Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(99,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.99");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.u (of order \(18\), degree \(6\), not 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: | \(7.58578819202\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\Q(\zeta_{36})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{6} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 199.2 | ||
Root | \(-0.342020 - 0.939693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 950.199 |
Dual form | 950.2.u.d.549.2 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{4}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.984808 | − | 0.173648i | 0.696364 | − | 0.122788i | ||||
\(3\) | 0.565258 | + | 0.673648i | 0.326352 | + | 0.388931i | 0.904126 | − | 0.427266i | \(-0.140523\pi\) |
−0.577774 | + | 0.816197i | \(0.696079\pi\) | |||||||
\(4\) | 0.939693 | − | 0.342020i | 0.469846 | − | 0.171010i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.673648 | + | 0.565258i | 0.275016 | + | 0.230766i | ||||
\(7\) | 0.460802 | + | 0.266044i | 0.174167 | + | 0.100555i | 0.584549 | − | 0.811358i | \(-0.301271\pi\) |
−0.410382 | + | 0.911914i | \(0.634605\pi\) | |||||||
\(8\) | 0.866025 | − | 0.500000i | 0.306186 | − | 0.176777i | ||||
\(9\) | 0.386659 | − | 2.19285i | 0.128886 | − | 0.730951i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0.761570 | + | 0.439693i | 0.219846 | + | 0.126928i | ||||
\(13\) | −0.419550 | + | 0.500000i | −0.116362 | + | 0.138675i | −0.821081 | − | 0.570812i | \(-0.806629\pi\) |
0.704719 | + | 0.709487i | \(0.251073\pi\) | |||||||
\(14\) | 0.500000 | + | 0.181985i | 0.133631 | + | 0.0486376i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.766044 | − | 0.642788i | 0.191511 | − | 0.160697i | ||||
\(17\) | 3.82045 | − | 0.673648i | 0.926595 | − | 0.163384i | 0.310065 | − | 0.950715i | \(-0.399649\pi\) |
0.616530 | + | 0.787332i | \(0.288538\pi\) | |||||||
\(18\) | − | 2.22668i | − | 0.524834i | ||||||
\(19\) | 4.21688 | − | 1.10359i | 0.967419 | − | 0.253181i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0812519 | + | 0.460802i | 0.0177306 | + | 0.100555i | ||||
\(22\) | 0.642788 | + | 0.766044i | 0.137043 | + | 0.163321i | ||||
\(23\) | 1.55007 | + | 4.25877i | 0.323211 | + | 0.888015i | 0.989784 | + | 0.142575i | \(0.0455383\pi\) |
−0.666573 | + | 0.745440i | \(0.732239\pi\) | |||||||
\(24\) | 0.826352 | + | 0.300767i | 0.168678 | + | 0.0613939i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.326352 | + | 0.565258i | −0.0640029 | + | 0.110856i | ||||
\(27\) | 3.98048 | − | 2.29813i | 0.766044 | − | 0.442276i | ||||
\(28\) | 0.524005 | + | 0.0923963i | 0.0990277 | + | 0.0174613i | ||||
\(29\) | 0.773318 | − | 4.38571i | 0.143602 | − | 0.814405i | −0.824878 | − | 0.565311i | \(-0.808756\pi\) |
0.968479 | − | 0.249094i | \(-0.0801328\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.37939 | + | 2.38917i | −0.247745 | + | 0.429107i | −0.962900 | − | 0.269859i | \(-0.913023\pi\) |
0.715155 | + | 0.698966i | \(0.246356\pi\) | |||||||
\(32\) | 0.642788 | − | 0.766044i | 0.113630 | − | 0.135419i | ||||
\(33\) | −0.300767 | + | 0.826352i | −0.0523569 | + | 0.143849i | ||||
\(34\) | 3.64543 | − | 1.32683i | 0.625186 | − | 0.227549i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.386659 | − | 2.19285i | −0.0644432 | − | 0.365476i | ||||
\(37\) | 0.958111i | 0.157512i | 0.996894 | + | 0.0787562i | \(0.0250949\pi\) | ||||
−0.996894 | + | 0.0787562i | \(0.974905\pi\) | |||||||
\(38\) | 3.96118 | − | 1.81908i | 0.642588 | − | 0.295093i | ||||
\(39\) | −0.573978 | −0.0919100 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.78699 | + | 4.01676i | −0.747602 | + | 0.627313i | −0.934868 | − | 0.354997i | \(-0.884482\pi\) |
0.187265 | + | 0.982309i | \(0.440038\pi\) | |||||||
\(42\) | 0.160035 | + | 0.439693i | 0.0246939 | + | 0.0678460i | ||||
\(43\) | −1.71275 | + | 4.70574i | −0.261192 | + | 0.717618i | 0.737896 | + | 0.674914i | \(0.235819\pi\) |
−0.999088 | + | 0.0427039i | \(0.986403\pi\) | |||||||
\(44\) | 0.766044 | + | 0.642788i | 0.115486 | + | 0.0969039i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.26604 | + | 3.92490i | 0.334110 | + | 0.578696i | ||||
\(47\) | −0.761570 | − | 0.134285i | −0.111086 | − | 0.0195875i | 0.117829 | − | 0.993034i | \(-0.462407\pi\) |
−0.228915 | + | 0.973446i | \(0.573518\pi\) | |||||||
\(48\) | 0.866025 | + | 0.152704i | 0.125000 | + | 0.0220409i | ||||
\(49\) | −3.35844 | − | 5.81699i | −0.479777 | − | 0.830999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.61334 | + | 2.19285i | 0.365941 | + | 0.307061i | ||||
\(52\) | −0.223238 | + | 0.613341i | −0.0309575 | + | 0.0850551i | ||||
\(53\) | 1.31920 | + | 3.62449i | 0.181207 | + | 0.497861i | 0.996725 | − | 0.0808705i | \(-0.0257700\pi\) |
−0.815518 | + | 0.578732i | \(0.803548\pi\) | |||||||
\(54\) | 3.52094 | − | 2.95442i | 0.479140 | − | 0.402046i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.532089 | 0.0711034 | ||||||||
\(57\) | 3.12706 | + | 2.21688i | 0.414189 | + | 0.293633i | ||||
\(58\) | − | 4.45336i | − | 0.584755i | ||||||
\(59\) | −1.08853 | − | 6.17334i | −0.141714 | − | 0.803700i | −0.969947 | − | 0.243316i | \(-0.921765\pi\) |
0.828233 | − | 0.560384i | \(-0.189346\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.62449 | + | 1.68317i | −0.592105 | + | 0.215508i | −0.620655 | − | 0.784084i | \(-0.713133\pi\) |
0.0285502 | + | 0.999592i | \(0.490911\pi\) | |||||||
\(62\) | −0.943555 | + | 2.59240i | −0.119832 | + | 0.329235i | ||||
\(63\) | 0.761570 | − | 0.907604i | 0.0959488 | − | 0.114347i | ||||
\(64\) | 0.500000 | − | 0.866025i | 0.0625000 | − | 0.108253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.152704 | + | 0.866025i | −0.0187965 | + | 0.106600i | ||||
\(67\) | −1.32683 | − | 0.233956i | −0.162098 | − | 0.0285822i | 0.0920102 | − | 0.995758i | \(-0.470671\pi\) |
−0.254108 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(68\) | 3.35965 | − | 1.93969i | 0.407417 | − | 0.235222i | ||||
\(69\) | −1.99273 | + | 3.45150i | −0.239896 | + | 0.415512i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.33275 | − | 1.94096i | −0.632881 | − | 0.230350i | 0.00560389 | − | 0.999984i | \(-0.498216\pi\) |
−0.638485 | + | 0.769635i | \(0.720438\pi\) | |||||||
\(72\) | −0.761570 | − | 2.09240i | −0.0897519 | − | 0.246591i | ||||
\(73\) | 4.80526 | + | 5.72668i | 0.562413 | + | 0.670257i | 0.970055 | − | 0.242884i | \(-0.0780935\pi\) |
−0.407643 | + | 0.913142i | \(0.633649\pi\) | |||||||
\(74\) | 0.166374 | + | 0.943555i | 0.0193406 | + | 0.109686i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.58512 | − | 2.47929i | 0.411242 | − | 0.284395i | ||||
\(77\) | 0.532089i | 0.0606372i | ||||||||
\(78\) | −0.565258 | + | 0.0996702i | −0.0640029 | + | 0.0112854i | ||||
\(79\) | 0.543233 | − | 0.455827i | 0.0611185 | − | 0.0512845i | −0.611717 | − | 0.791077i | \(-0.709521\pi\) |
0.672835 | + | 0.739792i | \(0.265076\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.47906 | − | 0.902302i | −0.275451 | − | 0.100256i | ||||
\(82\) | −4.01676 | + | 4.78699i | −0.443577 | + | 0.528634i | ||||
\(83\) | 9.15144 | + | 5.28359i | 1.00450 | + | 0.579949i | 0.909577 | − | 0.415536i | \(-0.136406\pi\) |
0.0949240 | + | 0.995485i | \(0.469739\pi\) | |||||||
\(84\) | 0.233956 | + | 0.405223i | 0.0255266 | + | 0.0442134i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.869585 | + | 4.93166i | −0.0937698 | + | 0.531795i | ||||
\(87\) | 3.39155 | − | 1.95811i | 0.363612 | − | 0.209932i | ||||
\(88\) | 0.866025 | + | 0.500000i | 0.0923186 | + | 0.0533002i | ||||
\(89\) | −3.75877 | − | 3.15398i | −0.398429 | − | 0.334322i | 0.421457 | − | 0.906848i | \(-0.361519\pi\) |
−0.819886 | + | 0.572527i | \(0.805963\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.326352 | + | 0.118782i | −0.0342110 | + | 0.0124518i | ||||
\(92\) | 2.91317 | + | 3.47178i | 0.303719 | + | 0.361958i | ||||
\(93\) | −2.38917 | + | 0.421274i | −0.247745 | + | 0.0436841i | ||||
\(94\) | −0.773318 | −0.0797617 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.879385 | 0.0897519 | ||||||||
\(97\) | 0.0994798 | − | 0.0175410i | 0.0101006 | − | 0.00178102i | −0.168596 | − | 0.985685i | \(-0.553923\pi\) |
0.178696 | + | 0.983904i | \(0.442812\pi\) | |||||||
\(98\) | −4.31753 | − | 5.14543i | −0.436136 | − | 0.519767i | ||||
\(99\) | 2.09240 | − | 0.761570i | 0.210294 | − | 0.0765407i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.9816 | − | 9.21464i | −1.09271 | − | 0.916891i | −0.0957949 | − | 0.995401i | \(-0.530539\pi\) |
−0.996913 | + | 0.0785100i | \(0.974984\pi\) | |||||||
\(102\) | 2.95442 | + | 1.70574i | 0.292531 | + | 0.168893i | ||||
\(103\) | −5.35619 | + | 3.09240i | −0.527761 | + | 0.304703i | −0.740104 | − | 0.672492i | \(-0.765224\pi\) |
0.212343 | + | 0.977195i | \(0.431890\pi\) | |||||||
\(104\) | −0.113341 | + | 0.642788i | −0.0111140 | + | 0.0630305i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.92855 | + | 3.34034i | 0.187317 | + | 0.324443i | ||||
\(107\) | −8.47065 | − | 4.89053i | −0.818888 | − | 0.472785i | 0.0311447 | − | 0.999515i | \(-0.490085\pi\) |
−0.850033 | + | 0.526730i | \(0.823418\pi\) | |||||||
\(108\) | 2.95442 | − | 3.52094i | 0.284290 | − | 0.338803i | ||||
\(109\) | −12.0360 | − | 4.38073i | −1.15284 | − | 0.419598i | −0.306303 | − | 0.951934i | \(-0.599092\pi\) |
−0.846533 | + | 0.532336i | \(0.821314\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.645430 | + | 0.541580i | −0.0612615 | + | 0.0514045i | ||||
\(112\) | 0.524005 | − | 0.0923963i | 0.0495138 | − | 0.00873063i | ||||
\(113\) | − | 5.47565i | − | 0.515106i | −0.966264 | − | 0.257553i | \(-0.917084\pi\) | ||
0.966264 | − | 0.257553i | \(-0.0829162\pi\) | |||||||
\(114\) | 3.46451 | + | 1.64019i | 0.324481 | + | 0.153618i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.773318 | − | 4.38571i | −0.0718008 | − | 0.407203i | ||||
\(117\) | 0.934204 | + | 1.11334i | 0.0863672 | + | 0.102928i | ||||
\(118\) | −2.14398 | − | 5.89053i | −0.197369 | − | 0.542267i | ||||
\(119\) | 1.93969 | + | 0.705990i | 0.177811 | + | 0.0647180i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | −4.26195 | + | 2.46064i | −0.385859 | + | 0.222776i | ||||
\(123\) | −5.41177 | − | 0.954241i | −0.487963 | − | 0.0860410i | ||||
\(124\) | −0.479055 | + | 2.71686i | −0.0430205 | + | 0.243981i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.592396 | − | 1.02606i | 0.0527749 | − | 0.0914087i | ||||
\(127\) | −6.61046 | + | 7.87804i | −0.586584 | + | 0.699063i | −0.974946 | − | 0.222444i | \(-0.928597\pi\) |
0.388362 | + | 0.921507i | \(0.373041\pi\) | |||||||
\(128\) | 0.342020 | − | 0.939693i | 0.0302306 | − | 0.0830579i | ||||
\(129\) | −4.13816 | + | 1.50617i | −0.364344 | + | 0.132610i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.46404 | − | 8.30299i | −0.127914 | − | 0.725435i | −0.979534 | − | 0.201277i | \(-0.935491\pi\) |
0.851621 | − | 0.524159i | \(-0.175620\pi\) | |||||||
\(132\) | 0.879385i | 0.0765407i | ||||||||
\(133\) | 2.23675 | + | 0.613341i | 0.193951 | + | 0.0531834i | ||||
\(134\) | −1.34730 | −0.116389 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.97178 | − | 2.49362i | 0.254828 | − | 0.213826i | ||||
\(137\) | 2.72621 | + | 7.49020i | 0.232916 | + | 0.639931i | 0.999999 | − | 0.00161707i | \(-0.000514729\pi\) |
−0.767083 | + | 0.641548i | \(0.778293\pi\) | |||||||
\(138\) | −1.36310 | + | 3.74510i | −0.116035 | + | 0.318804i | ||||
\(139\) | 4.83409 | + | 4.05629i | 0.410022 | + | 0.344050i | 0.824352 | − | 0.566077i | \(-0.191540\pi\) |
−0.414330 | + | 0.910127i | \(0.635984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.340022 | − | 0.588936i | −0.0286351 | − | 0.0495974i | ||||
\(142\) | −5.58878 | − | 0.985452i | −0.469000 | − | 0.0826973i | ||||
\(143\) | −0.642788 | − | 0.113341i | −0.0537526 | − | 0.00947803i | ||||
\(144\) | −1.11334 | − | 1.92836i | −0.0927784 | − | 0.160697i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.72668 | + | 4.80526i | 0.473944 | + | 0.397686i | ||||
\(147\) | 2.02022 | − | 5.55051i | 0.166625 | − | 0.457798i | ||||
\(148\) | 0.327693 | + | 0.900330i | 0.0269362 | + | 0.0740067i | ||||
\(149\) | −13.8589 | + | 11.6290i | −1.13537 | + | 0.952685i | −0.999277 | − | 0.0380115i | \(-0.987898\pi\) |
−0.136089 | + | 0.990697i | \(0.543453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2071 | 0.830640 | 0.415320 | − | 0.909675i | \(-0.363670\pi\) | ||||
0.415320 | + | 0.909675i | \(0.363670\pi\) | |||||||
\(152\) | 3.10013 | − | 3.06418i | 0.251454 | − | 0.248538i | ||||
\(153\) | − | 8.63816i | − | 0.698353i | ||||||
\(154\) | 0.0923963 | + | 0.524005i | 0.00744550 | + | 0.0422255i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.539363 | + | 0.196312i | −0.0431836 | + | 0.0157175i | ||||
\(157\) | −5.45475 | + | 14.9868i | −0.435336 | + | 1.19608i | 0.507158 | + | 0.861853i | \(0.330696\pi\) |
−0.942494 | + | 0.334223i | \(0.891526\pi\) | |||||||
\(158\) | 0.455827 | − | 0.543233i | 0.0362636 | − | 0.0432173i | ||||
\(159\) | −1.69594 | + | 2.93745i | −0.134497 | + | 0.232955i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.418748 | + | 2.37484i | −0.0330020 | + | 0.187163i | ||||
\(162\) | −2.59808 | − | 0.458111i | −0.204124 | − | 0.0359926i | ||||
\(163\) | −14.3113 | + | 8.26264i | −1.12095 | + | 0.647180i | −0.941643 | − | 0.336613i | \(-0.890718\pi\) |
−0.179306 | + | 0.983793i | \(0.557385\pi\) | |||||||
\(164\) | −3.12449 | + | 5.41177i | −0.243981 | + | 0.422588i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.92989 | + | 3.61419i | 0.770709 | + | 0.280515i | ||||
\(167\) | −8.13533 | − | 22.3516i | −0.629531 | − | 1.72962i | −0.682359 | − | 0.731018i | \(-0.739046\pi\) |
0.0528278 | − | 0.998604i | \(-0.483177\pi\) | |||||||
\(168\) | 0.300767 | + | 0.358441i | 0.0232047 | + | 0.0276543i | ||||
\(169\) | 2.18345 | + | 12.3830i | 0.167958 | + | 0.952535i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.789515 | − | 9.67372i | −0.0603757 | − | 0.739768i | ||||
\(172\) | 5.00774i | 0.381837i | ||||||||
\(173\) | 3.02525 | − | 0.533433i | 0.230005 | − | 0.0405562i | −0.0574574 | − | 0.998348i | \(-0.518299\pi\) |
0.287463 | + | 0.957792i | \(0.407188\pi\) | |||||||
\(174\) | 3.00000 | − | 2.51730i | 0.227429 | − | 0.190836i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.939693 | + | 0.342020i | 0.0708320 | + | 0.0257807i | ||||
\(177\) | 3.54336 | − | 4.22281i | 0.266335 | − | 0.317406i | ||||
\(178\) | −4.24935 | − | 2.45336i | −0.318502 | − | 0.183887i | ||||
\(179\) | 7.98680 | + | 13.8335i | 0.596961 | + | 1.03397i | 0.993267 | + | 0.115848i | \(0.0369587\pi\) |
−0.396306 | + | 0.918119i | \(0.629708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.69728 | + | 9.62576i | −0.126158 | + | 0.715477i | 0.854455 | + | 0.519525i | \(0.173891\pi\) |
−0.980613 | + | 0.195952i | \(0.937220\pi\) | |||||||
\(182\) | −0.300767 | + | 0.173648i | −0.0222944 | + | 0.0128717i | ||||
\(183\) | −3.74789 | − | 2.16385i | −0.277052 | − | 0.159956i | ||||
\(184\) | 3.47178 | + | 2.91317i | 0.255943 | + | 0.214762i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.27972 | + | 0.829748i | −0.167157 | + | 0.0608401i | ||||
\(187\) | 2.49362 | + | 2.97178i | 0.182352 | + | 0.217318i | ||||
\(188\) | −0.761570 | + | 0.134285i | −0.0555432 | + | 0.00979376i | ||||
\(189\) | 2.44562 | 0.177893 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.52023 | 0.544145 | 0.272072 | − | 0.962277i | \(-0.412291\pi\) | ||||
0.272072 | + | 0.962277i | \(0.412291\pi\) | |||||||
\(192\) | 0.866025 | − | 0.152704i | 0.0625000 | − | 0.0110204i | ||||
\(193\) | −15.7739 | − | 18.7986i | −1.13543 | − | 1.35315i | −0.926976 | − | 0.375121i | \(-0.877601\pi\) |
−0.208454 | − | 0.978032i | \(-0.566843\pi\) | |||||||
\(194\) | 0.0949225 | − | 0.0345490i | 0.00681504 | − | 0.00248047i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.14543 | − | 4.31753i | −0.367531 | − | 0.308395i | ||||
\(197\) | −12.4740 | − | 7.20187i | −0.888736 | − | 0.513112i | −0.0152069 | − | 0.999884i | \(-0.504841\pi\) |
−0.873529 | + | 0.486773i | \(0.838174\pi\) | |||||||
\(198\) | 1.92836 | − | 1.11334i | 0.137043 | − | 0.0791217i | ||||
\(199\) | 0.771097 | − | 4.37311i | 0.0546616 | − | 0.310001i | −0.945203 | − | 0.326485i | \(-0.894136\pi\) |
0.999864 | + | 0.0164832i | \(0.00524699\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.592396 | − | 1.02606i | −0.0417844 | − | 0.0723727i | ||||
\(202\) | −12.4149 | − | 7.16772i | −0.873506 | − | 0.504319i | ||||
\(203\) | 1.52314 | − | 1.81521i | 0.106903 | − | 0.127403i | ||||
\(204\) | 3.20574 | + | 1.16679i | 0.224446 | + | 0.0816918i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.73783 | + | 3.97551i | −0.330100 | + | 0.276987i | ||||
\(207\) | 9.93821 | − | 1.75237i | 0.690753 | − | 0.121798i | ||||
\(208\) | 0.652704i | 0.0452569i | ||||||||
\(209\) | 3.06418 | + | 3.10013i | 0.211954 | + | 0.214441i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.95218 | − | 11.0714i | −0.134394 | − | 0.762185i | −0.975280 | − | 0.220973i | \(-0.929077\pi\) |
0.840886 | − | 0.541212i | \(-0.182034\pi\) | |||||||
\(212\) | 2.47929 | + | 2.95471i | 0.170279 | + | 0.202930i | ||||
\(213\) | −1.70685 | − | 4.68954i | −0.116952 | − | 0.321322i | ||||
\(214\) | −9.19119 | − | 3.34532i | −0.628297 | − | 0.228681i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2.29813 | − | 3.98048i | 0.156368 | − | 0.270838i | ||||
\(217\) | −1.27125 | + | 0.733956i | −0.0862980 | + | 0.0498241i | ||||
\(218\) | −12.6138 | − | 2.22416i | −0.854315 | − | 0.150639i | ||||
\(219\) | −1.14156 | + | 6.47410i | −0.0771394 | + | 0.437479i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.26604 | + | 2.19285i | −0.0851634 | + | 0.147507i | ||||
\(222\) | −0.541580 | + | 0.645430i | −0.0363485 | + | 0.0433184i | ||||
\(223\) | −4.10597 | + | 11.2811i | −0.274956 | + | 0.755436i | 0.722959 | + | 0.690891i | \(0.242782\pi\) |
−0.997915 | + | 0.0645444i | \(0.979441\pi\) | |||||||
\(224\) | 0.500000 | − | 0.181985i | 0.0334077 | − | 0.0121594i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.950837 | − | 5.39246i | −0.0632487 | − | 0.358701i | ||||
\(227\) | − | 25.8871i | − | 1.71819i | −0.511817 | − | 0.859094i | \(-0.671027\pi\) | ||
0.511817 | − | 0.859094i | \(-0.328973\pi\) | |||||||
\(228\) | 3.69669 | + | 1.01367i | 0.244819 | + | 0.0671320i | ||||
\(229\) | −11.1138 | −0.734421 | −0.367211 | − | 0.930138i | \(-0.619687\pi\) | ||||
−0.367211 | + | 0.930138i | \(0.619687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.358441 | + | 0.300767i | −0.0235837 | + | 0.0197890i | ||||
\(232\) | −1.52314 | − | 4.18479i | −0.0999990 | − | 0.274745i | ||||
\(233\) | 0.433877 | − | 1.19207i | 0.0284242 | − | 0.0780949i | −0.924669 | − | 0.380772i | \(-0.875658\pi\) |
0.953093 | + | 0.302677i | \(0.0978804\pi\) | |||||||
\(234\) | 1.11334 | + | 0.934204i | 0.0727814 | + | 0.0610708i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.13429 | − | 5.42874i | −0.204025 | − | 0.353381i | ||||
\(237\) | 0.614134 | + | 0.108288i | 0.0398923 | + | 0.00703408i | ||||
\(238\) | 2.03282 | + | 0.358441i | 0.131768 | + | 0.0232343i | ||||
\(239\) | 2.13429 | + | 3.69669i | 0.138055 | + | 0.239119i | 0.926761 | − | 0.375653i | \(-0.122581\pi\) |
−0.788705 | + | 0.614772i | \(0.789248\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 22.5214 | + | 18.8977i | 1.45073 | + | 1.21731i | 0.932044 | + | 0.362344i | \(0.118024\pi\) |
0.518687 | + | 0.854964i | \(0.326421\pi\) | |||||||
\(242\) | 3.42020 | − | 9.39693i | 0.219859 | − | 0.604057i | ||||
\(243\) | −5.50952 | − | 15.1373i | −0.353436 | − | 0.971057i | ||||
\(244\) | −3.76991 | + | 3.16333i | −0.241344 | + | 0.202512i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.49525 | −0.350364 | ||||||||
\(247\) | −1.21740 | + | 2.57145i | −0.0774611 | + | 0.163618i | ||||
\(248\) | 2.75877i | 0.175182i | ||||||||
\(249\) | 1.61365 | + | 9.15144i | 0.102261 | + | 0.579949i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.14290 | + | 3.32774i | −0.577095 | + | 0.210045i | −0.614044 | − | 0.789272i | \(-0.710458\pi\) |
0.0369491 | + | 0.999317i | \(0.488236\pi\) | |||||||
\(252\) | 0.405223 | − | 1.11334i | 0.0255266 | − | 0.0701339i | ||||
\(253\) | −2.91317 | + | 3.47178i | −0.183149 | + | 0.218269i | ||||
\(254\) | −5.14203 | + | 8.90625i | −0.322639 | + | 0.558828i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.173648 | − | 0.984808i | 0.0108530 | − | 0.0615505i | ||||
\(257\) | 4.44393 | + | 0.783585i | 0.277205 | + | 0.0488787i | 0.310522 | − | 0.950566i | \(-0.399496\pi\) |
−0.0333173 | + | 0.999445i | \(0.510607\pi\) | |||||||
\(258\) | −3.81374 | + | 2.20187i | −0.237433 | + | 0.137082i | ||||
\(259\) | −0.254900 | + | 0.441500i | −0.0158387 | + | 0.0274335i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.31820 | − | 3.39155i | −0.576782 | − | 0.209932i | ||||
\(262\) | −2.88360 | − | 7.92262i | −0.178149 | − | 0.489461i | ||||
\(263\) | 19.3618 | + | 23.0744i | 1.19390 | + | 1.42283i | 0.881047 | + | 0.473029i | \(0.156839\pi\) |
0.312850 | + | 0.949802i | \(0.398716\pi\) | |||||||
\(264\) | 0.152704 | + | 0.866025i | 0.00939826 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.30928 | + | 0.215615i | 0.141591 | + | 0.0132202i | ||||
\(267\) | − | 4.31490i | − | 0.264068i | ||||||
\(268\) | −1.32683 | + | 0.233956i | −0.0810489 | + | 0.0142911i | ||||
\(269\) | 3.31315 | − | 2.78006i | 0.202006 | − | 0.169503i | −0.536173 | − | 0.844108i | \(-0.680130\pi\) |
0.738179 | + | 0.674605i | \(0.235686\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.3491 | + | 9.22632i | 1.53985 | + | 0.560459i | 0.966009 | − | 0.258509i | \(-0.0832310\pi\) |
0.573840 | + | 0.818968i | \(0.305453\pi\) | |||||||
\(272\) | 2.49362 | − | 2.97178i | 0.151198 | − | 0.180191i | ||||
\(273\) | −0.264490 | − | 0.152704i | −0.0160077 | − | 0.00924205i | ||||
\(274\) | 3.98545 | + | 6.90301i | 0.240770 | + | 0.417026i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.692066 | + | 3.92490i | −0.0416575 | + | 0.236251i | ||||
\(277\) | −1.90906 | + | 1.10220i | −0.114704 | + | 0.0662246i | −0.556255 | − | 0.831012i | \(-0.687762\pi\) |
0.441550 | + | 0.897237i | \(0.354429\pi\) | |||||||
\(278\) | 5.46502 | + | 3.15523i | 0.327770 | + | 0.189238i | ||||
\(279\) | 4.70574 | + | 3.94858i | 0.281725 | + | 0.236395i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.8341 | + | 6.49108i | −1.06389 | + | 0.387225i | −0.813889 | − | 0.581020i | \(-0.802654\pi\) |
−0.250003 | + | 0.968245i | \(0.580432\pi\) | |||||||
\(282\) | −0.437124 | − | 0.520945i | −0.0260304 | − | 0.0310218i | ||||
\(283\) | −14.3189 | + | 2.52481i | −0.851172 | + | 0.150085i | −0.582182 | − | 0.813058i | \(-0.697801\pi\) |
−0.268990 | + | 0.963143i | \(0.586690\pi\) | |||||||
\(284\) | −5.67499 | −0.336749 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.652704 | −0.0385952 | ||||||||
\(287\) | −3.27449 | + | 0.577382i | −0.193287 | + | 0.0340818i | ||||
\(288\) | −1.43128 | − | 1.70574i | −0.0843392 | − | 0.100512i | ||||
\(289\) | −1.83275 | + | 0.667066i | −0.107809 | + | 0.0392392i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0680482 | + | 0.0570992i | 0.00398905 | + | 0.00334721i | ||||
\(292\) | 6.47410 | + | 3.73783i | 0.378868 | + | 0.218740i | ||||
\(293\) | 5.42285 | − | 3.13088i | 0.316806 | − | 0.182908i | −0.333162 | − | 0.942870i | \(-0.608116\pi\) |
0.649968 | + | 0.759962i | \(0.274782\pi\) | |||||||
\(294\) | 1.02569 | − | 5.81699i | 0.0598196 | − | 0.339254i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.479055 | + | 0.829748i | 0.0278445 | + | 0.0482281i | ||||
\(297\) | 3.98048 | + | 2.29813i | 0.230971 | + | 0.133351i | ||||
\(298\) | −11.6290 | + | 13.8589i | −0.673650 | + | 0.802825i | ||||
\(299\) | −2.77972 | − | 1.01173i | −0.160755 | − | 0.0585101i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.04117 | + | 1.71275i | −0.117651 | + | 0.0987212i | ||||
\(302\) | 10.0520 | − | 1.77244i | 0.578428 | − | 0.101993i | ||||
\(303\) | − | 12.6064i | − | 0.724217i | ||||||
\(304\) | 2.52094 | − | 3.55596i | 0.144586 | − | 0.203948i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | − | 8.50692i | −0.0857493 | − | 0.486308i | ||||
\(307\) | −5.00097 | − | 5.95992i | −0.285420 | − | 0.340151i | 0.604216 | − | 0.796821i | \(-0.293486\pi\) |
−0.889636 | + | 0.456670i | \(0.849042\pi\) | |||||||
\(308\) | 0.181985 | + | 0.500000i | 0.0103696 | + | 0.0284901i | ||||
\(309\) | −5.11081 | − | 1.86018i | −0.290744 | − | 0.105822i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5189 | − | 26.8795i | 0.879995 | − | 1.52420i | 0.0286507 | − | 0.999589i | \(-0.490879\pi\) |
0.851345 | − | 0.524607i | \(-0.175788\pi\) | |||||||
\(312\) | −0.497079 | + | 0.286989i | −0.0281416 | + | 0.0162476i | ||||
\(313\) | −9.08651 | − | 1.60220i | −0.513600 | − | 0.0905615i | −0.0891594 | − | 0.996017i | \(-0.528418\pi\) |
−0.424440 | + | 0.905456i | \(0.639529\pi\) | |||||||
\(314\) | −2.76945 | + | 15.7063i | −0.156289 | + | 0.886359i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.354570 | − | 0.614134i | 0.0199461 | − | 0.0345477i | ||||
\(317\) | −15.4308 | + | 18.3897i | −0.866677 | + | 1.03287i | 0.132454 | + | 0.991189i | \(0.457714\pi\) |
−0.999131 | + | 0.0416766i | \(0.986730\pi\) | |||||||
\(318\) | −1.16009 | + | 3.18732i | −0.0650546 | + | 0.178736i | ||||
\(319\) | 4.18479 | − | 1.52314i | 0.234303 | − | 0.0852795i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.49360 | − | 8.47065i | −0.0833648 | − | 0.472785i | ||||
\(322\) | 2.41147i | 0.134386i | ||||||||
\(323\) | 15.3669 | − | 7.05690i | 0.855040 | − | 0.392657i | ||||
\(324\) | −2.63816 | −0.146564 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −12.6591 | + | 10.6222i | −0.701123 | + | 0.588312i | ||||
\(327\) | −3.85235 | − | 10.5842i | −0.213035 | − | 0.585310i | ||||
\(328\) | −2.13727 | + | 5.87211i | −0.118011 | + | 0.324233i | ||||
\(329\) | −0.315207 | − | 0.264490i | −0.0173780 | − | 0.0145818i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2724 | + | 21.2565i | 0.674554 | + | 1.16836i | 0.976599 | + | 0.215069i | \(0.0689975\pi\) |
−0.302045 | + | 0.953294i | \(0.597669\pi\) | |||||||
\(332\) | 10.4066 | + | 1.83497i | 0.571138 | + | 0.100707i | ||||
\(333\) | 2.10100 | + | 0.370462i | 0.115134 | + | 0.0203012i | ||||
\(334\) | −11.8931 | − | 20.5994i | −0.650759 | − | 1.12715i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.358441 | + | 0.300767i | 0.0195545 | + | 0.0164082i | ||||
\(337\) | −10.4842 | + | 28.8050i | −0.571109 | + | 1.56911i | 0.231647 | + | 0.972800i | \(0.425589\pi\) |
−0.802756 | + | 0.596308i | \(0.796634\pi\) | |||||||
\(338\) | 4.30055 | + | 11.8157i | 0.233919 | + | 0.642688i | ||||
\(339\) | 3.68866 | − | 3.09516i | 0.200341 | − | 0.168106i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.75877 | −0.149396 | ||||||||
\(342\) | −2.45734 | − | 9.38965i | −0.132878 | − | 0.507734i | ||||
\(343\) | − | 7.29860i | − | 0.394087i | ||||||
\(344\) | 0.869585 | + | 4.93166i | 0.0468849 | + | 0.265897i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.88666 | − | 1.05066i | 0.155188 | − | 0.0564837i | ||||
\(347\) | −2.65366 | + | 7.29086i | −0.142456 | + | 0.391394i | −0.990317 | − | 0.138824i | \(-0.955668\pi\) |
0.847861 | + | 0.530218i | \(0.177890\pi\) | |||||||
\(348\) | 2.51730 | − | 3.00000i | 0.134941 | − | 0.160817i | ||||
\(349\) | −6.37551 | + | 11.0427i | −0.341273 | + | 0.591103i | −0.984669 | − | 0.174431i | \(-0.944192\pi\) |
0.643396 | + | 0.765534i | \(0.277525\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.520945 | + | 2.95442i | −0.0278060 | + | 0.157695i | ||||
\(352\) | 0.984808 | + | 0.173648i | 0.0524904 | + | 0.00925548i | ||||
\(353\) | −8.19275 | + | 4.73009i | −0.436056 | + | 0.251757i | −0.701923 | − | 0.712253i | \(-0.747675\pi\) |
0.265867 | + | 0.964010i | \(0.414342\pi\) | |||||||
\(354\) | 2.75624 | − | 4.77396i | 0.146493 | − | 0.253733i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.61081 | − | 1.67820i | −0.244373 | − | 0.0889444i | ||||
\(357\) | 0.620838 | + | 1.70574i | 0.0328582 | + | 0.0902772i | ||||
\(358\) | 10.2676 | + | 12.2365i | 0.542661 | + | 0.646718i | ||||
\(359\) | 0.181799 | + | 1.03104i | 0.00959501 | + | 0.0544160i | 0.989229 | − | 0.146374i | \(-0.0467603\pi\) |
−0.979634 | + | 0.200790i | \(0.935649\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.5642 | − | 9.30742i | 0.871799 | − | 0.489864i | ||||
\(362\) | 9.77425i | 0.513723i | ||||||||
\(363\) | 8.66025 | − | 1.52704i | 0.454545 | − | 0.0801486i | ||||
\(364\) | −0.266044 | + | 0.223238i | −0.0139445 | + | 0.0117008i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −4.06670 | − | 1.48016i | −0.212570 | − | 0.0773692i | ||||
\(367\) | 6.35359 | − | 7.57192i | 0.331655 | − | 0.395251i | −0.574286 | − | 0.818655i | \(-0.694720\pi\) |
0.905941 | + | 0.423404i | \(0.139165\pi\) | |||||||
\(368\) | 3.92490 | + | 2.26604i | 0.204600 | + | 0.118126i | ||||
\(369\) | 6.95723 | + | 12.0503i | 0.362179 | + | 0.627313i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.356381 | + | 2.02114i | −0.0185024 | + | 0.104932i | ||||
\(372\) | −2.10100 | + | 1.21301i | −0.108932 | + | 0.0628917i | ||||
\(373\) | 24.0079 | + | 13.8610i | 1.24308 | + | 0.717694i | 0.969720 | − | 0.244218i | \(-0.0785312\pi\) |
0.273361 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(374\) | 2.97178 | + | 2.49362i | 0.153667 | + | 0.128942i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.726682 | + | 0.264490i | −0.0374757 | + | 0.0136401i | ||||
\(377\) | 1.86841 | + | 2.22668i | 0.0962279 | + | 0.114680i | ||||
\(378\) | 2.40847 | − | 0.424678i | 0.123878 | − | 0.0218431i | ||||
\(379\) | 13.0787 | 0.671809 | 0.335905 | − | 0.941896i | \(-0.390958\pi\) | ||||
0.335905 | + | 0.941896i | \(0.390958\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.04364 | −0.463320 | ||||||||
\(382\) | 7.40598 | − | 1.30587i | 0.378923 | − | 0.0668143i | ||||
\(383\) | −6.40268 | − | 7.63041i | −0.327162 | − | 0.389896i | 0.577243 | − | 0.816573i | \(-0.304129\pi\) |
−0.904404 | + | 0.426677i | \(0.859684\pi\) | |||||||
\(384\) | 0.826352 | − | 0.300767i | 0.0421696 | − | 0.0153485i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −18.7986 | − | 15.7739i | −0.956824 | − | 0.802870i | ||||
\(387\) | 9.65674 | + | 5.57532i | 0.490880 | + | 0.283410i | ||||
\(388\) | 0.0874810 | − | 0.0505072i | 0.00444118 | − | 0.00256411i | ||||
\(389\) | 4.18850 | − | 23.7542i | 0.212365 | − | 1.20438i | −0.673055 | − | 0.739593i | \(-0.735018\pi\) |
0.885420 | − | 0.464791i | \(-0.153871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.79086 | + | 15.2262i | 0.444573 | + | 0.770023i | ||||
\(392\) | −5.81699 | − | 3.35844i | −0.293802 | − | 0.169627i | ||||
\(393\) | 4.76573 | − | 5.67958i | 0.240399 | − | 0.286497i | ||||
\(394\) | −13.5351 | − | 4.92637i | −0.681888 | − | 0.248187i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.70574 | − | 1.43128i | 0.0857165 | − | 0.0719247i | ||||
\(397\) | 24.9842 | − | 4.40538i | 1.25392 | − | 0.221100i | 0.493048 | − | 0.870002i | \(-0.335883\pi\) |
0.760872 | + | 0.648902i | \(0.224772\pi\) | |||||||
\(398\) | − | 4.44057i | − | 0.222586i | ||||||
\(399\) | 0.851167 | + | 1.85348i | 0.0426116 | + | 0.0927901i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.30810 | − | 24.4324i | −0.215136 | − | 1.22010i | −0.880670 | − | 0.473730i | \(-0.842907\pi\) |
0.665534 | − | 0.746367i | \(-0.268204\pi\) | |||||||
\(402\) | −0.761570 | − | 0.907604i | −0.0379837 | − | 0.0452672i | ||||
\(403\) | −0.615862 | − | 1.69207i | −0.0306783 | − | 0.0842878i | ||||
\(404\) | −13.4709 | − | 4.90301i | −0.670203 | − | 0.243934i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.18479 | − | 2.05212i | 0.0588003 | − | 0.101845i | ||||
\(407\) | −0.829748 | + | 0.479055i | −0.0411291 | + | 0.0237459i | ||||
\(408\) | 3.35965 | + | 0.592396i | 0.166327 | + | 0.0293280i | ||||
\(409\) | 5.20692 | − | 29.5299i | 0.257466 | − | 1.46016i | −0.532198 | − | 0.846620i | \(-0.678634\pi\) |
0.789664 | − | 0.613540i | \(-0.210255\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.50475 | + | 6.07040i | −0.172876 | + | 0.299431i | ||||
\(412\) | −3.97551 | + | 4.73783i | −0.195859 | + | 0.233416i | ||||
\(413\) | 1.14079 | − | 3.13429i | 0.0561344 | − | 0.154228i | ||||
\(414\) | 9.48293 | − | 3.45150i | 0.466060 | − | 0.169632i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.113341 | + | 0.642788i | 0.00555699 | + | 0.0315153i | ||||
\(417\) | 5.54933i | 0.271752i | ||||||||
\(418\) | 3.55596 | + | 2.52094i | 0.173928 | + | 0.123303i | ||||
\(419\) | 17.7196 | 0.865658 | 0.432829 | − | 0.901476i | \(-0.357515\pi\) | ||||
0.432829 | + | 0.901476i | \(0.357515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.22462 | + | 7.74038i | −0.449581 | + | 0.377243i | −0.839280 | − | 0.543699i | \(-0.817023\pi\) |
0.389700 | + | 0.920942i | \(0.372579\pi\) | |||||||
\(422\) | −3.84505 | − | 10.5642i | −0.187174 | − | 0.514256i | ||||
\(423\) | −0.588936 | + | 1.61809i | −0.0286351 | + | 0.0786742i | ||||
\(424\) | 2.95471 | + | 2.47929i | 0.143493 | + | 0.120405i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.49525 | − | 4.32190i | −0.120895 | − | 0.209397i | ||||
\(427\) | −2.57877 | − | 0.454707i | −0.124796 | − | 0.0220048i | ||||
\(428\) | −9.63246 | − | 1.69846i | −0.465603 | − | 0.0820983i | ||||
\(429\) | −0.286989 | − | 0.497079i | −0.0138560 | − | 0.0239992i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0913 | + | 22.7323i | 1.30494 | + | 1.09498i | 0.989269 | + | 0.146107i | \(0.0466743\pi\) |
0.315672 | + | 0.948868i | \(0.397770\pi\) | |||||||
\(432\) | 1.57202 | − | 4.31908i | 0.0756336 | − | 0.207802i | ||||
\(433\) | −9.16496 | − | 25.1805i | −0.440440 | − | 1.21010i | −0.939204 | − | 0.343360i | \(-0.888435\pi\) |
0.498764 | − | 0.866738i | \(-0.333787\pi\) | |||||||
\(434\) | −1.12449 | + | 0.943555i | −0.0539770 | + | 0.0452921i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.8084 | −0.613411 | ||||||||
\(437\) | 11.2364 | + | 16.2481i | 0.537509 | + | 0.777252i | ||||
\(438\) | 6.57398i | 0.314117i | ||||||||
\(439\) | −4.14244 | − | 23.4929i | −0.197708 | − | 1.12126i | −0.908510 | − | 0.417864i | \(-0.862779\pi\) |
0.710802 | − | 0.703392i | \(-0.248332\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −14.0544 | + | 5.11538i | −0.669256 | + | 0.243589i | ||||
\(442\) | −0.866025 | + | 2.37939i | −0.0411926 | + | 0.113176i | ||||
\(443\) | 21.6640 | − | 25.8182i | 1.02929 | − | 1.22666i | 0.0556780 | − | 0.998449i | \(-0.482268\pi\) |
0.973612 | − | 0.228211i | \(-0.0732876\pi\) | |||||||
\(444\) | −0.421274 | + | 0.729669i | −0.0199928 | + | 0.0346285i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.08466 | + | 11.8227i | −0.0987113 | + | 0.559820i | ||||
\(447\) | −15.6677 | − | 2.76264i | −0.741057 | − | 0.130668i | ||||
\(448\) | 0.460802 | − | 0.266044i | 0.0217709 | − | 0.0125694i | ||||
\(449\) | 6.45605 | − | 11.1822i | 0.304680 | − | 0.527721i | −0.672510 | − | 0.740088i | \(-0.734784\pi\) |
0.977190 | + | 0.212367i | \(0.0681172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.87211 | − | 2.13727i | −0.276507 | − | 0.100640i | ||||
\(452\) | −1.87278 | − | 5.14543i | −0.0880883 | − | 0.242021i | ||||
\(453\) | 5.76963 | + | 6.87598i | 0.271081 | + | 0.323062i | ||||
\(454\) | −4.49525 | − | 25.4938i | −0.210973 | − | 1.19649i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.81655 | + | 0.356347i | 0.178726 | + | 0.0166875i | ||||
\(457\) | 36.0779i | 1.68765i | 0.536616 | + | 0.843827i | \(0.319702\pi\) | ||||
−0.536616 | + | 0.843827i | \(0.680298\pi\) | |||||||
\(458\) | −10.9450 | + | 1.92989i | −0.511425 | + | 0.0901780i | ||||
\(459\) | 13.6591 | − | 11.4613i | 0.637552 | − | 0.534970i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.0530334 | + | 0.0193026i | 0.00247001 | + | 0.000899011i | 0.343255 | − | 0.939242i | \(-0.388471\pi\) |
−0.340785 | + | 0.940141i | \(0.610693\pi\) | |||||||
\(462\) | −0.300767 | + | 0.358441i | −0.0139930 | + | 0.0166762i | ||||
\(463\) | 24.3792 | + | 14.0753i | 1.13300 | + | 0.654136i | 0.944687 | − | 0.327974i | \(-0.106366\pi\) |
0.188310 | + | 0.982110i | \(0.439699\pi\) | |||||||
\(464\) | −2.22668 | − | 3.85673i | −0.103371 | − | 0.179044i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.220285 | − | 1.24930i | 0.0102045 | − | 0.0578726i | ||||
\(467\) | 0.266819 | − | 0.154048i | 0.0123469 | − | 0.00712848i | −0.493814 | − | 0.869568i | \(-0.664398\pi\) |
0.506161 | + | 0.862439i | \(0.331064\pi\) | |||||||
\(468\) | 1.25865 | + | 0.726682i | 0.0581811 | + | 0.0335909i | ||||
\(469\) | −0.549163 | − | 0.460802i | −0.0253580 | − | 0.0212779i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1792 | + | 4.79682i | −0.607264 | + | 0.221026i | ||||
\(472\) | −4.02936 | − | 4.80200i | −0.185466 | − | 0.221030i | ||||
\(473\) | −4.93166 | + | 0.869585i | −0.226758 | + | 0.0399836i | ||||
\(474\) | 0.623608 | 0.0286433 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.06418 | 0.0946114 | ||||||||
\(477\) | 8.45805 | − | 1.49138i | 0.387267 | − | 0.0682857i | ||||
\(478\) | 2.74378 | + | 3.26991i | 0.125498 | + | 0.149562i | ||||
\(479\) | 28.4021 | − | 10.3375i | 1.29773 | − | 0.472334i | 0.401471 | − | 0.915872i | \(-0.368499\pi\) |
0.896256 | + | 0.443538i | \(0.146277\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.479055 | − | 0.401975i | −0.0218430 | − | 0.0183285i | ||||
\(482\) | 25.4608 | + | 14.6998i | 1.15971 | + | 0.669558i | ||||
\(483\) | −1.83651 | + | 1.06031i | −0.0835639 | + | 0.0482457i | ||||
\(484\) | 1.73648 | − | 9.84808i | 0.0789310 | − | 0.447640i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.05438 | − | 13.9506i | −0.365354 | − | 0.632812i | ||||
\(487\) | 25.8956 | + | 14.9508i | 1.17344 | + | 0.677487i | 0.954488 | − | 0.298248i | \(-0.0964023\pi\) |
0.218954 | + | 0.975735i | \(0.429736\pi\) | |||||||
\(488\) | −3.16333 | + | 3.76991i | −0.143197 | + | 0.170656i | ||||
\(489\) | −13.6557 | − | 4.97027i | −0.617532 | − | 0.224763i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.98680 | + | 2.50622i | −0.134792 | + | 0.113104i | −0.707691 | − | 0.706522i | \(-0.750263\pi\) |
0.572899 | + | 0.819626i | \(0.305819\pi\) | |||||||
\(492\) | −5.41177 | + | 0.954241i | −0.243981 | + | 0.0430205i | ||||
\(493\) | − | 17.2763i | − | 0.778086i | ||||||
\(494\) | −0.752374 | + | 2.74378i | −0.0338509 | + | 0.123449i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.479055 | + | 2.71686i | 0.0215102 | + | 0.121991i | ||||
\(497\) | −1.94096 | − | 2.31315i | −0.0870640 | − | 0.103759i | ||||
\(498\) | 3.17826 | + | 8.73220i | 0.142421 | + | 0.391299i | ||||
\(499\) | −22.9231 | − | 8.34332i | −1.02618 | − | 0.373498i | −0.226554 | − | 0.973999i | \(-0.572746\pi\) |
−0.799625 | + | 0.600500i | \(0.794968\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 10.4586 | − | 18.1148i | 0.467255 | − | 0.809309i | ||||
\(502\) | −8.42615 | + | 4.86484i | −0.376077 | + | 0.217128i | ||||
\(503\) | −13.4283 | − | 2.36777i | −0.598739 | − | 0.105574i | −0.133939 | − | 0.990990i | \(-0.542763\pi\) |
−0.464800 | + | 0.885416i | \(0.653874\pi\) | |||||||
\(504\) | 0.205737 | − | 1.16679i | 0.00916426 | − | 0.0519731i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.26604 | + | 3.92490i | −0.100738 | + | 0.174483i | ||||
\(507\) | −7.10754 | + | 8.47044i | −0.315657 | + | 0.376185i | ||||
\(508\) | −3.51735 | + | 9.66385i | −0.156057 | + | 0.428764i | ||||
\(509\) | −7.18004 | + | 2.61332i | −0.318250 | + | 0.115833i | −0.496206 | − | 0.868205i | \(-0.665274\pi\) |
0.177956 | + | 0.984038i | \(0.443052\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.690722 | + | 3.91728i | 0.0305558 | + | 0.173290i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 14.2490 | − | 14.0838i | 0.629110 | − | 0.621814i | ||||
\(514\) | 4.51249 | 0.199037 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3.37346 | + | 2.83067i | −0.148508 | + | 0.124613i | ||||
\(517\) | −0.264490 | − | 0.726682i | −0.0116323 | − | 0.0319594i | ||||
\(518\) | −0.174362 | + | 0.479055i | −0.00766102 | + | 0.0210485i | ||||
\(519\) | 2.06939 | + | 1.73643i | 0.0908362 | + | 0.0762207i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.52734 | − | 11.3057i | −0.285968 | − | 0.495311i | 0.686875 | − | 0.726775i | \(-0.258982\pi\) |
−0.972843 | + | 0.231464i | \(0.925648\pi\) | |||||||
\(522\) | −9.76557 | − | 1.72193i | −0.427427 | − | 0.0753670i | ||||
\(523\) | 17.5065 | + | 3.08688i | 0.765508 | + | 0.134980i | 0.542750 | − | 0.839894i | \(-0.317383\pi\) |
0.222758 | + | 0.974874i | \(0.428494\pi\) | |||||||
\(524\) | −4.21554 | − | 7.30152i | −0.184157 | − | 0.318969i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 23.0744 | + | 19.3618i | 1.00609 | + | 0.844213i | ||||
\(527\) | −3.66041 | + | 10.0569i | −0.159450 | + | 0.438086i | ||||
\(528\) | 0.300767 | + | 0.826352i | 0.0130892 | + | 0.0359623i | ||||
\(529\) | 1.88460 | − | 1.58137i | 0.0819391 | − | 0.0687551i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −13.9581 | −0.605730 | ||||||||
\(532\) | 2.31164 | − | 0.188663i | 0.100222 | − | 0.00817958i | ||||
\(533\) | − | 4.07873i | − | 0.176669i | ||||||
\(534\) | −0.749275 | − | 4.24935i | −0.0324243 | − | 0.183887i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.26604 | + | 0.460802i | −0.0546848 | + | 0.0199036i | ||||
\(537\) | −4.80434 | + | 13.1998i | −0.207322 | + | 0.569614i | ||||
\(538\) | 2.78006 | − | 3.31315i | 0.119857 | − | 0.142840i | ||||
\(539\) | 3.35844 | − | 5.81699i | 0.144658 | − | 0.250555i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.67008 | + | 37.8279i | −0.286769 | + | 1.62635i | 0.412127 | + | 0.911126i | \(0.364786\pi\) |
−0.698896 | + | 0.715223i | \(0.746325\pi\) | |||||||
\(542\) | 26.5661 | + | 4.68433i | 1.14111 | + | 0.201209i | ||||
\(543\) | −7.44378 | + | 4.29767i | −0.319443 | + | 0.184431i | ||||
\(544\) | 1.93969 | − | 3.35965i | 0.0831636 | − | 0.144044i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.286989 | − | 0.104455i | −0.0122820 | − | 0.00447028i | ||||
\(547\) | −9.24076 | − | 25.3888i | −0.395106 | − | 1.08555i | −0.964638 | − | 0.263577i | \(-0.915098\pi\) |
0.569532 | − | 0.821969i | \(-0.307124\pi\) | |||||||
\(548\) | 5.12360 | + | 6.10607i | 0.218869 | + | 0.260838i | ||||
\(549\) | 1.90286 | + | 10.7916i | 0.0812119 | + | 0.460576i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.57903 | − | 19.3474i | −0.0672690 | − | 0.824228i | ||||
\(552\) | 3.98545i | 0.169632i | ||||||||
\(553\) | 0.371593 | − | 0.0655219i | 0.0158018 | − | 0.00278628i | ||||
\(554\) | −1.68866 | + | 1.41696i | −0.0717444 | + | 0.0602007i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.92989 | + | 2.15830i | 0.251483 | + | 0.0915325i | ||||
\(557\) | 7.72016 | − | 9.20052i | 0.327113 | − | 0.389839i | −0.577274 | − | 0.816550i | \(-0.695884\pi\) |
0.904388 | + | 0.426712i | \(0.140328\pi\) | |||||||
\(558\) | 5.31991 | + | 3.07145i | 0.225210 | + | 0.130025i | ||||
\(559\) | −1.63429 | − | 2.83067i | −0.0691229 | − | 0.119724i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.592396 | + | 3.35965i | −0.0250110 | + | 0.141844i | ||||
\(562\) | −16.4360 | + | 9.48932i | −0.693310 | + | 0.400283i | ||||
\(563\) | 12.7815 | + | 7.37939i | 0.538675 | + | 0.311004i | 0.744542 | − | 0.667576i | \(-0.232668\pi\) |
−0.205867 | + | 0.978580i | \(0.566001\pi\) | |||||||
\(564\) | −0.520945 | − | 0.437124i | −0.0219357 | − | 0.0184063i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.6630 | + | 4.97291i | −0.574297 | + | 0.209027i | ||||
\(567\) | −0.902302 | − | 1.07532i | −0.0378931 | − | 0.0451593i | ||||
\(568\) | −5.58878 | + | 0.985452i | −0.234500 | + | 0.0413487i | ||||
\(569\) | 41.7570 | 1.75055 | 0.875273 | − | 0.483630i | \(-0.160682\pi\) | ||||
0.875273 | + | 0.483630i | \(0.160682\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.2431 | 1.22379 | 0.611893 | − | 0.790941i | \(-0.290408\pi\) | ||||
0.611893 | + | 0.790941i | \(0.290408\pi\) | |||||||
\(572\) | −0.642788 | + | 0.113341i | −0.0268763 | + | 0.00473902i | ||||
\(573\) | 4.25087 | + | 5.06599i | 0.177583 | + | 0.211635i | ||||
\(574\) | −3.12449 | + | 1.13722i | −0.130413 | + | 0.0474666i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.70574 | − | 1.43128i | −0.0710724 | − | 0.0596368i | ||||
\(577\) | 1.06029 | + | 0.612159i | 0.0441405 | + | 0.0254845i | 0.521908 | − | 0.853002i | \(-0.325220\pi\) |
−0.477767 | + | 0.878486i | \(0.658554\pi\) | |||||||
\(578\) | −1.68907 | + | 0.975185i | −0.0702561 | + | 0.0405624i | ||||
\(579\) | 3.74732 | − | 21.2521i | 0.155733 | − | 0.883208i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.81134 | + | 4.86938i | 0.116634 | + | 0.202016i | ||||
\(582\) | 0.0769295 | + | 0.0444153i | 0.00318883 | + | 0.00184107i | ||||
\(583\) | −2.47929 | + | 2.95471i | −0.102682 | + | 0.122371i | ||||
\(584\) | 7.02481 | + | 2.55682i | 0.290689 | + | 0.105802i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.79679 | − | 4.02498i | 0.198154 | − | 0.166271i | ||||
\(587\) | 27.3868 | − | 4.82904i | 1.13038 | − | 0.199316i | 0.422984 | − | 0.906137i | \(-0.360983\pi\) |
0.707392 | + | 0.706821i | \(0.249872\pi\) | |||||||
\(588\) | − | 5.90673i | − | 0.243589i | ||||||
\(589\) | −3.18004 | + | 11.5971i | −0.131031 | + | 0.477850i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.19950 | − | 12.4740i | −0.0904754 | − | 0.513112i | ||||
\(592\) | 0.615862 | + | 0.733956i | 0.0253118 | + | 0.0301654i | ||||
\(593\) | −10.3596 | − | 28.4628i | −0.425418 | − | 1.16883i | −0.948565 | − | 0.316583i | \(-0.897464\pi\) |
0.523147 | − | 0.852242i | \(-0.324758\pi\) | |||||||
\(594\) | 4.31908 | + | 1.57202i | 0.177214 | + | 0.0645006i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9.04576 | + | 15.6677i | −0.370529 | + | 0.641775i | ||||
\(597\) | 3.38180 | − | 1.95249i | 0.138408 | − | 0.0799099i | ||||
\(598\) | −2.91317 | − | 0.513671i | −0.119128 | − | 0.0210056i | ||||
\(599\) | 2.09105 | − | 11.8589i | 0.0854381 | − | 0.484543i | −0.911823 | − | 0.410583i | \(-0.865325\pi\) |
0.997261 | − | 0.0739602i | \(-0.0235638\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.05572 | + | 12.2209i | −0.287809 | + | 0.498500i | −0.973286 | − | 0.229594i | \(-0.926260\pi\) |
0.685478 | + | 0.728094i | \(0.259593\pi\) | |||||||
\(602\) | −1.71275 | + | 2.04117i | −0.0698064 | + | 0.0831920i | ||||
\(603\) | −1.02606 | + | 2.81908i | −0.0417844 | + | 0.114802i | ||||
\(604\) | 9.59152 | − | 3.49103i | 0.390273 | − | 0.142048i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.18907 | − | 12.4149i | −0.0889250 | − | 0.504319i | ||||
\(607\) | − | 5.31727i | − | 0.215821i | −0.994161 | − | 0.107911i | \(-0.965584\pi\) | ||
0.994161 | − | 0.107911i | \(-0.0344160\pi\) | |||||||
\(608\) | 1.86516 | − | 3.93969i | 0.0756422 | − | 0.159776i | ||||
\(609\) | 2.08378 | 0.0844390 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.386659 | − | 0.324446i | 0.0156426 | − | 0.0131257i | ||||
\(612\) | −2.95442 | − | 8.11721i | −0.119425 | − | 0.328119i | ||||
\(613\) | −14.3961 | + | 39.5531i | −0.581455 | + | 1.59753i | 0.204241 | + | 0.978921i | \(0.434528\pi\) |
−0.785695 | + | 0.618614i | \(0.787695\pi\) | |||||||
\(614\) | −5.95992 | − | 5.00097i | −0.240523 | − | 0.201823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.266044 | + | 0.460802i | 0.0107192 | + | 0.0185663i | ||||
\(617\) | −15.3617 | − | 2.70867i | −0.618437 | − | 0.109047i | −0.144352 | − | 0.989526i | \(-0.546110\pi\) |
−0.474085 | + | 0.880479i | \(0.657221\pi\) | |||||||
\(618\) | −5.35619 | − | 0.944440i | −0.215457 | − | 0.0379910i | ||||
\(619\) | 11.1853 | + | 19.3734i | 0.449574 | + | 0.778684i | 0.998358 | − | 0.0572796i | \(-0.0182426\pi\) |
−0.548785 | + | 0.835964i | \(0.684909\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 15.9572 | + | 13.3897i | 0.640342 | + | 0.537311i | ||||
\(622\) | 10.6155 | − | 29.1660i | 0.425644 | − | 1.16945i | ||||
\(623\) | −0.892951 | − | 2.45336i | −0.0357753 | − | 0.0982919i | ||||
\(624\) | −0.439693 | + | 0.368946i | −0.0176018 | + | 0.0147697i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −9.22668 | −0.368772 | ||||||||
\(627\) | −0.356347 | + | 3.81655i | −0.0142311 | + | 0.152418i | ||||
\(628\) | 15.9486i | 0.636419i | ||||||||
\(629\) | 0.645430 | + | 3.66041i | 0.0257350 | + | 0.145950i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.58260 | + | 1.66793i | −0.182430 | + | 0.0663992i | −0.431620 | − | 0.902055i | \(-0.642058\pi\) |
0.249190 | + | 0.968455i | \(0.419836\pi\) | |||||||
\(632\) | 0.242540 | − | 0.666374i | 0.00964774 | − | 0.0265069i | ||||
\(633\) | 6.35472 | − | 7.57326i | 0.252578 | − | 0.301010i | ||||
\(634\) | −12.0030 | + | 20.7898i | −0.476700 | + | 0.825668i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.588993 | + | 3.34034i | −0.0233551 | + | 0.132453i | ||||
\(637\) | 4.31753 | + | 0.761297i | 0.171067 | + | 0.0301637i | ||||
\(638\) | 3.85673 | − | 2.22668i | 0.152689 | − | 0.0881552i | ||||
\(639\) | −6.31820 | + | 10.9434i | −0.249944 | + | 0.432916i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.32635 | + | 0.482753i | 0.0523877 | + | 0.0190676i | 0.368081 | − | 0.929794i | \(-0.380015\pi\) |
−0.315693 | + | 0.948861i | \(0.602237\pi\) | |||||||
\(642\) | −2.94182 | − | 8.08260i | −0.116105 | − | 0.318995i | ||||
\(643\) | 5.25346 | + | 6.26083i | 0.207176 | + | 0.246903i | 0.859620 | − | 0.510934i | \(-0.170700\pi\) |
−0.652444 | + | 0.757837i | \(0.726256\pi\) | |||||||
\(644\) | 0.418748 | + | 2.37484i | 0.0165010 | + | 0.0935817i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13.9081 | − | 9.61814i | 0.547206 | − | 0.378421i | ||||
\(647\) | − | 31.3773i | − | 1.23357i | −0.787132 | − | 0.616785i | \(-0.788435\pi\) | ||
0.787132 | − | 0.616785i | \(-0.211565\pi\) | |||||||
\(648\) | −2.59808 | + | 0.458111i | −0.102062 | + | 0.0179963i | ||||
\(649\) | 4.80200 | − | 4.02936i | 0.188495 | − | 0.158166i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.21301 | − | 0.441500i | −0.0475417 | − | 0.0173037i | ||||
\(652\) | −10.6222 | + | 12.6591i | −0.415999 | + | 0.495769i | ||||
\(653\) | 33.6780 | + | 19.4440i | 1.31792 | + | 0.760904i | 0.983394 | − | 0.181482i | \(-0.0580893\pi\) |
0.334530 | + | 0.942385i | \(0.391423\pi\) | |||||||
\(654\) | −5.63176 | − | 9.75449i | −0.220219 | − | 0.381431i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.08512 | + | 6.15403i | −0.0423669 | + | 0.240275i | ||||
\(657\) | 14.4158 | − | 8.32295i | 0.562413 | − | 0.324709i | ||||
\(658\) | −0.356347 | − | 0.205737i | −0.0138919 | − | 0.00802047i | ||||
\(659\) | −9.69047 | − | 8.13127i | −0.377487 | − | 0.316749i | 0.434228 | − | 0.900803i | \(-0.357021\pi\) |
−0.811715 | + | 0.584054i | \(0.801466\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −41.7708 | + | 15.2033i | −1.62470 | + | 0.591342i | −0.984269 | − | 0.176676i | \(-0.943466\pi\) |
−0.640429 | + | 0.768018i | \(0.721243\pi\) | |||||||
\(662\) | 15.7771 | + | 18.8025i | 0.613196 | + | 0.730779i | ||||
\(663\) | −2.19285 | + | 0.386659i | −0.0851634 | + | 0.0150166i | ||||
\(664\) | 10.5672 | 0.410086 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.13341 | 0.0826679 | ||||||||
\(667\) | 19.8764 | − | 3.50475i | 0.769618 | − | 0.135704i | ||||
\(668\) | −15.2894 | − | 18.2212i | −0.591565 | − | 0.705000i | ||||
\(669\) | −9.92040 | + | 3.61073i | −0.383545 | + | 0.139599i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.76991 | − | 3.16333i | −0.145536 | − | 0.122119i | ||||
\(672\) | 0.405223 | + | 0.233956i | 0.0156318 | + | 0.00902503i | ||||
\(673\) | 16.8909 | − | 9.75196i | 0.651096 | − | 0.375911i | −0.137780 | − | 0.990463i | \(-0.543997\pi\) |
0.788876 | + | 0.614552i | \(0.210663\pi\) | |||||||
\(674\) | −5.32295 | + | 30.1879i | −0.205032 | + | 1.16280i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.28699 | + | 10.8894i | 0.241807 | + | 0.418822i | ||||
\(677\) | −6.08738 | − | 3.51455i | −0.233957 | − | 0.135075i | 0.378439 | − | 0.925626i | \(-0.376461\pi\) |
−0.612396 | + | 0.790551i | \(0.709794\pi\) | |||||||
\(678\) | 3.09516 | − | 3.68866i | 0.118869 | − | 0.141662i | ||||
\(679\) | 0.0505072 | + | 0.0183831i | 0.00193829 | + | 0.000705479i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.4388 | − | 14.6329i | 0.668257 | − | 0.560734i | ||||
\(682\) | −2.71686 | + | 0.479055i | −0.104034 | + | 0.0183440i | ||||
\(683\) | 0.386821i | 0.0148013i | 0.999973 | + | 0.00740065i | \(0.00235572\pi\) | ||||
−0.999973 | + | 0.00740065i | \(0.997644\pi\) | |||||||
\(684\) | −4.05051 | − | 8.82029i | −0.154875 | − | 0.337252i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.26739 | − | 7.18772i | −0.0483891 | − | 0.274428i | ||||
\(687\) | −6.28217 | − | 7.48680i | −0.239680 | − | 0.285639i | ||||
\(688\) | 1.71275 | + | 4.70574i | 0.0652979 | + | 0.179405i | ||||
\(689\) | −2.36571 | − | 0.861050i | −0.0901266 | − | 0.0328034i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.2260 | − | 36.7645i | 0.807474 | − | 1.39859i | −0.107134 | − | 0.994245i | \(-0.534168\pi\) |
0.914608 | − | 0.404341i | \(-0.132499\pi\) | |||||||
\(692\) | 2.66036 | − | 1.53596i | 0.101132 | − | 0.0583884i | ||||
\(693\) | 1.16679 | + | 0.205737i | 0.0443228 | + | 0.00781530i | ||||
\(694\) | −1.34730 | + | 7.64090i | −0.0511427 | + | 0.290044i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.95811 | − | 3.39155i | 0.0742220 | − | 0.128556i | ||||
\(697\) | −15.5826 | + | 18.5706i | −0.590232 | + | 0.703411i | ||||
\(698\) | −4.36111 | + | 11.9820i | −0.165070 | + | 0.453527i | ||||
\(699\) | 1.04829 | − | 0.381545i | 0.0396498 | − | 0.0144313i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.96497 | − | 33.8291i | −0.225294 | − | 1.27771i | −0.862122 | − | 0.506700i | \(-0.830865\pi\) |
0.636828 | − | 0.771006i | \(-0.280246\pi\) | |||||||
\(702\) | 3.00000i | 0.113228i | ||||||||
\(703\) | 1.05736 | + | 4.04024i | 0.0398792 | + | 0.152381i | ||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.24691 | + | 6.08088i | −0.272741 | + | 0.228857i | ||||
\(707\) | −2.60884 | − | 7.16772i | −0.0981154 | − | 0.269570i | ||||
\(708\) | 1.88538 | − | 5.18004i | 0.0708570 | − | 0.194678i | ||||
\(709\) | 7.38144 | + | 6.19377i | 0.277216 | + | 0.232612i | 0.770786 | − | 0.637094i | \(-0.219864\pi\) |
−0.493570 | + | 0.869706i | \(0.664308\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.789515 | − | 1.36748i | −0.0296091 | − | 0.0512845i | ||||
\(712\) | −4.83218 | − | 0.852044i | −0.181094 | − | 0.0319317i | ||||
\(713\) | −12.3130 | − | 2.17112i | −0.461127 | − | 0.0813092i | ||||
\(714\) | 0.907604 | + | 1.57202i | 0.0339662 | + | 0.0588312i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.2365 | + | 10.2676i | 0.457299 | + | 0.383719i | ||||
\(717\) | −1.28385 | + | 3.52734i | −0.0479462 | + | 0.131731i | ||||
\(718\) | 0.358075 | + | 0.983803i | 0.0133632 | + | 0.0367152i | ||||
\(719\) | −35.3542 | + | 29.6657i | −1.31849 | + | 1.10634i | −0.331864 | + | 0.943327i | \(0.607678\pi\) |
−0.986624 | + | 0.163015i | \(0.947878\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.29086 | −0.122558 | ||||||||
\(722\) | 14.6963 | − | 12.0424i | 0.546940 | − | 0.448170i | ||||
\(723\) | 25.8536i | 0.961505i | ||||||||
\(724\) | 1.69728 | + | 9.62576i | 0.0630790 | + | 0.357739i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 8.26352 | − | 3.00767i | 0.306688 | − | 0.111625i | ||||
\(727\) | 1.12879 | − | 3.10132i | 0.0418644 | − | 0.115022i | −0.916999 | − | 0.398890i | \(-0.869396\pi\) |
0.958863 | + | 0.283868i | \(0.0916178\pi\) | |||||||
\(728\) | −0.223238 | + | 0.266044i | −0.00827374 | + | 0.00986026i | ||||
\(729\) | 3.12567 | − | 5.41381i | 0.115765 | − | 0.200512i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.37346 | + | 19.1318i | −0.124772 | + | 0.707616i | ||||
\(732\) | −4.26195 | − | 0.751497i | −0.157526 | − | 0.0277761i | ||||
\(733\) | −37.5450 | + | 21.6766i | −1.38676 | + | 0.800645i | −0.992948 | − | 0.118547i | \(-0.962176\pi\) |
−0.393809 | + | 0.919192i | \(0.628843\pi\) | |||||||
\(734\) | 4.94222 | − | 8.56017i | 0.182421 | − | 0.315962i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.25877 | + | 1.55007i | 0.156980 | + | 0.0571362i | ||||
\(737\) | −0.460802 | − | 1.26604i | −0.0169739 | − | 0.0466353i | ||||
\(738\) | 8.94405 | + | 10.6591i | 0.329235 | + | 0.392367i | ||||
\(739\) | 0.427204 | + | 2.42279i | 0.0157150 | + | 0.0891239i | 0.991657 | − | 0.128908i | \(-0.0411473\pi\) |
−0.975942 | + | 0.218032i | \(0.930036\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.42040 | + | 0.633436i | −0.0889155 | + | 0.0232699i | ||||
\(742\) | 2.05232i | 0.0753430i | ||||||||
\(743\) | −8.28104 | + | 1.46017i | −0.303802 | + | 0.0535685i | −0.323471 | − | 0.946238i | \(-0.604850\pi\) |
0.0196692 | + | 0.999807i | \(0.493739\pi\) | |||||||
\(744\) | −1.85844 | + | 1.55942i | −0.0681337 | + | 0.0571710i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 26.0501 | + | 9.48146i | 0.953762 | + | 0.347141i | ||||
\(747\) | 15.1246 | − | 18.0248i | 0.553381 | − | 0.659493i | ||||
\(748\) | 3.35965 | + | 1.93969i | 0.122841 | + | 0.0709222i | ||||
\(749\) | −2.60220 | − | 4.50714i | −0.0950822 | − | 0.164687i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.14502 | + | 6.49373i | −0.0417823 | + | 0.236959i | −0.998546 | − | 0.0539072i | \(-0.982832\pi\) |
0.956764 | + | 0.290867i | \(0.0939436\pi\) | |||||||
\(752\) | −0.669713 | + | 0.386659i | −0.0244219 | + | 0.0141000i | ||||
\(753\) | −7.40983 | − | 4.27807i | −0.270029 | − | 0.155901i | ||||
\(754\) | 2.22668 | + | 1.86841i | 0.0810910 | + | 0.0680434i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.29813 | − | 0.836452i | 0.0835823 | − | 0.0304215i | ||||
\(757\) | 1.66772 | + | 1.98751i | 0.0606143 | + | 0.0722373i | 0.795500 | − | 0.605954i | \(-0.207208\pi\) |
−0.734885 | + | 0.678191i | \(0.762764\pi\) | |||||||
\(758\) | 12.8800 | − | 2.27110i | 0.467824 | − | 0.0824900i | ||||
\(759\) | −3.98545 | −0.144663 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.9454 | 1.30302 | 0.651510 | − | 0.758640i | \(-0.274136\pi\) | ||||
0.651510 | + | 0.758640i | \(0.274136\pi\) | |||||||
\(762\) | −8.90625 | + | 1.57041i | −0.322639 | + | 0.0568900i | ||||
\(763\) | −4.38073 | − | 5.22075i | −0.158593 | − | 0.189004i | ||||
\(764\) | 7.06670 | − | 2.57207i | 0.255664 | − | 0.0930542i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.63041 | − | 6.40268i | −0.275698 | − | 0.231338i | ||||
\(767\) | 3.54336 | + | 2.04576i | 0.127943 | + | 0.0738681i | ||||
\(768\) | 0.761570 | − | 0.439693i | 0.0274808 | − | 0.0158660i | ||||
\(769\) | −3.00815 | + | 17.0601i | −0.108477 | + | 0.615202i | 0.881298 | + | 0.472561i | \(0.156670\pi\) |
−0.989775 | + | 0.142641i | \(0.954441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.98411 | + | 3.43658i | 0.0714559 | + | 0.123765i | ||||
\(772\) | −21.2521 | − | 12.2699i | −0.764880 | − | 0.441604i | ||||
\(773\) | −23.1790 | + | 27.6236i | −0.833689 | + | 0.993552i | 0.166283 | + | 0.986078i | \(0.446824\pi\) |
−0.999972 | + | 0.00747402i | \(0.997621\pi\) | |||||||
\(774\) | 10.4782 | + | 3.81374i | 0.376630 | + | 0.137082i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.0773815 | − | 0.0649308i | 0.00277783 | − | 0.00233088i | ||||
\(777\) | −0.441500 | + | 0.0778483i | −0.0158387 | + | 0.00279279i | ||||
\(778\) | − | 24.1206i | − | 0.864766i | ||||||
\(779\) | −15.7533 | + | 22.2211i | −0.564421 | + | 0.796153i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.985452 | − | 5.58878i | −0.0352622 | − | 0.199982i | ||||
\(782\) | 11.3013 | + | 13.4684i | 0.404134 | + | 0.481628i | ||||
\(783\) | −7.00076 | − | 19.2344i | −0.250187 | − | 0.687382i | ||||
\(784\) | −6.31180 | − | 2.29731i | −0.225422 | − | 0.0820467i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.70708 | − | 6.42085i | 0.132227 | − | 0.229024i | ||||
\(787\) | 10.0380 | − | 5.79544i | 0.357816 | − | 0.206585i | −0.310306 | − | 0.950637i | \(-0.600432\pi\) |
0.668122 | + | 0.744051i | \(0.267098\pi\) | |||||||
\(788\) | −14.1849 | − | 2.50118i | −0.505316 | − | 0.0891009i | ||||
\(789\) | −4.59967 | + | 26.0860i | −0.163753 | + | 0.928687i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.45677 | − | 2.52319i | 0.0517967 | − | 0.0897145i | ||||
\(792\) | 1.43128 | − | 1.70574i | 0.0508584 | − | 0.0606107i | ||||
\(793\) | 1.09861 | − | 3.01842i | 0.0390129 | − | 0.107187i | ||||
\(794\) | 23.8396 | − | 8.67691i | 0.846036 | − | 0.307932i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.771097 | − | 4.37311i | −0.0273308 | − | 0.155001i | ||||
\(797\) | − | 45.0634i | − | 1.59623i | −0.602508 | − | 0.798113i | \(-0.705832\pi\) | ||
0.602508 | − | 0.798113i | \(-0.294168\pi\) | |||||||
\(798\) | 1.16009 | + | 1.67752i | 0.0410667 | + | 0.0593835i | ||||
\(799\) | −3.00000 | −0.106132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.36959 | + | 7.02292i | −0.295725 | + | 0.248143i | ||||
\(802\) | −8.48529 | − | 23.3131i | −0.299626 | − | 0.823216i | ||||
\(803\) | −2.55682 | + | 7.02481i | −0.0902283 | + | 0.247900i | ||||
\(804\) | −0.907604 | − | 0.761570i | −0.0320087 | − | 0.0268585i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.900330 | − | 1.55942i | −0.0317128 | − | 0.0549281i | ||||
\(807\) | 3.74557 | + | 0.660444i | 0.131850 | + | 0.0232487i | ||||
\(808\) | −14.1176 | − | 2.48932i | −0.496657 | − | 0.0875741i | ||||
\(809\) | −2.82841 | − | 4.89895i | −0.0994416 | − | 0.172238i | 0.812012 | − | 0.583641i | \(-0.198372\pi\) |
−0.911454 | + | 0.411403i | \(0.865039\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.2781 | + | 17.8545i | 0.747176 | + | 0.626955i | 0.934754 | − | 0.355295i | \(-0.115619\pi\) |
−0.187578 | + | 0.982250i | \(0.560064\pi\) | |||||||
\(812\) | 0.810446 | − | 2.22668i | 0.0284411 | − | 0.0781412i | ||||
\(813\) | 8.11349 | + | 22.2916i | 0.284553 | + | 0.781802i | ||||
\(814\) | −0.733956 | + | 0.615862i | −0.0257251 | + | 0.0215859i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.41147 | 0.119425 | ||||||||
\(817\) | −2.02925 | + | 21.7337i | −0.0709945 | + | 0.760366i | ||||
\(818\) | − | 29.9855i | − | 1.04842i | ||||||
\(819\) | 0.134285 | + | 0.761570i | 0.00469231 | + | 0.0266114i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.1450 | + | 13.1557i | −1.26147 | + | 0.459137i | −0.884262 | − | 0.466991i | \(-0.845338\pi\) |
−0.377208 | + | 0.926129i | \(0.623116\pi\) | |||||||
\(822\) | −2.39739 | + | 6.58677i | −0.0836185 | + | 0.229740i | ||||
\(823\) | −6.00833 | + | 7.16044i | −0.209437 | + | 0.249597i | −0.860529 | − | 0.509402i | \(-0.829867\pi\) |
0.651092 | + | 0.758999i | \(0.274311\pi\) | |||||||
\(824\) | −3.09240 | + | 5.35619i | −0.107729 | + | 0.186592i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.579193 | − | 3.28476i | 0.0201527 | − | 0.114292i | ||||
\(827\) | −45.1237 | − | 7.95652i | −1.56910 | − | 0.276675i | −0.679593 | − | 0.733590i | \(-0.737843\pi\) |
−0.889511 | + | 0.456914i | \(0.848955\pi\) | |||||||
\(828\) | 8.73951 | − | 5.04576i | 0.303719 | − | 0.175352i | ||||
\(829\) | −20.7699 | + | 35.9745i | −0.721369 | + | 1.24945i | 0.239082 | + | 0.970999i | \(0.423153\pi\) |
−0.960451 | + | 0.278448i | \(0.910180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.82160 | − | 0.663010i | −0.0631907 | − | 0.0229996i | ||||
\(832\) | 0.223238 | + | 0.613341i | 0.00773938 | + | 0.0212638i | ||||
\(833\) | −16.7494 | − | 19.9611i | −0.580331 | − | 0.691611i | ||||
\(834\) | 0.963630 | + | 5.46502i | 0.0333678 | + | 0.189238i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.93969 | + | 1.86516i | 0.136257 | + | 0.0645079i | ||||
\(837\) | 12.6800i | 0.438286i | ||||||||
\(838\) | 17.4504 | − | 3.07697i | 0.602813 | − | 0.106292i | ||||
\(839\) | 18.0458 | − | 15.1422i | 0.623009 | − | 0.522766i | −0.275739 | − | 0.961233i | \(-0.588923\pi\) |
0.898748 | + | 0.438466i | \(0.144478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.61468 | + | 3.13549i | 0.297058 | + | 0.108120i | ||||
\(842\) | −7.74038 | + | 9.22462i | −0.266751 | + | 0.317901i | ||||
\(843\) | −14.4536 | − | 8.34477i | −0.497807 | − | 0.287409i | ||||
\(844\) | −5.62108 | − | 9.73600i | −0.193486 | − | 0.335127i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.299011 | + | 1.69577i | −0.0102802 | + | 0.0583019i | ||||
\(847\) | 4.60802 | − | 2.66044i | 0.158334 | − | 0.0914140i | ||||
\(848\) | 3.34034 | + | 1.92855i | 0.114708 | + | 0.0662266i | ||||
\(849\) | −9.79473 | − | 8.21875i | −0.336154 | − | 0.282067i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.08037 | + | 1.48513i | −0.139873 | + | 0.0509098i | ||||
\(852\) | −3.20783 | − | 3.82295i | −0.109899 | − | 0.130972i | ||||
\(853\) | 15.4840 | − | 2.73025i | 0.530162 | − | 0.0934819i | 0.0978418 | − | 0.995202i | \(-0.468806\pi\) |
0.432320 | + | 0.901720i | \(0.357695\pi\) | |||||||
\(854\) | −2.61856 | −0.0896051 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.78106 | −0.334310 | ||||||||
\(857\) | 2.57705 | − | 0.454403i | 0.0880302 | − | 0.0155221i | −0.129460 | − | 0.991585i | \(-0.541324\pi\) |
0.217490 | + | 0.976063i | \(0.430213\pi\) | |||||||
\(858\) | −0.368946 | − | 0.439693i | −0.0125956 | − | 0.0150109i | ||||
\(859\) | −20.7729 | + | 7.56072i | −0.708762 | + | 0.257968i | −0.671147 | − | 0.741324i | \(-0.734198\pi\) |
−0.0376150 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.23989 | − | 1.87949i | −0.0763351 | − | 0.0640527i | ||||
\(862\) | 30.6271 | + | 17.6826i | 1.04316 | + | 0.602271i | ||||
\(863\) | 2.76990 | − | 1.59920i | 0.0942885 | − | 0.0544375i | −0.452114 | − | 0.891960i | \(-0.649330\pi\) |
0.546403 | + | 0.837522i | \(0.315997\pi\) | |||||||
\(864\) | 0.798133 | − | 4.52644i | 0.0271530 | − | 0.153993i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.3983 | − | 23.2065i | −0.455292 | − | 0.788588i | ||||
\(867\) | −1.48534 | − | 0.857563i | −0.0504449 | − | 0.0291244i | ||||
\(868\) | −0.943555 | + | 1.12449i | −0.0320263 | + | 0.0381675i | ||||
\(869\) | 0.666374 | + | 0.242540i | 0.0226052 | + | 0.00822762i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.673648 | − | 0.565258i | 0.0228257 | − | 0.0191530i | ||||
\(872\) | −12.6138 | + | 2.22416i | −0.427158 | + | 0.0753194i | ||||
\(873\) | − | 0.224927i | − | 0.00761262i | ||||||
\(874\) | 13.8871 | + | 14.0501i | 0.469739 | + | 0.475251i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.14156 | + | 6.47410i | 0.0385697 | + | 0.218740i | ||||
\(877\) | −34.8227 | − | 41.5001i | −1.17588 | − | 1.40136i | −0.897574 | − | 0.440865i | \(-0.854672\pi\) |
−0.278305 | − | 0.960493i | \(-0.589773\pi\) | |||||||
\(878\) | −8.15901 | − | 22.4167i | −0.275353 | − | 0.756527i | ||||
\(879\) | 5.17442 | + | 1.88333i | 0.174529 | + | 0.0635233i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2670 | − | 43.7637i | 0.851266 | − | 1.47444i | −0.0288001 | − | 0.999585i | \(-0.509169\pi\) |
0.880066 | − | 0.474851i | \(-0.157498\pi\) | |||||||
\(882\) | −12.9526 | + | 7.47818i | −0.436136 | + | 0.251803i | ||||
\(883\) | −44.4756 | − | 7.84224i | −1.49672 | − | 0.263913i | −0.635484 | − | 0.772114i | \(-0.719199\pi\) |
−0.861238 | + | 0.508201i | \(0.830311\pi\) | |||||||
\(884\) | −0.439693 | + | 2.49362i | −0.0147885 | + | 0.0838695i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.8516 | − | 29.1879i | 0.566142 | − | 0.980586i | ||||
\(887\) | −34.7430 | + | 41.4051i | −1.16656 | + | 1.39025i | −0.261368 | + | 0.965239i | \(0.584174\pi\) |
−0.905189 | + | 0.425009i | \(0.860271\pi\) | |||||||
\(888\) | −0.288169 | + | 0.791737i | −0.00967030 | + | 0.0265689i | ||||
\(889\) | −5.14203 | + | 1.87154i | −0.172458 | + | 0.0627696i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.458111 | − | 2.59808i | −0.0153473 | − | 0.0870388i | ||||
\(892\) | 12.0051i | 0.401959i | ||||||||
\(893\) | −3.35965 | + | 0.274196i | −0.112426 | + | 0.00917561i | ||||
\(894\) | −15.9094 | −0.532090 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.407604 | − | 0.342020i | 0.0136171 | − | 0.0114261i | ||||
\(897\) | −0.889704 | − | 2.44444i | −0.0297063 | − | 0.0816175i | ||||
\(898\) | 4.41620 | − | 12.1334i | 0.147370 | − | 0.404897i | ||||
\(899\) | 9.41147 | + | 7.89716i | 0.313890 | + | 0.263385i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7.48158 | + | 12.9585i | 0.249248 | + | 0.431710i | ||||
\(902\) | −6.15403 | − | 1.08512i | −0.204907 | − | 0.0361306i | ||||
\(903\) | −2.30758 | − | 0.406889i | −0.0767914 | − | 0.0135404i | ||||
\(904\) | −2.73783 | − | 4.74205i | −0.0910587 | − | 0.157718i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.87598 | + | 5.76963i | 0.228439 | + | 0.191683i | ||||
\(907\) | −7.39744 | + | 20.3243i | −0.245628 | + | 0.674857i | 0.754206 | + | 0.656638i | \(0.228022\pi\) |
−0.999834 | + | 0.0182193i | \(0.994200\pi\) | |||||||
\(908\) | −8.85392 | − | 24.3259i | −0.293828 | − | 0.807285i | ||||
\(909\) | −24.4525 | + | 20.5181i | −0.811038 | + | 0.680541i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.0529 | −1.26075 | −0.630375 | − | 0.776291i | \(-0.717099\pi\) | ||||
−0.630375 | + | 0.776291i | \(0.717099\pi\) | |||||||
\(912\) | 3.82045 | − | 0.311804i | 0.126508 | − | 0.0103249i | ||||
\(913\) | 10.5672i | 0.349722i | ||||||||
\(914\) | 6.26486 | + | 35.5298i | 0.207223 | + | 1.17522i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −10.4436 | + | 3.80115i | −0.345065 | + | 0.125593i | ||||
\(917\) | 1.53433 | − | 4.21554i | 0.0506680 | − | 0.139209i | ||||
\(918\) | 11.4613 | − | 13.6591i | 0.378281 | − | 0.450817i | ||||
\(919\) | −10.7255 | + | 18.5771i | −0.353802 | + | 0.612802i | −0.986912 | − | 0.161259i | \(-0.948445\pi\) |
0.633111 | + | 0.774061i | \(0.281778\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.18805 | − | 6.73779i | 0.0391477 | − | 0.222018i | ||||
\(922\) | 0.0555796 | + | 0.00980018i | 0.00183042 | + | 0.000322752i | ||||
\(923\) | 3.20783 | − | 1.85204i | 0.105587 | − | 0.0609608i | ||||
\(924\) | −0.233956 | + | 0.405223i | −0.00769657 | + | 0.0133309i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 26.4530 | + | 9.62809i | 0.869298 | + | 0.316399i | ||||
\(927\) | 4.71015 | + | 12.9410i | 0.154702 | + | 0.425039i | ||||
\(928\) | −2.86257 | − | 3.41147i | −0.0939684 | − | 0.111987i | ||||
\(929\) | −3.81093 | − | 21.6128i | −0.125032 | − | 0.709094i | −0.981289 | − | 0.192543i | \(-0.938327\pi\) |
0.856256 | − | 0.516551i | \(-0.172785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.5817 | − | 20.8232i | −0.674539 | − | 0.682453i | ||||
\(932\) | − | 1.26857i | − | 0.0415534i | ||||||
\(933\) | 26.8795 | − | 4.73958i | 0.879995 | − | 0.155167i | ||||
\(934\) | 0.236015 | − | 0.198040i | 0.00772265 | − | 0.00648007i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.36571 | + | 0.497079i | 0.0446398 | + | 0.0162476i | ||||
\(937\) | 30.9934 | − | 36.9365i | 1.01251 | − | 1.20666i | 0.0342223 | − | 0.999414i | \(-0.489105\pi\) |
0.978288 | − | 0.207249i | \(-0.0664510\pi\) | |||||||
\(938\) | −0.620838 | − | 0.358441i | −0.0202711 | − | 0.0117035i | ||||
\(939\) | −4.05690 | − | 7.02676i | −0.132392 | − | 0.229310i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.49004 | − | 14.1217i | 0.0811729 | − | 0.460354i | −0.916944 | − | 0.399016i | \(-0.869352\pi\) |
0.998117 | − | 0.0613388i | \(-0.0195370\pi\) | |||||||
\(942\) | −12.1460 | + | 7.01249i | −0.395738 | + | 0.228479i | ||||
\(943\) | −24.5266 | − | 14.1604i | −0.798696 | − | 0.461128i | ||||
\(944\) | −4.80200 | − | 4.02936i | −0.156292 | − | 0.131144i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.70574 | + | 1.71275i | −0.152997 | + | 0.0556862i | ||||
\(947\) | −15.1025 | − | 17.9984i | −0.490764 | − | 0.584870i | 0.462648 | − | 0.886542i | \(-0.346900\pi\) |
−0.953412 | + | 0.301673i | \(0.902455\pi\) | |||||||
\(948\) | 0.614134 | − | 0.108288i | 0.0199461 | − | 0.00351704i | ||||
\(949\) | −4.87939 | −0.158392 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.1105 | −0.684555 | ||||||||
\(952\) | 2.03282 | − | 0.358441i | 0.0658840 | − | 0.0116171i | ||||
\(953\) | −27.4216 | − | 32.6798i | −0.888273 | − | 1.05860i | −0.997909 | − | 0.0646307i | \(-0.979413\pi\) |
0.109636 | − | 0.993972i | \(-0.465031\pi\) | |||||||
\(954\) | 8.07057 | − | 2.93745i | 0.261294 | − | 0.0951034i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.26991 | + | 2.74378i | 0.105757 | + | 0.0887403i | ||||
\(957\) | 3.39155 | + | 1.95811i | 0.109633 | + | 0.0632967i | ||||
\(958\) | 26.1756 | − | 15.1125i | 0.845694 | − | 0.488262i | ||||
\(959\) | −0.736482 | + | 4.17680i | −0.0237822 | + | 0.134876i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.6946 | + | 20.2556i | 0.377245 | + | 0.653407i | ||||
\(962\) | −0.541580 | − | 0.312681i | −0.0174612 | − | 0.0100812i | ||||
\(963\) | −13.9995 | + | 16.6839i | −0.451127 | + | 0.537632i | ||||
\(964\) | 27.6266 | + | 10.0553i | 0.889793 | + | 0.323858i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.62449 | + | 1.36310i | −0.0522670 | + | 0.0438572i | ||||
\(967\) | −17.7757 | + | 3.13434i | −0.571629 | + | 0.100794i | −0.451989 | − | 0.892024i | \(-0.649285\pi\) |
−0.119640 | + | 0.992817i | \(0.538174\pi\) | |||||||
\(968\) | − | 10.0000i | − | 0.321412i | ||||||
\(969\) | 13.4402 | + | 6.36295i | 0.431760 | + | 0.204407i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.87346 | − | 21.9675i | −0.124305 | − | 0.704969i | −0.981718 | − | 0.190340i | \(-0.939041\pi\) |
0.857413 | − | 0.514629i | \(-0.172070\pi\) | |||||||
\(972\) | −10.3545 | − | 12.3400i | −0.332121 | − | 0.395806i | ||||
\(973\) | 1.14841 | + | 3.15523i | 0.0368163 | + | 0.101152i | ||||
\(974\) | 28.0984 | + | 10.2270i | 0.900330 | + | 0.327693i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.46064 | + | 4.26195i | −0.0787631 | + | 0.136422i | ||||
\(977\) | 6.45918 | − | 3.72921i | 0.206647 | − | 0.119308i | −0.393105 | − | 0.919494i | \(-0.628599\pi\) |
0.599752 | + | 0.800186i | \(0.295266\pi\) | |||||||
\(978\) | −14.3113 | − | 2.52347i | −0.457625 | − | 0.0806917i | ||||
\(979\) | 0.852044 | − | 4.83218i | 0.0272314 | − | 0.154437i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.2601 | + | 24.6992i | −0.455290 | + | 0.788586i | ||||
\(982\) | −2.50622 | + | 2.98680i | −0.0799767 | + | 0.0953125i | ||||
\(983\) | 2.39354 | − | 6.57620i | 0.0763421 | − | 0.209748i | −0.895651 | − | 0.444758i | \(-0.853290\pi\) |
0.971993 | + | 0.235009i | \(0.0755121\pi\) | |||||||
\(984\) | −5.16385 | + | 1.87949i | −0.164617 | + | 0.0599159i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.00000 | − | 17.0138i | −0.0955395 | − | 0.541831i | ||||
\(987\) | − | 0.361844i | − | 0.0115176i | ||||||
\(988\) | −0.264490 | + | 2.83275i | −0.00841456 | + | 0.0901217i | ||||
\(989\) | −22.6955 | −0.721676 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.77900 | − | 6.52736i | 0.247108 | − | 0.207348i | −0.510818 | − | 0.859689i | \(-0.670657\pi\) |
0.757926 | + | 0.652341i | \(0.226213\pi\) | |||||||
\(992\) | 0.943555 | + | 2.59240i | 0.0299579 | + | 0.0823087i | ||||
\(993\) | −7.38230 | + | 20.2827i | −0.234270 | + | 0.643652i | ||||
\(994\) | −2.31315 | − | 1.94096i | −0.0733686 | − | 0.0615636i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.64631 | + | 8.04764i | 0.147224 | + | 0.254999i | ||||
\(997\) | −53.8731 | − | 9.49928i | −1.70618 | − | 0.300845i | −0.766333 | − | 0.642444i | \(-0.777921\pi\) |
−0.939846 | + | 0.341598i | \(0.889032\pi\) | |||||||
\(998\) | −24.0236 | − | 4.23601i | −0.760455 | − | 0.134089i | ||||
\(999\) | 2.20187 | + | 3.81374i | 0.0696640 | + | 0.120662i |
(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 | 950.2.u.d.199.2 | 12 | ||
5.2 | odd | 4 | 950.2.l.e.351.1 | yes | 6 | ||
5.3 | odd | 4 | 950.2.l.b.351.1 | ✓ | 6 | ||
5.4 | even | 2 | inner | 950.2.u.d.199.1 | 12 | ||
19.17 | even | 9 | inner | 950.2.u.d.549.1 | 12 | ||
95.17 | odd | 36 | 950.2.l.e.701.1 | yes | 6 | ||
95.74 | even | 18 | inner | 950.2.u.d.549.2 | 12 | ||
95.93 | odd | 36 | 950.2.l.b.701.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.l.b.351.1 | ✓ | 6 | 5.3 | odd | 4 | ||
950.2.l.b.701.1 | yes | 6 | 95.93 | odd | 36 | ||
950.2.l.e.351.1 | yes | 6 | 5.2 | odd | 4 | ||
950.2.l.e.701.1 | yes | 6 | 95.17 | odd | 36 | ||
950.2.u.d.199.1 | 12 | 5.4 | even | 2 | inner | ||
950.2.u.d.199.2 | 12 | 1.1 | even | 1 | trivial | ||
950.2.u.d.549.1 | 12 | 19.17 | even | 9 | inner | ||
950.2.u.d.549.2 | 12 | 95.74 | even | 18 | inner |