Properties

Label 48.11.e.d.17.4
Level $48$
Weight $11$
Character 48.17
Analytic conductor $30.497$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 11 \)
Character orbit: \([\chi]\) \(=\) 48.e (of order \(2\), degree \(1\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(30.4971481283\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{85})\)
Defining polynomial: \(x^{4} - 2 x^{3} - 37 x^{2} + 38 x + 531\)
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 17.4
Root \(-4.10977 - 1.41421i\) of defining polynomial
Character \(\chi\) \(=\) 48.17
Dual form 48.11.e.d.17.3

$q$-expansion

\(f(q)\) \(=\) \(q+(200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 + 55125.0i) q^{9} +O(q^{10})\) \(q+(200.269 + 137.627i) q^{3} -3630.47i q^{5} +23226.5 q^{7} +(21166.4 + 55125.0i) q^{9} -62442.7i q^{11} -170161. q^{13} +(499653. - 727072. i) q^{15} -2.66626e6i q^{17} -766825. q^{19} +(4.65156e6 + 3.19661e6i) q^{21} -1.40327e6i q^{23} -3.41471e6 q^{25} +(-3.34774e6 + 1.39529e7i) q^{27} +4.83245e6i q^{29} +4.18297e7 q^{31} +(8.59382e6 - 1.25053e7i) q^{33} -8.43233e7i q^{35} +5.01619e7 q^{37} +(-3.40779e7 - 2.34188e7i) q^{39} -1.49239e8i q^{41} +1.98719e8 q^{43} +(2.00130e8 - 7.68440e7i) q^{45} +1.55059e8i q^{47} +2.56996e8 q^{49} +(3.66951e8 - 5.33970e8i) q^{51} +4.21541e7i q^{53} -2.26696e8 q^{55} +(-1.53571e8 - 1.05536e8i) q^{57} -2.92026e8i q^{59} -5.30727e8 q^{61} +(4.91622e8 + 1.28036e9i) q^{63} +6.17764e8i q^{65} -5.22093e8 q^{67} +(1.93128e8 - 2.81031e8i) q^{69} -5.71364e8i q^{71} +2.18588e9 q^{73} +(-6.83861e8 - 4.69958e8i) q^{75} -1.45033e9i q^{77} -1.96592e9 q^{79} +(-2.59075e9 + 2.33360e9i) q^{81} +2.18558e9i q^{83} -9.67979e9 q^{85} +(-6.65078e8 + 9.67791e8i) q^{87} -2.38742e8i q^{89} -3.95224e9 q^{91} +(8.37720e9 + 5.75692e9i) q^{93} +2.78394e9i q^{95} -8.84112e9 q^{97} +(3.44215e9 - 1.32169e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9} + O(q^{10}) \) \( 4 q - 84 q^{3} + 45112 q^{7} + 159012 q^{9} + 275240 q^{13} + 1180800 q^{15} + 1568728 q^{19} + 9628008 q^{21} - 33732380 q^{25} - 34619508 q^{27} + 21785848 q^{31} + 25974144 q^{33} - 71014168 q^{37} - 217287240 q^{39} + 470688664 q^{43} + 312318720 q^{45} - 50058420 q^{49} + 708576768 q^{51} - 2701359360 q^{55} - 1058753208 q^{57} - 1184038744 q^{61} + 905007096 q^{63} + 297365848 q^{67} + 596268288 q^{69} + 6534269000 q^{73} + 5150031180 q^{75} - 199282568 q^{79} + 1458964548 q^{81} - 12880512000 q^{85} - 210268800 q^{87} - 8317232080 q^{91} + 31744468392 q^{93} - 39176355064 q^{97} + 2626912512 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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
\(3\) 200.269 + 137.627i 0.824153 + 0.566368i
\(4\) 0 0
\(5\) 3630.47i 1.16175i −0.813992 0.580876i \(-0.802710\pi\)
0.813992 0.580876i \(-0.197290\pi\)
\(6\) 0 0
\(7\) 23226.5 1.38196 0.690978 0.722876i \(-0.257180\pi\)
0.690978 + 0.722876i \(0.257180\pi\)
\(8\) 0 0
\(9\) 21166.4 + 55125.0i 0.358455 + 0.933547i
\(10\) 0 0
\(11\) 62442.7i 0.387720i −0.981029 0.193860i \(-0.937899\pi\)
0.981029 0.193860i \(-0.0621007\pi\)
\(12\) 0 0
\(13\) −170161. −0.458292 −0.229146 0.973392i \(-0.573593\pi\)
−0.229146 + 0.973392i \(0.573593\pi\)
\(14\) 0 0
\(15\) 499653. 727072.i 0.657979 0.957460i
\(16\) 0 0
\(17\) 2.66626e6i 1.87784i −0.344139 0.938919i \(-0.611829\pi\)
0.344139 0.938919i \(-0.388171\pi\)
\(18\) 0 0
\(19\) −766825. −0.309691 −0.154845 0.987939i \(-0.549488\pi\)
−0.154845 + 0.987939i \(0.549488\pi\)
\(20\) 0 0
\(21\) 4.65156e6 + 3.19661e6i 1.13894 + 0.782695i
\(22\) 0 0
\(23\) 1.40327e6i 0.218022i −0.994041 0.109011i \(-0.965232\pi\)
0.994041 0.109011i \(-0.0347684\pi\)
\(24\) 0 0
\(25\) −3.41471e6 −0.349667
\(26\) 0 0
\(27\) −3.34774e6 + 1.39529e7i −0.233310 + 0.972402i
\(28\) 0 0
\(29\) 4.83245e6i 0.235601i 0.993037 + 0.117801i \(0.0375844\pi\)
−0.993037 + 0.117801i \(0.962416\pi\)
\(30\) 0 0
\(31\) 4.18297e7 1.46109 0.730544 0.682865i \(-0.239266\pi\)
0.730544 + 0.682865i \(0.239266\pi\)
\(32\) 0 0
\(33\) 8.59382e6 1.25053e7i 0.219592 0.319540i
\(34\) 0 0
\(35\) 8.43233e7i 1.60549i
\(36\) 0 0
\(37\) 5.01619e7 0.723378 0.361689 0.932299i \(-0.382200\pi\)
0.361689 + 0.932299i \(0.382200\pi\)
\(38\) 0 0
\(39\) −3.40779e7 2.34188e7i −0.377702 0.259562i
\(40\) 0 0
\(41\) 1.49239e8i 1.28814i −0.764967 0.644069i \(-0.777245\pi\)
0.764967 0.644069i \(-0.222755\pi\)
\(42\) 0 0
\(43\) 1.98719e8 1.35175 0.675876 0.737015i \(-0.263765\pi\)
0.675876 + 0.737015i \(0.263765\pi\)
\(44\) 0 0
\(45\) 2.00130e8 7.68440e7i 1.08455 0.416435i
\(46\) 0 0
\(47\) 1.55059e8i 0.676093i 0.941129 + 0.338047i \(0.109766\pi\)
−0.941129 + 0.338047i \(0.890234\pi\)
\(48\) 0 0
\(49\) 2.56996e8 0.909802
\(50\) 0 0
\(51\) 3.66951e8 5.33970e8i 1.06355 1.54762i
\(52\) 0 0
\(53\) 4.21541e7i 0.100800i 0.998729 + 0.0503999i \(0.0160496\pi\)
−0.998729 + 0.0503999i \(0.983950\pi\)
\(54\) 0 0
\(55\) −2.26696e8 −0.450434
\(56\) 0 0
\(57\) −1.53571e8 1.05536e8i −0.255233 0.175399i
\(58\) 0 0
\(59\) 2.92026e8i 0.408471i −0.978922 0.204236i \(-0.934529\pi\)
0.978922 0.204236i \(-0.0654708\pi\)
\(60\) 0 0
\(61\) −5.30727e8 −0.628379 −0.314190 0.949360i \(-0.601733\pi\)
−0.314190 + 0.949360i \(0.601733\pi\)
\(62\) 0 0
\(63\) 4.91622e8 + 1.28036e9i 0.495369 + 1.29012i
\(64\) 0 0
\(65\) 6.17764e8i 0.532421i
\(66\) 0 0
\(67\) −5.22093e8 −0.386700 −0.193350 0.981130i \(-0.561935\pi\)
−0.193350 + 0.981130i \(0.561935\pi\)
\(68\) 0 0
\(69\) 1.93128e8 2.81031e8i 0.123481 0.179684i
\(70\) 0 0
\(71\) 5.71364e8i 0.316681i −0.987385 0.158340i \(-0.949386\pi\)
0.987385 0.158340i \(-0.0506143\pi\)
\(72\) 0 0
\(73\) 2.18588e9 1.05441 0.527207 0.849737i \(-0.323239\pi\)
0.527207 + 0.849737i \(0.323239\pi\)
\(74\) 0 0
\(75\) −6.83861e8 4.69958e8i −0.288179 0.198040i
\(76\) 0 0
\(77\) 1.45033e9i 0.535812i
\(78\) 0 0
\(79\) −1.96592e9 −0.638897 −0.319449 0.947604i \(-0.603498\pi\)
−0.319449 + 0.947604i \(0.603498\pi\)
\(80\) 0 0
\(81\) −2.59075e9 + 2.33360e9i −0.743020 + 0.669269i
\(82\) 0 0
\(83\) 2.18558e9i 0.554850i 0.960747 + 0.277425i \(0.0894810\pi\)
−0.960747 + 0.277425i \(0.910519\pi\)
\(84\) 0 0
\(85\) −9.67979e9 −2.18158
\(86\) 0 0
\(87\) −6.65078e8 + 9.67791e8i −0.133437 + 0.194171i
\(88\) 0 0
\(89\) 2.38742e8i 0.0427542i −0.999771 0.0213771i \(-0.993195\pi\)
0.999771 0.0213771i \(-0.00680506\pi\)
\(90\) 0 0
\(91\) −3.95224e9 −0.633339
\(92\) 0 0
\(93\) 8.37720e9 + 5.75692e9i 1.20416 + 0.827514i
\(94\) 0 0
\(95\) 2.78394e9i 0.359784i
\(96\) 0 0
\(97\) −8.84112e9 −1.02955 −0.514776 0.857324i \(-0.672125\pi\)
−0.514776 + 0.857324i \(0.672125\pi\)
\(98\) 0 0
\(99\) 3.44215e9 1.32169e9i 0.361955 0.138980i
\(100\) 0 0
\(101\) 1.67928e10i 1.59778i 0.601477 + 0.798890i \(0.294579\pi\)
−0.601477 + 0.798890i \(0.705421\pi\)
\(102\) 0 0
\(103\) −8.36865e9 −0.721887 −0.360944 0.932588i \(-0.617545\pi\)
−0.360944 + 0.932588i \(0.617545\pi\)
\(104\) 0 0
\(105\) 1.16052e10 1.68873e10i 0.909297 1.32317i
\(106\) 0 0
\(107\) 1.43555e10i 1.02353i 0.859126 + 0.511764i \(0.171008\pi\)
−0.859126 + 0.511764i \(0.828992\pi\)
\(108\) 0 0
\(109\) −4.72564e9 −0.307134 −0.153567 0.988138i \(-0.549076\pi\)
−0.153567 + 0.988138i \(0.549076\pi\)
\(110\) 0 0
\(111\) 1.00459e10 + 6.90365e9i 0.596174 + 0.409698i
\(112\) 0 0
\(113\) 1.32158e10i 0.717303i −0.933472 0.358651i \(-0.883237\pi\)
0.933472 0.358651i \(-0.116763\pi\)
\(114\) 0 0
\(115\) −5.09452e9 −0.253288
\(116\) 0 0
\(117\) −3.60169e9 9.38011e9i −0.164277 0.427837i
\(118\) 0 0
\(119\) 6.19280e10i 2.59509i
\(120\) 0 0
\(121\) 2.20383e10 0.849673
\(122\) 0 0
\(123\) 2.05393e10 2.98879e10i 0.729560 1.06162i
\(124\) 0 0
\(125\) 2.30568e10i 0.755526i
\(126\) 0 0
\(127\) 3.17814e10 0.961953 0.480976 0.876733i \(-0.340282\pi\)
0.480976 + 0.876733i \(0.340282\pi\)
\(128\) 0 0
\(129\) 3.97973e10 + 2.73492e10i 1.11405 + 0.765589i
\(130\) 0 0
\(131\) 5.01094e10i 1.29886i 0.760421 + 0.649430i \(0.224993\pi\)
−0.760421 + 0.649430i \(0.775007\pi\)
\(132\) 0 0
\(133\) −1.78107e10 −0.427979
\(134\) 0 0
\(135\) 5.06557e10 + 1.21539e10i 1.12969 + 0.271048i
\(136\) 0 0
\(137\) 2.74744e10i 0.569279i −0.958635 0.284639i \(-0.908126\pi\)
0.958635 0.284639i \(-0.0918738\pi\)
\(138\) 0 0
\(139\) −6.32488e10 −1.21893 −0.609464 0.792814i \(-0.708615\pi\)
−0.609464 + 0.792814i \(0.708615\pi\)
\(140\) 0 0
\(141\) −2.13403e10 + 3.10534e10i −0.382917 + 0.557204i
\(142\) 0 0
\(143\) 1.06253e10i 0.177689i
\(144\) 0 0
\(145\) 1.75441e10 0.273710
\(146\) 0 0
\(147\) 5.14684e10 + 3.53697e10i 0.749815 + 0.515282i
\(148\) 0 0
\(149\) 3.38479e10i 0.460893i 0.973085 + 0.230446i \(0.0740186\pi\)
−0.973085 + 0.230446i \(0.925981\pi\)
\(150\) 0 0
\(151\) −1.22386e11 −1.55901 −0.779503 0.626399i \(-0.784528\pi\)
−0.779503 + 0.626399i \(0.784528\pi\)
\(152\) 0 0
\(153\) 1.46978e11 5.64351e10i 1.75305 0.673120i
\(154\) 0 0
\(155\) 1.51862e11i 1.69742i
\(156\) 0 0
\(157\) −1.58971e11 −1.66656 −0.833279 0.552853i \(-0.813539\pi\)
−0.833279 + 0.552853i \(0.813539\pi\)
\(158\) 0 0
\(159\) −5.80155e9 + 8.44215e9i −0.0570898 + 0.0830745i
\(160\) 0 0
\(161\) 3.25930e10i 0.301297i
\(162\) 0 0
\(163\) 9.20831e10 0.800280 0.400140 0.916454i \(-0.368962\pi\)
0.400140 + 0.916454i \(0.368962\pi\)
\(164\) 0 0
\(165\) −4.54003e10 3.11996e10i −0.371226 0.255111i
\(166\) 0 0
\(167\) 2.12416e11i 1.63533i 0.575697 + 0.817663i \(0.304731\pi\)
−0.575697 + 0.817663i \(0.695269\pi\)
\(168\) 0 0
\(169\) −1.08904e11 −0.789968
\(170\) 0 0
\(171\) −1.62309e10 4.22713e10i −0.111010 0.289111i
\(172\) 0 0
\(173\) 3.04132e11i 1.96260i 0.192482 + 0.981300i \(0.438346\pi\)
−0.192482 + 0.981300i \(0.561654\pi\)
\(174\) 0 0
\(175\) −7.93119e10 −0.483224
\(176\) 0 0
\(177\) 4.01908e10 5.84837e10i 0.231345 0.336642i
\(178\) 0 0
\(179\) 7.07114e9i 0.0384791i −0.999815 0.0192395i \(-0.993875\pi\)
0.999815 0.0192395i \(-0.00612451\pi\)
\(180\) 0 0
\(181\) −1.27309e11 −0.655337 −0.327669 0.944793i \(-0.606263\pi\)
−0.327669 + 0.944793i \(0.606263\pi\)
\(182\) 0 0
\(183\) −1.06288e11 7.30425e10i −0.517880 0.355894i
\(184\) 0 0
\(185\) 1.82111e11i 0.840386i
\(186\) 0 0
\(187\) −1.66488e11 −0.728075
\(188\) 0 0
\(189\) −7.77563e10 + 3.24078e11i −0.322424 + 1.34382i
\(190\) 0 0
\(191\) 2.06460e11i 0.812209i 0.913827 + 0.406105i \(0.133113\pi\)
−0.913827 + 0.406105i \(0.866887\pi\)
\(192\) 0 0
\(193\) 3.11606e11 1.16364 0.581821 0.813317i \(-0.302340\pi\)
0.581821 + 0.813317i \(0.302340\pi\)
\(194\) 0 0
\(195\) −8.50212e10 + 1.23719e11i −0.301546 + 0.438796i
\(196\) 0 0
\(197\) 1.51694e11i 0.511255i −0.966775 0.255628i \(-0.917718\pi\)
0.966775 0.255628i \(-0.0822821\pi\)
\(198\) 0 0
\(199\) 1.11692e11 0.357895 0.178947 0.983859i \(-0.442731\pi\)
0.178947 + 0.983859i \(0.442731\pi\)
\(200\) 0 0
\(201\) −1.04559e11 7.18543e10i −0.318700 0.219014i
\(202\) 0 0
\(203\) 1.12241e11i 0.325591i
\(204\) 0 0
\(205\) −5.41807e11 −1.49650
\(206\) 0 0
\(207\) 7.73551e10 2.97021e10i 0.203534 0.0781512i
\(208\) 0 0
\(209\) 4.78826e10i 0.120073i
\(210\) 0 0
\(211\) −1.53066e11 −0.365987 −0.182994 0.983114i \(-0.558579\pi\)
−0.182994 + 0.983114i \(0.558579\pi\)
\(212\) 0 0
\(213\) 7.86354e10 1.14427e11i 0.179358 0.260993i
\(214\) 0 0
\(215\) 7.21444e11i 1.57040i
\(216\) 0 0
\(217\) 9.71560e11 2.01916
\(218\) 0 0
\(219\) 4.37763e11 + 3.00836e11i 0.868998 + 0.597186i
\(220\) 0 0
\(221\) 4.53693e11i 0.860598i
\(222\) 0 0
\(223\) 6.05759e11 1.09844 0.549219 0.835678i \(-0.314925\pi\)
0.549219 + 0.835678i \(0.314925\pi\)
\(224\) 0 0
\(225\) −7.22772e10 1.88236e11i −0.125340 0.326430i
\(226\) 0 0
\(227\) 6.70588e11i 1.11257i −0.830992 0.556284i \(-0.812227\pi\)
0.830992 0.556284i \(-0.187773\pi\)
\(228\) 0 0
\(229\) 3.53356e11 0.561094 0.280547 0.959840i \(-0.409484\pi\)
0.280547 + 0.959840i \(0.409484\pi\)
\(230\) 0 0
\(231\) 1.99605e11 2.90456e11i 0.303467 0.441591i
\(232\) 0 0
\(233\) 1.12390e12i 1.63662i −0.574779 0.818309i \(-0.694912\pi\)
0.574779 0.818309i \(-0.305088\pi\)
\(234\) 0 0
\(235\) 5.62936e11 0.785452
\(236\) 0 0
\(237\) −3.93714e11 2.70565e11i −0.526549 0.361851i
\(238\) 0 0
\(239\) 2.64603e11i 0.339317i 0.985503 + 0.169658i \(0.0542665\pi\)
−0.985503 + 0.169658i \(0.945734\pi\)
\(240\) 0 0
\(241\) 8.86768e11 1.09075 0.545375 0.838192i \(-0.316387\pi\)
0.545375 + 0.838192i \(0.316387\pi\)
\(242\) 0 0
\(243\) −8.40014e11 + 1.10789e11i −0.991414 + 0.130757i
\(244\) 0 0
\(245\) 9.33019e11i 1.05696i
\(246\) 0 0
\(247\) 1.30483e11 0.141929
\(248\) 0 0
\(249\) −3.00795e11 + 4.37704e11i −0.314249 + 0.457281i
\(250\) 0 0
\(251\) 8.59494e11i 0.862729i 0.902178 + 0.431364i \(0.141968\pi\)
−0.902178 + 0.431364i \(0.858032\pi\)
\(252\) 0 0
\(253\) −8.76237e10 −0.0845316
\(254\) 0 0
\(255\) −1.93856e12 1.33220e12i −1.79796 1.23558i
\(256\) 0 0
\(257\) 2.17900e12i 1.94353i 0.235954 + 0.971764i \(0.424179\pi\)
−0.235954 + 0.971764i \(0.575821\pi\)
\(258\) 0 0
\(259\) 1.16509e12 0.999677
\(260\) 0 0
\(261\) −2.66389e11 + 1.02286e11i −0.219945 + 0.0844524i
\(262\) 0 0
\(263\) 1.37942e12i 1.09627i 0.836391 + 0.548134i \(0.184661\pi\)
−0.836391 + 0.548134i \(0.815339\pi\)
\(264\) 0 0
\(265\) 1.53039e11 0.117104
\(266\) 0 0
\(267\) 3.28574e10 4.78126e10i 0.0242146 0.0352360i
\(268\) 0 0
\(269\) 1.18129e12i 0.838680i 0.907829 + 0.419340i \(0.137738\pi\)
−0.907829 + 0.419340i \(0.862262\pi\)
\(270\) 0 0
\(271\) 1.42251e12 0.973213 0.486606 0.873621i \(-0.338235\pi\)
0.486606 + 0.873621i \(0.338235\pi\)
\(272\) 0 0
\(273\) −7.91511e11 5.43937e11i −0.521968 0.358703i
\(274\) 0 0
\(275\) 2.13224e11i 0.135573i
\(276\) 0 0
\(277\) 5.29960e11 0.324971 0.162485 0.986711i \(-0.448049\pi\)
0.162485 + 0.986711i \(0.448049\pi\)
\(278\) 0 0
\(279\) 8.85385e11 + 2.30587e12i 0.523734 + 1.36400i
\(280\) 0 0
\(281\) 2.28441e12i 1.30389i −0.758265 0.651946i \(-0.773953\pi\)
0.758265 0.651946i \(-0.226047\pi\)
\(282\) 0 0
\(283\) −2.31274e12 −1.27408 −0.637038 0.770833i \(-0.719840\pi\)
−0.637038 + 0.770833i \(0.719840\pi\)
\(284\) 0 0
\(285\) −3.83146e11 + 5.57537e11i −0.203770 + 0.296517i
\(286\) 0 0
\(287\) 3.46630e12i 1.78015i
\(288\) 0 0
\(289\) −5.09295e12 −2.52627
\(290\) 0 0
\(291\) −1.77060e12 1.21678e12i −0.848509 0.583106i
\(292\) 0 0
\(293\) 1.05989e12i 0.490822i 0.969419 + 0.245411i \(0.0789229\pi\)
−0.969419 + 0.245411i \(0.921077\pi\)
\(294\) 0 0
\(295\) −1.06019e12 −0.474542
\(296\) 0 0
\(297\) 8.71257e11 + 2.09042e11i 0.377020 + 0.0904588i
\(298\) 0 0
\(299\) 2.38781e11i 0.0999179i
\(300\) 0 0
\(301\) 4.61555e12 1.86806
\(302\) 0 0
\(303\) −2.31115e12 + 3.36308e12i −0.904931 + 1.31681i
\(304\) 0 0
\(305\) 1.92679e12i 0.730020i
\(306\) 0 0
\(307\) −6.89209e11 −0.252731 −0.126366 0.991984i \(-0.540331\pi\)
−0.126366 + 0.991984i \(0.540331\pi\)
\(308\) 0 0
\(309\) −1.67598e12 1.15176e12i −0.594945 0.408854i
\(310\) 0 0
\(311\) 1.95674e12i 0.672559i 0.941762 + 0.336280i \(0.109169\pi\)
−0.941762 + 0.336280i \(0.890831\pi\)
\(312\) 0 0
\(313\) −2.48821e11 −0.0828256 −0.0414128 0.999142i \(-0.513186\pi\)
−0.0414128 + 0.999142i \(0.513186\pi\)
\(314\) 0 0
\(315\) 4.64832e12 1.78482e12i 1.49880 0.575495i
\(316\) 0 0
\(317\) 4.63675e12i 1.44850i −0.689539 0.724249i \(-0.742187\pi\)
0.689539 0.724249i \(-0.257813\pi\)
\(318\) 0 0
\(319\) 3.01751e11 0.0913473
\(320\) 0 0
\(321\) −1.97571e12 + 2.87497e12i −0.579694 + 0.843544i
\(322\) 0 0
\(323\) 2.04456e12i 0.581549i
\(324\) 0 0
\(325\) 5.81050e11 0.160249
\(326\) 0 0
\(327\) −9.46400e11 6.50378e11i −0.253125 0.173951i
\(328\) 0 0
\(329\) 3.60147e12i 0.934331i
\(330\) 0 0
\(331\) 1.41443e12 0.355994 0.177997 0.984031i \(-0.443038\pi\)
0.177997 + 0.984031i \(0.443038\pi\)
\(332\) 0 0
\(333\) 1.06175e12 + 2.76518e12i 0.259298 + 0.675308i
\(334\) 0 0
\(335\) 1.89545e12i 0.449249i
\(336\) 0 0
\(337\) 8.67755e11 0.199640 0.0998201 0.995006i \(-0.468173\pi\)
0.0998201 + 0.995006i \(0.468173\pi\)
\(338\) 0 0
\(339\) 1.81886e12 2.64672e12i 0.406257 0.591167i
\(340\) 0 0
\(341\) 2.61196e12i 0.566493i
\(342\) 0 0
\(343\) −5.91785e11 −0.124650
\(344\) 0 0
\(345\) −1.02028e12 7.01146e11i −0.208748 0.143454i
\(346\) 0 0
\(347\) 5.20712e12i 1.03502i −0.855676 0.517512i \(-0.826858\pi\)
0.855676 0.517512i \(-0.173142\pi\)
\(348\) 0 0
\(349\) 1.11953e12 0.216226 0.108113 0.994139i \(-0.465519\pi\)
0.108113 + 0.994139i \(0.465519\pi\)
\(350\) 0 0
\(351\) 5.69653e11 2.37424e12i 0.106924 0.445644i
\(352\) 0 0
\(353\) 3.73952e12i 0.682248i 0.940018 + 0.341124i \(0.110808\pi\)
−0.940018 + 0.341124i \(0.889192\pi\)
\(354\) 0 0
\(355\) −2.07432e12 −0.367904
\(356\) 0 0
\(357\) 8.52299e12 1.24023e13i 1.46977 2.13875i
\(358\) 0 0
\(359\) 3.54489e12i 0.594471i −0.954804 0.297235i \(-0.903935\pi\)
0.954804 0.297235i \(-0.0960646\pi\)
\(360\) 0 0
\(361\) −5.54305e12 −0.904092
\(362\) 0 0
\(363\) 4.41360e12 + 3.03308e12i 0.700260 + 0.481228i
\(364\) 0 0
\(365\) 7.93577e12i 1.22497i
\(366\) 0 0
\(367\) 1.01161e13 1.51944 0.759722 0.650248i \(-0.225335\pi\)
0.759722 + 0.650248i \(0.225335\pi\)
\(368\) 0 0
\(369\) 8.22679e12 3.15885e12i 1.20254 0.461739i
\(370\) 0 0
\(371\) 9.79093e11i 0.139301i
\(372\) 0 0
\(373\) 3.81055e12 0.527769 0.263885 0.964554i \(-0.414996\pi\)
0.263885 + 0.964554i \(0.414996\pi\)
\(374\) 0 0
\(375\) 3.17325e12 4.61757e12i 0.427906 0.622669i
\(376\) 0 0
\(377\) 8.22293e11i 0.107974i
\(378\) 0 0
\(379\) −1.11052e13 −1.42014 −0.710069 0.704132i \(-0.751336\pi\)
−0.710069 + 0.704132i \(0.751336\pi\)
\(380\) 0 0
\(381\) 6.36482e12 + 4.37399e12i 0.792796 + 0.544819i
\(382\) 0 0
\(383\) 4.29169e12i 0.520756i −0.965507 0.260378i \(-0.916153\pi\)
0.965507 0.260378i \(-0.0838472\pi\)
\(384\) 0 0
\(385\) −5.26537e12 −0.622480
\(386\) 0 0
\(387\) 4.20617e12 + 1.09544e13i 0.484542 + 1.26192i
\(388\) 0 0
\(389\) 1.50554e13i 1.69023i 0.534588 + 0.845113i \(0.320467\pi\)
−0.534588 + 0.845113i \(0.679533\pi\)
\(390\) 0 0
\(391\) −3.74148e12 −0.409411
\(392\) 0 0
\(393\) −6.89642e12 + 1.00354e13i −0.735633 + 1.07046i
\(394\) 0 0
\(395\) 7.13723e12i 0.742240i
\(396\) 0 0
\(397\) −1.11669e13 −1.13235 −0.566174 0.824286i \(-0.691577\pi\)
−0.566174 + 0.824286i \(0.691577\pi\)
\(398\) 0 0
\(399\) −3.56693e12 2.45124e12i −0.352720 0.242394i
\(400\) 0 0
\(401\) 1.15685e13i 1.11572i −0.829935 0.557861i \(-0.811622\pi\)
0.829935 0.557861i \(-0.188378\pi\)
\(402\) 0 0
\(403\) −7.11777e12 −0.669605
\(404\) 0 0
\(405\) 8.47206e12 + 9.40565e12i 0.777524 + 0.863205i
\(406\) 0 0
\(407\) 3.13224e12i 0.280468i
\(408\) 0 0
\(409\) −1.07411e13 −0.938498 −0.469249 0.883066i \(-0.655475\pi\)
−0.469249 + 0.883066i \(0.655475\pi\)
\(410\) 0 0
\(411\) 3.78123e12 5.50227e12i 0.322421 0.469172i
\(412\) 0 0
\(413\) 6.78275e12i 0.564489i
\(414\) 0 0
\(415\) 7.93468e12 0.644598
\(416\) 0 0
\(417\) −1.26668e13 8.70477e12i −1.00458 0.690362i
\(418\) 0 0
\(419\) 8.81717e12i 0.682746i 0.939928 + 0.341373i \(0.110892\pi\)
−0.939928 + 0.341373i \(0.889108\pi\)
\(420\) 0 0
\(421\) −5.69741e12 −0.430792 −0.215396 0.976527i \(-0.569104\pi\)
−0.215396 + 0.976527i \(0.569104\pi\)
\(422\) 0 0
\(423\) −8.54761e12 + 3.28203e12i −0.631165 + 0.242349i
\(424\) 0 0
\(425\) 9.10451e12i 0.656617i
\(426\) 0 0
\(427\) −1.23269e13 −0.868392
\(428\) 0 0
\(429\) −1.46233e12 + 2.12792e12i −0.100637 + 0.146443i
\(430\) 0 0
\(431\) 1.80323e13i 1.21245i 0.795293 + 0.606226i \(0.207317\pi\)
−0.795293 + 0.606226i \(0.792683\pi\)
\(432\) 0 0
\(433\) 2.06339e13 1.35563 0.677816 0.735232i \(-0.262927\pi\)
0.677816 + 0.735232i \(0.262927\pi\)
\(434\) 0 0
\(435\) 3.51354e12 + 2.41455e12i 0.225579 + 0.155021i
\(436\) 0 0
\(437\) 1.07606e12i 0.0675195i
\(438\) 0 0
\(439\) −1.95313e13 −1.19787 −0.598935 0.800798i \(-0.704409\pi\)
−0.598935 + 0.800798i \(0.704409\pi\)
\(440\) 0 0
\(441\) 5.43969e12 + 1.41669e13i 0.326123 + 0.849343i
\(442\) 0 0
\(443\) 2.97469e13i 1.74351i −0.489946 0.871753i \(-0.662984\pi\)
0.489946 0.871753i \(-0.337016\pi\)
\(444\) 0 0
\(445\) −8.66747e11 −0.0496698
\(446\) 0 0
\(447\) −4.65839e12 + 6.77868e12i −0.261035 + 0.379846i
\(448\) 0 0
\(449\) 1.37505e13i 0.753509i 0.926313 + 0.376754i \(0.122960\pi\)
−0.926313 + 0.376754i \(0.877040\pi\)
\(450\) 0 0
\(451\) −9.31887e12 −0.499437
\(452\) 0 0
\(453\) −2.45102e13 1.68437e13i −1.28486 0.882971i
\(454\) 0 0
\(455\) 1.43485e13i 0.735783i
\(456\) 0 0
\(457\) 4.10224e11 0.0205798 0.0102899 0.999947i \(-0.496725\pi\)
0.0102899 + 0.999947i \(0.496725\pi\)
\(458\) 0 0
\(459\) 3.72021e13 + 8.92594e12i 1.82601 + 0.438118i
\(460\) 0 0
\(461\) 2.10914e11i 0.0101298i 0.999987 + 0.00506490i \(0.00161221\pi\)
−0.999987 + 0.00506490i \(0.998388\pi\)
\(462\) 0 0
\(463\) 1.96738e13 0.924660 0.462330 0.886708i \(-0.347013\pi\)
0.462330 + 0.886708i \(0.347013\pi\)
\(464\) 0 0
\(465\) 2.09003e13 3.04132e13i 0.961365 1.39893i
\(466\) 0 0
\(467\) 1.21902e13i 0.548815i −0.961614 0.274407i \(-0.911518\pi\)
0.961614 0.274407i \(-0.0884817\pi\)
\(468\) 0 0
\(469\) −1.21264e13 −0.534402
\(470\) 0 0
\(471\) −3.18370e13 2.18788e13i −1.37350 0.943885i
\(472\) 0 0
\(473\) 1.24085e13i 0.524101i
\(474\) 0 0
\(475\) 2.61849e12 0.108289
\(476\) 0 0
\(477\) −2.32374e12 + 8.92250e11i −0.0941014 + 0.0361322i
\(478\) 0 0
\(479\) 5.00886e12i 0.198637i 0.995056 + 0.0993187i \(0.0316663\pi\)
−0.995056 + 0.0993187i \(0.968334\pi\)
\(480\) 0 0
\(481\) −8.53558e12 −0.331518
\(482\) 0 0
\(483\) 4.48569e12 6.52737e12i 0.170645 0.248315i
\(484\) 0 0
\(485\) 3.20975e13i 1.19608i
\(486\) 0 0
\(487\) 4.17000e13 1.52227 0.761134 0.648595i \(-0.224643\pi\)
0.761134 + 0.648595i \(0.224643\pi\)
\(488\) 0 0
\(489\) 1.84414e13 + 1.26732e13i 0.659553 + 0.453253i
\(490\) 0 0
\(491\) 2.10340e12i 0.0737081i −0.999321 0.0368540i \(-0.988266\pi\)
0.999321 0.0368540i \(-0.0117337\pi\)
\(492\) 0 0
\(493\) 1.28846e13 0.442421
\(494\) 0 0
\(495\) −4.79835e12 1.24966e13i −0.161460 0.420501i
\(496\) 0 0
\(497\) 1.32708e13i 0.437639i
\(498\) 0 0
\(499\) −2.74482e13 −0.887179 −0.443589 0.896230i \(-0.646295\pi\)
−0.443589 + 0.896230i \(0.646295\pi\)
\(500\) 0 0
\(501\) −2.92342e13 + 4.25403e13i −0.926197 + 1.34776i
\(502\) 0 0
\(503\) 2.26985e13i 0.704949i 0.935822 + 0.352474i \(0.114660\pi\)
−0.935822 + 0.352474i \(0.885340\pi\)
\(504\) 0 0
\(505\) 6.09659e13 1.85622
\(506\) 0 0
\(507\) −2.18101e13 1.49882e13i −0.651055 0.447413i
\(508\) 0 0
\(509\) 4.21460e13i 1.23358i −0.787127 0.616791i \(-0.788433\pi\)
0.787127 0.616791i \(-0.211567\pi\)
\(510\) 0 0
\(511\) 5.07703e13 1.45715
\(512\) 0 0
\(513\) 2.56713e12 1.06994e13i 0.0722539 0.301144i
\(514\) 0 0
\(515\) 3.03822e13i 0.838653i
\(516\) 0 0
\(517\) 9.68227e12 0.262135
\(518\) 0 0
\(519\) −4.18569e13 + 6.09083e13i −1.11155 + 1.61748i
\(520\) 0 0
\(521\) 6.54420e13i 1.70478i −0.522907 0.852390i \(-0.675152\pi\)
0.522907 0.852390i \(-0.324848\pi\)
\(522\) 0 0
\(523\) 6.14531e13 1.57049 0.785245 0.619185i \(-0.212537\pi\)
0.785245 + 0.619185i \(0.212537\pi\)
\(524\) 0 0
\(525\) −1.58837e13 1.09155e13i −0.398250 0.273682i
\(526\) 0 0
\(527\) 1.11529e14i 2.74369i
\(528\) 0 0
\(529\) 3.94574e13 0.952466
\(530\) 0 0
\(531\) 1.60979e13 6.18114e12i 0.381327 0.146418i
\(532\) 0 0
\(533\) 2.53946e13i 0.590343i
\(534\) 0 0
\(535\) 5.21173e13 1.18909
\(536\) 0 0
\(537\) 9.73183e11 1.41613e12i 0.0217933 0.0317126i
\(538\) 0 0
\(539\) 1.60475e13i 0.352748i
\(540\) 0 0
\(541\) 1.50207e13 0.324118 0.162059 0.986781i \(-0.448187\pi\)
0.162059 + 0.986781i \(0.448187\pi\)
\(542\) 0 0
\(543\) −2.54960e13 1.75211e13i −0.540098 0.371162i
\(544\) 0 0
\(545\) 1.71563e13i 0.356814i
\(546\) 0 0
\(547\) −7.15097e13 −1.46025 −0.730127 0.683312i \(-0.760539\pi\)
−0.730127 + 0.683312i \(0.760539\pi\)
\(548\) 0 0
\(549\) −1.12336e13 2.92563e13i −0.225245 0.586621i
\(550\) 0 0
\(551\) 3.70565e12i 0.0729636i
\(552\) 0 0
\(553\) −4.56616e13 −0.882928
\(554\) 0 0
\(555\) 2.50635e13 3.64713e13i 0.475967 0.692606i
\(556\) 0 0
\(557\) 7.34107e13i 1.36925i 0.728895 + 0.684626i \(0.240034\pi\)
−0.728895 + 0.684626i \(0.759966\pi\)
\(558\) 0 0
\(559\) −3.38141e13 −0.619497
\(560\) 0 0
\(561\) −3.33425e13 2.29134e13i −0.600045 0.412358i
\(562\) 0 0
\(563\) 4.77347e13i 0.843902i 0.906619 + 0.421951i \(0.138655\pi\)
−0.906619 + 0.421951i \(0.861345\pi\)
\(564\) 0 0
\(565\) −4.79797e13 −0.833327
\(566\) 0 0
\(567\) −6.01742e13 + 5.42013e13i −1.02682 + 0.924900i
\(568\) 0 0
\(569\) 1.90951e13i 0.320156i −0.987104 0.160078i \(-0.948825\pi\)
0.987104 0.160078i \(-0.0511745\pi\)
\(570\) 0 0
\(571\) 2.09448e13 0.345060 0.172530 0.985004i \(-0.444806\pi\)
0.172530 + 0.985004i \(0.444806\pi\)
\(572\) 0 0
\(573\) −2.84145e13 + 4.13475e13i −0.460009 + 0.669385i
\(574\) 0 0
\(575\) 4.79175e12i 0.0762351i
\(576\) 0 0
\(577\) 3.56688e13 0.557711 0.278855 0.960333i \(-0.410045\pi\)
0.278855 + 0.960333i \(0.410045\pi\)
\(578\) 0 0
\(579\) 6.24051e13 + 4.28856e13i 0.959019 + 0.659050i
\(580\) 0 0
\(581\) 5.07634e13i 0.766778i
\(582\) 0 0
\(583\) 2.63221e12 0.0390821
\(584\) 0 0
\(585\) −3.40542e13 + 1.30758e13i −0.497040 + 0.190849i
\(586\) 0 0
\(587\) 1.29418e14i 1.85697i 0.371375 + 0.928483i \(0.378886\pi\)
−0.371375 + 0.928483i \(0.621114\pi\)
\(588\) 0 0
\(589\) −3.20761e13 −0.452486
\(590\) 0 0
\(591\) 2.08773e13 3.03797e13i 0.289559 0.421352i
\(592\) 0 0
\(593\) 3.96596e13i 0.540848i 0.962741 + 0.270424i \(0.0871639\pi\)
−0.962741 + 0.270424i \(0.912836\pi\)
\(594\) 0 0
\(595\) −2.24828e14 −3.01485
\(596\) 0 0
\(597\) 2.23684e13 + 1.53718e13i 0.294960 + 0.202700i
\(598\) 0 0
\(599\) 4.57555e13i 0.593347i 0.954979 + 0.296674i \(0.0958774\pi\)
−0.954979 + 0.296674i \(0.904123\pi\)
\(600\) 0 0
\(601\) 1.06033e14 1.35229 0.676143 0.736770i \(-0.263650\pi\)
0.676143 + 0.736770i \(0.263650\pi\)
\(602\) 0 0
\(603\) −1.10508e13 2.87804e13i −0.138614 0.361003i
\(604\) 0 0
\(605\) 8.00096e13i 0.987109i
\(606\) 0 0
\(607\) 9.55067e13 1.15902 0.579509 0.814966i \(-0.303244\pi\)
0.579509 + 0.814966i \(0.303244\pi\)
\(608\) 0 0
\(609\) −1.54475e13 + 2.24784e13i −0.184404 + 0.268336i
\(610\) 0 0
\(611\) 2.63849e13i 0.309848i
\(612\) 0 0
\(613\) −5.18411e13 −0.598924 −0.299462 0.954108i \(-0.596807\pi\)
−0.299462 + 0.954108i \(0.596807\pi\)
\(614\) 0 0
\(615\) −1.08507e14 7.45675e13i −1.23334 0.847567i
\(616\) 0 0
\(617\) 8.05443e13i 0.900760i 0.892837 + 0.450380i \(0.148711\pi\)
−0.892837 + 0.450380i \(0.851289\pi\)
\(618\) 0 0
\(619\) 5.14946e13 0.566642 0.283321 0.959025i \(-0.408564\pi\)
0.283321 + 0.959025i \(0.408564\pi\)
\(620\) 0 0
\(621\) 1.95797e13 + 4.69777e12i 0.212005 + 0.0508667i
\(622\) 0 0
\(623\) 5.54515e12i 0.0590844i
\(624\) 0 0
\(625\) −1.17054e14 −1.22740
\(626\) 0 0
\(627\) −6.58996e12 + 9.58941e12i −0.0680057 + 0.0989587i
\(628\) 0 0
\(629\) 1.33745e14i 1.35839i
\(630\) 0 0
\(631\) 1.02922e13 0.102887 0.0514435 0.998676i \(-0.483618\pi\)
0.0514435 + 0.998676i \(0.483618\pi\)
\(632\) 0 0
\(633\) −3.06543e13 2.10660e13i −0.301629 0.207283i
\(634\) 0 0
\(635\) 1.15381e14i 1.11755i
\(636\) 0 0
\(637\) −4.37307e13 −0.416955
\(638\) 0 0
\(639\) 3.14965e13 1.20937e13i 0.295636 0.113516i
\(640\) 0 0
\(641\) 4.62451e13i 0.427342i −0.976906 0.213671i \(-0.931458\pi\)
0.976906 0.213671i \(-0.0685420\pi\)
\(642\) 0 0
\(643\) −2.73102e13 −0.248468 −0.124234 0.992253i \(-0.539647\pi\)
−0.124234 + 0.992253i \(0.539647\pi\)
\(644\) 0 0
\(645\) 9.92905e13 1.44483e14i 0.889424 1.29425i
\(646\) 0 0
\(647\) 1.34984e13i 0.119059i −0.998227 0.0595293i \(-0.981040\pi\)
0.998227 0.0595293i \(-0.0189600\pi\)
\(648\) 0 0
\(649\) −1.82349e13 −0.158372
\(650\) 0 0
\(651\) 1.94573e14 + 1.33713e14i 1.66410 + 1.14359i
\(652\) 0 0
\(653\) 8.41840e13i 0.709029i 0.935051 + 0.354514i \(0.115354\pi\)
−0.935051 + 0.354514i \(0.884646\pi\)
\(654\) 0 0
\(655\) 1.81921e14 1.50895
\(656\) 0 0
\(657\) 4.62671e13 + 1.20496e14i 0.377960 + 0.984345i
\(658\) 0 0
\(659\) 1.65464e14i 1.33130i −0.746264 0.665650i \(-0.768154\pi\)
0.746264 0.665650i \(-0.231846\pi\)
\(660\) 0 0
\(661\) 2.01681e14 1.59830 0.799148 0.601135i \(-0.205284\pi\)
0.799148 + 0.601135i \(0.205284\pi\)
\(662\) 0 0
\(663\) −6.24405e13 + 9.08606e13i −0.487415 + 0.709264i
\(664\) 0 0
\(665\) 6.46612e13i 0.497205i
\(666\) 0 0
\(667\) 6.78122e12 0.0513664
\(668\) 0 0
\(669\) 1.21315e14 + 8.33691e13i 0.905281 + 0.622120i
\(670\) 0 0
\(671\) 3.31400e13i 0.243635i
\(672\) 0 0
\(673\) 6.04368e12 0.0437750 0.0218875 0.999760i \(-0.493032\pi\)
0.0218875 + 0.999760i \(0.493032\pi\)
\(674\) 0 0
\(675\) 1.14316e13 4.76452e13i 0.0815806 0.340017i
\(676\) 0 0
\(677\) 1.21474e14i 0.854164i −0.904213 0.427082i \(-0.859542\pi\)
0.904213 0.427082i \(-0.140458\pi\)
\(678\) 0 0
\(679\) −2.05349e14 −1.42280
\(680\) 0 0
\(681\) 9.22913e13 1.34298e14i 0.630123 0.916926i
\(682\) 0 0
\(683\) 1.51629e14i 1.02019i −0.860119 0.510094i \(-0.829611\pi\)
0.860119 0.510094i \(-0.170389\pi\)
\(684\) 0 0
\(685\) −9.97450e13 −0.661360
\(686\) 0 0
\(687\) 7.07663e13 + 4.86315e13i 0.462427 + 0.317785i
\(688\) 0 0
\(689\) 7.17296e12i 0.0461958i
\(690\) 0 0
\(691\) −6.62249e13 −0.420369 −0.210185 0.977662i \(-0.567407\pi\)
−0.210185 + 0.977662i \(0.567407\pi\)
\(692\) 0 0
\(693\) 7.99493e13 3.06982e13i 0.500205 0.192064i
\(694\) 0 0
\(695\) 2.29623e14i 1.41609i
\(696\) 0 0
\(697\) −3.97909e14 −2.41891
\(698\) 0 0
\(699\) 1.54679e14 2.25082e14i 0.926928 1.34882i
\(700\) 0 0
\(701\) 5.78990e13i 0.342043i −0.985267 0.171022i \(-0.945293\pi\)
0.985267 0.171022i \(-0.0547068\pi\)
\(702\) 0 0
\(703\) −3.84654e13 −0.224024
\(704\) 0 0
\(705\) 1.12739e14 + 7.74754e13i 0.647332 + 0.444855i
\(706\) 0 0
\(707\) 3.90039e14i 2.20806i
\(708\) 0 0
\(709\) 2.70077e14 1.50750 0.753750 0.657162i \(-0.228243\pi\)
0.753750 + 0.657162i \(0.228243\pi\)
\(710\) 0 0
\(711\) −4.16115e13 1.08372e14i −0.229016 0.596441i
\(712\) 0 0
\(713\) 5.86983e13i 0.318550i
\(714\) 0 0
\(715\) 3.85748e13 0.206430
\(716\) 0 0
\(717\) −3.64166e13 + 5.29918e13i −0.192178 + 0.279649i
\(718\) 0 0
\(719\) 1.48102e14i 0.770755i −0.922759 0.385377i \(-0.874071\pi\)
0.922759 0.385377i \(-0.125929\pi\)
\(720\) 0 0
\(721\) −1.94375e14 −0.997616
\(722\) 0 0
\(723\) 1.77592e14 + 1.22044e14i 0.898944 + 0.617765i
\(724\) 0 0
\(725\) 1.65014e13i 0.0823819i
\(726\) 0 0
\(727\) −5.21602e13 −0.256842 −0.128421 0.991720i \(-0.540991\pi\)
−0.128421 + 0.991720i \(0.540991\pi\)
\(728\) 0 0
\(729\) −1.83476e14 9.34214e13i −0.891133 0.453742i
\(730\) 0 0
\(731\) 5.29837e14i 2.53837i
\(732\) 0 0
\(733\) 3.21782e14 1.52069 0.760346 0.649518i \(-0.225029\pi\)
0.760346 + 0.649518i \(0.225029\pi\)
\(734\) 0 0
\(735\) 1.28409e14 1.86855e14i 0.598630 0.871099i
\(736\) 0 0
\(737\) 3.26009e13i 0.149931i
\(738\) 0 0
\(739\) −1.66542e14 −0.755617 −0.377809 0.925884i \(-0.623322\pi\)
−0.377809 + 0.925884i \(0.623322\pi\)
\(740\) 0 0
\(741\) 2.61318e13 + 1.79581e13i 0.116971 + 0.0803839i
\(742\) 0 0
\(743\) 1.13631e14i 0.501825i 0.968010 + 0.250912i \(0.0807306\pi\)
−0.968010 + 0.250912i \(0.919269\pi\)
\(744\) 0 0
\(745\) 1.22884e14 0.535443
\(746\) 0 0
\(747\) −1.20480e14 + 4.62608e13i −0.517979 + 0.198889i
\(748\) 0 0
\(749\) 3.33429e14i 1.41447i
\(750\) 0 0
\(751\) 1.64956e14 0.690508 0.345254 0.938509i \(-0.387793\pi\)
0.345254 + 0.938509i \(0.387793\pi\)
\(752\) 0 0
\(753\) −1.18290e14 + 1.72130e14i −0.488622 + 0.711020i
\(754\) 0 0
\(755\) 4.44320e14i 1.81118i
\(756\) 0 0
\(757\) −2.67990e14 −1.07805 −0.539026 0.842289i \(-0.681207\pi\)
−0.539026 + 0.842289i \(0.681207\pi\)
\(758\) 0 0
\(759\) −1.75483e13 1.20594e13i −0.0696669 0.0478760i
\(760\) 0 0
\(761\) 1.29795e14i 0.508550i 0.967132 + 0.254275i \(0.0818368\pi\)
−0.967132 + 0.254275i \(0.918163\pi\)
\(762\) 0 0
\(763\) −1.09760e14 −0.424446
\(764\) 0 0
\(765\) −2.04886e14 5.33599e14i −0.781998 2.03661i
\(766\) 0 0
\(767\) 4.96913e13i 0.187199i
\(768\) 0 0
\(769\) −2.19185e14 −0.815041 −0.407521 0.913196i \(-0.633607\pi\)
−0.407521 + 0.913196i \(0.633607\pi\)
\(770\) 0 0
\(771\) −2.99890e14 + 4.36386e14i −1.10075 + 1.60176i
\(772\) 0 0
\(773\) 4.05042e14i 1.46758i −0.679374 0.733792i \(-0.737749\pi\)
0.679374 0.733792i \(-0.262251\pi\)
\(774\) 0 0
\(775\) −1.42837e14 −0.510894
\(776\) 0 0
\(777\) 2.33331e14 + 1.60348e14i 0.823886 + 0.566185i
\(778\) 0 0
\(779\) 1.14440e14i 0.398925i
\(780\) 0 0
\(781\) −3.56775e13 −0.122783
\(782\) 0 0
\(783\) −6.74268e13 1.61778e13i −0.229099 0.0549681i
\(784\) 0 0
\(785\) 5.77141e14i 1.93613i
\(786\) 0 0
\(787\) &mi