Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,2,Mod(23,169)]
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([5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.23");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.e (of order \(6\), 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: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 147.5 | ||
Root | \(-1.56052 + 0.900969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.147 |
Dual form | 169.2.e.b.23.5 |
$q$-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 \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.694498 | + | 0.400969i | 0.491085 | + | 0.283528i | 0.725024 | − | 0.688723i | \(-0.241829\pi\) |
−0.233940 | + | 0.972251i | \(0.575162\pi\) | |||||||
\(3\) | 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 | ||||
\(5\) | − | 0.246980i | − | 0.110453i | −0.998474 | − | 0.0552263i | \(-0.982412\pi\) | ||
0.998474 | − | 0.0552263i | \(-0.0175880\pi\) | |||||||
\(6\) | 1.56052 | − | 0.900969i | 0.637081 | − | 0.367819i | ||||
\(7\) | −2.04113 | + | 1.17845i | −0.771475 | + | 0.445411i | −0.833401 | − | 0.552669i | \(-0.813609\pi\) |
0.0619254 | + | 0.998081i | \(0.480276\pi\) | |||||||
\(8\) | − | 2.69202i | − | 0.951773i | ||||||
\(9\) | −1.02446 | − | 1.77441i | −0.341486 | − | 0.591471i | ||||
\(10\) | 0.0990311 | − | 0.171527i | 0.0313164 | − | 0.0542416i | ||||
\(11\) | 3.67799 | + | 2.12349i | 1.10896 | + | 0.640256i | 0.938559 | − | 0.345119i | \(-0.112161\pi\) |
0.170397 | + | 0.985375i | \(0.445495\pi\) | |||||||
\(12\) | −3.04892 | −0.880147 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.89008 | −0.505146 | ||||||||
\(15\) | −0.480608 | − | 0.277479i | −0.124092 | − | 0.0716448i | ||||
\(16\) | −0.277479 | + | 0.480608i | −0.0693698 | + | 0.120152i | ||||
\(17\) | 1.07942 | + | 1.86960i | 0.261797 | + | 0.453446i | 0.966720 | − | 0.255839i | \(-0.0823516\pi\) |
−0.704922 | + | 0.709284i | \(0.749018\pi\) | |||||||
\(18\) | − | 1.64310i | − | 0.387283i | ||||||
\(19\) | 0.0763367 | − | 0.0440730i | 0.0175128 | − | 0.0101110i | −0.491218 | − | 0.871037i | \(-0.663448\pi\) |
0.508731 | + | 0.860926i | \(0.330115\pi\) | |||||||
\(20\) | −0.290227 | + | 0.167563i | −0.0648968 | + | 0.0374682i | ||||
\(21\) | 5.29590i | 1.15566i | ||||||||
\(22\) | 1.70291 | + | 2.94952i | 0.363061 | + | 0.628840i | ||||
\(23\) | 0.746980 | − | 1.29381i | 0.155756 | − | 0.269777i | −0.777578 | − | 0.628786i | \(-0.783552\pi\) |
0.933334 | + | 0.359009i | \(0.116885\pi\) | |||||||
\(24\) | −5.23852 | − | 3.02446i | −1.06931 | − | 0.617365i | ||||
\(25\) | 4.93900 | 0.987800 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13706 | 0.411278 | ||||||||
\(28\) | 2.76960 | + | 1.59903i | 0.523406 | + | 0.302188i | ||||
\(29\) | −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 | ||||
\(31\) | 6.63102i | 1.19097i | 0.803368 | + | 0.595483i | \(0.203039\pi\) | ||||
−0.803368 | + | 0.595483i | \(0.796961\pi\) | |||||||
\(32\) | −5.04814 | + | 2.91454i | −0.892393 | + | 0.515223i | ||||
\(33\) | 8.26437 | − | 4.77144i | 1.43864 | − | 0.830601i | ||||
\(34\) | 1.73125i | 0.296907i | ||||||||
\(35\) | 0.291053 | + | 0.504118i | 0.0491969 | + | 0.0852115i | ||||
\(36\) | −1.39008 | + | 2.40770i | −0.231681 | + | 0.401283i | ||||
\(37\) | −4.92944 | − | 2.84601i | −0.810394 | − | 0.467881i | 0.0366986 | − | 0.999326i | \(-0.488316\pi\) |
−0.847093 | + | 0.531445i | \(0.821649\pi\) | |||||||
\(38\) | 0.0706876 | 0.0114670 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.664874 | −0.105126 | ||||||||
\(41\) | −10.0388 | − | 5.79590i | −1.56780 | − | 0.905167i | −0.996426 | − | 0.0844742i | \(-0.973079\pi\) |
−0.571370 | − | 0.820693i | \(-0.693588\pi\) | |||||||
\(42\) | −2.12349 | + | 3.67799i | −0.327662 | + | 0.567527i | ||||
\(43\) | −0.147948 | − | 0.256254i | −0.0225619 | − | 0.0390784i | 0.854524 | − | 0.519412i | \(-0.173849\pi\) |
−0.877086 | + | 0.480334i | \(0.840516\pi\) | |||||||
\(44\) | − | 5.76271i | − | 0.868761i | ||||||
\(45\) | −0.438244 | + | 0.253020i | −0.0653296 | + | 0.0377181i | ||||
\(46\) | 1.03755 | − | 0.599031i | 0.152979 | − | 0.0883223i | ||||
\(47\) | − | 7.35690i | − | 1.07311i | −0.843864 | − | 0.536557i | \(-0.819725\pi\) | ||
0.843864 | − | 0.536557i | \(-0.180275\pi\) | |||||||
\(48\) | 0.623490 | + | 1.07992i | 0.0899930 | + | 0.155872i | ||||
\(49\) | −0.722521 | + | 1.25144i | −0.103217 | + | 0.178778i | ||||
\(50\) | 3.43013 | + | 1.98039i | 0.485093 | + | 0.280069i | ||||
\(51\) | 4.85086 | 0.679256 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3937 | −1.42769 | −0.713844 | − | 0.700304i | \(-0.753048\pi\) | ||||
−0.713844 | + | 0.700304i | \(0.753048\pi\) | |||||||
\(54\) | 1.48419 | + | 0.856896i | 0.201972 | + | 0.116609i | ||||
\(55\) | 0.524459 | − | 0.908389i | 0.0707180 | − | 0.122487i | ||||
\(56\) | 3.17241 | + | 5.49477i | 0.423931 | + | 0.734270i | ||||
\(57\) | − | 0.198062i | − | 0.0262340i | ||||||
\(58\) | −3.21624 | + | 1.85690i | −0.422313 | + | 0.243822i | ||||
\(59\) | −5.87180 | + | 3.39008i | −0.764443 | + | 0.441351i | −0.830889 | − | 0.556439i | \(-0.812167\pi\) |
0.0664458 | + | 0.997790i | \(0.478834\pi\) | |||||||
\(60\) | 0.753020i | 0.0972145i | ||||||||
\(61\) | −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 | ||||
\(63\) | 4.18211 | + | 2.41454i | 0.526896 | + | 0.304204i | ||||
\(64\) | −3.56465 | −0.445581 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.65279 | 0.941994 | ||||||||
\(67\) | 6.65102 | + | 3.83997i | 0.812552 | + | 0.469127i | 0.847841 | − | 0.530250i | \(-0.177902\pi\) |
−0.0352895 | + | 0.999377i | \(0.511235\pi\) | |||||||
\(68\) | 1.46466 | − | 2.53686i | 0.177616 | − | 0.307639i | ||||
\(69\) | −1.67845 | − | 2.90716i | −0.202061 | − | 0.349981i | ||||
\(70\) | 0.466812i | 0.0557947i | ||||||||
\(71\) | 7.50400 | − | 4.33244i | 0.890561 | − | 0.514166i | 0.0164351 | − | 0.999865i | \(-0.494768\pi\) |
0.874126 | + | 0.485699i | \(0.161435\pi\) | |||||||
\(72\) | −4.77676 | + | 2.75786i | −0.562947 | + | 0.325017i | ||||
\(73\) | 6.73556i | 0.788338i | 0.919038 | + | 0.394169i | \(0.128968\pi\) | ||||
−0.919038 | + | 0.394169i | \(0.871032\pi\) | |||||||
\(74\) | −2.28232 | − | 3.95310i | −0.265315 | − | 0.459539i | ||||
\(75\) | 5.54892 | − | 9.61101i | 0.640734 | − | 1.10978i | ||||
\(76\) | −0.103581 | − | 0.0598025i | −0.0118815 | − | 0.00685981i | ||||
\(77\) | −10.0097 | −1.14071 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.97046 | 1.12176 | 0.560882 | − | 0.827896i | \(-0.310462\pi\) | ||||
0.560882 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(80\) | 0.118700 | + | 0.0685317i | 0.0132711 | + | 0.00766207i | ||||
\(81\) | 5.47434 | − | 9.48184i | 0.608261 | − | 1.05354i | ||||
\(82\) | −4.64795 | − | 8.05048i | −0.513280 | − | 0.889027i | ||||
\(83\) | − | 1.60925i | − | 0.176638i | −0.996092 | − | 0.0883192i | \(-0.971850\pi\) | ||
0.996092 | − | 0.0883192i | \(-0.0281495\pi\) | |||||||
\(84\) | 6.22324 | − | 3.59299i | 0.679011 | − | 0.392027i | ||||
\(85\) | 0.461754 | − | 0.266594i | 0.0500843 | − | 0.0289162i | ||||
\(86\) | − | 0.237291i | − | 0.0255877i | ||||||
\(87\) | 5.20291 | + | 9.01170i | 0.557810 | + | 0.966156i | ||||
\(88\) | 5.71648 | − | 9.90123i | 0.609379 | − | 1.05548i | ||||
\(89\) | 2.49823 | + | 1.44235i | 0.264812 | + | 0.152889i | 0.626528 | − | 0.779399i | \(-0.284476\pi\) |
−0.361716 | + | 0.932288i | \(0.617809\pi\) | |||||||
\(90\) | −0.405813 | −0.0427765 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.02715 | −0.211345 | ||||||||
\(93\) | 12.9036 | + | 7.44989i | 1.33804 | + | 0.772517i | ||||
\(94\) | 2.94989 | − | 5.10935i | 0.304258 | − | 0.526990i | ||||
\(95\) | −0.0108851 | − | 0.0188536i | −0.00111679 | − | 0.00193434i | ||||
\(96\) | 13.0978i | 1.33679i | ||||||||
\(97\) | 6.97896 | − | 4.02930i | 0.708606 | − | 0.409114i | −0.101939 | − | 0.994791i | \(-0.532505\pi\) |
0.810545 | + | 0.585677i | \(0.199171\pi\) | |||||||
\(98\) | −1.00358 | + | 0.579417i | −0.101377 | + | 0.0585299i | ||||
\(99\) | − | 8.70171i | − | 0.874555i | ||||||
\(100\) | −3.35086 | − | 5.80385i | −0.335086 | − | 0.580385i | ||||
\(101\) | −6.67725 | + | 11.5653i | −0.664411 | + | 1.15079i | 0.315033 | + | 0.949081i | \(0.397984\pi\) |
−0.979445 | + | 0.201714i | \(0.935349\pi\) | |||||||
\(102\) | 3.36891 | + | 1.94504i | 0.333572 | + | 0.192588i | ||||
\(103\) | −1.36227 | −0.134229 | −0.0671144 | − | 0.997745i | \(-0.521379\pi\) | ||||
−0.0671144 | + | 0.997745i | \(0.521379\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.30798 | 0.127646 | ||||||||
\(106\) | −7.21843 | − | 4.16756i | −0.701116 | − | 0.404789i | ||||
\(107\) | −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 | ||||
\(109\) | − | 15.7017i | − | 1.50395i | −0.659191 | − | 0.751976i | \(-0.729101\pi\) | ||
0.659191 | − | 0.751976i | \(-0.270899\pi\) | |||||||
\(110\) | 0.728471 | − | 0.420583i | 0.0694570 | − | 0.0401010i | ||||
\(111\) | −11.0763 | + | 6.39493i | −1.05132 | + | 0.606980i | ||||
\(112\) | − | 1.30798i | − | 0.123592i | ||||||
\(113\) | −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 | ||||
\(115\) | −0.319544 | − | 0.184489i | −0.0297976 | − | 0.0172037i | ||||
\(116\) | 6.28382 | 0.583438 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.43727 | −0.500541 | ||||||||
\(119\) | −4.40646 | − | 2.54407i | −0.403940 | − | 0.233215i | ||||
\(120\) | −0.746980 | + | 1.29381i | −0.0681896 | + | 0.118108i | ||||
\(121\) | 3.51842 | + | 6.09408i | 0.319856 | + | 0.554007i | ||||
\(122\) | − | 2.78448i | − | 0.252095i | ||||||
\(123\) | −22.5570 | + | 13.0233i | −2.03389 | + | 1.17427i | ||||
\(124\) | 7.79216 | − | 4.49880i | 0.699756 | − | 0.404004i | ||||
\(125\) | − | 2.45473i | − | 0.219558i | ||||||
\(126\) | 1.93631 | + | 3.35379i | 0.172500 | + | 0.298780i | ||||
\(127\) | −4.90366 | + | 8.49338i | −0.435129 | + | 0.753666i | −0.997306 | − | 0.0733510i | \(-0.976631\pi\) |
0.562177 | + | 0.827017i | \(0.309964\pi\) | |||||||
\(128\) | 7.62063 | + | 4.39977i | 0.673575 | + | 0.388889i | ||||
\(129\) | −0.664874 | −0.0585389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.57673 | −0.574611 | −0.287306 | − | 0.957839i | \(-0.592760\pi\) | ||||
−0.287306 | + | 0.957839i | \(0.592760\pi\) | |||||||
\(132\) | −11.2139 | − | 6.47434i | −0.976044 | − | 0.563519i | ||||
\(133\) | −0.103875 | + | 0.179918i | −0.00900715 | + | 0.0156008i | ||||
\(134\) | 3.07942 | + | 5.33371i | 0.266021 | + | 0.460762i | ||||
\(135\) | − | 0.527811i | − | 0.0454267i | ||||||
\(136\) | 5.03302 | − | 2.90581i | 0.431578 | − | 0.249171i | ||||
\(137\) | 5.38653 | − | 3.10992i | 0.460203 | − | 0.265698i | −0.251927 | − | 0.967746i | \(-0.581064\pi\) |
0.712129 | + | 0.702048i | \(0.247731\pi\) | |||||||
\(138\) | − | 2.69202i | − | 0.229160i | ||||||
\(139\) | 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 | ||||
\(141\) | −14.3161 | − | 8.26540i | −1.20563 | − | 0.696072i | ||||
\(142\) | 6.94869 | 0.583121 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.13706 | 0.0947553 | ||||||||
\(145\) | 0.990532 | + | 0.571884i | 0.0822592 | + | 0.0474924i | ||||
\(146\) | −2.70075 | + | 4.67784i | −0.223516 | + | 0.387141i | ||||
\(147\) | 1.62349 | + | 2.81197i | 0.133903 | + | 0.231927i | ||||
\(148\) | 7.72348i | 0.634866i | ||||||||
\(149\) | −3.75433 | + | 2.16756i | −0.307567 | + | 0.177574i | −0.645837 | − | 0.763475i | \(-0.723491\pi\) |
0.338270 | + | 0.941049i | \(0.390158\pi\) | |||||||
\(150\) | 7.70743 | − | 4.44989i | 0.629309 | − | 0.363332i | ||||
\(151\) | 3.94438i | 0.320989i | 0.987037 | + | 0.160494i | \(0.0513089\pi\) | ||||
−0.987037 | + | 0.160494i | \(0.948691\pi\) | |||||||
\(152\) | −0.118645 | − | 0.205500i | −0.00962342 | − | 0.0166682i | ||||
\(153\) | 2.21164 | − | 3.83067i | 0.178800 | − | 0.309691i | ||||
\(154\) | −6.95171 | − | 4.01357i | −0.560185 | − | 0.323423i | ||||
\(155\) | 1.63773 | 0.131545 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.45473 | 0.355526 | 0.177763 | − | 0.984073i | \(-0.443114\pi\) | ||||
0.177763 | + | 0.984073i | \(0.443114\pi\) | |||||||
\(158\) | 6.92447 | + | 3.99784i | 0.550881 | + | 0.318051i | ||||
\(159\) | −11.6773 | + | 20.2256i | −0.926066 | + | 1.60399i | ||||
\(160\) | 0.719833 | + | 1.24679i | 0.0569078 | + | 0.0985671i | ||||
\(161\) | 3.52111i | 0.277502i | ||||||||
\(162\) | 7.60385 | − | 4.39008i | 0.597415 | − | 0.344918i | ||||
\(163\) | 13.9940 | − | 8.07942i | 1.09609 | − | 0.632829i | 0.160900 | − | 0.986971i | \(-0.448560\pi\) |
0.935192 | + | 0.354142i | \(0.115227\pi\) | |||||||
\(164\) | 15.7289i | 1.22822i | ||||||||
\(165\) | −1.17845 | − | 2.04113i | −0.0917420 | − | 0.158902i | ||||
\(166\) | 0.645260 | − | 1.11762i | 0.0500819 | − | 0.0867444i | ||||
\(167\) | −13.9579 | − | 8.05861i | −1.08010 | − | 0.623594i | −0.149174 | − | 0.988811i | \(-0.547661\pi\) |
−0.930922 | + | 0.365217i | \(0.880995\pi\) | |||||||
\(168\) | 14.2567 | 1.09993 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0.427583 | 0.0327942 | ||||||||
\(171\) | −0.156408 | − | 0.0903019i | −0.0119608 | − | 0.00690556i | ||||
\(172\) | −0.200751 | + | 0.347710i | −0.0153071 | + | 0.0265127i | ||||
\(173\) | −10.7681 | − | 18.6509i | −0.818682 | − | 1.41800i | −0.906653 | − | 0.421876i | \(-0.861372\pi\) |
0.0879709 | − | 0.996123i | \(-0.471962\pi\) | |||||||
\(174\) | 8.34481i | 0.632619i | ||||||||
\(175\) | −10.0812 | + | 5.82036i | −0.762063 | + | 0.439978i | ||||
\(176\) | −2.04113 | + | 1.17845i | −0.153856 | + | 0.0888289i | ||||
\(177\) | 15.2349i | 1.14513i | ||||||||
\(178\) | 1.15668 | + | 2.00342i | 0.0866967 | + | 0.150163i | ||||
\(179\) | 5.71648 | − | 9.90123i | 0.427270 | − | 0.740053i | −0.569360 | − | 0.822089i | \(-0.692809\pi\) |
0.996629 | + | 0.0820356i | \(0.0261421\pi\) | |||||||
\(180\) | 0.594652 | + | 0.343322i | 0.0443227 | + | 0.0255897i | ||||
\(181\) | −20.9705 | −1.55872 | −0.779361 | − | 0.626575i | \(-0.784456\pi\) | ||||
−0.779361 | + | 0.626575i | \(0.784456\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.80194 | −0.576736 | ||||||||
\(184\) | −3.48296 | − | 2.01089i | −0.256767 | − | 0.148244i | ||||
\(185\) | −0.702907 | + | 1.21747i | −0.0516787 | + | 0.0895102i | ||||
\(186\) | 5.97434 | + | 10.3479i | 0.438060 | + | 0.758743i | ||||
\(187\) | 9.16852i | 0.670469i | ||||||||
\(188\) | −8.64513 | + | 4.99127i | −0.630511 | + | 0.364026i | ||||
\(189\) | −4.36203 | + | 2.51842i | −0.317291 | + | 0.183188i | ||||
\(190\) | − | 0.0174584i | − | 0.00126657i | ||||||
\(191\) | 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 | ||||
\(193\) | 11.7604 | + | 6.78986i | 0.846530 | + | 0.488745i | 0.859479 | − | 0.511172i | \(-0.170788\pi\) |
−0.0129483 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(194\) | 6.46250 | 0.463980 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.96077 | 0.140055 | ||||||||
\(197\) | −0.485264 | − | 0.280167i | −0.0345736 | − | 0.0199611i | 0.482614 | − | 0.875833i | \(-0.339688\pi\) |
−0.517187 | + | 0.855872i | \(0.673021\pi\) | |||||||
\(198\) | 3.48911 | − | 6.04332i | 0.247961 | − | 0.429480i | ||||
\(199\) | 5.74578 | + | 9.95199i | 0.407308 | + | 0.705478i | 0.994587 | − | 0.103907i | \(-0.0331343\pi\) |
−0.587279 | + | 0.809384i | \(0.699801\pi\) | |||||||
\(200\) | − | 13.2959i | − | 0.940162i | ||||||
\(201\) | 14.9447 | − | 8.62833i | 1.05412 | − | 0.608596i | ||||
\(202\) | −9.27468 | + | 5.35474i | −0.652564 | + | 0.376758i | ||||
\(203\) | − | 10.9148i | − | 0.766071i | ||||||
\(204\) | −3.29105 | − | 5.70027i | −0.230420 | − | 0.399099i | ||||
\(205\) | −1.43147 | + | 2.47938i | −0.0999781 | + | 0.173167i | ||||
\(206\) | −0.946096 | − | 0.546229i | −0.0659177 | − | 0.0380576i | ||||
\(207\) | −3.06100 | −0.212754 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.374354 | 0.0258946 | ||||||||
\(210\) | 0.908389 | + | 0.524459i | 0.0626848 | + | 0.0361911i | ||||
\(211\) | −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 | ||||
\(213\) | − | 19.4698i | − | 1.33405i | ||||||
\(214\) | −2.27014 | + | 1.31067i | −0.155184 | + | 0.0895953i | ||||
\(215\) | −0.0632896 | + | 0.0365403i | −0.00431631 | + | 0.00249202i | ||||
\(216\) | − | 5.75302i | − | 0.391443i | ||||||
\(217\) | −7.81431 | − | 13.5348i | −0.530470 | − | 0.918801i | ||||
\(218\) | 6.29590 | − | 10.9048i | 0.426412 | − | 0.738567i | ||||
\(219\) | 13.1070 | + | 7.56734i | 0.885690 | + | 0.511353i | ||||
\(220\) | −1.42327 | −0.0959570 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −10.2567 | −0.688383 | ||||||||
\(223\) | −1.95640 | − | 1.12953i | −0.131011 | − | 0.0756390i | 0.433062 | − | 0.901364i | \(-0.357433\pi\) |
−0.564073 | + | 0.825725i | \(0.690766\pi\) | |||||||
\(224\) | 6.86927 | − | 11.8979i | 0.458973 | − | 0.794964i | ||||
\(225\) | −5.05980 | − | 8.76383i | −0.337320 | − | 0.584256i | ||||
\(226\) | − | 9.66248i | − | 0.642739i | ||||||
\(227\) | 6.03286 | − | 3.48307i | 0.400415 | − | 0.231180i | −0.286248 | − | 0.958156i | \(-0.592408\pi\) |
0.686663 | + | 0.726976i | \(0.259075\pi\) | |||||||
\(228\) | −0.232744 | + | 0.134375i | −0.0154139 | + | 0.00889920i | ||||
\(229\) | − | 24.1739i | − | 1.59746i | −0.601692 | − | 0.798728i | \(-0.705507\pi\) | ||
0.601692 | − | 0.798728i | \(-0.294493\pi\) | |||||||
\(230\) | −0.147948 | − | 0.256254i | −0.00975543 | − | 0.0168969i | ||||
\(231\) | −11.2458 | + | 19.4783i | −0.739918 | + | 1.28158i | ||||
\(232\) | 10.7966 | + | 6.23341i | 0.708830 | + | 0.409243i | ||||
\(233\) | 3.06100 | 0.200533 | 0.100266 | − | 0.994961i | \(-0.468031\pi\) | ||||
0.100266 | + | 0.994961i | \(0.468031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.81700 | −0.118528 | ||||||||
\(236\) | 7.96742 | + | 4.59999i | 0.518635 | + | 0.299434i | ||||
\(237\) | 11.2017 | − | 19.4019i | 0.727629 | − | 1.26029i | ||||
\(238\) | −2.04019 | − | 3.53371i | −0.132246 | − | 0.229056i | ||||
\(239\) | 25.1468i | 1.62661i | 0.581839 | + | 0.813304i | \(0.302333\pi\) | ||||
−0.581839 | + | 0.813304i | \(0.697667\pi\) | |||||||
\(240\) | 0.266717 | − | 0.153989i | 0.0172165 | − | 0.00993996i | ||||
\(241\) | −17.5512 | + | 10.1332i | −1.13057 | + | 0.652735i | −0.944078 | − | 0.329721i | \(-0.893045\pi\) |
−0.186492 | + | 0.982456i | \(0.559712\pi\) | |||||||
\(242\) | 5.64310i | 0.362752i | ||||||||
\(243\) | −9.09515 | − | 15.7533i | −0.583454 | − | 1.01057i | ||||
\(244\) | −2.35570 | + | 4.08019i | −0.150808 | + | 0.261207i | ||||
\(245\) | 0.309081 | + | 0.178448i | 0.0197465 | + | 0.0114006i | ||||
\(246\) | −20.8877 | −1.33175 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 17.8509 | 1.13353 | ||||||||
\(249\) | −3.13151 | − | 1.80798i | −0.198451 | − | 0.114576i | ||||
\(250\) | 0.984271 | − | 1.70481i | 0.0622507 | − | 0.107821i | ||||
\(251\) | −11.8605 | − | 20.5431i | −0.748631 | − | 1.29667i | −0.948479 | − | 0.316840i | \(-0.897378\pi\) |
0.199848 | − | 0.979827i | \(-0.435955\pi\) | |||||||
\(252\) | − | 6.55257i | − | 0.412773i | ||||||
\(253\) | 5.49477 | − | 3.17241i | 0.345453 | − | 0.199448i | ||||
\(254\) | −6.81116 | + | 3.93243i | −0.427370 | + | 0.246742i | ||||
\(255\) | − | 1.19806i | − | 0.0750256i | ||||||
\(256\) | 7.09299 | + | 12.2854i | 0.443312 | + | 0.767839i | ||||
\(257\) | 7.11207 | − | 12.3185i | 0.443639 | − | 0.768405i | −0.554317 | − | 0.832305i | \(-0.687021\pi\) |
0.997956 | + | 0.0639003i | \(0.0203540\pi\) | |||||||
\(258\) | −0.461754 | − | 0.266594i | −0.0287476 | − | 0.0165974i | ||||
\(259\) | 13.4155 | 0.833599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.48858 | 0.587329 | ||||||||
\(262\) | −4.56753 | − | 2.63706i | −0.282183 | − | 0.162918i | ||||
\(263\) | 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 | ||||
\(265\) | 2.56704i | 0.157692i | ||||||||
\(266\) | −0.144283 | + | 0.0833017i | −0.00884654 | + | 0.00510755i | ||||
\(267\) | 5.61347 | − | 3.24094i | 0.343539 | − | 0.198342i | ||||
\(268\) | − | 10.4209i | − | 0.636556i | ||||||
\(269\) | 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 | ||||
\(271\) | −5.58415 | − | 3.22401i | −0.339213 | − | 0.195845i | 0.320711 | − | 0.947177i | \(-0.396078\pi\) |
−0.659924 | + | 0.751332i | \(0.729412\pi\) | |||||||
\(272\) | −1.19806 | −0.0726432 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.98792 | 0.301331 | ||||||||
\(275\) | 18.1656 | + | 10.4879i | 1.09543 | + | 0.632445i | ||||
\(276\) | −2.27748 | + | 3.94471i | −0.137088 | + | 0.237444i | ||||
\(277\) | 6.73005 | + | 11.6568i | 0.404370 | + | 0.700389i | 0.994248 | − | 0.107103i | \(-0.0341576\pi\) |
−0.589878 | + | 0.807492i | \(0.700824\pi\) | |||||||
\(278\) | 11.7942i | 0.707367i | ||||||||
\(279\) | 11.7662 | − | 6.79321i | 0.704423 | − | 0.406699i | ||||
\(280\) | 1.35710 | − | 0.783520i | 0.0811020 | − | 0.0468243i | ||||
\(281\) | 5.03684i | 0.300472i | 0.988650 | + | 0.150236i | \(0.0480034\pi\) | ||||
−0.988650 | + | 0.150236i | \(0.951997\pi\) | |||||||
\(282\) | −6.62833 | − | 11.4806i | −0.394712 | − | 0.683660i | ||||
\(283\) | 11.0640 | − | 19.1634i | 0.657686 | − | 1.13914i | −0.323528 | − | 0.946219i | \(-0.604869\pi\) |
0.981213 | − | 0.192926i | \(-0.0617977\pi\) | |||||||
\(284\) | −10.1821 | − | 5.87867i | −0.604199 | − | 0.348835i | ||||
\(285\) | −0.0489173 | −0.00289761 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 27.3207 | 1.61269 | ||||||||
\(288\) | 10.3432 | + | 5.97166i | 0.609480 | + | 0.351883i | ||||
\(289\) | 6.16972 | − | 10.6863i | 0.362925 | − | 0.628604i | ||||
\(290\) | 0.458615 | + | 0.794345i | 0.0269308 | + | 0.0466456i | ||||
\(291\) | − | 18.1075i | − | 1.06148i | ||||||
\(292\) | 7.91500 | − | 4.56973i | 0.463190 | − | 0.267423i | ||||
\(293\) | 12.9439 | − | 7.47315i | 0.756189 | − | 0.436586i | −0.0717367 | − | 0.997424i | \(-0.522854\pi\) |
0.827926 | + | 0.560838i | \(0.189521\pi\) | |||||||
\(294\) | 2.60388i | 0.151861i | ||||||||
\(295\) | 0.837282 | + | 1.45021i | 0.0487484 | + | 0.0844347i | ||||
\(296\) | −7.66152 | + | 13.2701i | −0.445317 | + | 0.771312i | ||||
\(297\) | 7.86010 | + | 4.53803i | 0.456089 | + | 0.263323i | ||||
\(298\) | −3.47650 | −0.201388 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −15.0586 | −0.869409 | ||||||||
\(301\) | 0.603965 | + | 0.348699i | 0.0348119 | + | 0.0200987i | ||||
\(302\) | −1.58157 | + | 2.73936i | −0.0910093 | + | 0.157633i | ||||
\(303\) | 15.0036 | + | 25.9871i | 0.861937 | + | 1.49292i | ||||
\(304\) | 0.0489173i | 0.00280560i | ||||||||
\(305\) | −0.742669 | + | 0.428780i | −0.0425251 | + | 0.0245519i | ||||
\(306\) | 3.07196 | − | 1.77359i | 0.175612 | − | 0.101390i | ||||
\(307\) | 19.1293i | 1.09177i | 0.837861 | + | 0.545883i | \(0.183806\pi\) | ||||
−0.837861 | + | 0.545883i | \(0.816194\pi\) | |||||||
\(308\) | 6.79105 | + | 11.7624i | 0.386956 | + | 0.670228i | ||||
\(309\) | −1.53050 | + | 2.65090i | −0.0870671 | + | 0.150805i | ||||
\(310\) | 1.13740 | + | 0.656678i | 0.0645999 | + | 0.0372968i | ||||
\(311\) | 0.269815 | 0.0152998 | 0.00764990 | − | 0.999971i | \(-0.497565\pi\) | ||||
0.00764990 | + | 0.999971i | \(0.497565\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.3937 | −1.32229 | −0.661146 | − | 0.750257i | \(-0.729930\pi\) | ||||
−0.661146 | + | 0.750257i | \(0.729930\pi\) | |||||||
\(314\) | 3.09380 | + | 1.78621i | 0.174593 | + | 0.100802i | ||||
\(315\) | 0.596343 | − | 1.03290i | 0.0336001 | − | 0.0581971i | ||||
\(316\) | −6.76444 | − | 11.7164i | −0.380529 | − | 0.659096i | ||||
\(317\) | 13.9952i | 0.786050i | 0.919528 | + | 0.393025i | \(0.128571\pi\) | ||||
−0.919528 | + | 0.393025i | \(0.871429\pi\) | |||||||
\(318\) | −16.2197 | + | 9.36443i | −0.909554 | + | 0.525131i | ||||
\(319\) | −17.0329 | + | 9.83393i | −0.953657 | + | 0.550594i | ||||
\(320\) | 0.880395i | 0.0492156i | ||||||||
\(321\) | 3.67241 | + | 6.36080i | 0.204974 | + | 0.355025i | ||||
\(322\) | −1.41185 | + | 2.44540i | −0.0786795 | + | 0.136277i | ||||
\(323\) | 0.164798 | + | 0.0951463i | 0.00916962 | + | 0.00529408i | ||||
\(324\) | −14.8562 | −0.825346 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 12.9584 | 0.717698 | ||||||||
\(327\) | −30.5546 | − | 17.6407i | −1.68967 | − | 0.975534i | ||||
\(328\) | −15.6027 | + | 27.0246i | −0.861514 | + | 1.49219i | ||||
\(329\) | 8.66972 | + | 15.0164i | 0.477977 | + | 0.827881i | ||||
\(330\) | − | 1.89008i | − | 0.104046i | ||||||
\(331\) | −15.4337 | + | 8.91066i | −0.848314 | + | 0.489774i | −0.860081 | − | 0.510157i | \(-0.829587\pi\) |
0.0117680 | + | 0.999931i | \(0.496254\pi\) | |||||||
\(332\) | −1.89104 | + | 1.09179i | −0.103784 | + | 0.0599200i | ||||
\(333\) | 11.6625i | 0.639100i | ||||||||
\(334\) | −6.46250 | − | 11.1934i | −0.353612 | − | 0.612474i | ||||
\(335\) | 0.948394 | − | 1.64267i | 0.0518163 | − | 0.0897485i | ||||
\(336\) | −2.54525 | − | 1.46950i | −0.138855 | − | 0.0801678i | ||||
\(337\) | 27.8485 | 1.51700 | 0.758501 | − | 0.651672i | \(-0.225932\pi\) | ||||
0.758501 | + | 0.651672i | \(0.225932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.0737 | −1.47044 | ||||||||
\(340\) | −0.626552 | − | 0.361740i | −0.0339796 | − | 0.0196181i | ||||
\(341\) | −14.0809 | + | 24.3888i | −0.762524 | + | 1.32073i | ||||
\(342\) | −0.0724165 | − | 0.125429i | −0.00391584 | − | 0.00678243i | ||||
\(343\) | − | 19.9041i | − | 1.07472i | ||||||
\(344\) | −0.689842 | + | 0.398280i | −0.0371938 | + | 0.0214738i | ||||
\(345\) | −0.718009 | + | 0.414542i | −0.0386563 | + | 0.0223182i | ||||
\(346\) | − | 17.2707i | − | 0.928477i | ||||||
\(347\) | −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 | ||||
\(349\) | 12.2854 | + | 7.09299i | 0.657623 | + | 0.379679i | 0.791371 | − | 0.611336i | \(-0.209368\pi\) |
−0.133747 | + | 0.991015i | \(0.542701\pi\) | |||||||
\(350\) | −9.33513 | −0.498983 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −24.7560 | −1.31950 | ||||||||
\(353\) | −6.20812 | − | 3.58426i | −0.330425 | − | 0.190771i | 0.325605 | − | 0.945506i | \(-0.394432\pi\) |
−0.656030 | + | 0.754735i | \(0.727765\pi\) | |||||||
\(354\) | −6.10872 | + | 10.5806i | −0.324675 | + | 0.562353i | ||||
\(355\) | −1.07002 | − | 1.85334i | −0.0567910 | − | 0.0983648i | ||||
\(356\) | − | 3.91425i | − | 0.207455i | ||||||
\(357\) | −9.90123 | + | 5.71648i | −0.524029 | + | 0.302548i | ||||
\(358\) | 7.94017 | − | 4.58426i | 0.419651 | − | 0.242286i | ||||
\(359\) | 19.8853i | 1.04951i | 0.851255 | + | 0.524753i | \(0.175842\pi\) | ||||
−0.851255 | + | 0.524753i | \(0.824158\pi\) | |||||||
\(360\) | 0.681136 | + | 1.17976i | 0.0358990 | + | 0.0621790i | ||||
\(361\) | −9.49612 | + | 16.4478i | −0.499796 | + | 0.865671i | ||||
\(362\) | −14.5640 | − | 8.40850i | −0.765464 | − | 0.441941i | ||||
\(363\) | 15.8116 | 0.829895 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.66355 | 0.0870740 | ||||||||
\(366\) | −5.41843 | − | 3.12833i | −0.283226 | − | 0.163521i | ||||
\(367\) | −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 | ||||
\(369\) | 23.7506i | 1.23641i | ||||||||
\(370\) | −0.976335 | + | 0.563687i | −0.0507572 | + | 0.0293047i | ||||
\(371\) | 21.2150 | − | 12.2485i | 1.10143 | − | 0.635909i | ||||
\(372\) | − | 20.2174i | − | 1.04823i | ||||||
\(373\) | 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 | ||||
\(375\) | −4.77676 | − | 2.75786i | −0.246671 | − | 0.142416i | ||||
\(376\) | −19.8049 | −1.02136 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −4.03923 | −0.207756 | ||||||||
\(379\) | −2.08608 | − | 1.20440i | −0.107155 | − | 0.0618658i | 0.445465 | − | 0.895299i | \(-0.353038\pi\) |
−0.552620 | + | 0.833434i | \(0.686372\pi\) | |||||||
\(380\) | −0.0147700 | + | 0.0255824i | −0.000757685 | + | 0.00131235i | ||||
\(381\) | 11.0184 | + | 19.0845i | 0.564491 | + | 0.977726i | ||||
\(382\) | 11.5778i | 0.592371i | ||||||||
\(383\) | 26.3197 | − | 15.1957i | 1.34487 | − | 0.776462i | 0.357354 | − | 0.933969i | \(-0.383679\pi\) |
0.987518 | + | 0.157506i | \(0.0503455\pi\) | |||||||
\(384\) | 17.1234 | − | 9.88620i | 0.873825 | − | 0.504503i | ||||
\(385\) | 2.47219i | 0.125994i | ||||||||
\(386\) | 5.44504 | + | 9.43109i | 0.277145 | + | 0.480030i | ||||
\(387\) | −0.303134 | + | 0.525044i | −0.0154092 | + | 0.0266895i | ||||
\(388\) | −9.46972 | − | 5.46734i | −0.480752 | − | 0.277562i | ||||
\(389\) | 15.9409 | 0.808237 | 0.404118 | − | 0.914707i | \(-0.367578\pi\) | ||||
0.404118 | + | 0.914707i | \(0.367578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.22521 | 0.163106 | ||||||||
\(392\) | 3.36891 | + | 1.94504i | 0.170156 | + | 0.0982394i | ||||
\(393\) | −7.38889 | + | 12.7979i | −0.372720 | + | 0.645570i | ||||
\(394\) | −0.224677 | − | 0.389152i | −0.0113191 | − | 0.0196052i | ||||
\(395\) | − | 2.46250i | − | 0.123902i | ||||||
\(396\) | −10.2254 | + | 5.90366i | −0.513847 | + | 0.296670i | ||||
\(397\) | 14.6487 | − | 8.45742i | 0.735196 | − | 0.424466i | −0.0851239 | − | 0.996370i | \(-0.527129\pi\) |
0.820320 | + | 0.571905i | \(0.193795\pi\) | |||||||
\(398\) | 9.21552i | 0.461932i | ||||||||
\(399\) | 0.233406 | + | 0.404271i | 0.0116849 | + | 0.0202389i | ||||
\(400\) | −1.37047 | + | 2.37372i | −0.0685235 | + | 0.118686i | ||||
\(401\) | −23.0904 | − | 13.3312i | −1.15308 | − | 0.665730i | −0.203443 | − | 0.979087i | \(-0.565213\pi\) |
−0.949636 | + | 0.313356i | \(0.898547\pi\) | |||||||
\(402\) | 13.8388 | 0.690215 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18.1207 | 0.901537 | ||||||||
\(405\) | −2.34182 | − | 1.35205i | −0.116366 | − | 0.0671840i | ||||
\(406\) | 4.37651 | − | 7.58034i | 0.217203 | − | 0.376206i | ||||
\(407\) | −12.0869 | − | 20.9352i | −0.599128 | − | 1.03772i | ||||
\(408\) | − | 13.0586i | − | 0.646497i | ||||||
\(409\) | −24.6959 | + | 14.2582i | −1.22113 | + | 0.705021i | −0.965159 | − | 0.261663i | \(-0.915729\pi\) |
−0.255972 | + | 0.966684i | \(0.582396\pi\) | |||||||
\(410\) | −1.98831 | + | 1.14795i | −0.0981954 | + | 0.0566931i | ||||
\(411\) | − | 13.9758i | − | 0.689377i | ||||||
\(412\) | 0.924231 | + | 1.60082i | 0.0455336 | + | 0.0788665i | ||||
\(413\) | 7.99007 | − | 13.8392i | 0.393166 | − | 0.680983i | ||||
\(414\) | −2.12586 | − | 1.22737i | −0.104480 | − | 0.0603217i | ||||
\(415\) | −0.397452 | −0.0195102 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 33.0465 | 1.61830 | ||||||||
\(418\) | 0.259988 | + | 0.150104i | 0.0127165 | + | 0.00734185i | ||||
\(419\) | 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 | ||||
\(421\) | 11.6606i | 0.568301i | 0.958780 | + | 0.284151i | \(0.0917115\pi\) | ||||
−0.958780 | + | 0.284151i | \(0.908288\pi\) | |||||||
\(422\) | −6.10081 | + | 3.52230i | −0.296983 | + | 0.171463i | ||||
\(423\) | −13.0542 | + | 7.53684i | −0.634716 | + | 0.366453i | ||||
\(424\) | 27.9801i | 1.35884i | ||||||||
\(425\) | 5.33124 | + | 9.23398i | 0.258603 | + | 0.447914i | ||||
\(426\) | 7.80678 | − | 13.5217i | 0.378240 | − | 0.655131i | ||||
\(427\) | 7.08719 | + | 4.09179i | 0.342973 | + | 0.198016i | ||||
\(428\) | 4.43535 | 0.214391 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.0586060 | −0.00282623 | ||||||||
\(431\) | 3.76645 | + | 2.17456i | 0.181424 | + | 0.104745i | 0.587961 | − | 0.808889i | \(-0.299931\pi\) |
−0.406538 | + | 0.913634i | \(0.633264\pi\) | |||||||
\(432\) | −0.592990 | + | 1.02709i | −0.0285303 | + | 0.0494159i | ||||
\(433\) | −7.19418 | − | 12.4607i | −0.345730 | − | 0.598822i | 0.639756 | − | 0.768578i | \(-0.279035\pi\) |
−0.985486 | + | 0.169756i | \(0.945702\pi\) | |||||||
\(434\) | − | 12.5332i | − | 0.601612i | ||||||
\(435\) | 2.22571 | − | 1.28501i | 0.106714 | − | 0.0616116i | ||||
\(436\) | −18.4512 | + | 10.6528i | −0.883651 | + | 0.510176i | ||||
\(437\) | − | 0.131687i | − | 0.00629942i | ||||||
\(438\) | 6.06853 | + | 10.5110i | 0.289966 | + | 0.502235i | ||||
\(439\) | −10.1163 | + | 17.5219i | −0.482822 | + | 0.836273i | −0.999805 | − | 0.0197227i | \(-0.993722\pi\) |
0.516983 | + | 0.855996i | \(0.327055\pi\) | |||||||
\(440\) | −2.44540 | − | 1.41185i | −0.116580 | − | 0.0673075i | ||||
\(441\) | 2.96077 | 0.140989 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.12200 | 0.385888 | 0.192944 | − | 0.981210i | \(-0.438196\pi\) | ||||
0.192944 | + | 0.981210i | \(0.438196\pi\) | |||||||
\(444\) | 15.0294 | + | 8.67725i | 0.713266 | + | 0.411804i | ||||
\(445\) | 0.356232 | − | 0.617012i | 0.0168870 | − | 0.0292492i | ||||
\(446\) | −0.905813 | − | 1.56891i | −0.0428915 | − | 0.0742903i | ||||
\(447\) | 9.74094i | 0.460731i | ||||||||
\(448\) | 7.27591 | − | 4.20075i | 0.343755 | − | 0.198467i | ||||
\(449\) | 10.8180 | − | 6.24578i | 0.510534 | − | 0.294757i | −0.222519 | − | 0.974928i | \(-0.571428\pi\) |
0.733053 | + | 0.680172i | \(0.238095\pi\) | |||||||
\(450\) | − | 8.11529i | − | 0.382559i | ||||||
\(451\) | −24.6151 | − | 42.6345i | −1.15908 | − | 2.00758i | ||||
\(452\) | −8.17456 | + | 14.1588i | −0.384499 | + | 0.665972i | ||||
\(453\) | 7.67553 | + | 4.43147i | 0.360628 | + | 0.208209i | ||||
\(454\) | 5.58642 | 0.262184 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.533188 | −0.0249688 | ||||||||
\(457\) | 5.17988 | + | 2.99061i | 0.242305 | + | 0.139895i | 0.616236 | − | 0.787562i | \(-0.288657\pi\) |
−0.373931 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(458\) | 9.69298 | − | 16.7887i | 0.452923 | − | 0.784486i | ||||
\(459\) | 2.30678 | + | 3.99546i | 0.107671 | + | 0.186492i | ||||
\(460\) | 0.500664i | 0.0233436i | ||||||||
\(461\) | 1.78114 | − | 1.02834i | 0.0829561 | − | 0.0478947i | −0.457948 | − | 0.888979i | \(-0.651415\pi\) |
0.540904 | + | 0.841084i | \(0.318082\pi\) | |||||||
\(462\) | −15.6204 | + | 9.01842i | −0.726725 | + | 0.419575i | ||||
\(463\) | − | 8.44935i | − | 0.392675i | −0.980536 | − | 0.196337i | \(-0.937095\pi\) | ||
0.980536 | − | 0.196337i | \(-0.0629048\pi\) | |||||||
\(464\) | −1.28501 | − | 2.22571i | −0.0596552 | − | 0.103326i | ||||
\(465\) | 1.83997 | − | 3.18692i | 0.0853266 | − | 0.147790i | ||||
\(466\) | 2.12586 | + | 1.22737i | 0.0984785 | + | 0.0568566i | ||||
\(467\) | −33.5139 | −1.55084 | −0.775420 | − | 0.631446i | \(-0.782462\pi\) | ||||
−0.775420 | + | 0.631446i | \(0.782462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.1008 | −0.835818 | ||||||||
\(470\) | −1.26191 | − | 0.728562i | −0.0582074 | − | 0.0336060i | ||||
\(471\) | 5.00484 | − | 8.66864i | 0.230611 | − | 0.399430i | ||||
\(472\) | 9.12618 | + | 15.8070i | 0.420066 | + | 0.727576i | ||||
\(473\) | − | 1.25667i | − | 0.0577817i | ||||||
\(474\) | 15.5591 | − | 8.98307i | 0.714655 | − | 0.412606i | ||||
\(475\) | 0.377027 | − | 0.217677i | 0.0172992 | − | 0.00998769i | ||||
\(476\) | 6.90408i | 0.316448i | ||||||||
\(477\) | 10.6479 | + | 18.4428i | 0.487536 | + | 0.844437i | ||||
\(478\) | −10.0831 | + | 17.4644i | −0.461189 | + | 0.798802i | ||||
\(479\) | 21.4179 | + | 12.3656i | 0.978608 | + | 0.565000i | 0.901850 | − | 0.432050i | \(-0.142210\pi\) |
0.0767587 | + | 0.997050i | \(0.475543\pi\) | |||||||
\(480\) | 3.23490 | 0.147652 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −16.2524 | −0.740275 | ||||||||
\(483\) | 6.85187 | + | 3.95593i | 0.311771 | + | 0.180001i | ||||
\(484\) | 4.77413 | − | 8.26903i | 0.217006 | − | 0.375865i | ||||
\(485\) | −0.995156 | − | 1.72366i | −0.0451877 | − | 0.0782674i | ||||
\(486\) | − | 14.5875i | − | 0.661702i | ||||||
\(487\) | 32.6972 | − | 18.8778i | 1.48165 | − | 0.855433i | 0.481870 | − | 0.876243i | \(-0.339958\pi\) |
0.999783 | + | 0.0208094i | \(0.00662430\pi\) | |||||||
\(488\) | −8.09492 | + | 4.67360i | −0.366440 | + | 0.211564i | ||||
\(489\) | − | 36.3086i | − | 1.64193i | ||||||
\(490\) | 0.143104 | + | 0.247864i | 0.00646479 | + | 0.0111973i | ||||
\(491\) | 15.6555 | − | 27.1161i | 0.706522 | − | 1.22373i | −0.259617 | − | 0.965712i | \(-0.583596\pi\) |
0.966139 | − | 0.258020i | \(-0.0830702\pi\) | |||||||
\(492\) | 30.6074 | + | 17.6712i | 1.37989 | + | 0.796680i | ||||
\(493\) | −9.99761 | −0.450270 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.14914 | −0.0965969 | ||||||||
\(496\) | −3.18692 | − | 1.83997i | −0.143097 | − | 0.0826171i | ||||
\(497\) | −10.2111 | + | 17.6861i | −0.458031 | + | 0.793332i | ||||
\(498\) | −1.44989 | − | 2.51128i | −0.0649710 | − | 0.112533i | ||||
\(499\) | − | 21.4873i | − | 0.961902i | −0.876748 | − | 0.480951i | \(-0.840292\pi\) | ||
0.876748 | − | 0.480951i | \(-0.159708\pi\) | |||||||
\(500\) | −2.88457 | + | 1.66541i | −0.129002 | + | 0.0744793i | ||||
\(501\) | −31.3632 | + | 18.1075i | −1.40120 | + | 0.808984i | ||||
\(502\) | − | 19.0228i | − | 0.849031i | ||||||
\(503\) | −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 | ||||
\(505\) | 2.85640 | + | 1.64914i | 0.127108 | + | 0.0733860i | ||||
\(506\) | 5.08815 | 0.226196 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.3075 | 0.590425 | ||||||||
\(509\) | −14.8155 | − | 8.55376i | −0.656688 | − | 0.379139i | 0.134326 | − | 0.990937i | \(-0.457113\pi\) |
−0.791014 | + | 0.611798i | \(0.790446\pi\) | |||||||
\(510\) | 0.480386 | − | 0.832052i | 0.0212718 | − | 0.0368439i | ||||
\(511\) | −7.93751 | − | 13.7482i | −0.351135 | − | 0.608183i | ||||
\(512\) | − | 6.22282i | − | 0.275012i | ||||||
\(513\) | 0.163136 | − | 0.0941868i | 0.00720264 | − | 0.00415845i | ||||
\(514\) | 9.87865 | − | 5.70344i | 0.435728 | − | 0.251568i | ||||
\(515\) | 0.336454i | 0.0148259i | ||||||||
\(516\) | 0.451083 | + | 0.781298i | 0.0198578 | + | 0.0343947i | ||||
\(517\) | 15.6223 | − | 27.0586i | 0.687068 | − | 1.19004i | ||||
\(518\) | 9.31705 | + | 5.37920i | 0.409367 | + | 0.236348i | ||||
\(519\) | −48.3913 | −2.12414 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19.8465 | −0.869493 | −0.434746 | − | 0.900553i | \(-0.643162\pi\) | ||||
−0.434746 | + | 0.900553i | \(0.643162\pi\) | |||||||
\(522\) | 6.58981 | + | 3.80463i | 0.288428 | + | 0.166524i | ||||
\(523\) | 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 | ||||
\(525\) | 26.1564i | 1.14156i | ||||||||
\(526\) | 11.8728 | − | 6.85474i | 0.517677 | − | 0.298881i | ||||
\(527\) | −12.3974 | + | 7.15764i | −0.540039 | + | 0.311792i | ||||
\(528\) | 5.29590i | 0.230474i | ||||||||
\(529\) | 10.3840 | + | 17.9857i | 0.451480 | + | 0.781987i | ||||
\(530\) | −1.02930 | + | 1.78281i | −0.0447101 | + | 0.0774401i | ||||
\(531\) | 12.0308 | + | 6.94600i | 0.522093 | + | 0.301431i | ||||
\(532\) | 0.281896 | 0.0122218 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.19806 | 0.224942 | ||||||||
\(535\) | 0.699155 | + | 0.403657i | 0.0302271 | + | 0.0174516i | ||||
\(536\) | 10.3373 | − | 17.9047i | 0.446503 | − | 0.773365i | ||||
\(537\) | −12.8448 | − | 22.2479i | −0.554295 | − | 0.960066i | ||||
\(538\) | 5.18598i | 0.223584i | ||||||||
\(539\) | −5.31485 | + | 3.06853i | −0.228927 | + | 0.132171i | ||||
\(540\) | −0.620234 | + | 0.358092i | −0.0266906 | + | 0.0154098i | ||||
\(541\) | 16.1884i | 0.695993i | 0.937496 | + | 0.347996i | \(0.113138\pi\) | ||||
−0.937496 | + | 0.347996i | \(0.886862\pi\) | |||||||
\(542\) | −2.58546 | − | 4.47814i | −0.111055 | − | 0.192353i | ||||
\(543\) | −23.5601 | + | 40.8073i | −1.01106 | + | 1.75121i | ||||
\(544\) | −10.8981 | − | 6.29201i | −0.467252 | − | 0.269768i | ||||
\(545\) | −3.87800 | −0.166115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.33081 | 0.227929 | 0.113965 | − | 0.993485i | \(-0.463645\pi\) | ||||
0.113965 | + | 0.993485i | \(0.463645\pi\) | |||||||
\(548\) | −7.30896 | − | 4.21983i | −0.312223 | − | 0.180262i | ||||
\(549\) | −3.55711 | + | 6.16110i | −0.151814 | + | 0.262949i | ||||
\(550\) | 8.41066 | + | 14.5677i | 0.358632 | + | 0.621168i | ||||
\(551\) | 0.408206i | 0.0173902i | ||||||||
\(552\) | −7.82613 | + | 4.51842i | −0.333102 | + | 0.192317i | ||||
\(553\) | −20.3510 | + | 11.7497i | −0.865413 | + | 0.499647i | ||||
\(554\) | 10.7942i | 0.458600i | ||||||||
\(555\) | 1.57942 | + | 2.73563i | 0.0670425 | + | 0.116121i | ||||
\(556\) | 9.97799 | − | 17.2824i | 0.423161 | − | 0.732937i | ||||
\(557\) | −6.40058 | − | 3.69537i | −0.271201 | − | 0.156578i | 0.358232 | − | 0.933633i | \(-0.383380\pi\) |
−0.629433 | + | 0.777054i | \(0.716713\pi\) | |||||||
\(558\) | 10.8955 | 0.461242 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −0.323044 | −0.0136511 | ||||||||
\(561\) | 17.8414 | + | 10.3007i | 0.753265 | + | 0.434898i | ||||
\(562\) | −2.01961 | + | 3.49807i | −0.0851923 | + | 0.147557i | ||||
\(563\) | −4.73945 | − | 8.20896i | −0.199744 | − | 0.345967i | 0.748701 | − | 0.662907i | \(-0.230678\pi\) |
−0.948445 | + | 0.316941i | \(0.897344\pi\) | |||||||
\(564\) | 22.4306i | 0.944497i | ||||||||
\(565\) | −2.57715 | + | 1.48792i | −0.108422 | + | 0.0625972i | ||||
\(566\) | 15.3678 | − | 8.87263i | 0.645958 | − | 0.372944i | ||||
\(567\) | 25.8049i | 1.08370i | ||||||||
\(568\) | −11.6630 | − | 20.2009i | −0.489369 | − | 0.847612i | ||||
\(569\) | −5.07188 | + | 8.78476i | −0.212624 | + | 0.368276i | −0.952535 | − | 0.304429i | \(-0.901534\pi\) |
0.739911 | + | 0.672705i | \(0.234868\pi\) | |||||||
\(570\) | −0.0339730 | − | 0.0196143i | −0.00142297 | − | 0.000821554i | ||||
\(571\) | 14.0925 | 0.589751 | 0.294876 | − | 0.955536i | \(-0.404722\pi\) | ||||
0.294876 | + | 0.955536i | \(0.404722\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.4403 | 1.35521 | ||||||||
\(574\) | 18.9741 | + | 10.9547i | 0.791966 | + | 0.457242i | ||||
\(575\) | 3.68933 | − | 6.39011i | 0.153856 | − | 0.266486i | ||||
\(576\) | 3.65183 | + | 6.32516i | 0.152160 | + | 0.263548i | ||||
\(577\) | − | 25.1545i | − | 1.04720i | −0.851965 | − | 0.523598i | \(-0.824589\pi\) | ||
0.851965 | − | 0.523598i | \(-0.175411\pi\) | |||||||
\(578\) | 8.56972 | − | 4.94773i | 0.356453 | − | 0.205798i | ||||
\(579\) | 26.4253 | − | 15.2567i | 1.09820 | − | 0.634045i | ||||
\(580\) | − | 1.55197i | − | 0.0644422i | ||||||
\(581\) | 1.89642 | + | 3.28470i | 0.0786768 | + | 0.136272i | ||||
\(582\) | 7.26055 | − | 12.5756i | 0.300960 | − | 0.521277i | ||||
\(583\) | −38.2281 | − | 22.0710i | −1.58324 | − | 0.914087i | ||||
\(584\) | 18.1323 | 0.750319 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 11.9860 | 0.495137 | ||||||||
\(587\) | 37.9625 | + | 21.9177i | 1.56688 | + | 0.904639i | 0.996530 | + | 0.0832369i | \(0.0265258\pi\) |
0.570350 | + | 0.821402i | \(0.306808\pi\) | |||||||
\(588\) | 2.20291 | − | 3.81555i | 0.0908463 | − | 0.157350i | ||||
\(589\) | 0.292249 | + | 0.506190i | 0.0120419 | + | 0.0208572i | ||||
\(590\) | 1.34290i | 0.0552861i | ||||||||
\(591\) | −1.09038 | + | 0.629531i | −0.0448522 | + | 0.0258954i | ||||
\(592\) | 2.73563 | − | 1.57942i | 0.112434 | − | 0.0649136i | ||||
\(593\) | − | 24.9965i | − | 1.02648i | −0.858244 | − | 0.513242i | \(-0.828444\pi\) | ||
0.858244 | − | 0.513242i | \(-0.171556\pi\) | |||||||
\(594\) | 3.63922 | + | 6.30331i | 0.149319 | + | 0.258628i | ||||
\(595\) | −0.628334 | + | 1.08831i | −0.0257592 | + | 0.0446162i | ||||
\(596\) | 5.09423 | + | 2.94116i | 0.208668 | + | 0.120474i | ||||
\(597\) | 25.8213 | 1.05680 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.24027 | −0.254971 | −0.127485 | − | 0.991840i | \(-0.540691\pi\) | ||||
−0.127485 | + | 0.991840i | \(0.540691\pi\) | |||||||
\(600\) | −25.8730 | − | 14.9378i | −1.05626 | − | 0.609833i | ||||
\(601\) | −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 | ||||
\(603\) | − | 15.7356i | − | 0.640802i | ||||||
\(604\) | 4.63506 | − | 2.67606i | 0.188598 | − | 0.108887i | ||||
\(605\) | 1.50511 | − | 0.868977i | 0.0611915 | − | 0.0353290i | ||||
\(606\) | 24.0640i | 0.977532i | ||||||||
\(607\) | 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 | ||||
\(609\) | −21.2396 | − | 12.2627i | −0.860673 | − | 0.496910i | ||||
\(610\) | −0.687710 | −0.0278445 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −6.00192 | −0.242613 | ||||||||
\(613\) | −22.4769 | − | 12.9770i | −0.907833 | − | 0.524137i | −0.0280995 | − | 0.999605i | \(-0.508946\pi\) |
−0.879733 | + | 0.475468i | \(0.842279\pi\) | |||||||
\(614\) | −7.67025 | + | 13.2853i | −0.309546 | + | 0.536150i | ||||
\(615\) | 3.21648 | + | 5.57111i | 0.129701 | + | 0.224649i | ||||
\(616\) | 26.9463i | 1.08570i | ||||||||
\(617\) | −39.7849 | + | 22.9698i | −1.60168 | + | 0.924729i | −0.610526 | + | 0.791996i | \(0.709042\pi\) |
−0.991152 | + | 0.132733i | \(0.957625\pi\) | |||||||
\(618\) | −2.12586 | + | 1.22737i | −0.0855146 | + | 0.0493719i | ||||
\(619\) | 6.73556i | 0.270725i | 0.990796 | + | 0.135363i | \(0.0432199\pi\) | ||||
−0.990796 | + | 0.135363i | \(0.956780\pi\) | |||||||
\(620\) | −1.11111 | − | 1.92450i | −0.0446234 | − | 0.0772899i | ||||
\(621\) | 1.59634 | − | 2.76495i | 0.0640590 | − | 0.110953i | ||||
\(622\) | 0.187386 | + | 0.108187i | 0.00751349 | + | 0.00433792i | ||||
\(623\) | −6.79895 | −0.272394 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.0887 | 0.963549 | ||||||||
\(626\) | −16.2469 | − | 9.38016i | −0.649357 | − | 0.374907i | ||||
\(627\) | 0.420583 | − | 0.728471i | 0.0167965 | − | 0.0290923i | ||||
\(628\) | −3.02230 | − | 5.23478i | −0.120603 | − | 0.208891i | ||||
\(629\) | − | 12.2881i | − | 0.489960i | ||||||
\(630\) | 0.828318 | − | 0.478230i | 0.0330010 | − | 0.0190531i | ||||
\(631\) | 39.0575 | − | 22.5499i | 1.55486 | − | 0.897696i | 0.557121 | − | 0.830432i | \(-0.311906\pi\) |
0.997735 | − | 0.0672649i | \(-0.0214273\pi\) | |||||||
\(632\) | − | 26.8407i | − | 1.06767i | ||||||
\(633\) | 9.86927 | + | 17.0941i | 0.392268 | + | 0.679429i | ||||
\(634\) | −5.61165 | + | 9.71965i | −0.222867 | + | 0.386017i | ||||
\(635\) | 2.09769 | + | 1.21110i | 0.0832444 | + | 0.0480612i | ||||
\(636\) | 31.6896 | 1.25658 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.7724 | −0.624435 | ||||||||
\(639\) | −15.3751 | − | 8.87681i | −0.608229 | − | 0.351161i | ||||
\(640\) | 1.08665 | − | 1.88214i | 0.0429538 | − | 0.0743981i | ||||
\(641\) | 16.2911 | + | 28.2169i | 0.643458 | + | 1.11450i | 0.984655 | + | 0.174510i | \(0.0558342\pi\) |
−0.341197 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(642\) | 5.89008i | 0.232463i | ||||||||
\(643\) | −22.1489 | + | 12.7877i | −0.873469 | + | 0.504298i | −0.868500 | − | 0.495690i | \(-0.834915\pi\) |
−0.00496965 | + | 0.999988i | \(0.501582\pi\) | |||||||
\(644\) | 4.13767 | − | 2.38889i | 0.163047 | − | 0.0941353i | ||||
\(645\) | 0.164210i | 0.00646578i | ||||||||
\(646\) | 0.0763014 | + | 0.132158i | 0.00300204 | + | 0.00519968i | ||||
\(647\) | −15.0858 | + | 26.1293i | −0.593082 | + | 1.02725i | 0.400732 | + | 0.916195i | \(0.368756\pi\) |
−0.993814 | + | 0.111053i | \(0.964578\pi\) | |||||||
\(648\) | −25.5253 | − | 14.7371i | −1.00273 | − | 0.578926i | ||||
\(649\) | −28.7952 | −1.13031 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.1172 | −1.37635 | ||||||||
\(652\) | −18.9883 | − | 10.9629i | −0.743641 | − | 0.429341i | ||||
\(653\) | −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 | ||||
\(655\) | 1.62432i | 0.0634673i | ||||||||
\(656\) | 5.57111 | − | 3.21648i | 0.217515 | − | 0.125582i | ||||
\(657\) | 11.9517 | − | 6.90030i | 0.466279 | − | 0.269207i | ||||
\(658\) | 13.9051i | 0.542079i | ||||||||
\(659\) | −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 | ||||
\(661\) | 27.5041 | + | 15.8795i | 1.06979 | + | 0.617641i | 0.928123 | − | 0.372274i | \(-0.121422\pi\) |
0.141662 | + | 0.989915i | \(0.454755\pi\) | |||||||
\(662\) | −14.2916 | −0.555458 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.33214 | −0.168120 | ||||||||
\(665\) | 0.0444360 | + | 0.0256551i | 0.00172315 | + | 0.000994863i | ||||
\(666\) | −4.67629 | + | 8.09958i | −0.181203 | + | 0.313852i | ||||
\(667\) | 3.45928 | + | 5.99165i | 0.133944 | + | 0.231998i | ||||
\(668\) | 21.8694i | 0.846152i | ||||||||
\(669\) | −4.39600 | + | 2.53803i | −0.169959 | + | 0.0981260i | ||||
\(670\) | 1.31732 | − | 0.760553i | 0.0508924 | − | 0.0293827i | ||||
\(671\) | − | 14.7463i | − | 0.569275i | ||||||
\(672\) | −15.4351 | − | 26.7344i | −0.595423 | − | 1.03130i | ||||
\(673\) | −3.75116 | + | 6.49720i | −0.144597 | + | 0.250449i | −0.929222 | − | 0.369521i | \(-0.879522\pi\) |
0.784626 | + | 0.619970i | \(0.212855\pi\) | |||||||
\(674\) | 19.3407 | + | 11.1664i | 0.744976 | + | 0.430112i | ||||
\(675\) | 10.5550 | 0.406261 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −35.0315 | −1.34637 | −0.673184 | − | 0.739475i | \(-0.735074\pi\) | ||||
−0.673184 | + | 0.739475i | \(0.735074\pi\) | |||||||
\(678\) | −18.8026 | − | 10.8557i | −0.722110 | − | 0.416911i | ||||
\(679\) | −9.49665 | + | 16.4487i | −0.364448 | + | 0.631242i | ||||
\(680\) | −0.717677 | − | 1.24305i | −0.0275216 | − | 0.0476689i | ||||
\(681\) | − | 15.6528i | − | 0.599816i | ||||||
\(682\) | −19.5583 | + | 11.2920i | −0.748927 | + | 0.432393i | ||||
\(683\) | −20.8568 | + | 12.0417i | −0.798063 | + | 0.460762i | −0.842794 | − | 0.538237i | \(-0.819091\pi\) |
0.0447302 | + | 0.998999i | \(0.485757\pi\) | |||||||
\(684\) | 0.245061i | 0.00937013i | ||||||||
\(685\) | −0.768086 | − | 1.33036i | −0.0293471 | − | 0.0508306i | ||||
\(686\) | 7.98092 | − | 13.8234i | 0.304713 | − | 0.527778i | ||||
\(687\) | −47.0410 | − | 27.1591i | −1.79473 | − | 1.03619i | ||||
\(688\) | 0.164210 | 0.00626046 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −0.664874 | −0.0253113 | ||||||||
\(691\) | 1.74459 | + | 1.00724i | 0.0663672 | + | 0.0383171i | 0.532816 | − | 0.846231i | \(-0.321134\pi\) |
−0.466449 | + | 0.884548i | \(0.654467\pi\) | |||||||
\(692\) | −14.6112 | + | 25.3073i | −0.555433 | + | 0.962039i | ||||
\(693\) | 10.2545 | + | 17.7613i | 0.389537 | + | 0.674697i | ||||
\(694\) | − | 1.20583i | − | 0.0457728i | ||||||
\(695\) | 3.14571 | − | 1.81618i | 0.119323 | − | 0.0688915i | ||||
\(696\) | 24.2597 | − | 14.0063i | 0.919561 | − | 0.530909i | ||||
\(697\) | − | 25.0248i | − | 0.947880i | ||||||
\(698\) | 5.68814 | + | 9.85214i | 0.215299 | + | 0.372909i | ||||
\(699\) | 3.43900 | − | 5.95652i | 0.130075 | − | 0.225296i | ||||
\(700\) | 13.6791 | + | 7.89762i | 0.517020 | + | 0.298502i | ||||
\(701\) | 48.8189 | 1.84387 | 0.921933 | − | 0.387350i | \(-0.126610\pi\) | ||||
0.921933 | + | 0.387350i | \(0.126610\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.501729 | −0.0189231 | ||||||||
\(704\) | −13.1107 | − | 7.56949i | −0.494130 | − | 0.285286i | ||||
\(705\) | −2.04138 | + | 3.53578i | −0.0768830 | + | 0.133165i | ||||
\(706\) | −2.87435 | − | 4.97853i | −0.108178 | − | 0.187369i | ||||
\(707\) | − | 31.4752i | − | 1.18375i | ||||||
\(708\) | 17.9026 | − | 10.3361i | 0.672822 | − | 0.388454i | ||||
\(709\) | −18.0185 | + | 10.4030i | −0.676699 | + | 0.390693i | −0.798610 | − | 0.601848i | \(-0.794431\pi\) |
0.121911 | + | 0.992541i | \(0.461098\pi\) | |||||||
\(710\) | − | 1.71618i | − | 0.0644073i | ||||||
\(711\) | −10.2143 | − | 17.6917i | −0.383067 | − | 0.663492i | ||||
\(712\) | 3.88285 | − | 6.72529i | 0.145516 | − | 0.252041i | ||||
\(713\) | 8.57926 | + | 4.95324i | 0.321296 | + | 0.185500i | ||||
\(714\) | −9.16852 | −0.343123 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.5133 | −0.579761 | ||||||||
\(717\) | 48.9341 | + | 28.2521i | 1.82748 | + | 1.05509i | ||||
\(718\) | −7.97339 | + | 13.8103i | −0.297564 | + | 0.515396i | ||||
\(719\) | 10.7153 | + | 18.5594i | 0.399613 | + | 0.692149i | 0.993678 | − | 0.112267i | \(-0.0358113\pi\) |
−0.594065 | + | 0.804417i | \(0.702478\pi\) | |||||||
\(720\) | − | 0.280831i | − | 0.0104660i | ||||||
\(721\) | 2.78058 | − | 1.60537i | 0.103554 | − | 0.0597870i | ||||
\(722\) | −13.1901 | + | 7.61529i | −0.490884 | + | 0.283412i | ||||
\(723\) | 45.5381i | 1.69358i | ||||||||
\(724\) | 14.2274 | + | 24.6425i | 0.528756 | + | 0.915832i | ||||
\(725\) | −11.4363 | + | 19.8083i | −0.424734 | + | 0.735661i | ||||
\(726\) | 10.9812 | + | 6.33997i | 0.407549 | + | 0.235298i | ||||
\(727\) | −13.4862 | −0.500175 | −0.250088 | − | 0.968223i | \(-0.580459\pi\) | ||||
−0.250088 | + | 0.968223i | \(0.580459\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.02715 | −0.297302 | ||||||||
\(730\) | 1.15533 | + | 0.667030i | 0.0427607 | + | 0.0246879i | ||||
\(731\) | 0.319396 | − | 0.553210i | 0.0118133 | − | 0.0204612i | ||||
\(732\) | 5.29321 | + | 9.16811i | 0.195643 | + | 0.338863i | ||||
\(733\) | 43.5424i | 1.60828i | 0.594443 | + | 0.804138i | \(0.297373\pi\) | ||||
−0.594443 | + | 0.804138i | \(0.702627\pi\) | |||||||
\(734\) | −0.752721 | + | 0.434584i | −0.0277834 | + | 0.0160408i | ||||
\(735\) | 0.694498 | − | 0.400969i | 0.0256170 | − | 0.0147900i | ||||
\(736\) | 8.70841i | 0.320996i | ||||||||
\(737\) | 16.3083 | + | 28.2468i | 0.600723 | + | 1.04048i | ||||
\(738\) | −9.52326 | + | 16.4948i | −0.350556 | + | 0.607181i | ||||
\(739\) | −17.3675 | − | 10.0271i | −0.638875 | − | 0.368855i | 0.145306 | − | 0.989387i | \(-0.453583\pi\) |
−0.784181 | + | 0.620532i | \(0.786917\pi\) | |||||||
\(740\) | 1.90754 | 0.0701226 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 19.6450 | 0.721191 | ||||||||
\(743\) | −28.7248 | − | 16.5843i | −1.05381 | − | 0.608418i | −0.130096 | − | 0.991501i | \(-0.541529\pi\) |
−0.923714 | + | 0.383084i | \(0.874862\pi\) | |||||||
\(744\) | 20.0553 | − | 34.7367i | 0.735261 | − | 1.27351i | ||||
\(745\) | 0.535344 | + | 0.927243i | 0.0196135 | + | 0.0339715i | ||||
\(746\) | 4.91617i | 0.179994i | ||||||||
\(747\) | −2.85548 | + | 1.64861i | −0.104477 | + | 0.0603196i | ||||
\(748\) | 10.7740 | − | 6.22037i | 0.393936 | − | 0.227439i | ||||
\(749\) | − | 7.70410i | − | 0.281502i | ||||||
\(750\) | −2.21164 | − | 3.83067i | −0.0807575 | − | 0.139876i | ||||
\(751\) | 19.6407 | − | 34.0187i | 0.716700 | − | 1.24136i | −0.245601 | − | 0.969371i | \(-0.578985\pi\) |
0.962300 | − | 0.271989i | \(-0.0876815\pi\) | |||||||
\(752\) | 3.53578 | + | 2.04138i | 0.128937 | + | 0.0744416i | ||||
\(753\) | −53.3008 | −1.94239 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.974181 | 0.0354541 | ||||||||
\(756\) | 5.91882 | + | 3.41723i | 0.215265 | + | 0.124283i | ||||
\(757\) | 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 | ||||
\(759\) | − | 14.2567i | − | 0.517484i | ||||||
\(760\) | −0.0507543 | + | 0.0293030i | −0.00184105 | + | 0.00106293i | ||||
\(761\) | −18.9646 | + | 10.9492i | −0.687467 | + | 0.396909i | −0.802662 | − | 0.596434i | \(-0.796584\pi\) |
0.115196 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(762\) | 17.6722i | 0.640195i | ||||||||
\(763\) | 18.5036 | + | 32.0493i | 0.669877 | + | 1.16026i | ||||
\(764\) | 9.79494 | − | 16.9653i | 0.354368 | − | 0.613784i | ||||
\(765\) | −0.946096 | − | 0.546229i | −0.0342062 | − | 0.0197489i | ||||
\(766\) | 24.3720 | 0.880595 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 31.8756 | 1.15021 | ||||||||
\(769\) | 40.4517 | + | 23.3548i | 1.45873 | + | 0.842196i | 0.998949 | − | 0.0458390i | \(-0.0145961\pi\) |
0.459777 | + | 0.888035i | \(0.347929\pi\) | |||||||
\(770\) | −0.991271 | + | 1.71693i | −0.0357229 | + | 0.0618739i | ||||
\(771\) | −15.9807 | − | 27.6794i | −0.575530 | − | 0.996848i | ||||
\(772\) | − | 18.4263i | − | 0.663175i | ||||||
\(773\) | 26.1900 | − | 15.1208i | 0.941989 | − | 0.543857i | 0.0514055 | − | 0.998678i | \(-0.483630\pi\) |
0.890583 | + | 0.454820i | \(0.150297\pi\) | |||||||
\(774\) | −0.421052 | + | 0.243095i | −0.0151344 | + | 0.00873786i | ||||
\(775\) | 32.7506i | 1.17644i | ||||||||
\(776\) | −10.8470 | − | 18.7875i | −0.389384 | − | 0.674432i | ||||
\(777\) | 15.0722 | − | 26.1058i | 0.540711 | − | 0.936540i | ||||
\(778\) | 11.0709 | + | 6.39181i | 0.396913 | + | 0.229158i | ||||
\(779\) | −1.02177 | −0.0366087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.7995 | 1.31679 | ||||||||
\(782\) | 2.23990 | + | 1.29321i | 0.0800988 | + | 0.0462450i | ||||
\(783\) | −4.94839 | + | 8.57087i | −0.176841 | + | 0.306298i | ||||
\(784\) | −0.400969 | − | 0.694498i | −0.0143203 | − | 0.0248035i | ||||
\(785\) | − | 1.10023i | − | 0.0392688i | ||||||
\(786\) | −10.2631 | + | 5.92543i | −0.366074 | + | 0.211353i | ||||
\(787\) | 24.8569 | − | 14.3512i | 0.886054 | − | 0.511563i | 0.0134040 | − | 0.999910i | \(-0.495733\pi\) |
0.872650 | + | 0.488347i | \(0.162400\pi\) | |||||||
\(788\) | 0.760316i | 0.0270851i | ||||||||
\(789\) | −19.2066 | − | 33.2667i | −0.683771 | − | 1.18433i | ||||
\(790\) | 0.987386 | − | 1.71020i | 0.0351296 | − | 0.0608463i | ||||
\(791\) | 24.5934 | + | 14.1990i | 0.874442 | + | 0.504859i | ||||
\(792\) | −23.4252 | −0.832378 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 13.5646 | 0.481391 | ||||||||
\(795\) | 4.99531 | + | 2.88404i | 0.177165 | + | 0.102286i | ||||
\(796\) | 7.79643 | − | 13.5038i | 0.276337 | − | 0.478630i | ||||
\(797\) | −9.27091 | − | 16.0577i | −0.328392 | − | 0.568792i | 0.653801 | − | 0.756667i | \(-0.273173\pi\) |
−0.982193 | + | 0.187875i | \(0.939840\pi\) | |||||||
\(798\) | 0.374354i | 0.0132520i | ||||||||
\(799\) | 13.7545 | − | 7.94116i | 0.486599 | − | 0.280938i | ||||
\(800\) | −24.9327 | + | 14.3949i | −0.881506 | + | 0.508938i | ||||
\(801\) | − | 5.91053i | − | 0.208838i | ||||||
\(802\) | −10.6908 | − | 18.5171i | −0.377506 | − | 0.653860i | ||||
\(803\) | −14.3029 | + | 24.7733i | −0.504738 | + | 0.874232i | ||||
\(804\) | −20.2784 | − | 11.7078i | −0.715165 | − | 0.412901i | ||||
\(805\) | 0.869641 | 0.0306508 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.5308 | 0.511508 | ||||||||
\(808\) | 31.1341 | + | 17.9753i | 1.09530 | + | 0.632369i | ||||
\(809\) | 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 | ||||
\(811\) | 10.0285i | 0.352147i | 0.984377 | + | 0.176074i | \(0.0563397\pi\) | ||||
−0.984377 | + | 0.176074i | \(0.943660\pi\) | |||||||
\(812\) | −12.8261 | + | 7.40515i | −0.450108 | + | 0.259870i | ||||
\(813\) | −12.5475 | + | 7.24429i | −0.440059 | + | 0.254068i | ||||
\(814\) | − | 19.3860i | − | 0.679478i | ||||||
\(815\) | −1.99545 | − | 3.45622i | −0.0698976 | − | 0.121066i | ||||
\(816\) | −1.34601 | + | 2.33136i | −0.0471198 | + | 0.0816139i | ||||
\(817\) | −0.0225878 | − | 0.0130411i | −0.000790247 | − | 0.000456249i | ||||
\(818\) | −22.8683 | −0.799572 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3.88471 | 0.135660 | ||||||||
\(821\) | −22.6643 | − | 13.0852i | −0.790988 | − | 0.456677i | 0.0493220 | − | 0.998783i | \(-0.484294\pi\) |
−0.840310 | + | 0.542106i | \(0.817627\pi\) | |||||||
\(822\) | 5.60388 | − | 9.70620i | 0.195458 | − | 0.338542i | ||||
\(823\) | 0.911190 | + | 1.57823i | 0.0317621 | + | 0.0550135i | 0.881470 | − | 0.472241i | \(-0.156555\pi\) |
−0.849707 | + | 0.527255i | \(0.823221\pi\) | |||||||
\(824\) | 3.66727i | 0.127755i | ||||||||
\(825\) | 40.8177 | − | 23.5661i | 1.42109 | − | 0.820468i | ||||
\(826\) | 11.0982 | − | 6.40754i | 0.386155 | − | 0.222947i | ||||
\(827\) | − | 32.2941i | − | 1.12298i | −0.827485 | − | 0.561488i | \(-0.810229\pi\) | ||
0.827485 | − | 0.561488i | \(-0.189771\pi\) | |||||||
\(828\) | 2.07673 | + | 3.59700i | 0.0721713 | + | 0.125004i | ||||
\(829\) | 7.55011 | − | 13.0772i | 0.262226 | − | 0.454189i | −0.704607 | − | 0.709598i | \(-0.748877\pi\) |
0.966833 | + | 0.255409i | \(0.0822100\pi\) | |||||||
\(830\) | −0.276030 | − | 0.159366i | −0.00958115 | − | 0.00553168i | ||||
\(831\) | 30.2446 | 1.04917 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.11960 | −0.108088 | ||||||||
\(834\) | 22.9508 | + | 13.2506i | 0.794720 | + | 0.458832i | ||||
\(835\) | −1.99031 | + | 3.44732i | −0.0688776 | + | 0.119299i | ||||
\(836\) | −0.253980 | − | 0.439906i | −0.00878408 | − | 0.0152145i | ||||
\(837\) | 14.1709i | 0.489818i | ||||||||
\(838\) | 20.5636 | − | 11.8724i | 0.710357 | − | 0.410125i | ||||
\(839\) | −28.5758 | + | 16.4983i | −0.986548 | + | 0.569584i | −0.904241 | − | 0.427023i | \(-0.859562\pi\) |
−0.0823071 | + | 0.996607i | \(0.526229\pi\) | |||||||
\(840\) | − | 3.52111i | − | 0.121490i | ||||||
\(841\) | 3.77682 | + | 6.54164i | 0.130235 | + | 0.225574i | ||||
\(842\) | −4.67552 | + | 8.09824i | −0.161129 | + | 0.279084i | ||||
\(843\) | 9.80139 | + | 5.65883i | 0.337578 | + | 0.194901i | ||||
\(844\) | 11.9196 | 0.410290 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −12.0881 | −0.415599 | ||||||||
\(847\) | −14.3631 | − | 8.29254i | −0.493522 | − | 0.284935i | ||||
\(848\) | 2.88404 | − | 4.99531i | 0.0990384 | − | 0.171540i | ||||
\(849\) | −24.8605 | − | 43.0597i | −0.853212 | − | 1.47781i | ||||
\(850\) | 8.55065i | 0.293285i | ||||||||
\(851\) | −7.36438 | + | 4.25182i | −0.252448 | + | 0.145751i | ||||
\(852\) | −22.8791 | + | 13.2092i | −0.783824 | + | 0.452541i | ||||
\(853\) | − | 37.7802i | − | 1.29357i | −0.762673 | − | 0.646784i | \(-0.776113\pi\) | ||
0.762673 | − | 0.646784i | \(-0.223887\pi\) | |||||||
\(854\) | 3.28136 | + | 5.68349i | 0.112286 | + | 0.194485i | ||||
\(855\) | −0.0223027 | + | 0.0386295i | −0.000762737 | + | 0.00132110i | ||||
\(856\) | 7.62063 | + | 4.39977i | 0.260468 | + | 0.150381i | ||||
\(857\) | −27.3623 | −0.934677 | −0.467339 | − | 0.884078i | \(-0.654787\pi\) | ||||
−0.467339 | + | 0.884078i | \(0.654787\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0629 | −0.684538 | −0.342269 | − | 0.939602i | \(-0.611195\pi\) | ||||
−0.342269 | + | 0.939602i | \(0.611195\pi\) | |||||||
\(860\) | 0.0858774 | + | 0.0495813i | 0.00292839 | + | 0.00169071i | ||||
\(861\) | 30.6945 | − | 53.1644i | 1.04606 | − | 1.81184i | ||||
\(862\) | 1.74386 | + | 3.02046i | 0.0593962 | + | 0.102877i | ||||
\(863\) | 6.14483i | 0.209173i | 0.994516 | + | 0.104586i | \(0.0333518\pi\) | ||||
−0.994516 | + | 0.104586i | \(0.966648\pi\) | |||||||
\(864\) | −10.7882 | + | 6.22856i | −0.367022 | + | 0.211900i | ||||
\(865\) | −4.60638 | + | 2.65950i | −0.156622 | + | 0.0904256i | ||||
\(866\) | − | 11.5386i | − | 0.392096i | ||||||
\(867\) | −13.8632 | − | 24.0118i | −0.470820 | − | 0.815484i | ||||
\(868\) | −10.6032 | + | 18.3653i | −0.359896 | + | 0.623359i | ||||
\(869\) | 36.6713 | + | 21.1722i | 1.24399 | + | 0.718217i | ||||
\(870\) | 2.06100 | 0.0698744 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −42.2693 | −1.43142 | ||||||||
\(873\) | −14.2993 | − | 8.25571i | −0.483958 | − | 0.279413i | ||||
\(874\) | 0.0528022 | − | 0.0914561i | 0.00178606 | − | 0.00309355i | ||||
\(875\) | 2.89277 | + | 5.01043i | 0.0977935 | + | 0.169383i | ||||
\(876\) | − | 20.5362i | − | 0.693853i | ||||||
\(877\) | 11.6980 | − | 6.75385i | 0.395014 | − | 0.228061i | −0.289317 | − | 0.957233i | \(-0.593428\pi\) |
0.684330 | + | 0.729172i | \(0.260095\pi\) | |||||||
\(878\) | −14.0514 | + | 8.11260i | −0.474213 | + | 0.273787i | ||||
\(879\) | − | 33.5840i | − | 1.13276i | ||||||
\(880\) | 0.291053 | + | 0.504118i | 0.00981138 | + | 0.0169938i | ||||
\(881\) | −2.61715 | + | 4.53304i | −0.0881741 | + | 0.152722i | −0.906739 | − | 0.421691i | \(-0.861437\pi\) |
0.818565 | + | 0.574414i | \(0.194770\pi\) | |||||||
\(882\) | 2.05625 | + | 1.18718i | 0.0692376 | + | 0.0399743i | ||||
\(883\) | 4.57301 | 0.153894 | 0.0769470 | − | 0.997035i | \(-0.475483\pi\) | ||||
0.0769470 | + | 0.997035i | \(0.475483\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.76271 | 0.126482 | ||||||||
\(886\) | 5.64071 | + | 3.25667i | 0.189504 | + | 0.109410i | ||||
\(887\) | 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 | ||||
\(889\) | − | 23.1148i | − | 0.775246i | ||||||
\(890\) | 0.494805 | − | 0.285676i | 0.0165859 | − | 0.00957587i | ||||
\(891\) | 40.2692 | − | 23.2494i | 1.34907 | − | 0.778885i | ||||
\(892\) | 3.06531i | 0.102634i | ||||||||
\(893\) | −0.324240 | − | 0.561601i | −0.0108503 | − | 0.0187933i | ||||
\(894\) | −3.90581 | + | 6.76507i | −0.130630 | + | 0.226258i | ||||
\(895\) | −2.44540 | − | 1.41185i | −0.0817408 | − | 0.0471931i | ||||
\(896\) | −20.7396 | −0.692862 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0175 | 0.334287 | ||||||||
\(899\) | −26.5943 | − | 15.3542i | −0.886968 | − | 0.512091i | ||||
\(900\) | −6.86563 | + | 11.8916i | −0.228854 | + | 0.396387i | ||||
\(901\) | −11.2192 | − | 19.4322i | −0.373765 | − | 0.647379i | ||||
\(902\) | − | 39.4795i | − | 1.31452i | ||||||
\(903\) | 1.35710 | − | 0.783520i | 0.0451613 | − | 0.0260739i | ||||
\(904\) | −28.0904 | + | 16.2180i | −0.934271 | + | 0.539402i | ||||
\(905\) | 5.17928i | 0.172165i | ||||||||
\(906\) | 3.55376 | + | 6.15530i | 0.118066 | + | 0.204496i | ||||
\(907\) | 4.05107 | − | 7.01666i | 0.134514 | − | 0.232985i | −0.790898 | − | 0.611948i | \(-0.790386\pi\) |
0.925412 | + | 0.378964i | \(0.123719\pi\) | |||||||
\(908\) | −8.18596 | − | 4.72617i | −0.271661 | − | 0.156843i | ||||
\(909\) | 27.3623 | 0.907549 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.18119 | −0.304187 | −0.152093 | − | 0.988366i | \(-0.548601\pi\) | ||||
−0.152093 | + | 0.988366i | \(0.548601\pi\) | |||||||
\(912\) | 0.0951903 | + | 0.0549581i | 0.00315207 | + | 0.00181985i | ||||
\(913\) | 3.41723 | − | 5.91882i | 0.113094 | − | 0.195884i | ||||
\(914\) | 2.39828 | + | 4.15394i | 0.0793281 | + | 0.137400i | ||||
\(915\) | 1.92692i | 0.0637020i | ||||||||
\(916\) | −28.4069 | + | 16.4007i | −0.938590 | + | 0.541895i | ||||
\(917\) | 13.4240 | − | 7.75033i | 0.443299 | − | 0.255939i | ||||
\(918\) | 3.69979i | 0.122111i | ||||||||
\(919\) | −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 | ||||
\(921\) | 37.2245 | + | 21.4916i | 1.22659 | + | 0.708171i | ||||
\(922\) | 1.64933 | 0.0543180 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 30.5187 | 1.00399 | ||||||||
\(925\) | −24.3465 | − | 14.0565i | −0.800508 | − | 0.462173i | ||||
\(926\) | 3.38793 | − | 5.86806i | 0.111334 | − | 0.192837i | ||||
\(927\) | 1.39559 | + | 2.41724i | 0.0458373 | + | 0.0793925i | ||||
\(928\) | − | 26.9946i | − | 0.886142i | ||||||
\(929\) | −20.9692 | + | 12.1066i | −0.687977 | + | 0.397203i | −0.802854 | − | 0.596176i | \(-0.796686\pi\) |
0.114877 | + | 0.993380i | \(0.463353\pi\) | |||||||
\(930\) | 2.55571 | − | 1.47554i | 0.0838051 | − | 0.0483849i | ||||
\(931\) | 0.127375i | 0.00417454i | ||||||||
\(932\) | −2.07673 | − | 3.59700i | −0.0680255 | − | 0.117824i | ||||
\(933\) | 0.303134 | − | 0.525044i | 0.00992417 | − | 0.0171892i | ||||
\(934\) | −23.2754 | − | 13.4380i | −0.761593 | − | 0.439706i | ||||
\(935\) | 2.26444 | 0.0740550 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1830 | 0.365333 | 0.182666 | − | 0.983175i | \(-0.441527\pi\) | ||||
0.182666 | + | 0.983175i | \(0.441527\pi\) | |||||||
\(938\) | −12.5710 | − | 7.25786i | −0.410457 | − | 0.236978i | ||||
\(939\) | −26.2826 | + | 45.5228i | −0.857701 | + | 1.48558i | ||||
\(940\) | 1.23274 | + | 2.13517i | 0.0402076 | + | 0.0696416i | ||||
\(941\) | 15.9638i | 0.520404i | 0.965554 | + | 0.260202i | \(0.0837891\pi\) | ||||
−0.965554 | + | 0.260202i | \(0.916211\pi\) | |||||||
\(942\) | 6.95171 | − | 4.01357i | 0.226499 | − | 0.130769i | ||||
\(943\) | −14.9975 | + | 8.65883i | −0.488387 | + | 0.281970i | ||||
\(944\) | − | 3.76271i | − | 0.122466i | ||||||
\(945\) | 0.621998 | + | 1.07733i | 0.0202336 | + | 0.0350456i | ||||
\(946\) | 0.503885 | − | 0.872754i | 0.0163827 | − | 0.0283757i | ||||
\(947\) | −5.64186 | − | 3.25733i | −0.183336 | − | 0.105849i | 0.405523 | − | 0.914085i | \(-0.367089\pi\) |
−0.588859 | + | 0.808236i | \(0.700423\pi\) | |||||||
\(948\) | −30.3991 | −0.987317 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0.349126 | 0.0113271 | ||||||||
\(951\) | 27.2339 | + | 15.7235i | 0.883119 | + | 0.509869i | ||||
\(952\) | −6.84870 | + | 11.8623i | −0.221968 | + | 0.384459i | ||||
\(953\) | 23.8235 | + | 41.2635i | 0.771718 | + | 1.33665i | 0.936621 | + | 0.350345i | \(0.113936\pi\) |
−0.164903 | + | 0.986310i | \(0.552731\pi\) | |||||||
\(954\) | 17.0780i | 0.552920i | ||||||||
\(955\) | 3.08800 | − | 1.78286i | 0.0999252 | − | 0.0576919i | ||||
\(956\) | 29.5501 | − | 17.0608i | 0.955719 | − | 0.551784i | ||||
\(957\) | 44.1933i | 1.42857i | ||||||||
\(958\) | 9.91646 | + | 17.1758i | 0.320386 | + | 0.554925i | ||||
\(959\) | −7.32975 | + | 12.6955i | −0.236690 | + | 0.409959i | ||||
\(960\) | 1.71320 | + | 0.989115i | 0.0552932 | + | 0.0319235i | ||||
\(961\) | −12.9705 | −0.418402 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.69740 | 0.215821 | ||||||||
\(964\) | 23.8151 | + | 13.7497i | 0.767033 | + | 0.442847i | ||||
\(965\) | 1.67696 | − | 2.90457i | 0.0539831 | − | 0.0935015i | ||||
\(966\) | 3.17241 | + | 5.49477i | 0.102071 | + | 0.176791i | ||||
\(967\) | 43.8122i | 1.40891i | 0.709751 | + | 0.704453i | \(0.248808\pi\) | ||||
−0.709751 | + | 0.704453i | \(0.751192\pi\) | |||||||
\(968\) | 16.4054 | − | 9.47166i | 0.527289 | − | 0.304431i | ||||
\(969\) | 0.370298 | − | 0.213792i | 0.0118957 | − | 0.00686798i | ||||
\(970\) | − | 1.59611i | − | 0.0512479i | ||||||
\(971\) | −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 | ||||
\(973\) | −30.0191 | − | 17.3315i | −0.962368 | − | 0.555624i | ||||
\(974\) | 30.2776 | 0.970156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.92692 | 0.0616792 | ||||||||
\(977\) | 23.2112 | + | 13.4010i | 0.742591 | + | 0.428735i | 0.823011 | − | 0.568026i | \(-0.192293\pi\) |
−0.0804198 | + | 0.996761i | \(0.525626\pi\) | |||||||
\(978\) | 14.5586 | − | 25.2162i | 0.465533 | − | 0.806327i | ||||
\(979\) | 6.12565 | + | 10.6099i | 0.195776 | + | 0.339095i | ||||
\(980\) | − | 0.484271i | − | 0.0154695i | ||||||
\(981\) | −27.8613 | + | 16.0858i | −0.889544 | + | 0.513579i | ||||
\(982\) | 21.7454 | − | 12.5547i | 0.693924 | − | 0.400637i | ||||
\(983\) | 27.2495i | 0.869124i | 0.900642 | + | 0.434562i | \(0.143097\pi\) | ||||
−0.900642 | + | 0.434562i | \(0.856903\pi\) | |||||||
\(984\) | 35.0589 | + | 60.7238i | 1.11764 | + | 1.93580i | ||||
\(985\) | −0.0691957 | + | 0.119850i | −0.00220476 | + | 0.00381875i | ||||
\(986\) | −6.94332 | − | 4.00873i | −0.221120 | − | 0.127664i | ||||
\(987\) | 38.9614 | 1.24015 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.442058 | −0.0140566 | ||||||||
\(990\) | −1.49258 | − | 0.861740i | −0.0474372 | − | 0.0273879i | ||||
\(991\) | −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 | ||||
\(993\) | 40.0441i | 1.27076i | ||||||||
\(994\) | −14.1832 | + | 8.18867i | −0.449863 | + | 0.259729i | ||||
\(995\) | 2.45794 | − | 1.41909i | 0.0779219 | − | 0.0449882i | ||||
\(996\) | 4.90648i | 0.155468i | ||||||||
\(997\) | −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 | ||||
\(999\) | −10.5345 | − | 6.08211i | −0.333297 | − | 0.192429i |
(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.e.b.147.5 | 12 | ||
13.2 | odd | 12 | 169.2.c.b.146.3 | 6 | |||
13.3 | even | 3 | inner | 169.2.e.b.23.2 | 12 | ||
13.4 | even | 6 | 169.2.b.b.168.5 | 6 | |||
13.5 | odd | 4 | 169.2.c.b.22.3 | 6 | |||
13.6 | odd | 12 | 169.2.a.c.1.1 | yes | 3 | ||
13.7 | odd | 12 | 169.2.a.b.1.3 | ✓ | 3 | ||
13.8 | odd | 4 | 169.2.c.c.22.1 | 6 | |||
13.9 | even | 3 | 169.2.b.b.168.2 | 6 | |||
13.10 | even | 6 | inner | 169.2.e.b.23.5 | 12 | ||
13.11 | odd | 12 | 169.2.c.c.146.1 | 6 | |||
13.12 | even | 2 | inner | 169.2.e.b.147.2 | 12 | ||
39.17 | odd | 6 | 1521.2.b.l.1351.2 | 6 | |||
39.20 | even | 12 | 1521.2.a.r.1.1 | 3 | |||
39.32 | even | 12 | 1521.2.a.o.1.3 | 3 | |||
39.35 | odd | 6 | 1521.2.b.l.1351.5 | 6 | |||
52.7 | even | 12 | 2704.2.a.z.1.3 | 3 | |||
52.19 | even | 12 | 2704.2.a.ba.1.3 | 3 | |||
52.35 | odd | 6 | 2704.2.f.o.337.5 | 6 | |||
52.43 | odd | 6 | 2704.2.f.o.337.6 | 6 | |||
65.19 | odd | 12 | 4225.2.a.bb.1.3 | 3 | |||
65.59 | odd | 12 | 4225.2.a.bg.1.1 | 3 | |||
91.6 | even | 12 | 8281.2.a.bj.1.1 | 3 | |||
91.20 | even | 12 | 8281.2.a.bf.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
169.2.a.b.1.3 | ✓ | 3 | 13.7 | odd | 12 | ||
169.2.a.c.1.1 | yes | 3 | 13.6 | odd | 12 | ||
169.2.b.b.168.2 | 6 | 13.9 | even | 3 | |||
169.2.b.b.168.5 | 6 | 13.4 | even | 6 | |||
169.2.c.b.22.3 | 6 | 13.5 | odd | 4 | |||
169.2.c.b.146.3 | 6 | 13.2 | odd | 12 | |||
169.2.c.c.22.1 | 6 | 13.8 | odd | 4 | |||
169.2.c.c.146.1 | 6 | 13.11 | odd | 12 | |||
169.2.e.b.23.2 | 12 | 13.3 | even | 3 | inner | ||
169.2.e.b.23.5 | 12 | 13.10 | even | 6 | inner | ||
169.2.e.b.147.2 | 12 | 13.12 | even | 2 | inner | ||
169.2.e.b.147.5 | 12 | 1.1 | even | 1 | trivial | ||
1521.2.a.o.1.3 | 3 | 39.32 | even | 12 | |||
1521.2.a.r.1.1 | 3 | 39.20 | even | 12 | |||
1521.2.b.l.1351.2 | 6 | 39.17 | odd | 6 | |||
1521.2.b.l.1351.5 | 6 | 39.35 | odd | 6 | |||
2704.2.a.z.1.3 | 3 | 52.7 | even | 12 | |||
2704.2.a.ba.1.3 | 3 | 52.19 | even | 12 | |||
2704.2.f.o.337.5 | 6 | 52.35 | odd | 6 | |||
2704.2.f.o.337.6 | 6 | 52.43 | odd | 6 | |||
4225.2.a.bb.1.3 | 3 | 65.19 | odd | 12 | |||
4225.2.a.bg.1.1 | 3 | 65.59 | odd | 12 | |||
8281.2.a.bf.1.3 | 3 | 91.20 | even | 12 | |||
8281.2.a.bj.1.1 | 3 | 91.6 | even | 12 |