Properties

Label 177.11.c.a.58.18
Level $177$
Weight $11$
Character 177.58
Analytic conductor $112.458$
Analytic rank $0$
Dimension $100$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(112.458233723\)
Analytic rank: \(0\)
Dimension: \(100\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.18
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.83

$q$-expansion

\(f(q)\) \(=\) \(q-46.3046i q^{2} +140.296 q^{3} -1120.11 q^{4} +3858.39 q^{5} -6496.35i q^{6} +22459.5 q^{7} +4450.45i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-46.3046i q^{2} +140.296 q^{3} -1120.11 q^{4} +3858.39 q^{5} -6496.35i q^{6} +22459.5 q^{7} +4450.45i q^{8} +19683.0 q^{9} -178661. i q^{10} -173626. i q^{11} -157147. q^{12} -674974. i q^{13} -1.03998e6i q^{14} +541318. q^{15} -940919. q^{16} +2.43219e6 q^{17} -911413. i q^{18} +1.33829e6 q^{19} -4.32184e6 q^{20} +3.15097e6 q^{21} -8.03968e6 q^{22} -562371. i q^{23} +624381. i q^{24} +5.12158e6 q^{25} -3.12544e7 q^{26} +2.76145e6 q^{27} -2.51571e7 q^{28} +7.41792e6 q^{29} -2.50655e7i q^{30} +3.31206e7i q^{31} +4.81261e7i q^{32} -2.43591e7i q^{33} -1.12621e8i q^{34} +8.66574e7 q^{35} -2.20472e7 q^{36} +7.74043e7i q^{37} -6.19690e7i q^{38} -9.46962e7i q^{39} +1.71716e7i q^{40} +1.51747e8 q^{41} -1.45905e8i q^{42} +1.64287e8i q^{43} +1.94481e8i q^{44} +7.59448e7 q^{45} -2.60403e7 q^{46} -2.27468e8i q^{47} -1.32007e8 q^{48} +2.21952e8 q^{49} -2.37152e8i q^{50} +3.41226e8 q^{51} +7.56047e8i q^{52} -6.16906e8 q^{53} -1.27868e8i q^{54} -6.69918e8i q^{55} +9.99547e7i q^{56} +1.87757e8 q^{57} -3.43484e8i q^{58} +(-6.62524e8 + 2.68661e8i) q^{59} -6.06337e8 q^{60} +5.94808e8i q^{61} +1.53363e9 q^{62} +4.42069e8 q^{63} +1.26496e9 q^{64} -2.60431e9i q^{65} -1.12794e9 q^{66} +1.29950e9i q^{67} -2.72432e9 q^{68} -7.88984e7i q^{69} -4.01263e9i q^{70} +2.19554e9 q^{71} +8.75982e7i q^{72} +1.44021e8i q^{73} +3.58417e9 q^{74} +7.18538e8 q^{75} -1.49904e9 q^{76} -3.89955e9i q^{77} -4.38487e9 q^{78} -5.52548e9 q^{79} -3.63044e9 q^{80} +3.87420e8 q^{81} -7.02659e9i q^{82} -2.03540e9i q^{83} -3.52945e9 q^{84} +9.38433e9 q^{85} +7.60724e9 q^{86} +1.04071e9 q^{87} +7.72714e8 q^{88} +2.60902e8i q^{89} -3.51659e9i q^{90} -1.51595e10i q^{91} +6.29918e8i q^{92} +4.64669e9i q^{93} -1.05328e10 q^{94} +5.16365e9 q^{95} +6.75191e9i q^{96} -9.73345e9i q^{97} -1.02774e10i q^{98} -3.41748e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 46.3046i 1.44702i −0.690315 0.723509i \(-0.742528\pi\)
0.690315 0.723509i \(-0.257472\pi\)
\(3\) 140.296 0.577350
\(4\) −1120.11 −1.09386
\(5\) 3858.39 1.23469 0.617343 0.786694i \(-0.288209\pi\)
0.617343 + 0.786694i \(0.288209\pi\)
\(6\) 6496.35i 0.835436i
\(7\) 22459.5 1.33632 0.668158 0.744020i \(-0.267083\pi\)
0.668158 + 0.744020i \(0.267083\pi\)
\(8\) 4450.45i 0.135817i
\(9\) 19683.0 0.333333
\(10\) 178661.i 1.78661i
\(11\) 173626.i 1.07808i −0.842280 0.539041i \(-0.818787\pi\)
0.842280 0.539041i \(-0.181213\pi\)
\(12\) −157147. −0.631540
\(13\) 674974.i 1.81790i −0.416904 0.908950i \(-0.636885\pi\)
0.416904 0.908950i \(-0.363115\pi\)
\(14\) 1.03998e6i 1.93367i
\(15\) 541318. 0.712846
\(16\) −940919. −0.897330
\(17\) 2.43219e6 1.71298 0.856490 0.516164i \(-0.172640\pi\)
0.856490 + 0.516164i \(0.172640\pi\)
\(18\) 911413.i 0.482339i
\(19\) 1.33829e6 0.540483 0.270242 0.962793i \(-0.412896\pi\)
0.270242 + 0.962793i \(0.412896\pi\)
\(20\) −4.32184e6 −1.35057
\(21\) 3.15097e6 0.771522
\(22\) −8.03968e6 −1.56000
\(23\) 562371.i 0.0873742i −0.999045 0.0436871i \(-0.986090\pi\)
0.999045 0.0436871i \(-0.0139105\pi\)
\(24\) 624381.i 0.0784140i
\(25\) 5.12158e6 0.524450
\(26\) −3.12544e7 −2.63053
\(27\) 2.76145e6 0.192450
\(28\) −2.51571e7 −1.46174
\(29\) 7.41792e6 0.361653 0.180827 0.983515i \(-0.442123\pi\)
0.180827 + 0.983515i \(0.442123\pi\)
\(30\) 2.50655e7i 1.03150i
\(31\) 3.31206e7i 1.15688i 0.815724 + 0.578442i \(0.196339\pi\)
−0.815724 + 0.578442i \(0.803661\pi\)
\(32\) 4.81261e7i 1.43427i
\(33\) 2.43591e7i 0.622431i
\(34\) 1.12621e8i 2.47871i
\(35\) 8.66574e7 1.64993
\(36\) −2.20472e7 −0.364620
\(37\) 7.74043e7i 1.11624i 0.829761 + 0.558119i \(0.188477\pi\)
−0.829761 + 0.558119i \(0.811523\pi\)
\(38\) 6.19690e7i 0.782089i
\(39\) 9.46962e7i 1.04957i
\(40\) 1.71716e7i 0.167691i
\(41\) 1.51747e8 1.30979 0.654894 0.755720i \(-0.272713\pi\)
0.654894 + 0.755720i \(0.272713\pi\)
\(42\) 1.45905e8i 1.11641i
\(43\) 1.64287e8i 1.11754i 0.829324 + 0.558768i \(0.188726\pi\)
−0.829324 + 0.558768i \(0.811274\pi\)
\(44\) 1.94481e8i 1.17927i
\(45\) 7.59448e7 0.411562
\(46\) −2.60403e7 −0.126432
\(47\) 2.27468e8i 0.991817i −0.868375 0.495909i \(-0.834835\pi\)
0.868375 0.495909i \(-0.165165\pi\)
\(48\) −1.32007e8 −0.518074
\(49\) 2.21952e8 0.785740
\(50\) 2.37152e8i 0.758888i
\(51\) 3.41226e8 0.988989
\(52\) 7.56047e8i 1.98853i
\(53\) −6.16906e8 −1.47516 −0.737581 0.675258i \(-0.764032\pi\)
−0.737581 + 0.675258i \(0.764032\pi\)
\(54\) 1.27868e8i 0.278479i
\(55\) 6.69918e8i 1.33109i
\(56\) 9.99547e7i 0.181494i
\(57\) 1.87757e8 0.312048
\(58\) 3.43484e8i 0.523318i
\(59\) −6.62524e8 + 2.68661e8i −0.926705 + 0.375790i
\(60\) −6.06337e8 −0.779754
\(61\) 5.94808e8i 0.704251i 0.935953 + 0.352126i \(0.114541\pi\)
−0.935953 + 0.352126i \(0.885459\pi\)
\(62\) 1.53363e9 1.67403
\(63\) 4.42069e8 0.445439
\(64\) 1.26496e9 1.17808
\(65\) 2.60431e9i 2.24454i
\(66\) −1.12794e9 −0.900668
\(67\) 1.29950e9i 0.962500i 0.876583 + 0.481250i \(0.159817\pi\)
−0.876583 + 0.481250i \(0.840183\pi\)
\(68\) −2.72432e9 −1.87376
\(69\) 7.88984e7i 0.0504455i
\(70\) 4.01263e9i 2.38748i
\(71\) 2.19554e9 1.21688 0.608442 0.793599i \(-0.291795\pi\)
0.608442 + 0.793599i \(0.291795\pi\)
\(72\) 8.75982e7i 0.0452723i
\(73\) 1.44021e8i 0.0694723i 0.999397 + 0.0347361i \(0.0110591\pi\)
−0.999397 + 0.0347361i \(0.988941\pi\)
\(74\) 3.58417e9 1.61521
\(75\) 7.18538e8 0.302791
\(76\) −1.49904e9 −0.591213
\(77\) 3.89955e9i 1.44066i
\(78\) −4.38487e9 −1.51874
\(79\) −5.52548e9 −1.79570 −0.897851 0.440298i \(-0.854873\pi\)
−0.897851 + 0.440298i \(0.854873\pi\)
\(80\) −3.63044e9 −1.10792
\(81\) 3.87420e8 0.111111
\(82\) 7.02659e9i 1.89529i
\(83\) 2.03540e9i 0.516726i −0.966048 0.258363i \(-0.916817\pi\)
0.966048 0.258363i \(-0.0831831\pi\)
\(84\) −3.52945e9 −0.843937
\(85\) 9.38433e9 2.11499
\(86\) 7.60724e9 1.61709
\(87\) 1.04071e9 0.208801
\(88\) 7.72714e8 0.146422
\(89\) 2.60902e8i 0.0467227i 0.999727 + 0.0233614i \(0.00743683\pi\)
−0.999727 + 0.0233614i \(0.992563\pi\)
\(90\) 3.51659e9i 0.595537i
\(91\) 1.51595e10i 2.42929i
\(92\) 6.29918e8i 0.0955752i
\(93\) 4.64669e9i 0.667927i
\(94\) −1.05328e10 −1.43518
\(95\) 5.16365e9 0.667327
\(96\) 6.75191e9i 0.828076i
\(97\) 9.73345e9i 1.13347i −0.823902 0.566733i \(-0.808207\pi\)
0.823902 0.566733i \(-0.191793\pi\)
\(98\) 1.02774e10i 1.13698i
\(99\) 3.41748e9i 0.359360i
\(100\) −5.73674e9 −0.573674
\(101\) 2.01714e10i 1.91924i 0.281293 + 0.959622i \(0.409237\pi\)
−0.281293 + 0.959622i \(0.590763\pi\)
\(102\) 1.58003e10i 1.43108i
\(103\) 8.11267e9i 0.699806i −0.936786 0.349903i \(-0.886215\pi\)
0.936786 0.349903i \(-0.113785\pi\)
\(104\) 3.00394e9 0.246902
\(105\) 1.21577e10 0.952588
\(106\) 2.85656e10i 2.13459i
\(107\) 7.83502e9 0.558626 0.279313 0.960200i \(-0.409893\pi\)
0.279313 + 0.960200i \(0.409893\pi\)
\(108\) −3.09313e9 −0.210513
\(109\) 1.58300e10i 1.02884i −0.857537 0.514422i \(-0.828007\pi\)
0.857537 0.514422i \(-0.171993\pi\)
\(110\) −3.10203e10 −1.92611
\(111\) 1.08595e10i 0.644460i
\(112\) −2.11325e10 −1.19912
\(113\) 3.34226e10i 1.81405i 0.421082 + 0.907023i \(0.361651\pi\)
−0.421082 + 0.907023i \(0.638349\pi\)
\(114\) 8.69400e9i 0.451539i
\(115\) 2.16985e9i 0.107880i
\(116\) −8.30891e9 −0.395598
\(117\) 1.32855e10i 0.605967i
\(118\) 1.24402e10 + 3.06779e10i 0.543774 + 1.34096i
\(119\) 5.46256e10 2.28908
\(120\) 2.40911e9i 0.0968166i
\(121\) −4.20859e9 −0.162259
\(122\) 2.75423e10 1.01906
\(123\) 2.12895e10 0.756207
\(124\) 3.70988e10i 1.26547i
\(125\) −1.79186e10 −0.587155
\(126\) 2.04698e10i 0.644557i
\(127\) −1.60679e10 −0.486341 −0.243171 0.969984i \(-0.578188\pi\)
−0.243171 + 0.969984i \(0.578188\pi\)
\(128\) 9.29216e9i 0.270437i
\(129\) 2.30488e10i 0.645209i
\(130\) −1.20592e11 −3.24788
\(131\) 3.56195e10i 0.923276i −0.887068 0.461638i \(-0.847262\pi\)
0.887068 0.461638i \(-0.152738\pi\)
\(132\) 2.72849e10i 0.680852i
\(133\) 3.00573e10 0.722256
\(134\) 6.01726e10 1.39275
\(135\) 1.06548e10 0.237615
\(136\) 1.08243e10i 0.232652i
\(137\) 4.47286e10 0.926793 0.463396 0.886151i \(-0.346631\pi\)
0.463396 + 0.886151i \(0.346631\pi\)
\(138\) −3.65336e9 −0.0729956
\(139\) −3.73592e10 −0.719986 −0.359993 0.932955i \(-0.617221\pi\)
−0.359993 + 0.932955i \(0.617221\pi\)
\(140\) −9.70661e10 −1.80479
\(141\) 3.19129e10i 0.572626i
\(142\) 1.01663e11i 1.76085i
\(143\) −1.17193e11 −1.95984
\(144\) −1.85201e10 −0.299110
\(145\) 2.86213e10 0.446528
\(146\) 6.66883e9 0.100528
\(147\) 3.11390e10 0.453647
\(148\) 8.67015e10i 1.22101i
\(149\) 5.72721e10i 0.779852i 0.920846 + 0.389926i \(0.127499\pi\)
−0.920846 + 0.389926i \(0.872501\pi\)
\(150\) 3.32716e10i 0.438144i
\(151\) 8.23203e10i 1.04863i 0.851525 + 0.524315i \(0.175678\pi\)
−0.851525 + 0.524315i \(0.824322\pi\)
\(152\) 5.95599e9i 0.0734068i
\(153\) 4.78727e10 0.570993
\(154\) −1.80567e11 −2.08466
\(155\) 1.27792e11i 1.42839i
\(156\) 1.06070e11i 1.14808i
\(157\) 6.15806e10i 0.645573i 0.946472 + 0.322787i \(0.104620\pi\)
−0.946472 + 0.322787i \(0.895380\pi\)
\(158\) 2.55855e11i 2.59841i
\(159\) −8.65496e10 −0.851686
\(160\) 1.85689e11i 1.77087i
\(161\) 1.26305e10i 0.116760i
\(162\) 1.79393e10i 0.160780i
\(163\) −1.86475e11 −1.62063 −0.810314 0.585996i \(-0.800703\pi\)
−0.810314 + 0.585996i \(0.800703\pi\)
\(164\) −1.69974e11 −1.43273
\(165\) 9.39869e10i 0.768506i
\(166\) −9.42485e10 −0.747712
\(167\) −1.33552e11 −1.02818 −0.514090 0.857736i \(-0.671870\pi\)
−0.514090 + 0.857736i \(0.671870\pi\)
\(168\) 1.40233e10i 0.104786i
\(169\) −3.17731e11 −2.30476
\(170\) 4.34537e11i 3.06043i
\(171\) 2.63416e10 0.180161
\(172\) 1.84020e11i 1.22243i
\(173\) 7.52751e10i 0.485759i −0.970056 0.242879i \(-0.921908\pi\)
0.970056 0.242879i \(-0.0780919\pi\)
\(174\) 4.81894e10i 0.302138i
\(175\) 1.15028e11 0.700830
\(176\) 1.63368e11i 0.967395i
\(177\) −9.29495e10 + 3.76921e10i −0.535033 + 0.216962i
\(178\) 1.20810e10 0.0676086
\(179\) 1.98766e11i 1.08162i −0.841143 0.540812i \(-0.818117\pi\)
0.841143 0.540812i \(-0.181883\pi\)
\(180\) −8.50667e10 −0.450191
\(181\) 1.84058e11 0.947460 0.473730 0.880670i \(-0.342907\pi\)
0.473730 + 0.880670i \(0.342907\pi\)
\(182\) −7.01956e11 −3.51522
\(183\) 8.34493e10i 0.406600i
\(184\) 2.50280e9 0.0118669
\(185\) 2.98656e11i 1.37820i
\(186\) 2.15163e11 0.966502
\(187\) 4.22291e11i 1.84673i
\(188\) 2.54790e11i 1.08491i
\(189\) 6.20206e10 0.257174
\(190\) 2.39101e11i 0.965634i
\(191\) 1.52877e11i 0.601418i 0.953716 + 0.300709i \(0.0972233\pi\)
−0.953716 + 0.300709i \(0.902777\pi\)
\(192\) 1.77469e11 0.680167
\(193\) −1.45253e11 −0.542423 −0.271212 0.962520i \(-0.587424\pi\)
−0.271212 + 0.962520i \(0.587424\pi\)
\(194\) −4.50703e11 −1.64014
\(195\) 3.65375e11i 1.29588i
\(196\) −2.48611e11 −0.859489
\(197\) −3.18108e11 −1.07212 −0.536061 0.844180i \(-0.680088\pi\)
−0.536061 + 0.844180i \(0.680088\pi\)
\(198\) −1.58245e11 −0.520001
\(199\) 4.37270e11 1.40115 0.700574 0.713580i \(-0.252927\pi\)
0.700574 + 0.713580i \(0.252927\pi\)
\(200\) 2.27933e10i 0.0712292i
\(201\) 1.82314e11i 0.555700i
\(202\) 9.34030e11 2.77718
\(203\) 1.66602e11 0.483283
\(204\) −3.82212e11 −1.08182
\(205\) 5.85500e11 1.61718
\(206\) −3.75654e11 −1.01263
\(207\) 1.10691e10i 0.0291247i
\(208\) 6.35096e11i 1.63126i
\(209\) 2.32362e11i 0.582685i
\(210\) 5.62957e11i 1.37841i
\(211\) 1.61677e11i 0.386577i 0.981142 + 0.193289i \(0.0619153\pi\)
−0.981142 + 0.193289i \(0.938085\pi\)
\(212\) 6.91005e11 1.61362
\(213\) 3.08025e11 0.702568
\(214\) 3.62797e11i 0.808342i
\(215\) 6.33885e11i 1.37981i
\(216\) 1.22897e10i 0.0261380i
\(217\) 7.43871e11i 1.54596i
\(218\) −7.33003e11 −1.48876
\(219\) 2.02056e10i 0.0401098i
\(220\) 7.50383e11i 1.45603i
\(221\) 1.64166e12i 3.11403i
\(222\) 5.02845e11 0.932545
\(223\) 7.52806e11 1.36508 0.682541 0.730847i \(-0.260875\pi\)
0.682541 + 0.730847i \(0.260875\pi\)
\(224\) 1.08089e12i 1.91664i
\(225\) 1.00808e11 0.174817
\(226\) 1.54762e12 2.62496
\(227\) 1.24261e11i 0.206160i −0.994673 0.103080i \(-0.967130\pi\)
0.994673 0.103080i \(-0.0328698\pi\)
\(228\) −2.10309e11 −0.341337
\(229\) 8.21422e11i 1.30433i −0.758075 0.652167i \(-0.773860\pi\)
0.758075 0.652167i \(-0.226140\pi\)
\(230\) −1.00474e11 −0.156104
\(231\) 5.47091e11i 0.831764i
\(232\) 3.30131e10i 0.0491186i
\(233\) 3.61168e11i 0.525932i 0.964805 + 0.262966i \(0.0847007\pi\)
−0.964805 + 0.262966i \(0.915299\pi\)
\(234\) −6.15180e11 −0.876845
\(235\) 8.77662e11i 1.22458i
\(236\) 7.42101e11 3.00931e11i 1.01369 0.411061i
\(237\) −7.75203e11 −1.03675
\(238\) 2.52941e12i 3.31234i
\(239\) 1.31812e12 1.69031 0.845156 0.534520i \(-0.179507\pi\)
0.845156 + 0.534520i \(0.179507\pi\)
\(240\) −5.09336e11 −0.639659
\(241\) −9.65434e11 −1.18751 −0.593755 0.804646i \(-0.702355\pi\)
−0.593755 + 0.804646i \(0.702355\pi\)
\(242\) 1.94877e11i 0.234792i
\(243\) 5.43536e10 0.0641500
\(244\) 6.66252e11i 0.770352i
\(245\) 8.56378e11 0.970142
\(246\) 9.85803e11i 1.09424i
\(247\) 9.03311e11i 0.982545i
\(248\) −1.47402e11 −0.157124
\(249\) 2.85559e11i 0.298332i
\(250\) 8.29711e11i 0.849624i
\(251\) −1.73925e12 −1.74580 −0.872898 0.487902i \(-0.837762\pi\)
−0.872898 + 0.487902i \(0.837762\pi\)
\(252\) −4.95168e11 −0.487247
\(253\) −9.76422e10 −0.0941965
\(254\) 7.44018e11i 0.703745i
\(255\) 1.31659e12 1.22109
\(256\) 8.65047e11 0.786756
\(257\) 2.30940e11 0.205984 0.102992 0.994682i \(-0.467158\pi\)
0.102992 + 0.994682i \(0.467158\pi\)
\(258\) 1.06727e12 0.933629
\(259\) 1.73846e12i 1.49165i
\(260\) 2.91713e12i 2.45521i
\(261\) 1.46007e11 0.120551
\(262\) −1.64935e12 −1.33600
\(263\) −1.00273e12 −0.796906 −0.398453 0.917189i \(-0.630453\pi\)
−0.398453 + 0.917189i \(0.630453\pi\)
\(264\) 1.08409e11 0.0845366
\(265\) −2.38027e12 −1.82136
\(266\) 1.39179e12i 1.04512i
\(267\) 3.66036e10i 0.0269754i
\(268\) 1.45558e12i 1.05284i
\(269\) 1.38574e12i 0.983827i 0.870644 + 0.491914i \(0.163702\pi\)
−0.870644 + 0.491914i \(0.836298\pi\)
\(270\) 4.93364e11i 0.343834i
\(271\) −3.34414e11 −0.228791 −0.114395 0.993435i \(-0.536493\pi\)
−0.114395 + 0.993435i \(0.536493\pi\)
\(272\) −2.28849e12 −1.53711
\(273\) 2.12683e12i 1.40255i
\(274\) 2.07114e12i 1.34109i
\(275\) 8.89240e11i 0.565399i
\(276\) 8.83751e10i 0.0551804i
\(277\) 6.23330e11 0.382225 0.191113 0.981568i \(-0.438790\pi\)
0.191113 + 0.981568i \(0.438790\pi\)
\(278\) 1.72990e12i 1.04183i
\(279\) 6.51913e11i 0.385628i
\(280\) 3.85665e11i 0.224088i
\(281\) −1.04987e12 −0.599247 −0.299623 0.954058i \(-0.596861\pi\)
−0.299623 + 0.954058i \(0.596861\pi\)
\(282\) −1.47771e12 −0.828600
\(283\) 1.82074e12i 1.00304i −0.865147 0.501518i \(-0.832775\pi\)
0.865147 0.501518i \(-0.167225\pi\)
\(284\) −2.45925e12 −1.33110
\(285\) 7.24440e11 0.385282
\(286\) 5.42657e12i 2.83593i
\(287\) 3.40816e12 1.75029
\(288\) 9.47266e11i 0.478090i
\(289\) 3.89954e12 1.93430
\(290\) 1.32529e12i 0.646134i
\(291\) 1.36557e12i 0.654407i
\(292\) 1.61320e11i 0.0759929i
\(293\) −1.89086e12 −0.875631 −0.437816 0.899065i \(-0.644248\pi\)
−0.437816 + 0.899065i \(0.644248\pi\)
\(294\) 1.44188e12i 0.656435i
\(295\) −2.55628e12 + 1.03660e12i −1.14419 + 0.463982i
\(296\) −3.44484e11 −0.151604
\(297\) 4.79459e11i 0.207477i
\(298\) 2.65196e12 1.12846
\(299\) −3.79585e11 −0.158838
\(300\) −8.04843e11 −0.331211
\(301\) 3.68980e12i 1.49338i
\(302\) 3.81180e12 1.51739
\(303\) 2.82998e12i 1.10808i
\(304\) −1.25922e12 −0.484992
\(305\) 2.29500e12i 0.869529i
\(306\) 2.21673e12i 0.826237i
\(307\) 3.11488e12 1.14222 0.571109 0.820874i \(-0.306513\pi\)
0.571109 + 0.820874i \(0.306513\pi\)
\(308\) 4.36793e12i 1.57588i
\(309\) 1.13818e12i 0.404033i
\(310\) 5.91737e12 2.06690
\(311\) −6.95987e11 −0.239221 −0.119610 0.992821i \(-0.538165\pi\)
−0.119610 + 0.992821i \(0.538165\pi\)
\(312\) 4.21441e11 0.142549
\(313\) 2.00121e12i 0.666149i −0.942900 0.333075i \(-0.891914\pi\)
0.942900 0.333075i \(-0.108086\pi\)
\(314\) 2.85146e12 0.934156
\(315\) 1.70568e12 0.549977
\(316\) 6.18916e12 1.96425
\(317\) 4.25638e12 1.32967 0.664835 0.746990i \(-0.268502\pi\)
0.664835 + 0.746990i \(0.268502\pi\)
\(318\) 4.00764e12i 1.23240i
\(319\) 1.28794e12i 0.389891i
\(320\) 4.88070e12 1.45456
\(321\) 1.09922e12 0.322523
\(322\) −5.84852e11 −0.168953
\(323\) 3.25497e12 0.925837
\(324\) −4.33955e11 −0.121540
\(325\) 3.45693e12i 0.953397i
\(326\) 8.63465e12i 2.34508i
\(327\) 2.22089e12i 0.594003i
\(328\) 6.75343e11i 0.177892i
\(329\) 5.10881e12i 1.32538i
\(330\) −4.35202e12 −1.11204
\(331\) −1.32140e12 −0.332578 −0.166289 0.986077i \(-0.553179\pi\)
−0.166289 + 0.986077i \(0.553179\pi\)
\(332\) 2.27988e12i 0.565226i
\(333\) 1.52355e12i 0.372079i
\(334\) 6.18409e12i 1.48780i
\(335\) 5.01397e12i 1.18839i
\(336\) −2.96481e12 −0.692310
\(337\) 2.23788e12i 0.514858i −0.966297 0.257429i \(-0.917125\pi\)
0.966297 0.257429i \(-0.0828754\pi\)
\(338\) 1.47124e13i 3.33503i
\(339\) 4.68906e12i 1.04734i
\(340\) −1.05115e13 −2.31351
\(341\) 5.75060e12 1.24721
\(342\) 1.21973e12i 0.260696i
\(343\) −1.35932e12 −0.286320
\(344\) −7.31152e11 −0.151780
\(345\) 3.04421e11i 0.0622844i
\(346\) −3.48558e12 −0.702902
\(347\) 3.33102e12i 0.662110i −0.943611 0.331055i \(-0.892595\pi\)
0.943611 0.331055i \(-0.107405\pi\)
\(348\) −1.16571e12 −0.228399
\(349\) 5.35080e11i 0.103346i −0.998664 0.0516728i \(-0.983545\pi\)
0.998664 0.0516728i \(-0.0164553\pi\)
\(350\) 5.32632e12i 1.01411i
\(351\) 1.86391e12i 0.349855i
\(352\) 8.35595e12 1.54626
\(353\) 1.27435e12i 0.232496i −0.993220 0.116248i \(-0.962913\pi\)
0.993220 0.116248i \(-0.0370868\pi\)
\(354\) 1.74532e12 + 4.30399e12i 0.313948 + 0.774203i
\(355\) 8.47124e12 1.50247
\(356\) 2.92240e11i 0.0511081i
\(357\) 7.66376e12 1.32160
\(358\) −9.20376e12 −1.56513
\(359\) −7.50199e12 −1.25807 −0.629034 0.777378i \(-0.716549\pi\)
−0.629034 + 0.777378i \(0.716549\pi\)
\(360\) 3.37988e11i 0.0558971i
\(361\) −4.34004e12 −0.707878
\(362\) 8.52270e12i 1.37099i
\(363\) −5.90449e11 −0.0936805
\(364\) 1.69804e13i 2.65730i
\(365\) 5.55690e11i 0.0857764i
\(366\) 3.86408e12 0.588357
\(367\) 2.92715e12i 0.439657i −0.975539 0.219829i \(-0.929450\pi\)
0.975539 0.219829i \(-0.0705498\pi\)
\(368\) 5.29145e11i 0.0784036i
\(369\) 2.98684e12 0.436596
\(370\) 1.38291e13 1.99428
\(371\) −1.38554e13 −1.97128
\(372\) 5.20482e12i 0.730619i
\(373\) 8.19998e12 1.13571 0.567856 0.823128i \(-0.307773\pi\)
0.567856 + 0.823128i \(0.307773\pi\)
\(374\) −1.95540e13 −2.67225
\(375\) −2.51390e12 −0.338994
\(376\) 1.01234e12 0.134706
\(377\) 5.00690e12i 0.657449i
\(378\) 2.87184e12i 0.372135i
\(379\) 7.57176e12 0.968279 0.484140 0.874991i \(-0.339133\pi\)
0.484140 + 0.874991i \(0.339133\pi\)
\(380\) −5.78387e12 −0.729963
\(381\) −2.25427e12 −0.280789
\(382\) 7.07892e12 0.870262
\(383\) 6.28768e12 0.762951 0.381475 0.924379i \(-0.375416\pi\)
0.381475 + 0.924379i \(0.375416\pi\)
\(384\) 1.30365e12i 0.156137i
\(385\) 1.50460e13i 1.77876i
\(386\) 6.72588e12i 0.784896i
\(387\) 3.23366e12i 0.372512i
\(388\) 1.09026e13i 1.23985i
\(389\) −8.97532e12 −1.00763 −0.503816 0.863811i \(-0.668071\pi\)
−0.503816 + 0.863811i \(0.668071\pi\)
\(390\) −1.69185e13 −1.87517
\(391\) 1.36779e12i 0.149670i
\(392\) 9.87786e11i 0.106717i
\(393\) 4.99728e12i 0.533054i
\(394\) 1.47299e13i 1.55138i
\(395\) −2.13195e13 −2.21713
\(396\) 3.82796e12i 0.393090i
\(397\) 3.49967e12i 0.354874i −0.984132 0.177437i \(-0.943219\pi\)
0.984132 0.177437i \(-0.0567806\pi\)
\(398\) 2.02476e13i 2.02749i
\(399\) 4.21692e12 0.416995
\(400\) −4.81899e12 −0.470605
\(401\) 5.14383e11i 0.0496095i −0.999692 0.0248047i \(-0.992104\pi\)
0.999692 0.0248047i \(-0.00789641\pi\)
\(402\) 8.44198e12 0.804107
\(403\) 2.23555e13 2.10310
\(404\) 2.25943e13i 2.09938i
\(405\) 1.49482e12 0.137187
\(406\) 7.71445e12i 0.699319i
\(407\) 1.34394e13 1.20339
\(408\) 1.51861e12i 0.134322i
\(409\) 1.55003e13i 1.35433i −0.735832 0.677164i \(-0.763209\pi\)
0.735832 0.677164i \(-0.236791\pi\)
\(410\) 2.71113e13i 2.34009i
\(411\) 6.27525e12 0.535084
\(412\) 9.08711e12i 0.765490i
\(413\) −1.48799e13 + 6.03399e12i −1.23837 + 0.502174i
\(414\) −5.12552e11 −0.0421440
\(415\) 7.85339e12i 0.637994i
\(416\) 3.24839e13 2.60736
\(417\) −5.24135e12 −0.415684
\(418\) −1.07594e13 −0.843156
\(419\) 9.66126e12i 0.748107i 0.927407 + 0.374054i \(0.122032\pi\)
−0.927407 + 0.374054i \(0.877968\pi\)
\(420\) −1.36180e13 −1.04200
\(421\) 1.11554e13i 0.843479i 0.906717 + 0.421740i \(0.138580\pi\)
−0.906717 + 0.421740i \(0.861420\pi\)
\(422\) 7.48638e12 0.559384
\(423\) 4.47726e12i 0.330606i
\(424\) 2.74551e12i 0.200352i
\(425\) 1.24566e13 0.898372
\(426\) 1.42630e13i 1.01663i
\(427\) 1.33591e13i 0.941102i
\(428\) −8.77611e12 −0.611059
\(429\) −1.64417e13 −1.13152
\(430\) 2.93517e13 1.99660
\(431\) 1.68009e13i 1.12966i 0.825208 + 0.564828i \(0.191058\pi\)
−0.825208 + 0.564828i \(0.808942\pi\)
\(432\) −2.59830e12 −0.172691
\(433\) −2.13329e13 −1.40156 −0.700779 0.713378i \(-0.747164\pi\)
−0.700779 + 0.713378i \(0.747164\pi\)
\(434\) 3.44446e13 2.23703
\(435\) 4.01545e12 0.257803
\(436\) 1.77314e13i 1.12541i
\(437\) 7.52615e11i 0.0472243i
\(438\) 9.35611e11 0.0580396
\(439\) −3.77036e12 −0.231239 −0.115619 0.993294i \(-0.536885\pi\)
−0.115619 + 0.993294i \(0.536885\pi\)
\(440\) 2.98144e12 0.180785
\(441\) 4.36868e12 0.261913
\(442\) −7.60164e13 −4.50605
\(443\) 2.05445e13i 1.20414i −0.798443 0.602070i \(-0.794343\pi\)
0.798443 0.602070i \(-0.205657\pi\)
\(444\) 1.21639e13i 0.704949i
\(445\) 1.00666e12i 0.0576879i
\(446\) 3.48584e13i 1.97530i
\(447\) 8.03506e12i 0.450247i
\(448\) 2.84103e13 1.57429
\(449\) 6.79517e12 0.372365 0.186182 0.982515i \(-0.440388\pi\)
0.186182 + 0.982515i \(0.440388\pi\)
\(450\) 4.66787e12i 0.252963i
\(451\) 2.63473e13i 1.41206i
\(452\) 3.74371e13i 1.98431i
\(453\) 1.15492e13i 0.605426i
\(454\) −5.75384e12 −0.298318
\(455\) 5.84915e13i 2.99941i
\(456\) 8.35603e11i 0.0423814i
\(457\) 2.65198e13i 1.33042i 0.746657 + 0.665209i \(0.231658\pi\)
−0.746657 + 0.665209i \(0.768342\pi\)
\(458\) −3.80356e13 −1.88739
\(459\) 6.71636e12 0.329663
\(460\) 2.43047e12i 0.118005i
\(461\) 2.21723e13 1.06490 0.532448 0.846463i \(-0.321272\pi\)
0.532448 + 0.846463i \(0.321272\pi\)
\(462\) −2.53328e13 −1.20358
\(463\) 7.92214e11i 0.0372338i −0.999827 0.0186169i \(-0.994074\pi\)
0.999827 0.0186169i \(-0.00592629\pi\)
\(464\) −6.97966e12 −0.324522
\(465\) 1.79288e13i 0.824680i
\(466\) 1.67237e13 0.761032
\(467\) 3.39537e13i 1.52863i 0.644842 + 0.764316i \(0.276923\pi\)
−0.644842 + 0.764316i \(0.723077\pi\)
\(468\) 1.48813e13i 0.662843i
\(469\) 2.91860e13i 1.28620i
\(470\) −4.06398e13 −1.77199
\(471\) 8.63951e12i 0.372722i
\(472\) −1.19566e12 2.94853e12i −0.0510386 0.125862i
\(473\) 2.85245e13 1.20479
\(474\) 3.58954e13i 1.50019i
\(475\) 6.85416e12 0.283456
\(476\) −6.11868e13 −2.50393
\(477\) −1.21426e13 −0.491721
\(478\) 6.10352e13i 2.44591i
\(479\) −4.75640e13 −1.88626 −0.943128 0.332430i \(-0.892131\pi\)
−0.943128 + 0.332430i \(0.892131\pi\)
\(480\) 2.60515e13i 1.02241i
\(481\) 5.22459e13 2.02921
\(482\) 4.47040e13i 1.71835i
\(483\) 1.77202e12i 0.0674112i
\(484\) 4.71410e12 0.177489
\(485\) 3.75555e13i 1.39947i
\(486\) 2.51682e12i 0.0928262i
\(487\) 3.51604e13 1.28354 0.641769 0.766898i \(-0.278201\pi\)
0.641769 + 0.766898i \(0.278201\pi\)
\(488\) −2.64716e12 −0.0956493
\(489\) −2.61618e13 −0.935670
\(490\) 3.96542e13i 1.40381i
\(491\) −1.27897e13 −0.448182 −0.224091 0.974568i \(-0.571941\pi\)
−0.224091 + 0.974568i \(0.571941\pi\)
\(492\) −2.38467e13 −0.827185
\(493\) 1.80418e13 0.619504
\(494\) −4.18274e13 −1.42176
\(495\) 1.31860e13i 0.443697i
\(496\) 3.11638e13i 1.03811i
\(497\) 4.93106e13 1.62614
\(498\) −1.32227e13 −0.431692
\(499\) −1.52080e13 −0.491553 −0.245776 0.969327i \(-0.579043\pi\)
−0.245776 + 0.969327i \(0.579043\pi\)
\(500\) 2.00708e13 0.642266
\(501\) −1.87369e13 −0.593621
\(502\) 8.05353e13i 2.52620i
\(503\) 2.33946e13i 0.726568i −0.931678 0.363284i \(-0.881656\pi\)
0.931678 0.363284i \(-0.118344\pi\)
\(504\) 1.96741e12i 0.0604981i
\(505\) 7.78294e13i 2.36966i
\(506\) 4.52128e12i 0.136304i
\(507\) −4.45764e13 −1.33066
\(508\) 1.79979e13 0.531989
\(509\) 5.67471e13i 1.66094i 0.557060 + 0.830472i \(0.311929\pi\)
−0.557060 + 0.830472i \(0.688071\pi\)
\(510\) 6.09639e13i 1.76694i
\(511\) 3.23463e12i 0.0928369i
\(512\) 4.95708e13i 1.40889i
\(513\) 3.69562e12 0.104016
\(514\) 1.06936e13i 0.298063i
\(515\) 3.13019e13i 0.864041i
\(516\) 2.58173e13i 0.705769i
\(517\) −3.94944e13 −1.06926
\(518\) 8.04986e13 2.15844
\(519\) 1.05608e13i 0.280453i
\(520\) 1.15904e13 0.304846
\(521\) −4.25643e13 −1.10881 −0.554405 0.832247i \(-0.687054\pi\)
−0.554405 + 0.832247i \(0.687054\pi\)
\(522\) 6.76079e12i 0.174439i
\(523\) −3.59058e13 −0.917606 −0.458803 0.888538i \(-0.651722\pi\)
−0.458803 + 0.888538i \(0.651722\pi\)
\(524\) 3.98979e13i 1.00993i
\(525\) 1.61380e13 0.404625
\(526\) 4.64312e13i 1.15314i
\(527\) 8.05555e13i 1.98172i
\(528\) 2.29199e13i 0.558526i
\(529\) 4.11103e13 0.992366
\(530\) 1.10217e14i 2.63554i
\(531\) −1.30405e13 + 5.28806e12i −0.308902 + 0.125263i
\(532\) −3.36675e13 −0.790047
\(533\) 1.02425e14i 2.38107i
\(534\) 1.69491e12 0.0390338
\(535\) 3.02306e13 0.689728
\(536\) −5.78334e12 −0.130724
\(537\) 2.78861e13i 0.624476i
\(538\) 6.41659e13 1.42362
\(539\) 3.85366e13i 0.847091i
\(540\) −1.19345e13 −0.259918
\(541\) 6.83733e13i 1.47537i −0.675147 0.737683i \(-0.735920\pi\)
0.675147 0.737683i \(-0.264080\pi\)
\(542\) 1.54849e13i 0.331064i
\(543\) 2.58226e13 0.547016
\(544\) 1.17052e14i 2.45688i
\(545\) 6.10785e13i 1.27030i
\(546\) −9.84817e13 −2.02952
\(547\) −1.27448e13 −0.260253 −0.130127 0.991497i \(-0.541538\pi\)
−0.130127 + 0.991497i \(0.541538\pi\)
\(548\) −5.01011e13 −1.01378
\(549\) 1.17076e13i 0.234750i
\(550\) −4.11759e13 −0.818143
\(551\) 9.92733e12 0.195468
\(552\) 3.51133e11 0.00685136
\(553\) −1.24099e14 −2.39963
\(554\) 2.88630e13i 0.553087i
\(555\) 4.19003e13i 0.795706i
\(556\) 4.18465e13 0.787563
\(557\) −3.48486e13 −0.649993 −0.324997 0.945715i \(-0.605363\pi\)
−0.324997 + 0.945715i \(0.605363\pi\)
\(558\) 3.01865e13 0.558010
\(559\) 1.10890e14 2.03157
\(560\) −8.15376e13 −1.48053
\(561\) 5.92458e13i 1.06621i
\(562\) 4.86140e13i 0.867121i
\(563\) 1.65945e12i 0.0293374i 0.999892 + 0.0146687i \(0.00466935\pi\)
−0.999892 + 0.0146687i \(0.995331\pi\)
\(564\) 3.57461e13i 0.626372i
\(565\) 1.28958e14i 2.23978i
\(566\) −8.43088e13 −1.45141
\(567\) 8.70125e12 0.148480
\(568\) 9.77112e12i 0.165273i
\(569\) 9.52495e13i 1.59699i 0.602003 + 0.798493i \(0.294369\pi\)
−0.602003 + 0.798493i \(0.705631\pi\)
\(570\) 3.35449e13i 0.557509i
\(571\) 3.48630e12i 0.0574360i 0.999588 + 0.0287180i \(0.00914248\pi\)
−0.999588 + 0.0287180i \(0.990858\pi\)
\(572\) 1.31269e14 2.14380
\(573\) 2.14481e13i 0.347229i
\(574\) 1.57813e14i 2.53270i
\(575\) 2.88022e12i 0.0458234i
\(576\) 2.48982e13 0.392694
\(577\) 5.15438e13 0.805930 0.402965 0.915215i \(-0.367980\pi\)
0.402965 + 0.915215i \(0.367980\pi\)
\(578\) 1.80566e14i 2.79897i
\(579\) −2.03784e13 −0.313168
\(580\) −3.20590e13 −0.488439
\(581\) 4.57141e13i 0.690509i
\(582\) −6.32319e13 −0.946938
\(583\) 1.07111e14i 1.59035i
\(584\) −6.40958e11 −0.00943551
\(585\) 5.12607e13i 0.748179i
\(586\) 8.75555e13i 1.26705i
\(587\) 4.23890e13i 0.608223i 0.952636 + 0.304112i \(0.0983596\pi\)
−0.952636 + 0.304112i \(0.901640\pi\)
\(588\) −3.48792e13 −0.496226
\(589\) 4.43250e13i 0.625276i
\(590\) 4.79994e13 + 1.18367e14i 0.671391 + 1.65566i
\(591\) −4.46294e13 −0.618989
\(592\) 7.28312e13i 1.00163i
\(593\) 4.77928e13 0.651762 0.325881 0.945411i \(-0.394339\pi\)
0.325881 + 0.945411i \(0.394339\pi\)
\(594\) −2.22012e13 −0.300223
\(595\) 2.10767e14 2.82630
\(596\) 6.41512e13i 0.853048i
\(597\) 6.13473e13 0.808953
\(598\) 1.75765e13i 0.229841i
\(599\) −4.04491e13 −0.524536 −0.262268 0.964995i \(-0.584470\pi\)
−0.262268 + 0.964995i \(0.584470\pi\)
\(600\) 3.19782e12i 0.0411242i
\(601\) 1.44431e14i 1.84199i 0.389572 + 0.920996i \(0.372623\pi\)
−0.389572 + 0.920996i \(0.627377\pi\)
\(602\) 1.70855e14 2.16095
\(603\) 2.55780e13i 0.320833i
\(604\) 9.22080e13i 1.14705i
\(605\) −1.62384e13 −0.200339
\(606\) 1.31041e14 1.60341
\(607\) −6.25111e13 −0.758601 −0.379301 0.925274i \(-0.623835\pi\)
−0.379301 + 0.925274i \(0.623835\pi\)
\(608\) 6.44067e13i 0.775199i
\(609\) 2.33737e13 0.279023
\(610\) 1.06269e14 1.25822
\(611\) −1.53535e14 −1.80302
\(612\) −5.36228e13 −0.624587
\(613\) 9.96934e13i 1.15177i 0.817532 + 0.575883i \(0.195342\pi\)
−0.817532 + 0.575883i \(0.804658\pi\)
\(614\) 1.44233e14i 1.65281i
\(615\) 8.21434e13 0.933678
\(616\) 1.73547e13 0.195666
\(617\) 1.57532e14 1.76174 0.880870 0.473358i \(-0.156958\pi\)
0.880870 + 0.473358i \(0.156958\pi\)
\(618\) −5.27028e13 −0.584643
\(619\) 9.05151e12 0.0996019 0.0498009 0.998759i \(-0.484141\pi\)
0.0498009 + 0.998759i \(0.484141\pi\)
\(620\) 1.43142e14i 1.56246i
\(621\) 1.55296e12i 0.0168152i
\(622\) 3.22274e13i 0.346157i
\(623\) 5.85973e12i 0.0624363i
\(624\) 8.91015e13i 0.941807i
\(625\) −1.19152e14 −1.24940
\(626\) −9.26653e13 −0.963930
\(627\) 3.25995e13i 0.336413i
\(628\) 6.89772e13i 0.706167i
\(629\) 1.88262e14i 1.91209i
\(630\) 7.89807e13i 0.795826i
\(631\) 1.60900e14 1.60845 0.804227 0.594322i \(-0.202580\pi\)
0.804227 + 0.594322i \(0.202580\pi\)
\(632\) 2.45909e13i 0.243887i
\(633\) 2.26827e13i 0.223190i
\(634\) 1.97090e14i 1.92406i
\(635\) −6.19964e13 −0.600479
\(636\) 9.69453e13 0.931625
\(637\) 1.49812e14i 1.42840i
\(638\) −5.96377e13 −0.564180
\(639\) 4.32147e13 0.405628
\(640\) 3.58528e13i 0.333905i
\(641\) −6.48002e13 −0.598806 −0.299403 0.954127i \(-0.596787\pi\)
−0.299403 + 0.954127i \(0.596787\pi\)
\(642\) 5.08991e13i 0.466697i
\(643\) −7.74552e13 −0.704686 −0.352343 0.935871i \(-0.614615\pi\)
−0.352343 + 0.935871i \(0.614615\pi\)
\(644\) 1.41476e13i 0.127719i
\(645\) 8.89315e13i 0.796631i
\(646\) 1.50720e14i 1.33970i
\(647\) 1.06247e14 0.937119 0.468559 0.883432i \(-0.344773\pi\)
0.468559 + 0.883432i \(0.344773\pi\)
\(648\) 1.72420e12i 0.0150908i
\(649\) 4.66466e13 + 1.15031e14i 0.405132 + 0.999063i
\(650\) −1.60072e14 −1.37958
\(651\) 1.04362e14i 0.892561i
\(652\) 2.08873e14 1.77274
\(653\) 1.19468e14 1.00620 0.503100 0.864228i \(-0.332193\pi\)
0.503100 + 0.864228i \(0.332193\pi\)
\(654\) −1.02837e14 −0.859533
\(655\) 1.37434e14i 1.13996i
\(656\) −1.42782e14 −1.17531
\(657\) 2.83477e12i 0.0231574i
\(658\) −2.36561e14 −1.91785
\(659\) 2.02038e14i 1.62557i 0.582566 + 0.812784i \(0.302049\pi\)
−0.582566 + 0.812784i \(0.697951\pi\)
\(660\) 1.05276e14i 0.840638i
\(661\) −6.65042e13 −0.527038 −0.263519 0.964654i \(-0.584883\pi\)
−0.263519 + 0.964654i \(0.584883\pi\)
\(662\) 6.11868e13i 0.481247i
\(663\) 2.30319e14i 1.79788i
\(664\) 9.05847e12 0.0701802
\(665\) 1.15973e14 0.891760
\(666\) 7.05473e13 0.538405
\(667\) 4.17162e12i 0.0315992i
\(668\) 1.49594e14 1.12469
\(669\) 1.05616e14 0.788131
\(670\) 2.32170e14 1.71962
\(671\) 1.03274e14 0.759240
\(672\) 1.51644e14i 1.10657i
\(673\) 1.75283e14i 1.26959i −0.772679 0.634796i \(-0.781084\pi\)
0.772679 0.634796i \(-0.218916\pi\)
\(674\) −1.03624e14 −0.745009
\(675\) 1.41430e13 0.100930
\(676\) 3.55895e14 2.52109
\(677\) −1.00815e13 −0.0708898 −0.0354449 0.999372i \(-0.511285\pi\)
−0.0354449 + 0.999372i \(0.511285\pi\)
\(678\) 2.17125e14 1.51552
\(679\) 2.18608e14i 1.51467i
\(680\) 4.17645e13i 0.287252i
\(681\) 1.74333e13i 0.119027i
\(682\) 2.66279e14i 1.80474i
\(683\) 1.10610e14i 0.744204i −0.928192 0.372102i \(-0.878637\pi\)
0.928192 0.372102i \(-0.121363\pi\)
\(684\) −2.95055e13 −0.197071
\(685\) 1.72581e14 1.14430
\(686\) 6.29427e13i 0.414310i
\(687\) 1.15242e14i 0.753058i
\(688\) 1.54581e14i 1.00280i
\(689\) 4.16396e14i 2.68170i
\(690\) −1.40961e13 −0.0901266
\(691\) 1.58453e13i 0.100580i 0.998735 + 0.0502898i \(0.0160145\pi\)
−0.998735 + 0.0502898i \(0.983985\pi\)
\(692\) 8.43166e13i 0.531352i
\(693\) 7.67548e13i 0.480219i
\(694\) −1.54241e14 −0.958084
\(695\) −1.44147e14 −0.888956
\(696\) 4.63161e12i 0.0283586i
\(697\) 3.69077e14 2.24364
\(698\) −2.47766e13 −0.149543
\(699\) 5.06704e13i 0.303647i
\(700\) −1.28844e14 −0.766610
\(701\) 4.46930e13i 0.264028i 0.991248 + 0.132014i \(0.0421443\pi\)
−0.991248 + 0.132014i \(0.957856\pi\)
\(702\) −8.63073e13 −0.506247
\(703\) 1.03589e14i 0.603308i
\(704\) 2.19630e14i 1.27007i
\(705\) 1.23133e14i 0.707013i
\(706\) −5.90083e13 −0.336426
\(707\) 4.53040e14i 2.56472i
\(708\) 1.04114e14 4.22194e13i 0.585252 0.237326i
\(709\) −2.60393e14 −1.45344 −0.726720 0.686933i \(-0.758956\pi\)
−0.726720 + 0.686933i \(0.758956\pi\)
\(710\) 3.92257e14i 2.17410i
\(711\) −1.08758e14 −0.598568
\(712\) −1.16113e12 −0.00634574
\(713\) 1.86260e13 0.101082
\(714\) 3.54867e14i 1.91238i
\(715\) −4.52177e14 −2.41979
\(716\) 2.22640e14i 1.18315i
\(717\) 1.84928e14 0.975902
\(718\) 3.47376e14i 1.82045i
\(719\) 2.80920e14i 1.46197i −0.682393 0.730985i \(-0.739061\pi\)
0.682393 0.730985i \(-0.260939\pi\)
\(720\) −7.14579e13 −0.369307
\(721\) 1.82206e14i 0.935162i
\(722\) 2.00964e14i 1.02431i
\(723\) −1.35447e14 −0.685609
\(724\) −2.06165e14 −1.03639
\(725\) 3.79915e13 0.189669
\(726\) 2.73405e13i 0.135557i
\(727\) 2.03091e14 1.00004 0.500022 0.866013i \(-0.333325\pi\)
0.500022 + 0.866013i \(0.333325\pi\)
\(728\) 6.74668e13 0.329939
\(729\) 7.62560e12 0.0370370
\(730\) 2.57310e13 0.124120
\(731\) 3.99577e14i 1.91432i
\(732\) 9.34726e13i 0.444763i
\(733\) −4.22591e13 −0.199710 −0.0998551 0.995002i \(-0.531838\pi\)
−0.0998551 + 0.995002i \(0.531838\pi\)
\(734\) −1.35540e14 −0.636192
\(735\) 1.20147e14 0.560112
\(736\) 2.70647e13 0.125318
\(737\) 2.25626e14 1.03765
\(738\) 1.38304e14i 0.631763i
\(739\) 7.28618e13i 0.330581i 0.986245 + 0.165290i \(0.0528561\pi\)
−0.986245 + 0.165290i \(0.947144\pi\)
\(740\) 3.34529e14i 1.50756i
\(741\) 1.26731e14i 0.567273i
\(742\) 6.41568e14i 2.85248i
\(743\) 1.84631e14 0.815381 0.407690 0.913120i \(-0.366334\pi\)
0.407690 + 0.913120i \(0.366334\pi\)
\(744\) −2.06799e13 −0.0907158
\(745\) 2.20978e14i 0.962872i
\(746\) 3.79696e14i 1.64340i
\(747\) 4.00629e13i 0.172242i
\(748\) 4.73013e14i 2.02007i
\(749\) 1.75970e14 0.746501
\(750\) 1.16405e14i 0.490531i
\(751\) 7.80965e13i 0.326913i 0.986551 + 0.163456i \(0.0522643\pi\)
−0.986551 + 0.163456i \(0.947736\pi\)
\(752\) 2.14029e14i 0.889988i
\(753\) −2.44010e14 −1.00794
\(754\) −2.31842e14 −0.951341
\(755\) 3.17624e14i 1.29473i
\(756\) −6.94701e13 −0.281312
\(757\) 3.97360e14 1.59847 0.799236 0.601017i \(-0.205238\pi\)
0.799236 + 0.601017i \(0.205238\pi\)
\(758\) 3.50607e14i 1.40112i
\(759\) −1.36988e13 −0.0543844
\(760\) 2.29806e13i 0.0906344i
\(761\) −1.06320e14 −0.416575 −0.208287 0.978068i \(-0.566789\pi\)
−0.208287 + 0.978068i \(0.566789\pi\)
\(762\) 1.04383e14i 0.406307i
\(763\) 3.55534e14i 1.37486i
\(764\) 1.71240e14i 0.657867i
\(765\) 1.84712e14 0.704997
\(766\) 2.91148e14i 1.10400i
\(767\) 1.81339e14 + 4.47186e14i 0.683148 + 1.68466i
\(768\) 1.21363e14 0.454234
\(769\) 2.09290e13i 0.0778246i −0.999243 0.0389123i \(-0.987611\pi\)
0.999243 0.0389123i \(-0.0123893\pi\)
\(770\) −6.96698e14 −2.57390
\(771\) 3.24000e13 0.118925
\(772\) 1.62700e14 0.593335
\(773\) 1.46588e14i 0.531132i 0.964093 + 0.265566i \(0.0855588\pi\)
−0.964093 + 0.265566i \(0.914441\pi\)
\(774\) 1.49733e14 0.539031
\(775\) 1.69630e14i 0.606727i
\(776\) 4.33182e13 0.153944
\(777\) 2.43899e14i 0.861202i
\(778\) 4.15598e14i 1.45806i
\(779\) 2.03082e14 0.707919