Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(1\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-20.3182\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −22.3182 | −1.97267 | −0.986336 | − | 0.164744i | \(-0.947320\pi\) | ||||
−0.986336 | + | 0.164744i | \(0.947320\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 370.104 | 2.89144 | ||||||||
\(5\) | −84.4166 | −0.302018 | −0.151009 | − | 0.988532i | \(-0.548252\pi\) | ||||
−0.151009 | + | 0.988532i | \(0.548252\pi\) | |||||||
\(6\) | −602.593 | −1.13892 | ||||||||
\(7\) | 1532.13 | 1.68831 | 0.844156 | − | 0.536097i | \(-0.180102\pi\) | ||||
0.844156 | + | 0.536097i | \(0.180102\pi\) | |||||||
\(8\) | −5403.34 | −3.73119 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 1884.03 | 0.595782 | ||||||||
\(11\) | 4639.41 | 1.05097 | 0.525483 | − | 0.850804i | \(-0.323885\pi\) | ||||
0.525483 | + | 0.850804i | \(0.323885\pi\) | |||||||
\(12\) | 9992.81 | 1.66937 | ||||||||
\(13\) | −1710.47 | −0.215930 | −0.107965 | − | 0.994155i | \(-0.534433\pi\) | ||||
−0.107965 | + | 0.994155i | \(0.534433\pi\) | |||||||
\(14\) | −34194.5 | −3.33049 | ||||||||
\(15\) | −2279.25 | −0.174370 | ||||||||
\(16\) | 73219.7 | 4.46897 | ||||||||
\(17\) | −14226.6 | −0.702310 | −0.351155 | − | 0.936317i | \(-0.614211\pi\) | ||||
−0.351155 | + | 0.936317i | \(0.614211\pi\) | |||||||
\(18\) | −16270.0 | −0.657558 | ||||||||
\(19\) | −21902.8 | −0.732590 | −0.366295 | − | 0.930499i | \(-0.619374\pi\) | ||||
−0.366295 | + | 0.930499i | \(0.619374\pi\) | |||||||
\(20\) | −31242.9 | −0.873266 | ||||||||
\(21\) | 41367.5 | 0.974748 | ||||||||
\(22\) | −103543. | −2.07321 | ||||||||
\(23\) | −107697. | −1.84567 | −0.922836 | − | 0.385194i | \(-0.874135\pi\) | ||||
−0.922836 | + | 0.385194i | \(0.874135\pi\) | |||||||
\(24\) | −145890. | −2.15420 | ||||||||
\(25\) | −70998.8 | −0.908785 | ||||||||
\(26\) | 38174.6 | 0.425959 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | 567048. | 4.88165 | ||||||||
\(29\) | −195131. | −1.48571 | −0.742853 | − | 0.669454i | \(-0.766528\pi\) | ||||
−0.742853 | + | 0.669454i | \(0.766528\pi\) | |||||||
\(30\) | 50868.8 | 0.343975 | ||||||||
\(31\) | −68117.7 | −0.410671 | −0.205336 | − | 0.978692i | \(-0.565829\pi\) | ||||
−0.205336 | + | 0.978692i | \(0.565829\pi\) | |||||||
\(32\) | −942507. | −5.08463 | ||||||||
\(33\) | 125264. | 0.606775 | ||||||||
\(34\) | 317512. | 1.38543 | ||||||||
\(35\) | −129337. | −0.509901 | ||||||||
\(36\) | 269806. | 0.963812 | ||||||||
\(37\) | −309640. | −1.00496 | −0.502482 | − | 0.864588i | \(-0.667580\pi\) | ||||
−0.502482 | + | 0.864588i | \(0.667580\pi\) | |||||||
\(38\) | 488831. | 1.44516 | ||||||||
\(39\) | −46182.6 | −0.124667 | ||||||||
\(40\) | 456131. | 1.12689 | ||||||||
\(41\) | 873409. | 1.97913 | 0.989565 | − | 0.144086i | \(-0.0460242\pi\) | ||||
0.989565 | + | 0.144086i | \(0.0460242\pi\) | |||||||
\(42\) | −923251. | −1.92286 | ||||||||
\(43\) | 159630. | 0.306179 | 0.153089 | − | 0.988212i | \(-0.451078\pi\) | ||||
0.153089 | + | 0.988212i | \(0.451078\pi\) | |||||||
\(44\) | 1.71706e6 | 3.03880 | ||||||||
\(45\) | −61539.7 | −0.100673 | ||||||||
\(46\) | 2.40360e6 | 3.64091 | ||||||||
\(47\) | −615386. | −0.864580 | −0.432290 | − | 0.901735i | \(-0.642294\pi\) | ||||
−0.432290 | + | 0.901735i | \(0.642294\pi\) | |||||||
\(48\) | 1.97693e6 | 2.58016 | ||||||||
\(49\) | 1.52388e6 | 1.85040 | ||||||||
\(50\) | 1.58457e6 | 1.79274 | ||||||||
\(51\) | −384117. | −0.405479 | ||||||||
\(52\) | −633051. | −0.624348 | ||||||||
\(53\) | −745946. | −0.688243 | −0.344121 | − | 0.938925i | \(-0.611823\pi\) | ||||
−0.344121 | + | 0.938925i | \(0.611823\pi\) | |||||||
\(54\) | −439290. | −0.379641 | ||||||||
\(55\) | −391643. | −0.317410 | ||||||||
\(56\) | −8.27862e6 | −6.29941 | ||||||||
\(57\) | −591374. | −0.422961 | ||||||||
\(58\) | 4.35498e6 | 2.93081 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | −843558. | −0.504180 | ||||||||
\(61\) | −2.69167e6 | −1.51833 | −0.759167 | − | 0.650896i | \(-0.774393\pi\) | ||||
−0.759167 | + | 0.650896i | \(0.774393\pi\) | |||||||
\(62\) | 1.52027e6 | 0.810119 | ||||||||
\(63\) | 1.11692e6 | 0.562771 | ||||||||
\(64\) | 1.16630e7 | 5.56135 | ||||||||
\(65\) | 144392. | 0.0652147 | ||||||||
\(66\) | −2.79567e6 | −1.19697 | ||||||||
\(67\) | 2.11862e6 | 0.860581 | 0.430290 | − | 0.902691i | \(-0.358411\pi\) | ||||
0.430290 | + | 0.902691i | \(0.358411\pi\) | |||||||
\(68\) | −5.26531e6 | −2.03068 | ||||||||
\(69\) | −2.90781e6 | −1.06560 | ||||||||
\(70\) | 2.88658e6 | 1.00587 | ||||||||
\(71\) | −1.64750e6 | −0.546289 | −0.273144 | − | 0.961973i | \(-0.588064\pi\) | ||||
−0.273144 | + | 0.961973i | \(0.588064\pi\) | |||||||
\(72\) | −3.93903e6 | −1.24373 | ||||||||
\(73\) | −2.91422e6 | −0.876783 | −0.438391 | − | 0.898784i | \(-0.644452\pi\) | ||||
−0.438391 | + | 0.898784i | \(0.644452\pi\) | |||||||
\(74\) | 6.91062e6 | 1.98247 | ||||||||
\(75\) | −1.91697e6 | −0.524687 | ||||||||
\(76\) | −8.10630e6 | −2.11824 | ||||||||
\(77\) | 7.10818e6 | 1.77436 | ||||||||
\(78\) | 1.03071e6 | 0.245928 | ||||||||
\(79\) | 171784. | 0.0392002 | 0.0196001 | − | 0.999808i | \(-0.493761\pi\) | ||||
0.0196001 | + | 0.999808i | \(0.493761\pi\) | |||||||
\(80\) | −6.18095e6 | −1.34971 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.94930e7 | −3.90418 | ||||||||
\(83\) | 4.94728e6 | 0.949714 | 0.474857 | − | 0.880063i | \(-0.342500\pi\) | ||||
0.474857 | + | 0.880063i | \(0.342500\pi\) | |||||||
\(84\) | 1.53103e7 | 2.81842 | ||||||||
\(85\) | 1.20096e6 | 0.212110 | ||||||||
\(86\) | −3.56266e6 | −0.603990 | ||||||||
\(87\) | −5.26854e6 | −0.857773 | ||||||||
\(88\) | −2.50683e7 | −3.92135 | ||||||||
\(89\) | −1.83391e6 | −0.275748 | −0.137874 | − | 0.990450i | \(-0.544027\pi\) | ||||
−0.137874 | + | 0.990450i | \(0.544027\pi\) | |||||||
\(90\) | 1.37346e6 | 0.198594 | ||||||||
\(91\) | −2.62066e6 | −0.364557 | ||||||||
\(92\) | −3.98589e7 | −5.33664 | ||||||||
\(93\) | −1.83918e6 | −0.237101 | ||||||||
\(94\) | 1.37343e7 | 1.70553 | ||||||||
\(95\) | 1.84896e6 | 0.221255 | ||||||||
\(96\) | −2.54477e7 | −2.93561 | ||||||||
\(97\) | −1.09662e7 | −1.21998 | −0.609992 | − | 0.792408i | \(-0.708827\pi\) | ||||
−0.609992 | + | 0.792408i | \(0.708827\pi\) | |||||||
\(98\) | −3.40104e7 | −3.65023 | ||||||||
\(99\) | 3.38213e6 | 0.350322 | ||||||||
\(100\) | −2.62770e7 | −2.62770 | ||||||||
\(101\) | −7.80317e6 | −0.753610 | −0.376805 | − | 0.926293i | \(-0.622977\pi\) | ||||
−0.376805 | + | 0.926293i | \(0.622977\pi\) | |||||||
\(102\) | 8.57282e6 | 0.799877 | ||||||||
\(103\) | −150244. | −0.0135477 | −0.00677386 | − | 0.999977i | \(-0.502156\pi\) | ||||
−0.00677386 | + | 0.999977i | \(0.502156\pi\) | |||||||
\(104\) | 9.24223e6 | 0.805675 | ||||||||
\(105\) | −3.49211e6 | −0.294391 | ||||||||
\(106\) | 1.66482e7 | 1.35768 | ||||||||
\(107\) | 8.15970e6 | 0.643918 | 0.321959 | − | 0.946754i | \(-0.395659\pi\) | ||||
0.321959 | + | 0.946754i | \(0.395659\pi\) | |||||||
\(108\) | 7.28476e6 | 0.556457 | ||||||||
\(109\) | 6.65386e6 | 0.492131 | 0.246066 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246066 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(110\) | 8.74078e6 | 0.626147 | ||||||||
\(111\) | −8.36027e6 | −0.580217 | ||||||||
\(112\) | 1.12182e8 | 7.54502 | ||||||||
\(113\) | 1.76235e7 | 1.14899 | 0.574496 | − | 0.818507i | \(-0.305198\pi\) | ||||
0.574496 | + | 0.818507i | \(0.305198\pi\) | |||||||
\(114\) | 1.31984e7 | 0.834364 | ||||||||
\(115\) | 9.09137e6 | 0.557426 | ||||||||
\(116\) | −7.22187e7 | −4.29583 | ||||||||
\(117\) | −1.24693e6 | −0.0719767 | ||||||||
\(118\) | 4.58370e6 | 0.256820 | ||||||||
\(119\) | −2.17970e7 | −1.18572 | ||||||||
\(120\) | 1.23155e7 | 0.650607 | ||||||||
\(121\) | 2.03695e6 | 0.104528 | ||||||||
\(122\) | 6.00733e7 | 2.99517 | ||||||||
\(123\) | 2.35821e7 | 1.14265 | ||||||||
\(124\) | −2.52106e7 | −1.18743 | ||||||||
\(125\) | 1.25885e7 | 0.576487 | ||||||||
\(126\) | −2.49278e7 | −1.11016 | ||||||||
\(127\) | −2.94003e7 | −1.27362 | −0.636808 | − | 0.771023i | \(-0.719745\pi\) | ||||
−0.636808 | + | 0.771023i | \(0.719745\pi\) | |||||||
\(128\) | −1.39656e8 | −5.88608 | ||||||||
\(129\) | 4.31001e6 | 0.176772 | ||||||||
\(130\) | −3.22257e6 | −0.128647 | ||||||||
\(131\) | 4.56665e6 | 0.177480 | 0.0887398 | − | 0.996055i | \(-0.471716\pi\) | ||||
0.0887398 | + | 0.996055i | \(0.471716\pi\) | |||||||
\(132\) | 4.63607e7 | 1.75445 | ||||||||
\(133\) | −3.35579e7 | −1.23684 | ||||||||
\(134\) | −4.72839e7 | −1.69764 | ||||||||
\(135\) | −1.66157e6 | −0.0581234 | ||||||||
\(136\) | 7.68709e7 | 2.62045 | ||||||||
\(137\) | 3.33611e6 | 0.110846 | 0.0554228 | − | 0.998463i | \(-0.482349\pi\) | ||||
0.0554228 | + | 0.998463i | \(0.482349\pi\) | |||||||
\(138\) | 6.48971e7 | 2.10208 | ||||||||
\(139\) | 2.57204e7 | 0.812317 | 0.406158 | − | 0.913803i | \(-0.366868\pi\) | ||||
0.406158 | + | 0.913803i | \(0.366868\pi\) | |||||||
\(140\) | −4.78682e7 | −1.47435 | ||||||||
\(141\) | −1.66154e7 | −0.499166 | ||||||||
\(142\) | 3.67694e7 | 1.07765 | ||||||||
\(143\) | −7.93556e6 | −0.226935 | ||||||||
\(144\) | 5.33771e7 | 1.48966 | ||||||||
\(145\) | 1.64723e7 | 0.448710 | ||||||||
\(146\) | 6.50402e7 | 1.72961 | ||||||||
\(147\) | 4.11448e7 | 1.06833 | ||||||||
\(148\) | −1.14599e8 | −2.90579 | ||||||||
\(149\) | −7.15213e7 | −1.77127 | −0.885633 | − | 0.464387i | \(-0.846275\pi\) | ||||
−0.885633 | + | 0.464387i | \(0.846275\pi\) | |||||||
\(150\) | 4.27834e7 | 1.03504 | ||||||||
\(151\) | 3.70730e7 | 0.876271 | 0.438135 | − | 0.898909i | \(-0.355639\pi\) | ||||
0.438135 | + | 0.898909i | \(0.355639\pi\) | |||||||
\(152\) | 1.18348e8 | 2.73343 | ||||||||
\(153\) | −1.03712e7 | −0.234103 | ||||||||
\(154\) | −1.58642e8 | −3.50023 | ||||||||
\(155\) | 5.75026e6 | 0.124030 | ||||||||
\(156\) | −1.70924e7 | −0.360467 | ||||||||
\(157\) | −5.84600e7 | −1.20562 | −0.602810 | − | 0.797885i | \(-0.705952\pi\) | ||||
−0.602810 | + | 0.797885i | \(0.705952\pi\) | |||||||
\(158\) | −3.83392e6 | −0.0773291 | ||||||||
\(159\) | −2.01405e7 | −0.397357 | ||||||||
\(160\) | 7.95632e7 | 1.53565 | ||||||||
\(161\) | −1.65005e8 | −3.11607 | ||||||||
\(162\) | −1.18608e7 | −0.219186 | ||||||||
\(163\) | 1.08299e8 | 1.95869 | 0.979346 | − | 0.202190i | \(-0.0648057\pi\) | ||||
0.979346 | + | 0.202190i | \(0.0648057\pi\) | |||||||
\(164\) | 3.23252e8 | 5.72253 | ||||||||
\(165\) | −1.05744e7 | −0.183257 | ||||||||
\(166\) | −1.10415e8 | −1.87347 | ||||||||
\(167\) | −6.99062e6 | −0.116147 | −0.0580735 | − | 0.998312i | \(-0.518496\pi\) | ||||
−0.0580735 | + | 0.998312i | \(0.518496\pi\) | |||||||
\(168\) | −2.23523e8 | −3.63697 | ||||||||
\(169\) | −5.98228e7 | −0.953374 | ||||||||
\(170\) | −2.68033e7 | −0.418424 | ||||||||
\(171\) | −1.59671e7 | −0.244197 | ||||||||
\(172\) | 5.90797e7 | 0.885296 | ||||||||
\(173\) | −9.78233e7 | −1.43642 | −0.718209 | − | 0.695827i | \(-0.755038\pi\) | ||||
−0.718209 | + | 0.695827i | \(0.755038\pi\) | |||||||
\(174\) | 1.17584e8 | 1.69211 | ||||||||
\(175\) | −1.08780e8 | −1.53431 | ||||||||
\(176\) | 3.39696e8 | 4.69674 | ||||||||
\(177\) | −5.54523e6 | −0.0751646 | ||||||||
\(178\) | 4.09296e7 | 0.543961 | ||||||||
\(179\) | 7.71690e7 | 1.00567 | 0.502837 | − | 0.864381i | \(-0.332290\pi\) | ||||
0.502837 | + | 0.864381i | \(0.332290\pi\) | |||||||
\(180\) | −2.27761e7 | −0.291089 | ||||||||
\(181\) | −6.26316e7 | −0.785088 | −0.392544 | − | 0.919733i | \(-0.628405\pi\) | ||||
−0.392544 | + | 0.919733i | \(0.628405\pi\) | |||||||
\(182\) | 5.84885e7 | 0.719152 | ||||||||
\(183\) | −7.26750e7 | −0.876610 | ||||||||
\(184\) | 5.81921e8 | 6.88655 | ||||||||
\(185\) | 2.61387e7 | 0.303517 | ||||||||
\(186\) | 4.10472e7 | 0.467723 | ||||||||
\(187\) | −6.60028e7 | −0.738103 | ||||||||
\(188\) | −2.27757e8 | −2.49988 | ||||||||
\(189\) | 3.01569e7 | 0.324916 | ||||||||
\(190\) | −4.12654e7 | −0.436464 | ||||||||
\(191\) | −2.82767e7 | −0.293638 | −0.146819 | − | 0.989163i | \(-0.546903\pi\) | ||||
−0.146819 | + | 0.989163i | \(0.546903\pi\) | |||||||
\(192\) | 3.14901e8 | 3.21084 | ||||||||
\(193\) | −3.31268e7 | −0.331688 | −0.165844 | − | 0.986152i | \(-0.553035\pi\) | ||||
−0.165844 | + | 0.986152i | \(0.553035\pi\) | |||||||
\(194\) | 2.44746e8 | 2.40663 | ||||||||
\(195\) | 3.89858e6 | 0.0376517 | ||||||||
\(196\) | 5.63995e8 | 5.35031 | ||||||||
\(197\) | −1.09797e8 | −1.02320 | −0.511598 | − | 0.859225i | \(-0.670946\pi\) | ||||
−0.511598 | + | 0.859225i | \(0.670946\pi\) | |||||||
\(198\) | −7.54832e7 | −0.691070 | ||||||||
\(199\) | 1.14654e8 | 1.03134 | 0.515671 | − | 0.856787i | \(-0.327543\pi\) | ||||
0.515671 | + | 0.856787i | \(0.327543\pi\) | |||||||
\(200\) | 3.83631e8 | 3.39085 | ||||||||
\(201\) | 5.72028e7 | 0.496856 | ||||||||
\(202\) | 1.74153e8 | 1.48663 | ||||||||
\(203\) | −2.98966e8 | −2.50834 | ||||||||
\(204\) | −1.42163e8 | −1.17242 | ||||||||
\(205\) | −7.37302e7 | −0.597733 | ||||||||
\(206\) | 3.35318e6 | 0.0267252 | ||||||||
\(207\) | −7.85108e7 | −0.615224 | ||||||||
\(208\) | −1.25240e8 | −0.964985 | ||||||||
\(209\) | −1.01616e8 | −0.769927 | ||||||||
\(210\) | 7.79377e7 | 0.580737 | ||||||||
\(211\) | −1.35295e8 | −0.991502 | −0.495751 | − | 0.868465i | \(-0.665107\pi\) | ||||
−0.495751 | + | 0.868465i | \(0.665107\pi\) | |||||||
\(212\) | −2.76077e8 | −1.99001 | ||||||||
\(213\) | −4.44826e7 | −0.315400 | ||||||||
\(214\) | −1.82110e8 | −1.27024 | ||||||||
\(215\) | −1.34754e7 | −0.0924714 | ||||||||
\(216\) | −1.06354e8 | −0.718067 | ||||||||
\(217\) | −1.04365e8 | −0.693341 | ||||||||
\(218\) | −1.48502e8 | −0.970814 | ||||||||
\(219\) | −7.86839e7 | −0.506211 | ||||||||
\(220\) | −1.44949e8 | −0.917772 | ||||||||
\(221\) | 2.43341e7 | 0.151650 | ||||||||
\(222\) | 1.86587e8 | 1.14458 | ||||||||
\(223\) | 9.14456e7 | 0.552199 | 0.276100 | − | 0.961129i | \(-0.410958\pi\) | ||||
0.276100 | + | 0.961129i | \(0.410958\pi\) | |||||||
\(224\) | −1.44404e9 | −8.58445 | ||||||||
\(225\) | −5.17582e7 | −0.302928 | ||||||||
\(226\) | −3.93325e8 | −2.26659 | ||||||||
\(227\) | −8.92462e7 | −0.506406 | −0.253203 | − | 0.967413i | \(-0.581484\pi\) | ||||
−0.253203 | + | 0.967413i | \(0.581484\pi\) | |||||||
\(228\) | −2.18870e8 | −1.22297 | ||||||||
\(229\) | 2.51758e8 | 1.38535 | 0.692673 | − | 0.721251i | \(-0.256433\pi\) | ||||
0.692673 | + | 0.721251i | \(0.256433\pi\) | |||||||
\(230\) | −2.02903e8 | −1.09962 | ||||||||
\(231\) | 1.91921e8 | 1.02443 | ||||||||
\(232\) | 1.05436e9 | 5.54345 | ||||||||
\(233\) | 3.50359e8 | 1.81455 | 0.907273 | − | 0.420542i | \(-0.138160\pi\) | ||||
0.907273 | + | 0.420542i | \(0.138160\pi\) | |||||||
\(234\) | 2.78293e7 | 0.141986 | ||||||||
\(235\) | 5.19488e7 | 0.261119 | ||||||||
\(236\) | −7.60116e7 | −0.376433 | ||||||||
\(237\) | 4.63817e6 | 0.0226322 | ||||||||
\(238\) | 4.86470e8 | 2.33903 | ||||||||
\(239\) | 1.94400e8 | 0.921092 | 0.460546 | − | 0.887636i | \(-0.347654\pi\) | ||||
0.460546 | + | 0.887636i | \(0.347654\pi\) | |||||||
\(240\) | −1.66886e8 | −0.779255 | ||||||||
\(241\) | 6.19386e7 | 0.285038 | 0.142519 | − | 0.989792i | \(-0.454480\pi\) | ||||
0.142519 | + | 0.989792i | \(0.454480\pi\) | |||||||
\(242\) | −4.54612e7 | −0.206199 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | −9.96197e8 | −4.39017 | ||||||||
\(245\) | −1.28641e8 | −0.558853 | ||||||||
\(246\) | −5.26310e8 | −2.25408 | ||||||||
\(247\) | 3.74639e7 | 0.158188 | ||||||||
\(248\) | 3.68063e8 | 1.53229 | ||||||||
\(249\) | 1.33576e8 | 0.548318 | ||||||||
\(250\) | −2.80954e8 | −1.13722 | ||||||||
\(251\) | 2.42156e8 | 0.966577 | 0.483289 | − | 0.875461i | \(-0.339442\pi\) | ||||
0.483289 | + | 0.875461i | \(0.339442\pi\) | |||||||
\(252\) | 4.13378e8 | 1.62722 | ||||||||
\(253\) | −4.99648e8 | −1.93974 | ||||||||
\(254\) | 6.56162e8 | 2.51243 | ||||||||
\(255\) | 3.24259e7 | 0.122462 | ||||||||
\(256\) | 1.62403e9 | 6.04996 | ||||||||
\(257\) | −3.80530e8 | −1.39837 | −0.699187 | − | 0.714939i | \(-0.746454\pi\) | ||||
−0.699187 | + | 0.714939i | \(0.746454\pi\) | |||||||
\(258\) | −9.61918e7 | −0.348714 | ||||||||
\(259\) | −4.74409e8 | −1.69669 | ||||||||
\(260\) | 5.34400e7 | 0.188564 | ||||||||
\(261\) | −1.42250e8 | −0.495236 | ||||||||
\(262\) | −1.01920e8 | −0.350109 | ||||||||
\(263\) | −1.88914e8 | −0.640353 | −0.320176 | − | 0.947358i | \(-0.603742\pi\) | ||||
−0.320176 | + | 0.947358i | \(0.603742\pi\) | |||||||
\(264\) | −6.76844e8 | −2.26399 | ||||||||
\(265\) | 6.29702e7 | 0.207862 | ||||||||
\(266\) | 7.48953e8 | 2.43988 | ||||||||
\(267\) | −4.95155e7 | −0.159203 | ||||||||
\(268\) | 7.84110e8 | 2.48832 | ||||||||
\(269\) | 2.07575e8 | 0.650194 | 0.325097 | − | 0.945681i | \(-0.394603\pi\) | ||||
0.325097 | + | 0.945681i | \(0.394603\pi\) | |||||||
\(270\) | 3.70834e7 | 0.114658 | ||||||||
\(271\) | −7.81832e7 | −0.238628 | −0.119314 | − | 0.992857i | \(-0.538069\pi\) | ||||
−0.119314 | + | 0.992857i | \(0.538069\pi\) | |||||||
\(272\) | −1.04166e9 | −3.13860 | ||||||||
\(273\) | −7.07578e7 | −0.210477 | ||||||||
\(274\) | −7.44562e7 | −0.218662 | ||||||||
\(275\) | −3.29393e8 | −0.955102 | ||||||||
\(276\) | −1.07619e9 | −3.08111 | ||||||||
\(277\) | −1.30983e8 | −0.370284 | −0.185142 | − | 0.982712i | \(-0.559274\pi\) | ||||
−0.185142 | + | 0.982712i | \(0.559274\pi\) | |||||||
\(278\) | −5.74033e8 | −1.60243 | ||||||||
\(279\) | −4.96578e7 | −0.136890 | ||||||||
\(280\) | 6.98853e8 | 1.90253 | ||||||||
\(281\) | 1.69682e8 | 0.456209 | 0.228105 | − | 0.973637i | \(-0.426747\pi\) | ||||
0.228105 | + | 0.973637i | \(0.426747\pi\) | |||||||
\(282\) | 3.70827e8 | 0.984691 | ||||||||
\(283\) | 2.01304e8 | 0.527958 | 0.263979 | − | 0.964528i | \(-0.414965\pi\) | ||||
0.263979 | + | 0.964528i | \(0.414965\pi\) | |||||||
\(284\) | −6.09748e8 | −1.57956 | ||||||||
\(285\) | 4.99218e7 | 0.127742 | ||||||||
\(286\) | 1.77108e8 | 0.447668 | ||||||||
\(287\) | 1.33818e9 | 3.34139 | ||||||||
\(288\) | −6.87088e8 | −1.69488 | ||||||||
\(289\) | −2.07944e8 | −0.506761 | ||||||||
\(290\) | −3.67632e8 | −0.885158 | ||||||||
\(291\) | −2.96087e8 | −0.704358 | ||||||||
\(292\) | −1.07856e9 | −2.53516 | ||||||||
\(293\) | −4.63019e7 | −0.107538 | −0.0537691 | − | 0.998553i | \(-0.517123\pi\) | ||||
−0.0537691 | + | 0.998553i | \(0.517123\pi\) | |||||||
\(294\) | −9.18280e8 | −2.10746 | ||||||||
\(295\) | 1.73374e7 | 0.0393194 | ||||||||
\(296\) | 1.67309e9 | 3.74971 | ||||||||
\(297\) | 9.13175e7 | 0.202258 | ||||||||
\(298\) | 1.59623e9 | 3.49413 | ||||||||
\(299\) | 1.84211e8 | 0.398536 | ||||||||
\(300\) | −7.09478e8 | −1.51710 | ||||||||
\(301\) | 2.44574e8 | 0.516925 | ||||||||
\(302\) | −8.27404e8 | −1.72859 | ||||||||
\(303\) | −2.10686e8 | −0.435097 | ||||||||
\(304\) | −1.60371e9 | −3.27393 | ||||||||
\(305\) | 2.27221e8 | 0.458564 | ||||||||
\(306\) | 2.31466e8 | 0.461809 | ||||||||
\(307\) | −8.24546e8 | −1.62641 | −0.813206 | − | 0.581975i | \(-0.802280\pi\) | ||||
−0.813206 | + | 0.581975i | \(0.802280\pi\) | |||||||
\(308\) | 2.63077e9 | 5.13044 | ||||||||
\(309\) | −4.05658e6 | −0.00782178 | ||||||||
\(310\) | −1.28336e8 | −0.244671 | ||||||||
\(311\) | 8.21297e8 | 1.54824 | 0.774121 | − | 0.633038i | \(-0.218192\pi\) | ||||
0.774121 | + | 0.633038i | \(0.218192\pi\) | |||||||
\(312\) | 2.49540e8 | 0.465157 | ||||||||
\(313\) | 4.00974e8 | 0.739113 | 0.369557 | − | 0.929208i | \(-0.379510\pi\) | ||||
0.369557 | + | 0.929208i | \(0.379510\pi\) | |||||||
\(314\) | 1.30472e9 | 2.37829 | ||||||||
\(315\) | −9.42868e7 | −0.169967 | ||||||||
\(316\) | 6.35779e7 | 0.113345 | ||||||||
\(317\) | 2.03257e8 | 0.358375 | 0.179187 | − | 0.983815i | \(-0.442653\pi\) | ||||
0.179187 | + | 0.983815i | \(0.442653\pi\) | |||||||
\(318\) | 4.49501e8 | 0.783855 | ||||||||
\(319\) | −9.05292e8 | −1.56143 | ||||||||
\(320\) | −9.84549e8 | −1.67963 | ||||||||
\(321\) | 2.20312e8 | 0.371766 | ||||||||
\(322\) | 3.68263e9 | 6.14699 | ||||||||
\(323\) | 3.11601e8 | 0.514505 | ||||||||
\(324\) | 1.96688e8 | 0.321271 | ||||||||
\(325\) | 1.21441e8 | 0.196234 | ||||||||
\(326\) | −2.41704e9 | −3.86386 | ||||||||
\(327\) | 1.79654e8 | 0.284132 | ||||||||
\(328\) | −4.71932e9 | −7.38451 | ||||||||
\(329\) | −9.42853e8 | −1.45968 | ||||||||
\(330\) | 2.36001e8 | 0.361506 | ||||||||
\(331\) | 4.59053e8 | 0.695769 | 0.347884 | − | 0.937537i | \(-0.386900\pi\) | ||||
0.347884 | + | 0.937537i | \(0.386900\pi\) | |||||||
\(332\) | 1.83101e9 | 2.74604 | ||||||||
\(333\) | −2.25727e8 | −0.334988 | ||||||||
\(334\) | 1.56018e8 | 0.229120 | ||||||||
\(335\) | −1.78847e8 | −0.259911 | ||||||||
\(336\) | 3.02892e9 | 4.35612 | ||||||||
\(337\) | −1.03100e9 | −1.46741 | −0.733706 | − | 0.679467i | \(-0.762211\pi\) | ||||
−0.733706 | + | 0.679467i | \(0.762211\pi\) | |||||||
\(338\) | 1.33514e9 | 1.88070 | ||||||||
\(339\) | 4.75834e8 | 0.663371 | ||||||||
\(340\) | 4.44479e8 | 0.613303 | ||||||||
\(341\) | −3.16026e8 | −0.431601 | ||||||||
\(342\) | 3.56358e8 | 0.481720 | ||||||||
\(343\) | 1.07301e9 | 1.43574 | ||||||||
\(344\) | −8.62534e8 | −1.14241 | ||||||||
\(345\) | 2.45467e8 | 0.321830 | ||||||||
\(346\) | 2.18324e9 | 2.83358 | ||||||||
\(347\) | 8.50881e8 | 1.09324 | 0.546620 | − | 0.837381i | \(-0.315914\pi\) | ||||
0.546620 | + | 0.837381i | \(0.315914\pi\) | |||||||
\(348\) | −1.94991e9 | −2.48020 | ||||||||
\(349\) | −7.28476e8 | −0.917331 | −0.458666 | − | 0.888609i | \(-0.651672\pi\) | ||||
−0.458666 | + | 0.888609i | \(0.651672\pi\) | |||||||
\(350\) | 2.42777e9 | 3.02670 | ||||||||
\(351\) | −3.36671e7 | −0.0415557 | ||||||||
\(352\) | −4.37268e9 | −5.34377 | ||||||||
\(353\) | 1.14502e9 | 1.38548 | 0.692741 | − | 0.721186i | \(-0.256403\pi\) | ||||
0.692741 | + | 0.721186i | \(0.256403\pi\) | |||||||
\(354\) | 1.23760e8 | 0.148275 | ||||||||
\(355\) | 1.39077e8 | 0.164989 | ||||||||
\(356\) | −6.78737e8 | −0.797309 | ||||||||
\(357\) | −5.88518e8 | −0.684575 | ||||||||
\(358\) | −1.72228e9 | −1.98387 | ||||||||
\(359\) | 4.66157e8 | 0.531743 | 0.265871 | − | 0.964008i | \(-0.414340\pi\) | ||||
0.265871 | + | 0.964008i | \(0.414340\pi\) | |||||||
\(360\) | 3.32520e8 | 0.375628 | ||||||||
\(361\) | −4.14141e8 | −0.463312 | ||||||||
\(362\) | 1.39783e9 | 1.54872 | ||||||||
\(363\) | 5.49977e7 | 0.0603491 | ||||||||
\(364\) | −9.69917e8 | −1.05409 | ||||||||
\(365\) | 2.46008e8 | 0.264804 | ||||||||
\(366\) | 1.62198e9 | 1.72926 | ||||||||
\(367\) | 1.98730e8 | 0.209861 | 0.104930 | − | 0.994480i | \(-0.466538\pi\) | ||||
0.104930 | + | 0.994480i | \(0.466538\pi\) | |||||||
\(368\) | −7.88551e9 | −8.24826 | ||||||||
\(369\) | 6.36716e8 | 0.659710 | ||||||||
\(370\) | −5.83370e8 | −0.598740 | ||||||||
\(371\) | −1.14289e9 | −1.16197 | ||||||||
\(372\) | −6.80687e8 | −0.685563 | ||||||||
\(373\) | 9.45866e8 | 0.943732 | 0.471866 | − | 0.881670i | \(-0.343581\pi\) | ||||
0.471866 | + | 0.881670i | \(0.343581\pi\) | |||||||
\(374\) | 1.47307e9 | 1.45604 | ||||||||
\(375\) | 3.39890e8 | 0.332835 | ||||||||
\(376\) | 3.32514e9 | 3.22591 | ||||||||
\(377\) | 3.33765e8 | 0.320809 | ||||||||
\(378\) | −6.73050e8 | −0.640953 | ||||||||
\(379\) | −1.07925e9 | −1.01832 | −0.509162 | − | 0.860671i | \(-0.670044\pi\) | ||||
−0.509162 | + | 0.860671i | \(0.670044\pi\) | |||||||
\(380\) | 6.84306e8 | 0.639746 | ||||||||
\(381\) | −7.93807e8 | −0.735322 | ||||||||
\(382\) | 6.31086e8 | 0.579251 | ||||||||
\(383\) | −5.46503e8 | −0.497046 | −0.248523 | − | 0.968626i | \(-0.579945\pi\) | ||||
−0.248523 | + | 0.968626i | \(0.579945\pi\) | |||||||
\(384\) | −3.77073e9 | −3.39833 | ||||||||
\(385\) | −6.00048e8 | −0.535888 | ||||||||
\(386\) | 7.39333e8 | 0.654311 | ||||||||
\(387\) | 1.16370e8 | 0.102060 | ||||||||
\(388\) | −4.05863e9 | −3.52751 | ||||||||
\(389\) | −6.83446e8 | −0.588682 | −0.294341 | − | 0.955700i | \(-0.595100\pi\) | ||||
−0.294341 | + | 0.955700i | \(0.595100\pi\) | |||||||
\(390\) | −8.70094e7 | −0.0742745 | ||||||||
\(391\) | 1.53215e9 | 1.29623 | ||||||||
\(392\) | −8.23405e9 | −6.90418 | ||||||||
\(393\) | 1.23300e8 | 0.102468 | ||||||||
\(394\) | 2.45048e9 | 2.01843 | ||||||||
\(395\) | −1.45014e7 | −0.0118391 | ||||||||
\(396\) | 1.25174e9 | 1.01293 | ||||||||
\(397\) | −1.21932e9 | −0.978030 | −0.489015 | − | 0.872275i | \(-0.662644\pi\) | ||||
−0.489015 | + | 0.872275i | \(0.662644\pi\) | |||||||
\(398\) | −2.55887e9 | −2.03450 | ||||||||
\(399\) | −9.06063e8 | −0.714091 | ||||||||
\(400\) | −5.19851e9 | −4.06134 | ||||||||
\(401\) | −1.27738e9 | −0.989268 | −0.494634 | − | 0.869101i | \(-0.664698\pi\) | ||||
−0.494634 | + | 0.869101i | \(0.664698\pi\) | |||||||
\(402\) | −1.27667e9 | −0.980135 | ||||||||
\(403\) | 1.16513e8 | 0.0886762 | ||||||||
\(404\) | −2.88799e9 | −2.17902 | ||||||||
\(405\) | −4.48624e7 | −0.0335575 | ||||||||
\(406\) | 6.67240e9 | 4.94813 | ||||||||
\(407\) | −1.43655e9 | −1.05618 | ||||||||
\(408\) | 2.07551e9 | 1.51292 | ||||||||
\(409\) | −1.52758e9 | −1.10401 | −0.552004 | − | 0.833842i | \(-0.686137\pi\) | ||||
−0.552004 | + | 0.833842i | \(0.686137\pi\) | |||||||
\(410\) | 1.64553e9 | 1.17913 | ||||||||
\(411\) | 9.00750e7 | 0.0639968 | ||||||||
\(412\) | −5.56058e7 | −0.0391724 | ||||||||
\(413\) | −3.14668e8 | −0.219800 | ||||||||
\(414\) | 1.75222e9 | 1.21364 | ||||||||
\(415\) | −4.17632e8 | −0.286831 | ||||||||
\(416\) | 1.61213e9 | 1.09792 | ||||||||
\(417\) | 6.94450e8 | 0.468991 | ||||||||
\(418\) | 2.26789e9 | 1.51881 | ||||||||
\(419\) | 2.15816e9 | 1.43329 | 0.716645 | − | 0.697438i | \(-0.245677\pi\) | ||||
0.716645 | + | 0.697438i | \(0.245677\pi\) | |||||||
\(420\) | −1.29244e9 | −0.851214 | ||||||||
\(421\) | −4.86121e8 | −0.317509 | −0.158755 | − | 0.987318i | \(-0.550748\pi\) | ||||
−0.158755 | + | 0.987318i | \(0.550748\pi\) | |||||||
\(422\) | 3.01955e9 | 1.95591 | ||||||||
\(423\) | −4.48617e8 | −0.288193 | ||||||||
\(424\) | 4.03059e9 | 2.56796 | ||||||||
\(425\) | 1.01007e9 | 0.638249 | ||||||||
\(426\) | 9.92773e8 | 0.622181 | ||||||||
\(427\) | −4.12399e9 | −2.56342 | ||||||||
\(428\) | 3.01994e9 | 1.86185 | ||||||||
\(429\) | −2.14260e8 | −0.131021 | ||||||||
\(430\) | 3.00747e8 | 0.182416 | ||||||||
\(431\) | 8.97584e8 | 0.540013 | 0.270007 | − | 0.962858i | \(-0.412974\pi\) | ||||
0.270007 | + | 0.962858i | \(0.412974\pi\) | |||||||
\(432\) | 1.44118e9 | 0.860054 | ||||||||
\(433\) | −1.07413e8 | −0.0635843 | −0.0317921 | − | 0.999495i | \(-0.510121\pi\) | ||||
−0.0317921 | + | 0.999495i | \(0.510121\pi\) | |||||||
\(434\) | 2.32925e9 | 1.36773 | ||||||||
\(435\) | 4.44752e8 | 0.259063 | ||||||||
\(436\) | 2.46262e9 | 1.42297 | ||||||||
\(437\) | 2.35885e9 | 1.35212 | ||||||||
\(438\) | 1.75609e9 | 0.998588 | ||||||||
\(439\) | −4.23839e8 | −0.239097 | −0.119549 | − | 0.992828i | \(-0.538145\pi\) | ||||
−0.119549 | + | 0.992828i | \(0.538145\pi\) | |||||||
\(440\) | 2.11618e9 | 1.18432 | ||||||||
\(441\) | 1.11091e9 | 0.616799 | ||||||||
\(442\) | −5.43094e8 | −0.299155 | ||||||||
\(443\) | −1.56918e9 | −0.857552 | −0.428776 | − | 0.903411i | \(-0.641055\pi\) | ||||
−0.428776 | + | 0.903411i | \(0.641055\pi\) | |||||||
\(444\) | −3.09417e9 | −1.67766 | ||||||||
\(445\) | 1.54812e8 | 0.0832809 | ||||||||
\(446\) | −2.04091e9 | −1.08931 | ||||||||
\(447\) | −1.93108e9 | −1.02264 | ||||||||
\(448\) | 1.78692e10 | 9.38929 | ||||||||
\(449\) | −6.52660e8 | −0.340271 | −0.170135 | − | 0.985421i | \(-0.554420\pi\) | ||||
−0.170135 | + | 0.985421i | \(0.554420\pi\) | |||||||
\(450\) | 1.15515e9 | 0.597579 | ||||||||
\(451\) | 4.05210e9 | 2.08000 | ||||||||
\(452\) | 6.52252e9 | 3.32224 | ||||||||
\(453\) | 1.00097e9 | 0.505915 | ||||||||
\(454\) | 1.99182e9 | 0.998974 | ||||||||
\(455\) | 2.21227e8 | 0.110103 | ||||||||
\(456\) | 3.19539e9 | 1.57815 | ||||||||
\(457\) | −3.14784e9 | −1.54278 | −0.771392 | − | 0.636360i | \(-0.780439\pi\) | ||||
−0.771392 | + | 0.636360i | \(0.780439\pi\) | |||||||
\(458\) | −5.61879e9 | −2.73284 | ||||||||
\(459\) | −2.80021e8 | −0.135160 | ||||||||
\(460\) | 3.36475e9 | 1.61176 | ||||||||
\(461\) | 3.81603e9 | 1.81409 | 0.907044 | − | 0.421037i | \(-0.138334\pi\) | ||||
0.907044 | + | 0.421037i | \(0.138334\pi\) | |||||||
\(462\) | −4.28334e9 | −2.02086 | ||||||||
\(463\) | 7.32034e8 | 0.342766 | 0.171383 | − | 0.985204i | \(-0.445176\pi\) | ||||
0.171383 | + | 0.985204i | \(0.445176\pi\) | |||||||
\(464\) | −1.42874e10 | −6.63958 | ||||||||
\(465\) | 1.55257e8 | 0.0716087 | ||||||||
\(466\) | −7.81941e9 | −3.57951 | ||||||||
\(467\) | −9.56937e8 | −0.434785 | −0.217392 | − | 0.976084i | \(-0.569755\pi\) | ||||
−0.217392 | + | 0.976084i | \(0.569755\pi\) | |||||||
\(468\) | −4.61494e8 | −0.208116 | ||||||||
\(469\) | 3.24601e9 | 1.45293 | ||||||||
\(470\) | −1.15941e9 | −0.515102 | ||||||||
\(471\) | −1.57842e9 | −0.696065 | ||||||||
\(472\) | 1.10973e9 | 0.485759 | ||||||||
\(473\) | 7.40589e8 | 0.321783 | ||||||||
\(474\) | −1.03516e8 | −0.0446460 | ||||||||
\(475\) | 1.55507e9 | 0.665767 | ||||||||
\(476\) | −8.06714e9 | −3.42843 | ||||||||
\(477\) | −5.43794e8 | −0.229414 | ||||||||
\(478\) | −4.33866e9 | −1.81701 | ||||||||
\(479\) | 3.19983e9 | 1.33031 | 0.665154 | − | 0.746706i | \(-0.268366\pi\) | ||||
0.665154 | + | 0.746706i | \(0.268366\pi\) | |||||||
\(480\) | 2.14821e9 | 0.886608 | ||||||||
\(481\) | 5.29629e8 | 0.217002 | ||||||||
\(482\) | −1.38236e9 | −0.562286 | ||||||||
\(483\) | −4.45514e9 | −1.79906 | ||||||||
\(484\) | 7.53884e8 | 0.302236 | ||||||||
\(485\) | 9.25727e8 | 0.368457 | ||||||||
\(486\) | −3.20242e8 | −0.126547 | ||||||||
\(487\) | −3.55741e8 | −0.139567 | −0.0697834 | − | 0.997562i | \(-0.522231\pi\) | ||||
−0.0697834 | + | 0.997562i | \(0.522231\pi\) | |||||||
\(488\) | 1.45440e10 | 5.66518 | ||||||||
\(489\) | 2.92406e9 | 1.13085 | ||||||||
\(490\) | 2.87104e9 | 1.10243 | ||||||||
\(491\) | −1.77516e7 | −0.00676788 | −0.00338394 | − | 0.999994i | \(-0.501077\pi\) | ||||
−0.00338394 | + | 0.999994i | \(0.501077\pi\) | |||||||
\(492\) | 8.72781e9 | 3.30391 | ||||||||
\(493\) | 2.77604e9 | 1.04343 | ||||||||
\(494\) | −8.36129e8 | −0.312054 | ||||||||
\(495\) | −2.85508e8 | −0.105803 | ||||||||
\(496\) | −4.98755e9 | −1.83528 | ||||||||
\(497\) | −2.52419e9 | −0.922306 | ||||||||
\(498\) | −2.98119e9 | −1.08165 | ||||||||
\(499\) | 1.97045e9 | 0.709927 | 0.354963 | − | 0.934880i | \(-0.384493\pi\) | ||||
0.354963 | + | 0.934880i | \(0.384493\pi\) | |||||||
\(500\) | 4.65906e9 | 1.66688 | ||||||||
\(501\) | −1.88747e8 | −0.0670575 | ||||||||
\(502\) | −5.40449e9 | −1.90674 | ||||||||
\(503\) | −4.77882e9 | −1.67430 | −0.837148 | − | 0.546976i | \(-0.815779\pi\) | ||||
−0.837148 | + | 0.546976i | \(0.815779\pi\) | |||||||
\(504\) | −6.03511e9 | −2.09980 | ||||||||
\(505\) | 6.58717e8 | 0.227604 | ||||||||
\(506\) | 1.11513e10 | 3.82647 | ||||||||
\(507\) | −1.61522e9 | −0.550431 | ||||||||
\(508\) | −1.08812e10 | −3.68258 | ||||||||
\(509\) | −2.21746e9 | −0.745321 | −0.372660 | − | 0.927968i | \(-0.621554\pi\) | ||||
−0.372660 | + | 0.927968i | \(0.621554\pi\) | |||||||
\(510\) | −7.23688e8 | −0.241577 | ||||||||
\(511\) | −4.46496e9 | −1.48028 | ||||||||
\(512\) | −1.83694e10 | −6.04852 | ||||||||
\(513\) | −4.31112e8 | −0.140987 | ||||||||
\(514\) | 8.49277e9 | 2.75853 | ||||||||
\(515\) | 1.26831e7 | 0.00409165 | ||||||||
\(516\) | 1.59515e9 | 0.511126 | ||||||||
\(517\) | −2.85503e9 | −0.908644 | ||||||||
\(518\) | 1.05880e10 | 3.34702 | ||||||||
\(519\) | −2.64123e9 | −0.829317 | ||||||||
\(520\) | −7.80197e8 | −0.243328 | ||||||||
\(521\) | −2.05916e9 | −0.637908 | −0.318954 | − | 0.947770i | \(-0.603332\pi\) | ||||
−0.318954 | + | 0.947770i | \(0.603332\pi\) | |||||||
\(522\) | 3.17478e9 | 0.976938 | ||||||||
\(523\) | 4.60384e9 | 1.40723 | 0.703614 | − | 0.710582i | \(-0.251568\pi\) | ||||
0.703614 | + | 0.710582i | \(0.251568\pi\) | |||||||
\(524\) | 1.69014e9 | 0.513171 | ||||||||
\(525\) | −2.93705e9 | −0.885836 | ||||||||
\(526\) | 4.21623e9 | 1.26321 | ||||||||
\(527\) | 9.69081e8 | 0.288418 | ||||||||
\(528\) | 9.17179e9 | 2.71166 | ||||||||
\(529\) | 8.19372e9 | 2.40650 | ||||||||
\(530\) | −1.40538e9 | −0.410043 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −1.24199e10 | −3.57625 | ||||||||
\(533\) | −1.49394e9 | −0.427354 | ||||||||
\(534\) | 1.10510e9 | 0.314056 | ||||||||
\(535\) | −6.88814e8 | −0.194475 | ||||||||
\(536\) | −1.14476e10 | −3.21099 | ||||||||
\(537\) | 2.08356e9 | 0.580626 | ||||||||
\(538\) | −4.63272e9 | −1.28262 | ||||||||
\(539\) | 7.06992e9 | 1.94470 | ||||||||
\(540\) | −6.14954e8 | −0.168060 | ||||||||
\(541\) | −5.44524e9 | −1.47852 | −0.739258 | − | 0.673422i | \(-0.764824\pi\) | ||||
−0.739258 | + | 0.673422i | \(0.764824\pi\) | |||||||
\(542\) | 1.74491e9 | 0.470735 | ||||||||
\(543\) | −1.69105e9 | −0.453271 | ||||||||
\(544\) | 1.34086e10 | 3.57099 | ||||||||
\(545\) | −5.61696e8 | −0.148632 | ||||||||
\(546\) | 1.57919e9 | 0.415203 | ||||||||
\(547\) | −2.09397e9 | −0.547035 | −0.273518 | − | 0.961867i | \(-0.588187\pi\) | ||||
−0.273518 | + | 0.961867i | \(0.588187\pi\) | |||||||
\(548\) | 1.23471e9 | 0.320503 | ||||||||
\(549\) | −1.96223e9 | −0.506111 | ||||||||
\(550\) | 7.35147e9 | 1.88410 | ||||||||
\(551\) | 4.27390e9 | 1.08841 | ||||||||
\(552\) | 1.57119e10 | 3.97595 | ||||||||
\(553\) | 2.63196e8 | 0.0661821 | ||||||||
\(554\) | 2.92330e9 | 0.730449 | ||||||||
\(555\) | 7.05746e8 | 0.175236 | ||||||||
\(556\) | 9.51921e9 | 2.34876 | ||||||||
\(557\) | 4.55263e9 | 1.11627 | 0.558135 | − | 0.829750i | \(-0.311517\pi\) | ||||
0.558135 | + | 0.829750i | \(0.311517\pi\) | |||||||
\(558\) | 1.10827e9 | 0.270040 | ||||||||
\(559\) | −2.73042e8 | −0.0661131 | ||||||||
\(560\) | −9.47003e9 | −2.27873 | ||||||||
\(561\) | −1.78208e9 | −0.426144 | ||||||||
\(562\) | −3.78701e9 | −0.899952 | ||||||||
\(563\) | −2.34649e9 | −0.554166 | −0.277083 | − | 0.960846i | \(-0.589368\pi\) | ||||
−0.277083 | + | 0.960846i | \(0.589368\pi\) | |||||||
\(564\) | −6.14944e9 | −1.44331 | ||||||||
\(565\) | −1.48771e9 | −0.347016 | ||||||||
\(566\) | −4.49274e9 | −1.04149 | ||||||||
\(567\) | 8.14237e8 | 0.187590 | ||||||||
\(568\) | 8.90202e9 | 2.03831 | ||||||||
\(569\) | −2.75800e9 | −0.627626 | −0.313813 | − | 0.949485i | \(-0.601606\pi\) | ||||
−0.313813 | + | 0.949485i | \(0.601606\pi\) | |||||||
\(570\) | −1.11417e9 | −0.251993 | ||||||||
\(571\) | −1.49430e9 | −0.335901 | −0.167950 | − | 0.985795i | \(-0.553715\pi\) | ||||
−0.167950 | + | 0.985795i | \(0.553715\pi\) | |||||||
\(572\) | −2.93698e9 | −0.656168 | ||||||||
\(573\) | −7.63470e8 | −0.169532 | ||||||||
\(574\) | −2.98658e10 | −6.59147 | ||||||||
\(575\) | 7.64633e9 | 1.67732 | ||||||||
\(576\) | 8.50232e9 | 1.85378 | ||||||||
\(577\) | −5.27606e8 | −0.114339 | −0.0571695 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571695 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(578\) | 4.64094e9 | 0.999673 | ||||||||
\(579\) | −8.94425e8 | −0.191500 | ||||||||
\(580\) | 6.09646e9 | 1.29742 | ||||||||
\(581\) | 7.57987e9 | 1.60341 | ||||||||
\(582\) | 6.60814e9 | 1.38947 | ||||||||
\(583\) | −3.46075e9 | −0.723319 | ||||||||
\(584\) | 1.57465e10 | 3.27144 | ||||||||
\(585\) | 1.05262e8 | 0.0217382 | ||||||||
\(586\) | 1.03338e9 | 0.212138 | ||||||||
\(587\) | −3.02681e9 | −0.617664 | −0.308832 | − | 0.951117i | \(-0.599938\pi\) | ||||
−0.308832 | + | 0.951117i | \(0.599938\pi\) | |||||||
\(588\) | 1.52279e10 | 3.08900 | ||||||||
\(589\) | 1.49197e9 | 0.300854 | ||||||||
\(590\) | −3.86940e8 | −0.0775643 | ||||||||
\(591\) | −2.96452e9 | −0.590743 | ||||||||
\(592\) | −2.26717e10 | −4.49116 | ||||||||
\(593\) | −7.55687e9 | −1.48816 | −0.744081 | − | 0.668089i | \(-0.767113\pi\) | ||||
−0.744081 | + | 0.668089i | \(0.767113\pi\) | |||||||
\(594\) | −2.03805e9 | −0.398990 | ||||||||
\(595\) | 1.84002e9 | 0.358108 | ||||||||
\(596\) | −2.64703e10 | −5.12150 | ||||||||
\(597\) | 3.09565e9 | 0.595445 | ||||||||
\(598\) | −4.11127e9 | −0.786181 | ||||||||
\(599\) | −7.21826e9 | −1.37227 | −0.686133 | − | 0.727476i | \(-0.740693\pi\) | ||||
−0.686133 | + | 0.727476i | \(0.740693\pi\) | |||||||
\(600\) | 1.03580e10 | 1.95771 | ||||||||
\(601\) | −4.11700e9 | −0.773607 | −0.386803 | − | 0.922162i | \(-0.626421\pi\) | ||||
−0.386803 | + | 0.922162i | \(0.626421\pi\) | |||||||
\(602\) | −5.45846e9 | −1.01972 | ||||||||
\(603\) | 1.54448e9 | 0.286860 | ||||||||
\(604\) | 1.37209e10 | 2.53368 | ||||||||
\(605\) | −1.71952e8 | −0.0315693 | ||||||||
\(606\) | 4.70213e9 | 0.858303 | ||||||||
\(607\) | 3.42535e9 | 0.621649 | 0.310824 | − | 0.950467i | \(-0.399395\pi\) | ||||
0.310824 | + | 0.950467i | \(0.399395\pi\) | |||||||
\(608\) | 2.06435e10 | 3.72495 | ||||||||
\(609\) | −8.07209e9 | −1.44819 | ||||||||
\(610\) | −5.07118e9 | −0.904596 | ||||||||
\(611\) | 1.05260e9 | 0.186689 | ||||||||
\(612\) | −3.83841e9 | −0.676895 | ||||||||
\(613\) | −8.07359e9 | −1.41565 | −0.707823 | − | 0.706390i | \(-0.750323\pi\) | ||||
−0.707823 | + | 0.706390i | \(0.750323\pi\) | |||||||
\(614\) | 1.84024e10 | 3.20838 | ||||||||
\(615\) | −1.99072e9 | −0.345101 | ||||||||
\(616\) | −3.84079e10 | −6.62046 | ||||||||
\(617\) | −7.36421e9 | −1.26220 | −0.631100 | − | 0.775702i | \(-0.717396\pi\) | ||||
−0.631100 | + | 0.775702i | \(0.717396\pi\) | |||||||
\(618\) | 9.05358e7 | 0.0154298 | ||||||||
\(619\) | 9.33576e9 | 1.58210 | 0.791048 | − | 0.611755i | \(-0.209536\pi\) | ||||
0.791048 | + | 0.611755i | \(0.209536\pi\) | |||||||
\(620\) | 2.12820e9 | 0.358625 | ||||||||
\(621\) | −2.11979e9 | −0.355200 | ||||||||
\(622\) | −1.83299e10 | −3.05417 | ||||||||
\(623\) | −2.80979e9 | −0.465549 | ||||||||
\(624\) | −3.38147e9 | −0.557134 | ||||||||
\(625\) | 4.48410e9 | 0.734676 | ||||||||
\(626\) | −8.94903e9 | −1.45803 | ||||||||
\(627\) | −2.74363e9 | −0.444517 | ||||||||
\(628\) | −2.16363e10 | −3.48597 | ||||||||
\(629\) | 4.40511e9 | 0.705796 | ||||||||
\(630\) | 2.10432e9 | 0.335289 | ||||||||
\(631\) | 1.58549e9 | 0.251225 | 0.125612 | − | 0.992079i | \(-0.459910\pi\) | ||||
0.125612 | + | 0.992079i | \(0.459910\pi\) | |||||||
\(632\) | −9.28206e8 | −0.146263 | ||||||||
\(633\) | −3.65297e9 | −0.572444 | ||||||||
\(634\) | −4.53633e9 | −0.706956 | ||||||||
\(635\) | 2.48187e9 | 0.384655 | ||||||||
\(636\) | −7.45409e9 | −1.14893 | ||||||||
\(637\) | −2.60655e9 | −0.399556 | ||||||||
\(638\) | 2.02045e10 | 3.08018 | ||||||||
\(639\) | −1.20103e9 | −0.182096 | ||||||||
\(640\) | 1.17893e10 | 1.77770 | ||||||||
\(641\) | 7.99377e9 | 1.19880 | 0.599402 | − | 0.800448i | \(-0.295405\pi\) | ||||
0.599402 | + | 0.800448i | \(0.295405\pi\) | |||||||
\(642\) | −4.91697e9 | −0.733373 | ||||||||
\(643\) | −2.26242e9 | −0.335610 | −0.167805 | − | 0.985820i | \(-0.553668\pi\) | ||||
−0.167805 | + | 0.985820i | \(0.553668\pi\) | |||||||
\(644\) | −6.10691e10 | −9.00992 | ||||||||
\(645\) | −3.63836e8 | −0.0533884 | ||||||||
\(646\) | −6.95438e9 | −1.01495 | ||||||||
\(647\) | 4.58044e8 | 0.0664879 | 0.0332439 | − | 0.999447i | \(-0.489416\pi\) | ||||
0.0332439 | + | 0.999447i | \(0.489416\pi\) | |||||||
\(648\) | −2.87155e9 | −0.414576 | ||||||||
\(649\) | −9.52837e8 | −0.136824 | ||||||||
\(650\) | −2.71035e9 | −0.387105 | ||||||||
\(651\) | −2.81786e9 | −0.400301 | ||||||||
\(652\) | 4.00818e10 | 5.66344 | ||||||||
\(653\) | 8.67155e9 | 1.21871 | 0.609355 | − | 0.792897i | \(-0.291428\pi\) | ||||
0.609355 | + | 0.792897i | \(0.291428\pi\) | |||||||
\(654\) | −4.00957e9 | −0.560500 | ||||||||
\(655\) | −3.85501e8 | −0.0536020 | ||||||||
\(656\) | 6.39507e10 | 8.84468 | ||||||||
\(657\) | −2.12446e9 | −0.292261 | ||||||||
\(658\) | 2.10428e10 | 2.87947 | ||||||||
\(659\) | 8.76494e9 | 1.19303 | 0.596513 | − | 0.802603i | \(-0.296552\pi\) | ||||
0.596513 | + | 0.802603i | \(0.296552\pi\) | |||||||
\(660\) | −3.91361e9 | −0.529876 | ||||||||
\(661\) | 1.58045e9 | 0.212850 | 0.106425 | − | 0.994321i | \(-0.466060\pi\) | ||||
0.106425 | + | 0.994321i | \(0.466060\pi\) | |||||||
\(662\) | −1.02453e10 | −1.37252 | ||||||||
\(663\) | 6.57020e8 | 0.0875550 | ||||||||
\(664\) | −2.67318e10 | −3.54356 | ||||||||
\(665\) | 2.83284e9 | 0.373548 | ||||||||
\(666\) | 5.03784e9 | 0.660822 | ||||||||
\(667\) | 2.10149e10 | 2.74213 | ||||||||
\(668\) | −2.58726e9 | −0.335832 | ||||||||
\(669\) | 2.46903e9 | 0.318812 | ||||||||
\(670\) | 3.99155e9 | 0.512719 | ||||||||
\(671\) | −1.24877e10 | −1.59572 | ||||||||
\(672\) | −3.89892e10 | −4.95623 | ||||||||
\(673\) | −2.26086e9 | −0.285905 | −0.142952 | − | 0.989730i | \(-0.545660\pi\) | ||||
−0.142952 | + | 0.989730i | \(0.545660\pi\) | |||||||
\(674\) | 2.30100e10 | 2.89472 | ||||||||
\(675\) | −1.39747e9 | −0.174896 | ||||||||
\(676\) | −2.21407e10 | −2.75662 | ||||||||
\(677\) | 6.78561e9 | 0.840483 | 0.420241 | − | 0.907412i | \(-0.361945\pi\) | ||||
0.420241 | + | 0.907412i | \(0.361945\pi\) | |||||||
\(678\) | −1.06198e10 | −1.30861 | ||||||||
\(679\) | −1.68016e10 | −2.05971 | ||||||||
\(680\) | −6.48918e9 | −0.791423 | ||||||||
\(681\) | −2.40965e9 | −0.292374 | ||||||||
\(682\) | 7.05314e9 | 0.851407 | ||||||||
\(683\) | −7.74627e9 | −0.930294 | −0.465147 | − | 0.885234i | \(-0.653998\pi\) | ||||
−0.465147 | + | 0.885234i | \(0.653998\pi\) | |||||||
\(684\) | −5.90949e9 | −0.706080 | ||||||||
\(685\) | −2.81623e8 | −0.0334774 | ||||||||
\(686\) | −2.39477e10 | −2.83224 | ||||||||
\(687\) | 6.79746e9 | 0.799830 | ||||||||
\(688\) | 1.16880e10 | 1.36830 | ||||||||
\(689\) | 1.27592e9 | 0.148612 | ||||||||
\(690\) | −5.47839e9 | −0.634865 | ||||||||
\(691\) | −5.90227e9 | −0.680528 | −0.340264 | − | 0.940330i | \(-0.610516\pi\) | ||||
−0.340264 | + | 0.940330i | \(0.610516\pi\) | |||||||
\(692\) | −3.62048e10 | −4.15331 | ||||||||
\(693\) | 5.18187e9 | 0.591452 | ||||||||
\(694\) | −1.89902e10 | −2.15660 | ||||||||
\(695\) | −2.17122e9 | −0.245334 | ||||||||
\(696\) | 2.84677e10 | 3.20051 | ||||||||
\(697\) | −1.24256e10 | −1.38996 | ||||||||
\(698\) | 1.62583e10 | 1.80959 | ||||||||
\(699\) | 9.45970e9 | 1.04763 | ||||||||
\(700\) | −4.02597e10 | −4.43637 | ||||||||
\(701\) | −1.01648e10 | −1.11452 | −0.557259 | − | 0.830339i | \(-0.688147\pi\) | ||||
−0.557259 | + | 0.830339i | \(0.688147\pi\) | |||||||
\(702\) | 7.51391e8 | 0.0819759 | ||||||||
\(703\) | 6.78196e9 | 0.736227 | ||||||||
\(704\) | 5.41094e10 | 5.84478 | ||||||||
\(705\) | 1.40262e9 | 0.150757 | ||||||||
\(706\) | −2.55548e10 | −2.73310 | ||||||||
\(707\) | −1.19555e10 | −1.27233 | ||||||||
\(708\) | −2.05231e9 | −0.217334 | ||||||||
\(709\) | −7.24332e9 | −0.763266 | −0.381633 | − | 0.924314i | \(-0.624638\pi\) | ||||
−0.381633 | + | 0.924314i | \(0.624638\pi\) | |||||||
\(710\) | −3.10395e9 | −0.325469 | ||||||||
\(711\) | 1.25231e8 | 0.0130667 | ||||||||
\(712\) | 9.90922e9 | 1.02887 | ||||||||
\(713\) | 7.33604e9 | 0.757964 | ||||||||
\(714\) | 1.31347e10 | 1.35044 | ||||||||
\(715\) | 6.69892e8 | 0.0685384 | ||||||||
\(716\) | 2.85606e10 | 2.90784 | ||||||||
\(717\) | 5.24879e9 | 0.531792 | ||||||||
\(718\) | −1.04038e10 | −1.04895 | ||||||||
\(719\) | 1.37810e10 | 1.38270 | 0.691350 | − | 0.722520i | \(-0.257016\pi\) | ||||
0.691350 | + | 0.722520i | \(0.257016\pi\) | |||||||
\(720\) | −4.50591e9 | −0.449903 | ||||||||
\(721\) | −2.30193e8 | −0.0228728 | ||||||||
\(722\) | 9.24290e9 | 0.913962 | ||||||||
\(723\) | 1.67234e9 | 0.164567 | ||||||||
\(724\) | −2.31802e10 | −2.27003 | ||||||||
\(725\) | 1.38541e10 | 1.35019 | ||||||||
\(726\) | −1.22745e9 | −0.119049 | ||||||||
\(727\) | −1.04638e10 | −1.00999 | −0.504996 | − | 0.863122i | \(-0.668506\pi\) | ||||
−0.504996 | + | 0.863122i | \(0.668506\pi\) | |||||||
\(728\) | 1.41603e10 | 1.36023 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −5.49047e9 | −0.522372 | ||||||||
\(731\) | −2.27099e9 | −0.215032 | ||||||||
\(732\) | −2.68973e10 | −2.53466 | ||||||||
\(733\) | −6.09625e9 | −0.571740 | −0.285870 | − | 0.958268i | \(-0.592283\pi\) | ||||
−0.285870 | + | 0.958268i | \(0.592283\pi\) | |||||||
\(734\) | −4.43530e9 | −0.413987 | ||||||||
\(735\) | −3.47331e9 | −0.322654 | ||||||||
\(736\) | 1.01505e11 | 9.38456 | ||||||||
\(737\) | 9.82915e9 | 0.904440 | ||||||||
\(738\) | −1.42104e10 | −1.30139 | ||||||||
\(739\) | 1.62223e10 | 1.47862 | 0.739308 | − | 0.673367i | \(-0.235153\pi\) | ||||
0.739308 | + | 0.673367i | \(0.235153\pi\) | |||||||
\(740\) | 9.67405e9 | 0.877601 | ||||||||
\(741\) | 1.01153e9 | 0.0913300 | ||||||||
\(742\) | 2.55072e10 | 2.29218 | ||||||||
\(743\) | −2.03461e10 | −1.81978 | −0.909891 | − | 0.414847i | \(-0.863835\pi\) | ||||
−0.909891 | + | 0.414847i | \(0.863835\pi\) | |||||||
\(744\) | 9.93770e9 | 0.884668 | ||||||||
\(745\) | 6.03758e9 | 0.534954 | ||||||||
\(746\) | −2.11101e10 | −1.86167 | ||||||||
\(747\) | 3.60656e9 | 0.316571 | ||||||||
\(748\) | −2.44279e10 | −2.13418 | ||||||||
\(749\) | 1.25017e10 | 1.08714 | ||||||||
\(750\) | −7.58575e9 | −0.656575 | ||||||||
\(751\) | 6.71015e9 | 0.578086 | 0.289043 | − | 0.957316i | \(-0.406663\pi\) | ||||
0.289043 | + | 0.957316i | \(0.406663\pi\) | |||||||
\(752\) | −4.50584e10 | −3.86379 | ||||||||
\(753\) | 6.53820e9 | 0.558054 | ||||||||
\(754\) | −7.44905e9 | −0.632850 | ||||||||
\(755\) | −3.12957e9 | −0.264649 | ||||||||
\(756\) | 1.11612e10 | 0.939474 | ||||||||
\(757\) | 7.51213e9 | 0.629401 | 0.314700 | − | 0.949191i | \(-0.398096\pi\) | ||||
0.314700 | + | 0.949191i | \(0.398096\pi\) | |||||||
\(758\) | 2.40870e10 | 2.00882 | ||||||||
\(759\) | −1.34905e10 | −1.11991 | ||||||||
\(760\) | −9.99053e9 | −0.825545 | ||||||||
\(761\) | 1.17043e10 | 0.962721 | 0.481361 | − | 0.876523i | \(-0.340143\pi\) | ||||
0.481361 | + | 0.876523i | \(0.340143\pi\) | |||||||
\(762\) | 1.77164e10 | 1.45055 | ||||||||
\(763\) | 1.01946e10 | 0.830871 | ||||||||
\(764\) | −1.04653e10 | −0.849035 | ||||||||
\(765\) | 8.75498e8 | 0.0707034 | ||||||||
\(766\) | 1.21970e10 | 0.980509 | ||||||||
\(767\) | 3.51294e8 | 0.0281117 | ||||||||
\(768\) | 4.38487e10 | 3.49295 | ||||||||
\(769\) | −2.01241e9 | −0.159579 | −0.0797894 | − | 0.996812i | \(-0.525425\pi\) | ||||
−0.0797894 | + | 0.996812i | \(0.525425\pi\) | |||||||
\(770\) | 1.33920e10 | 1.05713 | ||||||||
\(771\) | −1.02743e10 | −0.807351 | ||||||||
\(772\) | −1.22604e10 | −0.959055 | ||||||||
\(773\) | −5.06105e9 | −0.394105 | −0.197053 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197053 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(774\) | −2.59718e9 | −0.201330 | ||||||||
\(775\) | 4.83628e9 | 0.373212 | ||||||||
\(776\) | 5.92539e10 | 4.55199 | ||||||||
\(777\) | −1.28090e10 | −0.979587 | ||||||||
\(778\) | 1.52533e10 | 1.16128 | ||||||||
\(779\) | −1.91301e10 | −1.44989 | ||||||||
\(780\) | 1.44288e9 | 0.108868 | ||||||||
\(781\) | −7.64344e9 | −0.574130 | ||||||||
\(782\) | −3.41949e10 | −2.55704 | ||||||||
\(783\) | −3.84076e9 | −0.285924 | ||||||||
\(784\) | 1.11578e11 | 8.26938 | ||||||||
\(785\) | 4.93499e9 | 0.364119 | ||||||||
\(786\) | −2.75183e9 | −0.202136 | ||||||||
\(787\) | −1.29130e10 | −0.944311 | −0.472155 | − | 0.881515i | \(-0.656524\pi\) | ||||
−0.472155 | + | 0.881515i | \(0.656524\pi\) | |||||||
\(788\) | −4.06364e10 | −2.95851 | ||||||||
\(789\) | −5.10068e9 | −0.369708 | ||||||||
\(790\) | 3.23646e8 | 0.0233548 | ||||||||
\(791\) | 2.70015e10 | 1.93986 | ||||||||
\(792\) | −1.82748e10 | −1.30712 | ||||||||
\(793\) | 4.60401e9 | 0.327854 | ||||||||
\(794\) | 2.72132e10 | 1.92933 | ||||||||
\(795\) | 1.70019e9 | 0.120009 | ||||||||
\(796\) | 4.24338e10 | 2.98206 | ||||||||
\(797\) | −1.75345e10 | −1.22684 | −0.613422 | − | 0.789755i | \(-0.710208\pi\) | ||||
−0.613422 | + | 0.789755i | \(0.710208\pi\) | |||||||
\(798\) | 2.02217e10 | 1.40867 | ||||||||
\(799\) | 8.75483e9 | 0.607203 | ||||||||
\(800\) | 6.69169e10 | 4.62084 | ||||||||
\(801\) | −1.33692e9 | −0.0919161 | ||||||||
\(802\) | 2.85088e10 | 1.95150 | ||||||||
\(803\) | −1.35203e10 | −0.921468 | ||||||||
\(804\) | 2.11710e10 | 1.43663 | ||||||||
\(805\) | 1.39292e10 | 0.941109 | ||||||||
\(806\) | −2.60037e9 | −0.174929 | ||||||||
\(807\) | 5.60454e9 | 0.375390 | ||||||||
\(808\) | 4.21632e10 | 2.81186 | ||||||||
\(809\) | 3.03994e9 | 0.201858 | 0.100929 | − | 0.994894i | \(-0.467819\pi\) | ||||
0.100929 | + | 0.994894i | \(0.467819\pi\) | |||||||
\(810\) | 1.00125e9 | 0.0661980 | ||||||||
\(811\) | 1.35418e10 | 0.891465 | 0.445733 | − | 0.895166i | \(-0.352943\pi\) | ||||
0.445733 | + | 0.895166i | \(0.352943\pi\) | |||||||
\(812\) | −1.10649e11 | −7.25270 | ||||||||
\(813\) | −2.11095e9 | −0.137772 | ||||||||
\(814\) | 3.20612e10 | 2.08350 | ||||||||
\(815\) | −9.14220e9 | −0.591560 | ||||||||
\(816\) | −2.81249e10 | −1.81207 | ||||||||
\(817\) | −3.49634e9 | −0.224303 | ||||||||
\(818\) | 3.40929e10 | 2.17785 | ||||||||
\(819\) | −1.91046e9 | −0.121519 | ||||||||
\(820\) | −2.72879e10 | −1.72831 | ||||||||
\(821\) | −1.44424e10 | −0.910834 | −0.455417 | − | 0.890278i | \(-0.650510\pi\) | ||||
−0.455417 | + | 0.890278i | \(0.650510\pi\) | |||||||
\(822\) | −2.01032e9 | −0.126245 | ||||||||
\(823\) | 1.58161e10 | 0.989009 | 0.494504 | − | 0.869175i | \(-0.335350\pi\) | ||||
0.494504 | + | 0.869175i | \(0.335350\pi\) | |||||||
\(824\) | 8.11818e8 | 0.0505491 | ||||||||
\(825\) | −8.89360e9 | −0.551428 | ||||||||
\(826\) | 7.02283e9 | 0.433593 | ||||||||
\(827\) | −2.91022e10 | −1.78919 | −0.894594 | − | 0.446879i | \(-0.852535\pi\) | ||||
−0.894594 | + | 0.446879i | \(0.852535\pi\) | |||||||
\(828\) | −2.90572e10 | −1.77888 | ||||||||
\(829\) | −1.38090e10 | −0.841825 | −0.420913 | − | 0.907101i | \(-0.638290\pi\) | ||||
−0.420913 | + | 0.907101i | \(0.638290\pi\) | |||||||
\(830\) | 9.32081e9 | 0.565823 | ||||||||
\(831\) | −3.53653e9 | −0.213784 | ||||||||
\(832\) | −1.99492e10 | −1.20086 | ||||||||
\(833\) | −2.16796e10 | −1.29955 | ||||||||
\(834\) | −1.54989e10 | −0.925166 | ||||||||
\(835\) | 5.90124e8 | 0.0350785 | ||||||||
\(836\) | −3.76084e10 | −2.22620 | ||||||||
\(837\) | −1.34076e9 | −0.0790337 | ||||||||
\(838\) | −4.81663e10 | −2.82741 | ||||||||
\(839\) | 2.26960e10 | 1.32673 | 0.663366 | − | 0.748295i | \(-0.269127\pi\) | ||||
0.663366 | + | 0.748295i | \(0.269127\pi\) | |||||||
\(840\) | 1.88690e10 | 1.09843 | ||||||||
\(841\) | 2.08262e10 | 1.20732 | ||||||||
\(842\) | 1.08494e10 | 0.626342 | ||||||||
\(843\) | 4.58142e9 | 0.263393 | ||||||||
\(844\) | −5.00733e10 | −2.86687 | ||||||||
\(845\) | 5.05004e9 | 0.287936 | ||||||||
\(846\) | 1.00123e10 | 0.568511 | ||||||||
\(847\) | 3.12088e9 | 0.176476 | ||||||||
\(848\) | −5.46179e10 | −3.07574 | ||||||||
\(849\) | 5.43520e9 | 0.304817 | ||||||||
\(850\) | −2.25430e10 | −1.25906 | ||||||||
\(851\) | 3.33471e10 | 1.85483 | ||||||||
\(852\) | −1.64632e10 | −0.911959 | ||||||||
\(853\) | −2.76986e9 | −0.152804 | −0.0764022 | − | 0.997077i | \(-0.524343\pi\) | ||||
−0.0764022 | + | 0.997077i | \(0.524343\pi\) | |||||||
\(854\) | 9.20402e10 | 5.05679 | ||||||||
\(855\) | 1.34789e9 | 0.0737518 | ||||||||
\(856\) | −4.40896e10 | −2.40258 | ||||||||
\(857\) | 8.53606e9 | 0.463260 | 0.231630 | − | 0.972804i | \(-0.425594\pi\) | ||||
0.231630 | + | 0.972804i | \(0.425594\pi\) | |||||||
\(858\) | 4.78191e9 | 0.258461 | ||||||||
\(859\) | −7.27081e9 | −0.391387 | −0.195694 | − | 0.980665i | \(-0.562696\pi\) | ||||
−0.195694 | + | 0.980665i | \(0.562696\pi\) | |||||||
\(860\) | −4.98730e9 | −0.267375 | ||||||||
\(861\) | 3.61308e10 | 1.92915 | ||||||||
\(862\) | −2.00325e10 | −1.06527 | ||||||||
\(863\) | 2.06289e10 | 1.09254 | 0.546270 | − | 0.837609i | \(-0.316047\pi\) | ||||
0.546270 | + | 0.837609i | \(0.316047\pi\) | |||||||
\(864\) | −1.85514e10 | −0.978538 | ||||||||
\(865\) | 8.25791e9 | 0.433824 | ||||||||
\(866\) | 2.39727e9 | 0.125431 | ||||||||
\(867\) | −5.61448e9 | −0.292579 | ||||||||
\(868\) | −3.86260e10 | −2.00475 | ||||||||
\(869\) | 7.96976e8 | 0.0411980 | ||||||||
\(870\) | −9.92607e9 | −0.511046 | ||||||||
\(871\) | −3.62383e9 | −0.185825 | ||||||||
\(872\) | −3.59530e10 | −1.83623 | ||||||||
\(873\) | −7.99434e9 | −0.406661 | ||||||||
\(874\) | −5.26454e10 | −2.66729 | ||||||||
\(875\) | 1.92873e10 | 0.973291 | ||||||||
\(876\) | −2.91212e10 | −1.46368 | ||||||||
\(877\) | 1.04224e10 | 0.521760 | 0.260880 | − | 0.965371i | \(-0.415987\pi\) | ||||
0.260880 | + | 0.965371i | \(0.415987\pi\) | |||||||
\(878\) | 9.45934e9 | 0.471661 | ||||||||
\(879\) | −1.25015e9 | −0.0620872 | ||||||||
\(880\) | −2.86760e10 | −1.41850 | ||||||||
\(881\) | 3.28267e10 | 1.61738 | 0.808690 | − | 0.588235i | \(-0.200177\pi\) | ||||
0.808690 | + | 0.588235i | \(0.200177\pi\) | |||||||
\(882\) | −2.47936e10 | −1.21674 | ||||||||
\(883\) | 2.09738e10 | 1.02522 | 0.512608 | − | 0.858623i | \(-0.328680\pi\) | ||||
0.512608 | + | 0.858623i | \(0.328680\pi\) | |||||||
\(884\) | 9.00613e9 | 0.438486 | ||||||||
\(885\) | 4.68110e8 | 0.0227011 | ||||||||
\(886\) | 3.50214e10 | 1.69167 | ||||||||
\(887\) | 4.36272e9 | 0.209906 | 0.104953 | − | 0.994477i | \(-0.466531\pi\) | ||||
0.104953 | + | 0.994477i | \(0.466531\pi\) | |||||||
\(888\) | 4.51734e10 | 2.16490 | ||||||||
\(889\) | −4.50451e10 | −2.15026 | ||||||||
\(890\) | −3.45514e9 | −0.164286 | ||||||||
\(891\) | 2.46557e9 | 0.116774 | ||||||||
\(892\) | 3.38444e10 | 1.59665 | ||||||||
\(893\) | 1.34787e10 | 0.633383 | ||||||||
\(894\) | 4.30982e10 | 2.01733 | ||||||||
\(895\) | −6.51434e9 | −0.303732 | ||||||||
\(896\) | −2.13972e11 | −9.93754 | ||||||||
\(897\) | 4.97371e9 | 0.230095 | ||||||||
\(898\) | 1.45662e10 | 0.671243 | ||||||||
\(899\) | 1.32919e10 | 0.610137 | ||||||||
\(900\) | −1.91559e10 | −0.875899 | ||||||||
\(901\) | 1.06122e10 | 0.483360 | ||||||||
\(902\) | −9.04359e10 | −4.10315 | ||||||||
\(903\) | 6.60350e9 | 0.298447 | ||||||||
\(904\) | −9.52256e10 | −4.28711 | ||||||||
\(905\) | 5.28714e9 | 0.237111 | ||||||||
\(906\) | −2.23399e10 | −0.998005 | ||||||||
\(907\) | 9.67343e9 | 0.430482 | 0.215241 | − | 0.976561i | \(-0.430946\pi\) | ||||
0.215241 | + | 0.976561i | \(0.430946\pi\) | |||||||
\(908\) | −3.30304e10 | −1.46424 | ||||||||
\(909\) | −5.68851e9 | −0.251203 | ||||||||
\(910\) | −4.93740e9 | −0.217197 | ||||||||
\(911\) | 1.13862e10 | 0.498959 | 0.249480 | − | 0.968380i | \(-0.419740\pi\) | ||||
0.249480 | + | 0.968380i | \(0.419740\pi\) | |||||||
\(912\) | −4.33002e10 | −1.89020 | ||||||||
\(913\) | 2.29524e10 | 0.998116 | ||||||||
\(914\) | 7.02542e10 | 3.04341 | ||||||||
\(915\) | 6.13498e9 | 0.264752 | ||||||||
\(916\) | 9.31765e10 | 4.00564 | ||||||||
\(917\) | 6.99671e9 | 0.299641 | ||||||||
\(918\) | 6.24959e9 | 0.266626 | ||||||||
\(919\) | −1.74980e9 | −0.0743676 | −0.0371838 | − | 0.999308i | \(-0.511839\pi\) | ||||
−0.0371838 | + | 0.999308i | \(0.511839\pi\) | |||||||
\(920\) | −4.91237e10 | −2.07986 | ||||||||
\(921\) | −2.22628e10 | −0.939010 | ||||||||
\(922\) | −8.51670e10 | −3.57860 | ||||||||
\(923\) | 2.81800e9 | 0.117960 | ||||||||
\(924\) | 7.10307e10 | 2.96206 | ||||||||
\(925\) | 2.19841e10 | 0.913297 | ||||||||
\(926\) | −1.63377e10 | −0.676165 | ||||||||
\(927\) | −1.09528e8 | −0.00451591 | ||||||||
\(928\) | 1.83912e11 | 7.55428 | ||||||||
\(929\) | −5.01633e9 | −0.205273 | −0.102636 | − | 0.994719i | \(-0.532728\pi\) | ||||
−0.102636 | + | 0.994719i | \(0.532728\pi\) | |||||||
\(930\) | −3.46507e9 | −0.141261 | ||||||||
\(931\) | −3.33772e10 | −1.35558 | ||||||||
\(932\) | 1.29669e11 | 5.24665 | ||||||||
\(933\) | 2.21750e10 | 0.893878 | ||||||||
\(934\) | 2.13572e10 | 0.857688 | ||||||||
\(935\) | 5.57173e9 | 0.222920 | ||||||||
\(936\) | 6.73758e9 | 0.268558 | ||||||||
\(937\) | 2.41581e10 | 0.959343 | 0.479672 | − | 0.877448i | \(-0.340756\pi\) | ||||
0.479672 | + | 0.877448i | \(0.340756\pi\) | |||||||
\(938\) | −7.24452e10 | −2.86615 | ||||||||
\(939\) | 1.08263e10 | 0.426727 | ||||||||
\(940\) | 1.92265e10 | 0.755009 | ||||||||
\(941\) | −2.00603e10 | −0.784826 | −0.392413 | − | 0.919789i | \(-0.628360\pi\) | ||||
−0.392413 | + | 0.919789i | \(0.628360\pi\) | |||||||
\(942\) | 3.52276e10 | 1.37311 | ||||||||
\(943\) | −9.40632e10 | −3.65282 | ||||||||
\(944\) | −1.50378e10 | −0.581811 | ||||||||
\(945\) | −2.54574e9 | −0.0981304 | ||||||||
\(946\) | −1.65286e10 | −0.634772 | ||||||||
\(947\) | −1.33454e10 | −0.510632 | −0.255316 | − | 0.966858i | \(-0.582180\pi\) | ||||
−0.255316 | + | 0.966858i | \(0.582180\pi\) | |||||||
\(948\) | 1.71660e9 | 0.0654396 | ||||||||
\(949\) | 4.98467e9 | 0.189324 | ||||||||
\(950\) | −3.47064e10 | −1.31334 | ||||||||
\(951\) | 5.48793e9 | 0.206908 | ||||||||
\(952\) | 1.17776e11 | 4.42414 | ||||||||
\(953\) | −4.58477e10 | −1.71590 | −0.857950 | − | 0.513733i | \(-0.828262\pi\) | ||||
−0.857950 | + | 0.513733i | \(0.828262\pi\) | |||||||
\(954\) | 1.21365e10 | 0.452559 | ||||||||
\(955\) | 2.38702e9 | 0.0886838 | ||||||||
\(956\) | 7.19481e10 | 2.66328 | ||||||||
\(957\) | −2.44429e10 | −0.901490 | ||||||||
\(958\) | −7.14146e10 | −2.62426 | ||||||||
\(959\) | 5.11136e9 | 0.187142 | ||||||||
\(960\) | −2.65828e10 | −0.969732 | ||||||||
\(961\) | −2.28726e10 | −0.831349 | ||||||||
\(962\) | −1.18204e10 | −0.428074 | ||||||||
\(963\) | 5.94842e9 | 0.214639 | ||||||||
\(964\) | 2.29237e10 | 0.824168 | ||||||||
\(965\) | 2.79645e9 | 0.100176 | ||||||||
\(966\) | 9.94309e10 | 3.54896 | ||||||||
\(967\) | 2.81641e10 | 1.00162 | 0.500810 | − | 0.865557i | \(-0.333036\pi\) | ||||
0.500810 | + | 0.865557i | \(0.333036\pi\) | |||||||
\(968\) | −1.10063e10 | −0.390013 | ||||||||
\(969\) | 8.41322e9 | 0.297050 | ||||||||
\(970\) | −2.06606e10 | −0.726845 | ||||||||
\(971\) | 2.91527e10 | 1.02191 | 0.510954 | − | 0.859608i | \(-0.329292\pi\) | ||||
0.510954 | + | 0.859608i | \(0.329292\pi\) | |||||||
\(972\) | 5.31059e9 | 0.185486 | ||||||||
\(973\) | 3.94070e10 | 1.37144 | ||||||||
\(974\) | 7.93951e9 | 0.275320 | ||||||||
\(975\) | 3.27891e9 | 0.113296 | ||||||||
\(976\) | −1.97083e11 | −6.78539 | ||||||||
\(977\) | 2.18798e10 | 0.750607 | 0.375303 | − | 0.926902i | \(-0.377539\pi\) | ||||
0.375303 | + | 0.926902i | \(0.377539\pi\) | |||||||
\(978\) | −6.52599e10 | −2.23080 | ||||||||
\(979\) | −8.50825e9 | −0.289802 | ||||||||
\(980\) | −4.76105e10 | −1.61589 | ||||||||
\(981\) | 4.85066e9 | 0.164044 | ||||||||
\(982\) | 3.96185e8 | 0.0133508 | ||||||||
\(983\) | 7.16781e9 | 0.240685 | 0.120342 | − | 0.992732i | \(-0.461601\pi\) | ||||
0.120342 | + | 0.992732i | \(0.461601\pi\) | |||||||
\(984\) | −1.27422e11 | −4.26345 | ||||||||
\(985\) | 9.26870e9 | 0.309024 | ||||||||
\(986\) | −6.19564e10 | −2.05834 | ||||||||
\(987\) | −2.54570e10 | −0.842748 | ||||||||
\(988\) | 1.38656e10 | 0.457391 | ||||||||
\(989\) | −1.71916e10 | −0.565105 | ||||||||
\(990\) | 6.37203e9 | 0.208716 | ||||||||
\(991\) | −3.83800e9 | −0.125270 | −0.0626350 | − | 0.998037i | \(-0.519950\pi\) | ||||
−0.0626350 | + | 0.998037i | \(0.519950\pi\) | |||||||
\(992\) | 6.42014e10 | 2.08811 | ||||||||
\(993\) | 1.23944e10 | 0.401702 | ||||||||
\(994\) | 5.63355e10 | 1.81941 | ||||||||
\(995\) | −9.67868e9 | −0.311484 | ||||||||
\(996\) | 4.94372e10 | 1.58543 | ||||||||
\(997\) | 5.63360e10 | 1.80033 | 0.900166 | − | 0.435547i | \(-0.143445\pi\) | ||||
0.900166 | + | 0.435547i | \(0.143445\pi\) | |||||||
\(998\) | −4.39770e10 | −1.40045 | ||||||||
\(999\) | −6.09464e9 | −0.193406 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.8.a.b.1.1 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.d.1.17 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.1 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.d.1.17 | 17 | 3.2 | odd | 2 |