Properties

Label 252.9.z.d.145.2
Level $252$
Weight $9$
Character 252.145
Analytic conductor $102.659$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 252.z (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(102.659409735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Defining polynomial: \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + \cdots + 45\!\cdots\!96 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{10}\cdot 7^{4} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 145.2
Root \(221.993 + 384.503i\) of defining polynomial
Character \(\chi\) \(=\) 252.145
Dual form 252.9.z.d.73.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-632.551 - 365.204i) q^{5} +(984.437 + 2189.91i) q^{7} +O(q^{10})\) \(q+(-632.551 - 365.204i) q^{5} +(984.437 + 2189.91i) q^{7} +(-6353.95 - 11005.4i) q^{11} +21176.4i q^{13} +(82551.9 - 47661.3i) q^{17} +(-133336. - 76981.8i) q^{19} +(47111.5 - 81599.5i) q^{23} +(71435.0 + 123729. i) q^{25} -541664. q^{29} +(-185730. + 107231. i) q^{31} +(177055. - 1.74475e6i) q^{35} +(-370376. + 641510. i) q^{37} +782599. i q^{41} -221324. q^{43} +(-7.13230e6 - 4.11784e6i) q^{47} +(-3.82657e6 + 4.31165e6i) q^{49} +(-659083. - 1.14157e6i) q^{53} +9.28194e6i q^{55} +(7.52865e6 - 4.34667e6i) q^{59} +(1.31192e7 + 7.57439e6i) q^{61} +(7.73369e6 - 1.33951e7i) q^{65} +(1.99100e7 + 3.44851e7i) q^{67} +9.34713e6 q^{71} +(2.94520e7 - 1.70041e7i) q^{73} +(1.78456e7 - 2.47486e7i) q^{77} +(2.26450e7 - 3.92223e7i) q^{79} +6.58893e7i q^{83} -6.96244e7 q^{85} +(1.09902e7 + 6.34517e6i) q^{89} +(-4.63742e7 + 2.08468e7i) q^{91} +(5.62280e7 + 9.73898e7i) q^{95} -6.15780e6i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) −632.551 365.204i −1.01208 0.584326i −0.100282 0.994959i \(-0.531974\pi\)
−0.911801 + 0.410633i \(0.865308\pi\)
\(6\) 0 0
\(7\) 984.437 + 2189.91i 0.410011 + 0.912080i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −6353.95 11005.4i −0.433983 0.751681i 0.563229 0.826301i \(-0.309559\pi\)
−0.997212 + 0.0746198i \(0.976226\pi\)
\(12\) 0 0
\(13\) 21176.4i 0.741444i 0.928744 + 0.370722i \(0.120890\pi\)
−0.928744 + 0.370722i \(0.879110\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 82551.9 47661.3i 0.988397 0.570651i 0.0836020 0.996499i \(-0.473358\pi\)
0.904795 + 0.425848i \(0.140024\pi\)
\(18\) 0 0
\(19\) −133336. 76981.8i −1.02314 0.590709i −0.108126 0.994137i \(-0.534485\pi\)
−0.915011 + 0.403428i \(0.867818\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 47111.5 81599.5i 0.168351 0.291593i −0.769489 0.638660i \(-0.779489\pi\)
0.937840 + 0.347067i \(0.112822\pi\)
\(24\) 0 0
\(25\) 71435.0 + 123729.i 0.182874 + 0.316746i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −541664. −0.765840 −0.382920 0.923782i \(-0.625081\pi\)
−0.382920 + 0.923782i \(0.625081\pi\)
\(30\) 0 0
\(31\) −185730. + 107231.i −0.201110 + 0.116111i −0.597173 0.802112i \(-0.703710\pi\)
0.396063 + 0.918223i \(0.370376\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 177055. 1.74475e6i 0.117987 1.16268i
\(36\) 0 0
\(37\) −370376. + 641510.i −0.197622 + 0.342292i −0.947757 0.318993i \(-0.896655\pi\)
0.750135 + 0.661285i \(0.229989\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 782599.i 0.276952i 0.990366 + 0.138476i \(0.0442203\pi\)
−0.990366 + 0.138476i \(0.955780\pi\)
\(42\) 0 0
\(43\) −221324. −0.0647373 −0.0323687 0.999476i \(-0.510305\pi\)
−0.0323687 + 0.999476i \(0.510305\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −7.13230e6 4.11784e6i −1.46163 0.843874i −0.462546 0.886595i \(-0.653064\pi\)
−0.999087 + 0.0427209i \(0.986397\pi\)
\(48\) 0 0
\(49\) −3.82657e6 + 4.31165e6i −0.663782 + 0.747926i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −659083. 1.14157e6i −0.0835289 0.144676i 0.821235 0.570591i \(-0.193286\pi\)
−0.904763 + 0.425915i \(0.859952\pi\)
\(54\) 0 0
\(55\) 9.28194e6i 1.01435i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.52865e6 4.34667e6i 0.621311 0.358714i −0.156068 0.987746i \(-0.549882\pi\)
0.777379 + 0.629032i \(0.216549\pi\)
\(60\) 0 0
\(61\) 1.31192e7 + 7.57439e6i 0.947521 + 0.547052i 0.892310 0.451423i \(-0.149083\pi\)
0.0552112 + 0.998475i \(0.482417\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 7.73369e6 1.33951e7i 0.433245 0.750402i
\(66\) 0 0
\(67\) 1.99100e7 + 3.44851e7i 0.988033 + 1.71132i 0.627596 + 0.778539i \(0.284039\pi\)
0.360436 + 0.932784i \(0.382628\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9.34713e6 0.367828 0.183914 0.982942i \(-0.441123\pi\)
0.183914 + 0.982942i \(0.441123\pi\)
\(72\) 0 0
\(73\) 2.94520e7 1.70041e7i 1.03711 0.598774i 0.118094 0.993002i \(-0.462321\pi\)
0.919012 + 0.394229i \(0.128988\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.78456e7 2.47486e7i 0.507656 0.704025i
\(78\) 0 0
\(79\) 2.26450e7 3.92223e7i 0.581385 1.00699i −0.413931 0.910308i \(-0.635844\pi\)
0.995316 0.0966799i \(-0.0308223\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 6.58893e7i 1.38836i 0.719801 + 0.694180i \(0.244233\pi\)
−0.719801 + 0.694180i \(0.755767\pi\)
\(84\) 0 0
\(85\) −6.96244e7 −1.33378
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.09902e7 + 6.34517e6i 0.175164 + 0.101131i 0.585018 0.811020i \(-0.301087\pi\)
−0.409855 + 0.912151i \(0.634421\pi\)
\(90\) 0 0
\(91\) −4.63742e7 + 2.08468e7i −0.676256 + 0.304000i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 5.62280e7 + 9.73898e7i 0.690333 + 1.19569i
\(96\) 0 0
\(97\) 6.15780e6i 0.0695566i −0.999395 0.0347783i \(-0.988927\pi\)
0.999395 0.0347783i \(-0.0110725\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.15329e8 + 6.65855e7i −1.10829 + 0.639874i −0.938387 0.345587i \(-0.887680\pi\)
−0.169907 + 0.985460i \(0.554347\pi\)
\(102\) 0 0
\(103\) 4.81925e7 + 2.78240e7i 0.428184 + 0.247212i 0.698573 0.715539i \(-0.253819\pi\)
−0.270389 + 0.962751i \(0.587152\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −7.23667e6 + 1.25343e7i −0.0552082 + 0.0956234i −0.892309 0.451426i \(-0.850916\pi\)
0.837101 + 0.547049i \(0.184249\pi\)
\(108\) 0 0
\(109\) −9.01793e7 1.56195e8i −0.638853 1.10653i −0.985685 0.168598i \(-0.946076\pi\)
0.346832 0.937927i \(-0.387257\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.21791e7 0.136028 0.0680142 0.997684i \(-0.478334\pi\)
0.0680142 + 0.997684i \(0.478334\pi\)
\(114\) 0 0
\(115\) −5.96009e7 + 3.44106e7i −0.340770 + 0.196744i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.85641e8 + 1.33861e8i 0.925733 + 0.667524i
\(120\) 0 0
\(121\) 2.64341e7 4.57852e7i 0.123317 0.213591i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.80962e8i 0.741221i
\(126\) 0 0
\(127\) 1.77711e8 0.683123 0.341561 0.939859i \(-0.389044\pi\)
0.341561 + 0.939859i \(0.389044\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 4.83164e8 + 2.78955e8i 1.64062 + 0.947215i 0.980612 + 0.195960i \(0.0627823\pi\)
0.660012 + 0.751255i \(0.270551\pi\)
\(132\) 0 0
\(133\) 3.73216e7 3.67778e8i 0.119276 1.17538i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.96914e8 + 3.41064e8i 0.558977 + 0.968176i 0.997582 + 0.0694962i \(0.0221392\pi\)
−0.438606 + 0.898680i \(0.644528\pi\)
\(138\) 0 0
\(139\) 4.85677e8i 1.30103i 0.759492 + 0.650516i \(0.225447\pi\)
−0.759492 + 0.650516i \(0.774553\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.33054e8 1.34554e8i 0.557329 0.321774i
\(144\) 0 0
\(145\) 3.42630e8 + 1.97818e8i 0.775093 + 0.447500i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.60563e8 + 2.78103e8i −0.325762 + 0.564236i −0.981666 0.190608i \(-0.938954\pi\)
0.655905 + 0.754844i \(0.272287\pi\)
\(150\) 0 0
\(151\) 4.12702e8 + 7.14822e8i 0.793833 + 1.37496i 0.923577 + 0.383412i \(0.125251\pi\)
−0.129744 + 0.991547i \(0.541416\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.56645e8 0.271387
\(156\) 0 0
\(157\) 9.15549e8 5.28592e8i 1.50689 0.870006i 0.506926 0.861989i \(-0.330782\pi\)
0.999968 0.00801653i \(-0.00255177\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.25074e8 + 2.28402e7i 0.334982 + 0.0339935i
\(162\) 0 0
\(163\) −5.67831e8 + 9.83512e8i −0.804394 + 1.39325i 0.112306 + 0.993674i \(0.464176\pi\)
−0.916699 + 0.399577i \(0.869157\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.00076e9i 1.28666i −0.765591 0.643328i \(-0.777553\pi\)
0.765591 0.643328i \(-0.222447\pi\)
\(168\) 0 0
\(169\) 3.67292e8 0.450261
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 5.46649e8 + 3.15608e8i 0.610273 + 0.352341i 0.773072 0.634318i \(-0.218719\pi\)
−0.162799 + 0.986659i \(0.552052\pi\)
\(174\) 0 0
\(175\) −2.00632e8 + 2.78239e8i −0.213918 + 0.296665i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 5.77342e8 + 9.99986e8i 0.562369 + 0.974052i 0.997289 + 0.0735826i \(0.0234433\pi\)
−0.434920 + 0.900469i \(0.643223\pi\)
\(180\) 0 0
\(181\) 1.42212e9i 1.32502i 0.749052 + 0.662511i \(0.230509\pi\)
−0.749052 + 0.662511i \(0.769491\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 4.68564e8 2.70525e8i 0.400020 0.230952i
\(186\) 0 0
\(187\) −1.04906e9 6.05676e8i −0.857895 0.495306i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −3.05844e8 + 5.29737e8i −0.229809 + 0.398040i −0.957751 0.287598i \(-0.907143\pi\)
0.727943 + 0.685638i \(0.240477\pi\)
\(192\) 0 0
\(193\) 9.49542e8 + 1.64465e9i 0.684360 + 1.18535i 0.973637 + 0.228101i \(0.0732518\pi\)
−0.289277 + 0.957245i \(0.593415\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.00843e9 −0.669544 −0.334772 0.942299i \(-0.608659\pi\)
−0.334772 + 0.942299i \(0.608659\pi\)
\(198\) 0 0
\(199\) 2.76255e8 1.59496e8i 0.176156 0.101704i −0.409329 0.912387i \(-0.634237\pi\)
0.585485 + 0.810683i \(0.300904\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.33234e8 1.18619e9i −0.314003 0.698507i
\(204\) 0 0
\(205\) 2.85808e8 4.95034e8i 0.161830 0.280298i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.95655e9i 1.02543i
\(210\) 0 0
\(211\) −1.39969e9 −0.706160 −0.353080 0.935593i \(-0.614866\pi\)
−0.353080 + 0.935593i \(0.614866\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.39999e8 + 8.08283e7i 0.0655195 + 0.0378277i
\(216\) 0 0
\(217\) −4.17665e8 3.01168e8i −0.188360 0.135822i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.00929e9 + 1.74815e9i 0.423106 + 0.732840i
\(222\) 0 0
\(223\) 3.09118e9i 1.24999i −0.780630 0.624993i \(-0.785102\pi\)
0.780630 0.624993i \(-0.214898\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 3.27805e9 1.89258e9i 1.23456 0.712774i 0.266583 0.963812i \(-0.414105\pi\)
0.967977 + 0.251038i \(0.0807719\pi\)
\(228\) 0 0
\(229\) −2.74391e9 1.58420e9i −0.997763 0.576059i −0.0901773 0.995926i \(-0.528743\pi\)
−0.907586 + 0.419867i \(0.862077\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −2.76314e9 + 4.78590e9i −0.937518 + 1.62383i −0.167437 + 0.985883i \(0.553549\pi\)
−0.770081 + 0.637946i \(0.779784\pi\)
\(234\) 0 0
\(235\) 3.00770e9 + 5.20949e9i 0.986195 + 1.70814i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 3.93530e9 1.20611 0.603054 0.797701i \(-0.293951\pi\)
0.603054 + 0.797701i \(0.293951\pi\)
\(240\) 0 0
\(241\) 5.76301e9 3.32727e9i 1.70837 0.986326i 0.771780 0.635889i \(-0.219367\pi\)
0.936586 0.350437i \(-0.113967\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 3.99513e9 1.32986e9i 1.10883 0.369098i
\(246\) 0 0
\(247\) 1.63019e9 2.82358e9i 0.437977 0.758599i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 4.25680e9i 1.07248i 0.844066 + 0.536239i \(0.180155\pi\)
−0.844066 + 0.536239i \(0.819845\pi\)
\(252\) 0 0
\(253\) −1.19738e9 −0.292246
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 2.63398e9 + 1.52073e9i 0.603782 + 0.348593i 0.770528 0.637406i \(-0.219993\pi\)
−0.166746 + 0.986000i \(0.553326\pi\)
\(258\) 0 0
\(259\) −1.76946e9 1.79562e8i −0.393225 0.0399039i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −4.20815e9 7.28873e9i −0.879566 1.52345i −0.851818 0.523838i \(-0.824500\pi\)
−0.0277486 0.999615i \(-0.508834\pi\)
\(264\) 0 0
\(265\) 9.62798e8i 0.195232i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.40038e9 + 3.69526e9i −1.22235 + 0.705726i −0.965419 0.260703i \(-0.916046\pi\)
−0.256934 + 0.966429i \(0.582712\pi\)
\(270\) 0 0
\(271\) −3.72934e9 2.15314e9i −0.691441 0.399204i 0.112711 0.993628i \(-0.464047\pi\)
−0.804152 + 0.594424i \(0.797380\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 9.07789e8 1.57234e9i 0.158728 0.274925i
\(276\) 0 0
\(277\) −2.54312e7 4.40481e7i −0.00431964 0.00748183i 0.863858 0.503736i \(-0.168042\pi\)
−0.868177 + 0.496254i \(0.834708\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.03421e10 −1.65877 −0.829383 0.558680i \(-0.811308\pi\)
−0.829383 + 0.558680i \(0.811308\pi\)
\(282\) 0 0
\(283\) −2.55984e9 + 1.47792e9i −0.399086 + 0.230412i −0.686090 0.727517i \(-0.740674\pi\)
0.287003 + 0.957930i \(0.407341\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −1.71382e9 + 7.70419e8i −0.252602 + 0.113553i
\(288\) 0 0
\(289\) 1.05533e9 1.82788e9i 0.151285 0.262034i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 4.22563e9i 0.573351i −0.958028 0.286676i \(-0.907450\pi\)
0.958028 0.286676i \(-0.0925502\pi\)
\(294\) 0 0
\(295\) −6.34968e9 −0.838424
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.72798e9 + 9.97651e8i 0.216199 + 0.124823i
\(300\) 0 0
\(301\) −2.17880e8 4.84679e8i −0.0265430 0.0590456i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −5.53239e9 9.58238e9i −0.639313 1.10732i
\(306\) 0 0
\(307\) 2.96070e9i 0.333304i −0.986016 0.166652i \(-0.946704\pi\)
0.986016 0.166652i \(-0.0532956\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.74956e9 4.47421e9i 0.828391 0.478272i −0.0249101 0.999690i \(-0.507930\pi\)
0.853302 + 0.521418i \(0.174597\pi\)
\(312\) 0 0
\(313\) −5.04664e9 2.91368e9i −0.525806 0.303574i 0.213501 0.976943i \(-0.431513\pi\)
−0.739307 + 0.673369i \(0.764847\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.50614e9 + 4.34076e9i −0.248181 + 0.429861i −0.963021 0.269426i \(-0.913166\pi\)
0.714840 + 0.699288i \(0.246499\pi\)
\(318\) 0 0
\(319\) 3.44171e9 + 5.96121e9i 0.332362 + 0.575667i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −1.46762e10 −1.34835
\(324\) 0 0
\(325\) −2.62013e9 + 1.51273e9i −0.234850 + 0.135590i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.99637e9 1.96728e10i 0.170395 1.67912i
\(330\) 0 0
\(331\) 4.78357e9 8.28539e9i 0.398511 0.690242i −0.595031 0.803703i \(-0.702860\pi\)
0.993542 + 0.113461i \(0.0361937\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.90848e10i 2.30933i
\(336\) 0 0
\(337\) 2.32884e9 0.180560 0.0902798 0.995916i \(-0.471224\pi\)
0.0902798 + 0.995916i \(0.471224\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.36023e9 + 1.36268e9i 0.174557 + 0.100781i
\(342\) 0 0
\(343\) −1.32091e10 4.13528e9i −0.954327 0.298764i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.04233e10 1.80536e10i −0.718928 1.24522i −0.961425 0.275068i \(-0.911300\pi\)
0.242497 0.970152i \(-0.422034\pi\)
\(348\) 0 0
\(349\) 2.91490e10i 1.96482i 0.186745 + 0.982409i \(0.440206\pi\)
−0.186745 + 0.982409i \(0.559794\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.78829e8 + 5.65127e8i −0.0630388 + 0.0363955i −0.531188 0.847254i \(-0.678254\pi\)
0.468149 + 0.883649i \(0.344921\pi\)
\(354\) 0 0
\(355\) −5.91254e9 3.41361e9i −0.372272 0.214932i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.49405e9 + 9.51597e9i −0.330761 + 0.572896i −0.982661 0.185409i \(-0.940639\pi\)
0.651900 + 0.758305i \(0.273972\pi\)
\(360\) 0 0
\(361\) 3.36060e9 + 5.82073e9i 0.197874 + 0.342727i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.48399e10 −1.39952
\(366\) 0 0
\(367\) −2.47539e9 + 1.42917e9i −0.136452 + 0.0787805i −0.566672 0.823944i \(-0.691769\pi\)
0.430220 + 0.902724i \(0.358436\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.85109e9 2.56713e9i 0.0977086 0.135504i
\(372\) 0 0
\(373\) 8.91785e9 1.54462e10i 0.460707 0.797968i −0.538289 0.842760i \(-0.680929\pi\)
0.998996 + 0.0447919i \(0.0142625\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 1.14705e10i 0.567827i
\(378\) 0 0
\(379\) 3.25934e10 1.57969 0.789847 0.613303i \(-0.210160\pi\)
0.789847 + 0.613303i \(0.210160\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.90349e10 + 1.09898e10i 0.884619 + 0.510735i 0.872179 0.489187i \(-0.162707\pi\)
0.0124407 + 0.999923i \(0.496040\pi\)
\(384\) 0 0
\(385\) −2.03266e10 + 9.13749e9i −0.925170 + 0.415895i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.09555e10 + 1.89755e10i 0.478448 + 0.828695i 0.999695 0.0247103i \(-0.00786634\pi\)
−0.521247 + 0.853406i \(0.674533\pi\)
\(390\) 0 0
\(391\) 8.98159e9i 0.384279i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −2.86482e10 + 1.65401e10i −1.17682 + 0.679437i
\(396\) 0 0
\(397\) −4.10594e10 2.37057e10i −1.65292 0.954312i −0.975865 0.218376i \(-0.929924\pi\)
−0.677052 0.735936i \(-0.736743\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −6.47336e8 + 1.12122e9i −0.0250353 + 0.0433623i −0.878272 0.478162i \(-0.841303\pi\)
0.853236 + 0.521524i \(0.174636\pi\)
\(402\) 0 0
\(403\) −2.27076e9 3.93308e9i −0.0860898 0.149112i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 9.41340e9 0.343059
\(408\) 0 0
\(409\) 1.05517e10 6.09204e9i 0.377077 0.217705i −0.299469 0.954106i \(-0.596809\pi\)
0.676546 + 0.736401i \(0.263476\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 1.69303e10 + 1.22080e10i 0.581921 + 0.419609i
\(414\) 0 0
\(415\) 2.40630e10 4.16783e10i 0.811255 1.40514i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 2.83249e9i 0.0918992i 0.998944 + 0.0459496i \(0.0146314\pi\)
−0.998944 + 0.0459496i \(0.985369\pi\)
\(420\) 0 0
\(421\) 1.47344e10 0.469033 0.234517 0.972112i \(-0.424649\pi\)
0.234517 + 0.972112i \(0.424649\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.17942e10 + 6.80938e9i 0.361503 + 0.208714i
\(426\) 0 0
\(427\) −3.67214e9 + 3.61864e10i −0.110461 + 1.08851i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.99404e10 3.45377e10i −0.577862 1.00089i −0.995724 0.0923761i \(-0.970554\pi\)
0.417862 0.908510i \(-0.362780\pi\)
\(432\) 0 0
\(433\) 3.77901e10i 1.07505i −0.843249 0.537523i \(-0.819360\pi\)
0.843249 0.537523i \(-0.180640\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.25634e10 + 7.25345e9i −0.344493 + 0.198893i
\(438\) 0 0
\(439\) 7.02545e9 + 4.05614e9i 0.189154 + 0.109208i 0.591587 0.806242i \(-0.298502\pi\)
−0.402432 + 0.915450i \(0.631835\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −2.85877e10 + 4.95154e10i −0.742274 + 1.28566i 0.209183 + 0.977876i \(0.432919\pi\)
−0.951457 + 0.307780i \(0.900414\pi\)
\(444\) 0 0
\(445\) −4.63456e9 8.02729e9i −0.118187 0.204705i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.27811e10 1.54470 0.772349 0.635199i \(-0.219082\pi\)
0.772349 + 0.635199i \(0.219082\pi\)
\(450\) 0 0
\(451\) 8.61279e9 4.97259e9i 0.208179 0.120192i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.69474e10 + 3.74937e9i 0.862062 + 0.0874809i
\(456\) 0 0
\(457\) −8.34859e9 + 1.44602e10i −0.191403 + 0.331519i −0.945715 0.324996i \(-0.894637\pi\)
0.754313 + 0.656515i \(0.227970\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.39906e10i 0.309766i 0.987933 + 0.154883i \(0.0495001\pi\)
−0.987933 + 0.154883i \(0.950500\pi\)
\(462\) 0 0
\(463\) −2.56476e10 −0.558114 −0.279057 0.960274i \(-0.590022\pi\)
−0.279057 + 0.960274i \(0.590022\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 3.36726e10 + 1.94409e10i 0.707960 + 0.408741i 0.810305 0.586008i \(-0.199301\pi\)
−0.102345 + 0.994749i \(0.532635\pi\)
\(468\) 0 0
\(469\) −5.59189e10 + 7.75493e10i −1.15576 + 1.60283i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.40628e9 + 2.43575e9i 0.0280949 + 0.0486618i
\(474\) 0 0
\(475\) 2.19968e10i 0.432100i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −6.40797e9 + 3.69965e9i −0.121725 + 0.0702778i −0.559626 0.828745i \(-0.689055\pi\)
0.437901 + 0.899023i \(0.355722\pi\)
\(480\) 0 0
\(481\) −1.35849e10 7.84322e9i −0.253790 0.146526i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −2.24885e9 + 3.89512e9i −0.0406437 + 0.0703970i
\(486\) 0 0
\(487\) −1.11183e10 1.92575e10i −0.197662 0.342361i 0.750108 0.661316i \(-0.230002\pi\)
−0.947770 + 0.318954i \(0.896668\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.62576e10 −0.623839 −0.311920 0.950109i \(-0.600972\pi\)
−0.311920 + 0.950109i \(0.600972\pi\)
\(492\) 0 0
\(493\) −4.47154e10 + 2.58164e10i −0.756953 + 0.437027i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 9.20166e9 + 2.04693e10i 0.150814 + 0.335489i
\(498\) 0 0
\(499\) 3.67859e10 6.37151e10i 0.593307 1.02764i −0.400476 0.916307i \(-0.631155\pi\)
0.993783 0.111331i \(-0.0355114\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 5.49729e10i 0.858770i −0.903122 0.429385i \(-0.858730\pi\)
0.903122 0.429385i \(-0.141270\pi\)
\(504\) 0 0
\(505\) 9.72691e10 1.49558
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 5.64437e10 + 3.25878e10i 0.840900 + 0.485494i 0.857570 0.514367i \(-0.171973\pi\)
−0.0166697 + 0.999861i \(0.505306\pi\)
\(510\) 0 0
\(511\) 6.62311e10 + 4.77576e10i 0.971355 + 0.700421i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.03228e10 3.52002e10i −0.288905 0.500398i
\(516\) 0 0
\(517\) 1.04658e11i 1.46491i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −6.65862e9 + 3.84435e9i −0.0903718 + 0.0521762i −0.544505 0.838758i \(-0.683282\pi\)
0.454133 + 0.890934i \(0.349949\pi\)
\(522\) 0 0
\(523\) 1.07896e11 + 6.22937e10i 1.44211 + 0.832602i 0.997990 0.0633652i \(-0.0201833\pi\)
0.444119 + 0.895968i \(0.353517\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.02215e10 + 1.77042e10i −0.132518 + 0.229528i
\(528\) 0 0
\(529\) 3.47165e10 + 6.01307e10i 0.443316 + 0.767846i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.65726e10 −0.205344
\(534\) 0 0
\(535\) 9.15513e9 5.28572e9i 0.111750 0.0645191i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 7.17651e10 + 1.47168e10i 0.850272 + 0.174365i
\(540\) 0 0
\(541\) −4.97811e10 + 8.62233e10i −0.581132 + 1.00655i 0.414213 + 0.910180i \(0.364057\pi\)
−0.995346 + 0.0963708i \(0.969277\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.31735e11i 1.49319i
\(546\) 0 0
\(547\) −2.34938e10 −0.262424 −0.131212 0.991354i \(-0.541887\pi\)
−0.131212 + 0.991354i \(0.541887\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.22235e10 + 4.16982e10i 0.783559 + 0.452388i
\(552\) 0 0
\(553\) 1.08186e11 + 1.09785e10i 1.15683 + 0.117393i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −1.24108e10 2.14962e10i −0.128938 0.223327i 0.794328 0.607490i \(-0.207823\pi\)
−0.923265 + 0.384163i \(0.874490\pi\)
\(558\) 0 0
\(559\) 4.68684e9i 0.0479991i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.47632e11 8.52355e10i 1.46942 0.848373i 0.470013 0.882660i \(-0.344249\pi\)
0.999412 + 0.0342868i \(0.0109160\pi\)
\(564\) 0 0
\(565\) −1.40294e10 8.09988e9i −0.137672 0.0794849i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.03247e10 3.52033e10i 0.193898 0.335842i −0.752640 0.658432i \(-0.771220\pi\)
0.946539 + 0.322590i \(0.104553\pi\)
\(570\) 0 0
\(571\) 4.24414e9 + 7.35107e9i 0.0399250 + 0.0691522i 0.885297 0.465025i \(-0.153955\pi\)
−0.845372 + 0.534177i \(0.820621\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.34616e10 0.123148
\(576\) 0 0
\(577\) −5.94782e10 + 3.43397e10i −0.536604 + 0.309809i −0.743702 0.668512i \(-0.766932\pi\)
0.207097 + 0.978320i \(0.433598\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.44291e11 + 6.48638e10i −1.26630 + 0.569243i
\(582\) 0 0
\(583\) −8.37556e9 + 1.45069e10i −0.0725003 + 0.125574i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.43383e11i 1.20766i −0.797114 0.603829i \(-0.793641\pi\)
0.797114 0.603829i \(-0.206359\pi\)
\(588\) 0 0
\(589\) 3.30193e10 0.274351
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.30721e11 + 7.54720e10i 1.05713 + 0.610333i 0.924636 0.380851i \(-0.124369\pi\)
0.132491 + 0.991184i \(0.457702\pi\)
\(594\) 0 0
\(595\) −6.85408e10 1.52471e11i −0.546867 1.21652i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 8.29322e10 + 1.43643e11i 0.644193 + 1.11577i 0.984487 + 0.175456i \(0.0561399\pi\)
−0.340294 + 0.940319i \(0.610527\pi\)
\(600\) 0 0
\(601\) 7.04035e10i 0.539630i −0.962912 0.269815i \(-0.913037\pi\)
0.962912 0.269815i \(-0.0869625\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.34418e10 + 1.93076e10i −0.249614 + 0.144115i
\(606\) 0 0
\(607\) −5.15559e10 2.97658e10i −0.379773 0.219262i 0.297947 0.954583i \(-0.403698\pi\)
−0.677719 + 0.735321i \(0.737032\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 8.72009e10 1.51036e11i 0.625685 1.08372i
\(612\) 0 0
\(613\) 1.14654e11 + 1.98587e11i 0.811986 + 1.40640i 0.911472 + 0.411363i \(0.134947\pi\)
−0.0994852 + 0.995039i \(0.531720\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.93904e11 −1.33797 −0.668986 0.743275i \(-0.733272\pi\)
−0.668986 + 0.743275i \(0.733272\pi\)
\(618\) 0 0
\(619\) 1.77090e10 1.02243e10i 0.120623 0.0696418i −0.438474 0.898744i \(-0.644481\pi\)
0.559098 + 0.829102i \(0.311148\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.07621e9 + 3.03138e10i −0.0204203 + 0.201228i
\(624\) 0 0
\(625\) 9.39923e10 1.62799e11i 0.615988 1.06692i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.06105e10i 0.451094i
\(630\) 0 0
\(631\) −1.43159e11 −0.903030 −0.451515 0.892263i \(-0.649116\pi\)
−0.451515 + 0.892263i \(0.649116\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.12411e11 6.49006e10i −0.691377 0.399166i
\(636\) 0 0
\(637\) −9.13050e10 8.10328e10i −0.554545 0.492157i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.32450e11 + 2.29411e11i 0.784551 + 1.35888i 0.929267 + 0.369409i \(0.120440\pi\)
−0.144716 + 0.989473i \(0.546227\pi\)
\(642\) 0 0
\(643\) 1.18901e9i 0.00695572i 0.999994 + 0.00347786i \(0.00110704\pi\)
−0.999994 + 0.00347786i \(0.998893\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 8.24205e10 4.75855e10i 0.470347 0.271555i −0.246038 0.969260i \(-0.579129\pi\)
0.716385 + 0.697705i \(0.245796\pi\)
\(648\) 0 0
\(649\) −9.56733e10 5.52370e10i −0.539277 0.311352i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −1.66756e11 + 2.88829e11i −0.917124 + 1.58850i −0.113362 + 0.993554i \(0.536162\pi\)
−0.803762 + 0.594951i \(0.797171\pi\)
\(654\) 0 0
\(655\) −2.03751e11 3.52906e11i −1.10696 1.91732i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.17025e11 −0.620493 −0.310246 0.950656i \(-0.600412\pi\)
−0.310246 + 0.950656i \(0.600412\pi\)
\(660\) 0 0
\(661\) 2.68769e10 1.55174e10i 0.140791 0.0812855i −0.427950 0.903802i \(-0.640764\pi\)
0.568741 + 0.822517i \(0.307431\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.57922e11 + 2.19008e11i −0.807523 + 1.11989i
\(666\) 0 0
\(667\) −2.55186e10 + 4.41995e10i −0.128930 + 0.223313i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.92509e11i 0.949645i
\(672\) 0 0
\(673\) −2.12193e11 −1.03436 −0.517179 0.855877i \(-0.673018\pi\)
−0.517179 + 0.855877i \(0.673018\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.30441e10 5.37191e10i −0.442929 0.255725i 0.261910 0.965092i \(-0.415648\pi\)
−0.704839 + 0.709367i \(0.748981\pi\)
\(678\) 0 0
\(679\) 1.34850e10 6.06196e9i 0.0634412 0.0285190i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −5.88995e10 1.02017e11i −0.270663 0.468802i 0.698369 0.715738i \(-0.253909\pi\)
−0.969032 + 0.246936i \(0.920576\pi\)
\(684\) 0 0
\(685\) 2.87654e11i 1.30650i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.41742e10 1.39570e10i 0.107269 0.0619320i
\(690\) 0 0
\(691\) 2.96618e11 + 1.71253e11i 1.30103 + 0.751148i 0.980580 0.196119i \(-0.0628339\pi\)
0.320446 + 0.947267i \(0.396167\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.77371e11 3.07215e11i 0.760227 1.31675i
\(696\) 0 0
\(697\) 3.72997e10 + 6.46050e10i 0.158043 + 0.273738i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 1.15900e11 0.479967 0.239984 0.970777i \(-0.422858\pi\)
0.239984 + 0.970777i \(0.422858\pi\)
\(702\) 0 0
\(703\) 9.87691e10 5.70244e10i 0.404390 0.233474i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −2.59351e11 1.87011e11i −1.03803 0.748498i
\(708\) 0 0
\(709\) −7.71407e10 + 1.33612e11i −0.305280 + 0.528761i −0.977324 0.211751i \(-0.932083\pi\)
0.672044 + 0.740512i \(0.265417\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.02073e10i 0.0781897i
\(714\) 0 0
\(715\) −1.96558e11 −0.752084
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.82639e11 1.05447e11i −0.683404 0.394564i 0.117732 0.993045i \(-0.462438\pi\)
−0.801136 + 0.598482i \(0.795771\pi\)
\(720\) 0 0
\(721\) −1.34893e10 + 1.32928e11i −0.0499172 + 0.491898i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −3.86938e10 6.70195e10i −0.140052 0.242577i
\(726\) 0 0
\(727\) 2.28475e10i 0.0817900i −0.999163 0.0408950i \(-0.986979\pi\)
0.999163 0.0408950i \(-0.0130209\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.82707e10 + 1.05486e10i −0.0639861 + 0.0369424i
\(732\) 0 0
\(733\) 3.90685e11 + 2.25562e11i 1.35335 + 0.781358i 0.988717 0.149793i \(-0.0478609\pi\)
0.364634 + 0.931151i \(0.381194\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.53014e11 4.38233e11i 0.857579 1.48537i
\(738\) 0 0
\(739\) 8.06607e10 + 1.39708e11i 0.270448 + 0.468430i 0.968977 0.247152i \(-0.0794948\pi\)
−0.698528 + 0.715582i \(0.746161\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 2.11855e11 0.695159 0.347579 0.937651i \(-0.387004\pi\)
0.347579 + 0.937651i \(0.387004\pi\)
\(744\) 0 0
\(745\) 2.03129e11 1.17276e11i 0.659395 0.380702i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −3.45729e10 3.50841e9i −0.109852 0.0111477i
\(750\) 0 0
\(751\) −2.80633e11 + 4.86071e11i −0.882224 + 1.52806i −0.0333617 + 0.999443i \(0.510621\pi\)
−0.848862 + 0.528614i \(0.822712\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 6.02882e11i 1.85543i
\(756\) 0 0
\(757\) −2.12454e11 −0.646967 −0.323483 0.946234i \(-0.604854\pi\)
−0.323483 + 0.946234i \(0.604854\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.11683e11 1.79950e11i −0.929338 0.536554i −0.0427362 0.999086i \(-0.513607\pi\)
−0.886602 + 0.462533i \(0.846941\pi\)
\(762\) 0 0
\(763\) 2.53277e11 3.51248e11i 0.747304 1.03637i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 9.20467e10 + 1.59429e11i 0.265966 + 0.460667i
\(768\) 0 0
\(769\) 1.74232e11i 0.498222i −0.968475 0.249111i \(-0.919862\pi\)
0.968475 0.249111i \(-0.0801385\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −2.44377e11 + 1.41091e11i −0.684450 + 0.395168i −0.801530 0.597955i \(-0.795980\pi\)
0.117079 + 0.993123i \(0.462647\pi\)
\(774\) 0 0
\(775\) −2.65352e10 1.53201e10i −0.0735555 0.0424673i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 6.02458e10 1.04349e11i 0.163598 0.283360i
\(780\) 0 0
\(781\) −5.93912e10 1.02869e11i −0.159631 0.276490i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.72175e11 −2.03347
\(786\) 0 0
\(787\) 5.01252e11 2.89398e11i 1.30664 0.754391i 0.325110 0.945676i \(-0.394599\pi\)
0.981535 + 0.191285i \(0.0612654\pi\)
\(788\) 0 0
\(789\)