Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 13x^{5} + 16x^{4} + 19x^{3} - 8x^{2} - 10x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.340585\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.46450 | 1.54937 | 0.774685 | − | 0.632347i | \(-0.217908\pi\) | ||||
0.774685 | + | 0.632347i | \(0.217908\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.26047 | 0.476412 | 0.238206 | − | 0.971215i | \(-0.423441\pi\) | ||||
0.238206 | + | 0.971215i | \(0.423441\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.46450 | −1.09557 | ||||||||
\(11\) | −2.95054 | −0.889621 | −0.444810 | − | 0.895625i | \(-0.646729\pi\) | ||||
−0.444810 | + | 0.895625i | \(0.646729\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.89870 | −0.803955 | −0.401978 | − | 0.915649i | \(-0.631677\pi\) | ||||
−0.401978 | + | 0.915649i | \(0.631677\pi\) | |||||||
\(14\) | −1.26047 | −0.336874 | ||||||||
\(15\) | −3.46450 | −0.894529 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.513960 | −0.124654 | −0.0623268 | − | 0.998056i | \(-0.519852\pi\) | ||||
−0.0623268 | + | 0.998056i | \(0.519852\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −3.00622 | −0.689674 | −0.344837 | − | 0.938663i | \(-0.612066\pi\) | ||||
−0.344837 | + | 0.938663i | \(0.612066\pi\) | |||||||
\(20\) | 3.46450 | 0.774685 | ||||||||
\(21\) | −1.26047 | −0.275056 | ||||||||
\(22\) | 2.95054 | 0.629057 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 7.00274 | 1.40055 | ||||||||
\(26\) | 2.89870 | 0.568482 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.26047 | 0.238206 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 3.46450 | 0.632528 | ||||||||
\(31\) | −5.40982 | −0.971632 | −0.485816 | − | 0.874061i | \(-0.661478\pi\) | ||||
−0.485816 | + | 0.874061i | \(0.661478\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.95054 | 0.513623 | ||||||||
\(34\) | 0.513960 | 0.0881434 | ||||||||
\(35\) | 4.36688 | 0.738138 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.8799 | 1.78865 | 0.894323 | − | 0.447423i | \(-0.147658\pi\) | ||||
0.894323 | + | 0.447423i | \(0.147658\pi\) | |||||||
\(38\) | 3.00622 | 0.487673 | ||||||||
\(39\) | 2.89870 | 0.464164 | ||||||||
\(40\) | −3.46450 | −0.547785 | ||||||||
\(41\) | −7.03067 | −1.09801 | −0.549003 | − | 0.835821i | \(-0.684992\pi\) | ||||
−0.549003 | + | 0.835821i | \(0.684992\pi\) | |||||||
\(42\) | 1.26047 | 0.194494 | ||||||||
\(43\) | −7.06738 | −1.07777 | −0.538883 | − | 0.842381i | \(-0.681153\pi\) | ||||
−0.538883 | + | 0.842381i | \(0.681153\pi\) | |||||||
\(44\) | −2.95054 | −0.444810 | ||||||||
\(45\) | 3.46450 | 0.516457 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −4.98736 | −0.727481 | −0.363741 | − | 0.931500i | \(-0.618501\pi\) | ||||
−0.363741 | + | 0.931500i | \(0.618501\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.41122 | −0.773032 | ||||||||
\(50\) | −7.00274 | −0.990338 | ||||||||
\(51\) | 0.513960 | 0.0719688 | ||||||||
\(52\) | −2.89870 | −0.401978 | ||||||||
\(53\) | −7.84635 | −1.07778 | −0.538890 | − | 0.842376i | \(-0.681156\pi\) | ||||
−0.538890 | + | 0.842376i | \(0.681156\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −10.2221 | −1.37835 | ||||||||
\(56\) | −1.26047 | −0.168437 | ||||||||
\(57\) | 3.00622 | 0.398183 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | −4.54958 | −0.592304 | −0.296152 | − | 0.955141i | \(-0.595704\pi\) | ||||
−0.296152 | + | 0.955141i | \(0.595704\pi\) | |||||||
\(60\) | −3.46450 | −0.447265 | ||||||||
\(61\) | −7.47147 | −0.956624 | −0.478312 | − | 0.878190i | \(-0.658751\pi\) | ||||
−0.478312 | + | 0.878190i | \(0.658751\pi\) | |||||||
\(62\) | 5.40982 | 0.687048 | ||||||||
\(63\) | 1.26047 | 0.158804 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −10.0425 | −1.24562 | ||||||||
\(66\) | −2.95054 | −0.363186 | ||||||||
\(67\) | −8.80796 | −1.07606 | −0.538032 | − | 0.842925i | \(-0.680832\pi\) | ||||
−0.538032 | + | 0.842925i | \(0.680832\pi\) | |||||||
\(68\) | −0.513960 | −0.0623268 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −4.36688 | −0.521943 | ||||||||
\(71\) | 6.80747 | 0.807898 | 0.403949 | − | 0.914782i | \(-0.367637\pi\) | ||||
0.403949 | + | 0.914782i | \(0.367637\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 2.87765 | 0.336803 | 0.168402 | − | 0.985718i | \(-0.446139\pi\) | ||||
0.168402 | + | 0.985718i | \(0.446139\pi\) | |||||||
\(74\) | −10.8799 | −1.26476 | ||||||||
\(75\) | −7.00274 | −0.808607 | ||||||||
\(76\) | −3.00622 | −0.344837 | ||||||||
\(77\) | −3.71905 | −0.423826 | ||||||||
\(78\) | −2.89870 | −0.328213 | ||||||||
\(79\) | −9.61800 | −1.08211 | −0.541055 | − | 0.840987i | \(-0.681975\pi\) | ||||
−0.541055 | + | 0.840987i | \(0.681975\pi\) | |||||||
\(80\) | 3.46450 | 0.387343 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.03067 | 0.776407 | ||||||||
\(83\) | 0.492258 | 0.0540323 | 0.0270162 | − | 0.999635i | \(-0.491399\pi\) | ||||
0.0270162 | + | 0.999635i | \(0.491399\pi\) | |||||||
\(84\) | −1.26047 | −0.137528 | ||||||||
\(85\) | −1.78061 | −0.193135 | ||||||||
\(86\) | 7.06738 | 0.762095 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | 2.95054 | 0.314528 | ||||||||
\(89\) | 0.689007 | 0.0730346 | 0.0365173 | − | 0.999333i | \(-0.488374\pi\) | ||||
0.0365173 | + | 0.999333i | \(0.488374\pi\) | |||||||
\(90\) | −3.46450 | −0.365190 | ||||||||
\(91\) | −3.65372 | −0.383014 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 5.40982 | 0.560972 | ||||||||
\(94\) | 4.98736 | 0.514407 | ||||||||
\(95\) | −10.4150 | −1.06856 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.39041 | −0.242709 | −0.121355 | − | 0.992609i | \(-0.538724\pi\) | ||||
−0.121355 | + | 0.992609i | \(0.538724\pi\) | |||||||
\(98\) | 5.41122 | 0.546616 | ||||||||
\(99\) | −2.95054 | −0.296540 | ||||||||
\(100\) | 7.00274 | 0.700274 | ||||||||
\(101\) | 5.52770 | 0.550026 | 0.275013 | − | 0.961440i | \(-0.411318\pi\) | ||||
0.275013 | + | 0.961440i | \(0.411318\pi\) | |||||||
\(102\) | −0.513960 | −0.0508896 | ||||||||
\(103\) | −1.89297 | −0.186520 | −0.0932601 | − | 0.995642i | \(-0.529729\pi\) | ||||
−0.0932601 | + | 0.995642i | \(0.529729\pi\) | |||||||
\(104\) | 2.89870 | 0.284241 | ||||||||
\(105\) | −4.36688 | −0.426164 | ||||||||
\(106\) | 7.84635 | 0.762105 | ||||||||
\(107\) | 2.57025 | 0.248476 | 0.124238 | − | 0.992252i | \(-0.460351\pi\) | ||||
0.124238 | + | 0.992252i | \(0.460351\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 18.5551 | 1.77726 | 0.888628 | − | 0.458629i | \(-0.151659\pi\) | ||||
0.888628 | + | 0.458629i | \(0.151659\pi\) | |||||||
\(110\) | 10.2221 | 0.974642 | ||||||||
\(111\) | −10.8799 | −1.03267 | ||||||||
\(112\) | 1.26047 | 0.119103 | ||||||||
\(113\) | −3.26945 | −0.307564 | −0.153782 | − | 0.988105i | \(-0.549145\pi\) | ||||
−0.153782 | + | 0.988105i | \(0.549145\pi\) | |||||||
\(114\) | −3.00622 | −0.281558 | ||||||||
\(115\) | 3.46450 | 0.323066 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −2.89870 | −0.267985 | ||||||||
\(118\) | 4.54958 | 0.418822 | ||||||||
\(119\) | −0.647830 | −0.0593865 | ||||||||
\(120\) | 3.46450 | 0.316264 | ||||||||
\(121\) | −2.29433 | −0.208575 | ||||||||
\(122\) | 7.47147 | 0.676435 | ||||||||
\(123\) | 7.03067 | 0.633934 | ||||||||
\(124\) | −5.40982 | −0.485816 | ||||||||
\(125\) | 6.93850 | 0.620599 | ||||||||
\(126\) | −1.26047 | −0.112291 | ||||||||
\(127\) | −8.28653 | −0.735311 | −0.367655 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367655 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 7.06738 | 0.622248 | ||||||||
\(130\) | 10.0425 | 0.880790 | ||||||||
\(131\) | 11.3326 | 0.990131 | 0.495065 | − | 0.868856i | \(-0.335144\pi\) | ||||
0.495065 | + | 0.868856i | \(0.335144\pi\) | |||||||
\(132\) | 2.95054 | 0.256811 | ||||||||
\(133\) | −3.78924 | −0.328569 | ||||||||
\(134\) | 8.80796 | 0.760891 | ||||||||
\(135\) | −3.46450 | −0.298176 | ||||||||
\(136\) | 0.513960 | 0.0440717 | ||||||||
\(137\) | 9.35007 | 0.798830 | 0.399415 | − | 0.916770i | \(-0.369213\pi\) | ||||
0.399415 | + | 0.916770i | \(0.369213\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | −5.33044 | −0.452122 | −0.226061 | − | 0.974113i | \(-0.572585\pi\) | ||||
−0.226061 | + | 0.974113i | \(0.572585\pi\) | |||||||
\(140\) | 4.36688 | 0.369069 | ||||||||
\(141\) | 4.98736 | 0.420011 | ||||||||
\(142\) | −6.80747 | −0.571270 | ||||||||
\(143\) | 8.55273 | 0.715215 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 3.46450 | 0.287711 | ||||||||
\(146\) | −2.87765 | −0.238156 | ||||||||
\(147\) | 5.41122 | 0.446310 | ||||||||
\(148\) | 10.8799 | 0.894323 | ||||||||
\(149\) | −3.37859 | −0.276785 | −0.138392 | − | 0.990377i | \(-0.544193\pi\) | ||||
−0.138392 | + | 0.990377i | \(0.544193\pi\) | |||||||
\(150\) | 7.00274 | 0.571772 | ||||||||
\(151\) | 11.4581 | 0.932447 | 0.466223 | − | 0.884667i | \(-0.345614\pi\) | ||||
0.466223 | + | 0.884667i | \(0.345614\pi\) | |||||||
\(152\) | 3.00622 | 0.243836 | ||||||||
\(153\) | −0.513960 | −0.0415512 | ||||||||
\(154\) | 3.71905 | 0.299690 | ||||||||
\(155\) | −18.7423 | −1.50542 | ||||||||
\(156\) | 2.89870 | 0.232082 | ||||||||
\(157\) | −10.5662 | −0.843277 | −0.421638 | − | 0.906764i | \(-0.638545\pi\) | ||||
−0.421638 | + | 0.906764i | \(0.638545\pi\) | |||||||
\(158\) | 9.61800 | 0.765167 | ||||||||
\(159\) | 7.84635 | 0.622256 | ||||||||
\(160\) | −3.46450 | −0.273893 | ||||||||
\(161\) | 1.26047 | 0.0993387 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −22.6547 | −1.77445 | −0.887225 | − | 0.461336i | \(-0.847370\pi\) | ||||
−0.887225 | + | 0.461336i | \(0.847370\pi\) | |||||||
\(164\) | −7.03067 | −0.549003 | ||||||||
\(165\) | 10.2221 | 0.795792 | ||||||||
\(166\) | −0.492258 | −0.0382066 | ||||||||
\(167\) | 9.94700 | 0.769722 | 0.384861 | − | 0.922975i | \(-0.374249\pi\) | ||||
0.384861 | + | 0.922975i | \(0.374249\pi\) | |||||||
\(168\) | 1.26047 | 0.0972471 | ||||||||
\(169\) | −4.59753 | −0.353656 | ||||||||
\(170\) | 1.78061 | 0.136567 | ||||||||
\(171\) | −3.00622 | −0.229891 | ||||||||
\(172\) | −7.06738 | −0.538883 | ||||||||
\(173\) | −8.41406 | −0.639709 | −0.319854 | − | 0.947467i | \(-0.603634\pi\) | ||||
−0.319854 | + | 0.947467i | \(0.603634\pi\) | |||||||
\(174\) | 1.00000 | 0.0758098 | ||||||||
\(175\) | 8.82673 | 0.667238 | ||||||||
\(176\) | −2.95054 | −0.222405 | ||||||||
\(177\) | 4.54958 | 0.341967 | ||||||||
\(178\) | −0.689007 | −0.0516433 | ||||||||
\(179\) | −18.7011 | −1.39779 | −0.698894 | − | 0.715226i | \(-0.746324\pi\) | ||||
−0.698894 | + | 0.715226i | \(0.746324\pi\) | |||||||
\(180\) | 3.46450 | 0.258228 | ||||||||
\(181\) | 14.4459 | 1.07375 | 0.536877 | − | 0.843661i | \(-0.319604\pi\) | ||||
0.536877 | + | 0.843661i | \(0.319604\pi\) | |||||||
\(182\) | 3.65372 | 0.270832 | ||||||||
\(183\) | 7.47147 | 0.552307 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 37.6934 | 2.77127 | ||||||||
\(186\) | −5.40982 | −0.396667 | ||||||||
\(187\) | 1.51646 | 0.110894 | ||||||||
\(188\) | −4.98736 | −0.363741 | ||||||||
\(189\) | −1.26047 | −0.0916855 | ||||||||
\(190\) | 10.4150 | 0.755586 | ||||||||
\(191\) | 18.1975 | 1.31673 | 0.658364 | − | 0.752700i | \(-0.271249\pi\) | ||||
0.658364 | + | 0.752700i | \(0.271249\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −3.83991 | −0.276403 | −0.138201 | − | 0.990404i | \(-0.544132\pi\) | ||||
−0.138201 | + | 0.990404i | \(0.544132\pi\) | |||||||
\(194\) | 2.39041 | 0.171621 | ||||||||
\(195\) | 10.0425 | 0.719162 | ||||||||
\(196\) | −5.41122 | −0.386516 | ||||||||
\(197\) | 2.46376 | 0.175536 | 0.0877679 | − | 0.996141i | \(-0.472027\pi\) | ||||
0.0877679 | + | 0.996141i | \(0.472027\pi\) | |||||||
\(198\) | 2.95054 | 0.209686 | ||||||||
\(199\) | −27.5015 | −1.94953 | −0.974765 | − | 0.223233i | \(-0.928339\pi\) | ||||
−0.974765 | + | 0.223233i | \(0.928339\pi\) | |||||||
\(200\) | −7.00274 | −0.495169 | ||||||||
\(201\) | 8.80796 | 0.621265 | ||||||||
\(202\) | −5.52770 | −0.388927 | ||||||||
\(203\) | 1.26047 | 0.0884674 | ||||||||
\(204\) | 0.513960 | 0.0359844 | ||||||||
\(205\) | −24.3577 | −1.70122 | ||||||||
\(206\) | 1.89297 | 0.131890 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −2.89870 | −0.200989 | ||||||||
\(209\) | 8.86996 | 0.613548 | ||||||||
\(210\) | 4.36688 | 0.301344 | ||||||||
\(211\) | −2.76261 | −0.190186 | −0.0950929 | − | 0.995468i | \(-0.530315\pi\) | ||||
−0.0950929 | + | 0.995468i | \(0.530315\pi\) | |||||||
\(212\) | −7.84635 | −0.538890 | ||||||||
\(213\) | −6.80747 | −0.466440 | ||||||||
\(214\) | −2.57025 | −0.175699 | ||||||||
\(215\) | −24.4849 | −1.66986 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −6.81890 | −0.462897 | ||||||||
\(218\) | −18.5551 | −1.25671 | ||||||||
\(219\) | −2.87765 | −0.194453 | ||||||||
\(220\) | −10.2221 | −0.689176 | ||||||||
\(221\) | 1.48982 | 0.100216 | ||||||||
\(222\) | 10.8799 | 0.730211 | ||||||||
\(223\) | 21.6933 | 1.45269 | 0.726345 | − | 0.687331i | \(-0.241218\pi\) | ||||
0.726345 | + | 0.687331i | \(0.241218\pi\) | |||||||
\(224\) | −1.26047 | −0.0842185 | ||||||||
\(225\) | 7.00274 | 0.466850 | ||||||||
\(226\) | 3.26945 | 0.217481 | ||||||||
\(227\) | 26.6966 | 1.77191 | 0.885956 | − | 0.463769i | \(-0.153503\pi\) | ||||
0.885956 | + | 0.463769i | \(0.153503\pi\) | |||||||
\(228\) | 3.00622 | 0.199092 | ||||||||
\(229\) | −4.48624 | −0.296459 | −0.148230 | − | 0.988953i | \(-0.547357\pi\) | ||||
−0.148230 | + | 0.988953i | \(0.547357\pi\) | |||||||
\(230\) | −3.46450 | −0.228442 | ||||||||
\(231\) | 3.71905 | 0.244696 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −30.0147 | −1.96633 | −0.983164 | − | 0.182727i | \(-0.941508\pi\) | ||||
−0.983164 | + | 0.182727i | \(0.941508\pi\) | |||||||
\(234\) | 2.89870 | 0.189494 | ||||||||
\(235\) | −17.2787 | −1.12714 | ||||||||
\(236\) | −4.54958 | −0.296152 | ||||||||
\(237\) | 9.61800 | 0.624756 | ||||||||
\(238\) | 0.647830 | 0.0419926 | ||||||||
\(239\) | 5.58901 | 0.361523 | 0.180761 | − | 0.983527i | \(-0.442144\pi\) | ||||
0.180761 | + | 0.983527i | \(0.442144\pi\) | |||||||
\(240\) | −3.46450 | −0.223632 | ||||||||
\(241\) | 21.2451 | 1.36852 | 0.684259 | − | 0.729239i | \(-0.260126\pi\) | ||||
0.684259 | + | 0.729239i | \(0.260126\pi\) | |||||||
\(242\) | 2.29433 | 0.147485 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −7.47147 | −0.478312 | ||||||||
\(245\) | −18.7472 | −1.19771 | ||||||||
\(246\) | −7.03067 | −0.448259 | ||||||||
\(247\) | 8.71413 | 0.554467 | ||||||||
\(248\) | 5.40982 | 0.343524 | ||||||||
\(249\) | −0.492258 | −0.0311956 | ||||||||
\(250\) | −6.93850 | −0.438830 | ||||||||
\(251\) | −2.14014 | −0.135084 | −0.0675422 | − | 0.997716i | \(-0.521516\pi\) | ||||
−0.0675422 | + | 0.997716i | \(0.521516\pi\) | |||||||
\(252\) | 1.26047 | 0.0794019 | ||||||||
\(253\) | −2.95054 | −0.185499 | ||||||||
\(254\) | 8.28653 | 0.519943 | ||||||||
\(255\) | 1.78061 | 0.111506 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.3621 | 1.95632 | 0.978158 | − | 0.207862i | \(-0.0666505\pi\) | ||||
0.978158 | + | 0.207862i | \(0.0666505\pi\) | |||||||
\(258\) | −7.06738 | −0.439996 | ||||||||
\(259\) | 13.7138 | 0.852131 | ||||||||
\(260\) | −10.0425 | −0.622812 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | −11.3326 | −0.700128 | ||||||||
\(263\) | −14.8260 | −0.914211 | −0.457106 | − | 0.889412i | \(-0.651114\pi\) | ||||
−0.457106 | + | 0.889412i | \(0.651114\pi\) | |||||||
\(264\) | −2.95054 | −0.181593 | ||||||||
\(265\) | −27.1837 | −1.66988 | ||||||||
\(266\) | 3.78924 | 0.232333 | ||||||||
\(267\) | −0.689007 | −0.0421666 | ||||||||
\(268\) | −8.80796 | −0.538032 | ||||||||
\(269\) | 25.6253 | 1.56240 | 0.781200 | − | 0.624281i | \(-0.214608\pi\) | ||||
0.781200 | + | 0.624281i | \(0.214608\pi\) | |||||||
\(270\) | 3.46450 | 0.210843 | ||||||||
\(271\) | −13.5115 | −0.820764 | −0.410382 | − | 0.911914i | \(-0.634605\pi\) | ||||
−0.410382 | + | 0.911914i | \(0.634605\pi\) | |||||||
\(272\) | −0.513960 | −0.0311634 | ||||||||
\(273\) | 3.65372 | 0.221133 | ||||||||
\(274\) | −9.35007 | −0.564858 | ||||||||
\(275\) | −20.6619 | −1.24596 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | 18.8475 | 1.13244 | 0.566219 | − | 0.824255i | \(-0.308406\pi\) | ||||
0.566219 | + | 0.824255i | \(0.308406\pi\) | |||||||
\(278\) | 5.33044 | 0.319698 | ||||||||
\(279\) | −5.40982 | −0.323877 | ||||||||
\(280\) | −4.36688 | −0.260971 | ||||||||
\(281\) | −22.0826 | −1.31734 | −0.658669 | − | 0.752432i | \(-0.728880\pi\) | ||||
−0.658669 | + | 0.752432i | \(0.728880\pi\) | |||||||
\(282\) | −4.98736 | −0.296993 | ||||||||
\(283\) | 4.52701 | 0.269103 | 0.134551 | − | 0.990907i | \(-0.457041\pi\) | ||||
0.134551 | + | 0.990907i | \(0.457041\pi\) | |||||||
\(284\) | 6.80747 | 0.403949 | ||||||||
\(285\) | 10.4150 | 0.616933 | ||||||||
\(286\) | −8.55273 | −0.505733 | ||||||||
\(287\) | −8.86192 | −0.523103 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −16.7358 | −0.984461 | ||||||||
\(290\) | −3.46450 | −0.203442 | ||||||||
\(291\) | 2.39041 | 0.140128 | ||||||||
\(292\) | 2.87765 | 0.168402 | ||||||||
\(293\) | −14.9075 | −0.870906 | −0.435453 | − | 0.900211i | \(-0.643412\pi\) | ||||
−0.435453 | + | 0.900211i | \(0.643412\pi\) | |||||||
\(294\) | −5.41122 | −0.315589 | ||||||||
\(295\) | −15.7620 | −0.917699 | ||||||||
\(296\) | −10.8799 | −0.632382 | ||||||||
\(297\) | 2.95054 | 0.171208 | ||||||||
\(298\) | 3.37859 | 0.195716 | ||||||||
\(299\) | −2.89870 | −0.167636 | ||||||||
\(300\) | −7.00274 | −0.404304 | ||||||||
\(301\) | −8.90820 | −0.513460 | ||||||||
\(302\) | −11.4581 | −0.659339 | ||||||||
\(303\) | −5.52770 | −0.317558 | ||||||||
\(304\) | −3.00622 | −0.172418 | ||||||||
\(305\) | −25.8849 | −1.48216 | ||||||||
\(306\) | 0.513960 | 0.0293811 | ||||||||
\(307\) | −11.7337 | −0.669679 | −0.334839 | − | 0.942275i | \(-0.608682\pi\) | ||||
−0.334839 | + | 0.942275i | \(0.608682\pi\) | |||||||
\(308\) | −3.71905 | −0.211913 | ||||||||
\(309\) | 1.89297 | 0.107687 | ||||||||
\(310\) | 18.7423 | 1.06449 | ||||||||
\(311\) | −12.9143 | −0.732305 | −0.366152 | − | 0.930555i | \(-0.619325\pi\) | ||||
−0.366152 | + | 0.930555i | \(0.619325\pi\) | |||||||
\(312\) | −2.89870 | −0.164107 | ||||||||
\(313\) | −31.6900 | −1.79122 | −0.895612 | − | 0.444836i | \(-0.853262\pi\) | ||||
−0.895612 | + | 0.444836i | \(0.853262\pi\) | |||||||
\(314\) | 10.5662 | 0.596287 | ||||||||
\(315\) | 4.36688 | 0.246046 | ||||||||
\(316\) | −9.61800 | −0.541055 | ||||||||
\(317\) | 7.67149 | 0.430874 | 0.215437 | − | 0.976518i | \(-0.430882\pi\) | ||||
0.215437 | + | 0.976518i | \(0.430882\pi\) | |||||||
\(318\) | −7.84635 | −0.440002 | ||||||||
\(319\) | −2.95054 | −0.165198 | ||||||||
\(320\) | 3.46450 | 0.193671 | ||||||||
\(321\) | −2.57025 | −0.143458 | ||||||||
\(322\) | −1.26047 | −0.0702431 | ||||||||
\(323\) | 1.54508 | 0.0859703 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −20.2989 | −1.12598 | ||||||||
\(326\) | 22.6547 | 1.25473 | ||||||||
\(327\) | −18.5551 | −1.02610 | ||||||||
\(328\) | 7.03067 | 0.388204 | ||||||||
\(329\) | −6.28640 | −0.346580 | ||||||||
\(330\) | −10.2221 | −0.562710 | ||||||||
\(331\) | 8.13519 | 0.447151 | 0.223575 | − | 0.974687i | \(-0.428227\pi\) | ||||
0.223575 | + | 0.974687i | \(0.428227\pi\) | |||||||
\(332\) | 0.492258 | 0.0270162 | ||||||||
\(333\) | 10.8799 | 0.596215 | ||||||||
\(334\) | −9.94700 | −0.544276 | ||||||||
\(335\) | −30.5151 | −1.66722 | ||||||||
\(336\) | −1.26047 | −0.0687641 | ||||||||
\(337\) | −29.0056 | −1.58004 | −0.790018 | − | 0.613084i | \(-0.789929\pi\) | ||||
−0.790018 | + | 0.613084i | \(0.789929\pi\) | |||||||
\(338\) | 4.59753 | 0.250072 | ||||||||
\(339\) | 3.26945 | 0.177572 | ||||||||
\(340\) | −1.78061 | −0.0965673 | ||||||||
\(341\) | 15.9619 | 0.864384 | ||||||||
\(342\) | 3.00622 | 0.162558 | ||||||||
\(343\) | −15.6439 | −0.844693 | ||||||||
\(344\) | 7.06738 | 0.381048 | ||||||||
\(345\) | −3.46450 | −0.186522 | ||||||||
\(346\) | 8.41406 | 0.452343 | ||||||||
\(347\) | 4.85006 | 0.260365 | 0.130182 | − | 0.991490i | \(-0.458444\pi\) | ||||
0.130182 | + | 0.991490i | \(0.458444\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | 26.2742 | 1.40642 | 0.703212 | − | 0.710980i | \(-0.251748\pi\) | ||||
0.703212 | + | 0.710980i | \(0.251748\pi\) | |||||||
\(350\) | −8.82673 | −0.471808 | ||||||||
\(351\) | 2.89870 | 0.154721 | ||||||||
\(352\) | 2.95054 | 0.157264 | ||||||||
\(353\) | 12.6947 | 0.675670 | 0.337835 | − | 0.941205i | \(-0.390305\pi\) | ||||
0.337835 | + | 0.941205i | \(0.390305\pi\) | |||||||
\(354\) | −4.54958 | −0.241807 | ||||||||
\(355\) | 23.5845 | 1.25173 | ||||||||
\(356\) | 0.689007 | 0.0365173 | ||||||||
\(357\) | 0.647830 | 0.0342868 | ||||||||
\(358\) | 18.7011 | 0.988385 | ||||||||
\(359\) | 7.06962 | 0.373121 | 0.186560 | − | 0.982444i | \(-0.440266\pi\) | ||||
0.186560 | + | 0.982444i | \(0.440266\pi\) | |||||||
\(360\) | −3.46450 | −0.182595 | ||||||||
\(361\) | −9.96265 | −0.524350 | ||||||||
\(362\) | −14.4459 | −0.759258 | ||||||||
\(363\) | 2.29433 | 0.120421 | ||||||||
\(364\) | −3.65372 | −0.191507 | ||||||||
\(365\) | 9.96961 | 0.521833 | ||||||||
\(366\) | −7.47147 | −0.390540 | ||||||||
\(367\) | −38.1414 | −1.99096 | −0.995481 | − | 0.0949576i | \(-0.969728\pi\) | ||||
−0.995481 | + | 0.0949576i | \(0.969728\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −7.03067 | −0.366002 | ||||||||
\(370\) | −37.6934 | −1.95959 | ||||||||
\(371\) | −9.89007 | −0.513467 | ||||||||
\(372\) | 5.40982 | 0.280486 | ||||||||
\(373\) | −33.0377 | −1.71063 | −0.855315 | − | 0.518109i | \(-0.826636\pi\) | ||||
−0.855315 | + | 0.518109i | \(0.826636\pi\) | |||||||
\(374\) | −1.51646 | −0.0784142 | ||||||||
\(375\) | −6.93850 | −0.358303 | ||||||||
\(376\) | 4.98736 | 0.257203 | ||||||||
\(377\) | −2.89870 | −0.149291 | ||||||||
\(378\) | 1.26047 | 0.0648314 | ||||||||
\(379\) | 4.28909 | 0.220316 | 0.110158 | − | 0.993914i | \(-0.464864\pi\) | ||||
0.110158 | + | 0.993914i | \(0.464864\pi\) | |||||||
\(380\) | −10.4150 | −0.534280 | ||||||||
\(381\) | 8.28653 | 0.424532 | ||||||||
\(382\) | −18.1975 | −0.931067 | ||||||||
\(383\) | 22.5405 | 1.15177 | 0.575884 | − | 0.817531i | \(-0.304658\pi\) | ||||
0.575884 | + | 0.817531i | \(0.304658\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −12.8847 | −0.656663 | ||||||||
\(386\) | 3.83991 | 0.195446 | ||||||||
\(387\) | −7.06738 | −0.359255 | ||||||||
\(388\) | −2.39041 | −0.121355 | ||||||||
\(389\) | 36.1082 | 1.83076 | 0.915380 | − | 0.402590i | \(-0.131890\pi\) | ||||
0.915380 | + | 0.402590i | \(0.131890\pi\) | |||||||
\(390\) | −10.0425 | −0.508524 | ||||||||
\(391\) | −0.513960 | −0.0259921 | ||||||||
\(392\) | 5.41122 | 0.273308 | ||||||||
\(393\) | −11.3326 | −0.571652 | ||||||||
\(394\) | −2.46376 | −0.124123 | ||||||||
\(395\) | −33.3215 | −1.67659 | ||||||||
\(396\) | −2.95054 | −0.148270 | ||||||||
\(397\) | −4.49868 | −0.225782 | −0.112891 | − | 0.993607i | \(-0.536011\pi\) | ||||
−0.112891 | + | 0.993607i | \(0.536011\pi\) | |||||||
\(398\) | 27.5015 | 1.37853 | ||||||||
\(399\) | 3.78924 | 0.189699 | ||||||||
\(400\) | 7.00274 | 0.350137 | ||||||||
\(401\) | 18.7098 | 0.934321 | 0.467160 | − | 0.884173i | \(-0.345277\pi\) | ||||
0.467160 | + | 0.884173i | \(0.345277\pi\) | |||||||
\(402\) | −8.80796 | −0.439301 | ||||||||
\(403\) | 15.6815 | 0.781149 | ||||||||
\(404\) | 5.52770 | 0.275013 | ||||||||
\(405\) | 3.46450 | 0.172152 | ||||||||
\(406\) | −1.26047 | −0.0625559 | ||||||||
\(407\) | −32.1016 | −1.59122 | ||||||||
\(408\) | −0.513960 | −0.0254448 | ||||||||
\(409\) | −11.9465 | −0.590718 | −0.295359 | − | 0.955386i | \(-0.595439\pi\) | ||||
−0.295359 | + | 0.955386i | \(0.595439\pi\) | |||||||
\(410\) | 24.3577 | 1.20294 | ||||||||
\(411\) | −9.35007 | −0.461205 | ||||||||
\(412\) | −1.89297 | −0.0932601 | ||||||||
\(413\) | −5.73459 | −0.282181 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 1.70543 | 0.0837161 | ||||||||
\(416\) | 2.89870 | 0.142121 | ||||||||
\(417\) | 5.33044 | 0.261033 | ||||||||
\(418\) | −8.86996 | −0.433844 | ||||||||
\(419\) | 30.4419 | 1.48718 | 0.743591 | − | 0.668634i | \(-0.233121\pi\) | ||||
0.743591 | + | 0.668634i | \(0.233121\pi\) | |||||||
\(420\) | −4.36688 | −0.213082 | ||||||||
\(421\) | 35.5601 | 1.73309 | 0.866546 | − | 0.499098i | \(-0.166335\pi\) | ||||
0.866546 | + | 0.499098i | \(0.166335\pi\) | |||||||
\(422\) | 2.76261 | 0.134482 | ||||||||
\(423\) | −4.98736 | −0.242494 | ||||||||
\(424\) | 7.84635 | 0.381053 | ||||||||
\(425\) | −3.59913 | −0.174584 | ||||||||
\(426\) | 6.80747 | 0.329823 | ||||||||
\(427\) | −9.41754 | −0.455747 | ||||||||
\(428\) | 2.57025 | 0.124238 | ||||||||
\(429\) | −8.55273 | −0.412930 | ||||||||
\(430\) | 24.4849 | 1.18077 | ||||||||
\(431\) | −16.2501 | −0.782742 | −0.391371 | − | 0.920233i | \(-0.627999\pi\) | ||||
−0.391371 | + | 0.920233i | \(0.627999\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 21.5186 | 1.03412 | 0.517059 | − | 0.855950i | \(-0.327027\pi\) | ||||
0.517059 | + | 0.855950i | \(0.327027\pi\) | |||||||
\(434\) | 6.81890 | 0.327318 | ||||||||
\(435\) | −3.46450 | −0.166110 | ||||||||
\(436\) | 18.5551 | 0.888628 | ||||||||
\(437\) | −3.00622 | −0.143807 | ||||||||
\(438\) | 2.87765 | 0.137499 | ||||||||
\(439\) | 7.30169 | 0.348491 | 0.174245 | − | 0.984702i | \(-0.444251\pi\) | ||||
0.174245 | + | 0.984702i | \(0.444251\pi\) | |||||||
\(440\) | 10.2221 | 0.487321 | ||||||||
\(441\) | −5.41122 | −0.257677 | ||||||||
\(442\) | −1.48982 | −0.0708634 | ||||||||
\(443\) | −16.1535 | −0.767476 | −0.383738 | − | 0.923442i | \(-0.625363\pi\) | ||||
−0.383738 | + | 0.923442i | \(0.625363\pi\) | |||||||
\(444\) | −10.8799 | −0.516337 | ||||||||
\(445\) | 2.38706 | 0.113158 | ||||||||
\(446\) | −21.6933 | −1.02721 | ||||||||
\(447\) | 3.37859 | 0.159802 | ||||||||
\(448\) | 1.26047 | 0.0595515 | ||||||||
\(449\) | 2.04485 | 0.0965025 | 0.0482512 | − | 0.998835i | \(-0.484635\pi\) | ||||
0.0482512 | + | 0.998835i | \(0.484635\pi\) | |||||||
\(450\) | −7.00274 | −0.330113 | ||||||||
\(451\) | 20.7442 | 0.976808 | ||||||||
\(452\) | −3.26945 | −0.153782 | ||||||||
\(453\) | −11.4581 | −0.538348 | ||||||||
\(454\) | −26.6966 | −1.25293 | ||||||||
\(455\) | −12.6583 | −0.593430 | ||||||||
\(456\) | −3.00622 | −0.140779 | ||||||||
\(457\) | −26.9698 | −1.26160 | −0.630798 | − | 0.775947i | \(-0.717272\pi\) | ||||
−0.630798 | + | 0.775947i | \(0.717272\pi\) | |||||||
\(458\) | 4.48624 | 0.209628 | ||||||||
\(459\) | 0.513960 | 0.0239896 | ||||||||
\(460\) | 3.46450 | 0.161533 | ||||||||
\(461\) | 1.44799 | 0.0674395 | 0.0337197 | − | 0.999431i | \(-0.489265\pi\) | ||||
0.0337197 | + | 0.999431i | \(0.489265\pi\) | |||||||
\(462\) | −3.71905 | −0.173026 | ||||||||
\(463\) | −27.3529 | −1.27120 | −0.635598 | − | 0.772020i | \(-0.719246\pi\) | ||||
−0.635598 | + | 0.772020i | \(0.719246\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 18.7423 | 0.869154 | ||||||||
\(466\) | 30.0147 | 1.39040 | ||||||||
\(467\) | 5.17174 | 0.239320 | 0.119660 | − | 0.992815i | \(-0.461820\pi\) | ||||
0.119660 | + | 0.992815i | \(0.461820\pi\) | |||||||
\(468\) | −2.89870 | −0.133993 | ||||||||
\(469\) | −11.1021 | −0.512649 | ||||||||
\(470\) | 17.2787 | 0.797007 | ||||||||
\(471\) | 10.5662 | 0.486866 | ||||||||
\(472\) | 4.54958 | 0.209411 | ||||||||
\(473\) | 20.8526 | 0.958802 | ||||||||
\(474\) | −9.61800 | −0.441769 | ||||||||
\(475\) | −21.0518 | −0.965922 | ||||||||
\(476\) | −0.647830 | −0.0296932 | ||||||||
\(477\) | −7.84635 | −0.359260 | ||||||||
\(478\) | −5.58901 | −0.255635 | ||||||||
\(479\) | 13.5202 | 0.617754 | 0.308877 | − | 0.951102i | \(-0.400047\pi\) | ||||
0.308877 | + | 0.951102i | \(0.400047\pi\) | |||||||
\(480\) | 3.46450 | 0.158132 | ||||||||
\(481\) | −31.5376 | −1.43799 | ||||||||
\(482\) | −21.2451 | −0.967688 | ||||||||
\(483\) | −1.26047 | −0.0573532 | ||||||||
\(484\) | −2.29433 | −0.104288 | ||||||||
\(485\) | −8.28156 | −0.376046 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −6.08871 | −0.275906 | −0.137953 | − | 0.990439i | \(-0.544052\pi\) | ||||
−0.137953 | + | 0.990439i | \(0.544052\pi\) | |||||||
\(488\) | 7.47147 | 0.338218 | ||||||||
\(489\) | 22.6547 | 1.02448 | ||||||||
\(490\) | 18.7472 | 0.846911 | ||||||||
\(491\) | −43.4519 | −1.96096 | −0.980479 | − | 0.196622i | \(-0.937003\pi\) | ||||
−0.980479 | + | 0.196622i | \(0.937003\pi\) | |||||||
\(492\) | 7.03067 | 0.316967 | ||||||||
\(493\) | −0.513960 | −0.0231476 | ||||||||
\(494\) | −8.71413 | −0.392067 | ||||||||
\(495\) | −10.2221 | −0.459451 | ||||||||
\(496\) | −5.40982 | −0.242908 | ||||||||
\(497\) | 8.58059 | 0.384892 | ||||||||
\(498\) | 0.492258 | 0.0220586 | ||||||||
\(499\) | −13.3105 | −0.595859 | −0.297929 | − | 0.954588i | \(-0.596296\pi\) | ||||
−0.297929 | + | 0.954588i | \(0.596296\pi\) | |||||||
\(500\) | 6.93850 | 0.310299 | ||||||||
\(501\) | −9.94700 | −0.444399 | ||||||||
\(502\) | 2.14014 | 0.0955191 | ||||||||
\(503\) | −35.6652 | −1.59023 | −0.795117 | − | 0.606456i | \(-0.792590\pi\) | ||||
−0.795117 | + | 0.606456i | \(0.792590\pi\) | |||||||
\(504\) | −1.26047 | −0.0561457 | ||||||||
\(505\) | 19.1507 | 0.852194 | ||||||||
\(506\) | 2.95054 | 0.131167 | ||||||||
\(507\) | 4.59753 | 0.204183 | ||||||||
\(508\) | −8.28653 | −0.367655 | ||||||||
\(509\) | −6.42583 | −0.284820 | −0.142410 | − | 0.989808i | \(-0.545485\pi\) | ||||
−0.142410 | + | 0.989808i | \(0.545485\pi\) | |||||||
\(510\) | −1.78061 | −0.0788469 | ||||||||
\(511\) | 3.62718 | 0.160457 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 3.00622 | 0.132728 | ||||||||
\(514\) | −31.3621 | −1.38332 | ||||||||
\(515\) | −6.55820 | −0.288989 | ||||||||
\(516\) | 7.06738 | 0.311124 | ||||||||
\(517\) | 14.7154 | 0.647182 | ||||||||
\(518\) | −13.7138 | −0.602548 | ||||||||
\(519\) | 8.41406 | 0.369336 | ||||||||
\(520\) | 10.0425 | 0.440395 | ||||||||
\(521\) | 8.10399 | 0.355042 | 0.177521 | − | 0.984117i | \(-0.443192\pi\) | ||||
0.177521 | + | 0.984117i | \(0.443192\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | −30.8590 | −1.34937 | −0.674684 | − | 0.738106i | \(-0.735720\pi\) | ||||
−0.674684 | + | 0.738106i | \(0.735720\pi\) | |||||||
\(524\) | 11.3326 | 0.495065 | ||||||||
\(525\) | −8.82673 | −0.385230 | ||||||||
\(526\) | 14.8260 | 0.646445 | ||||||||
\(527\) | 2.78043 | 0.121117 | ||||||||
\(528\) | 2.95054 | 0.128406 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 27.1837 | 1.18078 | ||||||||
\(531\) | −4.54958 | −0.197435 | ||||||||
\(532\) | −3.78924 | −0.164284 | ||||||||
\(533\) | 20.3798 | 0.882747 | ||||||||
\(534\) | 0.689007 | 0.0298163 | ||||||||
\(535\) | 8.90464 | 0.384981 | ||||||||
\(536\) | 8.80796 | 0.380446 | ||||||||
\(537\) | 18.7011 | 0.807013 | ||||||||
\(538\) | −25.6253 | −1.10478 | ||||||||
\(539\) | 15.9660 | 0.687705 | ||||||||
\(540\) | −3.46450 | −0.149088 | ||||||||
\(541\) | −3.31760 | −0.142635 | −0.0713175 | − | 0.997454i | \(-0.522720\pi\) | ||||
−0.0713175 | + | 0.997454i | \(0.522720\pi\) | |||||||
\(542\) | 13.5115 | 0.580368 | ||||||||
\(543\) | −14.4459 | −0.619932 | ||||||||
\(544\) | 0.513960 | 0.0220359 | ||||||||
\(545\) | 64.2841 | 2.75363 | ||||||||
\(546\) | −3.65372 | −0.156365 | ||||||||
\(547\) | −9.46622 | −0.404746 | −0.202373 | − | 0.979308i | \(-0.564865\pi\) | ||||
−0.202373 | + | 0.979308i | \(0.564865\pi\) | |||||||
\(548\) | 9.35007 | 0.399415 | ||||||||
\(549\) | −7.47147 | −0.318875 | ||||||||
\(550\) | 20.6619 | 0.881025 | ||||||||
\(551\) | −3.00622 | −0.128069 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −12.1232 | −0.515530 | ||||||||
\(554\) | −18.8475 | −0.800754 | ||||||||
\(555\) | −37.6934 | −1.60000 | ||||||||
\(556\) | −5.33044 | −0.226061 | ||||||||
\(557\) | 19.6472 | 0.832477 | 0.416238 | − | 0.909256i | \(-0.363348\pi\) | ||||
0.416238 | + | 0.909256i | \(0.363348\pi\) | |||||||
\(558\) | 5.40982 | 0.229016 | ||||||||
\(559\) | 20.4862 | 0.866475 | ||||||||
\(560\) | 4.36688 | 0.184535 | ||||||||
\(561\) | −1.51646 | −0.0640249 | ||||||||
\(562\) | 22.0826 | 0.931499 | ||||||||
\(563\) | 22.8751 | 0.964069 | 0.482034 | − | 0.876152i | \(-0.339898\pi\) | ||||
0.482034 | + | 0.876152i | \(0.339898\pi\) | |||||||
\(564\) | 4.98736 | 0.210006 | ||||||||
\(565\) | −11.3270 | −0.476531 | ||||||||
\(566\) | −4.52701 | −0.190284 | ||||||||
\(567\) | 1.26047 | 0.0529346 | ||||||||
\(568\) | −6.80747 | −0.285635 | ||||||||
\(569\) | −21.5814 | −0.904741 | −0.452371 | − | 0.891830i | \(-0.649422\pi\) | ||||
−0.452371 | + | 0.891830i | \(0.649422\pi\) | |||||||
\(570\) | −10.4150 | −0.436238 | ||||||||
\(571\) | −28.2634 | −1.18279 | −0.591394 | − | 0.806383i | \(-0.701422\pi\) | ||||
−0.591394 | + | 0.806383i | \(0.701422\pi\) | |||||||
\(572\) | 8.55273 | 0.357608 | ||||||||
\(573\) | −18.1975 | −0.760213 | ||||||||
\(574\) | 8.86192 | 0.369889 | ||||||||
\(575\) | 7.00274 | 0.292035 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −31.5236 | −1.31234 | −0.656172 | − | 0.754611i | \(-0.727825\pi\) | ||||
−0.656172 | + | 0.754611i | \(0.727825\pi\) | |||||||
\(578\) | 16.7358 | 0.696119 | ||||||||
\(579\) | 3.83991 | 0.159581 | ||||||||
\(580\) | 3.46450 | 0.143855 | ||||||||
\(581\) | 0.620475 | 0.0257416 | ||||||||
\(582\) | −2.39041 | −0.0990856 | ||||||||
\(583\) | 23.1510 | 0.958815 | ||||||||
\(584\) | −2.87765 | −0.119078 | ||||||||
\(585\) | −10.0425 | −0.415208 | ||||||||
\(586\) | 14.9075 | 0.615824 | ||||||||
\(587\) | −9.43352 | −0.389363 | −0.194681 | − | 0.980867i | \(-0.562367\pi\) | ||||
−0.194681 | + | 0.980867i | \(0.562367\pi\) | |||||||
\(588\) | 5.41122 | 0.223155 | ||||||||
\(589\) | 16.2631 | 0.670109 | ||||||||
\(590\) | 15.7620 | 0.648911 | ||||||||
\(591\) | −2.46376 | −0.101346 | ||||||||
\(592\) | 10.8799 | 0.447161 | ||||||||
\(593\) | −6.36764 | −0.261488 | −0.130744 | − | 0.991416i | \(-0.541737\pi\) | ||||
−0.130744 | + | 0.991416i | \(0.541737\pi\) | |||||||
\(594\) | −2.95054 | −0.121062 | ||||||||
\(595\) | −2.24440 | −0.0920116 | ||||||||
\(596\) | −3.37859 | −0.138392 | ||||||||
\(597\) | 27.5015 | 1.12556 | ||||||||
\(598\) | 2.89870 | 0.118537 | ||||||||
\(599\) | −12.4811 | −0.509964 | −0.254982 | − | 0.966946i | \(-0.582070\pi\) | ||||
−0.254982 | + | 0.966946i | \(0.582070\pi\) | |||||||
\(600\) | 7.00274 | 0.285886 | ||||||||
\(601\) | 19.9100 | 0.812147 | 0.406074 | − | 0.913840i | \(-0.366898\pi\) | ||||
0.406074 | + | 0.913840i | \(0.366898\pi\) | |||||||
\(602\) | 8.90820 | 0.363071 | ||||||||
\(603\) | −8.80796 | −0.358688 | ||||||||
\(604\) | 11.4581 | 0.466223 | ||||||||
\(605\) | −7.94869 | −0.323160 | ||||||||
\(606\) | 5.52770 | 0.224547 | ||||||||
\(607\) | −5.64098 | −0.228960 | −0.114480 | − | 0.993426i | \(-0.536520\pi\) | ||||
−0.114480 | + | 0.993426i | \(0.536520\pi\) | |||||||
\(608\) | 3.00622 | 0.121918 | ||||||||
\(609\) | −1.26047 | −0.0510767 | ||||||||
\(610\) | 25.8849 | 1.04805 | ||||||||
\(611\) | 14.4569 | 0.584862 | ||||||||
\(612\) | −0.513960 | −0.0207756 | ||||||||
\(613\) | 6.27248 | 0.253343 | 0.126671 | − | 0.991945i | \(-0.459571\pi\) | ||||
0.126671 | + | 0.991945i | \(0.459571\pi\) | |||||||
\(614\) | 11.7337 | 0.473534 | ||||||||
\(615\) | 24.3577 | 0.982198 | ||||||||
\(616\) | 3.71905 | 0.149845 | ||||||||
\(617\) | 7.90980 | 0.318436 | 0.159218 | − | 0.987243i | \(-0.449103\pi\) | ||||
0.159218 | + | 0.987243i | \(0.449103\pi\) | |||||||
\(618\) | −1.89297 | −0.0761465 | ||||||||
\(619\) | −11.2820 | −0.453460 | −0.226730 | − | 0.973958i | \(-0.572804\pi\) | ||||
−0.226730 | + | 0.973958i | \(0.572804\pi\) | |||||||
\(620\) | −18.7423 | −0.752709 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | 12.9143 | 0.517818 | ||||||||
\(623\) | 0.868471 | 0.0347945 | ||||||||
\(624\) | 2.89870 | 0.116041 | ||||||||
\(625\) | −10.9753 | −0.439012 | ||||||||
\(626\) | 31.6900 | 1.26659 | ||||||||
\(627\) | −8.86996 | −0.354232 | ||||||||
\(628\) | −10.5662 | −0.421638 | ||||||||
\(629\) | −5.59184 | −0.222961 | ||||||||
\(630\) | −4.36688 | −0.173981 | ||||||||
\(631\) | 28.2132 | 1.12315 | 0.561574 | − | 0.827426i | \(-0.310196\pi\) | ||||
0.561574 | + | 0.827426i | \(0.310196\pi\) | |||||||
\(632\) | 9.61800 | 0.382584 | ||||||||
\(633\) | 2.76261 | 0.109804 | ||||||||
\(634\) | −7.67149 | −0.304674 | ||||||||
\(635\) | −28.7087 | −1.13927 | ||||||||
\(636\) | 7.84635 | 0.311128 | ||||||||
\(637\) | 15.6855 | 0.621483 | ||||||||
\(638\) | 2.95054 | 0.116813 | ||||||||
\(639\) | 6.80747 | 0.269299 | ||||||||
\(640\) | −3.46450 | −0.136946 | ||||||||
\(641\) | 49.8933 | 1.97067 | 0.985333 | − | 0.170642i | \(-0.0545843\pi\) | ||||
0.985333 | + | 0.170642i | \(0.0545843\pi\) | |||||||
\(642\) | 2.57025 | 0.101440 | ||||||||
\(643\) | −2.02052 | −0.0796814 | −0.0398407 | − | 0.999206i | \(-0.512685\pi\) | ||||
−0.0398407 | + | 0.999206i | \(0.512685\pi\) | |||||||
\(644\) | 1.26047 | 0.0496694 | ||||||||
\(645\) | 24.4849 | 0.964093 | ||||||||
\(646\) | −1.54508 | −0.0607902 | ||||||||
\(647\) | 0.309658 | 0.0121739 | 0.00608696 | − | 0.999981i | \(-0.498062\pi\) | ||||
0.00608696 | + | 0.999981i | \(0.498062\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | 13.4237 | 0.526926 | ||||||||
\(650\) | 20.2989 | 0.796187 | ||||||||
\(651\) | 6.81890 | 0.267254 | ||||||||
\(652\) | −22.6547 | −0.887225 | ||||||||
\(653\) | 28.5490 | 1.11721 | 0.558604 | − | 0.829434i | \(-0.311337\pi\) | ||||
0.558604 | + | 0.829434i | \(0.311337\pi\) | |||||||
\(654\) | 18.5551 | 0.725562 | ||||||||
\(655\) | 39.2616 | 1.53408 | ||||||||
\(656\) | −7.03067 | −0.274501 | ||||||||
\(657\) | 2.87765 | 0.112268 | ||||||||
\(658\) | 6.28640 | 0.245069 | ||||||||
\(659\) | −21.4565 | −0.835828 | −0.417914 | − | 0.908487i | \(-0.637239\pi\) | ||||
−0.417914 | + | 0.908487i | \(0.637239\pi\) | |||||||
\(660\) | 10.2221 | 0.397896 | ||||||||
\(661\) | −13.7477 | −0.534723 | −0.267362 | − | 0.963596i | \(-0.586152\pi\) | ||||
−0.267362 | + | 0.963596i | \(0.586152\pi\) | |||||||
\(662\) | −8.13519 | −0.316183 | ||||||||
\(663\) | −1.48982 | −0.0578597 | ||||||||
\(664\) | −0.492258 | −0.0191033 | ||||||||
\(665\) | −13.1278 | −0.509074 | ||||||||
\(666\) | −10.8799 | −0.421588 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 9.94700 | 0.384861 | ||||||||
\(669\) | −21.6933 | −0.838711 | ||||||||
\(670\) | 30.5151 | 1.17890 | ||||||||
\(671\) | 22.0449 | 0.851032 | ||||||||
\(672\) | 1.26047 | 0.0486236 | ||||||||
\(673\) | −5.90609 | −0.227663 | −0.113831 | − | 0.993500i | \(-0.536312\pi\) | ||||
−0.113831 | + | 0.993500i | \(0.536312\pi\) | |||||||
\(674\) | 29.0056 | 1.11725 | ||||||||
\(675\) | −7.00274 | −0.269536 | ||||||||
\(676\) | −4.59753 | −0.176828 | ||||||||
\(677\) | −7.44020 | −0.285950 | −0.142975 | − | 0.989726i | \(-0.545667\pi\) | ||||
−0.142975 | + | 0.989726i | \(0.545667\pi\) | |||||||
\(678\) | −3.26945 | −0.125563 | ||||||||
\(679\) | −3.01303 | −0.115629 | ||||||||
\(680\) | 1.78061 | 0.0682834 | ||||||||
\(681\) | −26.6966 | −1.02301 | ||||||||
\(682\) | −15.9619 | −0.611212 | ||||||||
\(683\) | 9.21980 | 0.352786 | 0.176393 | − | 0.984320i | \(-0.443557\pi\) | ||||
0.176393 | + | 0.984320i | \(0.443557\pi\) | |||||||
\(684\) | −3.00622 | −0.114946 | ||||||||
\(685\) | 32.3933 | 1.23768 | ||||||||
\(686\) | 15.6439 | 0.597288 | ||||||||
\(687\) | 4.48624 | 0.171161 | ||||||||
\(688\) | −7.06738 | −0.269441 | ||||||||
\(689\) | 22.7442 | 0.866487 | ||||||||
\(690\) | 3.46450 | 0.131891 | ||||||||
\(691\) | 28.3126 | 1.07706 | 0.538531 | − | 0.842606i | \(-0.318979\pi\) | ||||
0.538531 | + | 0.842606i | \(0.318979\pi\) | |||||||
\(692\) | −8.41406 | −0.319854 | ||||||||
\(693\) | −3.71905 | −0.141275 | ||||||||
\(694\) | −4.85006 | −0.184106 | ||||||||
\(695\) | −18.4673 | −0.700504 | ||||||||
\(696\) | 1.00000 | 0.0379049 | ||||||||
\(697\) | 3.61348 | 0.136870 | ||||||||
\(698\) | −26.2742 | −0.994492 | ||||||||
\(699\) | 30.0147 | 1.13526 | ||||||||
\(700\) | 8.82673 | 0.333619 | ||||||||
\(701\) | −27.6327 | −1.04367 | −0.521836 | − | 0.853046i | \(-0.674753\pi\) | ||||
−0.521836 | + | 0.853046i | \(0.674753\pi\) | |||||||
\(702\) | −2.89870 | −0.109404 | ||||||||
\(703\) | −32.7074 | −1.23358 | ||||||||
\(704\) | −2.95054 | −0.111203 | ||||||||
\(705\) | 17.2787 | 0.650753 | ||||||||
\(706\) | −12.6947 | −0.477771 | ||||||||
\(707\) | 6.96748 | 0.262039 | ||||||||
\(708\) | 4.54958 | 0.170984 | ||||||||
\(709\) | 35.8916 | 1.34794 | 0.673968 | − | 0.738760i | \(-0.264588\pi\) | ||||
0.673968 | + | 0.738760i | \(0.264588\pi\) | |||||||
\(710\) | −23.5845 | −0.885109 | ||||||||
\(711\) | −9.61800 | −0.360703 | ||||||||
\(712\) | −0.689007 | −0.0258216 | ||||||||
\(713\) | −5.40982 | −0.202599 | ||||||||
\(714\) | −0.647830 | −0.0242444 | ||||||||
\(715\) | 29.6309 | 1.10813 | ||||||||
\(716\) | −18.7011 | −0.698894 | ||||||||
\(717\) | −5.58901 | −0.208725 | ||||||||
\(718\) | −7.06962 | −0.263836 | ||||||||
\(719\) | 45.7915 | 1.70774 | 0.853868 | − | 0.520490i | \(-0.174251\pi\) | ||||
0.853868 | + | 0.520490i | \(0.174251\pi\) | |||||||
\(720\) | 3.46450 | 0.129114 | ||||||||
\(721\) | −2.38603 | −0.0888604 | ||||||||
\(722\) | 9.96265 | 0.370772 | ||||||||
\(723\) | −21.2451 | −0.790114 | ||||||||
\(724\) | 14.4459 | 0.536877 | ||||||||
\(725\) | 7.00274 | 0.260075 | ||||||||
\(726\) | −2.29433 | −0.0851505 | ||||||||
\(727\) | 19.0240 | 0.705562 | 0.352781 | − | 0.935706i | \(-0.385236\pi\) | ||||
0.352781 | + | 0.935706i | \(0.385236\pi\) | |||||||
\(728\) | 3.65372 | 0.135416 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.96961 | −0.368992 | ||||||||
\(731\) | 3.63235 | 0.134347 | ||||||||
\(732\) | 7.47147 | 0.276154 | ||||||||
\(733\) | −18.9003 | −0.698100 | −0.349050 | − | 0.937104i | \(-0.613496\pi\) | ||||
−0.349050 | + | 0.937104i | \(0.613496\pi\) | |||||||
\(734\) | 38.1414 | 1.40782 | ||||||||
\(735\) | 18.7472 | 0.691500 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 25.9882 | 0.957288 | ||||||||
\(738\) | 7.03067 | 0.258802 | ||||||||
\(739\) | −4.30945 | −0.158526 | −0.0792628 | − | 0.996854i | \(-0.525257\pi\) | ||||
−0.0792628 | + | 0.996854i | \(0.525257\pi\) | |||||||
\(740\) | 37.6934 | 1.38564 | ||||||||
\(741\) | −8.71413 | −0.320122 | ||||||||
\(742\) | 9.89007 | 0.363076 | ||||||||
\(743\) | −23.7569 | −0.871555 | −0.435777 | − | 0.900055i | \(-0.643526\pi\) | ||||
−0.435777 | + | 0.900055i | \(0.643526\pi\) | |||||||
\(744\) | −5.40982 | −0.198334 | ||||||||
\(745\) | −11.7051 | −0.428842 | ||||||||
\(746\) | 33.0377 | 1.20960 | ||||||||
\(747\) | 0.492258 | 0.0180108 | ||||||||
\(748\) | 1.51646 | 0.0554472 | ||||||||
\(749\) | 3.23972 | 0.118377 | ||||||||
\(750\) | 6.93850 | 0.253358 | ||||||||
\(751\) | 21.6384 | 0.789597 | 0.394799 | − | 0.918768i | \(-0.370814\pi\) | ||||
0.394799 | + | 0.918768i | \(0.370814\pi\) | |||||||
\(752\) | −4.98736 | −0.181870 | ||||||||
\(753\) | 2.14014 | 0.0779910 | ||||||||
\(754\) | 2.89870 | 0.105565 | ||||||||
\(755\) | 39.6965 | 1.44471 | ||||||||
\(756\) | −1.26047 | −0.0458427 | ||||||||
\(757\) | −35.9444 | −1.30642 | −0.653210 | − | 0.757176i | \(-0.726578\pi\) | ||||
−0.653210 | + | 0.757176i | \(0.726578\pi\) | |||||||
\(758\) | −4.28909 | −0.155787 | ||||||||
\(759\) | 2.95054 | 0.107098 | ||||||||
\(760\) | 10.4150 | 0.377793 | ||||||||
\(761\) | 1.00077 | 0.0362778 | 0.0181389 | − | 0.999835i | \(-0.494226\pi\) | ||||
0.0181389 | + | 0.999835i | \(0.494226\pi\) | |||||||
\(762\) | −8.28653 | −0.300189 | ||||||||
\(763\) | 23.3881 | 0.846706 | ||||||||
\(764\) | 18.1975 | 0.658364 | ||||||||
\(765\) | −1.78061 | −0.0643782 | ||||||||
\(766\) | −22.5405 | −0.814423 | ||||||||
\(767\) | 13.1879 | 0.476186 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −16.7679 | −0.604664 | −0.302332 | − | 0.953203i | \(-0.597765\pi\) | ||||
−0.302332 | + | 0.953203i | \(0.597765\pi\) | |||||||
\(770\) | 12.8847 | 0.464331 | ||||||||
\(771\) | −31.3621 | −1.12948 | ||||||||
\(772\) | −3.83991 | −0.138201 | ||||||||
\(773\) | 18.2576 | 0.656680 | 0.328340 | − | 0.944560i | \(-0.393511\pi\) | ||||
0.328340 | + | 0.944560i | \(0.393511\pi\) | |||||||
\(774\) | 7.06738 | 0.254032 | ||||||||
\(775\) | −37.8836 | −1.36082 | ||||||||
\(776\) | 2.39041 | 0.0858106 | ||||||||
\(777\) | −13.7138 | −0.491978 | ||||||||
\(778\) | −36.1082 | −1.29454 | ||||||||
\(779\) | 21.1357 | 0.757265 | ||||||||
\(780\) | 10.0425 | 0.359581 | ||||||||
\(781\) | −20.0857 | −0.718722 | ||||||||
\(782\) | 0.513960 | 0.0183792 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | −5.41122 | −0.193258 | ||||||||
\(785\) | −36.6067 | −1.30655 | ||||||||
\(786\) | 11.3326 | 0.404219 | ||||||||
\(787\) | 17.1358 | 0.610824 | 0.305412 | − | 0.952220i | \(-0.401206\pi\) | ||||
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(788\) | 2.46376 | 0.0877679 | ||||||||
\(789\) | 14.8260 | 0.527820 | ||||||||
\(790\) | 33.3215 | 1.18553 | ||||||||
\(791\) | −4.12104 | −0.146527 | ||||||||
\(792\) | 2.95054 | 0.104843 | ||||||||
\(793\) | 21.6576 | 0.769083 | ||||||||
\(794\) | 4.49868 | 0.159652 | ||||||||
\(795\) | 27.1837 | 0.964106 | ||||||||
\(796\) | −27.5015 | −0.974765 | ||||||||
\(797\) | 27.1842 | 0.962912 | 0.481456 | − | 0.876470i | \(-0.340108\pi\) | ||||
0.481456 | + | 0.876470i | \(0.340108\pi\) | |||||||
\(798\) | −3.78924 | −0.134138 | ||||||||
\(799\) | 2.56330 | 0.0906832 | ||||||||
\(800\) | −7.00274 | −0.247584 | ||||||||
\(801\) | 0.689007 | 0.0243449 | ||||||||
\(802\) | −18.7098 | −0.660665 | ||||||||
\(803\) | −8.49061 | −0.299627 | ||||||||
\(804\) | 8.80796 | 0.310633 | ||||||||
\(805\) | 4.36688 | 0.153912 | ||||||||
\(806\) | −15.6815 | −0.552356 | ||||||||
\(807\) | −25.6253 | −0.902052 | ||||||||
\(808\) | −5.52770 | −0.194464 | ||||||||
\(809\) | 8.38840 | 0.294920 | 0.147460 | − | 0.989068i | \(-0.452890\pi\) | ||||
0.147460 | + | 0.989068i | \(0.452890\pi\) | |||||||
\(810\) | −3.46450 | −0.121730 | ||||||||
\(811\) | −2.72534 | −0.0956995 | −0.0478498 | − | 0.998855i | \(-0.515237\pi\) | ||||
−0.0478498 | + | 0.998855i | \(0.515237\pi\) | |||||||
\(812\) | 1.26047 | 0.0442337 | ||||||||
\(813\) | 13.5115 | 0.473869 | ||||||||
\(814\) | 32.1016 | 1.12516 | ||||||||
\(815\) | −78.4871 | −2.74928 | ||||||||
\(816\) | 0.513960 | 0.0179922 | ||||||||
\(817\) | 21.2461 | 0.743307 | ||||||||
\(818\) | 11.9465 | 0.417700 | ||||||||
\(819\) | −3.65372 | −0.127671 | ||||||||
\(820\) | −24.3577 | −0.850609 | ||||||||
\(821\) | −14.2582 | −0.497613 | −0.248806 | − | 0.968553i | \(-0.580038\pi\) | ||||
−0.248806 | + | 0.968553i | \(0.580038\pi\) | |||||||
\(822\) | 9.35007 | 0.326121 | ||||||||
\(823\) | 22.7111 | 0.791660 | 0.395830 | − | 0.918324i | \(-0.370457\pi\) | ||||
0.395830 | + | 0.918324i | \(0.370457\pi\) | |||||||
\(824\) | 1.89297 | 0.0659448 | ||||||||
\(825\) | 20.6619 | 0.719354 | ||||||||
\(826\) | 5.73459 | 0.199532 | ||||||||
\(827\) | −49.9690 | −1.73759 | −0.868796 | − | 0.495171i | \(-0.835105\pi\) | ||||
−0.868796 | + | 0.495171i | \(0.835105\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 11.4162 | 0.396500 | 0.198250 | − | 0.980152i | \(-0.436474\pi\) | ||||
0.198250 | + | 0.980152i | \(0.436474\pi\) | |||||||
\(830\) | −1.70543 | −0.0591962 | ||||||||
\(831\) | −18.8475 | −0.653813 | ||||||||
\(832\) | −2.89870 | −0.100494 | ||||||||
\(833\) | 2.78115 | 0.0963613 | ||||||||
\(834\) | −5.33044 | −0.184578 | ||||||||
\(835\) | 34.4614 | 1.19258 | ||||||||
\(836\) | 8.86996 | 0.306774 | ||||||||
\(837\) | 5.40982 | 0.186991 | ||||||||
\(838\) | −30.4419 | −1.05160 | ||||||||
\(839\) | 24.5479 | 0.847487 | 0.423744 | − | 0.905782i | \(-0.360716\pi\) | ||||
0.423744 | + | 0.905782i | \(0.360716\pi\) | |||||||
\(840\) | 4.36688 | 0.150672 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −35.5601 | −1.22548 | ||||||||
\(843\) | 22.0826 | 0.760566 | ||||||||
\(844\) | −2.76261 | −0.0950929 | ||||||||
\(845\) | −15.9281 | −0.547944 | ||||||||
\(846\) | 4.98736 | 0.171469 | ||||||||
\(847\) | −2.89192 | −0.0993677 | ||||||||
\(848\) | −7.84635 | −0.269445 | ||||||||
\(849\) | −4.52701 | −0.155367 | ||||||||
\(850\) | 3.59913 | 0.123449 | ||||||||
\(851\) | 10.8799 | 0.372958 | ||||||||
\(852\) | −6.80747 | −0.233220 | ||||||||
\(853\) | 24.9890 | 0.855607 | 0.427803 | − | 0.903872i | \(-0.359288\pi\) | ||||
0.427803 | + | 0.903872i | \(0.359288\pi\) | |||||||
\(854\) | 9.41754 | 0.322262 | ||||||||
\(855\) | −10.4150 | −0.356187 | ||||||||
\(856\) | −2.57025 | −0.0878495 | ||||||||
\(857\) | 13.4262 | 0.458629 | 0.229314 | − | 0.973352i | \(-0.426352\pi\) | ||||
0.229314 | + | 0.973352i | \(0.426352\pi\) | |||||||
\(858\) | 8.55273 | 0.291985 | ||||||||
\(859\) | −46.2045 | −1.57648 | −0.788238 | − | 0.615370i | \(-0.789006\pi\) | ||||
−0.788238 | + | 0.615370i | \(0.789006\pi\) | |||||||
\(860\) | −24.4849 | −0.834929 | ||||||||
\(861\) | 8.86192 | 0.302013 | ||||||||
\(862\) | 16.2501 | 0.553482 | ||||||||
\(863\) | −46.7517 | −1.59144 | −0.795722 | − | 0.605661i | \(-0.792909\pi\) | ||||
−0.795722 | + | 0.605661i | \(0.792909\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −29.1505 | −0.991146 | ||||||||
\(866\) | −21.5186 | −0.731232 | ||||||||
\(867\) | 16.7358 | 0.568379 | ||||||||
\(868\) | −6.81890 | −0.231448 | ||||||||
\(869\) | 28.3783 | 0.962667 | ||||||||
\(870\) | 3.46450 | 0.117457 | ||||||||
\(871\) | 25.5316 | 0.865107 | ||||||||
\(872\) | −18.5551 | −0.628355 | ||||||||
\(873\) | −2.39041 | −0.0809030 | ||||||||
\(874\) | 3.00622 | 0.101687 | ||||||||
\(875\) | 8.74575 | 0.295660 | ||||||||
\(876\) | −2.87765 | −0.0972267 | ||||||||
\(877\) | −7.76520 | −0.262212 | −0.131106 | − | 0.991368i | \(-0.541853\pi\) | ||||
−0.131106 | + | 0.991368i | \(0.541853\pi\) | |||||||
\(878\) | −7.30169 | −0.246420 | ||||||||
\(879\) | 14.9075 | 0.502818 | ||||||||
\(880\) | −10.2221 | −0.344588 | ||||||||
\(881\) | 30.8212 | 1.03839 | 0.519195 | − | 0.854656i | \(-0.326232\pi\) | ||||
0.519195 | + | 0.854656i | \(0.326232\pi\) | |||||||
\(882\) | 5.41122 | 0.182205 | ||||||||
\(883\) | 5.27954 | 0.177671 | 0.0888353 | − | 0.996046i | \(-0.471686\pi\) | ||||
0.0888353 | + | 0.996046i | \(0.471686\pi\) | |||||||
\(884\) | 1.48982 | 0.0501080 | ||||||||
\(885\) | 15.7620 | 0.529834 | ||||||||
\(886\) | 16.1535 | 0.542688 | ||||||||
\(887\) | 21.5391 | 0.723213 | 0.361607 | − | 0.932331i | \(-0.382228\pi\) | ||||
0.361607 | + | 0.932331i | \(0.382228\pi\) | |||||||
\(888\) | 10.8799 | 0.365106 | ||||||||
\(889\) | −10.4449 | −0.350311 | ||||||||
\(890\) | −2.38706 | −0.0800146 | ||||||||
\(891\) | −2.95054 | −0.0988467 | ||||||||
\(892\) | 21.6933 | 0.726345 | ||||||||
\(893\) | 14.9931 | 0.501725 | ||||||||
\(894\) | −3.37859 | −0.112997 | ||||||||
\(895\) | −64.7900 | −2.16569 | ||||||||
\(896\) | −1.26047 | −0.0421092 | ||||||||
\(897\) | 2.89870 | 0.0967848 | ||||||||
\(898\) | −2.04485 | −0.0682376 | ||||||||
\(899\) | −5.40982 | −0.180428 | ||||||||
\(900\) | 7.00274 | 0.233425 | ||||||||
\(901\) | 4.03271 | 0.134349 | ||||||||
\(902\) | −20.7442 | −0.690708 | ||||||||
\(903\) | 8.90820 | 0.296446 | ||||||||
\(904\) | 3.26945 | 0.108740 | ||||||||
\(905\) | 50.0477 | 1.66364 | ||||||||
\(906\) | 11.4581 | 0.380670 | ||||||||
\(907\) | 17.7000 | 0.587718 | 0.293859 | − | 0.955849i | \(-0.405060\pi\) | ||||
0.293859 | + | 0.955849i | \(0.405060\pi\) | |||||||
\(908\) | 26.6966 | 0.885956 | ||||||||
\(909\) | 5.52770 | 0.183342 | ||||||||
\(910\) | 12.6583 | 0.419618 | ||||||||
\(911\) | 50.8581 | 1.68500 | 0.842502 | − | 0.538692i | \(-0.181082\pi\) | ||||
0.842502 | + | 0.538692i | \(0.181082\pi\) | |||||||
\(912\) | 3.00622 | 0.0995458 | ||||||||
\(913\) | −1.45243 | −0.0480683 | ||||||||
\(914\) | 26.9698 | 0.892083 | ||||||||
\(915\) | 25.8849 | 0.855728 | ||||||||
\(916\) | −4.48624 | −0.148230 | ||||||||
\(917\) | 14.2843 | 0.471710 | ||||||||
\(918\) | −0.513960 | −0.0169632 | ||||||||
\(919\) | −36.8992 | −1.21719 | −0.608596 | − | 0.793480i | \(-0.708267\pi\) | ||||
−0.608596 | + | 0.793480i | \(0.708267\pi\) | |||||||
\(920\) | −3.46450 | −0.114221 | ||||||||
\(921\) | 11.7337 | 0.386639 | ||||||||
\(922\) | −1.44799 | −0.0476869 | ||||||||
\(923\) | −19.7328 | −0.649514 | ||||||||
\(924\) | 3.71905 | 0.122348 | ||||||||
\(925\) | 76.1892 | 2.50509 | ||||||||
\(926\) | 27.3529 | 0.898871 | ||||||||
\(927\) | −1.89297 | −0.0621734 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 8.06811 | 0.264706 | 0.132353 | − | 0.991203i | \(-0.457747\pi\) | ||||
0.132353 | + | 0.991203i | \(0.457747\pi\) | |||||||
\(930\) | −18.7423 | −0.614584 | ||||||||
\(931\) | 16.2673 | 0.533140 | ||||||||
\(932\) | −30.0147 | −0.983164 | ||||||||
\(933\) | 12.9143 | 0.422796 | ||||||||
\(934\) | −5.17174 | −0.169225 | ||||||||
\(935\) | 5.25377 | 0.171817 | ||||||||
\(936\) | 2.89870 | 0.0947470 | ||||||||
\(937\) | −7.86456 | −0.256924 | −0.128462 | − | 0.991714i | \(-0.541004\pi\) | ||||
−0.128462 | + | 0.991714i | \(0.541004\pi\) | |||||||
\(938\) | 11.1021 | 0.362498 | ||||||||
\(939\) | 31.6900 | 1.03416 | ||||||||
\(940\) | −17.2787 | −0.563569 | ||||||||
\(941\) | −34.9867 | −1.14053 | −0.570266 | − | 0.821460i | \(-0.693160\pi\) | ||||
−0.570266 | + | 0.821460i | \(0.693160\pi\) | |||||||
\(942\) | −10.5662 | −0.344266 | ||||||||
\(943\) | −7.03067 | −0.228950 | ||||||||
\(944\) | −4.54958 | −0.148076 | ||||||||
\(945\) | −4.36688 | −0.142055 | ||||||||
\(946\) | −20.8526 | −0.677976 | ||||||||
\(947\) | 15.6316 | 0.507958 | 0.253979 | − | 0.967210i | \(-0.418261\pi\) | ||||
0.253979 | + | 0.967210i | \(0.418261\pi\) | |||||||
\(948\) | 9.61800 | 0.312378 | ||||||||
\(949\) | −8.34145 | −0.270775 | ||||||||
\(950\) | 21.0518 | 0.683010 | ||||||||
\(951\) | −7.67149 | −0.248765 | ||||||||
\(952\) | 0.647830 | 0.0209963 | ||||||||
\(953\) | −33.1722 | −1.07455 | −0.537277 | − | 0.843406i | \(-0.680547\pi\) | ||||
−0.537277 | + | 0.843406i | \(0.680547\pi\) | |||||||
\(954\) | 7.84635 | 0.254035 | ||||||||
\(955\) | 63.0453 | 2.04010 | ||||||||
\(956\) | 5.58901 | 0.180761 | ||||||||
\(957\) | 2.95054 | 0.0953773 | ||||||||
\(958\) | −13.5202 | −0.436818 | ||||||||
\(959\) | 11.7855 | 0.380572 | ||||||||
\(960\) | −3.46450 | −0.111816 | ||||||||
\(961\) | −1.73386 | −0.0559310 | ||||||||
\(962\) | 31.5376 | 1.01681 | ||||||||
\(963\) | 2.57025 | 0.0828253 | ||||||||
\(964\) | 21.2451 | 0.684259 | ||||||||
\(965\) | −13.3034 | −0.428250 | ||||||||
\(966\) | 1.26047 | 0.0405549 | ||||||||
\(967\) | 0.534347 | 0.0171834 | 0.00859172 | − | 0.999963i | \(-0.497265\pi\) | ||||
0.00859172 | + | 0.999963i | \(0.497265\pi\) | |||||||
\(968\) | 2.29433 | 0.0737425 | ||||||||
\(969\) | −1.54508 | −0.0496350 | ||||||||
\(970\) | 8.28156 | 0.265905 | ||||||||
\(971\) | −48.6158 | −1.56015 | −0.780077 | − | 0.625683i | \(-0.784820\pi\) | ||||
−0.780077 | + | 0.625683i | \(0.784820\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −6.71884 | −0.215396 | ||||||||
\(974\) | 6.08871 | 0.195095 | ||||||||
\(975\) | 20.2989 | 0.650084 | ||||||||
\(976\) | −7.47147 | −0.239156 | ||||||||
\(977\) | −40.1654 | −1.28500 | −0.642502 | − | 0.766284i | \(-0.722104\pi\) | ||||
−0.642502 | + | 0.766284i | \(0.722104\pi\) | |||||||
\(978\) | −22.6547 | −0.724417 | ||||||||
\(979\) | −2.03294 | −0.0649731 | ||||||||
\(980\) | −18.7472 | −0.598856 | ||||||||
\(981\) | 18.5551 | 0.592419 | ||||||||
\(982\) | 43.4519 | 1.38661 | ||||||||
\(983\) | 45.5704 | 1.45347 | 0.726735 | − | 0.686918i | \(-0.241037\pi\) | ||||
0.726735 | + | 0.686918i | \(0.241037\pi\) | |||||||
\(984\) | −7.03067 | −0.224129 | ||||||||
\(985\) | 8.53570 | 0.271970 | ||||||||
\(986\) | 0.513960 | 0.0163678 | ||||||||
\(987\) | 6.28640 | 0.200098 | ||||||||
\(988\) | 8.71413 | 0.277233 | ||||||||
\(989\) | −7.06738 | −0.224730 | ||||||||
\(990\) | 10.2221 | 0.324881 | ||||||||
\(991\) | 56.6411 | 1.79926 | 0.899632 | − | 0.436649i | \(-0.143835\pi\) | ||||
0.899632 | + | 0.436649i | \(0.143835\pi\) | |||||||
\(992\) | 5.40982 | 0.171762 | ||||||||
\(993\) | −8.13519 | −0.258163 | ||||||||
\(994\) | −8.58059 | −0.272160 | ||||||||
\(995\) | −95.2789 | −3.02054 | ||||||||
\(996\) | −0.492258 | −0.0155978 | ||||||||
\(997\) | 56.1383 | 1.77792 | 0.888959 | − | 0.457987i | \(-0.151429\pi\) | ||||
0.888959 | + | 0.457987i | \(0.151429\pi\) | |||||||
\(998\) | 13.3105 | 0.421336 | ||||||||
\(999\) | −10.8799 | −0.344225 |
(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 | 4002.2.a.bg.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.bg.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial |