Properties

Label 177.9.c.a.58.7
Level $177$
Weight $9$
Character 177.58
Analytic conductor $72.106$
Analytic rank $0$
Dimension $80$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 177.c (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(72.1060139808\)
Analytic rank: \(0\)
Dimension: \(80\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.7
Character \(\chi\) \(=\) 177.58
Dual form 177.9.c.a.58.74

$q$-expansion

\(f(q)\) \(=\) \(q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +O(q^{10})\) \(q-28.1432i q^{2} -46.7654 q^{3} -536.039 q^{4} -406.960 q^{5} +1316.13i q^{6} +2744.16 q^{7} +7881.18i q^{8} +2187.00 q^{9} +11453.1i q^{10} -5707.50i q^{11} +25068.1 q^{12} -49047.0i q^{13} -77229.3i q^{14} +19031.6 q^{15} +84575.7 q^{16} -62224.1 q^{17} -61549.1i q^{18} +167552. q^{19} +218146. q^{20} -128332. q^{21} -160627. q^{22} -321556. i q^{23} -368567. i q^{24} -225009. q^{25} -1.38034e6 q^{26} -102276. q^{27} -1.47097e6 q^{28} -340144. q^{29} -535610. i q^{30} -822696. i q^{31} -362646. i q^{32} +266913. i q^{33} +1.75118e6i q^{34} -1.11676e6 q^{35} -1.17232e6 q^{36} -506510. i q^{37} -4.71543e6i q^{38} +2.29370e6i q^{39} -3.20732e6i q^{40} +2.70031e6 q^{41} +3.61166e6i q^{42} -2.76851e6i q^{43} +3.05944e6i q^{44} -890021. q^{45} -9.04960e6 q^{46} +71974.2i q^{47} -3.95521e6 q^{48} +1.76559e6 q^{49} +6.33247e6i q^{50} +2.90993e6 q^{51} +2.62911e7i q^{52} +2.39637e6 q^{53} +2.87837e6i q^{54} +2.32272e6i q^{55} +2.16272e7i q^{56} -7.83561e6 q^{57} +9.57275e6i q^{58} +(6.01191e6 - 1.05208e7i) q^{59} -1.02017e7 q^{60} -5.73423e6i q^{61} -2.31533e7 q^{62} +6.00147e6 q^{63} +1.14454e7 q^{64} +1.99601e7i q^{65} +7.51179e6 q^{66} -1.33867e7i q^{67} +3.33545e7 q^{68} +1.50377e7i q^{69} +3.14292e7i q^{70} -2.76871e7 q^{71} +1.72362e7i q^{72} +1.83891e6i q^{73} -1.42548e7 q^{74} +1.05226e7 q^{75} -8.98141e7 q^{76} -1.56623e7i q^{77} +6.45521e7 q^{78} -3.52171e7 q^{79} -3.44189e7 q^{80} +4.78297e6 q^{81} -7.59953e7i q^{82} +3.28542e7i q^{83} +6.87907e7 q^{84} +2.53227e7 q^{85} -7.79145e7 q^{86} +1.59070e7 q^{87} +4.49818e7 q^{88} +8.29411e7i q^{89} +2.50480e7i q^{90} -1.34593e8i q^{91} +1.72366e8i q^{92} +3.84737e7i q^{93} +2.02558e6 q^{94} -6.81867e7 q^{95} +1.69593e7i q^{96} -2.69493e6i q^{97} -4.96894e7i q^{98} -1.24823e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} + O(q^{10}) \) \( 80q - 10240q^{4} + 160q^{7} + 174960q^{9} - 22680q^{12} - 59616q^{15} + 1199848q^{16} - 10608q^{17} - 27516q^{19} - 146436q^{20} - 974696q^{22} + 5718040q^{25} - 797484q^{26} - 3133000q^{28} + 1725924q^{29} + 4318800q^{35} - 22394880q^{36} - 732180q^{41} + 22752084q^{46} + 8703936q^{48} + 55899176q^{49} - 10373832q^{51} - 39265944q^{53} - 11408040q^{57} - 33575112q^{59} - 18034488q^{60} + 13038600q^{62} + 349920q^{63} - 241654260q^{64} - 35711928q^{66} + 36772608q^{68} - 235272660q^{71} - 63050712q^{74} + 74363184q^{75} + 9454680q^{76} - 10865988q^{78} + 17252580q^{79} + 318203976q^{80} + 382637520q^{81} - 20743128q^{84} - 27245820q^{85} + 105666984q^{86} + 29437992q^{87} + 82079788q^{88} + 121215992q^{94} - 690837276q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 28.1432i 1.75895i −0.475946 0.879475i \(-0.657894\pi\)
0.475946 0.879475i \(-0.342106\pi\)
\(3\) −46.7654 −0.577350
\(4\) −536.039 −2.09390
\(5\) −406.960 −0.651135 −0.325568 0.945519i \(-0.605555\pi\)
−0.325568 + 0.945519i \(0.605555\pi\)
\(6\) 1316.13i 1.01553i
\(7\) 2744.16 1.14292 0.571461 0.820629i \(-0.306377\pi\)
0.571461 + 0.820629i \(0.306377\pi\)
\(8\) 7881.18i 1.92412i
\(9\) 2187.00 0.333333
\(10\) 11453.1i 1.14531i
\(11\) 5707.50i 0.389830i −0.980820 0.194915i \(-0.937557\pi\)
0.980820 0.194915i \(-0.0624431\pi\)
\(12\) 25068.1 1.20891
\(13\) 49047.0i 1.71727i −0.512586 0.858636i \(-0.671312\pi\)
0.512586 0.858636i \(-0.328688\pi\)
\(14\) 77229.3i 2.01034i
\(15\) 19031.6 0.375933
\(16\) 84575.7 1.29052
\(17\) −62224.1 −0.745012 −0.372506 0.928030i \(-0.621501\pi\)
−0.372506 + 0.928030i \(0.621501\pi\)
\(18\) 61549.1i 0.586316i
\(19\) 167552. 1.28568 0.642842 0.765999i \(-0.277755\pi\)
0.642842 + 0.765999i \(0.277755\pi\)
\(20\) 218146. 1.36341
\(21\) −128332. −0.659867
\(22\) −160627. −0.685691
\(23\) 321556.i 1.14907i −0.818482 0.574533i \(-0.805184\pi\)
0.818482 0.574533i \(-0.194816\pi\)
\(24\) 368567.i 1.11089i
\(25\) −225009. −0.576023
\(26\) −1.38034e6 −3.02059
\(27\) −102276. −0.192450
\(28\) −1.47097e6 −2.39317
\(29\) −340144. −0.480918 −0.240459 0.970659i \(-0.577298\pi\)
−0.240459 + 0.970659i \(0.577298\pi\)
\(30\) 535610.i 0.661247i
\(31\) 822696.i 0.890825i −0.895325 0.445413i \(-0.853057\pi\)
0.895325 0.445413i \(-0.146943\pi\)
\(32\) 362646.i 0.345846i
\(33\) 266913.i 0.225068i
\(34\) 1.75118e6i 1.31044i
\(35\) −1.11676e6 −0.744197
\(36\) −1.17232e6 −0.697967
\(37\) 506510.i 0.270260i −0.990828 0.135130i \(-0.956855\pi\)
0.990828 0.135130i \(-0.0431451\pi\)
\(38\) 4.71543e6i 2.26145i
\(39\) 2.29370e6i 0.991467i
\(40\) 3.20732e6i 1.25286i
\(41\) 2.70031e6 0.955604 0.477802 0.878467i \(-0.341434\pi\)
0.477802 + 0.878467i \(0.341434\pi\)
\(42\) 3.61166e6i 1.16067i
\(43\) 2.76851e6i 0.809788i −0.914364 0.404894i \(-0.867308\pi\)
0.914364 0.404894i \(-0.132692\pi\)
\(44\) 3.05944e6i 0.816265i
\(45\) −890021. −0.217045
\(46\) −9.04960e6 −2.02115
\(47\) 71974.2i 0.0147498i 0.999973 + 0.00737489i \(0.00234752\pi\)
−0.999973 + 0.00737489i \(0.997652\pi\)
\(48\) −3.95521e6 −0.745084
\(49\) 1.76559e6 0.306271
\(50\) 6.33247e6i 1.01319i
\(51\) 2.90993e6 0.430133
\(52\) 2.62911e7i 3.59580i
\(53\) 2.39637e6 0.303704 0.151852 0.988403i \(-0.451476\pi\)
0.151852 + 0.988403i \(0.451476\pi\)
\(54\) 2.87837e6i 0.338510i
\(55\) 2.32272e6i 0.253832i
\(56\) 2.16272e7i 2.19912i
\(57\) −7.83561e6 −0.742290
\(58\) 9.57275e6i 0.845911i
\(59\) 6.01191e6 1.05208e7i 0.496141 0.868242i
\(60\) −1.02017e7 −0.787167
\(61\) 5.73423e6i 0.414148i −0.978325 0.207074i \(-0.933606\pi\)
0.978325 0.207074i \(-0.0663941\pi\)
\(62\) −2.31533e7 −1.56692
\(63\) 6.00147e6 0.380974
\(64\) 1.14454e7 0.682197
\(65\) 1.99601e7i 1.11818i
\(66\) 7.51179e6 0.395884
\(67\) 1.33867e7i 0.664315i −0.943224 0.332157i \(-0.892223\pi\)
0.943224 0.332157i \(-0.107777\pi\)
\(68\) 3.33545e7 1.55998
\(69\) 1.50377e7i 0.663413i
\(70\) 3.14292e7i 1.30900i
\(71\) −2.76871e7 −1.08954 −0.544771 0.838585i \(-0.683384\pi\)
−0.544771 + 0.838585i \(0.683384\pi\)
\(72\) 1.72362e7i 0.641372i
\(73\) 1.83891e6i 0.0647545i 0.999476 + 0.0323772i \(0.0103078\pi\)
−0.999476 + 0.0323772i \(0.989692\pi\)
\(74\) −1.42548e7 −0.475373
\(75\) 1.05226e7 0.332567
\(76\) −8.98141e7 −2.69209
\(77\) 1.56623e7i 0.445545i
\(78\) 6.45521e7 1.74394
\(79\) −3.52171e7 −0.904160 −0.452080 0.891977i \(-0.649318\pi\)
−0.452080 + 0.891977i \(0.649318\pi\)
\(80\) −3.44189e7 −0.840305
\(81\) 4.78297e6 0.111111
\(82\) 7.59953e7i 1.68086i
\(83\) 3.28542e7i 0.692275i 0.938184 + 0.346137i \(0.112507\pi\)
−0.938184 + 0.346137i \(0.887493\pi\)
\(84\) 6.87907e7 1.38170
\(85\) 2.53227e7 0.485103
\(86\) −7.79145e7 −1.42438
\(87\) 1.59070e7 0.277658
\(88\) 4.49818e7 0.750078
\(89\) 8.29411e7i 1.32193i 0.750415 + 0.660967i \(0.229854\pi\)
−0.750415 + 0.660967i \(0.770146\pi\)
\(90\) 2.50480e7i 0.381771i
\(91\) 1.34593e8i 1.96271i
\(92\) 1.72366e8i 2.40603i
\(93\) 3.84737e7i 0.514318i
\(94\) 2.02558e6 0.0259441
\(95\) −6.81867e7 −0.837154
\(96\) 1.69593e7i 0.199674i
\(97\) 2.69493e6i 0.0304411i −0.999884 0.0152205i \(-0.995155\pi\)
0.999884 0.0152205i \(-0.00484503\pi\)
\(98\) 4.96894e7i 0.538716i
\(99\) 1.24823e7i 0.129943i
\(100\) 1.20614e8 1.20614
\(101\) 8.66455e7i 0.832646i 0.909217 + 0.416323i \(0.136681\pi\)
−0.909217 + 0.416323i \(0.863319\pi\)
\(102\) 8.18948e7i 0.756581i
\(103\) 1.48893e8i 1.32290i −0.749990 0.661449i \(-0.769942\pi\)
0.749990 0.661449i \(-0.230058\pi\)
\(104\) 3.86549e8 3.30423
\(105\) 5.22257e7 0.429662
\(106\) 6.74416e7i 0.534201i
\(107\) −3.68069e7 −0.280798 −0.140399 0.990095i \(-0.544839\pi\)
−0.140399 + 0.990095i \(0.544839\pi\)
\(108\) 5.48238e7 0.402972
\(109\) 8.91124e7i 0.631295i −0.948877 0.315647i \(-0.897778\pi\)
0.948877 0.315647i \(-0.102222\pi\)
\(110\) 6.53687e7 0.446477
\(111\) 2.36871e7i 0.156034i
\(112\) 2.32089e8 1.47497
\(113\) 3.04104e8i 1.86513i 0.361007 + 0.932563i \(0.382433\pi\)
−0.361007 + 0.932563i \(0.617567\pi\)
\(114\) 2.20519e8i 1.30565i
\(115\) 1.30860e8i 0.748197i
\(116\) 1.82331e8 1.00700
\(117\) 1.07266e8i 0.572424i
\(118\) −2.96089e8 1.69194e8i −1.52719 0.872686i
\(119\) −1.70753e8 −0.851490
\(120\) 1.49992e8i 0.723340i
\(121\) 1.81783e8 0.848033
\(122\) −1.61379e8 −0.728465
\(123\) −1.26281e8 −0.551718
\(124\) 4.40997e8i 1.86530i
\(125\) 2.50538e8 1.02620
\(126\) 1.68900e8i 0.670114i
\(127\) 2.83628e8 1.09027 0.545135 0.838349i \(-0.316479\pi\)
0.545135 + 0.838349i \(0.316479\pi\)
\(128\) 4.14946e8i 1.54580i
\(129\) 1.29470e8i 0.467531i
\(130\) 5.61742e8 1.96682
\(131\) 2.19846e8i 0.746506i 0.927730 + 0.373253i \(0.121758\pi\)
−0.927730 + 0.373253i \(0.878242\pi\)
\(132\) 1.43076e8i 0.471271i
\(133\) 4.59788e8 1.46944
\(134\) −3.76744e8 −1.16850
\(135\) 4.16221e7 0.125311
\(136\) 4.90400e8i 1.43349i
\(137\) −1.43138e8 −0.406324 −0.203162 0.979145i \(-0.565122\pi\)
−0.203162 + 0.979145i \(0.565122\pi\)
\(138\) 4.23208e8 1.16691
\(139\) 1.34149e8 0.359358 0.179679 0.983725i \(-0.442494\pi\)
0.179679 + 0.983725i \(0.442494\pi\)
\(140\) 5.98627e8 1.55828
\(141\) 3.36590e6i 0.00851578i
\(142\) 7.79204e8i 1.91645i
\(143\) −2.79936e8 −0.669444
\(144\) 1.84967e8 0.430174
\(145\) 1.38425e8 0.313143
\(146\) 5.17529e7 0.113900
\(147\) −8.25687e7 −0.176826
\(148\) 2.71509e8i 0.565897i
\(149\) 2.11758e8i 0.429629i −0.976655 0.214815i \(-0.931085\pi\)
0.976655 0.214815i \(-0.0689147\pi\)
\(150\) 2.96140e8i 0.584968i
\(151\) 9.10554e8i 1.75145i 0.482809 + 0.875726i \(0.339617\pi\)
−0.482809 + 0.875726i \(0.660383\pi\)
\(152\) 1.32050e9i 2.47381i
\(153\) −1.36084e8 −0.248337
\(154\) −4.40786e8 −0.783691
\(155\) 3.34804e8i 0.580048i
\(156\) 1.22951e9i 2.07604i
\(157\) 1.77008e8i 0.291337i −0.989333 0.145668i \(-0.953467\pi\)
0.989333 0.145668i \(-0.0465333\pi\)
\(158\) 9.91121e8i 1.59037i
\(159\) −1.12067e8 −0.175344
\(160\) 1.47582e8i 0.225193i
\(161\) 8.82399e8i 1.31329i
\(162\) 1.34608e8i 0.195439i
\(163\) −9.70750e8 −1.37517 −0.687586 0.726103i \(-0.741330\pi\)
−0.687586 + 0.726103i \(0.741330\pi\)
\(164\) −1.44747e9 −2.00094
\(165\) 1.08623e8i 0.146550i
\(166\) 9.24622e8 1.21768
\(167\) −1.28578e9 −1.65311 −0.826556 0.562855i \(-0.809703\pi\)
−0.826556 + 0.562855i \(0.809703\pi\)
\(168\) 1.01140e9i 1.26966i
\(169\) −1.58988e9 −1.94902
\(170\) 7.12661e8i 0.853272i
\(171\) 3.66435e8 0.428561
\(172\) 1.48403e9i 1.69562i
\(173\) 1.10174e9i 1.22997i 0.788539 + 0.614984i \(0.210838\pi\)
−0.788539 + 0.614984i \(0.789162\pi\)
\(174\) 4.47673e8i 0.488387i
\(175\) −6.17460e8 −0.658349
\(176\) 4.82715e8i 0.503084i
\(177\) −2.81149e8 + 4.92009e8i −0.286447 + 0.501280i
\(178\) 2.33423e9 2.32521
\(179\) 2.16436e8i 0.210823i −0.994429 0.105411i \(-0.966384\pi\)
0.994429 0.105411i \(-0.0336159\pi\)
\(180\) 4.77086e8 0.454471
\(181\) −7.17258e8 −0.668284 −0.334142 0.942523i \(-0.608447\pi\)
−0.334142 + 0.942523i \(0.608447\pi\)
\(182\) −3.78787e9 −3.45230
\(183\) 2.68163e8i 0.239108i
\(184\) 2.53424e9 2.21094
\(185\) 2.06129e8i 0.175976i
\(186\) 1.08277e9 0.904660
\(187\) 3.55144e8i 0.290428i
\(188\) 3.85810e7i 0.0308846i
\(189\) −2.80661e8 −0.219956
\(190\) 1.91899e9i 1.47251i
\(191\) 8.84331e8i 0.664479i −0.943195 0.332240i \(-0.892196\pi\)
0.943195 0.332240i \(-0.107804\pi\)
\(192\) −5.35247e8 −0.393867
\(193\) 1.45097e9 1.04576 0.522878 0.852408i \(-0.324858\pi\)
0.522878 + 0.852408i \(0.324858\pi\)
\(194\) −7.58438e7 −0.0535443
\(195\) 9.33444e8i 0.645579i
\(196\) −9.46427e8 −0.641302
\(197\) −2.08279e9 −1.38287 −0.691434 0.722440i \(-0.743021\pi\)
−0.691434 + 0.722440i \(0.743021\pi\)
\(198\) −3.51292e8 −0.228564
\(199\) 1.28765e9 0.821078 0.410539 0.911843i \(-0.365341\pi\)
0.410539 + 0.911843i \(0.365341\pi\)
\(200\) 1.77334e9i 1.10834i
\(201\) 6.26033e8i 0.383542i
\(202\) 2.43848e9 1.46458
\(203\) −9.33410e8 −0.549652
\(204\) −1.55984e9 −0.900655
\(205\) −1.09892e9 −0.622228
\(206\) −4.19033e9 −2.32691
\(207\) 7.03242e8i 0.383022i
\(208\) 4.14818e9i 2.21618i
\(209\) 9.56300e8i 0.501198i
\(210\) 1.46980e9i 0.755754i
\(211\) 1.38402e9i 0.698253i 0.937076 + 0.349127i \(0.113522\pi\)
−0.937076 + 0.349127i \(0.886478\pi\)
\(212\) −1.28455e9 −0.635927
\(213\) 1.29480e9 0.629048
\(214\) 1.03586e9i 0.493909i
\(215\) 1.12667e9i 0.527282i
\(216\) 8.06055e8i 0.370297i
\(217\) 2.25761e9i 1.01814i
\(218\) −2.50791e9 −1.11042
\(219\) 8.59975e7i 0.0373860i
\(220\) 1.24507e9i 0.531499i
\(221\) 3.05191e9i 1.27939i
\(222\) 6.66631e8 0.274457
\(223\) −4.49221e9 −1.81652 −0.908261 0.418403i \(-0.862590\pi\)
−0.908261 + 0.418403i \(0.862590\pi\)
\(224\) 9.95157e8i 0.395275i
\(225\) −4.92094e8 −0.192008
\(226\) 8.55845e9 3.28066
\(227\) 2.37194e9i 0.893304i 0.894708 + 0.446652i \(0.147384\pi\)
−0.894708 + 0.446652i \(0.852616\pi\)
\(228\) 4.20019e9 1.55428
\(229\) 1.73293e9i 0.630142i 0.949068 + 0.315071i \(0.102028\pi\)
−0.949068 + 0.315071i \(0.897972\pi\)
\(230\) 3.68282e9 1.31604
\(231\) 7.32452e8i 0.257236i
\(232\) 2.68074e9i 0.925343i
\(233\) 9.85201e8i 0.334273i 0.985934 + 0.167136i \(0.0534520\pi\)
−0.985934 + 0.167136i \(0.946548\pi\)
\(234\) −3.01880e9 −1.00686
\(235\) 2.92906e7i 0.00960410i
\(236\) −3.22262e9 + 5.63956e9i −1.03887 + 1.81801i
\(237\) 1.64694e9 0.522017
\(238\) 4.80553e9i 1.49773i
\(239\) −1.03515e9 −0.317258 −0.158629 0.987338i \(-0.550707\pi\)
−0.158629 + 0.987338i \(0.550707\pi\)
\(240\) 1.60961e9 0.485150
\(241\) −4.76332e9 −1.41202 −0.706012 0.708200i \(-0.749507\pi\)
−0.706012 + 0.708200i \(0.749507\pi\)
\(242\) 5.11596e9i 1.49165i
\(243\) −2.23677e8 −0.0641500
\(244\) 3.07377e9i 0.867185i
\(245\) −7.18525e8 −0.199424
\(246\) 3.55395e9i 0.970444i
\(247\) 8.21790e9i 2.20787i
\(248\) 6.48382e9 1.71405
\(249\) 1.53644e9i 0.399685i
\(250\) 7.05094e9i 1.80504i
\(251\) 7.08834e9 1.78587 0.892935 0.450186i \(-0.148642\pi\)
0.892935 + 0.450186i \(0.148642\pi\)
\(252\) −3.21702e9 −0.797722
\(253\) −1.83528e9 −0.447940
\(254\) 7.98219e9i 1.91773i
\(255\) −1.18423e9 −0.280075
\(256\) −8.74790e9 −2.03678
\(257\) 3.07457e9 0.704778 0.352389 0.935854i \(-0.385369\pi\)
0.352389 + 0.935854i \(0.385369\pi\)
\(258\) 3.64370e9 0.822364
\(259\) 1.38994e9i 0.308886i
\(260\) 1.06994e10i 2.34135i
\(261\) −7.43896e8 −0.160306
\(262\) 6.18716e9 1.31307
\(263\) −4.06444e9 −0.849527 −0.424764 0.905304i \(-0.639643\pi\)
−0.424764 + 0.905304i \(0.639643\pi\)
\(264\) −2.10359e9 −0.433058
\(265\) −9.75227e8 −0.197753
\(266\) 1.29399e10i 2.58466i
\(267\) 3.87877e9i 0.763219i
\(268\) 7.17578e9i 1.39101i
\(269\) 1.25437e9i 0.239562i 0.992800 + 0.119781i \(0.0382192\pi\)
−0.992800 + 0.119781i \(0.961781\pi\)
\(270\) 1.17138e9i 0.220416i
\(271\) 1.02476e10 1.89996 0.949981 0.312308i \(-0.101102\pi\)
0.949981 + 0.312308i \(0.101102\pi\)
\(272\) −5.26265e9 −0.961454
\(273\) 6.29428e9i 1.13317i
\(274\) 4.02836e9i 0.714704i
\(275\) 1.28424e9i 0.224551i
\(276\) 8.06077e9i 1.38912i
\(277\) −9.16453e9 −1.55665 −0.778325 0.627861i \(-0.783930\pi\)
−0.778325 + 0.627861i \(0.783930\pi\)
\(278\) 3.77538e9i 0.632093i
\(279\) 1.79924e9i 0.296942i
\(280\) 8.80140e9i 1.43192i
\(281\) 1.18401e10 1.89902 0.949511 0.313735i \(-0.101580\pi\)
0.949511 + 0.313735i \(0.101580\pi\)
\(282\) −9.47271e7 −0.0149788
\(283\) 9.34560e9i 1.45701i −0.685043 0.728503i \(-0.740217\pi\)
0.685043 0.728503i \(-0.259783\pi\)
\(284\) 1.48414e10 2.28140
\(285\) 3.18878e9 0.483331
\(286\) 7.87828e9i 1.17752i
\(287\) 7.41007e9 1.09218
\(288\) 7.93107e8i 0.115282i
\(289\) −3.10392e9 −0.444958
\(290\) 3.89572e9i 0.550802i
\(291\) 1.26029e8i 0.0175752i
\(292\) 9.85729e8i 0.135590i
\(293\) −4.31608e9 −0.585625 −0.292812 0.956170i \(-0.594591\pi\)
−0.292812 + 0.956170i \(0.594591\pi\)
\(294\) 2.32375e9i 0.311028i
\(295\) −2.44661e9 + 4.28154e9i −0.323055 + 0.565343i
\(296\) 3.99190e9 0.520011
\(297\) 5.83739e8i 0.0750228i
\(298\) −5.95953e9 −0.755696
\(299\) −1.57713e10 −1.97326
\(300\) −5.64054e9 −0.696362
\(301\) 7.59721e9i 0.925525i
\(302\) 2.56259e10 3.08071
\(303\) 4.05201e9i 0.480728i
\(304\) 1.41708e10 1.65920
\(305\) 2.33360e9i 0.269666i
\(306\) 3.82984e9i 0.436812i
\(307\) −3.72885e9 −0.419780 −0.209890 0.977725i \(-0.567311\pi\)
−0.209890 + 0.977725i \(0.567311\pi\)
\(308\) 8.39558e9i 0.932928i
\(309\) 6.96305e9i 0.763775i
\(310\) 9.42245e9 1.02027
\(311\) −1.78526e10 −1.90835 −0.954177 0.299242i \(-0.903266\pi\)
−0.954177 + 0.299242i \(0.903266\pi\)
\(312\) −1.80771e10 −1.90770
\(313\) 1.65765e10i 1.72710i 0.504266 + 0.863548i \(0.331763\pi\)
−0.504266 + 0.863548i \(0.668237\pi\)
\(314\) −4.98158e9 −0.512447
\(315\) −2.44236e9 −0.248066
\(316\) 1.88777e10 1.89322
\(317\) −5.90897e9 −0.585160 −0.292580 0.956241i \(-0.594514\pi\)
−0.292580 + 0.956241i \(0.594514\pi\)
\(318\) 3.15393e9i 0.308421i
\(319\) 1.94137e9i 0.187476i
\(320\) −4.65780e9 −0.444202
\(321\) 1.72129e9 0.162119
\(322\) −2.48335e10 −2.31001
\(323\) −1.04257e10 −0.957849
\(324\) −2.56386e9 −0.232656
\(325\) 1.10360e10i 0.989188i
\(326\) 2.73200e10i 2.41886i
\(327\) 4.16738e9i 0.364478i
\(328\) 2.12816e10i 1.83869i
\(329\) 1.97508e8i 0.0168578i
\(330\) −3.05699e9 −0.257774
\(331\) 8.74322e9 0.728382 0.364191 0.931324i \(-0.381345\pi\)
0.364191 + 0.931324i \(0.381345\pi\)
\(332\) 1.76111e10i 1.44955i
\(333\) 1.10774e9i 0.0900865i
\(334\) 3.61861e10i 2.90774i
\(335\) 5.44784e9i 0.432559i
\(336\) −1.08537e10 −0.851573
\(337\) 9.50740e9i 0.737126i −0.929603 0.368563i \(-0.879850\pi\)
0.929603 0.368563i \(-0.120150\pi\)
\(338\) 4.47442e10i 3.42823i
\(339\) 1.42215e10i 1.07683i
\(340\) −1.35740e10 −1.01576
\(341\) −4.69553e9 −0.347270
\(342\) 1.03127e10i 0.753817i
\(343\) −1.09744e10 −0.792878
\(344\) 2.18191e10 1.55813
\(345\) 6.11972e9i 0.431972i
\(346\) 3.10064e10 2.16345
\(347\) 1.56359e10i 1.07846i −0.842157 0.539232i \(-0.818714\pi\)
0.842157 0.539232i \(-0.181286\pi\)
\(348\) −8.52676e9 −0.581389
\(349\) 1.05023e10i 0.707918i 0.935261 + 0.353959i \(0.115165\pi\)
−0.935261 + 0.353959i \(0.884835\pi\)
\(350\) 1.73773e10i 1.15800i
\(351\) 5.01633e9i 0.330489i
\(352\) −2.06980e9 −0.134821
\(353\) 1.77402e10i 1.14251i −0.820773 0.571254i \(-0.806457\pi\)
0.820773 0.571254i \(-0.193543\pi\)
\(354\) 1.38467e10 + 7.91244e9i 0.881726 + 0.503845i
\(355\) 1.12675e10 0.709440
\(356\) 4.44597e10i 2.76800i
\(357\) 7.98531e9 0.491608
\(358\) −6.09119e9 −0.370826
\(359\) −1.55105e10 −0.933787 −0.466894 0.884313i \(-0.654627\pi\)
−0.466894 + 0.884313i \(0.654627\pi\)
\(360\) 7.01442e9i 0.417620i
\(361\) 1.10900e10 0.652982
\(362\) 2.01859e10i 1.17548i
\(363\) −8.50117e9 −0.489612
\(364\) 7.21469e10i 4.10972i
\(365\) 7.48363e8i 0.0421639i
\(366\) 7.54697e9 0.420579
\(367\) 3.08457e10i 1.70032i −0.526527 0.850158i \(-0.676506\pi\)
0.526527 0.850158i \(-0.323494\pi\)
\(368\) 2.71958e10i 1.48289i
\(369\) 5.90558e9 0.318535
\(370\) 5.80113e9 0.309532
\(371\) 6.57603e9 0.347111
\(372\) 2.06234e10i 1.07693i
\(373\) −1.50923e10 −0.779687 −0.389844 0.920881i \(-0.627471\pi\)
−0.389844 + 0.920881i \(0.627471\pi\)
\(374\) 9.99488e9 0.510847
\(375\) −1.17165e10 −0.592479
\(376\) −5.67242e8 −0.0283803
\(377\) 1.66831e10i 0.825868i
\(378\) 7.89869e9i 0.386891i
\(379\) 2.73541e10 1.32576 0.662882 0.748724i \(-0.269333\pi\)
0.662882 + 0.748724i \(0.269333\pi\)
\(380\) 3.65507e10 1.75292
\(381\) −1.32640e10 −0.629467
\(382\) −2.48879e10 −1.16879
\(383\) 1.55369e10 0.722053 0.361026 0.932556i \(-0.382426\pi\)
0.361026 + 0.932556i \(0.382426\pi\)
\(384\) 1.94051e10i 0.892466i
\(385\) 6.37391e9i 0.290110i
\(386\) 4.08350e10i 1.83943i
\(387\) 6.05472e9i 0.269929i
\(388\) 1.44459e9i 0.0637406i
\(389\) −1.05981e10 −0.462840 −0.231420 0.972854i \(-0.574337\pi\)
−0.231420 + 0.972854i \(0.574337\pi\)
\(390\) −2.62701e10 −1.13554
\(391\) 2.00085e10i 0.856067i
\(392\) 1.39150e10i 0.589302i
\(393\) 1.02812e10i 0.430995i
\(394\) 5.86163e10i 2.43239i
\(395\) 1.43319e10 0.588730
\(396\) 6.69099e9i 0.272088i
\(397\) 2.46311e10i 0.991565i −0.868447 0.495783i \(-0.834881\pi\)
0.868447 0.495783i \(-0.165119\pi\)
\(398\) 3.62385e10i 1.44423i
\(399\) −2.15021e10 −0.848379
\(400\) −1.90303e10 −0.743370
\(401\) 3.11202e9i 0.120355i 0.998188 + 0.0601777i \(0.0191667\pi\)
−0.998188 + 0.0601777i \(0.980833\pi\)
\(402\) 1.76186e10 0.674631
\(403\) −4.03508e10 −1.52979
\(404\) 4.64453e10i 1.74348i
\(405\) −1.94648e9 −0.0723484
\(406\) 2.62691e10i 0.966810i
\(407\) −2.89090e9 −0.105355
\(408\) 2.29337e10i 0.827626i
\(409\) 1.95746e10i 0.699521i −0.936839 0.349760i \(-0.886263\pi\)
0.936839 0.349760i \(-0.113737\pi\)
\(410\) 3.09270e10i 1.09447i
\(411\) 6.69391e9 0.234592
\(412\) 7.98126e10i 2.77002i
\(413\) 1.64976e10 2.88707e10i 0.567050 0.992333i
\(414\) −1.97915e10 −0.673716
\(415\) 1.33703e10i 0.450764i
\(416\) −1.77867e10 −0.593912
\(417\) −6.27352e9 −0.207476
\(418\) −2.69133e10 −0.881581
\(419\) 5.13543e10i 1.66617i −0.553142 0.833087i \(-0.686571\pi\)
0.553142 0.833087i \(-0.313429\pi\)
\(420\) −2.79950e10 −0.899671
\(421\) 2.58050e10i 0.821439i 0.911762 + 0.410720i \(0.134722\pi\)
−0.911762 + 0.410720i \(0.865278\pi\)
\(422\) 3.89508e10 1.22819
\(423\) 1.57408e8i 0.00491659i
\(424\) 1.88863e10i 0.584363i
\(425\) 1.40010e10 0.429144
\(426\) 3.64397e10i 1.10646i
\(427\) 1.57356e10i 0.473339i
\(428\) 1.97299e10 0.587963
\(429\) 1.30913e10 0.386503
\(430\) 3.17081e10 0.927462
\(431\) 2.35267e10i 0.681793i −0.940101 0.340897i \(-0.889269\pi\)
0.940101 0.340897i \(-0.110731\pi\)
\(432\) −8.65005e9 −0.248361
\(433\) 2.29758e10 0.653612 0.326806 0.945091i \(-0.394028\pi\)
0.326806 + 0.945091i \(0.394028\pi\)
\(434\) −6.35362e10 −1.79086
\(435\) −6.47350e9 −0.180793
\(436\) 4.77677e10i 1.32187i
\(437\) 5.38771e10i 1.47733i
\(438\) −2.42024e9 −0.0657601
\(439\) 4.42515e10 1.19143 0.595717 0.803194i \(-0.296868\pi\)
0.595717 + 0.803194i \(0.296868\pi\)
\(440\) −1.83058e10 −0.488402
\(441\) 3.86135e9 0.102090
\(442\) 8.58904e10 2.25038
\(443\) 1.02222e9i 0.0265417i −0.999912 0.0132708i \(-0.995776\pi\)
0.999912 0.0132708i \(-0.00422436\pi\)
\(444\) 1.26972e10i 0.326721i
\(445\) 3.37537e10i 0.860758i
\(446\) 1.26425e11i 3.19517i
\(447\) 9.90292e9i 0.248047i
\(448\) 3.14079e10 0.779698
\(449\) 3.67444e10 0.904079 0.452039 0.891998i \(-0.350697\pi\)
0.452039 + 0.891998i \(0.350697\pi\)
\(450\) 1.38491e10i 0.337732i
\(451\) 1.54120e10i 0.372523i
\(452\) 1.63012e11i 3.90539i
\(453\) 4.25824e10i 1.01120i
\(454\) 6.67538e10 1.57128
\(455\) 5.47738e10i 1.27799i
\(456\) 6.17539e10i 1.42825i
\(457\) 4.00848e10i 0.918999i −0.888178 0.459499i \(-0.848029\pi\)
0.888178 0.459499i \(-0.151971\pi\)
\(458\) 4.87701e10 1.10839
\(459\) 6.36403e9 0.143378
\(460\) 7.01461e10i 1.56665i
\(461\) 4.68445e10 1.03718 0.518591 0.855022i \(-0.326457\pi\)
0.518591 + 0.855022i \(0.326457\pi\)
\(462\) 2.06135e10 0.452464
\(463\) 2.50947e10i 0.546082i 0.962002 + 0.273041i \(0.0880294\pi\)
−0.962002 + 0.273041i \(0.911971\pi\)
\(464\) −2.87679e10 −0.620636
\(465\) 1.56572e10i 0.334891i
\(466\) 2.77267e10 0.587969
\(467\) 2.89237e10i 0.608115i 0.952654 + 0.304058i \(0.0983416\pi\)
−0.952654 + 0.304058i \(0.901658\pi\)
\(468\) 5.74986e10i 1.19860i
\(469\) 3.67352e10i 0.759260i
\(470\) −8.24330e8 −0.0168931
\(471\) 8.27787e9i 0.168203i
\(472\) 8.29164e10 + 4.73810e10i 1.67060 + 0.954633i
\(473\) −1.58012e10 −0.315680
\(474\) 4.63502e10i 0.918201i
\(475\) −3.77006e10 −0.740583
\(476\) 9.15301e10 1.78294
\(477\) 5.24087e9 0.101235
\(478\) 2.91324e10i 0.558040i
\(479\) −6.00874e10 −1.14141 −0.570704 0.821156i \(-0.693330\pi\)
−0.570704 + 0.821156i \(0.693330\pi\)
\(480\) 6.90174e9i 0.130015i
\(481\) −2.48428e10 −0.464109
\(482\) 1.34055e11i 2.48368i
\(483\) 4.12657e10i 0.758230i
\(484\) −9.74429e10 −1.77570
\(485\) 1.09673e9i 0.0198213i
\(486\) 6.29499e9i 0.112837i
\(487\) 8.08677e10 1.43767 0.718835 0.695181i \(-0.244676\pi\)
0.718835 + 0.695181i \(0.244676\pi\)
\(488\) 4.51925e10 0.796869
\(489\) 4.53975e10 0.793956
\(490\) 2.02216e10i 0.350777i
\(491\) 2.29280e9 0.0394493 0.0197247 0.999805i \(-0.493721\pi\)
0.0197247 + 0.999805i \(0.493721\pi\)
\(492\) 6.76915e10 1.15524
\(493\) 2.11652e10 0.358290
\(494\) −2.31278e11 −3.88353
\(495\) 5.07979e9i 0.0846106i
\(496\) 6.95801e10i 1.14963i
\(497\) −7.59778e10 −1.24526
\(498\) −4.32403e10 −0.703025
\(499\) 9.12096e10 1.47109 0.735544 0.677477i \(-0.236927\pi\)
0.735544 + 0.677477i \(0.236927\pi\)
\(500\) −1.34298e11 −2.14877
\(501\) 6.01302e10 0.954424
\(502\) 1.99488e11i 3.14125i
\(503\) 4.30436e10i 0.672414i −0.941788 0.336207i \(-0.890856\pi\)
0.941788 0.336207i \(-0.109144\pi\)
\(504\) 4.72987e10i 0.733039i
\(505\) 3.52612e10i 0.542165i
\(506\) 5.16505e10i 0.787903i
\(507\) 7.43512e10 1.12527
\(508\) −1.52035e11 −2.28292
\(509\) 4.82412e10i 0.718699i 0.933203 + 0.359350i \(0.117001\pi\)
−0.933203 + 0.359350i \(0.882999\pi\)
\(510\) 3.33279e10i 0.492637i
\(511\) 5.04627e9i 0.0740093i
\(512\) 1.39967e11i 2.03679i
\(513\) −1.71365e10 −0.247430
\(514\) 8.65282e10i 1.23967i
\(515\) 6.05936e10i 0.861386i
\(516\) 6.94010e10i 0.978965i
\(517\) 4.10792e8 0.00574990
\(518\) −3.91174e10 −0.543314
\(519\) 5.15232e10i 0.710123i
\(520\) −1.57310e11 −2.15150
\(521\) −5.59642e10 −0.759555 −0.379777 0.925078i \(-0.623999\pi\)
−0.379777 + 0.925078i \(0.623999\pi\)
\(522\) 2.09356e10i 0.281970i
\(523\) 9.80172e10 1.31007 0.655037 0.755597i \(-0.272653\pi\)
0.655037 + 0.755597i \(0.272653\pi\)
\(524\) 1.17846e11i 1.56311i
\(525\) 2.88757e10 0.380098
\(526\) 1.14386e11i 1.49428i
\(527\) 5.11915e10i 0.663675i
\(528\) 2.25744e10i 0.290456i
\(529\) −2.50870e10 −0.320350
\(530\) 2.74460e10i 0.347837i
\(531\) 1.31481e10 2.30090e10i 0.165380 0.289414i
\(532\) −2.46464e11 −3.07686
\(533\) 1.32442e11i 1.64103i
\(534\) −1.09161e11 −1.34246
\(535\) 1.49789e10 0.182837
\(536\) 1.05503e11 1.27822
\(537\) 1.01217e10i 0.121718i
\(538\) 3.53020e10 0.421377
\(539\) 1.00771e10i 0.119394i
\(540\) −2.23111e10 −0.262389
\(541\) 8.07791e10i 0.942997i 0.881867 + 0.471498i \(0.156287\pi\)
−0.881867 + 0.471498i \(0.843713\pi\)
\(542\) 2.88400e11i 3.34194i
\(543\) 3.35429e10 0.385834
\(544\) 2.25653e10i 0.257659i
\(545\) 3.62652e10i 0.411058i
\(546\) 1.77141e11 1.99319
\(547\) 1.74965e9 0.0195435 0.00977176 0.999952i \(-0.496890\pi\)
0.00977176 + 0.999952i \(0.496890\pi\)
\(548\) 7.67276e10 0.850803
\(549\) 1.25408e10i 0.138049i
\(550\) 3.61425e10 0.394973
\(551\) −5.69917e10 −0.618309
\(552\) −1.18515e11 −1.27648
\(553\) −9.66412e10 −1.03338
\(554\) 2.57919e11i 2.73807i
\(555\) 9.63970e9i 0.101600i
\(556\) −7.19090e10 −0.752461
\(557\) −1.10540e11 −1.14841 −0.574207 0.818710i \(-0.694690\pi\)
−0.574207 + 0.818710i \(0.694690\pi\)
\(558\) −5.06362e10 −0.522305
\(559\) −1.35787e11 −1.39063
\(560\) −9.44508e10 −0.960403
\(561\) 1.66084e10i 0.167678i
\(562\) 3.33218e11i 3.34028i
\(563\) 5.32954e10i 0.530464i 0.964185 + 0.265232i \(0.0854485\pi\)
−0.964185 + 0.265232i \(0.914551\pi\)
\(564\) 1.80425e9i 0.0178312i
\(565\) 1.23758e11i 1.21445i
\(566\) −2.63015e11 −2.56280
\(567\) 1.31252e10 0.126991
\(568\) 2.18207e11i 2.09641i
\(569\) 5.27709e10i 0.503437i −0.967800 0.251719i \(-0.919004\pi\)
0.967800 0.251719i \(-0.0809957\pi\)
\(570\) 8.97423e10i 0.850155i
\(571\) 8.72877e10i 0.821124i −0.911833 0.410562i \(-0.865333\pi\)
0.911833 0.410562i \(-0.134667\pi\)
\(572\) 1.50056e11 1.40175
\(573\) 4.13561e10i 0.383637i
\(574\) 2.08543e11i 1.92109i
\(575\) 7.23529e10i 0.661888i
\(576\) 2.50310e10 0.227399
\(577\) −7.68360e8 −0.00693205 −0.00346602 0.999994i \(-0.501103\pi\)
−0.00346602 + 0.999994i \(0.501103\pi\)
\(578\) 8.73541e10i 0.782658i
\(579\) −6.78553e10 −0.603768
\(580\) −7.42012e10 −0.655691
\(581\) 9.01570e10i 0.791216i
\(582\) 3.54686e9 0.0309138
\(583\) 1.36773e10i 0.118393i
\(584\) −1.44928e10 −0.124595
\(585\) 4.36528e10i 0.372725i
\(586\) 1.21468e11i 1.03008i
\(587\) 7.08101e10i 0.596407i −0.954502 0.298203i \(-0.903613\pi\)
0.954502 0.298203i \(-0.0963874\pi\)
\(588\) 4.42600e10 0.370256
\(589\) 1.37844e11i 1.14532i
\(590\) 1.20496e11 + 6.88553e10i 0.994410 + 0.568237i
\(591\) 9.74024e10 0.798399
\(592\) 4.28384e10i 0.348776i
\(593\) −7.38587e10 −0.597287 −0.298643 0.954365i \(-0.596534\pi\)
−0.298643 + 0.954365i \(0.596534\pi\)
\(594\) 1.64283e10 0.131961
\(595\) 6.94895e10 0.554435
\(596\) 1.13510e11i 0.899601i
\(597\) −6.02173e10 −0.474050
\(598\) 4.43856e11i 3.47086i
\(599\) −6.39782e10 −0.496963 −0.248482 0.968637i \(-0.579932\pi\)
−0.248482 + 0.968637i \(0.579932\pi\)
\(600\) 8.29307e10i 0.639898i
\(601\) 4.79700e10i 0.367682i −0.982956 0.183841i \(-0.941147\pi\)
0.982956 0.183841i \(-0.0588531\pi\)
\(602\) −2.13810e11 −1.62795
\(603\) 2.92767e10i 0.221438i
\(604\) 4.88093e11i 3.66737i
\(605\) −7.39785e10 −0.552184
\(606\) −1.14036e11 −0.845577
\(607\) −1.76542e11 −1.30045 −0.650223 0.759743i \(-0.725325\pi\)
−0.650223 + 0.759743i \(0.725325\pi\)
\(608\) 6.07619e10i 0.444649i
\(609\) 4.36512e10 0.317342
\(610\) 6.56749e10 0.474329
\(611\) 3.53012e9 0.0253294
\(612\) 7.29464e10 0.519994
\(613\) 1.62572e11i 1.15134i 0.817681 + 0.575672i \(0.195259\pi\)
−0.817681 + 0.575672i \(0.804741\pi\)
\(614\) 1.04942e11i 0.738372i
\(615\) 5.13912e10 0.359243
\(616\) 1.23437e11 0.857281
\(617\) −9.33035e10 −0.643809 −0.321905 0.946772i \(-0.604323\pi\)
−0.321905 + 0.946772i \(0.604323\pi\)
\(618\) 1.95962e11 1.34344
\(619\) 2.34361e11 1.59633 0.798165 0.602439i \(-0.205804\pi\)
0.798165 + 0.602439i \(0.205804\pi\)
\(620\) 1.79468e11i 1.21456i
\(621\) 3.28874e10i 0.221138i
\(622\) 5.02428e11i 3.35670i
\(623\) 2.27603e11i 1.51087i
\(624\) 1.93991e11i 1.27951i
\(625\) −1.40648e10 −0.0921750
\(626\) 4.66517e11 3.03787
\(627\) 4.47217e10i 0.289367i
\(628\) 9.48834e10i 0.610031i
\(629\) 3.15171e10i 0.201346i
\(630\) 6.87357e10i 0.436335i
\(631\) −4.43112e10 −0.279509 −0.139755 0.990186i \(-0.544631\pi\)
−0.139755 + 0.990186i \(0.544631\pi\)
\(632\) 2.77552e11i 1.73971i
\(633\) 6.47243e10i 0.403137i
\(634\) 1.66297e11i 1.02927i
\(635\) −1.15425e11 −0.709913
\(636\) 6.00724e10 0.367153
\(637\) 8.65971e10i 0.525951i
\(638\) 5.46364e10 0.329761
\(639\) −6.05517e10 −0.363181
\(640\) 1.68866e11i 1.00652i
\(641\) −1.26538e11 −0.749528 −0.374764 0.927120i \(-0.622276\pi\)
−0.374764 + 0.927120i \(0.622276\pi\)
\(642\) 4.84425e10i 0.285159i
\(643\) 1.67234e11 0.978317 0.489158 0.872195i \(-0.337304\pi\)
0.489158 + 0.872195i \(0.337304\pi\)
\(644\) 4.73000e11i 2.74990i
\(645\) 5.26891e10i 0.304426i
\(646\) 2.93414e11i 1.68481i
\(647\) 1.60905e10 0.0918233 0.0459116 0.998946i \(-0.485381\pi\)
0.0459116 + 0.998946i \(0.485381\pi\)
\(648\) 3.76955e10i 0.213791i
\(649\) −6.00475e10 3.43130e10i −0.338467 0.193410i
\(650\) 3.10589e11 1.73993
\(651\) 1.05578e11i 0.587826i
\(652\) 5.20360e11 2.87948
\(653\) 1.82713e11 1.00489 0.502444 0.864610i \(-0.332434\pi\)
0.502444 + 0.864610i \(0.332434\pi\)
\(654\) 1.17283e11 0.641099
\(655\) 8.94684e10i 0.486076i
\(656\) 2.28381e11 1.23323
\(657\) 4.02170e9i 0.0215848i
\(658\) 5.55852e9 0.0296521
\(659\) 1.16823e11i 0.619425i 0.950830 + 0.309712i \(0.100233\pi\)
−0.950830 + 0.309712i \(0.899767\pi\)
\(660\) 5.82261e10i 0.306861i
\(661\) −2.78164e10 −0.145712 −0.0728560 0.997342i \(-0.523211\pi\)
−0.0728560 + 0.997342i \(0.523211\pi\)
\(662\) 2.46062e11i 1.28119i
\(663\) 1.42724e11i 0.738655i
\(664\) −2.58930e11 −1.33202
\(665\) −1.87115e11 −0.956802
\(666\) −3.11752e10 −0.158458
\(667\) 1.09375e11i 0.552606i
\(668\) 6.89230e11 3.46145
\(669\) 2.10080e11 1.04877
\(670\) 1.53320e11 0.760849
\(671\) −3.27281e10 −0.161447
\(672\) 4.65389e10i 0.228212i
\(673\) 1.70203e11i 0.829675i −0.909896 0.414837i \(-0.863838\pi\)
0.909896 0.414837i \(-0.136162\pi\)
\(674\) −2.67568e11 −1.29657
\(675\) 2.30130e10 0.110856
\(676\) 8.52236e11 4.08106
\(677\) −1.60157e11 −0.762413 −0.381207 0.924490i \(-0.624491\pi\)
−0.381207 + 0.924490i \(0.624491\pi\)
\(678\) −4.00239e11 −1.89409
\(679\) 7.39530e9i 0.0347918i
\(680\) 1.99573e11i 0.933396i
\(681\) 1.10924e11i 0.515749i
\(682\) 1.32147e11i 0.610831i
\(683\) 3.49843e11i 1.60765i −0.594868 0.803823i \(-0.702796\pi\)
0.594868 0.803823i \(-0.297204\pi\)
\(684\) −1.96424e11 −0.897365
\(685\) 5.82514e10 0.264572
\(686\) 3.08856e11i 1.39463i
\(687\) 8.10410e10i 0.363813i
\(688\) 2.34148e11i 1.04505i
\(689\) 1.17535e11i 0.521543i
\(690\) −1.72228e11 −0.759816
\(691\) 1.43170e11i 0.627973i 0.949427 + 0.313987i \(0.101665\pi\)
−0.949427 + 0.313987i \(0.898335\pi\)
\(692\) 5.90575e11i 2.57543i
\(693\) 3.42534e10i 0.148515i
\(694\) −4.40045e11 −1.89696
\(695\) −5.45931e10 −0.233991
\(696\) 1.25366e11i 0.534247i
\(697\) −1.68024e11 −0.711936
\(698\) 2.95568e11 1.24519
\(699\) 4.60733e10i 0.192992i
\(700\) 3.30982e11 1.37852
\(701\) 1.34207e11i 0.555781i −0.960613 0.277891i \(-0.910365\pi\)
0.960613 0.277891i \(-0.0896353\pi\)
\(702\) 1.41175e11 0.581314
\(703\) 8.48665e10i 0.347468i
\(704\) 6.53244e10i 0.265941i
\(705\) 1.36978e9i 0.00554493i
\(706\) −4.99265e11 −2.00961
\(707\) 2.37769e11i 0.951650i
\(708\) 1.50707e11 2.63736e11i 0.599792 1.04963i
\(709\) 2.30261e11 0.911245 0.455623 0.890173i \(-0.349417\pi\)
0.455623 + 0.890173i \(0.349417\pi\)
\(710\) 3.17104e11i 1.24787i
\(711\) −7.70198e10 −0.301387
\(712\) −6.53674e11 −2.54356
\(713\) −2.64542e11 −1.02362
\(714\) 2.24732e11i 0.864714i
\(715\) 1.13922e11 0.435898
\(716\) 1.16018e11i 0.441442i
\(717\) 4.84092e10 0.183169
\(718\) 4.36515e11i 1.64248i
\(719\) 3.23619e11i 1.21093i 0.795873 + 0.605464i \(0.207012\pi\)
−0.795873 + 0.605464i \(0.792988\pi\)
\(720\) −7.52741e10 −0.280102
\(721\) 4.08587e11i 1.51197i
\(722\) 3.12107e11i 1.14856i
\(723\) 2.22759e11 0.815232
\(724\) 3.84478e11 1.39932
\(725\) 7.65355e10 0.277020
\(726\) 2.39250e11i 0.861203i
\(727\) −8.18255e10 −0.292921 −0.146461 0.989216i \(-0.546788\pi\)
−0.146461 + 0.989216i \(0.546788\pi\)
\(728\) 1.06075e12 3.77648
\(729\) 1.04604e10 0.0370370
\(730\) −2.10613e10 −0.0741642
\(731\) 1.72268e11i 0.603302i
\(732\) 1.43746e11i 0.500669i
\(733\) −5.06458e10 −0.175440 −0.0877198 0.996145i \(-0.527958\pi\)
−0.0877198 + 0.996145i \(0.527958\pi\)
\(734\) −8.68095e11 −2.99077
\(735\) 3.36021e10 0.115138
\(736\) −1.16611e11 −0.397400
\(737\) −7.64045e10 −0.258970
\(738\) 1.66202e11i 0.560286i
\(739\) 2.40198e11i 0.805363i 0.915340 + 0.402682i \(0.131922\pi\)
−0.915340 + 0.402682i \(0.868078\pi\)
\(740\) 1.10493e11i 0.368475i
\(741\) 3.84313e11i 1.27471i
\(742\) 1.85070e11i 0.610550i
\(743\) −7.18154e10 −0.235647 −0.117824 0.993035i \(-0.537592\pi\)
−0.117824 + 0.993035i \(0.537592\pi\)
\(744\) −3.03218e11 −0.989609
\(745\) 8.61768e10i 0.279747i
\(746\) 4.24746e11i 1.37143i
\(747\) 7.18521e10i 0.230758i
\(748\) 1.90371e11i 0.608127i
\(749\) −1.01004e11 −0.320930
\(750\) 3.29740e11i 1.04214i
\(751\) 2.61941e11i 0.823461i 0.911306 + 0.411731i \(0.135076\pi\)
−0.911306 + 0.411731i \(0.864924\pi\)
\(752\) 6.08727e9i 0.0190349i
\(753\) −3.31489e11 −1.03107
\(754\) 4.69515e11 1.45266
\(755\) 3.70559e11i 1.14043i
\(756\) 1.50445e11 0.460565
\(757\) −2.95970e11 −0.901290 −0.450645 0.892703i \(-0.648806\pi\)
−0.450645 + 0.892703i \(0.648806\pi\)
\(758\) 7.69832e11i 2.33195i
\(759\) 8.58274e10 0.258618
\(760\) 5.37392e11i 1.61078i
\(761\) 2.40603e11 0.717402 0.358701 0.933453i \(-0.383220\pi\)
0.358701 + 0.933453i \(0.383220\pi\)
\(762\) 3.73290e11i 1.10720i
\(763\) 2.44538e11i 0.721521i
\(764\) 4.74036e11i 1.39135i
\(765\) 5.53807e10 0.161701
\(766\) 4.37258e11i 1.27005i
\(767\) −5.16014e11 2.94866e11i −1.49101 0.852008i
\(768\) 4.09099e11 1.17593
\(769\) 5.22952e11i 1.49540i −0.664038 0.747699i \(-0.731159\pi\)
0.664038 0.747699i \(-0.268841\pi\)
\(770\) 1.79382e11 0.510289
\(771\) −1.43784e11 −0.406904
\(772\) −7.77778e11 −2.18971
\(773\) 2.34322e11i 0.656289i −0.944628 0.328144i \(-0.893577\pi\)
0.944628 0.328144i \(-0.106423\pi\)
\(774\) −1.70399e11 −0.474792
\(775\) 1.85114e11i 0.513136i
\(776\) 2.12392e10 0.0585722
\(777\) 6.50012e10i 0.178335i
\(778\) 2.98265e11i 0.814111i
\(779\) 4.52441e11 1.22860
\(780\) 5.00362e11i 1.35178i
\(781\) 1.58024e11i 0.424736i
\(782\) 5.63103e11 1.50578