Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,10,Mod(49,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.49");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.b (of order \(2\), degree \(1\), not 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: | \(38.6276877123\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.49 |
Dual form | 75.10.b.b.49.1 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.0000i | 0.972272i | 0.873883 | + | 0.486136i | \(0.161594\pi\) | ||||
−0.873883 | + | 0.486136i | \(0.838406\pi\) | |||||||
\(3\) | 81.0000i | 0.577350i | ||||||||
\(4\) | 28.0000 | 0.0546875 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1782.00 | −0.561341 | ||||||||
\(7\) | − 5988.00i | − 0.942629i | −0.881965 | − | 0.471314i | \(-0.843780\pi\) | ||||
0.881965 | − | 0.471314i | \(-0.156220\pi\) | |||||||
\(8\) | 11880.0i | 1.02544i | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14648.0 | −0.301655 | −0.150828 | − | 0.988560i | \(-0.548194\pi\) | ||||
−0.150828 | + | 0.988560i | \(0.548194\pi\) | |||||||
\(12\) | 2268.00i | 0.0315738i | ||||||||
\(13\) | − 37906.0i | − 0.368098i | −0.982917 | − | 0.184049i | \(-0.941080\pi\) | ||||
0.982917 | − | 0.184049i | \(-0.0589204\pi\) | |||||||
\(14\) | 131736. | 0.916491 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −247024. | −0.942322 | ||||||||
\(17\) | − 441098.i | − 1.28090i | −0.768000 | − | 0.640450i | \(-0.778748\pi\) | ||||
0.768000 | − | 0.640450i | \(-0.221252\pi\) | |||||||
\(18\) | − 144342.i | − 0.324091i | ||||||||
\(19\) | −441820. | −0.777775 | −0.388888 | − | 0.921285i | \(-0.627141\pi\) | ||||
−0.388888 | + | 0.921285i | \(0.627141\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 485028. | 0.544227 | ||||||||
\(22\) | − 322256.i | − 0.293291i | ||||||||
\(23\) | − 2.26414e6i | − 1.68705i | −0.537092 | − | 0.843524i | \(-0.680477\pi\) | ||||
0.537092 | − | 0.843524i | \(-0.319523\pi\) | |||||||
\(24\) | −962280. | −0.592040 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 833932. | 0.357891 | ||||||||
\(27\) | − 531441.i | − 0.192450i | ||||||||
\(28\) | − 167664.i | − 0.0515500i | ||||||||
\(29\) | 1.04935e6 | 0.275505 | 0.137752 | − | 0.990467i | \(-0.456012\pi\) | ||||
0.137752 | + | 0.990467i | \(0.456012\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.91057e6 | −1.53844 | −0.769219 | − | 0.638985i | \(-0.779355\pi\) | ||||
−0.769219 | + | 0.638985i | \(0.779355\pi\) | |||||||
\(32\) | 648032.i | 0.109250i | ||||||||
\(33\) | − 1.18649e6i | − 0.174161i | ||||||||
\(34\) | 9.70416e6 | 1.24538 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −183708. | −0.0182292 | ||||||||
\(37\) | − 2.09926e7i | − 1.84144i | −0.390224 | − | 0.920720i | \(-0.627602\pi\) | ||||
0.390224 | − | 0.920720i | \(-0.372398\pi\) | |||||||
\(38\) | − 9.72004e6i | − 0.756209i | ||||||||
\(39\) | 3.07039e6 | 0.212521 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.32856e7 | 0.734265 | 0.367132 | − | 0.930169i | \(-0.380340\pi\) | ||||
0.367132 | + | 0.930169i | \(0.380340\pi\) | |||||||
\(42\) | 1.06706e7i | 0.529136i | ||||||||
\(43\) | 2.31308e7i | 1.03177i | 0.856659 | + | 0.515884i | \(0.172536\pi\) | ||||
−0.856659 | + | 0.515884i | \(0.827464\pi\) | |||||||
\(44\) | −410144. | −0.0164968 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.98110e7 | 1.64027 | ||||||||
\(47\) | − 1.38737e7i | − 0.414717i | −0.978265 | − | 0.207358i | \(-0.933513\pi\) | ||||
0.978265 | − | 0.207358i | \(-0.0664866\pi\) | |||||||
\(48\) | − 2.00089e7i | − 0.544050i | ||||||||
\(49\) | 4.49746e6 | 0.111451 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.57289e7 | 0.739527 | ||||||||
\(52\) | − 1.06137e6i | − 0.0201303i | ||||||||
\(53\) | 5.76352e7i | 1.00334i | 0.865060 | + | 0.501668i | \(0.167280\pi\) | ||||
−0.865060 | + | 0.501668i | \(0.832720\pi\) | |||||||
\(54\) | 1.16917e7 | 0.187114 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.11374e7 | 0.966612 | ||||||||
\(57\) | − 3.57874e7i | − 0.449049i | ||||||||
\(58\) | 2.30857e7i | 0.267866i | ||||||||
\(59\) | 3.20421e7 | 0.344260 | 0.172130 | − | 0.985074i | \(-0.444935\pi\) | ||||
0.172130 | + | 0.985074i | \(0.444935\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.10664e8 | 1.02335 | 0.511673 | − | 0.859180i | \(-0.329026\pi\) | ||||
0.511673 | + | 0.859180i | \(0.329026\pi\) | |||||||
\(62\) | − 1.74032e8i | − 1.49578i | ||||||||
\(63\) | 3.92873e7i | 0.314210i | ||||||||
\(64\) | −1.40733e8 | −1.04854 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.61027e7 | 0.169332 | ||||||||
\(67\) | − 1.18568e8i | − 0.718839i | −0.933176 | − | 0.359420i | \(-0.882975\pi\) | ||||
0.933176 | − | 0.359420i | \(-0.117025\pi\) | |||||||
\(68\) | − 1.23507e7i | − 0.0700492i | ||||||||
\(69\) | 1.83395e8 | 0.974017 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.76680e8 | 1.29216 | 0.646078 | − | 0.763272i | \(-0.276408\pi\) | ||||
0.646078 | + | 0.763272i | \(0.276408\pi\) | |||||||
\(72\) | − 7.79447e7i | − 0.341814i | ||||||||
\(73\) | 2.64023e8i | 1.08815i | 0.839036 | + | 0.544076i | \(0.183120\pi\) | ||||
−0.839036 | + | 0.544076i | \(0.816880\pi\) | |||||||
\(74\) | 4.61836e8 | 1.79038 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.23710e7 | −0.0425346 | ||||||||
\(77\) | 8.77122e7i | 0.284349i | ||||||||
\(78\) | 6.75485e7i | 0.206628i | ||||||||
\(79\) | −4.48203e8 | −1.29465 | −0.647325 | − | 0.762214i | \(-0.724112\pi\) | ||||
−0.647325 | + | 0.762214i | \(0.724112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | 2.92282e8i | 0.713905i | ||||||||
\(83\) | − 8.51016e8i | − 1.96828i | −0.177402 | − | 0.984138i | \(-0.556769\pi\) | ||||
0.177402 | − | 0.984138i | \(-0.443231\pi\) | |||||||
\(84\) | 1.35808e7 | 0.0297624 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.08877e8 | −1.00316 | ||||||||
\(87\) | 8.49974e7i | 0.159063i | ||||||||
\(88\) | − 1.74018e8i | − 0.309331i | ||||||||
\(89\) | −1.89895e8 | −0.320818 | −0.160409 | − | 0.987051i | \(-0.551281\pi\) | ||||
−0.160409 | + | 0.987051i | \(0.551281\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.26981e8 | −0.346979 | ||||||||
\(92\) | − 6.33958e7i | − 0.0922604i | ||||||||
\(93\) | − 6.40756e8i | − 0.888218i | ||||||||
\(94\) | 3.05221e8 | 0.403217 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.24906e7 | −0.0630755 | ||||||||
\(97\) | − 1.01415e9i | − 1.16313i | −0.813499 | − | 0.581566i | \(-0.802440\pi\) | ||||
0.813499 | − | 0.581566i | \(-0.197560\pi\) | |||||||
\(98\) | 9.89442e7i | 0.108361i | ||||||||
\(99\) | 9.61055e7 | 0.100552 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.31537e9 | −1.25777 | −0.628885 | − | 0.777498i | \(-0.716488\pi\) | ||||
−0.628885 | + | 0.777498i | \(0.716488\pi\) | |||||||
\(102\) | 7.86037e8i | 0.719022i | ||||||||
\(103\) | 1.82797e9i | 1.60030i | 0.599798 | + | 0.800151i | \(0.295248\pi\) | ||||
−0.599798 | + | 0.800151i | \(0.704752\pi\) | |||||||
\(104\) | 4.50323e8 | 0.377463 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.26797e9 | −0.975515 | ||||||||
\(107\) | 1.85367e8i | 0.136712i | 0.997661 | + | 0.0683559i | \(0.0217754\pi\) | ||||
−0.997661 | + | 0.0683559i | \(0.978225\pi\) | |||||||
\(108\) | − 1.48803e7i | − 0.0105246i | ||||||||
\(109\) | −1.97869e9 | −1.34264 | −0.671318 | − | 0.741169i | \(-0.734272\pi\) | ||||
−0.671318 | + | 0.741169i | \(0.734272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.70040e9 | 1.06316 | ||||||||
\(112\) | 1.47918e9i | 0.888259i | ||||||||
\(113\) | − 1.57875e9i | − 0.910876i | −0.890267 | − | 0.455438i | \(-0.849483\pi\) | ||||
0.890267 | − | 0.455438i | \(-0.150517\pi\) | |||||||
\(114\) | 7.87323e8 | 0.436597 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.93818e7 | 0.0150667 | ||||||||
\(117\) | 2.48701e8i | 0.122699i | ||||||||
\(118\) | 7.04927e8i | 0.334715i | ||||||||
\(119\) | −2.64129e9 | −1.20741 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.14338e9 | −0.909004 | ||||||||
\(122\) | 2.43461e9i | 0.994970i | ||||||||
\(123\) | 1.07613e9i | 0.423928i | ||||||||
\(124\) | −2.21496e8 | −0.0841333 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.64320e8 | −0.305497 | ||||||||
\(127\) | 2.40001e9i | 0.818645i | 0.912390 | + | 0.409322i | \(0.134235\pi\) | ||||
−0.912390 | + | 0.409322i | \(0.865765\pi\) | |||||||
\(128\) | − 2.76433e9i | − 0.910218i | ||||||||
\(129\) | −1.87359e9 | −0.595691 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.96840e9 | −0.583971 | −0.291986 | − | 0.956423i | \(-0.594316\pi\) | ||||
−0.291986 | + | 0.956423i | \(0.594316\pi\) | |||||||
\(132\) | − 3.32217e7i | − 0.00952442i | ||||||||
\(133\) | 2.64562e9i | 0.733153i | ||||||||
\(134\) | 2.60850e9 | 0.698907 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.24024e9 | 1.31349 | ||||||||
\(137\) | − 2.02909e9i | − 0.492107i | −0.969256 | − | 0.246054i | \(-0.920866\pi\) | ||||
0.969256 | − | 0.246054i | \(-0.0791339\pi\) | |||||||
\(138\) | 4.03469e9i | 0.947009i | ||||||||
\(139\) | 1.13673e9 | 0.258280 | 0.129140 | − | 0.991626i | \(-0.458778\pi\) | ||||
0.129140 | + | 0.991626i | \(0.458778\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.12377e9 | 0.239437 | ||||||||
\(142\) | 6.08695e9i | 1.25633i | ||||||||
\(143\) | 5.55247e8i | 0.111039i | ||||||||
\(144\) | 1.62072e9 | 0.314107 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −5.80851e9 | −1.05798 | ||||||||
\(147\) | 3.64295e8i | 0.0643465i | ||||||||
\(148\) | − 5.87792e8i | − 0.100704i | ||||||||
\(149\) | 4.73854e9 | 0.787601 | 0.393800 | − | 0.919196i | \(-0.371160\pi\) | ||||
0.393800 | + | 0.919196i | \(0.371160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.26216e9 | 0.354101 | 0.177051 | − | 0.984202i | \(-0.443344\pi\) | ||||
0.177051 | + | 0.984202i | \(0.443344\pi\) | |||||||
\(152\) | − 5.24882e9i | − 0.797564i | ||||||||
\(153\) | 2.89404e9i | 0.426966i | ||||||||
\(154\) | −1.92967e9 | −0.276465 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.59708e7 | 0.0116223 | ||||||||
\(157\) | − 1.17889e10i | − 1.54854i | −0.632853 | − | 0.774272i | \(-0.718116\pi\) | ||||
0.632853 | − | 0.774272i | \(-0.281884\pi\) | |||||||
\(158\) | − 9.86046e9i | − 1.25875i | ||||||||
\(159\) | −4.66845e9 | −0.579276 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.35576e10 | −1.59026 | ||||||||
\(162\) | 9.47028e8i | 0.108030i | ||||||||
\(163\) | − 1.14608e10i | − 1.27166i | −0.771830 | − | 0.635829i | \(-0.780658\pi\) | ||||
0.771830 | − | 0.635829i | \(-0.219342\pi\) | |||||||
\(164\) | 3.71996e8 | 0.0401551 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.87223e10 | 1.91370 | ||||||||
\(167\) | − 1.33707e10i | − 1.33024i | −0.746738 | − | 0.665118i | \(-0.768381\pi\) | ||||
0.746738 | − | 0.665118i | \(-0.231619\pi\) | |||||||
\(168\) | 5.76213e9i | 0.558074i | ||||||||
\(169\) | 9.16763e9 | 0.864504 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.89878e9 | 0.259258 | ||||||||
\(172\) | 6.47661e8i | 0.0564248i | ||||||||
\(173\) | − 1.06264e10i | − 0.901939i | −0.892539 | − | 0.450970i | \(-0.851078\pi\) | ||||
0.892539 | − | 0.450970i | \(-0.148922\pi\) | |||||||
\(174\) | −1.86994e9 | −0.154652 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.61841e9 | 0.284257 | ||||||||
\(177\) | 2.59541e9i | 0.198759i | ||||||||
\(178\) | − 4.17769e9i | − 0.311922i | ||||||||
\(179\) | −2.61254e10 | −1.90206 | −0.951031 | − | 0.309094i | \(-0.899974\pi\) | ||||
−0.951031 | + | 0.309094i | \(0.899974\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34689e9 | 0.162532 | 0.0812660 | − | 0.996692i | \(-0.474104\pi\) | ||||
0.0812660 | + | 0.996692i | \(0.474104\pi\) | |||||||
\(182\) | − 4.99358e9i | − 0.337358i | ||||||||
\(183\) | 8.96379e9i | 0.590829i | ||||||||
\(184\) | 2.68979e10 | 1.72997 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.40966e10 | 0.863589 | ||||||||
\(187\) | 6.46120e9i | 0.386390i | ||||||||
\(188\) | − 3.88463e8i | − 0.0226798i | ||||||||
\(189\) | −3.18227e9 | −0.181409 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.24064e10 | 1.21821 | 0.609105 | − | 0.793089i | \(-0.291529\pi\) | ||||
0.609105 | + | 0.793089i | \(0.291529\pi\) | |||||||
\(192\) | − 1.13994e10i | − 0.605376i | ||||||||
\(193\) | 3.65959e10i | 1.89856i | 0.314427 | + | 0.949282i | \(0.398188\pi\) | ||||
−0.314427 | + | 0.949282i | \(0.601812\pi\) | |||||||
\(194\) | 2.23113e10 | 1.13088 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.25929e8 | 0.00609499 | ||||||||
\(197\) | − 5.41546e9i | − 0.256175i | −0.991763 | − | 0.128088i | \(-0.959116\pi\) | ||||
0.991763 | − | 0.128088i | \(-0.0408839\pi\) | |||||||
\(198\) | 2.11432e9i | 0.0977637i | ||||||||
\(199\) | −2.62714e8 | −0.0118753 | −0.00593764 | − | 0.999982i | \(-0.501890\pi\) | ||||
−0.00593764 | + | 0.999982i | \(0.501890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.60403e9 | 0.415022 | ||||||||
\(202\) | − 2.89381e10i | − 1.22289i | ||||||||
\(203\) | − 6.28351e9i | − 0.259699i | ||||||||
\(204\) | 1.00041e9 | 0.0404429 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.02154e10 | −1.55593 | ||||||||
\(207\) | 1.48550e10i | 0.562349i | ||||||||
\(208\) | 9.36369e9i | 0.346866i | ||||||||
\(209\) | 6.47178e9 | 0.234620 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.34493e10 | 0.467121 | 0.233560 | − | 0.972342i | \(-0.424962\pi\) | ||||
0.233560 | + | 0.972342i | \(0.424962\pi\) | |||||||
\(212\) | 1.61378e9i | 0.0548699i | ||||||||
\(213\) | 2.24111e10i | 0.746026i | ||||||||
\(214\) | −4.07808e9 | −0.132921 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 6.31352e9 | 0.197347 | ||||||||
\(217\) | 4.73685e10i | 1.45018i | ||||||||
\(218\) | − 4.35312e10i | − 1.30541i | ||||||||
\(219\) | −2.13859e10 | −0.628245 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.67203e10 | −0.471496 | ||||||||
\(222\) | 3.74087e10i | 1.03368i | ||||||||
\(223\) | 2.66463e10i | 0.721547i | 0.932654 | + | 0.360773i | \(0.117487\pi\) | ||||
−0.932654 | + | 0.360773i | \(0.882513\pi\) | |||||||
\(224\) | 3.88042e9 | 0.102982 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.47324e10 | 0.885619 | ||||||||
\(227\) | 3.36318e10i | 0.840686i | 0.907365 | + | 0.420343i | \(0.138090\pi\) | ||||
−0.907365 | + | 0.420343i | \(0.861910\pi\) | |||||||
\(228\) | − 1.00205e9i | − 0.0245574i | ||||||||
\(229\) | −5.00453e10 | −1.20255 | −0.601276 | − | 0.799042i | \(-0.705341\pi\) | ||||
−0.601276 | + | 0.799042i | \(0.705341\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.10469e9 | −0.164169 | ||||||||
\(232\) | 1.24663e10i | 0.282515i | ||||||||
\(233\) | 3.29626e10i | 0.732688i | 0.930479 | + | 0.366344i | \(0.119391\pi\) | ||||
−0.930479 | + | 0.366344i | \(0.880609\pi\) | |||||||
\(234\) | −5.47143e9 | −0.119297 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.97179e8 | 0.0188267 | ||||||||
\(237\) | − 3.63044e10i | − 0.747467i | ||||||||
\(238\) | − 5.81085e10i | − 1.17393i | ||||||||
\(239\) | 7.95422e9 | 0.157691 | 0.0788455 | − | 0.996887i | \(-0.474877\pi\) | ||||
0.0788455 | + | 0.996887i | \(0.474877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.52477e10 | −1.43687 | −0.718434 | − | 0.695595i | \(-0.755141\pi\) | ||||
−0.718434 | + | 0.695595i | \(0.755141\pi\) | |||||||
\(242\) | − 4.71544e10i | − 0.883799i | ||||||||
\(243\) | 3.48678e9i | 0.0641500i | ||||||||
\(244\) | 3.09859e9 | 0.0559642 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.36749e10 | −0.412173 | ||||||||
\(247\) | 1.67476e10i | 0.286297i | ||||||||
\(248\) | − 9.39775e10i | − 1.57758i | ||||||||
\(249\) | 6.89323e10 | 1.13639 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.84631e10 | −1.56582 | −0.782910 | − | 0.622135i | \(-0.786266\pi\) | ||||
−0.782910 | + | 0.622135i | \(0.786266\pi\) | |||||||
\(252\) | 1.10004e9i | 0.0171833i | ||||||||
\(253\) | 3.31651e10i | 0.508907i | ||||||||
\(254\) | −5.28001e10 | −0.795945 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.12400e10 | −0.163563 | ||||||||
\(257\) | 8.52399e9i | 0.121883i | 0.998141 | + | 0.0609416i | \(0.0194103\pi\) | ||||
−0.998141 | + | 0.0609416i | \(0.980590\pi\) | |||||||
\(258\) | − 4.12190e10i | − 0.579174i | ||||||||
\(259\) | −1.25703e11 | −1.73579 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.88479e9 | −0.0918350 | ||||||||
\(262\) | − 4.33047e10i | − 0.567779i | ||||||||
\(263\) | − 5.90654e9i | − 0.0761259i | −0.999275 | − | 0.0380630i | \(-0.987881\pi\) | ||||
0.999275 | − | 0.0380630i | \(-0.0121187\pi\) | |||||||
\(264\) | 1.40955e10 | 0.178592 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −5.82036e10 | −0.712824 | ||||||||
\(267\) | − 1.53815e10i | − 0.185224i | ||||||||
\(268\) | − 3.31991e9i | − 0.0393115i | ||||||||
\(269\) | 7.15961e10 | 0.833689 | 0.416845 | − | 0.908978i | \(-0.363136\pi\) | ||||
0.416845 | + | 0.908978i | \(0.363136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.24755e11 | −1.40506 | −0.702530 | − | 0.711654i | \(-0.747946\pi\) | ||||
−0.702530 | + | 0.711654i | \(0.747946\pi\) | |||||||
\(272\) | 1.08962e11i | 1.20702i | ||||||||
\(273\) | − 1.83855e10i | − 0.200329i | ||||||||
\(274\) | 4.46401e10 | 0.478462 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.13506e9 | 0.0532666 | ||||||||
\(277\) | 1.12824e11i | 1.15145i | 0.817645 | + | 0.575723i | \(0.195279\pi\) | ||||
−0.817645 | + | 0.575723i | \(0.804721\pi\) | |||||||
\(278\) | 2.50080e10i | 0.251118i | ||||||||
\(279\) | 5.19012e10 | 0.512813 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.70208e10 | 0.832616 | 0.416308 | − | 0.909224i | \(-0.363324\pi\) | ||||
0.416308 | + | 0.909224i | \(0.363324\pi\) | |||||||
\(282\) | 2.47229e10i | 0.232798i | ||||||||
\(283\) | − 3.27696e9i | − 0.0303692i | −0.999885 | − | 0.0151846i | \(-0.995166\pi\) | ||||
0.999885 | − | 0.0151846i | \(-0.00483359\pi\) | |||||||
\(284\) | 7.74703e9 | 0.0706647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.22154e10 | −0.107960 | ||||||||
\(287\) | − 7.95539e10i | − 0.692139i | ||||||||
\(288\) | − 4.25174e9i | − 0.0364167i | ||||||||
\(289\) | −7.59796e10 | −0.640703 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.21461e10 | 0.671535 | ||||||||
\(292\) | 7.39265e9i | 0.0595083i | ||||||||
\(293\) | 1.49860e11i | 1.18791i | 0.804500 | + | 0.593953i | \(0.202433\pi\) | ||||
−0.804500 | + | 0.593953i | \(0.797567\pi\) | |||||||
\(294\) | −8.01448e9 | −0.0625622 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.49392e11 | 1.88829 | ||||||||
\(297\) | 7.78455e9i | 0.0580536i | ||||||||
\(298\) | 1.04248e11i | 0.765762i | ||||||||
\(299\) | −8.58243e10 | −0.620998 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.38507e11 | 0.972574 | ||||||||
\(302\) | 4.97676e10i | 0.344283i | ||||||||
\(303\) | − 1.06545e11i | − 0.726174i | ||||||||
\(304\) | 1.09140e11 | 0.732915 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.36690e10 | −0.415127 | ||||||||
\(307\) | − 1.84570e11i | − 1.18587i | −0.805249 | − | 0.592937i | \(-0.797968\pi\) | ||||
0.805249 | − | 0.592937i | \(-0.202032\pi\) | |||||||
\(308\) | 2.45594e9i | 0.0155503i | ||||||||
\(309\) | −1.48066e11 | −0.923935 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.04650e10 | 0.548351 | 0.274176 | − | 0.961680i | \(-0.411595\pi\) | ||||
0.274176 | + | 0.961680i | \(0.411595\pi\) | |||||||
\(312\) | 3.64762e10i | 0.217928i | ||||||||
\(313\) | − 1.07930e10i | − 0.0635615i | −0.999495 | − | 0.0317808i | \(-0.989882\pi\) | ||||
0.999495 | − | 0.0317808i | \(-0.0101178\pi\) | |||||||
\(314\) | 2.59355e11 | 1.50560 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.25497e10 | −0.0708012 | ||||||||
\(317\) | 4.18319e10i | 0.232670i | 0.993210 | + | 0.116335i | \(0.0371147\pi\) | ||||
−0.993210 | + | 0.116335i | \(0.962885\pi\) | |||||||
\(318\) | − 1.02706e11i | − 0.563214i | ||||||||
\(319\) | −1.53709e10 | −0.0831076 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.50148e10 | −0.0789306 | ||||||||
\(322\) | − 2.98268e11i | − 1.54616i | ||||||||
\(323\) | 1.94886e11i | 0.996252i | ||||||||
\(324\) | 1.20531e9 | 0.00607639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.52137e11 | 1.23640 | ||||||||
\(327\) | − 1.60274e11i | − 0.775172i | ||||||||
\(328\) | 1.57832e11i | 0.752946i | ||||||||
\(329\) | −8.30756e10 | −0.390924 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.23310e10 | −0.0564640 | −0.0282320 | − | 0.999601i | \(-0.508988\pi\) | ||||
−0.0282320 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(332\) | − 2.38284e10i | − 0.107640i | ||||||||
\(333\) | 1.37732e11i | 0.613813i | ||||||||
\(334\) | 2.94154e11 | 1.29335 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.19814e11 | −0.512837 | ||||||||
\(337\) | − 2.17976e10i | − 0.0920606i | −0.998940 | − | 0.0460303i | \(-0.985343\pi\) | ||||
0.998940 | − | 0.0460303i | \(-0.0146571\pi\) | |||||||
\(338\) | 2.01688e11i | 0.840533i | ||||||||
\(339\) | 1.27878e11 | 0.525895 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.15874e11 | 0.464078 | ||||||||
\(342\) | 6.37732e10i | 0.252070i | ||||||||
\(343\) | − 2.68568e11i | − 1.04769i | ||||||||
\(344\) | −2.74793e11 | −1.05802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.33780e11 | 0.876930 | ||||||||
\(347\) | − 8.43613e10i | − 0.312364i | −0.987728 | − | 0.156182i | \(-0.950081\pi\) | ||||
0.987728 | − | 0.156182i | \(-0.0499186\pi\) | |||||||
\(348\) | 2.37993e9i | 0.00869875i | ||||||||
\(349\) | 1.23295e9 | 0.00444867 | 0.00222434 | − | 0.999998i | \(-0.499292\pi\) | ||||
0.00222434 | + | 0.999998i | \(0.499292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.01448e10 | −0.0708404 | ||||||||
\(352\) | − 9.49237e9i | − 0.0329559i | ||||||||
\(353\) | − 1.73388e11i | − 0.594336i | −0.954825 | − | 0.297168i | \(-0.903958\pi\) | ||||
0.954825 | − | 0.297168i | \(-0.0960422\pi\) | |||||||
\(354\) | −5.70991e10 | −0.193248 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −5.31706e9 | −0.0175447 | ||||||||
\(357\) | − 2.13945e11i | − 0.697100i | ||||||||
\(358\) | − 5.74760e11i | − 1.84932i | ||||||||
\(359\) | −6.38159e10 | −0.202770 | −0.101385 | − | 0.994847i | \(-0.532327\pi\) | ||||
−0.101385 | + | 0.994847i | \(0.532327\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.27483e11 | −0.395066 | ||||||||
\(362\) | 5.16316e10i | 0.158025i | ||||||||
\(363\) | − 1.73614e11i | − 0.524814i | ||||||||
\(364\) | −6.35547e9 | −0.0189754 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.97203e11 | −0.574446 | ||||||||
\(367\) | 1.12242e11i | 0.322966i | 0.986876 | + | 0.161483i | \(0.0516277\pi\) | ||||
−0.986876 | + | 0.161483i | \(0.948372\pi\) | |||||||
\(368\) | 5.59296e11i | 1.58974i | ||||||||
\(369\) | −8.71666e10 | −0.244755 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.45119e11 | 0.945773 | ||||||||
\(372\) | − 1.79412e10i | − 0.0485744i | ||||||||
\(373\) | − 7.21004e11i | − 1.92863i | −0.264766 | − | 0.964313i | \(-0.585295\pi\) | ||||
0.264766 | − | 0.964313i | \(-0.414705\pi\) | |||||||
\(374\) | −1.42146e11 | −0.375676 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.64819e11 | 0.425268 | ||||||||
\(377\) | − 3.97767e10i | − 0.101413i | ||||||||
\(378\) | − 7.00099e10i | − 0.176379i | ||||||||
\(379\) | 2.04331e11 | 0.508695 | 0.254348 | − | 0.967113i | \(-0.418139\pi\) | ||||
0.254348 | + | 0.967113i | \(0.418139\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.94400e11 | −0.472645 | ||||||||
\(382\) | 4.92941e11i | 1.18443i | ||||||||
\(383\) | 5.47180e11i | 1.29938i | 0.760200 | + | 0.649689i | \(0.225101\pi\) | ||||
−0.760200 | + | 0.649689i | \(0.774899\pi\) | |||||||
\(384\) | 2.23911e11 | 0.525515 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.05111e11 | −1.84592 | ||||||||
\(387\) | − 1.51761e11i | − 0.343923i | ||||||||
\(388\) | − 2.83962e10i | − 0.0636088i | ||||||||
\(389\) | 3.46262e11 | 0.766711 | 0.383356 | − | 0.923601i | \(-0.374768\pi\) | ||||
0.383356 | + | 0.923601i | \(0.374768\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.98706e11 | −2.16094 | ||||||||
\(392\) | 5.34299e10i | 0.114287i | ||||||||
\(393\) | − 1.59440e11i | − 0.337156i | ||||||||
\(394\) | 1.19140e11 | 0.249072 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.69095e9 | 0.00549893 | ||||||||
\(397\) | 2.56758e11i | 0.518760i | 0.965775 | + | 0.259380i | \(0.0835181\pi\) | ||||
−0.965775 | + | 0.259380i | \(0.916482\pi\) | |||||||
\(398\) | − 5.77971e9i | − 0.0115460i | ||||||||
\(399\) | −2.14295e11 | −0.423286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.01679e10 | 0.0389504 | 0.0194752 | − | 0.999810i | \(-0.493800\pi\) | ||||
0.0194752 | + | 0.999810i | \(0.493800\pi\) | |||||||
\(402\) | 2.11289e11i | 0.403514i | ||||||||
\(403\) | 2.99858e11i | 0.566295i | ||||||||
\(404\) | −3.68303e10 | −0.0687843 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.38237e11 | 0.252498 | ||||||||
\(407\) | 3.07499e11i | 0.555481i | ||||||||
\(408\) | 4.24460e11i | 0.758343i | ||||||||
\(409\) | 4.33405e10 | 0.0765842 | 0.0382921 | − | 0.999267i | \(-0.487808\pi\) | ||||
0.0382921 | + | 0.999267i | \(0.487808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.64357e11 | 0.284118 | ||||||||
\(412\) | 5.11832e10i | 0.0875166i | ||||||||
\(413\) | − 1.91868e11i | − 0.324510i | ||||||||
\(414\) | −3.26810e11 | −0.546756 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.45643e10 | 0.0402147 | ||||||||
\(417\) | 9.20751e10i | 0.149118i | ||||||||
\(418\) | 1.42379e11i | 0.228115i | ||||||||
\(419\) | −5.10680e11 | −0.809443 | −0.404721 | − | 0.914440i | \(-0.632631\pi\) | ||||
−0.404721 | + | 0.914440i | \(0.632631\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.21228e11 | 0.498361 | 0.249181 | − | 0.968457i | \(-0.419839\pi\) | ||||
0.249181 | + | 0.968457i | \(0.419839\pi\) | |||||||
\(422\) | 2.95885e11i | 0.454168i | ||||||||
\(423\) | 9.10253e10i | 0.138239i | ||||||||
\(424\) | −6.84706e11 | −1.02886 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.93043e11 | −0.725340 | ||||||||
\(427\) | − 6.62656e11i | − 0.964635i | ||||||||
\(428\) | 5.19029e9i | 0.00747643i | ||||||||
\(429\) | −4.49750e10 | −0.0641082 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.47617e11 | 0.624826 | 0.312413 | − | 0.949946i | \(-0.398863\pi\) | ||||
0.312413 | + | 0.949946i | \(0.398863\pi\) | |||||||
\(432\) | 1.31279e11i | 0.181350i | ||||||||
\(433\) | 1.41186e11i | 0.193017i | 0.995332 | + | 0.0965085i | \(0.0307675\pi\) | ||||
−0.995332 | + | 0.0965085i | \(0.969233\pi\) | |||||||
\(434\) | −1.04211e12 | −1.40997 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.54033e10 | −0.0734254 | ||||||||
\(437\) | 1.00034e12i | 1.31214i | ||||||||
\(438\) | − 4.70490e11i | − 0.610824i | ||||||||
\(439\) | 8.50498e11 | 1.09291 | 0.546453 | − | 0.837490i | \(-0.315978\pi\) | ||||
0.546453 | + | 0.837490i | \(0.315978\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.95079e10 | −0.0371504 | ||||||||
\(442\) | − 3.67846e11i | − 0.458422i | ||||||||
\(443\) | − 3.03188e11i | − 0.374020i | −0.982358 | − | 0.187010i | \(-0.940120\pi\) | ||||
0.982358 | − | 0.187010i | \(-0.0598797\pi\) | |||||||
\(444\) | 4.76111e10 | 0.0581413 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.86218e11 | −0.701540 | ||||||||
\(447\) | 3.83822e11i | 0.454721i | ||||||||
\(448\) | 8.42709e11i | 0.988386i | ||||||||
\(449\) | 1.40328e12 | 1.62943 | 0.814714 | − | 0.579863i | \(-0.196894\pi\) | ||||
0.814714 | + | 0.579863i | \(0.196894\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.94607e11 | −0.221495 | ||||||||
\(452\) | − 4.42049e10i | − 0.0498136i | ||||||||
\(453\) | 1.83235e11i | 0.204440i | ||||||||
\(454\) | −7.39899e11 | −0.817375 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.25155e11 | 0.460474 | ||||||||
\(457\) | 3.35354e11i | 0.359650i | 0.983699 | + | 0.179825i | \(0.0575531\pi\) | ||||
−0.983699 | + | 0.179825i | \(0.942447\pi\) | |||||||
\(458\) | − 1.10100e12i | − 1.16921i | ||||||||
\(459\) | −2.34418e11 | −0.246509 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.04275e12 | 1.07529 | 0.537645 | − | 0.843171i | \(-0.319314\pi\) | ||||
0.537645 | + | 0.843171i | \(0.319314\pi\) | |||||||
\(462\) | − 1.56303e11i | − 0.159617i | ||||||||
\(463\) | 9.74084e11i | 0.985103i | 0.870283 | + | 0.492552i | \(0.163936\pi\) | ||||
−0.870283 | + | 0.492552i | \(0.836064\pi\) | |||||||
\(464\) | −2.59215e11 | −0.259614 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.25176e11 | −0.712372 | ||||||||
\(467\) | − 1.97851e11i | − 0.192492i | −0.995358 | − | 0.0962458i | \(-0.969317\pi\) | ||||
0.995358 | − | 0.0962458i | \(-0.0306835\pi\) | |||||||
\(468\) | 6.96364e9i | 0.00671011i | ||||||||
\(469\) | −7.09987e11 | −0.677599 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.54898e11 | 0.894052 | ||||||||
\(472\) | 3.80660e11i | 0.353019i | ||||||||
\(473\) | − 3.38819e11i | − 0.311238i | ||||||||
\(474\) | 7.98697e11 | 0.726741 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.39563e10 | −0.0660304 | ||||||||
\(477\) | − 3.78144e11i | − 0.334445i | ||||||||
\(478\) | 1.74993e11i | 0.153319i | ||||||||
\(479\) | 9.08731e11 | 0.788725 | 0.394362 | − | 0.918955i | \(-0.370965\pi\) | ||||
0.394362 | + | 0.918955i | \(0.370965\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.95744e11 | −0.677830 | ||||||||
\(482\) | − 1.65545e12i | − 1.39703i | ||||||||
\(483\) | − 1.09817e12i | − 0.918136i | ||||||||
\(484\) | −6.00147e10 | −0.0497112 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.67093e10 | −0.0623713 | ||||||||
\(487\) | 1.16963e12i | 0.942254i | 0.882065 | + | 0.471127i | \(0.156153\pi\) | ||||
−0.882065 | + | 0.471127i | \(0.843847\pi\) | |||||||
\(488\) | 1.31469e12i | 1.04938i | ||||||||
\(489\) | 9.28324e11 | 0.734192 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.49149e12 | −1.93460 | −0.967301 | − | 0.253630i | \(-0.918375\pi\) | ||||
−0.967301 | + | 0.253630i | \(0.918375\pi\) | |||||||
\(492\) | 3.01317e10i | 0.0231836i | ||||||||
\(493\) | − 4.62866e11i | − 0.352894i | ||||||||
\(494\) | −3.68448e11 | −0.278359 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.95410e12 | 1.44970 | ||||||||
\(497\) | − 1.65676e12i | − 1.21802i | ||||||||
\(498\) | 1.51651e12i | 1.10488i | ||||||||
\(499\) | 5.57571e11 | 0.402576 | 0.201288 | − | 0.979532i | \(-0.435487\pi\) | ||||
0.201288 | + | 0.979532i | \(0.435487\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.08302e12 | 0.768012 | ||||||||
\(502\) | − 2.16619e12i | − 1.52240i | ||||||||
\(503\) | − 1.80137e12i | − 1.25472i | −0.778730 | − | 0.627359i | \(-0.784136\pi\) | ||||
0.778730 | − | 0.627359i | \(-0.215864\pi\) | |||||||
\(504\) | −4.66733e11 | −0.322204 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.29631e11 | −0.494796 | ||||||||
\(507\) | 7.42578e11i | 0.499122i | ||||||||
\(508\) | 6.72001e10i | 0.0447696i | ||||||||
\(509\) | 2.40110e12 | 1.58555 | 0.792774 | − | 0.609515i | \(-0.208636\pi\) | ||||
0.792774 | + | 0.609515i | \(0.208636\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.58097e12 | 1.02572 | ||||||||
\(512\) | − 1.66262e12i | − 1.06925i | ||||||||
\(513\) | 2.34801e11i | 0.149683i | ||||||||
\(514\) | −1.87528e11 | −0.118504 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.24606e10 | −0.0325769 | ||||||||
\(517\) | 2.03222e11i | 0.125102i | ||||||||
\(518\) | − 2.76548e12i | − 1.68766i | ||||||||
\(519\) | 8.60735e11 | 0.520735 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.03008e12 | 0.612491 | 0.306246 | − | 0.951953i | \(-0.400927\pi\) | ||||
0.306246 | + | 0.951953i | \(0.400927\pi\) | |||||||
\(522\) | − 1.51465e11i | − 0.0892886i | ||||||||
\(523\) | − 1.06637e12i | − 0.623232i | −0.950208 | − | 0.311616i | \(-0.899130\pi\) | ||||
0.950208 | − | 0.311616i | \(-0.100870\pi\) | |||||||
\(524\) | −5.51151e10 | −0.0319359 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.29944e11 | 0.0740151 | ||||||||
\(527\) | 3.48934e12i | 1.97058i | ||||||||
\(528\) | 2.93091e11i | 0.164116i | ||||||||
\(529\) | −3.32516e12 | −1.84613 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.10228e11 | −0.114753 | ||||||||
\(532\) | 7.40773e10i | 0.0400943i | ||||||||
\(533\) | − 5.03603e11i | − 0.270281i | ||||||||
\(534\) | 3.38393e11 | 0.180088 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.40859e12 | 0.737129 | ||||||||
\(537\) | − 2.11616e12i | − 1.09816i | ||||||||
\(538\) | 1.57511e12i | 0.810572i | ||||||||
\(539\) | −6.58788e10 | −0.0336199 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.51749e12 | 1.26351 | 0.631756 | − | 0.775167i | \(-0.282334\pi\) | ||||
0.631756 | + | 0.775167i | \(0.282334\pi\) | |||||||
\(542\) | − 2.74460e12i | − 1.36610i | ||||||||
\(543\) | 1.90098e11i | 0.0938379i | ||||||||
\(544\) | 2.85846e11 | 0.139938 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.04480e11 | 0.194774 | ||||||||
\(547\) | − 1.10353e12i | − 0.527037i | −0.964654 | − | 0.263518i | \(-0.915117\pi\) | ||||
0.964654 | − | 0.263518i | \(-0.0848830\pi\) | |||||||
\(548\) | − 5.68146e10i | − 0.0269121i | ||||||||
\(549\) | −7.26067e11 | −0.341115 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.63624e11 | −0.214281 | ||||||||
\(552\) | 2.17873e12i | 0.998799i | ||||||||
\(553\) | 2.68384e12i | 1.22037i | ||||||||
\(554\) | −2.48213e12 | −1.11952 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.18284e10 | 0.0141247 | ||||||||
\(557\) | − 1.09072e12i | − 0.480137i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) | ||||
0.970756 | − | 0.240068i | \(-0.0771699\pi\) | |||||||
\(558\) | 1.14183e12i | 0.498593i | ||||||||
\(559\) | 8.76795e11 | 0.379791 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.23357e11 | −0.223083 | ||||||||
\(562\) | 1.91446e12i | 0.809529i | ||||||||
\(563\) | − 1.03081e12i | − 0.432403i | −0.976349 | − | 0.216202i | \(-0.930633\pi\) | ||||
0.976349 | − | 0.216202i | \(-0.0693668\pi\) | |||||||
\(564\) | 3.14655e10 | 0.0130942 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.20932e10 | 0.0295271 | ||||||||
\(567\) | − 2.57764e11i | − 0.104737i | ||||||||
\(568\) | 3.28695e12i | 1.32503i | ||||||||
\(569\) | 4.06618e12 | 1.62623 | 0.813113 | − | 0.582106i | \(-0.197771\pi\) | ||||
0.813113 | + | 0.582106i | \(0.197771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.86144e11 | 0.388220 | 0.194110 | − | 0.980980i | \(-0.437818\pi\) | ||||
0.194110 | + | 0.980980i | \(0.437818\pi\) | |||||||
\(572\) | 1.55469e10i | 0.00607243i | ||||||||
\(573\) | 1.81492e12i | 0.703334i | ||||||||
\(574\) | 1.75019e12 | 0.672947 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 9.23349e11 | 0.349514 | ||||||||
\(577\) | − 2.86947e12i | − 1.07773i | −0.842391 | − | 0.538866i | \(-0.818853\pi\) | ||||
0.842391 | − | 0.538866i | \(-0.181147\pi\) | |||||||
\(578\) | − 1.67155e12i | − 0.622937i | ||||||||
\(579\) | −2.96427e12 | −1.09614 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.09588e12 | −1.85535 | ||||||||
\(582\) | 1.80721e12i | 0.652914i | ||||||||
\(583\) | − 8.44240e11i | − 0.302662i | ||||||||
\(584\) | −3.13660e12 | −1.11584 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.29692e12 | −1.15497 | ||||||||
\(587\) | 1.14169e12i | 0.396898i | 0.980111 | + | 0.198449i | \(0.0635904\pi\) | ||||
−0.980111 | + | 0.198449i | \(0.936410\pi\) | |||||||
\(588\) | 1.02002e10i | 0.00351895i | ||||||||
\(589\) | 3.49505e12 | 1.19656 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.38652e11 | 0.147903 | ||||||||
\(592\) | 5.18567e12i | 1.73523i | ||||||||
\(593\) | 2.97176e12i | 0.986888i | 0.869777 | + | 0.493444i | \(0.164262\pi\) | ||||
−0.869777 | + | 0.493444i | \(0.835738\pi\) | |||||||
\(594\) | −1.71260e11 | −0.0564439 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.32679e11 | 0.0430719 | ||||||||
\(597\) | − 2.12798e10i | − 0.00685620i | ||||||||
\(598\) | − 1.88814e12i | − 0.603779i | ||||||||
\(599\) | −1.77262e12 | −0.562593 | −0.281297 | − | 0.959621i | \(-0.590764\pi\) | ||||
−0.281297 | + | 0.959621i | \(0.590764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.25838e12 | 0.393439 | 0.196719 | − | 0.980460i | \(-0.436971\pi\) | ||||
0.196719 | + | 0.980460i | \(0.436971\pi\) | |||||||
\(602\) | 3.04715e12i | 0.945606i | ||||||||
\(603\) | 7.77926e11i | 0.239613i | ||||||||
\(604\) | 6.33405e10 | 0.0193649 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 2.34399e12 | 0.706038 | ||||||||
\(607\) | 1.74535e11i | 0.0521834i | 0.999660 | + | 0.0260917i | \(0.00830619\pi\) | ||||
−0.999660 | + | 0.0260917i | \(0.991694\pi\) | |||||||
\(608\) | − 2.86313e11i | − 0.0849720i | ||||||||
\(609\) | 5.08964e11 | 0.149937 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.25896e11 | −0.152656 | ||||||||
\(612\) | 8.10332e10i | 0.0233497i | ||||||||
\(613\) | − 4.63037e12i | − 1.32447i | −0.749294 | − | 0.662237i | \(-0.769607\pi\) | ||||
0.749294 | − | 0.662237i | \(-0.230393\pi\) | |||||||
\(614\) | 4.06054e12 | 1.15299 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.04202e12 | −0.291584 | ||||||||
\(617\) | 2.50518e12i | 0.695914i | 0.937511 | + | 0.347957i | \(0.113124\pi\) | ||||
−0.937511 | + | 0.347957i | \(0.886876\pi\) | |||||||
\(618\) | − 3.25745e12i | − 0.898316i | ||||||||
\(619\) | −5.44228e11 | −0.148995 | −0.0744977 | − | 0.997221i | \(-0.523735\pi\) | ||||
−0.0744977 | + | 0.997221i | \(0.523735\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.20325e12 | −0.324672 | ||||||||
\(622\) | 1.99023e12i | 0.533146i | ||||||||
\(623\) | 1.13709e12i | 0.302412i | ||||||||
\(624\) | −7.58459e11 | −0.200263 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.37447e11 | 0.0617991 | ||||||||
\(627\) | 5.24214e11i | 0.135458i | ||||||||
\(628\) | − 3.30088e11i | − 0.0846860i | ||||||||
\(629\) | −9.25978e12 | −2.35870 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.51975e12 | −1.63719 | −0.818594 | − | 0.574372i | \(-0.805246\pi\) | ||||
−0.818594 | + | 0.574372i | \(0.805246\pi\) | |||||||
\(632\) | − 5.32465e12i | − 1.32759i | ||||||||
\(633\) | 1.08939e12i | 0.269692i | ||||||||
\(634\) | −9.20303e11 | −0.226219 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.30717e11 | −0.0316792 | ||||||||
\(637\) | − 1.70481e11i | − 0.0410250i | ||||||||
\(638\) | − 3.38159e11i | − 0.0808032i | ||||||||
\(639\) | −1.81530e12 | −0.430718 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.36297e12 | −0.786794 | −0.393397 | − | 0.919369i | \(-0.628700\pi\) | ||||
−0.393397 | + | 0.919369i | \(0.628700\pi\) | |||||||
\(642\) | − 3.30325e11i | − 0.0767420i | ||||||||
\(643\) | − 1.18082e12i | − 0.272417i | −0.990680 | − | 0.136208i | \(-0.956508\pi\) | ||||
0.990680 | − | 0.136208i | \(-0.0434917\pi\) | |||||||
\(644\) | −3.79614e11 | −0.0869673 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.28749e12 | −0.968628 | ||||||||
\(647\) | 6.63176e12i | 1.48785i | 0.668262 | + | 0.743926i | \(0.267038\pi\) | ||||
−0.668262 | + | 0.743926i | \(0.732962\pi\) | |||||||
\(648\) | 5.11395e11i | 0.113938i | ||||||||
\(649\) | −4.69353e11 | −0.103848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.83685e12 | −0.837259 | ||||||||
\(652\) | − 3.20902e11i | − 0.0695438i | ||||||||
\(653\) | − 8.25189e11i | − 0.177601i | −0.996049 | − | 0.0888003i | \(-0.971697\pi\) | ||||
0.996049 | − | 0.0888003i | \(-0.0283033\pi\) | |||||||
\(654\) | 3.52602e12 | 0.753677 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.28185e12 | −0.691913 | ||||||||
\(657\) | − 1.73226e12i | − 0.362717i | ||||||||
\(658\) | − 1.82766e12i | − 0.380084i | ||||||||
\(659\) | 4.40214e11 | 0.0909242 | 0.0454621 | − | 0.998966i | \(-0.485524\pi\) | ||||
0.0454621 | + | 0.998966i | \(0.485524\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.77788e12 | 1.99222 | 0.996112 | − | 0.0880914i | \(-0.0280767\pi\) | ||||
0.996112 | + | 0.0880914i | \(0.0280767\pi\) | |||||||
\(662\) | − 2.71281e11i | − 0.0548983i | ||||||||
\(663\) | − 1.35434e12i | − 0.272218i | ||||||||
\(664\) | 1.01101e13 | 2.01836 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.03011e12 | −0.596793 | ||||||||
\(667\) | − 2.37587e12i | − 0.464790i | ||||||||
\(668\) | − 3.74378e11i | − 0.0727473i | ||||||||
\(669\) | −2.15835e12 | −0.416585 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.62101e12 | −0.308698 | ||||||||
\(672\) | 3.14314e11i | 0.0594568i | ||||||||
\(673\) | − 4.22591e12i | − 0.794058i | −0.917806 | − | 0.397029i | \(-0.870041\pi\) | ||||
0.917806 | − | 0.397029i | \(-0.129959\pi\) | |||||||
\(674\) | 4.79547e11 | 0.0895079 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.56694e11 | 0.0472776 | ||||||||
\(677\) | − 7.56977e12i | − 1.38495i | −0.721442 | − | 0.692474i | \(-0.756521\pi\) | ||||
0.721442 | − | 0.692474i | \(-0.243479\pi\) | |||||||
\(678\) | 2.81333e12i | 0.511313i | ||||||||
\(679\) | −6.07273e12 | −1.09640 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2.72418e12 | −0.485370 | ||||||||
\(682\) | 2.54923e12i | 0.451210i | ||||||||
\(683\) | 1.92029e12i | 0.337655i | 0.985646 | + | 0.168827i | \(0.0539980\pi\) | ||||
−0.985646 | + | 0.168827i | \(0.946002\pi\) | |||||||
\(684\) | 8.11659e10 | 0.0141782 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.90850e12 | 1.01864 | ||||||||
\(687\) | − 4.05367e12i | − 0.694293i | ||||||||
\(688\) | − 5.71385e12i | − 0.972257i | ||||||||
\(689\) | 2.18472e12 | 0.369325 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.99839e12 | −0.667166 | −0.333583 | − | 0.942721i | \(-0.608258\pi\) | ||||
−0.333583 | + | 0.942721i | \(0.608258\pi\) | |||||||
\(692\) | − 2.97538e11i | − 0.0493248i | ||||||||
\(693\) | − 5.75480e11i | − 0.0947830i | ||||||||
\(694\) | 1.85595e12 | 0.303702 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.00977e12 | −0.163110 | ||||||||
\(697\) | − 5.86023e12i | − 0.940519i | ||||||||
\(698\) | 2.71249e10i | 0.00432532i | ||||||||
\(699\) | −2.66997e12 | −0.423018 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.12736e13 | 1.76332 | 0.881662 | − | 0.471881i | \(-0.156425\pi\) | ||||
0.881662 | + | 0.471881i | \(0.156425\pi\) | |||||||
\(702\) | − 4.43186e11i | − 0.0688761i | ||||||||
\(703\) | 9.27493e12i | 1.43223i | ||||||||
\(704\) | 2.06146e12 | 0.316299 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.81453e12 | 0.577856 | ||||||||
\(707\) | 7.87643e12i | 1.18561i | ||||||||
\(708\) | 7.26715e10i | 0.0108696i | ||||||||
\(709\) | −1.12679e13 | −1.67469 | −0.837346 | − | 0.546673i | \(-0.815894\pi\) | ||||
−0.837346 | + | 0.546673i | \(0.815894\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.94066e12 | 0.431550 | ||||||||
\(712\) | − 2.25595e12i | − 0.328980i | ||||||||
\(713\) | 1.79106e13i | 2.59542i | ||||||||
\(714\) | 4.70679e12 | 0.677770 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.31512e11 | −0.104019 | ||||||||
\(717\) | 6.44292e11i | 0.0910429i | ||||||||
\(718\) | − 1.40395e12i | − 0.197148i | ||||||||
\(719\) | 9.05247e12 | 1.26324 | 0.631622 | − | 0.775277i | \(-0.282390\pi\) | ||||
0.631622 | + | 0.775277i | \(0.282390\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.09459e13 | 1.50849 | ||||||||
\(722\) | − 2.80462e12i | − 0.384111i | ||||||||
\(723\) | − 6.09507e12i | − 0.829576i | ||||||||
\(724\) | 6.57129e10 | 0.00888847 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.81951e12 | 0.510262 | ||||||||
\(727\) | 1.34408e12i | 0.178452i | 0.996011 | + | 0.0892260i | \(0.0284393\pi\) | ||||
−0.996011 | + | 0.0892260i | \(0.971561\pi\) | |||||||
\(728\) | − 2.69654e12i | − 0.355807i | ||||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.02029e13 | 1.32159 | ||||||||
\(732\) | 2.50986e11i | 0.0323109i | ||||||||
\(733\) | − 6.57401e11i | − 0.0841129i | −0.999115 | − | 0.0420564i | \(-0.986609\pi\) | ||||
0.999115 | − | 0.0420564i | \(-0.0133909\pi\) | |||||||
\(734\) | −2.46932e12 | −0.314011 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.46723e12 | 0.184310 | ||||||||
\(737\) | 1.73679e12i | 0.216842i | ||||||||
\(738\) | − 1.91766e12i | − 0.237968i | ||||||||
\(739\) | −2.15587e12 | −0.265903 | −0.132951 | − | 0.991123i | \(-0.542445\pi\) | ||||
−0.132951 | + | 0.991123i | \(0.542445\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.35656e12 | −0.165294 | ||||||||
\(742\) | 7.59263e12i | 0.919548i | ||||||||
\(743\) | 7.73594e12i | 0.931244i | 0.884984 | + | 0.465622i | \(0.154169\pi\) | ||||
−0.884984 | + | 0.465622i | \(0.845831\pi\) | |||||||
\(744\) | 7.61218e12 | 0.910817 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.58621e13 | 1.87515 | ||||||||
\(747\) | 5.58351e12i | 0.656092i | ||||||||
\(748\) | 1.80914e11i | 0.0211307i | ||||||||
\(749\) | 1.10998e12 | 0.128869 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.12448e13 | −1.28995 | −0.644974 | − | 0.764205i | \(-0.723132\pi\) | ||||
−0.644974 | + | 0.764205i | \(0.723132\pi\) | |||||||
\(752\) | 3.42713e12i | 0.390797i | ||||||||
\(753\) | − 7.97551e12i | − 0.904027i | ||||||||
\(754\) | 8.75087e11 | 0.0986007 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.91035e10 | −0.00992080 | ||||||||
\(757\) | − 1.18544e13i | − 1.31205i | −0.754740 | − | 0.656024i | \(-0.772237\pi\) | ||||
0.754740 | − | 0.656024i | \(-0.227763\pi\) | |||||||
\(758\) | 4.49528e12i | 0.494590i | ||||||||
\(759\) | −2.68637e12 | −0.293818 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.24765e12 | −0.242939 | −0.121470 | − | 0.992595i | \(-0.538761\pi\) | ||||
−0.121470 | + | 0.992595i | \(0.538761\pi\) | |||||||
\(762\) | − 4.27681e12i | − 0.459539i | ||||||||
\(763\) | 1.18484e13i | 1.26561i | ||||||||
\(764\) | 6.27380e11 | 0.0666209 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.20380e13 | −1.26335 | ||||||||
\(767\) | − 1.21459e12i | − 0.126721i | ||||||||
\(768\) | − 9.10436e11i | − 0.0944331i | ||||||||
\(769\) | 1.44505e13 | 1.49010 | 0.745049 | − | 0.667009i | \(-0.232426\pi\) | ||||
0.745049 | + | 0.667009i | \(0.232426\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.90443e11 | −0.0703693 | ||||||||
\(772\) | 1.02469e12i | 0.103828i | ||||||||
\(773\) | − 5.19022e12i | − 0.522852i | −0.965224 | − | 0.261426i | \(-0.915807\pi\) | ||||
0.965224 | − | 0.261426i | \(-0.0841927\pi\) | |||||||
\(774\) | 3.33874e12 | 0.334386 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.20481e13 | 1.19273 | ||||||||
\(777\) | − 1.01820e13i | − 1.00216i | ||||||||
\(778\) | 7.61777e12i | 0.745452i | ||||||||
\(779\) | −5.86983e12 | −0.571093 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.05280e12 | −0.389786 | ||||||||
\(782\) | − 2.19715e13i | − 2.10102i | ||||||||
\(783\) | − 5.57668e11i | − 0.0530209i | ||||||||
\(784\) | −1.11098e12 | −0.105023 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.50768e12 | 0.327807 | ||||||||
\(787\) | − 1.39938e13i | − 1.30032i | −0.759797 | − | 0.650161i | \(-0.774701\pi\) | ||||
0.759797 | − | 0.650161i | \(-0.225299\pi\) | |||||||
\(788\) | − 1.51633e11i | − 0.0140096i | ||||||||
\(789\) | 4.78430e11 | 0.0439513 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.45354e12 | −0.858618 | ||||||||
\(792\) | 1.14173e12i | 0.103110i | ||||||||
\(793\) | − 4.19483e12i | − 0.376691i | ||||||||
\(794\) | −5.64867e12 | −0.504375 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.35599e9 | −0.000649430 0 | ||||||||
\(797\) | 2.01269e13i | 1.76691i | 0.468518 | + | 0.883454i | \(0.344788\pi\) | ||||
−0.468518 | + | 0.883454i | \(0.655212\pi\) | |||||||
\(798\) | − 4.71449e12i | − 0.411549i | ||||||||
\(799\) | −6.11966e12 | −0.531210 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.24590e12 | 0.106939 | ||||||||
\(802\) | 4.43695e11i | 0.0378704i | ||||||||
\(803\) | − 3.86741e12i | − 0.328247i | ||||||||
\(804\) | 2.68913e11 | 0.0226965 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.59688e12 | −0.550593 | ||||||||
\(807\) | 5.79928e12i | 0.481331i | ||||||||
\(808\) | − 1.56266e13i | − 1.28977i | ||||||||
\(809\) | 8.95775e12 | 0.735242 | 0.367621 | − | 0.929976i | \(-0.380172\pi\) | ||||
0.367621 | + | 0.929976i | \(0.380172\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.76446e12 | −0.143225 | −0.0716123 | − | 0.997433i | \(-0.522814\pi\) | ||||
−0.0716123 | + | 0.997433i | \(0.522814\pi\) | |||||||
\(812\) | − 1.75938e11i | − 0.0142023i | ||||||||
\(813\) | − 1.01051e13i | − 0.811212i | ||||||||
\(814\) | −6.76498e12 | −0.540078 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.82591e12 | −0.696873 | ||||||||
\(817\) | − 1.02196e13i | − 0.802483i | ||||||||
\(818\) | 9.53491e11i | 0.0744607i | ||||||||
\(819\) | 1.48922e12 | 0.115660 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.48082e13 | 1.13752 | 0.568758 | − | 0.822505i | \(-0.307424\pi\) | ||||
0.568758 | + | 0.822505i | \(0.307424\pi\) | |||||||
\(822\) | 3.61585e12i | 0.276240i | ||||||||
\(823\) | 3.39651e12i | 0.258067i | 0.991640 | + | 0.129034i | \(0.0411876\pi\) | ||||
−0.991640 | + | 0.129034i | \(0.958812\pi\) | |||||||
\(824\) | −2.17163e13 | −1.64102 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.22110e12 | 0.315512 | ||||||||
\(827\) | 1.88344e13i | 1.40016i | 0.714065 | + | 0.700080i | \(0.246852\pi\) | ||||
−0.714065 | + | 0.700080i | \(0.753148\pi\) | |||||||
\(828\) | 4.15940e11i | 0.0307535i | ||||||||
\(829\) | −1.18947e13 | −0.874695 | −0.437348 | − | 0.899292i | \(-0.644082\pi\) | ||||
−0.437348 | + | 0.899292i | \(0.644082\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.13876e12 | −0.664787 | ||||||||
\(832\) | 5.33462e12i | 0.385966i | ||||||||
\(833\) | − 1.98382e12i | − 0.142758i | ||||||||
\(834\) | −2.02565e12 | −0.144983 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.81210e11 | 0.0128308 | ||||||||
\(837\) | 4.20400e12i | 0.296073i | ||||||||
\(838\) | − 1.12350e13i | − 0.786998i | ||||||||
\(839\) | 1.22881e13 | 0.856165 | 0.428083 | − | 0.903740i | \(-0.359189\pi\) | ||||
0.428083 | + | 0.903740i | \(0.359189\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.34060e13 | −0.924097 | ||||||||
\(842\) | 7.06702e12i | 0.484543i | ||||||||
\(843\) | 7.04869e12i | 0.480711i | ||||||||
\(844\) | 3.76581e11 | 0.0255457 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.00256e12 | −0.134406 | ||||||||
\(847\) | 1.28346e13i | 0.856853i | ||||||||
\(848\) | − 1.42373e13i | − 0.945465i | ||||||||
\(849\) | 2.65434e11 | 0.0175336 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.75300e13 | −3.10660 | ||||||||
\(852\) | 6.27510e11i | 0.0407983i | ||||||||
\(853\) | 4.61355e12i | 0.298376i | 0.988809 | + | 0.149188i | \(0.0476660\pi\) | ||||
−0.988809 | + | 0.149188i | \(0.952334\pi\) | |||||||
\(854\) | 1.45784e13 | 0.937887 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.20216e12 | −0.140190 | ||||||||
\(857\) | − 4.29363e12i | − 0.271901i | −0.990716 | − | 0.135950i | \(-0.956591\pi\) | ||||
0.990716 | − | 0.135950i | \(-0.0434088\pi\) | |||||||
\(858\) | − 9.89450e11i | − 0.0623306i | ||||||||
\(859\) | 6.40428e12 | 0.401330 | 0.200665 | − | 0.979660i | \(-0.435690\pi\) | ||||
0.200665 | + | 0.979660i | \(0.435690\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.44387e12 | 0.399607 | ||||||||
\(862\) | 9.84758e12i | 0.607501i | ||||||||
\(863\) | 3.24421e12i | 0.199095i | 0.995033 | + | 0.0995474i | \(0.0317395\pi\) | ||||
−0.995033 | + | 0.0995474i | \(0.968260\pi\) | |||||||
\(864\) | 3.44391e11 | 0.0210252 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.10609e12 | −0.187665 | ||||||||
\(867\) | − 6.15435e12i | − 0.369910i | ||||||||
\(868\) | 1.32632e12i | 0.0793065i | ||||||||
\(869\) | 6.56527e12 | 0.390539 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.49445e12 | −0.264603 | ||||||||
\(872\) | − 2.35068e13i | − 1.37680i | ||||||||
\(873\) | 6.65383e12i | 0.387711i | ||||||||
\(874\) | −2.20075e13 | −1.27576 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.98805e11 | −0.0343571 | ||||||||
\(877\) | 2.89711e13i | 1.65374i | 0.562392 | + | 0.826871i | \(0.309881\pi\) | ||||
−0.562392 | + | 0.826871i | \(0.690119\pi\) | |||||||
\(878\) | 1.87109e13i | 1.06260i | ||||||||
\(879\) | −1.21387e13 | −0.685838 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.50447e12 | 0.419690 | 0.209845 | − | 0.977735i | \(-0.432704\pi\) | ||||
0.209845 | + | 0.977735i | \(0.432704\pi\) | |||||||
\(882\) | − 6.49173e11i | − 0.0361203i | ||||||||
\(883\) | − 2.87141e13i | − 1.58954i | −0.606908 | − | 0.794772i | \(-0.707590\pi\) | ||||
0.606908 | − | 0.794772i | \(-0.292410\pi\) | |||||||
\(884\) | −4.68167e11 | −0.0257849 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.67013e12 | 0.363649 | ||||||||
\(887\) | 9.99825e12i | 0.542335i | 0.962532 | + | 0.271168i | \(0.0874098\pi\) | ||||
−0.962532 | + | 0.271168i | \(0.912590\pi\) | |||||||
\(888\) | 2.02007e13i | 1.09021i | ||||||||
\(889\) | 1.43712e13 | 0.771678 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.30548e11 | −0.0335173 | ||||||||
\(892\) | 7.46095e11i | 0.0394596i | ||||||||
\(893\) | 6.12967e12i | 0.322556i | ||||||||
\(894\) | −8.44407e12 | −0.442113 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.65528e13 | −0.857998 | ||||||||
\(897\) | − 6.95177e12i | − 0.358533i | ||||||||
\(898\) | 3.08721e13i | 1.58425i | ||||||||
\(899\) | −8.30095e12 | −0.423847 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.54228e13 | 1.28517 | ||||||||
\(902\) | − 4.28135e12i | − 0.215353i | ||||||||
\(903\) | 1.12191e13i | 0.561516i | ||||||||
\(904\) | 1.87555e13 | 0.934052 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.03117e12 | −0.198772 | ||||||||
\(907\) | 4.70846e12i | 0.231018i | 0.993306 | + | 0.115509i | \(0.0368500\pi\) | ||||
−0.993306 | + | 0.115509i | \(0.963150\pi\) | |||||||
\(908\) | 9.41690e11i | 0.0459750i | ||||||||
\(909\) | 8.63013e12 | 0.419257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.69663e13 | 1.29714 | 0.648572 | − | 0.761154i | \(-0.275367\pi\) | ||||
0.648572 | + | 0.761154i | \(0.275367\pi\) | |||||||
\(912\) | 8.84035e12i | 0.423148i | ||||||||
\(913\) | 1.24657e13i | 0.593742i | ||||||||
\(914\) | −7.37778e12 | −0.349678 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.40127e12 | −0.0657645 | ||||||||
\(917\) | 1.17868e13i | 0.550468i | ||||||||
\(918\) | − 5.15719e12i | − 0.239674i | ||||||||
\(919\) | 3.96618e12 | 0.183422 | 0.0917112 | − | 0.995786i | \(-0.470766\pi\) | ||||
0.0917112 | + | 0.995786i | \(0.470766\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.49502e13 | 0.684664 | ||||||||
\(922\) | 2.29405e13i | 1.04547i | ||||||||
\(923\) | − 1.04878e13i | − 0.475639i | ||||||||
\(924\) | −1.98931e11 | −0.00897799 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −2.14298e13 | −0.957788 | ||||||||
\(927\) | − 1.19933e13i | − 0.533434i | ||||||||
\(928\) | 6.80012e11i | 0.0300989i | ||||||||
\(929\) | −1.96912e13 | −0.867365 | −0.433683 | − | 0.901066i | \(-0.642786\pi\) | ||||
−0.433683 | + | 0.901066i | \(0.642786\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.98707e12 | −0.0866841 | ||||||||
\(932\) | 9.22952e11i | 0.0400689i | ||||||||
\(933\) | 7.32766e12i | 0.316591i | ||||||||
\(934\) | 4.35271e12 | 0.187154 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.95457e12 | −0.125821 | ||||||||
\(937\) | − 2.11305e13i | − 0.895532i | −0.894151 | − | 0.447766i | \(-0.852220\pi\) | ||||
0.894151 | − | 0.447766i | \(-0.147780\pi\) | |||||||
\(938\) | − 1.56197e13i | − 0.658810i | ||||||||
\(939\) | 8.74236e11 | 0.0366973 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.41072e12 | 0.224958 | 0.112479 | − | 0.993654i | \(-0.464121\pi\) | ||||
0.112479 | + | 0.993654i | \(0.464121\pi\) | |||||||
\(942\) | 2.10077e13i | 0.869261i | ||||||||
\(943\) | − 3.00803e13i | − 1.23874i | ||||||||
\(944\) | −7.91517e12 | −0.324404 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.45403e12 | 0.302608 | ||||||||
\(947\) | 3.44259e12i | 0.139095i | 0.997579 | + | 0.0695473i | \(0.0221555\pi\) | ||||
−0.997579 | + | 0.0695473i | \(0.977845\pi\) | |||||||
\(948\) | − 1.01652e12i | − 0.0408771i | ||||||||
\(949\) | 1.00081e13 | 0.400546 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.38839e12 | −0.134332 | ||||||||
\(952\) | − 3.13786e13i | − 1.23813i | ||||||||
\(953\) | 4.18440e12i | 0.164329i | 0.996619 | + | 0.0821647i | \(0.0261834\pi\) | ||||
−0.996619 | + | 0.0821647i | \(0.973817\pi\) | |||||||
\(954\) | 8.31918e12 | 0.325172 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.22718e11 | 0.00862373 | ||||||||
\(957\) | − 1.24504e12i | − 0.0479822i | ||||||||
\(958\) | 1.99921e13i | 0.766855i | ||||||||
\(959\) | −1.21502e13 | −0.463874 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.61375e13 | 1.36679 | ||||||||
\(962\) | − 1.75064e13i | − 0.659035i | ||||||||
\(963\) | − 1.21620e12i | − 0.0455706i | ||||||||
\(964\) | −2.10694e12 | −0.0785787 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.41597e13 | 0.892678 | ||||||||
\(967\) | 1.49800e13i | 0.550926i | 0.961312 | + | 0.275463i | \(0.0888312\pi\) | ||||
−0.961312 | + | 0.275463i | \(0.911169\pi\) | |||||||
\(968\) | − 2.54634e13i | − 0.932132i | ||||||||
\(969\) | −1.57858e13 | −0.575186 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.82460e13 | −1.01970 | −0.509848 | − | 0.860264i | \(-0.670299\pi\) | ||||
−0.509848 | + | 0.860264i | \(0.670299\pi\) | |||||||
\(972\) | 9.76300e10i | 0.00350820i | ||||||||
\(973\) | − 6.80673e12i | − 0.243462i | ||||||||
\(974\) | −2.57318e13 | −0.916127 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.73367e13 | −0.964321 | ||||||||
\(977\) | − 4.62242e13i | − 1.62309i | −0.584287 | − | 0.811547i | \(-0.698626\pi\) | ||||
0.584287 | − | 0.811547i | \(-0.301374\pi\) | |||||||
\(978\) | 2.04231e13i | 0.713835i | ||||||||
\(979\) | 2.78158e12 | 0.0967764 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.29822e13 | 0.447545 | ||||||||
\(982\) | − 5.48127e13i | − 1.88096i | ||||||||
\(983\) | − 4.80363e13i | − 1.64089i | −0.571728 | − | 0.820443i | \(-0.693727\pi\) | ||||
0.571728 | − | 0.820443i | \(-0.306273\pi\) | |||||||
\(984\) | −1.27844e13 | −0.434714 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.01831e13 | 0.343109 | ||||||||
\(987\) | − 6.72913e12i | − 0.225700i | ||||||||
\(988\) | 4.68934e11i | 0.0156569i | ||||||||
\(989\) | 5.23712e13 | 1.74064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.31211e13 | 0.761512 | 0.380756 | − | 0.924675i | \(-0.375664\pi\) | ||||
0.380756 | + | 0.924675i | \(0.375664\pi\) | |||||||
\(992\) | − 5.12630e12i | − 0.168074i | ||||||||
\(993\) | − 9.98809e11i | − 0.0325995i | ||||||||
\(994\) | 3.64487e13 | 1.18425 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.93010e12 | 0.0621461 | ||||||||
\(997\) | − 1.35362e13i | − 0.433878i | −0.976185 | − | 0.216939i | \(-0.930393\pi\) | ||||
0.976185 | − | 0.216939i | \(-0.0696073\pi\) | |||||||
\(998\) | 1.22666e13i | 0.391413i | ||||||||
\(999\) | −1.11563e13 | −0.354385 |
(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 | 75.10.b.b.49.2 | 2 | ||
3.2 | odd | 2 | 225.10.b.b.199.1 | 2 | |||
5.2 | odd | 4 | 75.10.a.a.1.1 | 1 | |||
5.3 | odd | 4 | 15.10.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 75.10.b.b.49.1 | 2 | ||
15.2 | even | 4 | 225.10.a.f.1.1 | 1 | |||
15.8 | even | 4 | 45.10.a.a.1.1 | 1 | |||
15.14 | odd | 2 | 225.10.b.b.199.2 | 2 | |||
20.3 | even | 4 | 240.10.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.a.b.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
45.10.a.a.1.1 | 1 | 15.8 | even | 4 | |||
75.10.a.a.1.1 | 1 | 5.2 | odd | 4 | |||
75.10.b.b.49.1 | 2 | 5.4 | even | 2 | inner | ||
75.10.b.b.49.2 | 2 | 1.1 | even | 1 | trivial | ||
225.10.a.f.1.1 | 1 | 15.2 | even | 4 | |||
225.10.b.b.199.1 | 2 | 3.2 | odd | 2 | |||
225.10.b.b.199.2 | 2 | 15.14 | odd | 2 | |||
240.10.a.g.1.1 | 1 | 20.3 | even | 4 |