Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.4 | ||
Root | \(-1.16746 - 0.312819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.b.49.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.60976 | + | 1.55199i | −0.719905 | + | 0.694073i | ||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | − | 3.53919i | − | 1.33769i | −0.743403 | − | 0.668844i | \(-0.766789\pi\) | ||
0.743403 | − | 0.668844i | \(-0.233211\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.618092 | + | 2.14894i | −0.195458 | + | 0.679556i | ||||
\(11\) | 3.34017 | 1.00710 | 0.503550 | − | 0.863966i | \(-0.332027\pi\) | ||||
0.503550 | + | 0.863966i | \(0.332027\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 1.48028 | + | 0.854638i | 0.410555 | + | 0.237034i | 0.691028 | − | 0.722828i | \(-0.257158\pi\) |
−0.280473 | + | 0.959862i | \(0.590491\pi\) | |||||||
\(14\) | −1.76959 | − | 3.06503i | −0.472944 | − | 0.819163i | ||||
\(15\) | −0.618092 | + | 2.14894i | −0.159591 | + | 0.554855i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 3.29175 | − | 1.90049i | 0.798366 | − | 0.460937i | −0.0445332 | − | 0.999008i | \(-0.514180\pi\) |
0.842900 | + | 0.538071i | \(0.180847\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.30878 | − | 4.15777i | 0.300255 | − | 0.953859i | ||||
\(20\) | 0.539189 | + | 2.17009i | 0.120566 | + | 0.485246i | ||||
\(21\) | −1.76959 | − | 3.06503i | −0.386157 | − | 0.668844i | ||||
\(22\) | 2.89267 | − | 1.67009i | 0.616720 | − | 0.356064i | ||||
\(23\) | −7.33350 | − | 4.23400i | −1.52914 | − | 0.882850i | −0.999398 | − | 0.0346916i | \(-0.988955\pi\) |
−0.529743 | − | 0.848158i | \(-0.677712\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0.182626 | − | 4.99666i | 0.0365252 | − | 0.999333i | ||||
\(26\) | 1.70928 | 0.335216 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −3.06503 | − | 1.76959i | −0.579236 | − | 0.334422i | ||||
\(29\) | −3.97887 | + | 6.89160i | −0.738858 | + | 1.27974i | 0.214152 | + | 0.976800i | \(0.431301\pi\) |
−0.953010 | + | 0.302939i | \(0.902032\pi\) | |||||||
\(30\) | 0.539189 | + | 2.17009i | 0.0984420 | + | 0.396202i | ||||
\(31\) | 1.07838 | 0.193682 | 0.0968412 | − | 0.995300i | \(-0.469126\pi\) | ||||
0.0968412 | + | 0.995300i | \(0.469126\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 2.89267 | − | 1.67009i | 0.503550 | − | 0.290725i | ||||
\(34\) | 1.90049 | − | 3.29175i | 0.325932 | − | 0.564530i | ||||
\(35\) | 5.49280 | + | 5.69723i | 0.928453 | + | 0.963007i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 4.70928i | 0.774200i | 0.922038 | + | 0.387100i | \(0.126523\pi\) | ||||
−0.922038 | + | 0.387100i | \(0.873477\pi\) | |||||||
\(38\) | −0.945448 | − | 4.25513i | −0.153372 | − | 0.690273i | ||||
\(39\) | 1.70928 | 0.273703 | ||||||||
\(40\) | 1.55199 | + | 1.60976i | 0.245392 | + | 0.254525i | ||||
\(41\) | 5.96441 | + | 10.3307i | 0.931484 | + | 1.61338i | 0.780787 | + | 0.624797i | \(0.214818\pi\) |
0.150696 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(42\) | −3.06503 | − | 1.76959i | −0.472944 | − | 0.273054i | ||||
\(43\) | 4.39800 | − | 2.53919i | 0.670689 | − | 0.387223i | −0.125648 | − | 0.992075i | \(-0.540101\pi\) |
0.796338 | + | 0.604852i | \(0.206768\pi\) | |||||||
\(44\) | 1.67009 | − | 2.89267i | 0.251775 | − | 0.436087i | ||||
\(45\) | 0.539189 | + | 2.17009i | 0.0803775 | + | 0.323497i | ||||
\(46\) | −8.46800 | −1.24854 | ||||||||
\(47\) | −4.73543 | − | 2.73400i | −0.690733 | − | 0.398795i | 0.113154 | − | 0.993578i | \(-0.463905\pi\) |
−0.803887 | + | 0.594783i | \(0.797238\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | −5.52586 | −0.789408 | ||||||||
\(50\) | −2.34017 | − | 4.41855i | −0.330950 | − | 0.624877i | ||||
\(51\) | 1.90049 | − | 3.29175i | 0.266122 | − | 0.460937i | ||||
\(52\) | 1.48028 | − | 0.854638i | 0.205277 | − | 0.118517i | ||||
\(53\) | 10.8342 | + | 6.25513i | 1.48819 | + | 0.859208i | 0.999909 | − | 0.0134772i | \(-0.00429006\pi\) |
0.488283 | + | 0.872685i | \(0.337623\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −5.37686 | + | 5.18393i | −0.725016 | + | 0.699001i | ||||
\(56\) | −3.53919 | −0.472944 | ||||||||
\(57\) | −0.945448 | − | 4.25513i | −0.125228 | − | 0.563606i | ||||
\(58\) | 7.95774i | 1.04490i | ||||||||
\(59\) | 2.93302 | + | 5.08013i | 0.381846 | + | 0.661377i | 0.991326 | − | 0.131425i | \(-0.0419551\pi\) |
−0.609480 | + | 0.792801i | \(0.708622\pi\) | |||||||
\(60\) | 1.55199 | + | 1.60976i | 0.200362 | + | 0.207819i | ||||
\(61\) | −6.92522 | + | 11.9948i | −0.886683 | + | 1.53578i | −0.0429107 | + | 0.999079i | \(0.513663\pi\) |
−0.843772 | + | 0.536701i | \(0.819670\pi\) | |||||||
\(62\) | 0.933903 | − | 0.539189i | 0.118606 | − | 0.0684771i | ||||
\(63\) | −3.06503 | − | 1.76959i | −0.386157 | − | 0.222948i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.70928 | + | 0.921622i | −0.460079 | + | 0.114313i | ||||
\(66\) | 1.67009 | − | 2.89267i | 0.205573 | − | 0.356064i | ||||
\(67\) | −7.82551 | − | 4.51806i | −0.956038 | − | 0.551969i | −0.0610865 | − | 0.998132i | \(-0.519457\pi\) |
−0.894951 | + | 0.446164i | \(0.852790\pi\) | |||||||
\(68\) | − | 3.80098i | − | 0.460937i | ||||||
\(69\) | −8.46800 | −1.01943 | ||||||||
\(70\) | 7.60552 | + | 2.18754i | 0.909034 | + | 0.261462i | ||||
\(71\) | 4.04585 | + | 7.00763i | 0.480155 | + | 0.831652i | 0.999741 | − | 0.0227659i | \(-0.00724723\pi\) |
−0.519586 | + | 0.854418i | \(0.673914\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −5.11673 | + | 2.95415i | −0.598868 | + | 0.345757i | −0.768596 | − | 0.639734i | \(-0.779044\pi\) |
0.169728 | + | 0.985491i | \(0.445711\pi\) | |||||||
\(74\) | 2.35464 | + | 4.07835i | 0.273721 | + | 0.474099i | ||||
\(75\) | −2.34017 | − | 4.41855i | −0.270220 | − | 0.510210i | ||||
\(76\) | −2.94635 | − | 3.21233i | −0.337969 | − | 0.368479i | ||||
\(77\) | − | 11.8215i | − | 1.34719i | ||||||
\(78\) | 1.48028 | − | 0.854638i | 0.167608 | − | 0.0967687i | ||||
\(79\) | −3.53919 | − | 6.13005i | −0.398190 | − | 0.689685i | 0.595313 | − | 0.803494i | \(-0.297028\pi\) |
−0.993503 | + | 0.113809i | \(0.963695\pi\) | |||||||
\(80\) | 2.14894 | + | 0.618092i | 0.240259 | + | 0.0691048i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 10.3307 | + | 5.96441i | 1.14083 | + | 0.658658i | ||||
\(83\) | 4.68035i | 0.513735i | 0.966447 | + | 0.256867i | \(0.0826903\pi\) | ||||
−0.966447 | + | 0.256867i | \(0.917310\pi\) | |||||||
\(84\) | −3.53919 | −0.386157 | ||||||||
\(85\) | −2.34936 | + | 8.16810i | −0.254824 | + | 0.885955i | ||||
\(86\) | 2.53919 | − | 4.39800i | 0.273808 | − | 0.474249i | ||||
\(87\) | 7.95774i | 0.853159i | ||||||||
\(88\) | − | 3.34017i | − | 0.356064i | ||||||
\(89\) | 4.66229 | − | 8.07532i | 0.494201 | − | 0.855982i | −0.505776 | − | 0.862665i | \(-0.668794\pi\) |
0.999978 | + | 0.00668268i | \(0.00212718\pi\) | |||||||
\(90\) | 1.55199 | + | 1.60976i | 0.163595 | + | 0.169683i | ||||
\(91\) | 3.02472 | − | 5.23898i | 0.317077 | − | 0.549194i | ||||
\(92\) | −7.33350 | + | 4.23400i | −0.764570 | + | 0.441425i | ||||
\(93\) | 0.933903 | − | 0.539189i | 0.0968412 | − | 0.0559113i | ||||
\(94\) | −5.46800 | −0.563981 | ||||||||
\(95\) | 4.34602 | + | 8.72422i | 0.445892 | + | 0.895087i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.06662 | + | 2.92522i | −0.514438 | + | 0.297011i | −0.734656 | − | 0.678440i | \(-0.762656\pi\) |
0.220218 | + | 0.975451i | \(0.429323\pi\) | |||||||
\(98\) | −4.78553 | + | 2.76293i | −0.483412 | + | 0.279098i | ||||
\(99\) | 1.67009 | − | 2.89267i | 0.167850 | − | 0.290725i | ||||
\(100\) | −4.23592 | − | 2.65649i | −0.423592 | − | 0.265649i | ||||
\(101\) | 4.32684 | − | 7.49431i | 0.430537 | − | 0.745712i | −0.566383 | − | 0.824142i | \(-0.691658\pi\) |
0.996920 | + | 0.0784306i | \(0.0249909\pi\) | |||||||
\(102\) | − | 3.80098i | − | 0.376354i | ||||||
\(103\) | 0.751536i | 0.0740510i | 0.999314 | + | 0.0370255i | \(0.0117883\pi\) | ||||
−0.999314 | + | 0.0370255i | \(0.988212\pi\) | |||||||
\(104\) | 0.854638 | − | 1.48028i | 0.0838041 | − | 0.145153i | ||||
\(105\) | 7.60552 | + | 2.18754i | 0.742223 | + | 0.213482i | ||||
\(106\) | 12.5103 | 1.21510 | ||||||||
\(107\) | 9.82377i | 0.949700i | 0.880067 | + | 0.474850i | \(0.157498\pi\) | ||||
−0.880067 | + | 0.474850i | \(0.842502\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | −3.92522 | − | 6.79867i | −0.375968 | − | 0.651195i | 0.614504 | − | 0.788914i | \(-0.289356\pi\) |
−0.990471 | + | 0.137719i | \(0.956023\pi\) | |||||||
\(110\) | −2.06453 | + | 7.17785i | −0.196846 | + | 0.684381i | ||||
\(111\) | 2.35464 | + | 4.07835i | 0.223492 | + | 0.387100i | ||||
\(112\) | −3.06503 | + | 1.76959i | −0.289618 | + | 0.167211i | ||||
\(113\) | 7.98440i | 0.751109i | 0.926800 | + | 0.375555i | \(0.122548\pi\) | ||||
−0.926800 | + | 0.375555i | \(0.877452\pi\) | |||||||
\(114\) | −2.94635 | − | 3.21233i | −0.275951 | − | 0.300862i | ||||
\(115\) | 18.3763 | − | 4.56585i | 1.71360 | − | 0.425768i | ||||
\(116\) | 3.97887 | + | 6.89160i | 0.369429 | + | 0.639869i | ||||
\(117\) | 1.48028 | − | 0.854638i | 0.136852 | − | 0.0790113i | ||||
\(118\) | 5.08013 | + | 2.93302i | 0.467664 | + | 0.270006i | ||||
\(119\) | −6.72620 | − | 11.6501i | −0.616590 | − | 1.06796i | ||||
\(120\) | 2.14894 | + | 0.618092i | 0.196171 | + | 0.0564238i | ||||
\(121\) | 0.156755 | 0.0142505 | ||||||||
\(122\) | 13.8504i | 1.25396i | ||||||||
\(123\) | 10.3307 | + | 5.96441i | 0.931484 | + | 0.537792i | ||||
\(124\) | 0.539189 | − | 0.933903i | 0.0484206 | − | 0.0838669i | ||||
\(125\) | 7.46081 | + | 8.32684i | 0.667315 | + | 0.744775i | ||||
\(126\) | −3.53919 | −0.315296 | ||||||||
\(127\) | 16.1160 | + | 9.30458i | 1.43006 | + | 0.825648i | 0.997125 | − | 0.0757754i | \(-0.0241432\pi\) |
0.432939 | + | 0.901423i | \(0.357477\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 2.53919 | − | 4.39800i | 0.223563 | − | 0.387223i | ||||
\(130\) | −2.75152 | + | 2.65279i | −0.241324 | + | 0.232665i | ||||
\(131\) | 3.79072 | + | 6.56573i | 0.331197 | + | 0.573650i | 0.982747 | − | 0.184956i | \(-0.0592141\pi\) |
−0.651550 | + | 0.758606i | \(0.725881\pi\) | |||||||
\(132\) | − | 3.34017i | − | 0.290725i | ||||||
\(133\) | −14.7151 | − | 4.63203i | −1.27597 | − | 0.401648i | ||||
\(134\) | −9.03612 | −0.780602 | ||||||||
\(135\) | 1.55199 | + | 1.60976i | 0.133574 | + | 0.138546i | ||||
\(136\) | −1.90049 | − | 3.29175i | −0.162966 | − | 0.282265i | ||||
\(137\) | −9.88875 | − | 5.70928i | −0.844853 | − | 0.487776i | 0.0140576 | − | 0.999901i | \(-0.495525\pi\) |
−0.858911 | + | 0.512125i | \(0.828858\pi\) | |||||||
\(138\) | −7.33350 | + | 4.23400i | −0.624269 | + | 0.360422i | ||||
\(139\) | 1.80098 | − | 3.11940i | 0.152757 | − | 0.264584i | −0.779483 | − | 0.626424i | \(-0.784518\pi\) |
0.932240 | + | 0.361840i | \(0.117851\pi\) | |||||||
\(140\) | 7.68035 | − | 1.90829i | 0.649108 | − | 0.161280i | ||||
\(141\) | −5.46800 | −0.460489 | ||||||||
\(142\) | 7.00763 | + | 4.04585i | 0.588067 | + | 0.339521i | ||||
\(143\) | 4.94438 | + | 2.85464i | 0.413470 | + | 0.238717i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −4.29072 | − | 17.2690i | −0.356325 | − | 1.43411i | ||||
\(146\) | −2.95415 | + | 5.11673i | −0.244487 | + | 0.423464i | ||||
\(147\) | −4.78553 | + | 2.76293i | −0.394704 | + | 0.227883i | ||||
\(148\) | 4.07835 | + | 2.35464i | 0.335238 | + | 0.193550i | ||||
\(149\) | −5.14896 | − | 8.91825i | −0.421819 | − | 0.730612i | 0.574299 | − | 0.818646i | \(-0.305275\pi\) |
−0.996117 | + | 0.0880341i | \(0.971942\pi\) | |||||||
\(150\) | −4.23592 | − | 2.65649i | −0.345862 | − | 0.216902i | ||||
\(151\) | −4.69594 | −0.382151 | −0.191075 | − | 0.981575i | \(-0.561197\pi\) | ||||
−0.191075 | + | 0.981575i | \(0.561197\pi\) | |||||||
\(152\) | −4.15777 | − | 1.30878i | −0.337240 | − | 0.106156i | ||||
\(153\) | − | 3.80098i | − | 0.307291i | ||||||
\(154\) | −5.91075 | − | 10.2377i | −0.476302 | − | 0.824979i | ||||
\(155\) | −1.73592 | + | 1.67364i | −0.139433 | + | 0.134430i | ||||
\(156\) | 0.854638 | − | 1.48028i | 0.0684258 | − | 0.118517i | ||||
\(157\) | 9.10838 | − | 5.25872i | 0.726928 | − | 0.419692i | −0.0903695 | − | 0.995908i | \(-0.528805\pi\) |
0.817297 | + | 0.576216i | \(0.195471\pi\) | |||||||
\(158\) | −6.13005 | − | 3.53919i | −0.487681 | − | 0.281563i | ||||
\(159\) | 12.5103 | 0.992128 | ||||||||
\(160\) | 2.17009 | − | 0.539189i | 0.171560 | − | 0.0426266i | ||||
\(161\) | −14.9849 | + | 25.9546i | −1.18098 | + | 2.04551i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | 16.7792i | 1.31425i | 0.753781 | + | 0.657126i | \(0.228228\pi\) | ||||
−0.753781 | + | 0.657126i | \(0.771772\pi\) | |||||||
\(164\) | 11.9288 | 0.931484 | ||||||||
\(165\) | −2.06453 | + | 7.17785i | −0.160724 | + | 0.558795i | ||||
\(166\) | 2.34017 | + | 4.05330i | 0.181633 | + | 0.314597i | ||||
\(167\) | −10.0496 | − | 5.80212i | −0.777659 | − | 0.448981i | 0.0579413 | − | 0.998320i | \(-0.481546\pi\) |
−0.835600 | + | 0.549339i | \(0.814880\pi\) | |||||||
\(168\) | −3.06503 | + | 1.76959i | −0.236472 | + | 0.136527i | ||||
\(169\) | −5.03919 | − | 8.72813i | −0.387630 | − | 0.671395i | ||||
\(170\) | 2.04945 | + | 8.24846i | 0.157186 | + | 0.632628i | ||||
\(171\) | −2.94635 | − | 3.21233i | −0.225313 | − | 0.245653i | ||||
\(172\) | − | 5.07838i | − | 0.387223i | ||||||
\(173\) | 7.70752 | − | 4.44994i | 0.585992 | − | 0.338323i | −0.177519 | − | 0.984117i | \(-0.556807\pi\) |
0.763511 | + | 0.645795i | \(0.223474\pi\) | |||||||
\(174\) | 3.97887 | + | 6.89160i | 0.301637 | + | 0.522451i | ||||
\(175\) | −17.6841 | − | 0.646348i | −1.33680 | − | 0.0488593i | ||||
\(176\) | −1.67009 | − | 2.89267i | −0.125888 | − | 0.218044i | ||||
\(177\) | 5.08013 | + | 2.93302i | 0.381846 | + | 0.220459i | ||||
\(178\) | − | 9.32457i | − | 0.698906i | ||||||
\(179\) | −21.8599 | −1.63388 | −0.816942 | − | 0.576719i | \(-0.804333\pi\) | ||||
−0.816942 | + | 0.576719i | \(0.804333\pi\) | |||||||
\(180\) | 2.14894 | + | 0.618092i | 0.160173 | + | 0.0460699i | ||||
\(181\) | 2.66342 | − | 4.61318i | 0.197971 | − | 0.342895i | −0.749900 | − | 0.661551i | \(-0.769898\pi\) |
0.947870 | + | 0.318656i | \(0.103232\pi\) | |||||||
\(182\) | − | 6.04945i | − | 0.448415i | ||||||
\(183\) | 13.8504i | 1.02385i | ||||||||
\(184\) | −4.23400 | + | 7.33350i | −0.312135 | + | 0.540633i | ||||
\(185\) | −7.30877 | − | 7.58078i | −0.537351 | − | 0.557350i | ||||
\(186\) | 0.539189 | − | 0.933903i | 0.0395352 | − | 0.0684771i | ||||
\(187\) | 10.9950 | − | 6.34797i | 0.804035 | − | 0.464210i | ||||
\(188\) | −4.73543 | + | 2.73400i | −0.345366 | + | 0.199397i | ||||
\(189\) | −3.53919 | −0.257438 | ||||||||
\(190\) | 8.12588 | + | 5.38239i | 0.589513 | + | 0.390480i | ||||
\(191\) | 8.99386 | 0.650773 | 0.325386 | − | 0.945581i | \(-0.394506\pi\) | ||||
0.325386 | + | 0.945581i | \(0.394506\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −2.02042 | + | 1.16649i | −0.145433 | + | 0.0839660i | −0.570951 | − | 0.820984i | \(-0.693425\pi\) |
0.425518 | + | 0.904950i | \(0.360092\pi\) | |||||||
\(194\) | −2.92522 | + | 5.06662i | −0.210018 | + | 0.363762i | ||||
\(195\) | −2.75152 | + | 2.65279i | −0.197040 | + | 0.189970i | ||||
\(196\) | −2.76293 | + | 4.78553i | −0.197352 | + | 0.341824i | ||||
\(197\) | 24.0856i | 1.71603i | 0.513628 | + | 0.858013i | \(0.328301\pi\) | ||||
−0.513628 | + | 0.858013i | \(0.671699\pi\) | |||||||
\(198\) | − | 3.34017i | − | 0.237376i | ||||||
\(199\) | 0.652028 | − | 1.12935i | 0.0462210 | − | 0.0800572i | −0.841989 | − | 0.539494i | \(-0.818615\pi\) |
0.888210 | + | 0.459437i | \(0.151949\pi\) | |||||||
\(200\) | −4.99666 | − | 0.182626i | −0.353317 | − | 0.0129136i | ||||
\(201\) | −9.03612 | −0.637359 | ||||||||
\(202\) | − | 8.65368i | − | 0.608871i | ||||||
\(203\) | 24.3907 | + | 14.0820i | 1.71189 | + | 0.988361i | ||||
\(204\) | −1.90049 | − | 3.29175i | −0.133061 | − | 0.230469i | ||||
\(205\) | −25.6344 | − | 7.37310i | −1.79038 | − | 0.514960i | ||||
\(206\) | 0.375768 | + | 0.650849i | 0.0261810 | + | 0.0453468i | ||||
\(207\) | −7.33350 | + | 4.23400i | −0.509714 | + | 0.294283i | ||||
\(208\) | − | 1.70928i | − | 0.118517i | ||||||
\(209\) | 4.37156 | − | 13.8877i | 0.302387 | − | 0.960631i | ||||
\(210\) | 7.68035 | − | 1.90829i | 0.529994 | − | 0.131685i | ||||
\(211\) | −3.49220 | − | 6.04867i | −0.240413 | − | 0.416408i | 0.720419 | − | 0.693539i | \(-0.243950\pi\) |
−0.960832 | + | 0.277132i | \(0.910616\pi\) | |||||||
\(212\) | 10.8342 | − | 6.25513i | 0.744096 | − | 0.429604i | ||||
\(213\) | 7.00763 | + | 4.04585i | 0.480155 | + | 0.277217i | ||||
\(214\) | 4.91189 | + | 8.50763i | 0.335770 | + | 0.581570i | ||||
\(215\) | −3.13890 | + | 10.9132i | −0.214072 | + | 0.744271i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − | 3.81658i | − | 0.259087i | ||||||
\(218\) | −6.79867 | − | 3.92522i | −0.460464 | − | 0.265849i | ||||
\(219\) | −2.95415 | + | 5.11673i | −0.199623 | + | 0.345757i | ||||
\(220\) | 1.80098 | + | 7.24846i | 0.121422 | + | 0.488691i | ||||
\(221\) | 6.49693 | 0.437031 | ||||||||
\(222\) | 4.07835 | + | 2.35464i | 0.273721 | + | 0.158033i | ||||
\(223\) | 8.67180 | − | 5.00667i | 0.580707 | − | 0.335271i | −0.180708 | − | 0.983537i | \(-0.557839\pi\) |
0.761414 | + | 0.648266i | \(0.224505\pi\) | |||||||
\(224\) | −1.76959 | + | 3.06503i | −0.118236 | + | 0.204791i | ||||
\(225\) | −4.23592 | − | 2.65649i | −0.282395 | − | 0.177099i | ||||
\(226\) | 3.99220 | + | 6.91469i | 0.265557 | + | 0.459959i | ||||
\(227\) | − | 14.2485i | − | 0.945704i | −0.881142 | − | 0.472852i | \(-0.843225\pi\) | ||
0.881142 | − | 0.472852i | \(-0.156775\pi\) | |||||||
\(228\) | −4.15777 | − | 1.30878i | −0.275355 | − | 0.0866763i | ||||
\(229\) | 15.8576 | 1.04790 | 0.523951 | − | 0.851749i | \(-0.324458\pi\) | ||||
0.523951 | + | 0.851749i | \(0.324458\pi\) | |||||||
\(230\) | 13.6314 | − | 13.1423i | 0.898828 | − | 0.866577i | ||||
\(231\) | −5.91075 | − | 10.2377i | −0.388899 | − | 0.673593i | ||||
\(232\) | 6.89160 | + | 3.97887i | 0.452456 | + | 0.261226i | ||||
\(233\) | 21.3006 | − | 12.2979i | 1.39545 | − | 0.805663i | 0.401538 | − | 0.915843i | \(-0.368476\pi\) |
0.993912 | + | 0.110179i | \(0.0351426\pi\) | |||||||
\(234\) | 0.854638 | − | 1.48028i | 0.0558694 | − | 0.0967687i | ||||
\(235\) | 11.8660 | − | 2.94828i | 0.774055 | − | 0.192325i | ||||
\(236\) | 5.86603 | 0.381846 | ||||||||
\(237\) | −6.13005 | − | 3.53919i | −0.398190 | − | 0.229895i | ||||
\(238\) | −11.6501 | − | 6.72620i | −0.755165 | − | 0.435995i | ||||
\(239\) | −0.156755 | −0.0101397 | −0.00506983 | − | 0.999987i | \(-0.501614\pi\) | ||||
−0.00506983 | + | 0.999987i | \(0.501614\pi\) | |||||||
\(240\) | 2.17009 | − | 0.539189i | 0.140078 | − | 0.0348045i | ||||
\(241\) | 12.7968 | − | 22.1647i | 0.824313 | − | 1.42775i | −0.0781302 | − | 0.996943i | \(-0.524895\pi\) |
0.902443 | − | 0.430809i | \(-0.141772\pi\) | |||||||
\(242\) | 0.135754 | − | 0.0783777i | 0.00872661 | − | 0.00503831i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 6.92522 | + | 11.9948i | 0.443342 | + | 0.767890i | ||||
\(245\) | 8.89528 | − | 8.57610i | 0.568299 | − | 0.547907i | ||||
\(246\) | 11.9288 | 0.760553 | ||||||||
\(247\) | 5.49075 | − | 5.03612i | 0.349368 | − | 0.320440i | ||||
\(248\) | − | 1.07838i | − | 0.0684771i | ||||||
\(249\) | 2.34017 | + | 4.05330i | 0.148302 | + | 0.256867i | ||||
\(250\) | 10.6247 | + | 3.48085i | 0.671963 | + | 0.220148i | ||||
\(251\) | 5.32684 | − | 9.22636i | 0.336227 | − | 0.582363i | −0.647493 | − | 0.762072i | \(-0.724182\pi\) |
0.983720 | + | 0.179709i | \(0.0575156\pi\) | |||||||
\(252\) | −3.06503 | + | 1.76959i | −0.193079 | + | 0.111474i | ||||
\(253\) | −24.4952 | − | 14.1423i | −1.54000 | − | 0.889118i | ||||
\(254\) | 18.6092 | 1.16764 | ||||||||
\(255\) | 2.04945 | + | 8.24846i | 0.128341 | + | 0.516539i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −16.7899 | − | 9.69368i | −1.04733 | − | 0.604675i | −0.125428 | − | 0.992103i | \(-0.540030\pi\) |
−0.921900 | + | 0.387428i | \(0.873364\pi\) | |||||||
\(258\) | − | 5.07838i | − | 0.316166i | ||||||
\(259\) | 16.6670 | 1.03564 | ||||||||
\(260\) | −1.05649 | + | 3.67314i | −0.0655207 | + | 0.227798i | ||||
\(261\) | 3.97887 | + | 6.89160i | 0.246286 | + | 0.426580i | ||||
\(262\) | 6.56573 | + | 3.79072i | 0.405632 | + | 0.234192i | ||||
\(263\) | −26.5877 | + | 15.3504i | −1.63947 | + | 0.946548i | −0.658454 | + | 0.752621i | \(0.728789\pi\) |
−0.981016 | + | 0.193927i | \(0.937878\pi\) | |||||||
\(264\) | −1.67009 | − | 2.89267i | −0.102787 | − | 0.178032i | ||||
\(265\) | −27.1483 | + | 6.74539i | −1.66771 | + | 0.414366i | ||||
\(266\) | −15.0597 | + | 3.34612i | −0.923370 | + | 0.205164i | ||||
\(267\) | − | 9.32457i | − | 0.570655i | ||||||
\(268\) | −7.82551 | + | 4.51806i | −0.478019 | + | 0.275984i | ||||
\(269\) | −14.1334 | − | 24.4797i | −0.861726 | − | 1.49255i | −0.870262 | − | 0.492590i | \(-0.836050\pi\) |
0.00853563 | − | 0.999964i | \(-0.497283\pi\) | |||||||
\(270\) | 2.14894 | + | 0.618092i | 0.130781 | + | 0.0376159i | ||||
\(271\) | 5.80817 | + | 10.0600i | 0.352821 | + | 0.611104i | 0.986743 | − | 0.162293i | \(-0.0518890\pi\) |
−0.633921 | + | 0.773398i | \(0.718556\pi\) | |||||||
\(272\) | −3.29175 | − | 1.90049i | −0.199592 | − | 0.115234i | ||||
\(273\) | − | 6.04945i | − | 0.366129i | ||||||
\(274\) | −11.4186 | −0.689820 | ||||||||
\(275\) | 0.610003 | − | 16.6897i | 0.0367846 | − | 1.00643i | ||||
\(276\) | −4.23400 | + | 7.33350i | −0.254857 | + | 0.441425i | ||||
\(277\) | 26.1750i | 1.57270i | 0.617779 | + | 0.786352i | \(0.288033\pi\) | ||||
−0.617779 | + | 0.786352i | \(0.711967\pi\) | |||||||
\(278\) | − | 3.60197i | − | 0.216032i | ||||||
\(279\) | 0.539189 | − | 0.933903i | 0.0322804 | − | 0.0559113i | ||||
\(280\) | 5.69723 | − | 5.49280i | 0.340475 | − | 0.328258i | ||||
\(281\) | −12.0139 | + | 20.8086i | −0.716686 | + | 1.24134i | 0.245619 | + | 0.969366i | \(0.421009\pi\) |
−0.962305 | + | 0.271971i | \(0.912325\pi\) | |||||||
\(282\) | −4.73543 | + | 2.73400i | −0.281991 | + | 0.162807i | ||||
\(283\) | 17.5920 | − | 10.1568i | 1.04574 | − | 0.603756i | 0.124284 | − | 0.992247i | \(-0.460337\pi\) |
0.921453 | + | 0.388490i | \(0.127003\pi\) | |||||||
\(284\) | 8.09171 | 0.480155 | ||||||||
\(285\) | 8.12588 | + | 5.38239i | 0.481335 | + | 0.318825i | ||||
\(286\) | 5.70928 | 0.337597 | ||||||||
\(287\) | 36.5621 | − | 21.1092i | 2.15819 | − | 1.24603i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −1.27626 | + | 2.21055i | −0.0750741 | + | 0.130032i | ||||
\(290\) | −12.3504 | − | 12.8100i | −0.725239 | − | 0.752230i | ||||
\(291\) | −2.92522 | + | 5.06662i | −0.171479 | + | 0.297011i | ||||
\(292\) | 5.90829i | 0.345757i | ||||||||
\(293\) | 5.32457i | 0.311065i | 0.987831 | + | 0.155532i | \(0.0497093\pi\) | ||||
−0.987831 | + | 0.155532i | \(0.950291\pi\) | |||||||
\(294\) | −2.76293 | + | 4.78553i | −0.161137 | + | 0.279098i | ||||
\(295\) | −12.6058 | − | 3.62575i | −0.733937 | − | 0.211099i | ||||
\(296\) | 4.70928 | 0.273721 | ||||||||
\(297\) | − | 3.34017i | − | 0.193816i | ||||||
\(298\) | −8.91825 | − | 5.14896i | −0.516621 | − | 0.298271i | ||||
\(299\) | −7.23707 | − | 12.5350i | −0.418531 | − | 0.724916i | ||||
\(300\) | −4.99666 | − | 0.182626i | −0.288483 | − | 0.0105439i | ||||
\(301\) | −8.98667 | − | 15.5654i | −0.517983 | − | 0.897173i | ||||
\(302\) | −4.06681 | + | 2.34797i | −0.234018 | + | 0.135111i | ||||
\(303\) | − | 8.65368i | − | 0.497141i | ||||||
\(304\) | −4.25513 | + | 0.945448i | −0.244048 | + | 0.0542251i | ||||
\(305\) | −7.46800 | − | 30.0566i | −0.427616 | − | 1.72104i | ||||
\(306\) | −1.90049 | − | 3.29175i | −0.108644 | − | 0.188177i | ||||
\(307\) | 3.18301 | − | 1.83771i | 0.181664 | − | 0.104884i | −0.406410 | − | 0.913691i | \(-0.633220\pi\) |
0.588074 | + | 0.808807i | \(0.299886\pi\) | |||||||
\(308\) | −10.2377 | − | 5.91075i | −0.583348 | − | 0.336796i | ||||
\(309\) | 0.375768 | + | 0.650849i | 0.0213767 | + | 0.0370255i | ||||
\(310\) | −0.666537 | + | 2.31737i | −0.0378567 | + | 0.131618i | ||||
\(311\) | −13.7321 | −0.778674 | −0.389337 | − | 0.921095i | \(-0.627296\pi\) | ||||
−0.389337 | + | 0.921095i | \(0.627296\pi\) | |||||||
\(312\) | − | 1.70928i | − | 0.0967687i | ||||||
\(313\) | 15.5384 | + | 8.97107i | 0.878279 | + | 0.507075i | 0.870091 | − | 0.492892i | \(-0.164060\pi\) |
0.00818874 | + | 0.999966i | \(0.497393\pi\) | |||||||
\(314\) | 5.25872 | − | 9.10838i | 0.296767 | − | 0.514015i | ||||
\(315\) | 7.68035 | − | 1.90829i | 0.432738 | − | 0.107520i | ||||
\(316\) | −7.07838 | −0.398190 | ||||||||
\(317\) | −6.35055 | − | 3.66649i | −0.356682 | − | 0.205931i | 0.310942 | − | 0.950429i | \(-0.399355\pi\) |
−0.667625 | + | 0.744498i | \(0.732689\pi\) | |||||||
\(318\) | 10.8342 | − | 6.25513i | 0.607552 | − | 0.350770i | ||||
\(319\) | −13.2901 | + | 23.0192i | −0.744103 | + | 1.28883i | ||||
\(320\) | 1.60976 | − | 1.55199i | 0.0899881 | − | 0.0867591i | ||||
\(321\) | 4.91189 | + | 8.50763i | 0.274155 | + | 0.474850i | ||||
\(322\) | 29.9698i | 1.67015i | ||||||||
\(323\) | −3.59363 | − | 16.1737i | −0.199955 | − | 0.899928i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 4.54067 | − | 7.24036i | 0.251871 | − | 0.401623i | ||||
\(326\) | 8.38962 | + | 14.5313i | 0.464658 | + | 0.804812i | ||||
\(327\) | −6.79867 | − | 3.92522i | −0.375968 | − | 0.217065i | ||||
\(328\) | 10.3307 | − | 5.96441i | 0.570415 | − | 0.329329i | ||||
\(329\) | −9.67614 | + | 16.7596i | −0.533463 | + | 0.923985i | ||||
\(330\) | 1.80098 | + | 7.24846i | 0.0991409 | + | 0.399015i | ||||
\(331\) | 21.4813 | 1.18072 | 0.590360 | − | 0.807140i | \(-0.298986\pi\) | ||||
0.590360 | + | 0.807140i | \(0.298986\pi\) | |||||||
\(332\) | 4.05330 | + | 2.34017i | 0.222454 | + | 0.128434i | ||||
\(333\) | 4.07835 | + | 2.35464i | 0.223492 | + | 0.129033i | ||||
\(334\) | −11.6042 | −0.634956 | ||||||||
\(335\) | 19.6092 | − | 4.87217i | 1.07136 | − | 0.266195i | ||||
\(336\) | −1.76959 | + | 3.06503i | −0.0965393 | + | 0.167211i | ||||
\(337\) | −17.6151 | + | 10.1701i | −0.959556 | + | 0.554000i | −0.896036 | − | 0.443981i | \(-0.853566\pi\) |
−0.0635196 | + | 0.997981i | \(0.520233\pi\) | |||||||
\(338\) | −8.72813 | − | 5.03919i | −0.474748 | − | 0.274096i | ||||
\(339\) | 3.99220 | + | 6.91469i | 0.216827 | + | 0.375555i | ||||
\(340\) | 5.89911 | + | 6.11866i | 0.319924 | + | 0.331831i | ||||
\(341\) | 3.60197 | 0.195058 | ||||||||
\(342\) | −4.15777 | − | 1.30878i | −0.224827 | − | 0.0707709i | ||||
\(343\) | − | 5.21727i | − | 0.281706i | ||||||
\(344\) | −2.53919 | − | 4.39800i | −0.136904 | − | 0.237124i | ||||
\(345\) | 13.6314 | − | 13.1423i | 0.733890 | − | 0.707557i | ||||
\(346\) | 4.44994 | − | 7.70752i | 0.239230 | − | 0.414359i | ||||
\(347\) | −7.97084 | + | 4.60197i | −0.427897 | + | 0.247047i | −0.698450 | − | 0.715658i | \(-0.746127\pi\) |
0.270553 | + | 0.962705i | \(0.412793\pi\) | |||||||
\(348\) | 6.89160 | + | 3.97887i | 0.369429 | + | 0.213290i | ||||
\(349\) | −8.24846 | −0.441530 | −0.220765 | − | 0.975327i | \(-0.570855\pi\) | ||||
−0.220765 | + | 0.975327i | \(0.570855\pi\) | |||||||
\(350\) | −15.6381 | + | 8.28231i | −0.835891 | + | 0.442708i | ||||
\(351\) | 0.854638 | − | 1.48028i | 0.0456172 | − | 0.0790113i | ||||
\(352\) | −2.89267 | − | 1.67009i | −0.154180 | − | 0.0890159i | ||||
\(353\) | 6.24005i | 0.332125i | 0.986115 | + | 0.166062i | \(0.0531053\pi\) | ||||
−0.986115 | + | 0.166062i | \(0.946895\pi\) | |||||||
\(354\) | 5.86603 | 0.311776 | ||||||||
\(355\) | −17.3886 | − | 5.00142i | −0.922893 | − | 0.265448i | ||||
\(356\) | −4.66229 | − | 8.07532i | −0.247101 | − | 0.427991i | ||||
\(357\) | −11.6501 | − | 6.72620i | −0.616590 | − | 0.355988i | ||||
\(358\) | −18.9312 | + | 10.9299i | −1.00055 | + | 0.577665i | ||||
\(359\) | 0.401626 | + | 0.695636i | 0.0211970 | + | 0.0367143i | 0.876429 | − | 0.481531i | \(-0.159919\pi\) |
−0.855232 | + | 0.518245i | \(0.826586\pi\) | |||||||
\(360\) | 2.17009 | − | 0.539189i | 0.114374 | − | 0.0284177i | ||||
\(361\) | −15.5742 | − | 10.8833i | −0.819693 | − | 0.572803i | ||||
\(362\) | − | 5.32684i | − | 0.279973i | ||||||
\(363\) | 0.135754 | − | 0.0783777i | 0.00712525 | − | 0.00411376i | ||||
\(364\) | −3.02472 | − | 5.23898i | −0.158539 | − | 0.274597i | ||||
\(365\) | 3.65187 | − | 12.6966i | 0.191147 | − | 0.664570i | ||||
\(366\) | 6.92522 | + | 11.9948i | 0.361987 | + | 0.626980i | ||||
\(367\) | −2.54265 | − | 1.46800i | −0.132725 | − | 0.0766289i | 0.432167 | − | 0.901793i | \(-0.357749\pi\) |
−0.564892 | + | 0.825165i | \(0.691082\pi\) | |||||||
\(368\) | 8.46800i | 0.441425i | ||||||||
\(369\) | 11.9288 | 0.620989 | ||||||||
\(370\) | −10.1200 | − | 2.91077i | −0.526112 | − | 0.151323i | ||||
\(371\) | 22.1381 | − | 38.3443i | 1.14935 | − | 1.99074i | ||||
\(372\) | − | 1.07838i | − | 0.0559113i | ||||||
\(373\) | − | 25.5152i | − | 1.32113i | −0.750771 | − | 0.660563i | \(-0.770318\pi\) | ||
0.750771 | − | 0.660563i | \(-0.229682\pi\) | |||||||
\(374\) | 6.34797 | − | 10.9950i | 0.328246 | − | 0.568538i | ||||
\(375\) | 10.6247 | + | 3.48085i | 0.548656 | + | 0.179750i | ||||
\(376\) | −2.73400 | + | 4.73543i | −0.140995 | + | 0.244211i | ||||
\(377\) | −11.7797 | + | 6.80098i | −0.606683 | + | 0.350269i | ||||
\(378\) | −3.06503 | + | 1.76959i | −0.157648 | + | 0.0910181i | ||||
\(379\) | 26.6537 | 1.36911 | 0.684554 | − | 0.728962i | \(-0.259997\pi\) | ||||
0.684554 | + | 0.728962i | \(0.259997\pi\) | |||||||
\(380\) | 9.72841 | + | 0.598347i | 0.499057 | + | 0.0306946i | ||||
\(381\) | 18.6092 | 0.953376 | ||||||||
\(382\) | 7.78891 | − | 4.49693i | 0.398515 | − | 0.230083i | ||||
\(383\) | 8.35837 | − | 4.82571i | 0.427093 | − | 0.246582i | −0.271015 | − | 0.962575i | \(-0.587359\pi\) |
0.698107 | + | 0.715993i | \(0.254026\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 18.3469 | + | 19.0297i | 0.935045 | + | 0.969845i | ||||
\(386\) | −1.16649 | + | 2.02042i | −0.0593729 | + | 0.102837i | ||||
\(387\) | − | 5.07838i | − | 0.258148i | ||||||
\(388\) | 5.85043i | 0.297011i | ||||||||
\(389\) | −10.2407 | + | 17.7374i | −0.519222 | + | 0.899319i | 0.480528 | + | 0.876979i | \(0.340445\pi\) |
−0.999750 | + | 0.0223401i | \(0.992888\pi\) | |||||||
\(390\) | −1.05649 | + | 3.67314i | −0.0534974 | + | 0.185997i | ||||
\(391\) | −32.1867 | −1.62775 | ||||||||
\(392\) | 5.52586i | 0.279098i | ||||||||
\(393\) | 6.56573 | + | 3.79072i | 0.331197 | + | 0.191217i | ||||
\(394\) | 12.0428 | + | 20.8587i | 0.606707 | + | 1.05085i | ||||
\(395\) | 15.2110 | + | 4.37509i | 0.765351 | + | 0.220135i | ||||
\(396\) | −1.67009 | − | 2.89267i | −0.0839250 | − | 0.145362i | ||||
\(397\) | 0.296562 | − | 0.171220i | 0.0148840 | − | 0.00859330i | −0.492540 | − | 0.870290i | \(-0.663931\pi\) |
0.507424 | + | 0.861697i | \(0.330598\pi\) | |||||||
\(398\) | − | 1.30406i | − | 0.0653664i | ||||||
\(399\) | −15.0597 | + | 3.34612i | −0.753928 | + | 0.167515i | ||||
\(400\) | −4.41855 | + | 2.34017i | −0.220928 | + | 0.117009i | ||||
\(401\) | −4.06278 | − | 7.03694i | −0.202886 | − | 0.351408i | 0.746571 | − | 0.665305i | \(-0.231699\pi\) |
−0.949457 | + | 0.313897i | \(0.898365\pi\) | |||||||
\(402\) | −7.82551 | + | 4.51806i | −0.390301 | + | 0.225340i | ||||
\(403\) | 1.59630 | + | 0.921622i | 0.0795172 | + | 0.0459093i | ||||
\(404\) | −4.32684 | − | 7.49431i | −0.215268 | − | 0.372856i | ||||
\(405\) | 2.14894 | + | 0.618092i | 0.106782 | + | 0.0307132i | ||||
\(406\) | 28.1639 | 1.39775 | ||||||||
\(407\) | 15.7298i | 0.779697i | ||||||||
\(408\) | −3.29175 | − | 1.90049i | −0.162966 | − | 0.0940884i | ||||
\(409\) | 6.03725 | − | 10.4568i | 0.298523 | − | 0.517057i | −0.677275 | − | 0.735730i | \(-0.736839\pi\) |
0.975798 | + | 0.218673i | \(0.0701728\pi\) | |||||||
\(410\) | −25.8865 | + | 6.43188i | −1.27845 | + | 0.317648i | ||||
\(411\) | −11.4186 | −0.563236 | ||||||||
\(412\) | 0.650849 | + | 0.375768i | 0.0320650 | + | 0.0185128i | ||||
\(413\) | 17.9795 | − | 10.3805i | 0.884716 | − | 0.510791i | ||||
\(414\) | −4.23400 | + | 7.33350i | −0.208090 | + | 0.360422i | ||||
\(415\) | −7.26387 | − | 7.53421i | −0.356569 | − | 0.369840i | ||||
\(416\) | −0.854638 | − | 1.48028i | −0.0419021 | − | 0.0725765i | ||||
\(417\) | − | 3.60197i | − | 0.176389i | ||||||
\(418\) | −3.15796 | − | 14.2129i | −0.154461 | − | 0.695174i | ||||
\(419\) | 15.2290 | 0.743985 | 0.371992 | − | 0.928236i | \(-0.378675\pi\) | ||||
0.371992 | + | 0.928236i | \(0.378675\pi\) | |||||||
\(420\) | 5.69723 | − | 5.49280i | 0.277996 | − | 0.268021i | ||||
\(421\) | −4.80458 | − | 8.32177i | −0.234161 | − | 0.405578i | 0.724868 | − | 0.688888i | \(-0.241901\pi\) |
−0.959028 | + | 0.283310i | \(0.908568\pi\) | |||||||
\(422\) | −6.04867 | − | 3.49220i | −0.294445 | − | 0.169998i | ||||
\(423\) | −4.73543 | + | 2.73400i | −0.230244 | + | 0.132932i | ||||
\(424\) | 6.25513 | − | 10.8342i | 0.303776 | − | 0.526155i | ||||
\(425\) | −8.89496 | − | 16.7948i | −0.431469 | − | 0.814669i | ||||
\(426\) | 8.09171 | 0.392045 | ||||||||
\(427\) | 42.4520 | + | 24.5096i | 2.05439 | + | 1.18611i | ||||
\(428\) | 8.50763 | + | 4.91189i | 0.411232 | + | 0.237425i | ||||
\(429\) | 5.70928 | 0.275646 | ||||||||
\(430\) | 2.73820 | + | 11.0205i | 0.132048 | + | 0.531457i | ||||
\(431\) | 6.62730 | − | 11.4788i | 0.319226 | − | 0.552916i | −0.661101 | − | 0.750297i | \(-0.729910\pi\) |
0.980327 | + | 0.197381i | \(0.0632438\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 13.2965 | + | 7.67675i | 0.638990 | + | 0.368921i | 0.784225 | − | 0.620476i | \(-0.213061\pi\) |
−0.145235 | + | 0.989397i | \(0.546394\pi\) | |||||||
\(434\) | −1.90829 | − | 3.30526i | −0.0916009 | − | 0.158657i | ||||
\(435\) | −12.3504 | − | 12.8100i | −0.592155 | − | 0.614193i | ||||
\(436\) | −7.85043 | −0.375968 | ||||||||
\(437\) | −27.2020 | + | 24.9497i | −1.30125 | + | 1.19350i | ||||
\(438\) | 5.90829i | 0.282309i | ||||||||
\(439\) | 10.4263 | + | 18.0590i | 0.497623 | + | 0.861908i | 0.999996 | − | 0.00274309i | \(-0.000873154\pi\) |
−0.502374 | + | 0.864651i | \(0.667540\pi\) | |||||||
\(440\) | 5.18393 | + | 5.37686i | 0.247134 | + | 0.256332i | ||||
\(441\) | −2.76293 | + | 4.78553i | −0.131568 | + | 0.227883i | ||||
\(442\) | 5.62651 | − | 3.24846i | 0.267626 | − | 0.154514i | ||||
\(443\) | −22.0694 | − | 12.7418i | −1.04855 | − | 0.605381i | −0.126308 | − | 0.991991i | \(-0.540313\pi\) |
−0.922243 | + | 0.386610i | \(0.873646\pi\) | |||||||
\(444\) | 4.70928 | 0.223492 | ||||||||
\(445\) | 5.02771 | + | 20.2351i | 0.238336 | + | 0.959237i | ||||
\(446\) | 5.00667 | − | 8.67180i | 0.237072 | − | 0.410622i | ||||
\(447\) | −8.91825 | − | 5.14896i | −0.421819 | − | 0.243537i | ||||
\(448\) | 3.53919i | 0.167211i | ||||||||
\(449\) | 19.1412 | 0.903327 | 0.451664 | − | 0.892188i | \(-0.350831\pi\) | ||||
0.451664 | + | 0.892188i | \(0.350831\pi\) | |||||||
\(450\) | −4.99666 | − | 0.182626i | −0.235545 | − | 0.00860908i | ||||
\(451\) | 19.9221 | + | 34.5062i | 0.938097 | + | 1.62483i | ||||
\(452\) | 6.91469 | + | 3.99220i | 0.325240 | + | 0.187777i | ||||
\(453\) | −4.06681 | + | 2.34797i | −0.191075 | + | 0.110317i | ||||
\(454\) | −7.12423 | − | 12.3395i | −0.334357 | − | 0.579123i | ||||
\(455\) | 3.26180 | + | 13.1278i | 0.152915 | + | 0.615442i | ||||
\(456\) | −4.25513 | + | 0.945448i | −0.199265 | + | 0.0442746i | ||||
\(457\) | 32.0216i | 1.49791i | 0.662623 | + | 0.748953i | \(0.269443\pi\) | ||||
−0.662623 | + | 0.748953i | \(0.730557\pi\) | |||||||
\(458\) | 13.7331 | − | 7.92881i | 0.641706 | − | 0.370489i | ||||
\(459\) | −1.90049 | − | 3.29175i | −0.0887074 | − | 0.153646i | ||||
\(460\) | 5.23400 | − | 18.1973i | 0.244037 | − | 0.848452i | ||||
\(461\) | −20.6381 | − | 35.7462i | −0.961211 | − | 1.66487i | −0.719466 | − | 0.694527i | \(-0.755614\pi\) |
−0.241745 | − | 0.970340i | \(-0.577720\pi\) | |||||||
\(462\) | −10.2377 | − | 5.91075i | −0.476302 | − | 0.274993i | ||||
\(463\) | − | 8.16168i | − | 0.379305i | −0.981851 | − | 0.189653i | \(-0.939264\pi\) | ||
0.981851 | − | 0.189653i | \(-0.0607362\pi\) | |||||||
\(464\) | 7.95774 | 0.369429 | ||||||||
\(465\) | −0.666537 | + | 2.31737i | −0.0309099 | + | 0.107466i | ||||
\(466\) | 12.2979 | − | 21.3006i | 0.569690 | − | 0.986732i | ||||
\(467\) | 17.8238i | 0.824786i | 0.911006 | + | 0.412393i | \(0.135307\pi\) | ||||
−0.911006 | + | 0.412393i | \(0.864693\pi\) | |||||||
\(468\) | − | 1.70928i | − | 0.0790113i | ||||||
\(469\) | −15.9903 | + | 27.6959i | −0.738362 | + | 1.27888i | ||||
\(470\) | 8.80214 | − | 8.48630i | 0.406013 | − | 0.391444i | ||||
\(471\) | 5.25872 | − | 9.10838i | 0.242309 | − | 0.419692i | ||||
\(472\) | 5.08013 | − | 2.93302i | 0.233832 | − | 0.135003i | ||||
\(473\) | 14.6901 | − | 8.48133i | 0.675451 | − | 0.389972i | ||||
\(474\) | −7.07838 | −0.325121 | ||||||||
\(475\) | −20.5360 | − | 7.29887i | −0.942255 | − | 0.334895i | ||||
\(476\) | −13.4524 | −0.616590 | ||||||||
\(477\) | 10.8342 | − | 6.25513i | 0.496064 | − | 0.286403i | ||||
\(478\) | −0.135754 | + | 0.0783777i | −0.00620925 | + | 0.00358491i | ||||
\(479\) | −11.5694 | + | 20.0389i | −0.528621 | + | 0.915599i | 0.470822 | + | 0.882228i | \(0.343958\pi\) |
−0.999443 | + | 0.0333707i | \(0.989376\pi\) | |||||||
\(480\) | 1.60976 | − | 1.55199i | 0.0734750 | − | 0.0708385i | ||||
\(481\) | −4.02472 | + | 6.97103i | −0.183512 | + | 0.317851i | ||||
\(482\) | − | 25.5936i | − | 1.16575i | ||||||
\(483\) | 29.9698i | 1.36368i | ||||||||
\(484\) | 0.0783777 | − | 0.135754i | 0.00356262 | − | 0.00617065i | ||||
\(485\) | 3.61611 | − | 12.5723i | 0.164199 | − | 0.570877i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 10.8855i | 0.493269i | 0.969109 | + | 0.246635i | \(0.0793248\pi\) | ||||
−0.969109 | + | 0.246635i | \(0.920675\pi\) | |||||||
\(488\) | 11.9948 | + | 6.92522i | 0.542980 | + | 0.313490i | ||||
\(489\) | 8.38962 | + | 14.5313i | 0.379392 | + | 0.657126i | ||||
\(490\) | 3.41549 | − | 11.8748i | 0.154296 | − | 0.536447i | ||||
\(491\) | −15.3732 | − | 26.6272i | −0.693784 | − | 1.20167i | −0.970589 | − | 0.240743i | \(-0.922609\pi\) |
0.276805 | − | 0.960926i | \(-0.410724\pi\) | |||||||
\(492\) | 10.3307 | − | 5.96441i | 0.465742 | − | 0.268896i | ||||
\(493\) | 30.2472i | 1.36227i | ||||||||
\(494\) | 2.23707 | − | 7.10678i | 0.100651 | − | 0.319749i | ||||
\(495\) | 1.80098 | + | 7.24846i | 0.0809482 | + | 0.325794i | ||||
\(496\) | −0.539189 | − | 0.933903i | −0.0242103 | − | 0.0419335i | ||||
\(497\) | 24.8013 | − | 14.3190i | 1.11249 | − | 0.642297i | ||||
\(498\) | 4.05330 | + | 2.34017i | 0.181633 | + | 0.104866i | ||||
\(499\) | −3.29545 | − | 5.70789i | −0.147525 | − | 0.255520i | 0.782787 | − | 0.622289i | \(-0.213797\pi\) |
−0.930312 | + | 0.366769i | \(0.880464\pi\) | |||||||
\(500\) | 10.9417 | − | 2.29783i | 0.489326 | − | 0.102762i | ||||
\(501\) | −11.6042 | −0.518439 | ||||||||
\(502\) | − | 10.6537i | − | 0.475497i | ||||||
\(503\) | −11.1192 | − | 6.41968i | −0.495781 | − | 0.286240i | 0.231188 | − | 0.972909i | \(-0.425739\pi\) |
−0.726970 | + | 0.686669i | \(0.759072\pi\) | |||||||
\(504\) | −1.76959 | + | 3.06503i | −0.0788240 | + | 0.136527i | ||||
\(505\) | 4.66597 | + | 18.7792i | 0.207633 | + | 0.835665i | ||||
\(506\) | −28.2846 | −1.25740 | ||||||||
\(507\) | −8.72813 | − | 5.03919i | −0.387630 | − | 0.223798i | ||||
\(508\) | 16.1160 | − | 9.30458i | 0.715032 | − | 0.412824i | ||||
\(509\) | −11.4319 | + | 19.8006i | −0.506709 | + | 0.877646i | 0.493261 | + | 0.869882i | \(0.335805\pi\) |
−0.999970 | + | 0.00776458i | \(0.997528\pi\) | |||||||
\(510\) | 5.89911 | + | 6.11866i | 0.261217 | + | 0.270939i | ||||
\(511\) | 10.4553 | + | 18.1091i | 0.462514 | + | 0.801098i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.15777 | − | 1.30878i | −0.183570 | − | 0.0577842i | ||||
\(514\) | −19.3874 | −0.855140 | ||||||||
\(515\) | −1.16638 | − | 1.20979i | −0.0513968 | − | 0.0533097i | ||||
\(516\) | −2.53919 | − | 4.39800i | −0.111782 | − | 0.193611i | ||||
\(517\) | −15.8171 | − | 9.13203i | −0.695637 | − | 0.401626i | ||||
\(518\) | 14.4341 | − | 8.33351i | 0.634196 | − | 0.366153i | ||||
\(519\) | 4.44994 | − | 7.70752i | 0.195331 | − | 0.338323i | ||||
\(520\) | 0.921622 | + | 3.70928i | 0.0404158 | + | 0.162662i | ||||
\(521\) | 3.34632 | 0.146605 | 0.0733024 | − | 0.997310i | \(-0.476646\pi\) | ||||
0.0733024 | + | 0.997310i | \(0.476646\pi\) | |||||||
\(522\) | 6.89160 | + | 3.97887i | 0.301637 | + | 0.174150i | ||||
\(523\) | −38.8290 | − | 22.4179i | −1.69787 | − | 0.980268i | −0.947773 | − | 0.318944i | \(-0.896672\pi\) |
−0.750101 | − | 0.661324i | \(-0.769995\pi\) | |||||||
\(524\) | 7.58145 | 0.331197 | ||||||||
\(525\) | −15.6381 | + | 8.28231i | −0.682502 | + | 0.361470i | ||||
\(526\) | −15.3504 | + | 26.5877i | −0.669311 | + | 1.15928i | ||||
\(527\) | 3.54975 | − | 2.04945i | 0.154629 | − | 0.0892754i | ||||
\(528\) | −2.89267 | − | 1.67009i | −0.125888 | − | 0.0726812i | ||||
\(529\) | 24.3535 | + | 42.1815i | 1.05885 | + | 1.83398i | ||||
\(530\) | −20.1385 | + | 19.4159i | −0.874759 | + | 0.843371i | ||||
\(531\) | 5.86603 | 0.254564 | ||||||||
\(532\) | −11.3690 | + | 10.4277i | −0.492910 | + | 0.452097i | ||||
\(533\) | 20.3896i | 0.883173i | ||||||||
\(534\) | −4.66229 | − | 8.07532i | −0.201757 | − | 0.349453i | ||||
\(535\) | −15.2464 | − | 15.8139i | −0.659161 | − | 0.683693i | ||||
\(536\) | −4.51806 | + | 7.82551i | −0.195150 | + | 0.338010i | ||||
\(537\) | −18.9312 | + | 10.9299i | −0.816942 | + | 0.471662i | ||||
\(538\) | −24.4797 | − | 14.1334i | −1.05539 | − | 0.609332i | ||||
\(539\) | −18.4573 | −0.795013 | ||||||||
\(540\) | 2.17009 | − | 0.539189i | 0.0933857 | − | 0.0232030i | ||||
\(541\) | 3.98440 | − | 6.90119i | 0.171303 | − | 0.296705i | −0.767573 | − | 0.640962i | \(-0.778536\pi\) |
0.938876 | + | 0.344257i | \(0.111869\pi\) | |||||||
\(542\) | 10.0600 | + | 5.80817i | 0.432116 | + | 0.249482i | ||||
\(543\) | − | 5.32684i | − | 0.228597i | ||||||
\(544\) | −3.80098 | −0.162966 | ||||||||
\(545\) | 16.8701 | + | 4.85229i | 0.722638 | + | 0.207849i | ||||
\(546\) | −3.02472 | − | 5.23898i | −0.129446 | − | 0.224207i | ||||
\(547\) | 17.2203 | + | 9.94214i | 0.736287 | + | 0.425095i | 0.820718 | − | 0.571334i | \(-0.193574\pi\) |
−0.0844310 | + | 0.996429i | \(0.526907\pi\) | |||||||
\(548\) | −9.88875 | + | 5.70928i | −0.422427 | + | 0.243888i | ||||
\(549\) | 6.92522 | + | 11.9948i | 0.295561 | + | 0.511927i | ||||
\(550\) | −7.81658 | − | 14.7587i | −0.333300 | − | 0.629314i | ||||
\(551\) | 23.4463 | + | 25.5629i | 0.998844 | + | 1.08901i | ||||
\(552\) | 8.46800i | 0.360422i | ||||||||
\(553\) | −21.6954 | + | 12.5259i | −0.922583 | + | 0.532654i | ||||
\(554\) | 13.0875 | + | 22.6682i | 0.556035 | + | 0.963080i | ||||
\(555\) | −10.1200 | − | 2.91077i | −0.429569 | − | 0.123555i | ||||
\(556\) | −1.80098 | − | 3.11940i | −0.0763787 | − | 0.132292i | ||||
\(557\) | −17.1356 | − | 9.89322i | −0.726057 | − | 0.419189i | 0.0909212 | − | 0.995858i | \(-0.471019\pi\) |
−0.816978 | + | 0.576669i | \(0.804352\pi\) | |||||||
\(558\) | − | 1.07838i | − | 0.0456514i | ||||||
\(559\) | 8.68035 | 0.367140 | ||||||||
\(560\) | 2.18754 | − | 7.60552i | 0.0924406 | − | 0.321392i | ||||
\(561\) | 6.34797 | − | 10.9950i | 0.268012 | − | 0.464210i | ||||
\(562\) | 24.0277i | 1.01355i | ||||||||
\(563\) | 32.6681i | 1.37679i | 0.725334 | + | 0.688397i | \(0.241685\pi\) | ||||
−0.725334 | + | 0.688397i | \(0.758315\pi\) | |||||||
\(564\) | −2.73400 | + | 4.73543i | −0.115122 | + | 0.199397i | ||||
\(565\) | −12.3917 | − | 12.8529i | −0.521325 | − | 0.540727i | ||||
\(566\) | 10.1568 | − | 17.5920i | 0.426920 | − | 0.739448i | ||||
\(567\) | −3.06503 | + | 1.76959i | −0.128719 | + | 0.0743160i | ||||
\(568\) | 7.00763 | − | 4.04585i | 0.294033 | − | 0.169760i | ||||
\(569\) | −11.0650 | −0.463871 | −0.231935 | − | 0.972731i | \(-0.574506\pi\) | ||||
−0.231935 | + | 0.972731i | \(0.574506\pi\) | |||||||
\(570\) | 9.72841 | + | 0.598347i | 0.407478 | + | 0.0250620i | ||||
\(571\) | −30.4040 | −1.27237 | −0.636184 | − | 0.771538i | \(-0.719488\pi\) | ||||
−0.636184 | + | 0.771538i | \(0.719488\pi\) | |||||||
\(572\) | 4.94438 | − | 2.85464i | 0.206735 | − | 0.119358i | ||||
\(573\) | 7.78891 | − | 4.49693i | 0.325386 | − | 0.187862i | ||||
\(574\) | 21.1092 | − | 36.5621i | 0.881079 | − | 1.52607i | ||||
\(575\) | −22.4952 | + | 35.8698i | −0.938113 | + | 1.49587i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | − | 15.0010i | − | 0.624502i | −0.950000 | − | 0.312251i | \(-0.898917\pi\) | ||
0.950000 | − | 0.312251i | \(-0.101083\pi\) | |||||||
\(578\) | 2.55252i | 0.106171i | ||||||||
\(579\) | −1.16649 | + | 2.02042i | −0.0484778 | + | 0.0839660i | ||||
\(580\) | −17.1007 | − | 4.91862i | −0.710070 | − | 0.204234i | ||||
\(581\) | 16.5646 | 0.687217 | ||||||||
\(582\) | 5.85043i | 0.242508i | ||||||||
\(583\) | 36.1881 | + | 20.8932i | 1.49876 | + | 0.865309i | ||||
\(584\) | 2.95415 | + | 5.11673i | 0.122243 | + | 0.211732i | ||||
\(585\) | −1.05649 | + | 3.67314i | −0.0436805 | + | 0.151866i | ||||
\(586\) | 2.66229 | + | 4.61122i | 0.109978 | + | 0.190488i | ||||
\(587\) | −0.566107 | + | 0.326842i | −0.0233657 | + | 0.0134902i | −0.511637 | − | 0.859201i | \(-0.670961\pi\) |
0.488272 | + | 0.872692i | \(0.337628\pi\) | |||||||
\(588\) | 5.52586i | 0.227883i | ||||||||
\(589\) | 1.41136 | − | 4.48365i | 0.0581542 | − | 0.184746i | ||||
\(590\) | −12.7298 | + | 3.16290i | −0.524077 | + | 0.130214i | ||||
\(591\) | 12.0428 | + | 20.8587i | 0.495374 | + | 0.858013i | ||||
\(592\) | 4.07835 | − | 2.35464i | 0.167619 | − | 0.0967750i | ||||
\(593\) | 36.3095 | + | 20.9633i | 1.49105 | + | 0.860858i | 0.999948 | − | 0.0102432i | \(-0.00326056\pi\) |
0.491103 | + | 0.871102i | \(0.336594\pi\) | |||||||
\(594\) | −1.67009 | − | 2.89267i | −0.0685245 | − | 0.118688i | ||||
\(595\) | 28.9085 | + | 8.31482i | 1.18513 | + | 0.340874i | ||||
\(596\) | −10.2979 | −0.421819 | ||||||||
\(597\) | − | 1.30406i | − | 0.0533714i | ||||||
\(598\) | −12.5350 | − | 7.23707i | −0.512593 | − | 0.295946i | ||||
\(599\) | −8.45722 | + | 14.6483i | −0.345553 | + | 0.598515i | −0.985454 | − | 0.169942i | \(-0.945642\pi\) |
0.639901 | + | 0.768457i | \(0.278975\pi\) | |||||||
\(600\) | −4.41855 | + | 2.34017i | −0.180387 | + | 0.0955372i | ||||
\(601\) | −4.42243 | −0.180395 | −0.0901973 | − | 0.995924i | \(-0.528750\pi\) | ||||
−0.0901973 | + | 0.995924i | \(0.528750\pi\) | |||||||
\(602\) | −15.5654 | − | 8.98667i | −0.634397 | − | 0.366269i | ||||
\(603\) | −7.82551 | + | 4.51806i | −0.318679 | + | 0.183990i | ||||
\(604\) | −2.34797 | + | 4.06681i | −0.0955376 | + | 0.165476i | ||||
\(605\) | −0.252338 | + | 0.243284i | −0.0102590 | + | 0.00989089i | ||||
\(606\) | −4.32684 | − | 7.49431i | −0.175766 | − | 0.304436i | ||||
\(607\) | − | 15.6030i | − | 0.633307i | −0.948541 | − | 0.316653i | \(-0.897441\pi\) | ||
0.948541 | − | 0.316653i | \(-0.102559\pi\) | |||||||
\(608\) | −3.21233 | + | 2.94635i | −0.130277 | + | 0.119490i | ||||
\(609\) | 28.1639 | 1.14126 | ||||||||
\(610\) | −21.4958 | − | 22.2958i | −0.870339 | − | 0.902731i | ||||
\(611\) | −4.67316 | − | 8.09415i | −0.189056 | − | 0.327454i | ||||
\(612\) | −3.29175 | − | 1.90049i | −0.133061 | − | 0.0768228i | ||||
\(613\) | 3.51225 | − | 2.02780i | 0.141858 | − | 0.0819019i | −0.427391 | − | 0.904067i | \(-0.640567\pi\) |
0.569249 | + | 0.822165i | \(0.307234\pi\) | |||||||
\(614\) | 1.83771 | − | 3.18301i | 0.0741640 | − | 0.128456i | ||||
\(615\) | −25.8865 | + | 6.43188i | −1.04385 | + | 0.259359i | ||||
\(616\) | −11.8215 | −0.476302 | ||||||||
\(617\) | 17.4062 | + | 10.0494i | 0.700745 | + | 0.404576i | 0.807625 | − | 0.589696i | \(-0.200753\pi\) |
−0.106880 | + | 0.994272i | \(0.534086\pi\) | |||||||
\(618\) | 0.650849 | + | 0.375768i | 0.0261810 | + | 0.0151156i | ||||
\(619\) | 17.0917 | 0.686974 | 0.343487 | − | 0.939157i | \(-0.388392\pi\) | ||||
0.343487 | + | 0.939157i | \(0.388392\pi\) | |||||||
\(620\) | 0.581449 | + | 2.34017i | 0.0233516 | + | 0.0939836i | ||||
\(621\) | −4.23400 | + | 7.33350i | −0.169905 | + | 0.294283i | ||||
\(622\) | −11.8923 | + | 6.86603i | −0.476838 | + | 0.275303i | ||||
\(623\) | −28.5801 | − | 16.5007i | −1.14504 | − | 0.661087i | ||||
\(624\) | −0.854638 | − | 1.48028i | −0.0342129 | − | 0.0592585i | ||||
\(625\) | −24.9333 | − | 1.82504i | −0.997332 | − | 0.0730017i | ||||
\(626\) | 17.9421 | 0.717112 | ||||||||
\(627\) | −3.15796 | − | 14.2129i | −0.126117 | − | 0.567607i | ||||
\(628\) | − | 10.5174i | − | 0.419692i | ||||||
\(629\) | 8.94994 | + | 15.5018i | 0.356857 | + | 0.618095i | ||||
\(630\) | 5.69723 | − | 5.49280i | 0.226983 | − | 0.218838i | ||||
\(631\) | −5.80652 | + | 10.0572i | −0.231154 | + | 0.400370i | −0.958148 | − | 0.286274i | \(-0.907583\pi\) |
0.726994 | + | 0.686644i | \(0.240917\pi\) | |||||||
\(632\) | −6.13005 | + | 3.53919i | −0.243840 | + | 0.140781i | ||||
\(633\) | −6.04867 | − | 3.49220i | −0.240413 | − | 0.138803i | ||||
\(634\) | −7.33299 | −0.291230 | ||||||||
\(635\) | −40.3835 | + | 10.0338i | −1.60257 | + | 0.398181i | ||||
\(636\) | 6.25513 | − | 10.8342i | 0.248032 | − | 0.429604i | ||||
\(637\) | −8.17979 | − | 4.72261i | −0.324095 | − | 0.187116i | ||||
\(638\) | 26.5802i | 1.05232i | ||||||||
\(639\) | 8.09171 | 0.320103 | ||||||||
\(640\) | 0.618092 | − | 2.14894i | 0.0244322 | − | 0.0849445i | ||||
\(641\) | −3.14116 | − | 5.44064i | −0.124068 | − | 0.214893i | 0.797300 | − | 0.603583i | \(-0.206261\pi\) |
−0.921368 | + | 0.388691i | \(0.872928\pi\) | |||||||
\(642\) | 8.50763 | + | 4.91189i | 0.335770 | + | 0.193857i | ||||
\(643\) | −11.3358 | + | 6.54472i | −0.447040 | + | 0.258099i | −0.706579 | − | 0.707634i | \(-0.749763\pi\) |
0.259539 | + | 0.965733i | \(0.416429\pi\) | |||||||
\(644\) | 14.9849 | + | 25.9546i | 0.590489 | + | 1.02276i | ||||
\(645\) | 2.73820 | + | 11.0205i | 0.107817 | + | 0.433933i | ||||
\(646\) | −11.1990 | − | 12.2100i | −0.440619 | − | 0.480396i | ||||
\(647\) | − | 7.89496i | − | 0.310383i | −0.987884 | − | 0.155191i | \(-0.950401\pi\) | ||
0.987884 | − | 0.155191i | \(-0.0495994\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 9.79678 | + | 16.9685i | 0.384557 | + | 0.666073i | ||||
\(650\) | 0.312158 | − | 8.54067i | 0.0122439 | − | 0.334993i | ||||
\(651\) | −1.90829 | − | 3.30526i | −0.0747918 | − | 0.129543i | ||||
\(652\) | 14.5313 | + | 8.38962i | 0.569088 | + | 0.328563i | ||||
\(653\) | − | 36.7620i | − | 1.43861i | −0.694695 | − | 0.719305i | \(-0.744460\pi\) | ||
0.694695 | − | 0.719305i | \(-0.255540\pi\) | |||||||
\(654\) | −7.85043 | −0.306976 | ||||||||
\(655\) | −16.2921 | − | 4.68603i | −0.636586 | − | 0.183098i | ||||
\(656\) | 5.96441 | − | 10.3307i | 0.232871 | − | 0.403344i | ||||
\(657\) | 5.90829i | 0.230504i | ||||||||
\(658\) | 19.3523i | 0.754430i | ||||||||
\(659\) | −14.8805 | + | 25.7738i | −0.579662 | + | 1.00400i | 0.415856 | + | 0.909430i | \(0.363482\pi\) |
−0.995518 | + | 0.0945733i | \(0.969851\pi\) | |||||||
\(660\) | 5.18393 | + | 5.37686i | 0.201784 | + | 0.209294i | ||||
\(661\) | −2.94441 | + | 5.09987i | −0.114524 | + | 0.198362i | −0.917589 | − | 0.397529i | \(-0.869868\pi\) |
0.803065 | + | 0.595891i | \(0.203201\pi\) | |||||||
\(662\) | 18.6034 | − | 10.7407i | 0.723041 | − | 0.417448i | ||||
\(663\) | 5.62651 | − | 3.24846i | 0.218515 | − | 0.126160i | ||||
\(664\) | 4.68035 | 0.181633 | ||||||||
\(665\) | 30.8767 | − | 15.3814i | 1.19735 | − | 0.596465i | ||||
\(666\) | 4.70928 | 0.182481 | ||||||||
\(667\) | 58.3581 | − | 33.6931i | 2.25963 | − | 1.30460i | ||||
\(668\) | −10.0496 | + | 5.80212i | −0.388829 | + | 0.224491i | ||||
\(669\) | 5.00667 | − | 8.67180i | 0.193569 | − | 0.335271i | ||||
\(670\) | 14.5459 | − | 14.0240i | 0.561959 | − | 0.541795i | ||||
\(671\) | −23.1314 | + | 40.0648i | −0.892979 | + | 1.54668i | ||||
\(672\) | 3.53919i | 0.136527i | ||||||||
\(673\) | 8.96719i | 0.345660i | 0.984952 | + | 0.172830i | \(0.0552911\pi\) | ||||
−0.984952 | + | 0.172830i | \(0.944709\pi\) | |||||||
\(674\) | −10.1701 | + | 17.6151i | −0.391737 | + | 0.678509i | ||||
\(675\) | −4.99666 | − | 0.182626i | −0.192322 | − | 0.00702928i | ||||
\(676\) | −10.0784 | −0.387630 | ||||||||
\(677\) | − | 20.9721i | − | 0.806024i | −0.915195 | − | 0.403012i | \(-0.867963\pi\) | ||
0.915195 | − | 0.403012i | \(-0.132037\pi\) | |||||||
\(678\) | 6.91469 | + | 3.99220i | 0.265557 | + | 0.153320i | ||||
\(679\) | 10.3529 | + | 17.9317i | 0.397308 | + | 0.688157i | ||||
\(680\) | 8.16810 | + | 2.34936i | 0.313232 | + | 0.0900938i | ||||
\(681\) | −7.12423 | − | 12.3395i | −0.273001 | − | 0.472852i | ||||
\(682\) | 3.11940 | − | 1.80098i | 0.119448 | − | 0.0689632i | ||||
\(683\) | 7.46922i | 0.285802i | 0.989737 | + | 0.142901i | \(0.0456430\pi\) | ||||
−0.989737 | + | 0.142901i | \(0.954357\pi\) | |||||||
\(684\) | −4.25513 | + | 0.945448i | −0.162699 | + | 0.0361501i | ||||
\(685\) | 24.7792 | − | 6.15676i | 0.946766 | − | 0.235238i | ||||
\(686\) | −2.60863 | − | 4.51829i | −0.0995981 | − | 0.172509i | ||||
\(687\) | 13.7331 | − | 7.92881i | 0.523951 | − | 0.302503i | ||||
\(688\) | −4.39800 | − | 2.53919i | −0.167672 | − | 0.0968057i | ||||
\(689\) | 10.6917 | + | 18.5186i | 0.407323 | + | 0.705504i | ||||
\(690\) | 5.23400 | − | 18.1973i | 0.199255 | − | 0.692758i | ||||
\(691\) | 4.35804 | 0.165788 | 0.0828938 | − | 0.996558i | \(-0.473584\pi\) | ||||
0.0828938 | + | 0.996558i | \(0.473584\pi\) | |||||||
\(692\) | − | 8.89988i | − | 0.338323i | ||||||
\(693\) | −10.2377 | − | 5.91075i | −0.388899 | − | 0.224531i | ||||
\(694\) | −4.60197 | + | 7.97084i | −0.174688 | + | 0.302569i | ||||
\(695\) | 1.94214 | + | 7.81658i | 0.0736696 | + | 0.296500i | ||||
\(696\) | 7.95774 | 0.301637 | ||||||||
\(697\) | 39.2666 | + | 22.6706i | 1.48733 | + | 0.858711i | ||||
\(698\) | −7.14338 | + | 4.12423i | −0.270381 | + | 0.156104i | ||||
\(699\) | 12.2979 | − | 21.3006i | 0.465150 | − | 0.805663i | ||||
\(700\) | −9.40182 | + | 14.9917i | −0.355355 | + | 0.566634i | ||||
\(701\) | 10.1990 | + | 17.6652i | 0.385212 | + | 0.667206i | 0.991799 | − | 0.127811i | \(-0.0407952\pi\) |
−0.606587 | + | 0.795017i | \(0.707462\pi\) | |||||||
\(702\) | − | 1.70928i | − | 0.0645124i | ||||||
\(703\) | 19.5801 | + | 6.16342i | 0.738478 | + | 0.232458i | ||||
\(704\) | −3.34017 | −0.125888 | ||||||||
\(705\) | 8.80214 | − | 8.48630i | 0.331508 | − | 0.319613i | ||||
\(706\) | 3.12003 | + | 5.40405i | 0.117424 | + | 0.203384i | ||||
\(707\) | −26.5238 | − | 15.3135i | −0.997529 | − | 0.575924i | ||||
\(708\) | 5.08013 | − | 2.93302i | 0.190923 | − | 0.110229i | ||||
\(709\) | 14.4377 | − | 25.0069i | 0.542221 | − | 0.939154i | −0.456555 | − | 0.889695i | \(-0.650917\pi\) |
0.998776 | − | 0.0494590i | \(-0.0157497\pi\) | |||||||
\(710\) | −17.5597 | + | 4.36296i | −0.659004 | + | 0.163739i | ||||
\(711\) | −7.07838 | −0.265460 | ||||||||
\(712\) | −8.07532 | − | 4.66229i | −0.302635 | − | 0.174727i | ||||
\(713\) | −7.90829 | − | 4.56585i | −0.296168 | − | 0.170992i | ||||
\(714\) | −13.4524 | −0.503443 | ||||||||
\(715\) | −12.3896 | + | 3.07838i | −0.463346 | + | 0.115125i | ||||
\(716\) | −10.9299 | + | 18.9312i | −0.408471 | + | 0.707493i | ||||
\(717\) | −0.135754 | + | 0.0783777i | −0.00506983 | + | 0.00292707i | ||||
\(718\) | 0.695636 | + | 0.401626i | 0.0259609 | + | 0.0149885i | ||||
\(719\) | −18.1701 | − | 31.4715i | −0.677630 | − | 1.17369i | −0.975693 | − | 0.219143i | \(-0.929674\pi\) |
0.298063 | − | 0.954546i | \(-0.403660\pi\) | |||||||
\(720\) | 1.60976 | − | 1.55199i | 0.0599920 | − | 0.0578394i | ||||
\(721\) | 2.65983 | 0.0990571 | ||||||||
\(722\) | −18.9293 | − | 1.63809i | −0.704474 | − | 0.0609632i | ||||
\(723\) | − | 25.5936i | − | 0.951835i | ||||||
\(724\) | −2.66342 | − | 4.61318i | −0.0989853 | − | 0.171448i | ||||
\(725\) | 33.7084 | + | 21.1397i | 1.25190 | + | 0.785107i | ||||
\(726\) | 0.0783777 | − | 0.135754i | 0.00290887 | − | 0.00503831i | ||||
\(727\) | 25.7020 | − | 14.8390i | 0.953233 | − | 0.550350i | 0.0591495 | − | 0.998249i | \(-0.481161\pi\) |
0.894084 | + | 0.447900i | \(0.147828\pi\) | |||||||
\(728\) | −5.23898 | − | 3.02472i | −0.194169 | − | 0.112104i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.18568 | − | 12.8215i | −0.117907 | − | 0.474545i | ||||
\(731\) | 9.65142 | − | 16.7167i | 0.356971 | − | 0.618291i | ||||
\(732\) | 11.9948 | + | 6.92522i | 0.443342 | + | 0.255963i | ||||
\(733\) | − | 29.8248i | − | 1.10160i | −0.834636 | − | 0.550802i | \(-0.814322\pi\) | ||
0.834636 | − | 0.550802i | \(-0.185678\pi\) | |||||||
\(734\) | −2.93600 | −0.108370 | ||||||||
\(735\) | 3.41549 | − | 11.8748i | 0.125982 | − | 0.438007i | ||||
\(736\) | 4.23400 | + | 7.33350i | 0.156067 | + | 0.270316i | ||||
\(737\) | −26.1385 | − | 15.0911i | −0.962826 | − | 0.555888i | ||||
\(738\) | 10.3307 | − | 5.96441i | 0.380277 | − | 0.219553i | ||||
\(739\) | −26.6737 | − | 46.2002i | −0.981207 | − | 1.69950i | −0.657709 | − | 0.753272i | \(-0.728474\pi\) |
−0.323498 | − | 0.946229i | \(-0.604859\pi\) | |||||||
\(740\) | −10.2195 | + | 2.53919i | −0.375678 | + | 0.0933424i | ||||
\(741\) | 2.23707 | − | 7.10678i | 0.0821809 | − | 0.261074i | ||||
\(742\) | − | 44.2762i | − | 1.62543i | ||||||
\(743\) | −7.56947 | + | 4.37024i | −0.277697 | + | 0.160328i | −0.632380 | − | 0.774658i | \(-0.717922\pi\) |
0.354683 | + | 0.934986i | \(0.384589\pi\) | |||||||
\(744\) | −0.539189 | − | 0.933903i | −0.0197676 | − | 0.0342385i | ||||
\(745\) | 22.1296 | + | 6.36506i | 0.810767 | + | 0.233198i | ||||
\(746\) | −12.7576 | − | 22.0968i | −0.467089 | − | 0.809021i | ||||
\(747\) | 4.05330 | + | 2.34017i | 0.148302 | + | 0.0856225i | ||||
\(748\) | − | 12.6959i | − | 0.464210i | ||||||
\(749\) | 34.7682 | 1.27040 | ||||||||
\(750\) | 10.9417 | − | 2.29783i | 0.399533 | − | 0.0839049i | ||||
\(751\) | −19.4101 | + | 33.6193i | −0.708286 | + | 1.22679i | 0.257206 | + | 0.966356i | \(0.417198\pi\) |
−0.965492 | + | 0.260431i | \(0.916135\pi\) | |||||||
\(752\) | 5.46800i | 0.199397i | ||||||||
\(753\) | − | 10.6537i | − | 0.388242i | ||||||
\(754\) | −6.80098 | + | 11.7797i | −0.247677 | + | 0.428990i | ||||
\(755\) | 7.55932 | − | 7.28808i | 0.275112 | − | 0.265240i | ||||
\(756\) | −1.76959 | + | 3.06503i | −0.0643595 | + | 0.111474i | ||||
\(757\) | −44.1922 | + | 25.5144i | −1.60619 | + | 0.927336i | −0.615981 | + | 0.787761i | \(0.711240\pi\) |
−0.990212 | + | 0.139575i | \(0.955426\pi\) | |||||||
\(758\) | 23.0828 | − | 13.3268i | 0.838404 | − | 0.484053i | ||||
\(759\) | −28.2846 | −1.02667 | ||||||||
\(760\) | 8.72422 | − | 4.34602i | 0.316461 | − | 0.157647i | ||||
\(761\) | −24.2546 | −0.879229 | −0.439614 | − | 0.898187i | \(-0.644885\pi\) | ||||
−0.439614 | + | 0.898187i | \(0.644885\pi\) | |||||||
\(762\) | 16.1160 | − | 9.30458i | 0.583821 | − | 0.337069i | ||||
\(763\) | −24.0618 | + | 13.8921i | −0.871095 | + | 0.502927i | ||||
\(764\) | 4.49693 | − | 7.78891i | 0.162693 | − | 0.281793i | ||||
\(765\) | 5.89911 | + | 6.11866i | 0.213283 | + | 0.221220i | ||||
\(766\) | 4.82571 | − | 8.35837i | 0.174360 | − | 0.302000i | ||||
\(767\) | 10.0267i | 0.362042i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 8.02472 | − | 13.8992i | 0.289379 | − | 0.501219i | −0.684283 | − | 0.729217i | \(-0.739885\pi\) |
0.973662 | + | 0.227998i | \(0.0732179\pi\) | |||||||
\(770\) | 25.4038 | + | 7.30678i | 0.915488 | + | 0.263318i | ||||
\(771\) | −19.3874 | −0.698218 | ||||||||
\(772\) | 2.33299i | 0.0839660i | ||||||||
\(773\) | 6.20751 | + | 3.58391i | 0.223269 | + | 0.128904i | 0.607463 | − | 0.794348i | \(-0.292187\pi\) |
−0.384194 | + | 0.923252i | \(0.625521\pi\) | |||||||
\(774\) | −2.53919 | − | 4.39800i | −0.0912693 | − | 0.158083i | ||||
\(775\) | 0.196940 | − | 5.38829i | 0.00707429 | − | 0.193553i | ||||
\(776\) | 2.92522 | + | 5.06662i | 0.105009 | + | 0.181881i | ||||
\(777\) | 14.4341 | − | 8.33351i | 0.517819 | − | 0.298963i | ||||
\(778\) | 20.4813i | 0.734291i | ||||||||
\(779\) | 50.7586 | − | 11.2781i | 1.81862 | − | 0.404079i | ||||
\(780\) | 0.921622 | + | 3.70928i | 0.0329994 | + | 0.132813i | ||||
\(781\) | 13.5139 | + | 23.4067i | 0.483564 | + | 0.837557i | ||||
\(782\) | −27.8745 | + | 16.0934i | −0.996791 | + | 0.575498i | ||||
\(783\) | 6.89160 | + | 3.97887i | 0.246286 | + | 0.142193i | ||||
\(784\) | 2.76293 | + | 4.78553i | 0.0986760 | + | 0.170912i | ||||
\(785\) | −6.50075 | + | 22.6014i | −0.232022 | + | 0.806679i | ||||
\(786\) | 7.58145 | 0.270421 | ||||||||
\(787\) | − | 14.1001i | − | 0.502615i | −0.967907 | − | 0.251307i | \(-0.919139\pi\) | ||
0.967907 | − | 0.251307i | \(-0.0808605\pi\) | |||||||
\(788\) | 20.8587 | + | 12.0428i | 0.743061 | + | 0.429006i | ||||
\(789\) | −15.3504 | + | 26.5877i | −0.546490 | + | 0.946548i | ||||
\(790\) | 15.3607 | − | 3.81658i | 0.546509 | − | 0.135788i | ||||
\(791\) | 28.2583 | 1.00475 | ||||||||
\(792\) | −2.89267 | − | 1.67009i | −0.102787 | − | 0.0593439i | ||||
\(793\) | −20.5025 | + | 11.8371i | −0.728064 | + | 0.420348i | ||||
\(794\) | 0.171220 | − | 0.296562i | 0.00607638 | − | 0.0105246i | ||||
\(795\) | −20.1385 | + | 19.4159i | −0.714238 | + | 0.688609i | ||||
\(796\) | −0.652028 | − | 1.12935i | −0.0231105 | − | 0.0400286i | ||||
\(797\) | − | 11.3102i | − | 0.400628i | −0.979732 | − | 0.200314i | \(-0.935804\pi\) | ||
0.979732 | − | 0.200314i | \(-0.0641962\pi\) | |||||||
\(798\) | −11.3690 | + | 10.4277i | −0.402459 | + | 0.369136i | ||||
\(799\) | −20.7838 | −0.735277 | ||||||||
\(800\) | −2.65649 | + | 4.23592i | −0.0939211 | + | 0.149763i | ||||
\(801\) | −4.66229 | − | 8.07532i | −0.164734 | − | 0.285327i | ||||
\(802\) | −7.03694 | − | 4.06278i | −0.248483 | − | 0.143462i | ||||
\(803\) | −17.0908 | + | 9.86736i | −0.603120 | + | 0.348211i | ||||
\(804\) | −4.51806 | + | 7.82551i | −0.159340 | + | 0.275984i | ||||
\(805\) | −16.1594 | − | 65.0372i | −0.569544 | − | 2.29226i | ||||
\(806\) | 1.84324 | 0.0649255 | ||||||||
\(807\) | −24.4797 | − | 14.1334i | −0.861726 | − | 0.497518i | ||||
\(808\) | −7.49431 | − | 4.32684i | −0.263649 | − | 0.152218i | ||||
\(809\) | 22.9132 | 0.805586 | 0.402793 | − | 0.915291i | \(-0.368040\pi\) | ||||
0.402793 | + | 0.915291i | \(0.368040\pi\) | |||||||
\(810\) | 2.17009 | − | 0.539189i | 0.0762491 | − | 0.0189452i | ||||
\(811\) | 14.1140 | − | 24.4461i | 0.495609 | − | 0.858419i | −0.504379 | − | 0.863483i | \(-0.668278\pi\) |
0.999987 | + | 0.00506334i | \(0.00161172\pi\) | |||||||
\(812\) | 24.3907 | − | 14.0820i | 0.855945 | − | 0.494180i | ||||
\(813\) | 10.0600 | + | 5.80817i | 0.352821 | + | 0.203701i | ||||
\(814\) | 7.86490 | + | 13.6224i | 0.275665 | + | 0.477465i | ||||
\(815\) | −26.0413 | − | 27.0105i | −0.912187 | − | 0.946136i | ||||
\(816\) | −3.80098 | −0.133061 | ||||||||
\(817\) | −4.80134 | − | 21.6092i | −0.167978 | − | 0.756009i | ||||
\(818\) | − | 12.0745i | − | 0.422175i | ||||||
\(819\) | −3.02472 | − | 5.23898i | −0.105692 | − | 0.183065i | ||||
\(820\) | −19.2025 | + | 18.5134i | −0.670579 | + | 0.646518i | ||||
\(821\) | −23.0856 | + | 39.9854i | −0.805692 | + | 1.39550i | 0.110131 | + | 0.993917i | \(0.464873\pi\) |
−0.915823 | + | 0.401582i | \(0.868460\pi\) | |||||||
\(822\) | −9.88875 | + | 5.70928i | −0.344910 | + | 0.199134i | ||||
\(823\) | 4.05420 | + | 2.34070i | 0.141321 | + | 0.0815915i | 0.568993 | − | 0.822342i | \(-0.307333\pi\) |
−0.427673 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(824\) | 0.751536 | 0.0261810 | ||||||||
\(825\) | −7.81658 | − | 14.7587i | −0.272138 | − | 0.513833i | ||||
\(826\) | 10.3805 | − | 17.9795i | 0.361184 | − | 0.625588i | ||||
\(827\) | −19.7336 | − | 11.3932i | −0.686205 | − | 0.396181i | 0.115983 | − | 0.993251i | \(-0.462998\pi\) |
−0.802189 | + | 0.597070i | \(0.796331\pi\) | |||||||
\(828\) | 8.46800i | 0.294283i | ||||||||
\(829\) | 5.39189 | 0.187268 | 0.0936340 | − | 0.995607i | \(-0.470152\pi\) | ||||
0.0936340 | + | 0.995607i | \(0.470152\pi\) | |||||||
\(830\) | −10.0578 | − | 2.89288i | −0.349111 | − | 0.100413i | ||||
\(831\) | 13.0875 | + | 22.6682i | 0.454000 | + | 0.786352i | ||||
\(832\) | −1.48028 | − | 0.854638i | −0.0513193 | − | 0.0296292i | ||||
\(833\) | −18.1897 | + | 10.5018i | −0.630237 | + | 0.363868i | ||||
\(834\) | −1.80098 | − | 3.11940i | −0.0623630 | − | 0.108016i | ||||
\(835\) | 25.1822 | − | 6.25687i | 0.871466 | − | 0.216528i | ||||
\(836\) | −9.84131 | − | 10.7297i | −0.340369 | − | 0.371095i | ||||
\(837\) | − | 1.07838i | − | 0.0372742i | ||||||
\(838\) | 13.1887 | − | 7.61450i | 0.455596 | − | 0.263038i | ||||
\(839\) | 20.8732 | + | 36.1535i | 0.720624 | + | 1.24816i | 0.960750 | + | 0.277415i | \(0.0894777\pi\) |
−0.240127 | + | 0.970742i | \(0.577189\pi\) | |||||||
\(840\) | 2.18754 | − | 7.60552i | 0.0754774 | − | 0.262415i | ||||
\(841\) | −17.1628 | − | 29.7269i | −0.591821 | − | 1.02506i | ||||
\(842\) | −8.32177 | − | 4.80458i | −0.286787 | − | 0.165577i | ||||
\(843\) | 24.0277i | 0.827558i | ||||||||
\(844\) | −6.98440 | −0.240413 | ||||||||
\(845\) | 21.6579 | + | 6.22936i | 0.745054 | + | 0.214297i | ||||
\(846\) | −2.73400 | + | 4.73543i | −0.0939968 | + | 0.162807i | ||||
\(847\) | − | 0.554787i | − | 0.0190627i | ||||||
\(848\) | − | 12.5103i | − | 0.429604i | ||||||
\(849\) | 10.1568 | − | 17.5920i | 0.348579 | − | 0.603756i | ||||
\(850\) | −16.1007 | − | 10.0973i | −0.552249 | − | 0.346334i | ||||
\(851\) | 19.9391 | − | 34.5355i | 0.683503 | − | 1.18386i | ||||
\(852\) | 7.00763 | − | 4.04585i | 0.240077 | − | 0.138609i | ||||
\(853\) | 26.5700 | − | 15.3402i | 0.909738 | − | 0.525238i | 0.0293912 | − | 0.999568i | \(-0.490643\pi\) |
0.880347 | + | 0.474330i | \(0.157310\pi\) | |||||||
\(854\) | 49.0193 | 1.67741 | ||||||||
\(855\) | 9.72841 | + | 0.598347i | 0.332705 | + | 0.0204630i | ||||
\(856\) | 9.82377 | 0.335770 | ||||||||
\(857\) | −36.7427 | + | 21.2134i | −1.25511 | + | 0.724636i | −0.972119 | − | 0.234488i | \(-0.924659\pi\) |
−0.282987 | + | 0.959124i | \(0.591325\pi\) | |||||||
\(858\) | 4.94438 | − | 2.85464i | 0.168798 | − | 0.0974557i | ||||
\(859\) | −19.5983 | + | 33.9452i | −0.668685 | + | 1.15820i | 0.309587 | + | 0.950871i | \(0.399809\pi\) |
−0.978272 | + | 0.207325i | \(0.933524\pi\) | |||||||
\(860\) | 7.88161 | + | 8.17495i | 0.268761 | + | 0.278763i | ||||
\(861\) | 21.1092 | − | 36.5621i | 0.719398 | − | 1.24603i | ||||
\(862\) | − | 13.2546i | − | 0.451454i | ||||||
\(863\) | − | 30.9565i | − | 1.05377i | −0.849936 | − | 0.526886i | \(-0.823359\pi\) | ||
0.849936 | − | 0.526886i | \(-0.176641\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −5.50094 | + | 19.1253i | −0.187038 | + | 0.650281i | ||||
\(866\) | 15.3535 | 0.521733 | ||||||||
\(867\) | 2.55252i | 0.0866881i | ||||||||
\(868\) | −3.30526 | − | 1.90829i | −0.112188 | − | 0.0647716i | ||||
\(869\) | −11.8215 | − | 20.4754i | −0.401017 | − | 0.694582i | ||||
\(870\) | −17.1007 | − | 4.91862i | −0.579769 | − | 0.166757i | ||||
\(871\) | −7.72261 | − | 13.3759i | −0.261671 | − | 0.453227i | ||||
\(872\) | −6.79867 | + | 3.92522i | −0.230232 | + | 0.132925i | ||||
\(873\) | 5.85043i | 0.198007i | ||||||||
\(874\) | −11.0828 | + | 35.2080i | −0.374880 | + | 1.19093i | ||||
\(875\) | 29.4703 | − | 26.4052i | 0.996277 | − | 0.892659i | ||||
\(876\) | 2.95415 | + | 5.11673i | 0.0998113 | + | 0.172878i | ||||
\(877\) | −10.3903 | + | 5.99887i | −0.350857 | + | 0.202567i | −0.665063 | − | 0.746788i | \(-0.731595\pi\) |
0.314206 | + | 0.949355i | \(0.398262\pi\) | |||||||
\(878\) | 18.0590 | + | 10.4263i | 0.609461 | + | 0.351872i | ||||
\(879\) | 2.66229 | + | 4.61122i | 0.0897967 | + | 0.155532i | ||||
\(880\) | 7.17785 | + | 2.06453i | 0.241965 | + | 0.0695954i | ||||
\(881\) | −5.79872 | −0.195364 | −0.0976819 | − | 0.995218i | \(-0.531143\pi\) | ||||
−0.0976819 | + | 0.995218i | \(0.531143\pi\) | |||||||
\(882\) | 5.52586i | 0.186065i | ||||||||
\(883\) | 24.0657 | + | 13.8943i | 0.809876 | + | 0.467582i | 0.846913 | − | 0.531732i | \(-0.178459\pi\) |
−0.0370369 | + | 0.999314i | \(0.511792\pi\) | |||||||
\(884\) | 3.24846 | − | 5.62651i | 0.109258 | − | 0.189240i | ||||
\(885\) | −12.7298 | + | 3.16290i | −0.427907 | + | 0.106320i | ||||
\(886\) | −25.4836 | −0.856138 | ||||||||
\(887\) | −9.90849 | − | 5.72067i | −0.332694 | − | 0.192081i | 0.324342 | − | 0.945940i | \(-0.394857\pi\) |
−0.657037 | + | 0.753859i | \(0.728190\pi\) | |||||||
\(888\) | 4.07835 | − | 2.35464i | 0.136861 | − | 0.0790165i | ||||
\(889\) | 32.9307 | − | 57.0376i | 1.10446 | − | 1.91298i | ||||
\(890\) | 14.4717 | + | 15.0103i | 0.485092 | + | 0.503146i | ||||
\(891\) | −1.67009 | − | 2.89267i | −0.0559500 | − | 0.0969082i | ||||
\(892\) | − | 10.0133i | − | 0.335271i | ||||||
\(893\) | −17.5650 | + | 16.1106i | −0.587790 | + | 0.539121i | ||||
\(894\) | −10.2979 | −0.344414 | ||||||||
\(895\) | 35.1891 | − | 33.9264i | 1.17624 | − | 1.13404i | ||||
\(896\) | 1.76959 | + | 3.06503i | 0.0591180 | + | 0.102395i | ||||
\(897\) | −12.5350 | − | 7.23707i | −0.418531 | − | 0.241639i | ||||
\(898\) | 16.5767 | − | 9.57058i | 0.553173 | − | 0.319374i | ||||
\(899\) | −4.29072 | + | 7.43175i | −0.143104 | + | 0.247863i | ||||
\(900\) | −4.41855 | + | 2.34017i | −0.147285 | + | 0.0780058i | ||||
\(901\) | 47.5513 | 1.58416 | ||||||||
\(902\) | 34.5062 | + | 19.9221i | 1.14893 | + | 0.663335i | ||||
\(903\) | −15.5654 | − | 8.98667i | −0.517983 | − | 0.299058i | ||||
\(904\) | 7.98440 | 0.265557 | ||||||||
\(905\) | 2.87217 | + | 11.5597i | 0.0954743 | + | 0.384258i | ||||
\(906\) | −2.34797 | + | 4.06681i | −0.0780062 | + | 0.135111i | ||||
\(907\) | 12.3187 | − | 7.11223i | 0.409037 | − | 0.236158i | −0.281339 | − | 0.959608i | \(-0.590778\pi\) |
0.690376 | + | 0.723451i | \(0.257445\pi\) | |||||||
\(908\) | −12.3395 | − | 7.12423i | −0.409502 | − | 0.236426i | ||||
\(909\) | −4.32684 | − | 7.49431i | −0.143512 | − | 0.248571i | ||||
\(910\) | 9.38871 | + | 9.73813i | 0.311233 | + | 0.322816i | ||||
\(911\) | −14.4391 | −0.478388 | −0.239194 | − | 0.970972i | \(-0.576883\pi\) | ||||
−0.239194 | + | 0.970972i | \(0.576883\pi\) | |||||||
\(912\) | −3.21233 | + | 2.94635i | −0.106371 | + | 0.0975633i | ||||
\(913\) | 15.6332i | 0.517382i | ||||||||
\(914\) | 16.0108 | + | 27.7315i | 0.529590 | + | 0.917276i | ||||
\(915\) | −21.4958 | − | 22.2958i | −0.710629 | − | 0.737077i | ||||
\(916\) | 7.92881 | − | 13.7331i | 0.261975 | − | 0.453754i | ||||
\(917\) | 23.2374 | − | 13.4161i | 0.767365 | − | 0.443038i | ||||
\(918\) | −3.29175 | − | 1.90049i | −0.108644 | − | 0.0627256i | ||||
\(919\) | −31.4030 | −1.03589 | −0.517944 | − | 0.855415i | \(-0.673302\pi\) | ||||
−0.517944 | + | 0.855415i | \(0.673302\pi\) | |||||||
\(920\) | −4.56585 | − | 18.3763i | −0.150532 | − | 0.605848i | ||||
\(921\) | 1.83771 | − | 3.18301i | 0.0605547 | − | 0.104884i | ||||
\(922\) | −35.7462 | − | 20.6381i | −1.17724 | − | 0.679679i | ||||
\(923\) | 13.8310i | 0.455252i | ||||||||
\(924\) | −11.8215 | −0.388899 | ||||||||
\(925\) | 23.5307 | + | 0.860037i | 0.773684 | + | 0.0282778i | ||||
\(926\) | −4.08084 | − | 7.06822i | −0.134105 | − | 0.232276i | ||||
\(927\) | 0.650849 | + | 0.375768i | 0.0213767 | + | 0.0123418i | ||||
\(928\) | 6.89160 | − | 3.97887i | 0.226228 | − | 0.130613i | ||||
\(929\) | −4.50780 | − | 7.80774i | −0.147896 | − | 0.256164i | 0.782554 | − | 0.622583i | \(-0.213917\pi\) |
−0.930450 | + | 0.366420i | \(0.880583\pi\) | |||||||
\(930\) | 0.581449 | + | 2.34017i | 0.0190665 | + | 0.0767373i | ||||
\(931\) | −7.23215 | + | 22.9753i | −0.237024 | + | 0.752984i | ||||
\(932\) | − | 24.5958i | − | 0.805663i | ||||||
\(933\) | −11.8923 | + | 6.86603i | −0.389337 | + | 0.224784i | ||||
\(934\) | 8.91189 | + | 15.4358i | 0.291606 | + | 0.505076i | ||||
\(935\) | −7.84726 | + | 27.2829i | −0.256633 | + | 0.892246i | ||||
\(936\) | −0.854638 | − | 1.48028i | −0.0279347 | − | 0.0483843i | ||||
\(937\) | 3.87759 | + | 2.23873i | 0.126675 | + | 0.0731360i | 0.561999 | − | 0.827138i | \(-0.310033\pi\) |
−0.435323 | + | 0.900274i | \(0.643366\pi\) | |||||||
\(938\) | 31.9805i | 1.04420i | ||||||||
\(939\) | 17.9421 | 0.585520 | ||||||||
\(940\) | 3.37973 | − | 11.7504i | 0.110235 | − | 0.383257i | ||||
\(941\) | 25.5603 | − | 44.2718i | 0.833243 | − | 1.44322i | −0.0622107 | − | 0.998063i | \(-0.519815\pi\) |
0.895453 | − | 0.445155i | \(-0.146852\pi\) | |||||||
\(942\) | − | 10.5174i | − | 0.342677i | ||||||
\(943\) | − | 101.013i | − | 3.28944i | ||||||
\(944\) | 2.93302 | − | 5.08013i | 0.0954615 | − | 0.165344i | ||||
\(945\) | 5.69723 | − | 5.49280i | 0.185331 | − | 0.178681i | ||||
\(946\) | 8.48133 | − | 14.6901i | 0.275752 | − | 0.477616i | ||||
\(947\) | 38.2595 | − | 22.0892i | 1.24327 | − | 0.717801i | 0.273510 | − | 0.961869i | \(-0.411815\pi\) |
0.969758 | + | 0.244068i | \(0.0784820\pi\) | |||||||
\(948\) | −6.13005 | + | 3.53919i | −0.199095 | + | 0.114948i | ||||
\(949\) | −10.0989 | −0.327824 | ||||||||
\(950\) | −21.4341 | + | 3.94699i | −0.695415 | + | 0.128057i | ||||
\(951\) | −7.33299 | −0.237788 | ||||||||
\(952\) | −11.6501 | + | 6.72620i | −0.377583 | + | 0.217997i | ||||
\(953\) | 28.4107 | − | 16.4030i | 0.920314 | − | 0.531344i | 0.0365790 | − | 0.999331i | \(-0.488354\pi\) |
0.883735 | + | 0.467987i | \(0.155021\pi\) | |||||||
\(954\) | 6.25513 | − | 10.8342i | 0.202517 | − | 0.350770i | ||||
\(955\) | −14.4779 | + | 13.9584i | −0.468494 | + | 0.451684i | ||||
\(956\) | −0.0783777 | + | 0.135754i | −0.00253492 | + | 0.00439061i | ||||
\(957\) | 26.5802i | 0.859217i | ||||||||
\(958\) | 23.1389i | 0.747584i | ||||||||
\(959\) | −20.2062 | + | 34.9982i | −0.652492 | + | 1.13015i | ||||
\(960\) | 0.618092 | − | 2.14894i | 0.0199488 | − | 0.0693569i | ||||
\(961\) | −29.8371 | −0.962487 | ||||||||
\(962\) | 8.04945i | 0.259525i | ||||||||
\(963\) | 8.50763 | + | 4.91189i | 0.274155 | + | 0.158283i | ||||
\(964\) | −12.7968 | − | 22.1647i | −0.412156 | − | 0.713876i | ||||
\(965\) | 1.44200 | − | 5.01346i | 0.0464196 | − | 0.161389i | ||||
\(966\) | 14.9849 | + | 25.9546i | 0.482132 | + | 0.835077i | ||||
\(967\) | 0.442803 | − | 0.255652i | 0.0142396 | − | 0.00822122i | −0.492863 | − | 0.870107i | \(-0.664050\pi\) |
0.507103 | + | 0.861886i | \(0.330716\pi\) | |||||||
\(968\) | − | 0.156755i | − | 0.00503831i | ||||||
\(969\) | −11.1990 | − | 12.2100i | −0.359764 | − | 0.392242i | ||||
\(970\) | −3.15449 | − | 12.6959i | −0.101285 | − | 0.407642i | ||||
\(971\) | 27.4482 | + | 47.5417i | 0.880855 | + | 1.52568i | 0.850392 | + | 0.526149i | \(0.176365\pi\) |
0.0304620 | + | 0.999536i | \(0.490302\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | −11.0401 | − | 6.37402i | −0.353930 | − | 0.204342i | ||||
\(974\) | 5.44275 | + | 9.42712i | 0.174397 | + | 0.302065i | ||||
\(975\) | 0.312158 | − | 8.54067i | 0.00999707 | − | 0.273520i | ||||
\(976\) | 13.8504 | 0.443342 | ||||||||
\(977\) | 16.6114i | 0.531447i | 0.964049 | + | 0.265723i | \(0.0856107\pi\) | ||||
−0.964049 | + | 0.265723i | \(0.914389\pi\) | |||||||
\(978\) | 14.5313 | + | 8.38962i | 0.464658 | + | 0.268271i | ||||
\(979\) | 15.5728 | − | 26.9730i | 0.497710 | − | 0.862060i | ||||
\(980\) | −2.97948 | − | 11.9916i | −0.0951760 | − | 0.383057i | ||||
\(981\) | −7.85043 | −0.250645 | ||||||||
\(982\) | −26.6272 | − | 15.3732i | −0.849708 | − | 0.490579i | ||||
\(983\) | 11.6583 | − | 6.73093i | 0.371842 | − | 0.214683i | −0.302421 | − | 0.953175i | \(-0.597795\pi\) |
0.674263 | + | 0.738491i | \(0.264461\pi\) | |||||||
\(984\) | 5.96441 | − | 10.3307i | 0.190138 | − | 0.329329i | ||||
\(985\) | −37.3807 | − | 38.7719i | −1.19105 | − | 1.23537i | ||||
\(986\) | 15.1236 | + | 26.1949i | 0.481634 | + | 0.834215i | ||||
\(987\) | 19.3523i | 0.615990i | ||||||||
\(988\) | −1.61603 | − | 7.27319i | −0.0514128 | − | 0.231391i | ||||
\(989\) | −43.0037 | −1.36744 | ||||||||
\(990\) | 5.18393 | + | 5.37686i | 0.164756 | + | 0.170888i | ||||
\(991\) | −12.9077 | − | 22.3568i | −0.410026 | − | 0.710186i | 0.584866 | − | 0.811130i | \(-0.301147\pi\) |
−0.994892 | + | 0.100944i | \(0.967814\pi\) | |||||||
\(992\) | −0.933903 | − | 0.539189i | −0.0296514 | − | 0.0171193i | ||||
\(993\) | 18.6034 | − | 10.7407i | 0.590360 | − | 0.340845i | ||||
\(994\) | 14.3190 | − | 24.8013i | 0.454172 | − | 0.786650i | ||||
\(995\) | 0.703132 | + | 2.82991i | 0.0222908 | + | 0.0897143i | ||||
\(996\) | 4.68035 | 0.148302 | ||||||||
\(997\) | −18.8310 | − | 10.8721i | −0.596384 | − | 0.344322i | 0.171234 | − | 0.985230i | \(-0.445225\pi\) |
−0.767618 | + | 0.640908i | \(0.778558\pi\) | |||||||
\(998\) | −5.70789 | − | 3.29545i | −0.180680 | − | 0.104316i | ||||
\(999\) | 4.70928 | 0.148995 |
(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 | 570.2.q.b.349.4 | yes | 12 | |
3.2 | odd | 2 | 1710.2.t.b.919.3 | 12 | |||
5.4 | even | 2 | inner | 570.2.q.b.349.3 | yes | 12 | |
15.14 | odd | 2 | 1710.2.t.b.919.4 | 12 | |||
19.11 | even | 3 | inner | 570.2.q.b.49.3 | ✓ | 12 | |
57.11 | odd | 6 | 1710.2.t.b.1189.4 | 12 | |||
95.49 | even | 6 | inner | 570.2.q.b.49.4 | yes | 12 | |
285.239 | odd | 6 | 1710.2.t.b.1189.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.b.49.3 | ✓ | 12 | 19.11 | even | 3 | inner | |
570.2.q.b.49.4 | yes | 12 | 95.49 | even | 6 | inner | |
570.2.q.b.349.3 | yes | 12 | 5.4 | even | 2 | inner | |
570.2.q.b.349.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1710.2.t.b.919.3 | 12 | 3.2 | odd | 2 | |||
1710.2.t.b.919.4 | 12 | 15.14 | odd | 2 | |||
1710.2.t.b.1189.3 | 12 | 285.239 | odd | 6 | |||
1710.2.t.b.1189.4 | 12 | 57.11 | odd | 6 |