Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 273) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.273891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27389 | −0.900777 | −0.450388 | − | 0.892833i | \(-0.648714\pi\) | ||||
−0.450388 | + | 0.892833i | \(0.648714\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.377203 | −0.188601 | ||||||||
\(5\) | 1.10331 | 0.493416 | 0.246708 | − | 0.969090i | \(-0.420651\pi\) | ||||
0.246708 | + | 0.969090i | \(0.420651\pi\) | |||||||
\(6\) | 1.27389 | 0.520064 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 3.02830 | 1.07066 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.40550 | −0.444458 | ||||||||
\(11\) | −0.348907 | −0.105199 | −0.0525996 | − | 0.998616i | \(-0.516751\pi\) | ||||
−0.0525996 | + | 0.998616i | \(0.516751\pi\) | |||||||
\(12\) | 0.377203 | 0.108889 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.27389 | 0.340462 | ||||||||
\(15\) | −1.10331 | −0.284874 | ||||||||
\(16\) | −3.10331 | −0.775828 | ||||||||
\(17\) | 0.726109 | 0.176107 | 0.0880537 | − | 0.996116i | \(-0.471935\pi\) | ||||
0.0880537 | + | 0.996116i | \(0.471935\pi\) | |||||||
\(18\) | −1.27389 | −0.300259 | ||||||||
\(19\) | 2.30219 | 0.528158 | 0.264079 | − | 0.964501i | \(-0.414932\pi\) | ||||
0.264079 | + | 0.964501i | \(0.414932\pi\) | |||||||
\(20\) | −0.416173 | −0.0930590 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | 0.444469 | 0.0947611 | ||||||||
\(23\) | 0.0750160 | 0.0156419 | 0.00782096 | − | 0.999969i | \(-0.497510\pi\) | ||||
0.00782096 | + | 0.999969i | \(0.497510\pi\) | |||||||
\(24\) | −3.02830 | −0.618148 | ||||||||
\(25\) | −3.78270 | −0.756540 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.377203 | 0.0712846 | ||||||||
\(29\) | 0.480515 | 0.0892294 | 0.0446147 | − | 0.999004i | \(-0.485794\pi\) | ||||
0.0446147 | + | 0.999004i | \(0.485794\pi\) | |||||||
\(30\) | 1.40550 | 0.256608 | ||||||||
\(31\) | −6.85772 | −1.23168 | −0.615841 | − | 0.787870i | \(-0.711184\pi\) | ||||
−0.615841 | + | 0.787870i | \(0.711184\pi\) | |||||||
\(32\) | −2.10331 | −0.371817 | ||||||||
\(33\) | 0.348907 | 0.0607368 | ||||||||
\(34\) | −0.924984 | −0.158633 | ||||||||
\(35\) | −1.10331 | −0.186494 | ||||||||
\(36\) | −0.377203 | −0.0628671 | ||||||||
\(37\) | −1.10331 | −0.181383 | −0.0906917 | − | 0.995879i | \(-0.528908\pi\) | ||||
−0.0906917 | + | 0.995879i | \(0.528908\pi\) | |||||||
\(38\) | −2.93273 | −0.475752 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.34116 | 0.528283 | ||||||||
\(41\) | 3.09556 | 0.483446 | 0.241723 | − | 0.970345i | \(-0.422288\pi\) | ||||
0.241723 | + | 0.970345i | \(0.422288\pi\) | |||||||
\(42\) | −1.27389 | −0.196566 | ||||||||
\(43\) | −4.62280 | −0.704970 | −0.352485 | − | 0.935817i | \(-0.614663\pi\) | ||||
−0.352485 | + | 0.935817i | \(0.614663\pi\) | |||||||
\(44\) | 0.131609 | 0.0198407 | ||||||||
\(45\) | 1.10331 | 0.164472 | ||||||||
\(46\) | −0.0955622 | −0.0140899 | ||||||||
\(47\) | 4.70769 | 0.686687 | 0.343343 | − | 0.939210i | \(-0.388441\pi\) | ||||
0.343343 | + | 0.939210i | \(0.388441\pi\) | |||||||
\(48\) | 3.10331 | 0.447925 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 4.81875 | 0.681474 | ||||||||
\(51\) | −0.726109 | −0.101676 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.54778 | 0.762046 | 0.381023 | − | 0.924565i | \(-0.375572\pi\) | ||||
0.381023 | + | 0.924565i | \(0.375572\pi\) | |||||||
\(54\) | 1.27389 | 0.173355 | ||||||||
\(55\) | −0.384953 | −0.0519070 | ||||||||
\(56\) | −3.02830 | −0.404673 | ||||||||
\(57\) | −2.30219 | −0.304932 | ||||||||
\(58\) | −0.612124 | −0.0803758 | ||||||||
\(59\) | −3.92498 | −0.510989 | −0.255495 | − | 0.966810i | \(-0.582238\pi\) | ||||
−0.255495 | + | 0.966810i | \(0.582238\pi\) | |||||||
\(60\) | 0.416173 | 0.0537276 | ||||||||
\(61\) | 5.54778 | 0.710321 | 0.355160 | − | 0.934805i | \(-0.384426\pi\) | ||||
0.355160 | + | 0.934805i | \(0.384426\pi\) | |||||||
\(62\) | 8.73598 | 1.10947 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 8.88601 | 1.11075 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.444469 | −0.0547103 | ||||||||
\(67\) | 8.12386 | 0.992487 | 0.496244 | − | 0.868183i | \(-0.334712\pi\) | ||||
0.496244 | + | 0.868183i | \(0.334712\pi\) | |||||||
\(68\) | −0.273891 | −0.0332141 | ||||||||
\(69\) | −0.0750160 | −0.00903087 | ||||||||
\(70\) | 1.40550 | 0.167989 | ||||||||
\(71\) | −9.52936 | −1.13093 | −0.565463 | − | 0.824773i | \(-0.691303\pi\) | ||||
−0.565463 | + | 0.824773i | \(0.691303\pi\) | |||||||
\(72\) | 3.02830 | 0.356888 | ||||||||
\(73\) | −10.4338 | −1.22118 | −0.610592 | − | 0.791946i | \(-0.709068\pi\) | ||||
−0.610592 | + | 0.791946i | \(0.709068\pi\) | |||||||
\(74\) | 1.40550 | 0.163386 | ||||||||
\(75\) | 3.78270 | 0.436789 | ||||||||
\(76\) | −0.868391 | −0.0996113 | ||||||||
\(77\) | 0.348907 | 0.0397616 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.1054 | 1.92451 | 0.962256 | − | 0.272146i | \(-0.0877335\pi\) | ||||
0.962256 | + | 0.272146i | \(0.0877335\pi\) | |||||||
\(80\) | −3.42392 | −0.382806 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.94341 | −0.435477 | ||||||||
\(83\) | −11.9143 | −1.30777 | −0.653883 | − | 0.756596i | \(-0.726861\pi\) | ||||
−0.653883 | + | 0.756596i | \(0.726861\pi\) | |||||||
\(84\) | −0.377203 | −0.0411562 | ||||||||
\(85\) | 0.801125 | 0.0868943 | ||||||||
\(86\) | 5.88894 | 0.635020 | ||||||||
\(87\) | −0.480515 | −0.0515166 | ||||||||
\(88\) | −1.05659 | −0.112633 | ||||||||
\(89\) | −11.9610 | −1.26787 | −0.633933 | − | 0.773388i | \(-0.718561\pi\) | ||||
−0.633933 | + | 0.773388i | \(0.718561\pi\) | |||||||
\(90\) | −1.40550 | −0.148153 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.0282963 | −0.00295009 | ||||||||
\(93\) | 6.85772 | 0.711112 | ||||||||
\(94\) | −5.99708 | −0.618551 | ||||||||
\(95\) | 2.54003 | 0.260602 | ||||||||
\(96\) | 2.10331 | 0.214668 | ||||||||
\(97\) | 10.1033 | 1.02584 | 0.512918 | − | 0.858438i | \(-0.328564\pi\) | ||||
0.512918 | + | 0.858438i | \(0.328564\pi\) | |||||||
\(98\) | −1.27389 | −0.128682 | ||||||||
\(99\) | −0.348907 | −0.0350664 | ||||||||
\(100\) | 1.42685 | 0.142685 | ||||||||
\(101\) | 4.07502 | 0.405479 | 0.202740 | − | 0.979233i | \(-0.435015\pi\) | ||||
0.202740 | + | 0.979233i | \(0.435015\pi\) | |||||||
\(102\) | 0.924984 | 0.0915871 | ||||||||
\(103\) | −4.11106 | −0.405075 | −0.202538 | − | 0.979275i | \(-0.564919\pi\) | ||||
−0.202538 | + | 0.979275i | \(0.564919\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.10331 | 0.107672 | ||||||||
\(106\) | −7.06727 | −0.686434 | ||||||||
\(107\) | −6.17058 | −0.596532 | −0.298266 | − | 0.954483i | \(-0.596408\pi\) | ||||
−0.298266 | + | 0.954483i | \(0.596408\pi\) | |||||||
\(108\) | 0.377203 | 0.0362964 | ||||||||
\(109\) | −8.82167 | −0.844963 | −0.422481 | − | 0.906372i | \(-0.638841\pi\) | ||||
−0.422481 | + | 0.906372i | \(0.638841\pi\) | |||||||
\(110\) | 0.490388 | 0.0467567 | ||||||||
\(111\) | 1.10331 | 0.104722 | ||||||||
\(112\) | 3.10331 | 0.293235 | ||||||||
\(113\) | 12.0099 | 1.12979 | 0.564897 | − | 0.825161i | \(-0.308916\pi\) | ||||
0.564897 | + | 0.825161i | \(0.308916\pi\) | |||||||
\(114\) | 2.93273 | 0.274676 | ||||||||
\(115\) | 0.0827661 | 0.00771798 | ||||||||
\(116\) | −0.181252 | −0.0168288 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.00000 | 0.460287 | ||||||||
\(119\) | −0.726109 | −0.0665623 | ||||||||
\(120\) | −3.34116 | −0.305004 | ||||||||
\(121\) | −10.8783 | −0.988933 | ||||||||
\(122\) | −7.06727 | −0.639840 | ||||||||
\(123\) | −3.09556 | −0.279117 | ||||||||
\(124\) | 2.58675 | 0.232297 | ||||||||
\(125\) | −9.69006 | −0.866706 | ||||||||
\(126\) | 1.27389 | 0.113487 | ||||||||
\(127\) | −5.85772 | −0.519788 | −0.259894 | − | 0.965637i | \(-0.583688\pi\) | ||||
−0.259894 | + | 0.965637i | \(0.583688\pi\) | |||||||
\(128\) | −7.11319 | −0.628723 | ||||||||
\(129\) | 4.62280 | 0.407015 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.4055 | 1.95758 | 0.978789 | − | 0.204872i | \(-0.0656778\pi\) | ||||
0.978789 | + | 0.204872i | \(0.0656778\pi\) | |||||||
\(132\) | −0.131609 | −0.0114551 | ||||||||
\(133\) | −2.30219 | −0.199625 | ||||||||
\(134\) | −10.3489 | −0.894009 | ||||||||
\(135\) | −1.10331 | −0.0949580 | ||||||||
\(136\) | 2.19887 | 0.188552 | ||||||||
\(137\) | 20.2087 | 1.72655 | 0.863275 | − | 0.504734i | \(-0.168409\pi\) | ||||
0.863275 | + | 0.504734i | \(0.168409\pi\) | |||||||
\(138\) | 0.0955622 | 0.00813480 | ||||||||
\(139\) | 4.27389 | 0.362507 | 0.181253 | − | 0.983436i | \(-0.441985\pi\) | ||||
0.181253 | + | 0.983436i | \(0.441985\pi\) | |||||||
\(140\) | 0.416173 | 0.0351730 | ||||||||
\(141\) | −4.70769 | −0.396459 | ||||||||
\(142\) | 12.1394 | 1.01871 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −3.10331 | −0.258609 | ||||||||
\(145\) | 0.530158 | 0.0440272 | ||||||||
\(146\) | 13.2915 | 1.10001 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 0.416173 | 0.0342092 | ||||||||
\(149\) | −4.89669 | −0.401152 | −0.200576 | − | 0.979678i | \(-0.564281\pi\) | ||||
−0.200576 | + | 0.979678i | \(0.564281\pi\) | |||||||
\(150\) | −4.81875 | −0.393449 | ||||||||
\(151\) | −8.94553 | −0.727977 | −0.363988 | − | 0.931403i | \(-0.618585\pi\) | ||||
−0.363988 | + | 0.931403i | \(0.618585\pi\) | |||||||
\(152\) | 6.97170 | 0.565480 | ||||||||
\(153\) | 0.726109 | 0.0587025 | ||||||||
\(154\) | −0.444469 | −0.0358163 | ||||||||
\(155\) | −7.56620 | −0.607732 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.59450 | 0.526298 | 0.263149 | − | 0.964755i | \(-0.415239\pi\) | ||||
0.263149 | + | 0.964755i | \(0.415239\pi\) | |||||||
\(158\) | −21.7905 | −1.73356 | ||||||||
\(159\) | −5.54778 | −0.439968 | ||||||||
\(160\) | −2.32061 | −0.183460 | ||||||||
\(161\) | −0.0750160 | −0.00591209 | ||||||||
\(162\) | −1.27389 | −0.100086 | ||||||||
\(163\) | −9.90444 | −0.775775 | −0.387888 | − | 0.921707i | \(-0.626795\pi\) | ||||
−0.387888 | + | 0.921707i | \(0.626795\pi\) | |||||||
\(164\) | −1.16765 | −0.0911785 | ||||||||
\(165\) | 0.384953 | 0.0299685 | ||||||||
\(166\) | 15.1775 | 1.17800 | ||||||||
\(167\) | −16.7565 | −1.29666 | −0.648330 | − | 0.761360i | \(-0.724532\pi\) | ||||
−0.648330 | + | 0.761360i | \(0.724532\pi\) | |||||||
\(168\) | 3.02830 | 0.233638 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1.02055 | −0.0782723 | ||||||||
\(171\) | 2.30219 | 0.176053 | ||||||||
\(172\) | 1.74373 | 0.132958 | ||||||||
\(173\) | 13.7184 | 1.04299 | 0.521494 | − | 0.853255i | \(-0.325375\pi\) | ||||
0.521494 | + | 0.853255i | \(0.325375\pi\) | |||||||
\(174\) | 0.612124 | 0.0464050 | ||||||||
\(175\) | 3.78270 | 0.285945 | ||||||||
\(176\) | 1.08277 | 0.0816166 | ||||||||
\(177\) | 3.92498 | 0.295020 | ||||||||
\(178\) | 15.2370 | 1.14206 | ||||||||
\(179\) | −22.0304 | −1.64663 | −0.823315 | − | 0.567584i | \(-0.807878\pi\) | ||||
−0.823315 | + | 0.567584i | \(0.807878\pi\) | |||||||
\(180\) | −0.416173 | −0.0310197 | ||||||||
\(181\) | 9.43380 | 0.701208 | 0.350604 | − | 0.936524i | \(-0.385976\pi\) | ||||
0.350604 | + | 0.936524i | \(0.385976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.54778 | −0.410104 | ||||||||
\(184\) | 0.227171 | 0.0167473 | ||||||||
\(185\) | −1.21730 | −0.0894975 | ||||||||
\(186\) | −8.73598 | −0.640553 | ||||||||
\(187\) | −0.253344 | −0.0185264 | ||||||||
\(188\) | −1.77575 | −0.129510 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −3.23572 | −0.234744 | ||||||||
\(191\) | −3.37720 | −0.244366 | −0.122183 | − | 0.992508i | \(-0.538989\pi\) | ||||
−0.122183 | + | 0.992508i | \(0.538989\pi\) | |||||||
\(192\) | −8.88601 | −0.641293 | ||||||||
\(193\) | 22.3227 | 1.60683 | 0.803413 | − | 0.595423i | \(-0.203015\pi\) | ||||
0.803413 | + | 0.595423i | \(0.203015\pi\) | |||||||
\(194\) | −12.8705 | −0.924049 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.377203 | −0.0269431 | ||||||||
\(197\) | −25.4514 | −1.81334 | −0.906669 | − | 0.421842i | \(-0.861384\pi\) | ||||
−0.906669 | + | 0.421842i | \(0.861384\pi\) | |||||||
\(198\) | 0.444469 | 0.0315870 | ||||||||
\(199\) | −22.3404 | −1.58367 | −0.791833 | − | 0.610738i | \(-0.790873\pi\) | ||||
−0.791833 | + | 0.610738i | \(0.790873\pi\) | |||||||
\(200\) | −11.4551 | −0.810001 | ||||||||
\(201\) | −8.12386 | −0.573013 | ||||||||
\(202\) | −5.19112 | −0.365246 | ||||||||
\(203\) | −0.480515 | −0.0337256 | ||||||||
\(204\) | 0.273891 | 0.0191762 | ||||||||
\(205\) | 3.41537 | 0.238540 | ||||||||
\(206\) | 5.23704 | 0.364882 | ||||||||
\(207\) | 0.0750160 | 0.00521397 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.803248 | −0.0555618 | ||||||||
\(210\) | −1.40550 | −0.0969887 | ||||||||
\(211\) | 10.0382 | 0.691056 | 0.345528 | − | 0.938408i | \(-0.387700\pi\) | ||||
0.345528 | + | 0.938408i | \(0.387700\pi\) | |||||||
\(212\) | −2.09264 | −0.143723 | ||||||||
\(213\) | 9.52936 | 0.652941 | ||||||||
\(214\) | 7.86064 | 0.537342 | ||||||||
\(215\) | −5.10039 | −0.347844 | ||||||||
\(216\) | −3.02830 | −0.206049 | ||||||||
\(217\) | 6.85772 | 0.465532 | ||||||||
\(218\) | 11.2378 | 0.761123 | ||||||||
\(219\) | 10.4338 | 0.705051 | ||||||||
\(220\) | 0.145205 | 0.00978974 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −1.40550 | −0.0943309 | ||||||||
\(223\) | −5.13453 | −0.343834 | −0.171917 | − | 0.985111i | \(-0.554996\pi\) | ||||
−0.171917 | + | 0.985111i | \(0.554996\pi\) | |||||||
\(224\) | 2.10331 | 0.140533 | ||||||||
\(225\) | −3.78270 | −0.252180 | ||||||||
\(226\) | −15.2993 | −1.01769 | ||||||||
\(227\) | −28.9709 | −1.92287 | −0.961433 | − | 0.275039i | \(-0.911309\pi\) | ||||
−0.961433 | + | 0.275039i | \(0.911309\pi\) | |||||||
\(228\) | 0.868391 | 0.0575106 | ||||||||
\(229\) | 0.679390 | 0.0448953 | 0.0224477 | − | 0.999748i | \(-0.492854\pi\) | ||||
0.0224477 | + | 0.999748i | \(0.492854\pi\) | |||||||
\(230\) | −0.105435 | −0.00695218 | ||||||||
\(231\) | −0.348907 | −0.0229564 | ||||||||
\(232\) | 1.45514 | 0.0955348 | ||||||||
\(233\) | −18.3022 | −1.19902 | −0.599508 | − | 0.800369i | \(-0.704637\pi\) | ||||
−0.599508 | + | 0.800369i | \(0.704637\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.19405 | 0.338822 | ||||||||
\(236\) | 1.48052 | 0.0963733 | ||||||||
\(237\) | −17.1054 | −1.11112 | ||||||||
\(238\) | 0.924984 | 0.0599578 | ||||||||
\(239\) | −5.45222 | −0.352675 | −0.176337 | − | 0.984330i | \(-0.556425\pi\) | ||||
−0.176337 | + | 0.984330i | \(0.556425\pi\) | |||||||
\(240\) | 3.42392 | 0.221013 | ||||||||
\(241\) | −15.4621 | −0.996001 | −0.498000 | − | 0.867177i | \(-0.665932\pi\) | ||||
−0.498000 | + | 0.867177i | \(0.665932\pi\) | |||||||
\(242\) | 13.8577 | 0.890808 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −2.09264 | −0.133967 | ||||||||
\(245\) | 1.10331 | 0.0704880 | ||||||||
\(246\) | 3.94341 | 0.251422 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −20.7672 | −1.31872 | ||||||||
\(249\) | 11.9143 | 0.755039 | ||||||||
\(250\) | 12.3441 | 0.780708 | ||||||||
\(251\) | −8.29444 | −0.523540 | −0.261770 | − | 0.965130i | \(-0.584306\pi\) | ||||
−0.261770 | + | 0.965130i | \(0.584306\pi\) | |||||||
\(252\) | 0.377203 | 0.0237615 | ||||||||
\(253\) | −0.0261736 | −0.00164552 | ||||||||
\(254\) | 7.46209 | 0.468213 | ||||||||
\(255\) | −0.801125 | −0.0501684 | ||||||||
\(256\) | −8.71061 | −0.544413 | ||||||||
\(257\) | −15.0382 | −0.938055 | −0.469028 | − | 0.883184i | \(-0.655396\pi\) | ||||
−0.469028 | + | 0.883184i | \(0.655396\pi\) | |||||||
\(258\) | −5.88894 | −0.366629 | ||||||||
\(259\) | 1.10331 | 0.0685565 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.480515 | 0.0297431 | ||||||||
\(262\) | −28.5422 | −1.76334 | ||||||||
\(263\) | −17.2448 | −1.06336 | −0.531680 | − | 0.846945i | \(-0.678439\pi\) | ||||
−0.531680 | + | 0.846945i | \(0.678439\pi\) | |||||||
\(264\) | 1.05659 | 0.0650288 | ||||||||
\(265\) | 6.12094 | 0.376006 | ||||||||
\(266\) | 2.93273 | 0.179817 | ||||||||
\(267\) | 11.9610 | 0.732003 | ||||||||
\(268\) | −3.06434 | −0.187185 | ||||||||
\(269\) | −24.2944 | −1.48126 | −0.740629 | − | 0.671914i | \(-0.765472\pi\) | ||||
−0.740629 | + | 0.671914i | \(0.765472\pi\) | |||||||
\(270\) | 1.40550 | 0.0855360 | ||||||||
\(271\) | 18.3326 | 1.11363 | 0.556813 | − | 0.830638i | \(-0.312024\pi\) | ||||
0.556813 | + | 0.830638i | \(0.312024\pi\) | |||||||
\(272\) | −2.25334 | −0.136629 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −25.7437 | −1.55524 | ||||||||
\(275\) | 1.31981 | 0.0795875 | ||||||||
\(276\) | 0.0282963 | 0.00170323 | ||||||||
\(277\) | 8.45434 | 0.507972 | 0.253986 | − | 0.967208i | \(-0.418258\pi\) | ||||
0.253986 | + | 0.967208i | \(0.418258\pi\) | |||||||
\(278\) | −5.44447 | −0.326538 | ||||||||
\(279\) | −6.85772 | −0.410561 | ||||||||
\(280\) | −3.34116 | −0.199672 | ||||||||
\(281\) | −25.0120 | −1.49209 | −0.746045 | − | 0.665895i | \(-0.768050\pi\) | ||||
−0.746045 | + | 0.665895i | \(0.768050\pi\) | |||||||
\(282\) | 5.99708 | 0.357121 | ||||||||
\(283\) | 27.1415 | 1.61339 | 0.806697 | − | 0.590966i | \(-0.201253\pi\) | ||||
0.806697 | + | 0.590966i | \(0.201253\pi\) | |||||||
\(284\) | 3.59450 | 0.213294 | ||||||||
\(285\) | −2.54003 | −0.150458 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.09556 | −0.182725 | ||||||||
\(288\) | −2.10331 | −0.123939 | ||||||||
\(289\) | −16.4728 | −0.968986 | ||||||||
\(290\) | −0.675364 | −0.0396587 | ||||||||
\(291\) | −10.1033 | −0.592267 | ||||||||
\(292\) | 3.93566 | 0.230317 | ||||||||
\(293\) | −10.5400 | −0.615755 | −0.307878 | − | 0.951426i | \(-0.599619\pi\) | ||||
−0.307878 | + | 0.951426i | \(0.599619\pi\) | |||||||
\(294\) | 1.27389 | 0.0742948 | ||||||||
\(295\) | −4.33048 | −0.252130 | ||||||||
\(296\) | −3.34116 | −0.194201 | ||||||||
\(297\) | 0.348907 | 0.0202456 | ||||||||
\(298\) | 6.23784 | 0.361349 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.42685 | −0.0823790 | ||||||||
\(301\) | 4.62280 | 0.266454 | ||||||||
\(302\) | 11.3956 | 0.655745 | ||||||||
\(303\) | −4.07502 | −0.234104 | ||||||||
\(304\) | −7.14440 | −0.409760 | ||||||||
\(305\) | 6.12094 | 0.350484 | ||||||||
\(306\) | −0.924984 | −0.0528778 | ||||||||
\(307\) | −4.40842 | −0.251602 | −0.125801 | − | 0.992055i | \(-0.540150\pi\) | ||||
−0.125801 | + | 0.992055i | \(0.540150\pi\) | |||||||
\(308\) | −0.131609 | −0.00749909 | ||||||||
\(309\) | 4.11106 | 0.233870 | ||||||||
\(310\) | 9.63852 | 0.547431 | ||||||||
\(311\) | −2.32836 | −0.132029 | −0.0660146 | − | 0.997819i | \(-0.521028\pi\) | ||||
−0.0660146 | + | 0.997819i | \(0.521028\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6687 | 0.716078 | 0.358039 | − | 0.933707i | \(-0.383445\pi\) | ||||
0.358039 | + | 0.933707i | \(0.383445\pi\) | |||||||
\(314\) | −8.40067 | −0.474077 | ||||||||
\(315\) | −1.10331 | −0.0621646 | ||||||||
\(316\) | −6.45222 | −0.362966 | ||||||||
\(317\) | −12.2915 | −0.690360 | −0.345180 | − | 0.938536i | \(-0.612182\pi\) | ||||
−0.345180 | + | 0.938536i | \(0.612182\pi\) | |||||||
\(318\) | 7.06727 | 0.396313 | ||||||||
\(319\) | −0.167655 | −0.00938687 | ||||||||
\(320\) | 9.80405 | 0.548063 | ||||||||
\(321\) | 6.17058 | 0.344408 | ||||||||
\(322\) | 0.0955622 | 0.00532547 | ||||||||
\(323\) | 1.67164 | 0.0930125 | ||||||||
\(324\) | −0.377203 | −0.0209557 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.6172 | 0.698800 | ||||||||
\(327\) | 8.82167 | 0.487840 | ||||||||
\(328\) | 9.37428 | 0.517608 | ||||||||
\(329\) | −4.70769 | −0.259543 | ||||||||
\(330\) | −0.490388 | −0.0269950 | ||||||||
\(331\) | 13.2915 | 0.730568 | 0.365284 | − | 0.930896i | \(-0.380972\pi\) | ||||
0.365284 | + | 0.930896i | \(0.380972\pi\) | |||||||
\(332\) | 4.49411 | 0.246646 | ||||||||
\(333\) | −1.10331 | −0.0604611 | ||||||||
\(334\) | 21.3460 | 1.16800 | ||||||||
\(335\) | 8.96315 | 0.489709 | ||||||||
\(336\) | −3.10331 | −0.169300 | ||||||||
\(337\) | −3.40550 | −0.185509 | −0.0927547 | − | 0.995689i | \(-0.529567\pi\) | ||||
−0.0927547 | + | 0.995689i | \(0.529567\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.0099 | −0.652287 | ||||||||
\(340\) | −0.302187 | −0.0163884 | ||||||||
\(341\) | 2.39270 | 0.129572 | ||||||||
\(342\) | −2.93273 | −0.158584 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −13.9992 | −0.754786 | ||||||||
\(345\) | −0.0827661 | −0.00445598 | ||||||||
\(346\) | −17.4757 | −0.939499 | ||||||||
\(347\) | −33.4981 | −1.79827 | −0.899137 | − | 0.437667i | \(-0.855805\pi\) | ||||
−0.899137 | + | 0.437667i | \(0.855805\pi\) | |||||||
\(348\) | 0.181252 | 0.00971611 | ||||||||
\(349\) | −28.1805 | −1.50846 | −0.754232 | − | 0.656607i | \(-0.771991\pi\) | ||||
−0.754232 | + | 0.656607i | \(0.771991\pi\) | |||||||
\(350\) | −4.81875 | −0.257573 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.733860 | 0.0391148 | ||||||||
\(353\) | −2.99225 | −0.159261 | −0.0796307 | − | 0.996824i | \(-0.525374\pi\) | ||||
−0.0796307 | + | 0.996824i | \(0.525374\pi\) | |||||||
\(354\) | −5.00000 | −0.265747 | ||||||||
\(355\) | −10.5139 | −0.558018 | ||||||||
\(356\) | 4.51173 | 0.239121 | ||||||||
\(357\) | 0.726109 | 0.0384298 | ||||||||
\(358\) | 28.0643 | 1.48325 | ||||||||
\(359\) | 3.80888 | 0.201025 | 0.100512 | − | 0.994936i | \(-0.467952\pi\) | ||||
0.100512 | + | 0.994936i | \(0.467952\pi\) | |||||||
\(360\) | 3.34116 | 0.176094 | ||||||||
\(361\) | −13.6999 | −0.721049 | ||||||||
\(362\) | −12.0176 | −0.631632 | ||||||||
\(363\) | 10.8783 | 0.570961 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.5117 | −0.602552 | ||||||||
\(366\) | 7.06727 | 0.369412 | ||||||||
\(367\) | −26.4514 | −1.38075 | −0.690376 | − | 0.723450i | \(-0.742555\pi\) | ||||
−0.690376 | + | 0.723450i | \(0.742555\pi\) | |||||||
\(368\) | −0.232798 | −0.0121354 | ||||||||
\(369\) | 3.09556 | 0.161149 | ||||||||
\(370\) | 1.55070 | 0.0806173 | ||||||||
\(371\) | −5.54778 | −0.288026 | ||||||||
\(372\) | −2.58675 | −0.134117 | ||||||||
\(373\) | 2.13161 | 0.110371 | 0.0551853 | − | 0.998476i | \(-0.482425\pi\) | ||||
0.0551853 | + | 0.998476i | \(0.482425\pi\) | |||||||
\(374\) | 0.322733 | 0.0166881 | ||||||||
\(375\) | 9.69006 | 0.500393 | ||||||||
\(376\) | 14.2563 | 0.735211 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.27389 | −0.0655219 | ||||||||
\(379\) | −13.9434 | −0.716225 | −0.358112 | − | 0.933678i | \(-0.616580\pi\) | ||||
−0.358112 | + | 0.933678i | \(0.616580\pi\) | |||||||
\(380\) | −0.958107 | −0.0491498 | ||||||||
\(381\) | 5.85772 | 0.300100 | ||||||||
\(382\) | 4.30219 | 0.220119 | ||||||||
\(383\) | −18.6044 | −0.950639 | −0.475320 | − | 0.879813i | \(-0.657668\pi\) | ||||
−0.475320 | + | 0.879813i | \(0.657668\pi\) | |||||||
\(384\) | 7.11319 | 0.362993 | ||||||||
\(385\) | 0.384953 | 0.0196190 | ||||||||
\(386\) | −28.4367 | −1.44739 | ||||||||
\(387\) | −4.62280 | −0.234990 | ||||||||
\(388\) | −3.81100 | −0.193474 | ||||||||
\(389\) | −1.23009 | −0.0623682 | −0.0311841 | − | 0.999514i | \(-0.509928\pi\) | ||||
−0.0311841 | + | 0.999514i | \(0.509928\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0544699 | 0.00275466 | ||||||||
\(392\) | 3.02830 | 0.152952 | ||||||||
\(393\) | −22.4055 | −1.13021 | ||||||||
\(394\) | 32.4223 | 1.63341 | ||||||||
\(395\) | 18.8726 | 0.949585 | ||||||||
\(396\) | 0.131609 | 0.00661358 | ||||||||
\(397\) | 29.6142 | 1.48630 | 0.743148 | − | 0.669127i | \(-0.233332\pi\) | ||||
0.743148 | + | 0.669127i | \(0.233332\pi\) | |||||||
\(398\) | 28.4592 | 1.42653 | ||||||||
\(399\) | 2.30219 | 0.115253 | ||||||||
\(400\) | 11.7389 | 0.586945 | ||||||||
\(401\) | 8.18045 | 0.408512 | 0.204256 | − | 0.978917i | \(-0.434522\pi\) | ||||
0.204256 | + | 0.978917i | \(0.434522\pi\) | |||||||
\(402\) | 10.3489 | 0.516157 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.53711 | −0.0764740 | ||||||||
\(405\) | 1.10331 | 0.0548240 | ||||||||
\(406\) | 0.612124 | 0.0303792 | ||||||||
\(407\) | 0.384953 | 0.0190814 | ||||||||
\(408\) | −2.19887 | −0.108861 | ||||||||
\(409\) | 10.0673 | 0.497794 | 0.248897 | − | 0.968530i | \(-0.419932\pi\) | ||||
0.248897 | + | 0.968530i | \(0.419932\pi\) | |||||||
\(410\) | −4.35081 | −0.214871 | ||||||||
\(411\) | −20.2087 | −0.996824 | ||||||||
\(412\) | 1.55070 | 0.0763977 | ||||||||
\(413\) | 3.92498 | 0.193136 | ||||||||
\(414\) | −0.0955622 | −0.00469663 | ||||||||
\(415\) | −13.1452 | −0.645273 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.27389 | −0.209293 | ||||||||
\(418\) | 1.02325 | 0.0500488 | ||||||||
\(419\) | 9.45997 | 0.462150 | 0.231075 | − | 0.972936i | \(-0.425776\pi\) | ||||
0.231075 | + | 0.972936i | \(0.425776\pi\) | |||||||
\(420\) | −0.416173 | −0.0203071 | ||||||||
\(421\) | 31.0643 | 1.51398 | 0.756992 | − | 0.653424i | \(-0.226668\pi\) | ||||
0.756992 | + | 0.653424i | \(0.226668\pi\) | |||||||
\(422\) | −12.7875 | −0.622487 | ||||||||
\(423\) | 4.70769 | 0.228896 | ||||||||
\(424\) | 16.8003 | 0.815896 | ||||||||
\(425\) | −2.74666 | −0.133232 | ||||||||
\(426\) | −12.1394 | −0.588154 | ||||||||
\(427\) | −5.54778 | −0.268476 | ||||||||
\(428\) | 2.32756 | 0.112507 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.49734 | 0.313329 | ||||||||
\(431\) | −25.2186 | −1.21474 | −0.607369 | − | 0.794420i | \(-0.707775\pi\) | ||||
−0.607369 | + | 0.794420i | \(0.707775\pi\) | |||||||
\(432\) | 3.10331 | 0.149308 | ||||||||
\(433\) | 3.76991 | 0.181170 | 0.0905851 | − | 0.995889i | \(-0.471126\pi\) | ||||
0.0905851 | + | 0.995889i | \(0.471126\pi\) | |||||||
\(434\) | −8.73598 | −0.419341 | ||||||||
\(435\) | −0.530158 | −0.0254191 | ||||||||
\(436\) | 3.32756 | 0.159361 | ||||||||
\(437\) | 0.172701 | 0.00826141 | ||||||||
\(438\) | −13.2915 | −0.635093 | ||||||||
\(439\) | −22.6348 | −1.08030 | −0.540150 | − | 0.841569i | \(-0.681632\pi\) | ||||
−0.540150 | + | 0.841569i | \(0.681632\pi\) | |||||||
\(440\) | −1.16575 | −0.0555750 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.64334 | 0.220612 | 0.110306 | − | 0.993898i | \(-0.464817\pi\) | ||||
0.110306 | + | 0.993898i | \(0.464817\pi\) | |||||||
\(444\) | −0.416173 | −0.0197507 | ||||||||
\(445\) | −13.1968 | −0.625586 | ||||||||
\(446\) | 6.54083 | 0.309717 | ||||||||
\(447\) | 4.89669 | 0.231605 | ||||||||
\(448\) | −8.88601 | −0.419825 | ||||||||
\(449\) | 9.42312 | 0.444705 | 0.222352 | − | 0.974966i | \(-0.428626\pi\) | ||||
0.222352 | + | 0.974966i | \(0.428626\pi\) | |||||||
\(450\) | 4.81875 | 0.227158 | ||||||||
\(451\) | −1.08006 | −0.0508581 | ||||||||
\(452\) | −4.53016 | −0.213081 | ||||||||
\(453\) | 8.94553 | 0.420298 | ||||||||
\(454\) | 36.9058 | 1.73207 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −6.97170 | −0.326480 | ||||||||
\(457\) | 12.7162 | 0.594840 | 0.297420 | − | 0.954747i | \(-0.403874\pi\) | ||||
0.297420 | + | 0.954747i | \(0.403874\pi\) | |||||||
\(458\) | −0.865468 | −0.0404407 | ||||||||
\(459\) | −0.726109 | −0.0338919 | ||||||||
\(460\) | −0.0312196 | −0.00145562 | ||||||||
\(461\) | −29.7253 | −1.38445 | −0.692223 | − | 0.721684i | \(-0.743368\pi\) | ||||
−0.692223 | + | 0.721684i | \(0.743368\pi\) | |||||||
\(462\) | 0.444469 | 0.0206786 | ||||||||
\(463\) | −15.2838 | −0.710297 | −0.355148 | − | 0.934810i | \(-0.615570\pi\) | ||||
−0.355148 | + | 0.934810i | \(0.615570\pi\) | |||||||
\(464\) | −1.49119 | −0.0692267 | ||||||||
\(465\) | 7.56620 | 0.350874 | ||||||||
\(466\) | 23.3150 | 1.08005 | ||||||||
\(467\) | −26.6503 | −1.23323 | −0.616614 | − | 0.787265i | \(-0.711496\pi\) | ||||
−0.616614 | + | 0.787265i | \(0.711496\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.12386 | −0.375125 | ||||||||
\(470\) | −6.61665 | −0.305203 | ||||||||
\(471\) | −6.59450 | −0.303859 | ||||||||
\(472\) | −11.8860 | −0.547098 | ||||||||
\(473\) | 1.61292 | 0.0741623 | ||||||||
\(474\) | 21.7905 | 1.00087 | ||||||||
\(475\) | −8.70849 | −0.399573 | ||||||||
\(476\) | 0.273891 | 0.0125538 | ||||||||
\(477\) | 5.54778 | 0.254015 | ||||||||
\(478\) | 6.94553 | 0.317681 | ||||||||
\(479\) | −22.2117 | −1.01488 | −0.507439 | − | 0.861688i | \(-0.669408\pi\) | ||||
−0.507439 | + | 0.861688i | \(0.669408\pi\) | |||||||
\(480\) | 2.32061 | 0.105921 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 19.6970 | 0.897174 | ||||||||
\(483\) | 0.0750160 | 0.00341335 | ||||||||
\(484\) | 4.10331 | 0.186514 | ||||||||
\(485\) | 11.1471 | 0.506164 | ||||||||
\(486\) | 1.27389 | 0.0577848 | ||||||||
\(487\) | −0.971704 | −0.0440321 | −0.0220160 | − | 0.999758i | \(-0.507008\pi\) | ||||
−0.0220160 | + | 0.999758i | \(0.507008\pi\) | |||||||
\(488\) | 16.8003 | 0.760515 | ||||||||
\(489\) | 9.90444 | 0.447894 | ||||||||
\(490\) | −1.40550 | −0.0634940 | ||||||||
\(491\) | 26.9349 | 1.21555 | 0.607777 | − | 0.794108i | \(-0.292062\pi\) | ||||
0.607777 | + | 0.794108i | \(0.292062\pi\) | |||||||
\(492\) | 1.16765 | 0.0526419 | ||||||||
\(493\) | 0.348907 | 0.0157140 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.384953 | −0.0173023 | ||||||||
\(496\) | 21.2816 | 0.955574 | ||||||||
\(497\) | 9.52936 | 0.427450 | ||||||||
\(498\) | −15.1775 | −0.680121 | ||||||||
\(499\) | −21.1239 | −0.945634 | −0.472817 | − | 0.881161i | \(-0.656763\pi\) | ||||
−0.472817 | + | 0.881161i | \(0.656763\pi\) | |||||||
\(500\) | 3.65512 | 0.163462 | ||||||||
\(501\) | 16.7565 | 0.748626 | ||||||||
\(502\) | 10.5662 | 0.471593 | ||||||||
\(503\) | 12.5654 | 0.560264 | 0.280132 | − | 0.959962i | \(-0.409622\pi\) | ||||
0.280132 | + | 0.959962i | \(0.409622\pi\) | |||||||
\(504\) | −3.02830 | −0.134891 | ||||||||
\(505\) | 4.49602 | 0.200070 | ||||||||
\(506\) | 0.0333423 | 0.00148225 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.20955 | 0.0980328 | ||||||||
\(509\) | 27.6065 | 1.22364 | 0.611818 | − | 0.790998i | \(-0.290438\pi\) | ||||
0.611818 | + | 0.790998i | \(0.290438\pi\) | |||||||
\(510\) | 1.02055 | 0.0451905 | ||||||||
\(511\) | 10.4338 | 0.461564 | ||||||||
\(512\) | 25.3227 | 1.11912 | ||||||||
\(513\) | −2.30219 | −0.101644 | ||||||||
\(514\) | 19.1570 | 0.844978 | ||||||||
\(515\) | −4.53579 | −0.199871 | ||||||||
\(516\) | −1.74373 | −0.0767635 | ||||||||
\(517\) | −1.64254 | −0.0722389 | ||||||||
\(518\) | −1.40550 | −0.0617541 | ||||||||
\(519\) | −13.7184 | −0.602169 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.8783 | −1.61567 | −0.807833 | − | 0.589411i | \(-0.799360\pi\) | ||||
−0.807833 | + | 0.589411i | \(0.799360\pi\) | |||||||
\(522\) | −0.612124 | −0.0267919 | ||||||||
\(523\) | 30.8054 | 1.34702 | 0.673512 | − | 0.739176i | \(-0.264785\pi\) | ||||
0.673512 | + | 0.739176i | \(0.264785\pi\) | |||||||
\(524\) | −8.45142 | −0.369202 | ||||||||
\(525\) | −3.78270 | −0.165091 | ||||||||
\(526\) | 21.9680 | 0.957849 | ||||||||
\(527\) | −4.97945 | −0.216908 | ||||||||
\(528\) | −1.08277 | −0.0471213 | ||||||||
\(529\) | −22.9944 | −0.999755 | ||||||||
\(530\) | −7.79740 | −0.338697 | ||||||||
\(531\) | −3.92498 | −0.170330 | ||||||||
\(532\) | 0.868391 | 0.0376495 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −15.2370 | −0.659371 | ||||||||
\(535\) | −6.80807 | −0.294339 | ||||||||
\(536\) | 24.6015 | 1.06262 | ||||||||
\(537\) | 22.0304 | 0.950683 | ||||||||
\(538\) | 30.9485 | 1.33428 | ||||||||
\(539\) | −0.348907 | −0.0150285 | ||||||||
\(540\) | 0.416173 | 0.0179092 | ||||||||
\(541\) | −41.4981 | −1.78414 | −0.892072 | − | 0.451893i | \(-0.850749\pi\) | ||||
−0.892072 | + | 0.451893i | \(0.850749\pi\) | |||||||
\(542\) | −23.3537 | −1.00313 | ||||||||
\(543\) | −9.43380 | −0.404843 | ||||||||
\(544\) | −1.52723 | −0.0654797 | ||||||||
\(545\) | −9.73306 | −0.416918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.3716 | −1.76892 | −0.884460 | − | 0.466615i | \(-0.845473\pi\) | ||||
−0.884460 | + | 0.466615i | \(0.845473\pi\) | |||||||
\(548\) | −7.62280 | −0.325630 | ||||||||
\(549\) | 5.54778 | 0.236774 | ||||||||
\(550\) | −1.68129 | −0.0716906 | ||||||||
\(551\) | 1.10624 | 0.0471272 | ||||||||
\(552\) | −0.227171 | −0.00966903 | ||||||||
\(553\) | −17.1054 | −0.727397 | ||||||||
\(554\) | −10.7699 | −0.457569 | ||||||||
\(555\) | 1.21730 | 0.0516714 | ||||||||
\(556\) | −1.61212 | −0.0683693 | ||||||||
\(557\) | 30.0149 | 1.27177 | 0.635886 | − | 0.771783i | \(-0.280635\pi\) | ||||
0.635886 | + | 0.771783i | \(0.280635\pi\) | |||||||
\(558\) | 8.73598 | 0.369824 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 3.42392 | 0.144687 | ||||||||
\(561\) | 0.253344 | 0.0106962 | ||||||||
\(562\) | 31.8625 | 1.34404 | ||||||||
\(563\) | 25.9349 | 1.09302 | 0.546512 | − | 0.837451i | \(-0.315955\pi\) | ||||
0.546512 | + | 0.837451i | \(0.315955\pi\) | |||||||
\(564\) | 1.77575 | 0.0747727 | ||||||||
\(565\) | 13.2506 | 0.557459 | ||||||||
\(566\) | −34.5753 | −1.45331 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −28.8577 | −1.21084 | ||||||||
\(569\) | −6.56620 | −0.275270 | −0.137635 | − | 0.990483i | \(-0.543950\pi\) | ||||
−0.137635 | + | 0.990483i | \(0.543950\pi\) | |||||||
\(570\) | 3.23572 | 0.135529 | ||||||||
\(571\) | −30.0539 | −1.25772 | −0.628858 | − | 0.777520i | \(-0.716477\pi\) | ||||
−0.628858 | + | 0.777520i | \(0.716477\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.37720 | 0.141085 | ||||||||
\(574\) | 3.94341 | 0.164595 | ||||||||
\(575\) | −0.283763 | −0.0118337 | ||||||||
\(576\) | 8.88601 | 0.370251 | ||||||||
\(577\) | 21.1706 | 0.881343 | 0.440671 | − | 0.897669i | \(-0.354740\pi\) | ||||
0.440671 | + | 0.897669i | \(0.354740\pi\) | |||||||
\(578\) | 20.9845 | 0.872840 | ||||||||
\(579\) | −22.3227 | −0.927701 | ||||||||
\(580\) | −0.199977 | −0.00830360 | ||||||||
\(581\) | 11.9143 | 0.494289 | ||||||||
\(582\) | 12.8705 | 0.533500 | ||||||||
\(583\) | −1.93566 | −0.0801667 | ||||||||
\(584\) | −31.5966 | −1.30748 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.4268 | 0.554658 | ||||||||
\(587\) | 0.0312196 | 0.00128857 | 0.000644286 | − | 1.00000i | \(-0.499795\pi\) | ||||
0.000644286 | 1.00000i | \(0.499795\pi\) | ||||||||
\(588\) | 0.377203 | 0.0155556 | ||||||||
\(589\) | −15.7877 | −0.650523 | ||||||||
\(590\) | 5.51656 | 0.227113 | ||||||||
\(591\) | 25.4514 | 1.04693 | ||||||||
\(592\) | 3.42392 | 0.140722 | ||||||||
\(593\) | −10.3150 | −0.423586 | −0.211793 | − | 0.977315i | \(-0.567930\pi\) | ||||
−0.211793 | + | 0.977315i | \(0.567930\pi\) | |||||||
\(594\) | −0.444469 | −0.0182368 | ||||||||
\(595\) | −0.801125 | −0.0328429 | ||||||||
\(596\) | 1.84704 | 0.0756579 | ||||||||
\(597\) | 22.3404 | 0.914330 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 44.0176 | 1.79851 | 0.899256 | − | 0.437423i | \(-0.144109\pi\) | ||||
0.899256 | + | 0.437423i | \(0.144109\pi\) | |||||||
\(600\) | 11.4551 | 0.467654 | ||||||||
\(601\) | 5.04672 | 0.205860 | 0.102930 | − | 0.994689i | \(-0.467178\pi\) | ||||
0.102930 | + | 0.994689i | \(0.467178\pi\) | |||||||
\(602\) | −5.88894 | −0.240015 | ||||||||
\(603\) | 8.12386 | 0.330829 | ||||||||
\(604\) | 3.37428 | 0.137297 | ||||||||
\(605\) | −12.0021 | −0.487956 | ||||||||
\(606\) | 5.19112 | 0.210875 | ||||||||
\(607\) | 16.6482 | 0.675728 | 0.337864 | − | 0.941195i | \(-0.390296\pi\) | ||||
0.337864 | + | 0.941195i | \(0.390296\pi\) | |||||||
\(608\) | −4.84222 | −0.196378 | ||||||||
\(609\) | 0.480515 | 0.0194715 | ||||||||
\(610\) | −7.79740 | −0.315708 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.273891 | −0.0110714 | ||||||||
\(613\) | 38.0120 | 1.53529 | 0.767645 | − | 0.640875i | \(-0.221428\pi\) | ||||
0.767645 | + | 0.640875i | \(0.221428\pi\) | |||||||
\(614\) | 5.61585 | 0.226637 | ||||||||
\(615\) | −3.41537 | −0.137721 | ||||||||
\(616\) | 1.05659 | 0.0425713 | ||||||||
\(617\) | 15.6666 | 0.630713 | 0.315357 | − | 0.948973i | \(-0.397876\pi\) | ||||
0.315357 | + | 0.948973i | \(0.397876\pi\) | |||||||
\(618\) | −5.23704 | −0.210665 | ||||||||
\(619\) | 3.26109 | 0.131074 | 0.0655372 | − | 0.997850i | \(-0.479124\pi\) | ||||
0.0655372 | + | 0.997850i | \(0.479124\pi\) | |||||||
\(620\) | 2.85399 | 0.114619 | ||||||||
\(621\) | −0.0750160 | −0.00301029 | ||||||||
\(622\) | 2.96608 | 0.118929 | ||||||||
\(623\) | 11.9610 | 0.479209 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.22234 | 0.328894 | ||||||||
\(626\) | −16.1386 | −0.645027 | ||||||||
\(627\) | 0.803248 | 0.0320786 | ||||||||
\(628\) | −2.48746 | −0.0992606 | ||||||||
\(629\) | −0.801125 | −0.0319430 | ||||||||
\(630\) | 1.40550 | 0.0559964 | ||||||||
\(631\) | 1.59955 | 0.0636770 | 0.0318385 | − | 0.999493i | \(-0.489864\pi\) | ||||
0.0318385 | + | 0.999493i | \(0.489864\pi\) | |||||||
\(632\) | 51.8003 | 2.06051 | ||||||||
\(633\) | −10.0382 | −0.398981 | ||||||||
\(634\) | 15.6580 | 0.621860 | ||||||||
\(635\) | −6.46289 | −0.256472 | ||||||||
\(636\) | 2.09264 | 0.0829785 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.213574 | 0.00845548 | ||||||||
\(639\) | −9.52936 | −0.376976 | ||||||||
\(640\) | −7.84806 | −0.310222 | ||||||||
\(641\) | 31.3559 | 1.23848 | 0.619241 | − | 0.785201i | \(-0.287440\pi\) | ||||
0.619241 | + | 0.785201i | \(0.287440\pi\) | |||||||
\(642\) | −7.86064 | −0.310235 | ||||||||
\(643\) | −18.6631 | −0.736000 | −0.368000 | − | 0.929826i | \(-0.619957\pi\) | ||||
−0.368000 | + | 0.929826i | \(0.619957\pi\) | |||||||
\(644\) | 0.0282963 | 0.00111503 | ||||||||
\(645\) | 5.10039 | 0.200828 | ||||||||
\(646\) | −2.12949 | −0.0837835 | ||||||||
\(647\) | 6.53711 | 0.257000 | 0.128500 | − | 0.991709i | \(-0.458984\pi\) | ||||
0.128500 | + | 0.991709i | \(0.458984\pi\) | |||||||
\(648\) | 3.02830 | 0.118963 | ||||||||
\(649\) | 1.36945 | 0.0537557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.85772 | −0.268775 | ||||||||
\(652\) | 3.73598 | 0.146312 | ||||||||
\(653\) | 15.8521 | 0.620340 | 0.310170 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310170 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(654\) | −11.2378 | −0.439434 | ||||||||
\(655\) | 24.7203 | 0.965901 | ||||||||
\(656\) | −9.60650 | −0.375071 | ||||||||
\(657\) | −10.4338 | −0.407061 | ||||||||
\(658\) | 5.99708 | 0.233790 | ||||||||
\(659\) | −49.7974 | −1.93983 | −0.969916 | − | 0.243441i | \(-0.921724\pi\) | ||||
−0.969916 | + | 0.243441i | \(0.921724\pi\) | |||||||
\(660\) | −0.145205 | −0.00565211 | ||||||||
\(661\) | 3.57103 | 0.138897 | 0.0694485 | − | 0.997586i | \(-0.477876\pi\) | ||||
0.0694485 | + | 0.997586i | \(0.477876\pi\) | |||||||
\(662\) | −16.9319 | −0.658078 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −36.0801 | −1.40018 | ||||||||
\(665\) | −2.54003 | −0.0984982 | ||||||||
\(666\) | 1.40550 | 0.0544620 | ||||||||
\(667\) | 0.0360463 | 0.00139572 | ||||||||
\(668\) | 6.32061 | 0.244552 | ||||||||
\(669\) | 5.13453 | 0.198512 | ||||||||
\(670\) | −11.4181 | −0.441119 | ||||||||
\(671\) | −1.93566 | −0.0747252 | ||||||||
\(672\) | −2.10331 | −0.0811370 | ||||||||
\(673\) | 11.7339 | 0.452307 | 0.226154 | − | 0.974092i | \(-0.427385\pi\) | ||||
0.226154 | + | 0.974092i | \(0.427385\pi\) | |||||||
\(674\) | 4.33823 | 0.167102 | ||||||||
\(675\) | 3.78270 | 0.145596 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.3326 | 0.666146 | 0.333073 | − | 0.942901i | \(-0.391914\pi\) | ||||
0.333073 | + | 0.942901i | \(0.391914\pi\) | |||||||
\(678\) | 15.2993 | 0.587565 | ||||||||
\(679\) | −10.1033 | −0.387730 | ||||||||
\(680\) | 2.42605 | 0.0930346 | ||||||||
\(681\) | 28.9709 | 1.11017 | ||||||||
\(682\) | −3.04804 | −0.116716 | ||||||||
\(683\) | 16.9640 | 0.649108 | 0.324554 | − | 0.945867i | \(-0.394786\pi\) | ||||
0.324554 | + | 0.945867i | \(0.394786\pi\) | |||||||
\(684\) | −0.868391 | −0.0332038 | ||||||||
\(685\) | 22.2966 | 0.851908 | ||||||||
\(686\) | 1.27389 | 0.0486374 | ||||||||
\(687\) | −0.679390 | −0.0259203 | ||||||||
\(688\) | 14.3460 | 0.546935 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.105435 | 0.00401384 | ||||||||
\(691\) | 36.6425 | 1.39395 | 0.696974 | − | 0.717096i | \(-0.254529\pi\) | ||||
0.696974 | + | 0.717096i | \(0.254529\pi\) | |||||||
\(692\) | −5.17460 | −0.196709 | ||||||||
\(693\) | 0.348907 | 0.0132539 | ||||||||
\(694\) | 42.6730 | 1.61984 | ||||||||
\(695\) | 4.71544 | 0.178867 | ||||||||
\(696\) | −1.45514 | −0.0551570 | ||||||||
\(697\) | 2.24772 | 0.0851384 | ||||||||
\(698\) | 35.8988 | 1.35879 | ||||||||
\(699\) | 18.3022 | 0.692252 | ||||||||
\(700\) | −1.42685 | −0.0539297 | ||||||||
\(701\) | −14.6092 | −0.551782 | −0.275891 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275891 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.54003 | −0.0957991 | ||||||||
\(704\) | −3.10039 | −0.116850 | ||||||||
\(705\) | −5.19405 | −0.195619 | ||||||||
\(706\) | 3.81180 | 0.143459 | ||||||||
\(707\) | −4.07502 | −0.153257 | ||||||||
\(708\) | −1.48052 | −0.0556412 | ||||||||
\(709\) | −23.5860 | −0.885789 | −0.442894 | − | 0.896574i | \(-0.646048\pi\) | ||||
−0.442894 | + | 0.896574i | \(0.646048\pi\) | |||||||
\(710\) | 13.3935 | 0.502649 | ||||||||
\(711\) | 17.1054 | 0.641504 | ||||||||
\(712\) | −36.2215 | −1.35746 | ||||||||
\(713\) | −0.514439 | −0.0192659 | ||||||||
\(714\) | −0.924984 | −0.0346167 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.30994 | 0.310557 | ||||||||
\(717\) | 5.45222 | 0.203617 | ||||||||
\(718\) | −4.85209 | −0.181078 | ||||||||
\(719\) | 34.1337 | 1.27297 | 0.636487 | − | 0.771288i | \(-0.280387\pi\) | ||||
0.636487 | + | 0.771288i | \(0.280387\pi\) | |||||||
\(720\) | −3.42392 | −0.127602 | ||||||||
\(721\) | 4.11106 | 0.153104 | ||||||||
\(722\) | 17.4522 | 0.649504 | ||||||||
\(723\) | 15.4621 | 0.575041 | ||||||||
\(724\) | −3.55845 | −0.132249 | ||||||||
\(725\) | −1.81765 | −0.0675057 | ||||||||
\(726\) | −13.8577 | −0.514308 | ||||||||
\(727\) | −15.3481 | −0.569230 | −0.284615 | − | 0.958642i | \(-0.591866\pi\) | ||||
−0.284615 | + | 0.958642i | \(0.591866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 14.6647 | 0.542765 | ||||||||
\(731\) | −3.35666 | −0.124150 | ||||||||
\(732\) | 2.09264 | 0.0773462 | ||||||||
\(733\) | 23.2894 | 0.860213 | 0.430107 | − | 0.902778i | \(-0.358476\pi\) | ||||
0.430107 | + | 0.902778i | \(0.358476\pi\) | |||||||
\(734\) | 33.6962 | 1.24375 | ||||||||
\(735\) | −1.10331 | −0.0406963 | ||||||||
\(736\) | −0.157782 | −0.00581593 | ||||||||
\(737\) | −2.83447 | −0.104409 | ||||||||
\(738\) | −3.94341 | −0.145159 | ||||||||
\(739\) | −10.2661 | −0.377646 | −0.188823 | − | 0.982011i | \(-0.560467\pi\) | ||||
−0.188823 | + | 0.982011i | \(0.560467\pi\) | |||||||
\(740\) | 0.459168 | 0.0168794 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.06727 | 0.259447 | ||||||||
\(743\) | −45.3481 | −1.66366 | −0.831830 | − | 0.555030i | \(-0.812707\pi\) | ||||
−0.831830 | + | 0.555030i | \(0.812707\pi\) | |||||||
\(744\) | 20.7672 | 0.761363 | ||||||||
\(745\) | −5.40258 | −0.197935 | ||||||||
\(746\) | −2.71544 | −0.0994192 | ||||||||
\(747\) | −11.9143 | −0.435922 | ||||||||
\(748\) | 0.0955622 | 0.00349410 | ||||||||
\(749\) | 6.17058 | 0.225468 | ||||||||
\(750\) | −12.3441 | −0.450742 | ||||||||
\(751\) | −29.6113 | −1.08053 | −0.540266 | − | 0.841494i | \(-0.681676\pi\) | ||||
−0.540266 | + | 0.841494i | \(0.681676\pi\) | |||||||
\(752\) | −14.6094 | −0.532751 | ||||||||
\(753\) | 8.29444 | 0.302266 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.86971 | −0.359196 | ||||||||
\(756\) | −0.377203 | −0.0137187 | ||||||||
\(757\) | −25.9816 | −0.944316 | −0.472158 | − | 0.881514i | \(-0.656525\pi\) | ||||
−0.472158 | + | 0.881514i | \(0.656525\pi\) | |||||||
\(758\) | 17.7624 | 0.645159 | ||||||||
\(759\) | 0.0261736 | 0.000950041 0 | ||||||||
\(760\) | 7.69197 | 0.279017 | ||||||||
\(761\) | −54.0665 | −1.95991 | −0.979954 | − | 0.199224i | \(-0.936158\pi\) | ||||
−0.979954 | + | 0.199224i | \(0.936158\pi\) | |||||||
\(762\) | −7.46209 | −0.270323 | ||||||||
\(763\) | 8.82167 | 0.319366 | ||||||||
\(764\) | 1.27389 | 0.0460877 | ||||||||
\(765\) | 0.801125 | 0.0289648 | ||||||||
\(766\) | 23.6999 | 0.856313 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 8.71061 | 0.314317 | ||||||||
\(769\) | 25.7934 | 0.930133 | 0.465066 | − | 0.885276i | \(-0.346030\pi\) | ||||
0.465066 | + | 0.885276i | \(0.346030\pi\) | |||||||
\(770\) | −0.490388 | −0.0176724 | ||||||||
\(771\) | 15.0382 | 0.541586 | ||||||||
\(772\) | −8.42020 | −0.303050 | ||||||||
\(773\) | −0.121736 | −0.00437853 | −0.00218927 | − | 0.999998i | \(-0.500697\pi\) | ||||
−0.00218927 | + | 0.999998i | \(0.500697\pi\) | |||||||
\(774\) | 5.88894 | 0.211673 | ||||||||
\(775\) | 25.9407 | 0.931818 | ||||||||
\(776\) | 30.5958 | 1.09833 | ||||||||
\(777\) | −1.10331 | −0.0395811 | ||||||||
\(778\) | 1.56701 | 0.0561799 | ||||||||
\(779\) | 7.12656 | 0.255336 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32486 | 0.118973 | ||||||||
\(782\) | −0.0693886 | −0.00248133 | ||||||||
\(783\) | −0.480515 | −0.0171722 | ||||||||
\(784\) | −3.10331 | −0.110833 | ||||||||
\(785\) | 7.27579 | 0.259684 | ||||||||
\(786\) | 28.5422 | 1.01806 | ||||||||
\(787\) | −20.2215 | −0.720820 | −0.360410 | − | 0.932794i | \(-0.617363\pi\) | ||||
−0.360410 | + | 0.932794i | \(0.617363\pi\) | |||||||
\(788\) | 9.60035 | 0.341998 | ||||||||
\(789\) | 17.2448 | 0.613931 | ||||||||
\(790\) | −24.0417 | −0.855364 | ||||||||
\(791\) | −12.0099 | −0.427022 | ||||||||
\(792\) | −1.05659 | −0.0375444 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −37.7253 | −1.33882 | ||||||||
\(795\) | −6.12094 | −0.217087 | ||||||||
\(796\) | 8.42685 | 0.298682 | ||||||||
\(797\) | 32.4124 | 1.14811 | 0.574054 | − | 0.818818i | \(-0.305370\pi\) | ||||
0.574054 | + | 0.818818i | \(0.305370\pi\) | |||||||
\(798\) | −2.93273 | −0.103818 | ||||||||
\(799\) | 3.41830 | 0.120931 | ||||||||
\(800\) | 7.95620 | 0.281294 | ||||||||
\(801\) | −11.9610 | −0.422622 | ||||||||
\(802\) | −10.4210 | −0.367978 | ||||||||
\(803\) | 3.64042 | 0.128468 | ||||||||
\(804\) | 3.06434 | 0.108071 | ||||||||
\(805\) | −0.0827661 | −0.00291712 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.2944 | 0.855205 | ||||||||
\(808\) | 12.3404 | 0.434132 | ||||||||
\(809\) | 24.4629 | 0.860069 | 0.430035 | − | 0.902812i | \(-0.358501\pi\) | ||||
0.430035 | + | 0.902812i | \(0.358501\pi\) | |||||||
\(810\) | −1.40550 | −0.0493842 | ||||||||
\(811\) | −45.2448 | −1.58876 | −0.794380 | − | 0.607421i | \(-0.792204\pi\) | ||||
−0.794380 | + | 0.607421i | \(0.792204\pi\) | |||||||
\(812\) | 0.181252 | 0.00636069 | ||||||||
\(813\) | −18.3326 | −0.642953 | ||||||||
\(814\) | −0.490388 | −0.0171881 | ||||||||
\(815\) | −10.9277 | −0.382780 | ||||||||
\(816\) | 2.25334 | 0.0788828 | ||||||||
\(817\) | −10.6425 | −0.372335 | ||||||||
\(818\) | −12.8246 | −0.448401 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.28829 | −0.0449890 | ||||||||
\(821\) | 36.7331 | 1.28199 | 0.640996 | − | 0.767544i | \(-0.278521\pi\) | ||||
0.640996 | + | 0.767544i | \(0.278521\pi\) | |||||||
\(822\) | 25.7437 | 0.897916 | ||||||||
\(823\) | 42.6476 | 1.48660 | 0.743301 | − | 0.668957i | \(-0.233259\pi\) | ||||
0.743301 | + | 0.668957i | \(0.233259\pi\) | |||||||
\(824\) | −12.4495 | −0.433699 | ||||||||
\(825\) | −1.31981 | −0.0459499 | ||||||||
\(826\) | −5.00000 | −0.173972 | ||||||||
\(827\) | −50.0635 | −1.74088 | −0.870440 | − | 0.492275i | \(-0.836166\pi\) | ||||
−0.870440 | + | 0.492275i | \(0.836166\pi\) | |||||||
\(828\) | −0.0282963 | −0.000983363 0 | ||||||||
\(829\) | 25.8911 | 0.899234 | 0.449617 | − | 0.893222i | \(-0.351561\pi\) | ||||
0.449617 | + | 0.893222i | \(0.351561\pi\) | |||||||
\(830\) | 16.7456 | 0.581247 | ||||||||
\(831\) | −8.45434 | −0.293278 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.726109 | 0.0251582 | ||||||||
\(834\) | 5.44447 | 0.188527 | ||||||||
\(835\) | −18.4877 | −0.639793 | ||||||||
\(836\) | 0.302987 | 0.0104790 | ||||||||
\(837\) | 6.85772 | 0.237037 | ||||||||
\(838\) | −12.0510 | −0.416294 | ||||||||
\(839\) | −28.9349 | −0.998942 | −0.499471 | − | 0.866331i | \(-0.666472\pi\) | ||||
−0.499471 | + | 0.866331i | \(0.666472\pi\) | |||||||
\(840\) | 3.34116 | 0.115281 | ||||||||
\(841\) | −28.7691 | −0.992038 | ||||||||
\(842\) | −39.5726 | −1.36376 | ||||||||
\(843\) | 25.0120 | 0.861459 | ||||||||
\(844\) | −3.78643 | −0.130334 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.99708 | −0.206184 | ||||||||
\(847\) | 10.8783 | 0.373782 | ||||||||
\(848\) | −17.2165 | −0.591217 | ||||||||
\(849\) | −27.1415 | −0.931493 | ||||||||
\(850\) | 3.49894 | 0.120013 | ||||||||
\(851\) | −0.0827661 | −0.00283719 | ||||||||
\(852\) | −3.59450 | −0.123146 | ||||||||
\(853\) | 40.3094 | 1.38017 | 0.690083 | − | 0.723730i | \(-0.257574\pi\) | ||||
0.690083 | + | 0.723730i | \(0.257574\pi\) | |||||||
\(854\) | 7.06727 | 0.241837 | ||||||||
\(855\) | 2.54003 | 0.0868672 | ||||||||
\(856\) | −18.6863 | −0.638686 | ||||||||
\(857\) | 40.0459 | 1.36794 | 0.683971 | − | 0.729509i | \(-0.260251\pi\) | ||||
0.683971 | + | 0.729509i | \(0.260251\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.66659 | 0.227461 | 0.113731 | − | 0.993512i | \(-0.463720\pi\) | ||||
0.113731 | + | 0.993512i | \(0.463720\pi\) | |||||||
\(860\) | 1.92388 | 0.0656038 | ||||||||
\(861\) | 3.09556 | 0.105496 | ||||||||
\(862\) | 32.1258 | 1.09421 | ||||||||
\(863\) | −5.85289 | −0.199235 | −0.0996174 | − | 0.995026i | \(-0.531762\pi\) | ||||
−0.0996174 | + | 0.995026i | \(0.531762\pi\) | |||||||
\(864\) | 2.10331 | 0.0715561 | ||||||||
\(865\) | 15.1356 | 0.514627 | ||||||||
\(866\) | −4.80245 | −0.163194 | ||||||||
\(867\) | 16.4728 | 0.559444 | ||||||||
\(868\) | −2.58675 | −0.0878000 | ||||||||
\(869\) | −5.96820 | −0.202457 | ||||||||
\(870\) | 0.675364 | 0.0228970 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −26.7146 | −0.904672 | ||||||||
\(873\) | 10.1033 | 0.341945 | ||||||||
\(874\) | −0.220002 | −0.00744168 | ||||||||
\(875\) | 9.69006 | 0.327584 | ||||||||
\(876\) | −3.93566 | −0.132974 | ||||||||
\(877\) | 4.36733 | 0.147474 | 0.0737371 | − | 0.997278i | \(-0.476507\pi\) | ||||
0.0737371 | + | 0.997278i | \(0.476507\pi\) | |||||||
\(878\) | 28.8342 | 0.973109 | ||||||||
\(879\) | 10.5400 | 0.355506 | ||||||||
\(880\) | 1.19463 | 0.0402709 | ||||||||
\(881\) | 3.14733 | 0.106036 | 0.0530181 | − | 0.998594i | \(-0.483116\pi\) | ||||
0.0530181 | + | 0.998594i | \(0.483116\pi\) | |||||||
\(882\) | −1.27389 | −0.0428941 | ||||||||
\(883\) | 14.9554 | 0.503289 | 0.251645 | − | 0.967820i | \(-0.419029\pi\) | ||||
0.251645 | + | 0.967820i | \(0.419029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.33048 | 0.145568 | ||||||||
\(886\) | −5.91511 | −0.198722 | ||||||||
\(887\) | 22.5264 | 0.756364 | 0.378182 | − | 0.925731i | \(-0.376549\pi\) | ||||
0.378182 | + | 0.925731i | \(0.376549\pi\) | |||||||
\(888\) | 3.34116 | 0.112122 | ||||||||
\(889\) | 5.85772 | 0.196462 | ||||||||
\(890\) | 16.8112 | 0.563513 | ||||||||
\(891\) | −0.348907 | −0.0116888 | ||||||||
\(892\) | 1.93676 | 0.0648475 | ||||||||
\(893\) | 10.8380 | 0.362679 | ||||||||
\(894\) | −6.23784 | −0.208625 | ||||||||
\(895\) | −24.3064 | −0.812474 | ||||||||
\(896\) | 7.11319 | 0.237635 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.0040 | −0.400580 | ||||||||
\(899\) | −3.29524 | −0.109902 | ||||||||
\(900\) | 1.42685 | 0.0475615 | ||||||||
\(901\) | 4.02830 | 0.134202 | ||||||||
\(902\) | 1.37588 | 0.0458118 | ||||||||
\(903\) | −4.62280 | −0.153837 | ||||||||
\(904\) | 36.3695 | 1.20963 | ||||||||
\(905\) | 10.4084 | 0.345988 | ||||||||
\(906\) | −11.3956 | −0.378594 | ||||||||
\(907\) | −18.6532 | −0.619370 | −0.309685 | − | 0.950839i | \(-0.600224\pi\) | ||||
−0.309685 | + | 0.950839i | \(0.600224\pi\) | |||||||
\(908\) | 10.9279 | 0.362655 | ||||||||
\(909\) | 4.07502 | 0.135160 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.3278 | 0.607226 | 0.303613 | − | 0.952795i | \(-0.401807\pi\) | ||||
0.303613 | + | 0.952795i | \(0.401807\pi\) | |||||||
\(912\) | 7.14440 | 0.236575 | ||||||||
\(913\) | 4.15698 | 0.137576 | ||||||||
\(914\) | −16.1991 | −0.535818 | ||||||||
\(915\) | −6.12094 | −0.202352 | ||||||||
\(916\) | −0.256268 | −0.00846732 | ||||||||
\(917\) | −22.4055 | −0.739895 | ||||||||
\(918\) | 0.924984 | 0.0305290 | ||||||||
\(919\) | 15.1054 | 0.498282 | 0.249141 | − | 0.968467i | \(-0.419852\pi\) | ||||
0.249141 | + | 0.968467i | \(0.419852\pi\) | |||||||
\(920\) | 0.250640 | 0.00826337 | ||||||||
\(921\) | 4.40842 | 0.145262 | ||||||||
\(922\) | 37.8668 | 1.24708 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.131609 | 0.00432960 | ||||||||
\(925\) | 4.17350 | 0.137224 | ||||||||
\(926\) | 19.4698 | 0.639819 | ||||||||
\(927\) | −4.11106 | −0.135025 | ||||||||
\(928\) | −1.01067 | −0.0331770 | ||||||||
\(929\) | −6.25817 | −0.205324 | −0.102662 | − | 0.994716i | \(-0.532736\pi\) | ||||
−0.102662 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(930\) | −9.63852 | −0.316059 | ||||||||
\(931\) | 2.30219 | 0.0754511 | ||||||||
\(932\) | 6.90364 | 0.226136 | ||||||||
\(933\) | 2.32836 | 0.0762271 | ||||||||
\(934\) | 33.9496 | 1.11086 | ||||||||
\(935\) | −0.279518 | −0.00914121 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.6610 | −0.740301 | −0.370151 | − | 0.928972i | \(-0.620694\pi\) | ||||
−0.370151 | + | 0.928972i | \(0.620694\pi\) | |||||||
\(938\) | 10.3489 | 0.337904 | ||||||||
\(939\) | −12.6687 | −0.413428 | ||||||||
\(940\) | −1.95921 | −0.0639024 | ||||||||
\(941\) | 17.2944 | 0.563783 | 0.281891 | − | 0.959446i | \(-0.409038\pi\) | ||||
0.281891 | + | 0.959446i | \(0.409038\pi\) | |||||||
\(942\) | 8.40067 | 0.273709 | ||||||||
\(943\) | 0.232217 | 0.00756202 | ||||||||
\(944\) | 12.1805 | 0.396440 | ||||||||
\(945\) | 1.10331 | 0.0358908 | ||||||||
\(946\) | −2.05469 | −0.0668037 | ||||||||
\(947\) | −27.6121 | −0.897273 | −0.448637 | − | 0.893714i | \(-0.648090\pi\) | ||||
−0.448637 | + | 0.893714i | \(0.648090\pi\) | |||||||
\(948\) | 6.45222 | 0.209558 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 11.0937 | 0.359926 | ||||||||
\(951\) | 12.2915 | 0.398580 | ||||||||
\(952\) | −2.19887 | −0.0712659 | ||||||||
\(953\) | 4.39080 | 0.142232 | 0.0711160 | − | 0.997468i | \(-0.477344\pi\) | ||||
0.0711160 | + | 0.997468i | \(0.477344\pi\) | |||||||
\(954\) | −7.06727 | −0.228811 | ||||||||
\(955\) | −3.72611 | −0.120574 | ||||||||
\(956\) | 2.05659 | 0.0665150 | ||||||||
\(957\) | 0.167655 | 0.00541951 | ||||||||
\(958\) | 28.2952 | 0.914178 | ||||||||
\(959\) | −20.2087 | −0.652574 | ||||||||
\(960\) | −9.80405 | −0.316424 | ||||||||
\(961\) | 16.0283 | 0.517042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.17058 | −0.198844 | ||||||||
\(964\) | 5.83235 | 0.187847 | ||||||||
\(965\) | 24.6289 | 0.792834 | ||||||||
\(966\) | −0.0955622 | −0.00307466 | ||||||||
\(967\) | −18.4875 | −0.594517 | −0.297258 | − | 0.954797i | \(-0.596072\pi\) | ||||
−0.297258 | + | 0.954797i | \(0.596072\pi\) | |||||||
\(968\) | −32.9426 | −1.05882 | ||||||||
\(969\) | −1.67164 | −0.0537008 | ||||||||
\(970\) | −14.2002 | −0.455941 | ||||||||
\(971\) | −52.3374 | −1.67959 | −0.839794 | − | 0.542905i | \(-0.817324\pi\) | ||||
−0.839794 | + | 0.542905i | \(0.817324\pi\) | |||||||
\(972\) | 0.377203 | 0.0120988 | ||||||||
\(973\) | −4.27389 | −0.137015 | ||||||||
\(974\) | 1.23784 | 0.0396631 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.2165 | −0.551087 | ||||||||
\(977\) | 51.6447 | 1.65226 | 0.826130 | − | 0.563480i | \(-0.190538\pi\) | ||||
0.826130 | + | 0.563480i | \(0.190538\pi\) | |||||||
\(978\) | −12.6172 | −0.403453 | ||||||||
\(979\) | 4.17328 | 0.133379 | ||||||||
\(980\) | −0.416173 | −0.0132941 | ||||||||
\(981\) | −8.82167 | −0.281654 | ||||||||
\(982\) | −34.3121 | −1.09494 | ||||||||
\(983\) | 37.5419 | 1.19740 | 0.598701 | − | 0.800973i | \(-0.295684\pi\) | ||||
0.598701 | + | 0.800973i | \(0.295684\pi\) | |||||||
\(984\) | −9.37428 | −0.298841 | ||||||||
\(985\) | −28.0809 | −0.894731 | ||||||||
\(986\) | −0.444469 | −0.0141548 | ||||||||
\(987\) | 4.70769 | 0.149847 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.346784 | −0.0110271 | ||||||||
\(990\) | 0.490388 | 0.0155856 | ||||||||
\(991\) | −50.5724 | −1.60648 | −0.803242 | − | 0.595653i | \(-0.796893\pi\) | ||||
−0.803242 | + | 0.595653i | \(0.796893\pi\) | |||||||
\(992\) | 14.4239 | 0.457960 | ||||||||
\(993\) | −13.2915 | −0.421793 | ||||||||
\(994\) | −12.1394 | −0.385037 | ||||||||
\(995\) | −24.6484 | −0.781406 | ||||||||
\(996\) | −4.49411 | −0.142401 | ||||||||
\(997\) | −25.9221 | −0.820960 | −0.410480 | − | 0.911870i | \(-0.634639\pi\) | ||||
−0.410480 | + | 0.911870i | \(0.634639\pi\) | |||||||
\(998\) | 26.9095 | 0.851805 | ||||||||
\(999\) | 1.10331 | 0.0349073 |
(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 | 3549.2.a.h.1.2 | 3 | ||
13.3 | even | 3 | 273.2.k.d.22.2 | ✓ | 6 | ||
13.9 | even | 3 | 273.2.k.d.211.2 | yes | 6 | ||
13.12 | even | 2 | 3549.2.a.s.1.2 | 3 | |||
39.29 | odd | 6 | 819.2.o.d.568.2 | 6 | |||
39.35 | odd | 6 | 819.2.o.d.757.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.k.d.22.2 | ✓ | 6 | 13.3 | even | 3 | ||
273.2.k.d.211.2 | yes | 6 | 13.9 | even | 3 | ||
819.2.o.d.568.2 | 6 | 39.29 | odd | 6 | |||
819.2.o.d.757.2 | 6 | 39.35 | odd | 6 | |||
3549.2.a.h.1.2 | 3 | 1.1 | even | 1 | trivial | ||
3549.2.a.s.1.2 | 3 | 13.12 | even | 2 |