Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(373,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.373");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.k (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 445.1 | ||
Root | \(2.07085 - 3.58682i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.445 |
Dual form | 546.2.k.e.373.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −2.07085 | − | 3.58682i | −0.926112 | − | 1.60407i | −0.789763 | − | 0.613413i | \(-0.789796\pi\) |
−0.136350 | − | 0.990661i | \(-0.543537\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 2.11344 | − | 1.59166i | 0.798803 | − | 0.601592i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −4.14170 | −1.30972 | ||||||||
\(11\) | 0.523095 | 0.157719 | 0.0788595 | − | 0.996886i | \(-0.474872\pi\) | ||||
0.0788595 | + | 0.996886i | \(0.474872\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −3.28981 | + | 1.47551i | −0.912430 | + | 0.409234i | ||||
\(14\) | −0.321703 | − | 2.62612i | −0.0859787 | − | 0.701860i | ||||
\(15\) | 2.07085 | + | 3.58682i | 0.534691 | + | 0.926112i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.26155 | + | 2.18506i | 0.305970 | + | 0.529956i | 0.977477 | − | 0.211043i | \(-0.0676859\pi\) |
−0.671507 | + | 0.740998i | \(0.734353\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −5.69993 | −1.30765 | −0.653827 | − | 0.756644i | \(-0.726838\pi\) | ||||
−0.653827 | + | 0.756644i | \(0.726838\pi\) | |||||||
\(20\) | −2.07085 | + | 3.58682i | −0.463056 | + | 0.802037i | ||||
\(21\) | −2.11344 | + | 1.59166i | −0.461189 | + | 0.347329i | ||||
\(22\) | 0.261547 | − | 0.453013i | 0.0557621 | − | 0.0965827i | ||||
\(23\) | 3.69669 | − | 6.40285i | 0.770812 | − | 1.33509i | −0.166306 | − | 0.986074i | \(-0.553184\pi\) |
0.937118 | − | 0.349012i | \(-0.113483\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −6.07684 | + | 10.5254i | −1.21537 | + | 2.10508i | ||||
\(26\) | −0.367074 | + | 3.58682i | −0.0719891 | + | 0.703433i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.43514 | − | 1.03446i | −0.460198 | − | 0.195494i | ||||
\(29\) | −1.54066 | − | 2.66851i | −0.286094 | − | 0.495530i | 0.686780 | − | 0.726866i | \(-0.259024\pi\) |
−0.972874 | + | 0.231336i | \(0.925690\pi\) | |||||||
\(30\) | 4.14170 | 0.756167 | ||||||||
\(31\) | −2.17638 | + | 3.76959i | −0.390889 | + | 0.677039i | −0.992567 | − | 0.121699i | \(-0.961166\pi\) |
0.601678 | + | 0.798739i | \(0.294499\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −0.523095 | −0.0910591 | ||||||||
\(34\) | 2.52309 | 0.432707 | ||||||||
\(35\) | −10.0856 | − | 4.28441i | −1.70478 | − | 0.724198i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 2.83240 | − | 4.90586i | 0.465643 | − | 0.806518i | −0.533587 | − | 0.845745i | \(-0.679156\pi\) |
0.999230 | + | 0.0392274i | \(0.0124897\pi\) | |||||||
\(38\) | −2.84997 | + | 4.93629i | −0.462326 | + | 0.800772i | ||||
\(39\) | 3.28981 | − | 1.47551i | 0.526791 | − | 0.236271i | ||||
\(40\) | 2.07085 | + | 3.58682i | 0.327430 | + | 0.567126i | ||||
\(41\) | 2.33240 | + | 4.03983i | 0.364259 | + | 0.630915i | 0.988657 | − | 0.150191i | \(-0.0479889\pi\) |
−0.624398 | + | 0.781107i | \(0.714656\pi\) | |||||||
\(42\) | 0.321703 | + | 2.62612i | 0.0496398 | + | 0.405219i | ||||
\(43\) | −4.81529 | + | 8.34033i | −0.734325 | + | 1.27189i | 0.220694 | + | 0.975343i | \(0.429168\pi\) |
−0.955019 | + | 0.296545i | \(0.904166\pi\) | |||||||
\(44\) | −0.261547 | − | 0.453013i | −0.0394297 | − | 0.0682943i | ||||
\(45\) | −2.07085 | − | 3.58682i | −0.308704 | − | 0.534691i | ||||
\(46\) | −3.69669 | − | 6.40285i | −0.545047 | − | 0.944048i | ||||
\(47\) | −5.58154 | − | 9.66752i | −0.814152 | − | 1.41015i | −0.909935 | − | 0.414750i | \(-0.863869\pi\) |
0.0957835 | − | 0.995402i | \(-0.469464\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 1.93322 | − | 6.72775i | 0.276174 | − | 0.961108i | ||||
\(50\) | 6.07684 | + | 10.5254i | 0.859395 | + | 1.48852i | ||||
\(51\) | −1.26155 | − | 2.18506i | −0.176652 | − | 0.305970i | ||||
\(52\) | 2.92274 | + | 2.11130i | 0.405311 | + | 0.292785i | ||||
\(53\) | −0.00192073 | + | 0.00332680i | −0.000263832 | + | 0.000456971i | −0.866157 | − | 0.499771i | \(-0.833417\pi\) |
0.865893 | + | 0.500228i | \(0.166751\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −1.08325 | − | 1.87624i | −0.146065 | − | 0.252993i | ||||
\(56\) | −2.11344 | + | 1.59166i | −0.282420 | + | 0.212695i | ||||
\(57\) | 5.69993 | 0.754975 | ||||||||
\(58\) | −3.08133 | −0.404598 | ||||||||
\(59\) | −4.05374 | − | 7.02129i | −0.527752 | − | 0.914094i | −0.999477 | − | 0.0323479i | \(-0.989702\pi\) |
0.471724 | − | 0.881746i | \(-0.343632\pi\) | |||||||
\(60\) | 2.07085 | − | 3.58682i | 0.267346 | − | 0.463056i | ||||
\(61\) | 6.01198 | 0.769755 | 0.384877 | − | 0.922968i | \(-0.374244\pi\) | ||||
0.384877 | + | 0.922968i | \(0.374244\pi\) | |||||||
\(62\) | 2.17638 | + | 3.76959i | 0.276400 | + | 0.478739i | ||||
\(63\) | 2.11344 | − | 1.59166i | 0.266268 | − | 0.200531i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.1051 | + | 8.74439i | 1.50145 | + | 1.08461i | ||||
\(66\) | −0.261547 | + | 0.453013i | −0.0321942 | + | 0.0557621i | ||||
\(67\) | 3.23244 | 0.394906 | 0.197453 | − | 0.980312i | \(-0.436733\pi\) | ||||
0.197453 | + | 0.980312i | \(0.436733\pi\) | |||||||
\(68\) | 1.26155 | − | 2.18506i | 0.152985 | − | 0.264978i | ||||
\(69\) | −3.69669 | + | 6.40285i | −0.445029 | + | 0.770812i | ||||
\(70\) | −8.75321 | + | 6.59219i | −1.04621 | + | 0.787917i | ||||
\(71\) | 3.98568 | − | 6.90340i | 0.473013 | − | 0.819283i | −0.526510 | − | 0.850169i | \(-0.676500\pi\) |
0.999523 | + | 0.0308864i | \(0.00983301\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 5.99080 | − | 10.3764i | 0.701170 | − | 1.21446i | −0.266886 | − | 0.963728i | \(-0.585995\pi\) |
0.968056 | − | 0.250734i | \(-0.0806721\pi\) | |||||||
\(74\) | −2.83240 | − | 4.90586i | −0.329259 | − | 0.570294i | ||||
\(75\) | 6.07684 | − | 10.5254i | 0.701693 | − | 1.21537i | ||||
\(76\) | 2.84997 | + | 4.93629i | 0.326914 | + | 0.566231i | ||||
\(77\) | 1.10553 | − | 0.832590i | 0.125986 | − | 0.0948825i | ||||
\(78\) | 0.367074 | − | 3.58682i | 0.0415629 | − | 0.406127i | ||||
\(79\) | 1.15602 | + | 2.00229i | 0.130063 | + | 0.225275i | 0.923700 | − | 0.383115i | \(-0.125149\pi\) |
−0.793638 | + | 0.608390i | \(0.791816\pi\) | |||||||
\(80\) | 4.14170 | 0.463056 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.66479 | 0.515140 | ||||||||
\(83\) | 3.08133 | 0.338220 | 0.169110 | − | 0.985597i | \(-0.445911\pi\) | ||||
0.169110 | + | 0.985597i | \(0.445911\pi\) | |||||||
\(84\) | 2.43514 | + | 1.03446i | 0.265695 | + | 0.112869i | ||||
\(85\) | 5.22495 | − | 9.04988i | 0.566725 | − | 0.981597i | ||||
\(86\) | 4.81529 | + | 8.34033i | 0.519246 | + | 0.899361i | ||||
\(87\) | 1.54066 | + | 2.66851i | 0.165177 | + | 0.286094i | ||||
\(88\) | −0.523095 | −0.0557621 | ||||||||
\(89\) | 5.42599 | − | 9.39808i | 0.575153 | − | 0.996195i | −0.420871 | − | 0.907120i | \(-0.638276\pi\) |
0.996025 | − | 0.0890747i | \(-0.0283910\pi\) | |||||||
\(90\) | −4.14170 | −0.436573 | ||||||||
\(91\) | −4.60428 | + | 8.35467i | −0.482660 | + | 0.875808i | ||||
\(92\) | −7.39337 | −0.770812 | ||||||||
\(93\) | 2.17638 | − | 3.76959i | 0.225680 | − | 0.390889i | ||||
\(94\) | −11.1631 | −1.15138 | ||||||||
\(95\) | 11.8037 | + | 20.4446i | 1.21103 | + | 2.09757i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −1.31892 | + | 2.28443i | −0.133916 | + | 0.231949i | −0.925183 | − | 0.379522i | \(-0.876089\pi\) |
0.791267 | + | 0.611471i | \(0.209422\pi\) | |||||||
\(98\) | −4.85980 | − | 5.03809i | −0.490914 | − | 0.508924i | ||||
\(99\) | 0.523095 | 0.0525730 | ||||||||
\(100\) | 12.1537 | 1.21537 | ||||||||
\(101\) | −12.1845 | −1.21240 | −0.606200 | − | 0.795312i | \(-0.707307\pi\) | ||||
−0.606200 | + | 0.795312i | \(0.707307\pi\) | |||||||
\(102\) | −2.52309 | −0.249824 | ||||||||
\(103\) | 6.81529 | + | 11.8044i | 0.671531 | + | 1.16313i | 0.977470 | + | 0.211074i | \(0.0676961\pi\) |
−0.305940 | + | 0.952051i | \(0.598971\pi\) | |||||||
\(104\) | 3.28981 | − | 1.47551i | 0.322593 | − | 0.144686i | ||||
\(105\) | 10.0856 | + | 4.28441i | 0.984255 | + | 0.418116i | ||||
\(106\) | 0.00192073 | + | 0.00332680i | 0.000186558 | + | 0.000323127i | ||||
\(107\) | −2.69861 | + | 4.67412i | −0.260884 | + | 0.451865i | −0.966477 | − | 0.256753i | \(-0.917347\pi\) |
0.705593 | + | 0.708617i | \(0.250681\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 5.58133 | − | 9.66715i | 0.534594 | − | 0.925945i | −0.464588 | − | 0.885527i | \(-0.653798\pi\) |
0.999183 | − | 0.0404180i | \(-0.0128689\pi\) | |||||||
\(110\) | −2.16650 | −0.206568 | ||||||||
\(111\) | −2.83240 | + | 4.90586i | −0.268839 | + | 0.465643i | ||||
\(112\) | 0.321703 | + | 2.62612i | 0.0303981 | + | 0.248145i | ||||
\(113\) | 2.03617 | − | 3.52676i | 0.191547 | − | 0.331769i | −0.754216 | − | 0.656626i | \(-0.771983\pi\) |
0.945763 | + | 0.324857i | \(0.105316\pi\) | |||||||
\(114\) | 2.84997 | − | 4.93629i | 0.266924 | − | 0.462326i | ||||
\(115\) | −30.6211 | −2.85543 | ||||||||
\(116\) | −1.54066 | + | 2.66851i | −0.143047 | + | 0.247765i | ||||
\(117\) | −3.28981 | + | 1.47551i | −0.304143 | + | 0.136411i | ||||
\(118\) | −8.10749 | −0.746355 | ||||||||
\(119\) | 6.14408 | + | 2.61003i | 0.563227 | + | 0.239261i | ||||
\(120\) | −2.07085 | − | 3.58682i | −0.189042 | − | 0.327430i | ||||
\(121\) | −10.7264 | −0.975125 | ||||||||
\(122\) | 3.00599 | − | 5.20652i | 0.272149 | − | 0.471377i | ||||
\(123\) | −2.33240 | − | 4.03983i | −0.210305 | − | 0.364259i | ||||
\(124\) | 4.35275 | 0.390889 | ||||||||
\(125\) | 29.6284 | 2.65004 | ||||||||
\(126\) | −0.321703 | − | 2.62612i | −0.0286596 | − | 0.233953i | ||||
\(127\) | −3.83432 | − | 6.64123i | −0.340241 | − | 0.589314i | 0.644237 | − | 0.764826i | \(-0.277175\pi\) |
−0.984477 | + | 0.175512i | \(0.943842\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 4.81529 | − | 8.34033i | 0.423963 | − | 0.734325i | ||||
\(130\) | 13.6254 | − | 6.11113i | 1.19503 | − | 0.535982i | ||||
\(131\) | −5.62392 | − | 9.74091i | −0.491364 | − | 0.851067i | 0.508587 | − | 0.861011i | \(-0.330168\pi\) |
−0.999951 | + | 0.00994375i | \(0.996835\pi\) | |||||||
\(132\) | 0.261547 | + | 0.453013i | 0.0227648 | + | 0.0394297i | ||||
\(133\) | −12.0464 | + | 9.07238i | −1.04456 | + | 0.786675i | ||||
\(134\) | 1.61622 | − | 2.79938i | 0.139620 | − | 0.241829i | ||||
\(135\) | 2.07085 | + | 3.58682i | 0.178230 | + | 0.308704i | ||||
\(136\) | −1.26155 | − | 2.18506i | −0.108177 | − | 0.187368i | ||||
\(137\) | 3.51116 | + | 6.08150i | 0.299978 | + | 0.519578i | 0.976131 | − | 0.217184i | \(-0.0696872\pi\) |
−0.676152 | + | 0.736762i | \(0.736354\pi\) | |||||||
\(138\) | 3.69669 | + | 6.40285i | 0.314683 | + | 0.545047i | ||||
\(139\) | 6.59202 | − | 11.4177i | 0.559128 | − | 0.968438i | −0.438441 | − | 0.898760i | \(-0.644469\pi\) |
0.997569 | − | 0.0696786i | \(-0.0221974\pi\) | |||||||
\(140\) | 1.33240 | + | 10.8766i | 0.112608 | + | 0.919241i | ||||
\(141\) | 5.58154 | + | 9.66752i | 0.470051 | + | 0.814152i | ||||
\(142\) | −3.98568 | − | 6.90340i | −0.334471 | − | 0.579320i | ||||
\(143\) | −1.72088 | + | 0.771833i | −0.143907 | + | 0.0645439i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | −6.38097 | + | 11.0522i | −0.529911 | + | 0.917832i | ||||
\(146\) | −5.99080 | − | 10.3764i | −0.495802 | − | 0.858755i | ||||
\(147\) | −1.93322 | + | 6.72775i | −0.159449 | + | 0.554896i | ||||
\(148\) | −5.66479 | −0.465643 | ||||||||
\(149\) | 18.1322 | 1.48545 | 0.742726 | − | 0.669596i | \(-0.233533\pi\) | ||||
0.742726 | + | 0.669596i | \(0.233533\pi\) | |||||||
\(150\) | −6.07684 | − | 10.5254i | −0.496172 | − | 0.859395i | ||||
\(151\) | −2.53343 | + | 4.38804i | −0.206168 | + | 0.357093i | −0.950504 | − | 0.310712i | \(-0.899433\pi\) |
0.744336 | + | 0.667805i | \(0.232766\pi\) | |||||||
\(152\) | 5.69993 | 0.462326 | ||||||||
\(153\) | 1.26155 | + | 2.18506i | 0.101990 | + | 0.176652i | ||||
\(154\) | −0.168281 | − | 1.37371i | −0.0135605 | − | 0.110697i | ||||
\(155\) | 18.0278 | 1.44803 | ||||||||
\(156\) | −2.92274 | − | 2.11130i | −0.234006 | − | 0.169040i | ||||
\(157\) | 5.80481 | − | 10.0542i | 0.463274 | − | 0.802415i | −0.535847 | − | 0.844315i | \(-0.680008\pi\) |
0.999122 | + | 0.0419001i | \(0.0133411\pi\) | |||||||
\(158\) | 2.31204 | 0.183936 | ||||||||
\(159\) | 0.00192073 | − | 0.00332680i | 0.000152324 | − | 0.000263832i | ||||
\(160\) | 2.07085 | − | 3.58682i | 0.163715 | − | 0.283563i | ||||
\(161\) | −2.37847 | − | 19.4159i | −0.187450 | − | 1.53019i | ||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | −19.9927 | −1.56595 | −0.782976 | − | 0.622051i | \(-0.786299\pi\) | ||||
−0.782976 | + | 0.622051i | \(0.786299\pi\) | |||||||
\(164\) | 2.33240 | − | 4.03983i | 0.182130 | − | 0.315458i | ||||
\(165\) | 1.08325 | + | 1.87624i | 0.0843309 | + | 0.146065i | ||||
\(166\) | 1.54066 | − | 2.66851i | 0.119579 | − | 0.207117i | ||||
\(167\) | −8.82851 | − | 15.2914i | −0.683171 | − | 1.18329i | −0.974008 | − | 0.226514i | \(-0.927267\pi\) |
0.290837 | − | 0.956772i | \(-0.406066\pi\) | |||||||
\(168\) | 2.11344 | − | 1.59166i | 0.163055 | − | 0.122799i | ||||
\(169\) | 8.64572 | − | 9.70832i | 0.665055 | − | 0.746794i | ||||
\(170\) | −5.22495 | − | 9.04988i | −0.400735 | − | 0.694094i | ||||
\(171\) | −5.69993 | −0.435885 | ||||||||
\(172\) | 9.63058 | 0.734325 | ||||||||
\(173\) | −3.86985 | −0.294219 | −0.147110 | − | 0.989120i | \(-0.546997\pi\) | ||||
−0.147110 | + | 0.989120i | \(0.546997\pi\) | |||||||
\(174\) | 3.08133 | 0.233595 | ||||||||
\(175\) | 3.90987 | + | 31.9170i | 0.295559 | + | 2.41270i | ||||
\(176\) | −0.261547 | + | 0.453013i | −0.0197149 | + | 0.0341472i | ||||
\(177\) | 4.05374 | + | 7.02129i | 0.304698 | + | 0.527752i | ||||
\(178\) | −5.42599 | − | 9.39808i | −0.406695 | − | 0.704416i | ||||
\(179\) | −3.51968 | −0.263073 | −0.131537 | − | 0.991311i | \(-0.541991\pi\) | ||||
−0.131537 | + | 0.991311i | \(0.541991\pi\) | |||||||
\(180\) | −2.07085 | + | 3.58682i | −0.154352 | + | 0.267346i | ||||
\(181\) | 8.47129 | 0.629666 | 0.314833 | − | 0.949147i | \(-0.398052\pi\) | ||||
0.314833 | + | 0.949147i | \(0.398052\pi\) | |||||||
\(182\) | 4.93322 | + | 8.16476i | 0.365674 | + | 0.605213i | ||||
\(183\) | −6.01198 | −0.444418 | ||||||||
\(184\) | −3.69669 | + | 6.40285i | −0.272523 | + | 0.472024i | ||||
\(185\) | −23.4619 | −1.72495 | ||||||||
\(186\) | −2.17638 | − | 3.76959i | −0.159580 | − | 0.276400i | ||||
\(187\) | 0.659909 | + | 1.14300i | 0.0482573 | + | 0.0835841i | ||||
\(188\) | −5.58154 | + | 9.66752i | −0.407076 | + | 0.705076i | ||||
\(189\) | −2.11344 | + | 1.59166i | −0.153730 | + | 0.115776i | ||||
\(190\) | 23.6074 | 1.71266 | ||||||||
\(191\) | −21.9508 | −1.58830 | −0.794151 | − | 0.607721i | \(-0.792084\pi\) | ||||
−0.794151 | + | 0.607721i | \(0.792084\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 12.8592 | 0.925624 | 0.462812 | − | 0.886456i | \(-0.346840\pi\) | ||||
0.462812 | + | 0.886456i | \(0.346840\pi\) | |||||||
\(194\) | 1.31892 | + | 2.28443i | 0.0946928 | + | 0.164013i | ||||
\(195\) | −12.1051 | − | 8.74439i | −0.866864 | − | 0.626198i | ||||
\(196\) | −6.79301 | + | 1.68966i | −0.485215 | + | 0.120690i | ||||
\(197\) | −5.27054 | − | 9.12883i | −0.375510 | − | 0.650403i | 0.614893 | − | 0.788610i | \(-0.289199\pi\) |
−0.990403 | + | 0.138208i | \(0.955866\pi\) | |||||||
\(198\) | 0.261547 | − | 0.453013i | 0.0185874 | − | 0.0321942i | ||||
\(199\) | −6.55182 | − | 11.3481i | −0.464446 | − | 0.804445i | 0.534730 | − | 0.845023i | \(-0.320413\pi\) |
−0.999176 | + | 0.0405782i | \(0.987080\pi\) | |||||||
\(200\) | 6.07684 | − | 10.5254i | 0.429697 | − | 0.744258i | ||||
\(201\) | −3.23244 | −0.227999 | ||||||||
\(202\) | −6.09224 | + | 10.5521i | −0.428648 | + | 0.742441i | ||||
\(203\) | −7.50346 | − | 3.18750i | −0.526640 | − | 0.223719i | ||||
\(204\) | −1.26155 | + | 2.18506i | −0.0883260 | + | 0.152985i | ||||
\(205\) | 9.66009 | − | 16.7318i | 0.674690 | − | 1.16860i | ||||
\(206\) | 13.6306 | 0.949688 | ||||||||
\(207\) | 3.69669 | − | 6.40285i | 0.256937 | − | 0.445029i | ||||
\(208\) | 0.367074 | − | 3.58682i | 0.0254520 | − | 0.248701i | ||||
\(209\) | −2.98160 | −0.206242 | ||||||||
\(210\) | 8.75321 | − | 6.59219i | 0.604029 | − | 0.454904i | ||||
\(211\) | −0.979430 | − | 1.69642i | −0.0674267 | − | 0.116787i | 0.830341 | − | 0.557255i | \(-0.188146\pi\) |
−0.897768 | + | 0.440469i | \(0.854812\pi\) | |||||||
\(212\) | 0.00384145 | 0.000263832 | ||||||||
\(213\) | −3.98568 | + | 6.90340i | −0.273094 | + | 0.473013i | ||||
\(214\) | 2.69861 | + | 4.67412i | 0.184473 | + | 0.319516i | ||||
\(215\) | 39.8870 | 2.72027 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.40029 | + | 11.4309i | 0.0950581 | + | 0.775977i | ||||
\(218\) | −5.58133 | − | 9.66715i | −0.378015 | − | 0.654742i | ||||
\(219\) | −5.99080 | + | 10.3764i | −0.404821 | + | 0.701170i | ||||
\(220\) | −1.08325 | + | 1.87624i | −0.0730327 | + | 0.126496i | ||||
\(221\) | −7.37434 | − | 5.32702i | −0.496052 | − | 0.358334i | ||||
\(222\) | 2.83240 | + | 4.90586i | 0.190098 | + | 0.329259i | ||||
\(223\) | 6.26821 | + | 10.8569i | 0.419751 | + | 0.727029i | 0.995914 | − | 0.0903050i | \(-0.0287842\pi\) |
−0.576164 | + | 0.817334i | \(0.695451\pi\) | |||||||
\(224\) | 2.43514 | + | 1.03446i | 0.162705 | + | 0.0691176i | ||||
\(225\) | −6.07684 | + | 10.5254i | −0.405123 | + | 0.701693i | ||||
\(226\) | −2.03617 | − | 3.52676i | −0.135444 | − | 0.234596i | ||||
\(227\) | 10.8649 | + | 18.8186i | 0.721132 | + | 1.24904i | 0.960547 | + | 0.278119i | \(0.0897110\pi\) |
−0.239415 | + | 0.970917i | \(0.576956\pi\) | |||||||
\(228\) | −2.84997 | − | 4.93629i | −0.188744 | − | 0.326914i | ||||
\(229\) | −7.77570 | − | 13.4679i | −0.513833 | − | 0.889985i | −0.999871 | − | 0.0160474i | \(-0.994892\pi\) |
0.486038 | − | 0.873938i | \(-0.338442\pi\) | |||||||
\(230\) | −15.3106 | + | 26.5187i | −1.00955 | + | 1.74859i | ||||
\(231\) | −1.10553 | + | 0.832590i | −0.0727383 | + | 0.0547804i | ||||
\(232\) | 1.54066 | + | 2.66851i | 0.101150 | + | 0.175196i | ||||
\(233\) | 10.3320 | + | 17.8955i | 0.676870 | + | 1.17237i | 0.975919 | + | 0.218135i | \(0.0699974\pi\) |
−0.299048 | + | 0.954238i | \(0.596669\pi\) | |||||||
\(234\) | −0.367074 | + | 3.58682i | −0.0239964 | + | 0.234478i | ||||
\(235\) | −23.1171 | + | 40.0400i | −1.50799 | + | 2.61192i | ||||
\(236\) | −4.05374 | + | 7.02129i | −0.263876 | + | 0.457047i | ||||
\(237\) | −1.15602 | − | 2.00229i | −0.0750916 | − | 0.130063i | ||||
\(238\) | 5.33240 | − | 4.01592i | 0.345648 | − | 0.260313i | ||||
\(239\) | −30.0971 | −1.94682 | −0.973410 | − | 0.229071i | \(-0.926431\pi\) | ||||
−0.973410 | + | 0.229071i | \(0.926431\pi\) | |||||||
\(240\) | −4.14170 | −0.267346 | ||||||||
\(241\) | −1.02609 | − | 1.77725i | −0.0660965 | − | 0.114483i | 0.831083 | − | 0.556148i | \(-0.187721\pi\) |
−0.897180 | + | 0.441665i | \(0.854388\pi\) | |||||||
\(242\) | −5.36319 | + | 9.28931i | −0.344759 | + | 0.597140i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.00599 | − | 5.20652i | −0.192439 | − | 0.333314i | ||||
\(245\) | −28.1346 | + | 6.99807i | −1.79746 | + | 0.447090i | ||||
\(246\) | −4.66479 | −0.297416 | ||||||||
\(247\) | 18.7517 | − | 8.41033i | 1.19314 | − | 0.535136i | ||||
\(248\) | 2.17638 | − | 3.76959i | 0.138200 | − | 0.239369i | ||||
\(249\) | −3.08133 | −0.195271 | ||||||||
\(250\) | 14.8142 | − | 25.6589i | 0.936932 | − | 1.62281i | ||||
\(251\) | −8.23457 | + | 14.2627i | −0.519761 | + | 0.900253i | 0.479975 | + | 0.877282i | \(0.340646\pi\) |
−0.999736 | + | 0.0229705i | \(0.992688\pi\) | |||||||
\(252\) | −2.43514 | − | 1.03446i | −0.153399 | − | 0.0651647i | ||||
\(253\) | 1.93372 | − | 3.34929i | 0.121572 | − | 0.210568i | ||||
\(254\) | −7.66864 | −0.481173 | ||||||||
\(255\) | −5.22495 | + | 9.04988i | −0.327199 | + | 0.566725i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.93711 | + | 10.2834i | −0.370346 | + | 0.641459i | −0.989619 | − | 0.143717i | \(-0.954094\pi\) |
0.619272 | + | 0.785176i | \(0.287428\pi\) | |||||||
\(258\) | −4.81529 | − | 8.34033i | −0.299787 | − | 0.519246i | ||||
\(259\) | −1.82238 | − | 14.8764i | −0.113237 | − | 0.924376i | ||||
\(260\) | 1.52031 | − | 14.8555i | 0.0942856 | − | 0.921300i | ||||
\(261\) | −1.54066 | − | 2.66851i | −0.0953648 | − | 0.165177i | ||||
\(262\) | −11.2478 | −0.694893 | ||||||||
\(263\) | 25.0317 | 1.54352 | 0.771760 | − | 0.635914i | \(-0.219377\pi\) | ||||
0.771760 | + | 0.635914i | \(0.219377\pi\) | |||||||
\(264\) | 0.523095 | 0.0321942 | ||||||||
\(265\) | 0.0159101 | 0.000977353 | ||||||||
\(266\) | 1.83369 | + | 14.9687i | 0.112430 | + | 0.917791i | ||||
\(267\) | −5.42599 | + | 9.39808i | −0.332065 | + | 0.575153i | ||||
\(268\) | −1.61622 | − | 2.79938i | −0.0987264 | − | 0.170999i | ||||
\(269\) | 7.76501 | + | 13.4494i | 0.473441 | + | 0.820024i | 0.999538 | − | 0.0304008i | \(-0.00967836\pi\) |
−0.526097 | + | 0.850425i | \(0.676345\pi\) | |||||||
\(270\) | 4.14170 | 0.252056 | ||||||||
\(271\) | 2.63845 | − | 4.56993i | 0.160274 | − | 0.277604i | −0.774693 | − | 0.632338i | \(-0.782095\pi\) |
0.934967 | + | 0.354734i | \(0.115429\pi\) | |||||||
\(272\) | −2.52309 | −0.152985 | ||||||||
\(273\) | 4.60428 | − | 8.35467i | 0.278664 | − | 0.505648i | ||||
\(274\) | 7.02232 | 0.424234 | ||||||||
\(275\) | −3.17876 | + | 5.50578i | −0.191686 | + | 0.332011i | ||||
\(276\) | 7.39337 | 0.445029 | ||||||||
\(277\) | 5.56594 | + | 9.64049i | 0.334425 | + | 0.579241i | 0.983374 | − | 0.181591i | \(-0.0581246\pi\) |
−0.648949 | + | 0.760832i | \(0.724791\pi\) | |||||||
\(278\) | −6.59202 | − | 11.4177i | −0.395363 | − | 0.684789i | ||||
\(279\) | −2.17638 | + | 3.76959i | −0.130296 | + | 0.225680i | ||||
\(280\) | 10.0856 | + | 4.28441i | 0.602731 | + | 0.256043i | ||||
\(281\) | 19.3908 | 1.15676 | 0.578379 | − | 0.815768i | \(-0.303686\pi\) | ||||
0.578379 | + | 0.815768i | \(0.303686\pi\) | |||||||
\(282\) | 11.1631 | 0.664752 | ||||||||
\(283\) | 26.0359 | 1.54768 | 0.773838 | − | 0.633384i | \(-0.218335\pi\) | ||||
0.773838 | + | 0.633384i | \(0.218335\pi\) | |||||||
\(284\) | −7.97136 | −0.473013 | ||||||||
\(285\) | −11.8037 | − | 20.4446i | −0.699191 | − | 1.21103i | ||||
\(286\) | −0.192014 | + | 1.87624i | −0.0113540 | + | 0.110945i | ||||
\(287\) | 11.3594 | + | 4.82553i | 0.670525 | + | 0.284842i | ||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 5.31700 | − | 9.20931i | 0.312765 | − | 0.541724i | ||||
\(290\) | 6.38097 | + | 11.0522i | 0.374703 | + | 0.649005i | ||||
\(291\) | 1.31892 | − | 2.28443i | 0.0773163 | − | 0.133916i | ||||
\(292\) | −11.9816 | −0.701170 | ||||||||
\(293\) | −6.46216 | + | 11.1928i | −0.377523 | + | 0.653890i | −0.990701 | − | 0.136055i | \(-0.956558\pi\) |
0.613178 | + | 0.789945i | \(0.289891\pi\) | |||||||
\(294\) | 4.85980 | + | 5.03809i | 0.283429 | + | 0.293828i | ||||
\(295\) | −16.7894 | + | 29.0801i | −0.977516 | + | 1.69311i | ||||
\(296\) | −2.83240 | + | 4.90586i | −0.164630 | + | 0.285147i | ||||
\(297\) | −0.523095 | −0.0303530 | ||||||||
\(298\) | 9.06612 | − | 15.7030i | 0.525186 | − | 0.909649i | ||||
\(299\) | −2.71391 | + | 26.5187i | −0.156950 | + | 1.53361i | ||||
\(300\) | −12.1537 | −0.701693 | ||||||||
\(301\) | 3.09819 | + | 25.2911i | 0.178577 | + | 1.45775i | ||||
\(302\) | 2.53343 | + | 4.38804i | 0.145783 | + | 0.252503i | ||||
\(303\) | 12.1845 | 0.699980 | ||||||||
\(304\) | 2.84997 | − | 4.93629i | 0.163457 | − | 0.283116i | ||||
\(305\) | −12.4499 | − | 21.5639i | −0.712879 | − | 1.23474i | ||||
\(306\) | 2.52309 | 0.144236 | ||||||||
\(307\) | 20.0771 | 1.14586 | 0.572931 | − | 0.819604i | \(-0.305806\pi\) | ||||
0.572931 | + | 0.819604i | \(0.305806\pi\) | |||||||
\(308\) | −1.27381 | − | 0.541119i | −0.0725819 | − | 0.0308331i | ||||
\(309\) | −6.81529 | − | 11.8044i | −0.387708 | − | 0.671531i | ||||
\(310\) | 9.01390 | − | 15.6125i | 0.511955 | − | 0.886732i | ||||
\(311\) | 10.4837 | − | 18.1583i | 0.594475 | − | 1.02966i | −0.399145 | − | 0.916888i | \(-0.630693\pi\) |
0.993621 | − | 0.112774i | \(-0.0359736\pi\) | |||||||
\(312\) | −3.28981 | + | 1.47551i | −0.186249 | + | 0.0835345i | ||||
\(313\) | 9.55610 | + | 16.5517i | 0.540143 | + | 0.935555i | 0.998895 | + | 0.0469909i | \(0.0149632\pi\) |
−0.458752 | + | 0.888564i | \(0.651703\pi\) | |||||||
\(314\) | −5.80481 | − | 10.0542i | −0.327584 | − | 0.567393i | ||||
\(315\) | −10.0856 | − | 4.28441i | −0.568260 | − | 0.241399i | ||||
\(316\) | 1.15602 | − | 2.00229i | 0.0650313 | − | 0.112637i | ||||
\(317\) | 9.13122 | + | 15.8157i | 0.512860 | + | 0.888300i | 0.999889 | + | 0.0149141i | \(0.00474749\pi\) |
−0.487028 | + | 0.873386i | \(0.661919\pi\) | |||||||
\(318\) | −0.00192073 | − | 0.00332680i | −0.000107709 | − | 0.000186558i | ||||
\(319\) | −0.805913 | − | 1.39588i | −0.0451225 | − | 0.0781544i | ||||
\(320\) | −2.07085 | − | 3.58682i | −0.115764 | − | 0.200509i | ||||
\(321\) | 2.69861 | − | 4.67412i | 0.150622 | − | 0.260884i | ||||
\(322\) | −18.0039 | − | 7.64813i | −1.00332 | − | 0.426213i | ||||
\(323\) | −7.19074 | − | 12.4547i | −0.400103 | − | 0.692999i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 4.46130 | − | 43.5930i | 0.247468 | − | 2.41811i | ||||
\(326\) | −9.99637 | + | 17.3142i | −0.553648 | + | 0.958946i | ||||
\(327\) | −5.58133 | + | 9.66715i | −0.308648 | + | 0.534594i | ||||
\(328\) | −2.33240 | − | 4.03983i | −0.128785 | − | 0.223062i | ||||
\(329\) | −27.1837 | − | 11.5477i | −1.49868 | − | 0.636647i | ||||
\(330\) | 2.16650 | 0.119262 | ||||||||
\(331\) | −10.2440 | −0.563061 | −0.281530 | − | 0.959552i | \(-0.590842\pi\) | ||||
−0.281530 | + | 0.959552i | \(0.590842\pi\) | |||||||
\(332\) | −1.54066 | − | 2.66851i | −0.0845550 | − | 0.146453i | ||||
\(333\) | 2.83240 | − | 4.90586i | 0.155214 | − | 0.268839i | ||||
\(334\) | −17.6570 | −0.966149 | ||||||||
\(335\) | −6.69390 | − | 11.5942i | −0.365727 | − | 0.633457i | ||||
\(336\) | −0.321703 | − | 2.62612i | −0.0175503 | − | 0.143267i | ||||
\(337\) | −32.6266 | −1.77728 | −0.888642 | − | 0.458601i | \(-0.848351\pi\) | ||||
−0.888642 | + | 0.458601i | \(0.848351\pi\) | |||||||
\(338\) | −4.08479 | − | 12.3416i | −0.222183 | − | 0.671293i | ||||
\(339\) | −2.03617 | + | 3.52676i | −0.110590 | + | 0.191547i | ||||
\(340\) | −10.4499 | −0.566725 | ||||||||
\(341\) | −1.13845 | + | 1.97185i | −0.0616506 | + | 0.106782i | ||||
\(342\) | −2.84997 | + | 4.93629i | −0.154109 | + | 0.266924i | ||||
\(343\) | −6.62259 | − | 17.2957i | −0.357586 | − | 0.933880i | ||||
\(344\) | 4.81529 | − | 8.34033i | 0.259623 | − | 0.449680i | ||||
\(345\) | 30.6211 | 1.64859 | ||||||||
\(346\) | −1.93492 | + | 3.35139i | −0.104022 | + | 0.180172i | ||||
\(347\) | −4.21596 | − | 7.30226i | −0.226325 | − | 0.392006i | 0.730391 | − | 0.683029i | \(-0.239338\pi\) |
−0.956716 | + | 0.291023i | \(0.906004\pi\) | |||||||
\(348\) | 1.54066 | − | 2.66851i | 0.0825883 | − | 0.143047i | ||||
\(349\) | 18.3077 | + | 31.7099i | 0.979990 | + | 1.69739i | 0.662373 | + | 0.749174i | \(0.269549\pi\) |
0.317617 | + | 0.948219i | \(0.397117\pi\) | |||||||
\(350\) | 29.5959 | + | 12.5725i | 1.58197 | + | 0.672026i | ||||
\(351\) | 3.28981 | − | 1.47551i | 0.175597 | − | 0.0787571i | ||||
\(352\) | 0.261547 | + | 0.453013i | 0.0139405 | + | 0.0241457i | ||||
\(353\) | −5.23894 | −0.278841 | −0.139420 | − | 0.990233i | \(-0.544524\pi\) | ||||
−0.139420 | + | 0.990233i | \(0.544524\pi\) | |||||||
\(354\) | 8.10749 | 0.430908 | ||||||||
\(355\) | −33.0150 | −1.75225 | ||||||||
\(356\) | −10.8520 | −0.575153 | ||||||||
\(357\) | −6.14408 | − | 2.61003i | −0.325179 | − | 0.138138i | ||||
\(358\) | −1.75984 | + | 3.04813i | −0.0930105 | + | 0.161099i | ||||
\(359\) | −2.54006 | − | 4.39951i | −0.134059 | − | 0.232197i | 0.791178 | − | 0.611585i | \(-0.209468\pi\) |
−0.925238 | + | 0.379388i | \(0.876135\pi\) | |||||||
\(360\) | 2.07085 | + | 3.58682i | 0.109143 | + | 0.189042i | ||||
\(361\) | 13.4893 | 0.709961 | ||||||||
\(362\) | 4.23564 | − | 7.33635i | 0.222621 | − | 0.385590i | ||||
\(363\) | 10.7264 | 0.562989 | ||||||||
\(364\) | 9.53750 | − | 0.189910i | 0.499901 | − | 0.00995398i | ||||
\(365\) | −49.6242 | −2.59745 | ||||||||
\(366\) | −3.00599 | + | 5.20652i | −0.157126 | + | 0.272149i | ||||
\(367\) | 4.86302 | 0.253848 | 0.126924 | − | 0.991912i | \(-0.459490\pi\) | ||||
0.126924 | + | 0.991912i | \(0.459490\pi\) | |||||||
\(368\) | 3.69669 | + | 6.40285i | 0.192703 | + | 0.333771i | ||||
\(369\) | 2.33240 | + | 4.03983i | 0.121420 | + | 0.210305i | ||||
\(370\) | −11.7309 | + | 20.3186i | −0.609862 | + | 1.05631i | ||||
\(371\) | 0.00123581 | + | 0.0100881i | 6.41599e−5 | + | 0.000523749i | ||||
\(372\) | −4.35275 | −0.225680 | ||||||||
\(373\) | 28.8122 | 1.49184 | 0.745919 | − | 0.666036i | \(-0.232010\pi\) | ||||
0.745919 | + | 0.666036i | \(0.232010\pi\) | |||||||
\(374\) | 1.31982 | 0.0682461 | ||||||||
\(375\) | −29.6284 | −1.53000 | ||||||||
\(376\) | 5.58154 | + | 9.66752i | 0.287846 | + | 0.498564i | ||||
\(377\) | 9.00592 | + | 6.50562i | 0.463828 | + | 0.335057i | ||||
\(378\) | 0.321703 | + | 2.62612i | 0.0165466 | + | 0.135073i | ||||
\(379\) | −14.1550 | − | 24.5172i | −0.727094 | − | 1.25936i | −0.958106 | − | 0.286413i | \(-0.907537\pi\) |
0.231013 | − | 0.972951i | \(-0.425796\pi\) | |||||||
\(380\) | 11.8037 | − | 20.4446i | 0.605517 | − | 1.04879i | ||||
\(381\) | 3.83432 | + | 6.64123i | 0.196438 | + | 0.340241i | ||||
\(382\) | −10.9754 | + | 19.0099i | −0.561549 | + | 0.972632i | ||||
\(383\) | −18.7363 | −0.957380 | −0.478690 | − | 0.877984i | \(-0.658888\pi\) | ||||
−0.478690 | + | 0.877984i | \(0.658888\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −5.27573 | − | 2.24115i | −0.268876 | − | 0.114220i | ||||
\(386\) | 6.42959 | − | 11.1364i | 0.327258 | − | 0.566827i | ||||
\(387\) | −4.81529 | + | 8.34033i | −0.244775 | + | 0.423963i | ||||
\(388\) | 2.63784 | 0.133916 | ||||||||
\(389\) | 3.55307 | − | 6.15409i | 0.180148 | − | 0.312025i | −0.761783 | − | 0.647832i | \(-0.775676\pi\) |
0.941931 | + | 0.335807i | \(0.109009\pi\) | |||||||
\(390\) | −13.6254 | + | 6.11113i | −0.689950 | + | 0.309449i | ||||
\(391\) | 18.6542 | 0.943382 | ||||||||
\(392\) | −1.93322 | + | 6.72775i | −0.0976422 | + | 0.339803i | ||||
\(393\) | 5.62392 | + | 9.74091i | 0.283689 | + | 0.491364i | ||||
\(394\) | −10.5411 | −0.531051 | ||||||||
\(395\) | 4.78789 | − | 8.29287i | 0.240905 | − | 0.417260i | ||||
\(396\) | −0.261547 | − | 0.453013i | −0.0131432 | − | 0.0227648i | ||||
\(397\) | 39.3266 | 1.97374 | 0.986872 | − | 0.161503i | \(-0.0516340\pi\) | ||||
0.986872 | + | 0.161503i | \(0.0516340\pi\) | |||||||
\(398\) | −13.1036 | −0.656826 | ||||||||
\(399\) | 12.0464 | − | 9.07238i | 0.603076 | − | 0.454187i | ||||
\(400\) | −6.07684 | − | 10.5254i | −0.303842 | − | 0.526270i | ||||
\(401\) | 4.30153 | − | 7.45048i | 0.214808 | − | 0.372059i | −0.738405 | − | 0.674358i | \(-0.764421\pi\) |
0.953213 | + | 0.302299i | \(0.0977540\pi\) | |||||||
\(402\) | −1.61622 | + | 2.79938i | −0.0806098 | + | 0.139620i | ||||
\(403\) | 1.59778 | − | 15.6125i | 0.0795912 | − | 0.777715i | ||||
\(404\) | 6.09224 | + | 10.5521i | 0.303100 | + | 0.524985i | ||||
\(405\) | −2.07085 | − | 3.58682i | −0.102901 | − | 0.178230i | ||||
\(406\) | −6.51219 | + | 4.90444i | −0.323195 | + | 0.243403i | ||||
\(407\) | 1.48161 | − | 2.56623i | 0.0734408 | − | 0.127203i | ||||
\(408\) | 1.26155 | + | 2.18506i | 0.0624559 | + | 0.108177i | ||||
\(409\) | 18.2662 | + | 31.6381i | 0.903208 | + | 1.56440i | 0.823305 | + | 0.567599i | \(0.192128\pi\) |
0.0799027 | + | 0.996803i | \(0.474539\pi\) | |||||||
\(410\) | −9.66009 | − | 16.7318i | −0.477078 | − | 0.826323i | ||||
\(411\) | −3.51116 | − | 6.08150i | −0.173193 | − | 0.299978i | ||||
\(412\) | 6.81529 | − | 11.8044i | 0.335765 | − | 0.581563i | ||||
\(413\) | −19.7429 | − | 8.38685i | −0.971482 | − | 0.412690i | ||||
\(414\) | −3.69669 | − | 6.40285i | −0.181682 | − | 0.314683i | ||||
\(415\) | −6.38097 | − | 11.0522i | −0.313230 | − | 0.542529i | ||||
\(416\) | −2.92274 | − | 2.11130i | −0.143299 | − | 0.103515i | ||||
\(417\) | −6.59202 | + | 11.4177i | −0.322813 | + | 0.559128i | ||||
\(418\) | −1.49080 | + | 2.58215i | −0.0729175 | + | 0.126297i | ||||
\(419\) | 6.77818 | + | 11.7402i | 0.331136 | + | 0.573544i | 0.982735 | − | 0.185019i | \(-0.0592348\pi\) |
−0.651599 | + | 0.758564i | \(0.725901\pi\) | |||||||
\(420\) | −1.33240 | − | 10.8766i | −0.0650143 | − | 0.530724i | ||||
\(421\) | 4.50209 | 0.219418 | 0.109709 | − | 0.993964i | \(-0.465008\pi\) | ||||
0.109709 | + | 0.993964i | \(0.465008\pi\) | |||||||
\(422\) | −1.95886 | −0.0953558 | ||||||||
\(423\) | −5.58154 | − | 9.66752i | −0.271384 | − | 0.470051i | ||||
\(424\) | 0.00192073 | − | 0.00332680i | 9.32788e−5 | − | 0.000161564i | ||||
\(425\) | −30.6649 | −1.48746 | ||||||||
\(426\) | 3.98568 | + | 6.90340i | 0.193107 | + | 0.334471i | ||||
\(427\) | 12.7059 | − | 9.56904i | 0.614883 | − | 0.463078i | ||||
\(428\) | 5.39721 | 0.260884 | ||||||||
\(429\) | 1.72088 | − | 0.771833i | 0.0830850 | − | 0.0372644i | ||||
\(430\) | 19.9435 | − | 34.5431i | 0.961760 | − | 1.66582i | ||||
\(431\) | −0.507706 | −0.0244553 | −0.0122277 | − | 0.999925i | \(-0.503892\pi\) | ||||
−0.0122277 | + | 0.999925i | \(0.503892\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −6.41093 | + | 11.1041i | −0.308090 | + | 0.533627i | −0.977944 | − | 0.208865i | \(-0.933023\pi\) |
0.669855 | + | 0.742492i | \(0.266356\pi\) | |||||||
\(434\) | 10.5996 | + | 4.50274i | 0.508795 | + | 0.216138i | ||||
\(435\) | 6.38097 | − | 11.0522i | 0.305944 | − | 0.529911i | ||||
\(436\) | −11.1627 | −0.534594 | ||||||||
\(437\) | −21.0709 | + | 36.4958i | −1.00796 | + | 1.74583i | ||||
\(438\) | 5.99080 | + | 10.3764i | 0.286252 | + | 0.495802i | ||||
\(439\) | 0.216640 | − | 0.375232i | 0.0103397 | − | 0.0179088i | −0.860809 | − | 0.508928i | \(-0.830042\pi\) |
0.871149 | + | 0.491019i | \(0.163375\pi\) | |||||||
\(440\) | 1.08325 | + | 1.87624i | 0.0516419 | + | 0.0894464i | ||||
\(441\) | 1.93322 | − | 6.72775i | 0.0920580 | − | 0.320369i | ||||
\(442\) | −8.30051 | + | 3.72286i | −0.394815 | + | 0.177078i | ||||
\(443\) | −7.03339 | − | 12.1822i | −0.334166 | − | 0.578793i | 0.649158 | − | 0.760654i | \(-0.275121\pi\) |
−0.983324 | + | 0.181861i | \(0.941788\pi\) | |||||||
\(444\) | 5.66479 | 0.268839 | ||||||||
\(445\) | −44.9456 | −2.13063 | ||||||||
\(446\) | 12.5364 | 0.593617 | ||||||||
\(447\) | −18.1322 | −0.857626 | ||||||||
\(448\) | 2.11344 | − | 1.59166i | 0.0998504 | − | 0.0751990i | ||||
\(449\) | 15.2892 | − | 26.4817i | 0.721542 | − | 1.24975i | −0.238840 | − | 0.971059i | \(-0.576767\pi\) |
0.960382 | − | 0.278688i | \(-0.0898997\pi\) | |||||||
\(450\) | 6.07684 | + | 10.5254i | 0.286465 | + | 0.496172i | ||||
\(451\) | 1.22006 | + | 2.11321i | 0.0574506 | + | 0.0995073i | ||||
\(452\) | −4.07235 | −0.191547 | ||||||||
\(453\) | 2.53343 | − | 4.38804i | 0.119031 | − | 0.206168i | ||||
\(454\) | 21.7299 | 1.01983 | ||||||||
\(455\) | 39.5015 | − | 0.786550i | 1.85186 | − | 0.0368740i | ||||
\(456\) | −5.69993 | −0.266924 | ||||||||
\(457\) | −1.15513 | + | 2.00074i | −0.0540346 | + | 0.0935907i | −0.891778 | − | 0.452474i | \(-0.850541\pi\) |
0.837743 | + | 0.546065i | \(0.183875\pi\) | |||||||
\(458\) | −15.5514 | −0.726670 | ||||||||
\(459\) | −1.26155 | − | 2.18506i | −0.0588840 | − | 0.101990i | ||||
\(460\) | 15.3106 | + | 26.5187i | 0.713859 | + | 1.23644i | ||||
\(461\) | −15.0409 | + | 26.0516i | −0.700524 | + | 1.21334i | 0.267759 | + | 0.963486i | \(0.413717\pi\) |
−0.968283 | + | 0.249857i | \(0.919617\pi\) | |||||||
\(462\) | 0.168281 | + | 1.37371i | 0.00782914 | + | 0.0639107i | ||||
\(463\) | 29.4727 | 1.36971 | 0.684856 | − | 0.728679i | \(-0.259865\pi\) | ||||
0.684856 | + | 0.728679i | \(0.259865\pi\) | |||||||
\(464\) | 3.08133 | 0.143047 | ||||||||
\(465\) | −18.0278 | −0.836019 | ||||||||
\(466\) | 20.6639 | 0.957239 | ||||||||
\(467\) | 2.92442 | + | 5.06525i | 0.135326 | + | 0.234392i | 0.925722 | − | 0.378205i | \(-0.123458\pi\) |
−0.790396 | + | 0.612596i | \(0.790125\pi\) | |||||||
\(468\) | 2.92274 | + | 2.11130i | 0.135104 | + | 0.0975951i | ||||
\(469\) | 6.83156 | − | 5.14496i | 0.315452 | − | 0.237572i | ||||
\(470\) | 23.1171 | + | 40.0400i | 1.06631 | + | 1.84691i | ||||
\(471\) | −5.80481 | + | 10.0542i | −0.267472 | + | 0.463274i | ||||
\(472\) | 4.05374 | + | 7.02129i | 0.186589 | + | 0.323181i | ||||
\(473\) | −2.51885 | + | 4.36278i | −0.115817 | + | 0.200601i | ||||
\(474\) | −2.31204 | −0.106196 | ||||||||
\(475\) | 34.6376 | − | 59.9940i | 1.58928 | − | 2.75272i | ||||
\(476\) | −0.811687 | − | 6.62595i | −0.0372036 | − | 0.303700i | ||||
\(477\) | −0.00192073 | + | 0.00332680i | −8.79441e−5 | + | 0.000152324i | ||||
\(478\) | −15.0486 | + | 26.0649i | −0.688305 | + | 1.19218i | ||||
\(479\) | 17.3275 | 0.791713 | 0.395856 | − | 0.918312i | \(-0.370448\pi\) | ||||
0.395856 | + | 0.918312i | \(0.370448\pi\) | |||||||
\(480\) | −2.07085 | + | 3.58682i | −0.0945209 | + | 0.163715i | ||||
\(481\) | −2.07940 | + | 20.3186i | −0.0948124 | + | 0.926448i | ||||
\(482\) | −2.05219 | −0.0934746 | ||||||||
\(483\) | 2.37847 | + | 19.4159i | 0.108224 | + | 0.883453i | ||||
\(484\) | 5.36319 | + | 9.28931i | 0.243781 | + | 0.422241i | ||||
\(485\) | 10.9251 | 0.496084 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | 19.0323 | + | 32.9648i | 0.862434 | + | 1.49378i | 0.869573 | + | 0.493805i | \(0.164394\pi\) |
−0.00713845 | + | 0.999975i | \(0.502272\pi\) | |||||||
\(488\) | −6.01198 | −0.272149 | ||||||||
\(489\) | 19.9927 | 0.904103 | ||||||||
\(490\) | −8.00681 | + | 27.8643i | −0.361711 | + | 1.25878i | ||||
\(491\) | −8.22130 | − | 14.2397i | −0.371022 | − | 0.642629i | 0.618701 | − | 0.785627i | \(-0.287659\pi\) |
−0.989723 | + | 0.142997i | \(0.954326\pi\) | |||||||
\(492\) | −2.33240 | + | 4.03983i | −0.105153 | + | 0.182130i | ||||
\(493\) | 3.88724 | − | 6.73290i | 0.175073 | − | 0.303235i | ||||
\(494\) | 2.09230 | − | 20.4446i | 0.0941369 | − | 0.919847i | ||||
\(495\) | −1.08325 | − | 1.87624i | −0.0486885 | − | 0.0843309i | ||||
\(496\) | −2.17638 | − | 3.76959i | −0.0977222 | − | 0.169260i | ||||
\(497\) | −2.56441 | − | 20.9337i | −0.115029 | − | 0.939007i | ||||
\(498\) | −1.54066 | + | 2.66851i | −0.0690388 | + | 0.119579i | ||||
\(499\) | −3.74298 | − | 6.48304i | −0.167559 | − | 0.290221i | 0.770002 | − | 0.638041i | \(-0.220255\pi\) |
−0.937561 | + | 0.347821i | \(0.886922\pi\) | |||||||
\(500\) | −14.8142 | − | 25.6589i | −0.662511 | − | 1.14750i | ||||
\(501\) | 8.82851 | + | 15.2914i | 0.394429 | + | 0.683171i | ||||
\(502\) | 8.23457 | + | 14.2627i | 0.367527 | + | 0.636575i | ||||
\(503\) | 1.27275 | − | 2.20447i | 0.0567492 | − | 0.0982925i | −0.836255 | − | 0.548340i | \(-0.815260\pi\) |
0.893004 | + | 0.450048i | \(0.148593\pi\) | |||||||
\(504\) | −2.11344 | + | 1.59166i | −0.0941399 | + | 0.0708983i | ||||
\(505\) | 25.2322 | + | 43.7035i | 1.12282 | + | 1.94478i | ||||
\(506\) | −1.93372 | − | 3.34929i | −0.0859642 | − | 0.148894i | ||||
\(507\) | −8.64572 | + | 9.70832i | −0.383970 | + | 0.431162i | ||||
\(508\) | −3.83432 | + | 6.64123i | −0.170120 | + | 0.294657i | ||||
\(509\) | 17.2213 | − | 29.8281i | 0.763320 | − | 1.32211i | −0.177811 | − | 0.984065i | \(-0.556901\pi\) |
0.941130 | − | 0.338044i | \(-0.109765\pi\) | |||||||
\(510\) | 5.22495 | + | 9.04988i | 0.231365 | + | 0.400735i | ||||
\(511\) | −3.85452 | − | 31.4651i | −0.170514 | − | 1.39194i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.69993 | 0.251658 | ||||||||
\(514\) | 5.93711 | + | 10.2834i | 0.261874 | + | 0.453580i | ||||
\(515\) | 28.2269 | − | 48.8904i | 1.24383 | − | 2.15437i | ||||
\(516\) | −9.63058 | −0.423963 | ||||||||
\(517\) | −2.91968 | − | 5.05703i | −0.128407 | − | 0.222408i | ||||
\(518\) | −13.7946 | − | 5.85999i | −0.606098 | − | 0.257473i | ||||
\(519\) | 3.86985 | 0.169867 | ||||||||
\(520\) | −12.1051 | − | 8.74439i | −0.530844 | − | 0.383467i | ||||
\(521\) | 21.9782 | − | 38.0673i | 0.962881 | − | 1.66776i | 0.247677 | − | 0.968843i | \(-0.420333\pi\) |
0.715204 | − | 0.698916i | \(-0.246334\pi\) | |||||||
\(522\) | −3.08133 | −0.134866 | ||||||||
\(523\) | 14.2468 | − | 24.6763i | 0.622971 | − | 1.07902i | −0.365958 | − | 0.930631i | \(-0.619259\pi\) |
0.988929 | − | 0.148386i | \(-0.0474080\pi\) | |||||||
\(524\) | −5.62392 | + | 9.74091i | −0.245682 | + | 0.425533i | ||||
\(525\) | −3.90987 | − | 31.9170i | −0.170641 | − | 1.39297i | ||||
\(526\) | 12.5158 | − | 21.6781i | 0.545717 | − | 0.945209i | ||||
\(527\) | −10.9824 | −0.478401 | ||||||||
\(528\) | 0.261547 | − | 0.453013i | 0.0113824 | − | 0.0197149i | ||||
\(529\) | −15.8310 | − | 27.4200i | −0.688303 | − | 1.19218i | ||||
\(530\) | 0.00795507 | − | 0.0137786i | 0.000345546 | − | 0.000598504i | ||||
\(531\) | −4.05374 | − | 7.02129i | −0.175917 | − | 0.304698i | ||||
\(532\) | 13.8801 | + | 5.89634i | 0.601780 | + | 0.255639i | ||||
\(533\) | −13.6340 | − | 9.84880i | −0.590553 | − | 0.426599i | ||||
\(534\) | 5.42599 | + | 9.39808i | 0.234805 | + | 0.406695i | ||||
\(535\) | 22.3536 | 0.966432 | ||||||||
\(536\) | −3.23244 | −0.139620 | ||||||||
\(537\) | 3.51968 | 0.151885 | ||||||||
\(538\) | 15.5300 | 0.669547 | ||||||||
\(539\) | 1.01126 | − | 3.51925i | 0.0435579 | − | 0.151585i | ||||
\(540\) | 2.07085 | − | 3.58682i | 0.0891152 | − | 0.154352i | ||||
\(541\) | 0.327013 | + | 0.566403i | 0.0140594 | + | 0.0243516i | 0.872969 | − | 0.487775i | \(-0.162191\pi\) |
−0.858910 | + | 0.512126i | \(0.828858\pi\) | |||||||
\(542\) | −2.63845 | − | 4.56993i | −0.113331 | − | 0.196295i | ||||
\(543\) | −8.47129 | −0.363538 | ||||||||
\(544\) | −1.26155 | + | 2.18506i | −0.0540884 | + | 0.0936838i | ||||
\(545\) | −46.2324 | −1.98038 | ||||||||
\(546\) | −4.93322 | − | 8.16476i | −0.211122 | − | 0.349420i | ||||
\(547\) | 4.52174 | 0.193336 | 0.0966678 | − | 0.995317i | \(-0.469182\pi\) | ||||
0.0966678 | + | 0.995317i | \(0.469182\pi\) | |||||||
\(548\) | 3.51116 | − | 6.08150i | 0.149989 | − | 0.259789i | ||||
\(549\) | 6.01198 | 0.256585 | ||||||||
\(550\) | 3.17876 | + | 5.50578i | 0.135543 | + | 0.234767i | ||||
\(551\) | 8.78169 | + | 15.2103i | 0.374113 | + | 0.647982i | ||||
\(552\) | 3.69669 | − | 6.40285i | 0.157341 | − | 0.272523i | ||||
\(553\) | 5.63014 | + | 2.39171i | 0.239418 | + | 0.101706i | ||||
\(554\) | 11.1319 | 0.472948 | ||||||||
\(555\) | 23.4619 | 0.995901 | ||||||||
\(556\) | −13.1840 | −0.559128 | ||||||||
\(557\) | −2.19422 | −0.0929719 | −0.0464859 | − | 0.998919i | \(-0.514802\pi\) | ||||
−0.0464859 | + | 0.998919i | \(0.514802\pi\) | |||||||
\(558\) | 2.17638 | + | 3.76959i | 0.0921334 | + | 0.159580i | ||||
\(559\) | 3.53513 | − | 34.5431i | 0.149520 | − | 1.46102i | ||||
\(560\) | 8.75321 | − | 6.59219i | 0.369891 | − | 0.278571i | ||||
\(561\) | −0.659909 | − | 1.14300i | −0.0278614 | − | 0.0482573i | ||||
\(562\) | 9.69540 | − | 16.7929i | 0.408976 | − | 0.708367i | ||||
\(563\) | 7.51839 | + | 13.0222i | 0.316862 | + | 0.548822i | 0.979832 | − | 0.199825i | \(-0.0640374\pi\) |
−0.662969 | + | 0.748647i | \(0.730704\pi\) | |||||||
\(564\) | 5.58154 | − | 9.66752i | 0.235025 | − | 0.407076i | ||||
\(565\) | −16.8664 | −0.709576 | ||||||||
\(566\) | 13.0180 | − | 22.5478i | 0.547186 | − | 0.947754i | ||||
\(567\) | 2.11344 | − | 1.59166i | 0.0887559 | − | 0.0668436i | ||||
\(568\) | −3.98568 | + | 6.90340i | −0.167235 | + | 0.289660i | ||||
\(569\) | 9.08664 | − | 15.7385i | 0.380932 | − | 0.659793i | −0.610264 | − | 0.792198i | \(-0.708937\pi\) |
0.991196 | + | 0.132405i | \(0.0422700\pi\) | |||||||
\(570\) | −23.6074 | −0.988806 | ||||||||
\(571\) | −18.3240 | + | 31.7382i | −0.766837 | + | 1.32820i | 0.172433 | + | 0.985021i | \(0.444837\pi\) |
−0.939270 | + | 0.343180i | \(0.888496\pi\) | |||||||
\(572\) | 1.52887 | + | 1.10441i | 0.0639252 | + | 0.0461778i | ||||
\(573\) | 21.9508 | 0.917006 | ||||||||
\(574\) | 9.85874 | − | 7.42478i | 0.411496 | − | 0.309904i | ||||
\(575\) | 44.9283 | + | 77.8181i | 1.87364 | + | 3.24524i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −14.3809 | + | 24.9085i | −0.598686 | + | 1.03695i | 0.394330 | + | 0.918969i | \(0.370977\pi\) |
−0.993015 | + | 0.117985i | \(0.962357\pi\) | |||||||
\(578\) | −5.31700 | − | 9.20931i | −0.221158 | − | 0.383057i | ||||
\(579\) | −12.8592 | −0.534409 | ||||||||
\(580\) | 12.7619 | 0.529911 | ||||||||
\(581\) | 6.51219 | − | 4.90444i | 0.270171 | − | 0.203470i | ||||
\(582\) | −1.31892 | − | 2.28443i | −0.0546709 | − | 0.0946928i | ||||
\(583\) | −0.00100472 | + | 0.00174023i | −4.16113e−5 | + | 7.20729e-5i | ||||
\(584\) | −5.99080 | + | 10.3764i | −0.247901 | + | 0.429377i | ||||
\(585\) | 12.1051 | + | 8.74439i | 0.500484 | + | 0.361536i | ||||
\(586\) | 6.46216 | + | 11.1928i | 0.266949 | + | 0.462370i | ||||
\(587\) | −7.20528 | − | 12.4799i | −0.297394 | − | 0.515101i | 0.678145 | − | 0.734928i | \(-0.262784\pi\) |
−0.975539 | + | 0.219827i | \(0.929451\pi\) | |||||||
\(588\) | 6.79301 | − | 1.68966i | 0.280139 | − | 0.0696805i | ||||
\(589\) | 12.4052 | − | 21.4864i | 0.511147 | − | 0.885333i | ||||
\(590\) | 16.7894 | + | 29.0801i | 0.691208 | + | 1.19721i | ||||
\(591\) | 5.27054 | + | 9.12883i | 0.216801 | + | 0.375510i | ||||
\(592\) | 2.83240 | + | 4.90586i | 0.116411 | + | 0.201629i | ||||
\(593\) | 9.75838 | + | 16.9020i | 0.400729 | + | 0.694083i | 0.993814 | − | 0.111057i | \(-0.0354236\pi\) |
−0.593085 | + | 0.805140i | \(0.702090\pi\) | |||||||
\(594\) | −0.261547 | + | 0.453013i | −0.0107314 | + | 0.0185874i | ||||
\(595\) | −3.36176 | − | 27.4427i | −0.137819 | − | 1.12504i | ||||
\(596\) | −9.06612 | − | 15.7030i | −0.371363 | − | 0.643219i | ||||
\(597\) | 6.55182 | + | 11.3481i | 0.268148 | + | 0.464446i | ||||
\(598\) | 21.6089 | + | 15.6097i | 0.883653 | + | 0.638326i | ||||
\(599\) | 0.837961 | − | 1.45139i | 0.0342382 | − | 0.0593022i | −0.848399 | − | 0.529358i | \(-0.822433\pi\) |
0.882637 | + | 0.470056i | \(0.155766\pi\) | |||||||
\(600\) | −6.07684 | + | 10.5254i | −0.248086 | + | 0.429697i | ||||
\(601\) | −7.12111 | − | 12.3341i | −0.290476 | − | 0.503119i | 0.683446 | − | 0.730001i | \(-0.260480\pi\) |
−0.973922 | + | 0.226882i | \(0.927147\pi\) | |||||||
\(602\) | 23.4518 | + | 9.96242i | 0.955824 | + | 0.406038i | ||||
\(603\) | 3.23244 | 0.131635 | ||||||||
\(604\) | 5.06687 | 0.206168 | ||||||||
\(605\) | 22.2127 | + | 38.4735i | 0.903075 | + | 1.56417i | ||||
\(606\) | 6.09224 | − | 10.5521i | 0.247480 | − | 0.428648i | ||||
\(607\) | −34.3019 | −1.39227 | −0.696135 | − | 0.717911i | \(-0.745099\pi\) | ||||
−0.696135 | + | 0.717911i | \(0.745099\pi\) | |||||||
\(608\) | −2.84997 | − | 4.93629i | −0.115581 | − | 0.200193i | ||||
\(609\) | 7.50346 | + | 3.18750i | 0.304056 | + | 0.129164i | ||||
\(610\) | −24.8998 | −1.00816 | ||||||||
\(611\) | 32.6268 | + | 23.5687i | 1.31994 | + | 0.953486i | ||||
\(612\) | 1.26155 | − | 2.18506i | 0.0509950 | − | 0.0883260i | ||||
\(613\) | −3.65538 | −0.147639 | −0.0738197 | − | 0.997272i | \(-0.523519\pi\) | ||||
−0.0738197 | + | 0.997272i | \(0.523519\pi\) | |||||||
\(614\) | 10.0386 | − | 17.3873i | 0.405123 | − | 0.701694i | ||||
\(615\) | −9.66009 | + | 16.7318i | −0.389532 | + | 0.674690i | ||||
\(616\) | −1.10553 | + | 0.832590i | −0.0445429 | + | 0.0335460i | ||||
\(617\) | 2.31545 | − | 4.01048i | 0.0932167 | − | 0.161456i | −0.815646 | − | 0.578551i | \(-0.803618\pi\) |
0.908863 | + | 0.417095i | \(0.136952\pi\) | |||||||
\(618\) | −13.6306 | −0.548302 | ||||||||
\(619\) | −0.674947 | + | 1.16904i | −0.0271284 | + | 0.0469878i | −0.879271 | − | 0.476322i | \(-0.841970\pi\) |
0.852142 | + | 0.523310i | \(0.175303\pi\) | |||||||
\(620\) | −9.01390 | − | 15.6125i | −0.362007 | − | 0.627014i | ||||
\(621\) | −3.69669 | + | 6.40285i | −0.148343 | + | 0.256937i | ||||
\(622\) | −10.4837 | − | 18.1583i | −0.420358 | − | 0.728081i | ||||
\(623\) | −3.49111 | − | 28.4986i | −0.139868 | − | 1.14177i | ||||
\(624\) | −0.367074 | + | 3.58682i | −0.0146947 | + | 0.143588i | ||||
\(625\) | −30.9717 | − | 53.6446i | −1.23887 | − | 2.14578i | ||||
\(626\) | 19.1122 | 0.763877 | ||||||||
\(627\) | 2.98160 | 0.119074 | ||||||||
\(628\) | −11.6096 | −0.463274 | ||||||||
\(629\) | 14.2928 | 0.569892 | ||||||||
\(630\) | −8.75321 | + | 6.59219i | −0.348736 | + | 0.262639i | ||||
\(631\) | −20.8686 | + | 36.1455i | −0.830766 | + | 1.43893i | 0.0666652 | + | 0.997775i | \(0.478764\pi\) |
−0.897431 | + | 0.441154i | \(0.854569\pi\) | |||||||
\(632\) | −1.15602 | − | 2.00229i | −0.0459840 | − | 0.0796467i | ||||
\(633\) | 0.979430 | + | 1.69642i | 0.0389289 | + | 0.0674267i | ||||
\(634\) | 18.2624 | 0.725294 | ||||||||
\(635\) | −15.8806 | + | 27.5060i | −0.630202 | + | 1.09154i | ||||
\(636\) | −0.00384145 | −0.000152324 | ||||||||
\(637\) | 3.56697 | + | 24.9855i | 0.141328 | + | 0.989963i | ||||
\(638\) | −1.61183 | −0.0638128 | ||||||||
\(639\) | 3.98568 | − | 6.90340i | 0.157671 | − | 0.273094i | ||||
\(640\) | −4.14170 | −0.163715 | ||||||||
\(641\) | 7.90110 | + | 13.6851i | 0.312075 | + | 0.540529i | 0.978811 | − | 0.204764i | \(-0.0656427\pi\) |
−0.666737 | + | 0.745293i | \(0.732309\pi\) | |||||||
\(642\) | −2.69861 | − | 4.67412i | −0.106505 | − | 0.184473i | ||||
\(643\) | 17.7586 | − | 30.7588i | 0.700330 | − | 1.21301i | −0.268021 | − | 0.963413i | \(-0.586370\pi\) |
0.968351 | − | 0.249594i | \(-0.0802971\pi\) | |||||||
\(644\) | −15.6254 | + | 11.7678i | −0.615727 | + | 0.463715i | ||||
\(645\) | −39.8870 | −1.57055 | ||||||||
\(646\) | −14.3815 | −0.565832 | ||||||||
\(647\) | −7.99092 | −0.314156 | −0.157078 | − | 0.987586i | \(-0.550207\pi\) | ||||
−0.157078 | + | 0.987586i | \(0.550207\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −2.12049 | − | 3.67280i | −0.0832366 | − | 0.144170i | ||||
\(650\) | −35.5220 | − | 25.6601i | −1.39329 | − | 1.00647i | ||||
\(651\) | −1.40029 | − | 11.4309i | −0.0548818 | − | 0.448010i | ||||
\(652\) | 9.99637 | + | 17.3142i | 0.391488 | + | 0.678077i | ||||
\(653\) | −21.7485 | + | 37.6696i | −0.851086 | + | 1.47412i | 0.0291423 | + | 0.999575i | \(0.490722\pi\) |
−0.880229 | + | 0.474550i | \(0.842611\pi\) | |||||||
\(654\) | 5.58133 | + | 9.66715i | 0.218247 | + | 0.378015i | ||||
\(655\) | −23.2926 | + | 40.3439i | −0.910116 | + | 1.57637i | ||||
\(656\) | −4.66479 | −0.182130 | ||||||||
\(657\) | 5.99080 | − | 10.3764i | 0.233723 | − | 0.404821i | ||||
\(658\) | −23.5925 | + | 17.7679i | −0.919730 | + | 0.692664i | ||||
\(659\) | 2.30892 | − | 3.99917i | 0.0899429 | − | 0.155786i | −0.817544 | − | 0.575866i | \(-0.804665\pi\) |
0.907487 | + | 0.420081i | \(0.137998\pi\) | |||||||
\(660\) | 1.08325 | − | 1.87624i | 0.0421655 | − | 0.0730327i | ||||
\(661\) | 25.8552 | 1.00565 | 0.502824 | − | 0.864389i | \(-0.332294\pi\) | ||||
0.502824 | + | 0.864389i | \(0.332294\pi\) | |||||||
\(662\) | −5.12199 | + | 8.87155i | −0.199072 | + | 0.344803i | ||||
\(663\) | 7.37434 | + | 5.32702i | 0.286396 | + | 0.206884i | ||||
\(664\) | −3.08133 | −0.119579 | ||||||||
\(665\) | 57.4873 | + | 24.4209i | 2.22926 | + | 0.947000i | ||||
\(666\) | −2.83240 | − | 4.90586i | −0.109753 | − | 0.190098i | ||||
\(667\) | −22.7814 | −0.882100 | ||||||||
\(668\) | −8.82851 | + | 15.2914i | −0.341585 | + | 0.591643i | ||||
\(669\) | −6.26821 | − | 10.8569i | −0.242343 | − | 0.419751i | ||||
\(670\) | −13.3878 | −0.517216 | ||||||||
\(671\) | 3.14483 | 0.121405 | ||||||||
\(672\) | −2.43514 | − | 1.03446i | −0.0939375 | − | 0.0399051i | ||||
\(673\) | 6.36967 | + | 11.0326i | 0.245533 | + | 0.425275i | 0.962281 | − | 0.272056i | \(-0.0877038\pi\) |
−0.716748 | + | 0.697332i | \(0.754370\pi\) | |||||||
\(674\) | −16.3133 | + | 28.2555i | −0.628365 | + | 1.08836i | ||||
\(675\) | 6.07684 | − | 10.5254i | 0.233898 | − | 0.405123i | ||||
\(676\) | −12.7305 | − | 2.63325i | −0.489635 | − | 0.101279i | ||||
\(677\) | 12.1455 | + | 21.0367i | 0.466791 | + | 0.808505i | 0.999280 | − | 0.0379314i | \(-0.0120768\pi\) |
−0.532490 | + | 0.846436i | \(0.678744\pi\) | |||||||
\(678\) | 2.03617 | + | 3.52676i | 0.0781988 | + | 0.135444i | ||||
\(679\) | 0.848599 | + | 6.92727i | 0.0325663 | + | 0.265844i | ||||
\(680\) | −5.22495 | + | 9.04988i | −0.200368 | + | 0.347047i | ||||
\(681\) | −10.8649 | − | 18.8186i | −0.416346 | − | 0.721132i | ||||
\(682\) | 1.13845 | + | 1.97185i | 0.0435935 | + | 0.0755062i | ||||
\(683\) | −4.98049 | − | 8.62645i | −0.190573 | − | 0.330082i | 0.754867 | − | 0.655878i | \(-0.227701\pi\) |
−0.945440 | + | 0.325795i | \(0.894368\pi\) | |||||||
\(684\) | 2.84997 | + | 4.93629i | 0.108971 | + | 0.188744i | ||||
\(685\) | 14.5422 | − | 25.1878i | 0.555627 | − | 0.962375i | ||||
\(686\) | −18.2898 | − | 2.91252i | −0.698308 | − | 0.111201i | ||||
\(687\) | 7.77570 | + | 13.4679i | 0.296662 | + | 0.513833i | ||||
\(688\) | −4.81529 | − | 8.34033i | −0.183581 | − | 0.317972i | ||||
\(689\) | 0.00141010 | − | 0.0137786i | 5.37204e−5 | − | 0.000524923i | ||||
\(690\) | 15.3106 | − | 26.5187i | 0.582863 | − | 1.00955i | ||||
\(691\) | 14.1115 | − | 24.4419i | 0.536827 | − | 0.929812i | −0.462245 | − | 0.886752i | \(-0.652956\pi\) |
0.999072 | − | 0.0430600i | \(-0.0137107\pi\) | |||||||
\(692\) | 1.93492 | + | 3.35139i | 0.0735548 | + | 0.127401i | ||||
\(693\) | 1.10553 | − | 0.832590i | 0.0419955 | − | 0.0316275i | ||||
\(694\) | −8.43192 | −0.320071 | ||||||||
\(695\) | −54.6044 | −2.07126 | ||||||||
\(696\) | −1.54066 | − | 2.66851i | −0.0583987 | − | 0.101150i | ||||
\(697\) | −5.88486 | + | 10.1929i | −0.222905 | + | 0.386083i | ||||
\(698\) | 36.6155 | 1.38592 | ||||||||
\(699\) | −10.3320 | − | 17.8955i | −0.390791 | − | 0.676870i | ||||
\(700\) | 25.6860 | − | 19.3446i | 0.970840 | − | 0.731156i | ||||
\(701\) | −1.33647 | −0.0504778 | −0.0252389 | − | 0.999681i | \(-0.508035\pi\) | ||||
−0.0252389 | + | 0.999681i | \(0.508035\pi\) | |||||||
\(702\) | 0.367074 | − | 3.58682i | 0.0138543 | − | 0.135376i | ||||
\(703\) | −16.1445 | + | 27.9631i | −0.608901 | + | 1.05465i | ||||
\(704\) | 0.523095 | 0.0197149 | ||||||||
\(705\) | 23.1171 | − | 40.0400i | 0.870640 | − | 1.50799i | ||||
\(706\) | −2.61947 | + | 4.53705i | −0.0985850 | + | 0.170754i | ||||
\(707\) | −25.7511 | + | 19.3936i | −0.968470 | + | 0.729371i | ||||
\(708\) | 4.05374 | − | 7.02129i | 0.152349 | − | 0.263876i | ||||
\(709\) | −33.5104 | −1.25851 | −0.629254 | − | 0.777200i | \(-0.716639\pi\) | ||||
−0.629254 | + | 0.777200i | \(0.716639\pi\) | |||||||
\(710\) | −16.5075 | + | 28.5918i | −0.619515 | + | 1.07303i | ||||
\(711\) | 1.15602 | + | 2.00229i | 0.0433542 | + | 0.0750916i | ||||
\(712\) | −5.42599 | + | 9.39808i | −0.203347 | + | 0.352208i | ||||
\(713\) | 16.0908 | + | 27.8700i | 0.602604 | + | 1.04374i | ||||
\(714\) | −5.33240 | + | 4.01592i | −0.199560 | + | 0.150292i | ||||
\(715\) | 6.33211 | + | 4.57414i | 0.236808 | + | 0.171063i | ||||
\(716\) | 1.75984 | + | 3.04813i | 0.0657683 | + | 0.113914i | ||||
\(717\) | 30.0971 | 1.12400 | ||||||||
\(718\) | −5.08012 | −0.189588 | ||||||||
\(719\) | −7.06328 | −0.263416 | −0.131708 | − | 0.991289i | \(-0.542046\pi\) | ||||
−0.131708 | + | 0.991289i | \(0.542046\pi\) | |||||||
\(720\) | 4.14170 | 0.154352 | ||||||||
\(721\) | 33.1924 | + | 14.1003i | 1.23615 | + | 0.525121i | ||||
\(722\) | 6.74463 | − | 11.6820i | 0.251009 | − | 0.434760i | ||||
\(723\) | 1.02609 | + | 1.77725i | 0.0381609 | + | 0.0660965i | ||||
\(724\) | −4.23564 | − | 7.33635i | −0.157416 | − | 0.272653i | ||||
\(725\) | 37.4495 | 1.39084 | ||||||||
\(726\) | 5.36319 | − | 9.28931i | 0.199047 | − | 0.344759i | ||||
\(727\) | −22.2264 | −0.824331 | −0.412166 | − | 0.911109i | \(-0.635228\pi\) | ||||
−0.412166 | + | 0.911109i | \(0.635228\pi\) | |||||||
\(728\) | 4.60428 | − | 8.35467i | 0.170646 | − | 0.309645i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −24.8121 | + | 42.9758i | −0.918337 | + | 1.59061i | ||||
\(731\) | −24.2989 | −0.898726 | ||||||||
\(732\) | 3.00599 | + | 5.20652i | 0.111105 | + | 0.192439i | ||||
\(733\) | 7.77847 | + | 13.4727i | 0.287304 | + | 0.497626i | 0.973165 | − | 0.230107i | \(-0.0739076\pi\) |
−0.685861 | + | 0.727732i | \(0.740574\pi\) | |||||||
\(734\) | 2.43151 | − | 4.21150i | 0.0897487 | − | 0.155449i | ||||
\(735\) | 28.1346 | − | 6.99807i | 1.03776 | − | 0.258128i | ||||
\(736\) | 7.39337 | 0.272523 | ||||||||
\(737\) | 1.69087 | 0.0622841 | ||||||||
\(738\) | 4.66479 | 0.171713 | ||||||||
\(739\) | −6.38799 | −0.234986 | −0.117493 | − | 0.993074i | \(-0.537486\pi\) | ||||
−0.117493 | + | 0.993074i | \(0.537486\pi\) | |||||||
\(740\) | 11.7309 | + | 20.3186i | 0.431238 | + | 0.746926i | ||||
\(741\) | −18.7517 | + | 8.41033i | −0.688861 | + | 0.308961i | ||||
\(742\) | 0.00935447 | + | 0.00397382i | 0.000343413 | + | 0.000145884i | ||||
\(743\) | −5.24875 | − | 9.09109i | −0.192558 | − | 0.333520i | 0.753539 | − | 0.657403i | \(-0.228345\pi\) |
−0.946097 | + | 0.323883i | \(0.895012\pi\) | |||||||
\(744\) | −2.17638 | + | 3.76959i | −0.0797898 | + | 0.138200i | ||||
\(745\) | −37.5491 | − | 65.0370i | −1.37569 | − | 2.38277i | ||||
\(746\) | 14.4061 | − | 24.9521i | 0.527445 | − | 0.913561i | ||||
\(747\) | 3.08133 | 0.112740 | ||||||||
\(748\) | 0.659909 | − | 1.14300i | 0.0241286 | − | 0.0417920i | ||||
\(749\) | 1.73630 | + | 14.1737i | 0.0634430 | + | 0.517897i | ||||
\(750\) | −14.8142 | + | 25.6589i | −0.540938 | + | 0.936932i | ||||
\(751\) | −8.28166 | + | 14.3443i | −0.302202 | + | 0.523430i | −0.976634 | − | 0.214907i | \(-0.931055\pi\) |
0.674432 | + | 0.738337i | \(0.264388\pi\) | |||||||
\(752\) | 11.1631 | 0.407076 | ||||||||
\(753\) | 8.23457 | − | 14.2627i | 0.300084 | − | 0.519761i | ||||
\(754\) | 10.1370 | − | 4.54654i | 0.369168 | − | 0.165575i | ||||
\(755\) | 20.9854 | 0.763739 | ||||||||
\(756\) | 2.43514 | + | 1.03446i | 0.0885651 | + | 0.0376228i | ||||
\(757\) | −13.5475 | − | 23.4649i | −0.492391 | − | 0.852847i | 0.507570 | − | 0.861610i | \(-0.330544\pi\) |
−0.999962 | + | 0.00876370i | \(0.997210\pi\) | |||||||
\(758\) | −28.3100 | −1.02827 | ||||||||
\(759\) | −1.93372 | + | 3.34929i | −0.0701894 | + | 0.121572i | ||||
\(760\) | −11.8037 | − | 20.4446i | −0.428166 | − | 0.741604i | ||||
\(761\) | −2.80358 | −0.101630 | −0.0508148 | − | 0.998708i | \(-0.516182\pi\) | ||||
−0.0508148 | + | 0.998708i | \(0.516182\pi\) | |||||||
\(762\) | 7.66864 | 0.277805 | ||||||||
\(763\) | −3.59106 | − | 29.3145i | −0.130005 | − | 1.06126i | ||||
\(764\) | 10.9754 | + | 19.0099i | 0.397075 | + | 0.687755i | ||||
\(765\) | 5.22495 | − | 9.04988i | 0.188908 | − | 0.327199i | ||||
\(766\) | −9.36815 | + | 16.2261i | −0.338485 | + | 0.586273i | ||||
\(767\) | 23.6961 | + | 17.1174i | 0.855615 | + | 0.618072i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −4.67209 | − | 8.09231i | −0.168480 | − | 0.291816i | 0.769406 | − | 0.638761i | \(-0.220553\pi\) |
−0.937886 | + | 0.346945i | \(0.887219\pi\) | |||||||
\(770\) | −4.57876 | + | 3.44834i | −0.165007 | + | 0.124270i | ||||
\(771\) | 5.93711 | − | 10.2834i | 0.213820 | − | 0.370346i | ||||
\(772\) | −6.42959 | − | 11.1364i | −0.231406 | − | 0.400807i | ||||
\(773\) | −25.2786 | − | 43.7838i | −0.909207 | − | 1.57479i | −0.815168 | − | 0.579225i | \(-0.803355\pi\) |
−0.0940393 | − | 0.995568i | \(-0.529978\pi\) | |||||||
\(774\) | 4.81529 | + | 8.34033i | 0.173082 | + | 0.299787i | ||||
\(775\) | −26.4510 | − | 45.8144i | −0.950147 | − | 1.64570i | ||||
\(776\) | 1.31892 | − | 2.28443i | 0.0473464 | − | 0.0820063i | ||||
\(777\) | 1.82238 | + | 14.8764i | 0.0653776 | + | 0.533689i | ||||
\(778\) | −3.55307 | − | 6.15409i | −0.127384 | − | 0.220635i | ||||
\(779\) | −13.2945 | − | 23.0268i | −0.476325 | − | 0.825020i | ||||
\(780\) | −1.52031 | + | 14.8555i | −0.0544358 | + | 0.531913i | ||||
\(781\) | 2.08489 | − | 3.61113i | 0.0746031 | − | 0.129216i | ||||
\(782\) | 9.32709 | − | 16.1550i | 0.333536 | − | 0.577701i | ||||
\(783\) | 1.54066 | + | 2.66851i | 0.0550589 | + | 0.0953648i | ||||
\(784\) | 4.85980 | + | 5.03809i | 0.173564 | + | 0.179932i | ||||
\(785\) | −48.0836 | −1.71618 | ||||||||
\(786\) | 11.2478 | 0.401197 | ||||||||
\(787\) | −2.77011 | − | 4.79796i | −0.0987436 | − | 0.171029i | 0.812421 | − | 0.583071i | \(-0.198149\pi\) |
−0.911165 | + | 0.412042i | \(0.864816\pi\) | |||||||
\(788\) | −5.27054 | + | 9.12883i | −0.187755 | + | 0.325201i | ||||
\(789\) | −25.0317 | −0.891151 | ||||||||
\(790\) | −4.78789 | − | 8.29287i | −0.170346 | − | 0.295047i | ||||
\(791\) | −1.31009 | − | 10.6945i | −0.0465813 | − | 0.380252i | ||||
\(792\) | −0.523095 | −0.0185874 | ||||||||
\(793\) | −19.7783 | + | 8.87075i | −0.702347 | + | 0.315010i | ||||
\(794\) | 19.6633 | − | 34.0578i | 0.697824 | − | 1.20867i | ||||
\(795\) | −0.0159101 | −0.000564275 | ||||||||
\(796\) | −6.55182 | + | 11.3481i | −0.232223 | + | 0.402222i | ||||
\(797\) | −4.90846 | + | 8.50171i | −0.173867 | + | 0.301146i | −0.939768 | − | 0.341812i | \(-0.888960\pi\) |
0.765902 | + | 0.642958i | \(0.222293\pi\) | |||||||
\(798\) | −1.83369 | − | 14.9687i | −0.0649118 | − | 0.529887i | ||||
\(799\) | 14.0828 | − | 24.3921i | 0.498212 | − | 0.862929i | ||||
\(800\) | −12.1537 | −0.429697 | ||||||||
\(801\) | 5.42599 | − | 9.39808i | 0.191718 | − | 0.332065i | ||||
\(802\) | −4.30153 | − | 7.45048i | −0.151892 | − | 0.263085i | ||||
\(803\) | 3.13376 | − | 5.42782i | 0.110588 | − | 0.191544i | ||||
\(804\) | 1.61622 | + | 2.79938i | 0.0569997 | + | 0.0987264i | ||||
\(805\) | −64.7158 | + | 48.7385i | −2.28093 | + | 1.71781i | ||||
\(806\) | −12.7220 | − | 9.18998i | −0.448112 | − | 0.323703i | ||||
\(807\) | −7.76501 | − | 13.4494i | −0.273341 | − | 0.473441i | ||||
\(808\) | 12.1845 | 0.428648 | ||||||||
\(809\) | −40.7368 | −1.43223 | −0.716114 | − | 0.697983i | \(-0.754081\pi\) | ||||
−0.716114 | + | 0.697983i | \(0.754081\pi\) | |||||||
\(810\) | −4.14170 | −0.145524 | ||||||||
\(811\) | −23.9184 | −0.839887 | −0.419944 | − | 0.907550i | \(-0.637950\pi\) | ||||
−0.419944 | + | 0.907550i | \(0.637950\pi\) | |||||||
\(812\) | 0.991273 | + | 8.09194i | 0.0347869 | + | 0.283971i | ||||
\(813\) | −2.63845 | + | 4.56993i | −0.0925345 | + | 0.160274i | ||||
\(814\) | −1.48161 | − | 2.56623i | −0.0519305 | − | 0.0899462i | ||||
\(815\) | 41.4020 | + | 71.7103i | 1.45025 | + | 2.51190i | ||||
\(816\) | 2.52309 | 0.0883260 | ||||||||
\(817\) | 27.4468 | − | 47.5393i | 0.960243 | − | 1.66319i | ||||
\(818\) | 36.5325 | 1.27733 | ||||||||
\(819\) | −4.60428 | + | 8.35467i | −0.160887 | + | 0.291936i | ||||
\(820\) | −19.3202 | −0.674690 | ||||||||
\(821\) | 10.9625 | − | 18.9876i | 0.382594 | − | 0.662672i | −0.608839 | − | 0.793294i | \(-0.708364\pi\) |
0.991432 | + | 0.130623i | \(0.0416976\pi\) | |||||||
\(822\) | −7.02232 | −0.244931 | ||||||||
\(823\) | 1.29499 | + | 2.24299i | 0.0451404 | + | 0.0781856i | 0.887713 | − | 0.460398i | \(-0.152293\pi\) |
−0.842572 | + | 0.538583i | \(0.818960\pi\) | |||||||
\(824\) | −6.81529 | − | 11.8044i | −0.237422 | − | 0.411227i | ||||
\(825\) | 3.17876 | − | 5.50578i | 0.110670 | − | 0.191686i | ||||
\(826\) | −17.1346 | + | 12.9044i | −0.596191 | + | 0.449001i | ||||
\(827\) | 8.21658 | 0.285718 | 0.142859 | − | 0.989743i | \(-0.454370\pi\) | ||||
0.142859 | + | 0.989743i | \(0.454370\pi\) | |||||||
\(828\) | −7.39337 | −0.256937 | ||||||||
\(829\) | −8.62987 | −0.299728 | −0.149864 | − | 0.988707i | \(-0.547884\pi\) | ||||
−0.149864 | + | 0.988707i | \(0.547884\pi\) | |||||||
\(830\) | −12.7619 | −0.442973 | ||||||||
\(831\) | −5.56594 | − | 9.64049i | −0.193080 | − | 0.334425i | ||||
\(832\) | −3.28981 | + | 1.47551i | −0.114054 | + | 0.0511542i | ||||
\(833\) | 17.1394 | − | 4.26318i | 0.593846 | − | 0.147710i | ||||
\(834\) | 6.59202 | + | 11.4177i | 0.228263 | + | 0.395363i | ||||
\(835\) | −36.5650 | + | 63.3325i | −1.26539 | + | 2.19171i | ||||
\(836\) | 1.49080 | + | 2.58215i | 0.0515605 | + | 0.0893054i | ||||
\(837\) | 2.17638 | − | 3.76959i | 0.0752266 | − | 0.130296i | ||||
\(838\) | 13.5564 | 0.468297 | ||||||||
\(839\) | 0.656067 | − | 1.13634i | 0.0226499 | − | 0.0392309i | −0.854478 | − | 0.519487i | \(-0.826123\pi\) |
0.877128 | + | 0.480256i | \(0.159456\pi\) | |||||||
\(840\) | −10.0856 | − | 4.28441i | −0.347987 | − | 0.147826i | ||||
\(841\) | 9.75270 | − | 16.8922i | 0.336300 | − | 0.582489i | ||||
\(842\) | 2.25104 | − | 3.89892i | 0.0775761 | − | 0.134366i | ||||
\(843\) | −19.3908 | −0.667854 | ||||||||
\(844\) | −0.979430 | + | 1.69642i | −0.0337134 | + | 0.0583933i | ||||
\(845\) | −52.7260 | − | 10.9061i | −1.81383 | − | 0.375183i | ||||
\(846\) | −11.1631 | −0.383795 | ||||||||
\(847\) | −22.6695 | + | 17.0728i | −0.778933 | + | 0.586627i | ||||
\(848\) | −0.00192073 | − | 0.00332680i | −6.59580e−5 | − | 0.000114243i | ||||
\(849\) | −26.0359 | −0.893551 | ||||||||
\(850\) | −15.3324 | + | 26.5566i | −0.525898 | + | 0.910882i | ||||
\(851\) | −20.9410 | − | 36.2708i | −0.717847 | − | 1.24335i | ||||
\(852\) | 7.97136 | 0.273094 | ||||||||
\(853\) | 3.91347 | 0.133995 | 0.0669974 | − | 0.997753i | \(-0.478658\pi\) | ||||
0.0669974 | + | 0.997753i | \(0.478658\pi\) | |||||||
\(854\) | −1.93407 | − | 15.7882i | −0.0661825 | − | 0.540260i | ||||
\(855\) | 11.8037 | + | 20.4446i | 0.403678 | + | 0.699191i | ||||
\(856\) | 2.69861 | − | 4.67412i | 0.0922365 | − | 0.159758i | ||||
\(857\) | −20.7141 | + | 35.8779i | −0.707580 | + | 1.22556i | 0.258172 | + | 0.966099i | \(0.416880\pi\) |
−0.965752 | + | 0.259466i | \(0.916454\pi\) | |||||||
\(858\) | 0.192014 | − | 1.87624i | 0.00655526 | − | 0.0640539i | ||||
\(859\) | −6.13898 | − | 10.6330i | −0.209459 | − | 0.362794i | 0.742085 | − | 0.670306i | \(-0.233837\pi\) |
−0.951544 | + | 0.307511i | \(0.900504\pi\) | |||||||
\(860\) | −19.9435 | − | 34.5431i | −0.680067 | − | 1.17791i | ||||
\(861\) | −11.3594 | − | 4.82553i | −0.387128 | − | 0.164454i | ||||
\(862\) | −0.253853 | + | 0.439686i | −0.00864626 | + | 0.0149758i | ||||
\(863\) | 18.8040 | + | 32.5694i | 0.640095 | + | 1.10868i | 0.985411 | + | 0.170191i | \(0.0544383\pi\) |
−0.345316 | + | 0.938486i | \(0.612228\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 8.01387 | + | 13.8804i | 0.272480 | + | 0.471949i | ||||
\(866\) | 6.41093 | + | 11.1041i | 0.217852 | + | 0.377331i | ||||
\(867\) | −5.31700 | + | 9.20931i | −0.180575 | + | 0.312765i | ||||
\(868\) | 9.19926 | − | 6.92812i | 0.312243 | − | 0.235156i | ||||
\(869\) | 0.604708 | + | 1.04739i | 0.0205133 | + | 0.0355301i | ||||
\(870\) | −6.38097 | − | 11.0522i | −0.216335 | − | 0.374703i | ||||
\(871\) | −10.6341 | + | 4.76951i | −0.360323 | + | 0.161609i | ||||
\(872\) | −5.58133 | + | 9.66715i | −0.189008 | + | 0.327371i | ||||
\(873\) | −1.31892 | + | 2.28443i | −0.0446386 | + | 0.0773163i | ||||
\(874\) | 21.0709 | + | 36.4958i | 0.712733 | + | 1.23449i | ||||
\(875\) | 62.6177 | − | 47.1584i | 2.11686 | − | 1.59424i | ||||
\(876\) | 11.9816 | 0.404821 | ||||||||
\(877\) | −23.1321 | −0.781114 | −0.390557 | − | 0.920579i | \(-0.627718\pi\) | ||||
−0.390557 | + | 0.920579i | \(0.627718\pi\) | |||||||
\(878\) | −0.216640 | − | 0.375232i | −0.00731125 | − | 0.0126635i | ||||
\(879\) | 6.46216 | − | 11.1928i | 0.217963 | − | 0.377523i | ||||
\(880\) | 2.16650 | 0.0730327 | ||||||||
\(881\) | −25.2659 | − | 43.7618i | −0.851229 | − | 1.47437i | −0.880100 | − | 0.474788i | \(-0.842525\pi\) |
0.0288713 | − | 0.999583i | \(-0.490809\pi\) | |||||||
\(882\) | −4.85980 | − | 5.03809i | −0.163638 | − | 0.169641i | ||||
\(883\) | 30.7977 | 1.03643 | 0.518213 | − | 0.855251i | \(-0.326597\pi\) | ||||
0.518213 | + | 0.855251i | \(0.326597\pi\) | |||||||
\(884\) | −0.926162 | + | 9.04988i | −0.0311502 | + | 0.304380i | ||||
\(885\) | 16.7894 | − | 29.0801i | 0.564369 | − | 0.977516i | ||||
\(886\) | −14.0668 | −0.472583 | ||||||||
\(887\) | −10.0158 | + | 17.3479i | −0.336299 | + | 0.582486i | −0.983733 | − | 0.179635i | \(-0.942508\pi\) |
0.647435 | + | 0.762121i | \(0.275842\pi\) | |||||||
\(888\) | 2.83240 | − | 4.90586i | 0.0950490 | − | 0.164630i | ||||
\(889\) | −18.6742 | − | 7.93287i | −0.626312 | − | 0.266060i | ||||
\(890\) | −22.4728 | + | 38.9240i | −0.753290 | + | 1.30474i | ||||
\(891\) | 0.523095 | 0.0175243 | ||||||||
\(892\) | 6.26821 | − | 10.8569i | 0.209875 | − | 0.363515i | ||||
\(893\) | 31.8144 | + | 55.1042i | 1.06463 | + | 1.84399i | ||||
\(894\) | −9.06612 | + | 15.7030i | −0.303216 | + | 0.525186i | ||||
\(895\) | 7.28873 | + | 12.6245i | 0.243635 | + | 0.421989i | ||||
\(896\) | −0.321703 | − | 2.62612i | −0.0107473 | − | 0.0877325i | ||||
\(897\) | 2.71391 | − | 26.5187i | 0.0906149 | − | 0.885433i | ||||
\(898\) | −15.2892 | − | 26.4817i | −0.510207 | − | 0.883705i | ||||
\(899\) | 13.4123 | 0.447324 | ||||||||
\(900\) | 12.1537 | 0.405123 | ||||||||
\(901\) | −0.00969235 | −0.000322899 | ||||||||
\(902\) | 2.44013 | 0.0812474 | ||||||||
\(903\) | −3.09819 | − | 25.2911i | −0.103101 | − | 0.841634i | ||||
\(904\) | −2.03617 | + | 3.52676i | −0.0677221 | + | 0.117298i | ||||
\(905\) | −17.5428 | − | 30.3850i | −0.583141 | − | 1.01003i | ||||
\(906\) | −2.53343 | − | 4.38804i | −0.0841677 | − | 0.145783i | ||||
\(907\) | 15.6640 | 0.520114 | 0.260057 | − | 0.965593i | \(-0.416259\pi\) | ||||
0.260057 | + | 0.965593i | \(0.416259\pi\) | |||||||
\(908\) | 10.8649 | − | 18.8186i | 0.360566 | − | 0.624518i | ||||
\(909\) | −12.1845 | −0.404134 | ||||||||
\(910\) | 19.0696 | − | 34.6025i | 0.632150 | − | 1.14706i | ||||
\(911\) | 6.84991 | 0.226948 | 0.113474 | − | 0.993541i | \(-0.463802\pi\) | ||||
0.113474 | + | 0.993541i | \(0.463802\pi\) | |||||||
\(912\) | −2.84997 | + | 4.93629i | −0.0943718 | + | 0.163457i | ||||
\(913\) | 1.61183 | 0.0533437 | ||||||||
\(914\) | 1.15513 | + | 2.00074i | 0.0382082 | + | 0.0661786i | ||||
\(915\) | 12.4499 | + | 21.5639i | 0.411581 | + | 0.712879i | ||||
\(916\) | −7.77570 | + | 13.4679i | −0.256917 | + | 0.444992i | ||||
\(917\) | −27.3900 | − | 11.6354i | −0.904498 | − | 0.384235i | ||||
\(918\) | −2.52309 | −0.0832745 | ||||||||
\(919\) | 9.54874 | 0.314984 | 0.157492 | − | 0.987520i | \(-0.449659\pi\) | ||||
0.157492 | + | 0.987520i | \(0.449659\pi\) | |||||||
\(920\) | 30.6211 | 1.00955 | ||||||||
\(921\) | −20.0771 | −0.661563 | ||||||||
\(922\) | 15.0409 | + | 26.0516i | 0.495345 | + | 0.857963i | ||||
\(923\) | −2.92608 | + | 28.5918i | −0.0963130 | + | 0.941111i | ||||
\(924\) | 1.27381 | + | 0.541119i | 0.0419052 | + | 0.0178015i | ||||
\(925\) | 34.4240 | + | 59.6242i | 1.13186 | + | 1.96043i | ||||
\(926\) | 14.7363 | − | 25.5241i | 0.484266 | − | 0.838773i | ||||
\(927\) | 6.81529 | + | 11.8044i | 0.223844 | + | 0.387708i | ||||
\(928\) | 1.54066 | − | 2.66851i | 0.0505748 | − | 0.0875981i | ||||
\(929\) | −39.8657 | −1.30795 | −0.653975 | − | 0.756516i | \(-0.726900\pi\) | ||||
−0.653975 | + | 0.756516i | \(0.726900\pi\) | |||||||
\(930\) | −9.01390 | + | 15.6125i | −0.295577 | + | 0.511955i | ||||
\(931\) | −11.0192 | + | 38.3478i | −0.361140 | + | 1.25680i | ||||
\(932\) | 10.3320 | − | 17.8955i | 0.338435 | − | 0.586187i | ||||
\(933\) | −10.4837 | + | 18.1583i | −0.343221 | + | 0.594475i | ||||
\(934\) | 5.84884 | 0.191380 | ||||||||
\(935\) | 2.73314 | − | 4.73394i | 0.0893833 | − | 0.154816i | ||||
\(936\) | 3.28981 | − | 1.47551i | 0.107531 | − | 0.0482287i | ||||
\(937\) | −11.4259 | −0.373268 | −0.186634 | − | 0.982430i | \(-0.559758\pi\) | ||||
−0.186634 | + | 0.982430i | \(0.559758\pi\) | |||||||
\(938\) | −1.03989 | − | 8.48878i | −0.0339535 | − | 0.277168i | ||||
\(939\) | −9.55610 | − | 16.5517i | −0.311852 | − | 0.540143i | ||||
\(940\) | 46.2342 | 1.50799 | ||||||||
\(941\) | 19.0547 | − | 33.0037i | 0.621165 | − | 1.07589i | −0.368105 | − | 0.929784i | \(-0.619993\pi\) |
0.989269 | − | 0.146104i | \(-0.0466735\pi\) | |||||||
\(942\) | 5.80481 | + | 10.0542i | 0.189131 | + | 0.327584i | ||||
\(943\) | 34.4886 | 1.12310 | ||||||||
\(944\) | 8.10749 | 0.263876 | ||||||||
\(945\) | 10.0856 | + | 4.28441i | 0.328085 | + | 0.139372i | ||||
\(946\) | 2.51885 | + | 4.36278i | 0.0818950 | + | 0.141846i | ||||
\(947\) | 4.04628 | − | 7.00835i | 0.131486 | − | 0.227741i | −0.792763 | − | 0.609529i | \(-0.791358\pi\) |
0.924250 | + | 0.381789i | \(0.124692\pi\) | |||||||
\(948\) | −1.15602 | + | 2.00229i | −0.0375458 | + | 0.0650313i | ||||
\(949\) | −4.39813 | + | 42.9758i | −0.142769 | + | 1.39505i | ||||
\(950\) | −34.6376 | − | 59.9940i | −1.12379 | − | 1.94646i | ||||
\(951\) | −9.13122 | − | 15.8157i | −0.296100 | − | 0.512860i | ||||
\(952\) | −6.14408 | − | 2.61003i | −0.199131 | − | 0.0845917i | ||||
\(953\) | −2.17357 | + | 3.76473i | −0.0704088 | + | 0.121952i | −0.899081 | − | 0.437783i | \(-0.855764\pi\) |
0.828672 | + | 0.559735i | \(0.189097\pi\) | |||||||
\(954\) | 0.00192073 | + | 0.00332680i | 6.21858e−5 | + | 0.000107709i | ||||
\(955\) | 45.4567 | + | 78.7334i | 1.47094 | + | 2.54775i | ||||
\(956\) | 15.0486 | + | 26.0649i | 0.486705 | + | 0.842998i | ||||
\(957\) | 0.805913 | + | 1.39588i | 0.0260515 | + | 0.0451225i | ||||
\(958\) | 8.66374 | − | 15.0060i | 0.279913 | − | 0.484823i | ||||
\(959\) | 17.1003 | + | 7.26428i | 0.552198 | + | 0.234576i | ||||
\(960\) | 2.07085 | + | 3.58682i | 0.0668364 | + | 0.115764i | ||||
\(961\) | 6.02677 | + | 10.4387i | 0.194412 | + | 0.336731i | ||||
\(962\) | 16.5567 | + | 11.9601i | 0.533810 | + | 0.385609i | ||||
\(963\) | −2.69861 | + | 4.67412i | −0.0869614 | + | 0.150622i | ||||
\(964\) | −1.02609 | + | 1.77725i | −0.0330483 | + | 0.0572413i | ||||
\(965\) | −26.6294 | − | 46.1235i | −0.857232 | − | 1.48477i | ||||
\(966\) | 18.0039 | + | 7.64813i | 0.579265 | + | 0.246074i | ||||
\(967\) | −6.10945 | −0.196467 | −0.0982333 | − | 0.995163i | \(-0.531319\pi\) | ||||
−0.0982333 | + | 0.995163i | \(0.531319\pi\) | |||||||
\(968\) | 10.7264 | 0.344759 | ||||||||
\(969\) | 7.19074 | + | 12.4547i | 0.231000 | + | 0.400103i | ||||
\(970\) | 5.46256 | − | 9.46143i | 0.175392 | − | 0.303788i | ||||
\(971\) | 7.04259 | 0.226007 | 0.113004 | − | 0.993595i | \(-0.463953\pi\) | ||||
0.113004 | + | 0.993595i | \(0.463953\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | −4.24135 | − | 34.6229i | −0.135971 | − | 1.10996i | ||||
\(974\) | 38.0645 | 1.21967 | ||||||||
\(975\) | −4.46130 | + | 43.5930i | −0.142876 | + | 1.39609i | ||||
\(976\) | −3.00599 | + | 5.20652i | −0.0962193 | + | 0.166657i | ||||
\(977\) | 30.9306 | 0.989557 | 0.494779 | − | 0.869019i | \(-0.335249\pi\) | ||||
0.494779 | + | 0.869019i | \(0.335249\pi\) | |||||||
\(978\) | 9.99637 | − | 17.3142i | 0.319649 | − | 0.553648i | ||||
\(979\) | 2.83830 | − | 4.91609i | 0.0907126 | − | 0.157119i | ||||
\(980\) | 20.1278 | + | 20.8663i | 0.642960 | + | 0.666548i | ||||
\(981\) | 5.58133 | − | 9.66715i | 0.178198 | − | 0.308648i | ||||
\(982\) | −16.4426 | −0.524704 | ||||||||
\(983\) | 14.5237 | − | 25.1559i | 0.463235 | − | 0.802347i | −0.535885 | − | 0.844291i | \(-0.680022\pi\) |
0.999120 | + | 0.0419441i | \(0.0133551\pi\) | |||||||
\(984\) | 2.33240 | + | 4.03983i | 0.0743541 | + | 0.128785i | ||||
\(985\) | −21.8290 | + | 37.8089i | −0.695529 | + | 1.20469i | ||||
\(986\) | −3.88724 | − | 6.73290i | −0.123795 | − | 0.214419i | ||||
\(987\) | 27.1837 | + | 11.5477i | 0.865266 | + | 0.367568i | ||||
\(988\) | −16.6594 | − | 12.0343i | −0.530007 | − | 0.382862i | ||||
\(989\) | 35.6012 | + | 61.6631i | 1.13205 | + | 1.96077i | ||||
\(990\) | −2.16650 | −0.0688559 | ||||||||
\(991\) | −13.9391 | −0.442790 | −0.221395 | − | 0.975184i | \(-0.571061\pi\) | ||||
−0.221395 | + | 0.975184i | \(0.571061\pi\) | |||||||
\(992\) | −4.35275 | −0.138200 | ||||||||
\(993\) | 10.2440 | 0.325083 | ||||||||
\(994\) | −19.4114 | − | 8.24603i | −0.615691 | − | 0.261548i | ||||
\(995\) | −27.1357 | + | 47.0004i | −0.860259 | + | 1.49001i | ||||
\(996\) | 1.54066 | + | 2.66851i | 0.0488178 | + | 0.0845550i | ||||
\(997\) | 18.4125 | + | 31.8914i | 0.583129 | + | 1.01001i | 0.995106 | + | 0.0988150i | \(0.0315052\pi\) |
−0.411977 | + | 0.911194i | \(0.635161\pi\) | |||||||
\(998\) | −7.48597 | −0.236964 | ||||||||
\(999\) | −2.83240 | + | 4.90586i | −0.0896131 | + | 0.155214i |
(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 | 546.2.k.e.445.1 | yes | 10 | |
3.2 | odd | 2 | 1638.2.p.j.991.5 | 10 | |||
7.2 | even | 3 | 546.2.j.e.289.1 | ✓ | 10 | ||
13.9 | even | 3 | 546.2.j.e.529.1 | yes | 10 | ||
21.2 | odd | 6 | 1638.2.m.k.289.5 | 10 | |||
39.35 | odd | 6 | 1638.2.m.k.1621.5 | 10 | |||
91.9 | even | 3 | inner | 546.2.k.e.373.1 | yes | 10 | |
273.191 | odd | 6 | 1638.2.p.j.919.5 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.j.e.289.1 | ✓ | 10 | 7.2 | even | 3 | ||
546.2.j.e.529.1 | yes | 10 | 13.9 | even | 3 | ||
546.2.k.e.373.1 | yes | 10 | 91.9 | even | 3 | inner | |
546.2.k.e.445.1 | yes | 10 | 1.1 | even | 1 | trivial | |
1638.2.m.k.289.5 | 10 | 21.2 | odd | 6 | |||
1638.2.m.k.1621.5 | 10 | 39.35 | odd | 6 | |||
1638.2.p.j.919.5 | 10 | 273.191 | odd | 6 | |||
1638.2.p.j.991.5 | 10 | 3.2 | odd | 2 |