Properties

Label 84.12.i.b.25.3
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: \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) Copy content Toggle raw display
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 25.3
Root \(2410.13 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.12.i.b.37.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 + 210.444i) q^{3} +(-1339.81 - 2320.63i) q^{5} +(-28039.7 - 34512.4i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 + 210.444i) q^{3} +(-1339.81 - 2320.63i) q^{5} +(-28039.7 - 34512.4i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(-239334. + 414539. i) q^{11} -1.17059e6 q^{13} +651149. q^{15} +(-2.40839e6 + 4.17145e6i) q^{17} +(-4.55281e6 - 7.88570e6i) q^{19} +(1.06697e7 - 1.70754e6i) q^{21} +(-4.21644e6 - 7.30309e6i) q^{23} +(2.08239e7 - 3.60680e7i) q^{25} +1.43489e7 q^{27} +3.65821e7 q^{29} +(-1.20947e7 + 2.09487e7i) q^{31} +(-5.81582e7 - 1.00733e8i) q^{33} +(-4.25223e7 + 1.11310e8i) q^{35} +(-1.66789e8 - 2.88888e8i) q^{37} +(1.42226e8 - 2.46343e8i) q^{39} +5.86887e7 q^{41} +8.57155e8 q^{43} +(-7.91147e7 + 1.37031e8i) q^{45} +(4.75883e8 + 8.24254e8i) q^{47} +(-4.04880e8 + 1.93543e9i) q^{49} +(-5.85239e8 - 1.01366e9i) q^{51} +(-9.09651e8 + 1.57556e9i) q^{53} +1.28265e9 q^{55} +2.21267e9 q^{57} +(8.43761e8 - 1.46144e9i) q^{59} +(3.82941e9 + 6.63273e9i) q^{61} +(-9.37033e8 + 2.45285e9i) q^{63} +(1.56837e9 + 2.71649e9i) q^{65} +(-2.92346e9 + 5.06358e9i) q^{67} +2.04919e9 q^{69} +1.03360e10 q^{71} +(4.61314e9 - 7.99018e9i) q^{73} +(5.06020e9 + 8.76452e9i) q^{75} +(2.10176e10 - 3.36355e9i) q^{77} +(9.94865e9 + 1.72316e10i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} +4.78020e10 q^{83} +1.29072e10 q^{85} +(-4.44472e9 + 7.69849e9i) q^{87} +(-9.70762e9 - 1.68141e10i) q^{89} +(3.28229e10 + 4.03997e10i) q^{91} +(-2.93902e9 - 5.09054e9i) q^{93} +(-1.21998e10 + 2.11307e10i) q^{95} +8.32856e10 q^{97} +2.82649e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) −1339.81 2320.63i −0.191739 0.332101i 0.754088 0.656773i \(-0.228079\pi\)
−0.945826 + 0.324673i \(0.894746\pi\)
\(6\) 0 0
\(7\) −28039.7 34512.4i −0.630571 0.776132i
\(8\) 0 0
\(9\) −29524.5 51137.9i −0.166667 0.288675i
\(10\) 0 0
\(11\) −239334. + 414539.i −0.448069 + 0.776079i −0.998260 0.0589601i \(-0.981222\pi\)
0.550191 + 0.835039i \(0.314555\pi\)
\(12\) 0 0
\(13\) −1.17059e6 −0.874410 −0.437205 0.899362i \(-0.644032\pi\)
−0.437205 + 0.899362i \(0.644032\pi\)
\(14\) 0 0
\(15\) 651149. 0.221401
\(16\) 0 0
\(17\) −2.40839e6 + 4.17145e6i −0.411394 + 0.712555i −0.995042 0.0994514i \(-0.968291\pi\)
0.583649 + 0.812006i \(0.301625\pi\)
\(18\) 0 0
\(19\) −4.55281e6 7.88570e6i −0.421827 0.730626i 0.574291 0.818651i \(-0.305278\pi\)
−0.996118 + 0.0880250i \(0.971944\pi\)
\(20\) 0 0
\(21\) 1.06697e7 1.70754e6i 0.570096 0.0912354i
\(22\) 0 0
\(23\) −4.21644e6 7.30309e6i −0.136598 0.236594i 0.789609 0.613610i \(-0.210283\pi\)
−0.926207 + 0.377016i \(0.876950\pi\)
\(24\) 0 0
\(25\) 2.08239e7 3.60680e7i 0.426473 0.738672i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) 3.65821e7 0.331192 0.165596 0.986194i \(-0.447045\pi\)
0.165596 + 0.986194i \(0.447045\pi\)
\(30\) 0 0
\(31\) −1.20947e7 + 2.09487e7i −0.0758765 + 0.131422i −0.901467 0.432848i \(-0.857509\pi\)
0.825591 + 0.564270i \(0.190842\pi\)
\(32\) 0 0
\(33\) −5.81582e7 1.00733e8i −0.258693 0.448069i
\(34\) 0 0
\(35\) −4.25223e7 + 1.11310e8i −0.136849 + 0.358227i
\(36\) 0 0
\(37\) −1.66789e8 2.88888e8i −0.395420 0.684888i 0.597734 0.801694i \(-0.296068\pi\)
−0.993155 + 0.116806i \(0.962734\pi\)
\(38\) 0 0
\(39\) 1.42226e8 2.46343e8i 0.252420 0.437205i
\(40\) 0 0
\(41\) 5.86887e7 0.0791122 0.0395561 0.999217i \(-0.487406\pi\)
0.0395561 + 0.999217i \(0.487406\pi\)
\(42\) 0 0
\(43\) 8.57155e8 0.889166 0.444583 0.895738i \(-0.353352\pi\)
0.444583 + 0.895738i \(0.353352\pi\)
\(44\) 0 0
\(45\) −7.91147e7 + 1.37031e8i −0.0639128 + 0.110700i
\(46\) 0 0
\(47\) 4.75883e8 + 8.24254e8i 0.302665 + 0.524231i 0.976739 0.214433i \(-0.0687904\pi\)
−0.674074 + 0.738664i \(0.735457\pi\)
\(48\) 0 0
\(49\) −4.04880e8 + 1.93543e9i −0.204761 + 0.978812i
\(50\) 0 0
\(51\) −5.85239e8 1.01366e9i −0.237518 0.411394i
\(52\) 0 0
\(53\) −9.09651e8 + 1.57556e9i −0.298784 + 0.517509i −0.975858 0.218406i \(-0.929914\pi\)
0.677074 + 0.735915i \(0.263248\pi\)
\(54\) 0 0
\(55\) 1.28265e9 0.343649
\(56\) 0 0
\(57\) 2.21267e9 0.487084
\(58\) 0 0
\(59\) 8.43761e8 1.46144e9i 0.153650 0.266130i −0.778916 0.627128i \(-0.784230\pi\)
0.932567 + 0.360998i \(0.117564\pi\)
\(60\) 0 0
\(61\) 3.82941e9 + 6.63273e9i 0.580521 + 1.00549i 0.995418 + 0.0956231i \(0.0304843\pi\)
−0.414897 + 0.909868i \(0.636182\pi\)
\(62\) 0 0
\(63\) −9.37033e8 + 2.45285e9i −0.118955 + 0.311385i
\(64\) 0 0
\(65\) 1.56837e9 + 2.71649e9i 0.167658 + 0.290392i
\(66\) 0 0
\(67\) −2.92346e9 + 5.06358e9i −0.264537 + 0.458191i −0.967442 0.253093i \(-0.918552\pi\)
0.702906 + 0.711283i \(0.251886\pi\)
\(68\) 0 0
\(69\) 2.04919e9 0.157729
\(70\) 0 0
\(71\) 1.03360e10 0.679877 0.339939 0.940448i \(-0.389594\pi\)
0.339939 + 0.940448i \(0.389594\pi\)
\(72\) 0 0
\(73\) 4.61314e9 7.99018e9i 0.260448 0.451109i −0.705913 0.708298i \(-0.749463\pi\)
0.966361 + 0.257190i \(0.0827965\pi\)
\(74\) 0 0
\(75\) 5.06020e9 + 8.76452e9i 0.246224 + 0.426473i
\(76\) 0 0
\(77\) 2.10176e10 3.36355e9i 0.884879 0.141612i
\(78\) 0 0
\(79\) 9.94865e9 + 1.72316e10i 0.363760 + 0.630051i 0.988576 0.150721i \(-0.0481594\pi\)
−0.624816 + 0.780772i \(0.714826\pi\)
\(80\) 0 0
\(81\) −1.74339e9 + 3.01964e9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.78020e10 1.33204 0.666018 0.745935i \(-0.267997\pi\)
0.666018 + 0.745935i \(0.267997\pi\)
\(84\) 0 0
\(85\) 1.29072e10 0.315520
\(86\) 0 0
\(87\) −4.44472e9 + 7.69849e9i −0.0956068 + 0.165596i
\(88\) 0 0
\(89\) −9.70762e9 1.68141e10i −0.184276 0.319175i 0.759057 0.651025i \(-0.225661\pi\)
−0.943332 + 0.331850i \(0.892327\pi\)
\(90\) 0 0
\(91\) 3.28229e10 + 4.03997e10i 0.551377 + 0.678657i
\(92\) 0 0
\(93\) −2.93902e9 5.09054e9i −0.0438073 0.0758765i
\(94\) 0 0
\(95\) −1.21998e10 + 2.11307e10i −0.161761 + 0.280178i
\(96\) 0 0
\(97\) 8.32856e10 0.984749 0.492374 0.870383i \(-0.336129\pi\)
0.492374 + 0.870383i \(0.336129\pi\)
\(98\) 0 0
\(99\) 2.82649e10 0.298713
\(100\) 0 0
\(101\) −7.46928e10 + 1.29372e11i −0.707149 + 1.22482i 0.258761 + 0.965941i \(0.416686\pi\)
−0.965910 + 0.258877i \(0.916648\pi\)
\(102\) 0 0
\(103\) 3.62922e10 + 6.28600e10i 0.308467 + 0.534281i 0.978027 0.208477i \(-0.0668507\pi\)
−0.669560 + 0.742758i \(0.733517\pi\)
\(104\) 0 0
\(105\) −1.82580e10 2.24727e10i −0.139609 0.171836i
\(106\) 0 0
\(107\) 1.26123e11 + 2.18451e11i 0.869326 + 1.50572i 0.862687 + 0.505738i \(0.168780\pi\)
0.00663879 + 0.999978i \(0.497887\pi\)
\(108\) 0 0
\(109\) 6.84739e10 1.18600e11i 0.426265 0.738312i −0.570273 0.821455i \(-0.693162\pi\)
0.996538 + 0.0831430i \(0.0264958\pi\)
\(110\) 0 0
\(111\) 8.10597e10 0.456592
\(112\) 0 0
\(113\) 2.33958e11 1.19456 0.597279 0.802034i \(-0.296249\pi\)
0.597279 + 0.802034i \(0.296249\pi\)
\(114\) 0 0
\(115\) −1.12985e10 + 1.95696e10i −0.0523821 + 0.0907284i
\(116\) 0 0
\(117\) 3.45610e10 + 5.98614e10i 0.145735 + 0.252420i
\(118\) 0 0
\(119\) 2.11497e11 3.38470e10i 0.812449 0.130020i
\(120\) 0 0
\(121\) 2.80940e10 + 4.86603e10i 0.0984679 + 0.170551i
\(122\) 0 0
\(123\) −7.13068e9 + 1.23507e10i −0.0228377 + 0.0395561i
\(124\) 0 0
\(125\) −2.42442e11 −0.710562
\(126\) 0 0
\(127\) −2.05552e11 −0.552078 −0.276039 0.961146i \(-0.589022\pi\)
−0.276039 + 0.961146i \(0.589022\pi\)
\(128\) 0 0
\(129\) −1.04144e11 + 1.80383e11i −0.256680 + 0.444583i
\(130\) 0 0
\(131\) −1.71371e10 2.96824e10i −0.0388102 0.0672213i 0.845968 0.533234i \(-0.179023\pi\)
−0.884778 + 0.466013i \(0.845690\pi\)
\(132\) 0 0
\(133\) −1.44495e11 + 3.78241e11i −0.301070 + 0.788105i
\(134\) 0 0
\(135\) −1.92249e10 3.32984e10i −0.0369001 0.0639128i
\(136\) 0 0
\(137\) 7.70171e10 1.33397e11i 0.136340 0.236148i −0.789768 0.613405i \(-0.789799\pi\)
0.926109 + 0.377257i \(0.123133\pi\)
\(138\) 0 0
\(139\) −1.11480e11 −0.182228 −0.0911138 0.995840i \(-0.529043\pi\)
−0.0911138 + 0.995840i \(0.529043\pi\)
\(140\) 0 0
\(141\) −2.31279e11 −0.349487
\(142\) 0 0
\(143\) 2.80161e11 4.85254e11i 0.391796 0.678611i
\(144\) 0 0
\(145\) −4.90132e10 8.48933e10i −0.0635022 0.109989i
\(146\) 0 0
\(147\) −3.58107e11 3.20359e11i −0.430297 0.384939i
\(148\) 0 0
\(149\) −8.33795e11 1.44418e12i −0.930112 1.61100i −0.783127 0.621862i \(-0.786377\pi\)
−0.146985 0.989139i \(-0.546957\pi\)
\(150\) 0 0
\(151\) 3.71218e11 6.42968e11i 0.384818 0.666524i −0.606926 0.794758i \(-0.707598\pi\)
0.991744 + 0.128234i \(0.0409309\pi\)
\(152\) 0 0
\(153\) 2.84426e11 0.274262
\(154\) 0 0
\(155\) 6.48188e10 0.0581938
\(156\) 0 0
\(157\) −4.37190e11 + 7.57235e11i −0.365782 + 0.633552i −0.988901 0.148574i \(-0.952532\pi\)
0.623120 + 0.782126i \(0.285865\pi\)
\(158\) 0 0
\(159\) −2.21045e11 3.82861e11i −0.172503 0.298784i
\(160\) 0 0
\(161\) −1.33819e11 + 3.50296e11i −0.0974937 + 0.255207i
\(162\) 0 0
\(163\) −5.70121e11 9.87478e11i −0.388092 0.672196i 0.604101 0.796908i \(-0.293533\pi\)
−0.992193 + 0.124712i \(0.960199\pi\)
\(164\) 0 0
\(165\) −1.55842e11 + 2.69927e11i −0.0992028 + 0.171824i
\(166\) 0 0
\(167\) 1.67533e12 0.998068 0.499034 0.866582i \(-0.333688\pi\)
0.499034 + 0.866582i \(0.333688\pi\)
\(168\) 0 0
\(169\) −4.21888e11 −0.235408
\(170\) 0 0
\(171\) −2.68839e11 + 4.65643e11i −0.140609 + 0.243542i
\(172\) 0 0
\(173\) −1.84651e12 3.19825e12i −0.905937 1.56913i −0.819655 0.572858i \(-0.805835\pi\)
−0.0862817 0.996271i \(-0.527498\pi\)
\(174\) 0 0
\(175\) −1.82869e12 + 2.92654e11i −0.842228 + 0.134786i
\(176\) 0 0
\(177\) 2.05034e11 + 3.55129e11i 0.0887100 + 0.153650i
\(178\) 0 0
\(179\) −8.10662e11 + 1.40411e12i −0.329722 + 0.571096i −0.982457 0.186491i \(-0.940288\pi\)
0.652734 + 0.757587i \(0.273622\pi\)
\(180\) 0 0
\(181\) −3.72161e12 −1.42396 −0.711982 0.702198i \(-0.752202\pi\)
−0.711982 + 0.702198i \(0.752202\pi\)
\(182\) 0 0
\(183\) −1.86109e12 −0.670328
\(184\) 0 0
\(185\) −4.46934e11 + 7.74112e11i −0.151635 + 0.262639i
\(186\) 0 0
\(187\) −1.15282e12 1.99674e12i −0.368666 0.638548i
\(188\) 0 0
\(189\) −4.02339e11 4.95215e11i −0.121353 0.149367i
\(190\) 0 0
\(191\) 1.15479e12 + 2.00015e12i 0.328714 + 0.569349i 0.982257 0.187540i \(-0.0600516\pi\)
−0.653543 + 0.756889i \(0.726718\pi\)
\(192\) 0 0
\(193\) 6.67031e11 1.15533e12i 0.179300 0.310557i −0.762341 0.647176i \(-0.775950\pi\)
0.941641 + 0.336619i \(0.109283\pi\)
\(194\) 0 0
\(195\) −7.62227e11 −0.193595
\(196\) 0 0
\(197\) 3.95053e12 0.948618 0.474309 0.880359i \(-0.342698\pi\)
0.474309 + 0.880359i \(0.342698\pi\)
\(198\) 0 0
\(199\) −5.18976e11 + 8.98893e11i −0.117884 + 0.204181i −0.918929 0.394423i \(-0.870944\pi\)
0.801045 + 0.598604i \(0.204278\pi\)
\(200\) 0 0
\(201\) −7.10401e11 1.23045e12i −0.152730 0.264537i
\(202\) 0 0
\(203\) −1.02575e12 1.26253e12i −0.208840 0.257048i
\(204\) 0 0
\(205\) −7.86320e10 1.36195e11i −0.0151689 0.0262732i
\(206\) 0 0
\(207\) −2.48977e11 + 4.31240e11i −0.0455325 + 0.0788647i
\(208\) 0 0
\(209\) 4.35857e12 0.756031
\(210\) 0 0
\(211\) 4.91335e12 0.808769 0.404385 0.914589i \(-0.367486\pi\)
0.404385 + 0.914589i \(0.367486\pi\)
\(212\) 0 0
\(213\) −1.25582e12 + 2.17515e12i −0.196264 + 0.339939i
\(214\) 0 0
\(215\) −1.14843e12 1.98914e12i −0.170487 0.295293i
\(216\) 0 0
\(217\) 1.06212e12 1.69977e11i 0.149846 0.0239807i
\(218\) 0 0
\(219\) 1.12099e12 + 1.94161e12i 0.150370 + 0.260448i
\(220\) 0 0
\(221\) 2.81923e12 4.88305e12i 0.359727 0.623065i
\(222\) 0 0
\(223\) −8.25284e12 −1.00214 −0.501068 0.865408i \(-0.667059\pi\)
−0.501068 + 0.865408i \(0.667059\pi\)
\(224\) 0 0
\(225\) −2.45926e12 −0.284315
\(226\) 0 0
\(227\) 6.55247e12 1.13492e13i 0.721544 1.24975i −0.238837 0.971060i \(-0.576766\pi\)
0.960381 0.278691i \(-0.0899005\pi\)
\(228\) 0 0
\(229\) 3.18856e12 + 5.52274e12i 0.334579 + 0.579508i 0.983404 0.181430i \(-0.0580724\pi\)
−0.648825 + 0.760938i \(0.724739\pi\)
\(230\) 0 0
\(231\) −1.84580e12 + 4.83170e12i −0.184637 + 0.483319i
\(232\) 0 0
\(233\) 3.04721e12 + 5.27793e12i 0.290700 + 0.503507i 0.973975 0.226653i \(-0.0727785\pi\)
−0.683275 + 0.730161i \(0.739445\pi\)
\(234\) 0 0
\(235\) 1.27519e12 2.20869e12i 0.116065 0.201031i
\(236\) 0 0
\(237\) −4.83504e12 −0.420034
\(238\) 0 0
\(239\) 1.63982e13 1.36022 0.680108 0.733112i \(-0.261933\pi\)
0.680108 + 0.733112i \(0.261933\pi\)
\(240\) 0 0
\(241\) −7.93321e12 + 1.37407e13i −0.628573 + 1.08872i 0.359266 + 0.933235i \(0.383027\pi\)
−0.987838 + 0.155484i \(0.950306\pi\)
\(242\) 0 0
\(243\) −4.23644e11 7.33773e11i −0.0320750 0.0555556i
\(244\) 0 0
\(245\) 5.03387e12 1.65354e12i 0.364325 0.119675i
\(246\) 0 0
\(247\) 5.32946e12 + 9.23089e12i 0.368850 + 0.638867i
\(248\) 0 0
\(249\) −5.80794e12 + 1.00596e13i −0.384526 + 0.666018i
\(250\) 0 0
\(251\) 2.61416e13 1.65625 0.828125 0.560544i \(-0.189408\pi\)
0.828125 + 0.560544i \(0.189408\pi\)
\(252\) 0 0
\(253\) 4.03656e12 0.244821
\(254\) 0 0
\(255\) −1.56822e12 + 2.71624e12i −0.0910828 + 0.157760i
\(256\) 0 0
\(257\) 9.97426e12 + 1.72759e13i 0.554943 + 0.961190i 0.997908 + 0.0646509i \(0.0205934\pi\)
−0.442965 + 0.896539i \(0.646073\pi\)
\(258\) 0 0
\(259\) −5.29348e12 + 1.38566e13i −0.282223 + 0.738769i
\(260\) 0 0
\(261\) −1.08007e12 1.87073e12i −0.0551986 0.0956068i
\(262\) 0 0
\(263\) 1.90133e13 3.29321e13i 0.931755 1.61385i 0.151434 0.988467i \(-0.451611\pi\)
0.780321 0.625379i \(-0.215056\pi\)
\(264\) 0 0
\(265\) 4.87505e12 0.229154
\(266\) 0 0
\(267\) 4.71790e12 0.212783
\(268\) 0 0
\(269\) −6.11726e12 + 1.05954e13i −0.264801 + 0.458649i −0.967511 0.252827i \(-0.918640\pi\)
0.702710 + 0.711476i \(0.251973\pi\)
\(270\) 0 0
\(271\) −4.65635e12 8.06503e12i −0.193515 0.335177i 0.752898 0.658137i \(-0.228655\pi\)
−0.946413 + 0.322960i \(0.895322\pi\)
\(272\) 0 0
\(273\) −1.24899e13 + 1.99882e12i −0.498497 + 0.0797771i
\(274\) 0 0
\(275\) 9.96773e12 + 1.72646e13i 0.382179 + 0.661953i
\(276\) 0 0
\(277\) −1.90071e13 + 3.29212e13i −0.700288 + 1.21293i 0.268077 + 0.963397i \(0.413612\pi\)
−0.968365 + 0.249537i \(0.919722\pi\)
\(278\) 0 0
\(279\) 1.42837e12 0.0505844
\(280\) 0 0
\(281\) 3.06527e13 1.04372 0.521860 0.853031i \(-0.325238\pi\)
0.521860 + 0.853031i \(0.325238\pi\)
\(282\) 0 0
\(283\) 3.55669e12 6.16037e12i 0.116472 0.201735i −0.801895 0.597465i \(-0.796175\pi\)
0.918367 + 0.395729i \(0.129508\pi\)
\(284\) 0 0
\(285\) −2.96456e12 5.13477e12i −0.0933928 0.161761i
\(286\) 0 0
\(287\) −1.64561e12 2.02549e12i −0.0498859 0.0614015i
\(288\) 0 0
\(289\) 5.53527e12 + 9.58736e12i 0.161510 + 0.279744i
\(290\) 0 0
\(291\) −1.01192e13 + 1.75270e13i −0.284273 + 0.492374i
\(292\) 0 0
\(293\) 4.95279e12 0.133992 0.0669959 0.997753i \(-0.478659\pi\)
0.0669959 + 0.997753i \(0.478659\pi\)
\(294\) 0 0
\(295\) −4.52193e12 −0.117843
\(296\) 0 0
\(297\) −3.43419e12 + 5.94818e12i −0.0862310 + 0.149356i
\(298\) 0 0
\(299\) 4.93571e12 + 8.54890e12i 0.119442 + 0.206880i
\(300\) 0 0
\(301\) −2.40343e13 2.95824e13i −0.560682 0.690110i
\(302\) 0 0
\(303\) −1.81503e13 3.14373e13i −0.408273 0.707149i
\(304\) 0 0
\(305\) 1.02614e13 1.77733e13i 0.222616 0.385583i
\(306\) 0 0
\(307\) 2.23542e13 0.467842 0.233921 0.972256i \(-0.424844\pi\)
0.233921 + 0.972256i \(0.424844\pi\)
\(308\) 0 0
\(309\) −1.76380e13 −0.356187
\(310\) 0 0
\(311\) 2.65812e13 4.60399e13i 0.518074 0.897330i −0.481706 0.876333i \(-0.659983\pi\)
0.999780 0.0209972i \(-0.00668410\pi\)
\(312\) 0 0
\(313\) −2.79998e13 4.84971e13i −0.526819 0.912476i −0.999512 0.0312493i \(-0.990051\pi\)
0.472693 0.881227i \(-0.343282\pi\)
\(314\) 0 0
\(315\) 6.94760e12 1.11186e12i 0.126220 0.0201996i
\(316\) 0 0
\(317\) −3.41827e13 5.92062e13i −0.599764 1.03882i −0.992856 0.119322i \(-0.961928\pi\)
0.393092 0.919499i \(-0.371406\pi\)
\(318\) 0 0
\(319\) −8.75535e12 + 1.51647e13i −0.148397 + 0.257031i
\(320\) 0 0
\(321\) −6.12956e13 −1.00381
\(322\) 0 0
\(323\) 4.38598e13 0.694148
\(324\) 0 0
\(325\) −2.43761e13 + 4.22207e13i −0.372912 + 0.645902i
\(326\) 0 0
\(327\) 1.66392e13 + 2.88199e13i 0.246104 + 0.426265i
\(328\) 0 0
\(329\) 1.51033e13 3.95357e13i 0.216021 0.565473i
\(330\) 0 0
\(331\) −1.92107e13 3.32739e13i −0.265759 0.460309i 0.702003 0.712174i \(-0.252289\pi\)
−0.967762 + 0.251865i \(0.918956\pi\)
\(332\) 0 0
\(333\) −9.84875e12 + 1.70585e13i −0.131807 + 0.228296i
\(334\) 0 0
\(335\) 1.56676e13 0.202887
\(336\) 0 0
\(337\) −1.59403e14 −1.99771 −0.998855 0.0478440i \(-0.984765\pi\)
−0.998855 + 0.0478440i \(0.984765\pi\)
\(338\) 0 0
\(339\) −2.84259e13 + 4.92352e13i −0.344839 + 0.597279i
\(340\) 0 0
\(341\) −5.78938e12 1.00275e13i −0.0679959 0.117772i
\(342\) 0 0
\(343\) 7.81490e13 4.02955e13i 0.888803 0.458289i
\(344\) 0 0
\(345\) −2.74553e12 4.75541e12i −0.0302428 0.0523821i
\(346\) 0 0
\(347\) 3.76248e13 6.51680e13i 0.401478 0.695380i −0.592426 0.805625i \(-0.701830\pi\)
0.993905 + 0.110244i \(0.0351633\pi\)
\(348\) 0 0
\(349\) −1.81299e14 −1.87437 −0.937187 0.348828i \(-0.886580\pi\)
−0.937187 + 0.348828i \(0.886580\pi\)
\(350\) 0 0
\(351\) −1.67966e13 −0.168280
\(352\) 0 0
\(353\) −6.08571e12 + 1.05408e13i −0.0590949 + 0.102355i −0.894059 0.447948i \(-0.852155\pi\)
0.834964 + 0.550304i \(0.185488\pi\)
\(354\) 0 0
\(355\) −1.38483e13 2.39859e13i −0.130359 0.225788i
\(356\) 0 0
\(357\) −1.85740e13 + 4.86208e13i −0.169524 + 0.443758i
\(358\) 0 0
\(359\) −4.61043e13 7.98551e13i −0.408058 0.706778i 0.586614 0.809867i \(-0.300461\pi\)
−0.994672 + 0.103089i \(0.967127\pi\)
\(360\) 0 0
\(361\) 1.67890e13 2.90794e13i 0.144123 0.249629i
\(362\) 0 0
\(363\) −1.36537e13 −0.113701
\(364\) 0 0
\(365\) −2.47230e13 −0.199751
\(366\) 0 0
\(367\) −3.47460e13 + 6.01818e13i −0.272421 + 0.471847i −0.969481 0.245165i \(-0.921158\pi\)
0.697060 + 0.717013i \(0.254491\pi\)
\(368\) 0 0
\(369\) −1.73276e12 3.00122e12i −0.0131854 0.0228377i
\(370\) 0 0
\(371\) 7.98826e13 1.27840e13i 0.590060 0.0944303i
\(372\) 0 0
\(373\) 2.75190e13 + 4.76643e13i 0.197349 + 0.341818i 0.947668 0.319258i \(-0.103434\pi\)
−0.750319 + 0.661076i \(0.770100\pi\)
\(374\) 0 0
\(375\) 2.94566e13 5.10204e13i 0.205122 0.355281i
\(376\) 0 0
\(377\) −4.28225e13 −0.289597
\(378\) 0 0
\(379\) 1.64609e14 1.08128 0.540640 0.841254i \(-0.318182\pi\)
0.540640 + 0.841254i \(0.318182\pi\)
\(380\) 0 0
\(381\) 2.49745e13 4.32571e13i 0.159371 0.276039i
\(382\) 0 0
\(383\) 2.37086e13 + 4.10645e13i 0.146998 + 0.254609i 0.930117 0.367264i \(-0.119705\pi\)
−0.783118 + 0.621873i \(0.786372\pi\)
\(384\) 0 0
\(385\) −3.59652e13 4.42674e13i −0.216695 0.266717i
\(386\) 0 0
\(387\) −2.53071e13 4.38331e13i −0.148194 0.256680i
\(388\) 0 0
\(389\) −1.47659e14 + 2.55752e14i −0.840496 + 1.45578i 0.0489795 + 0.998800i \(0.484403\pi\)
−0.889476 + 0.456982i \(0.848930\pi\)
\(390\) 0 0
\(391\) 4.06194e13 0.224782
\(392\) 0 0
\(393\) 8.32865e12 0.0448142
\(394\) 0 0
\(395\) 2.66587e13 4.61742e13i 0.139494 0.241610i
\(396\) 0 0
\(397\) 1.02252e14 + 1.77106e14i 0.520386 + 0.901335i 0.999719 + 0.0237017i \(0.00754518\pi\)
−0.479333 + 0.877633i \(0.659121\pi\)
\(398\) 0 0
\(399\) −6.20424e13 7.63643e13i −0.307141 0.378042i
\(400\) 0 0
\(401\) −7.18349e13 1.24422e14i −0.345972 0.599242i 0.639558 0.768743i \(-0.279118\pi\)
−0.985530 + 0.169502i \(0.945784\pi\)
\(402\) 0 0
\(403\) 1.41579e13 2.45223e13i 0.0663472 0.114917i
\(404\) 0 0
\(405\) 9.34328e12 0.0426086
\(406\) 0 0
\(407\) 1.59674e14 0.708703
\(408\) 0 0
\(409\) −5.12511e13 + 8.87695e13i −0.221424 + 0.383518i −0.955241 0.295830i \(-0.904404\pi\)
0.733816 + 0.679348i \(0.237737\pi\)
\(410\) 0 0
\(411\) 1.87151e13 + 3.24156e13i 0.0787160 + 0.136340i
\(412\) 0 0
\(413\) −7.40964e13 + 1.18580e13i −0.303439 + 0.0485610i
\(414\) 0 0
\(415\) −6.40457e13 1.10930e14i −0.255403 0.442371i
\(416\) 0 0
\(417\) 1.35448e13 2.34603e13i 0.0526046 0.0911138i
\(418\) 0 0
\(419\) 2.06951e14 0.782871 0.391436 0.920206i \(-0.371979\pi\)
0.391436 + 0.920206i \(0.371979\pi\)
\(420\) 0 0
\(421\) −2.28895e13 −0.0843498 −0.0421749 0.999110i \(-0.513429\pi\)
−0.0421749 + 0.999110i \(0.513429\pi\)
\(422\) 0 0
\(423\) 2.81004e13 4.86714e13i 0.100888 0.174744i
\(424\) 0 0
\(425\) 1.00304e14 + 1.73732e14i 0.350896 + 0.607770i
\(426\) 0 0
\(427\) 1.21536e14 3.18142e14i 0.414335 1.08459i
\(428\) 0 0
\(429\) 6.80792e13 + 1.17917e14i 0.226204 + 0.391796i
\(430\) 0 0
\(431\) −6.89096e13 + 1.19355e14i −0.223180 + 0.386559i −0.955772 0.294109i \(-0.904977\pi\)
0.732592 + 0.680668i \(0.238310\pi\)
\(432\) 0 0
\(433\) 1.37606e14 0.434463 0.217231 0.976120i \(-0.430297\pi\)
0.217231 + 0.976120i \(0.430297\pi\)
\(434\) 0 0
\(435\) 2.38204e13 0.0733261
\(436\) 0 0
\(437\) −3.83933e13 + 6.64992e13i −0.115241 + 0.199604i
\(438\) 0 0
\(439\) 2.24449e14 + 3.88757e14i 0.656996 + 1.13795i 0.981389 + 0.192028i \(0.0615066\pi\)
−0.324393 + 0.945922i \(0.605160\pi\)
\(440\) 0 0
\(441\) 1.10928e14 3.64379e13i 0.316686 0.104026i
\(442\) 0 0
\(443\) 9.09994e13 + 1.57616e14i 0.253407 + 0.438913i 0.964462 0.264223i \(-0.0851156\pi\)
−0.711055 + 0.703137i \(0.751782\pi\)
\(444\) 0 0
\(445\) −2.60128e13 + 4.50555e13i −0.0706654 + 0.122396i
\(446\) 0 0
\(447\) 4.05225e14 1.07400
\(448\) 0 0
\(449\) 7.82493e13 0.202360 0.101180 0.994868i \(-0.467738\pi\)
0.101180 + 0.994868i \(0.467738\pi\)
\(450\) 0 0
\(451\) −1.40462e13 + 2.43288e13i −0.0354478 + 0.0613973i
\(452\) 0 0
\(453\) 9.02059e13 + 1.56241e14i 0.222175 + 0.384818i
\(454\) 0 0
\(455\) 4.97760e13 1.30298e14i 0.119662 0.313238i
\(456\) 0 0
\(457\) 6.37712e12 + 1.10455e13i 0.0149653 + 0.0259206i 0.873411 0.486984i \(-0.161903\pi\)
−0.858446 + 0.512904i \(0.828570\pi\)
\(458\) 0 0
\(459\) −3.45578e13 + 5.98558e13i −0.0791728 + 0.137131i
\(460\) 0 0
\(461\) −4.11130e14 −0.919653 −0.459826 0.888009i \(-0.652088\pi\)
−0.459826 + 0.888009i \(0.652088\pi\)
\(462\) 0 0
\(463\) 8.91432e14 1.94712 0.973560 0.228430i \(-0.0733593\pi\)
0.973560 + 0.228430i \(0.0733593\pi\)
\(464\) 0 0
\(465\) −7.87549e12 + 1.36407e13i −0.0167991 + 0.0290969i
\(466\) 0 0
\(467\) 9.36710e13 + 1.62243e14i 0.195147 + 0.338005i 0.946949 0.321384i \(-0.104148\pi\)
−0.751802 + 0.659389i \(0.770815\pi\)
\(468\) 0 0
\(469\) 2.56729e14 4.10857e13i 0.522425 0.0836064i
\(470\) 0 0
\(471\) −1.06237e14 1.84008e14i −0.211184 0.365782i
\(472\) 0 0
\(473\) −2.05147e14 + 3.55324e14i −0.398408 + 0.690063i
\(474\) 0 0
\(475\) −3.79228e14 −0.719591
\(476\) 0 0
\(477\) 1.07428e14 0.199189
\(478\) 0 0
\(479\) −3.54805e14 + 6.14540e14i −0.642901 + 1.11354i 0.341881 + 0.939743i \(0.388936\pi\)
−0.984782 + 0.173794i \(0.944397\pi\)
\(480\) 0 0
\(481\) 1.95241e14 + 3.38168e14i 0.345759 + 0.598873i
\(482\) 0 0
\(483\) −5.74587e13 7.07224e13i −0.0994595 0.122419i
\(484\) 0 0
\(485\) −1.11587e14 1.93275e14i −0.188814 0.327036i
\(486\) 0 0
\(487\) 1.72334e14 2.98491e14i 0.285077 0.493768i −0.687551 0.726136i \(-0.741314\pi\)
0.972628 + 0.232368i \(0.0746475\pi\)
\(488\) 0 0
\(489\) 2.77079e14 0.448130
\(490\) 0 0
\(491\) 2.50906e12 0.00396791 0.00198396 0.999998i \(-0.499368\pi\)
0.00198396 + 0.999998i \(0.499368\pi\)
\(492\) 0 0
\(493\) −8.81039e13 + 1.52601e14i −0.136250 + 0.235992i
\(494\) 0 0
\(495\) −3.78697e13 6.55922e13i −0.0572748 0.0992028i
\(496\) 0 0
\(497\) −2.89817e14 3.56719e14i −0.428711 0.527674i
\(498\) 0 0
\(499\) 3.62370e12 + 6.27644e12i 0.00524324 + 0.00908155i 0.868635 0.495452i \(-0.164998\pi\)
−0.863392 + 0.504534i \(0.831664\pi\)
\(500\) 0 0
\(501\) −2.03553e14 + 3.52564e14i −0.288118 + 0.499034i
\(502\) 0 0
\(503\) −1.22748e15 −1.69977 −0.849887 0.526965i \(-0.823330\pi\)
−0.849887 + 0.526965i \(0.823330\pi\)
\(504\) 0 0
\(505\) 4.00297e14 0.542351
\(506\) 0 0
\(507\) 5.12594e13 8.87839e13i 0.0679563 0.117704i
\(508\) 0 0
\(509\) −1.64697e13 2.85263e13i −0.0213667 0.0370082i 0.855144 0.518390i \(-0.173468\pi\)
−0.876511 + 0.481382i \(0.840135\pi\)
\(510\) 0 0
\(511\) −4.05111e14 + 6.48320e13i −0.514350 + 0.0823142i
\(512\) 0 0
\(513\) −6.53278e13 1.13151e14i −0.0811807 0.140609i
\(514\) 0 0
\(515\) 9.72497e13 1.68441e14i 0.118290 0.204884i
\(516\) 0 0
\(517\) −4.55581e14 −0.542459
\(518\) 0 0
\(519\) 8.97403e14 1.04609
\(520\) 0 0
\(521\) −4.69615e14 + 8.13397e14i −0.535962 + 0.928314i 0.463154 + 0.886278i \(0.346718\pi\)
−0.999116 + 0.0420361i \(0.986616\pi\)
\(522\) 0 0
\(523\) −4.77717e14 8.27430e14i −0.533840 0.924639i −0.999219 0.0395267i \(-0.987415\pi\)
0.465378 0.885112i \(-0.345918\pi\)
\(524\) 0 0
\(525\) 1.60598e14 4.20394e14i 0.175737 0.460024i
\(526\) 0 0
\(527\) −5.82577e13 1.00905e14i −0.0624303 0.108132i
\(528\) 0 0
\(529\) 4.40848e14 7.63571e14i 0.462682 0.801389i
\(530\) 0 0
\(531\) −9.96465e13 −0.102433
\(532\) 0 0
\(533\) −6.87002e13 −0.0691765
\(534\) 0 0
\(535\) 3.37962e14 5.85367e14i 0.333366 0.577408i
\(536\) 0 0
\(537\) −1.96991e14 3.41198e14i −0.190365 0.329722i
\(538\) 0 0
\(539\) −7.05410e14 6.31053e14i −0.667888 0.597486i
\(540\) 0 0
\(541\) −5.37113e14 9.30307e14i −0.498289 0.863061i 0.501709 0.865036i \(-0.332705\pi\)
−0.999998 + 0.00197505i \(0.999371\pi\)
\(542\) 0 0
\(543\) 4.52176e14 7.83191e14i 0.411063 0.711982i
\(544\) 0 0
\(545\) −3.66969e14 −0.326926
\(546\) 0 0
\(547\) 1.38381e15 1.20822 0.604111 0.796900i \(-0.293528\pi\)
0.604111 + 0.796900i \(0.293528\pi\)
\(548\) 0 0
\(549\) 2.26123e14 3.91656e14i 0.193507 0.335164i
\(550\) 0 0
\(551\) −1.66551e14 2.88475e14i −0.139706 0.241977i
\(552\) 0 0
\(553\) 3.15745e14 8.26519e14i 0.259626 0.679618i
\(554\) 0 0
\(555\) −1.08605e14 1.88109e14i −0.0875463 0.151635i
\(556\) 0 0
\(557\) −7.14824e14 + 1.23811e15i −0.564931 + 0.978490i 0.432125 + 0.901814i \(0.357764\pi\)
−0.997056 + 0.0766761i \(0.975569\pi\)
\(558\) 0 0
\(559\) −1.00337e15 −0.777495
\(560\) 0 0
\(561\) 5.60271e14 0.425699
\(562\) 0 0
\(563\) −1.27988e15 + 2.21682e15i −0.953615 + 1.65171i −0.216108 + 0.976370i \(0.569336\pi\)
−0.737507 + 0.675340i \(0.763997\pi\)
\(564\) 0 0
\(565\) −3.13461e14 5.42930e14i −0.229043 0.396714i
\(566\) 0 0
\(567\) 1.53099e14 2.45013e13i 0.109715 0.0175583i
\(568\) 0 0
\(569\) −1.13256e15 1.96165e15i −0.796056 1.37881i −0.922166 0.386794i \(-0.873583\pi\)
0.126110 0.992016i \(-0.459751\pi\)
\(570\) 0 0
\(571\) −5.49376e14 + 9.51547e14i −0.378766 + 0.656042i −0.990883 0.134725i \(-0.956985\pi\)
0.612117 + 0.790767i \(0.290318\pi\)
\(572\) 0 0
\(573\) −5.61226e14 −0.379566
\(574\) 0 0
\(575\) −3.51211e14 −0.233021
\(576\) 0 0
\(577\) −1.22669e15 + 2.12470e15i −0.798490 + 1.38303i 0.122109 + 0.992517i \(0.461034\pi\)
−0.920599 + 0.390509i \(0.872299\pi\)
\(578\) 0 0
\(579\) 1.62089e14 + 2.80746e14i 0.103519 + 0.179300i
\(580\) 0 0
\(581\) −1.34035e15 1.64976e15i −0.839943 1.03384i
\(582\) 0 0
\(583\) −4.35421e14 7.54172e14i −0.267752 0.463760i
\(584\) 0 0
\(585\) 9.26105e13 1.60406e14i 0.0558860 0.0967974i
\(586\) 0 0
\(587\) −3.57451e14 −0.211693 −0.105847 0.994382i \(-0.533755\pi\)
−0.105847 + 0.994382i \(0.533755\pi\)
\(588\) 0 0
\(589\) 2.20260e14 0.128027
\(590\) 0 0
\(591\) −4.79990e14 + 8.31366e14i −0.273842 + 0.474309i
\(592\) 0 0
\(593\) 3.47719e14 + 6.02267e14i 0.194728 + 0.337278i 0.946811 0.321790i \(-0.104284\pi\)
−0.752084 + 0.659068i \(0.770951\pi\)
\(594\) 0 0
\(595\) −3.61913e14 4.45457e14i −0.198958 0.244885i
\(596\) 0 0
\(597\) −1.26111e14 2.18431e14i −0.0680604 0.117884i
\(598\) 0 0
\(599\) 1.18753e14 2.05685e14i 0.0629210 0.108982i −0.832849 0.553500i \(-0.813292\pi\)
0.895770 + 0.444518i \(0.146625\pi\)
\(600\) 0 0
\(601\) 2.93732e15 1.52806 0.764032 0.645178i \(-0.223217\pi\)
0.764032 + 0.645178i \(0.223217\pi\)
\(602\) 0 0
\(603\) 3.45255e14 0.176358
\(604\) 0 0
\(605\) 7.52816e13 1.30391e14i 0.0377602 0.0654026i
\(606\) 0 0
\(607\) 8.62651e14 + 1.49416e15i 0.424910 + 0.735966i 0.996412 0.0846345i \(-0.0269723\pi\)
−0.571502 + 0.820601i \(0.693639\pi\)
\(608\) 0 0
\(609\) 3.90322e14 6.24652e13i 0.188811 0.0302164i
\(610\) 0 0
\(611\) −5.57062e14 9.64860e14i −0.264653 0.458393i
\(612\) 0 0
\(613\) −5.07686e14 + 8.79338e14i −0.236899 + 0.410320i −0.959823 0.280607i \(-0.909464\pi\)
0.722924 + 0.690927i \(0.242798\pi\)
\(614\) 0 0
\(615\) 3.82151e13 0.0175155
\(616\) 0 0
\(617\) 4.29465e15 1.93357 0.966784 0.255595i \(-0.0822714\pi\)
0.966784 + 0.255595i \(0.0822714\pi\)
\(618\) 0 0
\(619\) −8.18875e14 + 1.41833e15i −0.362175 + 0.627306i −0.988319 0.152402i \(-0.951299\pi\)
0.626143 + 0.779708i \(0.284633\pi\)
\(620\) 0 0
\(621\) −6.05014e13 1.04791e14i −0.0262882 0.0455325i
\(622\) 0 0
\(623\) −3.08095e14 + 8.06495e14i −0.131523 + 0.344284i
\(624\) 0 0
\(625\) −6.91964e14 1.19852e15i −0.290231 0.502694i
\(626\) 0 0
\(627\) −5.29567e14 + 9.17236e14i −0.218247 + 0.378016i
\(628\) 0 0
\(629\) 1.60678e15 0.650694
\(630\) 0 0
\(631\) 2.24346e15 0.892804 0.446402 0.894832i \(-0.352705\pi\)
0.446402 + 0.894832i \(0.352705\pi\)
\(632\) 0 0
\(633\) −5.96972e14 + 1.03399e15i −0.233472 + 0.404385i
\(634\) 0 0
\(635\) 2.75401e14 + 4.77008e14i 0.105855 + 0.183346i
\(636\) 0 0
\(637\) 4.73946e14 2.26559e15i 0.179045 0.855883i
\(638\) 0 0
\(639\) −3.05164e14 5.28560e14i −0.113313 0.196264i
\(640\) 0 0
\(641\) 9.60927e14 1.66437e15i 0.350729 0.607480i −0.635649 0.771978i \(-0.719267\pi\)
0.986377 + 0.164499i \(0.0526007\pi\)
\(642\) 0 0
\(643\) −8.48487e14 −0.304428 −0.152214 0.988348i \(-0.548640\pi\)
−0.152214 + 0.988348i \(0.548640\pi\)
\(644\) 0 0
\(645\) 5.58136e14 0.196862
\(646\) 0 0
\(647\) −1.54367e15 + 2.67372e15i −0.535280 + 0.927132i 0.463870 + 0.885903i \(0.346461\pi\)
−0.999150 + 0.0412287i \(0.986873\pi\)
\(648\) 0 0
\(649\) 4.03882e14 + 6.99544e14i 0.137692 + 0.238489i
\(650\) 0 0
\(651\) −9.32772e13 + 2.44170e14i −0.0312666 + 0.0818458i
\(652\) 0 0
\(653\) 4.33958e14 + 7.51637e14i 0.143029 + 0.247734i 0.928636 0.370992i \(-0.120982\pi\)
−0.785607 + 0.618726i \(0.787649\pi\)
\(654\) 0 0
\(655\) −4.59211e13 + 7.95378e13i −0.0148828 + 0.0257778i
\(656\) 0 0
\(657\) −5.44802e14 −0.173632
\(658\) 0 0
\(659\) 3.99805e15 1.25308 0.626540 0.779389i \(-0.284471\pi\)
0.626540 + 0.779389i \(0.284471\pi\)
\(660\) 0 0
\(661\) −1.60004e15 + 2.77135e15i −0.493200 + 0.854247i −0.999969 0.00783472i \(-0.997506\pi\)
0.506770 + 0.862081i \(0.330839\pi\)
\(662\) 0 0
\(663\) 6.85072e14 + 1.18658e15i 0.207688 + 0.359727i
\(664\) 0 0
\(665\) 1.07135e15 1.71454e14i 0.319457 0.0511244i
\(666\) 0 0
\(667\) −1.54246e14 2.67163e14i −0.0452400 0.0783580i
\(668\) 0 0
\(669\) 1.00272e15 1.73676e15i 0.289292 0.501068i
\(670\) 0 0
\(671\) −3.66604e15 −1.04045
\(672\) 0 0
\(673\) 6.83323e15 1.90785 0.953923 0.300052i \(-0.0970041\pi\)
0.953923 + 0.300052i \(0.0970041\pi\)
\(674\) 0 0
\(675\) 2.98800e14 5.17536e14i 0.0820747 0.142158i
\(676\) 0 0
\(677\) 1.59834e15 + 2.76841e15i 0.431949 + 0.748158i 0.997041 0.0768700i \(-0.0244926\pi\)
−0.565092 + 0.825028i \(0.691159\pi\)
\(678\) 0 0
\(679\) −2.33530e15 2.87438e15i −0.620954 0.764295i
\(680\) 0 0
\(681\) 1.59225e15 + 2.75786e15i 0.416584 + 0.721544i
\(682\) 0 0
\(683\) −1.63286e14 + 2.82819e14i −0.0420372 + 0.0728106i −0.886278 0.463153i \(-0.846718\pi\)
0.844241 + 0.535963i \(0.180051\pi\)
\(684\) 0 0
\(685\) −4.12754e14 −0.104567
\(686\) 0 0
\(687\) −1.54964e15 −0.386339
\(688\) 0 0
\(689\) 1.06482e15 1.84433e15i 0.261260 0.452515i
\(690\) 0 0
\(691\) −1.77293e12 3.07081e12i −0.000428117 0.000741521i 0.865811 0.500371i \(-0.166803\pi\)
−0.866239 + 0.499629i \(0.833470\pi\)
\(692\) 0 0
\(693\) −7.92539e14 9.75488e14i −0.188360 0.231841i
\(694\) 0 0
\(695\) 1.49362e14 + 2.58703e14i 0.0349401 + 0.0605180i
\(696\) 0 0
\(697\) −1.41345e14 + 2.44817e14i −0.0325463 + 0.0563718i
\(698\) 0 0
\(699\) −1.48095e15 −0.335672
\(700\) 0 0
\(701\) 6.37107e15 1.42155 0.710777 0.703418i \(-0.248344\pi\)
0.710777 + 0.703418i \(0.248344\pi\)
\(702\) 0 0
\(703\) −1.51872e15 + 2.63050e15i −0.333598 + 0.577809i
\(704\) 0 0
\(705\) 3.09871e14 + 5.36712e14i 0.0670102 + 0.116065i
\(706\) 0 0
\(707\) 6.55928e15 1.04972e15i 1.39653 0.223494i
\(708\) 0 0
\(709\) 3.87624e13 + 6.71385e13i 0.00812562 + 0.0140740i 0.870060 0.492946i \(-0.164080\pi\)
−0.861934 + 0.507020i \(0.830747\pi\)
\(710\) 0 0
\(711\) 5.87458e14 1.01751e15i 0.121253 0.210017i
\(712\) 0 0
\(713\) 2.03987e14 0.0414582
\(714\) 0 0
\(715\) −1.50146e15 −0.300490
\(716\) 0 0
\(717\) −1.99238e15 + 3.45090e15i −0.392660 + 0.680108i
\(718\) 0 0
\(719\) 2.30995e15 + 4.00095e15i 0.448326 + 0.776523i 0.998277 0.0586734i \(-0.0186870\pi\)
−0.549951 + 0.835197i \(0.685354\pi\)
\(720\) 0 0
\(721\) 1.15182e15 3.01511e15i 0.220162 0.576313i
\(722\) 0 0
\(723\) −1.92777e15 3.33900e15i −0.362907 0.628573i
\(724\) 0 0
\(725\) 7.61781e14 1.31944e15i 0.141244 0.244642i
\(726\) 0 0
\(727\) −2.05407e14 −0.0375124 −0.0187562 0.999824i \(-0.505971\pi\)
−0.0187562 + 0.999824i \(0.505971\pi\)
\(728\) 0 0
\(729\) 2.05891e14 0.0370370
\(730\) 0 0
\(731\) −2.06436e15 + 3.57558e15i −0.365797 + 0.633579i
\(732\) 0 0
\(733\) 4.30318e15 + 7.45332e15i 0.751134 + 1.30100i 0.947274 + 0.320426i \(0.103826\pi\)
−0.196140 + 0.980576i \(0.562841\pi\)
\(734\) 0 0
\(735\) −2.63637e14 + 1.26025e15i −0.0453342 + 0.216710i
\(736\) 0 0
\(737\) −1.39937e15 2.42378e15i −0.237061 0.410602i
\(738\) 0 0
\(739\) −4.84230e15 + 8.38712e15i −0.808179 + 1.39981i 0.105945 + 0.994372i \(0.466213\pi\)
−0.914124 + 0.405435i \(0.867120\pi\)
\(740\) 0 0
\(741\) −2.59012e15 −0.425911
\(742\) 0 0
\(743\) 4.55474e15 0.737947 0.368974 0.929440i \(-0.379709\pi\)
0.368974 + 0.929440i \(0.379709\pi\)
\(744\) 0 0
\(745\) −2.23426e15 + 3.86985e15i −0.356676 + 0.617782i
\(746\) 0 0
\(747\) −1.41133e15 2.44449e15i −0.222006 0.384526i
\(748\) 0 0
\(749\) 4.00282e15 1.04781e16i 0.620463 1.62417i
\(750\) 0 0
\(751\) −4.98893e15 8.64108e15i −0.762058 1.31992i −0.941788 0.336206i \(-0.890856\pi\)
0.179731 0.983716i \(-0.442477\pi\)
\(752\) 0 0
\(753\) −3.17620e15 + 5.50134e15i −0.478118 + 0.828125i
\(754\) 0 0
\(755\) −1.98945e15 −0.295138
\(756\) 0 0
\(757\) 2.16914e15 0.317146 0.158573 0.987347i \(-0.449311\pi\)
0.158573 + 0.987347i \(0.449311\pi\)
\(758\) 0 0
\(759\) −4.90442e14 + 8.49470e14i −0.0706737 + 0.122410i
\(760\) 0 0
\(761\) −4.02973e15 6.97970e15i −0.572349 0.991337i −0.996324 0.0856631i \(-0.972699\pi\)
0.423976 0.905674i \(-0.360634\pi\)
\(762\) 0 0
\(763\) −6.01316e15 + 9.62318e14i −0.841818 + 0.134720i
\(764\) 0 0
\(765\) −3.81078e14 6.60046e14i −0.0525867 0.0910828i
\(766\) 0 0
\(767\) −9.87695e14 + 1.71074e15i −0.134353 + 0.232707i
\(768\) 0 0
\(769\) −2.54259e15 −0.340943 −0.170472 0.985363i \(-0.554529\pi\)
−0.170472 + 0.985363i \(0.554529\pi\)
\(770\) 0 0
\(771\) −4.84749e15 −0.640793
\(772\) 0 0
\(773\) 6.44824e15 1.11687e16i 0.840338 1.45551i −0.0492707 0.998785i \(-0.515690\pi\)
0.889609 0.456723i \(-0.150977\pi\)
\(774\) 0 0
\(775\) 5.03719e14 + 8.72466e14i 0.0647185 + 0.112096i
\(776\) 0