Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(109,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.w (of order \(10\), degree \(4\), 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: | \(7.18653618192\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{10})\) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Character | \(\chi\) | \(=\) | 900.289 |
Dual form | 900.2.w.c.109.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{3}{10}\right)\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.913250 | + | 2.04107i | −0.408418 | + | 0.912795i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.62675i | 1.74875i | 0.485254 | + | 0.874373i | \(0.338727\pi\) | ||||
−0.485254 | + | 0.874373i | \(0.661273\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00366 | + | 2.90883i | −1.20715 | + | 0.877045i | −0.994969 | − | 0.100185i | \(-0.968056\pi\) |
−0.212180 | + | 0.977231i | \(0.568056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.21170 | − | 3.04414i | 0.613415 | − | 0.844294i | −0.383438 | − | 0.923567i | \(-0.625260\pi\) |
0.996853 | + | 0.0792730i | \(0.0252599\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.55872 | + | 0.831378i | −0.620580 | + | 0.201639i | −0.602398 | − | 0.798196i | \(-0.705788\pi\) |
−0.0181824 | + | 0.999835i | \(0.505788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81426 | − | 5.58371i | −0.416219 | − | 1.28099i | −0.911156 | − | 0.412062i | \(-0.864809\pi\) |
0.494937 | − | 0.868929i | \(-0.335191\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.92540 | − | 5.40285i | −0.818502 | − | 1.12657i | −0.989955 | − | 0.141379i | \(-0.954846\pi\) |
0.171453 | − | 0.985192i | \(-0.445154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.33195 | − | 3.72802i | −0.666390 | − | 0.745603i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.370972 | − | 1.14173i | 0.0688878 | − | 0.212015i | −0.910686 | − | 0.413099i | \(-0.864446\pi\) |
0.979574 | + | 0.201084i | \(0.0644464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02048 | + | 3.14072i | 0.183284 | + | 0.564090i | 0.999915 | − | 0.0130708i | \(-0.00416068\pi\) |
−0.816631 | + | 0.577161i | \(0.804161\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.44353 | − | 4.22538i | −1.59625 | − | 0.714219i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.10342 | − | 1.51873i | 0.181401 | − | 0.249677i | −0.708627 | − | 0.705584i | \(-0.750685\pi\) |
0.890028 | + | 0.455907i | \(0.150685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.45366 | − | 1.78269i | −0.383198 | − | 0.278410i | 0.379464 | − | 0.925206i | \(-0.376108\pi\) |
−0.762663 | + | 0.646797i | \(0.776108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6626i | 1.62603i | 0.582244 | + | 0.813014i | \(0.302175\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.246527 | − | 0.0801015i | −0.0359597 | − | 0.0116840i | 0.290982 | − | 0.956729i | \(-0.406018\pi\) |
−0.326942 | + | 0.945045i | \(0.606018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.4068 | −2.05811 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.31711 | + | 3.02731i | 1.27980 | + | 0.415833i | 0.868511 | − | 0.495670i | \(-0.165078\pi\) |
0.411292 | + | 0.911504i | \(0.365078\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.28079 | − | 10.8282i | −0.307542 | − | 1.46008i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.78643 | + | 5.65717i | 1.01371 | + | 0.736501i | 0.964983 | − | 0.262311i | \(-0.0844847\pi\) |
0.0487233 | + | 0.998812i | \(0.484485\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.07552 | + | 3.68758i | −0.649854 | + | 0.472147i | −0.863222 | − | 0.504825i | \(-0.831557\pi\) |
0.213367 | + | 0.976972i | \(0.431557\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.19348 | + | 7.29430i | 0.520138 | + | 0.904747i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.43521 | + | 0.791247i | −0.297508 | + | 0.0966662i | −0.453968 | − | 0.891018i | \(-0.649992\pi\) |
0.156460 | + | 0.987684i | \(0.449992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.68143 | + | 8.25259i | −0.318227 | + | 0.979403i | 0.656178 | + | 0.754606i | \(0.272172\pi\) |
−0.974406 | + | 0.224797i | \(0.927828\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86534 | + | 3.94381i | 0.335363 | + | 0.461588i | 0.943080 | − | 0.332566i | \(-0.107914\pi\) |
−0.607717 | + | 0.794154i | \(0.707914\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.4584 | − | 18.5239i | −1.53373 | − | 2.11100i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.85443 | + | 11.8627i | −0.433657 | + | 1.33466i | 0.460800 | + | 0.887504i | \(0.347563\pi\) |
−0.894457 | + | 0.447155i | \(0.852437\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.45513 | − | 2.74724i | 0.928071 | − | 0.301549i | 0.194298 | − | 0.980943i | \(-0.437757\pi\) |
0.733774 | + | 0.679394i | \(0.237757\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.639846 | − | 5.98178i | 0.0694011 | − | 0.648816i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.7934 | + | 8.56841i | −1.25010 | + | 0.908249i | −0.998228 | − | 0.0595118i | \(-0.981046\pi\) |
−0.251870 | + | 0.967761i | \(0.581046\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0845 | + | 10.2330i | 1.47646 | + | 1.07271i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.0536 | + | 1.39629i | 1.33927 | + | 0.143256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.79176 | − | 1.23202i | −0.384995 | − | 0.125092i | 0.110123 | − | 0.993918i | \(-0.464875\pi\) |
−0.495119 | + | 0.868825i | \(0.664875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.36896 | −0.932246 | −0.466123 | − | 0.884720i | \(-0.654350\pi\) | ||||
−0.466123 | + | 0.884720i | \(0.654350\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.91391 | − | 3.22123i | −0.976847 | − | 0.317397i | −0.223270 | − | 0.974757i | \(-0.571673\pi\) |
−0.753577 | + | 0.657360i | \(0.771673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.220683i | 0.0213342i | 0.999943 | + | 0.0106671i | \(0.00339551\pi\) | ||||
−0.999943 | + | 0.0106671i | \(0.996604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.40941 | + | 3.93017i | 0.518127 | + | 0.376442i | 0.815898 | − | 0.578196i | \(-0.196243\pi\) |
−0.297771 | + | 0.954637i | \(0.596243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.64782 | − | 7.77355i | 0.531302 | − | 0.731274i | −0.456026 | − | 0.889966i | \(-0.650728\pi\) |
0.987328 | + | 0.158692i | \(0.0507277\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.6125 | − | 3.07787i | 1.36262 | − | 0.287013i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.84658 | − | 11.8385i | −0.352615 | − | 1.08524i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.16882 | − | 12.8303i | 0.378984 | − | 1.16639i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6521 | − | 3.39614i | 0.952749 | − | 0.303760i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.40003 | − | 12.9380i | −0.834118 | − | 1.14806i | −0.987143 | − | 0.159842i | \(-0.948902\pi\) |
0.153025 | − | 0.988222i | \(-0.451098\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.80795 | + | 11.7197i | 0.332702 | + | 1.02395i | 0.967843 | + | 0.251556i | \(0.0809422\pi\) |
−0.635140 | + | 0.772397i | \(0.719058\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 25.8344 | − | 8.39411i | 2.24013 | − | 0.727862i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.34717 | − | 4.60698i | 0.285968 | − | 0.393601i | −0.641731 | − | 0.766930i | \(-0.721784\pi\) |
0.927699 | + | 0.373329i | \(0.121784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5598 | + | 10.5783i | −1.23495 | + | 0.897242i | −0.997251 | − | 0.0740969i | \(-0.976393\pi\) |
−0.237697 | + | 0.971339i | \(0.576393\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 18.6212i | 1.55718i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.99157 | + | 1.79987i | 0.165391 | + | 0.149471i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.09001 | −0.0892972 | −0.0446486 | − | 0.999003i | \(-0.514217\pi\) | ||||
−0.0446486 | + | 0.999003i | \(0.514217\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3789 | 0.926004 | 0.463002 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463002 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −7.34239 | − | 0.785384i | −0.589755 | − | 0.0630836i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.98415i | − | 0.317970i | −0.987281 | − | 0.158985i | \(-0.949178\pi\) | ||
0.987281 | − | 0.158985i | \(-0.0508221\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24.9976 | − | 18.1618i | 1.97009 | − | 1.43135i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.8322 | + | 17.6620i | −1.00509 | + | 1.38339i | −0.0829441 | + | 0.996554i | \(0.526432\pi\) |
−0.922148 | + | 0.386837i | \(0.873568\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7118 | + | 4.78015i | −1.13843 | + | 0.369899i | −0.816775 | − | 0.576957i | \(-0.804240\pi\) |
−0.321658 | + | 0.946856i | \(0.604240\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.357976 | − | 1.10174i | −0.0275366 | − | 0.0847490i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −10.0925 | − | 13.8911i | −0.767317 | − | 1.05612i | −0.996570 | − | 0.0827547i | \(-0.973628\pi\) |
0.229253 | − | 0.973367i | \(-0.426372\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.2486 | − | 15.4161i | 1.30387 | − | 1.16535i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.46392 | + | 13.7385i | −0.333649 | + | 1.02687i | 0.633734 | + | 0.773551i | \(0.281521\pi\) |
−0.967384 | + | 0.253316i | \(0.918479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.83071 | + | 11.7897i | 0.284734 | + | 0.876322i | 0.986478 | + | 0.163893i | \(0.0524051\pi\) |
−0.701744 | + | 0.712429i | \(0.747595\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.09213 | + | 3.63913i | 0.153817 | + | 0.267554i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.82590 | − | 10.7714i | 0.572287 | − | 0.787685i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.33930 | − | 0.973056i | −0.0969081 | − | 0.0704078i | 0.538276 | − | 0.842769i | \(-0.319076\pi\) |
−0.635184 | + | 0.772361i | \(0.719076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 16.3253i | − | 1.17512i | −0.809181 | − | 0.587560i | \(-0.800089\pi\) | ||
0.809181 | − | 0.587560i | \(-0.199911\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9652 | + | 4.21264i | 0.923730 | + | 0.300138i | 0.731996 | − | 0.681309i | \(-0.238589\pi\) |
0.191734 | + | 0.981447i | \(0.438589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.07817 | 0.430870 | 0.215435 | − | 0.976518i | \(-0.430883\pi\) | ||||
0.215435 | + | 0.976518i | \(0.430883\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.28252 | + | 1.71639i | 0.370760 | + | 0.120467i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.87941 | − | 3.38006i | 0.410636 | − | 0.236074i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 23.5057 | + | 17.0779i | 1.62593 | + | 1.18130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.8200 | + | 10.0408i | −0.951409 | + | 0.691239i | −0.951140 | − | 0.308761i | \(-0.900086\pi\) |
−0.000268984 | 1.00000i | \(0.500086\pi\) | ||||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.7631 | − | 9.73760i | −1.48423 | − | 0.664099i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −14.5313 | + | 4.72151i | −0.986450 | + | 0.320517i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.12828 | + | 9.62787i | −0.210431 | + | 0.647640i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.460700 | + | 0.634100i | 0.0308508 | + | 0.0424624i | 0.824164 | − | 0.566352i | \(-0.191646\pi\) |
−0.793313 | + | 0.608814i | \(0.791646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0771 | + | 19.3755i | 0.934331 | + | 1.28600i | 0.958146 | + | 0.286280i | \(0.0924186\pi\) |
−0.0238153 | + | 0.999716i | \(0.507581\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.71005 | − | 5.26299i | 0.113003 | − | 0.347788i | −0.878522 | − | 0.477702i | \(-0.841470\pi\) |
0.991525 | + | 0.129914i | \(0.0414700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.863314 | + | 0.280508i | −0.0565576 | + | 0.0183767i | −0.337159 | − | 0.941448i | \(-0.609466\pi\) |
0.280602 | + | 0.959824i | \(0.409466\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.388634 | − | 0.430027i | 0.0253517 | − | 0.0280519i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.09227 | − | 6.60592i | 0.588130 | − | 0.427302i | −0.253516 | − | 0.967331i | \(-0.581587\pi\) |
0.841646 | + | 0.540030i | \(0.181587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3840 | + | 11.9037i | 1.05539 | + | 0.766783i | 0.973229 | − | 0.229837i | \(-0.0738193\pi\) |
0.0821564 | + | 0.996619i | \(0.473819\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.1570 | − | 29.4053i | 0.840570 | − | 1.87864i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.0102 | − | 6.82663i | −1.33685 | − | 0.434368i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.6919 | 1.93725 | 0.968627 | − | 0.248520i | \(-0.0799442\pi\) | ||||
0.968627 | + | 0.248520i | \(0.0799442\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 31.4319 | + | 10.2129i | 1.97611 | + | 0.642077i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 4.77543i | − | 0.297883i | −0.988846 | − | 0.148941i | \(-0.952413\pi\) | ||
0.988846 | − | 0.148941i | \(-0.0475866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.02676 | + | 5.10524i | 0.436622 | + | 0.317224i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.711022 | − | 0.978638i | 0.0438435 | − | 0.0603454i | −0.786532 | − | 0.617549i | \(-0.788126\pi\) |
0.830376 | + | 0.557204i | \(0.188126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.6878 | + | 16.2522i | −0.902265 | + | 0.998364i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.88763 | − | 24.2756i | −0.480917 | − | 1.48011i | −0.837808 | − | 0.545965i | \(-0.816163\pi\) |
0.356891 | − | 0.934146i | \(-0.383837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.81499 | + | 5.58596i | −0.110253 | + | 0.339323i | −0.990927 | − | 0.134399i | \(-0.957090\pi\) |
0.880675 | + | 0.473722i | \(0.157090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 24.1842 | + | 5.23364i | 1.45836 | + | 0.315600i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.88332 | + | 3.96855i | 0.173242 | + | 0.238447i | 0.886805 | − | 0.462144i | \(-0.152920\pi\) |
−0.713563 | + | 0.700591i | \(0.752920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.400257 | + | 1.23186i | 0.0238773 | + | 0.0734868i | 0.962285 | − | 0.272043i | \(-0.0876993\pi\) |
−0.938408 | + | 0.345530i | \(0.887699\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.7501 | − | 9.34149i | 1.70902 | − | 0.555294i | 0.718849 | − | 0.695166i | \(-0.244669\pi\) |
0.990169 | + | 0.139873i | \(0.0446693\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.24807 | − | 11.3525i | 0.486868 | − | 0.670116i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.89744 | + | 5.73783i | −0.464555 | + | 0.337519i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.06831i | 0.471356i | 0.971831 | + | 0.235678i | \(0.0757310\pi\) | ||||
−0.971831 | + | 0.235678i | \(0.924269\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −18.6576 | + | 10.7263i | −1.08629 | + | 0.624506i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −25.1289 | −1.45324 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −49.3331 | −2.84351 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.89140 | − | 13.7272i | −0.165561 | − | 0.786017i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 14.7750i | − | 0.843255i | −0.906769 | − | 0.421628i | \(-0.861459\pi\) | ||
0.906769 | − | 0.421628i | \(-0.138541\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.40552 | + | 5.38043i | −0.419929 | + | 0.305096i | −0.777609 | − | 0.628748i | \(-0.783568\pi\) |
0.357680 | + | 0.933844i | \(0.383568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.79128 | − | 10.7238i | 0.440389 | − | 0.606144i | −0.529909 | − | 0.848054i | \(-0.677774\pi\) |
0.970299 | + | 0.241910i | \(0.0777740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.751858 | + | 0.244293i | −0.0422286 | + | 0.0137209i | −0.330055 | − | 0.943962i | \(-0.607067\pi\) |
0.287827 | + | 0.957683i | \(0.407067\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.83587 | + | 5.65021i | 0.102789 | + | 0.316351i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.28434 | + | 12.7788i | 0.516595 | + | 0.711032i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.7179 | + | 1.89768i | −1.03828 | + | 0.105264i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.370610 | − | 1.14062i | 0.0204324 | − | 0.0628844i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.04253 | − | 3.20858i | −0.0573026 | − | 0.176359i | 0.918308 | − | 0.395866i | \(-0.129555\pi\) |
−0.975611 | + | 0.219506i | \(0.929555\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.608960 | − | 5.69304i | 0.0332711 | − | 0.311044i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.6189 | + | 14.6157i | −0.578449 | + | 0.796166i | −0.993524 | − | 0.113621i | \(-0.963755\pi\) |
0.415076 | + | 0.909787i | \(0.363755\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.2215 | − | 9.60597i | −0.715983 | − | 0.520192i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 34.2694i | − | 1.85037i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.90284 | + | 0.943191i | 0.155833 | + | 0.0506332i | 0.385895 | − | 0.922543i | \(-0.373893\pi\) |
−0.230062 | + | 0.973176i | \(0.573893\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.628744 | 0.0336559 | 0.0168280 | − | 0.999858i | \(-0.494643\pi\) | ||||
0.0168280 | + | 0.999858i | \(0.494643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.9651 | + | 5.83721i | 0.956184 | + | 0.310683i | 0.745226 | − | 0.666812i | \(-0.232342\pi\) |
0.210958 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.3953 | − | 13.0097i | −0.764024 | − | 0.690482i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4087 | − | 17.0074i | −1.23546 | − | 0.897617i | −0.238176 | − | 0.971222i | \(-0.576550\pi\) |
−0.997287 | + | 0.0736053i | \(0.976550\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5149 | + | 9.09264i | −0.658681 | + | 0.478560i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.6664 | + | 2.24669i | −0.558303 | + | 0.117597i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.11949 | − | 1.66342i | 0.267235 | − | 0.0868299i | −0.172334 | − | 0.985038i | \(-0.555131\pi\) |
0.439570 | + | 0.898209i | \(0.355131\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −14.0066 | + | 43.1079i | −0.727187 | + | 2.23805i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.46415 | + | 8.89714i | 0.334701 | + | 0.460677i | 0.942884 | − | 0.333120i | \(-0.108101\pi\) |
−0.608183 | + | 0.793797i | \(0.708101\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.65513 | − | 3.65447i | −0.136746 | − | 0.188215i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.18405 | + | 6.72183i | −0.112187 | + | 0.345277i | −0.991350 | − | 0.131245i | \(-0.958103\pi\) |
0.879163 | + | 0.476522i | \(0.158103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.70484 | − | 2.50346i | 0.393699 | − | 0.127921i | −0.105476 | − | 0.994422i | \(-0.533637\pi\) |
0.499175 | + | 0.866501i | \(0.333637\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 50.0996 | − | 10.5526i | 2.55331 | − | 0.537812i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −26.7325 | + | 19.4223i | −1.35539 | + | 0.984750i | −0.356669 | + | 0.934231i | \(0.616088\pi\) |
−0.998723 | + | 0.0505192i | \(0.983912\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.5358 | + | 10.5609i | 0.735107 | + | 0.534086i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.6926 | − | 18.7008i | −1.04116 | − | 0.940938i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.7615 | + | 3.82155i | 0.590294 | + | 0.191798i | 0.588907 | − | 0.808201i | \(-0.299559\pi\) |
0.00138688 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.7983 | 0.738993 | 0.369496 | − | 0.929232i | \(-0.379530\pi\) | ||||
0.369496 | + | 0.929232i | \(0.379530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.8178 | + | 3.83984i | 0.588687 | + | 0.191276i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.29012i | 0.460494i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.1618 | − | 13.9219i | −0.947491 | − | 0.688392i | 0.00272132 | − | 0.999996i | \(-0.499134\pi\) |
−0.950212 | + | 0.311604i | \(0.899134\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −26.1743 | + | 36.0258i | −1.28795 | + | 1.77272i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.11433 | + | 19.7664i | −0.103789 | + | 0.970297i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.477059 | + | 1.46824i | 0.0233058 | + | 0.0717280i | 0.962033 | − | 0.272933i | \(-0.0879938\pi\) |
−0.938727 | + | 0.344661i | \(0.887994\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.43760 | + | 16.7352i | −0.265013 | + | 0.815625i | 0.726678 | + | 0.686978i | \(0.241063\pi\) |
−0.991691 | + | 0.128647i | \(0.958937\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 11.6249 | + | 6.76883i | 0.563891 | + | 0.328337i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −17.0615 | − | 23.4832i | −0.825665 | − | 1.13643i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.83527 | − | 14.8814i | −0.232907 | − | 0.716814i | −0.997392 | − | 0.0721724i | \(-0.977007\pi\) |
0.764485 | − | 0.644641i | \(-0.222993\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.217772 | − | 0.0707586i | 0.0104655 | − | 0.00340044i | −0.303780 | − | 0.952742i | \(-0.598249\pi\) |
0.314245 | + | 0.949342i | \(0.398249\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −23.0462 | + | 31.7204i | −1.10245 | + | 1.51739i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7111 | − | 11.4147i | 0.749848 | − | 0.544796i | −0.145932 | − | 0.989295i | \(-0.546618\pi\) |
0.895780 | + | 0.444498i | \(0.146618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 12.7980i | − | 0.608051i | −0.952664 | − | 0.304026i | \(-0.901669\pi\) | ||
0.952664 | − | 0.304026i | \(-0.0983309\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.71842 | − | 31.8963i | −0.318483 | − | 1.51203i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.1499 | −0.998124 | −0.499062 | − | 0.866566i | \(-0.666322\pi\) | ||||
−0.499062 | + | 0.866566i | \(0.666322\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0092 | 0.706755 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.7489 | + | 19.4022i | −1.58217 | + | 0.909589i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 8.97118i | − | 0.419654i | −0.977739 | − | 0.209827i | \(-0.932710\pi\) | ||
0.977739 | − | 0.209827i | \(-0.0672901\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.2764 | − | 16.1847i | 1.03751 | − | 0.753797i | 0.0677146 | − | 0.997705i | \(-0.478429\pi\) |
0.969799 | + | 0.243907i | \(0.0784293\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2815 | + | 23.7859i | −0.803140 | + | 1.10543i | 0.189206 | + | 0.981937i | \(0.439409\pi\) |
−0.992346 | + | 0.123489i | \(0.960591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6119 | − | 4.09785i | 0.583609 | − | 0.189626i | −0.00230768 | − | 0.999997i | \(-0.500735\pi\) |
0.585917 | + | 0.810371i | \(0.300735\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.66090 | − | 11.2671i | −0.169045 | − | 0.520266i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −31.0156 | − | 42.6893i | −1.42610 | − | 1.96286i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −14.7711 | + | 25.3682i | −0.677747 | + | 1.16397i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.58057 | + | 17.1752i | −0.254983 | + | 0.784757i | 0.738850 | + | 0.673870i | \(0.235369\pi\) |
−0.993833 | + | 0.110887i | \(0.964631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.18279 | − | 6.71793i | −0.0995266 | − | 0.306311i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 5.97746 | − | 6.61412i | 0.271423 | − | 0.300332i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.26258 | − | 11.3725i | 0.374413 | − | 0.515336i | −0.579681 | − | 0.814844i | \(-0.696823\pi\) |
0.954094 | + | 0.299508i | \(0.0968226\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0310 | − | 16.0065i | −0.994247 | − | 0.722363i | −0.0334000 | − | 0.999442i | \(-0.510634\pi\) |
−0.960847 | + | 0.277079i | \(0.910634\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.22980i | 0.145463i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −38.1827 | − | 12.4063i | −1.71273 | − | 0.556499i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.17654 | 0.366032 | 0.183016 | − | 0.983110i | \(-0.441414\pi\) | ||||
0.183016 | + | 0.983110i | \(0.441414\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.45805 | + | 3.07311i | 0.421714 | + | 0.137023i | 0.512183 | − | 0.858876i | \(-0.328837\pi\) |
−0.0904697 | + | 0.995899i | \(0.528837\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.55620 | − | 19.1227i | 0.380746 | − | 0.850950i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.9758 | − | 10.1540i | −0.619464 | − | 0.450067i | 0.233270 | − | 0.972412i | \(-0.425057\pi\) |
−0.852734 | + | 0.522345i | \(0.825057\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18.2470 | + | 13.2572i | −0.807200 | + | 0.586465i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.6286 | − | 17.2932i | 0.688680 | − | 0.762031i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.22001 | − | 0.396406i | 0.0536561 | − | 0.0174339i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.43786 | − | 10.5807i | 0.150615 | − | 0.463547i | −0.847075 | − | 0.531474i | \(-0.821638\pi\) |
0.997690 | + | 0.0679269i | \(0.0216385\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.20585 | − | 3.03609i | −0.0964551 | − | 0.132759i | 0.758062 | − | 0.652183i | \(-0.226147\pi\) |
−0.854517 | + | 0.519424i | \(0.826147\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.22225 | − | 7.18781i | −0.227485 | − | 0.313106i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.67462 | + | 20.5424i | −0.290201 | + | 0.893146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.8535 | + | 3.52653i | −0.470119 | + | 0.152751i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.450429 | − | 0.201538i | −0.0194738 | − | 0.00871326i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 57.6799 | − | 41.9069i | 2.48445 | − | 1.80506i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.2752 | − | 11.0981i | −0.656731 | − | 0.477143i | 0.208826 | − | 0.977953i | \(-0.433036\pi\) |
−0.865557 | + | 0.500810i | \(0.833036\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.9619 | + | 7.45177i | −0.555226 | + | 0.319199i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.147706 | + | 0.0479926i | 0.00631545 | + | 0.00205201i | 0.312173 | − | 0.950025i | \(-0.398943\pi\) |
−0.305858 | + | 0.952077i | \(0.598943\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.04815 | −0.300261 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −54.8858 | − | 17.8335i | −2.33398 | − | 0.758356i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19.0371i | 0.806626i | 0.915062 | + | 0.403313i | \(0.132141\pi\) | ||||
−0.915062 | + | 0.403313i | \(0.867859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 32.4584 | + | 23.5824i | 1.37285 | + | 0.997430i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.2630 | + | 25.1369i | −0.769694 | + | 1.05939i | 0.226652 | + | 0.973976i | \(0.427222\pi\) |
−0.996345 | + | 0.0854166i | \(0.972778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.7085 | + | 18.6268i | 0.450510 | + | 0.783635i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 12.1573 | + | 37.4162i | 0.509659 | + | 1.56857i | 0.792794 | + | 0.609490i | \(0.208626\pi\) |
−0.283135 | + | 0.959080i | \(0.591374\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.78632 | − | 27.0415i | 0.367696 | − | 1.13165i | −0.580580 | − | 0.814203i | \(-0.697174\pi\) |
0.948276 | − | 0.317448i | \(-0.102826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.06267 | + | 32.6360i | −0.294534 | + | 1.36101i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.2014 | + | 18.1701i | 0.549581 | + | 0.756433i | 0.989955 | − | 0.141381i | \(-0.0451544\pi\) |
−0.440375 | + | 0.897814i | \(0.645154\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.7108 | + | 39.1198i | 0.527332 | + | 1.62296i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −46.1085 | + | 14.9815i | −1.90962 | + | 0.620472i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.45335 | − | 13.0114i | 0.390182 | − | 0.537039i | −0.568064 | − | 0.822984i | \(-0.692308\pi\) |
0.958246 | + | 0.285945i | \(0.0923076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.6854 | − | 11.3961i | 0.646307 | − | 0.469570i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.4648i | 0.840389i | 0.907434 | + | 0.420194i | \(0.138038\pi\) | ||||
−0.907434 | + | 0.420194i | \(0.861962\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.6762 | + | 2.96041i | 1.13461 | + | 0.121365i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5688 | 0.758699 | 0.379349 | − | 0.925253i | \(-0.376148\pi\) | ||||
0.379349 | + | 0.925253i | \(0.376148\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 47.2047 | 1.92552 | 0.962761 | − | 0.270355i | \(-0.0871409\pi\) | ||||
0.962761 | + | 0.270355i | \(0.0871409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.3804 | + | 20.2261i | 0.909894 | + | 0.822310i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0786576i | 0.00319261i | 0.999999 | + | 0.00159631i | \(0.000508121\pi\) | ||||
−0.999999 | + | 0.00159631i | \(0.999492\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.789085 | + | 0.573304i | −0.0319230 | + | 0.0231934i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.12162 | + | 4.29654i | −0.126081 | + | 0.173536i | −0.867391 | − | 0.497627i | \(-0.834205\pi\) |
0.741310 | + | 0.671163i | \(0.234205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.9429 | − | 9.40411i | 1.16520 | − | 0.378595i | 0.338349 | − | 0.941021i | \(-0.390132\pi\) |
0.826848 | + | 0.562426i | \(0.190132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.77918 | + | 30.0972i | 0.393058 | + | 1.20971i | 0.930463 | + | 0.366385i | \(0.119405\pi\) |
−0.537405 | + | 0.843324i | \(0.680595\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −39.6439 | − | 54.5651i | −1.58830 | − | 2.18610i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.79622 | + | 24.8431i | −0.111849 | + | 0.993725i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.56070 | + | 4.80335i | −0.0622293 | + | 0.191522i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.4722 | − | 32.2301i | −0.416891 | − | 1.28306i | −0.910548 | − | 0.413403i | \(-0.864340\pi\) |
0.493657 | − | 0.869657i | \(-0.335660\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 34.9920 | − | 7.37048i | 1.38862 | − | 0.292489i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.8635 | + | 43.8564i | −1.26248 | + | 1.73765i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −39.6699 | − | 28.8219i | −1.56687 | − | 1.13840i | −0.930080 | − | 0.367358i | \(-0.880263\pi\) |
−0.636788 | − | 0.771039i | \(-0.719737\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.2509i | 0.562000i | 0.959708 | + | 0.281000i | \(0.0906660\pi\) | ||||
−0.959708 | + | 0.281000i | \(0.909334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.2623 | − | 13.0820i | −1.58287 | − | 0.514307i | −0.620079 | − | 0.784539i | \(-0.712899\pi\) |
−0.962795 | + | 0.270233i | \(0.912899\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −47.6300 | −1.86964 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 44.7274 | + | 14.5328i | 1.75032 | + | 0.568713i | 0.996126 | − | 0.0879407i | \(-0.0280286\pi\) |
0.754192 | + | 0.656654i | \(0.228029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −27.3983 | − | 2.93068i | −1.07054 | − | 0.114511i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.05013 | + | 6.57531i | 0.352543 | + | 0.256138i | 0.749935 | − | 0.661511i | \(-0.230085\pi\) |
−0.397392 | + | 0.917649i | \(0.630085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7102 | − | 27.3981i | 1.46676 | − | 1.06566i | 0.485218 | − | 0.874393i | \(-0.338740\pi\) |
0.981538 | − | 0.191268i | \(-0.0612599\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.46029 | + | 60.3958i | −0.250519 | + | 2.34205i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.62483 | + | 2.47746i | −0.295235 | + | 0.0959276i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.59412 | − | 29.5277i | 0.370377 | − | 1.13990i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.07264 | − | 11.1110i | −0.311178 | − | 0.428299i | 0.624570 | − | 0.780968i | \(-0.285274\pi\) |
−0.935748 | + | 0.352669i | \(0.885274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6428 | + | 29.7888i | 0.831801 | + | 1.14488i | 0.987585 | + | 0.157085i | \(0.0502095\pi\) |
−0.155784 | + | 0.987791i | \(0.549790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.70024 | − | 17.5435i | 0.218755 | − | 0.673259i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.6179 | − | 9.29850i | 1.09503 | − | 0.355797i | 0.294843 | − | 0.955546i | \(-0.404733\pi\) |
0.800189 | + | 0.599748i | \(0.204733\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.34638 | + | 11.0391i | 0.242483 | + | 0.421784i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 29.8222 | − | 21.6671i | 1.13614 | − | 0.825451i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.76839 | + | 4.91752i | 0.257482 | + | 0.187071i | 0.709036 | − | 0.705172i | \(-0.249130\pi\) |
−0.451554 | + | 0.892244i | \(0.649130\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.29438 | − | 39.3783i | −0.314624 | − | 1.49370i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.76033 | + | 2.52148i | 0.293943 | + | 0.0955080i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.42495 | 0.129359 | 0.0646794 | − | 0.997906i | \(-0.479398\pi\) | ||||
0.0646794 | + | 0.997906i | \(0.479398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.4820 | − | 3.40581i | −0.395336 | − | 0.128453i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 43.3478i | − | 1.63026i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.0330 | − | 29.0857i | −1.50347 | − | 1.09234i | −0.968973 | − | 0.247168i | \(-0.920500\pi\) |
−0.534499 | − | 0.845169i | \(-0.679500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.9630 | − | 17.8421i | 0.485469 | − | 0.668191i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.0072 | − | 17.0058i | −1.42139 | − | 0.635980i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.08148 | + | 24.8722i | 0.301388 | + | 0.927578i | 0.981000 | + | 0.194006i | \(0.0621481\pi\) |
−0.679612 | + | 0.733572i | \(0.737852\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.9038 | − | 45.8692i | 0.555046 | − | 1.70826i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.49247 | + | 2.42121i | −0.203985 | + | 0.0899216i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.3475 | + | 28.0059i | 0.754647 | + | 1.03868i | 0.997640 | + | 0.0686545i | \(0.0218706\pi\) |
−0.242994 | + | 0.970028i | \(0.578129\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.86463 | − | 27.2825i | −0.327870 | − | 1.00908i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.6104 | − | 5.39704i | 0.613518 | − | 0.199344i | 0.0142577 | − | 0.999898i | \(-0.495461\pi\) |
0.599260 | + | 0.800554i | \(0.295461\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.44814 | − | 10.2515i | 0.274356 | − | 0.377618i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.2358 | − | 11.7960i | 0.597243 | − | 0.433922i | −0.247656 | − | 0.968848i | \(-0.579660\pi\) |
0.844899 | + | 0.534926i | \(0.179660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.84644i | 0.214485i | 0.994233 | + | 0.107243i | \(0.0342022\pi\) | ||||
−0.994233 | + | 0.107243i | \(0.965798\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.995453 | − | 2.22479i | 0.0364706 | − | 0.0815101i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.02104 | −0.0373081 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.7925 | −1.19662 | −0.598308 | − | 0.801266i | \(-0.704160\pi\) | ||||
−0.598308 | + | 0.801266i | \(0.704160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −10.3918 | + | 23.2252i | −0.378196 | + | 0.845252i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 22.6371i | 0.822759i | 0.911464 | + | 0.411379i | \(0.134953\pi\) | ||||
−0.911464 | + | 0.411379i | \(0.865047\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3923 | + | 21.3547i | −1.06547 | + | 0.774109i | −0.975092 | − | 0.221799i | \(-0.928807\pi\) |
−0.0903767 | + | 0.995908i | \(0.528807\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.1839 | + | 25.0280i | −0.658301 | + | 0.906073i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 34.4425 | − | 11.1910i | 1.24365 | − | 0.404085i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.51902 | − | 13.9081i | −0.162960 | − | 0.501539i | 0.835920 | − | 0.548851i | \(-0.184935\pi\) |
−0.998880 | + | 0.0473119i | \(0.984935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.9422 | − | 24.6953i | −0.645336 | − | 0.888229i | 0.353550 | − | 0.935416i | \(-0.384975\pi\) |
−0.998886 | + | 0.0471864i | \(0.984975\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.30846 | − | 14.2691i | 0.298449 | − | 0.512561i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.50245 | + | 16.9348i | −0.197146 | + | 0.606752i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.2699 | − | 40.8404i | −0.474833 | − | 1.46138i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.13194 | + | 3.63852i | 0.290241 | + | 0.129865i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.8905 | − | 39.7644i | 1.02984 | − | 1.41745i | 0.124766 | − | 0.992186i | \(-0.460182\pi\) |
0.905070 | − | 0.425262i | \(-0.139818\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.9663 | + | 26.1310i | 1.27881 | + | 0.929112i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 23.6065i | 0.838290i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.3529 | + | 13.7613i | 1.50022 | + | 0.487450i | 0.940081 | − | 0.340951i | \(-0.110749\pi\) |
0.560136 | + | 0.828401i | \(0.310749\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.697388 | 0.0246718 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.9437 | − | 7.45487i | −0.809667 | − | 0.263077i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 14.2405 | + | 67.6082i | 0.501913 | + | 2.38288i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.5060 | + | 17.8046i | 0.861584 | + | 0.625978i | 0.928316 | − | 0.371793i | \(-0.121257\pi\) |
−0.0667312 | + | 0.997771i | \(0.521257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.05382 | + | 3.67182i | −0.177464 | + | 0.128935i | −0.672971 | − | 0.739669i | \(-0.734982\pi\) |
0.495507 | + | 0.868604i | \(0.334982\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −24.3304 | − | 42.3211i | −0.852255 | − | 1.48244i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 59.5367 | − | 19.3447i | 2.08293 | − | 0.676784i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.95524 | − | 18.3284i | 0.207839 | − | 0.639664i | −0.791745 | − | 0.610851i | \(-0.790827\pi\) |
0.999585 | − | 0.0288127i | \(-0.00917263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.44218 | − | 6.11414i | −0.154845 | − | 0.213126i | 0.724546 | − | 0.689227i | \(-0.242050\pi\) |
−0.879391 | + | 0.476101i | \(0.842050\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4412 | − | 25.3821i | −0.641262 | − | 0.882621i | 0.357420 | − | 0.933944i | \(-0.383656\pi\) |
−0.998682 | + | 0.0513225i | \(0.983656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55625 | + | 26.3334i | −0.297171 | + | 0.914597i | 0.685313 | + | 0.728249i | \(0.259665\pi\) |
−0.982484 | + | 0.186349i | \(0.940335\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36.8629 | − | 11.9775i | 1.27723 | − | 0.414996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.67890 | − | 34.3933i | 0.127314 | − | 1.19023i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 30.5642 | − | 22.2062i | 1.05519 | − | 0.766643i | 0.0819999 | − | 0.996632i | \(-0.473869\pi\) |
0.973193 | + | 0.229990i | \(0.0738693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.2956 | + | 16.1987i | 0.768812 | + | 0.558575i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.57565 | + | 0.275506i | 0.0886049 | + | 0.00947770i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59.3626 | + | 19.2881i | 2.03972 | + | 0.662747i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.5368 | −0.429756 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.9508 | + | 15.2552i | 1.60756 | + | 0.522329i | 0.968962 | − | 0.247208i | \(-0.0795131\pi\) |
0.638602 | + | 0.769537i | \(0.279513\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.7692i | 0.538667i | 0.963047 | + | 0.269333i | \(0.0868034\pi\) | ||||
−0.963047 | + | 0.269333i | \(0.913197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.60223 | + | 5.52335i | 0.259385 | + | 0.188454i | 0.709876 | − | 0.704327i | \(-0.248751\pi\) |
−0.450491 | + | 0.892781i | \(0.648751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.5040 | + | 14.4575i | −0.357560 | + | 0.492140i | −0.949467 | − | 0.313867i | \(-0.898375\pi\) |
0.591907 | + | 0.806007i | \(0.298375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37.5697 | − | 7.91343i | 1.27741 | − | 0.269065i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19.0748 | − | 58.7061i | −0.647068 | − | 1.99147i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.97728 | + | 9.16312i | −0.100881 | + | 0.310481i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 15.7131 | + | 49.2844i | 0.531199 | + | 1.66612i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.4069 | + | 14.3238i | 0.351415 | + | 0.483681i | 0.947732 | − | 0.319068i | \(-0.103370\pi\) |
−0.596317 | + | 0.802749i | \(0.703370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.82007 | + | 30.2231i | 0.330847 | + | 1.01824i | 0.968732 | + | 0.248110i | \(0.0798094\pi\) |
−0.637885 | + | 0.770131i | \(0.720191\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.9158 | − | 10.6950i | 1.10771 | − | 0.359916i | 0.302643 | − | 0.953104i | \(-0.402131\pi\) |
0.805064 | + | 0.593188i | \(0.202131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.7639 | + | 23.0735i | −0.562876 | + | 0.774732i | −0.991689 | − | 0.128661i | \(-0.958932\pi\) |
0.428813 | + | 0.903393i | \(0.358932\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 59.8610 | − | 43.4916i | 2.00767 | − | 1.45866i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.52186i | 0.0509271i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −23.9647 | − | 21.6579i | −0.801051 | − | 0.723944i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.96444 | 0.132221 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.3567 | −0.878069 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −27.5620 | − | 2.94819i | −0.916193 | − | 0.0980013i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.01754i | 0.233013i | 0.993190 | + | 0.116507i | \(0.0371697\pi\) | ||||
−0.993190 | + | 0.116507i | \(0.962830\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9145 | + | 12.2891i | −0.560403 | + | 0.407157i | −0.831606 | − | 0.555365i | \(-0.812578\pi\) |
0.271203 | + | 0.962522i | \(0.412578\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.8602 | + | 35.5936i | −0.855849 | + | 1.17797i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −54.2240 | + | 17.6184i | −1.79063 | + | 0.581812i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.4658 | − | 56.8320i | −0.609132 | − | 1.87471i | −0.465406 | − | 0.885097i | \(-0.654092\pi\) |
−0.143726 | − | 0.989618i | \(-0.545908\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 19.1916 | + | 26.4149i | 0.631698 | + | 0.869458i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.33837 | + | 0.946755i | −0.307044 | + | 0.0311291i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.4320 | + | 38.2618i | −0.407881 | + | 1.25533i | 0.510585 | + | 0.859828i | \(0.329429\pi\) |
−0.918466 | + | 0.395501i | \(0.870571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.1376 | + | 80.4434i | 0.856626 | + | 2.63642i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.8383 | + | 25.8102i | 0.485263 | + | 0.844085i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.0457 | + | 39.9780i | −0.948881 | + | 1.30602i | 0.00314114 | + | 0.999995i | \(0.499000\pi\) |
−0.952022 | + | 0.306028i | \(0.901000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0130 | + | 13.0872i | 0.587207 | + | 0.426631i | 0.841315 | − | 0.540545i | \(-0.181782\pi\) |
−0.254108 | + | 0.967176i | \(0.581782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 20.2546i | 0.659579i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.9316 | + | 11.0251i | 1.10263 | + | 0.358266i | 0.803114 | − | 0.595825i | \(-0.203175\pi\) |
0.299516 | + | 0.954091i | \(0.403175\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.3428 | 0.595433 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.66940 | + | 0.867341i | 0.0864704 | + | 0.0280959i | 0.351933 | − | 0.936025i | \(-0.385525\pi\) |
−0.265462 | + | 0.964121i | \(0.585525\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.20919 | − | 1.84496i | 0.103847 | − | 0.0597014i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.3153 | + | 15.4865i | 0.688308 | + | 0.500085i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.2568 | − | 11.8113i | 0.524413 | − | 0.381008i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 33.3211 | + | 14.9091i | 1.07264 | + | 0.479940i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.9640 | − | 3.56243i | 0.352580 | − | 0.114560i | −0.127372 | − | 0.991855i | \(-0.540654\pi\) |
0.479952 | + | 0.877295i | \(0.340654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.15578 | + | 22.0232i | −0.229640 | + | 0.706759i | 0.768148 | + | 0.640273i | \(0.221179\pi\) |
−0.997787 | + | 0.0664858i | \(0.978821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.9433 | − | 67.3646i | −1.56905 | − | 2.15961i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.85551 | + | 6.68304i | 0.155342 | + | 0.213809i | 0.879593 | − | 0.475726i | \(-0.157815\pi\) |
−0.724252 | + | 0.689536i | \(0.757815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 22.2927 | − | 68.6100i | 0.712479 | − | 2.19278i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.8202 | − | 6.11506i | 0.600271 | − | 0.195040i | 0.00690994 | − | 0.999976i | \(-0.497800\pi\) |
0.593361 | + | 0.804936i | \(0.297800\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.4387 | + | 22.6157i | −0.651232 | + | 0.720595i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57.6083 | − | 41.8549i | 1.83184 | − | 1.33091i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3036 | − | 12.5718i | −0.549666 | − | 0.399355i | 0.277997 | − | 0.960582i | \(-0.410330\pi\) |
−0.827662 | + | 0.561227i | \(0.810330\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.55089 | + | 12.4060i | −0.175975 | + | 0.393296i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.7226 | − | 5.43350i | −0.529610 | − | 0.172081i | 0.0319923 | − | 0.999488i | \(-0.489815\pi\) |
−0.561602 | + | 0.827407i | \(0.689815\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 900.2.w.c.289.3 | 24 | ||
3.2 | odd | 2 | 300.2.o.a.289.2 | yes | 24 | ||
15.2 | even | 4 | 1500.2.m.d.301.1 | 24 | |||
15.8 | even | 4 | 1500.2.m.c.301.6 | 24 | |||
15.14 | odd | 2 | 1500.2.o.c.949.6 | 24 | |||
25.9 | even | 10 | inner | 900.2.w.c.109.3 | 24 | ||
75.29 | odd | 10 | 7500.2.d.g.1249.13 | 24 | |||
75.38 | even | 20 | 1500.2.m.c.1201.6 | 24 | |||
75.41 | odd | 10 | 1500.2.o.c.49.6 | 24 | |||
75.47 | even | 20 | 7500.2.a.m.1.1 | 12 | |||
75.53 | even | 20 | 7500.2.a.n.1.12 | 12 | |||
75.59 | odd | 10 | 300.2.o.a.109.2 | ✓ | 24 | ||
75.62 | even | 20 | 1500.2.m.d.1201.1 | 24 | |||
75.71 | odd | 10 | 7500.2.d.g.1249.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.2 | ✓ | 24 | 75.59 | odd | 10 | ||
300.2.o.a.289.2 | yes | 24 | 3.2 | odd | 2 | ||
900.2.w.c.109.3 | 24 | 25.9 | even | 10 | inner | ||
900.2.w.c.289.3 | 24 | 1.1 | even | 1 | trivial | ||
1500.2.m.c.301.6 | 24 | 15.8 | even | 4 | |||
1500.2.m.c.1201.6 | 24 | 75.38 | even | 20 | |||
1500.2.m.d.301.1 | 24 | 15.2 | even | 4 | |||
1500.2.m.d.1201.1 | 24 | 75.62 | even | 20 | |||
1500.2.o.c.49.6 | 24 | 75.41 | odd | 10 | |||
1500.2.o.c.949.6 | 24 | 15.14 | odd | 2 | |||
7500.2.a.m.1.1 | 12 | 75.47 | even | 20 | |||
7500.2.a.n.1.12 | 12 | 75.53 | even | 20 | |||
7500.2.d.g.1249.12 | 24 | 75.71 | odd | 10 | |||
7500.2.d.g.1249.13 | 24 | 75.29 | odd | 10 |