Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,18,Mod(1,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.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: | \(12.8255461141\) |
Analytic rank: | \(1\) |
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: | \( x^{4} - 2x^{3} - 2290x^{2} - 4009x + 1104138 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-32.8226\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 465.279 | 1.28516 | 0.642582 | − | 0.766217i | \(-0.277863\pi\) | ||||
0.642582 | + | 0.766217i | \(0.277863\pi\) | |||||||
\(3\) | 749.859 | 0.0659856 | 0.0329928 | − | 0.999456i | \(-0.489496\pi\) | ||||
0.0329928 | + | 0.999456i | \(0.489496\pi\) | |||||||
\(4\) | 85412.5 | 0.651646 | ||||||||
\(5\) | −1.54763e6 | −1.77183 | −0.885917 | − | 0.463844i | \(-0.846470\pi\) | ||||
−0.885917 | + | 0.463844i | \(0.846470\pi\) | |||||||
\(6\) | 348894. | 0.0848023 | ||||||||
\(7\) | −5.76480e6 | −0.377964 | ||||||||
\(8\) | −2.12444e7 | −0.447692 | ||||||||
\(9\) | −1.28578e8 | −0.995646 | ||||||||
\(10\) | −7.20081e8 | −2.27710 | ||||||||
\(11\) | 1.32989e9 | 1.87059 | 0.935296 | − | 0.353865i | \(-0.115133\pi\) | ||||
0.935296 | + | 0.353865i | \(0.115133\pi\) | |||||||
\(12\) | 6.40473e7 | 0.0429992 | ||||||||
\(13\) | −1.07693e9 | −0.366157 | −0.183078 | − | 0.983098i | \(-0.558606\pi\) | ||||
−0.183078 | + | 0.983098i | \(0.558606\pi\) | |||||||
\(14\) | −2.68224e9 | −0.485746 | ||||||||
\(15\) | −1.16051e9 | −0.116915 | ||||||||
\(16\) | −2.10798e10 | −1.22700 | ||||||||
\(17\) | 1.37139e10 | 0.476809 | 0.238404 | − | 0.971166i | \(-0.423376\pi\) | ||||
0.238404 | + | 0.971166i | \(0.423376\pi\) | |||||||
\(18\) | −5.98246e10 | −1.27957 | ||||||||
\(19\) | −1.11230e11 | −1.50250 | −0.751252 | − | 0.660015i | \(-0.770550\pi\) | ||||
−0.751252 | + | 0.660015i | \(0.770550\pi\) | |||||||
\(20\) | −1.32187e11 | −1.15461 | ||||||||
\(21\) | −4.32279e9 | −0.0249402 | ||||||||
\(22\) | 6.18772e11 | 2.40402 | ||||||||
\(23\) | −1.98008e11 | −0.527225 | −0.263613 | − | 0.964629i | \(-0.584914\pi\) | ||||
−0.263613 | + | 0.964629i | \(0.584914\pi\) | |||||||
\(24\) | −1.59303e10 | −0.0295412 | ||||||||
\(25\) | 1.63223e12 | 2.13940 | ||||||||
\(26\) | −5.01071e11 | −0.470571 | ||||||||
\(27\) | −1.93252e11 | −0.131684 | ||||||||
\(28\) | −4.92386e11 | −0.246299 | ||||||||
\(29\) | 2.36257e12 | 0.877003 | 0.438502 | − | 0.898730i | \(-0.355509\pi\) | ||||
0.438502 | + | 0.898730i | \(0.355509\pi\) | |||||||
\(30\) | −5.39959e11 | −0.150256 | ||||||||
\(31\) | 2.01083e11 | 0.0423450 | 0.0211725 | − | 0.999776i | \(-0.493260\pi\) | ||||
0.0211725 | + | 0.999776i | \(0.493260\pi\) | |||||||
\(32\) | −7.02342e12 | −1.12921 | ||||||||
\(33\) | 9.97233e11 | 0.123432 | ||||||||
\(34\) | 6.38078e12 | 0.612778 | ||||||||
\(35\) | 8.92180e12 | 0.669690 | ||||||||
\(36\) | −1.09822e13 | −0.648808 | ||||||||
\(37\) | 5.35305e12 | 0.250546 | 0.125273 | − | 0.992122i | \(-0.460019\pi\) | ||||
0.125273 | + | 0.992122i | \(0.460019\pi\) | |||||||
\(38\) | −5.17529e13 | −1.93096 | ||||||||
\(39\) | −8.07542e11 | −0.0241611 | ||||||||
\(40\) | 3.28786e13 | 0.793237 | ||||||||
\(41\) | −6.77967e13 | −1.32601 | −0.663004 | − | 0.748616i | \(-0.730719\pi\) | ||||
−0.663004 | + | 0.748616i | \(0.730719\pi\) | |||||||
\(42\) | −2.01130e12 | −0.0320522 | ||||||||
\(43\) | −6.36640e13 | −0.830639 | −0.415319 | − | 0.909676i | \(-0.636330\pi\) | ||||
−0.415319 | + | 0.909676i | \(0.636330\pi\) | |||||||
\(44\) | 1.13590e14 | 1.21896 | ||||||||
\(45\) | 1.98991e14 | 1.76412 | ||||||||
\(46\) | −9.21289e13 | −0.677571 | ||||||||
\(47\) | 2.71873e13 | 0.166546 | 0.0832729 | − | 0.996527i | \(-0.473463\pi\) | ||||
0.0832729 | + | 0.996527i | \(0.473463\pi\) | |||||||
\(48\) | −1.58069e13 | −0.0809645 | ||||||||
\(49\) | 3.32329e13 | 0.142857 | ||||||||
\(50\) | 7.59442e14 | 2.74947 | ||||||||
\(51\) | 1.02835e13 | 0.0314625 | ||||||||
\(52\) | −9.19828e13 | −0.238604 | ||||||||
\(53\) | −2.63554e14 | −0.581468 | −0.290734 | − | 0.956804i | \(-0.593899\pi\) | ||||
−0.290734 | + | 0.956804i | \(0.593899\pi\) | |||||||
\(54\) | −8.99162e13 | −0.169235 | ||||||||
\(55\) | −2.05819e15 | −3.31438 | ||||||||
\(56\) | 1.22470e14 | 0.169212 | ||||||||
\(57\) | −8.34067e13 | −0.0991436 | ||||||||
\(58\) | 1.09925e15 | 1.12709 | ||||||||
\(59\) | −1.31652e15 | −1.16731 | −0.583655 | − | 0.812002i | \(-0.698378\pi\) | ||||
−0.583655 | + | 0.812002i | \(0.698378\pi\) | |||||||
\(60\) | −9.91218e13 | −0.0761875 | ||||||||
\(61\) | 8.86874e14 | 0.592322 | 0.296161 | − | 0.955138i | \(-0.404293\pi\) | ||||
0.296161 | + | 0.955138i | \(0.404293\pi\) | |||||||
\(62\) | 9.35599e13 | 0.0544202 | ||||||||
\(63\) | 7.41226e14 | 0.376319 | ||||||||
\(64\) | −5.04884e14 | −0.224213 | ||||||||
\(65\) | 1.66669e15 | 0.648769 | ||||||||
\(66\) | 4.63992e14 | 0.158630 | ||||||||
\(67\) | −2.21612e15 | −0.666741 | −0.333371 | − | 0.942796i | \(-0.608186\pi\) | ||||
−0.333371 | + | 0.942796i | \(0.608186\pi\) | |||||||
\(68\) | 1.17134e15 | 0.310710 | ||||||||
\(69\) | −1.48478e14 | −0.0347892 | ||||||||
\(70\) | 4.15112e15 | 0.860662 | ||||||||
\(71\) | 3.25484e15 | 0.598183 | 0.299091 | − | 0.954224i | \(-0.403316\pi\) | ||||
0.299091 | + | 0.954224i | \(0.403316\pi\) | |||||||
\(72\) | 2.73156e15 | 0.445743 | ||||||||
\(73\) | −8.03322e15 | −1.16586 | −0.582929 | − | 0.812523i | \(-0.698093\pi\) | ||||
−0.582929 | + | 0.812523i | \(0.698093\pi\) | |||||||
\(74\) | 2.49066e15 | 0.321992 | ||||||||
\(75\) | 1.22394e15 | 0.141169 | ||||||||
\(76\) | −9.50042e15 | −0.979100 | ||||||||
\(77\) | −7.66657e15 | −0.707018 | ||||||||
\(78\) | −3.75732e14 | −0.0310509 | ||||||||
\(79\) | 6.85931e15 | 0.508687 | 0.254343 | − | 0.967114i | \(-0.418141\pi\) | ||||
0.254343 | + | 0.967114i | \(0.418141\pi\) | |||||||
\(80\) | 3.26237e16 | 2.17405 | ||||||||
\(81\) | 1.64597e16 | 0.986957 | ||||||||
\(82\) | −3.15444e16 | −1.70414 | ||||||||
\(83\) | −1.23496e16 | −0.601851 | −0.300926 | − | 0.953648i | \(-0.597296\pi\) | ||||
−0.300926 | + | 0.953648i | \(0.597296\pi\) | |||||||
\(84\) | −3.69220e14 | −0.0162522 | ||||||||
\(85\) | −2.12241e16 | −0.844826 | ||||||||
\(86\) | −2.96215e16 | −1.06751 | ||||||||
\(87\) | 1.77159e15 | 0.0578696 | ||||||||
\(88\) | −2.82528e16 | −0.837450 | ||||||||
\(89\) | −5.51807e16 | −1.48584 | −0.742920 | − | 0.669380i | \(-0.766560\pi\) | ||||
−0.742920 | + | 0.669380i | \(0.766560\pi\) | |||||||
\(90\) | 9.25865e16 | 2.26718 | ||||||||
\(91\) | 6.20826e15 | 0.138394 | ||||||||
\(92\) | −1.69124e16 | −0.343564 | ||||||||
\(93\) | 1.50784e14 | 0.00279416 | ||||||||
\(94\) | 1.26497e16 | 0.214039 | ||||||||
\(95\) | 1.72143e17 | 2.66219 | ||||||||
\(96\) | −5.26658e15 | −0.0745114 | ||||||||
\(97\) | 2.92905e16 | 0.379461 | 0.189731 | − | 0.981836i | \(-0.439239\pi\) | ||||
0.189731 | + | 0.981836i | \(0.439239\pi\) | |||||||
\(98\) | 1.54626e16 | 0.183595 | ||||||||
\(99\) | −1.70995e17 | −1.86245 | ||||||||
\(100\) | 1.39413e17 | 1.39413 | ||||||||
\(101\) | 1.89051e16 | 0.173719 | 0.0868595 | − | 0.996221i | \(-0.472317\pi\) | ||||
0.0868595 | + | 0.996221i | \(0.472317\pi\) | |||||||
\(102\) | 4.78468e15 | 0.0404345 | ||||||||
\(103\) | 4.43270e16 | 0.344788 | 0.172394 | − | 0.985028i | \(-0.444850\pi\) | ||||
0.172394 | + | 0.985028i | \(0.444850\pi\) | |||||||
\(104\) | 2.28786e16 | 0.163926 | ||||||||
\(105\) | 6.69009e15 | 0.0441899 | ||||||||
\(106\) | −1.22626e17 | −0.747281 | ||||||||
\(107\) | −1.42299e17 | −0.800646 | −0.400323 | − | 0.916374i | \(-0.631102\pi\) | ||||
−0.400323 | + | 0.916374i | \(0.631102\pi\) | |||||||
\(108\) | −1.65062e16 | −0.0858112 | ||||||||
\(109\) | 1.57889e17 | 0.758975 | 0.379488 | − | 0.925197i | \(-0.376100\pi\) | ||||
0.379488 | + | 0.925197i | \(0.376100\pi\) | |||||||
\(110\) | −9.57632e17 | −4.25952 | ||||||||
\(111\) | 4.01403e15 | 0.0165324 | ||||||||
\(112\) | 1.21521e17 | 0.463764 | ||||||||
\(113\) | 2.33144e17 | 0.825007 | 0.412503 | − | 0.910956i | \(-0.364655\pi\) | ||||
0.412503 | + | 0.910956i | \(0.364655\pi\) | |||||||
\(114\) | −3.88074e16 | −0.127416 | ||||||||
\(115\) | 3.06444e17 | 0.934155 | ||||||||
\(116\) | 2.01793e17 | 0.571495 | ||||||||
\(117\) | 1.38469e17 | 0.364562 | ||||||||
\(118\) | −6.12550e17 | −1.50018 | ||||||||
\(119\) | −7.90578e16 | −0.180217 | ||||||||
\(120\) | 2.46543e16 | 0.0523422 | ||||||||
\(121\) | 1.26317e18 | 2.49912 | ||||||||
\(122\) | 4.12644e17 | 0.761231 | ||||||||
\(123\) | −5.08380e16 | −0.0874973 | ||||||||
\(124\) | 1.71750e16 | 0.0275939 | ||||||||
\(125\) | −1.34534e18 | −2.01882 | ||||||||
\(126\) | 3.44877e17 | 0.483631 | ||||||||
\(127\) | −2.52229e17 | −0.330722 | −0.165361 | − | 0.986233i | \(-0.552879\pi\) | ||||
−0.165361 | + | 0.986233i | \(0.552879\pi\) | |||||||
\(128\) | 6.85662e17 | 0.841057 | ||||||||
\(129\) | −4.77390e16 | −0.0548102 | ||||||||
\(130\) | 7.75474e17 | 0.833774 | ||||||||
\(131\) | −6.73780e17 | −0.678754 | −0.339377 | − | 0.940650i | \(-0.610216\pi\) | ||||
−0.339377 | + | 0.940650i | \(0.610216\pi\) | |||||||
\(132\) | 8.51762e16 | 0.0804340 | ||||||||
\(133\) | 6.41218e17 | 0.567893 | ||||||||
\(134\) | −1.03111e18 | −0.856872 | ||||||||
\(135\) | 2.99084e17 | 0.233322 | ||||||||
\(136\) | −2.91343e17 | −0.213464 | ||||||||
\(137\) | −2.04921e18 | −1.41079 | −0.705394 | − | 0.708815i | \(-0.749230\pi\) | ||||
−0.705394 | + | 0.708815i | \(0.749230\pi\) | |||||||
\(138\) | −6.90837e16 | −0.0447099 | ||||||||
\(139\) | 1.81878e18 | 1.10702 | 0.553509 | − | 0.832843i | \(-0.313289\pi\) | ||||
0.553509 | + | 0.832843i | \(0.313289\pi\) | |||||||
\(140\) | 7.62033e17 | 0.436401 | ||||||||
\(141\) | 2.03866e16 | 0.0109896 | ||||||||
\(142\) | 1.51441e18 | 0.768763 | ||||||||
\(143\) | −1.43220e18 | −0.684930 | ||||||||
\(144\) | 2.71039e18 | 1.22166 | ||||||||
\(145\) | −3.65639e18 | −1.55390 | ||||||||
\(146\) | −3.73769e18 | −1.49832 | ||||||||
\(147\) | 2.49200e16 | 0.00942651 | ||||||||
\(148\) | 4.57217e17 | 0.163267 | ||||||||
\(149\) | −2.78229e18 | −0.938252 | −0.469126 | − | 0.883131i | \(-0.655431\pi\) | ||||
−0.469126 | + | 0.883131i | \(0.655431\pi\) | |||||||
\(150\) | 5.69475e17 | 0.181426 | ||||||||
\(151\) | 7.81424e17 | 0.235279 | 0.117639 | − | 0.993056i | \(-0.462467\pi\) | ||||
0.117639 | + | 0.993056i | \(0.462467\pi\) | |||||||
\(152\) | 2.36301e18 | 0.672660 | ||||||||
\(153\) | −1.76330e18 | −0.474733 | ||||||||
\(154\) | −3.56710e18 | −0.908633 | ||||||||
\(155\) | −3.11203e17 | −0.0750283 | ||||||||
\(156\) | −6.89742e16 | −0.0157444 | ||||||||
\(157\) | 6.17912e18 | 1.33592 | 0.667959 | − | 0.744198i | \(-0.267168\pi\) | ||||
0.667959 | + | 0.744198i | \(0.267168\pi\) | |||||||
\(158\) | 3.19149e18 | 0.653746 | ||||||||
\(159\) | −1.97629e17 | −0.0383685 | ||||||||
\(160\) | 1.08697e19 | 2.00077 | ||||||||
\(161\) | 1.14148e18 | 0.199272 | ||||||||
\(162\) | 7.65833e18 | 1.26840 | ||||||||
\(163\) | −3.74440e18 | −0.588556 | −0.294278 | − | 0.955720i | \(-0.595079\pi\) | ||||
−0.294278 | + | 0.955720i | \(0.595079\pi\) | |||||||
\(164\) | −5.79069e18 | −0.864087 | ||||||||
\(165\) | −1.54335e18 | −0.218701 | ||||||||
\(166\) | −5.74601e18 | −0.773478 | ||||||||
\(167\) | 1.01080e19 | 1.29293 | 0.646465 | − | 0.762944i | \(-0.276247\pi\) | ||||
0.646465 | + | 0.762944i | \(0.276247\pi\) | |||||||
\(168\) | 9.18351e16 | 0.0111655 | ||||||||
\(169\) | −7.49065e18 | −0.865929 | ||||||||
\(170\) | −9.87510e18 | −1.08574 | ||||||||
\(171\) | 1.43017e19 | 1.49596 | ||||||||
\(172\) | −5.43770e18 | −0.541282 | ||||||||
\(173\) | 1.48327e19 | 1.40549 | 0.702744 | − | 0.711443i | \(-0.251958\pi\) | ||||
0.702744 | + | 0.711443i | \(0.251958\pi\) | |||||||
\(174\) | 8.24285e17 | 0.0743719 | ||||||||
\(175\) | −9.40948e18 | −0.808616 | ||||||||
\(176\) | −2.80339e19 | −2.29522 | ||||||||
\(177\) | −9.87207e17 | −0.0770256 | ||||||||
\(178\) | −2.56744e19 | −1.90955 | ||||||||
\(179\) | −1.04723e19 | −0.742659 | −0.371330 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(180\) | 1.69964e19 | 1.14958 | ||||||||
\(181\) | −4.33572e18 | −0.279765 | −0.139883 | − | 0.990168i | \(-0.544672\pi\) | ||||
−0.139883 | + | 0.990168i | \(0.544672\pi\) | |||||||
\(182\) | 2.88857e18 | 0.177859 | ||||||||
\(183\) | 6.65030e17 | 0.0390847 | ||||||||
\(184\) | 4.20656e18 | 0.236035 | ||||||||
\(185\) | −8.28456e18 | −0.443925 | ||||||||
\(186\) | 7.01567e16 | 0.00359095 | ||||||||
\(187\) | 1.82380e19 | 0.891915 | ||||||||
\(188\) | 2.32213e18 | 0.108529 | ||||||||
\(189\) | 1.11406e18 | 0.0497718 | ||||||||
\(190\) | 8.00945e19 | 3.42135 | ||||||||
\(191\) | 1.00097e18 | 0.0408919 | 0.0204460 | − | 0.999791i | \(-0.493491\pi\) | ||||
0.0204460 | + | 0.999791i | \(0.493491\pi\) | |||||||
\(192\) | −3.78592e17 | −0.0147948 | ||||||||
\(193\) | −1.73634e19 | −0.649230 | −0.324615 | − | 0.945846i | \(-0.605235\pi\) | ||||
−0.324615 | + | 0.945846i | \(0.605235\pi\) | |||||||
\(194\) | 1.36283e19 | 0.487670 | ||||||||
\(195\) | 1.24978e18 | 0.0428094 | ||||||||
\(196\) | 2.83851e18 | 0.0930922 | ||||||||
\(197\) | 3.42729e19 | 1.07644 | 0.538218 | − | 0.842805i | \(-0.319098\pi\) | ||||
0.538218 | + | 0.842805i | \(0.319098\pi\) | |||||||
\(198\) | −7.95604e19 | −2.39355 | ||||||||
\(199\) | −1.35620e19 | −0.390906 | −0.195453 | − | 0.980713i | \(-0.562618\pi\) | ||||
−0.195453 | + | 0.980713i | \(0.562618\pi\) | |||||||
\(200\) | −3.46758e19 | −0.957792 | ||||||||
\(201\) | −1.66178e18 | −0.0439953 | ||||||||
\(202\) | 8.79614e18 | 0.223257 | ||||||||
\(203\) | −1.36197e19 | −0.331476 | ||||||||
\(204\) | 8.78337e17 | 0.0205024 | ||||||||
\(205\) | 1.04924e20 | 2.34946 | ||||||||
\(206\) | 2.06244e19 | 0.443108 | ||||||||
\(207\) | 2.54594e19 | 0.524930 | ||||||||
\(208\) | 2.27013e19 | 0.449276 | ||||||||
\(209\) | −1.47924e20 | −2.81057 | ||||||||
\(210\) | 3.11276e18 | 0.0567913 | ||||||||
\(211\) | −2.80278e19 | −0.491121 | −0.245560 | − | 0.969381i | \(-0.578972\pi\) | ||||
−0.245560 | + | 0.969381i | \(0.578972\pi\) | |||||||
\(212\) | −2.25108e19 | −0.378911 | ||||||||
\(213\) | 2.44067e18 | 0.0394714 | ||||||||
\(214\) | −6.62089e19 | −1.02896 | ||||||||
\(215\) | 9.85285e19 | 1.47175 | ||||||||
\(216\) | 4.10553e18 | 0.0589539 | ||||||||
\(217\) | −1.15921e18 | −0.0160049 | ||||||||
\(218\) | 7.34626e19 | 0.975407 | ||||||||
\(219\) | −6.02379e18 | −0.0769298 | ||||||||
\(220\) | −1.75795e20 | −2.15980 | ||||||||
\(221\) | −1.47688e19 | −0.174587 | ||||||||
\(222\) | 1.86765e18 | 0.0212468 | ||||||||
\(223\) | 8.41954e19 | 0.921928 | 0.460964 | − | 0.887419i | \(-0.347504\pi\) | ||||
0.460964 | + | 0.887419i | \(0.347504\pi\) | |||||||
\(224\) | 4.04886e19 | 0.426800 | ||||||||
\(225\) | −2.09869e20 | −2.13008 | ||||||||
\(226\) | 1.08477e20 | 1.06027 | ||||||||
\(227\) | 1.64163e20 | 1.54545 | 0.772725 | − | 0.634741i | \(-0.218893\pi\) | ||||
0.772725 | + | 0.634741i | \(0.218893\pi\) | |||||||
\(228\) | −7.12398e18 | −0.0646065 | ||||||||
\(229\) | −1.03358e20 | −0.903117 | −0.451558 | − | 0.892242i | \(-0.649132\pi\) | ||||
−0.451558 | + | 0.892242i | \(0.649132\pi\) | |||||||
\(230\) | 1.42582e20 | 1.20054 | ||||||||
\(231\) | −5.74885e18 | −0.0466530 | ||||||||
\(232\) | −5.01913e19 | −0.392628 | ||||||||
\(233\) | −1.59667e20 | −1.20417 | −0.602086 | − | 0.798431i | \(-0.705664\pi\) | ||||
−0.602086 | + | 0.798431i | \(0.705664\pi\) | |||||||
\(234\) | 6.44266e19 | 0.468522 | ||||||||
\(235\) | −4.20759e19 | −0.295091 | ||||||||
\(236\) | −1.12447e20 | −0.760672 | ||||||||
\(237\) | 5.14352e18 | 0.0335660 | ||||||||
\(238\) | −3.67839e19 | −0.231608 | ||||||||
\(239\) | 1.16789e20 | 0.709612 | 0.354806 | − | 0.934940i | \(-0.384547\pi\) | ||||
0.354806 | + | 0.934940i | \(0.384547\pi\) | |||||||
\(240\) | 2.44632e19 | 0.143456 | ||||||||
\(241\) | 1.47720e20 | 0.836170 | 0.418085 | − | 0.908408i | \(-0.362701\pi\) | ||||
0.418085 | + | 0.908408i | \(0.362701\pi\) | |||||||
\(242\) | 5.87727e20 | 3.21177 | ||||||||
\(243\) | 3.72990e19 | 0.196809 | ||||||||
\(244\) | 7.57501e19 | 0.385984 | ||||||||
\(245\) | −5.14324e19 | −0.253119 | ||||||||
\(246\) | −2.36538e19 | −0.112448 | ||||||||
\(247\) | 1.19786e20 | 0.550152 | ||||||||
\(248\) | −4.27190e18 | −0.0189575 | ||||||||
\(249\) | −9.26046e18 | −0.0397135 | ||||||||
\(250\) | −6.25960e20 | −2.59452 | ||||||||
\(251\) | −1.55508e20 | −0.623053 | −0.311526 | − | 0.950237i | \(-0.600840\pi\) | ||||
−0.311526 | + | 0.950237i | \(0.600840\pi\) | |||||||
\(252\) | 6.33099e19 | 0.245226 | ||||||||
\(253\) | −2.63330e20 | −0.986223 | ||||||||
\(254\) | −1.17357e20 | −0.425031 | ||||||||
\(255\) | −1.59150e19 | −0.0557463 | ||||||||
\(256\) | 3.85200e20 | 1.30511 | ||||||||
\(257\) | −3.21984e20 | −1.05537 | −0.527683 | − | 0.849442i | \(-0.676939\pi\) | ||||
−0.527683 | + | 0.849442i | \(0.676939\pi\) | |||||||
\(258\) | −2.22120e19 | −0.0704400 | ||||||||
\(259\) | −3.08593e19 | −0.0946973 | ||||||||
\(260\) | 1.42356e20 | 0.422767 | ||||||||
\(261\) | −3.03774e20 | −0.873185 | ||||||||
\(262\) | −3.13496e20 | −0.872310 | ||||||||
\(263\) | −6.40953e20 | −1.72664 | −0.863321 | − | 0.504655i | \(-0.831620\pi\) | ||||
−0.863321 | + | 0.504655i | \(0.831620\pi\) | |||||||
\(264\) | −2.11856e19 | −0.0552596 | ||||||||
\(265\) | 4.07886e20 | 1.03026 | ||||||||
\(266\) | 2.98345e20 | 0.729836 | ||||||||
\(267\) | −4.13777e19 | −0.0980440 | ||||||||
\(268\) | −1.89284e20 | −0.434479 | ||||||||
\(269\) | 7.35147e20 | 1.63486 | 0.817429 | − | 0.576030i | \(-0.195399\pi\) | ||||
0.817429 | + | 0.576030i | \(0.195399\pi\) | |||||||
\(270\) | 1.39157e20 | 0.299857 | ||||||||
\(271\) | −1.53576e20 | −0.320688 | −0.160344 | − | 0.987061i | \(-0.551260\pi\) | ||||
−0.160344 | + | 0.987061i | \(0.551260\pi\) | |||||||
\(272\) | −2.89085e20 | −0.585046 | ||||||||
\(273\) | 4.65532e18 | 0.00913202 | ||||||||
\(274\) | −9.53455e20 | −1.81309 | ||||||||
\(275\) | 2.17069e21 | 4.00194 | ||||||||
\(276\) | −1.26819e19 | −0.0226703 | ||||||||
\(277\) | 2.43681e20 | 0.422419 | 0.211210 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211210 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(278\) | 8.46240e20 | 1.42270 | ||||||||
\(279\) | −2.58549e19 | −0.0421606 | ||||||||
\(280\) | −1.89538e20 | −0.299815 | ||||||||
\(281\) | −4.74614e20 | −0.728344 | −0.364172 | − | 0.931332i | \(-0.618648\pi\) | ||||
−0.364172 | + | 0.931332i | \(0.618648\pi\) | |||||||
\(282\) | 9.48546e18 | 0.0141235 | ||||||||
\(283\) | 5.03809e20 | 0.727916 | 0.363958 | − | 0.931415i | \(-0.381425\pi\) | ||||
0.363958 | + | 0.931415i | \(0.381425\pi\) | |||||||
\(284\) | 2.78004e20 | 0.389803 | ||||||||
\(285\) | 1.29083e20 | 0.175666 | ||||||||
\(286\) | −6.66371e20 | −0.880247 | ||||||||
\(287\) | 3.90835e20 | 0.501184 | ||||||||
\(288\) | 9.03057e20 | 1.12429 | ||||||||
\(289\) | −6.39170e20 | −0.772653 | ||||||||
\(290\) | −1.70124e21 | −1.99702 | ||||||||
\(291\) | 2.19638e19 | 0.0250390 | ||||||||
\(292\) | −6.86138e20 | −0.759726 | ||||||||
\(293\) | −1.74476e21 | −1.87655 | −0.938276 | − | 0.345886i | \(-0.887578\pi\) | ||||
−0.938276 | + | 0.345886i | \(0.887578\pi\) | |||||||
\(294\) | 1.15948e19 | 0.0121146 | ||||||||
\(295\) | 2.03749e21 | 2.06828 | ||||||||
\(296\) | −1.13722e20 | −0.112167 | ||||||||
\(297\) | −2.57005e20 | −0.246327 | ||||||||
\(298\) | −1.29454e21 | −1.20581 | ||||||||
\(299\) | 2.13240e20 | 0.193047 | ||||||||
\(300\) | 1.04540e20 | 0.0919923 | ||||||||
\(301\) | 3.67010e20 | 0.313952 | ||||||||
\(302\) | 3.63580e20 | 0.302372 | ||||||||
\(303\) | 1.41762e19 | 0.0114629 | ||||||||
\(304\) | 2.34470e21 | 1.84358 | ||||||||
\(305\) | −1.37256e21 | −1.04950 | ||||||||
\(306\) | −8.20427e20 | −0.610109 | ||||||||
\(307\) | −6.26704e20 | −0.453300 | −0.226650 | − | 0.973976i | \(-0.572777\pi\) | ||||
−0.226650 | + | 0.973976i | \(0.572777\pi\) | |||||||
\(308\) | −6.54821e20 | −0.460725 | ||||||||
\(309\) | 3.32390e19 | 0.0227510 | ||||||||
\(310\) | −1.44796e20 | −0.0964236 | ||||||||
\(311\) | −2.07324e21 | −1.34334 | −0.671671 | − | 0.740849i | \(-0.734423\pi\) | ||||
−0.671671 | + | 0.740849i | \(0.734423\pi\) | |||||||
\(312\) | 1.71558e19 | 0.0108167 | ||||||||
\(313\) | 2.88951e21 | 1.77295 | 0.886476 | − | 0.462775i | \(-0.153146\pi\) | ||||
0.886476 | + | 0.462775i | \(0.153146\pi\) | |||||||
\(314\) | 2.87501e21 | 1.71687 | ||||||||
\(315\) | −1.14715e21 | −0.666774 | ||||||||
\(316\) | 5.85871e20 | 0.331483 | ||||||||
\(317\) | −3.48578e21 | −1.91998 | −0.959989 | − | 0.280038i | \(-0.909653\pi\) | ||||
−0.959989 | + | 0.280038i | \(0.909653\pi\) | |||||||
\(318\) | −9.19525e19 | −0.0493098 | ||||||||
\(319\) | 3.14196e21 | 1.64052 | ||||||||
\(320\) | 7.81375e20 | 0.397269 | ||||||||
\(321\) | −1.06704e20 | −0.0528311 | ||||||||
\(322\) | 5.31105e20 | 0.256098 | ||||||||
\(323\) | −1.52539e21 | −0.716408 | ||||||||
\(324\) | 1.40586e21 | 0.643146 | ||||||||
\(325\) | −1.75779e21 | −0.783354 | ||||||||
\(326\) | −1.74219e21 | −0.756391 | ||||||||
\(327\) | 1.18395e20 | 0.0500814 | ||||||||
\(328\) | 1.44030e21 | 0.593643 | ||||||||
\(329\) | −1.56729e20 | −0.0629484 | ||||||||
\(330\) | −7.18089e20 | −0.281067 | ||||||||
\(331\) | 9.92801e20 | 0.378725 | 0.189363 | − | 0.981907i | \(-0.439358\pi\) | ||||
0.189363 | + | 0.981907i | \(0.439358\pi\) | |||||||
\(332\) | −1.05481e21 | −0.392194 | ||||||||
\(333\) | −6.88284e20 | −0.249455 | ||||||||
\(334\) | 4.70304e21 | 1.66163 | ||||||||
\(335\) | 3.42974e21 | 1.18136 | ||||||||
\(336\) | 9.11233e19 | 0.0306017 | ||||||||
\(337\) | −1.57640e21 | −0.516194 | −0.258097 | − | 0.966119i | \(-0.583095\pi\) | ||||
−0.258097 | + | 0.966119i | \(0.583095\pi\) | |||||||
\(338\) | −3.48524e21 | −1.11286 | ||||||||
\(339\) | 1.74825e20 | 0.0544385 | ||||||||
\(340\) | −1.81280e21 | −0.550527 | ||||||||
\(341\) | 2.67420e20 | 0.0792102 | ||||||||
\(342\) | 6.65428e21 | 1.92256 | ||||||||
\(343\) | −1.91581e20 | −0.0539949 | ||||||||
\(344\) | 1.35250e21 | 0.371871 | ||||||||
\(345\) | 2.29790e20 | 0.0616408 | ||||||||
\(346\) | 6.90132e21 | 1.80628 | ||||||||
\(347\) | −4.26241e21 | −1.08856 | −0.544282 | − | 0.838902i | \(-0.683198\pi\) | ||||
−0.544282 | + | 0.838902i | \(0.683198\pi\) | |||||||
\(348\) | 1.51316e20 | 0.0377104 | ||||||||
\(349\) | −3.75476e21 | −0.913200 | −0.456600 | − | 0.889672i | \(-0.650933\pi\) | ||||
−0.456600 | + | 0.889672i | \(0.650933\pi\) | |||||||
\(350\) | −4.37803e21 | −1.03920 | ||||||||
\(351\) | 2.08118e20 | 0.0482169 | ||||||||
\(352\) | −9.34041e21 | −2.11229 | ||||||||
\(353\) | 3.18901e20 | 0.0703998 | 0.0351999 | − | 0.999380i | \(-0.488793\pi\) | ||||
0.0351999 | + | 0.999380i | \(0.488793\pi\) | |||||||
\(354\) | −4.59326e20 | −0.0989905 | ||||||||
\(355\) | −5.03730e21 | −1.05988 | ||||||||
\(356\) | −4.71312e21 | −0.968241 | ||||||||
\(357\) | −5.92822e19 | −0.0118917 | ||||||||
\(358\) | −4.87252e21 | −0.954439 | ||||||||
\(359\) | 4.86841e21 | 0.931289 | 0.465644 | − | 0.884972i | \(-0.345823\pi\) | ||||
0.465644 | + | 0.884972i | \(0.345823\pi\) | |||||||
\(360\) | −4.22746e21 | −0.789783 | ||||||||
\(361\) | 6.89170e21 | 1.25752 | ||||||||
\(362\) | −2.01732e21 | −0.359544 | ||||||||
\(363\) | 9.47200e20 | 0.164906 | ||||||||
\(364\) | 5.30263e20 | 0.0901840 | ||||||||
\(365\) | 1.24325e22 | 2.06571 | ||||||||
\(366\) | 3.09425e20 | 0.0502303 | ||||||||
\(367\) | −8.97341e21 | −1.42330 | −0.711649 | − | 0.702535i | \(-0.752052\pi\) | ||||
−0.711649 | + | 0.702535i | \(0.752052\pi\) | |||||||
\(368\) | 4.17396e21 | 0.646907 | ||||||||
\(369\) | 8.71716e21 | 1.32023 | ||||||||
\(370\) | −3.85463e21 | −0.570517 | ||||||||
\(371\) | 1.51934e21 | 0.219774 | ||||||||
\(372\) | 1.28789e19 | 0.00182080 | ||||||||
\(373\) | −3.60949e21 | −0.498794 | −0.249397 | − | 0.968401i | \(-0.580232\pi\) | ||||
−0.249397 | + | 0.968401i | \(0.580232\pi\) | |||||||
\(374\) | 8.48576e21 | 1.14626 | ||||||||
\(375\) | −1.00882e21 | −0.133213 | ||||||||
\(376\) | −5.77577e20 | −0.0745613 | ||||||||
\(377\) | −2.54431e21 | −0.321121 | ||||||||
\(378\) | 5.18349e20 | 0.0639649 | ||||||||
\(379\) | 7.79019e21 | 0.939972 | 0.469986 | − | 0.882674i | \(-0.344259\pi\) | ||||
0.469986 | + | 0.882674i | \(0.344259\pi\) | |||||||
\(380\) | 1.47032e22 | 1.73480 | ||||||||
\(381\) | −1.89136e20 | −0.0218229 | ||||||||
\(382\) | 4.65731e20 | 0.0525528 | ||||||||
\(383\) | −1.02337e22 | −1.12939 | −0.564694 | − | 0.825300i | \(-0.691006\pi\) | ||||
−0.564694 | + | 0.825300i | \(0.691006\pi\) | |||||||
\(384\) | 5.14150e20 | 0.0554976 | ||||||||
\(385\) | 1.18650e22 | 1.25272 | ||||||||
\(386\) | −8.07885e21 | −0.834367 | ||||||||
\(387\) | 8.18578e21 | 0.827022 | ||||||||
\(388\) | 2.50178e21 | 0.247274 | ||||||||
\(389\) | −7.22837e21 | −0.698987 | −0.349493 | − | 0.936939i | \(-0.613646\pi\) | ||||
−0.349493 | + | 0.936939i | \(0.613646\pi\) | |||||||
\(390\) | 5.81496e20 | 0.0550171 | ||||||||
\(391\) | −2.71546e21 | −0.251386 | ||||||||
\(392\) | −7.06014e20 | −0.0639561 | ||||||||
\(393\) | −5.05240e20 | −0.0447880 | ||||||||
\(394\) | 1.59465e22 | 1.38340 | ||||||||
\(395\) | −1.06157e22 | −0.901309 | ||||||||
\(396\) | −1.46051e22 | −1.21366 | ||||||||
\(397\) | 1.30171e21 | 0.105875 | 0.0529377 | − | 0.998598i | \(-0.483142\pi\) | ||||
0.0529377 | + | 0.998598i | \(0.483142\pi\) | |||||||
\(398\) | −6.31011e21 | −0.502378 | ||||||||
\(399\) | 4.80823e20 | 0.0374728 | ||||||||
\(400\) | −3.44070e22 | −2.62505 | ||||||||
\(401\) | −1.37644e22 | −1.02809 | −0.514044 | − | 0.857764i | \(-0.671853\pi\) | ||||
−0.514044 | + | 0.857764i | \(0.671853\pi\) | |||||||
\(402\) | −7.73190e20 | −0.0565412 | ||||||||
\(403\) | −2.16552e20 | −0.0155049 | ||||||||
\(404\) | 1.61473e21 | 0.113203 | ||||||||
\(405\) | −2.54735e22 | −1.74872 | ||||||||
\(406\) | −6.33697e21 | −0.426001 | ||||||||
\(407\) | 7.11899e21 | 0.468669 | ||||||||
\(408\) | −2.18466e20 | −0.0140855 | ||||||||
\(409\) | 1.13861e22 | 0.718996 | 0.359498 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359498 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(410\) | 4.88191e22 | 3.01945 | ||||||||
\(411\) | −1.53662e21 | −0.0930917 | ||||||||
\(412\) | 3.78608e21 | 0.224679 | ||||||||
\(413\) | 7.58949e21 | 0.441202 | ||||||||
\(414\) | 1.18457e22 | 0.674620 | ||||||||
\(415\) | 1.91127e22 | 1.06638 | ||||||||
\(416\) | 7.56370e21 | 0.413467 | ||||||||
\(417\) | 1.36383e21 | 0.0730472 | ||||||||
\(418\) | −6.88259e22 | −3.61205 | ||||||||
\(419\) | 1.84138e22 | 0.946946 | 0.473473 | − | 0.880808i | \(-0.343000\pi\) | ||||
0.473473 | + | 0.880808i | \(0.343000\pi\) | |||||||
\(420\) | 5.71417e20 | 0.0287962 | ||||||||
\(421\) | 1.63841e22 | 0.809144 | 0.404572 | − | 0.914506i | \(-0.367421\pi\) | ||||
0.404572 | + | 0.914506i | \(0.367421\pi\) | |||||||
\(422\) | −1.30407e22 | −0.631170 | ||||||||
\(423\) | −3.49568e21 | −0.165821 | ||||||||
\(424\) | 5.59906e21 | 0.260319 | ||||||||
\(425\) | 2.23842e22 | 1.02008 | ||||||||
\(426\) | 1.13559e21 | 0.0507272 | ||||||||
\(427\) | −5.11265e21 | −0.223877 | ||||||||
\(428\) | −1.21541e22 | −0.521738 | ||||||||
\(429\) | −1.07395e21 | −0.0451955 | ||||||||
\(430\) | 4.58433e22 | 1.89144 | ||||||||
\(431\) | −4.09149e22 | −1.65510 | −0.827551 | − | 0.561391i | \(-0.810266\pi\) | ||||
−0.827551 | + | 0.561391i | \(0.810266\pi\) | |||||||
\(432\) | 4.07371e21 | 0.161577 | ||||||||
\(433\) | −1.62847e22 | −0.633333 | −0.316666 | − | 0.948537i | \(-0.602564\pi\) | ||||
−0.316666 | + | 0.948537i | \(0.602564\pi\) | |||||||
\(434\) | −5.39354e20 | −0.0205689 | ||||||||
\(435\) | −2.74178e21 | −0.102535 | ||||||||
\(436\) | 1.34857e22 | 0.494583 | ||||||||
\(437\) | 2.20244e22 | 0.792158 | ||||||||
\(438\) | −2.80274e21 | −0.0988674 | ||||||||
\(439\) | −5.29627e22 | −1.83240 | −0.916202 | − | 0.400716i | \(-0.868761\pi\) | ||||
−0.916202 | + | 0.400716i | \(0.868761\pi\) | |||||||
\(440\) | 4.37250e22 | 1.48382 | ||||||||
\(441\) | −4.27302e21 | −0.142235 | ||||||||
\(442\) | −6.87162e21 | −0.224373 | ||||||||
\(443\) | 1.42402e21 | 0.0456127 | 0.0228064 | − | 0.999740i | \(-0.492740\pi\) | ||||
0.0228064 | + | 0.999740i | \(0.492740\pi\) | |||||||
\(444\) | 3.42849e20 | 0.0107733 | ||||||||
\(445\) | 8.53995e22 | 2.63266 | ||||||||
\(446\) | 3.91743e22 | 1.18483 | ||||||||
\(447\) | −2.08633e21 | −0.0619111 | ||||||||
\(448\) | 2.91055e21 | 0.0847447 | ||||||||
\(449\) | −4.49500e22 | −1.28421 | −0.642104 | − | 0.766617i | \(-0.721938\pi\) | ||||
−0.642104 | + | 0.766617i | \(0.721938\pi\) | |||||||
\(450\) | −9.76475e22 | −2.73750 | ||||||||
\(451\) | −9.01624e22 | −2.48042 | ||||||||
\(452\) | 1.99134e22 | 0.537612 | ||||||||
\(453\) | 5.85958e20 | 0.0155250 | ||||||||
\(454\) | 7.63815e22 | 1.98616 | ||||||||
\(455\) | −9.60811e21 | −0.245212 | ||||||||
\(456\) | 1.77193e21 | 0.0443859 | ||||||||
\(457\) | 6.28849e22 | 1.54617 | 0.773087 | − | 0.634300i | \(-0.218711\pi\) | ||||
0.773087 | + | 0.634300i | \(0.218711\pi\) | |||||||
\(458\) | −4.80905e22 | −1.16065 | ||||||||
\(459\) | −2.65024e21 | −0.0627880 | ||||||||
\(460\) | 2.61741e22 | 0.608738 | ||||||||
\(461\) | 1.81575e22 | 0.414570 | 0.207285 | − | 0.978281i | \(-0.433537\pi\) | ||||
0.207285 | + | 0.978281i | \(0.433537\pi\) | |||||||
\(462\) | −2.67482e21 | −0.0599567 | ||||||||
\(463\) | −1.23298e22 | −0.271341 | −0.135671 | − | 0.990754i | \(-0.543319\pi\) | ||||
−0.135671 | + | 0.990754i | \(0.543319\pi\) | |||||||
\(464\) | −4.98024e22 | −1.07609 | ||||||||
\(465\) | −2.33359e20 | −0.00495078 | ||||||||
\(466\) | −7.42895e22 | −1.54756 | ||||||||
\(467\) | 5.52860e22 | 1.13089 | 0.565447 | − | 0.824785i | \(-0.308704\pi\) | ||||
0.565447 | + | 0.824785i | \(0.308704\pi\) | |||||||
\(468\) | 1.18270e22 | 0.237565 | ||||||||
\(469\) | 1.27755e22 | 0.252005 | ||||||||
\(470\) | −1.95770e22 | −0.379241 | ||||||||
\(471\) | 4.63347e21 | 0.0881513 | ||||||||
\(472\) | 2.79688e22 | 0.522596 | ||||||||
\(473\) | −8.46664e22 | −1.55379 | ||||||||
\(474\) | 2.39317e21 | 0.0431378 | ||||||||
\(475\) | −1.81553e23 | −3.21445 | ||||||||
\(476\) | −6.75252e21 | −0.117438 | ||||||||
\(477\) | 3.38873e22 | 0.578936 | ||||||||
\(478\) | 5.43396e22 | 0.911968 | ||||||||
\(479\) | 6.10024e22 | 1.00576 | 0.502880 | − | 0.864356i | \(-0.332274\pi\) | ||||
0.502880 | + | 0.864356i | \(0.332274\pi\) | |||||||
\(480\) | 8.15073e21 | 0.132022 | ||||||||
\(481\) | −5.76484e21 | −0.0917389 | ||||||||
\(482\) | 6.87311e22 | 1.07462 | ||||||||
\(483\) | 8.55947e20 | 0.0131491 | ||||||||
\(484\) | 1.07891e23 | 1.62854 | ||||||||
\(485\) | −4.53310e22 | −0.672342 | ||||||||
\(486\) | 1.73545e22 | 0.252931 | ||||||||
\(487\) | −7.45003e22 | −1.06699 | −0.533497 | − | 0.845802i | \(-0.679123\pi\) | ||||
−0.533497 | + | 0.845802i | \(0.679123\pi\) | |||||||
\(488\) | −1.88411e22 | −0.265178 | ||||||||
\(489\) | −2.80777e21 | −0.0388362 | ||||||||
\(490\) | −2.39304e22 | −0.325300 | ||||||||
\(491\) | 1.41363e23 | 1.88862 | 0.944308 | − | 0.329063i | \(-0.106733\pi\) | ||||
0.944308 | + | 0.329063i | \(0.106733\pi\) | |||||||
\(492\) | −4.34220e21 | −0.0570172 | ||||||||
\(493\) | 3.24000e22 | 0.418163 | ||||||||
\(494\) | 5.57340e22 | 0.707036 | ||||||||
\(495\) | 2.64638e23 | 3.29995 | ||||||||
\(496\) | −4.23879e21 | −0.0519574 | ||||||||
\(497\) | −1.87635e22 | −0.226092 | ||||||||
\(498\) | −4.30870e21 | −0.0510384 | ||||||||
\(499\) | 9.89380e22 | 1.15215 | 0.576074 | − | 0.817397i | \(-0.304584\pi\) | ||||
0.576074 | + | 0.817397i | \(0.304584\pi\) | |||||||
\(500\) | −1.14909e23 | −1.31556 | ||||||||
\(501\) | 7.57957e21 | 0.0853147 | ||||||||
\(502\) | −7.23544e22 | −0.800725 | ||||||||
\(503\) | −1.48681e23 | −1.61781 | −0.808905 | − | 0.587939i | \(-0.799940\pi\) | ||||
−0.808905 | + | 0.587939i | \(0.799940\pi\) | |||||||
\(504\) | −1.57469e22 | −0.168475 | ||||||||
\(505\) | −2.92582e22 | −0.307801 | ||||||||
\(506\) | −1.22522e23 | −1.26746 | ||||||||
\(507\) | −5.61693e21 | −0.0571388 | ||||||||
\(508\) | −2.15435e22 | −0.215513 | ||||||||
\(509\) | 5.94577e22 | 0.584934 | 0.292467 | − | 0.956276i | \(-0.405524\pi\) | ||||
0.292467 | + | 0.956276i | \(0.405524\pi\) | |||||||
\(510\) | −7.40494e21 | −0.0716432 | ||||||||
\(511\) | 4.63099e22 | 0.440653 | ||||||||
\(512\) | 8.93545e22 | 0.836222 | ||||||||
\(513\) | 2.14954e22 | 0.197856 | ||||||||
\(514\) | −1.49812e23 | −1.35632 | ||||||||
\(515\) | −6.86019e22 | −0.610906 | ||||||||
\(516\) | −4.07751e21 | −0.0357168 | ||||||||
\(517\) | 3.61562e22 | 0.311539 | ||||||||
\(518\) | −1.43582e22 | −0.121702 | ||||||||
\(519\) | 1.11224e22 | 0.0927419 | ||||||||
\(520\) | −3.54077e22 | −0.290449 | ||||||||
\(521\) | −1.56747e22 | −0.126496 | −0.0632482 | − | 0.997998i | \(-0.520146\pi\) | ||||
−0.0632482 | + | 0.997998i | \(0.520146\pi\) | |||||||
\(522\) | −1.41340e23 | −1.12219 | ||||||||
\(523\) | −8.69704e22 | −0.679371 | −0.339686 | − | 0.940539i | \(-0.610321\pi\) | ||||
−0.339686 | + | 0.940539i | \(0.610321\pi\) | |||||||
\(524\) | −5.75493e22 | −0.442307 | ||||||||
\(525\) | −7.05578e21 | −0.0533570 | ||||||||
\(526\) | −2.98222e23 | −2.21902 | ||||||||
\(527\) | 2.75763e21 | 0.0201905 | ||||||||
\(528\) | −2.10214e22 | −0.151452 | ||||||||
\(529\) | −1.01843e23 | −0.722034 | ||||||||
\(530\) | 1.89781e23 | 1.32406 | ||||||||
\(531\) | 1.69276e23 | 1.16223 | ||||||||
\(532\) | 5.47680e22 | 0.370065 | ||||||||
\(533\) | 7.30120e22 | 0.485526 | ||||||||
\(534\) | −1.92522e22 | −0.126003 | ||||||||
\(535\) | 2.20227e23 | 1.41861 | ||||||||
\(536\) | 4.70802e22 | 0.298495 | ||||||||
\(537\) | −7.85272e21 | −0.0490048 | ||||||||
\(538\) | 3.42048e23 | 2.10106 | ||||||||
\(539\) | 4.41963e22 | 0.267228 | ||||||||
\(540\) | 2.55455e22 | 0.152043 | ||||||||
\(541\) | 2.08084e23 | 1.21916 | 0.609580 | − | 0.792724i | \(-0.291338\pi\) | ||||
0.609580 | + | 0.792724i | \(0.291338\pi\) | |||||||
\(542\) | −7.14555e22 | −0.412137 | ||||||||
\(543\) | −3.25118e21 | −0.0184605 | ||||||||
\(544\) | −9.63183e22 | −0.538416 | ||||||||
\(545\) | −2.44355e23 | −1.34478 | ||||||||
\(546\) | 2.16602e21 | 0.0117361 | ||||||||
\(547\) | −1.78764e23 | −0.953645 | −0.476822 | − | 0.879000i | \(-0.658212\pi\) | ||||
−0.476822 | + | 0.879000i | \(0.658212\pi\) | |||||||
\(548\) | −1.75028e23 | −0.919334 | ||||||||
\(549\) | −1.14032e23 | −0.589743 | ||||||||
\(550\) | 1.00998e24 | 5.14315 | ||||||||
\(551\) | −2.62788e23 | −1.31770 | ||||||||
\(552\) | 3.15433e21 | 0.0155749 | ||||||||
\(553\) | −3.95426e22 | −0.192266 | ||||||||
\(554\) | 1.13380e23 | 0.542878 | ||||||||
\(555\) | −6.21225e21 | −0.0292927 | ||||||||
\(556\) | 1.55347e23 | 0.721383 | ||||||||
\(557\) | −3.57210e23 | −1.63363 | −0.816816 | − | 0.576898i | \(-0.804263\pi\) | ||||
−0.816816 | + | 0.576898i | \(0.804263\pi\) | |||||||
\(558\) | −1.20297e22 | −0.0541833 | ||||||||
\(559\) | 6.85614e22 | 0.304144 | ||||||||
\(560\) | −1.88069e23 | −0.821712 | ||||||||
\(561\) | 1.36759e22 | 0.0588535 | ||||||||
\(562\) | −2.20828e23 | −0.936041 | ||||||||
\(563\) | 1.12350e23 | 0.469085 | 0.234543 | − | 0.972106i | \(-0.424641\pi\) | ||||
0.234543 | + | 0.972106i | \(0.424641\pi\) | |||||||
\(564\) | 1.74127e21 | 0.00716133 | ||||||||
\(565\) | −3.60821e23 | −1.46177 | ||||||||
\(566\) | 2.34412e23 | 0.935491 | ||||||||
\(567\) | −9.48866e22 | −0.373035 | ||||||||
\(568\) | −6.91472e22 | −0.267802 | ||||||||
\(569\) | 1.43918e23 | 0.549110 | 0.274555 | − | 0.961571i | \(-0.411469\pi\) | ||||
0.274555 | + | 0.961571i | \(0.411469\pi\) | |||||||
\(570\) | 6.00596e22 | 0.225760 | ||||||||
\(571\) | 2.79666e23 | 1.03570 | 0.517848 | − | 0.855473i | \(-0.326733\pi\) | ||||
0.517848 | + | 0.855473i | \(0.326733\pi\) | |||||||
\(572\) | −1.22327e23 | −0.446332 | ||||||||
\(573\) | 7.50587e20 | 0.00269828 | ||||||||
\(574\) | 1.81847e23 | 0.644103 | ||||||||
\(575\) | −3.23195e23 | −1.12794 | ||||||||
\(576\) | 6.49169e22 | 0.223237 | ||||||||
\(577\) | 5.19840e23 | 1.76147 | 0.880734 | − | 0.473610i | \(-0.157050\pi\) | ||||
0.880734 | + | 0.473610i | \(0.157050\pi\) | |||||||
\(578\) | −2.97392e23 | −0.992986 | ||||||||
\(579\) | −1.30201e22 | −0.0428398 | ||||||||
\(580\) | −3.12301e23 | −1.01259 | ||||||||
\(581\) | 7.11930e22 | 0.227478 | ||||||||
\(582\) | 1.02193e22 | 0.0321792 | ||||||||
\(583\) | −3.50500e23 | −1.08769 | ||||||||
\(584\) | 1.70661e23 | 0.521946 | ||||||||
\(585\) | −2.14299e23 | −0.645944 | ||||||||
\(586\) | −8.11800e23 | −2.41168 | ||||||||
\(587\) | −7.53472e22 | −0.220619 | −0.110310 | − | 0.993897i | \(-0.535184\pi\) | ||||
−0.110310 | + | 0.993897i | \(0.535184\pi\) | |||||||
\(588\) | 2.12848e21 | 0.00614274 | ||||||||
\(589\) | −2.23665e22 | −0.0636235 | ||||||||
\(590\) | 9.48003e23 | 2.65808 | ||||||||
\(591\) | 2.56999e22 | 0.0710293 | ||||||||
\(592\) | −1.12841e23 | −0.307420 | ||||||||
\(593\) | 5.01094e23 | 1.34572 | 0.672860 | − | 0.739770i | \(-0.265066\pi\) | ||||
0.672860 | + | 0.739770i | \(0.265066\pi\) | |||||||
\(594\) | −1.19579e23 | −0.316570 | ||||||||
\(595\) | 1.22352e23 | 0.319314 | ||||||||
\(596\) | −2.37642e23 | −0.611408 | ||||||||
\(597\) | −1.01696e22 | −0.0257941 | ||||||||
\(598\) | 9.92160e22 | 0.248097 | ||||||||
\(599\) | 6.18716e23 | 1.52533 | 0.762664 | − | 0.646795i | \(-0.223891\pi\) | ||||
0.762664 | + | 0.646795i | \(0.223891\pi\) | |||||||
\(600\) | −2.60019e22 | −0.0632004 | ||||||||
\(601\) | −5.02644e23 | −1.20456 | −0.602278 | − | 0.798286i | \(-0.705740\pi\) | ||||
−0.602278 | + | 0.798286i | \(0.705740\pi\) | |||||||
\(602\) | 1.70762e23 | 0.403480 | ||||||||
\(603\) | 2.84944e23 | 0.663838 | ||||||||
\(604\) | 6.67434e22 | 0.153318 | ||||||||
\(605\) | −1.95493e24 | −4.42802 | ||||||||
\(606\) | 6.59587e21 | 0.0147318 | ||||||||
\(607\) | 4.38165e23 | 0.965014 | 0.482507 | − | 0.875892i | \(-0.339726\pi\) | ||||
0.482507 | + | 0.875892i | \(0.339726\pi\) | |||||||
\(608\) | 7.81214e23 | 1.69664 | ||||||||
\(609\) | −1.02129e22 | −0.0218726 | ||||||||
\(610\) | −6.38621e23 | −1.34878 | ||||||||
\(611\) | −2.92786e22 | −0.0609818 | ||||||||
\(612\) | −1.50608e23 | −0.309358 | ||||||||
\(613\) | 4.18811e23 | 0.848406 | 0.424203 | − | 0.905567i | \(-0.360554\pi\) | ||||
0.424203 | + | 0.905567i | \(0.360554\pi\) | |||||||
\(614\) | −2.91592e23 | −0.582565 | ||||||||
\(615\) | 7.86786e22 | 0.155031 | ||||||||
\(616\) | 1.62872e23 | 0.316526 | ||||||||
\(617\) | 3.18614e23 | 0.610718 | 0.305359 | − | 0.952237i | \(-0.401224\pi\) | ||||
0.305359 | + | 0.952237i | \(0.401224\pi\) | |||||||
\(618\) | 1.54654e22 | 0.0292388 | ||||||||
\(619\) | 8.77483e23 | 1.63632 | 0.818160 | − | 0.574991i | \(-0.194994\pi\) | ||||
0.818160 | + | 0.574991i | \(0.194994\pi\) | |||||||
\(620\) | −2.65807e22 | −0.0488918 | ||||||||
\(621\) | 3.82655e22 | 0.0694270 | ||||||||
\(622\) | −9.64636e23 | −1.72642 | ||||||||
\(623\) | 3.18106e23 | 0.561595 | ||||||||
\(624\) | 1.70228e22 | 0.0296457 | ||||||||
\(625\) | 8.36805e23 | 1.43762 | ||||||||
\(626\) | 1.34443e24 | 2.27853 | ||||||||
\(627\) | −1.10922e23 | −0.185457 | ||||||||
\(628\) | 5.27774e23 | 0.870544 | ||||||||
\(629\) | 7.34111e22 | 0.119462 | ||||||||
\(630\) | −5.33743e23 | −0.856914 | ||||||||
\(631\) | 7.40986e23 | 1.17371 | 0.586854 | − | 0.809693i | \(-0.300366\pi\) | ||||
0.586854 | + | 0.809693i | \(0.300366\pi\) | |||||||
\(632\) | −1.45722e23 | −0.227735 | ||||||||
\(633\) | −2.10169e22 | −0.0324069 | ||||||||
\(634\) | −1.62186e24 | −2.46749 | ||||||||
\(635\) | 3.90357e23 | 0.585984 | ||||||||
\(636\) | −1.68800e22 | −0.0250026 | ||||||||
\(637\) | −3.57894e22 | −0.0523081 | ||||||||
\(638\) | 1.46189e24 | 2.10833 | ||||||||
\(639\) | −4.18501e23 | −0.595578 | ||||||||
\(640\) | −1.06115e24 | −1.49021 | ||||||||
\(641\) | −2.59277e23 | −0.359311 | −0.179656 | − | 0.983730i | \(-0.557498\pi\) | ||||
−0.179656 | + | 0.983730i | \(0.557498\pi\) | |||||||
\(642\) | −4.96473e22 | −0.0678966 | ||||||||
\(643\) | −8.69513e23 | −1.17350 | −0.586749 | − | 0.809769i | \(-0.699593\pi\) | ||||
−0.586749 | + | 0.809769i | \(0.699593\pi\) | |||||||
\(644\) | 9.74964e22 | 0.129855 | ||||||||
\(645\) | 7.38825e22 | 0.0971145 | ||||||||
\(646\) | −7.09733e23 | −0.920701 | ||||||||
\(647\) | −6.37263e23 | −0.815891 | −0.407946 | − | 0.913006i | \(-0.633755\pi\) | ||||
−0.407946 | + | 0.913006i | \(0.633755\pi\) | |||||||
\(648\) | −3.49676e23 | −0.441853 | ||||||||
\(649\) | −1.75084e24 | −2.18356 | ||||||||
\(650\) | −8.17862e23 | −1.00674 | ||||||||
\(651\) | −8.69241e20 | −0.00105609 | ||||||||
\(652\) | −3.19819e23 | −0.383530 | ||||||||
\(653\) | −1.08875e23 | −0.128874 | −0.0644372 | − | 0.997922i | \(-0.520525\pi\) | ||||
−0.0644372 | + | 0.997922i | \(0.520525\pi\) | |||||||
\(654\) | 5.50866e22 | 0.0643628 | ||||||||
\(655\) | 1.04277e24 | 1.20264 | ||||||||
\(656\) | 1.42914e24 | 1.62702 | ||||||||
\(657\) | 1.03289e24 | 1.16078 | ||||||||
\(658\) | −7.29228e22 | −0.0808990 | ||||||||
\(659\) | −7.22617e23 | −0.791374 | −0.395687 | − | 0.918385i | \(-0.629494\pi\) | ||||
−0.395687 | + | 0.918385i | \(0.629494\pi\) | |||||||
\(660\) | −1.31821e23 | −0.142516 | ||||||||
\(661\) | −8.97949e22 | −0.0958383 | −0.0479192 | − | 0.998851i | \(-0.515259\pi\) | ||||
−0.0479192 | + | 0.998851i | \(0.515259\pi\) | |||||||
\(662\) | 4.61929e23 | 0.486724 | ||||||||
\(663\) | −1.10745e22 | −0.0115202 | ||||||||
\(664\) | 2.62360e23 | 0.269444 | ||||||||
\(665\) | −9.92371e23 | −1.00621 | ||||||||
\(666\) | −3.20244e23 | −0.320590 | ||||||||
\(667\) | −4.67807e23 | −0.462378 | ||||||||
\(668\) | 8.63349e23 | 0.842532 | ||||||||
\(669\) | 6.31347e22 | 0.0608339 | ||||||||
\(670\) | 1.59579e24 | 1.51823 | ||||||||
\(671\) | 1.17945e24 | 1.10799 | ||||||||
\(672\) | 3.03608e22 | 0.0281627 | ||||||||
\(673\) | −4.69165e23 | −0.429732 | −0.214866 | − | 0.976644i | \(-0.568931\pi\) | ||||
−0.214866 | + | 0.976644i | \(0.568931\pi\) | |||||||
\(674\) | −7.33467e23 | −0.663394 | ||||||||
\(675\) | −3.15432e23 | −0.281724 | ||||||||
\(676\) | −6.39795e23 | −0.564279 | ||||||||
\(677\) | 8.56181e23 | 0.745696 | 0.372848 | − | 0.927892i | \(-0.378381\pi\) | ||||
0.372848 | + | 0.927892i | \(0.378381\pi\) | |||||||
\(678\) | 8.13424e22 | 0.0699624 | ||||||||
\(679\) | −1.68854e23 | −0.143423 | ||||||||
\(680\) | 4.50893e23 | 0.378222 | ||||||||
\(681\) | 1.23099e23 | 0.101977 | ||||||||
\(682\) | 1.24425e23 | 0.101798 | ||||||||
\(683\) | −5.24073e23 | −0.423464 | −0.211732 | − | 0.977328i | \(-0.567910\pi\) | ||||
−0.211732 | + | 0.977328i | \(0.567910\pi\) | |||||||
\(684\) | 1.22154e24 | 0.974837 | ||||||||
\(685\) | 3.17143e24 | 2.49968 | ||||||||
\(686\) | −8.91387e22 | −0.0693923 | ||||||||
\(687\) | −7.75042e22 | −0.0595927 | ||||||||
\(688\) | 1.34202e24 | 1.01920 | ||||||||
\(689\) | 2.83828e23 | 0.212908 | ||||||||
\(690\) | 1.06916e23 | 0.0792185 | ||||||||
\(691\) | 5.63344e23 | 0.412297 | 0.206149 | − | 0.978521i | \(-0.433907\pi\) | ||||
0.206149 | + | 0.978521i | \(0.433907\pi\) | |||||||
\(692\) | 1.26689e24 | 0.915880 | ||||||||
\(693\) | 9.85752e23 | 0.703939 | ||||||||
\(694\) | −1.98321e24 | −1.39898 | ||||||||
\(695\) | −2.81480e24 | −1.96145 | ||||||||
\(696\) | −3.76364e22 | −0.0259078 | ||||||||
\(697\) | −9.29756e23 | −0.632252 | ||||||||
\(698\) | −1.74701e24 | −1.17361 | ||||||||
\(699\) | −1.19727e23 | −0.0794580 | ||||||||
\(700\) | −8.03687e23 | −0.526931 | ||||||||
\(701\) | 7.87779e23 | 0.510272 | 0.255136 | − | 0.966905i | \(-0.417880\pi\) | ||||
0.255136 | + | 0.966905i | \(0.417880\pi\) | |||||||
\(702\) | 9.68330e22 | 0.0619666 | ||||||||
\(703\) | −5.95419e23 | −0.376446 | ||||||||
\(704\) | −6.71442e23 | −0.419412 | ||||||||
\(705\) | −3.15510e22 | −0.0194718 | ||||||||
\(706\) | 1.48378e23 | 0.0904753 | ||||||||
\(707\) | −1.08984e23 | −0.0656596 | ||||||||
\(708\) | −8.43198e22 | −0.0501934 | ||||||||
\(709\) | −1.71248e24 | −1.00724 | −0.503619 | − | 0.863926i | \(-0.667998\pi\) | ||||
−0.503619 | + | 0.863926i | \(0.667998\pi\) | |||||||
\(710\) | −2.34375e24 | −1.36212 | ||||||||
\(711\) | −8.81956e23 | −0.506472 | ||||||||
\(712\) | 1.17228e24 | 0.665199 | ||||||||
\(713\) | −3.98161e22 | −0.0223253 | ||||||||
\(714\) | −2.75828e22 | −0.0152828 | ||||||||
\(715\) | 2.21651e24 | 1.21358 | ||||||||
\(716\) | −8.94462e23 | −0.483951 | ||||||||
\(717\) | 8.75756e22 | 0.0468242 | ||||||||
\(718\) | 2.26517e24 | 1.19686 | ||||||||
\(719\) | −2.27774e24 | −1.18935 | −0.594674 | − | 0.803967i | \(-0.702719\pi\) | ||||
−0.594674 | + | 0.803967i | \(0.702719\pi\) | |||||||
\(720\) | −4.19469e24 | −2.16458 | ||||||||
\(721\) | −2.55536e23 | −0.130317 | ||||||||
\(722\) | 3.20656e24 | 1.61612 | ||||||||
\(723\) | 1.10769e23 | 0.0551752 | ||||||||
\(724\) | −3.70325e23 | −0.182308 | ||||||||
\(725\) | 3.85625e24 | 1.87626 | ||||||||
\(726\) | 4.40712e23 | 0.211931 | ||||||||
\(727\) | 1.30389e24 | 0.619724 | 0.309862 | − | 0.950782i | \(-0.399717\pi\) | ||||
0.309862 | + | 0.950782i | \(0.399717\pi\) | |||||||
\(728\) | −1.31891e23 | −0.0619581 | ||||||||
\(729\) | −2.09763e24 | −0.973970 | ||||||||
\(730\) | 5.78457e24 | 2.65477 | ||||||||
\(731\) | −8.73080e23 | −0.396056 | ||||||||
\(732\) | 5.68019e22 | 0.0254694 | ||||||||
\(733\) | −1.60454e24 | −0.711158 | −0.355579 | − | 0.934646i | \(-0.615716\pi\) | ||||
−0.355579 | + | 0.934646i | \(0.615716\pi\) | |||||||
\(734\) | −4.17514e24 | −1.82917 | ||||||||
\(735\) | −3.85670e22 | −0.0167022 | ||||||||
\(736\) | 1.39069e24 | 0.595347 | ||||||||
\(737\) | −2.94720e24 | −1.24720 | ||||||||
\(738\) | 4.05591e24 | 1.69672 | ||||||||
\(739\) | −2.93894e24 | −1.21538 | −0.607691 | − | 0.794173i | \(-0.707904\pi\) | ||||
−0.607691 | + | 0.794173i | \(0.707904\pi\) | |||||||
\(740\) | −7.07605e23 | −0.289282 | ||||||||
\(741\) | 8.98228e22 | 0.0363021 | ||||||||
\(742\) | 7.06917e23 | 0.282446 | ||||||||
\(743\) | −3.72586e24 | −1.47171 | −0.735854 | − | 0.677141i | \(-0.763219\pi\) | ||||
−0.735854 | + | 0.677141i | \(0.763219\pi\) | |||||||
\(744\) | −3.20332e21 | −0.00125092 | ||||||||
\(745\) | 4.30597e24 | 1.66243 | ||||||||
\(746\) | −1.67942e24 | −0.641032 | ||||||||
\(747\) | 1.58789e24 | 0.599231 | ||||||||
\(748\) | 1.55775e24 | 0.581213 | ||||||||
\(749\) | 8.20327e23 | 0.302616 | ||||||||
\(750\) | −4.69381e23 | −0.171201 | ||||||||
\(751\) | 2.38800e24 | 0.861183 | 0.430591 | − | 0.902547i | \(-0.358305\pi\) | ||||
0.430591 | + | 0.902547i | \(0.358305\pi\) | |||||||
\(752\) | −5.73101e23 | −0.204352 | ||||||||
\(753\) | −1.16609e23 | −0.0411125 | ||||||||
\(754\) | −1.18381e24 | −0.412693 | ||||||||
\(755\) | −1.20936e24 | −0.416875 | ||||||||
\(756\) | 9.51547e22 | 0.0324336 | ||||||||
\(757\) | 3.27592e24 | 1.10413 | 0.552063 | − | 0.833802i | \(-0.313841\pi\) | ||||
0.552063 | + | 0.833802i | \(0.313841\pi\) | |||||||
\(758\) | 3.62461e24 | 1.20802 | ||||||||
\(759\) | −1.97460e23 | −0.0650765 | ||||||||
\(760\) | −3.65708e24 | −1.19184 | ||||||||
\(761\) | 6.93571e22 | 0.0223523 | 0.0111761 | − | 0.999938i | \(-0.496442\pi\) | ||||
0.0111761 | + | 0.999938i | \(0.496442\pi\) | |||||||
\(762\) | −8.80009e22 | −0.0280459 | ||||||||
\(763\) | −9.10201e23 | −0.286866 | ||||||||
\(764\) | 8.54954e22 | 0.0266471 | ||||||||
\(765\) | 2.72894e24 | 0.841148 | ||||||||
\(766\) | −4.76153e24 | −1.45145 | ||||||||
\(767\) | 1.41780e24 | 0.427418 | ||||||||
\(768\) | 2.88846e23 | 0.0861184 | ||||||||
\(769\) | −3.58174e24 | −1.05614 | −0.528068 | − | 0.849202i | \(-0.677083\pi\) | ||||
−0.528068 | + | 0.849202i | \(0.677083\pi\) | |||||||
\(770\) | 5.52056e24 | 1.60995 | ||||||||
\(771\) | −2.41443e23 | −0.0696389 | ||||||||
\(772\) | −1.48306e24 | −0.423068 | ||||||||
\(773\) | 3.28514e23 | 0.0926889 | 0.0463445 | − | 0.998926i | \(-0.485243\pi\) | ||||
0.0463445 | + | 0.998926i | \(0.485243\pi\) | |||||||
\(774\) | 3.80867e24 | 1.06286 | ||||||||
\(775\) | 3.28214e23 | 0.0905927 | ||||||||
\(776\) | −6.22260e23 | −0.169882 | ||||||||
\(777\) | −2.31401e22 | −0.00624866 | ||||||||
\(778\) | −3.36321e24 | −0.898312 | ||||||||
\(779\) | 7.54102e24 | 1.99233 | ||||||||
\(780\) | 1.06747e23 | 0.0278965 | ||||||||
\(781\) | 4.32859e24 | 1.11896 | ||||||||
\(782\) | −1.26344e24 | −0.323072 | ||||||||
\(783\) | −4.56571e23 | −0.115487 | ||||||||
\(784\) | −7.00542e23 | −0.175286 | ||||||||
\(785\) | −9.56301e24 | −2.36702 | ||||||||
\(786\) | −2.35078e23 | −0.0575599 | ||||||||
\(787\) | −3.43665e24 | −0.832436 | −0.416218 | − | 0.909265i | \(-0.636645\pi\) | ||||
−0.416218 | + | 0.909265i | \(0.636645\pi\) | |||||||
\(788\) | 2.92734e24 | 0.701455 | ||||||||
\(789\) | −4.80624e23 | −0.113933 | ||||||||
\(790\) | −4.93926e24 | −1.15833 | ||||||||
\(791\) | −1.34403e24 | −0.311823 | ||||||||
\(792\) | 3.63269e24 | 0.833804 | ||||||||
\(793\) | −9.55097e23 | −0.216883 | ||||||||
\(794\) | 6.05658e23 | 0.136067 | ||||||||
\(795\) | 3.05857e23 | 0.0679826 | ||||||||
\(796\) | −1.15836e24 | −0.254732 | ||||||||
\(797\) | 6.38674e24 | 1.38958 | 0.694790 | − | 0.719212i | \(-0.255497\pi\) | ||||
0.694790 | + | 0.719212i | \(0.255497\pi\) | |||||||
\(798\) | 2.23717e23 | 0.0481586 | ||||||||
\(799\) | 3.72843e23 | 0.0794105 | ||||||||
\(800\) | −1.14638e25 | −2.41582 | ||||||||
\(801\) | 7.09502e24 | 1.47937 | ||||||||
\(802\) | −6.40429e24 | −1.32126 | ||||||||
\(803\) | −1.06833e25 | −2.18085 | ||||||||
\(804\) | −1.41937e23 | −0.0286693 | ||||||||
\(805\) | −1.76659e24 | −0.353078 | ||||||||
\(806\) | −1.00757e23 | −0.0199263 | ||||||||
\(807\) | 5.51257e23 | 0.107877 | ||||||||
\(808\) | −4.01628e23 | −0.0777727 | ||||||||
\(809\) | 4.24605e24 | 0.813622 | 0.406811 | − | 0.913512i | \(-0.366641\pi\) | ||||
0.406811 | + | 0.913512i | \(0.366641\pi\) | |||||||
\(810\) | −1.18523e25 | −2.24740 | ||||||||
\(811\) | 2.80844e24 | 0.526972 | 0.263486 | − | 0.964663i | \(-0.415128\pi\) | ||||
0.263486 | + | 0.964663i | \(0.415128\pi\) | |||||||
\(812\) | −1.16329e24 | −0.216005 | ||||||||
\(813\) | −1.15160e23 | −0.0211608 | ||||||||
\(814\) | 3.31232e24 | 0.602316 | ||||||||
\(815\) | 5.79496e24 | 1.04282 | ||||||||
\(816\) | −2.16773e23 | −0.0386046 | ||||||||
\(817\) | 7.08134e24 | 1.24804 | ||||||||
\(818\) | 5.29771e24 | 0.924028 | ||||||||
\(819\) | −7.98245e23 | −0.137792 | ||||||||
\(820\) | 8.96186e24 | 1.53102 | ||||||||
\(821\) | −2.46315e24 | −0.416461 | −0.208230 | − | 0.978080i | \(-0.566770\pi\) | ||||
−0.208230 | + | 0.978080i | \(0.566770\pi\) | |||||||
\(822\) | −7.14957e23 | −0.119638 | ||||||||
\(823\) | 1.97971e24 | 0.327871 | 0.163936 | − | 0.986471i | \(-0.447581\pi\) | ||||
0.163936 | + | 0.986471i | \(0.447581\pi\) | |||||||
\(824\) | −9.41700e23 | −0.154359 | ||||||||
\(825\) | 1.62771e24 | 0.264070 | ||||||||
\(826\) | 3.53123e24 | 0.567016 | ||||||||
\(827\) | 5.87046e23 | 0.0932986 | 0.0466493 | − | 0.998911i | \(-0.485146\pi\) | ||||
0.0466493 | + | 0.998911i | \(0.485146\pi\) | |||||||
\(828\) | 2.17455e24 | 0.342068 | ||||||||
\(829\) | 3.47007e24 | 0.540287 | 0.270144 | − | 0.962820i | \(-0.412929\pi\) | ||||
0.270144 | + | 0.962820i | \(0.412929\pi\) | |||||||
\(830\) | 8.89272e24 | 1.37047 | ||||||||
\(831\) | 1.82726e23 | 0.0278736 | ||||||||
\(832\) | 5.43722e23 | 0.0820972 | ||||||||
\(833\) | 4.55752e23 | 0.0681156 | ||||||||
\(834\) | 6.34561e23 | 0.0938776 | ||||||||
\(835\) | −1.56435e25 | −2.29086 | ||||||||
\(836\) | −1.26346e25 | −1.83150 | ||||||||
\(837\) | −3.88598e22 | −0.00557615 | ||||||||
\(838\) | 8.56757e24 | 1.21698 | ||||||||
\(839\) | 1.07122e25 | 1.50626 | 0.753131 | − | 0.657871i | \(-0.228543\pi\) | ||||
0.753131 | + | 0.657871i | \(0.228543\pi\) | |||||||
\(840\) | −1.42127e23 | −0.0197835 | ||||||||
\(841\) | −1.67542e24 | −0.230865 | ||||||||
\(842\) | 7.62319e24 | 1.03988 | ||||||||
\(843\) | −3.55893e23 | −0.0480602 | ||||||||
\(844\) | −2.39392e24 | −0.320037 | ||||||||
\(845\) | 1.15928e25 | 1.53428 | ||||||||
\(846\) | −1.62647e24 | −0.213107 | ||||||||
\(847\) | −7.28193e24 | −0.944577 | ||||||||
\(848\) | 5.55567e24 | 0.713463 | ||||||||
\(849\) | 3.77786e23 | 0.0480319 | ||||||||
\(850\) | 1.04149e25 | 1.31097 | ||||||||
\(851\) | −1.05995e24 | −0.132094 | ||||||||
\(852\) | 2.08464e23 | 0.0257214 | ||||||||
\(853\) | −1.40685e25 | −1.71863 | −0.859313 | − | 0.511450i | \(-0.829109\pi\) | ||||
−0.859313 | + | 0.511450i | \(0.829109\pi\) | |||||||
\(854\) | −2.37881e24 | −0.287718 | ||||||||
\(855\) | −2.21338e25 | −2.65060 | ||||||||
\(856\) | 3.02307e24 | 0.358443 | ||||||||
\(857\) | −4.51107e24 | −0.529593 | −0.264797 | − | 0.964304i | \(-0.585305\pi\) | ||||
−0.264797 | + | 0.964304i | \(0.585305\pi\) | |||||||
\(858\) | −4.99684e23 | −0.0580836 | ||||||||
\(859\) | 1.65234e24 | 0.190177 | 0.0950887 | − | 0.995469i | \(-0.469687\pi\) | ||||
0.0950887 | + | 0.995469i | \(0.469687\pi\) | |||||||
\(860\) | 8.41557e24 | 0.959062 | ||||||||
\(861\) | 2.93071e23 | 0.0330709 | ||||||||
\(862\) | −1.90368e25 | −2.12708 | ||||||||
\(863\) | 4.01430e24 | 0.444138 | 0.222069 | − | 0.975031i | \(-0.428719\pi\) | ||||
0.222069 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(864\) | 1.35729e24 | 0.148698 | ||||||||
\(865\) | −2.29555e25 | −2.49029 | ||||||||
\(866\) | −7.57692e24 | −0.813936 | ||||||||
\(867\) | −4.79287e23 | −0.0509840 | ||||||||
\(868\) | −9.90107e22 | −0.0104295 | ||||||||
\(869\) | 9.12216e24 | 0.951546 | ||||||||
\(870\) | −1.27569e24 | −0.131775 | ||||||||
\(871\) | 2.38660e24 | 0.244132 | ||||||||
\(872\) | −3.35427e24 | −0.339788 | ||||||||
\(873\) | −3.76611e24 | −0.377809 | ||||||||
\(874\) | 1.02475e25 | 1.01805 | ||||||||
\(875\) | 7.75563e24 | 0.763043 | ||||||||
\(876\) | −5.14507e23 | −0.0501310 | ||||||||
\(877\) | −1.74406e25 | −1.68293 | −0.841464 | − | 0.540313i | \(-0.818306\pi\) | ||||
−0.841464 | + | 0.540313i | \(0.818306\pi\) | |||||||
\(878\) | −2.46424e25 | −2.35494 | ||||||||
\(879\) | −1.30832e24 | −0.123825 | ||||||||
\(880\) | 4.33861e25 | 4.06676 | ||||||||
\(881\) | −1.07521e25 | −0.998155 | −0.499078 | − | 0.866557i | \(-0.666328\pi\) | ||||
−0.499078 | + | 0.866557i | \(0.666328\pi\) | |||||||
\(882\) | −1.98815e24 | −0.182795 | ||||||||
\(883\) | 1.57828e25 | 1.43720 | 0.718600 | − | 0.695423i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695423i | \(0.244783\pi\) | |||||||
\(884\) | −1.26144e24 | −0.113769 | ||||||||
\(885\) | 1.52783e24 | 0.136477 | ||||||||
\(886\) | 6.62569e23 | 0.0586198 | ||||||||
\(887\) | −1.00351e25 | −0.879365 | −0.439683 | − | 0.898153i | \(-0.644909\pi\) | ||||
−0.439683 | + | 0.898153i | \(0.644909\pi\) | |||||||
\(888\) | −8.52758e22 | −0.00740143 | ||||||||
\(889\) | 1.45405e24 | 0.125001 | ||||||||
\(890\) | 3.97346e25 | 3.38340 | ||||||||
\(891\) | 2.18896e25 | 1.84619 | ||||||||
\(892\) | 7.19134e24 | 0.600770 | ||||||||
\(893\) | −3.02404e24 | −0.250236 | ||||||||
\(894\) | −9.70724e23 | −0.0795659 | ||||||||
\(895\) | 1.62072e25 | 1.31587 | ||||||||
\(896\) | −3.95271e24 | −0.317890 | ||||||||
\(897\) | 1.59900e23 | 0.0127383 | ||||||||
\(898\) | −2.09143e25 | −1.65042 | ||||||||
\(899\) | 4.75073e23 | 0.0371367 | ||||||||
\(900\) | −1.79254e25 | −1.38806 | ||||||||
\(901\) | −3.61435e24 | −0.277249 | ||||||||
\(902\) | −4.19507e25 | −3.18774 | ||||||||
\(903\) | 2.75206e23 | 0.0207163 | ||||||||
\(904\) | −4.95301e24 | −0.369349 | ||||||||
\(905\) | 6.71011e24 | 0.495697 | ||||||||
\(906\) | 2.72634e23 | 0.0199522 | ||||||||
\(907\) | 9.12638e24 | 0.661663 | 0.330831 | − | 0.943690i | \(-0.392671\pi\) | ||||
0.330831 | + | 0.943690i | \(0.392671\pi\) | |||||||
\(908\) | 1.40216e25 | 1.00709 | ||||||||
\(909\) | −2.43078e24 | −0.172963 | ||||||||
\(910\) | −4.47045e24 | −0.315137 | ||||||||
\(911\) | 2.27252e25 | 1.58709 | 0.793544 | − | 0.608513i | \(-0.208234\pi\) | ||||
0.793544 | + | 0.608513i | \(0.208234\pi\) | |||||||
\(912\) | 1.75819e24 | 0.121650 | ||||||||
\(913\) | −1.64237e25 | −1.12582 | ||||||||
\(914\) | 2.92590e25 | 1.98709 | ||||||||
\(915\) | −1.02922e24 | −0.0692517 | ||||||||
\(916\) | −8.82809e24 | −0.588512 | ||||||||
\(917\) | 3.88421e24 | 0.256545 | ||||||||
\(918\) | −1.23310e24 | −0.0806929 | ||||||||
\(919\) | 8.98037e24 | 0.582254 | 0.291127 | − | 0.956684i | \(-0.405970\pi\) | ||||
0.291127 | + | 0.956684i | \(0.405970\pi\) | |||||||
\(920\) | −6.51022e24 | −0.418214 | ||||||||
\(921\) | −4.69939e23 | −0.0299113 | ||||||||
\(922\) | 8.44830e24 | 0.532791 | ||||||||
\(923\) | −3.50522e24 | −0.219029 | ||||||||
\(924\) | −4.91024e23 | −0.0304012 | ||||||||
\(925\) | 8.73741e24 | 0.536016 | ||||||||
\(926\) | −5.73677e24 | −0.348718 | ||||||||
\(927\) | −5.69947e24 | −0.343286 | ||||||||
\(928\) | −1.65933e25 | −0.990319 | ||||||||
\(929\) | 9.60504e24 | 0.568022 | 0.284011 | − | 0.958821i | \(-0.408335\pi\) | ||||
0.284011 | + | 0.958821i | \(0.408335\pi\) | |||||||
\(930\) | −1.08577e23 | −0.00636257 | ||||||||
\(931\) | −3.69649e24 | −0.214644 | ||||||||
\(932\) | −1.36375e25 | −0.784694 | ||||||||
\(933\) | −1.55464e24 | −0.0886412 | ||||||||
\(934\) | 2.57234e25 | 1.45338 | ||||||||
\(935\) | −2.82257e25 | −1.58033 | ||||||||
\(936\) | −2.94169e24 | −0.163212 | ||||||||
\(937\) | 5.46544e24 | 0.300496 | 0.150248 | − | 0.988648i | \(-0.451993\pi\) | ||||
0.150248 | + | 0.988648i | \(0.451993\pi\) | |||||||
\(938\) | 5.94417e24 | 0.323867 | ||||||||
\(939\) | 2.16672e24 | 0.116989 | ||||||||
\(940\) | −3.59381e24 | −0.192295 | ||||||||
\(941\) | 9.15810e24 | 0.485617 | 0.242808 | − | 0.970074i | \(-0.421931\pi\) | ||||
0.242808 | + | 0.970074i | \(0.421931\pi\) | |||||||
\(942\) | 2.15586e24 | 0.113289 | ||||||||
\(943\) | 1.34243e25 | 0.699104 | ||||||||
\(944\) | 2.77520e25 | 1.43229 | ||||||||
\(945\) | −1.72416e24 | −0.0881874 | ||||||||
\(946\) | −3.93935e25 | −1.99687 | ||||||||
\(947\) | 6.69133e24 | 0.336154 | 0.168077 | − | 0.985774i | \(-0.446244\pi\) | ||||
0.168077 | + | 0.985774i | \(0.446244\pi\) | |||||||
\(948\) | 4.39321e23 | 0.0218731 | ||||||||
\(949\) | 8.65118e24 | 0.426887 | ||||||||
\(950\) | −8.44727e25 | −4.13110 | ||||||||
\(951\) | −2.61384e24 | −0.126691 | ||||||||
\(952\) | 1.67954e24 | 0.0806817 | ||||||||
\(953\) | −1.80291e25 | −0.858389 | −0.429194 | − | 0.903212i | \(-0.641202\pi\) | ||||
−0.429194 | + | 0.903212i | \(0.641202\pi\) | |||||||
\(954\) | 1.57670e25 | 0.744027 | ||||||||
\(955\) | −1.54914e24 | −0.0724538 | ||||||||
\(956\) | 9.97527e24 | 0.462416 | ||||||||
\(957\) | 2.35603e24 | 0.108250 | ||||||||
\(958\) | 2.83831e25 | 1.29257 | ||||||||
\(959\) | 1.18133e25 | 0.533228 | ||||||||
\(960\) | 5.85921e23 | 0.0262140 | ||||||||
\(961\) | −2.25097e25 | −0.998207 | ||||||||
\(962\) | −2.68226e24 | −0.117900 | ||||||||
\(963\) | 1.82965e25 | 0.797160 | ||||||||
\(964\) | 1.26171e25 | 0.544887 | ||||||||
\(965\) | 2.68722e25 | 1.15033 | ||||||||
\(966\) | 3.98254e23 | 0.0168987 | ||||||||
\(967\) | −4.09280e24 | −0.172145 | −0.0860726 | − | 0.996289i | \(-0.527432\pi\) | ||||
−0.0860726 | + | 0.996289i | \(0.527432\pi\) | |||||||
\(968\) | −2.68353e25 | −1.11884 | ||||||||
\(969\) | −1.14383e24 | −0.0472726 | ||||||||
\(970\) | −2.10916e25 | −0.864070 | ||||||||
\(971\) | 3.60792e25 | 1.46519 | 0.732595 | − | 0.680665i | \(-0.238309\pi\) | ||||
0.732595 | + | 0.680665i | \(0.238309\pi\) | |||||||
\(972\) | 3.18580e24 | 0.128250 | ||||||||
\(973\) | −1.04849e25 | −0.418413 | ||||||||
\(974\) | −3.46634e25 | −1.37126 | ||||||||
\(975\) | −1.31809e24 | −0.0516901 | ||||||||
\(976\) | −1.86951e25 | −0.726782 | ||||||||
\(977\) | 2.84870e25 | 1.09785 | 0.548925 | − | 0.835872i | \(-0.315037\pi\) | ||||
0.548925 | + | 0.835872i | \(0.315037\pi\) | |||||||
\(978\) | −1.30640e24 | −0.0499109 | ||||||||
\(979\) | −7.33845e25 | −2.77940 | ||||||||
\(980\) | −4.39297e24 | −0.164944 | ||||||||
\(981\) | −2.03011e25 | −0.755671 | ||||||||
\(982\) | 6.57733e25 | 2.42718 | ||||||||
\(983\) | −3.93479e25 | −1.43952 | −0.719758 | − | 0.694225i | \(-0.755747\pi\) | ||||
−0.719758 | + | 0.694225i | \(0.755747\pi\) | |||||||
\(984\) | 1.08002e24 | 0.0391719 | ||||||||
\(985\) | −5.30420e25 | −1.90727 | ||||||||
\(986\) | 1.50750e25 | 0.537408 | ||||||||
\(987\) | −1.17525e23 | −0.00415368 | ||||||||
\(988\) | 1.02312e25 | 0.358504 | ||||||||
\(989\) | 1.26060e25 | 0.437934 | ||||||||
\(990\) | 1.23130e26 | 4.24097 | ||||||||
\(991\) | 4.30174e25 | 1.46899 | 0.734494 | − | 0.678615i | \(-0.237420\pi\) | ||||
0.734494 | + | 0.678615i | \(0.237420\pi\) | |||||||
\(992\) | −1.41229e24 | −0.0478163 | ||||||||
\(993\) | 7.44461e23 | 0.0249904 | ||||||||
\(994\) | −8.73027e24 | −0.290565 | ||||||||
\(995\) | 2.09890e25 | 0.692620 | ||||||||
\(996\) | −7.90959e23 | −0.0258791 | ||||||||
\(997\) | 3.14767e25 | 1.02113 | 0.510565 | − | 0.859839i | \(-0.329436\pi\) | ||||
0.510565 | + | 0.859839i | \(0.329436\pi\) | |||||||
\(998\) | 4.60338e25 | 1.48070 | ||||||||
\(999\) | −1.03449e24 | −0.0329928 |
(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 | 7.18.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 63.18.a.b.1.1 | 4 | |||
4.3 | odd | 2 | 112.18.a.f.1.2 | 4 | |||
7.6 | odd | 2 | 49.18.a.c.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.18.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
49.18.a.c.1.4 | 4 | 7.6 | odd | 2 | |||
63.18.a.b.1.1 | 4 | 3.2 | odd | 2 | |||
112.18.a.f.1.2 | 4 | 4.3 | odd | 2 |