Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (of order \(4\), 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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.4 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.b.43.4 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.994632 | − | 2.00267i | −0.444813 | − | 0.895623i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 0.593998 | + | 0.593998i | 0.224510 | + | 0.224510i | 0.810395 | − | 0.585884i | \(-0.199253\pi\) |
−0.585884 | + | 0.810395i | \(0.699253\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 2.00267 | − | 0.994632i | 0.633301 | − | 0.314530i | ||||
\(11\) | 2.21854i | 0.668914i | 0.942411 | + | 0.334457i | \(0.108553\pi\) | ||||
−0.942411 | + | 0.334457i | \(0.891447\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 0.163340i | 0.0453024i | 0.999743 | + | 0.0226512i | \(0.00721072\pi\) | ||||
−0.999743 | + | 0.0226512i | \(0.992789\pi\) | |||||||
\(14\) | −0.593998 | + | 0.593998i | −0.158753 | + | 0.158753i | ||||
\(15\) | −0.712794 | + | 2.11942i | −0.184043 | + | 0.547231i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.23332 | 1.26927 | 0.634634 | − | 0.772813i | \(-0.281151\pi\) | ||||
0.634634 | + | 0.772813i | \(0.281151\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.67943 | − | 1.67943i | −0.385289 | − | 0.385289i | 0.487715 | − | 0.873003i | \(-0.337831\pi\) |
−0.873003 | + | 0.487715i | \(0.837831\pi\) | |||||||
\(20\) | 0.994632 | + | 2.00267i | 0.222407 | + | 0.447812i | ||||
\(21\) | − | 0.840040i | − | 0.183312i | ||||||
\(22\) | −2.21854 | −0.472993 | ||||||||
\(23\) | − | 3.86710i | − | 0.806346i | −0.915124 | − | 0.403173i | \(-0.867907\pi\) | ||
0.915124 | − | 0.403173i | \(-0.132093\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | −3.02141 | + | 3.98385i | −0.604283 | + | 0.796770i | ||||
\(26\) | −0.163340 | −0.0320336 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −0.593998 | − | 0.593998i | −0.112255 | − | 0.112255i | ||||
\(29\) | 4.79365 | − | 4.79365i | 0.890159 | − | 0.890159i | −0.104379 | − | 0.994538i | \(-0.533285\pi\) |
0.994538 | + | 0.104379i | \(0.0332854\pi\) | |||||||
\(30\) | −2.11942 | − | 0.712794i | −0.386951 | − | 0.130138i | ||||
\(31\) | −5.64797 | − | 5.64797i | −1.01441 | − | 1.01441i | −0.999895 | − | 0.0145112i | \(-0.995381\pi\) |
−0.0145112 | − | 0.999895i | \(-0.504619\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.56874 | − | 1.56874i | 0.273083 | − | 0.273083i | ||||
\(34\) | 5.23332i | 0.897508i | ||||||||
\(35\) | 0.598775 | − | 1.78039i | 0.101212 | − | 0.300942i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −4.51960 | + | 4.07102i | −0.743018 | + | 0.669271i | ||||
\(38\) | 1.67943 | − | 1.67943i | 0.272440 | − | 0.272440i | ||||
\(39\) | 0.115499 | − | 0.115499i | 0.0184946 | − | 0.0184946i | ||||
\(40\) | −2.00267 | + | 0.994632i | −0.316651 | + | 0.157265i | ||||
\(41\) | − | 5.85724i | − | 0.914748i | −0.889275 | − | 0.457374i | \(-0.848790\pi\) | ||
0.889275 | − | 0.457374i | \(-0.151210\pi\) | |||||||
\(42\) | 0.840040 | 0.129621 | ||||||||
\(43\) | − | 8.94207i | − | 1.36365i | −0.731514 | − | 0.681826i | \(-0.761186\pi\) | ||
0.731514 | − | 0.681826i | \(-0.238814\pi\) | |||||||
\(44\) | − | 2.21854i | − | 0.334457i | ||||||
\(45\) | 2.00267 | − | 0.994632i | 0.298541 | − | 0.148271i | ||||
\(46\) | 3.86710 | 0.570173 | ||||||||
\(47\) | −7.97291 | − | 7.97291i | −1.16297 | − | 1.16297i | −0.983823 | − | 0.179146i | \(-0.942667\pi\) |
−0.179146 | − | 0.983823i | \(-0.557333\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | − | 6.29433i | − | 0.899190i | ||||||
\(50\) | −3.98385 | − | 3.02141i | −0.563401 | − | 0.427292i | ||||
\(51\) | −3.70052 | − | 3.70052i | −0.518176 | − | 0.518176i | ||||
\(52\) | − | 0.163340i | − | 0.0226512i | ||||||
\(53\) | −7.94704 | + | 7.94704i | −1.09161 | + | 1.09161i | −0.0962535 | + | 0.995357i | \(0.530686\pi\) |
−0.995357 | + | 0.0962535i | \(0.969314\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | 4.44300 | − | 2.20663i | 0.599095 | − | 0.297541i | ||||
\(56\) | 0.593998 | − | 0.593998i | 0.0793763 | − | 0.0793763i | ||||
\(57\) | 2.37508i | 0.314587i | ||||||||
\(58\) | 4.79365 | + | 4.79365i | 0.629438 | + | 0.629438i | ||||
\(59\) | 1.00057 | + | 1.00057i | 0.130263 | + | 0.130263i | 0.769232 | − | 0.638969i | \(-0.220639\pi\) |
−0.638969 | + | 0.769232i | \(0.720639\pi\) | |||||||
\(60\) | 0.712794 | − | 2.11942i | 0.0920213 | − | 0.273615i | ||||
\(61\) | −7.50634 | − | 7.50634i | −0.961088 | − | 0.961088i | 0.0381827 | − | 0.999271i | \(-0.487843\pi\) |
−0.999271 | + | 0.0381827i | \(0.987843\pi\) | |||||||
\(62\) | 5.64797 | − | 5.64797i | 0.717293 | − | 0.717293i | ||||
\(63\) | −0.593998 | + | 0.593998i | −0.0748367 | + | 0.0748367i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.327117 | − | 0.162463i | 0.0405739 | − | 0.0201511i | ||||
\(66\) | 1.56874 | + | 1.56874i | 0.193099 | + | 0.193099i | ||||
\(67\) | 5.39694 | − | 5.39694i | 0.659341 | − | 0.659341i | −0.295883 | − | 0.955224i | \(-0.595614\pi\) |
0.955224 | + | 0.295883i | \(0.0956138\pi\) | |||||||
\(68\) | −5.23332 | −0.634634 | ||||||||
\(69\) | −2.73445 | + | 2.73445i | −0.329189 | + | 0.329189i | ||||
\(70\) | 1.78039 | + | 0.598775i | 0.212798 | + | 0.0715673i | ||||
\(71\) | 14.9530 | 1.77460 | 0.887299 | − | 0.461194i | \(-0.152579\pi\) | ||||
0.887299 | + | 0.461194i | \(0.152579\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 0.258848 | + | 0.258848i | 0.0302959 | + | 0.0302959i | 0.722092 | − | 0.691797i | \(-0.243181\pi\) |
−0.691797 | + | 0.722092i | \(0.743181\pi\) | |||||||
\(74\) | −4.07102 | − | 4.51960i | −0.473246 | − | 0.525393i | ||||
\(75\) | 4.95347 | − | 0.680545i | 0.571977 | − | 0.0785826i | ||||
\(76\) | 1.67943 | + | 1.67943i | 0.192644 | + | 0.192644i | ||||
\(77\) | −1.31781 | + | 1.31781i | −0.150178 | + | 0.150178i | ||||
\(78\) | 0.115499 | + | 0.115499i | 0.0130777 | + | 0.0130777i | ||||
\(79\) | −1.08732 | − | 1.08732i | −0.122333 | − | 0.122333i | 0.643290 | − | 0.765623i | \(-0.277569\pi\) |
−0.765623 | + | 0.643290i | \(0.777569\pi\) | |||||||
\(80\) | −0.994632 | − | 2.00267i | −0.111203 | − | 0.223906i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 5.85724 | 0.646824 | ||||||||
\(83\) | −4.08091 | + | 4.08091i | −0.447938 | + | 0.447938i | −0.894669 | − | 0.446731i | \(-0.852588\pi\) |
0.446731 | + | 0.894669i | \(0.352588\pi\) | |||||||
\(84\) | 0.840040i | 0.0916559i | ||||||||
\(85\) | −5.20523 | − | 10.4806i | −0.564587 | − | 1.13679i | ||||
\(86\) | 8.94207 | 0.964248 | ||||||||
\(87\) | −6.77925 | −0.726812 | ||||||||
\(88\) | 2.21854 | 0.236497 | ||||||||
\(89\) | 12.5864 | − | 12.5864i | 1.33415 | − | 1.33415i | 0.432539 | − | 0.901615i | \(-0.357618\pi\) |
0.901615 | − | 0.432539i | \(-0.142382\pi\) | |||||||
\(90\) | 0.994632 | + | 2.00267i | 0.104843 | + | 0.211100i | ||||
\(91\) | −0.0970237 | + | 0.0970237i | −0.0101708 | + | 0.0101708i | ||||
\(92\) | 3.86710i | 0.403173i | ||||||||
\(93\) | 7.98744i | 0.828259i | ||||||||
\(94\) | 7.97291 | − | 7.97291i | 0.822343 | − | 0.822343i | ||||
\(95\) | −1.69294 | + | 5.03378i | −0.173692 | + | 0.516455i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | −12.7909 | −1.29872 | −0.649359 | − | 0.760482i | \(-0.724963\pi\) | ||||
−0.649359 | + | 0.760482i | \(0.724963\pi\) | |||||||
\(98\) | 6.29433 | 0.635824 | ||||||||
\(99\) | −2.21854 | −0.222971 | ||||||||
\(100\) | 3.02141 | − | 3.98385i | 0.302141 | − | 0.398385i | ||||
\(101\) | 4.31584i | 0.429442i | 0.976675 | + | 0.214721i | \(0.0688842\pi\) | ||||
−0.976675 | + | 0.214721i | \(0.931116\pi\) | |||||||
\(102\) | 3.70052 | − | 3.70052i | 0.366406 | − | 0.366406i | ||||
\(103\) | −13.9487 | −1.37440 | −0.687202 | − | 0.726467i | \(-0.741161\pi\) | ||||
−0.687202 | + | 0.726467i | \(0.741161\pi\) | |||||||
\(104\) | 0.163340 | 0.0160168 | ||||||||
\(105\) | −1.68233 | + | 0.835531i | −0.164178 | + | 0.0815395i | ||||
\(106\) | −7.94704 | − | 7.94704i | −0.771885 | − | 0.771885i | ||||
\(107\) | 5.53603 | + | 5.53603i | 0.535189 | + | 0.535189i | 0.922112 | − | 0.386923i | \(-0.126462\pi\) |
−0.386923 | + | 0.922112i | \(0.626462\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 9.96395 | + | 9.96395i | 0.954373 | + | 0.954373i | 0.999004 | − | 0.0446302i | \(-0.0142109\pi\) |
−0.0446302 | + | 0.999004i | \(0.514211\pi\) | |||||||
\(110\) | 2.20663 | + | 4.44300i | 0.210394 | + | 0.423624i | ||||
\(111\) | 6.07449 | + | 0.317197i | 0.576565 | + | 0.0301070i | ||||
\(112\) | 0.593998 | + | 0.593998i | 0.0561275 | + | 0.0561275i | ||||
\(113\) | 18.7870 | 1.76733 | 0.883665 | − | 0.468120i | \(-0.155068\pi\) | ||||
0.883665 | + | 0.468120i | \(0.155068\pi\) | |||||||
\(114\) | −2.37508 | −0.222447 | ||||||||
\(115\) | −7.74455 | + | 3.84634i | −0.722183 | + | 0.358673i | ||||
\(116\) | −4.79365 | + | 4.79365i | −0.445080 | + | 0.445080i | ||||
\(117\) | −0.163340 | −0.0151008 | ||||||||
\(118\) | −1.00057 | + | 1.00057i | −0.0921100 | + | 0.0921100i | ||||
\(119\) | 3.10858 | + | 3.10858i | 0.284963 | + | 0.284963i | ||||
\(120\) | 2.11942 | + | 0.712794i | 0.193475 | + | 0.0650689i | ||||
\(121\) | 6.07810 | 0.552555 | ||||||||
\(122\) | 7.50634 | − | 7.50634i | 0.679592 | − | 0.679592i | ||||
\(123\) | −4.14170 | + | 4.14170i | −0.373444 | + | 0.373444i | ||||
\(124\) | 5.64797 | + | 5.64797i | 0.507203 | + | 0.507203i | ||||
\(125\) | 10.9836 | + | 2.08844i | 0.982399 | + | 0.186796i | ||||
\(126\) | −0.593998 | − | 0.593998i | −0.0529175 | − | 0.0529175i | ||||
\(127\) | 4.61246 | + | 4.61246i | 0.409290 | + | 0.409290i | 0.881491 | − | 0.472201i | \(-0.156540\pi\) |
−0.472201 | + | 0.881491i | \(0.656540\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −6.32300 | + | 6.32300i | −0.556709 | + | 0.556709i | ||||
\(130\) | 0.162463 | + | 0.327117i | 0.0142490 | + | 0.0286901i | ||||
\(131\) | −11.9955 | − | 11.9955i | −1.04805 | − | 1.04805i | −0.998786 | − | 0.0492667i | \(-0.984312\pi\) |
−0.0492667 | − | 0.998786i | \(-0.515688\pi\) | |||||||
\(132\) | −1.56874 | + | 1.56874i | −0.136541 | + | 0.136541i | ||||
\(133\) | − | 1.99516i | − | 0.173002i | ||||||
\(134\) | 5.39694 | + | 5.39694i | 0.466225 | + | 0.466225i | ||||
\(135\) | −2.11942 | − | 0.712794i | −0.182410 | − | 0.0613475i | ||||
\(136\) | − | 5.23332i | − | 0.448754i | ||||||
\(137\) | −2.69211 | − | 2.69211i | −0.230002 | − | 0.230002i | 0.582691 | − | 0.812694i | \(-0.302000\pi\) |
−0.812694 | + | 0.582691i | \(0.802000\pi\) | |||||||
\(138\) | −2.73445 | − | 2.73445i | −0.232772 | − | 0.232772i | ||||
\(139\) | −1.30467 | −0.110661 | −0.0553305 | − | 0.998468i | \(-0.517621\pi\) | ||||
−0.0553305 | + | 0.998468i | \(0.517621\pi\) | |||||||
\(140\) | −0.598775 | + | 1.78039i | −0.0506058 | + | 0.150471i | ||||
\(141\) | 11.2754i | 0.949560i | ||||||||
\(142\) | 14.9530i | 1.25483i | ||||||||
\(143\) | −0.362376 | −0.0303034 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −14.3681 | − | 4.83221i | −1.19320 | − | 0.401293i | ||||
\(146\) | −0.258848 | + | 0.258848i | −0.0214224 | + | 0.0214224i | ||||
\(147\) | −4.45077 | + | 4.45077i | −0.367093 | + | 0.367093i | ||||
\(148\) | 4.51960 | − | 4.07102i | 0.371509 | − | 0.334636i | ||||
\(149\) | 9.07290i | 0.743281i | 0.928377 | + | 0.371640i | \(0.121205\pi\) | ||||
−0.928377 | + | 0.371640i | \(0.878795\pi\) | |||||||
\(150\) | 0.680545 | + | 4.95347i | 0.0555663 | + | 0.404449i | ||||
\(151\) | 0.0622104i | 0.00506261i | 0.999997 | + | 0.00253130i | \(0.000805740\pi\) | ||||
−0.999997 | + | 0.00253130i | \(0.999194\pi\) | |||||||
\(152\) | −1.67943 | + | 1.67943i | −0.136220 | + | 0.136220i | ||||
\(153\) | 5.23332i | 0.423089i | ||||||||
\(154\) | −1.31781 | − | 1.31781i | −0.106192 | − | 0.106192i | ||||
\(155\) | −5.69340 | + | 16.9287i | −0.457305 | + | 1.35975i | ||||
\(156\) | −0.115499 | + | 0.115499i | −0.00924731 | + | 0.00924731i | ||||
\(157\) | −5.08868 | − | 5.08868i | −0.406121 | − | 0.406121i | 0.474263 | − | 0.880383i | \(-0.342715\pi\) |
−0.880383 | + | 0.474263i | \(0.842715\pi\) | |||||||
\(158\) | 1.08732 | − | 1.08732i | 0.0865023 | − | 0.0865023i | ||||
\(159\) | 11.2388 | 0.891296 | ||||||||
\(160\) | 2.00267 | − | 0.994632i | 0.158325 | − | 0.0786326i | ||||
\(161\) | 2.29705 | − | 2.29705i | 0.181033 | − | 0.181033i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −19.1109 | −1.49688 | −0.748441 | − | 0.663201i | \(-0.769197\pi\) | ||||
−0.748441 | + | 0.663201i | \(0.769197\pi\) | |||||||
\(164\) | 5.85724i | 0.457374i | ||||||||
\(165\) | −4.70200 | − | 1.58136i | −0.366050 | − | 0.123109i | ||||
\(166\) | −4.08091 | − | 4.08091i | −0.316740 | − | 0.316740i | ||||
\(167\) | −7.28469 | −0.563706 | −0.281853 | − | 0.959458i | \(-0.590949\pi\) | ||||
−0.281853 | + | 0.959458i | \(0.590949\pi\) | |||||||
\(168\) | −0.840040 | −0.0648105 | ||||||||
\(169\) | 12.9733 | 0.997948 | ||||||||
\(170\) | 10.4806 | − | 5.20523i | 0.803829 | − | 0.399223i | ||||
\(171\) | 1.67943 | − | 1.67943i | 0.128430 | − | 0.128430i | ||||
\(172\) | 8.94207i | 0.681826i | ||||||||
\(173\) | 8.94815 | + | 8.94815i | 0.680315 | + | 0.680315i | 0.960071 | − | 0.279756i | \(-0.0902536\pi\) |
−0.279756 | + | 0.960071i | \(0.590254\pi\) | |||||||
\(174\) | − | 6.77925i | − | 0.513934i | ||||||
\(175\) | −4.16111 | + | 0.571685i | −0.314551 | + | 0.0432154i | ||||
\(176\) | 2.21854i | 0.167228i | ||||||||
\(177\) | − | 1.41502i | − | 0.106359i | ||||||
\(178\) | 12.5864 | + | 12.5864i | 0.943390 | + | 0.943390i | ||||
\(179\) | 17.4301 | − | 17.4301i | 1.30279 | − | 1.30279i | 0.376287 | − | 0.926503i | \(-0.377201\pi\) |
0.926503 | − | 0.376287i | \(-0.122799\pi\) | |||||||
\(180\) | −2.00267 | + | 0.994632i | −0.149271 | + | 0.0741355i | ||||
\(181\) | 3.39361 | 0.252245 | 0.126122 | − | 0.992015i | \(-0.459747\pi\) | ||||
0.126122 | + | 0.992015i | \(0.459747\pi\) | |||||||
\(182\) | −0.0970237 | − | 0.0970237i | −0.00719188 | − | 0.00719188i | ||||
\(183\) | 10.6156i | 0.784725i | ||||||||
\(184\) | −3.86710 | −0.285086 | ||||||||
\(185\) | 12.6483 | + | 5.00213i | 0.929919 | + | 0.367764i | ||||
\(186\) | −7.98744 | −0.585668 | ||||||||
\(187\) | 11.6103i | 0.849030i | ||||||||
\(188\) | 7.97291 | + | 7.97291i | 0.581484 | + | 0.581484i | ||||
\(189\) | 0.840040 | 0.0611039 | ||||||||
\(190\) | −5.03378 | − | 1.69294i | −0.365189 | − | 0.122819i | ||||
\(191\) | 1.08400 | − | 1.08400i | 0.0784355 | − | 0.0784355i | −0.666801 | − | 0.745236i | \(-0.732337\pi\) |
0.745236 | + | 0.666801i | \(0.232337\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | − | 4.04039i | − | 0.290834i | −0.989370 | − | 0.145417i | \(-0.953548\pi\) | ||
0.989370 | − | 0.145417i | \(-0.0464523\pi\) | |||||||
\(194\) | − | 12.7909i | − | 0.918332i | ||||||
\(195\) | −0.346186 | − | 0.116428i | −0.0247909 | − | 0.00833757i | ||||
\(196\) | 6.29433i | 0.449595i | ||||||||
\(197\) | −12.3544 | − | 12.3544i | −0.880214 | − | 0.880214i | 0.113342 | − | 0.993556i | \(-0.463844\pi\) |
−0.993556 | + | 0.113342i | \(0.963844\pi\) | |||||||
\(198\) | − | 2.21854i | − | 0.157664i | ||||||
\(199\) | −5.19861 | + | 5.19861i | −0.368519 | + | 0.368519i | −0.866937 | − | 0.498418i | \(-0.833915\pi\) |
0.498418 | + | 0.866937i | \(0.333915\pi\) | |||||||
\(200\) | 3.98385 | + | 3.02141i | 0.281701 | + | 0.213646i | ||||
\(201\) | −7.63243 | −0.538350 | ||||||||
\(202\) | −4.31584 | −0.303661 | ||||||||
\(203\) | 5.69484 | 0.399699 | ||||||||
\(204\) | 3.70052 | + | 3.70052i | 0.259088 | + | 0.259088i | ||||
\(205\) | −11.7302 | + | 5.82580i | −0.819269 | + | 0.406892i | ||||
\(206\) | − | 13.9487i | − | 0.971850i | ||||||
\(207\) | 3.86710 | 0.268782 | ||||||||
\(208\) | 0.163340i | 0.0113256i | ||||||||
\(209\) | 3.72588 | − | 3.72588i | 0.257725 | − | 0.257725i | ||||
\(210\) | −0.835531 | − | 1.68233i | −0.0576571 | − | 0.116092i | ||||
\(211\) | −15.2308 | −1.04853 | −0.524264 | − | 0.851556i | \(-0.675660\pi\) | ||||
−0.524264 | + | 0.851556i | \(0.675660\pi\) | |||||||
\(212\) | 7.94704 | − | 7.94704i | 0.545805 | − | 0.545805i | ||||
\(213\) | −10.5734 | − | 10.5734i | −0.724477 | − | 0.724477i | ||||
\(214\) | −5.53603 | + | 5.53603i | −0.378435 | + | 0.378435i | ||||
\(215\) | −17.9081 | + | 8.89407i | −1.22132 | + | 0.606571i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | − | 6.70977i | − | 0.455489i | ||||||
\(218\) | −9.96395 | + | 9.96395i | −0.674844 | + | 0.674844i | ||||
\(219\) | − | 0.366066i | − | 0.0247365i | ||||||
\(220\) | −4.44300 | + | 2.20663i | −0.299547 | + | 0.148771i | ||||
\(221\) | 0.854812i | 0.0575009i | ||||||||
\(222\) | −0.317197 | + | 6.07449i | −0.0212888 | + | 0.407693i | ||||
\(223\) | 9.25821 | − | 9.25821i | 0.619976 | − | 0.619976i | −0.325549 | − | 0.945525i | \(-0.605549\pi\) |
0.945525 | + | 0.325549i | \(0.105549\pi\) | |||||||
\(224\) | −0.593998 | + | 0.593998i | −0.0396882 | + | 0.0396882i | ||||
\(225\) | −3.98385 | − | 3.02141i | −0.265590 | − | 0.201428i | ||||
\(226\) | 18.7870i | 1.24969i | ||||||||
\(227\) | −12.5313 | −0.831734 | −0.415867 | − | 0.909425i | \(-0.636522\pi\) | ||||
−0.415867 | + | 0.909425i | \(0.636522\pi\) | |||||||
\(228\) | − | 2.37508i | − | 0.157293i | ||||||
\(229\) | 7.37486i | 0.487345i | 0.969858 | + | 0.243672i | \(0.0783521\pi\) | ||||
−0.969858 | + | 0.243672i | \(0.921648\pi\) | |||||||
\(230\) | −3.84634 | − | 7.74455i | −0.253620 | − | 0.510660i | ||||
\(231\) | 1.86366 | 0.122620 | ||||||||
\(232\) | −4.79365 | − | 4.79365i | −0.314719 | − | 0.314719i | ||||
\(233\) | 18.4468 | + | 18.4468i | 1.20849 | + | 1.20849i | 0.971517 | + | 0.236971i | \(0.0761545\pi\) |
0.236971 | + | 0.971517i | \(0.423846\pi\) | |||||||
\(234\) | − | 0.163340i | − | 0.0106779i | ||||||
\(235\) | −8.03703 | + | 23.8973i | −0.524278 | + | 1.55889i | ||||
\(236\) | −1.00057 | − | 1.00057i | −0.0651316 | − | 0.0651316i | ||||
\(237\) | 1.53770i | 0.0998843i | ||||||||
\(238\) | −3.10858 | + | 3.10858i | −0.201500 | + | 0.201500i | ||||
\(239\) | −10.9427 | − | 10.9427i | −0.707825 | − | 0.707825i | 0.258252 | − | 0.966077i | \(-0.416853\pi\) |
−0.966077 | + | 0.258252i | \(0.916853\pi\) | |||||||
\(240\) | −0.712794 | + | 2.11942i | −0.0460106 | + | 0.136808i | ||||
\(241\) | 11.4584 | − | 11.4584i | 0.738102 | − | 0.738102i | −0.234108 | − | 0.972211i | \(-0.575217\pi\) |
0.972211 | + | 0.234108i | \(0.0752170\pi\) | |||||||
\(242\) | 6.07810i | 0.390715i | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 7.50634 | + | 7.50634i | 0.480544 | + | 0.480544i | ||||
\(245\) | −12.6055 | + | 6.26055i | −0.805336 | + | 0.399972i | ||||
\(246\) | −4.14170 | − | 4.14170i | −0.264065 | − | 0.264065i | ||||
\(247\) | 0.274319 | − | 0.274319i | 0.0174545 | − | 0.0174545i | ||||
\(248\) | −5.64797 | + | 5.64797i | −0.358647 | + | 0.358647i | ||||
\(249\) | 5.77128 | 0.365740 | ||||||||
\(250\) | −2.08844 | + | 10.9836i | −0.132085 | + | 0.694661i | ||||
\(251\) | −4.90961 | − | 4.90961i | −0.309892 | − | 0.309892i | 0.534976 | − | 0.844867i | \(-0.320321\pi\) |
−0.844867 | + | 0.534976i | \(0.820321\pi\) | |||||||
\(252\) | 0.593998 | − | 0.593998i | 0.0374184 | − | 0.0374184i | ||||
\(253\) | 8.57930 | 0.539376 | ||||||||
\(254\) | −4.61246 | + | 4.61246i | −0.289412 | + | 0.289412i | ||||
\(255\) | −3.73028 | + | 11.0916i | −0.233599 | + | 0.694582i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.1402 | 1.25631 | 0.628155 | − | 0.778088i | \(-0.283810\pi\) | ||||
0.628155 | + | 0.778088i | \(0.283810\pi\) | |||||||
\(258\) | −6.32300 | − | 6.32300i | −0.393653 | − | 0.393653i | ||||
\(259\) | −5.10281 | − | 0.266458i | −0.317073 | − | 0.0165569i | ||||
\(260\) | −0.327117 | + | 0.162463i | −0.0202869 | + | 0.0100756i | ||||
\(261\) | 4.79365 | + | 4.79365i | 0.296720 | + | 0.296720i | ||||
\(262\) | 11.9955 | − | 11.9955i | 0.741085 | − | 0.741085i | ||||
\(263\) | −5.00770 | − | 5.00770i | −0.308788 | − | 0.308788i | 0.535651 | − | 0.844439i | \(-0.320066\pi\) |
−0.844439 | + | 0.535651i | \(0.820066\pi\) | |||||||
\(264\) | −1.56874 | − | 1.56874i | −0.0965493 | − | 0.0965493i | ||||
\(265\) | 23.8197 | + | 8.01096i | 1.46323 | + | 0.492109i | ||||
\(266\) | 1.99516 | 0.122331 | ||||||||
\(267\) | −17.7998 | −1.08933 | ||||||||
\(268\) | −5.39694 | + | 5.39694i | −0.329671 | + | 0.329671i | ||||
\(269\) | − | 12.0216i | − | 0.732969i | −0.930424 | − | 0.366485i | \(-0.880561\pi\) | ||
0.930424 | − | 0.366485i | \(-0.119439\pi\) | |||||||
\(270\) | 0.712794 | − | 2.11942i | 0.0433792 | − | 0.128984i | ||||
\(271\) | −11.5944 | −0.704308 | −0.352154 | − | 0.935942i | \(-0.614551\pi\) | ||||
−0.352154 | + | 0.935942i | \(0.614551\pi\) | |||||||
\(272\) | 5.23332 | 0.317317 | ||||||||
\(273\) | 0.137212 | 0.00830446 | ||||||||
\(274\) | 2.69211 | − | 2.69211i | 0.162636 | − | 0.162636i | ||||
\(275\) | −8.83831 | − | 6.70311i | −0.532970 | − | 0.404213i | ||||
\(276\) | 2.73445 | − | 2.73445i | 0.164595 | − | 0.164595i | ||||
\(277\) | 1.48164i | 0.0890229i | 0.999009 | + | 0.0445115i | \(0.0141731\pi\) | ||||
−0.999009 | + | 0.0445115i | \(0.985827\pi\) | |||||||
\(278\) | − | 1.30467i | − | 0.0782491i | ||||||
\(279\) | 5.64797 | − | 5.64797i | 0.338135 | − | 0.338135i | ||||
\(280\) | −1.78039 | − | 0.598775i | −0.106399 | − | 0.0357837i | ||||
\(281\) | 2.20394 | − | 2.20394i | 0.131476 | − | 0.131476i | −0.638306 | − | 0.769782i | \(-0.720365\pi\) |
0.769782 | + | 0.638306i | \(0.220365\pi\) | |||||||
\(282\) | −11.2754 | −0.671440 | ||||||||
\(283\) | 12.9583 | 0.770291 | 0.385145 | − | 0.922856i | \(-0.374151\pi\) | ||||
0.385145 | + | 0.922856i | \(0.374151\pi\) | |||||||
\(284\) | −14.9530 | −0.887299 | ||||||||
\(285\) | 4.75651 | − | 2.36233i | 0.281751 | − | 0.139932i | ||||
\(286\) | − | 0.362376i | − | 0.0214277i | ||||||
\(287\) | 3.47919 | − | 3.47919i | 0.205370 | − | 0.205370i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 10.3877 | 0.611040 | ||||||||
\(290\) | 4.83221 | − | 14.3681i | 0.283757 | − | 0.843721i | ||||
\(291\) | 9.04452 | + | 9.04452i | 0.530199 | + | 0.530199i | ||||
\(292\) | −0.258848 | − | 0.258848i | −0.0151479 | − | 0.0151479i | ||||
\(293\) | −15.2639 | + | 15.2639i | −0.891729 | + | 0.891729i | −0.994686 | − | 0.102956i | \(-0.967170\pi\) |
0.102956 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(294\) | −4.45077 | − | 4.45077i | −0.259574 | − | 0.259574i | ||||
\(295\) | 1.00862 | − | 2.99902i | 0.0587240 | − | 0.174610i | ||||
\(296\) | 4.07102 | + | 4.51960i | 0.236623 | + | 0.262697i | ||||
\(297\) | 1.56874 | + | 1.56874i | 0.0910276 | + | 0.0910276i | ||||
\(298\) | −9.07290 | −0.525579 | ||||||||
\(299\) | 0.631653 | 0.0365294 | ||||||||
\(300\) | −4.95347 | + | 0.680545i | −0.285989 | + | 0.0392913i | ||||
\(301\) | 5.31157 | − | 5.31157i | 0.306154 | − | 0.306154i | ||||
\(302\) | −0.0622104 | −0.00357980 | ||||||||
\(303\) | 3.05176 | − | 3.05176i | 0.175319 | − | 0.175319i | ||||
\(304\) | −1.67943 | − | 1.67943i | −0.0963222 | − | 0.0963222i | ||||
\(305\) | −7.56671 | + | 22.4988i | −0.433268 | + | 1.28828i | ||||
\(306\) | −5.23332 | −0.299169 | ||||||||
\(307\) | −20.5532 | + | 20.5532i | −1.17303 | + | 1.17303i | −0.191547 | + | 0.981483i | \(0.561350\pi\) |
−0.981483 | + | 0.191547i | \(0.938650\pi\) | |||||||
\(308\) | 1.31781 | − | 1.31781i | 0.0750889 | − | 0.0750889i | ||||
\(309\) | 9.86320 | + | 9.86320i | 0.561098 | + | 0.561098i | ||||
\(310\) | −16.9287 | − | 5.69340i | −0.961486 | − | 0.323363i | ||||
\(311\) | 0.612480 | + | 0.612480i | 0.0347305 | + | 0.0347305i | 0.724259 | − | 0.689528i | \(-0.242182\pi\) |
−0.689528 | + | 0.724259i | \(0.742182\pi\) | |||||||
\(312\) | −0.115499 | − | 0.115499i | −0.00653884 | − | 0.00653884i | ||||
\(313\) | − | 3.56579i | − | 0.201550i | −0.994909 | − | 0.100775i | \(-0.967868\pi\) | ||
0.994909 | − | 0.100775i | \(-0.0321322\pi\) | |||||||
\(314\) | 5.08868 | − | 5.08868i | 0.287171 | − | 0.287171i | ||||
\(315\) | 1.78039 | + | 0.598775i | 0.100314 | + | 0.0337372i | ||||
\(316\) | 1.08732 | + | 1.08732i | 0.0611664 | + | 0.0611664i | ||||
\(317\) | 4.20992 | − | 4.20992i | 0.236453 | − | 0.236453i | −0.578927 | − | 0.815380i | \(-0.696528\pi\) |
0.815380 | + | 0.578927i | \(0.196528\pi\) | |||||||
\(318\) | 11.2388i | 0.630242i | ||||||||
\(319\) | 10.6349 | + | 10.6349i | 0.595439 | + | 0.595439i | ||||
\(320\) | 0.994632 | + | 2.00267i | 0.0556016 | + | 0.111953i | ||||
\(321\) | − | 7.82913i | − | 0.436980i | ||||||
\(322\) | 2.29705 | + | 2.29705i | 0.128010 | + | 0.128010i | ||||
\(323\) | −8.78902 | − | 8.78902i | −0.489034 | − | 0.489034i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −0.650723 | − | 0.493518i | −0.0360956 | − | 0.0273755i | ||||
\(326\) | − | 19.1109i | − | 1.05846i | ||||||
\(327\) | − | 14.0912i | − | 0.779243i | ||||||
\(328\) | −5.85724 | −0.323412 | ||||||||
\(329\) | − | 9.47178i | − | 0.522196i | ||||||
\(330\) | 1.58136 | − | 4.70200i | 0.0870509 | − | 0.258837i | ||||
\(331\) | 14.0919 | − | 14.0919i | 0.774561 | − | 0.774561i | −0.204339 | − | 0.978900i | \(-0.565505\pi\) |
0.978900 | + | 0.204339i | \(0.0655045\pi\) | |||||||
\(332\) | 4.08091 | − | 4.08091i | 0.223969 | − | 0.223969i | ||||
\(333\) | −4.07102 | − | 4.51960i | −0.223090 | − | 0.247673i | ||||
\(334\) | − | 7.28469i | − | 0.398601i | ||||||
\(335\) | −16.1763 | − | 5.44035i | −0.883805 | − | 0.297238i | ||||
\(336\) | − | 0.840040i | − | 0.0458279i | ||||||
\(337\) | −17.5011 | + | 17.5011i | −0.953348 | + | 0.953348i | −0.998959 | − | 0.0456112i | \(-0.985476\pi\) |
0.0456112 | + | 0.998959i | \(0.485476\pi\) | |||||||
\(338\) | 12.9733i | 0.705656i | ||||||||
\(339\) | −13.2844 | − | 13.2844i | −0.721510 | − | 0.721510i | ||||
\(340\) | 5.20523 | + | 10.4806i | 0.282293 | + | 0.568393i | ||||
\(341\) | 12.5302 | − | 12.5302i | 0.678550 | − | 0.678550i | ||||
\(342\) | 1.67943 | + | 1.67943i | 0.0908134 | + | 0.0908134i | ||||
\(343\) | 7.89681 | − | 7.89681i | 0.426388 | − | 0.426388i | ||||
\(344\) | −8.94207 | −0.482124 | ||||||||
\(345\) | 8.19600 | + | 2.75645i | 0.441258 | + | 0.148402i | ||||
\(346\) | −8.94815 | + | 8.94815i | −0.481055 | + | 0.481055i | ||||
\(347\) | 19.3835i | 1.04056i | 0.853996 | + | 0.520280i | \(0.174173\pi\) | ||||
−0.853996 | + | 0.520280i | \(0.825827\pi\) | |||||||
\(348\) | 6.77925 | 0.363406 | ||||||||
\(349\) | 14.5408i | 0.778350i | 0.921164 | + | 0.389175i | \(0.127240\pi\) | ||||
−0.921164 | + | 0.389175i | \(0.872760\pi\) | |||||||
\(350\) | −0.571685 | − | 4.16111i | −0.0305579 | − | 0.222421i | ||||
\(351\) | 0.115499 | + | 0.115499i | 0.00616488 | + | 0.00616488i | ||||
\(352\) | −2.21854 | −0.118248 | ||||||||
\(353\) | 26.3150 | 1.40060 | 0.700302 | − | 0.713847i | \(-0.253049\pi\) | ||||
0.700302 | + | 0.713847i | \(0.253049\pi\) | |||||||
\(354\) | 1.41502 | 0.0752075 | ||||||||
\(355\) | −14.8728 | − | 29.9461i | −0.789365 | − | 1.58937i | ||||
\(356\) | −12.5864 | + | 12.5864i | −0.667077 | + | 0.667077i | ||||
\(357\) | − | 4.39620i | − | 0.232672i | ||||||
\(358\) | 17.4301 | + | 17.4301i | 0.921212 | + | 0.921212i | ||||
\(359\) | − | 6.12864i | − | 0.323457i | −0.986835 | − | 0.161729i | \(-0.948293\pi\) | ||
0.986835 | − | 0.161729i | \(-0.0517069\pi\) | |||||||
\(360\) | −0.994632 | − | 2.00267i | −0.0524217 | − | 0.105550i | ||||
\(361\) | − | 13.3590i | − | 0.703105i | ||||||
\(362\) | 3.39361i | 0.178364i | ||||||||
\(363\) | −4.29787 | − | 4.29787i | −0.225580 | − | 0.225580i | ||||
\(364\) | 0.0970237 | − | 0.0970237i | 0.00508542 | − | 0.00508542i | ||||
\(365\) | 0.260930 | − | 0.775847i | 0.0136577 | − | 0.0406097i | ||||
\(366\) | −10.6156 | −0.554884 | ||||||||
\(367\) | 21.0105 | + | 21.0105i | 1.09674 | + | 1.09674i | 0.994789 | + | 0.101950i | \(0.0325083\pi\) |
0.101950 | + | 0.994789i | \(0.467492\pi\) | |||||||
\(368\) | − | 3.86710i | − | 0.201587i | ||||||
\(369\) | 5.85724 | 0.304916 | ||||||||
\(370\) | −5.00213 | + | 12.6483i | −0.260048 | + | 0.657552i | ||||
\(371\) | −9.44106 | −0.490155 | ||||||||
\(372\) | − | 7.98744i | − | 0.414129i | ||||||
\(373\) | 2.15543 | + | 2.15543i | 0.111604 | + | 0.111604i | 0.760703 | − | 0.649100i | \(-0.224854\pi\) |
−0.649100 | + | 0.760703i | \(0.724854\pi\) | |||||||
\(374\) | −11.6103 | −0.600355 | ||||||||
\(375\) | −6.28979 | − | 9.24330i | −0.324803 | − | 0.477322i | ||||
\(376\) | −7.97291 | + | 7.97291i | −0.411171 | + | 0.411171i | ||||
\(377\) | 0.782996 | + | 0.782996i | 0.0403263 | + | 0.0403263i | ||||
\(378\) | 0.840040i | 0.0432070i | ||||||||
\(379\) | 37.8733i | 1.94542i | 0.232022 | + | 0.972711i | \(0.425466\pi\) | ||||
−0.232022 | + | 0.972711i | \(0.574534\pi\) | |||||||
\(380\) | 1.69294 | − | 5.03378i | 0.0868461 | − | 0.258228i | ||||
\(381\) | − | 6.52301i | − | 0.334184i | ||||||
\(382\) | 1.08400 | + | 1.08400i | 0.0554622 | + | 0.0554622i | ||||
\(383\) | 33.6750i | 1.72071i | 0.509695 | + | 0.860355i | \(0.329758\pi\) | ||||
−0.509695 | + | 0.860355i | \(0.670242\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | 3.94987 | + | 1.32840i | 0.201304 | + | 0.0677017i | ||||
\(386\) | 4.04039 | 0.205650 | ||||||||
\(387\) | 8.94207 | 0.454551 | ||||||||
\(388\) | 12.7909 | 0.649359 | ||||||||
\(389\) | 6.96706 | + | 6.96706i | 0.353244 | + | 0.353244i | 0.861315 | − | 0.508071i | \(-0.169641\pi\) |
−0.508071 | + | 0.861315i | \(0.669641\pi\) | |||||||
\(390\) | 0.116428 | − | 0.346186i | 0.00589555 | − | 0.0175298i | ||||
\(391\) | − | 20.2378i | − | 1.02347i | ||||||
\(392\) | −6.29433 | −0.317912 | ||||||||
\(393\) | 16.9642i | 0.855731i | ||||||||
\(394\) | 12.3544 | − | 12.3544i | 0.622405 | − | 0.622405i | ||||
\(395\) | −1.09606 | + | 3.25902i | −0.0551489 | + | 0.163979i | ||||
\(396\) | 2.21854 | 0.111486 | ||||||||
\(397\) | −2.14584 | + | 2.14584i | −0.107697 | + | 0.107697i | −0.758902 | − | 0.651205i | \(-0.774264\pi\) |
0.651205 | + | 0.758902i | \(0.274264\pi\) | |||||||
\(398\) | −5.19861 | − | 5.19861i | −0.260583 | − | 0.260583i | ||||
\(399\) | −1.41079 | + | 1.41079i | −0.0706279 | + | 0.0706279i | ||||
\(400\) | −3.02141 | + | 3.98385i | −0.151071 | + | 0.199192i | ||||
\(401\) | 3.17371 | + | 3.17371i | 0.158488 | + | 0.158488i | 0.781896 | − | 0.623409i | \(-0.214253\pi\) |
−0.623409 | + | 0.781896i | \(0.714253\pi\) | |||||||
\(402\) | − | 7.63243i | − | 0.380671i | ||||||
\(403\) | 0.922541 | − | 0.922541i | 0.0459550 | − | 0.0459550i | ||||
\(404\) | − | 4.31584i | − | 0.214721i | ||||||
\(405\) | 0.994632 | + | 2.00267i | 0.0494237 | + | 0.0995137i | ||||
\(406\) | 5.69484i | 0.282630i | ||||||||
\(407\) | −9.03170 | − | 10.0269i | −0.447685 | − | 0.497015i | ||||
\(408\) | −3.70052 | + | 3.70052i | −0.183203 | + | 0.183203i | ||||
\(409\) | −7.23143 | + | 7.23143i | −0.357571 | + | 0.357571i | −0.862917 | − | 0.505346i | \(-0.831365\pi\) |
0.505346 | + | 0.862917i | \(0.331365\pi\) | |||||||
\(410\) | −5.82580 | − | 11.7302i | −0.287716 | − | 0.579311i | ||||
\(411\) | 3.80721i | 0.187796i | ||||||||
\(412\) | 13.9487 | 0.687202 | ||||||||
\(413\) | 1.18867i | 0.0584908i | ||||||||
\(414\) | 3.86710i | 0.190058i | ||||||||
\(415\) | 12.2317 | + | 4.11373i | 0.600432 | + | 0.201935i | ||||
\(416\) | −0.163340 | −0.00800841 | ||||||||
\(417\) | 0.922543 | + | 0.922543i | 0.0451771 | + | 0.0451771i | ||||
\(418\) | 3.72588 | + | 3.72588i | 0.182239 | + | 0.182239i | ||||
\(419\) | 1.66410i | 0.0812966i | 0.999174 | + | 0.0406483i | \(0.0129423\pi\) | ||||
−0.999174 | + | 0.0406483i | \(0.987058\pi\) | |||||||
\(420\) | 1.68233 | − | 0.835531i | 0.0820892 | − | 0.0407697i | ||||
\(421\) | −1.49656 | − | 1.49656i | −0.0729381 | − | 0.0729381i | 0.669697 | − | 0.742635i | \(-0.266424\pi\) |
−0.742635 | + | 0.669697i | \(0.766424\pi\) | |||||||
\(422\) | − | 15.2308i | − | 0.741422i | ||||||
\(423\) | 7.97291 | − | 7.97291i | 0.387656 | − | 0.387656i | ||||
\(424\) | 7.94704 | + | 7.94704i | 0.385943 | + | 0.385943i | ||||
\(425\) | −15.8120 | + | 20.8488i | −0.766996 | + | 1.01131i | ||||
\(426\) | 10.5734 | − | 10.5734i | 0.512283 | − | 0.512283i | ||||
\(427\) | − | 8.91750i | − | 0.431548i | ||||||
\(428\) | −5.53603 | − | 5.53603i | −0.267594 | − | 0.267594i | ||||
\(429\) | 0.256238 | + | 0.256238i | 0.0123713 | + | 0.0123713i | ||||
\(430\) | −8.89407 | − | 17.9081i | −0.428910 | − | 0.863603i | ||||
\(431\) | 1.82566 | + | 1.82566i | 0.0879392 | + | 0.0879392i | 0.749708 | − | 0.661769i | \(-0.230194\pi\) |
−0.661769 | + | 0.749708i | \(0.730194\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | 8.92738 | − | 8.92738i | 0.429023 | − | 0.429023i | −0.459273 | − | 0.888295i | \(-0.651890\pi\) |
0.888295 | + | 0.459273i | \(0.151890\pi\) | |||||||
\(434\) | 6.70977 | 0.322079 | ||||||||
\(435\) | 6.74286 | + | 13.5766i | 0.323295 | + | 0.650950i | ||||
\(436\) | −9.96395 | − | 9.96395i | −0.477187 | − | 0.477187i | ||||
\(437\) | −6.49454 | + | 6.49454i | −0.310676 | + | 0.310676i | ||||
\(438\) | 0.366066 | 0.0174913 | ||||||||
\(439\) | −12.1430 | + | 12.1430i | −0.579555 | + | 0.579555i | −0.934781 | − | 0.355225i | \(-0.884404\pi\) |
0.355225 | + | 0.934781i | \(0.384404\pi\) | |||||||
\(440\) | −2.20663 | − | 4.44300i | −0.105197 | − | 0.211812i | ||||
\(441\) | 6.29433 | 0.299730 | ||||||||
\(442\) | −0.854812 | −0.0406593 | ||||||||
\(443\) | −20.3377 | − | 20.3377i | −0.966271 | − | 0.966271i | 0.0331781 | − | 0.999449i | \(-0.489437\pi\) |
−0.999449 | + | 0.0331781i | \(0.989437\pi\) | |||||||
\(444\) | −6.07449 | − | 0.317197i | −0.288282 | − | 0.0150535i | ||||
\(445\) | −37.7253 | − | 12.6876i | −1.78835 | − | 0.601451i | ||||
\(446\) | 9.25821 | + | 9.25821i | 0.438389 | + | 0.438389i | ||||
\(447\) | 6.41551 | − | 6.41551i | 0.303443 | − | 0.303443i | ||||
\(448\) | −0.593998 | − | 0.593998i | −0.0280638 | − | 0.0280638i | ||||
\(449\) | −5.53101 | − | 5.53101i | −0.261024 | − | 0.261024i | 0.564446 | − | 0.825470i | \(-0.309090\pi\) |
−0.825470 | + | 0.564446i | \(0.809090\pi\) | |||||||
\(450\) | 3.02141 | − | 3.98385i | 0.142431 | − | 0.187800i | ||||
\(451\) | 12.9945 | 0.611887 | ||||||||
\(452\) | −18.7870 | −0.883665 | ||||||||
\(453\) | 0.0439894 | − | 0.0439894i | 0.00206680 | − | 0.00206680i | ||||
\(454\) | − | 12.5313i | − | 0.588125i | ||||||
\(455\) | 0.290810 | + | 0.0978040i | 0.0136334 | + | 0.00458512i | ||||
\(456\) | 2.37508 | 0.111223 | ||||||||
\(457\) | −23.3394 | −1.09177 | −0.545884 | − | 0.837861i | \(-0.683806\pi\) | ||||
−0.545884 | + | 0.837861i | \(0.683806\pi\) | |||||||
\(458\) | −7.37486 | −0.344605 | ||||||||
\(459\) | 3.70052 | − | 3.70052i | 0.172725 | − | 0.172725i | ||||
\(460\) | 7.74455 | − | 3.84634i | 0.361091 | − | 0.179337i | ||||
\(461\) | 22.7009 | − | 22.7009i | 1.05728 | − | 1.05728i | 0.0590285 | − | 0.998256i | \(-0.481200\pi\) |
0.998256 | − | 0.0590285i | \(-0.0188003\pi\) | |||||||
\(462\) | 1.86366i | 0.0867052i | ||||||||
\(463\) | − | 0.607463i | − | 0.0282312i | −0.999900 | − | 0.0141156i | \(-0.995507\pi\) | ||
0.999900 | − | 0.0141156i | \(-0.00449329\pi\) | |||||||
\(464\) | 4.79365 | − | 4.79365i | 0.222540 | − | 0.222540i | ||||
\(465\) | 15.9962 | − | 7.94457i | 0.741808 | − | 0.368420i | ||||
\(466\) | −18.4468 | + | 18.4468i | −0.854530 | + | 0.854530i | ||||
\(467\) | −8.76294 | −0.405500 | −0.202750 | − | 0.979230i | \(-0.564988\pi\) | ||||
−0.202750 | + | 0.979230i | \(0.564988\pi\) | |||||||
\(468\) | 0.163340 | 0.00755040 | ||||||||
\(469\) | 6.41155 | 0.296058 | ||||||||
\(470\) | −23.8973 | − | 8.03703i | −1.10230 | − | 0.370721i | ||||
\(471\) | 7.19648i | 0.331596i | ||||||||
\(472\) | 1.00057 | − | 1.00057i | 0.0460550 | − | 0.0460550i | ||||
\(473\) | 19.8383 | 0.912166 | ||||||||
\(474\) | −1.53770 | −0.0706288 | ||||||||
\(475\) | 11.7649 | − | 1.61635i | 0.539810 | − | 0.0741632i | ||||
\(476\) | −3.10858 | − | 3.10858i | −0.142482 | − | 0.142482i | ||||
\(477\) | −7.94704 | − | 7.94704i | −0.363870 | − | 0.363870i | ||||
\(478\) | 10.9427 | − | 10.9427i | 0.500508 | − | 0.500508i | ||||
\(479\) | −6.88917 | − | 6.88917i | −0.314774 | − | 0.314774i | 0.531982 | − | 0.846756i | \(-0.321448\pi\) |
−0.846756 | + | 0.531982i | \(0.821448\pi\) | |||||||
\(480\) | −2.11942 | − | 0.712794i | −0.0967377 | − | 0.0325344i | ||||
\(481\) | −0.664961 | − | 0.738233i | −0.0303196 | − | 0.0336605i | ||||
\(482\) | 11.4584 | + | 11.4584i | 0.521917 | + | 0.521917i | ||||
\(483\) | −3.24852 | −0.147813 | ||||||||
\(484\) | −6.07810 | −0.276277 | ||||||||
\(485\) | 12.7222 | + | 25.6160i | 0.577686 | + | 1.16316i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | 18.0453 | 0.817709 | 0.408855 | − | 0.912599i | \(-0.365928\pi\) | ||||
0.408855 | + | 0.912599i | \(0.365928\pi\) | |||||||
\(488\) | −7.50634 | + | 7.50634i | −0.339796 | + | 0.339796i | ||||
\(489\) | 13.5135 | + | 13.5135i | 0.611100 | + | 0.611100i | ||||
\(490\) | −6.26055 | − | 12.6055i | −0.282823 | − | 0.569459i | ||||
\(491\) | 41.7594 | 1.88457 | 0.942287 | − | 0.334807i | \(-0.108671\pi\) | ||||
0.942287 | + | 0.334807i | \(0.108671\pi\) | |||||||
\(492\) | 4.14170 | − | 4.14170i | 0.186722 | − | 0.186722i | ||||
\(493\) | 25.0867 | − | 25.0867i | 1.12985 | − | 1.12985i | ||||
\(494\) | 0.274319 | + | 0.274319i | 0.0123422 | + | 0.0123422i | ||||
\(495\) | 2.20663 | + | 4.44300i | 0.0991805 | + | 0.199698i | ||||
\(496\) | −5.64797 | − | 5.64797i | −0.253601 | − | 0.253601i | ||||
\(497\) | 8.88207 | + | 8.88207i | 0.398415 | + | 0.398415i | ||||
\(498\) | 5.77128i | 0.258617i | ||||||||
\(499\) | −6.17352 | + | 6.17352i | −0.276365 | + | 0.276365i | −0.831656 | − | 0.555291i | \(-0.812607\pi\) |
0.555291 | + | 0.831656i | \(0.312607\pi\) | |||||||
\(500\) | −10.9836 | − | 2.08844i | −0.491199 | − | 0.0933980i | ||||
\(501\) | 5.15105 | + | 5.15105i | 0.230132 | + | 0.230132i | ||||
\(502\) | 4.90961 | − | 4.90961i | 0.219127 | − | 0.219127i | ||||
\(503\) | 0.796966i | 0.0355350i | 0.999842 | + | 0.0177675i | \(0.00565586\pi\) | ||||
−0.999842 | + | 0.0177675i | \(0.994344\pi\) | |||||||
\(504\) | 0.593998 | + | 0.593998i | 0.0264588 | + | 0.0264588i | ||||
\(505\) | 8.64322 | − | 4.29267i | 0.384618 | − | 0.191021i | ||||
\(506\) | 8.57930i | 0.381396i | ||||||||
\(507\) | −9.17352 | − | 9.17352i | −0.407410 | − | 0.407410i | ||||
\(508\) | −4.61246 | − | 4.61246i | −0.204645 | − | 0.204645i | ||||
\(509\) | 4.90293 | 0.217319 | 0.108659 | − | 0.994079i | \(-0.465344\pi\) | ||||
0.108659 | + | 0.994079i | \(0.465344\pi\) | |||||||
\(510\) | −11.0916 | − | 3.73028i | −0.491144 | − | 0.165180i | ||||
\(511\) | 0.307510i | 0.0136035i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.37508 | −0.104862 | ||||||||
\(514\) | 20.1402i | 0.888346i | ||||||||
\(515\) | 13.8738 | + | 27.9347i | 0.611353 | + | 1.23095i | ||||
\(516\) | 6.32300 | − | 6.32300i | 0.278354 | − | 0.278354i | ||||
\(517\) | 17.6882 | − | 17.6882i | 0.777925 | − | 0.777925i | ||||
\(518\) | 0.266458 | − | 5.10281i | 0.0117075 | − | 0.224205i | ||||
\(519\) | − | 12.6546i | − | 0.555475i | ||||||
\(520\) | −0.162463 | − | 0.327117i | −0.00712449 | − | 0.0143450i | ||||
\(521\) | − | 27.5443i | − | 1.20674i | −0.797462 | − | 0.603369i | \(-0.793825\pi\) | ||
0.797462 | − | 0.603369i | \(-0.206175\pi\) | |||||||
\(522\) | −4.79365 | + | 4.79365i | −0.209813 | + | 0.209813i | ||||
\(523\) | − | 43.9195i | − | 1.92046i | −0.279204 | − | 0.960232i | \(-0.590070\pi\) | ||
0.279204 | − | 0.960232i | \(-0.409930\pi\) | |||||||
\(524\) | 11.9955 | + | 11.9955i | 0.524026 | + | 0.524026i | ||||
\(525\) | 3.34659 | + | 2.53811i | 0.146057 | + | 0.110772i | ||||
\(526\) | 5.00770 | − | 5.00770i | 0.218346 | − | 0.218346i | ||||
\(527\) | −29.5577 | − | 29.5577i | −1.28755 | − | 1.28755i | ||||
\(528\) | 1.56874 | − | 1.56874i | 0.0682707 | − | 0.0682707i | ||||
\(529\) | 8.04553 | 0.349806 | ||||||||
\(530\) | −8.01096 | + | 23.8197i | −0.347974 | + | 1.03466i | ||||
\(531\) | −1.00057 | + | 1.00057i | −0.0434211 | + | 0.0434211i | ||||
\(532\) | 1.99516i | 0.0865012i | ||||||||
\(533\) | 0.956723 | 0.0414403 | ||||||||
\(534\) | − | 17.7998i | − | 0.770274i | ||||||
\(535\) | 5.58056 | − | 16.5932i | 0.241269 | − | 0.717386i | ||||
\(536\) | −5.39694 | − | 5.39694i | −0.233112 | − | 0.233112i | ||||
\(537\) | −24.6499 | −1.06372 | ||||||||
\(538\) | 12.0216 | 0.518288 | ||||||||
\(539\) | 13.9642 | 0.601481 | ||||||||
\(540\) | 2.11942 | + | 0.712794i | 0.0912052 | + | 0.0306738i | ||||
\(541\) | 6.90527 | − | 6.90527i | 0.296881 | − | 0.296881i | −0.542910 | − | 0.839791i | \(-0.682678\pi\) |
0.839791 | + | 0.542910i | \(0.182678\pi\) | |||||||
\(542\) | − | 11.5944i | − | 0.498021i | ||||||
\(543\) | −2.39964 | − | 2.39964i | −0.102979 | − | 0.102979i | ||||
\(544\) | 5.23332i | 0.224377i | ||||||||
\(545\) | 10.0441 | − | 29.8650i | 0.430241 | − | 1.27928i | ||||
\(546\) | 0.137212i | 0.00587214i | ||||||||
\(547\) | 19.7636i | 0.845030i | 0.906356 | + | 0.422515i | \(0.138853\pi\) | ||||
−0.906356 | + | 0.422515i | \(0.861147\pi\) | |||||||
\(548\) | 2.69211 | + | 2.69211i | 0.115001 | + | 0.115001i | ||||
\(549\) | 7.50634 | − | 7.50634i | 0.320363 | − | 0.320363i | ||||
\(550\) | 6.70311 | − | 8.83831i | 0.285822 | − | 0.376867i | ||||
\(551\) | −16.1013 | −0.685936 | ||||||||
\(552\) | 2.73445 | + | 2.73445i | 0.116386 | + | 0.116386i | ||||
\(553\) | − | 1.29173i | − | 0.0549299i | ||||||
\(554\) | −1.48164 | −0.0629487 | ||||||||
\(555\) | −5.40664 | − | 12.4807i | −0.229499 | − | 0.529777i | ||||
\(556\) | 1.30467 | 0.0553305 | ||||||||
\(557\) | 32.5498i | 1.37918i | 0.724201 | + | 0.689589i | \(0.242209\pi\) | ||||
−0.724201 | + | 0.689589i | \(0.757791\pi\) | |||||||
\(558\) | 5.64797 | + | 5.64797i | 0.239098 | + | 0.239098i | ||||
\(559\) | 1.46060 | 0.0617767 | ||||||||
\(560\) | 0.598775 | − | 1.78039i | 0.0253029 | − | 0.0752354i | ||||
\(561\) | 8.20973 | − | 8.20973i | 0.346615 | − | 0.346615i | ||||
\(562\) | 2.20394 | + | 2.20394i | 0.0929675 | + | 0.0929675i | ||||
\(563\) | 9.04112i | 0.381038i | 0.981684 | + | 0.190519i | \(0.0610170\pi\) | ||||
−0.981684 | + | 0.190519i | \(0.938983\pi\) | |||||||
\(564\) | − | 11.2754i | − | 0.474780i | ||||||
\(565\) | −18.6861 | − | 37.6242i | −0.786132 | − | 1.58286i | ||||
\(566\) | 12.9583i | 0.544678i | ||||||||
\(567\) | −0.593998 | − | 0.593998i | −0.0249456 | − | 0.0249456i | ||||
\(568\) | − | 14.9530i | − | 0.627415i | ||||||
\(569\) | −20.6513 | + | 20.6513i | −0.865749 | + | 0.865749i | −0.991999 | − | 0.126249i | \(-0.959706\pi\) |
0.126249 | + | 0.991999i | \(0.459706\pi\) | |||||||
\(570\) | 2.36233 | + | 4.75651i | 0.0989471 | + | 0.199228i | ||||
\(571\) | 18.5622 | 0.776802 | 0.388401 | − | 0.921490i | \(-0.373027\pi\) | ||||
0.388401 | + | 0.921490i | \(0.373027\pi\) | |||||||
\(572\) | 0.362376 | 0.0151517 | ||||||||
\(573\) | −1.53301 | −0.0640423 | ||||||||
\(574\) | 3.47919 | + | 3.47919i | 0.145219 | + | 0.145219i | ||||
\(575\) | 15.4060 | + | 11.6841i | 0.642473 | + | 0.487261i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | 43.8508 | 1.82553 | 0.912766 | − | 0.408483i | \(-0.133942\pi\) | ||||
0.912766 | + | 0.408483i | \(0.133942\pi\) | |||||||
\(578\) | 10.3877i | 0.432070i | ||||||||
\(579\) | −2.85699 | + | 2.85699i | −0.118732 | + | 0.118732i | ||||
\(580\) | 14.3681 | + | 4.83221i | 0.596601 | + | 0.200646i | ||||
\(581\) | −4.84810 | −0.201133 | ||||||||
\(582\) | −9.04452 | + | 9.04452i | −0.374907 | + | 0.374907i | ||||
\(583\) | −17.6308 | − | 17.6308i | −0.730193 | − | 0.730193i | ||||
\(584\) | 0.258848 | − | 0.258848i | 0.0107112 | − | 0.0107112i | ||||
\(585\) | 0.162463 | + | 0.327117i | 0.00671703 | + | 0.0135246i | ||||
\(586\) | −15.2639 | − | 15.2639i | −0.630548 | − | 0.630548i | ||||
\(587\) | 29.8581i | 1.23238i | 0.787599 | + | 0.616188i | \(0.211324\pi\) | ||||
−0.787599 | + | 0.616188i | \(0.788676\pi\) | |||||||
\(588\) | 4.45077 | − | 4.45077i | 0.183546 | − | 0.183546i | ||||
\(589\) | 18.9708i | 0.781678i | ||||||||
\(590\) | 2.99902 | + | 1.00862i | 0.123468 | + | 0.0415241i | ||||
\(591\) | 17.4717i | 0.718692i | ||||||||
\(592\) | −4.51960 | + | 4.07102i | −0.185755 | + | 0.167318i | ||||
\(593\) | 28.1350 | − | 28.1350i | 1.15537 | − | 1.15537i | 0.169905 | − | 0.985460i | \(-0.445654\pi\) |
0.985460 | − | 0.169905i | \(-0.0543461\pi\) | |||||||
\(594\) | −1.56874 | + | 1.56874i | −0.0643662 | + | 0.0643662i | ||||
\(595\) | 3.13359 | − | 9.31738i | 0.128464 | − | 0.381975i | ||||
\(596\) | − | 9.07290i | − | 0.371640i | ||||||
\(597\) | 7.35194 | 0.300895 | ||||||||
\(598\) | 0.631653i | 0.0258302i | ||||||||
\(599\) | − | 18.0057i | − | 0.735692i | −0.929887 | − | 0.367846i | \(-0.880095\pi\) | ||
0.929887 | − | 0.367846i | \(-0.119905\pi\) | |||||||
\(600\) | −0.680545 | − | 4.95347i | −0.0277831 | − | 0.202225i | ||||
\(601\) | −3.53685 | −0.144271 | −0.0721356 | − | 0.997395i | \(-0.522981\pi\) | ||||
−0.0721356 | + | 0.997395i | \(0.522981\pi\) | |||||||
\(602\) | 5.31157 | + | 5.31157i | 0.216483 | + | 0.216483i | ||||
\(603\) | 5.39694 | + | 5.39694i | 0.219780 | + | 0.219780i | ||||
\(604\) | − | 0.0622104i | − | 0.00253130i | ||||||
\(605\) | −6.04548 | − | 12.1725i | −0.245784 | − | 0.494881i | ||||
\(606\) | 3.05176 | + | 3.05176i | 0.123969 | + | 0.123969i | ||||
\(607\) | 4.86568i | 0.197492i | 0.995113 | + | 0.0987459i | \(0.0314831\pi\) | ||||
−0.995113 | + | 0.0987459i | \(0.968517\pi\) | |||||||
\(608\) | 1.67943 | − | 1.67943i | 0.0681101 | − | 0.0681101i | ||||
\(609\) | −4.02686 | − | 4.02686i | −0.163177 | − | 0.163177i | ||||
\(610\) | −22.4988 | − | 7.56671i | −0.910950 | − | 0.306367i | ||||
\(611\) | 1.30230 | − | 1.30230i | 0.0526853 | − | 0.0526853i | ||||
\(612\) | − | 5.23332i | − | 0.211545i | ||||||
\(613\) | 23.1044 | + | 23.1044i | 0.933179 | + | 0.933179i | 0.997903 | − | 0.0647244i | \(-0.0206168\pi\) |
−0.0647244 | + | 0.997903i | \(0.520617\pi\) | |||||||
\(614\) | −20.5532 | − | 20.5532i | −0.829458 | − | 0.829458i | ||||
\(615\) | 12.4139 | + | 4.17501i | 0.500578 | + | 0.168353i | ||||
\(616\) | 1.31781 | + | 1.31781i | 0.0530959 | + | 0.0530959i | ||||
\(617\) | −25.4761 | + | 25.4761i | −1.02563 | + | 1.02563i | −0.0259665 | + | 0.999663i | \(0.508266\pi\) |
−0.999663 | + | 0.0259665i | \(0.991734\pi\) | |||||||
\(618\) | −9.86320 | + | 9.86320i | −0.396756 | + | 0.396756i | ||||
\(619\) | 31.1893 | 1.25360 | 0.626801 | − | 0.779179i | \(-0.284364\pi\) | ||||
0.626801 | + | 0.779179i | \(0.284364\pi\) | |||||||
\(620\) | 5.69340 | − | 16.9287i | 0.228652 | − | 0.679873i | ||||
\(621\) | −2.73445 | − | 2.73445i | −0.109730 | − | 0.109730i | ||||
\(622\) | −0.612480 | + | 0.612480i | −0.0245582 | + | 0.0245582i | ||||
\(623\) | 14.9526 | 0.599062 | ||||||||
\(624\) | 0.115499 | − | 0.115499i | 0.00462366 | − | 0.00462366i | ||||
\(625\) | −6.74212 | − | 24.0737i | −0.269685 | − | 0.962949i | ||||
\(626\) | 3.56579 | 0.142517 | ||||||||
\(627\) | −5.26920 | −0.210431 | ||||||||
\(628\) | 5.08868 | + | 5.08868i | 0.203060 | + | 0.203060i | ||||
\(629\) | −23.6525 | + | 21.3050i | −0.943089 | + | 0.849484i | ||||
\(630\) | −0.598775 | + | 1.78039i | −0.0238558 | + | 0.0709326i | ||||
\(631\) | 19.9604 | + | 19.9604i | 0.794612 | + | 0.794612i | 0.982240 | − | 0.187628i | \(-0.0600800\pi\) |
−0.187628 | + | 0.982240i | \(0.560080\pi\) | |||||||
\(632\) | −1.08732 | + | 1.08732i | −0.0432512 | + | 0.0432512i | ||||
\(633\) | 10.7698 | + | 10.7698i | 0.428060 | + | 0.428060i | ||||
\(634\) | 4.20992 | + | 4.20992i | 0.167197 | + | 0.167197i | ||||
\(635\) | 4.64956 | − | 13.8250i | 0.184512 | − | 0.548627i | ||||
\(636\) | −11.2388 | −0.445648 | ||||||||
\(637\) | 1.02812 | 0.0407355 | ||||||||
\(638\) | −10.6349 | + | 10.6349i | −0.421039 | + | 0.421039i | ||||
\(639\) | 14.9530i | 0.591533i | ||||||||
\(640\) | −2.00267 | + | 0.994632i | −0.0791627 | + | 0.0393163i | ||||
\(641\) | −0.397393 | −0.0156961 | −0.00784804 | − | 0.999969i | \(-0.502498\pi\) | ||||
−0.00784804 | + | 0.999969i | \(0.502498\pi\) | |||||||
\(642\) | 7.82913 | 0.308991 | ||||||||
\(643\) | 21.4396 | 0.845495 | 0.422748 | − | 0.906247i | \(-0.361066\pi\) | ||||
0.422748 | + | 0.906247i | \(0.361066\pi\) | |||||||
\(644\) | −2.29705 | + | 2.29705i | −0.0905165 | + | 0.0905165i | ||||
\(645\) | 18.9520 | + | 6.37385i | 0.746233 | + | 0.250970i | ||||
\(646\) | 8.78902 | − | 8.78902i | 0.345800 | − | 0.345800i | ||||
\(647\) | − | 5.00707i | − | 0.196848i | −0.995145 | − | 0.0984241i | \(-0.968620\pi\) | ||
0.995145 | − | 0.0984241i | \(-0.0313802\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −2.21980 | + | 2.21980i | −0.0871348 | + | 0.0871348i | ||||
\(650\) | 0.493518 | − | 0.650723i | 0.0193574 | − | 0.0255234i | ||||
\(651\) | −4.74452 | + | 4.74452i | −0.185953 | + | 0.185953i | ||||
\(652\) | 19.1109 | 0.748441 | ||||||||
\(653\) | −28.3624 | −1.10991 | −0.554954 | − | 0.831881i | \(-0.687264\pi\) | ||||
−0.554954 | + | 0.831881i | \(0.687264\pi\) | |||||||
\(654\) | 14.0912 | 0.551008 | ||||||||
\(655\) | −12.0920 | + | 35.9542i | −0.472473 | + | 1.40485i | ||||
\(656\) | − | 5.85724i | − | 0.228687i | ||||||
\(657\) | −0.258848 | + | 0.258848i | −0.0100986 | + | 0.0100986i | ||||
\(658\) | 9.47178 | 0.369249 | ||||||||
\(659\) | 13.0798 | 0.509518 | 0.254759 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254759 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(660\) | 4.70200 | + | 1.58136i | 0.183025 | + | 0.0615543i | ||||
\(661\) | −21.4953 | − | 21.4953i | −0.836072 | − | 0.836072i | 0.152267 | − | 0.988339i | \(-0.451343\pi\) |
−0.988339 | + | 0.152267i | \(0.951343\pi\) | |||||||
\(662\) | 14.0919 | + | 14.0919i | 0.547697 | + | 0.547697i | ||||
\(663\) | 0.604443 | − | 0.604443i | 0.0234746 | − | 0.0234746i | ||||
\(664\) | 4.08091 | + | 4.08091i | 0.158370 | + | 0.158370i | ||||
\(665\) | −3.99566 | + | 1.98445i | −0.154945 | + | 0.0769537i | ||||
\(666\) | 4.51960 | − | 4.07102i | 0.175131 | − | 0.157749i | ||||
\(667\) | −18.5375 | − | 18.5375i | −0.717776 | − | 0.717776i | ||||
\(668\) | 7.28469 | 0.281853 | ||||||||
\(669\) | −13.0931 | −0.506208 | ||||||||
\(670\) | 5.44035 | − | 16.1763i | 0.210179 | − | 0.624945i | ||||
\(671\) | 16.6531 | − | 16.6531i | 0.642885 | − | 0.642885i | ||||
\(672\) | 0.840040 | 0.0324052 | ||||||||
\(673\) | 17.5609 | − | 17.5609i | 0.676922 | − | 0.676922i | −0.282380 | − | 0.959303i | \(-0.591124\pi\) |
0.959303 | + | 0.282380i | \(0.0911240\pi\) | |||||||
\(674\) | −17.5011 | − | 17.5011i | −0.674119 | − | 0.674119i | ||||
\(675\) | 0.680545 | + | 4.95347i | 0.0261942 | + | 0.190659i | ||||
\(676\) | −12.9733 | −0.498974 | ||||||||
\(677\) | 27.0147 | − | 27.0147i | 1.03826 | − | 1.03826i | 0.0390206 | − | 0.999238i | \(-0.487576\pi\) |
0.999238 | − | 0.0390206i | \(-0.0124238\pi\) | |||||||
\(678\) | 13.2844 | − | 13.2844i | 0.510184 | − | 0.510184i | ||||
\(679\) | −7.59776 | − | 7.59776i | −0.291575 | − | 0.291575i | ||||
\(680\) | −10.4806 | + | 5.20523i | −0.401914 | + | 0.199612i | ||||
\(681\) | 8.86099 | + | 8.86099i | 0.339554 | + | 0.339554i | ||||
\(682\) | 12.5302 | + | 12.5302i | 0.479807 | + | 0.479807i | ||||
\(683\) | − | 24.3629i | − | 0.932219i | −0.884727 | − | 0.466109i | \(-0.845655\pi\) | ||
0.884727 | − | 0.466109i | \(-0.154345\pi\) | |||||||
\(684\) | −1.67943 | + | 1.67943i | −0.0642148 | + | 0.0642148i | ||||
\(685\) | −2.71376 | + | 8.06907i | −0.103687 | + | 0.308303i | ||||
\(686\) | 7.89681 | + | 7.89681i | 0.301502 | + | 0.301502i | ||||
\(687\) | 5.21481 | − | 5.21481i | 0.198958 | − | 0.198958i | ||||
\(688\) | − | 8.94207i | − | 0.340913i | ||||||
\(689\) | −1.29807 | − | 1.29807i | −0.0494526 | − | 0.0494526i | ||||
\(690\) | −2.75645 | + | 8.19600i | −0.104936 | + | 0.312016i | ||||
\(691\) | 37.9850i | 1.44502i | 0.691361 | + | 0.722509i | \(0.257011\pi\) | ||||
−0.691361 | + | 0.722509i | \(0.742989\pi\) | |||||||
\(692\) | −8.94815 | − | 8.94815i | −0.340158 | − | 0.340158i | ||||
\(693\) | −1.31781 | − | 1.31781i | −0.0500593 | − | 0.0500593i | ||||
\(694\) | −19.3835 | −0.735787 | ||||||||
\(695\) | 1.29767 | + | 2.61284i | 0.0492234 | + | 0.0991105i | ||||
\(696\) | 6.77925i | 0.256967i | ||||||||
\(697\) | − | 30.6528i | − | 1.16106i | ||||||
\(698\) | −14.5408 | −0.550377 | ||||||||
\(699\) | − | 26.0877i | − | 0.986726i | ||||||
\(700\) | 4.16111 | − | 0.571685i | 0.157275 | − | 0.0216077i | ||||
\(701\) | −2.11618 | + | 2.11618i | −0.0799271 | + | 0.0799271i | −0.745940 | − | 0.666013i | \(-0.768000\pi\) |
0.666013 | + | 0.745940i | \(0.268000\pi\) | |||||||
\(702\) | −0.115499 | + | 0.115499i | −0.00435923 | + | 0.00435923i | ||||
\(703\) | 14.4274 | + | 0.753367i | 0.544139 | + | 0.0284138i | ||||
\(704\) | − | 2.21854i | − | 0.0836142i | ||||||
\(705\) | 22.5810 | − | 11.2149i | 0.850448 | − | 0.422377i | ||||
\(706\) | 26.3150i | 0.990376i | ||||||||
\(707\) | −2.56360 | + | 2.56360i | −0.0964141 | + | 0.0964141i | ||||
\(708\) | 1.41502i | 0.0531797i | ||||||||
\(709\) | −10.3418 | − | 10.3418i | −0.388395 | − | 0.388395i | 0.485720 | − | 0.874114i | \(-0.338557\pi\) |
−0.874114 | + | 0.485720i | \(0.838557\pi\) | |||||||
\(710\) | 29.9461 | − | 14.8728i | 1.12386 | − | 0.558165i | ||||
\(711\) | 1.08732 | − | 1.08732i | 0.0407776 | − | 0.0407776i | ||||
\(712\) | −12.5864 | − | 12.5864i | −0.471695 | − | 0.471695i | ||||
\(713\) | −21.8413 | + | 21.8413i | −0.817962 | + | 0.817962i | ||||
\(714\) | 4.39620 | 0.164524 | ||||||||
\(715\) | 0.360431 | + | 0.725721i | 0.0134793 | + | 0.0271404i | ||||
\(716\) | −17.4301 | + | 17.4301i | −0.651395 | + | 0.651395i | ||||
\(717\) | 15.4753i | 0.577937i | ||||||||
\(718\) | 6.12864 | 0.228719 | ||||||||
\(719\) | 8.49669i | 0.316873i | 0.987369 | + | 0.158436i | \(0.0506453\pi\) | ||||
−0.987369 | + | 0.158436i | \(0.949355\pi\) | |||||||
\(720\) | 2.00267 | − | 0.994632i | 0.0746353 | − | 0.0370678i | ||||
\(721\) | −8.28548 | − | 8.28548i | −0.308568 | − | 0.308568i | ||||
\(722\) | 13.3590 | 0.497170 | ||||||||
\(723\) | −16.2047 | −0.602658 | ||||||||
\(724\) | −3.39361 | −0.126122 | ||||||||
\(725\) | 4.61359 | + | 33.5808i | 0.171344 | + | 1.24716i | ||||
\(726\) | 4.29787 | − | 4.29787i | 0.159509 | − | 0.159509i | ||||
\(727\) | 4.28583i | 0.158953i | 0.996837 | + | 0.0794764i | \(0.0253248\pi\) | ||||
−0.996837 | + | 0.0794764i | \(0.974675\pi\) | |||||||
\(728\) | 0.0970237 | + | 0.0970237i | 0.00359594 | + | 0.00359594i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0.775847 | + | 0.260930i | 0.0287154 | + | 0.00965745i | ||||
\(731\) | − | 46.7967i | − | 1.73084i | ||||||
\(732\) | − | 10.6156i | − | 0.392363i | ||||||
\(733\) | 2.83283 | + | 2.83283i | 0.104633 | + | 0.104633i | 0.757485 | − | 0.652852i | \(-0.226428\pi\) |
−0.652852 | + | 0.757485i | \(0.726428\pi\) | |||||||
\(734\) | −21.0105 | + | 21.0105i | −0.775512 | + | 0.775512i | ||||
\(735\) | 13.3403 | + | 4.48656i | 0.492065 | + | 0.165489i | ||||
\(736\) | 3.86710 | 0.142543 | ||||||||
\(737\) | 11.9733 | + | 11.9733i | 0.441042 | + | 0.441042i | ||||
\(738\) | 5.85724i | 0.215608i | ||||||||
\(739\) | −41.7623 | −1.53625 | −0.768126 | − | 0.640299i | \(-0.778810\pi\) | ||||
−0.768126 | + | 0.640299i | \(0.778810\pi\) | |||||||
\(740\) | −12.6483 | − | 5.00213i | −0.464960 | − | 0.183882i | ||||
\(741\) | −0.387946 | −0.0142515 | ||||||||
\(742\) | − | 9.44106i | − | 0.346592i | ||||||
\(743\) | −36.8937 | − | 36.8937i | −1.35350 | − | 1.35350i | −0.881712 | − | 0.471788i | \(-0.843609\pi\) |
−0.471788 | − | 0.881712i | \(-0.656391\pi\) | |||||||
\(744\) | 7.98744 | 0.292834 | ||||||||
\(745\) | 18.1701 | − | 9.02420i | 0.665700 | − | 0.330621i | ||||
\(746\) | −2.15543 | + | 2.15543i | −0.0789157 | + | 0.0789157i | ||||
\(747\) | −4.08091 | − | 4.08091i | −0.149313 | − | 0.149313i | ||||
\(748\) | − | 11.6103i | − | 0.424515i | ||||||
\(749\) | 6.57679i | 0.240311i | ||||||||
\(750\) | 9.24330 | − | 6.28979i | 0.337517 | − | 0.229671i | ||||
\(751\) | − | 26.9870i | − | 0.984768i | −0.870378 | − | 0.492384i | \(-0.836125\pi\) | ||
0.870378 | − | 0.492384i | \(-0.163875\pi\) | |||||||
\(752\) | −7.97291 | − | 7.97291i | −0.290742 | − | 0.290742i | ||||
\(753\) | 6.94324i | 0.253026i | ||||||||
\(754\) | −0.782996 | + | 0.782996i | −0.0285150 | + | 0.0285150i | ||||
\(755\) | 0.124587 | − | 0.0618764i | 0.00453419 | − | 0.00225191i | ||||
\(756\) | −0.840040 | −0.0305520 | ||||||||
\(757\) | −36.8457 | −1.33918 | −0.669590 | − | 0.742731i | \(-0.733530\pi\) | ||||
−0.669590 | + | 0.742731i | \(0.733530\pi\) | |||||||
\(758\) | −37.8733 | −1.37562 | ||||||||
\(759\) | −6.06648 | − | 6.06648i | −0.220199 | − | 0.220199i | ||||
\(760\) | 5.03378 | + | 1.69294i | 0.182594 | + | 0.0614094i | ||||
\(761\) | − | 38.2000i | − | 1.38475i | −0.721538 | − | 0.692374i | \(-0.756565\pi\) | ||
0.721538 | − | 0.692374i | \(-0.243435\pi\) | |||||||
\(762\) | 6.52301 | 0.236304 | ||||||||
\(763\) | 11.8371i | 0.428533i | ||||||||
\(764\) | −1.08400 | + | 1.08400i | −0.0392177 | + | 0.0392177i | ||||
\(765\) | 10.4806 | − | 5.20523i | 0.378929 | − | 0.188196i | ||||
\(766\) | −33.6750 | −1.21673 | ||||||||
\(767\) | −0.163433 | + | 0.163433i | −0.00590124 | + | 0.00590124i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | −23.0452 | + | 23.0452i | −0.831031 | + | 0.831031i | −0.987658 | − | 0.156627i | \(-0.949938\pi\) |
0.156627 | + | 0.987658i | \(0.449938\pi\) | |||||||
\(770\) | −1.32840 | + | 3.94987i | −0.0478724 | + | 0.142343i | ||||
\(771\) | −14.2413 | − | 14.2413i | −0.512887 | − | 0.512887i | ||||
\(772\) | 4.04039i | 0.145417i | ||||||||
\(773\) | −15.2548 | + | 15.2548i | −0.548676 | + | 0.548676i | −0.926058 | − | 0.377382i | \(-0.876824\pi\) |
0.377382 | + | 0.926058i | \(0.376824\pi\) | |||||||
\(774\) | 8.94207i | 0.321416i | ||||||||
\(775\) | 39.5655 | − | 5.43582i | 1.42124 | − | 0.195260i | ||||
\(776\) | 12.7909i | 0.459166i | ||||||||
\(777\) | 3.41982 | + | 3.79665i | 0.122685 | + | 0.136204i | ||||
\(778\) | −6.96706 | + | 6.96706i | −0.249781 | + | 0.249781i | ||||
\(779\) | −9.83686 | + | 9.83686i | −0.352442 | + | 0.352442i | ||||
\(780\) | 0.346186 | + | 0.116428i | 0.0123954 | + | 0.00416879i | ||||
\(781\) | 33.1738i | 1.18705i | ||||||||
\(782\) | 20.2378 | 0.723702 | ||||||||
\(783\) | − | 6.77925i | − | 0.242271i | ||||||
\(784\) | − | 6.29433i | − | 0.224798i | ||||||
\(785\) | −5.12961 | + | 15.2523i | −0.183084 | + | 0.544379i | ||||
\(786\) | −16.9642 | −0.605093 | ||||||||
\(787\) | −24.1643 | − | 24.1643i | −0.861365 | − | 0.861365i | 0.130132 | − | 0.991497i | \(-0.458460\pi\) |
−0.991497 | + | 0.130132i | \(0.958460\pi\) | |||||||
\(788\) | 12.3544 | + | 12.3544i | 0.440107 | + | 0.440107i | ||||
\(789\) | 7.08196i | 0.252124i | ||||||||
\(790\) | −3.25902 | − | 1.09606i | −0.115951 | − | 0.0389961i | ||||
\(791\) | 11.1594 | + | 11.1594i | 0.396784 | + | 0.396784i | ||||
\(792\) | 2.21854i | 0.0788322i | ||||||||
\(793\) | 1.22609 | − | 1.22609i | 0.0435396 | − | 0.0435396i | ||||
\(794\) | −2.14584 | − | 2.14584i | −0.0761529 | − | 0.0761529i | ||||
\(795\) | −11.1785 | − | 22.5077i | −0.396460 | − | 0.798266i | ||||
\(796\) | 5.19861 | − | 5.19861i | 0.184260 | − | 0.184260i | ||||
\(797\) | 32.2456i | 1.14220i | 0.820881 | + | 0.571099i | \(0.193483\pi\) | ||||
−0.820881 | + | 0.571099i | \(0.806517\pi\) | |||||||
\(798\) | −1.41079 | − | 1.41079i | −0.0499415 | − | 0.0499415i | ||||
\(799\) | −41.7248 | − | 41.7248i | −1.47612 | − | 1.47612i | ||||
\(800\) | −3.98385 | − | 3.02141i | −0.140850 | − | 0.106823i | ||||
\(801\) | 12.5864 | + | 12.5864i | 0.444718 | + | 0.444718i | ||||
\(802\) | −3.17371 | + | 3.17371i | −0.112068 | + | 0.112068i | ||||
\(803\) | −0.574263 | + | 0.574263i | −0.0202653 | + | 0.0202653i | ||||
\(804\) | 7.63243 | 0.269175 | ||||||||
\(805\) | −6.88497 | − | 2.31552i | −0.242663 | − | 0.0816115i | ||||
\(806\) | 0.922541 | + | 0.922541i | 0.0324951 | + | 0.0324951i | ||||
\(807\) | −8.50055 | + | 8.50055i | −0.299234 | + | 0.299234i | ||||
\(808\) | 4.31584 | 0.151831 | ||||||||
\(809\) | −16.4950 | + | 16.4950i | −0.579933 | + | 0.579933i | −0.934885 | − | 0.354952i | \(-0.884497\pi\) |
0.354952 | + | 0.934885i | \(0.384497\pi\) | |||||||
\(810\) | −2.00267 | + | 0.994632i | −0.0703668 | + | 0.0349478i | ||||
\(811\) | −36.1279 | −1.26862 | −0.634310 | − | 0.773078i | \(-0.718716\pi\) | ||||
−0.634310 | + | 0.773078i | \(0.718716\pi\) | |||||||
\(812\) | −5.69484 | −0.199850 | ||||||||
\(813\) | 8.19846 | + | 8.19846i | 0.287533 | + | 0.287533i | ||||
\(814\) | 10.0269 | − | 9.03170i | 0.351443 | − | 0.316561i | ||||
\(815\) | 19.0083 | + | 38.2729i | 0.665833 | + | 1.34064i | ||||
\(816\) | −3.70052 | − | 3.70052i | −0.129544 | − | 0.129544i | ||||
\(817\) | −15.0176 | + | 15.0176i | −0.525400 | + | 0.525400i | ||||
\(818\) | −7.23143 | − | 7.23143i | −0.252841 | − | 0.252841i | ||||
\(819\) | −0.0970237 | − | 0.0970237i | −0.00339028 | − | 0.00339028i | ||||
\(820\) | 11.7302 | − | 5.82580i | 0.409635 | − | 0.203446i | ||||
\(821\) | −49.5091 | −1.72788 | −0.863939 | − | 0.503597i | \(-0.832010\pi\) | ||||
−0.863939 | + | 0.503597i | \(0.832010\pi\) | |||||||
\(822\) | −3.80721 | −0.132792 | ||||||||
\(823\) | 5.45635 | − | 5.45635i | 0.190196 | − | 0.190196i | −0.605585 | − | 0.795781i | \(-0.707061\pi\) |
0.795781 | + | 0.605585i | \(0.207061\pi\) | |||||||
\(824\) | 13.9487i | 0.485925i | ||||||||
\(825\) | 1.50981 | + | 10.9894i | 0.0525650 | + | 0.382603i | ||||
\(826\) | −1.18867 | −0.0413593 | ||||||||
\(827\) | −9.24721 | −0.321557 | −0.160778 | − | 0.986991i | \(-0.551400\pi\) | ||||
−0.160778 | + | 0.986991i | \(0.551400\pi\) | |||||||
\(828\) | −3.86710 | −0.134391 | ||||||||
\(829\) | 15.9624 | − | 15.9624i | 0.554396 | − | 0.554396i | −0.373311 | − | 0.927706i | \(-0.621777\pi\) |
0.927706 | + | 0.373311i | \(0.121777\pi\) | |||||||
\(830\) | −4.11373 | + | 12.2317i | −0.142790 | + | 0.424570i | ||||
\(831\) | 1.04768 | − | 1.04768i | 0.0363435 | − | 0.0363435i | ||||
\(832\) | − | 0.163340i | − | 0.00566280i | ||||||
\(833\) | − | 32.9403i | − | 1.14131i | ||||||
\(834\) | −0.922543 | + | 0.922543i | −0.0319451 | + | 0.0319451i | ||||
\(835\) | 7.24559 | + | 14.5889i | 0.250744 | + | 0.504869i | ||||
\(836\) | −3.72588 | + | 3.72588i | −0.128862 | + | 0.128862i | ||||
\(837\) | −7.98744 | −0.276086 | ||||||||
\(838\) | −1.66410 | −0.0574854 | ||||||||
\(839\) | 8.15311 | 0.281477 | 0.140738 | − | 0.990047i | \(-0.455052\pi\) | ||||
0.140738 | + | 0.990047i | \(0.455052\pi\) | |||||||
\(840\) | 0.835531 | + | 1.68233i | 0.0288286 | + | 0.0580458i | ||||
\(841\) | − | 16.9582i | − | 0.584766i | ||||||
\(842\) | 1.49656 | − | 1.49656i | 0.0515750 | − | 0.0515750i | ||||
\(843\) | −3.11684 | −0.107350 | ||||||||
\(844\) | 15.2308 | 0.524264 | ||||||||
\(845\) | −12.9037 | − | 25.9813i | −0.443900 | − | 0.893785i | ||||
\(846\) | 7.97291 | + | 7.97291i | 0.274114 | + | 0.274114i | ||||
\(847\) | 3.61038 | + | 3.61038i | 0.124054 | + | 0.124054i | ||||
\(848\) | −7.94704 | + | 7.94704i | −0.272903 | + | 0.272903i | ||||
\(849\) | −9.16290 | − | 9.16290i | −0.314470 | − | 0.314470i | ||||
\(850\) | −20.8488 | − | 15.8120i | −0.715107 | − | 0.542348i | ||||
\(851\) | 15.7430 | + | 17.4778i | 0.539664 | + | 0.599130i | ||||
\(852\) | 10.5734 | + | 10.5734i | 0.362238 | + | 0.362238i | ||||
\(853\) | 39.7229 | 1.36009 | 0.680044 | − | 0.733172i | \(-0.261961\pi\) | ||||
0.680044 | + | 0.733172i | \(0.261961\pi\) | |||||||
\(854\) | 8.91750 | 0.305151 | ||||||||
\(855\) | −5.03378 | − | 1.69294i | −0.172152 | − | 0.0578974i | ||||
\(856\) | 5.53603 | − | 5.53603i | 0.189218 | − | 0.189218i | ||||
\(857\) | 36.5325 | 1.24793 | 0.623964 | − | 0.781453i | \(-0.285521\pi\) | ||||
0.623964 | + | 0.781453i | \(0.285521\pi\) | |||||||
\(858\) | −0.256238 | + | 0.256238i | −0.00874784 | + | 0.00874784i | ||||
\(859\) | 7.62822 | + | 7.62822i | 0.260272 | + | 0.260272i | 0.825164 | − | 0.564893i | \(-0.191082\pi\) |
−0.564893 | + | 0.825164i | \(0.691082\pi\) | |||||||
\(860\) | 17.9081 | − | 8.89407i | 0.610660 | − | 0.303285i | ||||
\(861\) | −4.92032 | −0.167684 | ||||||||
\(862\) | −1.82566 | + | 1.82566i | −0.0621824 | + | 0.0621824i | ||||
\(863\) | −2.11127 | + | 2.11127i | −0.0718684 | + | 0.0718684i | −0.742127 | − | 0.670259i | \(-0.766183\pi\) |
0.670259 | + | 0.742127i | \(0.266183\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | 9.02011 | − | 26.8203i | 0.306693 | − | 0.911919i | ||||
\(866\) | 8.92738 | + | 8.92738i | 0.303365 | + | 0.303365i | ||||
\(867\) | −7.34519 | − | 7.34519i | −0.249456 | − | 0.249456i | ||||
\(868\) | 6.70977i | 0.227744i | ||||||||
\(869\) | 2.41225 | − | 2.41225i | 0.0818300 | − | 0.0818300i | ||||
\(870\) | −13.5766 | + | 6.74286i | −0.460291 | + | 0.228604i | ||||
\(871\) | 0.881537 | + | 0.881537i | 0.0298698 | + | 0.0298698i | ||||
\(872\) | 9.96395 | − | 9.96395i | 0.337422 | − | 0.337422i | ||||
\(873\) | − | 12.7909i | − | 0.432906i | ||||||
\(874\) | −6.49454 | − | 6.49454i | −0.219681 | − | 0.219681i | ||||
\(875\) | 5.28368 | + | 7.76474i | 0.178621 | + | 0.262496i | ||||
\(876\) | 0.366066i | 0.0123682i | ||||||||
\(877\) | −14.3455 | − | 14.3455i | −0.484412 | − | 0.484412i | 0.422126 | − | 0.906537i | \(-0.361284\pi\) |
−0.906537 | + | 0.422126i | \(0.861284\pi\) | |||||||
\(878\) | −12.1430 | − | 12.1430i | −0.409807 | − | 0.409807i | ||||
\(879\) | 21.5865 | 0.728094 | ||||||||
\(880\) | 4.44300 | − | 2.20663i | 0.149774 | − | 0.0743854i | ||||
\(881\) | 55.0941i | 1.85617i | 0.372373 | + | 0.928083i | \(0.378544\pi\) | ||||
−0.372373 | + | 0.928083i | \(0.621456\pi\) | |||||||
\(882\) | 6.29433i | 0.211941i | ||||||||
\(883\) | −11.4724 | −0.386078 | −0.193039 | − | 0.981191i | \(-0.561834\pi\) | ||||
−0.193039 | + | 0.981191i | \(0.561834\pi\) | |||||||
\(884\) | − | 0.854812i | − | 0.0287504i | ||||||
\(885\) | −2.83383 | + | 1.40743i | −0.0952580 | + | 0.0473101i | ||||
\(886\) | 20.3377 | − | 20.3377i | 0.683257 | − | 0.683257i | ||||
\(887\) | 5.30617 | − | 5.30617i | 0.178164 | − | 0.178164i | −0.612391 | − | 0.790555i | \(-0.709792\pi\) |
0.790555 | + | 0.612391i | \(0.209792\pi\) | |||||||
\(888\) | 0.317197 | − | 6.07449i | 0.0106444 | − | 0.203846i | ||||
\(889\) | 5.47959i | 0.183779i | ||||||||
\(890\) | 12.6876 | − | 37.7253i | 0.425290 | − | 1.26455i | ||||
\(891\) | − | 2.21854i | − | 0.0743237i | ||||||
\(892\) | −9.25821 | + | 9.25821i | −0.309988 | + | 0.309988i | ||||
\(893\) | 26.7800i | 0.896157i | ||||||||
\(894\) | 6.41551 | + | 6.41551i | 0.214567 | + | 0.214567i | ||||
\(895\) | −52.2435 | − | 17.5703i | −1.74631 | − | 0.587311i | ||||
\(896\) | 0.593998 | − | 0.593998i | 0.0198441 | − | 0.0198441i | ||||
\(897\) | −0.446646 | − | 0.446646i | −0.0149131 | − | 0.0149131i | ||||
\(898\) | 5.53101 | − | 5.53101i | 0.184572 | − | 0.184572i | ||||
\(899\) | −54.1488 | −1.80597 | ||||||||
\(900\) | 3.98385 | + | 3.02141i | 0.132795 | + | 0.100714i | ||||
\(901\) | −41.5894 | + | 41.5894i | −1.38555 | + | 1.38555i | ||||
\(902\) | 12.9945i | 0.432669i | ||||||||
\(903\) | −7.51170 | −0.249974 | ||||||||
\(904\) | − | 18.7870i | − | 0.624846i | ||||||
\(905\) | −3.37539 | − | 6.79629i | −0.112202 | − | 0.225916i | ||||
\(906\) | 0.0439894 | + | 0.0439894i | 0.00146145 | + | 0.00146145i | ||||
\(907\) | 31.7782 | 1.05518 | 0.527589 | − | 0.849500i | \(-0.323096\pi\) | ||||
0.527589 | + | 0.849500i | \(0.323096\pi\) | |||||||
\(908\) | 12.5313 | 0.415867 | ||||||||
\(909\) | −4.31584 | −0.143147 | ||||||||
\(910\) | −0.0978040 | + | 0.290810i | −0.00324217 | + | 0.00964025i | ||||
\(911\) | −33.4412 | + | 33.4412i | −1.10796 | + | 1.10796i | −0.114539 | + | 0.993419i | \(0.536539\pi\) |
−0.993419 | + | 0.114539i | \(0.963461\pi\) | |||||||
\(912\) | 2.37508i | 0.0786467i | ||||||||
\(913\) | −9.05364 | − | 9.05364i | −0.299632 | − | 0.299632i | ||||
\(914\) | − | 23.3394i | − | 0.771997i | ||||||
\(915\) | 21.2595 | − | 10.5586i | 0.702818 | − | 0.349056i | ||||
\(916\) | − | 7.37486i | − | 0.243672i | ||||||
\(917\) | − | 14.2506i | − | 0.470597i | ||||||
\(918\) | 3.70052 | + | 3.70052i | 0.122135 | + | 0.122135i | ||||
\(919\) | −2.92019 | + | 2.92019i | −0.0963281 | + | 0.0963281i | −0.753629 | − | 0.657300i | \(-0.771698\pi\) |
0.657300 | + | 0.753629i | \(0.271698\pi\) | |||||||
\(920\) | 3.84634 | + | 7.74455i | 0.126810 | + | 0.255330i | ||||
\(921\) | 29.0665 | 0.957775 | ||||||||
\(922\) | 22.7009 | + | 22.7009i | 0.747613 | + | 0.747613i | ||||
\(923\) | 2.44243i | 0.0803936i | ||||||||
\(924\) | −1.86366 | −0.0613099 | ||||||||
\(925\) | −2.56274 | − | 30.3056i | −0.0842624 | − | 0.996444i | ||||
\(926\) | 0.607463 | 0.0199625 | ||||||||
\(927\) | − | 13.9487i | − | 0.458134i | ||||||
\(928\) | 4.79365 | + | 4.79365i | 0.157359 | + | 0.157359i | ||||
\(929\) | 6.30230 | 0.206772 | 0.103386 | − | 0.994641i | \(-0.467032\pi\) | ||||
0.103386 | + | 0.994641i | \(0.467032\pi\) | |||||||
\(930\) | 7.94457 | + | 15.9962i | 0.260513 | + | 0.524538i | ||||
\(931\) | −10.5709 | + | 10.5709i | −0.346448 | + | 0.346448i | ||||
\(932\) | −18.4468 | − | 18.4468i | −0.604244 | − | 0.604244i | ||||
\(933\) | − | 0.866177i | − | 0.0283574i | ||||||
\(934\) | − | 8.76294i | − | 0.286732i | ||||||
\(935\) | 23.2517 | − | 11.5480i | 0.760411 | − | 0.377660i | ||||
\(936\) | 0.163340i | 0.00533894i | ||||||||
\(937\) | −1.82017 | − | 1.82017i | −0.0594623 | − | 0.0594623i | 0.676750 | − | 0.736213i | \(-0.263388\pi\) |
−0.736213 | + | 0.676750i | \(0.763388\pi\) | |||||||
\(938\) | 6.41155i | 0.209344i | ||||||||
\(939\) | −2.52139 | + | 2.52139i | −0.0822825 | + | 0.0822825i | ||||
\(940\) | 8.03703 | − | 23.8973i | 0.262139 | − | 0.779443i | ||||
\(941\) | −34.3191 | −1.11877 | −0.559385 | − | 0.828908i | \(-0.688962\pi\) | ||||
−0.559385 | + | 0.828908i | \(0.688962\pi\) | |||||||
\(942\) | −7.19648 | −0.234474 | ||||||||
\(943\) | −22.6505 | −0.737603 | ||||||||
\(944\) | 1.00057 | + | 1.00057i | 0.0325658 | + | 0.0325658i | ||||
\(945\) | −0.835531 | − | 1.68233i | −0.0271798 | − | 0.0547261i | ||||
\(946\) | 19.8383i | 0.644999i | ||||||||
\(947\) | 8.75872 | 0.284620 | 0.142310 | − | 0.989822i | \(-0.454547\pi\) | ||||
0.142310 | + | 0.989822i | \(0.454547\pi\) | |||||||
\(948\) | − | 1.53770i | − | 0.0499421i | ||||||
\(949\) | −0.0422803 | + | 0.0422803i | −0.00137248 | + | 0.00137248i | ||||
\(950\) | 1.61635 | + | 11.7649i | 0.0524413 | + | 0.381703i | ||||
\(951\) | −5.95373 | −0.193063 | ||||||||
\(952\) | 3.10858 | − | 3.10858i | 0.100750 | − | 0.100750i | ||||
\(953\) | −10.3887 | − | 10.3887i | −0.336523 | − | 0.336523i | 0.518534 | − | 0.855057i | \(-0.326478\pi\) |
−0.855057 | + | 0.518534i | \(0.826478\pi\) | |||||||
\(954\) | 7.94704 | − | 7.94704i | 0.257295 | − | 0.257295i | ||||
\(955\) | −3.24908 | − | 1.09272i | −0.105138 | − | 0.0353595i | ||||
\(956\) | 10.9427 | + | 10.9427i | 0.353913 | + | 0.353913i | ||||
\(957\) | − | 15.0400i | − | 0.486174i | ||||||
\(958\) | 6.88917 | − | 6.88917i | 0.222579 | − | 0.222579i | ||||
\(959\) | − | 3.19821i | − | 0.103276i | ||||||
\(960\) | 0.712794 | − | 2.11942i | 0.0230053 | − | 0.0684039i | ||||
\(961\) | 32.7992i | 1.05804i | ||||||||
\(962\) | 0.738233 | − | 0.664961i | 0.0238016 | − | 0.0214392i | ||||
\(963\) | −5.53603 | + | 5.53603i | −0.178396 | + | 0.178396i | ||||
\(964\) | −11.4584 | + | 11.4584i | −0.369051 | + | 0.369051i | ||||
\(965\) | −8.09159 | + | 4.01870i | −0.260477 | + | 0.129367i | ||||
\(966\) | − | 3.24852i | − | 0.104519i | ||||||
\(967\) | 13.8109 | 0.444129 | 0.222065 | − | 0.975032i | \(-0.428720\pi\) | ||||
0.222065 | + | 0.975032i | \(0.428720\pi\) | |||||||
\(968\) | − | 6.07810i | − | 0.195358i | ||||||
\(969\) | 12.4296i | 0.399295i | ||||||||
\(970\) | −25.6160 | + | 12.7222i | −0.822479 | + | 0.408486i | ||||
\(971\) | −47.3586 | −1.51981 | −0.759905 | − | 0.650034i | \(-0.774755\pi\) | ||||
−0.759905 | + | 0.650034i | \(0.774755\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −0.774973 | − | 0.774973i | −0.0248445 | − | 0.0248445i | ||||
\(974\) | 18.0453i | 0.578208i | ||||||||
\(975\) | 0.111160 | + | 0.809100i | 0.00355998 | + | 0.0259119i | ||||
\(976\) | −7.50634 | − | 7.50634i | −0.240272 | − | 0.240272i | ||||
\(977\) | 10.0505i | 0.321543i | 0.986992 | + | 0.160771i | \(0.0513982\pi\) | ||||
−0.986992 | + | 0.160771i | \(0.948602\pi\) | |||||||
\(978\) | −13.5135 | + | 13.5135i | −0.432113 | + | 0.432113i | ||||
\(979\) | 27.9233 | + | 27.9233i | 0.892434 | + | 0.892434i | ||||
\(980\) | 12.6055 | − | 6.26055i | 0.402668 | − | 0.199986i | ||||
\(981\) | −9.96395 | + | 9.96395i | −0.318124 | + | 0.318124i | ||||
\(982\) | 41.7594i | 1.33259i | ||||||||
\(983\) | −16.0348 | − | 16.0348i | −0.511429 | − | 0.511429i | 0.403535 | − | 0.914964i | \(-0.367781\pi\) |
−0.914964 | + | 0.403535i | \(0.867781\pi\) | |||||||
\(984\) | 4.14170 | + | 4.14170i | 0.132032 | + | 0.132032i | ||||
\(985\) | −12.4538 | + | 37.0299i | −0.396810 | + | 1.17987i | ||||
\(986\) | 25.0867 | + | 25.0867i | 0.798924 | + | 0.798924i | ||||
\(987\) | −6.69756 | + | 6.69756i | −0.213186 | + | 0.213186i | ||||
\(988\) | −0.274319 | + | 0.274319i | −0.00872725 | + | 0.00872725i | ||||
\(989\) | −34.5799 | −1.09958 | ||||||||
\(990\) | −4.44300 | + | 2.20663i | −0.141208 | + | 0.0701312i | ||||
\(991\) | 18.3342 | + | 18.3342i | 0.582404 | + | 0.582404i | 0.935563 | − | 0.353160i | \(-0.114893\pi\) |
−0.353160 | + | 0.935563i | \(0.614893\pi\) | |||||||
\(992\) | 5.64797 | − | 5.64797i | 0.179323 | − | 0.179323i | ||||
\(993\) | −19.9290 | −0.632426 | ||||||||
\(994\) | −8.88207 | + | 8.88207i | −0.281722 | + | 0.281722i | ||||
\(995\) | 15.5818 | + | 5.24042i | 0.493977 | + | 0.166132i | ||||
\(996\) | −5.77128 | −0.182870 | ||||||||
\(997\) | 36.8722 | 1.16775 | 0.583877 | − | 0.811842i | \(-0.301535\pi\) | ||||
0.583877 | + | 0.811842i | \(0.301535\pi\) | |||||||
\(998\) | −6.17352 | − | 6.17352i | −0.195419 | − | 0.195419i | ||||
\(999\) | −0.317197 | + | 6.07449i | −0.0100357 | + | 0.192188i |
(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 | 1110.2.l.b.697.4 | yes | 40 | |
5.3 | odd | 4 | 1110.2.o.b.253.17 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.o.b.487.17 | yes | 40 | ||
185.43 | even | 4 | inner | 1110.2.l.b.43.4 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.4 | ✓ | 40 | 185.43 | even | 4 | inner | |
1110.2.l.b.697.4 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.253.17 | yes | 40 | 5.3 | odd | 4 | ||
1110.2.o.b.487.17 | yes | 40 | 37.6 | odd | 4 |