Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [297,2,Mod(37,297)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(297, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([10, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("297.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 297 = 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 297.n (of order \(15\), degree \(8\), 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: | \(2.37155694003\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 235.4 | ||
Character | \(\chi\) | \(=\) | 297.235 |
Dual form | 297.2.n.b.91.4 |
$q$-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 \(\left(\mathbb{Z}/297\mathbb{Z}\right)^\times\).
\(n\) | \(56\) | \(244\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.527858 | + | 0.235017i | −0.373252 | + | 0.166182i | −0.584785 | − | 0.811188i | \(-0.698821\pi\) |
0.211533 | + | 0.977371i | \(0.432154\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.11486 | + | 1.23818i | −0.557430 | + | 0.619089i | ||||
\(5\) | −2.74468 | − | 1.22201i | −1.22746 | − | 0.546500i | −0.312450 | − | 0.949934i | \(-0.601150\pi\) |
−0.915009 | + | 0.403434i | \(0.867816\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.13888 | + | 0.242076i | 0.430455 | + | 0.0914960i | 0.418044 | − | 0.908427i | \(-0.362716\pi\) |
0.0124114 | + | 0.999923i | \(0.496049\pi\) | |||||||
\(8\) | 0.654602 | − | 2.01466i | 0.231437 | − | 0.712289i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73599 | 0.548970 | ||||||||
\(11\) | 2.54741 | − | 2.12385i | 0.768072 | − | 0.640364i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.412487 | − | 3.92455i | 0.114403 | − | 1.08848i | −0.775192 | − | 0.631726i | \(-0.782347\pi\) |
0.889595 | − | 0.456750i | \(-0.150986\pi\) | |||||||
\(14\) | −0.658057 | + | 0.139874i | −0.175873 | + | 0.0373830i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.220374 | − | 2.09672i | −0.0550935 | − | 0.524179i | ||||
\(17\) | −0.254185 | + | 0.184677i | −0.0616490 | + | 0.0447906i | −0.618183 | − | 0.786034i | \(-0.712131\pi\) |
0.556534 | + | 0.830825i | \(0.312131\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.96794 | − | 6.05670i | 0.451477 | − | 1.38950i | −0.423746 | − | 0.905781i | \(-0.639285\pi\) |
0.875222 | − | 0.483721i | \(-0.160715\pi\) | |||||||
\(20\) | 4.57300 | − | 2.03603i | 1.02255 | − | 0.455271i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.845527 | + | 1.71977i | −0.180267 | + | 0.366657i | ||||
\(23\) | −0.0427501 | − | 0.0740453i | −0.00891401 | − | 0.0154395i | 0.861534 | − | 0.507700i | \(-0.169504\pi\) |
−0.870448 | + | 0.492260i | \(0.836171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.69431 | + | 2.99234i | 0.538862 | + | 0.598467i | ||||
\(26\) | 0.704604 | + | 2.16855i | 0.138184 | + | 0.425287i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.56942 | + | 1.14025i | −0.296593 | + | 0.215487i | ||||
\(29\) | −7.53156 | − | 1.60088i | −1.39858 | − | 0.297276i | −0.553913 | − | 0.832575i | \(-0.686866\pi\) |
−0.844663 | + | 0.535298i | \(0.820199\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.682449 | + | 6.49307i | −0.122571 | + | 1.16619i | 0.744366 | + | 0.667772i | \(0.232752\pi\) |
−0.866937 | + | 0.498418i | \(0.833915\pi\) | |||||||
\(32\) | 2.72743 | + | 4.72404i | 0.482146 | + | 0.835101i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0907715 | − | 0.157221i | 0.0155672 | − | 0.0269632i | ||||
\(35\) | −2.83004 | − | 2.05614i | −0.478363 | − | 0.347551i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.92922 | − | 5.93753i | −0.317162 | − | 0.976124i | −0.974855 | − | 0.222838i | \(-0.928468\pi\) |
0.657694 | − | 0.753286i | \(-0.271532\pi\) | |||||||
\(38\) | 0.384637 | + | 3.65957i | 0.0623963 | + | 0.593661i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.25861 | + | 4.72966i | −0.673345 | + | 0.747825i | ||||
\(41\) | 5.68213 | − | 1.20777i | 0.887399 | − | 0.188623i | 0.258409 | − | 0.966036i | \(-0.416802\pi\) |
0.628990 | + | 0.777413i | \(0.283468\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.39229 | − | 5.87562i | 0.517320 | − | 0.896024i | −0.482478 | − | 0.875908i | \(-0.660263\pi\) |
0.999798 | − | 0.0201157i | \(-0.00640347\pi\) | |||||||
\(44\) | −0.210303 | + | 5.52194i | −0.0317043 | + | 0.832463i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0399679 | + | 0.0290384i | 0.00589294 | + | 0.00428147i | ||||
\(47\) | 0.219298 | + | 0.243555i | 0.0319879 | + | 0.0355262i | 0.758926 | − | 0.651176i | \(-0.225724\pi\) |
−0.726939 | + | 0.686703i | \(0.759058\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.15638 | − | 2.29577i | −0.736625 | − | 0.327967i | ||||
\(50\) | −2.12546 | − | 0.946318i | −0.300586 | − | 0.133830i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.39943 | + | 4.88606i | 0.610091 | + | 0.677575i | ||||
\(53\) | −1.96000 | − | 1.42402i | −0.269227 | − | 0.195605i | 0.444978 | − | 0.895541i | \(-0.353211\pi\) |
−0.714205 | + | 0.699937i | \(0.753211\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.58718 | + | 2.71632i | −1.29274 | + | 0.366269i | ||||
\(56\) | 1.23321 | − | 2.13598i | 0.164795 | − | 0.285433i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.35183 | − | 0.925009i | 0.571423 | − | 0.121460i | ||||
\(59\) | 1.53634 | − | 1.70628i | 0.200015 | − | 0.222139i | −0.634790 | − | 0.772685i | \(-0.718913\pi\) |
0.834805 | + | 0.550545i | \(0.185580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.43070 | + | 13.6122i | 0.183183 | + | 1.74287i | 0.570839 | + | 0.821062i | \(0.306618\pi\) |
−0.387656 | + | 0.921804i | \(0.626715\pi\) | |||||||
\(62\) | −1.16575 | − | 3.58780i | −0.148050 | − | 0.455652i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.861321 | + | 0.625787i | 0.107665 | + | 0.0782233i | ||||
\(65\) | −5.92799 | + | 10.2676i | −0.735277 | + | 1.27354i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.83989 | − | 10.1150i | −0.713456 | − | 1.23574i | −0.963552 | − | 0.267521i | \(-0.913795\pi\) |
0.250096 | − | 0.968221i | \(-0.419538\pi\) | |||||||
\(68\) | 0.0547189 | − | 0.520616i | 0.00663564 | − | 0.0631339i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.97708 | + | 0.420242i | 0.236307 | + | 0.0502286i | ||||
\(71\) | 7.05272 | − | 5.12410i | 0.837004 | − | 0.608119i | −0.0845279 | − | 0.996421i | \(-0.526938\pi\) |
0.921532 | + | 0.388302i | \(0.126938\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.910538 | + | 2.80235i | 0.106570 | + | 0.327990i | 0.990096 | − | 0.140393i | \(-0.0448367\pi\) |
−0.883525 | + | 0.468383i | \(0.844837\pi\) | |||||||
\(74\) | 2.41378 | + | 2.68077i | 0.280596 | + | 0.311633i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.30529 | + | 9.18904i | 0.608559 | + | 1.05405i | ||||
\(77\) | 3.41531 | − | 1.80213i | 0.389211 | − | 0.205372i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.11886 | + | 3.61475i | −0.913443 | + | 0.406691i | −0.808979 | − | 0.587838i | \(-0.799979\pi\) |
−0.104464 | + | 0.994529i | \(0.533313\pi\) | |||||||
\(80\) | −1.95735 | + | 6.02412i | −0.218839 | + | 0.673517i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.71551 | + | 1.97293i | −0.299878 | + | 0.217874i | ||||
\(83\) | 0.518229 | + | 4.93062i | 0.0568831 | + | 0.541206i | 0.985441 | + | 0.170018i | \(0.0543827\pi\) |
−0.928558 | + | 0.371188i | \(0.878951\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.923335 | − | 0.196261i | 0.100150 | − | 0.0212875i | ||||
\(86\) | −0.409774 | + | 3.89874i | −0.0441871 | + | 0.420412i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.61129 | − | 6.52242i | −0.278364 | − | 0.695293i | ||||
\(89\) | −2.12862 | −0.225634 | −0.112817 | − | 0.993616i | \(-0.535987\pi\) | ||||
−0.112817 | + | 0.993616i | \(0.535987\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.41981 | − | 4.36973i | 0.148837 | − | 0.458072i | ||||
\(92\) | 0.139342 | + | 0.0296180i | 0.0145274 | + | 0.00308789i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.172998 | − | 0.0770236i | −0.0178434 | − | 0.00794437i | ||||
\(95\) | −12.8027 | + | 14.2189i | −1.31353 | + | 1.45882i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.0811587 | + | 0.0361342i | −0.00824041 | + | 0.00366887i | −0.410853 | − | 0.911702i | \(-0.634769\pi\) |
0.402612 | + | 0.915371i | \(0.368102\pi\) | |||||||
\(98\) | 3.26138 | 0.329449 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.70883 | −0.670883 | ||||||||
\(101\) | 1.87869 | − | 0.836447i | 0.186937 | − | 0.0832296i | −0.311134 | − | 0.950366i | \(-0.600709\pi\) |
0.498071 | + | 0.867137i | \(0.334042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.01858 | + | 2.24186i | −0.198896 | + | 0.220897i | −0.834340 | − | 0.551251i | \(-0.814151\pi\) |
0.635443 | + | 0.772148i | \(0.280817\pi\) | |||||||
\(104\) | −7.63662 | − | 3.40004i | −0.748832 | − | 0.333401i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.36927 | + | 0.291048i | 0.132995 | + | 0.0282690i | ||||
\(107\) | −3.70600 | + | 11.4059i | −0.358272 | + | 1.10265i | 0.595815 | + | 0.803121i | \(0.296829\pi\) |
−0.954088 | + | 0.299527i | \(0.903171\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.20013 | 0.498082 | 0.249041 | − | 0.968493i | \(-0.419885\pi\) | ||||
0.249041 | + | 0.968493i | \(0.419885\pi\) | |||||||
\(110\) | 4.42228 | − | 3.68699i | 0.421648 | − | 0.351540i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.256586 | − | 2.44125i | 0.0242451 | − | 0.230676i | ||||
\(113\) | 18.8074 | − | 3.99763i | 1.76925 | − | 0.376066i | 0.795907 | − | 0.605419i | \(-0.206995\pi\) |
0.973343 | + | 0.229354i | \(0.0736612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0268512 | + | 0.255472i | 0.00250389 | + | 0.0238229i | ||||
\(116\) | 10.3788 | − | 7.54065i | 0.963649 | − | 0.700132i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.409965 | + | 1.26174i | −0.0377403 | + | 0.116153i | ||||
\(119\) | −0.334192 | + | 0.148792i | −0.0306353 | + | 0.0136397i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.97856 | − | 10.8206i | 0.179869 | − | 0.983691i | ||||
\(122\) | −3.95432 | − | 6.84907i | −0.358007 | − | 0.620086i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.27874 | − | 8.08386i | −0.653650 | − | 0.725952i | ||||
\(125\) | 0.903736 | + | 2.78141i | 0.0808326 | + | 0.248777i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.6652 | − | 7.74873i | 0.946384 | − | 0.687588i | −0.00356461 | − | 0.999994i | \(-0.501135\pi\) |
0.949949 | + | 0.312405i | \(0.101135\pi\) | |||||||
\(128\) | −11.2730 | − | 2.39616i | −0.996405 | − | 0.211792i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.716076 | − | 6.81300i | 0.0628040 | − | 0.597540i | ||||
\(131\) | −8.98588 | − | 15.5640i | −0.785100 | − | 1.35983i | −0.928939 | − | 0.370233i | \(-0.879278\pi\) |
0.143839 | − | 0.989601i | \(-0.454055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.70742 | − | 6.42144i | 0.321474 | − | 0.556810i | ||||
\(134\) | 5.45983 | + | 3.96680i | 0.471657 | + | 0.342679i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.205670 | + | 0.632986i | 0.0176360 | + | 0.0542781i | ||||
\(137\) | −1.71445 | − | 16.3119i | −0.146475 | − | 1.39362i | −0.782836 | − | 0.622228i | \(-0.786228\pi\) |
0.636361 | − | 0.771391i | \(-0.280439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.96373 | + | 8.84461i | −0.675475 | + | 0.750190i | −0.979273 | − | 0.202546i | \(-0.935078\pi\) |
0.303798 | + | 0.952736i | \(0.401745\pi\) | |||||||
\(140\) | 5.70096 | − | 1.21178i | 0.481819 | − | 0.102414i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.51858 | + | 4.36231i | −0.211355 | + | 0.366077i | ||||
\(143\) | −7.28438 | − | 10.8735i | −0.609150 | − | 0.909287i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.7154 | + | 13.5976i | 1.55423 | + | 1.12922i | ||||
\(146\) | −1.13923 | − | 1.26525i | −0.0942837 | − | 0.104713i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.50253 | + | 4.23080i | 0.781103 | + | 0.347770i | ||||
\(149\) | 4.13993 | + | 1.84321i | 0.339156 | + | 0.151002i | 0.569246 | − | 0.822167i | \(-0.307235\pi\) |
−0.230090 | + | 0.973169i | \(0.573902\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.96113 | − | 2.17806i | −0.159595 | − | 0.177248i | 0.658044 | − | 0.752979i | \(-0.271384\pi\) |
−0.817639 | + | 0.575732i | \(0.804717\pi\) | |||||||
\(152\) | −10.9140 | − | 7.92945i | −0.885239 | − | 0.643164i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.37927 | + | 1.75393i | −0.111144 | + | 0.141336i | ||||
\(155\) | 9.80771 | − | 16.9874i | 0.787774 | − | 1.36446i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.6591 | − | 3.75356i | 1.40935 | − | 0.299567i | 0.560481 | − | 0.828167i | \(-0.310616\pi\) |
0.848871 | + | 0.528600i | \(0.177283\pi\) | |||||||
\(158\) | 3.43607 | − | 3.81614i | 0.273359 | − | 0.303596i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.71309 | − | 16.2989i | −0.135431 | − | 1.28854i | ||||
\(161\) | −0.0307625 | − | 0.0946773i | −0.00242443 | − | 0.00746161i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.71129 | + | 3.42295i | 0.369017 | + | 0.268106i | 0.756803 | − | 0.653643i | \(-0.226760\pi\) |
−0.387786 | + | 0.921749i | \(0.626760\pi\) | |||||||
\(164\) | −4.83934 | + | 8.38199i | −0.377889 | + | 0.654523i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.43233 | − | 2.48087i | −0.111171 | − | 0.192553i | ||||
\(167\) | −0.524913 | + | 4.99422i | −0.0406190 | + | 0.386464i | 0.955260 | + | 0.295769i | \(0.0955757\pi\) |
−0.995879 | + | 0.0906956i | \(0.971091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.51606 | − | 0.534805i | −0.193543 | − | 0.0411388i | ||||
\(170\) | −0.441265 | + | 0.320598i | −0.0338435 | + | 0.0245887i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.49313 | + | 10.7508i | 0.266349 | + | 0.819738i | ||||
\(173\) | 10.4317 | + | 11.5855i | 0.793104 | + | 0.880831i | 0.995132 | − | 0.0985486i | \(-0.0314200\pi\) |
−0.202028 | + | 0.979380i | \(0.564753\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.34412 | + | 4.06013i | 0.177199 | + | 0.306917i | ||||
\(176\) | −5.01449 | − | 4.87315i | −0.377981 | − | 0.367327i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.12361 | − | 0.500263i | 0.0842181 | − | 0.0374963i | ||||
\(179\) | −2.17822 | + | 6.70387i | −0.162808 | + | 0.501071i | −0.998868 | − | 0.0475668i | \(-0.984853\pi\) |
0.836060 | + | 0.548638i | \(0.184853\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.02068 | + | 1.46811i | −0.150196 | + | 0.109124i | −0.660345 | − | 0.750962i | \(-0.729590\pi\) |
0.510149 | + | 0.860086i | \(0.329590\pi\) | |||||||
\(182\) | 0.277504 | + | 2.64028i | 0.0205700 | + | 0.195710i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.177160 | + | 0.0376566i | −0.0130604 | + | 0.00277608i | ||||
\(185\) | −1.96063 | + | 18.6542i | −0.144148 | + | 1.37148i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.255289 | + | 1.01030i | −0.0186686 | + | 0.0738802i | ||||
\(188\) | −0.546051 | −0.0398249 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.41633 | − | 10.5144i | 0.247847 | − | 0.762795i | ||||
\(191\) | −11.5646 | − | 2.45814i | −0.836786 | − | 0.177864i | −0.230461 | − | 0.973081i | \(-0.574024\pi\) |
−0.606325 | + | 0.795217i | \(0.707357\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.16338 | + | 2.74411i | 0.443650 | + | 0.197526i | 0.616389 | − | 0.787442i | \(-0.288595\pi\) |
−0.172739 | + | 0.984968i | \(0.555262\pi\) | |||||||
\(194\) | 0.0343481 | − | 0.0381474i | 0.00246605 | − | 0.00273882i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.59121 | − | 3.82505i | 0.613658 | − | 0.273218i | ||||
\(197\) | 20.6474 | 1.47107 | 0.735534 | − | 0.677488i | \(-0.236931\pi\) | ||||
0.735534 | + | 0.677488i | \(0.236931\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.2862 | −0.941832 | −0.470916 | − | 0.882178i | \(-0.656077\pi\) | ||||
−0.470916 | + | 0.882178i | \(0.656077\pi\) | |||||||
\(200\) | 7.79224 | − | 3.46933i | 0.550994 | − | 0.245318i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.795102 | + | 0.883050i | −0.0559432 | + | 0.0621312i | ||||
\(203\) | −8.18999 | − | 3.64642i | −0.574824 | − | 0.255928i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.0715 | − | 3.62867i | −1.19233 | − | 0.253437i | ||||
\(206\) | 0.538646 | − | 1.65778i | 0.0375292 | − | 0.115503i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.31958 | −0.576859 | ||||||||
\(209\) | −7.85035 | − | 19.6085i | −0.543020 | − | 1.35635i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.872292 | − | 8.29930i | 0.0600510 | − | 0.571348i | −0.922584 | − | 0.385797i | \(-0.873926\pi\) |
0.982635 | − | 0.185551i | \(-0.0594068\pi\) | |||||||
\(212\) | 3.94832 | − | 0.839242i | 0.271172 | − | 0.0576394i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.724343 | − | 6.89166i | −0.0495150 | − | 0.471104i | ||||
\(215\) | −16.4908 | + | 11.9813i | −1.12467 | + | 0.817117i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.34904 | + | 7.22960i | −0.159463 | + | 0.490778i | ||||
\(218\) | −2.74493 | + | 1.22212i | −0.185910 | + | 0.0827724i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 7.32508 | − | 14.8990i | 0.493857 | − | 1.00449i | ||||
\(221\) | 0.619925 | + | 1.07374i | 0.0417007 | + | 0.0722277i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.256716 | − | 0.285112i | −0.0171910 | − | 0.0190925i | 0.734488 | − | 0.678622i | \(-0.237422\pi\) |
−0.751679 | + | 0.659529i | \(0.770756\pi\) | |||||||
\(224\) | 1.96263 | + | 6.04035i | 0.131134 | + | 0.403588i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −8.98811 | + | 6.53024i | −0.597880 | + | 0.434385i | ||||
\(227\) | 17.6204 | + | 3.74533i | 1.16951 | + | 0.248586i | 0.751422 | − | 0.659822i | \(-0.229368\pi\) |
0.418084 | + | 0.908408i | \(0.362702\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.40359 | + | 13.3543i | −0.0927521 | + | 0.882478i | 0.844905 | + | 0.534916i | \(0.179657\pi\) |
−0.937657 | + | 0.347561i | \(0.887010\pi\) | |||||||
\(230\) | −0.0742139 | − | 0.128542i | −0.00489352 | − | 0.00847583i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.15540 | + | 14.1256i | −0.535428 | + | 0.927389i | ||||
\(233\) | −2.72611 | − | 1.98063i | −0.178593 | − | 0.129756i | 0.494897 | − | 0.868952i | \(-0.335206\pi\) |
−0.673490 | + | 0.739196i | \(0.735206\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.304276 | − | 0.936466i | −0.0198488 | − | 0.0610883i | ||||
\(236\) | 0.399873 | + | 3.80454i | 0.0260295 | + | 0.247654i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.141437 | − | 0.157082i | 0.00916800 | − | 0.0101821i | ||||
\(239\) | −22.6899 | + | 4.82289i | −1.46769 | + | 0.311967i | −0.871308 | − | 0.490736i | \(-0.836728\pi\) |
−0.596379 | + | 0.802703i | \(0.703394\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.58206 | + | 13.1325i | −0.488404 | + | 0.845940i | −0.999911 | − | 0.0133389i | \(-0.995754\pi\) |
0.511507 | + | 0.859279i | \(0.329087\pi\) | |||||||
\(242\) | 1.49863 | + | 6.17673i | 0.0963358 | + | 0.397055i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −18.4494 | − | 13.4043i | −1.18110 | − | 0.858120i | ||||
\(245\) | 11.3472 | + | 12.6023i | 0.724944 | + | 0.805131i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.9581 | − | 10.2216i | −1.46079 | − | 0.650385i | ||||
\(248\) | 12.6346 | + | 5.62528i | 0.802297 | + | 0.357205i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.13072 | − | 1.25580i | −0.0715133 | − | 0.0794235i | ||||
\(251\) | −0.471095 | − | 0.342271i | −0.0297353 | − | 0.0216039i | 0.572818 | − | 0.819682i | \(-0.305850\pi\) |
−0.602554 | + | 0.798078i | \(0.705850\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.266163 | − | 0.0978289i | −0.0167335 | − | 0.00615045i | ||||
\(254\) | −3.80863 | + | 6.59673i | −0.238974 | + | 0.413916i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.43092 | − | 0.941821i | 0.276933 | − | 0.0588638i | ||||
\(257\) | 7.34131 | − | 8.15335i | 0.457939 | − | 0.508592i | −0.469313 | − | 0.883032i | \(-0.655498\pi\) |
0.927251 | + | 0.374440i | \(0.122165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.759813 | − | 7.22913i | −0.0472125 | − | 0.449197i | ||||
\(260\) | −6.10421 | − | 18.7868i | −0.378567 | − | 1.16511i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.40108 | + | 6.10374i | 0.519020 | + | 0.377090i | ||||
\(263\) | −7.19768 | + | 12.4668i | −0.443828 | + | 0.768733i | −0.997970 | − | 0.0636896i | \(-0.979713\pi\) |
0.554142 | + | 0.832422i | \(0.313047\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.63940 | + | 6.30363i | 0.223567 | + | 0.387229i | ||||
\(266\) | −0.447840 | + | 4.26092i | −0.0274589 | + | 0.261254i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.0348 | + | 4.04598i | 1.16274 | + | 0.247147i | ||||
\(269\) | 0.395590 | − | 0.287413i | 0.0241195 | − | 0.0175239i | −0.575660 | − | 0.817689i | \(-0.695255\pi\) |
0.599780 | + | 0.800165i | \(0.295255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.77950 | + | 20.8652i | 0.411825 | + | 1.26747i | 0.915060 | + | 0.403318i | \(0.132143\pi\) |
−0.503234 | + | 0.864150i | \(0.667857\pi\) | |||||||
\(272\) | 0.443230 | + | 0.492257i | 0.0268748 | + | 0.0298475i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.73856 | + | 8.20743i | 0.286267 | + | 0.495829i | ||||
\(275\) | 13.2188 | + | 1.90039i | 0.797122 | + | 0.114598i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62144 | − | 1.16714i | 0.157507 | − | 0.0701267i | −0.326469 | − | 0.945208i | \(-0.605859\pi\) |
0.483976 | + | 0.875081i | \(0.339192\pi\) | |||||||
\(278\) | 2.12508 | − | 6.54031i | 0.127454 | − | 0.392262i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.99497 | + | 4.35560i | −0.358268 | + | 0.260297i | ||||
\(281\) | 1.90013 | + | 18.0785i | 0.113352 | + | 1.07847i | 0.892318 | + | 0.451406i | \(0.149078\pi\) |
−0.778967 | + | 0.627066i | \(0.784256\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.0883 | − | 4.26991i | 1.19413 | − | 0.253820i | 0.432378 | − | 0.901692i | \(-0.357674\pi\) |
0.761749 | + | 0.647873i | \(0.224341\pi\) | |||||||
\(284\) | −1.51825 | + | 14.4452i | −0.0900916 | + | 0.857164i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.40057 | + | 4.02770i | 0.378474 | + | 0.238163i | ||||
\(287\) | 6.76362 | 0.399244 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.22278 | + | 16.0741i | −0.307223 | + | 0.945534i | ||||
\(290\) | −13.0747 | − | 2.77912i | −0.767776 | − | 0.163196i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.48493 | − | 1.99682i | −0.262461 | − | 0.116855i | ||||
\(293\) | −0.575497 | + | 0.639154i | −0.0336209 | + | 0.0373398i | −0.759721 | − | 0.650250i | \(-0.774664\pi\) |
0.726100 | + | 0.687589i | \(0.241331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.30187 | + | 2.80578i | −0.366909 | + | 0.163359i | ||||
\(296\) | −13.2250 | −0.768685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.61848 | −0.151684 | ||||||||
\(299\) | −0.308229 | + | 0.137232i | −0.0178253 | + | 0.00793635i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.28575 | − | 5.87042i | 0.304665 | − | 0.338365i | ||||
\(302\) | 1.54708 | + | 0.688804i | 0.0890244 | + | 0.0396362i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −13.1329 | − | 2.79148i | −0.753221 | − | 0.160102i | ||||
\(305\) | 12.7075 | − | 39.1095i | 0.727627 | − | 2.23941i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.48920 | 0.199139 | 0.0995696 | − | 0.995031i | \(-0.468253\pi\) | ||||
0.0995696 | + | 0.995031i | \(0.468253\pi\) | |||||||
\(308\) | −1.57624 | + | 6.23790i | −0.0898144 | + | 0.355437i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.18473 | + | 11.2719i | −0.0672880 | + | 0.640203i | ||||
\(311\) | 10.6083 | − | 2.25486i | 0.601542 | − | 0.127862i | 0.102932 | − | 0.994688i | \(-0.467178\pi\) |
0.498610 | + | 0.866827i | \(0.333844\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.95618 | + | 28.1261i | 0.167093 | + | 1.58978i | 0.681226 | + | 0.732073i | \(0.261447\pi\) |
−0.514133 | + | 0.857710i | \(0.671886\pi\) | |||||||
\(314\) | −8.43935 | + | 6.13155i | −0.476260 | + | 0.346023i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.57569 | − | 14.0825i | 0.257403 | − | 0.792204i | ||||
\(317\) | 1.01634 | − | 0.452505i | 0.0570836 | − | 0.0254152i | −0.377996 | − | 0.925807i | \(-0.623387\pi\) |
0.435080 | + | 0.900392i | \(0.356720\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −22.5860 | + | 11.9178i | −1.26457 | + | 0.667267i | ||||
\(320\) | −1.59933 | − | 2.77013i | −0.0894055 | − | 0.154855i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0384890 | + | 0.0427464i | 0.00214491 | + | 0.00238216i | ||||
\(323\) | 0.618308 | + | 1.90296i | 0.0344036 | + | 0.105883i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.8550 | − | 9.33967i | 0.713065 | − | 0.518072i | ||||
\(326\) | −3.29134 | − | 0.699597i | −0.182291 | − | 0.0387471i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.28628 | − | 12.2382i | 0.0710230 | − | 0.675739i | ||||
\(329\) | 0.190795 | + | 0.330466i | 0.0105188 | + | 0.0182192i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.18915 | − | 10.7199i | 0.340187 | − | 0.589221i | −0.644281 | − | 0.764789i | \(-0.722843\pi\) |
0.984467 | + | 0.175569i | \(0.0561764\pi\) | |||||||
\(332\) | −6.68275 | − | 4.85530i | −0.366763 | − | 0.266469i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.896648 | − | 2.75960i | −0.0490624 | − | 0.150999i | ||||
\(335\) | 3.66801 | + | 34.8988i | 0.200405 | + | 1.90673i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.01561 | − | 10.0128i | 0.491112 | − | 0.545435i | −0.445740 | − | 0.895163i | \(-0.647059\pi\) |
0.936851 | + | 0.349728i | \(0.113726\pi\) | |||||||
\(338\) | 1.45381 | − | 0.309017i | 0.0790768 | − | 0.0168083i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.786384 | + | 1.36206i | −0.0426477 | + | 0.0738679i | ||||
\(341\) | 12.0518 | + | 17.9899i | 0.652642 | + | 0.974208i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.9104 | − | 8.65342i | −0.643102 | − | 0.467241i | ||||
\(344\) | −9.61676 | − | 10.6805i | −0.518501 | − | 0.575854i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.22923 | − | 3.66389i | −0.442406 | − | 0.196972i | ||||
\(347\) | −8.89717 | − | 3.96128i | −0.477625 | − | 0.212652i | 0.153781 | − | 0.988105i | \(-0.450855\pi\) |
−0.631406 | + | 0.775453i | \(0.717522\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.97107 | − | 3.29971i | −0.159038 | − | 0.176629i | 0.658360 | − | 0.752703i | \(-0.271251\pi\) |
−0.817397 | + | 0.576074i | \(0.804584\pi\) | |||||||
\(350\) | −2.19156 | − | 1.59226i | −0.117144 | − | 0.0851100i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.9810 | + | 6.24142i | 0.905090 | + | 0.332669i | ||||
\(353\) | 16.2618 | − | 28.1662i | 0.865527 | − | 1.49914i | −0.000996749 | − | 1.00000i | \(-0.500317\pi\) |
0.866523 | − | 0.499137i | \(-0.166349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −25.6192 | + | 5.44553i | −1.35973 | + | 0.289019i | ||||
\(356\) | 2.37312 | − | 2.63561i | 0.125775 | − | 0.139687i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.425736 | − | 4.05061i | −0.0225008 | − | 0.214081i | ||||
\(359\) | 8.58143 | + | 26.4109i | 0.452911 | + | 1.39392i | 0.873571 | + | 0.486697i | \(0.161799\pi\) |
−0.420660 | + | 0.907218i | \(0.638201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4395 | − | 12.6705i | −0.917868 | − | 0.666870i | ||||
\(362\) | 0.721600 | − | 1.24985i | 0.0379264 | − | 0.0656905i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.82761 | + | 6.62962i | 0.200621 | + | 0.347487i | ||||
\(365\) | 0.925362 | − | 8.80424i | 0.0484357 | − | 0.460835i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.14658 | − | 0.243713i | −0.0598511 | − | 0.0127217i | 0.177889 | − | 0.984051i | \(-0.443073\pi\) |
−0.237740 | + | 0.971329i | \(0.576407\pi\) | |||||||
\(368\) | −0.145831 | + | 0.105952i | −0.00760197 | + | 0.00552315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.34912 | − | 10.3075i | −0.174112 | − | 0.535862i | ||||
\(371\) | −1.88748 | − | 2.09626i | −0.0979929 | − | 0.108832i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.8834 | − | 18.8506i | −0.563520 | − | 0.976046i | −0.997186 | − | 0.0749719i | \(-0.976113\pi\) |
0.433665 | − | 0.901074i | \(-0.357220\pi\) | |||||||
\(374\) | −0.102681 | − | 0.593290i | −0.00530951 | − | 0.0306783i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.634233 | − | 0.282379i | 0.0327081 | − | 0.0145626i | ||||
\(377\) | −9.38942 | + | 28.8977i | −0.483580 | + | 1.48831i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.1440 | − | 9.54967i | 0.675161 | − | 0.490533i | −0.196588 | − | 0.980486i | \(-0.562986\pi\) |
0.871749 | + | 0.489953i | \(0.162986\pi\) | |||||||
\(380\) | −3.33224 | − | 31.7041i | −0.170940 | − | 1.62639i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.68218 | − | 1.42034i | 0.341890 | − | 0.0726709i | ||||
\(383\) | 0.647381 | − | 6.15942i | 0.0330796 | − | 0.314732i | −0.965453 | − | 0.260577i | \(-0.916087\pi\) |
0.998533 | − | 0.0541542i | \(-0.0172463\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.5762 | + | 0.772734i | −0.589977 | + | 0.0393821i | ||||
\(386\) | −3.89830 | −0.198418 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0.0457401 | − | 0.140773i | 0.00232210 | − | 0.00714669i | ||||
\(389\) | −0.707409 | − | 0.150365i | −0.0358671 | − | 0.00762378i | 0.189943 | − | 0.981795i | \(-0.439170\pi\) |
−0.225810 | + | 0.974171i | \(0.572503\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0245409 | + | 0.0109263i | 0.00124109 | + | 0.000552567i | ||||
\(392\) | −8.00056 | + | 8.88552i | −0.404089 | + | 0.448787i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.8989 | + | 4.85250i | −0.549079 | + | 0.244466i | ||||
\(395\) | 26.7009 | 1.34347 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.08994 | 0.205268 | 0.102634 | − | 0.994719i | \(-0.467273\pi\) | ||||
0.102634 | + | 0.994719i | \(0.467273\pi\) | |||||||
\(398\) | 7.01321 | − | 3.12248i | 0.351540 | − | 0.156516i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.68033 | − | 6.30864i | 0.284016 | − | 0.315432i | ||||
\(401\) | 5.15812 | + | 2.29654i | 0.257584 | + | 0.114684i | 0.531466 | − | 0.847079i | \(-0.321641\pi\) |
−0.273882 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.2009 | + | 5.35662i | 1.25535 | + | 0.266832i | ||||
\(404\) | −1.05881 | + | 3.25868i | −0.0526777 | + | 0.162125i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.18012 | 0.257085 | ||||||||
\(407\) | −17.5249 | − | 11.0279i | −0.868677 | − | 0.546634i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.987666 | + | 9.39701i | −0.0488369 | + | 0.464652i | 0.942586 | + | 0.333962i | \(0.108386\pi\) |
−0.991423 | + | 0.130690i | \(0.958281\pi\) | |||||||
\(410\) | 9.86414 | − | 2.09669i | 0.487155 | − | 0.103548i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.525386 | − | 4.99871i | −0.0258839 | − | 0.246269i | ||||
\(413\) | 2.16276 | − | 1.57134i | 0.106422 | − | 0.0773204i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.60290 | − | 14.1663i | 0.225948 | − | 0.695395i | ||||
\(416\) | 19.6648 | − | 8.75533i | 0.964145 | − | 0.429265i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.75220 | + | 8.50551i | 0.428084 | + | 0.416018i | ||||
\(419\) | 0.0757820 | + | 0.131258i | 0.00370219 | + | 0.00641238i | 0.867871 | − | 0.496790i | \(-0.165488\pi\) |
−0.864168 | + | 0.503203i | \(0.832155\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.3595 | + | 12.6160i | 0.553630 | + | 0.614868i | 0.953386 | − | 0.301753i | \(-0.0975719\pi\) |
−0.399756 | + | 0.916622i | \(0.630905\pi\) | |||||||
\(422\) | 1.49003 | + | 4.58585i | 0.0725337 | + | 0.223236i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.15194 | + | 3.01656i | −0.201636 | + | 0.146497i | ||||
\(425\) | −1.23747 | − | 0.263032i | −0.0600261 | − | 0.0127589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.66580 | + | 15.8490i | −0.0806135 | + | 0.766986i | ||||
\(428\) | −9.99085 | − | 17.3047i | −0.482926 | − | 0.836453i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.88900 | − | 10.2000i | 0.283993 | − | 0.491890i | ||||
\(431\) | −20.5242 | − | 14.9117i | −0.988618 | − | 0.718273i | −0.0289998 | − | 0.999579i | \(-0.509232\pi\) |
−0.959618 | + | 0.281307i | \(0.909232\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.10950 | + | 15.7254i | 0.245547 | + | 0.755716i | 0.995546 | + | 0.0942769i | \(0.0300539\pi\) |
−0.749999 | + | 0.661439i | \(0.769946\pi\) | |||||||
\(434\) | −0.459123 | − | 4.36827i | −0.0220386 | − | 0.209684i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.79742 | + | 6.43868i | −0.277646 | + | 0.308357i | ||||
\(437\) | −0.532600 | + | 0.113208i | −0.0254777 | + | 0.00541545i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.6207 | − | 33.9840i | 0.936443 | − | 1.62197i | 0.164403 | − | 0.986393i | \(-0.447430\pi\) |
0.772040 | − | 0.635574i | \(-0.219237\pi\) | |||||||
\(440\) | −0.803326 | + | 21.0930i | −0.0382971 | + | 1.00557i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.579580 | − | 0.421089i | −0.0275678 | − | 0.0200292i | ||||
\(443\) | −21.5389 | − | 23.9214i | −1.02334 | − | 1.13654i | −0.990561 | − | 0.137075i | \(-0.956230\pi\) |
−0.0327827 | − | 0.999463i | \(-0.510437\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.84239 | + | 2.60120i | 0.276956 | + | 0.123309i | ||||
\(446\) | 0.202515 | + | 0.0901657i | 0.00958939 | + | 0.00426947i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.829451 | + | 0.921199i | 0.0391879 | + | 0.0435226i | ||||
\(449\) | −20.9085 | − | 15.1909i | −0.986731 | − | 0.716902i | −0.0275281 | − | 0.999621i | \(-0.508764\pi\) |
−0.959203 | + | 0.282719i | \(0.908764\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.9096 | − | 15.1447i | 0.560799 | − | 0.713134i | ||||
\(452\) | −16.0178 | + | 27.7437i | −0.753415 | + | 1.30495i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.1813 | + | 2.16410i | −0.477831 | + | 0.101566i | ||||
\(455\) | −9.23679 | + | 10.2585i | −0.433027 | + | 0.480926i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.32921 | + | 12.6466i | 0.0621780 | + | 0.591584i | 0.980605 | + | 0.195994i | \(0.0627932\pi\) |
−0.918427 | + | 0.395590i | \(0.870540\pi\) | |||||||
\(458\) | −2.39760 | − | 7.37904i | −0.112032 | − | 0.344800i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.346255 | − | 0.251569i | −0.0161442 | − | 0.0117295i | ||||
\(461\) | −9.51087 | + | 16.4733i | −0.442965 | + | 0.767238i | −0.997908 | − | 0.0646502i | \(-0.979407\pi\) |
0.554943 | + | 0.831889i | \(0.312740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.4334 | + | 19.8032i | 0.531353 | + | 0.920331i | 0.999330 | + | 0.0365903i | \(0.0116497\pi\) |
−0.467977 | + | 0.883741i | \(0.655017\pi\) | |||||||
\(464\) | −1.69684 | + | 16.1443i | −0.0787738 | + | 0.749482i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.90448 | + | 0.404810i | 0.0882233 | + | 0.0187524i | ||||
\(467\) | 12.8819 | − | 9.35921i | 0.596101 | − | 0.433093i | −0.248392 | − | 0.968660i | \(-0.579902\pi\) |
0.844493 | + | 0.535567i | \(0.179902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.20232 | − | 12.9334i | −0.194045 | − | 0.597210i | ||||
\(470\) | 0.380700 | + | 0.422810i | 0.0175604 | + | 0.0195028i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.43188 | − | 4.21215i | −0.111936 | − | 0.193880i | ||||
\(473\) | −3.83737 | − | 22.1723i | −0.176443 | − | 1.01948i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 23.4259 | − | 10.4299i | 1.07486 | − | 0.478556i | ||||
\(476\) | 0.188347 | − | 0.579671i | 0.00863285 | − | 0.0265692i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.8436 | − | 7.87832i | 0.495973 | − | 0.360346i | ||||
\(479\) | −1.71322 | − | 16.3002i | −0.0782789 | − | 0.744774i | −0.961312 | − | 0.275463i | \(-0.911169\pi\) |
0.883033 | − | 0.469311i | \(-0.155498\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0979 | + | 5.12217i | −1.09877 | + | 0.233551i | ||||
\(482\) | 0.915880 | − | 8.71402i | 0.0417172 | − | 0.396913i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.1920 | + | 14.5133i | 0.508728 | + | 0.659694i | ||||
\(485\) | 0.266911 | 0.0121198 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.04142 | − | 21.6713i | 0.319077 | − | 0.982019i | −0.654966 | − | 0.755658i | \(-0.727317\pi\) |
0.974044 | − | 0.226361i | \(-0.0726828\pi\) | |||||||
\(488\) | 28.3605 | + | 6.02821i | 1.28382 | + | 0.272884i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.95145 | − | 3.98544i | −0.404385 | − | 0.180044i | ||||
\(491\) | 29.2029 | − | 32.4331i | 1.31791 | − | 1.46368i | 0.529836 | − | 0.848100i | \(-0.322253\pi\) |
0.788071 | − | 0.615584i | \(-0.211080\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.21006 | − | 0.983982i | 0.0995360 | − | 0.0443163i | ||||
\(494\) | 14.5209 | 0.653324 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.7645 | 0.618045 | ||||||||
\(497\) | 9.27261 | − | 4.12843i | 0.415933 | − | 0.185185i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4519 | + | 14.9398i | −0.602189 | + | 0.668798i | −0.964752 | − | 0.263161i | \(-0.915235\pi\) |
0.362563 | + | 0.931959i | \(0.381902\pi\) | |||||||
\(500\) | −4.45142 | − | 1.98190i | −0.199074 | − | 0.0886333i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.329111 | + | 0.0699546i | 0.0146889 | + | 0.00312223i | ||||
\(503\) | 3.27815 | − | 10.0891i | 0.146165 | − | 0.449850i | −0.850994 | − | 0.525176i | \(-0.824000\pi\) |
0.997159 | + | 0.0753254i | \(0.0239995\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.17856 | −0.274942 | ||||||||
\(506\) | 0.163487 | − | 0.0109131i | 0.00726791 | − | 0.000485148i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.29592 | + | 21.8442i | −0.101865 | + | 0.969179i | ||||
\(509\) | −43.4966 | + | 9.24549i | −1.92795 | + | 0.409799i | −0.928715 | + | 0.370794i | \(0.879086\pi\) |
−0.999239 | + | 0.0390051i | \(0.987581\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.358610 | + | 3.41195i | 0.0158640 | + | 0.150936i | ||||
\(512\) | 16.5301 | − | 12.0098i | 0.730534 | − | 0.530764i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.95899 | + | 6.02915i | −0.0864073 | + | 0.265934i | ||||
\(515\) | 8.27992 | − | 3.68646i | 0.364857 | − | 0.162445i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.07591 | + | 0.154679i | 0.0473187 | + | 0.00680275i | ||||
\(518\) | 2.10004 | + | 3.63738i | 0.0922707 | + | 0.159817i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 16.8052 | + | 18.6641i | 0.736956 | + | 0.818473i | ||||
\(521\) | −5.23819 | − | 16.1215i | −0.229489 | − | 0.706296i | −0.997805 | − | 0.0662243i | \(-0.978905\pi\) |
0.768315 | − | 0.640071i | \(-0.221095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.4438 | + | 17.7595i | −1.06885 | + | 0.776567i | −0.975706 | − | 0.219085i | \(-0.929693\pi\) |
−0.0931472 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(524\) | 29.2890 | + | 6.22557i | 1.27950 | + | 0.271965i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.869448 | − | 8.27225i | 0.0379098 | − | 0.360687i | ||||
\(527\) | −1.02565 | − | 1.77648i | −0.0446780 | − | 0.0773845i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4963 | − | 19.9123i | 0.499841 | − | 0.865750i | ||||
\(530\) | −3.40255 | − | 2.47210i | −0.147797 | − | 0.107381i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.81763 | + | 11.7495i | 0.165515 | + | 0.509404i | ||||
\(533\) | −2.39617 | − | 22.7980i | −0.103790 | − | 0.987491i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.1099 | − | 26.7768i | 1.04236 | − | 1.15766i | ||||
\(536\) | −24.2010 | + | 5.14409i | −1.04533 | + | 0.222191i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.141268 | + | 0.244683i | −0.00609050 | + | 0.0105491i | ||||
\(539\) | −18.0112 | + | 5.10310i | −0.775799 | + | 0.219806i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.57164 | − | 6.95421i | −0.411517 | − | 0.298985i | 0.362699 | − | 0.931906i | \(-0.381855\pi\) |
−0.774216 | + | 0.632922i | \(0.781855\pi\) | |||||||
\(542\) | −8.48229 | − | 9.42053i | −0.364345 | − | 0.404647i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.56569 | − | 0.697091i | −0.0671285 | − | 0.0298875i | ||||
\(545\) | −14.2727 | − | 6.35461i | −0.611375 | − | 0.272202i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.70348 | + | 1.89190i | 0.0728355 | + | 0.0808920i | 0.778461 | − | 0.627693i | \(-0.216001\pi\) |
−0.705626 | + | 0.708585i | \(0.749334\pi\) | |||||||
\(548\) | 22.1084 | + | 16.0627i | 0.944424 | + | 0.686164i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7.42425 | + | 2.10350i | −0.316571 | + | 0.0896937i | ||||
\(551\) | −24.5177 | + | 42.4659i | −1.04449 | + | 1.80911i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.1214 | + | 2.15137i | −0.430407 | + | 0.0914857i | ||||
\(554\) | −1.10945 | + | 1.23217i | −0.0471360 | + | 0.0523498i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.07276 | − | 19.7210i | −0.0879048 | − | 0.836358i | ||||
\(557\) | −2.98987 | − | 9.20189i | −0.126685 | − | 0.389896i | 0.867519 | − | 0.497404i | \(-0.165713\pi\) |
−0.994204 | + | 0.107507i | \(0.965713\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.6599 | − | 15.7368i | −0.916117 | − | 0.665598i | ||||
\(560\) | −3.68748 | + | 6.38690i | −0.155824 | + | 0.269896i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.25175 | − | 9.09630i | −0.221532 | − | 0.383704i | ||||
\(563\) | −2.50735 | + | 23.8558i | −0.105672 | + | 1.00540i | 0.805281 | + | 0.592893i | \(0.202014\pi\) |
−0.910953 | + | 0.412510i | \(0.864652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −56.5054 | − | 12.0106i | −2.37720 | − | 0.505290i | ||||
\(566\) | −9.60027 | + | 6.97501i | −0.403530 | + | 0.293181i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.70659 | − | 17.5631i | −0.239443 | − | 0.736930i | ||||
\(569\) | 25.1721 | + | 27.9565i | 1.05527 | + | 1.17200i | 0.984659 | + | 0.174492i | \(0.0558283\pi\) |
0.0706111 | + | 0.997504i | \(0.477505\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.37740 | + | 12.7780i | 0.308735 | + | 0.534744i | 0.978086 | − | 0.208202i | \(-0.0667612\pi\) |
−0.669351 | + | 0.742946i | \(0.733428\pi\) | |||||||
\(572\) | 21.5844 | + | 3.10307i | 0.902488 | + | 0.129746i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.57023 | + | 1.58957i | −0.149018 | + | 0.0663473i | ||||
\(575\) | 0.106386 | − | 0.327424i | 0.00443662 | − | 0.0136545i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.0466 | − | 13.1116i | 0.751289 | − | 0.545843i | −0.144937 | − | 0.989441i | \(-0.546298\pi\) |
0.896226 | + | 0.443598i | \(0.146298\pi\) | |||||||
\(578\) | −1.02080 | − | 9.71227i | −0.0424597 | − | 0.403977i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −37.7013 | + | 8.01366i | −1.56546 | + | 0.332749i | ||||
\(581\) | −0.603385 | + | 5.74083i | −0.0250326 | + | 0.238170i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.01732 | + | 0.535173i | −0.332044 | + | 0.0221646i | ||||
\(584\) | 6.24181 | 0.258288 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.153568 | − | 0.472634i | 0.00634384 | − | 0.0195243i | ||||
\(587\) | −2.44553 | − | 0.519814i | −0.100938 | − | 0.0214550i | 0.157166 | − | 0.987572i | \(-0.449764\pi\) |
−0.258104 | + | 0.966117i | \(0.583098\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 37.9836 | + | 16.9114i | 1.56508 | + | 0.696821i | ||||
\(590\) | 2.66709 | − | 2.96210i | 0.109802 | − | 0.121948i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −12.0242 | + | 5.35351i | −0.494190 | + | 0.220028i | ||||
\(593\) | 10.8953 | 0.447417 | 0.223708 | − | 0.974656i | \(-0.428184\pi\) | ||||
0.223708 | + | 0.974656i | \(0.428184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.09907 | 0.0450577 | ||||||||
\(596\) | −6.89767 | + | 3.07104i | −0.282540 | + | 0.125795i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.130449 | − | 0.144878i | 0.00533445 | − | 0.00592451i | ||||
\(599\) | 33.6533 | + | 14.9834i | 1.37504 | + | 0.612205i | 0.955353 | − | 0.295466i | \(-0.0954749\pi\) |
0.419682 | + | 0.907671i | \(0.362142\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.1166 | + | 3.21313i | 0.616618 | + | 0.131066i | 0.505623 | − | 0.862755i | \(-0.331263\pi\) |
0.110995 | + | 0.993821i | \(0.464596\pi\) | |||||||
\(602\) | −1.41047 | + | 4.34099i | −0.0574866 | + | 0.176925i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.88321 | 0.198695 | ||||||||
\(605\) | −18.6534 | + | 27.2813i | −0.758368 | + | 1.10914i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.66306 | − | 25.3373i | 0.108090 | − | 1.02841i | −0.797228 | − | 0.603678i | \(-0.793701\pi\) |
0.905319 | − | 0.424733i | \(-0.139632\pi\) | |||||||
\(608\) | 33.9795 | − | 7.22257i | 1.37805 | − | 0.292914i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.48369 | + | 23.6307i | 0.100562 | + | 0.956781i | ||||
\(611\) | 1.04630 | − | 0.760183i | 0.0423289 | − | 0.0307537i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.6728 | + | 35.9252i | −0.471461 | + | 1.45101i | 0.379211 | + | 0.925310i | \(0.376195\pi\) |
−0.850672 | + | 0.525697i | \(0.823805\pi\) | |||||||
\(614\) | −1.84180 | + | 0.820023i | −0.0743290 | + | 0.0330934i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.39501 | − | 8.06037i | −0.0562066 | − | 0.324761i | ||||
\(617\) | 20.9464 | + | 36.2802i | 0.843271 | + | 1.46059i | 0.887115 | + | 0.461549i | \(0.152706\pi\) |
−0.0438437 | + | 0.999038i | \(0.513960\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.00783 | − | 4.45115i | −0.161088 | − | 0.178907i | 0.657197 | − | 0.753719i | \(-0.271742\pi\) |
−0.818286 | + | 0.574812i | \(0.805075\pi\) | |||||||
\(620\) | 10.0993 | + | 31.0823i | 0.405596 | + | 1.24830i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.06974 | + | 3.68338i | −0.203278 | + | 0.147690i | ||||
\(623\) | −2.42424 | − | 0.515288i | −0.0971251 | − | 0.0206446i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.02291 | − | 28.7611i | 0.120917 | − | 1.15044i | ||||
\(626\) | −8.17057 | − | 14.1518i | −0.326562 | − | 0.565621i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15.0399 | + | 26.0498i | −0.600157 | + | 1.03950i | ||||
\(629\) | 1.58690 | + | 1.15295i | 0.0632739 | + | 0.0459712i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.64368 | − | 20.4471i | −0.264481 | − | 0.813988i | −0.991813 | − | 0.127702i | \(-0.959240\pi\) |
0.727332 | − | 0.686286i | \(-0.240760\pi\) | |||||||
\(632\) | 1.96786 | + | 18.7229i | 0.0782772 | + | 0.744758i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −0.430138 | + | 0.477717i | −0.0170830 | + | 0.0189726i | ||||
\(635\) | −38.7416 | + | 8.23479i | −1.53741 | + | 0.326788i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −11.1368 | + | 19.2895i | −0.441256 | + | 0.764278i | ||||
\(638\) | 9.12129 | − | 11.5990i | 0.361115 | − | 0.459208i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 28.0127 | + | 20.3525i | 1.10730 | + | 0.804501i | ||||
\(641\) | −8.58963 | − | 9.53975i | −0.339270 | − | 0.376798i | 0.549232 | − | 0.835670i | \(-0.314920\pi\) |
−0.888502 | + | 0.458872i | \(0.848254\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 25.9041 | + | 11.5332i | 1.02156 | + | 0.454827i | 0.848000 | − | 0.529997i | \(-0.177807\pi\) |
0.173558 | + | 0.984824i | \(0.444473\pi\) | |||||||
\(644\) | 0.151523 | + | 0.0674625i | 0.00597085 | + | 0.00265839i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.773607 | − | 0.859177i | −0.0304372 | − | 0.0338039i | ||||
\(647\) | −14.1536 | − | 10.2832i | −0.556436 | − | 0.404274i | 0.273717 | − | 0.961810i | \(-0.411747\pi\) |
−0.830153 | + | 0.557536i | \(0.811747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.289810 | − | 7.60956i | 0.0113760 | − | 0.298701i | ||||
\(650\) | −4.59060 | + | 7.95116i | −0.180058 | + | 0.311870i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.49066 | + | 2.01730i | −0.371683 | + | 0.0790036i | ||||
\(653\) | 19.6070 | − | 21.7758i | 0.767282 | − | 0.852152i | −0.225230 | − | 0.974306i | \(-0.572313\pi\) |
0.992511 | + | 0.122153i | \(0.0389799\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.64400 | + | 53.6991i | 0.220529 | + | 2.09820i | ||||
\(656\) | −3.78455 | − | 11.6477i | −0.147762 | − | 0.454764i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.178378 | − | 0.129599i | −0.00695388 | − | 0.00505229i | ||||
\(659\) | 13.7935 | − | 23.8911i | 0.537319 | − | 0.930664i | −0.461728 | − | 0.887021i | \(-0.652771\pi\) |
0.999047 | − | 0.0436422i | \(-0.0138961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.8776 | − | 25.7688i | −0.578672 | − | 1.00229i | −0.995632 | − | 0.0933649i | \(-0.970238\pi\) |
0.416960 | − | 0.908925i | \(-0.363096\pi\) | |||||||
\(662\) | −0.747623 | + | 7.11315i | −0.0290572 | + | 0.276461i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.2728 | + | 2.18354i | 0.398660 | + | 0.0847378i | ||||
\(665\) | −18.0228 | + | 13.0943i | −0.698893 | + | 0.507775i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.203437 | + | 0.626115i | 0.00787711 | + | 0.0242433i | ||||
\(668\) | −5.59853 | − | 6.21779i | −0.216613 | − | 0.240574i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.1380 | − | 17.5596i | −0.391666 | − | 0.678385i | ||||
\(671\) | 32.5548 | + | 31.6373i | 1.25677 | + | 1.22134i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.81907 | − | 3.92650i | 0.339950 | − | 0.151356i | −0.229659 | − | 0.973271i | \(-0.573761\pi\) |
0.569609 | + | 0.821916i | \(0.307094\pi\) | |||||||
\(674\) | −2.40577 | + | 7.40418i | −0.0926666 | + | 0.285198i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.46724 | − | 2.51910i | 0.133355 | − | 0.0968883i | ||||
\(677\) | −0.0102558 | − | 0.0975777i | −0.000394163 | − | 0.00375021i | 0.994323 | − | 0.106403i | \(-0.0339335\pi\) |
−0.994717 | + | 0.102653i | \(0.967267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.101177 | + | 0.0215058i | −0.00388281 | + | 0.000825318i | ||||
\(680\) | 0.209018 | − | 1.98868i | 0.00801549 | − | 0.0762623i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.5896 | − | 6.66372i | −0.405496 | − | 0.255167i | ||||
\(683\) | −30.5246 | −1.16799 | −0.583996 | − | 0.811756i | \(-0.698512\pi\) | ||||
−0.583996 | + | 0.811756i | \(0.698512\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.2277 | + | 46.8660i | −0.581820 | + | 1.79066i | ||||
\(686\) | 8.32071 | + | 1.76862i | 0.317686 | + | 0.0675263i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −13.0671 | − | 5.81784i | −0.498178 | − | 0.221803i | ||||
\(689\) | −6.39713 | + | 7.10473i | −0.243711 | + | 0.270669i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.9658 | − | 13.3416i | 1.13995 | − | 0.507540i | 0.252116 | − | 0.967697i | \(-0.418873\pi\) |
0.887838 | + | 0.460157i | \(0.152207\pi\) | |||||||
\(692\) | −25.9748 | −0.987413 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.62741 | 0.213614 | ||||||||
\(695\) | 32.6661 | − | 14.5439i | 1.23910 | − | 0.551681i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.22127 | + | 1.35635i | −0.0462588 | + | 0.0513756i | ||||
\(698\) | 2.34379 | + | 1.04352i | 0.0887138 | + | 0.0394979i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −7.64053 | − | 1.62405i | −0.288785 | − | 0.0613831i | ||||
\(701\) | 2.70365 | − | 8.32098i | 0.102115 | − | 0.314279i | −0.886927 | − | 0.461909i | \(-0.847165\pi\) |
0.989043 | + | 0.147630i | \(0.0471646\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.7584 | −1.49952 | ||||||||
\(704\) | 3.52321 | − | 0.235181i | 0.132786 | − | 0.00886373i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.96435 | + | 18.6895i | −0.0739293 | + | 0.703390i | ||||
\(707\) | 2.34208 | − | 0.497825i | 0.0880831 | − | 0.0187226i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.79884 | − | 26.6292i | −0.105113 | − | 1.00008i | −0.912227 | − | 0.409685i | \(-0.865639\pi\) |
0.807114 | − | 0.590395i | \(-0.201028\pi\) | |||||||
\(710\) | 12.2435 | − | 8.89542i | 0.459490 | − | 0.333839i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.39340 | + | 4.28845i | −0.0522199 | + | 0.160716i | ||||
\(713\) | 0.509956 | − | 0.227047i | 0.0190980 | − | 0.00850298i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.70577 | + | 38.7459i | 0.250781 | + | 1.44901i | ||||
\(716\) | −5.87217 | − | 10.1709i | −0.219453 | − | 0.380105i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.7368 | − | 11.9244i | −0.400694 | − | 0.445016i | ||||
\(719\) | 4.63672 | + | 14.2703i | 0.172920 | + | 0.532194i | 0.999532 | − | 0.0305782i | \(-0.00973486\pi\) |
−0.826612 | + | 0.562772i | \(0.809735\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.84161 | + | 2.06455i | −0.105827 | + | 0.0768879i | ||||
\(722\) | 12.1834 | + | 2.58965i | 0.453418 | + | 0.0963769i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.434995 | − | 4.13870i | 0.0161665 | − | 0.153814i | ||||
\(725\) | −15.5020 | − | 26.8502i | −0.575730 | − | 0.997193i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.7663 | + | 23.8438i | −0.510562 | + | 0.884319i | 0.489363 | + | 0.872080i | \(0.337229\pi\) |
−0.999925 | + | 0.0122391i | \(0.996104\pi\) | |||||||
\(728\) | −7.87410 | − | 5.72087i | −0.291834 | − | 0.212029i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.58069 | + | 4.86486i | 0.0585039 | + | 0.180057i | ||||
\(731\) | 0.222818 | + | 2.11997i | 0.00824123 | + | 0.0784101i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.9441 | − | 35.4775i | 1.17988 | − | 1.31039i | 0.239251 | − | 0.970958i | \(-0.423098\pi\) |
0.940630 | − | 0.339433i | \(-0.110235\pi\) | |||||||
\(734\) | 0.662509 | − | 0.140821i | 0.0244536 | − | 0.00519778i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.233195 | − | 0.403906i | 0.00859570 | − | 0.0148882i | ||||
\(737\) | −36.3593 | − | 13.3640i | −1.33931 | − | 0.492267i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.20421 | − | 0.874910i | −0.0442976 | − | 0.0321841i | 0.565416 | − | 0.824806i | \(-0.308716\pi\) |
−0.609714 | + | 0.792622i | \(0.708716\pi\) | |||||||
\(740\) | −20.9113 | − | 23.2244i | −0.768716 | − | 0.853746i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.48898 | + | 0.662935i | 0.0546620 | + | 0.0243371i | ||||
\(743\) | 16.5901 | + | 7.38641i | 0.608633 | + | 0.270981i | 0.687823 | − | 0.725879i | \(-0.258567\pi\) |
−0.0791896 | + | 0.996860i | \(0.525233\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.11035 | − | 10.1181i | −0.333778 | − | 0.370698i | ||||
\(746\) | 10.1751 | + | 7.39264i | 0.372537 | + | 0.270664i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.966316 | − | 1.44243i | −0.0353320 | − | 0.0527406i | ||||
\(749\) | −6.98177 | + | 12.0928i | −0.255108 | + | 0.441860i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.29862 | − | 0.913700i | 0.156859 | − | 0.0333414i | −0.128813 | − | 0.991669i | \(-0.541117\pi\) |
0.285672 | + | 0.958328i | \(0.407783\pi\) | |||||||
\(752\) | 0.462338 | − | 0.513479i | 0.0168597 | − | 0.0187246i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.83518 | − | 17.4605i | −0.0668332 | − | 0.635875i | ||||
\(755\) | 2.72107 | + | 8.37459i | 0.0990299 | + | 0.304783i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.1369 | + | 8.09140i | 0.404776 | + | 0.294087i | 0.771483 | − | 0.636249i | \(-0.219515\pi\) |
−0.366708 | + | 0.930336i | \(0.619515\pi\) | |||||||
\(758\) | −4.69382 | + | 8.12993i | −0.170487 | + | 0.295292i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.2655 | + | 35.1008i | 0.735105 | + | 1.27324i | ||||
\(761\) | −3.25147 | + | 30.9357i | −0.117866 | + | 1.12142i | 0.762456 | + | 0.647041i | \(0.223994\pi\) |
−0.880321 | + | 0.474378i | \(0.842673\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.92230 | + | 1.25882i | 0.214402 | + | 0.0455725i | ||||
\(764\) | 15.9365 | − | 11.5786i | 0.576564 | − | 0.418898i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.10585 | + | 3.40344i | 0.0399558 | + | 0.122971i | ||||
\(767\) | −6.06268 | − | 6.73329i | −0.218911 | − | 0.243125i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.9677 | − | 18.9966i | −0.395504 | − | 0.685034i | 0.597661 | − | 0.801749i | \(-0.296097\pi\) |
−0.993165 | + | 0.116715i | \(0.962764\pi\) | |||||||
\(770\) | 5.92897 | − | 3.12850i | 0.213665 | − | 0.112743i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.2690 | + | 4.57206i | −0.369590 | + | 0.164552i | ||||
\(773\) | 3.92965 | − | 12.0942i | 0.141340 | − | 0.434999i | −0.855182 | − | 0.518327i | \(-0.826555\pi\) |
0.996522 | + | 0.0833281i | \(0.0265549\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.2682 | + | 15.4522i | −0.763976 | + | 0.555061i | ||||
\(776\) | 0.0196714 | + | 0.187160i | 0.000706160 | + | 0.00671867i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.408750 | − | 0.0868824i | 0.0146544 | − | 0.00311489i | ||||
\(779\) | 3.86697 | − | 36.7918i | 0.138549 | − | 1.31820i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.08334 | − | 28.0321i | 0.253462 | − | 1.00307i | ||||
\(782\) | −0.0155220 | −0.000555064 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.67724 | + | 11.3174i | −0.131330 | + | 0.404193i | ||||
\(785\) | −53.0556 | − | 11.2773i | −1.89363 | − | 0.402504i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.7693 | − | 7.02095i | −0.562115 | − | 0.250270i | 0.105951 | − | 0.994371i | \(-0.466211\pi\) |
−0.668067 | + | 0.744102i | \(0.732878\pi\) | |||||||
\(788\) | −23.0190 | + | 25.5652i | −0.820018 | + | 0.910722i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −14.0943 | + | 6.27518i | −0.501452 | + | 0.223261i | ||||
\(791\) | 22.3870 | 0.795991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 54.0120 | 1.91802 | ||||||||
\(794\) | −2.15890 | + | 0.961206i | −0.0766166 | + | 0.0341119i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.8122 | − | 16.4507i | 0.525006 | − | 0.583078i | ||||
\(797\) | −32.1582 | − | 14.3177i | −1.13910 | − | 0.507161i | −0.251538 | − | 0.967847i | \(-0.580936\pi\) |
−0.887563 | + | 0.460687i | \(0.847603\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.100721 | − | 0.0214090i | −0.00356326 | − | 0.000757395i | ||||
\(800\) | −6.78739 | + | 20.8894i | −0.239970 | + | 0.738553i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.26248 | −0.115202 | ||||||||
\(803\) | 8.27126 | + | 5.20487i | 0.291887 | + | 0.183676i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0312634 | + | 0.297451i | −0.00110189 | + | 0.0104838i | ||||
\(806\) | −14.5614 | + | 3.09512i | −0.512903 | + | 0.109021i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −0.455360 | − | 4.33246i | −0.0160195 | − | 0.152415i | ||||
\(809\) | −15.4367 | + | 11.2154i | −0.542725 | + | 0.394313i | −0.825096 | − | 0.564992i | \(-0.808879\pi\) |
0.282371 | + | 0.959305i | \(0.408879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.59769 | + | 29.5387i | −0.337020 | + | 1.03724i | 0.628698 | + | 0.777650i | \(0.283588\pi\) |
−0.965718 | + | 0.259593i | \(0.916412\pi\) | |||||||
\(812\) | 13.6456 | − | 6.07542i | 0.478867 | − | 0.213205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11.8424 | + | 1.70252i | 0.415076 | + | 0.0596733i | ||||
\(815\) | −8.74810 | − | 15.1522i | −0.306433 | − | 0.530757i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28.9110 | − | 32.1090i | −1.01147 | − | 1.12335i | ||||
\(818\) | −1.68711 | − | 5.19240i | −0.0589885 | − | 0.181548i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.5253 | − | 17.0922i | 0.821540 | − | 0.596884i | ||||
\(821\) | 33.2653 | + | 7.07077i | 1.16097 | + | 0.246771i | 0.747826 | − | 0.663895i | \(-0.231098\pi\) |
0.413143 | + | 0.910666i | \(0.364431\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.62605 | + | 15.4708i | −0.0566804 | + | 0.539278i | 0.928931 | + | 0.370252i | \(0.120729\pi\) |
−0.985612 | + | 0.169026i | \(0.945938\pi\) | |||||||
\(824\) | 3.19521 | + | 5.53426i | 0.111310 | + | 0.192795i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.772337 | + | 1.33773i | −0.0268730 | + | 0.0465455i | ||||
\(827\) | 12.9667 | + | 9.42084i | 0.450895 | + | 0.327595i | 0.789949 | − | 0.613172i | \(-0.210107\pi\) |
−0.339054 | + | 0.940767i | \(0.610107\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.90205 | + | 18.1646i | 0.204987 | + | 0.630884i | 0.999714 | + | 0.0239173i | \(0.00761382\pi\) |
−0.794727 | + | 0.606967i | \(0.792386\pi\) | |||||||
\(830\) | 0.899644 | + | 8.55954i | 0.0312271 | + | 0.297106i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.81122 | − | 3.12217i | 0.0974614 | − | 0.108242i | ||||
\(833\) | 1.73465 | − | 0.368711i | 0.0601021 | − | 0.0127751i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.54371 | − | 13.0661i | 0.261061 | − | 0.452171i | ||||
\(836\) | 33.0308 | + | 12.1406i | 1.14240 | + | 0.419891i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.0708501 | − | 0.0514756i | −0.00244747 | − | 0.00177819i | ||||
\(839\) | −0.995613 | − | 1.10574i | −0.0343724 | − | 0.0381744i | 0.725713 | − | 0.687997i | \(-0.241510\pi\) |
−0.760086 | + | 0.649823i | \(0.774843\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.6687 | + | 12.3189i | 0.954095 | + | 0.424790i | ||||
\(842\) | −8.96121 | − | 3.98979i | −0.308824 | − | 0.137497i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.30353 | + | 10.3326i | 0.320241 | + | 0.355663i | ||||
\(845\) | 6.25224 | + | 4.54252i | 0.215084 | + | 0.156267i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.87274 | − | 11.8444i | 0.167429 | − | 0.406977i | ||||
\(848\) | −2.55384 | + | 4.42338i | −0.0876993 | + | 0.151900i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.715025 | − | 0.151983i | 0.0245252 | − | 0.00521298i | ||||
\(851\) | −0.357172 | + | 0.396680i | −0.0122437 | + | 0.0135980i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.95139 | − | 37.5950i | −0.135293 | − | 1.28723i | −0.825825 | − | 0.563926i | \(-0.809290\pi\) |
0.690532 | − | 0.723302i | \(-0.257376\pi\) | |||||||
\(854\) | −2.84548 | − | 8.75750i | −0.0973704 | − | 0.299675i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.5530 | + | 14.9326i | 0.702487 | + | 0.510387i | ||||
\(857\) | 9.91348 | − | 17.1706i | 0.338638 | − | 0.586538i | −0.645539 | − | 0.763727i | \(-0.723367\pi\) |
0.984177 | + | 0.177189i | \(0.0567005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.85764 | + | 13.6098i | 0.268099 | + | 0.464362i | 0.968371 | − | 0.249515i | \(-0.0802711\pi\) |
−0.700272 | + | 0.713876i | \(0.746938\pi\) | |||||||
\(860\) | 3.55001 | − | 33.7761i | 0.121054 | − | 1.15175i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 14.3384 | + | 3.04772i | 0.488368 | + | 0.103806i | ||||
\(863\) | 6.57548 | − | 4.77736i | 0.223832 | − | 0.162623i | −0.470218 | − | 0.882550i | \(-0.655825\pi\) |
0.694050 | + | 0.719927i | \(0.255825\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.4739 | − | 44.5462i | −0.492128 | − | 1.51462i | ||||
\(866\) | −6.39284 | − | 7.09997i | −0.217237 | − | 0.241267i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.33269 | − | 10.9685i | −0.214945 | − | 0.372296i | ||||
\(869\) | −13.0049 | + | 26.4514i | −0.441159 | + | 0.897303i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.1057 | + | 18.7467i | −1.42670 | + | 0.635206i | ||||
\(872\) | 3.40401 | − | 10.4765i | 0.115274 | − | 0.354778i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.254531 | − | 0.184928i | 0.00860964 | − | 0.00625527i | ||||
\(875\) | 0.355931 | + | 3.38646i | 0.0120327 | + | 0.114483i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.47817 | − | 0.526750i | 0.0836817 | − | 0.0177871i | −0.165881 | − | 0.986146i | \(-0.553047\pi\) |
0.249562 | + | 0.968359i | \(0.419713\pi\) | |||||||
\(878\) | −2.37009 | + | 22.5499i | −0.0799867 | + | 0.761022i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.80812 | + | 19.5030i | 0.263212 | + | 0.657446i | ||||
\(881\) | 47.4109 | 1.59731 | 0.798657 | − | 0.601786i | \(-0.205544\pi\) | ||||
0.798657 | + | 0.601786i | \(0.205544\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.19295 | − | 25.2153i | 0.275715 | − | 0.848563i | −0.713315 | − | 0.700844i | \(-0.752807\pi\) |
0.989029 | − | 0.147719i | \(-0.0471930\pi\) | |||||||
\(884\) | −2.02061 | − | 0.429495i | −0.0679606 | − | 0.0144455i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.9914 | + | 7.56506i | 0.570837 | + | 0.254153i | ||||
\(887\) | 32.0041 | − | 35.5441i | 1.07459 | − | 1.19345i | 0.0943729 | − | 0.995537i | \(-0.469915\pi\) |
0.980219 | − | 0.197918i | \(-0.0634179\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.0221 | − | 6.24306i | 0.470288 | − | 0.209386i | ||||
\(890\) | −3.69528 | −0.123866 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.639221 | 0.0214027 | ||||||||
\(893\) | 1.90671 | − | 0.848920i | 0.0638055 | − | 0.0284080i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1707 | − | 15.7382i | 0.473675 | − | 0.526069i | ||||
\(896\) | −12.2585 | − | 5.45786i | −0.409529 | − | 0.182334i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.6068 | + | 3.10477i | 0.487435 | + | 0.103608i | ||||
\(899\) | 15.5345 | − | 47.8104i | 0.518106 | − | 1.59457i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.761187 | 0.0253588 | ||||||||
\(902\) | −2.72730 | + | 10.7932i | −0.0908090 | + | 0.359373i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.25749 | − | 40.5073i | 0.141602 | − | 1.34725i | ||||
\(905\) | 7.34017 | − | 1.56020i | 0.243995 | − | 0.0518628i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.96075 | − | 47.1984i | −0.164719 | − | 1.56720i | −0.694771 | − | 0.719231i | \(-0.744494\pi\) |
0.530052 | − | 0.847965i | \(-0.322172\pi\) | |||||||
\(908\) | −24.2817 | + | 17.6417i | −0.805815 | + | 0.585459i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.46479 | − | 7.58583i | 0.0817068 | − | 0.251468i | ||||
\(911\) | 25.9741 | − | 11.5644i | 0.860561 | − | 0.383147i | 0.0714850 | − | 0.997442i | \(-0.477226\pi\) |
0.789076 | + | 0.614295i | \(0.210560\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.7920 | + | 11.4597i | 0.390259 | + | 0.379259i | ||||
\(914\) | −3.67381 | − | 6.36322i | −0.121519 | − | 0.210477i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −14.9702 | − | 16.6261i | −0.494629 | − | 0.549342i | ||||
\(917\) | −6.46615 | − | 19.9008i | −0.213531 | − | 0.657181i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −31.0442 | + | 22.5550i | −1.02406 | + | 0.744020i | −0.967110 | − | 0.254358i | \(-0.918136\pi\) |
−0.0569449 | + | 0.998377i | \(0.518136\pi\) | |||||||
\(920\) | 0.532265 | + | 0.113136i | 0.0175483 | + | 0.00373000i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.14887 | − | 10.9308i | 0.0378361 | − | 0.359986i | ||||
\(923\) | −17.2007 | − | 29.7924i | −0.566167 | − | 0.980629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 12.5692 | − | 21.7704i | 0.413272 | − | 0.715808i | ||||
\(926\) | −10.6893 | − | 7.76621i | −0.351271 | − | 0.255214i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −12.9791 | − | 39.9457i | −0.426061 | − | 1.31128i | ||||
\(929\) | 1.39939 | + | 13.3143i | 0.0459126 | + | 0.436829i | 0.993198 | + | 0.116438i | \(0.0371476\pi\) |
−0.947285 | + | 0.320391i | \(0.896186\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0522 | + | 26.7127i | −0.788280 | + | 0.875473i | ||||
\(932\) | 5.49160 | − | 1.16728i | 0.179883 | − | 0.0382354i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.60021 | + | 7.96779i | −0.150523 | + | 0.260714i | ||||
\(935\) | 1.93528 | − | 2.46098i | 0.0632905 | − | 0.0804826i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.9588 | + | 14.5010i | 0.652027 | + | 0.473725i | 0.863961 | − | 0.503559i | \(-0.167976\pi\) |
−0.211934 | + | 0.977284i | \(0.567976\pi\) | |||||||
\(938\) | 5.25781 | + | 5.83939i | 0.171674 | + | 0.190663i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.49874 | + | 0.667281i | 0.0488834 | + | 0.0217643i | ||||
\(941\) | −7.58453 | − | 3.37685i | −0.247249 | − | 0.110082i | 0.279371 | − | 0.960183i | \(-0.409874\pi\) |
−0.526620 | + | 0.850101i | \(0.676541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.332341 | − | 0.369103i | −0.0108225 | − | 0.0120196i | ||||
\(944\) | −3.91616 | − | 2.84526i | −0.127460 | − | 0.0926053i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.23646 | + | 10.8020i | 0.235278 | + | 0.351202i | ||||
\(947\) | 18.9748 | − | 32.8653i | 0.616598 | − | 1.06798i | −0.373503 | − | 0.927629i | \(-0.621844\pi\) |
0.990102 | − | 0.140351i | \(-0.0448231\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.3735 | − | 2.41752i | 0.369201 | − | 0.0784761i | ||||
\(950\) | −9.91435 | + | 11.0110i | −0.321664 | + | 0.357244i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.0810019 | + | 0.770681i | 0.00262529 | + | 0.0249779i | ||||
\(953\) | 15.0400 | + | 46.2884i | 0.487194 | + | 1.49943i | 0.828778 | + | 0.559578i | \(0.189037\pi\) |
−0.341583 | + | 0.939852i | \(0.610963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.7373 | + | 20.8789i | 0.929918 | + | 0.675625i | ||||
\(956\) | 19.3245 | − | 33.4710i | 0.624998 | − | 1.08253i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.73516 | + | 8.20154i | 0.152986 | + | 0.264980i | ||||
\(959\) | 1.99617 | − | 18.9923i | 0.0644596 | − | 0.613292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.3716 | − | 2.41712i | −0.366827 | − | 0.0779716i | ||||
\(962\) | 11.5165 | − | 8.36721i | 0.371306 | − | 0.269770i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.80746 | − | 24.0289i | −0.251461 | − | 0.773918i | ||||
\(965\) | −13.5632 | − | 15.0634i | −0.436614 | − | 0.484909i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.48901 | − | 9.50724i | −0.176515 | − | 0.305732i | 0.764170 | − | 0.645015i | \(-0.223149\pi\) |
−0.940684 | + | 0.339283i | \(0.889816\pi\) | |||||||
\(968\) | −20.5046 | − | 11.0693i | −0.659044 | − | 0.355781i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.140891 | + | 0.0627287i | −0.00452374 | + | 0.00201410i | ||||
\(971\) | −4.03687 | + | 12.4242i | −0.129549 | + | 0.398712i | −0.994702 | − | 0.102796i | \(-0.967221\pi\) |
0.865153 | + | 0.501508i | \(0.167221\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2108 | + | 8.14510i | −0.359401 | + | 0.261120i | ||||
\(974\) | 1.37626 | + | 13.0942i | 0.0440981 | + | 0.419565i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 28.2257 | − | 5.99955i | 0.903482 | − | 0.192041i | ||||
\(977\) | −1.15779 | + | 11.0156i | −0.0370410 | + | 0.352421i | 0.960266 | + | 0.279085i | \(0.0900312\pi\) |
−0.997307 | + | 0.0733360i | \(0.976635\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.42247 | + | 4.52087i | −0.173303 | + | 0.144488i | ||||
\(980\) | −28.2544 | −0.902554 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.79262 | + | 23.9832i | −0.248673 | + | 0.765336i | ||||
\(983\) | −25.8539 | − | 5.49541i | −0.824611 | − | 0.175277i | −0.223767 | − | 0.974643i | \(-0.571835\pi\) |
−0.600844 | + | 0.799366i | \(0.705169\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −56.6706 | − | 25.2314i | −1.80568 | − | 0.803938i | ||||
\(986\) | −0.935344 | + | 1.03880i | −0.0297874 | + | 0.0330823i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.2512 | − | 17.0305i | 1.21693 | − | 0.541814i | ||||
\(989\) | −0.580083 | −0.0184456 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.9911 | −0.603272 | −0.301636 | − | 0.953423i | \(-0.597533\pi\) | ||||
−0.301636 | + | 0.953423i | \(0.597533\pi\) | |||||||
\(992\) | −32.5349 | + | 14.4855i | −1.03298 | + | 0.459914i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.92436 | + | 4.35845i | −0.124473 | + | 0.138242i | ||||
\(995\) | 36.4663 | + | 16.2359i | 1.15606 | + | 0.514711i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.6299 | − | 4.59758i | −0.685027 | − | 0.145607i | −0.147765 | − | 0.989022i | \(-0.547208\pi\) |
−0.537262 | + | 0.843416i | \(0.680541\pi\) | |||||||
\(998\) | 3.58956 | − | 11.0475i | 0.113625 | − | 0.349703i | ||||
\(999\) | 0 | 0 |
(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 | 297.2.n.b.235.4 | 72 | ||
3.2 | odd | 2 | 99.2.m.b.70.6 | yes | 72 | ||
9.2 | odd | 6 | 891.2.f.f.730.4 | 36 | |||
9.4 | even | 3 | inner | 297.2.n.b.37.6 | 72 | ||
9.5 | odd | 6 | 99.2.m.b.4.4 | ✓ | 72 | ||
9.7 | even | 3 | 891.2.f.e.730.6 | 36 | |||
11.3 | even | 5 | inner | 297.2.n.b.289.6 | 72 | ||
33.5 | odd | 10 | 1089.2.e.p.727.8 | 36 | |||
33.14 | odd | 10 | 99.2.m.b.25.4 | yes | 72 | ||
33.17 | even | 10 | 1089.2.e.o.727.11 | 36 | |||
99.5 | odd | 30 | 1089.2.e.p.364.8 | 36 | |||
99.14 | odd | 30 | 99.2.m.b.58.6 | yes | 72 | ||
99.16 | even | 15 | 9801.2.a.cp.1.8 | 18 | |||
99.25 | even | 15 | 891.2.f.e.487.6 | 36 | |||
99.38 | odd | 30 | 9801.2.a.cm.1.11 | 18 | |||
99.47 | odd | 30 | 891.2.f.f.487.4 | 36 | |||
99.50 | even | 30 | 1089.2.e.o.364.11 | 36 | |||
99.58 | even | 15 | inner | 297.2.n.b.91.4 | 72 | ||
99.61 | odd | 30 | 9801.2.a.cn.1.11 | 18 | |||
99.83 | even | 30 | 9801.2.a.co.1.8 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.2.m.b.4.4 | ✓ | 72 | 9.5 | odd | 6 | ||
99.2.m.b.25.4 | yes | 72 | 33.14 | odd | 10 | ||
99.2.m.b.58.6 | yes | 72 | 99.14 | odd | 30 | ||
99.2.m.b.70.6 | yes | 72 | 3.2 | odd | 2 | ||
297.2.n.b.37.6 | 72 | 9.4 | even | 3 | inner | ||
297.2.n.b.91.4 | 72 | 99.58 | even | 15 | inner | ||
297.2.n.b.235.4 | 72 | 1.1 | even | 1 | trivial | ||
297.2.n.b.289.6 | 72 | 11.3 | even | 5 | inner | ||
891.2.f.e.487.6 | 36 | 99.25 | even | 15 | |||
891.2.f.e.730.6 | 36 | 9.7 | even | 3 | |||
891.2.f.f.487.4 | 36 | 99.47 | odd | 30 | |||
891.2.f.f.730.4 | 36 | 9.2 | odd | 6 | |||
1089.2.e.o.364.11 | 36 | 99.50 | even | 30 | |||
1089.2.e.o.727.11 | 36 | 33.17 | even | 10 | |||
1089.2.e.p.364.8 | 36 | 99.5 | odd | 30 | |||
1089.2.e.p.727.8 | 36 | 33.5 | odd | 10 | |||
9801.2.a.cm.1.11 | 18 | 99.38 | odd | 30 | |||
9801.2.a.cn.1.11 | 18 | 99.61 | odd | 30 | |||
9801.2.a.co.1.8 | 18 | 99.83 | even | 30 | |||
9801.2.a.cp.1.8 | 18 | 99.16 | even | 15 |