Properties

Label 252.8.k.e.37.4
Level $252$
Weight $8$
Character 252.37
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 37.4
Root \(-50.1630 + 86.8849i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.8.k.e.109.4

$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

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

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 −0.995986 0.0895111i \(-0.971470\pi\)
0.575512 + 0.817793i \(0.304803\pi\)
\(6\) 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 0.838451 + 0.544977i \(0.183462\pi\)
0.0527383 + 0.998608i \(0.483205\pi\)
\(12\) 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 0.940722 0.339179i \(-0.110149\pi\)
−0.764098 + 0.645100i \(0.776816\pi\)
\(18\) 0 0
\(19\) −19965.0 + 34580.3i −0.667776 + 1.15662i 0.310749 + 0.950492i \(0.399420\pi\)
−0.978525 + 0.206130i \(0.933913\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 28266.6 48959.2i 0.484425 0.839048i −0.515415 0.856940i \(-0.672362\pi\)
0.999840 + 0.0178925i \(0.00569567\pi\)
\(24\) 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 0.777784 0.628532i \(-0.216344\pi\)
−0.933216 + 0.359315i \(0.883010\pi\)
\(32\) 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 −0.544824 0.838550i \(-0.683404\pi\)
0.998618 + 0.0525566i \(0.0167370\pi\)
\(38\) 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 0.395489 + 0.918471i \(0.370575\pi\)
−0.993164 + 0.116731i \(0.962758\pi\)
\(48\) 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 −0.998018 0.0629273i \(-0.979956\pi\)
0.444512 0.895773i \(-0.353377\pi\)
\(54\) 0 0
\(55\) −1.84943e6 −1.49889
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −856228. 1.48303e6i −0.542759 0.940086i −0.998744 0.0500990i \(-0.984046\pi\)
0.455985 0.889987i \(-0.349287\pi\)
\(60\) 0 0
\(61\) −1.22726e6 + 2.12568e6i −0.692282 + 1.19907i 0.278806 + 0.960347i \(0.410061\pi\)
−0.971088 + 0.238721i \(0.923272\pi\)
\(62\) 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 0.795296 0.606222i \(-0.207316\pi\)
−0.922651 + 0.385635i \(0.873982\pi\)
\(68\) 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 0.928747 0.370714i \(-0.120887\pi\)
−0.785421 + 0.618962i \(0.787554\pi\)
\(74\) 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 0.302952 + 0.953006i \(0.402028\pi\)
−0.976803 + 0.214139i \(0.931305\pi\)
\(80\) 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 −0.992408 0.122989i \(-0.960752\pi\)
0.602716 + 0.797956i \(0.294085\pi\)
\(90\) 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 0.947446 0.319916i \(-0.103655\pi\)
−0.750778 + 0.660554i \(0.770321\pi\)
\(102\) 0 0
\(103\) −7.15804e6 + 1.23981e7i −0.645452 + 1.11795i 0.338745 + 0.940878i \(0.389997\pi\)
−0.984197 + 0.177077i \(0.943336\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 9.47668e6 1.64141e7i 0.747847 1.29531i −0.201005 0.979590i \(-0.564421\pi\)
0.948853 0.315720i \(-0.102246\pi\)
\(108\) 0 0
\(109\) −2.83878e6 4.91690e6i −0.209961 0.363663i 0.741741 0.670686i \(-0.234000\pi\)
−0.951702 + 0.307023i \(0.900667\pi\)
\(110\) 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 −0.996419 0.0845554i \(-0.973053\pi\)
0.571436 + 0.820646i \(0.306386\pi\)
\(132\) 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 0.988945 + 0.148283i \(0.0473746\pi\)
−0.366056 + 0.930593i \(0.619292\pi\)
\(138\) 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 −0.744961 0.667108i \(-0.767532\pi\)
0.950213 + 0.311601i \(0.100865\pi\)
\(150\) 0 0
\(151\) 3.11762e7 + 5.39987e7i 0.736891 + 1.27633i 0.953888 + 0.300161i \(0.0970405\pi\)
−0.216997 + 0.976172i \(0.569626\pi\)
\(152\) 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 0.584497 0.811396i \(-0.301292\pi\)
−0.994938 + 0.100491i \(0.967959\pi\)
\(158\) 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 −0.673866 0.738854i \(-0.735367\pi\)
0.976799 + 0.214158i \(0.0687008\pi\)
\(164\) 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 −0.450718 0.892666i \(-0.648832\pi\)
0.998431 0.0560000i \(-0.0178347\pi\)
\(174\) 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 0.743245 + 0.669019i \(0.233286\pi\)
0.207765 + 0.978179i \(0.433381\pi\)
\(180\) 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 −0.900442 0.434976i \(-0.856757\pi\)
0.826921 + 0.562318i \(0.190090\pi\)
\(192\) 0 0
\(193\) −5.70040e6 9.87338e6i −0.0570761 0.0988588i 0.836076 0.548614i \(-0.184844\pi\)
−0.893152 + 0.449756i \(0.851511\pi\)
\(194\) 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 0.988630 0.150369i \(-0.0480461\pi\)
−0.624538 + 0.780994i \(0.714713\pi\)
\(200\) 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 0.566286 0.824209i \(-0.308380\pi\)
−0.996929 + 0.0783137i \(0.975046\pi\)
\(228\) 0 0
\(229\) 1.01394e8 1.75620e8i 0.557942 0.966384i −0.439726 0.898132i \(-0.644924\pi\)
0.997668 0.0682522i \(-0.0217423\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.53553e8 2.65962e8i 0.795266 1.37744i −0.127403 0.991851i \(-0.540664\pi\)
0.922670 0.385591i \(-0.126002\pi\)
\(234\) 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 0.864421 0.502769i \(-0.167685\pi\)
−0.867621 + 0.497226i \(0.834352\pi\)
\(242\) 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 0.354857 + 0.934921i \(0.384530\pi\)
−0.987093 + 0.160146i \(0.948804\pi\)
\(258\) 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 0.880908 0.473288i \(-0.156933\pi\)
−0.850333 + 0.526244i \(0.823600\pi\)
\(264\) 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 0.897530 0.440954i \(-0.145360\pi\)
−0.830642 + 0.556806i \(0.812027\pi\)
\(270\) 0 0
\(271\) 7.46844e7 1.29357e8i 0.227949 0.394819i −0.729251 0.684246i \(-0.760131\pi\)
0.957200 + 0.289427i \(0.0934648\pi\)
\(272\) 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 −0.999945 0.0104821i \(-0.996663\pi\)
0.490895 0.871219i \(-0.336670\pi\)
\(278\) 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 0.892793 0.450467i \(-0.148742\pi\)
−0.836512 + 0.547948i \(0.815409\pi\)
\(284\) 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 0.608292 0.793714i \(-0.291855\pi\)
−0.991522 + 0.129939i \(0.958522\pi\)
\(312\) 0 0
\(313\) 2.29934e8 3.98258e8i 0.423837 0.734107i −0.572474 0.819923i \(-0.694016\pi\)
0.996311 + 0.0858160i \(0.0273497\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.06886e8 5.31543e8i 0.541091 0.937197i −0.457751 0.889081i \(-0.651345\pi\)
0.998842 0.0481166i \(-0.0153219\pi\)
\(318\) 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 0.000808163 1.00000i \(-0.499743\pi\)
0.865621 0.500700i \(-0.166924\pi\)
\(332\) 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 0.650128 0.759825i \(-0.274715\pi\)
−0.983092 + 0.183114i \(0.941382\pi\)
\(348\) 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 0.764048 + 0.645160i \(0.223209\pi\)
0.176701 + 0.984265i \(0.443458\pi\)
\(354\) 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 −0.425395 + 0.905008i \(0.639865\pi\)
−0.571062 + 0.820907i \(0.693469\pi\)
\(360\) 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 0.932074 0.362267i \(-0.117997\pi\)
−0.779769 + 0.626067i \(0.784664\pi\)
\(368\) 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 −0.907633 0.419764i \(-0.862113\pi\)
0.817343 + 0.576152i \(0.195446\pi\)
\(374\) 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 −0.0895186 0.995985i \(-0.528533\pi\)
0.907308 0.420467i \(-0.138134\pi\)
\(384\) 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 0.925875 0.377831i \(-0.123330\pi\)
−0.790148 + 0.612916i \(0.789997\pi\)
\(390\) 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 0.317861 + 0.948137i \(0.397036\pi\)
−0.980041 + 0.198793i \(0.936298\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −5.17565e8 + 8.96449e8i −0.400830 + 0.694257i −0.993826 0.110948i \(-0.964611\pi\)
0.592997 + 0.805205i \(0.297945\pi\)
\(402\) 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 0.980058 0.198710i \(-0.0636751\pi\)
−0.662117 + 0.749401i \(0.730342\pi\)
\(410\) 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 0.980410 + 0.196969i \(0.0631097\pi\)
−0.319625 + 0.947544i \(0.603557\pi\)
\(432\) 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 −0.958296 0.285776i \(-0.907749\pi\)
0.726637 + 0.687021i \(0.241082\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −6.27229e8 + 1.08639e9i −0.342778 + 0.593709i −0.984948 0.172854i \(-0.944701\pi\)
0.642169 + 0.766563i \(0.278035\pi\)
\(444\) 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 −0.910901 0.412624i \(-0.864612\pi\)
0.812794 + 0.582552i \(0.197946\pi\)
\(458\) 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 −0.986733 0.162352i \(-0.948092\pi\)
0.633968 + 0.773359i \(0.281425\pi\)
\(468\) 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 0.714352 0.699787i \(-0.246722\pi\)
−0.963209 + 0.268753i \(0.913388\pi\)
\(480\) 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 0.660754 0.750602i \(-0.270237\pi\)
−0.980418 + 0.196929i \(0.936903\pi\)
\(488\) 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 −0.779985 0.625798i \(-0.784774\pi\)
0.931949 + 0.362588i \(0.118107\pi\)
\(500\) 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 −0.285601 0.958348i \(-0.592193\pi\)
0.972755 0.231836i \(-0.0744733\pi\)
\(510\) 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 0.854327 0.519736i \(-0.173970\pi\)
−0.877268 + 0.480001i \(0.840636\pi\)
\(522\) 0 0
\(523\) −8.06974e8 + 1.39772e9i −0.246663 + 0.427232i −0.962598 0.270934i \(-0.912667\pi\)
0.715935 + 0.698167i \(0.246001\pi\)
\(524\) 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 −0.485499 0.874237i \(-0.661362\pi\)
0.999861 0.0166643i \(-0.00530466\pi\)
\(542\) 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 0.877683 0.479241i \(-0.159088\pi\)
−0.853877 + 0.520476i \(0.825755\pi\)
\(558\) 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 0.984213 0.176989i \(-0.0566356\pi\)
−0.645383 + 0.763859i \(0.723302\pi\)
\(564\) 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 −0.361625 0.932324i \(-0.617778\pi\)
0.988228 0.152986i \(-0.0488888\pi\)
\(570\) 0 0
\(571\) 2.55175e9 + 4.41975e9i 0.573603 + 0.993509i 0.996192 + 0.0871876i \(0.0277880\pi\)
−0.422589 + 0.906321i \(0.638879\pi\)
\(572\) 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 0.615552 0.788097i \(-0.288933\pi\)
−0.990287 + 0.139035i \(0.955600\pi\)
\(578\) 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 0.148665 + 0.988888i \(0.452502\pi\)
−0.930734 + 0.365696i \(0.880831\pi\)
\(594\) 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 0.642541 0.766252i \(-0.277880\pi\)
−0.984864 + 0.173331i \(0.944547\pi\)
\(600\) 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 −0.247174 0.968971i \(-0.579502\pi\)
0.962741 0.270426i \(-0.0871646\pi\)
\(608\) 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 −0.838433 0.545004i \(-0.816528\pi\)
−0.0527708 0.998607i \(-0.516805\pi\)
\(614\) 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 0.633838 + 0.773466i \(0.281479\pi\)
0.352922 + 0.935653i \(0.385188\pi\)
\(620\) 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 0.937439 + 0.348148i \(0.113189\pi\)
−0.167215 + 0.985921i \(0.553477\pi\)
\(642\) 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 0.738649 0.674090i \(-0.235464\pi\)
−0.953104 + 0.302644i \(0.902131\pi\)
\(648\) 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 −0.985062 0.172199i \(-0.944913\pi\)
0.641660 + 0.766990i \(0.278246\pi\)
\(654\) 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 0.996927 0.0783406i \(-0.0249622\pi\)
−0.566308 + 0.824193i \(0.691629\pi\)
\(662\) 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 0.0523818 + 0.998627i \(0.483319\pi\)
−0.891027 + 0.453950i \(0.850015\pi\)
\(678\) 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 0.944484 0.328557i \(-0.106562\pi\)
−0.756781 + 0.653669i \(0.773229\pi\)
\(684\) 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 −0.567605 0.823301i \(-0.692130\pi\)
0.996802 + 0.0799095i \(0.0254631\pi\)
\(692\) 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 0.225211 0.974310i \(-0.427693\pi\)
0.731172 0.682193i \(-0.238974\pi\)
\(710\) 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 −0.266771 0.963760i \(-0.585957\pi\)
0.968026 0.250850i \(-0.0807100\pi\)
\(720\) 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 0.459879 + 0.887982i \(0.347893\pi\)
−0.998954 + 0.0457245i \(0.985440\pi\)
\(734\) 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 0.833657 0.552282i \(-0.186243\pi\)
−0.895119 + 0.445827i \(0.852910\pi\)
\(740\) 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 −0.661669 0.749796i \(-0.730152\pi\)
0.980177 + 0.198125i \(0.0634850\pi\)
\(752\) 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 −0.462890 0.886416i \(-0.653188\pi\)
0.999104 0.0423334i \(-0.0134792\pi\)
\(762\) 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 0.995511 0.0946470i \(-0.0301722\pi\)
−0.579722 + 0.814814i \(0.696839\pi\)
\(774\) 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 0.896923 + 0.442187i \(0.145797\pi\)
−0.0655160 + 0.997852i \(0.520869\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −5.59204e9 1.36470e9i −0.401747 0.0980440i
\(792\) 0 0
\(793\) 7.07262e9 1.22501e10i