Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.b (of order \(2\), degree \(1\), 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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.324000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 26x^{4} + 24x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.5 | ||
Root | \(1.33826i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.d.1249.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.209057i | 0.147826i | 0.997265 | + | 0.0739128i | \(0.0235486\pi\) | ||||
−0.997265 | + | 0.0739128i | \(0.976451\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.95630 | 0.978148 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.209057 | 0.0853471 | ||||||||
\(7\) | − 0.591023i | − 0.223386i | −0.993743 | − | 0.111693i | \(-0.964373\pi\) | ||||
0.993743 | − | 0.111693i | \(-0.0356273\pi\) | |||||||
\(8\) | 0.827091i | 0.292421i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.870796 | −0.262555 | −0.131277 | − | 0.991346i | \(-0.541908\pi\) | ||||
−0.131277 | + | 0.991346i | \(0.541908\pi\) | |||||||
\(12\) | − 1.95630i | − 0.564734i | ||||||||
\(13\) | 1.15057i | 0.319110i | 0.987189 | + | 0.159555i | \(0.0510060\pi\) | ||||
−0.987189 | + | 0.159555i | \(0.948994\pi\) | |||||||
\(14\) | 0.123557 | 0.0330221 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.73968 | 0.934920 | ||||||||
\(17\) | 4.93395i | 1.19666i | 0.801250 | + | 0.598330i | \(0.204169\pi\) | ||||
−0.801250 | + | 0.598330i | \(0.795831\pi\) | |||||||
\(18\) | − 0.209057i | − 0.0492752i | ||||||||
\(19\) | 2.84943 | 0.653704 | 0.326852 | − | 0.945075i | \(-0.394012\pi\) | ||||
0.326852 | + | 0.945075i | \(0.394012\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.591023 | −0.128972 | ||||||||
\(22\) | − 0.182046i | − 0.0388123i | ||||||||
\(23\) | 6.91259i | 1.44137i | 0.693260 | + | 0.720687i | \(0.256174\pi\) | ||||
−0.693260 | + | 0.720687i | \(0.743826\pi\) | |||||||
\(24\) | 0.827091 | 0.168829 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.240534 | −0.0471727 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − 1.15622i | − 0.218504i | ||||||||
\(29\) | 7.48883 | 1.39064 | 0.695320 | − | 0.718700i | \(-0.255262\pi\) | ||||
0.695320 | + | 0.718700i | \(0.255262\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.45991 | 0.621418 | 0.310709 | − | 0.950505i | \(-0.399434\pi\) | ||||
0.310709 | + | 0.950505i | \(0.399434\pi\) | |||||||
\(32\) | 2.43599i | 0.430626i | ||||||||
\(33\) | 0.870796i | 0.151586i | ||||||||
\(34\) | −1.03148 | −0.176897 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.95630 | −0.326049 | ||||||||
\(37\) | − 10.1681i | − 1.67163i | −0.549013 | − | 0.835814i | \(-0.684996\pi\) | ||||
0.549013 | − | 0.835814i | \(-0.315004\pi\) | |||||||
\(38\) | 0.595693i | 0.0966342i | ||||||||
\(39\) | 1.15057 | 0.184238 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.11409 | 1.42338 | 0.711691 | − | 0.702493i | \(-0.247930\pi\) | ||||
0.711691 | + | 0.702493i | \(0.247930\pi\) | |||||||
\(42\) | − 0.123557i | − 0.0190653i | ||||||||
\(43\) | − 2.81486i | − 0.429263i | −0.976695 | − | 0.214631i | \(-0.931145\pi\) | ||||
0.976695 | − | 0.214631i | \(-0.0688550\pi\) | |||||||
\(44\) | −1.70353 | −0.256817 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.44512 | −0.213072 | ||||||||
\(47\) | − 6.68842i | − 0.975606i | −0.872954 | − | 0.487803i | \(-0.837798\pi\) | ||||
0.872954 | − | 0.487803i | \(-0.162202\pi\) | |||||||
\(48\) | − 3.73968i | − 0.539777i | ||||||||
\(49\) | 6.65069 | 0.950099 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.93395 | 0.690892 | ||||||||
\(52\) | 2.25085i | 0.312137i | ||||||||
\(53\) | 3.87238i | 0.531912i | 0.963985 | + | 0.265956i | \(0.0856875\pi\) | ||||
−0.963985 | + | 0.265956i | \(0.914312\pi\) | |||||||
\(54\) | −0.209057 | −0.0284490 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.488830 | 0.0653226 | ||||||||
\(57\) | − 2.84943i | − 0.377416i | ||||||||
\(58\) | 1.56559i | 0.205572i | ||||||||
\(59\) | 11.5277 | 1.50078 | 0.750392 | − | 0.660993i | \(-0.229865\pi\) | ||||
0.750392 | + | 0.660993i | \(0.229865\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.7564 | −1.63329 | −0.816643 | − | 0.577143i | \(-0.804168\pi\) | ||||
−0.816643 | + | 0.577143i | \(0.804168\pi\) | |||||||
\(62\) | 0.723318i | 0.0918615i | ||||||||
\(63\) | 0.591023i | 0.0744619i | ||||||||
\(64\) | 6.97010 | 0.871263 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.182046 | −0.0224083 | ||||||||
\(67\) | 7.60292i | 0.928845i | 0.885614 | + | 0.464422i | \(0.153738\pi\) | ||||
−0.885614 | + | 0.464422i | \(0.846262\pi\) | |||||||
\(68\) | 9.65227i | 1.17051i | ||||||||
\(69\) | 6.91259 | 0.832178 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0566 | −1.78689 | −0.893444 | − | 0.449175i | \(-0.851718\pi\) | ||||
−0.893444 | + | 0.449175i | \(0.851718\pi\) | |||||||
\(72\) | − 0.827091i | − 0.0974736i | ||||||||
\(73\) | − 2.98798i | − 0.349716i | −0.984594 | − | 0.174858i | \(-0.944053\pi\) | ||||
0.984594 | − | 0.174858i | \(-0.0559467\pi\) | |||||||
\(74\) | 2.12571 | 0.247109 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.57433 | 0.639419 | ||||||||
\(77\) | 0.514660i | 0.0586510i | ||||||||
\(78\) | 0.240534i | 0.0272351i | ||||||||
\(79\) | −3.33728 | −0.375474 | −0.187737 | − | 0.982219i | \(-0.560115\pi\) | ||||
−0.187737 | + | 0.982219i | \(0.560115\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.90536i | 0.210412i | ||||||||
\(83\) | − 9.73310i | − 1.06835i | −0.845375 | − | 0.534173i | \(-0.820623\pi\) | ||||
0.845375 | − | 0.534173i | \(-0.179377\pi\) | |||||||
\(84\) | −1.15622 | −0.126153 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.588467 | 0.0634560 | ||||||||
\(87\) | − 7.48883i | − 0.802887i | ||||||||
\(88\) | − 0.720227i | − 0.0767765i | ||||||||
\(89\) | −0.645045 | −0.0683746 | −0.0341873 | − | 0.999415i | \(-0.510884\pi\) | ||||
−0.0341873 | + | 0.999415i | \(0.510884\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.680012 | 0.0712847 | ||||||||
\(92\) | 13.5231i | 1.40988i | ||||||||
\(93\) | − 3.45991i | − 0.358776i | ||||||||
\(94\) | 1.39826 | 0.144220 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.43599 | 0.248622 | ||||||||
\(97\) | − 11.6970i | − 1.18765i | −0.804596 | − | 0.593823i | \(-0.797618\pi\) | ||||
0.804596 | − | 0.593823i | \(-0.202382\pi\) | |||||||
\(98\) | 1.39037i | 0.140449i | ||||||||
\(99\) | 0.870796 | 0.0875183 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7636 | −1.46903 | −0.734517 | − | 0.678591i | \(-0.762591\pi\) | ||||
−0.734517 | + | 0.678591i | \(0.762591\pi\) | |||||||
\(102\) | 1.03148i | 0.102131i | ||||||||
\(103\) | − 1.41969i | − 0.139887i | −0.997551 | − | 0.0699433i | \(-0.977718\pi\) | ||||
0.997551 | − | 0.0699433i | \(-0.0222818\pi\) | |||||||
\(104\) | −0.951625 | −0.0933145 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.809547 | −0.0786301 | ||||||||
\(107\) | 14.9579i | 1.44603i | 0.690831 | + | 0.723016i | \(0.257245\pi\) | ||||
−0.690831 | + | 0.723016i | \(0.742755\pi\) | |||||||
\(108\) | 1.95630i | 0.188245i | ||||||||
\(109\) | 11.0977 | 1.06297 | 0.531485 | − | 0.847068i | \(-0.321634\pi\) | ||||
0.531485 | + | 0.847068i | \(0.321634\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.1681 | −0.965115 | ||||||||
\(112\) | − 2.21024i | − 0.208848i | ||||||||
\(113\) | − 12.1069i | − 1.13892i | −0.822020 | − | 0.569459i | \(-0.807153\pi\) | ||||
0.822020 | − | 0.569459i | \(-0.192847\pi\) | |||||||
\(114\) | 0.595693 | 0.0557918 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 14.6504 | 1.36025 | ||||||||
\(117\) | − 1.15057i | − 0.106370i | ||||||||
\(118\) | 2.40995i | 0.221854i | ||||||||
\(119\) | 2.91608 | 0.267317 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2417 | −0.931065 | ||||||||
\(122\) | − 2.66681i | − 0.241442i | ||||||||
\(123\) | − 9.11409i | − 0.821790i | ||||||||
\(124\) | 6.76860 | 0.607838 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.123557 | −0.0110074 | ||||||||
\(127\) | − 0.541671i | − 0.0480656i | −0.999711 | − | 0.0240328i | \(-0.992349\pi\) | ||||
0.999711 | − | 0.0240328i | \(-0.00765061\pi\) | |||||||
\(128\) | 6.32912i | 0.559421i | ||||||||
\(129\) | −2.81486 | −0.247835 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.46747 | −0.215583 | −0.107792 | − | 0.994173i | \(-0.534378\pi\) | ||||
−0.107792 | + | 0.994173i | \(0.534378\pi\) | |||||||
\(132\) | 1.70353i | 0.148274i | ||||||||
\(133\) | − 1.68408i | − 0.146028i | ||||||||
\(134\) | −1.58944 | −0.137307 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.08083 | −0.349928 | ||||||||
\(137\) | 5.64471i | 0.482261i | 0.970493 | + | 0.241130i | \(0.0775181\pi\) | ||||
−0.970493 | + | 0.241130i | \(0.922482\pi\) | |||||||
\(138\) | 1.44512i | 0.123017i | ||||||||
\(139\) | 0.326034 | 0.0276538 | 0.0138269 | − | 0.999904i | \(-0.495599\pi\) | ||||
0.0138269 | + | 0.999904i | \(0.495599\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.68842 | −0.563267 | ||||||||
\(142\) | − 3.14768i | − 0.264148i | ||||||||
\(143\) | − 1.00191i | − 0.0837839i | ||||||||
\(144\) | −3.73968 | −0.311640 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.624657 | 0.0516970 | ||||||||
\(147\) | − 6.65069i | − 0.548540i | ||||||||
\(148\) | − 19.8918i | − 1.63510i | ||||||||
\(149\) | 0.637614 | 0.0522354 | 0.0261177 | − | 0.999659i | \(-0.491686\pi\) | ||||
0.0261177 | + | 0.999659i | \(0.491686\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.3948 | 0.927299 | 0.463649 | − | 0.886019i | \(-0.346540\pi\) | ||||
0.463649 | + | 0.886019i | \(0.346540\pi\) | |||||||
\(152\) | 2.35674i | 0.191157i | ||||||||
\(153\) | − 4.93395i | − 0.398887i | ||||||||
\(154\) | −0.107593 | −0.00867011 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.25085 | 0.180212 | ||||||||
\(157\) | − 2.86068i | − 0.228307i | −0.993463 | − | 0.114154i | \(-0.963584\pi\) | ||||
0.993463 | − | 0.114154i | \(-0.0364156\pi\) | |||||||
\(158\) | − 0.697683i | − 0.0555046i | ||||||||
\(159\) | 3.87238 | 0.307099 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.08550 | 0.321982 | ||||||||
\(162\) | 0.209057i | 0.0164251i | ||||||||
\(163\) | 14.1106i | 1.10523i | 0.833437 | + | 0.552614i | \(0.186370\pi\) | ||||
−0.833437 | + | 0.552614i | \(0.813630\pi\) | |||||||
\(164\) | 17.8299 | 1.39228 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.03477 | 0.157929 | ||||||||
\(167\) | 7.49041i | 0.579625i | 0.957083 | + | 0.289813i | \(0.0935930\pi\) | ||||
−0.957083 | + | 0.289813i | \(0.906407\pi\) | |||||||
\(168\) | − 0.488830i | − 0.0377140i | ||||||||
\(169\) | 11.6762 | 0.898169 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.84943 | −0.217901 | ||||||||
\(172\) | − 5.50670i | − 0.419882i | ||||||||
\(173\) | 20.3231i | 1.54514i | 0.634929 | + | 0.772570i | \(0.281029\pi\) | ||||
−0.634929 | + | 0.772570i | \(0.718971\pi\) | |||||||
\(174\) | 1.56559 | 0.118687 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.25650 | −0.245468 | ||||||||
\(177\) | − 11.5277i | − 0.866478i | ||||||||
\(178\) | − 0.134851i | − 0.0101075i | ||||||||
\(179\) | −1.13209 | −0.0846164 | −0.0423082 | − | 0.999105i | \(-0.513471\pi\) | ||||
−0.0423082 | + | 0.999105i | \(0.513471\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.96450 | 0.369008 | 0.184504 | − | 0.982832i | \(-0.440932\pi\) | ||||
0.184504 | + | 0.982832i | \(0.440932\pi\) | |||||||
\(182\) | 0.142161i | 0.0105377i | ||||||||
\(183\) | 12.7564i | 0.942978i | ||||||||
\(184\) | −5.71734 | −0.421488 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.723318 | 0.0530362 | ||||||||
\(187\) | − 4.29647i | − 0.314189i | ||||||||
\(188\) | − 13.0845i | − 0.954287i | ||||||||
\(189\) | 0.591023 | 0.0429906 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.44610 | 0.466424 | 0.233212 | − | 0.972426i | \(-0.425076\pi\) | ||||
0.233212 | + | 0.972426i | \(0.425076\pi\) | |||||||
\(192\) | − 6.97010i | − 0.503024i | ||||||||
\(193\) | − 18.4312i | − 1.32671i | −0.748307 | − | 0.663353i | \(-0.769133\pi\) | ||||
0.748307 | − | 0.663353i | \(-0.230867\pi\) | |||||||
\(194\) | 2.44533 | 0.175564 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 13.0107 | 0.929337 | ||||||||
\(197\) | 16.8343i | 1.19940i | 0.800227 | + | 0.599698i | \(0.204713\pi\) | ||||
−0.800227 | + | 0.599698i | \(0.795287\pi\) | |||||||
\(198\) | 0.182046i | 0.0129374i | ||||||||
\(199\) | −16.9968 | −1.20487 | −0.602435 | − | 0.798168i | \(-0.705803\pi\) | ||||
−0.602435 | + | 0.798168i | \(0.705803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.60292 | 0.536269 | ||||||||
\(202\) | − 3.08643i | − 0.217161i | ||||||||
\(203\) | − 4.42607i | − 0.310649i | ||||||||
\(204\) | 9.65227 | 0.675794 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.296797 | 0.0206788 | ||||||||
\(207\) | − 6.91259i | − 0.480458i | ||||||||
\(208\) | 4.30276i | 0.298343i | ||||||||
\(209\) | −2.48127 | −0.171633 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.00874 | 0.344816 | 0.172408 | − | 0.985026i | \(-0.444845\pi\) | ||||
0.172408 | + | 0.985026i | \(0.444845\pi\) | |||||||
\(212\) | 7.57551i | 0.520288i | ||||||||
\(213\) | 15.0566i | 1.03166i | ||||||||
\(214\) | −3.12705 | −0.213761 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.827091 | −0.0562764 | ||||||||
\(217\) | − 2.04489i | − 0.138816i | ||||||||
\(218\) | 2.32006i | 0.157134i | ||||||||
\(219\) | −2.98798 | −0.201909 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.67685 | −0.381866 | ||||||||
\(222\) | − 2.12571i | − 0.142669i | ||||||||
\(223\) | 15.9452i | 1.06777i | 0.845556 | + | 0.533886i | \(0.179269\pi\) | ||||
−0.845556 | + | 0.533886i | \(0.820731\pi\) | |||||||
\(224\) | 1.43972 | 0.0961957 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.53102 | 0.168361 | ||||||||
\(227\) | 26.8967i | 1.78520i | 0.450850 | + | 0.892600i | \(0.351121\pi\) | ||||
−0.450850 | + | 0.892600i | \(0.648879\pi\) | |||||||
\(228\) | − 5.57433i | − 0.369169i | ||||||||
\(229\) | 2.94598 | 0.194676 | 0.0973378 | − | 0.995251i | \(-0.468967\pi\) | ||||
0.0973378 | + | 0.995251i | \(0.468967\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.514660 | 0.0338622 | ||||||||
\(232\) | 6.19394i | 0.406652i | ||||||||
\(233\) | − 23.4054i | − 1.53334i | −0.642041 | − | 0.766670i | \(-0.721912\pi\) | ||||
0.642041 | − | 0.766670i | \(-0.278088\pi\) | |||||||
\(234\) | 0.240534 | 0.0157242 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.5517 | 1.46799 | ||||||||
\(237\) | 3.33728i | 0.216780i | ||||||||
\(238\) | 0.609627i | 0.0395162i | ||||||||
\(239\) | −14.7790 | −0.955973 | −0.477987 | − | 0.878367i | \(-0.658633\pi\) | ||||
−0.477987 | + | 0.878367i | \(0.658633\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.3894 | −0.926903 | −0.463451 | − | 0.886122i | \(-0.653389\pi\) | ||||
−0.463451 | + | 0.886122i | \(0.653389\pi\) | |||||||
\(242\) | − 2.14110i | − 0.137635i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | −24.9552 | −1.59760 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.90536 | 0.121482 | ||||||||
\(247\) | 3.27847i | 0.208604i | ||||||||
\(248\) | 2.86166i | 0.181716i | ||||||||
\(249\) | −9.73310 | −0.616810 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7342 | −1.18249 | −0.591247 | − | 0.806490i | \(-0.701364\pi\) | ||||
−0.591247 | + | 0.806490i | \(0.701364\pi\) | |||||||
\(252\) | 1.15622i | 0.0728347i | ||||||||
\(253\) | − 6.01945i | − 0.378440i | ||||||||
\(254\) | 0.113240 | 0.00710532 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 12.6171 | 0.788566 | ||||||||
\(257\) | 6.42218i | 0.400605i | 0.979734 | + | 0.200302i | \(0.0641924\pi\) | ||||
−0.979734 | + | 0.200302i | \(0.935808\pi\) | |||||||
\(258\) | − 0.588467i | − 0.0366363i | ||||||||
\(259\) | −6.00959 | −0.373418 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.48883 | −0.463547 | ||||||||
\(262\) | − 0.515841i | − 0.0318687i | ||||||||
\(263\) | − 14.2071i | − 0.876050i | −0.898963 | − | 0.438025i | \(-0.855678\pi\) | ||||
0.898963 | − | 0.438025i | \(-0.144322\pi\) | |||||||
\(264\) | −0.720227 | −0.0443269 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.352068 | 0.0215867 | ||||||||
\(267\) | 0.645045i | 0.0394761i | ||||||||
\(268\) | 14.8736i | 0.908547i | ||||||||
\(269\) | 8.67115 | 0.528689 | 0.264345 | − | 0.964428i | \(-0.414844\pi\) | ||||
0.264345 | + | 0.964428i | \(0.414844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.5697 | 0.702807 | 0.351403 | − | 0.936224i | \(-0.385705\pi\) | ||||
0.351403 | + | 0.936224i | \(0.385705\pi\) | |||||||
\(272\) | 18.4514i | 1.11878i | ||||||||
\(273\) | − 0.680012i | − 0.0411562i | ||||||||
\(274\) | −1.18007 | −0.0712904 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 13.5231 | 0.813993 | ||||||||
\(277\) | − 19.2540i | − 1.15686i | −0.815732 | − | 0.578431i | \(-0.803665\pi\) | ||||
0.815732 | − | 0.578431i | \(-0.196335\pi\) | |||||||
\(278\) | 0.0681596i | 0.00408794i | ||||||||
\(279\) | −3.45991 | −0.207139 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.21917 | −0.192040 | −0.0960198 | − | 0.995379i | \(-0.530611\pi\) | ||||
−0.0960198 | + | 0.995379i | \(0.530611\pi\) | |||||||
\(282\) | − 1.39826i | − 0.0832652i | ||||||||
\(283\) | 30.6086i | 1.81949i | 0.415167 | + | 0.909745i | \(0.363723\pi\) | ||||
−0.415167 | + | 0.909745i | \(0.636277\pi\) | |||||||
\(284\) | −29.4551 | −1.74784 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.209456 | 0.0123854 | ||||||||
\(287\) | − 5.38664i | − 0.317963i | ||||||||
\(288\) | − 2.43599i | − 0.143542i | ||||||||
\(289\) | −7.34391 | −0.431995 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.6970 | −0.685688 | ||||||||
\(292\) | − 5.84536i | − 0.342074i | ||||||||
\(293\) | − 12.6725i | − 0.740333i | −0.928965 | − | 0.370166i | \(-0.879301\pi\) | ||||
0.928965 | − | 0.370166i | \(-0.120699\pi\) | |||||||
\(294\) | 1.39037 | 0.0810882 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 8.40995 | 0.488819 | ||||||||
\(297\) | − 0.870796i | − 0.0505287i | ||||||||
\(298\) | 0.133298i | 0.00772173i | ||||||||
\(299\) | −7.95341 | −0.459958 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.66365 | −0.0958911 | ||||||||
\(302\) | 2.38217i | 0.137078i | ||||||||
\(303\) | 14.7636i | 0.848147i | ||||||||
\(304\) | 10.6560 | 0.611162 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.03148 | 0.0589656 | ||||||||
\(307\) | − 28.0055i | − 1.59836i | −0.601092 | − | 0.799180i | \(-0.705268\pi\) | ||||
0.601092 | − | 0.799180i | \(-0.294732\pi\) | |||||||
\(308\) | 1.00683i | 0.0573693i | ||||||||
\(309\) | −1.41969 | −0.0807636 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.1437 | 1.65259 | 0.826293 | − | 0.563241i | \(-0.190446\pi\) | ||||
0.826293 | + | 0.563241i | \(0.190446\pi\) | |||||||
\(312\) | 0.951625i | 0.0538751i | ||||||||
\(313\) | 19.1782i | 1.08402i | 0.840373 | + | 0.542009i | \(0.182336\pi\) | ||||
−0.840373 | + | 0.542009i | \(0.817664\pi\) | |||||||
\(314\) | 0.598045 | 0.0337497 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.52871 | −0.367269 | ||||||||
\(317\) | − 19.8985i | − 1.11761i | −0.829300 | − | 0.558804i | \(-0.811260\pi\) | ||||
0.829300 | − | 0.558804i | \(-0.188740\pi\) | |||||||
\(318\) | 0.809547i | 0.0453971i | ||||||||
\(319\) | −6.52124 | −0.365119 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 14.9579 | 0.834867 | ||||||||
\(322\) | 0.854102i | 0.0475972i | ||||||||
\(323\) | 14.0590i | 0.782262i | ||||||||
\(324\) | 1.95630 | 0.108683 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.94992 | −0.163381 | ||||||||
\(327\) | − 11.0977i | − 0.613706i | ||||||||
\(328\) | 7.53818i | 0.416226i | ||||||||
\(329\) | −3.95301 | −0.217936 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.8128 | −1.52873 | −0.764366 | − | 0.644783i | \(-0.776948\pi\) | ||||
−0.764366 | + | 0.644783i | \(0.776948\pi\) | |||||||
\(332\) | − 19.0408i | − 1.04500i | ||||||||
\(333\) | 10.1681i | 0.557209i | ||||||||
\(334\) | −1.56592 | −0.0856834 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.21024 | −0.120578 | ||||||||
\(337\) | 31.7776i | 1.73104i | 0.500877 | + | 0.865518i | \(0.333011\pi\) | ||||
−0.500877 | + | 0.865518i | \(0.666989\pi\) | |||||||
\(338\) | 2.44099i | 0.132772i | ||||||||
\(339\) | −12.1069 | −0.657555 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.01287 | −0.163156 | ||||||||
\(342\) | − 0.595693i | − 0.0322114i | ||||||||
\(343\) | − 8.06787i | − 0.435624i | ||||||||
\(344\) | 2.32815 | 0.125525 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.24869 | −0.228411 | ||||||||
\(347\) | 27.6962i | 1.48681i | 0.668842 | + | 0.743404i | \(0.266790\pi\) | ||||
−0.668842 | + | 0.743404i | \(0.733210\pi\) | |||||||
\(348\) | − 14.6504i | − 0.785342i | ||||||||
\(349\) | 11.3435 | 0.607206 | 0.303603 | − | 0.952799i | \(-0.401810\pi\) | ||||
0.303603 | + | 0.952799i | \(0.401810\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.15057 | −0.0614128 | ||||||||
\(352\) | − 2.12125i | − 0.113063i | ||||||||
\(353\) | − 13.2761i | − 0.706614i | −0.935507 | − | 0.353307i | \(-0.885057\pi\) | ||||
0.935507 | − | 0.353307i | \(-0.114943\pi\) | |||||||
\(354\) | 2.40995 | 0.128088 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.26190 | −0.0668805 | ||||||||
\(357\) | − 2.91608i | − 0.154335i | ||||||||
\(358\) | − 0.236671i | − 0.0125085i | ||||||||
\(359\) | −0.547922 | −0.0289182 | −0.0144591 | − | 0.999895i | \(-0.504603\pi\) | ||||
−0.0144591 | + | 0.999895i | \(0.504603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8807 | −0.572671 | ||||||||
\(362\) | 1.03786i | 0.0545489i | ||||||||
\(363\) | 10.2417i | 0.537551i | ||||||||
\(364\) | 1.33030 | 0.0697269 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.66681 | −0.139396 | ||||||||
\(367\) | − 32.3147i | − 1.68681i | −0.537277 | − | 0.843406i | \(-0.680547\pi\) | ||||
0.537277 | − | 0.843406i | \(-0.319453\pi\) | |||||||
\(368\) | 25.8509i | 1.34757i | ||||||||
\(369\) | −9.11409 | −0.474461 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.28866 | 0.118821 | ||||||||
\(372\) | − 6.76860i | − 0.350936i | ||||||||
\(373\) | − 15.2740i | − 0.790860i | −0.918496 | − | 0.395430i | \(-0.870596\pi\) | ||||
0.918496 | − | 0.395430i | \(-0.129404\pi\) | |||||||
\(374\) | 0.898206 | 0.0464451 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.53193 | 0.285288 | ||||||||
\(377\) | 8.61641i | 0.443768i | ||||||||
\(378\) | 0.123557i | 0.00635511i | ||||||||
\(379\) | −11.5928 | −0.595482 | −0.297741 | − | 0.954647i | \(-0.596233\pi\) | ||||
−0.297741 | + | 0.954647i | \(0.596233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.541671 | −0.0277507 | ||||||||
\(382\) | 1.34760i | 0.0689493i | ||||||||
\(383\) | − 27.1864i | − 1.38916i | −0.719416 | − | 0.694580i | \(-0.755590\pi\) | ||||
0.719416 | − | 0.694580i | \(-0.244410\pi\) | |||||||
\(384\) | 6.32912 | 0.322982 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.85317 | 0.196121 | ||||||||
\(387\) | 2.81486i | 0.143088i | ||||||||
\(388\) | − 22.8827i | − 1.16169i | ||||||||
\(389\) | −36.2825 | −1.83959 | −0.919797 | − | 0.392394i | \(-0.871647\pi\) | ||||
−0.919797 | + | 0.392394i | \(0.871647\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −34.1064 | −1.72484 | ||||||||
\(392\) | 5.50073i | 0.277829i | ||||||||
\(393\) | 2.46747i | 0.124467i | ||||||||
\(394\) | −3.51933 | −0.177301 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.70353 | 0.0856058 | ||||||||
\(397\) | 24.6879i | 1.23905i | 0.784977 | + | 0.619525i | \(0.212675\pi\) | ||||
−0.784977 | + | 0.619525i | \(0.787325\pi\) | |||||||
\(398\) | − 3.55330i | − 0.178111i | ||||||||
\(399\) | −1.68408 | −0.0843094 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.4435 | −1.72003 | −0.860014 | − | 0.510271i | \(-0.829545\pi\) | ||||
−0.860014 | + | 0.510271i | \(0.829545\pi\) | |||||||
\(402\) | 1.58944i | 0.0792742i | ||||||||
\(403\) | 3.98086i | 0.198301i | ||||||||
\(404\) | −28.8820 | −1.43693 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.925301 | 0.0459219 | ||||||||
\(407\) | 8.85435i | 0.438894i | ||||||||
\(408\) | 4.08083i | 0.202031i | ||||||||
\(409\) | 12.9896 | 0.642294 | 0.321147 | − | 0.947029i | \(-0.395932\pi\) | ||||
0.321147 | + | 0.947029i | \(0.395932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.64471 | 0.278433 | ||||||||
\(412\) | − 2.77734i | − 0.136830i | ||||||||
\(413\) | − 6.81316i | − 0.335254i | ||||||||
\(414\) | 1.44512 | 0.0710240 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.80277 | −0.137417 | ||||||||
\(417\) | − 0.326034i | − 0.0159659i | ||||||||
\(418\) | − 0.518727i | − 0.0253718i | ||||||||
\(419\) | −18.5116 | −0.904353 | −0.452177 | − | 0.891928i | \(-0.649352\pi\) | ||||
−0.452177 | + | 0.891928i | \(0.649352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.8357 | 1.16168 | 0.580841 | − | 0.814017i | \(-0.302724\pi\) | ||||
0.580841 | + | 0.814017i | \(0.302724\pi\) | |||||||
\(422\) | 1.04711i | 0.0509726i | ||||||||
\(423\) | 6.68842i | 0.325202i | ||||||||
\(424\) | −3.20281 | −0.155542 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.14768 | −0.152506 | ||||||||
\(427\) | 7.53931i | 0.364853i | ||||||||
\(428\) | 29.2620i | 1.41443i | ||||||||
\(429\) | −1.00191 | −0.0483727 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.6800 | −1.42963 | −0.714817 | − | 0.699312i | \(-0.753490\pi\) | ||||
−0.714817 | + | 0.699312i | \(0.753490\pi\) | |||||||
\(432\) | 3.73968i | 0.179926i | ||||||||
\(433\) | − 18.0164i | − 0.865811i | −0.901439 | − | 0.432906i | \(-0.857488\pi\) | ||||
0.901439 | − | 0.432906i | \(-0.142512\pi\) | |||||||
\(434\) | 0.427497 | 0.0205205 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 21.7104 | 1.03974 | ||||||||
\(437\) | 19.6970i | 0.942233i | ||||||||
\(438\) | − 0.624657i | − 0.0298473i | ||||||||
\(439\) | −21.0442 | −1.00438 | −0.502191 | − | 0.864757i | \(-0.667473\pi\) | ||||
−0.502191 | + | 0.864757i | \(0.667473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.65069 | −0.316700 | ||||||||
\(442\) | − 1.18679i | − 0.0564496i | ||||||||
\(443\) | − 4.15877i | − 0.197589i | −0.995108 | − | 0.0987946i | \(-0.968501\pi\) | ||||
0.995108 | − | 0.0987946i | \(-0.0314987\pi\) | |||||||
\(444\) | −19.8918 | −0.944024 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.33346 | −0.157844 | ||||||||
\(447\) | − 0.637614i | − 0.0301581i | ||||||||
\(448\) | − 4.11949i | − 0.194628i | ||||||||
\(449\) | 7.39256 | 0.348876 | 0.174438 | − | 0.984668i | \(-0.444189\pi\) | ||||
0.174438 | + | 0.984668i | \(0.444189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.93651 | −0.373716 | ||||||||
\(452\) | − 23.6846i | − 1.11403i | ||||||||
\(453\) | − 11.3948i | − 0.535376i | ||||||||
\(454\) | −5.62295 | −0.263898 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.35674 | 0.110364 | ||||||||
\(457\) | 0.573353i | 0.0268203i | 0.999910 | + | 0.0134102i | \(0.00426871\pi\) | ||||
−0.999910 | + | 0.0134102i | \(0.995731\pi\) | |||||||
\(458\) | 0.615877i | 0.0287780i | ||||||||
\(459\) | −4.93395 | −0.230297 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.74666 | 0.174499 | 0.0872497 | − | 0.996186i | \(-0.472192\pi\) | ||||
0.0872497 | + | 0.996186i | \(0.472192\pi\) | |||||||
\(462\) | 0.107593i | 0.00500569i | ||||||||
\(463\) | 17.3803i | 0.807732i | 0.914818 | + | 0.403866i | \(0.132334\pi\) | ||||
−0.914818 | + | 0.403866i | \(0.867666\pi\) | |||||||
\(464\) | 28.0058 | 1.30014 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.89307 | 0.226667 | ||||||||
\(467\) | − 10.0211i | − 0.463720i | −0.972749 | − | 0.231860i | \(-0.925519\pi\) | ||||
0.972749 | − | 0.231860i | \(-0.0744811\pi\) | |||||||
\(468\) | − 2.25085i | − 0.104046i | ||||||||
\(469\) | 4.49350 | 0.207491 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.86068 | −0.131813 | ||||||||
\(472\) | 9.53449i | 0.438860i | ||||||||
\(473\) | 2.45117i | 0.112705i | ||||||||
\(474\) | −0.697683 | −0.0320456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.70471 | 0.261475 | ||||||||
\(477\) | − 3.87238i | − 0.177304i | ||||||||
\(478\) | − 3.08965i | − 0.141317i | ||||||||
\(479\) | −18.6136 | −0.850476 | −0.425238 | − | 0.905082i | \(-0.639810\pi\) | ||||
−0.425238 | + | 0.905082i | \(0.639810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.6991 | 0.533433 | ||||||||
\(482\) | − 3.00820i | − 0.137020i | ||||||||
\(483\) | − 4.08550i | − 0.185897i | ||||||||
\(484\) | −20.0358 | −0.910719 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.209057 | 0.00948301 | ||||||||
\(487\) | − 2.07209i | − 0.0938954i | −0.998897 | − | 0.0469477i | \(-0.985051\pi\) | ||||
0.998897 | − | 0.0469477i | \(-0.0149494\pi\) | |||||||
\(488\) | − 10.5507i | − 0.477607i | ||||||||
\(489\) | 14.1106 | 0.638103 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.2355 | −1.00348 | −0.501738 | − | 0.865020i | \(-0.667306\pi\) | ||||
−0.501738 | + | 0.865020i | \(0.667306\pi\) | |||||||
\(492\) | − 17.8299i | − 0.803832i | ||||||||
\(493\) | 36.9495i | 1.66412i | ||||||||
\(494\) | −0.685386 | −0.0308370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.9390 | 0.580976 | ||||||||
\(497\) | 8.89878i | 0.399165i | ||||||||
\(498\) | − 2.03477i | − 0.0911803i | ||||||||
\(499\) | −28.2713 | −1.26560 | −0.632798 | − | 0.774317i | \(-0.718094\pi\) | ||||
−0.632798 | + | 0.774317i | \(0.718094\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.49041 | 0.334647 | ||||||||
\(502\) | − 3.91652i | − 0.174803i | ||||||||
\(503\) | − 3.39793i | − 0.151506i | −0.997127 | − | 0.0757531i | \(-0.975864\pi\) | ||||
0.997127 | − | 0.0757531i | \(-0.0241361\pi\) | |||||||
\(504\) | −0.488830 | −0.0217742 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.25841 | 0.0559431 | ||||||||
\(507\) | − 11.6762i | − 0.518558i | ||||||||
\(508\) | − 1.05967i | − 0.0470152i | ||||||||
\(509\) | 10.8405 | 0.480497 | 0.240248 | − | 0.970711i | \(-0.422771\pi\) | ||||
0.240248 | + | 0.970711i | \(0.422771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.76596 | −0.0781216 | ||||||||
\(512\) | 15.2959i | 0.675991i | ||||||||
\(513\) | 2.84943i | 0.125805i | ||||||||
\(514\) | −1.34260 | −0.0592196 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.50670 | −0.242419 | ||||||||
\(517\) | 5.82425i | 0.256150i | ||||||||
\(518\) | − 1.25635i | − 0.0552007i | ||||||||
\(519\) | 20.3231 | 0.892087 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.6473 | 0.685519 | 0.342760 | − | 0.939423i | \(-0.388638\pi\) | ||||
0.342760 | + | 0.939423i | \(0.388638\pi\) | |||||||
\(522\) | − 1.56559i | − 0.0685241i | ||||||||
\(523\) | − 18.3578i | − 0.802729i | −0.915918 | − | 0.401364i | \(-0.868536\pi\) | ||||
0.915918 | − | 0.401364i | \(-0.131464\pi\) | |||||||
\(524\) | −4.82709 | −0.210872 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.97010 | 0.129503 | ||||||||
\(527\) | 17.0710i | 0.743626i | ||||||||
\(528\) | 3.25650i | 0.141721i | ||||||||
\(529\) | −24.7839 | −1.07756 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.5277 | −0.500261 | ||||||||
\(532\) | − 3.29456i | − 0.142837i | ||||||||
\(533\) | 10.4864i | 0.454216i | ||||||||
\(534\) | −0.134851 | −0.00583558 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.28831 | −0.271613 | ||||||||
\(537\) | 1.13209i | 0.0488533i | ||||||||
\(538\) | 1.81276i | 0.0781538i | ||||||||
\(539\) | −5.79139 | −0.249453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.8856 | −0.596988 | −0.298494 | − | 0.954412i | \(-0.596484\pi\) | ||||
−0.298494 | + | 0.954412i | \(0.596484\pi\) | |||||||
\(542\) | 2.41872i | 0.103893i | ||||||||
\(543\) | − 4.96450i | − 0.213047i | ||||||||
\(544\) | −12.0191 | −0.515313 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.142161 | 0.00608394 | ||||||||
\(547\) | − 41.9134i | − 1.79209i | −0.443966 | − | 0.896043i | \(-0.646429\pi\) | ||||
0.443966 | − | 0.896043i | \(-0.353571\pi\) | |||||||
\(548\) | 11.0427i | 0.471722i | ||||||||
\(549\) | 12.7564 | 0.544429 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.3389 | 0.909068 | ||||||||
\(552\) | 5.71734i | 0.243346i | ||||||||
\(553\) | 1.97241i | 0.0838755i | ||||||||
\(554\) | 4.02518 | 0.171014 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.637818 | 0.0270495 | ||||||||
\(557\) | 8.04257i | 0.340774i | 0.985377 | + | 0.170387i | \(0.0545019\pi\) | ||||
−0.985377 | + | 0.170387i | \(0.945498\pi\) | |||||||
\(558\) | − 0.723318i | − 0.0306205i | ||||||||
\(559\) | 3.23869 | 0.136982 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.29647 | −0.181397 | ||||||||
\(562\) | − 0.672990i | − 0.0283884i | ||||||||
\(563\) | 5.67464i | 0.239158i | 0.992825 | + | 0.119579i | \(0.0381544\pi\) | ||||
−0.992825 | + | 0.119579i | \(0.961846\pi\) | |||||||
\(564\) | −13.0845 | −0.550958 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −6.39893 | −0.268967 | ||||||||
\(567\) | − 0.591023i | − 0.0248206i | ||||||||
\(568\) | − 12.4532i | − 0.522523i | ||||||||
\(569\) | −8.25303 | −0.345985 | −0.172993 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172993 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.5703 | −0.735293 | −0.367646 | − | 0.929966i | \(-0.619836\pi\) | ||||
−0.367646 | + | 0.929966i | \(0.619836\pi\) | |||||||
\(572\) | − 1.96003i | − 0.0819531i | ||||||||
\(573\) | − 6.44610i | − 0.269290i | ||||||||
\(574\) | 1.12611 | 0.0470031 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6.97010 | −0.290421 | ||||||||
\(577\) | − 29.6207i | − 1.23313i | −0.787305 | − | 0.616564i | \(-0.788524\pi\) | ||||
0.787305 | − | 0.616564i | \(-0.211476\pi\) | |||||||
\(578\) | − 1.53529i | − 0.0638598i | ||||||||
\(579\) | −18.4312 | −0.765974 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.75249 | −0.238653 | ||||||||
\(582\) | − 2.44533i | − 0.101362i | ||||||||
\(583\) | − 3.37205i | − 0.139656i | ||||||||
\(584\) | 2.47133 | 0.102264 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.64926 | 0.109440 | ||||||||
\(587\) | 18.1475i | 0.749027i | 0.927222 | + | 0.374513i | \(0.122190\pi\) | ||||
−0.927222 | + | 0.374513i | \(0.877810\pi\) | |||||||
\(588\) | − 13.0107i | − 0.536553i | ||||||||
\(589\) | 9.85877 | 0.406224 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16.8343 | 0.692471 | ||||||||
\(592\) | − 38.0255i | − 1.56284i | ||||||||
\(593\) | − 26.0022i | − 1.06778i | −0.845553 | − | 0.533891i | \(-0.820729\pi\) | ||||
0.845553 | − | 0.533891i | \(-0.179271\pi\) | |||||||
\(594\) | 0.182046 | 0.00746943 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.24736 | 0.0510939 | ||||||||
\(597\) | 16.9968i | 0.695632i | ||||||||
\(598\) | − 1.66272i | − 0.0679935i | ||||||||
\(599\) | −20.6259 | −0.842753 | −0.421376 | − | 0.906886i | \(-0.638453\pi\) | ||||
−0.421376 | + | 0.906886i | \(0.638453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.7602 | −0.724452 | −0.362226 | − | 0.932090i | \(-0.617983\pi\) | ||||
−0.362226 | + | 0.932090i | \(0.617983\pi\) | |||||||
\(602\) | − 0.347797i | − 0.0141752i | ||||||||
\(603\) | − 7.60292i | − 0.309615i | ||||||||
\(604\) | 22.2917 | 0.907035 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.08643 | −0.125378 | ||||||||
\(607\) | 13.0143i | 0.528232i | 0.964491 | + | 0.264116i | \(0.0850803\pi\) | ||||
−0.964491 | + | 0.264116i | \(0.914920\pi\) | |||||||
\(608\) | 6.94118i | 0.281502i | ||||||||
\(609\) | −4.42607 | −0.179353 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.69548 | 0.311326 | ||||||||
\(612\) | − 9.65227i | − 0.390170i | ||||||||
\(613\) | − 21.9959i | − 0.888407i | −0.895926 | − | 0.444204i | \(-0.853487\pi\) | ||||
0.895926 | − | 0.444204i | \(-0.146513\pi\) | |||||||
\(614\) | 5.85475 | 0.236278 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.425671 | −0.0171508 | ||||||||
\(617\) | − 33.3091i | − 1.34097i | −0.741922 | − | 0.670487i | \(-0.766085\pi\) | ||||
0.741922 | − | 0.670487i | \(-0.233915\pi\) | |||||||
\(618\) | − 0.296797i | − 0.0119389i | ||||||||
\(619\) | 27.9714 | 1.12426 | 0.562132 | − | 0.827048i | \(-0.309981\pi\) | ||||
0.562132 | + | 0.827048i | \(0.309981\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.91259 | −0.277393 | ||||||||
\(622\) | 6.09268i | 0.244294i | ||||||||
\(623\) | 0.381236i | 0.0152739i | ||||||||
\(624\) | 4.30276 | 0.172248 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.00934 | −0.160245 | ||||||||
\(627\) | 2.48127i | 0.0990925i | ||||||||
\(628\) | − 5.59634i | − 0.223318i | ||||||||
\(629\) | 50.1690 | 2.00037 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.0172 | −0.916301 | −0.458150 | − | 0.888875i | \(-0.651488\pi\) | ||||
−0.458150 | + | 0.888875i | \(0.651488\pi\) | |||||||
\(632\) | − 2.76024i | − 0.109796i | ||||||||
\(633\) | − 5.00874i | − 0.199079i | ||||||||
\(634\) | 4.15991 | 0.165211 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 7.57551 | 0.300388 | ||||||||
\(637\) | 7.65208i | 0.303186i | ||||||||
\(638\) | − 1.36331i | − 0.0539740i | ||||||||
\(639\) | 15.0566 | 0.595629 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.1915 | 1.15300 | 0.576498 | − | 0.817099i | \(-0.304419\pi\) | ||||
0.576498 | + | 0.817099i | \(0.304419\pi\) | |||||||
\(642\) | 3.12705i | 0.123415i | ||||||||
\(643\) | − 29.6236i | − 1.16824i | −0.811668 | − | 0.584119i | \(-0.801440\pi\) | ||||
0.811668 | − | 0.584119i | \(-0.198560\pi\) | |||||||
\(644\) | 7.99244 | 0.314946 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.93912 | −0.115638 | ||||||||
\(647\) | − 49.0862i | − 1.92978i | −0.262657 | − | 0.964889i | \(-0.584599\pi\) | ||||
0.262657 | − | 0.964889i | \(-0.415401\pi\) | |||||||
\(648\) | 0.827091i | 0.0324912i | ||||||||
\(649\) | −10.0383 | −0.394038 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.04489 | −0.0801454 | ||||||||
\(652\) | 27.6045i | 1.08108i | ||||||||
\(653\) | − 11.6946i | − 0.457645i | −0.973468 | − | 0.228823i | \(-0.926512\pi\) | ||||
0.973468 | − | 0.228823i | \(-0.0734876\pi\) | |||||||
\(654\) | 2.32006 | 0.0907214 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 34.0838 | 1.33075 | ||||||||
\(657\) | 2.98798i | 0.116572i | ||||||||
\(658\) | − 0.826404i | − 0.0322166i | ||||||||
\(659\) | −1.18709 | −0.0462424 | −0.0231212 | − | 0.999733i | \(-0.507360\pi\) | ||||
−0.0231212 | + | 0.999733i | \(0.507360\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.72234 | 0.144782 | 0.0723912 | − | 0.997376i | \(-0.476937\pi\) | ||||
0.0723912 | + | 0.997376i | \(0.476937\pi\) | |||||||
\(662\) | − 5.81446i | − 0.225986i | ||||||||
\(663\) | 5.67685i | 0.220471i | ||||||||
\(664\) | 8.05016 | 0.312407 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.12571 | −0.0823698 | ||||||||
\(667\) | 51.7672i | 2.00443i | ||||||||
\(668\) | 14.6535i | 0.566959i | ||||||||
\(669\) | 15.9452 | 0.616479 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 11.1082 | 0.428827 | ||||||||
\(672\) | − 1.43972i | − 0.0555386i | ||||||||
\(673\) | 46.9935i | 1.81147i | 0.423847 | + | 0.905734i | \(0.360680\pi\) | ||||
−0.423847 | + | 0.905734i | \(0.639320\pi\) | |||||||
\(674\) | −6.64333 | −0.255892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 22.8421 | 0.878541 | ||||||||
\(677\) | − 36.4081i | − 1.39928i | −0.714497 | − | 0.699639i | \(-0.753344\pi\) | ||||
0.714497 | − | 0.699639i | \(-0.246656\pi\) | |||||||
\(678\) | − 2.53102i | − 0.0972034i | ||||||||
\(679\) | −6.91317 | −0.265303 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.8967 | 1.03069 | ||||||||
\(682\) | − 0.629862i | − 0.0241187i | ||||||||
\(683\) | 4.66507i | 0.178504i | 0.996009 | + | 0.0892519i | \(0.0284476\pi\) | ||||
−0.996009 | + | 0.0892519i | \(0.971552\pi\) | |||||||
\(684\) | −5.57433 | −0.213140 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.68664 | 0.0643964 | ||||||||
\(687\) | − 2.94598i | − 0.112396i | ||||||||
\(688\) | − 10.5267i | − 0.401326i | ||||||||
\(689\) | −4.45543 | −0.169738 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.9254 | 1.21450 | 0.607249 | − | 0.794511i | \(-0.292273\pi\) | ||||
0.607249 | + | 0.794511i | \(0.292273\pi\) | |||||||
\(692\) | 39.7581i | 1.51138i | ||||||||
\(693\) | − 0.514660i | − 0.0195503i | ||||||||
\(694\) | −5.79008 | −0.219788 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 6.19394 | 0.234781 | ||||||||
\(697\) | 44.9685i | 1.70330i | ||||||||
\(698\) | 2.37144i | 0.0897605i | ||||||||
\(699\) | −23.4054 | −0.885275 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.09598 | −0.116933 | −0.0584667 | − | 0.998289i | \(-0.518621\pi\) | ||||
−0.0584667 | + | 0.998289i | \(0.518621\pi\) | |||||||
\(702\) | − 0.240534i | − 0.00907838i | ||||||||
\(703\) | − 28.9733i | − 1.09275i | ||||||||
\(704\) | −6.06954 | −0.228754 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.77546 | 0.104456 | ||||||||
\(707\) | 8.72563i | 0.328161i | ||||||||
\(708\) | − 22.5517i | − 0.847543i | ||||||||
\(709\) | −47.0490 | −1.76696 | −0.883481 | − | 0.468468i | \(-0.844806\pi\) | ||||
−0.883481 | + | 0.468468i | \(0.844806\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.33728 | 0.125158 | ||||||||
\(712\) | − 0.533511i | − 0.0199942i | ||||||||
\(713\) | 23.9169i | 0.895696i | ||||||||
\(714\) | 0.609627 | 0.0228147 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.21470 | −0.0827674 | ||||||||
\(717\) | 14.7790i | 0.551931i | ||||||||
\(718\) | − 0.114547i | − 0.00427485i | ||||||||
\(719\) | −25.7083 | −0.958757 | −0.479378 | − | 0.877608i | \(-0.659138\pi\) | ||||
−0.479378 | + | 0.877608i | \(0.659138\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.839072 | −0.0312487 | ||||||||
\(722\) | − 2.27469i | − 0.0846553i | ||||||||
\(723\) | 14.3894i | 0.535147i | ||||||||
\(724\) | 9.71202 | 0.360945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.14110 | −0.0794637 | ||||||||
\(727\) | 35.4025i | 1.31301i | 0.754323 | + | 0.656504i | \(0.227965\pi\) | ||||
−0.754323 | + | 0.656504i | \(0.772035\pi\) | |||||||
\(728\) | 0.562432i | 0.0208451i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.8884 | 0.513681 | ||||||||
\(732\) | 24.9552i | 0.922372i | ||||||||
\(733\) | 25.7565i | 0.951336i | 0.879625 | + | 0.475668i | \(0.157794\pi\) | ||||
−0.879625 | + | 0.475668i | \(0.842206\pi\) | |||||||
\(734\) | 6.75560 | 0.249354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −16.8390 | −0.620693 | ||||||||
\(737\) | − 6.62059i | − 0.243873i | ||||||||
\(738\) | − 1.90536i | − 0.0701374i | ||||||||
\(739\) | 22.1071 | 0.813222 | 0.406611 | − | 0.913601i | \(-0.366711\pi\) | ||||
0.406611 | + | 0.913601i | \(0.366711\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.27847 | 0.120437 | ||||||||
\(742\) | 0.478461i | 0.0175648i | ||||||||
\(743\) | 20.2268i | 0.742049i | 0.928623 | + | 0.371025i | \(0.120993\pi\) | ||||
−0.928623 | + | 0.371025i | \(0.879007\pi\) | |||||||
\(744\) | 2.86166 | 0.104914 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.19314 | 0.116909 | ||||||||
\(747\) | 9.73310i | 0.356116i | ||||||||
\(748\) | − 8.40516i | − 0.307323i | ||||||||
\(749\) | 8.84045 | 0.323023 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.23206 | −0.0449584 | −0.0224792 | − | 0.999747i | \(-0.507156\pi\) | ||||
−0.0224792 | + | 0.999747i | \(0.507156\pi\) | |||||||
\(752\) | − 25.0126i | − 0.912114i | ||||||||
\(753\) | 18.7342i | 0.682714i | ||||||||
\(754\) | −1.80132 | −0.0656002 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.15622 | 0.0420511 | ||||||||
\(757\) | − 15.2062i | − 0.552678i | −0.961060 | − | 0.276339i | \(-0.910879\pi\) | ||||
0.961060 | − | 0.276339i | \(-0.0891212\pi\) | |||||||
\(758\) | − 2.42356i | − 0.0880275i | ||||||||
\(759\) | −6.01945 | −0.218492 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −32.3209 | −1.17163 | −0.585817 | − | 0.810444i | \(-0.699226\pi\) | ||||
−0.585817 | + | 0.810444i | \(0.699226\pi\) | |||||||
\(762\) | − 0.113240i | − 0.00410226i | ||||||||
\(763\) | − 6.55901i | − 0.237452i | ||||||||
\(764\) | 12.6105 | 0.456231 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 5.68350 | 0.205353 | ||||||||
\(767\) | 13.2635i | 0.478915i | ||||||||
\(768\) | − 12.6171i | − 0.455279i | ||||||||
\(769\) | 28.8068 | 1.03880 | 0.519400 | − | 0.854531i | \(-0.326155\pi\) | ||||
0.519400 | + | 0.854531i | \(0.326155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.42218 | 0.231289 | ||||||||
\(772\) | − 36.0569i | − 1.29771i | ||||||||
\(773\) | − 38.2458i | − 1.37561i | −0.725897 | − | 0.687803i | \(-0.758575\pi\) | ||||
0.725897 | − | 0.687803i | \(-0.241425\pi\) | |||||||
\(774\) | −0.588467 | −0.0211520 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.67444 | 0.347292 | ||||||||
\(777\) | 6.00959i | 0.215593i | ||||||||
\(778\) | − 7.58510i | − 0.271939i | ||||||||
\(779\) | 25.9700 | 0.930471 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.1112 | 0.469156 | ||||||||
\(782\) | − 7.13018i | − 0.254975i | ||||||||
\(783\) | 7.48883i | 0.267629i | ||||||||
\(784\) | 24.8715 | 0.888267 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.515841 | −0.0183994 | ||||||||
\(787\) | − 36.7934i | − 1.31154i | −0.754960 | − | 0.655771i | \(-0.772344\pi\) | ||||
0.754960 | − | 0.655771i | \(-0.227656\pi\) | |||||||
\(788\) | 32.9329i | 1.17319i | ||||||||
\(789\) | −14.2071 | −0.505788 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.15543 | −0.254418 | ||||||||
\(792\) | 0.720227i | 0.0255922i | ||||||||
\(793\) | − 14.6771i | − 0.521199i | ||||||||
\(794\) | −5.16117 | −0.183163 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.2507 | −1.17854 | ||||||||
\(797\) | − 36.6698i | − 1.29891i | −0.760399 | − | 0.649456i | \(-0.774997\pi\) | ||||
0.760399 | − | 0.649456i | \(-0.225003\pi\) | |||||||
\(798\) | − 0.352068i | − 0.0124631i | ||||||||
\(799\) | 33.0004 | 1.16747 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.645045 | 0.0227915 | ||||||||
\(802\) | − 7.20066i | − 0.254264i | ||||||||
\(803\) | 2.60192i | 0.0918197i | ||||||||
\(804\) | 14.8736 | 0.524550 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.832227 | −0.0293139 | ||||||||
\(807\) | − 8.67115i | − 0.305239i | ||||||||
\(808\) | − 12.2108i | − 0.429576i | ||||||||
\(809\) | 39.2361 | 1.37947 | 0.689735 | − | 0.724062i | \(-0.257727\pi\) | ||||
0.689735 | + | 0.724062i | \(0.257727\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.70444 | 0.235425 | 0.117712 | − | 0.993048i | \(-0.462444\pi\) | ||||
0.117712 | + | 0.993048i | \(0.462444\pi\) | |||||||
\(812\) | − 8.65870i | − 0.303861i | ||||||||
\(813\) | − 11.5697i | − 0.405766i | ||||||||
\(814\) | −1.85106 | −0.0648797 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 18.4514 | 0.645929 | ||||||||
\(817\) | − 8.02076i | − 0.280611i | ||||||||
\(818\) | 2.71557i | 0.0949475i | ||||||||
\(819\) | −0.680012 | −0.0237616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.1557 | −1.05244 | −0.526220 | − | 0.850348i | \(-0.676391\pi\) | ||||
−0.526220 | + | 0.850348i | \(0.676391\pi\) | |||||||
\(822\) | 1.18007i | 0.0411596i | ||||||||
\(823\) | − 1.90341i | − 0.0663487i | −0.999450 | − | 0.0331744i | \(-0.989438\pi\) | ||||
0.999450 | − | 0.0331744i | \(-0.0105617\pi\) | |||||||
\(824\) | 1.17422 | 0.0409057 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.42434 | 0.0495590 | ||||||||
\(827\) | 17.5652i | 0.610803i | 0.952224 | + | 0.305402i | \(0.0987907\pi\) | ||||
−0.952224 | + | 0.305402i | \(0.901209\pi\) | |||||||
\(828\) | − 13.5231i | − 0.469959i | ||||||||
\(829\) | 24.0291 | 0.834566 | 0.417283 | − | 0.908777i | \(-0.362982\pi\) | ||||
0.417283 | + | 0.908777i | \(0.362982\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −19.2540 | −0.667914 | ||||||||
\(832\) | 8.01958i | 0.278029i | ||||||||
\(833\) | 32.8142i | 1.13695i | ||||||||
\(834\) | 0.0681596 | 0.00236017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.85410 | −0.167883 | ||||||||
\(837\) | 3.45991i | 0.119592i | ||||||||
\(838\) | − 3.86999i | − 0.133687i | ||||||||
\(839\) | −1.07320 | −0.0370511 | −0.0185255 | − | 0.999828i | \(-0.505897\pi\) | ||||
−0.0185255 | + | 0.999828i | \(0.505897\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0826 | 0.933882 | ||||||||
\(842\) | 4.98302i | 0.171726i | ||||||||
\(843\) | 3.21917i | 0.110874i | ||||||||
\(844\) | 9.79857 | 0.337281 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.39826 | −0.0480732 | ||||||||
\(847\) | 6.05309i | 0.207987i | ||||||||
\(848\) | 14.4815i | 0.497295i | ||||||||
\(849\) | 30.6086 | 1.05048 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 70.2880 | 2.40944 | ||||||||
\(852\) | 29.4551i | 1.00912i | ||||||||
\(853\) | 17.2818i | 0.591716i | 0.955232 | + | 0.295858i | \(0.0956056\pi\) | ||||
−0.955232 | + | 0.295858i | \(0.904394\pi\) | |||||||
\(854\) | −1.57615 | −0.0539346 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.3715 | −0.422850 | ||||||||
\(857\) | 16.2742i | 0.555917i | 0.960593 | + | 0.277959i | \(0.0896578\pi\) | ||||
−0.960593 | + | 0.277959i | \(0.910342\pi\) | |||||||
\(858\) | − 0.209456i | − 0.00715072i | ||||||||
\(859\) | 11.2429 | 0.383604 | 0.191802 | − | 0.981434i | \(-0.438567\pi\) | ||||
0.191802 | + | 0.981434i | \(0.438567\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.38664 | −0.183576 | ||||||||
\(862\) | − 6.20480i | − 0.211336i | ||||||||
\(863\) | 33.3846i | 1.13642i | 0.822882 | + | 0.568212i | \(0.192365\pi\) | ||||
−0.822882 | + | 0.568212i | \(0.807635\pi\) | |||||||
\(864\) | −2.43599 | −0.0828740 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.76645 | 0.127989 | ||||||||
\(867\) | 7.34391i | 0.249412i | ||||||||
\(868\) | − 4.00040i | − 0.135782i | ||||||||
\(869\) | 2.90609 | 0.0985825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.74768 | −0.296404 | ||||||||
\(872\) | 9.17883i | 0.310834i | ||||||||
\(873\) | 11.6970i | 0.395882i | ||||||||
\(874\) | −4.11778 | −0.139286 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.84536 | −0.197497 | ||||||||
\(877\) | 16.1140i | 0.544130i | 0.962279 | + | 0.272065i | \(0.0877066\pi\) | ||||
−0.962279 | + | 0.272065i | \(0.912293\pi\) | |||||||
\(878\) | − 4.39943i | − 0.148473i | ||||||||
\(879\) | −12.6725 | −0.427431 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.2799 | 0.851701 | 0.425851 | − | 0.904793i | \(-0.359975\pi\) | ||||
0.425851 | + | 0.904793i | \(0.359975\pi\) | |||||||
\(882\) | − 1.39037i | − 0.0468163i | ||||||||
\(883\) | − 31.0260i | − 1.04411i | −0.852913 | − | 0.522053i | \(-0.825166\pi\) | ||||
0.852913 | − | 0.522053i | \(-0.174834\pi\) | |||||||
\(884\) | −11.1056 | −0.373522 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.869420 | 0.0292087 | ||||||||
\(887\) | − 38.1973i | − 1.28254i | −0.767316 | − | 0.641270i | \(-0.778408\pi\) | ||||
0.767316 | − | 0.641270i | \(-0.221592\pi\) | |||||||
\(888\) | − 8.40995i | − 0.282220i | ||||||||
\(889\) | −0.320140 | −0.0107372 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.870796 | −0.0291728 | ||||||||
\(892\) | 31.1936i | 1.04444i | ||||||||
\(893\) | − 19.0582i | − 0.637758i | ||||||||
\(894\) | 0.133298 | 0.00445814 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.74066 | 0.124967 | ||||||||
\(897\) | 7.95341i | 0.265557i | ||||||||
\(898\) | 1.54547i | 0.0515728i | ||||||||
\(899\) | 25.9107 | 0.864169 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.1061 | −0.636517 | ||||||||
\(902\) | − 1.65918i | − 0.0552447i | ||||||||
\(903\) | 1.66365i | 0.0553628i | ||||||||
\(904\) | 10.0135 | 0.333043 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.38217 | 0.0791423 | ||||||||
\(907\) | 40.9212i | 1.35877i | 0.733784 | + | 0.679383i | \(0.237753\pi\) | ||||
−0.733784 | + | 0.679383i | \(0.762247\pi\) | |||||||
\(908\) | 52.6180i | 1.74619i | ||||||||
\(909\) | 14.7636 | 0.489678 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45.6189 | −1.51142 | −0.755710 | − | 0.654906i | \(-0.772708\pi\) | ||||
−0.755710 | + | 0.654906i | \(0.772708\pi\) | |||||||
\(912\) | − 10.6560i | − 0.352854i | ||||||||
\(913\) | 8.47554i | 0.280500i | ||||||||
\(914\) | −0.119863 | −0.00396473 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.76320 | 0.190422 | ||||||||
\(917\) | 1.45833i | 0.0481583i | ||||||||
\(918\) | − 1.03148i | − 0.0340438i | ||||||||
\(919\) | −20.6582 | −0.681451 | −0.340725 | − | 0.940163i | \(-0.610673\pi\) | ||||
−0.340725 | + | 0.940163i | \(0.610673\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.0055 | −0.922813 | ||||||||
\(922\) | 0.783265i | 0.0257955i | ||||||||
\(923\) | − 17.3236i | − 0.570214i | ||||||||
\(924\) | 1.00683 | 0.0331222 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.63348 | −0.119404 | ||||||||
\(927\) | 1.41969i | 0.0466289i | ||||||||
\(928\) | 18.2427i | 0.598846i | ||||||||
\(929\) | 23.2327 | 0.762239 | 0.381119 | − | 0.924526i | \(-0.375539\pi\) | ||||
0.381119 | + | 0.924526i | \(0.375539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.9507 | 0.621084 | ||||||||
\(932\) | − 45.7879i | − 1.49983i | ||||||||
\(933\) | − 29.1437i | − 0.954121i | ||||||||
\(934\) | 2.09498 | 0.0685497 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.951625 | 0.0311048 | ||||||||
\(937\) | − 18.3122i | − 0.598232i | −0.954217 | − | 0.299116i | \(-0.903308\pi\) | ||||
0.954217 | − | 0.299116i | \(-0.0966918\pi\) | |||||||
\(938\) | 0.939397i | 0.0306724i | ||||||||
\(939\) | 19.1782 | 0.625858 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3075 | 0.564209 | 0.282104 | − | 0.959384i | \(-0.408968\pi\) | ||||
0.282104 | + | 0.959384i | \(0.408968\pi\) | |||||||
\(942\) | − 0.598045i | − 0.0194854i | ||||||||
\(943\) | 63.0020i | 2.05163i | ||||||||
\(944\) | 43.1101 | 1.40311 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.512434 | −0.0166607 | ||||||||
\(947\) | − 18.4829i | − 0.600613i | −0.953843 | − | 0.300307i | \(-0.902911\pi\) | ||||
0.953843 | − | 0.300307i | \(-0.0970890\pi\) | |||||||
\(948\) | 6.52871i | 0.212043i | ||||||||
\(949\) | 3.43787 | 0.111598 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.8985 | −0.645252 | ||||||||
\(952\) | 2.41186i | 0.0781689i | ||||||||
\(953\) | 20.8872i | 0.676604i | 0.941038 | + | 0.338302i | \(0.109852\pi\) | ||||
−0.941038 | + | 0.338302i | \(0.890148\pi\) | |||||||
\(954\) | 0.809547 | 0.0262100 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −28.9121 | −0.935083 | ||||||||
\(957\) | 6.52124i | 0.210802i | ||||||||
\(958\) | − 3.89130i | − 0.125722i | ||||||||
\(959\) | 3.33616 | 0.107730 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0290 | −0.613840 | ||||||||
\(962\) | 2.44578i | 0.0788551i | ||||||||
\(963\) | − 14.9579i | − 0.482011i | ||||||||
\(964\) | −28.1499 | −0.906647 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0.854102 | 0.0274803 | ||||||||
\(967\) | 51.2510i | 1.64812i | 0.566501 | + | 0.824061i | \(0.308297\pi\) | ||||
−0.566501 | + | 0.824061i | \(0.691703\pi\) | |||||||
\(968\) | − 8.47083i | − 0.272263i | ||||||||
\(969\) | 14.0590 | 0.451639 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.6012 | −1.23877 | −0.619385 | − | 0.785087i | \(-0.712618\pi\) | ||||
−0.619385 | + | 0.785087i | \(0.712618\pi\) | |||||||
\(972\) | − 1.95630i | − 0.0627482i | ||||||||
\(973\) | − 0.192693i | − 0.00617747i | ||||||||
\(974\) | 0.433185 | 0.0138801 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −47.7048 | −1.52699 | ||||||||
\(977\) | − 2.91913i | − 0.0933912i | −0.998909 | − | 0.0466956i | \(-0.985131\pi\) | ||||
0.998909 | − | 0.0466956i | \(-0.0148691\pi\) | |||||||
\(978\) | 2.94992i | 0.0943280i | ||||||||
\(979\) | 0.561702 | 0.0179521 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0977 | −0.354323 | ||||||||
\(982\) | − 4.64849i | − 0.148339i | ||||||||
\(983\) | 0.980138i | 0.0312615i | 0.999878 | + | 0.0156308i | \(0.00497563\pi\) | ||||
−0.999878 | + | 0.0156308i | \(0.995024\pi\) | |||||||
\(984\) | 7.53818 | 0.240308 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −7.72456 | −0.246000 | ||||||||
\(987\) | 3.95301i | 0.125826i | ||||||||
\(988\) | 6.41365i | 0.204045i | ||||||||
\(989\) | 19.4580 | 0.618728 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0913 | 1.17824 | 0.589122 | − | 0.808044i | \(-0.299474\pi\) | ||||
0.589122 | + | 0.808044i | \(0.299474\pi\) | |||||||
\(992\) | 8.42830i | 0.267599i | ||||||||
\(993\) | 27.8128i | 0.882613i | ||||||||
\(994\) | −1.86035 | −0.0590068 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −19.0408 | −0.603331 | ||||||||
\(997\) | − 16.7675i | − 0.531031i | −0.964107 | − | 0.265515i | \(-0.914458\pi\) | ||||
0.964107 | − | 0.265515i | \(-0.0855421\pi\) | |||||||
\(998\) | − 5.91031i | − 0.187088i | ||||||||
\(999\) | 10.1681 | 0.321705 |
(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 | 1875.2.b.d.1249.5 | 8 | ||
5.2 | odd | 4 | 1875.2.a.g.1.2 | yes | 4 | ||
5.3 | odd | 4 | 1875.2.a.f.1.3 | ✓ | 4 | ||
5.4 | even | 2 | inner | 1875.2.b.d.1249.4 | 8 | ||
15.2 | even | 4 | 5625.2.a.j.1.3 | 4 | |||
15.8 | even | 4 | 5625.2.a.m.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1875.2.a.f.1.3 | ✓ | 4 | 5.3 | odd | 4 | ||
1875.2.a.g.1.2 | yes | 4 | 5.2 | odd | 4 | ||
1875.2.b.d.1249.4 | 8 | 5.4 | even | 2 | inner | ||
1875.2.b.d.1249.5 | 8 | 1.1 | even | 1 | trivial | ||
5625.2.a.j.1.3 | 4 | 15.2 | even | 4 | |||
5625.2.a.m.1.2 | 4 | 15.8 | even | 4 |