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 | 97.8 | ||
Root | \(-0.424637 - 3.22544i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.e.1273.8 |
$q$-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 | \(0.0373389\pi\) |
0.117035 | + | 0.993128i | \(0.462661\pi\) | |||||||
\(14\) | 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 | −0.833598 | − | 0.552372i | \(-0.813723\pi\) |
0.552372 | + | 0.833598i | \(0.313723\pi\) | |||||||
\(18\) | −0.707107 | + | 0.707107i | −0.166667 | + | 0.166667i | ||||
\(19\) | −5.82646 | −1.33668 | −0.668341 | − | 0.743855i | \(-0.732995\pi\) | ||||
−0.668341 | + | 0.743855i | \(0.732995\pi\) | |||||||
\(20\) | 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 | \(0.000927359\pi\) | ||||
−0.999996 | + | 0.00291338i | \(0.999073\pi\) | |||||||
\(32\) | −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 | \(-0.673751\pi\) | ||
0.519149 | − | 0.854684i | \(-0.326249\pi\) | |||||||
\(42\) | 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 | −0.997857 | − | 0.0654279i | \(-0.979159\pi\) |
0.0654279 | + | 0.997857i | \(0.479159\pi\) | |||||||
\(48\) | −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 | \(-0.460163\pi\) | ||||
0.124824 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(60\) | −1.11507 | + | 1.93820i | −0.143955 | + | 0.250221i | ||||
\(61\) | 13.5554i | 1.73559i | 0.496925 | + | 0.867793i | \(0.334462\pi\) | ||||
−0.496925 | + | 0.867793i | \(0.665538\pi\) | |||||||
\(62\) | −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 | 0.518994 | − | 0.854778i | \(-0.326307\pi\) |
−0.854778 | + | 0.518994i | \(0.826307\pi\) | |||||||
\(74\) | 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 | 0.644861 | − | 0.764299i | \(-0.276915\pi\) |
−0.764299 | + | 0.644861i | \(0.776915\pi\) | |||||||
\(84\) | 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 | \(-0.707110\pi\) | ||||
−0.605708 | + | 0.795687i | \(0.707110\pi\) | |||||||
\(90\) | −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 | −0.823288 | − | 0.567624i | \(-0.807863\pi\) |
0.567624 | + | 0.823288i | \(0.307863\pi\) | |||||||
\(98\) | 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 | \(0.0720654\pi\) | ||||
−0.974481 | + | 0.224471i | \(0.927935\pi\) | |||||||
\(102\) | −1.15953 | − | 1.15953i | −0.114810 | − | 0.114810i | ||||
\(103\) | −10.4477 | − | 10.4477i | −1.02945 | − | 1.02945i | −0.999553 | − | 0.0298934i | \(-0.990483\pi\) |
−0.0298934 | − | 0.999553i | \(-0.509517\pi\) | |||||||
\(104\) | −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 | \(-0.688915\pi\) | ||
0.559261 | − | 0.828992i | \(-0.311085\pi\) | |||||||
\(132\) | −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 | \(-0.440937\pi\) | ||||
0.184489 | + | 0.982835i | \(0.440937\pi\) | |||||||
\(140\) | 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 | \(0.585191\pi\) |
−0.964399 | + | 0.264451i | \(0.914809\pi\) | |||||||
\(158\) | 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 | \(-0.427532\pi\) |
0.974196 | − | 0.225703i | \(-0.0724679\pi\) | |||||||
\(168\) | 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 | 0.918736 | − | 0.394873i | \(-0.129211\pi\) |
−0.394873 | + | 0.918736i | \(0.629211\pi\) | |||||||
\(174\) | −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 | \(0.158507\pi\) | ||||
−0.878556 | + | 0.477639i | \(0.841493\pi\) | |||||||
\(182\) | 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 | \(-0.388848\pi\) | ||||
0.342140 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(200\) | −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 | 0.374554 | − | 0.927205i | \(-0.377796\pi\) |
−0.927205 | + | 0.374554i | \(0.877796\pi\) | |||||||
\(224\) | 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 | \(-0.483816\pi\) |
0.998708 | − | 0.0508215i | \(-0.0161840\pi\) | |||||||
\(228\) | 4.11993 | − | 4.11993i | 0.272849 | − | 0.272849i | ||||
\(229\) | 4.96622 | 0.328177 | 0.164088 | − | 0.986446i | \(-0.447532\pi\) | ||||
0.164088 | + | 0.986446i | \(0.447532\pi\) | |||||||
\(230\) | 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 | \(0.0108444\pi\) | ||||
−0.999420 | + | 0.0340620i | \(0.989156\pi\) | |||||||
\(242\) | −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 | \(0.0643548\pi\) | ||||
−0.979632 | + | 0.200802i | \(0.935645\pi\) | |||||||
\(252\) | 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 | −0.440073 | − | 0.897962i | \(-0.645047\pi\) |
0.897962 | + | 0.440073i | \(0.145047\pi\) | |||||||
\(258\) | 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 | \(-0.513784\pi\) | ||||
−0.0432917 | + | 0.999062i | \(0.513784\pi\) | |||||||
\(270\) | −2.15899 | + | 0.582041i | −0.131392 | + | 0.0354219i | ||||
\(271\) | 0.353601i | 0.0214797i | 0.999942 | + | 0.0107399i | \(0.00341867\pi\) | ||||
−0.999942 | + | 0.0107399i | \(0.996581\pi\) | |||||||
\(272\) | 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 | 0.623705 | − | 0.781660i | \(-0.285627\pi\) |
−0.781660 | + | 0.623705i | \(0.785627\pi\) | |||||||
\(284\) | 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 | 0.574215 | − | 0.818705i | \(-0.305308\pi\) |
−0.818705 | + | 0.574215i | \(0.805308\pi\) | |||||||
\(294\) | 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 | \(0.510475\pi\) |
−0.999459 | + | 0.0329031i | \(0.989525\pi\) | |||||||
\(308\) | 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 | \(-0.597832\pi\) | ||
0.302531 | − | 0.953139i | \(-0.402168\pi\) | |||||||
\(312\) | −4.00275 | − | 4.00275i | −0.226611 | − | 0.226611i | ||||
\(313\) | −16.2383 | − | 16.2383i | −0.917843 | − | 0.917843i | 0.0790289 | − | 0.996872i | \(-0.474818\pi\) |
−0.996872 | + | 0.0790289i | \(0.974818\pi\) | |||||||
\(314\) | −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 | \(-0.358494\pi\) | ||||
0.430056 | + | 0.902802i | \(0.358494\pi\) | |||||||
\(350\) | 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 | \(-0.964049\pi\) |
−0.112703 | − | 0.993629i | \(-0.535951\pi\) | |||||||
\(354\) | 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 | −0.902221 | − | 0.431274i | \(-0.858064\pi\) |
0.431274 | + | 0.902221i | \(0.358064\pi\) | |||||||
\(368\) | −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 | 0.951354 | − | 0.308100i | \(-0.0996930\pi\) |
−0.308100 | + | 0.951354i | \(0.599693\pi\) | |||||||
\(384\) | 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 | −0.771840 | − | 0.635817i | \(-0.780663\pi\) |
0.635817 | + | 0.771840i | \(0.280663\pi\) | |||||||
\(398\) | 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 | \(-0.396737\pi\) | ||||
0.318751 | + | 0.947839i | \(0.396737\pi\) | |||||||
\(410\) | 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 | \(-0.338496\pi\) | ||||
0.485888 | + | 0.874021i | \(0.338496\pi\) | |||||||
\(420\) | 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 | 0.630080 | − | 0.776530i | \(-0.283022\pi\) |
−0.776530 | + | 0.630080i | \(0.783022\pi\) | |||||||
\(434\) | 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 | \(-0.844430\pi\) | ||||
−0.882926 | + | 0.469513i | \(0.844430\pi\) | |||||||
\(440\) | −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 | \(-0.992386\pi\) | ||
0.999714 | − | 0.0239189i | \(-0.00761434\pi\) | |||||||
\(462\) | 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 | −0.942109 | − | 0.335305i | \(-0.891160\pi\) |
0.335305 | + | 0.942109i | \(0.391160\pi\) | |||||||
\(468\) | −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 | \(-0.437960\pi\) | ||||
0.193672 | + | 0.981066i | \(0.437960\pi\) | |||||||
\(480\) | −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 | 0.872058 | − | 0.489402i | \(-0.162785\pi\) |
−0.489402 | + | 0.872058i | \(0.662785\pi\) | |||||||
\(504\) | 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 | \(-0.418789\pi\) | ||||
0.252374 | + | 0.967630i | \(0.418789\pi\) | |||||||
\(510\) | −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 | \(0.140494\pi\) | ||||
−0.904165 | + | 0.427183i | \(0.859506\pi\) | |||||||
\(522\) | −3.91576 | − | 3.91576i | −0.171388 | − | 0.171388i | ||||
\(523\) | 10.5304 | + | 10.5304i | 0.460462 | + | 0.460462i | 0.898807 | − | 0.438345i | \(-0.144435\pi\) |
−0.438345 | + | 0.898807i | \(0.644435\pi\) | |||||||
\(524\) | 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 | 0.704999 | − | 0.709208i | \(-0.250947\pi\) |
−0.709208 | + | 0.704999i | \(0.750947\pi\) | |||||||
\(564\) | − | 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 | −0.816628 | − | 0.577164i | \(-0.804159\pi\) |
0.577164 | + | 0.816628i | \(0.304159\pi\) | |||||||
\(578\) | −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 | −0.988914 | − | 0.148491i | \(-0.952558\pi\) |
0.148491 | + | 0.988914i | \(0.452558\pi\) | |||||||
\(588\) | 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 | 0.379819 | − | 0.925061i | \(-0.375986\pi\) |
−0.925061 | + | 0.379819i | \(0.875986\pi\) | |||||||
\(594\) | −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 | \(-0.857723\pi\) | ||
0.901758 | − | 0.432241i | \(-0.142277\pi\) | |||||||
\(602\) | 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 | −0.556923 | − | 0.830564i | \(-0.688018\pi\) |
0.830564 | + | 0.556923i | \(0.188018\pi\) | |||||||
\(608\) | 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 | \(-0.665481\pi\) | ||||
−0.496772 | + | 0.867881i | \(0.665481\pi\) | |||||||
\(620\) | −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 | 0.130906 | − | 0.991395i | \(-0.458211\pi\) |
−0.991395 | + | 0.130906i | \(0.958211\pi\) | |||||||
\(644\) | 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 | \(0.510587\pi\) |
−0.999447 | + | 0.0332527i | \(0.989413\pi\) | |||||||
\(648\) | 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 | \(0.228857\pi\) | ||||
−0.752482 | + | 0.658613i | \(0.771143\pi\) | |||||||
\(662\) | −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 | −0.904628 | − | 0.426203i | \(-0.859851\pi\) |
0.426203 | + | 0.904628i | \(0.359851\pi\) | |||||||
\(678\) | 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 | \(0.0179660\pi\) | ||||
−0.998408 | + | 0.0564118i | \(0.982034\pi\) | |||||||
\(692\) | −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 | \(-0.448658\pi\) | ||||
0.160596 | + | 0.987020i | \(0.448658\pi\) | |||||||
\(720\) | −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 | −0.903455 | − | 0.428682i | \(-0.858978\pi\) |
0.428682 | + | 0.903455i | \(0.358978\pi\) | |||||||
\(728\) | 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 | 0.991789 | − | 0.127886i | \(-0.0408192\pi\) |
−0.127886 | + | 0.991789i | \(0.540819\pi\) | |||||||
\(734\) | −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 | \(0.0997956\pi\) | ||||
−0.951255 | + | 0.308406i | \(0.900204\pi\) | |||||||
\(762\) | 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 | \(-0.544352\pi\) | ||||
−0.138884 | + | 0.990309i | \(0.544352\pi\) | |||||||
\(770\) | 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 | 0.744541 | − | 0.667577i | \(-0.232668\pi\) |
−0.667577 | + | 0.744541i | \(0.732668\pi\) | |||||||
\(774\) | 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 | −0.365726 | − | 0.930722i | \(-0.619179\pi\) |
0.930722 | + | 0.365726i | \(0.119179\pi\) | |||||||
\(788\) | 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 | −0.203545 | − | 0.979066i | \(-0.565246\pi\) |
0.979066 | + | 0.203545i | \(0.0652464\pi\) | |||||||
\(798\) | 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 | \(-0.797246\pi\) | ||
0.803901 | − | 0.594763i | \(-0.202754\pi\) | |||||||
\(812\) | 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 | \(-0.745436\pi\) | ||||
−0.696895 | + | 0.717173i | \(0.745436\pi\) | |||||||
\(830\) | −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 | \(-0.659371\pi\) | ||||
−0.480022 | + | 0.877256i | \(0.659371\pi\) | |||||||
\(840\) | 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 | 0.953889 | − | 0.300160i | \(-0.0970400\pi\) |
−0.300160 | + | 0.953889i | \(0.597040\pi\) | |||||||
\(854\) | 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 | −0.416617 | − | 0.909082i | \(-0.636784\pi\) |
0.909082 | + | 0.416617i | \(0.136784\pi\) | |||||||
\(858\) | −1.84573 | + | 1.84573i | −0.0630120 | + | 0.0630120i | ||||
\(859\) | 4.48341 | 0.152972 | 0.0764860 | − | 0.997071i | \(-0.475630\pi\) | ||||
0.0764860 | + | 0.997071i | \(0.475630\pi\) | |||||||
\(860\) | 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 | \(0.377707\pi\) | ||||
−0.374813 | + | 0.927100i | \(0.622293\pi\) | |||||||
\(882\) | 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 | −0.924550 | − | 0.381061i | \(-0.875559\pi\) |
0.381061 | + | 0.924550i | \(0.375559\pi\) | |||||||
\(888\) | −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 | \(-0.359612\pi\) | ||||
0.426883 | + | 0.904307i | \(0.359612\pi\) | |||||||
\(930\) | −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 | −0.369082 | − | 0.929397i | \(-0.620328\pi\) |
0.929397 | + | 0.369082i | \(0.120328\pi\) | |||||||
\(938\) | 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 | \(0.0873779\pi\) | ||||
−0.962559 | + | 0.271071i | \(0.912622\pi\) | |||||||
\(942\) | −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 | \(-0.871693\pi\) | ||
0.919854 | − | 0.392261i | \(-0.128307\pi\) | |||||||
\(972\) | 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 | 0.997739 | − | 0.0672080i | \(-0.0214091\pi\) |
−0.0672080 | + | 0.997739i | \(0.521409\pi\) | |||||||
\(984\) | 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 | −0.476732 | − | 0.879049i | \(-0.658179\pi\) |
0.879049 | + | 0.476732i | \(0.158179\pi\) | |||||||
\(998\) | 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.e.97.8 | 16 | ||
5.3 | odd | 4 | 1470.2.m.d.1273.5 | 16 | |||
7.4 | even | 3 | 210.2.u.b.187.1 | yes | 16 | ||
7.5 | odd | 6 | 210.2.u.a.157.4 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.d.97.5 | 16 | |||
21.5 | even | 6 | 630.2.bv.a.577.1 | 16 | |||
21.11 | odd | 6 | 630.2.bv.b.397.4 | 16 | |||
35.4 | even | 6 | 1050.2.bc.g.607.3 | 16 | |||
35.12 | even | 12 | 1050.2.bc.g.493.3 | 16 | |||
35.13 | even | 4 | inner | 1470.2.m.e.1273.8 | 16 | ||
35.18 | odd | 12 | 210.2.u.a.103.4 | ✓ | 16 | ||
35.19 | odd | 6 | 1050.2.bc.h.157.1 | 16 | |||
35.32 | odd | 12 | 1050.2.bc.h.943.1 | 16 | |||
35.33 | even | 12 | 210.2.u.b.73.1 | yes | 16 | ||
105.53 | even | 12 | 630.2.bv.a.523.1 | 16 | |||
105.68 | odd | 12 | 630.2.bv.b.73.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.4 | ✓ | 16 | 35.18 | odd | 12 | ||
210.2.u.a.157.4 | yes | 16 | 7.5 | odd | 6 | ||
210.2.u.b.73.1 | yes | 16 | 35.33 | even | 12 | ||
210.2.u.b.187.1 | yes | 16 | 7.4 | even | 3 | ||
630.2.bv.a.523.1 | 16 | 105.53 | even | 12 | |||
630.2.bv.a.577.1 | 16 | 21.5 | even | 6 | |||
630.2.bv.b.73.4 | 16 | 105.68 | odd | 12 | |||
630.2.bv.b.397.4 | 16 | 21.11 | odd | 6 | |||
1050.2.bc.g.493.3 | 16 | 35.12 | even | 12 | |||
1050.2.bc.g.607.3 | 16 | 35.4 | even | 6 | |||
1050.2.bc.h.157.1 | 16 | 35.19 | odd | 6 | |||
1050.2.bc.h.943.1 | 16 | 35.32 | odd | 12 | |||
1470.2.m.d.97.5 | 16 | 7.6 | odd | 2 | |||
1470.2.m.d.1273.5 | 16 | 5.3 | odd | 4 | |||
1470.2.m.e.97.8 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.e.1273.8 | 16 | 35.13 | even | 4 | inner |