Properties

Label 43.9.b.b.42.8
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 42.8
Character \(\chi\) \(=\) 43.42
Dual form 43.9.b.b.42.21

$q$-expansion

\(f(q)\) \(=\) \(q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} +O(q^{10})\) \(q-17.7707i q^{2} +152.462i q^{3} -59.7986 q^{4} -783.269i q^{5} +2709.35 q^{6} +1147.99i q^{7} -3486.64i q^{8} -16683.5 q^{9} -13919.3 q^{10} +21355.1 q^{11} -9116.98i q^{12} +16947.7 q^{13} +20400.5 q^{14} +119418. q^{15} -77268.6 q^{16} +104612. q^{17} +296478. i q^{18} +142642. i q^{19} +46838.4i q^{20} -175024. q^{21} -379495. i q^{22} +376231. q^{23} +531579. q^{24} -222885. q^{25} -301172. i q^{26} -1.54329e6i q^{27} -68647.9i q^{28} +245109. i q^{29} -2.12215e6i q^{30} +373811. q^{31} +480538. i q^{32} +3.25582e6i q^{33} -1.85903e6i q^{34} +899182. q^{35} +997650. q^{36} -1.72624e6i q^{37} +2.53484e6 q^{38} +2.58387e6i q^{39} -2.73098e6 q^{40} -3.57800e6 q^{41} +3.11030e6i q^{42} +(3.19345e6 + 1.22070e6i) q^{43} -1.27700e6 q^{44} +1.30677e7i q^{45} -6.68589e6i q^{46} +6.89105e6 q^{47} -1.17805e7i q^{48} +4.44693e6 q^{49} +3.96083e6i q^{50} +1.59493e7i q^{51} -1.01345e6 q^{52} -3.52143e6 q^{53} -2.74255e7 q^{54} -1.67268e7i q^{55} +4.00262e6 q^{56} -2.17474e7 q^{57} +4.35576e6 q^{58} -1.55268e6 q^{59} -7.14105e6 q^{60} -3.86782e6i q^{61} -6.64288e6i q^{62} -1.91524e7i q^{63} -1.12412e7 q^{64} -1.32746e7i q^{65} +5.78584e7 q^{66} -1.77748e7 q^{67} -6.25565e6 q^{68} +5.73607e7i q^{69} -1.59791e7i q^{70} -3.92801e7i q^{71} +5.81694e7i q^{72} +2.65149e7i q^{73} -3.06764e7 q^{74} -3.39814e7i q^{75} -8.52976e6i q^{76} +2.45153e7i q^{77} +4.59172e7 q^{78} -6.70808e7 q^{79} +6.05221e7i q^{80} +1.25832e8 q^{81} +6.35836e7i q^{82} -1.73713e7 q^{83} +1.04662e7 q^{84} -8.19394e7i q^{85} +(2.16926e7 - 5.67499e7i) q^{86} -3.73696e7 q^{87} -7.44574e7i q^{88} -1.06480e7i q^{89} +2.32222e8 q^{90} +1.94557e7i q^{91} -2.24981e7 q^{92} +5.69917e7i q^{93} -1.22459e8i q^{94} +1.11727e8 q^{95} -7.32636e7 q^{96} -1.23822e8 q^{97} -7.90251e7i q^{98} -3.56277e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + O(q^{10}) \) \( 28q - 4284q^{4} - 1794q^{6} - 80754q^{9} + 24982q^{10} + 4538q^{11} + 22086q^{13} + 24732q^{14} + 15388q^{15} + 525812q^{16} - 135136q^{17} - 261352q^{21} - 184432q^{23} + 1770326q^{24} - 2640434q^{25} - 110272q^{31} + 10947816q^{35} + 11602066q^{36} - 7189158q^{38} - 21389338q^{40} + 1301336q^{41} + 2473420q^{43} - 8818480q^{44} + 1983566q^{47} - 15560936q^{49} + 12927876q^{52} + 23942594q^{53} - 13757972q^{54} + 34967256q^{56} + 35225148q^{57} + 22565734q^{58} - 5554336q^{59} - 44902072q^{60} - 170444572q^{64} - 48457584q^{66} - 130953802q^{67} + 150021122q^{68} + 205870278q^{74} + 267860612q^{78} + 7380250q^{79} - 57601004q^{81} - 42603970q^{83} + 251931292q^{84} - 45482652q^{86} - 106687410q^{87} - 255044692q^{90} - 409532014q^{92} + 123322986q^{95} - 692987086q^{96} - 318744840q^{97} - 609707206q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 17.7707i 1.11067i −0.831627 0.555335i \(-0.812590\pi\)
0.831627 0.555335i \(-0.187410\pi\)
\(3\) 152.462i 1.88224i 0.338071 + 0.941121i \(0.390225\pi\)
−0.338071 + 0.941121i \(0.609775\pi\)
\(4\) −59.7986 −0.233588
\(5\) 783.269i 1.25323i −0.779329 0.626615i \(-0.784440\pi\)
0.779329 0.626615i \(-0.215560\pi\)
\(6\) 2709.35 2.09055
\(7\) 1147.99i 0.478128i 0.971004 + 0.239064i \(0.0768406\pi\)
−0.971004 + 0.239064i \(0.923159\pi\)
\(8\) 3486.64i 0.851231i
\(9\) −16683.5 −2.54283
\(10\) −13919.3 −1.39193
\(11\) 21355.1 1.45858 0.729290 0.684205i \(-0.239851\pi\)
0.729290 + 0.684205i \(0.239851\pi\)
\(12\) 9116.98i 0.439669i
\(13\) 16947.7 0.593385 0.296693 0.954973i \(-0.404116\pi\)
0.296693 + 0.954973i \(0.404116\pi\)
\(14\) 20400.5 0.531043
\(15\) 119418. 2.35888
\(16\) −77268.6 −1.17902
\(17\) 104612. 1.25252 0.626262 0.779613i \(-0.284584\pi\)
0.626262 + 0.779613i \(0.284584\pi\)
\(18\) 296478.i 2.82425i
\(19\) 142642.i 1.09454i 0.836956 + 0.547270i \(0.184333\pi\)
−0.836956 + 0.547270i \(0.815667\pi\)
\(20\) 46838.4i 0.292740i
\(21\) −175024. −0.899953
\(22\) 379495.i 1.62000i
\(23\) 376231. 1.34444 0.672222 0.740349i \(-0.265340\pi\)
0.672222 + 0.740349i \(0.265340\pi\)
\(24\) 531579. 1.60222
\(25\) −222885. −0.570586
\(26\) 301172.i 0.659055i
\(27\) 1.54329e6i 2.90398i
\(28\) 68647.9i 0.111685i
\(29\) 245109.i 0.346551i 0.984873 + 0.173275i \(0.0554350\pi\)
−0.984873 + 0.173275i \(0.944565\pi\)
\(30\) 2.12215e6i 2.61994i
\(31\) 373811. 0.404767 0.202383 0.979306i \(-0.435131\pi\)
0.202383 + 0.979306i \(0.435131\pi\)
\(32\) 480538.i 0.458277i
\(33\) 3.25582e6i 2.74540i
\(34\) 1.85903e6i 1.39114i
\(35\) 899182. 0.599205
\(36\) 997650. 0.593975
\(37\) 1.72624e6i 0.921071i −0.887641 0.460535i \(-0.847657\pi\)
0.887641 0.460535i \(-0.152343\pi\)
\(38\) 2.53484e6 1.21567
\(39\) 2.58387e6i 1.11689i
\(40\) −2.73098e6 −1.06679
\(41\) −3.57800e6 −1.26621 −0.633103 0.774067i \(-0.718219\pi\)
−0.633103 + 0.774067i \(0.718219\pi\)
\(42\) 3.11030e6i 0.999551i
\(43\) 3.19345e6 + 1.22070e6i 0.934084 + 0.357054i
\(44\) −1.27700e6 −0.340707
\(45\) 1.30677e7i 3.18675i
\(46\) 6.68589e6i 1.49323i
\(47\) 6.89105e6 1.41219 0.706096 0.708116i \(-0.250455\pi\)
0.706096 + 0.708116i \(0.250455\pi\)
\(48\) 1.17805e7i 2.21921i
\(49\) 4.44693e6 0.771393
\(50\) 3.96083e6i 0.633733i
\(51\) 1.59493e7i 2.35755i
\(52\) −1.01345e6 −0.138608
\(53\) −3.52143e6 −0.446288 −0.223144 0.974785i \(-0.571632\pi\)
−0.223144 + 0.974785i \(0.571632\pi\)
\(54\) −2.74255e7 −3.22536
\(55\) 1.67268e7i 1.82794i
\(56\) 4.00262e6 0.406998
\(57\) −2.17474e7 −2.06019
\(58\) 4.35576e6 0.384903
\(59\) −1.55268e6 −0.128137 −0.0640685 0.997946i \(-0.520408\pi\)
−0.0640685 + 0.997946i \(0.520408\pi\)
\(60\) −7.14105e6 −0.551007
\(61\) 3.86782e6i 0.279349i −0.990197 0.139674i \(-0.955394\pi\)
0.990197 0.139674i \(-0.0446056\pi\)
\(62\) 6.64288e6i 0.449562i
\(63\) 1.91524e7i 1.21580i
\(64\) −1.12412e7 −0.670030
\(65\) 1.32746e7i 0.743648i
\(66\) 5.78584e7 3.04923
\(67\) −1.77748e7 −0.882074 −0.441037 0.897489i \(-0.645389\pi\)
−0.441037 + 0.897489i \(0.645389\pi\)
\(68\) −6.25565e6 −0.292575
\(69\) 5.73607e7i 2.53057i
\(70\) 1.59791e7i 0.665519i
\(71\) 3.92801e7i 1.54575i −0.634557 0.772876i \(-0.718818\pi\)
0.634557 0.772876i \(-0.281182\pi\)
\(72\) 5.81694e7i 2.16454i
\(73\) 2.65149e7i 0.933680i 0.884342 + 0.466840i \(0.154608\pi\)
−0.884342 + 0.466840i \(0.845392\pi\)
\(74\) −3.06764e7 −1.02301
\(75\) 3.39814e7i 1.07398i
\(76\) 8.52976e6i 0.255672i
\(77\) 2.45153e7i 0.697388i
\(78\) 4.59172e7 1.24050
\(79\) −6.70808e7 −1.72223 −0.861113 0.508414i \(-0.830232\pi\)
−0.861113 + 0.508414i \(0.830232\pi\)
\(80\) 6.05221e7i 1.47759i
\(81\) 1.25832e8 2.92316
\(82\) 6.35836e7i 1.40634i
\(83\) −1.73713e7 −0.366033 −0.183017 0.983110i \(-0.558586\pi\)
−0.183017 + 0.983110i \(0.558586\pi\)
\(84\) 1.04662e7 0.210218
\(85\) 8.19394e7i 1.56970i
\(86\) 2.16926e7 5.67499e7i 0.396569 1.03746i
\(87\) −3.73696e7 −0.652292
\(88\) 7.44574e7i 1.24159i
\(89\) 1.06480e7i 0.169709i −0.996393 0.0848547i \(-0.972957\pi\)
0.996393 0.0848547i \(-0.0270426\pi\)
\(90\) 2.32222e8 3.53943
\(91\) 1.94557e7i 0.283714i
\(92\) −2.24981e7 −0.314046
\(93\) 5.69917e7i 0.761869i
\(94\) 1.22459e8i 1.56848i
\(95\) 1.11727e8 1.37171
\(96\) −7.32636e7 −0.862587
\(97\) −1.23822e8 −1.39866 −0.699330 0.714799i \(-0.746518\pi\)
−0.699330 + 0.714799i \(0.746518\pi\)
\(98\) 7.90251e7i 0.856763i
\(99\) −3.56277e8 −3.70892
\(100\) 1.33282e7 0.133282
\(101\) 2.90612e7 0.279273 0.139636 0.990203i \(-0.455407\pi\)
0.139636 + 0.990203i \(0.455407\pi\)
\(102\) 2.83431e8 2.61846
\(103\) 1.02737e7 0.0912806 0.0456403 0.998958i \(-0.485467\pi\)
0.0456403 + 0.998958i \(0.485467\pi\)
\(104\) 5.90905e7i 0.505108i
\(105\) 1.37091e8i 1.12785i
\(106\) 6.25783e7i 0.495679i
\(107\) −1.22323e8 −0.933195 −0.466597 0.884470i \(-0.654520\pi\)
−0.466597 + 0.884470i \(0.654520\pi\)
\(108\) 9.22868e7i 0.678335i
\(109\) 2.58957e8 1.83451 0.917257 0.398296i \(-0.130398\pi\)
0.917257 + 0.398296i \(0.130398\pi\)
\(110\) −2.97246e8 −2.03023
\(111\) 2.63184e8 1.73368
\(112\) 8.87033e7i 0.563725i
\(113\) 2.22666e8i 1.36565i 0.730581 + 0.682826i \(0.239249\pi\)
−0.730581 + 0.682826i \(0.760751\pi\)
\(114\) 3.86466e8i 2.28819i
\(115\) 2.94690e8i 1.68490i
\(116\) 1.46571e7i 0.0809501i
\(117\) −2.82747e8 −1.50888
\(118\) 2.75923e7i 0.142318i
\(119\) 1.20093e8i 0.598867i
\(120\) 4.16369e8i 2.00795i
\(121\) 2.41680e8 1.12745
\(122\) −6.87339e7 −0.310264
\(123\) 5.45507e8i 2.38331i
\(124\) −2.23533e7 −0.0945487
\(125\) 1.31385e8i 0.538155i
\(126\) −3.40353e8 −1.35035
\(127\) −7.23723e7 −0.278200 −0.139100 0.990278i \(-0.544421\pi\)
−0.139100 + 0.990278i \(0.544421\pi\)
\(128\) 3.22783e8i 1.20246i
\(129\) −1.86109e8 + 4.86878e8i −0.672061 + 1.75817i
\(130\) −2.35899e8 −0.825948
\(131\) 2.13462e8i 0.724828i 0.932017 + 0.362414i \(0.118047\pi\)
−0.932017 + 0.362414i \(0.881953\pi\)
\(132\) 1.94694e8i 0.641292i
\(133\) −1.63751e8 −0.523331
\(134\) 3.15871e8i 0.979693i
\(135\) −1.20881e9 −3.63936
\(136\) 3.64745e8i 1.06619i
\(137\) 2.73201e8i 0.775532i −0.921758 0.387766i \(-0.873247\pi\)
0.921758 0.387766i \(-0.126753\pi\)
\(138\) 1.01934e9 2.81063
\(139\) 3.27177e8 0.876442 0.438221 0.898867i \(-0.355609\pi\)
0.438221 + 0.898867i \(0.355609\pi\)
\(140\) −5.37698e7 −0.139967
\(141\) 1.05062e9i 2.65809i
\(142\) −6.98037e8 −1.71682
\(143\) 3.61919e8 0.865499
\(144\) 1.28911e9 2.99806
\(145\) 1.91986e8 0.434308
\(146\) 4.71189e8 1.03701
\(147\) 6.77985e8i 1.45195i
\(148\) 1.03226e8i 0.215151i
\(149\) 6.32543e8i 1.28335i −0.766977 0.641675i \(-0.778240\pi\)
0.766977 0.641675i \(-0.221760\pi\)
\(150\) −6.03874e8 −1.19284
\(151\) 4.30577e8i 0.828214i −0.910228 0.414107i \(-0.864094\pi\)
0.910228 0.414107i \(-0.135906\pi\)
\(152\) 4.97340e8 0.931706
\(153\) −1.74530e9 −3.18496
\(154\) 4.35655e8 0.774568
\(155\) 2.92794e8i 0.507266i
\(156\) 1.54512e8i 0.260893i
\(157\) 2.11312e8i 0.347797i 0.984764 + 0.173898i \(0.0556364\pi\)
−0.984764 + 0.173898i \(0.944364\pi\)
\(158\) 1.19207e9i 1.91282i
\(159\) 5.36882e8i 0.840022i
\(160\) 3.76391e8 0.574326
\(161\) 4.31908e8i 0.642817i
\(162\) 2.23613e9i 3.24667i
\(163\) 3.17331e7i 0.0449534i 0.999747 + 0.0224767i \(0.00715516\pi\)
−0.999747 + 0.0224767i \(0.992845\pi\)
\(164\) 2.13959e8 0.295771
\(165\) 2.55019e9 3.44062
\(166\) 3.08701e8i 0.406542i
\(167\) 1.72754e8 0.222107 0.111053 0.993814i \(-0.464578\pi\)
0.111053 + 0.993814i \(0.464578\pi\)
\(168\) 6.10245e8i 0.766068i
\(169\) −5.28507e8 −0.647894
\(170\) −1.45612e9 −1.74342
\(171\) 2.37976e9i 2.78323i
\(172\) −1.90964e8 7.29958e7i −0.218191 0.0834035i
\(173\) 3.49848e8 0.390567 0.195283 0.980747i \(-0.437437\pi\)
0.195283 + 0.980747i \(0.437437\pi\)
\(174\) 6.64086e8i 0.724481i
\(175\) 2.55869e8i 0.272813i
\(176\) −1.65007e9 −1.71970
\(177\) 2.36724e8i 0.241185i
\(178\) −1.89222e8 −0.188491
\(179\) 1.61233e9i 1.57052i 0.619169 + 0.785258i \(0.287469\pi\)
−0.619169 + 0.785258i \(0.712531\pi\)
\(180\) 7.81428e8i 0.744388i
\(181\) 1.47130e9 1.37084 0.685419 0.728149i \(-0.259619\pi\)
0.685419 + 0.728149i \(0.259619\pi\)
\(182\) 3.45742e8 0.315113
\(183\) 5.89693e8 0.525802
\(184\) 1.31178e9i 1.14443i
\(185\) −1.35211e9 −1.15431
\(186\) 1.01278e9 0.846185
\(187\) 2.23400e9 1.82691
\(188\) −4.12075e8 −0.329871
\(189\) 1.77168e9 1.38848
\(190\) 1.98546e9i 1.52352i
\(191\) 4.60059e8i 0.345685i 0.984949 + 0.172842i \(0.0552951\pi\)
−0.984949 + 0.172842i \(0.944705\pi\)
\(192\) 1.71386e9i 1.26116i
\(193\) −1.75432e9 −1.26439 −0.632193 0.774811i \(-0.717845\pi\)
−0.632193 + 0.774811i \(0.717845\pi\)
\(194\) 2.20041e9i 1.55345i
\(195\) 2.02386e9 1.39973
\(196\) −2.65920e8 −0.180188
\(197\) −2.67417e9 −1.77551 −0.887756 0.460314i \(-0.847737\pi\)
−0.887756 + 0.460314i \(0.847737\pi\)
\(198\) 6.33131e9i 4.11939i
\(199\) 9.42028e8i 0.600692i 0.953830 + 0.300346i \(0.0971021\pi\)
−0.953830 + 0.300346i \(0.902898\pi\)
\(200\) 7.77120e8i 0.485700i
\(201\) 2.70997e9i 1.66028i
\(202\) 5.16439e8i 0.310180i
\(203\) −2.81381e8 −0.165696
\(204\) 9.53746e8i 0.550696i
\(205\) 2.80253e9i 1.58685i
\(206\) 1.82571e8i 0.101383i
\(207\) −6.27685e9 −3.41870
\(208\) −1.30952e9 −0.699616
\(209\) 3.04612e9i 1.59647i
\(210\) 2.43620e9 1.25267
\(211\) 3.63936e9i 1.83610i 0.396469 + 0.918048i \(0.370236\pi\)
−0.396469 + 0.918048i \(0.629764\pi\)
\(212\) 2.10576e8 0.104248
\(213\) 5.98871e9 2.90948
\(214\) 2.17376e9i 1.03647i
\(215\) 9.56133e8 2.50133e9i 0.447470 1.17062i
\(216\) −5.38091e9 −2.47196
\(217\) 4.29129e8i 0.193530i
\(218\) 4.60184e9i 2.03754i
\(219\) −4.04250e9 −1.75741
\(220\) 1.00024e9i 0.426984i
\(221\) 1.77293e9 0.743229
\(222\) 4.67698e9i 1.92554i
\(223\) 1.86717e8i 0.0755032i 0.999287 + 0.0377516i \(0.0120196\pi\)
−0.999287 + 0.0377516i \(0.987980\pi\)
\(224\) −5.51651e8 −0.219115
\(225\) 3.71851e9 1.45090
\(226\) 3.95694e9 1.51679
\(227\) 2.20237e9i 0.829445i −0.909948 0.414722i \(-0.863879\pi\)
0.909948 0.414722i \(-0.136121\pi\)
\(228\) 1.30046e9 0.481236
\(229\) −1.37546e9 −0.500155 −0.250077 0.968226i \(-0.580456\pi\)
−0.250077 + 0.968226i \(0.580456\pi\)
\(230\) −5.23685e9 −1.87137
\(231\) −3.73764e9 −1.31265
\(232\) 8.54606e8 0.294995
\(233\) 1.56426e9i 0.530743i 0.964146 + 0.265372i \(0.0854946\pi\)
−0.964146 + 0.265372i \(0.914505\pi\)
\(234\) 5.02462e9i 1.67587i
\(235\) 5.39754e9i 1.76980i
\(236\) 9.28482e7 0.0299313
\(237\) 1.02272e10i 3.24164i
\(238\) 2.13414e9 0.665144
\(239\) −2.61367e9 −0.801048 −0.400524 0.916286i \(-0.631172\pi\)
−0.400524 + 0.916286i \(0.631172\pi\)
\(240\) −9.22729e9 −2.78118
\(241\) 3.69579e8i 0.109557i 0.998499 + 0.0547784i \(0.0174453\pi\)
−0.998499 + 0.0547784i \(0.982555\pi\)
\(242\) 4.29482e9i 1.25223i
\(243\) 9.05905e9i 2.59811i
\(244\) 2.31290e8i 0.0652526i
\(245\) 3.48314e9i 0.966733i
\(246\) −9.69405e9 −2.64707
\(247\) 2.41744e9i 0.649484i
\(248\) 1.30334e9i 0.344550i
\(249\) 2.64846e9i 0.688962i
\(250\) −2.33481e9 −0.597713
\(251\) 2.82275e9 0.711177 0.355588 0.934643i \(-0.384280\pi\)
0.355588 + 0.934643i \(0.384280\pi\)
\(252\) 1.14529e9i 0.283996i
\(253\) 8.03443e9 1.96098
\(254\) 1.28611e9i 0.308989i
\(255\) 1.24926e10 2.95456
\(256\) 2.85832e9 0.665506
\(257\) 1.95053e9i 0.447115i 0.974691 + 0.223558i \(0.0717671\pi\)
−0.974691 + 0.223558i \(0.928233\pi\)
\(258\) 8.65217e9 + 3.30729e9i 1.95275 + 0.746438i
\(259\) 1.98169e9 0.440390
\(260\) 7.93801e8i 0.173707i
\(261\) 4.08927e9i 0.881220i
\(262\) 3.79337e9 0.805045
\(263\) 1.40497e9i 0.293659i 0.989162 + 0.146830i \(0.0469069\pi\)
−0.989162 + 0.146830i \(0.953093\pi\)
\(264\) 1.13519e10 2.33697
\(265\) 2.75822e9i 0.559302i
\(266\) 2.90997e9i 0.581248i
\(267\) 1.62340e9 0.319434
\(268\) 1.06291e9 0.206042
\(269\) −8.25785e8 −0.157709 −0.0788547 0.996886i \(-0.525126\pi\)
−0.0788547 + 0.996886i \(0.525126\pi\)
\(270\) 2.14815e10i 4.04212i
\(271\) 6.82085e8 0.126462 0.0632312 0.997999i \(-0.479859\pi\)
0.0632312 + 0.997999i \(0.479859\pi\)
\(272\) −8.08322e9 −1.47676
\(273\) −2.96625e9 −0.534019
\(274\) −4.85498e9 −0.861360
\(275\) −4.75972e9 −0.832245
\(276\) 3.43009e9i 0.591111i
\(277\) 1.59599e9i 0.271089i 0.990771 + 0.135544i \(0.0432784\pi\)
−0.990771 + 0.135544i \(0.956722\pi\)
\(278\) 5.81417e9i 0.973438i
\(279\) −6.23647e9 −1.02925
\(280\) 3.13512e9i 0.510062i
\(281\) −9.84477e9 −1.57899 −0.789497 0.613755i \(-0.789658\pi\)
−0.789497 + 0.613755i \(0.789658\pi\)
\(282\) 1.86703e10 2.95226
\(283\) 5.66632e9 0.883395 0.441698 0.897164i \(-0.354376\pi\)
0.441698 + 0.897164i \(0.354376\pi\)
\(284\) 2.34890e9i 0.361069i
\(285\) 1.70340e10i 2.58189i
\(286\) 6.43156e9i 0.961284i
\(287\) 4.10749e9i 0.605409i
\(288\) 8.01706e9i 1.16532i
\(289\) 3.96793e9 0.568816
\(290\) 3.41173e9i 0.482373i
\(291\) 1.88781e10i 2.63261i
\(292\) 1.58555e9i 0.218097i
\(293\) −8.29340e9 −1.12528 −0.562642 0.826701i \(-0.690215\pi\)
−0.562642 + 0.826701i \(0.690215\pi\)
\(294\) 1.20483e10 1.61264
\(295\) 1.21617e9i 0.160585i
\(296\) −6.01876e9 −0.784044
\(297\) 3.29571e10i 4.23569i
\(298\) −1.12407e10 −1.42538
\(299\) 6.37624e9 0.797774
\(300\) 2.03204e9i 0.250869i
\(301\) −1.40134e9 + 3.66603e9i −0.170717 + 0.446612i
\(302\) −7.65166e9 −0.919873
\(303\) 4.43072e9i 0.525659i
\(304\) 1.10217e10i 1.29049i
\(305\) −3.02954e9 −0.350088
\(306\) 3.10152e10i 3.53744i
\(307\) −2.49145e9 −0.280478 −0.140239 0.990118i \(-0.544787\pi\)
−0.140239 + 0.990118i \(0.544787\pi\)
\(308\) 1.46598e9i 0.162902i
\(309\) 1.56635e9i 0.171812i
\(310\) −5.20316e9 −0.563405
\(311\) 8.34587e9 0.892134 0.446067 0.894999i \(-0.352824\pi\)
0.446067 + 0.894999i \(0.352824\pi\)
\(312\) 9.00902e9 0.950735
\(313\) 1.49570e10i 1.55836i −0.626803 0.779178i \(-0.715637\pi\)
0.626803 0.779178i \(-0.284363\pi\)
\(314\) 3.75517e9 0.386288
\(315\) −1.50015e10 −1.52368
\(316\) 4.01134e9 0.402292
\(317\) −4.93098e9 −0.488311 −0.244156 0.969736i \(-0.578511\pi\)
−0.244156 + 0.969736i \(0.578511\pi\)
\(318\) −9.54078e9 −0.932987
\(319\) 5.23431e9i 0.505472i
\(320\) 8.80492e9i 0.839702i
\(321\) 1.86495e10i 1.75650i
\(322\) 7.67531e9 0.713958
\(323\) 1.49220e10i 1.37094i
\(324\) −7.52460e9 −0.682815
\(325\) −3.77738e9 −0.338577
\(326\) 5.63921e8 0.0499284
\(327\) 3.94809e10i 3.45300i
\(328\) 1.24752e10i 1.07783i
\(329\) 7.91083e9i 0.675209i
\(330\) 4.53186e10i 3.82139i
\(331\) 1.01229e10i 0.843322i −0.906754 0.421661i \(-0.861447\pi\)
0.906754 0.421661i \(-0.138553\pi\)
\(332\) 1.03878e9 0.0855010
\(333\) 2.87997e10i 2.34213i
\(334\) 3.06996e9i 0.246687i
\(335\) 1.39224e10i 1.10544i
\(336\) 1.35238e10 1.06107
\(337\) −2.62618e9 −0.203613 −0.101807 0.994804i \(-0.532462\pi\)
−0.101807 + 0.994804i \(0.532462\pi\)
\(338\) 9.39195e9i 0.719596i
\(339\) −3.39480e10 −2.57049
\(340\) 4.89986e9i 0.366664i
\(341\) 7.98275e9 0.590384
\(342\) −4.22901e10 −3.09125
\(343\) 1.17229e10i 0.846953i
\(344\) 4.25613e9 1.11344e10i 0.303935 0.795121i
\(345\) 4.49289e10 3.17139
\(346\) 6.21706e9i 0.433791i
\(347\) 5.33379e9i 0.367890i 0.982937 + 0.183945i \(0.0588868\pi\)
−0.982937 + 0.183945i \(0.941113\pi\)
\(348\) 2.23465e9 0.152368
\(349\) 1.76395e9i 0.118901i −0.998231 0.0594504i \(-0.981065\pi\)
0.998231 0.0594504i \(-0.0189348\pi\)
\(350\) −4.54698e9 −0.303006
\(351\) 2.61553e10i 1.72318i
\(352\) 1.02619e10i 0.668433i
\(353\) −1.49693e10 −0.964056 −0.482028 0.876156i \(-0.660100\pi\)
−0.482028 + 0.876156i \(0.660100\pi\)
\(354\) −4.20676e9 −0.267877
\(355\) −3.07669e10 −1.93718
\(356\) 6.36732e8i 0.0396421i
\(357\) −1.83096e10 −1.12721
\(358\) 2.86523e10 1.74432
\(359\) 1.00539e10 0.605279 0.302639 0.953105i \(-0.402132\pi\)
0.302639 + 0.953105i \(0.402132\pi\)
\(360\) 4.55623e10 2.71266
\(361\) −3.36306e9 −0.198018
\(362\) 2.61460e10i 1.52255i
\(363\) 3.68468e10i 2.12214i
\(364\) 1.16342e9i 0.0662723i
\(365\) 2.07683e10 1.17012
\(366\) 1.04793e10i 0.583992i
\(367\) −2.25533e10 −1.24321 −0.621606 0.783330i \(-0.713519\pi\)
−0.621606 + 0.783330i \(0.713519\pi\)
\(368\) −2.90708e10 −1.58513
\(369\) 5.96936e10 3.21975
\(370\) 2.40279e10i 1.28206i
\(371\) 4.04255e9i 0.213383i
\(372\) 3.40802e9i 0.177963i
\(373\) 4.92003e9i 0.254175i −0.991892 0.127087i \(-0.959437\pi\)
0.991892 0.127087i \(-0.0405629\pi\)
\(374\) 3.96997e10i 2.02909i
\(375\) 2.00312e10 1.01294
\(376\) 2.40266e10i 1.20210i
\(377\) 4.15402e9i 0.205638i
\(378\) 3.14840e10i 1.54214i
\(379\) 1.13510e9 0.0550147 0.0275073 0.999622i \(-0.491243\pi\)
0.0275073 + 0.999622i \(0.491243\pi\)
\(380\) −6.68110e9 −0.320415
\(381\) 1.10340e10i 0.523640i
\(382\) 8.17558e9 0.383942
\(383\) 2.87658e10i 1.33685i 0.743782 + 0.668423i \(0.233030\pi\)
−0.743782 + 0.668423i \(0.766970\pi\)
\(384\) −4.92120e10 −2.26332
\(385\) 1.92021e10 0.873988
\(386\) 3.11755e10i 1.40432i
\(387\) −5.32779e10 2.03655e10i −2.37522 0.907927i
\(388\) 7.40440e9 0.326710
\(389\) 2.92780e10i 1.27862i 0.768947 + 0.639312i \(0.220781\pi\)
−0.768947 + 0.639312i \(0.779219\pi\)
\(390\) 3.59655e10i 1.55463i
\(391\) 3.93583e10 1.68395
\(392\) 1.55048e10i 0.656634i
\(393\) −3.25447e10 −1.36430
\(394\) 4.75219e10i 1.97201i
\(395\) 5.25423e10i 2.15835i
\(396\) 2.13049e10 0.866360
\(397\) −2.75612e10 −1.10952 −0.554761 0.832009i \(-0.687190\pi\)
−0.554761 + 0.832009i \(0.687190\pi\)
\(398\) 1.67405e10 0.667170
\(399\) 2.49657e10i 0.985035i
\(400\) 1.72220e10 0.672735
\(401\) 2.55883e10 0.989608 0.494804 0.869005i \(-0.335240\pi\)
0.494804 + 0.869005i \(0.335240\pi\)
\(402\) −4.81581e10 −1.84402
\(403\) 6.33522e9 0.240183
\(404\) −1.73782e9 −0.0652348
\(405\) 9.85606e10i 3.66339i
\(406\) 5.00035e9i 0.184033i
\(407\) 3.68639e10i 1.34345i
\(408\) 5.56095e10 2.00682
\(409\) 4.26629e10i 1.52461i −0.647220 0.762303i \(-0.724069\pi\)
0.647220 0.762303i \(-0.275931\pi\)
\(410\) 4.98031e10 1.76247
\(411\) 4.16526e10 1.45974
\(412\) −6.14354e8 −0.0213221
\(413\) 1.78246e9i 0.0612659i
\(414\) 1.11544e11i 3.79704i
\(415\) 1.36064e10i 0.458724i
\(416\) 8.14400e9i 0.271935i
\(417\) 4.98819e10i 1.64968i
\(418\) 5.41317e10 1.77316
\(419\) 5.09397e10i 1.65272i −0.563140 0.826362i \(-0.690407\pi\)
0.563140 0.826362i \(-0.309593\pi\)
\(420\) 8.19782e9i 0.263452i
\(421\) 3.53233e8i 0.0112443i −0.999984 0.00562216i \(-0.998210\pi\)
0.999984 0.00562216i \(-0.00178960\pi\)
\(422\) 6.46741e10 2.03930
\(423\) −1.14967e11 −3.59097
\(424\) 1.22780e10i 0.379894i
\(425\) −2.33165e10 −0.714672
\(426\) 1.06424e11i 3.23147i
\(427\) 4.44020e9 0.133565
\(428\) 7.31473e9 0.217983
\(429\) 5.51787e10i 1.62908i
\(430\) −4.44504e10 1.69912e10i −1.30017 0.496992i
\(431\) −1.09238e9 −0.0316566 −0.0158283 0.999875i \(-0.505039\pi\)
−0.0158283 + 0.999875i \(0.505039\pi\)
\(432\) 1.19248e11i 3.42386i
\(433\) 6.70639e10i 1.90782i −0.300092 0.953910i \(-0.597017\pi\)
0.300092 0.953910i \(-0.402983\pi\)
\(434\) 7.62594e9 0.214949
\(435\) 2.92705e10i 0.817472i
\(436\) −1.54852e10 −0.428521
\(437\) 5.36662e10i 1.47155i
\(438\) 7.18381e10i 1.95190i
\(439\) −3.53135e10 −0.950785 −0.475393 0.879774i \(-0.657694\pi\)
−0.475393 + 0.879774i \(0.657694\pi\)
\(440\) −5.83202e10 −1.55599
\(441\) −7.41904e10 −1.96152
\(442\) 3.15063e10i 0.825483i
\(443\) −6.26941e9 −0.162784 −0.0813921 0.996682i \(-0.525937\pi\)
−0.0813921 + 0.996682i \(0.525937\pi\)
\(444\) −1.57381e10 −0.404967
\(445\) −8.34021e9 −0.212685
\(446\) 3.31810e9 0.0838592
\(447\) 9.64384e10 2.41557
\(448\) 1.29048e10i 0.320361i
\(449\) 7.40849e10i 1.82282i −0.411497 0.911411i \(-0.634994\pi\)
0.411497 0.911411i \(-0.365006\pi\)
\(450\) 6.60805e10i 1.61147i
\(451\) −7.64083e10 −1.84686
\(452\) 1.33151e10i 0.319000i
\(453\) 6.56464e10 1.55890
\(454\) −3.91378e10 −0.921240
\(455\) 1.52390e10 0.355559
\(456\) 7.58252e10i 1.75370i
\(457\) 6.33445e10i 1.45226i 0.687558 + 0.726129i \(0.258683\pi\)
−0.687558 + 0.726129i \(0.741317\pi\)
\(458\) 2.44428e10i 0.555507i
\(459\) 1.61447e11i 3.63730i
\(460\) 1.76220e10i 0.393572i
\(461\) 4.30565e10 0.953313 0.476656 0.879090i \(-0.341849\pi\)
0.476656 + 0.879090i \(0.341849\pi\)
\(462\) 6.64206e10i 1.45792i
\(463\) 2.59095e10i 0.563812i −0.959442 0.281906i \(-0.909033\pi\)
0.959442 0.281906i \(-0.0909667\pi\)
\(464\) 1.89392e10i 0.408592i
\(465\) 4.46398e10 0.954797
\(466\) 2.77980e10 0.589481
\(467\) 3.07472e10i 0.646455i 0.946321 + 0.323228i \(0.104768\pi\)
−0.946321 + 0.323228i \(0.895232\pi\)
\(468\) 1.69079e10 0.352456
\(469\) 2.04052e10i 0.421745i
\(470\) −9.59182e10 −1.96567
\(471\) −3.22170e10 −0.654637
\(472\) 5.41365e9i 0.109074i
\(473\) 6.81962e10 + 2.60680e10i 1.36244 + 0.520791i
\(474\) −1.81746e11 −3.60040
\(475\) 3.17927e10i 0.624529i
\(476\) 7.18140e9i 0.139888i
\(477\) 5.87498e10 1.13484
\(478\) 4.64467e10i 0.889700i
\(479\) 4.25414e10 0.808109 0.404054 0.914735i \(-0.367601\pi\)
0.404054 + 0.914735i \(0.367601\pi\)
\(480\) 5.73851e10i 1.08102i
\(481\) 2.92557e10i 0.546550i
\(482\) 6.56769e9 0.121682
\(483\) −6.58493e10 −1.20994
\(484\) −1.44521e10 −0.263360
\(485\) 9.69862e10i 1.75284i
\(486\) 1.60986e11 2.88564
\(487\) −8.19028e10 −1.45607 −0.728036 0.685539i \(-0.759567\pi\)
−0.728036 + 0.685539i \(0.759567\pi\)
\(488\) −1.34857e10 −0.237790
\(489\) −4.83808e9 −0.0846132
\(490\) −6.18979e10 −1.07372
\(491\) 9.90164e10i 1.70365i −0.523824 0.851827i \(-0.675495\pi\)
0.523824 0.851827i \(-0.324505\pi\)
\(492\) 3.26205e10i 0.556712i
\(493\) 2.56413e10i 0.434063i
\(494\) 4.29597e10 0.721363
\(495\) 2.79061e11i 4.64813i
\(496\) −2.88838e10 −0.477230
\(497\) 4.50931e10 0.739068
\(498\) −4.70650e10 −0.765210
\(499\) 2.10144e10i 0.338934i −0.985536 0.169467i \(-0.945795\pi\)
0.985536 0.169467i \(-0.0542046\pi\)
\(500\) 7.85666e9i 0.125707i
\(501\) 2.63383e10i 0.418058i
\(502\) 5.01623e10i 0.789883i
\(503\) 4.46332e10i 0.697246i −0.937263 0.348623i \(-0.886649\pi\)
0.937263 0.348623i \(-0.113351\pi\)
\(504\) −6.67777e10 −1.03493
\(505\) 2.27628e10i 0.349993i
\(506\) 1.42778e11i 2.17800i
\(507\) 8.05770e10i 1.21949i
\(508\) 4.32776e9 0.0649842
\(509\) −8.81999e10 −1.31400 −0.657002 0.753889i \(-0.728176\pi\)
−0.657002 + 0.753889i \(0.728176\pi\)
\(510\) 2.22003e11i 3.28154i
\(511\) −3.04387e10 −0.446419
\(512\) 3.18379e10i 0.463302i
\(513\) 2.20138e11 3.17852
\(514\) 3.46623e10 0.496597
\(515\) 8.04708e9i 0.114396i
\(516\) 1.11291e10 2.91146e10i 0.156985 0.410688i
\(517\) 1.47159e11 2.05979
\(518\) 3.52161e10i 0.489128i
\(519\) 5.33384e10i 0.735141i
\(520\) −4.62837e10 −0.633016
\(521\) 7.84546e10i 1.06480i 0.846493 + 0.532400i \(0.178710\pi\)
−0.846493 + 0.532400i \(0.821290\pi\)
\(522\) −7.26694e10 −0.978744
\(523\) 7.85221e10i 1.04951i −0.851254 0.524753i \(-0.824158\pi\)
0.851254 0.524753i \(-0.175842\pi\)
\(524\) 1.27647e10i 0.169311i
\(525\) 3.90102e10 0.513500
\(526\) 2.49673e10 0.326158
\(527\) 3.91051e10 0.506980
\(528\) 2.51573e11i 3.23689i
\(529\) 6.32386e10 0.807532
\(530\) 4.90156e10 0.621200
\(531\) 2.59042e10 0.325831
\(532\) 9.79205e9 0.122244
\(533\) −6.06387e10 −0.751348
\(534\) 2.88490e10i 0.354786i
\(535\) 9.58116e10i 1.16951i
\(536\) 6.19743e10i 0.750848i
\(537\) −2.45818e11 −2.95609
\(538\) 1.46748e10i 0.175163i
\(539\) 9.49644e10 1.12514
\(540\) 7.22854e10 0.850110
\(541\) −1.01935e11 −1.18997 −0.594984 0.803737i \(-0.702842\pi\)
−0.594984 + 0.803737i \(0.702842\pi\)
\(542\) 1.21211e10i 0.140458i
\(543\) 2.24316e11i 2.58025i
\(544\) 5.02701e10i 0.574003i
\(545\) 2.02833e11i 2.29907i
\(546\) 5.27123e10i 0.593119i
\(547\) 3.06187e10 0.342009 0.171004 0.985270i \(-0.445299\pi\)
0.171004 + 0.985270i \(0.445299\pi\)
\(548\) 1.63370e10i 0.181155i
\(549\) 6.45288e10i 0.710337i
\(550\) 8.45837e10i 0.924349i
\(551\) −3.49627e10 −0.379314
\(552\) 1.99996e11 2.15410
\(553\) 7.70079e10i 0.823445i
\(554\) 2.83619e10 0.301090
\(555\) 2.06144e11i 2.17270i
\(556\) −1.95647e10 −0.204727
\(557\) 1.28205e11 1.33194 0.665971 0.745978i \(-0.268017\pi\)
0.665971 + 0.745978i \(0.268017\pi\)
\(558\) 1.10827e11i 1.14316i
\(559\) 5.41215e10 + 2.06879e10i 0.554272 + 0.211870i
\(560\) −6.94785e10 −0.706477
\(561\) 3.40599e11i 3.43868i
\(562\) 1.74949e11i 1.75374i
\(563\) −1.75852e11 −1.75031 −0.875153 0.483847i \(-0.839239\pi\)
−0.875153 + 0.483847i \(0.839239\pi\)
\(564\) 6.28255e10i 0.620897i
\(565\) 1.74407e11 1.71148
\(566\) 1.00695e11i 0.981161i
\(567\) 1.44454e11i 1.39765i
\(568\) −1.36956e11 −1.31579
\(569\) 1.96827e11 1.87774 0.938872 0.344266i \(-0.111872\pi\)
0.938872 + 0.344266i \(0.111872\pi\)
\(570\) 3.02707e11 2.86763
\(571\) 8.11931e10i 0.763791i 0.924205 + 0.381896i \(0.124729\pi\)
−0.924205 + 0.381896i \(0.875271\pi\)
\(572\) −2.16422e10 −0.202170
\(573\) −7.01413e10 −0.650662
\(574\) −7.29931e10 −0.672410
\(575\) −8.38562e10 −0.767121
\(576\) 1.87543e11 1.70377
\(577\) 3.27137e10i 0.295139i −0.989052 0.147569i \(-0.952855\pi\)
0.989052 0.147569i \(-0.0471449\pi\)
\(578\) 7.05129e10i 0.631768i
\(579\) 2.67466e11i 2.37988i
\(580\) −1.14805e10 −0.101449
\(581\) 1.99420e10i 0.175011i
\(582\) −3.35478e11 −2.92397
\(583\) −7.52003e10 −0.650946
\(584\) 9.24479e10 0.794777
\(585\) 2.21467e11i 1.89097i
\(586\) 1.47380e11i 1.24982i
\(587\) 4.75906e10i 0.400838i −0.979710 0.200419i \(-0.935770\pi\)
0.979710 0.200419i \(-0.0642303\pi\)
\(588\) 4.05426e10i 0.339158i
\(589\) 5.33209e10i 0.443033i
\(590\) 2.16122e10 0.178357
\(591\) 4.07708e11i 3.34194i
\(592\) 1.33384e11i 1.08597i
\(593\) 3.97667e9i 0.0321589i 0.999871 + 0.0160794i \(0.00511847\pi\)
−0.999871 + 0.0160794i \(0.994882\pi\)
\(594\) −5.85672e11 −4.70445
\(595\) 9.40653e10 0.750519
\(596\) 3.78252e10i 0.299775i
\(597\) −1.43623e11 −1.13065
\(598\) 1.13310e11i 0.886064i
\(599\) 1.36562e11 1.06077 0.530387 0.847756i \(-0.322047\pi\)
0.530387 + 0.847756i \(0.322047\pi\)
\(600\) −1.18481e11 −0.914205
\(601\) 3.99717e10i 0.306376i 0.988197 + 0.153188i \(0.0489540\pi\)
−0.988197 + 0.153188i \(0.951046\pi\)
\(602\) 6.51481e10 + 2.49029e10i 0.496039 + 0.189611i
\(603\) 2.96546e11 2.24297
\(604\) 2.57479e10i 0.193461i
\(605\) 1.89300e11i 1.41296i
\(606\) 7.87371e10 0.583833
\(607\) 1.12940e11i 0.831945i −0.909377 0.415973i \(-0.863441\pi\)
0.909377 0.415973i \(-0.136559\pi\)
\(608\) −6.85447e10 −0.501602
\(609\) 4.28998e10i 0.311879i
\(610\) 5.38371e10i 0.388833i
\(611\) 1.16787e11 0.837974
\(612\) 1.04366e11 0.743968
\(613\) 8.37139e10 0.592865 0.296432 0.955054i \(-0.404203\pi\)
0.296432 + 0.955054i \(0.404203\pi\)
\(614\) 4.42748e10i 0.311518i
\(615\) −4.27279e11 −2.98683
\(616\) 8.54761e10 0.593638
\(617\) 1.29479e11 0.893423 0.446712 0.894678i \(-0.352595\pi\)
0.446712 + 0.894678i \(0.352595\pi\)
\(618\) 2.78351e10 0.190827
\(619\) −1.67421e11 −1.14037 −0.570187 0.821515i \(-0.693129\pi\)
−0.570187 + 0.821515i \(0.693129\pi\)
\(620\) 1.75087e10i 0.118491i
\(621\) 5.80635e11i 3.90424i
\(622\) 1.48312e11i 0.990867i
\(623\) 1.22237e10 0.0811429
\(624\) 1.99652e11i 1.31685i
\(625\) −1.89975e11 −1.24502
\(626\) −2.65796e11 −1.73082
\(627\) −4.64416e11 −3.00495
\(628\) 1.26362e10i 0.0812412i
\(629\) 1.80585e11i 1.15366i
\(630\) 2.66588e11i 1.69230i
\(631\) 3.06797e11i 1.93523i 0.252427 + 0.967616i \(0.418771\pi\)
−0.252427 + 0.967616i \(0.581229\pi\)
\(632\) 2.33887e11i 1.46601i
\(633\) −5.54863e11 −3.45598
\(634\) 8.76271e10i 0.542352i
\(635\) 5.66869e10i 0.348649i
\(636\) 3.21048e10i 0.196219i
\(637\) 7.53651e10 0.457733
\(638\) 9.30175e10 0.561412
\(639\) 6.55331e11i 3.93059i
\(640\) 2.52826e11 1.50696
\(641\) 9.47904e9i 0.0561477i 0.999606 + 0.0280739i \(0.00893736\pi\)
−0.999606 + 0.0280739i \(0.991063\pi\)
\(642\) −3.31415e11 −1.95089
\(643\) −6.87672e10 −0.402288 −0.201144 0.979562i \(-0.564466\pi\)
−0.201144 + 0.979562i \(0.564466\pi\)
\(644\) 2.58275e10i 0.150155i
\(645\) 3.81356e11 + 1.45773e11i 2.20339 + 0.842247i
\(646\) 2.65175e11 1.52266
\(647\) 2.26638e11i 1.29335i 0.762767 + 0.646673i \(0.223840\pi\)
−0.762767 + 0.646673i \(0.776160\pi\)
\(648\) 4.38732e11i 2.48828i
\(649\) −3.31576e10 −0.186898
\(650\) 6.71268e10i 0.376048i
\(651\) −6.54257e10 −0.364271
\(652\) 1.89760e9i 0.0105006i
\(653\) 1.26350e11i 0.694898i −0.937699 0.347449i \(-0.887048\pi\)
0.937699 0.347449i \(-0.112952\pi\)
\(654\) 7.01604e11 3.83514
\(655\) 1.67198e11 0.908377
\(656\) 2.76467e11 1.49289
\(657\) 4.42361e11i 2.37419i
\(658\) 1.40581e11 0.749935
\(659\) 5.31715e10 0.281927 0.140964 0.990015i \(-0.454980\pi\)
0.140964 + 0.990015i \(0.454980\pi\)
\(660\) −1.52497e11 −0.803687
\(661\) −2.49891e11 −1.30901 −0.654506 0.756056i \(-0.727124\pi\)
−0.654506 + 0.756056i \(0.727124\pi\)
\(662\) −1.79891e11 −0.936653
\(663\) 2.70304e11i 1.39894i
\(664\) 6.05675e10i 0.311579i
\(665\) 1.28261e11i 0.655854i
\(666\) 5.11791e11 2.60133
\(667\) 9.22174e10i 0.465918i
\(668\) −1.03304e10 −0.0518815
\(669\) −2.84672e10 −0.142115
\(670\) 2.47412e11 1.22778
\(671\) 8.25975e10i 0.407452i
\(672\) 8.41056e10i 0.412428i
\(673\) 6.74617e10i 0.328849i −0.986390 0.164425i \(-0.947423\pi\)
0.986390 0.164425i \(-0.0525768\pi\)
\(674\) 4.66692e10i 0.226147i
\(675\) 3.43977e11i 1.65697i
\(676\) 3.16040e10 0.151340
\(677\) 3.99956e11i 1.90396i 0.306164 + 0.951979i \(0.400954\pi\)
−0.306164 + 0.951979i \(0.599046\pi\)
\(678\) 6.03281e11i 2.85496i
\(679\) 1.42146e11i 0.668739i
\(680\) −2.85693e11 −1.33618
\(681\) 3.35777e11 1.56122
\(682\) 1.41859e11i 0.655722i
\(683\) −2.49767e11 −1.14776 −0.573882 0.818938i \(-0.694563\pi\)
−0.573882 + 0.818938i \(0.694563\pi\)
\(684\) 1.42306e11i 0.650130i
\(685\) −2.13990e11 −0.971920
\(686\) 2.08325e11 0.940686
\(687\) 2.09704e11i 0.941412i
\(688\) −2.46753e11 9.43214e10i −1.10131 0.420975i
\(689\) −5.96800e10 −0.264821
\(690\) 7.98418e11i 3.52236i
\(691\) 8.07032e10i 0.353980i 0.984213 + 0.176990i \(0.0566360\pi\)
−0.984213 + 0.176990i \(0.943364\pi\)
\(692\) −2.09204e10 −0.0912318
\(693\) 4.09002e11i 1.77334i
\(694\) 9.47853e10 0.408604
\(695\) 2.56267e11i 1.09838i
\(696\) 1.30295e11i 0.555251i
\(697\) −3.74302e11 −1.58595
\(698\) −3.13467e10 −0.132059
\(699\) −2.38489e11 −0.998987
\(700\) 1.53006e10i 0.0637260i
\(701\) −1.82574e11 −0.756078 −0.378039 0.925790i \(-0.623401\pi\)
−0.378039 + 0.925790i \(0.623401\pi\)
\(702\) −4.64798e11 −1.91388
\(703\) 2.46233e11 1.00815
\(704\) −2.40057e11 −0.977292
\(705\) 8.22918e11 3.33119
\(706\) 2.66015e11i 1.07075i
\(707\) 3.33619e10i 0.133528i
\(708\) 1.41558e10i 0.0563379i
\(709\) −2.09260e11 −0.828137 −0.414069 0.910246i \(-0.635893\pi\)
−0.414069 + 0.910246i \(0.635893\pi\)
\(710\) 5.46750e11i 2.15157i
\(711\) 1.11914e12 4.37933
\(712\) −3.71256e10 −0.144462
\(713\) 1.40639e11 0.544187
\(714\) 3.25375e11i 1.25196i
\(715\) 2.83480e11i 1.08467i
\(716\) 9.64151e10i 0.366854i
\(717\) 3.98484e11i 1.50777i
\(718\) 1.78665e11i 0.672265i
\(719\) 2.93803e10 0.109936 0.0549682 0.998488i \(-0.482494\pi\)
0.0549682 + 0.998488i \(0.482494\pi\)
\(720\) 1.00972e12i 3.75726i
\(721\) 1.17941e10i 0.0436439i
\(722\) 5.97639e10i 0.219933i
\(723\) −5.63467e10 −0.206212
\(724\) −8.79815e10 −0.320211
\(725\) 5.46311e10i 0.197737i
\(726\) 6.54795e11 2.35700
\(727\) 2.83587e11i 1.01519i −0.861595 0.507597i \(-0.830534\pi\)
0.861595 0.507597i \(-0.169466\pi\)
\(728\) 6.78351e10 0.241506
\(729\) −5.55570e11 −1.96711
\(730\) 3.69067e11i 1.29961i
\(731\) 3.34073e11 + 1.27699e11i 1.16996 + 0.447218i
\(732\) −3.52628e10 −0.122821
\(733\) 1.36753e11i 0.473720i 0.971544 + 0.236860i \(0.0761183\pi\)
−0.971544 + 0.236860i \(0.923882\pi\)
\(734\) 4.00788e11i 1.38080i
\(735\) 5.31045e11 1.81962
\(736\) 1.80793e11i 0.616128i
\(737\) −3.79581e11 −1.28657
\(738\) 1.06080e12i 3.57608i
\(739\) 1.82315e10i 0.0611285i 0.999533 + 0.0305643i \(0.00973042\pi\)
−0.999533 + 0.0305643i \(0.990270\pi\)
\(740\) 8.08540e10 0.269634
\(741\) −3.68567e11 −1.22249
\(742\) −7.18390e10 −0.236998
\(743\) 2.39818e11i 0.786913i 0.919343 + 0.393456i \(0.128721\pi\)
−0.919343 + 0.393456i \(0.871279\pi\)
\(744\) 1.98710e11 0.648526
\(745\) −4.95451e11 −1.60833
\(746\) −8.74325e10 −0.282304
\(747\) 2.89815e11 0.930760
\(748\) −1.33590e11 −0.426744
\(749\) 1.40425e11i 0.446187i
\(750\) 3.55969e11i 1.12504i
\(751\) 2.50813e11i 0.788478i −0.919008 0.394239i \(-0.871008\pi\)
0.919008 0.394239i \(-0.128992\pi\)
\(752\) −5.32461e11 −1.66501
\(753\) 4.30361e11i 1.33861i
\(754\) 7.38200e10 0.228396
\(755\) −3.37257e11 −1.03794
\(756\) −1.05944e11 −0.324331
\(757\) 2.52893e11i 0.770111i −0.922893 0.385056i \(-0.874182\pi\)
0.922893 0.385056i \(-0.125818\pi\)
\(758\) 2.01716e10i 0.0611032i
\(759\) 1.22494e12i 3.69104i
\(760\) 3.89551e11i 1.16764i
\(761\) 2.33691e10i 0.0696791i 0.999393 + 0.0348396i \(0.0110920\pi\)
−0.999393 + 0.0348396i \(0.988908\pi\)
\(762\) −1.96082e11 −0.581591
\(763\) 2.97279e11i 0.877133i
\(764\) 2.75109e10i 0.0807479i
\(765\) 1.36704e12i 3.99148i
\(766\) 5.11189e11 1.48479
\(767\) −2.63144e10 −0.0760346
\(768\) 4.35785e11i 1.25264i
\(769\) −2.10074e11 −0.600713 −0.300356 0.953827i \(-0.597106\pi\)
−0.300356 + 0.953827i \(0.597106\pi\)
\(770\) 3.41235e11i 0.970712i
\(771\) −2.97380e11 −0.841578
\(772\) 1.04906e11 0.295346
\(773\) 6.38984e10i 0.178966i −0.995988 0.0894832i \(-0.971478\pi\)
0.995988 0.0894832i \(-0.0285215\pi\)
\(774\) −3.61909e11 + 9.46787e11i −1.00841 + 2.63808i
\(775\) −8.33168e10 −0.230954
\(776\) 4.31724e11i 1.19058i
\(777\) 3.02132e11i 0.828921i
\(778\) 5.20291e11 1.42013
\(779\) 5.10371e11i 1.38591i
\(780\) −1.21024e11 −0.326959
\(781\) 8.38830e11i 2.25460i
\(782\) 6.99425e11i