Properties

Label 252.9.z.d.145.5
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: \(x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + 576413321817541 x^{6} + 47217566733462528 x^{5} + 5214056955297543333 x^{4} + 358752845334081085965 x^{3} + 30962072851910211245661 x^{2} + 1221542968331193193318500 x + 45396580558961892385326096\)
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 145.5
Root \(-72.3408 - 125.298i\) of defining polynomial
Character \(\chi\) \(=\) 252.145
Dual form 252.9.z.d.73.5

$q$-expansion

\(f(q)\) \(=\) \(q+(225.043 + 129.928i) q^{5} +(597.275 - 2325.52i) q^{7} +O(q^{10})\) \(q+(225.043 + 129.928i) q^{5} +(597.275 - 2325.52i) q^{7} +(-9723.49 - 16841.6i) q^{11} -46381.7i q^{13} +(105886. - 61133.6i) q^{17} +(18446.7 + 10650.2i) q^{19} +(-152199. + 263616. i) q^{23} +(-161550. - 279812. i) q^{25} -88119.4 q^{29} +(-1.54998e6 + 894884. i) q^{31} +(436564. - 445739. i) q^{35} +(755092. - 1.30786e6i) q^{37} +188022. i q^{41} -123402. q^{43} +(5.58909e6 + 3.22686e6i) q^{47} +(-5.05133e6 - 2.77796e6i) q^{49} +(6.88508e6 + 1.19253e7i) q^{53} -5.05343e6i q^{55} +(-1.00305e7 + 5.79109e6i) q^{59} +(-1.92663e7 - 1.11234e7i) q^{61} +(6.02630e6 - 1.04379e7i) q^{65} +(5.75873e6 + 9.97442e6i) q^{67} +3.11345e7 q^{71} +(-1.08437e7 + 6.26059e6i) q^{73} +(-4.49731e7 + 1.25532e7i) q^{77} +(2.13222e7 - 3.69312e7i) q^{79} -7.19982e7i q^{83} +3.17720e7 q^{85} +(-4.37683e7 - 2.52696e7i) q^{89} +(-1.07862e8 - 2.77026e7i) q^{91} +(2.76753e6 + 4.79351e6i) q^{95} +1.16642e8i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 285 q^{5} + 198 q^{7} + O(q^{10}) \) \( 12 q - 285 q^{5} + 198 q^{7} + 17919 q^{11} + 205782 q^{17} + 74313 q^{19} + 62832 q^{23} + 878679 q^{25} + 575454 q^{29} + 1442952 q^{31} + 3989514 q^{35} - 2058621 q^{37} + 7721322 q^{43} - 12088194 q^{47} - 16964694 q^{49} + 5506743 q^{53} - 7511901 q^{59} - 37215576 q^{61} - 5047122 q^{65} - 36824553 q^{67} + 30011556 q^{71} + 95080185 q^{73} + 38333727 q^{77} + 8514456 q^{79} + 20121540 q^{85} - 83038554 q^{89} - 198538635 q^{91} + 221605224 q^{95} + O(q^{100}) \)

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
\(5\) 225.043 + 129.928i 0.360068 + 0.207885i 0.669111 0.743163i \(-0.266675\pi\)
−0.309042 + 0.951048i \(0.600009\pi\)
\(6\) 0 0
\(7\) 597.275 2325.52i 0.248761 0.968565i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −9723.49 16841.6i −0.664127 1.15030i −0.979521 0.201341i \(-0.935470\pi\)
0.315394 0.948961i \(-0.397863\pi\)
\(12\) 0 0
\(13\) 46381.7i 1.62395i −0.583690 0.811976i \(-0.698392\pi\)
0.583690 0.811976i \(-0.301608\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 105886. 61133.6i 1.26778 0.731955i 0.293215 0.956047i \(-0.405275\pi\)
0.974568 + 0.224092i \(0.0719416\pi\)
\(18\) 0 0
\(19\) 18446.7 + 10650.2i 0.141548 + 0.0817230i 0.569102 0.822267i \(-0.307291\pi\)
−0.427553 + 0.903990i \(0.640624\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −152199. + 263616.i −0.543876 + 0.942020i 0.454801 + 0.890593i \(0.349710\pi\)
−0.998677 + 0.0514271i \(0.983623\pi\)
\(24\) 0 0
\(25\) −161550. 279812.i −0.413567 0.716320i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −88119.4 −0.124589 −0.0622945 0.998058i \(-0.519842\pi\)
−0.0622945 + 0.998058i \(0.519842\pi\)
\(30\) 0 0
\(31\) −1.54998e6 + 894884.i −1.67834 + 0.968991i −0.715624 + 0.698486i \(0.753857\pi\)
−0.962718 + 0.270505i \(0.912809\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 436564. 445739.i 0.290921 0.297036i
\(36\) 0 0
\(37\) 755092. 1.30786e6i 0.402896 0.697836i −0.591178 0.806541i \(-0.701337\pi\)
0.994074 + 0.108705i \(0.0346703\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 188022.i 0.0665385i 0.999446 + 0.0332692i \(0.0105919\pi\)
−0.999446 + 0.0332692i \(0.989408\pi\)
\(42\) 0 0
\(43\) −123402. −0.0360953 −0.0180476 0.999837i \(-0.505745\pi\)
−0.0180476 + 0.999837i \(0.505745\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 5.58909e6 + 3.22686e6i 1.14538 + 0.661285i 0.947757 0.318993i \(-0.103345\pi\)
0.197623 + 0.980278i \(0.436678\pi\)
\(48\) 0 0
\(49\) −5.05133e6 2.77796e6i −0.876236 0.481882i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.88508e6 + 1.19253e7i 0.872580 + 1.51135i 0.859318 + 0.511441i \(0.170888\pi\)
0.0132616 + 0.999912i \(0.495779\pi\)
\(54\) 0 0
\(55\) 5.05343e6i 0.552250i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.00305e7 + 5.79109e6i −0.827776 + 0.477917i −0.853090 0.521763i \(-0.825275\pi\)
0.0253148 + 0.999680i \(0.491941\pi\)
\(60\) 0 0
\(61\) −1.92663e7 1.11234e7i −1.39149 0.803375i −0.398007 0.917383i \(-0.630298\pi\)
−0.993480 + 0.114007i \(0.963631\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 6.02630e6 1.04379e7i 0.337596 0.584734i
\(66\) 0 0
\(67\) 5.75873e6 + 9.97442e6i 0.285777 + 0.494981i 0.972797 0.231658i \(-0.0744149\pi\)
−0.687020 + 0.726638i \(0.741082\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.11345e7 1.22520 0.612602 0.790392i \(-0.290123\pi\)
0.612602 + 0.790392i \(0.290123\pi\)
\(72\) 0 0
\(73\) −1.08437e7 + 6.26059e6i −0.381843 + 0.220457i −0.678620 0.734490i \(-0.737422\pi\)
0.296777 + 0.954947i \(0.404088\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.49731e7 + 1.25532e7i −1.27935 + 0.357100i
\(78\) 0 0
\(79\) 2.13222e7 3.69312e7i 0.547424 0.948167i −0.451026 0.892511i \(-0.648942\pi\)
0.998450 0.0556558i \(-0.0177249\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 7.19982e7i 1.51708i −0.651625 0.758541i \(-0.725912\pi\)
0.651625 0.758541i \(-0.274088\pi\)
\(84\) 0 0
\(85\) 3.17720e7 0.608651
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −4.37683e7 2.52696e7i −0.697589 0.402753i 0.108860 0.994057i \(-0.465280\pi\)
−0.806449 + 0.591304i \(0.798613\pi\)
\(90\) 0 0
\(91\) −1.07862e8 2.77026e7i −1.57290 0.403976i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.76753e6 + 4.79351e6i 0.0339781 + 0.0588517i
\(96\) 0 0
\(97\) 1.16642e8i 1.31755i 0.752339 + 0.658776i \(0.228925\pi\)
−0.752339 + 0.658776i \(0.771075\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −9.23786e7 + 5.33348e7i −0.887740 + 0.512537i −0.873203 0.487357i \(-0.837961\pi\)
−0.0145374 + 0.999894i \(0.504628\pi\)
\(102\) 0 0
\(103\) 1.77725e8 + 1.02609e8i 1.57906 + 0.911671i 0.994991 + 0.0999675i \(0.0318739\pi\)
0.584070 + 0.811703i \(0.301459\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −8.90703e7 + 1.54274e8i −0.679513 + 1.17695i 0.295615 + 0.955307i \(0.404476\pi\)
−0.975128 + 0.221644i \(0.928858\pi\)
\(108\) 0 0
\(109\) −5.48168e7 9.49454e7i −0.388336 0.672617i 0.603890 0.797068i \(-0.293617\pi\)
−0.992226 + 0.124450i \(0.960283\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −2.74592e8 −1.68413 −0.842063 0.539379i \(-0.818659\pi\)
−0.842063 + 0.539379i \(0.818659\pi\)
\(114\) 0 0
\(115\) −6.85024e7 + 3.95499e7i −0.391665 + 0.226128i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −7.89243e7 2.82755e8i −0.393571 1.41001i
\(120\) 0 0
\(121\) −8.19129e7 + 1.41877e8i −0.382130 + 0.661868i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.85466e8i 0.759669i
\(126\) 0 0
\(127\) −3.97605e7 −0.152840 −0.0764199 0.997076i \(-0.524349\pi\)
−0.0764199 + 0.997076i \(0.524349\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.31807e7 1.91569e7i −0.112668 0.0650490i 0.442607 0.896716i \(-0.354054\pi\)
−0.555275 + 0.831667i \(0.687387\pi\)
\(132\) 0 0
\(133\) 3.57851e7 3.65372e7i 0.114366 0.116769i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −2.07018e8 3.58565e8i −0.587659 1.01786i −0.994538 0.104374i \(-0.966716\pi\)
0.406879 0.913482i \(-0.366617\pi\)
\(138\) 0 0
\(139\) 2.15646e8i 0.577674i −0.957378 0.288837i \(-0.906731\pi\)
0.957378 0.288837i \(-0.0932686\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −7.81141e8 + 4.50992e8i −1.86804 + 1.07851i
\(144\) 0 0
\(145\) −1.98306e7 1.14492e7i −0.0448605 0.0259002i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.59668e8 4.49759e8i 0.526834 0.912503i −0.472677 0.881236i \(-0.656712\pi\)
0.999511 0.0312676i \(-0.00995442\pi\)
\(150\) 0 0
\(151\) −1.65131e8 2.86015e8i −0.317630 0.550151i 0.662363 0.749183i \(-0.269554\pi\)
−0.979993 + 0.199032i \(0.936220\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −4.65083e8 −0.805757
\(156\) 0 0
\(157\) −2.58909e8 + 1.49481e8i −0.426137 + 0.246030i −0.697700 0.716390i \(-0.745793\pi\)
0.271563 + 0.962421i \(0.412460\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 5.22141e8 + 5.11393e8i 0.777113 + 0.761117i
\(162\) 0 0
\(163\) 2.92142e8 5.06004e8i 0.413850 0.716810i −0.581457 0.813577i \(-0.697517\pi\)
0.995307 + 0.0967676i \(0.0308504\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 7.46657e8i 0.959965i 0.877278 + 0.479983i \(0.159357\pi\)
−0.877278 + 0.479983i \(0.840643\pi\)
\(168\) 0 0
\(169\) −1.33553e9 −1.63722
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −9.08205e8 5.24352e8i −1.01391 0.585381i −0.101576 0.994828i \(-0.532388\pi\)
−0.912334 + 0.409447i \(0.865722\pi\)
\(174\) 0 0
\(175\) −7.47200e8 + 2.08563e8i −0.796681 + 0.222374i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 1.24237e8 + 2.15185e8i 0.121015 + 0.209604i 0.920168 0.391523i \(-0.128052\pi\)
−0.799153 + 0.601127i \(0.794718\pi\)
\(180\) 0 0
\(181\) 4.91957e8i 0.458366i 0.973383 + 0.229183i \(0.0736055\pi\)
−0.973383 + 0.229183i \(0.926394\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.39856e8 1.96216e8i 0.290140 0.167512i
\(186\) 0 0
\(187\) −2.05917e9 1.18886e9i −1.68394 0.972222i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −9.53669e8 + 1.65180e9i −0.716579 + 1.24115i 0.245768 + 0.969329i \(0.420960\pi\)
−0.962347 + 0.271823i \(0.912374\pi\)
\(192\) 0 0
\(193\) −4.70293e8 8.14571e8i −0.338953 0.587083i 0.645283 0.763943i \(-0.276739\pi\)
−0.984236 + 0.176860i \(0.943406\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1.22807e9 −0.815379 −0.407689 0.913121i \(-0.633665\pi\)
−0.407689 + 0.913121i \(0.633665\pi\)
\(198\) 0 0
\(199\) 9.98896e7 5.76713e7i 0.0636954 0.0367745i −0.467814 0.883827i \(-0.654958\pi\)
0.531509 + 0.847052i \(0.321625\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −5.26315e7 + 2.04924e8i −0.0309929 + 0.120672i
\(204\) 0 0
\(205\) −2.44294e7 + 4.23129e7i −0.0138324 + 0.0239584i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 4.14229e8i 0.217098i
\(210\) 0 0
\(211\) 2.33973e9 1.18042 0.590209 0.807250i \(-0.299045\pi\)
0.590209 + 0.807250i \(0.299045\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.77708e7 1.60335e7i −0.0129968 0.00750368i
\(216\) 0 0
\(217\) 1.15531e9 + 4.13902e9i 0.521025 + 1.86663i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.83548e9 4.91120e9i −1.18866 2.05882i
\(222\) 0 0
\(223\) 1.14133e9i 0.461523i −0.973010 0.230762i \(-0.925878\pi\)
0.973010 0.230762i \(-0.0741218\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1.82252e8 1.05223e8i 0.0686387 0.0396285i −0.465288 0.885159i \(-0.654049\pi\)
0.533927 + 0.845531i \(0.320716\pi\)
\(228\) 0 0
\(229\) −3.18730e9 1.84019e9i −1.15899 0.669146i −0.207932 0.978143i \(-0.566673\pi\)
−0.951063 + 0.308997i \(0.900007\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.42196e8 + 2.46291e8i −0.0482464 + 0.0835652i −0.889140 0.457635i \(-0.848697\pi\)
0.840894 + 0.541200i \(0.182030\pi\)
\(234\) 0 0
\(235\) 8.38522e8 + 1.45236e9i 0.274943 + 0.476216i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.62607e9 −0.804850 −0.402425 0.915453i \(-0.631833\pi\)
−0.402425 + 0.915453i \(0.631833\pi\)
\(240\) 0 0
\(241\) 2.05781e8 1.18808e8i 0.0610011 0.0352190i −0.469189 0.883098i \(-0.655454\pi\)
0.530190 + 0.847879i \(0.322120\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −7.75828e8 1.28147e9i −0.215328 0.355667i
\(246\) 0 0
\(247\) 4.93976e8 8.55591e8i 0.132714 0.229868i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.49203e9i 0.879797i −0.898047 0.439899i \(-0.855014\pi\)
0.898047 0.439899i \(-0.144986\pi\)
\(252\) 0 0
\(253\) 5.91961e9 1.44481
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.36384e9 + 1.94211e9i 0.771086 + 0.445187i 0.833262 0.552879i \(-0.186471\pi\)
−0.0621759 + 0.998065i \(0.519804\pi\)
\(258\) 0 0
\(259\) −2.59046e9 2.53714e9i −0.575675 0.563825i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.40863e8 + 1.62962e9i 0.196654 + 0.340615i 0.947442 0.319929i \(-0.103659\pi\)
−0.750787 + 0.660544i \(0.770326\pi\)
\(264\) 0 0
\(265\) 3.57827e9i 0.725587i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.78854e9 + 1.60997e9i −0.532559 + 0.307473i −0.742058 0.670336i \(-0.766150\pi\)
0.209499 + 0.977809i \(0.432817\pi\)
\(270\) 0 0
\(271\) 4.42388e9 + 2.55413e9i 0.820212 + 0.473550i 0.850490 0.525992i \(-0.176306\pi\)
−0.0302773 + 0.999542i \(0.509639\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −3.14165e9 + 5.44150e9i −0.549323 + 0.951455i
\(276\) 0 0
\(277\) 5.20091e9 + 9.00825e9i 0.883406 + 1.53010i 0.847529 + 0.530749i \(0.178089\pi\)
0.0358772 + 0.999356i \(0.488577\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.79146e9 1.57044 0.785222 0.619215i \(-0.212549\pi\)
0.785222 + 0.619215i \(0.212549\pi\)
\(282\) 0 0
\(283\) −9.03261e8 + 5.21498e8i −0.140821 + 0.0813031i −0.568755 0.822507i \(-0.692575\pi\)
0.427934 + 0.903810i \(0.359242\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.37249e8 + 1.12301e8i 0.0644468 + 0.0165522i
\(288\) 0 0
\(289\) 3.98675e9 6.90526e9i 0.571515 0.989893i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 2.83834e9i 0.385118i −0.981285 0.192559i \(-0.938321\pi\)
0.981285 0.192559i \(-0.0616787\pi\)
\(294\) 0 0
\(295\) −3.00971e9 −0.397408
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.22270e10 + 7.05924e9i 1.52980 + 0.883228i
\(300\) 0 0
\(301\) −7.37052e7 + 2.86975e8i −0.00897909 + 0.0349606i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.89049e9 5.00648e9i −0.334020 0.578540i
\(306\) 0 0
\(307\) 1.01655e10i 1.14439i −0.820116 0.572197i \(-0.806091\pi\)
0.820116 0.572197i \(-0.193909\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 9.35774e9 5.40269e9i 1.00030 0.577522i 0.0919614 0.995763i \(-0.470686\pi\)
0.908336 + 0.418240i \(0.137353\pi\)
\(312\) 0 0
\(313\) −7.81261e9 4.51061e9i −0.813989 0.469957i 0.0343502 0.999410i \(-0.489064\pi\)
−0.848339 + 0.529453i \(0.822397\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −2.10486e9 + 3.64573e9i −0.208443 + 0.361034i −0.951224 0.308500i \(-0.900173\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(318\) 0 0
\(319\) 8.56828e8 + 1.48407e9i 0.0827429 + 0.143315i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 2.60435e9 0.239270
\(324\) 0 0
\(325\) −1.29782e10 + 7.49295e9i −1.16327 + 0.671614i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 1.08424e10 1.10702e10i 0.925424 0.944873i
\(330\) 0 0
\(331\) 5.98155e9 1.03603e10i 0.498312 0.863102i −0.501686 0.865050i \(-0.667287\pi\)
0.999998 + 0.00194777i \(0.000619995\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.99289e9i 0.237636i
\(336\) 0 0
\(337\) 8.47484e9 0.657070 0.328535 0.944492i \(-0.393445\pi\)
0.328535 + 0.944492i \(0.393445\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 3.01425e10 + 1.74028e10i 2.22927 + 1.28707i
\(342\) 0 0
\(343\) −9.47723e9 + 1.00878e10i −0.684708 + 0.728818i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7.92809e9 + 1.37319e10i 0.546828 + 0.947134i 0.998489 + 0.0549447i \(0.0174983\pi\)
−0.451661 + 0.892190i \(0.649168\pi\)
\(348\) 0 0
\(349\) 7.90260e9i 0.532682i 0.963879 + 0.266341i \(0.0858148\pi\)
−0.963879 + 0.266341i \(0.914185\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −8.28745e9 + 4.78476e9i −0.533731 + 0.308150i −0.742534 0.669808i \(-0.766376\pi\)
0.208804 + 0.977958i \(0.433043\pi\)
\(354\) 0 0
\(355\) 7.00658e9 + 4.04525e9i 0.441157 + 0.254702i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −5.12021e9 + 8.86847e9i −0.308255 + 0.533914i −0.977981 0.208695i \(-0.933078\pi\)
0.669726 + 0.742609i \(0.266412\pi\)
\(360\) 0 0
\(361\) −8.26493e9 1.43153e10i −0.486643 0.842890i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −3.25371e9 −0.183319
\(366\) 0 0
\(367\) 2.80339e10 1.61854e10i 1.54532 0.892193i 0.546834 0.837241i \(-0.315833\pi\)
0.998489 0.0549514i \(-0.0175004\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 3.18449e10 8.88873e9i 1.68091 0.469185i
\(372\) 0 0
\(373\) 1.25975e10 2.18195e10i 0.650803 1.12722i −0.332126 0.943235i \(-0.607766\pi\)
0.982928 0.183988i \(-0.0589008\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 4.08713e9i 0.202327i
\(378\) 0 0
\(379\) −6.03658e9 −0.292573 −0.146287 0.989242i \(-0.546732\pi\)
−0.146287 + 0.989242i \(0.546732\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 9.57427e9 + 5.52771e9i 0.444949 + 0.256892i 0.705695 0.708516i \(-0.250635\pi\)
−0.260745 + 0.965408i \(0.583968\pi\)
\(384\) 0 0
\(385\) −1.17519e10 3.01829e9i −0.534890 0.137378i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.58412e10 2.74378e10i −0.691814 1.19826i −0.971243 0.238091i \(-0.923478\pi\)
0.279428 0.960167i \(-0.409855\pi\)
\(390\) 0 0
\(391\) 3.72178e10i 1.59237i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 9.59682e9 5.54072e9i 0.394220 0.227603i
\(396\) 0 0
\(397\) −1.81623e10 1.04860e10i −0.731155 0.422132i 0.0876897 0.996148i \(-0.472052\pi\)
−0.818844 + 0.574015i \(0.805385\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 5.84375e9 1.01217e10i 0.226003 0.391449i −0.730617 0.682788i \(-0.760767\pi\)
0.956620 + 0.291339i \(0.0941007\pi\)
\(402\) 0 0
\(403\) 4.15062e10 + 7.18909e10i 1.57360 + 2.72555i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −2.93685e10 −1.07030
\(408\) 0 0
\(409\) 2.98804e10 1.72515e10i 1.06781 0.616499i 0.140226 0.990119i \(-0.455217\pi\)
0.927582 + 0.373620i \(0.121884\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 7.47637e9 + 2.67849e10i 0.256975 + 0.920642i
\(414\) 0 0
\(415\) 9.35461e9 1.62027e10i 0.315379 0.546253i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.71261e10i 0.555652i −0.960631 0.277826i \(-0.910386\pi\)
0.960631 0.277826i \(-0.0896139\pi\)
\(420\) 0 0
\(421\) 3.64524e10 1.16037 0.580187 0.814484i \(-0.302980\pi\)
0.580187 + 0.814484i \(0.302980\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −3.42119e10 1.97522e10i −1.04863 0.605425i
\(426\) 0 0
\(427\) −3.73750e10 + 3.81605e10i −1.12427 + 1.14790i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −1.09904e10 1.90360e10i −0.318497 0.551654i 0.661677 0.749789i \(-0.269845\pi\)
−0.980175 + 0.198135i \(0.936512\pi\)
\(432\) 0 0
\(433\) 1.35544e10i 0.385593i 0.981239 + 0.192796i \(0.0617557\pi\)
−0.981239 + 0.192796i \(0.938244\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −5.61514e9 + 3.24190e9i −0.153969 + 0.0888943i
\(438\) 0 0
\(439\) −4.13004e10 2.38448e10i −1.11198 0.642001i −0.172637 0.984986i \(-0.555229\pi\)
−0.939341 + 0.342985i \(0.888562\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −9.20913e9 + 1.59507e10i −0.239113 + 0.414156i −0.960460 0.278418i \(-0.910190\pi\)
0.721347 + 0.692574i \(0.243523\pi\)
\(444\) 0 0
\(445\) −6.56648e9 1.13735e10i −0.167453 0.290037i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −4.72530e10 −1.16264 −0.581319 0.813676i \(-0.697463\pi\)
−0.581319 + 0.813676i \(0.697463\pi\)
\(450\) 0 0
\(451\) 3.16658e9 1.82823e9i 0.0765393 0.0441900i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −2.06741e10 2.02486e10i −0.482372 0.472443i
\(456\) 0 0
\(457\) 9.30524e9 1.61172e10i 0.213335 0.369508i −0.739421 0.673243i \(-0.764901\pi\)
0.952756 + 0.303736i \(0.0982340\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.20893e9i 0.203895i −0.994790 0.101947i \(-0.967493\pi\)
0.994790 0.101947i \(-0.0325073\pi\)
\(462\) 0 0
\(463\) −1.42010e10 −0.309025 −0.154513 0.987991i \(-0.549381\pi\)
−0.154513 + 0.987991i \(0.549381\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.95507e10 + 1.70611e10i 0.621299 + 0.358707i 0.777374 0.629038i \(-0.216551\pi\)
−0.156076 + 0.987745i \(0.549884\pi\)
\(468\) 0 0
\(469\) 2.66353e10 7.43460e9i 0.550511 0.153662i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.19990e9 + 2.07829e9i 0.0239718 + 0.0415204i
\(474\) 0 0
\(475\) 6.88216e9i 0.135192i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −7.59507e9 + 4.38502e9i −0.144275 + 0.0832970i −0.570400 0.821367i \(-0.693212\pi\)
0.426125 + 0.904664i \(0.359878\pi\)
\(480\) 0 0
\(481\) −6.06607e10 3.50225e10i −1.13325 0.654284i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.51551e10 + 2.62494e10i −0.273900 + 0.474408i
\(486\) 0 0
\(487\) −6.41038e9 1.11031e10i −0.113964 0.197392i 0.803401 0.595438i \(-0.203022\pi\)
−0.917365 + 0.398047i \(0.869688\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −6.34320e10 −1.09140 −0.545698 0.837982i \(-0.683735\pi\)
−0.545698 + 0.837982i \(0.683735\pi\)
\(492\) 0 0
\(493\) −9.33065e9 + 5.38705e9i −0.157952 + 0.0911934i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.85958e10 7.24040e10i 0.304783 1.18669i
\(498\) 0 0
\(499\) −3.36380e10 + 5.82628e10i −0.542536 + 0.939700i 0.456222 + 0.889866i \(0.349202\pi\)
−0.998758 + 0.0498336i \(0.984131\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 1.04697e11i 1.63554i −0.575542 0.817772i \(-0.695209\pi\)
0.575542 0.817772i \(-0.304791\pi\)
\(504\) 0 0
\(505\) −2.77188e10 −0.426196
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.94469e10 + 2.85482e10i 0.736662 + 0.425312i 0.820854 0.571137i \(-0.193498\pi\)
−0.0841923 + 0.996450i \(0.526831\pi\)
\(510\) 0 0
\(511\) 8.08251e9 + 2.89565e10i 0.118539 + 0.424680i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 2.66637e10 + 4.61830e10i 0.379046 + 0.656527i
\(516\) 0 0
\(517\) 1.25505e11i 1.75671i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.48609e10 + 4.32210e10i −1.01602 + 0.586602i −0.912950 0.408072i \(-0.866201\pi\)
−0.103074 + 0.994674i \(0.532868\pi\)
\(522\) 0 0
\(523\) 1.27623e10 + 7.36833e9i 0.170578 + 0.0984832i 0.582858 0.812574i \(-0.301934\pi\)
−0.412280 + 0.911057i \(0.635268\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −1.09415e11 + 1.89512e11i −1.41852 + 2.45694i
\(528\) 0 0
\(529\) −7.17338e9 1.24247e10i −0.0916012 0.158658i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 8.72077e9 0.108055
\(534\) 0 0
\(535\) −4.00892e10 + 2.31455e10i −0.489342 + 0.282522i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.33136e9 + 1.12084e11i 0.0276220 + 1.32797i
\(540\) 0 0
\(541\) −5.99660e10 + 1.03864e11i −0.700029 + 1.21249i 0.268427 + 0.963300i \(0.413496\pi\)
−0.968456 + 0.249185i \(0.919837\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.84890e10i 0.322917i
\(546\) 0 0
\(547\) −7.72241e10 −0.862588 −0.431294 0.902211i \(-0.641943\pi\)
−0.431294 + 0.902211i \(0.641943\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.62551e9 9.38491e8i −0.0176354 0.0101818i
\(552\) 0 0
\(553\) −7.31491e10 7.16434e10i −0.782183 0.766083i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −8.89933e10 1.54141e11i −0.924564 1.60139i −0.792262 0.610182i \(-0.791096\pi\)
−0.132302 0.991209i \(-0.542237\pi\)
\(558\) 0 0
\(559\) 5.72362e9i 0.0586170i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.36022e11 7.85323e10i 1.35386 0.781654i 0.365076 0.930978i \(-0.381043\pi\)
0.988788 + 0.149323i \(0.0477096\pi\)
\(564\) 0 0
\(565\) −6.17950e10 3.56774e10i −0.606400 0.350105i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.78668e8 4.82667e8i 0.00265851 0.00460467i −0.864693 0.502301i \(-0.832487\pi\)
0.867352 + 0.497696i \(0.165820\pi\)
\(570\) 0 0
\(571\) 1.85718e10 + 3.21672e10i 0.174706 + 0.302600i 0.940060 0.341010i \(-0.110769\pi\)
−0.765353 + 0.643610i \(0.777436\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 9.83506e10 0.899716
\(576\) 0 0
\(577\) 3.46036e10 1.99784e10i 0.312189 0.180243i −0.335716 0.941963i \(-0.608978\pi\)
0.647906 + 0.761721i \(0.275645\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.67434e11 4.30027e10i −1.46939 0.377391i
\(582\) 0 0
\(583\) 1.33894e11 2.31911e11i 1.15901 2.00746i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.12252e11i 0.945460i 0.881207 + 0.472730i \(0.156731\pi\)
−0.881207 + 0.472730i \(0.843269\pi\)
\(588\) 0 0
\(589\) −3.81229e10 −0.316756
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.84487e10 2.79719e10i −0.391799 0.226205i 0.291140 0.956680i \(-0.405965\pi\)
−0.682939 + 0.730475i \(0.739299\pi\)
\(594\) 0 0
\(595\) 1.89766e10 7.38865e10i 0.151409 0.589518i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.46361e10 2.53505e10i −0.113689 0.196916i 0.803566 0.595216i \(-0.202933\pi\)
−0.917255 + 0.398300i \(0.869600\pi\)
\(600\) 0 0
\(601\) 3.04406e10i 0.233322i −0.993172 0.116661i \(-0.962781\pi\)
0.993172 0.116661i \(-0.0372191\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.68678e10 + 2.12856e10i −0.275186 + 0.158879i
\(606\) 0 0
\(607\) 1.87228e11 + 1.08096e11i 1.37917 + 0.796262i 0.992059 0.125772i \(-0.0401409\pi\)
0.387107 + 0.922035i \(0.373474\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 1.49667e11 2.59232e11i 1.07390 1.86004i
\(612\) 0 0
\(613\) 3.15010e10 + 5.45613e10i 0.223091 + 0.386405i 0.955745 0.294196i \(-0.0950519\pi\)
−0.732654 + 0.680601i \(0.761719\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.31396e11 −1.59667 −0.798336 0.602213i \(-0.794286\pi\)
−0.798336 + 0.602213i \(0.794286\pi\)
\(618\) 0 0
\(619\) −8.62110e10 + 4.97739e10i −0.587219 + 0.339031i −0.763997 0.645220i \(-0.776766\pi\)
0.176778 + 0.984251i \(0.443432\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −8.49068e10 + 8.66913e10i −0.563625 + 0.575471i
\(624\) 0 0
\(625\) −3.90080e10 + 6.75639e10i −0.255643 + 0.442787i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 1.84646e11i 1.17961i
\(630\) 0 0
\(631\) −3.88355e10 −0.244969 −0.122485 0.992470i \(-0.539086\pi\)
−0.122485 + 0.992470i \(0.539086\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.94780e9 5.16602e9i −0.0550328 0.0317732i
\(636\) 0 0
\(637\) −1.28846e11 + 2.34289e11i −0.782554 + 1.42297i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.01203e11 + 1.75289e11i 0.599462 + 1.03830i 0.992901 + 0.118948i \(0.0379521\pi\)
−0.393439 + 0.919351i \(0.628715\pi\)
\(642\) 0 0
\(643\) 1.46591e11i 0.857558i 0.903409 + 0.428779i \(0.141056\pi\)
−0.903409 + 0.428779i \(0.858944\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −2.40431e11 + 1.38813e11i −1.37206 + 0.792158i −0.991187 0.132470i \(-0.957709\pi\)
−0.380871 + 0.924628i \(0.624376\pi\)
\(648\) 0 0
\(649\) 1.95062e11 + 1.12619e11i 1.09950 + 0.634795i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.35533e11 2.34750e11i 0.745406 1.29108i −0.204598 0.978846i \(-0.565589\pi\)
0.950005 0.312236i \(-0.101078\pi\)
\(654\) 0 0
\(655\) −4.97805e9 8.62224e9i −0.0270455 0.0468441i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −8.76828e10 −0.464914 −0.232457 0.972607i \(-0.574676\pi\)
−0.232457 + 0.972607i \(0.574676\pi\)
\(660\) 0 0
\(661\) −3.77894e10 + 2.18177e10i −0.197954 + 0.114289i −0.595701 0.803206i \(-0.703126\pi\)
0.397747 + 0.917495i \(0.369792\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 1.28004e10 3.57292e9i 0.0654541 0.0182699i
\(666\) 0 0
\(667\) 1.34117e10 2.32297e10i 0.0677609 0.117365i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 4.32633e11i 2.13417i
\(672\) 0 0
\(673\) 1.88626e11 0.919480 0.459740 0.888054i \(-0.347943\pi\)
0.459740 + 0.888054i \(0.347943\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.41068e10 1.96916e10i −0.162363 0.0937401i 0.416617 0.909082i \(-0.363216\pi\)
−0.578980 + 0.815342i \(0.696549\pi\)
\(678\) 0 0
\(679\) 2.71253e11 + 6.96673e10i 1.27613 + 0.327755i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.05360e11 + 1.82490e11i 0.484167 + 0.838601i 0.999835 0.0181874i \(-0.00578954\pi\)
−0.515668 + 0.856788i \(0.672456\pi\)
\(684\) 0 0
\(685\) 1.07590e11i 0.488663i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 5.53116e11 3.19342e11i 2.45437 1.41703i
\(690\) 0 0
\(691\) −3.03078e10 1.74982e10i −0.132936 0.0767505i 0.432057 0.901846i \(-0.357788\pi\)
−0.564993 + 0.825096i \(0.691121\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 2.80186e10 4.85296e10i 0.120090 0.208002i
\(696\) 0 0
\(697\) 1.14944e10 + 1.99090e10i 0.0487031 + 0.0843563i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.58032e10 −0.355330 −0.177665 0.984091i \(-0.556854\pi\)
−0.177665 + 0.984091i \(0.556854\pi\)
\(702\) 0 0
\(703\) 2.78580e10 1.60838e10i 0.114059 0.0658517i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.88559e10 + 2.46684e11i 0.275590 + 0.987333i
\(708\) 0 0
\(709\) 9.74057e10 1.68712e11i 0.385478 0.667668i −0.606357 0.795192i \(-0.707370\pi\)
0.991835 + 0.127525i \(0.0407032\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 5.44801e11i 2.10804i
\(714\) 0 0
\(715\) −2.34387e11 −0.896827
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 2.89871e11 + 1.67357e11i 1.08465 + 0.626222i 0.932147 0.362081i \(-0.117934\pi\)
0.152502 + 0.988303i \(0.451267\pi\)
\(720\) 0 0
\(721\) 3.44771e11 3.52017e11i 1.27582 1.30263i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.42357e10 + 2.46569e10i 0.0515259 + 0.0892455i
\(726\) 0 0
\(727\) 9.86180e10i 0.353035i −0.984297 0.176518i \(-0.943517\pi\)
0.984297 0.176518i \(-0.0564833\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.30667e10 + 7.54404e9i −0.0457609 + 0.0264201i
\(732\) 0 0
\(733\) 2.61192e11 + 1.50799e11i 0.904782 + 0.522376i 0.878749 0.477285i \(-0.158379\pi\)
0.0260337 + 0.999661i \(0.491712\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.11990e11 1.93972e11i 0.379585 0.657460i
\(738\) 0 0
\(739\) −1.82846e11 3.16698e11i −0.613065 1.06186i −0.990721 0.135914i \(-0.956603\pi\)
0.377655 0.925946i \(-0.376730\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.52082e11 1.15528 0.577642 0.816290i \(-0.303973\pi\)
0.577642 + 0.816290i \(0.303973\pi\)
\(744\) 0 0
\(745\) 1.16873e11 6.74766e10i 0.379392 0.219042i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 3.05569e11 + 2.99279e11i 0.970917 + 0.950932i
\(750\) 0 0
\(751\) −1.44039e11 + 2.49484e11i −0.452816 + 0.784300i −0.998560 0.0536517i \(-0.982914\pi\)
0.545744 + 0.837952i \(0.316247\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 8.58209e10i 0.264122i
\(756\) 0 0
\(757\) −5.34615e11 −1.62801 −0.814006 0.580857i \(-0.802718\pi\)
−0.814006 + 0.580857i \(0.802718\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −2.20516e10 1.27315e10i −0.0657507 0.0379612i 0.466764 0.884382i \(-0.345420\pi\)
−0.532515 + 0.846421i \(0.678753\pi\)
\(762\) 0 0
\(763\) −2.53539e11 + 7.07692e10i −0.748076 + 0.208807i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 2.68601e11 + 4.65230e11i 0.776114 + 1.34427i
\(768\) 0 0
\(769\) 1.61134e11i 0.460768i −0.973100 0.230384i \(-0.926002\pi\)
0.973100 0.230384i \(-0.0739982\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 2.00134e11 1.15547e11i 0.560535 0.323625i −0.192825 0.981233i \(-0.561765\pi\)
0.753360 + 0.657608i \(0.228432\pi\)
\(774\) 0 0
\(775\) 5.00799e11 + 2.89136e11i 1.38821 + 0.801486i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.00247e9 + 3.46839e9i −0.00543772 + 0.00941841i
\(780\) 0 0
\(781\) −3.02736e11 5.24353e11i −0.813691 1.40935i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.76875e10 −0.204585
\(786\) 0 0
\(787\) 8.19226e9 4.72980e9i 0.0213553 0.0123295i −0.489284 0.872124i \(-0.662742\pi\)
0.510640 + 0.859795i \(0.329409\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0