.904298\pi\)
0.734042 + 0.679104i \(0.237632\pi\)
\(80\) 0 0
\(81\) −2.39148e6 4.14217e6i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 6.82663e7i 1.43845i 0.694779 + 0.719223i \(0.255502\pi\)
−0.694779 + 0.719223i \(0.744498\pi\)
\(84\) 0 0
\(85\) 1.14930e8 2.20169
\(86\) 0 0
\(87\) −2.29849e7 + 1.32703e7i −0.401205 + 0.231636i
\(88\) 0 0
\(89\) −7.87155e7 4.54464e7i −1.25459 0.724335i −0.282569 0.959247i \(-0.591186\pi\)
−0.972017 + 0.234912i \(0.924520\pi\)
\(90\) 0 0
\(91\) 1.90457e7 1.44553e7i 0.277735 0.210796i
\(92\) 0 0
\(93\) 1.48297e7 2.56858e7i 0.198244 0.343369i
\(94\) 0 0
\(95\) −9.24895e7 1.60197e8i −1.13553 1.96679i
\(96\) 0 0
\(97\) 3.95376e7i 0.446605i 0.974749 + 0.223302i \(0.0716837\pi\)
−0.974749 + 0.223302i \(0.928316\pi\)
\(98\) 0 0
\(99\) −3.68968e7 −0.384103
\(100\) 0 0
\(101\) 1.01453e8 5.85738e7i 0.974941 0.562882i 0.0742019 0.997243i \(-0.476359\pi\)
0.900739 + 0.434361i \(0.143026\pi\)
\(102\) 0 0
\(103\) −4.22305e7 2.43818e7i −0.375212 0.216629i 0.300521 0.953775i \(-0.402839\pi\)
−0.675733 + 0.737146i \(0.736173\pi\)
\(104\) 0 0
\(105\) −7.36516e7 9.70398e7i −0.605934 0.798349i
\(106\) 0 0
\(107\) 5.90508e7 1.02279e8i 0.450496 0.780282i −0.547921 0.836530i \(-0.684580\pi\)
0.998417 + 0.0562482i \(0.0179138\pi\)
\(108\) 0 0
\(109\) −7.54688e6 1.30716e7i −0.0534640 0.0926024i 0.838055 0.545586i \(-0.183693\pi\)
−0.891519 + 0.452984i \(0.850360\pi\)
\(110\) 0 0
\(111\) 1.00770e8i 0.663802i
\(112\) 0 0
\(113\) −6.94293e7 −0.425823 −0.212911 0.977072i \(-0.568295\pi\)
−0.212911 + 0.977072i \(0.568295\pi\)
\(114\) 0 0
\(115\) 1.98623e8 1.14675e8i 1.13563 0.655658i
\(116\) 0 0
\(117\) −1.88612e7 1.08895e7i −0.100653 0.0581119i
\(118\) 0 0
\(119\) −2.34458e8 9.85671e7i −1.16917 0.491523i
\(120\) 0 0
\(121\) −3.51352e7 + 6.08560e7i −0.163908 + 0.283898i
\(122\) 0 0
\(123\) 1.27536e8 + 2.20898e8i 0.557200 + 0.965099i
\(124\) 0 0
\(125\) 4.29561e8i 1.75948i
\(126\) 0 0
\(127\) −1.00139e8 −0.384934 −0.192467 0.981303i \(-0.561649\pi\)
−0.192467 + 0.981303i \(0.561649\pi\)
\(128\) 0 0
\(129\) 2.25474e8 1.30177e8i 0.814212 0.470085i
\(130\) 0 0
\(131\) −6.73342e6 3.88754e6i −0.0228639 0.0132005i 0.488524 0.872550i \(-0.337535\pi\)
−0.511388 + 0.859350i \(0.670869\pi\)
\(132\) 0 0
\(133\) 5.12902e7 + 4.06125e8i 0.163919 + 1.29793i
\(134\) 0 0
\(135\) −5.54833e7 + 9.60999e7i −0.167043 + 0.289326i
\(136\) 0 0
\(137\) −5.53803e7 9.59215e7i −0.157207 0.272291i 0.776653 0.629928i \(-0.216916\pi\)
−0.933861 + 0.357637i \(0.883582\pi\)
\(138\) 0 0
\(139\) 3.31664e8i 0.888464i −0.895912 0.444232i \(-0.853477\pi\)
0.895912 0.444232i \(-0.146523\pi\)
\(140\) 0 0
\(141\) 1.49439e8 0.378083
\(142\) 0 0
\(143\) −1.45499e8 + 8.40040e7i −0.347949 + 0.200889i
\(144\) 0 0
\(145\) 5.33258e8 + 3.07877e8i 1.20633 + 0.696474i
\(146\) 0 0
\(147\) 6.70258e7 + 2.61128e8i 0.143540 + 0.559222i
\(148\) 0 0
\(149\) 3.47265e8 6.01481e8i 0.704557 1.22033i −0.262294 0.964988i \(-0.584479\pi\)
0.966851 0.255341i \(-0.0821877\pi\)
\(150\) 0 0
\(151\) −4.10896e8 7.11694e8i −0.790359 1.36894i −0.925745 0.378150i \(-0.876561\pi\)
0.135385 0.990793i \(-0.456773\pi\)
\(152\) 0 0
\(153\) 2.31665e8i 0.422762i
\(154\) 0 0
\(155\) −6.88109e8 −1.19215
\(156\) 0 0
\(157\) −4.16332e8 + 2.40369e8i −0.685238 + 0.395622i −0.801825 0.597558i \(-0.796138\pi\)
0.116588 + 0.993180i \(0.462804\pi\)
\(158\) 0 0
\(159\) 3.55000e8 + 2.04959e8i 0.555443 + 0.320685i
\(160\) 0 0
\(161\) −5.03542e8 + 6.35933e7i −0.749432 + 0.0946472i
\(162\) 0 0
\(163\) −3.04664e8 + 5.27694e8i −0.431590 + 0.747536i −0.997010 0.0772671i \(-0.975381\pi\)
0.565420 + 0.824803i \(0.308714\pi\)
\(164\) 0 0
\(165\) 4.28010e8 + 7.41334e8i 0.577454 + 1.00018i
\(166\) 0 0
\(167\) 1.84576e8i 0.237307i 0.992936 + 0.118653i \(0.0378577\pi\)
−0.992936 + 0.118653i \(0.962142\pi\)
\(168\) 0 0
\(169\) 7.16561e8 0.878428
\(170\) 0 0
\(171\) 3.22911e8 1.86433e8i 0.377658 0.218041i
\(172\) 0 0
\(173\) −2.92420e8 1.68829e8i −0.326454 0.188478i 0.327812 0.944743i \(-0.393689\pi\)
−0.654266 + 0.756265i \(0.727022\pi\)
\(174\) 0 0
\(175\) −7.31884e8 + 1.74090e9i −0.780351 + 1.85619i
\(176\) 0 0
\(177\) −2.18313e8 + 3.78129e8i −0.222426 + 0.385254i
\(178\) 0 0
\(179\) 2.92703e8 + 5.06977e8i 0.285112 + 0.493828i 0.972636 0.232333i \(-0.0746359\pi\)
−0.687524 + 0.726161i \(0.741303\pi\)
\(180\) 0 0
\(181\) 1.29407e9i 1.20571i 0.797850 + 0.602856i \(0.205971\pi\)
−0.797850 + 0.602856i \(0.794029\pi\)
\(182\) 0 0
\(183\) −1.15424e9 −1.02918
\(184\) 0 0
\(185\) 2.02468e9 1.16895e9i 1.72850 0.997950i
\(186\) 0 0
\(187\) 1.54769e9 + 8.93557e8i 1.26566 + 0.730728i
\(188\) 0 0
\(189\) 1.95605e8 1.48461e8i 0.153297 0.116349i
\(190\) 0 0
\(191\) −7.80043e8 + 1.35107e9i −0.586118 + 1.01519i 0.408617 + 0.912706i \(0.366011\pi\)
−0.994735 + 0.102480i \(0.967322\pi\)
\(192\) 0 0
\(193\) 8.76806e8 + 1.51867e9i 0.631937 + 1.09455i 0.987155 + 0.159764i \(0.0510734\pi\)
−0.355218 + 0.934784i \(0.615593\pi\)
\(194\) 0 0
\(195\) 5.05282e8i 0.349458i
\(196\) 0 0
\(197\) −1.78624e9 −1.18598 −0.592988 0.805212i \(-0.702052\pi\)
−0.592988 + 0.805212i \(0.702052\pi\)
\(198\) 0 0
\(199\) −2.60521e9 + 1.50412e9i −1.66123 + 0.959114i −0.689107 + 0.724660i \(0.741997\pi\)
−0.972127 + 0.234454i \(0.924670\pi\)
\(200\) 0 0
\(201\) −5.60341e8 3.23513e8i −0.343295 0.198202i
\(202\) 0 0
\(203\) −8.23809e8 1.08541e9i −0.485112 0.639161i
\(204\) 0 0
\(205\) 2.95888e9 5.12492e9i 1.67537 2.90183i
\(206\) 0 0
\(207\) 2.31152e8 + 4.00368e8i 0.125897 + 0.218061i
\(208\) 0 0
\(209\) 2.87636e9i 1.50750i
\(210\) 0 0
\(211\) 3.33988e9 1.68501 0.842503 0.538692i \(-0.181081\pi\)
0.842503 + 0.538692i \(0.181081\pi\)
\(212\) 0 0
\(213\) 4.82714e8 2.78695e8i 0.234515 0.135398i
\(214\) 0 0
\(215\) −5.23108e9 3.02016e9i −2.44815 1.41344i
\(216\) 0 0
\(217\) 1.40375e9 + 5.90143e8i 0.633069 + 0.266145i
\(218\) 0 0
\(219\) −4.94911e8 + 8.57210e8i −0.215154 + 0.372658i
\(220\) 0 0
\(221\) 5.27439e8 + 9.13552e8i 0.221107 + 0.382969i
\(222\) 0 0
\(223\) 1.94513e9i 0.786556i 0.919420 + 0.393278i \(0.128659\pi\)
−0.919420 + 0.393278i \(0.871341\pi\)
\(224\) 0 0
\(225\) 1.72017e9 0.671184
\(226\) 0 0
\(227\) 1.17894e9 6.80660e8i 0.444004 0.256346i −0.261290 0.965260i \(-0.584148\pi\)
0.705295 + 0.708914i \(0.250815\pi\)
\(228\) 0 0
\(229\) −3.23205e9 1.86603e9i −1.17527 0.678541i −0.220352 0.975420i \(-0.570721\pi\)
−0.954915 + 0.296880i \(0.904054\pi\)
\(230\) 0 0
\(231\) −2.37354e8 1.87940e9i −0.0833581 0.660043i
\(232\) 0 0
\(233\) −1.72263e8 + 2.98368e8i −0.0584477 + 0.101234i −0.893769 0.448528i \(-0.851948\pi\)
0.835321 + 0.549762i \(0.185282\pi\)
\(234\) 0 0
\(235\) −1.73352e9 3.00254e9i −0.568404 0.984505i
\(236\) 0 0
\(237\) 8.05477e8i 0.255305i
\(238\) 0 0
\(239\) 3.17982e9 0.974565 0.487283 0.873244i \(-0.337988\pi\)
0.487283 + 0.873244i \(0.337988\pi\)
\(240\) 0 0
\(241\) −4.09977e9 + 2.36701e9i −1.21532 + 0.701667i −0.963914 0.266214i \(-0.914227\pi\)
−0.251409 + 0.967881i \(0.580894\pi\)
\(242\) 0 0
\(243\) −1.93710e8 1.11839e8i −0.0555556 0.0320750i
\(244\) 0 0
\(245\) 4.46911e9 4.37583e9i 1.24038 1.21449i
\(246\) 0 0
\(247\) 8.48913e8 1.47036e9i 0.228074 0.395035i
\(248\) 0 0
\(249\) 1.59625e9 + 2.76478e9i 0.415244 + 0.719223i
\(250\) 0 0
\(251\) 7.03152e9i 1.77155i 0.464112 + 0.885776i \(0.346373\pi\)
−0.464112 + 0.885776i \(0.653627\pi\)
\(252\) 0 0
\(253\) 3.56631e9 0.870437
\(254\) 0 0
\(255\) 4.65465e9 2.68736e9i 1.10084 0.635573i
\(256\) 0 0
\(257\) −1.10931e9 6.40462e8i −0.254286 0.146812i 0.367439 0.930047i \(-0.380235\pi\)
−0.621725 + 0.783236i \(0.713568\pi\)
\(258\) 0 0
\(259\) −5.13289e9 + 6.48243e8i −1.14068 + 0.144058i
\(260\) 0 0
\(261\) −6.20593e8 + 1.07490e9i −0.133735 + 0.231636i
\(262\) 0 0
\(263\) 2.37972e8 + 4.12179e8i 0.0497396 + 0.0861516i 0.889823 0.456305i \(-0.150828\pi\)
−0.840084 + 0.542457i \(0.817494\pi\)
\(264\) 0 0
\(265\) 9.51027e9i 1.92845i
\(266\) 0 0
\(267\) −4.25064e9 −0.836390
\(268\) 0 0
\(269\) −4.95417e9 + 2.86029e9i −0.946154 + 0.546262i −0.891884 0.452264i \(-0.850616\pi\)
−0.0542696 + 0.998526i \(0.517283\pi\)
\(270\) 0 0
\(271\) −5.53293e9 3.19444e9i −1.02584 0.592267i −0.110048 0.993926i \(-0.535100\pi\)
−0.915789 + 0.401659i \(0.868434\pi\)
\(272\) 0 0
\(273\) 4.33345e8 1.03078e9i 0.0780159 0.185573i
\(274\) 0 0
\(275\) 6.63487e9 1.14919e10i 1.16012 2.00938i
\(276\) 0 0
\(277\) −2.63656e9 4.56666e9i −0.447836 0.775675i 0.550409 0.834895i \(-0.314472\pi\)
−0.998245 + 0.0592204i \(0.981139\pi\)
\(278\) 0 0
\(279\) 1.38703e9i 0.228913i
\(280\) 0 0
\(281\) 7.48748e9 1.20091 0.600455 0.799658i \(-0.294986\pi\)
0.600455 + 0.799658i \(0.294986\pi\)
\(282\) 0 0
\(283\) −3.62475e9 + 2.09275e9i −0.565109 + 0.326266i −0.755193 0.655502i \(-0.772457\pi\)
0.190085 + 0.981768i \(0.439124\pi\)
\(284\) 0 0
\(285\) −7.49165e9 4.32531e9i −1.13553 0.655598i
\(286\) 0 0
\(287\) −1.04314e10 + 7.91728e9i −1.53750 + 1.16694i
\(288\) 0 0
\(289\) 2.12254e9 3.67634e9i 0.304273 0.527017i
\(290\) 0 0
\(291\) 9.24495e8 + 1.60127e9i 0.128924 + 0.223302i
\(292\) 0 0
\(293\) 1.12022e9i 0.151997i 0.997108 + 0.0759983i \(0.0242143\pi\)
−0.997108 + 0.0759983i \(0.975786\pi\)
\(294\) 0 0
\(295\) 1.01299e10 1.33757
\(296\) 0 0
\(297\) −1.49432e9 + 8.62746e8i −0.192052 + 0.110881i
\(298\) 0 0
\(299\) 1.82306e9 + 1.05254e9i 0.228095 + 0.131691i
\(300\) 0 0
\(301\) 8.08127e9 + 1.06475e10i 0.984496 + 1.29712i
\(302\) 0 0
\(303\) 2.73922e9 4.74447e9i 0.324980 0.562882i
\(304\) 0 0
\(305\) 1.33894e10 + 2.31911e10i 1.54725 + 2.67992i
\(306\) 0 0
\(307\) 1.02340e10i 1.15210i 0.817413 + 0.576051i \(0.195407\pi\)
−0.817413 + 0.576051i \(0.804593\pi\)
\(308\) 0 0
\(309\) −2.28044e9 −0.250141
\(310\) 0 0
\(311\) 5.99552e9 3.46151e9i 0.640892 0.370019i −0.144066 0.989568i \(-0.546018\pi\)
0.784958 + 0.619549i \(0.212684\pi\)
\(312\) 0 0
\(313\) 4.79188e8 + 2.76659e8i 0.0499262 + 0.0288249i 0.524755 0.851253i \(-0.324157\pi\)
−0.474829 + 0.880078i \(0.657490\pi\)
\(314\) 0 0
\(315\) −5.25194e9 2.20794e9i −0.533430 0.224257i
\(316\) 0 0
\(317\) −6.72093e8 + 1.16410e9i −0.0665568 + 0.115280i −0.897384 0.441251i \(-0.854535\pi\)
0.830827 + 0.556531i \(0.187868\pi\)
\(318\) 0 0
\(319\) 4.78738e9 + 8.29198e9i 0.462312 + 0.800747i
\(320\) 0 0
\(321\) 5.52307e9i 0.520188i
\(322\) 0 0
\(323\) −1.80599e10 −1.65923
\(324\) 0 0
\(325\) 6.78333e9 3.91636e9i 0.608009 0.351034i
\(326\) 0 0
\(327\) −6.11298e8 3.52933e8i −0.0534640 0.0308675i
\(328\) 0 0
\(329\) 9.61326e8 + 7.61194e9i 0.0820516 + 0.649698i
\(330\) 0 0
\(331\) 3.38567e8 5.86414e8i 0.0282054 0.0488532i −0.851578 0.524228i \(-0.824354\pi\)
0.879784 + 0.475374i \(0.157687\pi\)
\(332\) 0 0
\(333\) 2.35627e9 + 4.08118e9i 0.191623 + 0.331901i
\(334\) 0 0
\(335\) 1.50112e10i 1.19189i
\(336\) 0 0
\(337\) −1.73692e10 −1.34667 −0.673333 0.739340i \(-0.735138\pi\)
−0.673333 + 0.739340i \(0.735138\pi\)
\(338\) 0 0
\(339\) −2.81189e9 + 1.62344e9i −0.212911 + 0.122924i
\(340\) 0 0
\(341\) −9.26634e9 5.34992e9i −0.685316 0.395667i
\(342\) 0 0
\(343\) −1.28699e10 + 5.09389e9i −0.929817 + 0.368022i
\(344\) 0 0
\(345\) 5.36282e9 9.28868e9i 0.378545 0.655658i
\(346\) 0 0
\(347\) 8.82405e9 + 1.52837e10i 0.608626 + 1.05417i 0.991467 + 0.130356i \(0.0416122\pi\)
−0.382842 + 0.923814i \(0.625054\pi\)
\(348\) 0 0
\(349\) 9.49559e9i 0.640059i −0.947408 0.320030i \(-0.896307\pi\)
0.947408 0.320030i \(-0.103693\pi\)
\(350\) 0 0
\(351\) −1.01850e9 −0.0671019
\(352\) 0 0
\(353\) 6.12231e9 3.53472e9i 0.394290 0.227644i −0.289727 0.957109i \(-0.593565\pi\)
0.684017 + 0.729466i \(0.260231\pi\)
\(354\) 0 0
\(355\) −1.11991e10 6.46583e9i −0.705134 0.407109i
\(356\) 0 0
\(357\) −1.18003e10 + 1.49028e9i −0.726474 + 0.0917478i
\(358\) 0 0
\(359\) −6.55145e9 + 1.13474e10i −0.394421 + 0.683157i −0.993027 0.117887i \(-0.962388\pi\)
0.598606 + 0.801043i \(0.295721\pi\)
\(360\) 0 0
\(361\) 6.04193e9 + 1.04649e10i 0.355752 + 0.616180i
\(362\) 0 0
\(363\) 3.28622e9i 0.189265i
\(364\) 0 0
\(365\) 2.29642e10 1.29384
\(366\) 0 0
\(367\) 2.12630e10 1.22762e10i 1.17209 0.676707i 0.217919 0.975967i \(-0.430073\pi\)
0.954172 + 0.299260i \(0.0967399\pi\)
\(368\) 0 0
\(369\) 1.03304e10 + 5.96426e9i 0.557200 + 0.321700i
\(370\) 0 0
\(371\) −8.15629e9 + 1.94011e10i −0.430524 + 1.02407i
\(372\) 0 0
\(373\) 5.64618e9 9.77947e9i 0.291689 0.505219i −0.682521 0.730866i \(-0.739116\pi\)
0.974209 + 0.225647i \(0.0724496\pi\)
\(374\) 0 0
\(375\) −1.00443e10 1.73972e10i −0.507919 0.879741i
\(376\) 0 0
\(377\) 5.65168e9i 0.279777i
\(378\) 0 0
\(379\) −3.52545e9 −0.170867 −0.0854335 0.996344i \(-0.527228\pi\)
−0.0854335 + 0.996344i \(0.527228\pi\)
\(380\) 0 0
\(381\) −4.05561e9 + 2.34151e9i −0.192467 + 0.111121i
\(382\) 0 0
\(383\) 2.74394e10 + 1.58422e10i 1.27521 + 0.736240i 0.975963 0.217937i \(-0.0699326\pi\)
0.299243 + 0.954177i \(0.403266\pi\)
\(384\) 0 0
\(385\) −3.50079e10 + 2.65704e10i −1.59339 + 1.20936i
\(386\) 0 0
\(387\) 6.08779e9 1.05444e10i 0.271404 0.470085i
\(388\) 0 0
\(389\) 2.01146e9 + 3.48396e9i 0.0878443 + 0.152151i 0.906600 0.421992i \(-0.138669\pi\)
−0.818755 + 0.574143i \(0.805336\pi\)
\(390\) 0 0
\(391\) 2.23920e10i 0.958043i
\(392\) 0 0
\(393\) −3.63605e8 −0.0152426
\(394\) 0 0
\(395\) 1.61837e10 9.34368e9i 0.664799 0.383822i
\(396\) 0 0
\(397\) −3.37145e10 1.94651e10i −1.35724 0.783600i −0.367985 0.929832i \(-0.619952\pi\)
−0.989250 + 0.146232i \(0.953286\pi\)
\(398\) 0 0
\(399\) 1.15735e10 + 1.52487e10i 0.456641 + 0.601648i
\(400\) 0 0
\(401\) 2.03692e10 3.52804e10i 0.787764 1.36445i −0.139571 0.990212i \(-0.544572\pi\)
0.927334 0.374234i \(-0.122094\pi\)
\(402\) 0 0
\(403\) −3.15790e9 5.46963e9i −0.119723 0.207366i
\(404\) 0 0
\(405\) 5.18940e9i 0.192884i
\(406\) 0 0
\(407\) 3.63535e10 1.32486
\(408\) 0 0
\(409\) −1.08712e10 + 6.27648e9i −0.388493 + 0.224297i −0.681507 0.731812i \(-0.738675\pi\)
0.293014 + 0.956108i \(0.405342\pi\)
\(410\) 0 0
\(411\) −4.48580e9 2.58988e9i −0.157207 0.0907637i
\(412\) 0 0
\(413\) −2.06651e10 8.68769e9i −0.710291 0.298610i
\(414\) 0 0
\(415\) 3.70336e10 6.41440e10i 1.24854 2.16254i
\(416\) 0 0
\(417\) −7.75521e9 1.34324e10i −0.256477 0.444232i
\(418\) 0 0
\(419\) 1.94158e9i 0.0629941i 0.999504 + 0.0314970i \(0.0100275\pi\)
−0.999504 + 0.0314970i \(0.989973\pi\)
\(420\) 0 0
\(421\) 1.38803e9 0.0441846 0.0220923 0.999756i \(-0.492967\pi\)
0.0220923 + 0.999756i \(0.492967\pi\)
\(422\) 0 0
\(423\) 6.05228e9 3.49428e9i 0.189042 0.109143i
\(424\) 0 0
\(425\) −7.21549e10 4.16586e10i −2.21162 1.27688i
\(426\) 0 0
\(427\) −7.42511e9 5.87932e10i −0.223353 1.76854i
\(428\) 0 0
\(429\) −3.92848e9 + 6.80432e9i −0.115983 + 0.200889i
\(430\) 0 0
\(431\) −1.62135e10 2.80826e10i −0.469860 0.813821i 0.529546 0.848281i \(-0.322362\pi\)
−0.999406 + 0.0344602i \(0.989029\pi\)
\(432\) 0 0
\(433\) 4.65333e10i 1.32377i 0.749606 + 0.661884i \(0.230243\pi\)
−0.749606 + 0.661884i \(0.769757\pi\)
\(434\) 0 0
\(435\) 2.87960e10 0.804219
\(436\) 0 0
\(437\) −3.12114e10 + 1.80199e10i −0.855831 + 0.494114i
\(438\) 0 0
\(439\) −4.44106e10 2.56404e10i −1.19572 0.690347i −0.236119 0.971724i \(-0.575876\pi\)
−0.959597 + 0.281377i \(0.909209\pi\)
\(440\) 0 0
\(441\) 8.82042e9 + 9.00845e9i 0.233204 + 0.238175i
\(442\) 0 0
\(443\) 2.09215e10 3.62371e10i 0.543223 0.940891i −0.455493 0.890239i \(-0.650537\pi\)
0.998716 0.0506512i \(-0.0161297\pi\)
\(444\) 0 0
\(445\) 4.93082e10 + 8.54042e10i 1.25742 + 2.17791i
\(446\) 0 0
\(447\) 3.24800e10i 0.813553i
\(448\) 0 0
\(449\) 2.89337e10 0.711900 0.355950 0.934505i \(-0.384157\pi\)
0.355950 + 0.934505i \(0.384157\pi\)
\(450\) 0 0
\(451\) 7.96907e10 4.60095e10i 1.92620 1.11209i
\(452\) 0 0
\(453\) −3.32826e10 1.92157e10i −0.790359 0.456314i
\(454\) 0 0
\(455\) −2.57374e10 + 3.25043e9i −0.600509 + 0.0758394i
\(456\) 0 0
\(457\) −3.38299e10 + 5.85951e10i −0.775597 + 1.34337i 0.158862 + 0.987301i \(0.449218\pi\)
−0.934458 + 0.356072i \(0.884116\pi\)
\(458\) 0 0
\(459\) 5.41696e9 + 9.38245e9i 0.122041 + 0.211381i
\(460\) 0 0
\(461\) 2.13195e10i 0.472035i 0.971749 + 0.236017i \(0.0758422\pi\)
−0.971749 + 0.236017i \(0.924158\pi\)
\(462\) 0 0
\(463\) 5.73662e10 1.24834 0.624168 0.781290i \(-0.285438\pi\)
0.624168 + 0.781290i \(0.285438\pi\)
\(464\) 0 0
\(465\) −2.78684e10 + 1.60898e10i −0.596074 + 0.344144i
\(466\) 0 0
\(467\) −1.40331e10 8.10202e9i −0.295044 0.170343i 0.345171 0.938540i \(-0.387821\pi\)
−0.640214 + 0.768196i \(0.721154\pi\)
\(468\) 0 0
\(469\) 1.28741e10 3.06231e10i 0.266088 0.632933i
\(470\) 0 0
\(471\) −1.12410e10 + 1.94699e10i −0.228413 + 0.395622i
\(472\) 0 0
\(473\) −4.69625e10 8.13414e10i −0.938224 1.62505i
\(474\) 0 0
\(475\) 1.34099e11i 2.63422i
\(476\) 0 0
\(477\) 1.91700e10 0.370296
\(478\) 0 0
\(479\) −8.47162e10 + 4.89109e10i −1.60925 + 0.929103i −0.619716 + 0.784826i \(0.712752\pi\)
−0.989537 + 0.144276i \(0.953915\pi\)
\(480\) 0 0
\(481\) 1.85835e10 + 1.07292e10i 0.347173 + 0.200441i
\(482\) 0 0
\(483\) −1.89065e10 + 1.43497e10i −0.347394 + 0.263666i
\(484\) 0 0
\(485\) 2.14486e10 3.71501e10i 0.387644 0.671418i
\(486\) 0 0
\(487\) 2.47120e10 + 4.28025e10i 0.439332 + 0.760945i 0.997638 0.0686896i \(-0.0218818\pi\)
−0.558306 + 0.829635i \(0.688548\pi\)
\(488\) 0 0
\(489\) 2.84955e10i 0.498357i
\(490\) 0 0
\(491\) 4.36304e10 0.750695 0.375348 0.926884i \(-0.377523\pi\)
0.375348 + 0.926884i \(0.377523\pi\)
\(492\) 0 0
\(493\) 5.20632e10 3.00587e10i 0.881340 0.508842i
\(494\) 0 0
\(495\) 3.46688e10 + 2.00160e10i 0.577454 + 0.333393i
\(496\) 0 0
\(497\) 1.73011e10 + 2.27951e10i 0.283562 + 0.373608i
\(498\) 0 0
\(499\) 1.70928e10 2.96057e10i 0.275684 0.477499i −0.694623 0.719374i \(-0.744429\pi\)
0.970308 + 0.241874i \(0.0777622\pi\)
\(500\) 0 0
\(501\) 4.31589e9 + 7.47534e9i 0.0685045 + 0.118653i
\(502\) 0 0
\(503\) 1.10624e10i 0.172813i −0.996260 0.0864063i \(-0.972462\pi\)
0.996260 0.0864063i \(-0.0275383\pi\)
\(504\) 0 0
\(505\) −1.27102e11 −1.95428
\(506\) 0 0
\(507\) 2.90207e10 1.67551e10i 0.439214 0.253580i
\(508\) 0 0
\(509\) −9.58080e10 5.53148e10i −1.42735 0.824081i −0.430440 0.902619i \(-0.641642\pi\)
−0.996911 + 0.0785379i \(0.974975\pi\)
\(510\) 0 0
\(511\) −4.68473e10 1.96948e10i −0.687069 0.288847i
\(512\) 0 0
\(513\) 8.71859e9 1.51010e10i 0.125886 0.218041i
\(514\) 0 0
\(515\) 2.64536e10 + 4.58189e10i 0.376059 + 0.651353i
\(516\) 0 0
\(517\) 5.39112e10i 0.754600i
\(518\) 0 0
\(519\) −1.57907e10 −0.217636
\(520\) 0 0
\(521\) 1.11862e11 6.45834e10i 1.51820 0.876536i 0.518434 0.855118i \(-0.326515\pi\)
0.999771 0.0214183i \(-0.00681818\pi\)
\(522\) 0 0
\(523\) 4.41818e10 + 2.55084e10i 0.590523 + 0.340939i 0.765304 0.643669i \(-0.222588\pi\)
−0.174781 + 0.984607i \(0.555922\pi\)
\(524\) 0 0
\(525\) 1.10657e10 + 8.76200e10i 0.145660 + 1.15336i
\(526\) 0 0
\(527\) −3.35908e10 + 5.81810e10i −0.435490 + 0.754290i
\(528\) 0 0
\(529\) 1.68131e10 + 2.91212e10i 0.214697 + 0.371866i
\(530\) 0 0
\(531\) 2.04190e10i 0.256836i
\(532\) 0 0
\(533\) 5.43159e10 0.673005
\(534\) 0 0
\(535\) −1.10970e11 + 6.40686e10i −1.35454 + 0.782042i
\(536\) 0 0
\(537\) 2.37090e10 + 1.36884e10i 0.285112 + 0.164609i
\(538\) 0 0
\(539\) 9.42040e10 2.41801e10i 1.11613 0.286485i
\(540\) 0 0
\(541\) −5.42593e10 + 9.39799e10i −0.633410 + 1.09710i 0.353439 + 0.935457i \(0.385012\pi\)
−0.986850 + 0.161641i \(0.948321\pi\)
\(542\) 0 0
\(543\) 3.02588e10 + 5.24098e10i 0.348059 + 0.602856i
\(544\) 0 0
\(545\) 1.63763e10i 0.185623i
\(546\) 0 0
\(547\) −6.18018e10 −0.690322 −0.345161 0.938544i \(-0.612176\pi\)
−0.345161 + 0.938544i \(0.612176\pi\)
\(548\) 0 0
\(549\) −4.67467e10 + 2.69892e10i −0.514590 + 0.297099i
\(550\) 0 0
\(551\) −8.37957e10 4.83795e10i −0.909108 0.524874i
\(552\) 0 0
\(553\) −4.10284e10 + 5.18156e9i −0.438717 + 0.0554064i
\(554\) 0 0
\(555\) 5.46663e10 9.46849e10i 0.576166 0.997950i
\(556\) 0 0
\(557\) 2.68485e10 + 4.65029e10i 0.278932 + 0.483125i 0.971120 0.238593i \(-0.0766862\pi\)
−0.692188 + 0.721718i \(0.743353\pi\)
\(558\) 0 0
\(559\) 5.54410e10i 0.567785i
\(560\) 0 0
\(561\) 8.35751e10 0.843772
\(562\) 0 0
\(563\) −1.24343e11 + 7.17894e10i −1.23762 + 0.714540i −0.968607 0.248596i \(-0.920031\pi\)
−0.269013 + 0.963137i \(0.586697\pi\)
\(564\) 0 0
\(565\) 6.52368e10 + 3.76645e10i 0.640175 + 0.369605i
\(566\) 0 0
\(567\) 4.45058e9 1.05864e10i 0.0430611 0.102428i
\(568\) 0 0
\(569\) 4.80492e10 8.32237e10i 0.458392 0.793958i −0.540484 0.841354i \(-0.681759\pi\)
0.998876 + 0.0473959i \(0.0150922\pi\)
\(570\) 0 0
\(571\) 1.02075e11 + 1.76799e11i 0.960231 + 1.66317i 0.721915 + 0.691981i \(0.243262\pi\)
0.238316 + 0.971188i \(0.423405\pi\)
\(572\) 0 0
\(573\) 7.29580e10i 0.676790i
\(574\) 0 0
\(575\) −1.66266e11 −1.52101
\(576\) 0 0
\(577\) −1.23039e10 + 7.10368e9i −0.111005 + 0.0640885i −0.554474 0.832201i \(-0.687081\pi\)
0.443470 + 0.896289i \(0.353747\pi\)
\(578\) 0 0
\(579\) 7.10213e10 + 4.10041e10i 0.631937 + 0.364849i
\(580\) 0 0
\(581\) −1.30561e11 + 9.90934e10i −1.14580 + 0.869641i
\(582\) 0 0
\(583\) 7.39406e10 1.28069e11i 0.640043 1.10859i
\(584\) 0 0
\(585\) 1.18148e10 + 2.04639e10i 0.100880 + 0.174729i
\(586\) 0 0
\(587\) 6.63318e10i 0.558688i −0.960191 0.279344i \(-0.909883\pi\)
0.960191 0.279344i \(-0.0901170\pi\)
\(588\) 0 0
\(589\) 1.08129e11 0.898421
\(590\) 0 0
\(591\) −7.23428e10 + 4.17672e10i −0.592988 + 0.342362i
\(592\) 0 0
\(593\) 9.13541e10 + 5.27433e10i 0.738770 + 0.426529i 0.821622 0.570033i \(-0.193070\pi\)
−0.0828520 + 0.996562i \(0.526403\pi\)
\(594\) 0 0
\(595\) 1.66829e11 + 2.19805e11i 1.33107 + 1.75376i
\(596\) 0 0
\(597\) −7.03407e10 + 1.21834e11i −0.553745 + 0.959114i
\(598\) 0 0
\(599\) −7.35115e10 1.27326e11i −0.571016 0.989028i −0.996462 0.0840447i \(-0.973216\pi\)
0.425446 0.904984i \(-0.360117\pi\)
\(600\) 0 0
\(601\) 1.86033e11i 1.42591i −0.701210 0.712954i \(-0.747357\pi\)
0.701210 0.712954i \(-0.252643\pi\)
\(602\) 0 0
\(603\) −3.02584e10 −0.228864
\(604\) 0 0
\(605\) 6.60272e10 3.81208e10i 0.492834 0.284538i
\(606\) 0 0
\(607\) −5.85799e10 3.38211e10i −0.431513 0.249134i 0.268478 0.963286i \(-0.413479\pi\)
−0.699991 + 0.714152i \(0.746813\pi\)
\(608\) 0 0
\(609\) −5.87441e10 2.46963e10i −0.427066 0.179541i
\(610\) 0 0
\(611\) 1.59111e10 2.75588e10i 0.114165 0.197740i
\(612\) 0 0
\(613\) −1.19635e11 2.07214e11i −0.847261 1.46750i −0.883643 0.468161i \(-0.844917\pi\)
0.0363824 0.999338i \(-0.488417\pi\)
\(614\) 0 0
\(615\) 2.76746e11i 1.93455i
\(616\) 0 0
\(617\) −3.40881e10 −0.235214 −0.117607 0.993060i \(-0.537522\pi\)
−0.117607 + 0.993060i \(0.537522\pi\)
\(618\) 0 0
\(619\) 8.42286e10 4.86294e10i 0.573716 0.331235i −0.184916 0.982754i \(-0.559201\pi\)
0.758632 + 0.651519i \(0.225868\pi\)
\(620\) 0 0
\(621\) 1.87233e10 + 1.08099e10i 0.125897 + 0.0726870i
\(622\) 0 0
\(623\) −2.73439e10 2.16514e11i −0.181513 1.43725i
\(624\) 0 0
\(625\) −7.94095e10 + 1.37541e11i −0.520418 + 0.901391i
\(626\) 0 0
\(627\) −6.72570e10 1.16493e11i −0.435178 0.753751i
\(628\) 0 0
\(629\) 2.28254e11i 1.45820i
\(630\) 0 0
\(631\) −1.63168e11 −1.02924 −0.514621 0.857418i \(-0.672067\pi\)
−0.514621 + 0.857418i \(0.672067\pi\)
\(632\) 0 0
\(633\) 1.35265e11 7.80954e10i 0.842503 0.486419i
\(634\) 0 0
\(635\) 9.40916e10 + 5.43238e10i 0.578704 + 0.334115i
\(636\) 0 0
\(637\) 5.52923e10 + 1.54423e10i 0.335820 + 0.0937895i
\(638\) 0 0
\(639\) 1.30333e10 2.25743e10i 0.0781718 0.135398i
\(640\) 0 0
\(641\) −2.04255e10 3.53779e10i −0.120987 0.209556i 0.799170 0.601105i \(-0.205273\pi\)
−0.920157 + 0.391549i \(0.871939\pi\)
\(642\) 0 0
\(643\) 1.66499e11i 0.974022i −0.873396 0.487011i \(-0.838087\pi\)
0.873396 0.487011i \(-0.161913\pi\)
\(644\) 0 0
\(645\) −2.82478e11 −1.63210
\(646\) 0 0
\(647\) −4.33764e10 + 2.50434e10i −0.247535 + 0.142914i −0.618635 0.785678i \(-0.712314\pi\)
0.371100 + 0.928593i \(0.378981\pi\)
\(648\) 0 0
\(649\) 1.36413e11 + 7.87580e10i 0.768912 + 0.443931i
\(650\) 0 0
\(651\) 7.06510e10 8.92265e9i 0.393364 0.0496786i
\(652\) 0 0
\(653\) −2.99393e10 + 5.18564e10i −0.164660 + 0.285200i −0.936535 0.350575i \(-0.885986\pi\)
0.771874 + 0.635775i \(0.219319\pi\)
\(654\) 0 0
\(655\) 4.21788e9 + 7.30558e9i 0.0229155 + 0.0396908i
\(656\) 0 0
\(657\) 4.62893e10i 0.248439i
\(658\) 0 0
\(659\) −5.62292e10 −0.298140 −0.149070 0.988827i \(-0.547628\pi\)
−0.149070 + 0.988827i \(0.547628\pi\)
\(660\) 0 0
\(661\) 1.99084e11 1.14941e11i 1.04287 0.602102i 0.122226 0.992502i \(-0.460997\pi\)
0.920645 + 0.390400i \(0.127663\pi\)
\(662\) 0 0
\(663\) 4.27226e10 + 2.46659e10i 0.221107 + 0.127656i
\(664\) 0 0
\(665\) 1.72124e11 4.09425e11i 0.880147 2.09357i
\(666\) 0 0
\(667\) 5.99843e10 1.03896e11i 0.303064 0.524922i
\(668\) 0 0
\(669\) 4.54824e10 + 7.87779e10i 0.227059 + 0.393278i
\(670\) 0 0
\(671\) 4.16400e11i 2.05410i
\(672\) 0 0
\(673\) 9.84906e10 0.480103 0.240052 0.970760i \(-0.422836\pi\)
0.240052 + 0.970760i \(0.422836\pi\)
\(674\) 0 0
\(675\) 6.96669e10 4.02222e10i 0.335592 0.193754i
\(676\) 0 0
\(677\) 1.28763e11 + 7.43413e10i 0.612965 + 0.353896i 0.774125 0.633033i \(-0.218190\pi\)
−0.161160 + 0.986928i \(0.551523\pi\)
\(678\) 0 0
\(679\) −7.56165e10 + 5.73917e10i −0.355744 + 0.270004i
\(680\) 0 0
\(681\) 3.18313e10 5.51334e10i 0.148001 0.256346i
\(682\) 0 0
\(683\) 1.76448e11 + 3.05616e11i 0.810836 + 1.40441i 0.912280 + 0.409568i \(0.134320\pi\)
−0.101444 + 0.994841i \(0.532346\pi\)
\(684\) 0 0
\(685\) 1.20172e11i 0.545811i
\(686\) 0 0
\(687\) −1.74531e11 −0.783511
\(688\) 0 0
\(689\) 7.55951e10 4.36449e10i 0.335442 0.193667i
\(690\) 0 0
\(691\) −2.91147e11 1.68094e11i −1.27703 0.737291i −0.300725 0.953711i \(-0.597229\pi\)
−0.976300 + 0.216420i \(0.930562\pi\)
\(692\) 0 0
\(693\) −5.35583e10 7.05659e10i −0.232217 0.305958i
\(694\) 0 0
\(695\) −1.79924e11 + 3.11637e11i −0.771168 + 1.33570i
\(696\) 0 0
\(697\) −2.88882e11 5.00358e11i −1.22402 2.12007i
\(698\) 0 0
\(699\) 1.61119e10i 0.0674896i
\(700\) 0 0
\(701\) 4.11369e11 1.70357 0.851784 0.523893i \(-0.175521\pi\)
0.851784 + 0.523893i \(0.175521\pi\)
\(702\) 0 0
\(703\) −3.18156e11 + 1.83687e11i −1.30262 + 0.752070i
\(704\) 0 0
\(705\) −1.40415e11 8.10687e10i −0.568404 0.328168i
\(706\) 0 0
\(707\) 2.59290e11 + 1.09007e11i 1.03778 + 0.436290i
\(708\) 0 0
\(709\) −6.95122e10 + 1.20399e11i −0.275091 + 0.476472i −0.970158 0.242473i \(-0.922041\pi\)
0.695067 + 0.718945i \(0.255375\pi\)
\(710\) 0 0
\(711\) 1.88342e10 + 3.26218e10i 0.0737003 + 0.127653i
\(712\) 0 0
\(713\) 1.34066e11i 0.518751i
\(714\) 0 0
\(715\) 1.82284e11 0.697469
\(716\) 0 0
\(717\) 1.28783e11 7.43527e10i 0.487283 0.281333i
\(718\) 0 0
\(719\) −1.01094e11 5.83667e10i −0.378277 0.218398i 0.298791 0.954318i \(-0.403417\pi\)
−0.677068 + 0.735920i \(0.736750\pi\)
\(720\) 0 0
\(721\) −1.46699e10 1.16159e11i −0.0542857 0.429843i
\(722\) 0 0
\(723\) −1.10694e11 + 1.91727e11i −0.405108 + 0.701667i
\(724\) 0 0
\(725\) −2.23193e11 3.86581e11i −0.807846 1.39923i
\(726\) 0 0
\(727\) 2.43338e11i 0.871109i −0.900162 0.435555i \(-0.856552\pi\)
0.900162 0.435555i \(-0.143448\pi\)
\(728\) 0 0
\(729\) −1.04604e10 −0.0370370
\(730\) 0 0
\(731\) −5.10722e11 + 2.94865e11i −1.78861 + 1.03265i
\(732\) 0 0
\(733\) 4.20029e11 + 2.42504e11i 1.45500 + 0.840046i 0.998759 0.0498097i \(-0.0158615\pi\)
0.456243 + 0.889855i \(0.349195\pi\)
\(734\) 0 0
\(735\) 7.86802e10 2.81721e11i 0.269598 0.965315i
\(736\) 0 0
\(737\) −1.16710e11 + 2.02147e11i −0.395582 + 0.685169i
\(738\) 0 0
\(739\) −1.98657e11 3.44083e11i −0.666078 1.15368i −0.978992 0.203900i \(-0.934638\pi\)
0.312913 0.949782i \(-0.398695\pi\)
\(740\) 0 0
\(741\) 7.93995e10i 0.263357i
\(742\) 0 0
\(743\) 2.20639e11 0.723980 0.361990 0.932182i \(-0.382097\pi\)
0.361990 + 0.932182i \(0.382097\pi\)
\(744\) 0 0
\(745\) −6.52591e11 + 3.76774e11i −2.11844 + 1.22308i
\(746\) 0 0
\(747\) 1.29296e11 + 7.46492e10i 0.415244 + 0.239741i
\(748\) 0 0
\(749\) 2.81327e11 3.55294e10i 0.893892 0.112891i
\(750\) 0 0
\(751\) 2.44854e8 4.24099e8i 0.000769745 0.00133324i −0.865640 0.500666i \(-0.833088\pi\)
0.866410 + 0.499333i \(0.166422\pi\)
\(752\) 0 0
\(753\) 1.64416e11 + 2.84776e11i 0.511403 + 0.885776i
\(754\) 0 0
\(755\) 8.91624e11i 2.74406i
\(756\) 0 0
\(757\) −6.35724e10 −0.193591 −0.0967955 0.995304i \(-0.530859\pi\)
−0.0967955 + 0.995304i \(0.530859\pi\)
\(758\) 0 0
\(759\) 1.44436e11 8.33900e10i 0.435219 0.251274i
\(760\) 0 0
\(761\) 5.15892e10 + 2.97850e10i 0.153823 + 0.0888095i 0.574936 0.818199i \(-0.305027\pi\)
−0.421113 + 0.907008i \(0.638360\pi\)
\(762\) 0 0
\(763\) 1.40449e10 3.34079e10i 0.0414399 0.0985715i
\(764\) 0 0
\(765\) 1.25675e11 2.17676e11i 0.366948 0.635573i
\(766\) 0 0
\(767\) 4.64884e10 + 8.05203e10i 0.134327 + 0.232661i
\(768\) 0 0
\(769\) 3.28466e11i 0.939259i 0.882864 + 0.469629i \(0.155612\pi\)
−0.882864 + 0.469629i \(0.844388\pi\)
\(770\) 0 0
\(771\) −5.99029e10 −0.169524
\(772\) 0 0
\(773\) 4.19975e11 2.42473e11i 1.17627 0.679117i 0.221118 0.975247i \(-0.429030\pi\)
0.955148 + 0.296130i \(0.0956962\pi\)
\(774\) 0 0
\(775\) 4.32007e11 + 2.49420e11i 1.19752 + 0.691391i
\(776\) 0 0
\(777\) −1.92725e11 + 1.46275e11i −0.528753 + 0.401315i
\(778\) 0 0
\(779\) −4.64955e11 + 8.05325e11i −1.26259 + 2.18686i
\(780\) 0 0
\(781\) −1.00541e11 1.74143e11i −0.270234 0.468060i