Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,2,Mod(493,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.f (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: | \(7.58578819202\) |
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 | 493.3 | ||
Character | \(\chi\) | \(=\) | 950.493 |
Dual form | 950.2.f.d.607.3 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −0.267657 | + | 0.267657i | −0.154532 | + | 0.154532i | −0.780139 | − | 0.625607i | \(-0.784851\pi\) |
0.625607 | + | 0.780139i | \(0.284851\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.378524 | 0.154532 | ||||||||
\(7\) | −0.709827 | + | 0.709827i | −0.268289 | + | 0.268289i | −0.828411 | − | 0.560121i | \(-0.810755\pi\) |
0.560121 | + | 0.828411i | \(0.310755\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.85672i | 0.952240i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59543 | −1.68709 | −0.843543 | − | 0.537061i | \(-0.819534\pi\) | ||||
−0.843543 | + | 0.537061i | \(0.819534\pi\) | |||||||
\(12\) | −0.267657 | − | 0.267657i | −0.0772659 | − | 0.0772659i | ||||
\(13\) | 2.99477 | − | 2.99477i | 0.830600 | − | 0.830600i | −0.156999 | − | 0.987599i | \(-0.550182\pi\) |
0.987599 | + | 0.156999i | \(0.0501820\pi\) | |||||||
\(14\) | 1.00385 | 0.268289 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.20326 | − | 2.20326i | 0.534369 | − | 0.534369i | −0.387501 | − | 0.921869i | \(-0.626662\pi\) |
0.921869 | + | 0.387501i | \(0.126662\pi\) | |||||||
\(18\) | 2.02001 | − | 2.02001i | 0.476120 | − | 0.476120i | ||||
\(19\) | −3.84194 | + | 2.05900i | −0.881402 | + | 0.472368i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 0.379980i | − | 0.0829185i | ||||||
\(22\) | 3.95657 | + | 3.95657i | 0.843543 | + | 0.843543i | ||||
\(23\) | −5.89692 | − | 5.89692i | −1.22959 | − | 1.22959i | −0.964118 | − | 0.265475i | \(-0.914471\pi\) |
−0.265475 | − | 0.964118i | \(-0.585529\pi\) | |||||||
\(24\) | 0.378524i | 0.0772659i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.23524 | −0.830600 | ||||||||
\(27\) | −1.56759 | − | 1.56759i | −0.301683 | − | 0.301683i | ||||
\(28\) | −0.709827 | − | 0.709827i | −0.134145 | − | 0.134145i | ||||
\(29\) | 9.34335 | 1.73502 | 0.867508 | − | 0.497423i | \(-0.165720\pi\) | ||||
0.867508 | + | 0.497423i | \(0.165720\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 1.49766 | − | 1.49766i | 0.260709 | − | 0.260709i | ||||
\(34\) | −3.11588 | −0.534369 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.85672 | −0.476120 | ||||||||
\(37\) | −6.61320 | − | 6.61320i | −1.08720 | − | 1.08720i | −0.995815 | − | 0.0913885i | \(-0.970869\pi\) |
−0.0913885 | − | 0.995815i | \(-0.529131\pi\) | |||||||
\(38\) | 4.17260 | + | 1.26073i | 0.676885 | + | 0.204517i | ||||
\(39\) | 1.60314i | 0.256708i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.14029i | − | 1.42747i | −0.700414 | − | 0.713737i | \(-0.747001\pi\) | ||
0.700414 | − | 0.713737i | \(-0.252999\pi\) | |||||||
\(42\) | −0.268687 | + | 0.268687i | −0.0414592 | + | 0.0414592i | ||||
\(43\) | 0.927191 | + | 0.927191i | 0.141395 | + | 0.141395i | 0.774261 | − | 0.632866i | \(-0.218122\pi\) |
−0.632866 | + | 0.774261i | \(0.718122\pi\) | |||||||
\(44\) | − | 5.59543i | − | 0.843543i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.33950i | 1.22959i | ||||||||
\(47\) | 4.20858 | − | 4.20858i | 0.613884 | − | 0.613884i | −0.330072 | − | 0.943956i | \(-0.607073\pi\) |
0.943956 | + | 0.330072i | \(0.107073\pi\) | |||||||
\(48\) | 0.267657 | − | 0.267657i | 0.0386329 | − | 0.0386329i | ||||
\(49\) | 5.99229i | 0.856042i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17943i | 0.165154i | ||||||||
\(52\) | 2.99477 | + | 2.99477i | 0.415300 | + | 0.415300i | ||||
\(53\) | −2.44104 | + | 2.44104i | −0.335303 | + | 0.335303i | −0.854596 | − | 0.519293i | \(-0.826195\pi\) |
0.519293 | + | 0.854596i | \(0.326195\pi\) | |||||||
\(54\) | 2.21691i | 0.301683i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00385i | 0.134145i | ||||||||
\(57\) | 0.477216 | − | 1.57943i | 0.0632087 | − | 0.209200i | ||||
\(58\) | −6.60675 | − | 6.60675i | −0.867508 | − | 0.867508i | ||||
\(59\) | −12.5001 | −1.62737 | −0.813684 | − | 0.581307i | \(-0.802541\pi\) | ||||
−0.813684 | + | 0.581307i | \(0.802541\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | −2.44949 | + | 2.44949i | −0.311086 | + | 0.311086i | ||||
\(63\) | −2.02778 | − | 2.02778i | −0.255476 | − | 0.255476i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.11801 | −0.260709 | ||||||||
\(67\) | 5.72134 | + | 5.72134i | 0.698973 | + | 0.698973i | 0.964189 | − | 0.265216i | \(-0.0854433\pi\) |
−0.265216 | + | 0.964189i | \(0.585443\pi\) | |||||||
\(68\) | 2.20326 | + | 2.20326i | 0.267184 | + | 0.267184i | ||||
\(69\) | 3.15670 | 0.380022 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.9114i | − | 1.65097i | −0.564421 | − | 0.825487i | \(-0.690901\pi\) | ||
0.564421 | − | 0.825487i | \(-0.309099\pi\) | |||||||
\(72\) | 2.02001 | + | 2.02001i | 0.238060 | + | 0.238060i | ||||
\(73\) | −4.33274 | − | 4.33274i | −0.507109 | − | 0.507109i | 0.406529 | − | 0.913638i | \(-0.366739\pi\) |
−0.913638 | + | 0.406529i | \(0.866739\pi\) | |||||||
\(74\) | 9.35248i | 1.08720i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.05900 | − | 3.84194i | −0.236184 | − | 0.440701i | ||||
\(77\) | 3.97179 | − | 3.97179i | 0.452627 | − | 0.452627i | ||||
\(78\) | 1.13359 | − | 1.13359i | 0.128354 | − | 0.128354i | ||||
\(79\) | 5.47180 | 0.615625 | 0.307813 | − | 0.951447i | \(-0.400403\pi\) | ||||
0.307813 | + | 0.951447i | \(0.400403\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.73101 | −0.859001 | ||||||||
\(82\) | −6.46316 | + | 6.46316i | −0.713737 | + | 0.713737i | ||||
\(83\) | −5.53597 | − | 5.53597i | −0.607652 | − | 0.607652i | 0.334680 | − | 0.942332i | \(-0.391372\pi\) |
−0.942332 | + | 0.334680i | \(0.891372\pi\) | |||||||
\(84\) | 0.379980 | 0.0414592 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.31125i | − | 0.141395i | ||||||
\(87\) | −2.50081 | + | 2.50081i | −0.268115 | + | 0.268115i | ||||
\(88\) | −3.95657 | + | 3.95657i | −0.421772 | + | 0.421772i | ||||
\(89\) | −8.99513 | −0.953482 | −0.476741 | − | 0.879044i | \(-0.658182\pi\) | ||||
−0.476741 | + | 0.879044i | \(0.658182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.25154i | 0.445682i | ||||||||
\(92\) | 5.89692 | − | 5.89692i | 0.614796 | − | 0.614796i | ||||
\(93\) | 0.927191 | + | 0.927191i | 0.0961452 | + | 0.0961452i | ||||
\(94\) | −5.95183 | −0.613884 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.378524 | −0.0386329 | ||||||||
\(97\) | −9.16155 | − | 9.16155i | −0.930215 | − | 0.930215i | 0.0675043 | − | 0.997719i | \(-0.478496\pi\) |
−0.997719 | + | 0.0675043i | \(0.978496\pi\) | |||||||
\(98\) | 4.23719 | − | 4.23719i | 0.428021 | − | 0.428021i | ||||
\(99\) | − | 15.9846i | − | 1.60651i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 0.833986 | − | 0.833986i | 0.0825769 | − | 0.0825769i | ||||
\(103\) | −4.91891 | + | 4.91891i | −0.484675 | + | 0.484675i | −0.906621 | − | 0.421946i | \(-0.861347\pi\) |
0.421946 | + | 0.906621i | \(0.361347\pi\) | |||||||
\(104\) | − | 4.23524i | − | 0.415300i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.45215 | 0.335303 | ||||||||
\(107\) | 2.21021 | + | 2.21021i | 0.213669 | + | 0.213669i | 0.805824 | − | 0.592155i | \(-0.201723\pi\) |
−0.592155 | + | 0.805824i | \(0.701723\pi\) | |||||||
\(108\) | 1.56759 | − | 1.56759i | 0.150842 | − | 0.150842i | ||||
\(109\) | 0.858684 | 0.0822471 | 0.0411235 | − | 0.999154i | \(-0.486906\pi\) | ||||
0.0411235 | + | 0.999154i | \(0.486906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.54014 | 0.336015 | ||||||||
\(112\) | 0.709827 | − | 0.709827i | 0.0670723 | − | 0.0670723i | ||||
\(113\) | −8.19921 | + | 8.19921i | −0.771317 | + | 0.771317i | −0.978337 | − | 0.207020i | \(-0.933623\pi\) |
0.207020 | + | 0.978337i | \(0.433623\pi\) | |||||||
\(114\) | −1.45427 | + | 0.779382i | −0.136205 | + | 0.0729958i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.34335i | 0.867508i | ||||||||
\(117\) | 8.55522 | + | 8.55522i | 0.790930 | + | 0.790930i | ||||
\(118\) | 8.83887 | + | 8.83887i | 0.813684 | + | 0.813684i | ||||
\(119\) | 3.12786i | 0.286731i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 20.3089 | 1.84626 | ||||||||
\(122\) | 1.41421 | + | 1.41421i | 0.128037 | + | 0.128037i | ||||
\(123\) | 2.44646 | + | 2.44646i | 0.220590 | + | 0.220590i | ||||
\(124\) | 3.46410 | 0.311086 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.86771i | 0.255476i | ||||||||
\(127\) | −2.85436 | − | 2.85436i | −0.253283 | − | 0.253283i | 0.569032 | − | 0.822315i | \(-0.307318\pi\) |
−0.822315 | + | 0.569032i | \(0.807318\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −0.496338 | −0.0437001 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.7134 | 1.19815 | 0.599074 | − | 0.800693i | \(-0.295535\pi\) | ||||
0.599074 | + | 0.800693i | \(0.295535\pi\) | |||||||
\(132\) | 1.49766 | + | 1.49766i | 0.130354 | + | 0.130354i | ||||
\(133\) | 1.26558 | − | 4.18865i | 0.109739 | − | 0.363202i | ||||
\(134\) | − | 8.09119i | − | 0.698973i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.11588i | − | 0.267184i | ||||||
\(137\) | −12.3591 | + | 12.3591i | −1.05591 | + | 1.05591i | −0.0575711 | + | 0.998341i | \(0.518336\pi\) |
−0.998341 | + | 0.0575711i | \(0.981664\pi\) | |||||||
\(138\) | −2.23213 | − | 2.23213i | −0.190011 | − | 0.190011i | ||||
\(139\) | 11.0729i | 0.939188i | 0.882883 | + | 0.469594i | \(0.155600\pi\) | ||||
−0.882883 | + | 0.469594i | \(0.844400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.25291i | 0.189729i | ||||||||
\(142\) | −9.83681 | + | 9.83681i | −0.825487 | + | 0.825487i | ||||
\(143\) | −16.7570 | + | 16.7570i | −1.40129 | + | 1.40129i | ||||
\(144\) | − | 2.85672i | − | 0.238060i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6.12742i | 0.507109i | ||||||||
\(147\) | −1.60388 | − | 1.60388i | −0.132286 | − | 0.132286i | ||||
\(148\) | 6.61320 | − | 6.61320i | 0.543602 | − | 0.543602i | ||||
\(149\) | − | 5.19087i | − | 0.425252i | −0.977134 | − | 0.212626i | \(-0.931798\pi\) | ||
0.977134 | − | 0.212626i | \(-0.0682017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.37692i | 0.518946i | 0.965750 | + | 0.259473i | \(0.0835489\pi\) | ||||
−0.965750 | + | 0.259473i | \(0.916451\pi\) | |||||||
\(152\) | −1.26073 | + | 4.17260i | −0.102258 | + | 0.338442i | ||||
\(153\) | 6.29409 | + | 6.29409i | 0.508847 | + | 0.508847i | ||||
\(154\) | −5.61696 | −0.452627 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.60314 | −0.128354 | ||||||||
\(157\) | 4.30387 | − | 4.30387i | 0.343486 | − | 0.343486i | −0.514190 | − | 0.857676i | \(-0.671907\pi\) |
0.857676 | + | 0.514190i | \(0.171907\pi\) | |||||||
\(158\) | −3.86914 | − | 3.86914i | −0.307813 | − | 0.307813i | ||||
\(159\) | − | 1.30672i | − | 0.103630i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.37158 | 0.659773 | ||||||||
\(162\) | 5.46665 | + | 5.46665i | 0.429500 | + | 0.429500i | ||||
\(163\) | 9.73720 | + | 9.73720i | 0.762676 | + | 0.762676i | 0.976805 | − | 0.214129i | \(-0.0686914\pi\) |
−0.214129 | + | 0.976805i | \(0.568691\pi\) | |||||||
\(164\) | 9.14029 | 0.713737 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.82904i | 0.607652i | ||||||||
\(167\) | −15.5454 | − | 15.5454i | −1.20294 | − | 1.20294i | −0.973267 | − | 0.229676i | \(-0.926233\pi\) |
−0.229676 | − | 0.973267i | \(-0.573767\pi\) | |||||||
\(168\) | −0.268687 | − | 0.268687i | −0.0207296 | − | 0.0207296i | ||||
\(169\) | − | 4.93729i | − | 0.379791i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.88199 | − | 10.9753i | −0.449807 | − | 0.839306i | ||||
\(172\) | −0.927191 | + | 0.927191i | −0.0706976 | + | 0.0706976i | ||||
\(173\) | 11.9265 | − | 11.9265i | 0.906753 | − | 0.906753i | −0.0892559 | − | 0.996009i | \(-0.528449\pi\) |
0.996009 | + | 0.0892559i | \(0.0284489\pi\) | |||||||
\(174\) | 3.53668 | 0.268115 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.59543 | 0.421772 | ||||||||
\(177\) | 3.34573 | − | 3.34573i | 0.251480 | − | 0.251480i | ||||
\(178\) | 6.36052 | + | 6.36052i | 0.476741 | + | 0.476741i | ||||
\(179\) | 5.34131 | 0.399229 | 0.199614 | − | 0.979875i | \(-0.436031\pi\) | ||||
0.199614 | + | 0.979875i | \(0.436031\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.1836i | 0.905599i | 0.891612 | + | 0.452799i | \(0.149575\pi\) | ||||
−0.891612 | + | 0.452799i | \(0.850425\pi\) | |||||||
\(182\) | 3.00629 | − | 3.00629i | 0.222841 | − | 0.222841i | ||||
\(183\) | 0.535314 | − | 0.535314i | 0.0395715 | − | 0.0395715i | ||||
\(184\) | −8.33950 | −0.614796 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 1.31125i | − | 0.0961452i | ||||||
\(187\) | −12.3282 | + | 12.3282i | −0.901526 | + | 0.901526i | ||||
\(188\) | 4.20858 | + | 4.20858i | 0.306942 | + | 0.306942i | ||||
\(189\) | 2.22544 | 0.161877 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.54014 | 0.545585 | 0.272793 | − | 0.962073i | \(-0.412053\pi\) | ||||
0.272793 | + | 0.962073i | \(0.412053\pi\) | |||||||
\(192\) | 0.267657 | + | 0.267657i | 0.0193165 | + | 0.0193165i | ||||
\(193\) | 5.88017 | − | 5.88017i | 0.423264 | − | 0.423264i | −0.463062 | − | 0.886326i | \(-0.653249\pi\) |
0.886326 | + | 0.463062i | \(0.153249\pi\) | |||||||
\(194\) | 12.9564i | 0.930215i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.99229 | −0.428021 | ||||||||
\(197\) | 12.8237 | − | 12.8237i | 0.913649 | − | 0.913649i | −0.0829081 | − | 0.996557i | \(-0.526421\pi\) |
0.996557 | + | 0.0829081i | \(0.0264208\pi\) | |||||||
\(198\) | −11.3028 | + | 11.3028i | −0.803256 | + | 0.803256i | ||||
\(199\) | − | 8.00986i | − | 0.567804i | −0.958853 | − | 0.283902i | \(-0.908371\pi\) | ||
0.958853 | − | 0.283902i | \(-0.0916290\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.06271 | −0.216027 | ||||||||
\(202\) | 4.24264 | + | 4.24264i | 0.298511 | + | 0.298511i | ||||
\(203\) | −6.63216 | + | 6.63216i | −0.465486 | + | 0.465486i | ||||
\(204\) | −1.17943 | −0.0825769 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.95639 | 0.484675 | ||||||||
\(207\) | 16.8458 | − | 16.8458i | 1.17087 | − | 1.17087i | ||||
\(208\) | −2.99477 | + | 2.99477i | −0.207650 | + | 0.207650i | ||||
\(209\) | 21.4973 | − | 11.5210i | 1.48700 | − | 0.796925i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.88184i | 0.680294i | 0.940372 | + | 0.340147i | \(0.110477\pi\) | ||||
−0.940372 | + | 0.340147i | \(0.889523\pi\) | |||||||
\(212\) | −2.44104 | − | 2.44104i | −0.167651 | − | 0.167651i | ||||
\(213\) | 3.72347 | + | 3.72347i | 0.255128 | + | 0.255128i | ||||
\(214\) | − | 3.12571i | − | 0.213669i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.21691 | −0.150842 | ||||||||
\(217\) | 2.45891 | + | 2.45891i | 0.166922 | + | 0.166922i | ||||
\(218\) | −0.607182 | − | 0.607182i | −0.0411235 | − | 0.0411235i | ||||
\(219\) | 2.31938 | 0.156729 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.1965i | − | 0.887693i | ||||||
\(222\) | −2.50326 | − | 2.50326i | −0.168008 | − | 0.168008i | ||||
\(223\) | −1.07063 | + | 1.07063i | −0.0716945 | + | 0.0716945i | −0.742045 | − | 0.670350i | \(-0.766144\pi\) |
0.670350 | + | 0.742045i | \(0.266144\pi\) | |||||||
\(224\) | −1.00385 | −0.0670723 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.5954 | 0.771317 | ||||||||
\(227\) | 10.0734 | + | 10.0734i | 0.668592 | + | 0.668592i | 0.957390 | − | 0.288798i | \(-0.0932557\pi\) |
−0.288798 | + | 0.957390i | \(0.593256\pi\) | |||||||
\(228\) | 1.57943 | + | 0.477216i | 0.104600 | + | 0.0316044i | ||||
\(229\) | 13.4423i | 0.888292i | 0.895954 | + | 0.444146i | \(0.146493\pi\) | ||||
−0.895954 | + | 0.444146i | \(0.853507\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.12615i | 0.139891i | ||||||||
\(232\) | 6.60675 | − | 6.60675i | 0.433754 | − | 0.433754i | ||||
\(233\) | 10.9619 | + | 10.9619i | 0.718141 | + | 0.718141i | 0.968224 | − | 0.250084i | \(-0.0804581\pi\) |
−0.250084 | + | 0.968224i | \(0.580458\pi\) | |||||||
\(234\) | − | 12.0989i | − | 0.790930i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 12.5001i | − | 0.813684i | ||||||
\(237\) | −1.46456 | + | 1.46456i | −0.0951336 | + | 0.0951336i | ||||
\(238\) | 2.21173 | − | 2.21173i | 0.143365 | − | 0.143365i | ||||
\(239\) | − | 20.6959i | − | 1.33870i | −0.742945 | − | 0.669352i | \(-0.766572\pi\) | ||
0.742945 | − | 0.669352i | \(-0.233428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.82904i | 0.504313i | 0.967686 | + | 0.252157i | \(0.0811398\pi\) | ||||
−0.967686 | + | 0.252157i | \(0.918860\pi\) | |||||||
\(242\) | −14.3605 | − | 14.3605i | −0.923131 | − | 0.923131i | ||||
\(243\) | 6.77203 | − | 6.77203i | 0.434426 | − | 0.434426i | ||||
\(244\) | − | 2.00000i | − | 0.128037i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 3.45982i | − | 0.220590i | ||||||
\(247\) | −5.33949 | + | 17.6720i | −0.339743 | + | 1.12444i | ||||
\(248\) | −2.44949 | − | 2.44949i | −0.155543 | − | 0.155543i | ||||
\(249\) | 2.96348 | 0.187803 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.07286 | 0.193957 | 0.0969786 | − | 0.995286i | \(-0.469082\pi\) | ||||
0.0969786 | + | 0.995286i | \(0.469082\pi\) | |||||||
\(252\) | 2.02778 | − | 2.02778i | 0.127738 | − | 0.127738i | ||||
\(253\) | 32.9958 | + | 32.9958i | 2.07443 | + | 2.07443i | ||||
\(254\) | 4.03667i | 0.253283i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5836 | − | 11.5836i | −0.722567 | − | 0.722567i | 0.246560 | − | 0.969127i | \(-0.420700\pi\) |
−0.969127 | + | 0.246560i | \(0.920700\pi\) | |||||||
\(258\) | 0.350964 | + | 0.350964i | 0.0218501 | + | 0.0218501i | ||||
\(259\) | 9.38846 | 0.583370 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 26.6913i | 1.65215i | ||||||||
\(262\) | −9.69687 | − | 9.69687i | −0.599074 | − | 0.599074i | ||||
\(263\) | 5.28880 | + | 5.28880i | 0.326121 | + | 0.326121i | 0.851109 | − | 0.524988i | \(-0.175930\pi\) |
−0.524988 | + | 0.851109i | \(0.675930\pi\) | |||||||
\(264\) | − | 2.11801i | − | 0.130354i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.85672 | + | 2.06692i | −0.236471 | + | 0.126731i | ||||
\(267\) | 2.40761 | − | 2.40761i | 0.147343 | − | 0.147343i | ||||
\(268\) | −5.72134 | + | 5.72134i | −0.349486 | + | 0.349486i | ||||
\(269\) | 18.5605 | 1.13165 | 0.565827 | − | 0.824524i | \(-0.308557\pi\) | ||||
0.565827 | + | 0.824524i | \(0.308557\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9219 | 0.845693 | 0.422847 | − | 0.906201i | \(-0.361031\pi\) | ||||
0.422847 | + | 0.906201i | \(0.361031\pi\) | |||||||
\(272\) | −2.20326 | + | 2.20326i | −0.133592 | + | 0.133592i | ||||
\(273\) | −1.13795 | − | 1.13795i | −0.0688720 | − | 0.0688720i | ||||
\(274\) | 17.4785 | 1.05591 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.15670i | 0.190011i | ||||||||
\(277\) | −18.3178 | + | 18.3178i | −1.10061 | + | 1.10061i | −0.106270 | + | 0.994337i | \(0.533891\pi\) |
−0.994337 | + | 0.106270i | \(0.966109\pi\) | |||||||
\(278\) | 7.82969 | − | 7.82969i | 0.469594 | − | 0.469594i | ||||
\(279\) | 9.89597 | 0.592456 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9436i | 0.652840i | 0.945225 | + | 0.326420i | \(0.105842\pi\) | ||||
−0.945225 | + | 0.326420i | \(0.894158\pi\) | |||||||
\(282\) | 1.59305 | − | 1.59305i | 0.0948647 | − | 0.0948647i | ||||
\(283\) | −19.1004 | − | 19.1004i | −1.13540 | − | 1.13540i | −0.989264 | − | 0.146138i | \(-0.953316\pi\) |
−0.146138 | − | 0.989264i | \(-0.546684\pi\) | |||||||
\(284\) | 13.9114 | 0.825487 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 23.6980 | 1.40129 | ||||||||
\(287\) | 6.48802 | + | 6.48802i | 0.382976 | + | 0.382976i | ||||
\(288\) | −2.02001 | + | 2.02001i | −0.119030 | + | 0.119030i | ||||
\(289\) | 7.29131i | 0.428900i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.90431 | 0.287495 | ||||||||
\(292\) | 4.33274 | − | 4.33274i | 0.253554 | − | 0.253554i | ||||
\(293\) | 8.41216 | − | 8.41216i | 0.491444 | − | 0.491444i | −0.417317 | − | 0.908761i | \(-0.637030\pi\) |
0.908761 | + | 0.417317i | \(0.137030\pi\) | |||||||
\(294\) | 2.26823i | 0.132286i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −9.35248 | −0.543602 | ||||||||
\(297\) | 8.77135 | + | 8.77135i | 0.508966 | + | 0.508966i | ||||
\(298\) | −3.67050 | + | 3.67050i | −0.212626 | + | 0.212626i | ||||
\(299\) | −35.3198 | −2.04260 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.31629 | −0.0758697 | ||||||||
\(302\) | 4.50916 | − | 4.50916i | 0.259473 | − | 0.259473i | ||||
\(303\) | 1.60594 | − | 1.60594i | 0.0922589 | − | 0.0922589i | ||||
\(304\) | 3.84194 | − | 2.05900i | 0.220350 | − | 0.118092i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 8.90119i | − | 0.508847i | ||||||
\(307\) | 12.9256 | + | 12.9256i | 0.737705 | + | 0.737705i | 0.972133 | − | 0.234428i | \(-0.0753217\pi\) |
−0.234428 | + | 0.972133i | \(0.575322\pi\) | |||||||
\(308\) | 3.97179 | + | 3.97179i | 0.226314 | + | 0.226314i | ||||
\(309\) | − | 2.63316i | − | 0.149795i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.7233 | −0.664767 | −0.332384 | − | 0.943144i | \(-0.607853\pi\) | ||||
−0.332384 | + | 0.943144i | \(0.607853\pi\) | |||||||
\(312\) | 1.13359 | + | 1.13359i | 0.0641770 | + | 0.0641770i | ||||
\(313\) | −16.3409 | − | 16.3409i | −0.923643 | − | 0.923643i | 0.0736417 | − | 0.997285i | \(-0.476538\pi\) |
−0.997285 | + | 0.0736417i | \(0.976538\pi\) | |||||||
\(314\) | −6.08659 | −0.343486 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.47180i | 0.307813i | ||||||||
\(317\) | −7.39624 | − | 7.39624i | −0.415414 | − | 0.415414i | 0.468205 | − | 0.883620i | \(-0.344901\pi\) |
−0.883620 | + | 0.468205i | \(0.844901\pi\) | |||||||
\(318\) | −0.923993 | + | 0.923993i | −0.0518149 | + | 0.0518149i | ||||
\(319\) | −52.2801 | −2.92712 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.18316 | −0.0660374 | ||||||||
\(322\) | −5.91960 | − | 5.91960i | −0.329887 | − | 0.329887i | ||||
\(323\) | −3.92827 | + | 13.0013i | −0.218575 | + | 0.723412i | ||||
\(324\) | − | 7.73101i | − | 0.429500i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 13.7705i | − | 0.762676i | ||||||
\(327\) | −0.229833 | + | 0.229833i | −0.0127098 | + | 0.0127098i | ||||
\(328\) | −6.46316 | − | 6.46316i | −0.356868 | − | 0.356868i | ||||
\(329\) | 5.97473i | 0.329397i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.4836i | − | 1.01595i | −0.861371 | − | 0.507976i | \(-0.830394\pi\) | ||
0.861371 | − | 0.507976i | \(-0.169606\pi\) | |||||||
\(332\) | 5.53597 | − | 5.53597i | 0.303826 | − | 0.303826i | ||||
\(333\) | 18.8921 | − | 18.8921i | 1.03528 | − | 1.03528i | ||||
\(334\) | 21.9846i | 1.20294i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.379980i | 0.0207296i | ||||||||
\(337\) | −23.8856 | − | 23.8856i | −1.30113 | − | 1.30113i | −0.927629 | − | 0.373504i | \(-0.878156\pi\) |
−0.373504 | − | 0.927629i | \(-0.621844\pi\) | |||||||
\(338\) | −3.49119 | + | 3.49119i | −0.189896 | + | 0.189896i | ||||
\(339\) | − | 4.38915i | − | 0.238386i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 19.3831i | 1.04966i | ||||||||
\(342\) | −3.60154 | + | 11.9199i | −0.194749 | + | 0.644557i | ||||
\(343\) | −9.22228 | − | 9.22228i | −0.497956 | − | 0.497956i | ||||
\(344\) | 1.31125 | 0.0706976 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −16.8666 | −0.906753 | ||||||||
\(347\) | −7.59564 | + | 7.59564i | −0.407755 | + | 0.407755i | −0.880955 | − | 0.473200i | \(-0.843099\pi\) |
0.473200 | + | 0.880955i | \(0.343099\pi\) | |||||||
\(348\) | −2.50081 | − | 2.50081i | −0.134058 | − | 0.134058i | ||||
\(349\) | 32.0798i | 1.71719i | 0.512655 | + | 0.858595i | \(0.328662\pi\) | ||||
−0.512655 | + | 0.858595i | \(0.671338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.38915 | −0.501156 | ||||||||
\(352\) | −3.95657 | − | 3.95657i | −0.210886 | − | 0.210886i | ||||
\(353\) | −1.84231 | − | 1.84231i | −0.0980562 | − | 0.0980562i | 0.656377 | − | 0.754433i | \(-0.272088\pi\) |
−0.754433 | + | 0.656377i | \(0.772088\pi\) | |||||||
\(354\) | −4.73157 | −0.251480 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 8.99513i | − | 0.476741i | ||||||
\(357\) | −0.837194 | − | 0.837194i | −0.0443090 | − | 0.0443090i | ||||
\(358\) | −3.77688 | − | 3.77688i | −0.199614 | − | 0.199614i | ||||
\(359\) | 8.46972i | 0.447015i | 0.974702 | + | 0.223507i | \(0.0717507\pi\) | ||||
−0.974702 | + | 0.223507i | \(0.928249\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.5210 | − | 15.8211i | 0.553738 | − | 0.832691i | ||||
\(362\) | 8.61510 | − | 8.61510i | 0.452799 | − | 0.452799i | ||||
\(363\) | −5.43581 | + | 5.43581i | −0.285306 | + | 0.285306i | ||||
\(364\) | −4.25154 | −0.222841 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.757048 | −0.0395715 | ||||||||
\(367\) | −12.3312 | + | 12.3312i | −0.643684 | + | 0.643684i | −0.951459 | − | 0.307775i | \(-0.900416\pi\) |
0.307775 | + | 0.951459i | \(0.400416\pi\) | |||||||
\(368\) | 5.89692 | + | 5.89692i | 0.307398 | + | 0.307398i | ||||
\(369\) | 26.1112 | 1.35930 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.46543i | − | 0.179916i | ||||||
\(372\) | −0.927191 | + | 0.927191i | −0.0480726 | + | 0.0480726i | ||||
\(373\) | −5.47155 | + | 5.47155i | −0.283306 | + | 0.283306i | −0.834426 | − | 0.551120i | \(-0.814201\pi\) |
0.551120 | + | 0.834426i | \(0.314201\pi\) | |||||||
\(374\) | 17.4347 | 0.901526 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 5.95183i | − | 0.306942i | ||||||
\(377\) | 27.9812 | − | 27.9812i | 1.44110 | − | 1.44110i | ||||
\(378\) | −1.57362 | − | 1.57362i | −0.0809384 | − | 0.0809384i | ||||
\(379\) | 13.3179 | 0.684095 | 0.342048 | − | 0.939683i | \(-0.388880\pi\) | ||||
0.342048 | + | 0.939683i | \(0.388880\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.52798 | 0.0782806 | ||||||||
\(382\) | −5.33168 | − | 5.33168i | −0.272793 | − | 0.272793i | ||||
\(383\) | −14.0425 | + | 14.0425i | −0.717541 | + | 0.717541i | −0.968101 | − | 0.250560i | \(-0.919385\pi\) |
0.250560 | + | 0.968101i | \(0.419385\pi\) | |||||||
\(384\) | − | 0.378524i | − | 0.0193165i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.31581 | −0.423264 | ||||||||
\(387\) | −2.64872 | + | 2.64872i | −0.134642 | + | 0.134642i | ||||
\(388\) | 9.16155 | − | 9.16155i | 0.465107 | − | 0.465107i | ||||
\(389\) | − | 12.5072i | − | 0.634138i | −0.948402 | − | 0.317069i | \(-0.897301\pi\) | ||
0.948402 | − | 0.317069i | \(-0.102699\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.9849 | −1.31411 | ||||||||
\(392\) | 4.23719 | + | 4.23719i | 0.214010 | + | 0.214010i | ||||
\(393\) | −3.67050 | + | 3.67050i | −0.185152 | + | 0.185152i | ||||
\(394\) | −18.1354 | −0.913649 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 15.9846 | 0.803256 | ||||||||
\(397\) | −18.2540 | + | 18.2540i | −0.916141 | + | 0.916141i | −0.996746 | − | 0.0806055i | \(-0.974315\pi\) |
0.0806055 | + | 0.996746i | \(0.474315\pi\) | |||||||
\(398\) | −5.66382 | + | 5.66382i | −0.283902 | + | 0.283902i | ||||
\(399\) | 0.782380 | + | 1.45986i | 0.0391680 | + | 0.0730845i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9.54641i | − | 0.476725i | −0.971176 | − | 0.238363i | \(-0.923389\pi\) | ||
0.971176 | − | 0.238363i | \(-0.0766106\pi\) | |||||||
\(402\) | 2.16566 | + | 2.16566i | 0.108014 | + | 0.108014i | ||||
\(403\) | −10.3742 | − | 10.3742i | −0.516775 | − | 0.516775i | ||||
\(404\) | − | 6.00000i | − | 0.298511i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.37929 | 0.465486 | ||||||||
\(407\) | 37.0037 | + | 37.0037i | 1.83421 | + | 1.83421i | ||||
\(408\) | 0.833986 | + | 0.833986i | 0.0412885 | + | 0.0412885i | ||||
\(409\) | −11.2029 | −0.553949 | −0.276975 | − | 0.960877i | \(-0.589332\pi\) | ||||
−0.276975 | + | 0.960877i | \(0.589332\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 6.61602i | − | 0.326344i | ||||||
\(412\) | −4.91891 | − | 4.91891i | −0.242337 | − | 0.242337i | ||||
\(413\) | 8.87287 | − | 8.87287i | 0.436606 | − | 0.436606i | ||||
\(414\) | −23.8236 | −1.17087 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.23524 | 0.207650 | ||||||||
\(417\) | −2.96373 | − | 2.96373i | −0.145134 | − | 0.145134i | ||||
\(418\) | −23.3475 | − | 7.05431i | −1.14196 | − | 0.345038i | ||||
\(419\) | − | 6.91172i | − | 0.337660i | −0.985645 | − | 0.168830i | \(-0.946001\pi\) | ||
0.985645 | − | 0.168830i | \(-0.0539988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.98100i | − | 0.437707i | −0.975758 | − | 0.218854i | \(-0.929768\pi\) | ||
0.975758 | − | 0.218854i | \(-0.0702317\pi\) | |||||||
\(422\) | 6.98752 | − | 6.98752i | 0.340147 | − | 0.340147i | ||||
\(423\) | 12.0227 | + | 12.0227i | 0.584565 | + | 0.584565i | ||||
\(424\) | 3.45215i | 0.167651i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 5.26578i | − | 0.255128i | ||||||
\(427\) | 1.41965 | − | 1.41965i | 0.0687019 | − | 0.0687019i | ||||
\(428\) | −2.21021 | + | 2.21021i | −0.106835 | + | 0.106835i | ||||
\(429\) | − | 8.97027i | − | 0.433089i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.5052i | 0.650524i | 0.945624 | + | 0.325262i | \(0.105453\pi\) | ||||
−0.945624 | + | 0.325262i | \(0.894547\pi\) | |||||||
\(432\) | 1.56759 | + | 1.56759i | 0.0754208 | + | 0.0754208i | ||||
\(433\) | 16.9664 | − | 16.9664i | 0.815353 | − | 0.815353i | −0.170077 | − | 0.985431i | \(-0.554402\pi\) |
0.985431 | + | 0.170077i | \(0.0544018\pi\) | |||||||
\(434\) | − | 3.47743i | − | 0.166922i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.858684i | 0.0411235i | ||||||||
\(437\) | 34.7974 | + | 10.5138i | 1.66458 | + | 0.502945i | ||||
\(438\) | −1.64005 | − | 1.64005i | −0.0783644 | − | 0.0783644i | ||||
\(439\) | −34.2082 | −1.63267 | −0.816334 | − | 0.577580i | \(-0.803997\pi\) | ||||
−0.816334 | + | 0.577580i | \(0.803997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.1183 | −0.815157 | ||||||||
\(442\) | −9.33134 | + | 9.33134i | −0.443846 | + | 0.443846i | ||||
\(443\) | −9.98134 | − | 9.98134i | −0.474228 | − | 0.474228i | 0.429052 | − | 0.903280i | \(-0.358848\pi\) |
−0.903280 | + | 0.429052i | \(0.858848\pi\) | |||||||
\(444\) | 3.54014i | 0.168008i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.51410 | 0.0716945 | ||||||||
\(447\) | 1.38937 | + | 1.38937i | 0.0657150 | + | 0.0657150i | ||||
\(448\) | 0.709827 | + | 0.709827i | 0.0335362 | + | 0.0335362i | ||||
\(449\) | 15.8684 | 0.748875 | 0.374438 | − | 0.927252i | \(-0.377836\pi\) | ||||
0.374438 | + | 0.927252i | \(0.377836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 51.1439i | 2.40827i | ||||||||
\(452\) | −8.19921 | − | 8.19921i | −0.385658 | − | 0.385658i | ||||
\(453\) | −1.70683 | − | 1.70683i | −0.0801937 | − | 0.0801937i | ||||
\(454\) | − | 14.2459i | − | 0.668592i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.779382 | − | 1.45427i | −0.0364979 | − | 0.0681023i | ||||
\(457\) | 20.0286 | − | 20.0286i | 0.936896 | − | 0.936896i | −0.0612274 | − | 0.998124i | \(-0.519501\pi\) |
0.998124 | + | 0.0612274i | \(0.0195015\pi\) | |||||||
\(458\) | 9.50514 | − | 9.50514i | 0.444146 | − | 0.444146i | ||||
\(459\) | −6.90762 | −0.322420 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −39.5726 | −1.84308 | −0.921540 | − | 0.388284i | \(-0.873068\pi\) | ||||
−0.921540 | + | 0.388284i | \(0.873068\pi\) | |||||||
\(462\) | 1.50342 | − | 1.50342i | 0.0699453 | − | 0.0699453i | ||||
\(463\) | −8.32792 | − | 8.32792i | −0.387031 | − | 0.387031i | 0.486596 | − | 0.873627i | \(-0.338238\pi\) |
−0.873627 | + | 0.486596i | \(0.838238\pi\) | |||||||
\(464\) | −9.34335 | −0.433754 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 15.5025i | − | 0.718141i | ||||||
\(467\) | −18.6687 | + | 18.6687i | −0.863886 | + | 0.863886i | −0.991787 | − | 0.127901i | \(-0.959176\pi\) |
0.127901 | + | 0.991787i | \(0.459176\pi\) | |||||||
\(468\) | −8.55522 | + | 8.55522i | −0.395465 | + | 0.395465i | ||||
\(469\) | −8.12232 | −0.375054 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.30392i | 0.106159i | ||||||||
\(472\) | −8.83887 | + | 8.83887i | −0.406842 | + | 0.406842i | ||||
\(473\) | −5.18803 | − | 5.18803i | −0.238546 | − | 0.238546i | ||||
\(474\) | 2.07121 | 0.0951336 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.12786 | −0.143365 | ||||||||
\(477\) | −6.97337 | − | 6.97337i | −0.319289 | − | 0.319289i | ||||
\(478\) | −14.6342 | + | 14.6342i | −0.669352 | + | 0.669352i | ||||
\(479\) | − | 14.5449i | − | 0.664573i | −0.943179 | − | 0.332286i | \(-0.892180\pi\) | ||
0.943179 | − | 0.332286i | \(-0.107820\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −39.6100 | −1.80606 | ||||||||
\(482\) | 5.53597 | − | 5.53597i | 0.252157 | − | 0.252157i | ||||
\(483\) | −2.24071 | + | 2.24071i | −0.101956 | + | 0.101956i | ||||
\(484\) | 20.3089i | 0.923131i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.57710 | −0.434426 | ||||||||
\(487\) | 22.3869 | + | 22.3869i | 1.01445 | + | 1.01445i | 0.999894 | + | 0.0145519i | \(0.00463216\pi\) |
0.0145519 | + | 0.999894i | \(0.495368\pi\) | |||||||
\(488\) | −1.41421 | + | 1.41421i | −0.0640184 | + | 0.0640184i | ||||
\(489\) | −5.21246 | −0.235715 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.90431 | −0.311587 | −0.155793 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155793 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(492\) | −2.44646 | + | 2.44646i | −0.110295 | + | 0.110295i | ||||
\(493\) | 20.5858 | − | 20.5858i | 0.927138 | − | 0.927138i | ||||
\(494\) | 16.2716 | − | 8.72038i | 0.732092 | − | 0.392348i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.46410i | 0.155543i | ||||||||
\(497\) | 9.87465 | + | 9.87465i | 0.442939 | + | 0.442939i | ||||
\(498\) | −2.09550 | − | 2.09550i | −0.0939015 | − | 0.0939015i | ||||
\(499\) | 27.6980i | 1.23993i | 0.784628 | + | 0.619967i | \(0.212854\pi\) | ||||
−0.784628 | + | 0.619967i | \(0.787146\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.32169 | 0.371786 | ||||||||
\(502\) | −2.17284 | − | 2.17284i | −0.0969786 | − | 0.0969786i | ||||
\(503\) | −7.10527 | − | 7.10527i | −0.316808 | − | 0.316808i | 0.530732 | − | 0.847540i | \(-0.321917\pi\) |
−0.847540 | + | 0.530732i | \(0.821917\pi\) | |||||||
\(504\) | −2.86771 | −0.127738 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 46.6631i | − | 2.07443i | ||||||
\(507\) | 1.32150 | + | 1.32150i | 0.0586898 | + | 0.0586898i | ||||
\(508\) | 2.85436 | − | 2.85436i | 0.126642 | − | 0.126642i | ||||
\(509\) | −20.7950 | −0.921723 | −0.460861 | − | 0.887472i | \(-0.652459\pi\) | ||||
−0.460861 | + | 0.887472i | \(0.652459\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.15099 | 0.272104 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 9.25027 | + | 2.79492i | 0.408409 | + | 0.123399i | ||||
\(514\) | 16.3817i | 0.722567i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 0.496338i | − | 0.0218501i | ||||||
\(517\) | −23.5488 | + | 23.5488i | −1.03568 | + | 1.03568i | ||||
\(518\) | −6.63864 | − | 6.63864i | −0.291685 | − | 0.291685i | ||||
\(519\) | 6.38440i | 0.280244i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.8270i | − | 1.21912i | −0.792739 | − | 0.609561i | \(-0.791346\pi\) | ||
0.792739 | − | 0.609561i | \(-0.208654\pi\) | |||||||
\(522\) | 18.8736 | − | 18.8736i | 0.826076 | − | 0.826076i | ||||
\(523\) | 8.18242 | − | 8.18242i | 0.357792 | − | 0.357792i | −0.505206 | − | 0.862999i | \(-0.668584\pi\) |
0.862999 | + | 0.505206i | \(0.168584\pi\) | |||||||
\(524\) | 13.7134i | 0.599074i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 7.47949i | − | 0.326121i | ||||||
\(527\) | −7.63231 | − | 7.63231i | −0.332469 | − | 0.332469i | ||||
\(528\) | −1.49766 | + | 1.49766i | −0.0651771 | + | 0.0651771i | ||||
\(529\) | 46.5473i | 2.02380i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 35.7091i | − | 1.54964i | ||||||
\(532\) | 4.18865 | + | 1.26558i | 0.181601 | + | 0.0548697i | ||||
\(533\) | −27.3731 | − | 27.3731i | −1.18566 | − | 1.18566i | ||||
\(534\) | −3.40487 | −0.147343 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.09119 | 0.349486 | ||||||||
\(537\) | −1.42964 | + | 1.42964i | −0.0616935 | + | 0.0616935i | ||||
\(538\) | −13.1243 | − | 13.1243i | −0.565827 | − | 0.565827i | ||||
\(539\) | − | 33.5295i | − | 1.44422i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.27114 | 0.183631 | 0.0918154 | − | 0.995776i | \(-0.470733\pi\) | ||||
0.0918154 | + | 0.995776i | \(0.470733\pi\) | |||||||
\(542\) | −9.84425 | − | 9.84425i | −0.422847 | − | 0.422847i | ||||
\(543\) | −3.26102 | − | 3.26102i | −0.139944 | − | 0.139944i | ||||
\(544\) | 3.11588 | 0.133592 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.60931i | 0.0688720i | ||||||||
\(547\) | −13.1550 | − | 13.1550i | −0.562465 | − | 0.562465i | 0.367542 | − | 0.930007i | \(-0.380199\pi\) |
−0.930007 | + | 0.367542i | \(0.880199\pi\) | |||||||
\(548\) | −12.3591 | − | 12.3591i | −0.527956 | − | 0.527956i | ||||
\(549\) | − | 5.71344i | − | 0.243844i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.8966 | + | 19.2380i | −1.52925 | + | 0.819566i | ||||
\(552\) | 2.23213 | − | 2.23213i | 0.0950056 | − | 0.0950056i | ||||
\(553\) | −3.88403 | + | 3.88403i | −0.165166 | + | 0.165166i | ||||
\(554\) | 25.9052 | 1.10061 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.0729 | −0.469594 | ||||||||
\(557\) | −11.7550 | + | 11.7550i | −0.498075 | + | 0.498075i | −0.910838 | − | 0.412764i | \(-0.864564\pi\) |
0.412764 | + | 0.910838i | \(0.364564\pi\) | |||||||
\(558\) | −6.99751 | − | 6.99751i | −0.296228 | − | 0.296228i | ||||
\(559\) | 5.55345 | 0.234886 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 6.59945i | − | 0.278629i | ||||||
\(562\) | 7.73829 | − | 7.73829i | 0.326420 | − | 0.326420i | ||||
\(563\) | 5.14713 | − | 5.14713i | 0.216926 | − | 0.216926i | −0.590276 | − | 0.807202i | \(-0.700981\pi\) |
0.807202 | + | 0.590276i | \(0.200981\pi\) | |||||||
\(564\) | −2.25291 | −0.0948647 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.0121i | 1.13540i | ||||||||
\(567\) | 5.48768 | − | 5.48768i | 0.230461 | − | 0.230461i | ||||
\(568\) | −9.83681 | − | 9.83681i | −0.412743 | − | 0.412743i | ||||
\(569\) | −23.4663 | −0.983760 | −0.491880 | − | 0.870663i | \(-0.663690\pi\) | ||||
−0.491880 | + | 0.870663i | \(0.663690\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.94945 | 0.332674 | 0.166337 | − | 0.986069i | \(-0.446806\pi\) | ||||
0.166337 | + | 0.986069i | \(0.446806\pi\) | |||||||
\(572\) | −16.7570 | − | 16.7570i | −0.700647 | − | 0.700647i | ||||
\(573\) | −2.01817 | + | 2.01817i | −0.0843103 | + | 0.0843103i | ||||
\(574\) | − | 9.17545i | − | 0.382976i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.85672 | 0.119030 | ||||||||
\(577\) | 18.2440 | − | 18.2440i | 0.759507 | − | 0.759507i | −0.216726 | − | 0.976233i | \(-0.569538\pi\) |
0.976233 | + | 0.216726i | \(0.0695377\pi\) | |||||||
\(578\) | 5.15573 | − | 5.15573i | 0.214450 | − | 0.214450i | ||||
\(579\) | 3.14773i | 0.130815i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.85916 | 0.326053 | ||||||||
\(582\) | −3.46787 | − | 3.46787i | −0.143748 | − | 0.143748i | ||||
\(583\) | 13.6587 | − | 13.6587i | 0.565685 | − | 0.565685i | ||||
\(584\) | −6.12742 | −0.253554 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8966 | −0.491444 | ||||||||
\(587\) | 32.3528 | − | 32.3528i | 1.33534 | − | 1.33534i | 0.434829 | − | 0.900513i | \(-0.356809\pi\) |
0.900513 | − | 0.434829i | \(-0.143191\pi\) | |||||||
\(588\) | 1.60388 | − | 1.60388i | 0.0661428 | − | 0.0661428i | ||||
\(589\) | 7.13260 | + | 13.3089i | 0.293893 | + | 0.548383i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.86469i | 0.282376i | ||||||||
\(592\) | 6.61320 | + | 6.61320i | 0.271801 | + | 0.271801i | ||||
\(593\) | 10.0317 | + | 10.0317i | 0.411953 | + | 0.411953i | 0.882419 | − | 0.470465i | \(-0.155914\pi\) |
−0.470465 | + | 0.882419i | \(0.655914\pi\) | |||||||
\(594\) | − | 12.4046i | − | 0.508966i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.19087 | 0.212626 | ||||||||
\(597\) | 2.14389 | + | 2.14389i | 0.0877437 | + | 0.0877437i | ||||
\(598\) | 24.9749 | + | 24.9749i | 1.02130 | + | 1.02130i | ||||
\(599\) | 9.68729 | 0.395812 | 0.197906 | − | 0.980221i | \(-0.436586\pi\) | ||||
0.197906 | + | 0.980221i | \(0.436586\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.610515i | 0.0249034i | 0.999922 | + | 0.0124517i | \(0.00396361\pi\) | ||||
−0.999922 | + | 0.0124517i | \(0.996036\pi\) | |||||||
\(602\) | 0.930757 | + | 0.930757i | 0.0379348 | + | 0.0379348i | ||||
\(603\) | −16.3443 | + | 16.3443i | −0.665590 | + | 0.665590i | ||||
\(604\) | −6.37692 | −0.259473 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.27114 | −0.0922589 | ||||||||
\(607\) | 3.31601 | + | 3.31601i | 0.134593 | + | 0.134593i | 0.771193 | − | 0.636601i | \(-0.219660\pi\) |
−0.636601 | + | 0.771193i | \(0.719660\pi\) | |||||||
\(608\) | −4.17260 | − | 1.26073i | −0.169221 | − | 0.0511292i | ||||
\(609\) | − | 3.55029i | − | 0.143865i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 25.2075i | − | 1.01978i | ||||||
\(612\) | −6.29409 | + | 6.29409i | −0.254424 | + | 0.254424i | ||||
\(613\) | −8.70433 | − | 8.70433i | −0.351565 | − | 0.351565i | 0.509127 | − | 0.860691i | \(-0.329968\pi\) |
−0.860691 | + | 0.509127i | \(0.829968\pi\) | |||||||
\(614\) | − | 18.2796i | − | 0.737705i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 5.61696i | − | 0.226314i | ||||||
\(617\) | −18.5096 | + | 18.5096i | −0.745170 | + | 0.745170i | −0.973568 | − | 0.228398i | \(-0.926651\pi\) |
0.228398 | + | 0.973568i | \(0.426651\pi\) | |||||||
\(618\) | −1.86193 | + | 1.86193i | −0.0748977 | + | 0.0748977i | ||||
\(619\) | − | 24.7937i | − | 0.996544i | −0.867021 | − | 0.498272i | \(-0.833968\pi\) | ||
0.867021 | − | 0.498272i | \(-0.166032\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.4879i | 0.741895i | ||||||||
\(622\) | 8.28962 | + | 8.28962i | 0.332384 | + | 0.332384i | ||||
\(623\) | 6.38498 | − | 6.38498i | 0.255809 | − | 0.255809i | ||||
\(624\) | − | 1.60314i | − | 0.0641770i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23.1095i | 0.923643i | ||||||||
\(627\) | −2.67023 | + | 8.83759i | −0.106639 | + | 0.352939i | ||||
\(628\) | 4.30387 | + | 4.30387i | 0.171743 | + | 0.171743i | ||||
\(629\) | −29.1412 | −1.16194 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.4997 | 1.01513 | 0.507564 | − | 0.861614i | \(-0.330546\pi\) | ||||
0.507564 | + | 0.861614i | \(0.330546\pi\) | |||||||
\(632\) | 3.86914 | − | 3.86914i | 0.153906 | − | 0.153906i | ||||
\(633\) | −2.64494 | − | 2.64494i | −0.105127 | − | 0.105127i | ||||
\(634\) | 10.4599i | 0.415414i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.30672 | 0.0518149 | ||||||||
\(637\) | 17.9455 | + | 17.9455i | 0.711028 | + | 0.711028i | ||||
\(638\) | 36.9676 | + | 36.9676i | 1.46356 | + | 1.46356i | ||||
\(639\) | 39.7408 | 1.57212 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.36066i | − | 0.172236i | −0.996285 | − | 0.0861178i | \(-0.972554\pi\) | ||
0.996285 | − | 0.0861178i | \(-0.0274462\pi\) | |||||||
\(642\) | 0.836619 | + | 0.836619i | 0.0330187 | + | 0.0330187i | ||||
\(643\) | 17.0826 | + | 17.0826i | 0.673673 | + | 0.673673i | 0.958561 | − | 0.284888i | \(-0.0919563\pi\) |
−0.284888 | + | 0.958561i | \(0.591956\pi\) | |||||||
\(644\) | 8.37158i | 0.329887i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.9710 | − | 6.41560i | 0.470993 | − | 0.252418i | ||||
\(647\) | −14.0709 | + | 14.0709i | −0.553183 | + | 0.553183i | −0.927358 | − | 0.374175i | \(-0.877926\pi\) |
0.374175 | + | 0.927358i | \(0.377926\pi\) | |||||||
\(648\) | −5.46665 | + | 5.46665i | −0.214750 | + | 0.214750i | ||||
\(649\) | 69.9432 | 2.74551 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.31629 | −0.0515895 | ||||||||
\(652\) | −9.73720 | + | 9.73720i | −0.381338 | + | 0.381338i | ||||
\(653\) | 3.12836 | + | 3.12836i | 0.122422 | + | 0.122422i | 0.765664 | − | 0.643241i | \(-0.222411\pi\) |
−0.643241 | + | 0.765664i | \(0.722411\pi\) | |||||||
\(654\) | 0.325033 | 0.0127098 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 9.14029i | 0.356868i | ||||||||
\(657\) | 12.3774 | − | 12.3774i | 0.482889 | − | 0.482889i | ||||
\(658\) | 4.22477 | − | 4.22477i | 0.164699 | − | 0.164699i | ||||
\(659\) | −34.5113 | −1.34437 | −0.672185 | − | 0.740383i | \(-0.734644\pi\) | ||||
−0.672185 | + | 0.740383i | \(0.734644\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.89056i | 0.0735344i | 0.999324 | + | 0.0367672i | \(0.0117060\pi\) | ||||
−0.999324 | + | 0.0367672i | \(0.988294\pi\) | |||||||
\(662\) | −13.0699 | + | 13.0699i | −0.507976 | + | 0.507976i | ||||
\(663\) | 3.53213 | + | 3.53213i | 0.137177 | + | 0.137177i | ||||
\(664\) | −7.82904 | −0.303826 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −26.7174 | −1.03528 | ||||||||
\(667\) | −55.0970 | − | 55.0970i | −2.13336 | − | 2.13336i | ||||
\(668\) | 15.5454 | − | 15.5454i | 0.601471 | − | 0.601471i | ||||
\(669\) | − | 0.573122i | − | 0.0221582i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1909 | 0.432019 | ||||||||
\(672\) | 0.268687 | − | 0.268687i | 0.0103648 | − | 0.0103648i | ||||
\(673\) | −0.499570 | + | 0.499570i | −0.0192570 | + | 0.0192570i | −0.716670 | − | 0.697413i | \(-0.754334\pi\) |
0.697413 | + | 0.716670i | \(0.254334\pi\) | |||||||
\(674\) | 33.7794i | 1.30113i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.93729 | 0.189896 | ||||||||
\(677\) | 24.8658 | + | 24.8658i | 0.955671 | + | 0.955671i | 0.999058 | − | 0.0433869i | \(-0.0138148\pi\) |
−0.0433869 | + | 0.999058i | \(0.513815\pi\) | |||||||
\(678\) | −3.10360 | + | 3.10360i | −0.119193 | + | 0.119193i | ||||
\(679\) | 13.0062 | 0.499133 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.39240 | −0.206637 | ||||||||
\(682\) | 13.7060 | − | 13.7060i | 0.524828 | − | 0.524828i | ||||
\(683\) | −20.7651 | + | 20.7651i | −0.794555 | + | 0.794555i | −0.982231 | − | 0.187676i | \(-0.939905\pi\) |
0.187676 | + | 0.982231i | \(0.439905\pi\) | |||||||
\(684\) | 10.9753 | − | 5.88199i | 0.419653 | − | 0.224904i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 13.0423i | 0.497956i | ||||||||
\(687\) | −3.59792 | − | 3.59792i | −0.137269 | − | 0.137269i | ||||
\(688\) | −0.927191 | − | 0.927191i | −0.0353488 | − | 0.0353488i | ||||
\(689\) | 14.6207i | 0.557005i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.67571 | −0.177872 | −0.0889362 | − | 0.996037i | \(-0.528347\pi\) | ||||
−0.0889362 | + | 0.996037i | \(0.528347\pi\) | |||||||
\(692\) | 11.9265 | + | 11.9265i | 0.453376 | + | 0.453376i | ||||
\(693\) | 11.3463 | + | 11.3463i | 0.431010 | + | 0.431010i | ||||
\(694\) | 10.7419 | 0.407755 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.53668i | 0.134058i | ||||||||
\(697\) | −20.1384 | − | 20.1384i | −0.762797 | − | 0.762797i | ||||
\(698\) | 22.6838 | − | 22.6838i | 0.858595 | − | 0.858595i | ||||
\(699\) | −5.86808 | −0.221951 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.2106 | 0.498957 | 0.249478 | − | 0.968380i | \(-0.419741\pi\) | ||||
0.249478 | + | 0.968380i | \(0.419741\pi\) | |||||||
\(702\) | 6.63913 | + | 6.63913i | 0.250578 | + | 0.250578i | ||||
\(703\) | 39.0241 | + | 11.7909i | 1.47182 | + | 0.444703i | ||||
\(704\) | 5.59543i | 0.210886i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.60542i | 0.0980562i | ||||||||
\(707\) | 4.25896 | − | 4.25896i | 0.160175 | − | 0.160175i | ||||
\(708\) | 3.34573 | + | 3.34573i | 0.125740 | + | 0.125740i | ||||
\(709\) | − | 4.01972i | − | 0.150964i | −0.997147 | − | 0.0754818i | \(-0.975951\pi\) | ||
0.997147 | − | 0.0754818i | \(-0.0240495\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 15.6314i | 0.586223i | ||||||||
\(712\) | −6.36052 | + | 6.36052i | −0.238370 | + | 0.238370i | ||||
\(713\) | −20.4275 | + | 20.4275i | −0.765017 | + | 0.765017i | ||||
\(714\) | 1.18397i | 0.0443090i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.34131i | 0.199614i | ||||||||
\(717\) | 5.53939 | + | 5.53939i | 0.206872 | + | 0.206872i | ||||
\(718\) | 5.98900 | − | 5.98900i | 0.223507 | − | 0.223507i | ||||
\(719\) | 7.54014i | 0.281200i | 0.990067 | + | 0.140600i | \(0.0449031\pi\) | ||||
−0.990067 | + | 0.140600i | \(0.955097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 6.98315i | − | 0.260066i | ||||||
\(722\) | −18.6267 | + | 3.74775i | −0.693214 | + | 0.139477i | ||||
\(723\) | −2.09550 | − | 2.09550i | −0.0779324 | − | 0.0779324i | ||||
\(724\) | −12.1836 | −0.452799 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.68740 | 0.285306 | ||||||||
\(727\) | 35.6576 | − | 35.6576i | 1.32247 | − | 1.32247i | 0.410691 | − | 0.911775i | \(-0.365287\pi\) |
0.911775 | − | 0.410691i | \(-0.134713\pi\) | |||||||
\(728\) | 3.00629 | + | 3.00629i | 0.111421 | + | 0.111421i | ||||
\(729\) | − | 19.5679i | − | 0.724735i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.08568 | 0.151114 | ||||||||
\(732\) | 0.535314 | + | 0.535314i | 0.0197858 | + | 0.0197858i | ||||
\(733\) | −26.5296 | − | 26.5296i | −0.979894 | − | 0.979894i | 0.0199075 | − | 0.999802i | \(-0.493663\pi\) |
−0.999802 | + | 0.0199075i | \(0.993663\pi\) | |||||||
\(734\) | 17.4390 | 0.643684 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.33950i | − | 0.307398i | ||||||
\(737\) | −32.0134 | − | 32.0134i | −1.17923 | − | 1.17923i | ||||
\(738\) | −18.4634 | − | 18.4634i | −0.679648 | − | 0.679648i | ||||
\(739\) | 38.6023i | 1.42001i | 0.704197 | + | 0.710005i | \(0.251307\pi\) | ||||
−0.704197 | + | 0.710005i | \(0.748693\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.30087 | − | 6.15917i | −0.121261 | − | 0.226263i | ||||
\(742\) | −2.45043 | + | 2.45043i | −0.0899581 | + | 0.0899581i | ||||
\(743\) | 20.8219 | − | 20.8219i | 0.763881 | − | 0.763881i | −0.213141 | − | 0.977022i | \(-0.568369\pi\) |
0.977022 | + | 0.213141i | \(0.0683692\pi\) | |||||||
\(744\) | 1.31125 | 0.0480726 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.73795 | 0.283306 | ||||||||
\(747\) | 15.8147 | − | 15.8147i | 0.578630 | − | 0.578630i | ||||
\(748\) | −12.3282 | − | 12.3282i | −0.450763 | − | 0.450763i | ||||
\(749\) | −3.13774 | −0.114650 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 35.9437i | − | 1.31160i | −0.754933 | − | 0.655802i | \(-0.772331\pi\) | ||
0.754933 | − | 0.655802i | \(-0.227669\pi\) | |||||||
\(752\) | −4.20858 | + | 4.20858i | −0.153471 | + | 0.153471i | ||||
\(753\) | −0.822472 | + | 0.822472i | −0.0299726 | + | 0.0299726i | ||||
\(754\) | −39.5714 | −1.44110 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.22544i | 0.0809384i | ||||||||
\(757\) | 7.77714 | − | 7.77714i | 0.282665 | − | 0.282665i | −0.551506 | − | 0.834171i | \(-0.685947\pi\) |
0.834171 | + | 0.551506i | \(0.185947\pi\) | |||||||
\(758\) | −9.41719 | − | 9.41719i | −0.342048 | − | 0.342048i | ||||
\(759\) | −17.6631 | −0.641131 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.7886 | 1.26109 | 0.630543 | − | 0.776154i | \(-0.282832\pi\) | ||||
0.630543 | + | 0.776154i | \(0.282832\pi\) | |||||||
\(762\) | −1.08044 | − | 1.08044i | −0.0391403 | − | 0.0391403i | ||||
\(763\) | −0.609517 | + | 0.609517i | −0.0220660 | + | 0.0220660i | ||||
\(764\) | 7.54014i | 0.272793i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8592 | 0.717541 | ||||||||
\(767\) | −37.4348 | + | 37.4348i | −1.35169 | + | 1.35169i | ||||
\(768\) | −0.267657 | + | 0.267657i | −0.00965824 | + | 0.00965824i | ||||
\(769\) | − | 25.7435i | − | 0.928333i | −0.885748 | − | 0.464166i | \(-0.846354\pi\) | ||
0.885748 | − | 0.464166i | \(-0.153646\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.20088 | 0.223319 | ||||||||
\(772\) | 5.88017 | + | 5.88017i | 0.211632 | + | 0.211632i | ||||
\(773\) | −1.08904 | + | 1.08904i | −0.0391701 | + | 0.0391701i | −0.726421 | − | 0.687250i | \(-0.758818\pi\) |
0.687250 | + | 0.726421i | \(0.258818\pi\) | |||||||
\(774\) | 3.74586 | 0.134642 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.9564 | −0.465107 | ||||||||
\(777\) | −2.51289 | + | 2.51289i | −0.0901493 | + | 0.0901493i | ||||
\(778\) | −8.84389 | + | 8.84389i | −0.317069 | + | 0.317069i | ||||
\(779\) | 18.8199 | + | 35.1164i | 0.674292 | + | 1.25818i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 77.8401i | 2.78534i | ||||||||
\(782\) | 18.3741 | + | 18.3741i | 0.657056 | + | 0.657056i | ||||
\(783\) | −14.6466 | − | 14.6466i | −0.523425 | − | 0.523425i | ||||
\(784\) | − | 5.99229i | − | 0.214010i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.19087 | 0.185152 | ||||||||
\(787\) | −24.4918 | − | 24.4918i | −0.873040 | − | 0.873040i | 0.119763 | − | 0.992803i | \(-0.461787\pi\) |
−0.992803 | + | 0.119763i | \(0.961787\pi\) | |||||||
\(788\) | 12.8237 | + | 12.8237i | 0.456825 | + | 0.456825i | ||||
\(789\) | −2.83117 | −0.100792 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.6400i | − | 0.413872i | ||||||
\(792\) | −11.3028 | − | 11.3028i | −0.401628 | − | 0.401628i | ||||
\(793\) | −5.98954 | + | 5.98954i | −0.212695 | + | 0.212695i | ||||
\(794\) | 25.8150 | 0.916141 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.00986 | 0.283902 | ||||||||
\(797\) | −8.41216 | − | 8.41216i | −0.297974 | − | 0.297974i | 0.542246 | − | 0.840220i | \(-0.317574\pi\) |
−0.840220 | + | 0.542246i | \(0.817574\pi\) | |||||||
\(798\) | 0.479051 | − | 1.58550i | 0.0169582 | − | 0.0561262i | ||||
\(799\) | − | 18.5452i | − | 0.656081i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 25.6966i | − | 0.907943i | ||||||
\(802\) | −6.75033 | + | 6.75033i | −0.238363 | + | 0.238363i | ||||
\(803\) | 24.2436 | + | 24.2436i | 0.855536 | + | 0.855536i | ||||
\(804\) | − | 3.06271i | − | 0.108014i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 14.6713i | 0.516775i | ||||||||
\(807\) | −4.96785 | + | 4.96785i | −0.174876 | + | 0.174876i | ||||
\(808\) | −4.24264 | + | 4.24264i | −0.149256 | + | 0.149256i | ||||
\(809\) | − | 3.30643i | − | 0.116248i | −0.998309 | − | 0.0581240i | \(-0.981488\pi\) | ||
0.998309 | − | 0.0581240i | \(-0.0185119\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29.3864i | − | 1.03190i | −0.856620 | − | 0.515948i | \(-0.827440\pi\) | ||
0.856620 | − | 0.515948i | \(-0.172560\pi\) | |||||||
\(812\) | −6.63216 | − | 6.63216i | −0.232743 | − | 0.232743i | ||||
\(813\) | −3.72629 | + | 3.72629i | −0.130687 | + | 0.130687i | ||||
\(814\) | − | 52.3312i | − | 1.83421i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 1.17943i | − | 0.0412885i | ||||||
\(817\) | −5.47130 | − | 1.65312i | −0.191417 | − | 0.0578355i | ||||
\(818\) | 7.92167 | + | 7.92167i | 0.276975 | + | 0.276975i | ||||
\(819\) | −12.1454 | −0.424396 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −48.0995 | −1.67868 | −0.839342 | − | 0.543604i | \(-0.817059\pi\) | ||||
−0.839342 | + | 0.543604i | \(0.817059\pi\) | |||||||
\(822\) | −4.67823 | + | 4.67823i | −0.163172 | + | 0.163172i | ||||
\(823\) | 1.98892 | + | 1.98892i | 0.0693295 | + | 0.0693295i | 0.740921 | − | 0.671592i | \(-0.234389\pi\) |
−0.671592 | + | 0.740921i | \(0.734389\pi\) | |||||||
\(824\) | 6.95639i | 0.242337i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.5481 | −0.436606 | ||||||||
\(827\) | 36.0051 | + | 36.0051i | 1.25202 | + | 1.25202i | 0.954813 | + | 0.297207i | \(0.0960552\pi\) |
0.297207 | + | 0.954813i | \(0.403945\pi\) | |||||||
\(828\) | 16.8458 | + | 16.8458i | 0.585434 | + | 0.585434i | ||||
\(829\) | 49.7577 | 1.72815 | 0.864077 | − | 0.503359i | \(-0.167903\pi\) | ||||
0.864077 | + | 0.503359i | \(0.167903\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 9.80575i | − | 0.340158i | ||||||
\(832\) | −2.99477 | − | 2.99477i | −0.103825 | − | 0.103825i | ||||
\(833\) | 13.2026 | + | 13.2026i | 0.457442 | + | 0.457442i | ||||
\(834\) | 4.19134i | 0.145134i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 11.5210 | + | 21.4973i | 0.398463 | + | 0.743500i | ||||
\(837\) | −5.43030 | + | 5.43030i | −0.187698 | + | 0.187698i | ||||
\(838\) | −4.88733 | + | 4.88733i | −0.168830 | + | 0.168830i | ||||
\(839\) | 44.3918 | 1.53258 | 0.766288 | − | 0.642497i | \(-0.222102\pi\) | ||||
0.766288 | + | 0.642497i | \(0.222102\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 58.2982 | 2.01028 | ||||||||
\(842\) | −6.35053 | + | 6.35053i | −0.218854 | + | 0.218854i | ||||
\(843\) | −2.92913 | − | 2.92913i | −0.100885 | − | 0.100885i | ||||
\(844\) | −9.88184 | −0.340147 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 17.0027i | − | 0.584565i | ||||||
\(847\) | −14.4158 | + | 14.4158i | −0.495332 | + | 0.495332i | ||||
\(848\) | 2.44104 | − | 2.44104i | 0.0838257 | − | 0.0838257i | ||||
\(849\) | 10.2247 | 0.350912 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 77.9951i | 2.67364i | ||||||||
\(852\) | −3.72347 | + | 3.72347i | −0.127564 | + | 0.127564i | ||||
\(853\) | 37.8438 | + | 37.8438i | 1.29575 | + | 1.29575i | 0.931175 | + | 0.364574i | \(0.118785\pi\) |
0.364574 | + | 0.931175i | \(0.381215\pi\) | |||||||
\(854\) | −2.00769 | −0.0687019 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.12571 | 0.106835 | ||||||||
\(857\) | −20.1772 | − | 20.1772i | −0.689240 | − | 0.689240i | 0.272824 | − | 0.962064i | \(-0.412042\pi\) |
−0.962064 | + | 0.272824i | \(0.912042\pi\) | |||||||
\(858\) | −6.34294 | + | 6.34294i | −0.216544 | + | 0.216544i | ||||
\(859\) | − | 6.94256i | − | 0.236877i | −0.992961 | − | 0.118438i | \(-0.962211\pi\) | ||
0.992961 | − | 0.118438i | \(-0.0377888\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.47313 | −0.118364 | ||||||||
\(862\) | 9.54964 | − | 9.54964i | 0.325262 | − | 0.325262i | ||||
\(863\) | −12.0170 | + | 12.0170i | −0.409063 | + | 0.409063i | −0.881412 | − | 0.472349i | \(-0.843406\pi\) |
0.472349 | + | 0.881412i | \(0.343406\pi\) | |||||||
\(864\) | − | 2.21691i | − | 0.0754208i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −23.9941 | −0.815353 | ||||||||
\(867\) | −1.95157 | − | 1.95157i | −0.0662787 | − | 0.0662787i | ||||
\(868\) | −2.45891 | + | 2.45891i | −0.0834609 | + | 0.0834609i | ||||
\(869\) | −30.6171 | −1.03861 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 34.2682 | 1.16113 | ||||||||
\(872\) | 0.607182 | − | 0.607182i | 0.0205618 | − | 0.0205618i | ||||
\(873\) | 26.1720 | − | 26.1720i | 0.885787 | − | 0.885787i | ||||
\(874\) | −17.1711 | − | 32.0399i | −0.580820 | − | 1.08377i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.31938i | 0.0783644i | ||||||||
\(877\) | 32.4987 | + | 32.4987i | 1.09740 | + | 1.09740i | 0.994714 | + | 0.102689i | \(0.0327446\pi\) |
0.102689 | + | 0.994714i | \(0.467255\pi\) | |||||||
\(878\) | 24.1888 | + | 24.1888i | 0.816334 | + | 0.816334i | ||||
\(879\) | 4.50315i | 0.151887i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 38.5449 | 1.29861 | 0.649305 | − | 0.760528i | \(-0.275060\pi\) | ||||
0.649305 | + | 0.760528i | \(0.275060\pi\) | |||||||
\(882\) | 12.1045 | + | 12.1045i | 0.407578 | + | 0.407578i | ||||
\(883\) | 2.14041 | + | 2.14041i | 0.0720305 | + | 0.0720305i | 0.742204 | − | 0.670174i | \(-0.233780\pi\) |
−0.670174 | + | 0.742204i | \(0.733780\pi\) | |||||||
\(884\) | 13.1965 | 0.443846 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 14.1157i | 0.474228i | ||||||||
\(887\) | 0.280827 | + | 0.280827i | 0.00942925 | + | 0.00942925i | 0.711806 | − | 0.702376i | \(-0.247878\pi\) |
−0.702376 | + | 0.711806i | \(0.747878\pi\) | |||||||
\(888\) | 2.50326 | − | 2.50326i | 0.0840038 | − | 0.0840038i | ||||
\(889\) | 4.05220 | 0.135906 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43.2583 | 1.44921 | ||||||||
\(892\) | −1.07063 | − | 1.07063i | −0.0358473 | − | 0.0358473i | ||||
\(893\) | −7.50363 | + | 24.8346i | −0.251100 | + | 0.831058i | ||||
\(894\) | − | 1.96487i | − | 0.0657150i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1.00385i | − | 0.0335362i | ||||||
\(897\) | 9.45360 | − | 9.45360i | 0.315646 | − | 0.315646i | ||||
\(898\) | −11.2206 | − | 11.2206i | −0.374438 | − | 0.374438i | ||||
\(899\) | − | 32.3663i | − | 1.07948i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7565i | 0.358350i | ||||||||
\(902\) | 36.1642 | − | 36.1642i | 1.20414 | − | 1.20414i | ||||
\(903\) | 0.352314 | − | 0.352314i | 0.0117243 | − | 0.0117243i | ||||
\(904\) | 11.5954i | 0.385658i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.41382i | 0.0801937i | ||||||||
\(907\) | −8.68507 | − | 8.68507i | −0.288383 | − | 0.288383i | 0.548058 | − | 0.836441i | \(-0.315367\pi\) |
−0.836441 | + | 0.548058i | \(0.815367\pi\) | |||||||
\(908\) | −10.0734 | + | 10.0734i | −0.334296 | + | 0.334296i | ||||
\(909\) | − | 17.1403i | − | 0.568508i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.99084i | 0.297880i | 0.988846 | + | 0.148940i | \(0.0475861\pi\) | ||||
−0.988846 | + | 0.148940i | \(0.952414\pi\) | |||||||
\(912\) | −0.477216 | + | 1.57943i | −0.0158022 | + | 0.0523001i | ||||
\(913\) | 30.9761 | + | 30.9761i | 1.02516 | + | 1.02516i | ||||
\(914\) | −28.3247 | −0.936896 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.4423 | −0.444146 | ||||||||
\(917\) | −9.73417 | + | 9.73417i | −0.321451 | + | 0.321451i | ||||
\(918\) | 4.88442 | + | 4.88442i | 0.161210 | + | 0.161210i | ||||
\(919\) | − | 20.8360i | − | 0.687317i | −0.939095 | − | 0.343659i | \(-0.888334\pi\) | ||
0.939095 | − | 0.343659i | \(-0.111666\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.91928 | −0.227998 | ||||||||
\(922\) | 27.9821 | + | 27.9821i | 0.921540 | + | 0.921540i | ||||
\(923\) | −41.6613 | − | 41.6613i | −1.37130 | − | 1.37130i | ||||
\(924\) | −2.12615 | −0.0699453 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 11.7775i | 0.387031i | ||||||||
\(927\) | −14.0520 | − | 14.0520i | −0.461527 | − | 0.461527i | ||||
\(928\) | 6.60675 | + | 6.60675i | 0.216877 | + | 0.216877i | ||||
\(929\) | − | 27.9065i | − | 0.915581i | −0.889060 | − | 0.457791i | \(-0.848641\pi\) | ||
0.889060 | − | 0.457791i | \(-0.151359\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.3381 | − | 23.0220i | −0.404366 | − | 0.754516i | ||||
\(932\) | −10.9619 | + | 10.9619i | −0.359070 | + | 0.359070i | ||||
\(933\) | 3.13782 | − | 3.13782i | 0.102728 | − | 0.102728i | ||||
\(934\) | 26.4016 | 0.863886 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.0989 | 0.395465 | ||||||||
\(937\) | −11.2974 | + | 11.2974i | −0.369070 | + | 0.369070i | −0.867138 | − | 0.498068i | \(-0.834043\pi\) |
0.498068 | + | 0.867138i | \(0.334043\pi\) | |||||||
\(938\) | 5.74335 | + | 5.74335i | 0.187527 | + | 0.187527i | ||||
\(939\) | 8.74752 | 0.285464 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 4.26784i | − | 0.139128i | −0.997578 | − | 0.0695638i | \(-0.977839\pi\) | ||
0.997578 | − | 0.0695638i | \(-0.0221607\pi\) | |||||||
\(942\) | 1.62912 | − | 1.62912i | 0.0530796 | − | 0.0530796i | ||||
\(943\) | −53.8996 | + | 53.8996i | −1.75521 | + | 1.75521i | ||||
\(944\) | 12.5001 | 0.406842 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.33699i | 0.238546i | ||||||||
\(947\) | 12.7848 | − | 12.7848i | 0.415451 | − | 0.415451i | −0.468181 | − | 0.883632i | \(-0.655091\pi\) |
0.883632 | + | 0.468181i | \(0.155091\pi\) | |||||||
\(948\) | −1.46456 | − | 1.46456i | −0.0475668 | − | 0.0475668i | ||||
\(949\) | −25.9511 | −0.842409 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.95931 | 0.128389 | ||||||||
\(952\) | 2.21173 | + | 2.21173i | 0.0716827 | + | 0.0716827i | ||||
\(953\) | −37.5706 | + | 37.5706i | −1.21703 | + | 1.21703i | −0.248366 | + | 0.968666i | \(0.579894\pi\) |
−0.968666 | + | 0.248366i | \(0.920106\pi\) | |||||||
\(954\) | 9.86183i | 0.319289i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 20.6959 | 0.669352 | ||||||||
\(957\) | 13.9931 | − | 13.9931i | 0.452334 | − | 0.452334i | ||||
\(958\) | −10.2848 | + | 10.2848i | −0.332286 | + | 0.332286i | ||||
\(959\) | − | 17.5457i | − | 0.566580i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | 28.0085 | + | 28.0085i | 0.903031 | + | 0.903031i | ||||
\(963\) | −6.31396 | + | 6.31396i | −0.203465 | + | 0.203465i | ||||
\(964\) | −7.82904 | −0.252157 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.16885 | 0.101956 | ||||||||
\(967\) | 2.45555 | − | 2.45555i | 0.0789650 | − | 0.0789650i | −0.666521 | − | 0.745486i | \(-0.732217\pi\) |
0.745486 | + | 0.666521i | \(0.232217\pi\) | |||||||
\(968\) | 14.3605 | − | 14.3605i | 0.461565 | − | 0.461565i | ||||
\(969\) | −2.42846 | − | 4.53132i | −0.0780134 | − | 0.145567i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.95882i | 0.127045i | 0.997980 | + | 0.0635223i | \(0.0202334\pi\) | ||||
−0.997980 | + | 0.0635223i | \(0.979767\pi\) | |||||||
\(972\) | 6.77203 | + | 6.77203i | 0.217213 | + | 0.217213i | ||||
\(973\) | −7.85981 | − | 7.85981i | −0.251974 | − | 0.251974i | ||||
\(974\) | − | 31.6598i | − | 1.01445i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | 0.0640184 | ||||||||
\(977\) | −7.80485 | − | 7.80485i | −0.249699 | − | 0.249699i | 0.571148 | − | 0.820847i | \(-0.306498\pi\) |
−0.820847 | + | 0.571148i | \(0.806498\pi\) | |||||||
\(978\) | 3.68576 | + | 3.68576i | 0.117858 | + | 0.117858i | ||||
\(979\) | 50.3316 | 1.60861 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.45302i | 0.0783189i | ||||||||
\(982\) | 4.88208 | + | 4.88208i | 0.155793 | + | 0.155793i | ||||
\(983\) | 17.7520 | − | 17.7520i | 0.566202 | − | 0.566202i | −0.364860 | − | 0.931062i | \(-0.618883\pi\) |
0.931062 | + | 0.364860i | \(0.118883\pi\) | |||||||
\(984\) | 3.45982 | 0.110295 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −29.1127 | −0.927138 | ||||||||
\(987\) | −1.59918 | − | 1.59918i | −0.0509024 | − | 0.0509024i | ||||
\(988\) | −17.6720 | − | 5.33949i | −0.562220 | − | 0.169872i | ||||
\(989\) | − | 10.9351i | − | 0.347717i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 23.1109i | − | 0.734141i | −0.930193 | − | 0.367071i | \(-0.880361\pi\) | ||
0.930193 | − | 0.367071i | \(-0.119639\pi\) | |||||||
\(992\) | 2.44949 | − | 2.44949i | 0.0777714 | − | 0.0777714i | ||||
\(993\) | 4.94727 | + | 4.94727i | 0.156997 | + | 0.156997i | ||||
\(994\) | − | 13.9649i | − | 0.442939i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.96348i | 0.0939015i | ||||||||
\(997\) | 0.574345 | − | 0.574345i | 0.0181897 | − | 0.0181897i | −0.697953 | − | 0.716143i | \(-0.745906\pi\) |
0.716143 | + | 0.697953i | \(0.245906\pi\) | |||||||
\(998\) | 19.5855 | − | 19.5855i | 0.619967 | − | 0.619967i | ||||
\(999\) | 20.7336i | 0.655982i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 950.2.f.d.493.3 | ✓ | 32 | |
5.2 | odd | 4 | inner | 950.2.f.d.607.13 | yes | 32 | |
5.3 | odd | 4 | inner | 950.2.f.d.607.4 | yes | 32 | |
5.4 | even | 2 | inner | 950.2.f.d.493.14 | yes | 32 | |
19.18 | odd | 2 | inner | 950.2.f.d.493.13 | yes | 32 | |
95.18 | even | 4 | inner | 950.2.f.d.607.14 | yes | 32 | |
95.37 | even | 4 | inner | 950.2.f.d.607.3 | yes | 32 | |
95.94 | odd | 2 | inner | 950.2.f.d.493.4 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.2.f.d.493.3 | ✓ | 32 | 1.1 | even | 1 | trivial | |
950.2.f.d.493.4 | yes | 32 | 95.94 | odd | 2 | inner | |
950.2.f.d.493.13 | yes | 32 | 19.18 | odd | 2 | inner | |
950.2.f.d.493.14 | yes | 32 | 5.4 | even | 2 | inner | |
950.2.f.d.607.3 | yes | 32 | 95.37 | even | 4 | inner | |
950.2.f.d.607.4 | yes | 32 | 5.3 | odd | 4 | inner | |
950.2.f.d.607.13 | yes | 32 | 5.2 | odd | 4 | inner | |
950.2.f.d.607.14 | yes | 32 | 95.18 | even | 4 | inner |