Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4031,2,Mod(1,4031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4031, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4031 = 29 \cdot 139 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4031.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: | \(32.1876970548\) |
Analytic rank: | \(1\) |
Dimension: | \(59\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33108 | −0.941215 | −0.470608 | − | 0.882343i | \(-0.655965\pi\) | ||||
−0.470608 | + | 0.882343i | \(0.655965\pi\) | |||||||
\(3\) | 2.24902 | 1.29847 | 0.649235 | − | 0.760588i | \(-0.275089\pi\) | ||||
0.649235 | + | 0.760588i | \(0.275089\pi\) | |||||||
\(4\) | −0.228227 | −0.114114 | ||||||||
\(5\) | −0.768051 | −0.343483 | −0.171741 | − | 0.985142i | \(-0.554939\pi\) | ||||
−0.171741 | + | 0.985142i | \(0.554939\pi\) | |||||||
\(6\) | −2.99362 | −1.22214 | ||||||||
\(7\) | 2.32195 | 0.877615 | 0.438807 | − | 0.898581i | \(-0.355401\pi\) | ||||
0.438807 | + | 0.898581i | \(0.355401\pi\) | |||||||
\(8\) | 2.96595 | 1.04862 | ||||||||
\(9\) | 2.05807 | 0.686023 | ||||||||
\(10\) | 1.02234 | 0.323291 | ||||||||
\(11\) | 2.75683 | 0.831217 | 0.415608 | − | 0.909544i | \(-0.363569\pi\) | ||||
0.415608 | + | 0.909544i | \(0.363569\pi\) | |||||||
\(12\) | −0.513286 | −0.148173 | ||||||||
\(13\) | −2.32328 | −0.644363 | −0.322181 | − | 0.946678i | \(-0.604416\pi\) | ||||
−0.322181 | + | 0.946678i | \(0.604416\pi\) | |||||||
\(14\) | −3.09070 | −0.826024 | ||||||||
\(15\) | −1.72736 | −0.446002 | ||||||||
\(16\) | −3.49146 | −0.872865 | ||||||||
\(17\) | −5.07020 | −1.22970 | −0.614852 | − | 0.788642i | \(-0.710784\pi\) | ||||
−0.614852 | + | 0.788642i | \(0.710784\pi\) | |||||||
\(18\) | −2.73946 | −0.645696 | ||||||||
\(19\) | 2.16559 | 0.496820 | 0.248410 | − | 0.968655i | \(-0.420092\pi\) | ||||
0.248410 | + | 0.968655i | \(0.420092\pi\) | |||||||
\(20\) | 0.175290 | 0.0391960 | ||||||||
\(21\) | 5.22210 | 1.13956 | ||||||||
\(22\) | −3.66957 | −0.782354 | ||||||||
\(23\) | −6.25765 | −1.30481 | −0.652405 | − | 0.757871i | \(-0.726240\pi\) | ||||
−0.652405 | + | 0.757871i | \(0.726240\pi\) | |||||||
\(24\) | 6.67046 | 1.36160 | ||||||||
\(25\) | −4.41010 | −0.882020 | ||||||||
\(26\) | 3.09247 | 0.606484 | ||||||||
\(27\) | −2.11841 | −0.407689 | ||||||||
\(28\) | −0.529932 | −0.100148 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 2.29925 | 0.419784 | ||||||||
\(31\) | 1.13865 | 0.204508 | 0.102254 | − | 0.994758i | \(-0.467395\pi\) | ||||
0.102254 | + | 0.994758i | \(0.467395\pi\) | |||||||
\(32\) | −1.28449 | −0.227067 | ||||||||
\(33\) | 6.20016 | 1.07931 | ||||||||
\(34\) | 6.74884 | 1.15742 | ||||||||
\(35\) | −1.78338 | −0.301445 | ||||||||
\(36\) | −0.469707 | −0.0782846 | ||||||||
\(37\) | −10.8474 | −1.78331 | −0.891653 | − | 0.452719i | \(-0.850454\pi\) | ||||
−0.891653 | + | 0.452719i | \(0.850454\pi\) | |||||||
\(38\) | −2.88257 | −0.467614 | ||||||||
\(39\) | −5.22510 | −0.836685 | ||||||||
\(40\) | −2.27800 | −0.360183 | ||||||||
\(41\) | −5.07743 | −0.792961 | −0.396481 | − | 0.918043i | \(-0.629769\pi\) | ||||
−0.396481 | + | 0.918043i | \(0.629769\pi\) | |||||||
\(42\) | −6.95103 | −1.07257 | ||||||||
\(43\) | 8.93812 | 1.36305 | 0.681525 | − | 0.731795i | \(-0.261317\pi\) | ||||
0.681525 | + | 0.731795i | \(0.261317\pi\) | |||||||
\(44\) | −0.629184 | −0.0948531 | ||||||||
\(45\) | −1.58070 | −0.235637 | ||||||||
\(46\) | 8.32943 | 1.22811 | ||||||||
\(47\) | −0.680566 | −0.0992707 | −0.0496353 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496353 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(48\) | −7.85234 | −1.13339 | ||||||||
\(49\) | −1.60855 | −0.229792 | ||||||||
\(50\) | 5.87019 | 0.830170 | ||||||||
\(51\) | −11.4030 | −1.59673 | ||||||||
\(52\) | 0.530236 | 0.0735305 | ||||||||
\(53\) | 0.403466 | 0.0554203 | 0.0277101 | − | 0.999616i | \(-0.491178\pi\) | ||||
0.0277101 | + | 0.999616i | \(0.491178\pi\) | |||||||
\(54\) | 2.81978 | 0.383723 | ||||||||
\(55\) | −2.11739 | −0.285509 | ||||||||
\(56\) | 6.88678 | 0.920285 | ||||||||
\(57\) | 4.87044 | 0.645105 | ||||||||
\(58\) | −1.33108 | −0.174779 | ||||||||
\(59\) | −1.09579 | −0.142660 | −0.0713301 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713301 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(60\) | 0.394230 | 0.0508949 | ||||||||
\(61\) | −11.3179 | −1.44911 | −0.724554 | − | 0.689218i | \(-0.757954\pi\) | ||||
−0.724554 | + | 0.689218i | \(0.757954\pi\) | |||||||
\(62\) | −1.51564 | −0.192486 | ||||||||
\(63\) | 4.77874 | 0.602064 | ||||||||
\(64\) | 8.69267 | 1.08658 | ||||||||
\(65\) | 1.78440 | 0.221327 | ||||||||
\(66\) | −8.25291 | −1.01586 | ||||||||
\(67\) | −13.1384 | −1.60511 | −0.802557 | − | 0.596576i | \(-0.796527\pi\) | ||||
−0.802557 | + | 0.596576i | \(0.796527\pi\) | |||||||
\(68\) | 1.15716 | 0.140326 | ||||||||
\(69\) | −14.0735 | −1.69426 | ||||||||
\(70\) | 2.37381 | 0.283725 | ||||||||
\(71\) | 6.87462 | 0.815868 | 0.407934 | − | 0.913011i | \(-0.366249\pi\) | ||||
0.407934 | + | 0.913011i | \(0.366249\pi\) | |||||||
\(72\) | 6.10413 | 0.719379 | ||||||||
\(73\) | −7.85139 | −0.918935 | −0.459468 | − | 0.888195i | \(-0.651960\pi\) | ||||
−0.459468 | + | 0.888195i | \(0.651960\pi\) | |||||||
\(74\) | 14.4388 | 1.67848 | ||||||||
\(75\) | −9.91838 | −1.14528 | ||||||||
\(76\) | −0.494246 | −0.0566939 | ||||||||
\(77\) | 6.40123 | 0.729488 | ||||||||
\(78\) | 6.95502 | 0.787501 | ||||||||
\(79\) | −13.6784 | −1.53894 | −0.769471 | − | 0.638682i | \(-0.779480\pi\) | ||||
−0.769471 | + | 0.638682i | \(0.779480\pi\) | |||||||
\(80\) | 2.68162 | 0.299814 | ||||||||
\(81\) | −10.9386 | −1.21540 | ||||||||
\(82\) | 6.75846 | 0.746347 | ||||||||
\(83\) | −8.61588 | −0.945716 | −0.472858 | − | 0.881139i | \(-0.656778\pi\) | ||||
−0.472858 | + | 0.881139i | \(0.656778\pi\) | |||||||
\(84\) | −1.19183 | −0.130039 | ||||||||
\(85\) | 3.89417 | 0.422382 | ||||||||
\(86\) | −11.8973 | −1.28292 | ||||||||
\(87\) | 2.24902 | 0.241120 | ||||||||
\(88\) | 8.17663 | 0.871631 | ||||||||
\(89\) | 9.20872 | 0.976122 | 0.488061 | − | 0.872809i | \(-0.337704\pi\) | ||||
0.488061 | + | 0.872809i | \(0.337704\pi\) | |||||||
\(90\) | 2.10404 | 0.221785 | ||||||||
\(91\) | −5.39455 | −0.565502 | ||||||||
\(92\) | 1.42816 | 0.148896 | ||||||||
\(93\) | 2.56085 | 0.265548 | ||||||||
\(94\) | 0.905887 | 0.0934351 | ||||||||
\(95\) | −1.66328 | −0.170649 | ||||||||
\(96\) | −2.88883 | −0.294840 | ||||||||
\(97\) | 7.77949 | 0.789887 | 0.394944 | − | 0.918705i | \(-0.370764\pi\) | ||||
0.394944 | + | 0.918705i | \(0.370764\pi\) | |||||||
\(98\) | 2.14110 | 0.216284 | ||||||||
\(99\) | 5.67376 | 0.570234 | ||||||||
\(100\) | 1.00650 | 0.100650 | ||||||||
\(101\) | −2.00970 | −0.199972 | −0.0999861 | − | 0.994989i | \(-0.531880\pi\) | ||||
−0.0999861 | + | 0.994989i | \(0.531880\pi\) | |||||||
\(102\) | 15.1783 | 1.50287 | ||||||||
\(103\) | 15.6871 | 1.54569 | 0.772847 | − | 0.634592i | \(-0.218832\pi\) | ||||
0.772847 | + | 0.634592i | \(0.218832\pi\) | |||||||
\(104\) | −6.89073 | −0.675692 | ||||||||
\(105\) | −4.01084 | −0.391418 | ||||||||
\(106\) | −0.537045 | −0.0521624 | ||||||||
\(107\) | 4.88257 | 0.472016 | 0.236008 | − | 0.971751i | \(-0.424161\pi\) | ||||
0.236008 | + | 0.971751i | \(0.424161\pi\) | |||||||
\(108\) | 0.483480 | 0.0465228 | ||||||||
\(109\) | 17.3395 | 1.66082 | 0.830410 | − | 0.557152i | \(-0.188106\pi\) | ||||
0.830410 | + | 0.557152i | \(0.188106\pi\) | |||||||
\(110\) | 2.81841 | 0.268725 | ||||||||
\(111\) | −24.3960 | −2.31557 | ||||||||
\(112\) | −8.10699 | −0.766039 | ||||||||
\(113\) | 10.0953 | 0.949687 | 0.474844 | − | 0.880070i | \(-0.342505\pi\) | ||||
0.474844 | + | 0.880070i | \(0.342505\pi\) | |||||||
\(114\) | −6.48294 | −0.607183 | ||||||||
\(115\) | 4.80619 | 0.448180 | ||||||||
\(116\) | −0.228227 | −0.0211904 | ||||||||
\(117\) | −4.78148 | −0.442048 | ||||||||
\(118\) | 1.45859 | 0.134274 | ||||||||
\(119\) | −11.7728 | −1.07921 | ||||||||
\(120\) | −5.12325 | −0.467687 | ||||||||
\(121\) | −3.39987 | −0.309079 | ||||||||
\(122\) | 15.0650 | 1.36392 | ||||||||
\(123\) | −11.4192 | −1.02964 | ||||||||
\(124\) | −0.259872 | −0.0233372 | ||||||||
\(125\) | 7.22743 | 0.646441 | ||||||||
\(126\) | −6.36088 | −0.566672 | ||||||||
\(127\) | −0.124099 | −0.0110120 | −0.00550599 | − | 0.999985i | \(-0.501753\pi\) | ||||
−0.00550599 | + | 0.999985i | \(0.501753\pi\) | |||||||
\(128\) | −9.00166 | −0.795642 | ||||||||
\(129\) | 20.1020 | 1.76988 | ||||||||
\(130\) | −2.37518 | −0.208317 | ||||||||
\(131\) | 4.65193 | 0.406441 | 0.203220 | − | 0.979133i | \(-0.434859\pi\) | ||||
0.203220 | + | 0.979133i | \(0.434859\pi\) | |||||||
\(132\) | −1.41505 | −0.123164 | ||||||||
\(133\) | 5.02838 | 0.436016 | ||||||||
\(134\) | 17.4883 | 1.51076 | ||||||||
\(135\) | 1.62705 | 0.140034 | ||||||||
\(136\) | −15.0380 | −1.28949 | ||||||||
\(137\) | −9.87736 | −0.843880 | −0.421940 | − | 0.906624i | \(-0.638651\pi\) | ||||
−0.421940 | + | 0.906624i | \(0.638651\pi\) | |||||||
\(138\) | 18.7330 | 1.59466 | ||||||||
\(139\) | 1.00000 | 0.0848189 | ||||||||
\(140\) | 0.407015 | 0.0343990 | ||||||||
\(141\) | −1.53060 | −0.128900 | ||||||||
\(142\) | −9.15067 | −0.767907 | ||||||||
\(143\) | −6.40490 | −0.535605 | ||||||||
\(144\) | −7.18567 | −0.598806 | ||||||||
\(145\) | −0.768051 | −0.0637831 | ||||||||
\(146\) | 10.4508 | 0.864916 | ||||||||
\(147\) | −3.61765 | −0.298379 | ||||||||
\(148\) | 2.47568 | 0.203499 | ||||||||
\(149\) | −2.25689 | −0.184892 | −0.0924458 | − | 0.995718i | \(-0.529469\pi\) | ||||
−0.0924458 | + | 0.995718i | \(0.529469\pi\) | |||||||
\(150\) | 13.2022 | 1.07795 | ||||||||
\(151\) | 4.35064 | 0.354050 | 0.177025 | − | 0.984206i | \(-0.443353\pi\) | ||||
0.177025 | + | 0.984206i | \(0.443353\pi\) | |||||||
\(152\) | 6.42302 | 0.520975 | ||||||||
\(153\) | −10.4348 | −0.843606 | ||||||||
\(154\) | −8.52055 | −0.686605 | ||||||||
\(155\) | −0.874543 | −0.0702450 | ||||||||
\(156\) | 1.19251 | 0.0954771 | ||||||||
\(157\) | 21.4917 | 1.71522 | 0.857612 | − | 0.514296i | \(-0.171947\pi\) | ||||
0.857612 | + | 0.514296i | \(0.171947\pi\) | |||||||
\(158\) | 18.2071 | 1.44848 | ||||||||
\(159\) | 0.907400 | 0.0719615 | ||||||||
\(160\) | 0.986551 | 0.0779937 | ||||||||
\(161\) | −14.5299 | −1.14512 | ||||||||
\(162\) | 14.5601 | 1.14395 | ||||||||
\(163\) | 0.586869 | 0.0459672 | 0.0229836 | − | 0.999736i | \(-0.492683\pi\) | ||||
0.0229836 | + | 0.999736i | \(0.492683\pi\) | |||||||
\(164\) | 1.15881 | 0.0904876 | ||||||||
\(165\) | −4.76204 | −0.370724 | ||||||||
\(166\) | 11.4684 | 0.890122 | ||||||||
\(167\) | 24.7861 | 1.91801 | 0.959003 | − | 0.283394i | \(-0.0914605\pi\) | ||||
0.959003 | + | 0.283394i | \(0.0914605\pi\) | |||||||
\(168\) | 15.4885 | 1.19496 | ||||||||
\(169\) | −7.60236 | −0.584797 | ||||||||
\(170\) | −5.18345 | −0.397553 | ||||||||
\(171\) | 4.45693 | 0.340830 | ||||||||
\(172\) | −2.03992 | −0.155543 | ||||||||
\(173\) | −2.49813 | −0.189929 | −0.0949646 | − | 0.995481i | \(-0.530274\pi\) | ||||
−0.0949646 | + | 0.995481i | \(0.530274\pi\) | |||||||
\(174\) | −2.99362 | −0.226946 | ||||||||
\(175\) | −10.2400 | −0.774073 | ||||||||
\(176\) | −9.62537 | −0.725540 | ||||||||
\(177\) | −2.46446 | −0.185240 | ||||||||
\(178\) | −12.2575 | −0.918741 | ||||||||
\(179\) | −17.6921 | −1.32237 | −0.661184 | − | 0.750224i | \(-0.729946\pi\) | ||||
−0.661184 | + | 0.750224i | \(0.729946\pi\) | |||||||
\(180\) | 0.360759 | 0.0268894 | ||||||||
\(181\) | −13.0882 | −0.972838 | −0.486419 | − | 0.873726i | \(-0.661697\pi\) | ||||
−0.486419 | + | 0.873726i | \(0.661697\pi\) | |||||||
\(182\) | 7.18057 | 0.532259 | ||||||||
\(183\) | −25.4541 | −1.88162 | ||||||||
\(184\) | −18.5599 | −1.36825 | ||||||||
\(185\) | 8.33138 | 0.612535 | ||||||||
\(186\) | −3.40869 | −0.249938 | ||||||||
\(187\) | −13.9777 | −1.02215 | ||||||||
\(188\) | 0.155323 | 0.0113281 | ||||||||
\(189\) | −4.91885 | −0.357794 | ||||||||
\(190\) | 2.21396 | 0.160617 | ||||||||
\(191\) | 3.03234 | 0.219412 | 0.109706 | − | 0.993964i | \(-0.465009\pi\) | ||||
0.109706 | + | 0.993964i | \(0.465009\pi\) | |||||||
\(192\) | 19.5499 | 1.41090 | ||||||||
\(193\) | 3.21536 | 0.231447 | 0.115723 | − | 0.993281i | \(-0.463081\pi\) | ||||
0.115723 | + | 0.993281i | \(0.463081\pi\) | |||||||
\(194\) | −10.3551 | −0.743454 | ||||||||
\(195\) | 4.01314 | 0.287387 | ||||||||
\(196\) | 0.367114 | 0.0262224 | ||||||||
\(197\) | −14.9217 | −1.06313 | −0.531564 | − | 0.847018i | \(-0.678396\pi\) | ||||
−0.531564 | + | 0.847018i | \(0.678396\pi\) | |||||||
\(198\) | −7.55222 | −0.536713 | ||||||||
\(199\) | −24.0928 | −1.70789 | −0.853945 | − | 0.520363i | \(-0.825797\pi\) | ||||
−0.853945 | + | 0.520363i | \(0.825797\pi\) | |||||||
\(200\) | −13.0801 | −0.924904 | ||||||||
\(201\) | −29.5485 | −2.08419 | ||||||||
\(202\) | 2.67507 | 0.188217 | ||||||||
\(203\) | 2.32195 | 0.162969 | ||||||||
\(204\) | 2.60247 | 0.182209 | ||||||||
\(205\) | 3.89972 | 0.272368 | ||||||||
\(206\) | −20.8808 | −1.45483 | ||||||||
\(207\) | −12.8787 | −0.895130 | ||||||||
\(208\) | 8.11164 | 0.562441 | ||||||||
\(209\) | 5.97016 | 0.412965 | ||||||||
\(210\) | 5.33875 | 0.368408 | ||||||||
\(211\) | 7.47712 | 0.514746 | 0.257373 | − | 0.966312i | \(-0.417143\pi\) | ||||
0.257373 | + | 0.966312i | \(0.417143\pi\) | |||||||
\(212\) | −0.0920818 | −0.00632420 | ||||||||
\(213\) | 15.4611 | 1.05938 | ||||||||
\(214\) | −6.49909 | −0.444269 | ||||||||
\(215\) | −6.86493 | −0.468184 | ||||||||
\(216\) | −6.28311 | −0.427511 | ||||||||
\(217\) | 2.64390 | 0.179479 | ||||||||
\(218\) | −23.0802 | −1.56319 | ||||||||
\(219\) | −17.6579 | −1.19321 | ||||||||
\(220\) | 0.483245 | 0.0325804 | ||||||||
\(221\) | 11.7795 | 0.792376 | ||||||||
\(222\) | 32.4731 | 2.17945 | ||||||||
\(223\) | −20.2984 | −1.35928 | −0.679642 | − | 0.733544i | \(-0.737865\pi\) | ||||
−0.679642 | + | 0.733544i | \(0.737865\pi\) | |||||||
\(224\) | −2.98251 | −0.199278 | ||||||||
\(225\) | −9.07629 | −0.605086 | ||||||||
\(226\) | −13.4377 | −0.893860 | ||||||||
\(227\) | −12.0679 | −0.800978 | −0.400489 | − | 0.916302i | \(-0.631160\pi\) | ||||
−0.400489 | + | 0.916302i | \(0.631160\pi\) | |||||||
\(228\) | −1.11157 | −0.0736152 | ||||||||
\(229\) | −3.51211 | −0.232087 | −0.116043 | − | 0.993244i | \(-0.537021\pi\) | ||||
−0.116043 | + | 0.993244i | \(0.537021\pi\) | |||||||
\(230\) | −6.39742 | −0.421834 | ||||||||
\(231\) | 14.3965 | 0.947218 | ||||||||
\(232\) | 2.96595 | 0.194724 | ||||||||
\(233\) | 5.01658 | 0.328647 | 0.164324 | − | 0.986406i | \(-0.447456\pi\) | ||||
0.164324 | + | 0.986406i | \(0.447456\pi\) | |||||||
\(234\) | 6.36453 | 0.416062 | ||||||||
\(235\) | 0.522709 | 0.0340978 | ||||||||
\(236\) | 0.250090 | 0.0162795 | ||||||||
\(237\) | −30.7630 | −1.99827 | ||||||||
\(238\) | 15.6705 | 1.01577 | ||||||||
\(239\) | 6.78054 | 0.438597 | 0.219298 | − | 0.975658i | \(-0.429623\pi\) | ||||
0.219298 | + | 0.975658i | \(0.429623\pi\) | |||||||
\(240\) | 6.03100 | 0.389299 | ||||||||
\(241\) | −3.39678 | −0.218806 | −0.109403 | − | 0.993997i | \(-0.534894\pi\) | ||||
−0.109403 | + | 0.993997i | \(0.534894\pi\) | |||||||
\(242\) | 4.52549 | 0.290910 | ||||||||
\(243\) | −18.2457 | −1.17046 | ||||||||
\(244\) | 2.58305 | 0.165363 | ||||||||
\(245\) | 1.23545 | 0.0789297 | ||||||||
\(246\) | 15.1999 | 0.969110 | ||||||||
\(247\) | −5.03127 | −0.320132 | ||||||||
\(248\) | 3.37719 | 0.214452 | ||||||||
\(249\) | −19.3772 | −1.22798 | ||||||||
\(250\) | −9.62029 | −0.608440 | ||||||||
\(251\) | −12.5444 | −0.791793 | −0.395896 | − | 0.918295i | \(-0.629566\pi\) | ||||
−0.395896 | + | 0.918295i | \(0.629566\pi\) | |||||||
\(252\) | −1.09064 | −0.0687037 | ||||||||
\(253\) | −17.2513 | −1.08458 | ||||||||
\(254\) | 0.165185 | 0.0103646 | ||||||||
\(255\) | 8.75805 | 0.548451 | ||||||||
\(256\) | −5.40341 | −0.337713 | ||||||||
\(257\) | 3.42274 | 0.213505 | 0.106752 | − | 0.994286i | \(-0.465955\pi\) | ||||
0.106752 | + | 0.994286i | \(0.465955\pi\) | |||||||
\(258\) | −26.7573 | −1.66584 | ||||||||
\(259\) | −25.1872 | −1.56506 | ||||||||
\(260\) | −0.407248 | −0.0252565 | ||||||||
\(261\) | 2.05807 | 0.127391 | ||||||||
\(262\) | −6.19208 | −0.382548 | ||||||||
\(263\) | 18.9346 | 1.16756 | 0.583780 | − | 0.811912i | \(-0.301573\pi\) | ||||
0.583780 | + | 0.811912i | \(0.301573\pi\) | |||||||
\(264\) | 18.3894 | 1.13179 | ||||||||
\(265\) | −0.309882 | −0.0190359 | ||||||||
\(266\) | −6.69318 | −0.410385 | ||||||||
\(267\) | 20.7105 | 1.26746 | ||||||||
\(268\) | 2.99854 | 0.183165 | ||||||||
\(269\) | −7.14322 | −0.435530 | −0.217765 | − | 0.976001i | \(-0.569877\pi\) | ||||
−0.217765 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(270\) | −2.16573 | −0.131802 | ||||||||
\(271\) | 12.7937 | 0.777160 | 0.388580 | − | 0.921415i | \(-0.372966\pi\) | ||||
0.388580 | + | 0.921415i | \(0.372966\pi\) | |||||||
\(272\) | 17.7024 | 1.07337 | ||||||||
\(273\) | −12.1324 | −0.734287 | ||||||||
\(274\) | 13.1476 | 0.794273 | ||||||||
\(275\) | −12.1579 | −0.733150 | ||||||||
\(276\) | 3.21197 | 0.193338 | ||||||||
\(277\) | 4.10099 | 0.246404 | 0.123202 | − | 0.992382i | \(-0.460684\pi\) | ||||
0.123202 | + | 0.992382i | \(0.460684\pi\) | |||||||
\(278\) | −1.33108 | −0.0798328 | ||||||||
\(279\) | 2.34343 | 0.140297 | ||||||||
\(280\) | −5.28940 | −0.316102 | ||||||||
\(281\) | −24.4067 | −1.45598 | −0.727992 | − | 0.685585i | \(-0.759546\pi\) | ||||
−0.727992 | + | 0.685585i | \(0.759546\pi\) | |||||||
\(282\) | 2.03735 | 0.121323 | ||||||||
\(283\) | 12.1523 | 0.722380 | 0.361190 | − | 0.932492i | \(-0.382371\pi\) | ||||
0.361190 | + | 0.932492i | \(0.382371\pi\) | |||||||
\(284\) | −1.56898 | −0.0931016 | ||||||||
\(285\) | −3.74074 | −0.221582 | ||||||||
\(286\) | 8.52544 | 0.504120 | ||||||||
\(287\) | −11.7895 | −0.695915 | ||||||||
\(288\) | −2.64356 | −0.155773 | ||||||||
\(289\) | 8.70695 | 0.512173 | ||||||||
\(290\) | 1.02234 | 0.0600337 | ||||||||
\(291\) | 17.4962 | 1.02564 | ||||||||
\(292\) | 1.79190 | 0.104863 | ||||||||
\(293\) | 19.7255 | 1.15237 | 0.576187 | − | 0.817318i | \(-0.304540\pi\) | ||||
0.576187 | + | 0.817318i | \(0.304540\pi\) | |||||||
\(294\) | 4.81538 | 0.280838 | ||||||||
\(295\) | 0.841626 | 0.0490013 | ||||||||
\(296\) | −32.1729 | −1.87001 | ||||||||
\(297\) | −5.84012 | −0.338878 | ||||||||
\(298\) | 3.00410 | 0.174023 | ||||||||
\(299\) | 14.5383 | 0.840771 | ||||||||
\(300\) | 2.26364 | 0.130691 | ||||||||
\(301\) | 20.7539 | 1.19623 | ||||||||
\(302\) | −5.79105 | −0.333237 | ||||||||
\(303\) | −4.51984 | −0.259658 | ||||||||
\(304\) | −7.56106 | −0.433656 | ||||||||
\(305\) | 8.69272 | 0.497744 | ||||||||
\(306\) | 13.8896 | 0.794015 | ||||||||
\(307\) | 0.274177 | 0.0156481 | 0.00782406 | − | 0.999969i | \(-0.497509\pi\) | ||||
0.00782406 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(308\) | −1.46093 | −0.0832445 | ||||||||
\(309\) | 35.2805 | 2.00704 | ||||||||
\(310\) | 1.16409 | 0.0661157 | ||||||||
\(311\) | −16.6056 | −0.941617 | −0.470808 | − | 0.882236i | \(-0.656038\pi\) | ||||
−0.470808 | + | 0.882236i | \(0.656038\pi\) | |||||||
\(312\) | −15.4974 | −0.877366 | ||||||||
\(313\) | 10.4619 | 0.591341 | 0.295670 | − | 0.955290i | \(-0.404457\pi\) | ||||
0.295670 | + | 0.955290i | \(0.404457\pi\) | |||||||
\(314\) | −28.6072 | −1.61440 | ||||||||
\(315\) | −3.67031 | −0.206799 | ||||||||
\(316\) | 3.12179 | 0.175614 | ||||||||
\(317\) | 1.05127 | 0.0590449 | 0.0295225 | − | 0.999564i | \(-0.490601\pi\) | ||||
0.0295225 | + | 0.999564i | \(0.490601\pi\) | |||||||
\(318\) | −1.20782 | −0.0677313 | ||||||||
\(319\) | 2.75683 | 0.154353 | ||||||||
\(320\) | −6.67641 | −0.373223 | ||||||||
\(321\) | 10.9810 | 0.612898 | ||||||||
\(322\) | 19.3405 | 1.07780 | ||||||||
\(323\) | −10.9800 | −0.610941 | ||||||||
\(324\) | 2.49648 | 0.138693 | ||||||||
\(325\) | 10.2459 | 0.568340 | ||||||||
\(326\) | −0.781170 | −0.0432650 | ||||||||
\(327\) | 38.9968 | 2.15653 | ||||||||
\(328\) | −15.0594 | −0.831516 | ||||||||
\(329\) | −1.58024 | −0.0871214 | ||||||||
\(330\) | 6.33865 | 0.348931 | ||||||||
\(331\) | −30.7798 | −1.69181 | −0.845905 | − | 0.533333i | \(-0.820939\pi\) | ||||
−0.845905 | + | 0.533333i | \(0.820939\pi\) | |||||||
\(332\) | 1.96638 | 0.107919 | ||||||||
\(333\) | −22.3248 | −1.22339 | ||||||||
\(334\) | −32.9923 | −1.80526 | ||||||||
\(335\) | 10.0910 | 0.551329 | ||||||||
\(336\) | −18.2328 | −0.994678 | ||||||||
\(337\) | 11.2395 | 0.612255 | 0.306127 | − | 0.951991i | \(-0.400967\pi\) | ||||
0.306127 | + | 0.951991i | \(0.400967\pi\) | |||||||
\(338\) | 10.1193 | 0.550420 | ||||||||
\(339\) | 22.7045 | 1.23314 | ||||||||
\(340\) | −0.888756 | −0.0481995 | ||||||||
\(341\) | 3.13908 | 0.169991 | ||||||||
\(342\) | −5.93253 | −0.320794 | ||||||||
\(343\) | −19.9886 | −1.07928 | ||||||||
\(344\) | 26.5100 | 1.42932 | ||||||||
\(345\) | 10.8092 | 0.581948 | ||||||||
\(346\) | 3.32521 | 0.178764 | ||||||||
\(347\) | 31.2320 | 1.67662 | 0.838310 | − | 0.545194i | \(-0.183544\pi\) | ||||
0.838310 | + | 0.545194i | \(0.183544\pi\) | |||||||
\(348\) | −0.513286 | −0.0275150 | ||||||||
\(349\) | 28.4236 | 1.52148 | 0.760740 | − | 0.649056i | \(-0.224836\pi\) | ||||
0.760740 | + | 0.649056i | \(0.224836\pi\) | |||||||
\(350\) | 13.6303 | 0.728570 | ||||||||
\(351\) | 4.92167 | 0.262700 | ||||||||
\(352\) | −3.54112 | −0.188742 | ||||||||
\(353\) | −22.0558 | −1.17391 | −0.586956 | − | 0.809619i | \(-0.699674\pi\) | ||||
−0.586956 | + | 0.809619i | \(0.699674\pi\) | |||||||
\(354\) | 3.28039 | 0.174351 | ||||||||
\(355\) | −5.28006 | −0.280236 | ||||||||
\(356\) | −2.10168 | −0.111389 | ||||||||
\(357\) | −26.4771 | −1.40132 | ||||||||
\(358\) | 23.5496 | 1.24463 | ||||||||
\(359\) | −1.53906 | −0.0812282 | −0.0406141 | − | 0.999175i | \(-0.512931\pi\) | ||||
−0.0406141 | + | 0.999175i | \(0.512931\pi\) | |||||||
\(360\) | −4.68828 | −0.247094 | ||||||||
\(361\) | −14.3102 | −0.753170 | ||||||||
\(362\) | 17.4214 | 0.915650 | ||||||||
\(363\) | −7.64635 | −0.401329 | ||||||||
\(364\) | 1.23118 | 0.0645314 | ||||||||
\(365\) | 6.03026 | 0.315638 | ||||||||
\(366\) | 33.8815 | 1.77101 | ||||||||
\(367\) | −17.4613 | −0.911471 | −0.455736 | − | 0.890115i | \(-0.650624\pi\) | ||||
−0.455736 | + | 0.890115i | \(0.650624\pi\) | |||||||
\(368\) | 21.8483 | 1.13892 | ||||||||
\(369\) | −10.4497 | −0.543990 | ||||||||
\(370\) | −11.0897 | −0.576527 | ||||||||
\(371\) | 0.936827 | 0.0486376 | ||||||||
\(372\) | −0.584455 | −0.0303026 | ||||||||
\(373\) | 13.6487 | 0.706701 | 0.353351 | − | 0.935491i | \(-0.385042\pi\) | ||||
0.353351 | + | 0.935491i | \(0.385042\pi\) | |||||||
\(374\) | 18.6054 | 0.962064 | ||||||||
\(375\) | 16.2546 | 0.839384 | ||||||||
\(376\) | −2.01852 | −0.104097 | ||||||||
\(377\) | −2.32328 | −0.119655 | ||||||||
\(378\) | 6.54738 | 0.336761 | ||||||||
\(379\) | −22.0759 | −1.13396 | −0.566982 | − | 0.823730i | \(-0.691889\pi\) | ||||
−0.566982 | + | 0.823730i | \(0.691889\pi\) | |||||||
\(380\) | 0.379606 | 0.0194734 | ||||||||
\(381\) | −0.279100 | −0.0142987 | ||||||||
\(382\) | −4.03628 | −0.206514 | ||||||||
\(383\) | −28.9119 | −1.47733 | −0.738665 | − | 0.674073i | \(-0.764543\pi\) | ||||
−0.738665 | + | 0.674073i | \(0.764543\pi\) | |||||||
\(384\) | −20.2449 | −1.03312 | ||||||||
\(385\) | −4.91647 | −0.250567 | ||||||||
\(386\) | −4.27991 | −0.217841 | ||||||||
\(387\) | 18.3953 | 0.935085 | ||||||||
\(388\) | −1.77549 | −0.0901369 | ||||||||
\(389\) | 3.82444 | 0.193907 | 0.0969535 | − | 0.995289i | \(-0.469090\pi\) | ||||
0.0969535 | + | 0.995289i | \(0.469090\pi\) | |||||||
\(390\) | −5.34181 | −0.270493 | ||||||||
\(391\) | 31.7275 | 1.60453 | ||||||||
\(392\) | −4.77087 | −0.240965 | ||||||||
\(393\) | 10.4623 | 0.527751 | ||||||||
\(394\) | 19.8620 | 1.00063 | ||||||||
\(395\) | 10.5057 | 0.528600 | ||||||||
\(396\) | −1.29491 | −0.0650715 | ||||||||
\(397\) | −10.3270 | −0.518295 | −0.259148 | − | 0.965838i | \(-0.583442\pi\) | ||||
−0.259148 | + | 0.965838i | \(0.583442\pi\) | |||||||
\(398\) | 32.0694 | 1.60749 | ||||||||
\(399\) | 11.3089 | 0.566154 | ||||||||
\(400\) | 15.3977 | 0.769884 | ||||||||
\(401\) | 5.34790 | 0.267061 | 0.133531 | − | 0.991045i | \(-0.457369\pi\) | ||||
0.133531 | + | 0.991045i | \(0.457369\pi\) | |||||||
\(402\) | 39.3314 | 1.96167 | ||||||||
\(403\) | −2.64541 | −0.131777 | ||||||||
\(404\) | 0.458667 | 0.0228195 | ||||||||
\(405\) | 8.40137 | 0.417467 | ||||||||
\(406\) | −3.09070 | −0.153389 | ||||||||
\(407\) | −29.9046 | −1.48231 | ||||||||
\(408\) | −33.8206 | −1.67437 | ||||||||
\(409\) | −21.1204 | −1.04434 | −0.522168 | − | 0.852843i | \(-0.674877\pi\) | ||||
−0.522168 | + | 0.852843i | \(0.674877\pi\) | |||||||
\(410\) | −5.19084 | −0.256357 | ||||||||
\(411\) | −22.2143 | −1.09575 | ||||||||
\(412\) | −3.58022 | −0.176385 | ||||||||
\(413\) | −2.54438 | −0.125201 | ||||||||
\(414\) | 17.1426 | 0.842510 | ||||||||
\(415\) | 6.61743 | 0.324837 | ||||||||
\(416\) | 2.98422 | 0.146314 | ||||||||
\(417\) | 2.24902 | 0.110135 | ||||||||
\(418\) | −7.94676 | −0.388689 | ||||||||
\(419\) | 7.62762 | 0.372634 | 0.186317 | − | 0.982490i | \(-0.440345\pi\) | ||||
0.186317 | + | 0.982490i | \(0.440345\pi\) | |||||||
\(420\) | 0.915382 | 0.0446661 | ||||||||
\(421\) | −2.98057 | −0.145264 | −0.0726321 | − | 0.997359i | \(-0.523140\pi\) | ||||
−0.0726321 | + | 0.997359i | \(0.523140\pi\) | |||||||
\(422\) | −9.95265 | −0.484487 | ||||||||
\(423\) | −1.40065 | −0.0681020 | ||||||||
\(424\) | 1.19666 | 0.0581148 | ||||||||
\(425\) | 22.3601 | 1.08462 | ||||||||
\(426\) | −20.5800 | −0.997104 | ||||||||
\(427\) | −26.2796 | −1.27176 | ||||||||
\(428\) | −1.11434 | −0.0538634 | ||||||||
\(429\) | −14.4047 | −0.695467 | ||||||||
\(430\) | 9.13777 | 0.440662 | ||||||||
\(431\) | −1.31983 | −0.0635739 | −0.0317870 | − | 0.999495i | \(-0.510120\pi\) | ||||
−0.0317870 | + | 0.999495i | \(0.510120\pi\) | |||||||
\(432\) | 7.39635 | 0.355857 | ||||||||
\(433\) | 22.2634 | 1.06991 | 0.534956 | − | 0.844880i | \(-0.320328\pi\) | ||||
0.534956 | + | 0.844880i | \(0.320328\pi\) | |||||||
\(434\) | −3.51924 | −0.168929 | ||||||||
\(435\) | −1.72736 | −0.0828205 | ||||||||
\(436\) | −3.95734 | −0.189522 | ||||||||
\(437\) | −13.5515 | −0.648255 | ||||||||
\(438\) | 23.5041 | 1.12307 | ||||||||
\(439\) | −10.5197 | −0.502079 | −0.251039 | − | 0.967977i | \(-0.580772\pi\) | ||||
−0.251039 | + | 0.967977i | \(0.580772\pi\) | |||||||
\(440\) | −6.28006 | −0.299390 | ||||||||
\(441\) | −3.31050 | −0.157643 | ||||||||
\(442\) | −15.6795 | −0.745796 | ||||||||
\(443\) | 33.3116 | 1.58268 | 0.791342 | − | 0.611374i | \(-0.209383\pi\) | ||||
0.791342 | + | 0.611374i | \(0.209383\pi\) | |||||||
\(444\) | 5.56784 | 0.264238 | ||||||||
\(445\) | −7.07276 | −0.335281 | ||||||||
\(446\) | 27.0188 | 1.27938 | ||||||||
\(447\) | −5.07578 | −0.240076 | ||||||||
\(448\) | 20.1839 | 0.953602 | ||||||||
\(449\) | −2.78879 | −0.131611 | −0.0658056 | − | 0.997832i | \(-0.520962\pi\) | ||||
−0.0658056 | + | 0.997832i | \(0.520962\pi\) | |||||||
\(450\) | 12.0813 | 0.569516 | ||||||||
\(451\) | −13.9976 | −0.659123 | ||||||||
\(452\) | −2.30402 | −0.108372 | ||||||||
\(453\) | 9.78465 | 0.459723 | ||||||||
\(454\) | 16.0634 | 0.753892 | ||||||||
\(455\) | 4.14328 | 0.194240 | ||||||||
\(456\) | 14.4455 | 0.676471 | ||||||||
\(457\) | 1.33846 | 0.0626104 | 0.0313052 | − | 0.999510i | \(-0.490034\pi\) | ||||
0.0313052 | + | 0.999510i | \(0.490034\pi\) | |||||||
\(458\) | 4.67490 | 0.218444 | ||||||||
\(459\) | 10.7408 | 0.501337 | ||||||||
\(460\) | −1.09690 | −0.0511434 | ||||||||
\(461\) | −14.9902 | −0.698164 | −0.349082 | − | 0.937092i | \(-0.613507\pi\) | ||||
−0.349082 | + | 0.937092i | \(0.613507\pi\) | |||||||
\(462\) | −19.1628 | −0.891536 | ||||||||
\(463\) | 0.0783710 | 0.00364221 | 0.00182110 | − | 0.999998i | \(-0.499420\pi\) | ||||
0.00182110 | + | 0.999998i | \(0.499420\pi\) | |||||||
\(464\) | −3.49146 | −0.162087 | ||||||||
\(465\) | −1.96686 | −0.0912110 | ||||||||
\(466\) | −6.67747 | −0.309328 | ||||||||
\(467\) | −14.9284 | −0.690802 | −0.345401 | − | 0.938455i | \(-0.612257\pi\) | ||||
−0.345401 | + | 0.938455i | \(0.612257\pi\) | |||||||
\(468\) | 1.09126 | 0.0504436 | ||||||||
\(469\) | −30.5068 | −1.40867 | ||||||||
\(470\) | −0.695767 | −0.0320933 | ||||||||
\(471\) | 48.3352 | 2.22717 | ||||||||
\(472\) | −3.25007 | −0.149597 | ||||||||
\(473\) | 24.6409 | 1.13299 | ||||||||
\(474\) | 40.9480 | 1.88080 | ||||||||
\(475\) | −9.55045 | −0.438205 | ||||||||
\(476\) | 2.68686 | 0.123152 | ||||||||
\(477\) | 0.830361 | 0.0380196 | ||||||||
\(478\) | −9.02544 | −0.412814 | ||||||||
\(479\) | 11.5980 | 0.529926 | 0.264963 | − | 0.964259i | \(-0.414640\pi\) | ||||
0.264963 | + | 0.964259i | \(0.414640\pi\) | |||||||
\(480\) | 2.21877 | 0.101272 | ||||||||
\(481\) | 25.2016 | 1.14910 | ||||||||
\(482\) | 4.52138 | 0.205943 | ||||||||
\(483\) | −32.6781 | −1.48690 | ||||||||
\(484\) | 0.775941 | 0.0352701 | ||||||||
\(485\) | −5.97504 | −0.271313 | ||||||||
\(486\) | 24.2865 | 1.10166 | ||||||||
\(487\) | −41.8745 | −1.89751 | −0.948756 | − | 0.316008i | \(-0.897657\pi\) | ||||
−0.948756 | + | 0.316008i | \(0.897657\pi\) | |||||||
\(488\) | −33.5683 | −1.51957 | ||||||||
\(489\) | 1.31988 | 0.0596870 | ||||||||
\(490\) | −1.64448 | −0.0742899 | ||||||||
\(491\) | 15.0652 | 0.679884 | 0.339942 | − | 0.940446i | \(-0.389593\pi\) | ||||
0.339942 | + | 0.940446i | \(0.389593\pi\) | |||||||
\(492\) | 2.60618 | 0.117495 | ||||||||
\(493\) | −5.07020 | −0.228350 | ||||||||
\(494\) | 6.69702 | 0.301313 | ||||||||
\(495\) | −4.35773 | −0.195866 | ||||||||
\(496\) | −3.97556 | −0.178508 | ||||||||
\(497\) | 15.9625 | 0.716018 | ||||||||
\(498\) | 25.7927 | 1.15580 | ||||||||
\(499\) | −7.40967 | −0.331703 | −0.165851 | − | 0.986151i | \(-0.553037\pi\) | ||||
−0.165851 | + | 0.986151i | \(0.553037\pi\) | |||||||
\(500\) | −1.64950 | −0.0737677 | ||||||||
\(501\) | 55.7443 | 2.49047 | ||||||||
\(502\) | 16.6975 | 0.745248 | ||||||||
\(503\) | 38.4356 | 1.71376 | 0.856880 | − | 0.515516i | \(-0.172400\pi\) | ||||
0.856880 | + | 0.515516i | \(0.172400\pi\) | |||||||
\(504\) | 14.1735 | 0.631337 | ||||||||
\(505\) | 1.54355 | 0.0686870 | ||||||||
\(506\) | 22.9629 | 1.02082 | ||||||||
\(507\) | −17.0978 | −0.759341 | ||||||||
\(508\) | 0.0283227 | 0.00125662 | ||||||||
\(509\) | 41.5698 | 1.84255 | 0.921275 | − | 0.388912i | \(-0.127149\pi\) | ||||
0.921275 | + | 0.388912i | \(0.127149\pi\) | |||||||
\(510\) | −11.6577 | −0.516210 | ||||||||
\(511\) | −18.2305 | −0.806471 | ||||||||
\(512\) | 25.1957 | 1.11350 | ||||||||
\(513\) | −4.58761 | −0.202548 | ||||||||
\(514\) | −4.55594 | −0.200954 | ||||||||
\(515\) | −12.0485 | −0.530919 | ||||||||
\(516\) | −4.58781 | −0.201967 | ||||||||
\(517\) | −1.87621 | −0.0825155 | ||||||||
\(518\) | 33.5262 | 1.47305 | ||||||||
\(519\) | −5.61833 | −0.246617 | ||||||||
\(520\) | 5.29243 | 0.232088 | ||||||||
\(521\) | −8.79559 | −0.385342 | −0.192671 | − | 0.981263i | \(-0.561715\pi\) | ||||
−0.192671 | + | 0.981263i | \(0.561715\pi\) | |||||||
\(522\) | −2.73946 | −0.119903 | ||||||||
\(523\) | −38.1154 | −1.66667 | −0.833336 | − | 0.552767i | \(-0.813572\pi\) | ||||
−0.833336 | + | 0.552767i | \(0.813572\pi\) | |||||||
\(524\) | −1.06170 | −0.0463804 | ||||||||
\(525\) | −23.0300 | −1.00511 | ||||||||
\(526\) | −25.2035 | −1.09893 | ||||||||
\(527\) | −5.77320 | −0.251485 | ||||||||
\(528\) | −21.6476 | −0.942091 | ||||||||
\(529\) | 16.1582 | 0.702529 | ||||||||
\(530\) | 0.412478 | 0.0179169 | ||||||||
\(531\) | −2.25522 | −0.0978683 | ||||||||
\(532\) | −1.14761 | −0.0497554 | ||||||||
\(533\) | 11.7963 | 0.510955 | ||||||||
\(534\) | −27.5674 | −1.19296 | ||||||||
\(535\) | −3.75006 | −0.162129 | ||||||||
\(536\) | −38.9679 | −1.68316 | ||||||||
\(537\) | −39.7898 | −1.71705 | ||||||||
\(538\) | 9.50819 | 0.409927 | ||||||||
\(539\) | −4.43450 | −0.191007 | ||||||||
\(540\) | −0.371337 | −0.0159798 | ||||||||
\(541\) | −21.8880 | −0.941039 | −0.470520 | − | 0.882390i | \(-0.655934\pi\) | ||||
−0.470520 | + | 0.882390i | \(0.655934\pi\) | |||||||
\(542\) | −17.0294 | −0.731475 | ||||||||
\(543\) | −29.4356 | −1.26320 | ||||||||
\(544\) | 6.51261 | 0.279226 | ||||||||
\(545\) | −13.3176 | −0.570463 | ||||||||
\(546\) | 16.1492 | 0.691122 | ||||||||
\(547\) | 11.1549 | 0.476950 | 0.238475 | − | 0.971149i | \(-0.423353\pi\) | ||||
0.238475 | + | 0.971149i | \(0.423353\pi\) | |||||||
\(548\) | 2.25428 | 0.0962981 | ||||||||
\(549\) | −23.2930 | −0.994123 | ||||||||
\(550\) | 16.1831 | 0.690052 | ||||||||
\(551\) | 2.16559 | 0.0922571 | ||||||||
\(552\) | −41.7414 | −1.77663 | ||||||||
\(553\) | −31.7606 | −1.35060 | ||||||||
\(554\) | −5.45874 | −0.231920 | ||||||||
\(555\) | 18.7374 | 0.795358 | ||||||||
\(556\) | −0.228227 | −0.00967898 | ||||||||
\(557\) | 18.4574 | 0.782064 | 0.391032 | − | 0.920377i | \(-0.372118\pi\) | ||||
0.391032 | + | 0.920377i | \(0.372118\pi\) | |||||||
\(558\) | −3.11929 | −0.132050 | ||||||||
\(559\) | −20.7658 | −0.878299 | ||||||||
\(560\) | 6.22658 | 0.263121 | ||||||||
\(561\) | −31.4361 | −1.32723 | ||||||||
\(562\) | 32.4873 | 1.37039 | ||||||||
\(563\) | −0.376010 | −0.0158469 | −0.00792346 | − | 0.999969i | \(-0.502522\pi\) | ||||
−0.00792346 | + | 0.999969i | \(0.502522\pi\) | |||||||
\(564\) | 0.349325 | 0.0147092 | ||||||||
\(565\) | −7.75371 | −0.326201 | ||||||||
\(566\) | −16.1757 | −0.679915 | ||||||||
\(567\) | −25.3988 | −1.06665 | ||||||||
\(568\) | 20.3898 | 0.855536 | ||||||||
\(569\) | 45.5041 | 1.90763 | 0.953816 | − | 0.300391i | \(-0.0971171\pi\) | ||||
0.953816 | + | 0.300391i | \(0.0971171\pi\) | |||||||
\(570\) | 4.97923 | 0.208557 | ||||||||
\(571\) | −39.3056 | −1.64489 | −0.822444 | − | 0.568846i | \(-0.807390\pi\) | ||||
−0.822444 | + | 0.568846i | \(0.807390\pi\) | |||||||
\(572\) | 1.46177 | 0.0611198 | ||||||||
\(573\) | 6.81977 | 0.284900 | ||||||||
\(574\) | 15.6928 | 0.655005 | ||||||||
\(575\) | 27.5968 | 1.15087 | ||||||||
\(576\) | 17.8901 | 0.745422 | ||||||||
\(577\) | −35.6677 | −1.48487 | −0.742433 | − | 0.669920i | \(-0.766328\pi\) | ||||
−0.742433 | + | 0.669920i | \(0.766328\pi\) | |||||||
\(578\) | −11.5896 | −0.482066 | ||||||||
\(579\) | 7.23140 | 0.300527 | ||||||||
\(580\) | 0.175290 | 0.00727852 | ||||||||
\(581\) | −20.0056 | −0.829974 | ||||||||
\(582\) | −23.2888 | −0.965353 | ||||||||
\(583\) | 1.11229 | 0.0460662 | ||||||||
\(584\) | −23.2868 | −0.963615 | ||||||||
\(585\) | 3.67242 | 0.151836 | ||||||||
\(586\) | −26.2562 | −1.08463 | ||||||||
\(587\) | 7.52414 | 0.310555 | 0.155277 | − | 0.987871i | \(-0.450373\pi\) | ||||
0.155277 | + | 0.987871i | \(0.450373\pi\) | |||||||
\(588\) | 0.825645 | 0.0340490 | ||||||||
\(589\) | 2.46585 | 0.101604 | ||||||||
\(590\) | −1.12027 | −0.0461208 | ||||||||
\(591\) | −33.5592 | −1.38044 | ||||||||
\(592\) | 37.8733 | 1.55658 | ||||||||
\(593\) | 6.90701 | 0.283637 | 0.141818 | − | 0.989893i | \(-0.454705\pi\) | ||||
0.141818 | + | 0.989893i | \(0.454705\pi\) | |||||||
\(594\) | 7.77366 | 0.318957 | ||||||||
\(595\) | 9.04207 | 0.370689 | ||||||||
\(596\) | 0.515084 | 0.0210986 | ||||||||
\(597\) | −54.1850 | −2.21764 | ||||||||
\(598\) | −19.3516 | −0.791346 | ||||||||
\(599\) | 18.0988 | 0.739496 | 0.369748 | − | 0.929132i | \(-0.379444\pi\) | ||||
0.369748 | + | 0.929132i | \(0.379444\pi\) | |||||||
\(600\) | −29.4174 | −1.20096 | ||||||||
\(601\) | 6.71850 | 0.274053 | 0.137027 | − | 0.990567i | \(-0.456245\pi\) | ||||
0.137027 | + | 0.990567i | \(0.456245\pi\) | |||||||
\(602\) | −27.6251 | −1.12591 | ||||||||
\(603\) | −27.0398 | −1.10115 | ||||||||
\(604\) | −0.992934 | −0.0404019 | ||||||||
\(605\) | 2.61127 | 0.106163 | ||||||||
\(606\) | 6.01626 | 0.244394 | ||||||||
\(607\) | −36.9855 | −1.50119 | −0.750597 | − | 0.660760i | \(-0.770234\pi\) | ||||
−0.750597 | + | 0.660760i | \(0.770234\pi\) | |||||||
\(608\) | −2.78167 | −0.112811 | ||||||||
\(609\) | 5.22210 | 0.211610 | ||||||||
\(610\) | −11.5707 | −0.468484 | ||||||||
\(611\) | 1.58115 | 0.0639663 | ||||||||
\(612\) | 2.38151 | 0.0962669 | ||||||||
\(613\) | 5.87449 | 0.237268 | 0.118634 | − | 0.992938i | \(-0.462148\pi\) | ||||
0.118634 | + | 0.992938i | \(0.462148\pi\) | |||||||
\(614\) | −0.364952 | −0.0147283 | ||||||||
\(615\) | 8.77054 | 0.353662 | ||||||||
\(616\) | 18.9857 | 0.764956 | ||||||||
\(617\) | 34.6078 | 1.39326 | 0.696628 | − | 0.717432i | \(-0.254683\pi\) | ||||
0.696628 | + | 0.717432i | \(0.254683\pi\) | |||||||
\(618\) | −46.9612 | −1.88906 | ||||||||
\(619\) | −40.2200 | −1.61658 | −0.808290 | − | 0.588785i | \(-0.799607\pi\) | ||||
−0.808290 | + | 0.588785i | \(0.799607\pi\) | |||||||
\(620\) | 0.199594 | 0.00801591 | ||||||||
\(621\) | 13.2563 | 0.531957 | ||||||||
\(622\) | 22.1034 | 0.886264 | ||||||||
\(623\) | 21.3822 | 0.856659 | ||||||||
\(624\) | 18.2432 | 0.730313 | ||||||||
\(625\) | 16.4995 | 0.659978 | ||||||||
\(626\) | −13.9256 | −0.556579 | ||||||||
\(627\) | 13.4270 | 0.536222 | ||||||||
\(628\) | −4.90499 | −0.195730 | ||||||||
\(629\) | 54.9987 | 2.19294 | ||||||||
\(630\) | 4.88548 | 0.194642 | ||||||||
\(631\) | −0.439056 | −0.0174785 | −0.00873927 | − | 0.999962i | \(-0.502782\pi\) | ||||
−0.00873927 | + | 0.999962i | \(0.502782\pi\) | |||||||
\(632\) | −40.5695 | −1.61377 | ||||||||
\(633\) | 16.8162 | 0.668382 | ||||||||
\(634\) | −1.39932 | −0.0555740 | ||||||||
\(635\) | 0.0953141 | 0.00378242 | ||||||||
\(636\) | −0.207093 | −0.00821178 | ||||||||
\(637\) | 3.73711 | 0.148070 | ||||||||
\(638\) | −3.66957 | −0.145280 | ||||||||
\(639\) | 14.1485 | 0.559704 | ||||||||
\(640\) | 6.91373 | 0.273289 | ||||||||
\(641\) | 22.0670 | 0.871592 | 0.435796 | − | 0.900045i | \(-0.356467\pi\) | ||||
0.435796 | + | 0.900045i | \(0.356467\pi\) | |||||||
\(642\) | −14.6166 | −0.576870 | ||||||||
\(643\) | −38.1072 | −1.50280 | −0.751401 | − | 0.659846i | \(-0.770622\pi\) | ||||
−0.751401 | + | 0.659846i | \(0.770622\pi\) | |||||||
\(644\) | 3.31613 | 0.130674 | ||||||||
\(645\) | −15.4393 | −0.607923 | ||||||||
\(646\) | 14.6152 | 0.575027 | ||||||||
\(647\) | 37.6194 | 1.47897 | 0.739485 | − | 0.673173i | \(-0.235069\pi\) | ||||
0.739485 | + | 0.673173i | \(0.235069\pi\) | |||||||
\(648\) | −32.4432 | −1.27449 | ||||||||
\(649\) | −3.02092 | −0.118582 | ||||||||
\(650\) | −13.6381 | −0.534931 | ||||||||
\(651\) | 5.94616 | 0.233049 | ||||||||
\(652\) | −0.133940 | −0.00524548 | ||||||||
\(653\) | 22.7015 | 0.888378 | 0.444189 | − | 0.895933i | \(-0.353492\pi\) | ||||
0.444189 | + | 0.895933i | \(0.353492\pi\) | |||||||
\(654\) | −51.9078 | −2.02975 | ||||||||
\(655\) | −3.57291 | −0.139605 | ||||||||
\(656\) | 17.7276 | 0.692148 | ||||||||
\(657\) | −16.1587 | −0.630411 | ||||||||
\(658\) | 2.10342 | 0.0820000 | ||||||||
\(659\) | −27.6992 | −1.07901 | −0.539505 | − | 0.841983i | \(-0.681388\pi\) | ||||
−0.539505 | + | 0.841983i | \(0.681388\pi\) | |||||||
\(660\) | 1.08683 | 0.0423047 | ||||||||
\(661\) | −14.7929 | −0.575379 | −0.287689 | − | 0.957724i | \(-0.592887\pi\) | ||||
−0.287689 | + | 0.957724i | \(0.592887\pi\) | |||||||
\(662\) | 40.9704 | 1.59236 | ||||||||
\(663\) | 26.4923 | 1.02888 | ||||||||
\(664\) | −25.5543 | −0.991697 | ||||||||
\(665\) | −3.86205 | −0.149764 | ||||||||
\(666\) | 29.7161 | 1.15147 | ||||||||
\(667\) | −6.25765 | −0.242297 | ||||||||
\(668\) | −5.65686 | −0.218871 | ||||||||
\(669\) | −45.6515 | −1.76499 | ||||||||
\(670\) | −13.4319 | −0.518919 | ||||||||
\(671\) | −31.2016 | −1.20452 | ||||||||
\(672\) | −6.70772 | −0.258756 | ||||||||
\(673\) | −21.4452 | −0.826651 | −0.413325 | − | 0.910583i | \(-0.635633\pi\) | ||||
−0.413325 | + | 0.910583i | \(0.635633\pi\) | |||||||
\(674\) | −14.9607 | −0.576264 | ||||||||
\(675\) | 9.34241 | 0.359590 | ||||||||
\(676\) | 1.73506 | 0.0667333 | ||||||||
\(677\) | −51.6540 | −1.98522 | −0.992612 | − | 0.121329i | \(-0.961284\pi\) | ||||
−0.992612 | + | 0.121329i | \(0.961284\pi\) | |||||||
\(678\) | −30.2215 | −1.16065 | ||||||||
\(679\) | 18.0636 | 0.693217 | ||||||||
\(680\) | 11.5499 | 0.442919 | ||||||||
\(681\) | −27.1410 | −1.04005 | ||||||||
\(682\) | −4.17836 | −0.159998 | ||||||||
\(683\) | −33.1623 | −1.26892 | −0.634459 | − | 0.772956i | \(-0.718777\pi\) | ||||
−0.634459 | + | 0.772956i | \(0.718777\pi\) | |||||||
\(684\) | −1.01719 | −0.0388933 | ||||||||
\(685\) | 7.58631 | 0.289858 | ||||||||
\(686\) | 26.6064 | 1.01584 | ||||||||
\(687\) | −7.89879 | −0.301358 | ||||||||
\(688\) | −31.2071 | −1.18976 | ||||||||
\(689\) | −0.937364 | −0.0357107 | ||||||||
\(690\) | −14.3879 | −0.547738 | ||||||||
\(691\) | −13.2094 | −0.502508 | −0.251254 | − | 0.967921i | \(-0.580843\pi\) | ||||
−0.251254 | + | 0.967921i | \(0.580843\pi\) | |||||||
\(692\) | 0.570141 | 0.0216735 | ||||||||
\(693\) | 13.1742 | 0.500446 | ||||||||
\(694\) | −41.5722 | −1.57806 | ||||||||
\(695\) | −0.768051 | −0.0291338 | ||||||||
\(696\) | 6.67046 | 0.252843 | ||||||||
\(697\) | 25.7436 | 0.975108 | ||||||||
\(698\) | −37.8341 | −1.43204 | ||||||||
\(699\) | 11.2824 | 0.426738 | ||||||||
\(700\) | 2.33705 | 0.0883323 | ||||||||
\(701\) | 9.98297 | 0.377051 | 0.188526 | − | 0.982068i | \(-0.439629\pi\) | ||||
0.188526 | + | 0.982068i | \(0.439629\pi\) | |||||||
\(702\) | −6.55114 | −0.247257 | ||||||||
\(703\) | −23.4910 | −0.885982 | ||||||||
\(704\) | 23.9643 | 0.903187 | ||||||||
\(705\) | 1.17558 | 0.0442749 | ||||||||
\(706\) | 29.3580 | 1.10490 | ||||||||
\(707\) | −4.66641 | −0.175499 | ||||||||
\(708\) | 0.562456 | 0.0211384 | ||||||||
\(709\) | 33.4638 | 1.25676 | 0.628380 | − | 0.777906i | \(-0.283718\pi\) | ||||
0.628380 | + | 0.777906i | \(0.283718\pi\) | |||||||
\(710\) | 7.02818 | 0.263763 | ||||||||
\(711\) | −28.1511 | −1.05575 | ||||||||
\(712\) | 27.3126 | 1.02358 | ||||||||
\(713\) | −7.12529 | −0.266844 | ||||||||
\(714\) | 35.2431 | 1.31894 | ||||||||
\(715\) | 4.91929 | 0.183971 | ||||||||
\(716\) | 4.03781 | 0.150900 | ||||||||
\(717\) | 15.2495 | 0.569505 | ||||||||
\(718\) | 2.04861 | 0.0764533 | ||||||||
\(719\) | 15.6418 | 0.583341 | 0.291670 | − | 0.956519i | \(-0.405789\pi\) | ||||
0.291670 | + | 0.956519i | \(0.405789\pi\) | |||||||
\(720\) | 5.51896 | 0.205679 | ||||||||
\(721\) | 36.4246 | 1.35652 | ||||||||
\(722\) | 19.0481 | 0.708895 | ||||||||
\(723\) | −7.63941 | −0.284113 | ||||||||
\(724\) | 2.98708 | 0.111014 | ||||||||
\(725\) | −4.41010 | −0.163787 | ||||||||
\(726\) | 10.1779 | 0.377737 | ||||||||
\(727\) | 16.4733 | 0.610962 | 0.305481 | − | 0.952198i | \(-0.401183\pi\) | ||||
0.305481 | + | 0.952198i | \(0.401183\pi\) | |||||||
\(728\) | −15.9999 | −0.592997 | ||||||||
\(729\) | −8.21928 | −0.304418 | ||||||||
\(730\) | −8.02676 | −0.297084 | ||||||||
\(731\) | −45.3181 | −1.67615 | ||||||||
\(732\) | 5.80932 | 0.214719 | ||||||||
\(733\) | 1.68644 | 0.0622901 | 0.0311450 | − | 0.999515i | \(-0.490085\pi\) | ||||
0.0311450 | + | 0.999515i | \(0.490085\pi\) | |||||||
\(734\) | 23.2424 | 0.857891 | ||||||||
\(735\) | 2.77854 | 0.102488 | ||||||||
\(736\) | 8.03787 | 0.296280 | ||||||||
\(737\) | −36.2204 | −1.33420 | ||||||||
\(738\) | 13.9094 | 0.512012 | ||||||||
\(739\) | 42.4536 | 1.56168 | 0.780840 | − | 0.624731i | \(-0.214791\pi\) | ||||
0.780840 | + | 0.624731i | \(0.214791\pi\) | |||||||
\(740\) | −1.90145 | −0.0698985 | ||||||||
\(741\) | −11.3154 | −0.415682 | ||||||||
\(742\) | −1.24699 | −0.0457785 | ||||||||
\(743\) | 10.2889 | 0.377462 | 0.188731 | − | 0.982029i | \(-0.439563\pi\) | ||||
0.188731 | + | 0.982029i | \(0.439563\pi\) | |||||||
\(744\) | 7.59534 | 0.278459 | ||||||||
\(745\) | 1.73341 | 0.0635071 | ||||||||
\(746\) | −18.1675 | −0.665158 | ||||||||
\(747\) | −17.7321 | −0.648783 | ||||||||
\(748\) | 3.19009 | 0.116641 | ||||||||
\(749\) | 11.3371 | 0.414248 | ||||||||
\(750\) | −21.6362 | −0.790041 | ||||||||
\(751\) | 45.9257 | 1.67585 | 0.837927 | − | 0.545782i | \(-0.183767\pi\) | ||||
0.837927 | + | 0.545782i | \(0.183767\pi\) | |||||||
\(752\) | 2.37617 | 0.0866499 | ||||||||
\(753\) | −28.2125 | −1.02812 | ||||||||
\(754\) | 3.09247 | 0.112621 | ||||||||
\(755\) | −3.34151 | −0.121610 | ||||||||
\(756\) | 1.12262 | 0.0408291 | ||||||||
\(757\) | 33.5253 | 1.21850 | 0.609249 | − | 0.792979i | \(-0.291471\pi\) | ||||
0.609249 | + | 0.792979i | \(0.291471\pi\) | |||||||
\(758\) | 29.3848 | 1.06730 | ||||||||
\(759\) | −38.7984 | −1.40829 | ||||||||
\(760\) | −4.93320 | −0.178946 | ||||||||
\(761\) | 36.3243 | 1.31676 | 0.658378 | − | 0.752688i | \(-0.271243\pi\) | ||||
0.658378 | + | 0.752688i | \(0.271243\pi\) | |||||||
\(762\) | 0.371504 | 0.0134582 | ||||||||
\(763\) | 40.2614 | 1.45756 | ||||||||
\(764\) | −0.692061 | −0.0250379 | ||||||||
\(765\) | 8.01448 | 0.289764 | ||||||||
\(766\) | 38.4840 | 1.39049 | ||||||||
\(767\) | 2.54584 | 0.0919249 | ||||||||
\(768\) | −12.1524 | −0.438510 | ||||||||
\(769\) | 50.3839 | 1.81689 | 0.908444 | − | 0.418006i | \(-0.137271\pi\) | ||||
0.908444 | + | 0.418006i | \(0.137271\pi\) | |||||||
\(770\) | 6.54421 | 0.235837 | ||||||||
\(771\) | 7.69779 | 0.277229 | ||||||||
\(772\) | −0.733833 | −0.0264112 | ||||||||
\(773\) | −8.49018 | −0.305371 | −0.152685 | − | 0.988275i | \(-0.548792\pi\) | ||||
−0.152685 | + | 0.988275i | \(0.548792\pi\) | |||||||
\(774\) | −24.4856 | −0.880116 | ||||||||
\(775\) | −5.02157 | −0.180380 | ||||||||
\(776\) | 23.0736 | 0.828292 | ||||||||
\(777\) | −56.6464 | −2.03218 | ||||||||
\(778\) | −5.09064 | −0.182508 | ||||||||
\(779\) | −10.9956 | −0.393959 | ||||||||
\(780\) | −0.915907 | −0.0327947 | ||||||||
\(781\) | 18.9522 | 0.678163 | ||||||||
\(782\) | −42.2319 | −1.51021 | ||||||||
\(783\) | −2.11841 | −0.0757059 | ||||||||
\(784\) | 5.61618 | 0.200578 | ||||||||
\(785\) | −16.5067 | −0.589150 | ||||||||
\(786\) | −13.9261 | −0.496727 | ||||||||
\(787\) | −0.537361 | −0.0191548 | −0.00957742 | − | 0.999954i | \(-0.503049\pi\) | ||||
−0.00957742 | + | 0.999954i | \(0.503049\pi\) | |||||||
\(788\) | 3.40554 | 0.121317 | ||||||||
\(789\) | 42.5843 | 1.51604 | ||||||||
\(790\) | −13.9839 | −0.497527 | ||||||||
\(791\) | 23.4408 | 0.833460 | ||||||||
\(792\) | 16.8281 | 0.597959 | ||||||||
\(793\) | 26.2947 | 0.933751 | ||||||||
\(794\) | 13.7460 | 0.487827 | ||||||||
\(795\) | −0.696929 | −0.0247175 | ||||||||
\(796\) | 5.49862 | 0.194893 | ||||||||
\(797\) | −0.203016 | −0.00719119 | −0.00359559 | − | 0.999994i | \(-0.501145\pi\) | ||||
−0.00359559 | + | 0.999994i | \(0.501145\pi\) | |||||||
\(798\) | −15.0531 | −0.532873 | ||||||||
\(799\) | 3.45060 | 0.122074 | ||||||||
\(800\) | 5.66471 | 0.200278 | ||||||||
\(801\) | 18.9522 | 0.669643 | ||||||||
\(802\) | −7.11848 | −0.251362 | ||||||||
\(803\) | −21.6450 | −0.763834 | ||||||||
\(804\) | 6.74377 | 0.237834 | ||||||||
\(805\) | 11.1597 | 0.393329 | ||||||||
\(806\) | 3.52125 | 0.124031 | ||||||||
\(807\) | −16.0652 | −0.565522 | ||||||||
\(808\) | −5.96065 | −0.209695 | ||||||||
\(809\) | −30.5469 | −1.07397 | −0.536985 | − | 0.843592i | \(-0.680437\pi\) | ||||
−0.536985 | + | 0.843592i | \(0.680437\pi\) | |||||||
\(810\) | −11.1829 | −0.392927 | ||||||||
\(811\) | 43.2311 | 1.51805 | 0.759024 | − | 0.651063i | \(-0.225677\pi\) | ||||
0.759024 | + | 0.651063i | \(0.225677\pi\) | |||||||
\(812\) | −0.529932 | −0.0185970 | ||||||||
\(813\) | 28.7732 | 1.00912 | ||||||||
\(814\) | 39.8054 | 1.39518 | ||||||||
\(815\) | −0.450745 | −0.0157889 | ||||||||
\(816\) | 39.8130 | 1.39373 | ||||||||
\(817\) | 19.3563 | 0.677190 | ||||||||
\(818\) | 28.1129 | 0.982945 | ||||||||
\(819\) | −11.1024 | −0.387948 | ||||||||
\(820\) | −0.890023 | −0.0310809 | ||||||||
\(821\) | −16.2042 | −0.565530 | −0.282765 | − | 0.959189i | \(-0.591252\pi\) | ||||
−0.282765 | + | 0.959189i | \(0.591252\pi\) | |||||||
\(822\) | 29.5690 | 1.03134 | ||||||||
\(823\) | −1.15493 | −0.0402583 | −0.0201292 | − | 0.999797i | \(-0.506408\pi\) | ||||
−0.0201292 | + | 0.999797i | \(0.506408\pi\) | |||||||
\(824\) | 46.5271 | 1.62085 | ||||||||
\(825\) | −27.3433 | −0.951972 | ||||||||
\(826\) | 3.38677 | 0.117841 | ||||||||
\(827\) | 43.7846 | 1.52254 | 0.761270 | − | 0.648436i | \(-0.224576\pi\) | ||||
0.761270 | + | 0.648436i | \(0.224576\pi\) | |||||||
\(828\) | 2.93926 | 0.102146 | ||||||||
\(829\) | −31.7976 | −1.10437 | −0.552187 | − | 0.833720i | \(-0.686207\pi\) | ||||
−0.552187 | + | 0.833720i | \(0.686207\pi\) | |||||||
\(830\) | −8.80833 | −0.305742 | ||||||||
\(831\) | 9.22318 | 0.319949 | ||||||||
\(832\) | −20.1955 | −0.700154 | ||||||||
\(833\) | 8.15566 | 0.282577 | ||||||||
\(834\) | −2.99362 | −0.103661 | ||||||||
\(835\) | −19.0370 | −0.658802 | ||||||||
\(836\) | −1.36255 | −0.0471249 | ||||||||
\(837\) | −2.41214 | −0.0833757 | ||||||||
\(838\) | −10.1530 | −0.350728 | ||||||||
\(839\) | −4.37059 | −0.150889 | −0.0754447 | − | 0.997150i | \(-0.524038\pi\) | ||||
−0.0754447 | + | 0.997150i | \(0.524038\pi\) | |||||||
\(840\) | −11.8959 | −0.410449 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 3.96738 | 0.136725 | ||||||||
\(843\) | −54.8911 | −1.89055 | ||||||||
\(844\) | −1.70648 | −0.0587395 | ||||||||
\(845\) | 5.83900 | 0.200868 | ||||||||
\(846\) | 1.86438 | 0.0640987 | ||||||||
\(847\) | −7.89432 | −0.271252 | ||||||||
\(848\) | −1.40868 | −0.0483744 | ||||||||
\(849\) | 27.3307 | 0.937988 | ||||||||
\(850\) | −29.7631 | −1.02086 | ||||||||
\(851\) | 67.8794 | 2.32688 | ||||||||
\(852\) | −3.52865 | −0.120890 | ||||||||
\(853\) | −12.8251 | −0.439125 | −0.219562 | − | 0.975598i | \(-0.570463\pi\) | ||||
−0.219562 | + | 0.975598i | \(0.570463\pi\) | |||||||
\(854\) | 34.9802 | 1.19700 | ||||||||
\(855\) | −3.42315 | −0.117069 | ||||||||
\(856\) | 14.4815 | 0.494966 | ||||||||
\(857\) | 5.10036 | 0.174225 | 0.0871125 | − | 0.996198i | \(-0.472236\pi\) | ||||
0.0871125 | + | 0.996198i | \(0.472236\pi\) | |||||||
\(858\) | 19.1738 | 0.654584 | ||||||||
\(859\) | −21.9547 | −0.749085 | −0.374543 | − | 0.927210i | \(-0.622200\pi\) | ||||
−0.374543 | + | 0.927210i | \(0.622200\pi\) | |||||||
\(860\) | 1.56676 | 0.0534262 | ||||||||
\(861\) | −26.5149 | −0.903624 | ||||||||
\(862\) | 1.75680 | 0.0598368 | ||||||||
\(863\) | 57.2311 | 1.94817 | 0.974085 | − | 0.226181i | \(-0.0726242\pi\) | ||||
0.974085 | + | 0.226181i | \(0.0726242\pi\) | |||||||
\(864\) | 2.72107 | 0.0925728 | ||||||||
\(865\) | 1.91869 | 0.0652374 | ||||||||
\(866\) | −29.6344 | −1.00702 | ||||||||
\(867\) | 19.5821 | 0.665042 | ||||||||
\(868\) | −0.603409 | −0.0204810 | ||||||||
\(869\) | −37.7091 | −1.27919 | ||||||||
\(870\) | 2.29925 | 0.0779519 | ||||||||
\(871\) | 30.5243 | 1.03427 | ||||||||
\(872\) | 51.4280 | 1.74157 | ||||||||
\(873\) | 16.0107 | 0.541881 | ||||||||
\(874\) | 18.0381 | 0.610148 | ||||||||
\(875\) | 16.7817 | 0.567326 | ||||||||
\(876\) | 4.03001 | 0.136161 | ||||||||
\(877\) | −51.6800 | −1.74511 | −0.872554 | − | 0.488517i | \(-0.837538\pi\) | ||||
−0.872554 | + | 0.488517i | \(0.837538\pi\) | |||||||
\(878\) | 14.0026 | 0.472564 | ||||||||
\(879\) | 44.3629 | 1.49632 | ||||||||
\(880\) | 7.39277 | 0.249210 | ||||||||
\(881\) | 16.1283 | 0.543377 | 0.271688 | − | 0.962385i | \(-0.412418\pi\) | ||||
0.271688 | + | 0.962385i | \(0.412418\pi\) | |||||||
\(882\) | 4.40654 | 0.148376 | ||||||||
\(883\) | −41.0614 | −1.38182 | −0.690912 | − | 0.722939i | \(-0.742791\pi\) | ||||
−0.690912 | + | 0.722939i | \(0.742791\pi\) | |||||||
\(884\) | −2.68840 | −0.0904208 | ||||||||
\(885\) | 1.89283 | 0.0636268 | ||||||||
\(886\) | −44.3404 | −1.48965 | ||||||||
\(887\) | −23.6138 | −0.792874 | −0.396437 | − | 0.918062i | \(-0.629753\pi\) | ||||
−0.396437 | + | 0.918062i | \(0.629753\pi\) | |||||||
\(888\) | −72.3574 | −2.42815 | ||||||||
\(889\) | −0.288151 | −0.00966427 | ||||||||
\(890\) | 9.41441 | 0.315572 | ||||||||
\(891\) | −30.1558 | −1.01026 | ||||||||
\(892\) | 4.63265 | 0.155113 | ||||||||
\(893\) | −1.47382 | −0.0493196 | ||||||||
\(894\) | 6.75627 | 0.225963 | ||||||||
\(895\) | 13.5884 | 0.454211 | ||||||||
\(896\) | −20.9014 | −0.698267 | ||||||||
\(897\) | 32.6968 | 1.09172 | ||||||||
\(898\) | 3.71210 | 0.123875 | ||||||||
\(899\) | 1.13865 | 0.0379762 | ||||||||
\(900\) | 2.07146 | 0.0690485 | ||||||||
\(901\) | −2.04565 | −0.0681505 | ||||||||
\(902\) | 18.6320 | 0.620377 | ||||||||
\(903\) | 46.6758 | 1.55327 | ||||||||
\(904\) | 29.9422 | 0.995862 | ||||||||
\(905\) | 10.0524 | 0.334153 | ||||||||
\(906\) | −13.0242 | −0.432698 | ||||||||
\(907\) | −16.5452 | −0.549375 | −0.274688 | − | 0.961534i | \(-0.588574\pi\) | ||||
−0.274688 | + | 0.961534i | \(0.588574\pi\) | |||||||
\(908\) | 2.75423 | 0.0914024 | ||||||||
\(909\) | −4.13610 | −0.137186 | ||||||||
\(910\) | −5.51504 | −0.182822 | ||||||||
\(911\) | −6.74786 | −0.223567 | −0.111783 | − | 0.993733i | \(-0.535656\pi\) | ||||
−0.111783 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(912\) | −17.0049 | −0.563090 | ||||||||
\(913\) | −23.7526 | −0.786095 | ||||||||
\(914\) | −1.78159 | −0.0589298 | ||||||||
\(915\) | 19.5501 | 0.646305 | ||||||||
\(916\) | 0.801558 | 0.0264842 | ||||||||
\(917\) | 10.8015 | 0.356698 | ||||||||
\(918\) | −14.2968 | −0.471866 | ||||||||
\(919\) | −25.1667 | −0.830172 | −0.415086 | − | 0.909782i | \(-0.636248\pi\) | ||||
−0.415086 | + | 0.909782i | \(0.636248\pi\) | |||||||
\(920\) | 14.2549 | 0.469970 | ||||||||
\(921\) | 0.616629 | 0.0203186 | ||||||||
\(922\) | 19.9532 | 0.657123 | ||||||||
\(923\) | −15.9717 | −0.525715 | ||||||||
\(924\) | −3.28566 | −0.108090 | ||||||||
\(925\) | 47.8382 | 1.57291 | ||||||||
\(926\) | −0.104318 | −0.00342810 | ||||||||
\(927\) | 32.2851 | 1.06038 | ||||||||
\(928\) | −1.28449 | −0.0421653 | ||||||||
\(929\) | 14.1028 | 0.462699 | 0.231349 | − | 0.972871i | \(-0.425686\pi\) | ||||
0.231349 | + | 0.972871i | \(0.425686\pi\) | |||||||
\(930\) | 2.61805 | 0.0858492 | ||||||||
\(931\) | −3.48345 | −0.114165 | ||||||||
\(932\) | −1.14492 | −0.0375031 | ||||||||
\(933\) | −37.3462 | −1.22266 | ||||||||
\(934\) | 19.8708 | 0.650193 | ||||||||
\(935\) | 10.7356 | 0.351091 | ||||||||
\(936\) | −14.1816 | −0.463541 | ||||||||
\(937\) | −16.0094 | −0.523005 | −0.261503 | − | 0.965203i | \(-0.584218\pi\) | ||||
−0.261503 | + | 0.965203i | \(0.584218\pi\) | |||||||
\(938\) | 40.6069 | 1.32586 | ||||||||
\(939\) | 23.5289 | 0.767838 | ||||||||
\(940\) | −0.119296 | −0.00389102 | ||||||||
\(941\) | −17.6384 | −0.574995 | −0.287498 | − | 0.957781i | \(-0.592823\pi\) | ||||
−0.287498 | + | 0.957781i | \(0.592823\pi\) | |||||||
\(942\) | −64.3380 | −2.09624 | ||||||||
\(943\) | 31.7728 | 1.03466 | ||||||||
\(944\) | 3.82592 | 0.124523 | ||||||||
\(945\) | 3.77793 | 0.122896 | ||||||||
\(946\) | −32.7990 | −1.06639 | ||||||||
\(947\) | −18.8627 | −0.612957 | −0.306478 | − | 0.951878i | \(-0.599151\pi\) | ||||
−0.306478 | + | 0.951878i | \(0.599151\pi\) | |||||||
\(948\) | 7.02094 | 0.228030 | ||||||||
\(949\) | 18.2410 | 0.592127 | ||||||||
\(950\) | 12.7124 | 0.412445 | ||||||||
\(951\) | 2.36431 | 0.0766680 | ||||||||
\(952\) | −34.9174 | −1.13168 | ||||||||
\(953\) | −7.39553 | −0.239565 | −0.119782 | − | 0.992800i | \(-0.538220\pi\) | ||||
−0.119782 | + | 0.992800i | \(0.538220\pi\) | |||||||
\(954\) | −1.10528 | −0.0357846 | ||||||||
\(955\) | −2.32899 | −0.0753643 | ||||||||
\(956\) | −1.54750 | −0.0500498 | ||||||||
\(957\) | 6.20016 | 0.200423 | ||||||||
\(958\) | −15.4379 | −0.498774 | ||||||||
\(959\) | −22.9347 | −0.740601 | ||||||||
\(960\) | −15.0154 | −0.484618 | ||||||||
\(961\) | −29.7035 | −0.958176 | ||||||||
\(962\) | −33.5454 | −1.08155 | ||||||||
\(963\) | 10.0487 | 0.323814 | ||||||||
\(964\) | 0.775237 | 0.0249687 | ||||||||
\(965\) | −2.46956 | −0.0794980 | ||||||||
\(966\) | 43.4971 | 1.39950 | ||||||||
\(967\) | 7.49708 | 0.241090 | 0.120545 | − | 0.992708i | \(-0.461536\pi\) | ||||
0.120545 | + | 0.992708i | \(0.461536\pi\) | |||||||
\(968\) | −10.0838 | −0.324106 | ||||||||
\(969\) | −24.6941 | −0.793289 | ||||||||
\(970\) | 7.95326 | 0.255364 | ||||||||
\(971\) | −10.0837 | −0.323602 | −0.161801 | − | 0.986823i | \(-0.551730\pi\) | ||||
−0.161801 | + | 0.986823i | \(0.551730\pi\) | |||||||
\(972\) | 4.16417 | 0.133566 | ||||||||
\(973\) | 2.32195 | 0.0744383 | ||||||||
\(974\) | 55.7382 | 1.78597 | ||||||||
\(975\) | 23.0432 | 0.737973 | ||||||||
\(976\) | 39.5160 | 1.26488 | ||||||||
\(977\) | −18.4119 | −0.589048 | −0.294524 | − | 0.955644i | \(-0.595161\pi\) | ||||
−0.294524 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(978\) | −1.75686 | −0.0561783 | ||||||||
\(979\) | 25.3869 | 0.811369 | ||||||||
\(980\) | −0.281962 | −0.00900695 | ||||||||
\(981\) | 35.6859 | 1.13936 | ||||||||
\(982\) | −20.0530 | −0.639917 | ||||||||
\(983\) | 20.7157 | 0.660729 | 0.330364 | − | 0.943853i | \(-0.392828\pi\) | ||||
0.330364 | + | 0.943853i | \(0.392828\pi\) | |||||||
\(984\) | −33.8688 | −1.07970 | ||||||||
\(985\) | 11.4606 | 0.365166 | ||||||||
\(986\) | 6.74884 | 0.214927 | ||||||||
\(987\) | −3.55398 | −0.113125 | ||||||||
\(988\) | 1.14827 | 0.0365314 | ||||||||
\(989\) | −55.9316 | −1.77852 | ||||||||
\(990\) | 5.80049 | 0.184352 | ||||||||
\(991\) | −7.41403 | −0.235514 | −0.117757 | − | 0.993042i | \(-0.537570\pi\) | ||||
−0.117757 | + | 0.993042i | \(0.537570\pi\) | |||||||
\(992\) | −1.46258 | −0.0464371 | ||||||||
\(993\) | −69.2242 | −2.19676 | ||||||||
\(994\) | −21.2474 | −0.673927 | ||||||||
\(995\) | 18.5045 | 0.586631 | ||||||||
\(996\) | 4.42241 | 0.140130 | ||||||||
\(997\) | 14.7768 | 0.467985 | 0.233992 | − | 0.972238i | \(-0.424821\pi\) | ||||
0.233992 | + | 0.972238i | \(0.424821\pi\) | |||||||
\(998\) | 9.86287 | 0.312204 | ||||||||
\(999\) | 22.9793 | 0.727034 |
(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 | 4031.2.a.b.1.18 | ✓ | 59 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4031.2.a.b.1.18 | ✓ | 59 | 1.1 | even | 1 | trivial |