Properties

Label 192.11.e.h.65.4
Level $192$
Weight $11$
Character 192.65
Analytic conductor $121.989$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 192.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(121.988592513\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{85})\)
Defining polynomial: \( x^{4} - 2x^{3} - 37x^{2} + 38x + 531 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{14}\cdot 3^{6} \)
Twist minimal: no (minimal twist has level 6)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 65.4
Root \(5.10977 + 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 192.65
Dual form 192.11.e.h.65.3

$q$-expansion

\(f(q)\) \(=\) \(q+(242.269 + 18.8335i) q^{3} -4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} +O(q^{10})\) \(q+(242.269 + 18.8335i) q^{3} -4818.41i q^{5} -670.530 q^{7} +(58339.6 + 9125.53i) q^{9} -233268. i q^{11} -307781. q^{13} +(90747.4 - 1.16735e6i) q^{15} -672324. i q^{17} -1.55119e6 q^{19} +(-162449. - 12628.4i) q^{21} +5.57551e6i q^{23} -1.34515e7 q^{25} +(1.39620e7 + 3.30957e6i) q^{27} -2.97313e7i q^{29} -3.09368e7 q^{31} +(4.39325e6 - 5.65137e7i) q^{33} +3.23089e6i q^{35} +8.56690e7 q^{37} +(-7.45657e7 - 5.79657e6i) q^{39} -3.59054e7i q^{41} -3.66253e7 q^{43} +(4.39706e7 - 2.81104e8i) q^{45} +3.28877e7i q^{47} -2.82026e8 q^{49} +(1.26622e7 - 1.62883e8i) q^{51} +4.59194e8i q^{53} -1.12398e9 q^{55} +(-3.75805e8 - 2.92143e7i) q^{57} +4.88657e8i q^{59} +6.12928e7 q^{61} +(-3.91184e7 - 6.11894e6i) q^{63} +1.48301e9i q^{65} -6.70776e8 q^{67} +(-1.05006e8 + 1.35077e9i) q^{69} +1.23330e9i q^{71} +1.08126e9 q^{73} +(-3.25888e9 - 2.53338e8i) q^{75} +1.56413e8i q^{77} +1.86628e9 q^{79} +(3.32023e9 + 1.06476e9i) q^{81} +1.09562e9i q^{83} -3.23953e9 q^{85} +(5.59944e8 - 7.20298e9i) q^{87} -5.19876e9i q^{89} +2.06376e8 q^{91} +(-7.49503e9 - 5.82647e8i) q^{93} +7.47427e9i q^{95} -1.07471e10 q^{97} +(2.12870e9 - 1.36088e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 84 q^{3} + 45112 q^{7} + 159012 q^{9} - 275240 q^{13} + 1180800 q^{15} - 1568728 q^{19} - 9628008 q^{21} - 33732380 q^{25} + 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} + 71014168 q^{37} - 217287240 q^{39} - 470688664 q^{43} - 312318720 q^{45} - 50058420 q^{49} - 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} + 1184038744 q^{61} + 905007096 q^{63} - 297365848 q^{67} - 596268288 q^{69} + 6534269000 q^{73} - 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} + 12880512000 q^{85} - 210268800 q^{87} + 8317232080 q^{91} - 31744468392 q^{93} - 39176355064 q^{97} - 2626912512 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 242.269 + 18.8335i 0.996992 + 0.0775039i
\(4\) 0 0
\(5\) 4818.41i 1.54189i −0.636900 0.770946i \(-0.719784\pi\)
0.636900 0.770946i \(-0.280216\pi\)
\(6\) 0 0
\(7\) −670.530 −0.0398959 −0.0199479 0.999801i \(-0.506350\pi\)
−0.0199479 + 0.999801i \(0.506350\pi\)
\(8\) 0 0
\(9\) 58339.6 + 9125.53i 0.987986 + 0.154542i
\(10\) 0 0
\(11\) 233268.i 1.44841i −0.689583 0.724206i \(-0.742206\pi\)
0.689583 0.724206i \(-0.257794\pi\)
\(12\) 0 0
\(13\) −307781. −0.828943 −0.414471 0.910062i \(-0.636033\pi\)
−0.414471 + 0.910062i \(0.636033\pi\)
\(14\) 0 0
\(15\) 90747.4 1.16735e6i 0.119503 1.53725i
\(16\) 0 0
\(17\) 672324.i 0.473515i −0.971569 0.236758i \(-0.923915\pi\)
0.971569 0.236758i \(-0.0760847\pi\)
\(18\) 0 0
\(19\) −1.55119e6 −0.626465 −0.313233 0.949676i \(-0.601412\pi\)
−0.313233 + 0.949676i \(0.601412\pi\)
\(20\) 0 0
\(21\) −162449. 12628.4i −0.0397758 0.00309209i
\(22\) 0 0
\(23\) 5.57551e6i 0.866255i 0.901333 + 0.433127i \(0.142590\pi\)
−0.901333 + 0.433127i \(0.857410\pi\)
\(24\) 0 0
\(25\) −1.34515e7 −1.37743
\(26\) 0 0
\(27\) 1.39620e7 + 3.30957e6i 0.973037 + 0.230650i
\(28\) 0 0
\(29\) 2.97313e7i 1.44952i −0.689001 0.724760i \(-0.741951\pi\)
0.689001 0.724760i \(-0.258049\pi\)
\(30\) 0 0
\(31\) −3.09368e7 −1.08061 −0.540303 0.841471i \(-0.681690\pi\)
−0.540303 + 0.841471i \(0.681690\pi\)
\(32\) 0 0
\(33\) 4.39325e6 5.65137e7i 0.112258 1.44406i
\(34\) 0 0
\(35\) 3.23089e6i 0.0615151i
\(36\) 0 0
\(37\) 8.56690e7 1.23542 0.617711 0.786406i \(-0.288060\pi\)
0.617711 + 0.786406i \(0.288060\pi\)
\(38\) 0 0
\(39\) −7.45657e7 5.79657e6i −0.826449 0.0642463i
\(40\) 0 0
\(41\) 3.59054e7i 0.309913i −0.987921 0.154957i \(-0.950476\pi\)
0.987921 0.154957i \(-0.0495238\pi\)
\(42\) 0 0
\(43\) −3.66253e7 −0.249137 −0.124569 0.992211i \(-0.539755\pi\)
−0.124569 + 0.992211i \(0.539755\pi\)
\(44\) 0 0
\(45\) 4.39706e7 2.81104e8i 0.238287 1.52337i
\(46\) 0 0
\(47\) 3.28877e7i 0.143398i 0.997426 + 0.0716992i \(0.0228421\pi\)
−0.997426 + 0.0716992i \(0.977158\pi\)
\(48\) 0 0
\(49\) −2.82026e8 −0.998408
\(50\) 0 0
\(51\) 1.26622e7 1.62883e8i 0.0366993 0.472091i
\(52\) 0 0
\(53\) 4.59194e8i 1.09804i 0.835810 + 0.549019i \(0.184998\pi\)
−0.835810 + 0.549019i \(0.815002\pi\)
\(54\) 0 0
\(55\) −1.12398e9 −2.23330
\(56\) 0 0
\(57\) −3.75805e8 2.92143e7i −0.624581 0.0485535i
\(58\) 0 0
\(59\) 4.88657e8i 0.683508i 0.939789 + 0.341754i \(0.111021\pi\)
−0.939789 + 0.341754i \(0.888979\pi\)
\(60\) 0 0
\(61\) 6.12928e7 0.0725705 0.0362852 0.999341i \(-0.488448\pi\)
0.0362852 + 0.999341i \(0.488448\pi\)
\(62\) 0 0
\(63\) −3.91184e7 6.11894e6i −0.0394166 0.00616557i
\(64\) 0 0
\(65\) 1.48301e9i 1.27814i
\(66\) 0 0
\(67\) −6.70776e8 −0.496825 −0.248413 0.968654i \(-0.579909\pi\)
−0.248413 + 0.968654i \(0.579909\pi\)
\(68\) 0 0
\(69\) −1.05006e8 + 1.35077e9i −0.0671382 + 0.863649i
\(70\) 0 0
\(71\) 1.23330e9i 0.683561i 0.939780 + 0.341781i \(0.111030\pi\)
−0.939780 + 0.341781i \(0.888970\pi\)
\(72\) 0 0
\(73\) 1.08126e9 0.521573 0.260787 0.965396i \(-0.416018\pi\)
0.260787 + 0.965396i \(0.416018\pi\)
\(74\) 0 0
\(75\) −3.25888e9 2.53338e8i −1.37329 0.106756i
\(76\) 0 0
\(77\) 1.56413e8i 0.0577857i
\(78\) 0 0
\(79\) 1.86628e9 0.606515 0.303258 0.952909i \(-0.401926\pi\)
0.303258 + 0.952909i \(0.401926\pi\)
\(80\) 0 0
\(81\) 3.32023e9 + 1.06476e9i 0.952234 + 0.305370i
\(82\) 0 0
\(83\) 1.09562e9i 0.278145i 0.990282 + 0.139072i \(0.0444121\pi\)
−0.990282 + 0.139072i \(0.955588\pi\)
\(84\) 0 0
\(85\) −3.23953e9 −0.730109
\(86\) 0 0
\(87\) 5.59944e8 7.20298e9i 0.112344 1.44516i
\(88\) 0 0
\(89\) 5.19876e9i 0.931000i −0.885048 0.465500i \(-0.845874\pi\)
0.885048 0.465500i \(-0.154126\pi\)
\(90\) 0 0
\(91\) 2.06376e8 0.0330714
\(92\) 0 0
\(93\) −7.49503e9 5.82647e8i −1.07735 0.0837512i
\(94\) 0 0
\(95\) 7.47427e9i 0.965941i
\(96\) 0 0
\(97\) −1.07471e10 −1.25150 −0.625750 0.780024i \(-0.715207\pi\)
−0.625750 + 0.780024i \(0.715207\pi\)
\(98\) 0 0
\(99\) 2.12870e9 1.36088e10i 0.223840 1.43101i
\(100\) 0 0
\(101\) 1.08154e10i 1.02905i −0.857475 0.514525i \(-0.827968\pi\)
0.857475 0.514525i \(-0.172032\pi\)
\(102\) 0 0
\(103\) 2.83446e9 0.244503 0.122251 0.992499i \(-0.460989\pi\)
0.122251 + 0.992499i \(0.460989\pi\)
\(104\) 0 0
\(105\) −6.08488e7 + 7.82744e8i −0.00476766 + 0.0613301i
\(106\) 0 0
\(107\) 2.41202e10i 1.71974i 0.510515 + 0.859869i \(0.329455\pi\)
−0.510515 + 0.859869i \(0.670545\pi\)
\(108\) 0 0
\(109\) 5.43424e9 0.353188 0.176594 0.984284i \(-0.443492\pi\)
0.176594 + 0.984284i \(0.443492\pi\)
\(110\) 0 0
\(111\) 2.07549e10 + 1.61344e9i 1.23170 + 0.0957500i
\(112\) 0 0
\(113\) 1.39305e10i 0.756092i −0.925787 0.378046i \(-0.876596\pi\)
0.925787 0.378046i \(-0.123404\pi\)
\(114\) 0 0
\(115\) 2.68651e10 1.33567
\(116\) 0 0
\(117\) −1.79558e10 2.80866e9i −0.818984 0.128106i
\(118\) 0 0
\(119\) 4.50813e8i 0.0188913i
\(120\) 0 0
\(121\) −2.84767e10 −1.09790
\(122\) 0 0
\(123\) 6.76223e8 8.69877e9i 0.0240195 0.308981i
\(124\) 0 0
\(125\) 1.77600e10i 0.581958i
\(126\) 0 0
\(127\) −4.08412e10 −1.23617 −0.618087 0.786110i \(-0.712092\pi\)
−0.618087 + 0.786110i \(0.712092\pi\)
\(128\) 0 0
\(129\) −8.87317e9 6.89781e8i −0.248388 0.0193091i
\(130\) 0 0
\(131\) 4.15498e10i 1.07699i −0.842628 0.538495i \(-0.818993\pi\)
0.842628 0.538495i \(-0.181007\pi\)
\(132\) 0 0
\(133\) 1.04012e9 0.0249934
\(134\) 0 0
\(135\) 1.59469e10 6.72748e10i 0.355637 1.50032i
\(136\) 0 0
\(137\) 9.25532e10i 1.91773i 0.283854 + 0.958867i \(0.408387\pi\)
−0.283854 + 0.958867i \(0.591613\pi\)
\(138\) 0 0
\(139\) 7.95575e10 1.53323 0.766615 0.642107i \(-0.221939\pi\)
0.766615 + 0.642107i \(0.221939\pi\)
\(140\) 0 0
\(141\) −6.19389e8 + 7.96767e9i −0.0111139 + 0.142967i
\(142\) 0 0
\(143\) 7.17955e10i 1.20065i
\(144\) 0 0
\(145\) −1.43258e11 −2.23500
\(146\) 0 0
\(147\) −6.83261e10 5.31152e9i −0.995405 0.0773806i
\(148\) 0 0
\(149\) 8.07804e10i 1.09995i 0.835180 + 0.549977i \(0.185364\pi\)
−0.835180 + 0.549977i \(0.814636\pi\)
\(150\) 0 0
\(151\) −3.08654e10 −0.393176 −0.196588 0.980486i \(-0.562986\pi\)
−0.196588 + 0.980486i \(0.562986\pi\)
\(152\) 0 0
\(153\) 6.13531e9 3.92231e10i 0.0731778 0.467827i
\(154\) 0 0
\(155\) 1.49066e11i 1.66618i
\(156\) 0 0
\(157\) −9.71322e10 −1.01828 −0.509138 0.860685i \(-0.670036\pi\)
−0.509138 + 0.860685i \(0.670036\pi\)
\(158\) 0 0
\(159\) −8.64822e9 + 1.11249e11i −0.0851023 + 1.09473i
\(160\) 0 0
\(161\) 3.73855e9i 0.0345600i
\(162\) 0 0
\(163\) −1.39440e11 −1.21185 −0.605927 0.795520i \(-0.707198\pi\)
−0.605927 + 0.795520i \(0.707198\pi\)
\(164\) 0 0
\(165\) −2.72306e11 2.11685e10i −2.22658 0.173089i
\(166\) 0 0
\(167\) 1.25840e11i 0.968804i −0.874845 0.484402i \(-0.839037\pi\)
0.874845 0.484402i \(-0.160963\pi\)
\(168\) 0 0
\(169\) −4.31296e10 −0.312854
\(170\) 0 0
\(171\) −9.04958e10 1.41554e10i −0.618939 0.0968149i
\(172\) 0 0
\(173\) 1.26257e11i 0.814750i −0.913261 0.407375i \(-0.866444\pi\)
0.913261 0.407375i \(-0.133556\pi\)
\(174\) 0 0
\(175\) 9.01961e9 0.0549538
\(176\) 0 0
\(177\) −9.20310e9 + 1.18386e11i −0.0529746 + 0.681452i
\(178\) 0 0
\(179\) 2.96543e11i 1.61370i −0.590758 0.806848i \(-0.701171\pi\)
0.590758 0.806848i \(-0.298829\pi\)
\(180\) 0 0
\(181\) −2.48451e11 −1.27893 −0.639466 0.768819i \(-0.720845\pi\)
−0.639466 + 0.768819i \(0.720845\pi\)
\(182\) 0 0
\(183\) 1.48493e10 + 1.15435e9i 0.0723522 + 0.00562450i
\(184\) 0 0
\(185\) 4.12789e11i 1.90489i
\(186\) 0 0
\(187\) −1.56832e11 −0.685846
\(188\) 0 0
\(189\) −9.36194e9 2.21916e9i −0.0388201 0.00920196i
\(190\) 0 0
\(191\) 1.58050e11i 0.621769i −0.950448 0.310884i \(-0.899375\pi\)
0.950448 0.310884i \(-0.100625\pi\)
\(192\) 0 0
\(193\) −3.78369e11 −1.41296 −0.706479 0.707734i \(-0.749717\pi\)
−0.706479 + 0.707734i \(0.749717\pi\)
\(194\) 0 0
\(195\) −2.79303e10 + 3.59288e11i −0.0990609 + 1.27430i
\(196\) 0 0
\(197\) 1.89406e11i 0.638356i −0.947695 0.319178i \(-0.896593\pi\)
0.947695 0.319178i \(-0.103407\pi\)
\(198\) 0 0
\(199\) −5.02942e10 −0.161158 −0.0805791 0.996748i \(-0.525677\pi\)
−0.0805791 + 0.996748i \(0.525677\pi\)
\(200\) 0 0
\(201\) −1.62508e11 1.26330e10i −0.495331 0.0385059i
\(202\) 0 0
\(203\) 1.99357e10i 0.0578298i
\(204\) 0 0
\(205\) −1.73007e11 −0.477853
\(206\) 0 0
\(207\) −5.08795e10 + 3.25273e11i −0.133872 + 0.855848i
\(208\) 0 0
\(209\) 3.61843e11i 0.907380i
\(210\) 0 0
\(211\) 4.74970e11 1.13567 0.567837 0.823141i \(-0.307780\pi\)
0.567837 + 0.823141i \(0.307780\pi\)
\(212\) 0 0
\(213\) −2.32273e10 + 2.98791e11i −0.0529787 + 0.681505i
\(214\) 0 0
\(215\) 1.76476e11i 0.384143i
\(216\) 0 0
\(217\) 2.07440e10 0.0431117
\(218\) 0 0
\(219\) 2.61955e11 + 2.03638e10i 0.520004 + 0.0404240i
\(220\) 0 0
\(221\) 2.06928e11i 0.392517i
\(222\) 0 0
\(223\) 2.35580e11 0.427183 0.213592 0.976923i \(-0.431484\pi\)
0.213592 + 0.976923i \(0.431484\pi\)
\(224\) 0 0
\(225\) −7.84754e11 1.22752e11i −1.36088 0.212870i
\(226\) 0 0
\(227\) 4.27026e11i 0.708475i −0.935155 0.354238i \(-0.884740\pi\)
0.935155 0.354238i \(-0.115260\pi\)
\(228\) 0 0
\(229\) −1.03671e12 −1.64619 −0.823096 0.567902i \(-0.807755\pi\)
−0.823096 + 0.567902i \(0.807755\pi\)
\(230\) 0 0
\(231\) −2.94580e9 + 3.78941e10i −0.00447862 + 0.0576119i
\(232\) 0 0
\(233\) 1.03766e12i 1.51103i 0.655130 + 0.755516i \(0.272614\pi\)
−0.655130 + 0.755516i \(0.727386\pi\)
\(234\) 0 0
\(235\) 1.58466e11 0.221105
\(236\) 0 0
\(237\) 4.52142e11 + 3.51485e10i 0.604691 + 0.0470073i
\(238\) 0 0
\(239\) 1.23687e12i 1.58612i −0.609144 0.793060i \(-0.708487\pi\)
0.609144 0.793060i \(-0.291513\pi\)
\(240\) 0 0
\(241\) −1.03912e12 −1.27814 −0.639072 0.769147i \(-0.720682\pi\)
−0.639072 + 0.769147i \(0.720682\pi\)
\(242\) 0 0
\(243\) 7.84337e11 + 3.20490e11i 0.925702 + 0.378253i
\(244\) 0 0
\(245\) 1.35892e12i 1.53944i
\(246\) 0 0
\(247\) 4.77426e11 0.519304
\(248\) 0 0
\(249\) −2.06344e10 + 2.65436e11i −0.0215573 + 0.277308i
\(250\) 0 0
\(251\) 5.66781e11i 0.568914i −0.958689 0.284457i \(-0.908187\pi\)
0.958689 0.284457i \(-0.0918133\pi\)
\(252\) 0 0
\(253\) 1.30059e12 1.25469
\(254\) 0 0
\(255\) −7.84839e11 6.10116e10i −0.727913 0.0565864i
\(256\) 0 0
\(257\) 1.27943e12i 1.14117i −0.821239 0.570584i \(-0.806717\pi\)
0.821239 0.570584i \(-0.193283\pi\)
\(258\) 0 0
\(259\) −5.74436e10 −0.0492882
\(260\) 0 0
\(261\) 2.71314e11 1.73451e12i 0.224011 1.43211i
\(262\) 0 0
\(263\) 1.68583e12i 1.33978i 0.742459 + 0.669892i \(0.233660\pi\)
−0.742459 + 0.669892i \(0.766340\pi\)
\(264\) 0 0
\(265\) 2.21259e12 1.69306
\(266\) 0 0
\(267\) 9.79107e10 1.25950e12i 0.0721562 0.928200i
\(268\) 0 0
\(269\) 1.34023e12i 0.951523i −0.879574 0.475761i \(-0.842173\pi\)
0.879574 0.475761i \(-0.157827\pi\)
\(270\) 0 0
\(271\) 1.75349e12 1.19966 0.599829 0.800129i \(-0.295235\pi\)
0.599829 + 0.800129i \(0.295235\pi\)
\(272\) 0 0
\(273\) 4.99985e10 + 3.88677e9i 0.0329719 + 0.00256316i
\(274\) 0 0
\(275\) 3.13780e12i 1.99509i
\(276\) 0 0
\(277\) −1.69580e12 −1.03986 −0.519930 0.854209i \(-0.674042\pi\)
−0.519930 + 0.854209i \(0.674042\pi\)
\(278\) 0 0
\(279\) −1.80484e12 2.82315e11i −1.06762 0.166999i
\(280\) 0 0
\(281\) 2.44175e11i 0.139370i −0.997569 0.0696851i \(-0.977801\pi\)
0.997569 0.0696851i \(-0.0221995\pi\)
\(282\) 0 0
\(283\) −9.96409e11 −0.548916 −0.274458 0.961599i \(-0.588498\pi\)
−0.274458 + 0.961599i \(0.588498\pi\)
\(284\) 0 0
\(285\) −1.40766e11 + 1.81078e12i −0.0748643 + 0.963036i
\(286\) 0 0
\(287\) 2.40756e10i 0.0123643i
\(288\) 0 0
\(289\) 1.56397e12 0.775783
\(290\) 0 0
\(291\) −2.60368e12 2.02404e11i −1.24774 0.0969962i
\(292\) 0 0
\(293\) 1.57571e12i 0.729690i −0.931068 0.364845i \(-0.881122\pi\)
0.931068 0.364845i \(-0.118878\pi\)
\(294\) 0 0
\(295\) 2.35455e12 1.05390
\(296\) 0 0
\(297\) 7.72018e11 3.25690e12i 0.334076 1.40936i
\(298\) 0 0
\(299\) 1.71603e12i 0.718076i
\(300\) 0 0
\(301\) 2.45583e10 0.00993955
\(302\) 0 0
\(303\) 2.03692e11 2.62024e12i 0.0797554 1.02595i
\(304\) 0 0
\(305\) 2.95334e11i 0.111896i
\(306\) 0 0
\(307\) −3.29823e12 −1.20945 −0.604726 0.796434i \(-0.706717\pi\)
−0.604726 + 0.796434i \(0.706717\pi\)
\(308\) 0 0
\(309\) 6.86702e11 + 5.33827e10i 0.243768 + 0.0189499i
\(310\) 0 0
\(311\) 1.67301e12i 0.575038i 0.957775 + 0.287519i \(0.0928304\pi\)
−0.957775 + 0.287519i \(0.907170\pi\)
\(312\) 0 0
\(313\) 1.73318e12 0.576930 0.288465 0.957490i \(-0.406855\pi\)
0.288465 + 0.957490i \(0.406855\pi\)
\(314\) 0 0
\(315\) −2.94836e10 + 1.88489e11i −0.00950664 + 0.0607761i
\(316\) 0 0
\(317\) 1.33100e12i 0.415798i −0.978150 0.207899i \(-0.933337\pi\)
0.978150 0.207899i \(-0.0666625\pi\)
\(318\) 0 0
\(319\) −6.93538e12 −2.09950
\(320\) 0 0
\(321\) −4.54267e11 + 5.84358e12i −0.133286 + 1.71456i
\(322\) 0 0
\(323\) 1.04290e12i 0.296641i
\(324\) 0 0
\(325\) 4.14010e12 1.14181
\(326\) 0 0
\(327\) 1.31655e12 + 1.02345e11i 0.352126 + 0.0273735i
\(328\) 0 0
\(329\) 2.20522e10i 0.00572100i
\(330\) 0 0
\(331\) 4.71961e12 1.18786 0.593931 0.804516i \(-0.297575\pi\)
0.593931 + 0.804516i \(0.297575\pi\)
\(332\) 0 0
\(333\) 4.99789e12 + 7.81775e11i 1.22058 + 0.190924i
\(334\) 0 0
\(335\) 3.23208e12i 0.766051i
\(336\) 0 0
\(337\) 4.15283e12 0.955422 0.477711 0.878517i \(-0.341467\pi\)
0.477711 + 0.878517i \(0.341467\pi\)
\(338\) 0 0
\(339\) 2.62360e11 3.37493e12i 0.0586001 0.753818i
\(340\) 0 0
\(341\) 7.21658e12i 1.56516i
\(342\) 0 0
\(343\) 3.78515e11 0.0797282
\(344\) 0 0
\(345\) 6.50859e12 + 5.05963e11i 1.33165 + 0.103520i
\(346\) 0 0
\(347\) 4.39939e12i 0.874470i 0.899347 + 0.437235i \(0.144042\pi\)
−0.899347 + 0.437235i \(0.855958\pi\)
\(348\) 0 0
\(349\) 9.24002e12 1.78462 0.892310 0.451423i \(-0.149083\pi\)
0.892310 + 0.451423i \(0.149083\pi\)
\(350\) 0 0
\(351\) −4.29724e12 1.01862e12i −0.806592 0.191195i
\(352\) 0 0
\(353\) 9.20733e11i 0.167981i −0.996467 0.0839905i \(-0.973233\pi\)
0.996467 0.0839905i \(-0.0267665\pi\)
\(354\) 0 0
\(355\) 5.94255e12 1.05398
\(356\) 0 0
\(357\) −8.49037e9 + 1.09218e11i −0.00146415 + 0.0188345i
\(358\) 0 0
\(359\) 6.17595e12i 1.03569i −0.855473 0.517847i \(-0.826733\pi\)
0.855473 0.517847i \(-0.173267\pi\)
\(360\) 0 0
\(361\) −3.72488e12 −0.607542
\(362\) 0 0
\(363\) −6.89902e12 5.36315e11i −1.09460 0.0850916i
\(364\) 0 0
\(365\) 5.20995e12i 0.804209i
\(366\) 0 0
\(367\) 8.19379e12 1.23071 0.615353 0.788252i \(-0.289013\pi\)
0.615353 + 0.788252i \(0.289013\pi\)
\(368\) 0 0
\(369\) 3.27656e11 2.09471e12i 0.0478945 0.306190i
\(370\) 0 0
\(371\) 3.07903e11i 0.0438072i
\(372\) 0 0
\(373\) 9.07322e12 1.25666 0.628329 0.777947i \(-0.283739\pi\)
0.628329 + 0.777947i \(0.283739\pi\)
\(374\) 0 0
\(375\) −3.34481e11 + 4.30269e12i −0.0451041 + 0.580208i
\(376\) 0 0
\(377\) 9.15072e12i 1.20157i
\(378\) 0 0
\(379\) 1.17817e13 1.50665 0.753324 0.657650i \(-0.228449\pi\)
0.753324 + 0.657650i \(0.228449\pi\)
\(380\) 0 0
\(381\) −9.89455e12 7.69180e11i −1.23246 0.0958083i
\(382\) 0 0
\(383\) 6.82336e12i 0.827950i 0.910288 + 0.413975i \(0.135860\pi\)
−0.910288 + 0.413975i \(0.864140\pi\)
\(384\) 0 0
\(385\) 7.53664e11 0.0890993
\(386\) 0 0
\(387\) −2.13670e12 3.34225e11i −0.246144 0.0385021i
\(388\) 0 0
\(389\) 7.07814e11i 0.0794642i 0.999210 + 0.0397321i \(0.0126504\pi\)
−0.999210 + 0.0397321i \(0.987350\pi\)
\(390\) 0 0
\(391\) 3.74855e12 0.410185
\(392\) 0 0
\(393\) 7.82526e11 1.00662e13i 0.0834710 1.07375i
\(394\) 0 0
\(395\) 8.99251e12i 0.935181i
\(396\) 0 0
\(397\) −1.26553e12 −0.128328 −0.0641639 0.997939i \(-0.520438\pi\)
−0.0641639 + 0.997939i \(0.520438\pi\)
\(398\) 0 0
\(399\) 2.51989e11 + 1.95890e10i 0.0249182 + 0.00193708i
\(400\) 0 0
\(401\) 1.50259e13i 1.44917i −0.689187 0.724583i \(-0.742032\pi\)
0.689187 0.724583i \(-0.257968\pi\)
\(402\) 0 0
\(403\) 9.52175e12 0.895760
\(404\) 0 0
\(405\) 5.13045e12 1.59983e13i 0.470848 1.46824i
\(406\) 0 0
\(407\) 1.99839e13i 1.78940i
\(408\) 0 0
\(409\) −1.70362e12 −0.148852 −0.0744261 0.997227i \(-0.523712\pi\)
−0.0744261 + 0.997227i \(0.523712\pi\)
\(410\) 0 0
\(411\) −1.74310e12 + 2.24228e13i −0.148632 + 1.91197i
\(412\) 0 0
\(413\) 3.27659e11i 0.0272692i
\(414\) 0 0
\(415\) 5.27917e12 0.428869
\(416\) 0 0
\(417\) 1.92743e13 + 1.49834e12i 1.52862 + 0.118831i
\(418\) 0 0
\(419\) 2.22448e13i 1.72250i −0.508185 0.861248i \(-0.669683\pi\)
0.508185 0.861248i \(-0.330317\pi\)
\(420\) 0 0
\(421\) −1.82948e11 −0.0138330 −0.00691650 0.999976i \(-0.502202\pi\)
−0.00691650 + 0.999976i \(0.502202\pi\)
\(422\) 0 0
\(423\) −3.00118e11 + 1.91865e12i −0.0221610 + 0.141676i
\(424\) 0 0
\(425\) 9.04375e12i 0.652235i
\(426\) 0 0
\(427\) −4.10986e10 −0.00289526
\(428\) 0 0
\(429\) −1.35216e12 + 1.73938e13i −0.0930552 + 1.19704i
\(430\) 0 0
\(431\) 6.64491e12i 0.446789i 0.974728 + 0.223395i \(0.0717139\pi\)
−0.974728 + 0.223395i \(0.928286\pi\)
\(432\) 0 0
\(433\) 7.28337e12 0.478512 0.239256 0.970956i \(-0.423096\pi\)
0.239256 + 0.970956i \(0.423096\pi\)
\(434\) 0 0
\(435\) −3.47069e13 2.69804e12i −2.22828 0.173222i
\(436\) 0 0
\(437\) 8.64868e12i 0.542678i
\(438\) 0 0
\(439\) 1.52600e13 0.935907 0.467954 0.883753i \(-0.344991\pi\)
0.467954 + 0.883753i \(0.344991\pi\)
\(440\) 0 0
\(441\) −1.64533e13 2.57363e12i −0.986414 0.154296i
\(442\) 0 0
\(443\) 1.83304e13i 1.07437i 0.843465 + 0.537184i \(0.180512\pi\)
−0.843465 + 0.537184i \(0.819488\pi\)
\(444\) 0 0
\(445\) −2.50498e13 −1.43550
\(446\) 0 0
\(447\) −1.52138e12 + 1.95706e13i −0.0852508 + 1.09665i
\(448\) 0 0
\(449\) 8.33876e12i 0.456951i −0.973550 0.228475i \(-0.926626\pi\)
0.973550 0.228475i \(-0.0733741\pi\)
\(450\) 0 0
\(451\) −8.37559e12 −0.448883
\(452\) 0 0
\(453\) −7.47774e12 5.81303e11i −0.391994 0.0304727i
\(454\) 0 0
\(455\) 9.94405e11i 0.0509925i
\(456\) 0 0
\(457\) 4.12288e11 0.0206833 0.0103416 0.999947i \(-0.496708\pi\)
0.0103416 + 0.999947i \(0.496708\pi\)
\(458\) 0 0
\(459\) 2.22510e12 9.38700e12i 0.109216 0.460748i
\(460\) 0 0
\(461\) 1.66247e11i 0.00798453i 0.999992 + 0.00399226i \(0.00127078\pi\)
−0.999992 + 0.00399226i \(0.998729\pi\)
\(462\) 0 0
\(463\) −1.27323e13 −0.598416 −0.299208 0.954188i \(-0.596722\pi\)
−0.299208 + 0.954188i \(0.596722\pi\)
\(464\) 0 0
\(465\) −2.80743e12 + 3.61142e13i −0.129135 + 1.66116i
\(466\) 0 0
\(467\) 2.26689e13i 1.02058i 0.860004 + 0.510288i \(0.170461\pi\)
−0.860004 + 0.510288i \(0.829539\pi\)
\(468\) 0 0
\(469\) 4.49775e11 0.0198213
\(470\) 0 0
\(471\) −2.35321e13 1.82934e12i −1.01521 0.0789203i
\(472\) 0 0
\(473\) 8.54352e12i 0.360854i
\(474\) 0 0
\(475\) 2.08658e13 0.862913
\(476\) 0 0
\(477\) −4.19039e12 + 2.67892e13i −0.169693 + 1.08485i
\(478\) 0 0
\(479\) 2.39654e13i 0.950402i −0.879877 0.475201i \(-0.842375\pi\)
0.879877 0.475201i \(-0.157625\pi\)
\(480\) 0 0
\(481\) −2.63673e13 −1.02409
\(482\) 0 0
\(483\) 7.04098e10 9.05734e11i 0.00267853 0.0344560i
\(484\) 0 0
\(485\) 5.17838e13i 1.92968i
\(486\) 0 0
\(487\) 1.13824e13 0.415516 0.207758 0.978180i \(-0.433383\pi\)
0.207758 + 0.978180i \(0.433383\pi\)
\(488\) 0 0
\(489\) −3.37821e13 2.62615e12i −1.20821 0.0939235i
\(490\) 0 0
\(491\) 3.59512e13i 1.25981i −0.776672 0.629906i \(-0.783094\pi\)
0.776672 0.629906i \(-0.216906\pi\)
\(492\) 0 0
\(493\) −1.99891e13 −0.686370
\(494\) 0 0
\(495\) −6.55727e13 1.02569e13i −2.20647 0.345137i
\(496\) 0 0
\(497\) 8.26965e11i 0.0272713i
\(498\) 0 0
\(499\) −1.33630e13 −0.431917 −0.215958 0.976403i \(-0.569288\pi\)
−0.215958 + 0.976403i \(0.569288\pi\)
\(500\) 0 0
\(501\) 2.37000e12 3.04871e13i 0.0750862 0.965890i
\(502\) 0 0
\(503\) 3.54934e13i 1.10232i 0.834399 + 0.551160i \(0.185815\pi\)
−0.834399 + 0.551160i \(0.814185\pi\)
\(504\) 0 0
\(505\) −5.21132e13 −1.58668
\(506\) 0 0
\(507\) −1.04490e13 8.12280e11i −0.311913 0.0242474i
\(508\) 0 0
\(509\) 6.07337e13i 1.77763i −0.458269 0.888813i \(-0.651530\pi\)
0.458269 0.888813i \(-0.348470\pi\)
\(510\) 0 0
\(511\) −7.25016e11 −0.0208086
\(512\) 0 0
\(513\) −2.16577e13 5.13377e12i −0.609574 0.144494i
\(514\) 0 0
\(515\) 1.36576e13i 0.376997i
\(516\) 0 0
\(517\) 7.67166e12 0.207700
\(518\) 0 0
\(519\) 2.37785e12 3.05881e13i 0.0631464 0.812299i
\(520\) 0 0
\(521\) 2.06244e13i 0.537270i 0.963242 + 0.268635i \(0.0865726\pi\)
−0.963242 + 0.268635i \(0.913427\pi\)
\(522\) 0 0
\(523\) 5.24376e13 1.34009 0.670045 0.742320i \(-0.266275\pi\)
0.670045 + 0.742320i \(0.266275\pi\)
\(524\) 0 0
\(525\) 2.18517e12 + 1.69871e11i 0.0547885 + 0.00425914i
\(526\) 0 0
\(527\) 2.07996e13i 0.511683i
\(528\) 0 0
\(529\) 1.03402e13 0.249603
\(530\) 0 0
\(531\) −4.45925e12 + 2.85080e13i −0.105631 + 0.675297i
\(532\) 0 0
\(533\) 1.10510e13i 0.256900i
\(534\) 0 0
\(535\) 1.16221e14 2.65165
\(536\) 0 0
\(537\) 5.58492e12 7.18431e13i 0.125068 1.60884i
\(538\) 0 0
\(539\) 6.57877e13i 1.44611i
\(540\) 0 0
\(541\) −8.20249e13 −1.76994 −0.884972 0.465645i \(-0.845822\pi\)
−0.884972 + 0.465645i \(0.845822\pi\)
\(542\) 0 0
\(543\) −6.01919e13 4.67919e12i −1.27509 0.0991223i
\(544\) 0 0
\(545\) 2.61844e13i 0.544578i
\(546\) 0 0
\(547\) −1.62332e13 −0.331488 −0.165744 0.986169i \(-0.553003\pi\)
−0.165744 + 0.986169i \(0.553003\pi\)
\(548\) 0 0
\(549\) 3.57580e12 + 5.59329e11i 0.0716987 + 0.0112152i
\(550\) 0 0
\(551\) 4.61189e13i 0.908074i
\(552\) 0 0
\(553\) −1.25140e12 −0.0241974
\(554\) 0 0
\(555\) 7.77424e12 1.00006e14i 0.147636 1.89916i
\(556\) 0 0
\(557\) 1.12168e13i 0.209215i −0.994514 0.104608i \(-0.966641\pi\)
0.994514 0.104608i \(-0.0333587\pi\)
\(558\) 0 0
\(559\) 1.12726e13 0.206521
\(560\) 0 0
\(561\) −3.79955e13 2.95369e12i −0.683783 0.0531557i
\(562\) 0 0
\(563\) 7.98522e13i 1.41171i 0.708357 + 0.705854i \(0.249437\pi\)
−0.708357 + 0.705854i \(0.750563\pi\)
\(564\) 0 0
\(565\) −6.71230e13 −1.16581
\(566\) 0 0
\(567\) −2.22632e12 7.13953e11i −0.0379902 0.0121830i
\(568\) 0 0
\(569\) 9.95594e11i 0.0166925i 0.999965 + 0.00834624i \(0.00265672\pi\)
−0.999965 + 0.00834624i \(0.997343\pi\)
\(570\) 0 0
\(571\) 1.07836e14 1.77657 0.888283 0.459297i \(-0.151899\pi\)
0.888283 + 0.459297i \(0.151899\pi\)
\(572\) 0 0
\(573\) 2.97664e12 3.82907e13i 0.0481895 0.619899i
\(574\) 0 0
\(575\) 7.49989e13i 1.19321i
\(576\) 0 0
\(577\) 3.31000e13 0.517546 0.258773 0.965938i \(-0.416682\pi\)
0.258773 + 0.965938i \(0.416682\pi\)
\(578\) 0 0
\(579\) −9.16671e13 7.12600e12i −1.40871 0.109510i
\(580\) 0 0
\(581\) 7.34648e11i 0.0110968i
\(582\) 0 0
\(583\) 1.07116e14 1.59041
\(584\) 0 0
\(585\) −1.35333e13 + 8.65184e13i −0.197526 + 1.26278i
\(586\) 0 0
\(587\) 1.21022e14i 1.73650i −0.496131 0.868248i \(-0.665246\pi\)
0.496131 0.868248i \(-0.334754\pi\)
\(588\) 0 0
\(589\) 4.79889e13 0.676961
\(590\) 0 0
\(591\) 3.56717e12 4.58873e13i 0.0494751 0.636436i
\(592\) 0 0
\(593\) 8.43944e12i 0.115091i 0.998343 + 0.0575453i \(0.0183274\pi\)
−0.998343 + 0.0575453i \(0.981673\pi\)
\(594\) 0 0
\(595\) 2.17220e12 0.0291283
\(596\) 0 0
\(597\) −1.21847e13 9.47213e11i −0.160673 0.0124904i
\(598\) 0 0
\(599\) 3.11882e13i 0.404443i 0.979340 + 0.202221i \(0.0648160\pi\)
−0.979340 + 0.202221i \(0.935184\pi\)
\(600\) 0 0
\(601\) 2.87401e13 0.366535 0.183267 0.983063i \(-0.441333\pi\)
0.183267 + 0.983063i \(0.441333\pi\)
\(602\) 0 0
\(603\) −3.91328e13 6.12119e12i −0.490857 0.0767802i
\(604\) 0 0
\(605\) 1.37212e14i 1.69284i
\(606\) 0 0
\(607\) 4.47536e13 0.543106 0.271553 0.962423i \(-0.412463\pi\)
0.271553 + 0.962423i \(0.412463\pi\)
\(608\) 0 0
\(609\) −3.75459e11 + 4.82981e12i −0.00448204 + 0.0576559i
\(610\) 0 0
\(611\) 1.01222e13i 0.118869i
\(612\) 0 0
\(613\) −6.78051e13 −0.783358 −0.391679 0.920102i \(-0.628106\pi\)
−0.391679 + 0.920102i \(0.628106\pi\)
\(614\) 0 0
\(615\) −4.19143e13 3.25832e12i −0.476416 0.0370355i
\(616\) 0 0
\(617\) 2.48261e12i 0.0277641i 0.999904 + 0.0138820i \(0.00441893\pi\)
−0.999904 + 0.0138820i \(0.995581\pi\)
\(618\) 0 0
\(619\) 1.64000e13 0.180464 0.0902320 0.995921i \(-0.471239\pi\)
0.0902320 + 0.995921i \(0.471239\pi\)
\(620\) 0 0
\(621\) −1.84526e13 + 7.78454e13i −0.199801 + 0.842898i
\(622\) 0 0
\(623\) 3.48592e12i 0.0371431i
\(624\) 0 0
\(625\) −4.57873e13 −0.480114
\(626\) 0 0
\(627\) −6.81476e12 + 8.76635e13i −0.0703255 + 0.904651i
\(628\) 0 0
\(629\) 5.75973e13i 0.584991i
\(630\) 0 0
\(631\) 1.37258e13 0.137211 0.0686056 0.997644i \(-0.478145\pi\)
0.0686056 + 0.997644i \(0.478145\pi\)
\(632\) 0 0
\(633\) 1.15070e14 + 8.94532e12i 1.13226 + 0.0880192i
\(634\) 0 0
\(635\) 1.96790e14i 1.90605i
\(636\) 0 0
\(637\) 8.68020e13 0.827623
\(638\) 0 0
\(639\) −1.12545e13 + 7.19503e13i −0.105639 + 0.675349i
\(640\) 0 0
\(641\) 5.42348e13i 0.501173i 0.968094 + 0.250587i \(0.0806235\pi\)
−0.968094 + 0.250587i \(0.919377\pi\)
\(642\) 0 0
\(643\) −5.54693e13 −0.504659 −0.252329 0.967641i \(-0.581197\pi\)
−0.252329 + 0.967641i \(0.581197\pi\)
\(644\) 0 0
\(645\) −3.32365e12 + 4.27546e13i −0.0297726 + 0.382987i
\(646\) 0 0
\(647\) 5.56652e13i 0.490979i 0.969399 + 0.245489i \(0.0789486\pi\)
−0.969399 + 0.245489i \(0.921051\pi\)
\(648\) 0 0
\(649\) 1.13988e14 0.990002
\(650\) 0 0
\(651\) 5.02564e12 + 3.90682e11i 0.0429820 + 0.00334132i
\(652\) 0 0
\(653\) 5.56792e13i 0.468951i −0.972122 0.234475i \(-0.924663\pi\)
0.972122 0.234475i \(-0.0753372\pi\)
\(654\) 0 0
\(655\) −2.00204e14 −1.66060
\(656\) 0 0
\(657\) 6.30802e13 + 9.86706e12i 0.515307 + 0.0806048i
\(658\) 0 0
\(659\) 1.52699e14i 1.22860i −0.789074 0.614298i \(-0.789439\pi\)
0.789074 0.614298i \(-0.210561\pi\)
\(660\) 0 0
\(661\) 2.08036e14 1.64866 0.824329 0.566111i \(-0.191553\pi\)
0.824329 + 0.566111i \(0.191553\pi\)
\(662\) 0 0
\(663\) −3.89717e12 + 5.01323e13i −0.0304216 + 0.391336i
\(664\) 0 0
\(665\) 5.01172e12i 0.0385371i
\(666\) 0 0
\(667\) 1.65767e14 1.25565
\(668\) 0 0
\(669\) 5.70737e13 + 4.43679e12i 0.425898 + 0.0331084i
\(670\) 0 0
\(671\) 1.42977e13i 0.105112i
\(672\) 0 0
\(673\) −9.45260e13 −0.684662 −0.342331 0.939579i \(-0.611216\pi\)
−0.342331 + 0.939579i \(0.611216\pi\)
\(674\) 0 0
\(675\) −1.87810e14 4.45186e13i −1.34029 0.317704i
\(676\) 0 0
\(677\) 1.70106e14i 1.19612i −0.801451 0.598060i \(-0.795938\pi\)
0.801451 0.598060i \(-0.204062\pi\)
\(678\) 0 0
\(679\) 7.20622e12 0.0499297
\(680\) 0 0
\(681\) 8.04237e12 1.03455e14i 0.0549096 0.706344i
\(682\) 0 0
\(683\) 2.23578e14i 1.50427i −0.659009 0.752135i \(-0.729024\pi\)
0.659009 0.752135i \(-0.270976\pi\)
\(684\) 0 0
\(685\) 4.45960e14 2.95694
\(686\) 0 0
\(687\) −2.51163e14 1.95249e13i −1.64124 0.127586i
\(688\) 0 0
\(689\) 1.41331e14i 0.910210i
\(690\) 0 0
\(691\) −1.10134e13 −0.0699090 −0.0349545 0.999389i \(-0.511129\pi\)
−0.0349545 + 0.999389i \(0.511129\pi\)
\(692\) 0 0
\(693\) −1.42735e12 + 9.12509e12i −0.00893029 + 0.0570915i
\(694\) 0 0
\(695\) 3.83341e14i 2.36408i
\(696\) 0 0
\(697\) −2.41401e13 −0.146749
\(698\) 0 0
\(699\) −1.95426e13 + 2.51392e14i −0.117111 + 1.50649i
\(700\) 0 0
\(701\) 1.10962e14i 0.655516i −0.944762 0.327758i \(-0.893707\pi\)
0.944762 0.327758i \(-0.106293\pi\)
\(702\) 0 0
\(703\) −1.32889e14 −0.773948
\(704\) 0 0
\(705\) 3.83915e13 + 2.98447e12i 0.220440 + 0.0171365i
\(706\) 0 0
\(707\) 7.25206e12i 0.0410548i
\(708\) 0 0
\(709\) −2.08219e14 −1.16222 −0.581112 0.813824i \(-0.697382\pi\)
−0.581112 + 0.813824i \(0.697382\pi\)
\(710\) 0 0
\(711\) 1.08878e14 + 1.70308e13i 0.599229 + 0.0937318i
\(712\) 0 0
\(713\) 1.72489e14i 0.936080i
\(714\) 0 0
\(715\) 3.45940e14 1.85127
\(716\) 0 0
\(717\) 2.32946e13 2.99656e14i 0.122931 1.58135i
\(718\) 0 0
\(719\) 2.74910e14i 1.43069i 0.698771 + 0.715346i \(0.253731\pi\)
−0.698771 + 0.715346i \(0.746269\pi\)
\(720\) 0 0
\(721\) −1.90059e12 −0.00975465
\(722\) 0 0
\(723\) −2.51746e14 1.95702e13i −1.27430 0.0990613i
\(724\) 0 0
\(725\) 3.99930e14i 1.99661i
\(726\) 0 0
\(727\) 2.99071e14 1.47266 0.736330 0.676622i \(-0.236557\pi\)
0.736330 + 0.676622i \(0.236557\pi\)
\(728\) 0 0
\(729\) 1.83985e14 + 9.24165e13i 0.893602 + 0.448861i
\(730\) 0 0
\(731\) 2.46241e13i 0.117970i
\(732\) 0 0
\(733\) −1.19922e14 −0.566734 −0.283367 0.959012i \(-0.591451\pi\)
−0.283367 + 0.959012i \(0.591451\pi\)
\(734\) 0 0
\(735\) −2.55931e13 + 3.29223e14i −0.119313 + 1.53481i
\(736\) 0 0
\(737\) 1.56471e14i 0.719608i
\(738\) 0 0
\(739\) −7.29345e13 −0.330911 −0.165455 0.986217i \(-0.552909\pi\)
−0.165455 + 0.986217i \(0.552909\pi\)
\(740\) 0 0
\(741\) 1.15666e14 + 8.99158e12i 0.517742 + 0.0402481i
\(742\) 0 0
\(743\) 1.07061e14i 0.472809i −0.971655 0.236405i \(-0.924031\pi\)
0.971655 0.236405i \(-0.0759691\pi\)
\(744\) 0 0
\(745\) 3.89234e14 1.69601
\(746\) 0 0
\(747\) −9.99815e12 + 6.39183e13i −0.0429850 + 0.274803i
\(748\) 0 0
\(749\) 1.61733e13i 0.0686104i
\(750\) 0 0
\(751\) −1.83777e14 −0.769292 −0.384646 0.923064i \(-0.625677\pi\)
−0.384646 + 0.923064i \(0.625677\pi\)
\(752\) 0 0
\(753\) 1.06744e13 1.37313e14i 0.0440931 0.567203i
\(754\) 0 0
\(755\) 1.48722e14i 0.606236i
\(756\) 0 0
\(757\) 1.73049e14 0.696130 0.348065 0.937470i \(-0.386839\pi\)
0.348065 + 0.937470i \(0.386839\pi\)
\(758\) 0 0
\(759\) 3.15093e14 + 2.44946e13i 1.25092 + 0.0972438i
\(760\) 0 0
\(761\) 1.10156e14i 0.431604i 0.976437 + 0.215802i \(0.0692365\pi\)
−0.976437 + 0.215802i \(0.930764\pi\)
\(762\) 0 0
\(763\) −3.64382e12 −0.0140907
\(764\) 0 0
\(765\) −1.88993e14 2.95625e13i −0.721338 0.112832i
\(766\) 0 0
\(767\) 1.50399e14i 0.566589i
\(768\) 0 0
\(769\) 2.30458e14 0.856959 0.428480 0.903551i \(-0.359049\pi\)
0.428480 + 0.903551i \(0.359049\pi\)
\(770\) 0 0
\(771\) 2.40960e13 3.09965e14i 0.0884451 1.13774i
\(772\) 0 0
\(773\) 1.50965e14i 0.546991i −0.961873 0.273495i \(-0.911820\pi\)
0.961873 0.273495i \(-0.0881798\pi\)
\(774\) 0 0
\(775\) 4.16146e14 1.48846
\(776\) 0 0
\(777\) −1.39168e13 1.08186e12i −0.0491399 0.00382003i
\(778\) 0 0
\(779\) 5.56961e13i 0.194150i
\(780\) 0 0
\(781\) 2.87690e14 0.990079
\(782\) 0 0
\(783\) 9.83979e13 4.15109e14i 0.334331 1.41044i
\(784\) 0 0
\(785\)