Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1502,2,Mod(1,1502)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1502, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1502.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1502 = 2 \cdot 751 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1502.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: | \(11.9935303836\) |
Analytic rank: | \(0\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 6 x^{18} - 23 x^{17} + 190 x^{16} + 128 x^{15} - 2394 x^{14} + 749 x^{13} + 15539 x^{12} - 11338 x^{11} - 56744 x^{10} + 50183 x^{9} + 120237 x^{8} - 102992 x^{7} + \cdots + 4222 \) |
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 | 1.3 | ||
Root | \(-2.13636\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1502.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.13636 | −1.23343 | −0.616713 | − | 0.787188i | \(-0.711536\pi\) | ||||
−0.616713 | + | 0.787188i | \(0.711536\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.42355 | −1.08385 | −0.541923 | − | 0.840428i | \(-0.682304\pi\) | ||||
−0.541923 | + | 0.840428i | \(0.682304\pi\) | |||||||
\(6\) | 2.13636 | 0.872164 | ||||||||
\(7\) | 4.87888 | 1.84404 | 0.922022 | − | 0.387137i | \(-0.126536\pi\) | ||||
0.922022 | + | 0.387137i | \(0.126536\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.56402 | 0.521341 | ||||||||
\(10\) | 2.42355 | 0.766395 | ||||||||
\(11\) | 4.17648 | 1.25926 | 0.629629 | − | 0.776896i | \(-0.283207\pi\) | ||||
0.629629 | + | 0.776896i | \(0.283207\pi\) | |||||||
\(12\) | −2.13636 | −0.616713 | ||||||||
\(13\) | 3.80781 | 1.05610 | 0.528048 | − | 0.849214i | \(-0.322924\pi\) | ||||
0.528048 | + | 0.849214i | \(0.322924\pi\) | |||||||
\(14\) | −4.87888 | −1.30394 | ||||||||
\(15\) | 5.17758 | 1.33684 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.58856 | −0.870354 | −0.435177 | − | 0.900345i | \(-0.643314\pi\) | ||||
−0.435177 | + | 0.900345i | \(0.643314\pi\) | |||||||
\(18\) | −1.56402 | −0.368643 | ||||||||
\(19\) | 2.08604 | 0.478570 | 0.239285 | − | 0.970949i | \(-0.423087\pi\) | ||||
0.239285 | + | 0.970949i | \(0.423087\pi\) | |||||||
\(20\) | −2.42355 | −0.541923 | ||||||||
\(21\) | −10.4230 | −2.27449 | ||||||||
\(22\) | −4.17648 | −0.890429 | ||||||||
\(23\) | 3.33317 | 0.695015 | 0.347507 | − | 0.937677i | \(-0.387028\pi\) | ||||
0.347507 | + | 0.937677i | \(0.387028\pi\) | |||||||
\(24\) | 2.13636 | 0.436082 | ||||||||
\(25\) | 0.873611 | 0.174722 | ||||||||
\(26\) | −3.80781 | −0.746773 | ||||||||
\(27\) | 3.06776 | 0.590391 | ||||||||
\(28\) | 4.87888 | 0.922022 | ||||||||
\(29\) | −9.07425 | −1.68505 | −0.842523 | − | 0.538660i | \(-0.818931\pi\) | ||||
−0.842523 | + | 0.538660i | \(0.818931\pi\) | |||||||
\(30\) | −5.17758 | −0.945292 | ||||||||
\(31\) | −1.55922 | −0.280044 | −0.140022 | − | 0.990148i | \(-0.544717\pi\) | ||||
−0.140022 | + | 0.990148i | \(0.544717\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −8.92246 | −1.55320 | ||||||||
\(34\) | 3.58856 | 0.615433 | ||||||||
\(35\) | −11.8242 | −1.99866 | ||||||||
\(36\) | 1.56402 | 0.260670 | ||||||||
\(37\) | −2.16036 | −0.355161 | −0.177580 | − | 0.984106i | \(-0.556827\pi\) | ||||
−0.177580 | + | 0.984106i | \(0.556827\pi\) | |||||||
\(38\) | −2.08604 | −0.338400 | ||||||||
\(39\) | −8.13485 | −1.30262 | ||||||||
\(40\) | 2.42355 | 0.383197 | ||||||||
\(41\) | 8.24485 | 1.28763 | 0.643815 | − | 0.765182i | \(-0.277351\pi\) | ||||
0.643815 | + | 0.765182i | \(0.277351\pi\) | |||||||
\(42\) | 10.4230 | 1.60831 | ||||||||
\(43\) | 2.98863 | 0.455761 | 0.227881 | − | 0.973689i | \(-0.426820\pi\) | ||||
0.227881 | + | 0.973689i | \(0.426820\pi\) | |||||||
\(44\) | 4.17648 | 0.629629 | ||||||||
\(45\) | −3.79049 | −0.565053 | ||||||||
\(46\) | −3.33317 | −0.491450 | ||||||||
\(47\) | −6.93762 | −1.01196 | −0.505978 | − | 0.862546i | \(-0.668868\pi\) | ||||
−0.505978 | + | 0.862546i | \(0.668868\pi\) | |||||||
\(48\) | −2.13636 | −0.308357 | ||||||||
\(49\) | 16.8035 | 2.40050 | ||||||||
\(50\) | −0.873611 | −0.123547 | ||||||||
\(51\) | 7.66645 | 1.07352 | ||||||||
\(52\) | 3.80781 | 0.528048 | ||||||||
\(53\) | −4.05475 | −0.556962 | −0.278481 | − | 0.960442i | \(-0.589831\pi\) | ||||
−0.278481 | + | 0.960442i | \(0.589831\pi\) | |||||||
\(54\) | −3.06776 | −0.417470 | ||||||||
\(55\) | −10.1219 | −1.36484 | ||||||||
\(56\) | −4.87888 | −0.651968 | ||||||||
\(57\) | −4.45652 | −0.590280 | ||||||||
\(58\) | 9.07425 | 1.19151 | ||||||||
\(59\) | 11.1211 | 1.44784 | 0.723921 | − | 0.689883i | \(-0.242338\pi\) | ||||
0.723921 | + | 0.689883i | \(0.242338\pi\) | |||||||
\(60\) | 5.17758 | 0.668422 | ||||||||
\(61\) | −8.56035 | −1.09604 | −0.548020 | − | 0.836465i | \(-0.684618\pi\) | ||||
−0.548020 | + | 0.836465i | \(0.684618\pi\) | |||||||
\(62\) | 1.55922 | 0.198021 | ||||||||
\(63\) | 7.63068 | 0.961375 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.22843 | −1.14465 | ||||||||
\(66\) | 8.92246 | 1.09828 | ||||||||
\(67\) | 1.12384 | 0.137299 | 0.0686495 | − | 0.997641i | \(-0.478131\pi\) | ||||
0.0686495 | + | 0.997641i | \(0.478131\pi\) | |||||||
\(68\) | −3.58856 | −0.435177 | ||||||||
\(69\) | −7.12085 | −0.857249 | ||||||||
\(70\) | 11.8242 | 1.41327 | ||||||||
\(71\) | 2.87963 | 0.341749 | 0.170875 | − | 0.985293i | \(-0.445341\pi\) | ||||
0.170875 | + | 0.985293i | \(0.445341\pi\) | |||||||
\(72\) | −1.56402 | −0.184322 | ||||||||
\(73\) | 5.17680 | 0.605898 | 0.302949 | − | 0.953007i | \(-0.402029\pi\) | ||||
0.302949 | + | 0.953007i | \(0.402029\pi\) | |||||||
\(74\) | 2.16036 | 0.251137 | ||||||||
\(75\) | −1.86634 | −0.215507 | ||||||||
\(76\) | 2.08604 | 0.239285 | ||||||||
\(77\) | 20.3766 | 2.32213 | ||||||||
\(78\) | 8.13485 | 0.921090 | ||||||||
\(79\) | 5.93193 | 0.667394 | 0.333697 | − | 0.942680i | \(-0.391704\pi\) | ||||
0.333697 | + | 0.942680i | \(0.391704\pi\) | |||||||
\(80\) | −2.42355 | −0.270961 | ||||||||
\(81\) | −11.2459 | −1.24954 | ||||||||
\(82\) | −8.24485 | −0.910491 | ||||||||
\(83\) | −2.08785 | −0.229171 | −0.114586 | − | 0.993413i | \(-0.536554\pi\) | ||||
−0.114586 | + | 0.993413i | \(0.536554\pi\) | |||||||
\(84\) | −10.4230 | −1.13725 | ||||||||
\(85\) | 8.69707 | 0.943329 | ||||||||
\(86\) | −2.98863 | −0.322272 | ||||||||
\(87\) | 19.3858 | 2.07838 | ||||||||
\(88\) | −4.17648 | −0.445215 | ||||||||
\(89\) | 5.27367 | 0.559007 | 0.279504 | − | 0.960145i | \(-0.409830\pi\) | ||||
0.279504 | + | 0.960145i | \(0.409830\pi\) | |||||||
\(90\) | 3.79049 | 0.399553 | ||||||||
\(91\) | 18.5779 | 1.94749 | ||||||||
\(92\) | 3.33317 | 0.347507 | ||||||||
\(93\) | 3.33104 | 0.345413 | ||||||||
\(94\) | 6.93762 | 0.715561 | ||||||||
\(95\) | −5.05562 | −0.518696 | ||||||||
\(96\) | 2.13636 | 0.218041 | ||||||||
\(97\) | 8.80362 | 0.893872 | 0.446936 | − | 0.894566i | \(-0.352515\pi\) | ||||
0.446936 | + | 0.894566i | \(0.352515\pi\) | |||||||
\(98\) | −16.8035 | −1.69741 | ||||||||
\(99\) | 6.53211 | 0.656502 | ||||||||
\(100\) | 0.873611 | 0.0873611 | ||||||||
\(101\) | −1.40231 | −0.139535 | −0.0697673 | − | 0.997563i | \(-0.522226\pi\) | ||||
−0.0697673 | + | 0.997563i | \(0.522226\pi\) | |||||||
\(102\) | −7.66645 | −0.759091 | ||||||||
\(103\) | 17.5860 | 1.73280 | 0.866401 | − | 0.499349i | \(-0.166427\pi\) | ||||
0.866401 | + | 0.499349i | \(0.166427\pi\) | |||||||
\(104\) | −3.80781 | −0.373387 | ||||||||
\(105\) | 25.2608 | 2.46520 | ||||||||
\(106\) | 4.05475 | 0.393832 | ||||||||
\(107\) | −2.16657 | −0.209450 | −0.104725 | − | 0.994501i | \(-0.533396\pi\) | ||||
−0.104725 | + | 0.994501i | \(0.533396\pi\) | |||||||
\(108\) | 3.06776 | 0.295196 | ||||||||
\(109\) | −14.8582 | −1.42316 | −0.711578 | − | 0.702607i | \(-0.752019\pi\) | ||||
−0.711578 | + | 0.702607i | \(0.752019\pi\) | |||||||
\(110\) | 10.1219 | 0.965088 | ||||||||
\(111\) | 4.61530 | 0.438065 | ||||||||
\(112\) | 4.87888 | 0.461011 | ||||||||
\(113\) | 20.4505 | 1.92382 | 0.961910 | − | 0.273367i | \(-0.0881374\pi\) | ||||
0.961910 | + | 0.273367i | \(0.0881374\pi\) | |||||||
\(114\) | 4.45652 | 0.417391 | ||||||||
\(115\) | −8.07812 | −0.753289 | ||||||||
\(116\) | −9.07425 | −0.842523 | ||||||||
\(117\) | 5.95550 | 0.550586 | ||||||||
\(118\) | −11.1211 | −1.02378 | ||||||||
\(119\) | −17.5082 | −1.60497 | ||||||||
\(120\) | −5.17758 | −0.472646 | ||||||||
\(121\) | 6.44301 | 0.585729 | ||||||||
\(122\) | 8.56035 | 0.775017 | ||||||||
\(123\) | −17.6139 | −1.58820 | ||||||||
\(124\) | −1.55922 | −0.140022 | ||||||||
\(125\) | 10.0005 | 0.894474 | ||||||||
\(126\) | −7.63068 | −0.679795 | ||||||||
\(127\) | −14.8677 | −1.31930 | −0.659648 | − | 0.751574i | \(-0.729295\pi\) | ||||
−0.659648 | + | 0.751574i | \(0.729295\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.38478 | −0.562148 | ||||||||
\(130\) | 9.22843 | 0.809387 | ||||||||
\(131\) | −8.50866 | −0.743405 | −0.371703 | − | 0.928352i | \(-0.621226\pi\) | ||||
−0.371703 | + | 0.928352i | \(0.621226\pi\) | |||||||
\(132\) | −8.92246 | −0.776601 | ||||||||
\(133\) | 10.1775 | 0.882504 | ||||||||
\(134\) | −1.12384 | −0.0970851 | ||||||||
\(135\) | −7.43489 | −0.639893 | ||||||||
\(136\) | 3.58856 | 0.307717 | ||||||||
\(137\) | 13.1946 | 1.12729 | 0.563644 | − | 0.826018i | \(-0.309399\pi\) | ||||
0.563644 | + | 0.826018i | \(0.309399\pi\) | |||||||
\(138\) | 7.12085 | 0.606167 | ||||||||
\(139\) | −4.26167 | −0.361470 | −0.180735 | − | 0.983532i | \(-0.557848\pi\) | ||||
−0.180735 | + | 0.983532i | \(0.557848\pi\) | |||||||
\(140\) | −11.8242 | −0.999330 | ||||||||
\(141\) | 14.8212 | 1.24817 | ||||||||
\(142\) | −2.87963 | −0.241653 | ||||||||
\(143\) | 15.9033 | 1.32990 | ||||||||
\(144\) | 1.56402 | 0.130335 | ||||||||
\(145\) | 21.9919 | 1.82633 | ||||||||
\(146\) | −5.17680 | −0.428435 | ||||||||
\(147\) | −35.8983 | −2.96084 | ||||||||
\(148\) | −2.16036 | −0.177580 | ||||||||
\(149\) | −12.4180 | −1.01732 | −0.508661 | − | 0.860967i | \(-0.669859\pi\) | ||||
−0.508661 | + | 0.860967i | \(0.669859\pi\) | |||||||
\(150\) | 1.86634 | 0.152386 | ||||||||
\(151\) | 21.1521 | 1.72133 | 0.860666 | − | 0.509169i | \(-0.170047\pi\) | ||||
0.860666 | + | 0.509169i | \(0.170047\pi\) | |||||||
\(152\) | −2.08604 | −0.169200 | ||||||||
\(153\) | −5.61259 | −0.453751 | ||||||||
\(154\) | −20.3766 | −1.64199 | ||||||||
\(155\) | 3.77885 | 0.303524 | ||||||||
\(156\) | −8.13485 | −0.651309 | ||||||||
\(157\) | 17.2057 | 1.37316 | 0.686582 | − | 0.727052i | \(-0.259110\pi\) | ||||
0.686582 | + | 0.727052i | \(0.259110\pi\) | |||||||
\(158\) | −5.93193 | −0.471919 | ||||||||
\(159\) | 8.66239 | 0.686972 | ||||||||
\(160\) | 2.42355 | 0.191599 | ||||||||
\(161\) | 16.2622 | 1.28164 | ||||||||
\(162\) | 11.2459 | 0.883561 | ||||||||
\(163\) | 1.80306 | 0.141226 | 0.0706132 | − | 0.997504i | \(-0.477504\pi\) | ||||
0.0706132 | + | 0.997504i | \(0.477504\pi\) | |||||||
\(164\) | 8.24485 | 0.643815 | ||||||||
\(165\) | 21.6241 | 1.68343 | ||||||||
\(166\) | 2.08785 | 0.162049 | ||||||||
\(167\) | −0.507845 | −0.0392982 | −0.0196491 | − | 0.999807i | \(-0.506255\pi\) | ||||
−0.0196491 | + | 0.999807i | \(0.506255\pi\) | |||||||
\(168\) | 10.4230 | 0.804155 | ||||||||
\(169\) | 1.49943 | 0.115341 | ||||||||
\(170\) | −8.69707 | −0.667035 | ||||||||
\(171\) | 3.26261 | 0.249498 | ||||||||
\(172\) | 2.98863 | 0.227881 | ||||||||
\(173\) | 16.6498 | 1.26586 | 0.632932 | − | 0.774208i | \(-0.281851\pi\) | ||||
0.632932 | + | 0.774208i | \(0.281851\pi\) | |||||||
\(174\) | −19.3858 | −1.46964 | ||||||||
\(175\) | 4.26225 | 0.322195 | ||||||||
\(176\) | 4.17648 | 0.314814 | ||||||||
\(177\) | −23.7586 | −1.78581 | ||||||||
\(178\) | −5.27367 | −0.395278 | ||||||||
\(179\) | −11.9707 | −0.894732 | −0.447366 | − | 0.894351i | \(-0.647638\pi\) | ||||
−0.447366 | + | 0.894351i | \(0.647638\pi\) | |||||||
\(180\) | −3.79049 | −0.282526 | ||||||||
\(181\) | 2.20077 | 0.163582 | 0.0817911 | − | 0.996649i | \(-0.473936\pi\) | ||||
0.0817911 | + | 0.996649i | \(0.473936\pi\) | |||||||
\(182\) | −18.5779 | −1.37708 | ||||||||
\(183\) | 18.2880 | 1.35188 | ||||||||
\(184\) | −3.33317 | −0.245725 | ||||||||
\(185\) | 5.23574 | 0.384939 | ||||||||
\(186\) | −3.33104 | −0.244244 | ||||||||
\(187\) | −14.9876 | −1.09600 | ||||||||
\(188\) | −6.93762 | −0.505978 | ||||||||
\(189\) | 14.9673 | 1.08871 | ||||||||
\(190\) | 5.05562 | 0.366773 | ||||||||
\(191\) | −5.90750 | −0.427452 | −0.213726 | − | 0.976894i | \(-0.568560\pi\) | ||||
−0.213726 | + | 0.976894i | \(0.568560\pi\) | |||||||
\(192\) | −2.13636 | −0.154178 | ||||||||
\(193\) | −13.4643 | −0.969178 | −0.484589 | − | 0.874742i | \(-0.661031\pi\) | ||||
−0.484589 | + | 0.874742i | \(0.661031\pi\) | |||||||
\(194\) | −8.80362 | −0.632063 | ||||||||
\(195\) | 19.7152 | 1.41184 | ||||||||
\(196\) | 16.8035 | 1.20025 | ||||||||
\(197\) | 12.7144 | 0.905867 | 0.452933 | − | 0.891544i | \(-0.350378\pi\) | ||||
0.452933 | + | 0.891544i | \(0.350378\pi\) | |||||||
\(198\) | −6.53211 | −0.464217 | ||||||||
\(199\) | 26.8112 | 1.90059 | 0.950296 | − | 0.311347i | \(-0.100780\pi\) | ||||
0.950296 | + | 0.311347i | \(0.100780\pi\) | |||||||
\(200\) | −0.873611 | −0.0617736 | ||||||||
\(201\) | −2.40093 | −0.169348 | ||||||||
\(202\) | 1.40231 | 0.0986659 | ||||||||
\(203\) | −44.2722 | −3.10730 | ||||||||
\(204\) | 7.66645 | 0.536759 | ||||||||
\(205\) | −19.9818 | −1.39559 | ||||||||
\(206\) | −17.5860 | −1.22528 | ||||||||
\(207\) | 5.21316 | 0.362339 | ||||||||
\(208\) | 3.80781 | 0.264024 | ||||||||
\(209\) | 8.71230 | 0.602642 | ||||||||
\(210\) | −25.2608 | −1.74316 | ||||||||
\(211\) | −10.9857 | −0.756286 | −0.378143 | − | 0.925747i | \(-0.623437\pi\) | ||||
−0.378143 | + | 0.925747i | \(0.623437\pi\) | |||||||
\(212\) | −4.05475 | −0.278481 | ||||||||
\(213\) | −6.15192 | −0.421523 | ||||||||
\(214\) | 2.16657 | 0.148104 | ||||||||
\(215\) | −7.24310 | −0.493975 | ||||||||
\(216\) | −3.06776 | −0.208735 | ||||||||
\(217\) | −7.60724 | −0.516413 | ||||||||
\(218\) | 14.8582 | 1.00632 | ||||||||
\(219\) | −11.0595 | −0.747331 | ||||||||
\(220\) | −10.1219 | −0.682420 | ||||||||
\(221\) | −13.6646 | −0.919178 | ||||||||
\(222\) | −4.61530 | −0.309758 | ||||||||
\(223\) | 27.6057 | 1.84861 | 0.924307 | − | 0.381650i | \(-0.124644\pi\) | ||||
0.924307 | + | 0.381650i | \(0.124644\pi\) | |||||||
\(224\) | −4.87888 | −0.325984 | ||||||||
\(225\) | 1.36635 | 0.0910898 | ||||||||
\(226\) | −20.4505 | −1.36035 | ||||||||
\(227\) | −26.2090 | −1.73955 | −0.869777 | − | 0.493444i | \(-0.835738\pi\) | ||||
−0.869777 | + | 0.493444i | \(0.835738\pi\) | |||||||
\(228\) | −4.45652 | −0.295140 | ||||||||
\(229\) | −22.1584 | −1.46427 | −0.732135 | − | 0.681159i | \(-0.761476\pi\) | ||||
−0.732135 | + | 0.681159i | \(0.761476\pi\) | |||||||
\(230\) | 8.07812 | 0.532656 | ||||||||
\(231\) | −43.5316 | −2.86417 | ||||||||
\(232\) | 9.07425 | 0.595754 | ||||||||
\(233\) | 14.4276 | 0.945182 | 0.472591 | − | 0.881282i | \(-0.343319\pi\) | ||||
0.472591 | + | 0.881282i | \(0.343319\pi\) | |||||||
\(234\) | −5.95550 | −0.389323 | ||||||||
\(235\) | 16.8137 | 1.09680 | ||||||||
\(236\) | 11.1211 | 0.723921 | ||||||||
\(237\) | −12.6727 | −0.823181 | ||||||||
\(238\) | 17.5082 | 1.13489 | ||||||||
\(239\) | 7.47287 | 0.483380 | 0.241690 | − | 0.970354i | \(-0.422298\pi\) | ||||
0.241690 | + | 0.970354i | \(0.422298\pi\) | |||||||
\(240\) | 5.17758 | 0.334211 | ||||||||
\(241\) | −5.81160 | −0.374358 | −0.187179 | − | 0.982326i | \(-0.559934\pi\) | ||||
−0.187179 | + | 0.982326i | \(0.559934\pi\) | |||||||
\(242\) | −6.44301 | −0.414173 | ||||||||
\(243\) | 14.8220 | 0.950830 | ||||||||
\(244\) | −8.56035 | −0.548020 | ||||||||
\(245\) | −40.7242 | −2.60177 | ||||||||
\(246\) | 17.6139 | 1.12302 | ||||||||
\(247\) | 7.94323 | 0.505416 | ||||||||
\(248\) | 1.55922 | 0.0990104 | ||||||||
\(249\) | 4.46039 | 0.282666 | ||||||||
\(250\) | −10.0005 | −0.632489 | ||||||||
\(251\) | 31.3685 | 1.97996 | 0.989982 | − | 0.141194i | \(-0.0450941\pi\) | ||||
0.989982 | + | 0.141194i | \(0.0450941\pi\) | |||||||
\(252\) | 7.63068 | 0.480688 | ||||||||
\(253\) | 13.9209 | 0.875202 | ||||||||
\(254\) | 14.8677 | 0.932884 | ||||||||
\(255\) | −18.5800 | −1.16353 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.79913 | 0.112227 | 0.0561133 | − | 0.998424i | \(-0.482129\pi\) | ||||
0.0561133 | + | 0.998424i | \(0.482129\pi\) | |||||||
\(258\) | 6.38478 | 0.397499 | ||||||||
\(259\) | −10.5401 | −0.654932 | ||||||||
\(260\) | −9.22843 | −0.572323 | ||||||||
\(261\) | −14.1923 | −0.878483 | ||||||||
\(262\) | 8.50866 | 0.525667 | ||||||||
\(263\) | −14.5641 | −0.898063 | −0.449032 | − | 0.893516i | \(-0.648231\pi\) | ||||
−0.449032 | + | 0.893516i | \(0.648231\pi\) | |||||||
\(264\) | 8.92246 | 0.549139 | ||||||||
\(265\) | 9.82690 | 0.603662 | ||||||||
\(266\) | −10.1775 | −0.624024 | ||||||||
\(267\) | −11.2664 | −0.689494 | ||||||||
\(268\) | 1.12384 | 0.0686495 | ||||||||
\(269\) | 9.22945 | 0.562729 | 0.281365 | − | 0.959601i | \(-0.409213\pi\) | ||||
0.281365 | + | 0.959601i | \(0.409213\pi\) | |||||||
\(270\) | 7.43489 | 0.452473 | ||||||||
\(271\) | −21.8990 | −1.33027 | −0.665134 | − | 0.746724i | \(-0.731625\pi\) | ||||
−0.665134 | + | 0.746724i | \(0.731625\pi\) | |||||||
\(272\) | −3.58856 | −0.217588 | ||||||||
\(273\) | −39.6890 | −2.40209 | ||||||||
\(274\) | −13.1946 | −0.797114 | ||||||||
\(275\) | 3.64862 | 0.220020 | ||||||||
\(276\) | −7.12085 | −0.428625 | ||||||||
\(277\) | 27.9450 | 1.67905 | 0.839525 | − | 0.543321i | \(-0.182833\pi\) | ||||
0.839525 | + | 0.543321i | \(0.182833\pi\) | |||||||
\(278\) | 4.26167 | 0.255598 | ||||||||
\(279\) | −2.43865 | −0.145998 | ||||||||
\(280\) | 11.8242 | 0.706633 | ||||||||
\(281\) | 11.7874 | 0.703177 | 0.351588 | − | 0.936155i | \(-0.385642\pi\) | ||||
0.351588 | + | 0.936155i | \(0.385642\pi\) | |||||||
\(282\) | −14.8212 | −0.882592 | ||||||||
\(283\) | 24.8420 | 1.47670 | 0.738352 | − | 0.674415i | \(-0.235604\pi\) | ||||
0.738352 | + | 0.674415i | \(0.235604\pi\) | |||||||
\(284\) | 2.87963 | 0.170875 | ||||||||
\(285\) | 10.8006 | 0.639773 | ||||||||
\(286\) | −15.9033 | −0.940380 | ||||||||
\(287\) | 40.2257 | 2.37445 | ||||||||
\(288\) | −1.56402 | −0.0921609 | ||||||||
\(289\) | −4.12223 | −0.242484 | ||||||||
\(290\) | −21.9919 | −1.29141 | ||||||||
\(291\) | −18.8077 | −1.10252 | ||||||||
\(292\) | 5.17680 | 0.302949 | ||||||||
\(293\) | −6.33434 | −0.370056 | −0.185028 | − | 0.982733i | \(-0.559238\pi\) | ||||
−0.185028 | + | 0.982733i | \(0.559238\pi\) | |||||||
\(294\) | 35.8983 | 2.09363 | ||||||||
\(295\) | −26.9525 | −1.56924 | ||||||||
\(296\) | 2.16036 | 0.125568 | ||||||||
\(297\) | 12.8125 | 0.743454 | ||||||||
\(298\) | 12.4180 | 0.719355 | ||||||||
\(299\) | 12.6921 | 0.734003 | ||||||||
\(300\) | −1.86634 | −0.107753 | ||||||||
\(301\) | 14.5812 | 0.840444 | ||||||||
\(302\) | −21.1521 | −1.21717 | ||||||||
\(303\) | 2.99583 | 0.172106 | ||||||||
\(304\) | 2.08604 | 0.119642 | ||||||||
\(305\) | 20.7465 | 1.18794 | ||||||||
\(306\) | 5.61259 | 0.320850 | ||||||||
\(307\) | −6.64633 | −0.379326 | −0.189663 | − | 0.981849i | \(-0.560740\pi\) | ||||
−0.189663 | + | 0.981849i | \(0.560740\pi\) | |||||||
\(308\) | 20.3766 | 1.16106 | ||||||||
\(309\) | −37.5700 | −2.13728 | ||||||||
\(310\) | −3.77885 | −0.214624 | ||||||||
\(311\) | 1.93843 | 0.109918 | 0.0549592 | − | 0.998489i | \(-0.482497\pi\) | ||||
0.0549592 | + | 0.998489i | \(0.482497\pi\) | |||||||
\(312\) | 8.13485 | 0.460545 | ||||||||
\(313\) | 12.7744 | 0.722054 | 0.361027 | − | 0.932555i | \(-0.382426\pi\) | ||||
0.361027 | + | 0.932555i | \(0.382426\pi\) | |||||||
\(314\) | −17.2057 | −0.970974 | ||||||||
\(315\) | −18.4934 | −1.04198 | ||||||||
\(316\) | 5.93193 | 0.333697 | ||||||||
\(317\) | 4.51399 | 0.253531 | 0.126765 | − | 0.991933i | \(-0.459540\pi\) | ||||
0.126765 | + | 0.991933i | \(0.459540\pi\) | |||||||
\(318\) | −8.66239 | −0.485763 | ||||||||
\(319\) | −37.8985 | −2.12191 | ||||||||
\(320\) | −2.42355 | −0.135481 | ||||||||
\(321\) | 4.62857 | 0.258341 | ||||||||
\(322\) | −16.2622 | −0.906255 | ||||||||
\(323\) | −7.48587 | −0.416525 | ||||||||
\(324\) | −11.2459 | −0.624772 | ||||||||
\(325\) | 3.32655 | 0.184524 | ||||||||
\(326\) | −1.80306 | −0.0998621 | ||||||||
\(327\) | 31.7424 | 1.75536 | ||||||||
\(328\) | −8.24485 | −0.455246 | ||||||||
\(329\) | −33.8478 | −1.86609 | ||||||||
\(330\) | −21.6241 | −1.19037 | ||||||||
\(331\) | −17.9117 | −0.984516 | −0.492258 | − | 0.870449i | \(-0.663828\pi\) | ||||
−0.492258 | + | 0.870449i | \(0.663828\pi\) | |||||||
\(332\) | −2.08785 | −0.114586 | ||||||||
\(333\) | −3.37885 | −0.185160 | ||||||||
\(334\) | 0.507845 | 0.0277880 | ||||||||
\(335\) | −2.72369 | −0.148811 | ||||||||
\(336\) | −10.4230 | −0.568623 | ||||||||
\(337\) | −25.7627 | −1.40338 | −0.701691 | − | 0.712482i | \(-0.747571\pi\) | ||||
−0.701691 | + | 0.712482i | \(0.747571\pi\) | |||||||
\(338\) | −1.49943 | −0.0815583 | ||||||||
\(339\) | −43.6895 | −2.37289 | ||||||||
\(340\) | 8.69707 | 0.471665 | ||||||||
\(341\) | −6.51204 | −0.352647 | ||||||||
\(342\) | −3.26261 | −0.176422 | ||||||||
\(343\) | 47.8302 | 2.58259 | ||||||||
\(344\) | −2.98863 | −0.161136 | ||||||||
\(345\) | 17.2578 | 0.929126 | ||||||||
\(346\) | −16.6498 | −0.895101 | ||||||||
\(347\) | 9.33419 | 0.501086 | 0.250543 | − | 0.968106i | \(-0.419391\pi\) | ||||
0.250543 | + | 0.968106i | \(0.419391\pi\) | |||||||
\(348\) | 19.3858 | 1.03919 | ||||||||
\(349\) | −23.3987 | −1.25250 | −0.626251 | − | 0.779621i | \(-0.715412\pi\) | ||||
−0.626251 | + | 0.779621i | \(0.715412\pi\) | |||||||
\(350\) | −4.26225 | −0.227827 | ||||||||
\(351\) | 11.6815 | 0.623510 | ||||||||
\(352\) | −4.17648 | −0.222607 | ||||||||
\(353\) | 16.7459 | 0.891296 | 0.445648 | − | 0.895208i | \(-0.352973\pi\) | ||||
0.445648 | + | 0.895208i | \(0.352973\pi\) | |||||||
\(354\) | 23.7586 | 1.26276 | ||||||||
\(355\) | −6.97894 | −0.370404 | ||||||||
\(356\) | 5.27367 | 0.279504 | ||||||||
\(357\) | 37.4037 | 1.97961 | ||||||||
\(358\) | 11.9707 | 0.632671 | ||||||||
\(359\) | 11.2319 | 0.592796 | 0.296398 | − | 0.955065i | \(-0.404215\pi\) | ||||
0.296398 | + | 0.955065i | \(0.404215\pi\) | |||||||
\(360\) | 3.79049 | 0.199776 | ||||||||
\(361\) | −14.6485 | −0.770971 | ||||||||
\(362\) | −2.20077 | −0.115670 | ||||||||
\(363\) | −13.7646 | −0.722453 | ||||||||
\(364\) | 18.5779 | 0.973745 | ||||||||
\(365\) | −12.5462 | −0.656701 | ||||||||
\(366\) | −18.2880 | −0.955927 | ||||||||
\(367\) | −36.8380 | −1.92293 | −0.961464 | − | 0.274931i | \(-0.911345\pi\) | ||||
−0.961464 | + | 0.274931i | \(0.911345\pi\) | |||||||
\(368\) | 3.33317 | 0.173754 | ||||||||
\(369\) | 12.8951 | 0.671293 | ||||||||
\(370\) | −5.23574 | −0.272193 | ||||||||
\(371\) | −19.7826 | −1.02706 | ||||||||
\(372\) | 3.33104 | 0.172707 | ||||||||
\(373\) | 17.1113 | 0.885991 | 0.442995 | − | 0.896524i | \(-0.353916\pi\) | ||||
0.442995 | + | 0.896524i | \(0.353916\pi\) | |||||||
\(374\) | 14.9876 | 0.774988 | ||||||||
\(375\) | −21.3647 | −1.10327 | ||||||||
\(376\) | 6.93762 | 0.357780 | ||||||||
\(377\) | −34.5530 | −1.77957 | ||||||||
\(378\) | −14.9673 | −0.769833 | ||||||||
\(379\) | 22.7500 | 1.16859 | 0.584293 | − | 0.811543i | \(-0.301372\pi\) | ||||
0.584293 | + | 0.811543i | \(0.301372\pi\) | |||||||
\(380\) | −5.05562 | −0.259348 | ||||||||
\(381\) | 31.7628 | 1.62726 | ||||||||
\(382\) | 5.90750 | 0.302254 | ||||||||
\(383\) | 14.2435 | 0.727806 | 0.363903 | − | 0.931437i | \(-0.381444\pi\) | ||||
0.363903 | + | 0.931437i | \(0.381444\pi\) | |||||||
\(384\) | 2.13636 | 0.109021 | ||||||||
\(385\) | −49.3837 | −2.51683 | ||||||||
\(386\) | 13.4643 | 0.685313 | ||||||||
\(387\) | 4.67428 | 0.237607 | ||||||||
\(388\) | 8.80362 | 0.446936 | ||||||||
\(389\) | −14.3431 | −0.727226 | −0.363613 | − | 0.931550i | \(-0.618457\pi\) | ||||
−0.363613 | + | 0.931550i | \(0.618457\pi\) | |||||||
\(390\) | −19.7152 | −0.998320 | ||||||||
\(391\) | −11.9613 | −0.604909 | ||||||||
\(392\) | −16.8035 | −0.848705 | ||||||||
\(393\) | 18.1775 | 0.916935 | ||||||||
\(394\) | −12.7144 | −0.640544 | ||||||||
\(395\) | −14.3763 | −0.723352 | ||||||||
\(396\) | 6.53211 | 0.328251 | ||||||||
\(397\) | −17.1101 | −0.858731 | −0.429366 | − | 0.903131i | \(-0.641263\pi\) | ||||
−0.429366 | + | 0.903131i | \(0.641263\pi\) | |||||||
\(398\) | −26.8112 | −1.34392 | ||||||||
\(399\) | −21.7428 | −1.08850 | ||||||||
\(400\) | 0.873611 | 0.0436805 | ||||||||
\(401\) | −5.89718 | −0.294491 | −0.147246 | − | 0.989100i | \(-0.547041\pi\) | ||||
−0.147246 | + | 0.989100i | \(0.547041\pi\) | |||||||
\(402\) | 2.40093 | 0.119747 | ||||||||
\(403\) | −5.93720 | −0.295753 | ||||||||
\(404\) | −1.40231 | −0.0697673 | ||||||||
\(405\) | 27.2550 | 1.35431 | ||||||||
\(406\) | 44.2722 | 2.19719 | ||||||||
\(407\) | −9.02270 | −0.447239 | ||||||||
\(408\) | −7.66645 | −0.379546 | ||||||||
\(409\) | 8.66087 | 0.428253 | 0.214126 | − | 0.976806i | \(-0.431310\pi\) | ||||
0.214126 | + | 0.976806i | \(0.431310\pi\) | |||||||
\(410\) | 19.9818 | 0.986832 | ||||||||
\(411\) | −28.1883 | −1.39043 | ||||||||
\(412\) | 17.5860 | 0.866401 | ||||||||
\(413\) | 54.2585 | 2.66989 | ||||||||
\(414\) | −5.21316 | −0.256213 | ||||||||
\(415\) | 5.06002 | 0.248386 | ||||||||
\(416\) | −3.80781 | −0.186693 | ||||||||
\(417\) | 9.10445 | 0.445847 | ||||||||
\(418\) | −8.71230 | −0.426132 | ||||||||
\(419\) | −15.7433 | −0.769112 | −0.384556 | − | 0.923102i | \(-0.625645\pi\) | ||||
−0.384556 | + | 0.923102i | \(0.625645\pi\) | |||||||
\(420\) | 25.2608 | 1.23260 | ||||||||
\(421\) | 27.7975 | 1.35477 | 0.677383 | − | 0.735631i | \(-0.263114\pi\) | ||||
0.677383 | + | 0.735631i | \(0.263114\pi\) | |||||||
\(422\) | 10.9857 | 0.534775 | ||||||||
\(423\) | −10.8506 | −0.527574 | ||||||||
\(424\) | 4.05475 | 0.196916 | ||||||||
\(425\) | −3.13501 | −0.152070 | ||||||||
\(426\) | 6.15192 | 0.298061 | ||||||||
\(427\) | −41.7649 | −2.02115 | ||||||||
\(428\) | −2.16657 | −0.104725 | ||||||||
\(429\) | −33.9751 | −1.64033 | ||||||||
\(430\) | 7.24310 | 0.349293 | ||||||||
\(431\) | −39.1696 | −1.88673 | −0.943366 | − | 0.331754i | \(-0.892360\pi\) | ||||
−0.943366 | + | 0.331754i | \(0.892360\pi\) | |||||||
\(432\) | 3.06776 | 0.147598 | ||||||||
\(433\) | 21.6849 | 1.04211 | 0.521055 | − | 0.853523i | \(-0.325539\pi\) | ||||
0.521055 | + | 0.853523i | \(0.325539\pi\) | |||||||
\(434\) | 7.60724 | 0.365159 | ||||||||
\(435\) | −46.9826 | −2.25264 | ||||||||
\(436\) | −14.8582 | −0.711578 | ||||||||
\(437\) | 6.95312 | 0.332613 | ||||||||
\(438\) | 11.0595 | 0.528443 | ||||||||
\(439\) | −13.8473 | −0.660895 | −0.330447 | − | 0.943824i | \(-0.607200\pi\) | ||||
−0.330447 | + | 0.943824i | \(0.607200\pi\) | |||||||
\(440\) | 10.1219 | 0.482544 | ||||||||
\(441\) | 26.2811 | 1.25148 | ||||||||
\(442\) | 13.6646 | 0.649957 | ||||||||
\(443\) | 30.0846 | 1.42936 | 0.714681 | − | 0.699451i | \(-0.246572\pi\) | ||||
0.714681 | + | 0.699451i | \(0.246572\pi\) | |||||||
\(444\) | 4.61530 | 0.219032 | ||||||||
\(445\) | −12.7810 | −0.605878 | ||||||||
\(446\) | −27.6057 | −1.30717 | ||||||||
\(447\) | 26.5293 | 1.25479 | ||||||||
\(448\) | 4.87888 | 0.230506 | ||||||||
\(449\) | 34.8294 | 1.64370 | 0.821850 | − | 0.569704i | \(-0.192942\pi\) | ||||
0.821850 | + | 0.569704i | \(0.192942\pi\) | |||||||
\(450\) | −1.36635 | −0.0644102 | ||||||||
\(451\) | 34.4345 | 1.62146 | ||||||||
\(452\) | 20.4505 | 0.961910 | ||||||||
\(453\) | −45.1884 | −2.12314 | ||||||||
\(454\) | 26.2090 | 1.23005 | ||||||||
\(455\) | −45.0245 | −2.11078 | ||||||||
\(456\) | 4.45652 | 0.208696 | ||||||||
\(457\) | 0.0780659 | 0.00365177 | 0.00182588 | − | 0.999998i | \(-0.499419\pi\) | ||||
0.00182588 | + | 0.999998i | \(0.499419\pi\) | |||||||
\(458\) | 22.1584 | 1.03540 | ||||||||
\(459\) | −11.0089 | −0.513849 | ||||||||
\(460\) | −8.07812 | −0.376644 | ||||||||
\(461\) | 20.0398 | 0.933345 | 0.466673 | − | 0.884430i | \(-0.345453\pi\) | ||||
0.466673 | + | 0.884430i | \(0.345453\pi\) | |||||||
\(462\) | 43.5316 | 2.02528 | ||||||||
\(463\) | 23.2743 | 1.08165 | 0.540824 | − | 0.841136i | \(-0.318113\pi\) | ||||
0.540824 | + | 0.841136i | \(0.318113\pi\) | |||||||
\(464\) | −9.07425 | −0.421262 | ||||||||
\(465\) | −8.07296 | −0.374375 | ||||||||
\(466\) | −14.4276 | −0.668345 | ||||||||
\(467\) | 2.21624 | 0.102555 | 0.0512776 | − | 0.998684i | \(-0.483671\pi\) | ||||
0.0512776 | + | 0.998684i | \(0.483671\pi\) | |||||||
\(468\) | 5.95550 | 0.275293 | ||||||||
\(469\) | 5.48309 | 0.253186 | ||||||||
\(470\) | −16.8137 | −0.775558 | ||||||||
\(471\) | −36.7575 | −1.69370 | ||||||||
\(472\) | −11.1211 | −0.511890 | ||||||||
\(473\) | 12.4820 | 0.573921 | ||||||||
\(474\) | 12.6727 | 0.582077 | ||||||||
\(475\) | 1.82238 | 0.0836167 | ||||||||
\(476\) | −17.5082 | −0.802486 | ||||||||
\(477\) | −6.34171 | −0.290367 | ||||||||
\(478\) | −7.47287 | −0.341801 | ||||||||
\(479\) | 7.59253 | 0.346912 | 0.173456 | − | 0.984842i | \(-0.444507\pi\) | ||||
0.173456 | + | 0.984842i | \(0.444507\pi\) | |||||||
\(480\) | −5.17758 | −0.236323 | ||||||||
\(481\) | −8.22624 | −0.375084 | ||||||||
\(482\) | 5.81160 | 0.264711 | ||||||||
\(483\) | −34.7418 | −1.58081 | ||||||||
\(484\) | 6.44301 | 0.292864 | ||||||||
\(485\) | −21.3360 | −0.968819 | ||||||||
\(486\) | −14.8220 | −0.672338 | ||||||||
\(487\) | 6.15247 | 0.278795 | 0.139397 | − | 0.990237i | \(-0.455483\pi\) | ||||
0.139397 | + | 0.990237i | \(0.455483\pi\) | |||||||
\(488\) | 8.56035 | 0.387509 | ||||||||
\(489\) | −3.85197 | −0.174192 | ||||||||
\(490\) | 40.7242 | 1.83973 | ||||||||
\(491\) | −37.0886 | −1.67378 | −0.836892 | − | 0.547369i | \(-0.815630\pi\) | ||||
−0.836892 | + | 0.547369i | \(0.815630\pi\) | |||||||
\(492\) | −17.6139 | −0.794098 | ||||||||
\(493\) | 32.5635 | 1.46659 | ||||||||
\(494\) | −7.94323 | −0.357383 | ||||||||
\(495\) | −15.8309 | −0.711547 | ||||||||
\(496\) | −1.55922 | −0.0700109 | ||||||||
\(497\) | 14.0494 | 0.630201 | ||||||||
\(498\) | −4.46039 | −0.199875 | ||||||||
\(499\) | −33.3384 | −1.49243 | −0.746217 | − | 0.665703i | \(-0.768132\pi\) | ||||
−0.746217 | + | 0.665703i | \(0.768132\pi\) | |||||||
\(500\) | 10.0005 | 0.447237 | ||||||||
\(501\) | 1.08494 | 0.0484714 | ||||||||
\(502\) | −31.3685 | −1.40005 | ||||||||
\(503\) | 19.4007 | 0.865036 | 0.432518 | − | 0.901625i | \(-0.357625\pi\) | ||||
0.432518 | + | 0.901625i | \(0.357625\pi\) | |||||||
\(504\) | −7.63068 | −0.339898 | ||||||||
\(505\) | 3.39856 | 0.151234 | ||||||||
\(506\) | −13.9209 | −0.618861 | ||||||||
\(507\) | −3.20332 | −0.142264 | ||||||||
\(508\) | −14.8677 | −0.659648 | ||||||||
\(509\) | 4.81858 | 0.213580 | 0.106790 | − | 0.994282i | \(-0.465943\pi\) | ||||
0.106790 | + | 0.994282i | \(0.465943\pi\) | |||||||
\(510\) | 18.5800 | 0.822738 | ||||||||
\(511\) | 25.2570 | 1.11730 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 6.39946 | 0.282543 | ||||||||
\(514\) | −1.79913 | −0.0793562 | ||||||||
\(515\) | −42.6207 | −1.87809 | ||||||||
\(516\) | −6.38478 | −0.281074 | ||||||||
\(517\) | −28.9749 | −1.27431 | ||||||||
\(518\) | 10.5401 | 0.463107 | ||||||||
\(519\) | −35.5700 | −1.56135 | ||||||||
\(520\) | 9.22843 | 0.404694 | ||||||||
\(521\) | −0.578491 | −0.0253441 | −0.0126721 | − | 0.999920i | \(-0.504034\pi\) | ||||
−0.0126721 | + | 0.999920i | \(0.504034\pi\) | |||||||
\(522\) | 14.1923 | 0.621181 | ||||||||
\(523\) | 13.8406 | 0.605209 | 0.302604 | − | 0.953116i | \(-0.402144\pi\) | ||||
0.302604 | + | 0.953116i | \(0.402144\pi\) | |||||||
\(524\) | −8.50866 | −0.371703 | ||||||||
\(525\) | −9.10568 | −0.397404 | ||||||||
\(526\) | 14.5641 | 0.635027 | ||||||||
\(527\) | 5.59534 | 0.243737 | ||||||||
\(528\) | −8.92246 | −0.388300 | ||||||||
\(529\) | −11.8900 | −0.516955 | ||||||||
\(530\) | −9.82690 | −0.426853 | ||||||||
\(531\) | 17.3936 | 0.754819 | ||||||||
\(532\) | 10.1775 | 0.441252 | ||||||||
\(533\) | 31.3948 | 1.35986 | ||||||||
\(534\) | 11.2664 | 0.487546 | ||||||||
\(535\) | 5.25080 | 0.227012 | ||||||||
\(536\) | −1.12384 | −0.0485426 | ||||||||
\(537\) | 25.5737 | 1.10359 | ||||||||
\(538\) | −9.22945 | −0.397910 | ||||||||
\(539\) | 70.1796 | 3.02285 | ||||||||
\(540\) | −7.43489 | −0.319947 | ||||||||
\(541\) | −25.9841 | −1.11714 | −0.558571 | − | 0.829457i | \(-0.688650\pi\) | ||||
−0.558571 | + | 0.829457i | \(0.688650\pi\) | |||||||
\(542\) | 21.8990 | 0.940641 | ||||||||
\(543\) | −4.70164 | −0.201767 | ||||||||
\(544\) | 3.58856 | 0.153858 | ||||||||
\(545\) | 36.0096 | 1.54248 | ||||||||
\(546\) | 39.6890 | 1.69853 | ||||||||
\(547\) | −11.4985 | −0.491639 | −0.245819 | − | 0.969316i | \(-0.579057\pi\) | ||||
−0.245819 | + | 0.969316i | \(0.579057\pi\) | |||||||
\(548\) | 13.1946 | 0.563644 | ||||||||
\(549\) | −13.3886 | −0.571410 | ||||||||
\(550\) | −3.64862 | −0.155578 | ||||||||
\(551\) | −18.9292 | −0.806412 | ||||||||
\(552\) | 7.12085 | 0.303083 | ||||||||
\(553\) | 28.9412 | 1.23070 | ||||||||
\(554\) | −27.9450 | −1.18727 | ||||||||
\(555\) | −11.1854 | −0.474795 | ||||||||
\(556\) | −4.26167 | −0.180735 | ||||||||
\(557\) | −40.1044 | −1.69928 | −0.849638 | − | 0.527366i | \(-0.823180\pi\) | ||||
−0.849638 | + | 0.527366i | \(0.823180\pi\) | |||||||
\(558\) | 2.43865 | 0.103236 | ||||||||
\(559\) | 11.3801 | 0.481328 | ||||||||
\(560\) | −11.8242 | −0.499665 | ||||||||
\(561\) | 32.0188 | 1.35183 | ||||||||
\(562\) | −11.7874 | −0.497221 | ||||||||
\(563\) | 38.1782 | 1.60902 | 0.804510 | − | 0.593940i | \(-0.202428\pi\) | ||||
0.804510 | + | 0.593940i | \(0.202428\pi\) | |||||||
\(564\) | 14.8212 | 0.624087 | ||||||||
\(565\) | −49.5628 | −2.08512 | ||||||||
\(566\) | −24.8420 | −1.04419 | ||||||||
\(567\) | −54.8674 | −2.30422 | ||||||||
\(568\) | −2.87963 | −0.120827 | ||||||||
\(569\) | 9.33767 | 0.391456 | 0.195728 | − | 0.980658i | \(-0.437293\pi\) | ||||
0.195728 | + | 0.980658i | \(0.437293\pi\) | |||||||
\(570\) | −10.8006 | −0.452388 | ||||||||
\(571\) | 37.0912 | 1.55222 | 0.776110 | − | 0.630597i | \(-0.217190\pi\) | ||||
0.776110 | + | 0.630597i | \(0.217190\pi\) | |||||||
\(572\) | 15.9033 | 0.664949 | ||||||||
\(573\) | 12.6205 | 0.527231 | ||||||||
\(574\) | −40.2257 | −1.67899 | ||||||||
\(575\) | 2.91190 | 0.121434 | ||||||||
\(576\) | 1.56402 | 0.0651676 | ||||||||
\(577\) | −16.1394 | −0.671893 | −0.335947 | − | 0.941881i | \(-0.609056\pi\) | ||||
−0.335947 | + | 0.941881i | \(0.609056\pi\) | |||||||
\(578\) | 4.12223 | 0.171462 | ||||||||
\(579\) | 28.7645 | 1.19541 | ||||||||
\(580\) | 21.9919 | 0.913165 | ||||||||
\(581\) | −10.1864 | −0.422602 | ||||||||
\(582\) | 18.8077 | 0.779603 | ||||||||
\(583\) | −16.9346 | −0.701359 | ||||||||
\(584\) | −5.17680 | −0.214217 | ||||||||
\(585\) | −14.4335 | −0.596751 | ||||||||
\(586\) | 6.33434 | 0.261669 | ||||||||
\(587\) | 27.8662 | 1.15016 | 0.575081 | − | 0.818097i | \(-0.304971\pi\) | ||||
0.575081 | + | 0.818097i | \(0.304971\pi\) | |||||||
\(588\) | −35.8983 | −1.48042 | ||||||||
\(589\) | −3.25258 | −0.134020 | ||||||||
\(590\) | 26.9525 | 1.10962 | ||||||||
\(591\) | −27.1626 | −1.11732 | ||||||||
\(592\) | −2.16036 | −0.0887902 | ||||||||
\(593\) | −39.1529 | −1.60782 | −0.803908 | − | 0.594754i | \(-0.797249\pi\) | ||||
−0.803908 | + | 0.594754i | \(0.797249\pi\) | |||||||
\(594\) | −12.8125 | −0.525702 | ||||||||
\(595\) | 42.4320 | 1.73954 | ||||||||
\(596\) | −12.4180 | −0.508661 | ||||||||
\(597\) | −57.2782 | −2.34424 | ||||||||
\(598\) | −12.6921 | −0.519018 | ||||||||
\(599\) | 9.56015 | 0.390617 | 0.195309 | − | 0.980742i | \(-0.437429\pi\) | ||||
0.195309 | + | 0.980742i | \(0.437429\pi\) | |||||||
\(600\) | 1.86634 | 0.0761932 | ||||||||
\(601\) | 31.3941 | 1.28059 | 0.640295 | − | 0.768129i | \(-0.278812\pi\) | ||||
0.640295 | + | 0.768129i | \(0.278812\pi\) | |||||||
\(602\) | −14.5812 | −0.594284 | ||||||||
\(603\) | 1.75771 | 0.0715796 | ||||||||
\(604\) | 21.1521 | 0.860666 | ||||||||
\(605\) | −15.6150 | −0.634840 | ||||||||
\(606\) | −2.99583 | −0.121697 | ||||||||
\(607\) | 5.95832 | 0.241841 | 0.120920 | − | 0.992662i | \(-0.461415\pi\) | ||||
0.120920 | + | 0.992662i | \(0.461415\pi\) | |||||||
\(608\) | −2.08604 | −0.0845999 | ||||||||
\(609\) | 94.5813 | 3.83263 | ||||||||
\(610\) | −20.7465 | −0.839999 | ||||||||
\(611\) | −26.4172 | −1.06872 | ||||||||
\(612\) | −5.61259 | −0.226875 | ||||||||
\(613\) | −7.81119 | −0.315491 | −0.157746 | − | 0.987480i | \(-0.550423\pi\) | ||||
−0.157746 | + | 0.987480i | \(0.550423\pi\) | |||||||
\(614\) | 6.64633 | 0.268224 | ||||||||
\(615\) | 42.6883 | 1.72136 | ||||||||
\(616\) | −20.3766 | −0.820996 | ||||||||
\(617\) | 4.71909 | 0.189983 | 0.0949916 | − | 0.995478i | \(-0.469718\pi\) | ||||
0.0949916 | + | 0.995478i | \(0.469718\pi\) | |||||||
\(618\) | 37.5700 | 1.51129 | ||||||||
\(619\) | −16.0858 | −0.646543 | −0.323271 | − | 0.946306i | \(-0.604783\pi\) | ||||
−0.323271 | + | 0.946306i | \(0.604783\pi\) | |||||||
\(620\) | 3.77885 | 0.151762 | ||||||||
\(621\) | 10.2254 | 0.410331 | ||||||||
\(622\) | −1.93843 | −0.0777241 | ||||||||
\(623\) | 25.7296 | 1.03083 | ||||||||
\(624\) | −8.13485 | −0.325654 | ||||||||
\(625\) | −28.6049 | −1.14419 | ||||||||
\(626\) | −12.7744 | −0.510569 | ||||||||
\(627\) | −18.6126 | −0.743315 | ||||||||
\(628\) | 17.2057 | 0.686582 | ||||||||
\(629\) | 7.75258 | 0.309115 | ||||||||
\(630\) | 18.4934 | 0.736793 | ||||||||
\(631\) | 17.1134 | 0.681273 | 0.340636 | − | 0.940195i | \(-0.389357\pi\) | ||||
0.340636 | + | 0.940195i | \(0.389357\pi\) | |||||||
\(632\) | −5.93193 | −0.235959 | ||||||||
\(633\) | 23.4694 | 0.932824 | ||||||||
\(634\) | −4.51399 | −0.179273 | ||||||||
\(635\) | 36.0327 | 1.42991 | ||||||||
\(636\) | 8.66239 | 0.343486 | ||||||||
\(637\) | 63.9846 | 2.53516 | ||||||||
\(638\) | 37.8985 | 1.50041 | ||||||||
\(639\) | 4.50380 | 0.178168 | ||||||||
\(640\) | 2.42355 | 0.0957994 | ||||||||
\(641\) | 21.9533 | 0.867102 | 0.433551 | − | 0.901129i | \(-0.357260\pi\) | ||||
0.433551 | + | 0.901129i | \(0.357260\pi\) | |||||||
\(642\) | −4.62857 | −0.182675 | ||||||||
\(643\) | 39.4200 | 1.55457 | 0.777287 | − | 0.629147i | \(-0.216596\pi\) | ||||
0.777287 | + | 0.629147i | \(0.216596\pi\) | |||||||
\(644\) | 16.2622 | 0.640819 | ||||||||
\(645\) | 15.4738 | 0.609282 | ||||||||
\(646\) | 7.48587 | 0.294528 | ||||||||
\(647\) | 25.1145 | 0.987354 | 0.493677 | − | 0.869645i | \(-0.335653\pi\) | ||||
0.493677 | + | 0.869645i | \(0.335653\pi\) | |||||||
\(648\) | 11.2459 | 0.441781 | ||||||||
\(649\) | 46.4470 | 1.82321 | ||||||||
\(650\) | −3.32655 | −0.130478 | ||||||||
\(651\) | 16.2518 | 0.636957 | ||||||||
\(652\) | 1.80306 | 0.0706132 | ||||||||
\(653\) | −28.4238 | −1.11231 | −0.556154 | − | 0.831079i | \(-0.687724\pi\) | ||||
−0.556154 | + | 0.831079i | \(0.687724\pi\) | |||||||
\(654\) | −31.7424 | −1.24123 | ||||||||
\(655\) | 20.6212 | 0.805737 | ||||||||
\(656\) | 8.24485 | 0.321907 | ||||||||
\(657\) | 8.09663 | 0.315879 | ||||||||
\(658\) | 33.8478 | 1.31953 | ||||||||
\(659\) | −27.9099 | −1.08722 | −0.543608 | − | 0.839339i | \(-0.682942\pi\) | ||||
−0.543608 | + | 0.839339i | \(0.682942\pi\) | |||||||
\(660\) | 21.6241 | 0.841715 | ||||||||
\(661\) | −4.83388 | −0.188016 | −0.0940081 | − | 0.995571i | \(-0.529968\pi\) | ||||
−0.0940081 | + | 0.995571i | \(0.529968\pi\) | |||||||
\(662\) | 17.9117 | 0.696158 | ||||||||
\(663\) | 29.1924 | 1.13374 | ||||||||
\(664\) | 2.08785 | 0.0810243 | ||||||||
\(665\) | −24.6658 | −0.956498 | ||||||||
\(666\) | 3.37885 | 0.130928 | ||||||||
\(667\) | −30.2461 | −1.17113 | ||||||||
\(668\) | −0.507845 | −0.0196491 | ||||||||
\(669\) | −58.9756 | −2.28013 | ||||||||
\(670\) | 2.72369 | 0.105225 | ||||||||
\(671\) | −35.7521 | −1.38020 | ||||||||
\(672\) | 10.4230 | 0.402077 | ||||||||
\(673\) | 22.1093 | 0.852253 | 0.426126 | − | 0.904664i | \(-0.359878\pi\) | ||||
0.426126 | + | 0.904664i | \(0.359878\pi\) | |||||||
\(674\) | 25.7627 | 0.992340 | ||||||||
\(675\) | 2.68003 | 0.103154 | ||||||||
\(676\) | 1.49943 | 0.0576704 | ||||||||
\(677\) | 14.1275 | 0.542964 | 0.271482 | − | 0.962444i | \(-0.412486\pi\) | ||||
0.271482 | + | 0.962444i | \(0.412486\pi\) | |||||||
\(678\) | 43.6895 | 1.67789 | ||||||||
\(679\) | 42.9518 | 1.64834 | ||||||||
\(680\) | −8.69707 | −0.333517 | ||||||||
\(681\) | 55.9919 | 2.14561 | ||||||||
\(682\) | 6.51204 | 0.249359 | ||||||||
\(683\) | −5.65598 | −0.216420 | −0.108210 | − | 0.994128i | \(-0.534512\pi\) | ||||
−0.108210 | + | 0.994128i | \(0.534512\pi\) | |||||||
\(684\) | 3.26261 | 0.124749 | ||||||||
\(685\) | −31.9778 | −1.22181 | ||||||||
\(686\) | −47.8302 | −1.82616 | ||||||||
\(687\) | 47.3383 | 1.80607 | ||||||||
\(688\) | 2.98863 | 0.113940 | ||||||||
\(689\) | −15.4397 | −0.588206 | ||||||||
\(690\) | −17.2578 | −0.656992 | ||||||||
\(691\) | 12.8809 | 0.490013 | 0.245006 | − | 0.969521i | \(-0.421210\pi\) | ||||
0.245006 | + | 0.969521i | \(0.421210\pi\) | |||||||
\(692\) | 16.6498 | 0.632932 | ||||||||
\(693\) | 31.8694 | 1.21062 | ||||||||
\(694\) | −9.33419 | −0.354321 | ||||||||
\(695\) | 10.3284 | 0.391778 | ||||||||
\(696\) | −19.3858 | −0.734818 | ||||||||
\(697\) | −29.5871 | −1.12069 | ||||||||
\(698\) | 23.3987 | 0.885653 | ||||||||
\(699\) | −30.8225 | −1.16581 | ||||||||
\(700\) | 4.26225 | 0.161098 | ||||||||
\(701\) | −14.0994 | −0.532529 | −0.266264 | − | 0.963900i | \(-0.585789\pi\) | ||||
−0.266264 | + | 0.963900i | \(0.585789\pi\) | |||||||
\(702\) | −11.6815 | −0.440888 | ||||||||
\(703\) | −4.50659 | −0.169969 | ||||||||
\(704\) | 4.17648 | 0.157407 | ||||||||
\(705\) | −35.9201 | −1.35283 | ||||||||
\(706\) | −16.7459 | −0.630242 | ||||||||
\(707\) | −6.84169 | −0.257308 | ||||||||
\(708\) | −23.7586 | −0.892903 | ||||||||
\(709\) | 19.9917 | 0.750806 | 0.375403 | − | 0.926862i | \(-0.377504\pi\) | ||||
0.375403 | + | 0.926862i | \(0.377504\pi\) | |||||||
\(710\) | 6.97894 | 0.261915 | ||||||||
\(711\) | 9.27766 | 0.347940 | ||||||||
\(712\) | −5.27367 | −0.197639 | ||||||||
\(713\) | −5.19714 | −0.194634 | ||||||||
\(714\) | −37.4037 | −1.39980 | ||||||||
\(715\) | −38.5424 | −1.44140 | ||||||||
\(716\) | −11.9707 | −0.447366 | ||||||||
\(717\) | −15.9647 | −0.596214 | ||||||||
\(718\) | −11.2319 | −0.419170 | ||||||||
\(719\) | −41.5863 | −1.55091 | −0.775454 | − | 0.631404i | \(-0.782479\pi\) | ||||
−0.775454 | + | 0.631404i | \(0.782479\pi\) | |||||||
\(720\) | −3.79049 | −0.141263 | ||||||||
\(721\) | 85.8002 | 3.19536 | ||||||||
\(722\) | 14.6485 | 0.545159 | ||||||||
\(723\) | 12.4156 | 0.461743 | ||||||||
\(724\) | 2.20077 | 0.0817911 | ||||||||
\(725\) | −7.92736 | −0.294415 | ||||||||
\(726\) | 13.7646 | 0.510852 | ||||||||
\(727\) | −1.73876 | −0.0644869 | −0.0322435 | − | 0.999480i | \(-0.510265\pi\) | ||||
−0.0322435 | + | 0.999480i | \(0.510265\pi\) | |||||||
\(728\) | −18.5779 | −0.688542 | ||||||||
\(729\) | 2.07267 | 0.0767656 | ||||||||
\(730\) | 12.5462 | 0.464357 | ||||||||
\(731\) | −10.7249 | −0.396674 | ||||||||
\(732\) | 18.2880 | 0.675942 | ||||||||
\(733\) | −13.9364 | −0.514754 | −0.257377 | − | 0.966311i | \(-0.582858\pi\) | ||||
−0.257377 | + | 0.966311i | \(0.582858\pi\) | |||||||
\(734\) | 36.8380 | 1.35972 | ||||||||
\(735\) | 87.0014 | 3.20910 | ||||||||
\(736\) | −3.33317 | −0.122862 | ||||||||
\(737\) | 4.69371 | 0.172895 | ||||||||
\(738\) | −12.8951 | −0.474676 | ||||||||
\(739\) | −3.48282 | −0.128117 | −0.0640587 | − | 0.997946i | \(-0.520404\pi\) | ||||
−0.0640587 | + | 0.997946i | \(0.520404\pi\) | |||||||
\(740\) | 5.23574 | 0.192470 | ||||||||
\(741\) | −16.9696 | −0.623393 | ||||||||
\(742\) | 19.7826 | 0.726244 | ||||||||
\(743\) | −42.2131 | −1.54865 | −0.774323 | − | 0.632790i | \(-0.781910\pi\) | ||||
−0.774323 | + | 0.632790i | \(0.781910\pi\) | |||||||
\(744\) | −3.33104 | −0.122122 | ||||||||
\(745\) | 30.0957 | 1.10262 | ||||||||
\(746\) | −17.1113 | −0.626490 | ||||||||
\(747\) | −3.26544 | −0.119476 | ||||||||
\(748\) | −14.9876 | −0.548000 | ||||||||
\(749\) | −10.5704 | −0.386236 | ||||||||
\(750\) | 21.3647 | 0.780128 | ||||||||
\(751\) | 1.00000 | 0.0364905 | ||||||||
\(752\) | −6.93762 | −0.252989 | ||||||||
\(753\) | −67.0144 | −2.44214 | ||||||||
\(754\) | 34.5530 | 1.25835 | ||||||||
\(755\) | −51.2632 | −1.86566 | ||||||||
\(756\) | 14.9673 | 0.544354 | ||||||||
\(757\) | 26.0282 | 0.946010 | 0.473005 | − | 0.881060i | \(-0.343169\pi\) | ||||
0.473005 | + | 0.881060i | \(0.343169\pi\) | |||||||
\(758\) | −22.7500 | −0.826315 | ||||||||
\(759\) | −29.7401 | −1.07950 | ||||||||
\(760\) | 5.05562 | 0.183387 | ||||||||
\(761\) | 15.2514 | 0.552864 | 0.276432 | − | 0.961033i | \(-0.410848\pi\) | ||||
0.276432 | + | 0.961033i | \(0.410848\pi\) | |||||||
\(762\) | −31.7628 | −1.15064 | ||||||||
\(763\) | −72.4913 | −2.62436 | ||||||||
\(764\) | −5.90750 | −0.213726 | ||||||||
\(765\) | 13.6024 | 0.491796 | ||||||||
\(766\) | −14.2435 | −0.514637 | ||||||||
\(767\) | 42.3470 | 1.52906 | ||||||||
\(768\) | −2.13636 | −0.0770891 | ||||||||
\(769\) | 8.24274 | 0.297241 | 0.148620 | − | 0.988894i | \(-0.452517\pi\) | ||||
0.148620 | + | 0.988894i | \(0.452517\pi\) | |||||||
\(770\) | 49.3837 | 1.77967 | ||||||||
\(771\) | −3.84358 | −0.138423 | ||||||||
\(772\) | −13.4643 | −0.484589 | ||||||||
\(773\) | 0.616153 | 0.0221615 | 0.0110807 | − | 0.999939i | \(-0.496473\pi\) | ||||
0.0110807 | + | 0.999939i | \(0.496473\pi\) | |||||||
\(774\) | −4.67428 | −0.168013 | ||||||||
\(775\) | −1.36215 | −0.0489298 | ||||||||
\(776\) | −8.80362 | −0.316031 | ||||||||
\(777\) | 22.5175 | 0.807811 | ||||||||
\(778\) | 14.3431 | 0.514226 | ||||||||
\(779\) | 17.1991 | 0.616220 | ||||||||
\(780\) | 19.7152 | 0.705919 | ||||||||
\(781\) | 12.0267 | 0.430350 | ||||||||
\(782\) | 11.9613 | 0.427735 | ||||||||
\(783\) | −27.8376 | −0.994836 | ||||||||
\(784\) | 16.8035 | 0.600125 | ||||||||
\(785\) | −41.6989 | −1.48830 | ||||||||
\(786\) | −18.1775 | −0.648371 | ||||||||
\(787\) | −40.1242 | −1.43027 | −0.715137 | − | 0.698985i | \(-0.753636\pi\) | ||||
−0.715137 | + | 0.698985i | \(0.753636\pi\) | |||||||
\(788\) | 12.7144 | 0.452933 | ||||||||
\(789\) | 31.1142 | 1.10770 | ||||||||
\(790\) | 14.3763 | 0.511487 | ||||||||
\(791\) | 99.7755 | 3.54761 | ||||||||
\(792\) | −6.53211 | −0.232108 | ||||||||
\(793\) | −32.5962 | −1.15752 | ||||||||
\(794\) | 17.1101 | 0.607215 | ||||||||
\(795\) | −20.9938 | −0.744572 | ||||||||
\(796\) | 26.8112 | 0.950296 | ||||||||
\(797\) | 31.9726 | 1.13253 | 0.566263 | − | 0.824225i | \(-0.308389\pi\) | ||||
0.566263 | + | 0.824225i | \(0.308389\pi\) | |||||||
\(798\) | 21.7428 | 0.769688 | ||||||||
\(799\) | 24.8961 | 0.880760 | ||||||||
\(800\) | −0.873611 | −0.0308868 | ||||||||
\(801\) | 8.24813 | 0.291433 | ||||||||
\(802\) | 5.89718 | 0.208237 | ||||||||
\(803\) | 21.6208 | 0.762982 | ||||||||
\(804\) | −2.40093 | −0.0846742 | ||||||||
\(805\) | −39.4122 | −1.38910 | ||||||||
\(806\) | 5.93720 | 0.209129 | ||||||||
\(807\) | −19.7174 | −0.694085 | ||||||||
\(808\) | 1.40231 | 0.0493330 | ||||||||
\(809\) | 7.06495 | 0.248390 | 0.124195 | − | 0.992258i | \(-0.460365\pi\) | ||||
0.124195 | + | 0.992258i | \(0.460365\pi\) | |||||||
\(810\) | −27.2550 | −0.957645 | ||||||||
\(811\) | 28.2760 | 0.992904 | 0.496452 | − | 0.868064i | \(-0.334636\pi\) | ||||
0.496452 | + | 0.868064i | \(0.334636\pi\) | |||||||
\(812\) | −44.2722 | −1.55365 | ||||||||
\(813\) | 46.7840 | 1.64079 | ||||||||
\(814\) | 9.02270 | 0.316245 | ||||||||
\(815\) | −4.36981 | −0.153068 | ||||||||
\(816\) | 7.66645 | 0.268379 | ||||||||
\(817\) | 6.23439 | 0.218114 | ||||||||
\(818\) | −8.66087 | −0.302820 | ||||||||
\(819\) | 29.0562 | 1.01531 | ||||||||
\(820\) | −19.9818 | −0.697796 | ||||||||
\(821\) | 30.3585 | 1.05952 | 0.529760 | − | 0.848148i | \(-0.322282\pi\) | ||||
0.529760 | + | 0.848148i | \(0.322282\pi\) | |||||||
\(822\) | 28.1883 | 0.983181 | ||||||||
\(823\) | −56.4647 | −1.96824 | −0.984118 | − | 0.177513i | \(-0.943195\pi\) | ||||
−0.984118 | + | 0.177513i | \(0.943195\pi\) | |||||||
\(824\) | −17.5860 | −0.612638 | ||||||||
\(825\) | −7.79476 | −0.271379 | ||||||||
\(826\) | −54.2585 | −1.88789 | ||||||||
\(827\) | 41.0454 | 1.42729 | 0.713644 | − | 0.700508i | \(-0.247043\pi\) | ||||
0.713644 | + | 0.700508i | \(0.247043\pi\) | |||||||
\(828\) | 5.21316 | 0.181170 | ||||||||
\(829\) | −29.9069 | −1.03871 | −0.519354 | − | 0.854559i | \(-0.673827\pi\) | ||||
−0.519354 | + | 0.854559i | \(0.673827\pi\) | |||||||
\(830\) | −5.06002 | −0.175636 | ||||||||
\(831\) | −59.7004 | −2.07099 | ||||||||
\(832\) | 3.80781 | 0.132012 | ||||||||
\(833\) | −60.3004 | −2.08929 | ||||||||
\(834\) | −9.10445 | −0.315261 | ||||||||
\(835\) | 1.23079 | 0.0425932 | ||||||||
\(836\) | 8.71230 | 0.301321 | ||||||||
\(837\) | −4.78331 | −0.165335 | ||||||||
\(838\) | 15.7433 | 0.543844 | ||||||||
\(839\) | 43.0763 | 1.48716 | 0.743579 | − | 0.668648i | \(-0.233127\pi\) | ||||
0.743579 | + | 0.668648i | \(0.233127\pi\) | |||||||
\(840\) | −25.2608 | −0.871580 | ||||||||
\(841\) | 53.3420 | 1.83938 | ||||||||
\(842\) | −27.7975 | −0.957964 | ||||||||
\(843\) | −25.1821 | −0.867317 | ||||||||
\(844\) | −10.9857 | −0.378143 | ||||||||
\(845\) | −3.63395 | −0.125012 | ||||||||
\(846\) | 10.8506 | 0.373051 | ||||||||
\(847\) | 31.4347 | 1.08011 | ||||||||
\(848\) | −4.05475 | −0.139241 | ||||||||
\(849\) | −53.0714 | −1.82141 | ||||||||
\(850\) | 3.13501 | 0.107530 | ||||||||
\(851\) | −7.20085 | −0.246842 | ||||||||
\(852\) | −6.15192 | −0.210761 | ||||||||
\(853\) | −43.1557 | −1.47762 | −0.738812 | − | 0.673912i | \(-0.764613\pi\) | ||||
−0.738812 | + | 0.673912i | \(0.764613\pi\) | |||||||
\(854\) | 41.7649 | 1.42917 | ||||||||
\(855\) | −7.90710 | −0.270417 | ||||||||
\(856\) | 2.16657 | 0.0740518 | ||||||||
\(857\) | 46.1759 | 1.57734 | 0.788670 | − | 0.614817i | \(-0.210770\pi\) | ||||
0.788670 | + | 0.614817i | \(0.210770\pi\) | |||||||
\(858\) | 33.9751 | 1.15989 | ||||||||
\(859\) | 9.73190 | 0.332048 | 0.166024 | − | 0.986122i | \(-0.446907\pi\) | ||||
0.166024 | + | 0.986122i | \(0.446907\pi\) | |||||||
\(860\) | −7.24310 | −0.246988 | ||||||||
\(861\) | −85.9364 | −2.92870 | ||||||||
\(862\) | 39.1696 | 1.33412 | ||||||||
\(863\) | 5.84488 | 0.198962 | 0.0994810 | − | 0.995039i | \(-0.468282\pi\) | ||||
0.0994810 | + | 0.995039i | \(0.468282\pi\) | |||||||
\(864\) | −3.06776 | −0.104367 | ||||||||
\(865\) | −40.3518 | −1.37200 | ||||||||
\(866\) | −21.6849 | −0.736883 | ||||||||
\(867\) | 8.80656 | 0.299087 | ||||||||
\(868\) | −7.60724 | −0.258206 | ||||||||
\(869\) | 24.7746 | 0.840420 | ||||||||
\(870\) | 46.9826 | 1.59286 | ||||||||
\(871\) | 4.27938 | 0.145001 | ||||||||
\(872\) | 14.8582 | 0.503161 | ||||||||
\(873\) | 13.7690 | 0.466012 | ||||||||
\(874\) | −6.95312 | −0.235193 | ||||||||
\(875\) | 48.7914 | 1.64945 | ||||||||
\(876\) | −11.0595 | −0.373666 | ||||||||
\(877\) | −42.5042 | −1.43526 | −0.717632 | − | 0.696422i | \(-0.754774\pi\) | ||||
−0.717632 | + | 0.696422i | \(0.754774\pi\) | |||||||
\(878\) | 13.8473 | 0.467323 | ||||||||
\(879\) | 13.5324 | 0.456437 | ||||||||
\(880\) | −10.1219 | −0.341210 | ||||||||
\(881\) | −33.2111 | −1.11891 | −0.559456 | − | 0.828860i | \(-0.688990\pi\) | ||||
−0.559456 | + | 0.828860i | \(0.688990\pi\) | |||||||
\(882\) | −26.2811 | −0.884929 | ||||||||
\(883\) | −29.9671 | −1.00847 | −0.504236 | − | 0.863566i | \(-0.668226\pi\) | ||||
−0.504236 | + | 0.863566i | \(0.668226\pi\) | |||||||
\(884\) | −13.6646 | −0.459589 | ||||||||
\(885\) | 57.5803 | 1.93554 | ||||||||
\(886\) | −30.0846 | −1.01071 | ||||||||
\(887\) | −32.1452 | −1.07933 | −0.539665 | − | 0.841880i | \(-0.681449\pi\) | ||||
−0.539665 | + | 0.841880i | \(0.681449\pi\) | |||||||
\(888\) | −4.61530 | −0.154879 | ||||||||
\(889\) | −72.5379 | −2.43284 | ||||||||
\(890\) | 12.7810 | 0.428420 | ||||||||
\(891\) | −46.9683 | −1.57350 | ||||||||
\(892\) | 27.6057 | 0.924307 | ||||||||
\(893\) | −14.4721 | −0.484291 | ||||||||
\(894\) | −26.5293 | −0.887271 | ||||||||
\(895\) | 29.0116 | 0.969752 | ||||||||
\(896\) | −4.87888 | −0.162992 | ||||||||
\(897\) | −27.1149 | −0.905339 | ||||||||
\(898\) | −34.8294 | −1.16227 | ||||||||
\(899\) | 14.1487 | 0.471886 | ||||||||
\(900\) | 1.36635 | 0.0455449 | ||||||||
\(901\) | 14.5507 | 0.484754 | ||||||||
\(902\) | −34.4345 | −1.14654 | ||||||||
\(903\) | −31.1506 | −1.03663 | ||||||||
\(904\) | −20.4505 | −0.680173 | ||||||||
\(905\) | −5.33369 | −0.177298 | ||||||||
\(906\) | 45.1884 | 1.50128 | ||||||||
\(907\) | 57.2241 | 1.90010 | 0.950048 | − | 0.312105i | \(-0.101034\pi\) | ||||
0.950048 | + | 0.312105i | \(0.101034\pi\) | |||||||
\(908\) | −26.2090 | −0.869777 | ||||||||
\(909\) | −2.19324 | −0.0727451 | ||||||||
\(910\) | 45.0245 | 1.49255 | ||||||||
\(911\) | −49.9403 | −1.65460 | −0.827299 | − | 0.561762i | \(-0.810124\pi\) | ||||
−0.827299 | + | 0.561762i | \(0.810124\pi\) | |||||||
\(912\) | −4.45652 | −0.147570 | ||||||||
\(913\) | −8.71987 | −0.288586 | ||||||||
\(914\) | −0.0780659 | −0.00258219 | ||||||||
\(915\) | −44.3218 | −1.46523 | ||||||||
\(916\) | −22.1584 | −0.732135 | ||||||||
\(917\) | −41.5128 | −1.37087 | ||||||||
\(918\) | 11.0089 | 0.363346 | ||||||||
\(919\) | −31.4234 | −1.03656 | −0.518282 | − | 0.855210i | \(-0.673428\pi\) | ||||
−0.518282 | + | 0.855210i | \(0.673428\pi\) | |||||||
\(920\) | 8.07812 | 0.266328 | ||||||||
\(921\) | 14.1989 | 0.467871 | ||||||||
\(922\) | −20.0398 | −0.659975 | ||||||||
\(923\) | 10.9651 | 0.360920 | ||||||||
\(924\) | −43.5316 | −1.43209 | ||||||||
\(925\) | −1.88731 | −0.0620544 | ||||||||
\(926\) | −23.2743 | −0.764840 | ||||||||
\(927\) | 27.5049 | 0.903380 | ||||||||
\(928\) | 9.07425 | 0.297877 | ||||||||
\(929\) | −31.7034 | −1.04015 | −0.520077 | − | 0.854119i | \(-0.674097\pi\) | ||||
−0.520077 | + | 0.854119i | \(0.674097\pi\) | |||||||
\(930\) | 8.07296 | 0.264723 | ||||||||
\(931\) | 35.0527 | 1.14881 | ||||||||
\(932\) | 14.4276 | 0.472591 | ||||||||
\(933\) | −4.14118 | −0.135576 | ||||||||
\(934\) | −2.21624 | −0.0725175 | ||||||||
\(935\) | 36.3232 | 1.18789 | ||||||||
\(936\) | −5.95550 | −0.194662 | ||||||||
\(937\) | −35.4887 | −1.15937 | −0.579683 | − | 0.814842i | \(-0.696823\pi\) | ||||
−0.579683 | + | 0.814842i | \(0.696823\pi\) | |||||||
\(938\) | −5.48309 | −0.179029 | ||||||||
\(939\) | −27.2908 | −0.890600 | ||||||||
\(940\) | 16.8137 | 0.548402 | ||||||||
\(941\) | −12.6223 | −0.411474 | −0.205737 | − | 0.978607i | \(-0.565959\pi\) | ||||
−0.205737 | + | 0.978607i | \(0.565959\pi\) | |||||||
\(942\) | 36.7575 | 1.19762 | ||||||||
\(943\) | 27.4815 | 0.894921 | ||||||||
\(944\) | 11.1211 | 0.361961 | ||||||||
\(945\) | −36.2739 | −1.17999 | ||||||||
\(946\) | −12.4820 | −0.405823 | ||||||||
\(947\) | −53.0576 | −1.72414 | −0.862070 | − | 0.506789i | \(-0.830832\pi\) | ||||
−0.862070 | + | 0.506789i | \(0.830832\pi\) | |||||||
\(948\) | −12.6727 | −0.411591 | ||||||||
\(949\) | 19.7123 | 0.639887 | ||||||||
\(950\) | −1.82238 | −0.0591259 | ||||||||
\(951\) | −9.64349 | −0.312712 | ||||||||
\(952\) | 17.5082 | 0.567443 | ||||||||
\(953\) | −9.79368 | −0.317248 | −0.158624 | − | 0.987339i | \(-0.550706\pi\) | ||||
−0.158624 | + | 0.987339i | \(0.550706\pi\) | |||||||
\(954\) | 6.34171 | 0.205321 | ||||||||
\(955\) | 14.3171 | 0.463292 | ||||||||
\(956\) | 7.47287 | 0.241690 | ||||||||
\(957\) | 80.9647 | 2.61722 | ||||||||
\(958\) | −7.59253 | −0.245304 | ||||||||
\(959\) | 64.3748 | 2.07877 | ||||||||
\(960\) | 5.17758 | 0.167106 | ||||||||
\(961\) | −28.5688 | −0.921576 | ||||||||
\(962\) | 8.22624 | 0.265225 | ||||||||
\(963\) | −3.38856 | −0.109195 | ||||||||
\(964\) | −5.81160 | −0.187179 | ||||||||
\(965\) | 32.6313 | 1.05044 | ||||||||
\(966\) | 34.7418 | 1.11780 | ||||||||
\(967\) | −16.6778 | −0.536321 | −0.268161 | − | 0.963374i | \(-0.586416\pi\) | ||||
−0.268161 | + | 0.963374i | \(0.586416\pi\) | |||||||
\(968\) | −6.44301 | −0.207086 | ||||||||
\(969\) | 15.9925 | 0.513753 | ||||||||
\(970\) | 21.3360 | 0.685059 | ||||||||
\(971\) | 0.0825230 | 0.00264829 | 0.00132414 | − | 0.999999i | \(-0.499579\pi\) | ||||
0.00132414 | + | 0.999999i | \(0.499579\pi\) | |||||||
\(972\) | 14.8220 | 0.475415 | ||||||||
\(973\) | −20.7922 | −0.666567 | ||||||||
\(974\) | −6.15247 | −0.197138 | ||||||||
\(975\) | −7.10669 | −0.227596 | ||||||||
\(976\) | −8.56035 | −0.274010 | ||||||||
\(977\) | −26.7169 | −0.854750 | −0.427375 | − | 0.904075i | \(-0.640562\pi\) | ||||
−0.427375 | + | 0.904075i | \(0.640562\pi\) | |||||||
\(978\) | 3.85197 | 0.123173 | ||||||||
\(979\) | 22.0254 | 0.703934 | ||||||||
\(980\) | −40.7242 | −1.30089 | ||||||||
\(981\) | −23.2385 | −0.741949 | ||||||||
\(982\) | 37.0886 | 1.18354 | ||||||||
\(983\) | 14.2752 | 0.455307 | 0.227653 | − | 0.973742i | \(-0.426895\pi\) | ||||
0.227653 | + | 0.973742i | \(0.426895\pi\) | |||||||
\(984\) | 17.6139 | 0.561512 | ||||||||
\(985\) | −30.8141 | −0.981820 | ||||||||
\(986\) | −32.5635 | −1.03703 | ||||||||
\(987\) | 72.3111 | 2.30169 | ||||||||
\(988\) | 7.94323 | 0.252708 | ||||||||
\(989\) | 9.96161 | 0.316761 | ||||||||
\(990\) | 15.8309 | 0.503140 | ||||||||
\(991\) | 42.8136 | 1.36002 | 0.680009 | − | 0.733203i | \(-0.261976\pi\) | ||||
0.680009 | + | 0.733203i | \(0.261976\pi\) | |||||||
\(992\) | 1.55922 | 0.0495052 | ||||||||
\(993\) | 38.2658 | 1.21433 | ||||||||
\(994\) | −14.0494 | −0.445619 | ||||||||
\(995\) | −64.9783 | −2.05995 | ||||||||
\(996\) | 4.46039 | 0.141333 | ||||||||
\(997\) | 5.28690 | 0.167438 | 0.0837189 | − | 0.996489i | \(-0.473320\pi\) | ||||
0.0837189 | + | 0.996489i | \(0.473320\pi\) | |||||||
\(998\) | 33.3384 | 1.05531 | ||||||||
\(999\) | −6.62746 | −0.209684 |
(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 | 1502.2.a.h.1.3 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1502.2.a.h.1.3 | ✓ | 19 | 1.1 | even | 1 | trivial |