Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,10,Mod(1,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.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: | \(6.69546587013\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{4} - x^{3} - 1602x^{2} + 1544x + 342272 \)
|
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(16.5360\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −24.5360 | −1.08435 | −0.542175 | − | 0.840266i | \(-0.682399\pi\) | ||||
−0.542175 | + | 0.840266i | \(0.682399\pi\) | |||||||
\(3\) | 49.9972 | 0.356369 | 0.178185 | − | 0.983997i | \(-0.442978\pi\) | ||||
0.178185 | + | 0.983997i | \(0.442978\pi\) | |||||||
\(4\) | 90.0171 | 0.175815 | ||||||||
\(5\) | 1814.98 | 1.29869 | 0.649346 | − | 0.760493i | \(-0.275043\pi\) | ||||
0.649346 | + | 0.760493i | \(0.275043\pi\) | |||||||
\(6\) | −1226.73 | −0.386429 | ||||||||
\(7\) | −8707.31 | −1.37070 | −0.685351 | − | 0.728213i | \(-0.740351\pi\) | ||||
−0.685351 | + | 0.728213i | \(0.740351\pi\) | |||||||
\(8\) | 10353.8 | 0.893705 | ||||||||
\(9\) | −17183.3 | −0.873001 | ||||||||
\(10\) | −44532.3 | −1.40824 | ||||||||
\(11\) | −82919.7 | −1.70762 | −0.853809 | − | 0.520587i | \(-0.825713\pi\) | ||||
−0.853809 | + | 0.520587i | \(0.825713\pi\) | |||||||
\(12\) | 4500.61 | 0.0626550 | ||||||||
\(13\) | −28561.0 | −0.277350 | ||||||||
\(14\) | 213643. | 1.48632 | ||||||||
\(15\) | 90743.8 | 0.462814 | ||||||||
\(16\) | −300130. | −1.14490 | ||||||||
\(17\) | 374907. | 1.08869 | 0.544344 | − | 0.838862i | \(-0.316779\pi\) | ||||
0.544344 | + | 0.838862i | \(0.316779\pi\) | |||||||
\(18\) | 421610. | 0.946638 | ||||||||
\(19\) | −361501. | −0.636383 | −0.318191 | − | 0.948026i | \(-0.603075\pi\) | ||||
−0.318191 | + | 0.948026i | \(0.603075\pi\) | |||||||
\(20\) | 163379. | 0.228329 | ||||||||
\(21\) | −435341. | −0.488476 | ||||||||
\(22\) | 2.03452e6 | 1.85165 | ||||||||
\(23\) | −2.31340e6 | −1.72376 | −0.861878 | − | 0.507116i | \(-0.830712\pi\) | ||||
−0.861878 | + | 0.507116i | \(0.830712\pi\) | |||||||
\(24\) | 517661. | 0.318489 | ||||||||
\(25\) | 1.34101e6 | 0.686599 | ||||||||
\(26\) | 700774. | 0.300745 | ||||||||
\(27\) | −1.84321e6 | −0.667480 | ||||||||
\(28\) | −783807. | −0.240989 | ||||||||
\(29\) | −649654. | −0.170565 | −0.0852827 | − | 0.996357i | \(-0.527179\pi\) | ||||
−0.0852827 | + | 0.996357i | \(0.527179\pi\) | |||||||
\(30\) | −2.22649e6 | −0.501852 | ||||||||
\(31\) | 4.32521e6 | 0.841162 | 0.420581 | − | 0.907255i | \(-0.361826\pi\) | ||||
0.420581 | + | 0.907255i | \(0.361826\pi\) | |||||||
\(32\) | 2.06285e6 | 0.347771 | ||||||||
\(33\) | −4.14575e6 | −0.608542 | ||||||||
\(34\) | −9.19873e6 | −1.18052 | ||||||||
\(35\) | −1.58036e7 | −1.78012 | ||||||||
\(36\) | −1.54679e6 | −0.153486 | ||||||||
\(37\) | 1.21021e7 | 1.06158 | 0.530790 | − | 0.847503i | \(-0.321895\pi\) | ||||
0.530790 | + | 0.847503i | \(0.321895\pi\) | |||||||
\(38\) | 8.86981e6 | 0.690062 | ||||||||
\(39\) | −1.42797e6 | −0.0988391 | ||||||||
\(40\) | 1.87919e7 | 1.16065 | ||||||||
\(41\) | 2.59960e6 | 0.143674 | 0.0718372 | − | 0.997416i | \(-0.477114\pi\) | ||||
0.0718372 | + | 0.997416i | \(0.477114\pi\) | |||||||
\(42\) | 1.06816e7 | 0.529679 | ||||||||
\(43\) | 3.08318e6 | 0.137528 | 0.0687640 | − | 0.997633i | \(-0.478094\pi\) | ||||
0.0687640 | + | 0.997633i | \(0.478094\pi\) | |||||||
\(44\) | −7.46419e6 | −0.300224 | ||||||||
\(45\) | −3.11872e7 | −1.13376 | ||||||||
\(46\) | 5.67617e7 | 1.86915 | ||||||||
\(47\) | 2.60298e7 | 0.778090 | 0.389045 | − | 0.921219i | \(-0.372805\pi\) | ||||
0.389045 | + | 0.921219i | \(0.372805\pi\) | |||||||
\(48\) | −1.50057e7 | −0.408009 | ||||||||
\(49\) | 3.54636e7 | 0.878822 | ||||||||
\(50\) | −3.29032e7 | −0.744513 | ||||||||
\(51\) | 1.87443e7 | 0.387975 | ||||||||
\(52\) | −2.57098e6 | −0.0487622 | ||||||||
\(53\) | −1.01982e8 | −1.77535 | −0.887673 | − | 0.460475i | \(-0.847679\pi\) | ||||
−0.887673 | + | 0.460475i | \(0.847679\pi\) | |||||||
\(54\) | 4.52251e7 | 0.723782 | ||||||||
\(55\) | −1.50497e8 | −2.21767 | ||||||||
\(56\) | −9.01536e7 | −1.22500 | ||||||||
\(57\) | −1.80741e7 | −0.226787 | ||||||||
\(58\) | 1.59399e7 | 0.184953 | ||||||||
\(59\) | 1.37562e8 | 1.47797 | 0.738985 | − | 0.673722i | \(-0.235305\pi\) | ||||
0.738985 | + | 0.673722i | \(0.235305\pi\) | |||||||
\(60\) | 8.16850e6 | 0.0813695 | ||||||||
\(61\) | −4.29579e7 | −0.397245 | −0.198623 | − | 0.980076i | \(-0.563647\pi\) | ||||
−0.198623 | + | 0.980076i | \(0.563647\pi\) | |||||||
\(62\) | −1.06124e8 | −0.912114 | ||||||||
\(63\) | 1.49620e8 | 1.19662 | ||||||||
\(64\) | 1.03052e8 | 0.767798 | ||||||||
\(65\) | −5.18375e7 | −0.360192 | ||||||||
\(66\) | 1.01720e8 | 0.659873 | ||||||||
\(67\) | 5.54479e7 | 0.336162 | 0.168081 | − | 0.985773i | \(-0.446243\pi\) | ||||
0.168081 | + | 0.985773i | \(0.446243\pi\) | |||||||
\(68\) | 3.37480e7 | 0.191407 | ||||||||
\(69\) | −1.15664e8 | −0.614294 | ||||||||
\(70\) | 3.87757e8 | 1.93027 | ||||||||
\(71\) | −1.43613e8 | −0.670706 | −0.335353 | − | 0.942093i | \(-0.608856\pi\) | ||||
−0.335353 | + | 0.942093i | \(0.608856\pi\) | |||||||
\(72\) | −1.77912e8 | −0.780205 | ||||||||
\(73\) | 3.37147e7 | 0.138952 | 0.0694762 | − | 0.997584i | \(-0.477867\pi\) | ||||
0.0694762 | + | 0.997584i | \(0.477867\pi\) | |||||||
\(74\) | −2.96937e8 | −1.15112 | ||||||||
\(75\) | 6.70469e7 | 0.244683 | ||||||||
\(76\) | −3.25413e7 | −0.111886 | ||||||||
\(77\) | 7.22007e8 | 2.34063 | ||||||||
\(78\) | 3.50367e7 | 0.107176 | ||||||||
\(79\) | −2.66652e8 | −0.770236 | −0.385118 | − | 0.922867i | \(-0.625839\pi\) | ||||
−0.385118 | + | 0.922867i | \(0.625839\pi\) | |||||||
\(80\) | −5.44728e8 | −1.48688 | ||||||||
\(81\) | 2.46063e8 | 0.635132 | ||||||||
\(82\) | −6.37839e7 | −0.155793 | ||||||||
\(83\) | −9.89542e7 | −0.228867 | −0.114433 | − | 0.993431i | \(-0.536505\pi\) | ||||
−0.114433 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(84\) | −3.91882e7 | −0.0858812 | ||||||||
\(85\) | 6.80447e8 | 1.41387 | ||||||||
\(86\) | −7.56490e7 | −0.149128 | ||||||||
\(87\) | −3.24809e7 | −0.0607843 | ||||||||
\(88\) | −8.58533e8 | −1.52611 | ||||||||
\(89\) | −5.08803e8 | −0.859597 | −0.429798 | − | 0.902925i | \(-0.641415\pi\) | ||||
−0.429798 | + | 0.902925i | \(0.641415\pi\) | |||||||
\(90\) | 7.65211e8 | 1.22939 | ||||||||
\(91\) | 2.48689e8 | 0.380164 | ||||||||
\(92\) | −2.08246e8 | −0.303062 | ||||||||
\(93\) | 2.16249e8 | 0.299764 | ||||||||
\(94\) | −6.38667e8 | −0.843722 | ||||||||
\(95\) | −6.56116e8 | −0.826465 | ||||||||
\(96\) | 1.03137e8 | 0.123935 | ||||||||
\(97\) | −4.53920e8 | −0.520603 | −0.260301 | − | 0.965527i | \(-0.583822\pi\) | ||||
−0.260301 | + | 0.965527i | \(0.583822\pi\) | |||||||
\(98\) | −8.70137e8 | −0.952950 | ||||||||
\(99\) | 1.42483e9 | 1.49075 | ||||||||
\(100\) | 1.20714e8 | 0.120714 | ||||||||
\(101\) | 6.44663e8 | 0.616434 | 0.308217 | − | 0.951316i | \(-0.400268\pi\) | ||||
0.308217 | + | 0.951316i | \(0.400268\pi\) | |||||||
\(102\) | −4.59911e8 | −0.420700 | ||||||||
\(103\) | −1.14825e9 | −1.00524 | −0.502620 | − | 0.864507i | \(-0.667631\pi\) | ||||
−0.502620 | + | 0.864507i | \(0.667631\pi\) | |||||||
\(104\) | −2.95715e8 | −0.247869 | ||||||||
\(105\) | −7.90134e8 | −0.634379 | ||||||||
\(106\) | 2.50224e9 | 1.92510 | ||||||||
\(107\) | 5.95299e8 | 0.439044 | 0.219522 | − | 0.975607i | \(-0.429550\pi\) | ||||
0.219522 | + | 0.975607i | \(0.429550\pi\) | |||||||
\(108\) | −1.65921e8 | −0.117353 | ||||||||
\(109\) | 1.00898e9 | 0.684645 | 0.342322 | − | 0.939583i | \(-0.388787\pi\) | ||||
0.342322 | + | 0.939583i | \(0.388787\pi\) | |||||||
\(110\) | 3.69261e9 | 2.40473 | ||||||||
\(111\) | 6.05071e8 | 0.378315 | ||||||||
\(112\) | 2.61332e9 | 1.56932 | ||||||||
\(113\) | −1.59931e9 | −0.922739 | −0.461370 | − | 0.887208i | \(-0.652642\pi\) | ||||
−0.461370 | + | 0.887208i | \(0.652642\pi\) | |||||||
\(114\) | 4.43466e8 | 0.245917 | ||||||||
\(115\) | −4.19877e9 | −2.23863 | ||||||||
\(116\) | −5.84800e7 | −0.0299879 | ||||||||
\(117\) | 4.90772e8 | 0.242127 | ||||||||
\(118\) | −3.37524e9 | −1.60264 | ||||||||
\(119\) | −3.26443e9 | −1.49226 | ||||||||
\(120\) | 9.39542e8 | 0.413619 | ||||||||
\(121\) | 4.51772e9 | 1.91596 | ||||||||
\(122\) | 1.05402e9 | 0.430753 | ||||||||
\(123\) | 1.29973e8 | 0.0512011 | ||||||||
\(124\) | 3.89343e8 | 0.147889 | ||||||||
\(125\) | −1.11097e9 | −0.407011 | ||||||||
\(126\) | −3.67108e9 | −1.29756 | ||||||||
\(127\) | −1.58816e9 | −0.541723 | −0.270861 | − | 0.962618i | \(-0.587308\pi\) | ||||
−0.270861 | + | 0.962618i | \(0.587308\pi\) | |||||||
\(128\) | −3.58467e9 | −1.18033 | ||||||||
\(129\) | 1.54151e8 | 0.0490107 | ||||||||
\(130\) | 1.27189e9 | 0.390574 | ||||||||
\(131\) | −3.54703e9 | −1.05231 | −0.526156 | − | 0.850388i | \(-0.676367\pi\) | ||||
−0.526156 | + | 0.850388i | \(0.676367\pi\) | |||||||
\(132\) | −3.73189e8 | −0.106991 | ||||||||
\(133\) | 3.14770e9 | 0.872291 | ||||||||
\(134\) | −1.36047e9 | −0.364517 | ||||||||
\(135\) | −3.34539e9 | −0.866850 | ||||||||
\(136\) | 3.88170e9 | 0.972965 | ||||||||
\(137\) | −3.79917e9 | −0.921395 | −0.460697 | − | 0.887557i | \(-0.652401\pi\) | ||||
−0.460697 | + | 0.887557i | \(0.652401\pi\) | |||||||
\(138\) | 2.83793e9 | 0.666109 | ||||||||
\(139\) | 3.81526e9 | 0.866878 | 0.433439 | − | 0.901183i | \(-0.357300\pi\) | ||||
0.433439 | + | 0.901183i | \(0.357300\pi\) | |||||||
\(140\) | −1.42259e9 | −0.312971 | ||||||||
\(141\) | 1.30142e9 | 0.277287 | ||||||||
\(142\) | 3.52370e9 | 0.727280 | ||||||||
\(143\) | 2.36827e9 | 0.473608 | ||||||||
\(144\) | 5.15721e9 | 0.999502 | ||||||||
\(145\) | −1.17911e9 | −0.221512 | ||||||||
\(146\) | −8.27225e8 | −0.150673 | ||||||||
\(147\) | 1.77308e9 | 0.313185 | ||||||||
\(148\) | 1.08940e9 | 0.186641 | ||||||||
\(149\) | 1.16149e10 | 1.93054 | 0.965269 | − | 0.261258i | \(-0.0841374\pi\) | ||||
0.965269 | + | 0.261258i | \(0.0841374\pi\) | |||||||
\(150\) | −1.64507e9 | −0.265322 | ||||||||
\(151\) | 3.19196e9 | 0.499645 | 0.249822 | − | 0.968292i | \(-0.419628\pi\) | ||||
0.249822 | + | 0.968292i | \(0.419628\pi\) | |||||||
\(152\) | −3.74291e9 | −0.568739 | ||||||||
\(153\) | −6.44213e9 | −0.950425 | ||||||||
\(154\) | −1.77152e10 | −2.53806 | ||||||||
\(155\) | 7.85016e9 | 1.09241 | ||||||||
\(156\) | −1.28542e8 | −0.0173774 | ||||||||
\(157\) | −5.05861e9 | −0.664481 | −0.332240 | − | 0.943195i | \(-0.607805\pi\) | ||||
−0.332240 | + | 0.943195i | \(0.607805\pi\) | |||||||
\(158\) | 6.54260e9 | 0.835205 | ||||||||
\(159\) | −5.09883e9 | −0.632679 | ||||||||
\(160\) | 3.74403e9 | 0.451647 | ||||||||
\(161\) | 2.01435e10 | 2.36275 | ||||||||
\(162\) | −6.03741e9 | −0.688705 | ||||||||
\(163\) | −7.83438e9 | −0.869282 | −0.434641 | − | 0.900604i | \(-0.643125\pi\) | ||||
−0.434641 | + | 0.900604i | \(0.643125\pi\) | |||||||
\(164\) | 2.34009e8 | 0.0252601 | ||||||||
\(165\) | −7.52444e9 | −0.790308 | ||||||||
\(166\) | 2.42794e9 | 0.248172 | ||||||||
\(167\) | −1.44048e8 | −0.0143312 | −0.00716559 | − | 0.999974i | \(-0.502281\pi\) | ||||
−0.00716559 | + | 0.999974i | \(0.502281\pi\) | |||||||
\(168\) | −4.50743e9 | −0.436553 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | −1.66955e10 | −1.53313 | ||||||||
\(171\) | 6.21178e9 | 0.555563 | ||||||||
\(172\) | 2.77539e8 | 0.0241794 | ||||||||
\(173\) | −1.36123e10 | −1.15538 | −0.577689 | − | 0.816257i | \(-0.696045\pi\) | ||||
−0.577689 | + | 0.816257i | \(0.696045\pi\) | |||||||
\(174\) | 7.96952e8 | 0.0659114 | ||||||||
\(175\) | −1.16766e10 | −0.941122 | ||||||||
\(176\) | 2.48867e10 | 1.95506 | ||||||||
\(177\) | 6.87774e9 | 0.526703 | ||||||||
\(178\) | 1.24840e10 | 0.932104 | ||||||||
\(179\) | 4.98195e8 | 0.0362711 | 0.0181355 | − | 0.999836i | \(-0.494227\pi\) | ||||
0.0181355 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(180\) | −2.80739e9 | −0.199331 | ||||||||
\(181\) | 2.86758e9 | 0.198592 | 0.0992961 | − | 0.995058i | \(-0.468341\pi\) | ||||
0.0992961 | + | 0.995058i | \(0.468341\pi\) | |||||||
\(182\) | −6.10185e9 | −0.412231 | ||||||||
\(183\) | −2.14777e9 | −0.141566 | ||||||||
\(184\) | −2.39525e10 | −1.54053 | ||||||||
\(185\) | 2.19650e10 | 1.37866 | ||||||||
\(186\) | −5.30588e9 | −0.325049 | ||||||||
\(187\) | −3.10871e10 | −1.85906 | ||||||||
\(188\) | 2.34312e9 | 0.136800 | ||||||||
\(189\) | 1.60494e10 | 0.914916 | ||||||||
\(190\) | 1.60985e10 | 0.896177 | ||||||||
\(191\) | −2.83331e10 | −1.54044 | −0.770218 | − | 0.637781i | \(-0.779852\pi\) | ||||
−0.770218 | + | 0.637781i | \(0.779852\pi\) | |||||||
\(192\) | 5.15232e9 | 0.273620 | ||||||||
\(193\) | 2.44273e10 | 1.26726 | 0.633632 | − | 0.773634i | \(-0.281563\pi\) | ||||
0.633632 | + | 0.773634i | \(0.281563\pi\) | |||||||
\(194\) | 1.11374e10 | 0.564516 | ||||||||
\(195\) | −2.59173e9 | −0.128361 | ||||||||
\(196\) | 3.19233e9 | 0.154510 | ||||||||
\(197\) | 1.37323e10 | 0.649601 | 0.324800 | − | 0.945783i | \(-0.394703\pi\) | ||||
0.324800 | + | 0.945783i | \(0.394703\pi\) | |||||||
\(198\) | −3.49597e10 | −1.61650 | ||||||||
\(199\) | −8.56614e9 | −0.387210 | −0.193605 | − | 0.981080i | \(-0.562018\pi\) | ||||
−0.193605 | + | 0.981080i | \(0.562018\pi\) | |||||||
\(200\) | 1.38846e10 | 0.613617 | ||||||||
\(201\) | 2.77224e9 | 0.119798 | ||||||||
\(202\) | −1.58175e10 | −0.668430 | ||||||||
\(203\) | 5.65673e9 | 0.233794 | ||||||||
\(204\) | 1.68731e9 | 0.0682117 | ||||||||
\(205\) | 4.71821e9 | 0.186589 | ||||||||
\(206\) | 2.81736e10 | 1.09003 | ||||||||
\(207\) | 3.97518e10 | 1.50484 | ||||||||
\(208\) | 8.57200e9 | 0.317539 | ||||||||
\(209\) | 2.99756e10 | 1.08670 | ||||||||
\(210\) | 1.93868e10 | 0.687889 | ||||||||
\(211\) | 2.70272e9 | 0.0938706 | 0.0469353 | − | 0.998898i | \(-0.485055\pi\) | ||||
0.0469353 | + | 0.998898i | \(0.485055\pi\) | |||||||
\(212\) | −9.18015e9 | −0.312132 | ||||||||
\(213\) | −7.18027e9 | −0.239019 | ||||||||
\(214\) | −1.46063e10 | −0.476078 | ||||||||
\(215\) | 5.59590e9 | 0.178606 | ||||||||
\(216\) | −1.90842e10 | −0.596530 | ||||||||
\(217\) | −3.76610e10 | −1.15298 | ||||||||
\(218\) | −2.47565e10 | −0.742394 | ||||||||
\(219\) | 1.68564e9 | 0.0495184 | ||||||||
\(220\) | −1.35473e10 | −0.389899 | ||||||||
\(221\) | −1.07077e10 | −0.301947 | ||||||||
\(222\) | −1.48460e10 | −0.410225 | ||||||||
\(223\) | −3.57969e10 | −0.969333 | −0.484667 | − | 0.874699i | \(-0.661059\pi\) | ||||
−0.484667 | + | 0.874699i | \(0.661059\pi\) | |||||||
\(224\) | −1.79619e10 | −0.476690 | ||||||||
\(225\) | −2.30430e10 | −0.599401 | ||||||||
\(226\) | 3.92407e10 | 1.00057 | ||||||||
\(227\) | −7.55373e10 | −1.88819 | −0.944094 | − | 0.329675i | \(-0.893061\pi\) | ||||
−0.944094 | + | 0.329675i | \(0.893061\pi\) | |||||||
\(228\) | −1.62698e9 | −0.0398726 | ||||||||
\(229\) | −5.69066e10 | −1.36742 | −0.683711 | − | 0.729753i | \(-0.739635\pi\) | ||||
−0.683711 | + | 0.729753i | \(0.739635\pi\) | |||||||
\(230\) | 1.03021e11 | 2.42745 | ||||||||
\(231\) | 3.60984e10 | 0.834130 | ||||||||
\(232\) | −6.72637e9 | −0.152435 | ||||||||
\(233\) | −4.68000e10 | −1.04026 | −0.520132 | − | 0.854086i | \(-0.674117\pi\) | ||||
−0.520132 | + | 0.854086i | \(0.674117\pi\) | |||||||
\(234\) | −1.20416e10 | −0.262550 | ||||||||
\(235\) | 4.72434e10 | 1.01050 | ||||||||
\(236\) | 1.23830e10 | 0.259849 | ||||||||
\(237\) | −1.33319e10 | −0.274488 | ||||||||
\(238\) | 8.00961e10 | 1.61814 | ||||||||
\(239\) | −8.79993e9 | −0.174457 | −0.0872285 | − | 0.996188i | \(-0.527801\pi\) | ||||
−0.0872285 | + | 0.996188i | \(0.527801\pi\) | |||||||
\(240\) | −2.72349e10 | −0.529877 | ||||||||
\(241\) | −1.76057e10 | −0.336183 | −0.168092 | − | 0.985771i | \(-0.553760\pi\) | ||||
−0.168092 | + | 0.985771i | \(0.553760\pi\) | |||||||
\(242\) | −1.10847e11 | −2.07757 | ||||||||
\(243\) | 4.85824e10 | 0.893821 | ||||||||
\(244\) | −3.86695e9 | −0.0698415 | ||||||||
\(245\) | 6.43656e10 | 1.14132 | ||||||||
\(246\) | −3.18902e9 | −0.0555200 | ||||||||
\(247\) | 1.03248e10 | 0.176501 | ||||||||
\(248\) | 4.47823e10 | 0.751751 | ||||||||
\(249\) | −4.94743e9 | −0.0815611 | ||||||||
\(250\) | 2.72588e10 | 0.441343 | ||||||||
\(251\) | −1.77113e10 | −0.281655 | −0.140828 | − | 0.990034i | \(-0.544976\pi\) | ||||
−0.140828 | + | 0.990034i | \(0.544976\pi\) | |||||||
\(252\) | 1.34684e10 | 0.210384 | ||||||||
\(253\) | 1.91826e11 | 2.94351 | ||||||||
\(254\) | 3.89671e10 | 0.587417 | ||||||||
\(255\) | 3.40204e10 | 0.503859 | ||||||||
\(256\) | 3.51910e10 | 0.512096 | ||||||||
\(257\) | −6.26733e10 | −0.896156 | −0.448078 | − | 0.893994i | \(-0.647891\pi\) | ||||
−0.448078 | + | 0.893994i | \(0.647891\pi\) | |||||||
\(258\) | −3.78224e9 | −0.0531448 | ||||||||
\(259\) | −1.05377e11 | −1.45511 | ||||||||
\(260\) | −4.66627e9 | −0.0633271 | ||||||||
\(261\) | 1.11632e10 | 0.148904 | ||||||||
\(262\) | 8.70301e10 | 1.14107 | ||||||||
\(263\) | 4.49501e10 | 0.579335 | 0.289667 | − | 0.957127i | \(-0.406455\pi\) | ||||
0.289667 | + | 0.957127i | \(0.406455\pi\) | |||||||
\(264\) | −4.29243e10 | −0.543857 | ||||||||
\(265\) | −1.85095e11 | −2.30563 | ||||||||
\(266\) | −7.72322e10 | −0.945869 | ||||||||
\(267\) | −2.54388e10 | −0.306334 | ||||||||
\(268\) | 4.99126e9 | 0.0591023 | ||||||||
\(269\) | −8.65536e10 | −1.00786 | −0.503930 | − | 0.863745i | \(-0.668113\pi\) | ||||
−0.503930 | + | 0.863745i | \(0.668113\pi\) | |||||||
\(270\) | 8.20825e10 | 0.939969 | ||||||||
\(271\) | 8.36056e10 | 0.941615 | 0.470808 | − | 0.882236i | \(-0.343963\pi\) | ||||
0.470808 | + | 0.882236i | \(0.343963\pi\) | |||||||
\(272\) | −1.12521e11 | −1.24644 | ||||||||
\(273\) | 1.24338e10 | 0.135479 | ||||||||
\(274\) | 9.32165e10 | 0.999114 | ||||||||
\(275\) | −1.11196e11 | −1.17245 | ||||||||
\(276\) | −1.04117e10 | −0.108002 | ||||||||
\(277\) | 1.73137e11 | 1.76698 | 0.883489 | − | 0.468452i | \(-0.155188\pi\) | ||||
0.883489 | + | 0.468452i | \(0.155188\pi\) | |||||||
\(278\) | −9.36114e10 | −0.939999 | ||||||||
\(279\) | −7.43213e10 | −0.734335 | ||||||||
\(280\) | −1.63627e11 | −1.59090 | ||||||||
\(281\) | 7.57598e10 | 0.724871 | 0.362435 | − | 0.932009i | \(-0.381945\pi\) | ||||
0.362435 | + | 0.932009i | \(0.381945\pi\) | |||||||
\(282\) | −3.19316e10 | −0.300676 | ||||||||
\(283\) | 1.68901e11 | 1.56528 | 0.782642 | − | 0.622472i | \(-0.213872\pi\) | ||||
0.782642 | + | 0.622472i | \(0.213872\pi\) | |||||||
\(284\) | −1.29277e10 | −0.117920 | ||||||||
\(285\) | −3.28040e10 | −0.294527 | ||||||||
\(286\) | −5.81079e10 | −0.513557 | ||||||||
\(287\) | −2.26355e10 | −0.196935 | ||||||||
\(288\) | −3.54466e10 | −0.303605 | ||||||||
\(289\) | 2.19672e10 | 0.185240 | ||||||||
\(290\) | 2.89306e10 | 0.240196 | ||||||||
\(291\) | −2.26947e10 | −0.185527 | ||||||||
\(292\) | 3.03490e9 | 0.0244299 | ||||||||
\(293\) | −1.18842e11 | −0.942030 | −0.471015 | − | 0.882125i | \(-0.656112\pi\) | ||||
−0.471015 | + | 0.882125i | \(0.656112\pi\) | |||||||
\(294\) | −4.35044e10 | −0.339602 | ||||||||
\(295\) | 2.49672e11 | 1.91943 | ||||||||
\(296\) | 1.25302e11 | 0.948740 | ||||||||
\(297\) | 1.52839e11 | 1.13980 | ||||||||
\(298\) | −2.84984e11 | −2.09338 | ||||||||
\(299\) | 6.60730e10 | 0.478084 | ||||||||
\(300\) | 6.03537e9 | 0.0430188 | ||||||||
\(301\) | −2.68462e10 | −0.188510 | ||||||||
\(302\) | −7.83181e10 | −0.541790 | ||||||||
\(303\) | 3.22313e10 | 0.219678 | ||||||||
\(304\) | 1.08497e11 | 0.728597 | ||||||||
\(305\) | −7.79675e10 | −0.515899 | ||||||||
\(306\) | 1.58064e11 | 1.03059 | ||||||||
\(307\) | −1.99530e11 | −1.28199 | −0.640997 | − | 0.767543i | \(-0.721479\pi\) | ||||
−0.640997 | + | 0.767543i | \(0.721479\pi\) | |||||||
\(308\) | 6.49930e10 | 0.411518 | ||||||||
\(309\) | −5.74095e10 | −0.358237 | ||||||||
\(310\) | −1.92612e11 | −1.18455 | ||||||||
\(311\) | 1.90145e11 | 1.15256 | 0.576281 | − | 0.817252i | \(-0.304503\pi\) | ||||
0.576281 | + | 0.817252i | \(0.304503\pi\) | |||||||
\(312\) | −1.47849e10 | −0.0883330 | ||||||||
\(313\) | −3.39674e10 | −0.200038 | −0.100019 | − | 0.994986i | \(-0.531890\pi\) | ||||
−0.100019 | + | 0.994986i | \(0.531890\pi\) | |||||||
\(314\) | 1.24118e11 | 0.720530 | ||||||||
\(315\) | 2.71557e11 | 1.55404 | ||||||||
\(316\) | −2.40033e10 | −0.135419 | ||||||||
\(317\) | −8.53565e9 | −0.0474756 | −0.0237378 | − | 0.999718i | \(-0.507557\pi\) | ||||
−0.0237378 | + | 0.999718i | \(0.507557\pi\) | |||||||
\(318\) | 1.25105e11 | 0.686045 | ||||||||
\(319\) | 5.38691e10 | 0.291260 | ||||||||
\(320\) | 1.87037e11 | 0.997133 | ||||||||
\(321\) | 2.97633e10 | 0.156462 | ||||||||
\(322\) | −4.94242e11 | −2.56205 | ||||||||
\(323\) | −1.35529e11 | −0.692822 | ||||||||
\(324\) | 2.21499e10 | 0.111665 | ||||||||
\(325\) | −3.83007e10 | −0.190428 | ||||||||
\(326\) | 1.92225e11 | 0.942606 | ||||||||
\(327\) | 5.04464e10 | 0.243986 | ||||||||
\(328\) | 2.69157e10 | 0.128403 | ||||||||
\(329\) | −2.26649e11 | −1.06653 | ||||||||
\(330\) | 1.84620e11 | 0.856971 | ||||||||
\(331\) | 5.09528e10 | 0.233315 | 0.116657 | − | 0.993172i | \(-0.462782\pi\) | ||||
0.116657 | + | 0.993172i | \(0.462782\pi\) | |||||||
\(332\) | −8.90757e9 | −0.0402381 | ||||||||
\(333\) | −2.07954e11 | −0.926760 | ||||||||
\(334\) | 3.53436e9 | 0.0155400 | ||||||||
\(335\) | 1.00637e11 | 0.436571 | ||||||||
\(336\) | 1.30659e11 | 0.559258 | ||||||||
\(337\) | 2.31891e11 | 0.979375 | 0.489688 | − | 0.871898i | \(-0.337111\pi\) | ||||
0.489688 | + | 0.871898i | \(0.337111\pi\) | |||||||
\(338\) | −2.00148e10 | −0.0834115 | ||||||||
\(339\) | −7.99609e10 | −0.328836 | ||||||||
\(340\) | 6.12519e10 | 0.248579 | ||||||||
\(341\) | −3.58645e11 | −1.43638 | ||||||||
\(342\) | −1.52412e11 | −0.602425 | ||||||||
\(343\) | 4.25786e10 | 0.166099 | ||||||||
\(344\) | 3.19226e10 | 0.122909 | ||||||||
\(345\) | −2.09927e11 | −0.797778 | ||||||||
\(346\) | 3.33992e11 | 1.25283 | ||||||||
\(347\) | −3.64138e10 | −0.134829 | −0.0674146 | − | 0.997725i | \(-0.521475\pi\) | ||||
−0.0674146 | + | 0.997725i | \(0.521475\pi\) | |||||||
\(348\) | −2.92384e9 | −0.0106868 | ||||||||
\(349\) | 9.86839e10 | 0.356067 | 0.178034 | − | 0.984024i | \(-0.443026\pi\) | ||||
0.178034 | + | 0.984024i | \(0.443026\pi\) | |||||||
\(350\) | 2.86498e11 | 1.02051 | ||||||||
\(351\) | 5.26440e10 | 0.185126 | ||||||||
\(352\) | −1.71051e11 | −0.593860 | ||||||||
\(353\) | −3.90458e11 | −1.33841 | −0.669204 | − | 0.743078i | \(-0.733365\pi\) | ||||
−0.669204 | + | 0.743078i | \(0.733365\pi\) | |||||||
\(354\) | −1.68752e11 | −0.571131 | ||||||||
\(355\) | −2.60655e11 | −0.871040 | ||||||||
\(356\) | −4.58010e10 | −0.151130 | ||||||||
\(357\) | −1.63212e11 | −0.531797 | ||||||||
\(358\) | −1.22237e10 | −0.0393305 | ||||||||
\(359\) | −3.86316e11 | −1.22749 | −0.613744 | − | 0.789505i | \(-0.710337\pi\) | ||||
−0.613744 | + | 0.789505i | \(0.710337\pi\) | |||||||
\(360\) | −3.22906e11 | −1.01325 | ||||||||
\(361\) | −1.92005e11 | −0.595017 | ||||||||
\(362\) | −7.03591e10 | −0.215343 | ||||||||
\(363\) | 2.25874e11 | 0.682788 | ||||||||
\(364\) | 2.23863e10 | 0.0668385 | ||||||||
\(365\) | 6.11914e10 | 0.180456 | ||||||||
\(366\) | 5.26979e10 | 0.153507 | ||||||||
\(367\) | 1.48155e11 | 0.426305 | 0.213152 | − | 0.977019i | \(-0.431627\pi\) | ||||
0.213152 | + | 0.977019i | \(0.431627\pi\) | |||||||
\(368\) | 6.94320e11 | 1.97353 | ||||||||
\(369\) | −4.46697e10 | −0.125428 | ||||||||
\(370\) | −5.38934e11 | −1.49495 | ||||||||
\(371\) | 8.87991e11 | 2.43347 | ||||||||
\(372\) | 1.94661e10 | 0.0527030 | ||||||||
\(373\) | −6.15338e11 | −1.64598 | −0.822989 | − | 0.568057i | \(-0.807695\pi\) | ||||
−0.822989 | + | 0.568057i | \(0.807695\pi\) | |||||||
\(374\) | 7.62755e11 | 2.01587 | ||||||||
\(375\) | −5.55453e10 | −0.145046 | ||||||||
\(376\) | 2.69507e11 | 0.695383 | ||||||||
\(377\) | 1.85548e10 | 0.0473063 | ||||||||
\(378\) | −3.93789e11 | −0.992089 | ||||||||
\(379\) | 2.48822e10 | 0.0619459 | 0.0309729 | − | 0.999520i | \(-0.490139\pi\) | ||||
0.0309729 | + | 0.999520i | \(0.490139\pi\) | |||||||
\(380\) | −5.90617e10 | −0.145305 | ||||||||
\(381\) | −7.94035e10 | −0.193053 | ||||||||
\(382\) | 6.95181e11 | 1.67037 | ||||||||
\(383\) | 4.82478e11 | 1.14573 | 0.572866 | − | 0.819649i | \(-0.305832\pi\) | ||||
0.572866 | + | 0.819649i | \(0.305832\pi\) | |||||||
\(384\) | −1.79224e11 | −0.420634 | ||||||||
\(385\) | 1.31043e12 | 3.03976 | ||||||||
\(386\) | −5.99349e11 | −1.37416 | ||||||||
\(387\) | −5.29792e10 | −0.120062 | ||||||||
\(388\) | −4.08606e10 | −0.0915297 | ||||||||
\(389\) | 3.80215e11 | 0.841890 | 0.420945 | − | 0.907086i | \(-0.361698\pi\) | ||||
0.420945 | + | 0.907086i | \(0.361698\pi\) | |||||||
\(390\) | 6.35909e10 | 0.139189 | ||||||||
\(391\) | −8.67310e11 | −1.87663 | ||||||||
\(392\) | 3.67183e11 | 0.785408 | ||||||||
\(393\) | −1.77342e11 | −0.375012 | ||||||||
\(394\) | −3.36937e11 | −0.704394 | ||||||||
\(395\) | −4.83968e11 | −1.00030 | ||||||||
\(396\) | 1.28259e11 | 0.262096 | ||||||||
\(397\) | 7.91759e11 | 1.59969 | 0.799845 | − | 0.600207i | \(-0.204915\pi\) | ||||
0.799845 | + | 0.600207i | \(0.204915\pi\) | |||||||
\(398\) | 2.10179e11 | 0.419871 | ||||||||
\(399\) | 1.57376e11 | 0.310858 | ||||||||
\(400\) | −4.02478e11 | −0.786090 | ||||||||
\(401\) | −3.06132e11 | −0.591234 | −0.295617 | − | 0.955307i | \(-0.595525\pi\) | ||||
−0.295617 | + | 0.955307i | \(0.595525\pi\) | |||||||
\(402\) | −6.80199e10 | −0.129903 | ||||||||
\(403\) | −1.23532e11 | −0.233296 | ||||||||
\(404\) | 5.80307e10 | 0.108378 | ||||||||
\(405\) | 4.46598e11 | 0.824840 | ||||||||
\(406\) | −1.38794e11 | −0.253515 | ||||||||
\(407\) | −1.00350e12 | −1.81277 | ||||||||
\(408\) | 1.94074e11 | 0.346735 | ||||||||
\(409\) | 9.04916e11 | 1.59902 | 0.799509 | − | 0.600654i | \(-0.205093\pi\) | ||||
0.799509 | + | 0.600654i | \(0.205093\pi\) | |||||||
\(410\) | −1.15766e11 | −0.202327 | ||||||||
\(411\) | −1.89948e11 | −0.328357 | ||||||||
\(412\) | −1.03362e11 | −0.176736 | ||||||||
\(413\) | −1.19780e12 | −2.02586 | ||||||||
\(414\) | −9.75352e11 | −1.63177 | ||||||||
\(415\) | −1.79599e11 | −0.297227 | ||||||||
\(416\) | −5.89172e10 | −0.0964544 | ||||||||
\(417\) | 1.90753e11 | 0.308929 | ||||||||
\(418\) | −7.35482e11 | −1.17836 | ||||||||
\(419\) | 3.36210e11 | 0.532903 | 0.266451 | − | 0.963848i | \(-0.414149\pi\) | ||||
0.266451 | + | 0.963848i | \(0.414149\pi\) | |||||||
\(420\) | −7.11256e10 | −0.111533 | ||||||||
\(421\) | −1.87100e11 | −0.290271 | −0.145135 | − | 0.989412i | \(-0.546362\pi\) | ||||
−0.145135 | + | 0.989412i | \(0.546362\pi\) | |||||||
\(422\) | −6.63140e10 | −0.101789 | ||||||||
\(423\) | −4.47276e11 | −0.679273 | ||||||||
\(424\) | −1.05590e12 | −1.58664 | ||||||||
\(425\) | 5.02755e11 | 0.747491 | ||||||||
\(426\) | 1.76175e11 | 0.259180 | ||||||||
\(427\) | 3.74048e11 | 0.544504 | ||||||||
\(428\) | 5.35872e10 | 0.0771905 | ||||||||
\(429\) | 1.18407e11 | 0.168779 | ||||||||
\(430\) | −1.37301e11 | −0.193672 | ||||||||
\(431\) | 9.60500e11 | 1.34076 | 0.670378 | − | 0.742020i | \(-0.266132\pi\) | ||||
0.670378 | + | 0.742020i | \(0.266132\pi\) | |||||||
\(432\) | 5.53203e11 | 0.764200 | ||||||||
\(433\) | 1.14812e12 | 1.56961 | 0.784806 | − | 0.619741i | \(-0.212762\pi\) | ||||
0.784806 | + | 0.619741i | \(0.212762\pi\) | |||||||
\(434\) | 9.24051e11 | 1.25024 | ||||||||
\(435\) | −5.89520e10 | −0.0789400 | ||||||||
\(436\) | 9.08259e10 | 0.120371 | ||||||||
\(437\) | 8.36297e11 | 1.09697 | ||||||||
\(438\) | −4.13590e10 | −0.0536953 | ||||||||
\(439\) | 5.44277e11 | 0.699407 | 0.349703 | − | 0.936860i | \(-0.386282\pi\) | ||||
0.349703 | + | 0.936860i | \(0.386282\pi\) | |||||||
\(440\) | −1.55822e12 | −1.98194 | ||||||||
\(441\) | −6.09381e11 | −0.767212 | ||||||||
\(442\) | 2.62725e11 | 0.327417 | ||||||||
\(443\) | −1.12065e11 | −0.138247 | −0.0691233 | − | 0.997608i | \(-0.522020\pi\) | ||||
−0.0691233 | + | 0.997608i | \(0.522020\pi\) | |||||||
\(444\) | 5.44668e10 | 0.0665133 | ||||||||
\(445\) | −9.23466e11 | −1.11635 | ||||||||
\(446\) | 8.78313e11 | 1.05110 | ||||||||
\(447\) | 5.80714e11 | 0.687984 | ||||||||
\(448\) | −8.97307e11 | −1.05242 | ||||||||
\(449\) | −1.11883e12 | −1.29913 | −0.649567 | − | 0.760304i | \(-0.725050\pi\) | ||||
−0.649567 | + | 0.760304i | \(0.725050\pi\) | |||||||
\(450\) | 5.65384e11 | 0.649961 | ||||||||
\(451\) | −2.15558e11 | −0.245341 | ||||||||
\(452\) | −1.43965e11 | −0.162231 | ||||||||
\(453\) | 1.59589e11 | 0.178058 | ||||||||
\(454\) | 1.85339e12 | 2.04746 | ||||||||
\(455\) | 4.51365e11 | 0.493716 | ||||||||
\(456\) | −1.87135e11 | −0.202681 | ||||||||
\(457\) | −1.38914e12 | −1.48978 | −0.744890 | − | 0.667188i | \(-0.767498\pi\) | ||||
−0.744890 | + | 0.667188i | \(0.767498\pi\) | |||||||
\(458\) | 1.39626e12 | 1.48276 | ||||||||
\(459\) | −6.91032e11 | −0.726677 | ||||||||
\(460\) | −3.77961e11 | −0.393583 | ||||||||
\(461\) | 1.06041e12 | 1.09350 | 0.546752 | − | 0.837294i | \(-0.315864\pi\) | ||||
0.546752 | + | 0.837294i | \(0.315864\pi\) | |||||||
\(462\) | −8.85711e11 | −0.904488 | ||||||||
\(463\) | 2.81576e11 | 0.284762 | 0.142381 | − | 0.989812i | \(-0.454524\pi\) | ||||
0.142381 | + | 0.989812i | \(0.454524\pi\) | |||||||
\(464\) | 1.94980e11 | 0.195281 | ||||||||
\(465\) | 3.92486e11 | 0.389301 | ||||||||
\(466\) | 1.14829e12 | 1.12801 | ||||||||
\(467\) | −9.91125e11 | −0.964278 | −0.482139 | − | 0.876095i | \(-0.660140\pi\) | ||||
−0.482139 | + | 0.876095i | \(0.660140\pi\) | |||||||
\(468\) | 4.41779e10 | 0.0425695 | ||||||||
\(469\) | −4.82802e11 | −0.460778 | ||||||||
\(470\) | −1.15917e12 | −1.09573 | ||||||||
\(471\) | −2.52916e11 | −0.236801 | ||||||||
\(472\) | 1.42429e12 | 1.32087 | ||||||||
\(473\) | −2.55656e11 | −0.234845 | ||||||||
\(474\) | 3.27112e11 | 0.297641 | ||||||||
\(475\) | −4.84778e11 | −0.436940 | ||||||||
\(476\) | −2.93855e11 | −0.262362 | ||||||||
\(477\) | 1.75239e12 | 1.54988 | ||||||||
\(478\) | 2.15915e11 | 0.189173 | ||||||||
\(479\) | −1.38074e12 | −1.19841 | −0.599203 | − | 0.800597i | \(-0.704516\pi\) | ||||
−0.599203 | + | 0.800597i | \(0.704516\pi\) | |||||||
\(480\) | 1.87191e11 | 0.160953 | ||||||||
\(481\) | −3.45648e11 | −0.294429 | ||||||||
\(482\) | 4.31974e11 | 0.364541 | ||||||||
\(483\) | 1.00712e12 | 0.842013 | ||||||||
\(484\) | 4.06673e11 | 0.336853 | ||||||||
\(485\) | −8.23854e11 | −0.676102 | ||||||||
\(486\) | −1.19202e12 | −0.969215 | ||||||||
\(487\) | 9.65212e11 | 0.777575 | 0.388788 | − | 0.921327i | \(-0.372894\pi\) | ||||
0.388788 | + | 0.921327i | \(0.372894\pi\) | |||||||
\(488\) | −4.44777e11 | −0.355020 | ||||||||
\(489\) | −3.91697e11 | −0.309785 | ||||||||
\(490\) | −1.57928e12 | −1.23759 | ||||||||
\(491\) | −1.10735e12 | −0.859841 | −0.429920 | − | 0.902867i | \(-0.641458\pi\) | ||||
−0.429920 | + | 0.902867i | \(0.641458\pi\) | |||||||
\(492\) | 1.16998e10 | 0.00900191 | ||||||||
\(493\) | −2.43559e11 | −0.185692 | ||||||||
\(494\) | −2.53331e11 | −0.191389 | ||||||||
\(495\) | 2.58604e12 | 1.93603 | ||||||||
\(496\) | −1.29812e12 | −0.963050 | ||||||||
\(497\) | 1.25049e12 | 0.919338 | ||||||||
\(498\) | 1.21390e11 | 0.0884407 | ||||||||
\(499\) | −2.24583e12 | −1.62153 | −0.810763 | − | 0.585374i | \(-0.800948\pi\) | ||||
−0.810763 | + | 0.585374i | \(0.800948\pi\) | |||||||
\(500\) | −1.00006e11 | −0.0715586 | ||||||||
\(501\) | −7.20198e9 | −0.00510719 | ||||||||
\(502\) | 4.34564e11 | 0.305413 | ||||||||
\(503\) | 3.98259e11 | 0.277402 | 0.138701 | − | 0.990334i | \(-0.455707\pi\) | ||||
0.138701 | + | 0.990334i | \(0.455707\pi\) | |||||||
\(504\) | 1.54913e12 | 1.06943 | ||||||||
\(505\) | 1.17005e12 | 0.800557 | ||||||||
\(506\) | −4.70666e12 | −3.19180 | ||||||||
\(507\) | 4.07843e10 | 0.0274130 | ||||||||
\(508\) | −1.42961e11 | −0.0952428 | ||||||||
\(509\) | 2.66411e12 | 1.75923 | 0.879615 | − | 0.475687i | \(-0.157800\pi\) | ||||
0.879615 | + | 0.475687i | \(0.157800\pi\) | |||||||
\(510\) | −8.34727e11 | −0.546360 | ||||||||
\(511\) | −2.93564e11 | −0.190462 | ||||||||
\(512\) | 9.71905e11 | 0.625042 | ||||||||
\(513\) | 6.66323e11 | 0.424773 | ||||||||
\(514\) | 1.53775e12 | 0.971747 | ||||||||
\(515\) | −2.08405e12 | −1.30550 | ||||||||
\(516\) | 1.38762e10 | 0.00861681 | ||||||||
\(517\) | −2.15838e12 | −1.32868 | ||||||||
\(518\) | 2.58553e12 | 1.57785 | ||||||||
\(519\) | −6.80577e11 | −0.411741 | ||||||||
\(520\) | −5.36715e11 | −0.321906 | ||||||||
\(521\) | −3.11961e12 | −1.85494 | −0.927472 | − | 0.373894i | \(-0.878022\pi\) | ||||
−0.927472 | + | 0.373894i | \(0.878022\pi\) | |||||||
\(522\) | −2.73900e11 | −0.161464 | ||||||||
\(523\) | −2.05566e12 | −1.20142 | −0.600709 | − | 0.799468i | \(-0.705115\pi\) | ||||
−0.600709 | + | 0.799468i | \(0.705115\pi\) | |||||||
\(524\) | −3.19294e11 | −0.185012 | ||||||||
\(525\) | −5.83798e11 | −0.335387 | ||||||||
\(526\) | −1.10290e12 | −0.628202 | ||||||||
\(527\) | 1.62155e12 | 0.915762 | ||||||||
\(528\) | 1.24426e12 | 0.696722 | ||||||||
\(529\) | 3.55067e12 | 1.97133 | ||||||||
\(530\) | 4.54150e12 | 2.50011 | ||||||||
\(531\) | −2.36377e12 | −1.29027 | ||||||||
\(532\) | 2.83347e11 | 0.153362 | ||||||||
\(533\) | −7.42472e10 | −0.0398481 | ||||||||
\(534\) | 6.24166e11 | 0.332173 | ||||||||
\(535\) | 1.08045e12 | 0.570183 | ||||||||
\(536\) | 5.74096e11 | 0.300430 | ||||||||
\(537\) | 2.49083e10 | 0.0129259 | ||||||||
\(538\) | 2.12368e12 | 1.09287 | ||||||||
\(539\) | −2.94063e12 | −1.50069 | ||||||||
\(540\) | −3.01142e11 | −0.152405 | ||||||||
\(541\) | 8.06876e11 | 0.404966 | 0.202483 | − | 0.979286i | \(-0.435099\pi\) | ||||
0.202483 | + | 0.979286i | \(0.435099\pi\) | |||||||
\(542\) | −2.05135e12 | −1.02104 | ||||||||
\(543\) | 1.43371e11 | 0.0707721 | ||||||||
\(544\) | 7.73378e11 | 0.378614 | ||||||||
\(545\) | 1.83128e12 | 0.889142 | ||||||||
\(546\) | −3.05076e11 | −0.146906 | ||||||||
\(547\) | 1.93370e12 | 0.923521 | 0.461760 | − | 0.887005i | \(-0.347218\pi\) | ||||
0.461760 | + | 0.887005i | \(0.347218\pi\) | |||||||
\(548\) | −3.41990e11 | −0.161995 | ||||||||
\(549\) | 7.38157e11 | 0.346795 | ||||||||
\(550\) | 2.72832e12 | 1.27134 | ||||||||
\(551\) | 2.34851e11 | 0.108545 | ||||||||
\(552\) | −1.19756e12 | −0.548997 | ||||||||
\(553\) | 2.32183e12 | 1.05576 | ||||||||
\(554\) | −4.24810e12 | −1.91602 | ||||||||
\(555\) | 1.09819e12 | 0.491314 | ||||||||
\(556\) | 3.43439e11 | 0.152410 | ||||||||
\(557\) | 3.06623e12 | 1.34976 | 0.674879 | − | 0.737928i | \(-0.264196\pi\) | ||||
0.674879 | + | 0.737928i | \(0.264196\pi\) | |||||||
\(558\) | 1.82355e12 | 0.796276 | ||||||||
\(559\) | −8.80587e10 | −0.0381434 | ||||||||
\(560\) | 4.74312e12 | 2.03806 | ||||||||
\(561\) | −1.55427e12 | −0.662512 | ||||||||
\(562\) | −1.85885e12 | −0.786013 | ||||||||
\(563\) | −2.59944e12 | −1.09042 | −0.545208 | − | 0.838301i | \(-0.683549\pi\) | ||||
−0.545208 | + | 0.838301i | \(0.683549\pi\) | |||||||
\(564\) | 1.17150e11 | 0.0487512 | ||||||||
\(565\) | −2.90270e12 | −1.19835 | ||||||||
\(566\) | −4.14416e12 | −1.69732 | ||||||||
\(567\) | −2.14255e12 | −0.870576 | ||||||||
\(568\) | −1.48694e12 | −0.599413 | ||||||||
\(569\) | −1.63182e12 | −0.652632 | −0.326316 | − | 0.945261i | \(-0.605807\pi\) | ||||
−0.326316 | + | 0.945261i | \(0.605807\pi\) | |||||||
\(570\) | 8.04880e11 | 0.319370 | ||||||||
\(571\) | −1.05673e12 | −0.416010 | −0.208005 | − | 0.978128i | \(-0.566697\pi\) | ||||
−0.208005 | + | 0.978128i | \(0.566697\pi\) | |||||||
\(572\) | 2.13185e11 | 0.0832672 | ||||||||
\(573\) | −1.41658e12 | −0.548964 | ||||||||
\(574\) | 5.55386e11 | 0.213546 | ||||||||
\(575\) | −3.10230e12 | −1.18353 | ||||||||
\(576\) | −1.77077e12 | −0.670289 | ||||||||
\(577\) | −8.51110e11 | −0.319665 | −0.159832 | − | 0.987144i | \(-0.551095\pi\) | ||||
−0.159832 | + | 0.987144i | \(0.551095\pi\) | |||||||
\(578\) | −5.38987e11 | −0.200865 | ||||||||
\(579\) | 1.22130e12 | 0.451614 | ||||||||
\(580\) | −1.06140e11 | −0.0389450 | ||||||||
\(581\) | 8.61624e11 | 0.313708 | ||||||||
\(582\) | 5.56839e11 | 0.201176 | ||||||||
\(583\) | 8.45633e12 | 3.03161 | ||||||||
\(584\) | 3.49075e11 | 0.124183 | ||||||||
\(585\) | 8.90739e11 | 0.314448 | ||||||||
\(586\) | 2.91591e12 | 1.02149 | ||||||||
\(587\) | 6.19927e11 | 0.215511 | 0.107755 | − | 0.994177i | \(-0.465634\pi\) | ||||
0.107755 | + | 0.994177i | \(0.465634\pi\) | |||||||
\(588\) | 1.59608e11 | 0.0550626 | ||||||||
\(589\) | −1.56357e12 | −0.535301 | ||||||||
\(590\) | −6.12597e12 | −2.08133 | ||||||||
\(591\) | 6.86579e11 | 0.231498 | ||||||||
\(592\) | −3.63220e12 | −1.21541 | ||||||||
\(593\) | −3.79034e12 | −1.25873 | −0.629364 | − | 0.777110i | \(-0.716685\pi\) | ||||
−0.629364 | + | 0.777110i | \(0.716685\pi\) | |||||||
\(594\) | −3.75005e12 | −1.23594 | ||||||||
\(595\) | −5.92486e12 | −1.93799 | ||||||||
\(596\) | 1.04554e12 | 0.339417 | ||||||||
\(597\) | −4.28283e11 | −0.137990 | ||||||||
\(598\) | −1.62117e12 | −0.518410 | ||||||||
\(599\) | 2.62045e12 | 0.831679 | 0.415839 | − | 0.909438i | \(-0.363488\pi\) | ||||
0.415839 | + | 0.909438i | \(0.363488\pi\) | |||||||
\(600\) | 6.94190e11 | 0.218674 | ||||||||
\(601\) | 1.11042e12 | 0.347178 | 0.173589 | − | 0.984818i | \(-0.444464\pi\) | ||||
0.173589 | + | 0.984818i | \(0.444464\pi\) | |||||||
\(602\) | 6.58700e11 | 0.204411 | ||||||||
\(603\) | −9.52777e11 | −0.293470 | ||||||||
\(604\) | 2.87331e11 | 0.0878449 | ||||||||
\(605\) | 8.19956e12 | 2.48824 | ||||||||
\(606\) | −7.90829e11 | −0.238208 | ||||||||
\(607\) | 4.57077e12 | 1.36660 | 0.683298 | − | 0.730140i | \(-0.260545\pi\) | ||||
0.683298 | + | 0.730140i | \(0.260545\pi\) | |||||||
\(608\) | −7.45724e11 | −0.221316 | ||||||||
\(609\) | 2.82821e11 | 0.0833171 | ||||||||
\(610\) | 1.91301e12 | 0.559415 | ||||||||
\(611\) | −7.43436e11 | −0.215803 | ||||||||
\(612\) | −5.79902e11 | −0.167099 | ||||||||
\(613\) | −5.61998e12 | −1.60754 | −0.803772 | − | 0.594938i | \(-0.797177\pi\) | ||||
−0.803772 | + | 0.594938i | \(0.797177\pi\) | |||||||
\(614\) | 4.89568e12 | 1.39013 | ||||||||
\(615\) | 2.35898e11 | 0.0664945 | ||||||||
\(616\) | 7.47551e12 | 2.09184 | ||||||||
\(617\) | 2.17420e12 | 0.603970 | 0.301985 | − | 0.953313i | \(-0.402351\pi\) | ||||
0.301985 | + | 0.953313i | \(0.402351\pi\) | |||||||
\(618\) | 1.40860e12 | 0.388454 | ||||||||
\(619\) | 5.91455e12 | 1.61925 | 0.809625 | − | 0.586947i | \(-0.199670\pi\) | ||||
0.809625 | + | 0.586947i | \(0.199670\pi\) | |||||||
\(620\) | 7.06649e11 | 0.192062 | ||||||||
\(621\) | 4.26409e12 | 1.15057 | ||||||||
\(622\) | −4.66542e12 | −1.24978 | ||||||||
\(623\) | 4.43031e12 | 1.17825 | ||||||||
\(624\) | 4.28576e11 | 0.113161 | ||||||||
\(625\) | −4.63555e12 | −1.21518 | ||||||||
\(626\) | 8.33426e11 | 0.216912 | ||||||||
\(627\) | 1.49869e12 | 0.387266 | ||||||||
\(628\) | −4.55361e11 | −0.116826 | ||||||||
\(629\) | 4.53716e12 | 1.15573 | ||||||||
\(630\) | −6.66293e12 | −1.68513 | ||||||||
\(631\) | −5.05658e12 | −1.26977 | −0.634884 | − | 0.772607i | \(-0.718952\pi\) | ||||
−0.634884 | + | 0.772607i | \(0.718952\pi\) | |||||||
\(632\) | −2.76086e12 | −0.688364 | ||||||||
\(633\) | 1.35128e11 | 0.0334526 | ||||||||
\(634\) | 2.09431e11 | 0.0514801 | ||||||||
\(635\) | −2.88247e12 | −0.703530 | ||||||||
\(636\) | −4.58982e11 | −0.111234 | ||||||||
\(637\) | −1.01288e12 | −0.243741 | ||||||||
\(638\) | −1.32173e12 | −0.315828 | ||||||||
\(639\) | 2.46775e12 | 0.585527 | ||||||||
\(640\) | −6.50609e12 | −1.53289 | ||||||||
\(641\) | 1.51370e12 | 0.354142 | 0.177071 | − | 0.984198i | \(-0.443338\pi\) | ||||
0.177071 | + | 0.984198i | \(0.443338\pi\) | |||||||
\(642\) | −7.30274e11 | −0.169660 | ||||||||
\(643\) | 3.90178e12 | 0.900146 | 0.450073 | − | 0.892992i | \(-0.351398\pi\) | ||||
0.450073 | + | 0.892992i | \(0.351398\pi\) | |||||||
\(644\) | 1.81326e12 | 0.415407 | ||||||||
\(645\) | 2.79779e11 | 0.0636498 | ||||||||
\(646\) | 3.32535e12 | 0.751261 | ||||||||
\(647\) | 7.88115e12 | 1.76815 | 0.884077 | − | 0.467341i | \(-0.154788\pi\) | ||||
0.884077 | + | 0.467341i | \(0.154788\pi\) | |||||||
\(648\) | 2.54768e12 | 0.567620 | ||||||||
\(649\) | −1.14066e13 | −2.52381 | ||||||||
\(650\) | 9.39747e11 | 0.206491 | ||||||||
\(651\) | −1.88294e12 | −0.410887 | ||||||||
\(652\) | −7.05229e11 | −0.152833 | ||||||||
\(653\) | −5.10697e12 | −1.09914 | −0.549571 | − | 0.835447i | \(-0.685209\pi\) | ||||
−0.549571 | + | 0.835447i | \(0.685209\pi\) | |||||||
\(654\) | −1.23776e12 | −0.264567 | ||||||||
\(655\) | −6.43778e12 | −1.36663 | ||||||||
\(656\) | −7.80217e11 | −0.164493 | ||||||||
\(657\) | −5.79329e11 | −0.121306 | ||||||||
\(658\) | 5.56107e12 | 1.15649 | ||||||||
\(659\) | −5.45308e11 | −0.112631 | −0.0563154 | − | 0.998413i | \(-0.517935\pi\) | ||||
−0.0563154 | + | 0.998413i | \(0.517935\pi\) | |||||||
\(660\) | −6.77329e11 | −0.138948 | ||||||||
\(661\) | −3.05503e12 | −0.622456 | −0.311228 | − | 0.950335i | \(-0.600740\pi\) | ||||
−0.311228 | + | 0.950335i | \(0.600740\pi\) | |||||||
\(662\) | −1.25018e12 | −0.252995 | ||||||||
\(663\) | −5.35356e11 | −0.107605 | ||||||||
\(664\) | −1.02455e12 | −0.204539 | ||||||||
\(665\) | 5.71301e12 | 1.13284 | ||||||||
\(666\) | 5.10236e12 | 1.00493 | ||||||||
\(667\) | 1.50291e12 | 0.294013 | ||||||||
\(668\) | −1.29668e10 | −0.00251963 | ||||||||
\(669\) | −1.78974e12 | −0.345441 | ||||||||
\(670\) | −2.46923e12 | −0.473395 | ||||||||
\(671\) | 3.56205e12 | 0.678343 | ||||||||
\(672\) | −8.98046e11 | −0.169878 | ||||||||
\(673\) | −1.57419e12 | −0.295795 | −0.147897 | − | 0.989003i | \(-0.547251\pi\) | ||||
−0.147897 | + | 0.989003i | \(0.547251\pi\) | |||||||
\(674\) | −5.68968e12 | −1.06199 | ||||||||
\(675\) | −2.47177e12 | −0.458291 | ||||||||
\(676\) | 7.34298e10 | 0.0135242 | ||||||||
\(677\) | −2.62249e11 | −0.0479805 | −0.0239903 | − | 0.999712i | \(-0.507637\pi\) | ||||
−0.0239903 | + | 0.999712i | \(0.507637\pi\) | |||||||
\(678\) | 1.96192e12 | 0.356573 | ||||||||
\(679\) | 3.95242e12 | 0.713591 | ||||||||
\(680\) | 7.04520e12 | 1.26358 | ||||||||
\(681\) | −3.77666e12 | −0.672892 | ||||||||
\(682\) | 8.79973e12 | 1.55754 | ||||||||
\(683\) | −3.64995e12 | −0.641791 | −0.320896 | − | 0.947115i | \(-0.603984\pi\) | ||||
−0.320896 | + | 0.947115i | \(0.603984\pi\) | |||||||
\(684\) | 5.59166e11 | 0.0976762 | ||||||||
\(685\) | −6.89539e12 | −1.19661 | ||||||||
\(686\) | −1.04471e12 | −0.180110 | ||||||||
\(687\) | −2.84517e12 | −0.487307 | ||||||||
\(688\) | −9.25354e11 | −0.157456 | ||||||||
\(689\) | 2.91271e12 | 0.492392 | ||||||||
\(690\) | 5.15077e12 | 0.865070 | ||||||||
\(691\) | −1.69603e12 | −0.282998 | −0.141499 | − | 0.989938i | \(-0.545192\pi\) | ||||
−0.141499 | + | 0.989938i | \(0.545192\pi\) | |||||||
\(692\) | −1.22534e12 | −0.203132 | ||||||||
\(693\) | −1.24065e13 | −2.04337 | ||||||||
\(694\) | 8.93451e11 | 0.146202 | ||||||||
\(695\) | 6.92461e12 | 1.12581 | ||||||||
\(696\) | −3.36300e11 | −0.0543232 | ||||||||
\(697\) | 9.74608e11 | 0.156416 | ||||||||
\(698\) | −2.42131e12 | −0.386101 | ||||||||
\(699\) | −2.33987e12 | −0.370718 | ||||||||
\(700\) | −1.05110e12 | −0.165463 | ||||||||
\(701\) | 1.15906e13 | 1.81291 | 0.906454 | − | 0.422304i | \(-0.138778\pi\) | ||||
0.906454 | + | 0.422304i | \(0.138778\pi\) | |||||||
\(702\) | −1.29167e12 | −0.200741 | ||||||||
\(703\) | −4.37492e12 | −0.675571 | ||||||||
\(704\) | −8.54505e12 | −1.31111 | ||||||||
\(705\) | 2.36204e12 | 0.360111 | ||||||||
\(706\) | 9.58030e12 | 1.45130 | ||||||||
\(707\) | −5.61328e12 | −0.844946 | ||||||||
\(708\) | 6.19114e11 | 0.0926022 | ||||||||
\(709\) | −6.98541e12 | −1.03821 | −0.519104 | − | 0.854711i | \(-0.673734\pi\) | ||||
−0.519104 | + | 0.854711i | \(0.673734\pi\) | |||||||
\(710\) | 6.39544e12 | 0.944512 | ||||||||
\(711\) | 4.58196e12 | 0.672417 | ||||||||
\(712\) | −5.26804e12 | −0.768226 | ||||||||
\(713\) | −1.00059e13 | −1.44996 | ||||||||
\(714\) | 4.00459e12 | 0.576654 | ||||||||
\(715\) | 4.29835e12 | 0.615070 | ||||||||
\(716\) | 4.48461e10 | 0.00637699 | ||||||||
\(717\) | −4.39972e11 | −0.0621711 | ||||||||
\(718\) | 9.47866e12 | 1.33103 | ||||||||
\(719\) | −3.43730e12 | −0.479665 | −0.239832 | − | 0.970814i | \(-0.577092\pi\) | ||||
−0.239832 | + | 0.970814i | \(0.577092\pi\) | |||||||
\(720\) | 9.36022e12 | 1.29804 | ||||||||
\(721\) | 9.99820e12 | 1.37788 | ||||||||
\(722\) | 4.71103e12 | 0.645206 | ||||||||
\(723\) | −8.80236e11 | −0.119805 | ||||||||
\(724\) | 2.58131e11 | 0.0349154 | ||||||||
\(725\) | −8.71194e11 | −0.117110 | ||||||||
\(726\) | −5.54205e12 | −0.740381 | ||||||||
\(727\) | 1.25723e12 | 0.166920 | 0.0834601 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834601 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(728\) | 2.57488e12 | 0.339755 | ||||||||
\(729\) | −2.41427e12 | −0.316601 | ||||||||
\(730\) | −1.50139e12 | −0.195678 | ||||||||
\(731\) | 1.15591e12 | 0.149725 | ||||||||
\(732\) | −1.93337e11 | −0.0248894 | ||||||||
\(733\) | −1.51950e12 | −0.194416 | −0.0972079 | − | 0.995264i | \(-0.530991\pi\) | ||||
−0.0972079 | + | 0.995264i | \(0.530991\pi\) | |||||||
\(734\) | −3.63515e12 | −0.462264 | ||||||||
\(735\) | 3.21810e12 | 0.406731 | ||||||||
\(736\) | −4.77221e12 | −0.599473 | ||||||||
\(737\) | −4.59772e12 | −0.574036 | ||||||||
\(738\) | 1.09602e12 | 0.136008 | ||||||||
\(739\) | 1.19661e13 | 1.47589 | 0.737944 | − | 0.674862i | \(-0.235797\pi\) | ||||
0.737944 | + | 0.674862i | \(0.235797\pi\) | |||||||
\(740\) | 1.97723e12 | 0.242390 | ||||||||
\(741\) | 5.16213e11 | 0.0628995 | ||||||||
\(742\) | −2.17878e13 | −2.63873 | ||||||||
\(743\) | 1.52097e12 | 0.183093 | 0.0915465 | − | 0.995801i | \(-0.470819\pi\) | ||||
0.0915465 | + | 0.995801i | \(0.470819\pi\) | |||||||
\(744\) | 2.23899e12 | 0.267901 | ||||||||
\(745\) | 2.10808e13 | 2.50717 | ||||||||
\(746\) | 1.50980e13 | 1.78482 | ||||||||
\(747\) | 1.70036e12 | 0.199801 | ||||||||
\(748\) | −2.79838e12 | −0.326850 | ||||||||
\(749\) | −5.18346e12 | −0.601799 | ||||||||
\(750\) | 1.36286e12 | 0.157281 | ||||||||
\(751\) | −8.06595e12 | −0.925286 | −0.462643 | − | 0.886545i | \(-0.653099\pi\) | ||||
−0.462643 | + | 0.886545i | \(0.653099\pi\) | |||||||
\(752\) | −7.81230e12 | −0.890838 | ||||||||
\(753\) | −8.85513e11 | −0.100373 | ||||||||
\(754\) | −4.55260e11 | −0.0512966 | ||||||||
\(755\) | 5.79333e12 | 0.648884 | ||||||||
\(756\) | 1.44472e12 | 0.160856 | ||||||||
\(757\) | 8.72882e12 | 0.966104 | 0.483052 | − | 0.875592i | \(-0.339528\pi\) | ||||
0.483052 | + | 0.875592i | \(0.339528\pi\) | |||||||
\(758\) | −6.10511e11 | −0.0671710 | ||||||||
\(759\) | 9.59079e12 | 1.04898 | ||||||||
\(760\) | −6.79329e12 | −0.738616 | ||||||||
\(761\) | 7.63407e11 | 0.0825135 | 0.0412568 | − | 0.999149i | \(-0.486864\pi\) | ||||
0.0412568 | + | 0.999149i | \(0.486864\pi\) | |||||||
\(762\) | 1.94825e12 | 0.209337 | ||||||||
\(763\) | −8.78554e12 | −0.938443 | ||||||||
\(764\) | −2.55046e12 | −0.270831 | ||||||||
\(765\) | −1.16923e13 | −1.23431 | ||||||||
\(766\) | −1.18381e13 | −1.24237 | ||||||||
\(767\) | −3.92892e12 | −0.409915 | ||||||||
\(768\) | 1.75945e12 | 0.182495 | ||||||||
\(769\) | −5.30538e12 | −0.547076 | −0.273538 | − | 0.961861i | \(-0.588194\pi\) | ||||
−0.273538 | + | 0.961861i | \(0.588194\pi\) | |||||||
\(770\) | −3.21527e13 | −3.29616 | ||||||||
\(771\) | −3.13349e12 | −0.319363 | ||||||||
\(772\) | 2.19887e12 | 0.222804 | ||||||||
\(773\) | −1.53974e12 | −0.155110 | −0.0775550 | − | 0.996988i | \(-0.524711\pi\) | ||||
−0.0775550 | + | 0.996988i | \(0.524711\pi\) | |||||||
\(774\) | 1.29990e12 | 0.130189 | ||||||||
\(775\) | 5.80017e12 | 0.577541 | ||||||||
\(776\) | −4.69979e12 | −0.465266 | ||||||||
\(777\) | −5.26854e12 | −0.518556 | ||||||||
\(778\) | −9.32896e12 | −0.912904 | ||||||||
\(779\) | −9.39759e11 | −0.0914319 | ||||||||
\(780\) | −2.33300e11 | −0.0225678 | ||||||||
\(781\) | 1.19084e13 | 1.14531 | ||||||||
\(782\) | 2.12803e13 | 2.03492 | ||||||||
\(783\) | 1.19745e12 | 0.113849 | ||||||||
\(784\) | −1.06437e13 | −1.00617 | ||||||||
\(785\) | −9.18125e12 | −0.862955 | ||||||||
\(786\) | 4.35127e12 | 0.406644 | ||||||||
\(787\) | −2.94759e12 | −0.273893 | −0.136946 | − | 0.990578i | \(-0.543729\pi\) | ||||
−0.136946 | + | 0.990578i | \(0.543729\pi\) | |||||||
\(788\) | 1.23615e12 | 0.114209 | ||||||||
\(789\) | 2.24738e12 | 0.206457 | ||||||||
\(790\) | 1.18747e13 | 1.08467 | ||||||||
\(791\) | 1.39257e13 | 1.26480 | ||||||||
\(792\) | 1.47524e13 | 1.33229 | ||||||||
\(793\) | 1.22692e12 | 0.110176 | ||||||||
\(794\) | −1.94266e13 | −1.73462 | ||||||||
\(795\) | −9.25425e12 | −0.821654 | ||||||||
\(796\) | −7.71099e11 | −0.0680772 | ||||||||
\(797\) | −1.83481e13 | −1.61075 | −0.805376 | − | 0.592764i | \(-0.798037\pi\) | ||||
−0.805376 | + | 0.592764i | \(0.798037\pi\) | |||||||
\(798\) | −3.86139e12 | −0.337079 | ||||||||
\(799\) | 9.75873e12 | 0.847096 | ||||||||
\(800\) | 2.76632e12 | 0.238779 | ||||||||
\(801\) | 8.74291e12 | 0.750429 | ||||||||
\(802\) | 7.51127e12 | 0.641104 | ||||||||
\(803\) | −2.79561e12 | −0.237278 | ||||||||
\(804\) | 2.49549e11 | 0.0210622 | ||||||||
\(805\) | 3.65600e13 | 3.06849 | ||||||||
\(806\) | 3.03099e12 | 0.252975 | ||||||||
\(807\) | −4.32744e12 | −0.359170 | ||||||||
\(808\) | 6.67470e12 | 0.550910 | ||||||||
\(809\) | −9.70701e12 | −0.796741 | −0.398371 | − | 0.917225i | \(-0.630424\pi\) | ||||
−0.398371 | + | 0.917225i | \(0.630424\pi\) | |||||||
\(810\) | −1.09578e13 | −0.894415 | ||||||||
\(811\) | 6.14421e12 | 0.498738 | 0.249369 | − | 0.968409i | \(-0.419777\pi\) | ||||
0.249369 | + | 0.968409i | \(0.419777\pi\) | |||||||
\(812\) | 5.09203e11 | 0.0411045 | ||||||||
\(813\) | 4.18005e12 | 0.335563 | ||||||||
\(814\) | 2.46220e13 | 1.96568 | ||||||||
\(815\) | −1.42192e13 | −1.12893 | ||||||||
\(816\) | −5.62572e12 | −0.444194 | ||||||||
\(817\) | −1.11457e12 | −0.0875205 | ||||||||
\(818\) | −2.22030e13 | −1.73389 | ||||||||
\(819\) | −4.27330e12 | −0.331884 | ||||||||
\(820\) | 4.24720e11 | 0.0328050 | ||||||||
\(821\) | 1.41092e13 | 1.08383 | 0.541913 | − | 0.840434i | \(-0.317700\pi\) | ||||
0.541913 | + | 0.840434i | \(0.317700\pi\) | |||||||
\(822\) | 4.66057e12 | 0.356054 | ||||||||
\(823\) | 7.99374e12 | 0.607366 | 0.303683 | − | 0.952773i | \(-0.401784\pi\) | ||||
0.303683 | + | 0.952773i | \(0.401784\pi\) | |||||||
\(824\) | −1.18888e13 | −0.898389 | ||||||||
\(825\) | −5.55951e12 | −0.417824 | ||||||||
\(826\) | 2.93892e13 | 2.19674 | ||||||||
\(827\) | −4.82994e12 | −0.359060 | −0.179530 | − | 0.983752i | \(-0.557458\pi\) | ||||
−0.179530 | + | 0.983752i | \(0.557458\pi\) | |||||||
\(828\) | 3.57834e12 | 0.264573 | ||||||||
\(829\) | 1.41648e13 | 1.04163 | 0.520816 | − | 0.853669i | \(-0.325628\pi\) | ||||
0.520816 | + | 0.853669i | \(0.325628\pi\) | |||||||
\(830\) | 4.40666e12 | 0.322298 | ||||||||
\(831\) | 8.65637e12 | 0.629697 | ||||||||
\(832\) | −2.94327e12 | −0.212949 | ||||||||
\(833\) | 1.32956e13 | 0.956762 | ||||||||
\(834\) | −4.68031e12 | −0.334987 | ||||||||
\(835\) | −2.61443e11 | −0.0186118 | ||||||||
\(836\) | 2.69831e12 | 0.191058 | ||||||||
\(837\) | −7.97228e12 | −0.561459 | ||||||||
\(838\) | −8.24927e12 | −0.577853 | ||||||||
\(839\) | 1.79477e13 | 1.25049 | 0.625246 | − | 0.780428i | \(-0.284999\pi\) | ||||
0.625246 | + | 0.780428i | \(0.284999\pi\) | |||||||
\(840\) | −8.18088e12 | −0.566948 | ||||||||
\(841\) | −1.40851e13 | −0.970907 | ||||||||
\(842\) | 4.59068e12 | 0.314755 | ||||||||
\(843\) | 3.78778e12 | 0.258322 | ||||||||
\(844\) | 2.43291e11 | 0.0165038 | ||||||||
\(845\) | 1.48053e12 | 0.0998993 | ||||||||
\(846\) | 1.09744e13 | 0.736570 | ||||||||
\(847\) | −3.93372e13 | −2.62620 | ||||||||
\(848\) | 3.06079e13 | 2.03260 | ||||||||
\(849\) | 8.44458e12 | 0.557819 | ||||||||
\(850\) | −1.23356e13 | −0.810542 | ||||||||
\(851\) | −2.79970e13 | −1.82990 | ||||||||
\(852\) | −6.46347e11 | −0.0420231 | ||||||||
\(853\) | −8.65463e12 | −0.559729 | −0.279865 | − | 0.960039i | \(-0.590290\pi\) | ||||
−0.279865 | + | 0.960039i | \(0.590290\pi\) | |||||||
\(854\) | −9.17764e12 | −0.590433 | ||||||||
\(855\) | 1.12742e13 | 0.721505 | ||||||||
\(856\) | 6.16360e12 | 0.392376 | ||||||||
\(857\) | −1.17199e13 | −0.742185 | −0.371092 | − | 0.928596i | \(-0.621017\pi\) | ||||
−0.371092 | + | 0.928596i | \(0.621017\pi\) | |||||||
\(858\) | −2.90524e12 | −0.183016 | ||||||||
\(859\) | −2.70022e13 | −1.69211 | −0.846057 | − | 0.533092i | \(-0.821030\pi\) | ||||
−0.846057 | + | 0.533092i | \(0.821030\pi\) | |||||||
\(860\) | 5.03727e11 | 0.0314016 | ||||||||
\(861\) | −1.13171e12 | −0.0701815 | ||||||||
\(862\) | −2.35669e13 | −1.45385 | ||||||||
\(863\) | 2.11111e13 | 1.29557 | 0.647786 | − | 0.761823i | \(-0.275695\pi\) | ||||
0.647786 | + | 0.761823i | \(0.275695\pi\) | |||||||
\(864\) | −3.80228e12 | −0.232130 | ||||||||
\(865\) | −2.47060e13 | −1.50048 | ||||||||
\(866\) | −2.81704e13 | −1.70201 | ||||||||
\(867\) | 1.09830e12 | 0.0660137 | ||||||||
\(868\) | −3.39013e12 | −0.202711 | ||||||||
\(869\) | 2.21107e13 | 1.31527 | ||||||||
\(870\) | 1.44645e12 | 0.0855986 | ||||||||
\(871\) | −1.58365e12 | −0.0932346 | ||||||||
\(872\) | 1.04468e13 | 0.611870 | ||||||||
\(873\) | 7.79984e12 | 0.454487 | ||||||||
\(874\) | −2.05194e13 | −1.18950 | ||||||||
\(875\) | 9.67354e12 | 0.557891 | ||||||||
\(876\) | 1.51737e11 | 0.00870606 | ||||||||
\(877\) | −1.48840e13 | −0.849614 | −0.424807 | − | 0.905284i | \(-0.639658\pi\) | ||||
−0.424807 | + | 0.905284i | \(0.639658\pi\) | |||||||
\(878\) | −1.33544e13 | −0.758402 | ||||||||
\(879\) | −5.94176e12 | −0.335711 | ||||||||
\(880\) | 4.51687e13 | 2.53902 | ||||||||
\(881\) | 8.21496e11 | 0.0459424 | 0.0229712 | − | 0.999736i | \(-0.492687\pi\) | ||||
0.0229712 | + | 0.999736i | \(0.492687\pi\) | |||||||
\(882\) | 1.49518e13 | 0.831926 | ||||||||
\(883\) | −5.06069e12 | −0.280147 | −0.140074 | − | 0.990141i | \(-0.544734\pi\) | ||||
−0.140074 | + | 0.990141i | \(0.544734\pi\) | |||||||
\(884\) | −9.63878e11 | −0.0530868 | ||||||||
\(885\) | 1.24829e13 | 0.684025 | ||||||||
\(886\) | 2.74964e12 | 0.149908 | ||||||||
\(887\) | −4.00796e12 | −0.217404 | −0.108702 | − | 0.994074i | \(-0.534669\pi\) | ||||
−0.108702 | + | 0.994074i | \(0.534669\pi\) | |||||||
\(888\) | 6.26478e12 | 0.338102 | ||||||||
\(889\) | 1.38286e13 | 0.742540 | ||||||||
\(890\) | 2.26582e13 | 1.21051 | ||||||||
\(891\) | −2.04035e13 | −1.08456 | ||||||||
\(892\) | −3.22233e12 | −0.170423 | ||||||||
\(893\) | −9.40979e12 | −0.495163 | ||||||||
\(894\) | −1.42484e13 | −0.746016 | ||||||||
\(895\) | 9.04211e11 | 0.0471049 | ||||||||
\(896\) | 3.12129e13 | 1.61788 | ||||||||
\(897\) | 3.30347e12 | 0.170374 | ||||||||
\(898\) | 2.74516e13 | 1.40872 | ||||||||
\(899\) | −2.80989e12 | −0.143473 | ||||||||
\(900\) | −2.07427e12 | −0.105384 | ||||||||
\(901\) | −3.82338e13 | −1.93280 | ||||||||
\(902\) | 5.28894e12 | 0.266035 | ||||||||
\(903\) | −1.34224e12 | −0.0671791 | ||||||||
\(904\) | −1.65589e13 | −0.824657 | ||||||||
\(905\) | 5.20459e12 | 0.257910 | ||||||||
\(906\) | −3.91569e12 | −0.193077 | ||||||||
\(907\) | 4.52189e12 | 0.221864 | 0.110932 | − | 0.993828i | \(-0.464616\pi\) | ||||
0.110932 | + | 0.993828i | \(0.464616\pi\) | |||||||
\(908\) | −6.79966e12 | −0.331971 | ||||||||
\(909\) | −1.10774e13 | −0.538147 | ||||||||
\(910\) | −1.10747e13 | −0.535361 | ||||||||
\(911\) | −5.68437e12 | −0.273432 | −0.136716 | − | 0.990610i | \(-0.543655\pi\) | ||||
−0.136716 | + | 0.990610i | \(0.543655\pi\) | |||||||
\(912\) | 5.42456e12 | 0.259650 | ||||||||
\(913\) | 8.20525e12 | 0.390817 | ||||||||
\(914\) | 3.40839e13 | 1.61544 | ||||||||
\(915\) | −3.89816e12 | −0.183850 | ||||||||
\(916\) | −5.12257e12 | −0.240413 | ||||||||
\(917\) | 3.08851e13 | 1.44241 | ||||||||
\(918\) | 1.69552e13 | 0.787972 | ||||||||
\(919\) | 3.28047e13 | 1.51711 | 0.758555 | − | 0.651609i | \(-0.225906\pi\) | ||||
0.758555 | + | 0.651609i | \(0.225906\pi\) | |||||||
\(920\) | −4.34731e13 | −2.00067 | ||||||||
\(921\) | −9.97597e12 | −0.456864 | ||||||||
\(922\) | −2.60183e13 | −1.18574 | ||||||||
\(923\) | 4.10174e12 | 0.186020 | ||||||||
\(924\) | 3.24947e12 | 0.146652 | ||||||||
\(925\) | 1.62291e13 | 0.728880 | ||||||||
\(926\) | −6.90877e12 | −0.308782 | ||||||||
\(927\) | 1.97308e13 | 0.877576 | ||||||||
\(928\) | −1.34014e12 | −0.0593177 | ||||||||
\(929\) | 1.82868e13 | 0.805504 | 0.402752 | − | 0.915309i | \(-0.368054\pi\) | ||||
0.402752 | + | 0.915309i | \(0.368054\pi\) | |||||||
\(930\) | −9.63005e12 | −0.422139 | ||||||||
\(931\) | −1.28201e13 | −0.559267 | ||||||||
\(932\) | −4.21280e12 | −0.182894 | ||||||||
\(933\) | 9.50675e12 | 0.410738 | ||||||||
\(934\) | 2.43183e13 | 1.04562 | ||||||||
\(935\) | −5.64224e13 | −2.41435 | ||||||||
\(936\) | 5.08134e12 | 0.216390 | ||||||||
\(937\) | 2.71335e13 | 1.14995 | 0.574974 | − | 0.818171i | \(-0.305012\pi\) | ||||
0.574974 | + | 0.818171i | \(0.305012\pi\) | |||||||
\(938\) | 1.18461e13 | 0.499644 | ||||||||
\(939\) | −1.69828e12 | −0.0712875 | ||||||||
\(940\) | 4.25271e12 | 0.177660 | ||||||||
\(941\) | −9.48833e12 | −0.394490 | −0.197245 | − | 0.980354i | \(-0.563200\pi\) | ||||
−0.197245 | + | 0.980354i | \(0.563200\pi\) | |||||||
\(942\) | 6.20556e12 | 0.256775 | ||||||||
\(943\) | −6.01392e12 | −0.247660 | ||||||||
\(944\) | −4.12866e13 | −1.69213 | ||||||||
\(945\) | 2.91293e13 | 1.18819 | ||||||||
\(946\) | 6.27279e12 | 0.254654 | ||||||||
\(947\) | 1.99262e13 | 0.805100 | 0.402550 | − | 0.915398i | \(-0.368124\pi\) | ||||
0.402550 | + | 0.915398i | \(0.368124\pi\) | |||||||
\(948\) | −1.20010e12 | −0.0482591 | ||||||||
\(949\) | −9.62925e11 | −0.0385385 | ||||||||
\(950\) | 1.18945e13 | 0.473796 | ||||||||
\(951\) | −4.26759e11 | −0.0169188 | ||||||||
\(952\) | −3.37992e13 | −1.33364 | ||||||||
\(953\) | 2.48922e13 | 0.977565 | 0.488782 | − | 0.872406i | \(-0.337441\pi\) | ||||
0.488782 | + | 0.872406i | \(0.337441\pi\) | |||||||
\(954\) | −4.29967e13 | −1.68061 | ||||||||
\(955\) | −5.14238e13 | −2.00055 | ||||||||
\(956\) | −7.92144e11 | −0.0306721 | ||||||||
\(957\) | 2.69330e12 | 0.103796 | ||||||||
\(958\) | 3.38780e13 | 1.29949 | ||||||||
\(959\) | 3.30805e13 | 1.26296 | ||||||||
\(960\) | 9.35134e12 | 0.355347 | ||||||||
\(961\) | −7.73217e12 | −0.292446 | ||||||||
\(962\) | 8.48083e12 | 0.319264 | ||||||||
\(963\) | −1.02292e13 | −0.383286 | ||||||||
\(964\) | −1.58481e12 | −0.0591060 | ||||||||
\(965\) | 4.43349e13 | 1.64579 | ||||||||
\(966\) | −2.47107e13 | −0.913037 | ||||||||
\(967\) | −4.20642e13 | −1.54701 | −0.773505 | − | 0.633790i | \(-0.781499\pi\) | ||||
−0.773505 | + | 0.633790i | \(0.781499\pi\) | |||||||
\(968\) | 4.67756e13 | 1.71230 | ||||||||
\(969\) | −6.77609e12 | −0.246900 | ||||||||
\(970\) | 2.02141e13 | 0.733132 | ||||||||
\(971\) | −1.34740e12 | −0.0486418 | −0.0243209 | − | 0.999704i | \(-0.507742\pi\) | ||||
−0.0243209 | + | 0.999704i | \(0.507742\pi\) | |||||||
\(972\) | 4.37325e12 | 0.157147 | ||||||||
\(973\) | −3.32207e13 | −1.18823 | ||||||||
\(974\) | −2.36825e13 | −0.843164 | ||||||||
\(975\) | −1.91493e12 | −0.0678628 | ||||||||
\(976\) | 1.28929e13 | 0.454807 | ||||||||
\(977\) | −2.05822e13 | −0.722714 | −0.361357 | − | 0.932428i | \(-0.617686\pi\) | ||||
−0.361357 | + | 0.932428i | \(0.617686\pi\) | |||||||
\(978\) | 9.61070e12 | 0.335916 | ||||||||
\(979\) | 4.21898e13 | 1.46786 | ||||||||
\(980\) | 5.79401e12 | 0.200661 | ||||||||
\(981\) | −1.73377e13 | −0.597695 | ||||||||
\(982\) | 2.71700e13 | 0.932368 | ||||||||
\(983\) | −5.72322e13 | −1.95501 | −0.977506 | − | 0.210906i | \(-0.932359\pi\) | ||||
−0.977506 | + | 0.210906i | \(0.932359\pi\) | |||||||
\(984\) | 1.34571e12 | 0.0457587 | ||||||||
\(985\) | 2.49239e13 | 0.843631 | ||||||||
\(986\) | 5.97598e12 | 0.201355 | ||||||||
\(987\) | −1.13318e13 | −0.380078 | ||||||||
\(988\) | 9.29412e11 | 0.0310315 | ||||||||
\(989\) | −7.13263e12 | −0.237065 | ||||||||
\(990\) | −6.34511e13 | −2.09933 | ||||||||
\(991\) | 1.46766e13 | 0.483386 | 0.241693 | − | 0.970353i | \(-0.422297\pi\) | ||||
0.241693 | + | 0.970353i | \(0.422297\pi\) | |||||||
\(992\) | 8.92228e12 | 0.292532 | ||||||||
\(993\) | 2.54750e12 | 0.0831462 | ||||||||
\(994\) | −3.06820e13 | −0.996884 | ||||||||
\(995\) | −1.55473e13 | −0.502866 | ||||||||
\(996\) | −4.45354e11 | −0.0143396 | ||||||||
\(997\) | −5.31286e13 | −1.70294 | −0.851471 | − | 0.524402i | \(-0.824289\pi\) | ||||
−0.851471 | + | 0.524402i | \(0.824289\pi\) | |||||||
\(998\) | 5.51037e13 | 1.75830 | ||||||||
\(999\) | −2.23067e13 | −0.708583 |
(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 | 13.10.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 117.10.a.c.1.3 | 4 | |||
4.3 | odd | 2 | 208.10.a.g.1.1 | 4 | |||
5.4 | even | 2 | 325.10.a.a.1.3 | 4 | |||
13.12 | even | 2 | 169.10.a.a.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.10.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
117.10.a.c.1.3 | 4 | 3.2 | odd | 2 | |||
169.10.a.a.1.3 | 4 | 13.12 | even | 2 | |||
208.10.a.g.1.1 | 4 | 4.3 | odd | 2 | |||
325.10.a.a.1.3 | 4 | 5.4 | even | 2 |