Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,30,Mod(24,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(133.195105958\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25675x^{2} + 164788569 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{2}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.4 | ||
Root | \(113.802i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.30.b.a.24.1 |
$q$-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 \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 26073.9i | 1.12531i | 0.826693 | + | 0.562654i | \(0.190220\pi\) | ||||
−0.826693 | + | 0.562654i | \(0.809780\pi\) | |||||||
\(3\) | 1.44920e7i | 1.74932i | 0.484736 | + | 0.874660i | \(0.338916\pi\) | ||||
−0.484736 | + | 0.874660i | \(0.661084\pi\) | |||||||
\(4\) | −1.42978e8 | −0.266317 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.77862e11 | −1.96852 | ||||||||
\(7\) | − 3.40335e10i | − 0.0189664i | −0.999955 | − | 0.00948319i | \(-0.996981\pi\) | ||||
0.999955 | − | 0.00948319i | \(-0.00301864\pi\) | |||||||
\(8\) | 1.02703e13i | 0.825619i | ||||||||
\(9\) | −1.41387e14 | −2.06012 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −7.97271e14 | −0.633012 | −0.316506 | − | 0.948590i | \(-0.602510\pi\) | ||||
−0.316506 | + | 0.948590i | \(0.602510\pi\) | |||||||
\(12\) | − 2.07203e15i | − 0.465873i | ||||||||
\(13\) | − 1.10490e16i | − 0.778296i | −0.921175 | − | 0.389148i | \(-0.872769\pi\) | ||||
0.921175 | − | 0.389148i | \(-0.127231\pi\) | |||||||
\(14\) | 8.87385e14 | 0.0213430 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.44548e17 | −1.19539 | ||||||||
\(17\) | − 7.47691e17i | − 1.07699i | −0.842628 | − | 0.538496i | \(-0.818993\pi\) | ||||
0.842628 | − | 0.538496i | \(-0.181007\pi\) | |||||||
\(18\) | − 3.68651e18i | − 2.31827i | ||||||||
\(19\) | 2.49040e18 | 0.715060 | 0.357530 | − | 0.933902i | \(-0.383619\pi\) | ||||
0.357530 | + | 0.933902i | \(0.383619\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.93212e17 | 0.0331783 | ||||||||
\(22\) | − 2.07880e19i | − 0.712333i | ||||||||
\(23\) | 1.63712e18i | 0.0294461i | 0.999892 | + | 0.0147231i | \(0.00468667\pi\) | ||||
−0.999892 | + | 0.0147231i | \(0.995313\pi\) | |||||||
\(24\) | −1.48837e20 | −1.44427 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.88091e20 | 0.875822 | ||||||||
\(27\) | − 1.05439e21i | − 1.85449i | ||||||||
\(28\) | 4.86602e18i | 0.00505106i | ||||||||
\(29\) | −1.87750e21 | −1.17168 | −0.585839 | − | 0.810427i | \(-0.699235\pi\) | ||||
−0.585839 | + | 0.810427i | \(0.699235\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.79819e21 | −1.13850 | −0.569250 | − | 0.822165i | \(-0.692766\pi\) | ||||
−0.569250 | + | 0.822165i | \(0.692766\pi\) | |||||||
\(32\) | − 3.46987e21i | − 0.519564i | ||||||||
\(33\) | − 1.15540e22i | − 1.10734i | ||||||||
\(34\) | 1.94952e22 | 1.21195 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.02152e22 | 0.548645 | ||||||||
\(37\) | 7.91036e22i | 1.44302i | 0.692406 | + | 0.721508i | \(0.256551\pi\) | ||||
−0.692406 | + | 0.721508i | \(0.743449\pi\) | |||||||
\(38\) | 6.49345e22i | 0.804662i | ||||||||
\(39\) | 1.60122e23 | 1.36149 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.06439e21 | −0.0249702 | −0.0124851 | − | 0.999922i | \(-0.503974\pi\) | ||||
−0.0124851 | + | 0.999922i | \(0.503974\pi\) | |||||||
\(42\) | 1.28600e22i | 0.0373358i | ||||||||
\(43\) | − 6.72526e23i | − 1.38809i | −0.719933 | − | 0.694044i | \(-0.755827\pi\) | ||||
0.719933 | − | 0.694044i | \(-0.244173\pi\) | |||||||
\(44\) | 1.13992e23 | 0.168582 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.26862e22 | −0.0331359 | ||||||||
\(47\) | − 1.90366e24i | − 1.08186i | −0.841069 | − | 0.540928i | \(-0.818073\pi\) | ||||
0.841069 | − | 0.540928i | \(-0.181927\pi\) | |||||||
\(48\) | − 4.99319e24i | − 2.09112i | ||||||||
\(49\) | 3.21875e24 | 0.999640 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.08355e25 | 1.88401 | ||||||||
\(52\) | 1.57976e24i | 0.207273i | ||||||||
\(53\) | 1.65597e24i | 0.164836i | 0.996598 | + | 0.0824181i | \(0.0262643\pi\) | ||||
−0.996598 | + | 0.0824181i | \(0.973736\pi\) | |||||||
\(54\) | 2.74920e25 | 2.08688 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.49535e23 | 0.0156590 | ||||||||
\(57\) | 3.60909e25i | 1.25087i | ||||||||
\(58\) | − 4.89537e25i | − 1.31850i | ||||||||
\(59\) | 8.93685e25 | 1.87858 | 0.939292 | − | 0.343120i | \(-0.111484\pi\) | ||||
0.939292 | + | 0.343120i | \(0.111484\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.59924e25 | 0.596216 | 0.298108 | − | 0.954532i | \(-0.403644\pi\) | ||||
0.298108 | + | 0.954532i | \(0.403644\pi\) | |||||||
\(62\) | − 1.25108e26i | − 1.28116i | ||||||||
\(63\) | 4.81189e24i | 0.0390731i | ||||||||
\(64\) | −9.45048e25 | −0.610723 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.01259e26 | 1.24610 | ||||||||
\(67\) | − 1.04774e26i | − 0.348472i | −0.984704 | − | 0.174236i | \(-0.944254\pi\) | ||||
0.984704 | − | 0.174236i | \(-0.0557456\pi\) | |||||||
\(68\) | 1.06903e26i | 0.286821i | ||||||||
\(69\) | −2.37252e25 | −0.0515107 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.75243e26 | 0.251417 | 0.125709 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125709 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(72\) | − 1.45209e27i | − 1.70088i | ||||||||
\(73\) | 4.56674e26i | 0.437950i | 0.975730 | + | 0.218975i | \(0.0702713\pi\) | ||||
−0.975730 | + | 0.218975i | \(0.929729\pi\) | |||||||
\(74\) | −2.06254e27 | −1.62384 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.56072e26 | −0.190432 | ||||||||
\(77\) | 2.71339e25i | 0.0120059i | ||||||||
\(78\) | 4.17501e27i | 1.53209i | ||||||||
\(79\) | 3.28137e27 | 1.00107 | 0.500533 | − | 0.865717i | \(-0.333137\pi\) | ||||
0.500533 | + | 0.865717i | \(0.333137\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.57671e27 | 1.18398 | ||||||||
\(82\) | − 1.58122e26i | − 0.0280991i | ||||||||
\(83\) | 4.40086e27i | 0.656002i | 0.944677 | + | 0.328001i | \(0.106375\pi\) | ||||
−0.944677 | + | 0.328001i | \(0.893625\pi\) | |||||||
\(84\) | −7.05183e25 | −0.00883593 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.75354e28 | 1.56202 | ||||||||
\(87\) | − 2.72087e28i | − 2.04964i | ||||||||
\(88\) | − 8.18824e27i | − 0.522627i | ||||||||
\(89\) | 6.06897e26 | 0.0328821 | 0.0164411 | − | 0.999865i | \(-0.494766\pi\) | ||||
0.0164411 | + | 0.999865i | \(0.494766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.76036e26 | −0.0147615 | ||||||||
\(92\) | − 2.34072e26i | − 0.00784199i | ||||||||
\(93\) | − 6.95352e28i | − 1.99160i | ||||||||
\(94\) | 4.96357e28 | 1.21742 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.02853e28 | 0.908884 | ||||||||
\(97\) | 1.44471e28i | 0.224694i | 0.993669 | + | 0.112347i | \(0.0358368\pi\) | ||||
−0.993669 | + | 0.112347i | \(0.964163\pi\) | |||||||
\(98\) | 8.39253e28i | 1.12490i | ||||||||
\(99\) | 1.12724e29 | 1.30408 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.90236e28 | −0.424371 | −0.212185 | − | 0.977229i | \(-0.568058\pi\) | ||||
−0.212185 | + | 0.977229i | \(0.568058\pi\) | |||||||
\(102\) | 2.82524e29i | 2.12009i | ||||||||
\(103\) | − 1.31966e29i | − 0.859654i | −0.902911 | − | 0.429827i | \(-0.858574\pi\) | ||||
0.902911 | − | 0.429827i | \(-0.141426\pi\) | |||||||
\(104\) | 1.13477e29 | 0.642576 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.31776e28 | −0.185491 | ||||||||
\(107\) | − 2.31447e29i | − 0.867733i | −0.900977 | − | 0.433867i | \(-0.857149\pi\) | ||||
0.900977 | − | 0.433867i | \(-0.142851\pi\) | |||||||
\(108\) | 1.50754e29i | 0.493882i | ||||||||
\(109\) | −6.73768e29 | −1.93119 | −0.965597 | − | 0.260043i | \(-0.916263\pi\) | ||||
−0.965597 | + | 0.260043i | \(0.916263\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.14637e30 | −2.52430 | ||||||||
\(112\) | 1.17262e28i | 0.0226723i | ||||||||
\(113\) | − 5.10156e28i | − 0.0867092i | −0.999060 | − | 0.0433546i | \(-0.986195\pi\) | ||||
0.999060 | − | 0.0433546i | \(-0.0138045\pi\) | |||||||
\(114\) | −9.41029e29 | −1.40761 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.68440e29 | 0.312037 | ||||||||
\(117\) | 1.56219e30i | 1.60339i | ||||||||
\(118\) | 2.33019e30i | 2.11398i | ||||||||
\(119\) | −2.54465e28 | −0.0204267 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.50668e29 | −0.599296 | ||||||||
\(122\) | 1.19920e30i | 0.670926i | ||||||||
\(123\) | − 8.78850e28i | − 0.0436808i | ||||||||
\(124\) | 6.86034e29 | 0.303201 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.25465e29 | −0.0439692 | ||||||||
\(127\) | 3.46836e30i | 1.08385i | 0.840426 | + | 0.541926i | \(0.182305\pi\) | ||||
−0.840426 | + | 0.541926i | \(0.817695\pi\) | |||||||
\(128\) | − 4.32698e30i | − 1.20681i | ||||||||
\(129\) | 9.74624e30 | 2.42821 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.16207e30 | −0.231631 | −0.115816 | − | 0.993271i | \(-0.536948\pi\) | ||||
−0.115816 | + | 0.993271i | \(0.536948\pi\) | |||||||
\(132\) | 1.65197e30i | 0.294903i | ||||||||
\(133\) | − 8.47570e28i | − 0.0135621i | ||||||||
\(134\) | 2.73186e30 | 0.392138 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.67904e30 | 0.889186 | ||||||||
\(137\) | − 1.12214e31i | − 1.16842i | −0.811603 | − | 0.584210i | \(-0.801404\pi\) | ||||
0.811603 | − | 0.584210i | \(-0.198596\pi\) | |||||||
\(138\) | − 6.18608e29i | − 0.0579654i | ||||||||
\(139\) | 2.10245e30 | 0.177423 | 0.0887117 | − | 0.996057i | \(-0.471725\pi\) | ||||
0.0887117 | + | 0.996057i | \(0.471725\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.75877e31 | 1.89251 | ||||||||
\(142\) | 4.56927e30i | 0.282922i | ||||||||
\(143\) | 8.80906e30i | 0.492671i | ||||||||
\(144\) | 4.87146e31 | 2.46265 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.19073e31 | −0.492828 | ||||||||
\(147\) | 4.66460e31i | 1.74869i | ||||||||
\(148\) | − 1.13100e31i | − 0.384299i | ||||||||
\(149\) | 4.28030e30 | 0.131909 | 0.0659543 | − | 0.997823i | \(-0.478991\pi\) | ||||
0.0659543 | + | 0.997823i | \(0.478991\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.32731e30 | −0.236914 | −0.118457 | − | 0.992959i | \(-0.537795\pi\) | ||||
−0.118457 | + | 0.992959i | \(0.537795\pi\) | |||||||
\(152\) | 2.55773e31i | 0.590367i | ||||||||
\(153\) | 1.05714e32i | 2.21874i | ||||||||
\(154\) | −7.07486e29 | −0.0135104 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.28939e31 | −0.362587 | ||||||||
\(157\) | 2.58823e31i | 0.373644i | 0.982394 | + | 0.186822i | \(0.0598188\pi\) | ||||
−0.982394 | + | 0.186822i | \(0.940181\pi\) | |||||||
\(158\) | 8.55583e31i | 1.12651i | ||||||||
\(159\) | −2.39983e31 | −0.288351 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.57170e28 | 0.000558486 0 | ||||||||
\(162\) | 1.45407e32i | 1.33234i | ||||||||
\(163\) | − 1.19680e31i | − 0.100300i | −0.998742 | − | 0.0501501i | \(-0.984030\pi\) | ||||
0.998742 | − | 0.0501501i | \(-0.0159700\pi\) | |||||||
\(164\) | 8.67072e29 | 0.00664997 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.14748e32 | −0.738204 | ||||||||
\(167\) | 1.07804e32i | 0.635692i | 0.948142 | + | 0.317846i | \(0.102959\pi\) | ||||
−0.948142 | + | 0.317846i | \(0.897041\pi\) | |||||||
\(168\) | 5.06545e30i | 0.0273926i | ||||||||
\(169\) | 7.94575e31 | 0.394255 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.52110e32 | −1.47311 | ||||||||
\(172\) | 9.61562e31i | 0.369671i | ||||||||
\(173\) | − 3.82198e32i | − 1.35089i | −0.737410 | − | 0.675446i | \(-0.763951\pi\) | ||||
0.737410 | − | 0.675446i | \(-0.236049\pi\) | |||||||
\(174\) | 7.09436e32 | 2.30648 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.74698e32 | 0.756698 | ||||||||
\(177\) | 1.29513e33i | 3.28624i | ||||||||
\(178\) | 1.58242e31i | 0.0370025i | ||||||||
\(179\) | 5.24041e32 | 1.12979 | 0.564893 | − | 0.825164i | \(-0.308917\pi\) | ||||
0.564893 | + | 0.825164i | \(0.308917\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.54402e32 | −1.38441 | −0.692203 | − | 0.721703i | \(-0.743360\pi\) | ||||
−0.692203 | + | 0.721703i | \(0.743360\pi\) | |||||||
\(182\) | − 9.80473e30i | − 0.0166112i | ||||||||
\(183\) | 6.66521e32i | 1.04297i | ||||||||
\(184\) | −1.68138e31 | −0.0243113 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.81306e33 | 2.24116 | ||||||||
\(187\) | 5.96112e32i | 0.681750i | ||||||||
\(188\) | 2.72180e32i | 0.288116i | ||||||||
\(189\) | −3.58844e31 | −0.0351730 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.08024e33 | −0.908947 | −0.454473 | − | 0.890760i | \(-0.650173\pi\) | ||||
−0.454473 | + | 0.890760i | \(0.650173\pi\) | |||||||
\(192\) | − 1.36956e33i | − 1.06835i | ||||||||
\(193\) | − 1.91169e33i | − 1.38305i | −0.722354 | − | 0.691524i | \(-0.756940\pi\) | ||||
0.722354 | − | 0.691524i | \(-0.243060\pi\) | |||||||
\(194\) | −3.76693e32 | −0.252849 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.60209e32 | −0.266221 | ||||||||
\(197\) | − 2.82411e33i | − 1.51747i | −0.651397 | − | 0.758737i | \(-0.725817\pi\) | ||||
0.651397 | − | 0.758737i | \(-0.274183\pi\) | |||||||
\(198\) | 2.93915e33i | 1.46749i | ||||||||
\(199\) | −2.05181e33 | −0.952288 | −0.476144 | − | 0.879367i | \(-0.657966\pi\) | ||||
−0.476144 | + | 0.879367i | \(0.657966\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.51838e33 | 0.609590 | ||||||||
\(202\) | − 1.27824e33i | − 0.477547i | ||||||||
\(203\) | 6.38978e31i | 0.0222225i | ||||||||
\(204\) | −1.54924e33 | −0.501742 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.44088e33 | 0.967375 | ||||||||
\(207\) | − 2.31468e32i | − 0.0606626i | ||||||||
\(208\) | 3.80692e33i | 0.930369i | ||||||||
\(209\) | −1.98553e33 | −0.452641 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.24073e33 | −0.842063 | −0.421032 | − | 0.907046i | \(-0.638332\pi\) | ||||
−0.421032 | + | 0.907046i | \(0.638332\pi\) | |||||||
\(212\) | − 2.36767e32i | − 0.0438986i | ||||||||
\(213\) | 2.53962e33i | 0.439809i | ||||||||
\(214\) | 6.03472e33 | 0.976466 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.08289e34 | 1.53111 | ||||||||
\(217\) | 1.63299e32i | 0.0215932i | ||||||||
\(218\) | − 1.75678e34i | − 2.17319i | ||||||||
\(219\) | −6.61810e33 | −0.766115 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.26125e33 | −0.838219 | ||||||||
\(222\) | − 2.98903e34i | − 2.84061i | ||||||||
\(223\) | − 1.95826e34i | − 1.74362i | −0.489848 | − | 0.871808i | \(-0.662948\pi\) | ||||
0.489848 | − | 0.871808i | \(-0.337052\pi\) | |||||||
\(224\) | −1.18092e32 | −0.00985425 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.33017e33 | 0.0975745 | ||||||||
\(227\) | 1.22424e34i | 0.842345i | 0.906980 | + | 0.421173i | \(0.138381\pi\) | ||||
−0.906980 | + | 0.421173i | \(0.861619\pi\) | |||||||
\(228\) | − 5.16018e33i | − 0.333127i | ||||||||
\(229\) | −5.07275e33 | −0.307347 | −0.153673 | − | 0.988122i | \(-0.549110\pi\) | ||||
−0.153673 | + | 0.988122i | \(0.549110\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.93224e32 | −0.0210023 | ||||||||
\(232\) | − 1.92825e34i | − 0.967361i | ||||||||
\(233\) | 2.33456e34i | 1.10038i | 0.835038 | + | 0.550192i | \(0.185446\pi\) | ||||
−0.835038 | + | 0.550192i | \(0.814554\pi\) | |||||||
\(234\) | −4.07323e34 | −1.80430 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.27777e34 | −0.500298 | ||||||||
\(237\) | 4.75536e34i | 1.75119i | ||||||||
\(238\) | − 6.63490e32i | − 0.0229863i | ||||||||
\(239\) | 1.69274e34 | 0.551849 | 0.275925 | − | 0.961179i | \(-0.411016\pi\) | ||||
0.275925 | + | 0.961179i | \(0.411016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.26884e34 | −0.655476 | −0.327738 | − | 0.944769i | \(-0.606286\pi\) | ||||
−0.327738 | + | 0.944769i | \(0.606286\pi\) | |||||||
\(242\) | − 2.47876e34i | − 0.674392i | ||||||||
\(243\) | 8.45454e33i | 0.216670i | ||||||||
\(244\) | −6.57588e33 | −0.158782 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.29151e33 | 0.0491543 | ||||||||
\(247\) | − 2.75165e34i | − 0.556528i | ||||||||
\(248\) | − 4.92790e34i | − 0.939967i | ||||||||
\(249\) | −6.37771e34 | −1.14756 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.82834e34 | −1.57475 | −0.787374 | − | 0.616475i | \(-0.788560\pi\) | ||||
−0.787374 | + | 0.616475i | \(0.788560\pi\) | |||||||
\(252\) | − 6.87992e32i | − 0.0104058i | ||||||||
\(253\) | − 1.30523e33i | − 0.0186398i | ||||||||
\(254\) | −9.04337e34 | −1.21967 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 6.20845e34 | 0.747315 | ||||||||
\(257\) | − 8.53561e34i | − 0.970966i | −0.874246 | − | 0.485483i | \(-0.838644\pi\) | ||||
0.874246 | − | 0.485483i | \(-0.161356\pi\) | |||||||
\(258\) | 2.54122e35i | 2.73248i | ||||||||
\(259\) | 2.69217e33 | 0.0273688 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.65454e35 | 2.41380 | ||||||||
\(262\) | − 3.02996e34i | − 0.260656i | ||||||||
\(263\) | − 2.07906e35i | − 1.69243i | −0.532845 | − | 0.846213i | \(-0.678877\pi\) | ||||
0.532845 | − | 0.846213i | \(-0.321123\pi\) | |||||||
\(264\) | 1.18664e35 | 0.914242 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.20995e33 | 0.0152615 | ||||||||
\(267\) | 8.79513e33i | 0.0575214i | ||||||||
\(268\) | 1.49803e34i | 0.0928039i | ||||||||
\(269\) | 2.34883e35 | 1.37862 | 0.689309 | − | 0.724468i | \(-0.257914\pi\) | ||||
0.689309 | + | 0.724468i | \(0.257914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.82959e34 | −0.465463 | −0.232732 | − | 0.972541i | \(-0.574766\pi\) | ||||
−0.232732 | + | 0.972541i | \(0.574766\pi\) | |||||||
\(272\) | 2.57616e35i | 1.28743i | ||||||||
\(273\) | − 5.44951e33i | − 0.0258225i | ||||||||
\(274\) | 2.92586e35 | 1.31483 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.39217e33 | 0.0137182 | ||||||||
\(277\) | − 7.48695e34i | − 0.287308i | −0.989628 | − | 0.143654i | \(-0.954115\pi\) | ||||
0.989628 | − | 0.143654i | \(-0.0458853\pi\) | |||||||
\(278\) | 5.48191e34i | 0.199656i | ||||||||
\(279\) | 6.78402e35 | 2.34545 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.79424e35 | 1.18272 | 0.591361 | − | 0.806407i | \(-0.298591\pi\) | ||||
0.591361 | + | 0.806407i | \(0.298591\pi\) | |||||||
\(282\) | 7.19320e35i | 2.12966i | ||||||||
\(283\) | − 5.23811e35i | − 1.47323i | −0.676311 | − | 0.736616i | \(-0.736422\pi\) | ||||
0.676311 | − | 0.736616i | \(-0.263578\pi\) | |||||||
\(284\) | −2.50558e34 | −0.0669566 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.29686e35 | −0.554406 | ||||||||
\(287\) | 2.06392e32i | 0 0.000473593i | ||||||||
\(288\) | 4.90595e35i | 1.07037i | ||||||||
\(289\) | −7.70734e34 | −0.159914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.09367e35 | −0.393061 | ||||||||
\(292\) | − 6.52941e34i | − 0.116633i | ||||||||
\(293\) | 8.91980e35i | 1.51626i | 0.652102 | + | 0.758131i | \(0.273887\pi\) | ||||
−0.652102 | + | 0.758131i | \(0.726113\pi\) | |||||||
\(294\) | −1.21624e36 | −1.96782 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.12420e35 | −1.19138 | ||||||||
\(297\) | 8.40632e35i | 1.17392i | ||||||||
\(298\) | 1.11604e35i | 0.148438i | ||||||||
\(299\) | 1.80886e34 | 0.0229178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.28884e34 | −0.0263270 | ||||||||
\(302\) | − 2.43200e35i | − 0.266601i | ||||||||
\(303\) | − 7.10449e35i | − 0.742360i | ||||||||
\(304\) | −8.58064e35 | −0.854777 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.75637e36 | −2.49676 | ||||||||
\(307\) | 6.34791e35i | 0.548434i | 0.961668 | + | 0.274217i | \(0.0884187\pi\) | ||||
−0.961668 | + | 0.274217i | \(0.911581\pi\) | |||||||
\(308\) | − 3.87954e33i | − 0.00319738i | ||||||||
\(309\) | 1.91246e36 | 1.50381 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.79660e36 | 1.28655 | 0.643273 | − | 0.765637i | \(-0.277576\pi\) | ||||
0.643273 | + | 0.765637i | \(0.277576\pi\) | |||||||
\(312\) | 1.64451e36i | 1.12407i | ||||||||
\(313\) | 2.68729e36i | 1.75357i | 0.480886 | + | 0.876783i | \(0.340315\pi\) | ||||
−0.480886 | + | 0.876783i | \(0.659685\pi\) | |||||||
\(314\) | −6.74853e35 | −0.420465 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.69163e35 | −0.266601 | ||||||||
\(317\) | 1.03006e36i | 0.559119i | 0.960128 | + | 0.279559i | \(0.0901884\pi\) | ||||
−0.960128 | + | 0.279559i | \(0.909812\pi\) | |||||||
\(318\) | − 6.25729e35i | − 0.324484i | ||||||||
\(319\) | 1.49687e36 | 0.741687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.35412e36 | 1.51794 | ||||||||
\(322\) | 1.45276e33i | 0 0.000628469i | ||||||||
\(323\) | − 1.86205e36i | − 0.770114i | ||||||||
\(324\) | −7.97344e35 | −0.315314 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.12053e35 | 0.112869 | ||||||||
\(327\) | − 9.76422e36i | − 3.37828i | ||||||||
\(328\) | − 6.22833e34i | − 0.0206158i | ||||||||
\(329\) | −6.47880e34 | −0.0205189 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.57492e36 | 0.456827 | 0.228414 | − | 0.973564i | \(-0.426646\pi\) | ||||
0.228414 | + | 0.973564i | \(0.426646\pi\) | |||||||
\(332\) | − 6.29224e35i | − 0.174704i | ||||||||
\(333\) | − 1.11842e37i | − 2.97279i | ||||||||
\(334\) | −2.81087e36 | −0.715348 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.69935e35 | −0.0396611 | ||||||||
\(337\) | − 3.02595e36i | − 0.676438i | −0.941067 | − | 0.338219i | \(-0.890176\pi\) | ||||
0.941067 | − | 0.338219i | \(-0.109824\pi\) | |||||||
\(338\) | 2.07177e36i | 0.443658i | ||||||||
\(339\) | 7.39316e35 | 0.151682 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.82546e36 | 0.720684 | ||||||||
\(342\) | − 9.18090e36i | − 1.65770i | ||||||||
\(343\) | − 2.19130e35i | − 0.0379259i | ||||||||
\(344\) | 6.90707e36 | 1.14603 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.96541e36 | 1.52017 | ||||||||
\(347\) | 4.44778e36i | 0.650678i | 0.945597 | + | 0.325339i | \(0.105478\pi\) | ||||
−0.945597 | + | 0.325339i | \(0.894522\pi\) | |||||||
\(348\) | 3.89023e36i | 0.545854i | ||||||||
\(349\) | 9.68519e35 | 0.130359 | 0.0651793 | − | 0.997874i | \(-0.479238\pi\) | ||||
0.0651793 | + | 0.997874i | \(0.479238\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.16499e37 | −1.44335 | ||||||||
\(352\) | 2.76643e36i | 0.328890i | ||||||||
\(353\) | 9.40660e36i | 1.07325i | 0.843822 | + | 0.536623i | \(0.180300\pi\) | ||||
−0.843822 | + | 0.536623i | \(0.819700\pi\) | |||||||
\(354\) | −3.37690e37 | −3.69804 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.67726e34 | −0.00875705 | ||||||||
\(357\) | − 3.68770e35i | − 0.0357328i | ||||||||
\(358\) | 1.36638e37i | 1.27136i | ||||||||
\(359\) | −2.90920e36 | −0.259958 | −0.129979 | − | 0.991517i | \(-0.541491\pi\) | ||||
−0.129979 | + | 0.991517i | \(0.541491\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.92772e36 | −0.488690 | ||||||||
\(362\) | − 1.96702e37i | − 1.55788i | ||||||||
\(363\) | − 1.37771e37i | − 1.04836i | ||||||||
\(364\) | 5.37647e34 | 0.00393122 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.73788e37 | −1.17366 | ||||||||
\(367\) | 3.00435e36i | 0.195026i | 0.995234 | + | 0.0975131i | \(0.0310888\pi\) | ||||
−0.995234 | + | 0.0975131i | \(0.968911\pi\) | |||||||
\(368\) | − 5.64069e35i | − 0.0351997i | ||||||||
\(369\) | 8.57426e35 | 0.0514416 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.63584e34 | 0.00312634 | ||||||||
\(372\) | 9.94198e36i | 0.530396i | ||||||||
\(373\) | − 2.82375e37i | − 1.44893i | −0.689310 | − | 0.724466i | \(-0.742086\pi\) | ||||
0.689310 | − | 0.724466i | \(-0.257914\pi\) | |||||||
\(374\) | −1.55430e37 | −0.767178 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.95512e37 | 0.893201 | ||||||||
\(377\) | 2.07445e37i | 0.911913i | ||||||||
\(378\) | − 9.35647e35i | − 0.0395805i | ||||||||
\(379\) | −1.51814e37 | −0.618079 | −0.309039 | − | 0.951049i | \(-0.600007\pi\) | ||||
−0.309039 | + | 0.951049i | \(0.600007\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.02634e37 | −1.89601 | ||||||||
\(382\) | − 2.81662e37i | − 1.02284i | ||||||||
\(383\) | 2.59896e37i | 0.908692i | 0.890825 | + | 0.454346i | \(0.150127\pi\) | ||||
−0.890825 | + | 0.454346i | \(0.849873\pi\) | |||||||
\(384\) | 6.27065e37 | 2.11111 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.98453e37 | 1.55635 | ||||||||
\(387\) | 9.50865e37i | 2.85963i | ||||||||
\(388\) | − 2.06561e36i | − 0.0598397i | ||||||||
\(389\) | 4.80732e37 | 1.34163 | 0.670816 | − | 0.741623i | \(-0.265944\pi\) | ||||
0.670816 | + | 0.741623i | \(0.265944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.22406e36 | 0.0317133 | ||||||||
\(392\) | 3.30576e37i | 0.825322i | ||||||||
\(393\) | − 1.68406e37i | − 0.405197i | ||||||||
\(394\) | 7.36356e37 | 1.70762 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.61170e37 | −0.347299 | ||||||||
\(397\) | − 4.33277e37i | − 0.900126i | −0.892997 | − | 0.450063i | \(-0.851401\pi\) | ||||
0.892997 | − | 0.450063i | \(-0.148599\pi\) | |||||||
\(398\) | − 5.34988e37i | − 1.07162i | ||||||||
\(399\) | 1.22830e36 | 0.0237245 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.87417e37 | −0.516320 | −0.258160 | − | 0.966102i | \(-0.583116\pi\) | ||||
−0.258160 | + | 0.966102i | \(0.583116\pi\) | |||||||
\(402\) | 3.95901e37i | 0.685976i | ||||||||
\(403\) | 5.30153e37i | 0.886090i | ||||||||
\(404\) | 7.00928e36 | 0.113017 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.66606e36 | −0.0250072 | ||||||||
\(407\) | − 6.30670e37i | − 0.913446i | ||||||||
\(408\) | 1.11284e38i | 1.55547i | ||||||||
\(409\) | −8.54677e37 | −1.15296 | −0.576480 | − | 0.817112i | \(-0.695574\pi\) | ||||
−0.576480 | + | 0.817112i | \(0.695574\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.62620e38 | 2.04394 | ||||||||
\(412\) | 1.88683e37i | 0.228940i | ||||||||
\(413\) | − 3.04152e36i | − 0.0356299i | ||||||||
\(414\) | 6.03528e36 | 0.0682641 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.83387e37 | −0.404375 | ||||||||
\(417\) | 3.04686e37i | 0.310370i | ||||||||
\(418\) | − 5.17704e37i | − 0.509361i | ||||||||
\(419\) | 5.26548e37 | 0.500420 | 0.250210 | − | 0.968192i | \(-0.419500\pi\) | ||||
0.250210 | + | 0.968192i | \(0.419500\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.94249e37 | 0.881870 | 0.440935 | − | 0.897539i | \(-0.354647\pi\) | ||||
0.440935 | + | 0.897539i | \(0.354647\pi\) | |||||||
\(422\) | − 1.10572e38i | − 0.947580i | ||||||||
\(423\) | 2.69152e38i | 2.22876i | ||||||||
\(424\) | −1.70074e37 | −0.136092 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.62178e37 | −0.494921 | ||||||||
\(427\) | − 1.56528e36i | − 0.0113081i | ||||||||
\(428\) | 3.30917e37i | 0.231092i | ||||||||
\(429\) | −1.27661e38 | −0.861839 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.96737e38 | −1.24155 | −0.620777 | − | 0.783987i | \(-0.713183\pi\) | ||||
−0.620777 | + | 0.783987i | \(0.713183\pi\) | |||||||
\(432\) | 3.63287e38i | 2.21685i | ||||||||
\(433\) | − 8.93739e37i | − 0.527396i | −0.964605 | − | 0.263698i | \(-0.915058\pi\) | ||||
0.964605 | − | 0.263698i | \(-0.0849422\pi\) | |||||||
\(434\) | −4.25784e36 | −0.0242990 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.63337e37 | 0.514309 | ||||||||
\(437\) | 4.07710e36i | 0.0210557i | ||||||||
\(438\) | − 1.72560e38i | − 0.862115i | ||||||||
\(439\) | 3.31662e38 | 1.60310 | 0.801548 | − | 0.597930i | \(-0.204010\pi\) | ||||
0.801548 | + | 0.597930i | \(0.204010\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.55089e38 | −2.05938 | ||||||||
\(442\) | − 2.15403e38i | − 0.943254i | ||||||||
\(443\) | − 2.62823e38i | − 1.11380i | −0.830578 | − | 0.556902i | \(-0.811990\pi\) | ||||
0.830578 | − | 0.556902i | \(-0.188010\pi\) | |||||||
\(444\) | 1.63905e38 | 0.672262 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.10596e38 | 1.96210 | ||||||||
\(447\) | 6.20299e37i | 0.230750i | ||||||||
\(448\) | 3.21632e36i | 0.0115832i | ||||||||
\(449\) | −1.08508e38 | −0.378348 | −0.189174 | − | 0.981944i | \(-0.560581\pi\) | ||||
−0.189174 | + | 0.981944i | \(0.560581\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.83496e36 | 0.0158064 | ||||||||
\(452\) | 7.29408e36i | 0.0230921i | ||||||||
\(453\) | − 1.35171e38i | − 0.414439i | ||||||||
\(454\) | −3.19206e38 | −0.947897 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.70665e38 | −1.03274 | ||||||||
\(457\) | − 3.49142e38i | − 0.942360i | −0.882037 | − | 0.471180i | \(-0.843828\pi\) | ||||
0.882037 | − | 0.471180i | \(-0.156172\pi\) | |||||||
\(458\) | − 1.32266e38i | − 0.345860i | ||||||||
\(459\) | −7.88356e38 | −1.99728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.84500e38 | 1.39034 | 0.695171 | − | 0.718845i | \(-0.255329\pi\) | ||||
0.695171 | + | 0.718845i | \(0.255329\pi\) | |||||||
\(462\) | − 1.02529e37i | − 0.0236340i | ||||||||
\(463\) | − 2.77160e38i | − 0.619164i | −0.950873 | − | 0.309582i | \(-0.899811\pi\) | ||||
0.950873 | − | 0.309582i | \(-0.100189\pi\) | |||||||
\(464\) | 6.46889e38 | 1.40062 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.08712e38 | −1.23827 | ||||||||
\(467\) | − 9.01377e38i | − 1.77751i | −0.458384 | − | 0.888754i | \(-0.651571\pi\) | ||||
0.458384 | − | 0.888754i | \(-0.348429\pi\) | |||||||
\(468\) | − 2.23358e38i | − 0.427008i | ||||||||
\(469\) | −3.56582e36 | −0.00660926 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.75086e38 | −0.653623 | ||||||||
\(472\) | 9.17845e38i | 1.55099i | ||||||||
\(473\) | 5.36186e38i | 0.878676i | ||||||||
\(474\) | −1.23991e39 | −1.97062 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.63828e36 | 0.00543996 | ||||||||
\(477\) | − 2.34133e38i | − 0.339583i | ||||||||
\(478\) | 4.41363e38i | 0.621000i | ||||||||
\(479\) | −5.62143e38 | −0.767330 | −0.383665 | − | 0.923472i | \(-0.625338\pi\) | ||||
−0.383665 | + | 0.923472i | \(0.625338\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.74016e38 | 1.12309 | ||||||||
\(482\) | − 5.91575e38i | − 0.737612i | ||||||||
\(483\) | 8.07450e35i | 0 0.000976972i | ||||||||
\(484\) | 1.35924e38 | 0.159602 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.20443e38 | −0.243820 | ||||||||
\(487\) | − 1.05085e39i | − 1.12816i | −0.825720 | − | 0.564081i | \(-0.809231\pi\) | ||||
0.825720 | − | 0.564081i | \(-0.190769\pi\) | |||||||
\(488\) | 4.72358e38i | 0.492247i | ||||||||
\(489\) | 1.73440e38 | 0.175457 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.99399e38 | 0.762223 | 0.381112 | − | 0.924529i | \(-0.375541\pi\) | ||||
0.381112 | + | 0.924529i | \(0.375541\pi\) | |||||||
\(492\) | 1.25656e37i | 0.0116329i | ||||||||
\(493\) | 1.40379e39i | 1.26189i | ||||||||
\(494\) | 7.17462e38 | 0.626265 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.65321e39 | 1.36095 | ||||||||
\(497\) | − 5.96413e36i | − 0.00476848i | ||||||||
\(498\) | − 1.66292e39i | − 1.29136i | ||||||||
\(499\) | −1.14067e39 | −0.860401 | −0.430201 | − | 0.902733i | \(-0.641557\pi\) | ||||
−0.430201 | + | 0.902733i | \(0.641557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.56229e39 | −1.11203 | ||||||||
\(502\) | − 2.56263e39i | − 1.77208i | ||||||||
\(503\) | − 3.45164e38i | − 0.231894i | −0.993255 | − | 0.115947i | \(-0.963010\pi\) | ||||
0.993255 | − | 0.115947i | \(-0.0369903\pi\) | |||||||
\(504\) | −4.94197e37 | −0.0322595 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.40325e37 | 0.0209755 | ||||||||
\(507\) | 1.15150e39i | 0.689679i | ||||||||
\(508\) | − 4.95898e38i | − 0.288648i | ||||||||
\(509\) | 7.06121e37 | 0.0399458 | 0.0199729 | − | 0.999801i | \(-0.493642\pi\) | ||||
0.0199729 | + | 0.999801i | \(0.493642\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.55422e37 | 0.00830633 | ||||||||
\(512\) | − 7.04246e38i | − 0.365856i | ||||||||
\(513\) | − 2.62585e39i | − 1.32607i | ||||||||
\(514\) | 2.22557e39 | 1.09264 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.39349e39 | −0.646672 | ||||||||
\(517\) | 1.51773e39i | 0.684828i | ||||||||
\(518\) | 7.01953e37i | 0.0307983i | ||||||||
\(519\) | 5.53881e39 | 2.36314 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.46255e39 | 1.39717 | 0.698585 | − | 0.715528i | \(-0.253814\pi\) | ||||
0.698585 | + | 0.715528i | \(0.253814\pi\) | |||||||
\(522\) | 6.92142e39i | 2.71627i | ||||||||
\(523\) | 1.15392e39i | 0.440453i | 0.975449 | + | 0.220227i | \(0.0706797\pi\) | ||||
−0.975449 | + | 0.220227i | \(0.929320\pi\) | |||||||
\(524\) | 1.66149e38 | 0.0616872 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.42093e39 | 1.90450 | ||||||||
\(527\) | 3.58756e39i | 1.22616i | ||||||||
\(528\) | 3.98092e39i | 1.32371i | ||||||||
\(529\) | 3.08838e39 | 0.999133 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.26355e40 | −3.87011 | ||||||||
\(532\) | 1.21184e37i | 0.00361181i | ||||||||
\(533\) | 6.70055e37i | 0.0194342i | ||||||||
\(534\) | −2.29323e38 | −0.0647292 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.07606e39 | 0.287705 | ||||||||
\(537\) | 7.59439e39i | 1.97636i | ||||||||
\(538\) | 6.12432e39i | 1.55137i | ||||||||
\(539\) | −2.56621e39 | −0.632784 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.74672e39 | −0.641879 | −0.320940 | − | 0.947100i | \(-0.603999\pi\) | ||||
−0.320940 | + | 0.947100i | \(0.603999\pi\) | |||||||
\(542\) | − 2.30222e39i | − 0.523789i | ||||||||
\(543\) | − 1.09328e40i | − 2.42177i | ||||||||
\(544\) | −2.59439e39 | −0.559567 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.42090e38 | 0.0290583 | ||||||||
\(547\) | − 5.50487e39i | − 1.09630i | −0.836379 | − | 0.548152i | \(-0.815331\pi\) | ||||
0.836379 | − | 0.548152i | \(-0.184669\pi\) | |||||||
\(548\) | 1.60441e39i | 0.311170i | ||||||||
\(549\) | −6.50273e39 | −1.22828 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.67573e39 | −0.837820 | ||||||||
\(552\) | − 2.43666e38i | − 0.0425282i | ||||||||
\(553\) | − 1.11677e38i | − 0.0189866i | ||||||||
\(554\) | 1.95214e39 | 0.323310 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00603e38 | −0.0472508 | ||||||||
\(557\) | − 4.48537e39i | − 0.686908i | −0.939170 | − | 0.343454i | \(-0.888403\pi\) | ||||
0.939170 | − | 0.343454i | \(-0.111597\pi\) | |||||||
\(558\) | 1.76886e40i | 2.63935i | ||||||||
\(559\) | −7.43075e39 | −1.08034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.63885e39 | −1.19260 | ||||||||
\(562\) | 9.89305e39i | 1.33093i | ||||||||
\(563\) | − 6.55822e38i | − 0.0859834i | −0.999075 | − | 0.0429917i | \(-0.986311\pi\) | ||||
0.999075 | − | 0.0429917i | \(-0.0136889\pi\) | |||||||
\(564\) | −3.94443e39 | −0.504008 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.36578e40 | 1.65784 | ||||||||
\(567\) | − 1.89795e38i | − 0.0224559i | ||||||||
\(568\) | 1.79981e39i | 0.207575i | ||||||||
\(569\) | 1.62256e40 | 1.82420 | 0.912099 | − | 0.409970i | \(-0.134461\pi\) | ||||
0.912099 | + | 0.409970i | \(0.134461\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.28706e39 | 0.992327 | 0.496163 | − | 0.868229i | \(-0.334742\pi\) | ||||
0.496163 | + | 0.868229i | \(0.334742\pi\) | |||||||
\(572\) | − 1.25950e39i | − 0.131206i | ||||||||
\(573\) | − 1.56549e40i | − 1.59004i | ||||||||
\(574\) | −5.38145e36 | −0.000532938 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.33617e40 | 1.25816 | ||||||||
\(577\) | − 2.84801e39i | − 0.261513i | −0.991415 | − | 0.130756i | \(-0.958259\pi\) | ||||
0.991415 | − | 0.130756i | \(-0.0417406\pi\) | |||||||
\(578\) | − 2.00960e39i | − 0.179952i | ||||||||
\(579\) | 2.77042e40 | 2.41939 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.49776e38 | 0.0124420 | ||||||||
\(582\) | − 5.45902e39i | − 0.442315i | ||||||||
\(583\) | − 1.32026e39i | − 0.104343i | ||||||||
\(584\) | −4.69019e39 | −0.361580 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.32574e40 | −1.70626 | ||||||||
\(587\) | − 5.47078e39i | − 0.391559i | −0.980648 | − | 0.195779i | \(-0.937276\pi\) | ||||
0.980648 | − | 0.195779i | \(-0.0627236\pi\) | |||||||
\(588\) | − 6.66934e39i | − 0.465705i | ||||||||
\(589\) | −1.19494e40 | −0.814095 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.09269e40 | 2.65455 | ||||||||
\(592\) | − 2.72550e40i | − 1.72497i | ||||||||
\(593\) | − 2.22596e40i | − 1.37475i | −0.726302 | − | 0.687376i | \(-0.758762\pi\) | ||||
0.726302 | − | 0.687376i | \(-0.241238\pi\) | |||||||
\(594\) | −2.19186e40 | −1.32102 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.11986e38 | −0.0351294 | ||||||||
\(597\) | − 2.97348e40i | − 1.66586i | ||||||||
\(598\) | 4.71641e38i | 0.0257896i | ||||||||
\(599\) | −2.08204e39 | −0.111122 | −0.0555611 | − | 0.998455i | \(-0.517695\pi\) | ||||
−0.0555611 | + | 0.998455i | \(0.517695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.47384e40 | −0.749498 | −0.374749 | − | 0.927126i | \(-0.622271\pi\) | ||||
−0.374749 | + | 0.927126i | \(0.622271\pi\) | |||||||
\(602\) | − 5.96790e38i | − 0.0296260i | ||||||||
\(603\) | 1.48137e40i | 0.717895i | ||||||||
\(604\) | 1.33360e39 | 0.0630941 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.85242e40 | 0.835383 | ||||||||
\(607\) | 1.37809e40i | 0.606796i | 0.952864 | + | 0.303398i | \(0.0981211\pi\) | ||||
−0.952864 | + | 0.303398i | \(0.901879\pi\) | |||||||
\(608\) | − 8.64138e39i | − 0.371519i | ||||||||
\(609\) | −9.26005e38 | −0.0388743 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.10335e40 | −0.842004 | ||||||||
\(612\) | − 1.51147e40i | − 0.590886i | ||||||||
\(613\) | − 1.47390e40i | − 0.562717i | −0.959603 | − | 0.281358i | \(-0.909215\pi\) | ||||
0.959603 | − | 0.281358i | \(-0.0907850\pi\) | |||||||
\(614\) | −1.65515e40 | −0.617157 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.78674e38 | −0.00991234 | ||||||||
\(617\) | 4.06519e39i | 0.141236i | 0.997503 | + | 0.0706181i | \(0.0224971\pi\) | ||||
−0.997503 | + | 0.0706181i | \(0.977503\pi\) | |||||||
\(618\) | 4.98652e40i | 1.69225i | ||||||||
\(619\) | −3.64687e40 | −1.20894 | −0.604472 | − | 0.796627i | \(-0.706616\pi\) | ||||
−0.604472 | + | 0.796627i | \(0.706616\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.72616e39 | 0.0546077 | ||||||||
\(622\) | 4.68444e40i | 1.44776i | ||||||||
\(623\) | − 2.06548e37i | 0 0.000623655i | ||||||||
\(624\) | −5.51698e40 | −1.62751 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.00682e40 | −1.97330 | ||||||||
\(627\) | − 2.87742e40i | − 0.791815i | ||||||||
\(628\) | − 3.70059e39i | − 0.0995076i | ||||||||
\(629\) | 5.91450e40 | 1.55412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.88296e40 | −1.72723 | −0.863613 | − | 0.504155i | \(-0.831804\pi\) | ||||
−0.863613 | + | 0.504155i | \(0.831804\pi\) | |||||||
\(632\) | 3.37008e40i | 0.826500i | ||||||||
\(633\) | − 6.14565e40i | − 1.47304i | ||||||||
\(634\) | −2.68577e40 | −0.629181 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.43122e39 | 0.0767927 | ||||||||
\(637\) | − 3.55640e40i | − 0.778016i | ||||||||
\(638\) | 3.90294e40i | 0.834626i | ||||||||
\(639\) | −2.47771e40 | −0.517950 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.79208e40 | 1.15716 | 0.578580 | − | 0.815626i | \(-0.303607\pi\) | ||||
0.578580 | + | 0.815626i | \(0.303607\pi\) | |||||||
\(642\) | 8.74550e40i | 1.70815i | ||||||||
\(643\) | 6.13559e40i | 1.17165i | 0.810439 | + | 0.585824i | \(0.199229\pi\) | ||||
−0.810439 | + | 0.585824i | \(0.800771\pi\) | |||||||
\(644\) | −7.96629e36 | −0.000148734 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.85510e40 | 0.866615 | ||||||||
\(647\) | − 1.10620e40i | − 0.193074i | −0.995329 | − | 0.0965369i | \(-0.969223\pi\) | ||||
0.995329 | − | 0.0965369i | \(-0.0307766\pi\) | |||||||
\(648\) | 5.72747e40i | 0.977518i | ||||||||
\(649\) | −7.12509e40 | −1.18917 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.36652e39 | −0.0377735 | ||||||||
\(652\) | 1.71116e39i | 0.0267116i | ||||||||
\(653\) | − 9.61992e40i | − 1.46869i | −0.678776 | − | 0.734346i | \(-0.737489\pi\) | ||||
0.678776 | − | 0.734346i | \(-0.262511\pi\) | |||||||
\(654\) | 2.54591e41 | 3.80160 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.08948e39 | 0.0298491 | ||||||||
\(657\) | − 6.45677e40i | − 0.902231i | ||||||||
\(658\) | − 1.68928e39i | − 0.0230901i | ||||||||
\(659\) | −2.42717e40 | −0.324535 | −0.162268 | − | 0.986747i | \(-0.551881\pi\) | ||||
−0.162268 | + | 0.986747i | \(0.551881\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.66824e40 | −1.10920 | −0.554600 | − | 0.832117i | \(-0.687129\pi\) | ||||
−0.554600 | + | 0.832117i | \(0.687129\pi\) | |||||||
\(662\) | 4.10643e40i | 0.514071i | ||||||||
\(663\) | − 1.19722e41i | − 1.46631i | ||||||||
\(664\) | −4.51983e40 | −0.541608 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.91616e41 | 3.34530 | ||||||||
\(667\) | − 3.07370e39i | − 0.0345014i | ||||||||
\(668\) | − 1.54136e40i | − 0.169295i | ||||||||
\(669\) | 2.83791e41 | 3.05014 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.66684e40 | −0.377412 | ||||||||
\(672\) | − 1.71138e39i | − 0.0172382i | ||||||||
\(673\) | 8.20694e40i | 0.809027i | 0.914532 | + | 0.404513i | \(0.132559\pi\) | ||||
−0.914532 | + | 0.404513i | \(0.867441\pi\) | |||||||
\(674\) | 7.88983e40 | 0.761201 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.13606e40 | −0.104997 | ||||||||
\(677\) | 1.82761e41i | 1.65328i | 0.562730 | + | 0.826640i | \(0.309751\pi\) | ||||
−0.562730 | + | 0.826640i | \(0.690249\pi\) | |||||||
\(678\) | 1.92769e40i | 0.170689i | ||||||||
\(679\) | 4.91685e38 | 0.00426163 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.77416e41 | −1.47353 | ||||||||
\(682\) | 9.97446e40i | 0.810991i | ||||||||
\(683\) | 3.66780e39i | 0.0291948i | 0.999893 | + | 0.0145974i | \(0.00464666\pi\) | ||||
−0.999893 | + | 0.0145974i | \(0.995353\pi\) | |||||||
\(684\) | 5.03439e40 | 0.392314 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 5.71356e39 | 0.0426783 | ||||||||
\(687\) | − 7.35141e40i | − 0.537648i | ||||||||
\(688\) | 2.31718e41i | 1.65931i | ||||||||
\(689\) | 1.82968e40 | 0.128291 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.62493e40 | 0.378169 | 0.189084 | − | 0.981961i | \(-0.439448\pi\) | ||||
0.189084 | + | 0.981961i | \(0.439448\pi\) | |||||||
\(692\) | 5.46458e40i | 0.359765i | ||||||||
\(693\) | − 3.83638e39i | − 0.0247337i | ||||||||
\(694\) | −1.15971e41 | −0.732213 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.79442e41 | 1.69222 | ||||||||
\(697\) | 4.53429e39i | 0.0268927i | ||||||||
\(698\) | 2.52531e40i | 0.146693i | ||||||||
\(699\) | −3.38324e41 | −1.92493 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.31831e40 | 0.235724 | 0.117862 | − | 0.993030i | \(-0.462396\pi\) | ||||
0.117862 | + | 0.993030i | \(0.462396\pi\) | |||||||
\(702\) | − 3.03759e41i | − 1.62421i | ||||||||
\(703\) | 1.97000e41i | 1.03184i | ||||||||
\(704\) | 7.53459e40 | 0.386595 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.45267e41 | −1.20773 | ||||||||
\(707\) | 1.66844e39i | 0.00804878i | ||||||||
\(708\) | − 1.85174e41i | − 0.875181i | ||||||||
\(709\) | −3.70730e41 | −1.71667 | −0.858336 | − | 0.513088i | \(-0.828501\pi\) | ||||
−0.858336 | + | 0.513088i | \(0.828501\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.63944e41 | −2.06232 | ||||||||
\(712\) | 6.23303e39i | 0.0271481i | ||||||||
\(713\) | − 7.85524e39i | − 0.0335244i | ||||||||
\(714\) | 9.61528e39 | 0.0402104 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.49262e40 | −0.300881 | ||||||||
\(717\) | 2.45311e41i | 0.965361i | ||||||||
\(718\) | − 7.58541e40i | − 0.292533i | ||||||||
\(719\) | 3.14942e40 | 0.119031 | 0.0595157 | − | 0.998227i | \(-0.481044\pi\) | ||||
0.0595157 | + | 0.998227i | \(0.481044\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.49128e39 | −0.0163045 | ||||||||
\(722\) | − 1.54559e41i | − 0.549926i | ||||||||
\(723\) | − 3.28800e41i | − 1.14664i | ||||||||
\(724\) | 1.07863e41 | 0.368690 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.59222e41 | 1.17973 | ||||||||
\(727\) | 2.91745e41i | 0.939192i | 0.882881 | + | 0.469596i | \(0.155600\pi\) | ||||
−0.882881 | + | 0.469596i | \(0.844400\pi\) | |||||||
\(728\) | − 3.86202e39i | − 0.0121873i | ||||||||
\(729\) | 2.60209e41 | 0.804957 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.02842e41 | −1.49496 | ||||||||
\(732\) | − 9.52976e40i | − 0.277761i | ||||||||
\(733\) | 3.81345e41i | 1.08971i | 0.838531 | + | 0.544854i | \(0.183415\pi\) | ||||
−0.838531 | + | 0.544854i | \(0.816585\pi\) | |||||||
\(734\) | −7.83352e40 | −0.219464 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.68062e39 | 0.0152991 | ||||||||
\(737\) | 8.35331e40i | 0.220587i | ||||||||
\(738\) | 2.23564e40i | 0.0578876i | ||||||||
\(739\) | −5.69450e41 | −1.44581 | −0.722905 | − | 0.690947i | \(-0.757194\pi\) | ||||
−0.722905 | + | 0.690947i | \(0.757194\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.98768e41 | 0.973546 | ||||||||
\(742\) | 1.46948e39i | 0.00351810i | ||||||||
\(743\) | − 2.24951e41i | − 0.528140i | −0.964503 | − | 0.264070i | \(-0.914935\pi\) | ||||
0.964503 | − | 0.264070i | \(-0.0850650\pi\) | |||||||
\(744\) | 7.14150e41 | 1.64430 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.36262e41 | 1.63049 | ||||||||
\(747\) | − 6.22224e41i | − 1.35144i | ||||||||
\(748\) | − 8.52307e40i | − 0.181561i | ||||||||
\(749\) | −7.87693e39 | −0.0164578 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.45261e41 | −1.29705 | −0.648524 | − | 0.761194i | \(-0.724614\pi\) | ||||
−0.648524 | + | 0.761194i | \(0.724614\pi\) | |||||||
\(752\) | 6.55901e41i | 1.29324i | ||||||||
\(753\) | − 1.42432e42i | − 2.75474i | ||||||||
\(754\) | −5.40890e41 | −1.02618 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.13067e39 | 0.00936716 | ||||||||
\(757\) | − 8.68640e41i | − 1.55579i | −0.628397 | − | 0.777893i | \(-0.716289\pi\) | ||||
0.628397 | − | 0.777893i | \(-0.283711\pi\) | |||||||
\(758\) | − 3.95839e41i | − 0.695528i | ||||||||
\(759\) | 1.89154e40 | 0.0326069 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.39407e41 | 0.729104 | 0.364552 | − | 0.931183i | \(-0.381222\pi\) | ||||
0.364552 | + | 0.931183i | \(0.381222\pi\) | |||||||
\(762\) | − 1.31056e42i | − 2.13359i | ||||||||
\(763\) | 2.29306e40i | 0.0366278i | ||||||||
\(764\) | 1.54451e41 | 0.242068 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.77649e41 | −1.02256 | ||||||||
\(767\) | − 9.87434e41i | − 1.46209i | ||||||||
\(768\) | 8.99727e41i | 1.30729i | ||||||||
\(769\) | 3.86450e41 | 0.551012 | 0.275506 | − | 0.961299i | \(-0.411155\pi\) | ||||
0.275506 | + | 0.961299i | \(0.411155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.23698e42 | 1.69853 | ||||||||
\(772\) | 2.73329e41i | 0.368328i | ||||||||
\(773\) | − 3.89700e41i | − 0.515380i | −0.966228 | − | 0.257690i | \(-0.917039\pi\) | ||||
0.966228 | − | 0.257690i | \(-0.0829614\pi\) | |||||||
\(774\) | −2.47928e42 | −3.21796 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −1.48377e41 | −0.185511 | ||||||||
\(777\) | 3.90148e40i | 0.0478768i | ||||||||
\(778\) | 1.25346e42i | 1.50975i | ||||||||
\(779\) | −1.51028e40 | −0.0178552 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.39716e41 | −0.159150 | ||||||||
\(782\) | 3.19161e40i | 0.0356872i | ||||||||
\(783\) | 1.97961e42i | 2.17287i | ||||||||
\(784\) | −1.10901e42 | −1.19496 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 4.39101e41 | 0.455972 | ||||||||
\(787\) | 8.84928e41i | 0.902140i | 0.892488 | + | 0.451070i | \(0.148958\pi\) | ||||
−0.892488 | + | 0.451070i | \(0.851042\pi\) | |||||||
\(788\) | 4.03784e41i | 0.404128i | ||||||||
\(789\) | 3.01297e42 | 2.96059 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.73624e39 | −0.00164456 | ||||||||
\(792\) | 1.15771e42i | 1.07668i | ||||||||
\(793\) | − 5.08171e41i | − 0.464032i | ||||||||
\(794\) | 1.12972e42 | 1.01292 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.93363e41 | 0.253610 | ||||||||
\(797\) | − 6.26660e41i | − 0.531969i | −0.963977 | − | 0.265985i | \(-0.914303\pi\) | ||||
0.963977 | − | 0.265985i | \(-0.0856971\pi\) | |||||||
\(798\) | 3.20265e40i | 0.0266973i | ||||||||
\(799\) | −1.42335e42 | −1.16515 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.58073e40 | −0.0677412 | ||||||||
\(802\) | − 7.49409e41i | − 0.581019i | ||||||||
\(803\) | − 3.64093e41i | − 0.277228i | ||||||||
\(804\) | −2.17094e41 | −0.162344 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.38231e42 | −0.997123 | ||||||||
\(807\) | 3.40392e42i | 2.41164i | ||||||||
\(808\) | − 5.03489e41i | − 0.350369i | ||||||||
\(809\) | 8.71861e41 | 0.595928 | 0.297964 | − | 0.954577i | \(-0.403692\pi\) | ||||
0.297964 | + | 0.954577i | \(0.403692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.09697e41 | 0.599922 | 0.299961 | − | 0.953952i | \(-0.403026\pi\) | ||||
0.299961 | + | 0.953952i | \(0.403026\pi\) | |||||||
\(812\) | − 9.13595e39i | − 0.00591822i | ||||||||
\(813\) | − 1.27958e42i | − 0.814245i | ||||||||
\(814\) | 1.64440e42 | 1.02791 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.73336e42 | −2.25213 | ||||||||
\(817\) | − 1.67486e42i | − 0.992565i | ||||||||
\(818\) | − 2.22848e42i | − 1.29743i | ||||||||
\(819\) | 5.31666e40 | 0.0304104 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.52548e42 | 0.842231 | 0.421115 | − | 0.907007i | \(-0.361639\pi\) | ||||
0.421115 | + | 0.907007i | \(0.361639\pi\) | |||||||
\(822\) | 4.24015e42i | 2.30006i | ||||||||
\(823\) | 1.67746e42i | 0.894037i | 0.894525 | + | 0.447019i | \(0.147514\pi\) | ||||
−0.894525 | + | 0.447019i | \(0.852486\pi\) | |||||||
\(824\) | 1.35534e42 | 0.709747 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.93043e40 | 0.0400946 | ||||||||
\(827\) | − 3.12102e42i | − 1.55048i | −0.631665 | − | 0.775242i | \(-0.717628\pi\) | ||||
0.631665 | − | 0.775242i | \(-0.282372\pi\) | |||||||
\(828\) | 3.30948e40i | 0.0161555i | ||||||||
\(829\) | 1.01143e42 | 0.485174 | 0.242587 | − | 0.970130i | \(-0.422004\pi\) | ||||
0.242587 | + | 0.970130i | \(0.422004\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.08501e42 | 0.502595 | ||||||||
\(832\) | 1.04418e42i | 0.475323i | ||||||||
\(833\) | − 2.40663e42i | − 1.07661i | ||||||||
\(834\) | −7.94436e41 | −0.349262 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.83886e41 | 0.120546 | ||||||||
\(837\) | 5.05915e42i | 2.11134i | ||||||||
\(838\) | 1.37292e42i | 0.563126i | ||||||||
\(839\) | −1.10356e42 | −0.444887 | −0.222443 | − | 0.974946i | \(-0.571403\pi\) | ||||
−0.222443 | + | 0.974946i | \(0.571403\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.57314e41 | 0.372832 | ||||||||
\(842\) | 2.59240e42i | 0.992375i | ||||||||
\(843\) | 5.49860e42i | 2.06896i | ||||||||
\(844\) | 6.06329e41 | 0.224255 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.01785e42 | −2.50804 | ||||||||
\(847\) | 3.23545e40i | 0.0113665i | ||||||||
\(848\) | − 5.70562e41i | − 0.197044i | ||||||||
\(849\) | 7.59106e42 | 2.57716 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.29502e41 | −0.0424912 | ||||||||
\(852\) | − 3.63109e41i | − 0.117129i | ||||||||
\(853\) | − 1.80886e42i | − 0.573646i | −0.957984 | − | 0.286823i | \(-0.907401\pi\) | ||||
0.957984 | − | 0.286823i | \(-0.0925992\pi\) | |||||||
\(854\) | 4.08130e40 | 0.0127250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.37704e42 | 0.716417 | ||||||||
\(857\) | 3.58273e42i | 1.06168i | 0.847473 | + | 0.530838i | \(0.178123\pi\) | ||||
−0.847473 | + | 0.530838i | \(0.821877\pi\) | |||||||
\(858\) | − 3.32861e42i | − 0.969834i | ||||||||
\(859\) | −3.55534e42 | −1.01855 | −0.509273 | − | 0.860605i | \(-0.670086\pi\) | ||||
−0.509273 | + | 0.860605i | \(0.670086\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.99103e39 | −0.000828467 0 | ||||||||
\(862\) | − 5.12970e42i | − 1.39713i | ||||||||
\(863\) | 5.78959e42i | 1.55057i | 0.631612 | + | 0.775285i | \(0.282394\pi\) | ||||
−0.631612 | + | 0.775285i | \(0.717606\pi\) | |||||||
\(864\) | −3.65859e42 | −0.963528 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.33033e42 | 0.593482 | ||||||||
\(867\) | − 1.11695e42i | − 0.279740i | ||||||||
\(868\) | − 2.33481e40i | − 0.00575063i | ||||||||
\(869\) | −2.61614e42 | −0.633687 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.15765e42 | −0.271215 | ||||||||
\(872\) | − 6.91982e42i | − 1.59443i | ||||||||
\(873\) | − 2.04263e42i | − 0.462897i | ||||||||
\(874\) | −1.06306e41 | −0.0236942 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.46241e41 | 0.204029 | ||||||||
\(877\) | − 1.74620e42i | − 0.370340i | −0.982707 | − | 0.185170i | \(-0.940716\pi\) | ||||
0.982707 | − | 0.185170i | \(-0.0592835\pi\) | |||||||
\(878\) | 8.64771e42i | 1.80398i | ||||||||
\(879\) | −1.29265e43 | −2.65243 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.11305e42 | 1.21369 | 0.606844 | − | 0.794821i | \(-0.292435\pi\) | ||||
0.606844 | + | 0.794821i | \(0.292435\pi\) | |||||||
\(882\) | − 1.18659e43i | − 2.31744i | ||||||||
\(883\) | 5.67511e42i | 1.09029i | 0.838340 | + | 0.545147i | \(0.183526\pi\) | ||||
−0.838340 | + | 0.545147i | \(0.816474\pi\) | |||||||
\(884\) | 1.18117e42 | 0.223232 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.85281e42 | 1.25337 | ||||||||
\(887\) | 1.28948e42i | 0.232019i | 0.993248 | + | 0.116009i | \(0.0370102\pi\) | ||||
−0.993248 | + | 0.116009i | \(0.962990\pi\) | |||||||
\(888\) | − 1.17736e43i | − 2.08411i | ||||||||
\(889\) | 1.18040e41 | 0.0205568 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.44615e42 | −0.749475 | ||||||||
\(892\) | 2.79988e42i | 0.464354i | ||||||||
\(893\) | − 4.74087e42i | − 0.773592i | ||||||||
\(894\) | −1.61736e42 | −0.259665 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.47262e41 | −0.0228889 | ||||||||
\(897\) | 2.62140e41i | 0.0400906i | ||||||||
\(898\) | − 2.82924e42i | − 0.425758i | ||||||||
\(899\) | 9.00859e42 | 1.33396 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.23815e42 | 0.177527 | ||||||||
\(902\) | 1.26066e41i | 0.0177871i | ||||||||
\(903\) | − 3.31698e41i | − 0.0460543i | ||||||||
\(904\) | 5.23947e41 | 0.0715888 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.52444e42 | 0.466371 | ||||||||
\(907\) | − 6.85671e42i | − 0.892915i | −0.894805 | − | 0.446457i | \(-0.852685\pi\) | ||||
0.894805 | − | 0.446457i | \(-0.147315\pi\) | |||||||
\(908\) | − 1.75038e42i | − 0.224331i | ||||||||
\(909\) | 6.93130e42 | 0.874255 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.18262e42 | −0.755363 | −0.377682 | − | 0.925936i | \(-0.623279\pi\) | ||||
−0.377682 | + | 0.925936i | \(0.623279\pi\) | |||||||
\(912\) | − 1.24350e43i | − 1.49528i | ||||||||
\(913\) | − 3.50868e42i | − 0.415257i | ||||||||
\(914\) | 9.10348e42 | 1.06044 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.25289e41 | 0.0818516 | ||||||||
\(917\) | 3.95491e40i | 0.00439321i | ||||||||
\(918\) | − 2.05555e43i | − 2.24755i | ||||||||
\(919\) | −7.15141e42 | −0.769691 | −0.384846 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384846 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.19938e42 | −0.959387 | ||||||||
\(922\) | 1.52402e43i | 1.56456i | ||||||||
\(923\) | − 1.93626e42i | − 0.195677i | ||||||||
\(924\) | 5.62222e40 | 0.00559325 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.22663e42 | 0.696749 | ||||||||
\(927\) | 1.86583e43i | 1.77099i | ||||||||
\(928\) | 6.51468e42i | 0.608762i | ||||||||
\(929\) | −1.19347e43 | −1.09795 | −0.548975 | − | 0.835839i | \(-0.684982\pi\) | ||||
−0.548975 | + | 0.835839i | \(0.684982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.01598e42 | 0.714803 | ||||||||
\(932\) | − 3.33790e42i | − 0.293051i | ||||||||
\(933\) | 2.60363e43i | 2.25058i | ||||||||
\(934\) | 2.35024e43 | 2.00024 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.60442e43 | −1.32379 | ||||||||
\(937\) | − 4.02931e42i | − 0.327345i | −0.986515 | − | 0.163673i | \(-0.947666\pi\) | ||||
0.986515 | − | 0.163673i | \(-0.0523341\pi\) | |||||||
\(938\) | − 9.29747e40i | − 0.00743744i | ||||||||
\(939\) | −3.89442e43 | −3.06755 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.40592e42 | 0.718376 | 0.359188 | − | 0.933265i | \(-0.383054\pi\) | ||||
0.359188 | + | 0.933265i | \(0.383054\pi\) | |||||||
\(942\) | − 9.77996e42i | − 0.735527i | ||||||||
\(943\) | − 9.92816e39i | 0 0.000735274i | ||||||||
\(944\) | −3.07918e43 | −2.24564 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.39805e43 | −0.988781 | ||||||||
\(947\) | − 1.85611e43i | − 1.29279i | −0.763001 | − | 0.646397i | \(-0.776275\pi\) | ||||
0.763001 | − | 0.646397i | \(-0.223725\pi\) | |||||||
\(948\) | − 6.79910e42i | − 0.466370i | ||||||||
\(949\) | 5.04579e42 | 0.340855 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.49276e43 | −0.978078 | ||||||||
\(952\) | − 2.61344e41i | − 0.0168646i | ||||||||
\(953\) | 3.20332e42i | 0.203588i | 0.994805 | + | 0.101794i | \(0.0324583\pi\) | ||||
−0.994805 | + | 0.101794i | \(0.967542\pi\) | |||||||
\(954\) | 6.10475e42 | 0.382135 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.42024e42 | −0.146967 | ||||||||
\(957\) | 2.16927e43i | 1.29745i | ||||||||
\(958\) | − 1.46573e43i | − 0.863482i | ||||||||
\(959\) | −3.81903e41 | −0.0221607 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.26074e42 | 0.296181 | ||||||||
\(962\) | 2.27890e43i | 1.26383i | ||||||||
\(963\) | 3.27235e43i | 1.78764i | ||||||||
\(964\) | 3.24393e42 | 0.174564 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.10534e40 | −0.00109939 | ||||||||
\(967\) | 5.23025e42i | 0.269053i | 0.990910 | + | 0.134527i | \(0.0429514\pi\) | ||||
−0.990910 | + | 0.134527i | \(0.957049\pi\) | |||||||
\(968\) | − 9.76368e42i | − 0.494790i | ||||||||
\(969\) | 2.69848e43 | 1.34718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.58906e43 | −1.25448 | −0.627239 | − | 0.778827i | \(-0.715815\pi\) | ||||
−0.627239 | + | 0.778827i | \(0.715815\pi\) | |||||||
\(972\) | − 1.20881e42i | − 0.0577028i | ||||||||
\(973\) | − 7.15536e40i | − 0.00336508i | ||||||||
\(974\) | 2.73998e43 | 1.26953 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.58466e43 | −0.712712 | ||||||||
\(977\) | 6.80879e42i | 0.301716i | 0.988555 | + | 0.150858i | \(0.0482037\pi\) | ||||
−0.988555 | + | 0.150858i | \(0.951796\pi\) | |||||||
\(978\) | 4.52226e42i | 0.197443i | ||||||||
\(979\) | −4.83861e41 | −0.0208148 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.52620e43 | 3.97850 | ||||||||
\(982\) | 2.08435e43i | 0.857735i | ||||||||
\(983\) | 4.18545e43i | 1.69713i | 0.529089 | + | 0.848566i | \(0.322534\pi\) | ||||
−0.529089 | + | 0.848566i | \(0.677466\pi\) | |||||||
\(984\) | 9.02608e41 | 0.0360637 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.66023e43 | −1.42001 | ||||||||
\(987\) | − 9.38906e41i | − 0.0358941i | ||||||||
\(988\) | 3.93424e42i | 0.148213i | ||||||||
\(989\) | 1.10101e42 | 0.0408738 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.63339e43 | 0.949397 | 0.474699 | − | 0.880148i | \(-0.342557\pi\) | ||||
0.474699 | + | 0.880148i | \(0.342557\pi\) | |||||||
\(992\) | 1.66491e43i | 0.591523i | ||||||||
\(993\) | 2.28237e43i | 0.799138i | ||||||||
\(994\) | 1.55508e41 | 0.00536600 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 9.11870e42 | 0.305614 | ||||||||
\(997\) | − 1.61216e43i | − 0.532511i | −0.963903 | − | 0.266255i | \(-0.914214\pi\) | ||||
0.963903 | − | 0.266255i | \(-0.0857865\pi\) | |||||||
\(998\) | − 2.97416e43i | − 0.968216i | ||||||||
\(999\) | 8.34058e43 | 2.67606 |
(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 | 25.30.b.a.24.4 | 4 | ||
5.2 | odd | 4 | 25.30.a.a.1.1 | 2 | |||
5.3 | odd | 4 | 1.30.a.a.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 25.30.b.a.24.1 | 4 | ||
15.8 | even | 4 | 9.30.a.a.1.1 | 2 | |||
20.3 | even | 4 | 16.30.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.30.a.a.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
9.30.a.a.1.1 | 2 | 15.8 | even | 4 | |||
16.30.a.c.1.2 | 2 | 20.3 | even | 4 | |||
25.30.a.a.1.1 | 2 | 5.2 | odd | 4 | |||
25.30.b.a.24.1 | 4 | 5.4 | even | 2 | inner | ||
25.30.b.a.24.4 | 4 | 1.1 | even | 1 | trivial |