Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,37,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 37, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.b (of order \(2\), degree \(1\), 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: | \(32.8365034637\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + \cdots + 51\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.7 | ||
Root | \(8.47589e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.37.b.b.3.8 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −39525.7 | − | 259147.i | −0.150779 | − | 0.988568i | ||||
\(3\) | 1.35614e8i | 0.350044i | 0.984565 | + | 0.175022i | \(0.0559997\pi\) | ||||
−0.984565 | + | 0.175022i | \(0.944000\pi\) | |||||||
\(4\) | −6.55949e10 | + | 2.04859e10i | −0.954532 | + | 0.298110i | ||||
\(5\) | −1.24080e12 | −0.325268 | −0.162634 | − | 0.986686i | \(-0.551999\pi\) | ||||
−0.162634 | + | 0.986686i | \(0.551999\pi\) | |||||||
\(6\) | 3.51440e13 | − | 5.36025e12i | 0.346042 | − | 0.0527792i | ||||
\(7\) | − | 4.20496e14i | − | 0.258225i | −0.991630 | − | 0.129112i | \(-0.958787\pi\) | ||
0.991630 | − | 0.129112i | \(-0.0412128\pi\) | |||||||
\(8\) | 7.90156e15 | + | 1.61890e16i | 0.438625 | + | 0.898670i | ||||
\(9\) | 1.31703e17 | 0.877469 | ||||||||
\(10\) | 4.90435e16 | + | 3.21549e17i | 0.0490435 | + | 0.321549i | ||||
\(11\) | 3.22138e18i | 0.579394i | 0.957118 | + | 0.289697i | \(0.0935545\pi\) | ||||
−0.957118 | + | 0.289697i | \(0.906446\pi\) | |||||||
\(12\) | −2.77819e18 | − | 8.89561e18i | −0.104352 | − | 0.334128i | ||||
\(13\) | −2.28918e19 | −0.203563 | −0.101781 | − | 0.994807i | \(-0.532454\pi\) | ||||
−0.101781 | + | 0.994807i | \(0.532454\pi\) | |||||||
\(14\) | −1.08970e20 | + | 1.66204e19i | −0.255272 | + | 0.0389348i | ||||
\(15\) | − | 1.68270e20i | − | 0.113858i | ||||||
\(16\) | 3.88302e21 | − | 2.68755e21i | 0.822261 | − | 0.569110i | ||||
\(17\) | 6.53319e21 | 0.464563 | 0.232281 | − | 0.972649i | \(-0.425381\pi\) | ||||
0.232281 | + | 0.972649i | \(0.425381\pi\) | |||||||
\(18\) | −5.20567e21 | − | 3.41305e22i | −0.132304 | − | 0.867437i | ||||
\(19\) | − | 1.34943e23i | − | 1.29594i | −0.761665 | − | 0.647971i | \(-0.775618\pi\) | ||
0.761665 | − | 0.647971i | \(-0.224382\pi\) | |||||||
\(20\) | 8.13901e22 | − | 2.54189e22i | 0.310479 | − | 0.0969656i | ||||
\(21\) | 5.70253e22 | 0.0903900 | ||||||||
\(22\) | 8.34811e23 | − | 1.27327e23i | 0.572770 | − | 0.0873602i | ||||
\(23\) | 4.96373e22i | 0.0153006i | 0.999971 | + | 0.00765028i | \(0.00243518\pi\) | ||||
−0.999971 | + | 0.00765028i | \(0.997565\pi\) | |||||||
\(24\) | −2.19546e24 | + | 1.07156e24i | −0.314574 | + | 0.153538i | ||||
\(25\) | −1.30123e25 | −0.894201 | ||||||||
\(26\) | 9.04813e23 | + | 5.93233e24i | 0.0306930 | + | 0.201236i | ||||
\(27\) | 3.82158e25i | 0.657197i | ||||||||
\(28\) | 8.61427e24 | + | 2.75824e25i | 0.0769793 | + | 0.246484i | ||||
\(29\) | −1.19240e26 | −0.566577 | −0.283288 | − | 0.959035i | \(-0.591425\pi\) | ||||
−0.283288 | + | 0.959035i | \(0.591425\pi\) | |||||||
\(30\) | −4.36067e25 | + | 6.65100e24i | −0.112556 | + | 0.0171674i | ||||
\(31\) | − | 7.37399e26i | − | 1.05485i | −0.849601 | − | 0.527427i | \(-0.823157\pi\) | ||
0.849601 | − | 0.527427i | \(-0.176843\pi\) | |||||||
\(32\) | −8.49949e26 | − | 9.00045e26i | −0.686584 | − | 0.727051i | ||||
\(33\) | −4.36865e26 | −0.202813 | ||||||||
\(34\) | −2.58229e26 | − | 1.69306e27i | −0.0700462 | − | 0.459252i | ||||
\(35\) | 5.21751e26i | 0.0839922i | ||||||||
\(36\) | −8.63907e27 | + | 2.69807e27i | −0.837572 | + | 0.261582i | ||||
\(37\) | −2.48980e28 | −1.47412 | −0.737061 | − | 0.675826i | \(-0.763787\pi\) | ||||
−0.737061 | + | 0.675826i | \(0.763787\pi\) | |||||||
\(38\) | −3.49701e28 | + | 5.33372e27i | −1.28113 | + | 0.195400i | ||||
\(39\) | − | 3.10445e27i | − | 0.0712560i | ||||||
\(40\) | −9.80425e27 | − | 2.00873e28i | −0.142671 | − | 0.292309i | ||||
\(41\) | −1.04174e29 | −0.971968 | −0.485984 | − | 0.873968i | \(-0.661539\pi\) | ||||
−0.485984 | + | 0.873968i | \(0.661539\pi\) | |||||||
\(42\) | −2.25397e27 | − | 1.47779e28i | −0.0136289 | − | 0.0893566i | ||||
\(43\) | − | 2.34072e29i | − | 0.926651i | −0.886188 | − | 0.463326i | \(-0.846656\pi\) | ||
0.886188 | − | 0.463326i | \(-0.153344\pi\) | |||||||
\(44\) | −6.59930e28 | − | 2.11306e29i | −0.172723 | − | 0.553049i | ||||
\(45\) | −1.63417e29 | −0.285413 | ||||||||
\(46\) | 1.28634e28 | − | 1.96195e27i | 0.0151256 | − | 0.00230700i | ||||
\(47\) | 6.54567e29i | 0.522628i | 0.965254 | + | 0.261314i | \(0.0841557\pi\) | ||||
−0.965254 | + | 0.261314i | \(0.915844\pi\) | |||||||
\(48\) | 3.64470e29 | + | 5.26593e29i | 0.199214 | + | 0.287828i | ||||
\(49\) | 2.47491e30 | 0.933320 | ||||||||
\(50\) | 5.14322e29 | + | 3.37211e30i | 0.134826 | + | 0.883978i | ||||
\(51\) | 8.85993e29i | 0.162618i | ||||||||
\(52\) | 1.50158e30 | − | 4.68959e29i | 0.194307 | − | 0.0606841i | ||||
\(53\) | 8.42648e30 | 0.773893 | 0.386946 | − | 0.922102i | \(-0.373530\pi\) | ||||
0.386946 | + | 0.922102i | \(0.373530\pi\) | |||||||
\(54\) | 9.90352e30 | − | 1.51051e30i | 0.649684 | − | 0.0990913i | ||||
\(55\) | − | 3.99708e30i | − | 0.188458i | ||||||
\(56\) | 6.80742e30 | − | 3.32258e30i | 0.232059 | − | 0.113264i | ||||
\(57\) | 1.83002e31 | 0.453637 | ||||||||
\(58\) | 4.71306e30 | + | 3.09007e31i | 0.0854277 | + | 0.560099i | ||||
\(59\) | − | 6.65287e31i | − | 0.886488i | −0.896401 | − | 0.443244i | \(-0.853828\pi\) | ||
0.896401 | − | 0.443244i | \(-0.146172\pi\) | |||||||
\(60\) | 3.44717e30 | + | 1.10377e31i | 0.0339422 | + | 0.108681i | ||||
\(61\) | −1.74158e32 | −1.27352 | −0.636761 | − | 0.771062i | \(-0.719726\pi\) | ||||
−0.636761 | + | 0.771062i | \(0.719726\pi\) | |||||||
\(62\) | −1.91095e32 | + | 2.91462e31i | −1.04279 | + | 0.159049i | ||||
\(63\) | − | 5.53808e31i | − | 0.226584i | ||||||
\(64\) | −1.99649e32 | + | 2.55837e32i | −0.615217 | + | 0.788358i | ||||
\(65\) | 2.84041e31 | 0.0662125 | ||||||||
\(66\) | 1.72674e31 | + | 1.13212e32i | 0.0305799 | + | 0.200495i | ||||
\(67\) | − | 1.02480e33i | − | 1.38450i | −0.721656 | − | 0.692252i | \(-0.756619\pi\) | ||
0.721656 | − | 0.692252i | \(-0.243381\pi\) | |||||||
\(68\) | −4.28544e32 | + | 1.33839e32i | −0.443440 | + | 0.138491i | ||||
\(69\) | −6.73153e30 | −0.00535587 | ||||||||
\(70\) | 1.35210e32 | − | 2.06226e31i | 0.0830319 | − | 0.0126642i | ||||
\(71\) | − | 3.10980e33i | − | 1.47939i | −0.672942 | − | 0.739695i | \(-0.734970\pi\) | ||
0.672942 | − | 0.739695i | \(-0.265030\pi\) | |||||||
\(72\) | 1.04066e33 | + | 2.13215e33i | 0.384880 | + | 0.788555i | ||||
\(73\) | 3.37473e33 | 0.973704 | 0.486852 | − | 0.873484i | \(-0.338145\pi\) | ||||
0.486852 | + | 0.873484i | \(0.338145\pi\) | |||||||
\(74\) | 9.84112e32 | + | 6.45225e33i | 0.222266 | + | 1.45727i | ||||
\(75\) | − | 1.76466e33i | − | 0.313010i | ||||||
\(76\) | 2.76443e33 | + | 8.85157e33i | 0.386333 | + | 1.23702i | ||||
\(77\) | 1.35458e33 | 0.149614 | ||||||||
\(78\) | −8.04509e32 | + | 1.22706e32i | −0.0704414 | + | 0.0107439i | ||||
\(79\) | − | 1.58850e34i | − | 1.10586i | −0.833228 | − | 0.552929i | \(-0.813510\pi\) | ||
0.833228 | − | 0.552929i | \(-0.186490\pi\) | |||||||
\(80\) | −4.81804e33 | + | 3.33471e33i | −0.267455 | + | 0.185113i | ||||
\(81\) | 1.45854e34 | 0.647421 | ||||||||
\(82\) | 4.11757e33 | + | 2.69965e34i | 0.146552 | + | 0.960856i | ||||
\(83\) | − | 6.39239e34i | − | 1.82918i | −0.404377 | − | 0.914592i | \(-0.632512\pi\) | ||
0.404377 | − | 0.914592i | \(-0.367488\pi\) | |||||||
\(84\) | −3.74057e33 | + | 1.16822e33i | −0.0862801 | + | 0.0269461i | ||||
\(85\) | −8.10637e33 | −0.151107 | ||||||||
\(86\) | −6.06590e34 | + | 9.25185e33i | −0.916058 | + | 0.139719i | ||||
\(87\) | − | 1.61707e34i | − | 0.198327i | ||||||
\(88\) | −5.21509e34 | + | 2.54539e34i | −0.520684 | + | 0.254136i | ||||
\(89\) | −1.63956e35 | −1.33570 | −0.667849 | − | 0.744296i | \(-0.732785\pi\) | ||||
−0.667849 | + | 0.744296i | \(0.732785\pi\) | |||||||
\(90\) | 6.45919e33 | + | 4.23491e34i | 0.0430341 | + | 0.282150i | ||||
\(91\) | 9.62590e33i | 0.0525650i | ||||||||
\(92\) | −1.01687e33 | − | 3.25596e33i | −0.00456125 | − | 0.0146049i | ||||
\(93\) | 1.00002e35 | 0.369245 | ||||||||
\(94\) | 1.69629e35 | − | 2.58722e34i | 0.516653 | − | 0.0788011i | ||||
\(95\) | 1.67437e35i | 0.421528i | ||||||||
\(96\) | 1.22059e35 | − | 1.15265e35i | 0.254500 | − | 0.240335i | ||||
\(97\) | 3.39752e35 | 0.587855 | 0.293928 | − | 0.955828i | \(-0.405038\pi\) | ||||
0.293928 | + | 0.955828i | \(0.405038\pi\) | |||||||
\(98\) | −9.78227e34 | − | 6.41367e35i | −0.140725 | − | 0.922650i | ||||
\(99\) | 4.24267e35i | 0.508400i | ||||||||
\(100\) | 8.53543e35 | − | 2.66570e35i | 0.853543 | − | 0.266570i | ||||
\(101\) | 5.85528e35 | 0.489512 | 0.244756 | − | 0.969585i | \(-0.421292\pi\) | ||||
0.244756 | + | 0.969585i | \(0.421292\pi\) | |||||||
\(102\) | 2.29603e35 | − | 3.50195e34i | 0.160758 | − | 0.0245193i | ||||
\(103\) | 2.61949e36i | 1.53868i | 0.638842 | + | 0.769338i | \(0.279414\pi\) | ||||
−0.638842 | + | 0.769338i | \(0.720586\pi\) | |||||||
\(104\) | −1.80881e35 | − | 3.70595e35i | −0.0892877 | − | 0.182936i | ||||
\(105\) | −7.07570e34 | −0.0294010 | ||||||||
\(106\) | −3.33063e35 | − | 2.18370e36i | −0.116687 | − | 0.765045i | ||||
\(107\) | 3.83523e36i | 1.13471i | 0.823474 | + | 0.567354i | \(0.192033\pi\) | ||||
−0.823474 | + | 0.567354i | \(0.807967\pi\) | |||||||
\(108\) | −7.82888e35 | − | 2.50676e36i | −0.195917 | − | 0.627315i | ||||
\(109\) | −7.01177e36 | −1.48645 | −0.743226 | − | 0.669041i | \(-0.766705\pi\) | ||||
−0.743226 | + | 0.669041i | \(0.766705\pi\) | |||||||
\(110\) | −1.03583e36 | + | 1.57988e35i | −0.186304 | + | 0.0284155i | ||||
\(111\) | − | 3.37653e36i | − | 0.516008i | ||||||
\(112\) | −1.13010e36 | − | 1.63280e36i | −0.146958 | − | 0.212328i | ||||
\(113\) | 1.16771e36 | 0.129396 | 0.0646981 | − | 0.997905i | \(-0.479392\pi\) | ||||
0.0646981 | + | 0.997905i | \(0.479392\pi\) | |||||||
\(114\) | −7.23328e35 | − | 4.74244e36i | −0.0683987 | − | 0.448450i | ||||
\(115\) | − | 6.15900e34i | − | 0.00497678i | ||||||
\(116\) | 7.82155e36 | − | 2.44275e36i | 0.540815 | − | 0.168902i | ||||
\(117\) | −3.01492e36 | −0.178620 | ||||||||
\(118\) | −1.72407e37 | + | 2.62959e36i | −0.876353 | + | 0.133663i | ||||
\(119\) | − | 2.74718e36i | − | 0.119962i | ||||||
\(120\) | 2.72412e36 | − | 1.32960e36i | 0.102321 | − | 0.0499410i | ||||
\(121\) | 2.05354e37 | 0.664303 | ||||||||
\(122\) | 6.88372e36 | + | 4.51325e37i | 0.192020 | + | 1.25896i | ||||
\(123\) | − | 1.41275e37i | − | 0.340232i | ||||||
\(124\) | 1.51063e37 | + | 4.83696e37i | 0.314462 | + | 1.00689i | ||||
\(125\) | 3.42017e37 | 0.616123 | ||||||||
\(126\) | −1.43518e37 | + | 2.18897e36i | −0.223994 | + | 0.0341640i | ||||
\(127\) | − | 5.02086e37i | − | 0.679690i | −0.940481 | − | 0.339845i | \(-0.889625\pi\) | ||
0.940481 | − | 0.339845i | \(-0.110375\pi\) | |||||||
\(128\) | 7.41906e37 | + | 4.16264e37i | 0.872107 | + | 0.489316i | ||||
\(129\) | 3.17434e37 | 0.324369 | ||||||||
\(130\) | −1.12269e36 | − | 7.36083e36i | −0.00998343 | − | 0.0654555i | ||||
\(131\) | − | 1.96393e38i | − | 1.52140i | −0.649106 | − | 0.760698i | \(-0.724857\pi\) | ||
0.649106 | − | 0.760698i | \(-0.275143\pi\) | |||||||
\(132\) | 2.86561e37 | − | 8.94960e36i | 0.193592 | − | 0.0604606i | ||||
\(133\) | −5.67430e37 | −0.334644 | ||||||||
\(134\) | −2.65575e38 | + | 4.05061e37i | −1.36867 | + | 0.208754i | ||||
\(135\) | − | 4.74182e37i | − | 0.213765i | ||||||
\(136\) | 5.16224e37 | + | 1.05766e38i | 0.203769 | + | 0.417489i | ||||
\(137\) | −2.08851e38 | −0.722547 | −0.361273 | − | 0.932460i | \(-0.617658\pi\) | ||||
−0.361273 | + | 0.932460i | \(0.617658\pi\) | |||||||
\(138\) | 2.66069e35 | + | 1.74446e36i | 0.000807551 | + | 0.00529464i | ||||
\(139\) | 3.11254e38i | 0.829563i | 0.909921 | + | 0.414781i | \(0.136142\pi\) | ||||
−0.909921 | + | 0.414781i | \(0.863858\pi\) | |||||||
\(140\) | −1.06886e37 | − | 3.42242e37i | −0.0250389 | − | 0.0801732i | ||||
\(141\) | −8.87686e37 | −0.182943 | ||||||||
\(142\) | −8.05897e38 | + | 1.22917e38i | −1.46248 | + | 0.223060i | ||||
\(143\) | − | 7.37431e37i | − | 0.117943i | ||||||
\(144\) | 5.11407e38 | − | 3.53959e38i | 0.721509 | − | 0.499377i | ||||
\(145\) | 1.47953e38 | 0.184289 | ||||||||
\(146\) | −1.33389e38 | − | 8.74550e38i | −0.146814 | − | 0.962573i | ||||
\(147\) | 3.35634e38i | 0.326703i | ||||||||
\(148\) | 1.63318e39 | − | 5.10059e38i | 1.40710 | − | 0.439450i | ||||
\(149\) | 4.95139e38 | 0.377897 | 0.188949 | − | 0.981987i | \(-0.439492\pi\) | ||||
0.188949 | + | 0.981987i | \(0.439492\pi\) | |||||||
\(150\) | −4.57306e38 | + | 6.97494e37i | −0.309431 | + | 0.0471952i | ||||
\(151\) | 2.72979e39i | 1.63887i | 0.573171 | + | 0.819436i | \(0.305713\pi\) | ||||
−0.573171 | + | 0.819436i | \(0.694287\pi\) | |||||||
\(152\) | 2.18459e39 | − | 1.06626e39i | 1.16462 | − | 0.568432i | ||||
\(153\) | 8.60443e38 | 0.407640 | ||||||||
\(154\) | −5.35407e37 | − | 3.51035e38i | −0.0225585 | − | 0.147903i | ||||
\(155\) | 9.14964e38i | 0.343110i | ||||||||
\(156\) | 6.35976e37 | + | 2.03636e38i | 0.0212421 | + | 0.0680161i | ||||
\(157\) | −1.89635e39 | −0.564579 | −0.282290 | − | 0.959329i | \(-0.591094\pi\) | ||||
−0.282290 | + | 0.959329i | \(0.591094\pi\) | |||||||
\(158\) | −4.11655e39 | + | 6.27866e38i | −1.09322 | + | 0.166740i | ||||
\(159\) | 1.14275e39i | 0.270897i | ||||||||
\(160\) | 1.05462e39 | + | 1.11678e39i | 0.223324 | + | 0.236486i | ||||
\(161\) | 2.08723e37 | 0.00395098 | ||||||||
\(162\) | −5.76497e38 | − | 3.77975e39i | −0.0976173 | − | 0.640019i | ||||
\(163\) | − | 1.43646e38i | − | 0.0217730i | −0.999941 | − | 0.0108865i | \(-0.996535\pi\) | ||
0.999941 | − | 0.0108865i | \(-0.00346534\pi\) | |||||||
\(164\) | 6.83332e39 | − | 2.13411e39i | 0.927774 | − | 0.289753i | ||||
\(165\) | 5.42062e38 | 0.0659687 | ||||||||
\(166\) | −1.65657e40 | + | 2.52664e39i | −1.80827 | + | 0.275802i | ||||
\(167\) | − | 1.17608e40i | − | 1.15223i | −0.817368 | − | 0.576115i | \(-0.804568\pi\) | ||
0.817368 | − | 0.576115i | \(-0.195432\pi\) | |||||||
\(168\) | 4.50589e38 | + | 9.23183e38i | 0.0396473 | + | 0.0812308i | ||||
\(169\) | −1.21222e40 | −0.958562 | ||||||||
\(170\) | 3.20410e38 | + | 2.10074e39i | 0.0227838 | + | 0.149380i | ||||
\(171\) | − | 1.77724e40i | − | 1.13715i | ||||||
\(172\) | 4.79518e39 | + | 1.53539e40i | 0.276244 | + | 0.884518i | ||||
\(173\) | 1.17976e40 | 0.612297 | 0.306149 | − | 0.951984i | \(-0.400960\pi\) | ||||
0.306149 | + | 0.951984i | \(0.400960\pi\) | |||||||
\(174\) | −4.19058e39 | + | 6.39158e38i | −0.196060 | + | 0.0299035i | ||||
\(175\) | 5.47164e39i | 0.230905i | ||||||||
\(176\) | 8.65761e39 | + | 1.25087e40i | 0.329739 | + | 0.476413i | ||||
\(177\) | 9.02224e39 | 0.310310 | ||||||||
\(178\) | 6.48050e39 | + | 4.24888e40i | 0.201395 | + | 1.32043i | ||||
\(179\) | − | 1.15903e40i | − | 0.325643i | −0.986656 | − | 0.162821i | \(-0.947941\pi\) | ||
0.986656 | − | 0.162821i | \(-0.0520595\pi\) | |||||||
\(180\) | 1.07194e40 | − | 3.34776e39i | 0.272435 | − | 0.0850843i | ||||
\(181\) | 1.73830e40 | 0.399862 | 0.199931 | − | 0.979810i | \(-0.435928\pi\) | ||||
0.199931 | + | 0.979810i | \(0.435928\pi\) | |||||||
\(182\) | 2.49452e39 | − | 3.80471e38i | 0.0519640 | − | 0.00792568i | ||||
\(183\) | − | 2.36183e40i | − | 0.445789i | ||||||
\(184\) | −8.03579e38 | + | 3.92212e38i | −0.0137502 | + | 0.00671120i | ||||
\(185\) | 3.08934e40 | 0.479485 | ||||||||
\(186\) | −3.95265e39 | − | 2.59152e40i | −0.0556743 | − | 0.365024i | ||||
\(187\) | 2.10459e40i | 0.269165i | ||||||||
\(188\) | −1.34094e40 | − | 4.29362e40i | −0.155800 | − | 0.498865i | ||||
\(189\) | 1.60696e40 | 0.169704 | ||||||||
\(190\) | 4.33908e40 | − | 6.61807e39i | 0.416709 | − | 0.0635574i | ||||
\(191\) | 4.26867e40i | 0.372986i | 0.982456 | + | 0.186493i | \(0.0597121\pi\) | ||||
−0.982456 | + | 0.186493i | \(0.940288\pi\) | |||||||
\(192\) | −3.46951e40 | − | 2.70753e40i | −0.275960 | − | 0.215353i | ||||
\(193\) | −1.11984e41 | −0.811197 | −0.405599 | − | 0.914051i | \(-0.632937\pi\) | ||||
−0.405599 | + | 0.914051i | \(0.632937\pi\) | |||||||
\(194\) | −1.34289e40 | − | 8.80456e40i | −0.0886360 | − | 0.581135i | ||||
\(195\) | 3.85200e39i | 0.0231773i | ||||||||
\(196\) | −1.62342e41 | + | 5.07010e40i | −0.890883 | + | 0.278232i | ||||
\(197\) | −3.14173e41 | −1.57317 | −0.786586 | − | 0.617480i | \(-0.788153\pi\) | ||||
−0.786586 | + | 0.617480i | \(0.788153\pi\) | |||||||
\(198\) | 1.09947e41 | − | 1.67694e40i | 0.502588 | − | 0.0766559i | ||||
\(199\) | 4.13949e41i | 1.72819i | 0.503330 | + | 0.864094i | \(0.332108\pi\) | ||||
−0.503330 | + | 0.864094i | \(0.667892\pi\) | |||||||
\(200\) | −1.02818e41 | − | 2.10657e41i | −0.392219 | − | 0.803592i | ||||
\(201\) | 1.38978e41 | 0.484637 | ||||||||
\(202\) | −2.31434e40 | − | 1.51738e41i | −0.0738080 | − | 0.483916i | ||||
\(203\) | 5.01401e40i | 0.146304i | ||||||||
\(204\) | −1.81504e40 | − | 5.81167e40i | −0.0484779 | − | 0.155224i | ||||
\(205\) | 1.29260e41 | 0.316150 | ||||||||
\(206\) | 6.78834e41 | − | 1.03537e41i | 1.52108 | − | 0.231999i | ||||
\(207\) | 6.53741e39i | 0.0134258i | ||||||||
\(208\) | −8.88891e40 | + | 6.15227e40i | −0.167382 | + | 0.115850i | ||||
\(209\) | 4.34702e41 | 0.750860 | ||||||||
\(210\) | 2.79672e39 | + | 1.83365e40i | 0.00443304 | + | 0.0290649i | ||||
\(211\) | − | 5.11268e41i | − | 0.743985i | −0.928236 | − | 0.371992i | \(-0.878675\pi\) | ||
0.928236 | − | 0.371992i | \(-0.121325\pi\) | |||||||
\(212\) | −5.52735e41 | + | 1.72625e41i | −0.738705 | + | 0.230705i | ||||
\(213\) | 4.21734e41 | 0.517852 | ||||||||
\(214\) | 9.93889e41 | − | 1.51590e41i | 1.12173 | − | 0.171090i | ||||
\(215\) | 2.90436e41i | 0.301410i | ||||||||
\(216\) | −6.18676e41 | + | 3.01965e41i | −0.590604 | + | 0.288263i | ||||
\(217\) | −3.10074e41 | −0.272389 | ||||||||
\(218\) | 2.77145e41 | + | 1.81708e42i | 0.224125 | + | 1.46946i | ||||
\(219\) | 4.57661e41i | 0.340840i | ||||||||
\(220\) | 8.18841e40 | + | 2.62188e41i | 0.0561812 | + | 0.179889i | ||||
\(221\) | −1.49556e41 | −0.0945678 | ||||||||
\(222\) | −8.75017e41 | + | 1.33460e41i | −0.510109 | + | 0.0778030i | ||||
\(223\) | − | 2.98870e42i | − | 1.60692i | −0.595356 | − | 0.803462i | \(-0.702989\pi\) | ||
0.595356 | − | 0.803462i | \(-0.297011\pi\) | |||||||
\(224\) | −3.78466e41 | + | 3.57401e41i | −0.187742 | + | 0.177293i | ||||
\(225\) | −1.71377e42 | −0.784633 | ||||||||
\(226\) | −4.61544e40 | − | 3.02607e41i | −0.0195102 | − | 0.127917i | ||||
\(227\) | − | 3.18256e42i | − | 1.24254i | −0.783595 | − | 0.621272i | \(-0.786616\pi\) | ||
0.783595 | − | 0.621272i | \(-0.213384\pi\) | |||||||
\(228\) | −1.20040e42 | + | 3.74897e41i | −0.433011 | + | 0.135234i | ||||
\(229\) | −1.23648e41 | −0.0412238 | −0.0206119 | − | 0.999788i | \(-0.506561\pi\) | ||||
−0.0206119 | + | 0.999788i | \(0.506561\pi\) | |||||||
\(230\) | −1.59609e40 | + | 2.43439e39i | −0.00491989 | + | 0.000750393i | ||||
\(231\) | 1.83700e41i | 0.0523714i | ||||||||
\(232\) | −9.42184e41 | − | 1.93038e42i | −0.248515 | − | 0.509166i | ||||
\(233\) | 8.58420e41 | 0.209553 | 0.104776 | − | 0.994496i | \(-0.466587\pi\) | ||||
0.104776 | + | 0.994496i | \(0.466587\pi\) | |||||||
\(234\) | 1.19167e41 | + | 7.81308e41i | 0.0269321 | + | 0.176578i | ||||
\(235\) | − | 8.12185e41i | − | 0.169994i | ||||||
\(236\) | 1.36290e42 | + | 4.36394e42i | 0.264271 | + | 0.846181i | ||||
\(237\) | 2.15423e42 | 0.387099 | ||||||||
\(238\) | −7.11924e41 | + | 1.08584e41i | −0.118590 | + | 0.0180876i | ||||
\(239\) | 7.66299e42i | 1.18368i | 0.806054 | + | 0.591842i | \(0.201599\pi\) | ||||
−0.806054 | + | 0.591842i | \(0.798401\pi\) | |||||||
\(240\) | −4.52234e41 | − | 6.53396e41i | −0.0647979 | − | 0.0936211i | ||||
\(241\) | 1.20673e42 | 0.160437 | 0.0802183 | − | 0.996777i | \(-0.474438\pi\) | ||||
0.0802183 | + | 0.996777i | \(0.474438\pi\) | |||||||
\(242\) | −8.11676e41 | − | 5.32169e42i | −0.100163 | − | 0.656708i | ||||
\(243\) | 7.71398e42i | 0.883823i | ||||||||
\(244\) | 1.14239e43 | − | 3.56779e42i | 1.21562 | − | 0.379649i | ||||
\(245\) | −3.07087e42 | −0.303579 | ||||||||
\(246\) | −3.66111e42 | + | 5.58402e41i | −0.336342 | + | 0.0512997i | ||||
\(247\) | 3.08908e42i | 0.263806i | ||||||||
\(248\) | 1.19378e43 | − | 5.82660e42i | 0.947966 | − | 0.462685i | ||||
\(249\) | 8.66899e42 | 0.640296 | ||||||||
\(250\) | −1.35185e42 | − | 8.86327e42i | −0.0928982 | − | 0.609079i | ||||
\(251\) | 5.34548e42i | 0.341869i | 0.985282 | + | 0.170934i | \(0.0546786\pi\) | ||||
−0.985282 | + | 0.170934i | \(0.945321\pi\) | |||||||
\(252\) | 1.13453e42 | + | 3.63270e42i | 0.0675469 | + | 0.216282i | ||||
\(253\) | −1.59901e41 | −0.00886505 | ||||||||
\(254\) | −1.30114e43 | + | 1.98453e42i | −0.671920 | + | 0.102483i | ||||
\(255\) | − | 1.09934e42i | − | 0.0528943i | ||||||
\(256\) | 7.85492e42 | − | 2.08716e43i | 0.352227 | − | 0.935915i | ||||
\(257\) | −2.19858e43 | −0.919064 | −0.459532 | − | 0.888161i | \(-0.651983\pi\) | ||||
−0.459532 | + | 0.888161i | \(0.651983\pi\) | |||||||
\(258\) | −1.25468e42 | − | 8.22622e42i | −0.0489079 | − | 0.320661i | ||||
\(259\) | 1.04695e43i | 0.380655i | ||||||||
\(260\) | −1.86316e42 | + | 5.81884e41i | −0.0632019 | + | 0.0197386i | ||||
\(261\) | −1.57043e43 | −0.497154 | ||||||||
\(262\) | −5.08946e43 | + | 7.76257e42i | −1.50400 | + | 0.229394i | ||||
\(263\) | 2.34032e42i | 0.0645762i | 0.999479 | + | 0.0322881i | \(0.0102794\pi\) | ||||
−0.999479 | + | 0.0322881i | \(0.989721\pi\) | |||||||
\(264\) | −3.45192e42 | − | 7.07241e42i | −0.0889589 | − | 0.182262i | ||||
\(265\) | −1.04556e43 | −0.251723 | ||||||||
\(266\) | 2.24281e42 | + | 1.47048e43i | 0.0504572 | + | 0.330818i | ||||
\(267\) | − | 2.22348e43i | − | 0.467554i | ||||||
\(268\) | 2.09941e43 | + | 6.72219e43i | 0.412734 | + | 1.32155i | ||||
\(269\) | 5.58028e43 | 1.02592 | 0.512961 | − | 0.858412i | \(-0.328548\pi\) | ||||
0.512961 | + | 0.858412i | \(0.328548\pi\) | |||||||
\(270\) | −1.22883e43 | + | 1.87424e42i | −0.211321 | + | 0.0322312i | ||||
\(271\) | − | 5.41976e43i | − | 0.872033i | −0.899939 | − | 0.436017i | \(-0.856389\pi\) | ||
0.899939 | − | 0.436017i | \(-0.143611\pi\) | |||||||
\(272\) | 2.53685e43 | − | 1.75583e43i | 0.381992 | − | 0.264388i | ||||
\(273\) | −1.30541e42 | −0.0184001 | ||||||||
\(274\) | 8.25498e42 | + | 5.41231e43i | 0.108945 | + | 0.714286i | ||||
\(275\) | − | 4.19177e43i | − | 0.518094i | ||||||
\(276\) | 4.41554e41 | − | 1.37902e41i | 0.00511235 | − | 0.00159664i | ||||
\(277\) | −2.91199e43 | −0.315903 | −0.157952 | − | 0.987447i | \(-0.550489\pi\) | ||||
−0.157952 | + | 0.987447i | \(0.550489\pi\) | |||||||
\(278\) | 8.06607e43 | − | 1.23026e43i | 0.820079 | − | 0.125080i | ||||
\(279\) | − | 9.71180e43i | − | 0.925601i | ||||||
\(280\) | −8.44664e42 | + | 4.12265e42i | −0.0754813 | + | 0.0368410i | ||||
\(281\) | 1.85422e44 | 1.55399 | 0.776995 | − | 0.629507i | \(-0.216743\pi\) | ||||
0.776995 | + | 0.629507i | \(0.216743\pi\) | |||||||
\(282\) | 3.50864e42 | + | 2.30041e43i | 0.0275839 | + | 0.180851i | ||||
\(283\) | 5.61975e43i | 0.414535i | 0.978284 | + | 0.207268i | \(0.0664571\pi\) | ||||
−0.978284 | + | 0.207268i | \(0.933543\pi\) | |||||||
\(284\) | 6.37073e43 | + | 2.03987e44i | 0.441021 | + | 1.41212i | ||||
\(285\) | −2.27069e43 | −0.147553 | ||||||||
\(286\) | −1.91103e43 | + | 2.91475e42i | −0.116595 | + | 0.0177833i | ||||
\(287\) | 4.38050e43i | 0.250986i | ||||||||
\(288\) | −1.11941e44 | − | 1.18539e44i | −0.602456 | − | 0.637965i | ||||
\(289\) | −1.55088e44 | −0.784181 | ||||||||
\(290\) | −5.84795e42 | − | 3.83416e43i | −0.0277869 | − | 0.182182i | ||||
\(291\) | 4.60752e43i | 0.205775i | ||||||||
\(292\) | −2.21365e44 | + | 6.91345e43i | −0.929432 | + | 0.290271i | ||||
\(293\) | −6.61412e43 | −0.261129 | −0.130564 | − | 0.991440i | \(-0.541679\pi\) | ||||
−0.130564 | + | 0.991440i | \(0.541679\pi\) | |||||||
\(294\) | 8.69785e43 | − | 1.32662e43i | 0.322968 | − | 0.0492599i | ||||
\(295\) | 8.25487e43i | 0.288346i | ||||||||
\(296\) | −1.96733e44 | − | 4.03074e44i | −0.646586 | − | 1.32475i | ||||
\(297\) | −1.23108e44 | −0.380776 | ||||||||
\(298\) | −1.95707e43 | − | 1.28314e44i | −0.0569789 | − | 0.373577i | ||||
\(299\) | − | 1.13629e42i | − | 0.00311463i | ||||||
\(300\) | 3.61507e43 | + | 1.15753e44i | 0.0933113 | + | 0.298778i | ||||
\(301\) | −9.84262e43 | −0.239284 | ||||||||
\(302\) | 7.07418e44 | − | 1.07897e44i | 1.62014 | − | 0.247107i | ||||
\(303\) | 7.94060e43i | 0.171351i | ||||||||
\(304\) | −3.62666e44 | − | 5.23986e44i | −0.737534 | − | 1.06560i | ||||
\(305\) | 2.16095e44 | 0.414236 | ||||||||
\(306\) | −3.40096e43 | − | 2.22981e44i | −0.0614633 | − | 0.402979i | ||||
\(307\) | 6.49386e44i | 1.10666i | 0.832964 | + | 0.553328i | \(0.186642\pi\) | ||||
−0.832964 | + | 0.553328i | \(0.813358\pi\) | |||||||
\(308\) | −8.88535e43 | + | 2.77498e43i | −0.142811 | + | 0.0446013i | ||||
\(309\) | −3.55241e44 | −0.538604 | ||||||||
\(310\) | 2.37110e44 | − | 3.61646e43i | 0.339187 | − | 0.0517337i | ||||
\(311\) | 4.95093e44i | 0.668344i | 0.942512 | + | 0.334172i | \(0.108457\pi\) | ||||
−0.942512 | + | 0.334172i | \(0.891543\pi\) | |||||||
\(312\) | 5.02580e43 | − | 2.45300e43i | 0.0640357 | − | 0.0312547i | ||||
\(313\) | −5.21360e43 | −0.0627104 | −0.0313552 | − | 0.999508i | \(-0.509982\pi\) | ||||
−0.0313552 | + | 0.999508i | \(0.509982\pi\) | |||||||
\(314\) | 7.49546e43 | + | 4.91434e44i | 0.0851265 | + | 0.558125i | ||||
\(315\) | 6.87164e43i | 0.0737005i | ||||||||
\(316\) | 3.25419e44 | + | 1.04197e45i | 0.329667 | + | 1.05558i | ||||
\(317\) | 1.74925e45 | 1.67411 | 0.837056 | − | 0.547117i | \(-0.184275\pi\) | ||||
0.837056 | + | 0.547117i | \(0.184275\pi\) | |||||||
\(318\) | 2.96141e44 | − | 4.51681e43i | 0.267800 | − | 0.0408454i | ||||
\(319\) | − | 3.84118e44i | − | 0.328271i | ||||||
\(320\) | 2.47725e44 | − | 3.17442e44i | 0.200110 | − | 0.256428i | ||||
\(321\) | −5.20112e44 | −0.397198 | ||||||||
\(322\) | −8.24994e41 | − | 5.40900e42i | −0.000595724 | − | 0.00390581i | ||||
\(323\) | − | 8.81607e44i | − | 0.602046i | ||||||
\(324\) | −9.56725e44 | + | 2.98795e44i | −0.617984 | + | 0.193003i | ||||
\(325\) | 2.97875e44 | 0.182026 | ||||||||
\(326\) | −3.72255e43 | + | 5.67772e42i | −0.0215240 | + | 0.00328290i | ||||
\(327\) | − | 9.50897e44i | − | 0.520324i | ||||||
\(328\) | −8.23141e44 | − | 1.68648e45i | −0.426329 | − | 0.873479i | ||||
\(329\) | 2.75243e44 | 0.134955 | ||||||||
\(330\) | −2.14254e43 | − | 1.40474e44i | −0.00994667 | − | 0.0652145i | ||||
\(331\) | − | 3.93879e45i | − | 1.73164i | −0.500352 | − | 0.865822i | \(-0.666796\pi\) | ||
0.500352 | − | 0.865822i | \(-0.333204\pi\) | |||||||
\(332\) | 1.30954e45 | + | 4.19308e45i | 0.545298 | + | 1.74601i | ||||
\(333\) | −3.27915e45 | −1.29350 | ||||||||
\(334\) | −3.04777e45 | + | 4.64853e44i | −1.13906 | + | 0.173732i | ||||
\(335\) | 1.27157e45i | 0.450335i | ||||||||
\(336\) | 2.21430e44 | − | 1.53258e44i | 0.0743242 | − | 0.0514419i | ||||
\(337\) | −1.37207e45 | −0.436553 | −0.218277 | − | 0.975887i | \(-0.570044\pi\) | ||||
−0.218277 | + | 0.975887i | \(0.570044\pi\) | |||||||
\(338\) | 4.79138e44 | + | 3.14143e45i | 0.144531 | + | 0.947603i | ||||
\(339\) | 1.58358e44i | 0.0452944i | ||||||||
\(340\) | 5.31737e44 | − | 1.66067e44i | 0.144237 | − | 0.0450466i | ||||
\(341\) | 2.37544e45 | 0.611175 | ||||||||
\(342\) | −4.60568e45 | + | 7.02469e44i | −1.12415 | + | 0.171458i | ||||
\(343\) | − | 2.15574e45i | − | 0.499231i | ||||||
\(344\) | 3.78939e45 | − | 1.84953e45i | 0.832754 | − | 0.406452i | ||||
\(345\) | 8.35248e42 | 0.00174209 | ||||||||
\(346\) | −4.66307e44 | − | 3.05730e45i | −0.0923214 | − | 0.605297i | ||||
\(347\) | 3.78358e45i | 0.711169i | 0.934644 | + | 0.355585i | \(0.115718\pi\) | ||||
−0.934644 | + | 0.355585i | \(0.884282\pi\) | |||||||
\(348\) | 3.31272e44 | + | 1.06071e45i | 0.0591232 | + | 0.189309i | ||||
\(349\) | −1.87966e45 | −0.318581 | −0.159291 | − | 0.987232i | \(-0.550921\pi\) | ||||
−0.159291 | + | 0.987232i | \(0.550921\pi\) | |||||||
\(350\) | 1.41796e45 | − | 2.16271e44i | 0.228265 | − | 0.0348155i | ||||
\(351\) | − | 8.74828e44i | − | 0.133781i | ||||||
\(352\) | 2.89939e45 | − | 2.73801e45i | 0.421249 | − | 0.397802i | ||||
\(353\) | 1.31475e46 | 1.81509 | 0.907545 | − | 0.419954i | \(-0.137954\pi\) | ||||
0.907545 | + | 0.419954i | \(0.137954\pi\) | |||||||
\(354\) | −3.56611e44 | − | 2.33809e45i | −0.0467881 | − | 0.306762i | ||||
\(355\) | 3.85864e45i | 0.481198i | ||||||||
\(356\) | 1.07547e46 | − | 3.35880e45i | 1.27497 | − | 0.398185i | ||||
\(357\) | 3.72557e44 | 0.0419918 | ||||||||
\(358\) | −3.00360e45 | + | 4.58117e44i | −0.321920 | + | 0.0491000i | ||||
\(359\) | 1.37878e46i | 1.40539i | 0.711493 | + | 0.702693i | \(0.248019\pi\) | ||||
−0.711493 | + | 0.702693i | \(0.751981\pi\) | |||||||
\(360\) | −1.29125e45 | − | 2.64557e45i | −0.125189 | − | 0.256492i | ||||
\(361\) | −7.36708e45 | −0.679463 | ||||||||
\(362\) | −6.87076e44 | − | 4.50475e45i | −0.0602907 | − | 0.395291i | ||||
\(363\) | 2.78489e45i | 0.232535i | ||||||||
\(364\) | −1.97196e44 | − | 6.31410e44i | −0.0156701 | − | 0.0501749i | ||||
\(365\) | −4.18736e45 | −0.316715 | ||||||||
\(366\) | −6.12061e45 | + | 9.33531e44i | −0.440692 | + | 0.0672154i | ||||
\(367\) | 2.09789e45i | 0.143811i | 0.997411 | + | 0.0719057i | \(0.0229081\pi\) | ||||
−0.997411 | + | 0.0719057i | \(0.977092\pi\) | |||||||
\(368\) | 1.33403e44 | + | 1.92743e44i | 0.00870771 | + | 0.0125811i | ||||
\(369\) | −1.37201e46 | −0.852872 | ||||||||
\(370\) | −1.22108e45 | − | 8.00594e45i | −0.0722961 | − | 0.474003i | ||||
\(371\) | − | 3.54331e45i | − | 0.199838i | ||||||
\(372\) | −6.55961e45 | + | 2.04863e45i | −0.352456 | + | 0.110076i | ||||
\(373\) | −5.35973e45 | −0.274400 | −0.137200 | − | 0.990543i | \(-0.543810\pi\) | ||||
−0.137200 | + | 0.990543i | \(0.543810\pi\) | |||||||
\(374\) | 5.45398e45 | − | 8.31854e44i | 0.266088 | − | 0.0405843i | ||||
\(375\) | 4.63824e45i | 0.215670i | ||||||||
\(376\) | −1.05968e46 | + | 5.17210e45i | −0.469670 | + | 0.229237i | ||||
\(377\) | 2.72962e45 | 0.115334 | ||||||||
\(378\) | −6.35164e44 | − | 4.16440e45i | −0.0255878 | − | 0.167764i | ||||
\(379\) | − | 3.69366e45i | − | 0.141890i | −0.997480 | − | 0.0709449i | \(-0.977399\pi\) | ||
0.997480 | − | 0.0709449i | \(-0.0226014\pi\) | |||||||
\(380\) | −3.43011e45 | − | 1.09830e46i | −0.125662 | − | 0.402362i | ||||
\(381\) | 6.80900e45 | 0.237922 | ||||||||
\(382\) | 1.10621e46 | − | 1.68722e45i | 0.368722 | − | 0.0562383i | ||||
\(383\) | − | 4.03454e46i | − | 1.28297i | −0.767136 | − | 0.641485i | \(-0.778319\pi\) | ||
0.767136 | − | 0.641485i | \(-0.221681\pi\) | |||||||
\(384\) | −5.64513e45 | + | 1.00613e46i | −0.171282 | + | 0.305276i | ||||
\(385\) | −1.68076e45 | −0.0486645 | ||||||||
\(386\) | 4.42627e45 | + | 2.90205e46i | 0.122311 | + | 0.801923i | ||||
\(387\) | − | 3.08280e46i | − | 0.813108i | ||||||
\(388\) | −2.22860e46 | + | 6.96013e45i | −0.561126 | + | 0.175245i | ||||
\(389\) | 4.29638e46 | 1.03278 | 0.516392 | − | 0.856352i | \(-0.327275\pi\) | ||||
0.516392 | + | 0.856352i | \(0.327275\pi\) | |||||||
\(390\) | 9.98234e44 | − | 1.52253e44i | 0.0229123 | − | 0.00349464i | ||||
\(391\) | 3.24290e44i | 0.00710807i | ||||||||
\(392\) | 1.95557e46 | + | 4.00664e46i | 0.409377 | + | 0.838747i | ||||
\(393\) | 2.66337e46 | 0.532556 | ||||||||
\(394\) | 1.24179e46 | + | 8.14169e46i | 0.237201 | + | 1.55519i | ||||
\(395\) | 1.97101e46i | 0.359700i | ||||||||
\(396\) | −8.69151e45 | − | 2.78297e46i | −0.151559 | − | 0.485284i | ||||
\(397\) | −4.06613e46 | −0.677567 | −0.338784 | − | 0.940864i | \(-0.610015\pi\) | ||||
−0.338784 | + | 0.940864i | \(0.610015\pi\) | |||||||
\(398\) | 1.07274e47 | − | 1.63616e46i | 1.70843 | − | 0.260574i | ||||
\(399\) | − | 7.69516e45i | − | 0.117140i | ||||||
\(400\) | −5.05271e46 | + | 3.49713e46i | −0.735267 | + | 0.508899i | ||||
\(401\) | 3.03189e46 | 0.421808 | 0.210904 | − | 0.977507i | \(-0.432359\pi\) | ||||
0.210904 | + | 0.977507i | \(0.432359\pi\) | |||||||
\(402\) | −5.49320e45 | − | 3.60157e46i | −0.0730730 | − | 0.479097i | ||||
\(403\) | 1.68804e46i | 0.214729i | ||||||||
\(404\) | −3.84077e46 | + | 1.19951e46i | −0.467255 | + | 0.145928i | ||||
\(405\) | −1.80975e46 | −0.210585 | ||||||||
\(406\) | 1.29937e46 | − | 1.98182e45i | 0.144631 | − | 0.0220595i | ||||
\(407\) | − | 8.02060e46i | − | 0.854097i | ||||||
\(408\) | −1.43434e46 | + | 7.00073e45i | −0.146140 | + | 0.0713281i | ||||
\(409\) | −2.61966e46 | −0.255403 | −0.127701 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127701 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(410\) | −5.10908e45 | − | 3.34972e46i | −0.0476687 | − | 0.312536i | ||||
\(411\) | − | 2.83232e46i | − | 0.252923i | ||||||
\(412\) | −5.36628e46 | − | 1.71825e47i | −0.458694 | − | 1.46871i | ||||
\(413\) | −2.79751e46 | −0.228913 | ||||||||
\(414\) | 1.69415e45 | − | 2.58396e44i | 0.0132723 | − | 0.00202432i | ||||
\(415\) | 7.93167e46i | 0.594975i | ||||||||
\(416\) | 1.94568e46 | + | 2.06036e46i | 0.139763 | + | 0.148001i | ||||
\(417\) | −4.22106e46 | −0.290384 | ||||||||
\(418\) | −1.71819e46 | − | 1.12652e47i | −0.113214 | − | 0.742276i | ||||
\(419\) | 2.06412e47i | 1.30281i | 0.758730 | + | 0.651406i | \(0.225820\pi\) | ||||
−0.758730 | + | 0.651406i | \(0.774180\pi\) | |||||||
\(420\) | 4.64130e45 | − | 1.44952e45i | 0.0280642 | − | 0.00876472i | ||||
\(421\) | −3.68409e46 | −0.213429 | −0.106714 | − | 0.994290i | \(-0.534033\pi\) | ||||
−0.106714 | + | 0.994290i | \(0.534033\pi\) | |||||||
\(422\) | −1.32493e47 | + | 2.02082e46i | −0.735479 | + | 0.112177i | ||||
\(423\) | 8.62086e46i | 0.458590i | ||||||||
\(424\) | 6.65824e46 | + | 1.36416e47i | 0.339448 | + | 0.695474i | ||||
\(425\) | −8.50120e46 | −0.415412 | ||||||||
\(426\) | −1.66693e46 | − | 1.09291e47i | −0.0780810 | − | 0.511932i | ||||
\(427\) | 7.32328e46i | 0.328855i | ||||||||
\(428\) | −7.85684e46 | − | 2.51572e47i | −0.338267 | − | 1.08311i | ||||
\(429\) | 1.00006e46 | 0.0412853 | ||||||||
\(430\) | 7.52656e46 | − | 1.14797e46i | 0.297964 | − | 0.0454462i | ||||
\(431\) | 1.33320e47i | 0.506181i | 0.967443 | + | 0.253091i | \(0.0814470\pi\) | ||||
−0.967443 | + | 0.253091i | \(0.918553\pi\) | |||||||
\(432\) | 1.02707e47 | + | 1.48393e47i | 0.374018 | + | 0.540388i | ||||
\(433\) | 2.32639e47 | 0.812646 | 0.406323 | − | 0.913730i | \(-0.366811\pi\) | ||||
0.406323 | + | 0.913730i | \(0.366811\pi\) | |||||||
\(434\) | 1.22559e46 | + | 8.03547e46i | 0.0410705 | + | 0.269275i | ||||
\(435\) | 2.00646e46i | 0.0645094i | ||||||||
\(436\) | 4.59937e47 | − | 1.43643e47i | 1.41887 | − | 0.443126i | ||||
\(437\) | 6.69821e45 | 0.0198286 | ||||||||
\(438\) | 1.18602e47 | − | 1.80894e46i | 0.336943 | − | 0.0513913i | ||||
\(439\) | − | 1.54201e47i | − | 0.420462i | −0.977652 | − | 0.210231i | \(-0.932578\pi\) | ||
0.977652 | − | 0.210231i | \(-0.0674216\pi\) | |||||||
\(440\) | 6.47088e46 | − | 3.15832e46i | 0.169362 | − | 0.0826624i | ||||
\(441\) | 3.25955e47 | 0.818959 | ||||||||
\(442\) | 5.91131e45 | + | 3.87570e46i | 0.0142588 | + | 0.0934867i | ||||
\(443\) | − | 5.24128e47i | − | 1.21386i | −0.794754 | − | 0.606932i | \(-0.792400\pi\) | ||
0.794754 | − | 0.606932i | \(-0.207600\pi\) | |||||||
\(444\) | 6.91713e46 | + | 2.21483e47i | 0.153827 | + | 0.492546i | ||||
\(445\) | 2.03437e47 | 0.434460 | ||||||||
\(446\) | −7.74514e47 | + | 1.18131e47i | −1.58855 | + | 0.242290i | ||||
\(447\) | 6.71479e46i | 0.132281i | ||||||||
\(448\) | 1.07578e47 | + | 8.39518e46i | 0.203573 | + | 0.158864i | ||||
\(449\) | −6.42975e47 | −1.16885 | −0.584427 | − | 0.811447i | \(-0.698681\pi\) | ||||
−0.584427 | + | 0.811447i | \(0.698681\pi\) | |||||||
\(450\) | 6.77379e46 | + | 4.44118e47i | 0.118306 | + | 0.775663i | ||||
\(451\) | − | 3.35586e47i | − | 0.563152i | ||||||
\(452\) | −7.65955e46 | + | 2.39215e46i | −0.123513 | + | 0.0385742i | ||||
\(453\) | −3.70199e47 | −0.573678 | ||||||||
\(454\) | −8.24752e47 | + | 1.25793e47i | −1.22834 | + | 0.187349i | ||||
\(455\) | − | 1.19438e46i | − | 0.0170977i | ||||||
\(456\) | 1.44600e47 | + | 2.96262e47i | 0.198976 | + | 0.407670i | ||||
\(457\) | 9.18113e47 | 1.21452 | 0.607260 | − | 0.794503i | \(-0.292269\pi\) | ||||
0.607260 | + | 0.794503i | \(0.292269\pi\) | |||||||
\(458\) | 4.88727e45 | + | 3.20430e46i | 0.00621567 | + | 0.0407525i | ||||
\(459\) | 2.49671e47i | 0.305309i | ||||||||
\(460\) | 1.26173e45 | + | 4.03999e45i | 0.00148363 | + | 0.00475050i | ||||
\(461\) | −9.35047e47 | −1.05735 | −0.528673 | − | 0.848826i | \(-0.677310\pi\) | ||||
−0.528673 | + | 0.848826i | \(0.677310\pi\) | |||||||
\(462\) | 4.76054e46 | − | 7.26089e45i | 0.0517727 | − | 0.00789649i | ||||
\(463\) | − | 1.13538e48i | − | 1.18764i | −0.804599 | − | 0.593818i | \(-0.797620\pi\) | ||
0.804599 | − | 0.593818i | \(-0.202380\pi\) | |||||||
\(464\) | −4.63012e47 | + | 3.20464e47i | −0.465874 | + | 0.322445i | ||||
\(465\) | −1.24082e47 | −0.120104 | ||||||||
\(466\) | −3.39297e46 | − | 2.22457e47i | −0.0315961 | − | 0.207157i | ||||
\(467\) | − | 1.04572e48i | − | 0.936940i | −0.883479 | − | 0.468470i | \(-0.844805\pi\) | ||
0.883479 | − | 0.468470i | \(-0.155195\pi\) | |||||||
\(468\) | 1.97764e47 | − | 6.17635e46i | 0.170499 | − | 0.0532484i | ||||
\(469\) | −4.30926e47 | −0.357513 | ||||||||
\(470\) | −2.10475e47 | + | 3.21022e46i | −0.168051 | + | 0.0256315i | ||||
\(471\) | − | 2.57172e47i | − | 0.197628i | ||||||
\(472\) | 1.07703e48 | − | 5.25680e47i | 0.796660 | − | 0.388835i | ||||
\(473\) | 7.54033e47 | 0.536896 | ||||||||
\(474\) | −8.51476e46 | − | 5.58263e47i | −0.0583663 | − | 0.382674i | ||||
\(475\) | 1.75592e48i | 1.15883i | ||||||||
\(476\) | 5.62786e46 | + | 1.80201e47i | 0.0357617 | + | 0.114507i | ||||
\(477\) | 1.10980e48 | 0.679067 | ||||||||
\(478\) | 1.98584e48 | − | 3.02885e47i | 1.17015 | − | 0.178474i | ||||
\(479\) | 2.65599e48i | 1.50726i | 0.657300 | + | 0.753629i | \(0.271698\pi\) | ||||
−0.657300 | + | 0.753629i | \(0.728302\pi\) | |||||||
\(480\) | −1.51451e47 | + | 1.43021e47i | −0.0827807 | + | 0.0781731i | ||||
\(481\) | 5.69959e47 | 0.300077 | ||||||||
\(482\) | −4.76969e46 | − | 3.12721e47i | −0.0241904 | − | 0.158602i | ||||
\(483\) | 2.83059e45i | 0.00138302i | ||||||||
\(484\) | −1.34702e48 | + | 4.20687e47i | −0.634098 | + | 0.198035i | ||||
\(485\) | −4.21563e47 | −0.191210 | ||||||||
\(486\) | 1.99905e48 | − | 3.04900e47i | 0.873719 | − | 0.133262i | ||||
\(487\) | 3.04604e48i | 1.28296i | 0.767139 | + | 0.641481i | \(0.221680\pi\) | ||||
−0.767139 | + | 0.641481i | \(0.778320\pi\) | |||||||
\(488\) | −1.37612e48 | − | 2.81944e48i | −0.558598 | − | 1.14448i | ||||
\(489\) | 1.94805e46 | 0.00762150 | ||||||||
\(490\) | 1.21378e47 | + | 7.95807e47i | 0.0457733 | + | 0.300108i | ||||
\(491\) | − | 1.05583e48i | − | 0.383821i | −0.981412 | − | 0.191911i | \(-0.938532\pi\) | ||
0.981412 | − | 0.191911i | \(-0.0614683\pi\) | |||||||
\(492\) | 2.89416e47 | + | 9.26695e47i | 0.101426 | + | 0.324762i | ||||
\(493\) | −7.79019e47 | −0.263211 | ||||||||
\(494\) | 8.00526e47 | − | 1.22098e47i | 0.260790 | − | 0.0397763i | ||||
\(495\) | − | 5.26430e47i | − | 0.165366i | ||||||
\(496\) | −1.98180e48 | − | 2.86333e48i | −0.600328 | − | 0.867365i | ||||
\(497\) | −1.30766e48 | −0.382015 | ||||||||
\(498\) | −3.42648e47 | − | 2.24654e48i | −0.0965429 | − | 0.632975i | ||||
\(499\) | 4.01580e48i | 1.09135i | 0.837998 | + | 0.545673i | \(0.183726\pi\) | ||||
−0.837998 | + | 0.545673i | \(0.816274\pi\) | |||||||
\(500\) | −2.24346e48 | + | 7.00654e47i | −0.588109 | + | 0.183672i | ||||
\(501\) | 1.59493e48 | 0.403332 | ||||||||
\(502\) | 1.38527e48 | − | 2.11284e47i | 0.337961 | − | 0.0515465i | ||||
\(503\) | − | 5.68934e48i | − | 1.33918i | −0.742732 | − | 0.669589i | \(-0.766470\pi\) | ||
0.742732 | − | 0.669589i | \(-0.233530\pi\) | |||||||
\(504\) | 8.96560e47 | − | 4.37595e47i | 0.203624 | − | 0.0993854i | ||||
\(505\) | −7.26523e47 | −0.159223 | ||||||||
\(506\) | 6.32019e45 | + | 4.14378e46i | 0.00133666 | + | 0.00876370i | ||||
\(507\) | − | 1.64394e48i | − | 0.335539i | ||||||
\(508\) | 1.02857e48 | + | 3.29343e48i | 0.202622 | + | 0.648786i | ||||
\(509\) | −9.32459e48 | −1.77300 | −0.886501 | − | 0.462726i | \(-0.846871\pi\) | ||||
−0.886501 | + | 0.462726i | \(0.846871\pi\) | |||||||
\(510\) | −2.84891e47 | + | 4.34522e46i | −0.0522896 | + | 0.00797533i | ||||
\(511\) | − | 1.41906e48i | − | 0.251434i | ||||||
\(512\) | −5.71928e48 | − | 1.21061e48i | −0.978323 | − | 0.207084i | ||||
\(513\) | 5.15696e48 | 0.851689 | ||||||||
\(514\) | 8.69004e47 | + | 5.69755e48i | 0.138575 | + | 0.908556i | ||||
\(515\) | − | 3.25026e48i | − | 0.500482i | ||||||
\(516\) | −2.08221e48 | + | 6.50295e47i | −0.309620 | + | 0.0966976i | ||||
\(517\) | −2.10861e48 | −0.302807 | ||||||||
\(518\) | 2.71315e48 | − | 4.13815e47i | 0.376303 | − | 0.0573946i | ||||
\(519\) | 1.59992e48i | 0.214331i | ||||||||
\(520\) | 2.24436e47 | + | 4.59834e47i | 0.0290424 | + | 0.0595032i | ||||
\(521\) | 1.06132e49 | 1.32669 | 0.663344 | − | 0.748314i | \(-0.269137\pi\) | ||||
0.663344 | + | 0.748314i | \(0.269137\pi\) | |||||||
\(522\) | 6.20725e47 | + | 4.06973e48i | 0.0749602 | + | 0.491470i | ||||
\(523\) | − | 3.03586e47i | − | 0.0354202i | −0.999843 | − | 0.0177101i | \(-0.994362\pi\) | ||
0.999843 | − | 0.0177101i | \(-0.00563759\pi\) | |||||||
\(524\) | 4.02329e48 | + | 1.28824e49i | 0.453543 | + | 1.45222i | ||||
\(525\) | −7.42033e47 | −0.0808268 | ||||||||
\(526\) | 6.06488e47 | − | 9.25030e46i | 0.0638379 | − | 0.00973672i | ||||
\(527\) | − | 4.81757e48i | − | 0.490046i | ||||||
\(528\) | −1.69636e48 | + | 1.17410e48i | −0.166766 | + | 0.115423i | ||||
\(529\) | 1.05221e49 | 0.999766 | ||||||||
\(530\) | 4.13264e47 | + | 2.70953e48i | 0.0379544 | + | 0.248845i | ||||
\(531\) | − | 8.76205e48i | − | 0.777866i | ||||||
\(532\) | 3.72205e48 | − | 1.16243e48i | 0.319428 | − | 0.0997606i | ||||
\(533\) | 2.38474e48 | 0.197857 | ||||||||
\(534\) | −5.76209e48 | + | 8.78848e47i | −0.462208 | + | 0.0704971i | ||||
\(535\) | − | 4.75875e48i | − | 0.369084i | ||||||
\(536\) | 1.65905e49 | − | 8.09754e48i | 1.24421 | − | 0.607277i | ||||
\(537\) | 1.57182e48 | 0.113989 | ||||||||
\(538\) | −2.20564e48 | − | 1.44611e49i | −0.154687 | − | 1.01419i | ||||
\(539\) | 7.97264e48i | 0.540760i | ||||||||
\(540\) | 9.71406e47 | + | 3.11039e48i | 0.0637255 | + | 0.204046i | ||||
\(541\) | −2.03164e49 | −1.28913 | −0.644564 | − | 0.764550i | \(-0.722961\pi\) | ||||
−0.644564 | + | 0.764550i | \(0.722961\pi\) | |||||||
\(542\) | −1.40452e49 | + | 2.14220e48i | −0.862064 | + | 0.131484i | ||||
\(543\) | 2.35738e48i | 0.139969i | ||||||||
\(544\) | −5.55288e48 | − | 5.88016e48i | −0.318961 | − | 0.337761i | ||||
\(545\) | 8.70020e48 | 0.483495 | ||||||||
\(546\) | 5.15973e46 | + | 3.38293e47i | 0.00277434 | + | 0.0181897i | ||||
\(547\) | 1.38426e49i | 0.720187i | 0.932916 | + | 0.360093i | \(0.117255\pi\) | ||||
−0.932916 | + | 0.360093i | \(0.882745\pi\) | |||||||
\(548\) | 1.36996e49 | − | 4.27851e48i | 0.689694 | − | 0.215398i | ||||
\(549\) | −2.29372e49 | −1.11748 | ||||||||
\(550\) | −1.08628e49 | + | 1.65683e48i | −0.512171 | + | 0.0781175i | ||||
\(551\) | 1.60906e49i | 0.734250i | ||||||||
\(552\) | −5.31896e46 | − | 1.08977e47i | −0.00234922 | − | 0.00481316i | ||||
\(553\) | −6.67958e48 | −0.285560 | ||||||||
\(554\) | 1.15098e48 | + | 7.54633e48i | 0.0476315 | + | 0.312292i | ||||
\(555\) | 4.18959e48i | 0.167841i | ||||||||
\(556\) | −6.37634e48 | − | 2.04167e49i | −0.247301 | − | 0.791844i | ||||
\(557\) | −6.90930e48 | −0.259442 | −0.129721 | − | 0.991551i | \(-0.541408\pi\) | ||||
−0.129721 | + | 0.991551i | \(0.541408\pi\) | |||||||
\(558\) | −2.51678e49 | + | 3.83866e48i | −0.915019 | + | 0.139561i | ||||
\(559\) | 5.35831e48i | 0.188632i | ||||||||
\(560\) | 1.40223e48 | + | 2.02597e48i | 0.0478008 | + | 0.0690635i | ||||
\(561\) | −2.85412e48 | −0.0942196 | ||||||||
\(562\) | −7.32895e48 | − | 4.80517e49i | −0.234309 | − | 1.53622i | ||||
\(563\) | 1.68532e49i | 0.521834i | 0.965361 | + | 0.260917i | \(0.0840249\pi\) | ||||
−0.965361 | + | 0.260917i | \(0.915975\pi\) | |||||||
\(564\) | 5.82277e48 | − | 1.81851e48i | 0.174625 | − | 0.0545370i | ||||
\(565\) | −1.44889e48 | −0.0420884 | ||||||||
\(566\) | 1.45634e49 | − | 2.22125e48i | 0.409796 | − | 0.0625030i | ||||
\(567\) | − | 6.13309e48i | − | 0.167180i | ||||||
\(568\) | 5.03446e49 | − | 2.45723e49i | 1.32948 | − | 0.648897i | ||||
\(569\) | 6.09249e49 | 1.55874 | 0.779370 | − | 0.626564i | \(-0.215539\pi\) | ||||
0.779370 | + | 0.626564i | \(0.215539\pi\) | |||||||
\(570\) | 8.97505e47 | + | 5.88441e48i | 0.0222479 | + | 0.145867i | ||||
\(571\) | 1.00419e48i | 0.0241194i | 0.999927 | + | 0.0120597i | \(0.00383882\pi\) | ||||
−0.999927 | + | 0.0120597i | \(0.996161\pi\) | |||||||
\(572\) | 1.51070e48 | + | 4.83717e48i | 0.0351600 | + | 0.112580i | ||||
\(573\) | −5.78893e48 | −0.130561 | ||||||||
\(574\) | 1.13519e49 | − | 1.73142e48i | 0.248117 | − | 0.0378433i | ||||
\(575\) | − | 6.45898e47i | − | 0.0136818i | ||||||
\(576\) | −2.62945e49 | + | 3.36946e49i | −0.539834 | + | 0.691760i | ||||
\(577\) | 4.23848e49 | 0.843423 | 0.421711 | − | 0.906730i | \(-0.361430\pi\) | ||||
0.421711 | + | 0.906730i | \(0.361430\pi\) | |||||||
\(578\) | 6.12996e48 | + | 4.01906e49i | 0.118238 | + | 0.775216i | ||||
\(579\) | − | 1.51867e49i | − | 0.283955i | ||||||
\(580\) | −9.70497e48 | + | 3.03096e48i | −0.175910 | + | 0.0549384i | ||||
\(581\) | −2.68798e49 | −0.472341 | ||||||||
\(582\) | 1.19402e49 | − | 1.82115e48i | 0.203423 | − | 0.0310265i | ||||
\(583\) | 2.71449e49i | 0.448388i | ||||||||
\(584\) | 2.66656e49 | + | 5.46335e49i | 0.427091 | + | 0.875039i | ||||
\(585\) | 3.74091e48 | 0.0580994 | ||||||||
\(586\) | 2.61428e48 | + | 1.71403e49i | 0.0393727 | + | 0.258144i | ||||
\(587\) | − | 6.40630e49i | − | 0.935667i | −0.883817 | − | 0.467833i | \(-0.845035\pi\) | ||
0.883817 | − | 0.467833i | \(-0.154965\pi\) | |||||||
\(588\) | −6.87577e48 | − | 2.20159e49i | −0.0973934 | − | 0.311849i | ||||
\(589\) | −9.95068e49 | −1.36703 | ||||||||
\(590\) | 2.13923e49 | − | 3.26280e48i | 0.285050 | − | 0.0434764i | ||||
\(591\) | − | 4.26063e49i | − | 0.550680i | ||||||
\(592\) | −9.66794e49 | + | 6.69146e49i | −1.21211 | + | 0.838938i | ||||
\(593\) | 8.41910e49 | 1.02396 | 0.511978 | − | 0.858999i | \(-0.328913\pi\) | ||||
0.511978 | + | 0.858999i | \(0.328913\pi\) | |||||||
\(594\) | 4.86592e48 | + | 3.19030e49i | 0.0574129 | + | 0.376423i | ||||
\(595\) | 3.40870e48i | 0.0390196i | ||||||||
\(596\) | −3.24786e49 | + | 1.01434e49i | −0.360715 | + | 0.112655i | ||||
\(597\) | −5.61373e49 | −0.604942 | ||||||||
\(598\) | −2.94465e47 | + | 4.49125e46i | −0.00307902 | + | 0.000469620i | ||||
\(599\) | − | 1.23174e50i | − | 1.24978i | −0.780711 | − | 0.624892i | \(-0.785143\pi\) | ||
0.780711 | − | 0.624892i | \(-0.214857\pi\) | |||||||
\(600\) | 2.85681e49 | − | 1.39436e49i | 0.281293 | − | 0.137294i | ||||
\(601\) | 6.16907e49 | 0.589494 | 0.294747 | − | 0.955575i | \(-0.404765\pi\) | ||||
0.294747 | + | 0.955575i | \(0.404765\pi\) | |||||||
\(602\) | 3.89037e48 | + | 2.55069e49i | 0.0360790 | + | 0.236549i | ||||
\(603\) | − | 1.34970e50i | − | 1.21486i | ||||||
\(604\) | −5.59224e49 | − | 1.79061e50i | −0.488564 | − | 1.56435i | ||||
\(605\) | −2.54803e49 | −0.216077 | ||||||||
\(606\) | 2.05778e49 | − | 3.13858e48i | 0.169392 | − | 0.0258360i | ||||
\(607\) | 1.56513e50i | 1.25071i | 0.780342 | + | 0.625353i | \(0.215045\pi\) | ||||
−0.780342 | + | 0.625353i | \(0.784955\pi\) | |||||||
\(608\) | −1.21455e50 | + | 1.14695e50i | −0.942215 | + | 0.889772i | ||||
\(609\) | −6.79971e48 | −0.0512129 | ||||||||
\(610\) | −8.54131e48 | − | 5.60004e49i | −0.0624579 | − | 0.409500i | ||||
\(611\) | − | 1.49842e49i | − | 0.106388i | ||||||
\(612\) | −5.64407e49 | + | 1.76270e49i | −0.389105 | + | 0.121521i | ||||
\(613\) | −2.39697e50 | −1.60462 | −0.802312 | − | 0.596905i | \(-0.796397\pi\) | ||||
−0.802312 | + | 0.596905i | \(0.796397\pi\) | |||||||
\(614\) | 1.68287e50 | − | 2.56675e49i | 1.09400 | − | 0.166860i | ||||
\(615\) | 1.75294e49i | 0.110666i | ||||||||
\(616\) | 1.07033e49 | + | 2.19293e49i | 0.0656242 | + | 0.134453i | ||||
\(617\) | 2.72430e50 | 1.62227 | 0.811134 | − | 0.584861i | \(-0.198851\pi\) | ||||
0.811134 | + | 0.584861i | \(0.198851\pi\) | |||||||
\(618\) | 1.40411e49 | + | 9.20596e49i | 0.0812101 | + | 0.532447i | ||||
\(619\) | 2.09904e50i | 1.17920i | 0.807695 | + | 0.589601i | \(0.200715\pi\) | ||||
−0.807695 | + | 0.589601i | \(0.799285\pi\) | |||||||
\(620\) | −1.87439e49 | − | 6.00170e49i | −0.102284 | − | 0.327509i | ||||
\(621\) | −1.89693e48 | −0.0100555 | ||||||||
\(622\) | 1.28302e50 | − | 1.95689e49i | 0.660703 | − | 0.100772i | ||||
\(623\) | 6.89431e49i | 0.344910i | ||||||||
\(624\) | −8.34336e48 | − | 1.20546e49i | −0.0405526 | − | 0.0585911i | ||||
\(625\) | 1.46917e50 | 0.693796 | ||||||||
\(626\) | 2.06071e48 | + | 1.35109e49i | 0.00945538 | + | 0.0619934i | ||||
\(627\) | 5.89519e49i | 0.262834i | ||||||||
\(628\) | 1.24391e50 | − | 3.88485e49i | 0.538909 | − | 0.168307i | ||||
\(629\) | −1.62663e50 | −0.684823 | ||||||||
\(630\) | 1.78077e49 | − | 2.71607e48i | 0.0728580 | − | 0.0111125i | ||||
\(631\) | 3.26117e50i | 1.29672i | 0.761336 | + | 0.648358i | \(0.224544\pi\) | ||||
−0.761336 | + | 0.648358i | \(0.775456\pi\) | |||||||
\(632\) | 2.57162e50 | − | 1.25516e50i | 0.993802 | − | 0.485057i | ||||
\(633\) | 6.93352e49 | 0.260428 | ||||||||
\(634\) | −6.91403e49 | − | 4.53312e50i | −0.252420 | − | 1.65497i | ||||
\(635\) | 6.22987e49i | 0.221081i | ||||||||
\(636\) | −2.34104e49 | − | 7.49587e49i | −0.0807569 | − | 0.258579i | ||||
\(637\) | −5.66551e49 | −0.189989 | ||||||||
\(638\) | −9.95431e49 | + | 1.51825e49i | −0.324518 | + | 0.0494963i | ||||
\(639\) | − | 4.09572e50i | − | 1.29812i | ||||||
\(640\) | −9.20556e49 | − | 5.16500e49i | −0.283668 | − | 0.159159i | ||||
\(641\) | 4.77352e49 | 0.143019 | 0.0715095 | − | 0.997440i | \(-0.477218\pi\) | ||||
0.0715095 | + | 0.997440i | \(0.477218\pi\) | |||||||
\(642\) | 2.05578e49 | + | 1.34786e50i | 0.0598889 | + | 0.392657i | ||||
\(643\) | 3.60916e50i | 1.02237i | 0.859470 | + | 0.511186i | \(0.170794\pi\) | ||||
−0.859470 | + | 0.511186i | \(0.829206\pi\) | |||||||
\(644\) | −1.36912e48 | + | 4.27589e47i | −0.00377134 | + | 0.00117783i | ||||
\(645\) | −3.93872e49 | −0.105507 | ||||||||
\(646\) | −2.28466e50 | + | 3.48462e49i | −0.595163 | + | 0.0907757i | ||||
\(647\) | − | 2.90885e50i | − | 0.736962i | −0.929635 | − | 0.368481i | \(-0.879878\pi\) | ||
0.929635 | − | 0.368481i | \(-0.120122\pi\) | |||||||
\(648\) | 1.15247e50 | + | 2.36122e50i | 0.283975 | + | 0.581818i | ||||
\(649\) | 2.14314e50 | 0.513625 | ||||||||
\(650\) | −1.17737e49 | − | 7.71935e49i | −0.0274457 | − | 0.179945i | ||||
\(651\) | − | 4.20504e49i | − | 0.0953482i | ||||||
\(652\) | 2.94273e48 | + | 9.42246e48i | 0.00649073 | + | 0.0207830i | ||||
\(653\) | −7.81253e50 | −1.67631 | −0.838155 | − | 0.545432i | \(-0.816365\pi\) | ||||
−0.838155 | + | 0.545432i | \(0.816365\pi\) | |||||||
\(654\) | −2.46422e50 | + | 3.75849e49i | −0.514375 | + | 0.0784537i | ||||
\(655\) | 2.43684e50i | 0.494861i | ||||||||
\(656\) | −4.04511e50 | + | 2.79974e50i | −0.799211 | + | 0.553157i | ||||
\(657\) | 4.44463e50 | 0.854395 | ||||||||
\(658\) | −1.08792e49 | − | 7.13284e49i | −0.0203484 | − | 0.133412i | ||||
\(659\) | − | 7.80856e50i | − | 1.42113i | −0.703632 | − | 0.710565i | \(-0.748439\pi\) | ||
0.703632 | − | 0.710565i | \(-0.251561\pi\) | |||||||
\(660\) | −3.55565e49 | + | 1.11047e49i | −0.0629692 | + | 0.0196659i | ||||
\(661\) | −7.08006e50 | −1.22014 | −0.610072 | − | 0.792346i | \(-0.708859\pi\) | ||||
−0.610072 | + | 0.792346i | \(0.708859\pi\) | |||||||
\(662\) | −1.02073e51 | + | 1.55683e50i | −1.71185 | + | 0.261095i | ||||
\(663\) | − | 2.02819e49i | − | 0.0331029i | ||||||
\(664\) | 1.03486e51 | − | 5.05099e50i | 1.64383 | − | 0.802326i | ||||
\(665\) | 7.04067e49 | 0.108849 | ||||||||
\(666\) | 1.29611e50 | + | 8.49783e50i | 0.195032 | + | 1.27871i | ||||
\(667\) | − | 5.91877e48i | − | 0.00866894i | ||||||
\(668\) | 2.40931e50 | + | 7.71447e50i | 0.343491 | + | 1.09984i | ||||
\(669\) | 4.05311e50 | 0.562494 | ||||||||
\(670\) | 3.29525e50 | − | 5.02599e49i | 0.445186 | − | 0.0679008i | ||||
\(671\) | − | 5.61029e50i | − | 0.737870i | ||||||
\(672\) | −4.84686e49 | − | 5.13254e49i | −0.0620603 | − | 0.0657181i | ||||
\(673\) | 1.17951e51 | 1.47038 | 0.735190 | − | 0.677861i | \(-0.237093\pi\) | ||||
0.735190 | + | 0.677861i | \(0.237093\pi\) | |||||||
\(674\) | 5.42320e49 | + | 3.55567e50i | 0.0658229 | + | 0.431562i | ||||
\(675\) | − | 4.97277e50i | − | 0.587666i | ||||||
\(676\) | 7.95154e50 | − | 2.48334e50i | 0.914978 | − | 0.285757i | ||||
\(677\) | −3.48039e50 | −0.389971 | −0.194986 | − | 0.980806i | \(-0.562466\pi\) | ||||
−0.194986 | + | 0.980806i | \(0.562466\pi\) | |||||||
\(678\) | 4.10379e49 | − | 6.25919e48i | 0.0447765 | − | 0.00682942i | ||||
\(679\) | − | 1.42864e50i | − | 0.151799i | ||||||
\(680\) | −6.40530e49 | − | 1.31234e50i | −0.0662794 | − | 0.135796i | ||||
\(681\) | 4.31601e50 | 0.434945 | ||||||||
\(682\) | −9.38911e49 | − | 6.15589e50i | −0.0921522 | − | 0.604188i | ||||
\(683\) | − | 1.02243e49i | − | 0.00977376i | −0.999988 | − | 0.00488688i | \(-0.998444\pi\) | ||
0.999988 | − | 0.00488688i | \(-0.00155555\pi\) | |||||||
\(684\) | 3.64085e50 | + | 1.16578e51i | 0.338995 | + | 1.08544i | ||||
\(685\) | 2.59142e50 | 0.235021 | ||||||||
\(686\) | −5.58653e50 | + | 8.52070e49i | −0.493523 | + | 0.0752733i | ||||
\(687\) | − | 1.67684e49i | − | 0.0144301i | ||||||
\(688\) | −6.29079e50 | − | 9.08904e50i | −0.527367 | − | 0.761949i | ||||
\(689\) | −1.92897e50 | −0.157536 | ||||||||
\(690\) | −3.30138e47 | − | 2.16452e48i | −0.000262671 | − | 0.00172218i | ||||
\(691\) | 1.93134e51i | 1.49711i | 0.663072 | + | 0.748556i | \(0.269252\pi\) | ||||
−0.663072 | + | 0.748556i | \(0.730748\pi\) | |||||||
\(692\) | −7.73860e50 | + | 2.41684e50i | −0.584457 | + | 0.182532i | ||||
\(693\) | 1.78403e50 | 0.131281 | ||||||||
\(694\) | 9.80505e50 | − | 1.49549e50i | 0.703039 | − | 0.107229i | ||||
\(695\) | − | 3.86204e50i | − | 0.269830i | ||||||
\(696\) | 2.61787e50 | − | 1.27774e50i | 0.178231 | − | 0.0869911i | ||||
\(697\) | −6.80591e50 | −0.451540 | ||||||||
\(698\) | 7.42947e49 | + | 4.87107e50i | 0.0480353 | + | 0.314939i | ||||
\(699\) | 1.16414e50i | 0.0733527i | ||||||||
\(700\) | −1.12092e50 | − | 3.58912e50i | −0.0688349 | − | 0.220406i | ||||
\(701\) | −1.77887e51 | −1.06468 | −0.532342 | − | 0.846530i | \(-0.678688\pi\) | ||||
−0.532342 | + | 0.846530i | \(0.678688\pi\) | |||||||
\(702\) | −2.26709e50 | + | 3.45782e49i | −0.132252 | + | 0.0201713i | ||||
\(703\) | 3.35981e51i | 1.91038i | ||||||||
\(704\) | −8.24148e50 | − | 6.43146e50i | −0.456770 | − | 0.356453i | ||||
\(705\) | 1.10144e50 | 0.0595054 | ||||||||
\(706\) | −5.19664e50 | − | 3.40713e51i | −0.273677 | − | 1.79434i | ||||
\(707\) | − | 2.46213e50i | − | 0.126404i | ||||||
\(708\) | −5.91813e50 | + | 1.84829e50i | −0.296201 | + | 0.0925064i | ||||
\(709\) | −8.79132e50 | −0.428965 | −0.214483 | − | 0.976728i | \(-0.568807\pi\) | ||||
−0.214483 | + | 0.976728i | \(0.568807\pi\) | |||||||
\(710\) | 9.99955e50 | − | 1.52516e50i | 0.475697 | − | 0.0725544i | ||||
\(711\) | − | 2.09211e51i | − | 0.970356i | ||||||
\(712\) | −1.29551e51 | − | 2.65429e51i | −0.585870 | − | 1.20035i | ||||
\(713\) | 3.66025e49 | 0.0161399 | ||||||||
\(714\) | −1.47256e49 | − | 9.65471e49i | −0.00633147 | − | 0.0415118i | ||||
\(715\) | 9.15003e49i | 0.0383631i | ||||||||
\(716\) | 2.37439e50 | + | 7.60267e50i | 0.0970773 | + | 0.310836i | ||||
\(717\) | −1.03921e51 | −0.414342 | ||||||||
\(718\) | 3.57307e51 | − | 5.44974e50i | 1.38932 | − | 0.211902i | ||||
\(719\) | − | 4.94759e50i | − | 0.187618i | −0.995590 | − | 0.0938088i | \(-0.970096\pi\) | ||
0.995590 | − | 0.0938088i | \(-0.0299042\pi\) | |||||||
\(720\) | −6.34553e50 | + | 4.39192e50i | −0.234684 | + | 0.162431i | ||||
\(721\) | 1.10149e51 | 0.397324 | ||||||||
\(722\) | 2.91189e50 | + | 1.90916e51i | 0.102449 | + | 0.671695i | ||||
\(723\) | 1.63650e50i | 0.0561599i | ||||||||
\(724\) | −1.14024e51 | + | 3.56107e50i | −0.381681 | + | 0.119203i | ||||
\(725\) | 1.55159e51 | 0.506633 | ||||||||
\(726\) | 7.21697e50 | − | 1.10075e50i | 0.229877 | − | 0.0350614i | ||||
\(727\) | 4.79107e51i | 1.48872i | 0.667779 | + | 0.744359i | \(0.267245\pi\) | ||||
−0.667779 | + | 0.744359i | \(0.732755\pi\) | |||||||
\(728\) | −1.55834e50 | + | 7.60596e49i | −0.0472386 | + | 0.0230563i | ||||
\(729\) | 1.14306e51 | 0.338044 | ||||||||
\(730\) | 1.65508e50 | + | 1.08514e51i | 0.0477538 | + | 0.313094i | ||||
\(731\) | − | 1.52923e51i | − | 0.430488i | ||||||
\(732\) | 4.83843e50 | + | 1.54924e51i | 0.132894 | + | 0.425519i | ||||
\(733\) | 1.73318e50 | 0.0464486 | 0.0232243 | − | 0.999730i | \(-0.492607\pi\) | ||||
0.0232243 | + | 0.999730i | \(0.492607\pi\) | |||||||
\(734\) | 5.43661e50 | − | 8.29205e49i | 0.142167 | − | 0.0216837i | ||||
\(735\) | − | 4.16454e50i | − | 0.106266i | ||||||
\(736\) | 4.46759e49 | − | 4.21892e49i | 0.0111243 | − | 0.0105051i | ||||
\(737\) | 3.30128e51 | 0.802172 | ||||||||
\(738\) | 5.42298e50 | + | 3.55553e51i | 0.128595 | + | 0.843121i | ||||
\(739\) | 2.48623e51i | 0.575363i | 0.957726 | + | 0.287682i | \(0.0928845\pi\) | ||||
−0.957726 | + | 0.287682i | \(0.907115\pi\) | |||||||
\(740\) | −2.02645e51 | + | 6.32881e50i | −0.457683 | + | 0.142939i | ||||
\(741\) | −4.18923e50 | −0.0923436 | ||||||||
\(742\) | −9.18237e50 | + | 1.40052e50i | −0.197553 | + | 0.0301313i | ||||
\(743\) | − | 8.27336e51i | − | 1.73733i | −0.495396 | − | 0.868667i | \(-0.664977\pi\) | ||
0.495396 | − | 0.868667i | \(-0.335023\pi\) | |||||||
\(744\) | 7.90171e50 | + | 1.61893e51i | 0.161960 | + | 0.331830i | ||||
\(745\) | −6.14367e50 | −0.122918 | ||||||||
\(746\) | 2.11847e50 | + | 1.38896e51i | 0.0413737 | + | 0.271263i | ||||
\(747\) | − | 8.41900e51i | − | 1.60505i | ||||||
\(748\) | −4.31145e50 | − | 1.38050e51i | −0.0802406 | − | 0.256926i | ||||
\(749\) | 1.61270e51 | 0.293009 | ||||||||
\(750\) | 1.20199e51 | − | 1.83330e50i | 0.213205 | − | 0.0325185i | ||||
\(751\) | 9.42693e50i | 0.163249i | 0.996663 | + | 0.0816247i | \(0.0260109\pi\) | ||||
−0.996663 | + | 0.0816247i | \(0.973989\pi\) | |||||||
\(752\) | 1.75918e51 | + | 2.54169e51i | 0.297433 | + | 0.429736i | ||||
\(753\) | −7.24923e50 | −0.119669 | ||||||||
\(754\) | −1.07890e50 | − | 7.07373e50i | −0.0173899 | − | 0.114016i | ||||
\(755\) | − | 3.38713e51i | − | 0.533072i | ||||||
\(756\) | −1.05409e51 | + | 3.29202e50i | −0.161988 | + | 0.0505906i | ||||
\(757\) | −2.71850e51 | −0.407947 | −0.203974 | − | 0.978976i | \(-0.565386\pi\) | ||||
−0.203974 | + | 0.978976i | \(0.565386\pi\) | |||||||
\(758\) | −9.57201e50 | + | 1.45995e50i | −0.140268 | + | 0.0213939i | ||||
\(759\) | − | 2.16848e49i | − | 0.00310316i | ||||||
\(760\) | −2.71064e51 | + | 1.32301e51i | −0.378815 | + | 0.184893i | ||||
\(761\) | −4.38319e51 | −0.598227 | −0.299114 | − | 0.954218i | \(-0.596691\pi\) | ||||
−0.299114 | + | 0.954218i | \(0.596691\pi\) | |||||||
\(762\) | −2.69131e50 | − | 1.76453e51i | −0.0358735 | − | 0.235202i | ||||
\(763\) | 2.94843e51i | 0.383838i | ||||||||
\(764\) | −8.74478e50 | − | 2.80003e51i | −0.111191 | − | 0.356027i | ||||
\(765\) | −1.06764e51 | −0.132592 | ||||||||
\(766\) | −1.04554e52 | + | 1.59468e51i | −1.26830 | + | 0.193444i | ||||
\(767\) | 1.52296e51i | 0.180456i | ||||||||
\(768\) | 2.83049e51 | + | 1.06524e51i | 0.327612 | + | 0.123295i | ||||
\(769\) | −1.54036e52 | −1.74160 | −0.870802 | − | 0.491634i | \(-0.836400\pi\) | ||||
−0.870802 | + | 0.491634i | \(0.836400\pi\) | |||||||
\(770\) | 6.64333e49 | + | 4.35564e50i | 0.00733757 | + | 0.0481082i | ||||
\(771\) | − | 2.98159e51i | − | 0.321713i | ||||||
\(772\) | 7.34561e51 | − | 2.29411e51i | 0.774313 | − | 0.241826i | ||||
\(773\) | 1.47512e52 | 1.51914 | 0.759568 | − | 0.650428i | \(-0.225410\pi\) | ||||
0.759568 | + | 0.650428i | \(0.225410\pi\) | |||||||
\(774\) | −7.98899e51 | + | 1.21850e51i | −0.803812 | + | 0.122599i | ||||
\(775\) | 9.59528e51i | 0.943251i | ||||||||
\(776\) | 2.68457e51 | + | 5.50024e51i | 0.257848 | + | 0.528288i | ||||
\(777\) | −1.41982e51 | −0.133246 | ||||||||
\(778\) | −1.69817e51 | − | 1.11339e52i | −0.155722 | − | 1.02098i | ||||
\(779\) | 1.40576e52i | 1.25961i | ||||||||
\(780\) | −7.89118e49 | − | 2.52671e50i | −0.00690938 | − | 0.0221235i | ||||
\(781\) | 1.00179e52 | 0.857149 | ||||||||
\(782\) | 8.40388e49 | − | 1.28178e49i | 0.00702681 | − | 0.00107175i | ||||
\(783\) | − | 4.55687e51i | − | 0.372353i | ||||||
\(784\) | 9.61013e51 | − | 6.65145e51i | 0.767433 | − | 0.531162i | ||||
\(785\) | 2.35299e51 | 0.183640 | ||||||||
\(786\) | −1.05272e51 | − | 6.90204e51i | −0.0802981 | − | 0.526468i | ||||
\(787\) | 9.48013e51i | 0.706755i | 0.935481 | + | 0.353378i | \(0.114967\pi\) | ||||
−0.935481 | + | 0.353378i | \(0.885033\pi\) | |||||||
\(788\) | 2.06081e52 | − | 6.43613e51i | 1.50164 | − | 0.468978i | ||||
\(789\) | −3.17381e50 | −0.0226045 | ||||||||
\(790\) | 5.10781e51 | − | 7.79055e50i | 0.355588 | − | 0.0542351i | ||||
\(791\) | − | 4.91016e50i | − | 0.0334133i | ||||||
\(792\) | −6.86846e51 | + | 3.35237e51i | −0.456884 | + | 0.222997i | ||||
\(793\) | 3.98678e51 | 0.259242 | ||||||||
\(794\) | 1.60717e51 | + | 1.05373e52i | 0.102163 | + | 0.669821i | ||||
\(795\) | − | 1.41793e51i | − | 0.0881140i | ||||||
\(796\) | −8.48013e51 | − | 2.71529e52i | −0.515190 | − | 1.64961i | ||||
\(797\) | 1.29143e52 | 0.767045 | 0.383522 | − | 0.923532i | \(-0.374711\pi\) | ||||
0.383522 | + | 0.923532i | \(0.374711\pi\) | |||||||
\(798\) | −1.99418e51 | + | 3.04157e50i | −0.115801 | + | 0.0176622i | ||||
\(799\) | 4.27641e51i | 0.242793i | ||||||||
\(800\) | 1.10598e52 | + | 1.17117e52i | 0.613944 | + | 0.650129i | ||||
\(801\) | −2.15936e52 | −1.17203 | ||||||||
\(802\) | −1.19838e51 | − | 7.85705e51i | −0.0635996 | − | 0.416985i | ||||
\(803\) | 1.08713e52i | 0.564158i | ||||||||
\(804\) | −9.11625e51 | + | 2.84709e51i | −0.462602 | + | 0.144475i | ||||
\(805\) | −2.58984e49 | −0.00128513 | ||||||||
\(806\) | 4.37450e51 | − | 6.67209e50i | 0.212274 | − | 0.0323766i | ||||
\(807\) | 7.56765e51i | 0.359118i | ||||||||
\(808\) | 4.62659e51 | + | 9.47912e51i | 0.214712 | + | 0.439910i | ||||
\(809\) | −5.78633e51 | −0.262621 | −0.131310 | − | 0.991341i | \(-0.541918\pi\) | ||||
−0.131310 | + | 0.991341i | \(0.541918\pi\) | |||||||
\(810\) | 7.15317e50 | + | 4.68991e51i | 0.0317518 | + | 0.208178i | ||||
\(811\) | − | 1.48645e52i | − | 0.645320i | −0.946515 | − | 0.322660i | \(-0.895423\pi\) | ||
0.946515 | − | 0.322660i | \(-0.104577\pi\) | |||||||
\(812\) | −1.02717e51 | − | 3.28893e51i | −0.0436147 | − | 0.139652i | ||||
\(813\) | 7.34997e51 | 0.305250 | ||||||||
\(814\) | −2.07851e52 | + | 3.17020e51i | −0.844333 | + | 0.128780i | ||||
\(815\) | 1.78236e50i | 0.00708205i | ||||||||
\(816\) | 2.38115e51 | + | 3.44033e51i | 0.0925473 | + | 0.133714i | ||||
\(817\) | −3.15863e52 | −1.20089 | ||||||||
\(818\) | 1.03544e51 | + | 6.78877e51i | 0.0385093 | + | 0.252483i | ||||
\(819\) | 1.26776e51i | 0.0461241i | ||||||||
\(820\) | −8.47877e51 | + | 2.64800e51i | −0.301775 | + | 0.0942474i | ||||
\(821\) | −8.33480e51 | −0.290214 | −0.145107 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145107 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(822\) | −7.33986e51 | + | 1.11949e51i | −0.250032 | + | 0.0381354i | ||||
\(823\) | − | 4.87866e52i | − | 1.62594i | −0.582307 | − | 0.812969i | \(-0.697850\pi\) | ||
0.582307 | − | 0.812969i | \(-0.302150\pi\) | |||||||
\(824\) | −4.24070e52 | + | 2.06981e52i | −1.38276 | + | 0.674901i | ||||
\(825\) | 5.68464e51 | 0.181356 | ||||||||
\(826\) | 1.10574e51 | + | 7.24966e51i | 0.0345152 | + | 0.226296i | ||||
\(827\) | − | 4.32795e52i | − | 1.32185i | −0.750451 | − | 0.660926i | \(-0.770164\pi\) | ||
0.750451 | − | 0.660926i | \(-0.229836\pi\) | |||||||
\(828\) | −1.33925e50 | − | 4.28821e50i | −0.00400235 | − | 0.0128153i | ||||
\(829\) | 2.32097e52 | 0.678715 | 0.339358 | − | 0.940657i | \(-0.389790\pi\) | ||||
0.339358 | + | 0.940657i | \(0.389790\pi\) | |||||||
\(830\) | 2.05547e52 | − | 3.13505e51i | 0.588173 | − | 0.0897096i | ||||
\(831\) | − | 3.94907e51i | − | 0.110580i | ||||||
\(832\) | 4.57032e51 | − | 5.85655e51i | 0.125235 | − | 0.160481i | ||||
\(833\) | 1.61691e52 | 0.433586 | ||||||||
\(834\) | 1.66840e51 | + | 1.09387e52i | 0.0437836 | + | 0.287064i | ||||
\(835\) | 1.45928e52i | 0.374784i | ||||||||
\(836\) | −2.85143e52 | + | 8.90529e51i | −0.716720 | + | 0.223839i | ||||
\(837\) | 2.81803e52 | 0.693247 | ||||||||
\(838\) | 5.34909e52 | − | 8.15857e51i | 1.28792 | − | 0.196436i | ||||
\(839\) | − | 1.45030e52i | − | 0.341778i | −0.985290 | − | 0.170889i | \(-0.945336\pi\) | ||
0.985290 | − | 0.170889i | \(-0.0546639\pi\) | |||||||
\(840\) | −5.59090e50 | − | 1.14548e51i | −0.0128960 | − | 0.0264218i | ||||
\(841\) | −3.00740e52 | −0.678991 | ||||||||
\(842\) | 1.45616e51 | + | 9.54722e51i | 0.0321805 | + | 0.210989i | ||||
\(843\) | 2.51459e52i | 0.543965i | ||||||||
\(844\) | 1.04738e52 | + | 3.35366e52i | 0.221789 | + | 0.710157i | ||||
\(845\) | 1.50412e52 | 0.311790 | ||||||||
\(846\) | 2.23407e52 | − | 3.40746e51i | 0.453347 | − | 0.0691455i | ||||
\(847\) | − | 8.63506e51i | − | 0.171539i | ||||||
\(848\) | 3.27202e52 | − | 2.26466e52i | 0.636342 | − | 0.440430i | ||||
\(849\) | −7.62119e51 | −0.145106 | ||||||||
\(850\) | 3.36016e51 | + | 2.20306e52i | 0.0626353 | + | 0.410663i | ||||
\(851\) | − | 1.23587e51i | − | 0.0225549i | ||||||
\(852\) | −2.76636e52 | + | 8.63962e51i | −0.494306 | + | 0.154377i | ||||
\(853\) | 9.95728e52 | 1.74204 | 0.871020 | − | 0.491247i | \(-0.163459\pi\) | ||||
0.871020 | + | 0.491247i | \(0.163459\pi\) | |||||||
\(854\) | 1.89781e52 | − | 2.89458e51i | 0.325095 | − | 0.0495842i | ||||
\(855\) | 2.20520e52i | 0.369878i | ||||||||
\(856\) | −6.20886e52 | + | 3.03043e52i | −1.01973 | + | 0.497711i | ||||
\(857\) | −1.15586e53 | −1.85887 | −0.929436 | − | 0.368983i | \(-0.879706\pi\) | ||||
−0.929436 | + | 0.368983i | \(0.879706\pi\) | |||||||
\(858\) | −3.95281e50 | − | 2.59163e51i | −0.00622494 | − | 0.0408133i | ||||
\(859\) | 1.27482e52i | 0.196595i | 0.995157 | + | 0.0982977i | \(0.0313397\pi\) | ||||
−0.995157 | + | 0.0982977i | \(0.968660\pi\) | |||||||
\(860\) | −5.94985e51 | − | 1.90511e52i | −0.0898533 | − | 0.287705i | ||||
\(861\) | −5.94058e51 | −0.0878562 | ||||||||
\(862\) | 3.45496e52 | − | 5.26959e51i | 0.500394 | − | 0.0763213i | ||||
\(863\) | 1.07169e53i | 1.52011i | 0.649860 | + | 0.760054i | \(0.274827\pi\) | ||||
−0.649860 | + | 0.760054i | \(0.725173\pi\) | |||||||
\(864\) | 3.43960e52 | − | 3.24815e52i | 0.477816 | − | 0.451221i | ||||
\(865\) | −1.46384e52 | −0.199161 | ||||||||
\(866\) | −9.19524e51 | − | 6.02878e52i | −0.122530 | − | 0.803355i | ||||
\(867\) | − | 2.10321e52i | − | 0.274498i | ||||||
\(868\) | 2.03393e52 | − | 6.35215e51i | 0.260004 | − | 0.0812019i | ||||
\(869\) | 5.11716e52 | 0.640727 | ||||||||
\(870\) | 5.19967e51 | − | 7.93066e50i | 0.0637719 | − | 0.00972664i | ||||
\(871\) | 2.34595e52i | 0.281834i | ||||||||
\(872\) | −5.54039e52 | − | 1.13514e53i | −0.651994 | − | 1.33583i | ||||
\(873\) | 4.47464e52 | 0.515825 | ||||||||
\(874\) | −2.64751e50 | − | 1.73582e51i | −0.00298973 | − | 0.0196019i | ||||
\(875\) | − | 1.43817e52i | − | 0.159098i | ||||||
\(876\) | −9.37562e51 | − | 3.00202e52i | −0.101608 | − | 0.325342i | ||||
\(877\) | −7.34833e52 | −0.780182 | −0.390091 | − | 0.920776i | \(-0.627557\pi\) | ||||
−0.390091 | + | 0.920776i | \(0.627557\pi\) | |||||||
\(878\) | −3.99608e52 | + | 6.09492e51i | −0.415655 | + | 0.0633967i | ||||
\(879\) | − | 8.96969e51i | − | 0.0914066i | ||||||
\(880\) | −1.07424e52 | − | 1.55208e52i | −0.107254 | − | 0.154962i | ||||
\(881\) | −1.24738e53 | −1.22020 | −0.610100 | − | 0.792325i | \(-0.708871\pi\) | ||||
−0.610100 | + | 0.792325i | \(0.708871\pi\) | |||||||
\(882\) | −1.28836e52 | − | 8.44702e52i | −0.123482 | − | 0.809597i | ||||
\(883\) | 7.42343e51i | 0.0697128i | 0.999392 | + | 0.0348564i | \(0.0110974\pi\) | ||||
−0.999392 | + | 0.0348564i | \(0.988903\pi\) | |||||||
\(884\) | 9.81012e51 | − | 3.06380e51i | 0.0902680 | − | 0.0281916i | ||||
\(885\) | −1.11948e52 | −0.100934 | ||||||||
\(886\) | −1.35826e53 | + | 2.07165e52i | −1.19999 | + | 0.183025i | ||||
\(887\) | 2.59315e52i | 0.224493i | 0.993680 | + | 0.112247i | \(0.0358046\pi\) | ||||
−0.993680 | + | 0.112247i | \(0.964195\pi\) | |||||||
\(888\) | 5.46626e52 | − | 2.66798e52i | 0.463721 | − | 0.226334i | ||||
\(889\) | −2.11125e52 | −0.175513 | ||||||||
\(890\) | −8.04100e51 | − | 5.27201e52i | −0.0655073 | − | 0.429493i | ||||
\(891\) | 4.69850e52i | 0.375112i | ||||||||
\(892\) | 6.12264e52 | + | 1.96044e53i | 0.479040 | + | 1.53386i | ||||
\(893\) | 8.83291e52 | 0.677295 | ||||||||
\(894\) | 1.74012e52 | − | 2.65407e51i | 0.130769 | − | 0.0199451i | ||||
\(895\) | 1.43813e52i | 0.105921i | ||||||||
\(896\) | 1.75037e52 | − | 3.11969e52i | 0.126353 | − | 0.225199i | ||||
\(897\) | 1.54097e50 | 0.00109026 | ||||||||
\(898\) | 2.54141e52 | + | 1.66625e53i | 0.176238 | + | 1.15549i | ||||
\(899\) | 8.79276e52i | 0.597655i | ||||||||
\(900\) | 1.12414e53 | − | 3.51082e52i | 0.748957 | − | 0.233907i | ||||
\(901\) | 5.50518e52 | 0.359522 | ||||||||
\(902\) | −8.69660e52 | + | 1.32643e52i | −0.556714 | + | 0.0849113i | ||||
\(903\) | − | 1.33480e52i | − | 0.0837600i | ||||||
\(904\) | 9.22669e51 | + | 1.89040e52i | 0.0567563 | + | 0.116284i | ||||
\(905\) | −2.15688e52 | −0.130062 | ||||||||
\(906\) | 1.46324e52 | + | 9.59360e52i | 0.0864983 | + | 0.567119i | ||||
\(907\) | − | 2.36432e53i | − | 1.37017i | −0.728463 | − | 0.685085i | \(-0.759765\pi\) | ||
0.728463 | − | 0.685085i | \(-0.240235\pi\) | |||||||
\(908\) | 6.51978e52 | + | 2.08760e53i | 0.370414 | + | 1.18605i | ||||
\(909\) | 7.71161e52 | 0.429532 | ||||||||
\(910\) | −3.09520e51 | + | 4.72088e50i | −0.0169022 | + | 0.00257797i | ||||
\(911\) | − | 1.98515e53i | − | 1.06282i | −0.847113 | − | 0.531412i | \(-0.821662\pi\) | ||
0.847113 | − | 0.531412i | \(-0.178338\pi\) | |||||||
\(912\) | 7.10600e52 | − | 4.91826e52i | 0.373008 | − | 0.258169i | ||||
\(913\) | 2.05923e53 | 1.05982 | ||||||||
\(914\) | −3.62891e52 | − | 2.37926e53i | −0.183124 | − | 1.20063i | ||||
\(915\) | 2.93056e52i | 0.145001i | ||||||||
\(916\) | 8.11067e51 | − | 2.53304e51i | 0.0393494 | − | 0.0122892i | ||||
\(917\) | −8.25825e52 | −0.392862 | ||||||||
\(918\) | 6.47016e52 | − | 9.86844e51i | 0.301819 | − | 0.0460341i | ||||
\(919\) | − | 3.05673e53i | − | 1.39823i | −0.715010 | − | 0.699114i | \(-0.753578\pi\) | ||
0.715010 | − | 0.699114i | \(-0.246422\pi\) | |||||||
\(920\) | 9.97080e50 | − | 4.86657e50i | 0.00447249 | − | 0.00218294i | ||||
\(921\) | −8.80661e52 | −0.387378 | ||||||||
\(922\) | 3.69584e52 | + | 2.42315e53i | 0.159425 | + | 1.04526i | ||||
\(923\) | 7.11889e52i | 0.301149i | ||||||||
\(924\) | −3.76327e51 | − | 1.20498e52i | −0.0156124 | − | 0.0499902i | ||||
\(925\) | 3.23981e53 | 1.31816 | ||||||||
\(926\) | −2.94231e53 | + | 4.48767e52i | −1.17406 | + | 0.179070i | ||||
\(927\) | 3.44996e53i | 1.35014i | ||||||||
\(928\) | 1.01348e53 | + | 1.07322e53i | 0.389002 | + | 0.411930i | ||||
\(929\) | −6.70608e52 | −0.252456 | −0.126228 | − | 0.992001i | \(-0.540287\pi\) | ||||
−0.126228 | + | 0.992001i | \(0.540287\pi\) | |||||||
\(930\) | 4.90444e51 | + | 3.21555e52i | 0.0181091 | + | 0.118731i | ||||
\(931\) | − | 3.33972e53i | − | 1.20953i | ||||||
\(932\) | −5.63080e52 | + | 1.75855e52i | −0.200025 | + | 0.0624697i | ||||
\(933\) | −6.71417e52 | −0.233950 | ||||||||
\(934\) | −2.70995e53 | + | 4.13329e52i | −0.926228 | + | 0.141271i | ||||
\(935\) | − | 2.61137e52i | − | 0.0875507i | ||||||
\(936\) | −2.38226e52 | − | 4.88086e52i | −0.0783472 | − | 0.160521i | ||||
\(937\) | −1.81223e53 | −0.584657 | −0.292328 | − | 0.956318i | \(-0.594430\pi\) | ||||
−0.292328 | + | 0.956318i | \(0.594430\pi\) | |||||||
\(938\) | 1.70327e52 | + | 1.11673e53i | 0.0539053 | + | 0.353426i | ||||
\(939\) | − | 7.07038e51i | − | 0.0219514i | ||||||
\(940\) | 1.66384e52 | + | 5.32752e52i | 0.0506769 | + | 0.162265i | ||||
\(941\) | −6.50888e53 | −1.94488 | −0.972441 | − | 0.233149i | \(-0.925097\pi\) | ||||
−0.972441 | + | 0.233149i | \(0.925097\pi\) | |||||||
\(942\) | −6.66454e52 | + | 1.01649e52i | −0.195368 | + | 0.0297980i | ||||
\(943\) | − | 5.17094e51i | − | 0.0148717i | ||||||
\(944\) | −1.78799e53 | − | 2.58332e53i | −0.504509 | − | 0.728924i | ||||
\(945\) | −1.99392e52 | −0.0551994 | ||||||||
\(946\) | −2.98037e52 | − | 1.95406e53i | −0.0809524 | − | 0.530758i | ||||
\(947\) | 3.30949e53i | 0.881986i | 0.897511 | + | 0.440993i | \(0.145374\pi\) | ||||
−0.897511 | + | 0.440993i | \(0.854626\pi\) | |||||||
\(948\) | −1.41307e53 | + | 4.41315e52i | −0.369498 | + | 0.115398i | ||||
\(949\) | −7.72534e52 | −0.198210 | ||||||||
\(950\) | 4.55042e53 | − | 6.94041e52i | 1.14558 | − | 0.174727i | ||||
\(951\) | 2.37223e53i | 0.586013i | ||||||||
\(952\) | 4.44741e52 | − | 2.17070e52i | 0.107806 | − | 0.0526181i | ||||
\(953\) | 5.37052e53 | 1.27745 | 0.638726 | − | 0.769434i | \(-0.279462\pi\) | ||||
0.638726 | + | 0.769434i | \(0.279462\pi\) | |||||||
\(954\) | −4.38655e52 | − | 2.87601e53i | −0.102389 | − | 0.671304i | ||||
\(955\) | − | 5.29656e52i | − | 0.121320i | ||||||
\(956\) | −1.56984e53 | − | 5.02653e53i | −0.352868 | − | 1.12986i | ||||
\(957\) | 5.20919e52 | 0.114909 | ||||||||
\(958\) | 6.88293e53 | − | 1.04980e53i | 1.49003 | − | 0.227262i | ||||
\(959\) | 8.78210e52i | 0.186579i | ||||||||
\(960\) | 4.30497e52 | + | 3.35950e52i | 0.0897610 | + | 0.0700475i | ||||
\(961\) | −5.50815e52 | −0.112716 | ||||||||
\(962\) | −2.25280e52 | − | 1.47703e53i | −0.0452452 | − | 0.296646i | ||||
\(963\) | 5.05113e53i | 0.995670i | ||||||||
\(964\) | −7.91554e52 | + | 2.47210e52i | −0.153142 | + | 0.0478277i | ||||
\(965\) | 1.38950e53 | 0.263856 | ||||||||
\(966\) | 7.33538e50 | − | 1.11881e50i | 0.00136721 | − | 0.000208530i | ||||
\(967\) | − | 3.34104e53i | − | 0.611230i | −0.952155 | − | 0.305615i | \(-0.901138\pi\) | ||
0.952155 | − | 0.305615i | \(-0.0988621\pi\) | |||||||
\(968\) | 1.62262e53 | + | 3.32448e53i | 0.291380 | + | 0.596989i | ||||
\(969\) | 1.19559e53 | 0.210743 | ||||||||
\(970\) | 1.66626e52 | + | 1.09247e53i | 0.0288305 | + | 0.189024i | ||||
\(971\) | 6.83065e53i | 1.16016i | 0.814561 | + | 0.580078i | \(0.196978\pi\) | ||||
−0.814561 | + | 0.580078i | \(0.803022\pi\) | |||||||
\(972\) | −1.58028e53 | − | 5.05998e53i | −0.263476 | − | 0.843637i | ||||
\(973\) | 1.30881e53 | 0.214213 | ||||||||
\(974\) | 7.89372e53 | − | 1.20397e53i | 1.26829 | − | 0.193443i | ||||
\(975\) | 4.03961e52i | 0.0637172i | ||||||||
\(976\) | −6.76258e53 | + | 4.68058e53i | −1.04717 | + | 0.724774i | ||||
\(977\) | 6.41085e53 | 0.974571 | 0.487285 | − | 0.873243i | \(-0.337987\pi\) | ||||
0.487285 | + | 0.873243i | \(0.337987\pi\) | |||||||
\(978\) | −7.69980e50 | − | 5.04831e51i | −0.00114916 | − | 0.00753437i | ||||
\(979\) | − | 5.28166e53i | − | 0.773895i | ||||||
\(980\) | 2.01433e53 | − | 6.29097e52i | 0.289776 | − | 0.0904999i | ||||
\(981\) | −9.23474e53 | −1.30432 | ||||||||
\(982\) | −2.73616e53 | + | 4.17326e52i | −0.379433 | + | 0.0578720i | ||||
\(983\) | 1.20736e54i | 1.64390i | 0.569561 | + | 0.821949i | \(0.307113\pi\) | ||||
−0.569561 | + | 0.821949i | \(0.692887\pi\) | |||||||
\(984\) | 2.28711e53 | − | 1.11630e53i | 0.305756 | − | 0.149234i | ||||
\(985\) | 3.89825e53 | 0.511703 | ||||||||
\(986\) | 3.07913e52 | + | 2.01880e53i | 0.0396865 | + | 0.260201i | ||||
\(987\) | 3.73269e52i | 0.0472403i | ||||||||
\(988\) | −6.32827e52 | − | 2.02628e53i | −0.0786430 | − | 0.251811i | ||||
\(989\) | 1.16187e52 | 0.0141783 | ||||||||
\(990\) | −1.36423e53 | + | 2.08075e52i | −0.163476 | + | 0.0249337i | ||||
\(991\) | − | 9.10869e53i | − | 1.07184i | −0.844269 | − | 0.535920i | \(-0.819965\pi\) | ||
0.844269 | − | 0.535920i | \(-0.180035\pi\) | |||||||
\(992\) | −6.63693e53 | + | 6.26752e53i | −0.766932 | + | 0.724245i | ||||
\(993\) | 5.34156e53 | 0.606152 | ||||||||
\(994\) | 5.16863e52 | + | 3.38877e53i | 0.0575997 | + | 0.377648i | ||||
\(995\) | − | 5.13627e53i | − | 0.562124i | ||||||
\(996\) | −5.68642e53 | + | 1.77593e53i | −0.611182 | + | 0.190878i | ||||
\(997\) | −1.52141e54 | −1.60596 | −0.802979 | − | 0.596008i | \(-0.796753\pi\) | ||||
−0.802979 | + | 0.596008i | \(0.796753\pi\) | |||||||
\(998\) | 1.04068e54 | − | 1.58727e53i | 1.07887 | − | 0.164552i | ||||
\(999\) | − | 9.51498e53i | − | 0.968789i |
(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 | 4.37.b.b.3.7 | ✓ | 16 | |
4.3 | odd | 2 | inner | 4.37.b.b.3.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.37.b.b.3.7 | ✓ | 16 | 1.1 | even | 1 | trivial | |
4.37.b.b.3.8 | yes | 16 | 4.3 | odd | 2 | inner |