Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,10,Mod(1,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(22.1465409550\) |
Analytic rank: | \(1\) |
Dimension: | \(15\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{15} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{15} - 2 x^{14} - 5425 x^{13} + 14888 x^{12} + 11288030 x^{11} - 37600244 x^{10} - 11474166224 x^{9} + 47465836576 x^{8} + 5986976782464 x^{7} + \cdots + 52\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(-35.4490\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 33.4490 | 1.47825 | 0.739125 | − | 0.673569i | \(-0.235239\pi\) | ||||
0.739125 | + | 0.673569i | \(0.235239\pi\) | |||||||
\(3\) | 8.30450 | 0.0591927 | 0.0295963 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295963 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(4\) | 606.833 | 1.18522 | ||||||||
\(5\) | −752.925 | −0.538749 | −0.269375 | − | 0.963035i | \(-0.586817\pi\) | ||||
−0.269375 | + | 0.963035i | \(0.586817\pi\) | |||||||
\(6\) | 277.777 | 0.0875015 | ||||||||
\(7\) | −7164.62 | −1.12785 | −0.563926 | − | 0.825825i | \(-0.690710\pi\) | ||||
−0.563926 | + | 0.825825i | \(0.690710\pi\) | |||||||
\(8\) | 3172.07 | 0.273803 | ||||||||
\(9\) | −19614.0 | −0.996496 | ||||||||
\(10\) | −25184.6 | −0.796406 | ||||||||
\(11\) | −30954.5 | −0.637466 | −0.318733 | − | 0.947845i | \(-0.603257\pi\) | ||||
−0.318733 | + | 0.947845i | \(0.603257\pi\) | |||||||
\(12\) | 5039.45 | 0.0701564 | ||||||||
\(13\) | 41893.4 | 0.406818 | 0.203409 | − | 0.979094i | \(-0.434798\pi\) | ||||
0.203409 | + | 0.979094i | \(0.434798\pi\) | |||||||
\(14\) | −239649. | −1.66725 | ||||||||
\(15\) | −6252.67 | −0.0318900 | ||||||||
\(16\) | −204596. | −0.780472 | ||||||||
\(17\) | 187328. | 0.543980 | 0.271990 | − | 0.962300i | \(-0.412318\pi\) | ||||
0.271990 | + | 0.962300i | \(0.412318\pi\) | |||||||
\(18\) | −656069. | −1.47307 | ||||||||
\(19\) | 668619. | 1.17703 | 0.588515 | − | 0.808486i | \(-0.299713\pi\) | ||||
0.588515 | + | 0.808486i | \(0.299713\pi\) | |||||||
\(20\) | −456900. | −0.638537 | ||||||||
\(21\) | −59498.6 | −0.0667606 | ||||||||
\(22\) | −1.03540e6 | −0.942334 | ||||||||
\(23\) | −2.17863e6 | −1.62334 | −0.811669 | − | 0.584118i | \(-0.801440\pi\) | ||||
−0.811669 | + | 0.584118i | \(0.801440\pi\) | |||||||
\(24\) | 26342.4 | 0.0162071 | ||||||||
\(25\) | −1.38623e6 | −0.709749 | ||||||||
\(26\) | 1.40129e6 | 0.601379 | ||||||||
\(27\) | −326342. | −0.118178 | ||||||||
\(28\) | −4.34773e6 | −1.33675 | ||||||||
\(29\) | 2.40487e6 | 0.631393 | 0.315697 | − | 0.948860i | \(-0.397762\pi\) | ||||
0.315697 | + | 0.948860i | \(0.397762\pi\) | |||||||
\(30\) | −209145. | −0.0471414 | ||||||||
\(31\) | 8.05328e6 | 1.56619 | 0.783096 | − | 0.621901i | \(-0.213639\pi\) | ||||
0.783096 | + | 0.621901i | \(0.213639\pi\) | |||||||
\(32\) | −8.46763e6 | −1.42754 | ||||||||
\(33\) | −257062. | −0.0377333 | ||||||||
\(34\) | 6.26594e6 | 0.804138 | ||||||||
\(35\) | 5.39442e6 | 0.607629 | ||||||||
\(36\) | −1.19024e7 | −1.18107 | ||||||||
\(37\) | −1.64001e7 | −1.43860 | −0.719299 | − | 0.694701i | \(-0.755537\pi\) | ||||
−0.719299 | + | 0.694701i | \(0.755537\pi\) | |||||||
\(38\) | 2.23646e7 | 1.73994 | ||||||||
\(39\) | 347904. | 0.0240807 | ||||||||
\(40\) | −2.38833e6 | −0.147511 | ||||||||
\(41\) | 1.13061e7 | 0.624863 | 0.312431 | − | 0.949940i | \(-0.398857\pi\) | ||||
0.312431 | + | 0.949940i | \(0.398857\pi\) | |||||||
\(42\) | −1.99017e6 | −0.0986887 | ||||||||
\(43\) | −3.41880e6 | −0.152499 | ||||||||
\(44\) | −1.87842e7 | −0.755538 | ||||||||
\(45\) | 1.47679e7 | 0.536862 | ||||||||
\(46\) | −7.28730e7 | −2.39970 | ||||||||
\(47\) | −4.31570e7 | −1.29006 | −0.645031 | − | 0.764156i | \(-0.723156\pi\) | ||||
−0.645031 | + | 0.764156i | \(0.723156\pi\) | |||||||
\(48\) | −1.69907e6 | −0.0461983 | ||||||||
\(49\) | 1.09782e7 | 0.272049 | ||||||||
\(50\) | −4.63679e7 | −1.04919 | ||||||||
\(51\) | 1.55567e6 | 0.0321996 | ||||||||
\(52\) | 2.54223e7 | 0.482169 | ||||||||
\(53\) | −3.13129e7 | −0.545108 | −0.272554 | − | 0.962141i | \(-0.587868\pi\) | ||||
−0.272554 | + | 0.962141i | \(0.587868\pi\) | |||||||
\(54\) | −1.09158e7 | −0.174696 | ||||||||
\(55\) | 2.33064e7 | 0.343434 | ||||||||
\(56\) | −2.27267e7 | −0.308809 | ||||||||
\(57\) | 5.55255e6 | 0.0696716 | ||||||||
\(58\) | 8.04403e7 | 0.933357 | ||||||||
\(59\) | 4.51423e7 | 0.485009 | 0.242504 | − | 0.970150i | \(-0.422031\pi\) | ||||
0.242504 | + | 0.970150i | \(0.422031\pi\) | |||||||
\(60\) | −3.79433e6 | −0.0377967 | ||||||||
\(61\) | 7.25780e7 | 0.671152 | 0.335576 | − | 0.942013i | \(-0.391069\pi\) | ||||
0.335576 | + | 0.942013i | \(0.391069\pi\) | |||||||
\(62\) | 2.69374e8 | 2.31522 | ||||||||
\(63\) | 1.40527e8 | 1.12390 | ||||||||
\(64\) | −1.78480e8 | −1.32978 | ||||||||
\(65\) | −3.15426e7 | −0.219173 | ||||||||
\(66\) | −8.59845e6 | −0.0557792 | ||||||||
\(67\) | 2.83598e8 | 1.71936 | 0.859678 | − | 0.510836i | \(-0.170664\pi\) | ||||
0.859678 | + | 0.510836i | \(0.170664\pi\) | |||||||
\(68\) | 1.13677e8 | 0.644737 | ||||||||
\(69\) | −1.80925e7 | −0.0960897 | ||||||||
\(70\) | 1.80438e8 | 0.898228 | ||||||||
\(71\) | −1.90718e8 | −0.890695 | −0.445347 | − | 0.895358i | \(-0.646920\pi\) | ||||
−0.445347 | + | 0.895358i | \(0.646920\pi\) | |||||||
\(72\) | −6.22170e7 | −0.272843 | ||||||||
\(73\) | 2.75834e7 | 0.113683 | 0.0568415 | − | 0.998383i | \(-0.481897\pi\) | ||||
0.0568415 | + | 0.998383i | \(0.481897\pi\) | |||||||
\(74\) | −5.48567e8 | −2.12661 | ||||||||
\(75\) | −1.15119e7 | −0.0420120 | ||||||||
\(76\) | 4.05740e8 | 1.39504 | ||||||||
\(77\) | 2.21777e8 | 0.718967 | ||||||||
\(78\) | 1.16370e7 | 0.0355972 | ||||||||
\(79\) | 2.64422e8 | 0.763794 | 0.381897 | − | 0.924205i | \(-0.375271\pi\) | ||||
0.381897 | + | 0.924205i | \(0.375271\pi\) | |||||||
\(80\) | 1.54046e8 | 0.420479 | ||||||||
\(81\) | 3.83353e8 | 0.989501 | ||||||||
\(82\) | 3.78177e8 | 0.923703 | ||||||||
\(83\) | −5.42519e8 | −1.25477 | −0.627384 | − | 0.778710i | \(-0.715874\pi\) | ||||
−0.627384 | + | 0.778710i | \(0.715874\pi\) | |||||||
\(84\) | −3.61057e7 | −0.0791260 | ||||||||
\(85\) | −1.41044e8 | −0.293069 | ||||||||
\(86\) | −1.14355e8 | −0.225431 | ||||||||
\(87\) | 1.99712e7 | 0.0373739 | ||||||||
\(88\) | −9.81898e7 | −0.174540 | ||||||||
\(89\) | −2.40619e7 | −0.0406513 | −0.0203257 | − | 0.999793i | \(-0.506470\pi\) | ||||
−0.0203257 | + | 0.999793i | \(0.506470\pi\) | |||||||
\(90\) | 4.93971e8 | 0.793615 | ||||||||
\(91\) | −3.00150e8 | −0.458830 | ||||||||
\(92\) | −1.32207e9 | −1.92401 | ||||||||
\(93\) | 6.68785e7 | 0.0927071 | ||||||||
\(94\) | −1.44356e9 | −1.90703 | ||||||||
\(95\) | −5.03420e8 | −0.634124 | ||||||||
\(96\) | −7.03194e7 | −0.0844996 | ||||||||
\(97\) | −1.30561e9 | −1.49741 | −0.748704 | − | 0.662905i | \(-0.769323\pi\) | ||||
−0.748704 | + | 0.662905i | \(0.769323\pi\) | |||||||
\(98\) | 3.67209e8 | 0.402157 | ||||||||
\(99\) | 6.07143e8 | 0.635232 | ||||||||
\(100\) | −8.41209e8 | −0.841209 | ||||||||
\(101\) | 8.39059e8 | 0.802318 | 0.401159 | − | 0.916008i | \(-0.368607\pi\) | ||||
0.401159 | + | 0.916008i | \(0.368607\pi\) | |||||||
\(102\) | 5.20355e7 | 0.0475991 | ||||||||
\(103\) | −1.97091e9 | −1.72544 | −0.862720 | − | 0.505681i | \(-0.831241\pi\) | ||||
−0.862720 | + | 0.505681i | \(0.831241\pi\) | |||||||
\(104\) | 1.32889e8 | 0.111388 | ||||||||
\(105\) | 4.47980e7 | 0.0359672 | ||||||||
\(106\) | −1.04739e9 | −0.805805 | ||||||||
\(107\) | 1.26639e9 | 0.933983 | 0.466991 | − | 0.884262i | \(-0.345338\pi\) | ||||
0.466991 | + | 0.884262i | \(0.345338\pi\) | |||||||
\(108\) | −1.98035e8 | −0.140067 | ||||||||
\(109\) | −9.70279e8 | −0.658381 | −0.329191 | − | 0.944264i | \(-0.606776\pi\) | ||||
−0.329191 | + | 0.944264i | \(0.606776\pi\) | |||||||
\(110\) | 7.79576e8 | 0.507682 | ||||||||
\(111\) | −1.36195e8 | −0.0851544 | ||||||||
\(112\) | 1.46585e9 | 0.880257 | ||||||||
\(113\) | −1.93357e9 | −1.11559 | −0.557797 | − | 0.829977i | \(-0.688353\pi\) | ||||
−0.557797 | + | 0.829977i | \(0.688353\pi\) | |||||||
\(114\) | 1.85727e8 | 0.102992 | ||||||||
\(115\) | 1.64035e9 | 0.874572 | ||||||||
\(116\) | 1.45935e9 | 0.748341 | ||||||||
\(117\) | −8.21698e8 | −0.405393 | ||||||||
\(118\) | 1.50996e9 | 0.716964 | ||||||||
\(119\) | −1.34214e9 | −0.613529 | ||||||||
\(120\) | −1.98339e7 | −0.00873157 | ||||||||
\(121\) | −1.39977e9 | −0.593637 | ||||||||
\(122\) | 2.42766e9 | 0.992130 | ||||||||
\(123\) | 9.38914e7 | 0.0369873 | ||||||||
\(124\) | 4.88700e9 | 1.85628 | ||||||||
\(125\) | 2.51428e9 | 0.921126 | ||||||||
\(126\) | 4.70049e9 | 1.66140 | ||||||||
\(127\) | −2.17278e9 | −0.741137 | −0.370569 | − | 0.928805i | \(-0.620837\pi\) | ||||
−0.370569 | + | 0.928805i | \(0.620837\pi\) | |||||||
\(128\) | −1.63455e9 | −0.538212 | ||||||||
\(129\) | −2.83914e7 | −0.00902680 | ||||||||
\(130\) | −1.05507e9 | −0.323992 | ||||||||
\(131\) | −2.34464e9 | −0.695594 | −0.347797 | − | 0.937570i | \(-0.613070\pi\) | ||||
−0.347797 | + | 0.937570i | \(0.613070\pi\) | |||||||
\(132\) | −1.55994e8 | −0.0447223 | ||||||||
\(133\) | −4.79040e9 | −1.32752 | ||||||||
\(134\) | 9.48605e9 | 2.54164 | ||||||||
\(135\) | 2.45711e8 | 0.0636683 | ||||||||
\(136\) | 5.94218e8 | 0.148943 | ||||||||
\(137\) | 2.32762e9 | 0.564508 | 0.282254 | − | 0.959340i | \(-0.408918\pi\) | ||||
0.282254 | + | 0.959340i | \(0.408918\pi\) | |||||||
\(138\) | −6.05174e8 | −0.142044 | ||||||||
\(139\) | −3.92528e9 | −0.891875 | −0.445937 | − | 0.895064i | \(-0.647130\pi\) | ||||
−0.445937 | + | 0.895064i | \(0.647130\pi\) | |||||||
\(140\) | 3.27351e9 | 0.720175 | ||||||||
\(141\) | −3.58397e8 | −0.0763623 | ||||||||
\(142\) | −6.37932e9 | −1.31667 | ||||||||
\(143\) | −1.29679e9 | −0.259333 | ||||||||
\(144\) | 4.01296e9 | 0.777738 | ||||||||
\(145\) | −1.81068e9 | −0.340163 | ||||||||
\(146\) | 9.22637e8 | 0.168052 | ||||||||
\(147\) | 9.11683e7 | 0.0161033 | ||||||||
\(148\) | −9.95214e9 | −1.70506 | ||||||||
\(149\) | −3.42450e9 | −0.569192 | −0.284596 | − | 0.958648i | \(-0.591859\pi\) | ||||
−0.284596 | + | 0.958648i | \(0.591859\pi\) | |||||||
\(150\) | −3.85062e8 | −0.0621041 | ||||||||
\(151\) | −2.21822e9 | −0.347223 | −0.173611 | − | 0.984814i | \(-0.555544\pi\) | ||||
−0.173611 | + | 0.984814i | \(0.555544\pi\) | |||||||
\(152\) | 2.12090e9 | 0.322274 | ||||||||
\(153\) | −3.67426e9 | −0.542074 | ||||||||
\(154\) | 7.41822e9 | 1.06281 | ||||||||
\(155\) | −6.06352e9 | −0.843785 | ||||||||
\(156\) | 2.11119e8 | 0.0285409 | ||||||||
\(157\) | −1.02245e9 | −0.134306 | −0.0671530 | − | 0.997743i | \(-0.521392\pi\) | ||||
−0.0671530 | + | 0.997743i | \(0.521392\pi\) | |||||||
\(158\) | 8.84465e9 | 1.12908 | ||||||||
\(159\) | −2.60038e8 | −0.0322664 | ||||||||
\(160\) | 6.37549e9 | 0.769084 | ||||||||
\(161\) | 1.56091e10 | 1.83088 | ||||||||
\(162\) | 1.28228e10 | 1.46273 | ||||||||
\(163\) | 1.02522e10 | 1.13756 | 0.568778 | − | 0.822491i | \(-0.307416\pi\) | ||||
0.568778 | + | 0.822491i | \(0.307416\pi\) | |||||||
\(164\) | 6.86090e9 | 0.740601 | ||||||||
\(165\) | 1.93548e8 | 0.0203288 | ||||||||
\(166\) | −1.81467e10 | −1.85486 | ||||||||
\(167\) | −1.77286e10 | −1.76380 | −0.881901 | − | 0.471436i | \(-0.843736\pi\) | ||||
−0.881901 | + | 0.471436i | \(0.843736\pi\) | |||||||
\(168\) | −1.88734e8 | −0.0182792 | ||||||||
\(169\) | −8.84944e9 | −0.834499 | ||||||||
\(170\) | −4.71778e9 | −0.433229 | ||||||||
\(171\) | −1.31143e10 | −1.17291 | ||||||||
\(172\) | −2.07464e9 | −0.180744 | ||||||||
\(173\) | 1.17358e10 | 0.996104 | 0.498052 | − | 0.867147i | \(-0.334049\pi\) | ||||
0.498052 | + | 0.867147i | \(0.334049\pi\) | |||||||
\(174\) | 6.68017e8 | 0.0552479 | ||||||||
\(175\) | 9.93180e9 | 0.800492 | ||||||||
\(176\) | 6.33318e9 | 0.497525 | ||||||||
\(177\) | 3.74884e8 | 0.0287090 | ||||||||
\(178\) | −8.04846e8 | −0.0600928 | ||||||||
\(179\) | 7.44591e9 | 0.542100 | 0.271050 | − | 0.962565i | \(-0.412629\pi\) | ||||
0.271050 | + | 0.962565i | \(0.412629\pi\) | |||||||
\(180\) | 8.96165e9 | 0.636300 | ||||||||
\(181\) | 8.28250e8 | 0.0573599 | 0.0286799 | − | 0.999589i | \(-0.490870\pi\) | ||||
0.0286799 | + | 0.999589i | \(0.490870\pi\) | |||||||
\(182\) | −1.00397e10 | −0.678266 | ||||||||
\(183\) | 6.02724e8 | 0.0397273 | ||||||||
\(184\) | −6.91077e9 | −0.444474 | ||||||||
\(185\) | 1.23481e10 | 0.775043 | ||||||||
\(186\) | 2.23702e9 | 0.137044 | ||||||||
\(187\) | −5.79866e9 | −0.346769 | ||||||||
\(188\) | −2.61891e10 | −1.52901 | ||||||||
\(189\) | 2.33812e9 | 0.133287 | ||||||||
\(190\) | −1.68389e10 | −0.937394 | ||||||||
\(191\) | 1.78976e9 | 0.0973071 | 0.0486536 | − | 0.998816i | \(-0.484507\pi\) | ||||
0.0486536 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(192\) | −1.48219e9 | −0.0787133 | ||||||||
\(193\) | −1.53821e10 | −0.798007 | −0.399004 | − | 0.916949i | \(-0.630644\pi\) | ||||
−0.399004 | + | 0.916949i | \(0.630644\pi\) | |||||||
\(194\) | −4.36712e10 | −2.21354 | ||||||||
\(195\) | −2.61945e8 | −0.0129734 | ||||||||
\(196\) | 6.66192e9 | 0.322439 | ||||||||
\(197\) | 6.72162e9 | 0.317962 | 0.158981 | − | 0.987282i | \(-0.449179\pi\) | ||||
0.158981 | + | 0.987282i | \(0.449179\pi\) | |||||||
\(198\) | 2.03083e10 | 0.939032 | ||||||||
\(199\) | 2.38746e10 | 1.07919 | 0.539593 | − | 0.841926i | \(-0.318578\pi\) | ||||
0.539593 | + | 0.841926i | \(0.318578\pi\) | |||||||
\(200\) | −4.39721e9 | −0.194331 | ||||||||
\(201\) | 2.35514e9 | 0.101773 | ||||||||
\(202\) | 2.80657e10 | 1.18603 | ||||||||
\(203\) | −1.72300e10 | −0.712118 | ||||||||
\(204\) | 9.44031e8 | 0.0381637 | ||||||||
\(205\) | −8.51263e9 | −0.336645 | ||||||||
\(206\) | −6.59250e10 | −2.55063 | ||||||||
\(207\) | 4.27318e10 | 1.61765 | ||||||||
\(208\) | −8.57122e9 | −0.317510 | ||||||||
\(209\) | −2.06968e10 | −0.750317 | ||||||||
\(210\) | 1.49845e9 | 0.0531685 | ||||||||
\(211\) | −9.62380e9 | −0.334253 | −0.167127 | − | 0.985935i | \(-0.553449\pi\) | ||||
−0.167127 | + | 0.985935i | \(0.553449\pi\) | |||||||
\(212\) | −1.90017e10 | −0.646073 | ||||||||
\(213\) | −1.58382e9 | −0.0527226 | ||||||||
\(214\) | 4.23593e10 | 1.38066 | ||||||||
\(215\) | 2.57410e9 | 0.0821585 | ||||||||
\(216\) | −1.03518e9 | −0.0323574 | ||||||||
\(217\) | −5.76987e10 | −1.76643 | ||||||||
\(218\) | −3.24548e10 | −0.973251 | ||||||||
\(219\) | 2.29067e8 | 0.00672920 | ||||||||
\(220\) | 1.41431e10 | 0.407046 | ||||||||
\(221\) | 7.84781e9 | 0.221301 | ||||||||
\(222\) | −4.55558e9 | −0.125879 | ||||||||
\(223\) | 3.02591e10 | 0.819378 | 0.409689 | − | 0.912225i | \(-0.365637\pi\) | ||||
0.409689 | + | 0.912225i | \(0.365637\pi\) | |||||||
\(224\) | 6.06673e10 | 1.61005 | ||||||||
\(225\) | 2.71895e10 | 0.707262 | ||||||||
\(226\) | −6.46758e10 | −1.64913 | ||||||||
\(227\) | −1.66730e10 | −0.416771 | −0.208385 | − | 0.978047i | \(-0.566821\pi\) | ||||
−0.208385 | + | 0.978047i | \(0.566821\pi\) | |||||||
\(228\) | 3.36947e9 | 0.0825762 | ||||||||
\(229\) | 4.62782e10 | 1.11203 | 0.556015 | − | 0.831172i | \(-0.312330\pi\) | ||||
0.556015 | + | 0.831172i | \(0.312330\pi\) | |||||||
\(230\) | 5.48679e10 | 1.29284 | ||||||||
\(231\) | 1.84175e9 | 0.0425576 | ||||||||
\(232\) | 7.62840e9 | 0.172877 | ||||||||
\(233\) | 2.27489e10 | 0.505661 | 0.252830 | − | 0.967511i | \(-0.418639\pi\) | ||||
0.252830 | + | 0.967511i | \(0.418639\pi\) | |||||||
\(234\) | −2.74849e10 | −0.599271 | ||||||||
\(235\) | 3.24940e10 | 0.695021 | ||||||||
\(236\) | 2.73938e10 | 0.574843 | ||||||||
\(237\) | 2.19590e9 | 0.0452110 | ||||||||
\(238\) | −4.48930e10 | −0.906949 | ||||||||
\(239\) | 4.02770e10 | 0.798485 | 0.399242 | − | 0.916845i | \(-0.369273\pi\) | ||||
0.399242 | + | 0.916845i | \(0.369273\pi\) | |||||||
\(240\) | 1.27927e9 | 0.0248893 | ||||||||
\(241\) | −1.88067e10 | −0.359118 | −0.179559 | − | 0.983747i | \(-0.557467\pi\) | ||||
−0.179559 | + | 0.983747i | \(0.557467\pi\) | |||||||
\(242\) | −4.68207e10 | −0.877544 | ||||||||
\(243\) | 9.60695e9 | 0.176749 | ||||||||
\(244\) | 4.40427e10 | 0.795463 | ||||||||
\(245\) | −8.26574e9 | −0.146566 | ||||||||
\(246\) | 3.14057e9 | 0.0546765 | ||||||||
\(247\) | 2.80107e10 | 0.478837 | ||||||||
\(248\) | 2.55455e10 | 0.428827 | ||||||||
\(249\) | −4.50535e9 | −0.0742731 | ||||||||
\(250\) | 8.41002e10 | 1.36165 | ||||||||
\(251\) | 6.83951e10 | 1.08766 | 0.543830 | − | 0.839195i | \(-0.316973\pi\) | ||||
0.543830 | + | 0.839195i | \(0.316973\pi\) | |||||||
\(252\) | 8.52765e10 | 1.33207 | ||||||||
\(253\) | 6.74385e10 | 1.03482 | ||||||||
\(254\) | −7.26772e10 | −1.09559 | ||||||||
\(255\) | −1.17130e9 | −0.0173475 | ||||||||
\(256\) | 3.67078e10 | 0.534169 | ||||||||
\(257\) | −8.21993e10 | −1.17536 | −0.587678 | − | 0.809095i | \(-0.699958\pi\) | ||||
−0.587678 | + | 0.809095i | \(0.699958\pi\) | |||||||
\(258\) | −9.49664e8 | −0.0133439 | ||||||||
\(259\) | 1.17501e11 | 1.62252 | ||||||||
\(260\) | −1.91411e10 | −0.259768 | ||||||||
\(261\) | −4.71691e10 | −0.629181 | ||||||||
\(262\) | −7.84259e10 | −1.02826 | ||||||||
\(263\) | −1.78524e10 | −0.230089 | −0.115044 | − | 0.993360i | \(-0.536701\pi\) | ||||
−0.115044 | + | 0.993360i | \(0.536701\pi\) | |||||||
\(264\) | −8.15418e8 | −0.0103315 | ||||||||
\(265\) | 2.35763e10 | 0.293677 | ||||||||
\(266\) | −1.60234e11 | −1.96240 | ||||||||
\(267\) | −1.99822e8 | −0.00240626 | ||||||||
\(268\) | 1.72096e11 | 2.03782 | ||||||||
\(269\) | 1.12924e11 | 1.31492 | 0.657462 | − | 0.753488i | \(-0.271630\pi\) | ||||
0.657462 | + | 0.753488i | \(0.271630\pi\) | |||||||
\(270\) | 8.21879e9 | 0.0941176 | ||||||||
\(271\) | −1.05452e11 | −1.18766 | −0.593831 | − | 0.804590i | \(-0.702385\pi\) | ||||
−0.593831 | + | 0.804590i | \(0.702385\pi\) | |||||||
\(272\) | −3.83266e10 | −0.424562 | ||||||||
\(273\) | −2.49260e9 | −0.0271594 | ||||||||
\(274\) | 7.78565e10 | 0.834483 | ||||||||
\(275\) | 4.29101e10 | 0.452441 | ||||||||
\(276\) | −1.09791e10 | −0.113887 | ||||||||
\(277\) | −7.65554e10 | −0.781298 | −0.390649 | − | 0.920540i | \(-0.627749\pi\) | ||||
−0.390649 | + | 0.920540i | \(0.627749\pi\) | |||||||
\(278\) | −1.31296e11 | −1.31841 | ||||||||
\(279\) | −1.57957e11 | −1.56070 | ||||||||
\(280\) | 1.71115e10 | 0.166370 | ||||||||
\(281\) | −1.62567e11 | −1.55544 | −0.777721 | − | 0.628610i | \(-0.783624\pi\) | ||||
−0.777721 | + | 0.628610i | \(0.783624\pi\) | |||||||
\(282\) | −1.19880e10 | −0.112882 | ||||||||
\(283\) | 8.09281e10 | 0.749998 | 0.374999 | − | 0.927025i | \(-0.377643\pi\) | ||||
0.374999 | + | 0.927025i | \(0.377643\pi\) | |||||||
\(284\) | −1.15734e11 | −1.05567 | ||||||||
\(285\) | −4.18065e9 | −0.0375355 | ||||||||
\(286\) | −4.33763e10 | −0.383358 | ||||||||
\(287\) | −8.10038e10 | −0.704753 | ||||||||
\(288\) | 1.66084e11 | 1.42253 | ||||||||
\(289\) | −8.34960e10 | −0.704085 | ||||||||
\(290\) | −6.05655e10 | −0.502845 | ||||||||
\(291\) | −1.08424e10 | −0.0886355 | ||||||||
\(292\) | 1.67385e10 | 0.134739 | ||||||||
\(293\) | −1.52458e11 | −1.20849 | −0.604247 | − | 0.796797i | \(-0.706526\pi\) | ||||
−0.604247 | + | 0.796797i | \(0.706526\pi\) | |||||||
\(294\) | 3.04948e9 | 0.0238047 | ||||||||
\(295\) | −3.39888e10 | −0.261298 | ||||||||
\(296\) | −5.20223e10 | −0.393892 | ||||||||
\(297\) | 1.01018e10 | 0.0753344 | ||||||||
\(298\) | −1.14546e11 | −0.841408 | ||||||||
\(299\) | −9.12703e10 | −0.660403 | ||||||||
\(300\) | −6.98583e9 | −0.0497934 | ||||||||
\(301\) | 2.44944e10 | 0.171996 | ||||||||
\(302\) | −7.41972e10 | −0.513282 | ||||||||
\(303\) | 6.96797e9 | 0.0474913 | ||||||||
\(304\) | −1.36797e11 | −0.918640 | ||||||||
\(305\) | −5.46458e10 | −0.361583 | ||||||||
\(306\) | −1.22900e11 | −0.801321 | ||||||||
\(307\) | 2.31912e11 | 1.49005 | 0.745025 | − | 0.667037i | \(-0.232438\pi\) | ||||
0.745025 | + | 0.667037i | \(0.232438\pi\) | |||||||
\(308\) | 1.34582e11 | 0.852135 | ||||||||
\(309\) | −1.63675e10 | −0.102133 | ||||||||
\(310\) | −2.02818e11 | −1.24732 | ||||||||
\(311\) | 4.82364e10 | 0.292384 | 0.146192 | − | 0.989256i | \(-0.453298\pi\) | ||||
0.146192 | + | 0.989256i | \(0.453298\pi\) | |||||||
\(312\) | 1.10357e9 | 0.00659334 | ||||||||
\(313\) | 2.96278e11 | 1.74482 | 0.872408 | − | 0.488778i | \(-0.162557\pi\) | ||||
0.872408 | + | 0.488778i | \(0.162557\pi\) | |||||||
\(314\) | −3.42000e10 | −0.198538 | ||||||||
\(315\) | −1.05806e11 | −0.605500 | ||||||||
\(316\) | 1.60460e11 | 0.905264 | ||||||||
\(317\) | −4.42421e10 | −0.246076 | −0.123038 | − | 0.992402i | \(-0.539264\pi\) | ||||
−0.123038 | + | 0.992402i | \(0.539264\pi\) | |||||||
\(318\) | −8.69801e9 | −0.0476978 | ||||||||
\(319\) | −7.44415e10 | −0.402492 | ||||||||
\(320\) | 1.34382e11 | 0.716418 | ||||||||
\(321\) | 1.05167e10 | 0.0552849 | ||||||||
\(322\) | 5.22107e11 | 2.70650 | ||||||||
\(323\) | 1.25251e11 | 0.640281 | ||||||||
\(324\) | 2.32631e11 | 1.17278 | ||||||||
\(325\) | −5.80738e10 | −0.288739 | ||||||||
\(326\) | 3.42925e11 | 1.68159 | ||||||||
\(327\) | −8.05768e9 | −0.0389713 | ||||||||
\(328\) | 3.58637e10 | 0.171089 | ||||||||
\(329\) | 3.09204e11 | 1.45500 | ||||||||
\(330\) | 6.47399e9 | 0.0300510 | ||||||||
\(331\) | 1.85279e11 | 0.848399 | 0.424199 | − | 0.905569i | \(-0.360556\pi\) | ||||
0.424199 | + | 0.905569i | \(0.360556\pi\) | |||||||
\(332\) | −3.29218e11 | −1.48718 | ||||||||
\(333\) | 3.21673e11 | 1.43356 | ||||||||
\(334\) | −5.93002e11 | −2.60734 | ||||||||
\(335\) | −2.13528e11 | −0.926302 | ||||||||
\(336\) | 1.21732e10 | 0.0521048 | ||||||||
\(337\) | 3.97119e11 | 1.67720 | 0.838602 | − | 0.544744i | \(-0.183373\pi\) | ||||
0.838602 | + | 0.544744i | \(0.183373\pi\) | |||||||
\(338\) | −2.96005e11 | −1.23360 | ||||||||
\(339\) | −1.60573e10 | −0.0660350 | ||||||||
\(340\) | −8.55902e10 | −0.347351 | ||||||||
\(341\) | −2.49285e11 | −0.998394 | ||||||||
\(342\) | −4.38660e11 | −1.73385 | ||||||||
\(343\) | 2.10464e11 | 0.821020 | ||||||||
\(344\) | −1.08447e10 | −0.0417545 | ||||||||
\(345\) | 1.36223e10 | 0.0517682 | ||||||||
\(346\) | 3.92550e11 | 1.47249 | ||||||||
\(347\) | −3.90891e11 | −1.44735 | −0.723675 | − | 0.690141i | \(-0.757548\pi\) | ||||
−0.723675 | + | 0.690141i | \(0.757548\pi\) | |||||||
\(348\) | 1.21192e10 | 0.0442963 | ||||||||
\(349\) | 5.12370e10 | 0.184871 | 0.0924355 | − | 0.995719i | \(-0.470535\pi\) | ||||
0.0924355 | + | 0.995719i | \(0.470535\pi\) | |||||||
\(350\) | 3.32208e11 | 1.18333 | ||||||||
\(351\) | −1.36716e10 | −0.0480769 | ||||||||
\(352\) | 2.62111e11 | 0.910005 | ||||||||
\(353\) | 4.84133e9 | 0.0165950 | 0.00829752 | − | 0.999966i | \(-0.497359\pi\) | ||||
0.00829752 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(354\) | 1.25395e10 | 0.0424390 | ||||||||
\(355\) | 1.43596e11 | 0.479861 | ||||||||
\(356\) | −1.46016e10 | −0.0481808 | ||||||||
\(357\) | −1.11458e10 | −0.0363164 | ||||||||
\(358\) | 2.49058e11 | 0.801359 | ||||||||
\(359\) | −3.55635e11 | −1.13000 | −0.565001 | − | 0.825090i | \(-0.691124\pi\) | ||||
−0.565001 | + | 0.825090i | \(0.691124\pi\) | |||||||
\(360\) | 4.68448e10 | 0.146994 | ||||||||
\(361\) | 1.24364e11 | 0.385400 | ||||||||
\(362\) | 2.77041e10 | 0.0847922 | ||||||||
\(363\) | −1.16244e10 | −0.0351390 | ||||||||
\(364\) | −1.82141e11 | −0.543815 | ||||||||
\(365\) | −2.07683e10 | −0.0612466 | ||||||||
\(366\) | 2.01605e10 | 0.0587268 | ||||||||
\(367\) | −3.97521e11 | −1.14383 | −0.571917 | − | 0.820312i | \(-0.693800\pi\) | ||||
−0.571917 | + | 0.820312i | \(0.693800\pi\) | |||||||
\(368\) | 4.45740e11 | 1.26697 | ||||||||
\(369\) | −2.21758e11 | −0.622674 | ||||||||
\(370\) | 4.13030e11 | 1.14571 | ||||||||
\(371\) | 2.24345e11 | 0.614801 | ||||||||
\(372\) | 4.05841e10 | 0.109878 | ||||||||
\(373\) | −5.47884e11 | −1.46554 | −0.732772 | − | 0.680474i | \(-0.761774\pi\) | ||||
−0.732772 | + | 0.680474i | \(0.761774\pi\) | |||||||
\(374\) | −1.93959e11 | −0.512611 | ||||||||
\(375\) | 2.08799e10 | 0.0545239 | ||||||||
\(376\) | −1.36897e11 | −0.353222 | ||||||||
\(377\) | 1.00748e11 | 0.256862 | ||||||||
\(378\) | 7.82076e10 | 0.197032 | ||||||||
\(379\) | 6.83539e11 | 1.70171 | 0.850857 | − | 0.525397i | \(-0.176083\pi\) | ||||
0.850857 | + | 0.525397i | \(0.176083\pi\) | |||||||
\(380\) | −3.05492e11 | −0.751577 | ||||||||
\(381\) | −1.80438e10 | −0.0438699 | ||||||||
\(382\) | 5.98656e10 | 0.143844 | ||||||||
\(383\) | 5.16638e11 | 1.22685 | 0.613426 | − | 0.789753i | \(-0.289791\pi\) | ||||
0.613426 | + | 0.789753i | \(0.289791\pi\) | |||||||
\(384\) | −1.35741e10 | −0.0318582 | ||||||||
\(385\) | −1.66982e11 | −0.387343 | ||||||||
\(386\) | −5.14514e11 | −1.17965 | ||||||||
\(387\) | 6.70565e10 | 0.151964 | ||||||||
\(388\) | −7.92286e11 | −1.77476 | ||||||||
\(389\) | −4.39607e11 | −0.973399 | −0.486700 | − | 0.873569i | \(-0.661799\pi\) | ||||
−0.486700 | + | 0.873569i | \(0.661799\pi\) | |||||||
\(390\) | −8.76180e9 | −0.0191780 | ||||||||
\(391\) | −4.08119e11 | −0.883063 | ||||||||
\(392\) | 3.48235e10 | 0.0744878 | ||||||||
\(393\) | −1.94711e10 | −0.0411741 | ||||||||
\(394\) | 2.24831e11 | 0.470028 | ||||||||
\(395\) | −1.99090e11 | −0.411493 | ||||||||
\(396\) | 3.68434e11 | 0.752891 | ||||||||
\(397\) | 4.04283e11 | 0.816823 | 0.408411 | − | 0.912798i | \(-0.366083\pi\) | ||||
0.408411 | + | 0.912798i | \(0.366083\pi\) | |||||||
\(398\) | 7.98579e11 | 1.59531 | ||||||||
\(399\) | −3.97819e10 | −0.0785792 | ||||||||
\(400\) | 2.83617e11 | 0.553940 | ||||||||
\(401\) | −8.05560e11 | −1.55578 | −0.777890 | − | 0.628400i | \(-0.783710\pi\) | ||||
−0.777890 | + | 0.628400i | \(0.783710\pi\) | |||||||
\(402\) | 7.87769e10 | 0.150446 | ||||||||
\(403\) | 3.37379e11 | 0.637155 | ||||||||
\(404\) | 5.09169e11 | 0.950924 | ||||||||
\(405\) | −2.88636e11 | −0.533093 | ||||||||
\(406\) | −5.76324e11 | −1.05269 | ||||||||
\(407\) | 5.07658e11 | 0.917057 | ||||||||
\(408\) | 4.93468e9 | 0.00881634 | ||||||||
\(409\) | −4.85519e11 | −0.857929 | −0.428965 | − | 0.903321i | \(-0.641122\pi\) | ||||
−0.428965 | + | 0.903321i | \(0.641122\pi\) | |||||||
\(410\) | −2.84739e11 | −0.497644 | ||||||||
\(411\) | 1.93297e10 | 0.0334147 | ||||||||
\(412\) | −1.19602e12 | −2.04503 | ||||||||
\(413\) | −3.23428e11 | −0.547018 | ||||||||
\(414\) | 1.42933e12 | 2.39129 | ||||||||
\(415\) | 4.08476e11 | 0.676005 | ||||||||
\(416\) | −3.54737e11 | −0.580747 | ||||||||
\(417\) | −3.25975e10 | −0.0527925 | ||||||||
\(418\) | −6.92286e11 | −1.10915 | ||||||||
\(419\) | 6.38311e11 | 1.01174 | 0.505871 | − | 0.862609i | \(-0.331171\pi\) | ||||
0.505871 | + | 0.862609i | \(0.331171\pi\) | |||||||
\(420\) | 2.71849e10 | 0.0426291 | ||||||||
\(421\) | −3.95759e11 | −0.613991 | −0.306995 | − | 0.951711i | \(-0.599324\pi\) | ||||
−0.306995 | + | 0.951711i | \(0.599324\pi\) | |||||||
\(422\) | −3.21906e11 | −0.494110 | ||||||||
\(423\) | 8.46483e11 | 1.28554 | ||||||||
\(424\) | −9.93268e10 | −0.149252 | ||||||||
\(425\) | −2.59680e11 | −0.386090 | ||||||||
\(426\) | −5.29770e10 | −0.0779371 | ||||||||
\(427\) | −5.19994e11 | −0.756960 | ||||||||
\(428\) | 7.68485e11 | 1.10698 | ||||||||
\(429\) | −1.07692e10 | −0.0153506 | ||||||||
\(430\) | 8.61010e10 | 0.121451 | ||||||||
\(431\) | 5.11706e11 | 0.714287 | 0.357144 | − | 0.934049i | \(-0.383751\pi\) | ||||
0.357144 | + | 0.934049i | \(0.383751\pi\) | |||||||
\(432\) | 6.67684e10 | 0.0922346 | ||||||||
\(433\) | 5.74450e11 | 0.785337 | 0.392669 | − | 0.919680i | \(-0.371552\pi\) | ||||
0.392669 | + | 0.919680i | \(0.371552\pi\) | |||||||
\(434\) | −1.92996e12 | −2.61123 | ||||||||
\(435\) | −1.50368e10 | −0.0201351 | ||||||||
\(436\) | −5.88797e11 | −0.780327 | ||||||||
\(437\) | −1.45668e12 | −1.91072 | ||||||||
\(438\) | 7.66204e9 | 0.00994743 | ||||||||
\(439\) | 7.80007e11 | 1.00232 | 0.501162 | − | 0.865353i | \(-0.332906\pi\) | ||||
0.501162 | + | 0.865353i | \(0.332906\pi\) | |||||||
\(440\) | 7.39296e10 | 0.0940332 | ||||||||
\(441\) | −2.15326e11 | −0.271096 | ||||||||
\(442\) | 2.62501e11 | 0.327138 | ||||||||
\(443\) | 1.03032e12 | 1.27103 | 0.635517 | − | 0.772087i | \(-0.280787\pi\) | ||||
0.635517 | + | 0.772087i | \(0.280787\pi\) | |||||||
\(444\) | −8.26475e10 | −0.100927 | ||||||||
\(445\) | 1.81168e10 | 0.0219009 | ||||||||
\(446\) | 1.01214e12 | 1.21124 | ||||||||
\(447\) | −2.84388e10 | −0.0336920 | ||||||||
\(448\) | 1.27874e12 | 1.49980 | ||||||||
\(449\) | −5.64317e11 | −0.655262 | −0.327631 | − | 0.944806i | \(-0.606250\pi\) | ||||
−0.327631 | + | 0.944806i | \(0.606250\pi\) | |||||||
\(450\) | 9.09462e11 | 1.04551 | ||||||||
\(451\) | −3.49974e11 | −0.398329 | ||||||||
\(452\) | −1.17335e12 | −1.32223 | ||||||||
\(453\) | −1.84212e10 | −0.0205531 | ||||||||
\(454\) | −5.57694e11 | −0.616091 | ||||||||
\(455\) | 2.25991e11 | 0.247195 | ||||||||
\(456\) | 1.76131e10 | 0.0190762 | ||||||||
\(457\) | −2.62462e11 | −0.281478 | −0.140739 | − | 0.990047i | \(-0.544948\pi\) | ||||
−0.140739 | + | 0.990047i | \(0.544948\pi\) | |||||||
\(458\) | 1.54796e12 | 1.64386 | ||||||||
\(459\) | −6.11331e10 | −0.0642865 | ||||||||
\(460\) | 9.95417e11 | 1.03656 | ||||||||
\(461\) | −7.04852e11 | −0.726848 | −0.363424 | − | 0.931624i | \(-0.618392\pi\) | ||||
−0.363424 | + | 0.931624i | \(0.618392\pi\) | |||||||
\(462\) | 6.16047e10 | 0.0629107 | ||||||||
\(463\) | −1.58919e12 | −1.60717 | −0.803584 | − | 0.595191i | \(-0.797076\pi\) | ||||
−0.803584 | + | 0.595191i | \(0.797076\pi\) | |||||||
\(464\) | −4.92027e11 | −0.492785 | ||||||||
\(465\) | −5.03545e10 | −0.0499459 | ||||||||
\(466\) | 7.60928e11 | 0.747492 | ||||||||
\(467\) | −1.90216e12 | −1.85063 | −0.925317 | − | 0.379195i | \(-0.876201\pi\) | ||||
−0.925317 | + | 0.379195i | \(0.876201\pi\) | |||||||
\(468\) | −4.98634e11 | −0.480480 | ||||||||
\(469\) | −2.03187e12 | −1.93918 | ||||||||
\(470\) | 1.08689e12 | 1.02741 | ||||||||
\(471\) | −8.49098e9 | −0.00794993 | ||||||||
\(472\) | 1.43194e11 | 0.132797 | ||||||||
\(473\) | 1.05827e11 | 0.0972127 | ||||||||
\(474\) | 7.34504e10 | 0.0668331 | ||||||||
\(475\) | −9.26859e11 | −0.835396 | ||||||||
\(476\) | −8.14452e11 | −0.727167 | ||||||||
\(477\) | 6.14173e11 | 0.543198 | ||||||||
\(478\) | 1.34722e12 | 1.18036 | ||||||||
\(479\) | −4.06033e11 | −0.352412 | −0.176206 | − | 0.984353i | \(-0.556383\pi\) | ||||
−0.176206 | + | 0.984353i | \(0.556383\pi\) | |||||||
\(480\) | 5.29453e10 | 0.0455241 | ||||||||
\(481\) | −6.87056e11 | −0.585247 | ||||||||
\(482\) | −6.29066e11 | −0.530866 | ||||||||
\(483\) | 1.29626e11 | 0.108375 | ||||||||
\(484\) | −8.49424e11 | −0.703591 | ||||||||
\(485\) | 9.83025e11 | 0.806727 | ||||||||
\(486\) | 3.21343e11 | 0.261279 | ||||||||
\(487\) | −2.54024e11 | −0.204642 | −0.102321 | − | 0.994751i | \(-0.532627\pi\) | ||||
−0.102321 | + | 0.994751i | \(0.532627\pi\) | |||||||
\(488\) | 2.30222e11 | 0.183763 | ||||||||
\(489\) | 8.51394e10 | 0.0673350 | ||||||||
\(490\) | −2.76481e11 | −0.216662 | ||||||||
\(491\) | 5.49800e11 | 0.426911 | 0.213456 | − | 0.976953i | \(-0.431528\pi\) | ||||
0.213456 | + | 0.976953i | \(0.431528\pi\) | |||||||
\(492\) | 5.69764e10 | 0.0438381 | ||||||||
\(493\) | 4.50499e11 | 0.343466 | ||||||||
\(494\) | 9.36929e11 | 0.707841 | ||||||||
\(495\) | −4.57133e11 | −0.342231 | ||||||||
\(496\) | −1.64767e12 | −1.22237 | ||||||||
\(497\) | 1.36642e12 | 1.00457 | ||||||||
\(498\) | −1.50699e11 | −0.109794 | ||||||||
\(499\) | 2.09406e12 | 1.51195 | 0.755974 | − | 0.654601i | \(-0.227164\pi\) | ||||
0.755974 | + | 0.654601i | \(0.227164\pi\) | |||||||
\(500\) | 1.52575e12 | 1.09174 | ||||||||
\(501\) | −1.47227e11 | −0.104404 | ||||||||
\(502\) | 2.28775e12 | 1.60783 | ||||||||
\(503\) | 2.16997e12 | 1.51146 | 0.755730 | − | 0.654883i | \(-0.227282\pi\) | ||||
0.755730 | + | 0.654883i | \(0.227282\pi\) | |||||||
\(504\) | 4.45761e11 | 0.307727 | ||||||||
\(505\) | −6.31749e11 | −0.432248 | ||||||||
\(506\) | 2.25575e12 | 1.52973 | ||||||||
\(507\) | −7.34902e10 | −0.0493962 | ||||||||
\(508\) | −1.31851e12 | −0.878412 | ||||||||
\(509\) | −1.57264e12 | −1.03848 | −0.519242 | − | 0.854627i | \(-0.673786\pi\) | ||||
−0.519242 | + | 0.854627i | \(0.673786\pi\) | |||||||
\(510\) | −3.91788e10 | −0.0256440 | ||||||||
\(511\) | −1.97625e11 | −0.128217 | ||||||||
\(512\) | 2.06473e12 | 1.32785 | ||||||||
\(513\) | −2.18199e11 | −0.139099 | ||||||||
\(514\) | −2.74948e12 | −1.73747 | ||||||||
\(515\) | 1.48395e12 | 0.929580 | ||||||||
\(516\) | −1.72289e10 | −0.0106987 | ||||||||
\(517\) | 1.33590e12 | 0.822371 | ||||||||
\(518\) | 3.93027e12 | 2.39850 | ||||||||
\(519\) | 9.74599e10 | 0.0589621 | ||||||||
\(520\) | −1.00055e11 | −0.0600101 | ||||||||
\(521\) | 6.40632e11 | 0.380925 | 0.190462 | − | 0.981695i | \(-0.439001\pi\) | ||||
0.190462 | + | 0.981695i | \(0.439001\pi\) | |||||||
\(522\) | −1.57776e12 | −0.930087 | ||||||||
\(523\) | 1.66251e12 | 0.971642 | 0.485821 | − | 0.874058i | \(-0.338521\pi\) | ||||
0.485821 | + | 0.874058i | \(0.338521\pi\) | |||||||
\(524\) | −1.42281e12 | −0.824433 | ||||||||
\(525\) | 8.24787e10 | 0.0473833 | ||||||||
\(526\) | −5.97144e11 | −0.340129 | ||||||||
\(527\) | 1.50861e12 | 0.851978 | ||||||||
\(528\) | 5.25939e10 | 0.0294498 | ||||||||
\(529\) | 2.94529e12 | 1.63522 | ||||||||
\(530\) | 7.88603e11 | 0.434127 | ||||||||
\(531\) | −8.85423e11 | −0.483310 | ||||||||
\(532\) | −2.90697e12 | −1.57340 | ||||||||
\(533\) | 4.73650e11 | 0.254206 | ||||||||
\(534\) | −6.68384e9 | −0.00355706 | ||||||||
\(535\) | −9.53493e11 | −0.503183 | ||||||||
\(536\) | 8.99591e11 | 0.470764 | ||||||||
\(537\) | 6.18346e10 | 0.0320883 | ||||||||
\(538\) | 3.77719e12 | 1.94379 | ||||||||
\(539\) | −3.39824e11 | −0.173422 | ||||||||
\(540\) | 1.49106e11 | 0.0754610 | ||||||||
\(541\) | −3.01359e12 | −1.51250 | −0.756251 | − | 0.654282i | \(-0.772971\pi\) | ||||
−0.756251 | + | 0.654282i | \(0.772971\pi\) | |||||||
\(542\) | −3.52726e12 | −1.75566 | ||||||||
\(543\) | 6.87821e9 | 0.00339528 | ||||||||
\(544\) | −1.58623e12 | −0.776551 | ||||||||
\(545\) | 7.30547e11 | 0.354702 | ||||||||
\(546\) | −8.33748e10 | −0.0401484 | ||||||||
\(547\) | 5.31804e11 | 0.253985 | 0.126993 | − | 0.991904i | \(-0.459468\pi\) | ||||
0.126993 | + | 0.991904i | \(0.459468\pi\) | |||||||
\(548\) | 1.41248e12 | 0.669066 | ||||||||
\(549\) | −1.42355e12 | −0.668800 | ||||||||
\(550\) | 1.43530e12 | 0.668820 | ||||||||
\(551\) | 1.60794e12 | 0.743169 | ||||||||
\(552\) | −5.73905e10 | −0.0263096 | ||||||||
\(553\) | −1.89448e12 | −0.861446 | ||||||||
\(554\) | −2.56070e12 | −1.15495 | ||||||||
\(555\) | 1.02545e11 | 0.0458769 | ||||||||
\(556\) | −2.38199e12 | −1.05707 | ||||||||
\(557\) | −4.53326e12 | −1.99555 | −0.997775 | − | 0.0666751i | \(-0.978761\pi\) | ||||
−0.997775 | + | 0.0666751i | \(0.978761\pi\) | |||||||
\(558\) | −5.28351e12 | −2.30711 | ||||||||
\(559\) | −1.43225e11 | −0.0620392 | ||||||||
\(560\) | −1.10368e12 | −0.474238 | ||||||||
\(561\) | −4.81550e10 | −0.0205262 | ||||||||
\(562\) | −5.43770e12 | −2.29933 | ||||||||
\(563\) | 1.58678e12 | 0.665623 | 0.332811 | − | 0.942993i | \(-0.392003\pi\) | ||||
0.332811 | + | 0.942993i | \(0.392003\pi\) | |||||||
\(564\) | −2.17487e11 | −0.0905062 | ||||||||
\(565\) | 1.45583e12 | 0.601025 | ||||||||
\(566\) | 2.70696e12 | 1.10868 | ||||||||
\(567\) | −2.74658e12 | −1.11601 | ||||||||
\(568\) | −6.04970e11 | −0.243874 | ||||||||
\(569\) | −1.94543e12 | −0.778054 | −0.389027 | − | 0.921226i | \(-0.627189\pi\) | ||||
−0.389027 | + | 0.921226i | \(0.627189\pi\) | |||||||
\(570\) | −1.39839e11 | −0.0554868 | ||||||||
\(571\) | 5.49369e11 | 0.216273 | 0.108136 | − | 0.994136i | \(-0.465512\pi\) | ||||
0.108136 | + | 0.994136i | \(0.465512\pi\) | |||||||
\(572\) | −7.86935e11 | −0.307367 | ||||||||
\(573\) | 1.48631e10 | 0.00575987 | ||||||||
\(574\) | −2.70949e12 | −1.04180 | ||||||||
\(575\) | 3.02008e12 | 1.15216 | ||||||||
\(576\) | 3.50072e12 | 1.32512 | ||||||||
\(577\) | 1.70113e12 | 0.638922 | 0.319461 | − | 0.947599i | \(-0.396498\pi\) | ||||
0.319461 | + | 0.947599i | \(0.396498\pi\) | |||||||
\(578\) | −2.79285e12 | −1.04081 | ||||||||
\(579\) | −1.27740e11 | −0.0472362 | ||||||||
\(580\) | −1.09878e12 | −0.403168 | ||||||||
\(581\) | 3.88694e12 | 1.41519 | ||||||||
\(582\) | −3.62668e11 | −0.131025 | ||||||||
\(583\) | 9.69277e11 | 0.347488 | ||||||||
\(584\) | 8.74965e10 | 0.0311267 | ||||||||
\(585\) | 6.18677e11 | 0.218405 | ||||||||
\(586\) | −5.09955e12 | −1.78646 | ||||||||
\(587\) | −3.76857e12 | −1.31010 | −0.655051 | − | 0.755585i | \(-0.727353\pi\) | ||||
−0.655051 | + | 0.755585i | \(0.727353\pi\) | |||||||
\(588\) | 5.53239e10 | 0.0190860 | ||||||||
\(589\) | 5.38458e12 | 1.84346 | ||||||||
\(590\) | −1.13689e12 | −0.386264 | ||||||||
\(591\) | 5.58197e10 | 0.0188211 | ||||||||
\(592\) | 3.35540e12 | 1.12279 | ||||||||
\(593\) | 2.20370e12 | 0.731823 | 0.365912 | − | 0.930650i | \(-0.380757\pi\) | ||||
0.365912 | + | 0.930650i | \(0.380757\pi\) | |||||||
\(594\) | 3.37894e11 | 0.111363 | ||||||||
\(595\) | 1.01053e12 | 0.330538 | ||||||||
\(596\) | −2.07810e12 | −0.674619 | ||||||||
\(597\) | 1.98266e11 | 0.0638799 | ||||||||
\(598\) | −3.05290e12 | −0.976240 | ||||||||
\(599\) | 2.10006e12 | 0.666515 | 0.333258 | − | 0.942836i | \(-0.391852\pi\) | ||||
0.333258 | + | 0.942836i | \(0.391852\pi\) | |||||||
\(600\) | −3.65166e10 | −0.0115030 | ||||||||
\(601\) | −1.35259e12 | −0.422892 | −0.211446 | − | 0.977390i | \(-0.567817\pi\) | ||||
−0.211446 | + | 0.977390i | \(0.567817\pi\) | |||||||
\(602\) | 8.19313e11 | 0.254253 | ||||||||
\(603\) | −5.56249e12 | −1.71333 | ||||||||
\(604\) | −1.34609e12 | −0.411536 | ||||||||
\(605\) | 1.05392e12 | 0.319822 | ||||||||
\(606\) | 2.33071e11 | 0.0702040 | ||||||||
\(607\) | 4.40577e12 | 1.31726 | 0.658631 | − | 0.752466i | \(-0.271136\pi\) | ||||
0.658631 | + | 0.752466i | \(0.271136\pi\) | |||||||
\(608\) | −5.66162e12 | −1.68025 | ||||||||
\(609\) | −1.43086e11 | −0.0421522 | ||||||||
\(610\) | −1.82785e12 | −0.534509 | ||||||||
\(611\) | −1.80799e12 | −0.524821 | ||||||||
\(612\) | −2.22966e12 | −0.642478 | ||||||||
\(613\) | 2.69654e12 | 0.771320 | 0.385660 | − | 0.922641i | \(-0.373974\pi\) | ||||
0.385660 | + | 0.922641i | \(0.373974\pi\) | |||||||
\(614\) | 7.75722e12 | 2.20267 | ||||||||
\(615\) | −7.06932e10 | −0.0199269 | ||||||||
\(616\) | 7.03493e11 | 0.196855 | ||||||||
\(617\) | −2.92929e12 | −0.813727 | −0.406863 | − | 0.913489i | \(-0.633377\pi\) | ||||
−0.406863 | + | 0.913489i | \(0.633377\pi\) | |||||||
\(618\) | −5.47474e11 | −0.150979 | ||||||||
\(619\) | 5.71068e12 | 1.56343 | 0.781717 | − | 0.623633i | \(-0.214344\pi\) | ||||
0.781717 | + | 0.623633i | \(0.214344\pi\) | |||||||
\(620\) | −3.67954e12 | −1.00007 | ||||||||
\(621\) | 7.10980e11 | 0.191843 | ||||||||
\(622\) | 1.61346e12 | 0.432216 | ||||||||
\(623\) | 1.72394e11 | 0.0458487 | ||||||||
\(624\) | −7.11797e10 | −0.0187943 | ||||||||
\(625\) | 8.14411e11 | 0.213493 | ||||||||
\(626\) | 9.91019e12 | 2.57927 | ||||||||
\(627\) | −1.71876e11 | −0.0444133 | ||||||||
\(628\) | −6.20459e11 | −0.159182 | ||||||||
\(629\) | −3.07221e12 | −0.782569 | ||||||||
\(630\) | −3.53911e12 | −0.895080 | ||||||||
\(631\) | 6.26095e12 | 1.57220 | 0.786101 | − | 0.618099i | \(-0.212097\pi\) | ||||
0.786101 | + | 0.618099i | \(0.212097\pi\) | |||||||
\(632\) | 8.38765e11 | 0.209129 | ||||||||
\(633\) | −7.99209e10 | −0.0197853 | ||||||||
\(634\) | −1.47985e12 | −0.363762 | ||||||||
\(635\) | 1.63594e12 | 0.399287 | ||||||||
\(636\) | −1.57800e11 | −0.0382428 | ||||||||
\(637\) | 4.59913e11 | 0.110675 | ||||||||
\(638\) | −2.48999e12 | −0.594983 | ||||||||
\(639\) | 3.74075e12 | 0.887574 | ||||||||
\(640\) | 1.23069e12 | 0.289961 | ||||||||
\(641\) | −7.96482e12 | −1.86344 | −0.931718 | − | 0.363181i | \(-0.881691\pi\) | ||||
−0.931718 | + | 0.363181i | \(0.881691\pi\) | |||||||
\(642\) | 3.51773e11 | 0.0817249 | ||||||||
\(643\) | 5.28675e12 | 1.21966 | 0.609831 | − | 0.792532i | \(-0.291237\pi\) | ||||
0.609831 | + | 0.792532i | \(0.291237\pi\) | |||||||
\(644\) | 9.47210e12 | 2.17000 | ||||||||
\(645\) | 2.13766e10 | 0.00486318 | ||||||||
\(646\) | 4.18952e12 | 0.946495 | ||||||||
\(647\) | 2.49240e12 | 0.559176 | 0.279588 | − | 0.960120i | \(-0.409802\pi\) | ||||
0.279588 | + | 0.960120i | \(0.409802\pi\) | |||||||
\(648\) | 1.21602e12 | 0.270928 | ||||||||
\(649\) | −1.39736e12 | −0.309177 | ||||||||
\(650\) | −1.94251e12 | −0.426828 | ||||||||
\(651\) | −4.79159e11 | −0.104560 | ||||||||
\(652\) | 6.22137e12 | 1.34825 | ||||||||
\(653\) | −4.23455e12 | −0.911376 | −0.455688 | − | 0.890140i | \(-0.650607\pi\) | ||||
−0.455688 | + | 0.890140i | \(0.650607\pi\) | |||||||
\(654\) | −2.69521e11 | −0.0576093 | ||||||||
\(655\) | 1.76534e12 | 0.374751 | ||||||||
\(656\) | −2.31318e12 | −0.487688 | ||||||||
\(657\) | −5.41022e11 | −0.113285 | ||||||||
\(658\) | 1.03425e13 | 2.15085 | ||||||||
\(659\) | 9.53023e11 | 0.196843 | 0.0984213 | − | 0.995145i | \(-0.468621\pi\) | ||||
0.0984213 | + | 0.995145i | \(0.468621\pi\) | |||||||
\(660\) | 1.17452e11 | 0.0240941 | ||||||||
\(661\) | −6.93404e12 | −1.41280 | −0.706399 | − | 0.707814i | \(-0.749681\pi\) | ||||
−0.706399 | + | 0.707814i | \(0.749681\pi\) | |||||||
\(662\) | 6.19739e12 | 1.25414 | ||||||||
\(663\) | 6.51722e10 | 0.0130994 | ||||||||
\(664\) | −1.72091e12 | −0.343559 | ||||||||
\(665\) | 3.60681e12 | 0.715198 | ||||||||
\(666\) | 1.07596e13 | 2.11915 | ||||||||
\(667\) | −5.23932e12 | −1.02496 | ||||||||
\(668\) | −1.07583e13 | −2.09049 | ||||||||
\(669\) | 2.51287e11 | 0.0485012 | ||||||||
\(670\) | −7.14228e12 | −1.36931 | ||||||||
\(671\) | −2.24662e12 | −0.427837 | ||||||||
\(672\) | 5.03812e11 | 0.0953031 | ||||||||
\(673\) | −9.52595e11 | −0.178995 | −0.0894974 | − | 0.995987i | \(-0.528526\pi\) | ||||
−0.0894974 | + | 0.995987i | \(0.528526\pi\) | |||||||
\(674\) | 1.32832e13 | 2.47933 | ||||||||
\(675\) | 4.52385e11 | 0.0838767 | ||||||||
\(676\) | −5.37014e12 | −0.989066 | ||||||||
\(677\) | −9.34347e12 | −1.70946 | −0.854731 | − | 0.519072i | \(-0.826278\pi\) | ||||
−0.854731 | + | 0.519072i | \(0.826278\pi\) | |||||||
\(678\) | −5.37100e11 | −0.0976162 | ||||||||
\(679\) | 9.35418e12 | 1.68885 | ||||||||
\(680\) | −4.47401e11 | −0.0802430 | ||||||||
\(681\) | −1.38461e11 | −0.0246698 | ||||||||
\(682\) | −8.33834e12 | −1.47588 | ||||||||
\(683\) | −6.37568e12 | −1.12107 | −0.560535 | − | 0.828130i | \(-0.689405\pi\) | ||||
−0.560535 | + | 0.828130i | \(0.689405\pi\) | |||||||
\(684\) | −7.95820e12 | −1.39015 | ||||||||
\(685\) | −1.75252e12 | −0.304128 | ||||||||
\(686\) | 7.03980e12 | 1.21367 | ||||||||
\(687\) | 3.84317e11 | 0.0658241 | ||||||||
\(688\) | 6.99474e11 | 0.119021 | ||||||||
\(689\) | −1.31180e12 | −0.221760 | ||||||||
\(690\) | 4.55651e11 | 0.0765264 | ||||||||
\(691\) | 6.11546e12 | 1.02042 | 0.510208 | − | 0.860051i | \(-0.329568\pi\) | ||||
0.510208 | + | 0.860051i | \(0.329568\pi\) | |||||||
\(692\) | 7.12166e12 | 1.18060 | ||||||||
\(693\) | −4.34995e12 | −0.716448 | ||||||||
\(694\) | −1.30749e13 | −2.13954 | ||||||||
\(695\) | 2.95544e12 | 0.480497 | ||||||||
\(696\) | 6.33501e10 | 0.0102331 | ||||||||
\(697\) | 2.11795e12 | 0.339913 | ||||||||
\(698\) | 1.71382e12 | 0.273286 | ||||||||
\(699\) | 1.88918e11 | 0.0299314 | ||||||||
\(700\) | 6.02695e12 | 0.948760 | ||||||||
\(701\) | 3.82093e12 | 0.597638 | 0.298819 | − | 0.954310i | \(-0.403407\pi\) | ||||
0.298819 | + | 0.954310i | \(0.403407\pi\) | |||||||
\(702\) | −4.57300e11 | −0.0710697 | ||||||||
\(703\) | −1.09654e13 | −1.69327 | ||||||||
\(704\) | 5.52477e12 | 0.847690 | ||||||||
\(705\) | 2.69846e11 | 0.0411401 | ||||||||
\(706\) | 1.61937e11 | 0.0245316 | ||||||||
\(707\) | −6.01154e12 | −0.904896 | ||||||||
\(708\) | 2.27492e11 | 0.0340265 | ||||||||
\(709\) | −6.49775e11 | −0.0965728 | −0.0482864 | − | 0.998834i | \(-0.515376\pi\) | ||||
−0.0482864 | + | 0.998834i | \(0.515376\pi\) | |||||||
\(710\) | 4.80315e12 | 0.709354 | ||||||||
\(711\) | −5.18639e12 | −0.761118 | ||||||||
\(712\) | −7.63260e10 | −0.0111304 | ||||||||
\(713\) | −1.75451e13 | −2.54246 | ||||||||
\(714\) | −3.72814e11 | −0.0536847 | ||||||||
\(715\) | 9.76385e11 | 0.139715 | ||||||||
\(716\) | 4.51843e12 | 0.642508 | ||||||||
\(717\) | 3.34480e11 | 0.0472644 | ||||||||
\(718\) | −1.18956e13 | −1.67042 | ||||||||
\(719\) | 3.00170e12 | 0.418878 | 0.209439 | − | 0.977822i | \(-0.432836\pi\) | ||||
0.209439 | + | 0.977822i | \(0.432836\pi\) | |||||||
\(720\) | −3.02146e12 | −0.419006 | ||||||||
\(721\) | 1.41208e13 | 1.94604 | ||||||||
\(722\) | 4.15984e12 | 0.569717 | ||||||||
\(723\) | −1.56181e11 | −0.0212571 | ||||||||
\(724\) | 5.02610e11 | 0.0679841 | ||||||||
\(725\) | −3.33370e12 | −0.448131 | ||||||||
\(726\) | −3.88823e11 | −0.0519442 | ||||||||
\(727\) | −1.31825e13 | −1.75022 | −0.875109 | − | 0.483925i | \(-0.839211\pi\) | ||||
−0.875109 | + | 0.483925i | \(0.839211\pi\) | |||||||
\(728\) | −9.52096e11 | −0.125629 | ||||||||
\(729\) | −7.46576e12 | −0.979039 | ||||||||
\(730\) | −6.94676e11 | −0.0905377 | ||||||||
\(731\) | −6.40438e11 | −0.0829562 | ||||||||
\(732\) | 3.65753e11 | 0.0470856 | ||||||||
\(733\) | 1.12951e13 | 1.44519 | 0.722593 | − | 0.691274i | \(-0.242950\pi\) | ||||
0.722593 | + | 0.691274i | \(0.242950\pi\) | |||||||
\(734\) | −1.32967e13 | −1.69087 | ||||||||
\(735\) | −6.86429e10 | −0.00867566 | ||||||||
\(736\) | 1.84479e13 | 2.31737 | ||||||||
\(737\) | −8.77863e12 | −1.09603 | ||||||||
\(738\) | −7.41757e12 | −0.920467 | ||||||||
\(739\) | −1.22652e13 | −1.51278 | −0.756388 | − | 0.654124i | \(-0.773038\pi\) | ||||
−0.756388 | + | 0.654124i | \(0.773038\pi\) | |||||||
\(740\) | 7.49321e12 | 0.918598 | ||||||||
\(741\) | 2.32615e11 | 0.0283437 | ||||||||
\(742\) | 7.50412e12 | 0.908829 | ||||||||
\(743\) | −1.25794e13 | −1.51430 | −0.757149 | − | 0.653242i | \(-0.773408\pi\) | ||||
−0.757149 | + | 0.653242i | \(0.773408\pi\) | |||||||
\(744\) | 2.12143e11 | 0.0253834 | ||||||||
\(745\) | 2.57839e12 | 0.306652 | ||||||||
\(746\) | −1.83262e13 | −2.16644 | ||||||||
\(747\) | 1.06410e13 | 1.25037 | ||||||||
\(748\) | −3.51882e12 | −0.410998 | ||||||||
\(749\) | −9.07317e12 | −1.05339 | ||||||||
\(750\) | 6.98410e11 | 0.0806000 | ||||||||
\(751\) | 1.42829e13 | 1.63846 | 0.819231 | − | 0.573463i | \(-0.194400\pi\) | ||||
0.819231 | + | 0.573463i | \(0.194400\pi\) | |||||||
\(752\) | 8.82976e12 | 1.00686 | ||||||||
\(753\) | 5.67988e11 | 0.0643816 | ||||||||
\(754\) | 3.36992e12 | 0.379706 | ||||||||
\(755\) | 1.67015e12 | 0.187066 | ||||||||
\(756\) | 1.41885e12 | 0.157975 | ||||||||
\(757\) | −1.33564e12 | −0.147828 | −0.0739142 | − | 0.997265i | \(-0.523549\pi\) | ||||
−0.0739142 | + | 0.997265i | \(0.523549\pi\) | |||||||
\(758\) | 2.28637e13 | 2.51556 | ||||||||
\(759\) | 5.60043e11 | 0.0612539 | ||||||||
\(760\) | −1.59688e12 | −0.173625 | ||||||||
\(761\) | 1.24325e13 | 1.34378 | 0.671888 | − | 0.740653i | \(-0.265484\pi\) | ||||
0.671888 | + | 0.740653i | \(0.265484\pi\) | |||||||
\(762\) | −6.03548e11 | −0.0648507 | ||||||||
\(763\) | 6.95168e12 | 0.742556 | ||||||||
\(764\) | 1.08609e12 | 0.115330 | ||||||||
\(765\) | 2.76644e12 | 0.292042 | ||||||||
\(766\) | 1.72810e13 | 1.81359 | ||||||||
\(767\) | 1.89116e12 | 0.197310 | ||||||||
\(768\) | 3.04840e11 | 0.0316189 | ||||||||
\(769\) | −1.49843e13 | −1.54514 | −0.772569 | − | 0.634931i | \(-0.781028\pi\) | ||||
−0.772569 | + | 0.634931i | \(0.781028\pi\) | |||||||
\(770\) | −5.58537e12 | −0.572590 | ||||||||
\(771\) | −6.82624e11 | −0.0695724 | ||||||||
\(772\) | −9.33435e12 | −0.945815 | ||||||||
\(773\) | 8.29355e12 | 0.835473 | 0.417737 | − | 0.908568i | \(-0.362823\pi\) | ||||
0.417737 | + | 0.908568i | \(0.362823\pi\) | |||||||
\(774\) | 2.24297e12 | 0.224641 | ||||||||
\(775\) | −1.11637e13 | −1.11160 | ||||||||
\(776\) | −4.14148e12 | −0.409994 | ||||||||
\(777\) | 9.75784e11 | 0.0960416 | ||||||||
\(778\) | −1.47044e13 | −1.43893 | ||||||||
\(779\) | 7.55946e12 | 0.735482 | ||||||||
\(780\) | −1.58957e11 | −0.0153764 | ||||||||
\(781\) | 5.90358e12 | 0.567788 | ||||||||
\(782\) | −1.36512e13 | −1.30539 | ||||||||
\(783\) | −7.84810e11 | −0.0746168 | ||||||||
\(784\) | −2.24609e12 | −0.212327 | ||||||||
\(785\) | 7.69832e11 | 0.0723573 | ||||||||
\(786\) | −6.51288e11 | −0.0608656 | ||||||||
\(787\) | −1.33986e12 | −0.124501 | −0.0622505 | − | 0.998061i | \(-0.519828\pi\) | ||||
−0.0622505 | + | 0.998061i | \(0.519828\pi\) | |||||||
\(788\) | 4.07890e12 | 0.376856 | ||||||||
\(789\) | −1.48255e11 | −0.0136196 | ||||||||
\(790\) | −6.65936e12 | −0.608290 | ||||||||
\(791\) | 1.38533e13 | 1.25822 | ||||||||
\(792\) | 1.92590e12 | 0.173928 | ||||||||
\(793\) | 3.04054e12 | 0.273037 | ||||||||
\(794\) | 1.35228e13 | 1.20747 | ||||||||
\(795\) | 1.95789e11 | 0.0173835 | ||||||||
\(796\) | 1.44879e13 | 1.27907 | ||||||||
\(797\) | −3.09254e12 | −0.271489 | −0.135745 | − | 0.990744i | \(-0.543343\pi\) | ||||
−0.135745 | + | 0.990744i | \(0.543343\pi\) | |||||||
\(798\) | −1.33066e12 | −0.116160 | ||||||||
\(799\) | −8.08453e12 | −0.701769 | ||||||||
\(800\) | 1.17381e13 | 1.01319 | ||||||||
\(801\) | 4.71951e11 | 0.0405089 | ||||||||
\(802\) | −2.69452e13 | −2.29983 | ||||||||
\(803\) | −8.53832e11 | −0.0724690 | ||||||||
\(804\) | 1.42917e12 | 0.120624 | ||||||||
\(805\) | −1.17525e13 | −0.986387 | ||||||||
\(806\) | 1.12850e13 | 0.941874 | ||||||||
\(807\) | 9.37777e11 | 0.0778339 | ||||||||
\(808\) | 2.66155e12 | 0.219677 | ||||||||
\(809\) | −1.40195e13 | −1.15071 | −0.575353 | − | 0.817905i | \(-0.695135\pi\) | ||||
−0.575353 | + | 0.817905i | \(0.695135\pi\) | |||||||
\(810\) | −9.65458e12 | −0.788044 | ||||||||
\(811\) | −2.03904e13 | −1.65513 | −0.827565 | − | 0.561370i | \(-0.810274\pi\) | ||||
−0.827565 | + | 0.561370i | \(0.810274\pi\) | |||||||
\(812\) | −1.04557e13 | −0.844017 | ||||||||
\(813\) | −8.75726e11 | −0.0703009 | ||||||||
\(814\) | 1.69806e13 | 1.35564 | ||||||||
\(815\) | −7.71914e12 | −0.612857 | ||||||||
\(816\) | −3.18284e11 | −0.0251309 | ||||||||
\(817\) | −2.28588e12 | −0.179495 | ||||||||
\(818\) | −1.62401e13 | −1.26823 | ||||||||
\(819\) | 5.88715e12 | 0.457223 | ||||||||
\(820\) | −5.16575e12 | −0.398998 | ||||||||
\(821\) | 2.45678e13 | 1.88721 | 0.943607 | − | 0.331067i | \(-0.107408\pi\) | ||||
0.943607 | + | 0.331067i | \(0.107408\pi\) | |||||||
\(822\) | 6.46560e11 | 0.0493953 | ||||||||
\(823\) | −1.21005e13 | −0.919399 | −0.459699 | − | 0.888075i | \(-0.652043\pi\) | ||||
−0.459699 | + | 0.888075i | \(0.652043\pi\) | |||||||
\(824\) | −6.25187e12 | −0.472430 | ||||||||
\(825\) | 3.56347e11 | 0.0267812 | ||||||||
\(826\) | −1.08183e13 | −0.808629 | ||||||||
\(827\) | −4.05700e12 | −0.301599 | −0.150800 | − | 0.988564i | \(-0.548185\pi\) | ||||
−0.150800 | + | 0.988564i | \(0.548185\pi\) | |||||||
\(828\) | 2.59311e13 | 1.91727 | ||||||||
\(829\) | 1.18554e13 | 0.871809 | 0.435904 | − | 0.899993i | \(-0.356429\pi\) | ||||
0.435904 | + | 0.899993i | \(0.356429\pi\) | |||||||
\(830\) | 1.36631e13 | 0.999305 | ||||||||
\(831\) | −6.35754e11 | −0.0462471 | ||||||||
\(832\) | −7.47713e12 | −0.540979 | ||||||||
\(833\) | 2.05652e12 | 0.147990 | ||||||||
\(834\) | −1.09035e12 | −0.0780404 | ||||||||
\(835\) | 1.33483e13 | 0.950247 | ||||||||
\(836\) | −1.25595e13 | −0.889291 | ||||||||
\(837\) | −2.62813e12 | −0.185089 | ||||||||
\(838\) | 2.13508e13 | 1.49561 | ||||||||
\(839\) | −1.24519e13 | −0.867575 | −0.433787 | − | 0.901015i | \(-0.642823\pi\) | ||||
−0.433787 | + | 0.901015i | \(0.642823\pi\) | |||||||
\(840\) | 1.42102e11 | 0.00984791 | ||||||||
\(841\) | −8.72376e12 | −0.601342 | ||||||||
\(842\) | −1.32377e13 | −0.907632 | ||||||||
\(843\) | −1.35004e12 | −0.0920708 | ||||||||
\(844\) | −5.84004e12 | −0.396164 | ||||||||
\(845\) | 6.66297e12 | 0.449586 | ||||||||
\(846\) | 2.83140e13 | 1.90035 | ||||||||
\(847\) | 1.00288e13 | 0.669535 | ||||||||
\(848\) | 6.40651e12 | 0.425442 | ||||||||
\(849\) | 6.72067e11 | 0.0443944 | ||||||||
\(850\) | −8.68602e12 | −0.570737 | ||||||||
\(851\) | 3.57298e13 | 2.33533 | ||||||||
\(852\) | −9.61113e11 | −0.0624879 | ||||||||
\(853\) | 7.48447e12 | 0.484050 | 0.242025 | − | 0.970270i | \(-0.422188\pi\) | ||||
0.242025 | + | 0.970270i | \(0.422188\pi\) | |||||||
\(854\) | −1.73933e13 | −1.11898 | ||||||||
\(855\) | 9.87410e12 | 0.631902 | ||||||||
\(856\) | 4.01706e12 | 0.255727 | ||||||||
\(857\) | 1.28244e13 | 0.812129 | 0.406064 | − | 0.913844i | \(-0.366901\pi\) | ||||
0.406064 | + | 0.913844i | \(0.366901\pi\) | |||||||
\(858\) | −3.60218e11 | −0.0226920 | ||||||||
\(859\) | 1.30938e13 | 0.820536 | 0.410268 | − | 0.911965i | \(-0.365435\pi\) | ||||
0.410268 | + | 0.911965i | \(0.365435\pi\) | |||||||
\(860\) | 1.56205e12 | 0.0973760 | ||||||||
\(861\) | −6.72696e11 | −0.0417162 | ||||||||
\(862\) | 1.71160e13 | 1.05589 | ||||||||
\(863\) | −2.48587e13 | −1.52556 | −0.762780 | − | 0.646658i | \(-0.776166\pi\) | ||||
−0.762780 | + | 0.646658i | \(0.776166\pi\) | |||||||
\(864\) | 2.76335e12 | 0.168703 | ||||||||
\(865\) | −8.83617e12 | −0.536650 | ||||||||
\(866\) | 1.92147e13 | 1.16092 | ||||||||
\(867\) | −6.93393e11 | −0.0416767 | ||||||||
\(868\) | −3.50135e13 | −2.09361 | ||||||||
\(869\) | −8.18506e12 | −0.486893 | ||||||||
\(870\) | −5.02967e11 | −0.0297648 | ||||||||
\(871\) | 1.18809e13 | 0.699465 | ||||||||
\(872\) | −3.07779e12 | −0.180266 | ||||||||
\(873\) | 2.56082e13 | 1.49216 | ||||||||
\(874\) | −4.87243e13 | −2.82452 | ||||||||
\(875\) | −1.80139e13 | −1.03889 | ||||||||
\(876\) | 1.39005e11 | 0.00797558 | ||||||||
\(877\) | 2.55056e13 | 1.45592 | 0.727959 | − | 0.685621i | \(-0.240469\pi\) | ||||
0.727959 | + | 0.685621i | \(0.240469\pi\) | |||||||
\(878\) | 2.60904e13 | 1.48168 | ||||||||
\(879\) | −1.26608e12 | −0.0715340 | ||||||||
\(880\) | −4.76841e12 | −0.268041 | ||||||||
\(881\) | −4.40986e12 | −0.246623 | −0.123311 | − | 0.992368i | \(-0.539351\pi\) | ||||
−0.123311 | + | 0.992368i | \(0.539351\pi\) | |||||||
\(882\) | −7.20244e12 | −0.400748 | ||||||||
\(883\) | 7.48100e12 | 0.414130 | 0.207065 | − | 0.978327i | \(-0.433609\pi\) | ||||
0.207065 | + | 0.978327i | \(0.433609\pi\) | |||||||
\(884\) | 4.76231e12 | 0.262291 | ||||||||
\(885\) | −2.82260e11 | −0.0154669 | ||||||||
\(886\) | 3.44633e13 | 1.87890 | ||||||||
\(887\) | 1.64901e13 | 0.894473 | 0.447237 | − | 0.894416i | \(-0.352408\pi\) | ||||
0.447237 | + | 0.894416i | \(0.352408\pi\) | |||||||
\(888\) | −4.32019e11 | −0.0233155 | ||||||||
\(889\) | 1.55671e13 | 0.835893 | ||||||||
\(890\) | 6.05989e11 | 0.0323750 | ||||||||
\(891\) | −1.18665e13 | −0.630773 | ||||||||
\(892\) | 1.83622e13 | 0.971144 | ||||||||
\(893\) | −2.88556e13 | −1.51844 | ||||||||
\(894\) | −9.51247e11 | −0.0498052 | ||||||||
\(895\) | −5.60621e12 | −0.292056 | ||||||||
\(896\) | 1.17109e13 | 0.607023 | ||||||||
\(897\) | −7.57954e11 | −0.0390910 | ||||||||
\(898\) | −1.88758e13 | −0.968641 | ||||||||
\(899\) | 1.93671e13 | 0.988884 | ||||||||
\(900\) | 1.64995e13 | 0.838262 | ||||||||
\(901\) | −5.86580e12 | −0.296528 | ||||||||
\(902\) | −1.17063e13 | −0.588829 | ||||||||
\(903\) | 2.03414e11 | 0.0101809 | ||||||||
\(904\) | −6.13340e12 | −0.305452 | ||||||||
\(905\) | −6.23610e11 | −0.0309026 | ||||||||
\(906\) | −6.16171e11 | −0.0303825 | ||||||||
\(907\) | −2.16035e13 | −1.05997 | −0.529983 | − | 0.848008i | \(-0.677802\pi\) | ||||
−0.529983 | + | 0.848008i | \(0.677802\pi\) | |||||||
\(908\) | −1.01177e13 | −0.493965 | ||||||||
\(909\) | −1.64573e13 | −0.799507 | ||||||||
\(910\) | 7.55915e12 | 0.365415 | ||||||||
\(911\) | −6.95722e12 | −0.334659 | −0.167330 | − | 0.985901i | \(-0.553514\pi\) | ||||
−0.167330 | + | 0.985901i | \(0.553514\pi\) | |||||||
\(912\) | −1.13603e12 | −0.0543767 | ||||||||
\(913\) | 1.67934e13 | 0.799872 | ||||||||
\(914\) | −8.77910e12 | −0.416095 | ||||||||
\(915\) | −4.53806e11 | −0.0214030 | ||||||||
\(916\) | 2.80831e13 | 1.31800 | ||||||||
\(917\) | 1.67985e13 | 0.784527 | ||||||||
\(918\) | −2.04484e12 | −0.0950314 | ||||||||
\(919\) | 8.46725e12 | 0.391582 | 0.195791 | − | 0.980646i | \(-0.437273\pi\) | ||||
0.195791 | + | 0.980646i | \(0.437273\pi\) | |||||||
\(920\) | 5.20329e12 | 0.239460 | ||||||||
\(921\) | 1.92592e12 | 0.0882001 | ||||||||
\(922\) | −2.35766e13 | −1.07446 | ||||||||
\(923\) | −7.98982e12 | −0.362351 | ||||||||
\(924\) | 1.11764e12 | 0.0504401 | ||||||||
\(925\) | 2.27343e13 | 1.02104 | ||||||||
\(926\) | −5.31568e13 | −2.37580 | ||||||||
\(927\) | 3.86576e13 | 1.71940 | ||||||||
\(928\) | −2.03635e13 | −0.901336 | ||||||||
\(929\) | −3.72600e13 | −1.64124 | −0.820619 | − | 0.571475i | \(-0.806371\pi\) | ||||
−0.820619 | + | 0.571475i | \(0.806371\pi\) | |||||||
\(930\) | −1.68431e12 | −0.0738325 | ||||||||
\(931\) | 7.34022e12 | 0.320210 | ||||||||
\(932\) | 1.38048e13 | 0.599319 | ||||||||
\(933\) | 4.00579e11 | 0.0173070 | ||||||||
\(934\) | −6.36252e13 | −2.73570 | ||||||||
\(935\) | 4.36595e12 | 0.186822 | ||||||||
\(936\) | −2.60648e12 | −0.110998 | ||||||||
\(937\) | −1.23351e13 | −0.522774 | −0.261387 | − | 0.965234i | \(-0.584180\pi\) | ||||
−0.261387 | + | 0.965234i | \(0.584180\pi\) | |||||||
\(938\) | −6.79639e13 | −2.86659 | ||||||||
\(939\) | 2.46044e12 | 0.103280 | ||||||||
\(940\) | 1.97184e13 | 0.823753 | ||||||||
\(941\) | −1.46321e13 | −0.608348 | −0.304174 | − | 0.952617i | \(-0.598380\pi\) | ||||
−0.304174 | + | 0.952617i | \(0.598380\pi\) | |||||||
\(942\) | −2.84014e11 | −0.0117520 | ||||||||
\(943\) | −2.46318e13 | −1.01436 | ||||||||
\(944\) | −9.23594e12 | −0.378536 | ||||||||
\(945\) | −1.76043e12 | −0.0718084 | ||||||||
\(946\) | 3.53982e12 | 0.143705 | ||||||||
\(947\) | −1.11462e13 | −0.450353 | −0.225176 | − | 0.974318i | \(-0.572296\pi\) | ||||
−0.225176 | + | 0.974318i | \(0.572296\pi\) | |||||||
\(948\) | 1.33254e12 | 0.0535850 | ||||||||
\(949\) | 1.15556e12 | 0.0462483 | ||||||||
\(950\) | −3.10025e13 | −1.23492 | ||||||||
\(951\) | −3.67409e11 | −0.0145659 | ||||||||
\(952\) | −4.25734e12 | −0.167986 | ||||||||
\(953\) | 3.70196e13 | 1.45383 | 0.726915 | − | 0.686728i | \(-0.240954\pi\) | ||||
0.726915 | + | 0.686728i | \(0.240954\pi\) | |||||||
\(954\) | 2.05435e13 | 0.802982 | ||||||||
\(955\) | −1.34756e12 | −0.0524242 | ||||||||
\(956\) | 2.44414e13 | 0.946381 | ||||||||
\(957\) | −6.18200e11 | −0.0238246 | ||||||||
\(958\) | −1.35814e13 | −0.520953 | ||||||||
\(959\) | −1.66765e13 | −0.636681 | ||||||||
\(960\) | 1.11598e12 | 0.0424067 | ||||||||
\(961\) | 3.84157e13 | 1.45296 | ||||||||
\(962\) | −2.29813e13 | −0.865142 | ||||||||
\(963\) | −2.48389e13 | −0.930710 | ||||||||
\(964\) | −1.14126e13 | −0.425634 | ||||||||
\(965\) | 1.15815e13 | 0.429926 | ||||||||
\(966\) | 4.33584e12 | 0.160205 | ||||||||
\(967\) | −2.16109e13 | −0.794792 | −0.397396 | − | 0.917647i | \(-0.630086\pi\) | ||||
−0.397396 | + | 0.917647i | \(0.630086\pi\) | |||||||
\(968\) | −4.44015e12 | −0.162539 | ||||||||
\(969\) | 1.04015e12 | 0.0379000 | ||||||||
\(970\) | 3.28812e13 | 1.19254 | ||||||||
\(971\) | 1.75506e13 | 0.633586 | 0.316793 | − | 0.948495i | \(-0.397394\pi\) | ||||
0.316793 | + | 0.948495i | \(0.397394\pi\) | |||||||
\(972\) | 5.82982e12 | 0.209487 | ||||||||
\(973\) | 2.81231e13 | 1.00590 | ||||||||
\(974\) | −8.49684e12 | −0.302512 | ||||||||
\(975\) | −4.82274e11 | −0.0170912 | ||||||||
\(976\) | −1.48492e13 | −0.523816 | ||||||||
\(977\) | −2.50109e13 | −0.878219 | −0.439110 | − | 0.898433i | \(-0.644706\pi\) | ||||
−0.439110 | + | 0.898433i | \(0.644706\pi\) | |||||||
\(978\) | 2.84782e12 | 0.0995379 | ||||||||
\(979\) | 7.44825e11 | 0.0259139 | ||||||||
\(980\) | −5.01593e12 | −0.173714 | ||||||||
\(981\) | 1.90311e13 | 0.656074 | ||||||||
\(982\) | 1.83902e13 | 0.631081 | ||||||||
\(983\) | −2.10182e13 | −0.717966 | −0.358983 | − | 0.933344i | \(-0.616876\pi\) | ||||
−0.358983 | + | 0.933344i | \(0.616876\pi\) | |||||||
\(984\) | 2.97830e11 | 0.0101272 | ||||||||
\(985\) | −5.06088e12 | −0.171302 | ||||||||
\(986\) | 1.50687e13 | 0.507728 | ||||||||
\(987\) | 2.56778e12 | 0.0861253 | ||||||||
\(988\) | 1.69978e13 | 0.567528 | ||||||||
\(989\) | 7.44831e12 | 0.247557 | ||||||||
\(990\) | −1.52906e13 | −0.505903 | ||||||||
\(991\) | −5.45177e13 | −1.79559 | −0.897793 | − | 0.440417i | \(-0.854830\pi\) | ||||
−0.897793 | + | 0.440417i | \(0.854830\pi\) | |||||||
\(992\) | −6.81922e13 | −2.23580 | ||||||||
\(993\) | 1.53865e12 | 0.0502190 | ||||||||
\(994\) | 4.57054e13 | 1.48501 | ||||||||
\(995\) | −1.79757e13 | −0.581411 | ||||||||
\(996\) | −2.73399e12 | −0.0880300 | ||||||||
\(997\) | −6.06106e13 | −1.94276 | −0.971382 | − | 0.237522i | \(-0.923665\pi\) | ||||
−0.971382 | + | 0.237522i | \(0.923665\pi\) | |||||||
\(998\) | 7.00442e13 | 2.23504 | ||||||||
\(999\) | 5.35205e12 | 0.170011 |
(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 | 43.10.a.a.1.14 | ✓ | 15 | |
3.2 | odd | 2 | 387.10.a.c.1.2 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.10.a.a.1.14 | ✓ | 15 | 1.1 | even | 1 | trivial | |
387.10.a.c.1.2 | 15 | 3.2 | odd | 2 |