Properties

Label 84.12.i.b.25.8
Level $84$
Weight $12$
Character 84.25
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 25.8
Root \(-11427.1 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.25
Dual form 84.12.i.b.37.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 + 210.444i) q^{3} +(5578.82 + 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +(-29524.5 - 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 + 210.444i) q^{3} +(5578.82 + 9662.79i) q^{5} +(24922.9 + 36826.3i) q^{7} +(-29524.5 - 51137.9i) q^{9} +(-196201. + 339830. i) q^{11} -2.28291e6 q^{13} -2.71130e6 q^{15} +(-2.79207e6 + 4.83601e6i) q^{17} +(6.40868e6 + 1.11002e7i) q^{19} +(-1.07780e7 + 770481. i) q^{21} +(-1.12939e7 - 1.95616e7i) q^{23} +(-3.78323e7 + 6.55275e7i) q^{25} +1.43489e7 q^{27} +1.65025e8 q^{29} +(9.99385e7 - 1.73099e8i) q^{31} +(-4.76768e7 - 8.25786e7i) q^{33} +(-2.16805e8 + 4.46272e8i) q^{35} +(2.10302e8 + 3.64253e8i) q^{37} +(2.77373e8 - 4.80425e8i) q^{39} -7.64804e8 q^{41} -2.38223e8 q^{43} +(3.29423e8 - 5.70578e8i) q^{45} +(-9.33471e7 - 1.61682e8i) q^{47} +(-7.35026e8 + 1.83564e9i) q^{49} +(-6.78474e8 - 1.17515e9i) q^{51} +(1.62451e9 - 2.81374e9i) q^{53} -4.37827e9 q^{55} -3.11462e9 q^{57} +(6.84439e7 - 1.18548e8i) q^{59} +(1.63005e9 + 2.82334e9i) q^{61} +(1.14739e9 - 2.36178e9i) q^{63} +(-1.27359e10 - 2.20593e10i) q^{65} +(-7.66329e9 + 1.32732e10i) q^{67} +5.48883e9 q^{69} +1.53915e10 q^{71} +(1.23489e10 - 2.13889e10i) q^{73} +(-9.19325e9 - 1.59232e10i) q^{75} +(-1.74046e10 + 1.24419e9i) q^{77} +(1.05790e10 + 1.83233e10i) q^{79} +(-1.74339e9 + 3.01964e9i) q^{81} -5.62969e10 q^{83} -6.23059e10 q^{85} +(-2.00505e10 + 3.47285e10i) q^{87} +(-1.87036e10 - 3.23955e10i) q^{89} +(-5.68967e10 - 8.40711e10i) q^{91} +(2.42851e10 + 4.20630e10i) q^{93} +(-7.15057e10 + 1.23851e11i) q^{95} -7.72068e10 q^{97} +2.31709e10 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(43\) \(73\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 5578.82 + 9662.79i 0.798375 + 1.38283i 0.920674 + 0.390333i \(0.127640\pi\)
−0.122299 + 0.992493i \(0.539027\pi\)
\(6\) 0 0
\(7\) 24922.9 + 36826.3i 0.560479 + 0.828169i
\(8\) 0 0
\(9\) −29524.5 51137.9i −0.166667 0.288675i
\(10\) 0 0
\(11\) −196201. + 339830.i −0.367317 + 0.636211i −0.989145 0.146942i \(-0.953057\pi\)
0.621828 + 0.783154i \(0.286390\pi\)
\(12\) 0 0
\(13\) −2.28291e6 −1.70530 −0.852649 0.522484i \(-0.825005\pi\)
−0.852649 + 0.522484i \(0.825005\pi\)
\(14\) 0 0
\(15\) −2.71130e6 −0.921884
\(16\) 0 0
\(17\) −2.79207e6 + 4.83601e6i −0.476934 + 0.826073i −0.999651 0.0264331i \(-0.991585\pi\)
0.522717 + 0.852506i \(0.324918\pi\)
\(18\) 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
\(21\) −1.07780e7 + 770481.i −0.575881 + 0.0411676i
\(22\) 0 0
\(23\) −1.12939e7 1.95616e7i −0.365881 0.633725i 0.623036 0.782193i \(-0.285899\pi\)
−0.988917 + 0.148468i \(0.952566\pi\)
\(24\) 0 0
\(25\) −3.78323e7 + 6.55275e7i −0.774806 + 1.34200i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) 1.65025e8 1.49403 0.747016 0.664806i \(-0.231486\pi\)
0.747016 + 0.664806i \(0.231486\pi\)
\(30\) 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
\(33\) −4.76768e7 8.25786e7i −0.212070 0.367317i
\(34\) 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
\(39\) 2.77373e8 4.80425e8i 0.492277 0.852649i
\(40\) 0 0
\(41\) −7.64804e8 −1.03095 −0.515476 0.856904i \(-0.672385\pi\)
−0.515476 + 0.856904i \(0.672385\pi\)
\(42\) 0 0
\(43\) −2.38223e8 −0.247120 −0.123560 0.992337i \(-0.539431\pi\)
−0.123560 + 0.992337i \(0.539431\pi\)
\(44\) 0 0
\(45\) 3.29423e8 5.70578e8i 0.266125 0.460942i
\(46\) 0 0
\(47\) −9.33471e7 1.61682e8i −0.0593694 0.102831i 0.834813 0.550533i \(-0.185576\pi\)
−0.894183 + 0.447703i \(0.852242\pi\)
\(48\) 0 0
\(49\) −7.35026e8 + 1.83564e9i −0.371727 + 0.928342i
\(50\) 0 0
\(51\) −6.78474e8 1.17515e9i −0.275358 0.476934i
\(52\) 0 0
\(53\) 1.62451e9 2.81374e9i 0.533587 0.924200i −0.465643 0.884973i \(-0.654177\pi\)
0.999230 0.0392276i \(-0.0124897\pi\)
\(54\) 0 0
\(55\) −4.37827e9 −1.17303
\(56\) 0 0
\(57\) −3.11462e9 −0.685635
\(58\) 0 0
\(59\) 6.84439e7 1.18548e8i 0.0124637 0.0215878i −0.859726 0.510755i \(-0.829366\pi\)
0.872190 + 0.489167i \(0.162699\pi\)
\(60\) 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
\(63\) 1.14739e9 2.36178e9i 0.145659 0.299824i
\(64\) 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
\(69\) 5.48883e9 0.422483
\(70\) 0 0
\(71\) 1.53915e10 1.01242 0.506210 0.862410i \(-0.331046\pi\)
0.506210 + 0.862410i \(0.331046\pi\)
\(72\) 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
\(75\) −9.19325e9 1.59232e10i −0.447334 0.774806i
\(76\) 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
\(81\) −1.74339e9 + 3.01964e9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) −5.62969e10 −1.56875 −0.784377 0.620284i \(-0.787017\pi\)
−0.784377 + 0.620284i \(0.787017\pi\)
\(84\) 0 0
\(85\) −6.23059e10 −1.52309
\(86\) 0 0
\(87\) −2.00505e10 + 3.47285e10i −0.431290 + 0.747016i
\(88\) 0 0
\(89\) −1.87036e10 3.23955e10i −0.355041 0.614950i 0.632084 0.774900i \(-0.282200\pi\)
−0.987125 + 0.159950i \(0.948867\pi\)
\(90\) 0 0
\(91\) −5.68967e10 8.40711e10i −0.955783 1.41227i
\(92\) 0 0
\(93\) 2.42851e10 + 4.20630e10i 0.361979 + 0.626966i
\(94\) 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
\(99\) 2.31709e10 0.244878
\(100\) 0 0
\(101\) 6.27863e10 1.08749e11i 0.594426 1.02958i −0.399202 0.916863i \(-0.630713\pi\)
0.993628 0.112712i \(-0.0359539\pi\)
\(102\) 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
\(105\) −6.75735e10 9.98473e10i −0.516696 0.763476i
\(106\) 0 0
\(107\) 2.85938e10 + 4.95259e10i 0.197088 + 0.341367i 0.947583 0.319509i \(-0.103518\pi\)
−0.750495 + 0.660876i \(0.770185\pi\)
\(108\) 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
\(111\) −1.02207e11 −0.575709
\(112\) 0 0
\(113\) 4.16630e10 0.212726 0.106363 0.994327i \(-0.466080\pi\)
0.106363 + 0.994327i \(0.466080\pi\)
\(114\) 0 0
\(115\) 1.26013e11 2.18261e11i 0.584221 1.01190i
\(116\) 0 0
\(117\) 6.74018e10 + 1.16743e11i 0.284216 + 0.492277i
\(118\) 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
\(123\) 9.29237e10 1.60948e11i 0.297610 0.515476i
\(124\) 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
\(129\) 2.89441e10 5.01327e10i 0.0713374 0.123560i
\(130\) 0 0
\(131\) −1.98899e11 3.44503e11i −0.450443 0.780191i 0.547970 0.836498i \(-0.315401\pi\)
−0.998414 + 0.0563070i \(0.982067\pi\)
\(132\) 0 0
\(133\) −2.49055e11 + 5.12656e11i −0.518933 + 1.06817i
\(134\) 0 0
\(135\) 8.00499e10 + 1.38651e11i 0.153647 + 0.266125i
\(136\) 0 0
\(137\) −4.18742e11 + 7.25282e11i −0.741282 + 1.28394i 0.210630 + 0.977566i \(0.432448\pi\)
−0.951912 + 0.306372i \(0.900885\pi\)
\(138\) 0 0
\(139\) −6.68822e11 −1.09327 −0.546637 0.837370i \(-0.684092\pi\)
−0.546637 + 0.837370i \(0.684092\pi\)
\(140\) 0 0
\(141\) 4.53667e10 0.0685539
\(142\) 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
\(147\) −2.96993e11 3.77712e11i −0.356863 0.453853i
\(148\) 0 0
\(149\) 3.37890e11 + 5.85243e11i 0.376922 + 0.652847i 0.990613 0.136699i \(-0.0436493\pi\)
−0.613691 + 0.789546i \(0.710316\pi\)
\(150\) 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
\(153\) 3.29738e11 0.317956
\(154\) 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
\(159\) 3.94756e11 + 6.83738e11i 0.308067 + 0.533587i
\(160\) 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
\(165\) 5.31960e11 9.21381e11i 0.338623 0.586513i
\(166\) 0 0
\(167\) −2.62678e11 −0.156489 −0.0782445 0.996934i \(-0.524931\pi\)
−0.0782445 + 0.996934i \(0.524931\pi\)
\(168\) 0 0
\(169\) 3.41951e12 1.90804
\(170\) 0 0
\(171\) 3.78426e11 6.55453e11i 0.197926 0.342818i
\(172\) 0 0
\(173\) −9.72304e11 1.68408e12i −0.477033 0.826245i 0.522621 0.852565i \(-0.324954\pi\)
−0.999654 + 0.0263201i \(0.991621\pi\)
\(174\) 0 0
\(175\) −3.35602e12 + 2.39910e11i −1.54567 + 0.110494i
\(176\) 0 0
\(177\) 1.66319e10 + 2.88072e10i 0.00719594 + 0.0124637i
\(178\) 0 0
\(179\) −2.23898e12 + 3.87802e12i −0.910663 + 1.57732i −0.0975338 + 0.995232i \(0.531095\pi\)
−0.813129 + 0.582083i \(0.802238\pi\)
\(180\) 0 0
\(181\) 4.68844e12 1.79389 0.896945 0.442142i \(-0.145781\pi\)
0.896945 + 0.442142i \(0.145781\pi\)
\(182\) 0 0
\(183\) −7.92206e11 −0.285337
\(184\) 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
\(189\) 3.57616e11 + 5.28417e11i 0.107864 + 0.159381i
\(190\) 0 0
\(191\) 1.93575e12 + 3.35282e12i 0.551019 + 0.954393i 0.998201 + 0.0599500i \(0.0190941\pi\)
−0.447182 + 0.894443i \(0.647573\pi\)
\(192\) 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
\(195\) 6.18966e12 1.57209
\(196\) 0 0
\(197\) −3.10385e12 −0.745309 −0.372654 0.927970i \(-0.621552\pi\)
−0.372654 + 0.927970i \(0.621552\pi\)
\(198\) 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
\(201\) −1.86218e12 3.22539e12i −0.400353 0.693432i
\(202\) 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
\(207\) −6.66893e11 + 1.15509e12i −0.121960 + 0.211242i
\(208\) 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
\(213\) −1.87007e12 + 3.23906e12i −0.292260 + 0.506210i
\(214\) 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
\(219\) 3.00078e12 + 5.19751e12i 0.402524 + 0.697192i
\(220\) 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
\(225\) 4.46792e12 0.516537
\(226\) 0 0
\(227\) −6.86393e12 + 1.18887e13i −0.755841 + 1.30915i 0.189114 + 0.981955i \(0.439438\pi\)
−0.944955 + 0.327200i \(0.893895\pi\)
\(228\) 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
\(231\) 1.85282e12 3.81386e12i 0.185339 0.381503i
\(232\) 0 0
\(233\) −2.23260e12 3.86698e12i −0.212987 0.368904i 0.739661 0.672980i \(-0.234986\pi\)
−0.952648 + 0.304075i \(0.901653\pi\)
\(234\) 0 0
\(235\) 1.04153e12 1.80399e12i 0.0947981 0.164195i
\(236\) 0 0
\(237\) −5.14138e12 −0.446647
\(238\) 0 0
\(239\) −2.16228e13 −1.79359 −0.896795 0.442447i \(-0.854111\pi\)
−0.896795 + 0.442447i \(0.854111\pi\)
\(240\) 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
\(243\) −4.23644e11 7.33773e11i −0.0320750 0.0555556i
\(244\) 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
\(249\) 6.84007e12 1.18474e13i 0.452860 0.784377i
\(250\) 0 0
\(251\) −1.43958e13 −0.912075 −0.456037 0.889961i \(-0.650732\pi\)
−0.456037 + 0.889961i \(0.650732\pi\)
\(252\) 0 0
\(253\) 8.86347e12 0.537577
\(254\) 0 0
\(255\) 7.57016e12 1.31119e13i 0.439678 0.761544i
\(256\) 0 0
\(257\) −8.96043e12 1.55199e13i −0.498536 0.863490i 0.501463 0.865179i \(-0.332795\pi\)
−0.999999 + 0.00168967i \(0.999462\pi\)
\(258\) 0 0
\(259\) −8.17278e12 + 1.68229e13i −0.435734 + 0.896916i
\(260\) 0 0
\(261\) −4.87227e12 8.43902e12i −0.249005 0.431290i
\(262\) 0 0
\(263\) −3.34897e12 + 5.80059e12i −0.164117 + 0.284260i −0.936342 0.351091i \(-0.885811\pi\)
0.772224 + 0.635350i \(0.219144\pi\)
\(264\) 0 0
\(265\) 3.62514e13 1.70401
\(266\) 0 0
\(267\) 9.08993e12 0.409967
\(268\) 0 0
\(269\) −1.73220e13 + 3.00027e13i −0.749828 + 1.29874i 0.198077 + 0.980187i \(0.436531\pi\)
−0.947905 + 0.318554i \(0.896803\pi\)
\(270\) 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
\(273\) 2.46052e13 1.75894e12i 0.982048 0.0702030i
\(274\) 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
\(279\) −1.18025e13 −0.417977
\(280\) 0 0
\(281\) −1.40636e13 −0.478863 −0.239431 0.970913i \(-0.576961\pi\)
−0.239431 + 0.970913i \(0.576961\pi\)
\(282\) 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
\(285\) −1.73759e13 3.00959e13i −0.547394 0.948115i
\(286\) 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
\(291\) 9.38063e12 1.62477e13i 0.263524 0.456437i
\(292\) 0 0
\(293\) 2.56171e13 0.693040 0.346520 0.938043i \(-0.387363\pi\)
0.346520 + 0.938043i \(0.387363\pi\)
\(294\) 0 0
\(295\) 1.52734e12 0.0398030
\(296\) 0 0
\(297\) −2.81527e12 + 4.87618e12i −0.0706901 + 0.122439i
\(298\) 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
\(303\) 1.52571e13 + 2.64260e13i 0.343192 + 0.594426i
\(304\) 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
\(309\) 4.64620e13 0.938267
\(310\) 0 0
\(311\) −4.91286e13 + 8.50933e13i −0.957530 + 1.65849i −0.229061 + 0.973412i \(0.573566\pi\)
−0.728469 + 0.685079i \(0.759768\pi\)
\(312\) 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
\(315\) 2.92225e13 2.08901e12i 0.530895 0.0379518i
\(316\) 0 0
\(317\) 4.97132e13 + 8.61057e13i 0.872259 + 1.51080i 0.859654 + 0.510877i \(0.170679\pi\)
0.0126053 + 0.999921i \(0.495988\pi\)
\(318\) 0 0
\(319\) −3.23779e13 + 5.60802e13i −0.548783 + 0.950520i
\(320\) 0 0
\(321\) −1.38966e13 −0.227578
\(322\) 0 0
\(323\) −7.15741e13 −1.13277
\(324\) 0 0
\(325\) 8.63677e13 1.49593e14i 1.32127 2.28851i
\(326\) 0 0
\(327\) 2.95533e13 + 5.11879e13i 0.437113 + 0.757102i
\(328\) 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
\(333\) 1.24181e13 2.15088e13i 0.166193 0.287854i
\(334\) 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
\(339\) −5.06206e12 + 8.76775e12i −0.0614086 + 0.106363i
\(340\) 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
\(345\) 3.06212e13 + 5.30374e13i 0.337300 + 0.584221i
\(346\) 0 0
\(347\) −1.53483e10 + 2.65840e10i −0.000163775 + 0.000283666i −0.866107 0.499858i \(-0.833385\pi\)
0.865944 + 0.500142i \(0.166719\pi\)
\(348\) 0 0
\(349\) 1.00590e14 1.03995 0.519976 0.854181i \(-0.325941\pi\)
0.519976 + 0.854181i \(0.325941\pi\)
\(350\) 0 0
\(351\) −3.27573e13 −0.328185
\(352\) 0 0
\(353\) 9.13814e13 1.58277e14i 0.887354 1.53694i 0.0443634 0.999015i \(-0.485874\pi\)
0.842991 0.537928i \(-0.180793\pi\)
\(354\) 0 0
\(355\) 8.58665e13 + 1.48725e14i 0.808291 + 1.40000i
\(356\) 0 0
\(357\) 2.63670e13 5.42739e13i 0.240649 0.495354i
\(358\) 0 0
\(359\) 3.57145e13 + 6.18593e13i 0.316100 + 0.547502i 0.979671 0.200612i \(-0.0642930\pi\)
−0.663570 + 0.748114i \(0.730960\pi\)
\(360\) 0 0
\(361\) −2.38973e13 + 4.13913e13i −0.205144 + 0.355319i
\(362\) 0 0
\(363\) −3.19139e13 −0.265762
\(364\) 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
\(369\) 2.25804e13 + 3.91105e13i 0.171825 + 0.297610i
\(370\) 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
\(375\) 3.63809e13 6.30136e13i 0.253339 0.438796i
\(376\) 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
\(381\) 4.51223e12 7.81540e12i 0.0287941 0.0498728i
\(382\) 0 0
\(383\) −3.88422e13 6.72766e13i −0.240830 0.417130i 0.720121 0.693848i \(-0.244086\pi\)
−0.960951 + 0.276719i \(0.910753\pi\)
\(384\) 0 0
\(385\) −1.09119e14 1.61235e14i −0.657456 0.971464i
\(386\) 0 0
\(387\) 7.03342e12 + 1.21822e13i 0.0411867 + 0.0713374i
\(388\) 0 0
\(389\) 5.89738e13 1.02146e14i 0.335688 0.581429i −0.647928 0.761701i \(-0.724364\pi\)
0.983617 + 0.180272i \(0.0576977\pi\)
\(390\) 0 0
\(391\) 1.26133e14 0.698004
\(392\) 0 0
\(393\) 9.66649e13 0.520127
\(394\) 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
\(399\) −7.76253e13 1.14700e14i −0.384284 0.567822i
\(400\) 0 0
\(401\) 9.60090e13 + 1.66292e14i 0.462400 + 0.800900i 0.999080 0.0428855i \(-0.0136551\pi\)
−0.536680 + 0.843786i \(0.680322\pi\)
\(402\) 0 0
\(403\) −2.28151e14 + 3.95168e14i −1.06916 + 1.85184i
\(404\) 0 0
\(405\) −3.89043e13 −0.177417
\(406\) 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
\(411\) −1.01754e14 1.76244e14i −0.427979 0.741282i
\(412\) 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
\(417\) 8.12618e13 1.40750e14i 0.315601 0.546637i
\(418\) 0 0
\(419\) 3.40515e13 0.128813 0.0644064 0.997924i \(-0.479485\pi\)
0.0644064 + 0.997924i \(0.479485\pi\)
\(420\) 0 0
\(421\) −2.32682e14 −0.857456 −0.428728 0.903434i \(-0.641038\pi\)
−0.428728 + 0.903434i \(0.641038\pi\)
\(422\) 0 0
\(423\) −5.51205e12 + 9.54716e12i −0.0197898 + 0.0342769i
\(424\) 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
\(429\) 1.08842e14 + 1.88519e14i 0.361643 + 0.626384i
\(430\) 0 0
\(431\) −2.06089e14 + 3.56956e14i −0.667467 + 1.15609i 0.311144 + 0.950363i \(0.399288\pi\)
−0.978610 + 0.205723i \(0.934045\pi\)
\(432\) 0 0
\(433\) 3.16336e14 0.998770 0.499385 0.866380i \(-0.333559\pi\)
0.499385 + 0.866380i \(0.333559\pi\)
\(434\) 0 0
\(435\) −4.47432e14 −1.37732
\(436\) 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
\(441\) 1.15572e14 1.66085e13i 0.329944 0.0474153i
\(442\) 0 0
\(443\) −2.50000e14 4.33012e14i −0.696176 1.20581i −0.969783 0.243971i \(-0.921550\pi\)
0.273606 0.961842i \(-0.411783\pi\)
\(444\) 0 0
\(445\) 2.08687e14 3.61457e14i 0.566912 0.981921i
\(446\) 0 0
\(447\) −1.64215e14 −0.435232
\(448\) 0 0
\(449\) 1.51607e13 0.0392071 0.0196036 0.999808i \(-0.493760\pi\)
0.0196036 + 0.999808i \(0.493760\pi\)
\(450\) 0 0
\(451\) 1.50055e14 2.59903e14i 0.378686 0.655904i
\(452\) 0 0
\(453\) 5.32796e13 + 9.22829e13i 0.131226 + 0.227291i
\(454\) 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
\(459\) −4.00632e13 + 6.93915e13i −0.0917859 + 0.158978i
\(460\) 0 0
\(461\) 8.14992e14 1.82305 0.911524 0.411246i \(-0.134906\pi\)
0.911524 + 0.411246i \(0.134906\pi\)
\(462\) 0 0
\(463\) 7.98210e13 0.174350 0.0871749 0.996193i \(-0.472216\pi\)
0.0871749 + 0.996193i \(0.472216\pi\)
\(464\) 0 0
\(465\) −2.70964e14 + 4.69323e14i −0.577990 + 1.00111i
\(466\) 0 0
\(467\) 2.26295e14 + 3.91955e14i 0.471447 + 0.816570i 0.999466 0.0326623i \(-0.0103986\pi\)
−0.528020 + 0.849232i \(0.677065\pi\)
\(468\) 0 0
\(469\) −6.79794e14 + 4.85960e13i −1.38333 + 0.0988895i
\(470\) 0 0
\(471\) 3.59540e13 + 6.22742e13i 0.0714714 + 0.123792i
\(472\) 0 0
\(473\) 4.67396e13 8.09553e13i 0.0907713 0.157220i
\(474\) 0 0
\(475\) −9.69821e14 −1.84025
\(476\) 0 0
\(477\) −1.91852e14 −0.355725
\(478\) 0 0
\(479\) −3.51335e14 + 6.08530e14i −0.636614 + 1.10265i 0.349557 + 0.936915i \(0.386332\pi\)
−0.986171 + 0.165732i \(0.947001\pi\)
\(480\) 0 0
\(481\) −4.80100e14 8.31558e14i −0.850225 1.47263i
\(482\) 0 0
\(483\) 1.36797e14 + 2.02133e14i 0.236793 + 0.349888i
\(484\) 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
\(489\) −5.44723e14 −0.881002
\(490\) 0 0
\(491\) 7.12724e14 1.12713 0.563564 0.826073i \(-0.309430\pi\)
0.563564 + 0.826073i \(0.309430\pi\)
\(492\) 0 0
\(493\) −4.60761e14 + 7.98062e14i −0.712554 + 1.23418i
\(494\) 0 0
\(495\) 1.29266e14 + 2.23896e14i 0.195504 + 0.338623i
\(496\) 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
\(501\) 3.19154e13 5.52791e13i 0.0451745 0.0782445i
\(502\) 0 0
\(503\) −7.21102e14 −0.998556 −0.499278 0.866442i \(-0.666401\pi\)
−0.499278 + 0.866442i \(0.666401\pi\)
\(504\) 0 0
\(505\) 1.40109e15 1.89830
\(506\) 0 0
\(507\) −4.15471e14 + 7.19617e14i −0.550804 + 0.954020i
\(508\) 0 0
\(509\) −4.57952e13 7.93196e13i −0.0594117 0.102904i 0.834790 0.550569i \(-0.185589\pi\)
−0.894201 + 0.447665i \(0.852256\pi\)
\(510\) 0 0
\(511\) 1.09544e15 7.83094e13i 1.39083 0.0994257i
\(512\) 0 0
\(513\) 9.19576e13 + 1.59275e14i 0.114273 + 0.197926i
\(514\) 0 0
\(515\) 1.06668e15 1.84754e15i 1.29746 2.24727i
\(516\) 0 0
\(517\) 7.32591e13 0.0872295
\(518\) 0 0
\(519\) 4.72540e14 0.550830
\(520\) 0 0
\(521\) −7.21411e14 + 1.24952e15i −0.823332 + 1.42605i 0.0798550 + 0.996806i \(0.474554\pi\)
−0.903187 + 0.429247i \(0.858779\pi\)
\(522\) 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
\(525\) 3.57269e14 7.35405e14i 0.390949 0.804730i
\(526\) 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
\(531\) −8.08308e12 −0.00830916
\(532\) 0 0
\(533\) 1.74598e15 1.75808
\(534\) 0 0
\(535\) −3.19039e14 + 5.52592e14i −0.314701 + 0.545078i
\(536\) 0 0
\(537\) −5.44071e14 9.42359e14i −0.525772 0.910663i
\(538\) 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
\(543\) −5.69645e14 + 9.86654e14i −0.517852 + 0.896945i
\(544\) 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
\(549\) 9.62531e13 1.66715e14i 0.0823696 0.142668i
\(550\) 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
\(555\) −5.70192e14 9.87602e14i −0.459632 0.796105i
\(556\) 0 0
\(557\) −1.41948e14 + 2.45861e14i −0.112183 + 0.194306i −0.916650 0.399691i \(-0.869118\pi\)
0.804467 + 0.593997i \(0.202451\pi\)
\(558\) 0 0
\(559\) 5.43842e14 0.421413
\(560\) 0 0
\(561\) 5.32468e14 0.404574
\(562\) 0 0
\(563\) 1.12143e15 1.94238e15i 0.835559 1.44723i −0.0580164 0.998316i \(-0.518478\pi\)
0.893575 0.448914i \(-0.148189\pi\)
\(564\) 0 0
\(565\) 2.32430e14 + 4.02581e14i 0.169835 + 0.294162i
\(566\) 0 0
\(567\) −1.54653e14 + 1.10556e13i −0.110828 + 0.00792271i
\(568\) 0 0
\(569\) −3.11079e14 5.38804e14i −0.218652 0.378716i 0.735744 0.677259i \(-0.236833\pi\)
−0.954396 + 0.298544i \(0.903499\pi\)
\(570\) 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
\(573\) −9.40776e14 −0.636262
\(574\) 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
\(579\) 3.57087e14 + 6.18493e14i 0.228056 + 0.395005i
\(580\) 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
\(585\) −7.52044e14 + 1.30258e15i −0.453822 + 0.786043i
\(586\) 0 0
\(587\) −2.39872e15 −1.42059 −0.710297 0.703902i \(-0.751440\pi\)
−0.710297 + 0.703902i \(0.751440\pi\)
\(588\) 0 0
\(589\) 2.56190e15 1.48911
\(590\) 0 0
\(591\) 3.77117e14 6.53187e14i 0.215152 0.372654i
\(592\) 0 0
\(593\) 4.74884e13 + 8.22524e13i 0.0265942 + 0.0460625i 0.879016 0.476792i \(-0.158200\pi\)
−0.852422 + 0.522854i \(0.824867\pi\)
\(594\) 0 0
\(595\) −1.55284e15 2.29449e15i −0.853658 1.26137i
\(596\) 0 0
\(597\) 2.62999e14 + 4.55527e14i 0.141937 + 0.245842i
\(598\) 0 0
\(599\) 8.09261e14 1.40168e15i 0.428787 0.742680i −0.567979 0.823043i \(-0.692275\pi\)
0.996766 + 0.0803629i \(0.0256079\pi\)
\(600\) 0 0
\(601\) −6.48361e14 −0.337293 −0.168646 0.985677i \(-0.553940\pi\)
−0.168646 + 0.985677i \(0.553940\pi\)
\(602\) 0 0
\(603\) 9.05019e14 0.462288
\(604\) 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
\(609\) −1.77864e15 + 1.27148e14i −0.860384 + 0.0615057i
\(610\) 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
\(615\) 2.07362e15 0.950419
\(616\) 0 0
\(617\) 2.76415e15 1.24450 0.622248 0.782820i \(-0.286219\pi\)
0.622248 + 0.782820i \(0.286219\pi\)
\(618\) 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
\(621\) −1.62055e14 2.80687e14i −0.0704139 0.121960i
\(622\) 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
\(627\) 6.11090e14 1.05844e15i 0.251845 0.436209i
\(628\) 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
\(633\) −3.09517e14 + 5.36098e14i −0.121050 + 0.209664i
\(634\) 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
\(639\) −4.54427e14 7.87091e14i −0.168737 0.292260i
\(640\) 0 0
\(641\) −1.47446e15 + 2.55384e15i −0.538163 + 0.932126i 0.460840 + 0.887483i \(0.347548\pi\)
−0.999003 + 0.0446427i \(0.985785\pi\)
\(642\) 0 0
\(643\) −2.86149e15 −1.02667 −0.513337 0.858187i \(-0.671591\pi\)
−0.513337 + 0.858187i \(0.671591\pi\)
\(644\) 0 0
\(645\) 6.45896e14 0.227816
\(646\) 0 0
\(647\) −5.03509e14 + 8.72103e14i −0.174596 + 0.302409i −0.940021 0.341116i \(-0.889195\pi\)
0.765426 + 0.643524i \(0.222529\pi\)
\(648\) 0 0
\(649\) 2.68575e13 + 4.65185e13i 0.00915628 + 0.0158591i
\(650\) 0 0
\(651\) −9.43770e14 + 1.94266e15i −0.316352 + 0.651180i
\(652\) 0 0
\(653\) −1.08161e15 1.87340e15i −0.356489 0.617458i 0.630882 0.775878i \(-0.282693\pi\)
−0.987372 + 0.158421i \(0.949360\pi\)
\(654\) 0 0
\(655\) 2.21924e15 3.84384e15i 0.719246 1.24577i
\(656\) 0 0
\(657\) −1.45838e15 −0.464795
\(658\) 0 0
\(659\) 2.09934e15 0.657981 0.328991 0.944333i \(-0.393292\pi\)
0.328991 + 0.944333i \(0.393292\pi\)
\(660\) 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
\(663\) 1.54889e15 + 2.68276e15i 0.469567 + 0.813314i
\(664\) 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
\(669\) 5.31643e14 9.20833e14i 0.153383 0.265667i
\(670\) 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
\(675\) −5.42852e14 + 9.40248e14i −0.149111 + 0.258269i
\(676\) 0 0
\(677\) 9.92626e14 + 1.71928e15i 0.268255 + 0.464631i 0.968411 0.249358i \(-0.0802197\pi\)
−0.700156 + 0.713990i \(0.746886\pi\)
\(678\) 0 0
\(679\) −1.92422e15 2.84324e15i −0.511647 0.756014i
\(680\) 0 0
\(681\) −1.66793e15 2.88895e15i −0.436385 0.755841i
\(682\) 0 0
\(683\) −2.26798e15 + 3.92825e15i −0.583882 + 1.01131i 0.411132 + 0.911576i \(0.365134\pi\)
−0.995014 + 0.0997375i \(0.968200\pi\)
\(684\) 0 0
\(685\) −9.34433e15 −2.36728
\(686\) 0 0
\(687\) −2.81838e14 −0.0702648
\(688\) 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
\(693\) 5.77486e14 + 8.53299e14i 0.137249 + 0.202800i
\(694\) 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
\(699\) 1.08504e15 0.245936
\(700\) 0 0
\(701\) 1.04536e15 0.233247 0.116623 0.993176i \(-0.462793\pi\)
0.116623 + 0.993176i \(0.462793\pi\)
\(702\) 0 0
\(703\) −2.69551e15 + 4.66877e15i −0.592090 + 1.02553i
\(704\) 0 0
\(705\) 2.53092e14 + 4.38369e14i 0.0547317 + 0.0947981i
\(706\) 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
\(711\) 6.24678e14 1.08197e15i 0.128936 0.223323i
\(712\) 0 0
\(713\) −4.51478e15 −0.917580
\(714\) 0 0
\(715\) 9.99519e15 2.00036
\(716\) 0 0
\(717\) 2.62717e15 4.55039e15i 0.517765 0.896795i
\(718\) 0 0
\(719\) −1.91066e15 3.30937e15i −0.370830 0.642297i 0.618863 0.785499i \(-0.287594\pi\)
−0.989694 + 0.143202i \(0.954260\pi\)
\(720\) 0 0
\(721\) 3.71525e15 7.64750e15i 0.710141 1.46176i
\(722\) 0 0
\(723\) −2.35080e15 4.07170e15i −0.442542 0.766505i
\(724\) 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
\(729\) 2.05891e14 0.0370370
\(730\) 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
\(735\) 1.99288e15 4.97697e15i 0.342689 0.855824i
\(736\) 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
\(741\) 7.11039e15 1.16921
\(742\) 0 0
\(743\) −3.31622e15 −0.537286 −0.268643 0.963240i \(-0.586575\pi\)
−0.268643 + 0.963240i \(0.586575\pi\)
\(744\) 0 0
\(745\) −3.77005e15 + 6.52992e15i −0.601850 + 1.04243i
\(746\) 0 0
\(747\) 1.66214e15 + 2.87891e15i 0.261459 + 0.452860i
\(748\) 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
\(753\) 1.74909e15 3.02951e15i 0.263293 0.456037i
\(754\) 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
\(759\) −1.07691e15 + 1.86527e15i −0.155185 + 0.268789i
\(760\) 0 0
\(761\) 8.70949e14 + 1.50853e15i 0.123702 + 0.214258i 0.921225 0.389031i \(-0.127190\pi\)
−0.797523 + 0.603289i \(0.793857\pi\)
\(762\) 0 0
\(763\) 1.07885e16 7.71233e14i 1.51035 0.107969i
\(764\) 0 0
\(765\) 1.83955e15 + 3.18619e15i 0.253848 + 0.439678i
\(766\) 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
\(771\) 4.35477e15 0.575660
\(772\) 0 0
\(773\) 3.78929e15 6.56324e15i 0.493822 0.855325i −0.506152 0.862444i \(-0.668933\pi\)
0.999975 + 0.00711869i \(0.00226597\pi\)
\(774\) 0 0
\(775\) 7.56181e15 + 1.30974e16i 0.971553 + 1.68278i
\(776\) 0 0