Properties

Label 84.12.i.b.37.7
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 37.7
Root \(-10168.9 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 84.37
Dual form 84.12.i.b.25.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +O(q^{10})\) \(q+(-121.500 - 210.444i) q^{3} +(4949.72 - 8573.16i) q^{5} +(29163.1 + 33568.4i) q^{7} +(-29524.5 + 51137.9i) q^{9} +(25007.0 + 43313.5i) q^{11} +1.46252e6 q^{13} -2.40556e6 q^{15} +(3.16934e6 + 5.48946e6i) q^{17} +(-1.02494e7 + 1.77525e7i) q^{19} +(3.52097e6 - 1.02158e7i) q^{21} +(-2.36024e7 + 4.08806e7i) q^{23} +(-2.45854e7 - 4.25831e7i) q^{25} +1.43489e7 q^{27} -9.10208e7 q^{29} +(-4.83443e7 - 8.37349e7i) q^{31} +(6.07671e6 - 1.05252e7i) q^{33} +(4.32137e8 - 8.38657e7i) q^{35} +(-7.14098e7 + 1.23685e8i) q^{37} +(-1.77696e8 - 3.07778e8i) q^{39} +8.44357e8 q^{41} -1.55607e9 q^{43} +(2.92276e8 + 5.06237e8i) q^{45} +(-4.22680e8 + 7.32103e8i) q^{47} +(-2.76354e8 + 1.95792e9i) q^{49} +(7.70151e8 - 1.33394e9i) q^{51} +(1.26817e9 + 2.19654e9i) q^{53} +4.95111e8 q^{55} +4.98123e9 q^{57} +(2.80141e9 + 4.85219e9i) q^{59} +(-5.98273e8 + 1.03624e9i) q^{61} +(-2.57765e9 + 5.00249e8i) q^{63} +(7.23904e9 - 1.25384e10i) q^{65} +(-2.73114e9 - 4.73048e9i) q^{67} +1.14708e10 q^{69} +1.81232e10 q^{71} +(9.87533e9 + 1.71046e10i) q^{73} +(-5.97425e9 + 1.03477e10i) q^{75} +(-7.24683e8 + 2.10260e9i) q^{77} +(-2.14642e10 + 3.71770e10i) q^{79} +(-1.74339e9 - 3.01964e9i) q^{81} -5.21192e10 q^{83} +6.27494e10 q^{85} +(1.10590e10 + 1.91548e10i) q^{87} +(-1.39910e10 + 2.42332e10i) q^{89} +(4.26515e10 + 4.90944e10i) q^{91} +(-1.17477e10 + 2.03476e10i) q^{93} +(1.01464e11 + 1.75740e11i) q^{95} +5.42003e10 q^{97} -2.95328e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q - 1944 q^{3} - 2156 q^{5} + 50512 q^{7} - 472392 q^{9}+O(q^{10}) \) 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
\(5\) 4949.72 8573.16i 0.708346 1.22689i −0.257124 0.966378i \(-0.582775\pi\)
0.965470 0.260513i \(-0.0838917\pi\)
\(6\) 0 0
\(7\) 29163.1 + 33568.4i 0.655835 + 0.754904i
\(8\) 0 0
\(9\) −29524.5 + 51137.9i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 25007.0 + 43313.5i 0.0468169 + 0.0810892i 0.888484 0.458907i \(-0.151759\pi\)
−0.841667 + 0.539996i \(0.818426\pi\)
\(12\) 0 0
\(13\) 1.46252e6 1.09248 0.546238 0.837630i \(-0.316059\pi\)
0.546238 + 0.837630i \(0.316059\pi\)
\(14\) 0 0
\(15\) −2.40556e6 −0.817928
\(16\) 0 0
\(17\) 3.16934e6 + 5.48946e6i 0.541378 + 0.937693i 0.998825 + 0.0484569i \(0.0154304\pi\)
−0.457448 + 0.889237i \(0.651236\pi\)
\(18\) 0 0
\(19\) −1.02494e7 + 1.77525e7i −0.949632 + 1.64481i −0.203431 + 0.979089i \(0.565209\pi\)
−0.746201 + 0.665721i \(0.768124\pi\)
\(20\) 0 0
\(21\) 3.52097e6 1.02158e7i 0.188129 0.545840i
\(22\) 0 0
\(23\) −2.36024e7 + 4.08806e7i −0.764634 + 1.32438i 0.175806 + 0.984425i \(0.443747\pi\)
−0.940440 + 0.339960i \(0.889586\pi\)
\(24\) 0 0
\(25\) −2.45854e7 4.25831e7i −0.503508 0.872102i
\(26\) 0 0
\(27\) 1.43489e7 0.192450
\(28\) 0 0
\(29\) −9.10208e7 −0.824046 −0.412023 0.911173i \(-0.635178\pi\)
−0.412023 + 0.911173i \(0.635178\pi\)
\(30\) 0 0
\(31\) −4.83443e7 8.37349e7i −0.303289 0.525312i 0.673590 0.739105i \(-0.264751\pi\)
−0.976879 + 0.213794i \(0.931418\pi\)
\(32\) 0 0
\(33\) 6.07671e6 1.05252e7i 0.0270297 0.0468169i
\(34\) 0 0
\(35\) 4.32137e8 8.38657e7i 1.39074 0.269904i
\(36\) 0 0
\(37\) −7.14098e7 + 1.23685e8i −0.169297 + 0.293230i −0.938173 0.346167i \(-0.887483\pi\)
0.768876 + 0.639398i \(0.220816\pi\)
\(38\) 0 0
\(39\) −1.77696e8 3.07778e8i −0.315371 0.546238i
\(40\) 0 0
\(41\) 8.44357e8 1.13819 0.569095 0.822272i \(-0.307294\pi\)
0.569095 + 0.822272i \(0.307294\pi\)
\(42\) 0 0
\(43\) −1.55607e9 −1.61418 −0.807089 0.590430i \(-0.798958\pi\)
−0.807089 + 0.590430i \(0.798958\pi\)
\(44\) 0 0
\(45\) 2.92276e8 + 5.06237e8i 0.236115 + 0.408964i
\(46\) 0 0
\(47\) −4.22680e8 + 7.32103e8i −0.268827 + 0.465623i −0.968559 0.248783i \(-0.919969\pi\)
0.699732 + 0.714405i \(0.253303\pi\)
\(48\) 0 0
\(49\) −2.76354e8 + 1.95792e9i −0.139762 + 0.990185i
\(50\) 0 0
\(51\) 7.70151e8 1.33394e9i 0.312564 0.541378i
\(52\) 0 0
\(53\) 1.26817e9 + 2.19654e9i 0.416544 + 0.721476i 0.995589 0.0938196i \(-0.0299077\pi\)
−0.579045 + 0.815296i \(0.696574\pi\)
\(54\) 0 0
\(55\) 4.95111e8 0.132650
\(56\) 0 0
\(57\) 4.98123e9 1.09654
\(58\) 0 0
\(59\) 2.80141e9 + 4.85219e9i 0.510142 + 0.883592i 0.999931 + 0.0117512i \(0.00374060\pi\)
−0.489789 + 0.871841i \(0.662926\pi\)
\(60\) 0 0
\(61\) −5.98273e8 + 1.03624e9i −0.0906955 + 0.157089i −0.907804 0.419395i \(-0.862242\pi\)
0.817108 + 0.576484i \(0.195576\pi\)
\(62\) 0 0
\(63\) −2.57765e9 + 5.00249e8i −0.327228 + 0.0635058i
\(64\) 0 0
\(65\) 7.23904e9 1.25384e10i 0.773851 1.34035i
\(66\) 0 0
\(67\) −2.73114e9 4.73048e9i −0.247134 0.428049i 0.715595 0.698515i \(-0.246156\pi\)
−0.962730 + 0.270466i \(0.912822\pi\)
\(68\) 0 0
\(69\) 1.14708e10 0.882923
\(70\) 0 0
\(71\) 1.81232e10 1.19210 0.596051 0.802947i \(-0.296736\pi\)
0.596051 + 0.802947i \(0.296736\pi\)
\(72\) 0 0
\(73\) 9.87533e9 + 1.71046e10i 0.557540 + 0.965687i 0.997701 + 0.0677684i \(0.0215879\pi\)
−0.440161 + 0.897919i \(0.645079\pi\)
\(74\) 0 0
\(75\) −5.97425e9 + 1.03477e10i −0.290701 + 0.503508i
\(76\) 0 0
\(77\) −7.24683e8 + 2.10260e9i −0.0305105 + 0.0885234i
\(78\) 0 0
\(79\) −2.14642e10 + 3.71770e10i −0.784811 + 1.35933i 0.144301 + 0.989534i \(0.453907\pi\)
−0.929112 + 0.369799i \(0.879427\pi\)
\(80\) 0 0
\(81\) −1.74339e9 3.01964e9i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −5.21192e10 −1.45234 −0.726170 0.687515i \(-0.758701\pi\)
−0.726170 + 0.687515i \(0.758701\pi\)
\(84\) 0 0
\(85\) 6.27494e10 1.53393
\(86\) 0 0
\(87\) 1.10590e10 + 1.91548e10i 0.237882 + 0.412023i
\(88\) 0 0
\(89\) −1.39910e10 + 2.42332e10i −0.265586 + 0.460008i −0.967717 0.252039i \(-0.918899\pi\)
0.702131 + 0.712048i \(0.252232\pi\)
\(90\) 0 0
\(91\) 4.26515e10 + 4.90944e10i 0.716484 + 0.824715i
\(92\) 0 0
\(93\) −1.17477e10 + 2.03476e10i −0.175104 + 0.303289i
\(94\) 0 0
\(95\) 1.01464e11 + 1.75740e11i 1.34534 + 2.33019i
\(96\) 0 0
\(97\) 5.42003e10 0.640851 0.320426 0.947274i \(-0.396174\pi\)
0.320426 + 0.947274i \(0.396174\pi\)
\(98\) 0 0
\(99\) −2.95328e9 −0.0312112
\(100\) 0 0
\(101\) 6.07024e10 + 1.05140e11i 0.574696 + 0.995403i 0.996075 + 0.0885179i \(0.0282130\pi\)
−0.421379 + 0.906885i \(0.638454\pi\)
\(102\) 0 0
\(103\) 8.26479e10 1.43150e11i 0.702469 1.21671i −0.265128 0.964213i \(-0.585414\pi\)
0.967597 0.252499i \(-0.0812525\pi\)
\(104\) 0 0
\(105\) −7.01537e10 8.07510e10i −0.536425 0.617457i
\(106\) 0 0
\(107\) 1.05098e11 1.82035e11i 0.724410 1.25472i −0.234806 0.972042i \(-0.575446\pi\)
0.959216 0.282673i \(-0.0912211\pi\)
\(108\) 0 0
\(109\) −4.57197e10 7.91888e10i −0.284615 0.492967i 0.687901 0.725805i \(-0.258532\pi\)
−0.972516 + 0.232837i \(0.925199\pi\)
\(110\) 0 0
\(111\) 3.47052e10 0.195487
\(112\) 0 0
\(113\) −3.60006e9 −0.0183814 −0.00919068 0.999958i \(-0.502926\pi\)
−0.00919068 + 0.999958i \(0.502926\pi\)
\(114\) 0 0
\(115\) 2.33651e11 + 4.04695e11i 1.08325 + 1.87625i
\(116\) 0 0
\(117\) −4.31800e10 + 7.47900e10i −0.182079 + 0.315371i
\(118\) 0 0
\(119\) −9.18449e10 + 2.66480e11i −0.352815 + 1.02366i
\(120\) 0 0
\(121\) 1.41405e11 2.44921e11i 0.495616 0.858433i
\(122\) 0 0
\(123\) −1.02589e11 1.77690e11i −0.328567 0.569095i
\(124\) 0 0
\(125\) −3.39174e9 −0.00994071
\(126\) 0 0
\(127\) 6.33083e11 1.70036 0.850179 0.526494i \(-0.176494\pi\)
0.850179 + 0.526494i \(0.176494\pi\)
\(128\) 0 0
\(129\) 1.89062e11 + 3.27465e11i 0.465973 + 0.807089i
\(130\) 0 0
\(131\) −4.80539e10 + 8.32318e10i −0.108827 + 0.188494i −0.915295 0.402783i \(-0.868043\pi\)
0.806468 + 0.591277i \(0.201376\pi\)
\(132\) 0 0
\(133\) −8.94831e11 + 1.73662e11i −1.86448 + 0.361843i
\(134\) 0 0
\(135\) 7.10231e10 1.23016e11i 0.136321 0.236115i
\(136\) 0 0
\(137\) −1.83227e10 3.17359e10i −0.0324360 0.0561808i 0.849352 0.527827i \(-0.176993\pi\)
−0.881788 + 0.471647i \(0.843660\pi\)
\(138\) 0 0
\(139\) −7.27117e11 −1.18856 −0.594282 0.804257i \(-0.702564\pi\)
−0.594282 + 0.804257i \(0.702564\pi\)
\(140\) 0 0
\(141\) 2.05422e11 0.310415
\(142\) 0 0
\(143\) 3.65732e10 + 6.33466e10i 0.0511463 + 0.0885880i
\(144\) 0 0
\(145\) −4.50527e11 + 7.80336e11i −0.583710 + 1.01102i
\(146\) 0 0
\(147\) 4.45610e11 1.79730e11i 0.535438 0.215961i
\(148\) 0 0
\(149\) 5.76995e11 9.99385e11i 0.643647 1.11483i −0.340965 0.940076i \(-0.610754\pi\)
0.984612 0.174754i \(-0.0559129\pi\)
\(150\) 0 0
\(151\) −3.74264e11 6.48245e11i −0.387976 0.671995i 0.604201 0.796832i \(-0.293492\pi\)
−0.992177 + 0.124837i \(0.960159\pi\)
\(152\) 0 0
\(153\) −3.74293e11 −0.360918
\(154\) 0 0
\(155\) −9.57164e11 −0.859334
\(156\) 0 0
\(157\) −1.07175e12 1.85633e12i −0.896697 1.55312i −0.831691 0.555239i \(-0.812627\pi\)
−0.0650059 0.997885i \(-0.520707\pi\)
\(158\) 0 0
\(159\) 3.08166e11 5.33759e11i 0.240492 0.416544i
\(160\) 0 0
\(161\) −2.06062e12 + 3.99908e11i −1.50126 + 0.291352i
\(162\) 0 0
\(163\) 1.02063e10 1.76779e10i 0.00694765 0.0120337i −0.862531 0.506005i \(-0.831122\pi\)
0.869478 + 0.493971i \(0.164455\pi\)
\(164\) 0 0
\(165\) −6.01560e10 1.04193e11i −0.0382928 0.0663251i
\(166\) 0 0
\(167\) −2.47826e11 −0.147641 −0.0738204 0.997272i \(-0.523519\pi\)
−0.0738204 + 0.997272i \(0.523519\pi\)
\(168\) 0 0
\(169\) 3.46792e11 0.193505
\(170\) 0 0
\(171\) −6.05219e11 1.04827e12i −0.316544 0.548270i
\(172\) 0 0
\(173\) 9.53660e11 1.65179e12i 0.467886 0.810402i −0.531441 0.847096i \(-0.678349\pi\)
0.999327 + 0.0366932i \(0.0116824\pi\)
\(174\) 0 0
\(175\) 7.12463e11 2.06715e12i 0.328136 0.952056i
\(176\) 0 0
\(177\) 6.80744e11 1.17908e12i 0.294531 0.510142i
\(178\) 0 0
\(179\) 2.54501e11 + 4.40808e11i 0.103514 + 0.179291i 0.913130 0.407669i \(-0.133658\pi\)
−0.809616 + 0.586959i \(0.800325\pi\)
\(180\) 0 0
\(181\) −1.05292e12 −0.402869 −0.201434 0.979502i \(-0.564560\pi\)
−0.201434 + 0.979502i \(0.564560\pi\)
\(182\) 0 0
\(183\) 2.90761e11 0.104726
\(184\) 0 0
\(185\) 7.06917e11 + 1.22442e12i 0.239841 + 0.415417i
\(186\) 0 0
\(187\) −1.58512e11 + 2.74550e11i −0.0506912 + 0.0877997i
\(188\) 0 0
\(189\) 4.18459e11 + 4.81671e11i 0.126215 + 0.145281i
\(190\) 0 0
\(191\) −3.42442e12 + 5.93127e12i −0.974773 + 1.68836i −0.294092 + 0.955777i \(0.595017\pi\)
−0.680681 + 0.732580i \(0.738316\pi\)
\(192\) 0 0
\(193\) −1.13876e12 1.97240e12i −0.306104 0.530187i 0.671403 0.741093i \(-0.265692\pi\)
−0.977506 + 0.210906i \(0.932359\pi\)
\(194\) 0 0
\(195\) −3.51817e12 −0.893567
\(196\) 0 0
\(197\) 2.51939e12 0.604966 0.302483 0.953155i \(-0.402184\pi\)
0.302483 + 0.953155i \(0.402184\pi\)
\(198\) 0 0
\(199\) 5.73459e11 + 9.93260e11i 0.130260 + 0.225617i 0.923777 0.382932i \(-0.125086\pi\)
−0.793517 + 0.608548i \(0.791752\pi\)
\(200\) 0 0
\(201\) −6.63668e11 + 1.14951e12i −0.142683 + 0.247134i
\(202\) 0 0
\(203\) −2.65445e12 3.05543e12i −0.540438 0.622076i
\(204\) 0 0
\(205\) 4.17933e12 7.23881e12i 0.806233 1.39644i
\(206\) 0 0
\(207\) −1.39370e12 2.41396e12i −0.254878 0.441462i
\(208\) 0 0
\(209\) −1.02523e12 −0.177835
\(210\) 0 0
\(211\) −1.08695e12 −0.178919 −0.0894593 0.995990i \(-0.528514\pi\)
−0.0894593 + 0.995990i \(0.528514\pi\)
\(212\) 0 0
\(213\) −2.20197e12 3.81392e12i −0.344130 0.596051i
\(214\) 0 0
\(215\) −7.70209e12 + 1.33404e13i −1.14340 + 1.98042i
\(216\) 0 0
\(217\) 1.40098e12 4.06481e12i 0.197653 0.573472i
\(218\) 0 0
\(219\) 2.39970e12 4.15641e12i 0.321896 0.557540i
\(220\) 0 0
\(221\) 4.63521e12 + 8.02843e12i 0.591442 + 1.02441i
\(222\) 0 0
\(223\) 1.60167e13 1.94489 0.972447 0.233124i \(-0.0748949\pi\)
0.972447 + 0.233124i \(0.0748949\pi\)
\(224\) 0 0
\(225\) 2.90348e12 0.335672
\(226\) 0 0
\(227\) −5.82492e12 1.00891e13i −0.641428 1.11099i −0.985114 0.171901i \(-0.945009\pi\)
0.343686 0.939085i \(-0.388324\pi\)
\(228\) 0 0
\(229\) 4.67803e11 8.10258e11i 0.0490871 0.0850214i −0.840438 0.541908i \(-0.817702\pi\)
0.889525 + 0.456887i \(0.151035\pi\)
\(230\) 0 0
\(231\) 5.30529e11 1.02961e11i 0.0530693 0.0102993i
\(232\) 0 0
\(233\) −6.06338e12 + 1.05021e13i −0.578438 + 1.00188i 0.417220 + 0.908805i \(0.363004\pi\)
−0.995659 + 0.0930793i \(0.970329\pi\)
\(234\) 0 0
\(235\) 4.18429e12 + 7.24741e12i 0.380846 + 0.659644i
\(236\) 0 0
\(237\) 1.04316e13 0.906222
\(238\) 0 0
\(239\) 2.98561e12 0.247654 0.123827 0.992304i \(-0.460483\pi\)
0.123827 + 0.992304i \(0.460483\pi\)
\(240\) 0 0
\(241\) −4.35089e12 7.53596e12i −0.344734 0.597097i 0.640571 0.767899i \(-0.278698\pi\)
−0.985305 + 0.170802i \(0.945364\pi\)
\(242\) 0 0
\(243\) −4.23644e11 + 7.33773e11i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 1.54177e13 + 1.20604e13i 1.11585 + 0.872866i
\(246\) 0 0
\(247\) −1.49900e13 + 2.59634e13i −1.03745 + 1.79692i
\(248\) 0 0
\(249\) 6.33248e12 + 1.09682e13i 0.419254 + 0.726170i
\(250\) 0 0
\(251\) 1.10571e13 0.700544 0.350272 0.936648i \(-0.386089\pi\)
0.350272 + 0.936648i \(0.386089\pi\)
\(252\) 0 0
\(253\) −2.36091e12 −0.143191
\(254\) 0 0
\(255\) −7.62406e12 1.32053e13i −0.442808 0.766965i
\(256\) 0 0
\(257\) −1.27142e13 + 2.20217e13i −0.707387 + 1.22523i 0.258436 + 0.966028i \(0.416793\pi\)
−0.965823 + 0.259202i \(0.916540\pi\)
\(258\) 0 0
\(259\) −6.23446e12 + 1.20993e12i −0.332392 + 0.0645079i
\(260\) 0 0
\(261\) 2.68734e12 4.65461e12i 0.137341 0.237882i
\(262\) 0 0
\(263\) 1.68147e13 + 2.91239e13i 0.824011 + 1.42723i 0.902673 + 0.430327i \(0.141602\pi\)
−0.0786626 + 0.996901i \(0.525065\pi\)
\(264\) 0 0
\(265\) 2.51084e13 1.18023
\(266\) 0 0
\(267\) 6.79965e12 0.306672
\(268\) 0 0
\(269\) 7.46102e12 + 1.29229e13i 0.322969 + 0.559398i 0.981099 0.193506i \(-0.0619858\pi\)
−0.658130 + 0.752904i \(0.728652\pi\)
\(270\) 0 0
\(271\) 1.07841e13 1.86786e13i 0.448179 0.776269i −0.550089 0.835106i \(-0.685406\pi\)
0.998268 + 0.0588375i \(0.0187394\pi\)
\(272\) 0 0
\(273\) 5.14947e12 1.49407e13i 0.205527 0.596317i
\(274\) 0 0
\(275\) 1.22961e12 2.12975e12i 0.0471454 0.0816582i
\(276\) 0 0
\(277\) −1.45333e13 2.51724e13i −0.535457 0.927439i −0.999141 0.0414380i \(-0.986806\pi\)
0.463684 0.886001i \(-0.346527\pi\)
\(278\) 0 0
\(279\) 5.70937e12 0.202193
\(280\) 0 0
\(281\) 2.02171e13 0.688390 0.344195 0.938898i \(-0.388152\pi\)
0.344195 + 0.938898i \(0.388152\pi\)
\(282\) 0 0
\(283\) −2.44690e11 4.23815e11i −0.00801291 0.0138788i 0.861991 0.506923i \(-0.169217\pi\)
−0.870004 + 0.493045i \(0.835884\pi\)
\(284\) 0 0
\(285\) 2.46557e13 4.27049e13i 0.776730 1.34534i
\(286\) 0 0
\(287\) 2.46241e13 + 2.83438e13i 0.746465 + 0.859225i
\(288\) 0 0
\(289\) −2.95353e12 + 5.11566e12i −0.0861794 + 0.149267i
\(290\) 0 0
\(291\) −6.58534e12 1.14061e13i −0.184998 0.320426i
\(292\) 0 0
\(293\) −6.82921e13 −1.84756 −0.923780 0.382924i \(-0.874917\pi\)
−0.923780 + 0.382924i \(0.874917\pi\)
\(294\) 0 0
\(295\) 5.54649e13 1.44543
\(296\) 0 0
\(297\) 3.58824e11 + 6.21501e11i 0.00900991 + 0.0156056i
\(298\) 0 0
\(299\) −3.45189e13 + 5.97885e13i −0.835345 + 1.44686i
\(300\) 0 0
\(301\) −4.53797e13 5.22347e13i −1.05863 1.21855i
\(302\) 0 0
\(303\) 1.47507e13 2.55489e13i 0.331801 0.574696i
\(304\) 0 0
\(305\) 5.92257e12 + 1.02582e13i 0.128488 + 0.222547i
\(306\) 0 0
\(307\) −2.82225e13 −0.590655 −0.295328 0.955396i \(-0.595429\pi\)
−0.295328 + 0.955396i \(0.595429\pi\)
\(308\) 0 0
\(309\) −4.01669e13 −0.811142
\(310\) 0 0
\(311\) 3.53006e13 + 6.11425e13i 0.688019 + 1.19168i 0.972478 + 0.232996i \(0.0748528\pi\)
−0.284459 + 0.958688i \(0.591814\pi\)
\(312\) 0 0
\(313\) 1.75608e13 3.04162e13i 0.330408 0.572283i −0.652184 0.758061i \(-0.726147\pi\)
0.982592 + 0.185778i \(0.0594804\pi\)
\(314\) 0 0
\(315\) −8.46991e12 + 2.45747e13i −0.153876 + 0.446457i
\(316\) 0 0
\(317\) 1.54610e13 2.67792e13i 0.271275 0.469863i −0.697913 0.716182i \(-0.745888\pi\)
0.969189 + 0.246319i \(0.0792212\pi\)
\(318\) 0 0
\(319\) −2.27616e12 3.94242e12i −0.0385793 0.0668212i
\(320\) 0 0
\(321\) −5.10777e13 −0.836477
\(322\) 0 0
\(323\) −1.29936e14 −2.05644
\(324\) 0 0
\(325\) −3.59565e13 6.22785e13i −0.550071 0.952751i
\(326\) 0 0
\(327\) −1.11099e13 + 1.92429e13i −0.164322 + 0.284615i
\(328\) 0 0
\(329\) −3.69022e13 + 7.16169e12i −0.527807 + 0.102433i
\(330\) 0 0
\(331\) −1.86187e13 + 3.22486e13i −0.257571 + 0.446125i −0.965591 0.260067i \(-0.916255\pi\)
0.708020 + 0.706192i \(0.249589\pi\)
\(332\) 0 0
\(333\) −4.21668e12 7.30350e12i −0.0564322 0.0977435i
\(334\) 0 0
\(335\) −5.40736e13 −0.700227
\(336\) 0 0
\(337\) 9.01286e13 1.12953 0.564766 0.825251i \(-0.308967\pi\)
0.564766 + 0.825251i \(0.308967\pi\)
\(338\) 0 0
\(339\) 4.37407e11 + 7.57611e11i 0.00530624 + 0.00919068i
\(340\) 0 0
\(341\) 2.41790e12 4.18792e12i 0.0283981 0.0491869i
\(342\) 0 0
\(343\) −7.37837e13 + 4.78222e13i −0.839156 + 0.543891i
\(344\) 0 0
\(345\) 5.67771e13 9.83409e13i 0.625415 1.08325i
\(346\) 0 0
\(347\) −4.20561e13 7.28433e13i −0.448763 0.777280i 0.549543 0.835465i \(-0.314802\pi\)
−0.998306 + 0.0581855i \(0.981469\pi\)
\(348\) 0 0
\(349\) 1.62557e14 1.68061 0.840305 0.542114i \(-0.182376\pi\)
0.840305 + 0.542114i \(0.182376\pi\)
\(350\) 0 0
\(351\) 2.09855e13 0.210247
\(352\) 0 0
\(353\) −7.77383e13 1.34647e14i −0.754873 1.30748i −0.945437 0.325804i \(-0.894365\pi\)
0.190564 0.981675i \(-0.438968\pi\)
\(354\) 0 0
\(355\) 8.97046e13 1.55373e14i 0.844421 1.46258i
\(356\) 0 0
\(357\) 6.72383e13 1.30491e13i 0.613679 0.119098i
\(358\) 0 0
\(359\) −6.44669e13 + 1.11660e14i −0.570581 + 0.988275i 0.425925 + 0.904758i \(0.359949\pi\)
−0.996506 + 0.0835170i \(0.973385\pi\)
\(360\) 0 0
\(361\) −1.51857e14 2.63024e14i −1.30360 2.25790i
\(362\) 0 0
\(363\) −6.87229e13 −0.572288
\(364\) 0 0
\(365\) 1.95520e14 1.57972
\(366\) 0 0
\(367\) 8.09211e13 + 1.40159e14i 0.634452 + 1.09890i 0.986631 + 0.162970i \(0.0521074\pi\)
−0.352179 + 0.935933i \(0.614559\pi\)
\(368\) 0 0
\(369\) −2.49292e13 + 4.31787e13i −0.189698 + 0.328567i
\(370\) 0 0
\(371\) −3.67506e13 + 1.06629e14i −0.271461 + 0.787620i
\(372\) 0 0
\(373\) 7.49137e12 1.29754e13i 0.0537233 0.0930515i −0.837913 0.545804i \(-0.816224\pi\)
0.891636 + 0.452752i \(0.149558\pi\)
\(374\) 0 0
\(375\) 4.12096e11 + 7.13772e11i 0.00286964 + 0.00497035i
\(376\) 0 0
\(377\) −1.33119e14 −0.900251
\(378\) 0 0
\(379\) −1.46414e14 −0.961758 −0.480879 0.876787i \(-0.659682\pi\)
−0.480879 + 0.876787i \(0.659682\pi\)
\(380\) 0 0
\(381\) −7.69196e13 1.33229e14i −0.490851 0.850179i
\(382\) 0 0
\(383\) 1.03039e14 1.78468e14i 0.638861 1.10654i −0.346822 0.937931i \(-0.612739\pi\)
0.985683 0.168609i \(-0.0539275\pi\)
\(384\) 0 0
\(385\) 1.44390e13 + 1.66201e13i 0.0869966 + 0.100138i
\(386\) 0 0
\(387\) 4.59420e13 7.95740e13i 0.269030 0.465973i
\(388\) 0 0
\(389\) 4.28674e13 + 7.42485e13i 0.244008 + 0.422634i 0.961852 0.273569i \(-0.0882043\pi\)
−0.717844 + 0.696204i \(0.754871\pi\)
\(390\) 0 0
\(391\) −2.99217e14 −1.65582
\(392\) 0 0
\(393\) 2.33542e13 0.125663
\(394\) 0 0
\(395\) 2.12483e14 + 3.68032e14i 1.11184 + 1.92576i
\(396\) 0 0
\(397\) −5.18685e13 + 8.98388e13i −0.263971 + 0.457210i −0.967293 0.253660i \(-0.918366\pi\)
0.703323 + 0.710871i \(0.251699\pi\)
\(398\) 0 0
\(399\) 1.45268e14 + 1.67212e14i 0.719149 + 0.827783i
\(400\) 0 0
\(401\) 8.92898e13 1.54655e14i 0.430039 0.744850i −0.566837 0.823830i \(-0.691833\pi\)
0.996876 + 0.0789803i \(0.0251664\pi\)
\(402\) 0 0
\(403\) −7.07044e13 1.22464e14i −0.331336 0.573891i
\(404\) 0 0
\(405\) −3.45172e13 −0.157410
\(406\) 0 0
\(407\) −7.14299e12 −0.0317038
\(408\) 0 0
\(409\) 1.39715e14 + 2.41994e14i 0.603622 + 1.04550i 0.992268 + 0.124117i \(0.0396099\pi\)
−0.388645 + 0.921388i \(0.627057\pi\)
\(410\) 0 0
\(411\) −4.45243e12 + 7.71183e12i −0.0187269 + 0.0324360i
\(412\) 0 0
\(413\) −8.11826e13 + 2.35544e14i −0.332459 + 0.964599i
\(414\) 0 0
\(415\) −2.57975e14 + 4.46827e14i −1.02876 + 1.78186i
\(416\) 0 0
\(417\) 8.83447e13 + 1.53017e14i 0.343109 + 0.594282i
\(418\) 0 0
\(419\) 1.47340e14 0.557370 0.278685 0.960383i \(-0.410102\pi\)
0.278685 + 0.960383i \(0.410102\pi\)
\(420\) 0 0
\(421\) 1.13118e14 0.416852 0.208426 0.978038i \(-0.433166\pi\)
0.208426 + 0.978038i \(0.433166\pi\)
\(422\) 0 0
\(423\) −2.49588e13 4.32300e13i −0.0896091 0.155208i
\(424\) 0 0
\(425\) 1.55839e14 2.69921e14i 0.545176 0.944273i
\(426\) 0 0
\(427\) −5.22325e13 + 1.01369e13i −0.178069 + 0.0345581i
\(428\) 0 0
\(429\) 8.88728e12 1.53932e13i 0.0295293 0.0511463i
\(430\) 0 0
\(431\) 2.21901e14 + 3.84344e14i 0.718678 + 1.24479i 0.961524 + 0.274722i \(0.0885859\pi\)
−0.242845 + 0.970065i \(0.578081\pi\)
\(432\) 0 0
\(433\) 3.99750e14 1.26213 0.631067 0.775729i \(-0.282617\pi\)
0.631067 + 0.775729i \(0.282617\pi\)
\(434\) 0 0
\(435\) 2.18956e14 0.674010
\(436\) 0 0
\(437\) −4.83823e14 8.38006e14i −1.45224 2.51536i
\(438\) 0 0
\(439\) 2.14931e14 3.72271e14i 0.629134 1.08969i −0.358591 0.933495i \(-0.616743\pi\)
0.987726 0.156198i \(-0.0499239\pi\)
\(440\) 0 0
\(441\) −9.19647e13 7.19388e13i −0.262548 0.205377i
\(442\) 0 0
\(443\) −6.77263e13 + 1.17305e14i −0.188598 + 0.326661i −0.944783 0.327697i \(-0.893728\pi\)
0.756185 + 0.654358i \(0.227061\pi\)
\(444\) 0 0
\(445\) 1.38503e14 + 2.39895e14i 0.376254 + 0.651690i
\(446\) 0 0
\(447\) −2.80420e14 −0.743220
\(448\) 0 0
\(449\) 9.79795e13 0.253385 0.126692 0.991942i \(-0.459564\pi\)
0.126692 + 0.991942i \(0.459564\pi\)
\(450\) 0 0
\(451\) 2.11149e13 + 3.65720e13i 0.0532865 + 0.0922949i
\(452\) 0 0
\(453\) −9.09462e13 + 1.57523e14i −0.223998 + 0.387976i
\(454\) 0 0
\(455\) 6.32007e14 1.22655e14i 1.51935 0.294864i
\(456\) 0 0
\(457\) −3.69842e14 + 6.40586e14i −0.867916 + 1.50327i −0.00379321 + 0.999993i \(0.501207\pi\)
−0.864123 + 0.503281i \(0.832126\pi\)
\(458\) 0 0
\(459\) 4.54766e13 + 7.87678e13i 0.104188 + 0.180459i
\(460\) 0 0
\(461\) 2.05197e14 0.459003 0.229501 0.973308i \(-0.426290\pi\)
0.229501 + 0.973308i \(0.426290\pi\)
\(462\) 0 0
\(463\) 3.01270e14 0.658052 0.329026 0.944321i \(-0.393280\pi\)
0.329026 + 0.944321i \(0.393280\pi\)
\(464\) 0 0
\(465\) 1.16295e14 + 2.01430e14i 0.248068 + 0.429667i
\(466\) 0 0
\(467\) −1.92054e14 + 3.32648e14i −0.400111 + 0.693013i −0.993739 0.111727i \(-0.964362\pi\)
0.593628 + 0.804740i \(0.297695\pi\)
\(468\) 0 0
\(469\) 7.91463e13 2.29636e14i 0.161057 0.467293i
\(470\) 0 0
\(471\) −2.60435e14 + 4.51087e14i −0.517708 + 0.896697i
\(472\) 0 0
\(473\) −3.89126e13 6.73986e13i −0.0755707 0.130892i
\(474\) 0 0
\(475\) 1.00794e15 1.91259
\(476\) 0 0
\(477\) −1.49769e14 −0.277696
\(478\) 0 0
\(479\) −3.73993e14 6.47776e14i −0.677671 1.17376i −0.975681 0.219197i \(-0.929656\pi\)
0.298010 0.954563i \(-0.403677\pi\)
\(480\) 0 0
\(481\) −1.04438e14 + 1.80892e14i −0.184953 + 0.320347i
\(482\) 0 0
\(483\) 3.34523e14 + 3.85056e14i 0.579052 + 0.666523i
\(484\) 0 0
\(485\) 2.68276e14 4.64668e14i 0.453945 0.786255i
\(486\) 0 0
\(487\) 6.99482e13 + 1.21154e14i 0.115709 + 0.200414i 0.918063 0.396435i \(-0.129753\pi\)
−0.802354 + 0.596848i \(0.796419\pi\)
\(488\) 0 0
\(489\) −4.96028e12 −0.00802245
\(490\) 0 0
\(491\) 2.86402e13 0.0452926 0.0226463 0.999744i \(-0.492791\pi\)
0.0226463 + 0.999744i \(0.492791\pi\)
\(492\) 0 0
\(493\) −2.88476e14 4.99655e14i −0.446120 0.772703i
\(494\) 0 0
\(495\) −1.46179e13 + 2.53190e13i −0.0221084 + 0.0382928i
\(496\) 0 0
\(497\) 5.28528e14 + 6.08367e14i 0.781822 + 0.899923i
\(498\) 0 0
\(499\) −5.75867e14 + 9.97430e14i −0.833238 + 1.44321i 0.0622193 + 0.998063i \(0.480182\pi\)
−0.895457 + 0.445148i \(0.853151\pi\)
\(500\) 0 0
\(501\) 3.01109e13 + 5.21536e13i 0.0426202 + 0.0738204i
\(502\) 0 0
\(503\) −9.85521e14 −1.36472 −0.682358 0.731019i \(-0.739045\pi\)
−0.682358 + 0.731019i \(0.739045\pi\)
\(504\) 0 0
\(505\) 1.20184e15 1.62833
\(506\) 0 0
\(507\) −4.21352e13 7.29803e13i −0.0558601 0.0967525i
\(508\) 0 0
\(509\) 3.82938e14 6.63268e14i 0.496799 0.860481i −0.503194 0.864173i \(-0.667842\pi\)
0.999993 + 0.00369203i \(0.00117521\pi\)
\(510\) 0 0
\(511\) −2.86179e14 + 8.30322e14i −0.363348 + 1.05422i
\(512\) 0 0
\(513\) −1.47068e14 + 2.54730e14i −0.182757 + 0.316544i
\(514\) 0 0
\(515\) −8.18168e14 1.41711e15i −0.995183 1.72371i
\(516\) 0 0
\(517\) −4.22799e13 −0.0503426
\(518\) 0 0
\(519\) −4.63479e14 −0.540268
\(520\) 0 0
\(521\) −3.90199e14 6.75845e14i −0.445327 0.771329i 0.552748 0.833349i \(-0.313579\pi\)
−0.998075 + 0.0620194i \(0.980246\pi\)
\(522\) 0 0
\(523\) −1.32813e14 + 2.30039e14i −0.148416 + 0.257064i −0.930642 0.365930i \(-0.880751\pi\)
0.782226 + 0.622995i \(0.214084\pi\)
\(524\) 0 0
\(525\) −5.21584e14 + 1.01225e14i −0.570752 + 0.110767i
\(526\) 0 0
\(527\) 3.06440e14 5.30769e14i 0.328388 0.568784i
\(528\) 0 0
\(529\) −6.37744e14 1.10461e15i −0.669330 1.15931i
\(530\) 0 0
\(531\) −3.30841e14 −0.340095
\(532\) 0 0
\(533\) 1.23489e15 1.24345
\(534\) 0 0
\(535\) −1.04041e15 1.80205e15i −1.02627 1.77755i
\(536\) 0 0
\(537\) 6.18436e13 1.07116e14i 0.0597636 0.103514i
\(538\) 0 0
\(539\) −9.17151e13 + 3.69919e13i −0.0868365 + 0.0350242i
\(540\) 0 0
\(541\) −2.32642e14 + 4.02947e14i −0.215825 + 0.373820i −0.953528 0.301306i \(-0.902577\pi\)
0.737702 + 0.675126i \(0.235911\pi\)
\(542\) 0 0
\(543\) 1.27930e14 + 2.21581e14i 0.116298 + 0.201434i
\(544\) 0 0
\(545\) −9.05198e14 −0.806423
\(546\) 0 0
\(547\) −4.31654e14 −0.376882 −0.188441 0.982084i \(-0.560343\pi\)
−0.188441 + 0.982084i \(0.560343\pi\)
\(548\) 0 0
\(549\) −3.53274e13 6.11889e13i −0.0302318 0.0523631i
\(550\) 0 0
\(551\) 9.32912e14 1.61585e15i 0.782540 1.35540i
\(552\) 0 0
\(553\) −1.87394e15 + 3.63679e14i −1.54087 + 0.299040i
\(554\) 0 0
\(555\) 1.71781e14 2.97533e14i 0.138472 0.239841i
\(556\) 0 0
\(557\) 1.93906e13 + 3.35855e13i 0.0153246 + 0.0265429i 0.873586 0.486670i \(-0.161789\pi\)
−0.858261 + 0.513213i \(0.828455\pi\)
\(558\) 0 0
\(559\) −2.27577e15 −1.76345
\(560\) 0 0
\(561\) 7.70367e13 0.0585332
\(562\) 0 0
\(563\) −2.67759e14 4.63772e14i −0.199502 0.345548i 0.748865 0.662723i \(-0.230599\pi\)
−0.948367 + 0.317175i \(0.897266\pi\)
\(564\) 0 0
\(565\) −1.78193e13 + 3.08639e13i −0.0130204 + 0.0225519i
\(566\) 0 0
\(567\) 5.05220e13 1.46585e14i 0.0362055 0.105047i
\(568\) 0 0
\(569\) −4.33929e14 + 7.51587e14i −0.305001 + 0.528277i −0.977262 0.212038i \(-0.931990\pi\)
0.672261 + 0.740314i \(0.265323\pi\)
\(570\) 0 0
\(571\) 5.01450e14 + 8.68538e14i 0.345724 + 0.598811i 0.985485 0.169762i \(-0.0543000\pi\)
−0.639761 + 0.768574i \(0.720967\pi\)
\(572\) 0 0
\(573\) 1.66427e15 1.12557
\(574\) 0 0
\(575\) 2.32110e15 1.54000
\(576\) 0 0
\(577\) −1.70850e14 2.95920e14i −0.111211 0.192623i 0.805048 0.593210i \(-0.202140\pi\)
−0.916259 + 0.400587i \(0.868806\pi\)
\(578\) 0 0
\(579\) −2.76720e14 + 4.79292e14i −0.176729 + 0.306104i
\(580\) 0 0
\(581\) −1.51996e15 1.74956e15i −0.952495 1.09638i
\(582\) 0 0
\(583\) −6.34265e13 + 1.09858e14i −0.0390026 + 0.0675545i
\(584\) 0 0
\(585\) 4.27458e14 + 7.40379e14i 0.257950 + 0.446783i
\(586\) 0 0
\(587\) 1.31315e15 0.777689 0.388845 0.921303i \(-0.372874\pi\)
0.388845 + 0.921303i \(0.372874\pi\)
\(588\) 0 0
\(589\) 1.98201e15 1.15205
\(590\) 0 0
\(591\) −3.06106e14 5.30191e14i −0.174639 0.302483i
\(592\) 0 0
\(593\) −1.42951e15 + 2.47598e15i −0.800543 + 1.38658i 0.118715 + 0.992928i \(0.462122\pi\)
−0.919259 + 0.393654i \(0.871211\pi\)
\(594\) 0 0
\(595\) 1.82997e15 + 2.10640e15i 1.00601 + 1.15797i
\(596\) 0 0
\(597\) 1.39351e14 2.41362e14i 0.0752055 0.130260i
\(598\) 0 0
\(599\) −1.07552e15 1.86285e15i −0.569862 0.987030i −0.996579 0.0826451i \(-0.973663\pi\)
0.426717 0.904385i \(-0.359670\pi\)
\(600\) 0 0
\(601\) −3.46561e15 −1.80289 −0.901447 0.432889i \(-0.857494\pi\)
−0.901447 + 0.432889i \(0.857494\pi\)
\(602\) 0 0
\(603\) 3.22543e14 0.164756
\(604\) 0 0
\(605\) −1.39983e15 2.42458e15i −0.702136 1.21613i
\(606\) 0 0
\(607\) 8.39119e14 1.45340e15i 0.413319 0.715890i −0.581931 0.813238i \(-0.697703\pi\)
0.995250 + 0.0973481i \(0.0310360\pi\)
\(608\) 0 0
\(609\) −3.20481e14 + 9.29847e14i −0.155027 + 0.449797i
\(610\) 0 0
\(611\) −6.18176e14 + 1.07071e15i −0.293688 + 0.508682i
\(612\) 0 0
\(613\) 2.51033e14 + 4.34802e14i 0.117138 + 0.202889i 0.918632 0.395113i \(-0.129295\pi\)
−0.801494 + 0.598002i \(0.795961\pi\)
\(614\) 0 0
\(615\) −2.03115e15 −0.930957
\(616\) 0 0
\(617\) 3.06387e15 1.37944 0.689719 0.724077i \(-0.257734\pi\)
0.689719 + 0.724077i \(0.257734\pi\)
\(618\) 0 0
\(619\) 6.07837e14 + 1.05280e15i 0.268837 + 0.465639i 0.968562 0.248773i \(-0.0800275\pi\)
−0.699725 + 0.714412i \(0.746694\pi\)
\(620\) 0 0
\(621\) −3.38669e14 + 5.86592e14i −0.147154 + 0.254878i
\(622\) 0 0
\(623\) −1.22149e15 + 2.37058e14i −0.521443 + 0.101197i
\(624\) 0 0
\(625\) 1.18367e15 2.05018e15i 0.496467 0.859906i
\(626\) 0 0
\(627\) 1.24566e14 + 2.15754e14i 0.0513366 + 0.0889176i
\(628\) 0 0
\(629\) −9.05289e14 −0.366614
\(630\) 0 0
\(631\) 2.29369e15 0.912794 0.456397 0.889776i \(-0.349140\pi\)
0.456397 + 0.889776i \(0.349140\pi\)
\(632\) 0 0
\(633\) 1.32064e14 + 2.28742e14i 0.0516494 + 0.0894593i
\(634\) 0 0
\(635\) 3.13358e15 5.42753e15i 1.20444 2.08615i
\(636\) 0 0
\(637\) −4.04173e14 + 2.86349e15i −0.152686 + 1.08175i
\(638\) 0 0
\(639\) −5.35078e14 + 9.26782e14i −0.198684 + 0.344130i
\(640\) 0 0
\(641\) 9.49382e13 + 1.64438e14i 0.0346515 + 0.0600181i 0.882831 0.469691i \(-0.155635\pi\)
−0.848180 + 0.529709i \(0.822301\pi\)
\(642\) 0 0
\(643\) 1.75159e15 0.628452 0.314226 0.949348i \(-0.398255\pi\)
0.314226 + 0.949348i \(0.398255\pi\)
\(644\) 0 0
\(645\) 3.74321e15 1.32028
\(646\) 0 0
\(647\) 1.59994e15 + 2.77118e15i 0.554793 + 0.960930i 0.997920 + 0.0644710i \(0.0205360\pi\)
−0.443126 + 0.896459i \(0.646131\pi\)
\(648\) 0 0
\(649\) −1.40110e14 + 2.42678e14i −0.0477665 + 0.0827341i
\(650\) 0 0
\(651\) −1.02563e15 + 1.99047e14i −0.343793 + 0.0667206i
\(652\) 0 0
\(653\) −1.12815e15 + 1.95401e15i −0.371829 + 0.644026i −0.989847 0.142138i \(-0.954602\pi\)
0.618018 + 0.786164i \(0.287936\pi\)
\(654\) 0 0
\(655\) 4.75706e14 + 8.23948e14i 0.154174 + 0.267038i
\(656\) 0 0
\(657\) −1.16626e15 −0.371693
\(658\) 0 0
\(659\) 3.01218e15 0.944084 0.472042 0.881576i \(-0.343517\pi\)
0.472042 + 0.881576i \(0.343517\pi\)
\(660\) 0 0
\(661\) −1.47975e15 2.56300e15i −0.456121 0.790024i 0.542631 0.839971i \(-0.317428\pi\)
−0.998752 + 0.0499469i \(0.984095\pi\)
\(662\) 0 0
\(663\) 1.12636e15 1.95091e15i 0.341469 0.591442i
\(664\) 0 0
\(665\) −2.94033e15 + 8.53111e15i −0.876753 + 2.54382i
\(666\) 0 0
\(667\) 2.14831e15 3.72098e15i 0.630094 1.09135i
\(668\) 0 0
\(669\) −1.94603e15 3.37062e15i −0.561443 0.972447i
\(670\) 0 0
\(671\) −5.98442e13 −0.0169843
\(672\) 0 0
\(673\) 4.01157e15 1.12004 0.560018 0.828481i \(-0.310794\pi\)
0.560018 + 0.828481i \(0.310794\pi\)
\(674\) 0 0
\(675\) −3.52773e14 6.11021e14i −0.0969002 0.167836i
\(676\) 0 0
\(677\) −3.58231e15 + 6.20474e15i −0.968111 + 1.67682i −0.267096 + 0.963670i \(0.586064\pi\)
−0.701015 + 0.713147i \(0.747269\pi\)
\(678\) 0 0
\(679\) 1.58065e15 + 1.81942e15i 0.420293 + 0.483782i
\(680\) 0 0
\(681\) −1.41546e15 + 2.45164e15i −0.370329 + 0.641428i
\(682\) 0 0
\(683\) 7.37708e13 + 1.27775e14i 0.0189920 + 0.0328951i 0.875365 0.483462i \(-0.160621\pi\)
−0.856373 + 0.516357i \(0.827288\pi\)
\(684\) 0 0
\(685\) −3.62770e14 −0.0919037
\(686\) 0 0
\(687\) −2.27352e14 −0.0566809
\(688\) 0 0
\(689\) 1.85472e15 + 3.21248e15i 0.455065 + 0.788196i
\(690\) 0 0
\(691\) 1.43011e15 2.47703e15i 0.345335 0.598138i −0.640079 0.768309i \(-0.721099\pi\)
0.985415 + 0.170171i \(0.0544319\pi\)
\(692\) 0 0
\(693\) −8.61268e13 9.91370e13i −0.0204694 0.0235615i
\(694\) 0 0
\(695\) −3.59902e15 + 6.23369e15i −0.841915 + 1.45824i
\(696\) 0 0
\(697\) 2.67606e15 + 4.63507e15i 0.616191 + 1.06727i
\(698\) 0 0
\(699\) 2.94680e15 0.667923
\(700\) 0 0
\(701\) 3.67571e14 0.0820147 0.0410073 0.999159i \(-0.486943\pi\)
0.0410073 + 0.999159i \(0.486943\pi\)
\(702\) 0 0
\(703\) −1.46382e15 2.53541e15i −0.321539 0.556922i
\(704\) 0 0
\(705\) 1.01678e15 1.76112e15i 0.219881 0.380846i
\(706\) 0 0
\(707\) −1.75910e15 + 5.10388e15i −0.374528 + 1.08666i
\(708\) 0 0
\(709\) −3.52656e15 + 6.10818e15i −0.739259 + 1.28043i 0.213570 + 0.976928i \(0.431491\pi\)
−0.952829 + 0.303507i \(0.901842\pi\)
\(710\) 0 0
\(711\) −1.26744e15 2.19527e15i −0.261604 0.453111i
\(712\) 0 0
\(713\) 4.56418e15 0.927620
\(714\) 0 0
\(715\) 7.24108e14 0.144917
\(716\) 0 0
\(717\) −3.62752e14 6.28304e14i −0.0714914 0.123827i
\(718\) 0 0
\(719\) 3.63237e15 6.29146e15i 0.704988 1.22108i −0.261708 0.965147i \(-0.584286\pi\)
0.966696 0.255928i \(-0.0823810\pi\)
\(720\) 0 0
\(721\) 7.21561e15 1.40035e15i 1.37921 0.267665i
\(722\) 0 0
\(723\) −1.05727e15 + 1.83124e15i −0.199032 + 0.344734i
\(724\) 0 0
\(725\) 2.23778e15 + 3.87595e15i 0.414914 + 0.718652i
\(726\) 0 0
\(727\) −8.82541e15 −1.61174 −0.805871 0.592091i \(-0.798302\pi\)
−0.805871 + 0.592091i \(0.798302\pi\)
\(728\) 0 0
\(729\) 2.05891e14 0.0370370
\(730\) 0 0
\(731\) −4.93171e15 8.54196e15i −0.873880 1.51360i
\(732\) 0 0
\(733\) −3.25078e15 + 5.63051e15i −0.567434 + 0.982825i 0.429384 + 0.903122i \(0.358731\pi\)
−0.996819 + 0.0797030i \(0.974603\pi\)
\(734\) 0 0
\(735\) 6.64788e14 4.70990e15i 0.114315 0.809900i
\(736\) 0 0
\(737\) 1.36596e14 2.36591e14i 0.0231401 0.0400799i
\(738\) 0 0
\(739\) −4.66487e15 8.07979e15i −0.778565 1.34851i −0.932769 0.360475i \(-0.882615\pi\)
0.154204 0.988039i \(-0.450719\pi\)
\(740\) 0 0
\(741\) 7.28512e15 1.19794
\(742\) 0 0
\(743\) 7.14846e15 1.15817 0.579087 0.815266i \(-0.303409\pi\)
0.579087 + 0.815266i \(0.303409\pi\)
\(744\) 0 0
\(745\) −5.71193e15 9.89335e15i −0.911850 1.57937i
\(746\) 0 0
\(747\) 1.53879e15 2.66527e15i 0.242057 0.419254i
\(748\) 0 0
\(749\) 9.17564e15 1.78073e15i 1.42228 0.276025i
\(750\) 0 0
\(751\) 2.33373e15 4.04213e15i 0.356476 0.617434i −0.630893 0.775869i \(-0.717312\pi\)
0.987369 + 0.158435i \(0.0506448\pi\)
\(752\) 0 0
\(753\) −1.34344e15 2.32690e15i −0.202230 0.350272i
\(754\) 0 0
\(755\) −7.41001e15 −1.09929
\(756\) 0 0
\(757\) 4.72097e15 0.690246 0.345123 0.938557i \(-0.387837\pi\)
0.345123 + 0.938557i \(0.387837\pi\)
\(758\) 0 0
\(759\) 2.86850e14 + 4.96839e14i 0.0413357 + 0.0715955i
\(760\) 0 0
\(761\) 6.09532e14 1.05574e15i 0.0865727 0.149948i −0.819488 0.573097i \(-0.805742\pi\)
0.906060 + 0.423149i \(0.139075\pi\)
\(762\) 0 0
\(763\) 1.32492e15 3.84413e15i 0.185483 0.538162i
\(764\) 0 0
\(765\) −1.85265e15 + 3.20888e15i −0.255655 + 0.442808i
\(766\) 0 0
\(767\) 4.09711e15 + 7.09641e15i 0.557318 + 0.965304i
\(768\) 0 0
\(769\) 4.52570e15 0.606864 0.303432 0.952853i \(-0.401867\pi\)
0.303432 + 0.952853i \(0.401867\pi\)
\(770\) 0 0
\(771\) 6.17911e15 0.816820
\(772\) 0 0
\(773\) −2.34216e15 4.05675e15i −0.305232 0.528677i 0.672081 0.740478i \(-0.265401\pi\)
−0.977313 + 0.211800i \(0.932067\pi\)
\(774\) 0 0
\(775\) −2.37713e15 + 4.11731e15i −0.305417 + 0.528998i
\(776\) 0 0