Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,2,Mod(67,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.e (of order \(3\), degree \(2\), not 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: | \(1.17380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 147.67 |
Dual form | 147.2.e.e.79.1 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.207107 | − | 0.358719i | −0.146447 | − | 0.253653i | 0.783465 | − | 0.621436i | \(-0.213450\pi\) |
−0.929912 | + | 0.367783i | \(0.880117\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0.914214 | − | 1.58346i | 0.457107 | − | 0.791732i | ||||
\(5\) | 1.70711 | + | 2.95680i | 0.763441 | + | 1.32232i | 0.941067 | + | 0.338221i | \(0.109825\pi\) |
−0.177625 | + | 0.984098i | \(0.556842\pi\) | |||||||
\(6\) | −0.414214 | −0.169102 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.707107 | − | 1.22474i | 0.223607 | − | 0.387298i | ||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | −0.914214 | − | 1.58346i | −0.263911 | − | 0.457107i | ||||
\(13\) | −2.58579 | −0.717168 | −0.358584 | − | 0.933497i | \(-0.616740\pi\) | ||||
−0.358584 | + | 0.933497i | \(0.616740\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.41421 | 0.881546 | ||||||||
\(16\) | −1.50000 | − | 2.59808i | −0.375000 | − | 0.649519i | ||||
\(17\) | −1.12132 | + | 1.94218i | −0.271960 | + | 0.471049i | −0.969364 | − | 0.245630i | \(-0.921005\pi\) |
0.697404 | + | 0.716679i | \(0.254339\pi\) | |||||||
\(18\) | −0.207107 | + | 0.358719i | −0.0488155 | + | 0.0845510i | ||||
\(19\) | −1.41421 | − | 2.44949i | −0.324443 | − | 0.561951i | 0.656957 | − | 0.753928i | \(-0.271843\pi\) |
−0.981399 | + | 0.191977i | \(0.938510\pi\) | |||||||
\(20\) | 6.24264 | 1.39590 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.828427 | −0.176621 | ||||||||
\(23\) | 3.82843 | + | 6.63103i | 0.798282 | + | 1.38267i | 0.920734 | + | 0.390191i | \(0.127591\pi\) |
−0.122452 | + | 0.992474i | \(0.539076\pi\) | |||||||
\(24\) | −0.792893 | + | 1.37333i | −0.161849 | + | 0.280330i | ||||
\(25\) | −3.32843 | + | 5.76500i | −0.665685 | + | 1.15300i | ||||
\(26\) | 0.535534 | + | 0.927572i | 0.105027 | + | 0.181912i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.82843 | −1.26801 | −0.634004 | − | 0.773330i | \(-0.718590\pi\) | ||||
−0.634004 | + | 0.773330i | \(0.718590\pi\) | |||||||
\(30\) | −0.707107 | − | 1.22474i | −0.129099 | − | 0.223607i | ||||
\(31\) | −0.585786 | + | 1.01461i | −0.105210 | + | 0.182230i | −0.913824 | − | 0.406110i | \(-0.866885\pi\) |
0.808614 | + | 0.588340i | \(0.200218\pi\) | |||||||
\(32\) | −2.20711 | + | 3.82282i | −0.390165 | + | 0.675786i | ||||
\(33\) | −1.00000 | − | 1.73205i | −0.174078 | − | 0.301511i | ||||
\(34\) | 0.928932 | 0.159311 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.82843 | −0.304738 | ||||||||
\(37\) | 2.00000 | + | 3.46410i | 0.328798 | + | 0.569495i | 0.982274 | − | 0.187453i | \(-0.0600231\pi\) |
−0.653476 | + | 0.756948i | \(0.726690\pi\) | |||||||
\(38\) | −0.585786 | + | 1.01461i | −0.0950271 | + | 0.164592i | ||||
\(39\) | −1.29289 | + | 2.23936i | −0.207029 | + | 0.358584i | ||||
\(40\) | −2.70711 | − | 4.68885i | −0.428031 | − | 0.741372i | ||||
\(41\) | −6.24264 | −0.974937 | −0.487468 | − | 0.873141i | \(-0.662080\pi\) | ||||
−0.487468 | + | 0.873141i | \(0.662080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.65685 | 0.862662 | 0.431331 | − | 0.902194i | \(-0.358044\pi\) | ||||
0.431331 | + | 0.902194i | \(0.358044\pi\) | |||||||
\(44\) | −1.82843 | − | 3.16693i | −0.275646 | − | 0.477432i | ||||
\(45\) | 1.70711 | − | 2.95680i | 0.254480 | − | 0.440773i | ||||
\(46\) | 1.58579 | − | 2.74666i | 0.233811 | − | 0.404973i | ||||
\(47\) | −1.41421 | − | 2.44949i | −0.206284 | − | 0.357295i | 0.744257 | − | 0.667893i | \(-0.232804\pi\) |
−0.950541 | + | 0.310599i | \(0.899470\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.75736 | 0.389949 | ||||||||
\(51\) | 1.12132 | + | 1.94218i | 0.157016 | + | 0.271960i | ||||
\(52\) | −2.36396 | + | 4.09450i | −0.327822 | + | 0.567805i | ||||
\(53\) | 1.00000 | − | 1.73205i | 0.137361 | − | 0.237915i | −0.789136 | − | 0.614218i | \(-0.789471\pi\) |
0.926497 | + | 0.376303i | \(0.122805\pi\) | |||||||
\(54\) | 0.207107 | + | 0.358719i | 0.0281837 | + | 0.0488155i | ||||
\(55\) | 6.82843 | 0.920745 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 1.41421 | + | 2.44949i | 0.185695 | + | 0.321634i | ||||
\(59\) | −0.585786 | + | 1.01461i | −0.0762629 | + | 0.132091i | −0.901635 | − | 0.432498i | \(-0.857632\pi\) |
0.825372 | + | 0.564589i | \(0.190965\pi\) | |||||||
\(60\) | 3.12132 | − | 5.40629i | 0.402961 | − | 0.697948i | ||||
\(61\) | 6.12132 | + | 10.6024i | 0.783755 | + | 1.35750i | 0.929740 | + | 0.368216i | \(0.120031\pi\) |
−0.145985 | + | 0.989287i | \(0.546635\pi\) | |||||||
\(62\) | 0.485281 | 0.0616308 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −4.41421 | − | 7.64564i | −0.547516 | − | 0.948325i | ||||
\(66\) | −0.414214 | + | 0.717439i | −0.0509862 | + | 0.0883106i | ||||
\(67\) | 2.82843 | − | 4.89898i | 0.345547 | − | 0.598506i | −0.639906 | − | 0.768453i | \(-0.721027\pi\) |
0.985453 | + | 0.169948i | \(0.0543599\pi\) | |||||||
\(68\) | 2.05025 | + | 3.55114i | 0.248630 | + | 0.430639i | ||||
\(69\) | 7.65685 | 0.921777 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.31371 | 1.10533 | 0.552667 | − | 0.833402i | \(-0.313610\pi\) | ||||
0.552667 | + | 0.833402i | \(0.313610\pi\) | |||||||
\(72\) | 0.792893 | + | 1.37333i | 0.0934434 | + | 0.161849i | ||||
\(73\) | 6.94975 | − | 12.0373i | 0.813406 | − | 1.40886i | −0.0970601 | − | 0.995279i | \(-0.530944\pi\) |
0.910467 | − | 0.413583i | \(-0.135723\pi\) | |||||||
\(74\) | 0.828427 | − | 1.43488i | 0.0963027 | − | 0.166801i | ||||
\(75\) | 3.32843 | + | 5.76500i | 0.384334 | + | 0.665685i | ||||
\(76\) | −5.17157 | −0.593220 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.07107 | 0.121275 | ||||||||
\(79\) | −6.82843 | − | 11.8272i | −0.768258 | − | 1.33066i | −0.938507 | − | 0.345261i | \(-0.887790\pi\) |
0.170249 | − | 0.985401i | \(-0.445543\pi\) | |||||||
\(80\) | 5.12132 | − | 8.87039i | 0.572581 | − | 0.991739i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.29289 | + | 2.23936i | 0.142776 | + | 0.247296i | ||||
\(83\) | −7.31371 | −0.802784 | −0.401392 | − | 0.915906i | \(-0.631473\pi\) | ||||
−0.401392 | + | 0.915906i | \(0.631473\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | −1.17157 | − | 2.02922i | −0.126334 | − | 0.218817i | ||||
\(87\) | −3.41421 | + | 5.91359i | −0.366042 | + | 0.634004i | ||||
\(88\) | −1.58579 | + | 2.74666i | −0.169045 | + | 0.292795i | ||||
\(89\) | −7.12132 | − | 12.3345i | −0.754858 | − | 1.30745i | −0.945445 | − | 0.325783i | \(-0.894372\pi\) |
0.190586 | − | 0.981670i | \(-0.438961\pi\) | |||||||
\(90\) | −1.41421 | −0.149071 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 14.0000 | 1.45960 | ||||||||
\(93\) | 0.585786 | + | 1.01461i | 0.0607432 | + | 0.105210i | ||||
\(94\) | −0.585786 | + | 1.01461i | −0.0604193 | + | 0.104649i | ||||
\(95\) | 4.82843 | − | 8.36308i | 0.495386 | − | 0.858034i | ||||
\(96\) | 2.20711 | + | 3.82282i | 0.225262 | + | 0.390165i | ||||
\(97\) | −2.58579 | −0.262547 | −0.131273 | − | 0.991346i | \(-0.541907\pi\) | ||||
−0.131273 | + | 0.991346i | \(0.541907\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.00000 | −0.201008 | ||||||||
\(100\) | 6.08579 | + | 10.5409i | 0.608579 | + | 1.05409i | ||||
\(101\) | 1.46447 | − | 2.53653i | 0.145720 | − | 0.252394i | −0.783921 | − | 0.620860i | \(-0.786784\pi\) |
0.929641 | + | 0.368466i | \(0.120117\pi\) | |||||||
\(102\) | 0.464466 | − | 0.804479i | 0.0459890 | − | 0.0796553i | ||||
\(103\) | 2.24264 | + | 3.88437i | 0.220974 | + | 0.382738i | 0.955104 | − | 0.296271i | \(-0.0957431\pi\) |
−0.734130 | + | 0.679009i | \(0.762410\pi\) | |||||||
\(104\) | 4.10051 | 0.402088 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.828427 | −0.0804640 | ||||||||
\(107\) | 0.171573 | + | 0.297173i | 0.0165866 | + | 0.0287288i | 0.874200 | − | 0.485567i | \(-0.161387\pi\) |
−0.857613 | + | 0.514296i | \(0.828053\pi\) | |||||||
\(108\) | −0.914214 | + | 1.58346i | −0.0879702 | + | 0.152369i | ||||
\(109\) | 2.82843 | − | 4.89898i | 0.270914 | − | 0.469237i | −0.698182 | − | 0.715920i | \(-0.746007\pi\) |
0.969096 | + | 0.246683i | \(0.0793407\pi\) | |||||||
\(110\) | −1.41421 | − | 2.44949i | −0.134840 | − | 0.233550i | ||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.31371 | −0.499872 | −0.249936 | − | 0.968262i | \(-0.580410\pi\) | ||||
−0.249936 | + | 0.968262i | \(0.580410\pi\) | |||||||
\(114\) | 0.585786 | + | 1.01461i | 0.0548639 | + | 0.0950271i | ||||
\(115\) | −13.0711 | + | 22.6398i | −1.21888 | + | 2.11117i | ||||
\(116\) | −6.24264 | + | 10.8126i | −0.579615 | + | 1.00392i | ||||
\(117\) | 1.29289 | + | 2.23936i | 0.119528 | + | 0.207029i | ||||
\(118\) | 0.485281 | 0.0446738 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −5.41421 | −0.494248 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 2.53553 | − | 4.39167i | 0.229556 | − | 0.397603i | ||||
\(123\) | −3.12132 | + | 5.40629i | −0.281440 | + | 0.487468i | ||||
\(124\) | 1.07107 | + | 1.85514i | 0.0961847 | + | 0.166597i | ||||
\(125\) | −5.65685 | −0.505964 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.65685 | −0.147022 | −0.0735110 | − | 0.997294i | \(-0.523420\pi\) | ||||
−0.0735110 | + | 0.997294i | \(0.523420\pi\) | |||||||
\(128\) | 5.27817 | + | 9.14207i | 0.466529 | + | 0.808052i | ||||
\(129\) | 2.82843 | − | 4.89898i | 0.249029 | − | 0.431331i | ||||
\(130\) | −1.82843 | + | 3.16693i | −0.160364 | + | 0.277758i | ||||
\(131\) | −7.65685 | − | 13.2621i | −0.668982 | − | 1.15871i | −0.978189 | − | 0.207717i | \(-0.933397\pi\) |
0.309207 | − | 0.950995i | \(-0.399937\pi\) | |||||||
\(132\) | −3.65685 | −0.318288 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.34315 | −0.202417 | ||||||||
\(135\) | −1.70711 | − | 2.95680i | −0.146924 | − | 0.254480i | ||||
\(136\) | 1.77817 | − | 3.07989i | 0.152477 | − | 0.264098i | ||||
\(137\) | −7.07107 | + | 12.2474i | −0.604122 | + | 1.04637i | 0.388067 | + | 0.921631i | \(0.373143\pi\) |
−0.992190 | + | 0.124739i | \(0.960191\pi\) | |||||||
\(138\) | −1.58579 | − | 2.74666i | −0.134991 | − | 0.233811i | ||||
\(139\) | 17.6569 | 1.49763 | 0.748817 | − | 0.662776i | \(-0.230622\pi\) | ||||
0.748817 | + | 0.662776i | \(0.230622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.82843 | −0.238197 | ||||||||
\(142\) | −1.92893 | − | 3.34101i | −0.161872 | − | 0.280371i | ||||
\(143\) | −2.58579 | + | 4.47871i | −0.216234 | + | 0.374529i | ||||
\(144\) | −1.50000 | + | 2.59808i | −0.125000 | + | 0.216506i | ||||
\(145\) | −11.6569 | − | 20.1903i | −0.968049 | − | 1.67671i | ||||
\(146\) | −5.75736 | −0.476482 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.31371 | 0.601183 | ||||||||
\(149\) | −8.65685 | − | 14.9941i | −0.709197 | − | 1.22837i | −0.965155 | − | 0.261678i | \(-0.915724\pi\) |
0.255958 | − | 0.966688i | \(-0.417609\pi\) | |||||||
\(150\) | 1.37868 | − | 2.38794i | 0.112569 | − | 0.194975i | ||||
\(151\) | −6.00000 | + | 10.3923i | −0.488273 | + | 0.845714i | −0.999909 | − | 0.0134886i | \(-0.995706\pi\) |
0.511636 | + | 0.859202i | \(0.329040\pi\) | |||||||
\(152\) | 2.24264 | + | 3.88437i | 0.181902 | + | 0.315064i | ||||
\(153\) | 2.24264 | 0.181307 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 2.36396 | + | 4.09450i | 0.189268 | + | 0.327822i | ||||
\(157\) | 5.87868 | − | 10.1822i | 0.469170 | − | 0.812626i | −0.530209 | − | 0.847867i | \(-0.677887\pi\) |
0.999379 | + | 0.0352411i | \(0.0112199\pi\) | |||||||
\(158\) | −2.82843 | + | 4.89898i | −0.225018 | + | 0.389742i | ||||
\(159\) | −1.00000 | − | 1.73205i | −0.0793052 | − | 0.137361i | ||||
\(160\) | −15.0711 | −1.19147 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.414214 | 0.0325437 | ||||||||
\(163\) | 5.65685 | + | 9.79796i | 0.443079 | + | 0.767435i | 0.997916 | − | 0.0645236i | \(-0.0205528\pi\) |
−0.554837 | + | 0.831959i | \(0.687219\pi\) | |||||||
\(164\) | −5.70711 | + | 9.88500i | −0.445650 | + | 0.771889i | ||||
\(165\) | 3.41421 | − | 5.91359i | 0.265796 | − | 0.460372i | ||||
\(166\) | 1.51472 | + | 2.62357i | 0.117565 | + | 0.203628i | ||||
\(167\) | 19.7990 | 1.53209 | 0.766046 | − | 0.642786i | \(-0.222221\pi\) | ||||
0.766046 | + | 0.642786i | \(0.222221\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31371 | −0.485670 | ||||||||
\(170\) | 1.58579 | + | 2.74666i | 0.121624 | + | 0.210659i | ||||
\(171\) | −1.41421 | + | 2.44949i | −0.108148 | + | 0.187317i | ||||
\(172\) | 5.17157 | − | 8.95743i | 0.394329 | − | 0.682997i | ||||
\(173\) | 10.5355 | + | 18.2481i | 0.801002 | + | 1.38738i | 0.918957 | + | 0.394357i | \(0.129033\pi\) |
−0.117956 | + | 0.993019i | \(0.537634\pi\) | |||||||
\(174\) | 2.82843 | 0.214423 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | 0.585786 | + | 1.01461i | 0.0440304 | + | 0.0762629i | ||||
\(178\) | −2.94975 | + | 5.10911i | −0.221093 | + | 0.382944i | ||||
\(179\) | 9.82843 | − | 17.0233i | 0.734611 | − | 1.27238i | −0.220283 | − | 0.975436i | \(-0.570698\pi\) |
0.954894 | − | 0.296948i | \(-0.0959687\pi\) | |||||||
\(180\) | −3.12132 | − | 5.40629i | −0.232649 | − | 0.402961i | ||||
\(181\) | 2.58579 | 0.192200 | 0.0961000 | − | 0.995372i | \(-0.469363\pi\) | ||||
0.0961000 | + | 0.995372i | \(0.469363\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 12.2426 | 0.905002 | ||||||||
\(184\) | −6.07107 | − | 10.5154i | −0.447565 | − | 0.775205i | ||||
\(185\) | −6.82843 | + | 11.8272i | −0.502036 | + | 0.869552i | ||||
\(186\) | 0.242641 | − | 0.420266i | 0.0177913 | − | 0.0308154i | ||||
\(187\) | 2.24264 | + | 3.88437i | 0.163998 | + | 0.284053i | ||||
\(188\) | −5.17157 | −0.377176 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.00000 | −0.290191 | ||||||||
\(191\) | 9.00000 | + | 15.5885i | 0.651217 | + | 1.12794i | 0.982828 | + | 0.184525i | \(0.0590746\pi\) |
−0.331611 | + | 0.943416i | \(0.607592\pi\) | |||||||
\(192\) | −2.08579 | + | 3.61269i | −0.150529 | + | 0.260723i | ||||
\(193\) | −2.65685 | + | 4.60181i | −0.191245 | + | 0.331245i | −0.945663 | − | 0.325149i | \(-0.894586\pi\) |
0.754418 | + | 0.656394i | \(0.227919\pi\) | |||||||
\(194\) | 0.535534 | + | 0.927572i | 0.0384491 | + | 0.0665958i | ||||
\(195\) | −8.82843 | −0.632217 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0.414214 | + | 0.717439i | 0.0294369 | + | 0.0509862i | ||||
\(199\) | 10.8284 | − | 18.7554i | 0.767607 | − | 1.32953i | −0.171250 | − | 0.985228i | \(-0.554781\pi\) |
0.938857 | − | 0.344307i | \(-0.111886\pi\) | |||||||
\(200\) | 5.27817 | − | 9.14207i | 0.373223 | − | 0.646442i | ||||
\(201\) | −2.82843 | − | 4.89898i | −0.199502 | − | 0.345547i | ||||
\(202\) | −1.21320 | −0.0853607 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.10051 | 0.287093 | ||||||||
\(205\) | −10.6569 | − | 18.4582i | −0.744307 | − | 1.28918i | ||||
\(206\) | 0.928932 | − | 1.60896i | 0.0647218 | − | 0.112101i | ||||
\(207\) | 3.82843 | − | 6.63103i | 0.266094 | − | 0.460888i | ||||
\(208\) | 3.87868 | + | 6.71807i | 0.268938 | + | 0.465814i | ||||
\(209\) | −5.65685 | −0.391293 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.9706 | 0.892930 | 0.446465 | − | 0.894801i | \(-0.352683\pi\) | ||||
0.446465 | + | 0.894801i | \(0.352683\pi\) | |||||||
\(212\) | −1.82843 | − | 3.16693i | −0.125577 | − | 0.217506i | ||||
\(213\) | 4.65685 | − | 8.06591i | 0.319082 | − | 0.552667i | ||||
\(214\) | 0.0710678 | − | 0.123093i | 0.00485810 | − | 0.00841447i | ||||
\(215\) | 9.65685 | + | 16.7262i | 0.658592 | + | 1.14071i | ||||
\(216\) | 1.58579 | 0.107899 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.34315 | −0.158698 | ||||||||
\(219\) | −6.94975 | − | 12.0373i | −0.469620 | − | 0.813406i | ||||
\(220\) | 6.24264 | − | 10.8126i | 0.420879 | − | 0.728983i | ||||
\(221\) | 2.89949 | − | 5.02207i | 0.195041 | − | 0.337821i | ||||
\(222\) | −0.828427 | − | 1.43488i | −0.0556004 | − | 0.0963027i | ||||
\(223\) | −24.9706 | −1.67215 | −0.836076 | − | 0.548613i | \(-0.815156\pi\) | ||||
−0.836076 | + | 0.548613i | \(0.815156\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.65685 | 0.443790 | ||||||||
\(226\) | 1.10051 | + | 1.90613i | 0.0732045 | + | 0.126794i | ||||
\(227\) | 11.8995 | − | 20.6105i | 0.789797 | − | 1.36797i | −0.136294 | − | 0.990668i | \(-0.543519\pi\) |
0.926091 | − | 0.377300i | \(-0.123148\pi\) | |||||||
\(228\) | −2.58579 | + | 4.47871i | −0.171248 | + | 0.296610i | ||||
\(229\) | −0.121320 | − | 0.210133i | −0.00801707 | − | 0.0138860i | 0.861989 | − | 0.506927i | \(-0.169219\pi\) |
−0.870006 | + | 0.493041i | \(0.835885\pi\) | |||||||
\(230\) | 10.8284 | 0.714005 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.8284 | 0.710921 | ||||||||
\(233\) | 3.07107 | + | 5.31925i | 0.201192 | + | 0.348475i | 0.948913 | − | 0.315538i | \(-0.102185\pi\) |
−0.747721 | + | 0.664014i | \(0.768852\pi\) | |||||||
\(234\) | 0.535534 | − | 0.927572i | 0.0350089 | − | 0.0606373i | ||||
\(235\) | 4.82843 | − | 8.36308i | 0.314972 | − | 0.545547i | ||||
\(236\) | 1.07107 | + | 1.85514i | 0.0697206 | + | 0.120760i | ||||
\(237\) | −13.6569 | −0.887108 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −15.6569 | −1.01276 | −0.506379 | − | 0.862311i | \(-0.669016\pi\) | ||||
−0.506379 | + | 0.862311i | \(0.669016\pi\) | |||||||
\(240\) | −5.12132 | − | 8.87039i | −0.330580 | − | 0.572581i | ||||
\(241\) | −8.12132 | + | 14.0665i | −0.523140 | + | 0.906105i | 0.476497 | + | 0.879176i | \(0.341906\pi\) |
−0.999637 | + | 0.0269294i | \(0.991427\pi\) | |||||||
\(242\) | 1.44975 | − | 2.51104i | 0.0931933 | − | 0.161416i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 22.3848 | 1.43304 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.58579 | 0.164864 | ||||||||
\(247\) | 3.65685 | + | 6.33386i | 0.232680 | + | 0.403014i | ||||
\(248\) | 0.928932 | − | 1.60896i | 0.0589873 | − | 0.102169i | ||||
\(249\) | −3.65685 | + | 6.33386i | −0.231744 | + | 0.401392i | ||||
\(250\) | 1.17157 | + | 2.02922i | 0.0740968 | + | 0.128339i | ||||
\(251\) | 12.4853 | 0.788064 | 0.394032 | − | 0.919097i | \(-0.371080\pi\) | ||||
0.394032 | + | 0.919097i | \(0.371080\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137 | 0.962765 | ||||||||
\(254\) | 0.343146 | + | 0.594346i | 0.0215309 | + | 0.0372926i | ||||
\(255\) | −3.82843 | + | 6.63103i | −0.239745 | + | 0.415251i | ||||
\(256\) | −1.98528 | + | 3.43861i | −0.124080 | + | 0.214913i | ||||
\(257\) | 11.6066 | + | 20.1032i | 0.724000 | + | 1.25400i | 0.959384 | + | 0.282102i | \(0.0910318\pi\) |
−0.235384 | + | 0.971902i | \(0.575635\pi\) | |||||||
\(258\) | −2.34315 | −0.145878 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −16.1421 | −1.00109 | ||||||||
\(261\) | 3.41421 | + | 5.91359i | 0.211335 | + | 0.366042i | ||||
\(262\) | −3.17157 | + | 5.49333i | −0.195940 | + | 0.339379i | ||||
\(263\) | −2.65685 | + | 4.60181i | −0.163829 | + | 0.283760i | −0.936239 | − | 0.351365i | \(-0.885718\pi\) |
0.772410 | + | 0.635124i | \(0.219051\pi\) | |||||||
\(264\) | 1.58579 | + | 2.74666i | 0.0975984 | + | 0.169045i | ||||
\(265\) | 6.82843 | 0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.2426 | −0.871635 | ||||||||
\(268\) | −5.17157 | − | 8.95743i | −0.315904 | − | 0.547162i | ||||
\(269\) | −7.36396 | + | 12.7548i | −0.448989 | + | 0.777671i | −0.998320 | − | 0.0579332i | \(-0.981549\pi\) |
0.549332 | + | 0.835604i | \(0.314882\pi\) | |||||||
\(270\) | −0.707107 | + | 1.22474i | −0.0430331 | + | 0.0745356i | ||||
\(271\) | −5.07107 | − | 8.78335i | −0.308045 | − | 0.533550i | 0.669889 | − | 0.742461i | \(-0.266342\pi\) |
−0.977935 | + | 0.208911i | \(0.933008\pi\) | |||||||
\(272\) | 6.72792 | 0.407940 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.85786 | 0.353887 | ||||||||
\(275\) | 6.65685 | + | 11.5300i | 0.401423 | + | 0.695286i | ||||
\(276\) | 7.00000 | − | 12.1244i | 0.421350 | − | 0.729800i | ||||
\(277\) | 4.65685 | − | 8.06591i | 0.279803 | − | 0.484633i | −0.691532 | − | 0.722345i | \(-0.743064\pi\) |
0.971336 | + | 0.237712i | \(0.0763974\pi\) | |||||||
\(278\) | −3.65685 | − | 6.33386i | −0.219324 | − | 0.379880i | ||||
\(279\) | 1.17157 | 0.0701402 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.485281 | 0.0289495 | 0.0144747 | − | 0.999895i | \(-0.495392\pi\) | ||||
0.0144747 | + | 0.999895i | \(0.495392\pi\) | |||||||
\(282\) | 0.585786 | + | 1.01461i | 0.0348831 | + | 0.0604193i | ||||
\(283\) | −4.24264 | + | 7.34847i | −0.252199 | + | 0.436821i | −0.964131 | − | 0.265427i | \(-0.914487\pi\) |
0.711932 | + | 0.702248i | \(0.247820\pi\) | |||||||
\(284\) | 8.51472 | − | 14.7479i | 0.505256 | − | 0.875128i | ||||
\(285\) | −4.82843 | − | 8.36308i | −0.286011 | − | 0.495386i | ||||
\(286\) | 2.14214 | 0.126667 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 4.41421 | 0.260110 | ||||||||
\(289\) | 5.98528 | + | 10.3668i | 0.352075 | + | 0.609812i | ||||
\(290\) | −4.82843 | + | 8.36308i | −0.283535 | + | 0.491097i | ||||
\(291\) | −1.29289 | + | 2.23936i | −0.0757907 | + | 0.131273i | ||||
\(292\) | −12.7071 | − | 22.0094i | −0.743627 | − | 1.28800i | ||||
\(293\) | −16.5858 | −0.968952 | −0.484476 | − | 0.874805i | \(-0.660990\pi\) | ||||
−0.484476 | + | 0.874805i | \(0.660990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.00000 | −0.232889 | ||||||||
\(296\) | −3.17157 | − | 5.49333i | −0.184344 | − | 0.319293i | ||||
\(297\) | −1.00000 | + | 1.73205i | −0.0580259 | + | 0.100504i | ||||
\(298\) | −3.58579 | + | 6.21076i | −0.207719 | + | 0.359780i | ||||
\(299\) | −9.89949 | − | 17.1464i | −0.572503 | − | 0.991604i | ||||
\(300\) | 12.1716 | 0.702726 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.97056 | 0.286024 | ||||||||
\(303\) | −1.46447 | − | 2.53653i | −0.0841314 | − | 0.145720i | ||||
\(304\) | −4.24264 | + | 7.34847i | −0.243332 | + | 0.421464i | ||||
\(305\) | −20.8995 | + | 36.1990i | −1.19670 | + | 2.07275i | ||||
\(306\) | −0.464466 | − | 0.804479i | −0.0265518 | − | 0.0459890i | ||||
\(307\) | −30.1421 | −1.72030 | −0.860151 | − | 0.510039i | \(-0.829631\pi\) | ||||
−0.860151 | + | 0.510039i | \(0.829631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.48528 | 0.255159 | ||||||||
\(310\) | 0.828427 | + | 1.43488i | 0.0470515 | + | 0.0814956i | ||||
\(311\) | 3.07107 | − | 5.31925i | 0.174144 | − | 0.301627i | −0.765721 | − | 0.643173i | \(-0.777617\pi\) |
0.939865 | + | 0.341547i | \(0.110951\pi\) | |||||||
\(312\) | 2.05025 | − | 3.55114i | 0.116073 | − | 0.201044i | ||||
\(313\) | 0.949747 | + | 1.64501i | 0.0536829 | + | 0.0929815i | 0.891618 | − | 0.452788i | \(-0.149571\pi\) |
−0.837935 | + | 0.545770i | \(0.816237\pi\) | |||||||
\(314\) | −4.87006 | −0.274833 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −24.9706 | −1.40470 | ||||||||
\(317\) | −5.00000 | − | 8.66025i | −0.280828 | − | 0.486408i | 0.690761 | − | 0.723083i | \(-0.257276\pi\) |
−0.971589 | + | 0.236675i | \(0.923942\pi\) | |||||||
\(318\) | −0.414214 | + | 0.717439i | −0.0232279 | + | 0.0402320i | ||||
\(319\) | −6.82843 | + | 11.8272i | −0.382319 | + | 0.662195i | ||||
\(320\) | −7.12132 | − | 12.3345i | −0.398094 | − | 0.689519i | ||||
\(321\) | 0.343146 | 0.0191525 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.34315 | 0.352942 | ||||||||
\(324\) | 0.914214 | + | 1.58346i | 0.0507896 | + | 0.0879702i | ||||
\(325\) | 8.60660 | − | 14.9071i | 0.477408 | − | 0.826896i | ||||
\(326\) | 2.34315 | − | 4.05845i | 0.129775 | − | 0.224777i | ||||
\(327\) | −2.82843 | − | 4.89898i | −0.156412 | − | 0.270914i | ||||
\(328\) | 9.89949 | 0.546608 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.82843 | −0.155700 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | −6.68629 | + | 11.5810i | −0.366958 | + | 0.635590i | ||||
\(333\) | 2.00000 | − | 3.46410i | 0.109599 | − | 0.189832i | ||||
\(334\) | −4.10051 | − | 7.10228i | −0.224370 | − | 0.388620i | ||||
\(335\) | 19.3137 | 1.05522 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.6569 | −1.61551 | −0.807756 | − | 0.589517i | \(-0.799318\pi\) | ||||
−0.807756 | + | 0.589517i | \(0.799318\pi\) | |||||||
\(338\) | 1.30761 | + | 2.26485i | 0.0711247 | + | 0.123192i | ||||
\(339\) | −2.65685 | + | 4.60181i | −0.144301 | + | 0.249936i | ||||
\(340\) | −7.00000 | + | 12.1244i | −0.379628 | + | 0.657536i | ||||
\(341\) | 1.17157 | + | 2.02922i | 0.0634442 | + | 0.109889i | ||||
\(342\) | 1.17157 | 0.0633514 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.97056 | −0.483660 | ||||||||
\(345\) | 13.0711 | + | 22.6398i | 0.703723 | + | 1.21888i | ||||
\(346\) | 4.36396 | − | 7.55860i | 0.234608 | − | 0.406353i | ||||
\(347\) | −16.6569 | + | 28.8505i | −0.894187 | + | 1.54878i | −0.0593789 | + | 0.998236i | \(0.518912\pi\) |
−0.834808 | + | 0.550541i | \(0.814421\pi\) | |||||||
\(348\) | 6.24264 | + | 10.8126i | 0.334641 | + | 0.579615i | ||||
\(349\) | 9.89949 | 0.529908 | 0.264954 | − | 0.964261i | \(-0.414643\pi\) | ||||
0.264954 | + | 0.964261i | \(0.414643\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.58579 | 0.138019 | ||||||||
\(352\) | 4.41421 | + | 7.64564i | 0.235278 | + | 0.407514i | ||||
\(353\) | −7.36396 | + | 12.7548i | −0.391944 | + | 0.678867i | −0.992706 | − | 0.120561i | \(-0.961531\pi\) |
0.600762 | + | 0.799428i | \(0.294864\pi\) | |||||||
\(354\) | 0.242641 | − | 0.420266i | 0.0128962 | − | 0.0223369i | ||||
\(355\) | 15.8995 | + | 27.5387i | 0.843858 | + | 1.46160i | ||||
\(356\) | −26.0416 | −1.38020 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.14214 | −0.430325 | ||||||||
\(359\) | 0.171573 | + | 0.297173i | 0.00905527 | + | 0.0156842i | 0.870518 | − | 0.492137i | \(-0.163784\pi\) |
−0.861462 | + | 0.507822i | \(0.830451\pi\) | |||||||
\(360\) | −2.70711 | + | 4.68885i | −0.142677 | + | 0.247124i | ||||
\(361\) | 5.50000 | − | 9.52628i | 0.289474 | − | 0.501383i | ||||
\(362\) | −0.535534 | − | 0.927572i | −0.0281470 | − | 0.0487521i | ||||
\(363\) | 7.00000 | 0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 47.4558 | 2.48395 | ||||||||
\(366\) | −2.53553 | − | 4.39167i | −0.132534 | − | 0.229556i | ||||
\(367\) | −1.65685 | + | 2.86976i | −0.0864871 | + | 0.149800i | −0.906024 | − | 0.423226i | \(-0.860897\pi\) |
0.819537 | + | 0.573027i | \(0.194231\pi\) | |||||||
\(368\) | 11.4853 | − | 19.8931i | 0.598712 | − | 1.03700i | ||||
\(369\) | 3.12132 | + | 5.40629i | 0.162489 | + | 0.281440i | ||||
\(370\) | 5.65685 | 0.294086 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 2.14214 | 0.111065 | ||||||||
\(373\) | 5.34315 | + | 9.25460i | 0.276658 | + | 0.479185i | 0.970552 | − | 0.240892i | \(-0.0774399\pi\) |
−0.693894 | + | 0.720077i | \(0.744107\pi\) | |||||||
\(374\) | 0.928932 | − | 1.60896i | 0.0480339 | − | 0.0831972i | ||||
\(375\) | −2.82843 | + | 4.89898i | −0.146059 | + | 0.252982i | ||||
\(376\) | 2.24264 | + | 3.88437i | 0.115655 | + | 0.200321i | ||||
\(377\) | 17.6569 | 0.909374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.68629 | 0.446185 | 0.223092 | − | 0.974797i | \(-0.428385\pi\) | ||||
0.223092 | + | 0.974797i | \(0.428385\pi\) | |||||||
\(380\) | −8.82843 | − | 15.2913i | −0.452889 | − | 0.784426i | ||||
\(381\) | −0.828427 | + | 1.43488i | −0.0424416 | + | 0.0735110i | ||||
\(382\) | 3.72792 | − | 6.45695i | 0.190737 | − | 0.330366i | ||||
\(383\) | −9.17157 | − | 15.8856i | −0.468645 | − | 0.811718i | 0.530712 | − | 0.847552i | \(-0.321924\pi\) |
−0.999358 | + | 0.0358343i | \(0.988591\pi\) | |||||||
\(384\) | 10.5563 | 0.538701 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.20101 | 0.112028 | ||||||||
\(387\) | −2.82843 | − | 4.89898i | −0.143777 | − | 0.249029i | ||||
\(388\) | −2.36396 | + | 4.09450i | −0.120012 | + | 0.207867i | ||||
\(389\) | 9.07107 | − | 15.7116i | 0.459921 | − | 0.796607i | −0.539035 | − | 0.842283i | \(-0.681211\pi\) |
0.998956 | + | 0.0456762i | \(0.0145442\pi\) | |||||||
\(390\) | 1.82843 | + | 3.16693i | 0.0925860 | + | 0.160364i | ||||
\(391\) | −17.1716 | −0.868404 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.3137 | −0.772474 | ||||||||
\(394\) | −0.414214 | − | 0.717439i | −0.0208678 | − | 0.0361441i | ||||
\(395\) | 23.3137 | − | 40.3805i | 1.17304 | − | 2.03176i | ||||
\(396\) | −1.82843 | + | 3.16693i | −0.0918819 | + | 0.159144i | ||||
\(397\) | −1.19239 | − | 2.06528i | −0.0598442 | − | 0.103653i | 0.834551 | − | 0.550931i | \(-0.185727\pi\) |
−0.894395 | + | 0.447277i | \(0.852394\pi\) | |||||||
\(398\) | −8.97056 | −0.449654 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.9706 | 0.998528 | ||||||||
\(401\) | 3.07107 | + | 5.31925i | 0.153362 | + | 0.265630i | 0.932461 | − | 0.361270i | \(-0.117657\pi\) |
−0.779100 | + | 0.626900i | \(0.784323\pi\) | |||||||
\(402\) | −1.17157 | + | 2.02922i | −0.0584327 | + | 0.101208i | ||||
\(403\) | 1.51472 | − | 2.62357i | 0.0754535 | − | 0.130689i | ||||
\(404\) | −2.67767 | − | 4.63786i | −0.133219 | − | 0.230742i | ||||
\(405\) | −3.41421 | −0.169654 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | −1.77817 | − | 3.07989i | −0.0880328 | − | 0.152477i | ||||
\(409\) | −10.7071 | + | 18.5453i | −0.529432 | + | 0.917004i | 0.469978 | + | 0.882678i | \(0.344262\pi\) |
−0.999411 | + | 0.0343258i | \(0.989072\pi\) | |||||||
\(410\) | −4.41421 | + | 7.64564i | −0.218002 | + | 0.377591i | ||||
\(411\) | 7.07107 | + | 12.2474i | 0.348790 | + | 0.604122i | ||||
\(412\) | 8.20101 | 0.404035 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.17157 | −0.155874 | ||||||||
\(415\) | −12.4853 | − | 21.6251i | −0.612878 | − | 1.06154i | ||||
\(416\) | 5.70711 | − | 9.88500i | 0.279814 | − | 0.484652i | ||||
\(417\) | 8.82843 | − | 15.2913i | 0.432330 | − | 0.748817i | ||||
\(418\) | 1.17157 | + | 2.02922i | 0.0573035 | + | 0.0992526i | ||||
\(419\) | −33.1716 | −1.62054 | −0.810269 | − | 0.586059i | \(-0.800679\pi\) | ||||
−0.810269 | + | 0.586059i | \(0.800679\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.6274 | 0.810371 | 0.405185 | − | 0.914235i | \(-0.367207\pi\) | ||||
0.405185 | + | 0.914235i | \(0.367207\pi\) | |||||||
\(422\) | −2.68629 | − | 4.65279i | −0.130767 | − | 0.226494i | ||||
\(423\) | −1.41421 | + | 2.44949i | −0.0687614 | + | 0.119098i | ||||
\(424\) | −1.58579 | + | 2.74666i | −0.0770126 | + | 0.133390i | ||||
\(425\) | −7.46447 | − | 12.9288i | −0.362080 | − | 0.627141i | ||||
\(426\) | −3.85786 | −0.186914 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.627417 | 0.0303273 | ||||||||
\(429\) | 2.58579 | + | 4.47871i | 0.124843 | + | 0.216234i | ||||
\(430\) | 4.00000 | − | 6.92820i | 0.192897 | − | 0.334108i | ||||
\(431\) | 13.4853 | − | 23.3572i | 0.649563 | − | 1.12508i | −0.333664 | − | 0.942692i | \(-0.608285\pi\) |
0.983227 | − | 0.182384i | \(-0.0583815\pi\) | |||||||
\(432\) | 1.50000 | + | 2.59808i | 0.0721688 | + | 0.125000i | ||||
\(433\) | 20.2426 | 0.972799 | 0.486400 | − | 0.873736i | \(-0.338310\pi\) | ||||
0.486400 | + | 0.873736i | \(0.338310\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.3137 | −1.11781 | ||||||||
\(436\) | −5.17157 | − | 8.95743i | −0.247673 | − | 0.428983i | ||||
\(437\) | 10.8284 | − | 18.7554i | 0.517994 | − | 0.897192i | ||||
\(438\) | −2.87868 | + | 4.98602i | −0.137549 | + | 0.238241i | ||||
\(439\) | 6.34315 | + | 10.9867i | 0.302742 | + | 0.524364i | 0.976756 | − | 0.214354i | \(-0.0687647\pi\) |
−0.674014 | + | 0.738718i | \(0.735431\pi\) | |||||||
\(440\) | −10.8284 | −0.516225 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.40202 | −0.114252 | ||||||||
\(443\) | −17.4853 | − | 30.2854i | −0.830751 | − | 1.43890i | −0.897444 | − | 0.441129i | \(-0.854578\pi\) |
0.0666929 | − | 0.997774i | \(-0.478755\pi\) | |||||||
\(444\) | 3.65685 | − | 6.33386i | 0.173547 | − | 0.300592i | ||||
\(445\) | 24.3137 | − | 42.1126i | 1.15258 | − | 1.99633i | ||||
\(446\) | 5.17157 | + | 8.95743i | 0.244881 | + | 0.424146i | ||||
\(447\) | −17.3137 | −0.818910 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.31371 | −0.250769 | −0.125385 | − | 0.992108i | \(-0.540017\pi\) | ||||
−0.125385 | + | 0.992108i | \(0.540017\pi\) | |||||||
\(450\) | −1.37868 | − | 2.38794i | −0.0649916 | − | 0.112569i | ||||
\(451\) | −6.24264 | + | 10.8126i | −0.293954 | + | 0.509144i | ||||
\(452\) | −4.85786 | + | 8.41407i | −0.228495 | + | 0.395764i | ||||
\(453\) | 6.00000 | + | 10.3923i | 0.281905 | + | 0.488273i | ||||
\(454\) | −9.85786 | −0.462652 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.48528 | 0.210043 | ||||||||
\(457\) | 9.00000 | + | 15.5885i | 0.421002 | + | 0.729197i | 0.996038 | − | 0.0889312i | \(-0.0283451\pi\) |
−0.575036 | + | 0.818128i | \(0.695012\pi\) | |||||||
\(458\) | −0.0502525 | + | 0.0870399i | −0.00234815 | + | 0.00406711i | ||||
\(459\) | 1.12132 | − | 1.94218i | 0.0523388 | − | 0.0906534i | ||||
\(460\) | 23.8995 | + | 41.3951i | 1.11432 | + | 1.93006i | ||||
\(461\) | 16.5858 | 0.772477 | 0.386239 | − | 0.922399i | \(-0.373774\pi\) | ||||
0.386239 | + | 0.922399i | \(0.373774\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −26.6274 | −1.23748 | −0.618741 | − | 0.785595i | \(-0.712357\pi\) | ||||
−0.618741 | + | 0.785595i | \(0.712357\pi\) | |||||||
\(464\) | 10.2426 | + | 17.7408i | 0.475503 | + | 0.823595i | ||||
\(465\) | −2.00000 | + | 3.46410i | −0.0927478 | + | 0.160644i | ||||
\(466\) | 1.27208 | − | 2.20330i | 0.0589279 | − | 0.102066i | ||||
\(467\) | 0.100505 | + | 0.174080i | 0.00465082 | + | 0.00805546i | 0.868341 | − | 0.495967i | \(-0.165186\pi\) |
−0.863691 | + | 0.504022i | \(0.831853\pi\) | |||||||
\(468\) | 4.72792 | 0.218548 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −4.00000 | −0.184506 | ||||||||
\(471\) | −5.87868 | − | 10.1822i | −0.270875 | − | 0.469170i | ||||
\(472\) | 0.928932 | − | 1.60896i | 0.0427576 | − | 0.0740583i | ||||
\(473\) | 5.65685 | − | 9.79796i | 0.260102 | − | 0.450511i | ||||
\(474\) | 2.82843 | + | 4.89898i | 0.129914 | + | 0.225018i | ||||
\(475\) | 18.8284 | 0.863907 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.00000 | −0.0915737 | ||||||||
\(478\) | 3.24264 | + | 5.61642i | 0.148315 | + | 0.256889i | ||||
\(479\) | 0.928932 | − | 1.60896i | 0.0424440 | − | 0.0735152i | −0.844023 | − | 0.536307i | \(-0.819819\pi\) |
0.886467 | + | 0.462792i | \(0.153152\pi\) | |||||||
\(480\) | −7.53553 | + | 13.0519i | −0.343948 | + | 0.595736i | ||||
\(481\) | −5.17157 | − | 8.95743i | −0.235803 | − | 0.408424i | ||||
\(482\) | 6.72792 | 0.306448 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 12.7990 | 0.581772 | ||||||||
\(485\) | −4.41421 | − | 7.64564i | −0.200439 | − | 0.347171i | ||||
\(486\) | 0.207107 | − | 0.358719i | 0.00939455 | − | 0.0162718i | ||||
\(487\) | −13.3137 | + | 23.0600i | −0.603302 | + | 1.04495i | 0.389016 | + | 0.921231i | \(0.372815\pi\) |
−0.992317 | + | 0.123718i | \(0.960518\pi\) | |||||||
\(488\) | −9.70711 | − | 16.8132i | −0.439420 | − | 0.761098i | ||||
\(489\) | 11.3137 | 0.511624 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.02944 | 0.226975 | 0.113488 | − | 0.993539i | \(-0.463798\pi\) | ||||
0.113488 | + | 0.993539i | \(0.463798\pi\) | |||||||
\(492\) | 5.70711 | + | 9.88500i | 0.257296 | + | 0.445650i | ||||
\(493\) | 7.65685 | − | 13.2621i | 0.344847 | − | 0.597293i | ||||
\(494\) | 1.51472 | − | 2.62357i | 0.0681504 | − | 0.118040i | ||||
\(495\) | −3.41421 | − | 5.91359i | −0.153457 | − | 0.265796i | ||||
\(496\) | 3.51472 | 0.157816 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 3.02944 | 0.135752 | ||||||||
\(499\) | −1.65685 | − | 2.86976i | −0.0741710 | − | 0.128468i | 0.826554 | − | 0.562857i | \(-0.190298\pi\) |
−0.900725 | + | 0.434389i | \(0.856964\pi\) | |||||||
\(500\) | −5.17157 | + | 8.95743i | −0.231280 | + | 0.400588i | ||||
\(501\) | 9.89949 | − | 17.1464i | 0.442277 | − | 0.766046i | ||||
\(502\) | −2.58579 | − | 4.47871i | −0.115409 | − | 0.199895i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | −3.17157 | − | 5.49333i | −0.140994 | − | 0.244208i | ||||
\(507\) | −3.15685 | + | 5.46783i | −0.140201 | + | 0.242835i | ||||
\(508\) | −1.51472 | + | 2.62357i | −0.0672048 | + | 0.116402i | ||||
\(509\) | 2.77817 | + | 4.81194i | 0.123140 | + | 0.213285i | 0.921005 | − | 0.389552i | \(-0.127370\pi\) |
−0.797864 | + | 0.602837i | \(0.794037\pi\) | |||||||
\(510\) | 3.17157 | 0.140440 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | 1.41421 | + | 2.44949i | 0.0624391 | + | 0.108148i | ||||
\(514\) | 4.80761 | − | 8.32703i | 0.212055 | − | 0.367289i | ||||
\(515\) | −7.65685 | + | 13.2621i | −0.337401 | + | 0.584396i | ||||
\(516\) | −5.17157 | − | 8.95743i | −0.227666 | − | 0.394329i | ||||
\(517\) | −5.65685 | −0.248788 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 21.0711 | 0.924917 | ||||||||
\(520\) | 7.00000 | + | 12.1244i | 0.306970 | + | 0.531688i | ||||
\(521\) | −17.7071 | + | 30.6696i | −0.775762 | + | 1.34366i | 0.158603 | + | 0.987343i | \(0.449301\pi\) |
−0.934365 | + | 0.356317i | \(0.884032\pi\) | |||||||
\(522\) | 1.41421 | − | 2.44949i | 0.0618984 | − | 0.107211i | ||||
\(523\) | −12.8284 | − | 22.2195i | −0.560948 | − | 0.971590i | −0.997414 | − | 0.0718696i | \(-0.977103\pi\) |
0.436466 | − | 0.899721i | \(-0.356230\pi\) | |||||||
\(524\) | −28.0000 | −1.22319 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.20101 | 0.0959686 | ||||||||
\(527\) | −1.31371 | − | 2.27541i | −0.0572260 | − | 0.0991184i | ||||
\(528\) | −3.00000 | + | 5.19615i | −0.130558 | + | 0.226134i | ||||
\(529\) | −17.8137 | + | 30.8542i | −0.774509 | + | 1.34149i | ||||
\(530\) | −1.41421 | − | 2.44949i | −0.0614295 | − | 0.106399i | ||||
\(531\) | 1.17157 | 0.0508419 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 16.1421 | 0.699194 | ||||||||
\(534\) | 2.94975 | + | 5.10911i | 0.127648 | + | 0.221093i | ||||
\(535\) | −0.585786 | + | 1.01461i | −0.0253258 | + | 0.0438655i | ||||
\(536\) | −4.48528 | + | 7.76874i | −0.193735 | + | 0.335558i | ||||
\(537\) | −9.82843 | − | 17.0233i | −0.424128 | − | 0.734611i | ||||
\(538\) | 6.10051 | 0.263011 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −6.24264 | −0.268640 | ||||||||
\(541\) | −8.65685 | − | 14.9941i | −0.372187 | − | 0.644647i | 0.617715 | − | 0.786402i | \(-0.288059\pi\) |
−0.989902 | + | 0.141755i | \(0.954725\pi\) | |||||||
\(542\) | −2.10051 | + | 3.63818i | −0.0902244 | + | 0.156273i | ||||
\(543\) | 1.29289 | − | 2.23936i | 0.0554834 | − | 0.0961000i | ||||
\(544\) | −4.94975 | − | 8.57321i | −0.212219 | − | 0.367574i | ||||
\(545\) | 19.3137 | 0.827308 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −36.9706 | −1.58075 | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||||
−0.790374 | + | 0.612625i | \(0.790114\pi\) | |||||||
\(548\) | 12.9289 | + | 22.3936i | 0.552297 | + | 0.956606i | ||||
\(549\) | 6.12132 | − | 10.6024i | 0.261252 | − | 0.452501i | ||||
\(550\) | 2.75736 | − | 4.77589i | 0.117574 | − | 0.203644i | ||||
\(551\) | 9.65685 | + | 16.7262i | 0.411396 | + | 0.712558i | ||||
\(552\) | −12.1421 | −0.516804 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.85786 | −0.163905 | ||||||||
\(555\) | 6.82843 | + | 11.8272i | 0.289851 | + | 0.502036i | ||||
\(556\) | 16.1421 | − | 27.9590i | 0.684579 | − | 1.18573i | ||||
\(557\) | −13.0000 | + | 22.5167i | −0.550828 | + | 0.954062i | 0.447387 | + | 0.894340i | \(0.352355\pi\) |
−0.998215 | + | 0.0597213i | \(0.980979\pi\) | |||||||
\(558\) | −0.242641 | − | 0.420266i | −0.0102718 | − | 0.0177913i | ||||
\(559\) | −14.6274 | −0.618674 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.48528 | 0.189369 | ||||||||
\(562\) | −0.100505 | − | 0.174080i | −0.00423955 | − | 0.00734312i | ||||
\(563\) | −0.585786 | + | 1.01461i | −0.0246880 | + | 0.0427608i | −0.878105 | − | 0.478467i | \(-0.841193\pi\) |
0.853417 | + | 0.521228i | \(0.174526\pi\) | |||||||
\(564\) | −2.58579 | + | 4.47871i | −0.108881 | + | 0.188588i | ||||
\(565\) | −9.07107 | − | 15.7116i | −0.381623 | − | 0.660990i | ||||
\(566\) | 3.51472 | 0.147735 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.7696 | −0.619717 | ||||||||
\(569\) | 8.24264 | + | 14.2767i | 0.345549 | + | 0.598509i | 0.985453 | − | 0.169946i | \(-0.0543592\pi\) |
−0.639904 | + | 0.768455i | \(0.721026\pi\) | |||||||
\(570\) | −2.00000 | + | 3.46410i | −0.0837708 | + | 0.145095i | ||||
\(571\) | −11.1716 | + | 19.3497i | −0.467516 | + | 0.809761i | −0.999311 | − | 0.0371118i | \(-0.988184\pi\) |
0.531795 | + | 0.846873i | \(0.321518\pi\) | |||||||
\(572\) | 4.72792 | + | 8.18900i | 0.197684 | + | 0.342399i | ||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −50.9706 | −2.12562 | ||||||||
\(576\) | 2.08579 | + | 3.61269i | 0.0869078 | + | 0.150529i | ||||
\(577\) | −16.9497 | + | 29.3578i | −0.705627 | + | 1.22218i | 0.260837 | + | 0.965383i | \(0.416001\pi\) |
−0.966465 | + | 0.256799i | \(0.917332\pi\) | |||||||
\(578\) | 2.47918 | − | 4.29407i | 0.103120 | − | 0.178610i | ||||
\(579\) | 2.65685 | + | 4.60181i | 0.110415 | + | 0.191245i | ||||
\(580\) | −42.6274 | −1.77001 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.07107 | 0.0443972 | ||||||||
\(583\) | −2.00000 | − | 3.46410i | −0.0828315 | − | 0.143468i | ||||
\(584\) | −11.0208 | + | 19.0886i | −0.456045 | + | 0.789892i | ||||
\(585\) | −4.41421 | + | 7.64564i | −0.182505 | + | 0.316108i | ||||
\(586\) | 3.43503 | + | 5.94964i | 0.141900 | + | 0.245778i | ||||
\(587\) | 22.8284 | 0.942230 | 0.471115 | − | 0.882072i | \(-0.343852\pi\) | ||||
0.471115 | + | 0.882072i | \(0.343852\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.31371 | 0.136539 | ||||||||
\(590\) | 0.828427 | + | 1.43488i | 0.0341058 | + | 0.0590730i | ||||
\(591\) | 1.00000 | − | 1.73205i | 0.0411345 | − | 0.0712470i | ||||
\(592\) | 6.00000 | − | 10.3923i | 0.246598 | − | 0.427121i | ||||
\(593\) | −3.46447 | − | 6.00063i | −0.142269 | − | 0.246416i | 0.786082 | − | 0.618122i | \(-0.212106\pi\) |
−0.928351 | + | 0.371706i | \(0.878773\pi\) | |||||||
\(594\) | 0.828427 | 0.0339908 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −31.6569 | −1.29672 | ||||||||
\(597\) | −10.8284 | − | 18.7554i | −0.443178 | − | 0.767607i | ||||
\(598\) | −4.10051 | + | 7.10228i | −0.167682 | + | 0.290434i | ||||
\(599\) | 1.00000 | − | 1.73205i | 0.0408589 | − | 0.0707697i | −0.844873 | − | 0.534967i | \(-0.820324\pi\) |
0.885732 | + | 0.464198i | \(0.153657\pi\) | |||||||
\(600\) | −5.27817 | − | 9.14207i | −0.215481 | − | 0.373223i | ||||
\(601\) | 15.0711 | 0.614762 | 0.307381 | − | 0.951587i | \(-0.400547\pi\) | ||||
0.307381 | + | 0.951587i | \(0.400547\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | −0.230365 | ||||||||
\(604\) | 10.9706 | + | 19.0016i | 0.446386 | + | 0.773163i | ||||
\(605\) | −11.9497 | + | 20.6976i | −0.485826 | + | 0.841476i | ||||
\(606\) | −0.606602 | + | 1.05066i | −0.0246415 | + | 0.0426803i | ||||
\(607\) | −9.17157 | − | 15.8856i | −0.372263 | − | 0.644778i | 0.617651 | − | 0.786453i | \(-0.288085\pi\) |
−0.989913 | + | 0.141675i | \(0.954751\pi\) | |||||||
\(608\) | 12.4853 | 0.506345 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 17.3137 | 0.701012 | ||||||||
\(611\) | 3.65685 | + | 6.33386i | 0.147940 | + | 0.256240i | ||||
\(612\) | 2.05025 | − | 3.55114i | 0.0828765 | − | 0.143546i | ||||
\(613\) | −2.34315 | + | 4.05845i | −0.0946388 | + | 0.163919i | −0.909458 | − | 0.415796i | \(-0.863503\pi\) |
0.814819 | + | 0.579715i | \(0.196836\pi\) | |||||||
\(614\) | 6.24264 | + | 10.8126i | 0.251932 | + | 0.436360i | ||||
\(615\) | −21.3137 | −0.859452 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −24.4853 | −0.985740 | −0.492870 | − | 0.870103i | \(-0.664052\pi\) | ||||
−0.492870 | + | 0.870103i | \(0.664052\pi\) | |||||||
\(618\) | −0.928932 | − | 1.60896i | −0.0373671 | − | 0.0647218i | ||||
\(619\) | 14.4853 | − | 25.0892i | 0.582213 | − | 1.00842i | −0.413004 | − | 0.910729i | \(-0.635520\pi\) |
0.995217 | − | 0.0976926i | \(-0.0311462\pi\) | |||||||
\(620\) | −3.65685 | + | 6.33386i | −0.146863 | + | 0.254374i | ||||
\(621\) | −3.82843 | − | 6.63103i | −0.153629 | − | 0.266094i | ||||
\(622\) | −2.54416 | −0.102011 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 7.75736 | 0.310543 | ||||||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | 0.393398 | − | 0.681386i | 0.0157234 | − | 0.0272337i | ||||
\(627\) | −2.82843 | + | 4.89898i | −0.112956 | + | 0.195646i | ||||
\(628\) | −10.7487 | − | 18.6174i | −0.428921 | − | 0.742914i | ||||
\(629\) | −8.97056 | −0.357680 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3137 | 0.928104 | 0.464052 | − | 0.885808i | \(-0.346395\pi\) | ||||
0.464052 | + | 0.885808i | \(0.346395\pi\) | |||||||
\(632\) | 10.8284 | + | 18.7554i | 0.430732 | + | 0.746049i | ||||
\(633\) | 6.48528 | − | 11.2328i | 0.257767 | − | 0.446465i | ||||
\(634\) | −2.07107 | + | 3.58719i | −0.0822526 | + | 0.142466i | ||||
\(635\) | −2.82843 | − | 4.89898i | −0.112243 | − | 0.194410i | ||||
\(636\) | −3.65685 | −0.145004 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.65685 | 0.223957 | ||||||||
\(639\) | −4.65685 | − | 8.06591i | −0.184222 | − | 0.319082i | ||||
\(640\) | −18.0208 | + | 31.2130i | −0.712335 | + | 1.23380i | ||||
\(641\) | 5.41421 | − | 9.37769i | 0.213849 | − | 0.370397i | −0.739067 | − | 0.673632i | \(-0.764733\pi\) |
0.952916 | + | 0.303235i | \(0.0980668\pi\) | |||||||
\(642\) | −0.0710678 | − | 0.123093i | −0.00280482 | − | 0.00485810i | ||||
\(643\) | 34.4264 | 1.35764 | 0.678822 | − | 0.734302i | \(-0.262491\pi\) | ||||
0.678822 | + | 0.734302i | \(0.262491\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 19.3137 | 0.760477 | ||||||||
\(646\) | −1.31371 | − | 2.27541i | −0.0516872 | − | 0.0895248i | ||||
\(647\) | 13.4142 | − | 23.2341i | 0.527367 | − | 0.913427i | −0.472124 | − | 0.881532i | \(-0.656513\pi\) |
0.999491 | − | 0.0318946i | \(-0.0101541\pi\) | |||||||
\(648\) | 0.792893 | − | 1.37333i | 0.0311478 | − | 0.0539496i | ||||
\(649\) | 1.17157 | + | 2.02922i | 0.0459883 | + | 0.0796540i | ||||
\(650\) | −7.12994 | −0.279659 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6863 | 0.810138 | ||||||||
\(653\) | −18.2426 | − | 31.5972i | −0.713890 | − | 1.23649i | −0.963386 | − | 0.268118i | \(-0.913598\pi\) |
0.249497 | − | 0.968376i | \(-0.419735\pi\) | |||||||
\(654\) | −1.17157 | + | 2.02922i | −0.0458121 | + | 0.0793489i | ||||
\(655\) | 26.1421 | − | 45.2795i | 1.02146 | − | 1.76922i | ||||
\(656\) | 9.36396 | + | 16.2189i | 0.365601 | + | 0.633240i | ||||
\(657\) | −13.8995 | −0.542271 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.31371 | 0.362811 | 0.181405 | − | 0.983408i | \(-0.441935\pi\) | ||||
0.181405 | + | 0.983408i | \(0.441935\pi\) | |||||||
\(660\) | −6.24264 | − | 10.8126i | −0.242994 | − | 0.420879i | ||||
\(661\) | −11.7782 | + | 20.4004i | −0.458118 | + | 0.793483i | −0.998862 | − | 0.0477040i | \(-0.984810\pi\) |
0.540744 | + | 0.841187i | \(0.318143\pi\) | |||||||
\(662\) | 0.828427 | − | 1.43488i | 0.0321977 | − | 0.0557681i | ||||
\(663\) | −2.89949 | − | 5.02207i | −0.112607 | − | 0.195041i | ||||
\(664\) | 11.5980 | 0.450089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.65685 | −0.0642018 | ||||||||
\(667\) | −26.1421 | − | 45.2795i | −1.01223 | − | 1.75323i | ||||
\(668\) | 18.1005 | − | 31.3510i | 0.700330 | − | 1.21301i | ||||
\(669\) | −12.4853 | + | 21.6251i | −0.482709 | + | 0.836076i | ||||
\(670\) | −4.00000 | − | 6.92820i | −0.154533 | − | 0.267660i | ||||
\(671\) | 24.4853 | 0.945244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.3137 | 0.898677 | 0.449339 | − | 0.893361i | \(-0.351660\pi\) | ||||
0.449339 | + | 0.893361i | \(0.351660\pi\) | |||||||
\(674\) | 6.14214 | + | 10.6385i | 0.236586 | + | 0.409779i | ||||
\(675\) | 3.32843 | − | 5.76500i | 0.128111 | − | 0.221895i | ||||
\(676\) | −5.77208 | + | 9.99753i | −0.222003 | + | 0.384520i | ||||
\(677\) | 15.7071 | + | 27.2055i | 0.603673 | + | 1.04559i | 0.992260 | + | 0.124180i | \(0.0396301\pi\) |
−0.388587 | + | 0.921412i | \(0.627037\pi\) | |||||||
\(678\) | 2.20101 | 0.0845293 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.1421 | 0.465630 | ||||||||
\(681\) | −11.8995 | − | 20.6105i | −0.455990 | − | 0.789797i | ||||
\(682\) | 0.485281 | − | 0.840532i | 0.0185824 | − | 0.0321856i | ||||
\(683\) | 9.82843 | − | 17.0233i | 0.376074 | − | 0.651380i | −0.614413 | − | 0.788985i | \(-0.710607\pi\) |
0.990487 | + | 0.137605i | \(0.0439404\pi\) | |||||||
\(684\) | 2.58579 | + | 4.47871i | 0.0988700 | + | 0.171248i | ||||
\(685\) | −48.2843 | −1.84485 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.242641 | −0.00925732 | ||||||||
\(688\) | −8.48528 | − | 14.6969i | −0.323498 | − | 0.560316i | ||||
\(689\) | −2.58579 | + | 4.47871i | −0.0985106 | + | 0.170625i | ||||
\(690\) | 5.41421 | − | 9.37769i | 0.206116 | − | 0.357003i | ||||
\(691\) | −0.343146 | − | 0.594346i | −0.0130539 | − | 0.0226100i | 0.859425 | − | 0.511262i | \(-0.170822\pi\) |
−0.872479 | + | 0.488652i | \(0.837489\pi\) | |||||||
\(692\) | 38.5269 | 1.46457 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13.7990 | 0.523802 | ||||||||
\(695\) | 30.1421 | + | 52.2077i | 1.14336 | + | 1.98035i | ||||
\(696\) | 5.41421 | − | 9.37769i | 0.205225 | − | 0.355461i | ||||
\(697\) | 7.00000 | − | 12.1244i | 0.265144 | − | 0.459243i | ||||
\(698\) | −2.05025 | − | 3.55114i | −0.0776032 | − | 0.134413i | ||||
\(699\) | 6.14214 | 0.232317 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −17.1716 | −0.648561 | −0.324281 | − | 0.945961i | \(-0.605122\pi\) | ||||
−0.324281 | + | 0.945961i | \(0.605122\pi\) | |||||||
\(702\) | −0.535534 | − | 0.927572i | −0.0202124 | − | 0.0350089i | ||||
\(703\) | 5.65685 | − | 9.79796i | 0.213352 | − | 0.369537i | ||||
\(704\) | −4.17157 | + | 7.22538i | −0.157222 | + | 0.272317i | ||||
\(705\) | −4.82843 | − | 8.36308i | −0.181849 | − | 0.314972i | ||||
\(706\) | 6.10051 | 0.229596 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.14214 | 0.0805064 | ||||||||
\(709\) | 18.1421 | + | 31.4231i | 0.681342 | + | 1.18012i | 0.974571 | + | 0.224077i | \(0.0719368\pi\) |
−0.293229 | + | 0.956042i | \(0.594730\pi\) | |||||||
\(710\) | 6.58579 | − | 11.4069i | 0.247160 | − | 0.428094i | ||||
\(711\) | −6.82843 | + | 11.8272i | −0.256086 | + | 0.443554i | ||||
\(712\) | 11.2929 | + | 19.5599i | 0.423219 | + | 0.733037i | ||||
\(713\) | −8.97056 | −0.335950 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.6569 | −0.660329 | ||||||||
\(716\) | −17.9706 | − | 31.1259i | −0.671591 | − | 1.16323i | ||||
\(717\) | −7.82843 | + | 13.5592i | −0.292358 | + | 0.506379i | ||||
\(718\) | 0.0710678 | − | 0.123093i | 0.00265223 | − | 0.00459379i | ||||
\(719\) | 20.9706 | + | 36.3221i | 0.782070 | + | 1.35459i | 0.930734 | + | 0.365697i | \(0.119169\pi\) |
−0.148664 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(720\) | −10.2426 | −0.381721 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.55635 | −0.169570 | ||||||||
\(723\) | 8.12132 | + | 14.0665i | 0.302035 | + | 0.523140i | ||||
\(724\) | 2.36396 | − | 4.09450i | 0.0878559 | − | 0.152171i | ||||
\(725\) | 22.7279 | − | 39.3659i | 0.844094 | − | 1.46201i | ||||
\(726\) | −1.44975 | − | 2.51104i | −0.0538052 | − | 0.0931933i | ||||
\(727\) | −12.4853 | −0.463053 | −0.231527 | − | 0.972829i | \(-0.574372\pi\) | ||||
−0.231527 | + | 0.972829i | \(0.574372\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.82843 | − | 17.0233i | −0.363766 | − | 0.630062i | ||||
\(731\) | −6.34315 | + | 10.9867i | −0.234610 | + | 0.406356i | ||||
\(732\) | 11.1924 | − | 19.3858i | 0.413683 | − | 0.716519i | ||||
\(733\) | 24.8492 | + | 43.0402i | 0.917828 | + | 1.58972i | 0.802708 | + | 0.596373i | \(0.203392\pi\) |
0.115120 | + | 0.993352i | \(0.463275\pi\) | |||||||
\(734\) | 1.37258 | 0.0506630 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.7990 | −1.24585 | ||||||||
\(737\) | −5.65685 | − | 9.79796i | −0.208373 | − | 0.360912i | ||||
\(738\) | 1.29289 | − | 2.23936i | 0.0475921 | − | 0.0824319i | ||||
\(739\) | −2.34315 | + | 4.05845i | −0.0861940 | + | 0.149292i | −0.905899 | − | 0.423493i | \(-0.860804\pi\) |
0.819705 | + | 0.572785i | \(0.194137\pi\) | |||||||
\(740\) | 12.4853 | + | 21.6251i | 0.458968 | + | 0.794956i | ||||
\(741\) | 7.31371 | 0.268676 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −50.9706 | −1.86993 | −0.934964 | − | 0.354742i | \(-0.884569\pi\) | ||||
−0.934964 | + | 0.354742i | \(0.884569\pi\) | |||||||
\(744\) | −0.928932 | − | 1.60896i | −0.0340563 | − | 0.0589873i | ||||
\(745\) | 29.5563 | − | 51.1931i | 1.08286 | − | 1.87557i | ||||
\(746\) | 2.21320 | − | 3.83338i | 0.0810311 | − | 0.140350i | ||||
\(747\) | 3.65685 | + | 6.33386i | 0.133797 | + | 0.231744i | ||||
\(748\) | 8.20101 | 0.299859 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.34315 | 0.0855596 | ||||||||
\(751\) | −6.82843 | − | 11.8272i | −0.249173 | − | 0.431580i | 0.714124 | − | 0.700020i | \(-0.246825\pi\) |
−0.963297 | + | 0.268440i | \(0.913492\pi\) | |||||||
\(752\) | −4.24264 | + | 7.34847i | −0.154713 | + | 0.267971i | ||||
\(753\) | 6.24264 | − | 10.8126i | 0.227494 | − | 0.394032i | ||||
\(754\) | −3.65685 | − | 6.33386i | −0.133175 | − | 0.230665i | ||||
\(755\) | −40.9706 | −1.49107 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.3431 | 0.957458 | 0.478729 | − | 0.877963i | \(-0.341098\pi\) | ||||
0.478729 | + | 0.877963i | \(0.341098\pi\) | |||||||
\(758\) | −1.79899 | − | 3.11594i | −0.0653423 | − | 0.113176i | ||||
\(759\) | 7.65685 | − | 13.2621i | 0.277926 | − | 0.481382i | ||||
\(760\) | −7.65685 | + | 13.2621i | −0.277743 | + | 0.481065i | ||||
\(761\) | −9.26346 | − | 16.0448i | −0.335800 | − | 0.581623i | 0.647838 | − | 0.761778i | \(-0.275673\pi\) |
−0.983638 | + | 0.180155i | \(0.942340\pi\) | |||||||
\(762\) | 0.686292 | 0.0248617 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 32.9117 | 1.19070 | ||||||||
\(765\) | 3.82843 | + | 6.63103i | 0.138417 | + | 0.239745i | ||||
\(766\) | −3.79899 | + | 6.58004i | −0.137263 | + | 0.237747i | ||||
\(767\) | 1.51472 | − | 2.62357i | 0.0546933 | − | 0.0947316i | ||||
\(768\) | 1.98528 | + | 3.43861i | 0.0716377 | + | 0.124080i | ||||
\(769\) | −29.6985 | −1.07095 | −0.535477 | − | 0.844550i | \(-0.679868\pi\) | ||||
−0.535477 | + | 0.844550i | \(0.679868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.2132 | 0.836003 | ||||||||
\(772\) | 4.85786 | + | 8.41407i | 0.174838 | + | 0.302829i | ||||
\(773\) | −4.77817 | + | 8.27604i | −0.171859 | + | 0.297669i | −0.939070 | − | 0.343727i | \(-0.888311\pi\) |
0.767211 | + | 0.641395i | \(0.221644\pi\) | |||||||
\(774\) | −1.17157 | + | 2.02922i | −0.0421113 | + | 0.0729389i | ||||
\(775\) | −3.89949 | − | 6.75412i | −0.140074 | − | 0.242615i | ||||
\(776\) | 4.10051 | 0.147200 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.51472 | −0.269416 | ||||||||
\(779\) | 8.82843 | + | 15.2913i | 0.316311 | + | 0.547867i | ||||
\(780\) | −8.07107 | + | 13.9795i | −0.288991 | + | 0.500546i | ||||
\(781\) | 9.31371 | − | 16.1318i | 0.333271 | − | 0.577242i | ||||
\(782\) | 3.55635 | + | 6.15978i | 0.127175 | + | 0.220273i | ||||
\(783\) | 6.82843 | 0.244028 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 40.1421 | 1.43273 | ||||||||
\(786\) | 3.17157 | + | 5.49333i | 0.113126 | + | 0.195940i | ||||
\(787\) | 12.3431 | − | 21.3790i | 0.439986 | − | 0.762077i | −0.557702 | − | 0.830041i | \(-0.688317\pi\) |
0.997688 | + | 0.0679637i | \(0.0216502\pi\) | |||||||
\(788\) | 1.82843 | − | 3.16693i | 0.0651350 | − | 0.112817i | ||||
\(789\) | 2.65685 | + | 4.60181i | 0.0945865 | + | 0.163829i | ||||
\(790\) | −19.3137 | −0.687151 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.17157 | 0.112697 | ||||||||
\(793\) | −15.8284 | − | 27.4156i | −0.562084 | − | 0.973558i | ||||
\(794\) | −0.493903 | + | 0.855466i | −0.0175280 | + | 0.0303593i | ||||
\(795\) | 3.41421 | − | 5.91359i | 0.121090 | − | 0.209733i | ||||
\(796\) | −19.7990 | − | 34.2929i | −0.701757 | − | 1.21548i | ||||
\(797\) | 8.38478 | 0.297004 | 0.148502 | − | 0.988912i | \(-0.452555\pi\) | ||||
0.148502 | + | 0.988912i | \(0.452555\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.34315 | 0.224404 | ||||||||
\(800\) | −14.6924 | − | 25.4480i | −0.519454 | − | 0.899721i | ||||
\(801\) | −7.12132 | + | 12.3345i | −0.251619 | + | 0.435818i | ||||
\(802\) | 1.27208 | − | 2.20330i | 0.0449186 | − | 0.0778014i | ||||
\(803\) | −13.8995 | − | 24.0746i | −0.490503 | − | 0.849575i | ||||
\(804\) | −10.3431 | −0.364775 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.25483 | −0.0441996 | ||||||||
\(807\) | 7.36396 | + | 12.7548i | 0.259224 | + | 0.448989i | ||||
\(808\) | −2.32233 | + | 4.02239i | −0.0816993 | + | 0.141507i | ||||
\(809\) | −9.97056 | + | 17.2695i | −0.350546 | + | 0.607164i | −0.986345 | − | 0.164691i | \(-0.947337\pi\) |
0.635799 | + | 0.771855i | \(0.280671\pi\) | |||||||
\(810\) | 0.707107 | + | 1.22474i | 0.0248452 | + | 0.0430331i | ||||
\(811\) | 17.6569 | 0.620016 | 0.310008 | − | 0.950734i | \(-0.399668\pi\) | ||||
0.310008 | + | 0.950734i | \(0.399668\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.1421 | −0.355700 | ||||||||
\(814\) | −1.65685 | − | 2.86976i | −0.0580727 | − | 0.100585i | ||||
\(815\) | −19.3137 | + | 33.4523i | −0.676530 | + | 1.17178i | ||||
\(816\) | 3.36396 | − | 5.82655i | 0.117762 | − | 0.203970i | ||||
\(817\) | −8.00000 | − | 13.8564i | −0.279885 | − | 0.484774i | ||||
\(818\) | 8.87006 | 0.310134 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −38.9706 | −1.36091 | ||||||||
\(821\) | 5.34315 | + | 9.25460i | 0.186477 | + | 0.322988i | 0.944073 | − | 0.329736i | \(-0.106960\pi\) |
−0.757596 | + | 0.652724i | \(0.773626\pi\) | |||||||
\(822\) | 2.92893 | − | 5.07306i | 0.102158 | − | 0.176943i | ||||
\(823\) | −4.48528 | + | 7.76874i | −0.156347 | + | 0.270801i | −0.933549 | − | 0.358451i | \(-0.883305\pi\) |
0.777202 | + | 0.629252i | \(0.216639\pi\) | |||||||
\(824\) | −3.55635 | − | 6.15978i | −0.123891 | − | 0.214586i | ||||
\(825\) | 13.3137 | 0.463524 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 47.6569 | 1.65719 | 0.828596 | − | 0.559848i | \(-0.189140\pi\) | ||||
0.828596 | + | 0.559848i | \(0.189140\pi\) | |||||||
\(828\) | −7.00000 | − | 12.1244i | −0.243267 | − | 0.421350i | ||||
\(829\) | −0.363961 | + | 0.630399i | −0.0126409 | + | 0.0218947i | −0.872277 | − | 0.489013i | \(-0.837357\pi\) |
0.859636 | + | 0.510907i | \(0.170690\pi\) | |||||||
\(830\) | −5.17157 | + | 8.95743i | −0.179508 | + | 0.310917i | ||||
\(831\) | −4.65685 | − | 8.06591i | −0.161544 | − | 0.279803i | ||||
\(832\) | 10.7868 | 0.373965 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.31371 | −0.253253 | ||||||||
\(835\) | 33.7990 | + | 58.5416i | 1.16966 | + | 2.02591i | ||||
\(836\) | −5.17157 | + | 8.95743i | −0.178863 | + | 0.309799i | ||||
\(837\) | 0.585786 | − | 1.01461i | 0.0202477 | − | 0.0350701i | ||||
\(838\) | 6.87006 | + | 11.8993i | 0.237322 | + | 0.411054i | ||||
\(839\) | −50.8284 | −1.75479 | −0.877396 | − | 0.479767i | \(-0.840721\pi\) | ||||
−0.877396 | + | 0.479767i | \(0.840721\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.6274 | 0.607842 | ||||||||
\(842\) | −3.44365 | − | 5.96458i | −0.118676 | − | 0.205553i | ||||
\(843\) | 0.242641 | − | 0.420266i | 0.00835699 | − | 0.0144747i | ||||
\(844\) | 11.8579 | − | 20.5384i | 0.408165 | − | 0.706962i | ||||
\(845\) | −10.7782 | − | 18.6683i | −0.370780 | − | 0.642211i | ||||
\(846\) | 1.17157 | 0.0402795 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 4.24264 | + | 7.34847i | 0.145607 | + | 0.252199i | ||||
\(850\) | −3.09188 | + | 5.35530i | −0.106051 | + | 0.183685i | ||||
\(851\) | −15.3137 | + | 26.5241i | −0.524947 | + | 0.909235i | ||||
\(852\) | −8.51472 | − | 14.7479i | −0.291709 | − | 0.505256i | ||||
\(853\) | 49.4975 | 1.69476 | 0.847381 | − | 0.530986i | \(-0.178178\pi\) | ||||
0.847381 | + | 0.530986i | \(0.178178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.65685 | −0.330257 | ||||||||
\(856\) | −0.272078 | − | 0.471253i | −0.00929943 | − | 0.0161071i | ||||
\(857\) | 7.70711 | − | 13.3491i | 0.263270 | − | 0.455997i | −0.703839 | − | 0.710359i | \(-0.748532\pi\) |
0.967109 | + | 0.254363i | \(0.0818657\pi\) | |||||||
\(858\) | 1.07107 | − | 1.85514i | 0.0365657 | − | 0.0633336i | ||||
\(859\) | 28.7279 | + | 49.7582i | 0.980184 | + | 1.69773i | 0.661642 | + | 0.749820i | \(0.269860\pi\) |
0.318542 | + | 0.947909i | \(0.396807\pi\) | |||||||
\(860\) | 35.3137 | 1.20419 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.1716 | −0.380505 | ||||||||
\(863\) | −8.65685 | − | 14.9941i | −0.294683 | − | 0.510405i | 0.680228 | − | 0.733000i | \(-0.261881\pi\) |
−0.974911 | + | 0.222595i | \(0.928547\pi\) | |||||||
\(864\) | 2.20711 | − | 3.82282i | 0.0750873 | − | 0.130055i | ||||
\(865\) | −35.9706 | + | 62.3028i | −1.22304 | + | 2.11836i | ||||
\(866\) | −4.19239 | − | 7.26143i | −0.142463 | − | 0.246753i | ||||
\(867\) | 11.9706 | 0.406542 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.3137 | −0.926554 | ||||||||
\(870\) | 4.82843 | + | 8.36308i | 0.163699 | + | 0.283535i | ||||
\(871\) | −7.31371 | + | 12.6677i | −0.247816 | + | 0.429229i | ||||
\(872\) | −4.48528 | + | 7.76874i | −0.151891 | + | 0.263083i | ||||
\(873\) | 1.29289 | + | 2.23936i | 0.0437578 | + | 0.0757907i | ||||
\(874\) | −8.97056 | −0.303434 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.4142 | −0.858667 | ||||||||
\(877\) | 5.65685 | + | 9.79796i | 0.191018 | + | 0.330854i | 0.945588 | − | 0.325366i | \(-0.105488\pi\) |
−0.754570 | + | 0.656220i | \(0.772154\pi\) | |||||||
\(878\) | 2.62742 | − | 4.55082i | 0.0886710 | − | 0.153583i | ||||
\(879\) | −8.29289 | + | 14.3637i | −0.279712 | + | 0.484476i | ||||
\(880\) | −10.2426 | − | 17.7408i | −0.345279 | − | 0.598041i | ||||
\(881\) | −21.7574 | −0.733024 | −0.366512 | − | 0.930413i | \(-0.619448\pi\) | ||||
−0.366512 | + | 0.930413i | \(0.619448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.68629 | −0.157706 | −0.0788531 | − | 0.996886i | \(-0.525126\pi\) | ||||
−0.0788531 | + | 0.996886i | \(0.525126\pi\) | |||||||
\(884\) | −5.30152 | − | 9.18249i | −0.178309 | − | 0.308841i | ||||
\(885\) | −2.00000 | + | 3.46410i | −0.0672293 | + | 0.116445i | ||||
\(886\) | −7.24264 | + | 12.5446i | −0.243321 | + | 0.421445i | ||||
\(887\) | −1.41421 | − | 2.44949i | −0.0474846 | − | 0.0822458i | 0.841306 | − | 0.540559i | \(-0.181787\pi\) |
−0.888791 | + | 0.458313i | \(0.848454\pi\) | |||||||
\(888\) | −6.34315 | −0.212862 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −20.1421 | −0.675166 | ||||||||
\(891\) | 1.00000 | + | 1.73205i | 0.0335013 | + | 0.0580259i | ||||
\(892\) | −22.8284 | + | 39.5400i | −0.764352 | + | 1.32390i | ||||
\(893\) | −4.00000 | + | 6.92820i | −0.133855 | + | 0.231843i | ||||
\(894\) | 3.58579 | + | 6.21076i | 0.119927 | + | 0.207719i | ||||
\(895\) | 67.1127 | 2.24333 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.7990 | −0.661069 | ||||||||
\(898\) | 1.10051 | + | 1.90613i | 0.0367243 | + | 0.0636084i | ||||
\(899\) | 4.00000 | − | 6.92820i | 0.133407 | − | 0.231069i | ||||
\(900\) | 6.08579 | − | 10.5409i | 0.202860 | − | 0.351363i | ||||
\(901\) | 2.24264 | + | 3.88437i | 0.0747132 | + | 0.129407i | ||||
\(902\) | 5.17157 | 0.172195 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.42641 | 0.280258 | ||||||||
\(905\) | 4.41421 | + | 7.64564i | 0.146733 | + | 0.254150i | ||||
\(906\) | 2.48528 | − | 4.30463i | 0.0825679 | − | 0.143012i | ||||
\(907\) | 8.00000 | − | 13.8564i | 0.265636 | − | 0.460094i | −0.702094 | − | 0.712084i | \(-0.747752\pi\) |
0.967730 | + | 0.251990i | \(0.0810849\pi\) | |||||||
\(908\) | −21.7574 | − | 37.6849i | −0.722043 | − | 1.25062i | ||||
\(909\) | −2.92893 | −0.0971465 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.02944 | −0.0341068 | −0.0170534 | − | 0.999855i | \(-0.505429\pi\) | ||||
−0.0170534 | + | 0.999855i | \(0.505429\pi\) | |||||||
\(912\) | 4.24264 | + | 7.34847i | 0.140488 | + | 0.243332i | ||||
\(913\) | −7.31371 | + | 12.6677i | −0.242048 | + | 0.419240i | ||||
\(914\) | 3.72792 | − | 6.45695i | 0.123309 | − | 0.213577i | ||||
\(915\) | 20.8995 | + | 36.1990i | 0.690916 | + | 1.19670i | ||||
\(916\) | −0.443651 | −0.0146586 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −0.928932 | −0.0306593 | ||||||||
\(919\) | 4.14214 | + | 7.17439i | 0.136636 | + | 0.236661i | 0.926221 | − | 0.376980i | \(-0.123037\pi\) |
−0.789585 | + | 0.613641i | \(0.789704\pi\) | |||||||
\(920\) | 20.7279 | − | 35.9018i | 0.683379 | − | 1.18365i | ||||
\(921\) | −15.0711 | + | 26.1039i | −0.496609 | + | 0.860151i | ||||
\(922\) | −3.43503 | − | 5.94964i | −0.113127 | − | 0.195941i | ||||
\(923\) | −24.0833 | −0.792710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −26.6274 | −0.875504 | ||||||||
\(926\) | 5.51472 | + | 9.55177i | 0.181225 | + | 0.313891i | ||||
\(927\) | 2.24264 | − | 3.88437i | 0.0736580 | − | 0.127579i | ||||
\(928\) | 15.0711 | − | 26.1039i | 0.494732 | − | 0.856901i | ||||
\(929\) | −19.6066 | − | 33.9596i | −0.643272 | − | 1.11418i | −0.984698 | − | 0.174271i | \(-0.944243\pi\) |
0.341426 | − | 0.939909i | \(-0.389090\pi\) | |||||||
\(930\) | 1.65685 | 0.0543304 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 11.2304 | 0.367866 | ||||||||
\(933\) | −3.07107 | − | 5.31925i | −0.100542 | − | 0.174144i | ||||
\(934\) | 0.0416306 | − | 0.0721062i | 0.00136219 | − | 0.00235939i | ||||
\(935\) | −7.65685 | + | 13.2621i | −0.250406 | + | 0.433716i | ||||
\(936\) | −2.05025 | − | 3.55114i | −0.0670146 | − | 0.116073i | ||||
\(937\) | −30.5858 | −0.999194 | −0.499597 | − | 0.866258i | \(-0.666519\pi\) | ||||
−0.499597 | + | 0.866258i | \(0.666519\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.89949 | 0.0619877 | ||||||||
\(940\) | −8.82843 | − | 15.2913i | −0.287952 | − | 0.498747i | ||||
\(941\) | 17.6066 | − | 30.4955i | 0.573959 | − | 0.994126i | −0.422195 | − | 0.906505i | \(-0.638740\pi\) |
0.996154 | − | 0.0876208i | \(-0.0279264\pi\) | |||||||
\(942\) | −2.43503 | + | 4.21759i | −0.0793375 | + | 0.137417i | ||||
\(943\) | −23.8995 | − | 41.3951i | −0.778275 | − | 1.34801i | ||||
\(944\) | 3.51472 | 0.114394 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.68629 | −0.152364 | ||||||||
\(947\) | −15.3431 | − | 26.5751i | −0.498585 | − | 0.863575i | 0.501413 | − | 0.865208i | \(-0.332814\pi\) |
−0.999999 | + | 0.00163285i | \(0.999480\pi\) | |||||||
\(948\) | −12.4853 | + | 21.6251i | −0.405503 | + | 0.702352i | ||||
\(949\) | −17.9706 | + | 31.1259i | −0.583349 | + | 1.01039i | ||||
\(950\) | −3.89949 | − | 6.75412i | −0.126516 | − | 0.219133i | ||||
\(951\) | −10.0000 | −0.324272 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.00000 | 0.0647864 | 0.0323932 | − | 0.999475i | \(-0.489687\pi\) | ||||
0.0323932 | + | 0.999475i | \(0.489687\pi\) | |||||||
\(954\) | 0.414214 | + | 0.717439i | 0.0134107 | + | 0.0232279i | ||||
\(955\) | −30.7279 | + | 53.2223i | −0.994332 | + | 1.72223i | ||||
\(956\) | −14.3137 | + | 24.7921i | −0.462938 | + | 0.801833i | ||||
\(957\) | 6.82843 | + | 11.8272i | 0.220732 | + | 0.382319i | ||||
\(958\) | −0.769553 | −0.0248631 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −14.2426 | −0.459679 | ||||||||
\(961\) | 14.8137 | + | 25.6581i | 0.477862 | + | 0.827681i | ||||
\(962\) | −2.14214 | + | 3.71029i | −0.0690652 | + | 0.119624i | ||||
\(963\) | 0.171573 | − | 0.297173i | 0.00552886 | − | 0.00957626i | ||||
\(964\) | 14.8492 | + | 25.7196i | 0.478262 | + | 0.828374i | ||||
\(965\) | −18.1421 | −0.584016 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.6569 | 1.08233 | 0.541166 | − | 0.840916i | \(-0.317983\pi\) | ||||
0.541166 | + | 0.840916i | \(0.317983\pi\) | |||||||
\(968\) | −5.55025 | − | 9.61332i | −0.178392 | − | 0.308984i | ||||
\(969\) | 3.17157 | − | 5.49333i | 0.101886 | − | 0.176471i | ||||
\(970\) | −1.82843 | + | 3.16693i | −0.0587073 | + | 0.101684i | ||||
\(971\) | −25.3137 | − | 43.8446i | −0.812356 | − | 1.40704i | −0.911211 | − | 0.411939i | \(-0.864852\pi\) |
0.0988557 | − | 0.995102i | \(-0.468482\pi\) | |||||||
\(972\) | 1.82843 | 0.0586468 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.0294 | 0.353406 | ||||||||
\(975\) | −8.60660 | − | 14.9071i | −0.275632 | − | 0.477408i | ||||
\(976\) | 18.3640 | − | 31.8073i | 0.587816 | − | 1.01813i | ||||
\(977\) | 10.5858 | − | 18.3351i | 0.338669 | − | 0.586592i | −0.645513 | − | 0.763749i | \(-0.723357\pi\) |
0.984183 | + | 0.177157i | \(0.0566899\pi\) | |||||||
\(978\) | −2.34315 | − | 4.05845i | −0.0749255 | − | 0.129775i | ||||
\(979\) | −28.4853 | −0.910394 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.65685 | −0.180609 | ||||||||
\(982\) | −1.04163 | − | 1.80416i | −0.0332398 | − | 0.0575730i | ||||
\(983\) | −26.6274 | + | 46.1200i | −0.849283 | + | 1.47100i | 0.0325667 | + | 0.999470i | \(0.489632\pi\) |
−0.881849 | + | 0.471531i | \(0.843701\pi\) | |||||||
\(984\) | 4.94975 | − | 8.57321i | 0.157792 | − | 0.273304i | ||||
\(985\) | 3.41421 | + | 5.91359i | 0.108786 | + | 0.188423i | ||||
\(986\) | −6.34315 | −0.202007 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.3726 | 0.425439 | ||||||||
\(989\) | 21.6569 | + | 37.5108i | 0.688648 | + | 1.19277i | ||||
\(990\) | −1.41421 | + | 2.44949i | −0.0449467 | + | 0.0778499i | ||||
\(991\) | 6.48528 | − | 11.2328i | 0.206012 | − | 0.356823i | −0.744443 | − | 0.667686i | \(-0.767285\pi\) |
0.950455 | + | 0.310863i | \(0.100618\pi\) | |||||||
\(992\) | −2.58579 | − | 4.47871i | −0.0820988 | − | 0.142199i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 73.9411 | 2.34409 | ||||||||
\(996\) | 6.68629 | + | 11.5810i | 0.211863 | + | 0.366958i | ||||
\(997\) | 13.1924 | − | 22.8499i | 0.417807 | − | 0.723663i | −0.577911 | − | 0.816099i | \(-0.696132\pi\) |
0.995719 | + | 0.0924363i | \(0.0294654\pi\) | |||||||
\(998\) | −0.686292 | + | 1.18869i | −0.0217242 | + | 0.0376274i | ||||
\(999\) | −2.00000 | − | 3.46410i | −0.0632772 | − | 0.109599i |
(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 | 147.2.e.e.67.1 | 4 | ||
3.2 | odd | 2 | 441.2.e.f.361.2 | 4 | |||
4.3 | odd | 2 | 2352.2.q.bb.1537.2 | 4 | |||
7.2 | even | 3 | inner | 147.2.e.e.79.1 | 4 | ||
7.3 | odd | 6 | 147.2.a.e.1.2 | yes | 2 | ||
7.4 | even | 3 | 147.2.a.d.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 147.2.e.d.79.1 | 4 | |||
7.6 | odd | 2 | 147.2.e.d.67.1 | 4 | |||
21.2 | odd | 6 | 441.2.e.f.226.2 | 4 | |||
21.5 | even | 6 | 441.2.e.g.226.2 | 4 | |||
21.11 | odd | 6 | 441.2.a.j.1.1 | 2 | |||
21.17 | even | 6 | 441.2.a.i.1.1 | 2 | |||
21.20 | even | 2 | 441.2.e.g.361.2 | 4 | |||
28.3 | even | 6 | 2352.2.a.bc.1.2 | 2 | |||
28.11 | odd | 6 | 2352.2.a.be.1.1 | 2 | |||
28.19 | even | 6 | 2352.2.q.bd.961.1 | 4 | |||
28.23 | odd | 6 | 2352.2.q.bb.961.2 | 4 | |||
28.27 | even | 2 | 2352.2.q.bd.1537.1 | 4 | |||
35.4 | even | 6 | 3675.2.a.bf.1.1 | 2 | |||
35.24 | odd | 6 | 3675.2.a.bd.1.1 | 2 | |||
56.3 | even | 6 | 9408.2.a.dt.1.1 | 2 | |||
56.11 | odd | 6 | 9408.2.a.dq.1.2 | 2 | |||
56.45 | odd | 6 | 9408.2.a.di.1.1 | 2 | |||
56.53 | even | 6 | 9408.2.a.ef.1.2 | 2 | |||
84.11 | even | 6 | 7056.2.a.cv.1.2 | 2 | |||
84.59 | odd | 6 | 7056.2.a.cf.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.2.a.d.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
147.2.a.e.1.2 | yes | 2 | 7.3 | odd | 6 | ||
147.2.e.d.67.1 | 4 | 7.6 | odd | 2 | |||
147.2.e.d.79.1 | 4 | 7.5 | odd | 6 | |||
147.2.e.e.67.1 | 4 | 1.1 | even | 1 | trivial | ||
147.2.e.e.79.1 | 4 | 7.2 | even | 3 | inner | ||
441.2.a.i.1.1 | 2 | 21.17 | even | 6 | |||
441.2.a.j.1.1 | 2 | 21.11 | odd | 6 | |||
441.2.e.f.226.2 | 4 | 21.2 | odd | 6 | |||
441.2.e.f.361.2 | 4 | 3.2 | odd | 2 | |||
441.2.e.g.226.2 | 4 | 21.5 | even | 6 | |||
441.2.e.g.361.2 | 4 | 21.20 | even | 2 | |||
2352.2.a.bc.1.2 | 2 | 28.3 | even | 6 | |||
2352.2.a.be.1.1 | 2 | 28.11 | odd | 6 | |||
2352.2.q.bb.961.2 | 4 | 28.23 | odd | 6 | |||
2352.2.q.bb.1537.2 | 4 | 4.3 | odd | 2 | |||
2352.2.q.bd.961.1 | 4 | 28.19 | even | 6 | |||
2352.2.q.bd.1537.1 | 4 | 28.27 | even | 2 | |||
3675.2.a.bd.1.1 | 2 | 35.24 | odd | 6 | |||
3675.2.a.bf.1.1 | 2 | 35.4 | even | 6 | |||
7056.2.a.cf.1.1 | 2 | 84.59 | odd | 6 | |||
7056.2.a.cv.1.2 | 2 | 84.11 | even | 6 | |||
9408.2.a.di.1.1 | 2 | 56.45 | odd | 6 | |||
9408.2.a.dq.1.2 | 2 | 56.11 | odd | 6 | |||
9408.2.a.dt.1.1 | 2 | 56.3 | even | 6 | |||
9408.2.a.ef.1.2 | 2 | 56.53 | even | 6 |