Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,6,Mod(17,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.i (of order \(4\), 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: | \(9.62302918878\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{19} + 2 x^{18} - 382 x^{17} + 117610 x^{16} - 661518 x^{15} + 1160778 x^{14} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{14}\cdot 5^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.10 | ||
Root | \(-7.08001 - 5.69920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.17 |
Dual form | 60.6.i.a.53.10 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 15.5638 | − | 0.876355i | 0.998419 | − | 0.0562182i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −55.7692 | + | 3.84667i | −0.997630 | + | 0.0688114i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 151.287 | + | 151.287i | 1.16696 | + | 1.16696i | 0.982918 | + | 0.184044i | \(0.0589190\pi\) |
0.184044 | + | 0.982918i | \(0.441081\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 241.464 | − | 27.2788i | 0.993679 | − | 0.112259i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 504.939i | 1.25822i | 0.777315 | + | 0.629111i | \(0.216581\pi\) | ||||
−0.777315 | + | 0.629111i | \(0.783419\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 567.781 | − | 567.781i | 0.931799 | − | 0.931799i | −0.0660194 | − | 0.997818i | \(-0.521030\pi\) |
0.997818 | + | 0.0660194i | \(0.0210299\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −864.610 | + | 108.742i | −0.992183 | + | 0.124788i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 91.1681 | − | 91.1681i | 0.0765104 | − | 0.0765104i | −0.667816 | − | 0.744326i | \(-0.732771\pi\) |
0.744326 | + | 0.667816i | \(0.232771\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 600.852i | 0.381842i | 0.981605 | + | 0.190921i | \(0.0611474\pi\) | ||||
−0.981605 | + | 0.190921i | \(0.938853\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2487.18 | + | 2222.02i | 1.23072 | + | 1.09951i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2156.65 | + | 2156.65i | 0.850082 | + | 0.850082i | 0.990143 | − | 0.140061i | \(-0.0447297\pi\) |
−0.140061 | + | 0.990143i | \(0.544730\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3095.41 | − | 429.052i | 0.990530 | − | 0.137297i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3734.19 | − | 636.170i | 0.985797 | − | 0.167944i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5818.05 | −1.28464 | −0.642321 | − | 0.766436i | \(-0.722028\pi\) | ||||
−0.642321 | + | 0.766436i | \(0.722028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2220.29 | −0.414959 | −0.207479 | − | 0.978239i | \(-0.566526\pi\) | ||||
−0.207479 | + | 0.978239i | \(0.566526\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 442.506 | + | 7858.78i | 0.0707350 | + | 1.25623i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9019.11 | − | 7855.21i | −1.24450 | − | 1.08390i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6791.46 | − | 6791.46i | −0.815565 | − | 0.815565i | 0.169896 | − | 0.985462i | \(-0.445657\pi\) |
−0.985462 | + | 0.169896i | \(0.945657\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8339.25 | − | 9334.40i | 0.877941 | − | 0.982709i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 12164.1i | − | 1.13011i | −0.825055 | − | 0.565053i | \(-0.808856\pi\) | ||
0.825055 | − | 0.565053i | \(-0.191144\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5949.36 | + | 5949.36i | −0.490681 | + | 0.490681i | −0.908521 | − | 0.417840i | \(-0.862787\pi\) |
0.417840 | + | 0.908521i | \(0.362787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −13361.3 | + | 2450.15i | −0.983599 | + | 0.180369i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4500.58 | − | 4500.58i | 0.297183 | − | 0.297183i | −0.542727 | − | 0.839909i | \(-0.682608\pi\) |
0.839909 | + | 0.542727i | \(0.182608\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28968.6i | 1.72360i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1339.03 | − | 1498.82i | 0.0720882 | − | 0.0806907i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26033.6 | − | 26033.6i | −1.27305 | − | 1.27305i | −0.944480 | − | 0.328569i | \(-0.893434\pi\) |
−0.328569 | − | 0.944480i | \(-0.606566\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1942.34 | − | 28160.1i | −0.0865801 | − | 1.25524i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 526.559 | + | 9351.54i | 0.0214664 | + | 0.381238i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6530.45 | 0.244238 | 0.122119 | − | 0.992515i | \(-0.461031\pi\) | ||||
0.122119 | + | 0.992515i | \(0.461031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 28414.5 | 0.977722 | 0.488861 | − | 0.872362i | \(-0.337412\pi\) | ||||
0.488861 | + | 0.872362i | \(0.337412\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 40657.3 | + | 32403.5i | 1.29059 | + | 1.02858i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −29480.6 | + | 33848.7i | −0.865472 | + | 0.993709i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12318.8 | − | 12318.8i | −0.335259 | − | 0.335259i | 0.519321 | − | 0.854580i | \(-0.326185\pi\) |
−0.854580 | + | 0.519321i | \(0.826185\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 35455.7 | + | 31675.8i | 0.896528 | + | 0.800948i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 69210.3i | − | 1.62939i | −0.579890 | − | 0.814695i | \(-0.696905\pi\) | ||
0.579890 | − | 0.814695i | \(-0.303095\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −18264.0 | + | 18264.0i | −0.401133 | + | 0.401133i | −0.878632 | − | 0.477499i | \(-0.841543\pi\) |
0.477499 | + | 0.878632i | \(0.341543\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 47800.3 | − | 9390.35i | 0.981245 | − | 0.192765i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −76390.8 | + | 76390.8i | −1.46830 | + | 1.46830i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 41121.4i | − | 0.741311i | −0.928770 | − | 0.370655i | \(-0.879133\pi\) | ||
0.928770 | − | 0.370655i | \(-0.120867\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 57560.7 | − | 13173.7i | 0.974796 | − | 0.223098i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 56058.1 | + | 56058.1i | 0.893189 | + | 0.893189i | 0.994822 | − | 0.101633i | \(-0.0324068\pi\) |
−0.101633 | + | 0.994822i | \(0.532407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4733.68 | + | 5435.07i | −0.0710643 | + | 0.0815939i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −90550.9 | + | 5098.67i | −1.28261 | + | 0.0722202i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 54609.2 | 0.730787 | 0.365394 | − | 0.930853i | \(-0.380934\pi\) | ||||
0.365394 | + | 0.930853i | \(0.380934\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 171796. | 2.17475 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −34556.1 | + | 1945.76i | −0.414303 | + | 0.0233282i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2311.28 | − | 33509.0i | −0.0262751 | − | 0.380937i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17055.3 | + | 17055.3i | 0.184047 | + | 0.184047i | 0.793117 | − | 0.609070i | \(-0.208457\pi\) |
−0.609070 | + | 0.793117i | \(0.708457\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 13774.2 | + | 121925.i | 0.141246 | + | 1.25027i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 44798.8i | − | 0.436981i | −0.975839 | − | 0.218491i | \(-0.929887\pi\) | ||
0.975839 | − | 0.218491i | \(-0.0701133\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −112985. | + | 112985.i | −1.04937 | + | 1.04937i | −0.0506522 | + | 0.998716i | \(0.516130\pi\) |
−0.998716 | + | 0.0506522i | \(0.983870\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −147256. | − | 114353.i | −1.30346 | − | 1.01222i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 52567.6 | − | 52567.6i | 0.443873 | − | 0.443873i | −0.449438 | − | 0.893311i | \(-0.648376\pi\) |
0.893311 | + | 0.449438i | \(0.148376\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10619.5i | 0.0856125i | 0.999083 | + | 0.0428063i | \(0.0136298\pi\) | ||||
−0.999083 | + | 0.0428063i | \(0.986370\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −111653. | − | 99749.2i | −0.860125 | − | 0.768426i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 53690.7 | + | 53690.7i | 0.395552 | + | 0.395552i | 0.876661 | − | 0.481109i | \(-0.159766\pi\) |
−0.481109 | + | 0.876661i | \(0.659766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −128571. | − | 111979.i | −0.906563 | − | 0.789572i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 121610. | − | 152587.i | 0.821307 | − | 1.03051i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 27585.1 | 0.178570 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −93912.7 | −0.583124 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10660.0 | − | 189319.i | −0.0635325 | − | 1.12832i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −170978. | + | 35834.9i | −0.978735 | + | 0.205131i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −124569. | − | 124569.i | −0.685333 | − | 0.685333i | 0.275864 | − | 0.961197i | \(-0.411036\pi\) |
−0.961197 | + | 0.275864i | \(0.911036\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −87380.9 | + | 97808.4i | −0.462320 | + | 0.517490i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 46648.9i | − | 0.237500i | −0.992924 | − | 0.118750i | \(-0.962111\pi\) | ||
0.992924 | − | 0.118750i | \(-0.0378887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −90901.1 | + | 90901.1i | −0.445595 | + | 0.445595i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −205806. | + | 49842.9i | −0.971903 | + | 0.235380i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 123029. | − | 123029.i | 0.560025 | − | 0.560025i | −0.369289 | − | 0.929315i | \(-0.620399\pi\) |
0.929315 | + | 0.369289i | \(0.120399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 88863.2i | 0.390108i | 0.980793 | + | 0.195054i | \(0.0624882\pi\) | ||||
−0.980793 | + | 0.195054i | \(0.937512\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 66102.0 | − | 73990.2i | 0.280006 | − | 0.313420i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 286695. | + | 286695.i | 1.17241 | + | 1.17241i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 324468. | − | 22380.1i | 1.28160 | − | 0.0883980i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 25386.7 | + | 450861.i | 0.0968977 | + | 1.72088i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 280995. | 1.03689 | 0.518446 | − | 0.855110i | \(-0.326511\pi\) | ||||
0.518446 | + | 0.855110i | \(0.326511\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 381934. | 1.36316 | 0.681579 | − | 0.731745i | \(-0.261294\pi\) | ||||
0.681579 | + | 0.731745i | \(0.261294\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 19526.9 | − | 24500.8i | 0.0674379 | − | 0.0846158i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 123824. | − | 8540.72i | 0.413975 | − | 0.0285539i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −124075. | − | 124075.i | −0.401731 | − | 0.401731i | 0.477112 | − | 0.878843i | \(-0.341684\pi\) |
−0.878843 | + | 0.477112i | \(0.841684\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −427997. | − | 382368.i | −1.34260 | − | 1.19947i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 652548.i | 1.98403i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −131800. | + | 131800.i | −0.388549 | + | 0.388549i | −0.874170 | − | 0.485621i | \(-0.838594\pi\) |
0.485621 | + | 0.874170i | \(0.338594\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −54908.4 | − | 436575.i | −0.157010 | − | 1.24839i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −113051. | + | 113051.i | −0.313678 | + | 0.313678i | −0.846333 | − | 0.532654i | \(-0.821195\pi\) |
0.532654 | + | 0.846333i | \(0.321195\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 273457.i | − | 0.736499i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16390.5 | + | 145084.i | 0.0428650 | + | 0.379428i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −177634. | − | 177634.i | −0.451245 | − | 0.451245i | 0.444523 | − | 0.895767i | \(-0.353373\pi\) |
−0.895767 | + | 0.444523i | \(0.853373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 533205. | + | 403385.i | 1.31613 | + | 0.995691i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 101639. | − | 5722.99i | 0.243852 | − | 0.0137306i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −224850. | −0.524518 | −0.262259 | − | 0.964998i | \(-0.584467\pi\) | ||||
−0.262259 | + | 0.964998i | \(0.584467\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −430292. | −0.976263 | −0.488132 | − | 0.872770i | \(-0.662321\pi\) | ||||
−0.488132 | + | 0.872770i | \(0.662321\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 442238. | − | 24901.2i | 0.976176 | − | 0.0549658i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 404879. | + | 352630.i | 0.869753 | + | 0.757512i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 46034.4 | + | 46034.4i | 0.0962672 | + | 0.0962672i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 661180. | + | 468691.i | 1.34637 | + | 0.954403i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 479790.i | − | 0.951629i | −0.879546 | − | 0.475814i | \(-0.842153\pi\) | ||
0.879546 | − | 0.475814i | \(-0.157847\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 561095. | − | 561095.i | 1.08428 | − | 1.08428i | 0.0881793 | − | 0.996105i | \(-0.471895\pi\) |
0.996105 | − | 0.0881793i | \(-0.0281048\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −429167. | + | 552651.i | −0.808239 | + | 1.04079i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −264076. | + | 264076.i | −0.484801 | + | 0.484801i | −0.906661 | − | 0.421860i | \(-0.861377\pi\) |
0.421860 | + | 0.906661i | \(0.361377\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 111560.i | − | 0.199699i | −0.995003 | − | 0.0998494i | \(-0.968164\pi\) | ||
0.995003 | − | 0.0998494i | \(-0.0318361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −202523. | − | 180931.i | −0.353576 | − | 0.315881i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −880195. | − | 880195.i | −1.49913 | − | 1.49913i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 46791.2 | + | 678380.i | 0.0777642 | + | 1.12743i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 579585. | + | 461923.i | 0.940138 | + | 0.749280i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −303394. | −0.480442 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −932775. | −1.44235 | −0.721175 | − | 0.692753i | \(-0.756398\pi\) | ||||
−0.721175 | + | 0.692753i | \(0.756398\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −60652.8 | − | 1.07718e6i | −0.0916013 | − | 1.62681i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 308906. | − | 354676.i | 0.455753 | − | 0.523282i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −335901. | − | 335901.i | −0.484241 | − | 0.484241i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −268251. | + | 300263.i | −0.377947 | + | 0.423049i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 103527.i | − | 0.142585i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −866194. | + | 866194.i | −1.16642 | + | 1.16642i | −0.183372 | + | 0.983044i | \(0.558701\pi\) |
−0.983044 | + | 0.183372i | \(0.941299\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 735725. | − | 188040.i | 0.968856 | − | 0.247624i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 785260. | − | 785260.i | 1.01146 | − | 1.01146i | 0.0115270 | − | 0.999934i | \(-0.496331\pi\) |
0.999934 | − | 0.0115270i | \(-0.00366924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 1.35108e6i | − | 1.70252i | −0.524742 | − | 0.851261i | \(-0.675838\pi\) | ||
0.524742 | − | 0.851261i | \(-0.324162\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.12199e6 | + | 1.25588e6i | −1.38343 | + | 1.54852i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −211648. | − | 211648.i | −0.255403 | − | 0.255403i | 0.567779 | − | 0.823181i | \(-0.307803\pi\) |
−0.823181 | + | 0.567779i | \(0.807803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −233681. | + | 268306.i | −0.276029 | + | 0.316928i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −36036.9 | − | 640006.i | −0.0416751 | − | 0.740138i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.11134e6 | −1.25850 | −0.629251 | − | 0.777202i | \(-0.716638\pi\) | ||||
−0.629251 | + | 0.777202i | \(0.716638\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 501312. | 0.555988 | 0.277994 | − | 0.960583i | \(-0.410330\pi\) | ||||
0.277994 | + | 0.960583i | \(0.410330\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 884319. | − | 255477.i | 0.960712 | − | 0.277546i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −111433. | − | 1.61555e6i | −0.118603 | − | 1.71952i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 341152. | + | 341152.i | 0.355800 | + | 0.355800i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 921604. | + | 823351.i | 0.941989 | + | 0.841563i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 66926.4i | 0.0670522i | 0.999438 | + | 0.0335261i | \(0.0106737\pi\) | ||||
−0.999438 | + | 0.0335261i | \(0.989326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.08898e6 | + | 1.08898e6i | −1.06959 | + | 1.06959i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −68911.0 | + | 88738.7i | −0.0663648 | + | 0.0854599i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.10953e6 | + | 1.10953e6i | −1.04787 | + | 1.04787i | −0.0490726 | + | 0.998795i | \(0.515627\pi\) |
−0.998795 | + | 0.0490726i | \(0.984373\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 2.05492e6i | − | 1.90347i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.40485e6 | + | 158709.i | −1.27652 | + | 0.144212i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11345.4 | + | 11345.4i | 0.0101142 | + | 0.0101142i | 0.712146 | − | 0.702032i | \(-0.247723\pi\) |
−0.702032 | + | 0.712146i | \(0.747723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.55202e6 | + | 1.35173e6i | 1.35763 | + | 1.18243i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 849927. | − | 47857.1i | 0.729632 | − | 0.0410835i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.52047e6 | −1.28115 | −0.640573 | − | 0.767897i | \(-0.721303\pi\) | ||||
−0.640573 | + | 0.767897i | \(0.721303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.29409e6 | 1.89752 | 0.948761 | − | 0.315995i | \(-0.102338\pi\) | ||||
0.948761 | + | 0.315995i | \(0.102338\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.67380e6 | − | 150554.i | 2.17131 | − | 0.122260i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 216645. | + | 1.56299e6i | 0.172750 | + | 1.24631i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −53946.6 | − | 53946.6i | −0.0422440 | − | 0.0422440i | 0.685669 | − | 0.727913i | \(-0.259510\pi\) |
−0.727913 | + | 0.685669i | \(0.759510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −536120. | + | 60566.8i | −0.412336 | + | 0.0465827i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.07053e6i | 1.56428i | 0.623101 | + | 0.782141i | \(0.285873\pi\) | ||||
−0.623101 | + | 0.782141i | \(0.714127\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 826504. | − | 826504.i | 0.613450 | − | 0.613450i | −0.330394 | − | 0.943843i | \(-0.607181\pi\) |
0.943843 | + | 0.330394i | \(0.107181\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −65338.1 | − | 519502.i | −0.0476491 | − | 0.378857i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.84027e6 | − | 1.84027e6i | 1.31879 | − | 1.31879i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.40323e6i | 0.988292i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 280391. | + | 250498.i | 0.194103 | + | 0.173409i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 476780. | + | 476780.i | 0.324451 | + | 0.324451i | 0.850472 | − | 0.526021i | \(-0.176317\pi\) |
−0.526021 | + | 0.850472i | \(0.676317\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −364198. | + | 25120.5i | −0.243659 | + | 0.0168064i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 321227. | + | 1.88554e6i | 0.211311 | + | 1.24035i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.44901e6 | 1.58421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.80012e6 | −1.14521 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −39259.6 | − | 697240.i | −0.0245663 | − | 0.436290i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.58465e6 | + | 109301.i | −0.975405 | + | 0.0672784i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −517400. | − | 517400.i | −0.313314 | − | 0.313314i | 0.532878 | − | 0.846192i | \(-0.321111\pi\) |
−0.846192 | + | 0.532878i | \(0.821111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.65946e6 | + | 1.85749e6i | −0.988715 | + | 1.10670i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 580879.i | 0.340553i | 0.985396 | + | 0.170276i | \(0.0544661\pi\) | ||||
−0.985396 | + | 0.170276i | \(0.945534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −788946. | + | 788946.i | −0.455184 | + | 0.455184i | −0.897071 | − | 0.441887i | \(-0.854309\pi\) |
0.441887 | + | 0.897071i | \(0.354309\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.39207e6 | − | 1.65072e6i | −1.35831 | − | 0.937339i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 464640. | − | 464640.i | 0.259698 | − | 0.259698i | −0.565233 | − | 0.824931i | \(-0.691214\pi\) |
0.824931 | + | 0.565233i | \(0.191214\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 2.93776e6i | − | 1.61637i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 772084. | − | 864219.i | 0.418217 | − | 0.468125i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 54778.5 | + | 54778.5i | 0.0292149 | + | 0.0292149i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.51390e6 | − | 2.00112e6i | 0.795042 | − | 1.05091i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9306.43 | + | 165280.i | 0.00481298 | + | 0.0854771i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.36176e6 | 0.693602 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 376906. | 0.189088 | 0.0945439 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945439 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.82516e6 | − | 1.45463e6i | −0.901965 | − | 0.718856i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 734394. | + | 639622.i | 0.357534 | + | 0.311395i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.06686e6 | − | 1.06686e6i | −0.511719 | − | 0.511719i | 0.403334 | − | 0.915053i | \(-0.367851\pi\) |
−0.915053 | + | 0.403334i | \(0.867851\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 882684. | + | 788580.i | 0.417163 | + | 0.372689i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.12111e6i | − | 0.522111i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.83989e6 | + | 1.83989e6i | −0.844416 | + | 0.844416i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.09918e6 | − | 1.63014e6i | −0.949517 | − | 0.737358i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.95140e6 | + | 1.95140e6i | −0.870005 | + | 0.870005i | −0.992472 | − | 0.122468i | \(-0.960919\pi\) |
0.122468 | + | 0.992472i | \(0.460919\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.93764e6i | 1.73050i | 0.501337 | + | 0.865252i | \(0.332842\pi\) | ||||
−0.501337 | + | 0.865252i | \(0.667158\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.75900e6 | − | 2.48141e6i | 0.762074 | − | 1.07505i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 399857. | + | 399857.i | 0.170792 | + | 0.170792i | 0.787327 | − | 0.616535i | \(-0.211464\pi\) |
−0.616535 | + | 0.787327i | \(0.711464\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 266229. | + | 3.85980e6i | 0.112121 | + | 1.62553i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 429329. | − | 24174.3i | 0.178287 | − | 0.0100389i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 610242. | 0.249900 | 0.124950 | − | 0.992163i | \(-0.460123\pi\) | ||||
0.124950 | + | 0.992163i | \(0.460123\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.11508e6 | 0.854197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.46164e6 | + | 82300.8i | −0.582202 | + | 0.0327822i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 948311. | − | 1.08882e6i | 0.372579 | − | 0.427784i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.27572e6 | − | 2.27572e6i | −0.881969 | − | 0.881969i | 0.111765 | − | 0.993735i | \(-0.464350\pi\) |
−0.993735 | + | 0.111765i | \(0.964350\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −331821. | − | 2.93718e6i | −0.126864 | − | 1.12296i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.87711e6i | − | 2.97120i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.84940e6 | + | 1.84940e6i | −0.688269 | + | 0.688269i | −0.961849 | − | 0.273580i | \(-0.911792\pi\) |
0.273580 | + | 0.961849i | \(0.411792\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.62966e6 | + | 707565.i | −0.965655 | + | 0.259829i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.30337e6 | + | 3.30337e6i | −1.19703 | + | 1.19703i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 193997.i | 0.0693740i | 0.999398 | + | 0.0346870i | \(0.0110434\pi\) | ||||
−0.999398 | + | 0.0346870i | \(0.988957\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.04794e6 | − | 1.82961e6i | −0.722778 | − | 0.645721i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.31948e6 | + | 3.31948e6i | 1.15631 | + | 1.15631i | 0.985263 | + | 0.171045i | \(0.0547143\pi\) |
0.171045 | + | 0.985263i | \(0.445286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.96640e6 | − | 4.55410e6i | 1.36378 | − | 1.56585i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.27426e6 | + | 1.59885e6i | −0.432496 | + | 0.542662i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.87517e6 | 1.29842 | 0.649212 | − | 0.760608i | \(-0.275099\pi\) | ||||
0.649212 | + | 0.760608i | \(0.275099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 393236. | 0.130080 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −40881.0 | − | 726035.i | −0.0133518 | − | 0.237124i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 158181. | + | 2.29331e6i | 0.0510106 | + | 0.739554i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.13355e6 | − | 3.13355e6i | −0.997837 | − | 0.997837i | 0.00216047 | − | 0.999998i | \(-0.499312\pi\) |
−0.999998 | + | 0.00216047i | \(0.999312\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.33511e6 | + | 1.49443e6i | −0.419840 | + | 0.469941i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.10986e6i | 0.655229i | 0.944812 | + | 0.327614i | \(0.106245\pi\) | ||||
−0.944812 | + | 0.327614i | \(0.893755\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.26064e6 | + | 1.26064e6i | −0.386658 | + | 0.386658i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.15944e6 | + | 956105.i | −0.957134 | + | 0.289646i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.42928e6 | − | 3.42928e6i | 1.02616 | − | 1.02616i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.18131e6i | 0.349186i | 0.984641 | + | 0.174593i | \(0.0558609\pi\) | ||||
−0.984641 | + | 0.174593i | \(0.944139\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.80699e6 | − | 2.02262e6i | 0.527656 | − | 0.590623i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 987973. | + | 987973.i | 0.285017 | + | 0.285017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.34195e6 | − | 2.91068e6i | −0.952533 | − | 0.829610i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 77875.7 | + | 1.38305e6i | 0.0219312 | + | 0.389491i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.62127e6 | −1.28596 | −0.642978 | − | 0.765885i | \(-0.722301\pi\) | ||||
−0.642978 | + | 0.765885i | \(0.722301\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.46797e6 | 1.50356 | 0.751780 | − | 0.659414i | \(-0.229196\pi\) | ||||
0.751780 | + | 0.659414i | \(0.229196\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 963957. | − | 1.20950e6i | 0.261943 | − | 0.328666i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 243087. | − | 321318.i | 0.0652813 | − | 0.0862905i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.29875e6 | + | 4.29875e6i | 1.14096 | + | 1.14096i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.71331e6 | + | 4.21082e6i | 1.23647 | + | 1.10465i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.10096e6i | 1.84130i | 0.390393 | + | 0.920648i | \(0.372339\pi\) | ||||
−0.390393 | + | 0.920648i | \(0.627661\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 918303. | − | 918303.i | 0.235378 | − | 0.235378i | −0.579555 | − | 0.814933i | \(-0.696774\pi\) |
0.814933 | + | 0.579555i | \(0.196774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.03034e6 | − | 632669.i | 1.27460 | − | 0.160307i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.29583e6 | + | 1.29583e6i | −0.324597 | + | 0.324597i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 688839.i | 0.170591i | 0.996356 | + | 0.0852955i | \(0.0271834\pi\) | ||||
−0.996356 | + | 0.0852955i | \(0.972817\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 790229. | + | 6.99487e6i | 0.193489 | + | 1.71271i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −556700. | − | 556700.i | −0.134776 | − | 0.134776i | 0.636500 | − | 0.771276i | \(-0.280381\pi\) |
−0.771276 | + | 0.636500i | \(0.780381\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.04551e6 | + | 210064.i | −0.729055 | + | 0.0502865i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.37336e6 | − | 246252.i | 1.03525 | − | 0.0582922i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.83428e6 | 1.36575 | 0.682875 | − | 0.730535i | \(-0.260729\pi\) | ||||
0.682875 | + | 0.730535i | \(0.260729\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.14212e6 | 1.42192 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.94435e6 | − | 334710.i | 1.36100 | − | 0.0766342i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.58091e6 | + | 660842.i | −2.16959 | + | 0.149647i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −538370. | − | 538370.i | −0.120584 | − | 0.120584i | 0.644240 | − | 0.764824i | \(-0.277174\pi\) |
−0.764824 | + | 0.644240i | \(0.777174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 282441. | − | 398438.i | 0.0625743 | − | 0.0882732i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 8.26708e6i | − | 1.81176i | −0.423538 | − | 0.905878i | \(-0.639212\pi\) | ||
0.423538 | − | 0.905878i | \(-0.360788\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 228783. | − | 228783.i | 0.0495987 | − | 0.0495987i | −0.681872 | − | 0.731471i | \(-0.738834\pi\) |
0.731471 | + | 0.681872i | \(0.238834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.91968e6 | − | 241440.i | 0.411715 | − | 0.0517817i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.86350e6 | + | 3.86350e6i | −0.819763 | + | 0.819763i | −0.986073 | − | 0.166311i | \(-0.946815\pi\) |
0.166311 | + | 0.986073i | \(0.446815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 3.72734e6i | − | 0.782469i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.03981e6 | − | 1.82235e6i | −0.423680 | − | 0.378511i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00407e6 | − | 3.00407e6i | −0.617386 | − | 0.617386i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 257797. | + | 1.85988e6i | 0.0524256 | + | 0.378226i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.99635e6 | − | 5.57602e6i | −1.40791 | − | 1.12209i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.63939e6 | −0.923895 | −0.461947 | − | 0.886907i | \(-0.652849\pi\) | ||||
−0.461947 | + | 0.886907i | \(0.652849\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.71212e6 | −1.51989 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 571863. | + | 1.01561e7i | 0.111538 | + | 1.98089i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.01676e6 | − | 885552.i | −0.196275 | − | 0.170946i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.08733e6 | + | 3.08733e6i | 0.589875 | + | 0.589875i | 0.937598 | − | 0.347722i | \(-0.113045\pi\) |
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.93580e6 | + | 2.16681e6i | −0.366091 | + | 0.409778i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.63927e6i | 0.681256i | 0.940198 | + | 0.340628i | \(0.110640\pi\) | ||||
−0.940198 | + | 0.340628i | \(0.889360\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −530420. | + | 530420.i | −0.0982885 | + | 0.0982885i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.23718e6 | − | 6.74666e6i | −0.226944 | − | 1.23759i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.04706e7 | − | 1.04706e7i | 1.90144 | − | 1.90144i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.06954e6i | − | 1.09120i | −0.838046 | − | 0.545600i | \(-0.816302\pi\) | ||
0.838046 | − | 0.545600i | \(-0.183698\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.66044e6 | + | 1.85858e6i | −0.295548 | + | 0.330817i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 163619. | + | 163619.i | 0.0288346 | + | 0.0288346i | 0.721377 | − | 0.692543i | \(-0.243509\pi\) |
−0.692543 | + | 0.721377i | \(0.743509\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 172326. | + | 2.49839e6i | 0.0300693 | + | 0.435946i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −239645. | − | 4.25603e6i | −0.0414046 | − | 0.735334i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.60298e6 | −0.616407 | −0.308203 | − | 0.951321i | \(-0.599728\pi\) | ||||
−0.308203 | + | 0.951321i | \(0.599728\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.52620e6 | −0.936213 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 382244. | + | 2.24370e6i | 0.0641280 | + | 0.376418i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.86647e6 | − | 6.73570e6i | 0.974673 | − | 1.11909i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.27252e6 | + | 2.27252e6i | 0.373922 | + | 0.373922i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.92034e6 | − | 2.60900e6i | −0.475899 | − | 0.425163i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 3.06124e6i | − | 0.494087i | −0.969004 | − | 0.247043i | \(-0.920541\pi\) | ||
0.969004 | − | 0.247043i | \(-0.0794590\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.90090e6 | + | 1.90090e6i | −0.303882 | + | 0.303882i | −0.842530 | − | 0.538649i | \(-0.818935\pi\) |
0.538649 | + | 0.842530i | \(0.318935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.65221e6 | + | 5.81093e6i | 1.37003 | + | 0.920126i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −202419. | + | 202419.i | −0.0317487 | + | 0.0317487i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.86597e6i | 0.445280i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.57687e6 | − | 178143.i | 0.242694 | − | 0.0274178i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.90652e6 | − | 6.90652e6i | −1.05303 | − | 1.05303i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.72944e6 | + | 3.13386e6i | −0.412277 | + | 0.473364i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.49952e6 | + | 197048.i | −0.523689 | + | 0.0294875i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.46274e7 | −2.16867 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.55404e6 | −0.522071 | −0.261036 | − | 0.965329i | \(-0.584064\pi\) | ||||
−0.261036 | + | 0.965329i | \(0.584064\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.69698e6 | + | 377089.i | −0.974720 | + | 0.0548838i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40849.7 | − | 592240.i | −0.00589112 | − | 0.0854096i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.09378e6 | − | 4.09378e6i | −0.585001 | − | 0.585001i | 0.351272 | − | 0.936273i | \(-0.385749\pi\) |
−0.936273 | + | 0.351272i | \(0.885749\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.86108e6 | − | 775114.i | 0.971542 | − | 0.109758i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 3.49578e6i | − | 0.490530i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.22114e6 | − | 6.22114e6i | 0.865082 | − | 0.865082i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6.61048e6 | + | 5.13344e6i | 0.910963 | + | 0.707418i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.45849e6 | + | 3.45849e6i | −0.472334 | + | 0.472334i | −0.902669 | − | 0.430335i | \(-0.858395\pi\) |
0.430335 | + | 0.902669i | \(0.358395\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.75586e6i | 0.914432i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 756812. | + | 676127.i | 0.101527 | + | 0.0907029i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.34764e6 | − | 2.34764e6i | −0.312149 | − | 0.312149i | 0.533593 | − | 0.845741i | \(-0.320841\pi\) |
−0.845741 | + | 0.533593i | \(0.820841\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.20082e6 | − | 2.78776e6i | −0.421833 | − | 0.367396i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.07012e7 | + | 6.71518e6i | 1.39790 | + | 0.877203i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.86323e6 | 1.27714 | 0.638570 | − | 0.769564i | \(-0.279526\pi\) | ||||
0.638570 | + | 0.769564i | \(0.279526\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.01430e6 | −0.130190 | −0.0650949 | − | 0.997879i | \(-0.520735\pi\) | ||||
−0.0650949 | + | 0.997879i | \(0.520735\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −420466. | − | 7.46735e6i | −0.0534988 | − | 0.950124i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.60104e6 | + | 5.75040e6i | 0.958745 | + | 0.725319i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.10779e6 | + | 4.10779e6i | 0.513652 | + | 0.513652i | 0.915643 | − | 0.401991i | \(-0.131682\pi\) |
−0.401991 | + | 0.915643i | \(0.631682\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.24105e6 | − | 9.22449e6i | 1.02161 | − | 1.14353i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.69617e7i | 2.08463i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.31454e7 | − | 1.31454e7i | 1.60178 | − | 1.60178i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.19515e6 | + | 8.97745e6i | −0.748449 | + | 1.08458i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.58247e6 | + | 6.58247e6i | −0.788486 | + | 0.788486i | −0.981246 | − | 0.192760i | \(-0.938256\pi\) |
0.192760 | + | 0.981246i | \(0.438256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.33406e6i | − | 0.158449i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.87860e6 | + | 4.34145e6i | −0.456779 | + | 0.511289i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.18682e6 | − | 3.18682e6i | −0.372152 | − | 0.372152i | 0.496108 | − | 0.868261i | \(-0.334762\pi\) |
−0.868261 | + | 0.496108i | \(0.834762\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.53840e6 | + | 106111.i | −0.178146 | + | 0.0122876i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −97766.0 | − | 1.73630e6i | −0.0112267 | − | 0.199383i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.57885e6 | 0.635298 | 0.317649 | − | 0.948208i | \(-0.397107\pi\) | ||||
0.317649 | + | 0.948208i | \(0.397107\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45159e7 | −1.63930 | −0.819651 | − | 0.572863i | \(-0.805833\pi\) | ||||
−0.819651 | + | 0.572863i | \(0.805833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.31058e6 | − | 2.63850e6i | −0.370776 | − | 0.295504i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.23744e6 | − | 361252.i | 0.581742 | − | 0.0401256i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 121683. | + | 121683.i | 0.0134047 | + | 0.0134047i | 0.713777 | − | 0.700373i | \(-0.246983\pi\) |
−0.700373 | + | 0.713777i | \(0.746983\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.44705e7 | − | 1.29278e7i | −1.58104 | − | 1.41248i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5.11068e6i | − | 0.553829i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.08678e6 | − | 5.08678e6i | 0.546754 | − | 0.546754i | −0.378747 | − | 0.925500i | \(-0.623645\pi\) |
0.925500 | + | 0.378747i | \(0.123645\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.32275e6 | + | 1.05172e7i | 0.141023 | + | 1.12127i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 452387. | − | 452387.i | 0.0478407 | − | 0.0478407i | −0.682782 | − | 0.730622i | \(-0.739230\pi\) |
0.730622 | + | 0.682782i | \(0.239230\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04321e7i | 1.09432i | 0.837029 | + | 0.547159i | \(0.184291\pi\) | ||||
−0.837029 | + | 0.547159i | \(0.815709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.42536e6 | + | 6.68136e6i | 0.980774 | + | 0.695242i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.26167e6 | + | 8.26167e6i | 0.852801 | + | 0.852801i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.39745e6 | − | 2.65618e6i | 0.962299 | − | 0.271993i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.72196e6 | + | 265880.i | −0.479682 | + | 0.0270096i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.23833e6 | −0.124799 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 569289. | 0.0569193 | 0.0284597 | − | 0.999595i | \(-0.490940\pi\) | ||||
0.0284597 | + | 0.999595i | \(0.490940\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.45175e7 | + | 817442.i | −1.44007 | + | 0.0810863i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.42631e6 | + | 6.46795e6i | 0.730867 | + | 0.636550i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.64478e7 | + | 1.64478e7i | 1.60605 | + | 1.60605i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.88798e6 | − | 1.67118e7i | −0.182913 | − | 1.61909i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.83316e6i | 0.464607i | 0.972643 | + | 0.232304i | \(0.0746263\pi\) | ||||
−0.972643 | + | 0.232304i | \(0.925374\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.92195e6 | − | 6.92195e6i | 0.660239 | − | 0.660239i | −0.295197 | − | 0.955436i | \(-0.595385\pi\) |
0.955436 | + | 0.295197i | \(0.0953854\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4.49693e6 | − | 5.79082e6i | 0.425615 | − | 0.548076i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30646.6 | − | 30646.6i | 0.00287820 | − | 0.00287820i | −0.705666 | − | 0.708544i | \(-0.749352\pi\) |
0.708544 | + | 0.705666i | \(0.249352\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.29748e6i | 0.307306i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.52226e6 | − | 4.93353e6i | −0.510699 | − | 0.456252i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.22854e7 | + | 1.22854e7i | 1.12747 | + | 1.12747i | 0.990587 | + | 0.136886i | \(0.0437093\pi\) |
0.136886 | + | 0.990587i | \(0.456291\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 179443. | + | 2.60157e6i | 0.0163427 | + | 0.236937i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.91187e6 | + | 4.90831e6i | −0.353566 | + | 0.443628i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.98333e6 | 0.805794 | 0.402897 | − | 0.915245i | \(-0.368003\pi\) | ||||
0.402897 | + | 0.915245i | \(0.368003\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.77555e6 | 0.336106 | 0.168053 | − | 0.985778i | \(-0.446252\pi\) | ||||
0.168053 | + | 0.985778i | \(0.446252\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −90726.4 | − | 1.61127e6i | −0.00801585 | − | 0.142359i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.71982e6 | − | 5.41915e6i | 0.413877 | − | 0.475201i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.25475e7 | − | 1.25475e7i | −1.09205 | − | 1.09205i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.27222e7 | + | 1.42404e7i | −1.09900 | + | 1.23014i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.43476e7i | 1.23019i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.92841e6 | + | 3.92841e6i | −0.334333 | + | 0.334333i | −0.854229 | − | 0.519897i | \(-0.825970\pi\) |
0.519897 | + | 0.854229i | \(0.325970\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.12859e7 | − | 3.57137e6i | 0.953403 | − | 0.301700i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.42349e6 | − | 9.42349e6i | 0.790206 | − | 0.790206i | −0.191322 | − | 0.981527i | \(-0.561277\pi\) |
0.981527 | + | 0.191322i | \(0.0612773\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.16048e6i | 0.429552i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.15335e7 | − | 1.29098e7i | 0.952998 | − | 1.06672i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.25718e6 | − | 9.25718e6i | −0.759323 | − | 0.759323i | 0.216876 | − | 0.976199i | \(-0.430413\pi\) |
−0.976199 | + | 0.216876i | \(0.930413\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.38800e6 | + | 7.33451e6i | −0.520162 | + | 0.597234i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.18403e6 | − | 2.10280e7i | −0.0957127 | − | 1.69983i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.95628e7 | −2.37245 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.39289e6 | −0.668677 | −0.334339 | − | 0.942453i | \(-0.608513\pi\) | ||||
−0.334339 | + | 0.942453i | \(0.608513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.63618e7 | + | 2.05295e7i | −1.29419 | + | 1.62385i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −341828. | − | 4.95583e6i | −0.0268439 | − | 0.389183i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.10898e6 | − | 1.10898e6i | −0.0864649 | − | 0.0864649i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.47953e6 | − | 3.10858e6i | −0.269357 | − | 0.240640i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 70263.9i | − | 0.00540054i | −0.999996 | − | 0.00270027i | \(-0.999140\pi\) | ||
0.999996 | − | 0.00270027i | \(-0.000859523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.08066e6 | − | 4.08066e6i | 0.311417 | − | 0.311417i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.40184e6 | + | 4.38065e6i | −0.257775 | + | 0.331944i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.77748e6 | − | 6.77748e6i | 0.509941 | − | 0.509941i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1.88394e7i | − | 1.40751i | −0.710444 | − | 0.703753i | \(-0.751506\pi\) | ||
0.710444 | − | 0.703753i | \(-0.248494\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.12174e6 | − | 9.92934e6i | −0.0832185 | − | 0.736625i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.78839e6 | − | 4.78839e6i | −0.352749 | − | 0.352749i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.70916e7 | − | 1.48859e7i | −1.25031 | − | 1.08896i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.72967e7 | + | 973931.i | −1.25651 | + | 0.0707506i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.51796e7 | 1.81646 | 0.908232 | − | 0.418467i | \(-0.137432\pi\) | ||||
0.908232 | + | 0.418467i | \(0.137432\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.41864e7 | −2.44915 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.80232e6 | − | 439327.i | 0.555109 | − | 0.0312566i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.80092e7 | + | 2.49624e6i | −1.27248 | + | 0.176377i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.41853e6 | + | 6.41853e6i | 0.450401 | + | 0.450401i | 0.895488 | − | 0.445087i | \(-0.146827\pi\) |
−0.445087 | + | 0.895488i | \(0.646827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.35395e7 | − | 4.75117e6i | 0.943590 | − | 0.331117i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.08478e6i | 0.0750844i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −204706. | + | 204706.i | −0.0140725 | + | 0.0140725i | −0.714108 | − | 0.700036i | \(-0.753167\pi\) |
0.700036 | + | 0.714108i | \(0.253167\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.15011e6 | − | 2.50465e7i | −0.215084 | − | 1.71013i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.22023e6 | − | 6.22023e6i | 0.421830 | − | 0.421830i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.41366e6i | 0.297295i | 0.988890 | + | 0.148648i | \(0.0474920\pi\) | ||||
−0.988890 | + | 0.148648i | \(0.952508\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.60859e6 | + | 5.01065e6i | 0.375239 | + | 0.335235i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.20078e6 | + | 2.20078e6i | 0.146253 | + | 0.146253i | 0.776442 | − | 0.630189i | \(-0.217023\pi\) |
−0.630189 | + | 0.776442i | \(0.717023\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.56709e7 | + | 1.08090e6i | −1.03443 | + | 0.0713500i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.50652e7 | + | 1.20068e7i | 0.987811 | + | 0.787275i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.59056e7 | 1.03597 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.91761e7 | 1.24068 | 0.620342 | − | 0.784331i | \(-0.286994\pi\) | ||||
0.620342 | + | 0.784331i | \(0.286994\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 58651.2 | + | 1.04163e6i | 0.00376955 | + | 0.0669462i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.13002e7 | + | 1.46918e6i | −1.35993 | + | 0.0938008i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.86673e7 | + | 1.86673e7i | 1.18397 | + | 1.18397i | 0.978706 | + | 0.205268i | \(0.0658066\pi\) |
0.205268 | + | 0.978706i | \(0.434193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.59943e7 | + | 1.79030e7i | −1.00777 | + | 1.12803i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.47189e7i | − | 1.54727i | −0.633630 | − | 0.773636i | \(-0.718436\pi\) | ||
0.633630 | − | 0.773636i | \(-0.281564\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.60659e6 | + | 1.60659e6i | −0.0999066 | + | 0.0999066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −994751. | + | 1.44150e6i | −0.0614555 | + | 0.0890557i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.70787e6 | − | 3.70787e6i | 0.227581 | − | 0.227581i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.40867e7i | 1.46880i | 0.678718 | + | 0.734399i | \(0.262536\pi\) | ||||
−0.678718 | + | 0.734399i | \(0.737464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.62962e7 | + | 1.82409e7i | −0.987301 | + | 1.10512i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.74914e7 | + | 1.74914e7i | 1.05287 | + | 1.05287i | 0.998522 | + | 0.0543506i | \(0.0173089\pi\) |
0.0543506 | + | 0.998522i | \(0.482691\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.87269e6 | + | 952619.i | −0.411029 | + | 0.0569724i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.80084e6 | − | 3.19824e7i | −0.107010 | − | 1.90046i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.30880e6 | 0.431522 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.49470e7 | 2.05013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.17257e7 | + | 3.70127e6i | −1.26640 | + | 0.215748i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.39684e6 | + | 6.44229e6i | 0.428423 | + | 0.373135i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35513.6 | − | 35513.6i | −0.00204389 | − | 0.00204389i | 0.706084 | − | 0.708128i | \(-0.250460\pi\) |
−0.708128 | + | 0.706084i | \(0.750460\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 186520. | + | 166635.i | 0.0106668 | + | 0.00952958i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.62454e7i | 0.923188i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.61332e7 | − | 1.61332e7i | 0.911041 | − | 0.911041i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.53399e7 | + | 1.96780e7i | 1.42196 | + | 1.10424i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.28117e7 | + | 2.28117e7i | −1.27207 | + | 1.27207i | −0.327076 | + | 0.944998i | \(0.606063\pi\) |
−0.944998 | + | 0.327076i | \(0.893937\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 820618.i | − | 0.0454752i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.31862e7 | − | 1.48968e6i | 0.726168 | − | 0.0820371i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.22219e6 | − | 9.22219e6i | −0.504714 | − | 0.504714i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.51014e6 | − | 3.63921e7i | −0.136524 | − | 1.97933i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.36644e7 | + | 1.33248e6i | −1.27912 | + | 0.0720237i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.76782e7 | −1.48685 | −0.743424 | − | 0.668820i | \(-0.766800\pi\) | ||||
−0.743424 | + | 0.668820i | \(0.766800\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.48077e7 | 1.32445 | 0.662224 | − | 0.749306i | \(-0.269613\pi\) | ||||
0.662224 | + | 0.749306i | \(0.269613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.57047e7 | − | 2.01043e6i | 1.89452 | − | 0.106675i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.84338e6 | − | 7.85736e6i | 0.360892 | − | 0.414365i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.57468e6 | − | 3.57468e6i | −0.187362 | − | 0.187362i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.14825e7 | − | 4.68639e6i | 2.16100 | − | 0.244134i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.39255e7i | − | 1.23880i | −0.785074 | − | 0.619402i | \(-0.787375\pi\) | ||
0.785074 | − | 0.619402i | \(-0.212625\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.14187e7 | + | 2.14187e7i | −1.10228 | + | 1.10228i | −0.108147 | + | 0.994135i | \(0.534492\pi\) |
−0.994135 | + | 0.108147i | \(0.965508\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.74156e6 | + | 2.41362e7i | 0.242542 | + | 1.23462i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.79808e6 | + | 9.79808e6i | −0.498170 | + | 0.498170i | −0.910868 | − | 0.412698i | \(-0.864586\pi\) |
0.412698 | + | 0.910868i | \(0.364586\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 5.48957e6i | − | 0.277429i | −0.990332 | − | 0.138714i | \(-0.955703\pi\) | ||
0.990332 | − | 0.138714i | \(-0.0442970\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −886891. | − | 792338.i | −0.0445520 | − | 0.0398023i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.64101e6 | + | 2.64101e6i | 0.131874 | + | 0.131874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.86991e6 | − | 6.73966e6i | 0.291350 | − | 0.334520i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.29098e6 | + | 1.41248e6i | −0.409065 | + | 0.0696898i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.25564e7 | −1.10628 | −0.553139 | − | 0.833089i | \(-0.686570\pi\) | ||||
−0.553139 | + | 0.833089i | \(0.686570\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.33385e7 | 0.650305 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.81452e6 | + | 3.22253e7i | 0.0879411 | + | 1.56181i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.05190e6 | + | 1.52505e7i | 0.0506795 | + | 0.734753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.42078e7 | − | 1.42078e7i | −0.680484 | − | 0.680484i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.21392e7 | − | 1.35879e7i | 0.577992 | − | 0.646967i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.92937e7i | − | 1.38660i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.04195e7 | + | 2.04195e7i | −0.960889 | + | 0.960889i | −0.999263 | − | 0.0383747i | \(-0.987782\pi\) |
0.0383747 | + | 0.999263i | \(0.487782\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.47218e6 | − | 8.02817e6i | −0.0688724 | − | 0.375579i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.82606e7 | + | 1.82606e7i | −0.849301 | + | 0.849301i | −0.990046 | − | 0.140744i | \(-0.955050\pi\) |
0.140744 | + | 0.990046i | \(0.455050\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.20747e7i | 1.94553i | 0.231795 | + | 0.972765i | \(0.425540\pi\) | ||||
−0.231795 | + | 0.972765i | \(0.574460\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.70288e7 | − | 3.02543e7i | 1.24257 | − | 1.39085i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.06377e6 | + | 6.06377e6i | 0.277151 | + | 0.277151i | 0.831971 | − | 0.554820i | \(-0.187213\pi\) |
−0.554820 | + | 0.831971i | \(0.687213\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.05898e7 | + | 9.22323e6i | 0.481226 | + | 0.419124i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.22973e6 | + | 2.18397e7i | 0.0555600 | + | 0.986729i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.07638e7 | 0.932734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.39887e7 | −0.624788 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.58348e6 | + | 3.65298e6i | 0.203545 | + | 0.162223i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.12881e7 | − | 2.04454e7i | −1.38153 | − | 0.902766i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.55418e7 | − | 1.55418e7i | −0.682342 | − | 0.682342i | 0.278185 | − | 0.960527i | \(-0.410267\pi\) |
−0.960527 | + | 0.278185i | \(0.910267\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.83834e6 | + | 7.00268e6i | 0.342178 | + | 0.305698i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.84506e6i | − | 0.166902i | −0.996512 | − | 0.0834512i | \(-0.973406\pi\) | ||
0.996512 | − | 0.0834512i | \(-0.0265943\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.06162e7 | − | 3.06162e7i | 1.32145 | − | 1.32145i | 0.408843 | − | 0.912605i | \(-0.365932\pi\) |
0.912605 | − | 0.408843i | \(-0.134068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.64629e6 | + | 710138.i | −0.242329 | + | 0.0304779i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −6.56472e6 | + | 6.56472e6i | −0.280161 | + | 0.280161i | −0.833173 | − | 0.553012i | \(-0.813478\pi\) |
0.553012 | + | 0.833173i | \(0.313478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 3.76915e7i | − | 1.59952i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.65192e6 | + | 2.90647e7i | 0.280707 | + | 1.22651i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.70418e6 | + | 2.70418e6i | 0.113477 | + | 0.113477i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.25397e7 | − | 864925.i | 0.523275 | − | 0.0360928i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.81160e7 | − | 2.14620e6i | 1.58171 | − | 0.0890615i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.29177e7 | 0.533074 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.74687e6 | −0.194803 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.80168e7 | + | 1.57755e6i | −1.14340 | + | 0.0643817i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.39971e7 | − | 1.65519e6i | 0.973949 | − | 0.0671781i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.62226e6 | + | 6.62226e6i | 0.267293 | + | 0.267293i | 0.828009 | − | 0.560715i | \(-0.189474\pi\) |
−0.560715 | + | 0.828009i | \(0.689474\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.22206e6 | − | 1.08173e7i | −0.0490549 | − | 0.434219i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.25035e7i | − | 0.898368i | −0.893439 | − | 0.449184i | \(-0.851715\pi\) | ||
0.893439 | − | 0.449184i | \(-0.148285\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.83059e7 | + | 2.83059e7i | −1.12383 | + | 1.12383i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.45675e7 | + | 3.08986e6i | −0.970080 | + | 0.122008i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.05738e6 | − | 7.05738e6i | 0.277153 | − | 0.277153i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.33232e7i | 0.910960i | 0.890246 | + | 0.455480i | \(0.150532\pi\) | ||||
−0.890246 | + | 0.455480i | \(0.849468\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.50614e6 | − | 7.59928e6i | −0.330433 | − | 0.295205i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.92963e7 | − | 3.92963e7i | −1.51826 | − | 1.51826i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.39362e7 | − | 1.81084e7i | −0.919816 | − | 0.695868i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.41997e7 | + | 3.03639e7i | −0.924935 | + | 1.16054i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.09918e6 | −0.269879 | −0.134939 | − | 0.990854i | \(-0.543084\pi\) | ||||
−0.134939 | + | 0.990854i | \(0.543084\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.74058e7 | −0.658143 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 509056. | + | 9.04068e6i | 0.0191453 | + | 0.340014i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.74438e6 | − | 2.39022e6i | −0.102663 | − | 0.0894147i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.75325e6 | + | 6.75325e6i | 0.251284 | + | 0.251284i | 0.821497 | − | 0.570213i | \(-0.193139\pi\) |
−0.570213 | + | 0.821497i | \(0.693139\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.15876e7 | + | 1.29704e7i | −0.428874 | + | 0.480053i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1.55046e7i | − | 0.570802i | −0.958408 | − | 0.285401i | \(-0.907873\pi\) | ||
0.958408 | − | 0.285401i | \(-0.0921268\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.62337e7 | − | 2.62337e7i | 0.960683 | − | 0.960683i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.86764e7 | − | 2.35952e7i | −1.40885 | − | 0.859495i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.69942e7 | − | 1.69942e7i | 0.615779 | − | 0.615779i | −0.328667 | − | 0.944446i | \(-0.606599\pi\) |
0.944446 | + | 0.328667i | \(0.106599\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.07399e7i | 0.747550i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.82438e6 | − | 7.63876e6i | 0.244688 | − | 0.273887i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.69842e7 | − | 1.69842e7i | −0.605779 | − | 0.605779i | 0.336062 | − | 0.941840i | \(-0.390905\pi\) |
−0.941840 | + | 0.336062i | \(0.890905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.84560e6 | + | 2.67575e7i | 0.0654829 | + | 0.949373i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.57452e6 | − | 4.57227e7i | −0.0908691 | − | 1.61381i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.72255e7 | 1.30706 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.36995e7 | −0.827809 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.12592e7 | − | 1.41272e7i | 0.391239 | − | 0.490896i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.91335e7 | + | 3.34502e7i | −1.00710 | + | 1.15632i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.70755e7 | − | 3.70755e7i | −1.27503 | − | 1.27503i | −0.943415 | − | 0.331615i | \(-0.892406\pi\) |
−0.331615 | − | 0.943415i | \(-0.607594\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 900568. | + | 804557.i | 0.0308111 | + | 0.0275263i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.45718e6i | 0.0495982i | 0.999692 | + | 0.0247991i | \(0.00789460\pi\) | ||||
−0.999692 | + | 0.0247991i | \(0.992105\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.34439e7 | + | 1.34439e7i | −0.455241 | + | 0.455241i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.18084e7 | − | 3.24717e7i | 0.734705 | − | 1.09394i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.76383e7 | − | 1.76383e7i | 0.591182 | − | 0.591182i | −0.346769 | − | 0.937951i | \(-0.612721\pi\) |
0.937951 | + | 0.346769i | \(0.112721\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.75743e7i | 0.919493i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 289687. | + | 2.56422e6i | 0.00961073 | + | 0.0850713i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.17052e7 | + | 2.17052e7i | 0.716442 | + | 0.716442i | 0.967875 | − | 0.251433i | \(-0.0809018\pi\) |
−0.251433 | + | 0.967875i | \(0.580902\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.37115e7 | − | 1.57431e7i | 0.450292 | − | 0.517011i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.11941e7 | − | 1.19338e6i | 0.692505 | − | 0.0389930i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.56614e7 | −0.834238 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.38843e7 | −0.449095 | −0.224548 | − | 0.974463i | \(-0.572090\pi\) | ||||
−0.224548 | + | 0.974463i | \(0.572090\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.86609e6 | − | 330304.i | 0.188789 | − | 0.0106302i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 429134. | + | 6.22160e6i | 0.0137415 | + | 0.199225i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.43827e7 | + | 2.43827e7i | 0.776863 | + | 0.776863i | 0.979296 | − | 0.202433i | \(-0.0648849\pi\) |
−0.202433 | + | 0.979296i | \(0.564885\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.96811e7 | − | 2.10401e7i | −0.940951 | − | 0.667012i |
(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 | 60.6.i.a.17.10 | yes | 20 | |
3.2 | odd | 2 | inner | 60.6.i.a.17.5 | ✓ | 20 | |
5.2 | odd | 4 | 300.6.i.d.293.6 | 20 | |||
5.3 | odd | 4 | inner | 60.6.i.a.53.5 | yes | 20 | |
5.4 | even | 2 | 300.6.i.d.257.1 | 20 | |||
15.2 | even | 4 | 300.6.i.d.293.1 | 20 | |||
15.8 | even | 4 | inner | 60.6.i.a.53.10 | yes | 20 | |
15.14 | odd | 2 | 300.6.i.d.257.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.6.i.a.17.5 | ✓ | 20 | 3.2 | odd | 2 | inner | |
60.6.i.a.17.10 | yes | 20 | 1.1 | even | 1 | trivial | |
60.6.i.a.53.5 | yes | 20 | 5.3 | odd | 4 | inner | |
60.6.i.a.53.10 | yes | 20 | 15.8 | even | 4 | inner | |
300.6.i.d.257.1 | 20 | 5.4 | even | 2 | |||
300.6.i.d.257.6 | 20 | 15.14 | odd | 2 | |||
300.6.i.d.293.1 | 20 | 15.2 | even | 4 | |||
300.6.i.d.293.6 | 20 | 5.2 | odd | 4 |