Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2695,2,Mod(1,2695)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2695, 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("2695.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2695 = 5 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2695.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: | \(21.5196833447\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3x^{9} - 13x^{8} + 41x^{7} + 51x^{6} - 184x^{5} - 45x^{4} + 297x^{3} - 59x^{2} - 109x + 21 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 385) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.47520\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2695.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.47520 | −1.75023 | −0.875115 | − | 0.483916i | \(-0.839214\pi\) | ||||
−0.875115 | + | 0.483916i | \(0.839214\pi\) | |||||||
\(3\) | −3.19739 | −1.84601 | −0.923007 | − | 0.384784i | \(-0.874276\pi\) | ||||
−0.923007 | + | 0.384784i | \(0.874276\pi\) | |||||||
\(4\) | 4.12660 | 2.06330 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 7.91417 | 3.23095 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −5.26377 | −1.86102 | ||||||||
\(9\) | 7.22329 | 2.40776 | ||||||||
\(10\) | 2.47520 | 0.782726 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −13.1944 | −3.80888 | ||||||||
\(13\) | −1.36166 | −0.377658 | −0.188829 | − | 0.982010i | \(-0.560469\pi\) | ||||
−0.188829 | + | 0.982010i | \(0.560469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.19739 | 0.825562 | ||||||||
\(16\) | 4.77565 | 1.19391 | ||||||||
\(17\) | 2.83708 | 0.688092 | 0.344046 | − | 0.938953i | \(-0.388202\pi\) | ||||
0.344046 | + | 0.938953i | \(0.388202\pi\) | |||||||
\(18\) | −17.8791 | −4.21414 | ||||||||
\(19\) | −2.20953 | −0.506900 | −0.253450 | − | 0.967348i | \(-0.581565\pi\) | ||||
−0.253450 | + | 0.967348i | \(0.581565\pi\) | |||||||
\(20\) | −4.12660 | −0.922737 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.47520 | −0.527714 | ||||||||
\(23\) | 6.51211 | 1.35787 | 0.678935 | − | 0.734199i | \(-0.262442\pi\) | ||||
0.678935 | + | 0.734199i | \(0.262442\pi\) | |||||||
\(24\) | 16.8303 | 3.43547 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.37039 | 0.660988 | ||||||||
\(27\) | −13.5035 | −2.59875 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.29233 | 1.16846 | 0.584228 | − | 0.811590i | \(-0.301397\pi\) | ||||
0.584228 | + | 0.811590i | \(0.301397\pi\) | |||||||
\(30\) | −7.91417 | −1.44492 | ||||||||
\(31\) | 10.3303 | 1.85538 | 0.927688 | − | 0.373355i | \(-0.121793\pi\) | ||||
0.927688 | + | 0.373355i | \(0.121793\pi\) | |||||||
\(32\) | −1.29316 | −0.228600 | ||||||||
\(33\) | −3.19739 | −0.556594 | ||||||||
\(34\) | −7.02233 | −1.20432 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 29.8077 | 4.96795 | ||||||||
\(37\) | 7.81172 | 1.28424 | 0.642119 | − | 0.766605i | \(-0.278055\pi\) | ||||
0.642119 | + | 0.766605i | \(0.278055\pi\) | |||||||
\(38\) | 5.46902 | 0.887192 | ||||||||
\(39\) | 4.35377 | 0.697162 | ||||||||
\(40\) | 5.26377 | 0.832274 | ||||||||
\(41\) | 3.91618 | 0.611604 | 0.305802 | − | 0.952095i | \(-0.401075\pi\) | ||||
0.305802 | + | 0.952095i | \(0.401075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.47126 | −1.44435 | −0.722176 | − | 0.691709i | \(-0.756858\pi\) | ||||
−0.722176 | + | 0.691709i | \(0.756858\pi\) | |||||||
\(44\) | 4.12660 | 0.622109 | ||||||||
\(45\) | −7.22329 | −1.07679 | ||||||||
\(46\) | −16.1188 | −2.37658 | ||||||||
\(47\) | −1.14620 | −0.167191 | −0.0835954 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835954 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(48\) | −15.2696 | −2.20398 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.47520 | −0.350046 | ||||||||
\(51\) | −9.07124 | −1.27023 | ||||||||
\(52\) | −5.61905 | −0.779222 | ||||||||
\(53\) | 8.33037 | 1.14426 | 0.572132 | − | 0.820161i | \(-0.306116\pi\) | ||||
0.572132 | + | 0.820161i | \(0.306116\pi\) | |||||||
\(54\) | 33.4239 | 4.54841 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.06472 | 0.935745 | ||||||||
\(58\) | −15.5748 | −2.04507 | ||||||||
\(59\) | 2.25466 | 0.293532 | 0.146766 | − | 0.989171i | \(-0.453114\pi\) | ||||
0.146766 | + | 0.989171i | \(0.453114\pi\) | |||||||
\(60\) | 13.1944 | 1.70338 | ||||||||
\(61\) | 6.02240 | 0.771089 | 0.385545 | − | 0.922689i | \(-0.374014\pi\) | ||||
0.385545 | + | 0.922689i | \(0.374014\pi\) | |||||||
\(62\) | −25.5695 | −3.24733 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.35049 | −0.793811 | ||||||||
\(65\) | 1.36166 | 0.168894 | ||||||||
\(66\) | 7.91417 | 0.974167 | ||||||||
\(67\) | −8.71012 | −1.06411 | −0.532055 | − | 0.846710i | \(-0.678580\pi\) | ||||
−0.532055 | + | 0.846710i | \(0.678580\pi\) | |||||||
\(68\) | 11.7075 | 1.41974 | ||||||||
\(69\) | −20.8218 | −2.50664 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.86988 | −0.340592 | −0.170296 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170296 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(72\) | −38.0217 | −4.48090 | ||||||||
\(73\) | −11.7962 | −1.38064 | −0.690322 | − | 0.723503i | \(-0.742531\pi\) | ||||
−0.690322 | + | 0.723503i | \(0.742531\pi\) | |||||||
\(74\) | −19.3355 | −2.24771 | ||||||||
\(75\) | −3.19739 | −0.369203 | ||||||||
\(76\) | −9.11784 | −1.04589 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −10.7764 | −1.22019 | ||||||||
\(79\) | 8.75950 | 0.985520 | 0.492760 | − | 0.870165i | \(-0.335988\pi\) | ||||
0.492760 | + | 0.870165i | \(0.335988\pi\) | |||||||
\(80\) | −4.77565 | −0.533934 | ||||||||
\(81\) | 21.5061 | 2.38957 | ||||||||
\(82\) | −9.69331 | −1.07045 | ||||||||
\(83\) | 8.61026 | 0.945099 | 0.472549 | − | 0.881304i | \(-0.343334\pi\) | ||||
0.472549 | + | 0.881304i | \(0.343334\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.83708 | −0.307724 | ||||||||
\(86\) | 23.4432 | 2.52795 | ||||||||
\(87\) | −20.1190 | −2.15698 | ||||||||
\(88\) | −5.26377 | −0.561119 | ||||||||
\(89\) | −10.4755 | −1.11040 | −0.555200 | − | 0.831717i | \(-0.687358\pi\) | ||||
−0.555200 | + | 0.831717i | \(0.687358\pi\) | |||||||
\(90\) | 17.8791 | 1.88462 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 26.8729 | 2.80169 | ||||||||
\(93\) | −33.0300 | −3.42505 | ||||||||
\(94\) | 2.83708 | 0.292622 | ||||||||
\(95\) | 2.20953 | 0.226693 | ||||||||
\(96\) | 4.13472 | 0.421998 | ||||||||
\(97\) | 2.85280 | 0.289658 | 0.144829 | − | 0.989457i | \(-0.453737\pi\) | ||||
0.144829 | + | 0.989457i | \(0.453737\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.22329 | 0.725968 | ||||||||
\(100\) | 4.12660 | 0.412660 | ||||||||
\(101\) | −1.89945 | −0.189002 | −0.0945010 | − | 0.995525i | \(-0.530126\pi\) | ||||
−0.0945010 | + | 0.995525i | \(0.530126\pi\) | |||||||
\(102\) | 22.4531 | 2.22319 | ||||||||
\(103\) | −8.56203 | −0.843642 | −0.421821 | − | 0.906679i | \(-0.638609\pi\) | ||||
−0.421821 | + | 0.906679i | \(0.638609\pi\) | |||||||
\(104\) | 7.16749 | 0.702830 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −20.6193 | −2.00272 | ||||||||
\(107\) | 5.61803 | 0.543116 | 0.271558 | − | 0.962422i | \(-0.412461\pi\) | ||||
0.271558 | + | 0.962422i | \(0.412461\pi\) | |||||||
\(108\) | −55.7237 | −5.36201 | ||||||||
\(109\) | −9.65700 | −0.924972 | −0.462486 | − | 0.886626i | \(-0.653043\pi\) | ||||
−0.462486 | + | 0.886626i | \(0.653043\pi\) | |||||||
\(110\) | 2.47520 | 0.236001 | ||||||||
\(111\) | −24.9771 | −2.37072 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 14.0674 | 1.32335 | 0.661676 | − | 0.749790i | \(-0.269846\pi\) | ||||
0.661676 | + | 0.749790i | \(0.269846\pi\) | |||||||
\(114\) | −17.4866 | −1.63777 | ||||||||
\(115\) | −6.51211 | −0.607258 | ||||||||
\(116\) | 25.9659 | 2.41088 | ||||||||
\(117\) | −9.83571 | −0.909311 | ||||||||
\(118\) | −5.58073 | −0.513748 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −16.8303 | −1.53639 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −14.9066 | −1.34958 | ||||||||
\(123\) | −12.5215 | −1.12903 | ||||||||
\(124\) | 42.6291 | 3.82820 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.30320 | −0.825526 | −0.412763 | − | 0.910839i | \(-0.635436\pi\) | ||||
−0.412763 | + | 0.910839i | \(0.635436\pi\) | |||||||
\(128\) | 18.3050 | 1.61795 | ||||||||
\(129\) | 30.2833 | 2.66629 | ||||||||
\(130\) | −3.37039 | −0.295603 | ||||||||
\(131\) | −15.7807 | −1.37876 | −0.689381 | − | 0.724399i | \(-0.742118\pi\) | ||||
−0.689381 | + | 0.724399i | \(0.742118\pi\) | |||||||
\(132\) | −13.1944 | −1.14842 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 21.5593 | 1.86244 | ||||||||
\(135\) | 13.5035 | 1.16220 | ||||||||
\(136\) | −14.9337 | −1.28056 | ||||||||
\(137\) | 6.69088 | 0.571641 | 0.285820 | − | 0.958283i | \(-0.407734\pi\) | ||||
0.285820 | + | 0.958283i | \(0.407734\pi\) | |||||||
\(138\) | 51.5380 | 4.38720 | ||||||||
\(139\) | −3.57182 | −0.302958 | −0.151479 | − | 0.988461i | \(-0.548404\pi\) | ||||
−0.151479 | + | 0.988461i | \(0.548404\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.66485 | 0.308636 | ||||||||
\(142\) | 7.10353 | 0.596115 | ||||||||
\(143\) | −1.36166 | −0.113868 | ||||||||
\(144\) | 34.4960 | 2.87466 | ||||||||
\(145\) | −6.29233 | −0.522549 | ||||||||
\(146\) | 29.1980 | 2.41644 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 32.2359 | 2.64977 | ||||||||
\(149\) | −23.5761 | −1.93143 | −0.965717 | − | 0.259598i | \(-0.916410\pi\) | ||||
−0.965717 | + | 0.259598i | \(0.916410\pi\) | |||||||
\(150\) | 7.91417 | 0.646189 | ||||||||
\(151\) | 5.39014 | 0.438644 | 0.219322 | − | 0.975653i | \(-0.429616\pi\) | ||||
0.219322 | + | 0.975653i | \(0.429616\pi\) | |||||||
\(152\) | 11.6304 | 0.943353 | ||||||||
\(153\) | 20.4930 | 1.65676 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3303 | −0.829750 | ||||||||
\(156\) | 17.9663 | 1.43845 | ||||||||
\(157\) | 5.95318 | 0.475115 | 0.237558 | − | 0.971373i | \(-0.423653\pi\) | ||||
0.237558 | + | 0.971373i | \(0.423653\pi\) | |||||||
\(158\) | −21.6815 | −1.72489 | ||||||||
\(159\) | −26.6354 | −2.11233 | ||||||||
\(160\) | 1.29316 | 0.102233 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −53.2318 | −4.18229 | ||||||||
\(163\) | −12.4822 | −0.977679 | −0.488840 | − | 0.872374i | \(-0.662580\pi\) | ||||
−0.488840 | + | 0.872374i | \(0.662580\pi\) | |||||||
\(164\) | 16.1605 | 1.26192 | ||||||||
\(165\) | 3.19739 | 0.248916 | ||||||||
\(166\) | −21.3121 | −1.65414 | ||||||||
\(167\) | 17.6601 | 1.36658 | 0.683291 | − | 0.730146i | \(-0.260548\pi\) | ||||
0.683291 | + | 0.730146i | \(0.260548\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.1459 | −0.857374 | ||||||||
\(170\) | 7.02233 | 0.538588 | ||||||||
\(171\) | −15.9601 | −1.22050 | ||||||||
\(172\) | −39.0841 | −2.98014 | ||||||||
\(173\) | 2.91898 | 0.221926 | 0.110963 | − | 0.993825i | \(-0.464606\pi\) | ||||
0.110963 | + | 0.993825i | \(0.464606\pi\) | |||||||
\(174\) | 49.7985 | 3.77522 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.77565 | 0.359978 | ||||||||
\(177\) | −7.20903 | −0.541864 | ||||||||
\(178\) | 25.9289 | 1.94346 | ||||||||
\(179\) | −17.9474 | −1.34145 | −0.670725 | − | 0.741706i | \(-0.734017\pi\) | ||||
−0.670725 | + | 0.741706i | \(0.734017\pi\) | |||||||
\(180\) | −29.8077 | −2.22173 | ||||||||
\(181\) | 11.9052 | 0.884906 | 0.442453 | − | 0.896792i | \(-0.354108\pi\) | ||||
0.442453 | + | 0.896792i | \(0.354108\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.2559 | −1.42344 | ||||||||
\(184\) | −34.2782 | −2.52703 | ||||||||
\(185\) | −7.81172 | −0.574329 | ||||||||
\(186\) | 81.7557 | 5.99462 | ||||||||
\(187\) | 2.83708 | 0.207468 | ||||||||
\(188\) | −4.72992 | −0.344965 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5.46902 | −0.396764 | ||||||||
\(191\) | 6.88513 | 0.498190 | 0.249095 | − | 0.968479i | \(-0.419867\pi\) | ||||
0.249095 | + | 0.968479i | \(0.419867\pi\) | |||||||
\(192\) | 20.3050 | 1.46539 | ||||||||
\(193\) | 1.65966 | 0.119465 | 0.0597323 | − | 0.998214i | \(-0.480975\pi\) | ||||
0.0597323 | + | 0.998214i | \(0.480975\pi\) | |||||||
\(194\) | −7.06125 | −0.506968 | ||||||||
\(195\) | −4.35377 | −0.311780 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.7161 | 1.33347 | 0.666735 | − | 0.745295i | \(-0.267691\pi\) | ||||
0.666735 | + | 0.745295i | \(0.267691\pi\) | |||||||
\(198\) | −17.8791 | −1.27061 | ||||||||
\(199\) | 19.4444 | 1.37838 | 0.689189 | − | 0.724582i | \(-0.257967\pi\) | ||||
0.689189 | + | 0.724582i | \(0.257967\pi\) | |||||||
\(200\) | −5.26377 | −0.372204 | ||||||||
\(201\) | 27.8496 | 1.96436 | ||||||||
\(202\) | 4.70151 | 0.330797 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −37.4334 | −2.62086 | ||||||||
\(205\) | −3.91618 | −0.273518 | ||||||||
\(206\) | 21.1927 | 1.47657 | ||||||||
\(207\) | 47.0389 | 3.26943 | ||||||||
\(208\) | −6.50284 | −0.450891 | ||||||||
\(209\) | −2.20953 | −0.152836 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.35680 | −0.506463 | −0.253232 | − | 0.967406i | \(-0.581493\pi\) | ||||
−0.253232 | + | 0.967406i | \(0.581493\pi\) | |||||||
\(212\) | 34.3761 | 2.36096 | ||||||||
\(213\) | 9.17613 | 0.628738 | ||||||||
\(214\) | −13.9057 | −0.950577 | ||||||||
\(215\) | 9.47126 | 0.645934 | ||||||||
\(216\) | 71.0793 | 4.83634 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 23.9030 | 1.61891 | ||||||||
\(219\) | 37.7171 | 2.54869 | ||||||||
\(220\) | −4.12660 | −0.278216 | ||||||||
\(221\) | −3.86315 | −0.259864 | ||||||||
\(222\) | 61.8233 | 4.14931 | ||||||||
\(223\) | −1.41504 | −0.0947583 | −0.0473792 | − | 0.998877i | \(-0.515087\pi\) | ||||
−0.0473792 | + | 0.998877i | \(0.515087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.22329 | 0.481553 | ||||||||
\(226\) | −34.8196 | −2.31617 | ||||||||
\(227\) | 0.192342 | 0.0127662 | 0.00638309 | − | 0.999980i | \(-0.497968\pi\) | ||||
0.00638309 | + | 0.999980i | \(0.497968\pi\) | |||||||
\(228\) | 29.1533 | 1.93072 | ||||||||
\(229\) | 1.82401 | 0.120534 | 0.0602668 | − | 0.998182i | \(-0.480805\pi\) | ||||
0.0602668 | + | 0.998182i | \(0.480805\pi\) | |||||||
\(230\) | 16.1188 | 1.06284 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −33.1213 | −2.17452 | ||||||||
\(233\) | 20.1979 | 1.32321 | 0.661604 | − | 0.749853i | \(-0.269876\pi\) | ||||
0.661604 | + | 0.749853i | \(0.269876\pi\) | |||||||
\(234\) | 24.3453 | 1.59150 | ||||||||
\(235\) | 1.14620 | 0.0747700 | ||||||||
\(236\) | 9.30410 | 0.605645 | ||||||||
\(237\) | −28.0075 | −1.81928 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.5674 | 0.877603 | 0.438802 | − | 0.898584i | \(-0.355403\pi\) | ||||
0.438802 | + | 0.898584i | \(0.355403\pi\) | |||||||
\(240\) | 15.2696 | 0.985650 | ||||||||
\(241\) | −16.0107 | −1.03134 | −0.515670 | − | 0.856788i | \(-0.672457\pi\) | ||||
−0.515670 | + | 0.856788i | \(0.672457\pi\) | |||||||
\(242\) | −2.47520 | −0.159112 | ||||||||
\(243\) | −28.2528 | −1.81242 | ||||||||
\(244\) | 24.8521 | 1.59099 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 30.9933 | 1.97606 | ||||||||
\(247\) | 3.00864 | 0.191435 | ||||||||
\(248\) | −54.3763 | −3.45290 | ||||||||
\(249\) | −27.5303 | −1.74466 | ||||||||
\(250\) | 2.47520 | 0.156545 | ||||||||
\(251\) | −7.97654 | −0.503475 | −0.251737 | − | 0.967796i | \(-0.581002\pi\) | ||||
−0.251737 | + | 0.967796i | \(0.581002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.51211 | 0.409413 | ||||||||
\(254\) | 23.0273 | 1.44486 | ||||||||
\(255\) | 9.07124 | 0.568063 | ||||||||
\(256\) | −32.6076 | −2.03797 | ||||||||
\(257\) | 8.10095 | 0.505323 | 0.252662 | − | 0.967555i | \(-0.418694\pi\) | ||||
0.252662 | + | 0.967555i | \(0.418694\pi\) | |||||||
\(258\) | −74.9571 | −4.66663 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.61905 | 0.348479 | ||||||||
\(261\) | 45.4513 | 2.81337 | ||||||||
\(262\) | 39.0603 | 2.41315 | ||||||||
\(263\) | −6.09902 | −0.376082 | −0.188041 | − | 0.982161i | \(-0.560214\pi\) | ||||
−0.188041 | + | 0.982161i | \(0.560214\pi\) | |||||||
\(264\) | 16.8303 | 1.03583 | ||||||||
\(265\) | −8.33037 | −0.511731 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 33.4942 | 2.04981 | ||||||||
\(268\) | −35.9432 | −2.19558 | ||||||||
\(269\) | 27.7349 | 1.69103 | 0.845515 | − | 0.533952i | \(-0.179294\pi\) | ||||
0.845515 | + | 0.533952i | \(0.179294\pi\) | |||||||
\(270\) | −33.4239 | −2.03411 | ||||||||
\(271\) | 17.0261 | 1.03426 | 0.517132 | − | 0.855906i | \(-0.327000\pi\) | ||||
0.517132 | + | 0.855906i | \(0.327000\pi\) | |||||||
\(272\) | 13.5489 | 0.821523 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16.5613 | −1.00050 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −85.9231 | −5.17197 | ||||||||
\(277\) | 14.7376 | 0.885498 | 0.442749 | − | 0.896645i | \(-0.354003\pi\) | ||||
0.442749 | + | 0.896645i | \(0.354003\pi\) | |||||||
\(278\) | 8.84096 | 0.530245 | ||||||||
\(279\) | 74.6188 | 4.46731 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.54498 | −0.211476 | −0.105738 | − | 0.994394i | \(-0.533720\pi\) | ||||
−0.105738 | + | 0.994394i | \(0.533720\pi\) | |||||||
\(282\) | −9.07124 | −0.540184 | ||||||||
\(283\) | −22.6670 | −1.34741 | −0.673707 | − | 0.738999i | \(-0.735299\pi\) | ||||
−0.673707 | + | 0.738999i | \(0.735299\pi\) | |||||||
\(284\) | −11.8429 | −0.702745 | ||||||||
\(285\) | −7.06472 | −0.418478 | ||||||||
\(286\) | 3.37039 | 0.199295 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −9.34085 | −0.550415 | ||||||||
\(289\) | −8.95099 | −0.526529 | ||||||||
\(290\) | 15.5748 | 0.914581 | ||||||||
\(291\) | −9.12152 | −0.534713 | ||||||||
\(292\) | −48.6783 | −2.84868 | ||||||||
\(293\) | 5.90965 | 0.345245 | 0.172623 | − | 0.984988i | \(-0.444776\pi\) | ||||
0.172623 | + | 0.984988i | \(0.444776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.25466 | −0.131271 | ||||||||
\(296\) | −41.1191 | −2.39000 | ||||||||
\(297\) | −13.5035 | −0.783553 | ||||||||
\(298\) | 58.3556 | 3.38045 | ||||||||
\(299\) | −8.86732 | −0.512810 | ||||||||
\(300\) | −13.1944 | −0.761777 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −13.3417 | −0.767727 | ||||||||
\(303\) | 6.07327 | 0.348900 | ||||||||
\(304\) | −10.5519 | −0.605195 | ||||||||
\(305\) | −6.02240 | −0.344841 | ||||||||
\(306\) | −50.7243 | −2.89972 | ||||||||
\(307\) | −2.99704 | −0.171050 | −0.0855249 | − | 0.996336i | \(-0.527257\pi\) | ||||
−0.0855249 | + | 0.996336i | \(0.527257\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.3761 | 1.55737 | ||||||||
\(310\) | 25.5695 | 1.45225 | ||||||||
\(311\) | 0.595775 | 0.0337833 | 0.0168917 | − | 0.999857i | \(-0.494623\pi\) | ||||
0.0168917 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(312\) | −22.9172 | −1.29743 | ||||||||
\(313\) | 7.15763 | 0.404573 | 0.202287 | − | 0.979326i | \(-0.435163\pi\) | ||||
0.202287 | + | 0.979326i | \(0.435163\pi\) | |||||||
\(314\) | −14.7353 | −0.831561 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 36.1470 | 2.03343 | ||||||||
\(317\) | 12.1246 | 0.680987 | 0.340494 | − | 0.940247i | \(-0.389406\pi\) | ||||
0.340494 | + | 0.940247i | \(0.389406\pi\) | |||||||
\(318\) | 65.9280 | 3.69706 | ||||||||
\(319\) | 6.29233 | 0.352303 | ||||||||
\(320\) | 6.35049 | 0.355003 | ||||||||
\(321\) | −17.9630 | −1.00260 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.26860 | −0.348794 | ||||||||
\(324\) | 88.7472 | 4.93040 | ||||||||
\(325\) | −1.36166 | −0.0755316 | ||||||||
\(326\) | 30.8958 | 1.71116 | ||||||||
\(327\) | 30.8772 | 1.70751 | ||||||||
\(328\) | −20.6138 | −1.13821 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.91417 | −0.435661 | ||||||||
\(331\) | 11.8650 | 0.652159 | 0.326079 | − | 0.945342i | \(-0.394272\pi\) | ||||
0.326079 | + | 0.945342i | \(0.394272\pi\) | |||||||
\(332\) | 35.5311 | 1.95002 | ||||||||
\(333\) | 56.4263 | 3.09214 | ||||||||
\(334\) | −43.7123 | −2.39183 | ||||||||
\(335\) | 8.71012 | 0.475885 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.7226 | 1.29225 | 0.646125 | − | 0.763231i | \(-0.276388\pi\) | ||||
0.646125 | + | 0.763231i | \(0.276388\pi\) | |||||||
\(338\) | 27.5882 | 1.50060 | ||||||||
\(339\) | −44.9790 | −2.44292 | ||||||||
\(340\) | −11.7075 | −0.634928 | ||||||||
\(341\) | 10.3303 | 0.559417 | ||||||||
\(342\) | 39.5043 | 2.13615 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 49.8545 | 2.68797 | ||||||||
\(345\) | 20.8218 | 1.12101 | ||||||||
\(346\) | −7.22506 | −0.388422 | ||||||||
\(347\) | 0.619487 | 0.0332558 | 0.0166279 | − | 0.999862i | \(-0.494707\pi\) | ||||
0.0166279 | + | 0.999862i | \(0.494707\pi\) | |||||||
\(348\) | −83.0232 | −4.45051 | ||||||||
\(349\) | −14.0299 | −0.751005 | −0.375503 | − | 0.926821i | \(-0.622530\pi\) | ||||
−0.375503 | + | 0.926821i | \(0.622530\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.3873 | 0.981439 | ||||||||
\(352\) | −1.29316 | −0.0689254 | ||||||||
\(353\) | −25.3392 | −1.34867 | −0.674334 | − | 0.738427i | \(-0.735569\pi\) | ||||
−0.674334 | + | 0.738427i | \(0.735569\pi\) | |||||||
\(354\) | 17.8438 | 0.948386 | ||||||||
\(355\) | 2.86988 | 0.152318 | ||||||||
\(356\) | −43.2282 | −2.29109 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 44.4233 | 2.34784 | ||||||||
\(359\) | −11.5719 | −0.610743 | −0.305371 | − | 0.952233i | \(-0.598781\pi\) | ||||
−0.305371 | + | 0.952233i | \(0.598781\pi\) | |||||||
\(360\) | 38.0217 | 2.00392 | ||||||||
\(361\) | −14.1180 | −0.743052 | ||||||||
\(362\) | −29.4677 | −1.54879 | ||||||||
\(363\) | −3.19739 | −0.167819 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.7962 | 0.617442 | ||||||||
\(366\) | 47.6623 | 2.49135 | ||||||||
\(367\) | 7.05527 | 0.368282 | 0.184141 | − | 0.982900i | \(-0.441050\pi\) | ||||
0.184141 | + | 0.982900i | \(0.441050\pi\) | |||||||
\(368\) | 31.0996 | 1.62118 | ||||||||
\(369\) | 28.2877 | 1.47260 | ||||||||
\(370\) | 19.3355 | 1.00521 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −136.302 | −7.06691 | ||||||||
\(373\) | 2.22163 | 0.115032 | 0.0575158 | − | 0.998345i | \(-0.481682\pi\) | ||||
0.0575158 | + | 0.998345i | \(0.481682\pi\) | |||||||
\(374\) | −7.02233 | −0.363116 | ||||||||
\(375\) | 3.19739 | 0.165112 | ||||||||
\(376\) | 6.03334 | 0.311146 | ||||||||
\(377\) | −8.56804 | −0.441277 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.105060 | 0.00539655 | 0.00269828 | − | 0.999996i | \(-0.499141\pi\) | ||||
0.00269828 | + | 0.999996i | \(0.499141\pi\) | |||||||
\(380\) | 9.11784 | 0.467736 | ||||||||
\(381\) | 29.7460 | 1.52393 | ||||||||
\(382\) | −17.0421 | −0.871947 | ||||||||
\(383\) | 17.4751 | 0.892937 | 0.446469 | − | 0.894799i | \(-0.352681\pi\) | ||||
0.446469 | + | 0.894799i | \(0.352681\pi\) | |||||||
\(384\) | −58.5283 | −2.98676 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.10798 | −0.209090 | ||||||||
\(387\) | −68.4137 | −3.47766 | ||||||||
\(388\) | 11.7724 | 0.597653 | ||||||||
\(389\) | 26.2774 | 1.33231 | 0.666157 | − | 0.745811i | \(-0.267938\pi\) | ||||
0.666157 | + | 0.745811i | \(0.267938\pi\) | |||||||
\(390\) | 10.7764 | 0.545687 | ||||||||
\(391\) | 18.4754 | 0.934340 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 50.4569 | 2.54521 | ||||||||
\(394\) | −46.3261 | −2.33388 | ||||||||
\(395\) | −8.75950 | −0.440738 | ||||||||
\(396\) | 29.8077 | 1.49789 | ||||||||
\(397\) | 19.8732 | 0.997407 | 0.498703 | − | 0.866773i | \(-0.333810\pi\) | ||||
0.498703 | + | 0.866773i | \(0.333810\pi\) | |||||||
\(398\) | −48.1288 | −2.41248 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.77565 | 0.238783 | ||||||||
\(401\) | −20.1601 | −1.00675 | −0.503373 | − | 0.864069i | \(-0.667908\pi\) | ||||
−0.503373 | + | 0.864069i | \(0.667908\pi\) | |||||||
\(402\) | −68.9333 | −3.43808 | ||||||||
\(403\) | −14.0664 | −0.700698 | ||||||||
\(404\) | −7.83826 | −0.389968 | ||||||||
\(405\) | −21.5061 | −1.06865 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.81172 | 0.387213 | ||||||||
\(408\) | 47.7489 | 2.36392 | ||||||||
\(409\) | 20.3956 | 1.00850 | 0.504249 | − | 0.863558i | \(-0.331769\pi\) | ||||
0.504249 | + | 0.863558i | \(0.331769\pi\) | |||||||
\(410\) | 9.69331 | 0.478718 | ||||||||
\(411\) | −21.3934 | −1.05526 | ||||||||
\(412\) | −35.3321 | −1.74069 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −116.431 | −5.72225 | ||||||||
\(415\) | −8.61026 | −0.422661 | ||||||||
\(416\) | 1.76085 | 0.0863325 | ||||||||
\(417\) | 11.4205 | 0.559264 | ||||||||
\(418\) | 5.46902 | 0.267498 | ||||||||
\(419\) | 1.96618 | 0.0960541 | 0.0480270 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480270 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.9021 | −0.969969 | −0.484984 | − | 0.874523i | \(-0.661175\pi\) | ||||
−0.484984 | + | 0.874523i | \(0.661175\pi\) | |||||||
\(422\) | 18.2095 | 0.886427 | ||||||||
\(423\) | −8.27936 | −0.402556 | ||||||||
\(424\) | −43.8491 | −2.12950 | ||||||||
\(425\) | 2.83708 | 0.137618 | ||||||||
\(426\) | −22.7127 | −1.10044 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 23.1834 | 1.12061 | ||||||||
\(429\) | 4.35377 | 0.210202 | ||||||||
\(430\) | −23.4432 | −1.13053 | ||||||||
\(431\) | −25.5183 | −1.22918 | −0.614588 | − | 0.788849i | \(-0.710678\pi\) | ||||
−0.614588 | + | 0.788849i | \(0.710678\pi\) | |||||||
\(432\) | −64.4881 | −3.10269 | ||||||||
\(433\) | 21.5876 | 1.03743 | 0.518717 | − | 0.854946i | \(-0.326410\pi\) | ||||
0.518717 | + | 0.854946i | \(0.326410\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 20.1190 | 0.964633 | ||||||||
\(436\) | −39.8506 | −1.90850 | ||||||||
\(437\) | −14.3887 | −0.688304 | ||||||||
\(438\) | −93.3573 | −4.46078 | ||||||||
\(439\) | −29.2530 | −1.39617 | −0.698086 | − | 0.716014i | \(-0.745965\pi\) | ||||
−0.698086 | + | 0.716014i | \(0.745965\pi\) | |||||||
\(440\) | 5.26377 | 0.250940 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 9.56206 | 0.454821 | ||||||||
\(443\) | 6.49028 | 0.308363 | 0.154181 | − | 0.988043i | \(-0.450726\pi\) | ||||
0.154181 | + | 0.988043i | \(0.450726\pi\) | |||||||
\(444\) | −103.071 | −4.89151 | ||||||||
\(445\) | 10.4755 | 0.496586 | ||||||||
\(446\) | 3.50251 | 0.165849 | ||||||||
\(447\) | 75.3821 | 3.56545 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.1900 | 0.669668 | 0.334834 | − | 0.942277i | \(-0.391320\pi\) | ||||
0.334834 | + | 0.942277i | \(0.391320\pi\) | |||||||
\(450\) | −17.8791 | −0.842828 | ||||||||
\(451\) | 3.91618 | 0.184406 | ||||||||
\(452\) | 58.0507 | 2.73047 | ||||||||
\(453\) | −17.2344 | −0.809742 | ||||||||
\(454\) | −0.476084 | −0.0223437 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −37.1870 | −1.74144 | ||||||||
\(457\) | 16.8076 | 0.786224 | 0.393112 | − | 0.919491i | \(-0.371398\pi\) | ||||
0.393112 | + | 0.919491i | \(0.371398\pi\) | |||||||
\(458\) | −4.51477 | −0.210962 | ||||||||
\(459\) | −38.3105 | −1.78818 | ||||||||
\(460\) | −26.8729 | −1.25296 | ||||||||
\(461\) | −11.8158 | −0.550318 | −0.275159 | − | 0.961399i | \(-0.588730\pi\) | ||||
−0.275159 | + | 0.961399i | \(0.588730\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.7986 | −0.873644 | −0.436822 | − | 0.899548i | \(-0.643896\pi\) | ||||
−0.436822 | + | 0.899548i | \(0.643896\pi\) | |||||||
\(464\) | 30.0500 | 1.39503 | ||||||||
\(465\) | 33.0300 | 1.53173 | ||||||||
\(466\) | −49.9938 | −2.31592 | ||||||||
\(467\) | −18.0434 | −0.834950 | −0.417475 | − | 0.908689i | \(-0.637085\pi\) | ||||
−0.417475 | + | 0.908689i | \(0.637085\pi\) | |||||||
\(468\) | −40.5881 | −1.87618 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.83708 | −0.130865 | ||||||||
\(471\) | −19.0346 | −0.877069 | ||||||||
\(472\) | −11.8680 | −0.546269 | ||||||||
\(473\) | −9.47126 | −0.435489 | ||||||||
\(474\) | 69.3241 | 3.18416 | ||||||||
\(475\) | −2.20953 | −0.101380 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 60.1727 | 2.75512 | ||||||||
\(478\) | −33.5821 | −1.53601 | ||||||||
\(479\) | 16.2747 | 0.743611 | 0.371806 | − | 0.928311i | \(-0.378739\pi\) | ||||
0.371806 | + | 0.928311i | \(0.378739\pi\) | |||||||
\(480\) | −4.13472 | −0.188723 | ||||||||
\(481\) | −10.6369 | −0.485003 | ||||||||
\(482\) | 39.6296 | 1.80508 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.12660 | 0.187573 | ||||||||
\(485\) | −2.85280 | −0.129539 | ||||||||
\(486\) | 69.9313 | 3.17215 | ||||||||
\(487\) | 7.72075 | 0.349861 | 0.174930 | − | 0.984581i | \(-0.444030\pi\) | ||||
0.174930 | + | 0.984581i | \(0.444030\pi\) | |||||||
\(488\) | −31.7005 | −1.43501 | ||||||||
\(489\) | 39.9104 | 1.80481 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.6547 | −1.74446 | −0.872231 | − | 0.489095i | \(-0.837327\pi\) | ||||
−0.872231 | + | 0.489095i | \(0.837327\pi\) | |||||||
\(492\) | −51.6714 | −2.32953 | ||||||||
\(493\) | 17.8518 | 0.804005 | ||||||||
\(494\) | −7.44697 | −0.335055 | ||||||||
\(495\) | −7.22329 | −0.324663 | ||||||||
\(496\) | 49.3339 | 2.21516 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 68.1431 | 3.05356 | ||||||||
\(499\) | 40.1599 | 1.79780 | 0.898901 | − | 0.438151i | \(-0.144366\pi\) | ||||
0.898901 | + | 0.438151i | \(0.144366\pi\) | |||||||
\(500\) | −4.12660 | −0.184547 | ||||||||
\(501\) | −56.4663 | −2.52273 | ||||||||
\(502\) | 19.7435 | 0.881196 | ||||||||
\(503\) | −6.75989 | −0.301408 | −0.150704 | − | 0.988579i | \(-0.548154\pi\) | ||||
−0.150704 | + | 0.988579i | \(0.548154\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.89945 | 0.0845243 | ||||||||
\(506\) | −16.1188 | −0.716567 | ||||||||
\(507\) | 35.6377 | 1.58272 | ||||||||
\(508\) | −38.3906 | −1.70331 | ||||||||
\(509\) | 34.5690 | 1.53224 | 0.766121 | − | 0.642696i | \(-0.222184\pi\) | ||||
0.766121 | + | 0.642696i | \(0.222184\pi\) | |||||||
\(510\) | −22.4531 | −0.994240 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 44.1002 | 1.94897 | ||||||||
\(513\) | 29.8364 | 1.31731 | ||||||||
\(514\) | −20.0515 | −0.884432 | ||||||||
\(515\) | 8.56203 | 0.377288 | ||||||||
\(516\) | 124.967 | 5.50137 | ||||||||
\(517\) | −1.14620 | −0.0504099 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.33313 | −0.409679 | ||||||||
\(520\) | −7.16749 | −0.314315 | ||||||||
\(521\) | −23.3899 | −1.02473 | −0.512365 | − | 0.858768i | \(-0.671231\pi\) | ||||
−0.512365 | + | 0.858768i | \(0.671231\pi\) | |||||||
\(522\) | −112.501 | −4.92404 | ||||||||
\(523\) | −1.82225 | −0.0796815 | −0.0398407 | − | 0.999206i | \(-0.512685\pi\) | ||||
−0.0398407 | + | 0.999206i | \(0.512685\pi\) | |||||||
\(524\) | −65.1205 | −2.84480 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.0963 | 0.658229 | ||||||||
\(527\) | 29.3079 | 1.27667 | ||||||||
\(528\) | −15.2696 | −0.664525 | ||||||||
\(529\) | 19.4076 | 0.843809 | ||||||||
\(530\) | 20.6193 | 0.895646 | ||||||||
\(531\) | 16.2861 | 0.706756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.33252 | −0.230977 | ||||||||
\(534\) | −82.9049 | −3.58765 | ||||||||
\(535\) | −5.61803 | −0.242889 | ||||||||
\(536\) | 45.8480 | 1.98033 | ||||||||
\(537\) | 57.3847 | 2.47633 | ||||||||
\(538\) | −68.6495 | −2.95969 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 55.7237 | 2.39796 | ||||||||
\(541\) | −18.3946 | −0.790847 | −0.395424 | − | 0.918499i | \(-0.629402\pi\) | ||||
−0.395424 | + | 0.918499i | \(0.629402\pi\) | |||||||
\(542\) | −42.1431 | −1.81020 | ||||||||
\(543\) | −38.0655 | −1.63355 | ||||||||
\(544\) | −3.66878 | −0.157298 | ||||||||
\(545\) | 9.65700 | 0.413660 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.98726 | 0.170483 | 0.0852414 | − | 0.996360i | \(-0.472834\pi\) | ||||
0.0852414 | + | 0.996360i | \(0.472834\pi\) | |||||||
\(548\) | 27.6106 | 1.17947 | ||||||||
\(549\) | 43.5016 | 1.85660 | ||||||||
\(550\) | −2.47520 | −0.105543 | ||||||||
\(551\) | −13.9031 | −0.592290 | ||||||||
\(552\) | 109.601 | 4.66492 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −36.4786 | −1.54983 | ||||||||
\(555\) | 24.9771 | 1.06022 | ||||||||
\(556\) | −14.7395 | −0.625093 | ||||||||
\(557\) | 26.1553 | 1.10824 | 0.554119 | − | 0.832438i | \(-0.313055\pi\) | ||||
0.554119 | + | 0.832438i | \(0.313055\pi\) | |||||||
\(558\) | −184.696 | −7.81882 | ||||||||
\(559\) | 12.8967 | 0.545471 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.07124 | −0.382988 | ||||||||
\(562\) | 8.77453 | 0.370131 | ||||||||
\(563\) | −0.770882 | −0.0324888 | −0.0162444 | − | 0.999868i | \(-0.505171\pi\) | ||||
−0.0162444 | + | 0.999868i | \(0.505171\pi\) | |||||||
\(564\) | 15.1234 | 0.636810 | ||||||||
\(565\) | −14.0674 | −0.591821 | ||||||||
\(566\) | 56.1053 | 2.35828 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 15.1064 | 0.633850 | ||||||||
\(569\) | 20.0061 | 0.838700 | 0.419350 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419350 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(570\) | 17.4866 | 0.732432 | ||||||||
\(571\) | −4.52174 | −0.189229 | −0.0946145 | − | 0.995514i | \(-0.530162\pi\) | ||||
−0.0946145 | + | 0.995514i | \(0.530162\pi\) | |||||||
\(572\) | −5.61905 | −0.234944 | ||||||||
\(573\) | −22.0144 | −0.919666 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.51211 | 0.271574 | ||||||||
\(576\) | −45.8715 | −1.91131 | ||||||||
\(577\) | 27.6112 | 1.14947 | 0.574734 | − | 0.818340i | \(-0.305105\pi\) | ||||
0.574734 | + | 0.818340i | \(0.305105\pi\) | |||||||
\(578\) | 22.1555 | 0.921546 | ||||||||
\(579\) | −5.30656 | −0.220533 | ||||||||
\(580\) | −25.9659 | −1.07818 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 22.5776 | 0.935870 | ||||||||
\(583\) | 8.33037 | 0.345009 | ||||||||
\(584\) | 62.0925 | 2.56941 | ||||||||
\(585\) | 9.83571 | 0.406656 | ||||||||
\(586\) | −14.6276 | −0.604259 | ||||||||
\(587\) | −41.0780 | −1.69547 | −0.847734 | − | 0.530421i | \(-0.822034\pi\) | ||||
−0.847734 | + | 0.530421i | \(0.822034\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.8251 | −0.940491 | ||||||||
\(590\) | 5.58073 | 0.229755 | ||||||||
\(591\) | −59.8428 | −2.46160 | ||||||||
\(592\) | 37.3061 | 1.53327 | ||||||||
\(593\) | −38.7082 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(594\) | 33.4239 | 1.37140 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −97.2894 | −3.98513 | ||||||||
\(597\) | −62.1713 | −2.54450 | ||||||||
\(598\) | 21.9484 | 0.897535 | ||||||||
\(599\) | 1.50522 | 0.0615017 | 0.0307509 | − | 0.999527i | \(-0.490210\pi\) | ||||
0.0307509 | + | 0.999527i | \(0.490210\pi\) | |||||||
\(600\) | 16.8303 | 0.687094 | ||||||||
\(601\) | 31.9404 | 1.30287 | 0.651437 | − | 0.758702i | \(-0.274166\pi\) | ||||
0.651437 | + | 0.758702i | \(0.274166\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −62.9157 | −2.56213 | ||||||||
\(604\) | 22.2430 | 0.905054 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | −15.0325 | −0.610655 | ||||||||
\(607\) | −33.7368 | −1.36933 | −0.684667 | − | 0.728856i | \(-0.740053\pi\) | ||||
−0.684667 | + | 0.728856i | \(0.740053\pi\) | |||||||
\(608\) | 2.85726 | 0.115877 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 14.9066 | 0.603552 | ||||||||
\(611\) | 1.56074 | 0.0631409 | ||||||||
\(612\) | 84.5667 | 3.41841 | ||||||||
\(613\) | −35.6784 | −1.44104 | −0.720519 | − | 0.693435i | \(-0.756096\pi\) | ||||
−0.720519 | + | 0.693435i | \(0.756096\pi\) | |||||||
\(614\) | 7.41825 | 0.299376 | ||||||||
\(615\) | 12.5215 | 0.504917 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.170005 | −0.00684413 | −0.00342207 | − | 0.999994i | \(-0.501089\pi\) | ||||
−0.00342207 | + | 0.999994i | \(0.501089\pi\) | |||||||
\(618\) | −67.7613 | −2.72576 | ||||||||
\(619\) | 14.2539 | 0.572912 | 0.286456 | − | 0.958093i | \(-0.407523\pi\) | ||||
0.286456 | + | 0.958093i | \(0.407523\pi\) | |||||||
\(620\) | −42.6291 | −1.71202 | ||||||||
\(621\) | −87.9364 | −3.52877 | ||||||||
\(622\) | −1.47466 | −0.0591285 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 20.7921 | 0.832351 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −17.7165 | −0.708095 | ||||||||
\(627\) | 7.06472 | 0.282138 | ||||||||
\(628\) | 24.5664 | 0.980307 | ||||||||
\(629\) | 22.1625 | 0.883675 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.5090 | −0.697022 | −0.348511 | − | 0.937305i | \(-0.613313\pi\) | ||||
−0.348511 | + | 0.937305i | \(0.613313\pi\) | |||||||
\(632\) | −46.1079 | −1.83408 | ||||||||
\(633\) | 23.5226 | 0.934938 | ||||||||
\(634\) | −30.0109 | −1.19188 | ||||||||
\(635\) | 9.30320 | 0.369186 | ||||||||
\(636\) | −109.914 | −4.35837 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.5748 | −0.616610 | ||||||||
\(639\) | −20.7300 | −0.820067 | ||||||||
\(640\) | −18.3050 | −0.723570 | ||||||||
\(641\) | 38.5729 | 1.52354 | 0.761769 | − | 0.647849i | \(-0.224331\pi\) | ||||
0.761769 | + | 0.647849i | \(0.224331\pi\) | |||||||
\(642\) | 44.4621 | 1.75478 | ||||||||
\(643\) | −37.7939 | −1.49045 | −0.745223 | − | 0.666815i | \(-0.767657\pi\) | ||||
−0.745223 | + | 0.666815i | \(0.767657\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.2833 | −1.19240 | ||||||||
\(646\) | 15.5160 | 0.610470 | ||||||||
\(647\) | 17.6687 | 0.694630 | 0.347315 | − | 0.937749i | \(-0.387093\pi\) | ||||
0.347315 | + | 0.937749i | \(0.387093\pi\) | |||||||
\(648\) | −113.203 | −4.44704 | ||||||||
\(649\) | 2.25466 | 0.0885032 | ||||||||
\(650\) | 3.37039 | 0.132198 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −51.5090 | −2.01725 | ||||||||
\(653\) | −38.2713 | −1.49767 | −0.748837 | − | 0.662754i | \(-0.769387\pi\) | ||||
−0.748837 | + | 0.662754i | \(0.769387\pi\) | |||||||
\(654\) | −76.4271 | −2.98854 | ||||||||
\(655\) | 15.7807 | 0.616601 | ||||||||
\(656\) | 18.7023 | 0.730202 | ||||||||
\(657\) | −85.2076 | −3.32426 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.2280 | −0.476336 | −0.238168 | − | 0.971224i | \(-0.576547\pi\) | ||||
−0.238168 | + | 0.971224i | \(0.576547\pi\) | |||||||
\(660\) | 13.1944 | 0.513590 | ||||||||
\(661\) | 49.9188 | 1.94162 | 0.970808 | − | 0.239857i | \(-0.0771005\pi\) | ||||
0.970808 | + | 0.239857i | \(0.0771005\pi\) | |||||||
\(662\) | −29.3682 | −1.14143 | ||||||||
\(663\) | 12.3520 | 0.479711 | ||||||||
\(664\) | −45.3224 | −1.75885 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −139.666 | −5.41196 | ||||||||
\(667\) | 40.9763 | 1.58661 | ||||||||
\(668\) | 72.8763 | 2.81967 | ||||||||
\(669\) | 4.52444 | 0.174925 | ||||||||
\(670\) | −21.5593 | −0.832907 | ||||||||
\(671\) | 6.02240 | 0.232492 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6846 | −0.527502 | −0.263751 | − | 0.964591i | \(-0.584960\pi\) | ||||
−0.263751 | + | 0.964591i | \(0.584960\pi\) | |||||||
\(674\) | −58.7181 | −2.26173 | ||||||||
\(675\) | −13.5035 | −0.519750 | ||||||||
\(676\) | −45.9946 | −1.76902 | ||||||||
\(677\) | 8.96977 | 0.344736 | 0.172368 | − | 0.985033i | \(-0.444858\pi\) | ||||
0.172368 | + | 0.985033i | \(0.444858\pi\) | |||||||
\(678\) | 111.332 | 4.27568 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 14.9337 | 0.572682 | ||||||||
\(681\) | −0.614992 | −0.0235665 | ||||||||
\(682\) | −25.5695 | −0.979108 | ||||||||
\(683\) | −26.3119 | −1.00680 | −0.503399 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503399 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(684\) | −65.8609 | −2.51825 | ||||||||
\(685\) | −6.69088 | −0.255646 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.83205 | −0.222507 | ||||||||
\(688\) | −45.2314 | −1.72443 | ||||||||
\(689\) | −11.3432 | −0.432141 | ||||||||
\(690\) | −51.5380 | −1.96202 | ||||||||
\(691\) | 23.6024 | 0.897876 | 0.448938 | − | 0.893563i | \(-0.351802\pi\) | ||||
0.448938 | + | 0.893563i | \(0.351802\pi\) | |||||||
\(692\) | 12.0455 | 0.457901 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.53335 | −0.0582053 | ||||||||
\(695\) | 3.57182 | 0.135487 | ||||||||
\(696\) | 105.902 | 4.01420 | ||||||||
\(697\) | 11.1105 | 0.420840 | ||||||||
\(698\) | 34.7269 | 1.31443 | ||||||||
\(699\) | −64.5805 | −2.44266 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1198 | 0.684374 | 0.342187 | − | 0.939632i | \(-0.388832\pi\) | ||||
0.342187 | + | 0.939632i | \(0.388832\pi\) | |||||||
\(702\) | −45.5121 | −1.71774 | ||||||||
\(703\) | −17.2602 | −0.650981 | ||||||||
\(704\) | −6.35049 | −0.239343 | ||||||||
\(705\) | −3.66485 | −0.138026 | ||||||||
\(706\) | 62.7195 | 2.36048 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −29.7488 | −1.11803 | ||||||||
\(709\) | 43.5486 | 1.63550 | 0.817752 | − | 0.575571i | \(-0.195220\pi\) | ||||
0.817752 | + | 0.575571i | \(0.195220\pi\) | |||||||
\(710\) | −7.10353 | −0.266591 | ||||||||
\(711\) | 63.2724 | 2.37290 | ||||||||
\(712\) | 55.1406 | 2.06648 | ||||||||
\(713\) | 67.2721 | 2.51936 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.36166 | 0.0509234 | ||||||||
\(716\) | −74.0617 | −2.76782 | ||||||||
\(717\) | −43.3803 | −1.62007 | ||||||||
\(718\) | 28.6428 | 1.06894 | ||||||||
\(719\) | 45.1976 | 1.68559 | 0.842794 | − | 0.538237i | \(-0.180909\pi\) | ||||
0.842794 | + | 0.538237i | \(0.180909\pi\) | |||||||
\(720\) | −34.4960 | −1.28559 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 34.9448 | 1.30051 | ||||||||
\(723\) | 51.1924 | 1.90387 | ||||||||
\(724\) | 49.1280 | 1.82583 | ||||||||
\(725\) | 6.29233 | 0.233691 | ||||||||
\(726\) | 7.91417 | 0.293722 | ||||||||
\(727\) | 37.1901 | 1.37930 | 0.689652 | − | 0.724141i | \(-0.257763\pi\) | ||||
0.689652 | + | 0.724141i | \(0.257763\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 25.8169 | 0.956183 | ||||||||
\(730\) | −29.1980 | −1.08067 | ||||||||
\(731\) | −26.8707 | −0.993848 | ||||||||
\(732\) | −79.4617 | −2.93699 | ||||||||
\(733\) | −7.32991 | −0.270736 | −0.135368 | − | 0.990795i | \(-0.543222\pi\) | ||||
−0.135368 | + | 0.990795i | \(0.543222\pi\) | |||||||
\(734\) | −17.4632 | −0.644579 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.42118 | −0.310409 | ||||||||
\(737\) | −8.71012 | −0.320841 | ||||||||
\(738\) | −70.0176 | −2.57738 | ||||||||
\(739\) | 7.06120 | 0.259750 | 0.129875 | − | 0.991530i | \(-0.458542\pi\) | ||||
0.129875 | + | 0.991530i | \(0.458542\pi\) | |||||||
\(740\) | −32.2359 | −1.18501 | ||||||||
\(741\) | −9.61978 | −0.353391 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.2615 | −1.00013 | −0.500064 | − | 0.865988i | \(-0.666690\pi\) | ||||
−0.500064 | + | 0.865988i | \(0.666690\pi\) | |||||||
\(744\) | 173.862 | 6.37409 | ||||||||
\(745\) | 23.5761 | 0.863763 | ||||||||
\(746\) | −5.49897 | −0.201332 | ||||||||
\(747\) | 62.1944 | 2.27558 | ||||||||
\(748\) | 11.7075 | 0.428068 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −7.91417 | −0.288985 | ||||||||
\(751\) | 46.2169 | 1.68648 | 0.843239 | − | 0.537538i | \(-0.180646\pi\) | ||||
0.843239 | + | 0.537538i | \(0.180646\pi\) | |||||||
\(752\) | −5.47387 | −0.199611 | ||||||||
\(753\) | 25.5041 | 0.929421 | ||||||||
\(754\) | 21.2076 | 0.772335 | ||||||||
\(755\) | −5.39014 | −0.196167 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0891 | −0.657458 | −0.328729 | − | 0.944424i | \(-0.606620\pi\) | ||||
−0.328729 | + | 0.944424i | \(0.606620\pi\) | |||||||
\(758\) | −0.260043 | −0.00944520 | ||||||||
\(759\) | −20.8218 | −0.755782 | ||||||||
\(760\) | −11.6304 | −0.421880 | ||||||||
\(761\) | −11.8172 | −0.428374 | −0.214187 | − | 0.976793i | \(-0.568710\pi\) | ||||
−0.214187 | + | 0.976793i | \(0.568710\pi\) | |||||||
\(762\) | −73.6271 | −2.66723 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 28.4122 | 1.02792 | ||||||||
\(765\) | −20.4930 | −0.740928 | ||||||||
\(766\) | −43.2544 | −1.56284 | ||||||||
\(767\) | −3.07009 | −0.110855 | ||||||||
\(768\) | 104.259 | 3.76213 | ||||||||
\(769\) | 42.9075 | 1.54728 | 0.773642 | − | 0.633623i | \(-0.218433\pi\) | ||||
0.773642 | + | 0.633623i | \(0.218433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −25.9019 | −0.932834 | ||||||||
\(772\) | 6.84874 | 0.246492 | ||||||||
\(773\) | 17.9460 | 0.645473 | 0.322736 | − | 0.946489i | \(-0.395397\pi\) | ||||
0.322736 | + | 0.946489i | \(0.395397\pi\) | |||||||
\(774\) | 169.337 | 6.08671 | ||||||||
\(775\) | 10.3303 | 0.371075 | ||||||||
\(776\) | −15.0165 | −0.539061 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −65.0416 | −2.33186 | ||||||||
\(779\) | −8.65290 | −0.310022 | ||||||||
\(780\) | −17.9663 | −0.643297 | ||||||||
\(781\) | −2.86988 | −0.102692 | ||||||||
\(782\) | −45.7302 | −1.63531 | ||||||||
\(783\) | −84.9685 | −3.03653 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.95318 | −0.212478 | ||||||||
\(786\) | −124.891 | −4.45471 | ||||||||
\(787\) | 8.84623 | 0.315334 | 0.157667 | − | 0.987492i | \(-0.449603\pi\) | ||||
0.157667 | + | 0.987492i | \(0.449603\pi\) | |||||||
\(788\) | 77.2341 | 2.75135 | ||||||||
\(789\) | 19.5009 | 0.694252 | ||||||||
\(790\) | 21.6815 | 0.771393 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −38.0217 | −1.35104 | ||||||||
\(793\) | −8.20049 | −0.291208 | ||||||||
\(794\) | −49.1901 | −1.74569 | ||||||||
\(795\) | 26.6354 | 0.944661 | ||||||||
\(796\) | 80.2394 | 2.84401 | ||||||||
\(797\) | −23.9643 | −0.848859 | −0.424429 | − | 0.905461i | \(-0.639525\pi\) | ||||
−0.424429 | + | 0.905461i | \(0.639525\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.25186 | −0.115043 | ||||||||
\(800\) | −1.29316 | −0.0457200 | ||||||||
\(801\) | −75.6676 | −2.67358 | ||||||||
\(802\) | 49.9001 | 1.76204 | ||||||||
\(803\) | −11.7962 | −0.416280 | ||||||||
\(804\) | 114.924 | 4.05307 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 34.8171 | 1.22638 | ||||||||
\(807\) | −88.6794 | −3.12166 | ||||||||
\(808\) | 9.99824 | 0.351737 | ||||||||
\(809\) | 12.0434 | 0.423423 | 0.211712 | − | 0.977332i | \(-0.432096\pi\) | ||||
0.211712 | + | 0.977332i | \(0.432096\pi\) | |||||||
\(810\) | 53.2318 | 1.87038 | ||||||||
\(811\) | −2.30398 | −0.0809035 | −0.0404518 | − | 0.999181i | \(-0.512880\pi\) | ||||
−0.0404518 | + | 0.999181i | \(0.512880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.4392 | −1.90927 | ||||||||
\(814\) | −19.3355 | −0.677711 | ||||||||
\(815\) | 12.4822 | 0.437231 | ||||||||
\(816\) | −43.3211 | −1.51654 | ||||||||
\(817\) | 20.9270 | 0.732143 | ||||||||
\(818\) | −50.4832 | −1.76510 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.1605 | −0.564349 | ||||||||
\(821\) | 0.964222 | 0.0336516 | 0.0168258 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168258 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(822\) | 52.9528 | 1.84694 | ||||||||
\(823\) | 0.751163 | 0.0261839 | 0.0130919 | − | 0.999914i | \(-0.495833\pi\) | ||||
0.0130919 | + | 0.999914i | \(0.495833\pi\) | |||||||
\(824\) | 45.0685 | 1.57004 | ||||||||
\(825\) | −3.19739 | −0.111319 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.31121 | −0.0803685 | −0.0401843 | − | 0.999192i | \(-0.512794\pi\) | ||||
−0.0401843 | + | 0.999192i | \(0.512794\pi\) | |||||||
\(828\) | 194.111 | 6.74582 | ||||||||
\(829\) | 46.2419 | 1.60605 | 0.803024 | − | 0.595947i | \(-0.203223\pi\) | ||||
0.803024 | + | 0.595947i | \(0.203223\pi\) | |||||||
\(830\) | 21.3121 | 0.739754 | ||||||||
\(831\) | −47.1219 | −1.63464 | ||||||||
\(832\) | 8.64724 | 0.299789 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −28.2680 | −0.978840 | ||||||||
\(835\) | −17.6601 | −0.611154 | ||||||||
\(836\) | −9.11784 | −0.315347 | ||||||||
\(837\) | −139.495 | −4.82166 | ||||||||
\(838\) | −4.86668 | −0.168117 | ||||||||
\(839\) | 33.6375 | 1.16130 | 0.580648 | − | 0.814155i | \(-0.302799\pi\) | ||||
0.580648 | + | 0.814155i | \(0.302799\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.5934 | 0.365289 | ||||||||
\(842\) | 49.2616 | 1.69767 | ||||||||
\(843\) | 11.3347 | 0.390387 | ||||||||
\(844\) | −30.3586 | −1.04499 | ||||||||
\(845\) | 11.1459 | 0.383430 | ||||||||
\(846\) | 20.4930 | 0.704565 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 39.7830 | 1.36615 | ||||||||
\(849\) | 72.4752 | 2.48734 | ||||||||
\(850\) | −7.02233 | −0.240864 | ||||||||
\(851\) | 50.8708 | 1.74383 | ||||||||
\(852\) | 37.8663 | 1.29728 | ||||||||
\(853\) | 44.7072 | 1.53075 | 0.765373 | − | 0.643587i | \(-0.222554\pi\) | ||||
0.765373 | + | 0.643587i | \(0.222554\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.9601 | 0.545823 | ||||||||
\(856\) | −29.5720 | −1.01075 | ||||||||
\(857\) | 20.3336 | 0.694583 | 0.347292 | − | 0.937757i | \(-0.387101\pi\) | ||||
0.347292 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(858\) | −10.7764 | −0.367902 | ||||||||
\(859\) | −38.0627 | −1.29868 | −0.649341 | − | 0.760498i | \(-0.724955\pi\) | ||||
−0.649341 | + | 0.760498i | \(0.724955\pi\) | |||||||
\(860\) | 39.0841 | 1.33276 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 63.1629 | 2.15134 | ||||||||
\(863\) | −34.0330 | −1.15850 | −0.579248 | − | 0.815152i | \(-0.696654\pi\) | ||||
−0.579248 | + | 0.815152i | \(0.696654\pi\) | |||||||
\(864\) | 17.4621 | 0.594074 | ||||||||
\(865\) | −2.91898 | −0.0992484 | ||||||||
\(866\) | −53.4336 | −1.81575 | ||||||||
\(867\) | 28.6198 | 0.971979 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.75950 | 0.297146 | ||||||||
\(870\) | −49.7985 | −1.68833 | ||||||||
\(871\) | 11.8603 | 0.401870 | ||||||||
\(872\) | 50.8322 | 1.72139 | ||||||||
\(873\) | 20.6066 | 0.697429 | ||||||||
\(874\) | 35.6149 | 1.20469 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 155.644 | 5.25871 | ||||||||
\(877\) | 4.57143 | 0.154366 | 0.0771831 | − | 0.997017i | \(-0.475407\pi\) | ||||
0.0771831 | + | 0.997017i | \(0.475407\pi\) | |||||||
\(878\) | 72.4071 | 2.44362 | ||||||||
\(879\) | −18.8954 | −0.637328 | ||||||||
\(880\) | −4.77565 | −0.160987 | ||||||||
\(881\) | 21.3685 | 0.719922 | 0.359961 | − | 0.932967i | \(-0.382790\pi\) | ||||
0.359961 | + | 0.932967i | \(0.382790\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.7488 | 0.597294 | 0.298647 | − | 0.954364i | \(-0.403465\pi\) | ||||
0.298647 | + | 0.954364i | \(0.403465\pi\) | |||||||
\(884\) | −15.9417 | −0.536177 | ||||||||
\(885\) | 7.20903 | 0.242329 | ||||||||
\(886\) | −16.0647 | −0.539705 | ||||||||
\(887\) | 50.7758 | 1.70489 | 0.852443 | − | 0.522820i | \(-0.175120\pi\) | ||||
0.852443 | + | 0.522820i | \(0.175120\pi\) | |||||||
\(888\) | 131.474 | 4.41197 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −25.9289 | −0.869140 | ||||||||
\(891\) | 21.5061 | 0.720481 | ||||||||
\(892\) | −5.83932 | −0.195515 | ||||||||
\(893\) | 2.53256 | 0.0847491 | ||||||||
\(894\) | −186.586 | −6.24036 | ||||||||
\(895\) | 17.9474 | 0.599914 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.3523 | 0.946654 | ||||||||
\(898\) | −35.1231 | −1.17207 | ||||||||
\(899\) | 65.0016 | 2.16793 | ||||||||
\(900\) | 29.8077 | 0.993589 | ||||||||
\(901\) | 23.6339 | 0.787360 | ||||||||
\(902\) | −9.69331 | −0.322752 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −74.0476 | −2.46279 | ||||||||
\(905\) | −11.9052 | −0.395742 | ||||||||
\(906\) | 42.6585 | 1.41723 | ||||||||
\(907\) | 30.3479 | 1.00769 | 0.503843 | − | 0.863795i | \(-0.331919\pi\) | ||||
0.503843 | + | 0.863795i | \(0.331919\pi\) | |||||||
\(908\) | 0.793719 | 0.0263405 | ||||||||
\(909\) | −13.7203 | −0.455072 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.0080 | 1.12673 | 0.563367 | − | 0.826207i | \(-0.309506\pi\) | ||||
0.563367 | + | 0.826207i | \(0.309506\pi\) | |||||||
\(912\) | 33.7386 | 1.11720 | ||||||||
\(913\) | 8.61026 | 0.284958 | ||||||||
\(914\) | −41.6020 | −1.37607 | ||||||||
\(915\) | 19.2559 | 0.636582 | ||||||||
\(916\) | 7.52695 | 0.248697 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 94.8261 | 3.12973 | ||||||||
\(919\) | −31.0756 | −1.02509 | −0.512545 | − | 0.858660i | \(-0.671297\pi\) | ||||
−0.512545 | + | 0.858660i | \(0.671297\pi\) | |||||||
\(920\) | 34.2782 | 1.13012 | ||||||||
\(921\) | 9.58269 | 0.315760 | ||||||||
\(922\) | 29.2465 | 0.963182 | ||||||||
\(923\) | 3.90782 | 0.128627 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.81172 | 0.256848 | ||||||||
\(926\) | 46.5302 | 1.52908 | ||||||||
\(927\) | −61.8460 | −2.03129 | ||||||||
\(928\) | −8.13696 | −0.267109 | ||||||||
\(929\) | −32.5075 | −1.06654 | −0.533268 | − | 0.845947i | \(-0.679036\pi\) | ||||
−0.533268 | + | 0.845947i | \(0.679036\pi\) | |||||||
\(930\) | −81.7557 | −2.68088 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 83.3487 | 2.73018 | ||||||||
\(933\) | −1.90492 | −0.0623644 | ||||||||
\(934\) | 44.6610 | 1.46135 | ||||||||
\(935\) | −2.83708 | −0.0927824 | ||||||||
\(936\) | 51.7729 | 1.69225 | ||||||||
\(937\) | 19.7428 | 0.644968 | 0.322484 | − | 0.946575i | \(-0.395482\pi\) | ||||
0.322484 | + | 0.946575i | \(0.395482\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −22.8857 | −0.746847 | ||||||||
\(940\) | 4.72992 | 0.154273 | ||||||||
\(941\) | 36.4351 | 1.18775 | 0.593875 | − | 0.804557i | \(-0.297597\pi\) | ||||
0.593875 | + | 0.804557i | \(0.297597\pi\) | |||||||
\(942\) | 47.1145 | 1.53507 | ||||||||
\(943\) | 25.5026 | 0.830478 | ||||||||
\(944\) | 10.7675 | 0.350452 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23.4432 | 0.762205 | ||||||||
\(947\) | 33.1578 | 1.07749 | 0.538743 | − | 0.842470i | \(-0.318900\pi\) | ||||
0.538743 | + | 0.842470i | \(0.318900\pi\) | |||||||
\(948\) | −115.576 | −3.75373 | ||||||||
\(949\) | 16.0625 | 0.521411 | ||||||||
\(950\) | 5.46902 | 0.177438 | ||||||||
\(951\) | −38.7672 | −1.25711 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33.3590 | 1.08060 | 0.540302 | − | 0.841471i | \(-0.318310\pi\) | ||||
0.540302 | + | 0.841471i | \(0.318310\pi\) | |||||||
\(954\) | −148.939 | −4.82209 | ||||||||
\(955\) | −6.88513 | −0.222797 | ||||||||
\(956\) | 55.9874 | 1.81076 | ||||||||
\(957\) | −20.1190 | −0.650355 | ||||||||
\(958\) | −40.2832 | −1.30149 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −20.3050 | −0.655341 | ||||||||
\(961\) | 75.7151 | 2.44242 | ||||||||
\(962\) | 26.3285 | 0.848866 | ||||||||
\(963\) | 40.5807 | 1.30769 | ||||||||
\(964\) | −66.0698 | −2.12796 | ||||||||
\(965\) | −1.65966 | −0.0534262 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.1532 | −1.03398 | −0.516989 | − | 0.855992i | \(-0.672947\pi\) | ||||
−0.516989 | + | 0.855992i | \(0.672947\pi\) | |||||||
\(968\) | −5.26377 | −0.169184 | ||||||||
\(969\) | 20.0431 | 0.643879 | ||||||||
\(970\) | 7.06125 | 0.226723 | ||||||||
\(971\) | 11.2955 | 0.362489 | 0.181244 | − | 0.983438i | \(-0.441988\pi\) | ||||
0.181244 | + | 0.983438i | \(0.441988\pi\) | |||||||
\(972\) | −116.588 | −3.73957 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −19.1104 | −0.612336 | ||||||||
\(975\) | 4.35377 | 0.139432 | ||||||||
\(976\) | 28.7609 | 0.920614 | ||||||||
\(977\) | −45.9622 | −1.47046 | −0.735230 | − | 0.677818i | \(-0.762926\pi\) | ||||
−0.735230 | + | 0.677818i | \(0.762926\pi\) | |||||||
\(978\) | −98.7860 | −3.15883 | ||||||||
\(979\) | −10.4755 | −0.334798 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −69.7553 | −2.22712 | ||||||||
\(982\) | 95.6780 | 3.05321 | ||||||||
\(983\) | −9.75209 | −0.311043 | −0.155522 | − | 0.987832i | \(-0.549706\pi\) | ||||
−0.155522 | + | 0.987832i | \(0.549706\pi\) | |||||||
\(984\) | 65.9104 | 2.10115 | ||||||||
\(985\) | −18.7161 | −0.596346 | ||||||||
\(986\) | −44.1868 | −1.40719 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.4154 | 0.394988 | ||||||||
\(989\) | −61.6779 | −1.96124 | ||||||||
\(990\) | 17.8791 | 0.568235 | ||||||||
\(991\) | −3.15511 | −0.100225 | −0.0501127 | − | 0.998744i | \(-0.515958\pi\) | ||||
−0.0501127 | + | 0.998744i | \(0.515958\pi\) | |||||||
\(992\) | −13.3587 | −0.424139 | ||||||||
\(993\) | −37.9370 | −1.20389 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.4444 | −0.616429 | ||||||||
\(996\) | −113.607 | −3.59977 | ||||||||
\(997\) | −45.0881 | −1.42796 | −0.713978 | − | 0.700168i | \(-0.753108\pi\) | ||||
−0.713978 | + | 0.700168i | \(0.753108\pi\) | |||||||
\(998\) | −99.4036 | −3.14657 | ||||||||
\(999\) | −105.486 | −3.33742 |
(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 | 2695.2.a.y.1.1 | 10 | ||
7.2 | even | 3 | 385.2.i.d.221.10 | ✓ | 20 | ||
7.4 | even | 3 | 385.2.i.d.331.10 | yes | 20 | ||
7.6 | odd | 2 | 2695.2.a.z.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.i.d.221.10 | ✓ | 20 | 7.2 | even | 3 | ||
385.2.i.d.331.10 | yes | 20 | 7.4 | even | 3 | ||
2695.2.a.y.1.1 | 10 | 1.1 | even | 1 | trivial | ||
2695.2.a.z.1.1 | 10 | 7.6 | odd | 2 |