Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(101,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 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("1050.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.s (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 551.2 | ||
Root | \(-1.26217 + 1.18614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.551 |
Dual form | 1050.2.s.e.101.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 1.65831 | + | 0.500000i | 0.957427 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.18614 | − | 1.26217i | −0.484240 | − | 0.515278i | ||||
\(7\) | 0.866025 | − | 2.50000i | 0.327327 | − | 0.944911i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.50000 | + | 1.65831i | 0.833333 | + | 0.552771i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.68614 | + | 2.12819i | −1.11141 | + | 0.641675i | −0.939195 | − | 0.343384i | \(-0.888427\pi\) |
−0.172218 | + | 0.985059i | \(0.555093\pi\) | |||||||
\(12\) | 0.396143 | + | 1.68614i | 0.114357 | + | 0.486747i | ||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.31662 | + | 5.74456i | 0.804400 | + | 1.39326i | 0.916696 | + | 0.399586i | \(0.130846\pi\) |
−0.112296 | + | 0.993675i | \(0.535820\pi\) | |||||||
\(18\) | −1.33591 | − | 2.68614i | −0.314876 | − | 0.633129i | ||||
\(19\) | 3.00000 | + | 1.73205i | 0.688247 | + | 0.397360i | 0.802955 | − | 0.596040i | \(-0.203260\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.68614 | − | 3.71277i | 0.586164 | − | 0.810192i | ||||
\(22\) | 4.25639 | 0.907465 | ||||||||
\(23\) | 3.78651 | + | 2.18614i | 0.789541 | + | 0.455842i | 0.839801 | − | 0.542894i | \(-0.182672\pi\) |
−0.0502598 | + | 0.998736i | \(0.516005\pi\) | |||||||
\(24\) | 0.500000 | − | 1.65831i | 0.102062 | − | 0.338502i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 3.31662 | + | 4.00000i | 0.638285 | + | 0.769800i | ||||
\(28\) | 2.59808 | − | 0.500000i | 0.490990 | − | 0.0944911i | ||||
\(29\) | − | 3.31662i | − | 0.615882i | −0.951405 | − | 0.307941i | \(-0.900360\pi\) | ||
0.951405 | − | 0.307941i | \(-0.0996399\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.05842 | + | 1.18843i | −0.369704 | + | 0.213448i | −0.673329 | − | 0.739343i | \(-0.735136\pi\) |
0.303625 | + | 0.952791i | \(0.401803\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −7.17687 | + | 1.68614i | −1.24933 | + | 0.293519i | ||||
\(34\) | − | 6.63325i | − | 1.13759i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.186141 | + | 2.99422i | −0.0310234 | + | 0.499037i | ||||
\(37\) | 5.84096 | − | 10.1168i | 0.960248 | − | 1.66320i | 0.238376 | − | 0.971173i | \(-0.423385\pi\) |
0.721873 | − | 0.692026i | \(-0.243282\pi\) | |||||||
\(38\) | −1.73205 | − | 3.00000i | −0.280976 | − | 0.486664i | ||||
\(39\) | −1.00000 | + | 3.31662i | −0.160128 | + | 0.531085i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.62772 | −0.254207 | −0.127103 | − | 0.991889i | \(-0.540568\pi\) | ||||
−0.127103 | + | 0.991889i | \(0.540568\pi\) | |||||||
\(42\) | −4.18265 | + | 1.87228i | −0.645397 | + | 0.288899i | ||||
\(43\) | 11.0371 | 1.68314 | 0.841572 | − | 0.540145i | \(-0.181631\pi\) | ||||
0.841572 | + | 0.540145i | \(0.181631\pi\) | |||||||
\(44\) | −3.68614 | − | 2.12819i | −0.555707 | − | 0.320837i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.18614 | − | 3.78651i | −0.322329 | − | 0.558290i | ||||
\(47\) | 0.939764 | − | 1.62772i | 0.137079 | − | 0.237427i | −0.789311 | − | 0.613994i | \(-0.789562\pi\) |
0.926390 | + | 0.376566i | \(0.122895\pi\) | |||||||
\(48\) | −1.26217 | + | 1.18614i | −0.182178 | + | 0.171205i | ||||
\(49\) | −5.50000 | − | 4.33013i | −0.785714 | − | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.62772 | + | 11.1846i | 0.367954 | + | 1.56616i | ||||
\(52\) | −1.73205 | + | 1.00000i | −0.240192 | + | 0.138675i | ||||
\(53\) | −1.18843 | + | 0.686141i | −0.163243 | + | 0.0942487i | −0.579396 | − | 0.815046i | \(-0.696712\pi\) |
0.416153 | + | 0.909295i | \(0.363378\pi\) | |||||||
\(54\) | −0.872281 | − | 5.12241i | −0.118702 | − | 0.697072i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | − | 0.866025i | −0.334077 | − | 0.115728i | ||||
\(57\) | 4.10891 | + | 4.37228i | 0.544239 | + | 0.579123i | ||||
\(58\) | −1.65831 | + | 2.87228i | −0.217747 | + | 0.377149i | ||||
\(59\) | 2.05842 | + | 3.56529i | 0.267984 | + | 0.464161i | 0.968341 | − | 0.249631i | \(-0.0803093\pi\) |
−0.700357 | + | 0.713792i | \(0.746976\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.44158 | − | 1.40965i | −0.312612 | − | 0.180487i | 0.335483 | − | 0.942046i | \(-0.391101\pi\) |
−0.648095 | + | 0.761560i | \(0.724434\pi\) | |||||||
\(62\) | 2.37686 | 0.301862 | ||||||||
\(63\) | 6.31084 | − | 4.81386i | 0.795092 | − | 0.606489i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.05842 | + | 2.12819i | 0.868832 | + | 0.261963i | ||||
\(67\) | 3.78651 | + | 6.55842i | 0.462595 | + | 0.801239i | 0.999089 | − | 0.0426654i | \(-0.0135849\pi\) |
−0.536494 | + | 0.843904i | \(0.680252\pi\) | |||||||
\(68\) | −3.31662 | + | 5.74456i | −0.402200 | + | 0.696631i | ||||
\(69\) | 5.18614 | + | 5.51856i | 0.624338 | + | 0.664356i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.87953i | − | 0.223059i | −0.993761 | − | 0.111529i | \(-0.964425\pi\) | ||
0.993761 | − | 0.111529i | \(-0.0355749\pi\) | |||||||
\(72\) | 1.65831 | − | 2.50000i | 0.195434 | − | 0.294628i | ||||
\(73\) | 1.73205 | − | 1.00000i | 0.202721 | − | 0.117041i | −0.395203 | − | 0.918594i | \(-0.629326\pi\) |
0.597924 | + | 0.801553i | \(0.295992\pi\) | |||||||
\(74\) | −10.1168 | + | 5.84096i | −1.17606 | + | 0.678998i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46410i | 0.397360i | ||||||||
\(77\) | 2.12819 | + | 11.0584i | 0.242530 | + | 1.26022i | ||||
\(78\) | 2.52434 | − | 2.37228i | 0.285825 | − | 0.268608i | ||||
\(79\) | −4.05842 | + | 7.02939i | −0.456608 | + | 0.790869i | −0.998779 | − | 0.0493997i | \(-0.984269\pi\) |
0.542171 | + | 0.840268i | \(0.317603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50000 | + | 8.29156i | 0.388889 | + | 0.921285i | ||||
\(82\) | 1.40965 | + | 0.813859i | 0.155669 | + | 0.0898757i | ||||
\(83\) | 1.43710 | 0.157742 | 0.0788710 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788710 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(84\) | 4.55842 | + | 0.469882i | 0.497365 | + | 0.0512683i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −9.55842 | − | 5.51856i | −1.03071 | − | 0.595081i | ||||
\(87\) | 1.65831 | − | 5.50000i | 0.177790 | − | 0.589662i | ||||
\(88\) | 2.12819 | + | 3.68614i | 0.226866 | + | 0.392944i | ||||
\(89\) | 2.18614 | − | 3.78651i | 0.231730 | − | 0.401369i | −0.726587 | − | 0.687074i | \(-0.758895\pi\) |
0.958317 | + | 0.285706i | \(0.0922279\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | + | 1.73205i | 0.524142 | + | 0.181568i | ||||
\(92\) | 4.37228i | 0.455842i | ||||||||
\(93\) | −4.00772 | + | 0.941578i | −0.415581 | + | 0.0976371i | ||||
\(94\) | −1.62772 | + | 0.939764i | −0.167886 | + | 0.0969292i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.68614 | − | 0.396143i | 0.172091 | − | 0.0404312i | ||||
\(97\) | 2.11684i | 0.214933i | 0.994209 | + | 0.107466i | \(0.0342738\pi\) | ||||
−0.994209 | + | 0.107466i | \(0.965726\pi\) | |||||||
\(98\) | 2.59808 | + | 6.50000i | 0.262445 | + | 0.656599i | ||||
\(99\) | −12.7446 | − | 0.792287i | −1.28088 | − | 0.0796278i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.18614 | − | 14.1788i | −0.814551 | − | 1.41084i | −0.909650 | − | 0.415377i | \(-0.863650\pi\) |
0.0950981 | − | 0.995468i | \(-0.469684\pi\) | |||||||
\(102\) | 3.31662 | − | 11.0000i | 0.328395 | − | 1.08916i | ||||
\(103\) | −13.0916 | − | 7.55842i | −1.28995 | − | 0.744753i | −0.311306 | − | 0.950310i | \(-0.600766\pi\) |
−0.978645 | + | 0.205556i | \(0.934100\pi\) | |||||||
\(104\) | 2.00000 | 0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.37228 | 0.133288 | ||||||||
\(107\) | −15.3672 | − | 8.87228i | −1.48561 | − | 0.857716i | −0.485742 | − | 0.874102i | \(-0.661450\pi\) |
−0.999866 | + | 0.0163866i | \(0.994784\pi\) | |||||||
\(108\) | −1.80579 | + | 4.87228i | −0.173762 | + | 0.468835i | ||||
\(109\) | 4.55842 | + | 7.89542i | 0.436618 | + | 0.756244i | 0.997426 | − | 0.0717016i | \(-0.0228429\pi\) |
−0.560808 | + | 0.827946i | \(0.689510\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.7446 | − | 13.8564i | 1.39949 | − | 1.31519i | ||||
\(112\) | 1.73205 | + | 2.00000i | 0.163663 | + | 0.188982i | ||||
\(113\) | 3.25544i | 0.306246i | 0.988207 | + | 0.153123i | \(0.0489330\pi\) | ||||
−0.988207 | + | 0.153123i | \(0.951067\pi\) | |||||||
\(114\) | −1.37228 | − | 5.84096i | −0.128526 | − | 0.547056i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.87228 | − | 1.65831i | 0.266685 | − | 0.153970i | ||||
\(117\) | −3.31662 | + | 5.00000i | −0.306622 | + | 0.462250i | ||||
\(118\) | − | 4.11684i | − | 0.378986i | ||||||
\(119\) | 17.2337 | − | 3.31662i | 1.57981 | − | 0.304034i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.55842 | − | 6.16337i | 0.323493 | − | 0.560306i | ||||
\(122\) | 1.40965 | + | 2.44158i | 0.127623 | + | 0.221050i | ||||
\(123\) | −2.69927 | − | 0.813859i | −0.243385 | − | 0.0733832i | ||||
\(124\) | −2.05842 | − | 1.18843i | −0.184852 | − | 0.106724i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.87228 | + | 1.01350i | −0.701319 | + | 0.0902900i | ||||
\(127\) | −2.37686 | −0.210912 | −0.105456 | − | 0.994424i | \(-0.533630\pi\) | ||||
−0.105456 | + | 0.994424i | \(0.533630\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 18.3030 | + | 5.51856i | 1.61149 | + | 0.485882i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.31386 | + | 4.00772i | −0.202163 | + | 0.350156i | −0.949225 | − | 0.314598i | \(-0.898130\pi\) |
0.747062 | + | 0.664754i | \(0.231464\pi\) | |||||||
\(132\) | −5.04868 | − | 5.37228i | −0.439431 | − | 0.467597i | ||||
\(133\) | 6.92820 | − | 6.00000i | 0.600751 | − | 0.520266i | ||||
\(134\) | − | 7.57301i | − | 0.654209i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.74456 | − | 3.31662i | 0.492592 | − | 0.284398i | ||||
\(137\) | 2.37686 | − | 1.37228i | 0.203069 | − | 0.117242i | −0.395017 | − | 0.918674i | \(-0.629261\pi\) |
0.598086 | + | 0.801432i | \(0.295928\pi\) | |||||||
\(138\) | −1.73205 | − | 7.37228i | −0.147442 | − | 0.627570i | ||||
\(139\) | 11.6819i | 0.990848i | 0.868651 | + | 0.495424i | \(0.164987\pi\) | ||||
−0.868651 | + | 0.495424i | \(0.835013\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.37228 | − | 2.22938i | 0.199782 | − | 0.187748i | ||||
\(142\) | −0.939764 | + | 1.62772i | −0.0788632 | + | 0.136595i | ||||
\(143\) | −4.25639 | − | 7.37228i | −0.355937 | − | 0.616501i | ||||
\(144\) | −2.68614 | + | 1.33591i | −0.223845 | + | 0.111326i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | −6.95565 | − | 9.93070i | −0.573693 | − | 0.819071i | ||||
\(148\) | 11.6819 | 0.960248 | ||||||||
\(149\) | −12.3030 | − | 7.10313i | −1.00790 | − | 0.581911i | −0.0973237 | − | 0.995253i | \(-0.531028\pi\) |
−0.910576 | + | 0.413342i | \(0.864362\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.05842 | + | 7.02939i | 0.330270 | + | 0.572044i | 0.982565 | − | 0.185921i | \(-0.0595270\pi\) |
−0.652295 | + | 0.757965i | \(0.726194\pi\) | |||||||
\(152\) | 1.73205 | − | 3.00000i | 0.140488 | − | 0.243332i | ||||
\(153\) | −1.23472 | + | 19.8614i | −0.0998210 | + | 1.60570i | ||||
\(154\) | 3.68614 | − | 10.6410i | 0.297038 | − | 0.857474i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.37228 | + | 0.792287i | −0.269999 | + | 0.0634337i | ||||
\(157\) | −6.92820 | + | 4.00000i | −0.552931 | + | 0.319235i | −0.750303 | − | 0.661094i | \(-0.770093\pi\) |
0.197372 | + | 0.980329i | \(0.436759\pi\) | |||||||
\(158\) | 7.02939 | − | 4.05842i | 0.559228 | − | 0.322871i | ||||
\(159\) | −2.31386 | + | 0.543620i | −0.183501 | + | 0.0431119i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.74456 | − | 7.57301i | 0.689168 | − | 0.596837i | ||||
\(162\) | 1.11469 | − | 8.93070i | 0.0875785 | − | 0.701662i | ||||
\(163\) | 1.73205 | − | 3.00000i | 0.135665 | − | 0.234978i | −0.790186 | − | 0.612866i | \(-0.790016\pi\) |
0.925851 | + | 0.377888i | \(0.123350\pi\) | |||||||
\(164\) | −0.813859 | − | 1.40965i | −0.0635517 | − | 0.110075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.24456 | − | 0.718549i | −0.0965968 | − | 0.0557702i | ||||
\(167\) | 11.3321 | 0.876902 | 0.438451 | − | 0.898755i | \(-0.355527\pi\) | ||||
0.438451 | + | 0.898755i | \(0.355527\pi\) | |||||||
\(168\) | −3.71277 | − | 2.68614i | −0.286446 | − | 0.207240i | ||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.62772 | + | 9.30506i | 0.353890 | + | 0.711576i | ||||
\(172\) | 5.51856 | + | 9.55842i | 0.420786 | + | 0.728823i | ||||
\(173\) | 1.87953 | − | 3.25544i | 0.142898 | − | 0.247506i | −0.785689 | − | 0.618622i | \(-0.787691\pi\) |
0.928587 | + | 0.371116i | \(0.121025\pi\) | |||||||
\(174\) | −4.18614 | + | 3.93398i | −0.317351 | + | 0.298235i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 4.25639i | − | 0.320837i | ||||||
\(177\) | 1.63086 | + | 6.94158i | 0.122583 | + | 0.521761i | ||||
\(178\) | −3.78651 | + | 2.18614i | −0.283811 | + | 0.163858i | ||||
\(179\) | −2.48913 | + | 1.43710i | −0.186046 | + | 0.107414i | −0.590130 | − | 0.807308i | \(-0.700924\pi\) |
0.404084 | + | 0.914722i | \(0.367590\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9653i | 1.33535i | 0.744452 | + | 0.667676i | \(0.232711\pi\) | ||||
−0.744452 | + | 0.667676i | \(0.767289\pi\) | |||||||
\(182\) | −3.46410 | − | 4.00000i | −0.256776 | − | 0.296500i | ||||
\(183\) | −3.34408 | − | 3.55842i | −0.247201 | − | 0.263046i | ||||
\(184\) | 2.18614 | − | 3.78651i | 0.161164 | − | 0.279145i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.94158 | + | 1.18843i | 0.289011 | + | 0.0871400i | ||||
\(187\) | −24.4511 | − | 14.1168i | −1.78804 | − | 1.03233i | ||||
\(188\) | 1.87953 | 0.137079 | ||||||||
\(189\) | 12.8723 | − | 4.82746i | 0.936321 | − | 0.351146i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.25544 | − | 1.87953i | −0.235555 | − | 0.135998i | 0.377577 | − | 0.925978i | \(-0.376757\pi\) |
−0.613132 | + | 0.789980i | \(0.710091\pi\) | |||||||
\(192\) | −1.65831 | − | 0.500000i | −0.119678 | − | 0.0360844i | ||||
\(193\) | −4.00772 | − | 6.94158i | −0.288482 | − | 0.499666i | 0.684966 | − | 0.728575i | \(-0.259817\pi\) |
−0.973448 | + | 0.228910i | \(0.926484\pi\) | |||||||
\(194\) | 1.05842 | − | 1.83324i | 0.0759903 | − | 0.131619i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | − | 20.2337i | − | 1.44159i | −0.693148 | − | 0.720795i | \(-0.743777\pi\) | ||
0.693148 | − | 0.720795i | \(-0.256223\pi\) | |||||||
\(198\) | 10.6410 | + | 7.05842i | 0.756221 | + | 0.501620i | ||||
\(199\) | 16.1168 | − | 9.30506i | 1.14249 | − | 0.659619i | 0.195446 | − | 0.980714i | \(-0.437385\pi\) |
0.947047 | + | 0.321096i | \(0.104051\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.00000 | + | 12.7692i | 0.211604 | + | 0.900668i | ||||
\(202\) | 16.3723i | 1.15195i | ||||||||
\(203\) | −8.29156 | − | 2.87228i | −0.581954 | − | 0.201595i | ||||
\(204\) | −8.37228 | + | 7.86797i | −0.586177 | + | 0.550868i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.55842 | + | 13.0916i | 0.526620 | + | 0.912133i | ||||
\(207\) | 5.84096 | + | 11.7446i | 0.405975 | + | 0.816304i | ||||
\(208\) | −1.73205 | − | 1.00000i | −0.120096 | − | 0.0693375i | ||||
\(209\) | −14.7446 | −1.01990 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2337 | −1.25526 | −0.627629 | − | 0.778512i | \(-0.715975\pi\) | ||||
−0.627629 | + | 0.778512i | \(0.715975\pi\) | |||||||
\(212\) | −1.18843 | − | 0.686141i | −0.0816217 | − | 0.0471243i | ||||
\(213\) | 0.939764 | − | 3.11684i | 0.0643916 | − | 0.213563i | ||||
\(214\) | 8.87228 | + | 15.3672i | 0.606497 | + | 1.05048i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.00000 | − | 3.31662i | 0.272166 | − | 0.225668i | ||||
\(217\) | 1.18843 | + | 6.17527i | 0.0806759 | + | 0.419204i | ||||
\(218\) | − | 9.11684i | − | 0.617471i | ||||||
\(219\) | 3.37228 | − | 0.792287i | 0.227878 | − | 0.0535378i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4891 | + | 6.63325i | −0.772842 | + | 0.446201i | ||||
\(222\) | −19.6974 | + | 4.62772i | −1.32200 | + | 0.310592i | ||||
\(223\) | 18.1168i | 1.21319i | 0.795010 | + | 0.606597i | \(0.207466\pi\) | ||||
−0.795010 | + | 0.606597i | \(0.792534\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.62772 | − | 2.81929i | 0.108274 | − | 0.187536i | ||||
\(227\) | −7.82168 | − | 13.5475i | −0.519143 | − | 0.899182i | −0.999752 | − | 0.0222475i | \(-0.992918\pi\) |
0.480609 | − | 0.876935i | \(-0.340416\pi\) | |||||||
\(228\) | −1.73205 | + | 5.74456i | −0.114708 | + | 0.380443i | ||||
\(229\) | −12.0000 | − | 6.92820i | −0.792982 | − | 0.457829i | 0.0480291 | − | 0.998846i | \(-0.484706\pi\) |
−0.841011 | + | 0.541017i | \(0.818039\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.00000 | + | 19.4024i | −0.131590 | + | 1.27659i | ||||
\(232\) | −3.31662 | −0.217747 | ||||||||
\(233\) | −20.3422 | − | 11.7446i | −1.33266 | − | 0.769412i | −0.346954 | − | 0.937882i | \(-0.612784\pi\) |
−0.985707 | + | 0.168470i | \(0.946117\pi\) | |||||||
\(234\) | 5.37228 | − | 2.67181i | 0.351197 | − | 0.174662i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.05842 | + | 3.56529i | −0.133992 | + | 0.232081i | ||||
\(237\) | −10.2448 | + | 9.62772i | −0.665473 | + | 0.625388i | ||||
\(238\) | −16.5831 | − | 5.74456i | −1.07492 | − | 0.372365i | ||||
\(239\) | − | 2.87419i | − | 0.185916i | −0.995670 | − | 0.0929581i | \(-0.970368\pi\) | ||
0.995670 | − | 0.0929581i | \(-0.0296323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.17527 | − | 5.29734i | 0.591031 | − | 0.341232i | −0.174474 | − | 0.984662i | \(-0.555823\pi\) |
0.765505 | + | 0.643430i | \(0.222489\pi\) | |||||||
\(242\) | −6.16337 | + | 3.55842i | −0.396196 | + | 0.228744i | ||||
\(243\) | 1.65831 | + | 15.5000i | 0.106381 | + | 0.994325i | ||||
\(244\) | − | 2.81929i | − | 0.180487i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.93070 | + | 2.05446i | 0.123097 | + | 0.130987i | ||||
\(247\) | −3.46410 | + | 6.00000i | −0.220416 | + | 0.381771i | ||||
\(248\) | 1.18843 | + | 2.05842i | 0.0754654 | + | 0.130710i | ||||
\(249\) | 2.38316 | + | 0.718549i | 0.151026 | + | 0.0455362i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.1168 | −1.01729 | −0.508643 | − | 0.860977i | \(-0.669853\pi\) | ||||
−0.508643 | + | 0.860977i | \(0.669853\pi\) | |||||||
\(252\) | 7.32435 | + | 3.05842i | 0.461390 | + | 0.192662i | ||||
\(253\) | −18.6101 | −1.17001 | ||||||||
\(254\) | 2.05842 | + | 1.18843i | 0.129157 | + | 0.0745688i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.25639 | + | 7.37228i | −0.265506 | + | 0.459870i | −0.967696 | − | 0.252119i | \(-0.918872\pi\) |
0.702190 | + | 0.711990i | \(0.252206\pi\) | |||||||
\(258\) | −13.0916 | − | 13.9307i | −0.815046 | − | 0.867288i | ||||
\(259\) | −20.2337 | − | 23.3639i | −1.25726 | − | 1.45176i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.50000 | − | 8.29156i | 0.340441 | − | 0.513235i | ||||
\(262\) | 4.00772 | − | 2.31386i | 0.247598 | − | 0.142951i | ||||
\(263\) | −1.40965 | + | 0.813859i | −0.0869225 | + | 0.0501847i | −0.542831 | − | 0.839842i | \(-0.682648\pi\) |
0.455909 | + | 0.890027i | \(0.349314\pi\) | |||||||
\(264\) | 1.68614 | + | 7.17687i | 0.103775 | + | 0.441706i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.00000 | + | 1.73205i | −0.551825 | + | 0.106199i | ||||
\(267\) | 5.51856 | − | 5.18614i | 0.337730 | − | 0.317387i | ||||
\(268\) | −3.78651 | + | 6.55842i | −0.231298 | + | 0.400619i | ||||
\(269\) | 9.98913 | + | 17.3017i | 0.609048 | + | 1.05490i | 0.991398 | + | 0.130884i | \(0.0417815\pi\) |
−0.382350 | + | 0.924018i | \(0.624885\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1753 | − | 10.4935i | −1.10407 | − | 0.637434i | −0.166782 | − | 0.985994i | \(-0.553338\pi\) |
−0.937287 | + | 0.348559i | \(0.886671\pi\) | |||||||
\(272\) | −6.63325 | −0.402200 | ||||||||
\(273\) | 7.42554 | + | 5.37228i | 0.449414 | + | 0.325145i | ||||
\(274\) | −2.74456 | −0.165805 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.18614 | + | 7.25061i | −0.131590 | + | 0.436435i | ||||
\(277\) | −14.5012 | − | 25.1168i | −0.871294 | − | 1.50912i | −0.860659 | − | 0.509181i | \(-0.829948\pi\) |
−0.0106345 | − | 0.999943i | \(-0.503385\pi\) | |||||||
\(278\) | 5.84096 | − | 10.1168i | 0.350318 | − | 0.606768i | ||||
\(279\) | −7.11684 | − | 0.442430i | −0.426074 | − | 0.0264876i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.7793i | − | 1.29924i | −0.760258 | − | 0.649621i | \(-0.774927\pi\) | ||
0.760258 | − | 0.649621i | \(-0.225073\pi\) | |||||||
\(282\) | −3.16915 | + | 0.744563i | −0.188720 | + | 0.0443381i | ||||
\(283\) | −13.8564 | + | 8.00000i | −0.823678 | + | 0.475551i | −0.851683 | − | 0.524057i | \(-0.824418\pi\) |
0.0280052 | + | 0.999608i | \(0.491084\pi\) | |||||||
\(284\) | 1.62772 | − | 0.939764i | 0.0965873 | − | 0.0557647i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.51278i | 0.503371i | ||||||||
\(287\) | −1.40965 | + | 4.06930i | −0.0832088 | + | 0.240203i | ||||
\(288\) | 2.99422 | + | 0.186141i | 0.176436 | + | 0.0109684i | ||||
\(289\) | −13.5000 | + | 23.3827i | −0.794118 | + | 1.37545i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.05842 | + | 3.51039i | −0.0620458 | + | 0.205783i | ||||
\(292\) | 1.73205 | + | 1.00000i | 0.101361 | + | 0.0585206i | ||||
\(293\) | 25.0410 | 1.46291 | 0.731455 | − | 0.681889i | \(-0.238841\pi\) | ||||
0.731455 | + | 0.681889i | \(0.238841\pi\) | |||||||
\(294\) | 1.05842 | + | 12.0781i | 0.0617284 | + | 0.704407i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −10.1168 | − | 5.84096i | −0.588030 | − | 0.339499i | ||||
\(297\) | −20.7383 | − | 7.68614i | −1.20336 | − | 0.445995i | ||||
\(298\) | 7.10313 | + | 12.3030i | 0.411473 | + | 0.712693i | ||||
\(299\) | −4.37228 | + | 7.57301i | −0.252856 | + | 0.437959i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.55842 | − | 27.5928i | 0.550938 | − | 1.59042i | ||||
\(302\) | − | 8.11684i | − | 0.467072i | ||||||
\(303\) | −6.48577 | − | 27.6060i | −0.372598 | − | 1.58592i | ||||
\(304\) | −3.00000 | + | 1.73205i | −0.172062 | + | 0.0993399i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 11.0000 | − | 16.5831i | 0.628828 | − | 0.947994i | ||||
\(307\) | − | 6.88316i | − | 0.392842i | −0.980520 | − | 0.196421i | \(-0.937068\pi\) | ||
0.980520 | − | 0.196421i | \(-0.0629320\pi\) | |||||||
\(308\) | −8.51278 | + | 7.37228i | −0.485060 | + | 0.420075i | ||||
\(309\) | −17.9307 | − | 19.0800i | −1.02004 | − | 1.08542i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.11684 | + | 12.3267i | 0.403559 | + | 0.698985i | 0.994153 | − | 0.107984i | \(-0.0344396\pi\) |
−0.590593 | + | 0.806969i | \(0.701106\pi\) | |||||||
\(312\) | 3.31662 | + | 1.00000i | 0.187767 | + | 0.0566139i | ||||
\(313\) | 12.2255 | + | 7.05842i | 0.691029 | + | 0.398966i | 0.803997 | − | 0.594633i | \(-0.202703\pi\) |
−0.112969 | + | 0.993599i | \(0.536036\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.11684 | −0.456608 | ||||||||
\(317\) | −13.9576 | − | 8.05842i | −0.783937 | − | 0.452606i | 0.0538869 | − | 0.998547i | \(-0.482839\pi\) |
−0.837824 | + | 0.545941i | \(0.816172\pi\) | |||||||
\(318\) | 2.27567 | + | 0.686141i | 0.127613 | + | 0.0384769i | ||||
\(319\) | 7.05842 | + | 12.2255i | 0.395196 | + | 0.684499i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.0475 | − | 22.3966i | −1.17476 | − | 1.25006i | ||||
\(322\) | −11.3595 | + | 2.18614i | −0.633041 | + | 0.121829i | ||||
\(323\) | 22.9783i | 1.27854i | ||||||||
\(324\) | −5.43070 | + | 7.17687i | −0.301706 | + | 0.398715i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.00000 | + | 1.73205i | −0.166155 | + | 0.0959294i | ||||
\(327\) | 3.61158 | + | 15.3723i | 0.199721 | + | 0.850089i | ||||
\(328\) | 1.62772i | 0.0898757i | ||||||||
\(329\) | −3.25544 | − | 3.75906i | −0.179478 | − | 0.207243i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.11684 | + | 8.86263i | −0.281247 | + | 0.487134i | −0.971692 | − | 0.236250i | \(-0.924081\pi\) |
0.690445 | + | 0.723385i | \(0.257415\pi\) | |||||||
\(332\) | 0.718549 | + | 1.24456i | 0.0394355 | + | 0.0683042i | ||||
\(333\) | 31.3793 | − | 15.6060i | 1.71957 | − | 0.855202i | ||||
\(334\) | −9.81386 | − | 5.66603i | −0.536990 | − | 0.310032i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.87228 | + | 4.18265i | 0.102141 | + | 0.228182i | ||||
\(337\) | −9.30506 | −0.506879 | −0.253440 | − | 0.967351i | \(-0.581562\pi\) | ||||
−0.253440 | + | 0.967351i | \(0.581562\pi\) | |||||||
\(338\) | −7.79423 | − | 4.50000i | −0.423950 | − | 0.244768i | ||||
\(339\) | −1.62772 | + | 5.39853i | −0.0884055 | + | 0.293208i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.05842 | − | 8.76144i | 0.273929 | − | 0.474459i | ||||
\(342\) | 0.644810 | − | 10.3723i | 0.0348673 | − | 0.560869i | ||||
\(343\) | −15.5885 | + | 10.0000i | −0.841698 | + | 0.539949i | ||||
\(344\) | − | 11.0371i | − | 0.595081i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.25544 | + | 1.87953i | −0.175013 | + | 0.101044i | ||||
\(347\) | 16.5557 | − | 9.55842i | 0.888755 | − | 0.513123i | 0.0152200 | − | 0.999884i | \(-0.495155\pi\) |
0.873535 | + | 0.486761i | \(0.161822\pi\) | |||||||
\(348\) | 5.59230 | − | 1.31386i | 0.299779 | − | 0.0704303i | ||||
\(349\) | − | 24.0087i | − | 1.28515i | −0.766221 | − | 0.642577i | \(-0.777865\pi\) | ||
0.766221 | − | 0.642577i | \(-0.222135\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.00000 | + | 6.63325i | −0.427008 | + | 0.354057i | ||||
\(352\) | −2.12819 | + | 3.68614i | −0.113433 | + | 0.196472i | ||||
\(353\) | 9.45254 | + | 16.3723i | 0.503108 | + | 0.871409i | 0.999994 | + | 0.00359253i | \(0.00114354\pi\) |
−0.496886 | + | 0.867816i | \(0.665523\pi\) | |||||||
\(354\) | 2.05842 | − | 6.82701i | 0.109404 | − | 0.362852i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4.37228 | 0.231730 | ||||||||
\(357\) | 30.2372 | + | 3.11684i | 1.60032 | + | 0.164961i | ||||
\(358\) | 2.87419 | 0.151906 | ||||||||
\(359\) | 12.2554 | + | 7.07568i | 0.646817 | + | 0.373440i | 0.787236 | − | 0.616652i | \(-0.211511\pi\) |
−0.140419 | + | 0.990092i | \(0.544845\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.50000 | − | 6.06218i | −0.184211 | − | 0.319062i | ||||
\(362\) | 8.98266 | − | 15.5584i | 0.472118 | − | 0.817733i | ||||
\(363\) | 8.98266 | − | 8.44158i | 0.471467 | − | 0.443068i | ||||
\(364\) | 1.00000 | + | 5.19615i | 0.0524142 | + | 0.272352i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.11684 | + | 4.75372i | 0.0583784 | + | 0.248481i | ||||
\(367\) | 18.3889 | − | 10.6168i | 0.959893 | − | 0.554195i | 0.0637532 | − | 0.997966i | \(-0.479693\pi\) |
0.896140 | + | 0.443771i | \(0.146360\pi\) | |||||||
\(368\) | −3.78651 | + | 2.18614i | −0.197385 | + | 0.113960i | ||||
\(369\) | −4.06930 | − | 2.69927i | −0.211839 | − | 0.140518i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.686141 | + | 3.56529i | 0.0356226 | + | 0.185101i | ||||
\(372\) | −2.81929 | − | 3.00000i | −0.146173 | − | 0.155543i | ||||
\(373\) | 8.21782 | − | 14.2337i | 0.425503 | − | 0.736992i | −0.570964 | − | 0.820975i | \(-0.693431\pi\) |
0.996467 | + | 0.0839823i | \(0.0267639\pi\) | |||||||
\(374\) | 14.1168 | + | 24.4511i | 0.729965 | + | 1.26434i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.62772 | − | 0.939764i | −0.0839432 | − | 0.0484646i | ||||
\(377\) | 6.63325 | 0.341630 | ||||||||
\(378\) | −13.5615 | − | 2.25544i | −0.697526 | − | 0.116007i | ||||
\(379\) | −22.2337 | −1.14207 | −0.571034 | − | 0.820926i | \(-0.693458\pi\) | ||||
−0.571034 | + | 0.820926i | \(0.693458\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.94158 | − | 1.18843i | −0.201933 | − | 0.0608851i | ||||
\(382\) | 1.87953 | + | 3.25544i | 0.0961650 | + | 0.166563i | ||||
\(383\) | 10.4198 | − | 18.0475i | 0.532425 | − | 0.922187i | −0.466859 | − | 0.884332i | \(-0.654614\pi\) |
0.999283 | − | 0.0378546i | \(-0.0120524\pi\) | |||||||
\(384\) | 1.18614 | + | 1.26217i | 0.0605300 | + | 0.0644098i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.01544i | 0.407975i | ||||||||
\(387\) | 27.5928 | + | 18.3030i | 1.40262 | + | 0.930393i | ||||
\(388\) | −1.83324 | + | 1.05842i | −0.0930687 | + | 0.0537332i | ||||
\(389\) | −29.4891 | + | 17.0256i | −1.49516 | + | 0.863230i | −0.999985 | − | 0.00556424i | \(-0.998229\pi\) |
−0.495173 | + | 0.868794i | \(0.664896\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.0024i | 1.46672i | ||||||||
\(392\) | −4.33013 | + | 5.50000i | −0.218704 | + | 0.277792i | ||||
\(393\) | −5.84096 | + | 5.48913i | −0.294638 | + | 0.276890i | ||||
\(394\) | −10.1168 | + | 17.5229i | −0.509679 | + | 0.882790i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.68614 | − | 11.4333i | −0.285739 | − | 0.574543i | ||||
\(397\) | 6.92820 | + | 4.00000i | 0.347717 | + | 0.200754i | 0.663679 | − | 0.748017i | \(-0.268994\pi\) |
−0.315963 | + | 0.948772i | \(0.602327\pi\) | |||||||
\(398\) | −18.6101 | −0.932841 | ||||||||
\(399\) | 14.4891 | − | 6.48577i | 0.725364 | − | 0.324695i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.1861 | + | 9.92242i | 0.858235 | + | 0.495502i | 0.863421 | − | 0.504484i | \(-0.168317\pi\) |
−0.00518590 | + | 0.999987i | \(0.501651\pi\) | |||||||
\(402\) | 3.78651 | − | 12.5584i | 0.188854 | − | 0.626357i | ||||
\(403\) | −2.37686 | − | 4.11684i | −0.118400 | − | 0.205075i | ||||
\(404\) | 8.18614 | − | 14.1788i | 0.407276 | − | 0.705422i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.74456 | + | 6.63325i | 0.285098 | + | 0.329203i | ||||
\(407\) | 49.7228i | 2.46467i | ||||||||
\(408\) | 11.1846 | − | 2.62772i | 0.553720 | − | 0.130091i | ||||
\(409\) | 30.7337 | − | 17.7441i | 1.51968 | − | 0.877389i | 0.519952 | − | 0.854195i | \(-0.325950\pi\) |
0.999731 | − | 0.0231940i | \(-0.00738354\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.62772 | − | 1.08724i | 0.228269 | − | 0.0536296i | ||||
\(412\) | − | 15.1168i | − | 0.744753i | ||||||
\(413\) | 10.6959 | − | 2.05842i | 0.526310 | − | 0.101288i | ||||
\(414\) | 0.813859 | − | 13.0916i | 0.0399990 | − | 0.643416i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.00000 | + | 1.73205i | 0.0490290 | + | 0.0849208i | ||||
\(417\) | −5.84096 | + | 19.3723i | −0.286033 | + | 0.948665i | ||||
\(418\) | 12.7692 | + | 7.37228i | 0.624560 | + | 0.360590i | ||||
\(419\) | −29.4891 | −1.44064 | −0.720319 | − | 0.693643i | \(-0.756005\pi\) | ||||
−0.720319 | + | 0.693643i | \(0.756005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.1168 | 0.736750 | 0.368375 | − | 0.929677i | \(-0.379914\pi\) | ||||
0.368375 | + | 0.929677i | \(0.379914\pi\) | |||||||
\(422\) | 15.7908 | + | 9.11684i | 0.768686 | + | 0.443801i | ||||
\(423\) | 5.04868 | − | 2.51087i | 0.245475 | − | 0.122083i | ||||
\(424\) | 0.686141 | + | 1.18843i | 0.0333219 | + | 0.0577153i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.37228 | + | 2.22938i | −0.114937 | + | 0.108014i | ||||
\(427\) | −5.63858 | + | 4.88316i | −0.272870 | + | 0.236312i | ||||
\(428\) | − | 17.7446i | − | 0.857716i | ||||||
\(429\) | −3.37228 | − | 14.3537i | −0.162815 | − | 0.693005i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.25544 | − | 1.87953i | 0.156809 | − | 0.0905337i | −0.419542 | − | 0.907736i | \(-0.637809\pi\) |
0.576351 | + | 0.817202i | \(0.304476\pi\) | |||||||
\(432\) | −5.12241 | + | 0.872281i | −0.246452 | + | 0.0419677i | ||||
\(433\) | − | 34.0000i | − | 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | 2.05842 | − | 5.94215i | 0.0988074 | − | 0.285232i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.55842 | + | 7.89542i | −0.218309 | + | 0.378122i | ||||
\(437\) | 7.57301 | + | 13.1168i | 0.362266 | + | 0.627464i | ||||
\(438\) | −3.31662 | − | 1.00000i | −0.158474 | − | 0.0477818i | ||||
\(439\) | 11.0584 | + | 6.38458i | 0.527790 | + | 0.304720i | 0.740116 | − | 0.672479i | \(-0.234771\pi\) |
−0.212326 | + | 0.977199i | \(0.568104\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.56930 | − | 19.9460i | −0.312824 | − | 0.949811i | ||||
\(442\) | 13.2665 | 0.631023 | ||||||||
\(443\) | 7.79423 | + | 4.50000i | 0.370315 | + | 0.213801i | 0.673596 | − | 0.739100i | \(-0.264749\pi\) |
−0.303281 | + | 0.952901i | \(0.598082\pi\) | |||||||
\(444\) | 19.3723 | + | 5.84096i | 0.919368 | + | 0.277200i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.05842 | − | 15.6896i | 0.428929 | − | 0.742926i | ||||
\(447\) | −16.8506 | − | 17.9307i | −0.797007 | − | 0.848093i | ||||
\(448\) | −0.866025 | + | 2.50000i | −0.0409159 | + | 0.118114i | ||||
\(449\) | − | 35.9855i | − | 1.69826i | −0.528182 | − | 0.849131i | \(-0.677126\pi\) | ||
0.528182 | − | 0.849131i | \(-0.322874\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.00000 | − | 3.46410i | 0.282529 | − | 0.163118i | ||||
\(452\) | −2.81929 | + | 1.62772i | −0.132608 | + | 0.0765614i | ||||
\(453\) | 3.21543 | + | 13.6861i | 0.151074 | + | 0.643031i | ||||
\(454\) | 15.6434i | 0.734179i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.37228 | − | 4.10891i | 0.204751 | − | 0.192417i | ||||
\(457\) | 6.38458 | − | 11.0584i | 0.298658 | − | 0.517291i | −0.677171 | − | 0.735826i | \(-0.736794\pi\) |
0.975829 | + | 0.218534i | \(0.0701276\pi\) | |||||||
\(458\) | 6.92820 | + | 12.0000i | 0.323734 | + | 0.560723i | ||||
\(459\) | −11.9783 | + | 32.3191i | −0.559097 | + | 1.50852i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.510875 | 0.0237938 | 0.0118969 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118969 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(462\) | 11.4333 | − | 15.8030i | 0.531923 | − | 0.735221i | ||||
\(463\) | −36.5754 | −1.69981 | −0.849903 | − | 0.526940i | \(-0.823339\pi\) | ||||
−0.849903 | + | 0.526940i | \(0.823339\pi\) | |||||||
\(464\) | 2.87228 | + | 1.65831i | 0.133342 | + | 0.0769852i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.7446 | + | 20.3422i | 0.544056 | + | 0.942333i | ||||
\(467\) | −0.0274514 | + | 0.0475473i | −0.00127030 | + | 0.00220023i | −0.866660 | − | 0.498899i | \(-0.833738\pi\) |
0.865390 | + | 0.501100i | \(0.167071\pi\) | |||||||
\(468\) | −5.98844 | − | 0.372281i | −0.276816 | − | 0.0172087i | ||||
\(469\) | 19.6753 | − | 3.78651i | 0.908519 | − | 0.174845i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.4891 | + | 3.16915i | −0.621546 | + | 0.146027i | ||||
\(472\) | 3.56529 | − | 2.05842i | 0.164106 | − | 0.0947466i | ||||
\(473\) | −40.6844 | + | 23.4891i | −1.87067 | + | 1.08003i | ||||
\(474\) | 13.6861 | − | 3.21543i | 0.628625 | − | 0.147690i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.4891 | + | 13.2665i | 0.526603 | + | 0.608069i | ||||
\(477\) | −4.10891 | − | 0.255437i | −0.188134 | − | 0.0116957i | ||||
\(478\) | −1.43710 | + | 2.48913i | −0.0657313 | + | 0.113850i | ||||
\(479\) | −4.37228 | − | 7.57301i | −0.199775 | − | 0.346020i | 0.748681 | − | 0.662931i | \(-0.230688\pi\) |
−0.948455 | + | 0.316911i | \(0.897354\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2337 | + | 11.6819i | 0.922577 | + | 0.532650i | ||||
\(482\) | −10.5947 | −0.482575 | ||||||||
\(483\) | 18.2877 | − | 8.18614i | 0.832120 | − | 0.372482i | ||||
\(484\) | 7.11684 | 0.323493 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 6.31386 | − | 14.2525i | 0.286402 | − | 0.646509i | ||||
\(487\) | −2.27567 | − | 3.94158i | −0.103121 | − | 0.178610i | 0.809848 | − | 0.586639i | \(-0.199549\pi\) |
−0.912969 | + | 0.408029i | \(0.866216\pi\) | |||||||
\(488\) | −1.40965 | + | 2.44158i | −0.0638117 | + | 0.110525i | ||||
\(489\) | 4.37228 | − | 4.10891i | 0.197721 | − | 0.185811i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9205i | 1.21491i | 0.794355 | + | 0.607453i | \(0.207809\pi\) | ||||
−0.794355 | + | 0.607453i | \(0.792191\pi\) | |||||||
\(492\) | −0.644810 | − | 2.74456i | −0.0290703 | − | 0.123734i | ||||
\(493\) | 19.0526 | − | 11.0000i | 0.858084 | − | 0.495415i | ||||
\(494\) | 6.00000 | − | 3.46410i | 0.269953 | − | 0.155857i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.37686i | − | 0.106724i | ||||||
\(497\) | −4.69882 | − | 1.62772i | −0.210771 | − | 0.0730132i | ||||
\(498\) | −1.70460 | − | 1.81386i | −0.0763849 | − | 0.0812810i | ||||
\(499\) | 14.1168 | − | 24.4511i | 0.631957 | − | 1.09458i | −0.355195 | − | 0.934792i | \(-0.615585\pi\) |
0.987151 | − | 0.159789i | \(-0.0510813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 18.7921 | + | 5.66603i | 0.839570 | + | 0.253140i | ||||
\(502\) | 13.9576 | + | 8.05842i | 0.622958 | + | 0.359665i | ||||
\(503\) | 9.45254 | 0.421468 | 0.210734 | − | 0.977543i | \(-0.432415\pi\) | ||||
0.210734 | + | 0.977543i | \(0.432415\pi\) | |||||||
\(504\) | −4.81386 | − | 6.31084i | −0.214426 | − | 0.281107i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16.1168 | + | 9.30506i | 0.716481 | + | 0.413661i | ||||
\(507\) | 14.9248 | + | 4.50000i | 0.662834 | + | 0.199852i | ||||
\(508\) | −1.18843 | − | 2.05842i | −0.0527281 | − | 0.0913277i | ||||
\(509\) | −0.127719 | + | 0.221215i | −0.00566103 | + | 0.00980519i | −0.868842 | − | 0.495089i | \(-0.835135\pi\) |
0.863181 | + | 0.504895i | \(0.168469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00000 | − | 5.19615i | −0.0442374 | − | 0.229864i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.02167 | + | 17.7446i | 0.133410 | + | 0.783442i | ||||
\(514\) | 7.37228 | − | 4.25639i | 0.325177 | − | 0.187741i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 4.37228 | + | 18.6101i | 0.192479 | + | 0.819265i | ||||
\(517\) | 8.00000i | 0.351840i | ||||||||
\(518\) | 5.84096 | + | 30.3505i | 0.256637 | + | 1.33353i | ||||
\(519\) | 4.74456 | − | 4.45877i | 0.208263 | − | 0.195718i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.62772 | + | 2.81929i | 0.0713116 | + | 0.123515i | 0.899476 | − | 0.436969i | \(-0.143948\pi\) |
−0.828165 | + | 0.560485i | \(0.810615\pi\) | |||||||
\(522\) | −8.90892 | + | 4.43070i | −0.389933 | + | 0.193927i | ||||
\(523\) | 20.9870 | + | 12.1168i | 0.917697 | + | 0.529833i | 0.882900 | − | 0.469562i | \(-0.155588\pi\) |
0.0347974 | + | 0.999394i | \(0.488921\pi\) | |||||||
\(524\) | −4.62772 | −0.202163 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.62772 | 0.0709719 | ||||||||
\(527\) | −13.6540 | − | 7.88316i | −0.594779 | − | 0.343396i | ||||
\(528\) | 2.12819 | − | 7.05842i | 0.0926178 | − | 0.307178i | ||||
\(529\) | −1.94158 | − | 3.36291i | −0.0844164 | − | 0.146214i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.766312 | + | 12.3267i | −0.0332551 | + | 0.534935i | ||||
\(532\) | 8.66025 | + | 3.00000i | 0.375470 | + | 0.130066i | ||||
\(533\) | − | 3.25544i | − | 0.141009i | ||||||
\(534\) | −7.37228 | + | 1.73205i | −0.319030 | + | 0.0749532i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.55842 | − | 3.78651i | 0.283281 | − | 0.163552i | ||||
\(537\) | −4.84630 | + | 1.13859i | −0.209133 | + | 0.0491339i | ||||
\(538\) | − | 19.9783i | − | 0.861324i | ||||||
\(539\) | 29.4891 | + | 4.25639i | 1.27019 | + | 0.183336i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.67527 | − | 11.5619i | 0.286992 | − | 0.497085i | −0.686098 | − | 0.727509i | \(-0.740678\pi\) |
0.973090 | + | 0.230424i | \(0.0740113\pi\) | |||||||
\(542\) | 10.4935 | + | 18.1753i | 0.450734 | + | 0.780695i | ||||
\(543\) | −8.98266 | + | 29.7921i | −0.385483 | + | 1.27850i | ||||
\(544\) | 5.74456 | + | 3.31662i | 0.246296 | + | 0.142199i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.74456 | − | 8.36530i | −0.160252 | − | 0.358002i | ||||
\(547\) | −0.644810 | −0.0275701 | −0.0137850 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137850 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(548\) | 2.37686 | + | 1.37228i | 0.101534 | + | 0.0586210i | ||||
\(549\) | −3.76631 | − | 7.57301i | −0.160742 | − | 0.323208i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.74456 | − | 9.94987i | 0.244727 | − | 0.423879i | ||||
\(552\) | 5.51856 | − | 5.18614i | 0.234885 | − | 0.220737i | ||||
\(553\) | 14.0588 | + | 16.2337i | 0.597840 | + | 0.690327i | ||||
\(554\) | 29.0024i | 1.23220i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.1168 | + | 5.84096i | −0.429050 | + | 0.247712i | ||||
\(557\) | −0.746000 | + | 0.430703i | −0.0316090 | + | 0.0182495i | −0.515721 | − | 0.856756i | \(-0.672476\pi\) |
0.484112 | + | 0.875006i | \(0.339143\pi\) | |||||||
\(558\) | 5.94215 | + | 3.94158i | 0.251551 | + | 0.166860i | ||||
\(559\) | 22.0742i | 0.933640i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −33.4891 | − | 35.6357i | −1.41391 | − | 1.50454i | ||||
\(562\) | −10.8896 | + | 18.8614i | −0.459352 | + | 0.795620i | ||||
\(563\) | −5.91470 | − | 10.2446i | −0.249275 | − | 0.431757i | 0.714050 | − | 0.700095i | \(-0.246859\pi\) |
−0.963325 | + | 0.268338i | \(0.913526\pi\) | |||||||
\(564\) | 3.11684 | + | 0.939764i | 0.131243 | + | 0.0395712i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 16.0000 | 0.672530 | ||||||||
\(567\) | 23.7600 | − | 1.56930i | 0.997826 | − | 0.0659043i | ||||
\(568\) | −1.87953 | −0.0788632 | ||||||||
\(569\) | −18.8614 | − | 10.8896i | −0.790711 | − | 0.456517i | 0.0495016 | − | 0.998774i | \(-0.484237\pi\) |
−0.840213 | + | 0.542257i | \(0.817570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.1168 | − | 29.6472i | −0.716318 | − | 1.24070i | −0.962449 | − | 0.271462i | \(-0.912493\pi\) |
0.246132 | − | 0.969236i | \(-0.420840\pi\) | |||||||
\(572\) | 4.25639 | − | 7.37228i | 0.177969 | − | 0.308251i | ||||
\(573\) | −4.45877 | − | 4.74456i | −0.186268 | − | 0.198207i | ||||
\(574\) | 3.25544 | − | 2.81929i | 0.135879 | − | 0.117675i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.50000 | − | 1.65831i | −0.104167 | − | 0.0690963i | ||||
\(577\) | 15.4873 | − | 8.94158i | 0.644743 | − | 0.372243i | −0.141696 | − | 0.989910i | \(-0.545256\pi\) |
0.786439 | + | 0.617667i | \(0.211922\pi\) | |||||||
\(578\) | 23.3827 | − | 13.5000i | 0.972592 | − | 0.561526i | ||||
\(579\) | −3.17527 | − | 13.5152i | −0.131960 | − | 0.561671i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.24456 | − | 3.59274i | 0.0516332 | − | 0.149052i | ||||
\(582\) | 2.67181 | − | 2.51087i | 0.110750 | − | 0.104079i | ||||
\(583\) | 2.92048 | − | 5.05842i | 0.120954 | − | 0.209498i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −21.6861 | − | 12.5205i | −0.895846 | − | 0.517217i | ||||
\(587\) | 36.4280 | 1.50354 | 0.751772 | − | 0.659424i | \(-0.229200\pi\) | ||||
0.751772 | + | 0.659424i | \(0.229200\pi\) | |||||||
\(588\) | 5.12241 | − | 10.9891i | 0.211245 | − | 0.453184i | ||||
\(589\) | −8.23369 | −0.339263 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.1168 | − | 33.5538i | 0.416151 | − | 1.38022i | ||||
\(592\) | 5.84096 | + | 10.1168i | 0.240062 | + | 0.415800i | ||||
\(593\) | 7.07568 | − | 12.2554i | 0.290563 | − | 0.503270i | −0.683380 | − | 0.730063i | \(-0.739491\pi\) |
0.973943 | + | 0.226793i | \(0.0728240\pi\) | |||||||
\(594\) | 14.1168 | + | 17.0256i | 0.579221 | + | 0.698567i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 14.2063i | − | 0.581911i | ||||||
\(597\) | 31.3793 | − | 7.37228i | 1.28427 | − | 0.301727i | ||||
\(598\) | 7.57301 | − | 4.37228i | 0.309684 | − | 0.178796i | ||||
\(599\) | −7.37228 | + | 4.25639i | −0.301223 | + | 0.173911i | −0.642992 | − | 0.765873i | \(-0.722307\pi\) |
0.341769 | + | 0.939784i | \(0.388974\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 10.5947i | − | 0.432166i | −0.976375 | − | 0.216083i | \(-0.930672\pi\) | ||
0.976375 | − | 0.216083i | \(-0.0693282\pi\) | |||||||
\(602\) | −22.0742 | + | 19.1168i | −0.899678 | + | 0.779144i | ||||
\(603\) | −1.40965 | + | 22.6753i | −0.0574052 | + | 0.923408i | ||||
\(604\) | −4.05842 | + | 7.02939i | −0.165135 | + | 0.286022i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.18614 | + | 27.1504i | −0.332539 | + | 1.10291i | ||||
\(607\) | 23.7874 | + | 13.7337i | 0.965503 | + | 0.557433i | 0.897862 | − | 0.440277i | \(-0.145120\pi\) |
0.0676404 | + | 0.997710i | \(0.478453\pi\) | |||||||
\(608\) | 3.46410 | 0.140488 | ||||||||
\(609\) | −12.3139 | − | 8.90892i | −0.498983 | − | 0.361008i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.25544 | + | 1.87953i | 0.131701 | + | 0.0760375i | ||||
\(612\) | −17.8178 | + | 8.86141i | −0.720244 | + | 0.358201i | ||||
\(613\) | −6.48577 | − | 11.2337i | −0.261958 | − | 0.453724i | 0.704804 | − | 0.709402i | \(-0.251035\pi\) |
−0.966762 | + | 0.255677i | \(0.917701\pi\) | |||||||
\(614\) | −3.44158 | + | 5.96099i | −0.138891 | + | 0.240566i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.0584 | − | 2.12819i | 0.445557 | − | 0.0857474i | ||||
\(617\) | − | 1.02175i | − | 0.0411341i | −0.999788 | − | 0.0205670i | \(-0.993453\pi\) | ||
0.999788 | − | 0.0205670i | \(-0.00654715\pi\) | |||||||
\(618\) | 5.98844 | + | 25.4891i | 0.240890 | + | 1.02532i | ||||
\(619\) | −20.2337 | + | 11.6819i | −0.813261 | + | 0.469536i | −0.848087 | − | 0.529857i | \(-0.822246\pi\) |
0.0348263 | + | 0.999393i | \(0.488912\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.81386 | + | 22.3966i | 0.153045 | + | 0.898746i | ||||
\(622\) | − | 14.2337i | − | 0.570719i | ||||||
\(623\) | −7.57301 | − | 8.74456i | −0.303406 | − | 0.350344i | ||||
\(624\) | −2.37228 | − | 2.52434i | −0.0949673 | − | 0.101054i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −7.05842 | − | 12.2255i | −0.282111 | − | 0.488631i | ||||
\(627\) | −24.4511 | − | 7.37228i | −0.976483 | − | 0.294421i | ||||
\(628\) | −6.92820 | − | 4.00000i | −0.276465 | − | 0.159617i | ||||
\(629\) | 77.4891 | 3.08969 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.1168 | 1.19893 | 0.599466 | − | 0.800400i | \(-0.295380\pi\) | ||||
0.599466 | + | 0.800400i | \(0.295380\pi\) | |||||||
\(632\) | 7.02939 | + | 4.05842i | 0.279614 | + | 0.161435i | ||||
\(633\) | −30.2372 | − | 9.11684i | −1.20182 | − | 0.362362i | ||||
\(634\) | 8.05842 | + | 13.9576i | 0.320041 | + | 0.554327i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.62772 | − | 1.73205i | −0.0645432 | − | 0.0686803i | ||||
\(637\) | 8.66025 | − | 11.0000i | 0.343132 | − | 0.435836i | ||||
\(638\) | − | 14.1168i | − | 0.558891i | ||||||
\(639\) | 3.11684 | − | 4.69882i | 0.123300 | − | 0.185882i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −12.3030 | + | 7.10313i | −0.485939 | + | 0.280557i | −0.722888 | − | 0.690965i | \(-0.757186\pi\) |
0.236949 | + | 0.971522i | \(0.423852\pi\) | |||||||
\(642\) | 7.02939 | + | 29.9198i | 0.277428 | + | 1.18084i | ||||
\(643\) | 16.2337i | 0.640194i | 0.947385 | + | 0.320097i | \(0.103716\pi\) | ||||
−0.947385 | + | 0.320097i | \(0.896284\pi\) | |||||||
\(644\) | 10.9307 | + | 3.78651i | 0.430730 | + | 0.149209i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.4891 | − | 19.8997i | 0.452034 | − | 0.782945i | ||||
\(647\) | 12.7417 | + | 22.0693i | 0.500928 | + | 0.867634i | 0.999999 | + | 0.00107245i | \(0.000341372\pi\) |
−0.499071 | + | 0.866561i | \(0.666325\pi\) | |||||||
\(648\) | 8.29156 | − | 3.50000i | 0.325723 | − | 0.137493i | ||||
\(649\) | −15.1753 | − | 8.76144i | −0.595681 | − | 0.343917i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.11684 | + | 10.8347i | −0.0437726 | + | 0.424647i | ||||
\(652\) | 3.46410 | 0.135665 | ||||||||
\(653\) | −9.20387 | − | 5.31386i | −0.360175 | − | 0.207947i | 0.308982 | − | 0.951068i | \(-0.400012\pi\) |
−0.669158 | + | 0.743120i | \(0.733345\pi\) | |||||||
\(654\) | 4.55842 | − | 15.1186i | 0.178248 | − | 0.591183i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.813859 | − | 1.40965i | 0.0317759 | − | 0.0550374i | ||||
\(657\) | 5.98844 | + | 0.372281i | 0.233631 | + | 0.0145241i | ||||
\(658\) | 0.939764 | + | 4.88316i | 0.0366358 | + | 0.190365i | ||||
\(659\) | 36.9253i | 1.43841i | 0.694800 | + | 0.719203i | \(0.255493\pi\) | ||||
−0.694800 | + | 0.719203i | \(0.744507\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.44158 | − | 1.40965i | 0.0949664 | − | 0.0548289i | −0.451765 | − | 0.892137i | \(-0.649205\pi\) |
0.546731 | + | 0.837308i | \(0.315872\pi\) | |||||||
\(662\) | 8.86263 | − | 5.11684i | 0.344456 | − | 0.198872i | ||||
\(663\) | −22.3692 | + | 5.25544i | −0.868747 | + | 0.204104i | ||||
\(664\) | − | 1.43710i | − | 0.0557702i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −34.9783 | − | 2.17448i | −1.35538 | − | 0.0842594i | ||||
\(667\) | 7.25061 | − | 12.5584i | 0.280745 | − | 0.486264i | ||||
\(668\) | 5.66603 | + | 9.81386i | 0.219225 | + | 0.379710i | ||||
\(669\) | −9.05842 | + | 30.0434i | −0.350219 | + | 1.16154i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0.469882 | − | 4.55842i | 0.0181261 | − | 0.175845i | ||||
\(673\) | 17.1181 | 0.659855 | 0.329928 | − | 0.944006i | \(-0.392976\pi\) | ||||
0.329928 | + | 0.944006i | \(0.392976\pi\) | |||||||
\(674\) | 8.05842 | + | 4.65253i | 0.310399 | + | 0.179209i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | 22.4704 | − | 38.9198i | 0.863607 | − | 1.49581i | −0.00481749 | − | 0.999988i | \(-0.501533\pi\) |
0.868424 | − | 0.495822i | \(-0.165133\pi\) | |||||||
\(678\) | 4.10891 | − | 3.86141i | 0.157802 | − | 0.148296i | ||||
\(679\) | 5.29211 | + | 1.83324i | 0.203093 | + | 0.0703533i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.19702 | − | 26.3769i | −0.237470 | − | 1.01077i | ||||
\(682\) | −8.76144 | + | 5.05842i | −0.335493 | + | 0.193697i | ||||
\(683\) | 12.1055 | − | 6.98913i | 0.463205 | − | 0.267431i | −0.250186 | − | 0.968198i | \(-0.580492\pi\) |
0.713391 | + | 0.700766i | \(0.247158\pi\) | |||||||
\(684\) | −5.74456 | + | 8.66025i | −0.219649 | + | 0.331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 18.5000 | − | 0.866025i | 0.706333 | − | 0.0330650i | ||||
\(687\) | −16.4356 | − | 17.4891i | −0.627059 | − | 0.667252i | ||||
\(688\) | −5.51856 | + | 9.55842i | −0.210393 | + | 0.364411i | ||||
\(689\) | −1.37228 | − | 2.37686i | −0.0522798 | − | 0.0905512i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.2337 | − | 15.1460i | −0.997977 | − | 0.576182i | −0.0903276 | − | 0.995912i | \(-0.528791\pi\) |
−0.907649 | + | 0.419730i | \(0.862125\pi\) | |||||||
\(692\) | 3.75906 | 0.142898 | ||||||||
\(693\) | −13.0178 | + | 31.1753i | −0.494507 | + | 1.18425i | ||||
\(694\) | −19.1168 | −0.725665 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.50000 | − | 1.65831i | −0.208477 | − | 0.0628582i | ||||
\(697\) | −5.39853 | − | 9.35053i | −0.204484 | − | 0.354177i | ||||
\(698\) | −12.0043 | + | 20.7921i | −0.454371 | + | 0.786993i | ||||
\(699\) | −27.8614 | − | 29.6472i | −1.05382 | − | 1.12136i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 12.7143i | − | 0.480211i | −0.970747 | − | 0.240106i | \(-0.922818\pi\) | ||
0.970747 | − | 0.240106i | \(-0.0771821\pi\) | |||||||
\(702\) | 10.2448 | − | 1.74456i | 0.386666 | − | 0.0658443i | ||||
\(703\) | 35.0458 | − | 20.2337i | 1.32178 | − | 0.763128i | ||||
\(704\) | 3.68614 | − | 2.12819i | 0.138927 | − | 0.0802093i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.9051i | − | 0.711502i | ||||||
\(707\) | −42.5364 | + | 8.18614i | −1.59975 | + | 0.307872i | ||||
\(708\) | −5.19615 | + | 4.88316i | −0.195283 | + | 0.183520i | ||||
\(709\) | −2.55842 | + | 4.43132i | −0.0960836 | + | 0.166422i | −0.910060 | − | 0.414476i | \(-0.863965\pi\) |
0.813977 | + | 0.580897i | \(0.197298\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.8030 | + | 10.8434i | −0.817676 | + | 0.406657i | ||||
\(712\) | −3.78651 | − | 2.18614i | −0.141905 | − | 0.0819291i | ||||
\(713\) | −10.3923 | −0.389195 | ||||||||
\(714\) | −24.6277 | − | 17.8178i | −0.921669 | − | 0.666816i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.48913 | − | 1.43710i | −0.0930230 | − | 0.0537068i | ||||
\(717\) | 1.43710 | − | 4.76631i | 0.0536694 | − | 0.178001i | ||||
\(718\) | −7.07568 | − | 12.2554i | −0.264062 | − | 0.457369i | ||||
\(719\) | 16.6277 | − | 28.8001i | 0.620109 | − | 1.07406i | −0.369356 | − | 0.929288i | \(-0.620422\pi\) |
0.989465 | − | 0.144773i | \(-0.0462451\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.2337 | + | 26.1831i | −1.12596 | + | 0.975111i | ||||
\(722\) | 7.00000i | 0.260513i | ||||||||
\(723\) | 17.8641 | − | 4.19702i | 0.664374 | − | 0.156089i | ||||
\(724\) | −15.5584 | + | 8.98266i | −0.578224 | + | 0.333838i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −12.0000 | + | 2.81929i | −0.445362 | + | 0.104634i | ||||
\(727\) | 19.0000i | 0.704671i | 0.935874 | + | 0.352335i | \(0.114612\pi\) | ||||
−0.935874 | + | 0.352335i | \(0.885388\pi\) | |||||||
\(728\) | 1.73205 | − | 5.00000i | 0.0641941 | − | 0.185312i | ||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 36.6060 | + | 63.4034i | 1.35392 | + | 2.34506i | ||||
\(732\) | 1.40965 | − | 4.67527i | 0.0521020 | − | 0.172803i | ||||
\(733\) | −31.5817 | − | 18.2337i | −1.16650 | − | 0.673477i | −0.213644 | − | 0.976912i | \(-0.568533\pi\) |
−0.952852 | + | 0.303435i | \(0.901866\pi\) | |||||||
\(734\) | −21.2337 | −0.783750 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.37228 | 0.161164 | ||||||||
\(737\) | −27.9152 | − | 16.1168i | −1.02827 | − | 0.593672i | ||||
\(738\) | 2.17448 | + | 4.37228i | 0.0800438 | + | 0.160946i | ||||
\(739\) | −18.1168 | − | 31.3793i | −0.666439 | − | 1.15431i | −0.978893 | − | 0.204373i | \(-0.934484\pi\) |
0.312454 | − | 0.949933i | \(-0.398849\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.74456 | + | 8.21782i | −0.321240 | + | 0.301889i | ||||
\(742\) | 1.18843 | − | 3.43070i | 0.0436287 | − | 0.125945i | ||||
\(743\) | 18.6060i | 0.682587i | 0.939957 | + | 0.341293i | \(0.110865\pi\) | ||||
−0.939957 | + | 0.341293i | \(0.889135\pi\) | |||||||
\(744\) | 0.941578 | + | 4.00772i | 0.0345199 | + | 0.146930i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.2337 | + | 8.21782i | −0.521132 | + | 0.300876i | ||||
\(747\) | 3.59274 | + | 2.38316i | 0.131452 | + | 0.0871951i | ||||
\(748\) | − | 28.2337i | − | 1.03233i | ||||||
\(749\) | −35.4891 | + | 30.7345i | −1.29674 | + | 1.12301i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.0584 | + | 36.4743i | −0.768433 | + | 1.33096i | 0.169980 | + | 0.985448i | \(0.445630\pi\) |
−0.938412 | + | 0.345517i | \(0.887704\pi\) | |||||||
\(752\) | 0.939764 | + | 1.62772i | 0.0342697 | + | 0.0593568i | ||||
\(753\) | −26.7268 | − | 8.05842i | −0.973977 | − | 0.293665i | ||||
\(754\) | −5.74456 | − | 3.31662i | −0.209205 | − | 0.120784i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 10.6168 | + | 8.73399i | 0.386131 | + | 0.317652i | ||||
\(757\) | −5.63858 | −0.204938 | −0.102469 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102469 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(758\) | 19.2549 | + | 11.1168i | 0.699371 | + | 0.403782i | ||||
\(759\) | −30.8614 | − | 9.30506i | −1.12020 | − | 0.337752i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.4891 | + | 45.8805i | −0.960230 | + | 1.66317i | −0.238312 | + | 0.971189i | \(0.576594\pi\) |
−0.721918 | + | 0.691979i | \(0.756739\pi\) | |||||||
\(762\) | 2.81929 | + | 3.00000i | 0.102132 | + | 0.108679i | ||||
\(763\) | 23.6863 | − | 4.55842i | 0.857500 | − | 0.165026i | ||||
\(764\) | − | 3.75906i | − | 0.135998i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.0475 | + | 10.4198i | −0.652084 | + | 0.376481i | ||||
\(767\) | −7.13058 | + | 4.11684i | −0.257470 | + | 0.148651i | ||||
\(768\) | −0.396143 | − | 1.68614i | −0.0142946 | − | 0.0608434i | ||||
\(769\) | 40.4820i | 1.45982i | 0.683545 | + | 0.729909i | \(0.260437\pi\) | ||||
−0.683545 | + | 0.729909i | \(0.739563\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.7446 | + | 10.0974i | −0.386956 | + | 0.363647i | ||||
\(772\) | 4.00772 | − | 6.94158i | 0.144241 | − | 0.249833i | ||||
\(773\) | −0.939764 | − | 1.62772i | −0.0338010 | − | 0.0585450i | 0.848630 | − | 0.528987i | \(-0.177428\pi\) |
−0.882431 | + | 0.470442i | \(0.844095\pi\) | |||||||
\(774\) | −14.7446 | − | 29.6472i | −0.529982 | − | 1.06565i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.11684 | 0.0759903 | ||||||||
\(777\) | −21.8719 | − | 48.8614i | −0.784648 | − | 1.75289i | ||||
\(778\) | 34.0511 | 1.22079 | ||||||||
\(779\) | −4.88316 | − | 2.81929i | −0.174957 | − | 0.101012i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | + | 6.92820i | 0.143131 | + | 0.247911i | ||||
\(782\) | 14.5012 | − | 25.1168i | 0.518562 | − | 0.898177i | ||||
\(783\) | 13.2665 | − | 11.0000i | 0.474106 | − | 0.393108i | ||||
\(784\) | 6.50000 | − | 2.59808i | 0.232143 | − | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 7.80298 | − | 1.83324i | 0.278323 | − | 0.0653895i | ||||
\(787\) | −23.4839 | + | 13.5584i | −0.837110 | + | 0.483306i | −0.856281 | − | 0.516511i | \(-0.827231\pi\) |
0.0191710 | + | 0.999816i | \(0.493897\pi\) | |||||||
\(788\) | 17.5229 | − | 10.1168i | 0.624227 | − | 0.360398i | ||||
\(789\) | −2.74456 | + | 0.644810i | −0.0977090 | + | 0.0229558i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.13859 | + | 2.81929i | 0.289375 | + | 0.100242i | ||||
\(792\) | −0.792287 | + | 12.7446i | −0.0281527 | + | 0.452858i | ||||
\(793\) | 2.81929 | − | 4.88316i | 0.100116 | − | 0.173406i | ||||
\(794\) | −4.00000 | − | 6.92820i | −0.141955 | − | 0.245873i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.1168 | + | 9.30506i | 0.571246 | + | 0.329809i | ||||
\(797\) | −4.25639 | −0.150769 | −0.0753845 | − | 0.997155i | \(-0.524018\pi\) | ||||
−0.0753845 | + | 0.997155i | \(0.524018\pi\) | |||||||
\(798\) | −15.7908 | − | 1.62772i | −0.558990 | − | 0.0576206i | ||||
\(799\) | 12.4674 | 0.441064 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.7446 | − | 5.84096i | 0.414974 | − | 0.206380i | ||||
\(802\) | −9.92242 | − | 17.1861i | −0.350373 | − | 0.606864i | ||||
\(803\) | −4.25639 | + | 7.37228i | −0.150205 | + | 0.260162i | ||||
\(804\) | −9.55842 | + | 8.98266i | −0.337100 | + | 0.316794i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.75372i | 0.167443i | ||||||||
\(807\) | 7.91425 | + | 33.6861i | 0.278595 | + | 1.18581i | ||||
\(808\) | −14.1788 | + | 8.18614i | −0.498809 | + | 0.287987i | ||||
\(809\) | 22.0693 | − | 12.7417i | 0.775915 | − | 0.447975i | −0.0590655 | − | 0.998254i | \(-0.518812\pi\) |
0.834981 | + | 0.550279i | \(0.185479\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 10.3923i | − | 0.364923i | −0.983213 | − | 0.182462i | \(-0.941593\pi\) | ||
0.983213 | − | 0.182462i | \(-0.0584065\pi\) | |||||||
\(812\) | −1.65831 | − | 8.61684i | −0.0581954 | − | 0.302392i | ||||
\(813\) | −24.8935 | − | 26.4891i | −0.873054 | − | 0.929014i | ||||
\(814\) | 24.8614 | − | 43.0612i | 0.871392 | − | 1.50929i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −11.0000 | − | 3.31662i | −0.385077 | − | 0.116105i | ||||
\(817\) | 33.1113 | + | 19.1168i | 1.15842 | + | 0.668814i | ||||
\(818\) | −35.4882 | −1.24082 | ||||||||
\(819\) | 9.62772 | + | 12.6217i | 0.336420 | + | 0.441038i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.4307 | − | 10.6410i | −0.643236 | − | 0.371372i | 0.142624 | − | 0.989777i | \(-0.454446\pi\) |
−0.785860 | + | 0.618404i | \(0.787779\pi\) | |||||||
\(822\) | −4.55134 | − | 1.37228i | −0.158746 | − | 0.0478638i | ||||
\(823\) | 21.7518 | + | 37.6753i | 0.758221 | + | 1.31328i | 0.943757 | + | 0.330640i | \(0.107265\pi\) |
−0.185536 | + | 0.982637i | \(0.559402\pi\) | |||||||
\(824\) | −7.55842 | + | 13.0916i | −0.263310 | + | 0.456066i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −10.2921 | − | 3.56529i | −0.358108 | − | 0.124052i | ||||
\(827\) | 33.0000i | 1.14752i | 0.819023 | + | 0.573761i | \(0.194516\pi\) | ||||
−0.819023 | + | 0.573761i | \(0.805484\pi\) | |||||||
\(828\) | −7.25061 | + | 10.9307i | −0.251976 | + | 0.379868i | ||||
\(829\) | 16.1168 | − | 9.30506i | 0.559761 | − | 0.323178i | −0.193288 | − | 0.981142i | \(-0.561915\pi\) |
0.753050 | + | 0.657964i | \(0.228582\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4891 | − | 48.9022i | −0.398553 | − | 1.69640i | ||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | 6.63325 | − | 45.9565i | 0.229828 | − | 1.59230i | ||||
\(834\) | 14.7446 | − | 13.8564i | 0.510562 | − | 0.479808i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.37228 | − | 12.7692i | −0.254976 | − | 0.441631i | ||||
\(837\) | −11.5807 | − | 4.29211i | −0.400289 | − | 0.148357i | ||||
\(838\) | 25.5383 | + | 14.7446i | 0.882207 | + | 0.509342i | ||||
\(839\) | 1.72281 | 0.0594781 | 0.0297391 | − | 0.999558i | \(-0.490532\pi\) | ||||
0.0297391 | + | 0.999558i | \(0.490532\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.0000 | 0.620690 | ||||||||
\(842\) | −13.0916 | − | 7.55842i | −0.451165 | − | 0.260480i | ||||
\(843\) | 10.8896 | − | 36.1168i | 0.375059 | − | 1.24393i | ||||
\(844\) | −9.11684 | − | 15.7908i | −0.313815 | − | 0.543543i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.62772 | − | 0.349857i | −0.193485 | − | 0.0120283i | ||||
\(847\) | −12.3267 | − | 14.2337i | −0.423552 | − | 0.489075i | ||||
\(848\) | − | 1.37228i | − | 0.0471243i | ||||||
\(849\) | −26.9783 | + | 6.33830i | −0.925891 | + | 0.217530i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 44.2337 | − | 25.5383i | 1.51631 | − | 0.875443i | ||||
\(852\) | 3.16915 | − | 0.744563i | 0.108573 | − | 0.0255083i | ||||
\(853\) | 30.4674i | 1.04318i | 0.853195 | + | 0.521592i | \(0.174661\pi\) | ||||
−0.853195 | + | 0.521592i | \(0.825339\pi\) | |||||||
\(854\) | 7.32473 | − | 1.40965i | 0.250647 | − | 0.0482371i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.87228 | + | 15.3672i | −0.303248 | + | 0.525242i | ||||
\(857\) | 18.9051 | + | 32.7446i | 0.645785 | + | 1.11853i | 0.984120 | + | 0.177507i | \(0.0568032\pi\) |
−0.338334 | + | 0.941026i | \(0.609863\pi\) | |||||||
\(858\) | −4.25639 | + | 14.1168i | −0.145311 | + | 0.481941i | ||||
\(859\) | −28.4674 | − | 16.4356i | −0.971294 | − | 0.560777i | −0.0716637 | − | 0.997429i | \(-0.522831\pi\) |
−0.899631 | + | 0.436652i | \(0.856164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.37228 | + | 6.04334i | −0.149007 | + | 0.205957i | ||||
\(862\) | −3.75906 | −0.128034 | ||||||||
\(863\) | 6.60580 | + | 3.81386i | 0.224864 | + | 0.129825i | 0.608200 | − | 0.793783i | \(-0.291892\pi\) |
−0.383336 | + | 0.923609i | \(0.625225\pi\) | |||||||
\(864\) | 4.87228 | + | 1.80579i | 0.165758 | + | 0.0614342i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.0000 | + | 29.4449i | −0.577684 | + | 1.00058i | ||||
\(867\) | −34.0786 | + | 32.0258i | −1.15737 | + | 1.08765i | ||||
\(868\) | −4.75372 | + | 4.11684i | −0.161352 | + | 0.139735i | ||||
\(869\) | − | 34.5484i | − | 1.17198i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.1168 | + | 7.57301i | −0.444447 | + | 0.256602i | ||||
\(872\) | 7.89542 | − | 4.55842i | 0.267373 | − | 0.154368i | ||||
\(873\) | −3.51039 | + | 5.29211i | −0.118809 | + | 0.179111i | ||||
\(874\) | − | 15.1460i | − | 0.512322i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.37228 | + | 2.52434i | 0.0801520 | + | 0.0852895i | ||||
\(877\) | −15.7908 | + | 27.3505i | −0.533219 | + | 0.923562i | 0.466029 | + | 0.884770i | \(0.345684\pi\) |
−0.999247 | + | 0.0387922i | \(0.987649\pi\) | |||||||
\(878\) | −6.38458 | − | 11.0584i | −0.215469 | − | 0.373204i | ||||
\(879\) | 41.5258 | + | 12.5205i | 1.40063 | + | 0.422306i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3505 | 1.73004 | 0.865022 | − | 0.501734i | \(-0.167305\pi\) | ||||
0.865022 | + | 0.501734i | \(0.167305\pi\) | |||||||
\(882\) | −4.28384 | + | 20.5584i | −0.144244 | + | 0.692238i | ||||
\(883\) | −54.9455 | −1.84906 | −0.924532 | − | 0.381104i | \(-0.875544\pi\) | ||||
−0.924532 | + | 0.381104i | \(0.875544\pi\) | |||||||
\(884\) | −11.4891 | − | 6.63325i | −0.386421 | − | 0.223100i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.50000 | − | 7.79423i | −0.151180 | − | 0.261852i | ||||
\(887\) | 27.4453 | − | 47.5367i | 0.921523 | − | 1.59613i | 0.124464 | − | 0.992224i | \(-0.460279\pi\) |
0.797059 | − | 0.603901i | \(-0.206388\pi\) | |||||||
\(888\) | −13.8564 | − | 14.7446i | −0.464991 | − | 0.494795i | ||||
\(889\) | −2.05842 | + | 5.94215i | −0.0690373 | + | 0.199293i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.5475 | − | 23.1152i | −1.02338 | − | 0.774388i | ||||
\(892\) | −15.6896 | + | 9.05842i | −0.525328 | + | 0.303298i | ||||
\(893\) | 5.63858 | − | 3.25544i | 0.188688 | − | 0.108939i | ||||
\(894\) | 5.62772 | + | 23.9538i | 0.188219 | + | 0.801133i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.00000 | − | 1.73205i | 0.0668153 | − | 0.0578638i | ||||
\(897\) | −11.0371 | + | 10.3723i | −0.368519 | + | 0.346320i | ||||
\(898\) | −17.9928 | + | 31.1644i | −0.600427 | + | 1.03997i | ||||
\(899\) | 3.94158 | + | 6.82701i | 0.131459 | + | 0.227694i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.88316 | − | 4.55134i | −0.262626 | − | 0.151627i | ||||
\(902\) | −6.92820 | −0.230684 | ||||||||
\(903\) | 29.6472 | − | 40.9783i | 0.986598 | − | 1.36367i | ||||
\(904\) | 3.25544 | 0.108274 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.05842 | − | 13.4603i | 0.134832 | − | 0.447187i | ||||
\(907\) | 22.3966 | + | 38.7921i | 0.743668 | + | 1.28807i | 0.950814 | + | 0.309761i | \(0.100249\pi\) |
−0.207146 | + | 0.978310i | \(0.566418\pi\) | |||||||
\(908\) | 7.82168 | − | 13.5475i | 0.259572 | − | 0.449591i | ||||
\(909\) | 3.04755 | − | 49.0222i | 0.101081 | − | 1.62596i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.5437i | 0.813168i | 0.913613 | + | 0.406584i | \(0.133280\pi\) | ||||
−0.913613 | + | 0.406584i | \(0.866720\pi\) | |||||||
\(912\) | −5.84096 | + | 1.37228i | −0.193414 | + | 0.0454408i | ||||
\(913\) | −5.29734 | + | 3.05842i | −0.175316 | + | 0.101219i | ||||
\(914\) | −11.0584 | + | 6.38458i | −0.365780 | + | 0.211183i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 8.01544 | + | 9.25544i | 0.264693 | + | 0.305641i | ||||
\(918\) | 26.5330 | − | 22.0000i | 0.875719 | − | 0.726108i | ||||
\(919\) | −9.11684 | + | 15.7908i | −0.300737 | + | 0.520892i | −0.976303 | − | 0.216408i | \(-0.930566\pi\) |
0.675566 | + | 0.737299i | \(0.263899\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.44158 | − | 11.4144i | 0.113404 | − | 0.376118i | ||||
\(922\) | −0.442430 | − | 0.255437i | −0.0145707 | − | 0.00841238i | ||||
\(923\) | 3.75906 | 0.123731 | ||||||||
\(924\) | −17.8030 | + | 7.96916i | −0.585675 | + | 0.262166i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 31.6753 | + | 18.2877i | 1.04091 | + | 0.600972i | ||||
\(927\) | −20.1947 | − | 40.6060i | −0.663281 | − | 1.33368i | ||||
\(928\) | −1.65831 | − | 2.87228i | −0.0544368 | − | 0.0942873i | ||||
\(929\) | −8.44158 | + | 14.6212i | −0.276959 | + | 0.479707i | −0.970628 | − | 0.240587i | \(-0.922660\pi\) |
0.693668 | + | 0.720295i | \(0.255993\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.00000 | − | 22.5167i | −0.294963 | − | 0.737954i | ||||
\(932\) | − | 23.4891i | − | 0.769412i | ||||||
\(933\) | 5.63858 | + | 24.0000i | 0.184599 | + | 0.785725i | ||||
\(934\) | 0.0475473 | − | 0.0274514i | 0.00155579 | − | 0.000898238i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.00000 | + | 3.31662i | 0.163430 | + | 0.108407i | ||||
\(937\) | − | 50.3505i | − | 1.64488i | −0.568852 | − | 0.822440i | \(-0.692612\pi\) | ||
0.568852 | − | 0.822440i | \(-0.307388\pi\) | |||||||
\(938\) | −18.9325 | − | 6.55842i | −0.618169 | − | 0.214140i | ||||
\(939\) | 16.7446 | + | 17.8178i | 0.546438 | + | 0.581463i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.1753 | − | 21.0882i | −0.396902 | − | 0.687455i | 0.596440 | − | 0.802658i | \(-0.296582\pi\) |
−0.993342 | + | 0.115203i | \(0.963248\pi\) | |||||||
\(942\) | 13.2665 | + | 4.00000i | 0.432246 | + | 0.130327i | ||||
\(943\) | −6.16337 | − | 3.55842i | −0.200707 | − | 0.115878i | ||||
\(944\) | −4.11684 | −0.133992 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 46.9783 | 1.52739 | ||||||||
\(947\) | −37.3403 | − | 21.5584i | −1.21340 | − | 0.700555i | −0.249899 | − | 0.968272i | \(-0.580397\pi\) |
−0.963497 | + | 0.267717i | \(0.913731\pi\) | |||||||
\(948\) | −13.4603 | − | 4.05842i | −0.437169 | − | 0.131811i | ||||
\(949\) | 2.00000 | + | 3.46410i | 0.0649227 | + | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19.1168 | − | 20.3422i | −0.619906 | − | 0.659640i | ||||
\(952\) | −3.31662 | − | 17.2337i | −0.107492 | − | 0.558547i | ||||
\(953\) | 48.0000i | 1.55487i | 0.628962 | + | 0.777436i | \(0.283480\pi\) | ||||
−0.628962 | + | 0.777436i | \(0.716520\pi\) | |||||||
\(954\) | 3.43070 | + | 2.27567i | 0.111073 | + | 0.0736776i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 2.48913 | − | 1.43710i | 0.0805041 | − | 0.0464790i | ||||
\(957\) | 5.59230 | + | 23.8030i | 0.180773 | + | 0.769441i | ||||
\(958\) | 8.74456i | 0.282524i | ||||||||
\(959\) | −1.37228 | − | 7.13058i | −0.0443133 | − | 0.230259i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.6753 | + | 21.9542i | −0.408880 | + | 0.708200i | ||||
\(962\) | −11.6819 | − | 20.2337i | −0.376640 | − | 0.652360i | ||||
\(963\) | −23.7051 | − | 47.6644i | −0.763886 | − | 1.53596i | ||||
\(964\) | 9.17527 | + | 5.29734i | 0.295515 | + | 0.170616i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −19.9307 | − | 2.05446i | −0.641260 | − | 0.0661010i | ||||
\(967\) | −51.9239 | −1.66976 | −0.834879 | − | 0.550433i | \(-0.814463\pi\) | ||||
−0.834879 | + | 0.550433i | \(0.814463\pi\) | |||||||
\(968\) | −6.16337 | − | 3.55842i | −0.198098 | − | 0.114372i | ||||
\(969\) | −11.4891 | + | 38.1051i | −0.369084 | + | 1.22411i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 14.3139 | − | 24.7923i | 0.459354 | − | 0.795624i | −0.539573 | − | 0.841939i | \(-0.681414\pi\) |
0.998927 | + | 0.0463149i | \(0.0147478\pi\) | |||||||
\(972\) | −12.5942 | + | 9.18614i | −0.403960 | + | 0.294646i | ||||
\(973\) | 29.2048 | + | 10.1168i | 0.936263 | + | 0.324331i | ||||
\(974\) | 4.55134i | 0.145834i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.44158 | − | 1.40965i | 0.0781530 | − | 0.0451217i | ||||
\(977\) | −35.0458 | + | 20.2337i | −1.12121 | + | 0.647333i | −0.941710 | − | 0.336424i | \(-0.890782\pi\) |
−0.179503 | + | 0.983757i | \(0.557449\pi\) | |||||||
\(978\) | −5.84096 | + | 1.37228i | −0.186773 | + | 0.0438807i | ||||
\(979\) | 18.6101i | 0.594782i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.69702 | + | 27.2978i | −0.0541815 | + | 0.871553i | ||||
\(982\) | 13.4603 | − | 23.3139i | 0.429534 | − | 0.743975i | ||||
\(983\) | 10.8622 | + | 18.8139i | 0.346450 | + | 0.600069i | 0.985616 | − | 0.169000i | \(-0.0540537\pi\) |
−0.639166 | + | 0.769069i | \(0.720720\pi\) | |||||||
\(984\) | −0.813859 | + | 2.69927i | −0.0259449 | + | 0.0860495i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −22.0000 | −0.700623 | ||||||||
\(987\) | −3.51900 | − | 7.86141i | −0.112011 | − | 0.250231i | ||||
\(988\) | −6.92820 | −0.220416 | ||||||||
\(989\) | 41.7921 | + | 24.1287i | 1.32891 | + | 0.767248i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.1753 | + | 24.5523i | 0.450292 | + | 0.779929i | 0.998404 | − | 0.0564762i | \(-0.0179865\pi\) |
−0.548112 | + | 0.836405i | \(0.684653\pi\) | |||||||
\(992\) | −1.18843 | + | 2.05842i | −0.0377327 | + | 0.0653550i | ||||
\(993\) | −12.9166 | + | 12.1386i | −0.409897 | + | 0.385207i | ||||
\(994\) | 3.25544 | + | 3.75906i | 0.103256 | + | 0.119230i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0.569297 | + | 2.42315i | 0.0180389 | + | 0.0767804i | ||||
\(997\) | −26.3855 | + | 15.2337i | −0.835638 | + | 0.482456i | −0.855779 | − | 0.517341i | \(-0.826922\pi\) |
0.0201413 | + | 0.999797i | \(0.493588\pi\) | |||||||
\(998\) | −24.4511 | + | 14.1168i | −0.773986 | + | 0.446861i | ||||
\(999\) | 59.8397 | − | 10.1899i | 1.89324 | − | 0.322395i |
(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 | 1050.2.s.e.551.2 | 8 | ||
3.2 | odd | 2 | 1050.2.s.d.551.4 | 8 | |||
5.2 | odd | 4 | 210.2.t.d.89.1 | yes | 4 | ||
5.3 | odd | 4 | 210.2.t.a.89.2 | yes | 4 | ||
5.4 | even | 2 | inner | 1050.2.s.e.551.3 | 8 | ||
7.3 | odd | 6 | 1050.2.s.d.101.4 | 8 | |||
15.2 | even | 4 | 210.2.t.b.89.1 | yes | 4 | ||
15.8 | even | 4 | 210.2.t.c.89.2 | yes | 4 | ||
15.14 | odd | 2 | 1050.2.s.d.551.1 | 8 | |||
21.17 | even | 6 | inner | 1050.2.s.e.101.2 | 8 | ||
35.2 | odd | 12 | 1470.2.d.a.1469.4 | 4 | |||
35.3 | even | 12 | 210.2.t.b.59.1 | yes | 4 | ||
35.12 | even | 12 | 1470.2.d.b.1469.1 | 4 | |||
35.17 | even | 12 | 210.2.t.c.59.2 | yes | 4 | ||
35.23 | odd | 12 | 1470.2.d.d.1469.1 | 4 | |||
35.24 | odd | 6 | 1050.2.s.d.101.1 | 8 | |||
35.33 | even | 12 | 1470.2.d.c.1469.4 | 4 | |||
105.2 | even | 12 | 1470.2.d.c.1469.3 | 4 | |||
105.17 | odd | 12 | 210.2.t.a.59.1 | ✓ | 4 | ||
105.23 | even | 12 | 1470.2.d.b.1469.2 | 4 | |||
105.38 | odd | 12 | 210.2.t.d.59.2 | yes | 4 | ||
105.47 | odd | 12 | 1470.2.d.d.1469.2 | 4 | |||
105.59 | even | 6 | inner | 1050.2.s.e.101.3 | 8 | ||
105.68 | odd | 12 | 1470.2.d.a.1469.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.t.a.59.1 | ✓ | 4 | 105.17 | odd | 12 | ||
210.2.t.a.89.2 | yes | 4 | 5.3 | odd | 4 | ||
210.2.t.b.59.1 | yes | 4 | 35.3 | even | 12 | ||
210.2.t.b.89.1 | yes | 4 | 15.2 | even | 4 | ||
210.2.t.c.59.2 | yes | 4 | 35.17 | even | 12 | ||
210.2.t.c.89.2 | yes | 4 | 15.8 | even | 4 | ||
210.2.t.d.59.2 | yes | 4 | 105.38 | odd | 12 | ||
210.2.t.d.89.1 | yes | 4 | 5.2 | odd | 4 | ||
1050.2.s.d.101.1 | 8 | 35.24 | odd | 6 | |||
1050.2.s.d.101.4 | 8 | 7.3 | odd | 6 | |||
1050.2.s.d.551.1 | 8 | 15.14 | odd | 2 | |||
1050.2.s.d.551.4 | 8 | 3.2 | odd | 2 | |||
1050.2.s.e.101.2 | 8 | 21.17 | even | 6 | inner | ||
1050.2.s.e.101.3 | 8 | 105.59 | even | 6 | inner | ||
1050.2.s.e.551.2 | 8 | 1.1 | even | 1 | trivial | ||
1050.2.s.e.551.3 | 8 | 5.4 | even | 2 | inner | ||
1470.2.d.a.1469.3 | 4 | 105.68 | odd | 12 | |||
1470.2.d.a.1469.4 | 4 | 35.2 | odd | 12 | |||
1470.2.d.b.1469.1 | 4 | 35.12 | even | 12 | |||
1470.2.d.b.1469.2 | 4 | 105.23 | even | 12 | |||
1470.2.d.c.1469.3 | 4 | 105.2 | even | 12 | |||
1470.2.d.c.1469.4 | 4 | 35.33 | even | 12 | |||
1470.2.d.d.1469.1 | 4 | 35.23 | odd | 12 | |||
1470.2.d.d.1469.2 | 4 | 105.47 | odd | 12 |