Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(8.34436701122\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.36497.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 3x^{3} + 5x^{2} + x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.33419\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.584664 | −0.413420 | −0.206710 | − | 0.978402i | \(-0.566276\pi\) | ||||
−0.206710 | + | 0.978402i | \(0.566276\pi\) | |||||||
\(3\) | 0.334185 | 0.192942 | 0.0964709 | − | 0.995336i | \(-0.469245\pi\) | ||||
0.0964709 | + | 0.995336i | \(0.469245\pi\) | |||||||
\(4\) | −1.65817 | −0.829084 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −0.195386 | −0.0797660 | ||||||||
\(7\) | 1.85355 | 0.700578 | 0.350289 | − | 0.936642i | \(-0.386083\pi\) | ||||
0.350289 | + | 0.936642i | \(0.386083\pi\) | |||||||
\(8\) | 2.13880 | 0.756180 | ||||||||
\(9\) | −2.88832 | −0.962773 | ||||||||
\(10\) | 0.584664 | 0.184887 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | −0.554135 | −0.159965 | ||||||||
\(13\) | 2.56681 | 0.711906 | 0.355953 | − | 0.934504i | \(-0.384156\pi\) | ||||
0.355953 | + | 0.934504i | \(0.384156\pi\) | |||||||
\(14\) | −1.08371 | −0.289633 | ||||||||
\(15\) | −0.334185 | −0.0862862 | ||||||||
\(16\) | 2.06586 | 0.516464 | ||||||||
\(17\) | −7.56490 | −1.83476 | −0.917379 | − | 0.398015i | \(-0.869699\pi\) | ||||
−0.917379 | + | 0.398015i | \(0.869699\pi\) | |||||||
\(18\) | 1.68870 | 0.398030 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.65817 | 0.370778 | ||||||||
\(21\) | 0.619430 | 0.135171 | ||||||||
\(22\) | −0.584664 | −0.124651 | ||||||||
\(23\) | −1.73764 | −0.362322 | −0.181161 | − | 0.983453i | \(-0.557986\pi\) | ||||
−0.181161 | + | 0.983453i | \(0.557986\pi\) | |||||||
\(24\) | 0.714755 | 0.145899 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.50072 | −0.294316 | ||||||||
\(27\) | −1.96779 | −0.378701 | ||||||||
\(28\) | −3.07350 | −0.580838 | ||||||||
\(29\) | 9.32369 | 1.73137 | 0.865683 | − | 0.500593i | \(-0.166885\pi\) | ||||
0.865683 | + | 0.500593i | \(0.166885\pi\) | |||||||
\(30\) | 0.195386 | 0.0356724 | ||||||||
\(31\) | −4.31802 | −0.775539 | −0.387769 | − | 0.921756i | \(-0.626754\pi\) | ||||
−0.387769 | + | 0.921756i | \(0.626754\pi\) | |||||||
\(32\) | −5.48543 | −0.969696 | ||||||||
\(33\) | 0.334185 | 0.0581742 | ||||||||
\(34\) | 4.42292 | 0.758525 | ||||||||
\(35\) | −1.85355 | −0.313308 | ||||||||
\(36\) | 4.78932 | 0.798220 | ||||||||
\(37\) | −8.96941 | −1.47456 | −0.737281 | − | 0.675586i | \(-0.763891\pi\) | ||||
−0.737281 | + | 0.675586i | \(0.763891\pi\) | |||||||
\(38\) | −0.584664 | −0.0948450 | ||||||||
\(39\) | 0.857791 | 0.137357 | ||||||||
\(40\) | −2.13880 | −0.338174 | ||||||||
\(41\) | −10.6138 | −1.65760 | −0.828802 | − | 0.559543i | \(-0.810977\pi\) | ||||
−0.828802 | + | 0.559543i | \(0.810977\pi\) | |||||||
\(42\) | −0.362159 | −0.0558823 | ||||||||
\(43\) | 11.5068 | 1.75477 | 0.877387 | − | 0.479784i | \(-0.159285\pi\) | ||||
0.877387 | + | 0.479784i | \(0.159285\pi\) | |||||||
\(44\) | −1.65817 | −0.249978 | ||||||||
\(45\) | 2.88832 | 0.430565 | ||||||||
\(46\) | 1.01593 | 0.149791 | ||||||||
\(47\) | −6.50003 | −0.948126 | −0.474063 | − | 0.880491i | \(-0.657213\pi\) | ||||
−0.474063 | + | 0.880491i | \(0.657213\pi\) | |||||||
\(48\) | 0.690379 | 0.0996476 | ||||||||
\(49\) | −3.56434 | −0.509191 | ||||||||
\(50\) | −0.584664 | −0.0826840 | ||||||||
\(51\) | −2.52808 | −0.354002 | ||||||||
\(52\) | −4.25621 | −0.590230 | ||||||||
\(53\) | −8.73423 | −1.19974 | −0.599869 | − | 0.800098i | \(-0.704781\pi\) | ||||
−0.599869 | + | 0.800098i | \(0.704781\pi\) | |||||||
\(54\) | 1.15050 | 0.156563 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.96438 | 0.529763 | ||||||||
\(57\) | 0.334185 | 0.0442639 | ||||||||
\(58\) | −5.45123 | −0.715781 | ||||||||
\(59\) | −3.97991 | −0.518140 | −0.259070 | − | 0.965859i | \(-0.583416\pi\) | ||||
−0.259070 | + | 0.965859i | \(0.583416\pi\) | |||||||
\(60\) | 0.554135 | 0.0715385 | ||||||||
\(61\) | 0.649027 | 0.0830994 | 0.0415497 | − | 0.999136i | \(-0.486771\pi\) | ||||
0.0415497 | + | 0.999136i | \(0.486771\pi\) | |||||||
\(62\) | 2.52459 | 0.320623 | ||||||||
\(63\) | −5.35366 | −0.674497 | ||||||||
\(64\) | −0.924581 | −0.115573 | ||||||||
\(65\) | −2.56681 | −0.318374 | ||||||||
\(66\) | −0.195386 | −0.0240504 | ||||||||
\(67\) | −0.319933 | −0.0390861 | −0.0195430 | − | 0.999809i | \(-0.506221\pi\) | ||||
−0.0195430 | + | 0.999809i | \(0.506221\pi\) | |||||||
\(68\) | 12.5439 | 1.52117 | ||||||||
\(69\) | −0.580692 | −0.0699072 | ||||||||
\(70\) | 1.08371 | 0.129528 | ||||||||
\(71\) | −9.93130 | −1.17863 | −0.589314 | − | 0.807904i | \(-0.700602\pi\) | ||||
−0.589314 | + | 0.807904i | \(0.700602\pi\) | |||||||
\(72\) | −6.17754 | −0.728030 | ||||||||
\(73\) | −15.3646 | −1.79829 | −0.899146 | − | 0.437649i | \(-0.855811\pi\) | ||||
−0.899146 | + | 0.437649i | \(0.855811\pi\) | |||||||
\(74\) | 5.24409 | 0.609613 | ||||||||
\(75\) | 0.334185 | 0.0385884 | ||||||||
\(76\) | −1.65817 | −0.190205 | ||||||||
\(77\) | 1.85355 | 0.211232 | ||||||||
\(78\) | −0.501520 | −0.0567859 | ||||||||
\(79\) | −10.2604 | −1.15438 | −0.577192 | − | 0.816608i | \(-0.695852\pi\) | ||||
−0.577192 | + | 0.816608i | \(0.695852\pi\) | |||||||
\(80\) | −2.06586 | −0.230970 | ||||||||
\(81\) | 8.00735 | 0.889706 | ||||||||
\(82\) | 6.20553 | 0.685286 | ||||||||
\(83\) | 10.7036 | 1.17488 | 0.587439 | − | 0.809269i | \(-0.300136\pi\) | ||||
0.587439 | + | 0.809269i | \(0.300136\pi\) | |||||||
\(84\) | −1.02712 | −0.112068 | ||||||||
\(85\) | 7.56490 | 0.820529 | ||||||||
\(86\) | −6.72762 | −0.725458 | ||||||||
\(87\) | 3.11584 | 0.334053 | ||||||||
\(88\) | 2.13880 | 0.227997 | ||||||||
\(89\) | −13.3892 | −1.41925 | −0.709627 | − | 0.704577i | \(-0.751137\pi\) | ||||
−0.709627 | + | 0.704577i | \(0.751137\pi\) | |||||||
\(90\) | −1.68870 | −0.178004 | ||||||||
\(91\) | 4.75773 | 0.498746 | ||||||||
\(92\) | 2.88129 | 0.300396 | ||||||||
\(93\) | −1.44302 | −0.149634 | ||||||||
\(94\) | 3.80033 | 0.391974 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | −1.83315 | −0.187095 | ||||||||
\(97\) | −3.79273 | −0.385093 | −0.192547 | − | 0.981288i | \(-0.561675\pi\) | ||||
−0.192547 | + | 0.981288i | \(0.561675\pi\) | |||||||
\(98\) | 2.08394 | 0.210510 | ||||||||
\(99\) | −2.88832 | −0.290287 | ||||||||
\(100\) | −1.65817 | −0.165817 | ||||||||
\(101\) | −11.8733 | −1.18143 | −0.590717 | − | 0.806879i | \(-0.701155\pi\) | ||||
−0.590717 | + | 0.806879i | \(0.701155\pi\) | |||||||
\(102\) | 1.47808 | 0.146351 | ||||||||
\(103\) | 2.36415 | 0.232947 | 0.116473 | − | 0.993194i | \(-0.462841\pi\) | ||||
0.116473 | + | 0.993194i | \(0.462841\pi\) | |||||||
\(104\) | 5.48990 | 0.538329 | ||||||||
\(105\) | −0.619430 | −0.0604502 | ||||||||
\(106\) | 5.10659 | 0.495996 | ||||||||
\(107\) | 18.8479 | 1.82209 | 0.911046 | − | 0.412305i | \(-0.135276\pi\) | ||||
0.911046 | + | 0.412305i | \(0.135276\pi\) | |||||||
\(108\) | 3.26293 | 0.313975 | ||||||||
\(109\) | 4.97557 | 0.476573 | 0.238286 | − | 0.971195i | \(-0.423414\pi\) | ||||
0.238286 | + | 0.971195i | \(0.423414\pi\) | |||||||
\(110\) | 0.584664 | 0.0557455 | ||||||||
\(111\) | −2.99744 | −0.284505 | ||||||||
\(112\) | 3.82918 | 0.361823 | ||||||||
\(113\) | 6.56929 | 0.617987 | 0.308994 | − | 0.951064i | \(-0.400008\pi\) | ||||
0.308994 | + | 0.951064i | \(0.400008\pi\) | |||||||
\(114\) | −0.195386 | −0.0182996 | ||||||||
\(115\) | 1.73764 | 0.162035 | ||||||||
\(116\) | −15.4602 | −1.43545 | ||||||||
\(117\) | −7.41378 | −0.685405 | ||||||||
\(118\) | 2.32691 | 0.214209 | ||||||||
\(119\) | −14.0220 | −1.28539 | ||||||||
\(120\) | −0.714755 | −0.0652479 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −0.379463 | −0.0343549 | ||||||||
\(123\) | −3.54699 | −0.319821 | ||||||||
\(124\) | 7.16000 | 0.642987 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.13009 | 0.278851 | ||||||||
\(127\) | 1.09135 | 0.0968419 | 0.0484210 | − | 0.998827i | \(-0.484581\pi\) | ||||
0.0484210 | + | 0.998827i | \(0.484581\pi\) | |||||||
\(128\) | 11.5114 | 1.01748 | ||||||||
\(129\) | 3.84541 | 0.338569 | ||||||||
\(130\) | 1.50072 | 0.131622 | ||||||||
\(131\) | −0.274169 | −0.0239543 | −0.0119771 | − | 0.999928i | \(-0.503813\pi\) | ||||
−0.0119771 | + | 0.999928i | \(0.503813\pi\) | |||||||
\(132\) | −0.554135 | −0.0482313 | ||||||||
\(133\) | 1.85355 | 0.160724 | ||||||||
\(134\) | 0.187053 | 0.0161590 | ||||||||
\(135\) | 1.96779 | 0.169360 | ||||||||
\(136\) | −16.1798 | −1.38741 | ||||||||
\(137\) | 12.3503 | 1.05516 | 0.527579 | − | 0.849506i | \(-0.323100\pi\) | ||||
0.527579 | + | 0.849506i | \(0.323100\pi\) | |||||||
\(138\) | 0.339510 | 0.0289010 | ||||||||
\(139\) | 1.44278 | 0.122375 | 0.0611877 | − | 0.998126i | \(-0.480511\pi\) | ||||
0.0611877 | + | 0.998126i | \(0.480511\pi\) | |||||||
\(140\) | 3.07350 | 0.259758 | ||||||||
\(141\) | −2.17221 | −0.182933 | ||||||||
\(142\) | 5.80647 | 0.487268 | ||||||||
\(143\) | 2.56681 | 0.214648 | ||||||||
\(144\) | −5.96686 | −0.497238 | ||||||||
\(145\) | −9.32369 | −0.774290 | ||||||||
\(146\) | 8.98313 | 0.743449 | ||||||||
\(147\) | −1.19115 | −0.0982443 | ||||||||
\(148\) | 14.8728 | 1.22254 | ||||||||
\(149\) | −15.3857 | −1.26044 | −0.630222 | − | 0.776415i | \(-0.717036\pi\) | ||||
−0.630222 | + | 0.776415i | \(0.717036\pi\) | |||||||
\(150\) | −0.195386 | −0.0159532 | ||||||||
\(151\) | 13.9513 | 1.13534 | 0.567668 | − | 0.823257i | \(-0.307846\pi\) | ||||
0.567668 | + | 0.823257i | \(0.307846\pi\) | |||||||
\(152\) | 2.13880 | 0.173480 | ||||||||
\(153\) | 21.8499 | 1.76646 | ||||||||
\(154\) | −1.08371 | −0.0873275 | ||||||||
\(155\) | 4.31802 | 0.346832 | ||||||||
\(156\) | −1.42236 | −0.113880 | ||||||||
\(157\) | −1.01905 | −0.0813291 | −0.0406646 | − | 0.999173i | \(-0.512948\pi\) | ||||
−0.0406646 | + | 0.999173i | \(0.512948\pi\) | |||||||
\(158\) | 5.99888 | 0.477245 | ||||||||
\(159\) | −2.91885 | −0.231480 | ||||||||
\(160\) | 5.48543 | 0.433661 | ||||||||
\(161\) | −3.22080 | −0.253835 | ||||||||
\(162\) | −4.68161 | −0.367822 | ||||||||
\(163\) | 7.17421 | 0.561927 | 0.280964 | − | 0.959718i | \(-0.409346\pi\) | ||||
0.280964 | + | 0.959718i | \(0.409346\pi\) | |||||||
\(164\) | 17.5995 | 1.37429 | ||||||||
\(165\) | −0.334185 | −0.0260163 | ||||||||
\(166\) | −6.25803 | −0.485718 | ||||||||
\(167\) | −12.7807 | −0.989003 | −0.494502 | − | 0.869177i | \(-0.664649\pi\) | ||||
−0.494502 | + | 0.869177i | \(0.664649\pi\) | |||||||
\(168\) | 1.32484 | 0.102213 | ||||||||
\(169\) | −6.41146 | −0.493189 | ||||||||
\(170\) | −4.42292 | −0.339223 | ||||||||
\(171\) | −2.88832 | −0.220875 | ||||||||
\(172\) | −19.0802 | −1.45485 | ||||||||
\(173\) | −9.26126 | −0.704121 | −0.352060 | − | 0.935977i | \(-0.614519\pi\) | ||||
−0.352060 | + | 0.935977i | \(0.614519\pi\) | |||||||
\(174\) | −1.82172 | −0.138104 | ||||||||
\(175\) | 1.85355 | 0.140116 | ||||||||
\(176\) | 2.06586 | 0.155720 | ||||||||
\(177\) | −1.33003 | −0.0999709 | ||||||||
\(178\) | 7.82819 | 0.586748 | ||||||||
\(179\) | 1.36521 | 0.102041 | 0.0510204 | − | 0.998698i | \(-0.483753\pi\) | ||||
0.0510204 | + | 0.998698i | \(0.483753\pi\) | |||||||
\(180\) | −4.78932 | −0.356975 | ||||||||
\(181\) | 11.9402 | 0.887511 | 0.443755 | − | 0.896148i | \(-0.353646\pi\) | ||||
0.443755 | + | 0.896148i | \(0.353646\pi\) | |||||||
\(182\) | −2.78167 | −0.206191 | ||||||||
\(183\) | 0.216895 | 0.0160334 | ||||||||
\(184\) | −3.71646 | −0.273981 | ||||||||
\(185\) | 8.96941 | 0.659444 | ||||||||
\(186\) | 0.843680 | 0.0618616 | ||||||||
\(187\) | −7.56490 | −0.553200 | ||||||||
\(188\) | 10.7781 | 0.786076 | ||||||||
\(189\) | −3.64740 | −0.265310 | ||||||||
\(190\) | 0.584664 | 0.0424160 | ||||||||
\(191\) | 19.9632 | 1.44449 | 0.722243 | − | 0.691639i | \(-0.243111\pi\) | ||||
0.722243 | + | 0.691639i | \(0.243111\pi\) | |||||||
\(192\) | −0.308981 | −0.0222988 | ||||||||
\(193\) | 4.55437 | 0.327831 | 0.163915 | − | 0.986474i | \(-0.447588\pi\) | ||||
0.163915 | + | 0.986474i | \(0.447588\pi\) | |||||||
\(194\) | 2.21747 | 0.159205 | ||||||||
\(195\) | −0.857791 | −0.0614277 | ||||||||
\(196\) | 5.91027 | 0.422162 | ||||||||
\(197\) | 4.46917 | 0.318415 | 0.159208 | − | 0.987245i | \(-0.449106\pi\) | ||||
0.159208 | + | 0.987245i | \(0.449106\pi\) | |||||||
\(198\) | 1.68870 | 0.120010 | ||||||||
\(199\) | −13.4574 | −0.953968 | −0.476984 | − | 0.878912i | \(-0.658270\pi\) | ||||
−0.476984 | + | 0.878912i | \(0.658270\pi\) | |||||||
\(200\) | 2.13880 | 0.151236 | ||||||||
\(201\) | −0.106917 | −0.00754134 | ||||||||
\(202\) | 6.94187 | 0.488428 | ||||||||
\(203\) | 17.2820 | 1.21296 | ||||||||
\(204\) | 4.19198 | 0.293497 | ||||||||
\(205\) | 10.6138 | 0.741303 | ||||||||
\(206\) | −1.38223 | −0.0963048 | ||||||||
\(207\) | 5.01885 | 0.348834 | ||||||||
\(208\) | 5.30267 | 0.367674 | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0.362159 | 0.0249913 | ||||||||
\(211\) | −7.21902 | −0.496978 | −0.248489 | − | 0.968635i | \(-0.579934\pi\) | ||||
−0.248489 | + | 0.968635i | \(0.579934\pi\) | |||||||
\(212\) | 14.4828 | 0.994684 | ||||||||
\(213\) | −3.31889 | −0.227407 | ||||||||
\(214\) | −11.0197 | −0.753289 | ||||||||
\(215\) | −11.5068 | −0.784759 | ||||||||
\(216\) | −4.20871 | −0.286366 | ||||||||
\(217\) | −8.00368 | −0.543325 | ||||||||
\(218\) | −2.90903 | −0.197025 | ||||||||
\(219\) | −5.13462 | −0.346966 | ||||||||
\(220\) | 1.65817 | 0.111794 | ||||||||
\(221\) | −19.4177 | −1.30618 | ||||||||
\(222\) | 1.75250 | 0.117620 | ||||||||
\(223\) | 0.918786 | 0.0615265 | 0.0307632 | − | 0.999527i | \(-0.490206\pi\) | ||||
0.0307632 | + | 0.999527i | \(0.490206\pi\) | |||||||
\(224\) | −10.1675 | −0.679347 | ||||||||
\(225\) | −2.88832 | −0.192555 | ||||||||
\(226\) | −3.84083 | −0.255488 | ||||||||
\(227\) | −18.9477 | −1.25760 | −0.628800 | − | 0.777567i | \(-0.716454\pi\) | ||||
−0.628800 | + | 0.777567i | \(0.716454\pi\) | |||||||
\(228\) | −0.554135 | −0.0366985 | ||||||||
\(229\) | −8.46391 | −0.559311 | −0.279655 | − | 0.960100i | \(-0.590220\pi\) | ||||
−0.279655 | + | 0.960100i | \(0.590220\pi\) | |||||||
\(230\) | −1.01593 | −0.0669887 | ||||||||
\(231\) | 0.619430 | 0.0407555 | ||||||||
\(232\) | 19.9415 | 1.30922 | ||||||||
\(233\) | −10.8413 | −0.710238 | −0.355119 | − | 0.934821i | \(-0.615560\pi\) | ||||
−0.355119 | + | 0.934821i | \(0.615560\pi\) | |||||||
\(234\) | 4.33457 | 0.283360 | ||||||||
\(235\) | 6.50003 | 0.424015 | ||||||||
\(236\) | 6.59935 | 0.429581 | ||||||||
\(237\) | −3.42887 | −0.222729 | ||||||||
\(238\) | 8.19813 | 0.531406 | ||||||||
\(239\) | 3.48915 | 0.225694 | 0.112847 | − | 0.993612i | \(-0.464003\pi\) | ||||
0.112847 | + | 0.993612i | \(0.464003\pi\) | |||||||
\(240\) | −0.690379 | −0.0445638 | ||||||||
\(241\) | 12.3218 | 0.793718 | 0.396859 | − | 0.917880i | \(-0.370100\pi\) | ||||
0.396859 | + | 0.917880i | \(0.370100\pi\) | |||||||
\(242\) | −0.584664 | −0.0375836 | ||||||||
\(243\) | 8.57931 | 0.550363 | ||||||||
\(244\) | −1.07620 | −0.0688964 | ||||||||
\(245\) | 3.56434 | 0.227717 | ||||||||
\(246\) | 2.07380 | 0.132220 | ||||||||
\(247\) | 2.56681 | 0.163323 | ||||||||
\(248\) | −9.23537 | −0.586447 | ||||||||
\(249\) | 3.57700 | 0.226683 | ||||||||
\(250\) | 0.584664 | 0.0369774 | ||||||||
\(251\) | −18.0493 | −1.13926 | −0.569630 | − | 0.821901i | \(-0.692913\pi\) | ||||
−0.569630 | + | 0.821901i | \(0.692913\pi\) | |||||||
\(252\) | 8.87726 | 0.559215 | ||||||||
\(253\) | −1.73764 | −0.109244 | ||||||||
\(254\) | −0.638075 | −0.0400364 | ||||||||
\(255\) | 2.52808 | 0.158314 | ||||||||
\(256\) | −4.88116 | −0.305072 | ||||||||
\(257\) | 12.2032 | 0.761215 | 0.380608 | − | 0.924737i | \(-0.375715\pi\) | ||||
0.380608 | + | 0.924737i | \(0.375715\pi\) | |||||||
\(258\) | −2.24827 | −0.139971 | ||||||||
\(259\) | −16.6253 | −1.03305 | ||||||||
\(260\) | 4.25621 | 0.263959 | ||||||||
\(261\) | −26.9298 | −1.66691 | ||||||||
\(262\) | 0.160297 | 0.00990318 | ||||||||
\(263\) | −14.3679 | −0.885964 | −0.442982 | − | 0.896531i | \(-0.646079\pi\) | ||||
−0.442982 | + | 0.896531i | \(0.646079\pi\) | |||||||
\(264\) | 0.714755 | 0.0439901 | ||||||||
\(265\) | 8.73423 | 0.536539 | ||||||||
\(266\) | −1.08371 | −0.0664463 | ||||||||
\(267\) | −4.47448 | −0.273834 | ||||||||
\(268\) | 0.530503 | 0.0324056 | ||||||||
\(269\) | 26.3664 | 1.60759 | 0.803793 | − | 0.594910i | \(-0.202812\pi\) | ||||
0.803793 | + | 0.594910i | \(0.202812\pi\) | |||||||
\(270\) | −1.15050 | −0.0700169 | ||||||||
\(271\) | 14.5399 | 0.883233 | 0.441617 | − | 0.897204i | \(-0.354405\pi\) | ||||
0.441617 | + | 0.897204i | \(0.354405\pi\) | |||||||
\(272\) | −15.6280 | −0.947587 | ||||||||
\(273\) | 1.58996 | 0.0962289 | ||||||||
\(274\) | −7.22078 | −0.436223 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | 0.962886 | 0.0579589 | ||||||||
\(277\) | 18.6181 | 1.11866 | 0.559328 | − | 0.828947i | \(-0.311059\pi\) | ||||
0.559328 | + | 0.828947i | \(0.311059\pi\) | |||||||
\(278\) | −0.843544 | −0.0505924 | ||||||||
\(279\) | 12.4718 | 0.746668 | ||||||||
\(280\) | −3.96438 | −0.236917 | ||||||||
\(281\) | −21.3535 | −1.27385 | −0.636923 | − | 0.770928i | \(-0.719793\pi\) | ||||
−0.636923 | + | 0.770928i | \(0.719793\pi\) | |||||||
\(282\) | 1.27001 | 0.0756282 | ||||||||
\(283\) | 24.0828 | 1.43157 | 0.715787 | − | 0.698319i | \(-0.246068\pi\) | ||||
0.715787 | + | 0.698319i | \(0.246068\pi\) | |||||||
\(284\) | 16.4678 | 0.977182 | ||||||||
\(285\) | −0.334185 | −0.0197954 | ||||||||
\(286\) | −1.50072 | −0.0887397 | ||||||||
\(287\) | −19.6733 | −1.16128 | ||||||||
\(288\) | 15.8437 | 0.933598 | ||||||||
\(289\) | 40.2277 | 2.36634 | ||||||||
\(290\) | 5.45123 | 0.320107 | ||||||||
\(291\) | −1.26747 | −0.0743006 | ||||||||
\(292\) | 25.4771 | 1.49093 | ||||||||
\(293\) | −1.69328 | −0.0989223 | −0.0494612 | − | 0.998776i | \(-0.515750\pi\) | ||||
−0.0494612 | + | 0.998776i | \(0.515750\pi\) | |||||||
\(294\) | 0.696422 | 0.0406161 | ||||||||
\(295\) | 3.97991 | 0.231719 | ||||||||
\(296\) | −19.1838 | −1.11503 | ||||||||
\(297\) | −1.96779 | −0.114183 | ||||||||
\(298\) | 8.99545 | 0.521093 | ||||||||
\(299\) | −4.46019 | −0.257940 | ||||||||
\(300\) | −0.554135 | −0.0319930 | ||||||||
\(301\) | 21.3285 | 1.22935 | ||||||||
\(302\) | −8.15679 | −0.469371 | ||||||||
\(303\) | −3.96787 | −0.227948 | ||||||||
\(304\) | 2.06586 | 0.118485 | ||||||||
\(305\) | −0.649027 | −0.0371632 | ||||||||
\(306\) | −12.7748 | −0.730288 | ||||||||
\(307\) | 5.44517 | 0.310772 | 0.155386 | − | 0.987854i | \(-0.450338\pi\) | ||||
0.155386 | + | 0.987854i | \(0.450338\pi\) | |||||||
\(308\) | −3.07350 | −0.175129 | ||||||||
\(309\) | 0.790064 | 0.0449452 | ||||||||
\(310\) | −2.52459 | −0.143387 | ||||||||
\(311\) | −3.18004 | −0.180324 | −0.0901618 | − | 0.995927i | \(-0.528738\pi\) | ||||
−0.0901618 | + | 0.995927i | \(0.528738\pi\) | |||||||
\(312\) | 1.83464 | 0.103866 | ||||||||
\(313\) | 13.7658 | 0.778087 | 0.389044 | − | 0.921219i | \(-0.372805\pi\) | ||||
0.389044 | + | 0.921219i | \(0.372805\pi\) | |||||||
\(314\) | 0.595803 | 0.0336231 | ||||||||
\(315\) | 5.35366 | 0.301644 | ||||||||
\(316\) | 17.0134 | 0.957081 | ||||||||
\(317\) | 27.9418 | 1.56937 | 0.784684 | − | 0.619896i | \(-0.212825\pi\) | ||||
0.784684 | + | 0.619896i | \(0.212825\pi\) | |||||||
\(318\) | 1.70655 | 0.0956983 | ||||||||
\(319\) | 9.32369 | 0.522026 | ||||||||
\(320\) | 0.924581 | 0.0516856 | ||||||||
\(321\) | 6.29867 | 0.351558 | ||||||||
\(322\) | 1.88309 | 0.104940 | ||||||||
\(323\) | −7.56490 | −0.420922 | ||||||||
\(324\) | −13.2775 | −0.737641 | ||||||||
\(325\) | 2.56681 | 0.142381 | ||||||||
\(326\) | −4.19450 | −0.232312 | ||||||||
\(327\) | 1.66276 | 0.0919508 | ||||||||
\(328\) | −22.7009 | −1.25345 | ||||||||
\(329\) | −12.0481 | −0.664236 | ||||||||
\(330\) | 0.195386 | 0.0107556 | ||||||||
\(331\) | 25.4481 | 1.39875 | 0.699377 | − | 0.714753i | \(-0.253461\pi\) | ||||
0.699377 | + | 0.714753i | \(0.253461\pi\) | |||||||
\(332\) | −17.7484 | −0.974072 | ||||||||
\(333\) | 25.9065 | 1.41967 | ||||||||
\(334\) | 7.47244 | 0.408874 | ||||||||
\(335\) | 0.319933 | 0.0174798 | ||||||||
\(336\) | 1.27965 | 0.0698109 | ||||||||
\(337\) | 9.36359 | 0.510067 | 0.255034 | − | 0.966932i | \(-0.417913\pi\) | ||||
0.255034 | + | 0.966932i | \(0.417913\pi\) | |||||||
\(338\) | 3.74855 | 0.203894 | ||||||||
\(339\) | 2.19536 | 0.119236 | ||||||||
\(340\) | −12.5439 | −0.680287 | ||||||||
\(341\) | −4.31802 | −0.233834 | ||||||||
\(342\) | 1.68870 | 0.0913143 | ||||||||
\(343\) | −19.5816 | −1.05731 | ||||||||
\(344\) | 24.6108 | 1.32692 | ||||||||
\(345\) | 0.580692 | 0.0312634 | ||||||||
\(346\) | 5.41473 | 0.291098 | ||||||||
\(347\) | −15.3578 | −0.824450 | −0.412225 | − | 0.911082i | \(-0.635248\pi\) | ||||
−0.412225 | + | 0.911082i | \(0.635248\pi\) | |||||||
\(348\) | −5.16658 | −0.276958 | ||||||||
\(349\) | 25.1922 | 1.34851 | 0.674253 | − | 0.738501i | \(-0.264466\pi\) | ||||
0.674253 | + | 0.738501i | \(0.264466\pi\) | |||||||
\(350\) | −1.08371 | −0.0579265 | ||||||||
\(351\) | −5.05095 | −0.269600 | ||||||||
\(352\) | −5.48543 | −0.292374 | ||||||||
\(353\) | −2.98436 | −0.158842 | −0.0794208 | − | 0.996841i | \(-0.525307\pi\) | ||||
−0.0794208 | + | 0.996841i | \(0.525307\pi\) | |||||||
\(354\) | 0.777618 | 0.0413299 | ||||||||
\(355\) | 9.93130 | 0.527098 | ||||||||
\(356\) | 22.2016 | 1.17668 | ||||||||
\(357\) | −4.68593 | −0.248006 | ||||||||
\(358\) | −0.798191 | −0.0421857 | ||||||||
\(359\) | −18.5020 | −0.976496 | −0.488248 | − | 0.872705i | \(-0.662364\pi\) | ||||
−0.488248 | + | 0.872705i | \(0.662364\pi\) | |||||||
\(360\) | 6.17754 | 0.325585 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −6.98103 | −0.366915 | ||||||||
\(363\) | 0.334185 | 0.0175402 | ||||||||
\(364\) | −7.88912 | −0.413502 | ||||||||
\(365\) | 15.3646 | 0.804220 | ||||||||
\(366\) | −0.126811 | −0.00662851 | ||||||||
\(367\) | −11.2265 | −0.586021 | −0.293010 | − | 0.956109i | \(-0.594657\pi\) | ||||
−0.293010 | + | 0.956109i | \(0.594657\pi\) | |||||||
\(368\) | −3.58971 | −0.187127 | ||||||||
\(369\) | 30.6562 | 1.59590 | ||||||||
\(370\) | −5.24409 | −0.272627 | ||||||||
\(371\) | −16.1894 | −0.840510 | ||||||||
\(372\) | 2.39277 | 0.124059 | ||||||||
\(373\) | −4.82845 | −0.250007 | −0.125004 | − | 0.992156i | \(-0.539894\pi\) | ||||
−0.125004 | + | 0.992156i | \(0.539894\pi\) | |||||||
\(374\) | 4.42292 | 0.228704 | ||||||||
\(375\) | −0.334185 | −0.0172572 | ||||||||
\(376\) | −13.9022 | −0.716954 | ||||||||
\(377\) | 23.9322 | 1.23257 | ||||||||
\(378\) | 2.13251 | 0.109684 | ||||||||
\(379\) | −12.9178 | −0.663545 | −0.331772 | − | 0.943359i | \(-0.607647\pi\) | ||||
−0.331772 | + | 0.943359i | \(0.607647\pi\) | |||||||
\(380\) | 1.65817 | 0.0850622 | ||||||||
\(381\) | 0.364714 | 0.0186849 | ||||||||
\(382\) | −11.6718 | −0.597179 | ||||||||
\(383\) | −6.70039 | −0.342374 | −0.171187 | − | 0.985239i | \(-0.554760\pi\) | ||||
−0.171187 | + | 0.985239i | \(0.554760\pi\) | |||||||
\(384\) | 3.84695 | 0.196314 | ||||||||
\(385\) | −1.85355 | −0.0944659 | ||||||||
\(386\) | −2.66278 | −0.135532 | ||||||||
\(387\) | −33.2354 | −1.68945 | ||||||||
\(388\) | 6.28898 | 0.319275 | ||||||||
\(389\) | −26.0532 | −1.32095 | −0.660476 | − | 0.750847i | \(-0.729646\pi\) | ||||
−0.660476 | + | 0.750847i | \(0.729646\pi\) | |||||||
\(390\) | 0.501520 | 0.0253954 | ||||||||
\(391\) | 13.1450 | 0.664774 | ||||||||
\(392\) | −7.62340 | −0.385040 | ||||||||
\(393\) | −0.0916233 | −0.00462178 | ||||||||
\(394\) | −2.61296 | −0.131639 | ||||||||
\(395\) | 10.2604 | 0.516256 | ||||||||
\(396\) | 4.78932 | 0.240672 | ||||||||
\(397\) | 24.5643 | 1.23285 | 0.616423 | − | 0.787415i | \(-0.288581\pi\) | ||||
0.616423 | + | 0.787415i | \(0.288581\pi\) | |||||||
\(398\) | 7.86805 | 0.394389 | ||||||||
\(399\) | 0.619430 | 0.0310103 | ||||||||
\(400\) | 2.06586 | 0.103293 | ||||||||
\(401\) | −0.303645 | −0.0151633 | −0.00758165 | − | 0.999971i | \(-0.502413\pi\) | ||||
−0.00758165 | + | 0.999971i | \(0.502413\pi\) | |||||||
\(402\) | 0.0625105 | 0.00311774 | ||||||||
\(403\) | −11.0836 | −0.552111 | ||||||||
\(404\) | 19.6879 | 0.979508 | ||||||||
\(405\) | −8.00735 | −0.397889 | ||||||||
\(406\) | −10.1041 | −0.501460 | ||||||||
\(407\) | −8.96941 | −0.444597 | ||||||||
\(408\) | −5.40705 | −0.267689 | ||||||||
\(409\) | −16.8426 | −0.832812 | −0.416406 | − | 0.909179i | \(-0.636710\pi\) | ||||
−0.416406 | + | 0.909179i | \(0.636710\pi\) | |||||||
\(410\) | −6.20553 | −0.306469 | ||||||||
\(411\) | 4.12729 | 0.203584 | ||||||||
\(412\) | −3.92016 | −0.193132 | ||||||||
\(413\) | −7.37697 | −0.362997 | ||||||||
\(414\) | −2.93434 | −0.144215 | ||||||||
\(415\) | −10.7036 | −0.525421 | ||||||||
\(416\) | −14.0801 | −0.690333 | ||||||||
\(417\) | 0.482157 | 0.0236113 | ||||||||
\(418\) | −0.584664 | −0.0285969 | ||||||||
\(419\) | −36.4464 | −1.78052 | −0.890262 | − | 0.455449i | \(-0.849479\pi\) | ||||
−0.890262 | + | 0.455449i | \(0.849479\pi\) | |||||||
\(420\) | 1.02712 | 0.0501183 | ||||||||
\(421\) | −28.4297 | −1.38558 | −0.692789 | − | 0.721141i | \(-0.743618\pi\) | ||||
−0.692789 | + | 0.721141i | \(0.743618\pi\) | |||||||
\(422\) | 4.22070 | 0.205460 | ||||||||
\(423\) | 18.7742 | 0.912831 | ||||||||
\(424\) | −18.6808 | −0.907218 | ||||||||
\(425\) | −7.56490 | −0.366952 | ||||||||
\(426\) | 1.94044 | 0.0940144 | ||||||||
\(427\) | 1.20301 | 0.0582176 | ||||||||
\(428\) | −31.2529 | −1.51067 | ||||||||
\(429\) | 0.857791 | 0.0414146 | ||||||||
\(430\) | 6.72762 | 0.324435 | ||||||||
\(431\) | −20.8541 | −1.00451 | −0.502254 | − | 0.864720i | \(-0.667496\pi\) | ||||
−0.502254 | + | 0.864720i | \(0.667496\pi\) | |||||||
\(432\) | −4.06517 | −0.195586 | ||||||||
\(433\) | 8.63662 | 0.415049 | 0.207525 | − | 0.978230i | \(-0.433459\pi\) | ||||
0.207525 | + | 0.978230i | \(0.433459\pi\) | |||||||
\(434\) | 4.67946 | 0.224621 | ||||||||
\(435\) | −3.11584 | −0.149393 | ||||||||
\(436\) | −8.25032 | −0.395119 | ||||||||
\(437\) | −1.73764 | −0.0831224 | ||||||||
\(438\) | 3.00203 | 0.143443 | ||||||||
\(439\) | −27.9016 | −1.33167 | −0.665834 | − | 0.746100i | \(-0.731924\pi\) | ||||
−0.665834 | + | 0.746100i | \(0.731924\pi\) | |||||||
\(440\) | −2.13880 | −0.101963 | ||||||||
\(441\) | 10.2949 | 0.490236 | ||||||||
\(442\) | 11.3528 | 0.539999 | ||||||||
\(443\) | 2.53769 | 0.120569 | 0.0602846 | − | 0.998181i | \(-0.480799\pi\) | ||||
0.0602846 | + | 0.998181i | \(0.480799\pi\) | |||||||
\(444\) | 4.97027 | 0.235878 | ||||||||
\(445\) | 13.3892 | 0.634710 | ||||||||
\(446\) | −0.537181 | −0.0254363 | ||||||||
\(447\) | −5.14167 | −0.243192 | ||||||||
\(448\) | −1.71376 | −0.0809676 | ||||||||
\(449\) | 13.2827 | 0.626848 | 0.313424 | − | 0.949613i | \(-0.398524\pi\) | ||||
0.313424 | + | 0.949613i | \(0.398524\pi\) | |||||||
\(450\) | 1.68870 | 0.0796059 | ||||||||
\(451\) | −10.6138 | −0.499786 | ||||||||
\(452\) | −10.8930 | −0.512363 | ||||||||
\(453\) | 4.66230 | 0.219054 | ||||||||
\(454\) | 11.0780 | 0.519917 | ||||||||
\(455\) | −4.75773 | −0.223046 | ||||||||
\(456\) | 0.714755 | 0.0334715 | ||||||||
\(457\) | −31.2328 | −1.46101 | −0.730505 | − | 0.682907i | \(-0.760715\pi\) | ||||
−0.730505 | + | 0.682907i | \(0.760715\pi\) | |||||||
\(458\) | 4.94854 | 0.231230 | ||||||||
\(459\) | 14.8861 | 0.694825 | ||||||||
\(460\) | −2.88129 | −0.134341 | ||||||||
\(461\) | 5.04910 | 0.235160 | 0.117580 | − | 0.993063i | \(-0.462486\pi\) | ||||
0.117580 | + | 0.993063i | \(0.462486\pi\) | |||||||
\(462\) | −0.362159 | −0.0168491 | ||||||||
\(463\) | 23.0184 | 1.06976 | 0.534878 | − | 0.844929i | \(-0.320357\pi\) | ||||
0.534878 | + | 0.844929i | \(0.320357\pi\) | |||||||
\(464\) | 19.2614 | 0.894189 | ||||||||
\(465\) | 1.44302 | 0.0669183 | ||||||||
\(466\) | 6.33853 | 0.293627 | ||||||||
\(467\) | 19.1144 | 0.884510 | 0.442255 | − | 0.896889i | \(-0.354179\pi\) | ||||
0.442255 | + | 0.896889i | \(0.354179\pi\) | |||||||
\(468\) | 12.2933 | 0.568258 | ||||||||
\(469\) | −0.593014 | −0.0273828 | ||||||||
\(470\) | −3.80033 | −0.175296 | ||||||||
\(471\) | −0.340552 | −0.0156918 | ||||||||
\(472\) | −8.51222 | −0.391807 | ||||||||
\(473\) | 11.5068 | 0.529084 | ||||||||
\(474\) | 2.00474 | 0.0920806 | ||||||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 23.2507 | 1.06570 | ||||||||
\(477\) | 25.2272 | 1.15508 | ||||||||
\(478\) | −2.03998 | −0.0933066 | ||||||||
\(479\) | −29.7781 | −1.36059 | −0.680297 | − | 0.732936i | \(-0.738149\pi\) | ||||
−0.680297 | + | 0.732936i | \(0.738149\pi\) | |||||||
\(480\) | 1.83315 | 0.0836714 | ||||||||
\(481\) | −23.0228 | −1.04975 | ||||||||
\(482\) | −7.20413 | −0.328139 | ||||||||
\(483\) | −1.07634 | −0.0489754 | ||||||||
\(484\) | −1.65817 | −0.0753713 | ||||||||
\(485\) | 3.79273 | 0.172219 | ||||||||
\(486\) | −5.01601 | −0.227531 | ||||||||
\(487\) | −5.27518 | −0.239041 | −0.119521 | − | 0.992832i | \(-0.538136\pi\) | ||||
−0.119521 | + | 0.992832i | \(0.538136\pi\) | |||||||
\(488\) | 1.38814 | 0.0628381 | ||||||||
\(489\) | 2.39751 | 0.108419 | ||||||||
\(490\) | −2.08394 | −0.0941428 | ||||||||
\(491\) | −44.1380 | −1.99192 | −0.995960 | − | 0.0897969i | \(-0.971378\pi\) | ||||
−0.995960 | + | 0.0897969i | \(0.971378\pi\) | |||||||
\(492\) | 5.88150 | 0.265159 | ||||||||
\(493\) | −70.5328 | −3.17664 | ||||||||
\(494\) | −1.50072 | −0.0675208 | ||||||||
\(495\) | 2.88832 | 0.129820 | ||||||||
\(496\) | −8.92041 | −0.400538 | ||||||||
\(497\) | −18.4082 | −0.825720 | ||||||||
\(498\) | −2.09134 | −0.0937153 | ||||||||
\(499\) | −10.8222 | −0.484467 | −0.242233 | − | 0.970218i | \(-0.577880\pi\) | ||||
−0.242233 | + | 0.970218i | \(0.577880\pi\) | |||||||
\(500\) | 1.65817 | 0.0741555 | ||||||||
\(501\) | −4.27113 | −0.190820 | ||||||||
\(502\) | 10.5528 | 0.470993 | ||||||||
\(503\) | 35.5134 | 1.58346 | 0.791731 | − | 0.610869i | \(-0.209180\pi\) | ||||
0.791731 | + | 0.610869i | \(0.209180\pi\) | |||||||
\(504\) | −11.4504 | −0.510041 | ||||||||
\(505\) | 11.8733 | 0.528353 | ||||||||
\(506\) | 1.01593 | 0.0451638 | ||||||||
\(507\) | −2.14262 | −0.0951569 | ||||||||
\(508\) | −1.80965 | −0.0802901 | ||||||||
\(509\) | −29.8008 | −1.32090 | −0.660448 | − | 0.750871i | \(-0.729634\pi\) | ||||
−0.660448 | + | 0.750871i | \(0.729634\pi\) | |||||||
\(510\) | −1.47808 | −0.0654503 | ||||||||
\(511\) | −28.4791 | −1.25984 | ||||||||
\(512\) | −20.1690 | −0.891353 | ||||||||
\(513\) | −1.96779 | −0.0868800 | ||||||||
\(514\) | −7.13478 | −0.314701 | ||||||||
\(515\) | −2.36415 | −0.104177 | ||||||||
\(516\) | −6.37633 | −0.280702 | ||||||||
\(517\) | −6.50003 | −0.285871 | ||||||||
\(518\) | 9.72021 | 0.427081 | ||||||||
\(519\) | −3.09498 | −0.135854 | ||||||||
\(520\) | −5.48990 | −0.240748 | ||||||||
\(521\) | 2.21855 | 0.0971963 | 0.0485982 | − | 0.998818i | \(-0.484525\pi\) | ||||
0.0485982 | + | 0.998818i | \(0.484525\pi\) | |||||||
\(522\) | 15.7449 | 0.689135 | ||||||||
\(523\) | −13.4641 | −0.588745 | −0.294373 | − | 0.955691i | \(-0.595111\pi\) | ||||
−0.294373 | + | 0.955691i | \(0.595111\pi\) | |||||||
\(524\) | 0.454619 | 0.0198601 | ||||||||
\(525\) | 0.619430 | 0.0270342 | ||||||||
\(526\) | 8.40040 | 0.366275 | ||||||||
\(527\) | 32.6654 | 1.42293 | ||||||||
\(528\) | 0.690379 | 0.0300449 | ||||||||
\(529\) | −19.9806 | −0.868723 | ||||||||
\(530\) | −5.10659 | −0.221816 | ||||||||
\(531\) | 11.4952 | 0.498851 | ||||||||
\(532\) | −3.07350 | −0.133253 | ||||||||
\(533\) | −27.2438 | −1.18006 | ||||||||
\(534\) | 2.61607 | 0.113208 | ||||||||
\(535\) | −18.8479 | −0.814864 | ||||||||
\(536\) | −0.684273 | −0.0295561 | ||||||||
\(537\) | 0.456234 | 0.0196880 | ||||||||
\(538\) | −15.4155 | −0.664608 | ||||||||
\(539\) | −3.56434 | −0.153527 | ||||||||
\(540\) | −3.26293 | −0.140414 | ||||||||
\(541\) | 17.2003 | 0.739497 | 0.369749 | − | 0.929132i | \(-0.379444\pi\) | ||||
0.369749 | + | 0.929132i | \(0.379444\pi\) | |||||||
\(542\) | −8.50093 | −0.365146 | ||||||||
\(543\) | 3.99025 | 0.171238 | ||||||||
\(544\) | 41.4967 | 1.77916 | ||||||||
\(545\) | −4.97557 | −0.213130 | ||||||||
\(546\) | −0.929594 | −0.0397829 | ||||||||
\(547\) | 17.3636 | 0.742414 | 0.371207 | − | 0.928550i | \(-0.378944\pi\) | ||||
0.371207 | + | 0.928550i | \(0.378944\pi\) | |||||||
\(548\) | −20.4789 | −0.874815 | ||||||||
\(549\) | −1.87460 | −0.0800059 | ||||||||
\(550\) | −0.584664 | −0.0249302 | ||||||||
\(551\) | 9.32369 | 0.397203 | ||||||||
\(552\) | −1.24198 | −0.0528624 | ||||||||
\(553\) | −19.0182 | −0.808736 | ||||||||
\(554\) | −10.8854 | −0.462474 | ||||||||
\(555\) | 2.99744 | 0.127234 | ||||||||
\(556\) | −2.39238 | −0.101459 | ||||||||
\(557\) | 14.6832 | 0.622149 | 0.311075 | − | 0.950385i | \(-0.399311\pi\) | ||||
0.311075 | + | 0.950385i | \(0.399311\pi\) | |||||||
\(558\) | −7.29182 | −0.308688 | ||||||||
\(559\) | 29.5359 | 1.24923 | ||||||||
\(560\) | −3.82918 | −0.161812 | ||||||||
\(561\) | −2.52808 | −0.106735 | ||||||||
\(562\) | 12.4846 | 0.526633 | ||||||||
\(563\) | 12.2619 | 0.516778 | 0.258389 | − | 0.966041i | \(-0.416808\pi\) | ||||
0.258389 | + | 0.966041i | \(0.416808\pi\) | |||||||
\(564\) | 3.60189 | 0.151667 | ||||||||
\(565\) | −6.56929 | −0.276372 | ||||||||
\(566\) | −14.0803 | −0.591841 | ||||||||
\(567\) | 14.8421 | 0.623308 | ||||||||
\(568\) | −21.2410 | −0.891254 | ||||||||
\(569\) | −39.1105 | −1.63960 | −0.819799 | − | 0.572651i | \(-0.805915\pi\) | ||||
−0.819799 | + | 0.572651i | \(0.805915\pi\) | |||||||
\(570\) | 0.195386 | 0.00818382 | ||||||||
\(571\) | 12.2964 | 0.514589 | 0.257294 | − | 0.966333i | \(-0.417169\pi\) | ||||
0.257294 | + | 0.966333i | \(0.417169\pi\) | |||||||
\(572\) | −4.25621 | −0.177961 | ||||||||
\(573\) | 6.67141 | 0.278702 | ||||||||
\(574\) | 11.5023 | 0.480096 | ||||||||
\(575\) | −1.73764 | −0.0724645 | ||||||||
\(576\) | 2.67048 | 0.111270 | ||||||||
\(577\) | −10.4836 | −0.436439 | −0.218220 | − | 0.975900i | \(-0.570025\pi\) | ||||
−0.218220 | + | 0.975900i | \(0.570025\pi\) | |||||||
\(578\) | −23.5197 | −0.978290 | ||||||||
\(579\) | 1.52200 | 0.0632523 | ||||||||
\(580\) | 15.4602 | 0.641952 | ||||||||
\(581\) | 19.8398 | 0.823093 | ||||||||
\(582\) | 0.741046 | 0.0307174 | ||||||||
\(583\) | −8.73423 | −0.361735 | ||||||||
\(584\) | −32.8618 | −1.35983 | ||||||||
\(585\) | 7.41378 | 0.306522 | ||||||||
\(586\) | 0.989998 | 0.0408965 | ||||||||
\(587\) | −33.6559 | −1.38913 | −0.694563 | − | 0.719432i | \(-0.744402\pi\) | ||||
−0.694563 | + | 0.719432i | \(0.744402\pi\) | |||||||
\(588\) | 1.97512 | 0.0814528 | ||||||||
\(589\) | −4.31802 | −0.177921 | ||||||||
\(590\) | −2.32691 | −0.0957973 | ||||||||
\(591\) | 1.49353 | 0.0614356 | ||||||||
\(592\) | −18.5295 | −0.761559 | ||||||||
\(593\) | 38.1656 | 1.56727 | 0.783636 | − | 0.621220i | \(-0.213363\pi\) | ||||
0.783636 | + | 0.621220i | \(0.213363\pi\) | |||||||
\(594\) | 1.15050 | 0.0472054 | ||||||||
\(595\) | 14.0220 | 0.574844 | ||||||||
\(596\) | 25.5120 | 1.04501 | ||||||||
\(597\) | −4.49726 | −0.184060 | ||||||||
\(598\) | 2.60771 | 0.106637 | ||||||||
\(599\) | 40.9180 | 1.67186 | 0.835932 | − | 0.548832i | \(-0.184927\pi\) | ||||
0.835932 | + | 0.548832i | \(0.184927\pi\) | |||||||
\(600\) | 0.714755 | 0.0291797 | ||||||||
\(601\) | 18.0055 | 0.734458 | 0.367229 | − | 0.930131i | \(-0.380307\pi\) | ||||
0.367229 | + | 0.930131i | \(0.380307\pi\) | |||||||
\(602\) | −12.4700 | −0.508240 | ||||||||
\(603\) | 0.924070 | 0.0376310 | ||||||||
\(604\) | −23.1335 | −0.941290 | ||||||||
\(605\) | −1.00000 | −0.0406558 | ||||||||
\(606\) | 2.31987 | 0.0942382 | ||||||||
\(607\) | 24.9470 | 1.01257 | 0.506283 | − | 0.862367i | \(-0.331019\pi\) | ||||
0.506283 | + | 0.862367i | \(0.331019\pi\) | |||||||
\(608\) | −5.48543 | −0.222464 | ||||||||
\(609\) | 5.77538 | 0.234030 | ||||||||
\(610\) | 0.379463 | 0.0153640 | ||||||||
\(611\) | −16.6844 | −0.674977 | ||||||||
\(612\) | −36.2307 | −1.46454 | ||||||||
\(613\) | 33.8227 | 1.36608 | 0.683042 | − | 0.730379i | \(-0.260657\pi\) | ||||
0.683042 | + | 0.730379i | \(0.260657\pi\) | |||||||
\(614\) | −3.18359 | −0.128479 | ||||||||
\(615\) | 3.54699 | 0.143028 | ||||||||
\(616\) | 3.96438 | 0.159729 | ||||||||
\(617\) | −15.7001 | −0.632063 | −0.316031 | − | 0.948749i | \(-0.602350\pi\) | ||||
−0.316031 | + | 0.948749i | \(0.602350\pi\) | |||||||
\(618\) | −0.461922 | −0.0185812 | ||||||||
\(619\) | 15.6715 | 0.629892 | 0.314946 | − | 0.949110i | \(-0.398014\pi\) | ||||
0.314946 | + | 0.949110i | \(0.398014\pi\) | |||||||
\(620\) | −7.16000 | −0.287552 | ||||||||
\(621\) | 3.41930 | 0.137212 | ||||||||
\(622\) | 1.85926 | 0.0745494 | ||||||||
\(623\) | −24.8176 | −0.994298 | ||||||||
\(624\) | 1.77207 | 0.0709398 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.04835 | −0.321677 | ||||||||
\(627\) | 0.334185 | 0.0133461 | ||||||||
\(628\) | 1.68976 | 0.0674287 | ||||||||
\(629\) | 67.8527 | 2.70546 | ||||||||
\(630\) | −3.13009 | −0.124706 | ||||||||
\(631\) | −41.2356 | −1.64156 | −0.820781 | − | 0.571243i | \(-0.806461\pi\) | ||||
−0.820781 | + | 0.571243i | \(0.806461\pi\) | |||||||
\(632\) | −21.9449 | −0.872922 | ||||||||
\(633\) | −2.41249 | −0.0958878 | ||||||||
\(634\) | −16.3366 | −0.648808 | ||||||||
\(635\) | −1.09135 | −0.0433090 | ||||||||
\(636\) | 4.83994 | 0.191916 | ||||||||
\(637\) | −9.14899 | −0.362496 | ||||||||
\(638\) | −5.45123 | −0.215816 | ||||||||
\(639\) | 28.6848 | 1.13475 | ||||||||
\(640\) | −11.5114 | −0.455029 | ||||||||
\(641\) | 38.3845 | 1.51610 | 0.758049 | − | 0.652198i | \(-0.226153\pi\) | ||||
0.758049 | + | 0.652198i | \(0.226153\pi\) | |||||||
\(642\) | −3.68261 | −0.145341 | ||||||||
\(643\) | −17.9219 | −0.706772 | −0.353386 | − | 0.935478i | \(-0.614970\pi\) | ||||
−0.353386 | + | 0.935478i | \(0.614970\pi\) | |||||||
\(644\) | 5.34063 | 0.210450 | ||||||||
\(645\) | −3.84541 | −0.151413 | ||||||||
\(646\) | 4.42292 | 0.174018 | ||||||||
\(647\) | −25.4790 | −1.00168 | −0.500842 | − | 0.865539i | \(-0.666976\pi\) | ||||
−0.500842 | + | 0.865539i | \(0.666976\pi\) | |||||||
\(648\) | 17.1261 | 0.672778 | ||||||||
\(649\) | −3.97991 | −0.156225 | ||||||||
\(650\) | −1.50072 | −0.0588632 | ||||||||
\(651\) | −2.67471 | −0.104830 | ||||||||
\(652\) | −11.8960 | −0.465885 | ||||||||
\(653\) | −48.6094 | −1.90223 | −0.951117 | − | 0.308832i | \(-0.900062\pi\) | ||||
−0.951117 | + | 0.308832i | \(0.900062\pi\) | |||||||
\(654\) | −0.972156 | −0.0380143 | ||||||||
\(655\) | 0.274169 | 0.0107127 | ||||||||
\(656\) | −21.9267 | −0.856093 | ||||||||
\(657\) | 44.3779 | 1.73135 | ||||||||
\(658\) | 7.04412 | 0.274608 | ||||||||
\(659\) | 29.3918 | 1.14494 | 0.572470 | − | 0.819925i | \(-0.305985\pi\) | ||||
0.572470 | + | 0.819925i | \(0.305985\pi\) | |||||||
\(660\) | 0.554135 | 0.0215697 | ||||||||
\(661\) | −32.8576 | −1.27801 | −0.639006 | − | 0.769202i | \(-0.720654\pi\) | ||||
−0.639006 | + | 0.769202i | \(0.720654\pi\) | |||||||
\(662\) | −14.8786 | −0.578273 | ||||||||
\(663\) | −6.48911 | −0.252016 | ||||||||
\(664\) | 22.8929 | 0.888418 | ||||||||
\(665\) | −1.85355 | −0.0718777 | ||||||||
\(666\) | −15.1466 | −0.586920 | ||||||||
\(667\) | −16.2012 | −0.627313 | ||||||||
\(668\) | 21.1926 | 0.819967 | ||||||||
\(669\) | 0.307045 | 0.0118710 | ||||||||
\(670\) | −0.187053 | −0.00722651 | ||||||||
\(671\) | 0.649027 | 0.0250554 | ||||||||
\(672\) | −3.39784 | −0.131075 | ||||||||
\(673\) | −23.5619 | −0.908244 | −0.454122 | − | 0.890940i | \(-0.650047\pi\) | ||||
−0.454122 | + | 0.890940i | \(0.650047\pi\) | |||||||
\(674\) | −5.47456 | −0.210872 | ||||||||
\(675\) | −1.96779 | −0.0757402 | ||||||||
\(676\) | 10.6313 | 0.408895 | ||||||||
\(677\) | 10.2123 | 0.392490 | 0.196245 | − | 0.980555i | \(-0.437125\pi\) | ||||
0.196245 | + | 0.980555i | \(0.437125\pi\) | |||||||
\(678\) | −1.28355 | −0.0492944 | ||||||||
\(679\) | −7.03003 | −0.269788 | ||||||||
\(680\) | 16.1798 | 0.620467 | ||||||||
\(681\) | −6.33202 | −0.242644 | ||||||||
\(682\) | 2.52459 | 0.0966715 | ||||||||
\(683\) | −15.2708 | −0.584319 | −0.292160 | − | 0.956370i | \(-0.594374\pi\) | ||||
−0.292160 | + | 0.956370i | \(0.594374\pi\) | |||||||
\(684\) | 4.78932 | 0.183124 | ||||||||
\(685\) | −12.3503 | −0.471881 | ||||||||
\(686\) | 11.4486 | 0.437111 | ||||||||
\(687\) | −2.82851 | −0.107914 | ||||||||
\(688\) | 23.7714 | 0.906278 | ||||||||
\(689\) | −22.4191 | −0.854101 | ||||||||
\(690\) | −0.339510 | −0.0129249 | ||||||||
\(691\) | −30.0322 | −1.14248 | −0.571239 | − | 0.820783i | \(-0.693537\pi\) | ||||
−0.571239 | + | 0.820783i | \(0.693537\pi\) | |||||||
\(692\) | 15.3567 | 0.583775 | ||||||||
\(693\) | −5.35366 | −0.203369 | ||||||||
\(694\) | 8.97915 | 0.340844 | ||||||||
\(695\) | −1.44278 | −0.0547279 | ||||||||
\(696\) | 6.66415 | 0.252604 | ||||||||
\(697\) | 80.2926 | 3.04130 | ||||||||
\(698\) | −14.7289 | −0.557499 | ||||||||
\(699\) | −3.62301 | −0.137035 | ||||||||
\(700\) | −3.07350 | −0.116168 | ||||||||
\(701\) | 5.90462 | 0.223015 | 0.111507 | − | 0.993764i | \(-0.464432\pi\) | ||||
0.111507 | + | 0.993764i | \(0.464432\pi\) | |||||||
\(702\) | 2.95311 | 0.111458 | ||||||||
\(703\) | −8.96941 | −0.338288 | ||||||||
\(704\) | −0.924581 | −0.0348464 | ||||||||
\(705\) | 2.17221 | 0.0818102 | ||||||||
\(706\) | 1.74485 | 0.0656683 | ||||||||
\(707\) | −22.0077 | −0.827686 | ||||||||
\(708\) | 2.20541 | 0.0828842 | ||||||||
\(709\) | 17.5476 | 0.659013 | 0.329507 | − | 0.944153i | \(-0.393118\pi\) | ||||
0.329507 | + | 0.944153i | \(0.393118\pi\) | |||||||
\(710\) | −5.80647 | −0.217913 | ||||||||
\(711\) | 29.6353 | 1.11141 | ||||||||
\(712\) | −28.6369 | −1.07321 | ||||||||
\(713\) | 7.50315 | 0.280995 | ||||||||
\(714\) | 2.73969 | 0.102530 | ||||||||
\(715\) | −2.56681 | −0.0959934 | ||||||||
\(716\) | −2.26375 | −0.0846004 | ||||||||
\(717\) | 1.16602 | 0.0435459 | ||||||||
\(718\) | 10.8174 | 0.403703 | ||||||||
\(719\) | 3.99061 | 0.148825 | 0.0744124 | − | 0.997228i | \(-0.476292\pi\) | ||||
0.0744124 | + | 0.997228i | \(0.476292\pi\) | |||||||
\(720\) | 5.96686 | 0.222372 | ||||||||
\(721\) | 4.38208 | 0.163197 | ||||||||
\(722\) | −0.584664 | −0.0217589 | ||||||||
\(723\) | 4.11777 | 0.153142 | ||||||||
\(724\) | −19.7989 | −0.735821 | ||||||||
\(725\) | 9.32369 | 0.346273 | ||||||||
\(726\) | −0.195386 | −0.00725146 | ||||||||
\(727\) | 46.2696 | 1.71604 | 0.858021 | − | 0.513614i | \(-0.171694\pi\) | ||||
0.858021 | + | 0.513614i | \(0.171694\pi\) | |||||||
\(728\) | 10.1758 | 0.377141 | ||||||||
\(729\) | −21.1550 | −0.783518 | ||||||||
\(730\) | −8.98313 | −0.332481 | ||||||||
\(731\) | −87.0479 | −3.21958 | ||||||||
\(732\) | −0.359649 | −0.0132930 | ||||||||
\(733\) | −5.99820 | −0.221548 | −0.110774 | − | 0.993846i | \(-0.535333\pi\) | ||||
−0.110774 | + | 0.993846i | \(0.535333\pi\) | |||||||
\(734\) | 6.56376 | 0.242273 | ||||||||
\(735\) | 1.19115 | 0.0439362 | ||||||||
\(736\) | 9.53169 | 0.351343 | ||||||||
\(737\) | −0.319933 | −0.0117849 | ||||||||
\(738\) | −17.9236 | −0.659775 | ||||||||
\(739\) | 5.41614 | 0.199236 | 0.0996179 | − | 0.995026i | \(-0.468238\pi\) | ||||
0.0996179 | + | 0.995026i | \(0.468238\pi\) | |||||||
\(740\) | −14.8728 | −0.546735 | ||||||||
\(741\) | 0.857791 | 0.0315118 | ||||||||
\(742\) | 9.46534 | 0.347483 | ||||||||
\(743\) | 51.8360 | 1.90168 | 0.950838 | − | 0.309687i | \(-0.100224\pi\) | ||||
0.950838 | + | 0.309687i | \(0.100224\pi\) | |||||||
\(744\) | −3.08632 | −0.113150 | ||||||||
\(745\) | 15.3857 | 0.563688 | ||||||||
\(746\) | 2.82302 | 0.103358 | ||||||||
\(747\) | −30.9155 | −1.13114 | ||||||||
\(748\) | 12.5439 | 0.458649 | ||||||||
\(749\) | 34.9355 | 1.27652 | ||||||||
\(750\) | 0.195386 | 0.00713449 | ||||||||
\(751\) | 50.2801 | 1.83475 | 0.917373 | − | 0.398029i | \(-0.130306\pi\) | ||||
0.917373 | + | 0.398029i | \(0.130306\pi\) | |||||||
\(752\) | −13.4281 | −0.489673 | ||||||||
\(753\) | −6.03180 | −0.219811 | ||||||||
\(754\) | −13.9923 | −0.509569 | ||||||||
\(755\) | −13.9513 | −0.507738 | ||||||||
\(756\) | 6.04801 | 0.219964 | ||||||||
\(757\) | 19.0283 | 0.691597 | 0.345798 | − | 0.938309i | \(-0.387608\pi\) | ||||
0.345798 | + | 0.938309i | \(0.387608\pi\) | |||||||
\(758\) | 7.55260 | 0.274323 | ||||||||
\(759\) | −0.580692 | −0.0210778 | ||||||||
\(760\) | −2.13880 | −0.0775824 | ||||||||
\(761\) | 4.38531 | 0.158967 | 0.0794837 | − | 0.996836i | \(-0.474673\pi\) | ||||
0.0794837 | + | 0.996836i | \(0.474673\pi\) | |||||||
\(762\) | −0.213235 | −0.00772469 | ||||||||
\(763\) | 9.22248 | 0.333876 | ||||||||
\(764\) | −33.1023 | −1.19760 | ||||||||
\(765\) | −21.8499 | −0.789983 | ||||||||
\(766\) | 3.91748 | 0.141544 | ||||||||
\(767\) | −10.2157 | −0.368867 | ||||||||
\(768\) | −1.63121 | −0.0588612 | ||||||||
\(769\) | −11.9368 | −0.430453 | −0.215227 | − | 0.976564i | \(-0.569049\pi\) | ||||
−0.215227 | + | 0.976564i | \(0.569049\pi\) | |||||||
\(770\) | 1.08371 | 0.0390541 | ||||||||
\(771\) | 4.07813 | 0.146870 | ||||||||
\(772\) | −7.55191 | −0.271799 | ||||||||
\(773\) | 50.2033 | 1.80569 | 0.902843 | − | 0.429971i | \(-0.141476\pi\) | ||||
0.902843 | + | 0.429971i | \(0.141476\pi\) | |||||||
\(774\) | 19.4315 | 0.698452 | ||||||||
\(775\) | −4.31802 | −0.155108 | ||||||||
\(776\) | −8.11189 | −0.291200 | ||||||||
\(777\) | −5.55593 | −0.199318 | ||||||||
\(778\) | 15.2324 | 0.546108 | ||||||||
\(779\) | −10.6138 | −0.380280 | ||||||||
\(780\) | 1.42236 | 0.0509287 | ||||||||
\(781\) | −9.93130 | −0.355370 | ||||||||
\(782\) | −7.68544 | −0.274831 | ||||||||
\(783\) | −18.3471 | −0.655670 | ||||||||
\(784\) | −7.36341 | −0.262979 | ||||||||
\(785\) | 1.01905 | 0.0363715 | ||||||||
\(786\) | 0.0535688 | 0.00191074 | ||||||||
\(787\) | 4.84005 | 0.172529 | 0.0862647 | − | 0.996272i | \(-0.472507\pi\) | ||||
0.0862647 | + | 0.996272i | \(0.472507\pi\) | |||||||
\(788\) | −7.41063 | −0.263993 | ||||||||
\(789\) | −4.80154 | −0.170939 | ||||||||
\(790\) | −5.99888 | −0.213431 | ||||||||
\(791\) | 12.1765 | 0.432948 | ||||||||
\(792\) | −6.17754 | −0.219509 | ||||||||
\(793\) | 1.66593 | 0.0591590 | ||||||||
\(794\) | −14.3618 | −0.509683 | ||||||||
\(795\) | 2.91885 | 0.103521 | ||||||||
\(796\) | 22.3146 | 0.790920 | ||||||||
\(797\) | 26.3359 | 0.932865 | 0.466432 | − | 0.884557i | \(-0.345539\pi\) | ||||
0.466432 | + | 0.884557i | \(0.345539\pi\) | |||||||
\(798\) | −0.362159 | −0.0128203 | ||||||||
\(799\) | 49.1720 | 1.73958 | ||||||||
\(800\) | −5.48543 | −0.193939 | ||||||||
\(801\) | 38.6724 | 1.36642 | ||||||||
\(802\) | 0.177530 | 0.00626881 | ||||||||
\(803\) | −15.3646 | −0.542205 | ||||||||
\(804\) | 0.177286 | 0.00625241 | ||||||||
\(805\) | 3.22080 | 0.113518 | ||||||||
\(806\) | 6.48015 | 0.228254 | ||||||||
\(807\) | 8.81125 | 0.310171 | ||||||||
\(808\) | −25.3945 | −0.893376 | ||||||||
\(809\) | 4.63056 | 0.162802 | 0.0814009 | − | 0.996681i | \(-0.474061\pi\) | ||||
0.0814009 | + | 0.996681i | \(0.474061\pi\) | |||||||
\(810\) | 4.68161 | 0.164495 | ||||||||
\(811\) | 0.583214 | 0.0204794 | 0.0102397 | − | 0.999948i | \(-0.496741\pi\) | ||||
0.0102397 | + | 0.999948i | \(0.496741\pi\) | |||||||
\(812\) | −28.6564 | −1.00564 | ||||||||
\(813\) | 4.85900 | 0.170413 | ||||||||
\(814\) | 5.24409 | 0.183805 | ||||||||
\(815\) | −7.17421 | −0.251301 | ||||||||
\(816\) | −5.22265 | −0.182829 | ||||||||
\(817\) | 11.5068 | 0.402573 | ||||||||
\(818\) | 9.84725 | 0.344301 | ||||||||
\(819\) | −13.7418 | −0.480179 | ||||||||
\(820\) | −17.5995 | −0.614602 | ||||||||
\(821\) | 35.4319 | 1.23658 | 0.618290 | − | 0.785950i | \(-0.287826\pi\) | ||||
0.618290 | + | 0.785950i | \(0.287826\pi\) | |||||||
\(822\) | −2.41308 | −0.0841658 | ||||||||
\(823\) | −35.3477 | −1.23214 | −0.616072 | − | 0.787690i | \(-0.711277\pi\) | ||||
−0.616072 | + | 0.787690i | \(0.711277\pi\) | |||||||
\(824\) | 5.05645 | 0.176150 | ||||||||
\(825\) | 0.334185 | 0.0116348 | ||||||||
\(826\) | 4.31305 | 0.150070 | ||||||||
\(827\) | −16.7617 | −0.582861 | −0.291430 | − | 0.956592i | \(-0.594131\pi\) | ||||
−0.291430 | + | 0.956592i | \(0.594131\pi\) | |||||||
\(828\) | −8.32210 | −0.289213 | ||||||||
\(829\) | −19.2674 | −0.669186 | −0.334593 | − | 0.942363i | \(-0.608599\pi\) | ||||
−0.334593 | + | 0.942363i | \(0.608599\pi\) | |||||||
\(830\) | 6.25803 | 0.217219 | ||||||||
\(831\) | 6.22191 | 0.215836 | ||||||||
\(832\) | −2.37323 | −0.0822769 | ||||||||
\(833\) | 26.9639 | 0.934242 | ||||||||
\(834\) | −0.281900 | −0.00976139 | ||||||||
\(835\) | 12.7807 | 0.442296 | ||||||||
\(836\) | −1.65817 | −0.0573489 | ||||||||
\(837\) | 8.49695 | 0.293698 | ||||||||
\(838\) | 21.3089 | 0.736104 | ||||||||
\(839\) | 44.5687 | 1.53868 | 0.769341 | − | 0.638839i | \(-0.220585\pi\) | ||||
0.769341 | + | 0.638839i | \(0.220585\pi\) | |||||||
\(840\) | −1.32484 | −0.0457112 | ||||||||
\(841\) | 57.9312 | 1.99763 | ||||||||
\(842\) | 16.6218 | 0.572825 | ||||||||
\(843\) | −7.13604 | −0.245778 | ||||||||
\(844\) | 11.9703 | 0.412036 | ||||||||
\(845\) | 6.41146 | 0.220561 | ||||||||
\(846\) | −10.9766 | −0.377382 | ||||||||
\(847\) | 1.85355 | 0.0636889 | ||||||||
\(848\) | −18.0437 | −0.619622 | ||||||||
\(849\) | 8.04811 | 0.276210 | ||||||||
\(850\) | 4.42292 | 0.151705 | ||||||||
\(851\) | 15.5856 | 0.534267 | ||||||||
\(852\) | 5.50328 | 0.188539 | ||||||||
\(853\) | −1.06714 | −0.0365381 | −0.0182690 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182690 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(854\) | −0.703355 | −0.0240683 | ||||||||
\(855\) | 2.88832 | 0.0987785 | ||||||||
\(856\) | 40.3118 | 1.37783 | ||||||||
\(857\) | −24.2621 | −0.828777 | −0.414388 | − | 0.910100i | \(-0.636004\pi\) | ||||
−0.414388 | + | 0.910100i | \(0.636004\pi\) | |||||||
\(858\) | −0.501520 | −0.0171216 | ||||||||
\(859\) | −2.20953 | −0.0753882 | −0.0376941 | − | 0.999289i | \(-0.512001\pi\) | ||||
−0.0376941 | + | 0.999289i | \(0.512001\pi\) | |||||||
\(860\) | 19.0802 | 0.650631 | ||||||||
\(861\) | −6.57453 | −0.224059 | ||||||||
\(862\) | 12.1927 | 0.415283 | ||||||||
\(863\) | −6.31080 | −0.214822 | −0.107411 | − | 0.994215i | \(-0.534256\pi\) | ||||
−0.107411 | + | 0.994215i | \(0.534256\pi\) | |||||||
\(864\) | 10.7942 | 0.367225 | ||||||||
\(865\) | 9.26126 | 0.314892 | ||||||||
\(866\) | −5.04952 | −0.171590 | ||||||||
\(867\) | 13.4435 | 0.456565 | ||||||||
\(868\) | 13.2714 | 0.450462 | ||||||||
\(869\) | −10.2604 | −0.348060 | ||||||||
\(870\) | 1.82172 | 0.0617621 | ||||||||
\(871\) | −0.821210 | −0.0278256 | ||||||||
\(872\) | 10.6417 | 0.360375 | ||||||||
\(873\) | 10.9546 | 0.370758 | ||||||||
\(874\) | 1.01593 | 0.0343645 | ||||||||
\(875\) | −1.85355 | −0.0626616 | ||||||||
\(876\) | 8.51407 | 0.287664 | ||||||||
\(877\) | 1.50724 | 0.0508959 | 0.0254479 | − | 0.999676i | \(-0.491899\pi\) | ||||
0.0254479 | + | 0.999676i | \(0.491899\pi\) | |||||||
\(878\) | 16.3130 | 0.550538 | ||||||||
\(879\) | −0.565868 | −0.0190863 | ||||||||
\(880\) | −2.06586 | −0.0696400 | ||||||||
\(881\) | 21.1890 | 0.713877 | 0.356938 | − | 0.934128i | \(-0.383821\pi\) | ||||
0.356938 | + | 0.934128i | \(0.383821\pi\) | |||||||
\(882\) | −6.01909 | −0.202673 | ||||||||
\(883\) | −16.0935 | −0.541589 | −0.270794 | − | 0.962637i | \(-0.587286\pi\) | ||||
−0.270794 | + | 0.962637i | \(0.587286\pi\) | |||||||
\(884\) | 32.1978 | 1.08293 | ||||||||
\(885\) | 1.33003 | 0.0447083 | ||||||||
\(886\) | −1.48369 | −0.0498457 | ||||||||
\(887\) | 26.3625 | 0.885166 | 0.442583 | − | 0.896728i | \(-0.354062\pi\) | ||||
0.442583 | + | 0.896728i | \(0.354062\pi\) | |||||||
\(888\) | −6.41093 | −0.215137 | ||||||||
\(889\) | 2.02288 | 0.0678453 | ||||||||
\(890\) | −7.82819 | −0.262402 | ||||||||
\(891\) | 8.00735 | 0.268256 | ||||||||
\(892\) | −1.52350 | −0.0510106 | ||||||||
\(893\) | −6.50003 | −0.217515 | ||||||||
\(894\) | 3.00615 | 0.100541 | ||||||||
\(895\) | −1.36521 | −0.0456340 | ||||||||
\(896\) | 21.3371 | 0.712821 | ||||||||
\(897\) | −1.49053 | −0.0497674 | ||||||||
\(898\) | −7.76589 | −0.259151 | ||||||||
\(899\) | −40.2599 | −1.34274 | ||||||||
\(900\) | 4.78932 | 0.159644 | ||||||||
\(901\) | 66.0736 | 2.20123 | ||||||||
\(902\) | 6.20553 | 0.206622 | ||||||||
\(903\) | 7.12767 | 0.237194 | ||||||||
\(904\) | 14.0504 | 0.467309 | ||||||||
\(905\) | −11.9402 | −0.396907 | ||||||||
\(906\) | −2.72588 | −0.0905613 | ||||||||
\(907\) | 37.8709 | 1.25748 | 0.628742 | − | 0.777614i | \(-0.283570\pi\) | ||||
0.628742 | + | 0.777614i | \(0.283570\pi\) | |||||||
\(908\) | 31.4184 | 1.04266 | ||||||||
\(909\) | 34.2938 | 1.13745 | ||||||||
\(910\) | 2.78167 | 0.0922116 | ||||||||
\(911\) | −36.2441 | −1.20082 | −0.600410 | − | 0.799692i | \(-0.704996\pi\) | ||||
−0.600410 | + | 0.799692i | \(0.704996\pi\) | |||||||
\(912\) | 0.690379 | 0.0228607 | ||||||||
\(913\) | 10.7036 | 0.354239 | ||||||||
\(914\) | 18.2607 | 0.604011 | ||||||||
\(915\) | −0.216895 | −0.00717033 | ||||||||
\(916\) | 14.0346 | 0.463716 | ||||||||
\(917\) | −0.508188 | −0.0167818 | ||||||||
\(918\) | −8.70338 | −0.287254 | ||||||||
\(919\) | −57.6780 | −1.90262 | −0.951310 | − | 0.308235i | \(-0.900262\pi\) | ||||
−0.951310 | + | 0.308235i | \(0.900262\pi\) | |||||||
\(920\) | 3.71646 | 0.122528 | ||||||||
\(921\) | 1.81969 | 0.0599609 | ||||||||
\(922\) | −2.95202 | −0.0972198 | ||||||||
\(923\) | −25.4918 | −0.839073 | ||||||||
\(924\) | −1.02712 | −0.0337897 | ||||||||
\(925\) | −8.96941 | −0.294912 | ||||||||
\(926\) | −13.4580 | −0.442259 | ||||||||
\(927\) | −6.82843 | −0.224275 | ||||||||
\(928\) | −51.1445 | −1.67890 | ||||||||
\(929\) | 45.2673 | 1.48517 | 0.742586 | − | 0.669751i | \(-0.233599\pi\) | ||||
0.742586 | + | 0.669751i | \(0.233599\pi\) | |||||||
\(930\) | −0.843680 | −0.0276654 | ||||||||
\(931\) | −3.56434 | −0.116816 | ||||||||
\(932\) | 17.9767 | 0.588847 | ||||||||
\(933\) | −1.06272 | −0.0347920 | ||||||||
\(934\) | −11.1755 | −0.365674 | ||||||||
\(935\) | 7.56490 | 0.247399 | ||||||||
\(936\) | −15.8566 | −0.518289 | ||||||||
\(937\) | −49.0343 | −1.60188 | −0.800940 | − | 0.598745i | \(-0.795666\pi\) | ||||
−0.800940 | + | 0.598745i | \(0.795666\pi\) | |||||||
\(938\) | 0.346714 | 0.0113206 | ||||||||
\(939\) | 4.60032 | 0.150126 | ||||||||
\(940\) | −10.7781 | −0.351544 | ||||||||
\(941\) | 5.61799 | 0.183141 | 0.0915706 | − | 0.995799i | \(-0.470811\pi\) | ||||
0.0915706 | + | 0.995799i | \(0.470811\pi\) | |||||||
\(942\) | 0.199108 | 0.00648730 | ||||||||
\(943\) | 18.4430 | 0.600587 | ||||||||
\(944\) | −8.22192 | −0.267601 | ||||||||
\(945\) | 3.64740 | 0.118650 | ||||||||
\(946\) | −6.72762 | −0.218734 | ||||||||
\(947\) | −46.5630 | −1.51309 | −0.756547 | − | 0.653939i | \(-0.773115\pi\) | ||||
−0.756547 | + | 0.653939i | \(0.773115\pi\) | |||||||
\(948\) | 5.68564 | 0.184661 | ||||||||
\(949\) | −39.4381 | −1.28022 | ||||||||
\(950\) | −0.584664 | −0.0189690 | ||||||||
\(951\) | 9.33774 | 0.302797 | ||||||||
\(952\) | −29.9901 | −0.971986 | ||||||||
\(953\) | −13.6432 | −0.441948 | −0.220974 | − | 0.975280i | \(-0.570924\pi\) | ||||
−0.220974 | + | 0.975280i | \(0.570924\pi\) | |||||||
\(954\) | −14.7495 | −0.477531 | ||||||||
\(955\) | −19.9632 | −0.645994 | ||||||||
\(956\) | −5.78560 | −0.187120 | ||||||||
\(957\) | 3.11584 | 0.100721 | ||||||||
\(958\) | 17.4102 | 0.562497 | ||||||||
\(959\) | 22.8920 | 0.739220 | ||||||||
\(960\) | 0.308981 | 0.00997232 | ||||||||
\(961\) | −12.3547 | −0.398539 | ||||||||
\(962\) | 13.4606 | 0.433988 | ||||||||
\(963\) | −54.4387 | −1.75426 | ||||||||
\(964\) | −20.4316 | −0.658059 | ||||||||
\(965\) | −4.55437 | −0.146610 | ||||||||
\(966\) | 0.629300 | 0.0202474 | ||||||||
\(967\) | 7.80756 | 0.251074 | 0.125537 | − | 0.992089i | \(-0.459935\pi\) | ||||
0.125537 | + | 0.992089i | \(0.459935\pi\) | |||||||
\(968\) | 2.13880 | 0.0687436 | ||||||||
\(969\) | −2.52808 | −0.0812135 | ||||||||
\(970\) | −2.21747 | −0.0711988 | ||||||||
\(971\) | 8.59548 | 0.275842 | 0.137921 | − | 0.990443i | \(-0.455958\pi\) | ||||
0.137921 | + | 0.990443i | \(0.455958\pi\) | |||||||
\(972\) | −14.2259 | −0.456297 | ||||||||
\(973\) | 2.67428 | 0.0857334 | ||||||||
\(974\) | 3.08421 | 0.0988243 | ||||||||
\(975\) | 0.857791 | 0.0274713 | ||||||||
\(976\) | 1.34080 | 0.0429179 | ||||||||
\(977\) | 46.8731 | 1.49960 | 0.749801 | − | 0.661663i | \(-0.230149\pi\) | ||||
0.749801 | + | 0.661663i | \(0.230149\pi\) | |||||||
\(978\) | −1.40174 | −0.0448227 | ||||||||
\(979\) | −13.3892 | −0.427921 | ||||||||
\(980\) | −5.91027 | −0.188797 | ||||||||
\(981\) | −14.3710 | −0.458832 | ||||||||
\(982\) | 25.8059 | 0.823499 | ||||||||
\(983\) | −15.9451 | −0.508569 | −0.254284 | − | 0.967130i | \(-0.581840\pi\) | ||||
−0.254284 | + | 0.967130i | \(0.581840\pi\) | |||||||
\(984\) | −7.58629 | −0.241842 | ||||||||
\(985\) | −4.46917 | −0.142400 | ||||||||
\(986\) | 41.2380 | 1.31328 | ||||||||
\(987\) | −4.02631 | −0.128159 | ||||||||
\(988\) | −4.25621 | −0.135408 | ||||||||
\(989\) | −19.9947 | −0.635794 | ||||||||
\(990\) | −1.68870 | −0.0536703 | ||||||||
\(991\) | −5.95902 | −0.189295 | −0.0946473 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946473 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(992\) | 23.6862 | 0.752037 | ||||||||
\(993\) | 8.50438 | 0.269878 | ||||||||
\(994\) | 10.7626 | 0.341369 | ||||||||
\(995\) | 13.4574 | 0.426628 | ||||||||
\(996\) | −5.93126 | −0.187939 | ||||||||
\(997\) | 29.3619 | 0.929902 | 0.464951 | − | 0.885337i | \(-0.346072\pi\) | ||||
0.464951 | + | 0.885337i | \(0.346072\pi\) | |||||||
\(998\) | 6.32733 | 0.200288 | ||||||||
\(999\) | 17.6499 | 0.558419 |
(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 | 1045.2.a.e.1.3 | ✓ | 5 | |
3.2 | odd | 2 | 9405.2.a.u.1.3 | 5 | |||
5.4 | even | 2 | 5225.2.a.i.1.3 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.a.e.1.3 | ✓ | 5 | 1.1 | even | 1 | trivial | |
5225.2.a.i.1.3 | 5 | 5.4 | even | 2 | |||
9405.2.a.u.1.3 | 5 | 3.2 | odd | 2 |