Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6008,2,Mod(1,6008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6008, 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("6008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6008 = 2^{3} \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6008.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: | \(47.9741215344\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6008.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.93504 | −1.69454 | −0.847272 | − | 0.531159i | \(-0.821757\pi\) | ||||
−0.847272 | + | 0.531159i | \(0.821757\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.06805 | −0.924861 | −0.462430 | − | 0.886656i | \(-0.653022\pi\) | ||||
−0.462430 | + | 0.886656i | \(0.653022\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.42601 | 0.916947 | 0.458474 | − | 0.888708i | \(-0.348396\pi\) | ||||
0.458474 | + | 0.888708i | \(0.348396\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.61445 | 1.87148 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.57617 | −0.776744 | −0.388372 | − | 0.921503i | \(-0.626962\pi\) | ||||
−0.388372 | + | 0.921503i | \(0.626962\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.28339 | −0.355949 | −0.177975 | − | 0.984035i | \(-0.556954\pi\) | ||||
−0.177975 | + | 0.984035i | \(0.556954\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.06981 | 1.56722 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.19094 | 1.50152 | 0.750762 | − | 0.660573i | \(-0.229687\pi\) | ||||
0.750762 | + | 0.660573i | \(0.229687\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.69686 | 0.389285 | 0.194643 | − | 0.980874i | \(-0.437645\pi\) | ||||
0.194643 | + | 0.980874i | \(0.437645\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.12044 | −1.55381 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.28188 | 1.30986 | 0.654931 | − | 0.755689i | \(-0.272698\pi\) | ||||
0.654931 | + | 0.755689i | \(0.272698\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.723164 | −0.144633 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.67350 | −1.47676 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.09394 | 0.945920 | 0.472960 | − | 0.881084i | \(-0.343186\pi\) | ||||
0.472960 | + | 0.881084i | \(0.343186\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.11764 | 0.919156 | 0.459578 | − | 0.888137i | \(-0.348001\pi\) | ||||
0.459578 | + | 0.888137i | \(0.348001\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.56115 | 1.31623 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.01712 | −0.848048 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0401 | −1.65058 | −0.825291 | − | 0.564707i | \(-0.808989\pi\) | ||||
−0.825291 | + | 0.564707i | \(0.808989\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.76681 | 0.603172 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.199780 | −0.0312003 | −0.0156002 | − | 0.999878i | \(-0.504966\pi\) | ||||
−0.0156002 | + | 0.999878i | \(0.504966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.26243 | 1.26001 | 0.630005 | − | 0.776591i | \(-0.283053\pi\) | ||||
0.630005 | + | 0.776591i | \(0.283053\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.6110 | −1.73086 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.60927 | −0.818197 | −0.409098 | − | 0.912490i | \(-0.634157\pi\) | ||||
−0.409098 | + | 0.912490i | \(0.634157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.11445 | −0.159208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.1706 | −2.54440 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.03567 | −0.416982 | −0.208491 | − | 0.978024i | \(-0.566855\pi\) | ||||
−0.208491 | + | 0.978024i | \(0.566855\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.32765 | 0.718380 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.98033 | −0.659661 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.92521 | 0.511019 | 0.255509 | − | 0.966807i | \(-0.417757\pi\) | ||||
0.255509 | + | 0.966807i | \(0.417757\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50032 | 0.704244 | 0.352122 | − | 0.935954i | \(-0.385460\pi\) | ||||
0.352122 | + | 0.935954i | \(0.385460\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.6207 | 1.71605 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.65412 | 0.329203 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.34148 | 0.652565 | 0.326283 | − | 0.945272i | \(-0.394204\pi\) | ||||
0.326283 | + | 0.945272i | \(0.394204\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.4376 | −2.21962 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.73831 | −0.562334 | −0.281167 | − | 0.959659i | \(-0.590722\pi\) | ||||
−0.281167 | + | 0.959659i | \(0.590722\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.46890 | 0.523046 | 0.261523 | − | 0.965197i | \(-0.415775\pi\) | ||||
0.261523 | + | 0.965197i | \(0.415775\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.12251 | 0.245087 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.24982 | −0.712233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.736412 | −0.0828528 | −0.0414264 | − | 0.999142i | \(-0.513190\pi\) | ||||
−0.0414264 | + | 0.999142i | \(0.513190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.67866 | 0.630962 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.29873 | −0.801139 | −0.400570 | − | 0.916266i | \(-0.631188\pi\) | ||||
−0.400570 | + | 0.916266i | \(0.631188\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.8032 | −1.38870 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.9509 | −1.60290 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.85260 | 0.408375 | 0.204187 | − | 0.978932i | \(-0.434545\pi\) | ||||
0.204187 | + | 0.978932i | \(0.434545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.11353 | −0.326387 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.0205 | −1.55755 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.50918 | −0.360035 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.69150 | −0.171746 | −0.0858728 | − | 0.996306i | \(-0.527368\pi\) | ||||
−0.0858728 | + | 0.996306i | \(0.527368\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.4638 | −1.45366 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.23235 | −0.620142 | −0.310071 | − | 0.950713i | \(-0.600353\pi\) | ||||
−0.310071 | + | 0.950713i | \(0.600353\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.79770 | 0.571264 | 0.285632 | − | 0.958339i | \(-0.407796\pi\) | ||||
0.285632 | + | 0.958339i | \(0.407796\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 14.7254 | 1.43706 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.30489 | 0.222822 | 0.111411 | − | 0.993774i | \(-0.464463\pi\) | ||||
0.111411 | + | 0.993774i | \(0.464463\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.34406 | −0.224520 | −0.112260 | − | 0.993679i | \(-0.535809\pi\) | ||||
−0.112260 | + | 0.993679i | \(0.535809\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 29.4681 | 2.79699 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.06566 | −0.476537 | −0.238269 | − | 0.971199i | \(-0.576580\pi\) | ||||
−0.238269 | + | 0.971199i | \(0.576580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.9912 | −1.21144 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.20554 | −0.666152 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0193 | 1.37682 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.36335 | −0.396668 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.586361 | 0.0528704 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.8358 | 1.05863 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.81718 | 0.427456 | 0.213728 | − | 0.976893i | \(-0.431439\pi\) | ||||
0.213728 | + | 0.976893i | \(0.431439\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −24.2506 | −2.13514 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7616 | −1.11499 | −0.557494 | − | 0.830181i | \(-0.688237\pi\) | ||||
−0.557494 | + | 0.830181i | \(0.688237\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.11659 | 0.356954 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.8692 | 1.36580 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.55453 | −0.730863 | −0.365431 | − | 0.930838i | \(-0.619078\pi\) | ||||
−0.365431 | + | 0.930838i | \(0.619078\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.655924 | 0.0556348 | 0.0278174 | − | 0.999613i | \(-0.491144\pi\) | ||||
0.0278174 | + | 0.999613i | \(0.491144\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.4634 | 1.38647 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.30624 | 0.276481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.5345 | −0.874844 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.27097 | 0.269785 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.95189 | 0.405675 | 0.202837 | − | 0.979212i | \(-0.434984\pi\) | ||||
0.202837 | + | 0.979212i | \(0.434984\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.55315 | −0.126393 | −0.0631966 | − | 0.998001i | \(-0.520130\pi\) | ||||
−0.0631966 | + | 0.998001i | \(0.520130\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 34.7587 | 2.81007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.5836 | −0.850091 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.22482 | −0.337178 | −0.168589 | − | 0.985686i | \(-0.553921\pi\) | ||||
−0.168589 | + | 0.985686i | \(0.553921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.90982 | 0.706595 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2399 | 1.20107 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5311 | 1.52979 | 0.764895 | − | 0.644155i | \(-0.222791\pi\) | ||||
0.764895 | + | 0.644155i | \(0.222791\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −15.6369 | −1.21733 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.6163 | −1.59533 | −0.797667 | − | 0.603098i | \(-0.793933\pi\) | ||||
−0.797667 | + | 0.603098i | \(0.793933\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3529 | −0.873300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.52690 | 0.728540 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.1882 | −0.926649 | −0.463325 | − | 0.886189i | \(-0.653344\pi\) | ||||
−0.463325 | + | 0.886189i | \(0.653344\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.75441 | −0.132621 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −11.5206 | −0.865944 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.39333 | 0.702091 | 0.351045 | − | 0.936358i | \(-0.385826\pi\) | ||||
0.351045 | + | 0.936358i | \(0.385826\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.09033 | −0.601349 | −0.300675 | − | 0.953727i | \(-0.597212\pi\) | ||||
−0.300675 | + | 0.953727i | \(0.597212\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.1437 | −1.19337 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.7634 | 1.52656 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.9489 | −1.16630 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −18.6160 | −1.35412 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.4868 | 1.04823 | 0.524114 | − | 0.851648i | \(-0.324397\pi\) | ||||
0.524114 | + | 0.851648i | \(0.324397\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.99199 | −0.215368 | −0.107684 | − | 0.994185i | \(-0.534344\pi\) | ||||
−0.107684 | + | 0.994185i | \(0.534344\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.78995 | −0.557850 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.65268 | −0.402737 | −0.201368 | − | 0.979516i | \(-0.564539\pi\) | ||||
−0.201368 | + | 0.979516i | \(0.564539\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1790 | 1.35956 | 0.679782 | − | 0.733414i | \(-0.262075\pi\) | ||||
0.679782 | + | 0.733414i | \(0.262075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.6774 | −1.10580 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.3580 | 0.867359 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.413155 | 0.0288560 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 35.2693 | 2.45138 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.37139 | −0.302375 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.73576 | 0.532551 | 0.266276 | − | 0.963897i | \(-0.414207\pi\) | ||||
0.266276 | + | 0.963897i | \(0.414207\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.9071 | 0.952901 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −17.0871 | −1.16533 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.4155 | 0.842818 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.1164 | −0.886324 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.94541 | −0.534466 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.46039 | 0.298690 | 0.149345 | − | 0.988785i | \(-0.452284\pi\) | ||||
0.149345 | + | 0.988785i | \(0.452284\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.06016 | −0.270678 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.693983 | −0.0460613 | −0.0230306 | − | 0.999735i | \(-0.507332\pi\) | ||||
−0.0230306 | + | 0.999735i | \(0.507332\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.8794 | −0.851092 | −0.425546 | − | 0.904937i | \(-0.639918\pi\) | ||||
−0.425546 | + | 0.904937i | \(0.639918\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.3435 | 1.20691 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −15.9830 | −1.04708 | −0.523540 | − | 0.852001i | \(-0.675389\pi\) | ||||
−0.523540 | + | 0.852001i | \(0.675389\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.6003 | 0.756718 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.16140 | 0.140398 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.74647 | 0.436393 | 0.218196 | − | 0.975905i | \(-0.429983\pi\) | ||||
0.218196 | + | 0.975905i | \(0.429983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2087 | 1.04409 | 0.522047 | − | 0.852917i | \(-0.325169\pi\) | ||||
0.522047 | + | 0.852917i | \(0.325169\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.35340 | 0.407571 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.30475 | 0.147245 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.17773 | −0.138566 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.4220 | 1.35757 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.62965 | 0.229101 | 0.114551 | − | 0.993417i | \(-0.463457\pi\) | ||||
0.114551 | + | 0.993417i | \(0.463457\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.1832 | −1.01743 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.5778 | 2.35322 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 21.4727 | 1.33943 | 0.669716 | − | 0.742618i | \(-0.266416\pi\) | ||||
0.669716 | + | 0.742618i | \(0.266416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.3574 | −1.51350 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 28.5996 | 1.77027 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.124008 | −0.00764668 | −0.00382334 | − | 0.999993i | \(-0.501217\pi\) | ||||
−0.00382334 | + | 0.999993i | \(0.501217\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.27793 | 0.385650 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.3075 | −0.692009 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.24251 | −0.502555 | −0.251277 | − | 0.967915i | \(-0.580851\pi\) | ||||
−0.251277 | + | 0.967915i | \(0.580851\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9873 | 1.57861 | 0.789307 | − | 0.613998i | \(-0.210440\pi\) | ||||
0.789307 | + | 0.613998i | \(0.210440\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.13833 | 0.553077 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.86299 | 0.112343 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.14163 | 0.0685941 | 0.0342971 | − | 0.999412i | \(-0.489081\pi\) | ||||
0.0342971 | + | 0.999412i | \(0.489081\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 28.7327 | 1.72018 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.18883 | 0.309540 | 0.154770 | − | 0.987951i | \(-0.450536\pi\) | ||||
0.154770 | + | 0.987951i | \(0.450536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.4060 | 1.09412 | 0.547062 | − | 0.837092i | \(-0.315746\pi\) | ||||
0.547062 | + | 0.837092i | \(0.315746\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.2996 | 0.610095 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.484668 | −0.0286091 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 21.3278 | 1.25457 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.96461 | 0.291031 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 30.4604 | 1.77952 | 0.889758 | − | 0.456432i | \(-0.150873\pi\) | ||||
0.889758 | + | 0.456432i | \(0.150873\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.11753 | −0.472621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.7682 | 1.14707 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.06212 | −0.466244 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0448 | 1.15536 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 18.2922 | 1.05086 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.3749 | −0.651328 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.441213 | 0.0251814 | 0.0125907 | − | 0.999921i | \(-0.495992\pi\) | ||||
0.0125907 | + | 0.999921i | \(0.495992\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −17.0165 | −0.968033 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.426103 | 0.0241621 | 0.0120810 | − | 0.999927i | \(-0.496154\pi\) | ||||
0.0120810 | + | 0.999927i | \(0.496154\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.6708 | 0.603149 | 0.301575 | − | 0.953443i | \(-0.402488\pi\) | ||||
0.301575 | + | 0.953443i | \(0.402488\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −28.1684 | −1.58711 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.3371 | 1.42308 | 0.711538 | − | 0.702648i | \(-0.247999\pi\) | ||||
0.711538 | + | 0.702648i | \(0.247999\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.1228 | −0.734738 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.76494 | −0.377582 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5051 | 0.584521 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.928103 | 0.0514819 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.87991 | 0.380460 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6082 | −0.750243 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.9722 | 1.53749 | 0.768745 | − | 0.639555i | \(-0.220881\pi\) | ||||
0.768745 | + | 0.639555i | \(0.220881\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −56.3696 | −3.08904 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0465 | −0.603532 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.747034 | −0.0406935 | −0.0203468 | − | 0.999793i | \(-0.506477\pi\) | ||||
−0.0203468 | + | 0.999793i | \(0.506477\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.8679 | 0.807514 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.1839 | −0.713949 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.6858 | −1.06293 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 38.1298 | 2.05284 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.3371 | −0.930703 | −0.465351 | − | 0.885126i | \(-0.654072\pi\) | ||||
−0.465351 | + | 0.885126i | \(0.654072\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.97310 | −0.159147 | −0.0795733 | − | 0.996829i | \(-0.525356\pi\) | ||||
−0.0795733 | + | 0.996829i | \(0.525356\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.84811 | 0.525653 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.8009 | 1.21357 | 0.606784 | − | 0.794867i | \(-0.292459\pi\) | ||||
0.606784 | + | 0.794867i | \(0.292459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.79907 | 0.520081 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −44.0823 | −2.33308 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.2242 | −1.01461 | −0.507306 | − | 0.861766i | \(-0.669359\pi\) | ||||
−0.507306 | + | 0.861766i | \(0.669359\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1207 | −0.848457 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.8066 | 0.672172 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.24192 | −0.483744 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.91709 | 0.100071 | 0.0500357 | − | 0.998747i | \(-0.484066\pi\) | ||||
0.0500357 | + | 0.998747i | \(0.484066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.12165 | −0.0583909 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.36459 | −0.382350 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.6220 | 1.32666 | 0.663328 | − | 0.748328i | \(-0.269143\pi\) | ||||
0.663328 | + | 0.748328i | \(0.269143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −34.7385 | −1.79389 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −6.53752 | −0.336699 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.1324 | 1.85600 | 0.927998 | − | 0.372585i | \(-0.121528\pi\) | ||||
0.927998 | + | 0.372585i | \(0.121528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.1386 | −0.724343 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.79073 | −0.449186 | −0.224593 | − | 0.974453i | \(-0.572105\pi\) | ||||
−0.224593 | + | 0.974453i | \(0.572105\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12.9250 | 0.658717 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 46.3890 | 2.35808 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −35.0473 | −1.77697 | −0.888484 | − | 0.458907i | \(-0.848241\pi\) | ||||
−0.888484 | + | 0.458907i | \(0.848241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 38.8907 | 1.96679 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.4558 | 1.88940 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.52294 | 0.0766273 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.9137 | 1.20020 | 0.600098 | − | 0.799927i | \(-0.295128\pi\) | ||||
0.600098 | + | 0.799927i | \(0.295128\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.0824 | −0.604875 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.03703 | −0.0517867 | −0.0258933 | − | 0.999665i | \(-0.508243\pi\) | ||||
−0.0258933 | + | 0.999665i | \(0.508243\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.56795 | −0.327173 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.7438 | −0.583552 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 25.8650 | 1.28208 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.86456 | 0.438325 | 0.219162 | − | 0.975688i | \(-0.429668\pi\) | ||||
0.219162 | + | 0.975688i | \(0.429668\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 25.1079 | 1.23848 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.52261 | 0.468577 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0941 | 0.740942 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.92516 | −0.0942756 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.2682 | 0.941311 | 0.470656 | − | 0.882317i | \(-0.344017\pi\) | ||||
0.470656 | + | 0.882317i | \(0.344017\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.3278 | 0.795768 | 0.397884 | − | 0.917436i | \(-0.369745\pi\) | ||||
0.397884 | + | 0.917436i | \(0.369745\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −31.4930 | −1.53124 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.47706 | −0.217170 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.3439 | 0.645755 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.70393 | −0.468510 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.37338 | −0.403331 | −0.201666 | − | 0.979454i | \(-0.564635\pi\) | ||||
−0.201666 | + | 0.979454i | \(0.564635\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.553303 | 0.0265901 | 0.0132950 | − | 0.999912i | \(-0.495768\pi\) | ||||
0.0132950 | + | 0.999912i | \(0.495768\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 30.9192 | 1.48246 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.6594 | 0.509910 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9717 | 1.14411 | 0.572054 | − | 0.820216i | \(-0.306147\pi\) | ||||
0.572054 | + | 0.820216i | \(0.306147\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.25704 | −0.297954 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.9876 | 1.61480 | 0.807399 | − | 0.590005i | \(-0.200874\pi\) | ||||
0.807399 | + | 0.590005i | \(0.200874\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.96737 | −0.377690 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.5340 | −0.687434 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.87173 | 0.182718 | 0.0913590 | − | 0.995818i | \(-0.470879\pi\) | ||||
0.0913590 | + | 0.995818i | \(0.470879\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.514666 | 0.0242347 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.55854 | 0.214179 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.43894 | 0.301862 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.35380 | 0.110106 | 0.0550531 | − | 0.998483i | \(-0.482467\pi\) | ||||
0.0550531 | + | 0.998483i | \(0.482467\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −47.5062 | −2.21740 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.7486 | 0.780059 | 0.390030 | − | 0.920802i | \(-0.372465\pi\) | ||||
0.390030 | + | 0.920802i | \(0.372465\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.2328 | 1.03324 | 0.516622 | − | 0.856213i | \(-0.327189\pi\) | ||||
0.516622 | + | 0.856213i | \(0.327189\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.0631 | 1.44052 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.49920 | 0.254472 | 0.127236 | − | 0.991872i | \(-0.459389\pi\) | ||||
0.127236 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9585 | 0.598368 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.4000 | 0.571363 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.2854 | −0.978705 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.22710 | −0.0563034 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.0436 | −0.780374 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.98726 | 0.136491 | 0.0682456 | − | 0.997669i | \(-0.478260\pi\) | ||||
0.0682456 | + | 0.997669i | \(0.478260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12.8854 | 0.587524 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −44.7298 | −2.03527 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.49810 | 0.158841 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.0775 | 1.58951 | 0.794757 | − | 0.606928i | \(-0.207598\pi\) | ||||
0.794757 | + | 0.606928i | \(0.207598\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −57.3244 | −2.59230 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.1593 | −1.54159 | −0.770793 | − | 0.637086i | \(-0.780140\pi\) | ||||
−0.770793 | + | 0.637086i | \(0.780140\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 31.5363 | 1.42032 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 29.9118 | 1.34444 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −11.4952 | −0.515631 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.2523 | −0.996150 | −0.498075 | − | 0.867134i | \(-0.665960\pi\) | ||||
−0.498075 | + | 0.867134i | \(0.665960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 60.5095 | 2.70337 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2409 | −0.634971 | −0.317486 | − | 0.948263i | \(-0.602839\pi\) | ||||
−0.317486 | + | 0.948263i | \(0.602839\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.8888 | 0.573545 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.3212 | 1.47985 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1870 | 0.495855 | 0.247928 | − | 0.968779i | \(-0.420251\pi\) | ||||
0.247928 | + | 0.968779i | \(0.420251\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.8416 | 0.479605 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.0208 | −0.574883 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.9899 | −0.528340 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.4504 | 0.635530 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 35.7727 | 1.57025 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.2133 | −1.36748 | −0.683739 | − | 0.729727i | \(-0.739647\pi\) | ||||
−0.683739 | + | 0.729727i | \(0.739647\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.71810 | 0.250035 | 0.125017 | − | 0.992155i | \(-0.460101\pi\) | ||||
0.125017 | + | 0.992155i | \(0.460101\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.14925 | 0.224732 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 31.6830 | 1.38013 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.4620 | 0.715739 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.0379 | 0.956362 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.256396 | 0.0111057 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.76663 | −0.206079 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −27.5698 | −1.18972 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.87102 | 0.123664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.4407 | −0.534868 | −0.267434 | − | 0.963576i | \(-0.586176\pi\) | ||||
−0.267434 | + | 0.963576i | \(0.586176\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.7454 | 1.01901 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.84764 | 0.207650 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 25.6933 | 1.09857 | 0.549284 | − | 0.835636i | \(-0.314901\pi\) | ||||
0.549284 | + | 0.835636i | \(0.314901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.8813 | 1.31798 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.64367 | 0.368233 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.78655 | −0.0759717 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −60.9415 | −2.58682 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.5549 | −0.701453 | −0.350726 | − | 0.936478i | \(-0.614065\pi\) | ||||
−0.350726 | + | 0.936478i | \(0.614065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.6039 | −0.448499 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 46.8107 | 1.97635 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.5804 | 1.16237 | 0.581187 | − | 0.813770i | \(-0.302589\pi\) | ||||
0.581187 | + | 0.813770i | \(0.302589\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4760 | 0.440731 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 13.7765 | 0.578559 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.7709 | −0.828839 | −0.414420 | − | 0.910086i | \(-0.636015\pi\) | ||||
−0.414420 | + | 0.910086i | \(0.636015\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.71600 | 0.364753 | 0.182377 | − | 0.983229i | \(-0.441621\pi\) | ||||
0.182377 | + | 0.983229i | \(0.441621\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −42.5193 | −1.77627 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.54283 | −0.189449 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.83706 | −0.284631 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.78161 | 0.364951 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.7068 | −0.734603 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.82041 | 0.323888 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 14.9014 | 0.616098 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 12.2754 | 0.506660 | 0.253330 | − | 0.967380i | \(-0.418474\pi\) | ||||
0.253330 | + | 0.967380i | \(0.418474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.68390 | 0.357814 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.5908 | 0.682455 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −37.8978 | −1.55627 | −0.778137 | − | 0.628094i | \(-0.783835\pi\) | ||||
−0.778137 | + | 0.628094i | \(0.783835\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −31.0607 | −1.27337 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −56.2911 | −2.30384 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.7004 | 0.478066 | 0.239033 | − | 0.971011i | \(-0.423170\pi\) | ||||
0.239033 | + | 0.971011i | \(0.423170\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.21560 | 0.131167 | 0.0655835 | − | 0.997847i | \(-0.479109\pi\) | ||||
0.0655835 | + | 0.997847i | \(0.479109\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.9894 | 1.22126 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.02364 | 0.366863 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.2564 | 0.497471 | 0.248736 | − | 0.968571i | \(-0.419985\pi\) | ||||
0.248736 | + | 0.968571i | \(0.419985\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −36.2711 | −1.46978 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.19890 | 0.291236 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.70143 | 0.351447 | 0.175724 | − | 0.984440i | \(-0.443773\pi\) | ||||
0.175724 | + | 0.984440i | \(0.443773\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.21262 | −0.0488977 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.7520 | 0.795185 | 0.397593 | − | 0.917562i | \(-0.369846\pi\) | ||||
0.397593 | + | 0.917562i | \(0.369846\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.72356 | −0.270243 | −0.135121 | − | 0.990829i | \(-0.543142\pi\) | ||||
−0.135121 | + | 0.990829i | \(0.543142\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −48.2040 | −1.93436 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.34646 | 0.374458 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.8612 | −0.834449 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.8302 | 0.512388 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −62.1577 | −2.47839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6725 | −0.544292 | −0.272146 | − | 0.962256i | \(-0.587733\pi\) | ||||
−0.272146 | + | 0.962256i | \(0.587733\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.7047 | −0.902432 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.96218 | −0.395337 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.43028 | 0.0566699 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.6030 | −1.05240 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.7988 | −0.939994 | −0.469997 | − | 0.882668i | \(-0.655745\pi\) | ||||
−0.469997 | + | 0.882668i | \(0.655745\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −48.6919 | −1.92022 | −0.960110 | − | 0.279624i | \(-0.909790\pi\) | ||||
−0.960110 | + | 0.279624i | \(0.909790\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 50.1514 | 1.97471 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.5731 | 0.494298 | 0.247149 | − | 0.968977i | \(-0.420506\pi\) | ||||
0.247149 | + | 0.968977i | \(0.420506\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −10.1120 | −0.396931 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.4399 | −1.42819 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.85923 | −0.190156 | −0.0950782 | − | 0.995470i | \(-0.530310\pi\) | ||||
−0.0950782 | + | 0.995470i | \(0.530310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.3917 | 1.03121 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.0904 | 0.978870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.1649 | −1.52565 | −0.762824 | − | 0.646607i | \(-0.776188\pi\) | ||||
−0.762824 | + | 0.646607i | \(0.776188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8068 | 0.770395 | 0.385197 | − | 0.922834i | \(-0.374133\pi\) | ||||
0.385197 | + | 0.922834i | \(0.374133\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 23.3201 | 0.905677 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.51333 | −0.330133 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31.9995 | 1.23902 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.0914 | −0.506143 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.1698 | −0.547017 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3830 | −0.631517 | −0.315759 | − | 0.948840i | \(-0.602259\pi\) | ||||
−0.315759 | + | 0.948840i | \(0.602259\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.54919 | 0.213589 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −12.6860 | −0.487564 | −0.243782 | − | 0.969830i | \(-0.578388\pi\) | ||||
−0.243782 | + | 0.969830i | \(0.578388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.10360 | −0.157482 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.03687 | 0.0780529 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.1906 | −0.466460 | −0.233230 | − | 0.972422i | \(-0.574930\pi\) | ||||
−0.233230 | + | 0.972422i | \(0.574930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.6912 | 0.675946 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.8014 | 1.44221 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.89596 | 0.148424 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.2060 | 0.996925 | 0.498463 | − | 0.866911i | \(-0.333898\pi\) | ||||
0.498463 | + | 0.866911i | \(0.333898\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −35.0893 | −1.33293 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.35649 | −0.0514544 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.23682 | −0.0468481 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 46.9107 | 1.77432 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.3595 | −1.93982 | −0.969911 | − | 0.243461i | \(-0.921717\pi\) | ||||
−0.969911 | + | 0.243461i | \(0.921717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.0366 | −0.642547 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −34.0472 | −1.28229 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.1198 | −0.568637 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.8713 | −1.00917 | −0.504586 | − | 0.863361i | \(-0.668355\pi\) | ||||
−0.504586 | + | 0.863361i | \(0.668355\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.13454 | −0.155058 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 32.1484 | 1.20397 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.83747 | −0.255707 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.8011 | −0.739487 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.70033 | 0.0634115 | 0.0317058 | − | 0.999497i | \(-0.489906\pi\) | ||||
0.0317058 | + | 0.999497i | \(0.489906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.0653 | 0.523819 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.5731 | −1.76926 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.68375 | −0.136811 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.8931 | −0.441089 | −0.220545 | − | 0.975377i | \(-0.570783\pi\) | ||||
−0.220545 | + | 0.975377i | \(0.570783\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.6835 | −1.32161 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 51.1522 | 1.89193 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.7838 | 0.878475 | 0.439237 | − | 0.898371i | \(-0.355249\pi\) | ||||
0.439237 | + | 0.898371i | \(0.355249\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.76453 | −0.249513 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.7606 | −0.506876 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.2182 | −1.62659 | −0.813296 | − | 0.581851i | \(-0.802329\pi\) | ||||
−0.813296 | + | 0.581851i | \(0.802329\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.39172 | 0.234806 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −47.7735 | −1.75264 | −0.876320 | − | 0.481729i | \(-0.840009\pi\) | ||||
−0.876320 | + | 0.481729i | \(0.840009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.2408 | −0.375192 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −40.9783 | −1.49932 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.59170 | 0.204316 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −10.6531 | −0.388222 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.21199 | 0.116896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.4871 | 0.817308 | 0.408654 | − | 0.912689i | \(-0.365998\pi\) | ||||
0.408654 | + | 0.912689i | \(0.365998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 47.4982 | 1.72408 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.4890 | −0.742727 | −0.371364 | − | 0.928488i | \(-0.621110\pi\) | ||||
−0.371364 | + | 0.928488i | \(0.621110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.68673 | −0.205873 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −71.8828 | −2.59893 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.03758 | −0.181897 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.1392 | 1.30321 | 0.651607 | − | 0.758557i | \(-0.274095\pi\) | ||||
0.651607 | + | 0.758557i | \(0.274095\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −63.0232 | −2.26973 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 38.1243 | 1.37124 | 0.685618 | − | 0.727961i | \(-0.259532\pi\) | ||||
0.685618 | + | 0.727961i | \(0.259532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.70089 | −0.132940 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 71.4900 | 2.56469 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.338997 | −0.0121458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.2067 | 0.436790 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.0883 | −1.39690 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.73715 | 0.311842 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.91552 | −0.139573 | −0.0697867 | − | 0.997562i | \(-0.522232\pi\) | ||||
−0.0697867 | + | 0.997562i | \(0.522232\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.363969 | 0.0129576 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.2894 | −0.436959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.05907 | −0.250675 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −18.4260 | −0.653502 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.5703 | 1.08286 | 0.541429 | − | 0.840747i | \(-0.317884\pi\) | ||||
0.541429 | + | 0.840747i | \(0.317884\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.7267 | −1.22854 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.6302 | 0.764266 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.5126 | −0.406273 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −31.5170 | −1.11083 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.1921 | 0.851601 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.92027 | 0.208145 | 0.104073 | − | 0.994570i | \(-0.466813\pi\) | ||||
0.104073 | + | 0.994570i | \(0.466813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 53.6537 | 1.88404 | 0.942019 | − | 0.335561i | \(-0.108926\pi\) | ||||
0.942019 | + | 0.335561i | \(0.108926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −76.2736 | −2.67503 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40.3912 | −1.41484 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.0202 | 0.490503 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −17.4807 | −0.610827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.5637 | −1.03178 | −0.515891 | − | 0.856654i | \(-0.672539\pi\) | ||||
−0.515891 | + | 0.856654i | \(0.672539\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −44.3337 | −1.54538 | −0.772688 | − | 0.634786i | \(-0.781088\pi\) | ||||
−0.772688 | + | 0.634786i | \(0.781088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.46795 | −0.190370 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.9154 | 1.38800 | 0.693998 | − | 0.719977i | \(-0.255848\pi\) | ||||
0.693998 | + | 0.719977i | \(0.255848\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.35858 | −0.0819169 | −0.0409584 | − | 0.999161i | \(-0.513041\pi\) | ||||
−0.0409584 | + | 0.999161i | \(0.513041\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.35074 | −0.116236 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.89952 | −0.239054 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 42.6355 | 1.47546 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −39.2702 | −1.35738 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.9596 | −0.861702 | −0.430851 | − | 0.902423i | \(-0.641787\pi\) | ||||
−0.430851 | + | 0.902423i | \(0.641787\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.05182 | −0.105235 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.2294 | −0.524529 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.4784 | 0.807681 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5856 | −0.363724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −54.0224 | −1.85404 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −63.0707 | −2.16204 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.5205 | −0.360216 | −0.180108 | − | 0.983647i | \(-0.557645\pi\) | ||||
−0.180108 | + | 0.983647i | \(0.557645\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.7021 | −0.673798 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.7306 | 0.810621 | 0.405311 | − | 0.914179i | \(-0.367163\pi\) | ||||
0.405311 | + | 0.914179i | \(0.367163\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.2305 | −1.78208 | −0.891042 | − | 0.453922i | \(-0.850025\pi\) | ||||
−0.891042 | + | 0.453922i | \(0.850025\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.42252 | 0.0484793 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −41.2277 | −1.40341 | −0.701703 | − | 0.712469i | \(-0.747577\pi\) | ||||
−0.701703 | + | 0.712469i | \(0.747577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.2058 | 0.857021 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −62.5978 | −2.12593 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.89712 | 0.0643554 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.85522 | −0.232280 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.49682 | −0.321419 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28.7138 | 0.970704 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.3463 | 0.687047 | 0.343524 | − | 0.939144i | \(-0.388379\pi\) | ||||
0.343524 | + | 0.939144i | \(0.388379\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −89.4025 | −3.01547 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.3084 | −0.482062 | −0.241031 | − | 0.970517i | \(-0.577486\pi\) | ||||
−0.241031 | + | 0.970517i | \(0.577486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.3486 | −0.752090 | −0.376045 | − | 0.926601i | \(-0.622716\pi\) | ||||
−0.376045 | + | 0.926601i | \(0.622716\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.8253 | 0.800877 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.3194 | 1.38737 | 0.693685 | − | 0.720278i | \(-0.255986\pi\) | ||||
0.693685 | + | 0.720278i | \(0.255986\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.6865 | 0.391954 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.6292 | −0.490096 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.51813 | −0.318512 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.4259 | −0.649336 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.6626 | 0.790072 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26.0689 | 0.869448 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −18.7937 | −0.626108 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −58.8322 | −1.95781 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.7312 | 0.556164 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.8439 | −0.891338 | −0.445669 | − | 0.895198i | \(-0.647034\pi\) | ||||
−0.445669 | + | 0.895198i | \(0.647034\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −34.9912 | −1.16058 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.5951 | 0.384163 | 0.192081 | − | 0.981379i | \(-0.438476\pi\) | ||||
0.192081 | + | 0.981379i | \(0.438476\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8028 | 0.622280 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.3859 | 1.10370 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −30.9599 | −1.02238 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.7360 | −0.782980 | −0.391490 | − | 0.920182i | \(-0.628040\pi\) | ||||
−0.391490 | + | 0.920182i | \(0.628040\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.29498 | −0.0426709 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.08112 | 0.200162 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.26064 | 0.238728 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 32.5509 | 1.06911 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 14.8191 | 0.486200 | 0.243100 | − | 0.970001i | \(-0.421836\pi\) | ||||
0.243100 | + | 0.970001i | \(0.421836\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.89107 | −0.0619772 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.25063 | −0.0409437 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 32.9832 | 1.07867 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.9277 | 1.04303 | 0.521517 | − | 0.853241i | \(-0.325366\pi\) | ||||
0.521517 | + | 0.853241i | \(0.325366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −31.3192 | −1.02206 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5536 | 0.735225 | 0.367613 | − | 0.929979i | \(-0.380175\pi\) | ||||
0.367613 | + | 0.929979i | \(0.380175\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.25499 | −0.0408682 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.4989 | 1.25237 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 11.7270 | 0.381076 | 0.190538 | − | 0.981680i | \(-0.438977\pi\) | ||||
0.190538 | + | 0.981680i | \(0.438977\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.73536 | −0.186178 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −74.3654 | −2.41146 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 26.9121 | 0.871770 | 0.435885 | − | 0.900002i | \(-0.356435\pi\) | ||||
0.435885 | + | 0.900002i | \(0.356435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.9594 | −0.969464 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 38.5160 | 1.24505 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −20.7534 | −0.670162 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.80972 | −0.155152 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12.9407 | 0.417008 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.18760 | 0.199186 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 53.2753 | 1.71322 | 0.856609 | − | 0.515966i | \(-0.172567\pi\) | ||||
0.856609 | + | 0.515966i | \(0.172567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −30.8330 | −0.990497 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 34.3348 | 1.10186 | 0.550929 | − | 0.834552i | \(-0.314274\pi\) | ||||
0.550929 | + | 0.834552i | \(0.314274\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.59128 | 0.0510142 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.72402 | −0.0872384 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.7667 | 0.984315 | 0.492158 | − | 0.870506i | \(-0.336208\pi\) | ||||
0.492158 | + | 0.870506i | \(0.336208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.92494 | −0.317203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.1606 | −0.420186 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −51.2741 | −1.63539 | −0.817695 | − | 0.575652i | \(-0.804748\pi\) | ||||
−0.817695 | + | 0.575652i | \(0.804748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.6900 | 0.372475 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.9405 | 1.27132 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 51.9036 | 1.65044 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.79576 | −0.184108 | −0.0920542 | − | 0.995754i | \(-0.529343\pi\) | ||||
−0.0920542 | + | 0.995754i | \(0.529343\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −82.0994 | −2.60535 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.6632 | −1.25741 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.5585 | 1.12615 | 0.563075 | − | 0.826406i | \(-0.309618\pi\) | ||||
0.563075 | + | 0.826406i | \(0.309618\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 77.0427 | 2.43752 |
(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 | 6008.2.a.d.1.2 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6008.2.a.d.1.2 | ✓ | 49 | 1.1 | even | 1 | trivial |