Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [38,4,Mod(7,38)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(38, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("38.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 38 = 2 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 38.c (of order \(3\), 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: | \(2.24207258022\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 38.11 |
Dual form | 38.4.c.b.7.1 |
$q$-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 \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).
\(n\) | \(21\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 2.50000 | − | 4.33013i | 0.481125 | − | 0.833333i | −0.518640 | − | 0.854993i | \(-0.673562\pi\) |
0.999765 | + | 0.0216593i | \(0.00689490\pi\) | |||||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 6.00000 | − | 10.3923i | 0.536656 | − | 0.929516i | −0.462425 | − | 0.886658i | \(-0.653021\pi\) |
0.999081 | − | 0.0428575i | \(-0.0136462\pi\) | |||||||
\(6\) | 5.00000 | + | 8.66025i | 0.340207 | + | 0.589256i | ||||
\(7\) | 8.00000 | 0.431959 | 0.215980 | − | 0.976398i | \(-0.430705\pi\) | ||||
0.215980 | + | 0.976398i | \(0.430705\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.0370370 | + | 0.0641500i | ||||
\(10\) | 12.0000 | + | 20.7846i | 0.379473 | + | 0.657267i | ||||
\(11\) | 9.00000 | 0.246691 | 0.123346 | − | 0.992364i | \(-0.460638\pi\) | ||||
0.123346 | + | 0.992364i | \(0.460638\pi\) | |||||||
\(12\) | −20.0000 | −0.481125 | ||||||||
\(13\) | −13.0000 | − | 22.5167i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −8.00000 | + | 13.8564i | −0.152721 | + | 0.264520i | ||||
\(15\) | −30.0000 | − | 51.9615i | −0.516398 | − | 0.894427i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −57.0000 | + | 98.7269i | −0.813208 | + | 1.40852i | 0.0974001 | + | 0.995245i | \(0.468947\pi\) |
−0.910608 | + | 0.413272i | \(0.864386\pi\) | |||||||
\(18\) | −4.00000 | −0.0523783 | ||||||||
\(19\) | −66.5000 | − | 49.3634i | −0.802955 | − | 0.596040i | ||||
\(20\) | −48.0000 | −0.536656 | ||||||||
\(21\) | 20.0000 | − | 34.6410i | 0.207827 | − | 0.359966i | ||||
\(22\) | −9.00000 | + | 15.5885i | −0.0872185 | + | 0.151067i | ||||
\(23\) | 39.0000 | + | 67.5500i | 0.353568 | + | 0.612398i | 0.986872 | − | 0.161506i | \(-0.0516350\pi\) |
−0.633304 | + | 0.773903i | \(0.718302\pi\) | |||||||
\(24\) | 20.0000 | − | 34.6410i | 0.170103 | − | 0.294628i | ||||
\(25\) | −9.50000 | − | 16.4545i | −0.0760000 | − | 0.131636i | ||||
\(26\) | 52.0000 | 0.392232 | ||||||||
\(27\) | 145.000 | 1.03353 | ||||||||
\(28\) | −16.0000 | − | 27.7128i | −0.107990 | − | 0.187044i | ||||
\(29\) | 102.000 | + | 176.669i | 0.653135 | + | 1.13126i | 0.982358 | + | 0.187011i | \(0.0598801\pi\) |
−0.329222 | + | 0.944252i | \(0.606787\pi\) | |||||||
\(30\) | 120.000 | 0.730297 | ||||||||
\(31\) | 98.0000 | 0.567785 | 0.283892 | − | 0.958856i | \(-0.408374\pi\) | ||||
0.283892 | + | 0.958856i | \(0.408374\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 22.5000 | − | 38.9711i | 0.118689 | − | 0.205576i | ||||
\(34\) | −114.000 | − | 197.454i | −0.575025 | − | 0.995972i | ||||
\(35\) | 48.0000 | − | 83.1384i | 0.231814 | − | 0.401513i | ||||
\(36\) | 4.00000 | − | 6.92820i | 0.0185185 | − | 0.0320750i | ||||
\(37\) | −334.000 | −1.48403 | −0.742017 | − | 0.670381i | \(-0.766131\pi\) | ||||
−0.742017 | + | 0.670381i | \(0.766131\pi\) | |||||||
\(38\) | 152.000 | − | 65.8179i | 0.648886 | − | 0.280976i | ||||
\(39\) | −130.000 | −0.533761 | ||||||||
\(40\) | 48.0000 | − | 83.1384i | 0.189737 | − | 0.328634i | ||||
\(41\) | −88.5000 | + | 153.286i | −0.337107 | + | 0.583886i | −0.983887 | − | 0.178790i | \(-0.942782\pi\) |
0.646780 | + | 0.762676i | \(0.276115\pi\) | |||||||
\(42\) | 40.0000 | + | 69.2820i | 0.146956 | + | 0.254535i | ||||
\(43\) | 158.000 | − | 273.664i | 0.560344 | − | 0.970544i | −0.437123 | − | 0.899402i | \(-0.644002\pi\) |
0.997466 | − | 0.0711416i | \(-0.0226642\pi\) | |||||||
\(44\) | −18.0000 | − | 31.1769i | −0.0616728 | − | 0.106820i | ||||
\(45\) | 24.0000 | 0.0795046 | ||||||||
\(46\) | −156.000 | −0.500021 | ||||||||
\(47\) | 246.000 | + | 426.084i | 0.763464 | + | 1.32236i | 0.941055 | + | 0.338253i | \(0.109836\pi\) |
−0.177591 | + | 0.984104i | \(0.556831\pi\) | |||||||
\(48\) | 40.0000 | + | 69.2820i | 0.120281 | + | 0.208333i | ||||
\(49\) | −279.000 | −0.813411 | ||||||||
\(50\) | 38.0000 | 0.107480 | ||||||||
\(51\) | 285.000 | + | 493.634i | 0.782509 | + | 1.35535i | ||||
\(52\) | −52.0000 | + | 90.0666i | −0.138675 | + | 0.240192i | ||||
\(53\) | −339.000 | − | 587.165i | −0.878589 | − | 1.52176i | −0.852889 | − | 0.522092i | \(-0.825152\pi\) |
−0.0256998 | − | 0.999670i | \(-0.508181\pi\) | |||||||
\(54\) | −145.000 | + | 251.147i | −0.365407 | + | 0.632904i | ||||
\(55\) | 54.0000 | − | 93.5307i | 0.132388 | − | 0.229303i | ||||
\(56\) | 64.0000 | 0.152721 | ||||||||
\(57\) | −380.000 | + | 164.545i | −0.883022 | + | 0.382360i | ||||
\(58\) | −408.000 | −0.923673 | ||||||||
\(59\) | 289.500 | − | 501.429i | 0.638808 | − | 1.10645i | −0.346886 | − | 0.937907i | \(-0.612761\pi\) |
0.985695 | − | 0.168541i | \(-0.0539056\pi\) | |||||||
\(60\) | −120.000 | + | 207.846i | −0.258199 | + | 0.447214i | ||||
\(61\) | 176.000 | + | 304.841i | 0.369418 | + | 0.639851i | 0.989475 | − | 0.144706i | \(-0.0462238\pi\) |
−0.620057 | + | 0.784557i | \(0.712890\pi\) | |||||||
\(62\) | −98.0000 | + | 169.741i | −0.200742 | + | 0.347696i | ||||
\(63\) | 8.00000 | + | 13.8564i | 0.0159985 | + | 0.0277102i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −312.000 | −0.595367 | ||||||||
\(66\) | 45.0000 | + | 77.9423i | 0.0839260 | + | 0.145364i | ||||
\(67\) | −377.500 | − | 653.849i | −0.688343 | − | 1.19224i | −0.972374 | − | 0.233430i | \(-0.925005\pi\) |
0.284031 | − | 0.958815i | \(-0.408328\pi\) | |||||||
\(68\) | 456.000 | 0.813208 | ||||||||
\(69\) | 390.000 | 0.680442 | ||||||||
\(70\) | 96.0000 | + | 166.277i | 0.163917 | + | 0.283913i | ||||
\(71\) | −3.00000 | + | 5.19615i | −0.00501457 | + | 0.00868549i | −0.868522 | − | 0.495651i | \(-0.834930\pi\) |
0.863507 | + | 0.504336i | \(0.168263\pi\) | |||||||
\(72\) | 8.00000 | + | 13.8564i | 0.0130946 | + | 0.0226805i | ||||
\(73\) | 72.5000 | − | 125.574i | 0.116239 | − | 0.201333i | −0.802035 | − | 0.597277i | \(-0.796249\pi\) |
0.918275 | + | 0.395944i | \(0.129583\pi\) | |||||||
\(74\) | 334.000 | − | 578.505i | 0.524685 | − | 0.908782i | ||||
\(75\) | −95.0000 | −0.146262 | ||||||||
\(76\) | −38.0000 | + | 329.090i | −0.0573539 | + | 0.496700i | ||||
\(77\) | 72.0000 | 0.106561 | ||||||||
\(78\) | 130.000 | − | 225.167i | 0.188713 | − | 0.326860i | ||||
\(79\) | 158.000 | − | 273.664i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 96.0000 | + | 166.277i | 0.134164 | + | 0.232379i | ||||
\(81\) | 335.500 | − | 581.103i | 0.460219 | − | 0.797124i | ||||
\(82\) | −177.000 | − | 306.573i | −0.238370 | − | 0.412870i | ||||
\(83\) | −567.000 | −0.749835 | −0.374918 | − | 0.927058i | \(-0.622329\pi\) | ||||
−0.374918 | + | 0.927058i | \(0.622329\pi\) | |||||||
\(84\) | −160.000 | −0.207827 | ||||||||
\(85\) | 684.000 | + | 1184.72i | 0.872826 | + | 1.51178i | ||||
\(86\) | 316.000 | + | 547.328i | 0.396223 | + | 0.686278i | ||||
\(87\) | 1020.00 | 1.25696 | ||||||||
\(88\) | 72.0000 | 0.0872185 | ||||||||
\(89\) | 57.0000 | + | 98.7269i | 0.0678875 | + | 0.117585i | 0.897971 | − | 0.440054i | \(-0.145041\pi\) |
−0.830084 | + | 0.557639i | \(0.811707\pi\) | |||||||
\(90\) | −24.0000 | + | 41.5692i | −0.0281091 | + | 0.0486864i | ||||
\(91\) | −104.000 | − | 180.133i | −0.119804 | − | 0.207507i | ||||
\(92\) | 156.000 | − | 270.200i | 0.176784 | − | 0.306199i | ||||
\(93\) | 245.000 | − | 424.352i | 0.273175 | − | 0.473154i | ||||
\(94\) | −984.000 | −1.07970 | ||||||||
\(95\) | −912.000 | + | 394.908i | −0.984939 | + | 0.426491i | ||||
\(96\) | −160.000 | −0.170103 | ||||||||
\(97\) | 471.500 | − | 816.662i | 0.493542 | − | 0.854840i | −0.506430 | − | 0.862281i | \(-0.669035\pi\) |
0.999972 | + | 0.00744110i | \(0.00236860\pi\) | |||||||
\(98\) | 279.000 | − | 483.242i | 0.287584 | − | 0.498111i | ||||
\(99\) | 9.00000 | + | 15.5885i | 0.00913671 | + | 0.0158252i | ||||
\(100\) | −38.0000 | + | 65.8179i | −0.0380000 | + | 0.0658179i | ||||
\(101\) | 750.000 | + | 1299.04i | 0.738889 | + | 1.27979i | 0.952996 | + | 0.302983i | \(0.0979826\pi\) |
−0.214107 | + | 0.976810i | \(0.568684\pi\) | |||||||
\(102\) | −1140.00 | −1.10664 | ||||||||
\(103\) | −658.000 | −0.629463 | −0.314731 | − | 0.949181i | \(-0.601914\pi\) | ||||
−0.314731 | + | 0.949181i | \(0.601914\pi\) | |||||||
\(104\) | −104.000 | − | 180.133i | −0.0980581 | − | 0.169842i | ||||
\(105\) | −240.000 | − | 415.692i | −0.223063 | − | 0.386356i | ||||
\(106\) | 1356.00 | 1.24251 | ||||||||
\(107\) | −1440.00 | −1.30103 | −0.650514 | − | 0.759494i | \(-0.725447\pi\) | ||||
−0.650514 | + | 0.759494i | \(0.725447\pi\) | |||||||
\(108\) | −290.000 | − | 502.295i | −0.258382 | − | 0.447531i | ||||
\(109\) | −640.000 | + | 1108.51i | −0.562393 | + | 0.974094i | 0.434894 | + | 0.900482i | \(0.356786\pi\) |
−0.997287 | + | 0.0736121i | \(0.976547\pi\) | |||||||
\(110\) | 108.000 | + | 187.061i | 0.0936127 | + | 0.162142i | ||||
\(111\) | −835.000 | + | 1446.26i | −0.714006 | + | 1.23670i | ||||
\(112\) | −64.0000 | + | 110.851i | −0.0539949 | + | 0.0935220i | ||||
\(113\) | −369.000 | −0.307191 | −0.153596 | − | 0.988134i | \(-0.549085\pi\) | ||||
−0.153596 | + | 0.988134i | \(0.549085\pi\) | |||||||
\(114\) | 95.0000 | − | 822.724i | 0.0780488 | − | 0.675923i | ||||
\(115\) | 936.000 | 0.758978 | ||||||||
\(116\) | 408.000 | − | 706.677i | 0.326568 | − | 0.565632i | ||||
\(117\) | 26.0000 | − | 45.0333i | 0.0205445 | − | 0.0355840i | ||||
\(118\) | 579.000 | + | 1002.86i | 0.451706 | + | 0.782377i | ||||
\(119\) | −456.000 | + | 789.815i | −0.351273 | + | 0.608422i | ||||
\(120\) | −240.000 | − | 415.692i | −0.182574 | − | 0.316228i | ||||
\(121\) | −1250.00 | −0.939144 | ||||||||
\(122\) | −704.000 | −0.522436 | ||||||||
\(123\) | 442.500 | + | 766.432i | 0.324381 | + | 0.561845i | ||||
\(124\) | −196.000 | − | 339.482i | −0.141946 | − | 0.245858i | ||||
\(125\) | 1272.00 | 0.910169 | ||||||||
\(126\) | −32.0000 | −0.0226253 | ||||||||
\(127\) | −451.000 | − | 781.155i | −0.315116 | − | 0.545798i | 0.664346 | − | 0.747425i | \(-0.268710\pi\) |
−0.979462 | + | 0.201628i | \(0.935377\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −790.000 | − | 1368.32i | −0.539191 | − | 0.933906i | ||||
\(130\) | 312.000 | − | 540.400i | 0.210494 | − | 0.364586i | ||||
\(131\) | 226.500 | − | 392.310i | 0.151064 | − | 0.261651i | −0.780555 | − | 0.625087i | \(-0.785063\pi\) |
0.931619 | + | 0.363437i | \(0.118397\pi\) | |||||||
\(132\) | −180.000 | −0.118689 | ||||||||
\(133\) | −532.000 | − | 394.908i | −0.346844 | − | 0.257465i | ||||
\(134\) | 1510.00 | 0.973464 | ||||||||
\(135\) | 870.000 | − | 1506.88i | 0.554649 | − | 0.960681i | ||||
\(136\) | −456.000 | + | 789.815i | −0.287512 | + | 0.497986i | ||||
\(137\) | −1000.50 | − | 1732.92i | −0.623931 | − | 1.08068i | −0.988747 | − | 0.149600i | \(-0.952201\pi\) |
0.364816 | − | 0.931080i | \(-0.381132\pi\) | |||||||
\(138\) | −390.000 | + | 675.500i | −0.240572 | + | 0.416684i | ||||
\(139\) | 1467.50 | + | 2541.78i | 0.895480 | + | 1.55102i | 0.833209 | + | 0.552958i | \(0.186501\pi\) |
0.0622707 | + | 0.998059i | \(0.480166\pi\) | |||||||
\(140\) | −384.000 | −0.231814 | ||||||||
\(141\) | 2460.00 | 1.46929 | ||||||||
\(142\) | −6.00000 | − | 10.3923i | −0.00354584 | − | 0.00614157i | ||||
\(143\) | −117.000 | − | 202.650i | −0.0684198 | − | 0.118507i | ||||
\(144\) | −32.0000 | −0.0185185 | ||||||||
\(145\) | 2448.00 | 1.40204 | ||||||||
\(146\) | 145.000 | + | 251.147i | 0.0821937 | + | 0.142364i | ||||
\(147\) | −697.500 | + | 1208.11i | −0.391353 | + | 0.677843i | ||||
\(148\) | 668.000 | + | 1157.01i | 0.371009 | + | 0.642606i | ||||
\(149\) | −3.00000 | + | 5.19615i | −0.00164946 | + | 0.00285695i | −0.866849 | − | 0.498571i | \(-0.833858\pi\) |
0.865199 | + | 0.501428i | \(0.167192\pi\) | |||||||
\(150\) | 95.0000 | − | 164.545i | 0.0517115 | − | 0.0895669i | ||||
\(151\) | 2774.00 | 1.49500 | 0.747500 | − | 0.664262i | \(-0.231254\pi\) | ||||
0.747500 | + | 0.664262i | \(0.231254\pi\) | |||||||
\(152\) | −532.000 | − | 394.908i | −0.283887 | − | 0.210732i | ||||
\(153\) | −228.000 | −0.120475 | ||||||||
\(154\) | −72.0000 | + | 124.708i | −0.0376748 | + | 0.0652547i | ||||
\(155\) | 588.000 | − | 1018.45i | 0.304705 | − | 0.527765i | ||||
\(156\) | 260.000 | + | 450.333i | 0.133440 | + | 0.231125i | ||||
\(157\) | 1364.00 | − | 2362.52i | 0.693370 | − | 1.20095i | −0.277357 | − | 0.960767i | \(-0.589459\pi\) |
0.970727 | − | 0.240185i | \(-0.0772081\pi\) | |||||||
\(158\) | 316.000 | + | 547.328i | 0.159111 | + | 0.275589i | ||||
\(159\) | −3390.00 | −1.69085 | ||||||||
\(160\) | −384.000 | −0.189737 | ||||||||
\(161\) | 312.000 | + | 540.400i | 0.152727 | + | 0.264531i | ||||
\(162\) | 671.000 | + | 1162.21i | 0.325424 | + | 0.563651i | ||||
\(163\) | −1657.00 | −0.796235 | −0.398117 | − | 0.917334i | \(-0.630336\pi\) | ||||
−0.398117 | + | 0.917334i | \(0.630336\pi\) | |||||||
\(164\) | 708.000 | 0.337107 | ||||||||
\(165\) | −270.000 | − | 467.654i | −0.127391 | − | 0.220647i | ||||
\(166\) | 567.000 | − | 982.073i | 0.265107 | − | 0.459179i | ||||
\(167\) | −1392.00 | − | 2411.01i | −0.645007 | − | 1.11719i | −0.984300 | − | 0.176504i | \(-0.943521\pi\) |
0.339293 | − | 0.940681i | \(-0.389812\pi\) | |||||||
\(168\) | 160.000 | − | 277.128i | 0.0734778 | − | 0.127267i | ||||
\(169\) | 760.500 | − | 1317.22i | 0.346154 | − | 0.599556i | ||||
\(170\) | −2736.00 | −1.23436 | ||||||||
\(171\) | 19.0000 | − | 164.545i | 0.00849688 | − | 0.0735851i | ||||
\(172\) | −1264.00 | −0.560344 | ||||||||
\(173\) | −1191.00 | + | 2062.87i | −0.523411 | + | 0.906574i | 0.476218 | + | 0.879327i | \(0.342007\pi\) |
−0.999629 | + | 0.0272467i | \(0.991326\pi\) | |||||||
\(174\) | −1020.00 | + | 1766.69i | −0.444402 | + | 0.769727i | ||||
\(175\) | −76.0000 | − | 131.636i | −0.0328289 | − | 0.0568613i | ||||
\(176\) | −72.0000 | + | 124.708i | −0.0308364 | + | 0.0534102i | ||||
\(177\) | −1447.50 | − | 2507.14i | −0.614694 | − | 1.06468i | ||||
\(178\) | −228.000 | −0.0960074 | ||||||||
\(179\) | −3645.00 | −1.52201 | −0.761006 | − | 0.648745i | \(-0.775294\pi\) | ||||
−0.761006 | + | 0.648745i | \(0.775294\pi\) | |||||||
\(180\) | −48.0000 | − | 83.1384i | −0.0198762 | − | 0.0344265i | ||||
\(181\) | 953.000 | + | 1650.64i | 0.391359 | + | 0.677853i | 0.992629 | − | 0.121192i | \(-0.0386718\pi\) |
−0.601270 | + | 0.799046i | \(0.705338\pi\) | |||||||
\(182\) | 416.000 | 0.169428 | ||||||||
\(183\) | 1760.00 | 0.710945 | ||||||||
\(184\) | 312.000 | + | 540.400i | 0.125005 | + | 0.216515i | ||||
\(185\) | −2004.00 | + | 3471.03i | −0.796416 | + | 1.37943i | ||||
\(186\) | 490.000 | + | 848.705i | 0.193164 | + | 0.334570i | ||||
\(187\) | −513.000 | + | 888.542i | −0.200611 | + | 0.347469i | ||||
\(188\) | 984.000 | − | 1704.34i | 0.381732 | − | 0.661179i | ||||
\(189\) | 1160.00 | 0.446442 | ||||||||
\(190\) | 228.000 | − | 1974.54i | 0.0870572 | − | 0.753937i | ||||
\(191\) | 1332.00 | 0.504608 | 0.252304 | − | 0.967648i | \(-0.418812\pi\) | ||||
0.252304 | + | 0.967648i | \(0.418812\pi\) | |||||||
\(192\) | 160.000 | − | 277.128i | 0.0601407 | − | 0.104167i | ||||
\(193\) | −661.000 | + | 1144.89i | −0.246528 | + | 0.426998i | −0.962560 | − | 0.271069i | \(-0.912623\pi\) |
0.716032 | + | 0.698067i | \(0.245956\pi\) | |||||||
\(194\) | 943.000 | + | 1633.32i | 0.348987 | + | 0.604463i | ||||
\(195\) | −780.000 | + | 1351.00i | −0.286446 | + | 0.496139i | ||||
\(196\) | 558.000 | + | 966.484i | 0.203353 | + | 0.352217i | ||||
\(197\) | 3726.00 | 1.34755 | 0.673773 | − | 0.738939i | \(-0.264673\pi\) | ||||
0.673773 | + | 0.738939i | \(0.264673\pi\) | |||||||
\(198\) | −36.0000 | −0.0129213 | ||||||||
\(199\) | 239.000 | + | 413.960i | 0.0851370 | + | 0.147462i | 0.905450 | − | 0.424454i | \(-0.139534\pi\) |
−0.820313 | + | 0.571915i | \(0.806201\pi\) | |||||||
\(200\) | −76.0000 | − | 131.636i | −0.0268701 | − | 0.0465403i | ||||
\(201\) | −3775.00 | −1.32472 | ||||||||
\(202\) | −3000.00 | −1.04495 | ||||||||
\(203\) | 816.000 | + | 1413.35i | 0.282128 | + | 0.488660i | ||||
\(204\) | 1140.00 | − | 1974.54i | 0.391255 | − | 0.677673i | ||||
\(205\) | 1062.00 | + | 1839.44i | 0.361821 | + | 0.626692i | ||||
\(206\) | 658.000 | − | 1139.69i | 0.222549 | − | 0.385466i | ||||
\(207\) | −78.0000 | + | 135.100i | −0.0261902 | + | 0.0453628i | ||||
\(208\) | 416.000 | 0.138675 | ||||||||
\(209\) | −598.500 | − | 444.271i | −0.198082 | − | 0.147038i | ||||
\(210\) | 960.000 | 0.315459 | ||||||||
\(211\) | 410.000 | − | 710.141i | 0.133770 | − | 0.231697i | −0.791357 | − | 0.611355i | \(-0.790625\pi\) |
0.925127 | + | 0.379658i | \(0.123958\pi\) | |||||||
\(212\) | −1356.00 | + | 2348.66i | −0.439295 | + | 0.760881i | ||||
\(213\) | 15.0000 | + | 25.9808i | 0.00482527 | + | 0.00835762i | ||||
\(214\) | 1440.00 | − | 2494.15i | 0.459983 | − | 0.796714i | ||||
\(215\) | −1896.00 | − | 3283.97i | −0.601424 | − | 1.04170i | ||||
\(216\) | 1160.00 | 0.365407 | ||||||||
\(217\) | 784.000 | 0.245260 | ||||||||
\(218\) | −1280.00 | − | 2217.03i | −0.397672 | − | 0.688788i | ||||
\(219\) | −362.500 | − | 627.868i | −0.111852 | − | 0.193732i | ||||
\(220\) | −432.000 | −0.132388 | ||||||||
\(221\) | 2964.00 | 0.902173 | ||||||||
\(222\) | −1670.00 | − | 2892.52i | −0.504879 | − | 0.874475i | ||||
\(223\) | −463.000 | + | 801.940i | −0.139035 | + | 0.240815i | −0.927132 | − | 0.374736i | \(-0.877733\pi\) |
0.788097 | + | 0.615551i | \(0.211067\pi\) | |||||||
\(224\) | −128.000 | − | 221.703i | −0.0381802 | − | 0.0661300i | ||||
\(225\) | 19.0000 | − | 32.9090i | 0.00562963 | − | 0.00975080i | ||||
\(226\) | 369.000 | − | 639.127i | 0.108608 | − | 0.188115i | ||||
\(227\) | 4977.00 | 1.45522 | 0.727610 | − | 0.685991i | \(-0.240631\pi\) | ||||
0.727610 | + | 0.685991i | \(0.240631\pi\) | |||||||
\(228\) | 1330.00 | + | 987.269i | 0.386322 | + | 0.286770i | ||||
\(229\) | −4312.00 | −1.24430 | −0.622151 | − | 0.782898i | \(-0.713741\pi\) | ||||
−0.622151 | + | 0.782898i | \(0.713741\pi\) | |||||||
\(230\) | −936.000 | + | 1621.20i | −0.268339 | + | 0.464777i | ||||
\(231\) | 180.000 | − | 311.769i | 0.0512690 | − | 0.0888004i | ||||
\(232\) | 816.000 | + | 1413.35i | 0.230918 | + | 0.399962i | ||||
\(233\) | 910.500 | − | 1577.03i | 0.256004 | − | 0.443411i | −0.709164 | − | 0.705044i | \(-0.750927\pi\) |
0.965168 | + | 0.261632i | \(0.0842608\pi\) | |||||||
\(234\) | 52.0000 | + | 90.0666i | 0.0145271 | + | 0.0251617i | ||||
\(235\) | 5904.00 | 1.63887 | ||||||||
\(236\) | −2316.00 | −0.638808 | ||||||||
\(237\) | −790.000 | − | 1368.32i | −0.216523 | − | 0.375029i | ||||
\(238\) | −912.000 | − | 1579.63i | −0.248387 | − | 0.430219i | ||||
\(239\) | 324.000 | 0.0876896 | 0.0438448 | − | 0.999038i | \(-0.486039\pi\) | ||||
0.0438448 | + | 0.999038i | \(0.486039\pi\) | |||||||
\(240\) | 960.000 | 0.258199 | ||||||||
\(241\) | −170.500 | − | 295.315i | −0.0455721 | − | 0.0789332i | 0.842340 | − | 0.538947i | \(-0.181178\pi\) |
−0.887912 | + | 0.460014i | \(0.847844\pi\) | |||||||
\(242\) | 1250.00 | − | 2165.06i | 0.332037 | − | 0.575106i | ||||
\(243\) | 280.000 | + | 484.974i | 0.0739177 | + | 0.128029i | ||||
\(244\) | 704.000 | − | 1219.36i | 0.184709 | − | 0.319925i | ||||
\(245\) | −1674.00 | + | 2899.45i | −0.436522 | + | 0.756079i | ||||
\(246\) | −1770.00 | −0.458744 | ||||||||
\(247\) | −247.000 | + | 2139.08i | −0.0636285 | + | 0.551039i | ||||
\(248\) | 784.000 | 0.200742 | ||||||||
\(249\) | −1417.50 | + | 2455.18i | −0.360765 | + | 0.624863i | ||||
\(250\) | −1272.00 | + | 2203.17i | −0.321793 | + | 0.557362i | ||||
\(251\) | −2431.50 | − | 4211.48i | −0.611454 | − | 1.05907i | −0.990996 | − | 0.133895i | \(-0.957252\pi\) |
0.379542 | − | 0.925175i | \(-0.376082\pi\) | |||||||
\(252\) | 32.0000 | − | 55.4256i | 0.00799925 | − | 0.0138551i | ||||
\(253\) | 351.000 | + | 607.950i | 0.0872221 | + | 0.151073i | ||||
\(254\) | 1804.00 | 0.445642 | ||||||||
\(255\) | 6840.00 | 1.67975 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 1726.50 | + | 2990.39i | 0.419051 | + | 0.725818i | 0.995844 | − | 0.0910725i | \(-0.0290295\pi\) |
−0.576793 | + | 0.816890i | \(0.695696\pi\) | |||||||
\(258\) | 3160.00 | 0.762531 | ||||||||
\(259\) | −2672.00 | −0.641042 | ||||||||
\(260\) | 624.000 | + | 1080.80i | 0.148842 | + | 0.257801i | ||||
\(261\) | −204.000 | + | 353.338i | −0.0483804 | + | 0.0837973i | ||||
\(262\) | 453.000 | + | 784.619i | 0.106818 | + | 0.185015i | ||||
\(263\) | 60.0000 | − | 103.923i | 0.0140675 | − | 0.0243657i | −0.858906 | − | 0.512133i | \(-0.828855\pi\) |
0.872973 | + | 0.487768i | \(0.162189\pi\) | |||||||
\(264\) | 180.000 | − | 311.769i | 0.0419630 | − | 0.0726821i | ||||
\(265\) | −8136.00 | −1.88600 | ||||||||
\(266\) | 1216.00 | − | 526.543i | 0.280292 | − | 0.121370i | ||||
\(267\) | 570.000 | 0.130650 | ||||||||
\(268\) | −1510.00 | + | 2615.40i | −0.344171 | + | 0.596122i | ||||
\(269\) | 3534.00 | − | 6121.07i | 0.801010 | − | 1.38739i | −0.117941 | − | 0.993021i | \(-0.537629\pi\) |
0.918952 | − | 0.394370i | \(-0.129037\pi\) | |||||||
\(270\) | 1740.00 | + | 3013.77i | 0.392196 | + | 0.679304i | ||||
\(271\) | −694.000 | + | 1202.04i | −0.155563 | + | 0.269443i | −0.933264 | − | 0.359192i | \(-0.883052\pi\) |
0.777701 | + | 0.628634i | \(0.216386\pi\) | |||||||
\(272\) | −912.000 | − | 1579.63i | −0.203302 | − | 0.352129i | ||||
\(273\) | −1040.00 | −0.230563 | ||||||||
\(274\) | 4002.00 | 0.882371 | ||||||||
\(275\) | −85.5000 | − | 148.090i | −0.0187485 | − | 0.0324734i | ||||
\(276\) | −780.000 | − | 1351.00i | −0.170110 | − | 0.294640i | ||||
\(277\) | −5164.00 | −1.12013 | −0.560063 | − | 0.828450i | \(-0.689223\pi\) | ||||
−0.560063 | + | 0.828450i | \(0.689223\pi\) | |||||||
\(278\) | −5870.00 | −1.26640 | ||||||||
\(279\) | 98.0000 | + | 169.741i | 0.0210291 | + | 0.0364234i | ||||
\(280\) | 384.000 | − | 665.108i | 0.0819585 | − | 0.141956i | ||||
\(281\) | 322.500 | + | 558.586i | 0.0684653 | + | 0.118585i | 0.898226 | − | 0.439534i | \(-0.144856\pi\) |
−0.829761 | + | 0.558119i | \(0.811523\pi\) | |||||||
\(282\) | −2460.00 | + | 4260.84i | −0.519471 | + | 0.899750i | ||||
\(283\) | −3371.50 | + | 5839.61i | −0.708180 | + | 1.22660i | 0.257352 | + | 0.966318i | \(0.417150\pi\) |
−0.965532 | + | 0.260286i | \(0.916183\pi\) | |||||||
\(284\) | 24.0000 | 0.00501457 | ||||||||
\(285\) | −570.000 | + | 4936.34i | −0.118470 | + | 1.02598i | ||||
\(286\) | 468.000 | 0.0967602 | ||||||||
\(287\) | −708.000 | + | 1226.29i | −0.145616 | + | 0.252215i | ||||
\(288\) | 32.0000 | − | 55.4256i | 0.00654729 | − | 0.0113402i | ||||
\(289\) | −4041.50 | − | 7000.08i | −0.822613 | − | 1.42481i | ||||
\(290\) | −2448.00 | + | 4240.06i | −0.495695 | + | 0.858569i | ||||
\(291\) | −2357.50 | − | 4083.31i | −0.474911 | − | 0.822570i | ||||
\(292\) | −580.000 | −0.116239 | ||||||||
\(293\) | −252.000 | −0.0502457 | −0.0251229 | − | 0.999684i | \(-0.507998\pi\) | ||||
−0.0251229 | + | 0.999684i | \(0.507998\pi\) | |||||||
\(294\) | −1395.00 | − | 2416.21i | −0.276728 | − | 0.479307i | ||||
\(295\) | −3474.00 | − | 6017.14i | −0.685641 | − | 1.18757i | ||||
\(296\) | −2672.00 | −0.524685 | ||||||||
\(297\) | 1305.00 | 0.254962 | ||||||||
\(298\) | −6.00000 | − | 10.3923i | −0.00116634 | − | 0.00202017i | ||||
\(299\) | 1014.00 | − | 1756.30i | 0.196124 | − | 0.339697i | ||||
\(300\) | 190.000 | + | 329.090i | 0.0365655 | + | 0.0633333i | ||||
\(301\) | 1264.00 | − | 2189.31i | 0.242046 | − | 0.419235i | ||||
\(302\) | −2774.00 | + | 4804.71i | −0.528562 | + | 0.915496i | ||||
\(303\) | 7500.00 | 1.42199 | ||||||||
\(304\) | 1216.00 | − | 526.543i | 0.229416 | − | 0.0993399i | ||||
\(305\) | 4224.00 | 0.793002 | ||||||||
\(306\) | 228.000 | − | 394.908i | 0.0425944 | − | 0.0737757i | ||||
\(307\) | 3558.50 | − | 6163.50i | 0.661545 | − | 1.14583i | −0.318665 | − | 0.947868i | \(-0.603234\pi\) |
0.980210 | − | 0.197962i | \(-0.0634323\pi\) | |||||||
\(308\) | −144.000 | − | 249.415i | −0.0266401 | − | 0.0461421i | ||||
\(309\) | −1645.00 | + | 2849.22i | −0.302850 | + | 0.524552i | ||||
\(310\) | 1176.00 | + | 2036.89i | 0.215459 | + | 0.373186i | ||||
\(311\) | 4410.00 | 0.804078 | 0.402039 | − | 0.915623i | \(-0.368302\pi\) | ||||
0.402039 | + | 0.915623i | \(0.368302\pi\) | |||||||
\(312\) | −1040.00 | −0.188713 | ||||||||
\(313\) | −3362.50 | − | 5824.02i | −0.607220 | − | 1.05174i | −0.991696 | − | 0.128601i | \(-0.958951\pi\) |
0.384477 | − | 0.923135i | \(-0.374382\pi\) | |||||||
\(314\) | 2728.00 | + | 4725.03i | 0.490286 | + | 0.849201i | ||||
\(315\) | 192.000 | 0.0343428 | ||||||||
\(316\) | −1264.00 | −0.225018 | ||||||||
\(317\) | 2433.00 | + | 4214.08i | 0.431075 | + | 0.746644i | 0.996966 | − | 0.0778357i | \(-0.0248010\pi\) |
−0.565891 | + | 0.824480i | \(0.691468\pi\) | |||||||
\(318\) | 3390.00 | − | 5871.65i | 0.597804 | − | 1.03543i | ||||
\(319\) | 918.000 | + | 1590.02i | 0.161123 | + | 0.279073i | ||||
\(320\) | 384.000 | − | 665.108i | 0.0670820 | − | 0.116190i | ||||
\(321\) | −3600.00 | + | 6235.38i | −0.625958 | + | 1.08419i | ||||
\(322\) | −1248.00 | −0.215989 | ||||||||
\(323\) | 8664.00 | − | 3751.62i | 1.49250 | − | 0.646272i | ||||
\(324\) | −2684.00 | −0.460219 | ||||||||
\(325\) | −247.000 | + | 427.817i | −0.0421572 | + | 0.0730184i | ||||
\(326\) | 1657.00 | − | 2870.01i | 0.281511 | − | 0.487592i | ||||
\(327\) | 3200.00 | + | 5542.56i | 0.541163 | + | 0.937322i | ||||
\(328\) | −708.000 | + | 1226.29i | −0.119185 | + | 0.206435i | ||||
\(329\) | 1968.00 | + | 3408.68i | 0.329785 | + | 0.571205i | ||||
\(330\) | 1080.00 | 0.180158 | ||||||||
\(331\) | 2375.00 | 0.394386 | 0.197193 | − | 0.980365i | \(-0.436817\pi\) | ||||
0.197193 | + | 0.980365i | \(0.436817\pi\) | |||||||
\(332\) | 1134.00 | + | 1964.15i | 0.187459 | + | 0.324688i | ||||
\(333\) | −334.000 | − | 578.505i | −0.0549642 | − | 0.0952008i | ||||
\(334\) | 5568.00 | 0.912178 | ||||||||
\(335\) | −9060.00 | −1.47761 | ||||||||
\(336\) | 320.000 | + | 554.256i | 0.0519566 | + | 0.0899915i | ||||
\(337\) | 5166.50 | − | 8948.64i | 0.835125 | − | 1.44648i | −0.0588033 | − | 0.998270i | \(-0.518728\pi\) |
0.893928 | − | 0.448210i | \(-0.147938\pi\) | |||||||
\(338\) | 1521.00 | + | 2634.45i | 0.244768 | + | 0.423950i | ||||
\(339\) | −922.500 | + | 1597.82i | −0.147797 | + | 0.255993i | ||||
\(340\) | 2736.00 | − | 4738.89i | 0.436413 | − | 0.755890i | ||||
\(341\) | 882.000 | 0.140067 | ||||||||
\(342\) | 266.000 | + | 197.454i | 0.0420574 | + | 0.0312195i | ||||
\(343\) | −4976.00 | −0.783320 | ||||||||
\(344\) | 1264.00 | − | 2189.31i | 0.198111 | − | 0.343139i | ||||
\(345\) | 2340.00 | − | 4053.00i | 0.365163 | − | 0.632482i | ||||
\(346\) | −2382.00 | − | 4125.75i | −0.370107 | − | 0.641045i | ||||
\(347\) | −2554.50 | + | 4424.52i | −0.395195 | + | 0.684498i | −0.993126 | − | 0.117049i | \(-0.962656\pi\) |
0.597931 | + | 0.801548i | \(0.295990\pi\) | |||||||
\(348\) | −2040.00 | − | 3533.38i | −0.314240 | − | 0.544279i | ||||
\(349\) | −2044.00 | −0.313504 | −0.156752 | − | 0.987638i | \(-0.550102\pi\) | ||||
−0.156752 | + | 0.987638i | \(0.550102\pi\) | |||||||
\(350\) | 304.000 | 0.0464271 | ||||||||
\(351\) | −1885.00 | − | 3264.92i | −0.286649 | − | 0.496491i | ||||
\(352\) | −144.000 | − | 249.415i | −0.0218046 | − | 0.0377667i | ||||
\(353\) | −1701.00 | −0.256473 | −0.128237 | − | 0.991744i | \(-0.540932\pi\) | ||||
−0.128237 | + | 0.991744i | \(0.540932\pi\) | |||||||
\(354\) | 5790.00 | 0.869308 | ||||||||
\(355\) | 36.0000 | + | 62.3538i | 0.00538220 | + | 0.00932225i | ||||
\(356\) | 228.000 | − | 394.908i | 0.0339438 | − | 0.0587923i | ||||
\(357\) | 2280.00 | + | 3949.08i | 0.338012 | + | 0.585455i | ||||
\(358\) | 3645.00 | − | 6313.33i | 0.538112 | − | 0.932038i | ||||
\(359\) | −885.000 | + | 1532.86i | −0.130107 | + | 0.225352i | −0.923718 | − | 0.383074i | \(-0.874866\pi\) |
0.793610 | + | 0.608426i | \(0.208199\pi\) | |||||||
\(360\) | 192.000 | 0.0281091 | ||||||||
\(361\) | 1985.50 | + | 6565.34i | 0.289474 | + | 0.957186i | ||||
\(362\) | −3812.00 | −0.553465 | ||||||||
\(363\) | −3125.00 | + | 5412.66i | −0.451846 | + | 0.782620i | ||||
\(364\) | −416.000 | + | 720.533i | −0.0599020 | + | 0.103753i | ||||
\(365\) | −870.000 | − | 1506.88i | −0.124761 | − | 0.216093i | ||||
\(366\) | −1760.00 | + | 3048.41i | −0.251357 | + | 0.435363i | ||||
\(367\) | 5279.00 | + | 9143.50i | 0.750849 | + | 1.30051i | 0.947412 | + | 0.320017i | \(0.103689\pi\) |
−0.196563 | + | 0.980491i | \(0.562978\pi\) | |||||||
\(368\) | −1248.00 | −0.176784 | ||||||||
\(369\) | −354.000 | −0.0499417 | ||||||||
\(370\) | −4008.00 | − | 6942.06i | −0.563151 | − | 0.975407i | ||||
\(371\) | −2712.00 | − | 4697.32i | −0.379515 | − | 0.657339i | ||||
\(372\) | −1960.00 | −0.273175 | ||||||||
\(373\) | −124.000 | −0.0172131 | −0.00860654 | − | 0.999963i | \(-0.502740\pi\) | ||||
−0.00860654 | + | 0.999963i | \(0.502740\pi\) | |||||||
\(374\) | −1026.00 | − | 1777.08i | −0.141853 | − | 0.245697i | ||||
\(375\) | 3180.00 | − | 5507.92i | 0.437905 | − | 0.758474i | ||||
\(376\) | 1968.00 | + | 3408.68i | 0.269925 | + | 0.467524i | ||||
\(377\) | 2652.00 | − | 4593.40i | 0.362294 | − | 0.627512i | ||||
\(378\) | −1160.00 | + | 2009.18i | −0.157841 | + | 0.273389i | ||||
\(379\) | 44.0000 | 0.00596340 | 0.00298170 | − | 0.999996i | \(-0.499051\pi\) | ||||
0.00298170 | + | 0.999996i | \(0.499051\pi\) | |||||||
\(380\) | 3192.00 | + | 2369.45i | 0.430911 | + | 0.319868i | ||||
\(381\) | −4510.00 | −0.606442 | ||||||||
\(382\) | −1332.00 | + | 2307.09i | −0.178406 | + | 0.309008i | ||||
\(383\) | −4656.00 | + | 8064.43i | −0.621176 | + | 1.07591i | 0.368091 | + | 0.929790i | \(0.380012\pi\) |
−0.989267 | + | 0.146119i | \(0.953322\pi\) | |||||||
\(384\) | 320.000 | + | 554.256i | 0.0425259 | + | 0.0736570i | ||||
\(385\) | 432.000 | − | 748.246i | 0.0571864 | − | 0.0990497i | ||||
\(386\) | −1322.00 | − | 2289.77i | −0.174321 | − | 0.301933i | ||||
\(387\) | 632.000 | 0.0830139 | ||||||||
\(388\) | −3772.00 | −0.493542 | ||||||||
\(389\) | 5646.00 | + | 9779.16i | 0.735896 | + | 1.27461i | 0.954329 | + | 0.298757i | \(0.0965721\pi\) |
−0.218433 | + | 0.975852i | \(0.570095\pi\) | |||||||
\(390\) | −1560.00 | − | 2702.00i | −0.202548 | − | 0.350823i | ||||
\(391\) | −8892.00 | −1.15010 | ||||||||
\(392\) | −2232.00 | −0.287584 | ||||||||
\(393\) | −1132.50 | − | 1961.55i | −0.145361 | − | 0.251773i | ||||
\(394\) | −3726.00 | + | 6453.62i | −0.476429 | + | 0.825200i | ||||
\(395\) | −1896.00 | − | 3283.97i | −0.241514 | − | 0.418315i | ||||
\(396\) | 36.0000 | − | 62.3538i | 0.00456835 | − | 0.00791262i | ||||
\(397\) | 167.000 | − | 289.252i | 0.0211121 | − | 0.0365672i | −0.855276 | − | 0.518172i | \(-0.826613\pi\) |
0.876388 | + | 0.481605i | \(0.159946\pi\) | |||||||
\(398\) | −956.000 | −0.120402 | ||||||||
\(399\) | −3040.00 | + | 1316.36i | −0.381429 | + | 0.165164i | ||||
\(400\) | 304.000 | 0.0380000 | ||||||||
\(401\) | −2806.50 | + | 4861.00i | −0.349501 | + | 0.605354i | −0.986161 | − | 0.165791i | \(-0.946982\pi\) |
0.636660 | + | 0.771145i | \(0.280316\pi\) | |||||||
\(402\) | 3775.00 | − | 6538.49i | 0.468358 | − | 0.811220i | ||||
\(403\) | −1274.00 | − | 2206.63i | −0.157475 | − | 0.272755i | ||||
\(404\) | 3000.00 | − | 5196.15i | 0.369445 | − | 0.639897i | ||||
\(405\) | −4026.00 | − | 6973.24i | −0.493959 | − | 0.855563i | ||||
\(406\) | −3264.00 | −0.398989 | ||||||||
\(407\) | −3006.00 | −0.366098 | ||||||||
\(408\) | 2280.00 | + | 3949.08i | 0.276659 | + | 0.479187i | ||||
\(409\) | 1677.50 | + | 2905.52i | 0.202804 | + | 0.351268i | 0.949431 | − | 0.313976i | \(-0.101661\pi\) |
−0.746627 | + | 0.665243i | \(0.768328\pi\) | |||||||
\(410\) | −4248.00 | −0.511692 | ||||||||
\(411\) | −10005.0 | −1.20075 | ||||||||
\(412\) | 1316.00 | + | 2279.38i | 0.157366 | + | 0.272565i | ||||
\(413\) | 2316.00 | − | 4011.43i | 0.275939 | − | 0.477941i | ||||
\(414\) | −156.000 | − | 270.200i | −0.0185193 | − | 0.0320763i | ||||
\(415\) | −3402.00 | + | 5892.44i | −0.402404 | + | 0.696984i | ||||
\(416\) | −416.000 | + | 720.533i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 14675.0 | 1.72335 | ||||||||
\(418\) | 1368.00 | − | 592.361i | 0.160074 | − | 0.0693142i | ||||
\(419\) | 5796.00 | 0.675783 | 0.337892 | − | 0.941185i | \(-0.390286\pi\) | ||||
0.337892 | + | 0.941185i | \(0.390286\pi\) | |||||||
\(420\) | −960.000 | + | 1662.77i | −0.111531 | + | 0.193178i | ||||
\(421\) | −325.000 | + | 562.917i | −0.0376236 | + | 0.0651660i | −0.884224 | − | 0.467063i | \(-0.845312\pi\) |
0.846600 | + | 0.532229i | \(0.178645\pi\) | |||||||
\(422\) | 820.000 | + | 1420.28i | 0.0945900 | + | 0.163835i | ||||
\(423\) | −492.000 | + | 852.169i | −0.0565529 | + | 0.0979524i | ||||
\(424\) | −2712.00 | − | 4697.32i | −0.310628 | − | 0.538024i | ||||
\(425\) | 2166.00 | 0.247215 | ||||||||
\(426\) | −60.0000 | −0.00682397 | ||||||||
\(427\) | 1408.00 | + | 2438.73i | 0.159574 | + | 0.276389i | ||||
\(428\) | 2880.00 | + | 4988.31i | 0.325257 | + | 0.563362i | ||||
\(429\) | −1170.00 | −0.131674 | ||||||||
\(430\) | 7584.00 | 0.850542 | ||||||||
\(431\) | −2103.00 | − | 3642.50i | −0.235030 | − | 0.407084i | 0.724251 | − | 0.689536i | \(-0.242186\pi\) |
−0.959281 | + | 0.282452i | \(0.908852\pi\) | |||||||
\(432\) | −1160.00 | + | 2009.18i | −0.129191 | + | 0.223765i | ||||
\(433\) | 6539.00 | + | 11325.9i | 0.725737 | + | 1.25701i | 0.958670 | + | 0.284521i | \(0.0918346\pi\) |
−0.232932 | + | 0.972493i | \(0.574832\pi\) | |||||||
\(434\) | −784.000 | + | 1357.93i | −0.0867125 | + | 0.150190i | ||||
\(435\) | 6120.00 | − | 10600.2i | 0.674555 | − | 1.16836i | ||||
\(436\) | 5120.00 | 0.562393 | ||||||||
\(437\) | 741.000 | − | 6417.25i | 0.0811140 | − | 0.702468i | ||||
\(438\) | 1450.00 | 0.158182 | ||||||||
\(439\) | 1301.00 | − | 2253.40i | 0.141443 | − | 0.244986i | −0.786597 | − | 0.617466i | \(-0.788159\pi\) |
0.928040 | + | 0.372480i | \(0.121493\pi\) | |||||||
\(440\) | 432.000 | − | 748.246i | 0.0468063 | − | 0.0810710i | ||||
\(441\) | −279.000 | − | 483.242i | −0.0301263 | − | 0.0521803i | ||||
\(442\) | −2964.00 | + | 5133.80i | −0.318966 | + | 0.552466i | ||||
\(443\) | −3961.50 | − | 6861.52i | −0.424868 | − | 0.735893i | 0.571540 | − | 0.820574i | \(-0.306346\pi\) |
−0.996408 | + | 0.0846811i | \(0.973013\pi\) | |||||||
\(444\) | 6680.00 | 0.714006 | ||||||||
\(445\) | 1368.00 | 0.145729 | ||||||||
\(446\) | −926.000 | − | 1603.88i | −0.0983125 | − | 0.170282i | ||||
\(447\) | 15.0000 | + | 25.9808i | 0.00158719 | + | 0.00274910i | ||||
\(448\) | 512.000 | 0.0539949 | ||||||||
\(449\) | 2529.00 | 0.265815 | 0.132907 | − | 0.991128i | \(-0.457569\pi\) | ||||
0.132907 | + | 0.991128i | \(0.457569\pi\) | |||||||
\(450\) | 38.0000 | + | 65.8179i | 0.00398075 | + | 0.00689486i | ||||
\(451\) | −796.500 | + | 1379.58i | −0.0831612 | + | 0.144039i | ||||
\(452\) | 738.000 | + | 1278.25i | 0.0767978 | + | 0.133018i | ||||
\(453\) | 6935.00 | − | 12011.8i | 0.719282 | − | 1.24583i | ||||
\(454\) | −4977.00 | + | 8620.42i | −0.514498 | + | 0.891137i | ||||
\(455\) | −2496.00 | −0.257174 | ||||||||
\(456\) | −3040.00 | + | 1316.36i | −0.312195 | + | 0.135185i | ||||
\(457\) | 7037.00 | 0.720300 | 0.360150 | − | 0.932894i | \(-0.382726\pi\) | ||||
0.360150 | + | 0.932894i | \(0.382726\pi\) | |||||||
\(458\) | 4312.00 | − | 7468.60i | 0.439927 | − | 0.761976i | ||||
\(459\) | −8265.00 | + | 14315.4i | −0.840473 | + | 1.45574i | ||||
\(460\) | −1872.00 | − | 3242.40i | −0.189744 | − | 0.328647i | ||||
\(461\) | 5865.00 | − | 10158.5i | 0.592539 | − | 1.02631i | −0.401351 | − | 0.915924i | \(-0.631459\pi\) |
0.993889 | − | 0.110382i | \(-0.0352076\pi\) | |||||||
\(462\) | 360.000 | + | 623.538i | 0.0362526 | + | 0.0627914i | ||||
\(463\) | 11762.0 | 1.18062 | 0.590309 | − | 0.807177i | \(-0.299006\pi\) | ||||
0.590309 | + | 0.807177i | \(0.299006\pi\) | |||||||
\(464\) | −3264.00 | −0.326568 | ||||||||
\(465\) | −2940.00 | − | 5092.23i | −0.293203 | − | 0.507842i | ||||
\(466\) | 1821.00 | + | 3154.06i | 0.181022 | + | 0.313539i | ||||
\(467\) | −3465.00 | −0.343343 | −0.171671 | − | 0.985154i | \(-0.554917\pi\) | ||||
−0.171671 | + | 0.985154i | \(0.554917\pi\) | |||||||
\(468\) | −208.000 | −0.0205445 | ||||||||
\(469\) | −3020.00 | − | 5230.79i | −0.297336 | − | 0.515001i | ||||
\(470\) | −5904.00 | + | 10226.0i | −0.579428 | + | 1.00360i | ||||
\(471\) | −6820.00 | − | 11812.6i | −0.667195 | − | 1.15562i | ||||
\(472\) | 2316.00 | − | 4011.43i | 0.225853 | − | 0.391189i | ||||
\(473\) | 1422.00 | − | 2462.98i | 0.138232 | − | 0.239424i | ||||
\(474\) | 3160.00 | 0.306210 | ||||||||
\(475\) | −180.500 | + | 1563.18i | −0.0174356 | + | 0.150997i | ||||
\(476\) | 3648.00 | 0.351273 | ||||||||
\(477\) | 678.000 | − | 1174.33i | 0.0650807 | − | 0.112723i | ||||
\(478\) | −324.000 | + | 561.184i | −0.0310030 | + | 0.0536987i | ||||
\(479\) | 2010.00 | + | 3481.42i | 0.191731 | + | 0.332088i | 0.945824 | − | 0.324680i | \(-0.105256\pi\) |
−0.754093 | + | 0.656768i | \(0.771923\pi\) | |||||||
\(480\) | −960.000 | + | 1662.77i | −0.0912871 | + | 0.158114i | ||||
\(481\) | 4342.00 | + | 7520.56i | 0.411597 | + | 0.712907i | ||||
\(482\) | 682.000 | 0.0644486 | ||||||||
\(483\) | 3120.00 | 0.293923 | ||||||||
\(484\) | 2500.00 | + | 4330.13i | 0.234786 | + | 0.406661i | ||||
\(485\) | −5658.00 | − | 9799.94i | −0.529725 | − | 0.917510i | ||||
\(486\) | −1120.00 | −0.104535 | ||||||||
\(487\) | 18146.0 | 1.68845 | 0.844224 | − | 0.535991i | \(-0.180062\pi\) | ||||
0.844224 | + | 0.535991i | \(0.180062\pi\) | |||||||
\(488\) | 1408.00 | + | 2438.73i | 0.130609 | + | 0.226221i | ||||
\(489\) | −4142.50 | + | 7175.02i | −0.383089 | + | 0.663529i | ||||
\(490\) | −3348.00 | − | 5798.91i | −0.308668 | − | 0.534628i | ||||
\(491\) | −9264.00 | + | 16045.7i | −0.851484 | + | 1.47481i | 0.0283856 | + | 0.999597i | \(0.490963\pi\) |
−0.879869 | + | 0.475216i | \(0.842370\pi\) | |||||||
\(492\) | 1770.00 | − | 3065.73i | 0.162191 | − | 0.280922i | ||||
\(493\) | −23256.0 | −2.12454 | ||||||||
\(494\) | −3458.00 | − | 2566.90i | −0.314945 | − | 0.233786i | ||||
\(495\) | 216.000 | 0.0196131 | ||||||||
\(496\) | −784.000 | + | 1357.93i | −0.0709731 | + | 0.122929i | ||||
\(497\) | −24.0000 | + | 41.5692i | −0.00216609 | + | 0.00375178i | ||||
\(498\) | −2835.00 | − | 4910.36i | −0.255099 | − | 0.441845i | ||||
\(499\) | 8001.50 | − | 13859.0i | 0.717828 | − | 1.24332i | −0.244030 | − | 0.969768i | \(-0.578470\pi\) |
0.961858 | − | 0.273547i | \(-0.0881971\pi\) | |||||||
\(500\) | −2544.00 | − | 4406.34i | −0.227542 | − | 0.394115i | ||||
\(501\) | −13920.0 | −1.24132 | ||||||||
\(502\) | 9726.00 | 0.864726 | ||||||||
\(503\) | −6999.00 | − | 12122.6i | −0.620417 | − | 1.07459i | −0.989408 | − | 0.145161i | \(-0.953630\pi\) |
0.368991 | − | 0.929433i | \(-0.379703\pi\) | |||||||
\(504\) | 64.0000 | + | 110.851i | 0.00565632 | + | 0.00979704i | ||||
\(505\) | 18000.0 | 1.58612 | ||||||||
\(506\) | −1404.00 | −0.123351 | ||||||||
\(507\) | −3802.50 | − | 6586.12i | −0.333087 | − | 0.576923i | ||||
\(508\) | −1804.00 | + | 3124.62i | −0.157558 | + | 0.272899i | ||||
\(509\) | 5664.00 | + | 9810.34i | 0.493227 | + | 0.854294i | 0.999970 | − | 0.00780356i | \(-0.00248398\pi\) |
−0.506743 | + | 0.862097i | \(0.669151\pi\) | |||||||
\(510\) | −6840.00 | + | 11847.2i | −0.593883 | + | 1.02864i | ||||
\(511\) | 580.000 | − | 1004.59i | 0.0502107 | − | 0.0869676i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −9642.50 | − | 7157.70i | −0.829877 | − | 0.616024i | ||||
\(514\) | −6906.00 | −0.592628 | ||||||||
\(515\) | −3948.00 | + | 6838.14i | −0.337805 | + | 0.585096i | ||||
\(516\) | −3160.00 | + | 5473.28i | −0.269595 | + | 0.466953i | ||||
\(517\) | 2214.00 | + | 3834.76i | 0.188340 | + | 0.326214i | ||||
\(518\) | 2672.00 | − | 4628.04i | 0.226643 | − | 0.392557i | ||||
\(519\) | 5955.00 | + | 10314.4i | 0.503652 | + | 0.872351i | ||||
\(520\) | −2496.00 | −0.210494 | ||||||||
\(521\) | −1575.00 | −0.132441 | −0.0662207 | − | 0.997805i | \(-0.521094\pi\) | ||||
−0.0662207 | + | 0.997805i | \(0.521094\pi\) | |||||||
\(522\) | −408.000 | − | 706.677i | −0.0342101 | − | 0.0592536i | ||||
\(523\) | 10634.0 | + | 18418.6i | 0.889087 | + | 1.53994i | 0.840957 | + | 0.541102i | \(0.181993\pi\) |
0.0481299 | + | 0.998841i | \(0.484674\pi\) | |||||||
\(524\) | −1812.00 | −0.151064 | ||||||||
\(525\) | −760.000 | −0.0631793 | ||||||||
\(526\) | 120.000 | + | 207.846i | 0.00994724 | + | 0.0172291i | ||||
\(527\) | −5586.00 | + | 9675.24i | −0.461727 | + | 0.799734i | ||||
\(528\) | 360.000 | + | 623.538i | 0.0296723 | + | 0.0513940i | ||||
\(529\) | 3041.50 | − | 5268.03i | 0.249979 | − | 0.432977i | ||||
\(530\) | 8136.00 | − | 14092.0i | 0.666802 | − | 1.15494i | ||||
\(531\) | 1158.00 | 0.0946383 | ||||||||
\(532\) | −304.000 | + | 2632.72i | −0.0247746 | + | 0.214554i | ||||
\(533\) | 4602.00 | 0.373986 | ||||||||
\(534\) | −570.000 | + | 987.269i | −0.0461916 | + | 0.0800062i | ||||
\(535\) | −8640.00 | + | 14964.9i | −0.698205 | + | 1.20933i | ||||
\(536\) | −3020.00 | − | 5230.79i | −0.243366 | − | 0.421522i | ||||
\(537\) | −9112.50 | + | 15783.3i | −0.732278 | + | 1.26834i | ||||
\(538\) | 7068.00 | + | 12242.1i | 0.566400 | + | 0.981033i | ||||
\(539\) | −2511.00 | −0.200661 | ||||||||
\(540\) | −6960.00 | −0.554649 | ||||||||
\(541\) | −3874.00 | − | 6709.96i | −0.307867 | − | 0.533242i | 0.670028 | − | 0.742336i | \(-0.266282\pi\) |
−0.977896 | + | 0.209094i | \(0.932949\pi\) | |||||||
\(542\) | −1388.00 | − | 2404.09i | −0.109999 | − | 0.190525i | ||||
\(543\) | 9530.00 | 0.753170 | ||||||||
\(544\) | 3648.00 | 0.287512 | ||||||||
\(545\) | 7680.00 | + | 13302.2i | 0.603624 | + | 1.04551i | ||||
\(546\) | 1040.00 | − | 1801.33i | 0.0815163 | − | 0.141190i | ||||
\(547\) | −6898.00 | − | 11947.7i | −0.539190 | − | 0.933905i | −0.998948 | − | 0.0458607i | \(-0.985397\pi\) |
0.459757 | − | 0.888045i | \(-0.347936\pi\) | |||||||
\(548\) | −4002.00 | + | 6931.67i | −0.311965 | + | 0.540340i | ||||
\(549\) | −352.000 | + | 609.682i | −0.0273643 | + | 0.0473963i | ||||
\(550\) | 342.000 | 0.0265144 | ||||||||
\(551\) | 1938.00 | − | 16783.6i | 0.149840 | − | 1.29765i | ||||
\(552\) | 3120.00 | 0.240572 | ||||||||
\(553\) | 1264.00 | − | 2189.31i | 0.0971985 | − | 0.168353i | ||||
\(554\) | 5164.00 | − | 8944.31i | 0.396024 | − | 0.685934i | ||||
\(555\) | 10020.0 | + | 17355.1i | 0.766352 | + | 1.32736i | ||||
\(556\) | 5870.00 | − | 10167.1i | 0.447740 | − | 0.775508i | ||||
\(557\) | −7836.00 | − | 13572.4i | −0.596090 | − | 1.03246i | −0.993392 | − | 0.114770i | \(-0.963387\pi\) |
0.397302 | − | 0.917688i | \(-0.369946\pi\) | |||||||
\(558\) | −392.000 | −0.0297396 | ||||||||
\(559\) | −8216.00 | −0.621645 | ||||||||
\(560\) | 768.000 | + | 1330.22i | 0.0579534 | + | 0.100378i | ||||
\(561\) | 2565.00 | + | 4442.71i | 0.193038 | + | 0.334352i | ||||
\(562\) | −1290.00 | −0.0968245 | ||||||||
\(563\) | −12663.0 | −0.947925 | −0.473963 | − | 0.880545i | \(-0.657177\pi\) | ||||
−0.473963 | + | 0.880545i | \(0.657177\pi\) | |||||||
\(564\) | −4920.00 | − | 8521.69i | −0.367322 | − | 0.636220i | ||||
\(565\) | −2214.00 | + | 3834.76i | −0.164856 | + | 0.285539i | ||||
\(566\) | −6743.00 | − | 11679.2i | −0.500759 | − | 0.867340i | ||||
\(567\) | 2684.00 | − | 4648.82i | 0.198796 | − | 0.344325i | ||||
\(568\) | −24.0000 | + | 41.5692i | −0.00177292 | + | 0.00307078i | ||||
\(569\) | −14670.0 | −1.08084 | −0.540420 | − | 0.841395i | \(-0.681735\pi\) | ||||
−0.540420 | + | 0.841395i | \(0.681735\pi\) | |||||||
\(570\) | −7980.00 | − | 5923.61i | −0.586395 | − | 0.435286i | ||||
\(571\) | 4643.00 | 0.340286 | 0.170143 | − | 0.985419i | \(-0.445577\pi\) | ||||
0.170143 | + | 0.985419i | \(0.445577\pi\) | |||||||
\(572\) | −468.000 | + | 810.600i | −0.0342099 | + | 0.0592533i | ||||
\(573\) | 3330.00 | − | 5767.73i | 0.242780 | − | 0.420507i | ||||
\(574\) | −1416.00 | − | 2452.58i | −0.102966 | − | 0.178343i | ||||
\(575\) | 741.000 | − | 1283.45i | 0.0537423 | − | 0.0930844i | ||||
\(576\) | 64.0000 | + | 110.851i | 0.00462963 | + | 0.00801875i | ||||
\(577\) | −18277.0 | −1.31869 | −0.659343 | − | 0.751843i | \(-0.729165\pi\) | ||||
−0.659343 | + | 0.751843i | \(0.729165\pi\) | |||||||
\(578\) | 16166.0 | 1.16335 | ||||||||
\(579\) | 3305.00 | + | 5724.43i | 0.237221 | + | 0.410879i | ||||
\(580\) | −4896.00 | − | 8480.12i | −0.350509 | − | 0.607100i | ||||
\(581\) | −4536.00 | −0.323898 | ||||||||
\(582\) | 9430.00 | 0.671626 | ||||||||
\(583\) | −3051.00 | − | 5284.49i | −0.216740 | − | 0.375405i | ||||
\(584\) | 580.000 | − | 1004.59i | 0.0410969 | − | 0.0711819i | ||||
\(585\) | −312.000 | − | 540.400i | −0.0220506 | − | 0.0381928i | ||||
\(586\) | 252.000 | − | 436.477i | 0.0177645 | − | 0.0307691i | ||||
\(587\) | 6306.00 | − | 10922.3i | 0.443401 | − | 0.767993i | −0.554538 | − | 0.832158i | \(-0.687105\pi\) |
0.997939 | + | 0.0641650i | \(0.0204384\pi\) | |||||||
\(588\) | 5580.00 | 0.391353 | ||||||||
\(589\) | −6517.00 | − | 4837.62i | −0.455905 | − | 0.338422i | ||||
\(590\) | 13896.0 | 0.969643 | ||||||||
\(591\) | 9315.00 | − | 16134.1i | 0.648338 | − | 1.12295i | ||||
\(592\) | 2672.00 | − | 4628.04i | 0.185504 | − | 0.321303i | ||||
\(593\) | 11554.5 | + | 20013.0i | 0.800146 | + | 1.38589i | 0.919520 | + | 0.393044i | \(0.128578\pi\) |
−0.119374 | + | 0.992849i | \(0.538089\pi\) | |||||||
\(594\) | −1305.00 | + | 2260.33i | −0.0901428 | + | 0.156132i | ||||
\(595\) | 5472.00 | + | 9477.78i | 0.377025 | + | 0.653027i | ||||
\(596\) | 24.0000 | 0.00164946 | ||||||||
\(597\) | 2390.00 | 0.163846 | ||||||||
\(598\) | 2028.00 | + | 3512.60i | 0.138681 | + | 0.240202i | ||||
\(599\) | 39.0000 | + | 67.5500i | 0.00266026 | + | 0.00460771i | 0.867352 | − | 0.497694i | \(-0.165820\pi\) |
−0.864692 | + | 0.502302i | \(0.832487\pi\) | |||||||
\(600\) | −760.000 | −0.0517115 | ||||||||
\(601\) | 21707.0 | 1.47329 | 0.736645 | − | 0.676280i | \(-0.236409\pi\) | ||||
0.736645 | + | 0.676280i | \(0.236409\pi\) | |||||||
\(602\) | 2528.00 | + | 4378.62i | 0.171152 | + | 0.296444i | ||||
\(603\) | 755.000 | − | 1307.70i | 0.0509884 | − | 0.0883144i | ||||
\(604\) | −5548.00 | − | 9609.42i | −0.373750 | − | 0.647354i | ||||
\(605\) | −7500.00 | + | 12990.4i | −0.503997 | + | 0.872949i | ||||
\(606\) | −7500.00 | + | 12990.4i | −0.502750 | + | 0.870789i | ||||
\(607\) | 728.000 | 0.0486798 | 0.0243399 | − | 0.999704i | \(-0.492252\pi\) | ||||
0.0243399 | + | 0.999704i | \(0.492252\pi\) | |||||||
\(608\) | −304.000 | + | 2632.72i | −0.0202777 | + | 0.175610i | ||||
\(609\) | 8160.00 | 0.542955 | ||||||||
\(610\) | −4224.00 | + | 7316.18i | −0.280368 | + | 0.485612i | ||||
\(611\) | 6396.00 | − | 11078.2i | 0.423493 | − | 0.733512i | ||||
\(612\) | 456.000 | + | 789.815i | 0.0301188 | + | 0.0521673i | ||||
\(613\) | −4609.00 | + | 7983.02i | −0.303680 | + | 0.525989i | −0.976967 | − | 0.213393i | \(-0.931549\pi\) |
0.673287 | + | 0.739382i | \(0.264882\pi\) | |||||||
\(614\) | 7117.00 | + | 12327.0i | 0.467783 | + | 0.810224i | ||||
\(615\) | 10620.0 | 0.696325 | ||||||||
\(616\) | 576.000 | 0.0376748 | ||||||||
\(617\) | 13930.5 | + | 24128.3i | 0.908948 | + | 1.57434i | 0.815528 | + | 0.578717i | \(0.196446\pi\) |
0.0934194 | + | 0.995627i | \(0.470220\pi\) | |||||||
\(618\) | −3290.00 | − | 5698.45i | −0.214148 | − | 0.370915i | ||||
\(619\) | 23156.0 | 1.50358 | 0.751792 | − | 0.659401i | \(-0.229190\pi\) | ||||
0.751792 | + | 0.659401i | \(0.229190\pi\) | |||||||
\(620\) | −4704.00 | −0.304705 | ||||||||
\(621\) | 5655.00 | + | 9794.75i | 0.365422 | + | 0.632930i | ||||
\(622\) | −4410.00 | + | 7638.34i | −0.284284 | + | 0.492395i | ||||
\(623\) | 456.000 | + | 789.815i | 0.0293246 | + | 0.0507918i | ||||
\(624\) | 1040.00 | − | 1801.33i | 0.0667201 | − | 0.115563i | ||||
\(625\) | 8819.50 | − | 15275.8i | 0.564448 | − | 0.977653i | ||||
\(626\) | 13450.0 | 0.858738 | ||||||||
\(627\) | −3420.00 | + | 1480.90i | −0.217834 | + | 0.0943247i | ||||
\(628\) | −10912.0 | −0.693370 | ||||||||
\(629\) | 19038.0 | − | 32974.8i | 1.20683 | − | 2.09029i | ||||
\(630\) | −192.000 | + | 332.554i | −0.0121420 | + | 0.0210306i | ||||
\(631\) | −12568.0 | − | 21768.4i | −0.792907 | − | 1.37335i | −0.924160 | − | 0.382006i | \(-0.875233\pi\) |
0.131253 | − | 0.991349i | \(-0.458100\pi\) | |||||||
\(632\) | 1264.00 | − | 2189.31i | 0.0795557 | − | 0.137795i | ||||
\(633\) | −2050.00 | − | 3550.70i | −0.128721 | − | 0.222951i | ||||
\(634\) | −9732.00 | −0.609633 | ||||||||
\(635\) | −10824.0 | −0.676437 | ||||||||
\(636\) | 6780.00 | + | 11743.3i | 0.422711 | + | 0.732158i | ||||
\(637\) | 3627.00 | + | 6282.15i | 0.225600 | + | 0.390750i | ||||
\(638\) | −3672.00 | −0.227862 | ||||||||
\(639\) | −12.0000 | −0.000742899 | ||||||||
\(640\) | 768.000 | + | 1330.22i | 0.0474342 | + | 0.0821584i | ||||
\(641\) | −5200.50 | + | 9007.53i | −0.320448 | + | 0.555033i | −0.980581 | − | 0.196117i | \(-0.937167\pi\) |
0.660132 | + | 0.751149i | \(0.270500\pi\) | |||||||
\(642\) | −7200.00 | − | 12470.8i | −0.442619 | − | 0.766638i | ||||
\(643\) | 5868.50 | − | 10164.5i | 0.359924 | − | 0.623406i | −0.628024 | − | 0.778194i | \(-0.716136\pi\) |
0.987948 | + | 0.154788i | \(0.0494693\pi\) | |||||||
\(644\) | 1248.00 | − | 2161.60i | 0.0763635 | − | 0.132265i | ||||
\(645\) | −18960.0 | −1.15744 | ||||||||
\(646\) | −2166.00 | + | 18758.1i | −0.131920 | + | 1.14246i | ||||
\(647\) | −23058.0 | −1.40109 | −0.700544 | − | 0.713610i | \(-0.747059\pi\) | ||||
−0.700544 | + | 0.713610i | \(0.747059\pi\) | |||||||
\(648\) | 2684.00 | − | 4648.82i | 0.162712 | − | 0.281826i | ||||
\(649\) | 2605.50 | − | 4512.86i | 0.157588 | − | 0.272951i | ||||
\(650\) | −494.000 | − | 855.633i | −0.0298097 | − | 0.0516318i | ||||
\(651\) | 1960.00 | − | 3394.82i | 0.118001 | − | 0.204383i | ||||
\(652\) | 3314.00 | + | 5740.02i | 0.199059 | + | 0.344780i | ||||
\(653\) | −22860.0 | −1.36996 | −0.684978 | − | 0.728564i | \(-0.740188\pi\) | ||||
−0.684978 | + | 0.728564i | \(0.740188\pi\) | |||||||
\(654\) | −12800.0 | −0.765321 | ||||||||
\(655\) | −2718.00 | − | 4707.71i | −0.162139 | − | 0.280833i | ||||
\(656\) | −1416.00 | − | 2452.58i | −0.0842767 | − | 0.145972i | ||||
\(657\) | 290.000 | 0.0172207 | ||||||||
\(658\) | −7872.00 | −0.466387 | ||||||||
\(659\) | −1410.00 | − | 2442.19i | −0.0833472 | − | 0.144362i | 0.821339 | − | 0.570441i | \(-0.193228\pi\) |
−0.904686 | + | 0.426079i | \(0.859894\pi\) | |||||||
\(660\) | −1080.00 | + | 1870.61i | −0.0636954 | + | 0.110324i | ||||
\(661\) | 5930.00 | + | 10271.1i | 0.348941 | + | 0.604384i | 0.986062 | − | 0.166380i | \(-0.0532079\pi\) |
−0.637120 | + | 0.770764i | \(0.719875\pi\) | |||||||
\(662\) | −2375.00 | + | 4113.62i | −0.139437 | + | 0.241511i | ||||
\(663\) | 7410.00 | − | 12834.5i | 0.434058 | − | 0.751811i | ||||
\(664\) | −4536.00 | −0.265107 | ||||||||
\(665\) | −7296.00 | + | 3159.26i | −0.425454 | + | 0.184227i | ||||
\(666\) | 1336.00 | 0.0777312 | ||||||||
\(667\) | −7956.00 | + | 13780.2i | −0.461855 | + | 0.799957i | ||||
\(668\) | −5568.00 | + | 9644.06i | −0.322504 | + | 0.558593i | ||||
\(669\) | 2315.00 | + | 4009.70i | 0.133786 | + | 0.231725i | ||||
\(670\) | 9060.00 | − | 15692.4i | 0.522415 | − | 0.904850i | ||||
\(671\) | 1584.00 | + | 2743.57i | 0.0911321 | + | 0.157845i | ||||
\(672\) | −1280.00 | −0.0734778 | ||||||||
\(673\) | −31330.0 | −1.79448 | −0.897238 | − | 0.441547i | \(-0.854430\pi\) | ||||
−0.897238 | + | 0.441547i | \(0.854430\pi\) | |||||||
\(674\) | 10333.0 | + | 17897.3i | 0.590523 | + | 1.02282i | ||||
\(675\) | −1377.50 | − | 2385.90i | −0.0785481 | − | 0.136049i | ||||
\(676\) | −6084.00 | −0.346154 | ||||||||
\(677\) | −4410.00 | −0.250355 | −0.125177 | − | 0.992134i | \(-0.539950\pi\) | ||||
−0.125177 | + | 0.992134i | \(0.539950\pi\) | |||||||
\(678\) | −1845.00 | − | 3195.63i | −0.104509 | − | 0.181014i | ||||
\(679\) | 3772.00 | − | 6533.30i | 0.213190 | − | 0.369256i | ||||
\(680\) | 5472.00 | + | 9477.78i | 0.308591 | + | 0.534495i | ||||
\(681\) | 12442.5 | − | 21551.0i | 0.700143 | − | 1.21268i | ||||
\(682\) | −882.000 | + | 1527.67i | −0.0495213 | + | 0.0857734i | ||||
\(683\) | −180.000 | −0.0100842 | −0.00504210 | − | 0.999987i | \(-0.501605\pi\) | ||||
−0.00504210 | + | 0.999987i | \(0.501605\pi\) | |||||||
\(684\) | −608.000 | + | 263.272i | −0.0339875 | + | 0.0147170i | ||||
\(685\) | −24012.0 | −1.33935 | ||||||||
\(686\) | 4976.00 | − | 8618.68i | 0.276945 | − | 0.479684i | ||||
\(687\) | −10780.0 | + | 18671.5i | −0.598665 | + | 1.03692i | ||||
\(688\) | 2528.00 | + | 4378.62i | 0.140086 | + | 0.242636i | ||||
\(689\) | −8814.00 | + | 15266.3i | −0.487354 | + | 0.844121i | ||||
\(690\) | 4680.00 | + | 8106.00i | 0.258210 | + | 0.447232i | ||||
\(691\) | −27412.0 | −1.50912 | −0.754560 | − | 0.656231i | \(-0.772150\pi\) | ||||
−0.754560 | + | 0.656231i | \(0.772150\pi\) | |||||||
\(692\) | 9528.00 | 0.523411 | ||||||||
\(693\) | 72.0000 | + | 124.708i | 0.00394669 | + | 0.00683586i | ||||
\(694\) | −5109.00 | − | 8849.05i | −0.279445 | − | 0.484013i | ||||
\(695\) | 35220.0 | 1.92226 | ||||||||
\(696\) | 8160.00 | 0.444402 | ||||||||
\(697\) | −10089.0 | − | 17474.7i | −0.548276 | − | 0.949641i | ||||
\(698\) | 2044.00 | − | 3540.31i | 0.110840 | − | 0.191981i | ||||
\(699\) | −4552.50 | − | 7885.16i | −0.246340 | − | 0.426673i | ||||
\(700\) | −304.000 | + | 526.543i | −0.0164145 | + | 0.0284307i | ||||
\(701\) | −12918.0 | + | 22374.6i | −0.696014 | + | 1.20553i | 0.273823 | + | 0.961780i | \(0.411712\pi\) |
−0.969838 | + | 0.243752i | \(0.921622\pi\) | |||||||
\(702\) | 7540.00 | 0.405383 | ||||||||
\(703\) | 22211.0 | + | 16487.4i | 1.19161 | + | 0.884543i | ||||
\(704\) | 576.000 | 0.0308364 | ||||||||
\(705\) | 14760.0 | − | 25565.1i | 0.788502 | − | 1.36573i | ||||
\(706\) | 1701.00 | − | 2946.22i | 0.0906770 | − | 0.157057i | ||||
\(707\) | 6000.00 | + | 10392.3i | 0.319170 | + | 0.552819i | ||||
\(708\) | −5790.00 | + | 10028.6i | −0.307347 | + | 0.532340i | ||||
\(709\) | −7465.00 | − | 12929.8i | −0.395422 | − | 0.684890i | 0.597733 | − | 0.801695i | \(-0.296068\pi\) |
−0.993155 | + | 0.116805i | \(0.962735\pi\) | |||||||
\(710\) | −144.000 | −0.00761158 | ||||||||
\(711\) | 632.000 | 0.0333359 | ||||||||
\(712\) | 456.000 | + | 789.815i | 0.0240019 | + | 0.0415724i | ||||
\(713\) | 3822.00 | + | 6619.90i | 0.200750 | + | 0.347710i | ||||
\(714\) | −9120.00 | −0.478022 | ||||||||
\(715\) | −2808.00 | −0.146872 | ||||||||
\(716\) | 7290.00 | + | 12626.7i | 0.380503 | + | 0.659050i | ||||
\(717\) | 810.000 | − | 1402.96i | 0.0421897 | − | 0.0730747i | ||||
\(718\) | −1770.00 | − | 3065.73i | −0.0919997 | − | 0.159348i | ||||
\(719\) | −2073.00 | + | 3590.54i | −0.107524 | + | 0.186237i | −0.914767 | − | 0.403983i | \(-0.867626\pi\) |
0.807243 | + | 0.590220i | \(0.200959\pi\) | |||||||
\(720\) | −192.000 | + | 332.554i | −0.00993808 | + | 0.0172133i | ||||
\(721\) | −5264.00 | −0.271902 | ||||||||
\(722\) | −13357.0 | − | 3126.35i | −0.688499 | − | 0.161151i | ||||
\(723\) | −1705.00 | −0.0877035 | ||||||||
\(724\) | 3812.00 | − | 6602.58i | 0.195679 | − | 0.338927i | ||||
\(725\) | 1938.00 | − | 3356.71i | 0.0992766 | − | 0.171952i | ||||
\(726\) | −6250.00 | − | 10825.3i | −0.319503 | − | 0.553396i | ||||
\(727\) | 9428.00 | − | 16329.8i | 0.480970 | − | 0.833064i | −0.518792 | − | 0.854901i | \(-0.673618\pi\) |
0.999762 | + | 0.0218363i | \(0.00695127\pi\) | |||||||
\(728\) | −832.000 | − | 1441.07i | −0.0423571 | − | 0.0733647i | ||||
\(729\) | 20917.0 | 1.06269 | ||||||||
\(730\) | 3480.00 | 0.176439 | ||||||||
\(731\) | 18012.0 | + | 31197.7i | 0.911351 | + | 1.57851i | ||||
\(732\) | −3520.00 | − | 6096.82i | −0.177736 | − | 0.307848i | ||||
\(733\) | 17318.0 | 0.872653 | 0.436327 | − | 0.899788i | \(-0.356279\pi\) | ||||
0.436327 | + | 0.899788i | \(0.356279\pi\) | |||||||
\(734\) | −21116.0 | −1.06186 | ||||||||
\(735\) | 8370.00 | + | 14497.3i | 0.420044 | + | 0.727537i | ||||
\(736\) | 1248.00 | − | 2161.60i | 0.0625026 | − | 0.108258i | ||||
\(737\) | −3397.50 | − | 5884.64i | −0.169808 | − | 0.294116i | ||||
\(738\) | 354.000 | − | 613.146i | 0.0176571 | − | 0.0305829i | ||||
\(739\) | 12915.5 | − | 22370.3i | 0.642902 | − | 1.11354i | −0.341880 | − | 0.939744i | \(-0.611064\pi\) |
0.984782 | − | 0.173795i | \(-0.0556030\pi\) | |||||||
\(740\) | 16032.0 | 0.796416 | ||||||||
\(741\) | 8645.00 | + | 6417.25i | 0.428586 | + | 0.318142i | ||||
\(742\) | 10848.0 | 0.536715 | ||||||||
\(743\) | −255.000 | + | 441.673i | −0.0125909 | + | 0.0218081i | −0.872252 | − | 0.489056i | \(-0.837341\pi\) |
0.859661 | + | 0.510864i | \(0.170675\pi\) | |||||||
\(744\) | 1960.00 | − | 3394.82i | 0.0965821 | − | 0.167285i | ||||
\(745\) | 36.0000 | + | 62.3538i | 0.00177039 | + | 0.00306640i | ||||
\(746\) | 124.000 | − | 214.774i | 0.00608574 | − | 0.0105408i | ||||
\(747\) | −567.000 | − | 982.073i | −0.0277717 | − | 0.0481020i | ||||
\(748\) | 4104.00 | 0.200611 | ||||||||
\(749\) | −11520.0 | −0.561992 | ||||||||
\(750\) | 6360.00 | + | 11015.8i | 0.309646 | + | 0.536322i | ||||
\(751\) | 347.000 | + | 601.022i | 0.0168605 | + | 0.0292032i | 0.874333 | − | 0.485327i | \(-0.161300\pi\) |
−0.857472 | + | 0.514531i | \(0.827966\pi\) | |||||||
\(752\) | −7872.00 | −0.381732 | ||||||||
\(753\) | −24315.0 | −1.17674 | ||||||||
\(754\) | 5304.00 | + | 9186.80i | 0.256181 | + | 0.443718i | ||||
\(755\) | 16644.0 | − | 28828.3i | 0.802301 | − | 1.38963i | ||||
\(756\) | −2320.00 | − | 4018.36i | −0.111611 | − | 0.193315i | ||||
\(757\) | −2299.00 | + | 3981.98i | −0.110381 | + | 0.191186i | −0.915924 | − | 0.401352i | \(-0.868541\pi\) |
0.805543 | + | 0.592538i | \(0.201874\pi\) | |||||||
\(758\) | −44.0000 | + | 76.2102i | −0.00210838 | + | 0.00365182i | ||||
\(759\) | 3510.00 | 0.167859 | ||||||||
\(760\) | −7296.00 | + | 3159.26i | −0.348229 | + | 0.150787i | ||||
\(761\) | 32697.0 | 1.55751 | 0.778755 | − | 0.627328i | \(-0.215851\pi\) | ||||
0.778755 | + | 0.627328i | \(0.215851\pi\) | |||||||
\(762\) | 4510.00 | − | 7811.55i | 0.214410 | − | 0.371368i | ||||
\(763\) | −5120.00 | + | 8868.10i | −0.242931 | + | 0.420769i | ||||
\(764\) | −2664.00 | − | 4614.18i | −0.126152 | − | 0.218502i | ||||
\(765\) | −1368.00 | + | 2369.45i | −0.0646538 | + | 0.111984i | ||||
\(766\) | −9312.00 | − | 16128.9i | −0.439238 | − | 0.760782i | ||||
\(767\) | −15054.0 | −0.708694 | ||||||||
\(768\) | −1280.00 | −0.0601407 | ||||||||
\(769\) | 2255.00 | + | 3905.77i | 0.105744 | + | 0.183155i | 0.914042 | − | 0.405619i | \(-0.132944\pi\) |
−0.808298 | + | 0.588774i | \(0.799611\pi\) | |||||||
\(770\) | 864.000 | + | 1496.49i | 0.0404369 | + | 0.0700387i | ||||
\(771\) | 17265.0 | 0.806464 | ||||||||
\(772\) | 5288.00 | 0.246528 | ||||||||
\(773\) | 1506.00 | + | 2608.47i | 0.0700738 | + | 0.121371i | 0.898933 | − | 0.438085i | \(-0.144343\pi\) |
−0.828860 | + | 0.559457i | \(0.811010\pi\) | |||||||
\(774\) | −632.000 | + | 1094.66i | −0.0293498 | + | 0.0508354i | ||||
\(775\) | −931.000 | − | 1612.54i | −0.0431516 | − | 0.0747408i | ||||
\(776\) | 3772.00 | − | 6533.30i | 0.174493 | − | 0.302232i | ||||
\(777\) | −6680.00 | + | 11570.1i | −0.308422 | + | 0.534202i | ||||
\(778\) | −22584.0 | −1.04071 | ||||||||
\(779\) | 13452.0 | − | 5824.89i | 0.618701 | − | 0.267905i | ||||
\(780\) | 6240.00 | 0.286446 | ||||||||
\(781\) | −27.0000 | + | 46.7654i | −0.00123705 | + | 0.00214263i | ||||
\(782\) | 8892.00 | − | 15401.4i | 0.406621 | − | 0.704287i | ||||
\(783\) | 14790.0 | + | 25617.0i | 0.675034 | + | 1.16919i | ||||
\(784\) | 2232.00 | − | 3865.94i | 0.101676 | − | 0.176109i | ||||
\(785\) | −16368.0 | − | 28350.2i | −0.744203 | − | 1.28900i | ||||
\(786\) | 4530.00 | 0.205572 | ||||||||
\(787\) | 12131.0 | 0.549458 | 0.274729 | − | 0.961522i | \(-0.411412\pi\) | ||||
0.274729 | + | 0.961522i | \(0.411412\pi\) | |||||||
\(788\) | −7452.00 | − | 12907.2i | −0.336886 | − | 0.583504i | ||||
\(789\) | −300.000 | − | 519.615i | −0.0135365 | − | 0.0234459i | ||||
\(790\) | 7584.00 | 0.341553 | ||||||||
\(791\) | −2952.00 | −0.132694 | ||||||||
\(792\) | 72.0000 | + | 124.708i | 0.00323031 | + | 0.00559507i | ||||
\(793\) | 4576.00 | − | 7925.86i | 0.204916 | − | 0.354925i | ||||
\(794\) | 334.000 | + | 578.505i | 0.0149285 | + | 0.0258569i | ||||
\(795\) | −20340.0 | + | 35229.9i | −0.907403 | + | 1.57167i | ||||
\(796\) | 956.000 | − | 1655.84i | 0.0425685 | − | 0.0737308i | ||||
\(797\) | 8442.00 | 0.375196 | 0.187598 | − | 0.982246i | \(-0.439930\pi\) | ||||
0.187598 | + | 0.982246i | \(0.439930\pi\) | |||||||
\(798\) | 760.000 | − | 6581.79i | 0.0337139 | − | 0.291971i | ||||
\(799\) | −56088.0 | −2.48342 | ||||||||
\(800\) | −304.000 | + | 526.543i | −0.0134350 | + | 0.0232702i | ||||
\(801\) | −114.000 | + | 197.454i | −0.00502870 | + | 0.00870997i | ||||
\(802\) | −5613.00 | − | 9722.00i | −0.247135 | − | 0.428050i | ||||
\(803\) | 652.500 | − | 1130.16i | 0.0286752 | − | 0.0496670i | ||||
\(804\) | 7550.00 | + | 13077.0i | 0.331179 | + | 0.573619i | ||||
\(805\) | 7488.00 | 0.327848 | ||||||||
\(806\) | 5096.00 | 0.222703 | ||||||||
\(807\) | −17670.0 | − | 30605.3i | −0.770773 | − | 1.33502i | ||||
\(808\) | 6000.00 | + | 10392.3i | 0.261237 | + | 0.452475i | ||||
\(809\) | −8307.00 | −0.361012 | −0.180506 | − | 0.983574i | \(-0.557773\pi\) | ||||
−0.180506 | + | 0.983574i | \(0.557773\pi\) | |||||||
\(810\) | 16104.0 | 0.698564 | ||||||||
\(811\) | 8.00000 | + | 13.8564i | 0.000346385 | + | 0.000599956i | 0.866199 | − | 0.499700i | \(-0.166556\pi\) |
−0.865852 | + | 0.500300i | \(0.833223\pi\) | |||||||
\(812\) | 3264.00 | − | 5653.41i | 0.141064 | − | 0.244330i | ||||
\(813\) | 3470.00 | + | 6010.22i | 0.149690 | + | 0.259271i | ||||
\(814\) | 3006.00 | − | 5206.54i | 0.129435 | − | 0.224188i | ||||
\(815\) | −9942.00 | + | 17220.0i | −0.427304 | + | 0.740113i | ||||
\(816\) | −9120.00 | −0.391255 | ||||||||
\(817\) | −24016.0 | + | 10399.2i | −1.02841 | + | 0.445316i | ||||
\(818\) | −6710.00 | −0.286809 | ||||||||
\(819\) | 208.000 | − | 360.267i | 0.00887437 | − | 0.0153709i | ||||
\(820\) | 4248.00 | − | 7357.75i | 0.180910 | − | 0.313346i | ||||
\(821\) | 11127.0 | + | 19272.5i | 0.473002 | + | 0.819264i | 0.999523 | − | 0.0308985i | \(-0.00983685\pi\) |
−0.526520 | + | 0.850163i | \(0.676504\pi\) | |||||||
\(822\) | 10005.0 | − | 17329.2i | 0.424531 | − | 0.735309i | ||||
\(823\) | 19835.0 | + | 34355.2i | 0.840103 | + | 1.45510i | 0.889807 | + | 0.456337i | \(0.150839\pi\) |
−0.0497043 | + | 0.998764i | \(0.515828\pi\) | |||||||
\(824\) | −5264.00 | −0.222549 | ||||||||
\(825\) | −855.000 | −0.0360816 | ||||||||
\(826\) | 4632.00 | + | 8022.86i | 0.195119 | + | 0.337955i | ||||
\(827\) | −7741.50 | − | 13408.7i | −0.325512 | − | 0.563803i | 0.656104 | − | 0.754671i | \(-0.272203\pi\) |
−0.981616 | + | 0.190867i | \(0.938870\pi\) | |||||||
\(828\) | 624.000 | 0.0261902 | ||||||||
\(829\) | 27188.0 | 1.13906 | 0.569529 | − | 0.821972i | \(-0.307126\pi\) | ||||
0.569529 | + | 0.821972i | \(0.307126\pi\) | |||||||
\(830\) | −6804.00 | − | 11784.9i | −0.284543 | − | 0.492842i | ||||
\(831\) | −12910.0 | + | 22360.8i | −0.538921 | + | 0.933438i | ||||
\(832\) | −832.000 | − | 1441.07i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | 15903.0 | − | 27544.8i | 0.661472 | − | 1.14570i | ||||
\(834\) | −14675.0 | + | 25417.8i | −0.609297 | + | 1.05533i | ||||
\(835\) | −33408.0 | −1.38459 | ||||||||
\(836\) | −342.000 | + | 2961.81i | −0.0141487 | + | 0.122531i | ||||
\(837\) | 14210.0 | 0.586821 | ||||||||
\(838\) | −5796.00 | + | 10039.0i | −0.238925 | + | 0.413831i | ||||
\(839\) | −876.000 | + | 1517.28i | −0.0360463 | + | 0.0624341i | −0.883486 | − | 0.468458i | \(-0.844810\pi\) |
0.847439 | + | 0.530892i | \(0.178143\pi\) | |||||||
\(840\) | −1920.00 | − | 3325.54i | −0.0788646 | − | 0.136598i | ||||
\(841\) | −8613.50 | + | 14919.0i | −0.353172 | + | 0.611711i | ||||
\(842\) | −650.000 | − | 1125.83i | −0.0266039 | − | 0.0460793i | ||||
\(843\) | 3225.00 | 0.131761 | ||||||||
\(844\) | −3280.00 | −0.133770 | ||||||||
\(845\) | −9126.00 | − | 15806.7i | −0.371531 | − | 0.643511i | ||||
\(846\) | −984.000 | − | 1704.34i | −0.0399889 | − | 0.0692628i | ||||
\(847\) | −10000.0 | −0.405672 | ||||||||
\(848\) | 10848.0 | 0.439295 | ||||||||
\(849\) | 16857.5 | + | 29198.0i | 0.681446 | + | 1.18030i | ||||
\(850\) | −2166.00 | + | 3751.62i | −0.0874037 | + | 0.151388i | ||||
\(851\) | −13026.0 | − | 22561.7i | −0.524707 | − | 0.908819i | ||||
\(852\) | 60.0000 | − | 103.923i | 0.00241264 | − | 0.00417881i | ||||
\(853\) | 8231.00 | − | 14256.5i | 0.330392 | − | 0.572255i | −0.652197 | − | 0.758050i | \(-0.726153\pi\) |
0.982589 | + | 0.185794i | \(0.0594858\pi\) | |||||||
\(854\) | −5632.00 | −0.225671 | ||||||||
\(855\) | −1596.00 | − | 1184.72i | −0.0638387 | − | 0.0473879i | ||||
\(856\) | −11520.0 | −0.459983 | ||||||||
\(857\) | −11050.5 | + | 19140.0i | −0.440464 | + | 0.762907i | −0.997724 | − | 0.0674318i | \(-0.978519\pi\) |
0.557260 | + | 0.830338i | \(0.311853\pi\) | |||||||
\(858\) | 1170.00 | − | 2026.50i | 0.0465538 | − | 0.0806335i | ||||
\(859\) | −21779.5 | − | 37723.2i | −0.865084 | − | 1.49837i | −0.866964 | − | 0.498371i | \(-0.833932\pi\) |
0.00188022 | − | 0.999998i | \(-0.499402\pi\) | |||||||
\(860\) | −7584.00 | + | 13135.9i | −0.300712 | + | 0.520848i | ||||
\(861\) | 3540.00 | + | 6131.46i | 0.140119 | + | 0.242694i | ||||
\(862\) | 8412.00 | 0.332383 | ||||||||
\(863\) | 15570.0 | 0.614147 | 0.307074 | − | 0.951686i | \(-0.400650\pi\) | ||||
0.307074 | + | 0.951686i | \(0.400650\pi\) | |||||||
\(864\) | −2320.00 | − | 4018.36i | −0.0913519 | − | 0.158226i | ||||
\(865\) | 14292.0 | + | 24754.5i | 0.561783 | + | 0.973037i | ||||
\(866\) | −26156.0 | −1.02635 | ||||||||
\(867\) | −40415.0 | −1.58312 | ||||||||
\(868\) | −1568.00 | − | 2715.86i | −0.0613150 | − | 0.106201i | ||||
\(869\) | 1422.00 | − | 2462.98i | 0.0555098 | − | 0.0961459i | ||||
\(870\) | 12240.0 | + | 21200.3i | 0.476983 | + | 0.826158i | ||||
\(871\) | −9815.00 | + | 17000.1i | −0.381824 | + | 0.661338i | ||||
\(872\) | −5120.00 | + | 8868.10i | −0.198836 | + | 0.344394i | ||||
\(873\) | 1886.00 | 0.0731173 | ||||||||
\(874\) | 10374.0 | + | 7700.70i | 0.401494 | + | 0.298032i | ||||
\(875\) | 10176.0 | 0.393156 | ||||||||
\(876\) | −1450.00 | + | 2511.47i | −0.0559258 | + | 0.0968662i | ||||
\(877\) | 5072.00 | − | 8784.96i | 0.195290 | − | 0.338252i | −0.751706 | − | 0.659499i | \(-0.770769\pi\) |
0.946996 | + | 0.321247i | \(0.104102\pi\) | |||||||
\(878\) | 2602.00 | + | 4506.80i | 0.100015 | + | 0.173231i | ||||
\(879\) | −630.000 | + | 1091.19i | −0.0241745 | + | 0.0418714i | ||||
\(880\) | 864.000 | + | 1496.49i | 0.0330971 | + | 0.0573258i | ||||
\(881\) | 40887.0 | 1.56358 | 0.781792 | − | 0.623539i | \(-0.214306\pi\) | ||||
0.781792 | + | 0.623539i | \(0.214306\pi\) | |||||||
\(882\) | 1116.00 | 0.0426051 | ||||||||
\(883\) | −6299.50 | − | 10911.1i | −0.240085 | − | 0.415839i | 0.720653 | − | 0.693296i | \(-0.243842\pi\) |
−0.960738 | + | 0.277456i | \(0.910509\pi\) | |||||||
\(884\) | −5928.00 | − | 10267.6i | −0.225543 | − | 0.390652i | ||||
\(885\) | −34740.0 | −1.31952 | ||||||||
\(886\) | 15846.0 | 0.600854 | ||||||||
\(887\) | −24576.0 | − | 42566.9i | −0.930306 | − | 1.61134i | −0.782798 | − | 0.622276i | \(-0.786208\pi\) |
−0.147508 | − | 0.989061i | \(-0.547125\pi\) | |||||||
\(888\) | −6680.00 | + | 11570.1i | −0.252439 | + | 0.437238i | ||||
\(889\) | −3608.00 | − | 6249.24i | −0.136117 | − | 0.235762i | ||||
\(890\) | −1368.00 | + | 2369.45i | −0.0515230 | + | 0.0892404i | ||||
\(891\) | 3019.50 | − | 5229.93i | 0.113532 | − | 0.196643i | ||||
\(892\) | 3704.00 | 0.139035 | ||||||||
\(893\) | 4674.00 | − | 40478.0i | 0.175151 | − | 1.51685i | ||||
\(894\) | −60.0000 | −0.00224463 | ||||||||
\(895\) | −21870.0 | + | 37880.0i | −0.816797 | + | 1.41473i | ||||
\(896\) | −512.000 | + | 886.810i | −0.0190901 | + | 0.0330650i | ||||
\(897\) | −5070.00 | − | 8781.50i | −0.188721 | − | 0.326874i | ||||
\(898\) | −2529.00 | + | 4380.36i | −0.0939798 | + | 0.162778i | ||||
\(899\) | 9996.00 | + | 17313.6i | 0.370840 | + | 0.642314i | ||||
\(900\) | −152.000 | −0.00562963 | ||||||||
\(901\) | 77292.0 | 2.85790 | ||||||||
\(902\) | −1593.00 | − | 2759.16i | −0.0588039 | − | 0.101851i | ||||
\(903\) | −6320.00 | − | 10946.6i | −0.232909 | − | 0.403409i | ||||
\(904\) | −2952.00 | −0.108608 | ||||||||
\(905\) | 22872.0 | 0.840101 | ||||||||
\(906\) | 13870.0 | + | 24023.5i | 0.508609 | + | 0.880937i | ||||
\(907\) | 4494.50 | − | 7784.70i | 0.164540 | − | 0.284991i | −0.771952 | − | 0.635681i | \(-0.780719\pi\) |
0.936492 | + | 0.350690i | \(0.114053\pi\) | |||||||
\(908\) | −9954.00 | − | 17240.8i | −0.363805 | − | 0.630129i | ||||
\(909\) | −1500.00 | + | 2598.08i | −0.0547325 | + | 0.0947995i | ||||
\(910\) | 2496.00 | − | 4323.20i | 0.0909248 | − | 0.157486i | ||||
\(911\) | 26406.0 | 0.960340 | 0.480170 | − | 0.877175i | \(-0.340575\pi\) | ||||
0.480170 | + | 0.877175i | \(0.340575\pi\) | |||||||
\(912\) | 760.000 | − | 6581.79i | 0.0275944 | − | 0.238975i | ||||
\(913\) | −5103.00 | −0.184978 | ||||||||
\(914\) | −7037.00 | + | 12188.4i | −0.254664 | + | 0.441092i | ||||
\(915\) | 10560.0 | − | 18290.5i | 0.381533 | − | 0.660835i | ||||
\(916\) | 8624.00 | + | 14937.2i | 0.311075 | + | 0.538798i | ||||
\(917\) | 1812.00 | − | 3138.48i | 0.0652536 | − | 0.113022i | ||||
\(918\) | −16530.0 | − | 28630.8i | −0.594304 | − | 1.02937i | ||||
\(919\) | 43514.0 | 1.56191 | 0.780955 | − | 0.624588i | \(-0.214733\pi\) | ||||
0.780955 | + | 0.624588i | \(0.214733\pi\) | |||||||
\(920\) | 7488.00 | 0.268339 | ||||||||
\(921\) | −17792.5 | − | 30817.5i | −0.636572 | − | 1.10258i | ||||
\(922\) | 11730.0 | + | 20317.0i | 0.418988 | + | 0.725709i | ||||
\(923\) | 156.000 | 0.00556317 | ||||||||
\(924\) | −1440.00 | −0.0512690 | ||||||||
\(925\) | 3173.00 | + | 5495.80i | 0.112787 | + | 0.195352i | ||||
\(926\) | −11762.0 | + | 20372.4i | −0.417412 | + | 0.722978i | ||||
\(927\) | −658.000 | − | 1139.69i | −0.0233134 | − | 0.0403801i | ||||
\(928\) | 3264.00 | − | 5653.41i | 0.115459 | − | 0.199981i | ||||
\(929\) | −14074.5 | + | 24377.7i | −0.497061 | + | 0.860934i | −0.999994 | − | 0.00339072i | \(-0.998921\pi\) |
0.502934 | + | 0.864325i | \(0.332254\pi\) | |||||||
\(930\) | 11760.0 | 0.414651 | ||||||||
\(931\) | 18553.5 | + | 13772.4i | 0.653133 | + | 0.484825i | ||||
\(932\) | −7284.00 | −0.256004 | ||||||||
\(933\) | 11025.0 | − | 19095.9i | 0.386862 | − | 0.670065i | ||||
\(934\) | 3465.00 | − | 6001.56i | 0.121390 | − | 0.210254i | ||||
\(935\) | 6156.00 | + | 10662.5i | 0.215318 | + | 0.372942i | ||||
\(936\) | 208.000 | − | 360.267i | 0.00726356 | − | 0.0125809i | ||||
\(937\) | −17873.5 | − | 30957.8i | −0.623161 | − | 1.07935i | −0.988893 | − | 0.148626i | \(-0.952515\pi\) |
0.365732 | − | 0.930720i | \(-0.380819\pi\) | |||||||
\(938\) | 12080.0 | 0.420497 | ||||||||
\(939\) | −33625.0 | −1.16859 | ||||||||
\(940\) | −11808.0 | − | 20452.1i | −0.409718 | − | 0.709652i | ||||
\(941\) | −6495.00 | − | 11249.7i | −0.225006 | − | 0.389722i | 0.731315 | − | 0.682040i | \(-0.238907\pi\) |
−0.956321 | + | 0.292317i | \(0.905574\pi\) | |||||||
\(942\) | 27280.0 | 0.943557 | ||||||||
\(943\) | −13806.0 | −0.476761 | ||||||||
\(944\) | 4632.00 | + | 8022.86i | 0.159702 | + | 0.276612i | ||||
\(945\) | 6960.00 | − | 12055.1i | 0.239586 | − | 0.414975i | ||||
\(946\) | 2844.00 | + | 4925.95i | 0.0977446 | + | 0.169299i | ||||
\(947\) | −5862.00 | + | 10153.3i | −0.201150 | + | 0.348403i | −0.948899 | − | 0.315579i | \(-0.897801\pi\) |
0.747749 | + | 0.663982i | \(0.231135\pi\) | |||||||
\(948\) | −3160.00 | + | 5473.28i | −0.108262 | + | 0.187515i | ||||
\(949\) | −3770.00 | −0.128956 | ||||||||
\(950\) | −2527.00 | − | 1875.81i | −0.0863018 | − | 0.0640625i | ||||
\(951\) | 24330.0 | 0.829605 | ||||||||
\(952\) | −3648.00 | + | 6318.52i | −0.124194 | + | 0.215110i | ||||
\(953\) | −12508.5 | + | 21665.4i | −0.425173 | + | 0.736422i | −0.996437 | − | 0.0843452i | \(-0.973120\pi\) |
0.571263 | + | 0.820767i | \(0.306453\pi\) | |||||||
\(954\) | 1356.00 | + | 2348.66i | 0.0460190 | + | 0.0797072i | ||||
\(955\) | 7992.00 | − | 13842.6i | 0.270801 | − | 0.469041i | ||||
\(956\) | −648.000 | − | 1122.37i | −0.0219224 | − | 0.0379707i | ||||
\(957\) | 9180.00 | 0.310081 | ||||||||
\(958\) | −8040.00 | −0.271149 | ||||||||
\(959\) | −8004.00 | − | 13863.3i | −0.269513 | − | 0.466810i | ||||
\(960\) | −1920.00 | − | 3325.54i | −0.0645497 | − | 0.111803i | ||||
\(961\) | −20187.0 | −0.677621 | ||||||||
\(962\) | −17368.0 | −0.582086 | ||||||||
\(963\) | −1440.00 | − | 2494.15i | −0.0481862 | − | 0.0834610i | ||||
\(964\) | −682.000 | + | 1181.26i | −0.0227860 | + | 0.0394666i | ||||
\(965\) | 7932.00 | + | 13738.6i | 0.264601 | + | 0.458303i | ||||
\(966\) | −3120.00 | + | 5404.00i | −0.103918 | + | 0.179990i | ||||
\(967\) | 12947.0 | − | 22424.9i | 0.430556 | − | 0.745745i | −0.566365 | − | 0.824154i | \(-0.691651\pi\) |
0.996921 | + | 0.0784097i | \(0.0249842\pi\) | |||||||
\(968\) | −10000.0 | −0.332037 | ||||||||
\(969\) | 5415.00 | − | 46895.3i | 0.179520 | − | 1.55469i | ||||
\(970\) | 22632.0 | 0.749144 | ||||||||
\(971\) | −18295.5 | + | 31688.7i | −0.604666 | + | 1.04731i | 0.387438 | + | 0.921896i | \(0.373360\pi\) |
−0.992104 | + | 0.125416i | \(0.959973\pi\) | |||||||
\(972\) | 1120.00 | − | 1939.90i | 0.0369589 | − | 0.0640146i | ||||
\(973\) | 11740.0 | + | 20334.3i | 0.386811 | + | 0.669976i | ||||
\(974\) | −18146.0 | + | 31429.8i | −0.596956 | + | 1.03396i | ||||
\(975\) | 1235.00 | + | 2139.08i | 0.0405658 | + | 0.0702620i | ||||
\(976\) | −5632.00 | −0.184709 | ||||||||
\(977\) | −24687.0 | −0.808400 | −0.404200 | − | 0.914671i | \(-0.632450\pi\) | ||||
−0.404200 | + | 0.914671i | \(0.632450\pi\) | |||||||
\(978\) | −8285.00 | − | 14350.0i | −0.270885 | − | 0.469186i | ||||
\(979\) | 513.000 | + | 888.542i | 0.0167472 | + | 0.0290071i | ||||
\(980\) | 13392.0 | 0.436522 | ||||||||
\(981\) | −2560.00 | −0.0833175 | ||||||||
\(982\) | −18528.0 | − | 32091.4i | −0.602090 | − | 1.04285i | ||||
\(983\) | 12984.0 | − | 22488.9i | 0.421287 | − | 0.729691i | −0.574778 | − | 0.818309i | \(-0.694912\pi\) |
0.996066 | + | 0.0886183i | \(0.0282451\pi\) | |||||||
\(984\) | 3540.00 | + | 6131.46i | 0.114686 | + | 0.198642i | ||||
\(985\) | 22356.0 | − | 38721.7i | 0.723169 | − | 1.25257i | ||||
\(986\) | 23256.0 | − | 40280.6i | 0.751138 | − | 1.30101i | ||||
\(987\) | 19680.0 | 0.634672 | ||||||||
\(988\) | 7904.00 | − | 3422.53i | 0.254514 | − | 0.110208i | ||||
\(989\) | 24648.0 | 0.792478 | ||||||||
\(990\) | −216.000 | + | 374.123i | −0.00693427 | + | 0.0120105i | ||||
\(991\) | −9292.00 | + | 16094.2i | −0.297851 | + | 0.515893i | −0.975644 | − | 0.219360i | \(-0.929603\pi\) |
0.677793 | + | 0.735253i | \(0.262936\pi\) | |||||||
\(992\) | −1568.00 | − | 2715.86i | −0.0501855 | − | 0.0869239i | ||||
\(993\) | 5937.50 | − | 10284.1i | 0.189749 | − | 0.328655i | ||||
\(994\) | −48.0000 | − | 83.1384i | −0.00153166 | − | 0.00265291i | ||||
\(995\) | 5736.00 | 0.182757 | ||||||||
\(996\) | 11340.0 | 0.360765 | ||||||||
\(997\) | 24116.0 | + | 41770.1i | 0.766060 | + | 1.32685i | 0.939685 | + | 0.342042i | \(0.111119\pi\) |
−0.173625 | + | 0.984812i | \(0.555548\pi\) | |||||||
\(998\) | 16003.0 | + | 27718.0i | 0.507581 | + | 0.879157i | ||||
\(999\) | −48430.0 | −1.53379 |
(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 | 38.4.c.b.11.1 | yes | 2 | |
3.2 | odd | 2 | 342.4.g.c.163.1 | 2 | |||
4.3 | odd | 2 | 304.4.i.a.49.1 | 2 | |||
19.7 | even | 3 | inner | 38.4.c.b.7.1 | ✓ | 2 | |
19.8 | odd | 6 | 722.4.a.b.1.1 | 1 | |||
19.11 | even | 3 | 722.4.a.c.1.1 | 1 | |||
57.26 | odd | 6 | 342.4.g.c.235.1 | 2 | |||
76.7 | odd | 6 | 304.4.i.a.273.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
38.4.c.b.7.1 | ✓ | 2 | 19.7 | even | 3 | inner | |
38.4.c.b.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
304.4.i.a.49.1 | 2 | 4.3 | odd | 2 | |||
304.4.i.a.273.1 | 2 | 76.7 | odd | 6 | |||
342.4.g.c.163.1 | 2 | 3.2 | odd | 2 | |||
342.4.g.c.235.1 | 2 | 57.26 | odd | 6 | |||
722.4.a.b.1.1 | 1 | 19.8 | odd | 6 | |||
722.4.a.c.1.1 | 1 | 19.11 | even | 3 |