Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3344,2,Mod(1519,3344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3344.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3344 = 2^{4} \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3344.o (of order \(2\), degree \(1\), 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: | \(26.7019744359\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.19 | ||
Character | \(\chi\) | \(=\) | 3344.1519 |
Dual form | 3344.2.o.b.1519.20 |
$q$-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 \(\left(\mathbb{Z}/3344\mathbb{Z}\right)^\times\).
\(n\) | \(705\) | \(837\) | \(2433\) | \(2927\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.41745 | −0.818365 | −0.409182 | − | 0.912453i | \(-0.634186\pi\) | ||||
−0.409182 | + | 0.912453i | \(0.634186\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.36069 | 1.05573 | 0.527866 | − | 0.849328i | \(-0.322992\pi\) | ||||
0.527866 | + | 0.849328i | \(0.322992\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85642i | 1.07963i | 0.841785 | + | 0.539813i | \(0.181505\pi\) | ||||
−0.841785 | + | 0.539813i | \(0.818495\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.990838 | −0.330279 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000i | 0.301511i | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.49937i | − | 1.52525i | −0.646841 | − | 0.762625i | \(-0.723910\pi\) | ||
0.646841 | − | 0.762625i | \(-0.276090\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.34616 | −0.863974 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.747022 | −0.181179 | −0.0905897 | − | 0.995888i | \(-0.528875\pi\) | ||||
−0.0905897 | + | 0.995888i | \(0.528875\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.90515 | − | 3.92051i | −0.437072 | − | 0.899426i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.04883i | − | 0.883528i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.90067i | 1.43889i | 0.694549 | + | 0.719445i | \(0.255604\pi\) | ||||
−0.694549 | + | 0.719445i | \(0.744396\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.572849 | 0.114570 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.65681 | 1.08865 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.31965i | 0.430749i | 0.976532 | + | 0.215374i | \(0.0690972\pi\) | ||||
−0.976532 | + | 0.215374i | \(0.930903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.19493 | −0.214616 | −0.107308 | − | 0.994226i | \(-0.534223\pi\) | ||||
−0.107308 | + | 0.994226i | \(0.534223\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.41745i | − | 0.246746i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.74312i | 1.13980i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.00399i | − | 0.658252i | −0.944286 | − | 0.329126i | \(-0.893246\pi\) | ||
0.944286 | − | 0.329126i | \(-0.106754\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.79507i | 1.24821i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.90538i | 1.54696i | 0.633821 | + | 0.773480i | \(0.281486\pi\) | ||||
−0.633821 | + | 0.773480i | \(0.718514\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.59611i | 0.395904i | 0.980212 | + | 0.197952i | \(0.0634290\pi\) | ||||
−0.980212 | + | 0.197952i | \(0.936571\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.33906 | −0.348687 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.06027i | 1.17571i | 0.808966 | + | 0.587856i | \(0.200028\pi\) | ||||
−0.808966 | + | 0.587856i | \(0.799972\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.15915 | −0.165593 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.05887 | 0.148271 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.81166i | 0.248851i | 0.992229 | + | 0.124426i | \(0.0397088\pi\) | ||||
−0.992229 | + | 0.124426i | \(0.960291\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.36069i | 0.318315i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.70046 | + | 5.55712i | 0.357684 | + | 0.736059i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.29532 | 0.298825 | 0.149413 | − | 0.988775i | \(-0.452262\pi\) | ||||
0.149413 | + | 0.988775i | \(0.452262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.40218 | −1.20383 | −0.601913 | − | 0.798562i | \(-0.705595\pi\) | ||||
−0.601913 | + | 0.798562i | \(0.705595\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.83025i | − | 0.356578i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 12.9823i | − | 1.61026i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0326 | −1.47002 | −0.735008 | − | 0.678058i | \(-0.762822\pi\) | ||||
−0.735008 | + | 0.678058i | \(0.762822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 9.78135i | − | 1.17754i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.121811 | −0.0144563 | −0.00722815 | − | 0.999974i | \(-0.502301\pi\) | ||||
−0.00722815 | + | 0.999974i | \(0.502301\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.12024 | −0.599279 | −0.299640 | − | 0.954052i | \(-0.596866\pi\) | ||||
−0.299640 | + | 0.954052i | \(0.596866\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.811984 | −0.0937599 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.85642 | −0.325520 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.46660 | 0.502532 | 0.251266 | − | 0.967918i | \(-0.419153\pi\) | ||||
0.251266 | + | 0.967918i | \(0.419153\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.04572 | −0.560636 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5652i | 1.15969i | 0.814729 | + | 0.579843i | \(0.196886\pi\) | ||||
−0.814729 | + | 0.579843i | \(0.803114\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.76349 | −0.191277 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.28799i | − | 0.352510i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.36644i | − | 0.568841i | −0.958700 | − | 0.284421i | \(-0.908199\pi\) | ||
0.958700 | − | 0.284421i | \(-0.0918012\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.7085 | 1.64670 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.69376 | 0.175634 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.49747 | − | 9.25510i | −0.461431 | − | 0.949553i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.3695i | − | 1.05287i | −0.850217 | − | 0.526433i | \(-0.823529\pi\) | ||
0.850217 | − | 0.526433i | \(-0.176471\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 0.990838i | − | 0.0995830i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.49048 | −0.546323 | −0.273161 | − | 0.961968i | \(-0.588069\pi\) | ||||
−0.273161 | + | 0.961968i | \(0.588069\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.2513 | −1.60129 | −0.800643 | − | 0.599141i | \(-0.795509\pi\) | ||||
−0.800643 | + | 0.599141i | \(0.795509\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 9.55803i | − | 0.932768i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.82047 | 0.852707 | 0.426354 | − | 0.904557i | \(-0.359798\pi\) | ||||
0.426354 | + | 0.904557i | \(0.359798\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.68875i | − | 0.449101i | −0.974462 | − | 0.224551i | \(-0.927909\pi\) | ||
0.974462 | − | 0.224551i | \(-0.0720914\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.67546i | 0.538690i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.2668i | 1.05989i | 0.848032 | + | 0.529945i | \(0.177787\pi\) | ||||
−0.848032 | + | 0.529945i | \(0.822213\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.2903i | 1.51908i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.44898i | 0.503759i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 2.13381i | − | 0.195606i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 14.0404i | − | 1.26598i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.4511 | −0.934777 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.8349 | −1.40512 | −0.702559 | − | 0.711625i | \(-0.747959\pi\) | ||||
−0.702559 | + | 0.711625i | \(0.747959\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.67986i | − | 0.323994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.303222i | 0.0264926i | 0.999912 | + | 0.0132463i | \(0.00421655\pi\) | ||||
−0.999912 | + | 0.0132463i | \(0.995783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.1986 | − | 5.44192i | 0.971044 | − | 0.471875i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.3540 | 1.14933 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.9530 | 1.10665 | 0.553323 | − | 0.832967i | \(-0.313360\pi\) | ||||
0.553323 | + | 0.832967i | \(0.313360\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.77585i | 0.150626i | 0.997160 | + | 0.0753130i | \(0.0239956\pi\) | ||||
−0.997160 | + | 0.0753130i | \(0.976004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 11.4250i | − | 0.962160i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.49937 | 0.459880 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.47598i | 0.454755i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.64303 | 0.135515 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.89791 | −0.728946 | −0.364473 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364473 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.8154 | −1.28704 | −0.643519 | − | 0.765430i | \(-0.722526\pi\) | ||||
−0.643519 | + | 0.765430i | \(0.722526\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.740178 | 0.0598398 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.82086 | −0.226577 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.4342 | 1.63082 | 0.815412 | − | 0.578881i | \(-0.196511\pi\) | ||||
0.815412 | + | 0.578881i | \(0.196511\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 2.56794i | − | 0.203651i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.7112 | −1.55346 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.90104i | − | 0.540531i | −0.962786 | − | 0.270266i | \(-0.912888\pi\) | ||
0.962786 | − | 0.270266i | \(-0.0871115\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 3.34616i | − | 0.260498i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.6670 | −1.28973 | −0.644866 | − | 0.764296i | \(-0.723087\pi\) | ||||
−0.644866 | + | 0.764296i | \(0.723087\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −17.2430 | −1.32639 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.88770 | + | 3.88459i | 0.144356 | + | 0.297062i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.35319i | 0.483024i | 0.970398 | + | 0.241512i | \(0.0776434\pi\) | ||||
−0.970398 | + | 0.241512i | \(0.922357\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.63630i | 0.123693i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.25350 | −0.244548 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.6854 | −1.32187 | −0.660936 | − | 0.750442i | \(-0.729840\pi\) | ||||
−0.660936 | + | 0.750442i | \(0.729840\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.3156i | 1.80736i | 0.428205 | + | 0.903682i | \(0.359146\pi\) | ||||
−0.428205 | + | 0.903682i | \(0.640854\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.3271 | 0.985168 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 9.45218i | − | 0.694938i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 0.747022i | − | 0.0546276i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.1582i | 1.17534i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.41500i | 0.319458i | 0.987161 | + | 0.159729i | \(0.0510621\pi\) | ||||
−0.987161 | + | 0.159729i | \(0.948938\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.3885i | 1.39561i | 0.716287 | + | 0.697806i | \(0.245840\pi\) | ||||
−0.716287 | + | 0.697806i | \(0.754160\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.4017i | 1.31778i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.6160 | −1.32634 | −0.663169 | − | 0.748470i | \(-0.730789\pi\) | ||||
−0.663169 | + | 0.748470i | \(0.730789\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.43761i | 0.314574i | 0.987553 | + | 0.157287i | \(0.0502748\pi\) | ||||
−0.987553 | + | 0.157287i | \(0.949725\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.0556 | 1.20301 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.62591 | −0.465048 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.3835i | 1.63318i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.83745i | − | 0.475236i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.92051 | − | 1.90515i | 0.271187 | − | 0.131782i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.71830 | 0.600193 | 0.300096 | − | 0.953909i | \(-0.402981\pi\) | ||||
0.300096 | + | 0.953909i | \(0.402981\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.172661 | 0.0118305 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.12862i | 0.417968i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 3.41323i | − | 0.231705i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.25768 | 0.490429 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.10815i | 0.276344i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.12773 | 0.0755184 | 0.0377592 | − | 0.999287i | \(-0.487978\pi\) | ||||
0.0377592 | + | 0.999287i | \(0.487978\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.567601 | −0.0378401 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −13.7541 | −0.912895 | −0.456447 | − | 0.889750i | \(-0.650878\pi\) | ||||
−0.456447 | + | 0.889750i | \(0.650878\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.1290 | 0.999751 | 0.499876 | − | 0.866097i | \(-0.333379\pi\) | ||||
0.499876 | + | 0.866097i | \(0.333379\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.04883 | 0.266394 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.86111 | 0.646023 | 0.323012 | − | 0.946395i | \(-0.395305\pi\) | ||||
0.323012 | + | 0.946395i | \(0.395305\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.0278i | 1.24124i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.33118 | −0.411254 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.98810i | 0.322654i | 0.986901 | + | 0.161327i | \(0.0515773\pi\) | ||||
−0.986901 | + | 0.161327i | \(0.948423\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.56526i | 0.358490i | 0.983804 | + | 0.179245i | \(0.0573655\pi\) | ||||
−0.983804 | + | 0.179245i | \(0.942634\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −9.81837 | −0.629849 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.73639 | −0.174821 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.5603 | + | 10.4771i | −1.37185 | + | 0.666645i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 14.9757i | − | 0.949045i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.63885i | − | 0.103443i | −0.998662 | − | 0.0517215i | \(-0.983529\pi\) | ||
0.998662 | − | 0.0517215i | \(-0.0164708\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.90067 | −0.433842 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.49965 | 0.156534 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.23102i | 0.201546i | 0.994909 | + | 0.100773i | \(0.0321315\pi\) | ||||
−0.994909 | + | 0.100773i | \(0.967868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.4371 | 0.710667 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.29840i | − | 0.142268i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 16.6565i | − | 1.02709i | −0.858064 | − | 0.513543i | \(-0.828333\pi\) | ||
0.858064 | − | 0.513543i | \(-0.171667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.27677i | 0.262720i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.60665i | 0.465519i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 26.1317i | − | 1.59328i | −0.604454 | − | 0.796640i | \(-0.706609\pi\) | ||
0.604454 | − | 0.796640i | \(-0.293391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 1.63390i | − | 0.0992523i | −0.998768 | − | 0.0496262i | \(-0.984197\pi\) | ||
0.998768 | − | 0.0496262i | \(-0.0158030\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −22.2660 | −1.34760 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.572849i | 0.0345441i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.17565 | 0.250890 | 0.125445 | − | 0.992101i | \(-0.459964\pi\) | ||||
0.125445 | + | 0.992101i | \(0.459964\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.18399 | 0.0708834 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 14.9726i | − | 0.893192i | −0.894736 | − | 0.446596i | \(-0.852636\pi\) | ||
0.894736 | − | 0.446596i | \(-0.147364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 0.171136i | − | 0.0101730i | −0.999987 | − | 0.00508650i | \(-0.998381\pi\) | ||
0.999987 | − | 0.00508650i | \(-0.00161909\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.37494 | + | 13.1186i | 0.377619 | + | 0.777081i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.2939 | −1.67014 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.4420 | −0.967174 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6983i | 0.861629i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 21.0522i | 1.22988i | 0.788573 | + | 0.614941i | \(0.210820\pi\) | ||||
−0.788573 | + | 0.614941i | \(0.789180\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.41853 | 0.315479 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.65681i | 0.328241i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 37.9493 | 2.19467 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.41560 | −0.427428 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.78247 | 0.447091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −22.1956 | −1.27092 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.42551 | −0.366723 | −0.183361 | − | 0.983046i | \(-0.558698\pi\) | ||||
−0.183361 | + | 0.983046i | \(0.558698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.0354 | 1.31044 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.6582i | 1.73847i | 0.494401 | + | 0.869234i | \(0.335388\pi\) | ||||
−0.494401 | + | 0.869234i | \(0.664612\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0875 | 1.13541 | 0.567707 | − | 0.823231i | \(-0.307831\pi\) | ||||
0.567707 | + | 0.823231i | \(0.307831\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 6.68134i | − | 0.376451i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.2341i | 0.630971i | 0.948930 | + | 0.315485i | \(0.102167\pi\) | ||||
−0.948930 | + | 0.315485i | \(0.897833\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.31965 | −0.129876 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.5026 | −0.697826 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.42319 | + | 2.92871i | 0.0791885 | + | 0.162958i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.15031i | − | 0.174748i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.64607i | 0.367528i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −23.0235 | −1.26933 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7640 | −0.701571 | −0.350785 | − | 0.936456i | \(-0.614085\pi\) | ||||
−0.350785 | + | 0.936456i | \(0.614085\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.96731i | 0.217407i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −28.4052 | −1.55194 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 34.0522i | − | 1.85494i | −0.373893 | − | 0.927472i | \(-0.621977\pi\) | ||
0.373893 | − | 0.927472i | \(-0.378023\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 15.9701i | − | 0.867376i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.19493i | − | 0.0647093i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.6839i | 0.900848i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 23.0907i | − | 1.24316i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.89622i | 0.209160i | 0.994516 | + | 0.104580i | \(0.0333498\pi\) | ||||
−0.994516 | + | 0.104580i | \(0.966650\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.7263 | 0.627697 | 0.313849 | − | 0.949473i | \(-0.398382\pi\) | ||||
0.313849 | + | 0.949473i | \(0.398382\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 31.1089i | − | 1.66047i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.8518 | −1.00338 | −0.501691 | − | 0.865047i | \(-0.667288\pi\) | ||||
−0.501691 | + | 0.865047i | \(0.667288\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.287558 | −0.0152620 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.02457i | 0.160077i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.2241i | − | 1.27850i | −0.768999 | − | 0.639250i | \(-0.779245\pi\) | ||
0.768999 | − | 0.639250i | \(-0.220755\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.7408 | + | 14.9383i | −0.617936 | + | 0.786229i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.41745 | 0.0743968 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0873 | −0.632678 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.8522i | 1.40167i | 0.713322 | + | 0.700837i | \(0.247190\pi\) | ||||
−0.713322 | + | 0.700837i | \(0.752810\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 9.81463i | − | 0.510929i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.17488 | −0.268666 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.6582i | − | 1.17320i | −0.809877 | − | 0.586600i | \(-0.800466\pi\) | ||
0.809877 | − | 0.586600i | \(-0.199534\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.8139 | 0.764988 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.7566 | 0.657000 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.6082 | −1.16131 | −0.580654 | − | 0.814151i | \(-0.697203\pi\) | ||||
−0.580654 | + | 0.814151i | \(0.697203\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 22.4451 | 1.14990 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.6404 | 0.645893 | 0.322947 | − | 0.946417i | \(-0.395327\pi\) | ||||
0.322947 | + | 0.946417i | \(0.395327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.74312 | −0.343661 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 2.57233i | − | 0.130759i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6466 | −0.641206 | −0.320603 | − | 0.947214i | \(-0.603886\pi\) | ||||
−0.320603 | + | 0.947214i | \(0.603886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 5.15495i | − | 0.260697i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 0.429801i | − | 0.0216806i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5443 | 0.530539 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.2631 | 1.36830 | 0.684149 | − | 0.729342i | \(-0.260174\pi\) | ||||
0.684149 | + | 0.729342i | \(0.260174\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.8735 | + | 7.71365i | −0.794668 | + | 0.386165i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.9672i | 0.797363i | 0.917089 | + | 0.398682i | \(0.130532\pi\) | ||||
−0.917089 | + | 0.398682i | \(0.869468\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.57138i | 0.327344i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −11.9114 | −0.591881 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.00399 | 0.198471 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.6851i | 1.31949i | 0.751488 | + | 0.659747i | \(0.229337\pi\) | ||||
−0.751488 | + | 0.659747i | \(0.770663\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.3602 | −0.905640 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.55640i | 0.322619i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.9412i | 1.22432i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.51718i | − | 0.123267i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.48659i | 0.268038i | 0.990979 | + | 0.134019i | \(0.0427883\pi\) | ||||
−0.990979 | + | 0.134019i | \(0.957212\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.1252i | 1.61442i | 0.590264 | + | 0.807211i | \(0.299024\pi\) | ||||
−0.590264 | + | 0.807211i | \(0.700976\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 7.98643i | − | 0.388313i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.427931 | −0.0207577 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 26.8566i | − | 1.29968i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.79507 | −0.376350 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.09401 | 0.341706 | 0.170853 | − | 0.985296i | \(-0.445348\pi\) | ||||
0.170853 | + | 0.985296i | \(0.445348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.765804i | 0.0368022i | 0.999831 | + | 0.0184011i | \(0.00585759\pi\) | ||||
−0.999831 | + | 0.0184011i | \(0.994142\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 7.76192i | − | 0.372156i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.0542 | − | 13.1468i | 1.29418 | − | 0.628899i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7411 | −1.08537 | −0.542687 | − | 0.839935i | \(-0.682593\pi\) | ||||
−0.542687 | + | 0.839935i | \(0.682593\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.14853 | 0.0546918 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0871i | 0.669300i | 0.942343 | + | 0.334650i | \(0.108618\pi\) | ||||
−0.942343 | + | 0.334650i | \(0.891382\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 12.6685i | − | 0.600544i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.6123 | 0.596543 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 18.2937i | − | 0.863332i | −0.902034 | − | 0.431666i | \(-0.857926\pi\) | ||
0.902034 | − | 0.431666i | \(-0.142074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.90538 | −0.466426 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.4175 | 1.05327 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 37.0829 | 1.73847 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8553 | −0.835238 | −0.417619 | − | 0.908622i | \(-0.637135\pi\) | ||||
−0.417619 | + | 0.908622i | \(0.637135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.22576 | −0.197242 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0096 | 1.02509 | 0.512545 | − | 0.858660i | \(-0.328703\pi\) | ||||
0.512545 | + | 0.858660i | \(0.328703\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 21.2764i | − | 0.988799i | −0.869235 | − | 0.494399i | \(-0.835388\pi\) | ||
0.869235 | − | 0.494399i | \(-0.164612\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.99843 | 0.185423 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.06408i | 0.188063i | 0.995569 | + | 0.0940316i | \(0.0299755\pi\) | ||||
−0.995569 | + | 0.0940316i | \(0.970025\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 34.3702i | − | 1.58707i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −28.9644 | −1.33461 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −2.59611 | −0.119369 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.09137 | − | 2.24586i | −0.0500753 | − | 0.103047i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 1.79507i | − | 0.0821904i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 28.4469i | − | 1.29977i | −0.760032 | − | 0.649886i | \(-0.774817\pi\) | ||
0.760032 | − | 0.649886i | \(-0.225183\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.0194 | −1.00400 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 27.9397 | 1.27130 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 24.4792i | − | 1.11154i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.5512 | 0.931265 | 0.465632 | − | 0.884978i | \(-0.345827\pi\) | ||||
0.465632 | + | 0.884978i | \(0.345827\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.78188i | 0.442352i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.32477i | − | 0.104915i | −0.998623 | − | 0.0524577i | \(-0.983295\pi\) | ||
0.998623 | − | 0.0524577i | \(-0.0167055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.73283i | − | 0.0780428i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 2.33906i | − | 0.105133i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.347943i | − | 0.0156074i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.39830i | 0.152129i | 0.997103 | + | 0.0760645i | \(0.0242355\pi\) | ||||
−0.997103 | + | 0.0760645i | \(0.975765\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 23.6246 | 1.05547 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.1892i | − | 1.34607i | −0.739610 | − | 0.673035i | \(-0.764990\pi\) | ||
0.739610 | − | 0.673035i | \(-0.235010\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.9613 | −0.576770 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.4411 | 1.08547 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.0179i | 0.577010i | 0.957478 | + | 0.288505i | \(0.0931582\pi\) | ||||
−0.957478 | + | 0.288505i | \(0.906842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.6256i | − | 0.646997i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.7771 | − | 22.1776i | −0.475820 | − | 0.979164i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.3642 | −1.69053 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.06027 | −0.354490 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 9.00533i | − | 0.395290i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.20269i | 0.140312i | 0.997536 | + | 0.0701562i | \(0.0223498\pi\) | ||||
−0.997536 | + | 0.0701562i | \(0.977650\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.6892 | 1.07958 | 0.539791 | − | 0.841799i | \(-0.318503\pi\) | ||||
0.539791 | + | 0.841799i | \(0.318503\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 2.31937i | − | 0.101226i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.892641 | 0.0388841 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −24.6193 | −1.07040 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27429 | −0.0986958 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 54.4733 | 2.35950 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20.8224 | 0.900230 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.0682 | 1.08177 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.15915i | − | 0.0499280i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.1904 | −0.438120 | −0.219060 | − | 0.975711i | \(-0.570299\pi\) | ||||
−0.219060 | + | 0.975711i | \(0.570299\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 34.4661i | − | 1.47908i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 11.0687i | − | 0.474130i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2689 | 1.29421 | 0.647103 | − | 0.762403i | \(-0.275980\pi\) | ||||
0.647103 | + | 0.762403i | \(0.275980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.31604 | 0.397599 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.09422 | − | 4.41930i | 0.387427 | − | 0.188268i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7585i | 0.542546i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.3980i | 0.568713i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.0246473 | 0.00104434 | 0.000522169 | − | 1.00000i | \(-0.499834\pi\) | ||||
0.000522169 | 1.00000i | \(0.499834\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.2770 | 0.603852 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.05887i | 0.0447053i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.7494 | 1.04306 | 0.521531 | − | 0.853233i | \(-0.325361\pi\) | ||||
0.521531 | + | 0.853233i | \(0.325361\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.5974i | 1.11896i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 14.4127i | − | 0.605277i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.57504i | 0.107951i | 0.998542 | + | 0.0539756i | \(0.0171893\pi\) | ||||
−0.998542 | + | 0.0539756i | \(0.982811\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.52277i | 0.147423i | 0.997280 | + | 0.0737117i | \(0.0234845\pi\) | ||||
−0.997280 | + | 0.0737117i | \(0.976516\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.25804i | − | 0.261433i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.95304i | 0.164853i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.0816 | −0.544594 | −0.272297 | − | 0.962213i | \(-0.587783\pi\) | ||||
−0.272297 | + | 0.962213i | \(0.587783\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 27.4821i | − | 1.14212i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.1788 | −1.25203 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.81166 | −0.0750315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.8634i | 0.531834i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 26.5279i | − | 1.09492i | −0.836831 | − | 0.547461i | \(-0.815595\pi\) | ||
0.836831 | − | 0.547461i | \(-0.184405\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.27653 | + | 4.68475i | 0.0938028 | + | 0.193032i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 26.3873 | 1.08543 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.60973 | 0.312494 | 0.156247 | − | 0.987718i | \(-0.450060\pi\) | ||||
0.156247 | + | 0.987718i | \(0.450060\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 5.03726i | − | 0.206507i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 6.29009i | − | 0.257436i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.6027 | 1.49555 | 0.747773 | − | 0.663954i | \(-0.231123\pi\) | ||||
0.747773 | + | 0.663954i | \(0.231123\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 16.3639i | − | 0.667497i | −0.942662 | − | 0.333748i | \(-0.891686\pi\) | ||
0.942662 | − | 0.333748i | \(-0.108314\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.9224 | 0.485516 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.36069 | −0.0959756 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 46.9997 | 1.90766 | 0.953830 | − | 0.300347i | \(-0.0971023\pi\) | ||||
0.953830 | + | 0.300347i | \(0.0971023\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.39189 | 0.380579 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44.3264 | 1.79325 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.3632 | 1.91298 | 0.956490 | − | 0.291764i | \(-0.0942422\pi\) | ||||
0.956490 | + | 0.291764i | \(0.0942422\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 33.1449i | − | 1.33653i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.8329 | 0.838701 | 0.419350 | − | 0.907825i | \(-0.362258\pi\) | ||||
0.419350 | + | 0.907825i | \(0.362258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.1478i | 0.930389i | 0.885209 | + | 0.465194i | \(0.154016\pi\) | ||||
−0.885209 | + | 0.465194i | \(0.845984\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 39.0358i | 1.56645i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.3288 | 0.614136 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.5361 | −1.10144 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.55712 | + | 2.70046i | −0.221930 | + | 0.107846i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.99107i | 0.119262i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.2532i | 0.607219i | 0.952797 | + | 0.303609i | \(0.0981918\pi\) | ||||
−0.952797 | + | 0.303609i | \(0.901808\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −12.3578 | −0.491177 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −37.3812 | −1.48343 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.37458i | 0.252570i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.120695 | 0.00477462 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 37.6876i | 1.48857i | 0.667862 | + | 0.744285i | \(0.267210\pi\) | ||||
−0.667862 | + | 0.744285i | \(0.732790\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.12184i | − | 0.280858i | −0.990091 | − | 0.140429i | \(-0.955152\pi\) | ||
0.990091 | − | 0.140429i | \(-0.0448482\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 8.68700i | − | 0.342050i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 0.654870i | − | 0.0257456i | −0.999917 | − | 0.0128728i | \(-0.995902\pi\) | ||
0.999917 | − | 0.0128728i | \(-0.00409765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.29532i | 0.0900992i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.83808i | 0.189619i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.6710 | 1.70898 | 0.854489 | − | 0.519469i | \(-0.173870\pi\) | ||||
0.854489 | + | 0.519469i | \(0.173870\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.715812i | 0.0279691i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.07333 | 0.197930 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.2529 | −1.41221 | −0.706106 | − | 0.708106i | \(-0.749550\pi\) | ||||
−0.706106 | + | 0.708106i | \(0.749550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0067i | 0.467008i | 0.972356 | + | 0.233504i | \(0.0750192\pi\) | ||||
−0.972356 | + | 0.233504i | \(0.924981\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 5.82309i | − | 0.226150i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.4365 | − | 12.8467i | 1.02516 | − | 0.498173i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.0072 | −0.619800 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.59850 | −0.0618016 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 9.40218i | − | 0.362967i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 37.3402i | − | 1.43936i | −0.694307 | − | 0.719679i | \(-0.744289\pi\) | ||
0.694307 | − | 0.719679i | \(-0.255711\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.24050 | 0.124727 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.2570i | 1.58563i | 0.609460 | + | 0.792817i | \(0.291386\pi\) | ||||
−0.609460 | + | 0.792817i | \(0.708614\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 29.6198 | 1.13670 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.4958 | 0.747081 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7405 | −1.55889 | −0.779447 | − | 0.626469i | \(-0.784500\pi\) | ||||
−0.779447 | + | 0.626469i | \(0.784500\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30.5779 | 1.16832 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.4446 | −0.818161 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.96301 | 0.379560 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47735i | 0.132285i | 0.997810 | + | 0.0661424i | \(0.0210692\pi\) | ||||
−0.997810 | + | 0.0661424i | \(0.978931\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.83025 | 0.107512 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.19224i | 0.159021i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.39953i | − | 0.280277i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.9776 | −0.528682 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 39.9299 | 1.50813 | 0.754066 | − | 0.656799i | \(-0.228090\pi\) | ||||
0.754066 | + | 0.656799i | \(0.228090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.6977 | + | 7.62822i | −0.592050 | + | 0.287704i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 26.9709i | − | 1.01578i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 15.6831i | − | 0.589824i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.1202 | 1.16874 | 0.584371 | − | 0.811486i | \(-0.301341\pi\) | ||||
0.584371 | + | 0.811486i | \(0.301341\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.42568 | −0.165976 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 8.24584i | − | 0.308809i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9823 | 0.485510 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 7.07038i | − | 0.264048i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 40.6566i | − | 1.51624i | −0.652118 | − | 0.758118i | \(-0.726119\pi\) | ||
0.652118 | − | 0.758118i | \(-0.273881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 46.4205i | − | 1.72879i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.88848i | − | 0.293376i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.32881i | 0.0493508i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1161i | 0.894417i | 0.894430 | + | 0.447208i | \(0.147582\pi\) | ||||
−0.894430 | + | 0.447208i | \(0.852418\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0542 | 1.07608 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.93935i | − | 0.0717296i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.1403 | 1.03939 | 0.519693 | − | 0.854353i | \(-0.326046\pi\) | ||||
0.519693 | + | 0.854353i | \(0.326046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.87869 | 0.143068 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 12.0326i | − | 0.443227i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 45.6353i | − | 1.67872i | −0.543575 | − | 0.839361i | \(-0.682930\pi\) | ||
0.543575 | − | 0.839361i | \(-0.317070\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 30.5607 | − | 14.8508i | 1.12267 | − | 0.545558i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.05299 | −0.295436 | −0.147718 | − | 0.989030i | \(-0.547193\pi\) | ||||
−0.147718 | + | 0.989030i | \(0.547193\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −21.0052 | −0.769571 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 10.4684i | − | 0.383020i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.1950i | 0.920605i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.35756 | 0.159010 | 0.0795048 | − | 0.996834i | \(-0.474666\pi\) | ||||
0.0795048 | + | 0.996834i | \(0.474666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.32298i | 0.0846541i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.3352 | −1.35877 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.01051 | 0.182110 | 0.0910550 | − | 0.995846i | \(-0.470976\pi\) | ||||
0.0910550 | + | 0.995846i | \(0.470976\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.78135 | 0.355041 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 37.9954 | 1.37733 | 0.688666 | − | 0.725079i | \(-0.258197\pi\) | ||||
0.688666 | + | 0.725079i | \(0.258197\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.3931 | 0.484861 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.74733 | 0.0631748 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 12.6228i | − | 0.455783i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −36.2100 | −1.30577 | −0.652883 | − | 0.757459i | \(-0.726441\pi\) | ||||
−0.652883 | + | 0.757459i | \(0.726441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.57981i | − | 0.164938i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.0530i | 1.18883i | 0.804158 | + | 0.594416i | \(0.202617\pi\) | ||||
−0.804158 | + | 0.594416i | \(0.797383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.684516 | −0.0245886 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.2115 | −0.581584 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.8341 | − | 18.8713i | 1.39138 | − | 0.676133i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 0.121811i | − | 0.00435874i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 13.1218i | 0.468936i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.2387 | 1.72171 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2269 | 0.435842 | 0.217921 | − | 0.975966i | \(-0.430073\pi\) | ||||
0.217921 | + | 0.975966i | \(0.430073\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 23.6098i | 0.840531i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.1827 | −1.14428 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 51.7060i | 1.83614i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 6.06211i | − | 0.215001i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 38.6821i | − | 1.37019i | −0.728454 | − | 0.685094i | \(-0.759761\pi\) | ||
0.728454 | − | 0.685094i | \(-0.240239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 6.02120i | − | 0.213015i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.31727i | 0.187876i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 5.12024i | − | 0.180689i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −46.5321 | −1.64004 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 37.0404i | 1.30388i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −52.6496 | −1.85106 | −0.925531 | − | 0.378671i | \(-0.876381\pi\) | ||||
−0.925531 | + | 0.378671i | \(0.876381\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.02553 | 0.141355 | 0.0706777 | − | 0.997499i | \(-0.477484\pi\) | ||||
0.0706777 | + | 0.997499i | \(0.477484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.31597i | 0.0812246i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 16.2912i | − | 0.570656i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.1781 | − | 4.94600i | 0.356086 | − | 0.173038i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.5646 | −0.543871 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.5358 | −1.06571 | −0.532854 | − | 0.846207i | \(-0.678880\pi\) | ||||
−0.532854 | + | 0.846207i | \(0.678880\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.16634i | 0.284661i | 0.989819 | + | 0.142330i | \(0.0454596\pi\) | ||||
−0.989819 | + | 0.142330i | \(0.954540\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 0.811984i | − | 0.0282697i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.6480 | 0.439813 | 0.219907 | − | 0.975521i | \(-0.429425\pi\) | ||||
0.219907 | + | 0.975521i | \(0.429425\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.4740i | 0.467970i | 0.972240 | + | 0.233985i | \(0.0751766\pi\) | ||||
−0.972240 | + | 0.233985i | \(0.924823\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.91876 | −0.205320 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.865909 | 0.0300020 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −39.3456 | −1.36161 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.75951 | −0.233643 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.3291 | −0.632791 | −0.316396 | − | 0.948627i | \(-0.602473\pi\) | ||||
−0.316396 | + | 0.948627i | \(0.602473\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.6192 | 0.814455 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.2229i | 0.730956i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.7055 | −1.40031 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 2.85642i | − | 0.0981478i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.242577i | 0.00832522i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27.6303 | 0.947153 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.2794 | −1.37914 | −0.689569 | − | 0.724220i | \(-0.742200\pi\) | ||||
−0.689569 | + | 0.724220i | \(0.742200\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.45627 | + | 9.17031i | 0.152401 | + | 0.313618i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 13.5459i | − | 0.462719i | −0.972868 | − | 0.231359i | \(-0.925683\pi\) | ||
0.972868 | − | 0.231359i | \(-0.0743173\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 32.8595i | − | 1.12115i | −0.828103 | − | 0.560575i | \(-0.810580\pi\) | ||
0.828103 | − | 0.560575i | \(-0.189420\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.1052 | 1.36678 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.4320 | 1.03592 | 0.517958 | − | 0.855406i | \(-0.326692\pi\) | ||||
0.517958 | + | 0.855406i | \(0.326692\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.9979i | 0.509944i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 23.3056 | 0.791501 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.46660i | 0.151519i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 66.1717i | 2.24214i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.2745i | 0.347740i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 29.8528i | − | 1.00921i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 27.9946i | − | 0.945312i | −0.881247 | − | 0.472656i | \(-0.843295\pi\) | ||
0.881247 | − | 0.472656i | \(-0.156705\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 29.8404i | − | 1.00649i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.94901 | −0.335191 | −0.167595 | − | 0.985856i | \(-0.553600\pi\) | ||||
−0.167595 | + | 0.985856i | \(0.553600\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 45.8776i | − | 1.54390i | −0.635681 | − | 0.771952i | \(-0.719281\pi\) | ||
0.635681 | − | 0.771952i | \(-0.280719\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.68050 | −0.258177 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.1643 | 1.41574 | 0.707869 | − | 0.706344i | \(-0.249657\pi\) | ||||
0.707869 | + | 0.706344i | \(0.249657\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 45.2311i | − | 1.51700i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 5.04572i | − | 0.169038i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31.6004 | − | 15.3561i | 1.05747 | − | 0.513871i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.7498 | −1.39554 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −53.7913 | −1.79604 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.77183i | − | 0.0924458i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.35335i | − | 0.0450867i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.5112 | 0.349792 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 57.4015i | 1.90809i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.36055 | −0.177994 | −0.0889971 | − | 0.996032i | \(-0.528366\pi\) | ||||
−0.0889971 | + | 0.996032i | \(0.528366\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.44018 | 0.180439 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0968 | −1.19594 | −0.597970 | − | 0.801519i | \(-0.704026\pi\) | ||||
−0.597970 | + | 0.801519i | \(0.704026\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5652 | −0.349658 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 31.4611 | 1.04007 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.866129 | −0.0286021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.82205i | 0.0930907i | 0.998916 | + | 0.0465454i | \(0.0148212\pi\) | ||||
−0.998916 | + | 0.0465454i | \(0.985179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.10783 | 0.300113 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.669883i | 0.0220495i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.29368i | − | 0.0754159i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.1024 | 0.528872 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.0460 | 0.690498 | 0.345249 | − | 0.938511i | \(-0.387794\pi\) | ||||
0.345249 | + | 0.938511i | \(0.387794\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.20836 | + | 4.54445i | 0.0723759 | + | 0.148938i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 43.4565i | − | 1.42270i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.76349i | − | 0.0576721i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.8139 | −1.66002 | −0.830008 | − | 0.557751i | \(-0.811664\pi\) | ||||
−0.830008 | + | 0.557751i | \(0.811664\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.4730 | −0.929182 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.6197i | 1.19377i | 0.802327 | + | 0.596885i | \(0.203595\pi\) | ||||
−0.802327 | + | 0.596885i | \(0.796405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −68.3538 | −2.22591 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 38.1446i | 1.24084i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 40.3778i | − | 1.31210i | −0.754717 | − | 0.656051i | \(-0.772226\pi\) | ||
0.754717 | − | 0.656051i | \(-0.227774\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 28.1581i | 0.914050i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 15.9238i | − | 0.516364i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.9002i | 0.677022i | 0.940962 | + | 0.338511i | \(0.109923\pi\) | ||||
−0.940962 | + | 0.338511i | \(0.890077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 10.4224i | 0.337262i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.28799 | 0.106286 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 36.9991i | 1.19476i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.5721 | −0.953940 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.73966 | −0.281632 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.7701i | 1.47339i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.5238i | 0.917265i | 0.888626 | + | 0.458633i | \(0.151661\pi\) | ||||
−0.888626 | + | 0.458633i | \(0.848339\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.01730 | − | 4.15129i | −0.0648050 | − | 0.133359i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.3137 | 1.35791 | 0.678955 | − | 0.734180i | \(-0.262433\pi\) | ||||
0.678955 | + | 0.734180i | \(0.262433\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.07259 | −0.162620 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.46540i | 0.143007i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 10.3560i | − | 0.331317i | −0.986183 | − | 0.165659i | \(-0.947025\pi\) | ||
0.986183 | − | 0.165659i | \(-0.0529750\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.36644 | 0.171512 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.64580i | 0.148329i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 32.6772 | 1.04224 | 0.521120 | − | 0.853483i | \(-0.325514\pi\) | ||||
0.521120 | + | 0.853483i | \(0.325514\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −43.9467 | −1.40026 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.6347 | 1.03877 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17.9149 | −0.569662 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.3073 | −1.37570 | −0.687851 | − | 0.725852i | \(-0.741446\pi\) | ||||
−0.687851 | + | 0.725852i | \(0.741446\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.0923 | 0.574141 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.4758i | 0.332106i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.4845 | −1.53552 | −0.767760 | − | 0.640738i | \(-0.778628\pi\) | ||||
−0.767760 | + | 0.640738i | \(0.778628\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 22.6498i | − | 0.716609i |
(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 | 3344.2.o.b.1519.19 | ✓ | 64 | |
4.3 | odd | 2 | inner | 3344.2.o.b.1519.45 | yes | 64 | |
19.18 | odd | 2 | inner | 3344.2.o.b.1519.46 | yes | 64 | |
76.75 | even | 2 | inner | 3344.2.o.b.1519.20 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3344.2.o.b.1519.19 | ✓ | 64 | 1.1 | even | 1 | trivial | |
3344.2.o.b.1519.20 | yes | 64 | 76.75 | even | 2 | inner | |
3344.2.o.b.1519.45 | yes | 64 | 4.3 | odd | 2 | inner | |
3344.2.o.b.1519.46 | yes | 64 | 19.18 | odd | 2 | inner |