Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6047,2,Mod(1,6047)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6047, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6047.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6047 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6047.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: | \(48.2855381023\) |
Analytic rank: | \(0\) |
Dimension: | \(287\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 6047.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69892 | −1.90843 | −0.954214 | − | 0.299125i | \(-0.903305\pi\) | ||||
−0.954214 | + | 0.299125i | \(0.903305\pi\) | |||||||
\(3\) | 0.321066 | 0.185367 | 0.0926837 | − | 0.995696i | \(-0.470455\pi\) | ||||
0.0926837 | + | 0.995696i | \(0.470455\pi\) | |||||||
\(4\) | 5.28419 | 2.64210 | ||||||||
\(5\) | −2.61974 | −1.17158 | −0.585792 | − | 0.810461i | \(-0.699216\pi\) | ||||
−0.585792 | + | 0.810461i | \(0.699216\pi\) | |||||||
\(6\) | −0.866532 | −0.353760 | ||||||||
\(7\) | −2.02949 | −0.767076 | −0.383538 | − | 0.923525i | \(-0.625294\pi\) | ||||
−0.383538 | + | 0.923525i | \(0.625294\pi\) | |||||||
\(8\) | −8.86379 | −3.13382 | ||||||||
\(9\) | −2.89692 | −0.965639 | ||||||||
\(10\) | 7.07048 | 2.23588 | ||||||||
\(11\) | 0.150891 | 0.0454952 | 0.0227476 | − | 0.999741i | \(-0.492759\pi\) | ||||
0.0227476 | + | 0.999741i | \(0.492759\pi\) | |||||||
\(12\) | 1.69657 | 0.489758 | ||||||||
\(13\) | 3.48633 | 0.966934 | 0.483467 | − | 0.875363i | \(-0.339377\pi\) | ||||
0.483467 | + | 0.875363i | \(0.339377\pi\) | |||||||
\(14\) | 5.47745 | 1.46391 | ||||||||
\(15\) | −0.841109 | −0.217173 | ||||||||
\(16\) | 13.3543 | 3.33858 | ||||||||
\(17\) | −3.50370 | −0.849773 | −0.424887 | − | 0.905247i | \(-0.639686\pi\) | ||||
−0.424887 | + | 0.905247i | \(0.639686\pi\) | |||||||
\(18\) | 7.81856 | 1.84285 | ||||||||
\(19\) | −1.49640 | −0.343298 | −0.171649 | − | 0.985158i | \(-0.554909\pi\) | ||||
−0.171649 | + | 0.985158i | \(0.554909\pi\) | |||||||
\(20\) | −13.8432 | −3.09544 | ||||||||
\(21\) | −0.651600 | −0.142191 | ||||||||
\(22\) | −0.407242 | −0.0868244 | ||||||||
\(23\) | −3.96165 | −0.826061 | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||||
−0.413031 | + | 0.910717i | \(0.635530\pi\) | |||||||
\(24\) | −2.84586 | −0.580908 | ||||||||
\(25\) | 1.86304 | 0.372609 | ||||||||
\(26\) | −9.40934 | −1.84532 | ||||||||
\(27\) | −1.89330 | −0.364365 | ||||||||
\(28\) | −10.7242 | −2.02669 | ||||||||
\(29\) | −7.85969 | −1.45951 | −0.729754 | − | 0.683710i | \(-0.760365\pi\) | ||||
−0.729754 | + | 0.683710i | \(0.760365\pi\) | |||||||
\(30\) | 2.27009 | 0.414460 | ||||||||
\(31\) | 1.13379 | 0.203635 | 0.101818 | − | 0.994803i | \(-0.467534\pi\) | ||||
0.101818 | + | 0.994803i | \(0.467534\pi\) | |||||||
\(32\) | −18.3147 | −3.23761 | ||||||||
\(33\) | 0.0484458 | 0.00843333 | ||||||||
\(34\) | 9.45623 | 1.62173 | ||||||||
\(35\) | 5.31674 | 0.898694 | ||||||||
\(36\) | −15.3079 | −2.55131 | ||||||||
\(37\) | −2.38120 | −0.391467 | −0.195733 | − | 0.980657i | \(-0.562709\pi\) | ||||
−0.195733 | + | 0.980657i | \(0.562709\pi\) | |||||||
\(38\) | 4.03867 | 0.655159 | ||||||||
\(39\) | 1.11934 | 0.179238 | ||||||||
\(40\) | 23.2208 | 3.67153 | ||||||||
\(41\) | −9.49234 | −1.48245 | −0.741227 | − | 0.671254i | \(-0.765756\pi\) | ||||
−0.741227 | + | 0.671254i | \(0.765756\pi\) | |||||||
\(42\) | 1.75862 | 0.271361 | ||||||||
\(43\) | 10.8831 | 1.65965 | 0.829827 | − | 0.558021i | \(-0.188439\pi\) | ||||
0.829827 | + | 0.558021i | \(0.188439\pi\) | |||||||
\(44\) | 0.797335 | 0.120203 | ||||||||
\(45\) | 7.58917 | 1.13133 | ||||||||
\(46\) | 10.6922 | 1.57648 | ||||||||
\(47\) | −0.888951 | −0.129667 | −0.0648334 | − | 0.997896i | \(-0.520652\pi\) | ||||
−0.0648334 | + | 0.997896i | \(0.520652\pi\) | |||||||
\(48\) | 4.28761 | 0.618863 | ||||||||
\(49\) | −2.88116 | −0.411594 | ||||||||
\(50\) | −5.02821 | −0.711097 | ||||||||
\(51\) | −1.12492 | −0.157520 | ||||||||
\(52\) | 18.4224 | 2.55473 | ||||||||
\(53\) | −4.27646 | −0.587417 | −0.293708 | − | 0.955895i | \(-0.594889\pi\) | ||||
−0.293708 | + | 0.955895i | \(0.594889\pi\) | |||||||
\(54\) | 5.10987 | 0.695365 | ||||||||
\(55\) | −0.395294 | −0.0533015 | ||||||||
\(56\) | 17.9890 | 2.40388 | ||||||||
\(57\) | −0.480443 | −0.0636362 | ||||||||
\(58\) | 21.2127 | 2.78536 | ||||||||
\(59\) | 9.55046 | 1.24336 | 0.621682 | − | 0.783270i | \(-0.286450\pi\) | ||||
0.621682 | + | 0.783270i | \(0.286450\pi\) | |||||||
\(60\) | −4.44458 | −0.573793 | ||||||||
\(61\) | −11.6987 | −1.49786 | −0.748931 | − | 0.662648i | \(-0.769433\pi\) | ||||
−0.748931 | + | 0.662648i | \(0.769433\pi\) | |||||||
\(62\) | −3.06002 | −0.388623 | ||||||||
\(63\) | 5.87927 | 0.740718 | ||||||||
\(64\) | 22.7213 | 2.84017 | ||||||||
\(65\) | −9.13328 | −1.13284 | ||||||||
\(66\) | −0.130752 | −0.0160944 | ||||||||
\(67\) | −7.26318 | −0.887339 | −0.443670 | − | 0.896190i | \(-0.646324\pi\) | ||||
−0.443670 | + | 0.896190i | \(0.646324\pi\) | |||||||
\(68\) | −18.5142 | −2.24518 | ||||||||
\(69\) | −1.27195 | −0.153125 | ||||||||
\(70\) | −14.3495 | −1.71509 | ||||||||
\(71\) | 3.81577 | 0.452848 | 0.226424 | − | 0.974029i | \(-0.427296\pi\) | ||||
0.226424 | + | 0.974029i | \(0.427296\pi\) | |||||||
\(72\) | 25.6777 | 3.02614 | ||||||||
\(73\) | −14.3665 | −1.68147 | −0.840735 | − | 0.541448i | \(-0.817876\pi\) | ||||
−0.840735 | + | 0.541448i | \(0.817876\pi\) | |||||||
\(74\) | 6.42668 | 0.747086 | ||||||||
\(75\) | 0.598159 | 0.0690695 | ||||||||
\(76\) | −7.90727 | −0.907026 | ||||||||
\(77\) | −0.306231 | −0.0348983 | ||||||||
\(78\) | −3.02102 | −0.342063 | ||||||||
\(79\) | 3.40307 | 0.382875 | 0.191438 | − | 0.981505i | \(-0.438685\pi\) | ||||
0.191438 | + | 0.981505i | \(0.438685\pi\) | |||||||
\(80\) | −34.9848 | −3.91142 | ||||||||
\(81\) | 8.08288 | 0.898098 | ||||||||
\(82\) | 25.6191 | 2.82916 | ||||||||
\(83\) | 13.7854 | 1.51315 | 0.756574 | − | 0.653908i | \(-0.226872\pi\) | ||||
0.756574 | + | 0.653908i | \(0.226872\pi\) | |||||||
\(84\) | −3.44318 | −0.375682 | ||||||||
\(85\) | 9.17880 | 0.995581 | ||||||||
\(86\) | −29.3726 | −3.16733 | ||||||||
\(87\) | −2.52348 | −0.270545 | ||||||||
\(88\) | −1.33746 | −0.142574 | ||||||||
\(89\) | −15.9395 | −1.68959 | −0.844794 | − | 0.535092i | \(-0.820277\pi\) | ||||
−0.844794 | + | 0.535092i | \(0.820277\pi\) | |||||||
\(90\) | −20.4826 | −2.15906 | ||||||||
\(91\) | −7.07548 | −0.741712 | ||||||||
\(92\) | −20.9341 | −2.18253 | ||||||||
\(93\) | 0.364022 | 0.0377473 | ||||||||
\(94\) | 2.39921 | 0.247460 | ||||||||
\(95\) | 3.92018 | 0.402202 | ||||||||
\(96\) | −5.88021 | −0.600147 | ||||||||
\(97\) | −3.01739 | −0.306370 | −0.153185 | − | 0.988198i | \(-0.548953\pi\) | ||||
−0.153185 | + | 0.988198i | \(0.548953\pi\) | |||||||
\(98\) | 7.77603 | 0.785498 | ||||||||
\(99\) | −0.437118 | −0.0439320 | ||||||||
\(100\) | 9.84468 | 0.984468 | ||||||||
\(101\) | −19.8028 | −1.97045 | −0.985224 | − | 0.171268i | \(-0.945214\pi\) | ||||
−0.985224 | + | 0.171268i | \(0.945214\pi\) | |||||||
\(102\) | 3.03607 | 0.300616 | ||||||||
\(103\) | −16.1127 | −1.58764 | −0.793818 | − | 0.608156i | \(-0.791910\pi\) | ||||
−0.793818 | + | 0.608156i | \(0.791910\pi\) | |||||||
\(104\) | −30.9021 | −3.03020 | ||||||||
\(105\) | 1.70702 | 0.166588 | ||||||||
\(106\) | 11.5418 | 1.12104 | ||||||||
\(107\) | 0.218465 | 0.0211198 | 0.0105599 | − | 0.999944i | \(-0.496639\pi\) | ||||
0.0105599 | + | 0.999944i | \(0.496639\pi\) | |||||||
\(108\) | −10.0045 | −0.962688 | ||||||||
\(109\) | 1.59501 | 0.152775 | 0.0763873 | − | 0.997078i | \(-0.475661\pi\) | ||||
0.0763873 | + | 0.997078i | \(0.475661\pi\) | |||||||
\(110\) | 1.06687 | 0.101722 | ||||||||
\(111\) | −0.764521 | −0.0725652 | ||||||||
\(112\) | −27.1025 | −2.56094 | ||||||||
\(113\) | −5.92403 | −0.557286 | −0.278643 | − | 0.960395i | \(-0.589885\pi\) | ||||
−0.278643 | + | 0.960395i | \(0.589885\pi\) | |||||||
\(114\) | 1.29668 | 0.121445 | ||||||||
\(115\) | 10.3785 | 0.967800 | ||||||||
\(116\) | −41.5321 | −3.85616 | ||||||||
\(117\) | −10.0996 | −0.933709 | ||||||||
\(118\) | −25.7760 | −2.37287 | ||||||||
\(119\) | 7.11074 | 0.651841 | ||||||||
\(120\) | 7.45541 | 0.680583 | ||||||||
\(121\) | −10.9772 | −0.997930 | ||||||||
\(122\) | 31.5738 | 2.85856 | ||||||||
\(123\) | −3.04766 | −0.274799 | ||||||||
\(124\) | 5.99118 | 0.538024 | ||||||||
\(125\) | 8.21801 | 0.735042 | ||||||||
\(126\) | −15.8677 | −1.41361 | ||||||||
\(127\) | 8.29976 | 0.736484 | 0.368242 | − | 0.929730i | \(-0.379960\pi\) | ||||
0.368242 | + | 0.929730i | \(0.379960\pi\) | |||||||
\(128\) | −24.6938 | −2.18264 | ||||||||
\(129\) | 3.49418 | 0.307646 | ||||||||
\(130\) | 24.6500 | 2.16195 | ||||||||
\(131\) | −4.10600 | −0.358743 | −0.179371 | − | 0.983781i | \(-0.557406\pi\) | ||||
−0.179371 | + | 0.983781i | \(0.557406\pi\) | |||||||
\(132\) | 0.255997 | 0.0222817 | ||||||||
\(133\) | 3.03694 | 0.263336 | ||||||||
\(134\) | 19.6028 | 1.69342 | ||||||||
\(135\) | 4.95995 | 0.426884 | ||||||||
\(136\) | 31.0561 | 2.66304 | ||||||||
\(137\) | −12.4565 | −1.06423 | −0.532115 | − | 0.846672i | \(-0.678603\pi\) | ||||
−0.532115 | + | 0.846672i | \(0.678603\pi\) | |||||||
\(138\) | 3.43290 | 0.292228 | ||||||||
\(139\) | 1.93680 | 0.164278 | 0.0821388 | − | 0.996621i | \(-0.473825\pi\) | ||||
0.0821388 | + | 0.996621i | \(0.473825\pi\) | |||||||
\(140\) | 28.0947 | 2.37444 | ||||||||
\(141\) | −0.285412 | −0.0240360 | ||||||||
\(142\) | −10.2985 | −0.864228 | ||||||||
\(143\) | 0.526055 | 0.0439909 | ||||||||
\(144\) | −38.6863 | −3.22386 | ||||||||
\(145\) | 20.5903 | 1.70994 | ||||||||
\(146\) | 38.7740 | 3.20896 | ||||||||
\(147\) | −0.925042 | −0.0762962 | ||||||||
\(148\) | −12.5827 | −1.03429 | ||||||||
\(149\) | −0.825387 | −0.0676183 | −0.0338092 | − | 0.999428i | \(-0.510764\pi\) | ||||
−0.0338092 | + | 0.999428i | \(0.510764\pi\) | |||||||
\(150\) | −1.61439 | −0.131814 | ||||||||
\(151\) | −9.13818 | −0.743655 | −0.371827 | − | 0.928302i | \(-0.621269\pi\) | ||||
−0.371827 | + | 0.928302i | \(0.621269\pi\) | |||||||
\(152\) | 13.2638 | 1.07583 | ||||||||
\(153\) | 10.1499 | 0.820574 | ||||||||
\(154\) | 0.826495 | 0.0666009 | ||||||||
\(155\) | −2.97024 | −0.238576 | ||||||||
\(156\) | 5.91481 | 0.473564 | ||||||||
\(157\) | 5.68830 | 0.453976 | 0.226988 | − | 0.973898i | \(-0.427112\pi\) | ||||
0.226988 | + | 0.973898i | \(0.427112\pi\) | |||||||
\(158\) | −9.18462 | −0.730689 | ||||||||
\(159\) | −1.37302 | −0.108888 | ||||||||
\(160\) | 47.9797 | 3.79313 | ||||||||
\(161\) | 8.04014 | 0.633652 | ||||||||
\(162\) | −21.8151 | −1.71395 | ||||||||
\(163\) | 6.90941 | 0.541187 | 0.270594 | − | 0.962694i | \(-0.412780\pi\) | ||||
0.270594 | + | 0.962694i | \(0.412780\pi\) | |||||||
\(164\) | −50.1593 | −3.91679 | ||||||||
\(165\) | −0.126915 | −0.00988036 | ||||||||
\(166\) | −37.2058 | −2.88773 | ||||||||
\(167\) | −3.56096 | −0.275555 | −0.137778 | − | 0.990463i | \(-0.543996\pi\) | ||||
−0.137778 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(168\) | 5.77565 | 0.445601 | ||||||||
\(169\) | −0.845500 | −0.0650384 | ||||||||
\(170\) | −24.7729 | −1.89999 | ||||||||
\(171\) | 4.33495 | 0.331502 | ||||||||
\(172\) | 57.5083 | 4.38497 | ||||||||
\(173\) | −12.3995 | −0.942716 | −0.471358 | − | 0.881942i | \(-0.656236\pi\) | ||||
−0.471358 | + | 0.881942i | \(0.656236\pi\) | |||||||
\(174\) | 6.81067 | 0.516316 | ||||||||
\(175\) | −3.78103 | −0.285819 | ||||||||
\(176\) | 2.01504 | 0.151889 | ||||||||
\(177\) | 3.06632 | 0.230479 | ||||||||
\(178\) | 43.0196 | 3.22445 | ||||||||
\(179\) | 14.1371 | 1.05665 | 0.528327 | − | 0.849041i | \(-0.322819\pi\) | ||||
0.528327 | + | 0.849041i | \(0.322819\pi\) | |||||||
\(180\) | 40.1026 | 2.98907 | ||||||||
\(181\) | 11.3858 | 0.846300 | 0.423150 | − | 0.906060i | \(-0.360924\pi\) | ||||
0.423150 | + | 0.906060i | \(0.360924\pi\) | |||||||
\(182\) | 19.0962 | 1.41550 | ||||||||
\(183\) | −3.75604 | −0.277655 | ||||||||
\(184\) | 35.1152 | 2.58873 | ||||||||
\(185\) | 6.23813 | 0.458636 | ||||||||
\(186\) | −0.982468 | −0.0720380 | ||||||||
\(187\) | −0.528676 | −0.0386606 | ||||||||
\(188\) | −4.69739 | −0.342592 | ||||||||
\(189\) | 3.84243 | 0.279496 | ||||||||
\(190\) | −10.5803 | −0.767574 | ||||||||
\(191\) | −19.1249 | −1.38383 | −0.691914 | − | 0.721980i | \(-0.743232\pi\) | ||||
−0.691914 | + | 0.721980i | \(0.743232\pi\) | |||||||
\(192\) | 7.29504 | 0.526474 | ||||||||
\(193\) | 18.3081 | 1.31784 | 0.658921 | − | 0.752212i | \(-0.271013\pi\) | ||||
0.658921 | + | 0.752212i | \(0.271013\pi\) | |||||||
\(194\) | 8.14371 | 0.584684 | ||||||||
\(195\) | −2.93238 | −0.209992 | ||||||||
\(196\) | −15.2246 | −1.08747 | ||||||||
\(197\) | −3.84972 | −0.274281 | −0.137140 | − | 0.990552i | \(-0.543791\pi\) | ||||
−0.137140 | + | 0.990552i | \(0.543791\pi\) | |||||||
\(198\) | 1.17975 | 0.0838410 | ||||||||
\(199\) | −16.7193 | −1.18520 | −0.592601 | − | 0.805496i | \(-0.701899\pi\) | ||||
−0.592601 | + | 0.805496i | \(0.701899\pi\) | |||||||
\(200\) | −16.5136 | −1.16769 | ||||||||
\(201\) | −2.33196 | −0.164484 | ||||||||
\(202\) | 53.4462 | 3.76046 | ||||||||
\(203\) | 15.9512 | 1.11955 | ||||||||
\(204\) | −5.94429 | −0.416184 | ||||||||
\(205\) | 24.8675 | 1.73682 | ||||||||
\(206\) | 43.4871 | 3.02989 | ||||||||
\(207\) | 11.4766 | 0.797677 | ||||||||
\(208\) | 46.5575 | 3.22818 | ||||||||
\(209\) | −0.225793 | −0.0156184 | ||||||||
\(210\) | −4.60713 | −0.317922 | ||||||||
\(211\) | 7.06473 | 0.486356 | 0.243178 | − | 0.969982i | \(-0.421810\pi\) | ||||
0.243178 | + | 0.969982i | \(0.421810\pi\) | |||||||
\(212\) | −22.5976 | −1.55201 | ||||||||
\(213\) | 1.22511 | 0.0839432 | ||||||||
\(214\) | −0.589620 | −0.0403056 | ||||||||
\(215\) | −28.5108 | −1.94442 | ||||||||
\(216\) | 16.7818 | 1.14186 | ||||||||
\(217\) | −2.30102 | −0.156204 | ||||||||
\(218\) | −4.30482 | −0.291559 | ||||||||
\(219\) | −4.61258 | −0.311689 | ||||||||
\(220\) | −2.08881 | −0.140828 | ||||||||
\(221\) | −12.2151 | −0.821675 | ||||||||
\(222\) | 2.06339 | 0.138485 | ||||||||
\(223\) | −6.60472 | −0.442285 | −0.221142 | − | 0.975242i | \(-0.570979\pi\) | ||||
−0.221142 | + | 0.975242i | \(0.570979\pi\) | |||||||
\(224\) | 37.1695 | 2.48349 | ||||||||
\(225\) | −5.39708 | −0.359805 | ||||||||
\(226\) | 15.9885 | 1.06354 | ||||||||
\(227\) | 25.9948 | 1.72534 | 0.862668 | − | 0.505771i | \(-0.168792\pi\) | ||||
0.862668 | + | 0.505771i | \(0.168792\pi\) | |||||||
\(228\) | −2.53875 | −0.168133 | ||||||||
\(229\) | −1.96242 | −0.129680 | −0.0648400 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648400 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(230\) | −28.0108 | −1.84698 | ||||||||
\(231\) | −0.0983204 | −0.00646901 | ||||||||
\(232\) | 69.6666 | 4.57384 | ||||||||
\(233\) | 5.11916 | 0.335367 | 0.167684 | − | 0.985841i | \(-0.446371\pi\) | ||||
0.167684 | + | 0.985841i | \(0.446371\pi\) | |||||||
\(234\) | 27.2581 | 1.78192 | ||||||||
\(235\) | 2.32882 | 0.151916 | ||||||||
\(236\) | 50.4665 | 3.28509 | ||||||||
\(237\) | 1.09261 | 0.0709725 | ||||||||
\(238\) | −19.1914 | −1.24399 | ||||||||
\(239\) | −8.17753 | −0.528960 | −0.264480 | − | 0.964391i | \(-0.585200\pi\) | ||||
−0.264480 | + | 0.964391i | \(0.585200\pi\) | |||||||
\(240\) | −11.2324 | −0.725050 | ||||||||
\(241\) | −19.4770 | −1.25462 | −0.627312 | − | 0.778768i | \(-0.715845\pi\) | ||||
−0.627312 | + | 0.778768i | \(0.715845\pi\) | |||||||
\(242\) | 29.6267 | 1.90448 | ||||||||
\(243\) | 8.27503 | 0.530843 | ||||||||
\(244\) | −61.8181 | −3.95750 | ||||||||
\(245\) | 7.54789 | 0.482217 | ||||||||
\(246\) | 8.22541 | 0.524433 | ||||||||
\(247\) | −5.21695 | −0.331947 | ||||||||
\(248\) | −10.0497 | −0.638157 | ||||||||
\(249\) | 4.42603 | 0.280488 | ||||||||
\(250\) | −22.1798 | −1.40277 | ||||||||
\(251\) | −11.5525 | −0.729190 | −0.364595 | − | 0.931166i | \(-0.618793\pi\) | ||||
−0.364595 | + | 0.931166i | \(0.618793\pi\) | |||||||
\(252\) | 31.0672 | 1.95705 | ||||||||
\(253\) | −0.597776 | −0.0375819 | ||||||||
\(254\) | −22.4004 | −1.40553 | ||||||||
\(255\) | 2.94700 | 0.184548 | ||||||||
\(256\) | 21.2040 | 1.32525 | ||||||||
\(257\) | 13.3817 | 0.834725 | 0.417363 | − | 0.908740i | \(-0.362954\pi\) | ||||
0.417363 | + | 0.908740i | \(0.362954\pi\) | |||||||
\(258\) | −9.43053 | −0.587119 | ||||||||
\(259\) | 4.83263 | 0.300285 | ||||||||
\(260\) | −48.2620 | −2.99308 | ||||||||
\(261\) | 22.7689 | 1.40936 | ||||||||
\(262\) | 11.0818 | 0.684635 | ||||||||
\(263\) | 1.06515 | 0.0656799 | 0.0328399 | − | 0.999461i | \(-0.489545\pi\) | ||||
0.0328399 | + | 0.999461i | \(0.489545\pi\) | |||||||
\(264\) | −0.429413 | −0.0264286 | ||||||||
\(265\) | 11.2032 | 0.688208 | ||||||||
\(266\) | −8.19646 | −0.502557 | ||||||||
\(267\) | −5.11764 | −0.313194 | ||||||||
\(268\) | −38.3801 | −2.34444 | ||||||||
\(269\) | 28.8216 | 1.75729 | 0.878643 | − | 0.477480i | \(-0.158450\pi\) | ||||
0.878643 | + | 0.477480i | \(0.158450\pi\) | |||||||
\(270\) | −13.3865 | −0.814678 | ||||||||
\(271\) | 25.9706 | 1.57760 | 0.788802 | − | 0.614647i | \(-0.210702\pi\) | ||||
0.788802 | + | 0.614647i | \(0.210702\pi\) | |||||||
\(272\) | −46.7895 | −2.83703 | ||||||||
\(273\) | −2.27169 | −0.137489 | ||||||||
\(274\) | 33.6191 | 2.03101 | ||||||||
\(275\) | 0.281116 | 0.0169519 | ||||||||
\(276\) | −6.72123 | −0.404570 | ||||||||
\(277\) | −9.11553 | −0.547699 | −0.273850 | − | 0.961773i | \(-0.588297\pi\) | ||||
−0.273850 | + | 0.961773i | \(0.588297\pi\) | |||||||
\(278\) | −5.22729 | −0.313512 | ||||||||
\(279\) | −3.28450 | −0.196638 | ||||||||
\(280\) | −47.1265 | −2.81635 | ||||||||
\(281\) | −15.6130 | −0.931395 | −0.465697 | − | 0.884944i | \(-0.654196\pi\) | ||||
−0.465697 | + | 0.884944i | \(0.654196\pi\) | |||||||
\(282\) | 0.770305 | 0.0458710 | ||||||||
\(283\) | −7.36902 | −0.438043 | −0.219021 | − | 0.975720i | \(-0.570286\pi\) | ||||
−0.219021 | + | 0.975720i | \(0.570286\pi\) | |||||||
\(284\) | 20.1632 | 1.19647 | ||||||||
\(285\) | 1.25864 | 0.0745552 | ||||||||
\(286\) | −1.41978 | −0.0839535 | ||||||||
\(287\) | 19.2646 | 1.13715 | ||||||||
\(288\) | 53.0561 | 3.12636 | ||||||||
\(289\) | −4.72405 | −0.277885 | ||||||||
\(290\) | −55.5718 | −3.26329 | ||||||||
\(291\) | −0.968780 | −0.0567909 | ||||||||
\(292\) | −75.9152 | −4.44260 | ||||||||
\(293\) | −8.21519 | −0.479936 | −0.239968 | − | 0.970781i | \(-0.577137\pi\) | ||||
−0.239968 | + | 0.970781i | \(0.577137\pi\) | |||||||
\(294\) | 2.49662 | 0.145606 | ||||||||
\(295\) | −25.0197 | −1.45670 | ||||||||
\(296\) | 21.1064 | 1.22679 | ||||||||
\(297\) | −0.285681 | −0.0165769 | ||||||||
\(298\) | 2.22766 | 0.129045 | ||||||||
\(299\) | −13.8116 | −0.798747 | ||||||||
\(300\) | 3.16079 | 0.182488 | ||||||||
\(301\) | −22.0871 | −1.27308 | ||||||||
\(302\) | 24.6633 | 1.41921 | ||||||||
\(303\) | −6.35799 | −0.365257 | ||||||||
\(304\) | −19.9834 | −1.14613 | ||||||||
\(305\) | 30.6475 | 1.75487 | ||||||||
\(306\) | −27.3939 | −1.56601 | ||||||||
\(307\) | −19.0269 | −1.08592 | −0.542960 | − | 0.839759i | \(-0.682697\pi\) | ||||
−0.542960 | + | 0.839759i | \(0.682697\pi\) | |||||||
\(308\) | −1.61819 | −0.0922047 | ||||||||
\(309\) | −5.17325 | −0.294296 | ||||||||
\(310\) | 8.01646 | 0.455305 | ||||||||
\(311\) | 0.268523 | 0.0152265 | 0.00761326 | − | 0.999971i | \(-0.497577\pi\) | ||||
0.00761326 | + | 0.999971i | \(0.497577\pi\) | |||||||
\(312\) | −9.92160 | −0.561700 | ||||||||
\(313\) | −21.2263 | −1.19978 | −0.599892 | − | 0.800081i | \(-0.704790\pi\) | ||||
−0.599892 | + | 0.800081i | \(0.704790\pi\) | |||||||
\(314\) | −15.3523 | −0.866380 | ||||||||
\(315\) | −15.4022 | −0.867814 | ||||||||
\(316\) | 17.9825 | 1.01159 | ||||||||
\(317\) | 3.28812 | 0.184679 | 0.0923396 | − | 0.995728i | \(-0.470565\pi\) | ||||
0.0923396 | + | 0.995728i | \(0.470565\pi\) | |||||||
\(318\) | 3.70569 | 0.207805 | ||||||||
\(319\) | −1.18595 | −0.0664006 | ||||||||
\(320\) | −59.5240 | −3.32749 | ||||||||
\(321\) | 0.0701415 | 0.00391492 | ||||||||
\(322\) | −21.6997 | −1.20928 | ||||||||
\(323\) | 5.24295 | 0.291725 | ||||||||
\(324\) | 42.7115 | 2.37286 | ||||||||
\(325\) | 6.49518 | 0.360288 | ||||||||
\(326\) | −18.6480 | −1.03282 | ||||||||
\(327\) | 0.512104 | 0.0283194 | ||||||||
\(328\) | 84.1380 | 4.64575 | ||||||||
\(329\) | 1.80412 | 0.0994643 | ||||||||
\(330\) | 0.342535 | 0.0188559 | ||||||||
\(331\) | −19.2202 | −1.05644 | −0.528219 | − | 0.849108i | \(-0.677140\pi\) | ||||
−0.528219 | + | 0.849108i | \(0.677140\pi\) | |||||||
\(332\) | 72.8449 | 3.99788 | ||||||||
\(333\) | 6.89814 | 0.378016 | ||||||||
\(334\) | 9.61076 | 0.525877 | ||||||||
\(335\) | 19.0277 | 1.03959 | ||||||||
\(336\) | −8.70167 | −0.474715 | ||||||||
\(337\) | 9.01642 | 0.491155 | 0.245578 | − | 0.969377i | \(-0.421022\pi\) | ||||
0.245578 | + | 0.969377i | \(0.421022\pi\) | |||||||
\(338\) | 2.28194 | 0.124121 | ||||||||
\(339\) | −1.90200 | −0.103303 | ||||||||
\(340\) | 48.5025 | 2.63042 | ||||||||
\(341\) | 0.171079 | 0.00926443 | ||||||||
\(342\) | −11.6997 | −0.632647 | ||||||||
\(343\) | 20.0537 | 1.08280 | ||||||||
\(344\) | −96.4653 | −5.20106 | ||||||||
\(345\) | 3.33218 | 0.179399 | ||||||||
\(346\) | 33.4653 | 1.79911 | ||||||||
\(347\) | −11.1957 | −0.601019 | −0.300509 | − | 0.953779i | \(-0.597157\pi\) | ||||
−0.300509 | + | 0.953779i | \(0.597157\pi\) | |||||||
\(348\) | −13.3345 | −0.714806 | ||||||||
\(349\) | −22.4501 | −1.20172 | −0.600862 | − | 0.799352i | \(-0.705176\pi\) | ||||
−0.600862 | + | 0.799352i | \(0.705176\pi\) | |||||||
\(350\) | 10.2047 | 0.545465 | ||||||||
\(351\) | −6.60066 | −0.352317 | ||||||||
\(352\) | −2.76351 | −0.147296 | ||||||||
\(353\) | 27.9339 | 1.48677 | 0.743385 | − | 0.668864i | \(-0.233219\pi\) | ||||
0.743385 | + | 0.668864i | \(0.233219\pi\) | |||||||
\(354\) | −8.27578 | −0.439853 | ||||||||
\(355\) | −9.99632 | −0.530549 | ||||||||
\(356\) | −84.2276 | −4.46405 | ||||||||
\(357\) | 2.28302 | 0.120830 | ||||||||
\(358\) | −38.1549 | −2.01655 | ||||||||
\(359\) | −12.4775 | −0.658535 | −0.329268 | − | 0.944237i | \(-0.606802\pi\) | ||||
−0.329268 | + | 0.944237i | \(0.606802\pi\) | |||||||
\(360\) | −67.2688 | −3.54538 | ||||||||
\(361\) | −16.7608 | −0.882146 | ||||||||
\(362\) | −30.7294 | −1.61510 | ||||||||
\(363\) | −3.52441 | −0.184984 | ||||||||
\(364\) | −37.3882 | −1.95967 | ||||||||
\(365\) | 37.6365 | 1.96998 | ||||||||
\(366\) | 10.1373 | 0.529884 | ||||||||
\(367\) | 14.0317 | 0.732448 | 0.366224 | − | 0.930527i | \(-0.380650\pi\) | ||||
0.366224 | + | 0.930527i | \(0.380650\pi\) | |||||||
\(368\) | −52.9051 | −2.75787 | ||||||||
\(369\) | 27.4985 | 1.43152 | ||||||||
\(370\) | −16.8362 | −0.875274 | ||||||||
\(371\) | 8.67904 | 0.450593 | ||||||||
\(372\) | 1.92356 | 0.0997321 | ||||||||
\(373\) | 4.17402 | 0.216122 | 0.108061 | − | 0.994144i | \(-0.465536\pi\) | ||||
0.108061 | + | 0.994144i | \(0.465536\pi\) | |||||||
\(374\) | 1.42686 | 0.0737810 | ||||||||
\(375\) | 2.63852 | 0.136253 | ||||||||
\(376\) | 7.87947 | 0.406353 | ||||||||
\(377\) | −27.4015 | −1.41125 | ||||||||
\(378\) | −10.3704 | −0.533398 | ||||||||
\(379\) | −0.810957 | −0.0416560 | −0.0208280 | − | 0.999783i | \(-0.506630\pi\) | ||||
−0.0208280 | + | 0.999783i | \(0.506630\pi\) | |||||||
\(380\) | 20.7150 | 1.06266 | ||||||||
\(381\) | 2.66477 | 0.136520 | ||||||||
\(382\) | 51.6166 | 2.64094 | ||||||||
\(383\) | −17.1420 | −0.875914 | −0.437957 | − | 0.898996i | \(-0.644298\pi\) | ||||
−0.437957 | + | 0.898996i | \(0.644298\pi\) | |||||||
\(384\) | −7.92833 | −0.404591 | ||||||||
\(385\) | 0.802247 | 0.0408863 | ||||||||
\(386\) | −49.4121 | −2.51501 | ||||||||
\(387\) | −31.5274 | −1.60263 | ||||||||
\(388\) | −15.9445 | −0.809458 | ||||||||
\(389\) | 30.1258 | 1.52744 | 0.763720 | − | 0.645548i | \(-0.223371\pi\) | ||||
0.763720 | + | 0.645548i | \(0.223371\pi\) | |||||||
\(390\) | 7.91428 | 0.400755 | ||||||||
\(391\) | 13.8805 | 0.701965 | ||||||||
\(392\) | 25.5380 | 1.28986 | ||||||||
\(393\) | −1.31830 | −0.0664992 | ||||||||
\(394\) | 10.3901 | 0.523445 | ||||||||
\(395\) | −8.91516 | −0.448570 | ||||||||
\(396\) | −2.30981 | −0.116073 | ||||||||
\(397\) | 27.5147 | 1.38092 | 0.690461 | − | 0.723370i | \(-0.257408\pi\) | ||||
0.690461 | + | 0.723370i | \(0.257408\pi\) | |||||||
\(398\) | 45.1242 | 2.26187 | ||||||||
\(399\) | 0.975056 | 0.0488138 | ||||||||
\(400\) | 24.8796 | 1.24398 | ||||||||
\(401\) | 0.582299 | 0.0290786 | 0.0145393 | − | 0.999894i | \(-0.495372\pi\) | ||||
0.0145393 | + | 0.999894i | \(0.495372\pi\) | |||||||
\(402\) | 6.29378 | 0.313905 | ||||||||
\(403\) | 3.95278 | 0.196902 | ||||||||
\(404\) | −104.642 | −5.20612 | ||||||||
\(405\) | −21.1750 | −1.05220 | ||||||||
\(406\) | −43.0510 | −2.13659 | ||||||||
\(407\) | −0.359301 | −0.0178099 | ||||||||
\(408\) | 9.97104 | 0.493640 | ||||||||
\(409\) | −1.33729 | −0.0661249 | −0.0330624 | − | 0.999453i | \(-0.510526\pi\) | ||||
−0.0330624 | + | 0.999453i | \(0.510526\pi\) | |||||||
\(410\) | −67.1154 | −3.31459 | ||||||||
\(411\) | −3.99935 | −0.197274 | ||||||||
\(412\) | −85.1428 | −4.19469 | ||||||||
\(413\) | −19.3826 | −0.953755 | ||||||||
\(414\) | −30.9744 | −1.52231 | ||||||||
\(415\) | −36.1143 | −1.77278 | ||||||||
\(416\) | −63.8510 | −3.13055 | ||||||||
\(417\) | 0.621842 | 0.0304517 | ||||||||
\(418\) | 0.609398 | 0.0298066 | ||||||||
\(419\) | 24.4002 | 1.19203 | 0.596013 | − | 0.802975i | \(-0.296751\pi\) | ||||
0.596013 | + | 0.802975i | \(0.296751\pi\) | |||||||
\(420\) | 9.02024 | 0.440143 | ||||||||
\(421\) | 35.0410 | 1.70779 | 0.853896 | − | 0.520444i | \(-0.174233\pi\) | ||||
0.853896 | + | 0.520444i | \(0.174233\pi\) | |||||||
\(422\) | −19.0672 | −0.928176 | ||||||||
\(423\) | 2.57522 | 0.125211 | ||||||||
\(424\) | 37.9056 | 1.84086 | ||||||||
\(425\) | −6.52755 | −0.316633 | ||||||||
\(426\) | −3.30648 | −0.160200 | ||||||||
\(427\) | 23.7424 | 1.14897 | ||||||||
\(428\) | 1.15441 | 0.0558005 | ||||||||
\(429\) | 0.168898 | 0.00815448 | ||||||||
\(430\) | 76.9486 | 3.71079 | ||||||||
\(431\) | 24.9028 | 1.19952 | 0.599762 | − | 0.800178i | \(-0.295262\pi\) | ||||
0.599762 | + | 0.800178i | \(0.295262\pi\) | |||||||
\(432\) | −25.2837 | −1.21646 | ||||||||
\(433\) | 5.34569 | 0.256897 | 0.128449 | − | 0.991716i | \(-0.459000\pi\) | ||||
0.128449 | + | 0.991716i | \(0.459000\pi\) | |||||||
\(434\) | 6.21029 | 0.298103 | ||||||||
\(435\) | 6.61085 | 0.316966 | ||||||||
\(436\) | 8.42835 | 0.403645 | ||||||||
\(437\) | 5.92822 | 0.283585 | ||||||||
\(438\) | 12.4490 | 0.594837 | ||||||||
\(439\) | −5.57270 | −0.265971 | −0.132985 | − | 0.991118i | \(-0.542456\pi\) | ||||
−0.132985 | + | 0.991118i | \(0.542456\pi\) | |||||||
\(440\) | 3.50381 | 0.167037 | ||||||||
\(441\) | 8.34648 | 0.397452 | ||||||||
\(442\) | 32.9676 | 1.56811 | ||||||||
\(443\) | 35.9211 | 1.70666 | 0.853330 | − | 0.521370i | \(-0.174579\pi\) | ||||
0.853330 | + | 0.521370i | \(0.174579\pi\) | |||||||
\(444\) | −4.03988 | −0.191724 | ||||||||
\(445\) | 41.7574 | 1.97949 | ||||||||
\(446\) | 17.8256 | 0.844069 | ||||||||
\(447\) | −0.265003 | −0.0125342 | ||||||||
\(448\) | −46.1128 | −2.17862 | ||||||||
\(449\) | −18.0345 | −0.851101 | −0.425550 | − | 0.904935i | \(-0.639920\pi\) | ||||
−0.425550 | + | 0.904935i | \(0.639920\pi\) | |||||||
\(450\) | 14.5663 | 0.686663 | ||||||||
\(451\) | −1.43230 | −0.0674446 | ||||||||
\(452\) | −31.3037 | −1.47240 | ||||||||
\(453\) | −2.93396 | −0.137849 | ||||||||
\(454\) | −70.1580 | −3.29268 | ||||||||
\(455\) | 18.5359 | 0.868978 | ||||||||
\(456\) | 4.25854 | 0.199425 | ||||||||
\(457\) | 30.3530 | 1.41985 | 0.709927 | − | 0.704275i | \(-0.248728\pi\) | ||||
0.709927 | + | 0.704275i | \(0.248728\pi\) | |||||||
\(458\) | 5.29641 | 0.247485 | ||||||||
\(459\) | 6.63356 | 0.309628 | ||||||||
\(460\) | 54.8420 | 2.55702 | ||||||||
\(461\) | −14.4558 | −0.673273 | −0.336636 | − | 0.941635i | \(-0.609289\pi\) | ||||
−0.336636 | + | 0.941635i | \(0.609289\pi\) | |||||||
\(462\) | 0.265359 | 0.0123456 | ||||||||
\(463\) | 23.0813 | 1.07268 | 0.536340 | − | 0.844002i | \(-0.319806\pi\) | ||||
0.536340 | + | 0.844002i | \(0.319806\pi\) | |||||||
\(464\) | −104.961 | −4.87268 | ||||||||
\(465\) | −0.953643 | −0.0442242 | ||||||||
\(466\) | −13.8162 | −0.640024 | ||||||||
\(467\) | 25.1060 | 1.16177 | 0.580884 | − | 0.813986i | \(-0.302707\pi\) | ||||
0.580884 | + | 0.813986i | \(0.302707\pi\) | |||||||
\(468\) | −53.3683 | −2.46695 | ||||||||
\(469\) | 14.7406 | 0.680657 | ||||||||
\(470\) | −6.28531 | −0.289920 | ||||||||
\(471\) | 1.82632 | 0.0841523 | ||||||||
\(472\) | −84.6532 | −3.89648 | ||||||||
\(473\) | 1.64215 | 0.0755064 | ||||||||
\(474\) | −2.94887 | −0.135446 | ||||||||
\(475\) | −2.78786 | −0.127916 | ||||||||
\(476\) | 37.5745 | 1.72223 | ||||||||
\(477\) | 12.3885 | 0.567233 | ||||||||
\(478\) | 22.0705 | 1.00948 | ||||||||
\(479\) | −6.37443 | −0.291255 | −0.145628 | − | 0.989339i | \(-0.546520\pi\) | ||||
−0.145628 | + | 0.989339i | \(0.546520\pi\) | |||||||
\(480\) | 15.4046 | 0.703122 | ||||||||
\(481\) | −8.30165 | −0.378523 | ||||||||
\(482\) | 52.5669 | 2.39436 | ||||||||
\(483\) | 2.58141 | 0.117458 | ||||||||
\(484\) | −58.0058 | −2.63663 | ||||||||
\(485\) | 7.90478 | 0.358938 | ||||||||
\(486\) | −22.3337 | −1.01308 | ||||||||
\(487\) | 30.9180 | 1.40103 | 0.700514 | − | 0.713639i | \(-0.252954\pi\) | ||||
0.700514 | + | 0.713639i | \(0.252954\pi\) | |||||||
\(488\) | 103.695 | 4.69403 | ||||||||
\(489\) | 2.21838 | 0.100318 | ||||||||
\(490\) | −20.3712 | −0.920277 | ||||||||
\(491\) | 26.9153 | 1.21467 | 0.607335 | − | 0.794446i | \(-0.292239\pi\) | ||||
0.607335 | + | 0.794446i | \(0.292239\pi\) | |||||||
\(492\) | −16.1044 | −0.726044 | ||||||||
\(493\) | 27.5380 | 1.24025 | ||||||||
\(494\) | 14.0802 | 0.633496 | ||||||||
\(495\) | 1.14514 | 0.0514700 | ||||||||
\(496\) | 15.1410 | 0.679852 | ||||||||
\(497\) | −7.74407 | −0.347369 | ||||||||
\(498\) | −11.9455 | −0.535291 | ||||||||
\(499\) | −15.7800 | −0.706408 | −0.353204 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353204 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(500\) | 43.4256 | 1.94205 | ||||||||
\(501\) | −1.14330 | −0.0510789 | ||||||||
\(502\) | 31.1794 | 1.39161 | ||||||||
\(503\) | −41.0705 | −1.83124 | −0.915621 | − | 0.402043i | \(-0.868300\pi\) | ||||
−0.915621 | + | 0.402043i | \(0.868300\pi\) | |||||||
\(504\) | −52.1126 | −2.32128 | ||||||||
\(505\) | 51.8781 | 2.30855 | ||||||||
\(506\) | 1.61335 | 0.0717223 | ||||||||
\(507\) | −0.271461 | −0.0120560 | ||||||||
\(508\) | 43.8575 | 1.94586 | ||||||||
\(509\) | −14.8275 | −0.657220 | −0.328610 | − | 0.944466i | \(-0.606580\pi\) | ||||
−0.328610 | + | 0.944466i | \(0.606580\pi\) | |||||||
\(510\) | −7.95372 | −0.352197 | ||||||||
\(511\) | 29.1567 | 1.28981 | ||||||||
\(512\) | −7.84041 | −0.346501 | ||||||||
\(513\) | 2.83313 | 0.125086 | ||||||||
\(514\) | −36.1161 | −1.59301 | ||||||||
\(515\) | 42.2112 | 1.86005 | ||||||||
\(516\) | 18.4639 | 0.812829 | ||||||||
\(517\) | −0.134134 | −0.00589923 | ||||||||
\(518\) | −13.0429 | −0.573072 | ||||||||
\(519\) | −3.98105 | −0.174749 | ||||||||
\(520\) | 80.9555 | 3.55013 | ||||||||
\(521\) | −29.9782 | −1.31337 | −0.656683 | − | 0.754166i | \(-0.728041\pi\) | ||||
−0.656683 | + | 0.754166i | \(0.728041\pi\) | |||||||
\(522\) | −61.4514 | −2.68966 | ||||||||
\(523\) | −22.3504 | −0.977315 | −0.488657 | − | 0.872476i | \(-0.662513\pi\) | ||||
−0.488657 | + | 0.872476i | \(0.662513\pi\) | |||||||
\(524\) | −21.6969 | −0.947833 | ||||||||
\(525\) | −1.21396 | −0.0529815 | ||||||||
\(526\) | −2.87476 | −0.125345 | ||||||||
\(527\) | −3.97248 | −0.173044 | ||||||||
\(528\) | 0.646960 | 0.0281553 | ||||||||
\(529\) | −7.30532 | −0.317623 | ||||||||
\(530\) | −30.2366 | −1.31340 | ||||||||
\(531\) | −27.6669 | −1.20064 | ||||||||
\(532\) | 16.0477 | 0.695758 | ||||||||
\(533\) | −33.0934 | −1.43344 | ||||||||
\(534\) | 13.8121 | 0.597709 | ||||||||
\(535\) | −0.572321 | −0.0247436 | ||||||||
\(536\) | 64.3793 | 2.78076 | ||||||||
\(537\) | 4.53893 | 0.195869 | ||||||||
\(538\) | −77.7874 | −3.35365 | ||||||||
\(539\) | −0.434740 | −0.0187256 | ||||||||
\(540\) | 26.2093 | 1.12787 | ||||||||
\(541\) | −4.10382 | −0.176437 | −0.0882185 | − | 0.996101i | \(-0.528117\pi\) | ||||
−0.0882185 | + | 0.996101i | \(0.528117\pi\) | |||||||
\(542\) | −70.0928 | −3.01074 | ||||||||
\(543\) | 3.65559 | 0.156876 | ||||||||
\(544\) | 64.1692 | 2.75123 | ||||||||
\(545\) | −4.17852 | −0.178988 | ||||||||
\(546\) | 6.13113 | 0.262388 | ||||||||
\(547\) | −18.2627 | −0.780858 | −0.390429 | − | 0.920633i | \(-0.627673\pi\) | ||||
−0.390429 | + | 0.920633i | \(0.627673\pi\) | |||||||
\(548\) | −65.8225 | −2.81180 | ||||||||
\(549\) | 33.8901 | 1.44639 | ||||||||
\(550\) | −0.758710 | −0.0323515 | ||||||||
\(551\) | 11.7612 | 0.501046 | ||||||||
\(552\) | 11.2743 | 0.479866 | ||||||||
\(553\) | −6.90650 | −0.293694 | ||||||||
\(554\) | 24.6021 | 1.04524 | ||||||||
\(555\) | 2.00285 | 0.0850162 | ||||||||
\(556\) | 10.2344 | 0.434037 | ||||||||
\(557\) | −40.0463 | −1.69682 | −0.848409 | − | 0.529342i | \(-0.822439\pi\) | ||||
−0.848409 | + | 0.529342i | \(0.822439\pi\) | |||||||
\(558\) | 8.86463 | 0.375270 | ||||||||
\(559\) | 37.9420 | 1.60478 | ||||||||
\(560\) | 71.0014 | 3.00036 | ||||||||
\(561\) | −0.169740 | −0.00716642 | ||||||||
\(562\) | 42.1384 | 1.77750 | ||||||||
\(563\) | 20.1687 | 0.850007 | 0.425004 | − | 0.905192i | \(-0.360273\pi\) | ||||
0.425004 | + | 0.905192i | \(0.360273\pi\) | |||||||
\(564\) | −1.50817 | −0.0635054 | ||||||||
\(565\) | 15.5194 | 0.652907 | ||||||||
\(566\) | 19.8884 | 0.835973 | ||||||||
\(567\) | −16.4041 | −0.688909 | ||||||||
\(568\) | −33.8221 | −1.41915 | ||||||||
\(569\) | −16.7148 | −0.700720 | −0.350360 | − | 0.936615i | \(-0.613941\pi\) | ||||
−0.350360 | + | 0.936615i | \(0.613941\pi\) | |||||||
\(570\) | −3.39696 | −0.142283 | ||||||||
\(571\) | 4.23284 | 0.177139 | 0.0885693 | − | 0.996070i | \(-0.471771\pi\) | ||||
0.0885693 | + | 0.996070i | \(0.471771\pi\) | |||||||
\(572\) | 2.77977 | 0.116228 | ||||||||
\(573\) | −6.14035 | −0.256517 | ||||||||
\(574\) | −51.9938 | −2.17018 | ||||||||
\(575\) | −7.38073 | −0.307798 | ||||||||
\(576\) | −65.8218 | −2.74257 | ||||||||
\(577\) | −21.5958 | −0.899045 | −0.449522 | − | 0.893269i | \(-0.648406\pi\) | ||||
−0.449522 | + | 0.893269i | \(0.648406\pi\) | |||||||
\(578\) | 12.7499 | 0.530324 | ||||||||
\(579\) | 5.87809 | 0.244285 | ||||||||
\(580\) | 108.803 | 4.51781 | ||||||||
\(581\) | −27.9774 | −1.16070 | ||||||||
\(582\) | 2.61466 | 0.108381 | ||||||||
\(583\) | −0.645278 | −0.0267247 | ||||||||
\(584\) | 127.341 | 5.26942 | ||||||||
\(585\) | 26.4584 | 1.09392 | ||||||||
\(586\) | 22.1722 | 0.915924 | ||||||||
\(587\) | −13.0995 | −0.540672 | −0.270336 | − | 0.962766i | \(-0.587135\pi\) | ||||
−0.270336 | + | 0.962766i | \(0.587135\pi\) | |||||||
\(588\) | −4.88810 | −0.201582 | ||||||||
\(589\) | −1.69661 | −0.0699076 | ||||||||
\(590\) | 67.5264 | 2.78002 | ||||||||
\(591\) | −1.23601 | −0.0508427 | ||||||||
\(592\) | −31.7993 | −1.30694 | ||||||||
\(593\) | −8.44535 | −0.346809 | −0.173404 | − | 0.984851i | \(-0.555477\pi\) | ||||
−0.173404 | + | 0.984851i | \(0.555477\pi\) | |||||||
\(594\) | 0.771031 | 0.0316358 | ||||||||
\(595\) | −18.6283 | −0.763686 | ||||||||
\(596\) | −4.36150 | −0.178654 | ||||||||
\(597\) | −5.36801 | −0.219698 | ||||||||
\(598\) | 37.2765 | 1.52435 | ||||||||
\(599\) | −12.3576 | −0.504918 | −0.252459 | − | 0.967608i | \(-0.581239\pi\) | ||||
−0.252459 | + | 0.967608i | \(0.581239\pi\) | |||||||
\(600\) | −5.30195 | −0.216451 | ||||||||
\(601\) | −12.5192 | −0.510671 | −0.255335 | − | 0.966853i | \(-0.582186\pi\) | ||||
−0.255335 | + | 0.966853i | \(0.582186\pi\) | |||||||
\(602\) | 59.6115 | 2.42958 | ||||||||
\(603\) | 21.0408 | 0.856849 | ||||||||
\(604\) | −48.2879 | −1.96481 | ||||||||
\(605\) | 28.7575 | 1.16916 | ||||||||
\(606\) | 17.1597 | 0.697066 | ||||||||
\(607\) | 13.2252 | 0.536794 | 0.268397 | − | 0.963308i | \(-0.413506\pi\) | ||||
0.268397 | + | 0.963308i | \(0.413506\pi\) | |||||||
\(608\) | 27.4061 | 1.11146 | ||||||||
\(609\) | 5.12138 | 0.207529 | ||||||||
\(610\) | −82.7153 | −3.34904 | ||||||||
\(611\) | −3.09918 | −0.125379 | ||||||||
\(612\) | 53.6342 | 2.16804 | ||||||||
\(613\) | 32.2352 | 1.30197 | 0.650984 | − | 0.759091i | \(-0.274356\pi\) | ||||
0.650984 | + | 0.759091i | \(0.274356\pi\) | |||||||
\(614\) | 51.3520 | 2.07240 | ||||||||
\(615\) | 7.98409 | 0.321950 | ||||||||
\(616\) | 2.71437 | 0.109365 | ||||||||
\(617\) | 40.2697 | 1.62120 | 0.810598 | − | 0.585603i | \(-0.199142\pi\) | ||||
0.810598 | + | 0.585603i | \(0.199142\pi\) | |||||||
\(618\) | 13.9622 | 0.561642 | ||||||||
\(619\) | 37.3605 | 1.50165 | 0.750823 | − | 0.660503i | \(-0.229657\pi\) | ||||
0.750823 | + | 0.660503i | \(0.229657\pi\) | |||||||
\(620\) | −15.6953 | −0.630340 | ||||||||
\(621\) | 7.50058 | 0.300988 | ||||||||
\(622\) | −0.724723 | −0.0290587 | ||||||||
\(623\) | 32.3492 | 1.29604 | ||||||||
\(624\) | 14.9480 | 0.598400 | ||||||||
\(625\) | −30.8443 | −1.23377 | ||||||||
\(626\) | 57.2883 | 2.28970 | ||||||||
\(627\) | −0.0724944 | −0.00289515 | ||||||||
\(628\) | 30.0581 | 1.19945 | ||||||||
\(629\) | 8.34302 | 0.332658 | ||||||||
\(630\) | 41.5693 | 1.65616 | ||||||||
\(631\) | −26.8311 | −1.06813 | −0.534065 | − | 0.845443i | \(-0.679336\pi\) | ||||
−0.534065 | + | 0.845443i | \(0.679336\pi\) | |||||||
\(632\) | −30.1641 | −1.19986 | ||||||||
\(633\) | 2.26824 | 0.0901546 | ||||||||
\(634\) | −8.87439 | −0.352447 | ||||||||
\(635\) | −21.7432 | −0.862853 | ||||||||
\(636\) | −7.25532 | −0.287692 | ||||||||
\(637\) | −10.0447 | −0.397985 | ||||||||
\(638\) | 3.20080 | 0.126721 | ||||||||
\(639\) | −11.0540 | −0.437288 | ||||||||
\(640\) | 64.6913 | 2.55715 | ||||||||
\(641\) | −7.11609 | −0.281069 | −0.140534 | − | 0.990076i | \(-0.544882\pi\) | ||||
−0.140534 | + | 0.990076i | \(0.544882\pi\) | |||||||
\(642\) | −0.189307 | −0.00747134 | ||||||||
\(643\) | 6.71188 | 0.264691 | 0.132345 | − | 0.991204i | \(-0.457749\pi\) | ||||
0.132345 | + | 0.991204i | \(0.457749\pi\) | |||||||
\(644\) | 42.4856 | 1.67417 | ||||||||
\(645\) | −9.15385 | −0.360433 | ||||||||
\(646\) | −14.1503 | −0.556737 | ||||||||
\(647\) | 39.2170 | 1.54178 | 0.770890 | − | 0.636968i | \(-0.219812\pi\) | ||||
0.770890 | + | 0.636968i | \(0.219812\pi\) | |||||||
\(648\) | −71.6449 | −2.81448 | ||||||||
\(649\) | 1.44107 | 0.0565671 | ||||||||
\(650\) | −17.5300 | −0.687584 | ||||||||
\(651\) | −0.738780 | −0.0289551 | ||||||||
\(652\) | 36.5107 | 1.42987 | ||||||||
\(653\) | 17.2677 | 0.675736 | 0.337868 | − | 0.941193i | \(-0.390294\pi\) | ||||
0.337868 | + | 0.941193i | \(0.390294\pi\) | |||||||
\(654\) | −1.38213 | −0.0540455 | ||||||||
\(655\) | 10.7567 | 0.420297 | ||||||||
\(656\) | −126.764 | −4.94928 | ||||||||
\(657\) | 41.6185 | 1.62369 | ||||||||
\(658\) | −4.86918 | −0.189820 | ||||||||
\(659\) | −21.8381 | −0.850693 | −0.425347 | − | 0.905030i | \(-0.639848\pi\) | ||||
−0.425347 | + | 0.905030i | \(0.639848\pi\) | |||||||
\(660\) | −0.670646 | −0.0261048 | ||||||||
\(661\) | 12.9042 | 0.501915 | 0.250957 | − | 0.967998i | \(-0.419255\pi\) | ||||
0.250957 | + | 0.967998i | \(0.419255\pi\) | |||||||
\(662\) | 51.8739 | 2.01614 | ||||||||
\(663\) | −3.92184 | −0.152312 | ||||||||
\(664\) | −122.191 | −4.74194 | ||||||||
\(665\) | −7.95598 | −0.308520 | ||||||||
\(666\) | −18.6175 | −0.721415 | ||||||||
\(667\) | 31.1373 | 1.20564 | ||||||||
\(668\) | −18.8168 | −0.728043 | ||||||||
\(669\) | −2.12055 | −0.0819852 | ||||||||
\(670\) | −51.3542 | −1.98399 | ||||||||
\(671\) | −1.76522 | −0.0681456 | ||||||||
\(672\) | 11.9339 | 0.460358 | ||||||||
\(673\) | 10.2609 | 0.395529 | 0.197765 | − | 0.980250i | \(-0.436632\pi\) | ||||
0.197765 | + | 0.980250i | \(0.436632\pi\) | |||||||
\(674\) | −24.3346 | −0.937335 | ||||||||
\(675\) | −3.52729 | −0.135766 | ||||||||
\(676\) | −4.46778 | −0.171838 | ||||||||
\(677\) | −34.4667 | −1.32466 | −0.662331 | − | 0.749211i | \(-0.730433\pi\) | ||||
−0.662331 | + | 0.749211i | \(0.730433\pi\) | |||||||
\(678\) | 5.13336 | 0.197146 | ||||||||
\(679\) | 6.12377 | 0.235009 | ||||||||
\(680\) | −81.3589 | −3.11997 | ||||||||
\(681\) | 8.34604 | 0.319821 | ||||||||
\(682\) | −0.461729 | −0.0176805 | ||||||||
\(683\) | 20.5183 | 0.785111 | 0.392556 | − | 0.919728i | \(-0.371591\pi\) | ||||
0.392556 | + | 0.919728i | \(0.371591\pi\) | |||||||
\(684\) | 22.9067 | 0.875860 | ||||||||
\(685\) | 32.6328 | 1.24684 | ||||||||
\(686\) | −54.1235 | −2.06645 | ||||||||
\(687\) | −0.630064 | −0.0240385 | ||||||||
\(688\) | 145.336 | 5.54088 | ||||||||
\(689\) | −14.9091 | −0.567993 | ||||||||
\(690\) | −8.99330 | −0.342369 | ||||||||
\(691\) | 13.2697 | 0.504805 | 0.252402 | − | 0.967622i | \(-0.418779\pi\) | ||||
0.252402 | + | 0.967622i | \(0.418779\pi\) | |||||||
\(692\) | −65.5213 | −2.49075 | ||||||||
\(693\) | 0.887127 | 0.0336992 | ||||||||
\(694\) | 30.2164 | 1.14700 | ||||||||
\(695\) | −5.07393 | −0.192465 | ||||||||
\(696\) | 22.3675 | 0.847840 | ||||||||
\(697\) | 33.2583 | 1.25975 | ||||||||
\(698\) | 60.5911 | 2.29341 | ||||||||
\(699\) | 1.64359 | 0.0621661 | ||||||||
\(700\) | −19.9797 | −0.755162 | ||||||||
\(701\) | −23.7637 | −0.897542 | −0.448771 | − | 0.893647i | \(-0.648138\pi\) | ||||
−0.448771 | + | 0.893647i | \(0.648138\pi\) | |||||||
\(702\) | 17.8147 | 0.672372 | ||||||||
\(703\) | 3.56323 | 0.134390 | ||||||||
\(704\) | 3.42844 | 0.129214 | ||||||||
\(705\) | 0.747705 | 0.0281602 | ||||||||
\(706\) | −75.3914 | −2.83739 | ||||||||
\(707\) | 40.1896 | 1.51148 | ||||||||
\(708\) | 16.2030 | 0.608948 | ||||||||
\(709\) | 26.5440 | 0.996883 | 0.498441 | − | 0.866923i | \(-0.333906\pi\) | ||||
0.498441 | + | 0.866923i | \(0.333906\pi\) | |||||||
\(710\) | 26.9793 | 1.01252 | ||||||||
\(711\) | −9.85840 | −0.369719 | ||||||||
\(712\) | 141.285 | 5.29486 | ||||||||
\(713\) | −4.49169 | −0.168215 | ||||||||
\(714\) | −6.16168 | −0.230595 | ||||||||
\(715\) | −1.37813 | −0.0515390 | ||||||||
\(716\) | 74.7030 | 2.79178 | ||||||||
\(717\) | −2.62552 | −0.0980520 | ||||||||
\(718\) | 33.6757 | 1.25677 | ||||||||
\(719\) | 49.2247 | 1.83577 | 0.917886 | − | 0.396844i | \(-0.129895\pi\) | ||||
0.917886 | + | 0.396844i | \(0.129895\pi\) | |||||||
\(720\) | 101.348 | 3.77702 | ||||||||
\(721\) | 32.7007 | 1.21784 | ||||||||
\(722\) | 45.2361 | 1.68351 | ||||||||
\(723\) | −6.25339 | −0.232566 | ||||||||
\(724\) | 60.1647 | 2.23600 | ||||||||
\(725\) | −14.6429 | −0.543825 | ||||||||
\(726\) | 9.51212 | 0.353028 | ||||||||
\(727\) | −1.83788 | −0.0681631 | −0.0340815 | − | 0.999419i | \(-0.510851\pi\) | ||||
−0.0340815 | + | 0.999419i | \(0.510851\pi\) | |||||||
\(728\) | 62.7156 | 2.32439 | ||||||||
\(729\) | −21.5918 | −0.799697 | ||||||||
\(730\) | −101.578 | −3.75957 | ||||||||
\(731\) | −38.1311 | −1.41033 | ||||||||
\(732\) | −19.8477 | −0.733591 | ||||||||
\(733\) | 37.4778 | 1.38428 | 0.692138 | − | 0.721765i | \(-0.256669\pi\) | ||||
0.692138 | + | 0.721765i | \(0.256669\pi\) | |||||||
\(734\) | −37.8705 | −1.39782 | ||||||||
\(735\) | 2.42337 | 0.0893873 | ||||||||
\(736\) | 72.5564 | 2.67446 | ||||||||
\(737\) | −1.09595 | −0.0403697 | ||||||||
\(738\) | −74.2164 | −2.73194 | ||||||||
\(739\) | 31.9704 | 1.17605 | 0.588024 | − | 0.808843i | \(-0.299906\pi\) | ||||
0.588024 | + | 0.808843i | \(0.299906\pi\) | |||||||
\(740\) | 32.9635 | 1.21176 | ||||||||
\(741\) | −1.67498 | −0.0615320 | ||||||||
\(742\) | −23.4241 | −0.859925 | ||||||||
\(743\) | 25.3046 | 0.928334 | 0.464167 | − | 0.885748i | \(-0.346354\pi\) | ||||
0.464167 | + | 0.885748i | \(0.346354\pi\) | |||||||
\(744\) | −3.22661 | −0.118293 | ||||||||
\(745\) | 2.16230 | 0.0792205 | ||||||||
\(746\) | −11.2654 | −0.412454 | ||||||||
\(747\) | −39.9353 | −1.46115 | ||||||||
\(748\) | −2.79363 | −0.102145 | ||||||||
\(749\) | −0.443373 | −0.0162005 | ||||||||
\(750\) | −7.12117 | −0.260028 | ||||||||
\(751\) | −42.4211 | −1.54797 | −0.773984 | − | 0.633205i | \(-0.781739\pi\) | ||||
−0.773984 | + | 0.633205i | \(0.781739\pi\) | |||||||
\(752\) | −11.8713 | −0.432903 | ||||||||
\(753\) | −3.70913 | −0.135168 | ||||||||
\(754\) | 73.9545 | 2.69326 | ||||||||
\(755\) | 23.9397 | 0.871254 | ||||||||
\(756\) | 20.3042 | 0.738455 | ||||||||
\(757\) | 11.2347 | 0.408331 | 0.204165 | − | 0.978936i | \(-0.434552\pi\) | ||||
0.204165 | + | 0.978936i | \(0.434552\pi\) | |||||||
\(758\) | 2.18871 | 0.0794975 | ||||||||
\(759\) | −0.191925 | −0.00696645 | ||||||||
\(760\) | −34.7477 | −1.26043 | ||||||||
\(761\) | −2.74228 | −0.0994077 | −0.0497039 | − | 0.998764i | \(-0.515828\pi\) | ||||
−0.0497039 | + | 0.998764i | \(0.515828\pi\) | |||||||
\(762\) | −7.19200 | −0.260539 | ||||||||
\(763\) | −3.23707 | −0.117190 | ||||||||
\(764\) | −101.060 | −3.65621 | ||||||||
\(765\) | −26.5902 | −0.961371 | ||||||||
\(766\) | 46.2649 | 1.67162 | ||||||||
\(767\) | 33.2961 | 1.20225 | ||||||||
\(768\) | 6.80787 | 0.245658 | ||||||||
\(769\) | 46.7099 | 1.68440 | 0.842202 | − | 0.539163i | \(-0.181259\pi\) | ||||
0.842202 | + | 0.539163i | \(0.181259\pi\) | |||||||
\(770\) | −2.16520 | −0.0780285 | ||||||||
\(771\) | 4.29639 | 0.154731 | ||||||||
\(772\) | 96.7433 | 3.48187 | ||||||||
\(773\) | 5.36970 | 0.193135 | 0.0965673 | − | 0.995326i | \(-0.469214\pi\) | ||||
0.0965673 | + | 0.995326i | \(0.469214\pi\) | |||||||
\(774\) | 85.0900 | 3.05850 | ||||||||
\(775\) | 2.11231 | 0.0758762 | ||||||||
\(776\) | 26.7455 | 0.960108 | ||||||||
\(777\) | 1.55159 | 0.0556630 | ||||||||
\(778\) | −81.3073 | −2.91501 | ||||||||
\(779\) | 14.2043 | 0.508924 | ||||||||
\(780\) | −15.4953 | −0.554820 | ||||||||
\(781\) | 0.575763 | 0.0206024 | ||||||||
\(782\) | −37.4623 | −1.33965 | ||||||||
\(783\) | 14.8807 | 0.531794 | ||||||||
\(784\) | −38.4759 | −1.37414 | ||||||||
\(785\) | −14.9019 | −0.531871 | ||||||||
\(786\) | 3.55798 | 0.126909 | ||||||||
\(787\) | −27.7111 | −0.987795 | −0.493897 | − | 0.869520i | \(-0.664428\pi\) | ||||
−0.493897 | + | 0.869520i | \(0.664428\pi\) | |||||||
\(788\) | −20.3426 | −0.724677 | ||||||||
\(789\) | 0.341983 | 0.0121749 | ||||||||
\(790\) | 24.0613 | 0.856064 | ||||||||
\(791\) | 12.0228 | 0.427481 | ||||||||
\(792\) | 3.87452 | 0.137675 | ||||||||
\(793\) | −40.7855 | −1.44833 | ||||||||
\(794\) | −74.2600 | −2.63539 | ||||||||
\(795\) | 3.59697 | 0.127571 | ||||||||
\(796\) | −88.3482 | −3.13142 | ||||||||
\(797\) | 21.4896 | 0.761202 | 0.380601 | − | 0.924739i | \(-0.375717\pi\) | ||||
0.380601 | + | 0.924739i | \(0.375717\pi\) | |||||||
\(798\) | −2.63160 | −0.0931577 | ||||||||
\(799\) | 3.11462 | 0.110187 | ||||||||
\(800\) | −34.1210 | −1.20636 | ||||||||
\(801\) | 46.1755 | 1.63153 | ||||||||
\(802\) | −1.57158 | −0.0554945 | ||||||||
\(803\) | −2.16777 | −0.0764988 | ||||||||
\(804\) | −12.3225 | −0.434582 | ||||||||
\(805\) | −21.0631 | −0.742376 | ||||||||
\(806\) | −10.6682 | −0.375773 | ||||||||
\(807\) | 9.25363 | 0.325743 | ||||||||
\(808\) | 175.527 | 6.17504 | ||||||||
\(809\) | 37.9692 | 1.33493 | 0.667464 | − | 0.744642i | \(-0.267380\pi\) | ||||
0.667464 | + | 0.744642i | \(0.267380\pi\) | |||||||
\(810\) | 57.1498 | 2.00804 | ||||||||
\(811\) | 39.2690 | 1.37892 | 0.689460 | − | 0.724323i | \(-0.257848\pi\) | ||||
0.689460 | + | 0.724323i | \(0.257848\pi\) | |||||||
\(812\) | 84.2891 | 2.95797 | ||||||||
\(813\) | 8.33828 | 0.292436 | ||||||||
\(814\) | 0.969725 | 0.0339889 | ||||||||
\(815\) | −18.1009 | −0.634046 | ||||||||
\(816\) | −15.0225 | −0.525893 | ||||||||
\(817\) | −16.2855 | −0.569756 | ||||||||
\(818\) | 3.60925 | 0.126195 | ||||||||
\(819\) | 20.4971 | 0.716226 | ||||||||
\(820\) | 131.404 | 4.58884 | ||||||||
\(821\) | −33.8762 | −1.18229 | −0.591144 | − | 0.806566i | \(-0.701323\pi\) | ||||
−0.591144 | + | 0.806566i | \(0.701323\pi\) | |||||||
\(822\) | 10.7940 | 0.376482 | ||||||||
\(823\) | −39.5791 | −1.37964 | −0.689820 | − | 0.723981i | \(-0.742310\pi\) | ||||
−0.689820 | + | 0.723981i | \(0.742310\pi\) | |||||||
\(824\) | 142.820 | 4.97537 | ||||||||
\(825\) | 0.0902566 | 0.00314233 | ||||||||
\(826\) | 52.3121 | 1.82017 | ||||||||
\(827\) | 18.2126 | 0.633314 | 0.316657 | − | 0.948540i | \(-0.397440\pi\) | ||||
0.316657 | + | 0.948540i | \(0.397440\pi\) | |||||||
\(828\) | 60.6444 | 2.10754 | ||||||||
\(829\) | −37.7346 | −1.31058 | −0.655288 | − | 0.755379i | \(-0.727453\pi\) | ||||
−0.655288 | + | 0.755379i | \(0.727453\pi\) | |||||||
\(830\) | 97.4697 | 3.38322 | ||||||||
\(831\) | −2.92668 | −0.101526 | ||||||||
\(832\) | 79.2141 | 2.74625 | ||||||||
\(833\) | 10.0947 | 0.349762 | ||||||||
\(834\) | −1.67830 | −0.0581149 | ||||||||
\(835\) | 9.32879 | 0.322836 | ||||||||
\(836\) | −1.19313 | −0.0412654 | ||||||||
\(837\) | −2.14661 | −0.0741976 | ||||||||
\(838\) | −65.8542 | −2.27490 | ||||||||
\(839\) | −35.3946 | −1.22196 | −0.610978 | − | 0.791647i | \(-0.709224\pi\) | ||||
−0.610978 | + | 0.791647i | \(0.709224\pi\) | |||||||
\(840\) | −15.1307 | −0.522059 | ||||||||
\(841\) | 32.7747 | 1.13016 | ||||||||
\(842\) | −94.5729 | −3.25920 | ||||||||
\(843\) | −5.01281 | −0.172650 | ||||||||
\(844\) | 37.3314 | 1.28500 | ||||||||
\(845\) | 2.21499 | 0.0761980 | ||||||||
\(846\) | −6.95032 | −0.238957 | ||||||||
\(847\) | 22.2782 | 0.765488 | ||||||||
\(848\) | −57.1091 | −1.96114 | ||||||||
\(849\) | −2.36594 | −0.0811988 | ||||||||
\(850\) | 17.6174 | 0.604271 | ||||||||
\(851\) | 9.43348 | 0.323376 | ||||||||
\(852\) | 6.47372 | 0.221786 | ||||||||
\(853\) | 39.9327 | 1.36727 | 0.683635 | − | 0.729824i | \(-0.260398\pi\) | ||||
0.683635 | + | 0.729824i | \(0.260398\pi\) | |||||||
\(854\) | −64.0789 | −2.19273 | ||||||||
\(855\) | −11.3564 | −0.388382 | ||||||||
\(856\) | −1.93642 | −0.0661856 | ||||||||
\(857\) | −27.1751 | −0.928283 | −0.464142 | − | 0.885761i | \(-0.653637\pi\) | ||||
−0.464142 | + | 0.885761i | \(0.653637\pi\) | |||||||
\(858\) | −0.455843 | −0.0155622 | ||||||||
\(859\) | −18.0226 | −0.614923 | −0.307462 | − | 0.951560i | \(-0.599480\pi\) | ||||
−0.307462 | + | 0.951560i | \(0.599480\pi\) | |||||||
\(860\) | −150.657 | −5.13735 | ||||||||
\(861\) | 6.18521 | 0.210791 | ||||||||
\(862\) | −67.2107 | −2.28921 | ||||||||
\(863\) | −47.7757 | −1.62630 | −0.813152 | − | 0.582051i | \(-0.802250\pi\) | ||||
−0.813152 | + | 0.582051i | \(0.802250\pi\) | |||||||
\(864\) | 34.6751 | 1.17967 | ||||||||
\(865\) | 32.4835 | 1.10447 | ||||||||
\(866\) | −14.4276 | −0.490270 | ||||||||
\(867\) | −1.51673 | −0.0515109 | ||||||||
\(868\) | −12.1591 | −0.412705 | ||||||||
\(869\) | 0.513491 | 0.0174190 | ||||||||
\(870\) | −17.8422 | −0.604907 | ||||||||
\(871\) | −25.3219 | −0.857998 | ||||||||
\(872\) | −14.1379 | −0.478768 | ||||||||
\(873\) | 8.74113 | 0.295842 | ||||||||
\(874\) | −15.9998 | −0.541202 | ||||||||
\(875\) | −16.6784 | −0.563833 | ||||||||
\(876\) | −24.3738 | −0.823513 | ||||||||
\(877\) | 22.6238 | 0.763952 | 0.381976 | − | 0.924172i | \(-0.375244\pi\) | ||||
0.381976 | + | 0.924172i | \(0.375244\pi\) | |||||||
\(878\) | 15.0403 | 0.507586 | ||||||||
\(879\) | −2.63761 | −0.0889645 | ||||||||
\(880\) | −5.27888 | −0.177951 | ||||||||
\(881\) | 4.13858 | 0.139432 | 0.0697162 | − | 0.997567i | \(-0.477791\pi\) | ||||
0.0697162 | + | 0.997567i | \(0.477791\pi\) | |||||||
\(882\) | −22.5265 | −0.758508 | ||||||||
\(883\) | 16.8129 | 0.565801 | 0.282900 | − | 0.959149i | \(-0.408703\pi\) | ||||
0.282900 | + | 0.959149i | \(0.408703\pi\) | |||||||
\(884\) | −64.5468 | −2.17094 | ||||||||
\(885\) | −8.03298 | −0.270026 | ||||||||
\(886\) | −96.9482 | −3.25704 | ||||||||
\(887\) | 15.6404 | 0.525152 | 0.262576 | − | 0.964911i | \(-0.415428\pi\) | ||||
0.262576 | + | 0.964911i | \(0.415428\pi\) | |||||||
\(888\) | 6.77655 | 0.227406 | ||||||||
\(889\) | −16.8443 | −0.564939 | ||||||||
\(890\) | −112.700 | −3.77772 | ||||||||
\(891\) | 1.21963 | 0.0408592 | ||||||||
\(892\) | −34.9006 | −1.16856 | ||||||||
\(893\) | 1.33023 | 0.0445144 | ||||||||
\(894\) | 0.715224 | 0.0239207 | ||||||||
\(895\) | −37.0355 | −1.23796 | ||||||||
\(896\) | 50.1158 | 1.67425 | ||||||||
\(897\) | −4.43444 | −0.148062 | ||||||||
\(898\) | 48.6738 | 1.62426 | ||||||||
\(899\) | −8.91126 | −0.297207 | ||||||||
\(900\) | −28.5192 | −0.950640 | ||||||||
\(901\) | 14.9834 | 0.499171 | ||||||||
\(902\) | 3.86568 | 0.128713 | ||||||||
\(903\) | −7.09142 | −0.235988 | ||||||||
\(904\) | 52.5093 | 1.74643 | ||||||||
\(905\) | −29.8278 | −0.991511 | ||||||||
\(906\) | 7.91853 | 0.263075 | ||||||||
\(907\) | 49.8762 | 1.65611 | 0.828057 | − | 0.560644i | \(-0.189447\pi\) | ||||
0.828057 | + | 0.560644i | \(0.189447\pi\) | |||||||
\(908\) | 137.361 | 4.55850 | ||||||||
\(909\) | 57.3670 | 1.90274 | ||||||||
\(910\) | −50.0271 | −1.65838 | ||||||||
\(911\) | −23.7373 | −0.786453 | −0.393226 | − | 0.919442i | \(-0.628641\pi\) | ||||
−0.393226 | + | 0.919442i | \(0.628641\pi\) | |||||||
\(912\) | −6.41598 | −0.212454 | ||||||||
\(913\) | 2.08009 | 0.0688410 | ||||||||
\(914\) | −81.9205 | −2.70969 | ||||||||
\(915\) | 9.83986 | 0.325296 | ||||||||
\(916\) | −10.3698 | −0.342627 | ||||||||
\(917\) | 8.33309 | 0.275183 | ||||||||
\(918\) | −17.9035 | −0.590902 | ||||||||
\(919\) | −37.2320 | −1.22817 | −0.614085 | − | 0.789240i | \(-0.710475\pi\) | ||||
−0.614085 | + | 0.789240i | \(0.710475\pi\) | |||||||
\(920\) | −91.9928 | −3.03291 | ||||||||
\(921\) | −6.10887 | −0.201294 | ||||||||
\(922\) | 39.0151 | 1.28489 | ||||||||
\(923\) | 13.3030 | 0.437874 | ||||||||
\(924\) | −0.519544 | −0.0170917 | ||||||||
\(925\) | −4.43628 | −0.145864 | ||||||||
\(926\) | −62.2948 | −2.04713 | ||||||||
\(927\) | 46.6773 | 1.53308 | ||||||||
\(928\) | 143.948 | 4.72531 | ||||||||
\(929\) | 5.40545 | 0.177347 | 0.0886736 | − | 0.996061i | \(-0.471737\pi\) | ||||
0.0886736 | + | 0.996061i | \(0.471737\pi\) | |||||||
\(930\) | 2.57381 | 0.0843986 | ||||||||
\(931\) | 4.31137 | 0.141300 | ||||||||
\(932\) | 27.0506 | 0.886072 | ||||||||
\(933\) | 0.0862134 | 0.00282250 | ||||||||
\(934\) | −67.7593 | −2.21715 | ||||||||
\(935\) | 1.38500 | 0.0452942 | ||||||||
\(936\) | 89.5208 | 2.92608 | ||||||||
\(937\) | −8.17427 | −0.267042 | −0.133521 | − | 0.991046i | \(-0.542628\pi\) | ||||
−0.133521 | + | 0.991046i | \(0.542628\pi\) | |||||||
\(938\) | −39.7837 | −1.29898 | ||||||||
\(939\) | −6.81505 | −0.222401 | ||||||||
\(940\) | 12.3059 | 0.401376 | ||||||||
\(941\) | 34.2419 | 1.11625 | 0.558127 | − | 0.829756i | \(-0.311520\pi\) | ||||
0.558127 | + | 0.829756i | \(0.311520\pi\) | |||||||
\(942\) | −4.92909 | −0.160598 | ||||||||
\(943\) | 37.6053 | 1.22460 | ||||||||
\(944\) | 127.540 | 4.15106 | ||||||||
\(945\) | −10.0662 | −0.327453 | ||||||||
\(946\) | −4.43205 | −0.144098 | ||||||||
\(947\) | 4.85211 | 0.157672 | 0.0788362 | − | 0.996888i | \(-0.474880\pi\) | ||||
0.0788362 | + | 0.996888i | \(0.474880\pi\) | |||||||
\(948\) | 5.77355 | 0.187516 | ||||||||
\(949\) | −50.0863 | −1.62587 | ||||||||
\(950\) | 7.52422 | 0.244118 | ||||||||
\(951\) | 1.05570 | 0.0342335 | ||||||||
\(952\) | −63.0281 | −2.04275 | ||||||||
\(953\) | −29.8960 | −0.968427 | −0.484214 | − | 0.874950i | \(-0.660894\pi\) | ||||
−0.484214 | + | 0.874950i | \(0.660894\pi\) | |||||||
\(954\) | −33.4357 | −1.08252 | ||||||||
\(955\) | 50.1023 | 1.62127 | ||||||||
\(956\) | −43.2116 | −1.39756 | ||||||||
\(957\) | −0.380769 | −0.0123085 | ||||||||
\(958\) | 17.2041 | 0.555840 | ||||||||
\(959\) | 25.2804 | 0.816346 | ||||||||
\(960\) | −19.1111 | −0.616808 | ||||||||
\(961\) | −29.7145 | −0.958533 | ||||||||
\(962\) | 22.4055 | 0.722383 | ||||||||
\(963\) | −0.632874 | −0.0203941 | ||||||||
\(964\) | −102.920 | −3.31483 | ||||||||
\(965\) | −47.9624 | −1.54396 | ||||||||
\(966\) | −6.96704 | −0.224161 | ||||||||
\(967\) | −41.7370 | −1.34217 | −0.671085 | − | 0.741380i | \(-0.734171\pi\) | ||||
−0.671085 | + | 0.741380i | \(0.734171\pi\) | |||||||
\(968\) | 97.2998 | 3.12734 | ||||||||
\(969\) | 1.68333 | 0.0540764 | ||||||||
\(970\) | −21.3344 | −0.685006 | ||||||||
\(971\) | −18.5172 | −0.594247 | −0.297123 | − | 0.954839i | \(-0.596027\pi\) | ||||
−0.297123 | + | 0.954839i | \(0.596027\pi\) | |||||||
\(972\) | 43.7268 | 1.40254 | ||||||||
\(973\) | −3.93073 | −0.126013 | ||||||||
\(974\) | −83.4453 | −2.67376 | ||||||||
\(975\) | 2.08538 | 0.0667856 | ||||||||
\(976\) | −156.228 | −5.00073 | ||||||||
\(977\) | 8.81528 | 0.282026 | 0.141013 | − | 0.990008i | \(-0.454964\pi\) | ||||
0.141013 | + | 0.990008i | \(0.454964\pi\) | |||||||
\(978\) | −5.98723 | −0.191450 | ||||||||
\(979\) | −2.40513 | −0.0768682 | ||||||||
\(980\) | 39.8845 | 1.27406 | ||||||||
\(981\) | −4.62062 | −0.147525 | ||||||||
\(982\) | −72.6423 | −2.31811 | ||||||||
\(983\) | 52.1689 | 1.66393 | 0.831965 | − | 0.554828i | \(-0.187216\pi\) | ||||
0.831965 | + | 0.554828i | \(0.187216\pi\) | |||||||
\(984\) | 27.0138 | 0.861170 | ||||||||
\(985\) | 10.0853 | 0.321343 | ||||||||
\(986\) | −74.3230 | −2.36693 | ||||||||
\(987\) | 0.579241 | 0.0184374 | ||||||||
\(988\) | −27.5674 | −0.877035 | ||||||||
\(989\) | −43.1150 | −1.37098 | ||||||||
\(990\) | −3.09063 | −0.0982268 | ||||||||
\(991\) | 23.2262 | 0.737804 | 0.368902 | − | 0.929468i | \(-0.379734\pi\) | ||||
0.368902 | + | 0.929468i | \(0.379734\pi\) | |||||||
\(992\) | −20.7651 | −0.659291 | ||||||||
\(993\) | −6.17095 | −0.195829 | ||||||||
\(994\) | 20.9007 | 0.662928 | ||||||||
\(995\) | 43.8003 | 1.38856 | ||||||||
\(996\) | 23.3880 | 0.741077 | ||||||||
\(997\) | 0.0137954 | 0.000436903 0 | 0.000218452 | − | 1.00000i | \(-0.499930\pi\) | ||||
0.000218452 | 1.00000i | \(0.499930\pi\) | ||||||||
\(998\) | 42.5889 | 1.34813 | ||||||||
\(999\) | 4.50832 | 0.142637 |
(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 | 6047.2.a.b.1.6 | ✓ | 287 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6047.2.a.b.1.6 | ✓ | 287 | 1.1 | even | 1 | trivial |