Properties

Label 252.8.k.e.109.4
Level $252$
Weight $8$
Character 252.109
Analytic conductor $78.721$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(78.7210264220\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} - 993183560713460 x^{9} + 4531523101103784409 x^{8} - 25038421018919762700 x^{7} + 77467785793463920028824 x^{6} - 352418565495722251364640 x^{5} + 967025470523891143640719680 x^{4} - 1651641278575894088053178880 x^{3} + 7200793191683961412674394484736 x^{2} + 21939035854717669821876654243840 x + 34494438285389383231614325978300416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{20}\cdot 3^{13}\cdot 7^{8} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.4
Root \(-50.1630 - 86.8849i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.8.k.e.37.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-117.526 - 203.561i) q^{5} +(881.619 - 215.154i) q^{7} +O(q^{10})\) \(q+(-117.526 - 203.561i) q^{5} +(881.619 - 215.154i) q^{7} +(3934.09 - 6814.05i) q^{11} -5762.92 q^{13} +(3577.84 - 6196.99i) q^{17} +(-19965.0 - 34580.3i) q^{19} +(28266.6 + 48959.2i) q^{23} +(11437.7 - 19810.8i) q^{25} +130038. q^{29} +(-25781.5 + 44654.8i) q^{31} +(-147410. - 154177. i) q^{35} +(139818. + 242173. i) q^{37} +345556. q^{41} -111709. q^{43} +(-425409. - 736830. i) q^{47} +(730961. - 379368. i) q^{49} +(-599912. + 1.03908e6i) q^{53} -1.84943e6 q^{55} +(-856228. + 1.48303e6i) q^{59} +(-1.22726e6 - 2.12568e6i) q^{61} +(677294. + 1.17311e6i) q^{65} +(-313531. + 543052. i) q^{67} -2.97409e6 q^{71} +(476382. - 825118. i) q^{73} +(2.00230e6 - 6.85383e6i) q^{77} +(-2.95297e6 - 5.11469e6i) q^{79} +9.78669e6 q^{83} -1.68196e6 q^{85} +(-2.59171e6 - 4.48897e6i) q^{89} +(-5.08070e6 + 1.23992e6i) q^{91} +(-4.69281e6 + 8.12818e6i) q^{95} -4.87158e6 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 1680q^{7} + O(q^{10}) \) \( 16q + 1680q^{7} - 28280q^{13} + 42224q^{19} - 80460q^{25} + 164752q^{31} - 647980q^{37} + 1341440q^{43} + 230104q^{49} - 323120q^{55} - 4319336q^{61} - 3905760q^{67} + 6471780q^{73} - 6093104q^{79} + 456400q^{85} + 15969856q^{91} - 27141240q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(5\) −117.526 203.561i −0.420474 0.728282i 0.575512 0.817793i \(-0.304803\pi\)
−0.995986 + 0.0895111i \(0.971470\pi\)
\(6\) 0 0
\(7\) 881.619 215.154i 0.971489 0.237086i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3934.09 6814.05i 0.891189 1.54359i 0.0527383 0.998608i \(-0.483205\pi\)
0.838451 0.544977i \(-0.183462\pi\)
\(12\) 0 0
\(13\) −5762.92 −0.727514 −0.363757 0.931494i \(-0.618506\pi\)
−0.363757 + 0.931494i \(0.618506\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 3577.84 6196.99i 0.176624 0.305921i −0.764098 0.645100i \(-0.776816\pi\)
0.940722 + 0.339179i \(0.110149\pi\)
\(18\) 0 0
\(19\) −19965.0 34580.3i −0.667776 1.15662i −0.978525 0.206130i \(-0.933913\pi\)
0.310749 0.950492i \(-0.399420\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 28266.6 + 48959.2i 0.484425 + 0.839048i 0.999840 0.0178925i \(-0.00569567\pi\)
−0.515415 + 0.856940i \(0.672362\pi\)
\(24\) 0 0
\(25\) 11437.7 19810.8i 0.146403 0.253578i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 130038. 0.990096 0.495048 0.868866i \(-0.335150\pi\)
0.495048 + 0.868866i \(0.335150\pi\)
\(30\) 0 0
\(31\) −25781.5 + 44654.8i −0.155432 + 0.269217i −0.933216 0.359315i \(-0.883010\pi\)
0.777784 + 0.628532i \(0.216344\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −147410. 154177.i −0.581151 0.607830i
\(36\) 0 0
\(37\) 139818. + 242173.i 0.453794 + 0.785994i 0.998618 0.0525566i \(-0.0167370\pi\)
−0.544824 + 0.838550i \(0.683404\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 345556. 0.783024 0.391512 0.920173i \(-0.371952\pi\)
0.391512 + 0.920173i \(0.371952\pi\)
\(42\) 0 0
\(43\) −111709. −0.214264 −0.107132 0.994245i \(-0.534167\pi\)
−0.107132 + 0.994245i \(0.534167\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −425409. 736830.i −0.597674 1.03520i −0.993164 0.116731i \(-0.962758\pi\)
0.395489 0.918471i \(-0.370575\pi\)
\(48\) 0 0
\(49\) 730961. 379368.i 0.887580 0.460653i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −599912. + 1.03908e6i −0.553506 + 0.958700i 0.444512 + 0.895773i \(0.353377\pi\)
−0.998018 + 0.0629273i \(0.979956\pi\)
\(54\) 0 0
\(55\) −1.84943e6 −1.49889
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −856228. + 1.48303e6i −0.542759 + 0.940086i 0.455985 + 0.889987i \(0.349287\pi\)
−0.998744 + 0.0500990i \(0.984046\pi\)
\(60\) 0 0
\(61\) −1.22726e6 2.12568e6i −0.692282 1.19907i −0.971088 0.238721i \(-0.923272\pi\)
0.278806 0.960347i \(-0.410061\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 677294. + 1.17311e6i 0.305901 + 0.529835i
\(66\) 0 0
\(67\) −313531. + 543052.i −0.127356 + 0.220587i −0.922651 0.385635i \(-0.873982\pi\)
0.795296 + 0.606222i \(0.207316\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −2.97409e6 −0.986165 −0.493082 0.869983i \(-0.664130\pi\)
−0.493082 + 0.869983i \(0.664130\pi\)
\(72\) 0 0
\(73\) 476382. 825118.i 0.143326 0.248248i −0.785421 0.618962i \(-0.787554\pi\)
0.928747 + 0.370714i \(0.120887\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 2.00230e6 6.85383e6i 0.499818 1.71086i
\(78\) 0 0
\(79\) −2.95297e6 5.11469e6i −0.673852 1.16715i −0.976803 0.214139i \(-0.931305\pi\)
0.302952 0.953006i \(-0.402028\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 9.78669e6 1.87872 0.939361 0.342930i \(-0.111419\pi\)
0.939361 + 0.342930i \(0.111419\pi\)
\(84\) 0 0
\(85\) −1.68196e6 −0.297063
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −2.59171e6 4.48897e6i −0.389692 0.674966i 0.602716 0.797956i \(-0.294085\pi\)
−0.992408 + 0.122989i \(0.960752\pi\)
\(90\) 0 0
\(91\) −5.08070e6 + 1.23992e6i −0.706771 + 0.172483i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −4.69281e6 + 8.12818e6i −0.561565 + 0.972659i
\(96\) 0 0
\(97\) −4.87158e6 −0.541962 −0.270981 0.962585i \(-0.587348\pi\)
−0.270981 + 0.962585i \(0.587348\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.03637e6 3.52710e6i 0.196667 0.340638i −0.750778 0.660554i \(-0.770321\pi\)
0.947446 + 0.319916i \(0.103655\pi\)
\(102\) 0 0
\(103\) −7.15804e6 1.23981e7i −0.645452 1.11795i −0.984197 0.177077i \(-0.943336\pi\)
0.338745 0.940878i \(-0.389997\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.47668e6 + 1.64141e7i 0.747847 + 1.29531i 0.948853 + 0.315720i \(0.102246\pi\)
−0.201005 + 0.979590i \(0.564421\pi\)
\(108\) 0 0
\(109\) −2.83878e6 + 4.91690e6i −0.209961 + 0.363663i −0.951702 0.307023i \(-0.900667\pi\)
0.741741 + 0.670686i \(0.234000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.34292e6 −0.413537 −0.206769 0.978390i \(-0.566295\pi\)
−0.206769 + 0.978390i \(0.566295\pi\)
\(114\) 0 0
\(115\) 6.64412e6 1.15080e7i 0.407376 0.705596i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.82098e6 6.23317e6i 0.0990583 0.339074i
\(120\) 0 0
\(121\) −2.12106e7 3.67378e7i −1.08844 1.88523i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −2.37404e7 −1.08718
\(126\) 0 0
\(127\) −4.12014e7 −1.78484 −0.892420 0.451205i \(-0.850994\pi\)
−0.892420 + 0.451205i \(0.850994\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −1.09350e7 1.89400e7i −0.424982 0.736091i 0.571436 0.820646i \(-0.306386\pi\)
−0.996419 + 0.0845554i \(0.973053\pi\)
\(132\) 0 0
\(133\) −2.50416e7 2.61911e7i −0.922956 0.965324i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1.87470e7 3.24708e7i 0.622889 1.07888i −0.366056 0.930593i \(-0.619292\pi\)
0.988945 0.148283i \(-0.0473746\pi\)
\(138\) 0 0
\(139\) −3.15043e7 −0.994989 −0.497494 0.867467i \(-0.665746\pi\)
−0.497494 + 0.867467i \(0.665746\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −2.26719e7 + 3.92688e7i −0.648352 + 1.12298i
\(144\) 0 0
\(145\) −1.52829e7 2.64707e7i −0.416310 0.721070i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.28779e6 + 1.43549e7i 0.205252 + 0.355506i 0.950213 0.311601i \(-0.100865\pi\)
−0.744961 + 0.667108i \(0.767532\pi\)
\(150\) 0 0
\(151\) 3.11762e7 5.39987e7i 0.736891 1.27633i −0.216997 0.976172i \(-0.569626\pi\)
0.953888 0.300161i \(-0.0970405\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 1.21200e7 0.261421
\(156\) 0 0
\(157\) −1.99021e7 + 3.44715e7i −0.410441 + 0.710905i −0.994938 0.100491i \(-0.967959\pi\)
0.584497 + 0.811396i \(0.301292\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 3.54541e7 + 3.70817e7i 0.669540 + 0.700275i
\(162\) 0 0
\(163\) 1.67496e7 + 2.90111e7i 0.302933 + 0.524695i 0.976799 0.214158i \(-0.0687008\pi\)
−0.673866 + 0.738854i \(0.735367\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −8.31239e7 −1.38108 −0.690539 0.723295i \(-0.742627\pi\)
−0.690539 + 0.723295i \(0.742627\pi\)
\(168\) 0 0
\(169\) −2.95372e7 −0.470724
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.73005e7 + 6.46063e7i 0.547713 + 0.948666i 0.998431 + 0.0560000i \(0.0178347\pi\)
−0.450718 + 0.892666i \(0.648832\pi\)
\(174\) 0 0
\(175\) 5.82137e6 1.99264e7i 0.0821093 0.281058i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.29744e7 1.26395e8i 0.951010 1.64720i 0.207765 0.978179i \(-0.433381\pi\)
0.743245 0.669019i \(-0.233286\pi\)
\(180\) 0 0
\(181\) −8.25291e7 −1.03450 −0.517252 0.855833i \(-0.673045\pi\)
−0.517252 + 0.855833i \(0.673045\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3.28646e7 5.69232e7i 0.381617 0.660980i
\(186\) 0 0
\(187\) −2.81511e7 4.87591e7i −0.314810 0.545268i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −7.07989e6 1.22627e7i −0.0735207 0.127342i 0.826921 0.562318i \(-0.190090\pi\)
−0.900442 + 0.434976i \(0.856757\pi\)
\(192\) 0 0
\(193\) −5.70040e6 + 9.87338e6i −0.0570761 + 0.0988588i −0.893152 0.449756i \(-0.851511\pi\)
0.836076 + 0.548614i \(0.184844\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.08549e7 0.567106 0.283553 0.958957i \(-0.408487\pi\)
0.283553 + 0.958957i \(0.408487\pi\)
\(198\) 0 0
\(199\) 4.04759e7 7.01063e7i 0.364092 0.630625i −0.624538 0.780994i \(-0.714713\pi\)
0.988630 + 0.150369i \(0.0480461\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 1.14644e8 2.79782e7i 0.961867 0.234738i
\(204\) 0 0
\(205\) −4.06119e7 7.03418e7i −0.329241 0.570263i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −3.14176e8 −2.38046
\(210\) 0 0
\(211\) 5.64186e6 0.0413460 0.0206730 0.999786i \(-0.493419\pi\)
0.0206730 + 0.999786i \(0.493419\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.31288e7 + 2.27397e7i 0.0900926 + 0.156045i
\(216\) 0 0
\(217\) −1.31218e7 + 4.49155e7i −0.0871732 + 0.298392i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.06188e7 + 3.57128e7i −0.128496 + 0.222562i
\(222\) 0 0
\(223\) 1.69180e8 1.02160 0.510801 0.859699i \(-0.329349\pi\)
0.510801 + 0.859699i \(0.329349\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.58940e7 + 1.31452e8i −0.430643 + 0.745895i −0.996929 0.0783137i \(-0.975046\pi\)
0.566286 + 0.824209i \(0.308380\pi\)
\(228\) 0 0
\(229\) 1.01394e8 + 1.75620e8i 0.557942 + 0.966384i 0.997668 + 0.0682522i \(0.0217423\pi\)
−0.439726 + 0.898132i \(0.644924\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.53553e8 + 2.65962e8i 0.795266 + 1.37744i 0.922670 + 0.385591i \(0.126002\pi\)
−0.127403 + 0.991851i \(0.540664\pi\)
\(234\) 0 0
\(235\) −9.99934e7 + 1.73194e8i −0.502613 + 0.870551i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −2.38306e8 −1.12913 −0.564564 0.825389i \(-0.690956\pi\)
−0.564564 + 0.825389i \(0.690956\pi\)
\(240\) 0 0
\(241\) −695427. + 1.20451e6i −0.00320031 + 0.00554309i −0.867621 0.497226i \(-0.834352\pi\)
0.864421 + 0.502769i \(0.167685\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −1.63131e8 1.04210e8i −0.708690 0.452717i
\(246\) 0 0
\(247\) 1.15056e8 + 1.99284e8i 0.485816 + 0.841458i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.96244e8 1.58163 0.790815 0.612055i \(-0.209657\pi\)
0.790815 + 0.612055i \(0.209657\pi\)
\(252\) 0 0
\(253\) 4.44814e8 1.72686
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.72046e8 2.97993e8i −0.632237 1.09507i −0.987093 0.160146i \(-0.948804\pi\)
0.354857 0.934921i \(-0.384530\pi\)
\(258\) 0 0
\(259\) 1.75371e8 + 1.83421e8i 0.627203 + 0.655996i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 9.01986e6 1.56229e7i 0.0305742 0.0529560i −0.850333 0.526244i \(-0.823600\pi\)
0.880908 + 0.473288i \(0.156933\pi\)
\(264\) 0 0
\(265\) 2.82021e8 0.930939
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 2.13538e7 3.69859e7i 0.0668871 0.115852i −0.830642 0.556806i \(-0.812027\pi\)
0.897530 + 0.440954i \(0.145360\pi\)
\(270\) 0 0
\(271\) 7.46844e7 + 1.29357e8i 0.227949 + 0.394819i 0.957200 0.289427i \(-0.0934648\pi\)
−0.729251 + 0.684246i \(0.760131\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −8.99943e7 1.55875e8i −0.260946 0.451972i
\(276\) 0 0
\(277\) −1.80069e8 + 3.11889e8i −0.509050 + 0.881701i 0.490895 + 0.871219i \(0.336670\pi\)
−0.999945 + 0.0104821i \(0.996663\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.84959e8 0.497282 0.248641 0.968596i \(-0.420016\pi\)
0.248641 + 0.968596i \(0.420016\pi\)
\(282\) 0 0
\(283\) 2.14592e7 3.71684e7i 0.0562809 0.0974813i −0.836512 0.547948i \(-0.815409\pi\)
0.892793 + 0.450467i \(0.148742\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 3.04649e8 7.43478e7i 0.760699 0.185644i
\(288\) 0 0
\(289\) 1.79568e8 + 3.11020e8i 0.437608 + 0.757959i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 5.88345e8 1.36646 0.683228 0.730205i \(-0.260576\pi\)
0.683228 + 0.730205i \(0.260576\pi\)
\(294\) 0 0
\(295\) 4.02516e8 0.912865
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.62898e8 2.82148e8i −0.352425 0.610419i
\(300\) 0 0
\(301\) −9.84850e7 + 2.40347e7i −0.208155 + 0.0507991i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −2.88471e8 + 4.99646e8i −0.582173 + 1.00835i
\(306\) 0 0
\(307\) −4.17824e7 −0.0824155 −0.0412077 0.999151i \(-0.513121\pi\)
−0.0412077 + 0.999151i \(0.513121\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −2.03292e8 + 3.52113e8i −0.383230 + 0.663774i −0.991522 0.129939i \(-0.958522\pi\)
0.608292 + 0.793714i \(0.291855\pi\)
\(312\) 0 0
\(313\) 2.29934e8 + 3.98258e8i 0.423837 + 0.734107i 0.996311 0.0858160i \(-0.0273497\pi\)
−0.572474 + 0.819923i \(0.694016\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.06886e8 + 5.31543e8i 0.541091 + 0.937197i 0.998842 + 0.0481166i \(0.0153219\pi\)
−0.457751 + 0.889081i \(0.651345\pi\)
\(318\) 0 0
\(319\) 5.11581e8 8.86085e8i 0.882363 1.52830i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.85725e8 −0.471780
\(324\) 0 0
\(325\) −6.59149e7 + 1.14168e8i −0.106510 + 0.184481i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −5.33581e8 5.58075e8i −0.826066 0.863987i
\(330\) 0 0
\(331\) 5.71651e8 + 9.90129e8i 0.866429 + 1.50070i 0.865621 + 0.500700i \(0.166924\pi\)
0.000808163 1.00000i \(0.499743\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.47392e8 0.214199
\(336\) 0 0
\(337\) −8.58803e8 −1.22233 −0.611166 0.791503i \(-0.709299\pi\)
−0.611166 + 0.791503i \(0.709299\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 2.02853e8 + 3.51352e8i 0.277039 + 0.479846i
\(342\) 0 0
\(343\) 5.62806e8 4.91727e8i 0.753060 0.657952i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −2.59150e8 + 4.48860e8i −0.332964 + 0.576711i −0.983092 0.183114i \(-0.941382\pi\)
0.650128 + 0.759825i \(0.274715\pi\)
\(348\) 0 0
\(349\) −4.10903e8 −0.517428 −0.258714 0.965954i \(-0.583299\pi\)
−0.258714 + 0.965954i \(0.583299\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 7.77472e8 1.34662e9i 0.940749 1.62942i 0.176701 0.984265i \(-0.443458\pi\)
0.764048 0.645160i \(-0.223209\pi\)
\(354\) 0 0
\(355\) 3.49533e8 + 6.05409e8i 0.414657 + 0.718206i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −8.73553e8 1.51304e9i −0.996457 1.72591i −0.571062 0.820907i \(-0.693469\pi\)
−0.425395 0.905008i \(-0.639865\pi\)
\(360\) 0 0
\(361\) −3.50263e8 + 6.06673e8i −0.391849 + 0.678703i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.23949e8 −0.241060
\(366\) 0 0
\(367\) 1.44227e8 2.49808e8i 0.152305 0.263800i −0.779769 0.626067i \(-0.784664\pi\)
0.932074 + 0.362267i \(0.117997\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −3.05332e8 + 1.04514e9i −0.310430 + 1.06259i
\(372\) 0 0
\(373\) −9.04946e7 1.56741e8i −0.0902904 0.156388i 0.817343 0.576152i \(-0.195446\pi\)
−0.907633 + 0.419764i \(0.862113\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.49399e8 −0.720308
\(378\) 0 0
\(379\) 1.42653e9 1.34599 0.672997 0.739645i \(-0.265007\pi\)
0.672997 + 0.739645i \(0.265007\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 8.99160e8 + 1.55739e9i 0.817789 + 1.41645i 0.907308 + 0.420467i \(0.138134\pi\)
−0.0895186 + 0.995985i \(0.528533\pi\)
\(384\) 0 0
\(385\) −1.63049e9 + 3.97913e8i −1.45615 + 0.355366i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.57575e8 2.72928e8i 0.135726 0.235085i −0.790148 0.612916i \(-0.789997\pi\)
0.925875 + 0.377831i \(0.123330\pi\)
\(390\) 0 0
\(391\) 4.04533e8 0.342244
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −6.94102e8 + 1.20222e9i −0.566674 + 0.981509i
\(396\) 0 0
\(397\) −8.25550e8 1.42989e9i −0.662181 1.14693i −0.980041 0.198793i \(-0.936298\pi\)
0.317861 0.948137i \(-0.397036\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.17565e8 8.96449e8i −0.400830 0.694257i 0.592997 0.805205i \(-0.297945\pi\)
−0.993826 + 0.110948i \(0.964611\pi\)
\(402\) 0 0
\(403\) 1.48577e8 2.57342e8i 0.113079 0.195859i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 2.20023e9 1.61766
\(408\) 0 0
\(409\) 4.39925e8 7.61973e8i 0.317941 0.550691i −0.662117 0.749401i \(-0.730342\pi\)
0.980058 + 0.198710i \(0.0636751\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −4.35787e8 + 1.49169e9i −0.304403 + 1.04196i
\(414\) 0 0
\(415\) −1.15019e9 1.99219e9i −0.789954 1.36824i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 1.88360e8 0.125095 0.0625473 0.998042i \(-0.480078\pi\)
0.0625473 + 0.998042i \(0.480078\pi\)
\(420\) 0 0
\(421\) −2.55915e9 −1.67151 −0.835753 0.549106i \(-0.814968\pi\)
−0.835753 + 0.549106i \(0.814968\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −8.18448e7 1.41759e8i −0.0517166 0.0895757i
\(426\) 0 0
\(427\) −1.53933e9 1.60999e9i −0.956827 1.00075i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.09832e9 1.90235e9i 0.660785 1.14451i −0.319625 0.947544i \(-0.603557\pi\)
0.980410 0.196969i \(-0.0631097\pi\)
\(432\) 0 0
\(433\) −2.66829e9 −1.57952 −0.789761 0.613414i \(-0.789796\pi\)
−0.789761 + 0.613414i \(0.789796\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.12868e9 1.95494e9i 0.646974 1.12059i
\(438\) 0 0
\(439\) −4.10653e8 7.11272e8i −0.231659 0.401245i 0.726637 0.687021i \(-0.241082\pi\)
−0.958296 + 0.285776i \(0.907749\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.27229e8 1.08639e9i −0.342778 0.593709i 0.642169 0.766563i \(-0.278035\pi\)
−0.984948 + 0.172854i \(0.944701\pi\)
\(444\) 0 0
\(445\) −6.09187e8 + 1.05514e9i −0.327711 + 0.567612i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 8.34122e7 0.0434878 0.0217439 0.999764i \(-0.493078\pi\)
0.0217439 + 0.999764i \(0.493078\pi\)
\(450\) 0 0
\(451\) 1.35945e9 2.35464e9i 0.697823 1.20866i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 8.49513e8 + 8.88511e8i 0.422796 + 0.442204i
\(456\) 0 0
\(457\) −2.00176e8 3.46714e8i −0.0981080 0.169928i 0.812794 0.582552i \(-0.197946\pi\)
−0.910901 + 0.412624i \(0.864612\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −4.55230e7 −0.0216410 −0.0108205 0.999941i \(-0.503444\pi\)
−0.0108205 + 0.999941i \(0.503444\pi\)
\(462\) 0 0
\(463\) 1.41715e9 0.663565 0.331782 0.943356i \(-0.392350\pi\)
0.331782 + 0.943356i \(0.392350\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −7.76416e8 1.34479e9i −0.352765 0.611007i 0.633968 0.773359i \(-0.281425\pi\)
−0.986733 + 0.162352i \(0.948092\pi\)
\(468\) 0 0
\(469\) −1.59575e8 + 5.46222e8i −0.0714267 + 0.244492i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.39475e8 + 7.61192e8i −0.190950 + 0.330735i
\(474\) 0 0
\(475\) −9.13416e8 −0.391058
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −5.98584e8 + 1.03678e9i −0.248857 + 0.431034i −0.963209 0.268753i \(-0.913388\pi\)
0.714352 + 0.699787i \(0.246722\pi\)
\(480\) 0 0
\(481\) −8.05763e8 1.39562e9i −0.330141 0.571821i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 5.72538e8 + 9.91664e8i 0.227881 + 0.394701i
\(486\) 0 0
\(487\) −8.14788e8 + 1.41125e9i −0.319664 + 0.553674i −0.980418 0.196929i \(-0.936903\pi\)
0.660754 + 0.750602i \(0.270237\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.66094e9 −0.633240 −0.316620 0.948553i \(-0.602548\pi\)
−0.316620 + 0.948553i \(0.602548\pi\)
\(492\) 0 0
\(493\) 4.65255e8 8.05845e8i 0.174875 0.302892i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.62201e9 + 6.39887e8i −0.958048 + 0.233806i
\(498\) 0 0
\(499\) 4.21787e8 + 7.30556e8i 0.151964 + 0.263210i 0.931949 0.362588i \(-0.118107\pi\)
−0.779985 + 0.625798i \(0.784774\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −2.39033e7 −0.00837472 −0.00418736 0.999991i \(-0.501333\pi\)
−0.00418736 + 0.999991i \(0.501333\pi\)
\(504\) 0 0
\(505\) −9.57307e8 −0.330774
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.04440e9 + 3.54101e9i 0.687153 + 1.19018i 0.972755 + 0.231836i \(0.0744733\pi\)
−0.285601 + 0.958348i \(0.592193\pi\)
\(510\) 0 0
\(511\) 2.42460e8 8.29935e8i 0.0803836 0.275151i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.68251e9 + 2.91420e9i −0.542791 + 0.940142i
\(516\) 0 0
\(517\) −6.69440e9 −2.13056
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −7.40519e7 + 1.28262e8i −0.0229406 + 0.0397342i −0.877268 0.480001i \(-0.840636\pi\)
0.854327 + 0.519736i \(0.173970\pi\)
\(522\) 0 0
\(523\) −8.06974e8 1.39772e9i −0.246663 0.427232i 0.715935 0.698167i \(-0.246001\pi\)
−0.962598 + 0.270934i \(0.912667\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.84484e8 + 3.19535e8i 0.0549061 + 0.0951002i
\(528\) 0 0
\(529\) 1.04411e8 1.80846e8i 0.0306657 0.0531145i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.99141e9 −0.569661
\(534\) 0 0
\(535\) 2.22751e9 3.85817e9i 0.628901 1.08929i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 2.90638e8 6.47326e9i 0.0799450 1.78058i
\(540\) 0 0
\(541\) 1.89435e9 + 3.28111e9i 0.514362 + 0.890902i 0.999861 + 0.0166643i \(0.00530466\pi\)
−0.485499 + 0.874237i \(0.661362\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 1.33452e9 0.353132
\(546\) 0 0
\(547\) 2.21090e9 0.577582 0.288791 0.957392i \(-0.406747\pi\)
0.288791 + 0.957392i \(0.406747\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −2.59620e9 4.49676e9i −0.661162 1.14517i
\(552\) 0 0
\(553\) −3.70384e9 3.87387e9i −0.931353 0.974107i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 9.70947e7 1.68173e8i 0.0238069 0.0412347i −0.853877 0.520476i \(-0.825755\pi\)
0.877683 + 0.479241i \(0.159088\pi\)
\(558\) 0 0
\(559\) 6.43772e8 0.155880
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 1.43470e9 2.48497e9i 0.338830 0.586871i −0.645383 0.763859i \(-0.723302\pi\)
0.984213 + 0.176989i \(0.0566356\pi\)
\(564\) 0 0
\(565\) 7.45458e8 + 1.29117e9i 0.173882 + 0.301172i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 2.75350e9 + 4.76921e9i 0.626604 + 1.08531i 0.988228 + 0.152986i \(0.0488888\pi\)
−0.361625 + 0.932324i \(0.617778\pi\)
\(570\) 0 0
\(571\) 2.55175e9 4.41975e9i 0.573603 0.993509i −0.422589 0.906321i \(-0.638879\pi\)
0.996192 0.0871876i \(-0.0277880\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.29322e9 0.283685
\(576\) 0 0
\(577\) −1.72918e9 + 2.99503e9i −0.374736 + 0.649062i −0.990287 0.139035i \(-0.955600\pi\)
0.615552 + 0.788097i \(0.288933\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 8.62813e9 2.10564e9i 1.82516 0.445419i
\(582\) 0 0
\(583\) 4.72022e9 + 8.17566e9i 0.986557 + 1.70877i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.14732e9 0.846318 0.423159 0.906055i \(-0.360921\pi\)
0.423159 + 0.906055i \(0.360921\pi\)
\(588\) 0 0
\(589\) 2.05890e9 0.415176
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −3.97134e9 6.87856e9i −0.782069 1.35458i −0.930734 0.365696i \(-0.880831\pi\)
0.148665 0.988888i \(-0.452502\pi\)
\(594\) 0 0
\(595\) −1.48284e9 + 3.61879e8i −0.288593 + 0.0704295i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.80065e9 + 3.11882e9i −0.342323 + 0.592921i −0.984864 0.173331i \(-0.944547\pi\)
0.642541 + 0.766252i \(0.277880\pi\)
\(600\) 0 0
\(601\) −7.09831e8 −0.133381 −0.0666906 0.997774i \(-0.521244\pi\)
−0.0666906 + 0.997774i \(0.521244\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −4.98559e9 + 8.63529e9i −0.915319 + 1.58538i
\(606\) 0 0
\(607\) 3.94285e9 + 6.82922e9i 0.715566 + 1.23940i 0.962741 + 0.270426i \(0.0871646\pi\)
−0.247174 + 0.968971i \(0.579502\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 2.45160e9 + 4.24630e9i 0.434816 + 0.753123i
\(612\) 0 0
\(613\) −5.08263e9 + 8.80338e9i −0.891204 + 1.54361i −0.0527708 + 0.998607i \(0.516805\pi\)
−0.838433 + 0.545004i \(0.816528\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −5.64250e9 −0.967105 −0.483552 0.875315i \(-0.660654\pi\)
−0.483552 + 0.875315i \(0.660654\pi\)
\(618\) 0 0
\(619\) 5.82276e9 1.00853e10i 0.986760 1.70912i 0.352922 0.935653i \(-0.385188\pi\)
0.633838 0.773466i \(-0.281479\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.25072e9 3.39995e9i −0.538607 0.563332i
\(624\) 0 0
\(625\) 1.89654e9 + 3.28490e9i 0.310729 + 0.538199i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.00099e9 0.320603
\(630\) 0 0
\(631\) 1.07600e10 1.70494 0.852469 0.522777i \(-0.175104\pi\)
0.852469 + 0.522777i \(0.175104\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.84224e9 + 8.38701e9i 0.750479 + 1.29987i
\(636\) 0 0
\(637\) −4.21247e9 + 2.18627e9i −0.645727 + 0.335131i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 5.13595e9 8.89572e9i 0.770225 1.33407i −0.167215 0.985921i \(-0.553477\pi\)
0.937439 0.348148i \(-0.113189\pi\)
\(642\) 0 0
\(643\) 1.16555e10 1.72899 0.864497 0.502638i \(-0.167637\pi\)
0.864497 + 0.502638i \(0.167637\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −1.47741e9 + 2.55895e9i −0.214455 + 0.371447i −0.953104 0.302644i \(-0.902131\pi\)
0.738649 + 0.674090i \(0.235464\pi\)
\(648\) 0 0
\(649\) 6.73695e9 + 1.16687e10i 0.967402 + 1.67559i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −2.44343e9 4.23214e9i −0.343403 0.594791i 0.641660 0.766990i \(-0.278246\pi\)
−0.985062 + 0.172199i \(0.944913\pi\)
\(654\) 0 0
\(655\) −2.57030e9 + 4.45190e9i −0.357388 + 0.619014i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.12839e10 1.53589 0.767947 0.640513i \(-0.221278\pi\)
0.767947 + 0.640513i \(0.221278\pi\)
\(660\) 0 0
\(661\) 3.19740e9 5.53807e9i 0.430618 0.745853i −0.566308 0.824193i \(-0.691629\pi\)
0.996927 + 0.0783406i \(0.0249622\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.38846e9 + 8.17563e9i −0.314950 + 1.07807i
\(666\) 0 0
\(667\) 3.67573e9 + 6.36656e9i 0.479627 + 0.830738i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −1.93127e10 −2.46782
\(672\) 0 0
\(673\) 2.86561e8 0.0362380 0.0181190 0.999836i \(-0.494232\pi\)
0.0181190 + 0.999836i \(0.494232\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −6.77078e9 1.17273e10i −0.838646 1.45258i −0.891027 0.453950i \(-0.850015\pi\)
0.0523818 0.998627i \(-0.483319\pi\)
\(678\) 0 0
\(679\) −4.29488e9 + 1.04814e9i −0.526510 + 0.128492i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 1.56295e9 2.70711e9i 0.187704 0.325112i −0.756781 0.653669i \(-0.773229\pi\)
0.944484 + 0.328557i \(0.106562\pi\)
\(684\) 0 0
\(685\) −8.81307e9 −1.04763
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.45725e9 5.98813e9i 0.402683 0.697467i
\(690\) 0 0
\(691\) 3.72246e9 + 6.44749e9i 0.429197 + 0.743392i 0.996802 0.0799095i \(-0.0254631\pi\)
−0.567605 + 0.823301i \(0.692130\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.70258e9 + 6.41305e9i 0.418367 + 0.724633i
\(696\) 0 0
\(697\) 1.23634e9 2.14141e9i 0.138301 0.239544i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −8.02247e9 −0.879620 −0.439810 0.898091i \(-0.644954\pi\)
−0.439810 + 0.898091i \(0.644954\pi\)
\(702\) 0 0
\(703\) 5.58294e9 9.66993e9i 0.606065 1.04974i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.03643e9 3.54769e9i 0.110300 0.377553i
\(708\) 0 0
\(709\) 9.07598e9 + 1.57201e10i 0.956383 + 1.65650i 0.731172 + 0.682193i \(0.238974\pi\)
0.225211 + 0.974310i \(0.427693\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.91502e9 −0.301181
\(714\) 0 0
\(715\) 1.06581e10 1.09046
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 6.98920e9 + 1.21056e10i 0.701255 + 1.21461i 0.968026 + 0.250850i \(0.0807100\pi\)
−0.266771 + 0.963760i \(0.585957\pi\)
\(720\) 0 0
\(721\) −8.97816e9 9.39030e9i −0.892100 0.933053i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 1.48734e9 2.57615e9i 0.144953 0.251066i
\(726\) 0 0
\(727\) −6.81996e9 −0.658281 −0.329140 0.944281i \(-0.606759\pi\)
−0.329140 + 0.944281i \(0.606759\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −3.99678e8 + 6.92262e8i −0.0378442 + 0.0655480i
\(732\) 0 0
\(733\) −5.74796e9 9.95576e9i −0.539076 0.933706i −0.998954 0.0457245i \(-0.985440\pi\)
0.459879 0.887982i \(-0.347893\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.46692e9 + 4.27283e9i 0.226996 + 0.393169i
\(738\) 0 0
\(739\) −6.74312e8 + 1.16794e9i −0.0614618 + 0.106455i −0.895119 0.445827i \(-0.852910\pi\)
0.833657 + 0.552282i \(0.186243\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −2.00361e9 −0.179206 −0.0896029 0.995978i \(-0.528560\pi\)
−0.0896029 + 0.995978i \(0.528560\pi\)
\(744\) 0 0
\(745\) 1.94806e9 3.37414e9i 0.172606 0.298962i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.18864e10 + 1.24320e10i 1.03363 + 1.08107i
\(750\) 0 0
\(751\) 3.69709e9 + 6.40354e9i 0.318508 + 0.551671i 0.980177 0.198125i \(-0.0634850\pi\)
−0.661669 + 0.749796i \(0.730152\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −1.46561e10 −1.23937
\(756\) 0 0
\(757\) 1.79000e10 1.49975 0.749874 0.661581i \(-0.230114\pi\)
0.749874 + 0.661581i \(0.230114\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 6.51905e9 + 1.12913e10i 0.536214 + 0.928749i 0.999104 + 0.0423334i \(0.0134792\pi\)
−0.462890 + 0.886416i \(0.653188\pi\)
\(762\) 0 0
\(763\) −1.44483e9 + 4.94561e9i −0.117755 + 0.403073i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 4.93437e9 8.54658e9i 0.394865 0.683926i
\(768\) 0 0
\(769\) −1.72914e10 −1.37116 −0.685580 0.727997i \(-0.740451\pi\)
−0.685580 + 0.727997i \(0.740451\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 5.33950e9 9.24829e9i 0.415789 0.720167i −0.579722 0.814814i \(-0.696839\pi\)
0.995511 + 0.0946470i \(0.0301722\pi\)
\(774\) 0 0
\(775\) 5.89764e8 + 1.02150e9i 0.0455116 + 0.0788284i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −6.89902e9 1.19494e10i −0.522885 0.905663i
\(780\) 0 0
\(781\) −1.17003e10 + 2.02656e10i −0.878860 + 1.52223i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 9.35608e9 0.690319
\(786\) 0 0
\(787\) 1.13691e10 1.96918e10i 0.831407 1.44004i −0.0655160 0.997852i \(-0.520869\pi\)
0.896923 0.442187i \(-0.145797\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.59204e9 + 1.36470e9i −0.401747 + 0.0980440i
\(792\) 0 0
\(793\) 7.07262e9