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 | 109.3 | ||
Character | \(\chi\) | \(=\) | 900.109 |
Dual form | 900.2.w.c.289.3 |
$q$-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 \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{7}{10}\right)\) |
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 | \(-0.661273\pi\) | ||
0.485254 | − | 0.874373i | \(-0.338727\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00366 | − | 2.90883i | −1.20715 | − | 0.877045i | −0.212180 | − | 0.977231i | \(-0.568056\pi\) |
−0.994969 | + | 0.100185i | \(0.968056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.21170 | + | 3.04414i | 0.613415 | + | 0.844294i | 0.996853 | − | 0.0792730i | \(-0.0252599\pi\) |
−0.383438 | + | 0.923567i | \(0.625260\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.55872 | − | 0.831378i | −0.620580 | − | 0.201639i | −0.0181824 | − | 0.999835i | \(-0.505788\pi\) |
−0.602398 | + | 0.798196i | \(0.705788\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.81426 | + | 5.58371i | −0.416219 | + | 1.28099i | 0.494937 | + | 0.868929i | \(0.335191\pi\) |
−0.911156 | + | 0.412062i | \(0.864809\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.92540 | + | 5.40285i | −0.818502 | + | 1.12657i | 0.171453 | + | 0.985192i | \(0.445154\pi\) |
−0.989955 | + | 0.141379i | \(0.954846\pi\) | |||||||
\(24\) | 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 | 0.979574 | − | 0.201084i | \(-0.0644464\pi\) |
−0.910686 | + | 0.413099i | \(0.864446\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.02048 | − | 3.14072i | 0.183284 | − | 0.564090i | −0.816631 | − | 0.577161i | \(-0.804161\pi\) |
0.999915 | + | 0.0130708i | \(0.00416068\pi\) | |||||||
\(32\) | 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 | 0.890028 | − | 0.455907i | \(-0.150685\pi\) |
−0.708627 | + | 0.705584i | \(0.750685\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.45366 | + | 1.78269i | −0.383198 | + | 0.278410i | −0.762663 | − | 0.646797i | \(-0.776108\pi\) |
0.379464 | + | 0.925206i | \(0.376108\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.6626i | − | 1.62603i | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||
0.582244 | − | 0.813014i | \(-0.302175\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.246527 | + | 0.0801015i | −0.0359597 | + | 0.0116840i | −0.326942 | − | 0.945045i | \(-0.606018\pi\) |
0.290982 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(48\) | 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 | 0.411292 | − | 0.911504i | \(-0.365078\pi\) |
0.868511 | + | 0.495670i | \(0.165078\pi\) | |||||||
\(54\) | 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 | 0.0487233 | − | 0.998812i | \(-0.484485\pi\) |
0.964983 | + | 0.262311i | \(0.0844847\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.07552 | − | 3.68758i | −0.649854 | − | 0.472147i | 0.213367 | − | 0.976972i | \(-0.431557\pi\) |
−0.863222 | + | 0.504825i | \(0.831557\pi\) | |||||||
\(62\) | 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 | 0.156460 | − | 0.987684i | \(-0.449992\pi\) |
−0.453968 | + | 0.891018i | \(0.649992\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.68143 | − | 8.25259i | −0.318227 | − | 0.979403i | −0.974406 | − | 0.224797i | \(-0.927828\pi\) |
0.656178 | − | 0.754606i | \(-0.272172\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.86534 | − | 3.94381i | 0.335363 | − | 0.461588i | −0.607717 | − | 0.794154i | \(-0.707914\pi\) |
0.943080 | + | 0.332566i | \(0.107914\pi\) | |||||||
\(74\) | 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 | −0.894457 | − | 0.447155i | \(-0.852437\pi\) |
0.460800 | − | 0.887504i | \(-0.347563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.45513 | + | 2.74724i | 0.928071 | + | 0.301549i | 0.733774 | − | 0.679394i | \(-0.237757\pi\) |
0.194298 | + | 0.980943i | \(0.437757\pi\) | |||||||
\(84\) | 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 | −0.251870 | − | 0.967761i | \(-0.581046\pi\) |
−0.998228 | + | 0.0595118i | \(0.981046\pi\) | |||||||
\(90\) | 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 | −0.495119 | − | 0.868825i | \(-0.664875\pi\) |
0.110123 | + | 0.993918i | \(0.464875\pi\) | |||||||
\(98\) | 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 | −0.753577 | − | 0.657360i | \(-0.771673\pi\) |
−0.223270 | + | 0.974757i | \(0.571673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.220683i | − | 0.0213342i | −0.999943 | − | 0.0106671i | \(-0.996604\pi\) | ||
0.999943 | − | 0.0106671i | \(-0.00339551\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.40941 | − | 3.93017i | 0.518127 | − | 0.376442i | −0.297771 | − | 0.954637i | \(-0.596243\pi\) |
0.815898 | + | 0.578196i | \(0.196243\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.64782 | + | 7.77355i | 0.531302 | + | 0.731274i | 0.987328 | − | 0.158692i | \(-0.0507277\pi\) |
−0.456026 | + | 0.889966i | \(0.650728\pi\) | |||||||
\(114\) | 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 | 0.153025 | + | 0.988222i | \(0.451098\pi\) |
−0.987143 | + | 0.159842i | \(0.948902\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.80795 | − | 11.7197i | 0.332702 | − | 1.02395i | −0.635140 | − | 0.772397i | \(-0.719058\pi\) |
0.967843 | − | 0.251556i | \(-0.0809422\pi\) | |||||||
\(132\) | 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 | 0.927699 | − | 0.373329i | \(-0.121784\pi\) |
−0.641731 | + | 0.766930i | \(0.721784\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.5598 | − | 10.5783i | −1.23495 | − | 0.897242i | −0.237697 | − | 0.971339i | \(-0.576393\pi\) |
−0.997251 | + | 0.0740969i | \(0.976393\pi\) | |||||||
\(140\) | 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 | \(0.0508221\pi\) | ||||
−0.987281 | + | 0.158985i | \(0.949178\pi\) | |||||||
\(158\) | 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 | −0.922148 | − | 0.386837i | \(-0.873568\pi\) |
−0.0829441 | − | 0.996554i | \(-0.526432\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −14.7118 | − | 4.78015i | −1.13843 | − | 0.369899i | −0.321658 | − | 0.946856i | \(-0.604240\pi\) |
−0.816775 | + | 0.576957i | \(0.804240\pi\) | |||||||
\(168\) | 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 | 0.229253 | + | 0.973367i | \(0.426372\pi\) |
−0.996570 | + | 0.0827547i | \(0.973628\pi\) | |||||||
\(174\) | 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 | −0.967384 | − | 0.253316i | \(-0.918479\pi\) |
0.633734 | − | 0.773551i | \(-0.281521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.83071 | − | 11.7897i | 0.284734 | − | 0.876322i | −0.701744 | − | 0.712429i | \(-0.747595\pi\) |
0.986478 | − | 0.163893i | \(-0.0524051\pi\) | |||||||
\(182\) | 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 | −0.635184 | − | 0.772361i | \(-0.719076\pi\) |
0.538276 | + | 0.842769i | \(0.319076\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.3253i | 1.17512i | 0.809181 | + | 0.587560i | \(0.199911\pi\) | ||||
−0.809181 | + | 0.587560i | \(0.800089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.9652 | − | 4.21264i | 0.923730 | − | 0.300138i | 0.191734 | − | 0.981447i | \(-0.438589\pi\) |
0.731996 | + | 0.681309i | \(0.238589\pi\) | |||||||
\(198\) | 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 | −0.000268984 | − | 1.00000i | \(-0.500086\pi\) |
−0.951140 | + | 0.308761i | \(0.900086\pi\) | |||||||
\(212\) | 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 | −0.793313 | − | 0.608814i | \(-0.791646\pi\) |
0.824164 | + | 0.566352i | \(0.191646\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0771 | − | 19.3755i | 0.934331 | − | 1.28600i | −0.0238153 | − | 0.999716i | \(-0.507581\pi\) |
0.958146 | − | 0.286280i | \(-0.0924186\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.71005 | + | 5.26299i | 0.113003 | + | 0.347788i | 0.991525 | − | 0.129914i | \(-0.0414700\pi\) |
−0.878522 | + | 0.477702i | \(0.841470\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.863314 | − | 0.280508i | −0.0565576 | − | 0.0183767i | 0.280602 | − | 0.959824i | \(-0.409466\pi\) |
−0.337159 | + | 0.941448i | \(0.609466\pi\) | |||||||
\(234\) | 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 | 0.841646 | − | 0.540030i | \(-0.181587\pi\) |
−0.253516 | + | 0.967331i | \(0.581587\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3840 | − | 11.9037i | 1.05539 | − | 0.766783i | 0.0821564 | − | 0.996619i | \(-0.473819\pi\) |
0.973229 | + | 0.229837i | \(0.0738193\pi\) | |||||||
\(242\) | 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 | \(0.0475866\pi\) | ||||
−0.988846 | + | 0.148941i | \(0.952413\pi\) | |||||||
\(258\) | 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 | 0.830376 | − | 0.557204i | \(-0.188126\pi\) |
−0.786532 | + | 0.617549i | \(0.788126\pi\) | |||||||
\(264\) | 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 | 0.356891 | + | 0.934146i | \(0.383837\pi\) |
−0.837808 | + | 0.545965i | \(0.816163\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.81499 | − | 5.58596i | −0.110253 | − | 0.339323i | 0.880675 | − | 0.473722i | \(-0.157090\pi\) |
−0.990927 | + | 0.134399i | \(0.957090\pi\) | |||||||
\(272\) | 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 | −0.713563 | − | 0.700591i | \(-0.752920\pi\) |
0.886805 | + | 0.462144i | \(0.152920\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.400257 | − | 1.23186i | 0.0238773 | − | 0.0734868i | −0.938408 | − | 0.345530i | \(-0.887699\pi\) |
0.962285 | + | 0.272043i | \(0.0876993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 28.7501 | + | 9.34149i | 1.70902 | + | 0.555294i | 0.990169 | − | 0.139873i | \(-0.0446693\pi\) |
0.718849 | + | 0.695166i | \(0.244669\pi\) | |||||||
\(284\) | 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 | \(-0.924269\pi\) | ||
0.971831 | − | 0.235678i | \(-0.0757310\pi\) | |||||||
\(294\) | 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 | \(0.138541\pi\) | ||||
−0.906769 | + | 0.421628i | \(0.861459\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.40552 | − | 5.38043i | −0.419929 | − | 0.305096i | 0.357680 | − | 0.933844i | \(-0.383568\pi\) |
−0.777609 | + | 0.628748i | \(0.783568\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.79128 | + | 10.7238i | 0.440389 | + | 0.606144i | 0.970299 | − | 0.241910i | \(-0.0777740\pi\) |
−0.529909 | + | 0.848054i | \(0.677774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −0.751858 | − | 0.244293i | −0.0422286 | − | 0.0137209i | 0.287827 | − | 0.957683i | \(-0.407067\pi\) |
−0.330055 | + | 0.943962i | \(0.607067\pi\) | |||||||
\(318\) | 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 | −0.975611 | − | 0.219506i | \(-0.929555\pi\) |
0.918308 | + | 0.395866i | \(0.129555\pi\) | |||||||
\(332\) | 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 | 0.415076 | − | 0.909787i | \(-0.363755\pi\) |
−0.993524 | + | 0.113621i | \(0.963755\pi\) | |||||||
\(338\) | 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 | −0.230062 | − | 0.973176i | \(-0.573893\pi\) |
0.385895 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(348\) | 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 | 0.210958 | − | 0.977495i | \(-0.432342\pi\) |
0.745226 | + | 0.666812i | \(0.232342\pi\) | |||||||
\(354\) | 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 | −0.997287 | − | 0.0736053i | \(-0.976550\pi\) |
−0.238176 | + | 0.971222i | \(0.576550\pi\) | |||||||
\(360\) | 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 | 0.439570 | − | 0.898209i | \(-0.355131\pi\) |
−0.172334 | + | 0.985038i | \(0.555131\pi\) | |||||||
\(368\) | 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 | −0.608183 | − | 0.793797i | \(-0.708101\pi\) |
0.942884 | + | 0.333120i | \(0.108101\pi\) | |||||||
\(374\) | 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 | 0.879163 | − | 0.476522i | \(-0.158103\pi\) |
−0.991350 | + | 0.131245i | \(0.958103\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.70484 | + | 2.50346i | 0.393699 | + | 0.127921i | 0.499175 | − | 0.866501i | \(-0.333637\pi\) |
−0.105476 | + | 0.994422i | \(0.533637\pi\) | |||||||
\(384\) | 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 | −0.998723 | − | 0.0505192i | \(-0.983912\pi\) |
−0.356669 | − | 0.934231i | \(-0.616088\pi\) | |||||||
\(390\) | 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 | 0.00138688 | − | 0.999999i | \(-0.499559\pi\) |
0.588907 | + | 0.808201i | \(0.299559\pi\) | |||||||
\(398\) | 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 | −0.950212 | − | 0.311604i | \(-0.899134\pi\) |
0.00272132 | + | 0.999996i | \(0.499134\pi\) | |||||||
\(410\) | 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 | −0.938727 | − | 0.344661i | \(-0.887994\pi\) |
0.962033 | + | 0.272933i | \(0.0879938\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.43760 | − | 16.7352i | −0.265013 | − | 0.815625i | −0.991691 | − | 0.128647i | \(-0.958937\pi\) |
0.726678 | − | 0.686978i | \(-0.241063\pi\) | |||||||
\(422\) | 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 | 0.764485 | + | 0.644641i | \(0.222993\pi\) |
−0.997392 | + | 0.0721724i | \(0.977007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.217772 | + | 0.0707586i | 0.0104655 | + | 0.00340044i | 0.314245 | − | 0.949342i | \(-0.398249\pi\) |
−0.303780 | + | 0.952742i | \(0.598249\pi\) | |||||||
\(434\) | 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 | 0.895780 | − | 0.444498i | \(-0.146618\pi\) |
−0.145932 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.7980i | 0.608051i | 0.952664 | + | 0.304026i | \(0.0983309\pi\) | ||||
−0.952664 | + | 0.304026i | \(0.901669\pi\) | |||||||
\(444\) | 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 | \(0.0672901\pi\) | ||||
−0.977739 | + | 0.209827i | \(0.932710\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.2764 | + | 16.1847i | 1.03751 | + | 0.753797i | 0.969799 | − | 0.243907i | \(-0.0784293\pi\) |
0.0677146 | + | 0.997705i | \(0.478429\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2815 | − | 23.7859i | −0.803140 | − | 1.10543i | −0.992346 | − | 0.123489i | \(-0.960591\pi\) |
0.189206 | − | 0.981937i | \(-0.439409\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6119 | + | 4.09785i | 0.583609 | + | 0.189626i | 0.585917 | − | 0.810371i | \(-0.300735\pi\) |
−0.00230768 | + | 0.999997i | \(0.500735\pi\) | |||||||
\(468\) | 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 | −0.993833 | − | 0.110887i | \(-0.964631\pi\) |
0.738850 | − | 0.673870i | \(-0.235369\pi\) | |||||||
\(480\) | 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 | 0.954094 | − | 0.299508i | \(-0.0968226\pi\) |
−0.579681 | + | 0.814844i | \(0.696823\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0310 | + | 16.0065i | −0.994247 | + | 0.722363i | −0.960847 | − | 0.277079i | \(-0.910634\pi\) |
−0.0334000 | + | 0.999442i | \(0.510634\pi\) | |||||||
\(492\) | 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 | −0.0904697 | − | 0.995899i | \(-0.528837\pi\) |
0.512183 | + | 0.858876i | \(0.328837\pi\) | |||||||
\(504\) | 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 | −0.852734 | − | 0.522345i | \(-0.825057\pi\) |
0.233270 | + | 0.972412i | \(0.425057\pi\) | |||||||
\(510\) | 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 | 0.997690 | − | 0.0679269i | \(-0.0216385\pi\) |
−0.847075 | + | 0.531474i | \(0.821638\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.20585 | + | 3.03609i | −0.0964551 | + | 0.132759i | −0.854517 | − | 0.519424i | \(-0.826147\pi\) |
0.758062 | + | 0.652183i | \(0.226147\pi\) | |||||||
\(524\) | 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 | −0.865557 | − | 0.500810i | \(-0.833036\pi\) |
0.208826 | + | 0.977953i | \(0.433036\pi\) | |||||||
\(542\) | 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 | −0.305858 | − | 0.952077i | \(-0.598943\pi\) |
0.312173 | + | 0.950025i | \(0.398943\pi\) | |||||||
\(548\) | 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 | \(-0.867859\pi\) | ||
0.915062 | − | 0.403313i | \(-0.132141\pi\) | |||||||
\(558\) | 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 | −0.996345 | − | 0.0854166i | \(-0.972778\pi\) |
0.226652 | − | 0.973976i | \(-0.427222\pi\) | |||||||
\(564\) | 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 | −0.283135 | − | 0.959080i | \(-0.591374\pi\) |
0.792794 | − | 0.609490i | \(-0.208626\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.78632 | + | 27.0415i | 0.367696 | + | 1.13165i | 0.948276 | + | 0.317448i | \(0.102826\pi\) |
−0.580580 | + | 0.814203i | \(0.697174\pi\) | |||||||
\(572\) | 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 | −0.440375 | − | 0.897814i | \(-0.645154\pi\) |
0.989955 | + | 0.141381i | \(0.0451544\pi\) | |||||||
\(578\) | 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 | 0.958246 | − | 0.285945i | \(-0.0923076\pi\) |
−0.568064 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(588\) | 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 | \(-0.861962\pi\) | ||
0.907434 | − | 0.420194i | \(-0.138038\pi\) | |||||||
\(594\) | 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 | \(-0.999492\pi\) | ||
0.999999 | − | 0.00159631i | \(-0.000508121\pi\) | |||||||
\(608\) | 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 | 0.741310 | − | 0.671163i | \(-0.234205\pi\) |
−0.867391 | + | 0.497627i | \(0.834205\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 28.9429 | + | 9.40411i | 1.16520 | + | 0.378595i | 0.826848 | − | 0.562426i | \(-0.190132\pi\) |
0.338349 | + | 0.941021i | \(0.390132\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.77918 | − | 30.0972i | 0.393058 | − | 1.20971i | −0.537405 | − | 0.843324i | \(-0.680595\pi\) |
0.930463 | − | 0.366385i | \(-0.119405\pi\) | |||||||
\(620\) | 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 | 0.493657 | + | 0.869657i | \(0.335660\pi\) |
−0.910548 | + | 0.413403i | \(0.864340\pi\) | |||||||
\(632\) | 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 | −0.636788 | + | 0.771039i | \(0.719737\pi\) |
−0.930080 | + | 0.367358i | \(0.880263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 14.2509i | − | 0.562000i | −0.959708 | − | 0.281000i | \(-0.909334\pi\) | ||
0.959708 | − | 0.281000i | \(-0.0906660\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −40.2623 | + | 13.0820i | −1.58287 | + | 0.514307i | −0.962795 | − | 0.270233i | \(-0.912899\pi\) |
−0.620079 | + | 0.784539i | \(0.712899\pi\) | |||||||
\(648\) | 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 | 0.754192 | − | 0.656654i | \(-0.228029\pi\) |
0.996126 | + | 0.0879407i | \(0.0280286\pi\) | |||||||
\(654\) | 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 | −0.397392 | − | 0.917649i | \(-0.630085\pi\) |
0.749935 | + | 0.661511i | \(0.230085\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.7102 | + | 27.3981i | 1.46676 | + | 1.06566i | 0.981538 | + | 0.191268i | \(0.0612599\pi\) |
0.485218 | + | 0.874393i | \(0.338740\pi\) | |||||||
\(662\) | 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 | −0.935748 | − | 0.352669i | \(-0.885274\pi\) |
0.624570 | + | 0.780968i | \(0.285274\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.6428 | − | 29.7888i | 0.831801 | − | 1.14488i | −0.155784 | − | 0.987791i | \(-0.549790\pi\) |
0.987585 | − | 0.157085i | \(-0.0502095\pi\) | |||||||
\(678\) | 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 | 0.800189 | − | 0.599748i | \(-0.204733\pi\) |
0.294843 | + | 0.955546i | \(0.404733\pi\) | |||||||
\(684\) | 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 | −0.451554 | − | 0.892244i | \(-0.649130\pi\) |
0.709036 | + | 0.705172i | \(0.249130\pi\) | |||||||
\(692\) | 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 | −0.534499 | + | 0.845169i | \(0.679500\pi\) |
−0.968973 | + | 0.247168i | \(0.920500\pi\) | |||||||
\(710\) | 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 | −0.679612 | − | 0.733572i | \(-0.737852\pi\) |
0.981000 | − | 0.194006i | \(-0.0621481\pi\) | |||||||
\(720\) | 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 | −0.242994 | − | 0.970028i | \(-0.578129\pi\) |
0.997640 | − | 0.0686545i | \(-0.0218706\pi\) | |||||||
\(728\) | 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 | 0.599260 | − | 0.800554i | \(-0.295461\pi\) |
0.0142577 | + | 0.999898i | \(0.495461\pi\) | |||||||
\(734\) | 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 | 0.844899 | − | 0.534926i | \(-0.179660\pi\) |
−0.247656 | + | 0.968848i | \(0.579660\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.84644i | − | 0.214485i | −0.994233 | − | 0.107243i | \(-0.965798\pi\) | ||
0.994233 | − | 0.107243i | \(-0.0342022\pi\) | |||||||
\(744\) | 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 | \(-0.865047\pi\) | ||
0.911464 | − | 0.411379i | \(-0.134953\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.3923 | − | 21.3547i | −1.06547 | − | 0.774109i | −0.0903767 | − | 0.995908i | \(-0.528807\pi\) |
−0.975092 | + | 0.221799i | \(0.928807\pi\) | |||||||
\(762\) | 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 | −0.998880 | − | 0.0473119i | \(-0.984935\pi\) |
0.835920 | + | 0.548851i | \(0.184935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.9422 | + | 24.6953i | −0.645336 | + | 0.888229i | −0.998886 | − | 0.0471864i | \(-0.984975\pi\) |
0.353550 | + | 0.935416i | \(0.384975\pi\) | |||||||
\(774\) | 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 | 0.905070 | + | 0.425262i | \(0.139818\pi\) |
0.124766 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(788\) | 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 | 0.560136 | − | 0.828401i | \(-0.310749\pi\) |
0.940081 | + | 0.340951i | \(0.110749\pi\) | |||||||
\(798\) | 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 | −0.0667312 | − | 0.997771i | \(-0.521257\pi\) |
0.928316 | + | 0.371793i | \(0.121257\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.05382 | − | 3.67182i | −0.177464 | − | 0.128935i | 0.495507 | − | 0.868604i | \(-0.334982\pi\) |
−0.672971 | + | 0.739669i | \(0.734982\pi\) | |||||||
\(812\) | 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 | 0.999585 | + | 0.0288127i | \(0.00917263\pi\) |
−0.791745 | + | 0.610851i | \(0.790827\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.44218 | + | 6.11414i | −0.154845 | + | 0.213126i | −0.879391 | − | 0.476101i | \(-0.842050\pi\) |
0.724546 | + | 0.689227i | \(0.242050\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.4412 | + | 25.3821i | −0.641262 | + | 0.882621i | −0.998682 | − | 0.0513225i | \(-0.983656\pi\) |
0.357420 | + | 0.933944i | \(0.383656\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.55625 | − | 26.3334i | −0.297171 | − | 0.914597i | −0.982484 | − | 0.186349i | \(-0.940335\pi\) |
0.685313 | − | 0.728249i | \(-0.259665\pi\) | |||||||
\(830\) | 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 | 0.973193 | − | 0.229990i | \(-0.0738693\pi\) |
0.0819999 | + | 0.996632i | \(0.473869\pi\) | |||||||
\(840\) | 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 | 0.638602 | − | 0.769537i | \(-0.279513\pi\) |
0.968962 | + | 0.247208i | \(0.0795131\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.7692i | − | 0.538667i | −0.963047 | − | 0.269333i | \(-0.913197\pi\) | ||
0.963047 | − | 0.269333i | \(-0.0868034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.60223 | − | 5.52335i | 0.259385 | − | 0.188454i | −0.450491 | − | 0.892781i | \(-0.648751\pi\) |
0.709876 | + | 0.704327i | \(0.248751\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.5040 | − | 14.4575i | −0.357560 | − | 0.492140i | 0.591907 | − | 0.806007i | \(-0.298375\pi\) |
−0.949467 | + | 0.313867i | \(0.898375\pi\) | |||||||
\(864\) | 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 | −0.596317 | − | 0.802749i | \(-0.703370\pi\) |
0.947732 | + | 0.319068i | \(0.103370\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.82007 | − | 30.2231i | 0.330847 | − | 1.01824i | −0.637885 | − | 0.770131i | \(-0.720191\pi\) |
0.968732 | − | 0.248110i | \(-0.0798094\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.9158 | + | 10.6950i | 1.10771 | + | 0.359916i | 0.805064 | − | 0.593188i | \(-0.202131\pi\) |
0.302643 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.7639 | − | 23.0735i | −0.562876 | − | 0.774732i | 0.428813 | − | 0.903393i | \(-0.358932\pi\) |
−0.991689 | + | 0.128661i | \(0.958932\pi\) | |||||||
\(888\) | 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 | \(-0.962830\pi\) | ||
0.993190 | − | 0.116507i | \(-0.0371697\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9145 | − | 12.2891i | −0.560403 | − | 0.407157i | 0.271203 | − | 0.962522i | \(-0.412578\pi\) |
−0.831606 | + | 0.555365i | \(0.812578\pi\) | |||||||
\(912\) | 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 | −0.143726 | + | 0.989618i | \(0.545908\pi\) |
−0.465406 | + | 0.885097i | \(0.654092\pi\) | |||||||
\(920\) | 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 | −0.918466 | − | 0.395501i | \(-0.870571\pi\) |
0.510585 | − | 0.859828i | \(-0.329429\pi\) | |||||||
\(930\) | 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 | −0.952022 | − | 0.306028i | \(-0.901000\pi\) |
0.00314114 | − | 0.999995i | \(-0.499000\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.0130 | − | 13.0872i | 0.587207 | − | 0.426631i | −0.254108 | − | 0.967176i | \(-0.581782\pi\) |
0.841315 | + | 0.540545i | \(0.181782\pi\) | |||||||
\(942\) | 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 | 0.299516 | − | 0.954091i | \(-0.403175\pi\) |
0.803114 | + | 0.595825i | \(0.203175\pi\) | |||||||
\(948\) | 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 | −0.265462 | − | 0.964121i | \(-0.585525\pi\) |
0.351933 | + | 0.936025i | \(0.385525\pi\) | |||||||
\(954\) | 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 | 0.479952 | − | 0.877295i | \(-0.340654\pi\) |
−0.127372 | + | 0.991855i | \(0.540654\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.15578 | − | 22.0232i | −0.229640 | − | 0.706759i | −0.997787 | − | 0.0664858i | \(-0.978821\pi\) |
0.768148 | − | 0.640273i | \(-0.221179\pi\) | |||||||
\(972\) | 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 | −0.724252 | − | 0.689536i | \(-0.757815\pi\) |
0.879593 | + | 0.475726i | \(0.157815\pi\) | |||||||
\(978\) | 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 | 0.593361 | − | 0.804936i | \(-0.297800\pi\) |
0.00690994 | + | 0.999976i | \(0.497800\pi\) | |||||||
\(984\) | 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 | −0.827662 | − | 0.561227i | \(-0.810330\pi\) |
0.277997 | + | 0.960582i | \(0.410330\pi\) | |||||||
\(992\) | 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 | −0.561602 | − | 0.827407i | \(-0.689815\pi\) |
0.0319923 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(998\) | 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.109.3 | 24 | ||
3.2 | odd | 2 | 300.2.o.a.109.2 | ✓ | 24 | ||
15.2 | even | 4 | 1500.2.m.c.1201.6 | 24 | |||
15.8 | even | 4 | 1500.2.m.d.1201.1 | 24 | |||
15.14 | odd | 2 | 1500.2.o.c.49.6 | 24 | |||
25.14 | even | 10 | inner | 900.2.w.c.289.3 | 24 | ||
75.2 | even | 20 | 1500.2.m.c.301.6 | 24 | |||
75.8 | even | 20 | 7500.2.a.m.1.1 | 12 | |||
75.11 | odd | 10 | 1500.2.o.c.949.6 | 24 | |||
75.14 | odd | 10 | 300.2.o.a.289.2 | yes | 24 | ||
75.17 | even | 20 | 7500.2.a.n.1.12 | 12 | |||
75.23 | even | 20 | 1500.2.m.d.301.1 | 24 | |||
75.44 | odd | 10 | 7500.2.d.g.1249.12 | 24 | |||
75.56 | odd | 10 | 7500.2.d.g.1249.13 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.o.a.109.2 | ✓ | 24 | 3.2 | odd | 2 | ||
300.2.o.a.289.2 | yes | 24 | 75.14 | odd | 10 | ||
900.2.w.c.109.3 | 24 | 1.1 | even | 1 | trivial | ||
900.2.w.c.289.3 | 24 | 25.14 | even | 10 | inner | ||
1500.2.m.c.301.6 | 24 | 75.2 | even | 20 | |||
1500.2.m.c.1201.6 | 24 | 15.2 | even | 4 | |||
1500.2.m.d.301.1 | 24 | 75.23 | even | 20 | |||
1500.2.m.d.1201.1 | 24 | 15.8 | even | 4 | |||
1500.2.o.c.49.6 | 24 | 15.14 | odd | 2 | |||
1500.2.o.c.949.6 | 24 | 75.11 | odd | 10 | |||
7500.2.a.m.1.1 | 12 | 75.8 | even | 20 | |||
7500.2.a.n.1.12 | 12 | 75.17 | even | 20 | |||
7500.2.d.g.1249.12 | 24 | 75.44 | odd | 10 | |||
7500.2.d.g.1249.13 | 24 | 75.56 | odd | 10 |