Properties

Label 43.9.b.b.42.4
Level 43
Weight 9
Character 43.42
Analytic conductor 17.517
Analytic rank 0
Dimension 28
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 43.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(17.5172802326\)
Analytic rank: \(0\)
Dimension: \(28\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 42.4
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.25

$q$-expansion

\(f(q)\) \(=\) \(q-24.2897i q^{2} -13.8077i q^{3} -333.988 q^{4} +427.967i q^{5} -335.386 q^{6} +2563.83i q^{7} +1894.31i q^{8} +6370.35 q^{9} +O(q^{10})\) \(q-24.2897i q^{2} -13.8077i q^{3} -333.988 q^{4} +427.967i q^{5} -335.386 q^{6} +2563.83i q^{7} +1894.31i q^{8} +6370.35 q^{9} +10395.2 q^{10} +3299.24 q^{11} +4611.62i q^{12} +1783.00 q^{13} +62274.6 q^{14} +5909.26 q^{15} -39488.8 q^{16} +161819. q^{17} -154734. i q^{18} +188274. i q^{19} -142936. i q^{20} +35400.7 q^{21} -80137.4i q^{22} -430185. q^{23} +26156.2 q^{24} +207469. q^{25} -43308.5i q^{26} -178553. i q^{27} -856290. i q^{28} -1.23444e6i q^{29} -143534. i q^{30} +819928. q^{31} +1.44411e6i q^{32} -45555.0i q^{33} -3.93053e6i q^{34} -1.09724e6 q^{35} -2.12762e6 q^{36} +1.89464e6i q^{37} +4.57312e6 q^{38} -24619.2i q^{39} -810703. q^{40} +1.24331e6 q^{41} -859872. i q^{42} +(1.79787e6 + 2.90790e6i) q^{43} -1.10191e6 q^{44} +2.72630e6i q^{45} +1.04491e7i q^{46} +3.12874e6 q^{47} +545251. i q^{48} -808432. q^{49} -5.03936e6i q^{50} -2.23435e6i q^{51} -595502. q^{52} +6.47469e6 q^{53} -4.33699e6 q^{54} +1.41196e6i q^{55} -4.85670e6 q^{56} +2.59964e6 q^{57} -2.99841e7 q^{58} -177535. q^{59} -1.97362e6 q^{60} +1.30117e7i q^{61} -1.99158e7i q^{62} +1.63325e7i q^{63} +2.49679e7 q^{64} +763066. i q^{65} -1.10652e6 q^{66} -1.94324e7 q^{67} -5.40456e7 q^{68} +5.93988e6i q^{69} +2.66515e7i q^{70} +1.97077e7i q^{71} +1.20674e7i q^{72} -4.15914e7i q^{73} +4.60201e7 q^{74} -2.86468e6i q^{75} -6.28815e7i q^{76} +8.45869e6i q^{77} -597993. q^{78} +8.29308e6 q^{79} -1.68999e7i q^{80} +3.93304e7 q^{81} -3.01997e7i q^{82} +4.28237e7 q^{83} -1.18234e7 q^{84} +6.92532e7i q^{85} +(7.06319e7 - 4.36696e7i) q^{86} -1.70448e7 q^{87} +6.24978e6i q^{88} +2.70210e7i q^{89} +6.62209e7 q^{90} +4.57131e6i q^{91} +1.43677e8 q^{92} -1.13214e7i q^{93} -7.59960e7i q^{94} -8.05752e7 q^{95} +1.99400e7 q^{96} -1.00518e8 q^{97} +1.96366e7i q^{98} +2.10173e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 24.2897i 1.51810i −0.651030 0.759052i \(-0.725663\pi\)
0.651030 0.759052i \(-0.274337\pi\)
\(3\) 13.8077i 0.170466i −0.996361 0.0852330i \(-0.972837\pi\)
0.996361 0.0852330i \(-0.0271635\pi\)
\(4\) −333.988 −1.30464
\(5\) 427.967i 0.684747i 0.939564 + 0.342374i \(0.111231\pi\)
−0.939564 + 0.342374i \(0.888769\pi\)
\(6\) −335.386 −0.258785
\(7\) 2563.83i 1.06782i 0.845542 + 0.533909i \(0.179278\pi\)
−0.845542 + 0.533909i \(0.820722\pi\)
\(8\) 1894.31i 0.462478i
\(9\) 6370.35 0.970941
\(10\) 10395.2 1.03952
\(11\) 3299.24 0.225342 0.112671 0.993632i \(-0.464059\pi\)
0.112671 + 0.993632i \(0.464059\pi\)
\(12\) 4611.62i 0.222397i
\(13\) 1783.00 0.0624278 0.0312139 0.999513i \(-0.490063\pi\)
0.0312139 + 0.999513i \(0.490063\pi\)
\(14\) 62274.6 1.62106
\(15\) 5909.26 0.116726
\(16\) −39488.8 −0.602551
\(17\) 161819. 1.93746 0.968732 0.248109i \(-0.0798092\pi\)
0.968732 + 0.248109i \(0.0798092\pi\)
\(18\) 154734.i 1.47399i
\(19\) 188274.i 1.44470i 0.691529 + 0.722349i \(0.256937\pi\)
−0.691529 + 0.722349i \(0.743063\pi\)
\(20\) 142936.i 0.893350i
\(21\) 35400.7 0.182027
\(22\) 80137.4i 0.342093i
\(23\) −430185. −1.53725 −0.768624 0.639701i \(-0.779058\pi\)
−0.768624 + 0.639701i \(0.779058\pi\)
\(24\) 26156.2 0.0788368
\(25\) 207469. 0.531121
\(26\) 43308.5i 0.0947720i
\(27\) 178553.i 0.335978i
\(28\) 856290.i 1.39312i
\(29\) 1.23444e6i 1.74533i −0.488320 0.872665i \(-0.662390\pi\)
0.488320 0.872665i \(-0.337610\pi\)
\(30\) 143534.i 0.177202i
\(31\) 819928. 0.887828 0.443914 0.896069i \(-0.353589\pi\)
0.443914 + 0.896069i \(0.353589\pi\)
\(32\) 1.44411e6i 1.37721i
\(33\) 45555.0i 0.0384132i
\(34\) 3.93053e6i 2.94127i
\(35\) −1.09724e6 −0.731185
\(36\) −2.12762e6 −1.26673
\(37\) 1.89464e6i 1.01092i 0.862849 + 0.505462i \(0.168678\pi\)
−0.862849 + 0.505462i \(0.831322\pi\)
\(38\) 4.57312e6 2.19320
\(39\) 24619.2i 0.0106418i
\(40\) −810703. −0.316681
\(41\) 1.24331e6 0.439993 0.219996 0.975501i \(-0.429395\pi\)
0.219996 + 0.975501i \(0.429395\pi\)
\(42\) 859872.i 0.276336i
\(43\) 1.79787e6 + 2.90790e6i 0.525877 + 0.850561i
\(44\) −1.10191e6 −0.293991
\(45\) 2.72630e6i 0.664849i
\(46\) 1.04491e7i 2.33370i
\(47\) 3.12874e6 0.641176 0.320588 0.947219i \(-0.396119\pi\)
0.320588 + 0.947219i \(0.396119\pi\)
\(48\) 545251.i 0.102714i
\(49\) −808432. −0.140236
\(50\) 5.03936e6i 0.806298i
\(51\) 2.23435e6i 0.330272i
\(52\) −595502. −0.0814460
\(53\) 6.47469e6 0.820570 0.410285 0.911957i \(-0.365429\pi\)
0.410285 + 0.911957i \(0.365429\pi\)
\(54\) −4.33699e6 −0.510050
\(55\) 1.41196e6i 0.154303i
\(56\) −4.85670e6 −0.493843
\(57\) 2.59964e6 0.246272
\(58\) −2.99841e7 −2.64959
\(59\) −177535. −0.0146513 −0.00732565 0.999973i \(-0.502332\pi\)
−0.00732565 + 0.999973i \(0.502332\pi\)
\(60\) −1.97362e6 −0.152286
\(61\) 1.30117e7i 0.939753i 0.882732 + 0.469876i \(0.155702\pi\)
−0.882732 + 0.469876i \(0.844298\pi\)
\(62\) 1.99158e7i 1.34782i
\(63\) 1.63325e7i 1.03679i
\(64\) 2.49679e7 1.48820
\(65\) 763066.i 0.0427473i
\(66\) −1.10652e6 −0.0583153
\(67\) −1.94324e7 −0.964335 −0.482167 0.876079i \(-0.660150\pi\)
−0.482167 + 0.876079i \(0.660150\pi\)
\(68\) −5.40456e7 −2.52770
\(69\) 5.93988e6i 0.262048i
\(70\) 2.66515e7i 1.11002i
\(71\) 1.97077e7i 0.775536i 0.921757 + 0.387768i \(0.126754\pi\)
−0.921757 + 0.387768i \(0.873246\pi\)
\(72\) 1.20674e7i 0.449039i
\(73\) 4.15914e7i 1.46458i −0.680994 0.732289i \(-0.738452\pi\)
0.680994 0.732289i \(-0.261548\pi\)
\(74\) 4.60201e7 1.53469
\(75\) 2.86468e6i 0.0905381i
\(76\) 6.28815e7i 1.88481i
\(77\) 8.45869e6i 0.240625i
\(78\) −597993. −0.0161554
\(79\) 8.29308e6 0.212916 0.106458 0.994317i \(-0.466049\pi\)
0.106458 + 0.994317i \(0.466049\pi\)
\(80\) 1.68999e7i 0.412595i
\(81\) 3.93304e7 0.913668
\(82\) 3.01997e7i 0.667955i
\(83\) 4.28237e7 0.902344 0.451172 0.892437i \(-0.351006\pi\)
0.451172 + 0.892437i \(0.351006\pi\)
\(84\) −1.18234e7 −0.237480
\(85\) 6.92532e7i 1.32667i
\(86\) 7.06319e7 4.36696e7i 1.29124 0.798336i
\(87\) −1.70448e7 −0.297519
\(88\) 6.24978e6i 0.104216i
\(89\) 2.70210e7i 0.430666i 0.976541 + 0.215333i \(0.0690838\pi\)
−0.976541 + 0.215333i \(0.930916\pi\)
\(90\) 6.62209e7 1.00931
\(91\) 4.57131e6i 0.0666616i
\(92\) 1.43677e8 2.00556
\(93\) 1.13214e7i 0.151345i
\(94\) 7.59960e7i 0.973373i
\(95\) −8.05752e7 −0.989252
\(96\) 1.99400e7 0.234768
\(97\) −1.00518e8 −1.13542 −0.567708 0.823230i \(-0.692170\pi\)
−0.567708 + 0.823230i \(0.692170\pi\)
\(98\) 1.96366e7i 0.212893i
\(99\) 2.10173e7 0.218794
\(100\) −6.92923e7 −0.692923
\(101\) −7.93058e7 −0.762113 −0.381057 0.924552i \(-0.624440\pi\)
−0.381057 + 0.924552i \(0.624440\pi\)
\(102\) −5.42717e7 −0.501387
\(103\) 1.08221e8 0.961533 0.480767 0.876849i \(-0.340358\pi\)
0.480767 + 0.876849i \(0.340358\pi\)
\(104\) 3.37756e6i 0.0288715i
\(105\) 1.51503e7i 0.124642i
\(106\) 1.57268e8i 1.24571i
\(107\) −1.03278e8 −0.787907 −0.393953 0.919130i \(-0.628893\pi\)
−0.393953 + 0.919130i \(0.628893\pi\)
\(108\) 5.96345e7i 0.438332i
\(109\) −2.51482e8 −1.78156 −0.890782 0.454431i \(-0.849842\pi\)
−0.890782 + 0.454431i \(0.849842\pi\)
\(110\) 3.42962e7 0.234247
\(111\) 2.61606e7 0.172328
\(112\) 1.01243e8i 0.643415i
\(113\) 2.85143e8i 1.74884i −0.485171 0.874419i \(-0.661243\pi\)
0.485171 0.874419i \(-0.338757\pi\)
\(114\) 6.31445e7i 0.373866i
\(115\) 1.84105e8i 1.05263i
\(116\) 4.12288e8i 2.27703i
\(117\) 1.13583e7 0.0606138
\(118\) 4.31227e6i 0.0222422i
\(119\) 4.14877e8i 2.06886i
\(120\) 1.11940e7i 0.0539833i
\(121\) −2.03474e8 −0.949221
\(122\) 3.16049e8 1.42664
\(123\) 1.71674e7i 0.0750038i
\(124\) −2.73846e8 −1.15830
\(125\) 2.55965e8i 1.04843i
\(126\) 3.96711e8 1.57395
\(127\) −7.89136e7 −0.303345 −0.151673 0.988431i \(-0.548466\pi\)
−0.151673 + 0.988431i \(0.548466\pi\)
\(128\) 2.36770e8i 0.882036i
\(129\) 4.01515e7 2.48245e7i 0.144992 0.0896441i
\(130\) 1.85346e7 0.0648948
\(131\) 2.16717e8i 0.735882i 0.929849 + 0.367941i \(0.119937\pi\)
−0.929849 + 0.367941i \(0.880063\pi\)
\(132\) 1.52148e7i 0.0501155i
\(133\) −4.82704e8 −1.54267
\(134\) 4.72007e8i 1.46396i
\(135\) 7.64146e7 0.230060
\(136\) 3.06536e8i 0.896035i
\(137\) 4.99384e8i 1.41759i 0.705412 + 0.708797i \(0.250762\pi\)
−0.705412 + 0.708797i \(0.749238\pi\)
\(138\) 1.44278e8 0.397817
\(139\) −1.46570e7 −0.0392632 −0.0196316 0.999807i \(-0.506249\pi\)
−0.0196316 + 0.999807i \(0.506249\pi\)
\(140\) 3.66464e8 0.953935
\(141\) 4.32008e7i 0.109299i
\(142\) 4.78693e8 1.17735
\(143\) 5.88255e6 0.0140676
\(144\) −2.51557e8 −0.585042
\(145\) 5.28299e8 1.19511
\(146\) −1.01024e9 −2.22338
\(147\) 1.11626e7i 0.0239054i
\(148\) 6.32786e8i 1.31889i
\(149\) 7.39245e7i 0.149983i −0.997184 0.0749917i \(-0.976107\pi\)
0.997184 0.0749917i \(-0.0238930\pi\)
\(150\) −6.95822e7 −0.137446
\(151\) 7.14958e8i 1.37522i −0.726079 0.687611i \(-0.758660\pi\)
0.726079 0.687611i \(-0.241340\pi\)
\(152\) −3.56650e8 −0.668141
\(153\) 1.03084e9 1.88116
\(154\) 2.05459e8 0.365294
\(155\) 3.50902e8i 0.607938i
\(156\) 8.22253e6i 0.0138838i
\(157\) 1.90914e7i 0.0314224i −0.999877 0.0157112i \(-0.994999\pi\)
0.999877 0.0157112i \(-0.00500124\pi\)
\(158\) 2.01436e8i 0.323228i
\(159\) 8.94008e7i 0.139879i
\(160\) −6.18033e8 −0.943044
\(161\) 1.10292e9i 1.64150i
\(162\) 9.55323e8i 1.38704i
\(163\) 5.04417e8i 0.714561i 0.933997 + 0.357281i \(0.116296\pi\)
−0.933997 + 0.357281i \(0.883704\pi\)
\(164\) −4.15253e8 −0.574033
\(165\) 1.94960e7 0.0263033
\(166\) 1.04017e9i 1.36985i
\(167\) −6.01163e8 −0.772906 −0.386453 0.922309i \(-0.626300\pi\)
−0.386453 + 0.922309i \(0.626300\pi\)
\(168\) 6.70600e7i 0.0841834i
\(169\) −8.12552e8 −0.996103
\(170\) 1.68214e9 2.01403
\(171\) 1.19937e9i 1.40272i
\(172\) −6.00467e8 9.71204e8i −0.686081 1.10968i
\(173\) −8.47715e7 −0.0946380 −0.0473190 0.998880i \(-0.515068\pi\)
−0.0473190 + 0.998880i \(0.515068\pi\)
\(174\) 4.14013e8i 0.451665i
\(175\) 5.31916e8i 0.567141i
\(176\) −1.30283e8 −0.135780
\(177\) 2.45136e6i 0.00249755i
\(178\) 6.56331e8 0.653797
\(179\) 1.43087e8i 0.139376i 0.997569 + 0.0696882i \(0.0222004\pi\)
−0.997569 + 0.0696882i \(0.977800\pi\)
\(180\) 9.10552e8i 0.867390i
\(181\) 8.57397e8 0.798854 0.399427 0.916765i \(-0.369209\pi\)
0.399427 + 0.916765i \(0.369209\pi\)
\(182\) 1.11036e8 0.101199
\(183\) 1.79662e8 0.160196
\(184\) 8.14904e8i 0.710944i
\(185\) −8.10842e8 −0.692228
\(186\) −2.74992e8 −0.229757
\(187\) 5.33879e8 0.436593
\(188\) −1.04496e9 −0.836505
\(189\) 4.57779e8 0.358764
\(190\) 1.95715e9i 1.50179i
\(191\) 1.26564e9i 0.950990i −0.879718 0.475495i \(-0.842269\pi\)
0.879718 0.475495i \(-0.157731\pi\)
\(192\) 3.44751e8i 0.253688i
\(193\) 1.30174e9 0.938198 0.469099 0.883145i \(-0.344579\pi\)
0.469099 + 0.883145i \(0.344579\pi\)
\(194\) 2.44154e9i 1.72368i
\(195\) 1.05362e7 0.00728695
\(196\) 2.70007e8 0.182958
\(197\) 2.06607e9 1.37177 0.685885 0.727710i \(-0.259415\pi\)
0.685885 + 0.727710i \(0.259415\pi\)
\(198\) 5.10503e8i 0.332153i
\(199\) 9.02872e8i 0.575723i −0.957672 0.287862i \(-0.907056\pi\)
0.957672 0.287862i \(-0.0929443\pi\)
\(200\) 3.93012e8i 0.245632i
\(201\) 2.68318e8i 0.164386i
\(202\) 1.92631e9i 1.15697i
\(203\) 3.16489e9 1.86370
\(204\) 7.46248e8i 0.430886i
\(205\) 5.32098e8i 0.301284i
\(206\) 2.62866e9i 1.45971i
\(207\) −2.74043e9 −1.49258
\(208\) −7.04086e7 −0.0376160
\(209\) 6.21162e8i 0.325552i
\(210\) 3.67997e8 0.189220
\(211\) 2.34791e9i 1.18454i −0.805738 0.592272i \(-0.798231\pi\)
0.805738 0.592272i \(-0.201769\pi\)
\(212\) −2.16247e9 −1.07055
\(213\) 2.72119e8 0.132203
\(214\) 2.50860e9i 1.19612i
\(215\) −1.24448e9 + 7.69428e8i −0.582419 + 0.360093i
\(216\) 3.38234e8 0.155383
\(217\) 2.10216e9i 0.948039i
\(218\) 6.10842e9i 2.70460i
\(219\) −5.74284e8 −0.249661
\(220\) 4.71580e8i 0.201310i
\(221\) 2.88523e8 0.120952
\(222\) 6.35434e8i 0.261612i
\(223\) 2.77345e9i 1.12150i −0.827984 0.560752i \(-0.810512\pi\)
0.827984 0.560752i \(-0.189488\pi\)
\(224\) −3.70247e9 −1.47061
\(225\) 1.32165e9 0.515688
\(226\) −6.92604e9 −2.65492
\(227\) 2.06840e8i 0.0778989i −0.999241 0.0389494i \(-0.987599\pi\)
0.999241 0.0389494i \(-0.0124011\pi\)
\(228\) −8.68251e8 −0.321296
\(229\) −2.78916e9 −1.01422 −0.507110 0.861881i \(-0.669286\pi\)
−0.507110 + 0.861881i \(0.669286\pi\)
\(230\) −4.47185e9 −1.59800
\(231\) 1.16795e8 0.0410183
\(232\) 2.33841e9 0.807177
\(233\) 3.53341e9i 1.19887i −0.800425 0.599433i \(-0.795393\pi\)
0.800425 0.599433i \(-0.204607\pi\)
\(234\) 2.75890e8i 0.0920180i
\(235\) 1.33900e9i 0.439044i
\(236\) 5.92946e7 0.0191147
\(237\) 1.14509e8i 0.0362949i
\(238\) 1.00772e10 3.14075
\(239\) −2.07769e9 −0.636781 −0.318391 0.947960i \(-0.603142\pi\)
−0.318391 + 0.947960i \(0.603142\pi\)
\(240\) −2.33349e8 −0.0703334
\(241\) 2.64446e8i 0.0783916i −0.999232 0.0391958i \(-0.987520\pi\)
0.999232 0.0391958i \(-0.0124796\pi\)
\(242\) 4.94232e9i 1.44102i
\(243\) 1.71455e9i 0.491728i
\(244\) 4.34575e9i 1.22604i
\(245\) 3.45982e8i 0.0960261i
\(246\) −4.16990e8 −0.113864
\(247\) 3.35694e8i 0.0901893i
\(248\) 1.55320e9i 0.410602i
\(249\) 5.91299e8i 0.153819i
\(250\) 6.21730e9 1.59163
\(251\) 3.38964e9 0.854003 0.427001 0.904251i \(-0.359570\pi\)
0.427001 + 0.904251i \(0.359570\pi\)
\(252\) 5.45486e9i 1.35264i
\(253\) −1.41928e9 −0.346407
\(254\) 1.91679e9i 0.460510i
\(255\) 9.56230e8 0.226153
\(256\) 6.40731e8 0.149182
\(257\) 6.06881e9i 1.39114i −0.718458 0.695570i \(-0.755152\pi\)
0.718458 0.695570i \(-0.244848\pi\)
\(258\) −6.02979e8 9.75267e8i −0.136089 0.220112i
\(259\) −4.85753e9 −1.07948
\(260\) 2.54855e8i 0.0557699i
\(261\) 7.86380e9i 1.69461i
\(262\) 5.26399e9 1.11715
\(263\) 7.16640e9i 1.49788i 0.662635 + 0.748942i \(0.269438\pi\)
−0.662635 + 0.748942i \(0.730562\pi\)
\(264\) 8.62954e7 0.0177653
\(265\) 2.77095e9i 0.561883i
\(266\) 1.17247e10i 2.34194i
\(267\) 3.73099e8 0.0734140
\(268\) 6.49020e9 1.25811
\(269\) −1.04774e9 −0.200098 −0.100049 0.994982i \(-0.531900\pi\)
−0.100049 + 0.994982i \(0.531900\pi\)
\(270\) 1.85609e9i 0.349256i
\(271\) −8.61683e9 −1.59761 −0.798804 0.601591i \(-0.794534\pi\)
−0.798804 + 0.601591i \(0.794534\pi\)
\(272\) −6.39004e9 −1.16742
\(273\) 6.31195e7 0.0113635
\(274\) 1.21299e10 2.15206
\(275\) 6.84491e8 0.119684
\(276\) 1.98385e9i 0.341879i
\(277\) 8.11515e9i 1.37841i −0.724568 0.689204i \(-0.757961\pi\)
0.724568 0.689204i \(-0.242039\pi\)
\(278\) 3.56013e8i 0.0596056i
\(279\) 5.22323e9 0.862029
\(280\) 2.07851e9i 0.338158i
\(281\) −3.10778e9 −0.498454 −0.249227 0.968445i \(-0.580177\pi\)
−0.249227 + 0.968445i \(0.580177\pi\)
\(282\) −1.04933e9 −0.165927
\(283\) 9.84866e9 1.53544 0.767718 0.640788i \(-0.221392\pi\)
0.767718 + 0.640788i \(0.221392\pi\)
\(284\) 6.58214e9i 1.01180i
\(285\) 1.11256e9i 0.168634i
\(286\) 1.42885e8i 0.0213561i
\(287\) 3.18765e9i 0.469832i
\(288\) 9.19951e9i 1.33719i
\(289\) 1.92096e10 2.75377
\(290\) 1.28322e10i 1.81430i
\(291\) 1.38792e9i 0.193550i
\(292\) 1.38911e10i 1.91075i
\(293\) −1.18065e10 −1.60195 −0.800977 0.598695i \(-0.795686\pi\)
−0.800977 + 0.598695i \(0.795686\pi\)
\(294\) 2.71136e8 0.0362910
\(295\) 7.59791e7i 0.0100324i
\(296\) −3.58903e9 −0.467531
\(297\) 5.89088e8i 0.0757102i
\(298\) −1.79560e9 −0.227690
\(299\) −7.67020e8 −0.0959670
\(300\) 9.56771e8i 0.118120i
\(301\) −7.45536e9 + 4.60943e9i −0.908244 + 0.561541i
\(302\) −1.73661e10 −2.08773
\(303\) 1.09503e9i 0.129914i
\(304\) 7.43473e9i 0.870504i
\(305\) −5.56856e9 −0.643493
\(306\) 2.50388e10i 2.85580i
\(307\) −3.68250e9 −0.414561 −0.207281 0.978282i \(-0.566461\pi\)
−0.207281 + 0.978282i \(0.566461\pi\)
\(308\) 2.82510e9i 0.313929i
\(309\) 1.49429e9i 0.163909i
\(310\) 8.52330e9 0.922913
\(311\) 5.09479e9 0.544609 0.272305 0.962211i \(-0.412214\pi\)
0.272305 + 0.962211i \(0.412214\pi\)
\(312\) 4.66365e7 0.00492161
\(313\) 8.21077e9i 0.855473i −0.903903 0.427736i \(-0.859311\pi\)
0.903903 0.427736i \(-0.140689\pi\)
\(314\) −4.63725e8 −0.0477025
\(315\) −6.98977e9 −0.709938
\(316\) −2.76979e9 −0.277779
\(317\) 1.07248e10 1.06207 0.531034 0.847351i \(-0.321804\pi\)
0.531034 + 0.847351i \(0.321804\pi\)
\(318\) −2.17152e9 −0.212351
\(319\) 4.07271e9i 0.393297i
\(320\) 1.06854e10i 1.01904i
\(321\) 1.42604e9i 0.134311i
\(322\) −2.67896e10 −2.49197
\(323\) 3.04664e10i 2.79905i
\(324\) −1.31359e10 −1.19201
\(325\) 3.69918e8 0.0331568
\(326\) 1.22521e10 1.08478
\(327\) 3.47240e9i 0.303696i
\(328\) 2.35523e9i 0.203487i
\(329\) 8.02155e9i 0.684660i
\(330\) 4.73553e8i 0.0399312i
\(331\) 2.06009e9i 0.171623i 0.996311 + 0.0858114i \(0.0273482\pi\)
−0.996311 + 0.0858114i \(0.972652\pi\)
\(332\) −1.43026e10 −1.17724
\(333\) 1.20695e10i 0.981549i
\(334\) 1.46021e10i 1.17335i
\(335\) 8.31643e9i 0.660325i
\(336\) −1.39793e9 −0.109680
\(337\) 1.19620e10 0.927436 0.463718 0.885983i \(-0.346515\pi\)
0.463718 + 0.885983i \(0.346515\pi\)
\(338\) 1.97366e10i 1.51219i
\(339\) −3.93719e9 −0.298117
\(340\) 2.31297e10i 1.73083i
\(341\) 2.70514e9 0.200065
\(342\) 2.91324e10 2.12947
\(343\) 1.27073e10i 0.918072i
\(344\) −5.50846e9 + 3.40572e9i −0.393366 + 0.243207i
\(345\) −2.54207e9 −0.179437
\(346\) 2.05907e9i 0.143670i
\(347\) 3.44498e9i 0.237612i 0.992917 + 0.118806i \(0.0379067\pi\)
−0.992917 + 0.118806i \(0.962093\pi\)
\(348\) 5.69277e9 0.388156
\(349\) 8.41368e9i 0.567132i −0.958953 0.283566i \(-0.908482\pi\)
0.958953 0.283566i \(-0.0915176\pi\)
\(350\) 1.29201e10 0.860980
\(351\) 3.18360e8i 0.0209744i
\(352\) 4.76448e9i 0.310345i
\(353\) 1.58116e10 1.01830 0.509152 0.860677i \(-0.329959\pi\)
0.509152 + 0.860677i \(0.329959\pi\)
\(354\) 5.95427e7 0.00379154
\(355\) −8.43424e9 −0.531046
\(356\) 9.02469e9i 0.561865i
\(357\) 5.72851e9 0.352670
\(358\) 3.47555e9 0.211588
\(359\) −1.75353e10 −1.05568 −0.527842 0.849342i \(-0.676999\pi\)
−0.527842 + 0.849342i \(0.676999\pi\)
\(360\) −5.16446e9 −0.307478
\(361\) −1.84637e10 −1.08715
\(362\) 2.08259e10i 1.21274i
\(363\) 2.80952e9i 0.161810i
\(364\) 1.52677e9i 0.0869695i
\(365\) 1.77998e10 1.00287
\(366\) 4.36393e9i 0.243194i
\(367\) 1.96675e10 1.08414 0.542069 0.840334i \(-0.317641\pi\)
0.542069 + 0.840334i \(0.317641\pi\)
\(368\) 1.69875e10 0.926271
\(369\) 7.92034e9 0.427207
\(370\) 1.96951e10i 1.05087i
\(371\) 1.66000e10i 0.876219i
\(372\) 3.78120e9i 0.197450i
\(373\) 2.22528e10i 1.14961i −0.818291 0.574804i \(-0.805078\pi\)
0.818291 0.574804i \(-0.194922\pi\)
\(374\) 1.29678e10i 0.662794i
\(375\) 3.53429e9 0.178722
\(376\) 5.92680e9i 0.296530i
\(377\) 2.20101e9i 0.108957i
\(378\) 1.11193e10i 0.544641i
\(379\) −2.22479e10 −1.07828 −0.539141 0.842215i \(-0.681251\pi\)
−0.539141 + 0.842215i \(0.681251\pi\)
\(380\) 2.69112e10 1.29062
\(381\) 1.08962e9i 0.0517100i
\(382\) −3.07419e10 −1.44370
\(383\) 1.88396e10i 0.875542i −0.899087 0.437771i \(-0.855768\pi\)
0.899087 0.437771i \(-0.144232\pi\)
\(384\) −3.26925e9 −0.150357
\(385\) −3.62004e9 −0.164767
\(386\) 3.16188e10i 1.42428i
\(387\) 1.14530e10 + 1.85243e10i 0.510596 + 0.825845i
\(388\) 3.35717e10 1.48131
\(389\) 7.04839e9i 0.307816i 0.988085 + 0.153908i \(0.0491860\pi\)
−0.988085 + 0.153908i \(0.950814\pi\)
\(390\) 2.55921e8i 0.0110624i
\(391\) −6.96121e10 −2.97836
\(392\) 1.53142e9i 0.0648561i
\(393\) 2.99237e9 0.125443
\(394\) 5.01843e10i 2.08249i
\(395\) 3.54917e9i 0.145793i
\(396\) −7.01953e9 −0.285448
\(397\) −7.77464e9 −0.312981 −0.156491 0.987679i \(-0.550018\pi\)
−0.156491 + 0.987679i \(0.550018\pi\)
\(398\) −2.19305e10 −0.874008
\(399\) 6.66505e9i 0.262973i
\(400\) −8.19271e9 −0.320028
\(401\) 1.87199e9 0.0723980 0.0361990 0.999345i \(-0.488475\pi\)
0.0361990 + 0.999345i \(0.488475\pi\)
\(402\) 6.51735e9 0.249555
\(403\) 1.46193e9 0.0554252
\(404\) 2.64872e10 0.994285
\(405\) 1.68321e10i 0.625632i
\(406\) 7.68742e10i 2.82928i
\(407\) 6.25085e9i 0.227804i
\(408\) 4.23256e9 0.152744
\(409\) 1.64058e10i 0.586278i −0.956070 0.293139i \(-0.905300\pi\)
0.956070 0.293139i \(-0.0946999\pi\)
\(410\) 1.29245e10 0.457380
\(411\) 6.89536e9 0.241652
\(412\) −3.61447e10 −1.25446
\(413\) 4.55170e8i 0.0156449i
\(414\) 6.65641e10i 2.26589i
\(415\) 1.83271e10i 0.617877i
\(416\) 2.57486e9i 0.0859765i
\(417\) 2.02380e8i 0.00669304i
\(418\) 1.50878e10 0.494221
\(419\) 4.87108e10i 1.58041i −0.612844 0.790204i \(-0.709975\pi\)
0.612844 0.790204i \(-0.290025\pi\)
\(420\) 5.06004e9i 0.162613i
\(421\) 9.06047e9i 0.288418i 0.989547 + 0.144209i \(0.0460638\pi\)
−0.989547 + 0.144209i \(0.953936\pi\)
\(422\) −5.70299e10 −1.79826
\(423\) 1.99311e10 0.622545
\(424\) 1.22651e10i 0.379496i
\(425\) 3.35725e10 1.02903
\(426\) 6.60967e9i 0.200697i
\(427\) −3.33597e10 −1.00349
\(428\) 3.44938e10 1.02794
\(429\) 8.12247e7i 0.00239805i
\(430\) 1.86892e10 + 3.02281e10i 0.546658 + 0.884173i
\(431\) −4.56887e9 −0.132404 −0.0662019 0.997806i \(-0.521088\pi\)
−0.0662019 + 0.997806i \(0.521088\pi\)
\(432\) 7.05083e9i 0.202444i
\(433\) 1.09451e10i 0.311363i 0.987807 + 0.155681i \(0.0497573\pi\)
−0.987807 + 0.155681i \(0.950243\pi\)
\(434\) 5.10607e10 1.43922
\(435\) 7.29461e9i 0.203725i
\(436\) 8.39921e10 2.32430
\(437\) 8.09928e10i 2.22086i
\(438\) 1.39492e10i 0.379011i
\(439\) −8.95525e9 −0.241112 −0.120556 0.992706i \(-0.538468\pi\)
−0.120556 + 0.992706i \(0.538468\pi\)
\(440\) −2.67470e9 −0.0713616
\(441\) −5.14999e9 −0.136161
\(442\) 7.00814e9i 0.183617i
\(443\) 2.28878e10 0.594277 0.297139 0.954834i \(-0.403968\pi\)
0.297139 + 0.954834i \(0.403968\pi\)
\(444\) −8.73735e9 −0.224827
\(445\) −1.15641e10 −0.294898
\(446\) −6.73662e10 −1.70256
\(447\) −1.02073e9 −0.0255671
\(448\) 6.40136e10i 1.58913i
\(449\) 1.64061e10i 0.403664i 0.979420 + 0.201832i \(0.0646894\pi\)
−0.979420 + 0.201832i \(0.935311\pi\)
\(450\) 3.21025e10i 0.782868i
\(451\) 4.10199e9 0.0991490
\(452\) 9.52346e10i 2.28161i
\(453\) −9.87196e9 −0.234428
\(454\) −5.02408e9 −0.118259
\(455\) −1.95637e9 −0.0456463
\(456\) 4.92454e9i 0.113895i
\(457\) 6.73001e9i 0.154295i 0.997020 + 0.0771473i \(0.0245812\pi\)
−0.997020 + 0.0771473i \(0.975419\pi\)
\(458\) 6.77479e10i 1.53969i
\(459\) 2.88932e10i 0.650946i
\(460\) 6.14889e10i 1.37330i
\(461\) 9.84296e9 0.217932 0.108966 0.994045i \(-0.465246\pi\)
0.108966 + 0.994045i \(0.465246\pi\)
\(462\) 2.83692e9i 0.0622701i
\(463\) 6.34452e10i 1.38062i 0.723513 + 0.690311i \(0.242526\pi\)
−0.723513 + 0.690311i \(0.757474\pi\)
\(464\) 4.87465e10i 1.05165i
\(465\) 4.84517e9 0.103633
\(466\) −8.58254e10 −1.82000
\(467\) 3.63255e10i 0.763738i 0.924217 + 0.381869i \(0.124719\pi\)
−0.924217 + 0.381869i \(0.875281\pi\)
\(468\) −3.79355e9 −0.0790793
\(469\) 4.98215e10i 1.02973i
\(470\) 3.25238e10 0.666514
\(471\) −2.63610e8 −0.00535645
\(472\) 3.36307e8i 0.00677591i
\(473\) 5.93160e9 + 9.59385e9i 0.118502 + 0.191667i
\(474\) −2.78138e9 −0.0550994
\(475\) 3.90612e10i 0.767310i
\(476\) 1.38564e11i 2.69912i
\(477\) 4.12460e10 0.796725
\(478\) 5.04665e10i 0.966700i
\(479\) −6.24570e10 −1.18642 −0.593211 0.805047i \(-0.702140\pi\)
−0.593211 + 0.805047i \(0.702140\pi\)
\(480\) 8.53364e9i 0.160757i
\(481\) 3.37814e9i 0.0631098i
\(482\) −6.42332e9 −0.119007
\(483\) −1.52289e10 −0.279820
\(484\) 6.79579e10 1.23839
\(485\) 4.30182e10i 0.777473i
\(486\) −4.16458e10 −0.746494
\(487\) −7.05965e10 −1.25507 −0.627534 0.778589i \(-0.715936\pi\)
−0.627534 + 0.778589i \(0.715936\pi\)
\(488\) −2.46482e10 −0.434615
\(489\) 6.96486e9 0.121808
\(490\) −8.40380e9 −0.145778
\(491\) 4.83027e10i 0.831085i −0.909574 0.415542i \(-0.863592\pi\)
0.909574 0.415542i \(-0.136408\pi\)
\(492\) 5.73370e9i 0.0978531i
\(493\) 1.99756e11i 3.38151i
\(494\) 8.15389e9 0.136917
\(495\) 8.99470e9i 0.149819i
\(496\) −3.23780e10 −0.534962
\(497\) −5.05272e10 −0.828132
\(498\) −1.43625e10 −0.233513
\(499\) 6.67014e10i 1.07580i 0.843008 + 0.537901i \(0.180783\pi\)
−0.843008 + 0.537901i \(0.819217\pi\)
\(500\) 8.54892e10i 1.36783i
\(501\) 8.30071e9i 0.131754i
\(502\) 8.23333e10i 1.29647i
\(503\) 1.08689e11i 1.69791i 0.528468 + 0.848954i \(0.322767\pi\)
−0.528468 + 0.848954i \(0.677233\pi\)
\(504\) −3.09388e10 −0.479493
\(505\) 3.39403e10i 0.521855i
\(506\) 3.44739e10i 0.525882i
\(507\) 1.12195e10i 0.169802i
\(508\) 2.63562e10 0.395757
\(509\) 2.21280e10 0.329664 0.164832 0.986322i \(-0.447292\pi\)
0.164832 + 0.986322i \(0.447292\pi\)
\(510\) 2.32265e10i 0.343323i
\(511\) 1.06633e11 1.56390
\(512\) 7.61762e10i 1.10851i
\(513\) 3.36169e10 0.485387
\(514\) −1.47409e11 −2.11190
\(515\) 4.63152e10i 0.658407i
\(516\) −1.34101e10 + 8.29109e9i −0.189162 + 0.116953i
\(517\) 1.03224e10 0.144484
\(518\) 1.17988e11i 1.63877i
\(519\) 1.17050e9i 0.0161326i
\(520\) −1.44548e9 −0.0197697
\(521\) 8.18254e10i 1.11055i −0.831668 0.555274i \(-0.812613\pi\)
0.831668 0.555274i \(-0.187387\pi\)
\(522\) −1.91009e11 −2.57260
\(523\) 1.35833e10i 0.181552i −0.995871 0.0907758i \(-0.971065\pi\)
0.995871 0.0907758i \(-0.0289347\pi\)
\(524\) 7.23810e10i 0.960063i
\(525\) 7.34456e9 0.0966783
\(526\) 1.74070e11 2.27395
\(527\) 1.32680e11 1.72014
\(528\) 1.79891e9i 0.0231459i
\(529\) 1.06748e11 1.36313
\(530\) 6.73056e10 0.852997
\(531\) −1.13096e9 −0.0142255
\(532\) 1.61217e11 2.01264
\(533\) 2.21683e9 0.0274678
\(534\) 9.06244e9i 0.111450i
\(535\) 4.41998e10i 0.539517i
\(536\) 3.68111e10i 0.445984i
\(537\) 1.97571e9 0.0237589
\(538\) 2.54492e10i 0.303770i
\(539\) −2.66721e9 −0.0316011
\(540\) −2.55216e10 −0.300146
\(541\) −2.54665e10 −0.297289 −0.148645 0.988891i \(-0.547491\pi\)
−0.148645 + 0.988891i \(0.547491\pi\)
\(542\) 2.09300e11i 2.42534i
\(543\) 1.18387e10i 0.136177i
\(544\) 2.33685e11i 2.66830i
\(545\) 1.07626e11i 1.21992i
\(546\) 1.53315e9i 0.0172510i
\(547\) −1.06228e11 −1.18656 −0.593278 0.804998i \(-0.702167\pi\)
−0.593278 + 0.804998i \(0.702167\pi\)
\(548\) 1.66788e11i 1.84945i
\(549\) 8.28888e10i 0.912445i
\(550\) 1.66261e10i 0.181693i
\(551\) 2.32413e11 2.52147
\(552\) −1.12520e10 −0.121192
\(553\) 2.12621e10i 0.227355i
\(554\) −1.97114e11 −2.09257
\(555\) 1.11959e10i 0.118001i
\(556\) 4.89526e9 0.0512244
\(557\) −5.50843e10 −0.572278 −0.286139 0.958188i \(-0.592372\pi\)
−0.286139 + 0.958188i \(0.592372\pi\)
\(558\) 1.26870e11i 1.30865i
\(559\) 3.20560e9 + 5.18479e9i 0.0328293 + 0.0530987i
\(560\) 4.33285e10 0.440577
\(561\) 7.37167e9i 0.0744242i
\(562\) 7.54871e10i 0.756706i
\(563\) 1.49411e11 1.48713 0.743564 0.668664i \(-0.233134\pi\)
0.743564 + 0.668664i \(0.233134\pi\)
\(564\) 1.44286e10i 0.142596i
\(565\) 1.22032e11 1.19751
\(566\) 2.39221e11i 2.33095i
\(567\) 1.00837e11i 0.975632i
\(568\) −3.73325e10 −0.358669
\(569\) −1.27794e11 −1.21916 −0.609582 0.792723i \(-0.708663\pi\)
−0.609582 + 0.792723i \(0.708663\pi\)
\(570\) 2.70238e10 0.256004
\(571\) 1.25011e11i 1.17599i −0.808865 0.587995i \(-0.799918\pi\)
0.808865 0.587995i \(-0.200082\pi\)
\(572\) −1.96470e9 −0.0183532
\(573\) −1.74756e10 −0.162111
\(574\) 7.74270e10 0.713255
\(575\) −8.92502e10 −0.816465
\(576\) 1.59054e11 1.44496
\(577\) 1.59101e11i 1.43539i 0.696360 + 0.717693i \(0.254802\pi\)
−0.696360 + 0.717693i \(0.745198\pi\)
\(578\) 4.66595e11i 4.18051i
\(579\) 1.79741e10i 0.159931i
\(580\) −1.76446e11 −1.55919
\(581\) 1.09793e11i 0.963539i
\(582\) 3.37122e10 0.293829
\(583\) 2.13615e10 0.184909
\(584\) 7.87871e10 0.677336
\(585\) 4.86099e9i 0.0415051i
\(586\) 2.86776e11i 2.43193i
\(587\) 1.39779e10i 0.117731i 0.998266 + 0.0588654i \(0.0187483\pi\)
−0.998266 + 0.0588654i \(0.981252\pi\)
\(588\) 3.72819e9i 0.0311880i
\(589\) 1.54372e11i 1.28264i
\(590\) −1.84551e9 −0.0152303
\(591\) 2.85278e10i 0.233840i
\(592\) 7.48169e10i 0.609134i
\(593\) 8.73992e10i 0.706787i −0.935475 0.353394i \(-0.885028\pi\)
0.935475 0.353394i \(-0.114972\pi\)
\(594\) −1.43088e10 −0.114936
\(595\) −1.77553e11 −1.41665
\(596\) 2.46899e10i 0.195675i
\(597\) −1.24666e10 −0.0981412
\(598\) 1.86307e10i 0.145688i
\(599\) −1.57778e11 −1.22557 −0.612785 0.790250i \(-0.709951\pi\)
−0.612785 + 0.790250i \(0.709951\pi\)
\(600\) 5.42660e9 0.0418719
\(601\) 1.08858e11i 0.834381i −0.908819 0.417190i \(-0.863015\pi\)
0.908819 0.417190i \(-0.136985\pi\)
\(602\) 1.11962e11 + 1.81088e11i 0.852478 + 1.37881i
\(603\) −1.23791e11 −0.936312
\(604\) 2.38788e11i 1.79417i
\(605\) 8.70801e10i 0.649976i
\(606\) 2.65980e10 0.197224
\(607\) 2.80501e10i 0.206624i −0.994649 0.103312i \(-0.967056\pi\)
0.994649 0.103312i \(-0.0329440\pi\)
\(608\) −2.71890e11 −1.98966
\(609\) 4.37000e10i 0.317697i
\(610\) 1.35259e11i 0.976890i
\(611\) 5.57854e9 0.0400272
\(612\) −3.44289e11 −2.45425
\(613\) 9.06755e10 0.642167 0.321084 0.947051i \(-0.395953\pi\)
0.321084 + 0.947051i \(0.395953\pi\)
\(614\) 8.94466e10i 0.629348i
\(615\) 7.34707e9 0.0513586
\(616\) −1.60234e10 −0.111284
\(617\) 2.14084e11 1.47721 0.738607 0.674136i \(-0.235484\pi\)
0.738607 + 0.674136i \(0.235484\pi\)
\(618\) −3.62959e10 −0.248831
\(619\) −4.84848e10 −0.330250 −0.165125 0.986273i \(-0.552803\pi\)
−0.165125 + 0.986273i \(0.552803\pi\)
\(620\) 1.17197e11i 0.793141i
\(621\) 7.68107e10i 0.516482i
\(622\) 1.23751e11i 0.826774i
\(623\) −6.92772e10 −0.459873
\(624\) 9.72183e8i 0.00641224i
\(625\) −2.85017e10 −0.186789
\(626\) −1.99437e11 −1.29870
\(627\) 8.57685e9 0.0554955
\(628\) 6.37631e9i 0.0409950i
\(629\) 3.06588e11i 1.95863i
\(630\) 1.69779e11i 1.07776i
\(631\) 1.62923e11i 1.02770i −0.857881 0.513848i \(-0.828220\pi\)
0.857881 0.513848i \(-0.171780\pi\)
\(632\) 1.57097e10i 0.0984689i
\(633\) −3.24193e10 −0.201924
\(634\) 2.60502e11i 1.61233i
\(635\) 3.37724e10i 0.207715i
\(636\) 2.98588e10i 0.182492i
\(637\) −1.44144e9 −0.00875462
\(638\) −9.89247e10 −0.597066
\(639\) 1.25545e11i 0.753000i
\(640\) 1.01330e11 0.603971
\(641\) 1.93130e11i 1.14398i −0.820262 0.571988i \(-0.806172\pi\)
0.820262 0.571988i \(-0.193828\pi\)
\(642\) 3.46381e10 0.203899
\(643\) −2.75508e11 −1.61172 −0.805861 0.592105i \(-0.798297\pi\)
−0.805861 + 0.592105i \(0.798297\pi\)
\(644\) 3.68363e11i 2.14157i
\(645\) 1.06241e10 + 1.71835e10i 0.0613835 + 0.0992826i
\(646\) 7.40018e11 4.24925
\(647\) 1.84960e11i 1.05550i 0.849398 + 0.527752i \(0.176965\pi\)
−0.849398 + 0.527752i \(0.823035\pi\)
\(648\) 7.45041e10i 0.422552i
\(649\) −5.85730e8 −0.00330156
\(650\) 8.98519e9i 0.0503354i
\(651\) 2.90261e10 0.161608
\(652\) 1.68470e11i 0.932247i
\(653\) 2.03633e11i 1.11994i −0.828513 0.559970i \(-0.810813\pi\)
0.828513 0.559970i \(-0.189187\pi\)
\(654\) 8.43435e10 0.461042
\(655\) −9.27478e10 −0.503893
\(656\) −4.90970e10 −0.265118
\(657\) 2.64952e11i 1.42202i
\(658\) 1.94841e11 1.03939
\(659\) 3.21214e11 1.70315 0.851575 0.524232i \(-0.175648\pi\)
0.851575 + 0.524232i \(0.175648\pi\)
\(660\) −6.51145e9 −0.0343164
\(661\) −2.59186e11 −1.35771 −0.678853 0.734274i \(-0.737523\pi\)
−0.678853 + 0.734274i \(0.737523\pi\)
\(662\) 5.00390e10 0.260541
\(663\) 3.98386e9i 0.0206181i
\(664\) 8.11215e10i 0.417315i
\(665\) 2.06581e11i 1.05634i
\(666\) 2.93164e11 1.49009
\(667\) 5.31037e11i 2.68300i
\(668\) 2.00781e11 1.00837
\(669\) −3.82951e10 −0.191178
\(670\) −2.02003e11 −1.00244
\(671\) 4.29286e10i 0.211766i
\(672\) 5.11227e10i 0.250690i
\(673\) 1.82200e11i 0.888153i 0.895989 + 0.444077i \(0.146468\pi\)
−0.895989 + 0.444077i \(0.853532\pi\)
\(674\) 2.90553e11i 1.40794i
\(675\) 3.70442e10i 0.178445i
\(676\) 2.71383e11 1.29956
\(677\) 3.72816e11i 1.77476i 0.461040 + 0.887379i \(0.347476\pi\)
−0.461040 + 0.887379i \(0.652524\pi\)
\(678\) 9.56330e10i 0.452573i
\(679\) 2.57710e11i 1.21242i
\(680\) −1.31187e11 −0.613558
\(681\) −2.85599e9 −0.0132791
\(682\) 6.57069e10i 0.303720i
\(683\) −5.95037e10 −0.273439 −0.136720 0.990610i \(-0.543656\pi\)
−0.136720 + 0.990610i \(0.543656\pi\)
\(684\) 4.00577e11i 1.83004i
\(685\) −2.13720e11 −0.970694
\(686\) 3.08656e11 1.39373
\(687\) 3.85121e10i 0.172890i
\(688\) −7.09957e10 1.14829e11i −0.316868 0.512506i
\(689\) 1.15444e10 0.0512264
\(690\) 6.17461e10i 0.272404i
\(691\) 1.43990e11i 0.631568i −0.948831 0.315784i \(-0.897732\pi\)
0.948831 0.315784i \(-0.102268\pi\)
\(692\) 2.83127e10 0.123469
\(693\) 5.38848e10i 0.233633i
\(694\) 8.36775e10 0.360721
\(695\) 6.27271e9i 0.0268854i
\(696\) 3.22882e10i 0.137596i
\(697\) 2.01192e11 0.852470
\(698\) −2.04366e11 −0.860966
\(699\) −4.87884e10 −0.204366
\(700\) 1.77654e11i 0.739916i
\(701\) 3.56792e11 1.47755 0.738776 0.673951i \(-0.235404\pi\)
0.738776 + 0.673951i \(0.235404\pi\)
\(702\) −7.73285e9 −0.0318413
\(703\) −3.56711e11 −1.46048
\(704\) 8.23751e10 0.335356
\(705\) 1.84885e10 0.0748420
\(706\) 3.84059e11i 1.54589i
\(707\) 2.03327e11i 0.813798i
\(708\) 8.18725e8i 0.00325840i
\(709\) −1.69458e11 −0.670622 −0.335311 0.942107i \(-0.608841\pi\)
−0.335311 + 0.942107i \(0.608841\pi\)
\(710\) 2.04865e11i 0.806184i
\(711\) 5.28298e10 0.206729
\(712\) −5.11861e10 −0.199174
\(713\) −3.52721e11 −1.36481
\(714\) 1.39144e11i 0.535390i
\(715\) 2.51753e9i 0.00963277i
\(716\) 4.77895e10i 0.181836i
\(717\) 2.86883e10i 0.108549i
\(718\) 4.25926e11i 1.60264i
\(719\) −3.94401e11 −1.47578 −0.737892 0.674919i \(-0.764179\pi\)
−0.737892 + 0.674919i \(0.764179\pi\)
\(720\) 1.07658e11i 0.400606i
\(721\) 2.77462e11i 1.02674i
\(722\) 4.48477e11i 1.65041i
\(723\) −3.65141e9 −0.0133631
\(724\) −2.86360e11 −1.04222
\(725\) 2.56108e11i 0.926982i
\(726\) 6.82422e10 0.245644
\(727\) 4.40578e11i 1.57720i −0.614909 0.788598i \(-0.710807\pi\)
0.614909 0.788598i \(-0.289193\pi\)
\(728\) −8.65949e9 −0.0308295
\(729\) 2.34373e11 0.829846
\(730\) 4.32350e11i 1.52245i
\(731\) 2.90929e11 + 4.70553e11i 1.01887 + 1.64793i
\(732\) −6.00049e10 −0.208998
\(733\) 9.56982e10i 0.331503i 0.986168 + 0.165752i \(0.0530050\pi\)
−0.986168 + 0.165752i \(0.946995\pi\)
\(734\) 4.77716e11i 1.64583i
\(735\) −4.77723e9 −0.0163692
\(736\) 6.21236e11i 2.11712i
\(737\) −6.41122e10 −0.217305
\(738\) 1.92383e11i 0.648545i
\(739\) 2.11867e10i 0.0710373i 0.999369 + 0.0355186i \(0.0113083\pi\)
−0.999369 + 0.0355186i \(0.988692\pi\)
\(740\) 2.70812e11 0.903110
\(741\) 4.63517e9 0.0153742
\(742\) 4.03209e11 1.33019
\(743\) 5.43058e10i 0.178193i 0.996023 + 0.0890965i \(0.0283980\pi\)
−0.996023 + 0.0890965i \(0.971602\pi\)
\(744\) 2.14462e10 0.0699936
\(745\) 3.16372e10 0.102701
\(746\) −5.40514e11 −1.74523
\(747\) 2.72802e11 0.876123
\(748\) −1.78309e11 −0.569597
\(749\) 2.64789e11i 0.841341i
\(750\) 8.58468e10i 0.271318i
\(751\) 1.24175e11i 0.390367i 0.980767 + 0.195183i \(0.0625302\pi\)
−0.980767 + 0.195183i \(0.937470\pi\)
\(752\) −1.23550e11 −0.386342
\(753\) 4.68033e10i 0.145578i
\(754\) −5.34617e10 −0.165408
\(755\) 3.05978e11 0.941679
\(756\) −1.52893e11 −0.468058
\(757\) 2.64168e11i 0.804447i 0.915542 + 0.402223i \(0.131762\pi\)
−0.915542 + 0.402223i \(0.868238\pi\)
\(758\) 5.40395e11i 1.63695i
\(759\) 1.95971e10i 0.0590506i
\(760\) 1.52635e11i 0.457508i
\(761\) 2.13908e11i 0.637806i 0.947787 + 0.318903i \(0.103314\pi\)
−0.947787 + 0.318903i \(0.896686\pi\)
\(762\) 2.64665e10 0.0785012
\(763\) 6.44758e11i 1.90239i
\(764\) 4.22708e11i 1.24070i
\(765\) 4.41167e11i 1.28812i
\(766\) −4.57608e11 −1.32916
\(767\) −3.16545e8 −0.000914649
\(768\) 8.84705e9i 0.0254304i
\(769\) 1.42773e11 0.408263 0.204132 0.978943i \(-0.434563\pi\)
0.204132 + 0.978943i \(0.434563\pi\)
\(770\) 8.79296e10i 0.250134i
\(771\) −8.37966e10 −0.237142
\(772\) −4.34766e11 −1.22401
\(773\) 6.20070e9i 0.0173669i −0.999962 0.00868346i \(-0.997236\pi\)
0.999962 0.00868346i \(-0.00276407\pi\)
\(774\) 4.49950e11 2.78191e11i 1.25372 0.775138i
\(775\) 1.70110e11 0.471545
\(776\) 1.90412e11i 0.525106i
\(777\) 6.70715e10i 0.184015i
\(778\) 1.71203e11 0.467297
\(779\) 2.34084e11i 0.635657i
\(780\) −3.51897e9 −0.00950687
\(781\) 6.50203e10i 0.174761i
\(782\) 1.69085e12i