Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0759064919\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} - 2118 x^{6} - 710 x^{5} + 1113 x^{4} + 243 x^{3} - 183 x^{2} - 10 x + 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(0.256478\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.256478 | −0.181357 | −0.0906786 | − | 0.995880i | \(-0.528904\pi\) | ||||
−0.0906786 | + | 0.995880i | \(0.528904\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | −1.93422 | −0.967110 | ||||||||
\(5\) | −0.330746 | −0.147914 | −0.0739570 | − | 0.997261i | \(-0.523563\pi\) | ||||
−0.0739570 | + | 0.997261i | \(0.523563\pi\) | |||||||
\(6\) | −0.256478 | −0.104707 | ||||||||
\(7\) | 1.25226 | 0.473308 | 0.236654 | − | 0.971594i | \(-0.423949\pi\) | ||||
0.236654 | + | 0.971594i | \(0.423949\pi\) | |||||||
\(8\) | 1.00904 | 0.356750 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.0848290 | 0.0268253 | ||||||||
\(11\) | −0.708671 | −0.213672 | −0.106836 | − | 0.994277i | \(-0.534072\pi\) | ||||
−0.106836 | + | 0.994277i | \(0.534072\pi\) | |||||||
\(12\) | −1.93422 | −0.558361 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −0.321176 | −0.0858379 | ||||||||
\(15\) | −0.330746 | −0.0853982 | ||||||||
\(16\) | 3.60964 | 0.902410 | ||||||||
\(17\) | −5.11986 | −1.24175 | −0.620874 | − | 0.783910i | \(-0.713222\pi\) | ||||
−0.620874 | + | 0.783910i | \(0.713222\pi\) | |||||||
\(18\) | −0.256478 | −0.0604524 | ||||||||
\(19\) | 4.61143 | 1.05794 | 0.528968 | − | 0.848642i | \(-0.322579\pi\) | ||||
0.528968 | + | 0.848642i | \(0.322579\pi\) | |||||||
\(20\) | 0.639735 | 0.143049 | ||||||||
\(21\) | 1.25226 | 0.273265 | ||||||||
\(22\) | 0.181758 | 0.0387510 | ||||||||
\(23\) | 4.94053 | 1.03017 | 0.515086 | − | 0.857138i | \(-0.327760\pi\) | ||||
0.515086 | + | 0.857138i | \(0.327760\pi\) | |||||||
\(24\) | 1.00904 | 0.205969 | ||||||||
\(25\) | −4.89061 | −0.978121 | ||||||||
\(26\) | 0.256478 | 0.0502994 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.42214 | −0.457741 | ||||||||
\(29\) | −5.42929 | −1.00819 | −0.504097 | − | 0.863647i | \(-0.668175\pi\) | ||||
−0.504097 | + | 0.863647i | \(0.668175\pi\) | |||||||
\(30\) | 0.0848290 | 0.0154876 | ||||||||
\(31\) | −7.69609 | −1.38226 | −0.691130 | − | 0.722731i | \(-0.742887\pi\) | ||||
−0.691130 | + | 0.722731i | \(0.742887\pi\) | |||||||
\(32\) | −2.94387 | −0.520408 | ||||||||
\(33\) | −0.708671 | −0.123364 | ||||||||
\(34\) | 1.31313 | 0.225200 | ||||||||
\(35\) | −0.414179 | −0.0700089 | ||||||||
\(36\) | −1.93422 | −0.322370 | ||||||||
\(37\) | −10.3326 | −1.69868 | −0.849338 | − | 0.527850i | \(-0.822998\pi\) | ||||
−0.849338 | + | 0.527850i | \(0.822998\pi\) | |||||||
\(38\) | −1.18273 | −0.191864 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −0.333736 | −0.0527683 | ||||||||
\(41\) | 8.14897 | 1.27265 | 0.636327 | − | 0.771419i | \(-0.280453\pi\) | ||||
0.636327 | + | 0.771419i | \(0.280453\pi\) | |||||||
\(42\) | −0.321176 | −0.0495585 | ||||||||
\(43\) | 6.55836 | 1.00014 | 0.500070 | − | 0.865985i | \(-0.333308\pi\) | ||||
0.500070 | + | 0.865985i | \(0.333308\pi\) | |||||||
\(44\) | 1.37073 | 0.206645 | ||||||||
\(45\) | −0.330746 | −0.0493047 | ||||||||
\(46\) | −1.26714 | −0.186829 | ||||||||
\(47\) | −6.08641 | −0.887794 | −0.443897 | − | 0.896078i | \(-0.646404\pi\) | ||||
−0.443897 | + | 0.896078i | \(0.646404\pi\) | |||||||
\(48\) | 3.60964 | 0.521007 | ||||||||
\(49\) | −5.43185 | −0.775979 | ||||||||
\(50\) | 1.25433 | 0.177389 | ||||||||
\(51\) | −5.11986 | −0.716924 | ||||||||
\(52\) | 1.93422 | 0.268228 | ||||||||
\(53\) | 6.75068 | 0.927277 | 0.463638 | − | 0.886025i | \(-0.346544\pi\) | ||||
0.463638 | + | 0.886025i | \(0.346544\pi\) | |||||||
\(54\) | −0.256478 | −0.0349022 | ||||||||
\(55\) | 0.234390 | 0.0316051 | ||||||||
\(56\) | 1.26358 | 0.168853 | ||||||||
\(57\) | 4.61143 | 0.610799 | ||||||||
\(58\) | 1.39249 | 0.182843 | ||||||||
\(59\) | 13.2817 | 1.72912 | 0.864562 | − | 0.502526i | \(-0.167596\pi\) | ||||
0.864562 | + | 0.502526i | \(0.167596\pi\) | |||||||
\(60\) | 0.639735 | 0.0825894 | ||||||||
\(61\) | 0.799420 | 0.102355 | 0.0511776 | − | 0.998690i | \(-0.483703\pi\) | ||||
0.0511776 | + | 0.998690i | \(0.483703\pi\) | |||||||
\(62\) | 1.97388 | 0.250683 | ||||||||
\(63\) | 1.25226 | 0.157769 | ||||||||
\(64\) | −6.46425 | −0.808031 | ||||||||
\(65\) | 0.330746 | 0.0410240 | ||||||||
\(66\) | 0.181758 | 0.0223729 | ||||||||
\(67\) | −2.78601 | −0.340365 | −0.170183 | − | 0.985413i | \(-0.554436\pi\) | ||||
−0.170183 | + | 0.985413i | \(0.554436\pi\) | |||||||
\(68\) | 9.90293 | 1.20091 | ||||||||
\(69\) | 4.94053 | 0.594770 | ||||||||
\(70\) | 0.106228 | 0.0126966 | ||||||||
\(71\) | −4.43224 | −0.526011 | −0.263005 | − | 0.964794i | \(-0.584714\pi\) | ||||
−0.263005 | + | 0.964794i | \(0.584714\pi\) | |||||||
\(72\) | 1.00904 | 0.118917 | ||||||||
\(73\) | 14.2243 | 1.66483 | 0.832414 | − | 0.554155i | \(-0.186958\pi\) | ||||
0.832414 | + | 0.554155i | \(0.186958\pi\) | |||||||
\(74\) | 2.65009 | 0.308067 | ||||||||
\(75\) | −4.89061 | −0.564719 | ||||||||
\(76\) | −8.91952 | −1.02314 | ||||||||
\(77\) | −0.887438 | −0.101133 | ||||||||
\(78\) | 0.256478 | 0.0290404 | ||||||||
\(79\) | −0.500065 | −0.0562617 | −0.0281309 | − | 0.999604i | \(-0.508956\pi\) | ||||
−0.0281309 | + | 0.999604i | \(0.508956\pi\) | |||||||
\(80\) | −1.19387 | −0.133479 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.09003 | −0.230805 | ||||||||
\(83\) | −5.34068 | −0.586215 | −0.293108 | − | 0.956079i | \(-0.594689\pi\) | ||||
−0.293108 | + | 0.956079i | \(0.594689\pi\) | |||||||
\(84\) | −2.42214 | −0.264277 | ||||||||
\(85\) | 1.69337 | 0.183672 | ||||||||
\(86\) | −1.68207 | −0.181383 | ||||||||
\(87\) | −5.42929 | −0.582081 | ||||||||
\(88\) | −0.715077 | −0.0762275 | ||||||||
\(89\) | −10.3891 | −1.10125 | −0.550624 | − | 0.834754i | \(-0.685610\pi\) | ||||
−0.550624 | + | 0.834754i | \(0.685610\pi\) | |||||||
\(90\) | 0.0848290 | 0.00894176 | ||||||||
\(91\) | −1.25226 | −0.131272 | ||||||||
\(92\) | −9.55607 | −0.996289 | ||||||||
\(93\) | −7.69609 | −0.798048 | ||||||||
\(94\) | 1.56103 | 0.161008 | ||||||||
\(95\) | −1.52521 | −0.156483 | ||||||||
\(96\) | −2.94387 | −0.300458 | ||||||||
\(97\) | −9.27613 | −0.941848 | −0.470924 | − | 0.882174i | \(-0.656079\pi\) | ||||
−0.470924 | + | 0.882174i | \(0.656079\pi\) | |||||||
\(98\) | 1.39315 | 0.140729 | ||||||||
\(99\) | −0.708671 | −0.0712241 | ||||||||
\(100\) | 9.45951 | 0.945951 | ||||||||
\(101\) | −12.4389 | −1.23772 | −0.618858 | − | 0.785503i | \(-0.712404\pi\) | ||||
−0.618858 | + | 0.785503i | \(0.712404\pi\) | |||||||
\(102\) | 1.31313 | 0.130019 | ||||||||
\(103\) | 1.00000 | 0.0985329 | ||||||||
\(104\) | −1.00904 | −0.0989445 | ||||||||
\(105\) | −0.414179 | −0.0404197 | ||||||||
\(106\) | −1.73140 | −0.168168 | ||||||||
\(107\) | 9.17964 | 0.887429 | 0.443715 | − | 0.896168i | \(-0.353660\pi\) | ||||
0.443715 | + | 0.896168i | \(0.353660\pi\) | |||||||
\(108\) | −1.93422 | −0.186120 | ||||||||
\(109\) | −14.3027 | −1.36995 | −0.684975 | − | 0.728567i | \(-0.740187\pi\) | ||||
−0.684975 | + | 0.728567i | \(0.740187\pi\) | |||||||
\(110\) | −0.0601158 | −0.00573182 | ||||||||
\(111\) | −10.3326 | −0.980731 | ||||||||
\(112\) | 4.52020 | 0.427118 | ||||||||
\(113\) | −9.63960 | −0.906817 | −0.453409 | − | 0.891303i | \(-0.649792\pi\) | ||||
−0.453409 | + | 0.891303i | \(0.649792\pi\) | |||||||
\(114\) | −1.18273 | −0.110773 | ||||||||
\(115\) | −1.63406 | −0.152377 | ||||||||
\(116\) | 10.5014 | 0.975034 | ||||||||
\(117\) | −1.00000 | −0.0924500 | ||||||||
\(118\) | −3.40645 | −0.313589 | ||||||||
\(119\) | −6.41138 | −0.587730 | ||||||||
\(120\) | −0.333736 | −0.0304658 | ||||||||
\(121\) | −10.4978 | −0.954344 | ||||||||
\(122\) | −0.205034 | −0.0185629 | ||||||||
\(123\) | 8.14897 | 0.734768 | ||||||||
\(124\) | 14.8859 | 1.33680 | ||||||||
\(125\) | 3.27128 | 0.292592 | ||||||||
\(126\) | −0.321176 | −0.0286126 | ||||||||
\(127\) | −6.11083 | −0.542248 | −0.271124 | − | 0.962544i | \(-0.587395\pi\) | ||||
−0.271124 | + | 0.962544i | \(0.587395\pi\) | |||||||
\(128\) | 7.54568 | 0.666950 | ||||||||
\(129\) | 6.55836 | 0.577431 | ||||||||
\(130\) | −0.0848290 | −0.00743999 | ||||||||
\(131\) | −13.1424 | −1.14826 | −0.574128 | − | 0.818766i | \(-0.694659\pi\) | ||||
−0.574128 | + | 0.818766i | \(0.694659\pi\) | |||||||
\(132\) | 1.37073 | 0.119306 | ||||||||
\(133\) | 5.77470 | 0.500730 | ||||||||
\(134\) | 0.714550 | 0.0617277 | ||||||||
\(135\) | −0.330746 | −0.0284661 | ||||||||
\(136\) | −5.16614 | −0.442993 | ||||||||
\(137\) | −6.50977 | −0.556167 | −0.278084 | − | 0.960557i | \(-0.589699\pi\) | ||||
−0.278084 | + | 0.960557i | \(0.589699\pi\) | |||||||
\(138\) | −1.26714 | −0.107866 | ||||||||
\(139\) | 2.15233 | 0.182559 | 0.0912793 | − | 0.995825i | \(-0.470904\pi\) | ||||
0.0912793 | + | 0.995825i | \(0.470904\pi\) | |||||||
\(140\) | 0.801112 | 0.0677063 | ||||||||
\(141\) | −6.08641 | −0.512568 | ||||||||
\(142\) | 1.13677 | 0.0953958 | ||||||||
\(143\) | 0.708671 | 0.0592620 | ||||||||
\(144\) | 3.60964 | 0.300803 | ||||||||
\(145\) | 1.79572 | 0.149126 | ||||||||
\(146\) | −3.64822 | −0.301929 | ||||||||
\(147\) | −5.43185 | −0.448012 | ||||||||
\(148\) | 19.9856 | 1.64281 | ||||||||
\(149\) | −14.2020 | −1.16348 | −0.581738 | − | 0.813376i | \(-0.697627\pi\) | ||||
−0.581738 | + | 0.813376i | \(0.697627\pi\) | |||||||
\(150\) | 1.25433 | 0.102416 | ||||||||
\(151\) | 18.8801 | 1.53644 | 0.768219 | − | 0.640187i | \(-0.221143\pi\) | ||||
0.768219 | + | 0.640187i | \(0.221143\pi\) | |||||||
\(152\) | 4.65312 | 0.377418 | ||||||||
\(153\) | −5.11986 | −0.413916 | ||||||||
\(154\) | 0.227608 | 0.0183412 | ||||||||
\(155\) | 2.54545 | 0.204456 | ||||||||
\(156\) | 1.93422 | 0.154861 | ||||||||
\(157\) | −10.2255 | −0.816081 | −0.408040 | − | 0.912964i | \(-0.633788\pi\) | ||||
−0.408040 | + | 0.912964i | \(0.633788\pi\) | |||||||
\(158\) | 0.128256 | 0.0102035 | ||||||||
\(159\) | 6.75068 | 0.535363 | ||||||||
\(160\) | 0.973674 | 0.0769757 | ||||||||
\(161\) | 6.18681 | 0.487589 | ||||||||
\(162\) | −0.256478 | −0.0201508 | ||||||||
\(163\) | −18.7160 | −1.46595 | −0.732976 | − | 0.680255i | \(-0.761869\pi\) | ||||
−0.732976 | + | 0.680255i | \(0.761869\pi\) | |||||||
\(164\) | −15.7619 | −1.23080 | ||||||||
\(165\) | 0.234390 | 0.0182472 | ||||||||
\(166\) | 1.36977 | 0.106314 | ||||||||
\(167\) | −5.05071 | −0.390836 | −0.195418 | − | 0.980720i | \(-0.562606\pi\) | ||||
−0.195418 | + | 0.980720i | \(0.562606\pi\) | |||||||
\(168\) | 1.26358 | 0.0974871 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −0.434312 | −0.0333102 | ||||||||
\(171\) | 4.61143 | 0.352645 | ||||||||
\(172\) | −12.6853 | −0.967245 | ||||||||
\(173\) | −18.0644 | −1.37341 | −0.686704 | − | 0.726937i | \(-0.740943\pi\) | ||||
−0.686704 | + | 0.726937i | \(0.740943\pi\) | |||||||
\(174\) | 1.39249 | 0.105565 | ||||||||
\(175\) | −6.12429 | −0.462953 | ||||||||
\(176\) | −2.55805 | −0.192820 | ||||||||
\(177\) | 13.2817 | 0.998310 | ||||||||
\(178\) | 2.66459 | 0.199719 | ||||||||
\(179\) | 25.0335 | 1.87109 | 0.935545 | − | 0.353208i | \(-0.114909\pi\) | ||||
0.935545 | + | 0.353208i | \(0.114909\pi\) | |||||||
\(180\) | 0.639735 | 0.0476830 | ||||||||
\(181\) | −3.97181 | −0.295223 | −0.147611 | − | 0.989045i | \(-0.547158\pi\) | ||||
−0.147611 | + | 0.989045i | \(0.547158\pi\) | |||||||
\(182\) | 0.321176 | 0.0238071 | ||||||||
\(183\) | 0.799420 | 0.0590948 | ||||||||
\(184\) | 4.98519 | 0.367513 | ||||||||
\(185\) | 3.41748 | 0.251258 | ||||||||
\(186\) | 1.97388 | 0.144732 | ||||||||
\(187\) | 3.62830 | 0.265327 | ||||||||
\(188\) | 11.7724 | 0.858594 | ||||||||
\(189\) | 1.25226 | 0.0910882 | ||||||||
\(190\) | 0.391183 | 0.0283794 | ||||||||
\(191\) | 18.8856 | 1.36651 | 0.683256 | − | 0.730179i | \(-0.260564\pi\) | ||||
0.683256 | + | 0.730179i | \(0.260564\pi\) | |||||||
\(192\) | −6.46425 | −0.466517 | ||||||||
\(193\) | −15.7494 | −1.13367 | −0.566835 | − | 0.823831i | \(-0.691832\pi\) | ||||
−0.566835 | + | 0.823831i | \(0.691832\pi\) | |||||||
\(194\) | 2.37912 | 0.170811 | ||||||||
\(195\) | 0.330746 | 0.0236852 | ||||||||
\(196\) | 10.5064 | 0.750457 | ||||||||
\(197\) | −21.1867 | −1.50949 | −0.754743 | − | 0.656020i | \(-0.772239\pi\) | ||||
−0.754743 | + | 0.656020i | \(0.772239\pi\) | |||||||
\(198\) | 0.181758 | 0.0129170 | ||||||||
\(199\) | 0.295285 | 0.0209322 | 0.0104661 | − | 0.999945i | \(-0.496668\pi\) | ||||
0.0104661 | + | 0.999945i | \(0.496668\pi\) | |||||||
\(200\) | −4.93482 | −0.348944 | ||||||||
\(201\) | −2.78601 | −0.196510 | ||||||||
\(202\) | 3.19030 | 0.224469 | ||||||||
\(203\) | −6.79886 | −0.477187 | ||||||||
\(204\) | 9.90293 | 0.693344 | ||||||||
\(205\) | −2.69524 | −0.188244 | ||||||||
\(206\) | −0.256478 | −0.0178697 | ||||||||
\(207\) | 4.94053 | 0.343391 | ||||||||
\(208\) | −3.60964 | −0.250284 | ||||||||
\(209\) | −3.26799 | −0.226052 | ||||||||
\(210\) | 0.106228 | 0.00733040 | ||||||||
\(211\) | 0.815219 | 0.0561220 | 0.0280610 | − | 0.999606i | \(-0.491067\pi\) | ||||
0.0280610 | + | 0.999606i | \(0.491067\pi\) | |||||||
\(212\) | −13.0573 | −0.896778 | ||||||||
\(213\) | −4.43224 | −0.303692 | ||||||||
\(214\) | −2.35437 | −0.160942 | ||||||||
\(215\) | −2.16915 | −0.147935 | ||||||||
\(216\) | 1.00904 | 0.0686565 | ||||||||
\(217\) | −9.63748 | −0.654235 | ||||||||
\(218\) | 3.66832 | 0.248450 | ||||||||
\(219\) | 14.2243 | 0.961189 | ||||||||
\(220\) | −0.453362 | −0.0305656 | ||||||||
\(221\) | 5.11986 | 0.344399 | ||||||||
\(222\) | 2.65009 | 0.177863 | ||||||||
\(223\) | −7.97500 | −0.534045 | −0.267023 | − | 0.963690i | \(-0.586040\pi\) | ||||
−0.267023 | + | 0.963690i | \(0.586040\pi\) | |||||||
\(224\) | −3.68648 | −0.246314 | ||||||||
\(225\) | −4.89061 | −0.326040 | ||||||||
\(226\) | 2.47234 | 0.164458 | ||||||||
\(227\) | 6.13888 | 0.407452 | 0.203726 | − | 0.979028i | \(-0.434695\pi\) | ||||
0.203726 | + | 0.979028i | \(0.434695\pi\) | |||||||
\(228\) | −8.91952 | −0.590710 | ||||||||
\(229\) | −0.550057 | −0.0363488 | −0.0181744 | − | 0.999835i | \(-0.505785\pi\) | ||||
−0.0181744 | + | 0.999835i | \(0.505785\pi\) | |||||||
\(230\) | 0.419100 | 0.0276347 | ||||||||
\(231\) | −0.887438 | −0.0583891 | ||||||||
\(232\) | −5.47837 | −0.359673 | ||||||||
\(233\) | −6.24861 | −0.409360 | −0.204680 | − | 0.978829i | \(-0.565615\pi\) | ||||
−0.204680 | + | 0.978829i | \(0.565615\pi\) | |||||||
\(234\) | 0.256478 | 0.0167665 | ||||||||
\(235\) | 2.01305 | 0.131317 | ||||||||
\(236\) | −25.6896 | −1.67225 | ||||||||
\(237\) | −0.500065 | −0.0324827 | ||||||||
\(238\) | 1.64438 | 0.106589 | ||||||||
\(239\) | 14.1237 | 0.913589 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(240\) | −1.19387 | −0.0770642 | ||||||||
\(241\) | −6.98081 | −0.449674 | −0.224837 | − | 0.974396i | \(-0.572185\pi\) | ||||
−0.224837 | + | 0.974396i | \(0.572185\pi\) | |||||||
\(242\) | 2.69245 | 0.173077 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −1.54625 | −0.0989887 | ||||||||
\(245\) | 1.79656 | 0.114778 | ||||||||
\(246\) | −2.09003 | −0.133255 | ||||||||
\(247\) | −4.61143 | −0.293418 | ||||||||
\(248\) | −7.76567 | −0.493120 | ||||||||
\(249\) | −5.34068 | −0.338452 | ||||||||
\(250\) | −0.839010 | −0.0530637 | ||||||||
\(251\) | −10.4449 | −0.659279 | −0.329640 | − | 0.944107i | \(-0.606927\pi\) | ||||
−0.329640 | + | 0.944107i | \(0.606927\pi\) | |||||||
\(252\) | −2.42214 | −0.152580 | ||||||||
\(253\) | −3.50121 | −0.220119 | ||||||||
\(254\) | 1.56729 | 0.0983406 | ||||||||
\(255\) | 1.69337 | 0.106043 | ||||||||
\(256\) | 10.9932 | 0.687074 | ||||||||
\(257\) | 21.9346 | 1.36824 | 0.684121 | − | 0.729368i | \(-0.260186\pi\) | ||||
0.684121 | + | 0.729368i | \(0.260186\pi\) | |||||||
\(258\) | −1.68207 | −0.104721 | ||||||||
\(259\) | −12.9391 | −0.803997 | ||||||||
\(260\) | −0.639735 | −0.0396747 | ||||||||
\(261\) | −5.42929 | −0.336065 | ||||||||
\(262\) | 3.37073 | 0.208244 | ||||||||
\(263\) | 19.0663 | 1.17568 | 0.587840 | − | 0.808977i | \(-0.299978\pi\) | ||||
0.587840 | + | 0.808977i | \(0.299978\pi\) | |||||||
\(264\) | −0.715077 | −0.0440100 | ||||||||
\(265\) | −2.23276 | −0.137157 | ||||||||
\(266\) | −1.48108 | −0.0908109 | ||||||||
\(267\) | −10.3891 | −0.635806 | ||||||||
\(268\) | 5.38875 | 0.329171 | ||||||||
\(269\) | −11.3506 | −0.692059 | −0.346030 | − | 0.938224i | \(-0.612470\pi\) | ||||
−0.346030 | + | 0.938224i | \(0.612470\pi\) | |||||||
\(270\) | 0.0848290 | 0.00516253 | ||||||||
\(271\) | −12.7824 | −0.776478 | −0.388239 | − | 0.921559i | \(-0.626917\pi\) | ||||
−0.388239 | + | 0.921559i | \(0.626917\pi\) | |||||||
\(272\) | −18.4809 | −1.12057 | ||||||||
\(273\) | −1.25226 | −0.0757900 | ||||||||
\(274\) | 1.66961 | 0.100865 | ||||||||
\(275\) | 3.46583 | 0.208998 | ||||||||
\(276\) | −9.55607 | −0.575208 | ||||||||
\(277\) | −32.0113 | −1.92337 | −0.961686 | − | 0.274154i | \(-0.911602\pi\) | ||||
−0.961686 | + | 0.274154i | \(0.911602\pi\) | |||||||
\(278\) | −0.552026 | −0.0331083 | ||||||||
\(279\) | −7.69609 | −0.460753 | ||||||||
\(280\) | −0.417923 | −0.0249757 | ||||||||
\(281\) | −1.68742 | −0.100663 | −0.0503314 | − | 0.998733i | \(-0.516028\pi\) | ||||
−0.0503314 | + | 0.998733i | \(0.516028\pi\) | |||||||
\(282\) | 1.56103 | 0.0929579 | ||||||||
\(283\) | −27.5741 | −1.63911 | −0.819554 | − | 0.573002i | \(-0.805779\pi\) | ||||
−0.819554 | + | 0.573002i | \(0.805779\pi\) | |||||||
\(284\) | 8.57293 | 0.508710 | ||||||||
\(285\) | −1.52521 | −0.0903458 | ||||||||
\(286\) | −0.181758 | −0.0107476 | ||||||||
\(287\) | 10.2046 | 0.602358 | ||||||||
\(288\) | −2.94387 | −0.173469 | ||||||||
\(289\) | 9.21296 | 0.541939 | ||||||||
\(290\) | −0.460561 | −0.0270451 | ||||||||
\(291\) | −9.27613 | −0.543776 | ||||||||
\(292\) | −27.5129 | −1.61007 | ||||||||
\(293\) | −20.4622 | −1.19541 | −0.597706 | − | 0.801716i | \(-0.703921\pi\) | ||||
−0.597706 | + | 0.801716i | \(0.703921\pi\) | |||||||
\(294\) | 1.39315 | 0.0812502 | ||||||||
\(295\) | −4.39285 | −0.255762 | ||||||||
\(296\) | −10.4260 | −0.606002 | ||||||||
\(297\) | −0.708671 | −0.0411213 | ||||||||
\(298\) | 3.64251 | 0.211005 | ||||||||
\(299\) | −4.94053 | −0.285718 | ||||||||
\(300\) | 9.45951 | 0.546145 | ||||||||
\(301\) | 8.21275 | 0.473375 | ||||||||
\(302\) | −4.84232 | −0.278644 | ||||||||
\(303\) | −12.4389 | −0.714596 | ||||||||
\(304\) | 16.6456 | 0.954692 | ||||||||
\(305\) | −0.264405 | −0.0151398 | ||||||||
\(306\) | 1.31313 | 0.0750667 | ||||||||
\(307\) | −3.25494 | −0.185769 | −0.0928847 | − | 0.995677i | \(-0.529609\pi\) | ||||
−0.0928847 | + | 0.995677i | \(0.529609\pi\) | |||||||
\(308\) | 1.71650 | 0.0978066 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | −0.652852 | −0.0370795 | ||||||||
\(311\) | −27.2162 | −1.54329 | −0.771643 | − | 0.636055i | \(-0.780565\pi\) | ||||
−0.771643 | + | 0.636055i | \(0.780565\pi\) | |||||||
\(312\) | −1.00904 | −0.0571256 | ||||||||
\(313\) | 11.9023 | 0.672758 | 0.336379 | − | 0.941727i | \(-0.390798\pi\) | ||||
0.336379 | + | 0.941727i | \(0.390798\pi\) | |||||||
\(314\) | 2.62261 | 0.148002 | ||||||||
\(315\) | −0.414179 | −0.0233363 | ||||||||
\(316\) | 0.967235 | 0.0544112 | ||||||||
\(317\) | 20.6928 | 1.16222 | 0.581111 | − | 0.813824i | \(-0.302618\pi\) | ||||
0.581111 | + | 0.813824i | \(0.302618\pi\) | |||||||
\(318\) | −1.73140 | −0.0970920 | ||||||||
\(319\) | 3.84758 | 0.215423 | ||||||||
\(320\) | 2.13802 | 0.119519 | ||||||||
\(321\) | 9.17964 | 0.512357 | ||||||||
\(322\) | −1.58678 | −0.0884278 | ||||||||
\(323\) | −23.6099 | −1.31369 | ||||||||
\(324\) | −1.93422 | −0.107457 | ||||||||
\(325\) | 4.89061 | 0.271282 | ||||||||
\(326\) | 4.80024 | 0.265861 | ||||||||
\(327\) | −14.3027 | −0.790941 | ||||||||
\(328\) | 8.22263 | 0.454019 | ||||||||
\(329\) | −7.62174 | −0.420200 | ||||||||
\(330\) | −0.0601158 | −0.00330927 | ||||||||
\(331\) | 25.4281 | 1.39765 | 0.698826 | − | 0.715292i | \(-0.253706\pi\) | ||||
0.698826 | + | 0.715292i | \(0.253706\pi\) | |||||||
\(332\) | 10.3300 | 0.566934 | ||||||||
\(333\) | −10.3326 | −0.566225 | ||||||||
\(334\) | 1.29540 | 0.0708809 | ||||||||
\(335\) | 0.921461 | 0.0503448 | ||||||||
\(336\) | 4.52020 | 0.246597 | ||||||||
\(337\) | −11.8426 | −0.645110 | −0.322555 | − | 0.946551i | \(-0.604542\pi\) | ||||
−0.322555 | + | 0.946551i | \(0.604542\pi\) | |||||||
\(338\) | −0.256478 | −0.0139506 | ||||||||
\(339\) | −9.63960 | −0.523551 | ||||||||
\(340\) | −3.27535 | −0.177631 | ||||||||
\(341\) | 5.45400 | 0.295351 | ||||||||
\(342\) | −1.18273 | −0.0639547 | ||||||||
\(343\) | −15.5679 | −0.840586 | ||||||||
\(344\) | 6.61765 | 0.356800 | ||||||||
\(345\) | −1.63406 | −0.0879749 | ||||||||
\(346\) | 4.63311 | 0.249077 | ||||||||
\(347\) | 22.8076 | 1.22438 | 0.612189 | − | 0.790712i | \(-0.290289\pi\) | ||||
0.612189 | + | 0.790712i | \(0.290289\pi\) | |||||||
\(348\) | 10.5014 | 0.562936 | ||||||||
\(349\) | −1.31325 | −0.0702967 | −0.0351484 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351484 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(350\) | 1.57075 | 0.0839599 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.08624 | 0.111197 | ||||||||
\(353\) | 22.2826 | 1.18598 | 0.592992 | − | 0.805209i | \(-0.297947\pi\) | ||||
0.592992 | + | 0.805209i | \(0.297947\pi\) | |||||||
\(354\) | −3.40645 | −0.181051 | ||||||||
\(355\) | 1.46595 | 0.0778043 | ||||||||
\(356\) | 20.0949 | 1.06503 | ||||||||
\(357\) | −6.41138 | −0.339326 | ||||||||
\(358\) | −6.42053 | −0.339336 | ||||||||
\(359\) | −5.68425 | −0.300003 | −0.150002 | − | 0.988686i | \(-0.547928\pi\) | ||||
−0.150002 | + | 0.988686i | \(0.547928\pi\) | |||||||
\(360\) | −0.333736 | −0.0175894 | ||||||||
\(361\) | 2.26531 | 0.119227 | ||||||||
\(362\) | 1.01868 | 0.0535407 | ||||||||
\(363\) | −10.4978 | −0.550991 | ||||||||
\(364\) | 2.42214 | 0.126955 | ||||||||
\(365\) | −4.70463 | −0.246251 | ||||||||
\(366\) | −0.205034 | −0.0107173 | ||||||||
\(367\) | 25.9656 | 1.35539 | 0.677697 | − | 0.735341i | \(-0.262978\pi\) | ||||
0.677697 | + | 0.735341i | \(0.262978\pi\) | |||||||
\(368\) | 17.8336 | 0.929638 | ||||||||
\(369\) | 8.14897 | 0.424218 | ||||||||
\(370\) | −0.876507 | −0.0455674 | ||||||||
\(371\) | 8.45358 | 0.438888 | ||||||||
\(372\) | 14.8859 | 0.771800 | ||||||||
\(373\) | −34.2715 | −1.77451 | −0.887256 | − | 0.461278i | \(-0.847391\pi\) | ||||
−0.887256 | + | 0.461278i | \(0.847391\pi\) | |||||||
\(374\) | −0.930578 | −0.0481190 | ||||||||
\(375\) | 3.27128 | 0.168928 | ||||||||
\(376\) | −6.14143 | −0.316720 | ||||||||
\(377\) | 5.42929 | 0.279623 | ||||||||
\(378\) | −0.321176 | −0.0165195 | ||||||||
\(379\) | −28.4091 | −1.45928 | −0.729640 | − | 0.683832i | \(-0.760312\pi\) | ||||
−0.729640 | + | 0.683832i | \(0.760312\pi\) | |||||||
\(380\) | 2.95009 | 0.151337 | ||||||||
\(381\) | −6.11083 | −0.313067 | ||||||||
\(382\) | −4.84373 | −0.247827 | ||||||||
\(383\) | 27.4522 | 1.40274 | 0.701370 | − | 0.712798i | \(-0.252572\pi\) | ||||
0.701370 | + | 0.712798i | \(0.252572\pi\) | |||||||
\(384\) | 7.54568 | 0.385064 | ||||||||
\(385\) | 0.293516 | 0.0149590 | ||||||||
\(386\) | 4.03938 | 0.205599 | ||||||||
\(387\) | 6.55836 | 0.333380 | ||||||||
\(388\) | 17.9421 | 0.910870 | ||||||||
\(389\) | 27.9248 | 1.41584 | 0.707921 | − | 0.706292i | \(-0.249633\pi\) | ||||
0.707921 | + | 0.706292i | \(0.249633\pi\) | |||||||
\(390\) | −0.0848290 | −0.00429548 | ||||||||
\(391\) | −25.2948 | −1.27921 | ||||||||
\(392\) | −5.48096 | −0.276830 | ||||||||
\(393\) | −13.1424 | −0.662946 | ||||||||
\(394\) | 5.43391 | 0.273756 | ||||||||
\(395\) | 0.165394 | 0.00832190 | ||||||||
\(396\) | 1.37073 | 0.0688815 | ||||||||
\(397\) | 13.3500 | 0.670018 | 0.335009 | − | 0.942215i | \(-0.391261\pi\) | ||||
0.335009 | + | 0.942215i | \(0.391261\pi\) | |||||||
\(398\) | −0.0757339 | −0.00379620 | ||||||||
\(399\) | 5.77470 | 0.289096 | ||||||||
\(400\) | −17.6533 | −0.882667 | ||||||||
\(401\) | 15.1361 | 0.755863 | 0.377931 | − | 0.925834i | \(-0.376636\pi\) | ||||
0.377931 | + | 0.925834i | \(0.376636\pi\) | |||||||
\(402\) | 0.714550 | 0.0356385 | ||||||||
\(403\) | 7.69609 | 0.383370 | ||||||||
\(404\) | 24.0595 | 1.19701 | ||||||||
\(405\) | −0.330746 | −0.0164349 | ||||||||
\(406\) | 1.74376 | 0.0865413 | ||||||||
\(407\) | 7.32244 | 0.362960 | ||||||||
\(408\) | −5.16614 | −0.255762 | ||||||||
\(409\) | −0.521617 | −0.0257923 | −0.0128962 | − | 0.999917i | \(-0.504105\pi\) | ||||
−0.0128962 | + | 0.999917i | \(0.504105\pi\) | |||||||
\(410\) | 0.691269 | 0.0341393 | ||||||||
\(411\) | −6.50977 | −0.321103 | ||||||||
\(412\) | −1.93422 | −0.0952921 | ||||||||
\(413\) | 16.6320 | 0.818409 | ||||||||
\(414\) | −1.26714 | −0.0622764 | ||||||||
\(415\) | 1.76641 | 0.0867095 | ||||||||
\(416\) | 2.94387 | 0.144335 | ||||||||
\(417\) | 2.15233 | 0.105400 | ||||||||
\(418\) | 0.838167 | 0.0409961 | ||||||||
\(419\) | 38.7591 | 1.89351 | 0.946753 | − | 0.321961i | \(-0.104342\pi\) | ||||
0.946753 | + | 0.321961i | \(0.104342\pi\) | |||||||
\(420\) | 0.801112 | 0.0390903 | ||||||||
\(421\) | −20.4436 | −0.996358 | −0.498179 | − | 0.867074i | \(-0.665998\pi\) | ||||
−0.498179 | + | 0.867074i | \(0.665998\pi\) | |||||||
\(422\) | −0.209086 | −0.0101781 | ||||||||
\(423\) | −6.08641 | −0.295931 | ||||||||
\(424\) | 6.81170 | 0.330805 | ||||||||
\(425\) | 25.0392 | 1.21458 | ||||||||
\(426\) | 1.13677 | 0.0550768 | ||||||||
\(427\) | 1.00108 | 0.0484456 | ||||||||
\(428\) | −17.7554 | −0.858241 | ||||||||
\(429\) | 0.708671 | 0.0342150 | ||||||||
\(430\) | 0.556339 | 0.0268290 | ||||||||
\(431\) | −0.0783003 | −0.00377159 | −0.00188580 | − | 0.999998i | \(-0.500600\pi\) | ||||
−0.00188580 | + | 0.999998i | \(0.500600\pi\) | |||||||
\(432\) | 3.60964 | 0.173669 | ||||||||
\(433\) | −19.2156 | −0.923441 | −0.461721 | − | 0.887025i | \(-0.652768\pi\) | ||||
−0.461721 | + | 0.887025i | \(0.652768\pi\) | |||||||
\(434\) | 2.47180 | 0.118650 | ||||||||
\(435\) | 1.79572 | 0.0860980 | ||||||||
\(436\) | 27.6645 | 1.32489 | ||||||||
\(437\) | 22.7829 | 1.08986 | ||||||||
\(438\) | −3.64822 | −0.174319 | ||||||||
\(439\) | −31.7739 | −1.51648 | −0.758242 | − | 0.651973i | \(-0.773941\pi\) | ||||
−0.758242 | + | 0.651973i | \(0.773941\pi\) | |||||||
\(440\) | 0.236509 | 0.0112751 | ||||||||
\(441\) | −5.43185 | −0.258660 | ||||||||
\(442\) | −1.31313 | −0.0624593 | ||||||||
\(443\) | 22.2621 | 1.05770 | 0.528852 | − | 0.848714i | \(-0.322622\pi\) | ||||
0.528852 | + | 0.848714i | \(0.322622\pi\) | |||||||
\(444\) | 19.9856 | 0.948474 | ||||||||
\(445\) | 3.43617 | 0.162890 | ||||||||
\(446\) | 2.04541 | 0.0968530 | ||||||||
\(447\) | −14.2020 | −0.671733 | ||||||||
\(448\) | −8.09489 | −0.382448 | ||||||||
\(449\) | −35.2282 | −1.66252 | −0.831262 | − | 0.555882i | \(-0.812381\pi\) | ||||
−0.831262 | + | 0.555882i | \(0.812381\pi\) | |||||||
\(450\) | 1.25433 | 0.0591298 | ||||||||
\(451\) | −5.77494 | −0.271931 | ||||||||
\(452\) | 18.6451 | 0.876992 | ||||||||
\(453\) | 18.8801 | 0.887063 | ||||||||
\(454\) | −1.57449 | −0.0738943 | ||||||||
\(455\) | 0.414179 | 0.0194170 | ||||||||
\(456\) | 4.65312 | 0.217902 | ||||||||
\(457\) | 17.2978 | 0.809157 | 0.404579 | − | 0.914503i | \(-0.367418\pi\) | ||||
0.404579 | + | 0.914503i | \(0.367418\pi\) | |||||||
\(458\) | 0.141077 | 0.00659212 | ||||||||
\(459\) | −5.11986 | −0.238975 | ||||||||
\(460\) | 3.16063 | 0.147365 | ||||||||
\(461\) | 5.45741 | 0.254177 | 0.127089 | − | 0.991891i | \(-0.459437\pi\) | ||||
0.127089 | + | 0.991891i | \(0.459437\pi\) | |||||||
\(462\) | 0.227608 | 0.0105893 | ||||||||
\(463\) | 30.2868 | 1.40755 | 0.703773 | − | 0.710425i | \(-0.251497\pi\) | ||||
0.703773 | + | 0.710425i | \(0.251497\pi\) | |||||||
\(464\) | −19.5978 | −0.909805 | ||||||||
\(465\) | 2.54545 | 0.118042 | ||||||||
\(466\) | 1.60263 | 0.0742404 | ||||||||
\(467\) | −16.6959 | −0.772594 | −0.386297 | − | 0.922374i | \(-0.626246\pi\) | ||||
−0.386297 | + | 0.922374i | \(0.626246\pi\) | |||||||
\(468\) | 1.93422 | 0.0894093 | ||||||||
\(469\) | −3.48880 | −0.161098 | ||||||||
\(470\) | −0.516304 | −0.0238153 | ||||||||
\(471\) | −10.2255 | −0.471165 | ||||||||
\(472\) | 13.4017 | 0.616864 | ||||||||
\(473\) | −4.64772 | −0.213702 | ||||||||
\(474\) | 0.128256 | 0.00589097 | ||||||||
\(475\) | −22.5527 | −1.03479 | ||||||||
\(476\) | 12.4010 | 0.568399 | ||||||||
\(477\) | 6.75068 | 0.309092 | ||||||||
\(478\) | −3.62243 | −0.165686 | ||||||||
\(479\) | 21.5906 | 0.986499 | 0.493250 | − | 0.869888i | \(-0.335809\pi\) | ||||
0.493250 | + | 0.869888i | \(0.335809\pi\) | |||||||
\(480\) | 0.973674 | 0.0444419 | ||||||||
\(481\) | 10.3326 | 0.471128 | ||||||||
\(482\) | 1.79042 | 0.0815516 | ||||||||
\(483\) | 6.18681 | 0.281510 | ||||||||
\(484\) | 20.3050 | 0.922955 | ||||||||
\(485\) | 3.06804 | 0.139313 | ||||||||
\(486\) | −0.256478 | −0.0116341 | ||||||||
\(487\) | −19.7281 | −0.893968 | −0.446984 | − | 0.894542i | \(-0.647502\pi\) | ||||
−0.446984 | + | 0.894542i | \(0.647502\pi\) | |||||||
\(488\) | 0.806647 | 0.0365152 | ||||||||
\(489\) | −18.7160 | −0.846367 | ||||||||
\(490\) | −0.460779 | −0.0208159 | ||||||||
\(491\) | −8.40069 | −0.379118 | −0.189559 | − | 0.981869i | \(-0.560706\pi\) | ||||
−0.189559 | + | 0.981869i | \(0.560706\pi\) | |||||||
\(492\) | −15.7619 | −0.710601 | ||||||||
\(493\) | 27.7972 | 1.25192 | ||||||||
\(494\) | 1.18273 | 0.0532136 | ||||||||
\(495\) | 0.234390 | 0.0105350 | ||||||||
\(496\) | −27.7801 | −1.24737 | ||||||||
\(497\) | −5.55031 | −0.248965 | ||||||||
\(498\) | 1.36977 | 0.0613806 | ||||||||
\(499\) | −9.62383 | −0.430822 | −0.215411 | − | 0.976524i | \(-0.569109\pi\) | ||||
−0.215411 | + | 0.976524i | \(0.569109\pi\) | |||||||
\(500\) | −6.32737 | −0.282968 | ||||||||
\(501\) | −5.05071 | −0.225649 | ||||||||
\(502\) | 2.67890 | 0.119565 | ||||||||
\(503\) | −36.2219 | −1.61506 | −0.807528 | − | 0.589830i | \(-0.799195\pi\) | ||||
−0.807528 | + | 0.589830i | \(0.799195\pi\) | |||||||
\(504\) | 1.26358 | 0.0562842 | ||||||||
\(505\) | 4.11411 | 0.183076 | ||||||||
\(506\) | 0.897983 | 0.0399202 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 11.8197 | 0.524413 | ||||||||
\(509\) | 10.5162 | 0.466123 | 0.233062 | − | 0.972462i | \(-0.425126\pi\) | ||||
0.233062 | + | 0.972462i | \(0.425126\pi\) | |||||||
\(510\) | −0.434312 | −0.0192317 | ||||||||
\(511\) | 17.8125 | 0.787977 | ||||||||
\(512\) | −17.9109 | −0.791556 | ||||||||
\(513\) | 4.61143 | 0.203600 | ||||||||
\(514\) | −5.62574 | −0.248141 | ||||||||
\(515\) | −0.330746 | −0.0145744 | ||||||||
\(516\) | −12.6853 | −0.558439 | ||||||||
\(517\) | 4.31326 | 0.189697 | ||||||||
\(518\) | 3.31860 | 0.145811 | ||||||||
\(519\) | −18.0644 | −0.792937 | ||||||||
\(520\) | 0.333736 | 0.0146353 | ||||||||
\(521\) | −0.119135 | −0.00521938 | −0.00260969 | − | 0.999997i | \(-0.500831\pi\) | ||||
−0.00260969 | + | 0.999997i | \(0.500831\pi\) | |||||||
\(522\) | 1.39249 | 0.0609478 | ||||||||
\(523\) | 0.0576810 | 0.00252221 | 0.00126111 | − | 0.999999i | \(-0.499599\pi\) | ||||
0.00126111 | + | 0.999999i | \(0.499599\pi\) | |||||||
\(524\) | 25.4203 | 1.11049 | ||||||||
\(525\) | −6.12429 | −0.267286 | ||||||||
\(526\) | −4.89009 | −0.213218 | ||||||||
\(527\) | 39.4029 | 1.71642 | ||||||||
\(528\) | −2.55805 | −0.111325 | ||||||||
\(529\) | 1.40886 | 0.0612547 | ||||||||
\(530\) | 0.572653 | 0.0248745 | ||||||||
\(531\) | 13.2817 | 0.576375 | ||||||||
\(532\) | −11.1695 | −0.484260 | ||||||||
\(533\) | −8.14897 | −0.352971 | ||||||||
\(534\) | 2.66459 | 0.115308 | ||||||||
\(535\) | −3.03613 | −0.131263 | ||||||||
\(536\) | −2.81120 | −0.121425 | ||||||||
\(537\) | 25.0335 | 1.08027 | ||||||||
\(538\) | 2.91118 | 0.125510 | ||||||||
\(539\) | 3.84940 | 0.165805 | ||||||||
\(540\) | 0.639735 | 0.0275298 | ||||||||
\(541\) | −13.9639 | −0.600356 | −0.300178 | − | 0.953883i | \(-0.597046\pi\) | ||||
−0.300178 | + | 0.953883i | \(0.597046\pi\) | |||||||
\(542\) | 3.27841 | 0.140820 | ||||||||
\(543\) | −3.97181 | −0.170447 | ||||||||
\(544\) | 15.0722 | 0.646216 | ||||||||
\(545\) | 4.73055 | 0.202635 | ||||||||
\(546\) | 0.321176 | 0.0137451 | ||||||||
\(547\) | 34.6906 | 1.48326 | 0.741630 | − | 0.670809i | \(-0.234053\pi\) | ||||
0.741630 | + | 0.670809i | \(0.234053\pi\) | |||||||
\(548\) | 12.5913 | 0.537875 | ||||||||
\(549\) | 0.799420 | 0.0341184 | ||||||||
\(550\) | −0.888909 | −0.0379032 | ||||||||
\(551\) | −25.0368 | −1.06660 | ||||||||
\(552\) | 4.98519 | 0.212184 | ||||||||
\(553\) | −0.626210 | −0.0266291 | ||||||||
\(554\) | 8.21018 | 0.348817 | ||||||||
\(555\) | 3.41748 | 0.145064 | ||||||||
\(556\) | −4.16308 | −0.176554 | ||||||||
\(557\) | −7.20735 | −0.305385 | −0.152693 | − | 0.988274i | \(-0.548794\pi\) | ||||
−0.152693 | + | 0.988274i | \(0.548794\pi\) | |||||||
\(558\) | 1.97388 | 0.0835609 | ||||||||
\(559\) | −6.55836 | −0.277389 | ||||||||
\(560\) | −1.49504 | −0.0631768 | ||||||||
\(561\) | 3.62830 | 0.153187 | ||||||||
\(562\) | 0.432785 | 0.0182559 | ||||||||
\(563\) | −24.3619 | −1.02673 | −0.513366 | − | 0.858170i | \(-0.671602\pi\) | ||||
−0.513366 | + | 0.858170i | \(0.671602\pi\) | |||||||
\(564\) | 11.7724 | 0.495709 | ||||||||
\(565\) | 3.18826 | 0.134131 | ||||||||
\(566\) | 7.07214 | 0.297264 | ||||||||
\(567\) | 1.25226 | 0.0525898 | ||||||||
\(568\) | −4.47231 | −0.187654 | ||||||||
\(569\) | −8.76301 | −0.367364 | −0.183682 | − | 0.982986i | \(-0.558802\pi\) | ||||
−0.183682 | + | 0.982986i | \(0.558802\pi\) | |||||||
\(570\) | 0.391183 | 0.0163849 | ||||||||
\(571\) | 17.5523 | 0.734540 | 0.367270 | − | 0.930114i | \(-0.380293\pi\) | ||||
0.367270 | + | 0.930114i | \(0.380293\pi\) | |||||||
\(572\) | −1.37073 | −0.0573129 | ||||||||
\(573\) | 18.8856 | 0.788956 | ||||||||
\(574\) | −2.61725 | −0.109242 | ||||||||
\(575\) | −24.1622 | −1.00763 | ||||||||
\(576\) | −6.46425 | −0.269344 | ||||||||
\(577\) | 9.00167 | 0.374744 | 0.187372 | − | 0.982289i | \(-0.440003\pi\) | ||||
0.187372 | + | 0.982289i | \(0.440003\pi\) | |||||||
\(578\) | −2.36292 | −0.0982846 | ||||||||
\(579\) | −15.7494 | −0.654525 | ||||||||
\(580\) | −3.47331 | −0.144221 | ||||||||
\(581\) | −6.68789 | −0.277461 | ||||||||
\(582\) | 2.37912 | 0.0986178 | ||||||||
\(583\) | −4.78401 | −0.198133 | ||||||||
\(584\) | 14.3529 | 0.593926 | ||||||||
\(585\) | 0.330746 | 0.0136747 | ||||||||
\(586\) | 5.24809 | 0.216797 | ||||||||
\(587\) | −21.7448 | −0.897505 | −0.448752 | − | 0.893656i | \(-0.648131\pi\) | ||||
−0.448752 | + | 0.893656i | \(0.648131\pi\) | |||||||
\(588\) | 10.5064 | 0.433276 | ||||||||
\(589\) | −35.4900 | −1.46234 | ||||||||
\(590\) | 1.12667 | 0.0463842 | ||||||||
\(591\) | −21.1867 | −0.871503 | ||||||||
\(592\) | −37.2971 | −1.53290 | ||||||||
\(593\) | 43.0547 | 1.76805 | 0.884023 | − | 0.467443i | \(-0.154825\pi\) | ||||
0.884023 | + | 0.467443i | \(0.154825\pi\) | |||||||
\(594\) | 0.181758 | 0.00745764 | ||||||||
\(595\) | 2.12054 | 0.0869335 | ||||||||
\(596\) | 27.4698 | 1.12521 | ||||||||
\(597\) | 0.295285 | 0.0120852 | ||||||||
\(598\) | 1.26714 | 0.0518171 | ||||||||
\(599\) | −6.37811 | −0.260603 | −0.130301 | − | 0.991474i | \(-0.541594\pi\) | ||||
−0.130301 | + | 0.991474i | \(0.541594\pi\) | |||||||
\(600\) | −4.93482 | −0.201463 | ||||||||
\(601\) | −7.98434 | −0.325688 | −0.162844 | − | 0.986652i | \(-0.552067\pi\) | ||||
−0.162844 | + | 0.986652i | \(0.552067\pi\) | |||||||
\(602\) | −2.10639 | −0.0858500 | ||||||||
\(603\) | −2.78601 | −0.113455 | ||||||||
\(604\) | −36.5182 | −1.48590 | ||||||||
\(605\) | 3.47210 | 0.141161 | ||||||||
\(606\) | 3.19030 | 0.129597 | ||||||||
\(607\) | 42.7106 | 1.73357 | 0.866786 | − | 0.498681i | \(-0.166182\pi\) | ||||
0.866786 | + | 0.498681i | \(0.166182\pi\) | |||||||
\(608\) | −13.5755 | −0.550558 | ||||||||
\(609\) | −6.79886 | −0.275504 | ||||||||
\(610\) | 0.0678140 | 0.00274571 | ||||||||
\(611\) | 6.08641 | 0.246230 | ||||||||
\(612\) | 9.90293 | 0.400302 | ||||||||
\(613\) | 44.1711 | 1.78405 | 0.892027 | − | 0.451983i | \(-0.149283\pi\) | ||||
0.892027 | + | 0.451983i | \(0.149283\pi\) | |||||||
\(614\) | 0.834821 | 0.0336906 | ||||||||
\(615\) | −2.69524 | −0.108682 | ||||||||
\(616\) | −0.895460 | −0.0360791 | ||||||||
\(617\) | 11.8923 | 0.478766 | 0.239383 | − | 0.970925i | \(-0.423055\pi\) | ||||
0.239383 | + | 0.970925i | \(0.423055\pi\) | |||||||
\(618\) | −0.256478 | −0.0103171 | ||||||||
\(619\) | −3.87155 | −0.155611 | −0.0778054 | − | 0.996969i | \(-0.524791\pi\) | ||||
−0.0778054 | + | 0.996969i | \(0.524791\pi\) | |||||||
\(620\) | −4.92346 | −0.197731 | ||||||||
\(621\) | 4.94053 | 0.198257 | ||||||||
\(622\) | 6.98034 | 0.279886 | ||||||||
\(623\) | −13.0099 | −0.521230 | ||||||||
\(624\) | −3.60964 | −0.144501 | ||||||||
\(625\) | 23.3711 | 0.934843 | ||||||||
\(626\) | −3.05268 | −0.122010 | ||||||||
\(627\) | −3.26799 | −0.130511 | ||||||||
\(628\) | 19.7783 | 0.789240 | ||||||||
\(629\) | 52.9017 | 2.10933 | ||||||||
\(630\) | 0.106228 | 0.00423221 | ||||||||
\(631\) | −6.83787 | −0.272211 | −0.136106 | − | 0.990694i | \(-0.543459\pi\) | ||||
−0.136106 | + | 0.990694i | \(0.543459\pi\) | |||||||
\(632\) | −0.504586 | −0.0200713 | ||||||||
\(633\) | 0.815219 | 0.0324020 | ||||||||
\(634\) | −5.30724 | −0.210778 | ||||||||
\(635\) | 2.02113 | 0.0802061 | ||||||||
\(636\) | −13.0573 | −0.517755 | ||||||||
\(637\) | 5.43185 | 0.215218 | ||||||||
\(638\) | −0.986820 | −0.0390686 | ||||||||
\(639\) | −4.43224 | −0.175337 | ||||||||
\(640\) | −2.49570 | −0.0986513 | ||||||||
\(641\) | 30.7090 | 1.21293 | 0.606467 | − | 0.795108i | \(-0.292586\pi\) | ||||
0.606467 | + | 0.795108i | \(0.292586\pi\) | |||||||
\(642\) | −2.35437 | −0.0929197 | ||||||||
\(643\) | 6.11570 | 0.241180 | 0.120590 | − | 0.992702i | \(-0.461521\pi\) | ||||
0.120590 | + | 0.992702i | \(0.461521\pi\) | |||||||
\(644\) | −11.9667 | −0.471552 | ||||||||
\(645\) | −2.16915 | −0.0854102 | ||||||||
\(646\) | 6.05541 | 0.238247 | ||||||||
\(647\) | 5.89149 | 0.231618 | 0.115809 | − | 0.993271i | \(-0.463054\pi\) | ||||
0.115809 | + | 0.993271i | \(0.463054\pi\) | |||||||
\(648\) | 1.00904 | 0.0396388 | ||||||||
\(649\) | −9.41232 | −0.369466 | ||||||||
\(650\) | −1.25433 | −0.0491990 | ||||||||
\(651\) | −9.63748 | −0.377723 | ||||||||
\(652\) | 36.2009 | 1.41774 | ||||||||
\(653\) | −3.45013 | −0.135014 | −0.0675070 | − | 0.997719i | \(-0.521505\pi\) | ||||
−0.0675070 | + | 0.997719i | \(0.521505\pi\) | |||||||
\(654\) | 3.66832 | 0.143443 | ||||||||
\(655\) | 4.34679 | 0.169843 | ||||||||
\(656\) | 29.4149 | 1.14846 | ||||||||
\(657\) | 14.2243 | 0.554943 | ||||||||
\(658\) | 1.95481 | 0.0762064 | ||||||||
\(659\) | 8.74597 | 0.340695 | 0.170347 | − | 0.985384i | \(-0.445511\pi\) | ||||
0.170347 | + | 0.985384i | \(0.445511\pi\) | |||||||
\(660\) | −0.453362 | −0.0176471 | ||||||||
\(661\) | 33.0513 | 1.28555 | 0.642773 | − | 0.766057i | \(-0.277784\pi\) | ||||
0.642773 | + | 0.766057i | \(0.277784\pi\) | |||||||
\(662\) | −6.52173 | −0.253474 | ||||||||
\(663\) | 5.11986 | 0.198839 | ||||||||
\(664\) | −5.38896 | −0.209132 | ||||||||
\(665\) | −1.90996 | −0.0740649 | ||||||||
\(666\) | 2.65009 | 0.102689 | ||||||||
\(667\) | −26.8236 | −1.03861 | ||||||||
\(668\) | 9.76918 | 0.377981 | ||||||||
\(669\) | −7.97500 | −0.308331 | ||||||||
\(670\) | −0.236334 | −0.00913039 | ||||||||
\(671\) | −0.566526 | −0.0218705 | ||||||||
\(672\) | −3.68648 | −0.142209 | ||||||||
\(673\) | −12.3192 | −0.474869 | −0.237434 | − | 0.971404i | \(-0.576306\pi\) | ||||
−0.237434 | + | 0.971404i | \(0.576306\pi\) | |||||||
\(674\) | 3.03738 | 0.116995 | ||||||||
\(675\) | −4.89061 | −0.188240 | ||||||||
\(676\) | −1.93422 | −0.0743930 | ||||||||
\(677\) | −15.8012 | −0.607290 | −0.303645 | − | 0.952785i | \(-0.598204\pi\) | ||||
−0.303645 | + | 0.952785i | \(0.598204\pi\) | |||||||
\(678\) | 2.47234 | 0.0949498 | ||||||||
\(679\) | −11.6161 | −0.445785 | ||||||||
\(680\) | 1.70868 | 0.0655249 | ||||||||
\(681\) | 6.13888 | 0.235242 | ||||||||
\(682\) | −1.39883 | −0.0535640 | ||||||||
\(683\) | −6.68038 | −0.255618 | −0.127809 | − | 0.991799i | \(-0.540794\pi\) | ||||
−0.127809 | + | 0.991799i | \(0.540794\pi\) | |||||||
\(684\) | −8.91952 | −0.341046 | ||||||||
\(685\) | 2.15308 | 0.0822650 | ||||||||
\(686\) | 3.99281 | 0.152446 | ||||||||
\(687\) | −0.550057 | −0.0209860 | ||||||||
\(688\) | 23.6733 | 0.902537 | ||||||||
\(689\) | −6.75068 | −0.257180 | ||||||||
\(690\) | 0.419100 | 0.0159549 | ||||||||
\(691\) | −26.5969 | −1.01179 | −0.505896 | − | 0.862594i | \(-0.668838\pi\) | ||||
−0.505896 | + | 0.862594i | \(0.668838\pi\) | |||||||
\(692\) | 34.9404 | 1.32824 | ||||||||
\(693\) | −0.887438 | −0.0337110 | ||||||||
\(694\) | −5.84965 | −0.222050 | ||||||||
\(695\) | −0.711875 | −0.0270030 | ||||||||
\(696\) | −5.47837 | −0.207657 | ||||||||
\(697\) | −41.7216 | −1.58032 | ||||||||
\(698\) | 0.336820 | 0.0127488 | ||||||||
\(699\) | −6.24861 | −0.236344 | ||||||||
\(700\) | 11.8457 | 0.447726 | ||||||||
\(701\) | −32.8829 | −1.24197 | −0.620984 | − | 0.783823i | \(-0.713267\pi\) | ||||
−0.620984 | + | 0.783823i | \(0.713267\pi\) | |||||||
\(702\) | 0.256478 | 0.00968013 | ||||||||
\(703\) | −47.6483 | −1.79709 | ||||||||
\(704\) | 4.58102 | 0.172654 | ||||||||
\(705\) | 2.01305 | 0.0758160 | ||||||||
\(706\) | −5.71499 | −0.215087 | ||||||||
\(707\) | −15.5767 | −0.585821 | ||||||||
\(708\) | −25.6896 | −0.965475 | ||||||||
\(709\) | 10.1394 | 0.380793 | 0.190396 | − | 0.981707i | \(-0.439023\pi\) | ||||
0.190396 | + | 0.981707i | \(0.439023\pi\) | |||||||
\(710\) | −0.375983 | −0.0141104 | ||||||||
\(711\) | −0.500065 | −0.0187539 | ||||||||
\(712\) | −10.4831 | −0.392870 | ||||||||
\(713\) | −38.0228 | −1.42396 | ||||||||
\(714\) | 1.64438 | 0.0615392 | ||||||||
\(715\) | −0.234390 | −0.00876569 | ||||||||
\(716\) | −48.4202 | −1.80955 | ||||||||
\(717\) | 14.1237 | 0.527461 | ||||||||
\(718\) | 1.45788 | 0.0544077 | ||||||||
\(719\) | 42.3890 | 1.58084 | 0.790422 | − | 0.612563i | \(-0.209862\pi\) | ||||
0.790422 | + | 0.612563i | \(0.209862\pi\) | |||||||
\(720\) | −1.19387 | −0.0444931 | ||||||||
\(721\) | 1.25226 | 0.0466365 | ||||||||
\(722\) | −0.581002 | −0.0216227 | ||||||||
\(723\) | −6.98081 | −0.259619 | ||||||||
\(724\) | 7.68236 | 0.285513 | ||||||||
\(725\) | 26.5525 | 0.986136 | ||||||||
\(726\) | 2.69245 | 0.0999262 | ||||||||
\(727\) | −35.7924 | −1.32747 | −0.663733 | − | 0.747970i | \(-0.731029\pi\) | ||||
−0.663733 | + | 0.747970i | \(0.731029\pi\) | |||||||
\(728\) | −1.26358 | −0.0468313 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 1.20663 | 0.0446595 | ||||||||
\(731\) | −33.5779 | −1.24192 | ||||||||
\(732\) | −1.54625 | −0.0571512 | ||||||||
\(733\) | 6.61836 | 0.244455 | 0.122227 | − | 0.992502i | \(-0.460996\pi\) | ||||
0.122227 | + | 0.992502i | \(0.460996\pi\) | |||||||
\(734\) | −6.65960 | −0.245810 | ||||||||
\(735\) | 1.79656 | 0.0662672 | ||||||||
\(736\) | −14.5443 | −0.536110 | ||||||||
\(737\) | 1.97436 | 0.0727267 | ||||||||
\(738\) | −2.09003 | −0.0769351 | ||||||||
\(739\) | 33.1978 | 1.22120 | 0.610600 | − | 0.791939i | \(-0.290928\pi\) | ||||
0.610600 | + | 0.791939i | \(0.290928\pi\) | |||||||
\(740\) | −6.61015 | −0.242994 | ||||||||
\(741\) | −4.61143 | −0.169405 | ||||||||
\(742\) | −2.16815 | −0.0795955 | ||||||||
\(743\) | 23.5188 | 0.862821 | 0.431411 | − | 0.902156i | \(-0.358016\pi\) | ||||
0.431411 | + | 0.902156i | \(0.358016\pi\) | |||||||
\(744\) | −7.76567 | −0.284703 | ||||||||
\(745\) | 4.69726 | 0.172094 | ||||||||
\(746\) | 8.78988 | 0.321820 | ||||||||
\(747\) | −5.34068 | −0.195405 | ||||||||
\(748\) | −7.01792 | −0.256601 | ||||||||
\(749\) | 11.4953 | 0.420028 | ||||||||
\(750\) | −0.839010 | −0.0306363 | ||||||||
\(751\) | 37.5255 | 1.36932 | 0.684662 | − | 0.728861i | \(-0.259950\pi\) | ||||
0.684662 | + | 0.728861i | \(0.259950\pi\) | |||||||
\(752\) | −21.9698 | −0.801155 | ||||||||
\(753\) | −10.4449 | −0.380635 | ||||||||
\(754\) | −1.39249 | −0.0507116 | ||||||||
\(755\) | −6.24451 | −0.227261 | ||||||||
\(756\) | −2.42214 | −0.0880923 | ||||||||
\(757\) | −31.6614 | −1.15075 | −0.575376 | − | 0.817889i | \(-0.695144\pi\) | ||||
−0.575376 | + | 0.817889i | \(0.695144\pi\) | |||||||
\(758\) | 7.28631 | 0.264651 | ||||||||
\(759\) | −3.50121 | −0.127086 | ||||||||
\(760\) | −1.53900 | −0.0558254 | ||||||||
\(761\) | −6.36049 | −0.230568 | −0.115284 | − | 0.993333i | \(-0.536778\pi\) | ||||
−0.115284 | + | 0.993333i | \(0.536778\pi\) | |||||||
\(762\) | 1.56729 | 0.0567770 | ||||||||
\(763\) | −17.9106 | −0.648408 | ||||||||
\(764\) | −36.5288 | −1.32157 | ||||||||
\(765\) | 1.69337 | 0.0612240 | ||||||||
\(766\) | −7.04087 | −0.254397 | ||||||||
\(767\) | −13.2817 | −0.479573 | ||||||||
\(768\) | 10.9932 | 0.396683 | ||||||||
\(769\) | 37.3675 | 1.34750 | 0.673752 | − | 0.738957i | \(-0.264681\pi\) | ||||
0.673752 | + | 0.738957i | \(0.264681\pi\) | |||||||
\(770\) | −0.0752804 | −0.00271292 | ||||||||
\(771\) | 21.9346 | 0.789955 | ||||||||
\(772\) | 30.4629 | 1.09638 | ||||||||
\(773\) | −0.839820 | −0.0302062 | −0.0151031 | − | 0.999886i | \(-0.504808\pi\) | ||||
−0.0151031 | + | 0.999886i | \(0.504808\pi\) | |||||||
\(774\) | −1.68207 | −0.0604609 | ||||||||
\(775\) | 37.6386 | 1.35202 | ||||||||
\(776\) | −9.35998 | −0.336004 | ||||||||
\(777\) | −12.9391 | −0.464188 | ||||||||
\(778\) | −7.16208 | −0.256773 | ||||||||
\(779\) | 37.5784 | 1.34639 | ||||||||
\(780\) | −0.639735 | −0.0229062 | ||||||||
\(781\) | 3.14100 | 0.112394 | ||||||||
\(782\) | 6.48756 | 0.231995 | ||||||||
\(783\) | −5.42929 | −0.194027 | ||||||||
\(784\) | −19.6070 | −0.700252 | ||||||||
\(785\) | 3.38203 | 0.120710 | ||||||||
\(786\) | 3.37073 | 0.120230 | ||||||||
\(787\) | 34.0547 | 1.21392 | 0.606959 | − | 0.794733i | \(-0.292389\pi\) | ||||
0.606959 | + | 0.794733i | \(0.292389\pi\) | |||||||
\(788\) | 40.9796 | 1.45984 | ||||||||
\(789\) | 19.0663 | 0.678779 | ||||||||
\(790\) | −0.0424200 | −0.00150924 | ||||||||
\(791\) | −12.0712 | −0.429204 | ||||||||
\(792\) | −0.715077 | −0.0254092 | ||||||||
\(793\) | −0.799420 | −0.0283882 | ||||||||
\(794\) | −3.42398 | −0.121513 | ||||||||
\(795\) | −2.23276 | −0.0791878 | ||||||||
\(796\) | −0.571145 | −0.0202437 | ||||||||
\(797\) | 12.6514 | 0.448135 | 0.224067 | − | 0.974574i | \(-0.428066\pi\) | ||||
0.224067 | + | 0.974574i | \(0.428066\pi\) | |||||||
\(798\) | −1.48108 | −0.0524297 | ||||||||
\(799\) | 31.1616 | 1.10242 | ||||||||
\(800\) | 14.3973 | 0.509022 | ||||||||
\(801\) | −10.3891 | −0.367082 | ||||||||
\(802\) | −3.88208 | −0.137081 | ||||||||
\(803\) | −10.0803 | −0.355728 | ||||||||
\(804\) | 5.38875 | 0.190047 | ||||||||
\(805\) | −2.04626 | −0.0721213 | ||||||||
\(806\) | −1.97388 | −0.0695269 | ||||||||
\(807\) | −11.3506 | −0.399560 | ||||||||
\(808\) | −12.5513 | −0.441555 | ||||||||
\(809\) | −20.2253 | −0.711084 | −0.355542 | − | 0.934660i | \(-0.615704\pi\) | ||||
−0.355542 | + | 0.934660i | \(0.615704\pi\) | |||||||
\(810\) | 0.0848290 | 0.00298059 | ||||||||
\(811\) | −4.53408 | −0.159213 | −0.0796066 | − | 0.996826i | \(-0.525366\pi\) | ||||
−0.0796066 | + | 0.996826i | \(0.525366\pi\) | |||||||
\(812\) | 13.1505 | 0.461492 | ||||||||
\(813\) | −12.7824 | −0.448300 | ||||||||
\(814\) | −1.87804 | −0.0658254 | ||||||||
\(815\) | 6.19024 | 0.216835 | ||||||||
\(816\) | −18.4809 | −0.646960 | ||||||||
\(817\) | 30.2434 | 1.05808 | ||||||||
\(818\) | 0.133783 | 0.00467762 | ||||||||
\(819\) | −1.25226 | −0.0437574 | ||||||||
\(820\) | 5.21318 | 0.182052 | ||||||||
\(821\) | 52.6392 | 1.83712 | 0.918561 | − | 0.395279i | \(-0.129352\pi\) | ||||
0.918561 | + | 0.395279i | \(0.129352\pi\) | |||||||
\(822\) | 1.66961 | 0.0582344 | ||||||||
\(823\) | −46.9477 | −1.63649 | −0.818247 | − | 0.574867i | \(-0.805054\pi\) | ||||
−0.818247 | + | 0.574867i | \(0.805054\pi\) | |||||||
\(824\) | 1.00904 | 0.0351516 | ||||||||
\(825\) | 3.46583 | 0.120665 | ||||||||
\(826\) | −4.26575 | −0.148424 | ||||||||
\(827\) | 36.9321 | 1.28425 | 0.642127 | − | 0.766598i | \(-0.278052\pi\) | ||||
0.642127 | + | 0.766598i | \(0.278052\pi\) | |||||||
\(828\) | −9.55607 | −0.332096 | ||||||||
\(829\) | −36.0868 | −1.25335 | −0.626674 | − | 0.779282i | \(-0.715584\pi\) | ||||
−0.626674 | + | 0.779282i | \(0.715584\pi\) | |||||||
\(830\) | −0.453044 | −0.0157254 | ||||||||
\(831\) | −32.0113 | −1.11046 | ||||||||
\(832\) | 6.46425 | 0.224107 | ||||||||
\(833\) | 27.8103 | 0.963571 | ||||||||
\(834\) | −0.552026 | −0.0191151 | ||||||||
\(835\) | 1.67050 | 0.0578101 | ||||||||
\(836\) | 6.32101 | 0.218617 | ||||||||
\(837\) | −7.69609 | −0.266016 | ||||||||
\(838\) | −9.94085 | −0.343401 | ||||||||
\(839\) | 13.7228 | 0.473764 | 0.236882 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236882 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(840\) | −0.417923 | −0.0144197 | ||||||||
\(841\) | 0.477214 | 0.0164557 | ||||||||
\(842\) | 5.24332 | 0.180697 | ||||||||
\(843\) | −1.68742 | −0.0581177 | ||||||||
\(844\) | −1.57681 | −0.0542761 | ||||||||
\(845\) | −0.330746 | −0.0113780 | ||||||||
\(846\) | 1.56103 | 0.0536693 | ||||||||
\(847\) | −13.1459 | −0.451699 | ||||||||
\(848\) | 24.3675 | 0.836784 | ||||||||
\(849\) | −27.5741 | −0.946339 | ||||||||
\(850\) | −6.42201 | −0.220273 | ||||||||
\(851\) | −51.0487 | −1.74993 | ||||||||
\(852\) | 8.57293 | 0.293704 | ||||||||
\(853\) | 19.2984 | 0.660766 | 0.330383 | − | 0.943847i | \(-0.392822\pi\) | ||||
0.330383 | + | 0.943847i | \(0.392822\pi\) | |||||||
\(854\) | −0.256755 | −0.00878596 | ||||||||
\(855\) | −1.52521 | −0.0521612 | ||||||||
\(856\) | 9.26262 | 0.316590 | ||||||||
\(857\) | 22.9235 | 0.783053 | 0.391527 | − | 0.920167i | \(-0.371947\pi\) | ||||
0.391527 | + | 0.920167i | \(0.371947\pi\) | |||||||
\(858\) | −0.181758 | −0.00620513 | ||||||||
\(859\) | 21.4588 | 0.732164 | 0.366082 | − | 0.930583i | \(-0.380699\pi\) | ||||
0.366082 | + | 0.930583i | \(0.380699\pi\) | |||||||
\(860\) | 4.19561 | 0.143069 | ||||||||
\(861\) | 10.2046 | 0.347772 | ||||||||
\(862\) | 0.0200823 | 0.000684006 0 | ||||||||
\(863\) | 0.740930 | 0.0252216 | 0.0126108 | − | 0.999920i | \(-0.495986\pi\) | ||||
0.0126108 | + | 0.999920i | \(0.495986\pi\) | |||||||
\(864\) | −2.94387 | −0.100153 | ||||||||
\(865\) | 5.97471 | 0.203146 | ||||||||
\(866\) | 4.92837 | 0.167473 | ||||||||
\(867\) | 9.21296 | 0.312889 | ||||||||
\(868\) | 18.6410 | 0.632717 | ||||||||
\(869\) | 0.354382 | 0.0120216 | ||||||||
\(870\) | −0.460561 | −0.0156145 | ||||||||
\(871\) | 2.78601 | 0.0944004 | ||||||||
\(872\) | −14.4320 | −0.488729 | ||||||||
\(873\) | −9.27613 | −0.313949 | ||||||||
\(874\) | −5.84332 | −0.197653 | ||||||||
\(875\) | 4.09648 | 0.138486 | ||||||||
\(876\) | −27.5129 | −0.929575 | ||||||||
\(877\) | −50.6246 | −1.70947 | −0.854735 | − | 0.519064i | \(-0.826281\pi\) | ||||
−0.854735 | + | 0.519064i | \(0.826281\pi\) | |||||||
\(878\) | 8.14929 | 0.275025 | ||||||||
\(879\) | −20.4622 | −0.690171 | ||||||||
\(880\) | 0.846064 | 0.0285208 | ||||||||
\(881\) | −2.82396 | −0.0951417 | −0.0475708 | − | 0.998868i | \(-0.515148\pi\) | ||||
−0.0475708 | + | 0.998868i | \(0.515148\pi\) | |||||||
\(882\) | 1.39315 | 0.0469098 | ||||||||
\(883\) | 8.04046 | 0.270583 | 0.135291 | − | 0.990806i | \(-0.456803\pi\) | ||||
0.135291 | + | 0.990806i | \(0.456803\pi\) | |||||||
\(884\) | −9.90293 | −0.333072 | ||||||||
\(885\) | −4.39285 | −0.147664 | ||||||||
\(886\) | −5.70974 | −0.191822 | ||||||||
\(887\) | 35.8445 | 1.20354 | 0.601770 | − | 0.798670i | \(-0.294463\pi\) | ||||
0.601770 | + | 0.798670i | \(0.294463\pi\) | |||||||
\(888\) | −10.4260 | −0.349875 | ||||||||
\(889\) | −7.65232 | −0.256651 | ||||||||
\(890\) | −0.881301 | −0.0295413 | ||||||||
\(891\) | −0.708671 | −0.0237414 | ||||||||
\(892\) | 15.4254 | 0.516480 | ||||||||
\(893\) | −28.0671 | −0.939228 | ||||||||
\(894\) | 3.64251 | 0.121824 | ||||||||
\(895\) | −8.27972 | −0.276760 | ||||||||
\(896\) | 9.44913 | 0.315673 | ||||||||
\(897\) | −4.94053 | −0.164960 | ||||||||
\(898\) | 9.03526 | 0.301511 | ||||||||
\(899\) | 41.7843 | 1.39359 | ||||||||
\(900\) | 9.45951 | 0.315317 | ||||||||
\(901\) | −34.5625 | −1.15144 | ||||||||
\(902\) | 1.48114 | 0.0493167 | ||||||||
\(903\) | 8.21275 | 0.273303 | ||||||||
\(904\) | −9.72674 | −0.323507 | ||||||||
\(905\) | 1.31366 | 0.0436676 | ||||||||
\(906\) | −4.84232 | −0.160875 | ||||||||
\(907\) | 38.8272 | 1.28924 | 0.644618 | − | 0.764504i | \(-0.277016\pi\) | ||||
0.644618 | + | 0.764504i | \(0.277016\pi\) | |||||||
\(908\) | −11.8739 | −0.394050 | ||||||||
\(909\) | −12.4389 | −0.412572 | ||||||||
\(910\) | −0.106228 | −0.00352141 | ||||||||
\(911\) | 10.4250 | 0.345397 | 0.172699 | − | 0.984975i | \(-0.444751\pi\) | ||||
0.172699 | + | 0.984975i | \(0.444751\pi\) | |||||||
\(912\) | 16.6456 | 0.551192 | ||||||||
\(913\) | 3.78478 | 0.125258 | ||||||||
\(914\) | −4.43650 | −0.146747 | ||||||||
\(915\) | −0.264405 | −0.00874095 | ||||||||
\(916\) | 1.06393 | 0.0351533 | ||||||||
\(917\) | −16.4576 | −0.543479 | ||||||||
\(918\) | 1.31313 | 0.0433398 | ||||||||
\(919\) | 25.0699 | 0.826979 | 0.413490 | − | 0.910509i | \(-0.364310\pi\) | ||||
0.413490 | + | 0.910509i | \(0.364310\pi\) | |||||||
\(920\) | −1.64883 | −0.0543604 | ||||||||
\(921\) | −3.25494 | −0.107254 | ||||||||
\(922\) | −1.39971 | −0.0460968 | ||||||||
\(923\) | 4.43224 | 0.145889 | ||||||||
\(924\) | 1.71650 | 0.0564687 | ||||||||
\(925\) | 50.5329 | 1.66151 | ||||||||
\(926\) | −7.76789 | −0.255269 | ||||||||
\(927\) | 1.00000 | 0.0328443 | ||||||||
\(928\) | 15.9831 | 0.524673 | ||||||||
\(929\) | 2.55448 | 0.0838097 | 0.0419048 | − | 0.999122i | \(-0.486657\pi\) | ||||
0.0419048 | + | 0.999122i | \(0.486657\pi\) | |||||||
\(930\) | −0.652852 | −0.0214079 | ||||||||
\(931\) | −25.0486 | −0.820936 | ||||||||
\(932\) | 12.0862 | 0.395896 | ||||||||
\(933\) | −27.2162 | −0.891017 | ||||||||
\(934\) | 4.28213 | 0.140116 | ||||||||
\(935\) | −1.20004 | −0.0392456 | ||||||||
\(936\) | −1.00904 | −0.0329815 | ||||||||
\(937\) | −47.3948 | −1.54832 | −0.774161 | − | 0.632989i | \(-0.781828\pi\) | ||||
−0.774161 | + | 0.632989i | \(0.781828\pi\) | |||||||
\(938\) | 0.894800 | 0.0292162 | ||||||||
\(939\) | 11.9023 | 0.388417 | ||||||||
\(940\) | −3.89369 | −0.126998 | ||||||||
\(941\) | 15.2103 | 0.495842 | 0.247921 | − | 0.968780i | \(-0.420253\pi\) | ||||
0.247921 | + | 0.968780i | \(0.420253\pi\) | |||||||
\(942\) | 2.62261 | 0.0854491 | ||||||||
\(943\) | 40.2602 | 1.31105 | ||||||||
\(944\) | 47.9420 | 1.56038 | ||||||||
\(945\) | −0.414179 | −0.0134732 | ||||||||
\(946\) | 1.19204 | 0.0387565 | ||||||||
\(947\) | −16.6182 | −0.540018 | −0.270009 | − | 0.962858i | \(-0.587027\pi\) | ||||
−0.270009 | + | 0.962858i | \(0.587027\pi\) | |||||||
\(948\) | 0.967235 | 0.0314143 | ||||||||
\(949\) | −14.2243 | −0.461740 | ||||||||
\(950\) | 5.78427 | 0.187666 | ||||||||
\(951\) | 20.6928 | 0.671010 | ||||||||
\(952\) | −6.46934 | −0.209672 | ||||||||
\(953\) | −37.9356 | −1.22886 | −0.614428 | − | 0.788973i | \(-0.710613\pi\) | ||||
−0.614428 | + | 0.788973i | \(0.710613\pi\) | |||||||
\(954\) | −1.73140 | −0.0560561 | ||||||||
\(955\) | −6.24632 | −0.202126 | ||||||||
\(956\) | −27.3184 | −0.883541 | ||||||||
\(957\) | 3.84758 | 0.124375 | ||||||||
\(958\) | −5.53751 | −0.178909 | ||||||||
\(959\) | −8.15190 | −0.263239 | ||||||||
\(960\) | 2.13802 | 0.0690044 | ||||||||
\(961\) | 28.2299 | 0.910640 | ||||||||
\(962\) | −2.65009 | −0.0854424 | ||||||||
\(963\) | 9.17964 | 0.295810 | ||||||||
\(964\) | 13.5024 | 0.434884 | ||||||||
\(965\) | 5.20906 | 0.167686 | ||||||||
\(966\) | −1.58678 | −0.0510538 | ||||||||
\(967\) | −27.6609 | −0.889516 | −0.444758 | − | 0.895651i | \(-0.646710\pi\) | ||||
−0.444758 | + | 0.895651i | \(0.646710\pi\) | |||||||
\(968\) | −10.5927 | −0.340462 | ||||||||
\(969\) | −23.6099 | −0.758459 | ||||||||
\(970\) | −0.786884 | −0.0252653 | ||||||||
\(971\) | −45.4523 | −1.45863 | −0.729316 | − | 0.684177i | \(-0.760162\pi\) | ||||
−0.729316 | + | 0.684177i | \(0.760162\pi\) | |||||||
\(972\) | −1.93422 | −0.0620401 | ||||||||
\(973\) | 2.69527 | 0.0864065 | ||||||||
\(974\) | 5.05983 | 0.162127 | ||||||||
\(975\) | 4.89061 | 0.156625 | ||||||||
\(976\) | 2.88562 | 0.0923664 | ||||||||
\(977\) | 6.57078 | 0.210218 | 0.105109 | − | 0.994461i | \(-0.466481\pi\) | ||||
0.105109 | + | 0.994461i | \(0.466481\pi\) | |||||||
\(978\) | 4.80024 | 0.153495 | ||||||||
\(979\) | 7.36249 | 0.235306 | ||||||||
\(980\) | −3.47495 | −0.111003 | ||||||||
\(981\) | −14.3027 | −0.456650 | ||||||||
\(982\) | 2.15459 | 0.0687558 | ||||||||
\(983\) | 15.1444 | 0.483032 | 0.241516 | − | 0.970397i | \(-0.422355\pi\) | ||||
0.241516 | + | 0.970397i | \(0.422355\pi\) | |||||||
\(984\) | 8.22263 | 0.262128 | ||||||||
\(985\) | 7.00740 | 0.223274 | ||||||||
\(986\) | −7.12937 | −0.227045 | ||||||||
\(987\) | −7.62174 | −0.242603 | ||||||||
\(988\) | 8.91952 | 0.283768 | ||||||||
\(989\) | 32.4018 | 1.03032 | ||||||||
\(990\) | −0.0601158 | −0.00191061 | ||||||||
\(991\) | −4.66382 | −0.148151 | −0.0740756 | − | 0.997253i | \(-0.523601\pi\) | ||||
−0.0740756 | + | 0.997253i | \(0.523601\pi\) | |||||||
\(992\) | 22.6563 | 0.719339 | ||||||||
\(993\) | 25.4281 | 0.806935 | ||||||||
\(994\) | 1.42353 | 0.0451516 | ||||||||
\(995\) | −0.0976641 | −0.00309616 | ||||||||
\(996\) | 10.3300 | 0.327320 | ||||||||
\(997\) | −41.9785 | −1.32947 | −0.664736 | − | 0.747078i | \(-0.731456\pi\) | ||||
−0.664736 | + | 0.747078i | \(0.731456\pi\) | |||||||
\(998\) | 2.46830 | 0.0781326 | ||||||||
\(999\) | −10.3326 | −0.326910 |
(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 | 4017.2.a.e.1.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.e.1.8 | ✓ | 16 | 1.1 | even | 1 | trivial |