Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6013,2,Mod(1,6013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6013, 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("6013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6013 = 7 \cdot 859 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6013.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: | \(48.0140467354\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68972 | −1.90192 | −0.950959 | − | 0.309317i | \(-0.899900\pi\) | ||||
−0.950959 | + | 0.309317i | \(0.899900\pi\) | |||||||
\(3\) | 2.91852 | 1.68501 | 0.842504 | − | 0.538690i | \(-0.181081\pi\) | ||||
0.842504 | + | 0.538690i | \(0.181081\pi\) | |||||||
\(4\) | 5.23459 | 2.61729 | ||||||||
\(5\) | 0.347371 | 0.155349 | 0.0776744 | − | 0.996979i | \(-0.475251\pi\) | ||||
0.0776744 | + | 0.996979i | \(0.475251\pi\) | |||||||
\(6\) | −7.85000 | −3.20475 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −8.70012 | −3.07596 | ||||||||
\(9\) | 5.51776 | 1.83925 | ||||||||
\(10\) | −0.934329 | −0.295461 | ||||||||
\(11\) | −5.00686 | −1.50963 | −0.754813 | − | 0.655940i | \(-0.772272\pi\) | ||||
−0.754813 | + | 0.655940i | \(0.772272\pi\) | |||||||
\(12\) | 15.2772 | 4.41016 | ||||||||
\(13\) | 1.86596 | 0.517525 | 0.258762 | − | 0.965941i | \(-0.416685\pi\) | ||||
0.258762 | + | 0.965941i | \(0.416685\pi\) | |||||||
\(14\) | 2.68972 | 0.718858 | ||||||||
\(15\) | 1.01381 | 0.261764 | ||||||||
\(16\) | 12.9317 | 3.23293 | ||||||||
\(17\) | −2.63199 | −0.638351 | −0.319175 | − | 0.947696i | \(-0.603406\pi\) | ||||
−0.319175 | + | 0.947696i | \(0.603406\pi\) | |||||||
\(18\) | −14.8412 | −3.49811 | ||||||||
\(19\) | 4.88633 | 1.12100 | 0.560501 | − | 0.828154i | \(-0.310609\pi\) | ||||
0.560501 | + | 0.828154i | \(0.310609\pi\) | |||||||
\(20\) | 1.81834 | 0.406593 | ||||||||
\(21\) | −2.91852 | −0.636873 | ||||||||
\(22\) | 13.4671 | 2.87119 | ||||||||
\(23\) | −0.974596 | −0.203217 | −0.101609 | − | 0.994824i | \(-0.532399\pi\) | ||||
−0.101609 | + | 0.994824i | \(0.532399\pi\) | |||||||
\(24\) | −25.3915 | −5.18302 | ||||||||
\(25\) | −4.87933 | −0.975867 | ||||||||
\(26\) | −5.01891 | −0.984289 | ||||||||
\(27\) | 7.34813 | 1.41415 | ||||||||
\(28\) | −5.23459 | −0.989244 | ||||||||
\(29\) | 1.26823 | 0.235505 | 0.117753 | − | 0.993043i | \(-0.462431\pi\) | ||||
0.117753 | + | 0.993043i | \(0.462431\pi\) | |||||||
\(30\) | −2.72686 | −0.497854 | ||||||||
\(31\) | 8.76330 | 1.57393 | 0.786967 | − | 0.616995i | \(-0.211650\pi\) | ||||
0.786967 | + | 0.616995i | \(0.211650\pi\) | |||||||
\(32\) | −17.3824 | −3.07281 | ||||||||
\(33\) | −14.6126 | −2.54373 | ||||||||
\(34\) | 7.07931 | 1.21409 | ||||||||
\(35\) | −0.347371 | −0.0587164 | ||||||||
\(36\) | 28.8832 | 4.81386 | ||||||||
\(37\) | −8.53839 | −1.40370 | −0.701851 | − | 0.712324i | \(-0.747643\pi\) | ||||
−0.701851 | + | 0.712324i | \(0.747643\pi\) | |||||||
\(38\) | −13.1429 | −2.13205 | ||||||||
\(39\) | 5.44585 | 0.872033 | ||||||||
\(40\) | −3.02217 | −0.477847 | ||||||||
\(41\) | 6.41252 | 1.00147 | 0.500734 | − | 0.865601i | \(-0.333063\pi\) | ||||
0.500734 | + | 0.865601i | \(0.333063\pi\) | |||||||
\(42\) | 7.85000 | 1.21128 | ||||||||
\(43\) | −9.81142 | −1.49623 | −0.748114 | − | 0.663570i | \(-0.769040\pi\) | ||||
−0.748114 | + | 0.663570i | \(0.769040\pi\) | |||||||
\(44\) | −26.2089 | −3.95113 | ||||||||
\(45\) | 1.91671 | 0.285726 | ||||||||
\(46\) | 2.62139 | 0.386503 | ||||||||
\(47\) | −11.5629 | −1.68663 | −0.843314 | − | 0.537421i | \(-0.819399\pi\) | ||||
−0.843314 | + | 0.537421i | \(0.819399\pi\) | |||||||
\(48\) | 37.7415 | 5.44751 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 13.1240 | 1.85602 | ||||||||
\(51\) | −7.68151 | −1.07563 | ||||||||
\(52\) | 9.76754 | 1.35451 | ||||||||
\(53\) | −11.6945 | −1.60636 | −0.803180 | − | 0.595737i | \(-0.796860\pi\) | ||||
−0.803180 | + | 0.595737i | \(0.796860\pi\) | |||||||
\(54\) | −19.7644 | −2.68959 | ||||||||
\(55\) | −1.73924 | −0.234519 | ||||||||
\(56\) | 8.70012 | 1.16260 | ||||||||
\(57\) | 14.2609 | 1.88890 | ||||||||
\(58\) | −3.41119 | −0.447911 | ||||||||
\(59\) | −8.80181 | −1.14590 | −0.572949 | − | 0.819591i | \(-0.694201\pi\) | ||||
−0.572949 | + | 0.819591i | \(0.694201\pi\) | |||||||
\(60\) | 5.30687 | 0.685113 | ||||||||
\(61\) | 2.06284 | 0.264119 | 0.132060 | − | 0.991242i | \(-0.457841\pi\) | ||||
0.132060 | + | 0.991242i | \(0.457841\pi\) | |||||||
\(62\) | −23.5708 | −2.99349 | ||||||||
\(63\) | −5.51776 | −0.695172 | ||||||||
\(64\) | 20.8904 | 2.61130 | ||||||||
\(65\) | 0.648180 | 0.0803969 | ||||||||
\(66\) | 39.3039 | 4.83797 | ||||||||
\(67\) | −4.30305 | −0.525702 | −0.262851 | − | 0.964837i | \(-0.584663\pi\) | ||||
−0.262851 | + | 0.964837i | \(0.584663\pi\) | |||||||
\(68\) | −13.7774 | −1.67075 | ||||||||
\(69\) | −2.84438 | −0.342423 | ||||||||
\(70\) | 0.934329 | 0.111674 | ||||||||
\(71\) | −13.4124 | −1.59176 | −0.795879 | − | 0.605456i | \(-0.792991\pi\) | ||||
−0.795879 | + | 0.605456i | \(0.792991\pi\) | |||||||
\(72\) | −48.0052 | −5.65747 | ||||||||
\(73\) | −9.89942 | −1.15864 | −0.579320 | − | 0.815100i | \(-0.696682\pi\) | ||||
−0.579320 | + | 0.815100i | \(0.696682\pi\) | |||||||
\(74\) | 22.9659 | 2.66973 | ||||||||
\(75\) | −14.2404 | −1.64434 | ||||||||
\(76\) | 25.5779 | 2.93399 | ||||||||
\(77\) | 5.00686 | 0.570585 | ||||||||
\(78\) | −14.6478 | −1.65854 | ||||||||
\(79\) | 10.6020 | 1.19282 | 0.596411 | − | 0.802679i | \(-0.296593\pi\) | ||||
0.596411 | + | 0.802679i | \(0.296593\pi\) | |||||||
\(80\) | 4.49210 | 0.502232 | ||||||||
\(81\) | 4.89239 | 0.543599 | ||||||||
\(82\) | −17.2479 | −1.90471 | ||||||||
\(83\) | 6.24115 | 0.685056 | 0.342528 | − | 0.939508i | \(-0.388717\pi\) | ||||
0.342528 | + | 0.939508i | \(0.388717\pi\) | |||||||
\(84\) | −15.2772 | −1.66688 | ||||||||
\(85\) | −0.914275 | −0.0991671 | ||||||||
\(86\) | 26.3900 | 2.84570 | ||||||||
\(87\) | 3.70136 | 0.396828 | ||||||||
\(88\) | 43.5603 | 4.64355 | ||||||||
\(89\) | −0.489483 | −0.0518851 | −0.0259425 | − | 0.999663i | \(-0.508259\pi\) | ||||
−0.0259425 | + | 0.999663i | \(0.508259\pi\) | |||||||
\(90\) | −5.15540 | −0.543427 | ||||||||
\(91\) | −1.86596 | −0.195606 | ||||||||
\(92\) | −5.10161 | −0.531879 | ||||||||
\(93\) | 25.5759 | 2.65209 | ||||||||
\(94\) | 31.1011 | 3.20783 | ||||||||
\(95\) | 1.69737 | 0.174146 | ||||||||
\(96\) | −50.7309 | −5.17771 | ||||||||
\(97\) | 4.93383 | 0.500954 | 0.250477 | − | 0.968122i | \(-0.419412\pi\) | ||||
0.250477 | + | 0.968122i | \(0.419412\pi\) | |||||||
\(98\) | −2.68972 | −0.271703 | ||||||||
\(99\) | −27.6267 | −2.77658 | ||||||||
\(100\) | −25.5413 | −2.55413 | ||||||||
\(101\) | 11.8590 | 1.18002 | 0.590008 | − | 0.807398i | \(-0.299125\pi\) | ||||
0.590008 | + | 0.807398i | \(0.299125\pi\) | |||||||
\(102\) | 20.6611 | 2.04575 | ||||||||
\(103\) | −1.84566 | −0.181858 | −0.0909292 | − | 0.995857i | \(-0.528984\pi\) | ||||
−0.0909292 | + | 0.995857i | \(0.528984\pi\) | |||||||
\(104\) | −16.2341 | −1.59188 | ||||||||
\(105\) | −1.01381 | −0.0989375 | ||||||||
\(106\) | 31.4548 | 3.05516 | ||||||||
\(107\) | −1.62930 | −0.157510 | −0.0787550 | − | 0.996894i | \(-0.525094\pi\) | ||||
−0.0787550 | + | 0.996894i | \(0.525094\pi\) | |||||||
\(108\) | 38.4644 | 3.70124 | ||||||||
\(109\) | 2.27781 | 0.218175 | 0.109087 | − | 0.994032i | \(-0.465207\pi\) | ||||
0.109087 | + | 0.994032i | \(0.465207\pi\) | |||||||
\(110\) | 4.67806 | 0.446035 | ||||||||
\(111\) | −24.9195 | −2.36525 | ||||||||
\(112\) | −12.9317 | −1.22193 | ||||||||
\(113\) | 4.35334 | 0.409528 | 0.204764 | − | 0.978811i | \(-0.434357\pi\) | ||||
0.204764 | + | 0.978811i | \(0.434357\pi\) | |||||||
\(114\) | −38.3577 | −3.59253 | ||||||||
\(115\) | −0.338546 | −0.0315696 | ||||||||
\(116\) | 6.63868 | 0.616386 | ||||||||
\(117\) | 10.2959 | 0.951859 | ||||||||
\(118\) | 23.6744 | 2.17940 | ||||||||
\(119\) | 2.63199 | 0.241274 | ||||||||
\(120\) | −8.82026 | −0.805176 | ||||||||
\(121\) | 14.0687 | 1.27897 | ||||||||
\(122\) | −5.54845 | −0.502333 | ||||||||
\(123\) | 18.7151 | 1.68748 | ||||||||
\(124\) | 45.8722 | 4.11945 | ||||||||
\(125\) | −3.43179 | −0.306949 | ||||||||
\(126\) | 14.8412 | 1.32216 | ||||||||
\(127\) | −0.392058 | −0.0347895 | −0.0173948 | − | 0.999849i | \(-0.505537\pi\) | ||||
−0.0173948 | + | 0.999849i | \(0.505537\pi\) | |||||||
\(128\) | −21.4244 | −1.89367 | ||||||||
\(129\) | −28.6348 | −2.52116 | ||||||||
\(130\) | −1.74342 | −0.152908 | ||||||||
\(131\) | 20.8045 | 1.81770 | 0.908848 | − | 0.417128i | \(-0.136963\pi\) | ||||
0.908848 | + | 0.417128i | \(0.136963\pi\) | |||||||
\(132\) | −76.4911 | −6.65769 | ||||||||
\(133\) | −4.88633 | −0.423699 | ||||||||
\(134\) | 11.5740 | 0.999841 | ||||||||
\(135\) | 2.55252 | 0.219686 | ||||||||
\(136\) | 22.8986 | 1.96354 | ||||||||
\(137\) | −13.2735 | −1.13403 | −0.567014 | − | 0.823708i | \(-0.691902\pi\) | ||||
−0.567014 | + | 0.823708i | \(0.691902\pi\) | |||||||
\(138\) | 7.65058 | 0.651260 | ||||||||
\(139\) | −19.0691 | −1.61742 | −0.808710 | − | 0.588208i | \(-0.799834\pi\) | ||||
−0.808710 | + | 0.588208i | \(0.799834\pi\) | |||||||
\(140\) | −1.81834 | −0.153678 | ||||||||
\(141\) | −33.7467 | −2.84198 | ||||||||
\(142\) | 36.0755 | 3.02739 | ||||||||
\(143\) | −9.34261 | −0.781269 | ||||||||
\(144\) | 71.3541 | 5.94617 | ||||||||
\(145\) | 0.440547 | 0.0365854 | ||||||||
\(146\) | 26.6267 | 2.20364 | ||||||||
\(147\) | 2.91852 | 0.240715 | ||||||||
\(148\) | −44.6949 | −3.67390 | ||||||||
\(149\) | −3.85461 | −0.315782 | −0.157891 | − | 0.987457i | \(-0.550470\pi\) | ||||
−0.157891 | + | 0.987457i | \(0.550470\pi\) | |||||||
\(150\) | 38.3028 | 3.12741 | ||||||||
\(151\) | 12.3272 | 1.00317 | 0.501586 | − | 0.865108i | \(-0.332750\pi\) | ||||
0.501586 | + | 0.865108i | \(0.332750\pi\) | |||||||
\(152\) | −42.5117 | −3.44815 | ||||||||
\(153\) | −14.5227 | −1.17409 | ||||||||
\(154\) | −13.4671 | −1.08521 | ||||||||
\(155\) | 3.04411 | 0.244509 | ||||||||
\(156\) | 28.5067 | 2.28237 | ||||||||
\(157\) | −4.76344 | −0.380164 | −0.190082 | − | 0.981768i | \(-0.560875\pi\) | ||||
−0.190082 | + | 0.981768i | \(0.560875\pi\) | |||||||
\(158\) | −28.5165 | −2.26865 | ||||||||
\(159\) | −34.1305 | −2.70673 | ||||||||
\(160\) | −6.03814 | −0.477357 | ||||||||
\(161\) | 0.974596 | 0.0768089 | ||||||||
\(162\) | −13.1591 | −1.03388 | ||||||||
\(163\) | 12.5149 | 0.980242 | 0.490121 | − | 0.871654i | \(-0.336953\pi\) | ||||
0.490121 | + | 0.871654i | \(0.336953\pi\) | |||||||
\(164\) | 33.5669 | 2.62113 | ||||||||
\(165\) | −5.07600 | −0.395166 | ||||||||
\(166\) | −16.7869 | −1.30292 | ||||||||
\(167\) | −23.4047 | −1.81111 | −0.905554 | − | 0.424232i | \(-0.860544\pi\) | ||||
−0.905554 | + | 0.424232i | \(0.860544\pi\) | |||||||
\(168\) | 25.3915 | 1.95900 | ||||||||
\(169\) | −9.51819 | −0.732168 | ||||||||
\(170\) | 2.45914 | 0.188608 | ||||||||
\(171\) | 26.9616 | 2.06180 | ||||||||
\(172\) | −51.3587 | −3.91607 | ||||||||
\(173\) | −1.24837 | −0.0949120 | −0.0474560 | − | 0.998873i | \(-0.515111\pi\) | ||||
−0.0474560 | + | 0.998873i | \(0.515111\pi\) | |||||||
\(174\) | −9.95563 | −0.754734 | ||||||||
\(175\) | 4.87933 | 0.368843 | ||||||||
\(176\) | −64.7473 | −4.88051 | ||||||||
\(177\) | −25.6883 | −1.93085 | ||||||||
\(178\) | 1.31657 | 0.0986812 | ||||||||
\(179\) | 16.0148 | 1.19701 | 0.598503 | − | 0.801121i | \(-0.295763\pi\) | ||||
0.598503 | + | 0.801121i | \(0.295763\pi\) | |||||||
\(180\) | 10.0332 | 0.747828 | ||||||||
\(181\) | 3.08915 | 0.229615 | 0.114807 | − | 0.993388i | \(-0.463375\pi\) | ||||
0.114807 | + | 0.993388i | \(0.463375\pi\) | |||||||
\(182\) | 5.01891 | 0.372026 | ||||||||
\(183\) | 6.02043 | 0.445043 | ||||||||
\(184\) | 8.47911 | 0.625088 | ||||||||
\(185\) | −2.96599 | −0.218064 | ||||||||
\(186\) | −68.7919 | −5.04406 | ||||||||
\(187\) | 13.1780 | 0.963671 | ||||||||
\(188\) | −60.5272 | −4.41440 | ||||||||
\(189\) | −7.34813 | −0.534498 | ||||||||
\(190\) | −4.56544 | −0.331212 | ||||||||
\(191\) | 0.102395 | 0.00740901 | 0.00370450 | − | 0.999993i | \(-0.498821\pi\) | ||||
0.00370450 | + | 0.999993i | \(0.498821\pi\) | |||||||
\(192\) | 60.9690 | 4.40006 | ||||||||
\(193\) | 7.13913 | 0.513886 | 0.256943 | − | 0.966427i | \(-0.417285\pi\) | ||||
0.256943 | + | 0.966427i | \(0.417285\pi\) | |||||||
\(194\) | −13.2706 | −0.952774 | ||||||||
\(195\) | 1.89173 | 0.135469 | ||||||||
\(196\) | 5.23459 | 0.373899 | ||||||||
\(197\) | −17.8571 | −1.27227 | −0.636134 | − | 0.771579i | \(-0.719467\pi\) | ||||
−0.636134 | + | 0.771579i | \(0.719467\pi\) | |||||||
\(198\) | 74.3080 | 5.28084 | ||||||||
\(199\) | 6.29687 | 0.446373 | 0.223187 | − | 0.974776i | \(-0.428354\pi\) | ||||
0.223187 | + | 0.974776i | \(0.428354\pi\) | |||||||
\(200\) | 42.4508 | 3.00173 | ||||||||
\(201\) | −12.5585 | −0.885811 | ||||||||
\(202\) | −31.8974 | −2.24429 | ||||||||
\(203\) | −1.26823 | −0.0890125 | ||||||||
\(204\) | −40.2095 | −2.81523 | ||||||||
\(205\) | 2.22752 | 0.155577 | ||||||||
\(206\) | 4.96431 | 0.345880 | ||||||||
\(207\) | −5.37759 | −0.373768 | ||||||||
\(208\) | 24.1301 | 1.67312 | ||||||||
\(209\) | −24.4652 | −1.69229 | ||||||||
\(210\) | 2.72686 | 0.188171 | ||||||||
\(211\) | −4.70422 | −0.323852 | −0.161926 | − | 0.986803i | \(-0.551771\pi\) | ||||
−0.161926 | + | 0.986803i | \(0.551771\pi\) | |||||||
\(212\) | −61.2157 | −4.20431 | ||||||||
\(213\) | −39.1443 | −2.68212 | ||||||||
\(214\) | 4.38235 | 0.299571 | ||||||||
\(215\) | −3.40820 | −0.232437 | ||||||||
\(216\) | −63.9297 | −4.34986 | ||||||||
\(217\) | −8.76330 | −0.594891 | ||||||||
\(218\) | −6.12667 | −0.414950 | ||||||||
\(219\) | −28.8917 | −1.95232 | ||||||||
\(220\) | −9.10419 | −0.613804 | ||||||||
\(221\) | −4.91119 | −0.330362 | ||||||||
\(222\) | 67.0263 | 4.49851 | ||||||||
\(223\) | −6.77620 | −0.453768 | −0.226884 | − | 0.973922i | \(-0.572854\pi\) | ||||
−0.226884 | + | 0.973922i | \(0.572854\pi\) | |||||||
\(224\) | 17.3824 | 1.16141 | ||||||||
\(225\) | −26.9230 | −1.79487 | ||||||||
\(226\) | −11.7093 | −0.778889 | ||||||||
\(227\) | 8.97012 | 0.595368 | 0.297684 | − | 0.954665i | \(-0.403786\pi\) | ||||
0.297684 | + | 0.954665i | \(0.403786\pi\) | |||||||
\(228\) | 74.6497 | 4.94379 | ||||||||
\(229\) | −20.5561 | −1.35839 | −0.679194 | − | 0.733959i | \(-0.737670\pi\) | ||||
−0.679194 | + | 0.733959i | \(0.737670\pi\) | |||||||
\(230\) | 0.910594 | 0.0600428 | ||||||||
\(231\) | 14.6126 | 0.961441 | ||||||||
\(232\) | −11.0338 | −0.724404 | ||||||||
\(233\) | 22.0395 | 1.44386 | 0.721929 | − | 0.691967i | \(-0.243256\pi\) | ||||
0.721929 | + | 0.691967i | \(0.243256\pi\) | |||||||
\(234\) | −27.6931 | −1.81036 | ||||||||
\(235\) | −4.01663 | −0.262016 | ||||||||
\(236\) | −46.0738 | −2.99915 | ||||||||
\(237\) | 30.9423 | 2.00992 | ||||||||
\(238\) | −7.07931 | −0.458883 | ||||||||
\(239\) | −26.5936 | −1.72020 | −0.860099 | − | 0.510127i | \(-0.829598\pi\) | ||||
−0.860099 | + | 0.510127i | \(0.829598\pi\) | |||||||
\(240\) | 13.1103 | 0.846265 | ||||||||
\(241\) | −1.47059 | −0.0947293 | −0.0473646 | − | 0.998878i | \(-0.515082\pi\) | ||||
−0.0473646 | + | 0.998878i | \(0.515082\pi\) | |||||||
\(242\) | −37.8408 | −2.43250 | ||||||||
\(243\) | −7.76586 | −0.498180 | ||||||||
\(244\) | 10.7981 | 0.691277 | ||||||||
\(245\) | 0.347371 | 0.0221927 | ||||||||
\(246\) | −50.3383 | −3.20945 | ||||||||
\(247\) | 9.11771 | 0.580146 | ||||||||
\(248\) | −76.2418 | −4.84136 | ||||||||
\(249\) | 18.2149 | 1.15432 | ||||||||
\(250\) | 9.23055 | 0.583791 | ||||||||
\(251\) | 6.11694 | 0.386098 | 0.193049 | − | 0.981189i | \(-0.438162\pi\) | ||||
0.193049 | + | 0.981189i | \(0.438162\pi\) | |||||||
\(252\) | −28.8832 | −1.81947 | ||||||||
\(253\) | 4.87967 | 0.306782 | ||||||||
\(254\) | 1.05453 | 0.0661669 | ||||||||
\(255\) | −2.66833 | −0.167097 | ||||||||
\(256\) | 15.8449 | 0.990307 | ||||||||
\(257\) | 21.1245 | 1.31771 | 0.658856 | − | 0.752270i | \(-0.271041\pi\) | ||||
0.658856 | + | 0.752270i | \(0.271041\pi\) | |||||||
\(258\) | 77.0196 | 4.79503 | ||||||||
\(259\) | 8.53839 | 0.530550 | ||||||||
\(260\) | 3.39296 | 0.210422 | ||||||||
\(261\) | 6.99781 | 0.433153 | ||||||||
\(262\) | −55.9582 | −3.45711 | ||||||||
\(263\) | 29.3611 | 1.81048 | 0.905241 | − | 0.424899i | \(-0.139690\pi\) | ||||
0.905241 | + | 0.424899i | \(0.139690\pi\) | |||||||
\(264\) | 127.132 | 7.82442 | ||||||||
\(265\) | −4.06232 | −0.249546 | ||||||||
\(266\) | 13.1429 | 0.805840 | ||||||||
\(267\) | −1.42857 | −0.0874268 | ||||||||
\(268\) | −22.5247 | −1.37591 | ||||||||
\(269\) | −2.42218 | −0.147683 | −0.0738415 | − | 0.997270i | \(-0.523526\pi\) | ||||
−0.0738415 | + | 0.997270i | \(0.523526\pi\) | |||||||
\(270\) | −6.86557 | −0.417825 | ||||||||
\(271\) | −29.0499 | −1.76465 | −0.882327 | − | 0.470637i | \(-0.844024\pi\) | ||||
−0.882327 | + | 0.470637i | \(0.844024\pi\) | |||||||
\(272\) | −34.0361 | −2.06374 | ||||||||
\(273\) | −5.44585 | −0.329598 | ||||||||
\(274\) | 35.7019 | 2.15683 | ||||||||
\(275\) | 24.4302 | 1.47319 | ||||||||
\(276\) | −14.8891 | −0.896221 | ||||||||
\(277\) | 24.7085 | 1.48459 | 0.742294 | − | 0.670074i | \(-0.233738\pi\) | ||||
0.742294 | + | 0.670074i | \(0.233738\pi\) | |||||||
\(278\) | 51.2905 | 3.07620 | ||||||||
\(279\) | 48.3538 | 2.89486 | ||||||||
\(280\) | 3.02217 | 0.180609 | ||||||||
\(281\) | −20.3751 | −1.21548 | −0.607739 | − | 0.794137i | \(-0.707923\pi\) | ||||
−0.607739 | + | 0.794137i | \(0.707923\pi\) | |||||||
\(282\) | 90.7690 | 5.40522 | ||||||||
\(283\) | −16.9458 | −1.00732 | −0.503662 | − | 0.863901i | \(-0.668014\pi\) | ||||
−0.503662 | + | 0.863901i | \(0.668014\pi\) | |||||||
\(284\) | −70.2083 | −4.16610 | ||||||||
\(285\) | 4.95380 | 0.293438 | ||||||||
\(286\) | 25.1290 | 1.48591 | ||||||||
\(287\) | −6.41252 | −0.378519 | ||||||||
\(288\) | −95.9120 | −5.65167 | ||||||||
\(289\) | −10.0726 | −0.592508 | ||||||||
\(290\) | −1.18495 | −0.0695825 | ||||||||
\(291\) | 14.3995 | 0.844112 | ||||||||
\(292\) | −51.8194 | −3.03250 | ||||||||
\(293\) | −10.7707 | −0.629232 | −0.314616 | − | 0.949219i | \(-0.601876\pi\) | ||||
−0.314616 | + | 0.949219i | \(0.601876\pi\) | |||||||
\(294\) | −7.85000 | −0.457821 | ||||||||
\(295\) | −3.05749 | −0.178014 | ||||||||
\(296\) | 74.2850 | 4.31773 | ||||||||
\(297\) | −36.7911 | −2.13484 | ||||||||
\(298\) | 10.3678 | 0.600592 | ||||||||
\(299\) | −1.81856 | −0.105170 | ||||||||
\(300\) | −74.5428 | −4.30373 | ||||||||
\(301\) | 9.81142 | 0.565521 | ||||||||
\(302\) | −33.1566 | −1.90795 | ||||||||
\(303\) | 34.6107 | 1.98834 | ||||||||
\(304\) | 63.1886 | 3.62412 | ||||||||
\(305\) | 0.716569 | 0.0410306 | ||||||||
\(306\) | 39.0619 | 2.23302 | ||||||||
\(307\) | −32.8778 | −1.87644 | −0.938219 | − | 0.346042i | \(-0.887525\pi\) | ||||
−0.938219 | + | 0.346042i | \(0.887525\pi\) | |||||||
\(308\) | 26.2089 | 1.49339 | ||||||||
\(309\) | −5.38660 | −0.306433 | ||||||||
\(310\) | −8.18780 | −0.465036 | ||||||||
\(311\) | −17.2456 | −0.977909 | −0.488955 | − | 0.872309i | \(-0.662622\pi\) | ||||
−0.488955 | + | 0.872309i | \(0.662622\pi\) | |||||||
\(312\) | −47.3795 | −2.68234 | ||||||||
\(313\) | −3.49902 | −0.197776 | −0.0988881 | − | 0.995099i | \(-0.531529\pi\) | ||||
−0.0988881 | + | 0.995099i | \(0.531529\pi\) | |||||||
\(314\) | 12.8123 | 0.723041 | ||||||||
\(315\) | −1.91671 | −0.107994 | ||||||||
\(316\) | 55.4973 | 3.12196 | ||||||||
\(317\) | −16.1296 | −0.905928 | −0.452964 | − | 0.891529i | \(-0.649633\pi\) | ||||
−0.452964 | + | 0.891529i | \(0.649633\pi\) | |||||||
\(318\) | 91.8016 | 5.14798 | ||||||||
\(319\) | −6.34987 | −0.355525 | ||||||||
\(320\) | 7.25671 | 0.405662 | ||||||||
\(321\) | −4.75513 | −0.265406 | ||||||||
\(322\) | −2.62139 | −0.146084 | ||||||||
\(323\) | −12.8608 | −0.715592 | ||||||||
\(324\) | 25.6096 | 1.42276 | ||||||||
\(325\) | −9.10465 | −0.505035 | ||||||||
\(326\) | −33.6615 | −1.86434 | ||||||||
\(327\) | 6.64783 | 0.367626 | ||||||||
\(328\) | −55.7898 | −3.08047 | ||||||||
\(329\) | 11.5629 | 0.637485 | ||||||||
\(330\) | 13.6530 | 0.751573 | ||||||||
\(331\) | −7.42416 | −0.408069 | −0.204034 | − | 0.978964i | \(-0.565405\pi\) | ||||
−0.204034 | + | 0.978964i | \(0.565405\pi\) | |||||||
\(332\) | 32.6699 | 1.79299 | ||||||||
\(333\) | −47.1128 | −2.58176 | ||||||||
\(334\) | 62.9520 | 3.44458 | ||||||||
\(335\) | −1.49475 | −0.0816671 | ||||||||
\(336\) | −37.7415 | −2.05897 | ||||||||
\(337\) | −18.0698 | −0.984325 | −0.492162 | − | 0.870503i | \(-0.663793\pi\) | ||||
−0.492162 | + | 0.870503i | \(0.663793\pi\) | |||||||
\(338\) | 25.6012 | 1.39252 | ||||||||
\(339\) | 12.7053 | 0.690058 | ||||||||
\(340\) | −4.78585 | −0.259549 | ||||||||
\(341\) | −43.8766 | −2.37605 | ||||||||
\(342\) | −72.5191 | −3.92138 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 85.3606 | 4.60233 | ||||||||
\(345\) | −0.988054 | −0.0531950 | ||||||||
\(346\) | 3.35777 | 0.180515 | ||||||||
\(347\) | −4.36326 | −0.234232 | −0.117116 | − | 0.993118i | \(-0.537365\pi\) | ||||
−0.117116 | + | 0.993118i | \(0.537365\pi\) | |||||||
\(348\) | 19.3751 | 1.03861 | ||||||||
\(349\) | 5.28185 | 0.282731 | 0.141365 | − | 0.989957i | \(-0.454851\pi\) | ||||
0.141365 | + | 0.989957i | \(0.454851\pi\) | |||||||
\(350\) | −13.1240 | −0.701509 | ||||||||
\(351\) | 13.7113 | 0.731857 | ||||||||
\(352\) | 87.0314 | 4.63879 | ||||||||
\(353\) | 4.17885 | 0.222418 | 0.111209 | − | 0.993797i | \(-0.464528\pi\) | ||||
0.111209 | + | 0.993797i | \(0.464528\pi\) | |||||||
\(354\) | 69.0942 | 3.67231 | ||||||||
\(355\) | −4.65907 | −0.247278 | ||||||||
\(356\) | −2.56224 | −0.135798 | ||||||||
\(357\) | 7.68151 | 0.406549 | ||||||||
\(358\) | −43.0754 | −2.27661 | ||||||||
\(359\) | 31.3208 | 1.65305 | 0.826524 | − | 0.562902i | \(-0.190315\pi\) | ||||
0.826524 | + | 0.562902i | \(0.190315\pi\) | |||||||
\(360\) | −16.6756 | −0.878881 | ||||||||
\(361\) | 4.87623 | 0.256644 | ||||||||
\(362\) | −8.30895 | −0.436709 | ||||||||
\(363\) | 41.0597 | 2.15508 | ||||||||
\(364\) | −9.76754 | −0.511958 | ||||||||
\(365\) | −3.43877 | −0.179993 | ||||||||
\(366\) | −16.1933 | −0.846435 | ||||||||
\(367\) | 5.68976 | 0.297003 | 0.148501 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148501 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(368\) | −12.6032 | −0.656987 | ||||||||
\(369\) | 35.3828 | 1.84195 | ||||||||
\(370\) | 7.97767 | 0.414739 | ||||||||
\(371\) | 11.6945 | 0.607147 | ||||||||
\(372\) | 133.879 | 6.94130 | ||||||||
\(373\) | 28.8233 | 1.49241 | 0.746206 | − | 0.665715i | \(-0.231873\pi\) | ||||
0.746206 | + | 0.665715i | \(0.231873\pi\) | |||||||
\(374\) | −35.4451 | −1.83282 | ||||||||
\(375\) | −10.0157 | −0.517211 | ||||||||
\(376\) | 100.599 | 5.18800 | ||||||||
\(377\) | 2.36647 | 0.121880 | ||||||||
\(378\) | 19.7644 | 1.01657 | ||||||||
\(379\) | 16.8685 | 0.866478 | 0.433239 | − | 0.901279i | \(-0.357371\pi\) | ||||
0.433239 | + | 0.901279i | \(0.357371\pi\) | |||||||
\(380\) | 8.88502 | 0.455792 | ||||||||
\(381\) | −1.14423 | −0.0586207 | ||||||||
\(382\) | −0.275412 | −0.0140913 | ||||||||
\(383\) | −7.40623 | −0.378440 | −0.189220 | − | 0.981935i | \(-0.560596\pi\) | ||||
−0.189220 | + | 0.981935i | \(0.560596\pi\) | |||||||
\(384\) | −62.5276 | −3.19085 | ||||||||
\(385\) | 1.73924 | 0.0886397 | ||||||||
\(386\) | −19.2022 | −0.977368 | ||||||||
\(387\) | −54.1371 | −2.75194 | ||||||||
\(388\) | 25.8265 | 1.31114 | ||||||||
\(389\) | −20.1315 | −1.02071 | −0.510353 | − | 0.859965i | \(-0.670485\pi\) | ||||
−0.510353 | + | 0.859965i | \(0.670485\pi\) | |||||||
\(390\) | −5.08821 | −0.257652 | ||||||||
\(391\) | 2.56513 | 0.129724 | ||||||||
\(392\) | −8.70012 | −0.439423 | ||||||||
\(393\) | 60.7183 | 3.06283 | ||||||||
\(394\) | 48.0306 | 2.41975 | ||||||||
\(395\) | 3.68284 | 0.185304 | ||||||||
\(396\) | −144.614 | −7.26713 | ||||||||
\(397\) | −11.9766 | −0.601086 | −0.300543 | − | 0.953768i | \(-0.597168\pi\) | ||||
−0.300543 | + | 0.953768i | \(0.597168\pi\) | |||||||
\(398\) | −16.9368 | −0.848966 | ||||||||
\(399\) | −14.2609 | −0.713936 | ||||||||
\(400\) | −63.0981 | −3.15491 | ||||||||
\(401\) | −2.05154 | −0.102449 | −0.0512245 | − | 0.998687i | \(-0.516312\pi\) | ||||
−0.0512245 | + | 0.998687i | \(0.516312\pi\) | |||||||
\(402\) | 33.7790 | 1.68474 | ||||||||
\(403\) | 16.3520 | 0.814550 | ||||||||
\(404\) | 62.0770 | 3.08844 | ||||||||
\(405\) | 1.69947 | 0.0844475 | ||||||||
\(406\) | 3.41119 | 0.169295 | ||||||||
\(407\) | 42.7505 | 2.11907 | ||||||||
\(408\) | 66.8301 | 3.30858 | ||||||||
\(409\) | 4.28821 | 0.212038 | 0.106019 | − | 0.994364i | \(-0.466189\pi\) | ||||
0.106019 | + | 0.994364i | \(0.466189\pi\) | |||||||
\(410\) | −5.99141 | −0.295895 | ||||||||
\(411\) | −38.7389 | −1.91085 | ||||||||
\(412\) | −9.66127 | −0.475977 | ||||||||
\(413\) | 8.80181 | 0.433109 | ||||||||
\(414\) | 14.4642 | 0.710876 | ||||||||
\(415\) | 2.16799 | 0.106423 | ||||||||
\(416\) | −32.4349 | −1.59025 | ||||||||
\(417\) | −55.6535 | −2.72537 | ||||||||
\(418\) | 65.8045 | 3.21860 | ||||||||
\(419\) | 24.9168 | 1.21726 | 0.608632 | − | 0.793453i | \(-0.291719\pi\) | ||||
0.608632 | + | 0.793453i | \(0.291719\pi\) | |||||||
\(420\) | −5.30687 | −0.258949 | ||||||||
\(421\) | 15.3529 | 0.748256 | 0.374128 | − | 0.927377i | \(-0.377942\pi\) | ||||
0.374128 | + | 0.927377i | \(0.377942\pi\) | |||||||
\(422\) | 12.6530 | 0.615940 | ||||||||
\(423\) | −63.8015 | −3.10214 | ||||||||
\(424\) | 101.743 | 4.94109 | ||||||||
\(425\) | 12.8423 | 0.622945 | ||||||||
\(426\) | 105.287 | 5.10118 | ||||||||
\(427\) | −2.06284 | −0.0998276 | ||||||||
\(428\) | −8.52869 | −0.412250 | ||||||||
\(429\) | −27.2666 | −1.31644 | ||||||||
\(430\) | 9.16710 | 0.442077 | ||||||||
\(431\) | 30.5469 | 1.47139 | 0.735696 | − | 0.677312i | \(-0.236855\pi\) | ||||
0.735696 | + | 0.677312i | \(0.236855\pi\) | |||||||
\(432\) | 95.0239 | 4.57184 | ||||||||
\(433\) | 27.3984 | 1.31668 | 0.658342 | − | 0.752719i | \(-0.271258\pi\) | ||||
0.658342 | + | 0.752719i | \(0.271258\pi\) | |||||||
\(434\) | 23.5708 | 1.13143 | ||||||||
\(435\) | 1.28575 | 0.0616468 | ||||||||
\(436\) | 11.9234 | 0.571027 | ||||||||
\(437\) | −4.76220 | −0.227807 | ||||||||
\(438\) | 77.7104 | 3.71315 | ||||||||
\(439\) | −40.2473 | −1.92090 | −0.960450 | − | 0.278452i | \(-0.910179\pi\) | ||||
−0.960450 | + | 0.278452i | \(0.910179\pi\) | |||||||
\(440\) | 15.1316 | 0.721370 | ||||||||
\(441\) | 5.51776 | 0.262750 | ||||||||
\(442\) | 13.2097 | 0.628322 | ||||||||
\(443\) | −15.0260 | −0.713905 | −0.356952 | − | 0.934123i | \(-0.616184\pi\) | ||||
−0.356952 | + | 0.934123i | \(0.616184\pi\) | |||||||
\(444\) | −130.443 | −6.19055 | ||||||||
\(445\) | −0.170032 | −0.00806029 | ||||||||
\(446\) | 18.2261 | 0.863029 | ||||||||
\(447\) | −11.2498 | −0.532096 | ||||||||
\(448\) | −20.8904 | −0.986978 | ||||||||
\(449\) | −21.6326 | −1.02091 | −0.510453 | − | 0.859906i | \(-0.670522\pi\) | ||||
−0.510453 | + | 0.859906i | \(0.670522\pi\) | |||||||
\(450\) | 72.4153 | 3.41369 | ||||||||
\(451\) | −32.1066 | −1.51184 | ||||||||
\(452\) | 22.7880 | 1.07186 | ||||||||
\(453\) | 35.9771 | 1.69035 | ||||||||
\(454\) | −24.1271 | −1.13234 | ||||||||
\(455\) | −0.648180 | −0.0303872 | ||||||||
\(456\) | −124.071 | −5.81017 | ||||||||
\(457\) | 13.1071 | 0.613123 | 0.306562 | − | 0.951851i | \(-0.400821\pi\) | ||||
0.306562 | + | 0.951851i | \(0.400821\pi\) | |||||||
\(458\) | 55.2902 | 2.58354 | ||||||||
\(459\) | −19.3402 | −0.902723 | ||||||||
\(460\) | −1.77215 | −0.0826269 | ||||||||
\(461\) | −9.36134 | −0.436001 | −0.218000 | − | 0.975949i | \(-0.569953\pi\) | ||||
−0.218000 | + | 0.975949i | \(0.569953\pi\) | |||||||
\(462\) | −39.3039 | −1.82858 | ||||||||
\(463\) | 29.3049 | 1.36192 | 0.680958 | − | 0.732322i | \(-0.261564\pi\) | ||||
0.680958 | + | 0.732322i | \(0.261564\pi\) | |||||||
\(464\) | 16.4004 | 0.761371 | ||||||||
\(465\) | 8.88430 | 0.412000 | ||||||||
\(466\) | −59.2802 | −2.74610 | ||||||||
\(467\) | −36.7073 | −1.69861 | −0.849305 | − | 0.527903i | \(-0.822978\pi\) | ||||
−0.849305 | + | 0.527903i | \(0.822978\pi\) | |||||||
\(468\) | 53.8949 | 2.49129 | ||||||||
\(469\) | 4.30305 | 0.198697 | ||||||||
\(470\) | 10.8036 | 0.498333 | ||||||||
\(471\) | −13.9022 | −0.640579 | ||||||||
\(472\) | 76.5768 | 3.52473 | ||||||||
\(473\) | 49.1244 | 2.25874 | ||||||||
\(474\) | −83.2260 | −3.82269 | ||||||||
\(475\) | −23.8420 | −1.09395 | ||||||||
\(476\) | 13.7774 | 0.631484 | ||||||||
\(477\) | −64.5273 | −2.95450 | ||||||||
\(478\) | 71.5293 | 3.27168 | ||||||||
\(479\) | 4.72072 | 0.215695 | 0.107848 | − | 0.994167i | \(-0.465604\pi\) | ||||
0.107848 | + | 0.994167i | \(0.465604\pi\) | |||||||
\(480\) | −17.6224 | −0.804351 | ||||||||
\(481\) | −15.9323 | −0.726450 | ||||||||
\(482\) | 3.95548 | 0.180167 | ||||||||
\(483\) | 2.84438 | 0.129424 | ||||||||
\(484\) | 73.6437 | 3.34744 | ||||||||
\(485\) | 1.71387 | 0.0778227 | ||||||||
\(486\) | 20.8880 | 0.947498 | ||||||||
\(487\) | 37.8401 | 1.71470 | 0.857350 | − | 0.514734i | \(-0.172109\pi\) | ||||
0.857350 | + | 0.514734i | \(0.172109\pi\) | |||||||
\(488\) | −17.9469 | −0.812419 | ||||||||
\(489\) | 36.5250 | 1.65172 | ||||||||
\(490\) | −0.934329 | −0.0422087 | ||||||||
\(491\) | −8.58180 | −0.387291 | −0.193646 | − | 0.981072i | \(-0.562031\pi\) | ||||
−0.193646 | + | 0.981072i | \(0.562031\pi\) | |||||||
\(492\) | 97.9657 | 4.41663 | ||||||||
\(493\) | −3.33797 | −0.150335 | ||||||||
\(494\) | −24.5241 | −1.10339 | ||||||||
\(495\) | −9.59669 | −0.431339 | ||||||||
\(496\) | 113.324 | 5.08842 | ||||||||
\(497\) | 13.4124 | 0.601628 | ||||||||
\(498\) | −48.9930 | −2.19543 | ||||||||
\(499\) | −25.1559 | −1.12613 | −0.563066 | − | 0.826412i | \(-0.690378\pi\) | ||||
−0.563066 | + | 0.826412i | \(0.690378\pi\) | |||||||
\(500\) | −17.9640 | −0.803375 | ||||||||
\(501\) | −68.3070 | −3.05173 | ||||||||
\(502\) | −16.4528 | −0.734326 | ||||||||
\(503\) | −4.60886 | −0.205499 | −0.102749 | − | 0.994707i | \(-0.532764\pi\) | ||||
−0.102749 | + | 0.994707i | \(0.532764\pi\) | |||||||
\(504\) | 48.0052 | 2.13832 | ||||||||
\(505\) | 4.11947 | 0.183314 | ||||||||
\(506\) | −13.1249 | −0.583475 | ||||||||
\(507\) | −27.7790 | −1.23371 | ||||||||
\(508\) | −2.05226 | −0.0910544 | ||||||||
\(509\) | −17.3466 | −0.768875 | −0.384437 | − | 0.923151i | \(-0.625605\pi\) | ||||
−0.384437 | + | 0.923151i | \(0.625605\pi\) | |||||||
\(510\) | 7.17706 | 0.317805 | ||||||||
\(511\) | 9.89942 | 0.437925 | ||||||||
\(512\) | 0.230524 | 0.0101878 | ||||||||
\(513\) | 35.9054 | 1.58526 | ||||||||
\(514\) | −56.8190 | −2.50618 | ||||||||
\(515\) | −0.641128 | −0.0282515 | ||||||||
\(516\) | −149.891 | −6.59860 | ||||||||
\(517\) | 57.8941 | 2.54618 | ||||||||
\(518\) | −22.9659 | −1.00906 | ||||||||
\(519\) | −3.64340 | −0.159928 | ||||||||
\(520\) | −5.63925 | −0.247297 | ||||||||
\(521\) | 39.1629 | 1.71576 | 0.857879 | − | 0.513852i | \(-0.171782\pi\) | ||||
0.857879 | + | 0.513852i | \(0.171782\pi\) | |||||||
\(522\) | −18.8221 | −0.823822 | ||||||||
\(523\) | −4.70539 | −0.205752 | −0.102876 | − | 0.994694i | \(-0.532805\pi\) | ||||
−0.102876 | + | 0.994694i | \(0.532805\pi\) | |||||||
\(524\) | 108.903 | 4.75744 | ||||||||
\(525\) | 14.2404 | 0.621503 | ||||||||
\(526\) | −78.9730 | −3.44339 | ||||||||
\(527\) | −23.0649 | −1.00472 | ||||||||
\(528\) | −188.966 | −8.22371 | ||||||||
\(529\) | −22.0502 | −0.958703 | ||||||||
\(530\) | 10.9265 | 0.474616 | ||||||||
\(531\) | −48.5663 | −2.10760 | ||||||||
\(532\) | −25.5779 | −1.10894 | ||||||||
\(533\) | 11.9655 | 0.518284 | ||||||||
\(534\) | 3.84244 | 0.166279 | ||||||||
\(535\) | −0.565970 | −0.0244690 | ||||||||
\(536\) | 37.4371 | 1.61704 | ||||||||
\(537\) | 46.7396 | 2.01696 | ||||||||
\(538\) | 6.51499 | 0.280881 | ||||||||
\(539\) | −5.00686 | −0.215661 | ||||||||
\(540\) | 13.3614 | 0.574984 | ||||||||
\(541\) | 2.30598 | 0.0991416 | 0.0495708 | − | 0.998771i | \(-0.484215\pi\) | ||||
0.0495708 | + | 0.998771i | \(0.484215\pi\) | |||||||
\(542\) | 78.1360 | 3.35623 | ||||||||
\(543\) | 9.01576 | 0.386903 | ||||||||
\(544\) | 45.7503 | 1.96153 | ||||||||
\(545\) | 0.791244 | 0.0338932 | ||||||||
\(546\) | 14.6478 | 0.626868 | ||||||||
\(547\) | −6.01663 | −0.257253 | −0.128626 | − | 0.991693i | \(-0.541057\pi\) | ||||
−0.128626 | + | 0.991693i | \(0.541057\pi\) | |||||||
\(548\) | −69.4811 | −2.96808 | ||||||||
\(549\) | 11.3822 | 0.485782 | ||||||||
\(550\) | −65.7102 | −2.80189 | ||||||||
\(551\) | 6.19701 | 0.264001 | ||||||||
\(552\) | 24.7464 | 1.05328 | ||||||||
\(553\) | −10.6020 | −0.450844 | ||||||||
\(554\) | −66.4588 | −2.82357 | ||||||||
\(555\) | −8.65629 | −0.367439 | ||||||||
\(556\) | −99.8188 | −4.23326 | ||||||||
\(557\) | −7.45288 | −0.315789 | −0.157894 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157894 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(558\) | −130.058 | −5.50579 | ||||||||
\(559\) | −18.3077 | −0.774335 | ||||||||
\(560\) | −4.49210 | −0.189826 | ||||||||
\(561\) | 38.4603 | 1.62379 | ||||||||
\(562\) | 54.8033 | 2.31174 | ||||||||
\(563\) | 32.1826 | 1.35633 | 0.678167 | − | 0.734908i | \(-0.262775\pi\) | ||||
0.678167 | + | 0.734908i | \(0.262775\pi\) | |||||||
\(564\) | −176.650 | −7.43830 | ||||||||
\(565\) | 1.51222 | 0.0636197 | ||||||||
\(566\) | 45.5794 | 1.91585 | ||||||||
\(567\) | −4.89239 | −0.205461 | ||||||||
\(568\) | 116.689 | 4.89618 | ||||||||
\(569\) | −12.0767 | −0.506280 | −0.253140 | − | 0.967430i | \(-0.581463\pi\) | ||||
−0.253140 | + | 0.967430i | \(0.581463\pi\) | |||||||
\(570\) | −13.3243 | −0.558095 | ||||||||
\(571\) | −14.3032 | −0.598571 | −0.299286 | − | 0.954164i | \(-0.596748\pi\) | ||||
−0.299286 | + | 0.954164i | \(0.596748\pi\) | |||||||
\(572\) | −48.9047 | −2.04481 | ||||||||
\(573\) | 0.298840 | 0.0124842 | ||||||||
\(574\) | 17.2479 | 0.719913 | ||||||||
\(575\) | 4.75538 | 0.198313 | ||||||||
\(576\) | 115.268 | 4.80284 | ||||||||
\(577\) | −14.7782 | −0.615225 | −0.307612 | − | 0.951512i | \(-0.599530\pi\) | ||||
−0.307612 | + | 0.951512i | \(0.599530\pi\) | |||||||
\(578\) | 27.0926 | 1.12690 | ||||||||
\(579\) | 20.8357 | 0.865902 | ||||||||
\(580\) | 2.30608 | 0.0957548 | ||||||||
\(581\) | −6.24115 | −0.258927 | ||||||||
\(582\) | −38.7305 | −1.60543 | ||||||||
\(583\) | 58.5526 | 2.42500 | ||||||||
\(584\) | 86.1262 | 3.56393 | ||||||||
\(585\) | 3.57650 | 0.147870 | ||||||||
\(586\) | 28.9702 | 1.19675 | ||||||||
\(587\) | −38.8881 | −1.60509 | −0.802543 | − | 0.596595i | \(-0.796520\pi\) | ||||
−0.802543 | + | 0.596595i | \(0.796520\pi\) | |||||||
\(588\) | 15.2772 | 0.630023 | ||||||||
\(589\) | 42.8204 | 1.76438 | ||||||||
\(590\) | 8.22379 | 0.338568 | ||||||||
\(591\) | −52.1164 | −2.14378 | ||||||||
\(592\) | −110.416 | −4.53807 | ||||||||
\(593\) | −14.6422 | −0.601284 | −0.300642 | − | 0.953737i | \(-0.597201\pi\) | ||||
−0.300642 | + | 0.953737i | \(0.597201\pi\) | |||||||
\(594\) | 98.9577 | 4.06028 | ||||||||
\(595\) | 0.914275 | 0.0374816 | ||||||||
\(596\) | −20.1773 | −0.826495 | ||||||||
\(597\) | 18.3775 | 0.752143 | ||||||||
\(598\) | 4.89141 | 0.200025 | ||||||||
\(599\) | −42.7007 | −1.74470 | −0.872351 | − | 0.488880i | \(-0.837405\pi\) | ||||
−0.872351 | + | 0.488880i | \(0.837405\pi\) | |||||||
\(600\) | 123.894 | 5.05793 | ||||||||
\(601\) | 37.3644 | 1.52412 | 0.762062 | − | 0.647504i | \(-0.224187\pi\) | ||||
0.762062 | + | 0.647504i | \(0.224187\pi\) | |||||||
\(602\) | −26.3900 | −1.07557 | ||||||||
\(603\) | −23.7432 | −0.966898 | ||||||||
\(604\) | 64.5277 | 2.62559 | ||||||||
\(605\) | 4.88705 | 0.198687 | ||||||||
\(606\) | −93.0932 | −3.78165 | ||||||||
\(607\) | −0.633414 | −0.0257095 | −0.0128547 | − | 0.999917i | \(-0.504092\pi\) | ||||
−0.0128547 | + | 0.999917i | \(0.504092\pi\) | |||||||
\(608\) | −84.9363 | −3.44462 | ||||||||
\(609\) | −3.70136 | −0.149987 | ||||||||
\(610\) | −1.92737 | −0.0780368 | ||||||||
\(611\) | −21.5760 | −0.872871 | ||||||||
\(612\) | −76.0202 | −3.07293 | ||||||||
\(613\) | 15.6251 | 0.631090 | 0.315545 | − | 0.948911i | \(-0.397813\pi\) | ||||
0.315545 | + | 0.948911i | \(0.397813\pi\) | |||||||
\(614\) | 88.4321 | 3.56883 | ||||||||
\(615\) | 6.50107 | 0.262148 | ||||||||
\(616\) | −43.5603 | −1.75510 | ||||||||
\(617\) | −16.5528 | −0.666392 | −0.333196 | − | 0.942858i | \(-0.608127\pi\) | ||||
−0.333196 | + | 0.942858i | \(0.608127\pi\) | |||||||
\(618\) | 14.4884 | 0.582810 | ||||||||
\(619\) | 30.7945 | 1.23774 | 0.618868 | − | 0.785495i | \(-0.287592\pi\) | ||||
0.618868 | + | 0.785495i | \(0.287592\pi\) | |||||||
\(620\) | 15.9347 | 0.639952 | ||||||||
\(621\) | −7.16146 | −0.287380 | ||||||||
\(622\) | 46.3858 | 1.85990 | ||||||||
\(623\) | 0.489483 | 0.0196107 | ||||||||
\(624\) | 70.4241 | 2.81922 | ||||||||
\(625\) | 23.2046 | 0.928183 | ||||||||
\(626\) | 9.41137 | 0.376154 | ||||||||
\(627\) | −71.4022 | −2.85153 | ||||||||
\(628\) | −24.9346 | −0.995000 | ||||||||
\(629\) | 22.4729 | 0.896054 | ||||||||
\(630\) | 5.15540 | 0.205396 | ||||||||
\(631\) | −35.1859 | −1.40073 | −0.700364 | − | 0.713785i | \(-0.746979\pi\) | ||||
−0.700364 | + | 0.713785i | \(0.746979\pi\) | |||||||
\(632\) | −92.2390 | −3.66907 | ||||||||
\(633\) | −13.7294 | −0.545693 | ||||||||
\(634\) | 43.3841 | 1.72300 | ||||||||
\(635\) | −0.136190 | −0.00540452 | ||||||||
\(636\) | −178.659 | −7.08430 | ||||||||
\(637\) | 1.86596 | 0.0739321 | ||||||||
\(638\) | 17.0794 | 0.676179 | ||||||||
\(639\) | −74.0063 | −2.92764 | ||||||||
\(640\) | −7.44222 | −0.294180 | ||||||||
\(641\) | 14.0078 | 0.553275 | 0.276637 | − | 0.960974i | \(-0.410780\pi\) | ||||
0.276637 | + | 0.960974i | \(0.410780\pi\) | |||||||
\(642\) | 12.7900 | 0.504780 | ||||||||
\(643\) | 6.58680 | 0.259758 | 0.129879 | − | 0.991530i | \(-0.458541\pi\) | ||||
0.129879 | + | 0.991530i | \(0.458541\pi\) | |||||||
\(644\) | 5.10161 | 0.201032 | ||||||||
\(645\) | −9.94690 | −0.391659 | ||||||||
\(646\) | 34.5918 | 1.36100 | ||||||||
\(647\) | −4.05178 | −0.159292 | −0.0796460 | − | 0.996823i | \(-0.525379\pi\) | ||||
−0.0796460 | + | 0.996823i | \(0.525379\pi\) | |||||||
\(648\) | −42.5644 | −1.67209 | ||||||||
\(649\) | 44.0695 | 1.72988 | ||||||||
\(650\) | 24.4889 | 0.960535 | ||||||||
\(651\) | −25.5759 | −1.00240 | ||||||||
\(652\) | 65.5103 | 2.56558 | ||||||||
\(653\) | 27.8418 | 1.08953 | 0.544767 | − | 0.838587i | \(-0.316618\pi\) | ||||
0.544767 | + | 0.838587i | \(0.316618\pi\) | |||||||
\(654\) | −17.8808 | −0.699195 | ||||||||
\(655\) | 7.22687 | 0.282377 | ||||||||
\(656\) | 82.9249 | 3.23767 | ||||||||
\(657\) | −54.6226 | −2.13103 | ||||||||
\(658\) | −31.1011 | −1.21245 | ||||||||
\(659\) | −16.5191 | −0.643491 | −0.321745 | − | 0.946826i | \(-0.604270\pi\) | ||||
−0.321745 | + | 0.946826i | \(0.604270\pi\) | |||||||
\(660\) | −26.5708 | −1.03427 | ||||||||
\(661\) | −1.52023 | −0.0591301 | −0.0295651 | − | 0.999563i | \(-0.509412\pi\) | ||||
−0.0295651 | + | 0.999563i | \(0.509412\pi\) | |||||||
\(662\) | 19.9689 | 0.776114 | ||||||||
\(663\) | −14.3334 | −0.556663 | ||||||||
\(664\) | −54.2988 | −2.10720 | ||||||||
\(665\) | −1.69737 | −0.0658211 | ||||||||
\(666\) | 126.720 | 4.91030 | ||||||||
\(667\) | −1.23602 | −0.0478587 | ||||||||
\(668\) | −122.514 | −4.74020 | ||||||||
\(669\) | −19.7765 | −0.764602 | ||||||||
\(670\) | 4.02047 | 0.155324 | ||||||||
\(671\) | −10.3283 | −0.398721 | ||||||||
\(672\) | 50.7309 | 1.95699 | ||||||||
\(673\) | 14.8227 | 0.571371 | 0.285686 | − | 0.958323i | \(-0.407779\pi\) | ||||
0.285686 | + | 0.958323i | \(0.407779\pi\) | |||||||
\(674\) | 48.6027 | 1.87211 | ||||||||
\(675\) | −35.8540 | −1.38002 | ||||||||
\(676\) | −49.8238 | −1.91630 | ||||||||
\(677\) | −18.1691 | −0.698297 | −0.349148 | − | 0.937067i | \(-0.613529\pi\) | ||||
−0.349148 | + | 0.937067i | \(0.613529\pi\) | |||||||
\(678\) | −34.1737 | −1.31243 | ||||||||
\(679\) | −4.93383 | −0.189343 | ||||||||
\(680\) | 7.95431 | 0.305034 | ||||||||
\(681\) | 26.1795 | 1.00320 | ||||||||
\(682\) | 118.016 | 4.51906 | ||||||||
\(683\) | −1.32417 | −0.0506678 | −0.0253339 | − | 0.999679i | \(-0.508065\pi\) | ||||
−0.0253339 | + | 0.999679i | \(0.508065\pi\) | |||||||
\(684\) | 141.133 | 5.39635 | ||||||||
\(685\) | −4.61081 | −0.176170 | ||||||||
\(686\) | 2.68972 | 0.102694 | ||||||||
\(687\) | −59.9935 | −2.28889 | ||||||||
\(688\) | −126.878 | −4.83720 | ||||||||
\(689\) | −21.8214 | −0.831330 | ||||||||
\(690\) | 2.65759 | 0.101173 | ||||||||
\(691\) | −23.5124 | −0.894452 | −0.447226 | − | 0.894421i | \(-0.647588\pi\) | ||||
−0.447226 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(692\) | −6.53471 | −0.248413 | ||||||||
\(693\) | 27.6267 | 1.04945 | ||||||||
\(694\) | 11.7359 | 0.445490 | ||||||||
\(695\) | −6.62404 | −0.251264 | ||||||||
\(696\) | −32.2023 | −1.22063 | ||||||||
\(697\) | −16.8777 | −0.639288 | ||||||||
\(698\) | −14.2067 | −0.537731 | ||||||||
\(699\) | 64.3228 | 2.43291 | ||||||||
\(700\) | 25.5413 | 0.965370 | ||||||||
\(701\) | −38.8990 | −1.46919 | −0.734597 | − | 0.678504i | \(-0.762629\pi\) | ||||
−0.734597 | + | 0.678504i | \(0.762629\pi\) | |||||||
\(702\) | −36.8796 | −1.39193 | ||||||||
\(703\) | −41.7214 | −1.57355 | ||||||||
\(704\) | −104.595 | −3.94209 | ||||||||
\(705\) | −11.7226 | −0.441499 | ||||||||
\(706\) | −11.2399 | −0.423020 | ||||||||
\(707\) | −11.8590 | −0.446004 | ||||||||
\(708\) | −134.467 | −5.05359 | ||||||||
\(709\) | 7.05569 | 0.264982 | 0.132491 | − | 0.991184i | \(-0.457702\pi\) | ||||
0.132491 | + | 0.991184i | \(0.457702\pi\) | |||||||
\(710\) | 12.5316 | 0.470302 | ||||||||
\(711\) | 58.4995 | 2.19390 | ||||||||
\(712\) | 4.25856 | 0.159596 | ||||||||
\(713\) | −8.54068 | −0.319851 | ||||||||
\(714\) | −20.6611 | −0.773222 | ||||||||
\(715\) | −3.24535 | −0.121369 | ||||||||
\(716\) | 83.8311 | 3.13291 | ||||||||
\(717\) | −77.6140 | −2.89855 | ||||||||
\(718\) | −84.2441 | −3.14396 | ||||||||
\(719\) | −11.9386 | −0.445236 | −0.222618 | − | 0.974906i | \(-0.571460\pi\) | ||||
−0.222618 | + | 0.974906i | \(0.571460\pi\) | |||||||
\(720\) | 24.7863 | 0.923731 | ||||||||
\(721\) | 1.84566 | 0.0687360 | ||||||||
\(722\) | −13.1157 | −0.488115 | ||||||||
\(723\) | −4.29196 | −0.159620 | ||||||||
\(724\) | 16.1704 | 0.600970 | ||||||||
\(725\) | −6.18813 | −0.229821 | ||||||||
\(726\) | −110.439 | −4.09878 | ||||||||
\(727\) | −47.3986 | −1.75792 | −0.878958 | − | 0.476899i | \(-0.841761\pi\) | ||||
−0.878958 | + | 0.476899i | \(0.841761\pi\) | |||||||
\(728\) | 16.2341 | 0.601676 | ||||||||
\(729\) | −37.3420 | −1.38304 | ||||||||
\(730\) | 9.24932 | 0.342333 | ||||||||
\(731\) | 25.8235 | 0.955118 | ||||||||
\(732\) | 31.5144 | 1.16481 | ||||||||
\(733\) | 15.4114 | 0.569234 | 0.284617 | − | 0.958641i | \(-0.408134\pi\) | ||||
0.284617 | + | 0.958641i | \(0.408134\pi\) | |||||||
\(734\) | −15.3038 | −0.564875 | ||||||||
\(735\) | 1.01381 | 0.0373949 | ||||||||
\(736\) | 16.9408 | 0.624448 | ||||||||
\(737\) | 21.5448 | 0.793613 | ||||||||
\(738\) | −95.1697 | −3.50324 | ||||||||
\(739\) | −42.0082 | −1.54530 | −0.772649 | − | 0.634833i | \(-0.781069\pi\) | ||||
−0.772649 | + | 0.634833i | \(0.781069\pi\) | |||||||
\(740\) | −15.5257 | −0.570736 | ||||||||
\(741\) | 26.6102 | 0.977550 | ||||||||
\(742\) | −31.4548 | −1.15474 | ||||||||
\(743\) | −40.2222 | −1.47561 | −0.737805 | − | 0.675014i | \(-0.764137\pi\) | ||||
−0.737805 | + | 0.675014i | \(0.764137\pi\) | |||||||
\(744\) | −222.513 | −8.15773 | ||||||||
\(745\) | −1.33898 | −0.0490564 | ||||||||
\(746\) | −77.5265 | −2.83845 | ||||||||
\(747\) | 34.4372 | 1.25999 | ||||||||
\(748\) | 68.9814 | 2.52221 | ||||||||
\(749\) | 1.62930 | 0.0595332 | ||||||||
\(750\) | 26.9395 | 0.983693 | ||||||||
\(751\) | −15.0609 | −0.549580 | −0.274790 | − | 0.961504i | \(-0.588608\pi\) | ||||
−0.274790 | + | 0.961504i | \(0.588608\pi\) | |||||||
\(752\) | −149.529 | −5.45275 | ||||||||
\(753\) | 17.8524 | 0.650578 | ||||||||
\(754\) | −6.36515 | −0.231805 | ||||||||
\(755\) | 4.28210 | 0.155842 | ||||||||
\(756\) | −38.4644 | −1.39894 | ||||||||
\(757\) | −16.0338 | −0.582759 | −0.291380 | − | 0.956607i | \(-0.594114\pi\) | ||||
−0.291380 | + | 0.956607i | \(0.594114\pi\) | |||||||
\(758\) | −45.3716 | −1.64797 | ||||||||
\(759\) | 14.2414 | 0.516931 | ||||||||
\(760\) | −14.7673 | −0.535667 | ||||||||
\(761\) | −46.9757 | −1.70287 | −0.851433 | − | 0.524463i | \(-0.824266\pi\) | ||||
−0.851433 | + | 0.524463i | \(0.824266\pi\) | |||||||
\(762\) | 3.07766 | 0.111492 | ||||||||
\(763\) | −2.27781 | −0.0824622 | ||||||||
\(764\) | 0.535993 | 0.0193915 | ||||||||
\(765\) | −5.04475 | −0.182393 | ||||||||
\(766\) | 19.9207 | 0.719763 | ||||||||
\(767\) | −16.4238 | −0.593030 | ||||||||
\(768\) | 46.2437 | 1.66868 | ||||||||
\(769\) | −6.41739 | −0.231417 | −0.115709 | − | 0.993283i | \(-0.536914\pi\) | ||||
−0.115709 | + | 0.993283i | \(0.536914\pi\) | |||||||
\(770\) | −4.67806 | −0.168586 | ||||||||
\(771\) | 61.6523 | 2.22035 | ||||||||
\(772\) | 37.3704 | 1.34499 | ||||||||
\(773\) | 31.5449 | 1.13459 | 0.567296 | − | 0.823514i | \(-0.307990\pi\) | ||||
0.567296 | + | 0.823514i | \(0.307990\pi\) | |||||||
\(774\) | 145.613 | 5.23397 | ||||||||
\(775\) | −42.7590 | −1.53595 | ||||||||
\(776\) | −42.9249 | −1.54092 | ||||||||
\(777\) | 24.9195 | 0.893980 | ||||||||
\(778\) | 54.1480 | 1.94130 | ||||||||
\(779\) | 31.3337 | 1.12265 | ||||||||
\(780\) | 9.90241 | 0.354563 | ||||||||
\(781\) | 67.1540 | 2.40296 | ||||||||
\(782\) | −6.89946 | −0.246724 | ||||||||
\(783\) | 9.31914 | 0.333039 | ||||||||
\(784\) | 12.9317 | 0.461847 | ||||||||
\(785\) | −1.65468 | −0.0590580 | ||||||||
\(786\) | −163.315 | −5.82526 | ||||||||
\(787\) | 40.5997 | 1.44722 | 0.723612 | − | 0.690207i | \(-0.242480\pi\) | ||||
0.723612 | + | 0.690207i | \(0.242480\pi\) | |||||||
\(788\) | −93.4746 | −3.32990 | ||||||||
\(789\) | 85.6909 | 3.05068 | ||||||||
\(790\) | −9.90579 | −0.352432 | ||||||||
\(791\) | −4.35334 | −0.154787 | ||||||||
\(792\) | 240.355 | 8.54066 | ||||||||
\(793\) | 3.84917 | 0.136688 | ||||||||
\(794\) | 32.2136 | 1.14322 | ||||||||
\(795\) | −11.8559 | −0.420487 | ||||||||
\(796\) | 32.9615 | 1.16829 | ||||||||
\(797\) | 53.8734 | 1.90830 | 0.954148 | − | 0.299336i | \(-0.0967652\pi\) | ||||
0.954148 | + | 0.299336i | \(0.0967652\pi\) | |||||||
\(798\) | 38.3577 | 1.35785 | ||||||||
\(799\) | 30.4335 | 1.07666 | ||||||||
\(800\) | 84.8146 | 2.99865 | ||||||||
\(801\) | −2.70085 | −0.0954298 | ||||||||
\(802\) | 5.51807 | 0.194850 | ||||||||
\(803\) | 49.5650 | 1.74911 | ||||||||
\(804\) | −65.7388 | −2.31843 | ||||||||
\(805\) | 0.338546 | 0.0119322 | ||||||||
\(806\) | −43.9822 | −1.54921 | ||||||||
\(807\) | −7.06918 | −0.248847 | ||||||||
\(808\) | −103.175 | −3.62968 | ||||||||
\(809\) | 3.71273 | 0.130533 | 0.0652663 | − | 0.997868i | \(-0.479210\pi\) | ||||
0.0652663 | + | 0.997868i | \(0.479210\pi\) | |||||||
\(810\) | −4.57110 | −0.160612 | ||||||||
\(811\) | 3.54436 | 0.124459 | 0.0622296 | − | 0.998062i | \(-0.480179\pi\) | ||||
0.0622296 | + | 0.998062i | \(0.480179\pi\) | |||||||
\(812\) | −6.63868 | −0.232972 | ||||||||
\(813\) | −84.7826 | −2.97346 | ||||||||
\(814\) | −114.987 | −4.03029 | ||||||||
\(815\) | 4.34731 | 0.152280 | ||||||||
\(816\) | −99.3351 | −3.47742 | ||||||||
\(817\) | −47.9418 | −1.67727 | ||||||||
\(818\) | −11.5341 | −0.403280 | ||||||||
\(819\) | −10.2959 | −0.359769 | ||||||||
\(820\) | 11.6602 | 0.407190 | ||||||||
\(821\) | 13.1491 | 0.458908 | 0.229454 | − | 0.973319i | \(-0.426306\pi\) | ||||
0.229454 | + | 0.973319i | \(0.426306\pi\) | |||||||
\(822\) | 104.197 | 3.63427 | ||||||||
\(823\) | −18.9164 | −0.659383 | −0.329691 | − | 0.944089i | \(-0.606945\pi\) | ||||
−0.329691 | + | 0.944089i | \(0.606945\pi\) | |||||||
\(824\) | 16.0575 | 0.559389 | ||||||||
\(825\) | 71.2999 | 2.48234 | ||||||||
\(826\) | −23.6744 | −0.823737 | ||||||||
\(827\) | −17.2239 | −0.598935 | −0.299468 | − | 0.954106i | \(-0.596809\pi\) | ||||
−0.299468 | + | 0.954106i | \(0.596809\pi\) | |||||||
\(828\) | −28.1494 | −0.978261 | ||||||||
\(829\) | 26.1463 | 0.908099 | 0.454049 | − | 0.890977i | \(-0.349979\pi\) | ||||
0.454049 | + | 0.890977i | \(0.349979\pi\) | |||||||
\(830\) | −5.83129 | −0.202407 | ||||||||
\(831\) | 72.1122 | 2.50154 | ||||||||
\(832\) | 38.9807 | 1.35141 | ||||||||
\(833\) | −2.63199 | −0.0911930 | ||||||||
\(834\) | 149.692 | 5.18342 | ||||||||
\(835\) | −8.13009 | −0.281353 | ||||||||
\(836\) | −128.065 | −4.42923 | ||||||||
\(837\) | 64.3938 | 2.22578 | ||||||||
\(838\) | −67.0191 | −2.31513 | ||||||||
\(839\) | 43.4920 | 1.50151 | 0.750756 | − | 0.660580i | \(-0.229690\pi\) | ||||
0.750756 | + | 0.660580i | \(0.229690\pi\) | |||||||
\(840\) | 8.82026 | 0.304328 | ||||||||
\(841\) | −27.3916 | −0.944537 | ||||||||
\(842\) | −41.2951 | −1.42312 | ||||||||
\(843\) | −59.4652 | −2.04809 | ||||||||
\(844\) | −24.6247 | −0.847616 | ||||||||
\(845\) | −3.30634 | −0.113742 | ||||||||
\(846\) | 171.608 | 5.90001 | ||||||||
\(847\) | −14.0687 | −0.483406 | ||||||||
\(848\) | −151.230 | −5.19324 | ||||||||
\(849\) | −49.4567 | −1.69735 | ||||||||
\(850\) | −34.5423 | −1.18479 | ||||||||
\(851\) | 8.32148 | 0.285257 | ||||||||
\(852\) | −204.904 | −7.01991 | ||||||||
\(853\) | −48.2745 | −1.65289 | −0.826443 | − | 0.563020i | \(-0.809639\pi\) | ||||
−0.826443 | + | 0.563020i | \(0.809639\pi\) | |||||||
\(854\) | 5.54845 | 0.189864 | ||||||||
\(855\) | 9.36567 | 0.320299 | ||||||||
\(856\) | 14.1751 | 0.484494 | ||||||||
\(857\) | 36.8858 | 1.26000 | 0.629998 | − | 0.776597i | \(-0.283056\pi\) | ||||
0.629998 | + | 0.776597i | \(0.283056\pi\) | |||||||
\(858\) | 73.3395 | 2.50377 | ||||||||
\(859\) | −1.00000 | −0.0341196 | ||||||||
\(860\) | −17.8405 | −0.608356 | ||||||||
\(861\) | −18.7151 | −0.637808 | ||||||||
\(862\) | −82.1626 | −2.79847 | ||||||||
\(863\) | 34.5982 | 1.17774 | 0.588868 | − | 0.808229i | \(-0.299574\pi\) | ||||
0.588868 | + | 0.808229i | \(0.299574\pi\) | |||||||
\(864\) | −127.728 | −4.34541 | ||||||||
\(865\) | −0.433648 | −0.0147445 | ||||||||
\(866\) | −73.6940 | −2.50423 | ||||||||
\(867\) | −29.3972 | −0.998382 | ||||||||
\(868\) | −45.8722 | −1.55700 | ||||||||
\(869\) | −53.0829 | −1.80072 | ||||||||
\(870\) | −3.45829 | −0.117247 | ||||||||
\(871\) | −8.02933 | −0.272063 | ||||||||
\(872\) | −19.8172 | −0.671096 | ||||||||
\(873\) | 27.2237 | 0.921382 | ||||||||
\(874\) | 12.8090 | 0.433270 | ||||||||
\(875\) | 3.43179 | 0.116016 | ||||||||
\(876\) | −151.236 | −5.10979 | ||||||||
\(877\) | 15.8976 | 0.536825 | 0.268413 | − | 0.963304i | \(-0.413501\pi\) | ||||
0.268413 | + | 0.963304i | \(0.413501\pi\) | |||||||
\(878\) | 108.254 | 3.65340 | ||||||||
\(879\) | −31.4346 | −1.06026 | ||||||||
\(880\) | −22.4913 | −0.758182 | ||||||||
\(881\) | 26.0363 | 0.877186 | 0.438593 | − | 0.898686i | \(-0.355477\pi\) | ||||
0.438593 | + | 0.898686i | \(0.355477\pi\) | |||||||
\(882\) | −14.8412 | −0.499730 | ||||||||
\(883\) | −34.6382 | −1.16567 | −0.582835 | − | 0.812591i | \(-0.698057\pi\) | ||||
−0.582835 | + | 0.812591i | \(0.698057\pi\) | |||||||
\(884\) | −25.7080 | −0.864655 | ||||||||
\(885\) | −8.92335 | −0.299955 | ||||||||
\(886\) | 40.4156 | 1.35779 | ||||||||
\(887\) | 39.8386 | 1.33765 | 0.668824 | − | 0.743421i | \(-0.266798\pi\) | ||||
0.668824 | + | 0.743421i | \(0.266798\pi\) | |||||||
\(888\) | 216.802 | 7.27541 | ||||||||
\(889\) | 0.392058 | 0.0131492 | ||||||||
\(890\) | 0.457338 | 0.0153300 | ||||||||
\(891\) | −24.4955 | −0.820631 | ||||||||
\(892\) | −35.4706 | −1.18764 | ||||||||
\(893\) | −56.5003 | −1.89071 | ||||||||
\(894\) | 30.2587 | 1.01200 | ||||||||
\(895\) | 5.56309 | 0.185953 | ||||||||
\(896\) | 21.4244 | 0.715740 | ||||||||
\(897\) | −5.30750 | −0.177212 | ||||||||
\(898\) | 58.1856 | 1.94168 | ||||||||
\(899\) | 11.1139 | 0.370669 | ||||||||
\(900\) | −140.931 | −4.69769 | ||||||||
\(901\) | 30.7797 | 1.02542 | ||||||||
\(902\) | 86.3578 | 2.87540 | ||||||||
\(903\) | 28.6348 | 0.952907 | ||||||||
\(904\) | −37.8746 | −1.25969 | ||||||||
\(905\) | 1.07308 | 0.0356704 | ||||||||
\(906\) | −96.7683 | −3.21491 | ||||||||
\(907\) | −6.99072 | −0.232123 | −0.116062 | − | 0.993242i | \(-0.537027\pi\) | ||||
−0.116062 | + | 0.993242i | \(0.537027\pi\) | |||||||
\(908\) | 46.9548 | 1.55825 | ||||||||
\(909\) | 65.4351 | 2.17035 | ||||||||
\(910\) | 1.74342 | 0.0577939 | ||||||||
\(911\) | 51.2228 | 1.69709 | 0.848544 | − | 0.529125i | \(-0.177480\pi\) | ||||
0.848544 | + | 0.529125i | \(0.177480\pi\) | |||||||
\(912\) | 184.417 | 6.10667 | ||||||||
\(913\) | −31.2486 | −1.03418 | ||||||||
\(914\) | −35.2544 | −1.16611 | ||||||||
\(915\) | 2.09132 | 0.0691369 | ||||||||
\(916\) | −107.603 | −3.55530 | ||||||||
\(917\) | −20.8045 | −0.687024 | ||||||||
\(918\) | 52.0197 | 1.71690 | ||||||||
\(919\) | 17.7559 | 0.585715 | 0.292857 | − | 0.956156i | \(-0.405394\pi\) | ||||
0.292857 | + | 0.956156i | \(0.405394\pi\) | |||||||
\(920\) | 2.94539 | 0.0971068 | ||||||||
\(921\) | −95.9546 | −3.16181 | ||||||||
\(922\) | 25.1794 | 0.829238 | ||||||||
\(923\) | −25.0270 | −0.823774 | ||||||||
\(924\) | 76.4911 | 2.51637 | ||||||||
\(925\) | 41.6616 | 1.36983 | ||||||||
\(926\) | −78.8221 | −2.59025 | ||||||||
\(927\) | −10.1839 | −0.334484 | ||||||||
\(928\) | −22.0450 | −0.723661 | ||||||||
\(929\) | −13.4118 | −0.440027 | −0.220013 | − | 0.975497i | \(-0.570610\pi\) | ||||
−0.220013 | + | 0.975497i | \(0.570610\pi\) | |||||||
\(930\) | −23.8963 | −0.783590 | ||||||||
\(931\) | 4.88633 | 0.160143 | ||||||||
\(932\) | 115.368 | 3.77900 | ||||||||
\(933\) | −50.3317 | −1.64778 | ||||||||
\(934\) | 98.7322 | 3.23062 | ||||||||
\(935\) | 4.57765 | 0.149705 | ||||||||
\(936\) | −89.5758 | −2.92788 | ||||||||
\(937\) | −22.5056 | −0.735225 | −0.367612 | − | 0.929979i | \(-0.619825\pi\) | ||||
−0.367612 | + | 0.929979i | \(0.619825\pi\) | |||||||
\(938\) | −11.5740 | −0.377904 | ||||||||
\(939\) | −10.2120 | −0.333255 | ||||||||
\(940\) | −21.0254 | −0.685772 | ||||||||
\(941\) | 35.2001 | 1.14749 | 0.573746 | − | 0.819033i | \(-0.305490\pi\) | ||||
0.573746 | + | 0.819033i | \(0.305490\pi\) | |||||||
\(942\) | 37.3930 | 1.21833 | ||||||||
\(943\) | −6.24962 | −0.203516 | ||||||||
\(944\) | −113.822 | −3.70461 | ||||||||
\(945\) | −2.55252 | −0.0830336 | ||||||||
\(946\) | −132.131 | −4.29595 | ||||||||
\(947\) | 3.48739 | 0.113325 | 0.0566624 | − | 0.998393i | \(-0.481954\pi\) | ||||
0.0566624 | + | 0.998393i | \(0.481954\pi\) | |||||||
\(948\) | 161.970 | 5.26054 | ||||||||
\(949\) | −18.4719 | −0.599624 | ||||||||
\(950\) | 64.1284 | 2.08060 | ||||||||
\(951\) | −47.0746 | −1.52650 | ||||||||
\(952\) | −22.8986 | −0.742148 | ||||||||
\(953\) | −44.5458 | −1.44298 | −0.721490 | − | 0.692425i | \(-0.756543\pi\) | ||||
−0.721490 | + | 0.692425i | \(0.756543\pi\) | |||||||
\(954\) | 173.560 | 5.61922 | ||||||||
\(955\) | 0.0355689 | 0.00115098 | ||||||||
\(956\) | −139.207 | −4.50226 | ||||||||
\(957\) | −18.5322 | −0.599062 | ||||||||
\(958\) | −12.6974 | −0.410234 | ||||||||
\(959\) | 13.2735 | 0.428622 | ||||||||
\(960\) | 21.1789 | 0.683545 | ||||||||
\(961\) | 45.7954 | 1.47727 | ||||||||
\(962\) | 42.8534 | 1.38165 | ||||||||
\(963\) | −8.99006 | −0.289701 | ||||||||
\(964\) | −7.69795 | −0.247934 | ||||||||
\(965\) | 2.47992 | 0.0798316 | ||||||||
\(966\) | −7.65058 | −0.246153 | ||||||||
\(967\) | −23.4187 | −0.753095 | −0.376547 | − | 0.926397i | \(-0.622889\pi\) | ||||
−0.376547 | + | 0.926397i | \(0.622889\pi\) | |||||||
\(968\) | −122.399 | −3.93406 | ||||||||
\(969\) | −37.5344 | −1.20578 | ||||||||
\(970\) | −4.60982 | −0.148012 | ||||||||
\(971\) | 9.96733 | 0.319867 | 0.159933 | − | 0.987128i | \(-0.448872\pi\) | ||||
0.159933 | + | 0.987128i | \(0.448872\pi\) | |||||||
\(972\) | −40.6510 | −1.30388 | ||||||||
\(973\) | 19.0691 | 0.611327 | ||||||||
\(974\) | −101.779 | −3.26122 | ||||||||
\(975\) | −26.5721 | −0.850988 | ||||||||
\(976\) | 26.6760 | 0.853878 | ||||||||
\(977\) | 14.7814 | 0.472899 | 0.236449 | − | 0.971644i | \(-0.424016\pi\) | ||||
0.236449 | + | 0.971644i | \(0.424016\pi\) | |||||||
\(978\) | −98.2419 | −3.14143 | ||||||||
\(979\) | 2.45077 | 0.0783271 | ||||||||
\(980\) | 1.81834 | 0.0580848 | ||||||||
\(981\) | 12.5684 | 0.401278 | ||||||||
\(982\) | 23.0826 | 0.736596 | ||||||||
\(983\) | 48.6850 | 1.55281 | 0.776405 | − | 0.630234i | \(-0.217041\pi\) | ||||
0.776405 | + | 0.630234i | \(0.217041\pi\) | |||||||
\(984\) | −162.824 | −5.19062 | ||||||||
\(985\) | −6.20304 | −0.197645 | ||||||||
\(986\) | 8.97821 | 0.285924 | ||||||||
\(987\) | 33.7467 | 1.07417 | ||||||||
\(988\) | 47.7274 | 1.51841 | ||||||||
\(989\) | 9.56217 | 0.304059 | ||||||||
\(990\) | 25.8124 | 0.820372 | ||||||||
\(991\) | 48.7125 | 1.54740 | 0.773701 | − | 0.633551i | \(-0.218403\pi\) | ||||
0.773701 | + | 0.633551i | \(0.218403\pi\) | |||||||
\(992\) | −152.327 | −4.83640 | ||||||||
\(993\) | −21.6676 | −0.687600 | ||||||||
\(994\) | −36.0755 | −1.14425 | ||||||||
\(995\) | 2.18735 | 0.0693436 | ||||||||
\(996\) | 95.3476 | 3.02120 | ||||||||
\(997\) | 32.9908 | 1.04483 | 0.522414 | − | 0.852692i | \(-0.325031\pi\) | ||||
0.522414 | + | 0.852692i | \(0.325031\pi\) | |||||||
\(998\) | 67.6622 | 2.14181 | ||||||||
\(999\) | −62.7412 | −1.98504 |
(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 | 6013.2.a.c.1.5 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6013.2.a.c.1.5 | ✓ | 104 | 1.1 | even | 1 | trivial |