Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8034,2,Mod(1,8034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8034, 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("8034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8034.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: | \(64.1518129839\) |
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: | \( x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.194986\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8034.1 |
$q$-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 | ||||||||
\(5\) | 3.32958 | 1.48903 | 0.744516 | − | 0.667604i | \(-0.232680\pi\) | ||||
0.744516 | + | 0.667604i | \(0.232680\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.38443 | −0.523267 | −0.261634 | − | 0.965167i | \(-0.584261\pi\) | ||||
−0.261634 | + | 0.965167i | \(0.584261\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.32958 | −1.05290 | ||||||||
\(11\) | −2.60808 | −0.786365 | −0.393183 | − | 0.919460i | \(-0.628626\pi\) | ||||
−0.393183 | + | 0.919460i | \(0.628626\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 1.38443 | 0.370006 | ||||||||
\(15\) | −3.32958 | −0.859693 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.65277 | −0.400854 | −0.200427 | − | 0.979709i | \(-0.564233\pi\) | ||||
−0.200427 | + | 0.979709i | \(0.564233\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.38443 | −0.547027 | −0.273513 | − | 0.961868i | \(-0.588186\pi\) | ||||
−0.273513 | + | 0.961868i | \(0.588186\pi\) | |||||||
\(20\) | 3.32958 | 0.744516 | ||||||||
\(21\) | 1.38443 | 0.302108 | ||||||||
\(22\) | 2.60808 | 0.556044 | ||||||||
\(23\) | 0.437417 | 0.0912077 | 0.0456038 | − | 0.998960i | \(-0.485479\pi\) | ||||
0.0456038 | + | 0.998960i | \(0.485479\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 6.08609 | 1.21722 | ||||||||
\(26\) | −1.00000 | −0.196116 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.38443 | −0.261634 | ||||||||
\(29\) | 1.38942 | 0.258009 | 0.129004 | − | 0.991644i | \(-0.458822\pi\) | ||||
0.129004 | + | 0.991644i | \(0.458822\pi\) | |||||||
\(30\) | 3.32958 | 0.607895 | ||||||||
\(31\) | −5.09491 | −0.915072 | −0.457536 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457536 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.60808 | 0.454008 | ||||||||
\(34\) | 1.65277 | 0.283447 | ||||||||
\(35\) | −4.60958 | −0.779162 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.25229 | 1.02787 | 0.513935 | − | 0.857829i | \(-0.328187\pi\) | ||||
0.513935 | + | 0.857829i | \(0.328187\pi\) | |||||||
\(38\) | 2.38443 | 0.386806 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −3.32958 | −0.526452 | ||||||||
\(41\) | 2.88017 | 0.449807 | 0.224904 | − | 0.974381i | \(-0.427793\pi\) | ||||
0.224904 | + | 0.974381i | \(0.427793\pi\) | |||||||
\(42\) | −1.38443 | −0.213623 | ||||||||
\(43\) | 0.927277 | 0.141408 | 0.0707042 | − | 0.997497i | \(-0.477475\pi\) | ||||
0.0707042 | + | 0.997497i | \(0.477475\pi\) | |||||||
\(44\) | −2.60808 | −0.393183 | ||||||||
\(45\) | 3.32958 | 0.496344 | ||||||||
\(46\) | −0.437417 | −0.0644936 | ||||||||
\(47\) | −10.7983 | −1.57509 | −0.787545 | − | 0.616258i | \(-0.788648\pi\) | ||||
−0.787545 | + | 0.616258i | \(0.788648\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −5.08334 | −0.726192 | ||||||||
\(50\) | −6.08609 | −0.860702 | ||||||||
\(51\) | 1.65277 | 0.231433 | ||||||||
\(52\) | 1.00000 | 0.138675 | ||||||||
\(53\) | 8.01315 | 1.10069 | 0.550345 | − | 0.834937i | \(-0.314496\pi\) | ||||
0.550345 | + | 0.834937i | \(0.314496\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.68380 | −1.17092 | ||||||||
\(56\) | 1.38443 | 0.185003 | ||||||||
\(57\) | 2.38443 | 0.315826 | ||||||||
\(58\) | −1.38942 | −0.182440 | ||||||||
\(59\) | 3.33907 | 0.434709 | 0.217355 | − | 0.976093i | \(-0.430257\pi\) | ||||
0.217355 | + | 0.976093i | \(0.430257\pi\) | |||||||
\(60\) | −3.32958 | −0.429847 | ||||||||
\(61\) | −1.16385 | −0.149016 | −0.0745081 | − | 0.997220i | \(-0.523739\pi\) | ||||
−0.0745081 | + | 0.997220i | \(0.523739\pi\) | |||||||
\(62\) | 5.09491 | 0.647054 | ||||||||
\(63\) | −1.38443 | −0.174422 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.32958 | 0.412983 | ||||||||
\(66\) | −2.60808 | −0.321032 | ||||||||
\(67\) | 8.02334 | 0.980207 | 0.490104 | − | 0.871664i | \(-0.336959\pi\) | ||||
0.490104 | + | 0.871664i | \(0.336959\pi\) | |||||||
\(68\) | −1.65277 | −0.200427 | ||||||||
\(69\) | −0.437417 | −0.0526588 | ||||||||
\(70\) | 4.60958 | 0.550950 | ||||||||
\(71\) | 5.77612 | 0.685499 | 0.342750 | − | 0.939427i | \(-0.388642\pi\) | ||||
0.342750 | + | 0.939427i | \(0.388642\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −5.91373 | −0.692150 | −0.346075 | − | 0.938207i | \(-0.612486\pi\) | ||||
−0.346075 | + | 0.938207i | \(0.612486\pi\) | |||||||
\(74\) | −6.25229 | −0.726814 | ||||||||
\(75\) | −6.08609 | −0.702761 | ||||||||
\(76\) | −2.38443 | −0.273513 | ||||||||
\(77\) | 3.61071 | 0.411479 | ||||||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 5.61371 | 0.631592 | 0.315796 | − | 0.948827i | \(-0.397728\pi\) | ||||
0.315796 | + | 0.948827i | \(0.397728\pi\) | |||||||
\(80\) | 3.32958 | 0.372258 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.88017 | −0.318062 | ||||||||
\(83\) | −7.43809 | −0.816437 | −0.408218 | − | 0.912884i | \(-0.633850\pi\) | ||||
−0.408218 | + | 0.912884i | \(0.633850\pi\) | |||||||
\(84\) | 1.38443 | 0.151054 | ||||||||
\(85\) | −5.50301 | −0.596885 | ||||||||
\(86\) | −0.927277 | −0.0999909 | ||||||||
\(87\) | −1.38942 | −0.148961 | ||||||||
\(88\) | 2.60808 | 0.278022 | ||||||||
\(89\) | 17.2269 | 1.82605 | 0.913023 | − | 0.407908i | \(-0.133741\pi\) | ||||
0.913023 | + | 0.407908i | \(0.133741\pi\) | |||||||
\(90\) | −3.32958 | −0.350968 | ||||||||
\(91\) | −1.38443 | −0.145128 | ||||||||
\(92\) | 0.437417 | 0.0456038 | ||||||||
\(93\) | 5.09491 | 0.528317 | ||||||||
\(94\) | 10.7983 | 1.11376 | ||||||||
\(95\) | −7.93916 | −0.814541 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.80223 | −0.182989 | −0.0914945 | − | 0.995806i | \(-0.529164\pi\) | ||||
−0.0914945 | + | 0.995806i | \(0.529164\pi\) | |||||||
\(98\) | 5.08334 | 0.513495 | ||||||||
\(99\) | −2.60808 | −0.262122 | ||||||||
\(100\) | 6.08609 | 0.608609 | ||||||||
\(101\) | −2.58210 | −0.256929 | −0.128464 | − | 0.991714i | \(-0.541005\pi\) | ||||
−0.128464 | + | 0.991714i | \(0.541005\pi\) | |||||||
\(102\) | −1.65277 | −0.163648 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 4.60958 | 0.449849 | ||||||||
\(106\) | −8.01315 | −0.778306 | ||||||||
\(107\) | −12.0189 | −1.16191 | −0.580957 | − | 0.813934i | \(-0.697322\pi\) | ||||
−0.580957 | + | 0.813934i | \(0.697322\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −9.77876 | −0.936636 | −0.468318 | − | 0.883560i | \(-0.655140\pi\) | ||||
−0.468318 | + | 0.883560i | \(0.655140\pi\) | |||||||
\(110\) | 8.68380 | 0.827968 | ||||||||
\(111\) | −6.25229 | −0.593441 | ||||||||
\(112\) | −1.38443 | −0.130817 | ||||||||
\(113\) | −14.8934 | −1.40105 | −0.700527 | − | 0.713626i | \(-0.747051\pi\) | ||||
−0.700527 | + | 0.713626i | \(0.747051\pi\) | |||||||
\(114\) | −2.38443 | −0.223323 | ||||||||
\(115\) | 1.45641 | 0.135811 | ||||||||
\(116\) | 1.38942 | 0.129004 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | −3.33907 | −0.307386 | ||||||||
\(119\) | 2.28815 | 0.209754 | ||||||||
\(120\) | 3.32958 | 0.303947 | ||||||||
\(121\) | −4.19793 | −0.381630 | ||||||||
\(122\) | 1.16385 | 0.105370 | ||||||||
\(123\) | −2.88017 | −0.259696 | ||||||||
\(124\) | −5.09491 | −0.457536 | ||||||||
\(125\) | 3.61621 | 0.323443 | ||||||||
\(126\) | 1.38443 | 0.123335 | ||||||||
\(127\) | 6.22507 | 0.552385 | 0.276193 | − | 0.961102i | \(-0.410927\pi\) | ||||
0.276193 | + | 0.961102i | \(0.410927\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.927277 | −0.0816422 | ||||||||
\(130\) | −3.32958 | −0.292023 | ||||||||
\(131\) | −9.84125 | −0.859834 | −0.429917 | − | 0.902868i | \(-0.641457\pi\) | ||||
−0.429917 | + | 0.902868i | \(0.641457\pi\) | |||||||
\(132\) | 2.60808 | 0.227004 | ||||||||
\(133\) | 3.30109 | 0.286241 | ||||||||
\(134\) | −8.02334 | −0.693111 | ||||||||
\(135\) | −3.32958 | −0.286564 | ||||||||
\(136\) | 1.65277 | 0.141723 | ||||||||
\(137\) | −10.1134 | −0.864043 | −0.432022 | − | 0.901863i | \(-0.642200\pi\) | ||||
−0.432022 | + | 0.901863i | \(0.642200\pi\) | |||||||
\(138\) | 0.437417 | 0.0372354 | ||||||||
\(139\) | −22.7082 | −1.92608 | −0.963041 | − | 0.269356i | \(-0.913189\pi\) | ||||
−0.963041 | + | 0.269356i | \(0.913189\pi\) | |||||||
\(140\) | −4.60958 | −0.389581 | ||||||||
\(141\) | 10.7983 | 0.909378 | ||||||||
\(142\) | −5.77612 | −0.484721 | ||||||||
\(143\) | −2.60808 | −0.218098 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.62618 | 0.384183 | ||||||||
\(146\) | 5.91373 | 0.489424 | ||||||||
\(147\) | 5.08334 | 0.419267 | ||||||||
\(148\) | 6.25229 | 0.513935 | ||||||||
\(149\) | −5.39722 | −0.442158 | −0.221079 | − | 0.975256i | \(-0.570958\pi\) | ||||
−0.221079 | + | 0.975256i | \(0.570958\pi\) | |||||||
\(150\) | 6.08609 | 0.496927 | ||||||||
\(151\) | −2.23675 | −0.182024 | −0.0910122 | − | 0.995850i | \(-0.529010\pi\) | ||||
−0.0910122 | + | 0.995850i | \(0.529010\pi\) | |||||||
\(152\) | 2.38443 | 0.193403 | ||||||||
\(153\) | −1.65277 | −0.133618 | ||||||||
\(154\) | −3.61071 | −0.290960 | ||||||||
\(155\) | −16.9639 | −1.36257 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 16.1805 | 1.29134 | 0.645671 | − | 0.763616i | \(-0.276578\pi\) | ||||
0.645671 | + | 0.763616i | \(0.276578\pi\) | |||||||
\(158\) | −5.61371 | −0.446603 | ||||||||
\(159\) | −8.01315 | −0.635484 | ||||||||
\(160\) | −3.32958 | −0.263226 | ||||||||
\(161\) | −0.605575 | −0.0477260 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −11.0400 | −0.864722 | −0.432361 | − | 0.901701i | \(-0.642319\pi\) | ||||
−0.432361 | + | 0.901701i | \(0.642319\pi\) | |||||||
\(164\) | 2.88017 | 0.224904 | ||||||||
\(165\) | 8.68380 | 0.676033 | ||||||||
\(166\) | 7.43809 | 0.577308 | ||||||||
\(167\) | −16.6481 | −1.28827 | −0.644134 | − | 0.764913i | \(-0.722782\pi\) | ||||
−0.644134 | + | 0.764913i | \(0.722782\pi\) | |||||||
\(168\) | −1.38443 | −0.106811 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 5.50301 | 0.422062 | ||||||||
\(171\) | −2.38443 | −0.182342 | ||||||||
\(172\) | 0.927277 | 0.0707042 | ||||||||
\(173\) | −11.4486 | −0.870424 | −0.435212 | − | 0.900328i | \(-0.643327\pi\) | ||||
−0.435212 | + | 0.900328i | \(0.643327\pi\) | |||||||
\(174\) | 1.38942 | 0.105332 | ||||||||
\(175\) | −8.42579 | −0.636930 | ||||||||
\(176\) | −2.60808 | −0.196591 | ||||||||
\(177\) | −3.33907 | −0.250980 | ||||||||
\(178\) | −17.2269 | −1.29121 | ||||||||
\(179\) | −10.1335 | −0.757413 | −0.378706 | − | 0.925517i | \(-0.623631\pi\) | ||||
−0.378706 | + | 0.925517i | \(0.623631\pi\) | |||||||
\(180\) | 3.32958 | 0.248172 | ||||||||
\(181\) | −20.8197 | −1.54751 | −0.773757 | − | 0.633483i | \(-0.781625\pi\) | ||||
−0.773757 | + | 0.633483i | \(0.781625\pi\) | |||||||
\(182\) | 1.38443 | 0.102621 | ||||||||
\(183\) | 1.16385 | 0.0860345 | ||||||||
\(184\) | −0.437417 | −0.0322468 | ||||||||
\(185\) | 20.8175 | 1.53053 | ||||||||
\(186\) | −5.09491 | −0.373577 | ||||||||
\(187\) | 4.31054 | 0.315218 | ||||||||
\(188\) | −10.7983 | −0.787545 | ||||||||
\(189\) | 1.38443 | 0.100703 | ||||||||
\(190\) | 7.93916 | 0.575967 | ||||||||
\(191\) | −5.92513 | −0.428727 | −0.214364 | − | 0.976754i | \(-0.568768\pi\) | ||||
−0.214364 | + | 0.976754i | \(0.568768\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 20.0653 | 1.44433 | 0.722167 | − | 0.691718i | \(-0.243146\pi\) | ||||
0.722167 | + | 0.691718i | \(0.243146\pi\) | |||||||
\(194\) | 1.80223 | 0.129393 | ||||||||
\(195\) | −3.32958 | −0.238436 | ||||||||
\(196\) | −5.08334 | −0.363096 | ||||||||
\(197\) | 11.0734 | 0.788948 | 0.394474 | − | 0.918907i | \(-0.370927\pi\) | ||||
0.394474 | + | 0.918907i | \(0.370927\pi\) | |||||||
\(198\) | 2.60808 | 0.185348 | ||||||||
\(199\) | −7.37014 | −0.522455 | −0.261228 | − | 0.965277i | \(-0.584127\pi\) | ||||
−0.261228 | + | 0.965277i | \(0.584127\pi\) | |||||||
\(200\) | −6.08609 | −0.430351 | ||||||||
\(201\) | −8.02334 | −0.565923 | ||||||||
\(202\) | 2.58210 | 0.181676 | ||||||||
\(203\) | −1.92356 | −0.135007 | ||||||||
\(204\) | 1.65277 | 0.115717 | ||||||||
\(205\) | 9.58975 | 0.669777 | ||||||||
\(206\) | −1.00000 | −0.0696733 | ||||||||
\(207\) | 0.437417 | 0.0304026 | ||||||||
\(208\) | 1.00000 | 0.0693375 | ||||||||
\(209\) | 6.21879 | 0.430163 | ||||||||
\(210\) | −4.60958 | −0.318091 | ||||||||
\(211\) | 4.63742 | 0.319253 | 0.159627 | − | 0.987177i | \(-0.448971\pi\) | ||||
0.159627 | + | 0.987177i | \(0.448971\pi\) | |||||||
\(212\) | 8.01315 | 0.550345 | ||||||||
\(213\) | −5.77612 | −0.395773 | ||||||||
\(214\) | 12.0189 | 0.821598 | ||||||||
\(215\) | 3.08744 | 0.210562 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 7.05356 | 0.478827 | ||||||||
\(218\) | 9.77876 | 0.662301 | ||||||||
\(219\) | 5.91373 | 0.399613 | ||||||||
\(220\) | −8.68380 | −0.585462 | ||||||||
\(221\) | −1.65277 | −0.111177 | ||||||||
\(222\) | 6.25229 | 0.419626 | ||||||||
\(223\) | 2.11474 | 0.141613 | 0.0708067 | − | 0.997490i | \(-0.477443\pi\) | ||||
0.0708067 | + | 0.997490i | \(0.477443\pi\) | |||||||
\(224\) | 1.38443 | 0.0925014 | ||||||||
\(225\) | 6.08609 | 0.405739 | ||||||||
\(226\) | 14.8934 | 0.990694 | ||||||||
\(227\) | 6.63719 | 0.440526 | 0.220263 | − | 0.975441i | \(-0.429308\pi\) | ||||
0.220263 | + | 0.975441i | \(0.429308\pi\) | |||||||
\(228\) | 2.38443 | 0.157913 | ||||||||
\(229\) | −13.0876 | −0.864856 | −0.432428 | − | 0.901668i | \(-0.642343\pi\) | ||||
−0.432428 | + | 0.901668i | \(0.642343\pi\) | |||||||
\(230\) | −1.45641 | −0.0960330 | ||||||||
\(231\) | −3.61071 | −0.237567 | ||||||||
\(232\) | −1.38942 | −0.0912199 | ||||||||
\(233\) | −5.29335 | −0.346779 | −0.173389 | − | 0.984853i | \(-0.555472\pi\) | ||||
−0.173389 | + | 0.984853i | \(0.555472\pi\) | |||||||
\(234\) | −1.00000 | −0.0653720 | ||||||||
\(235\) | −35.9537 | −2.34536 | ||||||||
\(236\) | 3.33907 | 0.217355 | ||||||||
\(237\) | −5.61371 | −0.364650 | ||||||||
\(238\) | −2.28815 | −0.148318 | ||||||||
\(239\) | −14.4156 | −0.932465 | −0.466232 | − | 0.884662i | \(-0.654389\pi\) | ||||
−0.466232 | + | 0.884662i | \(0.654389\pi\) | |||||||
\(240\) | −3.32958 | −0.214923 | ||||||||
\(241\) | 13.6057 | 0.876417 | 0.438209 | − | 0.898873i | \(-0.355613\pi\) | ||||
0.438209 | + | 0.898873i | \(0.355613\pi\) | |||||||
\(242\) | 4.19793 | 0.269853 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −1.16385 | −0.0745081 | ||||||||
\(245\) | −16.9254 | −1.08132 | ||||||||
\(246\) | 2.88017 | 0.183633 | ||||||||
\(247\) | −2.38443 | −0.151718 | ||||||||
\(248\) | 5.09491 | 0.323527 | ||||||||
\(249\) | 7.43809 | 0.471370 | ||||||||
\(250\) | −3.61621 | −0.228709 | ||||||||
\(251\) | 27.1248 | 1.71210 | 0.856052 | − | 0.516890i | \(-0.172910\pi\) | ||||
0.856052 | + | 0.516890i | \(0.172910\pi\) | |||||||
\(252\) | −1.38443 | −0.0872112 | ||||||||
\(253\) | −1.14082 | −0.0717225 | ||||||||
\(254\) | −6.22507 | −0.390595 | ||||||||
\(255\) | 5.50301 | 0.344612 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 24.8096 | 1.54758 | 0.773791 | − | 0.633441i | \(-0.218358\pi\) | ||||
0.773791 | + | 0.633441i | \(0.218358\pi\) | |||||||
\(258\) | 0.927277 | 0.0577298 | ||||||||
\(259\) | −8.65588 | −0.537850 | ||||||||
\(260\) | 3.32958 | 0.206492 | ||||||||
\(261\) | 1.38942 | 0.0860029 | ||||||||
\(262\) | 9.84125 | 0.607994 | ||||||||
\(263\) | 17.4130 | 1.07373 | 0.536865 | − | 0.843668i | \(-0.319608\pi\) | ||||
0.536865 | + | 0.843668i | \(0.319608\pi\) | |||||||
\(264\) | −2.60808 | −0.160516 | ||||||||
\(265\) | 26.6804 | 1.63896 | ||||||||
\(266\) | −3.30109 | −0.202403 | ||||||||
\(267\) | −17.2269 | −1.05427 | ||||||||
\(268\) | 8.02334 | 0.490104 | ||||||||
\(269\) | −4.80067 | −0.292702 | −0.146351 | − | 0.989233i | \(-0.546753\pi\) | ||||
−0.146351 | + | 0.989233i | \(0.546753\pi\) | |||||||
\(270\) | 3.32958 | 0.202632 | ||||||||
\(271\) | 17.6247 | 1.07063 | 0.535313 | − | 0.844654i | \(-0.320194\pi\) | ||||
0.535313 | + | 0.844654i | \(0.320194\pi\) | |||||||
\(272\) | −1.65277 | −0.100214 | ||||||||
\(273\) | 1.38443 | 0.0837898 | ||||||||
\(274\) | 10.1134 | 0.610971 | ||||||||
\(275\) | −15.8730 | −0.957177 | ||||||||
\(276\) | −0.437417 | −0.0263294 | ||||||||
\(277\) | −20.2994 | −1.21967 | −0.609836 | − | 0.792527i | \(-0.708765\pi\) | ||||
−0.609836 | + | 0.792527i | \(0.708765\pi\) | |||||||
\(278\) | 22.7082 | 1.36195 | ||||||||
\(279\) | −5.09491 | −0.305024 | ||||||||
\(280\) | 4.60958 | 0.275475 | ||||||||
\(281\) | −3.46316 | −0.206595 | −0.103297 | − | 0.994651i | \(-0.532939\pi\) | ||||
−0.103297 | + | 0.994651i | \(0.532939\pi\) | |||||||
\(282\) | −10.7983 | −0.643028 | ||||||||
\(283\) | −16.2956 | −0.968671 | −0.484335 | − | 0.874882i | \(-0.660939\pi\) | ||||
−0.484335 | + | 0.874882i | \(0.660939\pi\) | |||||||
\(284\) | 5.77612 | 0.342750 | ||||||||
\(285\) | 7.93916 | 0.470275 | ||||||||
\(286\) | 2.60808 | 0.154219 | ||||||||
\(287\) | −3.98741 | −0.235369 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −14.2684 | −0.839316 | ||||||||
\(290\) | −4.62618 | −0.271659 | ||||||||
\(291\) | 1.80223 | 0.105649 | ||||||||
\(292\) | −5.91373 | −0.346075 | ||||||||
\(293\) | 16.2465 | 0.949132 | 0.474566 | − | 0.880220i | \(-0.342605\pi\) | ||||
0.474566 | + | 0.880220i | \(0.342605\pi\) | |||||||
\(294\) | −5.08334 | −0.296466 | ||||||||
\(295\) | 11.1177 | 0.647296 | ||||||||
\(296\) | −6.25229 | −0.363407 | ||||||||
\(297\) | 2.60808 | 0.151336 | ||||||||
\(298\) | 5.39722 | 0.312653 | ||||||||
\(299\) | 0.437417 | 0.0252965 | ||||||||
\(300\) | −6.08609 | −0.351380 | ||||||||
\(301\) | −1.28375 | −0.0739944 | ||||||||
\(302\) | 2.23675 | 0.128711 | ||||||||
\(303\) | 2.58210 | 0.148338 | ||||||||
\(304\) | −2.38443 | −0.136757 | ||||||||
\(305\) | −3.87514 | −0.221890 | ||||||||
\(306\) | 1.65277 | 0.0944823 | ||||||||
\(307\) | 22.2353 | 1.26903 | 0.634517 | − | 0.772909i | \(-0.281199\pi\) | ||||
0.634517 | + | 0.772909i | \(0.281199\pi\) | |||||||
\(308\) | 3.61071 | 0.205739 | ||||||||
\(309\) | −1.00000 | −0.0568880 | ||||||||
\(310\) | 16.9639 | 0.963484 | ||||||||
\(311\) | 16.5685 | 0.939515 | 0.469758 | − | 0.882795i | \(-0.344341\pi\) | ||||
0.469758 | + | 0.882795i | \(0.344341\pi\) | |||||||
\(312\) | 1.00000 | 0.0566139 | ||||||||
\(313\) | −31.5663 | −1.78423 | −0.892116 | − | 0.451807i | \(-0.850780\pi\) | ||||
−0.892116 | + | 0.451807i | \(0.850780\pi\) | |||||||
\(314\) | −16.1805 | −0.913117 | ||||||||
\(315\) | −4.60958 | −0.259721 | ||||||||
\(316\) | 5.61371 | 0.315796 | ||||||||
\(317\) | −21.3357 | −1.19833 | −0.599165 | − | 0.800625i | \(-0.704501\pi\) | ||||
−0.599165 | + | 0.800625i | \(0.704501\pi\) | |||||||
\(318\) | 8.01315 | 0.449355 | ||||||||
\(319\) | −3.62371 | −0.202889 | ||||||||
\(320\) | 3.32958 | 0.186129 | ||||||||
\(321\) | 12.0189 | 0.670832 | ||||||||
\(322\) | 0.605575 | 0.0337474 | ||||||||
\(323\) | 3.94091 | 0.219278 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.08609 | 0.337595 | ||||||||
\(326\) | 11.0400 | 0.611451 | ||||||||
\(327\) | 9.77876 | 0.540767 | ||||||||
\(328\) | −2.88017 | −0.159031 | ||||||||
\(329\) | 14.9495 | 0.824192 | ||||||||
\(330\) | −8.68380 | −0.478027 | ||||||||
\(331\) | −27.7441 | −1.52495 | −0.762476 | − | 0.647017i | \(-0.776016\pi\) | ||||
−0.762476 | + | 0.647017i | \(0.776016\pi\) | |||||||
\(332\) | −7.43809 | −0.408218 | ||||||||
\(333\) | 6.25229 | 0.342623 | ||||||||
\(334\) | 16.6481 | 0.910943 | ||||||||
\(335\) | 26.7143 | 1.45956 | ||||||||
\(336\) | 1.38443 | 0.0755271 | ||||||||
\(337\) | −20.7986 | −1.13297 | −0.566487 | − | 0.824071i | \(-0.691698\pi\) | ||||
−0.566487 | + | 0.824071i | \(0.691698\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 14.8934 | 0.808898 | ||||||||
\(340\) | −5.50301 | −0.298443 | ||||||||
\(341\) | 13.2879 | 0.719581 | ||||||||
\(342\) | 2.38443 | 0.128935 | ||||||||
\(343\) | 16.7286 | 0.903259 | ||||||||
\(344\) | −0.927277 | −0.0499955 | ||||||||
\(345\) | −1.45641 | −0.0784106 | ||||||||
\(346\) | 11.4486 | 0.615482 | ||||||||
\(347\) | −25.8264 | −1.38644 | −0.693218 | − | 0.720728i | \(-0.743808\pi\) | ||||
−0.693218 | + | 0.720728i | \(0.743808\pi\) | |||||||
\(348\) | −1.38942 | −0.0744807 | ||||||||
\(349\) | 2.17223 | 0.116277 | 0.0581383 | − | 0.998309i | \(-0.481484\pi\) | ||||
0.0581383 | + | 0.998309i | \(0.481484\pi\) | |||||||
\(350\) | 8.42579 | 0.450377 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.60808 | 0.139011 | ||||||||
\(353\) | 16.9804 | 0.903773 | 0.451887 | − | 0.892075i | \(-0.350751\pi\) | ||||
0.451887 | + | 0.892075i | \(0.350751\pi\) | |||||||
\(354\) | 3.33907 | 0.177469 | ||||||||
\(355\) | 19.2320 | 1.02073 | ||||||||
\(356\) | 17.2269 | 0.913023 | ||||||||
\(357\) | −2.28815 | −0.121101 | ||||||||
\(358\) | 10.1335 | 0.535572 | ||||||||
\(359\) | 16.9652 | 0.895390 | 0.447695 | − | 0.894186i | \(-0.352245\pi\) | ||||
0.447695 | + | 0.894186i | \(0.352245\pi\) | |||||||
\(360\) | −3.32958 | −0.175484 | ||||||||
\(361\) | −13.3145 | −0.700762 | ||||||||
\(362\) | 20.8197 | 1.09426 | ||||||||
\(363\) | 4.19793 | 0.220334 | ||||||||
\(364\) | −1.38443 | −0.0725641 | ||||||||
\(365\) | −19.6902 | −1.03063 | ||||||||
\(366\) | −1.16385 | −0.0608356 | ||||||||
\(367\) | −13.2181 | −0.689980 | −0.344990 | − | 0.938606i | \(-0.612118\pi\) | ||||
−0.344990 | + | 0.938606i | \(0.612118\pi\) | |||||||
\(368\) | 0.437417 | 0.0228019 | ||||||||
\(369\) | 2.88017 | 0.149936 | ||||||||
\(370\) | −20.8175 | −1.08225 | ||||||||
\(371\) | −11.0937 | −0.575955 | ||||||||
\(372\) | 5.09491 | 0.264159 | ||||||||
\(373\) | −4.80685 | −0.248889 | −0.124445 | − | 0.992227i | \(-0.539715\pi\) | ||||
−0.124445 | + | 0.992227i | \(0.539715\pi\) | |||||||
\(374\) | −4.31054 | −0.222893 | ||||||||
\(375\) | −3.61621 | −0.186740 | ||||||||
\(376\) | 10.7983 | 0.556878 | ||||||||
\(377\) | 1.38942 | 0.0715587 | ||||||||
\(378\) | −1.38443 | −0.0712076 | ||||||||
\(379\) | −31.6430 | −1.62539 | −0.812695 | − | 0.582689i | \(-0.802001\pi\) | ||||
−0.812695 | + | 0.582689i | \(0.802001\pi\) | |||||||
\(380\) | −7.93916 | −0.407270 | ||||||||
\(381\) | −6.22507 | −0.318920 | ||||||||
\(382\) | 5.92513 | 0.303156 | ||||||||
\(383\) | −0.530233 | −0.0270937 | −0.0135468 | − | 0.999908i | \(-0.504312\pi\) | ||||
−0.0135468 | + | 0.999908i | \(0.504312\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 12.0221 | 0.612705 | ||||||||
\(386\) | −20.0653 | −1.02130 | ||||||||
\(387\) | 0.927277 | 0.0471362 | ||||||||
\(388\) | −1.80223 | −0.0914945 | ||||||||
\(389\) | 19.6701 | 0.997315 | 0.498658 | − | 0.866799i | \(-0.333827\pi\) | ||||
0.498658 | + | 0.866799i | \(0.333827\pi\) | |||||||
\(390\) | 3.32958 | 0.168600 | ||||||||
\(391\) | −0.722947 | −0.0365610 | ||||||||
\(392\) | 5.08334 | 0.256747 | ||||||||
\(393\) | 9.84125 | 0.496425 | ||||||||
\(394\) | −11.0734 | −0.557871 | ||||||||
\(395\) | 18.6913 | 0.940461 | ||||||||
\(396\) | −2.60808 | −0.131061 | ||||||||
\(397\) | 8.59657 | 0.431450 | 0.215725 | − | 0.976454i | \(-0.430789\pi\) | ||||
0.215725 | + | 0.976454i | \(0.430789\pi\) | |||||||
\(398\) | 7.37014 | 0.369432 | ||||||||
\(399\) | −3.30109 | −0.165261 | ||||||||
\(400\) | 6.08609 | 0.304304 | ||||||||
\(401\) | −22.9750 | −1.14732 | −0.573659 | − | 0.819094i | \(-0.694477\pi\) | ||||
−0.573659 | + | 0.819094i | \(0.694477\pi\) | |||||||
\(402\) | 8.02334 | 0.400168 | ||||||||
\(403\) | −5.09491 | −0.253795 | ||||||||
\(404\) | −2.58210 | −0.128464 | ||||||||
\(405\) | 3.32958 | 0.165448 | ||||||||
\(406\) | 1.92356 | 0.0954647 | ||||||||
\(407\) | −16.3065 | −0.808281 | ||||||||
\(408\) | −1.65277 | −0.0818241 | ||||||||
\(409\) | −20.0669 | −0.992245 | −0.496122 | − | 0.868253i | \(-0.665243\pi\) | ||||
−0.496122 | + | 0.868253i | \(0.665243\pi\) | |||||||
\(410\) | −9.58975 | −0.473604 | ||||||||
\(411\) | 10.1134 | 0.498856 | ||||||||
\(412\) | 1.00000 | 0.0492665 | ||||||||
\(413\) | −4.62272 | −0.227469 | ||||||||
\(414\) | −0.437417 | −0.0214979 | ||||||||
\(415\) | −24.7657 | −1.21570 | ||||||||
\(416\) | −1.00000 | −0.0490290 | ||||||||
\(417\) | 22.7082 | 1.11202 | ||||||||
\(418\) | −6.21879 | −0.304171 | ||||||||
\(419\) | 16.5765 | 0.809813 | 0.404907 | − | 0.914358i | \(-0.367304\pi\) | ||||
0.404907 | + | 0.914358i | \(0.367304\pi\) | |||||||
\(420\) | 4.60958 | 0.224925 | ||||||||
\(421\) | −31.7963 | −1.54966 | −0.774829 | − | 0.632171i | \(-0.782164\pi\) | ||||
−0.774829 | + | 0.632171i | \(0.782164\pi\) | |||||||
\(422\) | −4.63742 | −0.225746 | ||||||||
\(423\) | −10.7983 | −0.525030 | ||||||||
\(424\) | −8.01315 | −0.389153 | ||||||||
\(425\) | −10.0589 | −0.487927 | ||||||||
\(426\) | 5.77612 | 0.279854 | ||||||||
\(427\) | 1.61128 | 0.0779752 | ||||||||
\(428\) | −12.0189 | −0.580957 | ||||||||
\(429\) | 2.60808 | 0.125919 | ||||||||
\(430\) | −3.08744 | −0.148890 | ||||||||
\(431\) | 10.6520 | 0.513090 | 0.256545 | − | 0.966532i | \(-0.417416\pi\) | ||||
0.256545 | + | 0.966532i | \(0.417416\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 7.06019 | 0.339291 | 0.169646 | − | 0.985505i | \(-0.445738\pi\) | ||||
0.169646 | + | 0.985505i | \(0.445738\pi\) | |||||||
\(434\) | −7.05356 | −0.338582 | ||||||||
\(435\) | −4.62618 | −0.221808 | ||||||||
\(436\) | −9.77876 | −0.468318 | ||||||||
\(437\) | −1.04299 | −0.0498930 | ||||||||
\(438\) | −5.91373 | −0.282569 | ||||||||
\(439\) | −36.1524 | −1.72546 | −0.862729 | − | 0.505666i | \(-0.831247\pi\) | ||||
−0.862729 | + | 0.505666i | \(0.831247\pi\) | |||||||
\(440\) | 8.68380 | 0.413984 | ||||||||
\(441\) | −5.08334 | −0.242064 | ||||||||
\(442\) | 1.65277 | 0.0786140 | ||||||||
\(443\) | 14.1150 | 0.670626 | 0.335313 | − | 0.942107i | \(-0.391158\pi\) | ||||
0.335313 | + | 0.942107i | \(0.391158\pi\) | |||||||
\(444\) | −6.25229 | −0.296720 | ||||||||
\(445\) | 57.3583 | 2.71904 | ||||||||
\(446\) | −2.11474 | −0.100136 | ||||||||
\(447\) | 5.39722 | 0.255280 | ||||||||
\(448\) | −1.38443 | −0.0654084 | ||||||||
\(449\) | 27.6663 | 1.30565 | 0.652827 | − | 0.757507i | \(-0.273583\pi\) | ||||
0.652827 | + | 0.757507i | \(0.273583\pi\) | |||||||
\(450\) | −6.08609 | −0.286901 | ||||||||
\(451\) | −7.51171 | −0.353713 | ||||||||
\(452\) | −14.8934 | −0.700527 | ||||||||
\(453\) | 2.23675 | 0.105092 | ||||||||
\(454\) | −6.63719 | −0.311499 | ||||||||
\(455\) | −4.60958 | −0.216101 | ||||||||
\(456\) | −2.38443 | −0.111661 | ||||||||
\(457\) | −11.8995 | −0.556634 | −0.278317 | − | 0.960489i | \(-0.589777\pi\) | ||||
−0.278317 | + | 0.960489i | \(0.589777\pi\) | |||||||
\(458\) | 13.0876 | 0.611546 | ||||||||
\(459\) | 1.65277 | 0.0771445 | ||||||||
\(460\) | 1.45641 | 0.0679056 | ||||||||
\(461\) | −8.74873 | −0.407469 | −0.203734 | − | 0.979026i | \(-0.565308\pi\) | ||||
−0.203734 | + | 0.979026i | \(0.565308\pi\) | |||||||
\(462\) | 3.61071 | 0.167986 | ||||||||
\(463\) | 5.98788 | 0.278280 | 0.139140 | − | 0.990273i | \(-0.455566\pi\) | ||||
0.139140 | + | 0.990273i | \(0.455566\pi\) | |||||||
\(464\) | 1.38942 | 0.0645022 | ||||||||
\(465\) | 16.9639 | 0.786681 | ||||||||
\(466\) | 5.29335 | 0.245210 | ||||||||
\(467\) | 42.2930 | 1.95709 | 0.978544 | − | 0.206038i | \(-0.0660569\pi\) | ||||
0.978544 | + | 0.206038i | \(0.0660569\pi\) | |||||||
\(468\) | 1.00000 | 0.0462250 | ||||||||
\(469\) | −11.1078 | −0.512910 | ||||||||
\(470\) | 35.9537 | 1.65842 | ||||||||
\(471\) | −16.1805 | −0.745557 | ||||||||
\(472\) | −3.33907 | −0.153693 | ||||||||
\(473\) | −2.41841 | −0.111199 | ||||||||
\(474\) | 5.61371 | 0.257846 | ||||||||
\(475\) | −14.5119 | −0.665850 | ||||||||
\(476\) | 2.28815 | 0.104877 | ||||||||
\(477\) | 8.01315 | 0.366897 | ||||||||
\(478\) | 14.4156 | 0.659352 | ||||||||
\(479\) | −17.9798 | −0.821519 | −0.410760 | − | 0.911744i | \(-0.634736\pi\) | ||||
−0.410760 | + | 0.911744i | \(0.634736\pi\) | |||||||
\(480\) | 3.32958 | 0.151974 | ||||||||
\(481\) | 6.25229 | 0.285080 | ||||||||
\(482\) | −13.6057 | −0.619721 | ||||||||
\(483\) | 0.605575 | 0.0275546 | ||||||||
\(484\) | −4.19793 | −0.190815 | ||||||||
\(485\) | −6.00067 | −0.272476 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 3.71623 | 0.168398 | 0.0841992 | − | 0.996449i | \(-0.473167\pi\) | ||||
0.0841992 | + | 0.996449i | \(0.473167\pi\) | |||||||
\(488\) | 1.16385 | 0.0526852 | ||||||||
\(489\) | 11.0400 | 0.499248 | ||||||||
\(490\) | 16.9254 | 0.764611 | ||||||||
\(491\) | 13.0876 | 0.590637 | 0.295318 | − | 0.955399i | \(-0.404574\pi\) | ||||
0.295318 | + | 0.955399i | \(0.404574\pi\) | |||||||
\(492\) | −2.88017 | −0.129848 | ||||||||
\(493\) | −2.29638 | −0.103424 | ||||||||
\(494\) | 2.38443 | 0.107281 | ||||||||
\(495\) | −8.68380 | −0.390308 | ||||||||
\(496\) | −5.09491 | −0.228768 | ||||||||
\(497\) | −7.99666 | −0.358699 | ||||||||
\(498\) | −7.43809 | −0.333309 | ||||||||
\(499\) | 16.4962 | 0.738472 | 0.369236 | − | 0.929336i | \(-0.379619\pi\) | ||||
0.369236 | + | 0.929336i | \(0.379619\pi\) | |||||||
\(500\) | 3.61621 | 0.161722 | ||||||||
\(501\) | 16.6481 | 0.743781 | ||||||||
\(502\) | −27.1248 | −1.21064 | ||||||||
\(503\) | −25.8610 | −1.15309 | −0.576543 | − | 0.817067i | \(-0.695599\pi\) | ||||
−0.576543 | + | 0.817067i | \(0.695599\pi\) | |||||||
\(504\) | 1.38443 | 0.0616676 | ||||||||
\(505\) | −8.59731 | −0.382575 | ||||||||
\(506\) | 1.14082 | 0.0507155 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.22507 | 0.276193 | ||||||||
\(509\) | 14.7923 | 0.655659 | 0.327830 | − | 0.944737i | \(-0.393683\pi\) | ||||
0.327830 | + | 0.944737i | \(0.393683\pi\) | |||||||
\(510\) | −5.50301 | −0.243677 | ||||||||
\(511\) | 8.18717 | 0.362179 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.38443 | 0.105275 | ||||||||
\(514\) | −24.8096 | −1.09431 | ||||||||
\(515\) | 3.32958 | 0.146719 | ||||||||
\(516\) | −0.927277 | −0.0408211 | ||||||||
\(517\) | 28.1627 | 1.23860 | ||||||||
\(518\) | 8.65588 | 0.380318 | ||||||||
\(519\) | 11.4486 | 0.502539 | ||||||||
\(520\) | −3.32958 | −0.146012 | ||||||||
\(521\) | −9.53815 | −0.417874 | −0.208937 | − | 0.977929i | \(-0.567000\pi\) | ||||
−0.208937 | + | 0.977929i | \(0.567000\pi\) | |||||||
\(522\) | −1.38942 | −0.0608132 | ||||||||
\(523\) | −5.66030 | −0.247508 | −0.123754 | − | 0.992313i | \(-0.539493\pi\) | ||||
−0.123754 | + | 0.992313i | \(0.539493\pi\) | |||||||
\(524\) | −9.84125 | −0.429917 | ||||||||
\(525\) | 8.42579 | 0.367731 | ||||||||
\(526\) | −17.4130 | −0.759242 | ||||||||
\(527\) | 8.42069 | 0.366811 | ||||||||
\(528\) | 2.60808 | 0.113502 | ||||||||
\(529\) | −22.8087 | −0.991681 | ||||||||
\(530\) | −26.6804 | −1.15892 | ||||||||
\(531\) | 3.33907 | 0.144903 | ||||||||
\(532\) | 3.30109 | 0.143121 | ||||||||
\(533\) | 2.88017 | 0.124754 | ||||||||
\(534\) | 17.2269 | 0.745480 | ||||||||
\(535\) | −40.0180 | −1.73013 | ||||||||
\(536\) | −8.02334 | −0.346556 | ||||||||
\(537\) | 10.1335 | 0.437292 | ||||||||
\(538\) | 4.80067 | 0.206971 | ||||||||
\(539\) | 13.2578 | 0.571052 | ||||||||
\(540\) | −3.32958 | −0.143282 | ||||||||
\(541\) | 25.4043 | 1.09222 | 0.546108 | − | 0.837715i | \(-0.316109\pi\) | ||||
0.546108 | + | 0.837715i | \(0.316109\pi\) | |||||||
\(542\) | −17.6247 | −0.757047 | ||||||||
\(543\) | 20.8197 | 0.893457 | ||||||||
\(544\) | 1.65277 | 0.0708617 | ||||||||
\(545\) | −32.5592 | −1.39468 | ||||||||
\(546\) | −1.38443 | −0.0592483 | ||||||||
\(547\) | −27.1325 | −1.16010 | −0.580050 | − | 0.814581i | \(-0.696967\pi\) | ||||
−0.580050 | + | 0.814581i | \(0.696967\pi\) | |||||||
\(548\) | −10.1134 | −0.432022 | ||||||||
\(549\) | −1.16385 | −0.0496721 | ||||||||
\(550\) | 15.8730 | 0.676826 | ||||||||
\(551\) | −3.31298 | −0.141138 | ||||||||
\(552\) | 0.437417 | 0.0186177 | ||||||||
\(553\) | −7.77182 | −0.330491 | ||||||||
\(554\) | 20.2994 | 0.862439 | ||||||||
\(555\) | −20.8175 | −0.883653 | ||||||||
\(556\) | −22.7082 | −0.963041 | ||||||||
\(557\) | −36.5462 | −1.54851 | −0.774257 | − | 0.632872i | \(-0.781876\pi\) | ||||
−0.774257 | + | 0.632872i | \(0.781876\pi\) | |||||||
\(558\) | 5.09491 | 0.215685 | ||||||||
\(559\) | 0.927277 | 0.0392197 | ||||||||
\(560\) | −4.60958 | −0.194790 | ||||||||
\(561\) | −4.31054 | −0.181991 | ||||||||
\(562\) | 3.46316 | 0.146085 | ||||||||
\(563\) | −18.2633 | −0.769708 | −0.384854 | − | 0.922977i | \(-0.625748\pi\) | ||||
−0.384854 | + | 0.922977i | \(0.625748\pi\) | |||||||
\(564\) | 10.7983 | 0.454689 | ||||||||
\(565\) | −49.5887 | −2.08621 | ||||||||
\(566\) | 16.2956 | 0.684954 | ||||||||
\(567\) | −1.38443 | −0.0581408 | ||||||||
\(568\) | −5.77612 | −0.242361 | ||||||||
\(569\) | 5.56719 | 0.233389 | 0.116694 | − | 0.993168i | \(-0.462770\pi\) | ||||
0.116694 | + | 0.993168i | \(0.462770\pi\) | |||||||
\(570\) | −7.93916 | −0.332535 | ||||||||
\(571\) | −9.09794 | −0.380737 | −0.190368 | − | 0.981713i | \(-0.560968\pi\) | ||||
−0.190368 | + | 0.981713i | \(0.560968\pi\) | |||||||
\(572\) | −2.60808 | −0.109049 | ||||||||
\(573\) | 5.92513 | 0.247526 | ||||||||
\(574\) | 3.98741 | 0.166431 | ||||||||
\(575\) | 2.66215 | 0.111020 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 11.1487 | 0.464125 | 0.232063 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232063 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(578\) | 14.2684 | 0.593486 | ||||||||
\(579\) | −20.0653 | −0.833887 | ||||||||
\(580\) | 4.62618 | 0.192092 | ||||||||
\(581\) | 10.2976 | 0.427215 | ||||||||
\(582\) | −1.80223 | −0.0747049 | ||||||||
\(583\) | −20.8989 | −0.865545 | ||||||||
\(584\) | 5.91373 | 0.244712 | ||||||||
\(585\) | 3.32958 | 0.137661 | ||||||||
\(586\) | −16.2465 | −0.671138 | ||||||||
\(587\) | 45.9447 | 1.89634 | 0.948170 | − | 0.317763i | \(-0.102932\pi\) | ||||
0.948170 | + | 0.317763i | \(0.102932\pi\) | |||||||
\(588\) | 5.08334 | 0.209633 | ||||||||
\(589\) | 12.1485 | 0.500569 | ||||||||
\(590\) | −11.1177 | −0.457708 | ||||||||
\(591\) | −11.0734 | −0.455500 | ||||||||
\(592\) | 6.25229 | 0.256967 | ||||||||
\(593\) | −27.5944 | −1.13317 | −0.566583 | − | 0.824005i | \(-0.691735\pi\) | ||||
−0.566583 | + | 0.824005i | \(0.691735\pi\) | |||||||
\(594\) | −2.60808 | −0.107011 | ||||||||
\(595\) | 7.61856 | 0.312330 | ||||||||
\(596\) | −5.39722 | −0.221079 | ||||||||
\(597\) | 7.37014 | 0.301640 | ||||||||
\(598\) | −0.437417 | −0.0178873 | ||||||||
\(599\) | 11.3793 | 0.464948 | 0.232474 | − | 0.972603i | \(-0.425318\pi\) | ||||
0.232474 | + | 0.972603i | \(0.425318\pi\) | |||||||
\(600\) | 6.08609 | 0.248463 | ||||||||
\(601\) | 15.5433 | 0.634025 | 0.317013 | − | 0.948421i | \(-0.397320\pi\) | ||||
0.317013 | + | 0.948421i | \(0.397320\pi\) | |||||||
\(602\) | 1.28375 | 0.0523219 | ||||||||
\(603\) | 8.02334 | 0.326736 | ||||||||
\(604\) | −2.23675 | −0.0910122 | ||||||||
\(605\) | −13.9773 | −0.568259 | ||||||||
\(606\) | −2.58210 | −0.104891 | ||||||||
\(607\) | 15.1565 | 0.615183 | 0.307591 | − | 0.951519i | \(-0.400477\pi\) | ||||
0.307591 | + | 0.951519i | \(0.400477\pi\) | |||||||
\(608\) | 2.38443 | 0.0967016 | ||||||||
\(609\) | 1.92356 | 0.0779466 | ||||||||
\(610\) | 3.87514 | 0.156900 | ||||||||
\(611\) | −10.7983 | −0.436851 | ||||||||
\(612\) | −1.65277 | −0.0668091 | ||||||||
\(613\) | 6.62987 | 0.267778 | 0.133889 | − | 0.990996i | \(-0.457253\pi\) | ||||
0.133889 | + | 0.990996i | \(0.457253\pi\) | |||||||
\(614\) | −22.2353 | −0.897342 | ||||||||
\(615\) | −9.58975 | −0.386696 | ||||||||
\(616\) | −3.61071 | −0.145480 | ||||||||
\(617\) | −8.30759 | −0.334451 | −0.167225 | − | 0.985919i | \(-0.553481\pi\) | ||||
−0.167225 | + | 0.985919i | \(0.553481\pi\) | |||||||
\(618\) | 1.00000 | 0.0402259 | ||||||||
\(619\) | −47.9531 | −1.92740 | −0.963699 | − | 0.266993i | \(-0.913970\pi\) | ||||
−0.963699 | + | 0.266993i | \(0.913970\pi\) | |||||||
\(620\) | −16.9639 | −0.681286 | ||||||||
\(621\) | −0.437417 | −0.0175529 | ||||||||
\(622\) | −16.5685 | −0.664338 | ||||||||
\(623\) | −23.8495 | −0.955510 | ||||||||
\(624\) | −1.00000 | −0.0400320 | ||||||||
\(625\) | −18.3900 | −0.735600 | ||||||||
\(626\) | 31.5663 | 1.26164 | ||||||||
\(627\) | −6.21879 | −0.248355 | ||||||||
\(628\) | 16.1805 | 0.645671 | ||||||||
\(629\) | −10.3336 | −0.412026 | ||||||||
\(630\) | 4.60958 | 0.183650 | ||||||||
\(631\) | −20.4276 | −0.813210 | −0.406605 | − | 0.913604i | \(-0.633287\pi\) | ||||
−0.406605 | + | 0.913604i | \(0.633287\pi\) | |||||||
\(632\) | −5.61371 | −0.223301 | ||||||||
\(633\) | −4.63742 | −0.184321 | ||||||||
\(634\) | 21.3357 | 0.847348 | ||||||||
\(635\) | 20.7268 | 0.822520 | ||||||||
\(636\) | −8.01315 | −0.317742 | ||||||||
\(637\) | −5.08334 | −0.201409 | ||||||||
\(638\) | 3.62371 | 0.143464 | ||||||||
\(639\) | 5.77612 | 0.228500 | ||||||||
\(640\) | −3.32958 | −0.131613 | ||||||||
\(641\) | 22.1765 | 0.875918 | 0.437959 | − | 0.898995i | \(-0.355701\pi\) | ||||
0.437959 | + | 0.898995i | \(0.355701\pi\) | |||||||
\(642\) | −12.0189 | −0.474350 | ||||||||
\(643\) | −14.7045 | −0.579889 | −0.289945 | − | 0.957043i | \(-0.593637\pi\) | ||||
−0.289945 | + | 0.957043i | \(0.593637\pi\) | |||||||
\(644\) | −0.605575 | −0.0238630 | ||||||||
\(645\) | −3.08744 | −0.121568 | ||||||||
\(646\) | −3.94091 | −0.155053 | ||||||||
\(647\) | 0.604244 | 0.0237553 | 0.0118776 | − | 0.999929i | \(-0.496219\pi\) | ||||
0.0118776 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −8.70854 | −0.341840 | ||||||||
\(650\) | −6.08609 | −0.238716 | ||||||||
\(651\) | −7.05356 | −0.276451 | ||||||||
\(652\) | −11.0400 | −0.432361 | ||||||||
\(653\) | −7.48013 | −0.292720 | −0.146360 | − | 0.989231i | \(-0.546756\pi\) | ||||
−0.146360 | + | 0.989231i | \(0.546756\pi\) | |||||||
\(654\) | −9.77876 | −0.382380 | ||||||||
\(655\) | −32.7672 | −1.28032 | ||||||||
\(656\) | 2.88017 | 0.112452 | ||||||||
\(657\) | −5.91373 | −0.230717 | ||||||||
\(658\) | −14.9495 | −0.582792 | ||||||||
\(659\) | −43.4268 | −1.69167 | −0.845834 | − | 0.533446i | \(-0.820897\pi\) | ||||
−0.845834 | + | 0.533446i | \(0.820897\pi\) | |||||||
\(660\) | 8.68380 | 0.338016 | ||||||||
\(661\) | −7.59732 | −0.295502 | −0.147751 | − | 0.989025i | \(-0.547203\pi\) | ||||
−0.147751 | + | 0.989025i | \(0.547203\pi\) | |||||||
\(662\) | 27.7441 | 1.07830 | ||||||||
\(663\) | 1.65277 | 0.0641881 | ||||||||
\(664\) | 7.43809 | 0.288654 | ||||||||
\(665\) | 10.9912 | 0.426222 | ||||||||
\(666\) | −6.25229 | −0.242271 | ||||||||
\(667\) | 0.607755 | 0.0235324 | ||||||||
\(668\) | −16.6481 | −0.644134 | ||||||||
\(669\) | −2.11474 | −0.0817606 | ||||||||
\(670\) | −26.7143 | −1.03206 | ||||||||
\(671\) | 3.03542 | 0.117181 | ||||||||
\(672\) | −1.38443 | −0.0534057 | ||||||||
\(673\) | 33.5644 | 1.29381 | 0.646906 | − | 0.762570i | \(-0.276063\pi\) | ||||
0.646906 | + | 0.762570i | \(0.276063\pi\) | |||||||
\(674\) | 20.7986 | 0.801134 | ||||||||
\(675\) | −6.08609 | −0.234254 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | −29.3775 | −1.12907 | −0.564534 | − | 0.825410i | \(-0.690944\pi\) | ||||
−0.564534 | + | 0.825410i | \(0.690944\pi\) | |||||||
\(678\) | −14.8934 | −0.571977 | ||||||||
\(679\) | 2.49507 | 0.0957521 | ||||||||
\(680\) | 5.50301 | 0.211031 | ||||||||
\(681\) | −6.63719 | −0.254338 | ||||||||
\(682\) | −13.2879 | −0.508821 | ||||||||
\(683\) | 7.29045 | 0.278961 | 0.139481 | − | 0.990225i | \(-0.455457\pi\) | ||||
0.139481 | + | 0.990225i | \(0.455457\pi\) | |||||||
\(684\) | −2.38443 | −0.0911711 | ||||||||
\(685\) | −33.6732 | −1.28659 | ||||||||
\(686\) | −16.7286 | −0.638701 | ||||||||
\(687\) | 13.0876 | 0.499325 | ||||||||
\(688\) | 0.927277 | 0.0353521 | ||||||||
\(689\) | 8.01315 | 0.305277 | ||||||||
\(690\) | 1.45641 | 0.0554447 | ||||||||
\(691\) | −36.1981 | −1.37704 | −0.688521 | − | 0.725216i | \(-0.741740\pi\) | ||||
−0.688521 | + | 0.725216i | \(0.741740\pi\) | |||||||
\(692\) | −11.4486 | −0.435212 | ||||||||
\(693\) | 3.61071 | 0.137160 | ||||||||
\(694\) | 25.8264 | 0.980358 | ||||||||
\(695\) | −75.6086 | −2.86800 | ||||||||
\(696\) | 1.38942 | 0.0526658 | ||||||||
\(697\) | −4.76025 | −0.180307 | ||||||||
\(698\) | −2.17223 | −0.0822200 | ||||||||
\(699\) | 5.29335 | 0.200213 | ||||||||
\(700\) | −8.42579 | −0.318465 | ||||||||
\(701\) | 17.7227 | 0.669376 | 0.334688 | − | 0.942329i | \(-0.391369\pi\) | ||||
0.334688 | + | 0.942329i | \(0.391369\pi\) | |||||||
\(702\) | 1.00000 | 0.0377426 | ||||||||
\(703\) | −14.9082 | −0.562272 | ||||||||
\(704\) | −2.60808 | −0.0982956 | ||||||||
\(705\) | 35.9537 | 1.35409 | ||||||||
\(706\) | −16.9804 | −0.639064 | ||||||||
\(707\) | 3.57475 | 0.134442 | ||||||||
\(708\) | −3.33907 | −0.125490 | ||||||||
\(709\) | 0.555936 | 0.0208786 | 0.0104393 | − | 0.999946i | \(-0.496677\pi\) | ||||
0.0104393 | + | 0.999946i | \(0.496677\pi\) | |||||||
\(710\) | −19.2320 | −0.721766 | ||||||||
\(711\) | 5.61371 | 0.210531 | ||||||||
\(712\) | −17.2269 | −0.645605 | ||||||||
\(713\) | −2.22860 | −0.0834616 | ||||||||
\(714\) | 2.28815 | 0.0856317 | ||||||||
\(715\) | −8.68380 | −0.324756 | ||||||||
\(716\) | −10.1335 | −0.378706 | ||||||||
\(717\) | 14.4156 | 0.538359 | ||||||||
\(718\) | −16.9652 | −0.633136 | ||||||||
\(719\) | 13.0890 | 0.488139 | 0.244069 | − | 0.969758i | \(-0.421518\pi\) | ||||
0.244069 | + | 0.969758i | \(0.421518\pi\) | |||||||
\(720\) | 3.32958 | 0.124086 | ||||||||
\(721\) | −1.38443 | −0.0515590 | ||||||||
\(722\) | 13.3145 | 0.495513 | ||||||||
\(723\) | −13.6057 | −0.506000 | ||||||||
\(724\) | −20.8197 | −0.773757 | ||||||||
\(725\) | 8.45613 | 0.314053 | ||||||||
\(726\) | −4.19793 | −0.155800 | ||||||||
\(727\) | 27.6975 | 1.02724 | 0.513622 | − | 0.858017i | \(-0.328303\pi\) | ||||
0.513622 | + | 0.858017i | \(0.328303\pi\) | |||||||
\(728\) | 1.38443 | 0.0513106 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.6902 | 0.728768 | ||||||||
\(731\) | −1.53257 | −0.0566842 | ||||||||
\(732\) | 1.16385 | 0.0430173 | ||||||||
\(733\) | −1.46711 | −0.0541888 | −0.0270944 | − | 0.999633i | \(-0.508625\pi\) | ||||
−0.0270944 | + | 0.999633i | \(0.508625\pi\) | |||||||
\(734\) | 13.2181 | 0.487890 | ||||||||
\(735\) | 16.9254 | 0.624302 | ||||||||
\(736\) | −0.437417 | −0.0161234 | ||||||||
\(737\) | −20.9255 | −0.770801 | ||||||||
\(738\) | −2.88017 | −0.106021 | ||||||||
\(739\) | 17.8199 | 0.655516 | 0.327758 | − | 0.944762i | \(-0.393707\pi\) | ||||
0.327758 | + | 0.944762i | \(0.393707\pi\) | |||||||
\(740\) | 20.8175 | 0.765266 | ||||||||
\(741\) | 2.38443 | 0.0875944 | ||||||||
\(742\) | 11.0937 | 0.407262 | ||||||||
\(743\) | 0.527700 | 0.0193594 | 0.00967972 | − | 0.999953i | \(-0.496919\pi\) | ||||
0.00967972 | + | 0.999953i | \(0.496919\pi\) | |||||||
\(744\) | −5.09491 | −0.186788 | ||||||||
\(745\) | −17.9705 | −0.658387 | ||||||||
\(746\) | 4.80685 | 0.175991 | ||||||||
\(747\) | −7.43809 | −0.272146 | ||||||||
\(748\) | 4.31054 | 0.157609 | ||||||||
\(749\) | 16.6394 | 0.607992 | ||||||||
\(750\) | 3.61621 | 0.132045 | ||||||||
\(751\) | 3.74134 | 0.136524 | 0.0682618 | − | 0.997667i | \(-0.478255\pi\) | ||||
0.0682618 | + | 0.997667i | \(0.478255\pi\) | |||||||
\(752\) | −10.7983 | −0.393772 | ||||||||
\(753\) | −27.1248 | −0.988484 | ||||||||
\(754\) | −1.38942 | −0.0505997 | ||||||||
\(755\) | −7.44744 | −0.271040 | ||||||||
\(756\) | 1.38443 | 0.0503514 | ||||||||
\(757\) | 8.05602 | 0.292801 | 0.146401 | − | 0.989225i | \(-0.453231\pi\) | ||||
0.146401 | + | 0.989225i | \(0.453231\pi\) | |||||||
\(758\) | 31.6430 | 1.14932 | ||||||||
\(759\) | 1.14082 | 0.0414090 | ||||||||
\(760\) | 7.93916 | 0.287984 | ||||||||
\(761\) | 32.4969 | 1.17801 | 0.589006 | − | 0.808129i | \(-0.299520\pi\) | ||||
0.589006 | + | 0.808129i | \(0.299520\pi\) | |||||||
\(762\) | 6.22507 | 0.225510 | ||||||||
\(763\) | 13.5381 | 0.490111 | ||||||||
\(764\) | −5.92513 | −0.214364 | ||||||||
\(765\) | −5.50301 | −0.198962 | ||||||||
\(766\) | 0.530233 | 0.0191581 | ||||||||
\(767\) | 3.33907 | 0.120567 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 0.887902 | 0.0320186 | 0.0160093 | − | 0.999872i | \(-0.494904\pi\) | ||||
0.0160093 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(770\) | −12.0221 | −0.433248 | ||||||||
\(771\) | −24.8096 | −0.893497 | ||||||||
\(772\) | 20.0653 | 0.722167 | ||||||||
\(773\) | 39.5626 | 1.42297 | 0.711484 | − | 0.702702i | \(-0.248023\pi\) | ||||
0.711484 | + | 0.702702i | \(0.248023\pi\) | |||||||
\(774\) | −0.927277 | −0.0333303 | ||||||||
\(775\) | −31.0080 | −1.11384 | ||||||||
\(776\) | 1.80223 | 0.0646964 | ||||||||
\(777\) | 8.65588 | 0.310528 | ||||||||
\(778\) | −19.6701 | −0.705208 | ||||||||
\(779\) | −6.86758 | −0.246057 | ||||||||
\(780\) | −3.32958 | −0.119218 | ||||||||
\(781\) | −15.0646 | −0.539053 | ||||||||
\(782\) | 0.722947 | 0.0258525 | ||||||||
\(783\) | −1.38942 | −0.0496538 | ||||||||
\(784\) | −5.08334 | −0.181548 | ||||||||
\(785\) | 53.8741 | 1.92285 | ||||||||
\(786\) | −9.84125 | −0.351026 | ||||||||
\(787\) | 6.84512 | 0.244002 | 0.122001 | − | 0.992530i | \(-0.461069\pi\) | ||||
0.122001 | + | 0.992530i | \(0.461069\pi\) | |||||||
\(788\) | 11.0734 | 0.394474 | ||||||||
\(789\) | −17.4130 | −0.619918 | ||||||||
\(790\) | −18.6913 | −0.665006 | ||||||||
\(791\) | 20.6189 | 0.733125 | ||||||||
\(792\) | 2.60808 | 0.0926740 | ||||||||
\(793\) | −1.16385 | −0.0413296 | ||||||||
\(794\) | −8.59657 | −0.305081 | ||||||||
\(795\) | −26.6804 | −0.946256 | ||||||||
\(796\) | −7.37014 | −0.261228 | ||||||||
\(797\) | 25.6291 | 0.907828 | 0.453914 | − | 0.891046i | \(-0.350027\pi\) | ||||
0.453914 | + | 0.891046i | \(0.350027\pi\) | |||||||
\(798\) | 3.30109 | 0.116857 | ||||||||
\(799\) | 17.8470 | 0.631382 | ||||||||
\(800\) | −6.08609 | −0.215176 | ||||||||
\(801\) | 17.2269 | 0.608682 | ||||||||
\(802\) | 22.9750 | 0.811276 | ||||||||
\(803\) | 15.4235 | 0.544282 | ||||||||
\(804\) | −8.02334 | −0.282961 | ||||||||
\(805\) | −2.01631 | −0.0710655 | ||||||||
\(806\) | 5.09491 | 0.179460 | ||||||||
\(807\) | 4.80067 | 0.168991 | ||||||||
\(808\) | 2.58210 | 0.0908381 | ||||||||
\(809\) | −35.4509 | −1.24639 | −0.623194 | − | 0.782067i | \(-0.714166\pi\) | ||||
−0.623194 | + | 0.782067i | \(0.714166\pi\) | |||||||
\(810\) | −3.32958 | −0.116989 | ||||||||
\(811\) | 15.2520 | 0.535571 | 0.267785 | − | 0.963479i | \(-0.413708\pi\) | ||||
0.267785 | + | 0.963479i | \(0.413708\pi\) | |||||||
\(812\) | −1.92356 | −0.0675037 | ||||||||
\(813\) | −17.6247 | −0.618126 | ||||||||
\(814\) | 16.3065 | 0.571541 | ||||||||
\(815\) | −36.7586 | −1.28760 | ||||||||
\(816\) | 1.65277 | 0.0578584 | ||||||||
\(817\) | −2.21103 | −0.0773542 | ||||||||
\(818\) | 20.0669 | 0.701623 | ||||||||
\(819\) | −1.38443 | −0.0483761 | ||||||||
\(820\) | 9.58975 | 0.334889 | ||||||||
\(821\) | −26.3835 | −0.920792 | −0.460396 | − | 0.887714i | \(-0.652293\pi\) | ||||
−0.460396 | + | 0.887714i | \(0.652293\pi\) | |||||||
\(822\) | −10.1134 | −0.352744 | ||||||||
\(823\) | −32.0115 | −1.11585 | −0.557925 | − | 0.829891i | \(-0.688402\pi\) | ||||
−0.557925 | + | 0.829891i | \(0.688402\pi\) | |||||||
\(824\) | −1.00000 | −0.0348367 | ||||||||
\(825\) | 15.8730 | 0.552626 | ||||||||
\(826\) | 4.62272 | 0.160845 | ||||||||
\(827\) | −30.7304 | −1.06860 | −0.534300 | − | 0.845295i | \(-0.679425\pi\) | ||||
−0.534300 | + | 0.845295i | \(0.679425\pi\) | |||||||
\(828\) | 0.437417 | 0.0152013 | ||||||||
\(829\) | −3.52821 | −0.122540 | −0.0612699 | − | 0.998121i | \(-0.519515\pi\) | ||||
−0.0612699 | + | 0.998121i | \(0.519515\pi\) | |||||||
\(830\) | 24.7657 | 0.859630 | ||||||||
\(831\) | 20.2994 | 0.704178 | ||||||||
\(832\) | 1.00000 | 0.0346688 | ||||||||
\(833\) | 8.40157 | 0.291097 | ||||||||
\(834\) | −22.7082 | −0.786319 | ||||||||
\(835\) | −55.4311 | −1.91827 | ||||||||
\(836\) | 6.21879 | 0.215081 | ||||||||
\(837\) | 5.09491 | 0.176106 | ||||||||
\(838\) | −16.5765 | −0.572624 | ||||||||
\(839\) | 1.10550 | 0.0381662 | 0.0190831 | − | 0.999818i | \(-0.493925\pi\) | ||||
0.0190831 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(840\) | −4.60958 | −0.159046 | ||||||||
\(841\) | −27.0695 | −0.933432 | ||||||||
\(842\) | 31.7963 | 1.09577 | ||||||||
\(843\) | 3.46316 | 0.119278 | ||||||||
\(844\) | 4.63742 | 0.159627 | ||||||||
\(845\) | 3.32958 | 0.114541 | ||||||||
\(846\) | 10.7983 | 0.371252 | ||||||||
\(847\) | 5.81176 | 0.199694 | ||||||||
\(848\) | 8.01315 | 0.275173 | ||||||||
\(849\) | 16.2956 | 0.559262 | ||||||||
\(850\) | 10.0589 | 0.345016 | ||||||||
\(851\) | 2.73485 | 0.0937496 | ||||||||
\(852\) | −5.77612 | −0.197887 | ||||||||
\(853\) | −17.7546 | −0.607907 | −0.303954 | − | 0.952687i | \(-0.598307\pi\) | ||||
−0.303954 | + | 0.952687i | \(0.598307\pi\) | |||||||
\(854\) | −1.61128 | −0.0551368 | ||||||||
\(855\) | −7.93916 | −0.271514 | ||||||||
\(856\) | 12.0189 | 0.410799 | ||||||||
\(857\) | 1.16759 | 0.0398841 | 0.0199421 | − | 0.999801i | \(-0.493652\pi\) | ||||
0.0199421 | + | 0.999801i | \(0.493652\pi\) | |||||||
\(858\) | −2.60808 | −0.0890383 | ||||||||
\(859\) | −26.6737 | −0.910094 | −0.455047 | − | 0.890467i | \(-0.650378\pi\) | ||||
−0.455047 | + | 0.890467i | \(0.650378\pi\) | |||||||
\(860\) | 3.08744 | 0.105281 | ||||||||
\(861\) | 3.98741 | 0.135891 | ||||||||
\(862\) | −10.6520 | −0.362809 | ||||||||
\(863\) | 16.6001 | 0.565075 | 0.282537 | − | 0.959256i | \(-0.408824\pi\) | ||||
0.282537 | + | 0.959256i | \(0.408824\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −38.1191 | −1.29609 | ||||||||
\(866\) | −7.06019 | −0.239915 | ||||||||
\(867\) | 14.2684 | 0.484579 | ||||||||
\(868\) | 7.05356 | 0.239414 | ||||||||
\(869\) | −14.6410 | −0.496662 | ||||||||
\(870\) | 4.62618 | 0.156842 | ||||||||
\(871\) | 8.02334 | 0.271861 | ||||||||
\(872\) | 9.77876 | 0.331151 | ||||||||
\(873\) | −1.80223 | −0.0609963 | ||||||||
\(874\) | 1.04299 | 0.0352797 | ||||||||
\(875\) | −5.00640 | −0.169247 | ||||||||
\(876\) | 5.91373 | 0.199806 | ||||||||
\(877\) | −45.6635 | −1.54195 | −0.770974 | − | 0.636867i | \(-0.780230\pi\) | ||||
−0.770974 | + | 0.636867i | \(0.780230\pi\) | |||||||
\(878\) | 36.1524 | 1.22008 | ||||||||
\(879\) | −16.2465 | −0.547982 | ||||||||
\(880\) | −8.68380 | −0.292731 | ||||||||
\(881\) | 30.4867 | 1.02712 | 0.513561 | − | 0.858053i | \(-0.328326\pi\) | ||||
0.513561 | + | 0.858053i | \(0.328326\pi\) | |||||||
\(882\) | 5.08334 | 0.171165 | ||||||||
\(883\) | −24.8086 | −0.834877 | −0.417439 | − | 0.908705i | \(-0.637072\pi\) | ||||
−0.417439 | + | 0.908705i | \(0.637072\pi\) | |||||||
\(884\) | −1.65277 | −0.0555885 | ||||||||
\(885\) | −11.1177 | −0.373717 | ||||||||
\(886\) | −14.1150 | −0.474204 | ||||||||
\(887\) | 4.40219 | 0.147811 | 0.0739055 | − | 0.997265i | \(-0.476454\pi\) | ||||
0.0739055 | + | 0.997265i | \(0.476454\pi\) | |||||||
\(888\) | 6.25229 | 0.209813 | ||||||||
\(889\) | −8.61820 | −0.289045 | ||||||||
\(890\) | −57.3583 | −1.92265 | ||||||||
\(891\) | −2.60808 | −0.0873739 | ||||||||
\(892\) | 2.11474 | 0.0708067 | ||||||||
\(893\) | 25.7478 | 0.861616 | ||||||||
\(894\) | −5.39722 | −0.180510 | ||||||||
\(895\) | −33.7402 | −1.12781 | ||||||||
\(896\) | 1.38443 | 0.0462507 | ||||||||
\(897\) | −0.437417 | −0.0146049 | ||||||||
\(898\) | −27.6663 | −0.923237 | ||||||||
\(899\) | −7.07896 | −0.236097 | ||||||||
\(900\) | 6.08609 | 0.202870 | ||||||||
\(901\) | −13.2439 | −0.441217 | ||||||||
\(902\) | 7.51171 | 0.250113 | ||||||||
\(903\) | 1.28375 | 0.0427207 | ||||||||
\(904\) | 14.8934 | 0.495347 | ||||||||
\(905\) | −69.3207 | −2.30430 | ||||||||
\(906\) | −2.23675 | −0.0743111 | ||||||||
\(907\) | 35.0714 | 1.16453 | 0.582264 | − | 0.813000i | \(-0.302167\pi\) | ||||
0.582264 | + | 0.813000i | \(0.302167\pi\) | |||||||
\(908\) | 6.63719 | 0.220263 | ||||||||
\(909\) | −2.58210 | −0.0856430 | ||||||||
\(910\) | 4.60958 | 0.152806 | ||||||||
\(911\) | −40.6258 | −1.34599 | −0.672997 | − | 0.739646i | \(-0.734993\pi\) | ||||
−0.672997 | + | 0.739646i | \(0.734993\pi\) | |||||||
\(912\) | 2.38443 | 0.0789565 | ||||||||
\(913\) | 19.3991 | 0.642018 | ||||||||
\(914\) | 11.8995 | 0.393599 | ||||||||
\(915\) | 3.87514 | 0.128108 | ||||||||
\(916\) | −13.0876 | −0.432428 | ||||||||
\(917\) | 13.6246 | 0.449923 | ||||||||
\(918\) | −1.65277 | −0.0545494 | ||||||||
\(919\) | −52.0533 | −1.71708 | −0.858540 | − | 0.512746i | \(-0.828628\pi\) | ||||
−0.858540 | + | 0.512746i | \(0.828628\pi\) | |||||||
\(920\) | −1.45641 | −0.0480165 | ||||||||
\(921\) | −22.2353 | −0.732677 | ||||||||
\(922\) | 8.74873 | 0.288124 | ||||||||
\(923\) | 5.77612 | 0.190123 | ||||||||
\(924\) | −3.61071 | −0.118784 | ||||||||
\(925\) | 38.0520 | 1.25114 | ||||||||
\(926\) | −5.98788 | −0.196774 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | −1.38942 | −0.0456099 | ||||||||
\(929\) | −50.7854 | −1.66622 | −0.833108 | − | 0.553111i | \(-0.813441\pi\) | ||||
−0.833108 | + | 0.553111i | \(0.813441\pi\) | |||||||
\(930\) | −16.9639 | −0.556268 | ||||||||
\(931\) | 12.1209 | 0.397246 | ||||||||
\(932\) | −5.29335 | −0.173389 | ||||||||
\(933\) | −16.5685 | −0.542429 | ||||||||
\(934\) | −42.2930 | −1.38387 | ||||||||
\(935\) | 14.3523 | 0.469370 | ||||||||
\(936\) | −1.00000 | −0.0326860 | ||||||||
\(937\) | 8.67062 | 0.283257 | 0.141628 | − | 0.989920i | \(-0.454766\pi\) | ||||
0.141628 | + | 0.989920i | \(0.454766\pi\) | |||||||
\(938\) | 11.1078 | 0.362682 | ||||||||
\(939\) | 31.5663 | 1.03013 | ||||||||
\(940\) | −35.9537 | −1.17268 | ||||||||
\(941\) | −12.9461 | −0.422032 | −0.211016 | − | 0.977483i | \(-0.567677\pi\) | ||||
−0.211016 | + | 0.977483i | \(0.567677\pi\) | |||||||
\(942\) | 16.1805 | 0.527188 | ||||||||
\(943\) | 1.25983 | 0.0410259 | ||||||||
\(944\) | 3.33907 | 0.108677 | ||||||||
\(945\) | 4.60958 | 0.149950 | ||||||||
\(946\) | 2.41841 | 0.0786294 | ||||||||
\(947\) | −34.0803 | −1.10746 | −0.553730 | − | 0.832696i | \(-0.686796\pi\) | ||||
−0.553730 | + | 0.832696i | \(0.686796\pi\) | |||||||
\(948\) | −5.61371 | −0.182325 | ||||||||
\(949\) | −5.91373 | −0.191968 | ||||||||
\(950\) | 14.5119 | 0.470827 | ||||||||
\(951\) | 21.3357 | 0.691856 | ||||||||
\(952\) | −2.28815 | −0.0741592 | ||||||||
\(953\) | 13.7710 | 0.446087 | 0.223044 | − | 0.974808i | \(-0.428401\pi\) | ||||
0.223044 | + | 0.974808i | \(0.428401\pi\) | |||||||
\(954\) | −8.01315 | −0.259435 | ||||||||
\(955\) | −19.7282 | −0.638389 | ||||||||
\(956\) | −14.4156 | −0.466232 | ||||||||
\(957\) | 3.62371 | 0.117138 | ||||||||
\(958\) | 17.9798 | 0.580902 | ||||||||
\(959\) | 14.0013 | 0.452125 | ||||||||
\(960\) | −3.32958 | −0.107462 | ||||||||
\(961\) | −5.04192 | −0.162643 | ||||||||
\(962\) | −6.25229 | −0.201582 | ||||||||
\(963\) | −12.0189 | −0.387305 | ||||||||
\(964\) | 13.6057 | 0.438209 | ||||||||
\(965\) | 66.8091 | 2.15066 | ||||||||
\(966\) | −0.605575 | −0.0194840 | ||||||||
\(967\) | 27.4535 | 0.882844 | 0.441422 | − | 0.897300i | \(-0.354474\pi\) | ||||
0.441422 | + | 0.897300i | \(0.354474\pi\) | |||||||
\(968\) | 4.19793 | 0.134927 | ||||||||
\(969\) | −3.94091 | −0.126600 | ||||||||
\(970\) | 6.00067 | 0.192670 | ||||||||
\(971\) | −57.3187 | −1.83945 | −0.919723 | − | 0.392568i | \(-0.871587\pi\) | ||||
−0.919723 | + | 0.392568i | \(0.871587\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 31.4380 | 1.00785 | ||||||||
\(974\) | −3.71623 | −0.119076 | ||||||||
\(975\) | −6.08609 | −0.194911 | ||||||||
\(976\) | −1.16385 | −0.0372540 | ||||||||
\(977\) | 24.8339 | 0.794505 | 0.397253 | − | 0.917709i | \(-0.369964\pi\) | ||||
0.397253 | + | 0.917709i | \(0.369964\pi\) | |||||||
\(978\) | −11.0400 | −0.353021 | ||||||||
\(979\) | −44.9291 | −1.43594 | ||||||||
\(980\) | −16.9254 | −0.540661 | ||||||||
\(981\) | −9.77876 | −0.312212 | ||||||||
\(982\) | −13.0876 | −0.417643 | ||||||||
\(983\) | 29.2824 | 0.933964 | 0.466982 | − | 0.884267i | \(-0.345341\pi\) | ||||
0.466982 | + | 0.884267i | \(0.345341\pi\) | |||||||
\(984\) | 2.88017 | 0.0918165 | ||||||||
\(985\) | 36.8698 | 1.17477 | ||||||||
\(986\) | 2.29638 | 0.0731318 | ||||||||
\(987\) | −14.9495 | −0.475848 | ||||||||
\(988\) | −2.38443 | −0.0758590 | ||||||||
\(989\) | 0.405607 | 0.0128975 | ||||||||
\(990\) | 8.68380 | 0.275989 | ||||||||
\(991\) | −17.4497 | −0.554309 | −0.277154 | − | 0.960825i | \(-0.589391\pi\) | ||||
−0.277154 | + | 0.960825i | \(0.589391\pi\) | |||||||
\(992\) | 5.09491 | 0.161763 | ||||||||
\(993\) | 27.7441 | 0.880431 | ||||||||
\(994\) | 7.99666 | 0.253639 | ||||||||
\(995\) | −24.5394 | −0.777953 | ||||||||
\(996\) | 7.43809 | 0.235685 | ||||||||
\(997\) | −44.9473 | −1.42350 | −0.711748 | − | 0.702435i | \(-0.752096\pi\) | ||||
−0.711748 | + | 0.702435i | \(0.752096\pi\) | |||||||
\(998\) | −16.4962 | −0.522179 | ||||||||
\(999\) | −6.25229 | −0.197814 |
(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 | 8034.2.a.o.1.7 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8034.2.a.o.1.7 | ✓ | 7 | 1.1 | even | 1 | trivial |