Properties

Label 84.12.i.b.37.1
Level $84$
Weight $12$
Character 84.37
Analytic conductor $64.541$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 84 = 2^{2} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 84.i (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(64.5408271670\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{42}\cdot 3^{15}\cdot 7^{9} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(13166.9 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.12.i.b.25.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 - 210.444i) q^{3} +(-6718.22 + 11636.3i) q^{5} +(41445.4 + 16112.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 - 210.444i) q^{3} +(-6718.22 + 11636.3i) q^{5} +(41445.4 + 16112.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(-425643. - 737235. i) q^{11} +2.13303e6 q^{13} +3.26505e6 q^{15} +(1.28105e6 + 2.21884e6i) q^{17} +(8.87791e6 - 1.53770e7i) q^{19} +(-1.64485e6 - 1.06796e7i) q^{21} +(-1.81716e7 + 3.14742e7i) q^{23} +(-6.58548e7 - 1.14064e8i) q^{25} +1.43489e7 q^{27} +571626. q^{29} +(1.07907e8 + 1.86901e8i) q^{31} +(-1.03431e8 + 1.79148e8i) q^{33} +(-4.65927e8 + 3.74024e8i) q^{35} +(-9.87524e7 + 1.71044e8i) q^{37} +(-2.59163e8 - 4.48883e8i) q^{39} -2.72342e8 q^{41} +1.11575e9 q^{43} +(-3.96704e8 - 6.87111e8i) q^{45} +(3.98664e8 - 6.90506e8i) q^{47} +(1.45811e9 + 1.33557e9i) q^{49} +(3.11295e8 - 5.39178e8i) q^{51} +(-6.76715e8 - 1.17210e9i) q^{53} +1.14382e10 q^{55} -4.31466e9 q^{57} +(3.81442e8 + 6.60677e8i) q^{59} +(-2.04039e9 + 3.53405e9i) q^{61} +(-2.04761e9 + 1.64372e9i) q^{63} +(-1.43301e10 + 2.48205e10i) q^{65} +(1.08784e9 + 1.88419e9i) q^{67} +8.83141e9 q^{69} +1.82655e10 q^{71} +(1.03329e10 + 1.78972e10i) q^{73} +(-1.60027e10 + 2.77175e10i) q^{75} +(-5.76230e9 - 3.74131e10i) q^{77} +(-1.28553e10 + 2.22661e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} +1.36264e10 q^{83} -3.44255e10 q^{85} +(-6.94525e7 - 1.20295e8i) q^{87} +(5.18461e9 - 8.98001e9i) q^{89} +(8.84041e10 + 3.43682e10i) q^{91} +(2.62214e10 - 4.54168e10i) q^{93} +(1.19287e11 + 2.06612e11i) q^{95} -1.14522e11 q^{97} +5.02675e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9} - 222796 q^{11} + 2703176 q^{13} + 1047816 q^{15} + 5114600 q^{17} + 6910556 q^{19} - 18340668 q^{21} - 51387712 q^{23} - 191456372 q^{25} + 229582512 q^{27} + 118854616 q^{29} + 164659160 q^{31} - 54139428 q^{33} + 55239344 q^{35} + 75658364 q^{37} - 328435884 q^{39} - 1815568608 q^{41} + 10754408 q^{43} - 127309644 q^{45} - 1034359464 q^{47} + 4123496848 q^{49} + 1242847800 q^{51} - 665159988 q^{53} - 1264543896 q^{55} - 3358530216 q^{57} + 1040514580 q^{59} - 14391208024 q^{61} + 1474099236 q^{63} - 20938150200 q^{65} - 33307097284 q^{67} + 24974428032 q^{69} + 65848902896 q^{71} + 17709749204 q^{73} - 46523898396 q^{75} + 8594484604 q^{77} - 26626784032 q^{79} - 27894275208 q^{81} - 210306955048 q^{83} - 25867402032 q^{85} - 14440835844 q^{87} - 55951560072 q^{89} + 66078280292 q^{91} + 40012175880 q^{93} + 106810047392 q^{95} - 156216030712 q^{97} + 26311762008 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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
\(3\) −121.500 210.444i −0.288675 0.500000i
\(4\) 0 0
\(5\) −6718.22 + 11636.3i −0.961433 + 1.66525i −0.242525 + 0.970145i \(0.577976\pi\)
−0.718908 + 0.695106i \(0.755358\pi\)
\(6\) 0 0
\(7\) 41445.4 + 16112.4i 0.932045 + 0.362344i
\(8\) 0 0
\(9\) −29524.5 + 51137.9i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −425643. 737235.i −0.796866 1.38021i −0.921647 0.388028i \(-0.873156\pi\)
0.124781 0.992184i \(-0.460177\pi\)
\(12\) 0 0
\(13\) 2.13303e6 1.59334 0.796669 0.604416i \(-0.206593\pi\)
0.796669 + 0.604416i \(0.206593\pi\)
\(14\) 0 0
\(15\) 3.26505e6 1.11017
\(16\) 0 0
\(17\) 1.28105e6 + 2.21884e6i 0.218825 + 0.379016i 0.954449 0.298374i \(-0.0964443\pi\)
−0.735624 + 0.677390i \(0.763111\pi\)
\(18\) 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
\(21\) −1.64485e6 1.06796e7i −0.0878862 0.570622i
\(22\) 0 0
\(23\) −1.81716e7 + 3.14742e7i −0.588695 + 1.01965i 0.405708 + 0.914003i \(0.367025\pi\)
−0.994404 + 0.105648i \(0.966308\pi\)
\(24\) 0 0
\(25\) −6.58548e7 1.14064e8i −1.34871 2.33603i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) 571626. 0.00517515 0.00258757 0.999997i \(-0.499176\pi\)
0.00258757 + 0.999997i \(0.499176\pi\)
\(30\) 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
\(33\) −1.03431e8 + 1.79148e8i −0.460071 + 0.796866i
\(34\) 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
\(39\) −2.59163e8 4.48883e8i −0.459957 0.796669i
\(40\) 0 0
\(41\) −2.72342e8 −0.367116 −0.183558 0.983009i \(-0.558762\pi\)
−0.183558 + 0.983009i \(0.558762\pi\)
\(42\) 0 0
\(43\) 1.11575e9 1.15741 0.578707 0.815536i \(-0.303558\pi\)
0.578707 + 0.815536i \(0.303558\pi\)
\(44\) 0 0
\(45\) −3.96704e8 6.87111e8i −0.320478 0.555084i
\(46\) 0 0
\(47\) 3.98664e8 6.90506e8i 0.253553 0.439167i −0.710949 0.703244i \(-0.751734\pi\)
0.964501 + 0.264077i \(0.0850675\pi\)
\(48\) 0 0
\(49\) 1.45811e9 + 1.33557e9i 0.737414 + 0.675441i
\(50\) 0 0
\(51\) 3.11295e8 5.39178e8i 0.126339 0.218825i
\(52\) 0 0
\(53\) −6.76715e8 1.17210e9i −0.222274 0.384990i 0.733224 0.679987i \(-0.238015\pi\)
−0.955498 + 0.294997i \(0.904681\pi\)
\(54\) 0 0
\(55\) 1.14382e10 3.06453
\(56\) 0 0
\(57\) −4.31466e9 −0.949807
\(58\) 0 0
\(59\) 3.81442e8 + 6.60677e8i 0.0694613 + 0.120310i 0.898664 0.438637i \(-0.144539\pi\)
−0.829203 + 0.558948i \(0.811205\pi\)
\(60\) 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
\(63\) −2.04761e9 + 1.64372e9i −0.259940 + 0.208667i
\(64\) 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
\(69\) 8.83141e9 0.679767
\(70\) 0 0
\(71\) 1.82655e10 1.20147 0.600733 0.799450i \(-0.294876\pi\)
0.600733 + 0.799450i \(0.294876\pi\)
\(72\) 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
\(75\) −1.60027e10 + 2.77175e10i −0.778676 + 1.34871i
\(76\) 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
\(81\) −1.74339e9 3.01964e9i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) 1.36264e10 0.379710 0.189855 0.981812i \(-0.439198\pi\)
0.189855 + 0.981812i \(0.439198\pi\)
\(84\) 0 0
\(85\) −3.44255e10 −0.841542
\(86\) 0 0
\(87\) −6.94525e7 1.20295e8i −0.00149394 0.00258757i
\(88\) 0 0
\(89\) 5.18461e9 8.98001e9i 0.0984173 0.170464i −0.812612 0.582804i \(-0.801955\pi\)
0.911030 + 0.412341i \(0.135289\pi\)
\(90\) 0 0
\(91\) 8.84041e10 + 3.43682e10i 1.48506 + 0.577336i
\(92\) 0 0
\(93\) 2.62214e10 4.54168e10i 0.390841 0.676956i
\(94\) 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
\(99\) 5.02675e10 0.531244
\(100\) 0 0
\(101\) 1.25331e10 + 2.17079e10i 0.118656 + 0.205518i 0.919235 0.393708i \(-0.128808\pi\)
−0.800579 + 0.599227i \(0.795475\pi\)
\(102\) 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
\(105\) 1.35321e11 + 5.26078e10i 1.03473 + 0.402262i
\(106\) 0 0
\(107\) −1.14704e11 + 1.98672e11i −0.790617 + 1.36939i 0.134969 + 0.990850i \(0.456907\pi\)
−0.925585 + 0.378539i \(0.876427\pi\)
\(108\) 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
\(111\) 4.79937e10 0.270338
\(112\) 0 0
\(113\) −2.19133e11 −1.11886 −0.559432 0.828877i \(-0.688981\pi\)
−0.559432 + 0.828877i \(0.688981\pi\)
\(114\) 0 0
\(115\) −2.44162e11 4.22901e11i −1.13198 1.96065i
\(116\) 0 0
\(117\) −6.29766e10 + 1.09079e11i −0.265556 + 0.459957i
\(118\) 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
\(123\) 3.30896e10 + 5.73128e10i 0.105977 + 0.183558i
\(124\) 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
\(129\) −1.35563e11 2.34802e11i −0.334117 0.578707i
\(130\) 0 0
\(131\) −2.19906e11 + 3.80889e11i −0.498018 + 0.862593i −0.999997 0.00228653i \(-0.999272\pi\)
0.501979 + 0.864880i \(0.332606\pi\)
\(132\) 0 0
\(133\) 6.15708e11 4.94261e11i 1.28289 1.02985i
\(134\) 0 0
\(135\) −9.63991e10 + 1.66968e11i −0.185028 + 0.320478i
\(136\) 0 0
\(137\) −2.51907e11 4.36315e11i −0.445940 0.772391i 0.552177 0.833727i \(-0.313797\pi\)
−0.998117 + 0.0613357i \(0.980464\pi\)
\(138\) 0 0
\(139\) 1.93201e11 0.315812 0.157906 0.987454i \(-0.449526\pi\)
0.157906 + 0.987454i \(0.449526\pi\)
\(140\) 0 0
\(141\) −1.93751e11 −0.292778
\(142\) 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
\(147\) 1.03902e11 4.69122e11i 0.124847 0.563690i
\(148\) 0 0
\(149\) 3.50276e10 6.06696e10i 0.0390738 0.0676778i −0.845827 0.533457i \(-0.820893\pi\)
0.884901 + 0.465779i \(0.154226\pi\)
\(150\) 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
\(153\) −1.51289e11 −0.145883
\(154\) 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
\(159\) −1.64442e11 + 2.84821e11i −0.128330 + 0.222274i
\(160\) 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
\(165\) −1.38975e12 2.40711e12i −0.884655 1.53227i
\(166\) 0 0
\(167\) 1.47522e12 0.878850 0.439425 0.898279i \(-0.355182\pi\)
0.439425 + 0.898279i \(0.355182\pi\)
\(168\) 0 0
\(169\) 2.75764e12 1.53873
\(170\) 0 0
\(171\) 5.24232e11 + 9.07996e11i 0.274186 + 0.474903i
\(172\) 0 0
\(173\) 7.02485e11 1.21674e12i 0.344654 0.596959i −0.640637 0.767844i \(-0.721330\pi\)
0.985291 + 0.170886i \(0.0546628\pi\)
\(174\) 0 0
\(175\) −8.91535e11 5.78850e12i −0.410610 2.66598i
\(176\) 0 0
\(177\) 9.26905e10 1.60545e11i 0.0401035 0.0694613i
\(178\) 0 0
\(179\) 1.25836e12 + 2.17955e12i 0.511816 + 0.886491i 0.999906 + 0.0136982i \(0.00436041\pi\)
−0.488090 + 0.872793i \(0.662306\pi\)
\(180\) 0 0
\(181\) −3.11043e12 −1.19011 −0.595056 0.803684i \(-0.702870\pi\)
−0.595056 + 0.803684i \(0.702870\pi\)
\(182\) 0 0
\(183\) 9.91627e11 0.357164
\(184\) 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
\(189\) 5.94696e11 + 2.31195e11i 0.179372 + 0.0697331i
\(190\) 0 0
\(191\) −5.63090e11 + 9.75301e11i −0.160286 + 0.277623i −0.934971 0.354724i \(-0.884575\pi\)
0.774686 + 0.632347i \(0.217908\pi\)
\(192\) 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
\(195\) 6.96445e12 1.76887
\(196\) 0 0
\(197\) 6.02832e12 1.44755 0.723773 0.690038i \(-0.242406\pi\)
0.723773 + 0.690038i \(0.242406\pi\)
\(198\) 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
\(201\) 2.64345e11 4.57859e11i 0.0568319 0.0984358i
\(202\) 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
\(207\) −1.07302e12 1.85852e12i −0.196232 0.339883i
\(208\) 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
\(213\) −2.21926e12 3.84387e12i −0.346833 0.600733i
\(214\) 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
\(219\) 2.51090e12 4.34901e12i 0.336812 0.583375i
\(220\) 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
\(225\) 7.77732e12 0.899138
\(226\) 0 0
\(227\) 7.58401e12 + 1.31359e13i 0.835135 + 1.44650i 0.893921 + 0.448226i \(0.147944\pi\)
−0.0587856 + 0.998271i \(0.518723\pi\)
\(228\) 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
\(231\) −7.17324e12 + 5.75833e12i −0.717546 + 0.576011i
\(232\) 0 0
\(233\) 6.03650e12 1.04555e13i 0.575874 0.997443i −0.420072 0.907491i \(-0.637995\pi\)
0.995946 0.0899524i \(-0.0286715\pi\)
\(234\) 0 0
\(235\) 5.35662e12 + 9.27794e12i 0.487548 + 0.844458i
\(236\) 0 0
\(237\) 6.24769e12 0.542755
\(238\) 0 0
\(239\) −1.62209e12 −0.134551 −0.0672756 0.997734i \(-0.521431\pi\)
−0.0672756 + 0.997734i \(0.521431\pi\)
\(240\) 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
\(243\) −4.23644e11 + 7.33773e11i −0.0320750 + 0.0555556i
\(244\) 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
\(249\) −1.65561e12 2.86760e12i −0.109613 0.189855i
\(250\) 0 0
\(251\) 1.41336e13 0.895461 0.447731 0.894169i \(-0.352232\pi\)
0.447731 + 0.894169i \(0.352232\pi\)
\(252\) 0 0
\(253\) 3.09385e13 1.87645
\(254\) 0 0
\(255\) 4.18269e12 + 7.24464e12i 0.242932 + 0.420771i
\(256\) 0 0
\(257\) −7.51915e12 + 1.30235e13i −0.418347 + 0.724598i −0.995773 0.0918448i \(-0.970724\pi\)
0.577427 + 0.816443i \(0.304057\pi\)
\(258\) 0 0
\(259\) −6.84876e12 + 5.49785e12i −0.365143 + 0.293119i
\(260\) 0 0
\(261\) −1.68770e10 + 2.92318e10i −0.000862525 + 0.00149394i
\(262\) 0 0
\(263\) −1.49881e13 2.59601e13i −0.734496 1.27218i −0.954944 0.296786i \(-0.904085\pi\)
0.220448 0.975399i \(-0.429248\pi\)
\(264\) 0 0
\(265\) 1.81853e13 0.854806
\(266\) 0 0
\(267\) −2.51972e12 −0.113642
\(268\) 0 0
\(269\) 2.23799e13 + 3.87631e13i 0.968769 + 1.67796i 0.699127 + 0.714997i \(0.253572\pi\)
0.269642 + 0.962961i \(0.413095\pi\)
\(270\) 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
\(273\) −3.50851e12 2.27799e13i −0.140032 0.909194i
\(274\) 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
\(279\) −1.27436e13 −0.451304
\(280\) 0 0
\(281\) 5.69959e12 0.194070 0.0970350 0.995281i \(-0.469064\pi\)
0.0970350 + 0.995281i \(0.469064\pi\)
\(282\) 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
\(285\) 2.89869e13 5.02067e13i 0.913176 1.58167i
\(286\) 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
\(291\) 1.39144e13 + 2.41005e13i 0.390889 + 0.677040i
\(292\) 0 0
\(293\) −1.60966e13 −0.435473 −0.217737 0.976008i \(-0.569867\pi\)
−0.217737 + 0.976008i \(0.569867\pi\)
\(294\) 0 0
\(295\) −1.02504e13 −0.267129
\(296\) 0 0
\(297\) −6.10751e12 1.05785e13i −0.153357 0.265622i
\(298\) 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
\(303\) 3.04554e12 5.27503e12i 0.0685062 0.118656i
\(304\) 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
\(309\) 1.89670e13 0.383024
\(310\) 0 0
\(311\) −2.92156e13 5.06029e13i −0.569420 0.986264i −0.996623 0.0821088i \(-0.973835\pi\)
0.427203 0.904156i \(-0.359499\pi\)
\(312\) 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
\(315\) −5.37053e12 3.48694e13i −0.0975684 0.633486i
\(316\) 0 0
\(317\) −1.47676e13 + 2.55782e13i −0.259109 + 0.448790i −0.966004 0.258529i \(-0.916762\pi\)
0.706894 + 0.707319i \(0.250096\pi\)
\(318\) 0 0
\(319\) −2.43308e11 4.21422e11i −0.00412390 0.00714281i
\(320\) 0 0
\(321\) 5.57459e13 0.912926
\(322\) 0 0
\(323\) 4.54921e13 0.719983
\(324\) 0 0
\(325\) −1.40470e14 2.43301e14i −2.14895 3.72208i
\(326\) 0 0
\(327\) 2.54225e13 4.40331e13i 0.376015 0.651278i
\(328\) 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
\(333\) −5.83123e12 1.01000e13i −0.0780400 0.135169i
\(334\) 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
\(339\) 2.66247e13 + 4.61153e13i 0.322988 + 0.559432i
\(340\) 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
\(345\) −5.93313e13 + 1.02765e14i −0.653550 + 1.13198i
\(346\) 0 0
\(347\) 5.22864e13 + 9.05626e13i 0.557926 + 0.966355i 0.997669 + 0.0682322i \(0.0217359\pi\)
−0.439744 + 0.898123i \(0.644931\pi\)
\(348\) 0 0
\(349\) 5.39858e13 0.558136 0.279068 0.960271i \(-0.409975\pi\)
0.279068 + 0.960271i \(0.409975\pi\)
\(350\) 0 0
\(351\) 3.06066e13 0.306638
\(352\) 0 0
\(353\) 1.09068e13 + 1.88911e13i 0.105910 + 0.183441i 0.914110 0.405467i \(-0.132891\pi\)
−0.808200 + 0.588909i \(0.799558\pi\)
\(354\) 0 0
\(355\) −1.22712e14 + 2.12543e14i −1.15513 + 2.00074i
\(356\) 0 0
\(357\) 2.15892e13 1.73307e13i 0.197043 0.158176i
\(358\) 0 0
\(359\) −6.99484e13 + 1.21154e14i −0.619096 + 1.07231i 0.370555 + 0.928811i \(0.379168\pi\)
−0.989651 + 0.143495i \(0.954166\pi\)
\(360\) 0 0
\(361\) −9.93895e13 1.72148e14i −0.853200 1.47779i
\(362\) 0 0
\(363\) 1.06768e14 0.889109
\(364\) 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
\(369\) 8.04077e12 1.39270e13i 0.0611860 0.105977i
\(370\) 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
\(375\) −1.35306e14 2.34357e14i −0.942206 1.63195i
\(376\) 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
\(381\) −3.12879e13 5.41922e13i −0.199659 0.345819i
\(382\) 0 0
\(383\) −1.81568e13 + 3.14486e13i −0.112576 + 0.194988i −0.916808 0.399328i \(-0.869244\pi\)
0.804232 + 0.594315i \(0.202577\pi\)
\(384\) 0 0
\(385\) 4.74062e14 + 1.84297e14i 2.85628 + 1.11041i
\(386\) 0 0
\(387\) −3.29418e13 + 5.70569e13i −0.192902 + 0.334117i
\(388\) 0 0
\(389\) 8.04933e13 + 1.39419e14i 0.458181 + 0.793593i 0.998865 0.0476332i \(-0.0151678\pi\)
−0.540684 + 0.841226i \(0.681835\pi\)
\(390\) 0 0
\(391\) −9.31149e13 −0.515285
\(392\) 0 0
\(393\) 1.06874e14 0.575062
\(394\) 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
\(399\) −1.78823e14 6.95196e13i −0.885262 0.344157i
\(400\) 0 0
\(401\) −8.22260e13 + 1.42420e14i −0.396018 + 0.685923i −0.993231 0.116160i \(-0.962942\pi\)
0.597213 + 0.802083i \(0.296275\pi\)
\(402\) 0 0
\(403\) 2.30169e14 + 3.98664e14i 1.07862 + 1.86823i
\(404\) 0 0
\(405\) 4.68499e13 0.213652
\(406\) 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
\(411\) −6.12133e13 + 1.06025e14i −0.257464 + 0.445940i
\(412\) 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
\(417\) −2.34739e13 4.06580e13i −0.0911669 0.157906i
\(418\) 0 0
\(419\) 8.23062e13 0.311355 0.155677 0.987808i \(-0.450244\pi\)
0.155677 + 0.987808i \(0.450244\pi\)
\(420\) 0 0
\(421\) −6.99072e13 −0.257614 −0.128807 0.991670i \(-0.541115\pi\)
−0.128807 + 0.991670i \(0.541115\pi\)
\(422\) 0 0
\(423\) 2.35407e13 + 4.07737e13i 0.0845176 + 0.146389i
\(424\) 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
\(429\) −2.20621e14 + 3.82128e14i −0.733048 + 1.26968i
\(430\) 0 0
\(431\) −1.23307e14 2.13574e14i −0.399358 0.691708i 0.594289 0.804252i \(-0.297434\pi\)
−0.993647 + 0.112544i \(0.964100\pi\)
\(432\) 0 0
\(433\) −4.21634e14 −1.33123 −0.665614 0.746296i \(-0.731830\pi\)
−0.665614 + 0.746296i \(0.731830\pi\)
\(434\) 0 0
\(435\) 1.86639e12 0.00574528
\(436\) 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
\(441\) −1.11348e14 + 3.51327e13i −0.317885 + 0.100300i
\(442\) 0 0
\(443\) −2.86748e14 + 4.96662e14i −0.798509 + 1.38306i 0.122078 + 0.992520i \(0.461044\pi\)
−0.920587 + 0.390537i \(0.872289\pi\)
\(444\) 0 0
\(445\) 6.96627e13 + 1.20659e14i 0.189243 + 0.327779i
\(446\) 0 0
\(447\) −1.70234e13 −0.0451185
\(448\) 0 0
\(449\) 6.33244e14 1.63763 0.818815 0.574057i \(-0.194631\pi\)
0.818815 + 0.574057i \(0.194631\pi\)
\(450\) 0 0
\(451\) 1.15920e14 + 2.00780e14i 0.292543 + 0.506699i
\(452\) 0 0
\(453\) 1.28709e14 2.22931e14i 0.317007 0.549073i
\(454\) 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
\(459\) 1.83816e13 + 3.18379e13i 0.0421129 + 0.0729416i
\(460\) 0 0
\(461\) 8.47695e14 1.89620 0.948101 0.317970i \(-0.103001\pi\)
0.948101 + 0.317970i \(0.103001\pi\)
\(462\) 0 0
\(463\) 7.99938e14 1.74727 0.873636 0.486579i \(-0.161756\pi\)
0.873636 + 0.486579i \(0.161756\pi\)
\(464\) 0 0
\(465\) 3.52322e14 + 6.10240e14i 0.751535 + 1.30170i
\(466\) 0 0
\(467\) 4.29125e14 7.43267e14i 0.894008 1.54847i 0.0589797 0.998259i \(-0.481215\pi\)
0.835028 0.550207i \(-0.185451\pi\)
\(468\) 0 0
\(469\) 1.47270e13 + 9.56187e13i 0.0299685 + 0.194577i
\(470\) 0 0
\(471\) −5.58203e13 + 9.66836e13i −0.110963 + 0.192193i
\(472\) 0 0
\(473\) −4.74909e14 8.22566e14i −0.922304 1.59748i
\(474\) 0 0
\(475\) −2.33861e15 −4.43755
\(476\) 0 0
\(477\) 7.99187e13 0.148183
\(478\) 0 0
\(479\) −6.28415e13 1.08845e14i −0.113868 0.197225i 0.803459 0.595360i \(-0.202991\pi\)
−0.917327 + 0.398135i \(0.869657\pi\)
\(480\) 0 0
\(481\) −2.10642e14 + 3.64842e14i −0.373032 + 0.646111i
\(482\) 0 0
\(483\) 3.66021e14 + 1.42295e14i 0.633573 + 0.246309i
\(484\) 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
\(489\) 6.94434e13 0.112314
\(490\) 0 0
\(491\) 1.14406e15 1.80926 0.904628 0.426201i \(-0.140148\pi\)
0.904628 + 0.426201i \(0.140148\pi\)
\(492\) 0 0
\(493\) 7.32281e11 + 1.26835e12i 0.00113245 + 0.00196146i
\(494\) 0 0
\(495\) −3.37708e14 + 5.84928e14i −0.510756 + 0.884655i
\(496\) 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
\(501\) −1.79239e14 3.10451e14i −0.253702 0.439425i
\(502\) 0 0
\(503\) 1.01920e15 1.41135 0.705677 0.708534i \(-0.250643\pi\)
0.705677 + 0.708534i \(0.250643\pi\)
\(504\) 0 0
\(505\) −3.36800e14 −0.456320
\(506\) 0 0
\(507\) −3.35054e14 5.80330e14i −0.444192 0.769363i
\(508\) 0 0
\(509\) −1.28883e14 + 2.23232e14i −0.167205 + 0.289607i −0.937436 0.348158i \(-0.886807\pi\)
0.770231 + 0.637765i \(0.220141\pi\)
\(510\) 0 0
\(511\) 1.39886e14 + 9.08242e14i 0.177607 + 1.15315i
\(512\) 0 0
\(513\) 1.27388e14 2.20643e14i 0.158301 0.274186i
\(514\) 0 0
\(515\) −5.24379e14 9.08252e14i −0.637831 1.10476i
\(516\) 0 0
\(517\) −6.78753e14 −0.808191
\(518\) 0 0
\(519\) −3.41408e14 −0.397972
\(520\) 0 0
\(521\) −1.50755e14 2.61115e14i −0.172053 0.298005i 0.767084 0.641546i \(-0.221707\pi\)
−0.939138 + 0.343541i \(0.888373\pi\)
\(522\) 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
\(525\) −1.10983e15 + 8.90921e14i −1.21446 + 0.974906i
\(526\) 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
\(531\) −4.50476e13 −0.0463075
\(532\) 0 0
\(533\) −5.80913e14 −0.584940
\(534\) 0 0
\(535\) −1.54121e15 2.66945e15i −1.52025 2.63315i
\(536\) 0 0
\(537\) 3.05782e14 5.29630e14i 0.295497 0.511816i
\(538\) 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
\(543\) 3.77917e14 + 6.54571e14i 0.343556 + 0.595056i
\(544\) 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
\(549\) −1.20483e14 2.08682e14i −0.103104 0.178582i
\(550\) 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
\(555\) −3.22432e14 + 5.58469e14i −0.259912 + 0.450181i
\(556\) 0 0
\(557\) −5.08145e14 8.80133e14i −0.401591 0.695576i 0.592327 0.805698i \(-0.298209\pi\)
−0.993918 + 0.110121i \(0.964876\pi\)
\(558\) 0 0
\(559\) 2.37992e15 1.84415
\(560\) 0 0
\(561\) −5.30001e14 −0.402700
\(562\) 0 0
\(563\) −6.05790e14 1.04926e15i −0.451363 0.781784i 0.547108 0.837062i \(-0.315729\pi\)
−0.998471 + 0.0552782i \(0.982395\pi\)
\(564\) 0 0
\(565\) 1.47219e15 2.54990e15i 1.07571 1.86319i
\(566\) 0 0
\(567\) −2.36018e13 1.53240e14i −0.0169137 0.109816i
\(568\) 0 0
\(569\) −7.24341e14 + 1.25460e15i −0.509126 + 0.881833i 0.490818 + 0.871262i \(0.336698\pi\)
−0.999944 + 0.0105706i \(0.996635\pi\)
\(570\) 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
\(573\) 2.73662e14 0.185082
\(574\) 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
\(579\) −2.62781e14 + 4.55150e14i −0.167827 + 0.290685i
\(580\) 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
\(585\) −8.46180e14 1.46563e15i −0.510629 0.884436i
\(586\) 0 0
\(587\) −7.59585e14 −0.449849 −0.224925 0.974376i \(-0.572214\pi\)
−0.224925 + 0.974376i \(0.572214\pi\)
\(588\) 0 0
\(589\) 3.83196e15 2.22734
\(590\) 0 0
\(591\) −7.32441e14 1.26863e15i −0.417870 0.723773i
\(592\) 0 0
\(593\) 1.64766e15 2.85384e15i 0.922715 1.59819i 0.127519 0.991836i \(-0.459299\pi\)
0.795196 0.606353i \(-0.207368\pi\)
\(594\) 0 0
\(595\) −1.42678e15 5.54676e14i −0.784354 0.304927i
\(596\) 0 0
\(597\) −3.47795e14 + 6.02399e14i −0.187700 + 0.325106i
\(598\) 0 0
\(599\) 1.26409e15 + 2.18947e15i 0.669777 + 1.16009i 0.977966 + 0.208763i \(0.0669437\pi\)
−0.308189 + 0.951325i \(0.599723\pi\)
\(600\) 0 0
\(601\) 1.40595e15 0.731410 0.365705 0.930731i \(-0.380828\pi\)
0.365705 + 0.930731i \(0.380828\pi\)
\(602\) 0 0
\(603\) −1.28472e14 −0.0656239
\(604\) 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
\(609\) −9.40240e11 6.10473e12i −0.000454824 0.00295305i
\(610\) 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
\(615\) −8.89212e14 −0.407560
\(616\) 0 0
\(617\) 6.41641e14 0.288884 0.144442 0.989513i \(-0.453861\pi\)
0.144442 + 0.989513i \(0.453861\pi\)
\(618\) 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
\(621\) −2.60743e14 + 4.51620e14i −0.113294 + 0.196232i
\(622\) 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
\(627\) 1.83651e15 + 3.18092e15i 0.756869 + 1.31094i
\(628\) 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
\(633\) 3.91601e14 + 6.78273e14i 0.153152 + 0.265268i
\(634\) 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
\(639\) −5.39280e14 + 9.34061e14i −0.200244 + 0.346833i
\(640\) 0 0
\(641\) 1.64178e15 + 2.84365e15i 0.599233 + 1.03790i 0.992934 + 0.118664i \(0.0378612\pi\)
−0.393701 + 0.919239i \(0.628805\pi\)
\(642\) 0 0
\(643\) 1.94429e15 0.697592 0.348796 0.937199i \(-0.386591\pi\)
0.348796 + 0.937199i \(0.386591\pi\)
\(644\) 0 0
\(645\) 3.64297e15 1.28492
\(646\) 0 0
\(647\) −3.24795e14 5.62562e14i −0.112625 0.195073i 0.804203 0.594355i \(-0.202593\pi\)
−0.916828 + 0.399282i \(0.869259\pi\)
\(648\) 0 0
\(649\) 3.24716e14 5.62425e14i 0.110703 0.191743i
\(650\) 0 0
\(651\) 1.81853e15 1.45983e15i 0.609572 0.489335i
\(652\) 0 0
\(653\) −1.92474e15 + 3.33375e15i −0.634380 + 1.09878i 0.352266 + 0.935900i \(0.385411\pi\)
−0.986646 + 0.162879i \(0.947922\pi\)
\(654\) 0 0
\(655\) −2.95476e15 5.11779e15i −0.957623 1.65865i
\(656\) 0 0
\(657\) −1.22030e15 −0.388917
\(658\) 0 0
\(659\) 1.40489e15 0.440324 0.220162 0.975463i \(-0.429341\pi\)
0.220162 + 0.975463i \(0.429341\pi\)
\(660\) 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
\(663\) 6.64000e14 1.15008e15i 0.201300 0.348662i
\(664\) 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
\(669\) 1.36519e15 + 2.36458e15i 0.393867 + 0.682198i
\(670\) 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
\(675\) −9.44945e14 1.63669e15i −0.259559 0.449569i
\(676\) 0 0
\(677\) −1.70181e15 + 2.94763e15i −0.459912 + 0.796590i −0.998956 0.0456873i \(-0.985452\pi\)
0.539044 + 0.842277i \(0.318786\pi\)
\(678\) 0 0
\(679\) −4.74640e15 1.84522e15i −1.26206 0.490642i
\(680\) 0 0
\(681\) 1.84291e15 3.19202e15i 0.482165 0.835135i
\(682\) 0 0
\(683\) 8.52660e14 + 1.47685e15i 0.219514 + 0.380209i 0.954659 0.297700i \(-0.0962195\pi\)
−0.735146 + 0.677909i \(0.762886\pi\)
\(684\) 0 0
\(685\) 6.76946e15 1.71497
\(686\) 0 0
\(687\) 8.85201e14 0.220689
\(688\) 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
\(693\) 2.08336e15 + 8.09930e14i 0.495143 + 0.192493i
\(694\) 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
\(699\) −2.93374e15 −0.664962
\(700\) 0 0
\(701\) −2.93440e15 −0.654741 −0.327371 0.944896i \(-0.606163\pi\)
−0.327371 + 0.944896i \(0.606163\pi\)
\(702\) 0 0
\(703\) 1.75343e15 + 3.03703e15i 0.385154 + 0.667106i
\(704\) 0 0
\(705\) 1.30166e15 2.25454e15i 0.281486 0.487548i
\(706\) 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
\(711\) −7.59094e14 1.31479e15i −0.156680 0.271377i
\(712\) 0 0
\(713\) −7.84339e15 −1.59408
\(714\) 0 0
\(715\) 2.43981e16 4.88284
\(716\) 0 0
\(717\) 1.97084e14 + 3.41360e14i 0.0388416 + 0.0672756i
\(718\) 0 0
\(719\) 1.47695e15 2.55816e15i 0.286654 0.496499i −0.686355 0.727266i \(-0.740790\pi\)
0.973009 + 0.230768i \(0.0741238\pi\)
\(720\) 0 0
\(721\) −2.70661e15 + 2.17273e15i −0.517347 + 0.415301i
\(722\) 0 0
\(723\) 1.86193e15 3.22496e15i 0.350512 0.607104i
\(724\) 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
\(729\) 2.05891e14 0.0370370
\(730\) 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
\(735\) 4.76080e15 + 4.36070e15i 0.818653 + 0.749852i
\(736\) 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
\(741\) −9.20330e15 −1.51336
\(742\) 0 0
\(743\) 5.66724e13 0.00918191 0.00459095 0.999989i \(-0.498539\pi\)
0.00459095 + 0.999989i \(0.498539\pi\)
\(744\) 0 0
\(745\) 4.70646e14 + 8.15182e14i 0.0751337 + 0.130135i
\(746\) 0 0
\(747\) −4.02313e14 + 6.96826e14i −0.0632850 + 0.109613i
\(748\) 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
\(753\) −1.71723e15 2.97433e15i −0.258497 0.447731i
\(754\) 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
\(759\) −3.75902e15 6.51082e15i −0.541683 0.938223i
\(760\) 0 0
\(761\) 3.73179e15 6.46364e15i 0.530031 0.918041i −0.469355 0.883009i \(-0.655514\pi\)
0.999386 0.0350311i \(-0.0111530\pi\)
\(762\) 0 0
\(763\) 1.41632e15 + 9.19582e15i 0.198279 + 1.28738i
\(764\) 0 0
\(765\) 1.01639e15 1.76045e15i 0.140257 0.242932i
\(766\) 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
\(771\) 3.65431e15 0.483065
\(772\) 0 0
\(773\) 3.32146e15 + 5.75293e15i 0.432854 + 0.749725i 0.997118 0.0758695i \(-0.0241732\pi\)
−0.564264 + 0.825595i \(0.690840\pi\)
\(774\) 0 0
\(775\) 1.42124e16 2.46166e16i 1.82603 3.16278i
\(776\) 0 0