Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.34947179416\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.64827.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 22.3 | ||
Root | \(-0.623490 + 1.07992i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.22 |
Dual form | 169.2.c.b.146.3 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.400969 | − | 0.694498i | 0.283528 | − | 0.491085i | −0.688723 | − | 0.725024i | \(-0.741829\pi\) |
0.972251 | + | 0.233940i | \(0.0751618\pi\) | |||||||
\(3\) | 1.12349 | − | 1.94594i | 0.648647 | − | 1.12349i | −0.334799 | − | 0.942290i | \(-0.608668\pi\) |
0.983446 | − | 0.181200i | \(-0.0579982\pi\) | |||||||
\(4\) | 0.678448 | + | 1.17511i | 0.339224 | + | 0.587553i | ||||
\(5\) | −0.246980 | −0.110453 | −0.0552263 | − | 0.998474i | \(-0.517588\pi\) | ||||
−0.0552263 | + | 0.998474i | \(0.517588\pi\) | |||||||
\(6\) | −0.900969 | − | 1.56052i | −0.367819 | − | 0.637081i | ||||
\(7\) | −1.17845 | − | 2.04113i | −0.445411 | − | 0.771475i | 0.552669 | − | 0.833401i | \(-0.313609\pi\) |
−0.998081 | + | 0.0619254i | \(0.980276\pi\) | |||||||
\(8\) | 2.69202 | 0.951773 | ||||||||
\(9\) | −1.02446 | − | 1.77441i | −0.341486 | − | 0.591471i | ||||
\(10\) | −0.0990311 | + | 0.171527i | −0.0313164 | + | 0.0542416i | ||||
\(11\) | −2.12349 | + | 3.67799i | −0.640256 | + | 1.10896i | 0.345119 | + | 0.938559i | \(0.387839\pi\) |
−0.985375 | + | 0.170397i | \(0.945495\pi\) | |||||||
\(12\) | 3.04892 | 0.880147 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.89008 | −0.505146 | ||||||||
\(15\) | −0.277479 | + | 0.480608i | −0.0716448 | + | 0.124092i | ||||
\(16\) | −0.277479 | + | 0.480608i | −0.0693698 | + | 0.120152i | ||||
\(17\) | −1.07942 | − | 1.86960i | −0.261797 | − | 0.453446i | 0.704922 | − | 0.709284i | \(-0.250982\pi\) |
−0.966720 | + | 0.255839i | \(0.917648\pi\) | |||||||
\(18\) | −1.64310 | −0.387283 | ||||||||
\(19\) | −0.0440730 | − | 0.0763367i | −0.0101110 | − | 0.0175128i | 0.860926 | − | 0.508731i | \(-0.169885\pi\) |
−0.871037 | + | 0.491218i | \(0.836552\pi\) | |||||||
\(20\) | −0.167563 | − | 0.290227i | −0.0374682 | − | 0.0648968i | ||||
\(21\) | −5.29590 | −1.15566 | ||||||||
\(22\) | 1.70291 | + | 2.94952i | 0.363061 | + | 0.628840i | ||||
\(23\) | −0.746980 | + | 1.29381i | −0.155756 | + | 0.269777i | −0.933334 | − | 0.359009i | \(-0.883115\pi\) |
0.777578 | + | 0.628786i | \(0.216448\pi\) | |||||||
\(24\) | 3.02446 | − | 5.23852i | 0.617365 | − | 1.06931i | ||||
\(25\) | −4.93900 | −0.987800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13706 | 0.411278 | ||||||||
\(28\) | 1.59903 | − | 2.76960i | 0.302188 | − | 0.523406i | ||||
\(29\) | −2.31551 | + | 4.01058i | −0.429980 | + | 0.744747i | −0.996871 | − | 0.0790460i | \(-0.974813\pi\) |
0.566891 | + | 0.823793i | \(0.308146\pi\) | |||||||
\(30\) | 0.222521 | + | 0.385418i | 0.0406266 | + | 0.0703673i | ||||
\(31\) | 6.63102 | 1.19097 | 0.595483 | − | 0.803368i | \(-0.296961\pi\) | ||||
0.595483 | + | 0.803368i | \(0.296961\pi\) | |||||||
\(32\) | 2.91454 | + | 5.04814i | 0.515223 | + | 0.892393i | ||||
\(33\) | 4.77144 | + | 8.26437i | 0.830601 | + | 1.43864i | ||||
\(34\) | −1.73125 | −0.296907 | ||||||||
\(35\) | 0.291053 | + | 0.504118i | 0.0491969 | + | 0.0852115i | ||||
\(36\) | 1.39008 | − | 2.40770i | 0.231681 | − | 0.401283i | ||||
\(37\) | 2.84601 | − | 4.92944i | 0.467881 | − | 0.810394i | −0.531445 | − | 0.847093i | \(-0.678351\pi\) |
0.999326 | + | 0.0366986i | \(0.0116841\pi\) | |||||||
\(38\) | −0.0706876 | −0.0114670 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.664874 | −0.105126 | ||||||||
\(41\) | −5.79590 | + | 10.0388i | −0.905167 | + | 1.56780i | −0.0844742 | + | 0.996426i | \(0.526921\pi\) |
−0.820693 | + | 0.571370i | \(0.806412\pi\) | |||||||
\(42\) | −2.12349 | + | 3.67799i | −0.327662 | + | 0.567527i | ||||
\(43\) | 0.147948 | + | 0.256254i | 0.0225619 | + | 0.0390784i | 0.877086 | − | 0.480334i | \(-0.159484\pi\) |
−0.854524 | + | 0.519412i | \(0.826151\pi\) | |||||||
\(44\) | −5.76271 | −0.868761 | ||||||||
\(45\) | 0.253020 | + | 0.438244i | 0.0377181 | + | 0.0653296i | ||||
\(46\) | 0.599031 | + | 1.03755i | 0.0883223 | + | 0.152979i | ||||
\(47\) | 7.35690 | 1.07311 | 0.536557 | − | 0.843864i | \(-0.319725\pi\) | ||||
0.536557 | + | 0.843864i | \(0.319725\pi\) | |||||||
\(48\) | 0.623490 | + | 1.07992i | 0.0899930 | + | 0.155872i | ||||
\(49\) | 0.722521 | − | 1.25144i | 0.103217 | − | 0.178778i | ||||
\(50\) | −1.98039 | + | 3.43013i | −0.280069 | + | 0.485093i | ||||
\(51\) | −4.85086 | −0.679256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3937 | −1.42769 | −0.713844 | − | 0.700304i | \(-0.753048\pi\) | ||||
−0.713844 | + | 0.700304i | \(0.753048\pi\) | |||||||
\(54\) | 0.856896 | − | 1.48419i | 0.116609 | − | 0.201972i | ||||
\(55\) | 0.524459 | − | 0.908389i | 0.0707180 | − | 0.122487i | ||||
\(56\) | −3.17241 | − | 5.49477i | −0.423931 | − | 0.734270i | ||||
\(57\) | −0.198062 | −0.0262340 | ||||||||
\(58\) | 1.85690 | + | 3.21624i | 0.243822 | + | 0.422313i | ||||
\(59\) | −3.39008 | − | 5.87180i | −0.441351 | − | 0.764443i | 0.556439 | − | 0.830889i | \(-0.312167\pi\) |
−0.997790 | + | 0.0664458i | \(0.978834\pi\) | |||||||
\(60\) | −0.753020 | −0.0972145 | ||||||||
\(61\) | −1.73609 | − | 3.00700i | −0.222284 | − | 0.385007i | 0.733217 | − | 0.679995i | \(-0.238018\pi\) |
−0.955501 | + | 0.294987i | \(0.904685\pi\) | |||||||
\(62\) | 2.65883 | − | 4.60523i | 0.337672 | − | 0.584865i | ||||
\(63\) | −2.41454 | + | 4.18211i | −0.304204 | + | 0.526896i | ||||
\(64\) | 3.56465 | 0.445581 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.65279 | 0.941994 | ||||||||
\(67\) | 3.83997 | − | 6.65102i | 0.469127 | − | 0.812552i | −0.530250 | − | 0.847841i | \(-0.677902\pi\) |
0.999377 | + | 0.0352895i | \(0.0112353\pi\) | |||||||
\(68\) | 1.46466 | − | 2.53686i | 0.177616 | − | 0.307639i | ||||
\(69\) | 1.67845 | + | 2.90716i | 0.202061 | + | 0.349981i | ||||
\(70\) | 0.466812 | 0.0557947 | ||||||||
\(71\) | −4.33244 | − | 7.50400i | −0.514166 | − | 0.890561i | −0.999865 | − | 0.0164351i | \(-0.994768\pi\) |
0.485699 | − | 0.874126i | \(-0.338565\pi\) | |||||||
\(72\) | −2.75786 | − | 4.77676i | −0.325017 | − | 0.562947i | ||||
\(73\) | −6.73556 | −0.788338 | −0.394169 | − | 0.919038i | \(-0.628968\pi\) | ||||
−0.394169 | + | 0.919038i | \(0.628968\pi\) | |||||||
\(74\) | −2.28232 | − | 3.95310i | −0.265315 | − | 0.459539i | ||||
\(75\) | −5.54892 | + | 9.61101i | −0.640734 | + | 1.10978i | ||||
\(76\) | 0.0598025 | − | 0.103581i | 0.00685981 | − | 0.0118815i | ||||
\(77\) | 10.0097 | 1.14071 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.97046 | 1.12176 | 0.560882 | − | 0.827896i | \(-0.310462\pi\) | ||||
0.560882 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(80\) | 0.0685317 | − | 0.118700i | 0.00766207 | − | 0.0132711i | ||||
\(81\) | 5.47434 | − | 9.48184i | 0.608261 | − | 1.05354i | ||||
\(82\) | 4.64795 | + | 8.05048i | 0.513280 | + | 0.889027i | ||||
\(83\) | −1.60925 | −0.176638 | −0.0883192 | − | 0.996092i | \(-0.528150\pi\) | ||||
−0.0883192 | + | 0.996092i | \(0.528150\pi\) | |||||||
\(84\) | −3.59299 | − | 6.22324i | −0.392027 | − | 0.679011i | ||||
\(85\) | 0.266594 | + | 0.461754i | 0.0289162 | + | 0.0500843i | ||||
\(86\) | 0.237291 | 0.0255877 | ||||||||
\(87\) | 5.20291 | + | 9.01170i | 0.557810 | + | 0.966156i | ||||
\(88\) | −5.71648 | + | 9.90123i | −0.609379 | + | 1.05548i | ||||
\(89\) | −1.44235 | + | 2.49823i | −0.152889 | + | 0.264812i | −0.932288 | − | 0.361716i | \(-0.882191\pi\) |
0.779399 | + | 0.626528i | \(0.215524\pi\) | |||||||
\(90\) | 0.405813 | 0.0427765 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.02715 | −0.211345 | ||||||||
\(93\) | 7.44989 | − | 12.9036i | 0.772517 | − | 1.33804i | ||||
\(94\) | 2.94989 | − | 5.10935i | 0.304258 | − | 0.526990i | ||||
\(95\) | 0.0108851 | + | 0.0188536i | 0.00111679 | + | 0.00193434i | ||||
\(96\) | 13.0978 | 1.33679 | ||||||||
\(97\) | −4.02930 | − | 6.97896i | −0.409114 | − | 0.708606i | 0.585677 | − | 0.810545i | \(-0.300829\pi\) |
−0.994791 | + | 0.101939i | \(0.967495\pi\) | |||||||
\(98\) | −0.579417 | − | 1.00358i | −0.0585299 | − | 0.101377i | ||||
\(99\) | 8.70171 | 0.874555 | ||||||||
\(100\) | −3.35086 | − | 5.80385i | −0.335086 | − | 0.580385i | ||||
\(101\) | 6.67725 | − | 11.5653i | 0.664411 | − | 1.15079i | −0.315033 | − | 0.949081i | \(-0.602016\pi\) |
0.979445 | − | 0.201714i | \(-0.0646510\pi\) | |||||||
\(102\) | −1.94504 | + | 3.36891i | −0.192588 | + | 0.333572i | ||||
\(103\) | 1.36227 | 0.134229 | 0.0671144 | − | 0.997745i | \(-0.478621\pi\) | ||||
0.0671144 | + | 0.997745i | \(0.478621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30798 | 0.127646 | ||||||||
\(106\) | −4.16756 | + | 7.21843i | −0.404789 | + | 0.701116i | ||||
\(107\) | −1.63437 | + | 2.83082i | −0.158001 | + | 0.273666i | −0.934148 | − | 0.356887i | \(-0.883838\pi\) |
0.776147 | + | 0.630552i | \(0.217172\pi\) | |||||||
\(108\) | 1.44989 | + | 2.51128i | 0.139515 | + | 0.241648i | ||||
\(109\) | −15.7017 | −1.50395 | −0.751976 | − | 0.659191i | \(-0.770899\pi\) | ||||
−0.751976 | + | 0.659191i | \(0.770899\pi\) | |||||||
\(110\) | −0.420583 | − | 0.728471i | −0.0401010 | − | 0.0694570i | ||||
\(111\) | −6.39493 | − | 11.0763i | −0.606980 | − | 1.05132i | ||||
\(112\) | 1.30798 | 0.123592 | ||||||||
\(113\) | −6.02446 | − | 10.4347i | −0.566733 | − | 0.981611i | −0.996886 | − | 0.0788549i | \(-0.974874\pi\) |
0.430153 | − | 0.902756i | \(-0.358460\pi\) | |||||||
\(114\) | −0.0794168 | + | 0.137554i | −0.00743806 | + | 0.0128831i | ||||
\(115\) | 0.184489 | − | 0.319544i | 0.0172037 | − | 0.0297976i | ||||
\(116\) | −6.28382 | −0.583438 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.43727 | −0.500541 | ||||||||
\(119\) | −2.54407 | + | 4.40646i | −0.233215 | + | 0.403940i | ||||
\(120\) | −0.746980 | + | 1.29381i | −0.0681896 | + | 0.118108i | ||||
\(121\) | −3.51842 | − | 6.09408i | −0.319856 | − | 0.554007i | ||||
\(122\) | −2.78448 | −0.252095 | ||||||||
\(123\) | 13.0233 | + | 22.5570i | 1.17427 | + | 2.03389i | ||||
\(124\) | 4.49880 | + | 7.79216i | 0.404004 | + | 0.699756i | ||||
\(125\) | 2.45473 | 0.219558 | ||||||||
\(126\) | 1.93631 | + | 3.35379i | 0.172500 | + | 0.298780i | ||||
\(127\) | 4.90366 | − | 8.49338i | 0.435129 | − | 0.753666i | −0.562177 | − | 0.827017i | \(-0.690036\pi\) |
0.997306 | + | 0.0733510i | \(0.0233694\pi\) | |||||||
\(128\) | −4.39977 | + | 7.62063i | −0.388889 | + | 0.673575i | ||||
\(129\) | 0.664874 | 0.0585389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.57673 | −0.574611 | −0.287306 | − | 0.957839i | \(-0.592760\pi\) | ||||
−0.287306 | + | 0.957839i | \(0.592760\pi\) | |||||||
\(132\) | −6.47434 | + | 11.2139i | −0.563519 | + | 0.976044i | ||||
\(133\) | −0.103875 | + | 0.179918i | −0.00900715 | + | 0.0156008i | ||||
\(134\) | −3.07942 | − | 5.33371i | −0.266021 | − | 0.460762i | ||||
\(135\) | −0.527811 | −0.0454267 | ||||||||
\(136\) | −2.90581 | − | 5.03302i | −0.249171 | − | 0.431578i | ||||
\(137\) | 3.10992 | + | 5.38653i | 0.265698 | + | 0.460203i | 0.967746 | − | 0.251927i | \(-0.0810642\pi\) |
−0.702048 | + | 0.712129i | \(0.747731\pi\) | |||||||
\(138\) | 2.69202 | 0.229160 | ||||||||
\(139\) | 7.35354 | + | 12.7367i | 0.623719 | + | 1.08031i | 0.988787 | + | 0.149333i | \(0.0477125\pi\) |
−0.365068 | + | 0.930981i | \(0.618954\pi\) | |||||||
\(140\) | −0.394928 | + | 0.684035i | −0.0333775 | + | 0.0578116i | ||||
\(141\) | 8.26540 | − | 14.3161i | 0.696072 | − | 1.20563i | ||||
\(142\) | −6.94869 | −0.583121 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.13706 | 0.0947553 | ||||||||
\(145\) | 0.571884 | − | 0.990532i | 0.0474924 | − | 0.0822592i | ||||
\(146\) | −2.70075 | + | 4.67784i | −0.223516 | + | 0.387141i | ||||
\(147\) | −1.62349 | − | 2.81197i | −0.133903 | − | 0.231927i | ||||
\(148\) | 7.72348 | 0.634866 | ||||||||
\(149\) | 2.16756 | + | 3.75433i | 0.177574 | + | 0.307567i | 0.941049 | − | 0.338270i | \(-0.109842\pi\) |
−0.763475 | + | 0.645837i | \(0.776509\pi\) | |||||||
\(150\) | 4.44989 | + | 7.70743i | 0.363332 | + | 0.629309i | ||||
\(151\) | −3.94438 | −0.320989 | −0.160494 | − | 0.987037i | \(-0.551309\pi\) | ||||
−0.160494 | + | 0.987037i | \(0.551309\pi\) | |||||||
\(152\) | −0.118645 | − | 0.205500i | −0.00962342 | − | 0.0166682i | ||||
\(153\) | −2.21164 | + | 3.83067i | −0.178800 | + | 0.309691i | ||||
\(154\) | 4.01357 | − | 6.95171i | 0.323423 | − | 0.560185i | ||||
\(155\) | −1.63773 | −0.131545 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.45473 | 0.355526 | 0.177763 | − | 0.984073i | \(-0.443114\pi\) | ||||
0.177763 | + | 0.984073i | \(0.443114\pi\) | |||||||
\(158\) | 3.99784 | − | 6.92447i | 0.318051 | − | 0.550881i | ||||
\(159\) | −11.6773 | + | 20.2256i | −0.926066 | + | 1.60399i | ||||
\(160\) | −0.719833 | − | 1.24679i | −0.0569078 | − | 0.0985671i | ||||
\(161\) | 3.52111 | 0.277502 | ||||||||
\(162\) | −4.39008 | − | 7.60385i | −0.344918 | − | 0.597415i | ||||
\(163\) | 8.07942 | + | 13.9940i | 0.632829 | + | 1.09609i | 0.986971 | + | 0.160900i | \(0.0514396\pi\) |
−0.354142 | + | 0.935192i | \(0.615227\pi\) | |||||||
\(164\) | −15.7289 | −1.22822 | ||||||||
\(165\) | −1.17845 | − | 2.04113i | −0.0917420 | − | 0.158902i | ||||
\(166\) | −0.645260 | + | 1.11762i | −0.0500819 | + | 0.0867444i | ||||
\(167\) | 8.05861 | − | 13.9579i | 0.623594 | − | 1.08010i | −0.365217 | − | 0.930922i | \(-0.619005\pi\) |
0.988811 | − | 0.149174i | \(-0.0476613\pi\) | |||||||
\(168\) | −14.2567 | −1.09993 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.427583 | 0.0327942 | ||||||||
\(171\) | −0.0903019 | + | 0.156408i | −0.00690556 | + | 0.0119608i | ||||
\(172\) | −0.200751 | + | 0.347710i | −0.0153071 | + | 0.0265127i | ||||
\(173\) | 10.7681 | + | 18.6509i | 0.818682 | + | 1.41800i | 0.906653 | + | 0.421876i | \(0.138628\pi\) |
−0.0879709 | + | 0.996123i | \(0.528038\pi\) | |||||||
\(174\) | 8.34481 | 0.632619 | ||||||||
\(175\) | 5.82036 | + | 10.0812i | 0.439978 | + | 0.762063i | ||||
\(176\) | −1.17845 | − | 2.04113i | −0.0888289 | − | 0.153856i | ||||
\(177\) | −15.2349 | −1.14513 | ||||||||
\(178\) | 1.15668 | + | 2.00342i | 0.0866967 | + | 0.150163i | ||||
\(179\) | −5.71648 | + | 9.90123i | −0.427270 | + | 0.740053i | −0.996629 | − | 0.0820356i | \(-0.973858\pi\) |
0.569360 | + | 0.822089i | \(0.307191\pi\) | |||||||
\(180\) | −0.343322 | + | 0.594652i | −0.0255897 | + | 0.0443227i | ||||
\(181\) | 20.9705 | 1.55872 | 0.779361 | − | 0.626575i | \(-0.215544\pi\) | ||||
0.779361 | + | 0.626575i | \(0.215544\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.80194 | −0.576736 | ||||||||
\(184\) | −2.01089 | + | 3.48296i | −0.148244 | + | 0.256767i | ||||
\(185\) | −0.702907 | + | 1.21747i | −0.0516787 | + | 0.0895102i | ||||
\(186\) | −5.97434 | − | 10.3479i | −0.438060 | − | 0.758743i | ||||
\(187\) | 9.16852 | 0.670469 | ||||||||
\(188\) | 4.99127 | + | 8.64513i | 0.364026 | + | 0.630511i | ||||
\(189\) | −2.51842 | − | 4.36203i | −0.183188 | − | 0.317291i | ||||
\(190\) | 0.0174584 | 0.00126657 | ||||||||
\(191\) | 7.21864 | + | 12.5030i | 0.522322 | + | 0.904689i | 0.999663 | + | 0.0259702i | \(0.00826749\pi\) |
−0.477341 | + | 0.878718i | \(0.658399\pi\) | |||||||
\(192\) | 4.00484 | − | 6.93659i | 0.289025 | − | 0.500606i | ||||
\(193\) | −6.78986 | + | 11.7604i | −0.488745 | + | 0.846530i | −0.999916 | − | 0.0129483i | \(-0.995878\pi\) |
0.511172 | + | 0.859479i | \(0.329212\pi\) | |||||||
\(194\) | −6.46250 | −0.463980 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.96077 | 0.140055 | ||||||||
\(197\) | −0.280167 | + | 0.485264i | −0.0199611 | + | 0.0345736i | −0.875833 | − | 0.482614i | \(-0.839688\pi\) |
0.855872 | + | 0.517187i | \(0.173021\pi\) | |||||||
\(198\) | 3.48911 | − | 6.04332i | 0.247961 | − | 0.429480i | ||||
\(199\) | −5.74578 | − | 9.95199i | −0.407308 | − | 0.705478i | 0.587279 | − | 0.809384i | \(-0.300199\pi\) |
−0.994587 | + | 0.103907i | \(0.966866\pi\) | |||||||
\(200\) | −13.2959 | −0.940162 | ||||||||
\(201\) | −8.62833 | − | 14.9447i | −0.608596 | − | 1.05412i | ||||
\(202\) | −5.35474 | − | 9.27468i | −0.376758 | − | 0.652564i | ||||
\(203\) | 10.9148 | 0.766071 | ||||||||
\(204\) | −3.29105 | − | 5.70027i | −0.230420 | − | 0.399099i | ||||
\(205\) | 1.43147 | − | 2.47938i | 0.0999781 | − | 0.173167i | ||||
\(206\) | 0.546229 | − | 0.946096i | 0.0380576 | − | 0.0659177i | ||||
\(207\) | 3.06100 | 0.212754 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.374354 | 0.0258946 | ||||||||
\(210\) | 0.524459 | − | 0.908389i | 0.0361911 | − | 0.0626848i | ||||
\(211\) | −4.39224 | + | 7.60758i | −0.302374 | + | 0.523728i | −0.976673 | − | 0.214731i | \(-0.931113\pi\) |
0.674299 | + | 0.738458i | \(0.264446\pi\) | |||||||
\(212\) | −7.05161 | − | 12.2137i | −0.484306 | − | 0.838843i | ||||
\(213\) | −19.4698 | −1.33405 | ||||||||
\(214\) | 1.31067 | + | 2.27014i | 0.0895953 | + | 0.155184i | ||||
\(215\) | −0.0365403 | − | 0.0632896i | −0.00249202 | − | 0.00431631i | ||||
\(216\) | 5.75302 | 0.391443 | ||||||||
\(217\) | −7.81431 | − | 13.5348i | −0.530470 | − | 0.918801i | ||||
\(218\) | −6.29590 | + | 10.9048i | −0.426412 | + | 0.738567i | ||||
\(219\) | −7.56734 | + | 13.1070i | −0.511353 | + | 0.885690i | ||||
\(220\) | 1.42327 | 0.0959570 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.2567 | −0.688383 | ||||||||
\(223\) | −1.12953 | + | 1.95640i | −0.0756390 | + | 0.131011i | −0.901364 | − | 0.433062i | \(-0.857433\pi\) |
0.825725 | + | 0.564073i | \(0.190766\pi\) | |||||||
\(224\) | 6.86927 | − | 11.8979i | 0.458973 | − | 0.794964i | ||||
\(225\) | 5.05980 | + | 8.76383i | 0.337320 | + | 0.584256i | ||||
\(226\) | −9.66248 | −0.642739 | ||||||||
\(227\) | −3.48307 | − | 6.03286i | −0.231180 | − | 0.400415i | 0.726976 | − | 0.686663i | \(-0.240925\pi\) |
−0.958156 | + | 0.286248i | \(0.907592\pi\) | |||||||
\(228\) | −0.134375 | − | 0.232744i | −0.00889920 | − | 0.0154139i | ||||
\(229\) | 24.1739 | 1.59746 | 0.798728 | − | 0.601692i | \(-0.205507\pi\) | ||||
0.798728 | + | 0.601692i | \(0.205507\pi\) | |||||||
\(230\) | −0.147948 | − | 0.256254i | −0.00975543 | − | 0.0168969i | ||||
\(231\) | 11.2458 | − | 19.4783i | 0.739918 | − | 1.28158i | ||||
\(232\) | −6.23341 | + | 10.7966i | −0.409243 | + | 0.708830i | ||||
\(233\) | −3.06100 | −0.200533 | −0.100266 | − | 0.994961i | \(-0.531969\pi\) | ||||
−0.100266 | + | 0.994961i | \(0.531969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81700 | −0.118528 | ||||||||
\(236\) | 4.59999 | − | 7.96742i | 0.299434 | − | 0.518635i | ||||
\(237\) | 11.2017 | − | 19.4019i | 0.727629 | − | 1.26029i | ||||
\(238\) | 2.04019 | + | 3.53371i | 0.132246 | + | 0.229056i | ||||
\(239\) | 25.1468 | 1.62661 | 0.813304 | − | 0.581839i | \(-0.197667\pi\) | ||||
0.813304 | + | 0.581839i | \(0.197667\pi\) | |||||||
\(240\) | −0.153989 | − | 0.266717i | −0.00993996 | − | 0.0172165i | ||||
\(241\) | −10.1332 | − | 17.5512i | −0.652735 | − | 1.13057i | −0.982456 | − | 0.186492i | \(-0.940288\pi\) |
0.329721 | − | 0.944078i | \(-0.393045\pi\) | |||||||
\(242\) | −5.64310 | −0.362752 | ||||||||
\(243\) | −9.09515 | − | 15.7533i | −0.583454 | − | 1.01057i | ||||
\(244\) | 2.35570 | − | 4.08019i | 0.150808 | − | 0.261207i | ||||
\(245\) | −0.178448 | + | 0.309081i | −0.0114006 | + | 0.0197465i | ||||
\(246\) | 20.8877 | 1.33175 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 17.8509 | 1.13353 | ||||||||
\(249\) | −1.80798 | + | 3.13151i | −0.114576 | + | 0.198451i | ||||
\(250\) | 0.984271 | − | 1.70481i | 0.0622507 | − | 0.107821i | ||||
\(251\) | 11.8605 | + | 20.5431i | 0.748631 | + | 1.29667i | 0.948479 | + | 0.316840i | \(0.102622\pi\) |
−0.199848 | + | 0.979827i | \(0.564045\pi\) | |||||||
\(252\) | −6.55257 | −0.412773 | ||||||||
\(253\) | −3.17241 | − | 5.49477i | −0.199448 | − | 0.345453i | ||||
\(254\) | −3.93243 | − | 6.81116i | −0.246742 | − | 0.427370i | ||||
\(255\) | 1.19806 | 0.0750256 | ||||||||
\(256\) | 7.09299 | + | 12.2854i | 0.443312 | + | 0.767839i | ||||
\(257\) | −7.11207 | + | 12.3185i | −0.443639 | + | 0.768405i | −0.997956 | − | 0.0639003i | \(-0.979646\pi\) |
0.554317 | + | 0.832305i | \(0.312979\pi\) | |||||||
\(258\) | 0.266594 | − | 0.461754i | 0.0165974 | − | 0.0287476i | ||||
\(259\) | −13.4155 | −0.833599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.48858 | 0.587329 | ||||||||
\(262\) | −2.63706 | + | 4.56753i | −0.162918 | + | 0.282183i | ||||
\(263\) | 8.54772 | − | 14.8051i | 0.527075 | − | 0.912921i | −0.472427 | − | 0.881370i | \(-0.656622\pi\) |
0.999502 | − | 0.0315510i | \(-0.0100447\pi\) | |||||||
\(264\) | 12.8448 | + | 22.2479i | 0.790544 | + | 1.36926i | ||||
\(265\) | 2.56704 | 0.157692 | ||||||||
\(266\) | 0.0833017 | + | 0.144283i | 0.00510755 | + | 0.00884654i | ||||
\(267\) | 3.24094 | + | 5.61347i | 0.198342 | + | 0.343539i | ||||
\(268\) | 10.4209 | 0.636556 | ||||||||
\(269\) | 3.23341 | + | 5.60042i | 0.197144 | + | 0.341464i | 0.947601 | − | 0.319455i | \(-0.103500\pi\) |
−0.750457 | + | 0.660919i | \(0.770167\pi\) | |||||||
\(270\) | −0.211636 | + | 0.366564i | −0.0128797 | + | 0.0223084i | ||||
\(271\) | 3.22401 | − | 5.58415i | 0.195845 | − | 0.339213i | −0.751332 | − | 0.659924i | \(-0.770588\pi\) |
0.947177 | + | 0.320711i | \(0.103922\pi\) | |||||||
\(272\) | 1.19806 | 0.0726432 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.98792 | 0.301331 | ||||||||
\(275\) | 10.4879 | − | 18.1656i | 0.632445 | − | 1.09543i | ||||
\(276\) | −2.27748 | + | 3.94471i | −0.137088 | + | 0.237444i | ||||
\(277\) | −6.73005 | − | 11.6568i | −0.404370 | − | 0.700389i | 0.589878 | − | 0.807492i | \(-0.299176\pi\) |
−0.994248 | + | 0.107103i | \(0.965842\pi\) | |||||||
\(278\) | 11.7942 | 0.707367 | ||||||||
\(279\) | −6.79321 | − | 11.7662i | −0.406699 | − | 0.704423i | ||||
\(280\) | 0.783520 | + | 1.35710i | 0.0468243 | + | 0.0811020i | ||||
\(281\) | −5.03684 | −0.300472 | −0.150236 | − | 0.988650i | \(-0.548003\pi\) | ||||
−0.150236 | + | 0.988650i | \(0.548003\pi\) | |||||||
\(282\) | −6.62833 | − | 11.4806i | −0.394712 | − | 0.683660i | ||||
\(283\) | −11.0640 | + | 19.1634i | −0.657686 | + | 1.13914i | 0.323528 | + | 0.946219i | \(0.395131\pi\) |
−0.981213 | + | 0.192926i | \(0.938202\pi\) | |||||||
\(284\) | 5.87867 | − | 10.1821i | 0.348835 | − | 0.604199i | ||||
\(285\) | 0.0489173 | 0.00289761 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.3207 | 1.61269 | ||||||||
\(288\) | 5.97166 | − | 10.3432i | 0.351883 | − | 0.609480i | ||||
\(289\) | 6.16972 | − | 10.6863i | 0.362925 | − | 0.628604i | ||||
\(290\) | −0.458615 | − | 0.794345i | −0.0269308 | − | 0.0466456i | ||||
\(291\) | −18.1075 | −1.06148 | ||||||||
\(292\) | −4.56973 | − | 7.91500i | −0.267423 | − | 0.463190i | ||||
\(293\) | 7.47315 | + | 12.9439i | 0.436586 | + | 0.756189i | 0.997424 | − | 0.0717367i | \(-0.0228541\pi\) |
−0.560838 | + | 0.827926i | \(0.689521\pi\) | |||||||
\(294\) | −2.60388 | −0.151861 | ||||||||
\(295\) | 0.837282 | + | 1.45021i | 0.0487484 | + | 0.0844347i | ||||
\(296\) | 7.66152 | − | 13.2701i | 0.445317 | − | 0.771312i | ||||
\(297\) | −4.53803 | + | 7.86010i | −0.263323 | + | 0.456089i | ||||
\(298\) | 3.47650 | 0.201388 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −15.0586 | −0.869409 | ||||||||
\(301\) | 0.348699 | − | 0.603965i | 0.0200987 | − | 0.0348119i | ||||
\(302\) | −1.58157 | + | 2.73936i | −0.0910093 | + | 0.157633i | ||||
\(303\) | −15.0036 | − | 25.9871i | −0.861937 | − | 1.49292i | ||||
\(304\) | 0.0489173 | 0.00280560 | ||||||||
\(305\) | 0.428780 | + | 0.742669i | 0.0245519 | + | 0.0425251i | ||||
\(306\) | 1.77359 | + | 3.07196i | 0.101390 | + | 0.175612i | ||||
\(307\) | −19.1293 | −1.09177 | −0.545883 | − | 0.837861i | \(-0.683806\pi\) | ||||
−0.545883 | + | 0.837861i | \(0.683806\pi\) | |||||||
\(308\) | 6.79105 | + | 11.7624i | 0.386956 | + | 0.670228i | ||||
\(309\) | 1.53050 | − | 2.65090i | 0.0870671 | − | 0.150805i | ||||
\(310\) | −0.656678 | + | 1.13740i | −0.0372968 | + | 0.0645999i | ||||
\(311\) | −0.269815 | −0.0152998 | −0.00764990 | − | 0.999971i | \(-0.502435\pi\) | ||||
−0.00764990 | + | 0.999971i | \(0.502435\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3937 | −1.32229 | −0.661146 | − | 0.750257i | \(-0.729930\pi\) | ||||
−0.661146 | + | 0.750257i | \(0.729930\pi\) | |||||||
\(314\) | 1.78621 | − | 3.09380i | 0.100802 | − | 0.174593i | ||||
\(315\) | 0.596343 | − | 1.03290i | 0.0336001 | − | 0.0581971i | ||||
\(316\) | 6.76444 | + | 11.7164i | 0.380529 | + | 0.659096i | ||||
\(317\) | 13.9952 | 0.786050 | 0.393025 | − | 0.919528i | \(-0.371429\pi\) | ||||
0.393025 | + | 0.919528i | \(0.371429\pi\) | |||||||
\(318\) | 9.36443 | + | 16.2197i | 0.525131 | + | 0.909554i | ||||
\(319\) | −9.83393 | − | 17.0329i | −0.550594 | − | 0.953657i | ||||
\(320\) | −0.880395 | −0.0492156 | ||||||||
\(321\) | 3.67241 | + | 6.36080i | 0.204974 | + | 0.355025i | ||||
\(322\) | 1.41185 | − | 2.44540i | 0.0786795 | − | 0.136277i | ||||
\(323\) | −0.0951463 | + | 0.164798i | −0.00529408 | + | 0.00916962i | ||||
\(324\) | 14.8562 | 0.825346 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.9584 | 0.717698 | ||||||||
\(327\) | −17.6407 | + | 30.5546i | −0.975534 | + | 1.68967i | ||||
\(328\) | −15.6027 | + | 27.0246i | −0.861514 | + | 1.49219i | ||||
\(329\) | −8.66972 | − | 15.0164i | −0.477977 | − | 0.827881i | ||||
\(330\) | −1.89008 | −0.104046 | ||||||||
\(331\) | 8.91066 | + | 15.4337i | 0.489774 | + | 0.848314i | 0.999931 | − | 0.0117680i | \(-0.00374594\pi\) |
−0.510157 | + | 0.860081i | \(0.670413\pi\) | |||||||
\(332\) | −1.09179 | − | 1.89104i | −0.0599200 | − | 0.103784i | ||||
\(333\) | −11.6625 | −0.639100 | ||||||||
\(334\) | −6.46250 | − | 11.1934i | −0.353612 | − | 0.612474i | ||||
\(335\) | −0.948394 | + | 1.64267i | −0.0518163 | + | 0.0897485i | ||||
\(336\) | 1.46950 | − | 2.54525i | 0.0801678 | − | 0.138855i | ||||
\(337\) | −27.8485 | −1.51700 | −0.758501 | − | 0.651672i | \(-0.774068\pi\) | ||||
−0.758501 | + | 0.651672i | \(0.774068\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.0737 | −1.47044 | ||||||||
\(340\) | −0.361740 | + | 0.626552i | −0.0196181 | + | 0.0339796i | ||||
\(341\) | −14.0809 | + | 24.3888i | −0.762524 | + | 1.32073i | ||||
\(342\) | 0.0724165 | + | 0.125429i | 0.00391584 | + | 0.00678243i | ||||
\(343\) | −19.9041 | −1.07472 | ||||||||
\(344\) | 0.398280 | + | 0.689842i | 0.0214738 | + | 0.0371938i | ||||
\(345\) | −0.414542 | − | 0.718009i | −0.0223182 | − | 0.0386563i | ||||
\(346\) | 17.2707 | 0.928477 | ||||||||
\(347\) | −0.751824 | − | 1.30220i | −0.0403600 | − | 0.0699056i | 0.845140 | − | 0.534545i | \(-0.179517\pi\) |
−0.885500 | + | 0.464640i | \(0.846184\pi\) | |||||||
\(348\) | −7.05980 | + | 12.2279i | −0.378445 | + | 0.655486i | ||||
\(349\) | −7.09299 | + | 12.2854i | −0.379679 | + | 0.657623i | −0.991015 | − | 0.133747i | \(-0.957299\pi\) |
0.611336 | + | 0.791371i | \(0.290632\pi\) | |||||||
\(350\) | 9.33513 | 0.498983 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.7560 | −1.31950 | ||||||||
\(353\) | −3.58426 | + | 6.20812i | −0.190771 | + | 0.330425i | −0.945506 | − | 0.325605i | \(-0.894432\pi\) |
0.754735 | + | 0.656030i | \(0.227765\pi\) | |||||||
\(354\) | −6.10872 | + | 10.5806i | −0.324675 | + | 0.562353i | ||||
\(355\) | 1.07002 | + | 1.85334i | 0.0567910 | + | 0.0983648i | ||||
\(356\) | −3.91425 | −0.207455 | ||||||||
\(357\) | 5.71648 | + | 9.90123i | 0.302548 | + | 0.524029i | ||||
\(358\) | 4.58426 | + | 7.94017i | 0.242286 | + | 0.419651i | ||||
\(359\) | −19.8853 | −1.04951 | −0.524753 | − | 0.851255i | \(-0.675842\pi\) | ||||
−0.524753 | + | 0.851255i | \(0.675842\pi\) | |||||||
\(360\) | 0.681136 | + | 1.17976i | 0.0358990 | + | 0.0621790i | ||||
\(361\) | 9.49612 | − | 16.4478i | 0.499796 | − | 0.865671i | ||||
\(362\) | 8.40850 | − | 14.5640i | 0.441941 | − | 0.765464i | ||||
\(363\) | −15.8116 | −0.829895 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.66355 | 0.0870740 | ||||||||
\(366\) | −3.12833 | + | 5.41843i | −0.163521 | + | 0.283226i | ||||
\(367\) | −0.541917 | + | 0.938628i | −0.0282878 | + | 0.0489960i | −0.879823 | − | 0.475302i | \(-0.842339\pi\) |
0.851535 | + | 0.524298i | \(0.175672\pi\) | |||||||
\(368\) | −0.414542 | − | 0.718009i | −0.0216095 | − | 0.0374288i | ||||
\(369\) | 23.7506 | 1.23641 | ||||||||
\(370\) | 0.563687 | + | 0.976335i | 0.0293047 | + | 0.0507572i | ||||
\(371\) | 12.2485 | + | 21.2150i | 0.635909 | + | 1.10143i | ||||
\(372\) | 20.2174 | 1.04823 | ||||||||
\(373\) | 3.06518 | + | 5.30905i | 0.158709 | + | 0.274892i | 0.934403 | − | 0.356217i | \(-0.115934\pi\) |
−0.775694 | + | 0.631109i | \(0.782600\pi\) | |||||||
\(374\) | 3.67629 | − | 6.36752i | 0.190097 | − | 0.329257i | ||||
\(375\) | 2.75786 | − | 4.77676i | 0.142416 | − | 0.246671i | ||||
\(376\) | 19.8049 | 1.02136 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.03923 | −0.207756 | ||||||||
\(379\) | −1.20440 | + | 2.08608i | −0.0618658 | + | 0.107155i | −0.895299 | − | 0.445465i | \(-0.853038\pi\) |
0.833434 | + | 0.552620i | \(0.186372\pi\) | |||||||
\(380\) | −0.0147700 | + | 0.0255824i | −0.000757685 | + | 0.00131235i | ||||
\(381\) | −11.0184 | − | 19.0845i | −0.564491 | − | 0.977726i | ||||
\(382\) | 11.5778 | 0.592371 | ||||||||
\(383\) | −15.1957 | − | 26.3197i | −0.776462 | − | 1.34487i | −0.933969 | − | 0.357354i | \(-0.883679\pi\) |
0.157506 | − | 0.987518i | \(-0.449655\pi\) | |||||||
\(384\) | 9.88620 | + | 17.1234i | 0.504503 | + | 0.873825i | ||||
\(385\) | −2.47219 | −0.125994 | ||||||||
\(386\) | 5.44504 | + | 9.43109i | 0.277145 | + | 0.480030i | ||||
\(387\) | 0.303134 | − | 0.525044i | 0.0154092 | − | 0.0266895i | ||||
\(388\) | 5.46734 | − | 9.46972i | 0.277562 | − | 0.480752i | ||||
\(389\) | −15.9409 | −0.808237 | −0.404118 | − | 0.914707i | \(-0.632422\pi\) | ||||
−0.404118 | + | 0.914707i | \(0.632422\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22521 | 0.163106 | ||||||||
\(392\) | 1.94504 | − | 3.36891i | 0.0982394 | − | 0.170156i | ||||
\(393\) | −7.38889 | + | 12.7979i | −0.372720 | + | 0.645570i | ||||
\(394\) | 0.224677 | + | 0.389152i | 0.0113191 | + | 0.0196052i | ||||
\(395\) | −2.46250 | −0.123902 | ||||||||
\(396\) | 5.90366 | + | 10.2254i | 0.296670 | + | 0.513847i | ||||
\(397\) | 8.45742 | + | 14.6487i | 0.424466 | + | 0.735196i | 0.996370 | − | 0.0851239i | \(-0.0271286\pi\) |
−0.571905 | + | 0.820320i | \(0.693795\pi\) | |||||||
\(398\) | −9.21552 | −0.461932 | ||||||||
\(399\) | 0.233406 | + | 0.404271i | 0.0116849 | + | 0.0202389i | ||||
\(400\) | 1.37047 | − | 2.37372i | 0.0685235 | − | 0.118686i | ||||
\(401\) | 13.3312 | − | 23.0904i | 0.665730 | − | 1.15308i | −0.313356 | − | 0.949636i | \(-0.601453\pi\) |
0.979087 | − | 0.203443i | \(-0.0652132\pi\) | |||||||
\(402\) | −13.8388 | −0.690215 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.1207 | 0.901537 | ||||||||
\(405\) | −1.35205 | + | 2.34182i | −0.0671840 | + | 0.116366i | ||||
\(406\) | 4.37651 | − | 7.58034i | 0.217203 | − | 0.376206i | ||||
\(407\) | 12.0869 | + | 20.9352i | 0.599128 | + | 1.03772i | ||||
\(408\) | −13.0586 | −0.646497 | ||||||||
\(409\) | 14.2582 | + | 24.6959i | 0.705021 | + | 1.22113i | 0.966684 | + | 0.255972i | \(0.0823956\pi\) |
−0.261663 | + | 0.965159i | \(0.584271\pi\) | |||||||
\(410\) | −1.14795 | − | 1.98831i | −0.0566931 | − | 0.0981954i | ||||
\(411\) | 13.9758 | 0.689377 | ||||||||
\(412\) | 0.924231 | + | 1.60082i | 0.0455336 | + | 0.0788665i | ||||
\(413\) | −7.99007 | + | 13.8392i | −0.393166 | + | 0.680983i | ||||
\(414\) | 1.22737 | − | 2.12586i | 0.0603217 | − | 0.104480i | ||||
\(415\) | 0.397452 | 0.0195102 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.0465 | 1.61830 | ||||||||
\(418\) | 0.150104 | − | 0.259988i | 0.00734185 | − | 0.0127165i | ||||
\(419\) | 14.8046 | − | 25.6424i | 0.723253 | − | 1.25271i | −0.236436 | − | 0.971647i | \(-0.575979\pi\) |
0.959689 | − | 0.281064i | \(-0.0906874\pi\) | |||||||
\(420\) | 0.887395 | + | 1.53701i | 0.0433005 | + | 0.0749986i | ||||
\(421\) | 11.6606 | 0.568301 | 0.284151 | − | 0.958780i | \(-0.408288\pi\) | ||||
0.284151 | + | 0.958780i | \(0.408288\pi\) | |||||||
\(422\) | 3.52230 | + | 6.10081i | 0.171463 | + | 0.296983i | ||||
\(423\) | −7.53684 | − | 13.0542i | −0.366453 | − | 0.634716i | ||||
\(424\) | −27.9801 | −1.35884 | ||||||||
\(425\) | 5.33124 | + | 9.23398i | 0.258603 | + | 0.447914i | ||||
\(426\) | −7.80678 | + | 13.5217i | −0.378240 | + | 0.655131i | ||||
\(427\) | −4.09179 | + | 7.08719i | −0.198016 | + | 0.342973i | ||||
\(428\) | −4.43535 | −0.214391 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0586060 | −0.00282623 | ||||||||
\(431\) | 2.17456 | − | 3.76645i | 0.104745 | − | 0.181424i | −0.808889 | − | 0.587961i | \(-0.799931\pi\) |
0.913634 | + | 0.406538i | \(0.133264\pi\) | |||||||
\(432\) | −0.592990 | + | 1.02709i | −0.0285303 | + | 0.0494159i | ||||
\(433\) | 7.19418 | + | 12.4607i | 0.345730 | + | 0.598822i | 0.985486 | − | 0.169756i | \(-0.0542979\pi\) |
−0.639756 | + | 0.768578i | \(0.720965\pi\) | |||||||
\(434\) | −12.5332 | −0.601612 | ||||||||
\(435\) | −1.28501 | − | 2.22571i | −0.0616116 | − | 0.106714i | ||||
\(436\) | −10.6528 | − | 18.4512i | −0.510176 | − | 0.883651i | ||||
\(437\) | 0.131687 | 0.00629942 | ||||||||
\(438\) | 6.06853 | + | 10.5110i | 0.289966 | + | 0.502235i | ||||
\(439\) | 10.1163 | − | 17.5219i | 0.482822 | − | 0.836273i | −0.516983 | − | 0.855996i | \(-0.672945\pi\) |
0.999805 | + | 0.0197227i | \(0.00627834\pi\) | |||||||
\(440\) | 1.41185 | − | 2.44540i | 0.0673075 | − | 0.116580i | ||||
\(441\) | −2.96077 | −0.140989 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.12200 | 0.385888 | 0.192944 | − | 0.981210i | \(-0.438196\pi\) | ||||
0.192944 | + | 0.981210i | \(0.438196\pi\) | |||||||
\(444\) | 8.67725 | − | 15.0294i | 0.411804 | − | 0.713266i | ||||
\(445\) | 0.356232 | − | 0.617012i | 0.0168870 | − | 0.0292492i | ||||
\(446\) | 0.905813 | + | 1.56891i | 0.0428915 | + | 0.0742903i | ||||
\(447\) | 9.74094 | 0.460731 | ||||||||
\(448\) | −4.20075 | − | 7.27591i | −0.198467 | − | 0.343755i | ||||
\(449\) | 6.24578 | + | 10.8180i | 0.294757 | + | 0.510534i | 0.974928 | − | 0.222519i | \(-0.0714281\pi\) |
−0.680172 | + | 0.733053i | \(0.738095\pi\) | |||||||
\(450\) | 8.11529 | 0.382559 | ||||||||
\(451\) | −24.6151 | − | 42.6345i | −1.15908 | − | 2.00758i | ||||
\(452\) | 8.17456 | − | 14.1588i | 0.384499 | − | 0.665972i | ||||
\(453\) | −4.43147 | + | 7.67553i | −0.208209 | + | 0.360628i | ||||
\(454\) | −5.58642 | −0.262184 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.533188 | −0.0249688 | ||||||||
\(457\) | 2.99061 | − | 5.17988i | 0.139895 | − | 0.242305i | −0.787562 | − | 0.616236i | \(-0.788657\pi\) |
0.927457 | + | 0.373931i | \(0.121990\pi\) | |||||||
\(458\) | 9.69298 | − | 16.7887i | 0.452923 | − | 0.784486i | ||||
\(459\) | −2.30678 | − | 3.99546i | −0.107671 | − | 0.186492i | ||||
\(460\) | 0.500664 | 0.0233436 | ||||||||
\(461\) | −1.02834 | − | 1.78114i | −0.0478947 | − | 0.0829561i | 0.841084 | − | 0.540904i | \(-0.181918\pi\) |
−0.888979 | + | 0.457948i | \(0.848585\pi\) | |||||||
\(462\) | −9.01842 | − | 15.6204i | −0.419575 | − | 0.726725i | ||||
\(463\) | 8.44935 | 0.392675 | 0.196337 | − | 0.980536i | \(-0.437095\pi\) | ||||
0.196337 | + | 0.980536i | \(0.437095\pi\) | |||||||
\(464\) | −1.28501 | − | 2.22571i | −0.0596552 | − | 0.103326i | ||||
\(465\) | −1.83997 | + | 3.18692i | −0.0853266 | + | 0.147790i | ||||
\(466\) | −1.22737 | + | 2.12586i | −0.0568566 | + | 0.0984785i | ||||
\(467\) | 33.5139 | 1.55084 | 0.775420 | − | 0.631446i | \(-0.217538\pi\) | ||||
0.775420 | + | 0.631446i | \(0.217538\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1008 | −0.835818 | ||||||||
\(470\) | −0.728562 | + | 1.26191i | −0.0336060 | + | 0.0582074i | ||||
\(471\) | 5.00484 | − | 8.66864i | 0.230611 | − | 0.399430i | ||||
\(472\) | −9.12618 | − | 15.8070i | −0.420066 | − | 0.727576i | ||||
\(473\) | −1.25667 | −0.0577817 | ||||||||
\(474\) | −8.98307 | − | 15.5591i | −0.412606 | − | 0.714655i | ||||
\(475\) | 0.217677 | + | 0.377027i | 0.00998769 | + | 0.0172992i | ||||
\(476\) | −6.90408 | −0.316448 | ||||||||
\(477\) | 10.6479 | + | 18.4428i | 0.487536 | + | 0.844437i | ||||
\(478\) | 10.0831 | − | 17.4644i | 0.461189 | − | 0.798802i | ||||
\(479\) | −12.3656 | + | 21.4179i | −0.565000 | + | 0.978608i | 0.432050 | + | 0.901850i | \(0.357790\pi\) |
−0.997050 | + | 0.0767587i | \(0.975543\pi\) | |||||||
\(480\) | −3.23490 | −0.147652 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2524 | −0.740275 | ||||||||
\(483\) | 3.95593 | − | 6.85187i | 0.180001 | − | 0.311771i | ||||
\(484\) | 4.77413 | − | 8.26903i | 0.217006 | − | 0.375865i | ||||
\(485\) | 0.995156 | + | 1.72366i | 0.0451877 | + | 0.0782674i | ||||
\(486\) | −14.5875 | −0.661702 | ||||||||
\(487\) | −18.8778 | − | 32.6972i | −0.855433 | − | 1.48165i | −0.876243 | − | 0.481870i | \(-0.839958\pi\) |
0.0208094 | − | 0.999783i | \(-0.493376\pi\) | |||||||
\(488\) | −4.67360 | − | 8.09492i | −0.211564 | − | 0.366440i | ||||
\(489\) | 36.3086 | 1.64193 | ||||||||
\(490\) | 0.143104 | + | 0.247864i | 0.00646479 | + | 0.0111973i | ||||
\(491\) | −15.6555 | + | 27.1161i | −0.706522 | + | 1.22373i | 0.259617 | + | 0.965712i | \(0.416404\pi\) |
−0.966139 | + | 0.258020i | \(0.916930\pi\) | |||||||
\(492\) | −17.6712 | + | 30.6074i | −0.796680 | + | 1.37989i | ||||
\(493\) | 9.99761 | 0.450270 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.14914 | −0.0965969 | ||||||||
\(496\) | −1.83997 | + | 3.18692i | −0.0826171 | + | 0.143097i | ||||
\(497\) | −10.2111 | + | 17.6861i | −0.458031 | + | 0.793332i | ||||
\(498\) | 1.44989 | + | 2.51128i | 0.0649710 | + | 0.112533i | ||||
\(499\) | −21.4873 | −0.961902 | −0.480951 | − | 0.876748i | \(-0.659708\pi\) | ||||
−0.480951 | + | 0.876748i | \(0.659708\pi\) | |||||||
\(500\) | 1.66541 | + | 2.88457i | 0.0744793 | + | 0.129002i | ||||
\(501\) | −18.1075 | − | 31.3632i | −0.808984 | − | 1.40120i | ||||
\(502\) | 19.0228 | 0.849031 | ||||||||
\(503\) | −18.7962 | − | 32.5560i | −0.838081 | − | 1.45160i | −0.891497 | − | 0.453026i | \(-0.850344\pi\) |
0.0534164 | − | 0.998572i | \(-0.482989\pi\) | |||||||
\(504\) | −6.50000 | + | 11.2583i | −0.289533 | + | 0.501486i | ||||
\(505\) | −1.64914 | + | 2.85640i | −0.0733860 | + | 0.127108i | ||||
\(506\) | −5.08815 | −0.226196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3075 | 0.590425 | ||||||||
\(509\) | −8.55376 | + | 14.8155i | −0.379139 | + | 0.656688i | −0.990937 | − | 0.134326i | \(-0.957113\pi\) |
0.611798 | + | 0.791014i | \(0.290446\pi\) | |||||||
\(510\) | 0.480386 | − | 0.832052i | 0.0212718 | − | 0.0368439i | ||||
\(511\) | 7.93751 | + | 13.7482i | 0.351135 | + | 0.608183i | ||||
\(512\) | −6.22282 | −0.275012 | ||||||||
\(513\) | −0.0941868 | − | 0.163136i | −0.00415845 | − | 0.00720264i | ||||
\(514\) | 5.70344 | + | 9.87865i | 0.251568 | + | 0.435728i | ||||
\(515\) | −0.336454 | −0.0148259 | ||||||||
\(516\) | 0.451083 | + | 0.781298i | 0.0198578 | + | 0.0343947i | ||||
\(517\) | −15.6223 | + | 27.0586i | −0.687068 | + | 1.19004i | ||||
\(518\) | −5.37920 | + | 9.31705i | −0.236348 | + | 0.409367i | ||||
\(519\) | 48.3913 | 2.12414 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8465 | −0.869493 | −0.434746 | − | 0.900553i | \(-0.643162\pi\) | ||||
−0.434746 | + | 0.900553i | \(0.643162\pi\) | |||||||
\(522\) | 3.80463 | − | 6.58981i | 0.166524 | − | 0.288428i | ||||
\(523\) | 5.71499 | − | 9.89865i | 0.249899 | − | 0.432838i | −0.713599 | − | 0.700555i | \(-0.752936\pi\) |
0.963498 | + | 0.267717i | \(0.0862693\pi\) | |||||||
\(524\) | −4.46197 | − | 7.72835i | −0.194922 | − | 0.337615i | ||||
\(525\) | 26.1564 | 1.14156 | ||||||||
\(526\) | −6.85474 | − | 11.8728i | −0.298881 | − | 0.517677i | ||||
\(527\) | −7.15764 | − | 12.3974i | −0.311792 | − | 0.540039i | ||||
\(528\) | −5.29590 | −0.230474 | ||||||||
\(529\) | 10.3840 | + | 17.9857i | 0.451480 | + | 0.781987i | ||||
\(530\) | 1.02930 | − | 1.78281i | 0.0447101 | − | 0.0774401i | ||||
\(531\) | −6.94600 | + | 12.0308i | −0.301431 | + | 0.522093i | ||||
\(532\) | −0.281896 | −0.0122218 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.19806 | 0.224942 | ||||||||
\(535\) | 0.403657 | − | 0.699155i | 0.0174516 | − | 0.0302271i | ||||
\(536\) | 10.3373 | − | 17.9047i | 0.446503 | − | 0.773365i | ||||
\(537\) | 12.8448 | + | 22.2479i | 0.554295 | + | 0.960066i | ||||
\(538\) | 5.18598 | 0.223584 | ||||||||
\(539\) | 3.06853 | + | 5.31485i | 0.132171 | + | 0.228927i | ||||
\(540\) | −0.358092 | − | 0.620234i | −0.0154098 | − | 0.0266906i | ||||
\(541\) | −16.1884 | −0.695993 | −0.347996 | − | 0.937496i | \(-0.613138\pi\) | ||||
−0.347996 | + | 0.937496i | \(0.613138\pi\) | |||||||
\(542\) | −2.58546 | − | 4.47814i | −0.111055 | − | 0.192353i | ||||
\(543\) | 23.5601 | − | 40.8073i | 1.01106 | − | 1.75121i | ||||
\(544\) | 6.29201 | − | 10.8981i | 0.269768 | − | 0.467252i | ||||
\(545\) | 3.87800 | 0.166115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.33081 | 0.227929 | 0.113965 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113965 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(548\) | −4.21983 | + | 7.30896i | −0.180262 | + | 0.312223i | ||||
\(549\) | −3.55711 | + | 6.16110i | −0.151814 | + | 0.262949i | ||||
\(550\) | −8.41066 | − | 14.5677i | −0.358632 | − | 0.621168i | ||||
\(551\) | 0.408206 | 0.0173902 | ||||||||
\(552\) | 4.51842 | + | 7.82613i | 0.192317 | + | 0.333102i | ||||
\(553\) | −11.7497 | − | 20.3510i | −0.499647 | − | 0.865413i | ||||
\(554\) | −10.7942 | −0.458600 | ||||||||
\(555\) | 1.57942 | + | 2.73563i | 0.0670425 | + | 0.116121i | ||||
\(556\) | −9.97799 | + | 17.2824i | −0.423161 | + | 0.732937i | ||||
\(557\) | 3.69537 | − | 6.40058i | 0.156578 | − | 0.271201i | −0.777054 | − | 0.629433i | \(-0.783287\pi\) |
0.933633 | + | 0.358232i | \(0.116620\pi\) | |||||||
\(558\) | −10.8955 | −0.461242 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.323044 | −0.0136511 | ||||||||
\(561\) | 10.3007 | − | 17.8414i | 0.434898 | − | 0.753265i | ||||
\(562\) | −2.01961 | + | 3.49807i | −0.0851923 | + | 0.147557i | ||||
\(563\) | 4.73945 | + | 8.20896i | 0.199744 | + | 0.345967i | 0.948445 | − | 0.316941i | \(-0.102656\pi\) |
−0.748701 | + | 0.662907i | \(0.769322\pi\) | |||||||
\(564\) | 22.4306 | 0.944497 | ||||||||
\(565\) | 1.48792 | + | 2.57715i | 0.0625972 | + | 0.108422i | ||||
\(566\) | 8.87263 | + | 15.3678i | 0.372944 | + | 0.645958i | ||||
\(567\) | −25.8049 | −1.08370 | ||||||||
\(568\) | −11.6630 | − | 20.2009i | −0.489369 | − | 0.847612i | ||||
\(569\) | 5.07188 | − | 8.78476i | 0.212624 | − | 0.368276i | −0.739911 | − | 0.672705i | \(-0.765132\pi\) |
0.952535 | + | 0.304429i | \(0.0984656\pi\) | |||||||
\(570\) | 0.0196143 | − | 0.0339730i | 0.000821554 | − | 0.00142297i | ||||
\(571\) | −14.0925 | −0.589751 | −0.294876 | − | 0.955536i | \(-0.595278\pi\) | ||||
−0.294876 | + | 0.955536i | \(0.595278\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.4403 | 1.35521 | ||||||||
\(574\) | 10.9547 | − | 18.9741i | 0.457242 | − | 0.791966i | ||||
\(575\) | 3.68933 | − | 6.39011i | 0.153856 | − | 0.266486i | ||||
\(576\) | −3.65183 | − | 6.32516i | −0.152160 | − | 0.263548i | ||||
\(577\) | −25.1545 | −1.04720 | −0.523598 | − | 0.851965i | \(-0.675411\pi\) | ||||
−0.523598 | + | 0.851965i | \(0.675411\pi\) | |||||||
\(578\) | −4.94773 | − | 8.56972i | −0.205798 | − | 0.356453i | ||||
\(579\) | 15.2567 | + | 26.4253i | 0.634045 | + | 1.09820i | ||||
\(580\) | 1.55197 | 0.0644422 | ||||||||
\(581\) | 1.89642 | + | 3.28470i | 0.0786768 | + | 0.136272i | ||||
\(582\) | −7.26055 | + | 12.5756i | −0.300960 | + | 0.521277i | ||||
\(583\) | 22.0710 | − | 38.2281i | 0.914087 | − | 1.58324i | ||||
\(584\) | −18.1323 | −0.750319 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.9860 | 0.495137 | ||||||||
\(587\) | 21.9177 | − | 37.9625i | 0.904639 | − | 1.56688i | 0.0832369 | − | 0.996530i | \(-0.473474\pi\) |
0.821402 | − | 0.570350i | \(-0.193192\pi\) | |||||||
\(588\) | 2.20291 | − | 3.81555i | 0.0908463 | − | 0.157350i | ||||
\(589\) | −0.292249 | − | 0.506190i | −0.0120419 | − | 0.0208572i | ||||
\(590\) | 1.34290 | 0.0552861 | ||||||||
\(591\) | 0.629531 | + | 1.09038i | 0.0258954 | + | 0.0448522i | ||||
\(592\) | 1.57942 | + | 2.73563i | 0.0649136 | + | 0.112434i | ||||
\(593\) | 24.9965 | 1.02648 | 0.513242 | − | 0.858244i | \(-0.328444\pi\) | ||||
0.513242 | + | 0.858244i | \(0.328444\pi\) | |||||||
\(594\) | 3.63922 | + | 6.30331i | 0.149319 | + | 0.258628i | ||||
\(595\) | 0.628334 | − | 1.08831i | 0.0257592 | − | 0.0446162i | ||||
\(596\) | −2.94116 | + | 5.09423i | −0.120474 | + | 0.208668i | ||||
\(597\) | −25.8213 | −1.05680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.24027 | −0.254971 | −0.127485 | − | 0.991840i | \(-0.540691\pi\) | ||||
−0.127485 | + | 0.991840i | \(0.540691\pi\) | |||||||
\(600\) | −14.9378 | + | 25.8730i | −0.609833 | + | 1.05626i | ||||
\(601\) | −3.16487 | + | 5.48172i | −0.129098 | + | 0.223604i | −0.923327 | − | 0.384014i | \(-0.874541\pi\) |
0.794229 | + | 0.607618i | \(0.207875\pi\) | |||||||
\(602\) | −0.279635 | − | 0.484342i | −0.0113971 | − | 0.0197403i | ||||
\(603\) | −15.7356 | −0.640802 | ||||||||
\(604\) | −2.67606 | − | 4.63506i | −0.108887 | − | 0.188598i | ||||
\(605\) | 0.868977 | + | 1.50511i | 0.0353290 | + | 0.0611915i | ||||
\(606\) | −24.0640 | −0.977532 | ||||||||
\(607\) | 21.8240 | + | 37.8003i | 0.885809 | + | 1.53427i | 0.844784 | + | 0.535108i | \(0.179729\pi\) |
0.0410253 | + | 0.999158i | \(0.486938\pi\) | |||||||
\(608\) | 0.256905 | − | 0.444973i | 0.0104189 | − | 0.0180460i | ||||
\(609\) | 12.2627 | − | 21.2396i | 0.496910 | − | 0.860673i | ||||
\(610\) | 0.687710 | 0.0278445 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.00192 | −0.242613 | ||||||||
\(613\) | −12.9770 | + | 22.4769i | −0.524137 | + | 0.907833i | 0.475468 | + | 0.879733i | \(0.342279\pi\) |
−0.999605 | + | 0.0280995i | \(0.991054\pi\) | |||||||
\(614\) | −7.67025 | + | 13.2853i | −0.309546 | + | 0.536150i | ||||
\(615\) | −3.21648 | − | 5.57111i | −0.129701 | − | 0.224649i | ||||
\(616\) | 26.9463 | 1.08570 | ||||||||
\(617\) | 22.9698 | + | 39.7849i | 0.924729 | + | 1.60168i | 0.791996 | + | 0.610526i | \(0.209042\pi\) |
0.132733 | + | 0.991152i | \(0.457625\pi\) | |||||||
\(618\) | −1.22737 | − | 2.12586i | −0.0493719 | − | 0.0855146i | ||||
\(619\) | −6.73556 | −0.270725 | −0.135363 | − | 0.990796i | \(-0.543220\pi\) | ||||
−0.135363 | + | 0.990796i | \(0.543220\pi\) | |||||||
\(620\) | −1.11111 | − | 1.92450i | −0.0446234 | − | 0.0772899i | ||||
\(621\) | −1.59634 | + | 2.76495i | −0.0640590 | + | 0.110953i | ||||
\(622\) | −0.108187 | + | 0.187386i | −0.00433792 | + | 0.00751349i | ||||
\(623\) | 6.79895 | 0.272394 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0887 | 0.963549 | ||||||||
\(626\) | −9.38016 | + | 16.2469i | −0.374907 | + | 0.649357i | ||||
\(627\) | 0.420583 | − | 0.728471i | 0.0167965 | − | 0.0290923i | ||||
\(628\) | 3.02230 | + | 5.23478i | 0.120603 | + | 0.208891i | ||||
\(629\) | −12.2881 | −0.489960 | ||||||||
\(630\) | −0.478230 | − | 0.828318i | −0.0190531 | − | 0.0330010i | ||||
\(631\) | 22.5499 | + | 39.0575i | 0.897696 | + | 1.55486i | 0.830432 | + | 0.557121i | \(0.188094\pi\) |
0.0672649 | + | 0.997735i | \(0.478573\pi\) | |||||||
\(632\) | 26.8407 | 1.06767 | ||||||||
\(633\) | 9.86927 | + | 17.0941i | 0.392268 | + | 0.679429i | ||||
\(634\) | 5.61165 | − | 9.71965i | 0.222867 | − | 0.386017i | ||||
\(635\) | −1.21110 | + | 2.09769i | −0.0480612 | + | 0.0832444i | ||||
\(636\) | −31.6896 | −1.25658 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.7724 | −0.624435 | ||||||||
\(639\) | −8.87681 | + | 15.3751i | −0.351161 | + | 0.608229i | ||||
\(640\) | 1.08665 | − | 1.88214i | 0.0429538 | − | 0.0743981i | ||||
\(641\) | −16.2911 | − | 28.2169i | −0.643458 | − | 1.11450i | −0.984655 | − | 0.174510i | \(-0.944166\pi\) |
0.341197 | − | 0.939992i | \(-0.389168\pi\) | |||||||
\(642\) | 5.89008 | 0.232463 | ||||||||
\(643\) | 12.7877 | + | 22.1489i | 0.504298 | + | 0.873469i | 0.999988 | + | 0.00496965i | \(0.00158190\pi\) |
−0.495690 | + | 0.868500i | \(0.665085\pi\) | |||||||
\(644\) | 2.38889 | + | 4.13767i | 0.0941353 | + | 0.163047i | ||||
\(645\) | −0.164210 | −0.00646578 | ||||||||
\(646\) | 0.0763014 | + | 0.132158i | 0.00300204 | + | 0.00519968i | ||||
\(647\) | 15.0858 | − | 26.1293i | 0.593082 | − | 1.02725i | −0.400732 | − | 0.916195i | \(-0.631244\pi\) |
0.993814 | − | 0.111053i | \(-0.0354224\pi\) | |||||||
\(648\) | 14.7371 | − | 25.5253i | 0.578926 | − | 1.00273i | ||||
\(649\) | 28.7952 | 1.13031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.1172 | −1.37635 | ||||||||
\(652\) | −10.9629 | + | 18.9883i | −0.429341 | + | 0.743641i | ||||
\(653\) | −18.4514 | + | 31.9587i | −0.722058 | + | 1.25064i | 0.238115 | + | 0.971237i | \(0.423470\pi\) |
−0.960173 | + | 0.279405i | \(0.909863\pi\) | |||||||
\(654\) | 14.1468 | + | 24.5029i | 0.553182 | + | 0.958139i | ||||
\(655\) | 1.62432 | 0.0634673 | ||||||||
\(656\) | −3.21648 | − | 5.57111i | −0.125582 | − | 0.217515i | ||||
\(657\) | 6.90030 | + | 11.9517i | 0.269207 | + | 0.466279i | ||||
\(658\) | −13.9051 | −0.542079 | ||||||||
\(659\) | −11.8433 | − | 20.5132i | −0.461350 | − | 0.799082i | 0.537678 | − | 0.843150i | \(-0.319302\pi\) |
−0.999029 | + | 0.0440679i | \(0.985968\pi\) | |||||||
\(660\) | 1.59903 | − | 2.76960i | 0.0622422 | − | 0.107807i | ||||
\(661\) | −15.8795 | + | 27.5041i | −0.617641 | + | 1.06979i | 0.372274 | + | 0.928123i | \(0.378578\pi\) |
−0.989915 | + | 0.141662i | \(0.954755\pi\) | |||||||
\(662\) | 14.2916 | 0.555458 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.33214 | −0.168120 | ||||||||
\(665\) | 0.0256551 | − | 0.0444360i | 0.000994863 | − | 0.00172315i | ||||
\(666\) | −4.67629 | + | 8.09958i | −0.181203 | + | 0.313852i | ||||
\(667\) | −3.45928 | − | 5.99165i | −0.133944 | − | 0.231998i | ||||
\(668\) | 21.8694 | 0.846152 | ||||||||
\(669\) | 2.53803 | + | 4.39600i | 0.0981260 | + | 0.169959i | ||||
\(670\) | 0.760553 | + | 1.31732i | 0.0293827 | + | 0.0508924i | ||||
\(671\) | 14.7463 | 0.569275 | ||||||||
\(672\) | −15.4351 | − | 26.7344i | −0.595423 | − | 1.03130i | ||||
\(673\) | 3.75116 | − | 6.49720i | 0.144597 | − | 0.250449i | −0.784626 | − | 0.619970i | \(-0.787145\pi\) |
0.929222 | + | 0.369521i | \(0.120478\pi\) | |||||||
\(674\) | −11.1664 | + | 19.3407i | −0.430112 | + | 0.744976i | ||||
\(675\) | −10.5550 | −0.406261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.0315 | −1.34637 | −0.673184 | − | 0.739475i | \(-0.735074\pi\) | ||||
−0.673184 | + | 0.739475i | \(0.735074\pi\) | |||||||
\(678\) | −10.8557 | + | 18.8026i | −0.416911 | + | 0.722110i | ||||
\(679\) | −9.49665 | + | 16.4487i | −0.364448 | + | 0.631242i | ||||
\(680\) | 0.717677 | + | 1.24305i | 0.0275216 | + | 0.0476689i | ||||
\(681\) | −15.6528 | −0.599816 | ||||||||
\(682\) | 11.2920 | + | 19.5583i | 0.432393 | + | 0.748927i | ||||
\(683\) | −12.0417 | − | 20.8568i | −0.460762 | − | 0.798063i | 0.538237 | − | 0.842794i | \(-0.319091\pi\) |
−0.998999 | + | 0.0447302i | \(0.985757\pi\) | |||||||
\(684\) | −0.245061 | −0.00937013 | ||||||||
\(685\) | −0.768086 | − | 1.33036i | −0.0293471 | − | 0.0508306i | ||||
\(686\) | −7.98092 | + | 13.8234i | −0.304713 | + | 0.527778i | ||||
\(687\) | 27.1591 | − | 47.0410i | 1.03619 | − | 1.79473i | ||||
\(688\) | −0.164210 | −0.00626046 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.664874 | −0.0253113 | ||||||||
\(691\) | 1.00724 | − | 1.74459i | 0.0383171 | − | 0.0663672i | −0.846231 | − | 0.532816i | \(-0.821134\pi\) |
0.884548 | + | 0.466449i | \(0.154467\pi\) | |||||||
\(692\) | −14.6112 | + | 25.3073i | −0.555433 | + | 0.962039i | ||||
\(693\) | −10.2545 | − | 17.7613i | −0.389537 | − | 0.674697i | ||||
\(694\) | −1.20583 | −0.0457728 | ||||||||
\(695\) | −1.81618 | − | 3.14571i | −0.0688915 | − | 0.119323i | ||||
\(696\) | 14.0063 | + | 24.2597i | 0.530909 | + | 0.919561i | ||||
\(697\) | 25.0248 | 0.947880 | ||||||||
\(698\) | 5.68814 | + | 9.85214i | 0.215299 | + | 0.372909i | ||||
\(699\) | −3.43900 | + | 5.95652i | −0.130075 | + | 0.225296i | ||||
\(700\) | −7.89762 | + | 13.6791i | −0.298502 | + | 0.517020i | ||||
\(701\) | −48.8189 | −1.84387 | −0.921933 | − | 0.387350i | \(-0.873390\pi\) | ||||
−0.921933 | + | 0.387350i | \(0.873390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.501729 | −0.0189231 | ||||||||
\(704\) | −7.56949 | + | 13.1107i | −0.285286 | + | 0.494130i | ||||
\(705\) | −2.04138 | + | 3.53578i | −0.0768830 | + | 0.133165i | ||||
\(706\) | 2.87435 | + | 4.97853i | 0.108178 | + | 0.187369i | ||||
\(707\) | −31.4752 | −1.18375 | ||||||||
\(708\) | −10.3361 | − | 17.9026i | −0.388454 | − | 0.672822i | ||||
\(709\) | −10.4030 | − | 18.0185i | −0.390693 | − | 0.676699i | 0.601848 | − | 0.798610i | \(-0.294431\pi\) |
−0.992541 | + | 0.121911i | \(0.961098\pi\) | |||||||
\(710\) | 1.71618 | 0.0644073 | ||||||||
\(711\) | −10.2143 | − | 17.6917i | −0.383067 | − | 0.663492i | ||||
\(712\) | −3.88285 | + | 6.72529i | −0.145516 | + | 0.252041i | ||||
\(713\) | −4.95324 | + | 8.57926i | −0.185500 | + | 0.321296i | ||||
\(714\) | 9.16852 | 0.343123 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.5133 | −0.579761 | ||||||||
\(717\) | 28.2521 | − | 48.9341i | 1.05509 | − | 1.82748i | ||||
\(718\) | −7.97339 | + | 13.8103i | −0.297564 | + | 0.515396i | ||||
\(719\) | −10.7153 | − | 18.5594i | −0.399613 | − | 0.692149i | 0.594065 | − | 0.804417i | \(-0.297522\pi\) |
−0.993678 | + | 0.112267i | \(0.964189\pi\) | |||||||
\(720\) | −0.280831 | −0.0104660 | ||||||||
\(721\) | −1.60537 | − | 2.78058i | −0.0597870 | − | 0.103554i | ||||
\(722\) | −7.61529 | − | 13.1901i | −0.283412 | − | 0.490884i | ||||
\(723\) | −45.5381 | −1.69358 | ||||||||
\(724\) | 14.2274 | + | 24.6425i | 0.528756 | + | 0.915832i | ||||
\(725\) | 11.4363 | − | 19.8083i | 0.424734 | − | 0.735661i | ||||
\(726\) | −6.33997 | + | 10.9812i | −0.235298 | + | 0.407549i | ||||
\(727\) | 13.4862 | 0.500175 | 0.250088 | − | 0.968223i | \(-0.419541\pi\) | ||||
0.250088 | + | 0.968223i | \(0.419541\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02715 | −0.297302 | ||||||||
\(730\) | 0.667030 | − | 1.15533i | 0.0246879 | − | 0.0427607i | ||||
\(731\) | 0.319396 | − | 0.553210i | 0.0118133 | − | 0.0204612i | ||||
\(732\) | −5.29321 | − | 9.16811i | −0.195643 | − | 0.338863i | ||||
\(733\) | 43.5424 | 1.60828 | 0.804138 | − | 0.594443i | \(-0.202627\pi\) | ||||
0.804138 | + | 0.594443i | \(0.202627\pi\) | |||||||
\(734\) | 0.434584 | + | 0.752721i | 0.0160408 | + | 0.0277834i | ||||
\(735\) | 0.400969 | + | 0.694498i | 0.0147900 | + | 0.0256170i | ||||
\(736\) | −8.70841 | −0.320996 | ||||||||
\(737\) | 16.3083 | + | 28.2468i | 0.600723 | + | 1.04048i | ||||
\(738\) | 9.52326 | − | 16.4948i | 0.350556 | − | 0.607181i | ||||
\(739\) | 10.0271 | − | 17.3675i | 0.368855 | − | 0.638875i | −0.620532 | − | 0.784181i | \(-0.713083\pi\) |
0.989387 | + | 0.145306i | \(0.0464167\pi\) | |||||||
\(740\) | −1.90754 | −0.0701226 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.6450 | 0.721191 | ||||||||
\(743\) | −16.5843 | + | 28.7248i | −0.608418 | + | 1.05381i | 0.383084 | + | 0.923714i | \(0.374862\pi\) |
−0.991501 | + | 0.130096i | \(0.958471\pi\) | |||||||
\(744\) | 20.0553 | − | 34.7367i | 0.735261 | − | 1.27351i | ||||
\(745\) | −0.535344 | − | 0.927243i | −0.0196135 | − | 0.0339715i | ||||
\(746\) | 4.91617 | 0.179994 | ||||||||
\(747\) | 1.64861 | + | 2.85548i | 0.0603196 | + | 0.104477i | ||||
\(748\) | 6.22037 | + | 10.7740i | 0.227439 | + | 0.393936i | ||||
\(749\) | 7.70410 | 0.281502 | ||||||||
\(750\) | −2.21164 | − | 3.83067i | −0.0807575 | − | 0.139876i | ||||
\(751\) | −19.6407 | + | 34.0187i | −0.716700 | + | 1.24136i | 0.245601 | + | 0.969371i | \(0.421015\pi\) |
−0.962300 | + | 0.271989i | \(0.912318\pi\) | |||||||
\(752\) | −2.04138 | + | 3.53578i | −0.0744416 | + | 0.128937i | ||||
\(753\) | 53.3008 | 1.94239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.974181 | 0.0354541 | ||||||||
\(756\) | 3.41723 | − | 5.91882i | 0.124283 | − | 0.215265i | ||||
\(757\) | 23.3213 | − | 40.3937i | 0.847628 | − | 1.46813i | −0.0356920 | − | 0.999363i | \(-0.511364\pi\) |
0.883320 | − | 0.468771i | \(-0.155303\pi\) | |||||||
\(758\) | 0.965853 | + | 1.67291i | 0.0350813 | + | 0.0607627i | ||||
\(759\) | −14.2567 | −0.517484 | ||||||||
\(760\) | 0.0293030 | + | 0.0507543i | 0.00106293 | + | 0.00184105i | ||||
\(761\) | −10.9492 | − | 18.9646i | −0.396909 | − | 0.687467i | 0.596434 | − | 0.802662i | \(-0.296584\pi\) |
−0.993343 | + | 0.115196i | \(0.963250\pi\) | |||||||
\(762\) | −17.6722 | −0.640195 | ||||||||
\(763\) | 18.5036 | + | 32.0493i | 0.669877 | + | 1.16026i | ||||
\(764\) | −9.79494 | + | 16.9653i | −0.354368 | + | 0.613784i | ||||
\(765\) | 0.546229 | − | 0.946096i | 0.0197489 | − | 0.0342062i | ||||
\(766\) | −24.3720 | −0.880595 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 31.8756 | 1.15021 | ||||||||
\(769\) | 23.3548 | − | 40.4517i | 0.842196 | − | 1.45873i | −0.0458390 | − | 0.998949i | \(-0.514596\pi\) |
0.888035 | − | 0.459777i | \(-0.152071\pi\) | |||||||
\(770\) | −0.991271 | + | 1.71693i | −0.0357229 | + | 0.0618739i | ||||
\(771\) | 15.9807 | + | 27.6794i | 0.575530 | + | 0.996848i | ||||
\(772\) | −18.4263 | −0.663175 | ||||||||
\(773\) | −15.1208 | − | 26.1900i | −0.543857 | − | 0.941989i | −0.998678 | − | 0.0514055i | \(-0.983630\pi\) |
0.454820 | − | 0.890583i | \(-0.349703\pi\) | |||||||
\(774\) | −0.243095 | − | 0.421052i | −0.00873786 | − | 0.0151344i | ||||
\(775\) | −32.7506 | −1.17644 | ||||||||
\(776\) | −10.8470 | − | 18.7875i | −0.389384 | − | 0.674432i | ||||
\(777\) | −15.0722 | + | 26.1058i | −0.540711 | + | 0.936540i | ||||
\(778\) | −6.39181 | + | 11.0709i | −0.229158 | + | 0.396913i | ||||
\(779\) | 1.02177 | 0.0366087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.7995 | 1.31679 | ||||||||
\(782\) | 1.29321 | − | 2.23990i | 0.0462450 | − | 0.0800988i | ||||
\(783\) | −4.94839 | + | 8.57087i | −0.176841 | + | 0.306298i | ||||
\(784\) | 0.400969 | + | 0.694498i | 0.0143203 | + | 0.0248035i | ||||
\(785\) | −1.10023 | −0.0392688 | ||||||||
\(786\) | 5.92543 | + | 10.2631i | 0.211353 | + | 0.366074i | ||||
\(787\) | 14.3512 | + | 24.8569i | 0.511563 | + | 0.886054i | 0.999910 | + | 0.0134040i | \(0.00426675\pi\) |
−0.488347 | + | 0.872650i | \(0.662400\pi\) | |||||||
\(788\) | −0.760316 | −0.0270851 | ||||||||
\(789\) | −19.2066 | − | 33.2667i | −0.683771 | − | 1.18433i | ||||
\(790\) | −0.987386 | + | 1.71020i | −0.0351296 | + | 0.0608463i | ||||
\(791\) | −14.1990 | + | 24.5934i | −0.504859 | + | 0.874442i | ||||
\(792\) | 23.4252 | 0.832378 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.5646 | 0.481391 | ||||||||
\(795\) | 2.88404 | − | 4.99531i | 0.102286 | − | 0.177165i | ||||
\(796\) | 7.79643 | − | 13.5038i | 0.276337 | − | 0.478630i | ||||
\(797\) | 9.27091 | + | 16.0577i | 0.328392 | + | 0.568792i | 0.982193 | − | 0.187875i | \(-0.0601599\pi\) |
−0.653801 | + | 0.756667i | \(0.726827\pi\) | |||||||
\(798\) | 0.374354 | 0.0132520 | ||||||||
\(799\) | −7.94116 | − | 13.7545i | −0.280938 | − | 0.486599i | ||||
\(800\) | −14.3949 | − | 24.9327i | −0.508938 | − | 0.881506i | ||||
\(801\) | 5.91053 | 0.208838 | ||||||||
\(802\) | −10.6908 | − | 18.5171i | −0.377506 | − | 0.653860i | ||||
\(803\) | 14.3029 | − | 24.7733i | 0.504738 | − | 0.874232i | ||||
\(804\) | 11.7078 | − | 20.2784i | 0.412901 | − | 0.715165i | ||||
\(805\) | −0.869641 | −0.0306508 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5308 | 0.511508 | ||||||||
\(808\) | 17.9753 | − | 31.1341i | 0.632369 | − | 1.09530i | ||||
\(809\) | 5.03385 | − | 8.71889i | 0.176981 | − | 0.306540i | −0.763864 | − | 0.645377i | \(-0.776700\pi\) |
0.940845 | + | 0.338837i | \(0.110034\pi\) | |||||||
\(810\) | 1.08426 | + | 1.87800i | 0.0380971 | + | 0.0659860i | ||||
\(811\) | 10.0285 | 0.352147 | 0.176074 | − | 0.984377i | \(-0.443660\pi\) | ||||
0.176074 | + | 0.984377i | \(0.443660\pi\) | |||||||
\(812\) | 7.40515 | + | 12.8261i | 0.259870 | + | 0.450108i | ||||
\(813\) | −7.24429 | − | 12.5475i | −0.254068 | − | 0.440059i | ||||
\(814\) | 19.3860 | 0.679478 | ||||||||
\(815\) | −1.99545 | − | 3.45622i | −0.0698976 | − | 0.121066i | ||||
\(816\) | 1.34601 | − | 2.33136i | 0.0471198 | − | 0.0816139i | ||||
\(817\) | 0.0130411 | − | 0.0225878i | 0.000456249 | − | 0.000790247i | ||||
\(818\) | 22.8683 | 0.799572 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.88471 | 0.135660 | ||||||||
\(821\) | −13.0852 | + | 22.6643i | −0.456677 | + | 0.790988i | −0.998783 | − | 0.0493220i | \(-0.984294\pi\) |
0.542106 | + | 0.840310i | \(0.317627\pi\) | |||||||
\(822\) | 5.60388 | − | 9.70620i | 0.195458 | − | 0.338542i | ||||
\(823\) | −0.911190 | − | 1.57823i | −0.0317621 | − | 0.0550135i | 0.849707 | − | 0.527255i | \(-0.176779\pi\) |
−0.881470 | + | 0.472241i | \(0.843445\pi\) | |||||||
\(824\) | 3.66727 | 0.127755 | ||||||||
\(825\) | −23.5661 | − | 40.8177i | −0.820468 | − | 1.42109i | ||||
\(826\) | 6.40754 | + | 11.0982i | 0.222947 | + | 0.386155i | ||||
\(827\) | 32.2941 | 1.12298 | 0.561488 | − | 0.827485i | \(-0.310229\pi\) | ||||
0.561488 | + | 0.827485i | \(0.310229\pi\) | |||||||
\(828\) | 2.07673 | + | 3.59700i | 0.0721713 | + | 0.125004i | ||||
\(829\) | −7.55011 | + | 13.0772i | −0.262226 | + | 0.454189i | −0.966833 | − | 0.255409i | \(-0.917790\pi\) |
0.704607 | + | 0.709598i | \(0.251123\pi\) | |||||||
\(830\) | 0.159366 | − | 0.276030i | 0.00553168 | − | 0.00958115i | ||||
\(831\) | −30.2446 | −1.04917 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.11960 | −0.108088 | ||||||||
\(834\) | 13.2506 | − | 22.9508i | 0.458832 | − | 0.794720i | ||||
\(835\) | −1.99031 | + | 3.44732i | −0.0688776 | + | 0.119299i | ||||
\(836\) | 0.253980 | + | 0.439906i | 0.00878408 | + | 0.0152145i | ||||
\(837\) | 14.1709 | 0.489818 | ||||||||
\(838\) | −11.8724 | − | 20.5636i | −0.410125 | − | 0.710357i | ||||
\(839\) | −16.4983 | − | 28.5758i | −0.569584 | − | 0.986548i | −0.996607 | − | 0.0823071i | \(-0.973771\pi\) |
0.427023 | − | 0.904241i | \(-0.359562\pi\) | |||||||
\(840\) | 3.52111 | 0.121490 | ||||||||
\(841\) | 3.77682 | + | 6.54164i | 0.130235 | + | 0.225574i | ||||
\(842\) | 4.67552 | − | 8.09824i | 0.161129 | − | 0.279084i | ||||
\(843\) | −5.65883 | + | 9.80139i | −0.194901 | + | 0.337578i | ||||
\(844\) | −11.9196 | −0.410290 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0881 | −0.415599 | ||||||||
\(847\) | −8.29254 | + | 14.3631i | −0.284935 | + | 0.493522i | ||||
\(848\) | 2.88404 | − | 4.99531i | 0.0990384 | − | 0.171540i | ||||
\(849\) | 24.8605 | + | 43.0597i | 0.853212 | + | 1.47781i | ||||
\(850\) | 8.55065 | 0.293285 | ||||||||
\(851\) | 4.25182 | + | 7.36438i | 0.145751 | + | 0.252448i | ||||
\(852\) | −13.2092 | − | 22.8791i | −0.452541 | − | 0.783824i | ||||
\(853\) | 37.7802 | 1.29357 | 0.646784 | − | 0.762673i | \(-0.276113\pi\) | ||||
0.646784 | + | 0.762673i | \(0.276113\pi\) | |||||||
\(854\) | 3.28136 | + | 5.68349i | 0.112286 | + | 0.194485i | ||||
\(855\) | 0.0223027 | − | 0.0386295i | 0.000762737 | − | 0.00132110i | ||||
\(856\) | −4.39977 | + | 7.62063i | −0.150381 | + | 0.260468i | ||||
\(857\) | 27.3623 | 0.934677 | 0.467339 | − | 0.884078i | \(-0.345213\pi\) | ||||
0.467339 | + | 0.884078i | \(0.345213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0629 | −0.684538 | −0.342269 | − | 0.939602i | \(-0.611195\pi\) | ||||
−0.342269 | + | 0.939602i | \(0.611195\pi\) | |||||||
\(860\) | 0.0495813 | − | 0.0858774i | 0.00169071 | − | 0.00292839i | ||||
\(861\) | 30.6945 | − | 53.1644i | 1.04606 | − | 1.81184i | ||||
\(862\) | −1.74386 | − | 3.02046i | −0.0593962 | − | 0.102877i | ||||
\(863\) | 6.14483 | 0.209173 | 0.104586 | − | 0.994516i | \(-0.466648\pi\) | ||||
0.104586 | + | 0.994516i | \(0.466648\pi\) | |||||||
\(864\) | 6.22856 | + | 10.7882i | 0.211900 | + | 0.367022i | ||||
\(865\) | −2.65950 | − | 4.60638i | −0.0904256 | − | 0.156622i | ||||
\(866\) | 11.5386 | 0.392096 | ||||||||
\(867\) | −13.8632 | − | 24.0118i | −0.470820 | − | 0.815484i | ||||
\(868\) | 10.6032 | − | 18.3653i | 0.359896 | − | 0.623359i | ||||
\(869\) | −21.1722 | + | 36.6713i | −0.718217 | + | 1.24399i | ||||
\(870\) | −2.06100 | −0.0698744 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −42.2693 | −1.43142 | ||||||||
\(873\) | −8.25571 | + | 14.2993i | −0.279413 | + | 0.483958i | ||||
\(874\) | 0.0528022 | − | 0.0914561i | 0.00178606 | − | 0.00309355i | ||||
\(875\) | −2.89277 | − | 5.01043i | −0.0977935 | − | 0.169383i | ||||
\(876\) | −20.5362 | −0.693853 | ||||||||
\(877\) | −6.75385 | − | 11.6980i | −0.228061 | − | 0.395014i | 0.729172 | − | 0.684330i | \(-0.239905\pi\) |
−0.957233 | + | 0.289317i | \(0.906572\pi\) | |||||||
\(878\) | −8.11260 | − | 14.0514i | −0.273787 | − | 0.474213i | ||||
\(879\) | 33.5840 | 1.13276 | ||||||||
\(880\) | 0.291053 | + | 0.504118i | 0.00981138 | + | 0.0169938i | ||||
\(881\) | 2.61715 | − | 4.53304i | 0.0881741 | − | 0.152722i | −0.818565 | − | 0.574414i | \(-0.805230\pi\) |
0.906739 | + | 0.421691i | \(0.138563\pi\) | |||||||
\(882\) | −1.18718 | + | 2.05625i | −0.0399743 | + | 0.0692376i | ||||
\(883\) | −4.57301 | −0.153894 | −0.0769470 | − | 0.997035i | \(-0.524517\pi\) | ||||
−0.0769470 | + | 0.997035i | \(0.524517\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.76271 | 0.126482 | ||||||||
\(886\) | 3.25667 | − | 5.64071i | 0.109410 | − | 0.189504i | ||||
\(887\) | 0.820356 | − | 1.42090i | 0.0275448 | − | 0.0477091i | −0.851924 | − | 0.523665i | \(-0.824564\pi\) |
0.879469 | + | 0.475956i | \(0.157898\pi\) | |||||||
\(888\) | −17.2153 | − | 29.8177i | −0.577707 | − | 1.00062i | ||||
\(889\) | −23.1148 | −0.775246 | ||||||||
\(890\) | −0.285676 | − | 0.494805i | −0.00957587 | − | 0.0165859i | ||||
\(891\) | 23.2494 | + | 40.2692i | 0.778885 | + | 1.34907i | ||||
\(892\) | −3.06531 | −0.102634 | ||||||||
\(893\) | −0.324240 | − | 0.561601i | −0.0108503 | − | 0.0187933i | ||||
\(894\) | 3.90581 | − | 6.76507i | 0.130630 | − | 0.226258i | ||||
\(895\) | 1.41185 | − | 2.44540i | 0.0471931 | − | 0.0817408i | ||||
\(896\) | 20.7396 | 0.692862 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0175 | 0.334287 | ||||||||
\(899\) | −15.3542 | + | 26.5943i | −0.512091 | + | 0.886968i | ||||
\(900\) | −6.86563 | + | 11.8916i | −0.228854 | + | 0.396387i | ||||
\(901\) | 11.2192 | + | 19.4322i | 0.373765 | + | 0.647379i | ||||
\(902\) | −39.4795 | −1.31452 | ||||||||
\(903\) | −0.783520 | − | 1.35710i | −0.0260739 | − | 0.0451613i | ||||
\(904\) | −16.2180 | − | 28.0904i | −0.539402 | − | 0.934271i | ||||
\(905\) | −5.17928 | −0.172165 | ||||||||
\(906\) | 3.55376 | + | 6.15530i | 0.118066 | + | 0.204496i | ||||
\(907\) | −4.05107 | + | 7.01666i | −0.134514 | + | 0.232985i | −0.925412 | − | 0.378964i | \(-0.876281\pi\) |
0.790898 | + | 0.611948i | \(0.209614\pi\) | |||||||
\(908\) | 4.72617 | − | 8.18596i | 0.156843 | − | 0.271661i | ||||
\(909\) | −27.3623 | −0.907549 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.18119 | −0.304187 | −0.152093 | − | 0.988366i | \(-0.548601\pi\) | ||||
−0.152093 | + | 0.988366i | \(0.548601\pi\) | |||||||
\(912\) | 0.0549581 | − | 0.0951903i | 0.00181985 | − | 0.00315207i | ||||
\(913\) | 3.41723 | − | 5.91882i | 0.113094 | − | 0.195884i | ||||
\(914\) | −2.39828 | − | 4.15394i | −0.0793281 | − | 0.137400i | ||||
\(915\) | 1.92692 | 0.0637020 | ||||||||
\(916\) | 16.4007 | + | 28.4069i | 0.541895 | + | 0.938590i | ||||
\(917\) | 7.75033 | + | 13.4240i | 0.255939 | + | 0.443299i | ||||
\(918\) | −3.69979 | −0.122111 | ||||||||
\(919\) | −13.7518 | − | 23.8189i | −0.453631 | − | 0.785712i | 0.544978 | − | 0.838451i | \(-0.316538\pi\) |
−0.998608 | + | 0.0527390i | \(0.983205\pi\) | |||||||
\(920\) | 0.496648 | − | 0.860219i | 0.0163740 | − | 0.0283606i | ||||
\(921\) | −21.4916 | + | 37.2245i | −0.708171 | + | 1.22659i | ||||
\(922\) | −1.64933 | −0.0543180 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 30.5187 | 1.00399 | ||||||||
\(925\) | −14.0565 | + | 24.3465i | −0.462173 | + | 0.800508i | ||||
\(926\) | 3.38793 | − | 5.86806i | 0.111334 | − | 0.192837i | ||||
\(927\) | −1.39559 | − | 2.41724i | −0.0458373 | − | 0.0793925i | ||||
\(928\) | −26.9946 | −0.886142 | ||||||||
\(929\) | 12.1066 | + | 20.9692i | 0.397203 | + | 0.687977i | 0.993380 | − | 0.114877i | \(-0.0366474\pi\) |
−0.596176 | + | 0.802854i | \(0.703314\pi\) | |||||||
\(930\) | 1.47554 | + | 2.55571i | 0.0483849 | + | 0.0838051i | ||||
\(931\) | −0.127375 | −0.00417454 | ||||||||
\(932\) | −2.07673 | − | 3.59700i | −0.0680255 | − | 0.117824i | ||||
\(933\) | −0.303134 | + | 0.525044i | −0.00992417 | + | 0.0171892i | ||||
\(934\) | 13.4380 | − | 23.2754i | 0.439706 | − | 0.761593i | ||||
\(935\) | −2.26444 | −0.0740550 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1830 | 0.365333 | 0.182666 | − | 0.983175i | \(-0.441527\pi\) | ||||
0.182666 | + | 0.983175i | \(0.441527\pi\) | |||||||
\(938\) | −7.25786 | + | 12.5710i | −0.236978 | + | 0.410457i | ||||
\(939\) | −26.2826 | + | 45.5228i | −0.857701 | + | 1.48558i | ||||
\(940\) | −1.23274 | − | 2.13517i | −0.0402076 | − | 0.0696416i | ||||
\(941\) | 15.9638 | 0.520404 | 0.260202 | − | 0.965554i | \(-0.416211\pi\) | ||||
0.260202 | + | 0.965554i | \(0.416211\pi\) | |||||||
\(942\) | −4.01357 | − | 6.95171i | −0.130769 | − | 0.226499i | ||||
\(943\) | −8.65883 | − | 14.9975i | −0.281970 | − | 0.488387i | ||||
\(944\) | 3.76271 | 0.122466 | ||||||||
\(945\) | 0.621998 | + | 1.07733i | 0.0202336 | + | 0.0350456i | ||||
\(946\) | −0.503885 | + | 0.872754i | −0.0163827 | + | 0.0283757i | ||||
\(947\) | 3.25733 | − | 5.64186i | 0.105849 | − | 0.183336i | −0.808236 | − | 0.588859i | \(-0.799577\pi\) |
0.914085 | + | 0.405523i | \(0.132911\pi\) | |||||||
\(948\) | 30.3991 | 0.987317 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.349126 | 0.0113271 | ||||||||
\(951\) | 15.7235 | − | 27.2339i | 0.509869 | − | 0.883119i | ||||
\(952\) | −6.84870 | + | 11.8623i | −0.221968 | + | 0.384459i | ||||
\(953\) | −23.8235 | − | 41.2635i | −0.771718 | − | 1.33665i | −0.936621 | − | 0.350345i | \(-0.886064\pi\) |
0.164903 | − | 0.986310i | \(-0.447269\pi\) | |||||||
\(954\) | 17.0780 | 0.552920 | ||||||||
\(955\) | −1.78286 | − | 3.08800i | −0.0576919 | − | 0.0999252i | ||||
\(956\) | 17.0608 | + | 29.5501i | 0.551784 | + | 0.955719i | ||||
\(957\) | −44.1933 | −1.42857 | ||||||||
\(958\) | 9.91646 | + | 17.1758i | 0.320386 | + | 0.554925i | ||||
\(959\) | 7.32975 | − | 12.6955i | 0.236690 | − | 0.409959i | ||||
\(960\) | −0.989115 | + | 1.71320i | −0.0319235 | + | 0.0552932i | ||||
\(961\) | 12.9705 | 0.418402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.69740 | 0.215821 | ||||||||
\(964\) | 13.7497 | − | 23.8151i | 0.442847 | − | 0.767033i | ||||
\(965\) | 1.67696 | − | 2.90457i | 0.0539831 | − | 0.0935015i | ||||
\(966\) | −3.17241 | − | 5.49477i | −0.102071 | − | 0.176791i | ||||
\(967\) | 43.8122 | 1.40891 | 0.704453 | − | 0.709751i | \(-0.251192\pi\) | ||||
0.704453 | + | 0.709751i | \(0.251192\pi\) | |||||||
\(968\) | −9.47166 | − | 16.4054i | −0.304431 | − | 0.527289i | ||||
\(969\) | 0.213792 | + | 0.370298i | 0.00686798 | + | 0.0118957i | ||||
\(970\) | 1.59611 | 0.0512479 | ||||||||
\(971\) | −2.14742 | − | 3.71943i | −0.0689139 | − | 0.119362i | 0.829510 | − | 0.558492i | \(-0.188620\pi\) |
−0.898423 | + | 0.439130i | \(0.855287\pi\) | |||||||
\(972\) | 12.3412 | − | 21.3755i | 0.395843 | − | 0.685620i | ||||
\(973\) | 17.3315 | − | 30.0191i | 0.555624 | − | 0.962368i | ||||
\(974\) | −30.2776 | −0.970156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.92692 | 0.0616792 | ||||||||
\(977\) | 13.4010 | − | 23.2112i | 0.428735 | − | 0.742591i | −0.568026 | − | 0.823011i | \(-0.692293\pi\) |
0.996761 | + | 0.0804198i | \(0.0256261\pi\) | |||||||
\(978\) | 14.5586 | − | 25.2162i | 0.465533 | − | 0.806327i | ||||
\(979\) | −6.12565 | − | 10.6099i | −0.195776 | − | 0.339095i | ||||
\(980\) | −0.484271 | −0.0154695 | ||||||||
\(981\) | 16.0858 | + | 27.8613i | 0.513579 | + | 0.889544i | ||||
\(982\) | 12.5547 | + | 21.7454i | 0.400637 | + | 0.693924i | ||||
\(983\) | −27.2495 | −0.869124 | −0.434562 | − | 0.900642i | \(-0.643097\pi\) | ||||
−0.434562 | + | 0.900642i | \(0.643097\pi\) | |||||||
\(984\) | 35.0589 | + | 60.7238i | 1.11764 | + | 1.93580i | ||||
\(985\) | 0.0691957 | − | 0.119850i | 0.00220476 | − | 0.00381875i | ||||
\(986\) | 4.00873 | − | 6.94332i | 0.127664 | − | 0.221120i | ||||
\(987\) | −38.9614 | −1.24015 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.442058 | −0.0140566 | ||||||||
\(990\) | −0.861740 | + | 1.49258i | −0.0273879 | + | 0.0474372i | ||||
\(991\) | −12.1945 | + | 21.1214i | −0.387370 | + | 0.670945i | −0.992095 | − | 0.125490i | \(-0.959950\pi\) |
0.604725 | + | 0.796435i | \(0.293283\pi\) | |||||||
\(992\) | 19.3264 | + | 33.4743i | 0.613614 | + | 1.06281i | ||||
\(993\) | 40.0441 | 1.27076 | ||||||||
\(994\) | 8.18867 | + | 14.1832i | 0.259729 | + | 0.449863i | ||||
\(995\) | 1.41909 | + | 2.45794i | 0.0449882 | + | 0.0779219i | ||||
\(996\) | −4.90648 | −0.155468 | ||||||||
\(997\) | −15.6603 | − | 27.1245i | −0.495967 | − | 0.859041i | 0.504022 | − | 0.863691i | \(-0.331853\pi\) |
−0.999989 | + | 0.00465010i | \(0.998520\pi\) | |||||||
\(998\) | −8.61572 | + | 14.9229i | −0.272726 | + | 0.472375i | ||||
\(999\) | 6.08211 | − | 10.5345i | 0.192429 | − | 0.333297i |
(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 | 169.2.c.b.22.3 | 6 | ||
13.2 | odd | 12 | 169.2.e.b.23.5 | 12 | |||
13.3 | even | 3 | inner | 169.2.c.b.146.3 | 6 | ||
13.4 | even | 6 | 169.2.a.b.1.3 | ✓ | 3 | ||
13.5 | odd | 4 | 169.2.e.b.147.2 | 12 | |||
13.6 | odd | 12 | 169.2.b.b.168.5 | 6 | |||
13.7 | odd | 12 | 169.2.b.b.168.2 | 6 | |||
13.8 | odd | 4 | 169.2.e.b.147.5 | 12 | |||
13.9 | even | 3 | 169.2.a.c.1.1 | yes | 3 | ||
13.10 | even | 6 | 169.2.c.c.146.1 | 6 | |||
13.11 | odd | 12 | 169.2.e.b.23.2 | 12 | |||
13.12 | even | 2 | 169.2.c.c.22.1 | 6 | |||
39.17 | odd | 6 | 1521.2.a.r.1.1 | 3 | |||
39.20 | even | 12 | 1521.2.b.l.1351.5 | 6 | |||
39.32 | even | 12 | 1521.2.b.l.1351.2 | 6 | |||
39.35 | odd | 6 | 1521.2.a.o.1.3 | 3 | |||
52.7 | even | 12 | 2704.2.f.o.337.5 | 6 | |||
52.19 | even | 12 | 2704.2.f.o.337.6 | 6 | |||
52.35 | odd | 6 | 2704.2.a.ba.1.3 | 3 | |||
52.43 | odd | 6 | 2704.2.a.z.1.3 | 3 | |||
65.4 | even | 6 | 4225.2.a.bg.1.1 | 3 | |||
65.9 | even | 6 | 4225.2.a.bb.1.3 | 3 | |||
91.48 | odd | 6 | 8281.2.a.bj.1.1 | 3 | |||
91.69 | odd | 6 | 8281.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.3 | ✓ | 3 | 13.4 | even | 6 | ||
169.2.a.c.1.1 | yes | 3 | 13.9 | even | 3 | ||
169.2.b.b.168.2 | 6 | 13.7 | odd | 12 | |||
169.2.b.b.168.5 | 6 | 13.6 | odd | 12 | |||
169.2.c.b.22.3 | 6 | 1.1 | even | 1 | trivial | ||
169.2.c.b.146.3 | 6 | 13.3 | even | 3 | inner | ||
169.2.c.c.22.1 | 6 | 13.12 | even | 2 | |||
169.2.c.c.146.1 | 6 | 13.10 | even | 6 | |||
169.2.e.b.23.2 | 12 | 13.11 | odd | 12 | |||
169.2.e.b.23.5 | 12 | 13.2 | odd | 12 | |||
169.2.e.b.147.2 | 12 | 13.5 | odd | 4 | |||
169.2.e.b.147.5 | 12 | 13.8 | odd | 4 | |||
1521.2.a.o.1.3 | 3 | 39.35 | odd | 6 | |||
1521.2.a.r.1.1 | 3 | 39.17 | odd | 6 | |||
1521.2.b.l.1351.2 | 6 | 39.32 | even | 12 | |||
1521.2.b.l.1351.5 | 6 | 39.20 | even | 12 | |||
2704.2.a.z.1.3 | 3 | 52.43 | odd | 6 | |||
2704.2.a.ba.1.3 | 3 | 52.35 | odd | 6 | |||
2704.2.f.o.337.5 | 6 | 52.7 | even | 12 | |||
2704.2.f.o.337.6 | 6 | 52.19 | even | 12 | |||
4225.2.a.bb.1.3 | 3 | 65.9 | even | 6 | |||
4225.2.a.bg.1.1 | 3 | 65.4 | even | 6 | |||
8281.2.a.bf.1.3 | 3 | 91.69 | odd | 6 | |||
8281.2.a.bj.1.1 | 3 | 91.48 | odd | 6 |