Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,8,Mod(1,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, 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("69.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.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: | \(21.5545667584\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 775x^{5} - 474x^{4} + 167184x^{3} - 33920x^{2} - 9348928x + 28965760 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-16.2020\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 69.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.2020 | −1.43207 | −0.716035 | − | 0.698064i | \(-0.754045\pi\) | ||||
−0.716035 | + | 0.698064i | \(0.754045\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 134.506 | 1.05083 | ||||||||
\(5\) | 395.951 | 1.41660 | 0.708299 | − | 0.705913i | \(-0.249463\pi\) | ||||
0.708299 | + | 0.705913i | \(0.249463\pi\) | |||||||
\(6\) | 437.455 | 0.826806 | ||||||||
\(7\) | 1527.96 | 1.68371 | 0.841856 | − | 0.539702i | \(-0.181463\pi\) | ||||
0.841856 | + | 0.539702i | \(0.181463\pi\) | |||||||
\(8\) | −105.404 | −0.0727852 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −6415.21 | −2.02867 | ||||||||
\(11\) | −977.157 | −0.221355 | −0.110678 | − | 0.993856i | \(-0.535302\pi\) | ||||
−0.110678 | + | 0.993856i | \(0.535302\pi\) | |||||||
\(12\) | −3631.65 | −0.606694 | ||||||||
\(13\) | 7625.78 | 0.962682 | 0.481341 | − | 0.876533i | \(-0.340150\pi\) | ||||
0.481341 | + | 0.876533i | \(0.340150\pi\) | |||||||
\(14\) | −24756.0 | −2.41119 | ||||||||
\(15\) | −10690.7 | −0.817873 | ||||||||
\(16\) | −15509.0 | −0.946592 | ||||||||
\(17\) | 13547.0 | 0.668763 | 0.334381 | − | 0.942438i | \(-0.391473\pi\) | ||||
0.334381 | + | 0.942438i | \(0.391473\pi\) | |||||||
\(18\) | −11811.3 | −0.477357 | ||||||||
\(19\) | 25.2152 | 0.000843384 0 | 0.000421692 | − | 1.00000i | \(-0.499866\pi\) | ||||
0.000421692 | 1.00000i | \(0.499866\pi\) | ||||||||
\(20\) | 53257.7 | 1.48860 | ||||||||
\(21\) | −41254.8 | −0.972092 | ||||||||
\(22\) | 15831.9 | 0.316996 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 2845.91 | 0.0420226 | ||||||||
\(25\) | 78652.3 | 1.00675 | ||||||||
\(26\) | −123553. | −1.37863 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 205519. | 1.76929 | ||||||||
\(29\) | −96873.1 | −0.737582 | −0.368791 | − | 0.929512i | \(-0.620228\pi\) | ||||
−0.368791 | + | 0.929512i | \(0.620228\pi\) | |||||||
\(30\) | 173211. | 1.17125 | ||||||||
\(31\) | 266572. | 1.60712 | 0.803561 | − | 0.595222i | \(-0.202936\pi\) | ||||
0.803561 | + | 0.595222i | \(0.202936\pi\) | |||||||
\(32\) | 264768. | 1.42837 | ||||||||
\(33\) | 26383.2 | 0.127800 | ||||||||
\(34\) | −219489. | −0.957715 | ||||||||
\(35\) | 604996. | 2.38514 | ||||||||
\(36\) | 98054.6 | 0.350275 | ||||||||
\(37\) | 39869.6 | 0.129400 | 0.0647002 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0647002 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(38\) | −408.538 | −0.00120779 | ||||||||
\(39\) | −205896. | −0.555805 | ||||||||
\(40\) | −41734.9 | −0.103107 | ||||||||
\(41\) | −746001. | −1.69042 | −0.845212 | − | 0.534431i | \(-0.820526\pi\) | ||||
−0.845212 | + | 0.534431i | \(0.820526\pi\) | |||||||
\(42\) | 668412. | 1.39210 | ||||||||
\(43\) | 579650. | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(44\) | −131433. | −0.232606 | ||||||||
\(45\) | 288648. | 0.472199 | ||||||||
\(46\) | 197130. | 0.298607 | ||||||||
\(47\) | −84917.9 | −0.119304 | −0.0596522 | − | 0.998219i | \(-0.518999\pi\) | ||||
−0.0596522 | + | 0.998219i | \(0.518999\pi\) | |||||||
\(48\) | 418742. | 0.546515 | ||||||||
\(49\) | 1.51111e6 | 1.83489 | ||||||||
\(50\) | −1.27433e6 | −1.44174 | ||||||||
\(51\) | −365769. | −0.386110 | ||||||||
\(52\) | 1.02571e6 | 1.01161 | ||||||||
\(53\) | −1.55729e6 | −1.43683 | −0.718413 | − | 0.695616i | \(-0.755131\pi\) | ||||
−0.718413 | + | 0.695616i | \(0.755131\pi\) | |||||||
\(54\) | 318904. | 0.275602 | ||||||||
\(55\) | −386906. | −0.313571 | ||||||||
\(56\) | −161053. | −0.122549 | ||||||||
\(57\) | −680.811 | −0.000486928 0 | ||||||||
\(58\) | 1.56954e6 | 1.05627 | ||||||||
\(59\) | −1.35938e6 | −0.861702 | −0.430851 | − | 0.902423i | \(-0.641787\pi\) | ||||
−0.430851 | + | 0.902423i | \(0.641787\pi\) | |||||||
\(60\) | −1.43796e6 | −0.859442 | ||||||||
\(61\) | 1.13718e6 | 0.641470 | 0.320735 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320735 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(62\) | −4.31901e6 | −2.30151 | ||||||||
\(63\) | 1.11388e6 | 0.561237 | ||||||||
\(64\) | −2.30464e6 | −1.09894 | ||||||||
\(65\) | 3.01944e6 | 1.36373 | ||||||||
\(66\) | −427462. | −0.183018 | ||||||||
\(67\) | 2.47935e6 | 1.00711 | 0.503555 | − | 0.863963i | \(-0.332025\pi\) | ||||
0.503555 | + | 0.863963i | \(0.332025\pi\) | |||||||
\(68\) | 1.82215e6 | 0.702753 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | −9.80216e6 | −3.41569 | ||||||||
\(71\) | −263847. | −0.0874879 | −0.0437439 | − | 0.999043i | \(-0.513929\pi\) | ||||
−0.0437439 | + | 0.999043i | \(0.513929\pi\) | |||||||
\(72\) | −76839.7 | −0.0242617 | ||||||||
\(73\) | −4.65126e6 | −1.39939 | −0.699697 | − | 0.714439i | \(-0.746682\pi\) | ||||
−0.699697 | + | 0.714439i | \(0.746682\pi\) | |||||||
\(74\) | −645968. | −0.185311 | ||||||||
\(75\) | −2.12361e6 | −0.581247 | ||||||||
\(76\) | 3391.59 | 0.000886249 0 | ||||||||
\(77\) | −1.49305e6 | −0.372699 | ||||||||
\(78\) | 3.33593e6 | 0.795951 | ||||||||
\(79\) | −4.49927e6 | −1.02671 | −0.513354 | − | 0.858177i | \(-0.671597\pi\) | ||||
−0.513354 | + | 0.858177i | \(0.671597\pi\) | |||||||
\(80\) | −6.14079e6 | −1.34094 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 1.20867e7 | 2.42081 | ||||||||
\(83\) | 5.06957e6 | 0.973191 | 0.486595 | − | 0.873627i | \(-0.338239\pi\) | ||||
0.486595 | + | 0.873627i | \(0.338239\pi\) | |||||||
\(84\) | −5.54901e6 | −1.02150 | ||||||||
\(85\) | 5.36395e6 | 0.947368 | ||||||||
\(86\) | −9.39150e6 | −1.59217 | ||||||||
\(87\) | 2.61557e6 | 0.425843 | ||||||||
\(88\) | 102996. | 0.0161114 | ||||||||
\(89\) | 1.01382e7 | 1.52438 | 0.762191 | − | 0.647352i | \(-0.224124\pi\) | ||||
0.762191 | + | 0.647352i | \(0.224124\pi\) | |||||||
\(90\) | −4.67669e6 | −0.676223 | ||||||||
\(91\) | 1.16519e7 | 1.62088 | ||||||||
\(92\) | −1.63653e6 | −0.219112 | ||||||||
\(93\) | −7.19745e6 | −0.927872 | ||||||||
\(94\) | 1.37584e6 | 0.170852 | ||||||||
\(95\) | 9984.00 | 0.00119474 | ||||||||
\(96\) | −7.14874e6 | −0.824670 | ||||||||
\(97\) | 1.22771e7 | 1.36583 | 0.682914 | − | 0.730499i | \(-0.260713\pi\) | ||||
0.682914 | + | 0.730499i | \(0.260713\pi\) | |||||||
\(98\) | −2.44830e7 | −2.62769 | ||||||||
\(99\) | −712347. | −0.0737851 | ||||||||
\(100\) | 1.05792e7 | 1.05792 | ||||||||
\(101\) | 1.93887e7 | 1.87250 | 0.936252 | − | 0.351329i | \(-0.114270\pi\) | ||||
0.936252 | + | 0.351329i | \(0.114270\pi\) | |||||||
\(102\) | 5.92620e6 | 0.552937 | ||||||||
\(103\) | 1.89953e6 | 0.171284 | 0.0856419 | − | 0.996326i | \(-0.472706\pi\) | ||||
0.0856419 | + | 0.996326i | \(0.472706\pi\) | |||||||
\(104\) | −803790. | −0.0700690 | ||||||||
\(105\) | −1.63349e7 | −1.37706 | ||||||||
\(106\) | 2.52313e7 | 2.05764 | ||||||||
\(107\) | −2.31415e6 | −0.182620 | −0.0913101 | − | 0.995823i | \(-0.529105\pi\) | ||||
−0.0913101 | + | 0.995823i | \(0.529105\pi\) | |||||||
\(108\) | −2.64747e6 | −0.202231 | ||||||||
\(109\) | −7.11020e6 | −0.525883 | −0.262942 | − | 0.964812i | \(-0.584693\pi\) | ||||
−0.262942 | + | 0.964812i | \(0.584693\pi\) | |||||||
\(110\) | 6.26867e6 | 0.449056 | ||||||||
\(111\) | −1.07648e6 | −0.0747094 | ||||||||
\(112\) | −2.36970e7 | −1.59379 | ||||||||
\(113\) | 1.94480e7 | 1.26794 | 0.633971 | − | 0.773357i | \(-0.281424\pi\) | ||||
0.633971 | + | 0.773357i | \(0.281424\pi\) | |||||||
\(114\) | 11030.5 | 0.000697315 0 | ||||||||
\(115\) | −4.81754e6 | −0.295381 | ||||||||
\(116\) | −1.30300e7 | −0.775069 | ||||||||
\(117\) | 5.55920e6 | 0.320894 | ||||||||
\(118\) | 2.20246e7 | 1.23402 | ||||||||
\(119\) | 2.06992e7 | 1.12600 | ||||||||
\(120\) | 1.12684e6 | 0.0595291 | ||||||||
\(121\) | −1.85323e7 | −0.951002 | ||||||||
\(122\) | −1.84247e7 | −0.918631 | ||||||||
\(123\) | 2.01420e7 | 0.975967 | ||||||||
\(124\) | 3.58555e7 | 1.68880 | ||||||||
\(125\) | 208794. | 0.00956168 | ||||||||
\(126\) | −1.80471e7 | −0.803731 | ||||||||
\(127\) | −2.18116e7 | −0.944877 | −0.472439 | − | 0.881364i | \(-0.656626\pi\) | ||||
−0.472439 | + | 0.881364i | \(0.656626\pi\) | |||||||
\(128\) | 3.44943e6 | 0.145382 | ||||||||
\(129\) | −1.56505e7 | −0.641897 | ||||||||
\(130\) | −4.89210e7 | −1.95296 | ||||||||
\(131\) | 3.40934e7 | 1.32502 | 0.662508 | − | 0.749054i | \(-0.269492\pi\) | ||||
0.662508 | + | 0.749054i | \(0.269492\pi\) | |||||||
\(132\) | 3.54869e6 | 0.134295 | ||||||||
\(133\) | 38527.8 | 0.00142002 | ||||||||
\(134\) | −4.01705e7 | −1.44225 | ||||||||
\(135\) | −7.79351e6 | −0.272624 | ||||||||
\(136\) | −1.42791e6 | −0.0486760 | ||||||||
\(137\) | −4.69929e7 | −1.56139 | −0.780693 | − | 0.624915i | \(-0.785133\pi\) | ||||
−0.780693 | + | 0.624915i | \(0.785133\pi\) | |||||||
\(138\) | −5.32251e6 | −0.172401 | ||||||||
\(139\) | 2.34403e7 | 0.740305 | 0.370153 | − | 0.928971i | \(-0.379305\pi\) | ||||
0.370153 | + | 0.928971i | \(0.379305\pi\) | |||||||
\(140\) | 8.13754e7 | 2.50637 | ||||||||
\(141\) | 2.29278e6 | 0.0688805 | ||||||||
\(142\) | 4.27485e6 | 0.125289 | ||||||||
\(143\) | −7.45159e6 | −0.213095 | ||||||||
\(144\) | −1.13060e7 | −0.315531 | ||||||||
\(145\) | −3.83570e7 | −1.04486 | ||||||||
\(146\) | 7.53598e7 | 2.00403 | ||||||||
\(147\) | −4.07999e7 | −1.05937 | ||||||||
\(148\) | 5.36269e6 | 0.135977 | ||||||||
\(149\) | −1.58376e7 | −0.392227 | −0.196113 | − | 0.980581i | \(-0.562832\pi\) | ||||
−0.196113 | + | 0.980581i | \(0.562832\pi\) | |||||||
\(150\) | 3.44068e7 | 0.832387 | ||||||||
\(151\) | 8.30927e7 | 1.96401 | 0.982005 | − | 0.188856i | \(-0.0604779\pi\) | ||||
0.982005 | + | 0.188856i | \(0.0604779\pi\) | |||||||
\(152\) | −2657.79 | −6.13859e−5 0 | ||||||||
\(153\) | 9.87577e6 | 0.222921 | ||||||||
\(154\) | 2.41905e7 | 0.533730 | ||||||||
\(155\) | 1.05550e8 | 2.27665 | ||||||||
\(156\) | −2.76942e7 | −0.584053 | ||||||||
\(157\) | −3.85096e7 | −0.794182 | −0.397091 | − | 0.917779i | \(-0.629980\pi\) | ||||
−0.397091 | + | 0.917779i | \(0.629980\pi\) | |||||||
\(158\) | 7.28973e7 | 1.47032 | ||||||||
\(159\) | 4.20469e7 | 0.829552 | ||||||||
\(160\) | 1.04835e8 | 2.02343 | ||||||||
\(161\) | −1.85906e7 | −0.351078 | ||||||||
\(162\) | −8.61042e6 | −0.159119 | ||||||||
\(163\) | 8.47299e6 | 0.153243 | 0.0766214 | − | 0.997060i | \(-0.475587\pi\) | ||||
0.0766214 | + | 0.997060i | \(0.475587\pi\) | |||||||
\(164\) | −1.00341e8 | −1.77634 | ||||||||
\(165\) | 1.04465e7 | 0.181041 | ||||||||
\(166\) | −8.21373e7 | −1.39368 | ||||||||
\(167\) | −1.12087e8 | −1.86228 | −0.931142 | − | 0.364656i | \(-0.881187\pi\) | ||||
−0.931142 | + | 0.364656i | \(0.881187\pi\) | |||||||
\(168\) | 4.34843e6 | 0.0707539 | ||||||||
\(169\) | −4.59595e6 | −0.0732439 | ||||||||
\(170\) | −8.69069e7 | −1.35670 | ||||||||
\(171\) | 18381.9 | 0.000281128 0 | ||||||||
\(172\) | 7.79662e7 | 1.16831 | ||||||||
\(173\) | −7.91886e7 | −1.16279 | −0.581395 | − | 0.813622i | \(-0.697493\pi\) | ||||
−0.581395 | + | 0.813622i | \(0.697493\pi\) | |||||||
\(174\) | −4.23776e7 | −0.609837 | ||||||||
\(175\) | 1.20177e8 | 1.69508 | ||||||||
\(176\) | 1.51547e7 | 0.209533 | ||||||||
\(177\) | 3.67031e7 | 0.497504 | ||||||||
\(178\) | −1.64259e8 | −2.18302 | ||||||||
\(179\) | −7.84923e7 | −1.02292 | −0.511459 | − | 0.859307i | \(-0.670895\pi\) | ||||
−0.511459 | + | 0.859307i | \(0.670895\pi\) | |||||||
\(180\) | 3.88248e7 | 0.496199 | ||||||||
\(181\) | −4.42911e7 | −0.555190 | −0.277595 | − | 0.960698i | \(-0.589537\pi\) | ||||
−0.277595 | + | 0.960698i | \(0.589537\pi\) | |||||||
\(182\) | −1.88784e8 | −2.32121 | ||||||||
\(183\) | −3.07040e7 | −0.370353 | ||||||||
\(184\) | 1.28245e6 | 0.0151768 | ||||||||
\(185\) | 1.57864e7 | 0.183308 | ||||||||
\(186\) | 1.16613e8 | 1.32878 | ||||||||
\(187\) | −1.32375e7 | −0.148034 | ||||||||
\(188\) | −1.14219e7 | −0.125368 | ||||||||
\(189\) | −3.00748e7 | −0.324031 | ||||||||
\(190\) | −161761. | −0.00171095 | ||||||||
\(191\) | 4.58471e7 | 0.476096 | 0.238048 | − | 0.971253i | \(-0.423492\pi\) | ||||
0.238048 | + | 0.971253i | \(0.423492\pi\) | |||||||
\(192\) | 6.22252e7 | 0.634471 | ||||||||
\(193\) | −2.93112e7 | −0.293483 | −0.146741 | − | 0.989175i | \(-0.546879\pi\) | ||||
−0.146741 | + | 0.989175i | \(0.546879\pi\) | |||||||
\(194\) | −1.98914e8 | −1.95596 | ||||||||
\(195\) | −8.15248e7 | −0.787352 | ||||||||
\(196\) | 2.03253e8 | 1.92815 | ||||||||
\(197\) | 1.71466e8 | 1.59789 | 0.798943 | − | 0.601407i | \(-0.205393\pi\) | ||||
0.798943 | + | 0.601407i | \(0.205393\pi\) | |||||||
\(198\) | 1.15415e7 | 0.105665 | ||||||||
\(199\) | 1.13235e8 | 1.01858 | 0.509288 | − | 0.860596i | \(-0.329909\pi\) | ||||
0.509288 | + | 0.860596i | \(0.329909\pi\) | |||||||
\(200\) | −8.29029e6 | −0.0732765 | ||||||||
\(201\) | −6.69425e7 | −0.581455 | ||||||||
\(202\) | −3.14135e8 | −2.68156 | ||||||||
\(203\) | −1.48018e8 | −1.24188 | ||||||||
\(204\) | −4.91980e7 | −0.405734 | ||||||||
\(205\) | −2.95380e8 | −2.39465 | ||||||||
\(206\) | −3.07763e7 | −0.245290 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | −1.18268e8 | −0.911266 | ||||||||
\(209\) | −24639.2 | −0.000186687 0 | ||||||||
\(210\) | 2.64658e8 | 1.97205 | ||||||||
\(211\) | −1.96433e8 | −1.43954 | −0.719772 | − | 0.694211i | \(-0.755754\pi\) | ||||
−0.719772 | + | 0.694211i | \(0.755754\pi\) | |||||||
\(212\) | −2.09464e8 | −1.50985 | ||||||||
\(213\) | 7.12387e6 | 0.0505111 | ||||||||
\(214\) | 3.74940e7 | 0.261525 | ||||||||
\(215\) | 2.29513e8 | 1.57497 | ||||||||
\(216\) | 2.07467e6 | 0.0140075 | ||||||||
\(217\) | 4.07311e8 | 2.70593 | ||||||||
\(218\) | 1.15200e8 | 0.753102 | ||||||||
\(219\) | 1.25584e8 | 0.807941 | ||||||||
\(220\) | −5.20411e7 | −0.329509 | ||||||||
\(221\) | 1.03307e8 | 0.643806 | ||||||||
\(222\) | 1.74411e7 | 0.106989 | ||||||||
\(223\) | 2.38859e8 | 1.44236 | 0.721180 | − | 0.692747i | \(-0.243600\pi\) | ||||
0.721180 | + | 0.692747i | \(0.243600\pi\) | |||||||
\(224\) | 4.04554e8 | 2.40497 | ||||||||
\(225\) | 5.73375e7 | 0.335583 | ||||||||
\(226\) | −3.15096e8 | −1.81578 | ||||||||
\(227\) | −8.13545e6 | −0.0461627 | −0.0230813 | − | 0.999734i | \(-0.507348\pi\) | ||||
−0.0230813 | + | 0.999734i | \(0.507348\pi\) | |||||||
\(228\) | −91572.9 | −0.000511676 0 | ||||||||
\(229\) | 2.29391e8 | 1.26227 | 0.631134 | − | 0.775674i | \(-0.282590\pi\) | ||||
0.631134 | + | 0.775674i | \(0.282590\pi\) | |||||||
\(230\) | 7.80539e7 | 0.423006 | ||||||||
\(231\) | 4.03124e7 | 0.215178 | ||||||||
\(232\) | 1.02108e7 | 0.0536850 | ||||||||
\(233\) | −1.37622e8 | −0.712756 | −0.356378 | − | 0.934342i | \(-0.615989\pi\) | ||||
−0.356378 | + | 0.934342i | \(0.615989\pi\) | |||||||
\(234\) | −9.00702e7 | −0.459543 | ||||||||
\(235\) | −3.36233e7 | −0.169006 | ||||||||
\(236\) | −1.82844e8 | −0.905499 | ||||||||
\(237\) | 1.21480e8 | 0.592771 | ||||||||
\(238\) | −3.35370e8 | −1.61252 | ||||||||
\(239\) | 4.68408e7 | 0.221938 | 0.110969 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110969 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(240\) | 1.65801e8 | 0.774192 | ||||||||
\(241\) | −4.15160e8 | −1.91054 | −0.955270 | − | 0.295735i | \(-0.904436\pi\) | ||||
−0.955270 | + | 0.295735i | \(0.904436\pi\) | |||||||
\(242\) | 3.00261e8 | 1.36190 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 1.52958e8 | 0.674073 | ||||||||
\(245\) | 5.98325e8 | 2.59930 | ||||||||
\(246\) | −3.26341e8 | −1.39765 | ||||||||
\(247\) | 192286. | 0.000811910 0 | ||||||||
\(248\) | −2.80978e7 | −0.116975 | ||||||||
\(249\) | −1.36878e8 | −0.561872 | ||||||||
\(250\) | −3.38289e6 | −0.0136930 | ||||||||
\(251\) | 3.43110e8 | 1.36954 | 0.684771 | − | 0.728759i | \(-0.259902\pi\) | ||||
0.684771 | + | 0.728759i | \(0.259902\pi\) | |||||||
\(252\) | 1.49823e8 | 0.589762 | ||||||||
\(253\) | 1.18891e7 | 0.0461558 | ||||||||
\(254\) | 3.53393e8 | 1.35313 | ||||||||
\(255\) | −1.44827e8 | −0.546963 | ||||||||
\(256\) | 2.39106e8 | 0.890738 | ||||||||
\(257\) | 3.10904e8 | 1.14251 | 0.571255 | − | 0.820773i | \(-0.306457\pi\) | ||||
0.571255 | + | 0.820773i | \(0.306457\pi\) | |||||||
\(258\) | 2.53571e8 | 0.919242 | ||||||||
\(259\) | 6.09190e7 | 0.217873 | ||||||||
\(260\) | 4.06131e8 | 1.43304 | ||||||||
\(261\) | −7.06205e7 | −0.245861 | ||||||||
\(262\) | −5.52383e8 | −1.89752 | ||||||||
\(263\) | −1.90372e8 | −0.645294 | −0.322647 | − | 0.946519i | \(-0.604573\pi\) | ||||
−0.322647 | + | 0.946519i | \(0.604573\pi\) | |||||||
\(264\) | −2.78090e6 | −0.00930191 | ||||||||
\(265\) | −6.16611e8 | −2.03541 | ||||||||
\(266\) | −624228. | −0.00203356 | ||||||||
\(267\) | −2.73730e8 | −0.880103 | ||||||||
\(268\) | 3.33487e8 | 1.05830 | ||||||||
\(269\) | 1.01060e8 | 0.316553 | 0.158277 | − | 0.987395i | \(-0.449406\pi\) | ||||
0.158277 | + | 0.987395i | \(0.449406\pi\) | |||||||
\(270\) | 1.26271e8 | 0.390417 | ||||||||
\(271\) | 5.89781e8 | 1.80011 | 0.900053 | − | 0.435780i | \(-0.143527\pi\) | ||||
0.900053 | + | 0.435780i | \(0.143527\pi\) | |||||||
\(272\) | −2.10100e8 | −0.633045 | ||||||||
\(273\) | −3.14600e8 | −0.935815 | ||||||||
\(274\) | 7.61380e8 | 2.23601 | ||||||||
\(275\) | −7.68556e7 | −0.222849 | ||||||||
\(276\) | 4.41863e7 | 0.126504 | ||||||||
\(277\) | −2.50265e8 | −0.707490 | −0.353745 | − | 0.935342i | \(-0.615092\pi\) | ||||
−0.353745 | + | 0.935342i | \(0.615092\pi\) | |||||||
\(278\) | −3.79780e8 | −1.06017 | ||||||||
\(279\) | 1.94331e8 | 0.535707 | ||||||||
\(280\) | −6.37692e7 | −0.173603 | ||||||||
\(281\) | −2.97671e7 | −0.0800322 | −0.0400161 | − | 0.999199i | \(-0.512741\pi\) | ||||
−0.0400161 | + | 0.999199i | \(0.512741\pi\) | |||||||
\(282\) | −3.71477e7 | −0.0986417 | ||||||||
\(283\) | −3.16316e8 | −0.829600 | −0.414800 | − | 0.909913i | \(-0.636148\pi\) | ||||
−0.414800 | + | 0.909913i | \(0.636148\pi\) | |||||||
\(284\) | −3.54889e7 | −0.0919344 | ||||||||
\(285\) | −269568. | −0.000689781 0 | ||||||||
\(286\) | 1.20731e8 | 0.305166 | ||||||||
\(287\) | −1.13986e9 | −2.84619 | ||||||||
\(288\) | 1.93016e8 | 0.476124 | ||||||||
\(289\) | −2.26817e8 | −0.552757 | ||||||||
\(290\) | 6.21461e8 | 1.49631 | ||||||||
\(291\) | −3.31483e8 | −0.788561 | ||||||||
\(292\) | −6.25620e8 | −1.47052 | ||||||||
\(293\) | −2.41195e7 | −0.0560185 | −0.0280092 | − | 0.999608i | \(-0.508917\pi\) | ||||
−0.0280092 | + | 0.999608i | \(0.508917\pi\) | |||||||
\(294\) | 6.61041e8 | 1.51710 | ||||||||
\(295\) | −5.38246e8 | −1.22069 | ||||||||
\(296\) | −4.20242e6 | −0.00941844 | ||||||||
\(297\) | 1.92334e7 | 0.0425998 | ||||||||
\(298\) | 2.56601e8 | 0.561696 | ||||||||
\(299\) | −9.27829e7 | −0.200733 | ||||||||
\(300\) | −2.85638e8 | −0.610789 | ||||||||
\(301\) | 8.85680e8 | 1.87195 | ||||||||
\(302\) | −1.34627e9 | −2.81260 | ||||||||
\(303\) | −5.23494e8 | −1.08109 | ||||||||
\(304\) | −391062. | −0.000798340 0 | ||||||||
\(305\) | 4.50270e8 | 0.908706 | ||||||||
\(306\) | −1.60007e8 | −0.319238 | ||||||||
\(307\) | 4.01012e8 | 0.790993 | 0.395496 | − | 0.918468i | \(-0.370573\pi\) | ||||
0.395496 | + | 0.918468i | \(0.370573\pi\) | |||||||
\(308\) | −2.00824e8 | −0.391641 | ||||||||
\(309\) | −5.12874e7 | −0.0988908 | ||||||||
\(310\) | −1.71012e9 | −3.26032 | ||||||||
\(311\) | −7.78223e8 | −1.46704 | −0.733522 | − | 0.679666i | \(-0.762125\pi\) | ||||
−0.733522 | + | 0.679666i | \(0.762125\pi\) | |||||||
\(312\) | 2.17023e7 | 0.0404544 | ||||||||
\(313\) | −7.95716e8 | −1.46674 | −0.733370 | − | 0.679830i | \(-0.762054\pi\) | ||||
−0.733370 | + | 0.679830i | \(0.762054\pi\) | |||||||
\(314\) | 6.23933e8 | 1.13732 | ||||||||
\(315\) | 4.41042e8 | 0.795048 | ||||||||
\(316\) | −6.05177e8 | −1.07889 | ||||||||
\(317\) | 8.52074e8 | 1.50235 | 0.751173 | − | 0.660106i | \(-0.229488\pi\) | ||||
0.751173 | + | 0.660106i | \(0.229488\pi\) | |||||||
\(318\) | −6.81245e8 | −1.18798 | ||||||||
\(319\) | 9.46602e7 | 0.163268 | ||||||||
\(320\) | −9.12523e8 | −1.55675 | ||||||||
\(321\) | 6.24821e7 | 0.105436 | ||||||||
\(322\) | 3.01206e8 | 0.502769 | ||||||||
\(323\) | 341591. | 0.000564024 0 | ||||||||
\(324\) | 7.14818e7 | 0.116758 | ||||||||
\(325\) | 5.99786e8 | 0.969180 | ||||||||
\(326\) | −1.37280e8 | −0.219454 | ||||||||
\(327\) | 1.91975e8 | 0.303619 | ||||||||
\(328\) | 7.86316e7 | 0.123038 | ||||||||
\(329\) | −1.29751e8 | −0.200874 | ||||||||
\(330\) | −1.69254e8 | −0.259263 | ||||||||
\(331\) | 2.06965e8 | 0.313689 | 0.156845 | − | 0.987623i | \(-0.449868\pi\) | ||||
0.156845 | + | 0.987623i | \(0.449868\pi\) | |||||||
\(332\) | 6.81886e8 | 1.02265 | ||||||||
\(333\) | 2.90649e7 | 0.0431335 | ||||||||
\(334\) | 1.81603e9 | 2.66692 | ||||||||
\(335\) | 9.81703e8 | 1.42667 | ||||||||
\(336\) | 6.39819e8 | 0.920174 | ||||||||
\(337\) | −1.17012e9 | −1.66543 | −0.832713 | − | 0.553705i | \(-0.813213\pi\) | ||||
−0.832713 | + | 0.553705i | \(0.813213\pi\) | |||||||
\(338\) | 7.44636e7 | 0.104890 | ||||||||
\(339\) | −5.25095e8 | −0.732047 | ||||||||
\(340\) | 7.21482e8 | 0.995518 | ||||||||
\(341\) | −2.60483e8 | −0.355745 | ||||||||
\(342\) | −297824. | −0.000402595 0 | ||||||||
\(343\) | 1.05057e9 | 1.40571 | ||||||||
\(344\) | −6.10975e7 | −0.0809225 | ||||||||
\(345\) | 1.30074e8 | 0.170538 | ||||||||
\(346\) | 1.28302e9 | 1.66520 | ||||||||
\(347\) | 1.74281e8 | 0.223921 | 0.111961 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111961 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(348\) | 3.51809e8 | 0.447486 | ||||||||
\(349\) | 5.92942e8 | 0.746661 | 0.373330 | − | 0.927698i | \(-0.378216\pi\) | ||||
0.373330 | + | 0.927698i | \(0.378216\pi\) | |||||||
\(350\) | −1.94712e9 | −2.42747 | ||||||||
\(351\) | −1.50098e8 | −0.185268 | ||||||||
\(352\) | −2.58720e8 | −0.316177 | ||||||||
\(353\) | −5.68861e8 | −0.688327 | −0.344164 | − | 0.938910i | \(-0.611838\pi\) | ||||
−0.344164 | + | 0.938910i | \(0.611838\pi\) | |||||||
\(354\) | −5.94665e8 | −0.712461 | ||||||||
\(355\) | −1.04470e8 | −0.123935 | ||||||||
\(356\) | 1.36364e9 | 1.60186 | ||||||||
\(357\) | −5.58879e8 | −0.650099 | ||||||||
\(358\) | 1.27173e9 | 1.46489 | ||||||||
\(359\) | 6.61337e8 | 0.754384 | 0.377192 | − | 0.926135i | \(-0.376890\pi\) | ||||
0.377192 | + | 0.926135i | \(0.376890\pi\) | |||||||
\(360\) | −3.04248e7 | −0.0343691 | ||||||||
\(361\) | −8.93871e8 | −0.999999 | ||||||||
\(362\) | 7.17606e8 | 0.795071 | ||||||||
\(363\) | 5.00373e8 | 0.549061 | ||||||||
\(364\) | 1.56724e9 | 1.70326 | ||||||||
\(365\) | −1.84167e9 | −1.98238 | ||||||||
\(366\) | 4.97467e8 | 0.530372 | ||||||||
\(367\) | 3.27583e8 | 0.345932 | 0.172966 | − | 0.984928i | \(-0.444665\pi\) | ||||
0.172966 | + | 0.984928i | \(0.444665\pi\) | |||||||
\(368\) | 1.88697e8 | 0.197378 | ||||||||
\(369\) | −5.43834e8 | −0.563475 | ||||||||
\(370\) | −2.55772e8 | −0.262511 | ||||||||
\(371\) | −2.37947e9 | −2.41920 | ||||||||
\(372\) | −9.68097e8 | −0.975032 | ||||||||
\(373\) | −1.50919e9 | −1.50578 | −0.752890 | − | 0.658146i | \(-0.771341\pi\) | ||||
−0.752890 | + | 0.658146i | \(0.771341\pi\) | |||||||
\(374\) | 2.14475e8 | 0.211995 | ||||||||
\(375\) | −5.63745e6 | −0.00552044 | ||||||||
\(376\) | 8.95071e6 | 0.00868360 | ||||||||
\(377\) | −7.38733e8 | −0.710056 | ||||||||
\(378\) | 4.87272e8 | 0.464035 | ||||||||
\(379\) | 1.60365e8 | 0.151312 | 0.0756560 | − | 0.997134i | \(-0.475895\pi\) | ||||
0.0756560 | + | 0.997134i | \(0.475895\pi\) | |||||||
\(380\) | 1.34290e6 | 0.00125546 | ||||||||
\(381\) | 5.88914e8 | 0.545525 | ||||||||
\(382\) | −7.42815e8 | −0.681803 | ||||||||
\(383\) | 6.86470e8 | 0.624347 | 0.312174 | − | 0.950025i | \(-0.398943\pi\) | ||||
0.312174 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(384\) | −9.31345e7 | −0.0839366 | ||||||||
\(385\) | −5.91176e8 | −0.527964 | ||||||||
\(386\) | 4.74901e8 | 0.420288 | ||||||||
\(387\) | 4.22565e8 | 0.370599 | ||||||||
\(388\) | 1.65134e9 | 1.43525 | ||||||||
\(389\) | −5.97929e8 | −0.515022 | −0.257511 | − | 0.966275i | \(-0.582902\pi\) | ||||
−0.257511 | + | 0.966275i | \(0.582902\pi\) | |||||||
\(390\) | 1.32087e9 | 1.12754 | ||||||||
\(391\) | −1.64826e8 | −0.139447 | ||||||||
\(392\) | −1.59277e8 | −0.133553 | ||||||||
\(393\) | −9.20523e8 | −0.764999 | ||||||||
\(394\) | −2.77809e9 | −2.28828 | ||||||||
\(395\) | −1.78149e9 | −1.45443 | ||||||||
\(396\) | −9.58147e7 | −0.0775352 | ||||||||
\(397\) | 1.06536e9 | 0.854534 | 0.427267 | − | 0.904125i | \(-0.359476\pi\) | ||||
0.427267 | + | 0.904125i | \(0.359476\pi\) | |||||||
\(398\) | −1.83463e9 | −1.45867 | ||||||||
\(399\) | −1.04025e6 | −0.000819847 0 | ||||||||
\(400\) | −1.21982e9 | −0.952981 | ||||||||
\(401\) | −2.90355e8 | −0.224866 | −0.112433 | − | 0.993659i | \(-0.535864\pi\) | ||||
−0.112433 | + | 0.993659i | \(0.535864\pi\) | |||||||
\(402\) | 1.08460e9 | 0.832684 | ||||||||
\(403\) | 2.03282e9 | 1.54715 | ||||||||
\(404\) | 2.60788e9 | 1.96767 | ||||||||
\(405\) | 2.10425e8 | 0.157400 | ||||||||
\(406\) | 2.39819e9 | 1.77845 | ||||||||
\(407\) | −3.89588e7 | −0.0286435 | ||||||||
\(408\) | 3.85536e7 | 0.0281031 | ||||||||
\(409\) | 1.99399e9 | 1.44109 | 0.720545 | − | 0.693408i | \(-0.243892\pi\) | ||||
0.720545 | + | 0.693408i | \(0.243892\pi\) | |||||||
\(410\) | 4.78575e9 | 3.42931 | ||||||||
\(411\) | 1.26881e9 | 0.901466 | ||||||||
\(412\) | 2.55498e8 | 0.179989 | ||||||||
\(413\) | −2.07707e9 | −1.45086 | ||||||||
\(414\) | 1.43708e8 | 0.0995358 | ||||||||
\(415\) | 2.00730e9 | 1.37862 | ||||||||
\(416\) | 2.01907e9 | 1.37507 | ||||||||
\(417\) | −6.32887e8 | −0.427415 | ||||||||
\(418\) | 399205. | 0.000267350 0 | ||||||||
\(419\) | −8.88709e8 | −0.590215 | −0.295108 | − | 0.955464i | \(-0.595356\pi\) | ||||
−0.295108 | + | 0.955464i | \(0.595356\pi\) | |||||||
\(420\) | −2.19714e9 | −1.44705 | ||||||||
\(421\) | −1.77426e9 | −1.15886 | −0.579430 | − | 0.815022i | \(-0.696725\pi\) | ||||
−0.579430 | + | 0.815022i | \(0.696725\pi\) | |||||||
\(422\) | 3.18261e9 | 2.06153 | ||||||||
\(423\) | −6.19051e7 | −0.0397682 | ||||||||
\(424\) | 1.64145e8 | 0.104580 | ||||||||
\(425\) | 1.06550e9 | 0.673277 | ||||||||
\(426\) | −1.15421e8 | −0.0723355 | ||||||||
\(427\) | 1.73757e9 | 1.08005 | ||||||||
\(428\) | −3.11267e8 | −0.191902 | ||||||||
\(429\) | 2.01193e8 | 0.123030 | ||||||||
\(430\) | −3.71858e9 | −2.25547 | ||||||||
\(431\) | −1.50258e9 | −0.904000 | −0.452000 | − | 0.892018i | \(-0.649289\pi\) | ||||
−0.452000 | + | 0.892018i | \(0.649289\pi\) | |||||||
\(432\) | 3.05263e8 | 0.182172 | ||||||||
\(433\) | −2.55359e8 | −0.151162 | −0.0755812 | − | 0.997140i | \(-0.524081\pi\) | ||||
−0.0755812 | + | 0.997140i | \(0.524081\pi\) | |||||||
\(434\) | −6.59926e9 | −3.87508 | ||||||||
\(435\) | 1.03564e9 | 0.603248 | ||||||||
\(436\) | −9.56362e8 | −0.552611 | ||||||||
\(437\) | −306794. | −0.000175858 0 | ||||||||
\(438\) | −2.03471e9 | −1.15703 | ||||||||
\(439\) | 2.86807e9 | 1.61795 | 0.808973 | − | 0.587846i | \(-0.200024\pi\) | ||||
0.808973 | + | 0.587846i | \(0.200024\pi\) | |||||||
\(440\) | 4.07816e7 | 0.0228234 | ||||||||
\(441\) | 1.10160e9 | 0.611629 | ||||||||
\(442\) | −1.67377e9 | −0.921975 | ||||||||
\(443\) | −1.44103e9 | −0.787520 | −0.393760 | − | 0.919213i | \(-0.628826\pi\) | ||||
−0.393760 | + | 0.919213i | \(0.628826\pi\) | |||||||
\(444\) | −1.44793e8 | −0.0785065 | ||||||||
\(445\) | 4.01421e9 | 2.15944 | ||||||||
\(446\) | −3.86999e9 | −2.06556 | ||||||||
\(447\) | 4.27615e8 | 0.226452 | ||||||||
\(448\) | −3.52138e9 | −1.85029 | ||||||||
\(449\) | −1.78535e9 | −0.930812 | −0.465406 | − | 0.885097i | \(-0.654092\pi\) | ||||
−0.465406 | + | 0.885097i | \(0.654092\pi\) | |||||||
\(450\) | −9.28984e8 | −0.480579 | ||||||||
\(451\) | 7.28959e8 | 0.374184 | ||||||||
\(452\) | 2.61586e9 | 1.33239 | ||||||||
\(453\) | −2.24350e9 | −1.13392 | ||||||||
\(454\) | 1.31811e8 | 0.0661082 | ||||||||
\(455\) | 4.61357e9 | 2.29613 | ||||||||
\(456\) | 71760.4 | 3.54412e−5 0 | ||||||||
\(457\) | −2.88464e8 | −0.141379 | −0.0706895 | − | 0.997498i | \(-0.522520\pi\) | ||||
−0.0706895 | + | 0.997498i | \(0.522520\pi\) | |||||||
\(458\) | −3.71659e9 | −1.80766 | ||||||||
\(459\) | −2.66646e8 | −0.128703 | ||||||||
\(460\) | −6.47986e8 | −0.310394 | ||||||||
\(461\) | −3.59417e8 | −0.170862 | −0.0854310 | − | 0.996344i | \(-0.527227\pi\) | ||||
−0.0854310 | + | 0.996344i | \(0.527227\pi\) | |||||||
\(462\) | −6.53143e8 | −0.308149 | ||||||||
\(463\) | 2.93665e8 | 0.137505 | 0.0687526 | − | 0.997634i | \(-0.478098\pi\) | ||||
0.0687526 | + | 0.997634i | \(0.478098\pi\) | |||||||
\(464\) | 1.50240e9 | 0.698189 | ||||||||
\(465\) | −2.84984e9 | −1.31442 | ||||||||
\(466\) | 2.22975e9 | 1.02072 | ||||||||
\(467\) | 3.19317e9 | 1.45082 | 0.725409 | − | 0.688318i | \(-0.241651\pi\) | ||||
0.725409 | + | 0.688318i | \(0.241651\pi\) | |||||||
\(468\) | 7.47743e8 | 0.337203 | ||||||||
\(469\) | 3.78834e9 | 1.69568 | ||||||||
\(470\) | 5.44766e8 | 0.242029 | ||||||||
\(471\) | 1.03976e9 | 0.458521 | ||||||||
\(472\) | 1.43284e8 | 0.0627192 | ||||||||
\(473\) | −5.66409e8 | −0.246102 | ||||||||
\(474\) | −1.96823e9 | −0.848889 | ||||||||
\(475\) | 1.98324e6 | 0.000849077 0 | ||||||||
\(476\) | 2.78416e9 | 1.18323 | ||||||||
\(477\) | −1.13527e9 | −0.478942 | ||||||||
\(478\) | −7.58917e8 | −0.317831 | ||||||||
\(479\) | 1.00355e9 | 0.417220 | 0.208610 | − | 0.977999i | \(-0.433106\pi\) | ||||
0.208610 | + | 0.977999i | \(0.433106\pi\) | |||||||
\(480\) | −2.83055e9 | −1.16823 | ||||||||
\(481\) | 3.04037e8 | 0.124571 | ||||||||
\(482\) | 6.72644e9 | 2.73603 | ||||||||
\(483\) | 5.01947e8 | 0.202695 | ||||||||
\(484\) | −2.49270e9 | −0.999337 | ||||||||
\(485\) | 4.86114e9 | 1.93483 | ||||||||
\(486\) | 2.32481e8 | 0.0918673 | ||||||||
\(487\) | 1.69071e9 | 0.663312 | 0.331656 | − | 0.943400i | \(-0.392393\pi\) | ||||
0.331656 | + | 0.943400i | \(0.392393\pi\) | |||||||
\(488\) | −1.19864e8 | −0.0466896 | ||||||||
\(489\) | −2.28771e8 | −0.0884747 | ||||||||
\(490\) | −9.69408e9 | −3.72238 | ||||||||
\(491\) | 1.44669e9 | 0.551559 | 0.275779 | − | 0.961221i | \(-0.411064\pi\) | ||||
0.275779 | + | 0.961221i | \(0.411064\pi\) | |||||||
\(492\) | 2.70921e9 | 1.02557 | ||||||||
\(493\) | −1.31234e9 | −0.493267 | ||||||||
\(494\) | −3.11542e6 | −0.00116271 | ||||||||
\(495\) | −2.82055e8 | −0.104524 | ||||||||
\(496\) | −4.13426e9 | −1.52129 | ||||||||
\(497\) | −4.03147e8 | −0.147304 | ||||||||
\(498\) | 2.21771e9 | 0.804640 | ||||||||
\(499\) | −2.74672e9 | −0.989605 | −0.494803 | − | 0.869005i | \(-0.664760\pi\) | ||||
−0.494803 | + | 0.869005i | \(0.664760\pi\) | |||||||
\(500\) | 2.80840e7 | 0.0100476 | ||||||||
\(501\) | 3.02634e9 | 1.07519 | ||||||||
\(502\) | −5.55907e9 | −1.96128 | ||||||||
\(503\) | 6.14861e8 | 0.215422 | 0.107711 | − | 0.994182i | \(-0.465648\pi\) | ||||
0.107711 | + | 0.994182i | \(0.465648\pi\) | |||||||
\(504\) | −1.17408e8 | −0.0408498 | ||||||||
\(505\) | 7.67696e9 | 2.65259 | ||||||||
\(506\) | −1.92627e8 | −0.0660983 | ||||||||
\(507\) | 1.24091e8 | 0.0422874 | ||||||||
\(508\) | −2.93379e9 | −0.992901 | ||||||||
\(509\) | −7.09303e7 | −0.0238407 | −0.0119204 | − | 0.999929i | \(-0.503794\pi\) | ||||
−0.0119204 | + | 0.999929i | \(0.503794\pi\) | |||||||
\(510\) | 2.34649e9 | 0.783290 | ||||||||
\(511\) | −7.10692e9 | −2.35618 | ||||||||
\(512\) | −4.31552e9 | −1.42098 | ||||||||
\(513\) | −496311. | −0.000162309 0 | ||||||||
\(514\) | −5.03727e9 | −1.63615 | ||||||||
\(515\) | 7.52122e8 | 0.242640 | ||||||||
\(516\) | −2.10509e9 | −0.674522 | ||||||||
\(517\) | 8.29781e7 | 0.0264087 | ||||||||
\(518\) | −9.87011e8 | −0.312010 | ||||||||
\(519\) | 2.13809e9 | 0.671337 | ||||||||
\(520\) | −3.18262e8 | −0.0992596 | ||||||||
\(521\) | −5.06862e9 | −1.57021 | −0.785104 | − | 0.619364i | \(-0.787391\pi\) | ||||
−0.785104 | + | 0.619364i | \(0.787391\pi\) | |||||||
\(522\) | 1.14419e9 | 0.352090 | ||||||||
\(523\) | −2.63435e9 | −0.805227 | −0.402613 | − | 0.915370i | \(-0.631898\pi\) | ||||
−0.402613 | + | 0.915370i | \(0.631898\pi\) | |||||||
\(524\) | 4.58576e9 | 1.39236 | ||||||||
\(525\) | −3.24479e9 | −0.978653 | ||||||||
\(526\) | 3.08441e9 | 0.924106 | ||||||||
\(527\) | 3.61125e9 | 1.07478 | ||||||||
\(528\) | −4.09176e8 | −0.120974 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 9.99035e9 | 2.91484 | ||||||||
\(531\) | −9.90984e8 | −0.287234 | ||||||||
\(532\) | 5.18220e6 | 0.00149219 | ||||||||
\(533\) | −5.68884e9 | −1.62734 | ||||||||
\(534\) | 4.43498e9 | 1.26037 | ||||||||
\(535\) | −9.16292e8 | −0.258699 | ||||||||
\(536\) | −2.61334e8 | −0.0733027 | ||||||||
\(537\) | 2.11929e9 | 0.590583 | ||||||||
\(538\) | −1.63738e9 | −0.453327 | ||||||||
\(539\) | −1.47659e9 | −0.406162 | ||||||||
\(540\) | −1.04827e9 | −0.286481 | ||||||||
\(541\) | −5.42527e9 | −1.47310 | −0.736548 | − | 0.676385i | \(-0.763545\pi\) | ||||
−0.736548 | + | 0.676385i | \(0.763545\pi\) | |||||||
\(542\) | −9.55564e9 | −2.57788 | ||||||||
\(543\) | 1.19586e9 | 0.320539 | ||||||||
\(544\) | 3.58682e9 | 0.955241 | ||||||||
\(545\) | −2.81529e9 | −0.744965 | ||||||||
\(546\) | 5.09716e9 | 1.34015 | ||||||||
\(547\) | −8.73776e8 | −0.228268 | −0.114134 | − | 0.993465i | \(-0.536409\pi\) | ||||
−0.114134 | + | 0.993465i | \(0.536409\pi\) | |||||||
\(548\) | −6.32081e9 | −1.64074 | ||||||||
\(549\) | 8.29008e8 | 0.213823 | ||||||||
\(550\) | 1.24522e9 | 0.319136 | ||||||||
\(551\) | −2.44268e6 | −0.000622065 0 | ||||||||
\(552\) | −3.46262e7 | −0.00876231 | ||||||||
\(553\) | −6.87469e9 | −1.72868 | ||||||||
\(554\) | 4.05480e9 | 1.01318 | ||||||||
\(555\) | −4.26233e8 | −0.105833 | ||||||||
\(556\) | 3.15285e9 | 0.777931 | ||||||||
\(557\) | 2.63557e9 | 0.646222 | 0.323111 | − | 0.946361i | \(-0.395271\pi\) | ||||
0.323111 | + | 0.946361i | \(0.395271\pi\) | |||||||
\(558\) | −3.14856e9 | −0.767171 | ||||||||
\(559\) | 4.42028e9 | 1.07031 | ||||||||
\(560\) | −9.38286e9 | −2.25776 | ||||||||
\(561\) | 3.57414e8 | 0.0854675 | ||||||||
\(562\) | 4.82288e8 | 0.114612 | ||||||||
\(563\) | −2.80648e9 | −0.662800 | −0.331400 | − | 0.943490i | \(-0.607521\pi\) | ||||
−0.331400 | + | 0.943490i | \(0.607521\pi\) | |||||||
\(564\) | 3.08392e8 | 0.0723813 | ||||||||
\(565\) | 7.70045e9 | 1.79617 | ||||||||
\(566\) | 5.12496e9 | 1.18805 | ||||||||
\(567\) | 8.12019e8 | 0.187079 | ||||||||
\(568\) | 2.78106e7 | 0.00636782 | ||||||||
\(569\) | 2.66168e8 | 0.0605706 | 0.0302853 | − | 0.999541i | \(-0.490358\pi\) | ||||
0.0302853 | + | 0.999541i | \(0.490358\pi\) | |||||||
\(570\) | 4.36755e6 | 0.000987815 0 | ||||||||
\(571\) | −4.42686e9 | −0.995107 | −0.497554 | − | 0.867433i | \(-0.665768\pi\) | ||||
−0.497554 | + | 0.867433i | \(0.665768\pi\) | |||||||
\(572\) | −1.00228e9 | −0.223925 | ||||||||
\(573\) | −1.23787e9 | −0.274874 | ||||||||
\(574\) | 1.84680e10 | 4.07594 | ||||||||
\(575\) | −9.56963e8 | −0.209922 | ||||||||
\(576\) | −1.68008e9 | −0.366312 | ||||||||
\(577\) | 2.24293e9 | 0.486072 | 0.243036 | − | 0.970017i | \(-0.421857\pi\) | ||||
0.243036 | + | 0.970017i | \(0.421857\pi\) | |||||||
\(578\) | 3.67490e9 | 0.791586 | ||||||||
\(579\) | 7.91402e8 | 0.169442 | ||||||||
\(580\) | −5.15923e9 | −1.09796 | ||||||||
\(581\) | 7.74609e9 | 1.63857 | ||||||||
\(582\) | 5.37069e9 | 1.12927 | ||||||||
\(583\) | 1.52172e9 | 0.318049 | ||||||||
\(584\) | 4.90262e8 | 0.101855 | ||||||||
\(585\) | 2.20117e9 | 0.454578 | ||||||||
\(586\) | 3.90784e8 | 0.0802224 | ||||||||
\(587\) | 8.36007e8 | 0.170599 | 0.0852995 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0852995 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(588\) | −5.48782e9 | −1.11322 | ||||||||
\(589\) | 6.72168e6 | 0.00135542 | ||||||||
\(590\) | 8.72068e9 | 1.74811 | ||||||||
\(591\) | −4.62958e9 | −0.922540 | ||||||||
\(592\) | −6.18336e8 | −0.122489 | ||||||||
\(593\) | 3.15873e9 | 0.622044 | 0.311022 | − | 0.950403i | \(-0.399329\pi\) | ||||
0.311022 | + | 0.950403i | \(0.399329\pi\) | |||||||
\(594\) | −3.11620e8 | −0.0610060 | ||||||||
\(595\) | 8.19589e9 | 1.59509 | ||||||||
\(596\) | −2.13024e9 | −0.412162 | ||||||||
\(597\) | −3.05734e9 | −0.588075 | ||||||||
\(598\) | 1.50327e9 | 0.287464 | ||||||||
\(599\) | −6.25625e9 | −1.18938 | −0.594689 | − | 0.803956i | \(-0.702725\pi\) | ||||
−0.594689 | + | 0.803956i | \(0.702725\pi\) | |||||||
\(600\) | 2.23838e8 | 0.0423062 | ||||||||
\(601\) | 6.43863e8 | 0.120985 | 0.0604927 | − | 0.998169i | \(-0.480733\pi\) | ||||
0.0604927 | + | 0.998169i | \(0.480733\pi\) | |||||||
\(602\) | −1.43498e10 | −2.68076 | ||||||||
\(603\) | 1.80745e9 | 0.335703 | ||||||||
\(604\) | 1.11764e10 | 2.06383 | ||||||||
\(605\) | −7.33790e9 | −1.34719 | ||||||||
\(606\) | 8.48166e9 | 1.54820 | ||||||||
\(607\) | 2.21655e9 | 0.402270 | 0.201135 | − | 0.979564i | \(-0.435537\pi\) | ||||
0.201135 | + | 0.979564i | \(0.435537\pi\) | |||||||
\(608\) | 6.67619e6 | 0.00120467 | ||||||||
\(609\) | 3.99648e9 | 0.716997 | ||||||||
\(610\) | −7.29528e9 | −1.30133 | ||||||||
\(611\) | −6.47565e8 | −0.114852 | ||||||||
\(612\) | 1.32835e9 | 0.234251 | ||||||||
\(613\) | 3.90045e9 | 0.683916 | 0.341958 | − | 0.939715i | \(-0.388910\pi\) | ||||
0.341958 | + | 0.939715i | \(0.388910\pi\) | |||||||
\(614\) | −6.49720e9 | −1.13276 | ||||||||
\(615\) | 7.97525e9 | 1.38255 | ||||||||
\(616\) | 1.57374e8 | 0.0271269 | ||||||||
\(617\) | 3.39587e8 | 0.0582040 | 0.0291020 | − | 0.999576i | \(-0.490735\pi\) | ||||
0.0291020 | + | 0.999576i | \(0.490735\pi\) | |||||||
\(618\) | 8.30959e8 | 0.141619 | ||||||||
\(619\) | −8.96930e9 | −1.51999 | −0.759996 | − | 0.649928i | \(-0.774799\pi\) | ||||
−0.759996 | + | 0.649928i | \(0.774799\pi\) | |||||||
\(620\) | 1.41970e10 | 2.39236 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | 1.26088e10 | 2.10091 | ||||||||
\(623\) | 1.54907e10 | 2.56662 | ||||||||
\(624\) | 3.19323e9 | 0.526120 | ||||||||
\(625\) | −6.06204e9 | −0.993205 | ||||||||
\(626\) | 1.28922e10 | 2.10047 | ||||||||
\(627\) | 665259. | 0.000107784 0 | ||||||||
\(628\) | −5.17975e9 | −0.834546 | ||||||||
\(629\) | 5.40114e8 | 0.0865382 | ||||||||
\(630\) | −7.14578e9 | −1.13856 | ||||||||
\(631\) | −1.32361e9 | −0.209728 | −0.104864 | − | 0.994487i | \(-0.533441\pi\) | ||||
−0.104864 | + | 0.994487i | \(0.533441\pi\) | |||||||
\(632\) | 4.74242e8 | 0.0747292 | ||||||||
\(633\) | 5.30368e9 | 0.831121 | ||||||||
\(634\) | −1.38053e10 | −2.15146 | ||||||||
\(635\) | −8.63635e9 | −1.33851 | ||||||||
\(636\) | 5.65554e9 | 0.871714 | ||||||||
\(637\) | 1.15234e10 | 1.76641 | ||||||||
\(638\) | −1.53369e9 | −0.233811 | ||||||||
\(639\) | −1.92344e8 | −0.0291626 | ||||||||
\(640\) | 1.36580e9 | 0.205948 | ||||||||
\(641\) | 3.41095e9 | 0.511531 | 0.255765 | − | 0.966739i | \(-0.417673\pi\) | ||||
0.255765 | + | 0.966739i | \(0.417673\pi\) | |||||||
\(642\) | −1.01234e9 | −0.150992 | ||||||||
\(643\) | −9.01499e9 | −1.33729 | −0.668647 | − | 0.743580i | \(-0.733126\pi\) | ||||
−0.668647 | + | 0.743580i | \(0.733126\pi\) | |||||||
\(644\) | −2.50055e9 | −0.368922 | ||||||||
\(645\) | −6.19685e9 | −0.909310 | ||||||||
\(646\) | −5.53446e6 | −0.000807722 0 | ||||||||
\(647\) | −3.32698e9 | −0.482932 | −0.241466 | − | 0.970409i | \(-0.577628\pi\) | ||||
−0.241466 | + | 0.970409i | \(0.577628\pi\) | |||||||
\(648\) | −5.60161e7 | −0.00808725 | ||||||||
\(649\) | 1.32832e9 | 0.190742 | ||||||||
\(650\) | −9.71774e9 | −1.38793 | ||||||||
\(651\) | −1.09974e10 | −1.56227 | ||||||||
\(652\) | 1.13966e9 | 0.161031 | ||||||||
\(653\) | −1.27437e10 | −1.79102 | −0.895510 | − | 0.445042i | \(-0.853189\pi\) | ||||
−0.895510 | + | 0.445042i | \(0.853189\pi\) | |||||||
\(654\) | −3.11039e9 | −0.434803 | ||||||||
\(655\) | 1.34993e10 | 1.87702 | ||||||||
\(656\) | 1.15697e10 | 1.60014 | ||||||||
\(657\) | −3.39077e9 | −0.466465 | ||||||||
\(658\) | 2.10223e9 | 0.287666 | ||||||||
\(659\) | 1.10663e10 | 1.50628 | 0.753138 | − | 0.657863i | \(-0.228539\pi\) | ||||
0.753138 | + | 0.657863i | \(0.228539\pi\) | |||||||
\(660\) | 1.40511e9 | 0.190242 | ||||||||
\(661\) | −1.44103e10 | −1.94074 | −0.970370 | − | 0.241624i | \(-0.922320\pi\) | ||||
−0.970370 | + | 0.241624i | \(0.922320\pi\) | |||||||
\(662\) | −3.35326e9 | −0.449225 | ||||||||
\(663\) | −2.78928e9 | −0.371701 | ||||||||
\(664\) | −5.34354e8 | −0.0708339 | ||||||||
\(665\) | 1.52551e7 | 0.00201159 | ||||||||
\(666\) | −4.70911e8 | −0.0617702 | ||||||||
\(667\) | 1.17865e9 | 0.153796 | ||||||||
\(668\) | −1.50763e10 | −1.95694 | ||||||||
\(669\) | −6.44918e9 | −0.832747 | ||||||||
\(670\) | −1.59056e10 | −2.04309 | ||||||||
\(671\) | −1.11121e9 | −0.141993 | ||||||||
\(672\) | −1.09230e10 | −1.38851 | ||||||||
\(673\) | −9.63239e9 | −1.21809 | −0.609047 | − | 0.793134i | \(-0.708448\pi\) | ||||
−0.609047 | + | 0.793134i | \(0.708448\pi\) | |||||||
\(674\) | 1.89583e10 | 2.38501 | ||||||||
\(675\) | −1.54811e9 | −0.193749 | ||||||||
\(676\) | −6.18181e8 | −0.0769665 | ||||||||
\(677\) | −1.92427e9 | −0.238344 | −0.119172 | − | 0.992874i | \(-0.538024\pi\) | ||||
−0.119172 | + | 0.992874i | \(0.538024\pi\) | |||||||
\(678\) | 8.50760e9 | 1.04834 | ||||||||
\(679\) | 1.87589e10 | 2.29966 | ||||||||
\(680\) | −5.65383e8 | −0.0689544 | ||||||||
\(681\) | 2.19657e8 | 0.0266520 | ||||||||
\(682\) | 4.22035e9 | 0.509452 | ||||||||
\(683\) | −8.38945e9 | −1.00754 | −0.503769 | − | 0.863839i | \(-0.668054\pi\) | ||||
−0.503769 | + | 0.863839i | \(0.668054\pi\) | |||||||
\(684\) | 2.47247e6 | 0.000295416 0 | ||||||||
\(685\) | −1.86069e10 | −2.21185 | ||||||||
\(686\) | −1.70214e10 | −2.01307 | ||||||||
\(687\) | −6.19355e9 | −0.728771 | ||||||||
\(688\) | −8.98976e9 | −1.05242 | ||||||||
\(689\) | −1.18756e10 | −1.38321 | ||||||||
\(690\) | −2.10745e9 | −0.244223 | ||||||||
\(691\) | 1.77731e9 | 0.204922 | 0.102461 | − | 0.994737i | \(-0.467328\pi\) | ||||
0.102461 | + | 0.994737i | \(0.467328\pi\) | |||||||
\(692\) | −1.06513e10 | −1.22189 | ||||||||
\(693\) | −1.08844e9 | −0.124233 | ||||||||
\(694\) | −2.82370e9 | −0.320671 | ||||||||
\(695\) | 9.28120e9 | 1.04871 | ||||||||
\(696\) | −2.75692e8 | −0.0309951 | ||||||||
\(697\) | −1.01061e10 | −1.13049 | ||||||||
\(698\) | −9.60686e9 | −1.06927 | ||||||||
\(699\) | 3.71579e9 | 0.411510 | ||||||||
\(700\) | 1.61645e10 | 1.78123 | ||||||||
\(701\) | −7.77870e9 | −0.852891 | −0.426446 | − | 0.904513i | \(-0.640234\pi\) | ||||
−0.426446 | + | 0.904513i | \(0.640234\pi\) | |||||||
\(702\) | 2.43190e9 | 0.265317 | ||||||||
\(703\) | 1.00532e6 | 0.000109134 0 | ||||||||
\(704\) | 2.25199e9 | 0.243255 | ||||||||
\(705\) | 9.07830e8 | 0.0975759 | ||||||||
\(706\) | 9.21671e9 | 0.985733 | ||||||||
\(707\) | 2.96250e10 | 3.15276 | ||||||||
\(708\) | 4.93678e9 | 0.522790 | ||||||||
\(709\) | −3.46303e9 | −0.364917 | −0.182459 | − | 0.983214i | \(-0.558406\pi\) | ||||
−0.182459 | + | 0.983214i | \(0.558406\pi\) | |||||||
\(710\) | 1.69263e9 | 0.177484 | ||||||||
\(711\) | −3.27997e9 | −0.342236 | ||||||||
\(712\) | −1.06860e9 | −0.110952 | ||||||||
\(713\) | −3.24338e9 | −0.335108 | ||||||||
\(714\) | 9.05498e9 | 0.930987 | ||||||||
\(715\) | −2.95046e9 | −0.301869 | ||||||||
\(716\) | −1.05577e10 | −1.07491 | ||||||||
\(717\) | −1.26470e9 | −0.128136 | ||||||||
\(718\) | −1.07150e10 | −1.08033 | ||||||||
\(719\) | −3.37019e9 | −0.338145 | −0.169072 | − | 0.985604i | \(-0.554077\pi\) | ||||
−0.169072 | + | 0.985604i | \(0.554077\pi\) | |||||||
\(720\) | −4.47664e9 | −0.446980 | ||||||||
\(721\) | 2.90240e9 | 0.288393 | ||||||||
\(722\) | 1.44825e10 | 1.43207 | ||||||||
\(723\) | 1.12093e10 | 1.10305 | ||||||||
\(724\) | −5.95741e9 | −0.583408 | ||||||||
\(725\) | −7.61929e9 | −0.742560 | ||||||||
\(726\) | −8.10706e9 | −0.786294 | ||||||||
\(727\) | −6.61011e8 | −0.0638026 | −0.0319013 | − | 0.999491i | \(-0.510156\pi\) | ||||
−0.0319013 | + | 0.999491i | \(0.510156\pi\) | |||||||
\(728\) | −1.22816e9 | −0.117976 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 2.98388e10 | 2.83891 | ||||||||
\(731\) | 7.85252e9 | 0.743529 | ||||||||
\(732\) | −4.12986e9 | −0.389176 | ||||||||
\(733\) | 1.05019e10 | 0.984931 | 0.492465 | − | 0.870332i | \(-0.336096\pi\) | ||||
0.492465 | + | 0.870332i | \(0.336096\pi\) | |||||||
\(734\) | −5.30751e9 | −0.495398 | ||||||||
\(735\) | −1.61548e10 | −1.50070 | ||||||||
\(736\) | −3.22144e9 | −0.297836 | ||||||||
\(737\) | −2.42272e9 | −0.222929 | ||||||||
\(738\) | 8.81122e9 | 0.806935 | ||||||||
\(739\) | −4.71267e9 | −0.429547 | −0.214774 | − | 0.976664i | \(-0.568901\pi\) | ||||
−0.214774 | + | 0.976664i | \(0.568901\pi\) | |||||||
\(740\) | 2.12336e9 | 0.192625 | ||||||||
\(741\) | −5.19172e6 | −0.000468757 0 | ||||||||
\(742\) | 3.85523e10 | 3.46447 | ||||||||
\(743\) | −1.38869e10 | −1.24206 | −0.621031 | − | 0.783786i | \(-0.713286\pi\) | ||||
−0.621031 | + | 0.783786i | \(0.713286\pi\) | |||||||
\(744\) | 7.58642e8 | 0.0675354 | ||||||||
\(745\) | −6.27091e9 | −0.555627 | ||||||||
\(746\) | 2.44519e10 | 2.15638 | ||||||||
\(747\) | 3.69572e9 | 0.324397 | ||||||||
\(748\) | −1.78052e9 | −0.155558 | ||||||||
\(749\) | −3.53593e9 | −0.307480 | ||||||||
\(750\) | 9.13381e7 | 0.00790565 | ||||||||
\(751\) | −1.37115e10 | −1.18126 | −0.590632 | − | 0.806941i | \(-0.701121\pi\) | ||||
−0.590632 | + | 0.806941i | \(0.701121\pi\) | |||||||
\(752\) | 1.31699e9 | 0.112933 | ||||||||
\(753\) | −9.26396e9 | −0.790705 | ||||||||
\(754\) | 1.19690e10 | 1.01685 | ||||||||
\(755\) | 3.29007e10 | 2.78221 | ||||||||
\(756\) | −4.04523e9 | −0.340499 | ||||||||
\(757\) | −1.08694e10 | −0.910685 | −0.455343 | − | 0.890316i | \(-0.650483\pi\) | ||||
−0.455343 | + | 0.890316i | \(0.650483\pi\) | |||||||
\(758\) | −2.59824e9 | −0.216689 | ||||||||
\(759\) | −3.21005e8 | −0.0266480 | ||||||||
\(760\) | −1.05236e6 | −8.69591e−5 0 | ||||||||
\(761\) | −8.48694e9 | −0.698079 | −0.349040 | − | 0.937108i | \(-0.613492\pi\) | ||||
−0.349040 | + | 0.937108i | \(0.613492\pi\) | |||||||
\(762\) | −9.54161e9 | −0.781230 | ||||||||
\(763\) | −1.08641e10 | −0.885436 | ||||||||
\(764\) | 6.16669e9 | 0.500294 | ||||||||
\(765\) | 3.91032e9 | 0.315789 | ||||||||
\(766\) | −1.11222e10 | −0.894109 | ||||||||
\(767\) | −1.03663e10 | −0.829545 | ||||||||
\(768\) | −6.45585e9 | −0.514268 | ||||||||
\(769\) | 1.66331e10 | 1.31896 | 0.659479 | − | 0.751723i | \(-0.270777\pi\) | ||||
0.659479 | + | 0.751723i | \(0.270777\pi\) | |||||||
\(770\) | 9.57825e9 | 0.756082 | ||||||||
\(771\) | −8.39440e9 | −0.659628 | ||||||||
\(772\) | −3.94252e9 | −0.308399 | ||||||||
\(773\) | 1.70231e10 | 1.32559 | 0.662796 | − | 0.748800i | \(-0.269370\pi\) | ||||
0.662796 | + | 0.748800i | \(0.269370\pi\) | |||||||
\(774\) | −6.84640e9 | −0.530725 | ||||||||
\(775\) | 2.09665e10 | 1.61797 | ||||||||
\(776\) | −1.29406e9 | −0.0994120 | ||||||||
\(777\) | −1.64481e9 | −0.125789 | ||||||||
\(778\) | 9.68765e9 | 0.737548 | ||||||||
\(779\) | −1.88106e7 | −0.00142568 | ||||||||
\(780\) | −1.09655e10 | −0.827369 | ||||||||
\(781\) | 2.57820e8 | 0.0193659 | ||||||||
\(782\) | 2.67052e9 | 0.199697 | ||||||||
\(783\) | 1.90675e9 | 0.141948 | ||||||||
\(784\) | −2.34357e10 | −1.73689 | ||||||||
\(785\) | −1.52479e10 | −1.12504 | ||||||||
\(786\) | 1.49143e10 | 1.09553 | ||||||||
\(787\) | 1.89829e10 | 1.38820 | 0.694100 | − | 0.719879i | \(-0.255803\pi\) | ||||
0.694100 | + | 0.719879i | \(0.255803\pi\) | |||||||
\(788\) | 2.30631e10 | 1.67910 | ||||||||
\(789\) | 5.14004e9 | 0.372560 | ||||||||
\(790\) | 2.88638e10 | 2.08285 | ||||||||
\(791\) | 2.97156e10 | 2.13485 | ||||||||
\(792\) | 7.50844e7 | 0.00537046 | ||||||||
\(793\) | 8.67192e9 | 0.617532 | ||||||||
\(794\) | −1.72610e10 | −1.22375 | ||||||||
\(795\) | 1.66485e10 | 1.17514 | ||||||||
\(796\) | 1.52307e10 | 1.07035 | ||||||||
\(797\) | −1.55539e10 | −1.08826 | −0.544131 | − | 0.839000i | \(-0.683141\pi\) | ||||
−0.544131 | + | 0.839000i | \(0.683141\pi\) | |||||||
\(798\) | 1.68542e7 | 0.00117408 | ||||||||
\(799\) | −1.15038e9 | −0.0797864 | ||||||||
\(800\) | 2.08246e10 | 1.43801 | ||||||||
\(801\) | 7.39071e9 | 0.508127 | ||||||||
\(802\) | 4.70435e9 | 0.322025 | ||||||||
\(803\) | 4.54501e9 | 0.309763 | ||||||||
\(804\) | −9.00415e9 | −0.611007 | ||||||||
\(805\) | −7.36099e9 | −0.497337 | ||||||||
\(806\) | −3.29358e10 | −2.21562 | ||||||||
\(807\) | −2.72862e9 | −0.182762 | ||||||||
\(808\) | −2.04365e9 | −0.136291 | ||||||||
\(809\) | −3.30592e9 | −0.219519 | −0.109760 | − | 0.993958i | \(-0.535008\pi\) | ||||
−0.109760 | + | 0.993958i | \(0.535008\pi\) | |||||||
\(810\) | −3.40931e9 | −0.225408 | ||||||||
\(811\) | 7.80890e9 | 0.514064 | 0.257032 | − | 0.966403i | \(-0.417256\pi\) | ||||
0.257032 | + | 0.966403i | \(0.417256\pi\) | |||||||
\(812\) | −1.99092e10 | −1.30499 | ||||||||
\(813\) | −1.59241e10 | −1.03929 | ||||||||
\(814\) | 6.31212e8 | 0.0410195 | ||||||||
\(815\) | 3.35489e9 | 0.217083 | ||||||||
\(816\) | 5.67270e9 | 0.365489 | ||||||||
\(817\) | 1.46160e7 | 0.000937673 0 | ||||||||
\(818\) | −3.23066e10 | −2.06374 | ||||||||
\(819\) | 8.49421e9 | 0.540293 | ||||||||
\(820\) | −3.97302e10 | −2.51636 | ||||||||
\(821\) | 2.03343e10 | 1.28242 | 0.641208 | − | 0.767367i | \(-0.278434\pi\) | ||||
0.641208 | + | 0.767367i | \(0.278434\pi\) | |||||||
\(822\) | −2.05573e10 | −1.29096 | ||||||||
\(823\) | −5.44877e9 | −0.340721 | −0.170360 | − | 0.985382i | \(-0.554493\pi\) | ||||
−0.170360 | + | 0.985382i | \(0.554493\pi\) | |||||||
\(824\) | −2.00219e8 | −0.0124669 | ||||||||
\(825\) | 2.07510e9 | 0.128662 | ||||||||
\(826\) | 3.36527e10 | 2.07773 | ||||||||
\(827\) | 1.46646e10 | 0.901571 | 0.450785 | − | 0.892632i | \(-0.351144\pi\) | ||||
0.450785 | + | 0.892632i | \(0.351144\pi\) | |||||||
\(828\) | −1.19303e9 | −0.0730374 | ||||||||
\(829\) | 1.62752e10 | 0.992171 | 0.496086 | − | 0.868274i | \(-0.334770\pi\) | ||||
0.496086 | + | 0.868274i | \(0.334770\pi\) | |||||||
\(830\) | −3.25224e10 | −1.97428 | ||||||||
\(831\) | 6.75715e9 | 0.408470 | ||||||||
\(832\) | −1.75747e10 | −1.05793 | ||||||||
\(833\) | 2.04710e10 | 1.22710 | ||||||||
\(834\) | 1.02541e10 | 0.612089 | ||||||||
\(835\) | −4.43808e10 | −2.63811 | ||||||||
\(836\) | −3.31412e6 | −0.000196176 0 | ||||||||
\(837\) | −5.24694e9 | −0.309291 | ||||||||
\(838\) | 1.43989e10 | 0.845230 | ||||||||
\(839\) | −2.08897e10 | −1.22114 | −0.610570 | − | 0.791962i | \(-0.709060\pi\) | ||||
−0.610570 | + | 0.791962i | \(0.709060\pi\) | |||||||
\(840\) | 1.72177e9 | 0.100230 | ||||||||
\(841\) | −7.86548e9 | −0.455973 | ||||||||
\(842\) | 2.87467e10 | 1.65957 | ||||||||
\(843\) | 8.03712e8 | 0.0462066 | ||||||||
\(844\) | −2.64213e10 | −1.51271 | ||||||||
\(845\) | −1.81977e9 | −0.103757 | ||||||||
\(846\) | 1.00299e9 | 0.0569508 | ||||||||
\(847\) | −2.83166e10 | −1.60121 | ||||||||
\(848\) | 2.41520e10 | 1.36009 | ||||||||
\(849\) | 8.54053e9 | 0.478970 | ||||||||
\(850\) | −1.72633e10 | −0.964179 | ||||||||
\(851\) | −4.85093e8 | −0.0269819 | ||||||||
\(852\) | 9.58200e8 | 0.0530784 | ||||||||
\(853\) | 8.63798e9 | 0.476530 | 0.238265 | − | 0.971200i | \(-0.423421\pi\) | ||||
0.238265 | + | 0.971200i | \(0.423421\pi\) | |||||||
\(854\) | −2.81521e10 | −1.54671 | ||||||||
\(855\) | 7.27834e6 | 0.000398245 0 | ||||||||
\(856\) | 2.43922e8 | 0.0132921 | ||||||||
\(857\) | −2.73211e10 | −1.48274 | −0.741370 | − | 0.671097i | \(-0.765823\pi\) | ||||
−0.741370 | + | 0.671097i | \(0.765823\pi\) | |||||||
\(858\) | −3.25973e9 | −0.176188 | ||||||||
\(859\) | 2.72853e10 | 1.46877 | 0.734383 | − | 0.678735i | \(-0.237471\pi\) | ||||
0.734383 | + | 0.678735i | \(0.237471\pi\) | |||||||
\(860\) | 3.08708e10 | 1.65502 | ||||||||
\(861\) | 3.07761e10 | 1.64325 | ||||||||
\(862\) | 2.43449e10 | 1.29459 | ||||||||
\(863\) | 1.11895e10 | 0.592617 | 0.296308 | − | 0.955092i | \(-0.404244\pi\) | ||||
0.296308 | + | 0.955092i | \(0.404244\pi\) | |||||||
\(864\) | −5.21143e9 | −0.274890 | ||||||||
\(865\) | −3.13548e10 | −1.64721 | ||||||||
\(866\) | 4.13733e9 | 0.216475 | ||||||||
\(867\) | 6.12407e9 | 0.319134 | ||||||||
\(868\) | 5.47856e10 | 2.84346 | ||||||||
\(869\) | 4.39649e9 | 0.227267 | ||||||||
\(870\) | −1.67795e10 | −0.863894 | ||||||||
\(871\) | 1.89070e10 | 0.969526 | ||||||||
\(872\) | 7.49446e8 | 0.0382765 | ||||||||
\(873\) | 8.95003e9 | 0.455276 | ||||||||
\(874\) | 4.97068e6 | 0.000251841 0 | ||||||||
\(875\) | 3.19029e8 | 0.0160991 | ||||||||
\(876\) | 1.68917e10 | 0.849005 | ||||||||
\(877\) | 2.05215e9 | 0.102733 | 0.0513667 | − | 0.998680i | \(-0.483642\pi\) | ||||
0.0513667 | + | 0.998680i | \(0.483642\pi\) | |||||||
\(878\) | −4.64685e10 | −2.31701 | ||||||||
\(879\) | 6.51226e8 | 0.0323423 | ||||||||
\(880\) | 6.00051e9 | 0.296824 | ||||||||
\(881\) | 2.13115e10 | 1.05002 | 0.525010 | − | 0.851096i | \(-0.324062\pi\) | ||||
0.525010 | + | 0.851096i | \(0.324062\pi\) | |||||||
\(882\) | −1.78481e10 | −0.875896 | ||||||||
\(883\) | −3.57525e9 | −0.174761 | −0.0873804 | − | 0.996175i | \(-0.527850\pi\) | ||||
−0.0873804 | + | 0.996175i | \(0.527850\pi\) | |||||||
\(884\) | 1.38953e10 | 0.676527 | ||||||||
\(885\) | 1.45326e10 | 0.704763 | ||||||||
\(886\) | 2.33477e10 | 1.12778 | ||||||||
\(887\) | −1.76896e9 | −0.0851107 | −0.0425554 | − | 0.999094i | \(-0.513550\pi\) | ||||
−0.0425554 | + | 0.999094i | \(0.513550\pi\) | |||||||
\(888\) | 1.13465e8 | 0.00543774 | ||||||||
\(889\) | −3.33273e10 | −1.59090 | ||||||||
\(890\) | −6.50384e10 | −3.09247 | ||||||||
\(891\) | −5.19301e8 | −0.0245950 | ||||||||
\(892\) | 3.21278e10 | 1.51567 | ||||||||
\(893\) | −2.14122e6 | −0.000100619 0 | ||||||||
\(894\) | −6.92823e9 | −0.324295 | ||||||||
\(895\) | −3.10791e10 | −1.44906 | ||||||||
\(896\) | 5.27057e9 | 0.244782 | ||||||||
\(897\) | 2.50514e9 | 0.115893 | ||||||||
\(898\) | 2.89263e10 | 1.33299 | ||||||||
\(899\) | −2.58237e10 | −1.18538 | ||||||||
\(900\) | 7.71222e9 | 0.352639 | ||||||||
\(901\) | −2.10966e10 | −0.960896 | ||||||||
\(902\) | −1.18106e10 | −0.535858 | ||||||||
\(903\) | −2.39134e10 | −1.08077 | ||||||||
\(904\) | −2.04990e9 | −0.0922875 | ||||||||
\(905\) | −1.75371e10 | −0.786481 | ||||||||
\(906\) | 3.63493e10 | 1.62386 | ||||||||
\(907\) | −3.18196e10 | −1.41602 | −0.708009 | − | 0.706203i | \(-0.750407\pi\) | ||||
−0.708009 | + | 0.706203i | \(0.750407\pi\) | |||||||
\(908\) | −1.09426e9 | −0.0485089 | ||||||||
\(909\) | 1.41343e10 | 0.624168 | ||||||||
\(910\) | −7.47492e10 | −3.28823 | ||||||||
\(911\) | −2.03709e10 | −0.892680 | −0.446340 | − | 0.894863i | \(-0.647273\pi\) | ||||
−0.446340 | + | 0.894863i | \(0.647273\pi\) | |||||||
\(912\) | 1.05587e7 | 0.000460922 0 | ||||||||
\(913\) | −4.95377e9 | −0.215421 | ||||||||
\(914\) | 4.67370e9 | 0.202465 | ||||||||
\(915\) | −1.21573e10 | −0.524641 | ||||||||
\(916\) | 3.08543e10 | 1.32642 | ||||||||
\(917\) | 5.20933e10 | 2.23095 | ||||||||
\(918\) | 4.32020e9 | 0.184312 | ||||||||
\(919\) | 2.27511e10 | 0.966936 | 0.483468 | − | 0.875362i | \(-0.339377\pi\) | ||||
0.483468 | + | 0.875362i | \(0.339377\pi\) | |||||||
\(920\) | 5.07789e8 | 0.0214994 | ||||||||
\(921\) | −1.08273e10 | −0.456680 | ||||||||
\(922\) | 5.82328e9 | 0.244686 | ||||||||
\(923\) | −2.01204e9 | −0.0842230 | ||||||||
\(924\) | 5.42225e9 | 0.226114 | ||||||||
\(925\) | 3.13584e9 | 0.130274 | ||||||||
\(926\) | −4.75797e9 | −0.196917 | ||||||||
\(927\) | 1.38476e9 | 0.0570946 | ||||||||
\(928\) | −2.56489e10 | −1.05354 | ||||||||
\(929\) | 2.74318e10 | 1.12253 | 0.561267 | − | 0.827635i | \(-0.310314\pi\) | ||||
0.561267 | + | 0.827635i | \(0.310314\pi\) | |||||||
\(930\) | 4.61732e10 | 1.88234 | ||||||||
\(931\) | 3.81030e7 | 0.00154751 | ||||||||
\(932\) | −1.85109e10 | −0.748982 | ||||||||
\(933\) | 2.10120e10 | 0.846998 | ||||||||
\(934\) | −5.17358e10 | −2.07767 | ||||||||
\(935\) | −5.24142e9 | −0.209705 | ||||||||
\(936\) | −5.85963e8 | −0.0233563 | ||||||||
\(937\) | 4.61149e10 | 1.83127 | 0.915635 | − | 0.402011i | \(-0.131689\pi\) | ||||
0.915635 | + | 0.402011i | \(0.131689\pi\) | |||||||
\(938\) | −6.13788e10 | −2.42834 | ||||||||
\(939\) | 2.14843e10 | 0.846822 | ||||||||
\(940\) | −4.52253e9 | −0.177596 | ||||||||
\(941\) | 2.61990e10 | 1.02499 | 0.512497 | − | 0.858689i | \(-0.328720\pi\) | ||||
0.512497 | + | 0.858689i | \(0.328720\pi\) | |||||||
\(942\) | −1.68462e10 | −0.656634 | ||||||||
\(943\) | 9.07659e9 | 0.352478 | ||||||||
\(944\) | 2.10825e10 | 0.815680 | ||||||||
\(945\) | −1.19081e10 | −0.459021 | ||||||||
\(946\) | 9.17697e9 | 0.352436 | ||||||||
\(947\) | 3.00640e10 | 1.15033 | 0.575165 | − | 0.818038i | \(-0.304938\pi\) | ||||
0.575165 | + | 0.818038i | \(0.304938\pi\) | |||||||
\(948\) | 1.63398e10 | 0.622898 | ||||||||
\(949\) | −3.54695e10 | −1.34717 | ||||||||
\(950\) | −3.21325e7 | −0.00121594 | ||||||||
\(951\) | −2.30060e10 | −0.867380 | ||||||||
\(952\) | −2.18179e9 | −0.0819564 | ||||||||
\(953\) | 6.39450e9 | 0.239321 | 0.119661 | − | 0.992815i | \(-0.461819\pi\) | ||||
0.119661 | + | 0.992815i | \(0.461819\pi\) | |||||||
\(954\) | 1.83936e10 | 0.685879 | ||||||||
\(955\) | 1.81532e10 | 0.674437 | ||||||||
\(956\) | 6.30036e9 | 0.233218 | ||||||||
\(957\) | −2.55582e9 | −0.0942626 | ||||||||
\(958\) | −1.62595e10 | −0.597488 | ||||||||
\(959\) | −7.18031e10 | −2.62892 | ||||||||
\(960\) | 2.46381e10 | 0.898790 | ||||||||
\(961\) | 4.35481e10 | 1.58284 | ||||||||
\(962\) | −4.92601e9 | −0.178395 | ||||||||
\(963\) | −1.68702e9 | −0.0608734 | ||||||||
\(964\) | −5.58414e10 | −2.00764 | ||||||||
\(965\) | −1.16058e10 | −0.415747 | ||||||||
\(966\) | −8.13257e9 | −0.290274 | ||||||||
\(967\) | −1.61416e10 | −0.574056 | −0.287028 | − | 0.957922i | \(-0.592667\pi\) | ||||
−0.287028 | + | 0.957922i | \(0.592667\pi\) | |||||||
\(968\) | 1.95339e9 | 0.0692189 | ||||||||
\(969\) | −9.22295e6 | −0.000325639 0 | ||||||||
\(970\) | −7.87604e10 | −2.77081 | ||||||||
\(971\) | 3.16346e10 | 1.10891 | 0.554454 | − | 0.832214i | \(-0.312927\pi\) | ||||
0.554454 | + | 0.832214i | \(0.312927\pi\) | |||||||
\(972\) | −1.93001e9 | −0.0674105 | ||||||||
\(973\) | 3.58157e10 | 1.24646 | ||||||||
\(974\) | −2.73929e10 | −0.949910 | ||||||||
\(975\) | −1.61942e10 | −0.559556 | ||||||||
\(976\) | −1.76365e10 | −0.607210 | ||||||||
\(977\) | 1.02749e10 | 0.352490 | 0.176245 | − | 0.984346i | \(-0.443605\pi\) | ||||
0.176245 | + | 0.984346i | \(0.443605\pi\) | |||||||
\(978\) | 3.70655e9 | 0.126702 | ||||||||
\(979\) | −9.90657e9 | −0.337430 | ||||||||
\(980\) | 8.04781e10 | 2.73141 | ||||||||
\(981\) | −5.18334e9 | −0.175294 | ||||||||
\(982\) | −2.34394e10 | −0.789871 | ||||||||
\(983\) | 1.83595e10 | 0.616487 | 0.308244 | − | 0.951307i | \(-0.400259\pi\) | ||||
0.308244 | + | 0.951307i | \(0.400259\pi\) | |||||||
\(984\) | −2.12305e9 | −0.0710359 | ||||||||
\(985\) | 6.78921e10 | 2.26356 | ||||||||
\(986\) | 2.12626e10 | 0.706393 | ||||||||
\(987\) | 3.50327e9 | 0.115975 | ||||||||
\(988\) | 2.58635e7 | 0.000853176 0 | ||||||||
\(989\) | −7.05260e9 | −0.231826 | ||||||||
\(990\) | 4.56986e9 | 0.149685 | ||||||||
\(991\) | −2.66502e10 | −0.869847 | −0.434924 | − | 0.900467i | \(-0.643225\pi\) | ||||
−0.434924 | + | 0.900467i | \(0.643225\pi\) | |||||||
\(992\) | 7.05799e10 | 2.29557 | ||||||||
\(993\) | −5.58806e9 | −0.181109 | ||||||||
\(994\) | 6.53179e9 | 0.210950 | ||||||||
\(995\) | 4.48354e10 | 1.44291 | ||||||||
\(996\) | −1.84109e10 | −0.590429 | ||||||||
\(997\) | −3.57015e10 | −1.14092 | −0.570458 | − | 0.821327i | \(-0.693234\pi\) | ||||
−0.570458 | + | 0.821327i | \(0.693234\pi\) | |||||||
\(998\) | 4.45024e10 | 1.41718 | ||||||||
\(999\) | −7.84753e8 | −0.0249031 |
(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 | 69.8.a.c.1.2 | ✓ | 7 | |
3.2 | odd | 2 | 207.8.a.d.1.6 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.c.1.2 | ✓ | 7 | 1.1 | even | 1 | trivial | |
207.8.a.d.1.6 | 7 | 3.2 | odd | 2 |