Properties

Label 252.12.k.d.37.8
Level $252$
Weight $12$
Character 252.37
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 37.8
Root \(13166.9 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 252.37
Dual form 252.12.k.d.109.8

$q$-expansion

\(f(q)\) \(=\) \(q+(6718.22 - 11636.3i) q^{5} +(41445.4 + 16112.4i) q^{7} +O(q^{10})\) \(q+(6718.22 - 11636.3i) q^{5} +(41445.4 + 16112.4i) q^{7} +(425643. + 737235. i) q^{11} +2.13303e6 q^{13} +(-1.28105e6 - 2.21884e6i) q^{17} +(8.87791e6 - 1.53770e7i) q^{19} +(1.81716e7 - 3.14742e7i) q^{23} +(-6.58548e7 - 1.14064e8i) q^{25} -571626. q^{29} +(1.07907e8 + 1.86901e8i) q^{31} +(4.65927e8 - 3.74024e8i) q^{35} +(-9.87524e7 + 1.71044e8i) q^{37} +2.72342e8 q^{41} +1.11575e9 q^{43} +(-3.98664e8 + 6.90506e8i) q^{47} +(1.45811e9 + 1.33557e9i) q^{49} +(6.76715e8 + 1.17210e9i) q^{53} +1.14382e10 q^{55} +(-3.81442e8 - 6.60677e8i) q^{59} +(-2.04039e9 + 3.53405e9i) q^{61} +(1.43301e10 - 2.48205e10i) q^{65} +(1.08784e9 + 1.88419e9i) q^{67} -1.82655e10 q^{71} +(1.03329e10 + 1.78972e10i) q^{73} +(5.76230e9 + 3.74131e10i) q^{77} +(-1.28553e10 + 2.22661e10i) q^{79} -1.36264e10 q^{83} -3.44255e10 q^{85} +(-5.18461e9 + 8.98001e9i) q^{89} +(8.84041e10 + 3.43682e10i) q^{91} +(-1.19287e11 - 2.06612e11i) q^{95} -1.14522e11 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 2156q^{5} + 50512q^{7} + O(q^{10}) \) \( 16q + 2156q^{5} + 50512q^{7} + 222796q^{11} + 2703176q^{13} - 5114600q^{17} + 6910556q^{19} + 51387712q^{23} - 191456372q^{25} - 118854616q^{29} + 164659160q^{31} - 55239344q^{35} + 75658364q^{37} + 1815568608q^{41} + 10754408q^{43} + 1034359464q^{47} + 4123496848q^{49} + 665159988q^{53} - 1264543896q^{55} - 1040514580q^{59} - 14391208024q^{61} + 20938150200q^{65} - 33307097284q^{67} - 65848902896q^{71} + 17709749204q^{73} - 8594484604q^{77} - 26626784032q^{79} + 210306955048q^{83} - 25867402032q^{85} + 55951560072q^{89} + 66078280292q^{91} - 106810047392q^{95} - 156216030712q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) 6718.22 11636.3i 0.961433 1.66525i 0.242525 0.970145i \(-0.422024\pi\)
0.718908 0.695106i \(-0.244642\pi\)
\(6\) 0 0
\(7\) 41445.4 + 16112.4i 0.932045 + 0.362344i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 425643. + 737235.i 0.796866 + 1.38021i 0.921647 + 0.388028i \(0.126844\pi\)
−0.124781 + 0.992184i \(0.539823\pi\)
\(12\) 0 0
\(13\) 2.13303e6 1.59334 0.796669 0.604416i \(-0.206593\pi\)
0.796669 + 0.604416i \(0.206593\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.28105e6 2.21884e6i −0.218825 0.379016i 0.735624 0.677390i \(-0.236889\pi\)
−0.954449 + 0.298374i \(0.903556\pi\)
\(18\) 0 0
\(19\) 8.87791e6 1.53770e7i 0.822557 1.42471i −0.0812152 0.996697i \(-0.525880\pi\)
0.903772 0.428014i \(-0.140787\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.81716e7 3.14742e7i 0.588695 1.01965i −0.405708 0.914003i \(-0.632975\pi\)
0.994404 0.105648i \(-0.0336915\pi\)
\(24\) 0 0
\(25\) −6.58548e7 1.14064e8i −1.34871 2.33603i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −571626. −0.00517515 −0.00258757 0.999997i \(-0.500824\pi\)
−0.00258757 + 0.999997i \(0.500824\pi\)
\(30\) 0 0
\(31\) 1.07907e8 + 1.86901e8i 0.676956 + 1.17252i 0.975893 + 0.218250i \(0.0700348\pi\)
−0.298936 + 0.954273i \(0.596632\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 4.65927e8 3.74024e8i 1.49949 1.20372i
\(36\) 0 0
\(37\) −9.87524e7 + 1.71044e8i −0.234120 + 0.405508i −0.959017 0.283350i \(-0.908554\pi\)
0.724897 + 0.688858i \(0.241887\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.72342e8 0.367116 0.183558 0.983009i \(-0.441238\pi\)
0.183558 + 0.983009i \(0.441238\pi\)
\(42\) 0 0
\(43\) 1.11575e9 1.15741 0.578707 0.815536i \(-0.303558\pi\)
0.578707 + 0.815536i \(0.303558\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.98664e8 + 6.90506e8i −0.253553 + 0.439167i −0.964501 0.264077i \(-0.914933\pi\)
0.710949 + 0.703244i \(0.248266\pi\)
\(48\) 0 0
\(49\) 1.45811e9 + 1.33557e9i 0.737414 + 0.675441i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.76715e8 + 1.17210e9i 0.222274 + 0.384990i 0.955498 0.294997i \(-0.0953188\pi\)
−0.733224 + 0.679987i \(0.761985\pi\)
\(54\) 0 0
\(55\) 1.14382e10 3.06453
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −3.81442e8 6.60677e8i −0.0694613 0.120310i 0.829203 0.558948i \(-0.188795\pi\)
−0.898664 + 0.438637i \(0.855461\pi\)
\(60\) 0 0
\(61\) −2.04039e9 + 3.53405e9i −0.309313 + 0.535746i −0.978212 0.207607i \(-0.933432\pi\)
0.668899 + 0.743353i \(0.266766\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 1.43301e10 2.48205e10i 1.53189 2.65331i
\(66\) 0 0
\(67\) 1.08784e9 + 1.88419e9i 0.0984358 + 0.170496i 0.911037 0.412324i \(-0.135283\pi\)
−0.812602 + 0.582820i \(0.801949\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −1.82655e10 −1.20147 −0.600733 0.799450i \(-0.705124\pi\)
−0.600733 + 0.799450i \(0.705124\pi\)
\(72\) 0 0
\(73\) 1.03329e10 + 1.78972e10i 0.583375 + 1.01043i 0.995076 + 0.0991158i \(0.0316014\pi\)
−0.411701 + 0.911319i \(0.635065\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 5.76230e9 + 3.74131e10i 0.242603 + 1.57516i
\(78\) 0 0
\(79\) −1.28553e10 + 2.22661e10i −0.470039 + 0.814132i −0.999413 0.0342567i \(-0.989094\pi\)
0.529374 + 0.848389i \(0.322427\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.36264e10 −0.379710 −0.189855 0.981812i \(-0.560802\pi\)
−0.189855 + 0.981812i \(0.560802\pi\)
\(84\) 0 0
\(85\) −3.44255e10 −0.841542
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.18461e9 + 8.98001e9i −0.0984173 + 0.170464i −0.911030 0.412341i \(-0.864711\pi\)
0.812612 + 0.582804i \(0.198045\pi\)
\(90\) 0 0
\(91\) 8.84041e10 + 3.43682e10i 1.48506 + 0.577336i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.19287e11 2.06612e11i −1.58167 2.73953i
\(96\) 0 0
\(97\) −1.14522e11 −1.35408 −0.677040 0.735947i \(-0.736737\pi\)
−0.677040 + 0.735947i \(0.736737\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −1.25331e10 2.17079e10i −0.118656 0.205518i 0.800579 0.599227i \(-0.204525\pi\)
−0.919235 + 0.393708i \(0.871192\pi\)
\(102\) 0 0
\(103\) −3.90267e10 + 6.75962e10i −0.331709 + 0.574536i −0.982847 0.184423i \(-0.940958\pi\)
0.651138 + 0.758959i \(0.274292\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.14704e11 1.98672e11i 0.790617 1.36939i −0.134969 0.990850i \(-0.543093\pi\)
0.925585 0.378539i \(-0.123573\pi\)
\(108\) 0 0
\(109\) 1.04619e11 + 1.81206e11i 0.651278 + 1.12805i 0.982813 + 0.184603i \(0.0591001\pi\)
−0.331535 + 0.943443i \(0.607567\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.19133e11 1.11886 0.559432 0.828877i \(-0.311019\pi\)
0.559432 + 0.828877i \(0.311019\pi\)
\(114\) 0 0
\(115\) −2.44162e11 4.22901e11i −1.13198 1.96065i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −1.73427e10 1.12601e11i −0.0666205 0.432549i
\(120\) 0 0
\(121\) −2.19687e11 + 3.80510e11i −0.769991 + 1.33366i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −1.11363e12 −3.26390
\(126\) 0 0
\(127\) 2.57513e11 0.691639 0.345819 0.938301i \(-0.387601\pi\)
0.345819 + 0.938301i \(0.387601\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 2.19906e11 3.80889e11i 0.498018 0.862593i −0.501979 0.864880i \(-0.667394\pi\)
0.999997 + 0.00228653i \(0.000727827\pi\)
\(132\) 0 0
\(133\) 6.15708e11 4.94261e11i 1.28289 1.02985i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 2.51907e11 + 4.36315e11i 0.445940 + 0.772391i 0.998117 0.0613357i \(-0.0195360\pi\)
−0.552177 + 0.833727i \(0.686203\pi\)
\(138\) 0 0
\(139\) 1.93201e11 0.315812 0.157906 0.987454i \(-0.449526\pi\)
0.157906 + 0.987454i \(0.449526\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 9.07907e11 + 1.57254e12i 1.26968 + 2.19915i
\(144\) 0 0
\(145\) −3.84031e9 + 6.65161e9i −0.00497556 + 0.00861792i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −3.50276e10 + 6.06696e10i −0.0390738 + 0.0676778i −0.884901 0.465779i \(-0.845774\pi\)
0.845827 + 0.533457i \(0.179107\pi\)
\(150\) 0 0
\(151\) 5.29667e11 + 9.17410e11i 0.549073 + 0.951022i 0.998338 + 0.0576234i \(0.0183523\pi\)
−0.449266 + 0.893398i \(0.648314\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 2.89977e12 2.60339
\(156\) 0 0
\(157\) −2.29713e11 3.97875e11i −0.192193 0.332888i 0.753784 0.657123i \(-0.228227\pi\)
−0.945977 + 0.324234i \(0.894893\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.26025e12 1.01167e12i 0.918154 0.737049i
\(162\) 0 0
\(163\) −1.42888e11 + 2.47489e11i −0.0972665 + 0.168470i −0.910552 0.413394i \(-0.864343\pi\)
0.813286 + 0.581864i \(0.197677\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.47522e12 −0.878850 −0.439425 0.898279i \(-0.644818\pi\)
−0.439425 + 0.898279i \(0.644818\pi\)
\(168\) 0 0
\(169\) 2.75764e12 1.53873
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −7.02485e11 + 1.21674e12i −0.344654 + 0.596959i −0.985291 0.170886i \(-0.945337\pi\)
0.640637 + 0.767844i \(0.278670\pi\)
\(174\) 0 0
\(175\) −8.91535e11 5.78850e12i −0.410610 2.66598i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.25836e12 2.17955e12i −0.511816 0.886491i −0.999906 0.0136982i \(-0.995640\pi\)
0.488090 0.872793i \(-0.337694\pi\)
\(180\) 0 0
\(181\) −3.11043e12 −1.19011 −0.595056 0.803684i \(-0.702870\pi\)
−0.595056 + 0.803684i \(0.702870\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 1.32688e12 + 2.29822e12i 0.450181 + 0.779737i
\(186\) 0 0
\(187\) 1.09054e12 1.88887e12i 0.348748 0.604049i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 5.63090e11 9.75301e11i 0.160286 0.277623i −0.774686 0.632347i \(-0.782092\pi\)
0.934971 + 0.354724i \(0.115425\pi\)
\(192\) 0 0
\(193\) −1.08140e12 1.87305e12i −0.290685 0.503482i 0.683287 0.730150i \(-0.260550\pi\)
−0.973972 + 0.226669i \(0.927217\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.02832e12 −1.44755 −0.723773 0.690038i \(-0.757594\pi\)
−0.723773 + 0.690038i \(0.757594\pi\)
\(198\) 0 0
\(199\) −1.43126e12 2.47901e12i −0.325106 0.563100i 0.656428 0.754389i \(-0.272067\pi\)
−0.981534 + 0.191289i \(0.938733\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −2.36912e10 9.21026e9i −0.00482347 0.00187518i
\(204\) 0 0
\(205\) 1.82965e12 3.16905e12i 0.352958 0.611341i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 1.51153e13 2.62187
\(210\) 0 0
\(211\) −3.22306e12 −0.530535 −0.265268 0.964175i \(-0.585460\pi\)
−0.265268 + 0.964175i \(0.585460\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 7.49582e12 1.29831e13i 1.11278 1.92738i
\(216\) 0 0
\(217\) 1.46083e12 + 9.48480e12i 0.206097 + 1.33813i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.73251e12 4.73285e12i −0.348662 0.603900i
\(222\) 0 0
\(223\) −1.12361e13 −1.36440 −0.682198 0.731167i \(-0.738976\pi\)
−0.682198 + 0.731167i \(0.738976\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.58401e12 1.31359e13i −0.835135 1.44650i −0.893921 0.448226i \(-0.852056\pi\)
0.0587856 0.998271i \(-0.481277\pi\)
\(228\) 0 0
\(229\) −1.82140e12 + 3.15476e12i −0.191122 + 0.331033i −0.945622 0.325267i \(-0.894546\pi\)
0.754500 + 0.656300i \(0.227879\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −6.03650e12 + 1.04555e13i −0.575874 + 0.997443i 0.420072 + 0.907491i \(0.362005\pi\)
−0.995946 + 0.0899524i \(0.971328\pi\)
\(234\) 0 0
\(235\) 5.35662e12 + 9.27794e12i 0.487548 + 0.844458i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 1.62209e12 0.134551 0.0672756 0.997734i \(-0.478569\pi\)
0.0672756 + 0.997734i \(0.478569\pi\)
\(240\) 0 0
\(241\) 7.66226e12 + 1.32714e13i 0.607104 + 1.05154i 0.991715 + 0.128456i \(0.0410022\pi\)
−0.384611 + 0.923079i \(0.625664\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 2.53369e13 7.99435e12i 1.83375 0.578588i
\(246\) 0 0
\(247\) 1.89368e13 3.27995e13i 1.31061 2.27005i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.41336e13 −0.895461 −0.447731 0.894169i \(-0.647768\pi\)
−0.447731 + 0.894169i \(0.647768\pi\)
\(252\) 0 0
\(253\) 3.09385e13 1.87645
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 7.51915e12 1.30235e13i 0.418347 0.724598i −0.577427 0.816443i \(-0.695943\pi\)
0.995773 + 0.0918448i \(0.0292764\pi\)
\(258\) 0 0
\(259\) −6.84876e12 + 5.49785e12i −0.365143 + 0.293119i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.49881e13 + 2.59601e13i 0.734496 + 1.27218i 0.954944 + 0.296786i \(0.0959147\pi\)
−0.220448 + 0.975399i \(0.570752\pi\)
\(264\) 0 0
\(265\) 1.81853e13 0.854806
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.23799e13 3.87631e13i −0.968769 1.67796i −0.699127 0.714997i \(-0.746428\pi\)
−0.269642 0.962961i \(-0.586905\pi\)
\(270\) 0 0
\(271\) 5.30406e12 9.18689e12i 0.220433 0.381801i −0.734506 0.678602i \(-0.762586\pi\)
0.954940 + 0.296800i \(0.0959196\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 5.60612e13 9.71009e13i 2.14948 3.72300i
\(276\) 0 0
\(277\) 2.06423e13 + 3.57535e13i 0.760536 + 1.31729i 0.942575 + 0.333996i \(0.108397\pi\)
−0.182039 + 0.983291i \(0.558270\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −5.69959e12 −0.194070 −0.0970350 0.995281i \(-0.530936\pi\)
−0.0970350 + 0.995281i \(0.530936\pi\)
\(282\) 0 0
\(283\) −2.13160e11 3.69205e11i −0.00698041 0.0120904i 0.862514 0.506033i \(-0.168889\pi\)
−0.869495 + 0.493943i \(0.835555\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 1.12873e13 + 4.38808e12i 0.342169 + 0.133022i
\(288\) 0 0
\(289\) 1.38538e13 2.39954e13i 0.404231 0.700149i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.60966e13 0.435473 0.217737 0.976008i \(-0.430133\pi\)
0.217737 + 0.976008i \(0.430133\pi\)
\(294\) 0 0
\(295\) −1.02504e13 −0.267129
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 3.87606e13 6.71353e13i 0.937991 1.62465i
\(300\) 0 0
\(301\) 4.62425e13 + 1.79773e13i 1.07876 + 0.419382i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 2.74155e13 + 4.74850e13i 0.594767 + 1.03017i
\(306\) 0 0
\(307\) −5.67881e13 −1.18849 −0.594246 0.804283i \(-0.702550\pi\)
−0.594246 + 0.804283i \(0.702550\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 2.92156e13 + 5.06029e13i 0.569420 + 0.986264i 0.996623 + 0.0821088i \(0.0261655\pi\)
−0.427203 + 0.904156i \(0.640501\pi\)
\(312\) 0 0
\(313\) 7.17860e12 1.24337e13i 0.135066 0.233941i −0.790557 0.612389i \(-0.790209\pi\)
0.925623 + 0.378448i \(0.123542\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.47676e13 2.55782e13i 0.259109 0.448790i −0.706894 0.707319i \(-0.749904\pi\)
0.966004 + 0.258529i \(0.0832377\pi\)
\(318\) 0 0
\(319\) −2.43308e11 4.21422e11i −0.00412390 0.00714281i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −4.54921e13 −0.719983
\(324\) 0 0
\(325\) −1.40470e14 2.43301e14i −2.14895 3.72208i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −2.76485e13 + 2.21948e13i −0.395452 + 0.317449i
\(330\) 0 0
\(331\) 5.55541e13 9.62225e13i 0.768532 1.33114i −0.169827 0.985474i \(-0.554321\pi\)
0.938359 0.345663i \(-0.112346\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 2.92334e13 0.378558
\(336\) 0 0
\(337\) −8.99428e13 −1.12720 −0.563601 0.826047i \(-0.690585\pi\)
−0.563601 + 0.826047i \(0.690585\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −9.18597e13 + 1.59106e14i −1.07889 + 1.86869i
\(342\) 0 0
\(343\) 3.89127e13 + 7.88467e13i 0.442561 + 0.896738i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.22864e13 9.05626e13i −0.557926 0.966355i −0.997669 0.0682322i \(-0.978264\pi\)
0.439744 0.898123i \(-0.355069\pi\)
\(348\) 0 0
\(349\) 5.39858e13 0.558136 0.279068 0.960271i \(-0.409975\pi\)
0.279068 + 0.960271i \(0.409975\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −1.09068e13 1.88911e13i −0.105910 0.183441i 0.808200 0.588909i \(-0.200442\pi\)
−0.914110 + 0.405467i \(0.867109\pi\)
\(354\) 0 0
\(355\) −1.22712e14 + 2.12543e14i −1.15513 + 2.00074i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.99484e13 1.21154e14i 0.619096 1.07231i −0.370555 0.928811i \(-0.620832\pi\)
0.989651 0.143495i \(-0.0458343\pi\)
\(360\) 0 0
\(361\) −9.93895e13 1.72148e14i −0.853200 1.47779i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.77675e14 2.24350
\(366\) 0 0
\(367\) −1.60223e13 2.77514e13i −0.125621 0.217581i 0.796355 0.604830i \(-0.206759\pi\)
−0.921975 + 0.387249i \(0.873426\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 9.16129e12 + 5.94818e13i 0.0676706 + 0.439367i
\(372\) 0 0
\(373\) 9.32722e13 1.61552e14i 0.668888 1.15855i −0.309327 0.950956i \(-0.600104\pi\)
0.978215 0.207593i \(-0.0665629\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −1.21929e12 −0.00824576
\(378\) 0 0
\(379\) 2.85750e13 0.187703 0.0938515 0.995586i \(-0.470082\pi\)
0.0938515 + 0.995586i \(0.470082\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.81568e13 3.14486e13i 0.112576 0.194988i −0.804232 0.594315i \(-0.797423\pi\)
0.916808 + 0.399328i \(0.130756\pi\)
\(384\) 0 0
\(385\) 4.74062e14 + 1.84297e14i 2.85628 + 1.11041i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −8.04933e13 1.39419e14i −0.458181 0.793593i 0.540684 0.841226i \(-0.318165\pi\)
−0.998865 + 0.0476332i \(0.984832\pi\)
\(390\) 0 0
\(391\) −9.31149e13 −0.515285
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 1.72730e14 + 2.99177e14i 0.903823 + 1.56547i
\(396\) 0 0
\(397\) 1.79387e14 3.10707e14i 0.912940 1.58126i 0.103052 0.994676i \(-0.467139\pi\)
0.809889 0.586583i \(-0.199527\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.22260e13 1.42420e14i 0.396018 0.685923i −0.597213 0.802083i \(-0.703725\pi\)
0.993231 + 0.116160i \(0.0370585\pi\)
\(402\) 0 0
\(403\) 2.30169e14 + 3.98664e14i 1.07862 + 1.86823i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.68133e14 −0.746249
\(408\) 0 0
\(409\) 3.13369e13 + 5.42771e13i 0.135387 + 0.234498i 0.925745 0.378148i \(-0.123439\pi\)
−0.790358 + 0.612645i \(0.790105\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −5.16392e12 3.35280e13i −0.0211473 0.137304i
\(414\) 0 0
\(415\) −9.15452e13 + 1.58561e14i −0.365066 + 0.632312i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −8.23062e13 −0.311355 −0.155677 0.987808i \(-0.549756\pi\)
−0.155677 + 0.987808i \(0.549756\pi\)
\(420\) 0 0
\(421\) −6.99072e13 −0.257614 −0.128807 0.991670i \(-0.541115\pi\)
−0.128807 + 0.991670i \(0.541115\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −1.68726e14 + 2.92243e14i −0.590261 + 1.02236i
\(426\) 0 0
\(427\) −1.41506e14 + 1.13595e14i −0.482417 + 0.387261i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.23307e14 + 2.13574e14i 0.399358 + 0.691708i 0.993647 0.112544i \(-0.0358998\pi\)
−0.594289 + 0.804252i \(0.702566\pi\)
\(432\) 0 0
\(433\) −4.21634e14 −1.33123 −0.665614 0.746296i \(-0.731830\pi\)
−0.665614 + 0.746296i \(0.731830\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −3.22652e14 5.58850e14i −0.968471 1.67744i
\(438\) 0 0
\(439\) −4.27459e13 + 7.40380e13i −0.125124 + 0.216720i −0.921781 0.387710i \(-0.873266\pi\)
0.796658 + 0.604431i \(0.206599\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.86748e14 4.96662e14i 0.798509 1.38306i −0.122078 0.992520i \(-0.538956\pi\)
0.920587 0.390537i \(-0.127711\pi\)
\(444\) 0 0
\(445\) 6.96627e13 + 1.20659e14i 0.189243 + 0.327779i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −6.33244e14 −1.63763 −0.818815 0.574057i \(-0.805369\pi\)
−0.818815 + 0.574057i \(0.805369\pi\)
\(450\) 0 0
\(451\) 1.15920e14 + 2.00780e14i 0.292543 + 0.506699i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 9.93836e14 7.97803e14i 2.38920 1.91793i
\(456\) 0 0
\(457\) 1.99228e13 3.45073e13i 0.0467532 0.0809788i −0.841702 0.539943i \(-0.818446\pi\)
0.888455 + 0.458964i \(0.151779\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.47695e14 −1.89620 −0.948101 0.317970i \(-0.896999\pi\)
−0.948101 + 0.317970i \(0.896999\pi\)
\(462\) 0 0
\(463\) 7.99938e14 1.74727 0.873636 0.486579i \(-0.161756\pi\)
0.873636 + 0.486579i \(0.161756\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −4.29125e14 + 7.43267e14i −0.894008 + 1.54847i −0.0589797 + 0.998259i \(0.518785\pi\)
−0.835028 + 0.550207i \(0.814549\pi\)
\(468\) 0 0
\(469\) 1.47270e13 + 9.56187e13i 0.0299685 + 0.194577i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.74909e14 + 8.22566e14i 0.922304 + 1.59748i
\(474\) 0 0
\(475\) −2.33861e15 −4.43755
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 6.28415e13 + 1.08845e14i 0.113868 + 0.197225i 0.917327 0.398135i \(-0.130343\pi\)
−0.803459 + 0.595360i \(0.797009\pi\)
\(480\) 0 0
\(481\) −2.10642e14 + 3.64842e14i −0.373032 + 0.646111i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.69383e14 + 1.33261e15i −1.30186 + 2.25488i
\(486\) 0 0
\(487\) 4.87117e14 + 8.43711e14i 0.805794 + 1.39568i 0.915754 + 0.401739i \(0.131594\pi\)
−0.109960 + 0.993936i \(0.535072\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.14406e15 −1.80926 −0.904628 0.426201i \(-0.859852\pi\)
−0.904628 + 0.426201i \(0.859852\pi\)
\(492\) 0 0
\(493\) 7.32281e11 + 1.26835e12i 0.00113245 + 0.00196146i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.57021e14 2.94301e14i −1.11982 0.435343i
\(498\) 0 0
\(499\) 6.44591e14 1.11646e15i 0.932677 1.61544i 0.153952 0.988078i \(-0.450800\pi\)
0.778725 0.627366i \(-0.215867\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −1.01920e15 −1.41135 −0.705677 0.708534i \(-0.749357\pi\)
−0.705677 + 0.708534i \(0.749357\pi\)
\(504\) 0 0
\(505\) −3.36800e14 −0.456320
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 1.28883e14 2.23232e14i 0.167205 0.289607i −0.770231 0.637765i \(-0.779859\pi\)
0.937436 + 0.348158i \(0.113193\pi\)
\(510\) 0 0
\(511\) 1.39886e14 + 9.08242e14i 0.177607 + 1.15315i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.24379e14 + 9.08252e14i 0.637831 + 1.10476i
\(516\) 0 0
\(517\) −6.78753e14 −0.808191
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.50755e14 + 2.61115e14i 0.172053 + 0.298005i 0.939138 0.343541i \(-0.111627\pi\)
−0.767084 + 0.641546i \(0.778293\pi\)
\(522\) 0 0
\(523\) −1.19275e14 + 2.06590e14i −0.133287 + 0.230860i −0.924942 0.380109i \(-0.875887\pi\)
0.791655 + 0.610969i \(0.209220\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2.76468e14 4.78857e14i 0.296270 0.513154i
\(528\) 0 0
\(529\) −1.84011e14 3.18716e14i −0.193124 0.334501i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 5.80913e14 0.584940
\(534\) 0 0
\(535\) −1.54121e15 2.66945e15i −1.52025 2.63315i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −3.63993e14 + 1.64344e15i −0.344632 + 1.55602i
\(540\) 0 0
\(541\) −7.15031e14 + 1.23847e15i −0.663346 + 1.14895i 0.316385 + 0.948631i \(0.397531\pi\)
−0.979731 + 0.200318i \(0.935803\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 2.81142e15 2.50464
\(546\) 0 0
\(547\) 9.19792e14 0.803081 0.401540 0.915841i \(-0.368475\pi\)
0.401540 + 0.915841i \(0.368475\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −5.07484e12 + 8.78989e12i −0.00425686 + 0.00737309i
\(552\) 0 0
\(553\) −8.91553e14 + 7.15696e14i −0.733093 + 0.588491i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.08145e14 + 8.80133e14i 0.401591 + 0.695576i 0.993918 0.110121i \(-0.0351239\pi\)
−0.592327 + 0.805698i \(0.701791\pi\)
\(558\) 0 0
\(559\) 2.37992e15 1.84415
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 6.05790e14 + 1.04926e15i 0.451363 + 0.781784i 0.998471 0.0552782i \(-0.0176046\pi\)
−0.547108 + 0.837062i \(0.684271\pi\)
\(564\) 0 0
\(565\) 1.47219e15 2.54990e15i 1.07571 1.86319i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 7.24341e14 1.25460e15i 0.509126 0.881833i −0.490818 0.871262i \(-0.663302\pi\)
0.999944 0.0105706i \(-0.00336477\pi\)
\(570\) 0 0
\(571\) −2.13063e14 3.69036e14i −0.146896 0.254431i 0.783183 0.621792i \(-0.213595\pi\)
−0.930079 + 0.367360i \(0.880262\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −4.78676e15 −3.17591
\(576\) 0 0
\(577\) 2.04431e14 + 3.54086e14i 0.133070 + 0.230484i 0.924859 0.380311i \(-0.124183\pi\)
−0.791788 + 0.610795i \(0.790850\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −5.64751e14 2.19554e14i −0.353907 0.137586i
\(582\) 0 0
\(583\) −5.76077e14 + 9.97795e14i −0.354245 + 0.613570i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.59585e14 0.449849 0.224925 0.974376i \(-0.427786\pi\)
0.224925 + 0.974376i \(0.427786\pi\)
\(588\) 0 0
\(589\) 3.83196e15 2.22734
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.64766e15 + 2.85384e15i −0.922715 + 1.59819i −0.127519 + 0.991836i \(0.540701\pi\)
−0.795196 + 0.606353i \(0.792632\pi\)
\(594\) 0 0
\(595\) −1.42678e15 5.54676e14i −0.784354 0.304927i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −1.26409e15 2.18947e15i −0.669777 1.16009i −0.977966 0.208763i \(-0.933056\pi\)
0.308189 0.951325i \(-0.400277\pi\)
\(600\) 0 0
\(601\) 1.40595e15 0.731410 0.365705 0.930731i \(-0.380828\pi\)
0.365705 + 0.930731i \(0.380828\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 2.95182e15 + 5.11270e15i 1.48059 + 2.56446i
\(606\) 0 0
\(607\) −1.31451e15 + 2.27680e15i −0.647480 + 1.12147i 0.336242 + 0.941776i \(0.390844\pi\)
−0.983723 + 0.179694i \(0.942489\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −8.50361e14 + 1.47287e15i −0.403995 + 0.699741i
\(612\) 0 0
\(613\) −2.36386e14 4.09433e14i −0.110304 0.191051i 0.805589 0.592475i \(-0.201849\pi\)
−0.915893 + 0.401423i \(0.868516\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −6.41641e14 −0.288884 −0.144442 0.989513i \(-0.546139\pi\)
−0.144442 + 0.989513i \(0.546139\pi\)
\(618\) 0 0
\(619\) −1.06581e15 1.84603e15i −0.471390 0.816471i 0.528074 0.849198i \(-0.322914\pi\)
−0.999464 + 0.0327268i \(0.989581\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −3.59568e14 + 2.88643e14i −0.153496 + 0.123219i
\(624\) 0 0
\(625\) −4.26605e15 + 7.38902e15i −1.78931 + 3.09918i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.06027e14 0.204925
\(630\) 0 0
\(631\) −2.49076e15 −0.991219 −0.495609 0.868545i \(-0.665055\pi\)
−0.495609 + 0.868545i \(0.665055\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 1.73003e15 2.99650e15i 0.664964 1.15175i
\(636\) 0 0
\(637\) 3.11018e15 + 2.84880e15i 1.17495 + 1.07621i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.64178e15 2.84365e15i −0.599233 1.03790i −0.992934 0.118664i \(-0.962139\pi\)
0.393701 0.919239i \(-0.371195\pi\)
\(642\) 0 0
\(643\) 1.94429e15 0.697592 0.348796 0.937199i \(-0.386591\pi\)
0.348796 + 0.937199i \(0.386591\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 3.24795e14 + 5.62562e14i 0.112625 + 0.195073i 0.916828 0.399282i \(-0.130741\pi\)
−0.804203 + 0.594355i \(0.797407\pi\)
\(648\) 0 0
\(649\) 3.24716e14 5.62425e14i 0.110703 0.191743i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 1.92474e15 3.33375e15i 0.634380 1.09878i −0.352266 0.935900i \(-0.614589\pi\)
0.986646 0.162879i \(-0.0520779\pi\)
\(654\) 0 0
\(655\) −2.95476e15 5.11779e15i −0.957623 1.65865i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −1.40489e15 −0.440324 −0.220162 0.975463i \(-0.570659\pi\)
−0.220162 + 0.975463i \(0.570659\pi\)
\(660\) 0 0
\(661\) −1.55113e15 2.68663e15i −0.478123 0.828134i 0.521562 0.853213i \(-0.325349\pi\)
−0.999685 + 0.0250796i \(0.992016\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.61490e15 1.04851e16i −0.481533 3.12647i
\(666\) 0 0
\(667\) −1.03874e13 + 1.79915e13i −0.00304659 + 0.00527684i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −3.47390e15 −0.985924
\(672\) 0 0
\(673\) −4.65798e15 −1.30051 −0.650256 0.759715i \(-0.725338\pi\)
−0.650256 + 0.759715i \(0.725338\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 1.70181e15 2.94763e15i 0.459912 0.796590i −0.539044 0.842277i \(-0.681214\pi\)
0.998956 + 0.0456873i \(0.0145478\pi\)
\(678\) 0 0
\(679\) −4.74640e15 1.84522e15i −1.26206 0.490642i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −8.52660e14 1.47685e15i −0.219514 0.380209i 0.735146 0.677909i \(-0.237114\pi\)
−0.954659 + 0.297700i \(0.903780\pi\)
\(684\) 0 0
\(685\) 6.76946e15 1.71497
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 1.44345e15 + 2.50013e15i 0.354157 + 0.613419i
\(690\) 0 0
\(691\) 2.28018e15 3.94939e15i 0.550606 0.953677i −0.447625 0.894221i \(-0.647730\pi\)
0.998231 0.0594557i \(-0.0189365\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 1.29797e15 2.24814e15i 0.303632 0.525905i
\(696\) 0 0
\(697\) −3.48884e14 6.04284e14i −0.0803341 0.139143i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 2.93440e15 0.654741 0.327371 0.944896i \(-0.393837\pi\)
0.327371 + 0.944896i \(0.393837\pi\)
\(702\) 0 0
\(703\) 1.75343e15 + 3.03703e15i 0.385154 + 0.667106i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.69671e14 1.10163e15i −0.0361245 0.234547i
\(708\) 0 0
\(709\) −1.47790e15 + 2.55980e15i −0.309807 + 0.536601i −0.978320 0.207099i \(-0.933598\pi\)
0.668513 + 0.743700i \(0.266931\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 7.84339e15 1.59408
\(714\) 0 0
\(715\) 2.43981e16 4.88284
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −1.47695e15 + 2.55816e15i −0.286654 + 0.496499i −0.973009 0.230768i \(-0.925876\pi\)
0.686355 + 0.727266i \(0.259210\pi\)
\(720\) 0 0
\(721\) −2.70661e15 + 2.17273e15i −0.517347 + 0.415301i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 3.76443e13 + 6.52019e13i 0.00697976 + 0.0120893i
\(726\) 0 0
\(727\) −5.57462e15 −1.01807 −0.509033 0.860747i \(-0.669997\pi\)
−0.509033 + 0.860747i \(0.669997\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −1.42932e15 2.47566e15i −0.253271 0.438678i
\(732\) 0 0
\(733\) −4.84328e15 + 8.38880e15i −0.845410 + 1.46429i 0.0398541 + 0.999206i \(0.487311\pi\)
−0.885264 + 0.465088i \(0.846023\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.26061e14 + 1.60399e15i −0.156880 + 0.271725i
\(738\) 0 0
\(739\) −9.18308e14 1.59056e15i −0.153265 0.265463i 0.779161 0.626824i \(-0.215646\pi\)
−0.932426 + 0.361361i \(0.882312\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −5.66724e13 −0.00918191 −0.00459095 0.999989i \(-0.501461\pi\)
−0.00459095 + 0.999989i \(0.501461\pi\)
\(744\) 0 0
\(745\) 4.70646e14 + 8.15182e14i 0.0751337 + 0.130135i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 7.95502e15 6.38590e15i 1.23308 0.989856i
\(750\) 0 0
\(751\) 8.39714e14 1.45443e15i 0.128266 0.222163i −0.794739 0.606952i \(-0.792392\pi\)
0.923005 + 0.384788i \(0.125726\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 1.42337e16 2.11159
\(756\) 0 0
\(757\) 5.82897e15 0.852245 0.426122 0.904666i \(-0.359879\pi\)
0.426122 + 0.904666i \(0.359879\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −3.73179e15 + 6.46364e15i −0.530031 + 0.918041i 0.469355 + 0.883009i \(0.344486\pi\)
−0.999386 + 0.0350311i \(0.988847\pi\)
\(762\) 0 0
\(763\) 1.41632e15 + 9.19582e15i 0.198279 + 1.28738i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −8.13627e14 1.40924e15i −0.110675 0.191695i
\(768\) 0 0
\(769\) 4.93564e15 0.661833 0.330917 0.943660i \(-0.392642\pi\)
0.330917 + 0.943660i \(0.392642\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −3.32146e15 5.75293e15i −0.432854 0.749725i 0.564264 0.825595i \(-0.309160\pi\)
−0.997118 + 0.0758695i \(0.975827\pi\)
\(774\) 0 0
\(775\) 1.42124e16 2.46166e16i 1.82603 3.16278i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 2.41783e15 4.18780e15i 0.301974 0.523034i
\(780\) 0 0
\(781\) −7.77458e15 1.34660e16i −0.957407 1.65828i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −6.17305e15 −0.739123