Properties

Label 252.12.k.d.109.1
Level $252$
Weight $12$
Character 252.109
Analytic conductor $193.622$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 252.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(193.622481501\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 581500324 x^{14} - 481772282104 x^{13} + 132272376701859942 x^{12} + \)\(18\!\cdots\!08\)\( x^{11} - \)\(14\!\cdots\!08\)\( x^{10} - \)\(25\!\cdots\!56\)\( x^{9} + \)\(80\!\cdots\!79\)\( x^{8} + \)\(11\!\cdots\!68\)\( x^{7} - \)\(19\!\cdots\!68\)\( x^{6} + \)\(59\!\cdots\!08\)\( x^{5} + \)\(21\!\cdots\!06\)\( x^{4} - \)\(37\!\cdots\!04\)\( x^{3} - \)\(31\!\cdots\!28\)\( x^{2} + \)\(25\!\cdots\!24\)\( x + \)\(79\!\cdots\!77\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 109.1
Root \(-11427.1 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.109
Dual form 252.12.k.d.37.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +O(q^{10})\) \(q+(-5578.82 - 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +(196201. - 339830. i) q^{11} -2.28291e6 q^{13} +(2.79207e6 - 4.83601e6i) q^{17} +(6.40868e6 + 1.11002e7i) q^{19} +(1.12939e7 + 1.95616e7i) q^{23} +(-3.78323e7 + 6.55275e7i) q^{25} -1.65025e8 q^{29} +(9.99385e7 - 1.73099e8i) q^{31} +(2.16805e8 - 4.46272e8i) q^{35} +(2.10302e8 + 3.64253e8i) q^{37} +7.64804e8 q^{41} -2.38223e8 q^{43} +(9.33471e7 + 1.61682e8i) q^{47} +(-7.35026e8 + 1.83564e9i) q^{49} +(-1.62451e9 + 2.81374e9i) q^{53} -4.37827e9 q^{55} +(-6.84439e7 + 1.18548e8i) q^{59} +(1.63005e9 + 2.82334e9i) q^{61} +(1.27359e10 + 2.20593e10i) q^{65} +(-7.66329e9 + 1.32732e10i) q^{67} -1.53915e10 q^{71} +(1.23489e10 - 2.13889e10i) q^{73} +(1.74046e10 - 1.24419e9i) q^{77} +(1.05790e10 + 1.83233e10i) q^{79} +5.62969e10 q^{83} -6.23059e10 q^{85} +(1.87036e10 + 3.23955e10i) q^{89} +(-5.68967e10 - 8.40711e10i) q^{91} +(7.15057e10 - 1.23851e11i) q^{95} -7.72068e10 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

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
\(5\) −5578.82 9662.79i −0.798375 1.38283i −0.920674 0.390333i \(-0.872360\pi\)
0.122299 0.992493i \(-0.460973\pi\)
\(6\) 0 0
\(7\) 24922.9 + 36826.3i 0.560479 + 0.828169i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 196201. 339830.i 0.367317 0.636211i −0.621828 0.783154i \(-0.713610\pi\)
0.989145 + 0.146942i \(0.0469432\pi\)
\(12\) 0 0
\(13\) −2.28291e6 −1.70530 −0.852649 0.522484i \(-0.825005\pi\)
−0.852649 + 0.522484i \(0.825005\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.79207e6 4.83601e6i 0.476934 0.826073i −0.522717 0.852506i \(-0.675082\pi\)
0.999651 + 0.0264331i \(0.00841489\pi\)
\(18\) 0 0
\(19\) 6.40868e6 + 1.11002e7i 0.593778 + 1.02845i 0.993718 + 0.111912i \(0.0356975\pi\)
−0.399940 + 0.916541i \(0.630969\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.12939e7 + 1.95616e7i 0.365881 + 0.633725i 0.988917 0.148468i \(-0.0474342\pi\)
−0.623036 + 0.782193i \(0.714101\pi\)
\(24\) 0 0
\(25\) −3.78323e7 + 6.55275e7i −0.774806 + 1.34200i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.65025e8 −1.49403 −0.747016 0.664806i \(-0.768514\pi\)
−0.747016 + 0.664806i \(0.768514\pi\)
\(30\) 0 0
\(31\) 9.99385e7 1.73099e8i 0.626966 1.08594i −0.361192 0.932492i \(-0.617630\pi\)
0.988157 0.153445i \(-0.0490367\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.16805e8 4.46272e8i 0.697741 1.43623i
\(36\) 0 0
\(37\) 2.10302e8 + 3.64253e8i 0.498579 + 0.863563i 0.999999 0.00164058i \(-0.000522215\pi\)
−0.501420 + 0.865204i \(0.667189\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 7.64804e8 1.03095 0.515476 0.856904i \(-0.327615\pi\)
0.515476 + 0.856904i \(0.327615\pi\)
\(42\) 0 0
\(43\) −2.38223e8 −0.247120 −0.123560 0.992337i \(-0.539431\pi\)
−0.123560 + 0.992337i \(0.539431\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 9.33471e7 + 1.61682e8i 0.0593694 + 0.102831i 0.894183 0.447703i \(-0.147758\pi\)
−0.834813 + 0.550533i \(0.814424\pi\)
\(48\) 0 0
\(49\) −7.35026e8 + 1.83564e9i −0.371727 + 0.928342i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.62451e9 + 2.81374e9i −0.533587 + 0.924200i 0.465643 + 0.884973i \(0.345823\pi\)
−0.999230 + 0.0392276i \(0.987510\pi\)
\(54\) 0 0
\(55\) −4.37827e9 −1.17303
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.84439e7 + 1.18548e8i −0.0124637 + 0.0215878i −0.872190 0.489167i \(-0.837301\pi\)
0.859726 + 0.510755i \(0.170634\pi\)
\(60\) 0 0
\(61\) 1.63005e9 + 2.82334e9i 0.247109 + 0.428005i 0.962722 0.270492i \(-0.0871862\pi\)
−0.715614 + 0.698496i \(0.753853\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.27359e10 + 2.20593e10i 1.36147 + 2.35813i
\(66\) 0 0
\(67\) −7.66329e9 + 1.32732e10i −0.693432 + 1.20106i 0.277275 + 0.960791i \(0.410569\pi\)
−0.970707 + 0.240268i \(0.922765\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.53915e10 −1.01242 −0.506210 0.862410i \(-0.668954\pi\)
−0.506210 + 0.862410i \(0.668954\pi\)
\(72\) 0 0
\(73\) 1.23489e10 2.13889e10i 0.697192 1.20757i −0.272244 0.962228i \(-0.587766\pi\)
0.969436 0.245344i \(-0.0789008\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.74046e10 1.24419e9i 0.732764 0.0523826i
\(78\) 0 0
\(79\) 1.05790e10 + 1.83233e10i 0.386807 + 0.669970i 0.992018 0.126095i \(-0.0402445\pi\)
−0.605211 + 0.796065i \(0.706911\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 5.62969e10 1.56875 0.784377 0.620284i \(-0.212983\pi\)
0.784377 + 0.620284i \(0.212983\pi\)
\(84\) 0 0
\(85\) −6.23059e10 −1.52309
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 1.87036e10 + 3.23955e10i 0.355041 + 0.614950i 0.987125 0.159950i \(-0.0511334\pi\)
−0.632084 + 0.774900i \(0.717800\pi\)
\(90\) 0 0
\(91\) −5.68967e10 8.40711e10i −0.955783 1.41227i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 7.15057e10 1.23851e11i 0.948115 1.64218i
\(96\) 0 0
\(97\) −7.72068e10 −0.912874 −0.456437 0.889756i \(-0.650875\pi\)
−0.456437 + 0.889756i \(0.650875\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −6.27863e10 + 1.08749e11i −0.594426 + 1.02958i 0.399202 + 0.916863i \(0.369287\pi\)
−0.993628 + 0.112712i \(0.964046\pi\)
\(102\) 0 0
\(103\) −9.56009e10 1.65586e11i −0.812563 1.40740i −0.911064 0.412264i \(-0.864738\pi\)
0.0985011 0.995137i \(-0.468595\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.85938e10 4.95259e10i −0.197088 0.341367i 0.750495 0.660876i \(-0.229815\pi\)
−0.947583 + 0.319509i \(0.896482\pi\)
\(108\) 0 0
\(109\) 1.21619e11 2.10650e11i 0.757102 1.31134i −0.187220 0.982318i \(-0.559948\pi\)
0.944322 0.329022i \(-0.106719\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −4.16630e10 −0.212726 −0.106363 0.994327i \(-0.533920\pi\)
−0.106363 + 0.994327i \(0.533920\pi\)
\(114\) 0 0
\(115\) 1.26013e11 2.18261e11i 0.584221 1.01190i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.47679e11 1.77057e10i 0.951439 0.0680149i
\(120\) 0 0
\(121\) 6.56664e10 + 1.13738e11i 0.230157 + 0.398643i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.99432e11 0.877592
\(126\) 0 0
\(127\) −3.71377e10 −0.0997457 −0.0498728 0.998756i \(-0.515882\pi\)
−0.0498728 + 0.998756i \(0.515882\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 1.98899e11 + 3.44503e11i 0.450443 + 0.780191i 0.998414 0.0563070i \(-0.0179326\pi\)
−0.547970 + 0.836498i \(0.684599\pi\)
\(132\) 0 0
\(133\) −2.49055e11 + 5.12656e11i −0.518933 + 1.06817i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 4.18742e11 7.25282e11i 0.741282 1.28394i −0.210630 0.977566i \(-0.567552\pi\)
0.951912 0.306372i \(-0.0991150\pi\)
\(138\) 0 0
\(139\) −6.68822e11 −1.09327 −0.546637 0.837370i \(-0.684092\pi\)
−0.546637 + 0.837370i \(0.684092\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −4.47908e11 + 7.75800e11i −0.626384 + 1.08493i
\(144\) 0 0
\(145\) 9.20642e11 + 1.59460e12i 1.19280 + 2.06599i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.37890e11 5.85243e11i −0.376922 0.652847i 0.613691 0.789546i \(-0.289684\pi\)
−0.990613 + 0.136699i \(0.956351\pi\)
\(150\) 0 0
\(151\) 2.19258e11 3.79765e11i 0.227291 0.393679i −0.729714 0.683753i \(-0.760347\pi\)
0.957004 + 0.290074i \(0.0936800\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.23015e12 −2.00221
\(156\) 0 0
\(157\) 1.47959e11 2.56272e11i 0.123792 0.214414i −0.797468 0.603361i \(-0.793828\pi\)
0.921260 + 0.388947i \(0.127161\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −4.38905e11 + 9.03443e11i −0.319763 + 0.658201i
\(162\) 0 0
\(163\) 1.12083e12 + 1.94133e12i 0.762971 + 1.32150i 0.941313 + 0.337535i \(0.109593\pi\)
−0.178342 + 0.983968i \(0.557073\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.62678e11 0.156489 0.0782445 0.996934i \(-0.475069\pi\)
0.0782445 + 0.996934i \(0.475069\pi\)
\(168\) 0 0
\(169\) 3.41951e12 1.90804
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 9.72304e11 + 1.68408e12i 0.477033 + 0.826245i 0.999654 0.0263201i \(-0.00837892\pi\)
−0.522621 + 0.852565i \(0.675046\pi\)
\(174\) 0 0
\(175\) −3.35602e12 + 2.39910e11i −1.54567 + 0.110494i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 2.23898e12 3.87802e12i 0.910663 1.57732i 0.0975338 0.995232i \(-0.468905\pi\)
0.813129 0.582083i \(-0.197762\pi\)
\(180\) 0 0
\(181\) 4.68844e12 1.79389 0.896945 0.442142i \(-0.145781\pi\)
0.896945 + 0.442142i \(0.145781\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.34647e12 4.06421e12i 0.796105 1.37889i
\(186\) 0 0
\(187\) −1.09561e12 1.89766e12i −0.350371 0.606861i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.93575e12 3.35282e12i −0.551019 0.954393i −0.998201 0.0599500i \(-0.980906\pi\)
0.447182 0.894443i \(-0.352427\pi\)
\(192\) 0 0
\(193\) 1.46950e12 2.54524e12i 0.395005 0.684169i −0.598097 0.801424i \(-0.704076\pi\)
0.993102 + 0.117255i \(0.0374094\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.10385e12 0.745309 0.372654 0.927970i \(-0.378448\pi\)
0.372654 + 0.927970i \(0.378448\pi\)
\(198\) 0 0
\(199\) 1.08230e12 1.87460e12i 0.245842 0.425810i −0.716526 0.697560i \(-0.754269\pi\)
0.962368 + 0.271750i \(0.0876023\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −4.11289e12 6.07725e12i −0.837373 1.23731i
\(204\) 0 0
\(205\) −4.26670e12 7.39014e12i −0.823087 1.42563i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 5.02955e12 0.872418
\(210\) 0 0
\(211\) 2.54746e12 0.419328 0.209664 0.977773i \(-0.432763\pi\)
0.209664 + 0.977773i \(0.432763\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.32900e12 + 2.30190e12i 0.197294 + 0.341724i
\(216\) 0 0
\(217\) 8.86534e12 6.33751e11i 1.25074 0.0894108i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −6.37405e12 + 1.10402e13i −0.813314 + 1.40870i
\(222\) 0 0
\(223\) −4.37566e12 −0.531333 −0.265667 0.964065i \(-0.585592\pi\)
−0.265667 + 0.964065i \(0.585592\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.86393e12 1.18887e13i 0.755841 1.30915i −0.189114 0.981955i \(-0.560562\pi\)
0.944955 0.327200i \(-0.106105\pi\)
\(228\) 0 0
\(229\) 5.79914e11 + 1.00444e12i 0.0608511 + 0.105397i 0.894846 0.446375i \(-0.147285\pi\)
−0.833995 + 0.551772i \(0.813952\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2.23260e12 + 3.86698e12i 0.212987 + 0.368904i 0.952648 0.304075i \(-0.0983474\pi\)
−0.739661 + 0.672980i \(0.765014\pi\)
\(234\) 0 0
\(235\) 1.04153e12 1.80399e12i 0.0947981 0.164195i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.16228e13 1.79359 0.896795 0.442447i \(-0.145889\pi\)
0.896795 + 0.442447i \(0.145889\pi\)
\(240\) 0 0
\(241\) −9.67406e12 + 1.67560e13i −0.766505 + 1.32763i 0.172942 + 0.984932i \(0.444673\pi\)
−0.939447 + 0.342694i \(0.888661\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.18379e13 3.13827e12i 1.58051 0.227131i
\(246\) 0 0
\(247\) −1.46304e13 2.53407e13i −1.01257 1.75382i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.43958e13 0.912075 0.456037 0.889961i \(-0.349268\pi\)
0.456037 + 0.889961i \(0.349268\pi\)
\(252\) 0 0
\(253\) 8.86347e12 0.537577
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.96043e12 + 1.55199e13i 0.498536 + 0.863490i 0.999999 0.00168967i \(-0.000537838\pi\)
−0.501463 + 0.865179i \(0.667205\pi\)
\(258\) 0 0
\(259\) −8.17278e12 + 1.68229e13i −0.435734 + 0.896916i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3.34897e12 5.80059e12i 0.164117 0.284260i −0.772224 0.635350i \(-0.780856\pi\)
0.936342 + 0.351091i \(0.114189\pi\)
\(264\) 0 0
\(265\) 3.62514e13 1.70401
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 1.73220e13 3.00027e13i 0.749828 1.29874i −0.198077 0.980187i \(-0.563469\pi\)
0.947905 0.318554i \(-0.103197\pi\)
\(270\) 0 0
\(271\) −7.52159e12 1.30278e13i −0.312593 0.541426i 0.666330 0.745657i \(-0.267864\pi\)
−0.978923 + 0.204231i \(0.934531\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 1.48454e13 + 2.57131e13i 0.569198 + 0.985880i
\(276\) 0 0
\(277\) −2.61416e12 + 4.52785e12i −0.0963148 + 0.166822i −0.910157 0.414264i \(-0.864039\pi\)
0.813842 + 0.581087i \(0.197372\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.40636e13 0.478863 0.239431 0.970913i \(-0.423039\pi\)
0.239431 + 0.970913i \(0.423039\pi\)
\(282\) 0 0
\(283\) 9.20998e12 1.59522e13i 0.301601 0.522389i −0.674897 0.737911i \(-0.735812\pi\)
0.976499 + 0.215523i \(0.0691455\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.90611e13 + 2.81649e13i 0.577827 + 0.853803i
\(288\) 0 0
\(289\) 1.54459e12 + 2.67531e12i 0.0450687 + 0.0780613i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −2.56171e13 −0.693040 −0.346520 0.938043i \(-0.612637\pi\)
−0.346520 + 0.938043i \(0.612637\pi\)
\(294\) 0 0
\(295\) 1.52734e12 0.0398030
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −2.57829e13 4.46573e13i −0.623937 1.08069i
\(300\) 0 0
\(301\) −5.93721e12 8.77288e12i −0.138505 0.204657i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 1.81875e13 3.15018e13i 0.394571 0.683417i
\(306\) 0 0
\(307\) 4.44656e13 0.930600 0.465300 0.885153i \(-0.345946\pi\)
0.465300 + 0.885153i \(0.345946\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 4.91286e13 8.50933e13i 0.957530 1.65849i 0.229061 0.973412i \(-0.426434\pi\)
0.728469 0.685079i \(-0.240232\pi\)
\(312\) 0 0
\(313\) −1.19408e13 2.06821e13i −0.224667 0.389135i 0.731552 0.681785i \(-0.238796\pi\)
−0.956220 + 0.292650i \(0.905463\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −4.97132e13 8.61057e13i −0.872259 1.51080i −0.859654 0.510877i \(-0.829321\pi\)
−0.0126053 0.999921i \(-0.504012\pi\)
\(318\) 0 0
\(319\) −3.23779e13 + 5.60802e13i −0.548783 + 0.950520i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.15741e13 1.13277
\(324\) 0 0
\(325\) 8.63677e13 1.49593e14i 1.32127 2.28851i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −3.62767e12 + 7.46721e12i −0.0518860 + 0.106802i
\(330\) 0 0
\(331\) 5.27130e12 + 9.13017e12i 0.0729229 + 0.126306i 0.900181 0.435516i \(-0.143434\pi\)
−0.827258 + 0.561822i \(0.810101\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.71008e14 2.21447
\(336\) 0 0
\(337\) 1.57113e14 1.96900 0.984502 0.175375i \(-0.0561139\pi\)
0.984502 + 0.175375i \(0.0561139\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −3.92160e13 6.79241e13i −0.460590 0.797765i
\(342\) 0 0
\(343\) −8.59186e13 + 1.86810e13i −0.977169 + 0.212463i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.53483e10 2.65840e10i 0.000163775 0.000283666i −0.865944 0.500142i \(-0.833281\pi\)
0.866107 + 0.499858i \(0.166615\pi\)
\(348\) 0 0
\(349\) 1.00590e14 1.03995 0.519976 0.854181i \(-0.325941\pi\)
0.519976 + 0.854181i \(0.325941\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9.13814e13 + 1.58277e14i −0.887354 + 1.53694i −0.0443634 + 0.999015i \(0.514126\pi\)
−0.842991 + 0.537928i \(0.819207\pi\)
\(354\) 0 0
\(355\) 8.58665e13 + 1.48725e14i 0.808291 + 1.40000i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.57145e13 6.18593e13i −0.316100 0.547502i 0.663570 0.748114i \(-0.269040\pi\)
−0.979671 + 0.200612i \(0.935707\pi\)
\(360\) 0 0
\(361\) −2.38973e13 + 4.13913e13i −0.205144 + 0.355319i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −2.75569e14 −2.22648
\(366\) 0 0
\(367\) 3.49074e13 6.04615e13i 0.273687 0.474040i −0.696116 0.717930i \(-0.745090\pi\)
0.969803 + 0.243889i \(0.0784233\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −1.44107e14 + 1.03017e13i −1.06446 + 0.0760942i
\(372\) 0 0
\(373\) −8.26603e13 1.43172e14i −0.592787 1.02674i −0.993855 0.110689i \(-0.964694\pi\)
0.401068 0.916048i \(-0.368639\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 3.76736e14 2.54777
\(378\) 0 0
\(379\) 3.93971e13 0.258791 0.129395 0.991593i \(-0.458696\pi\)
0.129395 + 0.991593i \(0.458696\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 3.88422e13 + 6.72766e13i 0.240830 + 0.417130i 0.960951 0.276719i \(-0.0892471\pi\)
−0.720121 + 0.693848i \(0.755914\pi\)
\(384\) 0 0
\(385\) −1.09119e14 1.61235e14i −0.657456 0.971464i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −5.89738e13 + 1.02146e14i −0.335688 + 0.581429i −0.983617 0.180272i \(-0.942302\pi\)
0.647928 + 0.761701i \(0.275636\pi\)
\(390\) 0 0
\(391\) 1.26133e14 0.698004
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.18036e14 2.04445e14i 0.617635 1.06977i
\(396\) 0 0
\(397\) 1.37279e14 + 2.37774e14i 0.698643 + 1.21009i 0.968937 + 0.247308i \(0.0795459\pi\)
−0.270294 + 0.962778i \(0.587121\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −9.60090e13 1.66292e14i −0.462400 0.800900i 0.536680 0.843786i \(-0.319678\pi\)
−0.999080 + 0.0428855i \(0.986345\pi\)
\(402\) 0 0
\(403\) −2.28151e14 + 3.95168e14i −1.06916 + 1.85184i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.65045e14 0.732545
\(408\) 0 0
\(409\) −1.84891e14 + 3.20240e14i −0.798798 + 1.38356i 0.121602 + 0.992579i \(0.461197\pi\)
−0.920399 + 0.390979i \(0.872136\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −6.07151e12 + 4.34030e11i −0.0248640 + 0.00177744i
\(414\) 0 0
\(415\) −3.14070e14 5.43985e14i −1.25245 2.16931i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −3.40515e13 −0.128813 −0.0644064 0.997924i \(-0.520515\pi\)
−0.0644064 + 0.997924i \(0.520515\pi\)
\(420\) 0 0
\(421\) −2.32682e14 −0.857456 −0.428728 0.903434i \(-0.641038\pi\)
−0.428728 + 0.903434i \(0.641038\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 2.11261e14 + 3.65915e14i 0.739062 + 1.28009i
\(426\) 0 0
\(427\) −6.33474e13 + 1.30395e14i −0.215961 + 0.444535i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2.06089e14 3.56956e14i 0.667467 1.15609i −0.311144 0.950363i \(-0.600712\pi\)
0.978610 0.205723i \(-0.0659547\pi\)
\(432\) 0 0
\(433\) 3.16336e14 0.998770 0.499385 0.866380i \(-0.333559\pi\)
0.499385 + 0.866380i \(0.333559\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.44758e14 + 2.50728e14i −0.434504 + 0.752584i
\(438\) 0 0
\(439\) 2.45107e14 + 4.24537e14i 0.717464 + 1.24268i 0.962002 + 0.273044i \(0.0880305\pi\)
−0.244538 + 0.969640i \(0.578636\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.50000e14 + 4.33012e14i 0.696176 + 1.20581i 0.969783 + 0.243971i \(0.0784501\pi\)
−0.273606 + 0.961842i \(0.588217\pi\)
\(444\) 0 0
\(445\) 2.08687e14 3.61457e14i 0.566912 0.981921i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −1.51607e13 −0.0392071 −0.0196036 0.999808i \(-0.506240\pi\)
−0.0196036 + 0.999808i \(0.506240\pi\)
\(450\) 0 0
\(451\) 1.50055e14 2.59903e14i 0.378686 0.655904i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −4.94945e14 + 1.01880e15i −1.18986 + 2.44921i
\(456\) 0 0
\(457\) −3.11245e14 5.39093e14i −0.730405 1.26510i −0.956710 0.291042i \(-0.905998\pi\)
0.226306 0.974056i \(-0.427335\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.14992e14 −1.82305 −0.911524 0.411246i \(-0.865094\pi\)
−0.911524 + 0.411246i \(0.865094\pi\)
\(462\) 0 0
\(463\) 7.98210e13 0.174350 0.0871749 0.996193i \(-0.472216\pi\)
0.0871749 + 0.996193i \(0.472216\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −2.26295e14 3.91955e14i −0.471447 0.816570i 0.528020 0.849232i \(-0.322935\pi\)
−0.999466 + 0.0326623i \(0.989601\pi\)
\(468\) 0 0
\(469\) −6.79794e14 + 4.85960e13i −1.38333 + 0.0988895i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −4.67396e13 + 8.09553e13i −0.0907713 + 0.157220i
\(474\) 0 0
\(475\) −9.69821e14 −1.84025
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 3.51335e14 6.08530e14i 0.636614 1.10265i −0.349557 0.936915i \(-0.613668\pi\)
0.986171 0.165732i \(-0.0529987\pi\)
\(480\) 0 0
\(481\) −4.80100e14 8.31558e14i −0.850225 1.47263i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 4.30723e14 + 7.46033e14i 0.728816 + 1.26235i
\(486\) 0 0
\(487\) −2.97188e14 + 5.14744e14i −0.491611 + 0.851495i −0.999953 0.00965994i \(-0.996925\pi\)
0.508342 + 0.861155i \(0.330258\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.12724e14 −1.12713 −0.563564 0.826073i \(-0.690570\pi\)
−0.563564 + 0.826073i \(0.690570\pi\)
\(492\) 0 0
\(493\) −4.60761e14 + 7.98062e14i −0.712554 + 1.23418i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −3.83601e14 5.66813e14i −0.567440 0.838455i
\(498\) 0 0
\(499\) −4.67371e14 8.09510e14i −0.676252 1.17130i −0.976101 0.217316i \(-0.930270\pi\)
0.299849 0.953987i \(-0.403064\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 7.21102e14 0.998556 0.499278 0.866442i \(-0.333599\pi\)
0.499278 + 0.866442i \(0.333599\pi\)
\(504\) 0 0
\(505\) 1.40109e15 1.89830
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.57952e13 + 7.93196e13i 0.0594117 + 0.102904i 0.894201 0.447665i \(-0.147744\pi\)
−0.834790 + 0.550569i \(0.814411\pi\)
\(510\) 0 0
\(511\) 1.09544e15 7.83094e13i 1.39083 0.0994257i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −1.06668e15 + 1.84754e15i −1.29746 + 2.24727i
\(516\) 0 0
\(517\) 7.32591e13 0.0872295
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.21411e14 1.24952e15i 0.823332 1.42605i −0.0798550 0.996806i \(-0.525446\pi\)
0.903187 0.429247i \(-0.141221\pi\)
\(522\) 0 0
\(523\) 6.15443e14 + 1.06598e15i 0.687746 + 1.19121i 0.972565 + 0.232630i \(0.0747332\pi\)
−0.284819 + 0.958581i \(0.591934\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −5.58072e14 9.66608e14i −0.598042 1.03584i
\(528\) 0 0
\(529\) 2.21301e14 3.83305e14i 0.232262 0.402289i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −1.74598e15 −1.75808
\(534\) 0 0
\(535\) −3.19039e14 + 5.52592e14i −0.314701 + 0.545078i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 4.79591e14 + 6.09937e14i 0.454080 + 0.577493i
\(540\) 0 0
\(541\) 2.37856e14 + 4.11979e14i 0.220663 + 0.382200i 0.955010 0.296575i \(-0.0958445\pi\)
−0.734346 + 0.678775i \(0.762511\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.71395e15 −2.41781
\(546\) 0 0
\(547\) −2.16232e14 −0.188795 −0.0943975 0.995535i \(-0.530092\pi\)
−0.0943975 + 0.995535i \(0.530092\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −1.05759e15 1.83180e15i −0.887123 1.53654i
\(552\) 0 0
\(553\) −4.11122e14 + 8.46255e14i −0.338051 + 0.695846i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.41948e14 2.45861e14i 0.112183 0.194306i −0.804467 0.593997i \(-0.797549\pi\)
0.916650 + 0.399691i \(0.130882\pi\)
\(558\) 0 0
\(559\) 5.43842e14 0.421413
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −1.12143e15 + 1.94238e15i −0.835559 + 1.44723i 0.0580164 + 0.998316i \(0.481522\pi\)
−0.893575 + 0.448914i \(0.851811\pi\)
\(564\) 0 0
\(565\) 2.32430e14 + 4.02581e14i 0.169835 + 0.294162i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 3.11079e14 + 5.38804e14i 0.218652 + 0.378716i 0.954396 0.298544i \(-0.0965008\pi\)
−0.735744 + 0.677259i \(0.763167\pi\)
\(570\) 0 0
\(571\) −1.28739e15 + 2.22982e15i −0.887585 + 1.53734i −0.0448633 + 0.998993i \(0.514285\pi\)
−0.842722 + 0.538349i \(0.819048\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −1.70909e15 −1.13395
\(576\) 0 0
\(577\) −1.24489e15 + 2.15621e15i −0.810332 + 1.40354i 0.102300 + 0.994754i \(0.467380\pi\)
−0.912632 + 0.408783i \(0.865953\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.40308e15 + 2.07321e15i 0.879253 + 1.29919i
\(582\) 0 0
\(583\) 6.37460e14 + 1.10411e15i 0.391991 + 0.678948i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 2.39872e15 1.42059 0.710297 0.703902i \(-0.248560\pi\)
0.710297 + 0.703902i \(0.248560\pi\)
\(588\) 0 0
\(589\) 2.56190e15 1.48911
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −4.74884e13 8.22524e13i −0.0265942 0.0460625i 0.852422 0.522854i \(-0.175133\pi\)
−0.879016 + 0.476792i \(0.841800\pi\)
\(594\) 0 0
\(595\) −1.55284e15 2.29449e15i −0.853658 1.26137i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −8.09261e14 + 1.40168e15i −0.428787 + 0.742680i −0.996766 0.0803629i \(-0.974392\pi\)
0.567979 + 0.823043i \(0.307725\pi\)
\(600\) 0 0
\(601\) −6.48361e14 −0.337293 −0.168646 0.985677i \(-0.553940\pi\)
−0.168646 + 0.985677i \(0.553940\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.32682e14 1.26904e15i 0.367503 0.636534i
\(606\) 0 0
\(607\) −8.47944e14 1.46868e15i −0.417666 0.723419i 0.578038 0.816010i \(-0.303819\pi\)
−0.995704 + 0.0925906i \(0.970485\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −2.13103e14 3.69105e14i −0.101243 0.175357i
\(612\) 0 0
\(613\) −6.00792e14 + 1.04060e15i −0.280344 + 0.485570i −0.971469 0.237165i \(-0.923782\pi\)
0.691125 + 0.722735i \(0.257115\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −2.76415e15 −1.24450 −0.622248 0.782820i \(-0.713781\pi\)
−0.622248 + 0.782820i \(0.713781\pi\)
\(618\) 0 0
\(619\) 1.21861e15 2.11070e15i 0.538972 0.933528i −0.459987 0.887926i \(-0.652146\pi\)
0.998960 0.0456021i \(-0.0145206\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −7.26860e14 + 1.49617e15i −0.310289 + 0.638700i
\(624\) 0 0
\(625\) 1.76807e14 + 3.06239e14i 0.0741582 + 0.128446i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 2.34871e15 0.951155
\(630\) 0 0
\(631\) 1.10045e15 0.437935 0.218968 0.975732i \(-0.429731\pi\)
0.218968 + 0.975732i \(0.429731\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 2.07184e14 + 3.58853e14i 0.0796345 + 0.137931i
\(636\) 0 0
\(637\) 1.67800e15 4.19059e15i 0.633906 1.58310i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 1.47446e15 2.55384e15i 0.538163 0.932126i −0.460840 0.887483i \(-0.652452\pi\)
0.999003 0.0446427i \(-0.0142149\pi\)
\(642\) 0 0
\(643\) −2.86149e15 −1.02667 −0.513337 0.858187i \(-0.671591\pi\)
−0.513337 + 0.858187i \(0.671591\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5.03509e14 8.72103e14i 0.174596 0.302409i −0.765426 0.643524i \(-0.777471\pi\)
0.940021 + 0.341116i \(0.110805\pi\)
\(648\) 0 0
\(649\) 2.68575e13 + 4.65185e13i 0.00915628 + 0.0158591i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.08161e15 + 1.87340e15i 0.356489 + 0.617458i 0.987372 0.158421i \(-0.0506403\pi\)
−0.630882 + 0.775878i \(0.717307\pi\)
\(654\) 0 0
\(655\) 2.21924e15 3.84384e15i 0.719246 1.24577i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −2.09934e15 −0.657981 −0.328991 0.944333i \(-0.606708\pi\)
−0.328991 + 0.944333i \(0.606708\pi\)
\(660\) 0 0
\(661\) −1.85165e15 + 3.20716e15i −0.570758 + 0.988581i 0.425731 + 0.904850i \(0.360017\pi\)
−0.996488 + 0.0837314i \(0.973316\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 6.34312e15 4.53447e14i 1.89140 0.135209i
\(666\) 0 0
\(667\) −1.86377e15 3.22814e15i −0.546638 0.946805i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.27927e15 0.363069
\(672\) 0 0
\(673\) 1.46499e15 0.409027 0.204513 0.978864i \(-0.434439\pi\)
0.204513 + 0.978864i \(0.434439\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −9.92626e14 1.71928e15i −0.268255 0.464631i 0.700156 0.713990i \(-0.253114\pi\)
−0.968411 + 0.249358i \(0.919780\pi\)
\(678\) 0 0
\(679\) −1.92422e15 2.84324e15i −0.511647 0.756014i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.26798e15 3.92825e15i 0.583882 1.01131i −0.411132 0.911576i \(-0.634866\pi\)
0.995014 0.0997375i \(-0.0318003\pi\)
\(684\) 0 0
\(685\) −9.34433e15 −2.36728
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 3.70861e15 6.42350e15i 0.909925 1.57604i
\(690\) 0 0
\(691\) 1.08860e15 + 1.88552e15i 0.262869 + 0.455303i 0.967003 0.254764i \(-0.0819978\pi\)
−0.704134 + 0.710067i \(0.748664\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 3.73123e15 + 6.46268e15i 0.872842 + 1.51181i
\(696\) 0 0
\(697\) 2.13539e15 3.69860e15i 0.491696 0.851642i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −1.04536e15 −0.233247 −0.116623 0.993176i \(-0.537207\pi\)
−0.116623 + 0.993176i \(0.537207\pi\)
\(702\) 0 0
\(703\) −2.69551e15 + 4.66877e15i −0.592090 + 1.02553i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.56964e15 + 3.98154e14i −1.18583 + 0.0847703i
\(708\) 0 0
\(709\) 1.92041e15 + 3.32625e15i 0.402569 + 0.697270i 0.994035 0.109060i \(-0.0347841\pi\)
−0.591466 + 0.806330i \(0.701451\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 4.51478e15 0.917580
\(714\) 0 0
\(715\) 9.99519e15 2.00036
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.91066e15 + 3.30937e15i 0.370830 + 0.642297i 0.989694 0.143202i \(-0.0457398\pi\)
−0.618863 + 0.785499i \(0.712406\pi\)
\(720\) 0 0
\(721\) 3.71525e15 7.64750e15i 0.710141 1.46176i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 6.24326e15 1.08136e16i 1.15758 2.00499i
\(726\) 0 0
\(727\) 1.10567e14 0.0201923 0.0100962 0.999949i \(-0.496786\pi\)
0.0100962 + 0.999949i \(0.496786\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −6.65137e14 + 1.15205e15i −0.117860 + 0.204139i
\(732\) 0 0
\(733\) −2.31452e15 4.00887e15i −0.404007 0.699761i 0.590198 0.807258i \(-0.299050\pi\)
−0.994205 + 0.107497i \(0.965716\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.00708e15 + 5.20842e15i 0.509418 + 0.882338i
\(738\) 0 0
\(739\) 3.10450e15 5.37716e15i 0.518141 0.897446i −0.481637 0.876371i \(-0.659958\pi\)
0.999778 0.0210753i \(-0.00670898\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.31622e15 0.537286 0.268643 0.963240i \(-0.413425\pi\)
0.268643 + 0.963240i \(0.413425\pi\)
\(744\) 0 0
\(745\) −3.77005e15 + 6.52992e15i −0.601850 + 1.04243i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.11122e15 2.28733e15i 0.172246 0.354551i
\(750\) 0 0
\(751\) 3.72462e15 + 6.45123e15i 0.568934 + 0.985423i 0.996672 + 0.0815203i \(0.0259775\pi\)
−0.427737 + 0.903903i \(0.640689\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −4.89279e15 −0.725852
\(756\) 0 0
\(757\) −9.51588e15 −1.39130 −0.695651 0.718380i \(-0.744884\pi\)
−0.695651 + 0.718380i \(0.744884\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −8.70949e14 1.50853e15i −0.123702 0.214258i 0.797523 0.603289i \(-0.206143\pi\)
−0.921225 + 0.389031i \(0.872810\pi\)
\(762\) 0 0
\(763\) 1.07885e16 7.71233e14i 1.51035 0.107969i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 1.56251e14 2.70635e14i 0.0212544 0.0368137i
\(768\) 0 0
\(769\) 8.11684e15 1.08841 0.544205 0.838953i \(-0.316832\pi\)
0.544205 + 0.838953i \(0.316832\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.78929e15 + 6.56324e15i −0.493822 + 0.855325i −0.999975 0.00711869i \(-0.997734\pi\)
0.506152 + 0.862444i \(0.331067\pi\)
\(774\) 0 0
\(775\) 7.56181e15 + 1.30974e16i 0.971553 + 1.68278i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 4.90138e15 + 8.48944e15i 0.612157 + 1.06029i
\(780\) 0 0
\(781\) −3.01983e15 + 5.23049e15i −0.371879 + 0.644113i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.30174e15 −0.395330