Properties

Label 177.11.c.a.58.13
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 58.13
Character \(\chi\) \(=\) 177.58
Dual form 177.11.c.a.58.88

$q$-expansion

\(f(q)\) \(=\) \(q-50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} -7140.06i q^{6} -26451.4 q^{7} +27587.7i q^{8} +19683.0 q^{9} +O(q^{10})\) \(q-50.8928i q^{2} +140.296 q^{3} -1566.07 q^{4} +2107.07 q^{5} -7140.06i q^{6} -26451.4 q^{7} +27587.7i q^{8} +19683.0 q^{9} -107235. i q^{10} -141491. i q^{11} -219714. q^{12} -258539. i q^{13} +1.34619e6i q^{14} +295614. q^{15} -199646. q^{16} +600229. q^{17} -1.00172e6i q^{18} -43051.6 q^{19} -3.29983e6 q^{20} -3.71103e6 q^{21} -7.20088e6 q^{22} -1.84919e6i q^{23} +3.87045e6i q^{24} -5.32588e6 q^{25} -1.31578e7 q^{26} +2.76145e6 q^{27} +4.14249e7 q^{28} +3.28651e6 q^{29} -1.50446e7i q^{30} -6.86797e6i q^{31} +3.84104e7i q^{32} -1.98507e7i q^{33} -3.05473e7i q^{34} -5.57350e7 q^{35} -3.08250e7 q^{36} -3.37758e7i q^{37} +2.19102e6i q^{38} -3.62720e7i q^{39} +5.81292e7i q^{40} -1.94974e8 q^{41} +1.88865e8i q^{42} -7.75843e7i q^{43} +2.21586e8i q^{44} +4.14735e7 q^{45} -9.41104e7 q^{46} +1.56607e8i q^{47} -2.80096e7 q^{48} +4.17203e8 q^{49} +2.71049e8i q^{50} +8.42097e7 q^{51} +4.04891e8i q^{52} -1.74257e8 q^{53} -1.40538e8i q^{54} -2.98132e8i q^{55} -7.29734e8i q^{56} -6.03998e6 q^{57} -1.67260e8i q^{58} +(6.14004e8 - 3.66219e8i) q^{59} -4.62953e8 q^{60} -1.60873e8i q^{61} -3.49530e8 q^{62} -5.20644e8 q^{63} +1.75037e9 q^{64} -5.44760e8i q^{65} -1.01026e9 q^{66} +1.29604e9i q^{67} -9.40003e8 q^{68} -2.59434e8i q^{69} +2.83651e9i q^{70} -1.68138e9 q^{71} +5.43009e8i q^{72} +3.06702e9i q^{73} -1.71895e9 q^{74} -7.47200e8 q^{75} +6.74221e7 q^{76} +3.74264e9i q^{77} -1.84598e9 q^{78} +1.15229e9 q^{79} -4.20669e8 q^{80} +3.87420e8 q^{81} +9.92277e9i q^{82} +7.52537e9i q^{83} +5.81176e9 q^{84} +1.26472e9 q^{85} -3.94848e9 q^{86} +4.61085e8 q^{87} +3.90341e9 q^{88} +5.42130e9i q^{89} -2.11070e9i q^{90} +6.83873e9i q^{91} +2.89597e9i q^{92} -9.63549e8i q^{93} +7.97019e9 q^{94} -9.07128e7 q^{95} +5.38882e9i q^{96} -3.52047e9i q^{97} -2.12326e10i q^{98} -2.78497e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + O(q^{10}) \) \( 100q - 51200q^{4} + 18392q^{7} + 1968300q^{9} + 620136q^{12} + 662904q^{15} + 27925160q^{16} - 2053136q^{17} - 5169828q^{19} - 1076324q^{20} - 1829224q^{22} + 215378180q^{25} - 22082700q^{26} - 102921320q^{28} - 112503588q^{29} - 76491392q^{35} - 1007769600q^{36} + 473464516q^{41} + 1215405588q^{46} - 1676272320q^{48} + 1975297276q^{49} + 733970808q^{51} + 3267506728q^{53} + 591502824q^{57} + 508142200q^{59} + 1264196808q^{60} - 6538206968q^{62} + 362009736q^{63} - 10324137972q^{64} - 2764346616q^{66} + 9997685952q^{68} + 14908523204q^{71} + 4863508712q^{74} + 1890481680q^{75} + 2044437240q^{76} - 758396196q^{78} - 3599839500q^{79} - 23217941144q^{80} + 38742048900q^{81} - 13094894808q^{84} + 23360564412q^{85} + 12186923752q^{86} + 7965322272q^{87} + 32415437996q^{88} - 22098322280q^{94} + 7834510028q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 50.8928i 1.59040i −0.606348 0.795200i \(-0.707366\pi\)
0.606348 0.795200i \(-0.292634\pi\)
\(3\) 140.296 0.577350
\(4\) −1566.07 −1.52937
\(5\) 2107.07 0.674262 0.337131 0.941458i \(-0.390543\pi\)
0.337131 + 0.941458i \(0.390543\pi\)
\(6\) 7140.06i 0.918217i
\(7\) −26451.4 −1.57383 −0.786917 0.617059i \(-0.788324\pi\)
−0.786917 + 0.617059i \(0.788324\pi\)
\(8\) 27587.7i 0.841910i
\(9\) 19683.0 0.333333
\(10\) 107235.i 1.07235i
\(11\) 141491.i 0.878549i −0.898353 0.439274i \(-0.855236\pi\)
0.898353 0.439274i \(-0.144764\pi\)
\(12\) −219714. −0.882982
\(13\) 258539.i 0.696320i −0.937435 0.348160i \(-0.886807\pi\)
0.937435 0.348160i \(-0.113193\pi\)
\(14\) 1.34619e6i 2.50303i
\(15\) 295614. 0.389286
\(16\) −199646. −0.190398
\(17\) 600229. 0.422739 0.211369 0.977406i \(-0.432208\pi\)
0.211369 + 0.977406i \(0.432208\pi\)
\(18\) 1.00172e6i 0.530133i
\(19\) −43051.6 −0.0173869 −0.00869344 0.999962i \(-0.502767\pi\)
−0.00869344 + 0.999962i \(0.502767\pi\)
\(20\) −3.29983e6 −1.03120
\(21\) −3.71103e6 −0.908654
\(22\) −7.20088e6 −1.39724
\(23\) 1.84919e6i 0.287304i −0.989628 0.143652i \(-0.954115\pi\)
0.989628 0.143652i \(-0.0458846\pi\)
\(24\) 3.87045e6i 0.486077i
\(25\) −5.32588e6 −0.545370
\(26\) −1.31578e7 −1.10743
\(27\) 2.76145e6 0.192450
\(28\) 4.14249e7 2.40698
\(29\) 3.28651e6 0.160231 0.0801153 0.996786i \(-0.474471\pi\)
0.0801153 + 0.996786i \(0.474471\pi\)
\(30\) 1.50446e7i 0.619120i
\(31\) 6.86797e6i 0.239894i −0.992780 0.119947i \(-0.961728\pi\)
0.992780 0.119947i \(-0.0382725\pi\)
\(32\) 3.84104e7i 1.14472i
\(33\) 1.98507e7i 0.507230i
\(34\) 3.05473e7i 0.672323i
\(35\) −5.57350e7 −1.06118
\(36\) −3.08250e7 −0.509790
\(37\) 3.37758e7i 0.487077i −0.969891 0.243538i \(-0.921692\pi\)
0.969891 0.243538i \(-0.0783082\pi\)
\(38\) 2.19102e6i 0.0276521i
\(39\) 3.62720e7i 0.402021i
\(40\) 5.81292e7i 0.567668i
\(41\) −1.94974e8 −1.68290 −0.841448 0.540338i \(-0.818297\pi\)
−0.841448 + 0.540338i \(0.818297\pi\)
\(42\) 1.88865e8i 1.44512i
\(43\) 7.75843e7i 0.527754i −0.964556 0.263877i \(-0.914999\pi\)
0.964556 0.263877i \(-0.0850014\pi\)
\(44\) 2.21586e8i 1.34363i
\(45\) 4.14735e7 0.224754
\(46\) −9.41104e7 −0.456929
\(47\) 1.56607e8i 0.682846i 0.939910 + 0.341423i \(0.110909\pi\)
−0.939910 + 0.341423i \(0.889091\pi\)
\(48\) −2.80096e7 −0.109926
\(49\) 4.17203e8 1.47696
\(50\) 2.71049e8i 0.867356i
\(51\) 8.42097e7 0.244068
\(52\) 4.04891e8i 1.06493i
\(53\) −1.74257e8 −0.416688 −0.208344 0.978056i \(-0.566807\pi\)
−0.208344 + 0.978056i \(0.566807\pi\)
\(54\) 1.40538e8i 0.306072i
\(55\) 2.98132e8i 0.592372i
\(56\) 7.29734e8i 1.32503i
\(57\) −6.03998e6 −0.0100383
\(58\) 1.67260e8i 0.254831i
\(59\) 6.14004e8 3.66219e8i 0.858837 0.512249i
\(60\) −4.62953e8 −0.595362
\(61\) 1.60873e8i 0.190473i −0.995455 0.0952365i \(-0.969639\pi\)
0.995455 0.0952365i \(-0.0303607\pi\)
\(62\) −3.49530e8 −0.381528
\(63\) −5.20644e8 −0.524611
\(64\) 1.75037e9 1.63016
\(65\) 5.44760e8i 0.469503i
\(66\) −1.01026e9 −0.806699
\(67\) 1.29604e9i 0.959938i 0.877285 + 0.479969i \(0.159352\pi\)
−0.877285 + 0.479969i \(0.840648\pi\)
\(68\) −9.40003e8 −0.646524
\(69\) 2.59434e8i 0.165875i
\(70\) 2.83651e9i 1.68770i
\(71\) −1.68138e9 −0.931910 −0.465955 0.884808i \(-0.654289\pi\)
−0.465955 + 0.884808i \(0.654289\pi\)
\(72\) 5.43009e8i 0.280637i
\(73\) 3.06702e9i 1.47946i 0.672905 + 0.739729i \(0.265046\pi\)
−0.672905 + 0.739729i \(0.734954\pi\)
\(74\) −1.71895e9 −0.774647
\(75\) −7.47200e8 −0.314870
\(76\) 6.74221e7 0.0265910
\(77\) 3.74264e9i 1.38269i
\(78\) −1.84598e9 −0.639374
\(79\) 1.15229e9 0.374476 0.187238 0.982315i \(-0.440046\pi\)
0.187238 + 0.982315i \(0.440046\pi\)
\(80\) −4.20669e8 −0.128378
\(81\) 3.87420e8 0.111111
\(82\) 9.92277e9i 2.67648i
\(83\) 7.52537e9i 1.91046i 0.295867 + 0.955229i \(0.404392\pi\)
−0.295867 + 0.955229i \(0.595608\pi\)
\(84\) 5.81176e9 1.38967
\(85\) 1.26472e9 0.285037
\(86\) −3.94848e9 −0.839340
\(87\) 4.61085e8 0.0925092
\(88\) 3.90341e9 0.739658
\(89\) 5.42130e9i 0.970854i 0.874277 + 0.485427i \(0.161336\pi\)
−0.874277 + 0.485427i \(0.838664\pi\)
\(90\) 2.11070e9i 0.357449i
\(91\) 6.83873e9i 1.09589i
\(92\) 2.89597e9i 0.439395i
\(93\) 9.63549e8i 0.138503i
\(94\) 7.97019e9 1.08600
\(95\) −9.07128e7 −0.0117233
\(96\) 5.38882e9i 0.660903i
\(97\) 3.52047e9i 0.409961i −0.978766 0.204980i \(-0.934287\pi\)
0.978766 0.204980i \(-0.0657131\pi\)
\(98\) 2.12326e10i 2.34895i
\(99\) 2.78497e9i 0.292850i
\(100\) 8.34073e9 0.834073
\(101\) 1.23159e10i 1.17182i 0.810377 + 0.585909i \(0.199262\pi\)
−0.810377 + 0.585909i \(0.800738\pi\)
\(102\) 4.28567e9i 0.388166i
\(103\) 4.05209e9i 0.349537i 0.984610 + 0.174769i \(0.0559177\pi\)
−0.984610 + 0.174769i \(0.944082\pi\)
\(104\) 7.13249e9 0.586239
\(105\) −7.81941e9 −0.612671
\(106\) 8.86843e9i 0.662701i
\(107\) −1.04529e10 −0.745277 −0.372638 0.927977i \(-0.621547\pi\)
−0.372638 + 0.927977i \(0.621547\pi\)
\(108\) −4.32463e9 −0.294327
\(109\) 1.90603e10i 1.23879i 0.785080 + 0.619395i \(0.212622\pi\)
−0.785080 + 0.619395i \(0.787378\pi\)
\(110\) −1.51728e10 −0.942109
\(111\) 4.73862e9i 0.281214i
\(112\) 5.28093e9 0.299654
\(113\) 2.03020e10i 1.10191i −0.834534 0.550956i \(-0.814263\pi\)
0.834534 0.550956i \(-0.185737\pi\)
\(114\) 3.07391e8i 0.0159649i
\(115\) 3.89637e9i 0.193718i
\(116\) −5.14693e9 −0.245052
\(117\) 5.08882e9i 0.232107i
\(118\) −1.86379e10 3.12483e10i −0.814680 1.36589i
\(119\) −1.58769e10 −0.665321
\(120\) 8.15530e9i 0.327743i
\(121\) 5.91768e9 0.228152
\(122\) −8.18726e9 −0.302928
\(123\) −2.73541e10 −0.971621
\(124\) 1.07558e10i 0.366887i
\(125\) −3.17989e10 −1.04199
\(126\) 2.64970e10i 0.834342i
\(127\) 4.04217e10 1.22348 0.611738 0.791060i \(-0.290470\pi\)
0.611738 + 0.791060i \(0.290470\pi\)
\(128\) 4.97491e10i 1.44789i
\(129\) 1.08848e10i 0.304699i
\(130\) −2.77243e10 −0.746697
\(131\) 3.47554e10i 0.900877i −0.892807 0.450439i \(-0.851268\pi\)
0.892807 0.450439i \(-0.148732\pi\)
\(132\) 3.10876e10i 0.775743i
\(133\) 1.13878e9 0.0273641
\(134\) 6.59589e10 1.52669
\(135\) 5.81857e9 0.129762
\(136\) 1.65589e10i 0.355908i
\(137\) 6.12256e10 1.26862 0.634308 0.773080i \(-0.281285\pi\)
0.634308 + 0.773080i \(0.281285\pi\)
\(138\) −1.32033e10 −0.263808
\(139\) −1.49800e10 −0.288694 −0.144347 0.989527i \(-0.546108\pi\)
−0.144347 + 0.989527i \(0.546108\pi\)
\(140\) 8.72852e10 1.62293
\(141\) 2.19714e10i 0.394242i
\(142\) 8.55701e10i 1.48211i
\(143\) −3.65810e10 −0.611751
\(144\) −3.92964e9 −0.0634659
\(145\) 6.92491e9 0.108037
\(146\) 1.56089e11 2.35293
\(147\) 5.85320e10 0.852720
\(148\) 5.28955e10i 0.744921i
\(149\) 1.48074e10i 0.201626i −0.994905 0.100813i \(-0.967856\pi\)
0.994905 0.100813i \(-0.0321444\pi\)
\(150\) 3.80271e10i 0.500768i
\(151\) 5.55513e10i 0.707635i −0.935314 0.353818i \(-0.884883\pi\)
0.935314 0.353818i \(-0.115117\pi\)
\(152\) 1.18770e9i 0.0146382i
\(153\) 1.18143e10 0.140913
\(154\) 1.90474e11 2.19903
\(155\) 1.44713e10i 0.161752i
\(156\) 5.68047e10i 0.614838i
\(157\) 1.11194e11i 1.16570i −0.812582 0.582848i \(-0.801938\pi\)
0.812582 0.582848i \(-0.198062\pi\)
\(158\) 5.86430e10i 0.595567i
\(159\) −2.44476e10 −0.240575
\(160\) 8.09333e10i 0.771840i
\(161\) 4.89137e10i 0.452169i
\(162\) 1.97169e10i 0.176711i
\(163\) 6.14155e10 0.533753 0.266876 0.963731i \(-0.414008\pi\)
0.266876 + 0.963731i \(0.414008\pi\)
\(164\) 3.05344e11 2.57377
\(165\) 4.18267e10i 0.342006i
\(166\) 3.82987e11 3.03839
\(167\) −6.25161e10 −0.481293 −0.240646 0.970613i \(-0.577359\pi\)
−0.240646 + 0.970613i \(0.577359\pi\)
\(168\) 1.02379e11i 0.765004i
\(169\) 7.10161e10 0.515138
\(170\) 6.43653e10i 0.453322i
\(171\) −8.47385e8 −0.00579563
\(172\) 1.21503e11i 0.807132i
\(173\) 1.32957e11i 0.857987i 0.903307 + 0.428994i \(0.141132\pi\)
−0.903307 + 0.428994i \(0.858868\pi\)
\(174\) 2.34659e10i 0.147127i
\(175\) 1.40877e11 0.858322
\(176\) 2.82482e10i 0.167274i
\(177\) 8.61423e10 5.13791e10i 0.495850 0.295747i
\(178\) 2.75905e11 1.54405
\(179\) 9.63839e9i 0.0524493i −0.999656 0.0262246i \(-0.991651\pi\)
0.999656 0.0262246i \(-0.00834852\pi\)
\(180\) −6.49505e10 −0.343732
\(181\) −1.12840e11 −0.580857 −0.290429 0.956897i \(-0.593798\pi\)
−0.290429 + 0.956897i \(0.593798\pi\)
\(182\) 3.48042e11 1.74291
\(183\) 2.25698e10i 0.109970i
\(184\) 5.10149e10 0.241884
\(185\) 7.11681e10i 0.328418i
\(186\) −4.90377e10 −0.220275
\(187\) 8.49270e10i 0.371397i
\(188\) 2.45259e11i 1.04432i
\(189\) −7.30443e10 −0.302885
\(190\) 4.61663e9i 0.0186448i
\(191\) 4.37205e11i 1.71996i 0.510329 + 0.859979i \(0.329524\pi\)
−0.510329 + 0.859979i \(0.670476\pi\)
\(192\) 2.45570e11 0.941174
\(193\) −4.25062e11 −1.58732 −0.793662 0.608359i \(-0.791828\pi\)
−0.793662 + 0.608359i \(0.791828\pi\)
\(194\) −1.79167e11 −0.652001
\(195\) 7.64277e10i 0.271068i
\(196\) −6.53371e11 −2.25881
\(197\) −8.09420e10 −0.272799 −0.136400 0.990654i \(-0.543553\pi\)
−0.136400 + 0.990654i \(0.543553\pi\)
\(198\) −1.41735e11 −0.465748
\(199\) −4.10305e11 −1.31475 −0.657373 0.753566i \(-0.728332\pi\)
−0.657373 + 0.753566i \(0.728332\pi\)
\(200\) 1.46929e11i 0.459152i
\(201\) 1.81829e11i 0.554221i
\(202\) 6.26791e11 1.86366
\(203\) −8.69330e10 −0.252176
\(204\) −1.31879e11 −0.373271
\(205\) −4.10824e11 −1.13471
\(206\) 2.06222e11 0.555904
\(207\) 3.63976e10i 0.0957681i
\(208\) 5.16164e10i 0.132578i
\(209\) 6.09143e9i 0.0152752i
\(210\) 3.97951e11i 0.974392i
\(211\) 4.72052e10i 0.112870i 0.998406 + 0.0564348i \(0.0179733\pi\)
−0.998406 + 0.0564348i \(0.982027\pi\)
\(212\) 2.72900e11 0.637271
\(213\) −2.35891e11 −0.538039
\(214\) 5.31977e11i 1.18529i
\(215\) 1.63476e11i 0.355845i
\(216\) 7.61820e10i 0.162026i
\(217\) 1.81668e11i 0.377554i
\(218\) 9.70032e11 1.97017
\(219\) 4.30291e11i 0.854165i
\(220\) 4.66897e11i 0.905957i
\(221\) 1.55182e11i 0.294362i
\(222\) −2.41161e11 −0.447242
\(223\) −3.57720e11 −0.648663 −0.324331 0.945943i \(-0.605139\pi\)
−0.324331 + 0.945943i \(0.605139\pi\)
\(224\) 1.01601e12i 1.80160i
\(225\) −1.04829e11 −0.181790
\(226\) −1.03323e12 −1.75248
\(227\) 2.97110e11i 0.492933i −0.969151 0.246466i \(-0.920731\pi\)
0.969151 0.246466i \(-0.0792695\pi\)
\(228\) 9.45906e9 0.0153523
\(229\) 6.05682e11i 0.961761i −0.876786 0.480880i \(-0.840317\pi\)
0.876786 0.480880i \(-0.159683\pi\)
\(230\) −1.98297e11 −0.308090
\(231\) 5.25078e11i 0.798297i
\(232\) 9.06673e10i 0.134900i
\(233\) 5.51638e11i 0.803294i −0.915795 0.401647i \(-0.868438\pi\)
0.915795 0.401647i \(-0.131562\pi\)
\(234\) −2.58984e11 −0.369143
\(235\) 3.29983e11i 0.460418i
\(236\) −9.61576e11 + 5.73526e11i −1.31348 + 0.783418i
\(237\) 1.61661e11 0.216204
\(238\) 8.08020e11i 1.05813i
\(239\) 9.48583e11 1.21643 0.608213 0.793774i \(-0.291887\pi\)
0.608213 + 0.793774i \(0.291887\pi\)
\(240\) −5.90182e10 −0.0741190
\(241\) −4.19889e11 −0.516475 −0.258238 0.966081i \(-0.583142\pi\)
−0.258238 + 0.966081i \(0.583142\pi\)
\(242\) 3.01167e11i 0.362853i
\(243\) 5.43536e10 0.0641500
\(244\) 2.51939e11i 0.291304i
\(245\) 8.79077e11 0.995855
\(246\) 1.39213e12i 1.54526i
\(247\) 1.11305e10i 0.0121068i
\(248\) 1.89471e11 0.201969
\(249\) 1.05578e12i 1.10300i
\(250\) 1.61833e12i 1.65717i
\(251\) 1.00757e12 1.01136 0.505680 0.862721i \(-0.331242\pi\)
0.505680 + 0.862721i \(0.331242\pi\)
\(252\) 8.15367e11 0.802325
\(253\) −2.61644e11 −0.252411
\(254\) 2.05717e12i 1.94582i
\(255\) 1.77436e11 0.164566
\(256\) −7.39488e11 −0.672560
\(257\) −9.37522e11 −0.836211 −0.418105 0.908399i \(-0.637306\pi\)
−0.418105 + 0.908399i \(0.637306\pi\)
\(258\) −5.53957e11 −0.484593
\(259\) 8.93419e11i 0.766578i
\(260\) 8.53134e11i 0.718043i
\(261\) 6.46884e10 0.0534102
\(262\) −1.76880e12 −1.43275
\(263\) 5.91121e11 0.469784 0.234892 0.972022i \(-0.424526\pi\)
0.234892 + 0.972022i \(0.424526\pi\)
\(264\) 5.47634e11 0.427042
\(265\) −3.67172e11 −0.280957
\(266\) 5.79556e10i 0.0435198i
\(267\) 7.60588e11i 0.560523i
\(268\) 2.02969e12i 1.46810i
\(269\) 6.67313e11i 0.473771i 0.971538 + 0.236885i \(0.0761266\pi\)
−0.971538 + 0.236885i \(0.923873\pi\)
\(270\) 2.96123e11i 0.206373i
\(271\) −1.30064e12 −0.889837 −0.444918 0.895571i \(-0.646767\pi\)
−0.444918 + 0.895571i \(0.646767\pi\)
\(272\) −1.19833e11 −0.0804884
\(273\) 9.59447e11i 0.632714i
\(274\) 3.11594e12i 2.01761i
\(275\) 7.53565e11i 0.479134i
\(276\) 4.06293e11i 0.253685i
\(277\) 1.95780e11 0.120052 0.0600261 0.998197i \(-0.480882\pi\)
0.0600261 + 0.998197i \(0.480882\pi\)
\(278\) 7.62375e11i 0.459140i
\(279\) 1.35182e11i 0.0799647i
\(280\) 1.53760e12i 0.893415i
\(281\) −2.19824e12 −1.25471 −0.627354 0.778734i \(-0.715862\pi\)
−0.627354 + 0.778734i \(0.715862\pi\)
\(282\) 1.11819e12 0.627001
\(283\) 6.67958e11i 0.367974i 0.982929 + 0.183987i \(0.0589004\pi\)
−0.982929 + 0.183987i \(0.941100\pi\)
\(284\) 2.63317e12 1.42524
\(285\) −1.27267e10 −0.00676846
\(286\) 1.86171e12i 0.972929i
\(287\) 5.15734e12 2.64860
\(288\) 7.56031e11i 0.381573i
\(289\) −1.65572e12 −0.821292
\(290\) 3.52428e11i 0.171823i
\(291\) 4.93909e11i 0.236691i
\(292\) 4.80318e12i 2.26264i
\(293\) 1.38989e12 0.643639 0.321820 0.946801i \(-0.395706\pi\)
0.321820 + 0.946801i \(0.395706\pi\)
\(294\) 2.97886e12i 1.35617i
\(295\) 1.29375e12 7.71649e11i 0.579082 0.345390i
\(296\) 9.31797e11 0.410075
\(297\) 3.90720e11i 0.169077i
\(298\) −7.53588e11 −0.320666
\(299\) −4.78087e11 −0.200056
\(300\) 1.17017e12 0.481552
\(301\) 2.05222e12i 0.830598i
\(302\) −2.82716e12 −1.12542
\(303\) 1.72788e12i 0.676549i
\(304\) 8.59510e9 0.00331042
\(305\) 3.38970e11i 0.128429i
\(306\) 6.01262e11i 0.224108i
\(307\) −9.19052e11 −0.337014 −0.168507 0.985700i \(-0.553895\pi\)
−0.168507 + 0.985700i \(0.553895\pi\)
\(308\) 5.86126e12i 2.11464i
\(309\) 5.68493e11i 0.201805i
\(310\) −7.36484e11 −0.257250
\(311\) −2.50050e12 −0.859458 −0.429729 0.902958i \(-0.641391\pi\)
−0.429729 + 0.902958i \(0.641391\pi\)
\(312\) 1.00066e12 0.338465
\(313\) 2.73877e12i 0.911664i 0.890066 + 0.455832i \(0.150658\pi\)
−0.890066 + 0.455832i \(0.849342\pi\)
\(314\) −5.65900e12 −1.85392
\(315\) −1.09703e12 −0.353726
\(316\) −1.80456e12 −0.572713
\(317\) −5.65807e12 −1.76755 −0.883776 0.467911i \(-0.845007\pi\)
−0.883776 + 0.467911i \(0.845007\pi\)
\(318\) 1.24421e12i 0.382611i
\(319\) 4.65012e11i 0.140770i
\(320\) 3.68816e12 1.09916
\(321\) −1.46650e12 −0.430286
\(322\) 2.48935e12 0.719130
\(323\) −2.58408e10 −0.00735011
\(324\) −6.06729e11 −0.169930
\(325\) 1.37695e12i 0.379752i
\(326\) 3.12561e12i 0.848880i
\(327\) 2.67409e12i 0.715215i
\(328\) 5.37888e12i 1.41685i
\(329\) 4.14249e12i 1.07469i
\(330\) −2.12868e12 −0.543927
\(331\) −5.78557e12 −1.45615 −0.728075 0.685498i \(-0.759585\pi\)
−0.728075 + 0.685498i \(0.759585\pi\)
\(332\) 1.17853e13i 2.92180i
\(333\) 6.64810e11i 0.162359i
\(334\) 3.18162e12i 0.765448i
\(335\) 2.73084e12i 0.647250i
\(336\) 7.40894e11 0.173006
\(337\) 3.77177e12i 0.867752i −0.900973 0.433876i \(-0.857146\pi\)
0.900973 0.433876i \(-0.142854\pi\)
\(338\) 3.61421e12i 0.819275i
\(339\) 2.84830e12i 0.636190i
\(340\) −1.98065e12 −0.435927
\(341\) −9.71757e11 −0.210759
\(342\) 4.31258e10i 0.00921736i
\(343\) −3.56375e12 −0.750648
\(344\) 2.14037e12 0.444321
\(345\) 5.46646e11i 0.111843i
\(346\) 6.76655e12 1.36454
\(347\) 1.54001e12i 0.306109i −0.988218 0.153054i \(-0.951089\pi\)
0.988218 0.153054i \(-0.0489109\pi\)
\(348\) −7.22094e11 −0.141481
\(349\) 4.66261e10i 0.00900538i −0.999990 0.00450269i \(-0.998567\pi\)
0.999990 0.00450269i \(-0.00143326\pi\)
\(350\) 7.16963e12i 1.36508i
\(351\) 7.13942e11i 0.134007i
\(352\) 5.43472e12 1.00569
\(353\) 1.25736e12i 0.229396i −0.993400 0.114698i \(-0.963410\pi\)
0.993400 0.114698i \(-0.0365900\pi\)
\(354\) −2.61483e12 4.38402e12i −0.470356 0.788599i
\(355\) −3.54278e12 −0.628352
\(356\) 8.49017e12i 1.48479i
\(357\) −2.22747e12 −0.384123
\(358\) −4.90525e11 −0.0834153
\(359\) 2.11731e12 0.355068 0.177534 0.984115i \(-0.443188\pi\)
0.177534 + 0.984115i \(0.443188\pi\)
\(360\) 1.14416e12i 0.189223i
\(361\) −6.12921e12 −0.999698
\(362\) 5.74273e12i 0.923795i
\(363\) 8.30228e11 0.131724
\(364\) 1.07100e13i 1.67603i
\(365\) 6.46243e12i 0.997542i
\(366\) −1.14864e12 −0.174896
\(367\) 3.76611e12i 0.565669i 0.959169 + 0.282834i \(0.0912747\pi\)
−0.959169 + 0.282834i \(0.908725\pi\)
\(368\) 3.69184e11i 0.0547020i
\(369\) −3.83767e12 −0.560966
\(370\) −3.62194e12 −0.522315
\(371\) 4.60935e12 0.655799
\(372\) 1.50899e12i 0.211822i
\(373\) −7.08756e12 −0.981641 −0.490821 0.871261i \(-0.663303\pi\)
−0.490821 + 0.871261i \(0.663303\pi\)
\(374\) −4.32217e12 −0.590669
\(375\) −4.46126e12 −0.601590
\(376\) −4.32044e12 −0.574895
\(377\) 8.49691e11i 0.111572i
\(378\) 3.71743e12i 0.481707i
\(379\) 1.17226e13 1.49910 0.749548 0.661950i \(-0.230271\pi\)
0.749548 + 0.661950i \(0.230271\pi\)
\(380\) 1.42063e11 0.0179293
\(381\) 5.67100e12 0.706375
\(382\) 2.22506e13 2.73542
\(383\) 9.52031e12 1.15520 0.577600 0.816320i \(-0.303989\pi\)
0.577600 + 0.816320i \(0.303989\pi\)
\(384\) 6.97960e12i 0.835939i
\(385\) 7.88601e12i 0.932296i
\(386\) 2.16326e13i 2.52448i
\(387\) 1.52709e12i 0.175918i
\(388\) 5.51332e12i 0.626982i
\(389\) −7.50109e12 −0.842125 −0.421063 0.907032i \(-0.638343\pi\)
−0.421063 + 0.907032i \(0.638343\pi\)
\(390\) −3.88962e12 −0.431106
\(391\) 1.10994e12i 0.121455i
\(392\) 1.15097e13i 1.24346i
\(393\) 4.87605e12i 0.520122i
\(394\) 4.11936e12i 0.433859i
\(395\) 2.42795e12 0.252495
\(396\) 4.36147e12i 0.447875i
\(397\) 6.39193e12i 0.648156i 0.946030 + 0.324078i \(0.105054\pi\)
−0.946030 + 0.324078i \(0.894946\pi\)
\(398\) 2.08816e13i 2.09097i
\(399\) 1.59766e11 0.0157987
\(400\) 1.06329e12 0.103837
\(401\) 3.14324e12i 0.303148i 0.988446 + 0.151574i \(0.0484342\pi\)
−0.988446 + 0.151574i \(0.951566\pi\)
\(402\) 9.25378e12 0.881432
\(403\) −1.77564e12 −0.167043
\(404\) 1.92876e13i 1.79214i
\(405\) 8.16322e11 0.0749181
\(406\) 4.42426e12i 0.401061i
\(407\) −4.77898e12 −0.427921
\(408\) 2.32315e12i 0.205483i
\(409\) 2.02712e13i 1.77118i −0.464471 0.885588i \(-0.653756\pi\)
0.464471 0.885588i \(-0.346244\pi\)
\(410\) 2.09080e13i 1.80465i
\(411\) 8.58972e12 0.732436
\(412\) 6.34588e12i 0.534572i
\(413\) −1.62413e13 + 9.68702e12i −1.35167 + 0.806195i
\(414\) −1.85237e12 −0.152310
\(415\) 1.58565e13i 1.28815i
\(416\) 9.93057e12 0.797090
\(417\) −2.10164e12 −0.166678
\(418\) 3.10010e11 0.0242937
\(419\) 1.62123e13i 1.25538i 0.778465 + 0.627688i \(0.215999\pi\)
−0.778465 + 0.627688i \(0.784001\pi\)
\(420\) 1.22458e13 0.937001
\(421\) 2.28667e13i 1.72899i −0.502642 0.864495i \(-0.667639\pi\)
0.502642 0.864495i \(-0.332361\pi\)
\(422\) 2.40240e12 0.179508
\(423\) 3.08250e12i 0.227615i
\(424\) 4.80735e12i 0.350814i
\(425\) −3.19675e12 −0.230549
\(426\) 1.20051e13i 0.855696i
\(427\) 4.25532e12i 0.299773i
\(428\) 1.63700e13 1.13980
\(429\) −5.13217e12 −0.353195
\(430\) −8.31973e12 −0.565936
\(431\) 3.91398e12i 0.263167i 0.991305 + 0.131584i \(0.0420062\pi\)
−0.991305 + 0.131584i \(0.957994\pi\)
\(432\) −5.51313e11 −0.0366420
\(433\) −2.66348e13 −1.74988 −0.874942 0.484227i \(-0.839101\pi\)
−0.874942 + 0.484227i \(0.839101\pi\)
\(434\) 9.24557e12 0.600461
\(435\) 9.71538e11 0.0623755
\(436\) 2.98499e13i 1.89457i
\(437\) 7.96106e10i 0.00499533i
\(438\) 2.18987e13 1.35846
\(439\) 1.22436e13 0.750910 0.375455 0.926841i \(-0.377486\pi\)
0.375455 + 0.926841i \(0.377486\pi\)
\(440\) 8.22477e12 0.498724
\(441\) 8.21181e12 0.492318
\(442\) −7.89766e12 −0.468152
\(443\) 8.44368e12i 0.494895i 0.968901 + 0.247447i \(0.0795918\pi\)
−0.968901 + 0.247447i \(0.920408\pi\)
\(444\) 7.42103e12i 0.430080i
\(445\) 1.14231e13i 0.654610i
\(446\) 1.82054e13i 1.03163i
\(447\) 2.07742e12i 0.116409i
\(448\) −4.62998e13 −2.56560
\(449\) −2.90029e12 −0.158931 −0.0794657 0.996838i \(-0.525321\pi\)
−0.0794657 + 0.996838i \(0.525321\pi\)
\(450\) 5.33505e12i 0.289119i
\(451\) 2.75871e13i 1.47851i
\(452\) 3.17945e13i 1.68523i
\(453\) 7.79363e12i 0.408553i
\(454\) −1.51207e13 −0.783960
\(455\) 1.44097e13i 0.738920i
\(456\) 1.66629e11i 0.00845136i
\(457\) 4.37141e12i 0.219301i −0.993970 0.109650i \(-0.965027\pi\)
0.993970 0.109650i \(-0.0349731\pi\)
\(458\) −3.08248e13 −1.52958
\(459\) 1.65750e12 0.0813561
\(460\) 6.10201e12i 0.296267i
\(461\) 2.45776e12 0.118042 0.0590208 0.998257i \(-0.481202\pi\)
0.0590208 + 0.998257i \(0.481202\pi\)
\(462\) 2.67227e13 1.26961
\(463\) 6.09401e12i 0.286417i 0.989693 + 0.143208i \(0.0457419\pi\)
−0.989693 + 0.143208i \(0.954258\pi\)
\(464\) −6.56140e11 −0.0305075
\(465\) 2.03027e12i 0.0933874i
\(466\) −2.80744e13 −1.27756
\(467\) 6.90328e12i 0.310793i −0.987852 0.155396i \(-0.950335\pi\)
0.987852 0.155396i \(-0.0496655\pi\)
\(468\) 7.96947e12i 0.354977i
\(469\) 3.42820e13i 1.51078i
\(470\) 1.67937e13 0.732248
\(471\) 1.56002e13i 0.673014i
\(472\) 1.01031e13 + 1.69389e13i 0.431267 + 0.723063i
\(473\) −1.09775e13 −0.463658
\(474\) 8.22738e12i 0.343851i
\(475\) 2.29288e11 0.00948229
\(476\) 2.48644e13 1.01752
\(477\) −3.42991e12 −0.138896
\(478\) 4.82760e13i 1.93460i
\(479\) −1.35835e13 −0.538686 −0.269343 0.963044i \(-0.586806\pi\)
−0.269343 + 0.963044i \(0.586806\pi\)
\(480\) 1.13546e13i 0.445622i
\(481\) −8.73237e12 −0.339162
\(482\) 2.13693e13i 0.821402i
\(483\) 6.86240e12i 0.261060i
\(484\) −9.26753e12 −0.348929
\(485\) 7.41789e12i 0.276421i
\(486\) 2.76621e12i 0.102024i
\(487\) 4.23136e12 0.154467 0.0772334 0.997013i \(-0.475391\pi\)
0.0772334 + 0.997013i \(0.475391\pi\)
\(488\) 4.43811e12 0.160361
\(489\) 8.61636e12 0.308162
\(490\) 4.47386e13i 1.58381i
\(491\) 6.30143e12 0.220816 0.110408 0.993886i \(-0.464784\pi\)
0.110408 + 0.993886i \(0.464784\pi\)
\(492\) 4.28386e13 1.48597
\(493\) 1.97266e12 0.0677357
\(494\) 5.66463e11 0.0192547
\(495\) 5.86813e12i 0.197457i
\(496\) 1.37116e12i 0.0456753i
\(497\) 4.44749e13 1.46667
\(498\) 5.37316e13 1.75422
\(499\) 6.90808e12 0.223282 0.111641 0.993749i \(-0.464389\pi\)
0.111641 + 0.993749i \(0.464389\pi\)
\(500\) 4.97994e13 1.59358
\(501\) −8.77077e12 −0.277875
\(502\) 5.12779e13i 1.60847i
\(503\) 5.01804e12i 0.155846i −0.996959 0.0779228i \(-0.975171\pi\)
0.996959 0.0779228i \(-0.0248288\pi\)
\(504\) 1.43634e13i 0.441675i
\(505\) 2.59505e13i 0.790112i
\(506\) 1.33158e13i 0.401434i
\(507\) 9.96329e12 0.297415
\(508\) −6.33034e13 −1.87115
\(509\) 3.38091e12i 0.0989565i 0.998775 + 0.0494783i \(0.0157559\pi\)
−0.998775 + 0.0494783i \(0.984244\pi\)
\(510\) 9.03020e12i 0.261726i
\(511\) 8.11271e13i 2.32842i
\(512\) 1.33085e13i 0.378249i
\(513\) −1.18885e11 −0.00334611
\(514\) 4.77131e13i 1.32991i
\(515\) 8.53805e12i 0.235680i
\(516\) 1.70464e13i 0.465998i
\(517\) 2.21586e13 0.599914
\(518\) 4.54686e13 1.21917
\(519\) 1.86534e13i 0.495359i
\(520\) 1.50287e13 0.395279
\(521\) 1.96892e13 0.512908 0.256454 0.966556i \(-0.417446\pi\)
0.256454 + 0.966556i \(0.417446\pi\)
\(522\) 3.29217e12i 0.0849435i
\(523\) −1.74191e13 −0.445162 −0.222581 0.974914i \(-0.571448\pi\)
−0.222581 + 0.974914i \(0.571448\pi\)
\(524\) 5.44295e13i 1.37777i
\(525\) 1.97645e13 0.495553
\(526\) 3.00838e13i 0.747143i
\(527\) 4.12235e12i 0.101413i
\(528\) 3.96311e12i 0.0965754i
\(529\) 3.80070e13 0.917456
\(530\) 1.86864e13i 0.446834i
\(531\) 1.20854e13 7.20829e12i 0.286279 0.170750i
\(532\) −1.78341e12 −0.0418498
\(533\) 5.04084e13i 1.17184i
\(534\) 3.87084e13 0.891455
\(535\) −2.20250e13 −0.502512
\(536\) −3.57547e13 −0.808181
\(537\) 1.35223e12i 0.0302816i
\(538\) 3.39614e13 0.753485
\(539\) 5.90306e13i 1.29758i
\(540\) −9.11231e12 −0.198454
\(541\) 3.09098e13i 0.666976i −0.942754 0.333488i \(-0.891774\pi\)
0.942754 0.333488i \(-0.108226\pi\)
\(542\) 6.61931e13i 1.41520i
\(543\) −1.58310e13 −0.335358
\(544\) 2.30550e13i 0.483917i
\(545\) 4.01614e13i 0.835269i
\(546\) 4.88289e13 1.00627
\(547\) 9.65358e13 1.97130 0.985648 0.168813i \(-0.0539936\pi\)
0.985648 + 0.168813i \(0.0539936\pi\)
\(548\) −9.58839e13 −1.94018
\(549\) 3.16646e12i 0.0634910i
\(550\) 3.83510e13 0.762015
\(551\) −1.41490e11 −0.00278591
\(552\) 7.15719e12 0.139652
\(553\) −3.04796e13 −0.589364
\(554\) 9.96381e12i 0.190931i
\(555\) 9.98460e12i 0.189612i
\(556\) 2.34598e13 0.441521
\(557\) −8.42715e13 −1.57183 −0.785914 0.618336i \(-0.787807\pi\)
−0.785914 + 0.618336i \(0.787807\pi\)
\(558\) −6.87980e12 −0.127176
\(559\) −2.00586e13 −0.367486
\(560\) 1.11273e13 0.202046
\(561\) 1.19149e13i 0.214426i
\(562\) 1.11874e14i 1.99549i
\(563\) 2.46985e13i 0.436644i 0.975877 + 0.218322i \(0.0700584\pi\)
−0.975877 + 0.218322i \(0.929942\pi\)
\(564\) 3.44089e13i 0.602941i
\(565\) 4.27778e13i 0.742978i
\(566\) 3.39942e13 0.585225
\(567\) −1.02478e13 −0.174870
\(568\) 4.63854e13i 0.784584i
\(569\) 5.13881e13i 0.861591i −0.902450 0.430796i \(-0.858233\pi\)
0.902450 0.430796i \(-0.141767\pi\)
\(570\) 6.47695e11i 0.0107646i
\(571\) 4.30960e13i 0.709997i 0.934867 + 0.354999i \(0.115519\pi\)
−0.934867 + 0.354999i \(0.884481\pi\)
\(572\) 5.72885e13 0.935594
\(573\) 6.13381e13i 0.993019i
\(574\) 2.62471e14i 4.21233i
\(575\) 9.84856e12i 0.156687i
\(576\) 3.44526e13 0.543387
\(577\) −3.50752e13 −0.548430 −0.274215 0.961668i \(-0.588418\pi\)
−0.274215 + 0.961668i \(0.588418\pi\)
\(578\) 8.42642e13i 1.30618i
\(579\) −5.96345e13 −0.916442
\(580\) −1.08449e13 −0.165229
\(581\) 1.99057e14i 3.00675i
\(582\) −2.51364e13 −0.376433
\(583\) 2.46559e13i 0.366081i
\(584\) −8.46120e13 −1.24557
\(585\) 1.07225e13i 0.156501i
\(586\) 7.07354e13i 1.02364i
\(587\) 8.69944e13i 1.24825i −0.781326 0.624124i \(-0.785456\pi\)
0.781326 0.624124i \(-0.214544\pi\)
\(588\) −9.16655e13 −1.30412
\(589\) 2.95677e11i 0.00417101i
\(590\) −3.92714e13 6.58425e13i −0.549308 0.920971i
\(591\) −1.13559e13 −0.157501
\(592\) 6.74322e12i 0.0927383i
\(593\) 9.80223e13 1.33675 0.668377 0.743823i \(-0.266989\pi\)
0.668377 + 0.743823i \(0.266989\pi\)
\(594\) −1.98849e13 −0.268900
\(595\) −3.34538e13 −0.448601
\(596\) 2.31894e13i 0.308361i
\(597\) −5.75642e13 −0.759069
\(598\) 2.43312e13i 0.318169i
\(599\) −6.56015e13 −0.850706 −0.425353 0.905028i \(-0.639850\pi\)
−0.425353 + 0.905028i \(0.639850\pi\)
\(600\) 2.06135e13i 0.265092i
\(601\) 7.31596e13i 0.933038i −0.884511 0.466519i \(-0.845508\pi\)
0.884511 0.466519i \(-0.154492\pi\)
\(602\) 1.04443e14 1.32098
\(603\) 2.55099e13i 0.319979i
\(604\) 8.69975e13i 1.08224i
\(605\) 1.24690e13 0.153834
\(606\) 8.79364e13 1.07598
\(607\) −5.58822e13 −0.678156 −0.339078 0.940758i \(-0.610115\pi\)
−0.339078 + 0.940758i \(0.610115\pi\)
\(608\) 1.65363e12i 0.0199031i
\(609\) −1.21964e13 −0.145594
\(610\) −1.72511e13 −0.204253
\(611\) 4.04891e13 0.475480
\(612\) −1.85021e13 −0.215508
\(613\) 4.28268e13i 0.494781i 0.968916 + 0.247391i \(0.0795731\pi\)
−0.968916 + 0.247391i \(0.920427\pi\)
\(614\) 4.67731e13i 0.535987i
\(615\) −5.76370e13 −0.655127
\(616\) −1.03251e14 −1.16410
\(617\) −1.09740e14 −1.22727 −0.613634 0.789590i \(-0.710293\pi\)
−0.613634 + 0.789590i \(0.710293\pi\)
\(618\) 2.89322e13 0.320951
\(619\) −7.95094e13 −0.874914 −0.437457 0.899239i \(-0.644121\pi\)
−0.437457 + 0.899239i \(0.644121\pi\)
\(620\) 2.26631e13i 0.247378i
\(621\) 5.10644e12i 0.0552917i
\(622\) 1.27257e14i 1.36688i
\(623\) 1.43401e14i 1.52796i
\(624\) 7.24157e12i 0.0765438i
\(625\) −1.49919e13 −0.157201
\(626\) 1.39384e14 1.44991
\(627\) 8.54603e11i 0.00881915i
\(628\) 1.74139e14i 1.78278i
\(629\) 2.02732e13i 0.205906i
\(630\) 5.58310e13i 0.562565i
\(631\) −1.06133e14 −1.06097 −0.530485 0.847694i \(-0.677990\pi\)
−0.530485 + 0.847694i \(0.677990\pi\)
\(632\) 3.17889e13i 0.315275i
\(633\) 6.62270e12i 0.0651653i
\(634\) 2.87955e14i 2.81111i
\(635\) 8.51713e13 0.824945
\(636\) 3.82868e13 0.367928
\(637\) 1.07863e14i 1.02843i
\(638\) −2.36658e13 −0.223881
\(639\) −3.30946e13 −0.310637
\(640\) 1.04825e14i 0.976257i
\(641\) −9.16379e13 −0.846808 −0.423404 0.905941i \(-0.639165\pi\)
−0.423404 + 0.905941i \(0.639165\pi\)
\(642\) 7.46343e13i 0.684326i
\(643\) 2.54312e13 0.231373 0.115686 0.993286i \(-0.463093\pi\)
0.115686 + 0.993286i \(0.463093\pi\)
\(644\) 7.66025e13i 0.691534i
\(645\) 2.29350e13i 0.205447i
\(646\) 1.31511e12i 0.0116896i
\(647\) −7.95829e13 −0.701937 −0.350969 0.936387i \(-0.614148\pi\)
−0.350969 + 0.936387i \(0.614148\pi\)
\(648\) 1.06880e13i 0.0935455i
\(649\) −5.18167e13 8.68761e13i −0.450035 0.754530i
\(650\) 7.00767e13 0.603958
\(651\) 2.54873e13i 0.217981i
\(652\) −9.61813e13 −0.816305
\(653\) 1.46937e13 0.123756 0.0618780 0.998084i \(-0.480291\pi\)
0.0618780 + 0.998084i \(0.480291\pi\)
\(654\) 1.36092e14 1.13748
\(655\) 7.32320e13i 0.607428i
\(656\) 3.89258e13 0.320419
\(657\) 6.03682e13i 0.493152i
\(658\) −2.10823e14 −1.70918
\(659\) 3.70636e13i 0.298209i −0.988821 0.149105i \(-0.952361\pi\)
0.988821 0.149105i \(-0.0476391\pi\)
\(660\) 6.55038e13i 0.523054i
\(661\) 1.96867e14 1.56015 0.780076 0.625685i \(-0.215181\pi\)
0.780076 + 0.625685i \(0.215181\pi\)
\(662\) 2.94444e14i 2.31586i
\(663\) 2.17715e13i 0.169950i
\(664\) −2.07608e14 −1.60843
\(665\) 2.39948e12 0.0184506
\(666\) −3.38340e13 −0.258216
\(667\) 6.07738e12i 0.0460349i
\(668\) 9.79049e13 0.736075
\(669\) −5.01867e13 −0.374506
\(670\) 1.38980e14 1.02939
\(671\) −2.27621e13 −0.167340
\(672\) 1.42542e14i 1.04015i
\(673\) 1.56435e14i 1.13307i 0.824037 + 0.566536i \(0.191717\pi\)
−0.824037 + 0.566536i \(0.808283\pi\)
\(674\) −1.91956e14 −1.38007
\(675\) −1.47071e13 −0.104957
\(676\) −1.11217e14 −0.787836
\(677\) −8.64965e13 −0.608212 −0.304106 0.952638i \(-0.598358\pi\)
−0.304106 + 0.952638i \(0.598358\pi\)
\(678\) −1.44958e14 −1.01180
\(679\) 9.31216e13i 0.645211i
\(680\) 3.48908e13i 0.239975i
\(681\) 4.16833e13i 0.284595i
\(682\) 4.94554e13i 0.335191i
\(683\) 2.51796e14i 1.69412i −0.531496 0.847061i \(-0.678370\pi\)
0.531496 0.847061i \(-0.321630\pi\)
\(684\) 1.32707e12 0.00886366
\(685\) 1.29007e14 0.855381
\(686\) 1.81369e14i 1.19383i
\(687\) 8.49748e13i 0.555273i
\(688\) 1.54894e13i 0.100483i
\(689\) 4.50523e13i 0.290149i
\(690\) −2.78203e13 −0.177876
\(691\) 8.92973e13i 0.566824i 0.958998 + 0.283412i \(0.0914663\pi\)
−0.958998 + 0.283412i \(0.908534\pi\)
\(692\) 2.08221e14i 1.31218i
\(693\) 7.36665e13i 0.460897i
\(694\) −7.83753e13 −0.486835
\(695\) −3.15640e13 −0.194656
\(696\) 1.27203e13i 0.0778843i
\(697\) −1.17029e14 −0.711426
\(698\) −2.37293e12 −0.0143221
\(699\) 7.73926e13i 0.463782i
\(700\) −2.20624e14 −1.31269
\(701\) 2.17405e14i 1.28434i 0.766563 + 0.642169i \(0.221965\pi\)
−0.766563 + 0.642169i \(0.778035\pi\)
\(702\) −3.63345e13 −0.213125
\(703\) 1.45411e12i 0.00846875i
\(704\) 2.47662e14i 1.43218i
\(705\) 4.62953e13i 0.265822i
\(706\) −6.39905e13 −0.364831
\(707\) 3.25774e14i 1.84425i
\(708\) −1.34905e14 + 8.04635e13i −0.758338 + 0.452306i
\(709\) 4.37689e13 0.244306 0.122153 0.992511i \(-0.461020\pi\)
0.122153 + 0.992511i \(0.461020\pi\)
\(710\) 1.80302e14i 0.999331i
\(711\) 2.26804e13 0.124825
\(712\) −1.49561e14 −0.817371
\(713\) −1.27002e13 −0.0689226
\(714\) 1.13362e14i 0.610909i
\(715\) −7.70787e13 −0.412481
\(716\) 1.50944e13i 0.0802143i
\(717\) 1.33082e14 0.702304
\(718\) 1.07756e14i 0.564700i
\(719\) 2.73736e14i 1.42458i −0.701885 0.712290i \(-0.747658\pi\)
0.701885 0.712290i \(-0.252342\pi\)
\(720\) −8.28003e12 −0.0427927
\(721\) 1.07184e14i 0.550114i
\(722\) 3.11933e14i 1.58992i
\(723\) −5.89089e13 −0.298187
\(724\) 1.76716e14 0.888345
\(725\) −1.75036e13 −0.0873850
\(726\) 4.22526e13i 0.209493i
\(727\) −6.53955e13 −0.322015 −0.161007 0.986953i \(-0.551474\pi\)
−0.161007 + 0.986953i \(0.551474\pi\)
\(728\) −1.88665e14 −0.922643
\(729\) 7.62560e12 0.0370370
\(730\) 3.28891e14 1.58649
\(731\) 4.65683e13i 0.223102i
\(732\) 3.53460e13i 0.168184i
\(733\) −6.74238e13 −0.318635 −0.159318 0.987227i \(-0.550929\pi\)
−0.159318 + 0.987227i \(0.550929\pi\)
\(734\) 1.91668e14 0.899639
\(735\) 1.23331e14 0.574957
\(736\) 7.10280e13 0.328882
\(737\) 1.83378e14 0.843353
\(738\) 1.95310e14i 0.892159i
\(739\) 1.38269e13i 0.0627341i 0.999508 + 0.0313671i \(0.00998608\pi\)
−0.999508 + 0.0313671i \(0.990014\pi\)
\(740\) 1.11455e14i 0.502272i
\(741\) 1.56157e12i 0.00698989i
\(742\) 2.34583e14i 1.04298i
\(743\) −3.62484e13 −0.160083 −0.0800414 0.996792i \(-0.525505\pi\)
−0.0800414 + 0.996792i \(0.525505\pi\)
\(744\) 2.65821e13 0.116607
\(745\) 3.12002e13i 0.135949i
\(746\) 3.60706e14i 1.56120i
\(747\) 1.48122e14i 0.636819i
\(748\) 1.33002e14i 0.568003i
\(749\) 2.76494e14 1.17294
\(750\) 2.27046e14i 0.956769i
\(751\) 1.53369e14i 0.642004i −0.947079 0.321002i \(-0.895980\pi\)
0.947079 0.321002i \(-0.104020\pi\)
\(752\) 3.12661e13i 0.130012i
\(753\) 1.41358e14 0.583909
\(754\) −4.32432e13 −0.177444
\(755\) 1.17050e14i 0.477132i
\(756\) 1.14393e14 0.463223
\(757\) −1.02440e14 −0.412088 −0.206044 0.978543i \(-0.566059\pi\)
−0.206044 + 0.978543i \(0.566059\pi\)
\(758\) 5.96598e14i 2.38416i
\(759\) −3.67076e13 −0.145729
\(760\) 2.50256e12i 0.00986998i
\(761\) 4.48293e13 0.175646 0.0878230 0.996136i \(-0.472009\pi\)
0.0878230 + 0.996136i \(0.472009\pi\)
\(762\) 2.88613e14i 1.12342i
\(763\) 5.04172e14i 1.94965i
\(764\) 6.84695e14i 2.63045i
\(765\) 2.48936e13 0.0950123
\(766\) 4.84515e14i 1.83723i
\(767\) −9.46819e13 1.58744e14i −0.356689 0.598026i
\(768\) −1.03747e14 −0.388303
\(769\) 7.98791e13i 0.297031i 0.988910 + 0.148515i \(0.0474494\pi\)
−0.988910 + 0.148515i \(0.952551\pi\)
\(770\) 4.01341e14 1.48272
\(771\) −1.31531e14 −0.482787
\(772\) 6.65679e14 2.42761
\(773\) 4.49751e14i 1.62958i −0.579760 0.814788i \(-0.696854\pi\)
0.579760 0.814788i \(-0.303146\pi\)
\(774\) −7.77180e13 −0.279780
\(775\) 3.65780e13i 0.130831i
\(776\) 9.71217e13 0.345150
\(777\) 1.25343e14i 0.442584i
\(778\) 3.81752e14i 1.33932i
\(779\) 8.39395e12 0.0292603