Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1457,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.s (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1793.4 | ||
Character | \(\chi\) | \(=\) | 2100.1793 |
Dual form | 2100.2.s.c.1457.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.28800 | + | 1.15804i | −0.743627 | + | 0.668595i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.317883 | − | 2.98311i | 0.105961 | − | 0.994370i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.81675i | − | 0.547772i | −0.961762 | − | 0.273886i | \(-0.911691\pi\) | ||
0.961762 | − | 0.273886i | \(-0.0883090\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28690 | + | 2.28690i | 0.634273 | + | 0.634273i | 0.949137 | − | 0.314864i | \(-0.101959\pi\) |
−0.314864 | + | 0.949137i | \(0.601959\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.614103 | − | 0.614103i | −0.148942 | − | 0.148942i | 0.628703 | − | 0.777645i | \(-0.283586\pi\) |
−0.777645 | + | 0.628703i | \(0.783586\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.915840i | 0.210108i | 0.994467 | + | 0.105054i | \(0.0335015\pi\) | ||||
−0.994467 | + | 0.105054i | \(0.966498\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.0918944 | − | 1.72961i | 0.0200530 | − | 0.377432i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.11658 | + | 3.11658i | −0.649851 | + | 0.649851i | −0.952957 | − | 0.303106i | \(-0.901976\pi\) |
0.303106 | + | 0.952957i | \(0.401976\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.04513 | + | 4.21037i | 0.586036 | + | 0.810285i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.83864 | −1.26990 | −0.634952 | − | 0.772552i | \(-0.718980\pi\) | ||||
−0.634952 | + | 0.772552i | \(0.718980\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.15001 | 1.46379 | 0.731893 | − | 0.681420i | \(-0.238637\pi\) | ||||
0.731893 | + | 0.681420i | \(0.238637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.10387 | + | 2.33998i | 0.366237 | + | 0.407338i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.57980 | − | 1.57980i | 0.259717 | − | 0.259717i | −0.565222 | − | 0.824939i | \(-0.691209\pi\) |
0.824939 | + | 0.565222i | \(0.191209\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.59386 | − | 0.297202i | −0.895734 | − | 0.0475904i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.926896i | − | 0.144757i | −0.997377 | − | 0.0723784i | \(-0.976941\pi\) | ||
0.997377 | − | 0.0723784i | \(-0.0230589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.34906 | + | 3.34906i | 0.510727 | + | 0.510727i | 0.914749 | − | 0.404022i | \(-0.132388\pi\) |
−0.404022 | + | 0.914749i | \(0.632388\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.74636 | + | 7.74636i | 1.12992 | + | 1.12992i | 0.990189 | + | 0.139734i | \(0.0446248\pi\) |
0.139734 | + | 0.990189i | \(0.455375\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.50212 | + | 0.0798077i | 0.210339 | + | 0.0111753i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.13170 | + | 3.13170i | −0.430172 | + | 0.430172i | −0.888687 | − | 0.458515i | \(-0.848382\pi\) |
0.458515 | + | 0.888687i | \(0.348382\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.06058 | − | 1.17960i | −0.140477 | − | 0.156242i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.50920 | −1.23799 | −0.618996 | − | 0.785394i | \(-0.712460\pi\) | ||||
−0.618996 | + | 0.785394i | \(0.712460\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.778193 | 0.0996374 | 0.0498187 | − | 0.998758i | \(-0.484136\pi\) | ||||
0.0498187 | + | 0.998758i | \(0.484136\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.88460 | + | 2.33416i | 0.237437 | + | 0.294076i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.95804 | + | 3.95804i | −0.483551 | + | 0.483551i | −0.906264 | − | 0.422713i | \(-0.861078\pi\) |
0.422713 | + | 0.906264i | \(0.361078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.405025 | − | 7.62327i | 0.0487592 | − | 0.917734i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.0067i | 1.18758i | 0.804620 | + | 0.593790i | \(0.202369\pi\) | ||||
−0.804620 | + | 0.593790i | \(0.797631\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.51085 | − | 3.51085i | −0.410913 | − | 0.410913i | 0.471143 | − | 0.882057i | \(-0.343841\pi\) |
−0.882057 | + | 0.471143i | \(0.843841\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.28464 | + | 1.28464i | 0.146398 | + | 0.146398i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.66336i | 0.974704i | 0.873206 | + | 0.487352i | \(0.162037\pi\) | ||||
−0.873206 | + | 0.487352i | \(0.837963\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.79790 | − | 1.89656i | −0.977545 | − | 0.210729i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.57830 | + | 9.57830i | −1.05135 | + | 1.05135i | −0.0527470 | + | 0.998608i | \(0.516798\pi\) |
−0.998608 | + | 0.0527470i | \(0.983202\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.80816 | − | 7.91942i | 0.944334 | − | 0.849051i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.12082 | −0.860805 | −0.430402 | − | 0.902637i | \(-0.641628\pi\) | ||||
−0.430402 | + | 0.902637i | \(0.641628\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23417 | −0.339033 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4972 | + | 9.43804i | −1.08851 | + | 0.978680i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.33732 | + | 3.33732i | −0.338854 | + | 0.338854i | −0.855936 | − | 0.517082i | \(-0.827018\pi\) |
0.517082 | + | 0.855936i | \(0.327018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.41958 | − | 0.577515i | −0.544688 | − | 0.0580424i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 13.9488i | − | 1.38796i | −0.719995 | − | 0.693980i | \(-0.755856\pi\) | ||
0.719995 | − | 0.693980i | \(-0.244144\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.36891 | − | 9.36891i | −0.923146 | − | 0.923146i | 0.0741044 | − | 0.997250i | \(-0.476390\pi\) |
−0.997250 | + | 0.0741044i | \(0.976390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.35305 | + | 2.35305i | 0.227477 | + | 0.227477i | 0.811638 | − | 0.584161i | \(-0.198576\pi\) |
−0.584161 | + | 0.811638i | \(0.698576\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.83168i | 0.462791i | 0.972860 | + | 0.231395i | \(0.0743291\pi\) | ||||
−0.972860 | + | 0.231395i | \(0.925671\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.205308 | + | 3.86425i | −0.0194869 | + | 0.366778i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.67956 | + | 7.67956i | −0.722432 | + | 0.722432i | −0.969100 | − | 0.246668i | \(-0.920664\pi\) |
0.246668 | + | 0.969100i | \(0.420664\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 7.54906 | − | 6.09512i | 0.697911 | − | 0.563494i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.868473 | 0.0796128 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.69941 | 0.699946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.07338 | + | 1.19384i | 0.0967837 | + | 0.107645i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.4839 | + | 15.4839i | −1.37397 | + | 1.37397i | −0.519507 | + | 0.854466i | \(0.673884\pi\) |
−0.854466 | + | 0.519507i | \(0.826116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.19194 | − | 0.435238i | −0.721260 | − | 0.0383206i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 13.4873i | − | 1.17839i | −0.807989 | − | 0.589197i | \(-0.799444\pi\) | ||
0.807989 | − | 0.589197i | \(-0.200556\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.647596 | − | 0.647596i | −0.0561537 | − | 0.0561537i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.329097 | + | 0.329097i | 0.0281166 | + | 0.0281166i | 0.721025 | − | 0.692909i | \(-0.243671\pi\) |
−0.692909 | + | 0.721025i | \(0.743671\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.8933i | 1.17841i | 0.807982 | + | 0.589207i | \(0.200560\pi\) | ||||
−0.807982 | + | 0.589207i | \(0.799440\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.9479 | − | 1.00670i | −1.59570 | − | 0.0847797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.15474 | − | 4.15474i | 0.347437 | − | 0.347437i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.15804 | + | 1.28800i | 0.0955136 | + | 0.106232i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.24564 | 0.511663 | 0.255831 | − | 0.966721i | \(-0.417651\pi\) | ||||
0.255831 | + | 0.966721i | \(0.417651\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.13878 | −0.662325 | −0.331162 | − | 0.943574i | \(-0.607441\pi\) | ||||
−0.331162 | + | 0.943574i | \(0.607441\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.02715 | + | 1.63672i | −0.163885 | + | 0.132321i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.08730 | − | 9.08730i | 0.725246 | − | 0.725246i | −0.244423 | − | 0.969669i | \(-0.578599\pi\) |
0.969669 | + | 0.244423i | \(0.0785985\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.406990 | − | 7.66025i | 0.0322764 | − | 0.607498i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.40750i | − | 0.347360i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.62179 | − | 8.62179i | −0.675310 | − | 0.675310i | 0.283625 | − | 0.958935i | \(-0.408463\pi\) |
−0.958935 | + | 0.283625i | \(0.908463\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.40121 | + | 4.40121i | 0.340576 | + | 0.340576i | 0.856584 | − | 0.516008i | \(-0.172582\pi\) |
−0.516008 | + | 0.856584i | \(0.672582\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 2.54014i | − | 0.195395i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.73205 | + | 0.291130i | 0.208925 | + | 0.0222633i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.75339 | + | 3.75339i | −0.285365 | + | 0.285365i | −0.835244 | − | 0.549879i | \(-0.814674\pi\) |
0.549879 | + | 0.835244i | \(0.314674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.2478 | − | 11.0120i | 0.920604 | − | 0.827715i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7357 | −0.951912 | −0.475956 | − | 0.879469i | \(-0.657898\pi\) | ||||
−0.475956 | + | 0.879469i | \(0.657898\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.3369 | −0.916995 | −0.458497 | − | 0.888696i | \(-0.651612\pi\) | ||||
−0.458497 | + | 0.888696i | \(0.651612\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00231 | + | 0.901179i | −0.0740930 | + | 0.0666171i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.11567 | + | 1.11567i | −0.0815861 | + | 0.0815861i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.13041 | − | 0.823945i | −0.373182 | − | 0.0599332i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 26.9639i | 1.95104i | 0.219906 | + | 0.975521i | \(0.429425\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.57391 | + | 6.57391i | 0.473201 | + | 0.473201i | 0.902949 | − | 0.429748i | \(-0.141398\pi\) |
−0.429748 | + | 0.902949i | \(0.641398\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.55416 | + | 2.55416i | 0.181976 | + | 0.181976i | 0.792216 | − | 0.610240i | \(-0.208927\pi\) |
−0.610240 | + | 0.792216i | \(0.708927\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.1790i | 1.35956i | 0.733415 | + | 0.679781i | \(0.237925\pi\) | ||||
−0.733415 | + | 0.679781i | \(0.762075\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.514379 | − | 9.68151i | 0.0362815 | − | 0.682881i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.83565 | − | 4.83565i | 0.339396 | − | 0.339396i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.30638 | + | 10.2878i | 0.577334 | + | 0.715051i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.66385 | 0.115091 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.59440 | −0.178606 | −0.0893031 | − | 0.996004i | \(-0.528464\pi\) | ||||
−0.0893031 | + | 0.996004i | \(0.528464\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.5882 | − | 12.8887i | −0.794011 | − | 0.883116i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.76293 | + | 5.76293i | −0.391213 | + | 0.391213i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.58767 | + | 0.456263i | 0.580301 | + | 0.0308314i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.80879i | − | 0.188940i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00759 | + | 1.00759i | 0.0674732 | + | 0.0674732i | 0.740038 | − | 0.672565i | \(-0.234807\pi\) |
−0.672565 | + | 0.740038i | \(0.734807\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.18906 | + | 6.18906i | 0.410782 | + | 0.410782i | 0.882011 | − | 0.471229i | \(-0.156189\pi\) |
−0.471229 | + | 0.882011i | \(0.656189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8649i | 1.18054i | 0.807204 | + | 0.590272i | \(0.200980\pi\) | ||||
−0.807204 | + | 0.590272i | \(0.799020\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.14228 | − | 0.166949i | −0.206747 | − | 0.0109845i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.5715 | + | 18.5715i | −1.21666 | + | 1.21666i | −0.247862 | + | 0.968795i | \(0.579728\pi\) |
−0.968795 | + | 0.247862i | \(0.920272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.0325 | − | 11.1584i | −0.651682 | − | 0.724816i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.40800 | 0.608553 | 0.304277 | − | 0.952584i | \(-0.401585\pi\) | ||||
0.304277 | + | 0.952584i | \(0.401585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.7004 | 1.65551 | 0.827756 | − | 0.561089i | \(-0.189617\pi\) | ||||
0.827756 | + | 0.561089i | \(0.189617\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5280 | − | 7.74556i | 0.867820 | − | 0.496878i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.09444 | + | 2.09444i | −0.133266 | + | 0.133266i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.24478 | − | 23.4289i | 0.0788847 | − | 1.48475i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.7942i | 1.37564i | 0.725884 | + | 0.687818i | \(0.241431\pi\) | ||||
−0.725884 | + | 0.687818i | \(0.758569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.66205 | + | 5.66205i | 0.355970 | + | 0.355970i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −14.7169 | − | 14.7169i | −0.918012 | − | 0.918012i | 0.0788726 | − | 0.996885i | \(-0.474868\pi\) |
−0.996885 | + | 0.0788726i | \(0.974868\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.23417i | 0.138825i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.17389 | + | 20.4004i | −0.134560 | + | 1.26275i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 22.0701 | − | 22.0701i | 1.36090 | − | 1.36090i | 0.488128 | − | 0.872772i | \(-0.337680\pi\) |
0.872772 | − | 0.488128i | \(-0.162320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.4596 | − | 9.40424i | 0.640117 | − | 0.575530i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.94878 | 0.362704 | 0.181352 | − | 0.983418i | \(-0.441953\pi\) | ||||
0.181352 | + | 0.983418i | \(0.441953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7968 | 0.655857 | 0.327928 | − | 0.944703i | \(-0.393650\pi\) | ||||
0.327928 | + | 0.944703i | \(0.393650\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.16561 | − | 3.74530i | 0.252114 | − | 0.226676i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.9527 | + | 16.9527i | −1.01859 | + | 1.01859i | −0.0187635 | + | 0.999824i | \(0.505973\pi\) |
−0.999824 | + | 0.0187635i | \(0.994027\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.59075 | − | 24.3124i | 0.155104 | − | 1.45554i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.4918i | − | 1.10313i | −0.834133 | − | 0.551563i | \(-0.814032\pi\) | ||
0.834133 | − | 0.551563i | \(-0.185968\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.26573 | − | 7.26573i | −0.431903 | − | 0.431903i | 0.457372 | − | 0.889275i | \(-0.348791\pi\) |
−0.889275 | + | 0.457372i | \(0.848791\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.655414 | + | 0.655414i | 0.0386879 | + | 0.0386879i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.2458i | − | 0.955633i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.433713 | − | 8.16322i | 0.0254247 | − | 0.478537i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.63645 | − | 1.63645i | 0.0956024 | − | 0.0956024i | −0.657688 | − | 0.753290i | \(-0.728465\pi\) |
0.753290 | + | 0.657688i | \(0.228465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.64919 | − | 5.53225i | 0.443851 | − | 0.321014i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.2546 | −0.824366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.73629 | −0.272995 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.1533 | + | 17.9661i | 0.927983 | + | 1.03212i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.74785 | + | 9.74785i | −0.556339 | + | 0.556339i | −0.928263 | − | 0.371924i | \(-0.878698\pi\) |
0.371924 | + | 0.928263i | \(0.378698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 22.9167 | + | 1.21757i | 1.30369 | + | 0.0692650i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.45205i | − | 0.365862i | −0.983126 | − | 0.182931i | \(-0.941442\pi\) | ||
0.983126 | − | 0.182931i | \(-0.0585585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3823 | + | 10.3823i | 0.586843 | + | 0.586843i | 0.936775 | − | 0.349932i | \(-0.113795\pi\) |
−0.349932 | + | 0.936775i | \(0.613795\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.2914 | − | 21.2914i | −1.19585 | − | 1.19585i | −0.975399 | − | 0.220448i | \(-0.929248\pi\) |
−0.220448 | − | 0.975399i | \(-0.570752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4241i | 0.695617i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.75564 | − | 0.305798i | −0.321249 | − | 0.0170680i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.562420 | − | 0.562420i | 0.0312939 | − | 0.0312939i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.59528 | − | 6.22320i | −0.309420 | − | 0.344144i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −10.9550 | −0.603969 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.5396 | 1.23889 | 0.619443 | − | 0.785041i | \(-0.287358\pi\) | ||||
0.619443 | + | 0.785041i | \(0.287358\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.21052 | − | 5.21490i | −0.230735 | − | 0.285775i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.64028 | + | 7.64028i | −0.416192 | + | 0.416192i | −0.883889 | − | 0.467697i | \(-0.845084\pi\) |
0.467697 | + | 0.883889i | \(0.345084\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.998022 | − | 18.7845i | 0.0542051 | − | 1.02023i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 14.8066i | − | 0.801820i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.92603 | + | 7.92603i | 0.425492 | + | 0.425492i | 0.887089 | − | 0.461598i | \(-0.152724\pi\) |
−0.461598 | + | 0.887089i | \(0.652724\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.7166i | 0.787761i | 0.919162 | + | 0.393880i | \(0.128868\pi\) | ||||
−0.919162 | + | 0.393880i | \(0.871132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.66478 | + | 16.5926i | −0.142235 | + | 0.885649i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.1607 | − | 21.1607i | 1.12627 | − | 1.12627i | 0.135491 | − | 0.990779i | \(-0.456739\pi\) |
0.990779 | − | 0.135491i | \(-0.0432610\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.11859 | + | 1.00573i | −0.0592022 | + | 0.0532287i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.2360 | 1.70135 | 0.850675 | − | 0.525692i | \(-0.176194\pi\) | ||||
0.850675 | + | 0.525692i | \(0.176194\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.1612 | 0.955855 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.91683 | + | 8.91623i | −0.520499 | + | 0.467981i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7264 | − | 13.7264i | 0.716510 | − | 0.716510i | −0.251378 | − | 0.967889i | \(-0.580884\pi\) |
0.967889 | + | 0.251378i | \(0.0808839\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.76503 | − | 0.294644i | −0.143942 | − | 0.0153386i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.42889i | − | 0.229936i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.2556 | − | 14.2556i | −0.738125 | − | 0.738125i | 0.234090 | − | 0.972215i | \(-0.424789\pi\) |
−0.972215 | + | 0.234090i | \(0.924789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −15.6393 | − | 15.6393i | −0.805465 | − | 0.805465i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.10982i | − | 0.365207i | −0.983187 | − | 0.182603i | \(-0.941548\pi\) | ||
0.983187 | − | 0.182603i | \(-0.0584524\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.01226 | − | 37.8742i | 0.103091 | − | 1.94035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.9109 | − | 25.9109i | 1.32398 | − | 1.32398i | 0.413461 | − | 0.910522i | \(-0.364320\pi\) |
0.910522 | − | 0.413461i | \(-0.135680\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.0552 | − | 8.92602i | 0.561969 | − | 0.453735i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.4040 | 0.983822 | 0.491911 | − | 0.870646i | \(-0.336299\pi\) | ||||
0.491911 | + | 0.870646i | \(0.336299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.82780 | 0.193580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.6189 | + | 17.3717i | 0.787869 | + | 0.876285i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.21357 | + | 7.21357i | −0.362039 | + | 0.362039i | −0.864563 | − | 0.502524i | \(-0.832405\pi\) |
0.502524 | + | 0.864563i | \(0.332405\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.58405 | + | 0.0841605i | 0.0793015 | + | 0.00421329i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.3956i | 1.61776i | 0.587974 | + | 0.808879i | \(0.299926\pi\) | ||||
−0.587974 | + | 0.808879i | \(0.700074\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.6383 | + | 18.6383i | 0.928439 | + | 0.928439i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.87010 | − | 2.87010i | −0.142266 | − | 0.142266i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.27721i | 0.260941i | 0.991452 | + | 0.130471i | \(0.0416488\pi\) | ||||
−0.991452 | + | 0.130471i | \(0.958351\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.804984 | − | 0.0427688i | −0.0397069 | − | 0.00210963i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.72402 | − | 6.72402i | 0.330867 | − | 0.330867i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0890 | − | 17.8945i | −0.787881 | − | 0.876300i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.9881 | 0.976480 | 0.488240 | − | 0.872709i | \(-0.337639\pi\) | ||||
0.488240 | + | 0.872709i | \(0.337639\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.48459 | 0.462251 | 0.231125 | − | 0.972924i | \(-0.425759\pi\) | ||||
0.231125 | + | 0.972924i | \(0.425759\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 25.5707 | − | 20.6458i | 1.24329 | − | 1.00383i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.550265 | + | 0.550265i | −0.0266292 | + | 0.0266292i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.539943 | + | 10.1627i | −0.0260687 | + | 0.490658i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 13.7200i | − | 0.660871i | −0.943829 | − | 0.330436i | \(-0.892804\pi\) | ||
0.943829 | − | 0.330436i | \(-0.107196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5650 | + | 18.5650i | 0.892178 | + | 0.892178i | 0.994728 | − | 0.102549i | \(-0.0327000\pi\) |
−0.102549 | + | 0.994728i | \(0.532700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.85428 | − | 2.85428i | −0.136539 | − | 0.136539i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 23.0045i | − | 1.09794i | −0.835840 | − | 0.548972i | \(-0.815019\pi\) | ||
0.835840 | − | 0.548972i | \(-0.184981\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.98311 | − | 0.317883i | −0.142053 | − | 0.0151373i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.3093 | + | 14.3093i | −0.679856 | + | 0.679856i | −0.959967 | − | 0.280112i | \(-0.909628\pi\) |
0.280112 | + | 0.959967i | \(0.409628\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.04438 | + | 7.23271i | −0.380486 | + | 0.342095i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.3590 | 1.81028 | 0.905138 | − | 0.425119i | \(-0.139768\pi\) | ||||
0.905138 | + | 0.425119i | \(0.139768\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.68394 | −0.0792937 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.4827 | − | 9.42504i | 0.492522 | − | 0.442827i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.2772 | + | 22.2772i | −1.04208 | + | 1.04208i | −0.0430065 | + | 0.999075i | \(0.513694\pi\) |
−0.999075 | + | 0.0430065i | \(0.986306\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.715574 | − | 4.45562i | 0.0334001 | − | 0.207971i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.1124i | 1.07645i | 0.842801 | + | 0.538226i | \(0.180905\pi\) | ||||
−0.842801 | + | 0.538226i | \(0.819095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.1962 | − | 23.1962i | −1.07802 | − | 1.07802i | −0.996687 | − | 0.0813329i | \(-0.974082\pi\) |
−0.0813329 | − | 0.996687i | \(-0.525918\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.4361 | + | 12.4361i | 0.575472 | + | 0.575472i | 0.933652 | − | 0.358180i | \(-0.116603\pi\) |
−0.358180 | + | 0.933652i | \(0.616603\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 5.59751i | − | 0.258469i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.18097 | + | 22.2279i | −0.0544162 | + | 1.02421i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.08442 | − | 6.08442i | 0.279762 | − | 0.279762i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.34668 | + | 10.3377i | 0.382168 | + | 0.473331i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.26702 | −0.286348 | −0.143174 | − | 0.989698i | \(-0.545731\pi\) | ||||
−0.143174 | + | 0.989698i | \(0.545731\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.22569 | 0.329463 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.10407 | + | 5.67686i | 0.232243 | + | 0.258306i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.4714 | − | 16.4714i | 0.746390 | − | 0.746390i | −0.227409 | − | 0.973799i | \(-0.573025\pi\) |
0.973799 | + | 0.227409i | \(0.0730254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.0892 | + | 1.12047i | 0.953688 | + | 0.0506695i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.5176i | 1.37724i | 0.725122 | + | 0.688621i | \(0.241784\pi\) | ||||
−0.725122 | + | 0.688621i | \(0.758216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.19963 | + | 4.19963i | 0.189142 | + | 0.189142i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −7.07583 | − | 7.07583i | −0.317394 | − | 0.317394i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.9169i | 0.488707i | 0.969686 | + | 0.244353i | \(0.0785757\pi\) | ||||
−0.969686 | + | 0.244353i | \(0.921424\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.7655 | − | 0.571974i | −0.480969 | − | 0.0255539i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.38329 | − | 2.38329i | 0.106266 | − | 0.106266i | −0.651975 | − | 0.758240i | \(-0.726059\pi\) |
0.758240 | + | 0.651975i | \(0.226059\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.94158 | + | 3.27170i | 0.130640 | + | 0.145301i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.79313 | −0.123804 | −0.0619018 | − | 0.998082i | \(-0.519717\pi\) | ||||
−0.0619018 | + | 0.998082i | \(0.519717\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.96509 | 0.219642 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.85602 | + | 2.78885i | −0.170247 | + | 0.123131i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.0732 | − | 14.0732i | 0.618940 | − | 0.618940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.487784 | − | 9.18095i | 0.0214114 | − | 0.402999i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.7166i | − | 1.21428i | −0.794593 | − | 0.607142i | \(-0.792316\pi\) | ||
0.794593 | − | 0.607142i | \(-0.207684\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.9685 | − | 28.9685i | −1.26670 | − | 1.26670i | −0.947781 | − | 0.318922i | \(-0.896679\pi\) |
−0.318922 | − | 0.947781i | \(-0.603321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.00494 | − | 5.00494i | −0.218019 | − | 0.218019i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.57392i | 0.155388i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.02281 | + | 28.3670i | −0.131179 | + | 1.23102i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.11972 | − | 2.11972i | 0.0918154 | − | 0.0918154i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 16.4036 | − | 14.7485i | 0.707867 | − | 0.636444i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.81675 | −0.0782531 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.67695 | 0.201078 | 0.100539 | − | 0.994933i | \(-0.467943\pi\) | ||||
0.100539 | + | 0.994933i | \(0.467943\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.8899 | − | 14.2866i | 0.681902 | − | 0.613098i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.58370 | + | 7.58370i | −0.324255 | + | 0.324255i | −0.850397 | − | 0.526142i | \(-0.823638\pi\) |
0.526142 | + | 0.850397i | \(0.323638\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.247374 | − | 2.32144i | 0.0105577 | − | 0.0990764i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 6.26309i | − | 0.266817i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.12592 | − | 6.12592i | −0.260501 | − | 0.260501i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.69726 | − | 2.69726i | −0.114287 | − | 0.114287i | 0.647651 | − | 0.761937i | \(-0.275752\pi\) |
−0.761937 | + | 0.647651i | \(0.775752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.3180i | 0.647881i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.144991 | − | 2.72898i | 0.00612152 | − | 0.115218i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5552 | − | 10.5552i | 0.444849 | − | 0.444849i | −0.448789 | − | 0.893638i | \(-0.648144\pi\) |
0.893638 | + | 0.448789i | \(0.148144\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.56213 | − | 4.87998i | 0.317579 | − | 0.204940i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.9498 | 1.75863 | 0.879313 | − | 0.476244i | \(-0.158002\pi\) | ||||
0.879313 | + | 0.476244i | \(0.158002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −40.1607 | −1.68067 | −0.840336 | − | 0.542066i | \(-0.817642\pi\) | ||||
−0.840336 | + | 0.542066i | \(0.817642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.2253 | − | 34.7295i | −1.30446 | − | 1.45085i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.8604 | + | 21.8604i | −0.910060 | + | 0.910060i | −0.996276 | − | 0.0862162i | \(-0.972522\pi\) |
0.0862162 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.0801 | − | 0.854334i | −0.668264 | − | 0.0355049i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 13.5458i | − | 0.561973i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.68952 | + | 5.68952i | 0.235636 | + | 0.235636i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.94407 | + | 3.94407i | 0.162789 | + | 0.162789i | 0.783801 | − | 0.621012i | \(-0.213278\pi\) |
−0.621012 | + | 0.783801i | \(0.713278\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.46410i | 0.307553i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.24757 | − | 0.331934i | −0.256991 | − | 0.0136539i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 29.0441 | − | 29.0441i | 1.19270 | − | 1.19270i | 0.216393 | − | 0.976306i | \(-0.430571\pi\) |
0.976306 | − | 0.216393i | \(-0.0694292\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.2100 | − | 24.7025i | −0.908996 | − | 1.01101i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.24338 | −0.377674 | −0.188837 | − | 0.982008i | \(-0.560472\pi\) | ||||
−0.188837 | + | 0.982008i | \(0.560472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.7255 | 1.25332 | 0.626660 | − | 0.779293i | \(-0.284421\pi\) | ||||
0.626660 | + | 0.779293i | \(0.284421\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5491 | + | 13.0655i | 0.429591 | + | 0.532066i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.82544 | + | 5.82544i | −0.236447 | + | 0.236447i | −0.815377 | − | 0.578930i | \(-0.803470\pi\) |
0.578930 | + | 0.815377i | \(0.303470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.628432 | + | 11.8282i | −0.0254654 | + | 0.479302i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.4304i | 1.43336i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.7731 | − | 22.7731i | −0.919797 | − | 0.919797i | 0.0772173 | − | 0.997014i | \(-0.475396\pi\) |
−0.997014 | + | 0.0772173i | \(0.975396\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.793772 | − | 0.793772i | −0.0319561 | − | 0.0319561i | 0.690948 | − | 0.722904i | \(-0.257193\pi\) |
−0.722904 | + | 0.690948i | \(0.757193\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.04339i | 0.363485i | 0.983346 | + | 0.181742i | \(0.0581737\pi\) | ||||
−0.983346 | + | 0.181742i | \(0.941826\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.6123 | − | 3.63154i | −0.907400 | − | 0.145729i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.74228 | − | 5.74228i | 0.230060 | − | 0.230060i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.14304 | + | 1.92681i | −0.0855849 | + | 0.0769494i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.94032 | −0.0773655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.3225 | −0.928453 | −0.464227 | − | 0.885716i | \(-0.653668\pi\) | ||||
−0.464227 | + | 0.885716i | \(0.653668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.34159 | − | 3.00443i | 0.132816 | − | 0.119415i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.28690 | − | 2.28690i | 0.0906104 | − | 0.0906104i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.8512 | + | 3.18097i | 1.18089 | + | 0.125837i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 37.4896i | − | 1.48075i | −0.672194 | − | 0.740375i | \(-0.734648\pi\) | ||
0.672194 | − | 0.740375i | \(-0.265352\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.0507 | + | 13.0507i | 0.514669 | + | 0.514669i | 0.915953 | − | 0.401285i | \(-0.131436\pi\) |
−0.401285 | + | 0.915953i | \(0.631436\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.9234 | − | 12.9234i | −0.508073 | − | 0.508073i | 0.405861 | − | 0.913935i | \(-0.366972\pi\) |
−0.913935 | + | 0.405861i | \(0.866972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.2759i | 0.678137i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.748940 | − | 14.0964i | 0.0293533 | − | 0.552480i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −31.8165 | + | 31.8165i | −1.24508 | + | 1.24508i | −0.287206 | + | 0.957869i | \(0.592727\pi\) |
−0.957869 | + | 0.287206i | \(0.907273\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.5893 | + | 9.35720i | −0.452141 | + | 0.365059i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −34.7626 | −1.35416 | −0.677079 | − | 0.735910i | \(-0.736754\pi\) | ||||
−0.677079 | + | 0.735910i | \(0.736754\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.2224 | −1.25331 | −0.626653 | − | 0.779299i | \(-0.715575\pi\) | ||||
−0.626653 | + | 0.779299i | \(0.715575\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.25269 | + | 3.61772i | 0.126324 | + | 0.140500i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 21.3131 | − | 21.3131i | 0.825248 | − | 0.825248i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.46460 | − | 0.130945i | −0.0952871 | − | 0.00506261i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.41378i | − | 0.0545785i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.83342 | − | 3.83342i | −0.147767 | − | 0.147767i | 0.629353 | − | 0.777120i | \(-0.283320\pi\) |
−0.777120 | + | 0.629353i | \(0.783320\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.73452 | − | 2.73452i | −0.105096 | − | 0.105096i | 0.652603 | − | 0.757700i | \(-0.273677\pi\) |
−0.757700 | + | 0.652603i | \(0.773677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 4.71969i | − | 0.181125i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.1387 | − | 0.804319i | −0.580116 | − | 0.0308216i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.43426 | − | 6.43426i | 0.246200 | − | 0.246200i | −0.573209 | − | 0.819409i | \(-0.694302\pi\) |
0.819409 | + | 0.573209i | \(0.194302\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −20.6883 | − | 23.0100i | −0.789307 | − | 0.877885i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.3238 | −0.545693 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3311 | −0.431054 | −0.215527 | − | 0.976498i | \(-0.569147\pi\) | ||||
−0.215527 | + | 0.976498i | \(0.569147\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4.24058 | − | 3.42385i | 0.161086 | − | 0.130061i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.569209 | + | 0.569209i | −0.0215603 | + | 0.0215603i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.41352 | − | 45.4265i | 0.0912875 | − | 1.71819i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.58848i | 0.248843i | 0.992229 | + | 0.124422i | \(0.0397076\pi\) | ||||
−0.992229 | + | 0.124422i | \(0.960292\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.44684 | + | 1.44684i | 0.0545686 | + | 0.0545686i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.86331 | + | 9.86331i | 0.370948 | + | 0.370948i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 21.3143i | − | 0.800475i | −0.916411 | − | 0.400238i | \(-0.868928\pi\) | ||
0.916411 | − | 0.400238i | \(-0.131072\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.8438 | + | 2.75393i | 0.969217 | + | 0.103281i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −25.4001 | + | 25.4001i | −0.951242 | + | 0.951242i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.1175 | + | 10.8949i | −0.452536 | + | 0.406876i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.6692 | 0.920007 | 0.460004 | − | 0.887917i | \(-0.347848\pi\) | ||||
0.460004 | + | 0.887917i | \(0.347848\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.2496 | 0.493442 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −33.1022 | + | 29.7622i | −1.23108 | + | 1.10687i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.8410 | − | 20.8410i | 0.772950 | − | 0.772950i | −0.205671 | − | 0.978621i | \(-0.565938\pi\) |
0.978621 | + | 0.205671i | \(0.0659378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.45435 | + | 25.6422i | −0.313124 | + | 0.949712i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 4.11334i | − | 0.152137i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1136 | + | 11.1136i | 0.410489 | + | 0.410489i | 0.881909 | − | 0.471420i | \(-0.156258\pi\) |
−0.471420 | + | 0.881909i | \(0.656258\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.19077 | + | 7.19077i | 0.264876 | + | 0.264876i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.2705i | 1.18709i | 0.804801 | + | 0.593544i | \(0.202272\pi\) | ||||
−0.804801 | + | 0.593544i | \(0.797728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.272189 | − | 5.12308i | 0.00999913 | − | 0.188201i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.15183 | − | 8.15183i | 0.299062 | − | 0.299062i | −0.541585 | − | 0.840646i | \(-0.682175\pi\) |
0.840646 | + | 0.541585i | \(0.182175\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.5284 | + | 31.6179i | 0.934033 | + | 1.15684i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.32771 | −0.121592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.8741 | −1.56450 | −0.782248 | − | 0.622967i | \(-0.785927\pi\) | ||||
−0.782248 | + | 0.622967i | \(0.785927\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −25.2385 | − | 28.0709i | −0.919743 | − | 1.02296i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3539 | − | 20.3539i | 0.739775 | − | 0.739775i | −0.232759 | − | 0.972534i | \(-0.574775\pi\) |
0.972534 | + | 0.232759i | \(0.0747755\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.8496 | − | 0.735830i | −0.502708 | − | 0.0267089i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 6.31471i | − | 0.228908i | −0.993429 | − | 0.114454i | \(-0.963488\pi\) | ||
0.993429 | − | 0.114454i | \(-0.0365119\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.41651 | − | 3.41651i | −0.123686 | − | 0.123686i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.7466 | − | 21.7466i | −0.785225 | − | 0.785225i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.2423i | 0.802078i | 0.916061 | + | 0.401039i | \(0.131351\pi\) | ||||
−0.916061 | + | 0.401039i | \(0.868649\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 35.9980 | + | 1.91258i | 1.29644 | + | 0.0688798i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.98186 | − | 5.98186i | 0.215153 | − | 0.215153i | −0.591299 | − | 0.806452i | \(-0.701385\pi\) |
0.806452 | + | 0.591299i | \(0.201385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.58726 | − | 2.87761i | −0.0928175 | − | 0.103234i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.848888 | 0.0304146 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.1798 | 0.650523 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.8245 | − | 28.7932i | −0.744209 | − | 1.02898i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.56921 | + | 7.56921i | −0.269813 | + | 0.269813i | −0.829025 | − | 0.559212i | \(-0.811104\pi\) |
0.559212 | + | 0.829025i | \(0.311104\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.86819 | + | 53.9843i | −0.102110 | + | 1.92189i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 10.8605i | − | 0.386156i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.77965 | + | 1.77965i | 0.0631973 | + | 0.0631973i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.62534 | − | 3.62534i | −0.128416 | − | 0.128416i | 0.639977 | − | 0.768394i | \(-0.278944\pi\) |
−0.768394 | + | 0.639977i | \(0.778944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 9.51413i | − | 0.336586i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.58147 | + | 24.2253i | −0.0912118 | + | 0.855959i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.37834 | + | 6.37834i | −0.225087 | + | 0.225087i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.66202 | + | 6.88893i | −0.269716 | + | 0.242502i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −43.5699 | −1.53184 | −0.765918 | − | 0.642939i | \(-0.777715\pi\) | ||||
−0.765918 | + | 0.642939i | \(0.777715\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −33.3205 | −1.17004 | −0.585021 | − | 0.811018i | \(-0.698914\pi\) | ||||
−0.585021 | + | 0.811018i | \(0.698914\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.9062 | + | 12.5031i | −0.487713 | + | 0.438503i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −3.06720 | + | 3.06720i | −0.107308 | + | 0.107308i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.02809 | + | 9.64789i | −0.0359243 | + | 0.337125i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.4901i | 1.44801i | 0.689792 | + | 0.724007i | \(0.257702\pi\) | ||||
−0.689792 | + | 0.724007i | \(0.742298\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.05418 | − | 3.05418i | −0.106462 | − | 0.106462i | 0.651869 | − | 0.758331i | \(-0.273985\pi\) |
−0.758331 | + | 0.651869i | \(0.773985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0224 | − | 12.0224i | −0.418059 | − | 0.418059i | 0.466475 | − | 0.884534i | \(-0.345524\pi\) |
−0.884534 | + | 0.466475i | \(0.845524\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16.7660i | − | 0.582309i | −0.956676 | − | 0.291154i | \(-0.905961\pi\) | ||
0.956676 | − | 0.291154i | \(-0.0940393\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.20314 | − | 41.4669i | 0.0764261 | − | 1.43847i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.614103 | + | 0.614103i | −0.0212774 | + | 0.0212774i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 24.8178 | + | 34.3145i | 0.857830 | + | 1.18608i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 53.8374 | 1.85867 | 0.929337 | − | 0.369232i | \(-0.120379\pi\) | ||||
0.929337 | + | 0.369232i | \(0.120379\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.7670 | 0.612654 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 21.4142 | + | 23.8174i | 0.737545 | + | 0.820314i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.44430 | + | 5.44430i | −0.187069 | + | 0.187069i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.7723 | + | 0.944241i | 0.609943 | + | 0.0324063i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.84712i | 0.337555i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 39.8451 | + | 39.8451i | 1.36427 | + | 1.36427i | 0.868392 | + | 0.495878i | \(0.165154\pi\) |
0.495878 | + | 0.868392i | \(0.334846\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 25.2268 | + | 25.2268i | 0.861730 | + | 0.861730i | 0.991539 | − | 0.129809i | \(-0.0414364\pi\) |
−0.129809 | + | 0.991539i | \(0.541436\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 40.9390i | − | 1.39682i | −0.715698 | − | 0.698410i | \(-0.753891\pi\) | ||
0.715698 | − | 0.698410i | \(-0.246109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.60317 | − | 0.0851765i | −0.0546359 | − | 0.00290281i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.4574 | + | 19.4574i | −0.662338 | + | 0.662338i | −0.955931 | − | 0.293592i | \(-0.905149\pi\) |
0.293592 | + | 0.955931i | \(0.405149\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.8132 | + | 20.9245i | 0.638931 | + | 0.710634i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 15.7392 | 0.533915 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.1033 | −0.613407 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.89473 | + | 11.0165i | 0.301041 | + | 0.372851i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.0431 | + | 30.0431i | −1.01448 | + | 1.01448i | −0.0145904 | + | 0.999894i | \(0.504644\pi\) |
−0.999894 | + | 0.0145904i | \(0.995356\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.212670 | + | 4.00282i | −0.00717318 | + | 0.135012i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.6290i | 0.560247i | 0.959964 | + | 0.280123i | \(0.0903753\pi\) | ||||
−0.959964 | + | 0.280123i | \(0.909625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.0848 | − | 28.0848i | −0.945128 | − | 0.945128i | 0.0534426 | − | 0.998571i | \(-0.482981\pi\) |
−0.998571 | + | 0.0534426i | \(0.982981\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.3800 | + | 20.3800i | 0.684293 | + | 0.684293i | 0.960965 | − | 0.276671i | \(-0.0892314\pi\) |
−0.276671 | + | 0.960965i | \(0.589231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 21.8975i | − | 0.734420i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.44558 | + | 15.9836i | −0.115431 | + | 0.535471i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.09442 | + | 7.09442i | −0.237406 | + | 0.237406i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.3599 | − | 16.5074i | 0.613020 | − | 0.551167i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −55.7350 | −1.85887 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.84637 | 0.128141 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.10034 | − | 5.48482i | 0.203007 | − | 0.182523i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.1542 | − | 25.1542i | 0.835230 | − | 0.835230i | −0.152997 | − | 0.988227i | \(-0.548892\pi\) |
0.988227 | + | 0.152997i | \(0.0488924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −41.6109 | − | 4.43409i | −1.38015 | − | 0.147070i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.1054i | 1.09683i | 0.836206 | + | 0.548416i | \(0.184769\pi\) | ||||
−0.836206 | + | 0.548416i | \(0.815231\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.4014 | + | 17.4014i | 0.575902 | + | 0.575902i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.53699 | + | 9.53699i | 0.314939 | + | 0.314939i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.1197i | − | 1.12550i | −0.826626 | − | 0.562752i | \(-0.809742\pi\) | ||
0.826626 | − | 0.562752i | \(-0.190258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.26681 | − | 23.8436i | 0.0417429 | − | 0.785674i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.8844 | + | 22.8844i | −0.753250 | + | 0.753250i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9267 | + | 24.9703i | −1.01577 | + | 0.820132i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −51.1795 | −1.67914 | −0.839572 | − | 0.543248i | \(-0.817194\pi\) | ||||
−0.839572 | + | 0.543248i | \(0.817194\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.915840 | 0.0300154 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.47173 | + | 8.31023i | 0.244614 | + | 0.272065i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.5430 | − | 26.5430i | 0.867123 | − | 0.867123i | −0.125030 | − | 0.992153i | \(-0.539903\pi\) |
0.992153 | + | 0.125030i | \(0.0399028\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3955 | − | 1.34927i | −0.828752 | − | 0.0440317i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 55.1606i | − | 1.79818i | −0.437761 | − | 0.899092i | \(-0.644228\pi\) | ||
0.437761 | − | 0.899092i | \(-0.355772\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.88874 | + | 2.88874i | 0.0940703 | + | 0.0940703i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.9440 | + | 27.9440i | 0.908057 | + | 0.908057i | 0.996115 | − | 0.0880583i | \(-0.0280662\pi\) |
−0.0880583 | + | 0.996115i | \(0.528066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 16.0579i | − | 0.521263i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 52.0797 | + | 2.76700i | 1.68880 | + | 0.0897261i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.2403 | + | 27.2403i | −0.882399 | + | 0.882399i | −0.993778 | − | 0.111379i | \(-0.964473\pi\) |
0.111379 | + | 0.993778i | \(0.464473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −14.3876 | − | 16.0022i | −0.465086 | − | 0.517279i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.465413 | −0.0150290 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 35.4227 | 1.14267 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.76739 | − | 6.27140i | 0.250301 | − | 0.202093i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.88371 | − | 8.88371i | 0.285681 | − | 0.285681i | −0.549689 | − | 0.835370i | \(-0.685254\pi\) |
0.835370 | + | 0.549689i | \(0.185254\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0730911 | + | 1.37570i | −0.00234802 | + | 0.0441939i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47.3377i | − | 1.51914i | −0.650426 | − | 0.759569i | \(-0.725410\pi\) | ||
0.650426 | − | 0.759569i | \(-0.274590\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.82404 | − | 9.82404i | −0.314944 | − | 0.314944i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 21.5847 | + | 21.5847i | 0.690557 | + | 0.690557i | 0.962354 | − | 0.271798i | \(-0.0876181\pi\) |
−0.271798 | + | 0.962354i | \(0.587618\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.7535i | 0.471524i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.4134 | + | 1.53591i | 0.460186 | + | 0.0490378i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.9392 | − | 27.9392i | 0.891121 | − | 0.891121i | −0.103508 | − | 0.994629i | \(-0.533007\pi\) |
0.994629 | + | 0.103508i | \(0.0330067\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.1100 | − | 12.6863i | 0.449128 | − | 0.403811i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −20.8752 | −0.663793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.2120 | 0.769119 | 0.384559 | − | 0.923100i | \(-0.374353\pi\) | ||||
0.384559 | + | 0.923100i | \(0.374353\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −29.0309 | + | 26.1017i | −0.921269 | + | 0.828314i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0723 | + | 12.0723i | −0.382334 | + | 0.382334i | −0.871942 | − | 0.489608i | \(-0.837140\pi\) |
0.489608 | + | 0.871942i | \(0.337140\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.4622 | + | 1.84083i | 0.362648 | + | 0.0582414i |
(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 | 2100.2.s.c.1793.4 | yes | 32 | |
3.2 | odd | 2 | inner | 2100.2.s.c.1793.12 | yes | 32 | |
5.2 | odd | 4 | inner | 2100.2.s.c.1457.12 | yes | 32 | |
5.3 | odd | 4 | inner | 2100.2.s.c.1457.5 | yes | 32 | |
5.4 | even | 2 | inner | 2100.2.s.c.1793.13 | yes | 32 | |
15.2 | even | 4 | inner | 2100.2.s.c.1457.4 | ✓ | 32 | |
15.8 | even | 4 | inner | 2100.2.s.c.1457.13 | yes | 32 | |
15.14 | odd | 2 | inner | 2100.2.s.c.1793.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.s.c.1457.4 | ✓ | 32 | 15.2 | even | 4 | inner | |
2100.2.s.c.1457.5 | yes | 32 | 5.3 | odd | 4 | inner | |
2100.2.s.c.1457.12 | yes | 32 | 5.2 | odd | 4 | inner | |
2100.2.s.c.1457.13 | yes | 32 | 15.8 | even | 4 | inner | |
2100.2.s.c.1793.4 | yes | 32 | 1.1 | even | 1 | trivial | |
2100.2.s.c.1793.5 | yes | 32 | 15.14 | odd | 2 | inner | |
2100.2.s.c.1793.12 | yes | 32 | 3.2 | odd | 2 | inner | |
2100.2.s.c.1793.13 | yes | 32 | 5.4 | even | 2 | inner |