Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (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: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 97.5 | ||
Root | \(-0.424637 - 3.22544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.d.1273.5 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | −2.15899 | + | 0.582041i | −0.965529 | + | 0.260297i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.93820 | − | 1.11507i | −0.612913 | − | 0.352616i | ||||
\(11\) | 0.461115 | 0.139031 | 0.0695156 | − | 0.997581i | \(-0.477855\pi\) | ||||
0.0695156 | + | 0.997581i | \(0.477855\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | −4.00275 | − | 4.00275i | −1.11016 | − | 1.11016i | −0.993128 | − | 0.117035i | \(-0.962661\pi\) |
−0.117035 | − | 0.993128i | \(-0.537339\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.93820 | + | 1.11507i | 0.500441 | + | 0.287910i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.15953 | − | 1.15953i | 0.281226 | − | 0.281226i | −0.552372 | − | 0.833598i | \(-0.686277\pi\) |
0.833598 | + | 0.552372i | \(0.186277\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | 5.82646 | 1.33668 | 0.668341 | − | 0.743855i | \(-0.267005\pi\) | ||||
0.668341 | + | 0.743855i | \(0.267005\pi\) | |||||||
\(20\) | −0.582041 | − | 2.15899i | −0.130148 | − | 0.482764i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.326057 | + | 0.326057i | 0.0695156 | + | 0.0695156i | ||||
\(23\) | 3.11997 | − | 3.11997i | 0.650559 | − | 0.650559i | −0.302568 | − | 0.953128i | \(-0.597844\pi\) |
0.953128 | + | 0.302568i | \(0.0978441\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.32246 | − | 2.51324i | 0.864491 | − | 0.502648i | ||||
\(26\) | − | 5.66074i | − | 1.11016i | ||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.53773i | 1.02833i | 0.857691 | + | 0.514165i | \(0.171898\pi\) | ||||
−0.857691 | + | 0.514165i | \(0.828102\pi\) | |||||||
\(30\) | 0.582041 | + | 2.15899i | 0.106266 | + | 0.394175i | ||||
\(31\) | − | 0.0324420i | − | 0.00582676i | −0.999996 | − | 0.00291338i | \(-0.999073\pi\) | ||
0.999996 | − | 0.00291338i | \(-0.000927359\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −0.326057 | − | 0.326057i | −0.0567593 | − | 0.0567593i | ||||
\(34\) | 1.63982 | 0.281226 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 5.70242 | + | 5.70242i | 0.937473 | + | 0.937473i | 0.998157 | − | 0.0606844i | \(-0.0193283\pi\) |
−0.0606844 | + | 0.998157i | \(0.519328\pi\) | |||||||
\(38\) | 4.11993 | + | 4.11993i | 0.668341 | + | 0.668341i | ||||
\(39\) | 5.66074i | 0.906444i | ||||||||
\(40\) | 1.11507 | − | 1.93820i | 0.176308 | − | 0.306456i | ||||
\(41\) | 10.9453i | 1.70937i | 0.519149 | + | 0.854684i | \(0.326249\pi\) | ||||
−0.519149 | + | 0.854684i | \(0.673751\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.75146 | − | 4.75146i | 0.724591 | − | 0.724591i | −0.244946 | − | 0.969537i | \(-0.578770\pi\) |
0.969537 | + | 0.244946i | \(0.0787703\pi\) | |||||||
\(44\) | 0.461115i | 0.0695156i | ||||||||
\(45\) | −0.582041 | − | 2.15899i | −0.0867655 | − | 0.321843i | ||||
\(46\) | 4.41231 | 0.650559 | ||||||||
\(47\) | 6.39241 | − | 6.39241i | 0.932429 | − | 0.932429i | −0.0654279 | − | 0.997857i | \(-0.520841\pi\) |
0.997857 | + | 0.0654279i | \(0.0208412\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.83357 | + | 1.27931i | 0.683570 | + | 0.180922i | ||||
\(51\) | −1.63982 | −0.229620 | ||||||||
\(52\) | 4.00275 | − | 4.00275i | 0.555081 | − | 0.555081i | ||||
\(53\) | 1.94214 | − | 1.94214i | 0.266773 | − | 0.266773i | −0.561025 | − | 0.827799i | \(-0.689593\pi\) |
0.827799 | + | 0.561025i | \(0.189593\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −0.995541 | + | 0.268388i | −0.134239 | + | 0.0361894i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.11993 | − | 4.11993i | −0.545698 | − | 0.545698i | ||||
\(58\) | −3.91576 | + | 3.91576i | −0.514165 | + | 0.514165i | ||||
\(59\) | −1.91758 | −0.249648 | −0.124824 | − | 0.992179i | \(-0.539837\pi\) | ||||
−0.124824 | + | 0.992179i | \(0.539837\pi\) | |||||||
\(60\) | −1.11507 | + | 1.93820i | −0.143955 | + | 0.250221i | ||||
\(61\) | − | 13.5554i | − | 1.73559i | −0.496925 | − | 0.867793i | \(-0.665538\pi\) | ||
0.496925 | − | 0.867793i | \(-0.334462\pi\) | |||||||
\(62\) | 0.0229400 | − | 0.0229400i | 0.00291338 | − | 0.00291338i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 10.9716 | + | 6.31212i | 1.36087 | + | 0.782922i | ||||
\(66\) | − | 0.461115i | − | 0.0567593i | ||||||
\(67\) | −2.69424 | − | 2.69424i | −0.329154 | − | 0.329154i | 0.523111 | − | 0.852265i | \(-0.324771\pi\) |
−0.852265 | + | 0.523111i | \(0.824771\pi\) | |||||||
\(68\) | 1.15953 | + | 1.15953i | 0.140613 | + | 0.140613i | ||||
\(69\) | −4.41231 | −0.531179 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.85877 | 1.05134 | 0.525671 | − | 0.850688i | \(-0.323814\pi\) | ||||
0.525671 | + | 0.850688i | \(0.323814\pi\) | |||||||
\(72\) | −0.707107 | − | 0.707107i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 2.86894 | + | 2.86894i | 0.335784 | + | 0.335784i | 0.854778 | − | 0.518994i | \(-0.173693\pi\) |
−0.518994 | + | 0.854778i | \(0.673693\pi\) | |||||||
\(74\) | 8.06444i | 0.937473i | ||||||||
\(75\) | −4.83357 | − | 1.27931i | −0.558132 | − | 0.147722i | ||||
\(76\) | 5.82646i | 0.668341i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.00275 | + | 4.00275i | −0.453222 | + | 0.453222i | ||||
\(79\) | − | 5.06128i | − | 0.569438i | −0.958611 | − | 0.284719i | \(-0.908100\pi\) | ||
0.958611 | − | 0.284719i | \(-0.0919003\pi\) | |||||||
\(80\) | 2.15899 | − | 0.582041i | 0.241382 | − | 0.0650741i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −7.73949 | + | 7.73949i | −0.854684 | + | 0.854684i | ||||
\(83\) | 1.08813 | + | 1.08813i | 0.119438 | + | 0.119438i | 0.764299 | − | 0.644861i | \(-0.223085\pi\) |
−0.644861 | + | 0.764299i | \(0.723085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.82851 | + | 3.17829i | −0.198330 | + | 0.344734i | ||||
\(86\) | 6.71958 | 0.724591 | ||||||||
\(87\) | 3.91576 | − | 3.91576i | 0.419814 | − | 0.419814i | ||||
\(88\) | −0.326057 | + | 0.326057i | −0.0347578 | + | 0.0347578i | ||||
\(89\) | 11.4285 | 1.21142 | 0.605708 | − | 0.795687i | \(-0.292890\pi\) | ||||
0.605708 | + | 0.795687i | \(0.292890\pi\) | |||||||
\(90\) | 1.11507 | − | 1.93820i | 0.117539 | − | 0.204304i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 3.11997 | + | 3.11997i | 0.325280 | + | 0.325280i | ||||
\(93\) | −0.0229400 | + | 0.0229400i | −0.00237876 | + | 0.00237876i | ||||
\(94\) | 9.04024 | 0.932429 | ||||||||
\(95\) | −12.5793 | + | 3.39124i | −1.29060 | + | 0.347934i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 2.51799 | − | 2.51799i | 0.255663 | − | 0.255663i | −0.567624 | − | 0.823288i | \(-0.692137\pi\) |
0.823288 | + | 0.567624i | \(0.192137\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.461115i | 0.0463438i | ||||||||
\(100\) | 2.51324 | + | 4.32246i | 0.251324 | + | 0.432246i | ||||
\(101\) | − | 4.51181i | − | 0.448942i | −0.974481 | − | 0.224471i | \(-0.927935\pi\) | ||
0.974481 | − | 0.224471i | \(-0.0720654\pi\) | |||||||
\(102\) | −1.15953 | − | 1.15953i | −0.114810 | − | 0.114810i | ||||
\(103\) | 10.4477 | + | 10.4477i | 1.02945 | + | 1.02945i | 0.999553 | + | 0.0298934i | \(0.00951679\pi\) |
0.0298934 | + | 0.999553i | \(0.490483\pi\) | |||||||
\(104\) | 5.66074 | 0.555081 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.74660 | 0.266773 | ||||||||
\(107\) | 4.17138 | + | 4.17138i | 0.403262 | + | 0.403262i | 0.879381 | − | 0.476119i | \(-0.157957\pi\) |
−0.476119 | + | 0.879381i | \(0.657957\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 16.6187i | − | 1.59179i | −0.605437 | − | 0.795893i | \(-0.707002\pi\) | ||
0.605437 | − | 0.795893i | \(-0.292998\pi\) | |||||||
\(110\) | −0.893732 | − | 0.514175i | −0.0852140 | − | 0.0490247i | ||||
\(111\) | − | 8.06444i | − | 0.765443i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.35390 | − | 6.35390i | 0.597724 | − | 0.597724i | −0.341982 | − | 0.939706i | \(-0.611098\pi\) |
0.939706 | + | 0.341982i | \(0.111098\pi\) | |||||||
\(114\) | − | 5.82646i | − | 0.545698i | ||||||
\(115\) | −4.92003 | + | 8.55193i | −0.458795 | + | 0.797472i | ||||
\(116\) | −5.53773 | −0.514165 | ||||||||
\(117\) | 4.00275 | − | 4.00275i | 0.370054 | − | 0.370054i | ||||
\(118\) | −1.35593 | − | 1.35593i | −0.124824 | − | 0.124824i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.15899 | + | 0.582041i | −0.197088 | + | 0.0531328i | ||||
\(121\) | −10.7874 | −0.980670 | ||||||||
\(122\) | 9.58509 | − | 9.58509i | 0.867793 | − | 0.867793i | ||||
\(123\) | 7.73949 | − | 7.73949i | 0.697847 | − | 0.697847i | ||||
\(124\) | 0.0324420 | 0.00291338 | ||||||||
\(125\) | −7.86932 | + | 7.94190i | −0.703854 | + | 0.710345i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.7757 | − | 11.7757i | −1.04493 | − | 1.04493i | −0.998942 | − | 0.0459856i | \(-0.985357\pi\) |
−0.0459856 | − | 0.998942i | \(-0.514643\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −6.71958 | −0.591626 | ||||||||
\(130\) | 3.29478 | + | 12.2215i | 0.288972 | + | 1.07189i | ||||
\(131\) | 18.9765i | 1.65798i | 0.559261 | + | 0.828992i | \(0.311085\pi\) | ||||
−0.559261 | + | 0.828992i | \(0.688915\pi\) | |||||||
\(132\) | 0.326057 | − | 0.326057i | 0.0283796 | − | 0.0283796i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 3.81023i | − | 0.329154i | ||||||
\(135\) | −1.11507 | + | 1.93820i | −0.0959699 | + | 0.166814i | ||||
\(136\) | 1.63982i | 0.140613i | ||||||||
\(137\) | −3.13179 | − | 3.13179i | −0.267567 | − | 0.267567i | 0.560552 | − | 0.828119i | \(-0.310589\pi\) |
−0.828119 | + | 0.560552i | \(0.810589\pi\) | |||||||
\(138\) | −3.11997 | − | 3.11997i | −0.265590 | − | 0.265590i | ||||
\(139\) | −4.35020 | −0.368979 | −0.184489 | − | 0.982835i | \(-0.559063\pi\) | ||||
−0.184489 | + | 0.982835i | \(0.559063\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.04024 | −0.761325 | ||||||||
\(142\) | 6.26410 | + | 6.26410i | 0.525671 | + | 0.525671i | ||||
\(143\) | −1.84573 | − | 1.84573i | −0.154347 | − | 0.154347i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | −3.22318 | − | 11.9559i | −0.267671 | − | 0.992882i | ||||
\(146\) | 4.05729i | 0.335784i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.70242 | + | 5.70242i | −0.468736 | + | 0.468736i | ||||
\(149\) | 4.34052i | 0.355589i | 0.984068 | + | 0.177794i | \(0.0568962\pi\) | ||||
−0.984068 | + | 0.177794i | \(0.943104\pi\) | |||||||
\(150\) | −2.51324 | − | 4.32246i | −0.205205 | − | 0.352927i | ||||
\(151\) | 8.18514 | 0.666098 | 0.333049 | − | 0.942910i | \(-0.391923\pi\) | ||||
0.333049 | + | 0.942910i | \(0.391923\pi\) | |||||||
\(152\) | −4.11993 | + | 4.11993i | −0.334170 | + | 0.334170i | ||||
\(153\) | 1.15953 | + | 1.15953i | 0.0937421 | + | 0.0937421i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0188826 | + | 0.0700419i | 0.00151669 | + | 0.00562590i | ||||
\(156\) | −5.66074 | −0.453222 | ||||||||
\(157\) | 15.3974 | − | 15.3974i | 1.22885 | − | 1.22885i | 0.264451 | − | 0.964399i | \(-0.414809\pi\) |
0.964399 | − | 0.264451i | \(-0.0851907\pi\) | |||||||
\(158\) | 3.57886 | − | 3.57886i | 0.284719 | − | 0.284719i | ||||
\(159\) | −2.74660 | −0.217820 | ||||||||
\(160\) | 1.93820 | + | 1.11507i | 0.153228 | + | 0.0881540i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −8.25527 | + | 8.25527i | −0.646602 | + | 0.646602i | −0.952170 | − | 0.305568i | \(-0.901154\pi\) |
0.305568 | + | 0.952170i | \(0.401154\pi\) | |||||||
\(164\) | −10.9453 | −0.854684 | ||||||||
\(165\) | 0.893732 | + | 0.514175i | 0.0695770 | + | 0.0400285i | ||||
\(166\) | 1.53885i | 0.119438i | ||||||||
\(167\) | −15.5061 | + | 15.5061i | −1.19990 | + | 1.19990i | −0.225703 | + | 0.974196i | \(0.572468\pi\) |
−0.974196 | + | 0.225703i | \(0.927532\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 19.0440i | 1.46492i | ||||||||
\(170\) | −3.54035 | + | 0.954441i | −0.271532 | + | 0.0732023i | ||||
\(171\) | 5.82646i | 0.445560i | ||||||||
\(172\) | 4.75146 | + | 4.75146i | 0.362295 | + | 0.362295i | ||||
\(173\) | −6.89034 | − | 6.89034i | −0.523863 | − | 0.523863i | 0.394873 | − | 0.918736i | \(-0.370789\pi\) |
−0.918736 | + | 0.394873i | \(0.870789\pi\) | |||||||
\(174\) | 5.53773 | 0.419814 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.461115 | −0.0347578 | ||||||||
\(177\) | 1.35593 | + | 1.35593i | 0.101918 | + | 0.101918i | ||||
\(178\) | 8.08115 | + | 8.08115i | 0.605708 | + | 0.605708i | ||||
\(179\) | − | 1.61515i | − | 0.120722i | −0.998177 | − | 0.0603611i | \(-0.980775\pi\) | ||
0.998177 | − | 0.0603611i | \(-0.0192252\pi\) | |||||||
\(180\) | 2.15899 | − | 0.582041i | 0.160921 | − | 0.0433828i | ||||
\(181\) | − | 12.8519i | − | 0.955277i | −0.878556 | − | 0.477639i | \(-0.841493\pi\) | ||
0.878556 | − | 0.477639i | \(-0.158507\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.58509 | + | 9.58509i | −0.708550 | + | 0.708550i | ||||
\(184\) | 4.41231i | 0.325280i | ||||||||
\(185\) | −15.6305 | − | 8.99242i | −1.14918 | − | 0.661136i | ||||
\(186\) | −0.0324420 | −0.00237876 | ||||||||
\(187\) | 0.534674 | − | 0.534674i | 0.0390993 | − | 0.0390993i | ||||
\(188\) | 6.39241 | + | 6.39241i | 0.466215 | + | 0.466215i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −11.2928 | − | 6.49691i | −0.819269 | − | 0.471335i | ||||
\(191\) | −10.6007 | −0.767036 | −0.383518 | − | 0.923533i | \(-0.625288\pi\) | ||||
−0.383518 | + | 0.923533i | \(0.625288\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | 5.10254 | − | 5.10254i | 0.367289 | − | 0.367289i | −0.499199 | − | 0.866487i | \(-0.666372\pi\) |
0.866487 | + | 0.499199i | \(0.166372\pi\) | |||||||
\(194\) | 3.56097 | 0.255663 | ||||||||
\(195\) | −3.29478 | − | 12.2215i | −0.235944 | − | 0.875198i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.72803 | − | 9.72803i | −0.693093 | − | 0.693093i | 0.269818 | − | 0.962911i | \(-0.413036\pi\) |
−0.962911 | + | 0.269818i | \(0.913036\pi\) | |||||||
\(198\) | −0.326057 | + | 0.326057i | −0.0231719 | + | 0.0231719i | ||||
\(199\) | −9.65296 | −0.684280 | −0.342140 | − | 0.939649i | \(-0.611152\pi\) | ||||
−0.342140 | + | 0.939649i | \(0.611152\pi\) | |||||||
\(200\) | −1.27931 | + | 4.83357i | −0.0904609 | + | 0.341785i | ||||
\(201\) | 3.81023i | 0.268753i | ||||||||
\(202\) | 3.19033 | − | 3.19033i | 0.224471 | − | 0.224471i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 1.63982i | − | 0.114810i | ||||||
\(205\) | −6.37061 | − | 23.6308i | −0.444943 | − | 1.65044i | ||||
\(206\) | 14.7753i | 1.02945i | ||||||||
\(207\) | 3.11997 | + | 3.11997i | 0.216853 | + | 0.216853i | ||||
\(208\) | 4.00275 | + | 4.00275i | 0.277541 | + | 0.277541i | ||||
\(209\) | 2.68667 | 0.185841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.33273 | 0.0917487 | 0.0458744 | − | 0.998947i | \(-0.485393\pi\) | ||||
0.0458744 | + | 0.998947i | \(0.485393\pi\) | |||||||
\(212\) | 1.94214 | + | 1.94214i | 0.133387 | + | 0.133387i | ||||
\(213\) | −6.26410 | − | 6.26410i | −0.429209 | − | 0.429209i | ||||
\(214\) | 5.89922i | 0.403262i | ||||||||
\(215\) | −7.49280 | + | 13.0239i | −0.511005 | + | 0.888221i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 11.7512 | − | 11.7512i | 0.795893 | − | 0.795893i | ||||
\(219\) | − | 4.05729i | − | 0.274166i | ||||||
\(220\) | −0.268388 | − | 0.995541i | −0.0180947 | − | 0.0671193i | ||||
\(221\) | −9.28258 | −0.624414 | ||||||||
\(222\) | 5.70242 | − | 5.70242i | 0.382722 | − | 0.382722i | ||||
\(223\) | 8.25284 | + | 8.25284i | 0.552651 | + | 0.552651i | 0.927205 | − | 0.374554i | \(-0.122204\pi\) |
−0.374554 | + | 0.927205i | \(0.622204\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.51324 | + | 4.32246i | 0.167549 | + | 0.288164i | ||||
\(226\) | 8.98577 | 0.597724 | ||||||||
\(227\) | −15.8128 | + | 15.8128i | −1.04953 | + | 1.04953i | −0.0508215 | + | 0.998708i | \(0.516184\pi\) |
−0.998708 | + | 0.0508215i | \(0.983816\pi\) | |||||||
\(228\) | 4.11993 | − | 4.11993i | 0.272849 | − | 0.272849i | ||||
\(229\) | −4.96622 | −0.328177 | −0.164088 | − | 0.986446i | \(-0.552468\pi\) | ||||
−0.164088 | + | 0.986446i | \(0.552468\pi\) | |||||||
\(230\) | −9.52612 | + | 2.56814i | −0.628134 | + | 0.169338i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.91576 | − | 3.91576i | −0.257082 | − | 0.257082i | ||||
\(233\) | 20.2472 | − | 20.2472i | 1.32644 | − | 1.32644i | 0.417980 | − | 0.908456i | \(-0.362738\pi\) |
0.908456 | − | 0.417980i | \(-0.137262\pi\) | |||||||
\(234\) | 5.66074 | 0.370054 | ||||||||
\(235\) | −10.0805 | + | 17.5218i | −0.657579 | + | 1.14300i | ||||
\(236\) | − | 1.91758i | − | 0.124824i | ||||||
\(237\) | −3.57886 | + | 3.57886i | −0.232472 | + | 0.232472i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.9230i | 0.900603i | 0.892877 | + | 0.450302i | \(0.148684\pi\) | ||||
−0.892877 | + | 0.450302i | \(0.851316\pi\) | |||||||
\(240\) | −1.93820 | − | 1.11507i | −0.125110 | − | 0.0719775i | ||||
\(241\) | − | 1.05757i | − | 0.0681239i | −0.999420 | − | 0.0340620i | \(-0.989156\pi\) | ||
0.999420 | − | 0.0340620i | \(-0.0108444\pi\) | |||||||
\(242\) | −7.62782 | − | 7.62782i | −0.490335 | − | 0.490335i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 13.5554 | 0.867793 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 10.9453 | 0.697847 | ||||||||
\(247\) | −23.3218 | − | 23.3218i | −1.48393 | − | 1.48393i | ||||
\(248\) | 0.0229400 | + | 0.0229400i | 0.00145669 | + | 0.00145669i | ||||
\(249\) | − | 1.53885i | − | 0.0975207i | ||||||
\(250\) | −11.1802 | + | 0.0513167i | −0.707099 | + | 0.00324555i | ||||
\(251\) | − | 6.36260i | − | 0.401604i | −0.979632 | − | 0.200802i | \(-0.935645\pi\) | ||
0.979632 | − | 0.200802i | \(-0.0643548\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.43866 | − | 1.43866i | 0.0904481 | − | 0.0904481i | ||||
\(254\) | − | 16.6534i | − | 1.04493i | ||||||
\(255\) | 3.54035 | − | 0.954441i | 0.221705 | − | 0.0597694i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −7.34052 | + | 7.34052i | −0.457889 | + | 0.457889i | −0.897962 | − | 0.440073i | \(-0.854953\pi\) |
0.440073 | + | 0.897962i | \(0.354953\pi\) | |||||||
\(258\) | −4.75146 | − | 4.75146i | −0.295813 | − | 0.295813i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −6.31212 | + | 10.9716i | −0.391461 | + | 0.680433i | ||||
\(261\) | −5.53773 | −0.342777 | ||||||||
\(262\) | −13.4184 | + | 13.4184i | −0.828992 | + | 0.828992i | ||||
\(263\) | 16.8022 | − | 16.8022i | 1.03607 | − | 1.03607i | 0.0367463 | − | 0.999325i | \(-0.488301\pi\) |
0.999325 | − | 0.0367463i | \(-0.0116993\pi\) | |||||||
\(264\) | 0.461115 | 0.0283796 | ||||||||
\(265\) | −3.06265 | + | 5.32346i | −0.188137 | + | 0.327018i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.08115 | − | 8.08115i | −0.494558 | − | 0.494558i | ||||
\(268\) | 2.69424 | − | 2.69424i | 0.164577 | − | 0.164577i | ||||
\(269\) | 1.42007 | 0.0865833 | 0.0432917 | − | 0.999062i | \(-0.486216\pi\) | ||||
0.0432917 | + | 0.999062i | \(0.486216\pi\) | |||||||
\(270\) | −2.15899 | + | 0.582041i | −0.131392 | + | 0.0354219i | ||||
\(271\) | − | 0.353601i | − | 0.0214797i | −0.999942 | − | 0.0107399i | \(-0.996581\pi\) | ||
0.999942 | − | 0.0107399i | \(-0.00341867\pi\) | |||||||
\(272\) | −1.15953 | + | 1.15953i | −0.0703066 | + | 0.0703066i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.42902i | − | 0.267567i | ||||||
\(275\) | 1.99315 | − | 1.15889i | 0.120191 | − | 0.0698837i | ||||
\(276\) | − | 4.41231i | − | 0.265590i | ||||||
\(277\) | −16.6182 | − | 16.6182i | −0.998492 | − | 0.998492i | 0.00150661 | − | 0.999999i | \(-0.499520\pi\) |
−0.999999 | + | 0.00150661i | \(0.999520\pi\) | |||||||
\(278\) | −3.07605 | − | 3.07605i | −0.184489 | − | 0.184489i | ||||
\(279\) | 0.0324420 | 0.00194225 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.4747 | 1.69866 | 0.849330 | − | 0.527862i | \(-0.177006\pi\) | ||||
0.849330 | + | 0.527862i | \(0.177006\pi\) | |||||||
\(282\) | −6.39241 | − | 6.39241i | −0.380663 | − | 0.380663i | ||||
\(283\) | 2.65722 | + | 2.65722i | 0.157956 | + | 0.157956i | 0.781660 | − | 0.623705i | \(-0.214373\pi\) |
−0.623705 | + | 0.781660i | \(0.714373\pi\) | |||||||
\(284\) | 8.85877i | 0.525671i | ||||||||
\(285\) | 11.2928 | + | 6.49691i | 0.668930 | + | 0.384844i | ||||
\(286\) | − | 2.61025i | − | 0.154347i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.707107 | − | 0.707107i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 14.3110i | 0.841823i | ||||||||
\(290\) | 6.17495 | − | 10.7332i | 0.362606 | − | 0.630276i | ||||
\(291\) | −3.56097 | −0.208748 | ||||||||
\(292\) | −2.86894 | + | 2.86894i | −0.167892 | + | 0.167892i | ||||
\(293\) | 4.18500 | + | 4.18500i | 0.244490 | + | 0.244490i | 0.818705 | − | 0.574215i | \(-0.194692\pi\) |
−0.574215 | + | 0.818705i | \(0.694692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.14003 | − | 1.11611i | 0.241042 | − | 0.0649825i | ||||
\(296\) | −8.06444 | −0.468736 | ||||||||
\(297\) | 0.326057 | − | 0.326057i | 0.0189198 | − | 0.0189198i | ||||
\(298\) | −3.06921 | + | 3.06921i | −0.177794 | + | 0.177794i | ||||
\(299\) | −24.9769 | −1.44445 | ||||||||
\(300\) | 1.27931 | − | 4.83357i | 0.0738610 | − | 0.279066i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 5.78777 | + | 5.78777i | 0.333049 | + | 0.333049i | ||||
\(303\) | −3.19033 | + | 3.19033i | −0.183280 | + | 0.183280i | ||||
\(304\) | −5.82646 | −0.334170 | ||||||||
\(305\) | 7.88978 | + | 29.2659i | 0.451767 | + | 1.67576i | ||||
\(306\) | 1.63982i | 0.0937421i | ||||||||
\(307\) | 18.0884 | − | 18.0884i | 1.03236 | − | 1.03236i | 0.0329031 | − | 0.999459i | \(-0.489525\pi\) |
0.999459 | − | 0.0329031i | \(-0.0104753\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 14.7753i | − | 0.840540i | ||||||
\(310\) | −0.0361751 | + | 0.0628791i | −0.00205461 | + | 0.00357130i | ||||
\(311\) | 33.6176i | 1.90628i | 0.302531 | + | 0.953139i | \(0.402168\pi\) | ||||
−0.302531 | + | 0.953139i | \(0.597832\pi\) | |||||||
\(312\) | −4.00275 | − | 4.00275i | −0.226611 | − | 0.226611i | ||||
\(313\) | 16.2383 | + | 16.2383i | 0.917843 | + | 0.917843i | 0.996872 | − | 0.0790289i | \(-0.0251819\pi\) |
−0.0790289 | + | 0.996872i | \(0.525182\pi\) | |||||||
\(314\) | 21.7753 | 1.22885 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.06128 | 0.284719 | ||||||||
\(317\) | 18.1316 | + | 18.1316i | 1.01837 | + | 1.01837i | 0.999828 | + | 0.0185453i | \(0.00590350\pi\) |
0.0185453 | + | 0.999828i | \(0.494096\pi\) | |||||||
\(318\) | −1.94214 | − | 1.94214i | −0.108910 | − | 0.108910i | ||||
\(319\) | 2.55353i | 0.142970i | ||||||||
\(320\) | 0.582041 | + | 2.15899i | 0.0325371 | + | 0.120691i | ||||
\(321\) | − | 5.89922i | − | 0.329262i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.75593 | − | 6.75593i | 0.375910 | − | 0.375910i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | −27.3616 | − | 7.24185i | −1.51775 | − | 0.401705i | ||||
\(326\) | −11.6747 | −0.646602 | ||||||||
\(327\) | −11.7512 | + | 11.7512i | −0.649844 | + | 0.649844i | ||||
\(328\) | −7.73949 | − | 7.73949i | −0.427342 | − | 0.427342i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.268388 | + | 0.995541i | 0.0147742 | + | 0.0548027i | ||||
\(331\) | −11.8648 | −0.652151 | −0.326076 | − | 0.945344i | \(-0.605726\pi\) | ||||
−0.326076 | + | 0.945344i | \(0.605726\pi\) | |||||||
\(332\) | −1.08813 | + | 1.08813i | −0.0597190 | + | 0.0597190i | ||||
\(333\) | −5.70242 | + | 5.70242i | −0.312491 | + | 0.312491i | ||||
\(334\) | −21.9290 | −1.19990 | ||||||||
\(335\) | 7.38499 | + | 4.24868i | 0.403485 | + | 0.232130i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.18746 | − | 3.18746i | −0.173632 | − | 0.173632i | 0.614941 | − | 0.788573i | \(-0.289180\pi\) |
−0.788573 | + | 0.614941i | \(0.789180\pi\) | |||||||
\(338\) | −13.4661 | + | 13.4661i | −0.732461 | + | 0.732461i | ||||
\(339\) | −8.98577 | −0.488040 | ||||||||
\(340\) | −3.17829 | − | 1.82851i | −0.172367 | − | 0.0991649i | ||||
\(341\) | − | 0.0149595i | − | 0.000810102i | ||||||
\(342\) | −4.11993 | + | 4.11993i | −0.222780 | + | 0.222780i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.71958i | 0.362295i | ||||||||
\(345\) | 9.52612 | − | 2.56814i | 0.512869 | − | 0.138264i | ||||
\(346\) | − | 9.74441i | − | 0.523863i | ||||||
\(347\) | −15.1477 | − | 15.1477i | −0.813172 | − | 0.813172i | 0.171936 | − | 0.985108i | \(-0.444998\pi\) |
−0.985108 | + | 0.171936i | \(0.944998\pi\) | |||||||
\(348\) | 3.91576 | + | 3.91576i | 0.209907 | + | 0.209907i | ||||
\(349\) | −16.0682 | −0.860113 | −0.430056 | − | 0.902802i | \(-0.641506\pi\) | ||||
−0.430056 | + | 0.902802i | \(0.641506\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.66074 | −0.302148 | ||||||||
\(352\) | −0.326057 | − | 0.326057i | −0.0173789 | − | 0.0173789i | ||||
\(353\) | 20.7861 | + | 20.7861i | 1.10633 | + | 1.10633i | 0.993629 | + | 0.112703i | \(0.0359508\pi\) |
0.112703 | + | 0.993629i | \(0.464049\pi\) | |||||||
\(354\) | 1.91758i | 0.101918i | ||||||||
\(355\) | −19.1260 | + | 5.15617i | −1.01510 | + | 0.273661i | ||||
\(356\) | 11.4285i | 0.605708i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.14209 | − | 1.14209i | 0.0603611 | − | 0.0603611i | ||||
\(359\) | − | 13.6274i | − | 0.719226i | −0.933102 | − | 0.359613i | \(-0.882909\pi\) | ||
0.933102 | − | 0.359613i | \(-0.117091\pi\) | |||||||
\(360\) | 1.93820 | + | 1.11507i | 0.102152 | + | 0.0587693i | ||||
\(361\) | 14.9476 | 0.786717 | ||||||||
\(362\) | 9.08769 | − | 9.08769i | 0.477639 | − | 0.477639i | ||||
\(363\) | 7.62782 | + | 7.62782i | 0.400357 | + | 0.400357i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.86384 | − | 4.52416i | −0.411612 | − | 0.236805i | ||||
\(366\) | −13.5554 | −0.708550 | ||||||||
\(367\) | 9.02205 | − | 9.02205i | 0.470947 | − | 0.470947i | −0.431274 | − | 0.902221i | \(-0.641936\pi\) |
0.902221 | + | 0.431274i | \(0.141936\pi\) | |||||||
\(368\) | −3.11997 | + | 3.11997i | −0.162640 | + | 0.162640i | ||||
\(369\) | −10.9453 | −0.569789 | ||||||||
\(370\) | −4.69384 | − | 17.4110i | −0.244021 | − | 0.905157i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0229400 | − | 0.0229400i | −0.00118938 | − | 0.00118938i | ||||
\(373\) | 2.82938 | − | 2.82938i | 0.146500 | − | 0.146500i | −0.630053 | − | 0.776552i | \(-0.716967\pi\) |
0.776552 | + | 0.630053i | \(0.216967\pi\) | |||||||
\(374\) | 0.756144 | 0.0390993 | ||||||||
\(375\) | 11.1802 | − | 0.0513167i | 0.577344 | − | 0.00264998i | ||||
\(376\) | 9.04024i | 0.466215i | ||||||||
\(377\) | 22.1661 | − | 22.1661i | 1.14161 | − | 1.14161i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00281i | 0.0515109i | 0.999668 | + | 0.0257555i | \(0.00819912\pi\) | ||||
−0.999668 | + | 0.0257555i | \(0.991801\pi\) | |||||||
\(380\) | −3.39124 | − | 12.5793i | −0.173967 | − | 0.645302i | ||||
\(381\) | 16.6534i | 0.853180i | ||||||||
\(382\) | −7.49579 | − | 7.49579i | −0.383518 | − | 0.383518i | ||||
\(383\) | −12.5887 | − | 12.5887i | −0.643255 | − | 0.643255i | 0.308100 | − | 0.951354i | \(-0.400307\pi\) |
−0.951354 | + | 0.308100i | \(0.900307\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.21608 | 0.367289 | ||||||||
\(387\) | 4.75146 | + | 4.75146i | 0.241530 | + | 0.241530i | ||||
\(388\) | 2.51799 | + | 2.51799i | 0.127832 | + | 0.127832i | ||||
\(389\) | 11.2587i | 0.570839i | 0.958403 | + | 0.285419i | \(0.0921329\pi\) | ||||
−0.958403 | + | 0.285419i | \(0.907867\pi\) | |||||||
\(390\) | 6.31212 | − | 10.9716i | 0.319627 | − | 0.555571i | ||||
\(391\) | − | 7.23538i | − | 0.365909i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.4184 | − | 13.4184i | 0.676869 | − | 0.676869i | ||||
\(394\) | − | 13.7575i | − | 0.693093i | ||||||
\(395\) | 2.94587 | + | 10.9272i | 0.148223 | + | 0.549809i | ||||
\(396\) | −0.461115 | −0.0231719 | ||||||||
\(397\) | 2.71023 | − | 2.71023i | 0.136022 | − | 0.136022i | −0.635817 | − | 0.771840i | \(-0.719337\pi\) |
0.771840 | + | 0.635817i | \(0.219337\pi\) | |||||||
\(398\) | −6.82567 | − | 6.82567i | −0.342140 | − | 0.342140i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.32246 | + | 2.51324i | −0.216123 | + | 0.125662i | ||||
\(401\) | 0.900044 | 0.0449461 | 0.0224730 | − | 0.999747i | \(-0.492846\pi\) | ||||
0.0224730 | + | 0.999747i | \(0.492846\pi\) | |||||||
\(402\) | −2.69424 | + | 2.69424i | −0.134377 | + | 0.134377i | ||||
\(403\) | −0.129857 | + | 0.129857i | −0.00646865 | + | 0.00646865i | ||||
\(404\) | 4.51181 | 0.224471 | ||||||||
\(405\) | 2.15899 | − | 0.582041i | 0.107281 | − | 0.0289218i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.62947 | + | 2.62947i | 0.130338 | + | 0.130338i | ||||
\(408\) | 1.15953 | − | 1.15953i | 0.0574051 | − | 0.0574051i | ||||
\(409\) | −12.8927 | −0.637501 | −0.318751 | − | 0.947839i | \(-0.603263\pi\) | ||||
−0.318751 | + | 0.947839i | \(0.603263\pi\) | |||||||
\(410\) | 12.2048 | − | 21.2142i | 0.602751 | − | 1.04769i | ||||
\(411\) | 4.42902i | 0.218468i | ||||||||
\(412\) | −10.4477 | + | 10.4477i | −0.514723 | + | 0.514723i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4.41231i | 0.216853i | ||||||||
\(415\) | −2.98260 | − | 1.71593i | −0.146410 | − | 0.0842315i | ||||
\(416\) | 5.66074i | 0.277541i | ||||||||
\(417\) | 3.07605 | + | 3.07605i | 0.150635 | + | 0.150635i | ||||
\(418\) | 1.89976 | + | 1.89976i | 0.0929203 | + | 0.0929203i | ||||
\(419\) | −19.8918 | −0.971777 | −0.485888 | − | 0.874021i | \(-0.661504\pi\) | ||||
−0.485888 | + | 0.874021i | \(0.661504\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12.6339 | −0.615740 | −0.307870 | − | 0.951428i | \(-0.599616\pi\) | ||||
−0.307870 | + | 0.951428i | \(0.599616\pi\) | |||||||
\(422\) | 0.942380 | + | 0.942380i | 0.0458744 | + | 0.0458744i | ||||
\(423\) | 6.39241 | + | 6.39241i | 0.310810 | + | 0.310810i | ||||
\(424\) | 2.74660i | 0.133387i | ||||||||
\(425\) | 2.09784 | − | 7.92617i | 0.101760 | − | 0.384476i | ||||
\(426\) | − | 8.85877i | − | 0.429209i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.17138 | + | 4.17138i | −0.201631 | + | 0.201631i | ||||
\(429\) | 2.61025i | 0.126024i | ||||||||
\(430\) | −14.5075 | + | 3.91107i | −0.699613 | + | 0.188608i | ||||
\(431\) | 30.7701 | 1.48215 | 0.741073 | − | 0.671425i | \(-0.234317\pi\) | ||||
0.741073 | + | 0.671425i | \(0.234317\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 3.04743 | + | 3.04743i | 0.146450 | + | 0.146450i | 0.776530 | − | 0.630080i | \(-0.216978\pi\) |
−0.630080 | + | 0.776530i | \(0.716978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.17495 | + | 10.7332i | −0.296066 | + | 0.514618i | ||||
\(436\) | 16.6187 | 0.795893 | ||||||||
\(437\) | 18.1784 | − | 18.1784i | 0.869590 | − | 0.869590i | ||||
\(438\) | 2.86894 | − | 2.86894i | 0.137083 | − | 0.137083i | ||||
\(439\) | 36.9987 | 1.76585 | 0.882926 | − | 0.469513i | \(-0.155570\pi\) | ||||
0.882926 | + | 0.469513i | \(0.155570\pi\) | |||||||
\(440\) | 0.514175 | − | 0.893732i | 0.0245123 | − | 0.0426070i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.56378 | − | 6.56378i | −0.312207 | − | 0.312207i | ||||
\(443\) | −12.5847 | + | 12.5847i | −0.597919 | + | 0.597919i | −0.939758 | − | 0.341839i | \(-0.888950\pi\) |
0.341839 | + | 0.939758i | \(0.388950\pi\) | |||||||
\(444\) | 8.06444 | 0.382722 | ||||||||
\(445\) | −24.6739 | + | 6.65183i | −1.16966 | + | 0.315327i | ||||
\(446\) | 11.6713i | 0.552651i | ||||||||
\(447\) | 3.06921 | − | 3.06921i | 0.145169 | − | 0.145169i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.41945i | 0.114181i | 0.998369 | + | 0.0570904i | \(0.0181823\pi\) | ||||
−0.998369 | + | 0.0570904i | \(0.981818\pi\) | |||||||
\(450\) | −1.27931 | + | 4.83357i | −0.0603073 | + | 0.227857i | ||||
\(451\) | 5.04704i | 0.237656i | ||||||||
\(452\) | 6.35390 | + | 6.35390i | 0.298862 | + | 0.298862i | ||||
\(453\) | −5.78777 | − | 5.78777i | −0.271933 | − | 0.271933i | ||||
\(454\) | −22.3626 | −1.04953 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5.82646 | 0.272849 | ||||||||
\(457\) | −19.4870 | − | 19.4870i | −0.911565 | − | 0.911565i | 0.0848308 | − | 0.996395i | \(-0.472965\pi\) |
−0.996395 | + | 0.0848308i | \(0.972965\pi\) | |||||||
\(458\) | −3.51165 | − | 3.51165i | −0.164088 | − | 0.164088i | ||||
\(459\) | − | 1.63982i | − | 0.0765401i | ||||||
\(460\) | −8.55193 | − | 4.92003i | −0.398736 | − | 0.229398i | ||||
\(461\) | 1.02712i | 0.0478378i | 0.999714 | + | 0.0239189i | \(0.00761434\pi\) | ||||
−0.999714 | + | 0.0239189i | \(0.992386\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.26507 | + | 8.26507i | −0.384111 | + | 0.384111i | −0.872581 | − | 0.488470i | \(-0.837555\pi\) |
0.488470 | + | 0.872581i | \(0.337555\pi\) | |||||||
\(464\) | − | 5.53773i | − | 0.257082i | ||||||
\(465\) | 0.0361751 | − | 0.0628791i | 0.00167758 | − | 0.00291595i | ||||
\(466\) | 28.6338 | 1.32644 | ||||||||
\(467\) | 13.1131 | − | 13.1131i | 0.606804 | − | 0.606804i | −0.335305 | − | 0.942109i | \(-0.608840\pi\) |
0.942109 | + | 0.335305i | \(0.108840\pi\) | |||||||
\(468\) | 4.00275 | + | 4.00275i | 0.185027 | + | 0.185027i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −19.5178 | + | 5.26179i | −0.900287 | + | 0.242708i | ||||
\(471\) | −21.7753 | −1.00335 | ||||||||
\(472\) | 1.35593 | − | 1.35593i | 0.0624120 | − | 0.0624120i | ||||
\(473\) | 2.19097 | − | 2.19097i | 0.100741 | − | 0.100741i | ||||
\(474\) | −5.06128 | −0.232472 | ||||||||
\(475\) | 25.1846 | − | 14.6433i | 1.15555 | − | 0.671880i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.94214 | + | 1.94214i | 0.0889245 | + | 0.0889245i | ||||
\(478\) | −9.84504 | + | 9.84504i | −0.450302 | + | 0.450302i | ||||
\(479\) | −8.47745 | −0.387344 | −0.193672 | − | 0.981066i | \(-0.562040\pi\) | ||||
−0.193672 | + | 0.981066i | \(0.562040\pi\) | |||||||
\(480\) | −0.582041 | − | 2.15899i | −0.0265664 | − | 0.0985439i | ||||
\(481\) | − | 45.6507i | − | 2.08149i | ||||||
\(482\) | 0.747813 | − | 0.747813i | 0.0340620 | − | 0.0340620i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 10.7874i | − | 0.490335i | ||||||
\(485\) | −3.97074 | + | 6.90188i | −0.180302 | + | 0.313398i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −3.43393 | − | 3.43393i | −0.155606 | − | 0.155606i | 0.625010 | − | 0.780617i | \(-0.285095\pi\) |
−0.780617 | + | 0.625010i | \(0.785095\pi\) | |||||||
\(488\) | 9.58509 | + | 9.58509i | 0.433897 | + | 0.433897i | ||||
\(489\) | 11.6747 | 0.527949 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.8594 | −1.70857 | −0.854286 | − | 0.519803i | \(-0.826005\pi\) | ||||
−0.854286 | + | 0.519803i | \(0.826005\pi\) | |||||||
\(492\) | 7.73949 | + | 7.73949i | 0.348923 | + | 0.348923i | ||||
\(493\) | 6.42114 | + | 6.42114i | 0.289193 | + | 0.289193i | ||||
\(494\) | − | 32.9821i | − | 1.48393i | ||||||
\(495\) | −0.268388 | − | 0.995541i | −0.0120631 | − | 0.0447462i | ||||
\(496\) | 0.0324420i | 0.00145669i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.08813 | − | 1.08813i | 0.0487604 | − | 0.0487604i | ||||
\(499\) | − | 0.512196i | − | 0.0229290i | −0.999934 | − | 0.0114645i | \(-0.996351\pi\) | ||
0.999934 | − | 0.0114645i | \(-0.00364935\pi\) | |||||||
\(500\) | −7.94190 | − | 7.86932i | −0.355172 | − | 0.351927i | ||||
\(501\) | 21.9290 | 0.979714 | ||||||||
\(502\) | 4.49904 | − | 4.49904i | 0.200802 | − | 0.200802i | ||||
\(503\) | −8.58209 | − | 8.58209i | −0.382657 | − | 0.382657i | 0.489402 | − | 0.872058i | \(-0.337215\pi\) |
−0.872058 | + | 0.489402i | \(0.837215\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.62606 | + | 9.74094i | 0.116858 | + | 0.433466i | ||||
\(506\) | 2.03458 | 0.0904481 | ||||||||
\(507\) | 13.4661 | − | 13.4661i | 0.598052 | − | 0.598052i | ||||
\(508\) | 11.7757 | − | 11.7757i | 0.522464 | − | 0.522464i | ||||
\(509\) | −11.3876 | −0.504748 | −0.252374 | − | 0.967630i | \(-0.581211\pi\) | ||||
−0.252374 | + | 0.967630i | \(0.581211\pi\) | |||||||
\(510\) | 3.17829 | + | 1.82851i | 0.140737 | + | 0.0809678i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.11993 | − | 4.11993i | 0.181899 | − | 0.181899i | ||||
\(514\) | −10.3811 | −0.457889 | ||||||||
\(515\) | −28.6376 | − | 16.4755i | −1.26192 | − | 0.725999i | ||||
\(516\) | − | 6.71958i | − | 0.295813i | ||||||
\(517\) | 2.94764 | − | 2.94764i | 0.129637 | − | 0.129637i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.74441i | 0.427732i | ||||||||
\(520\) | −12.2215 | + | 3.29478i | −0.535947 | + | 0.144486i | ||||
\(521\) | − | 19.5013i | − | 0.854365i | −0.904165 | − | 0.427183i | \(-0.859506\pi\) | ||
0.904165 | − | 0.427183i | \(-0.140494\pi\) | |||||||
\(522\) | −3.91576 | − | 3.91576i | −0.171388 | − | 0.171388i | ||||
\(523\) | −10.5304 | − | 10.5304i | −0.460462 | − | 0.460462i | 0.438345 | − | 0.898807i | \(-0.355565\pi\) |
−0.898807 | + | 0.438345i | \(0.855565\pi\) | |||||||
\(524\) | −18.9765 | −0.828992 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.7620 | 1.03607 | ||||||||
\(527\) | −0.0376174 | − | 0.0376174i | −0.00163864 | − | 0.00163864i | ||||
\(528\) | 0.326057 | + | 0.326057i | 0.0141898 | + | 0.0141898i | ||||
\(529\) | 3.53155i | 0.153546i | ||||||||
\(530\) | −5.92988 | + | 1.59863i | −0.257577 | + | 0.0694402i | ||||
\(531\) | − | 1.91758i | − | 0.0832159i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 43.8113 | − | 43.8113i | 1.89768 | − | 1.89768i | ||||
\(534\) | − | 11.4285i | − | 0.494558i | ||||||
\(535\) | −11.4339 | − | 6.57804i | −0.494329 | − | 0.284394i | ||||
\(536\) | 3.81023 | 0.164577 | ||||||||
\(537\) | −1.14209 | + | 1.14209i | −0.0492846 | + | 0.0492846i | ||||
\(538\) | 1.00414 | + | 1.00414i | 0.0432917 | + | 0.0432917i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.93820 | − | 1.11507i | −0.0834068 | − | 0.0479850i | ||||
\(541\) | 43.8119 | 1.88362 | 0.941810 | − | 0.336145i | \(-0.109123\pi\) | ||||
0.941810 | + | 0.336145i | \(0.109123\pi\) | |||||||
\(542\) | 0.250034 | − | 0.250034i | 0.0107399 | − | 0.0107399i | ||||
\(543\) | −9.08769 | + | 9.08769i | −0.389990 | + | 0.389990i | ||||
\(544\) | −1.63982 | −0.0703066 | ||||||||
\(545\) | 9.67279 | + | 35.8797i | 0.414337 | + | 1.53692i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.59346 | + | 8.59346i | 0.367430 | + | 0.367430i | 0.866539 | − | 0.499109i | \(-0.166339\pi\) |
−0.499109 | + | 0.866539i | \(0.666339\pi\) | |||||||
\(548\) | 3.13179 | − | 3.13179i | 0.133784 | − | 0.133784i | ||||
\(549\) | 13.5554 | 0.578529 | ||||||||
\(550\) | 2.22883 | + | 0.589909i | 0.0950375 | + | 0.0251538i | ||||
\(551\) | 32.2653i | 1.37455i | ||||||||
\(552\) | 3.11997 | − | 3.11997i | 0.132795 | − | 0.132795i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 23.5017i | − | 0.998492i | ||||||
\(555\) | 4.69384 | + | 17.4110i | 0.199242 | + | 0.739057i | ||||
\(556\) | − | 4.35020i | − | 0.184489i | ||||||
\(557\) | 6.03331 | + | 6.03331i | 0.255640 | + | 0.255640i | 0.823278 | − | 0.567638i | \(-0.192143\pi\) |
−0.567638 | + | 0.823278i | \(0.692143\pi\) | |||||||
\(558\) | 0.0229400 | + | 0.0229400i | 0.000971127 | + | 0.000971127i | ||||
\(559\) | −38.0378 | −1.60883 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.756144 | −0.0319244 | ||||||||
\(562\) | 20.1347 | + | 20.1347i | 0.849330 | + | 0.849330i | ||||
\(563\) | 0.0998745 | + | 0.0998745i | 0.00420921 | + | 0.00420921i | 0.709208 | − | 0.704999i | \(-0.249053\pi\) |
−0.704999 | + | 0.709208i | \(0.749053\pi\) | |||||||
\(564\) | − | 9.04024i | − | 0.380663i | ||||||
\(565\) | −10.0198 | + | 17.4162i | −0.421534 | + | 0.732706i | ||||
\(566\) | 3.75788i | 0.157956i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.26410 | + | 6.26410i | −0.262836 | + | 0.262836i | ||||
\(569\) | 4.19043i | 0.175672i | 0.996135 | + | 0.0878359i | \(0.0279951\pi\) | ||||
−0.996135 | + | 0.0878359i | \(0.972005\pi\) | |||||||
\(570\) | 3.39124 | + | 12.5793i | 0.142043 | + | 0.526887i | ||||
\(571\) | −9.79512 | −0.409913 | −0.204957 | − | 0.978771i | \(-0.565705\pi\) | ||||
−0.204957 | + | 0.978771i | \(0.565705\pi\) | |||||||
\(572\) | 1.84573 | − | 1.84573i | 0.0771737 | − | 0.0771737i | ||||
\(573\) | 7.49579 | + | 7.49579i | 0.313141 | + | 0.313141i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.64471 | − | 21.3272i | 0.235401 | − | 0.889405i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 5.75211 | − | 5.75211i | 0.239464 | − | 0.239464i | −0.577164 | − | 0.816628i | \(-0.695841\pi\) |
0.816628 | + | 0.577164i | \(0.195841\pi\) | |||||||
\(578\) | −10.1194 | + | 10.1194i | −0.420912 | + | 0.420912i | ||||
\(579\) | −7.21608 | −0.299890 | ||||||||
\(580\) | 11.9559 | − | 3.22318i | 0.496441 | − | 0.133835i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.51799 | − | 2.51799i | −0.104374 | − | 0.104374i | ||||
\(583\) | 0.895549 | − | 0.895549i | 0.0370899 | − | 0.0370899i | ||||
\(584\) | −4.05729 | −0.167892 | ||||||||
\(585\) | −6.31212 | + | 10.9716i | −0.260974 | + | 0.453622i | ||||
\(586\) | 5.91848i | 0.244490i | ||||||||
\(587\) | 20.3618 | − | 20.3618i | 0.840423 | − | 0.840423i | −0.148491 | − | 0.988914i | \(-0.547442\pi\) |
0.988914 | + | 0.148491i | \(0.0474416\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.189022i | − | 0.00778852i | ||||||
\(590\) | 3.71666 | + | 2.13824i | 0.153012 | + | 0.0880298i | ||||
\(591\) | 13.7575i | 0.565908i | ||||||||
\(592\) | −5.70242 | − | 5.70242i | −0.234368 | − | 0.234368i | ||||
\(593\) | 13.2775 | + | 13.2775i | 0.545242 | + | 0.545242i | 0.925061 | − | 0.379819i | \(-0.124014\pi\) |
−0.379819 | + | 0.925061i | \(0.624014\pi\) | |||||||
\(594\) | 0.461115 | 0.0189198 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.34052 | −0.177794 | ||||||||
\(597\) | 6.82567 | + | 6.82567i | 0.279356 | + | 0.279356i | ||||
\(598\) | −17.6614 | − | 17.6614i | −0.722226 | − | 0.722226i | ||||
\(599\) | 24.2998i | 0.992862i | 0.868076 | + | 0.496431i | \(0.165356\pi\) | ||||
−0.868076 | + | 0.496431i | \(0.834644\pi\) | |||||||
\(600\) | 4.32246 | − | 2.51324i | 0.176464 | − | 0.102603i | ||||
\(601\) | 21.1930i | 0.864481i | 0.901758 | + | 0.432241i | \(0.142277\pi\) | ||||
−0.901758 | + | 0.432241i | \(0.857723\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.69424 | − | 2.69424i | 0.109718 | − | 0.109718i | ||||
\(604\) | 8.18514i | 0.333049i | ||||||||
\(605\) | 23.2898 | − | 6.27869i | 0.946865 | − | 0.255265i | ||||
\(606\) | −4.51181 | −0.183280 | ||||||||
\(607\) | −6.74182 | + | 6.74182i | −0.273642 | + | 0.273642i | −0.830564 | − | 0.556923i | \(-0.811982\pi\) |
0.556923 | + | 0.830564i | \(0.311982\pi\) | |||||||
\(608\) | −4.11993 | − | 4.11993i | −0.167085 | − | 0.167085i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −15.1152 | + | 26.2730i | −0.611996 | + | 1.06376i | ||||
\(611\) | −51.1744 | −2.07030 | ||||||||
\(612\) | −1.15953 | + | 1.15953i | −0.0468711 | + | 0.0468711i | ||||
\(613\) | −15.7821 | + | 15.7821i | −0.637431 | + | 0.637431i | −0.949921 | − | 0.312490i | \(-0.898837\pi\) |
0.312490 | + | 0.949921i | \(0.398837\pi\) | |||||||
\(614\) | 25.5809 | 1.03236 | ||||||||
\(615\) | −12.2048 | + | 21.2142i | −0.492144 | + | 0.855438i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4571 | + | 15.4571i | 0.622278 | + | 0.622278i | 0.946113 | − | 0.323836i | \(-0.104973\pi\) |
−0.323836 | + | 0.946113i | \(0.604973\pi\) | |||||||
\(618\) | 10.4477 | − | 10.4477i | 0.420270 | − | 0.420270i | ||||
\(619\) | 24.7191 | 0.993543 | 0.496772 | − | 0.867881i | \(-0.334519\pi\) | ||||
0.496772 | + | 0.867881i | \(0.334519\pi\) | |||||||
\(620\) | −0.0700419 | + | 0.0188826i | −0.00281295 | + | 0.000758343i | ||||
\(621\) | − | 4.41231i | − | 0.177060i | ||||||
\(622\) | −23.7712 | + | 23.7712i | −0.953139 | + | 0.953139i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 5.66074i | − | 0.226611i | ||||||
\(625\) | 12.3673 | − | 21.7267i | 0.494691 | − | 0.869069i | ||||
\(626\) | 22.9644i | 0.917843i | ||||||||
\(627\) | −1.89976 | − | 1.89976i | −0.0758691 | − | 0.0758691i | ||||
\(628\) | 15.3974 | + | 15.3974i | 0.614425 | + | 0.614425i | ||||
\(629\) | 13.2242 | 0.527284 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 34.7305 | 1.38260 | 0.691299 | − | 0.722569i | \(-0.257039\pi\) | ||||
0.691299 | + | 0.722569i | \(0.257039\pi\) | |||||||
\(632\) | 3.57886 | + | 3.57886i | 0.142359 | + | 0.142359i | ||||
\(633\) | −0.942380 | − | 0.942380i | −0.0374563 | − | 0.0374563i | ||||
\(634\) | 25.6420i | 1.01837i | ||||||||
\(635\) | 32.2776 | + | 18.5697i | 1.28090 | + | 0.736917i | ||||
\(636\) | − | 2.74660i | − | 0.108910i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.80562 | + | 1.80562i | −0.0714850 | + | 0.0714850i | ||||
\(639\) | 8.85877i | 0.350448i | ||||||||
\(640\) | −1.11507 | + | 1.93820i | −0.0440770 | + | 0.0766141i | ||||
\(641\) | 11.6521 | 0.460229 | 0.230115 | − | 0.973164i | \(-0.426090\pi\) | ||||
0.230115 | + | 0.973164i | \(0.426090\pi\) | |||||||
\(642\) | 4.17138 | − | 4.17138i | 0.164631 | − | 0.164631i | ||||
\(643\) | 21.8198 | + | 21.8198i | 0.860489 | + | 0.860489i | 0.991395 | − | 0.130906i | \(-0.0417886\pi\) |
−0.130906 | + | 0.991395i | \(0.541789\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 14.5075 | − | 3.91107i | 0.571232 | − | 0.153998i | ||||
\(646\) | 9.55433 | 0.375910 | ||||||||
\(647\) | 26.2680 | − | 26.2680i | 1.03270 | − | 1.03270i | 0.0332527 | − | 0.999447i | \(-0.489413\pi\) |
0.999447 | − | 0.0332527i | \(-0.0105866\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −0.884225 | −0.0347089 | ||||||||
\(650\) | −14.2268 | − | 24.4683i | −0.558021 | − | 0.959726i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.25527 | − | 8.25527i | −0.323301 | − | 0.323301i | ||||
\(653\) | 22.3571 | − | 22.3571i | 0.874903 | − | 0.874903i | −0.118099 | − | 0.993002i | \(-0.537680\pi\) |
0.993002 | + | 0.118099i | \(0.0376801\pi\) | |||||||
\(654\) | −16.6187 | −0.649844 | ||||||||
\(655\) | −11.0451 | − | 40.9700i | −0.431568 | − | 1.60083i | ||||
\(656\) | − | 10.9453i | − | 0.427342i | ||||||
\(657\) | −2.86894 | + | 2.86894i | −0.111928 | + | 0.111928i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 38.7284i | 1.50864i | 0.656504 | + | 0.754322i | \(0.272034\pi\) | ||||
−0.656504 | + | 0.754322i | \(0.727966\pi\) | |||||||
\(660\) | −0.514175 | + | 0.893732i | −0.0200142 | + | 0.0347885i | ||||
\(661\) | − | 33.8658i | − | 1.31723i | −0.752482 | − | 0.658613i | \(-0.771143\pi\) | ||
0.752482 | − | 0.658613i | \(-0.228857\pi\) | |||||||
\(662\) | −8.38971 | − | 8.38971i | −0.326076 | − | 0.326076i | ||||
\(663\) | 6.56378 | + | 6.56378i | 0.254916 | + | 0.254916i | ||||
\(664\) | −1.53885 | −0.0597190 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.06444 | −0.312491 | ||||||||
\(667\) | 17.2775 | + | 17.2775i | 0.668989 | + | 0.668989i | ||||
\(668\) | −15.5061 | − | 15.5061i | −0.599950 | − | 0.599950i | ||||
\(669\) | − | 11.6713i | − | 0.451238i | ||||||
\(670\) | 2.21771 | + | 8.22625i | 0.0856777 | + | 0.317808i | ||||
\(671\) | − | 6.25058i | − | 0.241301i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7046 | + | 24.7046i | −0.952294 | + | 0.952294i | −0.998913 | − | 0.0466190i | \(-0.985155\pi\) |
0.0466190 | + | 0.998913i | \(0.485155\pi\) | |||||||
\(674\) | − | 4.50775i | − | 0.173632i | ||||||
\(675\) | 1.27931 | − | 4.83357i | 0.0492407 | − | 0.186044i | ||||
\(676\) | −19.0440 | −0.732461 | ||||||||
\(677\) | 12.4482 | − | 12.4482i | 0.478425 | − | 0.478425i | −0.426203 | − | 0.904628i | \(-0.640149\pi\) |
0.904628 | + | 0.426203i | \(0.140149\pi\) | |||||||
\(678\) | −6.35390 | − | 6.35390i | −0.244020 | − | 0.244020i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.954441 | − | 3.54035i | −0.0366011 | − | 0.135766i | ||||
\(681\) | 22.3626 | 0.856937 | ||||||||
\(682\) | 0.0105780 | − | 0.0105780i | 0.000405051 | − | 0.000405051i | ||||
\(683\) | −17.0933 | + | 17.0933i | −0.654057 | + | 0.654057i | −0.953967 | − | 0.299910i | \(-0.903043\pi\) |
0.299910 | + | 0.953967i | \(0.403043\pi\) | |||||||
\(684\) | −5.82646 | −0.222780 | ||||||||
\(685\) | 8.58433 | + | 4.93867i | 0.327991 | + | 0.188697i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.51165 | + | 3.51165i | 0.133978 | + | 0.133978i | ||||
\(688\) | −4.75146 | + | 4.75146i | −0.181148 | + | 0.181148i | ||||
\(689\) | −15.5478 | −0.592324 | ||||||||
\(690\) | 8.55193 | + | 4.92003i | 0.325567 | + | 0.187302i | ||||
\(691\) | − | 2.96578i | − | 0.112824i | −0.998408 | − | 0.0564118i | \(-0.982034\pi\) | ||
0.998408 | − | 0.0564118i | \(-0.0179660\pi\) | |||||||
\(692\) | 6.89034 | − | 6.89034i | 0.261931 | − | 0.261931i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 21.4221i | − | 0.813172i | ||||||
\(695\) | 9.39202 | − | 2.53199i | 0.356260 | − | 0.0960439i | ||||
\(696\) | 5.53773i | 0.209907i | ||||||||
\(697\) | 12.6914 | + | 12.6914i | 0.480719 | + | 0.480719i | ||||
\(698\) | −11.3620 | − | 11.3620i | −0.430056 | − | 0.430056i | ||||
\(699\) | −28.6338 | −1.08303 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.6815 | −0.705591 | −0.352795 | − | 0.935701i | \(-0.614769\pi\) | ||||
−0.352795 | + | 0.935701i | \(0.614769\pi\) | |||||||
\(702\) | −4.00275 | − | 4.00275i | −0.151074 | − | 0.151074i | ||||
\(703\) | 33.2249 | + | 33.2249i | 1.25310 | + | 1.25310i | ||||
\(704\) | − | 0.461115i | − | 0.0173789i | ||||||
\(705\) | 19.5178 | − | 5.26179i | 0.735082 | − | 0.198170i | ||||
\(706\) | 29.3960i | 1.10633i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −1.35593 | + | 1.35593i | −0.0509592 | + | 0.0509592i | ||||
\(709\) | 21.1525i | 0.794401i | 0.917732 | + | 0.397200i | \(0.130018\pi\) | ||||
−0.917732 | + | 0.397200i | \(0.869982\pi\) | |||||||
\(710\) | −17.1701 | − | 9.87815i | −0.644381 | − | 0.370720i | ||||
\(711\) | 5.06128 | 0.189813 | ||||||||
\(712\) | −8.08115 | + | 8.08115i | −0.302854 | + | 0.302854i | ||||
\(713\) | −0.101218 | − | 0.101218i | −0.00379065 | − | 0.00379065i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.05919 | + | 2.91061i | 0.189203 | + | 0.108851i | ||||
\(716\) | 1.61515 | 0.0603611 | ||||||||
\(717\) | 9.84504 | − | 9.84504i | 0.367670 | − | 0.367670i | ||||
\(718\) | 9.63602 | − | 9.63602i | 0.359613 | − | 0.359613i | ||||
\(719\) | −8.61250 | −0.321192 | −0.160596 | − | 0.987020i | \(-0.551342\pi\) | ||||
−0.160596 | + | 0.987020i | \(0.551342\pi\) | |||||||
\(720\) | 0.582041 | + | 2.15899i | 0.0216914 | + | 0.0804607i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.5696 | + | 10.5696i | 0.393359 | + | 0.393359i | ||||
\(723\) | −0.747813 | + | 0.747813i | −0.0278115 | + | 0.0278115i | ||||
\(724\) | 12.8519 | 0.477639 | ||||||||
\(725\) | 13.9176 | + | 23.9366i | 0.516888 | + | 0.888982i | ||||
\(726\) | 10.7874i | 0.400357i | ||||||||
\(727\) | 12.8013 | − | 12.8013i | 0.474774 | − | 0.474774i | −0.428682 | − | 0.903455i | \(-0.641022\pi\) |
0.903455 | + | 0.428682i | \(0.141022\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | −2.36151 | − | 8.75964i | −0.0874033 | − | 0.324209i | ||||
\(731\) | − | 11.0189i | − | 0.407548i | ||||||
\(732\) | −9.58509 | − | 9.58509i | −0.354275 | − | 0.354275i | ||||
\(733\) | −23.3893 | − | 23.3893i | −0.863903 | − | 0.863903i | 0.127886 | − | 0.991789i | \(-0.459181\pi\) |
−0.991789 | + | 0.127886i | \(0.959181\pi\) | |||||||
\(734\) | 12.7591 | 0.470947 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.41231 | −0.162640 | ||||||||
\(737\) | −1.24235 | − | 1.24235i | −0.0457627 | − | 0.0457627i | ||||
\(738\) | −7.73949 | − | 7.73949i | −0.284895 | − | 0.284895i | ||||
\(739\) | 47.3172i | 1.74059i | 0.492528 | + | 0.870296i | \(0.336073\pi\) | ||||
−0.492528 | + | 0.870296i | \(0.663927\pi\) | |||||||
\(740\) | 8.99242 | − | 15.6305i | 0.330568 | − | 0.574589i | ||||
\(741\) | 32.9821i | 1.21163i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.5587 | + | 21.5587i | −0.790914 | + | 0.790914i | −0.981643 | − | 0.190729i | \(-0.938915\pi\) |
0.190729 | + | 0.981643i | \(0.438915\pi\) | |||||||
\(744\) | − | 0.0324420i | − | 0.00118938i | ||||||
\(745\) | −2.52636 | − | 9.37112i | −0.0925586 | − | 0.343331i | ||||
\(746\) | 4.00135 | 0.146500 | ||||||||
\(747\) | −1.08813 | + | 1.08813i | −0.0398127 | + | 0.0398127i | ||||
\(748\) | 0.534674 | + | 0.534674i | 0.0195496 | + | 0.0195496i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 7.94190 | + | 7.86932i | 0.289997 | + | 0.287347i | ||||
\(751\) | 31.0138 | 1.13171 | 0.565854 | − | 0.824505i | \(-0.308547\pi\) | ||||
0.565854 | + | 0.824505i | \(0.308547\pi\) | |||||||
\(752\) | −6.39241 | + | 6.39241i | −0.233107 | + | 0.233107i | ||||
\(753\) | −4.49904 | + | 4.49904i | −0.163954 | + | 0.163954i | ||||
\(754\) | 31.3476 | 1.14161 | ||||||||
\(755\) | −17.6716 | + | 4.76409i | −0.643136 | + | 0.173383i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.7486 | − | 16.7486i | −0.608738 | − | 0.608738i | 0.333879 | − | 0.942616i | \(-0.391642\pi\) |
−0.942616 | + | 0.333879i | \(0.891642\pi\) | |||||||
\(758\) | −0.709094 | + | 0.709094i | −0.0257555 | + | 0.0257555i | ||||
\(759\) | −2.03458 | −0.0738505 | ||||||||
\(760\) | 6.49691 | − | 11.2928i | 0.235668 | − | 0.409634i | ||||
\(761\) | − | 17.0155i | − | 0.616813i | −0.951255 | − | 0.308406i | \(-0.900204\pi\) | ||
0.951255 | − | 0.308406i | \(-0.0997956\pi\) | |||||||
\(762\) | −11.7757 | + | 11.7757i | −0.426590 | + | 0.426590i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 10.6007i | − | 0.383518i | ||||||
\(765\) | −3.17829 | − | 1.82851i | −0.114911 | − | 0.0661100i | ||||
\(766\) | − | 17.8032i | − | 0.643255i | ||||||
\(767\) | 7.67560 | + | 7.67560i | 0.277150 | + | 0.277150i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 7.70275 | 0.277768 | 0.138884 | − | 0.990309i | \(-0.455648\pi\) | ||||
0.138884 | + | 0.990309i | \(0.455648\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3811 | 0.373865 | ||||||||
\(772\) | 5.10254 | + | 5.10254i | 0.183644 | + | 0.183644i | ||||
\(773\) | −2.13982 | − | 2.13982i | −0.0769640 | − | 0.0769640i | 0.667577 | − | 0.744541i | \(-0.267332\pi\) |
−0.744541 | + | 0.667577i | \(0.767332\pi\) | |||||||
\(774\) | 6.71958i | 0.241530i | ||||||||
\(775\) | −0.0815345 | − | 0.140229i | −0.00292881 | − | 0.00503718i | ||||
\(776\) | 3.56097i | 0.127832i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.96110 | + | 7.96110i | −0.285419 | + | 0.285419i | ||||
\(779\) | 63.7723i | 2.28488i | ||||||||
\(780\) | 12.2215 | − | 3.29478i | 0.437599 | − | 0.117972i | ||||
\(781\) | 4.08491 | 0.146170 | ||||||||
\(782\) | 5.11618 | − | 5.11618i | 0.182954 | − | 0.182954i | ||||
\(783\) | 3.91576 | + | 3.91576i | 0.139938 | + | 0.139938i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24.2810 | + | 42.2048i | −0.866624 | + | 1.50636i | ||||
\(786\) | 18.9765 | 0.676869 | ||||||||
\(787\) | −15.8501 | + | 15.8501i | −0.564996 | + | 0.564996i | −0.930722 | − | 0.365726i | \(-0.880821\pi\) |
0.365726 | + | 0.930722i | \(0.380821\pi\) | |||||||
\(788\) | 9.72803 | − | 9.72803i | 0.346547 | − | 0.346547i | ||||
\(789\) | −23.7620 | −0.845948 | ||||||||
\(790\) | −5.64368 | + | 9.80976i | −0.200793 | + | 0.349016i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −0.326057 | − | 0.326057i | −0.0115859 | − | 0.0115859i | ||||
\(793\) | −54.2587 | + | 54.2587i | −1.92678 | + | 1.92678i | ||||
\(794\) | 3.83284 | 0.136022 | ||||||||
\(795\) | 5.92988 | − | 1.59863i | 0.210311 | − | 0.0566977i | ||||
\(796\) | − | 9.65296i | − | 0.342140i | ||||||
\(797\) | −21.8939 | + | 21.8939i | −0.775520 | + | 0.775520i | −0.979066 | − | 0.203545i | \(-0.934754\pi\) |
0.203545 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 14.8243i | − | 0.524447i | ||||||
\(800\) | −4.83357 | − | 1.27931i | −0.170892 | − | 0.0452305i | ||||
\(801\) | 11.4285i | 0.403805i | ||||||||
\(802\) | 0.636428 | + | 0.636428i | 0.0224730 | + | 0.0224730i | ||||
\(803\) | 1.32291 | + | 1.32291i | 0.0466844 | + | 0.0466844i | ||||
\(804\) | −3.81023 | −0.134377 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.183646 | −0.00646865 | ||||||||
\(807\) | −1.00414 | − | 1.00414i | −0.0353475 | − | 0.0353475i | ||||
\(808\) | 3.19033 | + | 3.19033i | 0.112235 | + | 0.112235i | ||||
\(809\) | 1.08401i | 0.0381118i | 0.999818 | + | 0.0190559i | \(0.00606605\pi\) | ||||
−0.999818 | + | 0.0190559i | \(0.993934\pi\) | |||||||
\(810\) | 1.93820 | + | 1.11507i | 0.0681014 | + | 0.0391796i | ||||
\(811\) | 33.8754i | 1.18953i | 0.803901 | + | 0.594763i | \(0.202754\pi\) | ||||
−0.803901 | + | 0.594763i | \(0.797246\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.250034 | + | 0.250034i | −0.00876907 | + | 0.00876907i | ||||
\(814\) | 3.71863i | 0.130338i | ||||||||
\(815\) | 13.0181 | − | 22.6279i | 0.456005 | − | 0.792622i | ||||
\(816\) | 1.63982 | 0.0574051 | ||||||||
\(817\) | 27.6842 | − | 27.6842i | 0.968547 | − | 0.968547i | ||||
\(818\) | −9.11649 | − | 9.11649i | −0.318751 | − | 0.318751i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.6308 | − | 6.37061i | 0.825222 | − | 0.222471i | ||||
\(821\) | 4.86638 | 0.169838 | 0.0849190 | − | 0.996388i | \(-0.472937\pi\) | ||||
0.0849190 | + | 0.996388i | \(0.472937\pi\) | |||||||
\(822\) | −3.13179 | + | 3.13179i | −0.109234 | + | 0.109234i | ||||
\(823\) | −24.5590 | + | 24.5590i | −0.856072 | + | 0.856072i | −0.990873 | − | 0.134801i | \(-0.956961\pi\) |
0.134801 | + | 0.990873i | \(0.456961\pi\) | |||||||
\(824\) | −14.7753 | −0.514723 | ||||||||
\(825\) | −2.22883 | − | 0.589909i | −0.0775978 | − | 0.0205380i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.4936 | − | 38.4936i | −1.33855 | − | 1.33855i | −0.897461 | − | 0.441093i | \(-0.854591\pi\) |
−0.441093 | − | 0.897461i | \(-0.645409\pi\) | |||||||
\(828\) | −3.11997 | + | 3.11997i | −0.108427 | + | 0.108427i | ||||
\(829\) | 40.1305 | 1.39379 | 0.696895 | − | 0.717173i | \(-0.254564\pi\) | ||||
0.696895 | + | 0.717173i | \(0.254564\pi\) | |||||||
\(830\) | −0.895674 | − | 3.32236i | −0.0310893 | − | 0.115321i | ||||
\(831\) | 23.5017i | 0.815266i | ||||||||
\(832\) | −4.00275 | + | 4.00275i | −0.138770 | + | 0.138770i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 4.35020i | 0.150635i | ||||||||
\(835\) | 24.4523 | − | 42.5027i | 0.846207 | − | 1.47087i | ||||
\(836\) | 2.68667i | 0.0929203i | ||||||||
\(837\) | −0.0229400 | − | 0.0229400i | −0.000792922 | − | 0.000792922i | ||||
\(838\) | −14.0656 | − | 14.0656i | −0.485888 | − | 0.485888i | ||||
\(839\) | 27.8082 | 0.960044 | 0.480022 | − | 0.877256i | \(-0.340629\pi\) | ||||
0.480022 | + | 0.877256i | \(0.340629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.66640 | −0.0574621 | ||||||||
\(842\) | −8.93353 | − | 8.93353i | −0.307870 | − | 0.307870i | ||||
\(843\) | −20.1347 | − | 20.1347i | −0.693475 | − | 0.693475i | ||||
\(844\) | 1.33273i | 0.0458744i | ||||||||
\(845\) | −11.0844 | − | 41.1157i | −0.381314 | − | 1.41442i | ||||
\(846\) | 9.04024i | 0.310810i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.94214 | + | 1.94214i | −0.0666934 | + | 0.0666934i | ||||
\(849\) | − | 3.75788i | − | 0.128970i | ||||||
\(850\) | 7.08804 | − | 4.12125i | 0.243118 | − | 0.141358i | ||||
\(851\) | 35.5828 | 1.21976 | ||||||||
\(852\) | 6.26410 | − | 6.26410i | 0.214604 | − | 0.214604i | ||||
\(853\) | −19.0929 | − | 19.0929i | −0.653729 | − | 0.653729i | 0.300160 | − | 0.953889i | \(-0.402960\pi\) |
−0.953889 | + | 0.300160i | \(0.902960\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.39124 | − | 12.5793i | −0.115978 | − | 0.430201i | ||||
\(856\) | −5.89922 | −0.201631 | ||||||||
\(857\) | −14.4167 | + | 14.4167i | −0.492465 | + | 0.492465i | −0.909082 | − | 0.416617i | \(-0.863216\pi\) |
0.416617 | + | 0.909082i | \(0.363216\pi\) | |||||||
\(858\) | −1.84573 | + | 1.84573i | −0.0630120 | + | 0.0630120i | ||||
\(859\) | −4.48341 | −0.152972 | −0.0764860 | − | 0.997071i | \(-0.524370\pi\) | ||||
−0.0764860 | + | 0.997071i | \(0.524370\pi\) | |||||||
\(860\) | −13.0239 | − | 7.49280i | −0.444111 | − | 0.255502i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.7578 | + | 21.7578i | 0.741073 | + | 0.741073i | ||||
\(863\) | −13.8924 | + | 13.8924i | −0.472902 | + | 0.472902i | −0.902852 | − | 0.429951i | \(-0.858531\pi\) |
0.429951 | + | 0.902852i | \(0.358531\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 18.8866 | + | 10.8657i | 0.642164 | + | 0.369445i | ||||
\(866\) | 4.30971i | 0.146450i | ||||||||
\(867\) | 10.1194 | − | 10.1194i | 0.343673 | − | 0.343673i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.33383i | − | 0.0791697i | ||||||
\(870\) | −11.9559 | + | 3.22318i | −0.405342 | + | 0.109276i | ||||
\(871\) | 21.5687i | 0.730829i | ||||||||
\(872\) | 11.7512 | + | 11.7512i | 0.397947 | + | 0.397947i | ||||
\(873\) | 2.51799 | + | 2.51799i | 0.0852210 | + | 0.0852210i | ||||
\(874\) | 25.7081 | 0.869590 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.05729 | 0.137083 | ||||||||
\(877\) | 9.52443 | + | 9.52443i | 0.321617 | + | 0.321617i | 0.849387 | − | 0.527770i | \(-0.176972\pi\) |
−0.527770 | + | 0.849387i | \(0.676972\pi\) | |||||||
\(878\) | 26.1620 | + | 26.1620i | 0.882926 | + | 0.882926i | ||||
\(879\) | − | 5.91848i | − | 0.199625i | ||||||
\(880\) | 0.995541 | − | 0.268388i | 0.0335597 | − | 0.00904734i | ||||
\(881\) | − | 55.0357i | − | 1.85420i | −0.374813 | − | 0.927100i | \(-0.622293\pi\) | ||
0.374813 | − | 0.927100i | \(-0.377707\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.82147 | − | 3.82147i | 0.128603 | − | 0.128603i | −0.639876 | − | 0.768478i | \(-0.721014\pi\) |
0.768478 | + | 0.639876i | \(0.221014\pi\) | |||||||
\(884\) | − | 9.28258i | − | 0.312207i | ||||||
\(885\) | −3.71666 | − | 2.13824i | −0.124934 | − | 0.0718761i | ||||
\(886\) | −17.7975 | −0.597919 | ||||||||
\(887\) | 16.1865 | − | 16.1865i | 0.543489 | − | 0.543489i | −0.381061 | − | 0.924550i | \(-0.624441\pi\) |
0.924550 | + | 0.381061i | \(0.124441\pi\) | |||||||
\(888\) | 5.70242 | + | 5.70242i | 0.191361 | + | 0.191361i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −22.1507 | − | 12.7435i | −0.742492 | − | 0.427164i | ||||
\(891\) | −0.461115 | −0.0154479 | ||||||||
\(892\) | −8.25284 | + | 8.25284i | −0.276326 | + | 0.276326i | ||||
\(893\) | 37.2451 | − | 37.2451i | 1.24636 | − | 1.24636i | ||||
\(894\) | 4.34052 | 0.145169 | ||||||||
\(895\) | 0.940085 | + | 3.48710i | 0.0314236 | + | 0.116561i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 17.6614 | + | 17.6614i | 0.589695 | + | 0.589695i | ||||
\(898\) | −1.71081 | + | 1.71081i | −0.0570904 | + | 0.0570904i | ||||
\(899\) | 0.179655 | 0.00599183 | ||||||||
\(900\) | −4.32246 | + | 2.51324i | −0.144082 | + | 0.0837746i | ||||
\(901\) | − | 4.50392i | − | 0.150047i | ||||||
\(902\) | −3.56879 | + | 3.56879i | −0.118828 | + | 0.118828i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.98577i | 0.298862i | ||||||||
\(905\) | 7.48035 | + | 27.7472i | 0.248655 | + | 0.922347i | ||||
\(906\) | − | 8.18514i | − | 0.271933i | ||||||
\(907\) | 19.3481 | + | 19.3481i | 0.642444 | + | 0.642444i | 0.951156 | − | 0.308712i | \(-0.0998979\pi\) |
−0.308712 | + | 0.951156i | \(0.599898\pi\) | |||||||
\(908\) | −15.8128 | − | 15.8128i | −0.524765 | − | 0.524765i | ||||
\(909\) | 4.51181 | 0.149647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.5763 | −1.84132 | −0.920662 | − | 0.390360i | \(-0.872350\pi\) | ||||
−0.920662 | + | 0.390360i | \(0.872350\pi\) | |||||||
\(912\) | 4.11993 | + | 4.11993i | 0.136424 | + | 0.136424i | ||||
\(913\) | 0.501754 | + | 0.501754i | 0.0166056 | + | 0.0166056i | ||||
\(914\) | − | 27.5588i | − | 0.911565i | ||||||
\(915\) | 15.1152 | − | 26.2730i | 0.499692 | − | 0.868559i | ||||
\(916\) | − | 4.96622i | − | 0.164088i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.15953 | − | 1.15953i | 0.0382701 | − | 0.0382701i | ||||
\(919\) | 20.1259i | 0.663893i | 0.943298 | + | 0.331947i | \(0.107705\pi\) | ||||
−0.943298 | + | 0.331947i | \(0.892295\pi\) | |||||||
\(920\) | −2.56814 | − | 9.52612i | −0.0846692 | − | 0.314067i | ||||
\(921\) | −25.5809 | −0.842920 | ||||||||
\(922\) | −0.726284 | + | 0.726284i | −0.0239189 | + | 0.0239189i | ||||
\(923\) | −35.4594 | − | 35.4594i | −1.16716 | − | 1.16716i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.9800 | + | 10.3169i | 1.28166 | + | 0.339219i | ||||
\(926\) | −11.6886 | −0.384111 | ||||||||
\(927\) | −10.4477 | + | 10.4477i | −0.343149 | + | 0.343149i | ||||
\(928\) | 3.91576 | − | 3.91576i | 0.128541 | − | 0.128541i | ||||
\(929\) | −26.0224 | −0.853766 | −0.426883 | − | 0.904307i | \(-0.640388\pi\) | ||||
−0.426883 | + | 0.904307i | \(0.640388\pi\) | |||||||
\(930\) | 0.0700419 | − | 0.0188826i | 0.00229677 | − | 0.000619184i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.2472 | + | 20.2472i | 0.663218 | + | 0.663218i | ||||
\(933\) | 23.7712 | − | 23.7712i | 0.778235 | − | 0.778235i | ||||
\(934\) | 18.5448 | 0.606804 | ||||||||
\(935\) | −0.843153 | + | 1.46556i | −0.0275741 | + | 0.0479289i | ||||
\(936\) | 5.66074i | 0.185027i | ||||||||
\(937\) | −17.1515 | + | 17.1515i | −0.560314 | + | 0.560314i | −0.929397 | − | 0.369082i | \(-0.879672\pi\) |
0.369082 | + | 0.929397i | \(0.379672\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 22.9644i | − | 0.749416i | ||||||
\(940\) | −17.5218 | − | 10.0805i | −0.571498 | − | 0.328790i | ||||
\(941\) | − | 16.6306i | − | 0.542143i | −0.962559 | − | 0.271071i | \(-0.912622\pi\) | ||
0.962559 | − | 0.271071i | \(-0.0873779\pi\) | |||||||
\(942\) | −15.3974 | − | 15.3974i | −0.501676 | − | 0.501676i | ||||
\(943\) | 34.1490 | + | 34.1490i | 1.11204 | + | 1.11204i | ||||
\(944\) | 1.91758 | 0.0624120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.09849 | 0.100741 | ||||||||
\(947\) | −20.9961 | − | 20.9961i | −0.682281 | − | 0.682281i | 0.278233 | − | 0.960514i | \(-0.410251\pi\) |
−0.960514 | + | 0.278233i | \(0.910251\pi\) | |||||||
\(948\) | −3.57886 | − | 3.57886i | −0.116236 | − | 0.116236i | ||||
\(949\) | − | 22.9673i | − | 0.745549i | ||||||
\(950\) | 28.1626 | + | 7.45385i | 0.913715 | + | 0.241835i | ||||
\(951\) | − | 25.6420i | − | 0.831498i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −30.9752 | + | 30.9752i | −1.00339 | + | 1.00339i | −0.00339090 | + | 0.999994i | \(0.501079\pi\) |
−0.999994 | + | 0.00339090i | \(0.998921\pi\) | |||||||
\(954\) | 2.74660i | 0.0889245i | ||||||||
\(955\) | 22.8867 | − | 6.17001i | 0.740595 | − | 0.199657i | ||||
\(956\) | −13.9230 | −0.450302 | ||||||||
\(957\) | 1.80562 | − | 1.80562i | 0.0583673 | − | 0.0583673i | ||||
\(958\) | −5.99446 | − | 5.99446i | −0.193672 | − | 0.193672i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.11507 | − | 1.93820i | 0.0359887 | − | 0.0625551i | ||||
\(961\) | 30.9989 | 0.999966 | ||||||||
\(962\) | 32.2799 | − | 32.2799i | 1.04075 | − | 1.04075i | ||||
\(963\) | −4.17138 | + | 4.17138i | −0.134421 | + | 0.134421i | ||||
\(964\) | 1.05757 | 0.0340620 | ||||||||
\(965\) | −8.04643 | + | 13.9862i | −0.259024 | + | 0.450232i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.23140 | − | 9.23140i | −0.296862 | − | 0.296862i | 0.542922 | − | 0.839783i | \(-0.317318\pi\) |
−0.839783 | + | 0.542922i | \(0.817318\pi\) | |||||||
\(968\) | 7.62782 | − | 7.62782i | 0.245168 | − | 0.245168i | ||||
\(969\) | −9.55433 | −0.306929 | ||||||||
\(970\) | −7.68810 | + | 2.07263i | −0.246850 | + | 0.0665482i | ||||
\(971\) | 24.4464i | 0.784522i | 0.919854 | + | 0.392261i | \(0.128307\pi\) | ||||
−0.919854 | + | 0.392261i | \(0.871693\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 4.85631i | − | 0.155606i | ||||||
\(975\) | 14.2268 | + | 24.4683i | 0.455622 | + | 0.783613i | ||||
\(976\) | 13.5554i | 0.433897i | ||||||||
\(977\) | −19.8040 | − | 19.8040i | −0.633585 | − | 0.633585i | 0.315380 | − | 0.948965i | \(-0.397868\pi\) |
−0.948965 | + | 0.315380i | \(0.897868\pi\) | |||||||
\(978\) | 8.25527 | + | 8.25527i | 0.263974 | + | 0.263974i | ||||
\(979\) | 5.26983 | 0.168425 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.6187 | 0.530596 | ||||||||
\(982\) | −26.7707 | − | 26.7707i | −0.854286 | − | 0.854286i | ||||
\(983\) | −29.1748 | − | 29.1748i | −0.930531 | − | 0.930531i | 0.0672080 | − | 0.997739i | \(-0.478591\pi\) |
−0.997739 | + | 0.0672080i | \(0.978591\pi\) | |||||||
\(984\) | 10.9453i | 0.348923i | ||||||||
\(985\) | 26.6648 | + | 15.3406i | 0.849611 | + | 0.488792i | ||||
\(986\) | 9.08086i | 0.289193i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.3218 | − | 23.3218i | 0.741967 | − | 0.741967i | ||||
\(989\) | − | 29.6488i | − | 0.942778i | ||||||
\(990\) | 0.514175 | − | 0.893732i | 0.0163416 | − | 0.0284047i | ||||
\(991\) | −36.3648 | −1.15516 | −0.577582 | − | 0.816332i | \(-0.696004\pi\) | ||||
−0.577582 | + | 0.816332i | \(0.696004\pi\) | |||||||
\(992\) | −0.0229400 | + | 0.0229400i | −0.000728345 | + | 0.000728345i | ||||
\(993\) | 8.38971 | + | 8.38971i | 0.266240 | + | 0.266240i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.8406 | − | 5.61842i | 0.660692 | − | 0.178116i | ||||
\(996\) | 1.53885 | 0.0487604 | ||||||||
\(997\) | −12.7033 | + | 12.7033i | −0.402317 | + | 0.402317i | −0.879049 | − | 0.476732i | \(-0.841821\pi\) |
0.476732 | + | 0.879049i | \(0.341821\pi\) | |||||||
\(998\) | 0.362177 | − | 0.362177i | 0.0114645 | − | 0.0114645i | ||||
\(999\) | 8.06444 | 0.255148 |
(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 | 1470.2.m.d.97.5 | 16 | ||
5.3 | odd | 4 | 1470.2.m.e.1273.8 | 16 | |||
7.2 | even | 3 | 210.2.u.a.157.4 | yes | 16 | ||
7.3 | odd | 6 | 210.2.u.b.187.1 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.e.97.8 | 16 | |||
21.2 | odd | 6 | 630.2.bv.a.577.1 | 16 | |||
21.17 | even | 6 | 630.2.bv.b.397.4 | 16 | |||
35.2 | odd | 12 | 1050.2.bc.g.493.3 | 16 | |||
35.3 | even | 12 | 210.2.u.a.103.4 | ✓ | 16 | ||
35.9 | even | 6 | 1050.2.bc.h.157.1 | 16 | |||
35.13 | even | 4 | inner | 1470.2.m.d.1273.5 | 16 | ||
35.17 | even | 12 | 1050.2.bc.h.943.1 | 16 | |||
35.23 | odd | 12 | 210.2.u.b.73.1 | yes | 16 | ||
35.24 | odd | 6 | 1050.2.bc.g.607.3 | 16 | |||
105.23 | even | 12 | 630.2.bv.b.73.4 | 16 | |||
105.38 | odd | 12 | 630.2.bv.a.523.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.4 | ✓ | 16 | 35.3 | even | 12 | ||
210.2.u.a.157.4 | yes | 16 | 7.2 | even | 3 | ||
210.2.u.b.73.1 | yes | 16 | 35.23 | odd | 12 | ||
210.2.u.b.187.1 | yes | 16 | 7.3 | odd | 6 | ||
630.2.bv.a.523.1 | 16 | 105.38 | odd | 12 | |||
630.2.bv.a.577.1 | 16 | 21.2 | odd | 6 | |||
630.2.bv.b.73.4 | 16 | 105.23 | even | 12 | |||
630.2.bv.b.397.4 | 16 | 21.17 | even | 6 | |||
1050.2.bc.g.493.3 | 16 | 35.2 | odd | 12 | |||
1050.2.bc.g.607.3 | 16 | 35.24 | odd | 6 | |||
1050.2.bc.h.157.1 | 16 | 35.9 | even | 6 | |||
1050.2.bc.h.943.1 | 16 | 35.17 | even | 12 | |||
1470.2.m.d.97.5 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.d.1273.5 | 16 | 35.13 | even | 4 | inner | ||
1470.2.m.e.97.8 | 16 | 7.6 | odd | 2 | |||
1470.2.m.e.1273.8 | 16 | 5.3 | odd | 4 |