Properties

Label 84.12.i.b.25.4
Level $84$
Weight $12$
Character 84.25
Analytic conductor $64.541$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 581500324 x^{14} - 481772282104 x^{13} + 132272376701859942 x^{12} + \)\(18\!\cdots\!08\)\( x^{11} - \)\(14\!\cdots\!08\)\( x^{10} - \)\(25\!\cdots\!56\)\( x^{9} + \)\(80\!\cdots\!79\)\( x^{8} + \)\(11\!\cdots\!68\)\( x^{7} - \)\(19\!\cdots\!68\)\( x^{6} + \)\(59\!\cdots\!08\)\( x^{5} + \)\(21\!\cdots\!06\)\( x^{4} - \)\(37\!\cdots\!04\)\( x^{3} - \)\(31\!\cdots\!28\)\( x^{2} + \)\(25\!\cdots\!24\)\( x + \)\(79\!\cdots\!77\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 25.4
Root \(2396.04 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.12.i.b.37.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 + 210.444i) q^{3} +(-1332.77 - 2308.42i) q^{5} +(43648.5 + 8493.30i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 + 210.444i) q^{3} +(-1332.77 - 2308.42i) q^{5} +(43648.5 + 8493.30i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(262991. - 455515. i) q^{11} -1.10180e6 q^{13} +647726. q^{15} +(-222021. + 384552. i) q^{17} +(-1.58519e6 - 2.74562e6i) q^{19} +(-7.09066e6 + 8.15363e6i) q^{21} +(2.38816e7 + 4.13641e7i) q^{23} +(2.08615e7 - 3.61332e7i) q^{25} +1.43489e7 q^{27} -1.65232e8 q^{29} +(-8.05562e7 + 1.39527e8i) q^{31} +(6.39069e7 + 1.10690e8i) q^{33} +(-3.85672e7 - 1.12079e8i) q^{35} +(-1.73311e8 - 3.00184e8i) q^{37} +(1.33868e8 - 2.31866e8i) q^{39} -1.07369e9 q^{41} +1.10803e9 q^{43} +(-7.86987e7 + 1.36310e8i) q^{45} +(-4.49033e7 - 7.77748e7i) q^{47} +(1.83305e9 + 7.41439e8i) q^{49} +(-5.39512e7 - 9.34462e7i) q^{51} +(1.97953e8 - 3.42864e8i) q^{53} -1.40203e9 q^{55} +7.70401e8 q^{57} +(3.65401e9 - 6.32894e9i) q^{59} +(-6.05057e9 - 1.04799e10i) q^{61} +(-8.54370e8 - 2.48285e9i) q^{63} +(1.46844e9 + 2.54341e9i) q^{65} +(8.63592e9 - 1.49578e10i) q^{67} -1.16064e10 q^{69} -1.31065e10 q^{71} +(-7.39348e9 + 1.28059e10i) q^{73} +(5.06935e9 + 8.78037e9i) q^{75} +(1.53480e10 - 1.76489e10i) q^{77} +(-1.45406e10 - 2.51850e10i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} +2.43778e9 q^{83} +1.18361e9 q^{85} +(2.00757e10 - 3.47721e10i) q^{87} +(-4.46315e10 - 7.73040e10i) q^{89} +(-4.80917e10 - 9.35787e9i) q^{91} +(-1.95752e10 - 3.39052e10i) q^{93} +(-4.22537e9 + 7.31856e9i) q^{95} +6.63296e10 q^{97} -3.10588e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} + O(q^{10}) \) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
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
\(3\) −121.500 + 210.444i −0.288675 + 0.500000i
\(4\) 0 0
\(5\) −1332.77 2308.42i −0.190730 0.330355i 0.754762 0.655999i \(-0.227752\pi\)
−0.945492 + 0.325644i \(0.894419\pi\)
\(6\) 0 0
\(7\) 43648.5 + 8493.30i 0.981590 + 0.191002i
\(8\) 0 0
\(9\) −29524.5 51137.9i −0.166667 0.288675i
\(10\) 0 0
\(11\) 262991. 455515.i 0.492359 0.852791i −0.507602 0.861591i \(-0.669468\pi\)
0.999961 + 0.00880080i \(0.00280142\pi\)
\(12\) 0 0
\(13\) −1.10180e6 −0.823024 −0.411512 0.911404i \(-0.634999\pi\)
−0.411512 + 0.911404i \(0.634999\pi\)
\(14\) 0 0
\(15\) 647726. 0.220236
\(16\) 0 0
\(17\) −222021. + 384552.i −0.0379250 + 0.0656880i −0.884365 0.466796i \(-0.845408\pi\)
0.846440 + 0.532484i \(0.178741\pi\)
\(18\) 0 0
\(19\) −1.58519e6 2.74562e6i −0.146871 0.254388i 0.783199 0.621772i \(-0.213587\pi\)
−0.930069 + 0.367384i \(0.880253\pi\)
\(20\) 0 0
\(21\) −7.09066e6 + 8.15363e6i −0.378861 + 0.435657i
\(22\) 0 0
\(23\) 2.38816e7 + 4.13641e7i 0.773677 + 1.34005i 0.935535 + 0.353234i \(0.114918\pi\)
−0.161857 + 0.986814i \(0.551748\pi\)
\(24\) 0 0
\(25\) 2.08615e7 3.61332e7i 0.427244 0.740008i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) −1.65232e8 −1.49591 −0.747954 0.663750i \(-0.768964\pi\)
−0.747954 + 0.663750i \(0.768964\pi\)
\(30\) 0 0
\(31\) −8.05562e7 + 1.39527e8i −0.505370 + 0.875327i 0.494611 + 0.869115i \(0.335311\pi\)
−0.999981 + 0.00621203i \(0.998023\pi\)
\(32\) 0 0
\(33\) 6.39069e7 + 1.10690e8i 0.284264 + 0.492359i
\(34\) 0 0
\(35\) −3.85672e7 1.12079e8i −0.124121 0.360703i
\(36\) 0 0
\(37\) −1.73311e8 3.00184e8i −0.410882 0.711669i 0.584104 0.811679i \(-0.301446\pi\)
−0.994986 + 0.100010i \(0.968113\pi\)
\(38\) 0 0
\(39\) 1.33868e8 2.31866e8i 0.237586 0.411512i
\(40\) 0 0
\(41\) −1.07369e9 −1.44734 −0.723668 0.690148i \(-0.757545\pi\)
−0.723668 + 0.690148i \(0.757545\pi\)
\(42\) 0 0
\(43\) 1.10803e9 1.14941 0.574706 0.818360i \(-0.305117\pi\)
0.574706 + 0.818360i \(0.305117\pi\)
\(44\) 0 0
\(45\) −7.86987e7 + 1.36310e8i −0.0635768 + 0.110118i
\(46\) 0 0
\(47\) −4.49033e7 7.77748e7i −0.0285588 0.0494653i 0.851393 0.524529i \(-0.175758\pi\)
−0.879952 + 0.475063i \(0.842425\pi\)
\(48\) 0 0
\(49\) 1.83305e9 + 7.41439e8i 0.927037 + 0.374970i
\(50\) 0 0
\(51\) −5.39512e7 9.34462e7i −0.0218960 0.0379250i
\(52\) 0 0
\(53\) 1.97953e8 3.42864e8i 0.0650196 0.112617i −0.831683 0.555251i \(-0.812622\pi\)
0.896703 + 0.442633i \(0.145956\pi\)
\(54\) 0 0
\(55\) −1.40203e9 −0.375631
\(56\) 0 0
\(57\) 7.70401e8 0.169592
\(58\) 0 0
\(59\) 3.65401e9 6.32894e9i 0.665402 1.15251i −0.313774 0.949498i \(-0.601593\pi\)
0.979176 0.203012i \(-0.0650732\pi\)
\(60\) 0 0
\(61\) −6.05057e9 1.04799e10i −0.917238 1.58870i −0.803591 0.595182i \(-0.797080\pi\)
−0.113647 0.993521i \(-0.536253\pi\)
\(62\) 0 0
\(63\) −8.54370e8 2.48285e9i −0.108461 0.315194i
\(64\) 0 0
\(65\) 1.46844e9 + 2.54341e9i 0.156976 + 0.271890i
\(66\) 0 0
\(67\) 8.63592e9 1.49578e10i 0.781442 1.35350i −0.149659 0.988738i \(-0.547818\pi\)
0.931101 0.364760i \(-0.118849\pi\)
\(68\) 0 0
\(69\) −1.16064e10 −0.893366
\(70\) 0 0
\(71\) −1.31065e10 −0.862113 −0.431056 0.902325i \(-0.641859\pi\)
−0.431056 + 0.902325i \(0.641859\pi\)
\(72\) 0 0
\(73\) −7.39348e9 + 1.28059e10i −0.417420 + 0.722993i −0.995679 0.0928606i \(-0.970399\pi\)
0.578259 + 0.815853i \(0.303732\pi\)
\(74\) 0 0
\(75\) 5.06935e9 + 8.78037e9i 0.246669 + 0.427244i
\(76\) 0 0
\(77\) 1.53480e10 1.76489e10i 0.646179 0.743049i
\(78\) 0 0
\(79\) −1.45406e10 2.51850e10i −0.531658 0.920859i −0.999317 0.0369500i \(-0.988236\pi\)
0.467659 0.883909i \(-0.345098\pi\)
\(80\) 0 0
\(81\) −1.74339e9 + 3.01964e9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 2.43778e9 0.0679305 0.0339652 0.999423i \(-0.489186\pi\)
0.0339652 + 0.999423i \(0.489186\pi\)
\(84\) 0 0
\(85\) 1.18361e9 0.0289338
\(86\) 0 0
\(87\) 2.00757e10 3.47721e10i 0.431832 0.747954i
\(88\) 0 0
\(89\) −4.46315e10 7.73040e10i −0.847220 1.46743i −0.883679 0.468094i \(-0.844941\pi\)
0.0364584 0.999335i \(-0.488392\pi\)
\(90\) 0 0
\(91\) −4.80917e10 9.35787e9i −0.807872 0.157199i
\(92\) 0 0
\(93\) −1.95752e10 3.39052e10i −0.291776 0.505370i
\(94\) 0 0
\(95\) −4.22537e9 + 7.31856e9i −0.0560254 + 0.0970389i
\(96\) 0 0
\(97\) 6.63296e10 0.784265 0.392132 0.919909i \(-0.371738\pi\)
0.392132 + 0.919909i \(0.371738\pi\)
\(98\) 0 0
\(99\) −3.10588e10 −0.328239
\(100\) 0 0
\(101\) 1.40959e10 2.44149e10i 0.133452 0.231146i −0.791553 0.611101i \(-0.790727\pi\)
0.925005 + 0.379954i \(0.124060\pi\)
\(102\) 0 0
\(103\) −7.47509e10 1.29472e11i −0.635348 1.10045i −0.986441 0.164114i \(-0.947523\pi\)
0.351093 0.936340i \(-0.385810\pi\)
\(104\) 0 0
\(105\) 2.82722e10 + 5.50133e9i 0.216182 + 0.0420655i
\(106\) 0 0
\(107\) −1.31786e11 2.28259e11i −0.908358 1.57332i −0.816345 0.577564i \(-0.804003\pi\)
−0.0920128 0.995758i \(-0.529330\pi\)
\(108\) 0 0
\(109\) 2.35713e10 4.08266e10i 0.146736 0.254155i −0.783283 0.621665i \(-0.786456\pi\)
0.930019 + 0.367511i \(0.119790\pi\)
\(110\) 0 0
\(111\) 8.42293e10 0.474446
\(112\) 0 0
\(113\) 7.07560e10 0.361270 0.180635 0.983550i \(-0.442185\pi\)
0.180635 + 0.983550i \(0.442185\pi\)
\(114\) 0 0
\(115\) 6.36572e10 1.10258e11i 0.295128 0.511176i
\(116\) 0 0
\(117\) 3.25299e10 + 5.63435e10i 0.137171 + 0.237586i
\(118\) 0 0
\(119\) −1.29570e10 + 1.48994e10i −0.0497733 + 0.0572350i
\(120\) 0 0
\(121\) 4.32686e9 + 7.49434e9i 0.0151654 + 0.0262672i
\(122\) 0 0
\(123\) 1.30454e11 2.25953e11i 0.417810 0.723668i
\(124\) 0 0
\(125\) −2.41368e11 −0.707414
\(126\) 0 0
\(127\) −9.35541e10 −0.251271 −0.125635 0.992076i \(-0.540097\pi\)
−0.125635 + 0.992076i \(0.540097\pi\)
\(128\) 0 0
\(129\) −1.34626e11 + 2.33179e11i −0.331806 + 0.574706i
\(130\) 0 0
\(131\) 3.03929e10 + 5.26420e10i 0.0688303 + 0.119218i 0.898387 0.439205i \(-0.144740\pi\)
−0.829556 + 0.558423i \(0.811407\pi\)
\(132\) 0 0
\(133\) −4.58716e10 1.33306e11i −0.0955784 0.277757i
\(134\) 0 0
\(135\) −1.91238e10 3.31234e10i −0.0367061 0.0635768i
\(136\) 0 0
\(137\) 1.72230e11 2.98311e11i 0.304891 0.528087i −0.672346 0.740237i \(-0.734713\pi\)
0.977237 + 0.212150i \(0.0680465\pi\)
\(138\) 0 0
\(139\) 3.54339e11 0.579211 0.289606 0.957146i \(-0.406476\pi\)
0.289606 + 0.957146i \(0.406476\pi\)
\(140\) 0 0
\(141\) 2.18230e10 0.0329769
\(142\) 0 0
\(143\) −2.89763e11 + 5.01884e11i −0.405223 + 0.701867i
\(144\) 0 0
\(145\) 2.20216e11 + 3.81425e11i 0.285315 + 0.494180i
\(146\) 0 0
\(147\) −3.78748e11 + 2.95671e11i −0.455098 + 0.355274i
\(148\) 0 0
\(149\) 1.87394e11 + 3.24576e11i 0.209041 + 0.362069i 0.951413 0.307919i \(-0.0996325\pi\)
−0.742372 + 0.669988i \(0.766299\pi\)
\(150\) 0 0
\(151\) −2.29692e11 + 3.97838e11i −0.238107 + 0.412413i −0.960171 0.279413i \(-0.909860\pi\)
0.722064 + 0.691826i \(0.243194\pi\)
\(152\) 0 0
\(153\) 2.62203e10 0.0252833
\(154\) 0 0
\(155\) 4.29451e11 0.385558
\(156\) 0 0
\(157\) −6.37048e11 + 1.10340e12i −0.532996 + 0.923176i 0.466261 + 0.884647i \(0.345601\pi\)
−0.999257 + 0.0385292i \(0.987733\pi\)
\(158\) 0 0
\(159\) 4.81025e10 + 8.33160e10i 0.0375391 + 0.0650196i
\(160\) 0 0
\(161\) 6.91077e11 + 2.00831e12i 0.503482 + 1.46315i
\(162\) 0 0
\(163\) 8.84049e11 + 1.53122e12i 0.601790 + 1.04233i 0.992550 + 0.121838i \(0.0388787\pi\)
−0.390761 + 0.920492i \(0.627788\pi\)
\(164\) 0 0
\(165\) 1.70346e11 2.95048e11i 0.108435 0.187816i
\(166\) 0 0
\(167\) −1.36833e12 −0.815174 −0.407587 0.913166i \(-0.633630\pi\)
−0.407587 + 0.913166i \(0.633630\pi\)
\(168\) 0 0
\(169\) −5.78208e11 −0.322632
\(170\) 0 0
\(171\) −9.36037e10 + 1.62126e11i −0.0489569 + 0.0847959i
\(172\) 0 0
\(173\) −1.14381e12 1.98114e12i −0.561179 0.971990i −0.997394 0.0721478i \(-0.977015\pi\)
0.436215 0.899842i \(-0.356319\pi\)
\(174\) 0 0
\(175\) 1.21746e12 1.39998e12i 0.560721 0.644780i
\(176\) 0 0
\(177\) 8.87925e11 + 1.53793e12i 0.384170 + 0.665402i
\(178\) 0 0
\(179\) −1.28321e12 + 2.22258e12i −0.521922 + 0.903995i 0.477753 + 0.878494i \(0.341451\pi\)
−0.999675 + 0.0255010i \(0.991882\pi\)
\(180\) 0 0
\(181\) 4.37998e12 1.67587 0.837934 0.545771i \(-0.183763\pi\)
0.837934 + 0.545771i \(0.183763\pi\)
\(182\) 0 0
\(183\) 2.94058e12 1.05914
\(184\) 0 0
\(185\) −4.61968e11 + 8.00152e11i −0.156735 + 0.271474i
\(186\) 0 0
\(187\) 1.16779e11 + 2.02268e11i 0.0373454 + 0.0646842i
\(188\) 0 0
\(189\) 6.26308e11 + 1.21870e11i 0.188907 + 0.0367583i
\(190\) 0 0
\(191\) −8.48818e10 1.47020e11i −0.0241619 0.0418496i 0.853692 0.520779i \(-0.174358\pi\)
−0.877854 + 0.478929i \(0.841025\pi\)
\(192\) 0 0
\(193\) −1.61580e11 + 2.79865e11i −0.0434333 + 0.0752286i −0.886925 0.461914i \(-0.847163\pi\)
0.843492 + 0.537142i \(0.180496\pi\)
\(194\) 0 0
\(195\) −7.13661e11 −0.181260
\(196\) 0 0
\(197\) 8.26787e11 0.198531 0.0992657 0.995061i \(-0.468351\pi\)
0.0992657 + 0.995061i \(0.468351\pi\)
\(198\) 0 0
\(199\) −2.12706e12 + 3.68418e12i −0.483157 + 0.836853i −0.999813 0.0193401i \(-0.993843\pi\)
0.516656 + 0.856193i \(0.327177\pi\)
\(200\) 0 0
\(201\) 2.09853e12 + 3.63476e12i 0.451166 + 0.781442i
\(202\) 0 0
\(203\) −7.21213e12 1.40336e12i −1.46837 0.285721i
\(204\) 0 0
\(205\) 1.43099e12 + 2.47854e12i 0.276051 + 0.478134i
\(206\) 0 0
\(207\) 1.41018e12 2.44251e12i 0.257892 0.446683i
\(208\) 0 0
\(209\) −1.66756e12 −0.289253
\(210\) 0 0
\(211\) 6.58675e12 1.08422 0.542110 0.840307i \(-0.317626\pi\)
0.542110 + 0.840307i \(0.317626\pi\)
\(212\) 0 0
\(213\) 1.59243e12 2.75818e12i 0.248871 0.431056i
\(214\) 0 0
\(215\) −1.47675e12 2.55780e12i −0.219228 0.379713i
\(216\) 0 0
\(217\) −4.70120e12 + 5.40597e12i −0.663255 + 0.762685i
\(218\) 0 0
\(219\) −1.79662e12 3.11183e12i −0.240998 0.417420i
\(220\) 0 0
\(221\) 2.44622e11 4.23698e11i 0.0312132 0.0540628i
\(222\) 0 0
\(223\) −7.33282e11 −0.0890419 −0.0445209 0.999008i \(-0.514176\pi\)
−0.0445209 + 0.999008i \(0.514176\pi\)
\(224\) 0 0
\(225\) −2.46370e12 −0.284829
\(226\) 0 0
\(227\) 5.85905e11 1.01482e12i 0.0645186 0.111749i −0.831962 0.554833i \(-0.812782\pi\)
0.896480 + 0.443084i \(0.146115\pi\)
\(228\) 0 0
\(229\) −7.12391e12 1.23390e13i −0.747521 1.29474i −0.949008 0.315253i \(-0.897911\pi\)
0.201487 0.979491i \(-0.435423\pi\)
\(230\) 0 0
\(231\) 1.84932e12 + 5.37423e12i 0.184989 + 0.537589i
\(232\) 0 0
\(233\) −7.16183e12 1.24047e13i −0.683229 1.18339i −0.973990 0.226592i \(-0.927242\pi\)
0.290760 0.956796i \(-0.406092\pi\)
\(234\) 0 0
\(235\) −1.19692e11 + 2.07312e11i −0.0108941 + 0.0188691i
\(236\) 0 0
\(237\) 7.06672e12 0.613906
\(238\) 0 0
\(239\) −1.00149e13 −0.830728 −0.415364 0.909655i \(-0.636346\pi\)
−0.415364 + 0.909655i \(0.636346\pi\)
\(240\) 0 0
\(241\) 6.58907e12 1.14126e13i 0.522072 0.904255i −0.477598 0.878578i \(-0.658493\pi\)
0.999670 0.0256770i \(-0.00817415\pi\)
\(242\) 0 0
\(243\) −4.23644e11 7.33773e11i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) −7.31483e11 5.21963e12i −0.0529408 0.377769i
\(246\) 0 0
\(247\) 1.74655e12 + 3.02511e12i 0.120878 + 0.209367i
\(248\) 0 0
\(249\) −2.96190e11 + 5.13016e11i −0.0196098 + 0.0339652i
\(250\) 0 0
\(251\) −2.25032e13 −1.42574 −0.712868 0.701298i \(-0.752604\pi\)
−0.712868 + 0.701298i \(0.752604\pi\)
\(252\) 0 0
\(253\) 2.51226e13 1.52371
\(254\) 0 0
\(255\) −1.43809e11 + 2.49084e11i −0.00835247 + 0.0144669i
\(256\) 0 0
\(257\) −6.53000e12 1.13103e13i −0.363313 0.629276i 0.625191 0.780472i \(-0.285021\pi\)
−0.988504 + 0.151195i \(0.951688\pi\)
\(258\) 0 0
\(259\) −5.01523e12 1.45746e13i −0.267388 0.777046i
\(260\) 0 0
\(261\) 4.87839e12 + 8.44962e12i 0.249318 + 0.431832i
\(262\) 0 0
\(263\) 1.14385e13 1.98121e13i 0.560547 0.970897i −0.436901 0.899509i \(-0.643924\pi\)
0.997449 0.0713872i \(-0.0227426\pi\)
\(264\) 0 0
\(265\) −1.05530e12 −0.0496048
\(266\) 0 0
\(267\) 2.16909e13 0.978286
\(268\) 0 0
\(269\) −6.89726e12 + 1.19464e13i −0.298565 + 0.517130i −0.975808 0.218630i \(-0.929841\pi\)
0.677243 + 0.735760i \(0.263175\pi\)
\(270\) 0 0
\(271\) −5.69926e11 9.87141e11i −0.0236858 0.0410250i 0.853940 0.520372i \(-0.174207\pi\)
−0.877625 + 0.479347i \(0.840873\pi\)
\(272\) 0 0
\(273\) 7.81245e12 8.98363e12i 0.311812 0.358556i
\(274\) 0 0
\(275\) −1.09728e13 1.90054e13i −0.420715 0.728699i
\(276\) 0 0
\(277\) 2.28587e13 3.95924e13i 0.842195 1.45873i −0.0458392 0.998949i \(-0.514596\pi\)
0.888035 0.459777i \(-0.152070\pi\)
\(278\) 0 0
\(279\) 9.51352e12 0.336913
\(280\) 0 0
\(281\) −3.91820e13 −1.33414 −0.667072 0.744994i \(-0.732452\pi\)
−0.667072 + 0.744994i \(0.732452\pi\)
\(282\) 0 0
\(283\) −1.93169e12 + 3.34578e12i −0.0632574 + 0.109565i −0.895920 0.444216i \(-0.853482\pi\)
0.832662 + 0.553781i \(0.186816\pi\)
\(284\) 0 0
\(285\) −1.02677e12 1.77841e12i −0.0323463 0.0560254i
\(286\) 0 0
\(287\) −4.68651e13 9.11921e12i −1.42069 0.276444i
\(288\) 0 0
\(289\) 1.70374e13 + 2.95096e13i 0.497123 + 0.861043i
\(290\) 0 0
\(291\) −8.05904e12 + 1.39587e13i −0.226398 + 0.392132i
\(292\) 0 0
\(293\) −9.78633e12 −0.264757 −0.132379 0.991199i \(-0.542261\pi\)
−0.132379 + 0.991199i \(0.542261\pi\)
\(294\) 0 0
\(295\) −1.94798e13 −0.507649
\(296\) 0 0
\(297\) 3.77364e12 6.53614e12i 0.0947545 0.164120i
\(298\) 0 0
\(299\) −2.63126e13 4.55748e13i −0.636755 1.10289i
\(300\) 0 0
\(301\) 4.83639e13 + 9.41084e12i 1.12825 + 0.219539i
\(302\) 0 0
\(303\) 3.42531e12 + 5.93282e12i 0.0770488 + 0.133452i
\(304\) 0 0
\(305\) −1.61280e13 + 2.79346e13i −0.349890 + 0.606028i
\(306\) 0 0
\(307\) 9.68832e12 0.202762 0.101381 0.994848i \(-0.467674\pi\)
0.101381 + 0.994848i \(0.467674\pi\)
\(308\) 0 0
\(309\) 3.63289e13 0.733636
\(310\) 0 0
\(311\) −1.64052e13 + 2.84146e13i −0.319741 + 0.553808i −0.980434 0.196849i \(-0.936929\pi\)
0.660693 + 0.750656i \(0.270263\pi\)
\(312\) 0 0
\(313\) 4.65288e13 + 8.05902e13i 0.875443 + 1.51631i 0.856290 + 0.516496i \(0.172764\pi\)
0.0191533 + 0.999817i \(0.493903\pi\)
\(314\) 0 0
\(315\) −4.59280e12 + 5.28132e12i −0.0834391 + 0.0959476i
\(316\) 0 0
\(317\) 1.88239e13 + 3.26039e13i 0.330281 + 0.572063i 0.982567 0.185910i \(-0.0595232\pi\)
−0.652286 + 0.757973i \(0.726190\pi\)
\(318\) 0 0
\(319\) −4.34546e13 + 7.52656e13i −0.736524 + 1.27570i
\(320\) 0 0
\(321\) 6.40478e13 1.04888
\(322\) 0 0
\(323\) 1.40778e12 0.0222803
\(324\) 0 0
\(325\) −2.29851e13 + 3.98114e13i −0.351632 + 0.609044i
\(326\) 0 0
\(327\) 5.72782e12 + 9.92087e12i 0.0847182 + 0.146736i
\(328\) 0 0
\(329\) −1.29940e12 3.77613e12i −0.0185851 0.0540094i
\(330\) 0 0
\(331\) −5.00419e13 8.66751e13i −0.692276 1.19906i −0.971090 0.238713i \(-0.923275\pi\)
0.278814 0.960345i \(-0.410059\pi\)
\(332\) 0 0
\(333\) −1.02339e13 + 1.77256e13i −0.136961 + 0.237223i
\(334\) 0 0
\(335\) −4.60387e13 −0.596179
\(336\) 0 0
\(337\) 8.73473e13 1.09467 0.547337 0.836912i \(-0.315642\pi\)
0.547337 + 0.836912i \(0.315642\pi\)
\(338\) 0 0
\(339\) −8.59685e12 + 1.48902e13i −0.104290 + 0.180635i
\(340\) 0 0
\(341\) 4.23712e13 + 7.33890e13i 0.497647 + 0.861950i
\(342\) 0 0
\(343\) 7.37128e13 + 4.79314e13i 0.838350 + 0.545133i
\(344\) 0 0
\(345\) 1.54687e13 + 2.67926e13i 0.170392 + 0.295128i
\(346\) 0 0
\(347\) −3.55238e13 + 6.15290e13i −0.379059 + 0.656550i −0.990926 0.134411i \(-0.957086\pi\)
0.611866 + 0.790961i \(0.290419\pi\)
\(348\) 0 0
\(349\) −7.50390e13 −0.775796 −0.387898 0.921702i \(-0.626799\pi\)
−0.387898 + 0.921702i \(0.626799\pi\)
\(350\) 0 0
\(351\) −1.58096e13 −0.158391
\(352\) 0 0
\(353\) −6.79326e12 + 1.17663e13i −0.0659655 + 0.114256i −0.897122 0.441783i \(-0.854346\pi\)
0.831156 + 0.556039i \(0.187679\pi\)
\(354\) 0 0
\(355\) 1.74679e13 + 3.02552e13i 0.164431 + 0.284803i
\(356\) 0 0
\(357\) −1.56122e12 4.53701e12i −0.0142492 0.0414090i
\(358\) 0 0
\(359\) −7.02740e13 1.21718e14i −0.621978 1.07730i −0.989117 0.147131i \(-0.952996\pi\)
0.367139 0.930166i \(-0.380337\pi\)
\(360\) 0 0
\(361\) 5.32195e13 9.21789e13i 0.456858 0.791301i
\(362\) 0 0
\(363\) −2.10285e12 −0.0175115
\(364\) 0 0
\(365\) 3.94152e13 0.318459
\(366\) 0 0
\(367\) −1.75641e13 + 3.04219e13i −0.137709 + 0.238519i −0.926629 0.375977i \(-0.877307\pi\)
0.788920 + 0.614496i \(0.210641\pi\)
\(368\) 0 0
\(369\) 3.17003e13 + 5.49065e13i 0.241223 + 0.417810i
\(370\) 0 0
\(371\) 1.15524e13 1.32842e13i 0.0853326 0.0981251i
\(372\) 0 0
\(373\) 8.94455e13 + 1.54924e14i 0.641446 + 1.11102i 0.985110 + 0.171924i \(0.0549985\pi\)
−0.343664 + 0.939093i \(0.611668\pi\)
\(374\) 0 0
\(375\) 2.93262e13 5.07944e13i 0.204213 0.353707i
\(376\) 0 0
\(377\) 1.82052e14 1.23117
\(378\) 0 0
\(379\) −3.33296e13 −0.218935 −0.109467 0.993990i \(-0.534915\pi\)
−0.109467 + 0.993990i \(0.534915\pi\)
\(380\) 0 0
\(381\) 1.13668e13 1.96879e13i 0.0725357 0.125635i
\(382\) 0 0
\(383\) 1.37824e13 + 2.38718e13i 0.0854539 + 0.148010i 0.905585 0.424166i \(-0.139433\pi\)
−0.820131 + 0.572176i \(0.806099\pi\)
\(384\) 0 0
\(385\) −6.11964e13 1.19078e13i −0.368716 0.0717462i
\(386\) 0 0
\(387\) −3.27141e13 5.66624e13i −0.191569 0.331806i
\(388\) 0 0
\(389\) −1.16390e14 + 2.01594e14i −0.662513 + 1.14751i 0.317440 + 0.948278i \(0.397177\pi\)
−0.979953 + 0.199228i \(0.936156\pi\)
\(390\) 0 0
\(391\) −2.12089e13 −0.117367
\(392\) 0 0
\(393\) −1.47709e13 −0.0794784
\(394\) 0 0
\(395\) −3.87584e13 + 6.71316e13i −0.202807 + 0.351272i
\(396\) 0 0
\(397\) 7.15857e13 + 1.23990e14i 0.364316 + 0.631014i 0.988666 0.150131i \(-0.0479694\pi\)
−0.624350 + 0.781145i \(0.714636\pi\)
\(398\) 0 0
\(399\) 3.36268e13 + 6.54324e12i 0.166470 + 0.0323923i
\(400\) 0 0
\(401\) −1.44586e14 2.50431e14i −0.696359 1.20613i −0.969721 0.244217i \(-0.921469\pi\)
0.273362 0.961911i \(-0.411864\pi\)
\(402\) 0 0
\(403\) 8.87564e13 1.53731e14i 0.415932 0.720415i
\(404\) 0 0
\(405\) 9.29416e12 0.0423845
\(406\) 0 0
\(407\) −1.82318e14 −0.809206
\(408\) 0 0
\(409\) 4.66276e13 8.07613e13i 0.201449 0.348919i −0.747547 0.664209i \(-0.768768\pi\)
0.948995 + 0.315290i \(0.102102\pi\)
\(410\) 0 0
\(411\) 4.18518e13 + 7.24895e13i 0.176029 + 0.304891i
\(412\) 0 0
\(413\) 2.13246e14 2.45214e14i 0.873283 1.00420i
\(414\) 0 0
\(415\) −3.24900e12 5.62742e12i −0.0129564 0.0224412i
\(416\) 0 0
\(417\) −4.30521e13 + 7.45685e13i −0.167204 + 0.289606i
\(418\) 0 0
\(419\) −4.50519e14 −1.70426 −0.852130 0.523330i \(-0.824689\pi\)
−0.852130 + 0.523330i \(0.824689\pi\)
\(420\) 0 0
\(421\) 1.82722e14 0.673347 0.336673 0.941621i \(-0.390698\pi\)
0.336673 + 0.941621i \(0.390698\pi\)
\(422\) 0 0
\(423\) −2.65150e12 + 4.59253e12i −0.00951961 + 0.0164884i
\(424\) 0 0
\(425\) 9.26341e12 + 1.60447e13i 0.0324065 + 0.0561296i
\(426\) 0 0
\(427\) −1.75089e14 5.08821e14i −0.596907 1.73465i
\(428\) 0 0
\(429\) −7.04123e13 1.21958e14i −0.233956 0.405223i
\(430\) 0 0
\(431\) 7.13121e13 1.23516e14i 0.230961 0.400036i −0.727130 0.686500i \(-0.759146\pi\)
0.958091 + 0.286463i \(0.0924797\pi\)
\(432\) 0 0
\(433\) −1.67830e14 −0.529892 −0.264946 0.964263i \(-0.585354\pi\)
−0.264946 + 0.964263i \(0.585354\pi\)
\(434\) 0 0
\(435\) −1.07025e14 −0.329454
\(436\) 0 0
\(437\) 7.57135e13 1.31140e14i 0.227261 0.393628i
\(438\) 0 0
\(439\) −2.55296e14 4.42186e14i −0.747291 1.29435i −0.949117 0.314925i \(-0.898021\pi\)
0.201826 0.979421i \(-0.435313\pi\)
\(440\) 0 0
\(441\) −1.62044e13 1.15629e14i −0.0462615 0.330108i
\(442\) 0 0
\(443\) 1.38404e14 + 2.39723e14i 0.385415 + 0.667559i 0.991827 0.127592i \(-0.0407248\pi\)
−0.606411 + 0.795151i \(0.707391\pi\)
\(444\) 0 0
\(445\) −1.18967e14 + 2.06057e14i −0.323181 + 0.559766i
\(446\) 0 0
\(447\) −9.10735e13 −0.241380
\(448\) 0 0
\(449\) 7.18277e14 1.85754 0.928768 0.370661i \(-0.120869\pi\)
0.928768 + 0.370661i \(0.120869\pi\)
\(450\) 0 0
\(451\) −2.82372e14 + 4.89083e14i −0.712609 + 1.23428i
\(452\) 0 0
\(453\) −5.58151e13 9.66746e13i −0.137471 0.238107i
\(454\) 0 0
\(455\) 4.24932e13 + 1.23488e14i 0.102154 + 0.296867i
\(456\) 0 0
\(457\) −2.69134e14 4.66153e14i −0.631581 1.09393i −0.987229 0.159310i \(-0.949073\pi\)
0.355648 0.934620i \(-0.384260\pi\)
\(458\) 0 0
\(459\) −3.18576e12 + 5.51791e12i −0.00729867 + 0.0126417i
\(460\) 0 0
\(461\) 3.08940e14 0.691065 0.345532 0.938407i \(-0.387698\pi\)
0.345532 + 0.938407i \(0.387698\pi\)
\(462\) 0 0
\(463\) −3.55334e14 −0.776142 −0.388071 0.921630i \(-0.626858\pi\)
−0.388071 + 0.921630i \(0.626858\pi\)
\(464\) 0 0
\(465\) −5.21783e13 + 9.03755e13i −0.111301 + 0.192779i
\(466\) 0 0
\(467\) 1.09007e14 + 1.88806e14i 0.227097 + 0.393344i 0.956947 0.290264i \(-0.0937432\pi\)
−0.729849 + 0.683608i \(0.760410\pi\)
\(468\) 0 0
\(469\) 5.03986e14 5.79540e14i 1.02558 1.17932i
\(470\) 0 0
\(471\) −1.54803e14 2.68126e14i −0.307725 0.532996i
\(472\) 0 0
\(473\) 2.91403e14 5.04724e14i 0.565923 0.980207i
\(474\) 0 0
\(475\) −1.32278e14 −0.250999
\(476\) 0 0
\(477\) −2.33778e13 −0.0433464
\(478\) 0 0
\(479\) 3.15790e14 5.46965e14i 0.572207 0.991092i −0.424132 0.905601i \(-0.639421\pi\)
0.996339 0.0854915i \(-0.0272460\pi\)
\(480\) 0 0
\(481\) 1.90954e14 + 3.30741e14i 0.338166 + 0.585721i
\(482\) 0 0
\(483\) −5.06604e14 9.85770e13i −0.876919 0.170634i
\(484\) 0 0
\(485\) −8.84020e13 1.53117e14i −0.149583 0.259085i
\(486\) 0 0
\(487\) −1.36327e14 + 2.36125e14i −0.225513 + 0.390600i −0.956473 0.291820i \(-0.905739\pi\)
0.730960 + 0.682420i \(0.239072\pi\)
\(488\) 0 0
\(489\) −4.29648e14 −0.694887
\(490\) 0 0
\(491\) 1.03331e15 1.63411 0.817055 0.576560i \(-0.195605\pi\)
0.817055 + 0.576560i \(0.195605\pi\)
\(492\) 0 0
\(493\) 3.66850e13 6.35403e13i 0.0567324 0.0982633i
\(494\) 0 0
\(495\) 4.13941e13 + 7.16968e13i 0.0626052 + 0.108435i
\(496\) 0 0
\(497\) −5.72077e14 1.11317e14i −0.846241 0.164665i
\(498\) 0 0
\(499\) −1.89945e14 3.28995e14i −0.274837 0.476031i 0.695257 0.718761i \(-0.255291\pi\)
−0.970094 + 0.242730i \(0.921957\pi\)
\(500\) 0 0
\(501\) 1.66252e14 2.87957e14i 0.235321 0.407587i
\(502\) 0 0
\(503\) 2.88084e14 0.398928 0.199464 0.979905i \(-0.436080\pi\)
0.199464 + 0.979905i \(0.436080\pi\)
\(504\) 0 0
\(505\) −7.51465e13 −0.101814
\(506\) 0 0
\(507\) 7.02523e13 1.21681e14i 0.0931358 0.161316i
\(508\) 0 0
\(509\) 7.02577e14 + 1.21690e15i 0.911478 + 1.57873i 0.811977 + 0.583690i \(0.198392\pi\)
0.0995016 + 0.995037i \(0.468275\pi\)
\(510\) 0 0
\(511\) −4.31478e14 + 4.96162e14i −0.547828 + 0.629954i
\(512\) 0 0
\(513\) −2.27457e13 3.93967e13i −0.0282653 0.0489569i
\(514\) 0 0
\(515\) −1.99251e14 + 3.45113e14i −0.242360 + 0.419780i
\(516\) 0 0
\(517\) −4.72368e13 −0.0562448
\(518\) 0 0
\(519\) 5.55893e14 0.647993
\(520\) 0 0
\(521\) −8.31749e14 + 1.44063e15i −0.949259 + 1.64417i −0.202269 + 0.979330i \(0.564832\pi\)
−0.746990 + 0.664835i \(0.768502\pi\)
\(522\) 0 0
\(523\) 5.23224e13 + 9.06250e13i 0.0584693 + 0.101272i 0.893778 0.448509i \(-0.148045\pi\)
−0.835309 + 0.549781i \(0.814711\pi\)
\(524\) 0 0
\(525\) 1.46695e14 + 4.26305e14i 0.160524 + 0.466492i
\(526\) 0 0
\(527\) −3.57704e13 6.19561e13i −0.0383323 0.0663936i
\(528\) 0 0
\(529\) −6.64255e14 + 1.15052e15i −0.697154 + 1.20751i
\(530\) 0 0
\(531\) −4.31532e14 −0.443601
\(532\) 0 0
\(533\) 1.18299e15 1.19119
\(534\) 0 0
\(535\) −3.51279e14 + 6.08434e14i −0.346503 + 0.600161i
\(536\) 0 0
\(537\) −3.11820e14 5.40087e14i −0.301332 0.521922i
\(538\) 0 0
\(539\) 8.19814e14 6.39991e14i 0.776206 0.605948i
\(540\) 0 0
\(541\) 9.40174e13 + 1.62843e14i 0.0872215 + 0.151072i 0.906336 0.422558i \(-0.138868\pi\)
−0.819114 + 0.573630i \(0.805535\pi\)
\(542\) 0 0
\(543\) −5.32168e14 + 9.21741e14i −0.483782 + 0.837934i
\(544\) 0 0
\(545\) −1.25660e14 −0.111948
\(546\) 0 0
\(547\) 2.21322e15 1.93238 0.966192 0.257824i \(-0.0830056\pi\)
0.966192 + 0.257824i \(0.0830056\pi\)
\(548\) 0 0
\(549\) −3.57280e14 + 6.18827e14i −0.305746 + 0.529568i
\(550\) 0 0
\(551\) 2.61923e14 + 4.53665e14i 0.219705 + 0.380541i
\(552\) 0 0
\(553\) −4.20770e14 1.22279e15i −0.345985 1.00545i
\(554\) 0 0
\(555\) −1.12258e14 1.94437e14i −0.0904913 0.156735i
\(556\) 0 0
\(557\) −4.08922e14 + 7.08274e14i −0.323174 + 0.559755i −0.981141 0.193292i \(-0.938083\pi\)
0.657967 + 0.753047i \(0.271417\pi\)
\(558\) 0 0
\(559\) −1.22082e15 −0.945993
\(560\) 0 0
\(561\) −5.67548e13 −0.0431228
\(562\) 0 0
\(563\) −1.06151e15 + 1.83858e15i −0.790909 + 1.36989i 0.134495 + 0.990914i \(0.457059\pi\)
−0.925405 + 0.378981i \(0.876275\pi\)
\(564\) 0 0
\(565\) −9.43014e13 1.63335e14i −0.0689051 0.119347i
\(566\) 0 0
\(567\) −1.01743e14 + 1.16996e14i −0.0729119 + 0.0838423i
\(568\) 0 0
\(569\) 4.39692e14 + 7.61570e14i 0.309052 + 0.535294i 0.978155 0.207876i \(-0.0666549\pi\)
−0.669103 + 0.743169i \(0.733322\pi\)
\(570\) 0 0
\(571\) 3.97661e14 6.88769e14i 0.274166 0.474870i −0.695758 0.718276i \(-0.744931\pi\)
0.969924 + 0.243406i \(0.0782648\pi\)
\(572\) 0 0
\(573\) 4.12526e13 0.0278998
\(574\) 0 0
\(575\) 1.99282e15 1.32220
\(576\) 0 0
\(577\) −8.87379e14 + 1.53699e15i −0.577620 + 1.00047i 0.418132 + 0.908386i \(0.362685\pi\)
−0.995752 + 0.0920805i \(0.970648\pi\)
\(578\) 0 0
\(579\) −3.92640e13 6.80072e13i −0.0250762 0.0434333i
\(580\) 0 0
\(581\) 1.06405e14 + 2.07048e13i 0.0666799 + 0.0129748i
\(582\) 0 0
\(583\) −1.04120e14 1.80341e14i −0.0640260 0.110896i
\(584\) 0 0
\(585\) 8.67098e13 1.50186e14i 0.0523252 0.0906299i
\(586\) 0 0
\(587\) 1.91619e15 1.13482 0.567412 0.823434i \(-0.307945\pi\)
0.567412 + 0.823434i \(0.307945\pi\)
\(588\) 0 0
\(589\) 5.10786e14 0.296896
\(590\) 0 0
\(591\) −1.00455e14 + 1.73992e14i −0.0573111 + 0.0992657i
\(592\) 0 0
\(593\) 2.37770e14 + 4.11829e14i 0.133154 + 0.230630i 0.924891 0.380233i \(-0.124156\pi\)
−0.791736 + 0.610863i \(0.790823\pi\)
\(594\) 0 0
\(595\) 5.16629e13 + 1.00528e13i 0.0284011 + 0.00552640i
\(596\) 0 0
\(597\) −5.16877e14 8.95256e14i −0.278951 0.483157i
\(598\) 0 0
\(599\) 1.06635e15 1.84697e15i 0.565006 0.978618i −0.432044 0.901853i \(-0.642207\pi\)
0.997049 0.0767657i \(-0.0244593\pi\)
\(600\) 0 0
\(601\) 3.19165e12 0.00166037 0.000830187 1.00000i \(-0.499736\pi\)
0.000830187 1.00000i \(0.499736\pi\)
\(602\) 0 0
\(603\) −1.01988e15 −0.520962
\(604\) 0 0
\(605\) 1.15334e13 1.99765e13i 0.00578500 0.0100199i
\(606\) 0 0
\(607\) 6.33721e14 + 1.09764e15i 0.312148 + 0.540656i 0.978827 0.204689i \(-0.0656183\pi\)
−0.666679 + 0.745345i \(0.732285\pi\)
\(608\) 0 0
\(609\) 1.17160e15 1.34724e15i 0.566742 0.651704i
\(610\) 0 0
\(611\) 4.94743e13 + 8.56919e13i 0.0235046 + 0.0407111i
\(612\) 0 0
\(613\) 5.75304e14 9.96455e14i 0.268451 0.464970i −0.700011 0.714132i \(-0.746822\pi\)
0.968462 + 0.249162i \(0.0801550\pi\)
\(614\) 0 0
\(615\) −6.95460e14 −0.318756
\(616\) 0 0
\(617\) −1.65065e14 −0.0743169 −0.0371584 0.999309i \(-0.511831\pi\)
−0.0371584 + 0.999309i \(0.511831\pi\)
\(618\) 0 0
\(619\) −1.48618e15 + 2.57414e15i −0.657313 + 1.13850i 0.323995 + 0.946059i \(0.394974\pi\)
−0.981308 + 0.192441i \(0.938360\pi\)
\(620\) 0 0
\(621\) 3.42675e14 + 5.93530e14i 0.148894 + 0.257892i
\(622\) 0 0
\(623\) −1.29153e15 3.75327e15i −0.551342 1.60223i
\(624\) 0 0
\(625\) −6.96942e14 1.20714e15i −0.292319 0.506310i
\(626\) 0 0
\(627\) 2.02609e14 3.50929e14i 0.0835000 0.144626i
\(628\) 0 0
\(629\) 1.53915e14 0.0623309
\(630\) 0 0
\(631\) 4.28671e15 1.70594 0.852968 0.521964i \(-0.174800\pi\)
0.852968 + 0.521964i \(0.174800\pi\)
\(632\) 0 0
\(633\) −8.00290e14 + 1.38614e15i −0.312987 + 0.542110i
\(634\) 0 0
\(635\) 1.24686e14 + 2.15962e14i 0.0479250 + 0.0830085i
\(636\) 0 0
\(637\) −2.01965e15 8.16914e14i −0.762973 0.308610i
\(638\) 0 0
\(639\) 3.86961e14 + 6.70237e14i 0.143685 + 0.248871i
\(640\) 0 0
\(641\) −1.32146e15 + 2.28884e15i −0.482321 + 0.835404i −0.999794 0.0202954i \(-0.993539\pi\)
0.517473 + 0.855699i \(0.326873\pi\)
\(642\) 0 0
\(643\) −2.07428e15 −0.744228 −0.372114 0.928187i \(-0.621367\pi\)
−0.372114 + 0.928187i \(0.621367\pi\)
\(644\) 0 0
\(645\) 7.17700e14 0.253142
\(646\) 0 0
\(647\) −1.01990e15 + 1.76651e15i −0.353657 + 0.612552i −0.986887 0.161412i \(-0.948395\pi\)
0.633230 + 0.773964i \(0.281729\pi\)
\(648\) 0 0
\(649\) −1.92195e15 3.32891e15i −0.655233 1.13490i
\(650\) 0 0
\(651\) −5.66459e14 1.64617e15i −0.189877 0.551796i
\(652\) 0 0
\(653\) −2.93480e15 5.08322e15i −0.967289 1.67539i −0.703336 0.710858i \(-0.748307\pi\)
−0.263953 0.964536i \(-0.585026\pi\)
\(654\) 0 0
\(655\) 8.10133e13 1.40319e14i 0.0262561 0.0454768i
\(656\) 0 0
\(657\) 8.73155e14 0.278280
\(658\) 0 0
\(659\) 4.41751e15 1.38455 0.692274 0.721634i \(-0.256609\pi\)
0.692274 + 0.721634i \(0.256609\pi\)
\(660\) 0 0
\(661\) −5.04436e13 + 8.73709e13i −0.0155488 + 0.0269314i −0.873695 0.486474i \(-0.838283\pi\)
0.858146 + 0.513405i \(0.171616\pi\)
\(662\) 0 0
\(663\) 5.94432e13 + 1.02959e14i 0.0180209 + 0.0312132i
\(664\) 0 0
\(665\) −2.46590e14 + 2.83557e14i −0.0735286 + 0.0845514i
\(666\) 0 0
\(667\) −3.94600e15 6.83467e15i −1.15735 2.00459i
\(668\) 0 0
\(669\) 8.90938e13 1.54315e14i 0.0257042 0.0445209i
\(670\) 0 0
\(671\) −6.36499e15 −1.80644
\(672\) 0 0
\(673\) 2.37415e15 0.662866 0.331433 0.943479i \(-0.392468\pi\)
0.331433 + 0.943479i \(0.392468\pi\)
\(674\) 0 0
\(675\) 2.99340e14 5.18472e14i 0.0822231 0.142415i
\(676\) 0 0
\(677\) −1.65318e15 2.86340e15i −0.446769 0.773827i 0.551405 0.834238i \(-0.314092\pi\)
−0.998174 + 0.0604114i \(0.980759\pi\)
\(678\) 0 0
\(679\) 2.89519e15 + 5.63357e14i 0.769826 + 0.149796i
\(680\) 0 0
\(681\) 1.42375e14 + 2.46601e14i 0.0372498 + 0.0645186i
\(682\) 0 0
\(683\) 1.56905e15 2.71767e15i 0.403946 0.699654i −0.590253 0.807219i \(-0.700972\pi\)
0.994198 + 0.107564i \(0.0343052\pi\)
\(684\) 0 0
\(685\) −9.18170e14 −0.232608
\(686\) 0 0
\(687\) 3.46222e15 0.863163
\(688\) 0 0
\(689\) −2.18103e14 + 3.77766e14i −0.0535127 + 0.0926867i
\(690\) 0 0
\(691\) 3.74263e15 + 6.48243e15i 0.903749 + 1.56534i 0.822588 + 0.568638i \(0.192529\pi\)
0.0811608 + 0.996701i \(0.474137\pi\)
\(692\) 0 0
\(693\) −1.35567e15 2.63791e14i −0.322196 0.0626942i
\(694\) 0 0
\(695\) −4.72251e14 8.17963e14i −0.110473 0.191345i
\(696\) 0 0
\(697\) 2.38383e14 4.12892e14i 0.0548903 0.0950727i
\(698\) 0 0
\(699\) 3.48065e15 0.788925
\(700\) 0 0
\(701\) −4.02232e15 −0.897487 −0.448743 0.893661i \(-0.648128\pi\)
−0.448743 + 0.893661i \(0.648128\pi\)
\(702\) 0 0
\(703\) −5.49461e14 + 9.51695e14i −0.120693 + 0.209047i
\(704\) 0 0
\(705\) −2.90850e13 5.03768e13i −0.00628969 0.0108941i
\(706\) 0 0
\(707\) 8.22630e14 9.45952e14i 0.175145 0.201401i
\(708\) 0 0
\(709\) −6.43811e14 1.11511e15i −0.134960 0.233757i 0.790622 0.612304i \(-0.209757\pi\)
−0.925582 + 0.378547i \(0.876424\pi\)
\(710\) 0 0
\(711\) −8.58606e14 + 1.48715e15i −0.177219 + 0.306953i
\(712\) 0 0
\(713\) −7.69524e15 −1.56397
\(714\) 0 0
\(715\) 1.54475e15 0.309153
\(716\) 0 0
\(717\) 1.21681e15 2.10758e15i 0.239810 0.415364i
\(718\) 0 0
\(719\) −9.68896e14 1.67818e15i −0.188048 0.325708i 0.756552 0.653934i \(-0.226883\pi\)
−0.944599 + 0.328226i \(0.893549\pi\)
\(720\) 0 0
\(721\) −2.16312e15 6.28615e15i −0.413462 1.20155i
\(722\) 0 0
\(723\) 1.60114e15 + 2.77326e15i 0.301418 + 0.522072i
\(724\) 0 0
\(725\) −3.44699e15 + 5.97036e15i −0.639118 + 1.10698i
\(726\) 0 0
\(727\) 8.16531e15 1.49119 0.745596 0.666398i \(-0.232165\pi\)
0.745596 + 0.666398i \(0.232165\pi\)
\(728\) 0 0
\(729\) 2.05891e14 0.0370370
\(730\) 0 0
\(731\) −2.46007e14 + 4.26096e14i −0.0435914 + 0.0755026i
\(732\) 0 0
\(733\) 4.09691e15 + 7.09605e15i 0.715129 + 1.23864i 0.962910 + 0.269824i \(0.0869655\pi\)
−0.247781 + 0.968816i \(0.579701\pi\)
\(734\) 0 0
\(735\) 1.18732e15 + 4.80249e14i 0.204167 + 0.0825822i
\(736\) 0 0
\(737\) −4.54234e15 7.86757e15i −0.769500 1.33281i
\(738\) 0 0
\(739\) −2.53817e14 + 4.39624e14i −0.0423620 + 0.0733731i −0.886429 0.462865i \(-0.846822\pi\)
0.844067 + 0.536238i \(0.180155\pi\)
\(740\) 0 0
\(741\) −8.48823e14 −0.139578
\(742\) 0 0
\(743\) 7.56283e15 1.22531 0.612655 0.790350i \(-0.290101\pi\)
0.612655 + 0.790350i \(0.290101\pi\)
\(744\) 0 0
\(745\) 4.99506e14 8.65169e14i 0.0797409 0.138115i
\(746\) 0 0
\(747\) −7.19742e13 1.24663e14i −0.0113217 0.0196098i
\(748\) 0 0
\(749\) −3.81357e15 1.10825e16i −0.591128 1.71785i
\(750\) 0 0
\(751\) −1.98511e15 3.43832e15i −0.303226 0.525202i 0.673639 0.739061i \(-0.264730\pi\)
−0.976865 + 0.213858i \(0.931397\pi\)
\(752\) 0 0
\(753\) 2.73414e15 4.73567e15i 0.411575 0.712868i
\(754\) 0 0
\(755\) 1.22450e15 0.181657
\(756\) 0 0
\(757\) 5.28767e15 0.773103 0.386551 0.922268i \(-0.373666\pi\)
0.386551 + 0.922268i \(0.373666\pi\)
\(758\) 0 0
\(759\) −3.05240e15 + 5.28690e15i −0.439857 + 0.761854i
\(760\) 0 0
\(761\) 7.14612e14 + 1.23774e15i 0.101497 + 0.175798i 0.912302 0.409519i \(-0.134303\pi\)
−0.810804 + 0.585317i \(0.800970\pi\)
\(762\) 0 0
\(763\) 1.37560e15 1.58182e15i 0.192579 0.221449i
\(764\) 0 0
\(765\) −3.49456e13 6.05275e13i −0.00482230 0.00835247i
\(766\) 0 0
\(767\) −4.02597e15 + 6.97319e15i −0.547642 + 0.948543i
\(768\) 0 0
\(769\) −5.17246e15 −0.693589 −0.346795 0.937941i \(-0.612730\pi\)
−0.346795 + 0.937941i \(0.612730\pi\)
\(770\) 0 0
\(771\) 3.17358e15 0.419518
\(772\) 0 0
\(773\) −6.71899e15 + 1.16376e16i −0.875622 + 1.51662i −0.0195238 + 0.999809i \(0.506215\pi\)
−0.856098 + 0.516813i \(0.827118\pi\)
\(774\) 0 0
\(775\) 3.36105e15 + 5.82151e15i 0.431833 + 0.747956i
\(776\) 0