Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,7,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.31");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(17.0240021879\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 8470 x^{16} + 28007049 x^{14} + 45282701078 x^{12} + 36580026955844 x^{10} + \cdots + 65\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.6 | ||
Root | \(8.36225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.31 |
Dual form | 74.7.d.a.43.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.00000 | + | 4.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 12.3623i | 0.457861i | 0.973443 | + | 0.228931i | \(0.0735229\pi\) | ||||
−0.973443 | + | 0.228931i | \(0.926477\pi\) | |||||||
\(4\) | 32.0000i | 0.500000i | ||||||||
\(5\) | −142.025 | + | 142.025i | −1.13620 | + | 1.13620i | −0.147079 | + | 0.989125i | \(0.546987\pi\) |
−0.989125 | + | 0.147079i | \(0.953013\pi\) | |||||||
\(6\) | −49.4490 | + | 49.4490i | −0.228931 | + | 0.228931i | ||||
\(7\) | −327.411 | −0.954552 | −0.477276 | − | 0.878753i | \(-0.658376\pi\) | ||||
−0.477276 | + | 0.878753i | \(0.658376\pi\) | |||||||
\(8\) | −128.000 | + | 128.000i | −0.250000 | + | 0.250000i | ||||
\(9\) | 576.175 | 0.790363 | ||||||||
\(10\) | −1136.20 | −1.13620 | ||||||||
\(11\) | − | 1873.92i | − | 1.40790i | −0.710247 | − | 0.703952i | \(-0.751417\pi\) | ||
0.710247 | − | 0.703952i | \(-0.248583\pi\) | |||||||
\(12\) | −395.592 | −0.228931 | ||||||||
\(13\) | 471.226 | − | 471.226i | 0.214486 | − | 0.214486i | −0.591684 | − | 0.806170i | \(-0.701537\pi\) |
0.806170 | + | 0.591684i | \(0.201537\pi\) | |||||||
\(14\) | −1309.65 | − | 1309.65i | −0.477276 | − | 0.477276i | ||||
\(15\) | −1755.75 | − | 1755.75i | −0.520224 | − | 0.520224i | ||||
\(16\) | −1024.00 | −0.250000 | ||||||||
\(17\) | 1653.75 | − | 1653.75i | 0.336607 | − | 0.336607i | −0.518482 | − | 0.855089i | \(-0.673503\pi\) |
0.855089 | + | 0.518482i | \(0.173503\pi\) | |||||||
\(18\) | 2304.70 | + | 2304.70i | 0.395182 | + | 0.395182i | ||||
\(19\) | −331.819 | + | 331.819i | −0.0483771 | + | 0.0483771i | −0.730881 | − | 0.682504i | \(-0.760891\pi\) |
0.682504 | + | 0.730881i | \(0.260891\pi\) | |||||||
\(20\) | −4544.81 | − | 4544.81i | −0.568102 | − | 0.568102i | ||||
\(21\) | − | 4047.54i | − | 0.437052i | ||||||
\(22\) | 7495.68 | − | 7495.68i | 0.703952 | − | 0.703952i | ||||
\(23\) | −16501.6 | + | 16501.6i | −1.35626 | + | 1.35626i | −0.477778 | + | 0.878481i | \(0.658558\pi\) |
−0.878481 | + | 0.477778i | \(0.841442\pi\) | |||||||
\(24\) | −1582.37 | − | 1582.37i | −0.114465 | − | 0.114465i | ||||
\(25\) | − | 24717.5i | − | 1.58192i | ||||||
\(26\) | 3769.81 | 0.214486 | ||||||||
\(27\) | 16134.9i | 0.819738i | ||||||||
\(28\) | − | 10477.2i | − | 0.477276i | ||||||
\(29\) | −4645.17 | − | 4645.17i | −0.190462 | − | 0.190462i | 0.605434 | − | 0.795896i | \(-0.293000\pi\) |
−0.795896 | + | 0.605434i | \(0.793000\pi\) | |||||||
\(30\) | − | 14046.0i | − | 0.520224i | ||||||
\(31\) | −28352.1 | − | 28352.1i | −0.951700 | − | 0.951700i | 0.0471866 | − | 0.998886i | \(-0.484974\pi\) |
−0.998886 | + | 0.0471866i | \(0.984974\pi\) | |||||||
\(32\) | −4096.00 | − | 4096.00i | −0.125000 | − | 0.125000i | ||||
\(33\) | 23165.9 | 0.644625 | ||||||||
\(34\) | 13230.0 | 0.336607 | ||||||||
\(35\) | 46500.8 | − | 46500.8i | 1.08457 | − | 1.08457i | ||||
\(36\) | 18437.6i | 0.395182i | ||||||||
\(37\) | −23447.0 | + | 44899.5i | −0.462894 | + | 0.886413i | ||||
\(38\) | −2654.55 | −0.0483771 | ||||||||
\(39\) | 5825.41 | + | 5825.41i | 0.0982048 | + | 0.0982048i | ||||
\(40\) | − | 36358.5i | − | 0.568102i | ||||||
\(41\) | − | 70914.8i | − | 1.02893i | −0.857512 | − | 0.514464i | \(-0.827991\pi\) | ||
0.857512 | − | 0.514464i | \(-0.172009\pi\) | |||||||
\(42\) | 16190.2 | − | 16190.2i | 0.218526 | − | 0.218526i | ||||
\(43\) | −28595.9 | + | 28595.9i | −0.359665 | + | 0.359665i | −0.863690 | − | 0.504024i | \(-0.831852\pi\) |
0.504024 | + | 0.863690i | \(0.331852\pi\) | |||||||
\(44\) | 59965.5 | 0.703952 | ||||||||
\(45\) | −81831.5 | + | 81831.5i | −0.898014 | + | 0.898014i | ||||
\(46\) | −132013. | −1.35626 | ||||||||
\(47\) | −47680.7 | −0.459250 | −0.229625 | − | 0.973279i | \(-0.573750\pi\) | ||||
−0.229625 | + | 0.973279i | \(0.573750\pi\) | |||||||
\(48\) | − | 12658.9i | − | 0.114465i | ||||||
\(49\) | −10450.8 | −0.0888300 | ||||||||
\(50\) | 98869.9 | − | 98869.9i | 0.790959 | − | 0.790959i | ||||
\(51\) | 20444.1 | + | 20444.1i | 0.154119 | + | 0.154119i | ||||
\(52\) | 15079.2 | + | 15079.2i | 0.107243 | + | 0.107243i | ||||
\(53\) | 16731.9 | 0.112387 | 0.0561937 | − | 0.998420i | \(-0.482104\pi\) | ||||
0.0561937 | + | 0.998420i | \(0.482104\pi\) | |||||||
\(54\) | −64539.6 | + | 64539.6i | −0.409869 | + | 0.409869i | ||||
\(55\) | 266144. | + | 266144.i | 1.59967 | + | 1.59967i | ||||
\(56\) | 41908.7 | − | 41908.7i | 0.238638 | − | 0.238638i | ||||
\(57\) | −4102.03 | − | 4102.03i | −0.0221500 | − | 0.0221500i | ||||
\(58\) | − | 37161.4i | − | 0.190462i | ||||||
\(59\) | −160196. | + | 160196.i | −0.780001 | + | 0.780001i | −0.979831 | − | 0.199829i | \(-0.935961\pi\) |
0.199829 | + | 0.979831i | \(0.435961\pi\) | |||||||
\(60\) | 56184.1 | − | 56184.1i | 0.260112 | − | 0.260112i | ||||
\(61\) | −123654. | − | 123654.i | −0.544776 | − | 0.544776i | 0.380149 | − | 0.924925i | \(-0.375873\pi\) |
−0.924925 | + | 0.380149i | \(0.875873\pi\) | |||||||
\(62\) | − | 226817.i | − | 0.951700i | ||||||
\(63\) | −188646. | −0.754443 | ||||||||
\(64\) | − | 32768.0i | − | 0.125000i | ||||||
\(65\) | 133852.i | 0.487400i | ||||||||
\(66\) | 92663.5 | + | 92663.5i | 0.322312 | + | 0.322312i | ||||
\(67\) | 13293.2i | 0.0441984i | 0.999756 | + | 0.0220992i | \(0.00703496\pi\) | ||||
−0.999756 | + | 0.0220992i | \(0.992965\pi\) | |||||||
\(68\) | 52920.0 | + | 52920.0i | 0.168304 | + | 0.168304i | ||||
\(69\) | −203997. | − | 203997.i | −0.620978 | − | 0.620978i | ||||
\(70\) | 372006. | 1.08457 | ||||||||
\(71\) | 332247. | 0.928294 | 0.464147 | − | 0.885758i | \(-0.346361\pi\) | ||||
0.464147 | + | 0.885758i | \(0.346361\pi\) | |||||||
\(72\) | −73750.4 | + | 73750.4i | −0.197591 | + | 0.197591i | ||||
\(73\) | 656085.i | 1.68652i | 0.537506 | + | 0.843260i | \(0.319366\pi\) | ||||
−0.537506 | + | 0.843260i | \(0.680634\pi\) | |||||||
\(74\) | −273386. | + | 85810.0i | −0.674654 | + | 0.211760i | ||||
\(75\) | 305564. | 0.724299 | ||||||||
\(76\) | −10618.2 | − | 10618.2i | −0.0241886 | − | 0.0241886i | ||||
\(77\) | 613543.i | 1.34392i | ||||||||
\(78\) | 46603.3i | 0.0982048i | ||||||||
\(79\) | −570724. | + | 570724.i | −1.15756 | + | 1.15756i | −0.172567 | + | 0.984998i | \(0.555206\pi\) |
−0.984998 | + | 0.172567i | \(0.944794\pi\) | |||||||
\(80\) | 145434. | − | 145434.i | 0.284051 | − | 0.284051i | ||||
\(81\) | 220568. | 0.415037 | ||||||||
\(82\) | 283659. | − | 283659.i | 0.514464 | − | 0.514464i | ||||
\(83\) | 717191. | 1.25430 | 0.627149 | − | 0.778900i | \(-0.284222\pi\) | ||||
0.627149 | + | 0.778900i | \(0.284222\pi\) | |||||||
\(84\) | 129521. | 0.218526 | ||||||||
\(85\) | 469750.i | 0.764909i | ||||||||
\(86\) | −228767. | −0.359665 | ||||||||
\(87\) | 57424.8 | − | 57424.8i | 0.0872051 | − | 0.0872051i | ||||
\(88\) | 239862. | + | 239862.i | 0.351976 | + | 0.351976i | ||||
\(89\) | −176723. | − | 176723.i | −0.250682 | − | 0.250682i | 0.570568 | − | 0.821250i | \(-0.306723\pi\) |
−0.821250 | + | 0.570568i | \(0.806723\pi\) | |||||||
\(90\) | −654652. | −0.898014 | ||||||||
\(91\) | −154285. | + | 154285.i | −0.204738 | + | 0.204738i | ||||
\(92\) | −528051. | − | 528051.i | −0.678129 | − | 0.678129i | ||||
\(93\) | 350496. | − | 350496.i | 0.435746 | − | 0.435746i | ||||
\(94\) | −190723. | − | 190723.i | −0.229625 | − | 0.229625i | ||||
\(95\) | − | 94253.4i | − | 0.109933i | ||||||
\(96\) | 50635.8 | − | 50635.8i | 0.0572327 | − | 0.0572327i | ||||
\(97\) | 1.15438e6 | − | 1.15438e6i | 1.26484 | − | 1.26484i | 0.316120 | − | 0.948719i | \(-0.397620\pi\) |
0.948719 | − | 0.316120i | \(-0.102380\pi\) | |||||||
\(98\) | −41803.0 | − | 41803.0i | −0.0444150 | − | 0.0444150i | ||||
\(99\) | − | 1.07971e6i | − | 1.11276i | ||||||
\(100\) | 790959. | 0.790959 | ||||||||
\(101\) | − | 469134.i | − | 0.455337i | −0.973739 | − | 0.227668i | \(-0.926890\pi\) | ||
0.973739 | − | 0.227668i | \(-0.0731102\pi\) | |||||||
\(102\) | 163553.i | 0.154119i | ||||||||
\(103\) | −964602. | − | 964602.i | −0.882748 | − | 0.882748i | 0.111065 | − | 0.993813i | \(-0.464574\pi\) |
−0.993813 | + | 0.111065i | \(0.964574\pi\) | |||||||
\(104\) | 120634.i | 0.107243i | ||||||||
\(105\) | 574854. | + | 574854.i | 0.496581 | + | 0.496581i | ||||
\(106\) | 66927.6 | + | 66927.6i | 0.0561937 | + | 0.0561937i | ||||
\(107\) | −1.14372e6 | −0.933615 | −0.466807 | − | 0.884359i | \(-0.654596\pi\) | ||||
−0.466807 | + | 0.884359i | \(0.654596\pi\) | |||||||
\(108\) | −516317. | −0.409869 | ||||||||
\(109\) | −1.35097e6 | + | 1.35097e6i | −1.04320 | + | 1.04320i | −0.0441719 | + | 0.999024i | \(0.514065\pi\) |
−0.999024 | + | 0.0441719i | \(0.985935\pi\) | |||||||
\(110\) | 2.12916e6i | 1.59967i | ||||||||
\(111\) | −555059. | − | 289858.i | −0.405854 | − | 0.211941i | ||||
\(112\) | 335269. | 0.238638 | ||||||||
\(113\) | 215916. | + | 215916.i | 0.149641 | + | 0.149641i | 0.777957 | − | 0.628317i | \(-0.216256\pi\) |
−0.628317 | + | 0.777957i | \(0.716256\pi\) | |||||||
\(114\) | − | 32816.2i | − | 0.0221500i | ||||||
\(115\) | − | 4.68729e6i | − | 3.08197i | ||||||
\(116\) | 148646. | − | 148646.i | 0.0952309 | − | 0.0952309i | ||||
\(117\) | 271508. | − | 271508.i | 0.169522 | − | 0.169522i | ||||
\(118\) | −1.28157e6 | −0.780001 | ||||||||
\(119\) | −541457. | + | 541457.i | −0.321309 | + | 0.321309i | ||||
\(120\) | 449473. | 0.260112 | ||||||||
\(121\) | −1.74002e6 | −0.982194 | ||||||||
\(122\) | − | 989231.i | − | 0.544776i | ||||||
\(123\) | 876666. | 0.471106 | ||||||||
\(124\) | 907267. | − | 907267.i | 0.475850 | − | 0.475850i | ||||
\(125\) | 1.29136e6 | + | 1.29136e6i | 0.661177 | + | 0.661177i | ||||
\(126\) | −754585. | − | 754585.i | −0.377221 | − | 0.377221i | ||||
\(127\) | −693878. | −0.338744 | −0.169372 | − | 0.985552i | \(-0.554174\pi\) | ||||
−0.169372 | + | 0.985552i | \(0.554174\pi\) | |||||||
\(128\) | 131072. | − | 131072.i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −353510. | − | 353510.i | −0.164677 | − | 0.164677i | ||||
\(130\) | −535408. | + | 535408.i | −0.243700 | + | 0.243700i | ||||
\(131\) | −1.56710e6 | − | 1.56710e6i | −0.697081 | − | 0.697081i | 0.266699 | − | 0.963780i | \(-0.414067\pi\) |
−0.963780 | + | 0.266699i | \(0.914067\pi\) | |||||||
\(132\) | 741308.i | 0.322312i | ||||||||
\(133\) | 108641. | − | 108641.i | 0.0461785 | − | 0.0461785i | ||||
\(134\) | −53172.9 | + | 53172.9i | −0.0220992 | + | 0.0220992i | ||||
\(135\) | −2.29157e6 | − | 2.29157e6i | −0.931389 | − | 0.931389i | ||||
\(136\) | 423360.i | 0.168304i | ||||||||
\(137\) | 2.79547e6 | 1.08716 | 0.543579 | − | 0.839358i | \(-0.317069\pi\) | ||||
0.543579 | + | 0.839358i | \(0.317069\pi\) | |||||||
\(138\) | − | 1.63198e6i | − | 0.620978i | ||||||
\(139\) | 2.03481e6i | 0.757669i | 0.925464 | + | 0.378834i | \(0.123675\pi\) | ||||
−0.925464 | + | 0.378834i | \(0.876325\pi\) | |||||||
\(140\) | 1.48802e6 | + | 1.48802e6i | 0.542283 | + | 0.542283i | ||||
\(141\) | − | 589441.i | − | 0.210273i | ||||||
\(142\) | 1.32899e6 | + | 1.32899e6i | 0.464147 | + | 0.464147i | ||||
\(143\) | −883040. | − | 883040.i | −0.301976 | − | 0.301976i | ||||
\(144\) | −590003. | −0.197591 | ||||||||
\(145\) | 1.31947e6 | 0.432807 | ||||||||
\(146\) | −2.62434e6 | + | 2.62434e6i | −0.843260 | + | 0.843260i | ||||
\(147\) | − | 129195.i | − | 0.0406718i | ||||||
\(148\) | −1.43678e6 | − | 750304.i | −0.443207 | − | 0.231447i | ||||
\(149\) | 4.38790e6 | 1.32647 | 0.663236 | − | 0.748410i | \(-0.269183\pi\) | ||||
0.663236 | + | 0.748410i | \(0.269183\pi\) | |||||||
\(150\) | 1.22225e6 | + | 1.22225e6i | 0.362149 | + | 0.362149i | ||||
\(151\) | 2.00914e6i | 0.583551i | 0.956487 | + | 0.291775i | \(0.0942459\pi\) | ||||
−0.956487 | + | 0.291775i | \(0.905754\pi\) | |||||||
\(152\) | − | 84945.6i | − | 0.0241886i | ||||||
\(153\) | 952850. | − | 952850.i | 0.266042 | − | 0.266042i | ||||
\(154\) | −2.45417e6 | + | 2.45417e6i | −0.671959 | + | 0.671959i | ||||
\(155\) | 8.05343e6 | 2.16265 | ||||||||
\(156\) | −186413. | + | 186413.i | −0.0491024 | + | 0.0491024i | ||||
\(157\) | −2.11078e6 | −0.545437 | −0.272719 | − | 0.962094i | \(-0.587923\pi\) | ||||
−0.272719 | + | 0.962094i | \(0.587923\pi\) | |||||||
\(158\) | −4.56580e6 | −1.15756 | ||||||||
\(159\) | 206844.i | 0.0514578i | ||||||||
\(160\) | 1.16347e6 | 0.284051 | ||||||||
\(161\) | 5.40281e6 | − | 5.40281e6i | 1.29462 | − | 1.29462i | ||||
\(162\) | 882271. | + | 882271.i | 0.207518 | + | 0.207518i | ||||
\(163\) | 3.52676e6 | + | 3.52676e6i | 0.814353 | + | 0.814353i | 0.985283 | − | 0.170930i | \(-0.0546773\pi\) |
−0.170930 | + | 0.985283i | \(0.554677\pi\) | |||||||
\(164\) | 2.26927e6 | 0.514464 | ||||||||
\(165\) | −3.29014e6 | + | 3.29014e6i | −0.732425 | + | 0.732425i | ||||
\(166\) | 2.86876e6 | + | 2.86876e6i | 0.627149 | + | 0.627149i | ||||
\(167\) | −3.93036e6 | + | 3.93036e6i | −0.843884 | + | 0.843884i | −0.989362 | − | 0.145477i | \(-0.953528\pi\) |
0.145477 | + | 0.989362i | \(0.453528\pi\) | |||||||
\(168\) | 518085. | + | 518085.i | 0.109263 | + | 0.109263i | ||||
\(169\) | 4.38270e6i | 0.907992i | ||||||||
\(170\) | −1.87900e6 | + | 1.87900e6i | −0.382454 | + | 0.382454i | ||||
\(171\) | −191185. | + | 191185.i | −0.0382355 | + | 0.0382355i | ||||
\(172\) | −915069. | − | 915069.i | −0.179833 | − | 0.179833i | ||||
\(173\) | − | 924554.i | − | 0.178564i | −0.996006 | − | 0.0892820i | \(-0.971543\pi\) | ||
0.996006 | − | 0.0892820i | \(-0.0284572\pi\) | |||||||
\(174\) | 459398. | 0.0872051 | ||||||||
\(175\) | 8.09278e6i | 1.51002i | ||||||||
\(176\) | 1.91889e6i | 0.351976i | ||||||||
\(177\) | −1.98038e6 | − | 1.98038e6i | −0.357132 | − | 0.357132i | ||||
\(178\) | − | 1.41378e6i | − | 0.250682i | ||||||
\(179\) | 1.10687e6 | + | 1.10687e6i | 0.192991 | + | 0.192991i | 0.796987 | − | 0.603996i | \(-0.206426\pi\) |
−0.603996 | + | 0.796987i | \(0.706426\pi\) | |||||||
\(180\) | −2.61861e6 | − | 2.61861e6i | −0.449007 | − | 0.449007i | ||||
\(181\) | 1.06572e7 | 1.79725 | 0.898624 | − | 0.438720i | \(-0.144568\pi\) | ||||
0.898624 | + | 0.438720i | \(0.144568\pi\) | |||||||
\(182\) | −1.23428e6 | −0.204738 | ||||||||
\(183\) | 1.52864e6 | − | 1.52864e6i | 0.249432 | − | 0.249432i | ||||
\(184\) | − | 4.22441e6i | − | 0.678129i | ||||||
\(185\) | −3.04680e6 | − | 9.70694e6i | −0.481204 | − | 1.53309i | ||||
\(186\) | 2.80396e6 | 0.435746 | ||||||||
\(187\) | −3.09900e6 | − | 3.09900e6i | −0.473911 | − | 0.473911i | ||||
\(188\) | − | 1.52578e6i | − | 0.229625i | ||||||
\(189\) | − | 5.28275e6i | − | 0.782483i | ||||||
\(190\) | 377014. | − | 377014.i | 0.0549663 | − | 0.0549663i | ||||
\(191\) | −6.84260e6 | + | 6.84260e6i | −0.982021 | + | 0.982021i | −0.999841 | − | 0.0178203i | \(-0.994327\pi\) |
0.0178203 | + | 0.999841i | \(0.494327\pi\) | |||||||
\(192\) | 405086. | 0.0572327 | ||||||||
\(193\) | −8.04844e6 | + | 8.04844e6i | −1.11954 | + | 1.11954i | −0.127732 | + | 0.991809i | \(0.540770\pi\) |
−0.991809 | + | 0.127732i | \(0.959230\pi\) | |||||||
\(194\) | 9.23508e6 | 1.26484 | ||||||||
\(195\) | −1.65471e6 | −0.223161 | ||||||||
\(196\) | − | 334424.i | − | 0.0444150i | ||||||
\(197\) | −9.33067e6 | −1.22043 | −0.610217 | − | 0.792234i | \(-0.708918\pi\) | ||||
−0.610217 | + | 0.792234i | \(0.708918\pi\) | |||||||
\(198\) | 4.31882e6 | − | 4.31882e6i | 0.556378 | − | 0.556378i | ||||
\(199\) | −9.03343e6 | − | 9.03343e6i | −1.14629 | − | 1.14629i | −0.987277 | − | 0.159010i | \(-0.949170\pi\) |
−0.159010 | − | 0.987277i | \(-0.550830\pi\) | |||||||
\(200\) | 3.16384e6 | + | 3.16384e6i | 0.395479 | + | 0.395479i | ||||
\(201\) | −164334. | −0.0202367 | ||||||||
\(202\) | 1.87654e6 | − | 1.87654e6i | 0.227668 | − | 0.227668i | ||||
\(203\) | 1.52088e6 | + | 1.52088e6i | 0.181806 | + | 0.181806i | ||||
\(204\) | −654211. | + | 654211.i | −0.0770597 | + | 0.0770597i | ||||
\(205\) | 1.00717e7 | + | 1.00717e7i | 1.16907 | + | 1.16907i | ||||
\(206\) | − | 7.71682e6i | − | 0.882748i | ||||||
\(207\) | −9.50780e6 | + | 9.50780e6i | −1.07194 | + | 1.07194i | ||||
\(208\) | −482535. | + | 482535.i | −0.0536215 | + | 0.0536215i | ||||
\(209\) | 621802. | + | 621802.i | 0.0681103 | + | 0.0681103i | ||||
\(210\) | 4.59883e6i | 0.496581i | ||||||||
\(211\) | −5.29331e6 | −0.563482 | −0.281741 | − | 0.959491i | \(-0.590912\pi\) | ||||
−0.281741 | + | 0.959491i | \(0.590912\pi\) | |||||||
\(212\) | 535421.i | 0.0561937i | ||||||||
\(213\) | 4.10732e6i | 0.425030i | ||||||||
\(214\) | −4.57487e6 | − | 4.57487e6i | −0.466807 | − | 0.466807i | ||||
\(215\) | − | 8.12269e6i | − | 0.817306i | ||||||
\(216\) | −2.06527e6 | − | 2.06527e6i | −0.204934 | − | 0.204934i | ||||
\(217\) | 9.28280e6 | + | 9.28280e6i | 0.908447 | + | 0.908447i | ||||
\(218\) | −1.08078e7 | −1.04320 | ||||||||
\(219\) | −8.11069e6 | −0.772192 | ||||||||
\(220\) | −8.51662e6 | + | 8.51662e6i | −0.799833 | + | 0.799833i | ||||
\(221\) | − | 1.55858e6i | − | 0.144395i | ||||||
\(222\) | −1.06081e6 | − | 3.37967e6i | −0.0969565 | − | 0.308898i | ||||
\(223\) | 1.62356e6 | 0.146404 | 0.0732022 | − | 0.997317i | \(-0.476678\pi\) | ||||
0.0732022 | + | 0.997317i | \(0.476678\pi\) | |||||||
\(224\) | 1.34108e6 | + | 1.34108e6i | 0.119319 | + | 0.119319i | ||||
\(225\) | − | 1.42416e7i | − | 1.25029i | ||||||
\(226\) | 1.72733e6i | 0.149641i | ||||||||
\(227\) | 1.09499e7 | − | 1.09499e7i | 0.936126 | − | 0.936126i | −0.0619531 | − | 0.998079i | \(-0.519733\pi\) |
0.998079 | + | 0.0619531i | \(0.0197329\pi\) | |||||||
\(228\) | 131265. | − | 131265.i | 0.0110750 | − | 0.0110750i | ||||
\(229\) | 1.86754e7 | 1.55512 | 0.777559 | − | 0.628810i | \(-0.216458\pi\) | ||||
0.777559 | + | 0.628810i | \(0.216458\pi\) | |||||||
\(230\) | 1.87492e7 | − | 1.87492e7i | 1.54099 | − | 1.54099i | ||||
\(231\) | −7.58477e6 | −0.615328 | ||||||||
\(232\) | 1.18916e6 | 0.0952309 | ||||||||
\(233\) | − | 1.10713e7i | − | 0.875247i | −0.899158 | − | 0.437624i | \(-0.855820\pi\) | ||
0.899158 | − | 0.437624i | \(-0.144180\pi\) | |||||||
\(234\) | 2.17207e6 | 0.169522 | ||||||||
\(235\) | 6.77187e6 | − | 6.77187e6i | 0.521801 | − | 0.521801i | ||||
\(236\) | −5.12627e6 | − | 5.12627e6i | −0.390001 | − | 0.390001i | ||||
\(237\) | −7.05544e6 | − | 7.05544e6i | −0.530004 | − | 0.530004i | ||||
\(238\) | −4.33166e6 | −0.321309 | ||||||||
\(239\) | 8.90181e6 | − | 8.90181e6i | 0.652055 | − | 0.652055i | −0.301432 | − | 0.953488i | \(-0.597465\pi\) |
0.953488 | + | 0.301432i | \(0.0974647\pi\) | |||||||
\(240\) | 1.79789e6 | + | 1.79789e6i | 0.130056 | + | 0.130056i | ||||
\(241\) | −6.87750e6 | + | 6.87750e6i | −0.491337 | + | 0.491337i | −0.908727 | − | 0.417390i | \(-0.862945\pi\) |
0.417390 | + | 0.908727i | \(0.362945\pi\) | |||||||
\(242\) | −6.96007e6 | − | 6.96007e6i | −0.491097 | − | 0.491097i | ||||
\(243\) | 1.44891e7i | 1.00977i | ||||||||
\(244\) | 3.95693e6 | − | 3.95693e6i | 0.272388 | − | 0.272388i | ||||
\(245\) | 1.48427e6 | − | 1.48427e6i | 0.100929 | − | 0.100929i | ||||
\(246\) | 3.50666e6 | + | 3.50666e6i | 0.235553 | + | 0.235553i | ||||
\(247\) | 312723.i | 0.0207524i | ||||||||
\(248\) | 7.25813e6 | 0.475850 | ||||||||
\(249\) | 8.86609e6i | 0.574294i | ||||||||
\(250\) | 1.03309e7i | 0.661177i | ||||||||
\(251\) | −1.69595e7 | − | 1.69595e7i | −1.07248 | − | 1.07248i | −0.997159 | − | 0.0753248i | \(-0.976001\pi\) |
−0.0753248 | − | 0.997159i | \(-0.523999\pi\) | |||||||
\(252\) | − | 6.03668e6i | − | 0.377221i | ||||||
\(253\) | 3.09227e7 | + | 3.09227e7i | 1.90948 | + | 1.90948i | ||||
\(254\) | −2.77551e6 | − | 2.77551e6i | −0.169372 | − | 0.169372i | ||||
\(255\) | −5.80716e6 | −0.350222 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | −1.19740e7 | + | 1.19740e7i | −0.705409 | + | 0.705409i | −0.965566 | − | 0.260157i | \(-0.916226\pi\) |
0.260157 | + | 0.965566i | \(0.416226\pi\) | |||||||
\(258\) | − | 2.82808e6i | − | 0.164677i | ||||||
\(259\) | 7.67681e6 | − | 1.47006e7i | 0.441857 | − | 0.846128i | ||||
\(260\) | −4.28327e6 | −0.243700 | ||||||||
\(261\) | −2.67643e6 | − | 2.67643e6i | −0.150534 | − | 0.150534i | ||||
\(262\) | − | 1.25368e7i | − | 0.697081i | ||||||
\(263\) | 534794.i | 0.0293981i | 0.999892 | + | 0.0146990i | \(0.00467902\pi\) | ||||
−0.999892 | + | 0.0146990i | \(0.995321\pi\) | |||||||
\(264\) | −2.96523e6 | + | 2.96523e6i | −0.161156 | + | 0.161156i | ||||
\(265\) | −2.37636e6 | + | 2.37636e6i | −0.127695 | + | 0.127695i | ||||
\(266\) | 869130. | 0.0461785 | ||||||||
\(267\) | 2.18469e6 | − | 2.18469e6i | 0.114777 | − | 0.114777i | ||||
\(268\) | −425383. | −0.0220992 | ||||||||
\(269\) | 1.01521e7 | 0.521553 | 0.260776 | − | 0.965399i | \(-0.416021\pi\) | ||||
0.260776 | + | 0.965399i | \(0.416021\pi\) | |||||||
\(270\) | − | 1.83325e7i | − | 0.931389i | ||||||
\(271\) | −3.64203e7 | −1.82994 | −0.914968 | − | 0.403526i | \(-0.867784\pi\) | ||||
−0.914968 | + | 0.403526i | \(0.867784\pi\) | |||||||
\(272\) | −1.69344e6 | + | 1.69344e6i | −0.0841518 | + | 0.0841518i | ||||
\(273\) | −1.90731e6 | − | 1.90731e6i | −0.0937416 | − | 0.0937416i | ||||
\(274\) | 1.11819e7 | + | 1.11819e7i | 0.543579 | + | 0.543579i | ||||
\(275\) | −4.63186e7 | −2.22719 | ||||||||
\(276\) | 6.52790e6 | − | 6.52790e6i | 0.310489 | − | 0.310489i | ||||
\(277\) | 2.52880e7 | + | 2.52880e7i | 1.18980 | + | 1.18980i | 0.977122 | + | 0.212682i | \(0.0682197\pi\) |
0.212682 | + | 0.977122i | \(0.431780\pi\) | |||||||
\(278\) | −8.13924e6 | + | 8.13924e6i | −0.378834 | + | 0.378834i | ||||
\(279\) | −1.63358e7 | − | 1.63358e7i | −0.752188 | − | 0.752188i | ||||
\(280\) | 1.19042e7i | 0.542283i | ||||||||
\(281\) | −1.00784e7 | + | 1.00784e7i | −0.454225 | + | 0.454225i | −0.896754 | − | 0.442529i | \(-0.854081\pi\) |
0.442529 | + | 0.896754i | \(0.354081\pi\) | |||||||
\(282\) | 2.35776e6 | − | 2.35776e6i | 0.105136 | − | 0.105136i | ||||
\(283\) | 8.22079e6 | + | 8.22079e6i | 0.362706 | + | 0.362706i | 0.864808 | − | 0.502102i | \(-0.167440\pi\) |
−0.502102 | + | 0.864808i | \(0.667440\pi\) | |||||||
\(284\) | 1.06319e7i | 0.464147i | ||||||||
\(285\) | 1.16518e6 | 0.0503338 | ||||||||
\(286\) | − | 7.06432e6i | − | 0.301976i | ||||||
\(287\) | 2.32183e7i | 0.982166i | ||||||||
\(288\) | −2.36001e6 | − | 2.36001e6i | −0.0987954 | − | 0.0987954i | ||||
\(289\) | 1.86678e7i | 0.773391i | ||||||||
\(290\) | 5.27786e6 | + | 5.27786e6i | 0.216403 | + | 0.216403i | ||||
\(291\) | 1.42708e7 | + | 1.42708e7i | 0.579121 | + | 0.579121i | ||||
\(292\) | −2.09947e7 | −0.843260 | ||||||||
\(293\) | −2.01103e7 | −0.799496 | −0.399748 | − | 0.916625i | \(-0.630902\pi\) | ||||
−0.399748 | + | 0.916625i | \(0.630902\pi\) | |||||||
\(294\) | 516780. | − | 516780.i | 0.0203359 | − | 0.0203359i | ||||
\(295\) | − | 4.55038e7i | − | 1.77248i | ||||||
\(296\) | −2.74592e6 | − | 8.74835e6i | −0.105880 | − | 0.337327i | ||||
\(297\) | 3.02355e7 | 1.15411 | ||||||||
\(298\) | 1.75516e7 | + | 1.75516e7i | 0.663236 | + | 0.663236i | ||||
\(299\) | 1.55520e7i | 0.581797i | ||||||||
\(300\) | 9.77803e6i | 0.362149i | ||||||||
\(301\) | 9.36263e6 | − | 9.36263e6i | 0.343319 | − | 0.343319i | ||||
\(302\) | −8.03654e6 | + | 8.03654e6i | −0.291775 | + | 0.291775i | ||||
\(303\) | 5.79955e6 | 0.208481 | ||||||||
\(304\) | 339782. | − | 339782.i | 0.0120943 | − | 0.0120943i | ||||
\(305\) | 3.51240e7 | 1.23795 | ||||||||
\(306\) | 7.62280e6 | 0.266042 | ||||||||
\(307\) | 8.98342e6i | 0.310475i | 0.987877 | + | 0.155238i | \(0.0496143\pi\) | ||||
−0.987877 | + | 0.155238i | \(0.950386\pi\) | |||||||
\(308\) | −1.96334e7 | −0.671959 | ||||||||
\(309\) | 1.19247e7 | − | 1.19247e7i | 0.404176 | − | 0.404176i | ||||
\(310\) | 3.22137e7 | + | 3.22137e7i | 1.08132 | + | 1.08132i | ||||
\(311\) | 1.58018e7 | + | 1.58018e7i | 0.525320 | + | 0.525320i | 0.919173 | − | 0.393853i | \(-0.128858\pi\) |
−0.393853 | + | 0.919173i | \(0.628858\pi\) | |||||||
\(312\) | −1.49131e6 | −0.0491024 | ||||||||
\(313\) | −1.28316e7 | + | 1.28316e7i | −0.418454 | + | 0.418454i | −0.884671 | − | 0.466217i | \(-0.845617\pi\) |
0.466217 | + | 0.884671i | \(0.345617\pi\) | |||||||
\(314\) | −8.44314e6 | − | 8.44314e6i | −0.272719 | − | 0.272719i | ||||
\(315\) | 2.67926e7 | − | 2.67926e7i | 0.857201 | − | 0.857201i | ||||
\(316\) | −1.82632e7 | − | 1.82632e7i | −0.578782 | − | 0.578782i | ||||
\(317\) | − | 5.99898e7i | − | 1.88321i | −0.336714 | − | 0.941607i | \(-0.609316\pi\) | ||
0.336714 | − | 0.941607i | \(-0.390684\pi\) | |||||||
\(318\) | −827376. | + | 827376.i | −0.0257289 | + | 0.0257289i | ||||
\(319\) | −8.70469e6 | + | 8.70469e6i | −0.268152 | + | 0.268152i | ||||
\(320\) | 4.65389e6 | + | 4.65389e6i | 0.142025 | + | 0.142025i | ||||
\(321\) | − | 1.41389e7i | − | 0.427466i | ||||||
\(322\) | 4.32225e7 | 1.29462 | ||||||||
\(323\) | 1.09749e6i | 0.0325682i | ||||||||
\(324\) | 7.05817e6i | 0.207518i | ||||||||
\(325\) | −1.16475e7 | − | 1.16475e7i | −0.339299 | − | 0.339299i | ||||
\(326\) | 2.82140e7i | 0.814353i | ||||||||
\(327\) | −1.67010e7 | − | 1.67010e7i | −0.477639 | − | 0.477639i | ||||
\(328\) | 9.07709e6 | + | 9.07709e6i | 0.257232 | + | 0.257232i | ||||
\(329\) | 1.56112e7 | 0.438378 | ||||||||
\(330\) | −2.63212e7 | −0.732425 | ||||||||
\(331\) | 3.01418e7 | − | 3.01418e7i | 0.831162 | − | 0.831162i | −0.156514 | − | 0.987676i | \(-0.550026\pi\) |
0.987676 | + | 0.156514i | \(0.0500257\pi\) | |||||||
\(332\) | 2.29501e7i | 0.627149i | ||||||||
\(333\) | −1.35096e7 | + | 2.58700e7i | −0.365855 | + | 0.700588i | ||||
\(334\) | −3.14429e7 | −0.843884 | ||||||||
\(335\) | −1.88798e6 | − | 1.88798e6i | −0.0502183 | − | 0.0502183i | ||||
\(336\) | 4.14468e6i | 0.109263i | ||||||||
\(337\) | 4.33177e7i | 1.13182i | 0.824468 | + | 0.565908i | \(0.191474\pi\) | ||||
−0.824468 | + | 0.565908i | \(0.808526\pi\) | |||||||
\(338\) | −1.75308e7 | + | 1.75308e7i | −0.453996 | + | 0.453996i | ||||
\(339\) | −2.66921e6 | + | 2.66921e6i | −0.0685146 | + | 0.0685146i | ||||
\(340\) | −1.50320e7 | −0.382454 | ||||||||
\(341\) | −5.31295e7 | + | 5.31295e7i | −1.33990 | + | 1.33990i | ||||
\(342\) | −1.52948e6 | −0.0382355 | ||||||||
\(343\) | 4.19413e7 | 1.03935 | ||||||||
\(344\) | − | 7.32055e6i | − | 0.179833i | ||||||
\(345\) | 5.79455e7 | 1.41112 | ||||||||
\(346\) | 3.69822e6 | − | 3.69822e6i | 0.0892820 | − | 0.0892820i | ||||
\(347\) | −2.05380e7 | − | 2.05380e7i | −0.491553 | − | 0.491553i | 0.417242 | − | 0.908795i | \(-0.362997\pi\) |
−0.908795 | + | 0.417242i | \(0.862997\pi\) | |||||||
\(348\) | 1.83759e6 | + | 1.83759e6i | 0.0436025 | + | 0.0436025i | ||||
\(349\) | 4.37394e7 | 1.02895 | 0.514477 | − | 0.857504i | \(-0.327986\pi\) | ||||
0.514477 | + | 0.857504i | \(0.327986\pi\) | |||||||
\(350\) | −3.23711e7 | + | 3.23711e7i | −0.755012 | + | 0.755012i | ||||
\(351\) | 7.60318e6 | + | 7.60318e6i | 0.175822 | + | 0.175822i | ||||
\(352\) | −7.67558e6 | + | 7.67558e6i | −0.175988 | + | 0.175988i | ||||
\(353\) | 1.13326e7 | + | 1.13326e7i | 0.257636 | + | 0.257636i | 0.824092 | − | 0.566456i | \(-0.191686\pi\) |
−0.566456 | + | 0.824092i | \(0.691686\pi\) | |||||||
\(354\) | − | 1.58431e7i | − | 0.357132i | ||||||
\(355\) | −4.71875e7 | + | 4.71875e7i | −1.05473 | + | 1.05473i | ||||
\(356\) | 5.65513e6 | − | 5.65513e6i | 0.125341 | − | 0.125341i | ||||
\(357\) | −6.69363e6 | − | 6.69363e6i | −0.147115 | − | 0.147115i | ||||
\(358\) | 8.85493e6i | 0.192991i | ||||||||
\(359\) | 8.54266e6 | 0.184633 | 0.0923166 | − | 0.995730i | \(-0.470573\pi\) | ||||
0.0923166 | + | 0.995730i | \(0.470573\pi\) | |||||||
\(360\) | − | 2.09489e7i | − | 0.449007i | ||||||
\(361\) | 4.68257e7i | 0.995319i | ||||||||
\(362\) | 4.26289e7 | + | 4.26289e7i | 0.898624 | + | 0.898624i | ||||
\(363\) | − | 2.15105e7i | − | 0.449709i | ||||||
\(364\) | −4.93711e6 | − | 4.93711e6i | −0.102369 | − | 0.102369i | ||||
\(365\) | −9.31807e7 | − | 9.31807e7i | −1.91623 | − | 1.91623i | ||||
\(366\) | 1.22291e7 | 0.249432 | ||||||||
\(367\) | 4.25372e7 | 0.860539 | 0.430270 | − | 0.902700i | \(-0.358419\pi\) | ||||
0.430270 | + | 0.902700i | \(0.358419\pi\) | |||||||
\(368\) | 1.68976e7 | − | 1.68976e7i | 0.339065 | − | 0.339065i | ||||
\(369\) | − | 4.08593e7i | − | 0.813227i | ||||||
\(370\) | 2.66406e7 | − | 5.10150e7i | 0.525942 | − | 1.00715i | ||||
\(371\) | −5.47822e6 | −0.107280 | ||||||||
\(372\) | 1.12159e7 | + | 1.12159e7i | 0.217873 | + | 0.217873i | ||||
\(373\) | − | 3.73534e7i | − | 0.719787i | −0.932993 | − | 0.359894i | \(-0.882813\pi\) | ||
0.932993 | − | 0.359894i | \(-0.117187\pi\) | |||||||
\(374\) | − | 2.47920e7i | − | 0.473911i | ||||||
\(375\) | −1.59641e7 | + | 1.59641e7i | −0.302727 | + | 0.302727i | ||||
\(376\) | 6.10313e6 | − | 6.10313e6i | 0.114812 | − | 0.114812i | ||||
\(377\) | −4.37785e6 | −0.0817028 | ||||||||
\(378\) | 2.11310e7 | − | 2.11310e7i | 0.391241 | − | 0.391241i | ||||
\(379\) | −4.44387e7 | −0.816288 | −0.408144 | − | 0.912918i | \(-0.633824\pi\) | ||||
−0.408144 | + | 0.912918i | \(0.633824\pi\) | |||||||
\(380\) | 3.01611e6 | 0.0549663 | ||||||||
\(381\) | − | 8.57790e6i | − | 0.155098i | ||||||
\(382\) | −5.47408e7 | −0.982021 | ||||||||
\(383\) | 5.52203e7 | − | 5.52203e7i | 0.982885 | − | 0.982885i | −0.0169713 | − | 0.999856i | \(-0.505402\pi\) |
0.999856 | + | 0.0169713i | \(0.00540239\pi\) | |||||||
\(384\) | 1.62035e6 | + | 1.62035e6i | 0.0286163 | + | 0.0286163i | ||||
\(385\) | −8.71387e7 | − | 8.71387e7i | −1.52696 | − | 1.52696i | ||||
\(386\) | −6.43875e7 | −1.11954 | ||||||||
\(387\) | −1.64762e7 | + | 1.64762e7i | −0.284266 | + | 0.284266i | ||||
\(388\) | 3.69403e7 | + | 3.69403e7i | 0.632420 | + | 0.632420i | ||||
\(389\) | 5.95371e7 | − | 5.95371e7i | 1.01144 | − | 1.01144i | 0.0115037 | − | 0.999934i | \(-0.496338\pi\) |
0.999934 | − | 0.0115037i | \(-0.00366183\pi\) | |||||||
\(390\) | −6.61885e6 | − | 6.61885e6i | −0.111581 | − | 0.111581i | ||||
\(391\) | 5.45791e7i | 0.913053i | ||||||||
\(392\) | 1.33770e6 | − | 1.33770e6i | 0.0222075 | − | 0.0222075i | ||||
\(393\) | 1.93729e7 | − | 1.93729e7i | 0.319166 | − | 0.319166i | ||||
\(394\) | −3.73227e7 | − | 3.73227e7i | −0.610217 | − | 0.610217i | ||||
\(395\) | − | 1.62115e8i | − | 2.63046i | ||||||
\(396\) | 3.45506e7 | 0.556378 | ||||||||
\(397\) | 7.15452e7i | 1.14343i | 0.820453 | + | 0.571714i | \(0.193721\pi\) | ||||
−0.820453 | + | 0.571714i | \(0.806279\pi\) | |||||||
\(398\) | − | 7.22674e7i | − | 1.14629i | ||||||
\(399\) | 1.34305e6 | + | 1.34305e6i | 0.0211433 | + | 0.0211433i | ||||
\(400\) | 2.53107e7i | 0.395479i | ||||||||
\(401\) | −4.66890e7 | − | 4.66890e7i | −0.724072 | − | 0.724072i | 0.245360 | − | 0.969432i | \(-0.421094\pi\) |
−0.969432 | + | 0.245360i | \(0.921094\pi\) | |||||||
\(402\) | −657337. | − | 657337.i | −0.0101184 | − | 0.0101184i | ||||
\(403\) | −2.67205e7 | −0.408252 | ||||||||
\(404\) | 1.50123e7 | 0.227668 | ||||||||
\(405\) | −3.13262e7 | + | 3.13262e7i | −0.471567 | + | 0.471567i | ||||
\(406\) | 1.21671e7i | 0.181806i | ||||||||
\(407\) | 8.41381e7 | + | 4.39378e7i | 1.24799 | + | 0.651711i | ||||
\(408\) | −5.23369e6 | −0.0770597 | ||||||||
\(409\) | −1.42406e7 | − | 1.42406e7i | −0.208142 | − | 0.208142i | 0.595336 | − | 0.803477i | \(-0.297019\pi\) |
−0.803477 | + | 0.595336i | \(0.797019\pi\) | |||||||
\(410\) | 8.05736e7i | 1.16907i | ||||||||
\(411\) | 3.45583e7i | 0.497768i | ||||||||
\(412\) | 3.08673e7 | − | 3.08673e7i | 0.441374 | − | 0.441374i | ||||
\(413\) | 5.24500e7 | − | 5.24500e7i | 0.744552 | − | 0.744552i | ||||
\(414\) | −7.60624e7 | −1.07194 | ||||||||
\(415\) | −1.01859e8 | + | 1.01859e8i | −1.42514 | + | 1.42514i | ||||
\(416\) | −3.86028e6 | −0.0536215 | ||||||||
\(417\) | −2.51548e7 | −0.346907 | ||||||||
\(418\) | 4.97441e6i | 0.0681103i | ||||||||
\(419\) | 4.45066e7 | 0.605037 | 0.302519 | − | 0.953144i | \(-0.402173\pi\) | ||||
0.302519 | + | 0.953144i | \(0.402173\pi\) | |||||||
\(420\) | −1.83953e7 | + | 1.83953e7i | −0.248290 | + | 0.248290i | ||||
\(421\) | 9.01397e7 | + | 9.01397e7i | 1.20801 | + | 1.20801i | 0.971671 | + | 0.236336i | \(0.0759466\pi\) |
0.236336 | + | 0.971671i | \(0.424053\pi\) | |||||||
\(422\) | −2.11732e7 | − | 2.11732e7i | −0.281741 | − | 0.281741i | ||||
\(423\) | −2.74724e7 | −0.362974 | ||||||||
\(424\) | −2.14168e6 | + | 2.14168e6i | −0.0280969 | + | 0.0280969i | ||||
\(425\) | −4.08765e7 | − | 4.08765e7i | −0.532485 | − | 0.532485i | ||||
\(426\) | −1.64293e7 | + | 1.64293e7i | −0.212515 | + | 0.212515i | ||||
\(427\) | 4.04857e7 | + | 4.04857e7i | 0.520018 | + | 0.520018i | ||||
\(428\) | − | 3.65990e7i | − | 0.466807i | ||||||
\(429\) | 1.09164e7 | − | 1.09164e7i | 0.138263 | − | 0.138263i | ||||
\(430\) | 3.24908e7 | − | 3.24908e7i | 0.408653 | − | 0.408653i | ||||
\(431\) | 5.00465e6 | + | 5.00465e6i | 0.0625089 | + | 0.0625089i | 0.737670 | − | 0.675161i | \(-0.235926\pi\) |
−0.675161 | + | 0.737670i | \(0.735926\pi\) | |||||||
\(432\) | − | 1.65221e7i | − | 0.204934i | ||||||
\(433\) | −7.38688e7 | −0.909908 | −0.454954 | − | 0.890515i | \(-0.650344\pi\) | ||||
−0.454954 | + | 0.890515i | \(0.650344\pi\) | |||||||
\(434\) | 7.42624e7i | 0.908447i | ||||||||
\(435\) | 1.63116e7i | 0.198165i | ||||||||
\(436\) | −4.32310e7 | − | 4.32310e7i | −0.521598 | − | 0.521598i | ||||
\(437\) | − | 1.09511e7i | − | 0.131224i | ||||||
\(438\) | −3.24427e7 | − | 3.24427e7i | −0.386096 | − | 0.386096i | ||||
\(439\) | 4.68662e6 | + | 4.68662e6i | 0.0553944 | + | 0.0553944i | 0.734261 | − | 0.678867i | \(-0.237529\pi\) |
−0.678867 | + | 0.734261i | \(0.737529\pi\) | |||||||
\(440\) | −6.81330e7 | −0.799833 | ||||||||
\(441\) | −6.02146e6 | −0.0702079 | ||||||||
\(442\) | 6.23432e6 | − | 6.23432e6i | 0.0721975 | − | 0.0721975i | ||||
\(443\) | 1.06999e8i | 1.23075i | 0.788235 | + | 0.615374i | \(0.210995\pi\) | ||||
−0.788235 | + | 0.615374i | \(0.789005\pi\) | |||||||
\(444\) | 9.27544e6 | − | 1.77619e7i | 0.105971 | − | 0.202927i | ||||
\(445\) | 5.01983e7 | 0.569651 | ||||||||
\(446\) | 6.49424e6 | + | 6.49424e6i | 0.0732022 | + | 0.0732022i | ||||
\(447\) | 5.42444e7i | 0.607340i | ||||||||
\(448\) | 1.07286e7i | 0.119319i | ||||||||
\(449\) | 4.37631e7 | − | 4.37631e7i | 0.483469 | − | 0.483469i | −0.422769 | − | 0.906238i | \(-0.638942\pi\) |
0.906238 | + | 0.422769i | \(0.138942\pi\) | |||||||
\(450\) | 5.69663e7 | − | 5.69663e7i | 0.625145 | − | 0.625145i | ||||
\(451\) | −1.32889e8 | −1.44863 | ||||||||
\(452\) | −6.90931e6 | + | 6.90931e6i | −0.0748203 | + | 0.0748203i | ||||
\(453\) | −2.48374e7 | −0.267185 | ||||||||
\(454\) | 8.75995e7 | 0.936126 | ||||||||
\(455\) | − | 4.38247e7i | − | 0.465248i | ||||||
\(456\) | 1.05012e6 | 0.0110750 | ||||||||
\(457\) | −7.65822e7 | + | 7.65822e7i | −0.802378 | + | 0.802378i | −0.983467 | − | 0.181088i | \(-0.942038\pi\) |
0.181088 | + | 0.983467i | \(0.442038\pi\) | |||||||
\(458\) | 7.47016e7 | + | 7.47016e7i | 0.777559 | + | 0.777559i | ||||
\(459\) | 2.66831e7 | + | 2.66831e7i | 0.275930 | + | 0.275930i | ||||
\(460\) | 1.49993e8 | 1.54099 | ||||||||
\(461\) | 6.56687e7 | − | 6.56687e7i | 0.670279 | − | 0.670279i | −0.287501 | − | 0.957780i | \(-0.592825\pi\) |
0.957780 | + | 0.287501i | \(0.0928245\pi\) | |||||||
\(462\) | −3.03391e7 | − | 3.03391e7i | −0.307664 | − | 0.307664i | ||||
\(463\) | 7.49580e7 | − | 7.49580e7i | 0.755222 | − | 0.755222i | −0.220226 | − | 0.975449i | \(-0.570680\pi\) |
0.975449 | + | 0.220226i | \(0.0706796\pi\) | |||||||
\(464\) | 4.75666e6 | + | 4.75666e6i | 0.0476154 | + | 0.0476154i | ||||
\(465\) | 9.95586e7i | 0.990193i | ||||||||
\(466\) | 4.42852e7 | − | 4.42852e7i | 0.437624 | − | 0.437624i | ||||
\(467\) | 4.15210e7 | − | 4.15210e7i | 0.407678 | − | 0.407678i | −0.473250 | − | 0.880928i | \(-0.656919\pi\) |
0.880928 | + | 0.473250i | \(0.156919\pi\) | |||||||
\(468\) | 8.68827e6 | + | 8.68827e6i | 0.0847609 | + | 0.0847609i | ||||
\(469\) | − | 4.35236e6i | − | 0.0421896i | ||||||
\(470\) | 5.41750e7 | 0.521801 | ||||||||
\(471\) | − | 2.60941e7i | − | 0.249735i | ||||||
\(472\) | − | 4.10101e7i | − | 0.390001i | ||||||
\(473\) | 5.35865e7 | + | 5.35865e7i | 0.506374 | + | 0.506374i | ||||
\(474\) | − | 5.64435e7i | − | 0.530004i | ||||||
\(475\) | 8.20171e6 | + | 8.20171e6i | 0.0765286 | + | 0.0765286i | ||||
\(476\) | −1.73266e7 | − | 1.73266e7i | −0.160655 | − | 0.160655i | ||||
\(477\) | 9.64050e6 | 0.0888269 | ||||||||
\(478\) | 7.12145e7 | 0.652055 | ||||||||
\(479\) | −4.03691e7 | + | 4.03691e7i | −0.367318 | + | 0.367318i | −0.866498 | − | 0.499180i | \(-0.833635\pi\) |
0.499180 | + | 0.866498i | \(0.333635\pi\) | |||||||
\(480\) | 1.43831e7i | 0.130056i | ||||||||
\(481\) | 1.01090e7 | + | 3.22066e7i | 0.0908389 | + | 0.289408i | ||||
\(482\) | −5.50200e7 | −0.491337 | ||||||||
\(483\) | 6.67909e7 | + | 6.67909e7i | 0.592756 | + | 0.592756i | ||||
\(484\) | − | 5.56806e7i | − | 0.491097i | ||||||
\(485\) | 3.27904e8i | 2.87423i | ||||||||
\(486\) | −5.79562e7 | + | 5.79562e7i | −0.504884 | + | 0.504884i | ||||
\(487\) | −7.17600e7 | + | 7.17600e7i | −0.621292 | + | 0.621292i | −0.945862 | − | 0.324570i | \(-0.894780\pi\) |
0.324570 | + | 0.945862i | \(0.394780\pi\) | |||||||
\(488\) | 3.16554e7 | 0.272388 | ||||||||
\(489\) | −4.35986e7 | + | 4.35986e7i | −0.372861 | + | 0.372861i | ||||
\(490\) | 1.18742e7 | 0.100929 | ||||||||
\(491\) | 4.14336e7 | 0.350032 | 0.175016 | − | 0.984566i | \(-0.444002\pi\) | ||||
0.175016 | + | 0.984566i | \(0.444002\pi\) | |||||||
\(492\) | 2.80533e7i | 0.235553i | ||||||||
\(493\) | −1.53639e7 | −0.128222 | ||||||||
\(494\) | −1.25089e6 | + | 1.25089e6i | −0.0103762 | + | 0.0103762i | ||||
\(495\) | 1.53346e8 | + | 1.53346e8i | 1.26432 | + | 1.26432i | ||||
\(496\) | 2.90325e7 | + | 2.90325e7i | 0.237925 | + | 0.237925i | ||||
\(497\) | −1.08781e8 | −0.886105 | ||||||||
\(498\) | −3.54644e7 | + | 3.54644e7i | −0.287147 | + | 0.287147i | ||||
\(499\) | −1.30951e8 | − | 1.30951e8i | −1.05392 | − | 1.05392i | −0.998461 | − | 0.0554603i | \(-0.982337\pi\) |
−0.0554603 | − | 0.998461i | \(-0.517663\pi\) | |||||||
\(500\) | −4.13236e7 | + | 4.13236e7i | −0.330589 | + | 0.330589i | ||||
\(501\) | −4.85881e7 | − | 4.85881e7i | −0.386382 | − | 0.386382i | ||||
\(502\) | − | 1.35676e8i | − | 1.07248i | ||||||
\(503\) | 2.07372e6 | − | 2.07372e6i | 0.0162947 | − | 0.0162947i | −0.698913 | − | 0.715207i | \(-0.746332\pi\) |
0.715207 | + | 0.698913i | \(0.246332\pi\) | |||||||
\(504\) | 2.41467e7 | − | 2.41467e7i | 0.188611 | − | 0.188611i | ||||
\(505\) | 6.66290e7 | + | 6.66290e7i | 0.517355 | + | 0.517355i | ||||
\(506\) | 2.47381e8i | 1.90948i | ||||||||
\(507\) | −5.41801e7 | −0.415734 | ||||||||
\(508\) | − | 2.22041e7i | − | 0.169372i | ||||||
\(509\) | 1.23587e8i | 0.937175i | 0.883417 | + | 0.468588i | \(0.155237\pi\) | ||||
−0.883417 | + | 0.468588i | \(0.844763\pi\) | |||||||
\(510\) | −2.32287e7 | − | 2.32287e7i | −0.175111 | − | 0.175111i | ||||
\(511\) | − | 2.14810e8i | − | 1.60987i | ||||||
\(512\) | 4.19430e6 | + | 4.19430e6i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −5.35386e6 | − | 5.35386e6i | −0.0396565 | − | 0.0396565i | ||||
\(514\) | −9.57923e7 | −0.705409 | ||||||||
\(515\) | 2.73996e8 | 2.00596 | ||||||||
\(516\) | 1.13123e7 | − | 1.13123e7i | 0.0823384 | − | 0.0823384i | ||||
\(517\) | 8.93498e7i | 0.646580i | ||||||||
\(518\) | 8.95097e7 | − | 2.80952e7i | 0.643992 | − | 0.202136i | ||||
\(519\) | 1.14296e7 | 0.0817576 | ||||||||
\(520\) | −1.71331e7 | − | 1.71331e7i | −0.121850 | − | 0.121850i | ||||
\(521\) | 1.40526e8i | 0.993673i | 0.867844 | + | 0.496836i | \(0.165505\pi\) | ||||
−0.867844 | + | 0.496836i | \(0.834495\pi\) | |||||||
\(522\) | − | 2.14114e7i | − | 0.150534i | ||||||
\(523\) | −1.82286e6 | + | 1.82286e6i | −0.0127423 | + | 0.0127423i | −0.713449 | − | 0.700707i | \(-0.752868\pi\) |
0.700707 | + | 0.713449i | \(0.252868\pi\) | |||||||
\(524\) | 5.01472e7 | − | 5.01472e7i | 0.348540 | − | 0.348540i | ||||
\(525\) | −1.00045e8 | −0.691381 | ||||||||
\(526\) | −2.13918e6 | + | 2.13918e6i | −0.0146990 | + | 0.0146990i | ||||
\(527\) | −9.37746e7 | −0.640698 | ||||||||
\(528\) | −2.37219e7 | −0.161156 | ||||||||
\(529\) | − | 3.96570e8i | − | 2.67887i | ||||||
\(530\) | −1.90109e7 | −0.127695 | ||||||||
\(531\) | −9.23008e7 | + | 9.23008e7i | −0.616484 | + | 0.616484i | ||||
\(532\) | 3.47652e6 | + | 3.47652e6i | 0.0230892 | + | 0.0230892i | ||||
\(533\) | −3.34169e7 | − | 3.34169e7i | −0.220691 | − | 0.220691i | ||||
\(534\) | 1.74775e7 | 0.114777 | ||||||||
\(535\) | 1.62437e8 | − | 1.62437e8i | 1.06078 | − | 1.06078i | ||||
\(536\) | −1.70153e6 | − | 1.70153e6i | −0.0110496 | − | 0.0110496i | ||||
\(537\) | −1.36834e7 | + | 1.36834e7i | −0.0883629 | + | 0.0883629i | ||||
\(538\) | 4.06083e7 | + | 4.06083e7i | 0.260776 | + | 0.260776i | ||||
\(539\) | 1.95839e7i | 0.125064i | ||||||||
\(540\) | 7.33301e7 | − | 7.33301e7i | 0.465695 | − | 0.465695i | ||||
\(541\) | −1.79190e8 | + | 1.79190e8i | −1.13168 | + | 1.13168i | −0.141780 | + | 0.989898i | \(0.545283\pi\) |
−0.989898 | + | 0.141780i | \(0.954717\pi\) | |||||||
\(542\) | −1.45681e8 | − | 1.45681e8i | −0.914968 | − | 0.914968i | ||||
\(543\) | 1.31747e8i | 0.822890i | ||||||||
\(544\) | −1.35475e7 | −0.0841518 | ||||||||
\(545\) | − | 3.83744e8i | − | 2.37057i | ||||||
\(546\) | − | 1.52585e7i | − | 0.0937416i | ||||||
\(547\) | −1.12148e8 | − | 1.12148e8i | −0.685216 | − | 0.685216i | 0.275954 | − | 0.961171i | \(-0.411006\pi\) |
−0.961171 | + | 0.275954i | \(0.911006\pi\) | |||||||
\(548\) | 8.94550e7i | 0.543579i | ||||||||
\(549\) | −7.12463e7 | − | 7.12463e7i | −0.430571 | − | 0.430571i | ||||
\(550\) | −1.85274e8 | − | 1.85274e8i | −1.11359 | − | 1.11359i | ||||
\(551\) | 3.08271e6 | 0.0184280 | ||||||||
\(552\) | 5.22232e7 | 0.310489 | ||||||||
\(553\) | 1.86862e8 | − | 1.86862e8i | 1.10496 | − | 1.10496i | ||||
\(554\) | 2.02304e8i | 1.18980i | ||||||||
\(555\) | 1.20000e8 | − | 3.76653e7i | 0.701942 | − | 0.220325i | ||||
\(556\) | −6.51139e7 | −0.378834 | ||||||||
\(557\) | −4.61077e7 | − | 4.61077e7i | −0.266814 | − | 0.266814i | 0.561001 | − | 0.827815i | \(-0.310416\pi\) |
−0.827815 | + | 0.561001i | \(0.810416\pi\) | |||||||
\(558\) | − | 1.30686e8i | − | 0.752188i | ||||||
\(559\) | 2.69503e7i | 0.154286i | ||||||||
\(560\) | −4.76168e7 | + | 4.76168e7i | −0.271141 | + | 0.271141i | ||||
\(561\) | 3.83106e7 | − | 3.83106e7i | 0.216985 | − | 0.216985i | ||||
\(562\) | −8.06269e7 | −0.454225 | ||||||||
\(563\) | −8.28031e6 | + | 8.28031e6i | −0.0464003 | + | 0.0464003i | −0.729926 | − | 0.683526i | \(-0.760446\pi\) |
0.683526 | + | 0.729926i | \(0.260446\pi\) | |||||||
\(564\) | 1.88621e7 | 0.105136 | ||||||||
\(565\) | −6.13311e7 | −0.340044 | ||||||||
\(566\) | 6.57663e7i | 0.362706i | ||||||||
\(567\) | −7.22164e7 | −0.396174 | ||||||||
\(568\) | −4.25276e7 | + | 4.25276e7i | −0.232074 | + | 0.232074i | ||||
\(569\) | −4.71454e7 | − | 4.71454e7i | −0.255919 | − | 0.255919i | 0.567473 | − | 0.823392i | \(-0.307921\pi\) |
−0.823392 | + | 0.567473i | \(0.807921\pi\) | |||||||
\(570\) | 4.66074e6 | + | 4.66074e6i | 0.0251669 | + | 0.0251669i | ||||
\(571\) | 2.39611e8 | 1.28706 | 0.643529 | − | 0.765422i | \(-0.277470\pi\) | ||||
0.643529 | + | 0.765422i | \(0.277470\pi\) | |||||||
\(572\) | 2.82573e7 | − | 2.82573e7i | 0.150988 | − | 0.150988i | ||||
\(573\) | −8.45899e7 | − | 8.45899e7i | −0.449629 | − | 0.449629i | ||||
\(574\) | −9.28732e7 | + | 9.28732e7i | −0.491083 | + | 0.491083i | ||||
\(575\) | 4.07878e8 | + | 4.07878e8i | 2.14549 | + | 2.14549i | ||||
\(576\) | − | 1.88801e7i | − | 0.0987954i | ||||||
\(577\) | 8.40950e6 | − | 8.40950e6i | 0.0437767 | − | 0.0437767i | −0.684880 | − | 0.728656i | \(-0.740145\pi\) |
0.728656 | + | 0.684880i | \(0.240145\pi\) | |||||||
\(578\) | −7.46711e7 | + | 7.46711e7i | −0.386696 | + | 0.386696i | ||||
\(579\) | −9.94969e7 | − | 9.94969e7i | −0.512594 | − | 0.512594i | ||||
\(580\) | 4.22229e7i | 0.216403i | ||||||||
\(581\) | −2.34816e8 | −1.19729 | ||||||||
\(582\) | 1.14166e8i | 0.579121i | ||||||||
\(583\) | − | 3.13543e7i | − | 0.158231i | ||||||
\(584\) | −8.39789e7 | − | 8.39789e7i | −0.421630 | − | 0.421630i | ||||
\(585\) | 7.71222e7i | 0.385223i | ||||||||
\(586\) | −8.04414e7 | − | 8.04414e7i | −0.399748 | − | 0.399748i | ||||
\(587\) | 3.25252e7 | + | 3.25252e7i | 0.160807 | + | 0.160807i | 0.782924 | − | 0.622117i | \(-0.213727\pi\) |
−0.622117 | + | 0.782924i | \(0.713727\pi\) | |||||||
\(588\) | 4.13424e6 | 0.0203359 | ||||||||
\(589\) | 1.88155e7 | 0.0920809 | ||||||||
\(590\) | 1.82015e8 | − | 1.82015e8i | 0.886240 | − | 0.886240i | ||||
\(591\) | − | 1.15348e8i | − | 0.558789i | ||||||
\(592\) | 2.40097e7 | − | 4.59771e7i | 0.115724 | − | 0.221603i | ||||
\(593\) | −4.91588e7 | −0.235742 | −0.117871 | − | 0.993029i | \(-0.537607\pi\) | ||||
−0.117871 | + | 0.993029i | \(0.537607\pi\) | |||||||
\(594\) | 1.20942e8 | + | 1.20942e8i | 0.577056 | + | 0.577056i | ||||
\(595\) | − | 1.53801e8i | − | 0.730145i | ||||||
\(596\) | 1.40413e8i | 0.663236i | ||||||||
\(597\) | 1.11674e8 | − | 1.11674e8i | 0.524840 | − | 0.524840i | ||||
\(598\) | −6.22078e7 | + | 6.22078e7i | −0.290898 | + | 0.290898i | ||||
\(599\) | 9.79457e6 | 0.0455727 | 0.0227864 | − | 0.999740i | \(-0.492746\pi\) | ||||
0.0227864 | + | 0.999740i | \(0.492746\pi\) | |||||||
\(600\) | −3.91121e7 | + | 3.91121e7i | −0.181075 | + | 0.181075i | ||||
\(601\) | −3.08738e8 | −1.42222 | −0.711111 | − | 0.703080i | \(-0.751808\pi\) | ||||
−0.711111 | + | 0.703080i | \(0.751808\pi\) | |||||||
\(602\) | 7.49010e7 | 0.343319 | ||||||||
\(603\) | 7.65922e6i | 0.0349328i | ||||||||
\(604\) | −6.42924e7 | −0.291775 | ||||||||
\(605\) | 2.47127e8 | − | 2.47127e8i | 1.11597 | − | 1.11597i | ||||
\(606\) | 2.31982e7 | + | 2.31982e7i | 0.104241 | + | 0.104241i | ||||
\(607\) | −5.43133e7 | − | 5.43133e7i | −0.242851 | − | 0.242851i | 0.575178 | − | 0.818029i | \(-0.304933\pi\) |
−0.818029 | + | 0.575178i | \(0.804933\pi\) | |||||||
\(608\) | 2.71826e6 | 0.0120943 | ||||||||
\(609\) | −1.88015e7 | + | 1.88015e7i | −0.0832418 | + | 0.0832418i | ||||
\(610\) | 1.40496e8 | + | 1.40496e8i | 0.618977 | + | 0.618977i | ||||
\(611\) | −2.24684e7 | + | 2.24684e7i | −0.0985027 | + | 0.0985027i | ||||
\(612\) | 3.04912e7 | + | 3.04912e7i | 0.133021 | + | 0.133021i | ||||
\(613\) | − | 3.61934e8i | − | 1.57126i | −0.618697 | − | 0.785630i | \(-0.712339\pi\) | ||
0.618697 | − | 0.785630i | \(-0.287661\pi\) | |||||||
\(614\) | −3.59337e7 | + | 3.59337e7i | −0.155238 | + | 0.155238i | ||||
\(615\) | −1.24509e8 | + | 1.24509e8i | −0.535273 | + | 0.535273i | ||||
\(616\) | −7.85335e7 | − | 7.85335e7i | −0.335980 | − | 0.335980i | ||||
\(617\) | − | 3.23628e7i | − | 0.137781i | −0.997624 | − | 0.0688907i | \(-0.978054\pi\) | ||
0.997624 | − | 0.0688907i | \(-0.0219460\pi\) | |||||||
\(618\) | 9.53973e7 | 0.404176 | ||||||||
\(619\) | − | 2.42596e7i | − | 0.102285i | −0.998691 | − | 0.0511425i | \(-0.983714\pi\) | ||
0.998691 | − | 0.0511425i | \(-0.0162863\pi\) | |||||||
\(620\) | 2.57710e8i | 1.08132i | ||||||||
\(621\) | −2.66252e8 | − | 2.66252e8i | −1.11178 | − | 1.11178i | ||||
\(622\) | 1.26414e8i | 0.525320i | ||||||||
\(623\) | 5.78611e7 | + | 5.78611e7i | 0.239289 | + | 0.239289i | ||||
\(624\) | −5.96522e6 | − | 5.96522e6i | −0.0245512 | − | 0.0245512i | ||||
\(625\) | 1.93979e7 | 0.0794538 | ||||||||
\(626\) | −1.02653e8 | −0.418454 | ||||||||
\(627\) | −7.68687e6 | + | 7.68687e6i | −0.0311851 | + | 0.0311851i | ||||
\(628\) | − | 6.75451e7i | − | 0.272719i | ||||||
\(629\) | 3.54771e7 | + | 1.13028e8i | 0.142560 | + | 0.454187i | ||||
\(630\) | 2.14340e8 | 0.857201 | ||||||||
\(631\) | 9.57666e7 | + | 9.57666e7i | 0.381177 | + | 0.381177i | 0.871526 | − | 0.490349i | \(-0.163131\pi\) |
−0.490349 | + | 0.871526i | \(0.663131\pi\) | |||||||
\(632\) | − | 1.46105e8i | − | 0.578782i | ||||||
\(633\) | − | 6.54372e7i | − | 0.257996i | ||||||
\(634\) | 2.39959e8 | − | 2.39959e8i | 0.941607 | − | 0.941607i | ||||
\(635\) | 9.85484e7 | − | 9.85484e7i | 0.384883 | − | 0.384883i | ||||
\(636\) | −6.61901e6 | −0.0257289 | ||||||||
\(637\) | −4.92467e6 | + | 4.92467e6i | −0.0190528 | + | 0.0190528i | ||||
\(638\) | −6.96375e7 | −0.268152 | ||||||||
\(639\) | 1.91432e8 | 0.733689 | ||||||||
\(640\) | 3.72311e7i | 0.142025i | ||||||||
\(641\) | −2.72419e8 | −1.03434 | −0.517169 | − | 0.855883i | \(-0.673014\pi\) | ||||
−0.517169 | + | 0.855883i | \(0.673014\pi\) | |||||||
\(642\) | 5.65557e7 | − | 5.65557e7i | 0.213733 | − | 0.213733i | ||||
\(643\) | 6.05275e7 | + | 6.05275e7i | 0.227677 | + | 0.227677i | 0.811722 | − | 0.584044i | \(-0.198531\pi\) |
−0.584044 | + | 0.811722i | \(0.698531\pi\) | |||||||
\(644\) | 1.72890e8 | + | 1.72890e8i | 0.647310 | + | 0.647310i | ||||
\(645\) | 1.00415e8 | 0.374213 | ||||||||
\(646\) | −4.38996e6 | + | 4.38996e6i | −0.0162841 | + | 0.0162841i | ||||
\(647\) | −2.01584e8 | − | 2.01584e8i | −0.744291 | − | 0.744291i | 0.229109 | − | 0.973401i | \(-0.426419\pi\) |
−0.973401 | + | 0.229109i | \(0.926419\pi\) | |||||||
\(648\) | −2.82327e7 | + | 2.82327e7i | −0.103759 | + | 0.103759i | ||||
\(649\) | 3.00194e8 | + | 3.00194e8i | 1.09817 | + | 1.09817i | ||||
\(650\) | − | 9.31801e7i | − | 0.339299i | ||||||
\(651\) | −1.14756e8 | + | 1.14756e8i | −0.415943 | + | 0.415943i | ||||
\(652\) | −1.12856e8 | + | 1.12856e8i | −0.407176 | + | 0.407176i | ||||
\(653\) | 1.22917e7 | + | 1.22917e7i | 0.0441439 | + | 0.0441439i | 0.728834 | − | 0.684690i | \(-0.240063\pi\) |
−0.684690 | + | 0.728834i | \(0.740063\pi\) | |||||||
\(654\) | − | 1.33608e8i | − | 0.477639i | ||||||
\(655\) | 4.45137e8 | 1.58405 | ||||||||
\(656\) | 7.26167e7i | 0.257232i | ||||||||
\(657\) | 3.78019e8i | 1.33296i | ||||||||
\(658\) | 6.24448e7 | + | 6.24448e7i | 0.219189 | + | 0.219189i | ||||
\(659\) | − | 1.12317e8i | − | 0.392456i | −0.980558 | − | 0.196228i | \(-0.937131\pi\) | ||
0.980558 | − | 0.196228i | \(-0.0628693\pi\) | |||||||
\(660\) | −1.05285e8 | − | 1.05285e8i | −0.366213 | − | 0.366213i | ||||
\(661\) | −9.92510e6 | − | 9.92510e6i | −0.0343661 | − | 0.0343661i | 0.689715 | − | 0.724081i | \(-0.257736\pi\) |
−0.724081 | + | 0.689715i | \(0.757736\pi\) | |||||||
\(662\) | 2.41135e8 | 0.831162 | ||||||||
\(663\) | 1.92676e7 | 0.0661129 | ||||||||
\(664\) | −9.18004e7 | + | 9.18004e7i | −0.313574 | + | 0.313574i | ||||
\(665\) | 3.08596e7i | 0.104936i | ||||||||
\(666\) | −1.57518e8 | + | 4.94416e7i | −0.533222 | + | 0.167367i | ||||
\(667\) | 1.53306e8 | 0.516631 | ||||||||
\(668\) | −1.25772e8 | − | 1.25772e8i | −0.421942 | − | 0.421942i | ||||
\(669\) | 2.00709e7i | 0.0670329i | ||||||||
\(670\) | − | 1.51038e7i | − | 0.0502183i | ||||||
\(671\) | −2.31718e8 | + | 2.31718e8i | −0.766993 | + | 0.766993i | ||||
\(672\) | −1.65787e7 | + | 1.65787e7i | −0.0546316 | + | 0.0546316i | ||||
\(673\) | −1.62562e8 | −0.533301 | −0.266651 | − | 0.963793i | \(-0.585917\pi\) | ||||
−0.266651 | + | 0.963793i | \(0.585917\pi\) | |||||||
\(674\) | −1.73271e8 | + | 1.73271e8i | −0.565908 | + | 0.565908i | ||||
\(675\) | 3.98814e8 | 1.29676 | ||||||||
\(676\) | −1.40246e8 | −0.453996 | ||||||||
\(677\) | − | 3.93482e8i | − | 1.26811i | −0.773286 | − | 0.634057i | \(-0.781388\pi\) | ||
0.773286 | − | 0.634057i | \(-0.218612\pi\) | |||||||
\(678\) | −2.13537e7 | −0.0685146 | ||||||||
\(679\) | −3.77959e8 | + | 3.77959e8i | −1.20736 | + | 1.20736i | ||||
\(680\) | −6.01280e7 | − | 6.01280e7i | −0.191227 | − | 0.191227i | ||||
\(681\) | 1.35366e8 | + | 1.35366e8i | 0.428616 | + | 0.428616i | ||||
\(682\) | −4.25036e8 | −1.33990 | ||||||||
\(683\) | 3.93184e8 | − | 3.93184e8i | 1.23405 | − | 1.23405i | 0.271660 | − | 0.962393i | \(-0.412427\pi\) |
0.962393 | − | 0.271660i | \(-0.0875726\pi\) | |||||||
\(684\) | −6.11794e6 | − | 6.11794e6i | −0.0191177 | − | 0.0191177i | ||||
\(685\) | −3.97028e8 | + | 3.97028e8i | −1.23523 | + | 1.23523i | ||||
\(686\) | 1.67765e8 | + | 1.67765e8i | 0.519673 | + | 0.519673i | ||||
\(687\) | 2.30870e8i | 0.712028i | ||||||||
\(688\) | 2.92822e7 | − | 2.92822e7i | 0.0899163 | − | 0.0899163i | ||||
\(689\) | 7.88450e6 | − | 7.88450e6i | 0.0241055 | − | 0.0241055i | ||||
\(690\) | 2.31782e8 | + | 2.31782e8i | 0.705558 | + | 0.705558i | ||||
\(691\) | − | 2.50617e8i | − | 0.759585i | −0.925072 | − | 0.379792i | \(-0.875995\pi\) | ||
0.925072 | − | 0.379792i | \(-0.124005\pi\) | |||||||
\(692\) | 2.95857e7 | 0.0892820 | ||||||||
\(693\) | 3.53508e8i | 1.06218i | ||||||||
\(694\) | − | 1.64304e8i | − | 0.491553i | ||||||
\(695\) | −2.88995e8 | − | 2.88995e8i | −0.860866 | − | 0.860866i | ||||
\(696\) | 1.47007e7i | 0.0436025i | ||||||||
\(697\) | −1.17275e8 | − | 1.17275e8i | −0.346345 | − | 0.346345i | ||||
\(698\) | 1.74957e8 | + | 1.74957e8i | 0.514477 | + | 0.514477i | ||||
\(699\) | 1.36866e8 | 0.400742 | ||||||||
\(700\) | −2.58969e8 | −0.755012 | ||||||||
\(701\) | −1.54838e8 | + | 1.54838e8i | −0.449495 | + | 0.449495i | −0.895187 | − | 0.445692i | \(-0.852958\pi\) |
0.445692 | + | 0.895187i | \(0.352958\pi\) | |||||||
\(702\) | 6.08254e7i | 0.175822i | ||||||||
\(703\) | −7.11834e6 | − | 2.26786e7i | −0.0204886 | − | 0.0652756i | ||||
\(704\) | −6.14046e7 | −0.175988 | ||||||||
\(705\) | 8.37156e7 | + | 8.37156e7i | 0.238913 | + | 0.238913i | ||||
\(706\) | 9.06609e7i | 0.257636i | ||||||||
\(707\) | 1.53600e8i | 0.434643i | ||||||||
\(708\) | 6.33722e7 | − | 6.33722e7i | 0.178566 | − | 0.178566i | ||||
\(709\) | 1.16587e8 | − | 1.16587e8i | 0.327123 | − | 0.327123i | −0.524368 | − | 0.851492i | \(-0.675698\pi\) |
0.851492 | + | 0.524368i | \(0.175698\pi\) | |||||||
\(710\) | −3.77500e8 | −1.05473 | ||||||||
\(711\) | −3.28837e8 | + | 3.28837e8i | −0.914896 | + | 0.914896i | ||||
\(712\) | 4.52411e7 | 0.125341 | ||||||||
\(713\) | 9.35709e8 | 2.58150 | ||||||||
\(714\) | − | 5.35490e7i | − | 0.147115i | ||||||
\(715\) | 2.50828e8 | 0.686212 | ||||||||
\(716\) | −3.54197e7 | + | 3.54197e7i | −0.0964953 | + | 0.0964953i | ||||
\(717\) | 1.10046e8 | + | 1.10046e8i | 0.298551 | + | 0.298551i | ||||
\(718\) | 3.41706e7 | + | 3.41706e7i | 0.0923166 | + | 0.0923166i | ||||
\(719\) | −5.20524e8 | −1.40041 | −0.700203 | − | 0.713944i | \(-0.746907\pi\) | ||||
−0.700203 | + | 0.713944i | \(0.746907\pi\) | |||||||
\(720\) | 8.37954e7 | − | 8.37954e7i | 0.224503 | − | 0.224503i | ||||
\(721\) | 3.15822e8 | + | 3.15822e8i | 0.842629 | + | 0.842629i | ||||
\(722\) | −1.87303e8 | + | 1.87303e8i | −0.497660 | + | 0.497660i | ||||
\(723\) | −8.50214e7 | − | 8.50214e7i | −0.224964 | − | 0.224964i | ||||
\(724\) | 3.41031e8i | 0.898624i | ||||||||
\(725\) | −1.14817e8 | + | 1.14817e8i | −0.301295 | + | 0.301295i | ||||
\(726\) | 8.60421e7 | − | 8.60421e7i | 0.224854 | − | 0.224854i | ||||
\(727\) | −3.16206e8 | − | 3.16206e8i | −0.822938 | − | 0.822938i | 0.163590 | − | 0.986528i | \(-0.447693\pi\) |
−0.986528 | + | 0.163590i | \(0.947693\pi\) | |||||||
\(728\) | − | 3.94969e7i | − | 0.102369i | ||||||
\(729\) | −1.83235e7 | −0.0472962 | ||||||||
\(730\) | − | 7.45446e8i | − | 1.91623i | ||||||
\(731\) | 9.45811e7i | 0.242132i | ||||||||
\(732\) | 4.89165e7 | + | 4.89165e7i | 0.124716 | + | 0.124716i | ||||
\(733\) | − | 5.78289e8i | − | 1.46836i | −0.678954 | − | 0.734181i | \(-0.737566\pi\) | ||
0.678954 | − | 0.734181i | \(-0.262434\pi\) | |||||||
\(734\) | 1.70149e8 | + | 1.70149e8i | 0.430270 | + | 0.430270i | ||||
\(735\) | 1.83490e7 | + | 1.83490e7i | 0.0462115 | + | 0.0462115i | ||||
\(736\) | 1.35181e8 | 0.339065 | ||||||||
\(737\) | 2.49105e7 | 0.0622271 | ||||||||
\(738\) | 1.63437e8 | − | 1.63437e8i | 0.406613 | − | 0.406613i | ||||
\(739\) | − | 3.00683e8i | − | 0.745033i | −0.928026 | − | 0.372516i | \(-0.878495\pi\) | ||
0.928026 | − | 0.372516i | \(-0.121505\pi\) | |||||||
\(740\) | 3.10622e8 | − | 9.74977e7i | 0.766544 | − | 0.240602i | ||||
\(741\) | −3.86596e6 | −0.00950173 | ||||||||
\(742\) | −2.19129e7 | − | 2.19129e7i | −0.0536398 | − | 0.0536398i | ||||
\(743\) | 3.28721e8i | 0.801422i | 0.916204 | + | 0.400711i | \(0.131237\pi\) | ||||
−0.916204 | + | 0.400711i | \(0.868763\pi\) | |||||||
\(744\) | 8.97269e7i | 0.217873i | ||||||||
\(745\) | −6.23194e8 | + | 6.23194e8i | −1.50714 | + | 1.50714i | ||||
\(746\) | 1.49414e8 | − | 1.49414e8i | 0.359894 | − | 0.359894i | ||||
\(747\) | 4.13227e8 | 0.991350 | ||||||||
\(748\) | 9.91680e7 | − | 9.91680e7i | 0.236955 | − | 0.236955i | ||||
\(749\) | 3.74466e8 | 0.891184 | ||||||||
\(750\) | −1.27713e8 | −0.302727 | ||||||||
\(751\) | 1.89712e8i | 0.447893i | 0.974601 | + | 0.223946i | \(0.0718940\pi\) | ||||
−0.974601 | + | 0.223946i | \(0.928106\pi\) | |||||||
\(752\) | 4.88250e7 | 0.114812 | ||||||||
\(753\) | 2.09657e8 | − | 2.09657e8i | 0.491049 | − | 0.491049i | ||||
\(754\) | −1.75114e7 | − | 1.75114e7i | −0.0408514 | − | 0.0408514i | ||||
\(755\) | −2.85348e8 | − | 2.85348e8i | −0.663032 | − | 0.663032i | ||||
\(756\) | 1.69048e8 | 0.391241 | ||||||||
\(757\) | −1.29795e8 | + | 1.29795e8i | −0.299206 | + | 0.299206i | −0.840703 | − | 0.541497i | \(-0.817858\pi\) |
0.541497 | + | 0.840703i | \(0.317858\pi\) | |||||||
\(758\) | −1.77755e8 | − | 1.77755e8i | −0.408144 | − | 0.408144i | ||||
\(759\) | −3.82274e8 | + | 3.82274e8i | −0.874278 | + | 0.874278i | ||||
\(760\) | 1.20644e7 | + | 1.20644e7i | 0.0274831 | + | 0.0274831i | ||||
\(761\) | 4.83738e8i | 1.09763i | 0.835944 | + | 0.548815i | \(0.184921\pi\) | ||||
−0.835944 | + | 0.548815i | \(0.815079\pi\) | |||||||
\(762\) | 3.43116e7 | − | 3.43116e7i | 0.0775489 | − | 0.0775489i | ||||
\(763\) | 4.42323e8 | − | 4.42323e8i | 0.995785 | − | 0.995785i | ||||
\(764\) | −2.18963e8 | − | 2.18963e8i | −0.491010 | − | 0.491010i | ||||
\(765\) | 2.70658e8i | 0.604556i | ||||||||
\(766\) | 4.41763e8 | 0.982885 | ||||||||
\(767\) | 1.50977e8i | 0.334599i | ||||||||
\(768\) | 1.29628e7i | 0.0286163i | ||||||||
\(769\) | −3.16871e8 | − | 3.16871e8i | −0.696793 | − | 0.696793i | 0.266924 | − | 0.963718i | \(-0.413993\pi\) |
−0.963718 | + | 0.266924i | \(0.913993\pi\) | |||||||
\(770\) | − | 6.97110e8i | − | 1.52696i | ||||||
\(771\) | −1.48026e8 | − | 1.48026e8i | −0.322979 | − | 0.322979i | ||||
\(772\) | −2.57550e8 | − | 2.57550e8i | −0.559770 | − | 0.559770i | ||||
\(773\) | 4.67507e8 | 1.01216 | 0.506081 | − | 0.862486i | \(-0.331094\pi\) | ||||
0.506081 | + | 0.862486i | \(0.331094\pi\) | |||||||
\(774\) | −1.31810e8 | −0.284266 | ||||||||
\(775\) | −7.00792e8 | + | 7.00792e8i | −1.50551 | + | 1.50551i | ||||
\(776\) | 2.95522e8i | 0.632420i | ||||||||
\(777\) | 1.81733e8 | + | 9.49027e7i | 0.387409 | + | 0.202309i | ||||
\(778\) | 4.76297e8 | 1.01144 | ||||||||
\(779\) | 2.35308e7 | + | 2.35308e7i | 0.0497766 | + | 0.0497766i | ||||
\(780\) | − | 5.29508e7i | − | 0.111581i | ||||||
\(781\) | − | 6.22604e8i | − | 1.30695i | ||||||
\(782\) | −2.18316e8 | + | 2.18316e8i | −0.456526 | + | 0.456526i | ||||
\(783\) | 7.49494e7 | − | 7.49494e7i | 0.156129 | − | 0.156129i | ||||
\(784\) | 1.07016e7 | 0.0222075 | ||||||||
\(785\) | 2.99785e8 | − | 2.99785e8i | 0.619728 | − | 0.619728i | ||||
\(786\) | 1.54983e8 | 0.319166 | ||||||||
\(787\) | −2.54351e8 | −0.521807 | −0.260904 | − | 0.965365i | \(-0.584020\pi\) | ||||
−0.260904 | + | 0.965365i | \(0.584020\pi\) | |||||||
\(788\) | − | 2.98581e8i | − | 0.610217i | ||||||
\(789\) | −6.61126e6 | −0.0134602 | ||||||||
\(790\) | 6.48459e8 | − | 6.48459e8i | 1.31523 | − | 1.31523i | ||||
\(791\) | −7.06933e7 | − | 7.06933e7i | −0.142840 | − | 0.142840i | ||||
\(792\) | 1.38202e8 | + | 1.38202e8i | 0.278189 | + | 0.278189i | ||||
\(793\) | −1.16538e8 | −0.233694 | ||||||||
\(794\) | −2.86181e8 | + | 2.86181e8i | −0.571714 | + | 0.571714i | ||||
\(795\) | −2.93771e7 | − | 2.93771e7i | −0.0584666 | − | 0.0584666i | ||||
\(796\) | 2.89070e8 | − | 2.89070e8i | 0.573144 | − | 0.573144i | ||||
\(797\) | −5.94983e8 | − | 5.94983e8i | −1.17525 | − | 1.17525i | −0.980940 | − | 0.194309i | \(-0.937754\pi\) |
−0.194309 | − | 0.980940i | \(-0.562246\pi\) | |||||||
\(798\) | 1.07444e7i | 0.0211433i | ||||||||
\(799\) | −7.88520e7 | + | 7.88520e7i | −0.154587 | + | 0.154587i | ||||
\(800\) | −1.01243e8 | + | 1.01243e8i | −0.197740 | + | 0.197740i | ||||
\(801\) | −1.01823e8 | − | 1.01823e8i | −0.198130 | − | 0.198130i | ||||
\(802\) | − | 3.73512e8i | − | 0.724072i | ||||||
\(803\) | 1.22945e9 | 2.37446 | ||||||||
\(804\) | − | 5.25870e6i | − | 0.0101184i | ||||||
\(805\) | 1.53467e9i | 2.94190i | ||||||||
\(806\) | −1.06882e8 | − | 1.06882e8i | −0.204126 | − | 0.204126i | ||||
\(807\) | 1.25503e8i | 0.238799i | ||||||||
\(808\) | 6.00491e7 | + | 6.00491e7i | 0.113834 | + | 0.113834i | ||||
\(809\) | 5.05939e8 | + | 5.05939e8i | 0.955548 | + | 0.955548i | 0.999053 | − | 0.0435048i | \(-0.0138524\pi\) |
−0.0435048 | + | 0.999053i | \(0.513852\pi\) | |||||||
\(810\) | −2.50610e8 | −0.471567 | ||||||||
\(811\) | −4.34474e8 | −0.814519 | −0.407260 | − | 0.913312i | \(-0.633516\pi\) | ||||
−0.407260 | + | 0.913312i | \(0.633516\pi\) | |||||||
\(812\) | −4.86682e7 | + | 4.86682e7i | −0.0909029 | + | 0.0909029i | ||||
\(813\) | − | 4.50237e8i | − | 0.837857i | ||||||
\(814\) | 1.60801e8 | + | 5.12304e8i | 0.298137 | + | 0.949848i | ||||
\(815\) | −1.00178e9 | −1.85054 | ||||||||
\(816\) | −2.09348e7 | − | 2.09348e7i | −0.0385299 | − | 0.0385299i | ||||
\(817\) | − | 1.89773e7i | − | 0.0347991i | ||||||
\(818\) | − | 1.13925e8i | − | 0.208142i | ||||||
\(819\) | −8.88949e7 | + | 8.88949e7i | −0.161817 | + | 0.161817i | ||||
\(820\) | −3.22294e8 | + | 3.22294e8i | −0.584536 | + | 0.584536i | ||||
\(821\) | −8.19559e8 | −1.48098 | −0.740492 | − | 0.672065i | \(-0.765408\pi\) | ||||
−0.740492 | + | 0.672065i | \(0.765408\pi\) | |||||||
\(822\) | −1.38233e8 | + | 1.38233e8i | −0.248884 | + | 0.248884i | ||||
\(823\) | 5.56599e8 | 0.998488 | 0.499244 | − | 0.866462i | \(-0.333611\pi\) | ||||
0.499244 | + | 0.866462i | \(0.333611\pi\) | |||||||
\(824\) | 2.46938e8 | 0.441374 | ||||||||
\(825\) | − | 5.72602e8i | − | 1.01974i | ||||||
\(826\) | 4.19600e8 | 0.744552 | ||||||||
\(827\) | 5.01860e8 | − | 5.01860e8i | 0.887292 | − | 0.887292i | −0.106970 | − | 0.994262i | \(-0.534115\pi\) |
0.994262 | + | 0.106970i | \(0.0341150\pi\) | |||||||
\(828\) | −3.04250e8 | − | 3.04250e8i | −0.535968 | − | 0.535968i | ||||
\(829\) | −2.61267e8 | − | 2.61267e8i | −0.458587 | − | 0.458587i | 0.439605 | − | 0.898191i | \(-0.355119\pi\) |
−0.898191 | + | 0.439605i | \(0.855119\pi\) | |||||||
\(830\) | −8.14875e8 | −1.42514 | ||||||||
\(831\) | −3.12617e8 | + | 3.12617e8i | −0.544765 | + | 0.544765i | ||||
\(832\) | −1.54411e7 | − | 1.54411e7i | −0.0268108 | − | 0.0268108i | ||||
\(833\) | −1.72830e7 | + | 1.72830e7i | −0.0299008 | + | 0.0299008i | ||||
\(834\) | −1.00619e8 | − | 1.00619e8i | −0.173454 | − | 0.173454i | ||||
\(835\) | − | 1.11642e9i | − | 1.91765i | ||||||
\(836\) | −1.98977e7 | + | 1.98977e7i | −0.0340552 | + | 0.0340552i | ||||
\(837\) | 4.57458e8 | − | 4.57458e8i | 0.780144 | − | 0.780144i | ||||
\(838\) | 1.78026e8 | + | 1.78026e8i | 0.302519 | + | 0.302519i | ||||
\(839\) | − | 7.62696e7i | − | 0.129141i | −0.997913 | − | 0.0645707i | \(-0.979432\pi\) | ||
0.997913 | − | 0.0645707i | \(-0.0205678\pi\) | |||||||
\(840\) | −1.47163e8 | −0.248290 | ||||||||
\(841\) | − | 5.51668e8i | − | 0.927449i | ||||||
\(842\) | 7.21117e8i | 1.20801i | ||||||||
\(843\) | −1.24591e8 | − | 1.24591e8i | −0.207972 | − | 0.207972i | ||||
\(844\) | − | 1.69386e8i | − | 0.281741i | ||||||
\(845\) | −6.22455e8 | − | 6.22455e8i | −1.03166 | − | 1.03166i | ||||
\(846\) | −1.09890e8 | − | 1.09890e8i | −0.181487 | − | 0.181487i | ||||
\(847\) | 5.69702e8 | 0.937556 | ||||||||
\(848\) | −1.71335e7 | −0.0280969 | ||||||||
\(849\) | −1.01628e8 | + | 1.01628e8i | −0.166069 | + | 0.166069i | ||||
\(850\) | − | 3.27012e8i | − | 0.532485i | ||||||
\(851\) | −3.54001e8 | − | 1.12783e9i | −0.574401 | − | 1.83001i | ||||
\(852\) | −1.31434e8 | −0.212515 | ||||||||
\(853\) | 6.88104e8 | + | 6.88104e8i | 1.10868 | + | 1.10868i | 0.993324 | + | 0.115358i | \(0.0368014\pi\) |
0.115358 | + | 0.993324i | \(0.463199\pi\) | |||||||
\(854\) | 3.23886e8i | 0.520018i | ||||||||
\(855\) | − | 5.43064e7i | − | 0.0868866i | ||||||
\(856\) | 1.46396e8 | − | 1.46396e8i | 0.233404 | − | 0.233404i | ||||
\(857\) | −6.01650e8 | + | 6.01650e8i | −0.955875 | + | 0.955875i | −0.999067 | − | 0.0431914i | \(-0.986247\pi\) |
0.0431914 | + | 0.999067i | \(0.486247\pi\) | |||||||
\(858\) | 8.73309e7 | 0.138263 | ||||||||
\(859\) | −6.15477e8 | + | 6.15477e8i | −0.971029 | + | 0.971029i | −0.999592 | − | 0.0285627i | \(-0.990907\pi\) |
0.0285627 | + | 0.999592i | \(0.490907\pi\) | |||||||
\(860\) | 2.59926e8 | 0.408653 | ||||||||
\(861\) | −2.87030e8 | −0.449696 | ||||||||
\(862\) | 4.00372e7i | 0.0625089i | ||||||||
\(863\) | −6.18583e8 | −0.962422 | −0.481211 | − | 0.876605i | \(-0.659803\pi\) | ||||
−0.481211 | + | 0.876605i | \(0.659803\pi\) | |||||||
\(864\) | 6.60885e7 | − | 6.60885e7i | 0.102467 | − | 0.102467i | ||||
\(865\) | 1.31310e8 | + | 1.31310e8i | 0.202885 | + | 0.202885i | ||||
\(866\) | −2.95475e8 | − | 2.95475e8i | −0.454954 | − | 0.454954i | ||||
\(867\) | −2.30776e8 | −0.354106 | ||||||||
\(868\) | −2.97049e8 | + | 2.97049e8i | −0.454223 | + | 0.454223i | ||||
\(869\) | 1.06949e9 | + | 1.06949e9i | 1.62974 | + | 1.62974i | ||||
\(870\) | −6.52463e7 | + | 6.52463e7i | −0.0990827 | + | 0.0990827i | ||||
\(871\) | 6.26411e6 | + | 6.26411e6i | 0.00947993 | + | 0.00947993i | ||||
\(872\) | − | 3.45848e8i | − | 0.521598i | ||||||
\(873\) | 6.65127e8 | − | 6.65127e8i | 0.999682 | − | 0.999682i | ||||
\(874\) | 4.38043e7 | − | 4.38043e7i | 0.0656119 | − | 0.0656119i | ||||
\(875\) | −4.22807e8 | − | 4.22807e8i | −0.631128 | − | 0.631128i | ||||
\(876\) | − | 2.59542e8i | − | 0.386096i | ||||||
\(877\) | 6.14901e8 | 0.911605 | 0.455802 | − | 0.890081i | \(-0.349352\pi\) | ||||
0.455802 | + | 0.890081i | \(0.349352\pi\) | |||||||
\(878\) | 3.74929e7i | 0.0553944i | ||||||||
\(879\) | − | 2.48609e8i | − | 0.366058i | ||||||
\(880\) | −2.72532e8 | − | 2.72532e8i | −0.399917 | − | 0.399917i | ||||
\(881\) | − | 6.13106e8i | − | 0.896618i | −0.893879 | − | 0.448309i | \(-0.852026\pi\) | ||
0.893879 | − | 0.448309i | \(-0.147974\pi\) | |||||||
\(882\) | −2.40859e7 | − | 2.40859e7i | −0.0351040 | − | 0.0351040i | ||||
\(883\) | 3.62294e8 | + | 3.62294e8i | 0.526235 | + | 0.526235i | 0.919448 | − | 0.393213i | \(-0.128636\pi\) |
−0.393213 | + | 0.919448i | \(0.628636\pi\) | |||||||
\(884\) | 4.98746e7 | 0.0721975 | ||||||||
\(885\) | 5.62529e8 | 0.811550 | ||||||||
\(886\) | −4.27997e8 | + | 4.27997e8i | −0.615374 | + | 0.615374i | ||||
\(887\) | 7.06145e8i | 1.01187i | 0.862573 | + | 0.505933i | \(0.168852\pi\) | ||||
−0.862573 | + | 0.505933i | \(0.831148\pi\) | |||||||
\(888\) | 1.08149e8 | − | 3.39458e7i | 0.154449 | − | 0.0484782i | ||||
\(889\) | 2.27184e8 | 0.323349 | ||||||||
\(890\) | 2.00793e8 | + | 2.00793e8i | 0.284826 | + | 0.284826i | ||||
\(891\) | − | 4.13326e8i | − | 0.584332i | ||||||
\(892\) | 5.19539e7i | 0.0732022i | ||||||||
\(893\) | 1.58213e7 | − | 1.58213e7i | 0.0222172 | − | 0.0222172i | ||||
\(894\) | −2.16977e8 | + | 2.16977e8i | −0.303670 | + | 0.303670i | ||||
\(895\) | −3.14406e8 | −0.438553 | ||||||||
\(896\) | −4.29145e7 | + | 4.29145e7i | −0.0596595 | + | 0.0596595i | ||||
\(897\) | −1.92257e8 | −0.266382 | ||||||||
\(898\) | 3.50105e8 | 0.483469 | ||||||||
\(899\) | 2.63401e8i | 0.362525i | ||||||||
\(900\) | 4.55731e8 | 0.625145 | ||||||||
\(901\) | 2.76704e7 | − | 2.76704e7i | 0.0378304 | − | 0.0378304i | ||||
\(902\) | −5.31554e8 | − | 5.31554e8i | −0.724316 | − | 0.724316i | ||||
\(903\) | 1.15743e8 | + | 1.15743e8i | 0.157193 | + | 0.157193i | ||||
\(904\) | −5.52745e7 | −0.0748203 | ||||||||
\(905\) | −1.51360e9 | + | 1.51360e9i | −2.04204 | + | 2.04204i | ||||
\(906\) | −9.93498e7 | − | 9.93498e7i | −0.133593 | − | 0.133593i | ||||
\(907\) | −8.81378e8 | + | 8.81378e8i | −1.18125 | + | 1.18125i | −0.201825 | + | 0.979422i | \(0.564687\pi\) |
−0.979422 | + | 0.201825i | \(0.935313\pi\) | |||||||
\(908\) | 3.50398e8 | + | 3.50398e8i | 0.468063 | + | 0.468063i | ||||
\(909\) | − | 2.70303e8i | − | 0.359881i | ||||||
\(910\) | 1.75299e8 | − | 1.75299e8i | 0.232624 | − | 0.232624i | ||||
\(911\) | −4.90534e8 | + | 4.90534e8i | −0.648805 | + | 0.648805i | −0.952704 | − | 0.303899i | \(-0.901711\pi\) |
0.303899 | + | 0.952704i | \(0.401711\pi\) | |||||||
\(912\) | 4.20047e6 | + | 4.20047e6i | 0.00553750 | + | 0.00553750i | ||||
\(913\) | − | 1.34396e9i | − | 1.76593i | ||||||
\(914\) | −6.12658e8 | −0.802378 | ||||||||
\(915\) | 4.34212e8i | 0.566811i | ||||||||
\(916\) | 5.97613e8i | 0.777559i | ||||||||
\(917\) | 5.13087e8 | + | 5.13087e8i | 0.665400 | + | 0.665400i | ||||
\(918\) | 2.13465e8i | 0.275930i | ||||||||
\(919\) | 9.68659e8 | + | 9.68659e8i | 1.24803 | + | 1.24803i | 0.956590 | + | 0.291439i | \(0.0941339\pi\) |
0.291439 | + | 0.956590i | \(0.405866\pi\) | |||||||
\(920\) | 5.99974e8 | + | 5.99974e8i | 0.770493 | + | 0.770493i | ||||
\(921\) | −1.11055e8 | −0.142154 | ||||||||
\(922\) | 5.25350e8 | 0.670279 | ||||||||
\(923\) | 1.56563e8 | − | 1.56563e8i | 0.199106 | − | 0.199106i | ||||
\(924\) | − | 2.42713e8i | − | 0.307664i | ||||||
\(925\) | 1.10980e9 | + | 5.79550e8i | 1.40223 | + | 0.732261i | ||||
\(926\) | 5.99664e8 | 0.755222 | ||||||||
\(927\) | −5.55779e8 | − | 5.55779e8i | −0.697691 | − | 0.697691i | ||||
\(928\) | 3.80533e7i | 0.0476154i | ||||||||
\(929\) | − | 1.16565e8i | − | 0.145385i | −0.997354 | − | 0.0726925i | \(-0.976841\pi\) | ||
0.997354 | − | 0.0726925i | \(-0.0231592\pi\) | |||||||
\(930\) | −3.98234e8 | + | 3.98234e8i | −0.495097 | + | 0.495097i | ||||
\(931\) | 3.46776e6 | − | 3.46776e6i | 0.00429734 | − | 0.00429734i | ||||
\(932\) | 3.54282e8 | 0.437624 | ||||||||
\(933\) | −1.95345e8 | + | 1.95345e8i | −0.240524 | + | 0.240524i | ||||
\(934\) | 3.32168e8 | 0.407678 | ||||||||
\(935\) | 8.80274e8 | 1.07692 | ||||||||
\(936\) | 6.95061e7i | 0.0847609i | ||||||||
\(937\) | 1.71816e8 | 0.208855 | 0.104427 | − | 0.994533i | \(-0.466699\pi\) | ||||
0.104427 | + | 0.994533i | \(0.466699\pi\) | |||||||
\(938\) | 1.74094e7 | − | 1.74094e7i | 0.0210948 | − | 0.0210948i | ||||
\(939\) | −1.58627e8 | − | 1.58627e8i | −0.191594 | − | 0.191594i | ||||
\(940\) | 2.16700e8 | + | 2.16700e8i | 0.260901 | + | 0.260901i | ||||
\(941\) | 7.56964e8 | 0.908461 | 0.454230 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454230 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(942\) | 1.04376e8 | − | 1.04376e8i | 0.124867 | − | 0.124867i | ||||
\(943\) | 1.17021e9 | + | 1.17021e9i | 1.39549 | + | 1.39549i | ||||
\(944\) | 1.64041e8 | − | 1.64041e8i | 0.195000 | − | 0.195000i | ||||
\(945\) | 7.50285e8 | + | 7.50285e8i | 0.889060 | + | 0.889060i | ||||
\(946\) | 4.28692e8i | 0.506374i | ||||||||
\(947\) | 8.54941e8 | − | 8.54941e8i | 1.00667 | − | 1.00667i | 0.00669012 | − | 0.999978i | \(-0.497870\pi\) |
0.999978 | − | 0.00669012i | \(-0.00212955\pi\) | |||||||
\(948\) | 2.25774e8 | − | 2.25774e8i | 0.265002 | − | 0.265002i | ||||
\(949\) | 3.09164e8 | + | 3.09164e8i | 0.361735 | + | 0.361735i | ||||
\(950\) | 6.56137e7i | 0.0765286i | ||||||||
\(951\) | 7.41609e8 | 0.862251 | ||||||||
\(952\) | − | 1.38613e8i | − | 0.160655i | ||||||
\(953\) | − | 4.48598e8i | − | 0.518297i | −0.965838 | − | 0.259148i | \(-0.916558\pi\) | ||
0.965838 | − | 0.259148i | \(-0.0834418\pi\) | |||||||
\(954\) | 3.85620e7 | + | 3.85620e7i | 0.0444134 | + | 0.0444134i | ||||
\(955\) | − | 1.94365e9i | − | 2.23155i | ||||||
\(956\) | 2.84858e8 | + | 2.84858e8i | 0.326028 | + | 0.326028i | ||||
\(957\) | −1.07610e8 | − | 1.07610e8i | −0.122776 | − | 0.122776i | ||||
\(958\) | −3.22953e8 | −0.367318 | ||||||||
\(959\) | −9.15268e8 | −1.03775 | ||||||||
\(960\) | −5.75326e7 | + | 5.75326e7i | −0.0650280 | + | 0.0650280i | ||||
\(961\) | 7.20177e8i | 0.811464i | ||||||||
\(962\) | −8.83906e7 | + | 1.69262e8i | −0.0992844 | + | 0.190123i | ||||
\(963\) | −6.58982e8 | −0.737895 | ||||||||
\(964\) | −2.20080e8 | − | 2.20080e8i | −0.245668 | − | 0.245668i | ||||
\(965\) | − | 2.28617e9i | − | 2.54405i | ||||||
\(966\) | 5.34327e8i | 0.592756i | ||||||||
\(967\) | −5.61351e8 | + | 5.61351e8i | −0.620805 | + | 0.620805i | −0.945737 | − | 0.324933i | \(-0.894658\pi\) |
0.324933 | + | 0.945737i | \(0.394658\pi\) | |||||||
\(968\) | 2.22722e8 | − | 2.22722e8i | 0.245549 | − | 0.245549i | ||||
\(969\) | −1.35675e7 | −0.0149117 | ||||||||
\(970\) | −1.31162e9 | + | 1.31162e9i | −1.43711 | + | 1.43711i | ||||
\(971\) | −1.47808e9 | −1.61451 | −0.807254 | − | 0.590204i | \(-0.799047\pi\) | ||||
−0.807254 | + | 0.590204i | \(0.799047\pi\) | |||||||
\(972\) | −4.63650e8 | −0.504884 | ||||||||
\(973\) | − | 6.66220e8i | − | 0.723235i | ||||||
\(974\) | −5.74080e8 | −0.621292 | ||||||||
\(975\) | 1.43989e8 | − | 1.43989e8i | 0.155352 | − | 0.155352i | ||||
\(976\) | 1.26622e8 | + | 1.26622e8i | 0.136194 | + | 0.136194i | ||||
\(977\) | 1.14059e9 | + | 1.14059e9i | 1.22306 | + | 1.22306i | 0.966539 | + | 0.256521i | \(0.0825763\pi\) |
0.256521 | + | 0.966539i | \(0.417424\pi\) | |||||||
\(978\) | −3.48789e8 | −0.372861 | ||||||||
\(979\) | −3.31165e8 | + | 3.31165e8i | −0.352936 | + | 0.352936i | ||||
\(980\) | 4.74968e7 | + | 4.74968e7i | 0.0504645 | + | 0.0504645i | ||||
\(981\) | −7.78394e8 | + | 7.78394e8i | −0.824504 | + | 0.824504i | ||||
\(982\) | 1.65734e8 | + | 1.65734e8i | 0.175016 | + | 0.175016i | ||||
\(983\) | − | 1.93485e8i | − | 0.203698i | −0.994800 | − | 0.101849i | \(-0.967524\pi\) | ||
0.994800 | − | 0.101849i | \(-0.0324758\pi\) | |||||||
\(984\) | −1.12213e8 | + | 1.12213e8i | −0.117777 | + | 0.117777i | ||||
\(985\) | 1.32519e9 | − | 1.32519e9i | 1.38666 | − | 1.38666i | ||||
\(986\) | −6.14557e7 | − | 6.14557e7i | −0.0641108 | − | 0.0641108i | ||||
\(987\) | 1.92990e8i | 0.200716i | ||||||||
\(988\) | −1.00071e7 | −0.0103762 | ||||||||
\(989\) | − | 9.43756e8i | − | 0.975598i | ||||||
\(990\) | 1.22677e9i | 1.26432i | ||||||||
\(991\) | −9.22441e8 | − | 9.22441e8i | −0.947802 | − | 0.947802i | 0.0509016 | − | 0.998704i | \(-0.483791\pi\) |
−0.998704 | + | 0.0509016i | \(0.983791\pi\) | |||||||
\(992\) | 2.32260e8i | 0.237925i | ||||||||
\(993\) | 3.72621e8 | + | 3.72621e8i | 0.380557 | + | 0.380557i | ||||
\(994\) | −4.35125e8 | − | 4.35125e8i | −0.443053 | − | 0.443053i | ||||
\(995\) | 2.56595e9 | 2.60483 | ||||||||
\(996\) | −2.83715e8 | −0.287147 | ||||||||
\(997\) | −5.04009e8 | + | 5.04009e8i | −0.508573 | + | 0.508573i | −0.914088 | − | 0.405515i | \(-0.867092\pi\) |
0.405515 | + | 0.914088i | \(0.367092\pi\) | |||||||
\(998\) | − | 1.04761e9i | − | 1.05392i | ||||||
\(999\) | −7.24449e8 | − | 3.78315e8i | −0.726627 | − | 0.379452i |
(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 | 74.7.d.a.31.6 | ✓ | 18 | |
37.6 | odd | 4 | inner | 74.7.d.a.43.4 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.7.d.a.31.6 | ✓ | 18 | 1.1 | even | 1 | trivial | |
74.7.d.a.43.4 | yes | 18 | 37.6 | odd | 4 | inner |