Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [700,2,Mod(43,700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(700, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("700.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 700.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.58952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.3 | ||
Character | \(\chi\) | \(=\) | 700.43 |
Dual form | 700.2.k.b.407.3 |
$q$-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 \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(351\) | \(477\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29055 | + | 0.578354i | −0.912553 | + | 0.408958i | ||||
\(3\) | 1.27396 | − | 1.27396i | 0.735522 | − | 0.735522i | −0.236186 | − | 0.971708i | \(-0.575897\pi\) |
0.971708 | + | 0.236186i | \(0.0758975\pi\) | |||||||
\(4\) | 1.33101 | − | 1.49278i | 0.665507 | − | 0.746391i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.907305 | + | 2.38090i | −0.370406 | + | 0.972000i | ||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | −0.854378 | + | 2.69630i | −0.302068 | + | 0.953286i | ||||
\(9\) | − | 0.245954i | − | 0.0819847i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.36566i | − | 1.01478i | −0.861715 | − | 0.507392i | \(-0.830610\pi\) | ||
0.861715 | − | 0.507392i | \(-0.169390\pi\) | |||||||
\(12\) | −0.206087 | − | 3.59741i | −0.0594921 | − | 1.03848i | ||||
\(13\) | 2.69086 | + | 2.69086i | 0.746310 | + | 0.746310i | 0.973784 | − | 0.227474i | \(-0.0730468\pi\) |
−0.227474 | + | 0.973784i | \(0.573047\pi\) | |||||||
\(14\) | 1.32151 | + | 0.503596i | 0.353189 | + | 0.134592i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.456801 | − | 3.97383i | −0.114200 | − | 0.993458i | ||||
\(17\) | 1.60569 | − | 1.60569i | 0.389436 | − | 0.389436i | −0.485050 | − | 0.874486i | \(-0.661199\pi\) |
0.874486 | + | 0.485050i | \(0.161199\pi\) | |||||||
\(18\) | 0.142248 | + | 0.317415i | 0.0335283 | + | 0.0748154i | ||||
\(19\) | 1.20346 | 0.276092 | 0.138046 | − | 0.990426i | \(-0.455918\pi\) | ||||
0.138046 | + | 0.990426i | \(0.455918\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.80165 | −0.393153 | ||||||||
\(22\) | 1.94654 | + | 4.34353i | 0.415004 | + | 0.926045i | ||||
\(23\) | 5.40015 | − | 5.40015i | 1.12601 | − | 1.12601i | 0.135189 | − | 0.990820i | \(-0.456836\pi\) |
0.990820 | − | 0.135189i | \(-0.0431643\pi\) | |||||||
\(24\) | 2.34654 | + | 4.52343i | 0.478985 | + | 0.923341i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.02894 | − | 1.91641i | −0.986257 | − | 0.375838i | ||||
\(27\) | 3.50855 | + | 3.50855i | 0.675220 | + | 0.675220i | ||||
\(28\) | −1.99673 | + | 0.114388i | −0.377346 | + | 0.0216172i | ||||
\(29\) | − | 6.53311i | − | 1.21317i | −0.795020 | − | 0.606584i | \(-0.792540\pi\) | ||
0.795020 | − | 0.606584i | \(-0.207460\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.21966i | − | 0.757874i | −0.925423 | − | 0.378937i | \(-0.876290\pi\) | ||
0.925423 | − | 0.378937i | \(-0.123710\pi\) | |||||||
\(32\) | 2.88780 | + | 4.86422i | 0.510496 | + | 0.859880i | ||||
\(33\) | −4.28772 | − | 4.28772i | −0.746396 | − | 0.746396i | ||||
\(34\) | −1.14356 | + | 3.00087i | −0.196118 | + | 0.514644i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.367156 | − | 0.327368i | −0.0611927 | − | 0.0545614i | ||||
\(37\) | −1.99424 | + | 1.99424i | −0.327850 | + | 0.327850i | −0.851769 | − | 0.523918i | \(-0.824470\pi\) |
0.523918 | + | 0.851769i | \(0.324470\pi\) | |||||||
\(38\) | −1.55312 | + | 0.696024i | −0.251949 | + | 0.112910i | ||||
\(39\) | 6.85610 | 1.09785 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.68876 | −0.419914 | −0.209957 | − | 0.977711i | \(-0.567332\pi\) | ||||
−0.209957 | + | 0.977711i | \(0.567332\pi\) | |||||||
\(42\) | 2.32512 | − | 1.04199i | 0.358773 | − | 0.160783i | ||||
\(43\) | −1.90124 | + | 1.90124i | −0.289937 | + | 0.289937i | −0.837055 | − | 0.547118i | \(-0.815725\pi\) |
0.547118 | + | 0.837055i | \(0.315725\pi\) | |||||||
\(44\) | −5.02420 | − | 4.47974i | −0.757426 | − | 0.675346i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.84594 | + | 10.0923i | −0.567053 | + | 1.48803i | ||||
\(47\) | −7.59113 | − | 7.59113i | −1.10728 | − | 1.10728i | −0.993507 | − | 0.113774i | \(-0.963706\pi\) |
−0.113774 | − | 0.993507i | \(-0.536294\pi\) | |||||||
\(48\) | −5.64445 | − | 4.48056i | −0.814707 | − | 0.646713i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 4.09116i | − | 0.572877i | ||||||
\(52\) | 7.59844 | − | 0.435296i | 1.05371 | − | 0.0603647i | ||||
\(53\) | −9.24717 | − | 9.24717i | −1.27020 | − | 1.27020i | −0.945984 | − | 0.324213i | \(-0.894901\pi\) |
−0.324213 | − | 0.945984i | \(-0.605099\pi\) | |||||||
\(54\) | −6.55712 | − | 2.49876i | −0.892311 | − | 0.340038i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.51071 | − | 1.30244i | 0.335508 | − | 0.174045i | ||||
\(57\) | 1.53316 | − | 1.53316i | 0.203072 | − | 0.203072i | ||||
\(58\) | 3.77844 | + | 8.43127i | 0.496134 | + | 1.10708i | ||||
\(59\) | 7.21162 | 0.938873 | 0.469437 | − | 0.882966i | \(-0.344457\pi\) | ||||
0.469437 | + | 0.882966i | \(0.344457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.22203 | −0.668612 | −0.334306 | − | 0.942465i | \(-0.608502\pi\) | ||||
−0.334306 | + | 0.942465i | \(0.608502\pi\) | |||||||
\(62\) | 2.44046 | + | 5.44567i | 0.309938 | + | 0.691600i | ||||
\(63\) | −0.173916 | + | 0.173916i | −0.0219113 | + | 0.0219113i | ||||
\(64\) | −6.54008 | − | 4.60732i | −0.817510 | − | 0.575915i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.01331 | + | 3.05368i | 0.986370 | + | 0.375882i | ||||
\(67\) | 0.247826 | + | 0.247826i | 0.0302767 | + | 0.0302767i | 0.722083 | − | 0.691806i | \(-0.243185\pi\) |
−0.691806 | + | 0.722083i | \(0.743185\pi\) | |||||||
\(68\) | −0.259749 | − | 4.53413i | −0.0314992 | − | 0.549844i | ||||
\(69\) | − | 13.7592i | − | 1.65641i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5976i | 1.37638i | 0.725529 | + | 0.688192i | \(0.241595\pi\) | ||||
−0.725529 | + | 0.688192i | \(0.758405\pi\) | |||||||
\(72\) | 0.663166 | + | 0.210138i | 0.0781549 | + | 0.0247650i | ||||
\(73\) | 10.2421 | + | 10.2421i | 1.19875 | + | 1.19875i | 0.974542 | + | 0.224203i | \(0.0719779\pi\) |
0.224203 | + | 0.974542i | \(0.428022\pi\) | |||||||
\(74\) | 1.42028 | − | 3.72702i | 0.165104 | − | 0.433258i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.60182 | − | 1.79650i | 0.183741 | − | 0.206073i | ||||
\(77\) | −2.37988 | + | 2.37988i | −0.271212 | + | 0.271212i | ||||
\(78\) | −8.84810 | + | 3.96525i | −1.00185 | + | 0.448976i | ||||
\(79\) | 8.10604 | 0.912001 | 0.456000 | − | 0.889980i | \(-0.349282\pi\) | ||||
0.456000 | + | 0.889980i | \(0.349282\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.67737 | 1.07526 | ||||||||
\(82\) | 3.46997 | − | 1.55506i | 0.383194 | − | 0.171727i | ||||
\(83\) | 11.4358 | − | 11.4358i | 1.25524 | − | 1.25524i | 0.301900 | − | 0.953339i | \(-0.402379\pi\) |
0.953339 | − | 0.301900i | \(-0.0976210\pi\) | |||||||
\(84\) | −2.39803 | + | 2.68948i | −0.261646 | + | 0.293446i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.35405 | − | 3.55323i | 0.146011 | − | 0.383155i | ||||
\(87\) | −8.32292 | − | 8.32292i | −0.892311 | − | 0.892311i | ||||
\(88\) | 9.07483 | + | 2.87554i | 0.967380 | + | 0.306534i | ||||
\(89\) | 7.55643i | 0.800980i | 0.916301 | + | 0.400490i | \(0.131160\pi\) | ||||
−0.916301 | + | 0.400490i | \(0.868840\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.80545i | − | 0.398919i | ||||||
\(92\) | −0.873574 | − | 15.2489i | −0.0910764 | − | 1.58981i | ||||
\(93\) | −5.37569 | − | 5.37569i | −0.557433 | − | 0.557433i | ||||
\(94\) | 14.1871 | + | 5.40634i | 1.46328 | + | 0.557622i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.87577 | + | 2.51787i | 1.00794 | + | 0.256980i | ||||
\(97\) | −0.0167624 | + | 0.0167624i | −0.00170197 | + | 0.00170197i | −0.707957 | − | 0.706255i | \(-0.750383\pi\) |
0.706255 | + | 0.707957i | \(0.250383\pi\) | |||||||
\(98\) | −0.578354 | − | 1.29055i | −0.0584225 | − | 0.130365i | ||||
\(99\) | −0.827797 | −0.0831967 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.33818 | 0.232658 | 0.116329 | − | 0.993211i | \(-0.462887\pi\) | ||||
0.116329 | + | 0.993211i | \(0.462887\pi\) | |||||||
\(102\) | 2.36614 | + | 5.27983i | 0.234283 | + | 0.522781i | ||||
\(103\) | −5.19389 | + | 5.19389i | −0.511769 | + | 0.511769i | −0.915068 | − | 0.403299i | \(-0.867863\pi\) |
0.403299 | + | 0.915068i | \(0.367863\pi\) | |||||||
\(104\) | −9.55437 | + | 4.95635i | −0.936883 | + | 0.486010i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 17.2820 | + | 6.58576i | 1.67858 | + | 0.639666i | ||||
\(107\) | 8.66705 | + | 8.66705i | 0.837875 | + | 0.837875i | 0.988579 | − | 0.150704i | \(-0.0481540\pi\) |
−0.150704 | + | 0.988579i | \(0.548154\pi\) | |||||||
\(108\) | 9.90743 | − | 0.567572i | 0.953343 | − | 0.0546147i | ||||
\(109\) | 11.3693i | 1.08898i | 0.838766 | + | 0.544492i | \(0.183278\pi\) | ||||
−0.838766 | + | 0.544492i | \(0.816722\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.08116i | 0.482282i | ||||||||
\(112\) | −2.48692 | + | 3.13293i | −0.234991 | + | 0.296034i | ||||
\(113\) | −2.22660 | − | 2.22660i | −0.209461 | − | 0.209461i | 0.594577 | − | 0.804038i | \(-0.297319\pi\) |
−0.804038 | + | 0.594577i | \(0.797319\pi\) | |||||||
\(114\) | −1.09190 | + | 2.86532i | −0.102266 | + | 0.268361i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.75251 | − | 8.69566i | −0.905498 | − | 0.807372i | ||||
\(117\) | 0.661827 | − | 0.661827i | 0.0611860 | − | 0.0611860i | ||||
\(118\) | −9.30692 | + | 4.17087i | −0.856772 | + | 0.383959i | ||||
\(119\) | −2.27078 | −0.208162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.327654 | −0.0297867 | ||||||||
\(122\) | 6.73926 | − | 3.02018i | 0.610144 | − | 0.273434i | ||||
\(123\) | −3.42538 | + | 3.42538i | −0.308856 | + | 0.308856i | ||||
\(124\) | −6.29904 | − | 5.61643i | −0.565670 | − | 0.504370i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.123861 | − | 0.325031i | 0.0110344 | − | 0.0289561i | ||||
\(127\) | 2.39506 | + | 2.39506i | 0.212527 | + | 0.212527i | 0.805340 | − | 0.592813i | \(-0.201983\pi\) |
−0.592813 | + | 0.805340i | \(0.701983\pi\) | |||||||
\(128\) | 11.1049 | + | 2.16348i | 0.981546 | + | 0.191226i | ||||
\(129\) | 4.84422i | 0.426510i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.15491i | − | 0.712497i | −0.934391 | − | 0.356249i | \(-0.884056\pi\) | ||
0.934391 | − | 0.356249i | \(-0.115944\pi\) | |||||||
\(132\) | −12.1076 | + | 0.693618i | −1.05384 | + | 0.0603717i | ||||
\(133\) | −0.850973 | − | 0.850973i | −0.0737887 | − | 0.0737887i | ||||
\(134\) | −0.463161 | − | 0.176499i | −0.0400110 | − | 0.0152472i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.95755 | + | 5.70128i | 0.253608 | + | 0.488880i | ||||
\(137\) | −5.54560 | + | 5.54560i | −0.473793 | + | 0.473793i | −0.903140 | − | 0.429347i | \(-0.858744\pi\) |
0.429347 | + | 0.903140i | \(0.358744\pi\) | |||||||
\(138\) | 7.95766 | + | 17.7568i | 0.677401 | + | 1.51156i | ||||
\(139\) | −10.7453 | −0.911405 | −0.455702 | − | 0.890132i | \(-0.650612\pi\) | ||||
−0.455702 | + | 0.890132i | \(0.650612\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.3416 | −1.62886 | ||||||||
\(142\) | −6.70752 | − | 14.9673i | −0.562883 | − | 1.25602i | ||||
\(143\) | 9.05651 | − | 9.05651i | 0.757343 | − | 0.757343i | ||||
\(144\) | −0.977380 | + | 0.112352i | −0.0814483 | + | 0.00936268i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.1414 | − | 7.29433i | −1.58416 | − | 0.603683i | ||||
\(147\) | 1.27396 | + | 1.27396i | 0.105075 | + | 0.105075i | ||||
\(148\) | 0.322604 | + | 5.63132i | 0.0265179 | + | 0.462891i | ||||
\(149\) | 17.7579i | 1.45479i | 0.686221 | + | 0.727394i | \(0.259268\pi\) | ||||
−0.686221 | + | 0.727394i | \(0.740732\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.57930i | − | 0.291279i | −0.989338 | − | 0.145640i | \(-0.953476\pi\) | ||
0.989338 | − | 0.145640i | \(-0.0465240\pi\) | |||||||
\(152\) | −1.02821 | + | 3.24488i | −0.0833986 | + | 0.263195i | ||||
\(153\) | −0.394925 | − | 0.394925i | −0.0319278 | − | 0.0319278i | ||||
\(154\) | 1.69493 | − | 4.44775i | 0.136581 | − | 0.358410i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.12556 | − | 10.2347i | 0.730630 | − | 0.819429i | ||||
\(157\) | −2.41513 | + | 2.41513i | −0.192748 | + | 0.192748i | −0.796883 | − | 0.604134i | \(-0.793519\pi\) |
0.604134 | + | 0.796883i | \(0.293519\pi\) | |||||||
\(158\) | −10.4612 | + | 4.68816i | −0.832249 | + | 0.372970i | ||||
\(159\) | −23.5611 | −1.86852 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.63697 | −0.601877 | ||||||||
\(162\) | −12.4891 | + | 5.59694i | −0.981235 | + | 0.439737i | ||||
\(163\) | −0.475698 | + | 0.475698i | −0.0372595 | + | 0.0372595i | −0.725491 | − | 0.688232i | \(-0.758387\pi\) |
0.688232 | + | 0.725491i | \(0.258387\pi\) | |||||||
\(164\) | −3.57878 | + | 4.01374i | −0.279456 | + | 0.313420i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.14447 | + | 21.3723i | −0.632133 | + | 1.65881i | ||||
\(167\) | −7.18363 | − | 7.18363i | −0.555886 | − | 0.555886i | 0.372248 | − | 0.928133i | \(-0.378587\pi\) |
−0.928133 | + | 0.372248i | \(0.878587\pi\) | |||||||
\(168\) | 1.53929 | − | 4.85780i | 0.118759 | − | 0.374787i | ||||
\(169\) | 1.48144i | 0.113957i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 0.295995i | − | 0.0226353i | ||||||
\(172\) | 0.307561 | + | 5.36872i | 0.0234513 | + | 0.409361i | ||||
\(173\) | −1.21290 | − | 1.21290i | −0.0922149 | − | 0.0922149i | 0.659495 | − | 0.751709i | \(-0.270770\pi\) |
−0.751709 | + | 0.659495i | \(0.770770\pi\) | |||||||
\(174\) | 15.5547 | + | 5.92752i | 1.17920 | + | 0.449364i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −13.3746 | + | 1.53744i | −1.00815 | + | 0.115889i | ||||
\(177\) | 9.18732 | − | 9.18732i | 0.690562 | − | 0.690562i | ||||
\(178\) | −4.37029 | − | 9.75191i | −0.327567 | − | 0.730937i | ||||
\(179\) | −11.5214 | −0.861152 | −0.430576 | − | 0.902554i | \(-0.641690\pi\) | ||||
−0.430576 | + | 0.902554i | \(0.641690\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.4955 | 1.59775 | 0.798873 | − | 0.601500i | \(-0.205430\pi\) | ||||
0.798873 | + | 0.601500i | \(0.205430\pi\) | |||||||
\(182\) | 2.20089 | + | 4.91110i | 0.163141 | + | 0.364035i | ||||
\(183\) | −6.65266 | + | 6.65266i | −0.491779 | + | 0.491779i | ||||
\(184\) | 9.94666 | + | 19.1742i | 0.733278 | + | 1.41354i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 10.0466 | + | 3.82852i | 0.736653 | + | 0.280721i | ||||
\(187\) | −5.40419 | − | 5.40419i | −0.395194 | − | 0.395194i | ||||
\(188\) | −21.4358 | + | 1.22801i | −1.56337 | + | 0.0895616i | ||||
\(189\) | − | 4.96184i | − | 0.360920i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.2319i | 1.60864i | 0.594195 | + | 0.804321i | \(0.297471\pi\) | ||||
−0.594195 | + | 0.804321i | \(0.702529\pi\) | |||||||
\(192\) | −14.2014 | + | 2.46226i | −1.02489 | + | 0.177698i | ||||
\(193\) | 13.8546 | + | 13.8546i | 0.997276 | + | 0.997276i | 0.999996 | − | 0.00272045i | \(-0.000865947\pi\) |
−0.00272045 | + | 0.999996i | \(0.500866\pi\) | |||||||
\(194\) | 0.0119381 | − | 0.0313273i | 0.000857103 | − | 0.00224917i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.49278 | + | 1.33101i | 0.106627 | + | 0.0950725i | ||||
\(197\) | −16.2434 | + | 16.2434i | −1.15729 | + | 1.15729i | −0.172235 | + | 0.985056i | \(0.555099\pi\) |
−0.985056 | + | 0.172235i | \(0.944901\pi\) | |||||||
\(198\) | 1.06831 | − | 0.478759i | 0.0759215 | − | 0.0340240i | ||||
\(199\) | −3.80096 | −0.269443 | −0.134722 | − | 0.990884i | \(-0.543014\pi\) | ||||
−0.134722 | + | 0.990884i | \(0.543014\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.631441 | 0.0445384 | ||||||||
\(202\) | −3.01753 | + | 1.35230i | −0.212313 | + | 0.0951473i | ||||
\(203\) | −4.61960 | + | 4.61960i | −0.324233 | + | 0.324233i | ||||
\(204\) | −6.10722 | − | 5.44540i | −0.427591 | − | 0.381254i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.69905 | − | 9.70685i | 0.257725 | − | 0.676309i | ||||
\(207\) | −1.32819 | − | 1.32819i | −0.0923155 | − | 0.0923155i | ||||
\(208\) | 9.46383 | − | 11.9222i | 0.656198 | − | 0.826656i | ||||
\(209\) | − | 4.05042i | − | 0.280174i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.29202i | − | 0.295475i | −0.989027 | − | 0.147737i | \(-0.952801\pi\) | ||
0.989027 | − | 0.147737i | \(-0.0471990\pi\) | |||||||
\(212\) | −26.1121 | + | 1.49590i | −1.79339 | + | 0.102739i | ||||
\(213\) | 14.7749 | + | 14.7749i | 1.01236 | + | 1.01236i | ||||
\(214\) | −16.1978 | − | 6.17260i | −1.10726 | − | 0.421950i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −12.4577 | + | 6.46247i | −0.847641 | + | 0.439716i | ||||
\(217\) | −2.98375 | + | 2.98375i | −0.202550 | + | 0.202550i | ||||
\(218\) | −6.57549 | − | 14.6726i | −0.445349 | − | 0.993756i | ||||
\(219\) | 26.0960 | 1.76341 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.64135 | 0.581280 | ||||||||
\(222\) | −2.93870 | − | 6.55746i | −0.197233 | − | 0.440108i | ||||
\(223\) | −17.3042 | + | 17.3042i | −1.15877 | + | 1.15877i | −0.174035 | + | 0.984739i | \(0.555681\pi\) |
−0.984739 | + | 0.174035i | \(0.944319\pi\) | |||||||
\(224\) | 1.39754 | − | 5.48150i | 0.0933768 | − | 0.366248i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.16129 | + | 1.58577i | 0.276805 | + | 0.105484i | ||||
\(227\) | 2.06226 | + | 2.06226i | 0.136877 | + | 0.136877i | 0.772226 | − | 0.635349i | \(-0.219144\pi\) |
−0.635349 | + | 0.772226i | \(0.719144\pi\) | |||||||
\(228\) | −0.248017 | − | 4.32933i | −0.0164253 | − | 0.286717i | ||||
\(229\) | − | 3.85248i | − | 0.254579i | −0.991866 | − | 0.127290i | \(-0.959372\pi\) | ||
0.991866 | − | 0.127290i | \(-0.0406278\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.06375i | 0.398965i | ||||||||
\(232\) | 17.6152 | + | 5.58174i | 1.15650 | + | 0.366459i | ||||
\(233\) | 2.10259 | + | 2.10259i | 0.137745 | + | 0.137745i | 0.772617 | − | 0.634872i | \(-0.218947\pi\) |
−0.634872 | + | 0.772617i | \(0.718947\pi\) | |||||||
\(234\) | −0.471348 | + | 1.23689i | −0.0308130 | + | 0.0808579i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.59877 | − | 10.7654i | 0.624827 | − | 0.700767i | ||||
\(237\) | 10.3268 | − | 10.3268i | 0.670796 | − | 0.670796i | ||||
\(238\) | 2.93055 | − | 1.31332i | 0.189959 | − | 0.0851296i | ||||
\(239\) | −12.4700 | −0.806615 | −0.403308 | − | 0.915064i | \(-0.632140\pi\) | ||||
−0.403308 | + | 0.915064i | \(0.632140\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0460 | 0.775948 | 0.387974 | − | 0.921670i | \(-0.373175\pi\) | ||||
0.387974 | + | 0.921670i | \(0.373175\pi\) | |||||||
\(242\) | 0.422852 | − | 0.189500i | 0.0271819 | − | 0.0121815i | ||||
\(243\) | 1.80295 | − | 1.80295i | 0.115659 | − | 0.115659i | ||||
\(244\) | −6.95059 | + | 7.79535i | −0.444966 | + | 0.499046i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.43953 | − | 6.40169i | 0.155539 | − | 0.408157i | ||||
\(247\) | 3.23833 | + | 3.23833i | 0.206050 | + | 0.206050i | ||||
\(248\) | 11.3775 | + | 3.60519i | 0.722471 | + | 0.228930i | ||||
\(249\) | − | 29.1375i | − | 1.84651i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 9.65552i | − | 0.609451i | −0.952440 | − | 0.304725i | \(-0.901435\pi\) | ||
0.952440 | − | 0.304725i | \(-0.0985647\pi\) | |||||||
\(252\) | 0.0281341 | + | 0.491103i | 0.00177228 | + | 0.0309366i | ||||
\(253\) | −18.1751 | − | 18.1751i | −1.14266 | − | 1.14266i | ||||
\(254\) | −4.47612 | − | 1.70574i | −0.280857 | − | 0.107028i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.5827 | + | 3.63050i | −0.973917 | + | 0.226906i | ||||
\(257\) | −3.85614 | + | 3.85614i | −0.240539 | + | 0.240539i | −0.817073 | − | 0.576534i | \(-0.804405\pi\) |
0.576534 | + | 0.817073i | \(0.304405\pi\) | |||||||
\(258\) | −2.80167 | − | 6.25168i | −0.174424 | − | 0.389213i | ||||
\(259\) | 2.82027 | 0.175243 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.60684 | −0.0994611 | ||||||||
\(262\) | 4.71642 | + | 10.5243i | 0.291381 | + | 0.650192i | ||||
\(263\) | −12.3977 | + | 12.3977i | −0.764476 | + | 0.764476i | −0.977128 | − | 0.212652i | \(-0.931790\pi\) |
0.212652 | + | 0.977128i | \(0.431790\pi\) | |||||||
\(264\) | 15.2243 | − | 7.89764i | 0.936991 | − | 0.486066i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.59038 | + | 0.606056i | 0.0975126 | + | 0.0371597i | ||||
\(267\) | 9.62659 | + | 9.62659i | 0.589138 | + | 0.589138i | ||||
\(268\) | 0.699810 | − | 0.0400904i | 0.0427477 | − | 0.00244891i | ||||
\(269\) | − | 5.80512i | − | 0.353944i | −0.984216 | − | 0.176972i | \(-0.943370\pi\) | ||
0.984216 | − | 0.176972i | \(-0.0566302\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.9056i | 0.844703i | 0.906432 | + | 0.422351i | \(0.138795\pi\) | ||||
−0.906432 | + | 0.422351i | \(0.861205\pi\) | |||||||
\(272\) | −7.11421 | − | 5.64725i | −0.431362 | − | 0.342415i | ||||
\(273\) | −4.84799 | − | 4.84799i | −0.293414 | − | 0.293414i | ||||
\(274\) | 3.94953 | − | 10.3642i | 0.238600 | − | 0.626122i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −20.5394 | − | 18.3136i | −1.23633 | − | 1.10235i | ||||
\(277\) | 10.1031 | − | 10.1031i | 0.607038 | − | 0.607038i | −0.335133 | − | 0.942171i | \(-0.608781\pi\) |
0.942171 | + | 0.335133i | \(0.108781\pi\) | |||||||
\(278\) | 13.8673 | − | 6.21459i | 0.831706 | − | 0.372726i | ||||
\(279\) | −1.03784 | −0.0621340 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.575310 | −0.0343201 | −0.0171601 | − | 0.999853i | \(-0.505462\pi\) | ||||
−0.0171601 | + | 0.999853i | \(0.505462\pi\) | |||||||
\(282\) | 24.9612 | − | 11.1863i | 1.48642 | − | 0.666134i | ||||
\(283\) | −2.62044 | + | 2.62044i | −0.155769 | + | 0.155769i | −0.780689 | − | 0.624920i | \(-0.785132\pi\) |
0.624920 | + | 0.780689i | \(0.285132\pi\) | |||||||
\(284\) | 17.3127 | + | 15.4366i | 1.02732 | + | 0.915993i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.44997 | + | 16.9257i | −0.381395 | + | 1.00084i | ||||
\(287\) | 1.90124 | + | 1.90124i | 0.112227 | + | 0.112227i | ||||
\(288\) | 1.19637 | − | 0.710267i | 0.0704970 | − | 0.0418529i | ||||
\(289\) | 11.8435i | 0.696679i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.0427094i | 0.00250367i | ||||||||
\(292\) | 28.9216 | − | 1.65685i | 1.69251 | − | 0.0969596i | ||||
\(293\) | 14.2036 | + | 14.2036i | 0.829783 | + | 0.829783i | 0.987487 | − | 0.157703i | \(-0.0504090\pi\) |
−0.157703 | + | 0.987487i | \(0.550409\pi\) | |||||||
\(294\) | −2.38090 | − | 0.907305i | −0.138857 | − | 0.0529151i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.67323 | − | 7.08089i | −0.213502 | − | 0.411568i | ||||
\(297\) | 11.8086 | − | 11.8086i | 0.685203 | − | 0.685203i | ||||
\(298\) | −10.2704 | − | 22.9174i | −0.594946 | − | 1.32757i | ||||
\(299\) | 29.0621 | 1.68070 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.68876 | 0.154978 | ||||||||
\(302\) | 2.07010 | + | 4.61925i | 0.119121 | + | 0.265808i | ||||
\(303\) | 2.97875 | − | 2.97875i | 0.171125 | − | 0.171125i | ||||
\(304\) | −0.549741 | − | 4.78233i | −0.0315298 | − | 0.274286i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.738075 | + | 0.281262i | 0.0421929 | + | 0.0160787i | ||||
\(307\) | 1.65503 | + | 1.65503i | 0.0944578 | + | 0.0944578i | 0.752757 | − | 0.658299i | \(-0.228724\pi\) |
−0.658299 | + | 0.752757i | \(0.728724\pi\) | |||||||
\(308\) | 0.384990 | + | 6.72030i | 0.0219368 | + | 0.382924i | ||||
\(309\) | 13.2336i | 0.752835i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 32.5815i | − | 1.84753i | −0.382962 | − | 0.923764i | \(-0.625096\pi\) | ||
0.382962 | − | 0.923764i | \(-0.374904\pi\) | |||||||
\(312\) | −5.85770 | + | 18.4861i | −0.331627 | + | 1.04657i | ||||
\(313\) | 13.6347 | + | 13.6347i | 0.770676 | + | 0.770676i | 0.978225 | − | 0.207548i | \(-0.0665485\pi\) |
−0.207548 | + | 0.978225i | \(0.566548\pi\) | |||||||
\(314\) | 1.72003 | − | 4.51363i | 0.0970672 | − | 0.254719i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.7893 | − | 12.1006i | 0.606943 | − | 0.680709i | ||||
\(317\) | 1.67160 | − | 1.67160i | 0.0938866 | − | 0.0938866i | −0.658604 | − | 0.752490i | \(-0.728853\pi\) |
0.752490 | + | 0.658604i | \(0.228853\pi\) | |||||||
\(318\) | 30.4066 | − | 13.6266i | 1.70512 | − | 0.764144i | ||||
\(319\) | −21.9882 | −1.23110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.0830 | 1.23255 | ||||||||
\(322\) | 9.85585 | − | 4.41687i | 0.549245 | − | 0.246142i | ||||
\(323\) | 1.93237 | − | 1.93237i | 0.107520 | − | 0.107520i | ||||
\(324\) | 12.8807 | − | 14.4462i | 0.715595 | − | 0.802567i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.338788 | − | 0.889031i | 0.0187637 | − | 0.0492389i | ||||
\(327\) | 14.4841 | + | 14.4841i | 0.800972 | + | 0.800972i | ||||
\(328\) | 2.29722 | − | 7.24971i | 0.126843 | − | 0.400299i | ||||
\(329\) | 10.7355i | 0.591866i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.90436i | 0.214603i | 0.994227 | + | 0.107302i | \(0.0342210\pi\) | ||||
−0.994227 | + | 0.107302i | \(0.965779\pi\) | |||||||
\(332\) | −1.84995 | − | 32.2923i | −0.101529 | − | 1.77227i | ||||
\(333\) | 0.490490 | + | 0.490490i | 0.0268787 | + | 0.0268787i | ||||
\(334\) | 13.4255 | + | 5.11612i | 0.734609 | + | 0.279942i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.822998 | + | 7.15947i | 0.0448982 | + | 0.390581i | ||||
\(337\) | 10.4913 | − | 10.4913i | 0.571500 | − | 0.571500i | −0.361047 | − | 0.932547i | \(-0.617581\pi\) |
0.932547 | + | 0.361047i | \(0.117581\pi\) | |||||||
\(338\) | −0.856793 | − | 1.91186i | −0.0466034 | − | 0.103991i | ||||
\(339\) | −5.67321 | −0.308126 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.2019 | −0.769078 | ||||||||
\(342\) | 0.171190 | + | 0.381995i | 0.00925688 | + | 0.0206559i | ||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −3.50194 | − | 6.75070i | −0.188812 | − | 0.363974i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.26678 | + | 0.863815i | 0.121863 | + | 0.0464390i | ||||
\(347\) | 12.3223 | + | 12.3223i | 0.661495 | + | 0.661495i | 0.955732 | − | 0.294238i | \(-0.0950657\pi\) |
−0.294238 | + | 0.955732i | \(0.595066\pi\) | |||||||
\(348\) | −23.5022 | + | 1.34639i | −1.25985 | + | 0.0721739i | ||||
\(349\) | − | 16.2876i | − | 0.871854i | −0.899982 | − | 0.435927i | \(-0.856421\pi\) | ||
0.899982 | − | 0.435927i | \(-0.143579\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.8820i | 1.00785i | ||||||||
\(352\) | 16.3713 | − | 9.71935i | 0.872593 | − | 0.518043i | ||||
\(353\) | −9.05677 | − | 9.05677i | −0.482043 | − | 0.482043i | 0.423740 | − | 0.905784i | \(-0.360717\pi\) |
−0.905784 | + | 0.423740i | \(0.860717\pi\) | |||||||
\(354\) | −6.54314 | + | 17.1702i | −0.347764 | + | 0.912585i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 11.2801 | + | 10.0577i | 0.597844 | + | 0.533058i | ||||
\(357\) | −2.89289 | + | 2.89289i | −0.153108 | + | 0.153108i | ||||
\(358\) | 14.8689 | − | 6.66346i | 0.785848 | − | 0.352175i | ||||
\(359\) | −15.5546 | −0.820940 | −0.410470 | − | 0.911874i | \(-0.634635\pi\) | ||||
−0.410470 | + | 0.911874i | \(0.634635\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.5517 | −0.923773 | ||||||||
\(362\) | −27.7409 | + | 12.4320i | −1.45803 | + | 0.653410i | ||||
\(363\) | −0.417418 | + | 0.417418i | −0.0219088 | + | 0.0219088i | ||||
\(364\) | −5.68071 | − | 5.06511i | −0.297750 | − | 0.265484i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4.73797 | − | 12.4331i | 0.247658 | − | 0.649891i | ||||
\(367\) | −13.5723 | − | 13.5723i | −0.708469 | − | 0.708469i | 0.257744 | − | 0.966213i | \(-0.417021\pi\) |
−0.966213 | + | 0.257744i | \(0.917021\pi\) | |||||||
\(368\) | −23.9261 | − | 18.9925i | −1.24723 | − | 0.990052i | ||||
\(369\) | 0.661312i | 0.0344265i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 13.0775i | 0.678949i | ||||||||
\(372\) | −15.1798 | + | 0.869617i | −0.787038 | + | 0.0450875i | ||||
\(373\) | −3.46506 | − | 3.46506i | −0.179414 | − | 0.179414i | 0.611686 | − | 0.791100i | \(-0.290491\pi\) |
−0.791100 | + | 0.611686i | \(0.790491\pi\) | |||||||
\(374\) | 10.0999 | + | 3.84882i | 0.522253 | + | 0.199018i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.9537 | − | 13.9823i | 1.39003 | − | 0.721081i | ||||
\(377\) | 17.5797 | − | 17.5797i | 0.905399 | − | 0.905399i | ||||
\(378\) | 2.86970 | + | 6.40347i | 0.147601 | + | 0.329359i | ||||
\(379\) | 14.0417 | 0.721273 | 0.360636 | − | 0.932706i | \(-0.382560\pi\) | ||||
0.360636 | + | 0.932706i | \(0.382560\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.10243 | 0.312637 | ||||||||
\(382\) | −12.8579 | − | 28.6912i | −0.657866 | − | 1.46797i | ||||
\(383\) | 2.98618 | − | 2.98618i | 0.152586 | − | 0.152586i | −0.626686 | − | 0.779272i | \(-0.715589\pi\) |
0.779272 | + | 0.626686i | \(0.215589\pi\) | |||||||
\(384\) | 16.9034 | − | 11.3911i | 0.862600 | − | 0.581297i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −25.8928 | − | 9.86713i | −1.31791 | − | 0.502224i | ||||
\(387\) | 0.467618 | + | 0.467618i | 0.0237704 | + | 0.0237704i | ||||
\(388\) | 0.00271163 | + | 0.0473337i | 0.000137662 | + | 0.00240300i | ||||
\(389\) | − | 14.8325i | − | 0.752040i | −0.926612 | − | 0.376020i | \(-0.877292\pi\) | ||
0.926612 | − | 0.376020i | \(-0.122708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 17.3419i | − | 0.877017i | ||||||
\(392\) | −2.69630 | − | 0.854378i | −0.136184 | − | 0.0431526i | ||||
\(393\) | −10.3890 | − | 10.3890i | −0.524057 | − | 0.524057i | ||||
\(394\) | 11.5684 | − | 30.3572i | 0.582807 | − | 1.52937i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.10181 | + | 1.23572i | −0.0553680 | + | 0.0620973i | ||||
\(397\) | 1.69597 | − | 1.69597i | 0.0851182 | − | 0.0851182i | −0.663266 | − | 0.748384i | \(-0.730830\pi\) |
0.748384 | + | 0.663266i | \(0.230830\pi\) | |||||||
\(398\) | 4.90531 | − | 2.19830i | 0.245881 | − | 0.110191i | ||||
\(399\) | −2.16821 | −0.108546 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −27.6833 | −1.38244 | −0.691218 | − | 0.722646i | \(-0.742926\pi\) | ||||
−0.691218 | + | 0.722646i | \(0.742926\pi\) | |||||||
\(402\) | −0.814903 | + | 0.365196i | −0.0406437 | + | 0.0182143i | ||||
\(403\) | 11.3545 | − | 11.3545i | 0.565609 | − | 0.565609i | ||||
\(404\) | 3.11216 | − | 3.49040i | 0.154836 | − | 0.173654i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.29004 | − | 8.63357i | 0.163282 | − | 0.428477i | ||||
\(407\) | 6.71191 | + | 6.71191i | 0.332697 | + | 0.332697i | ||||
\(408\) | 11.0310 | + | 3.49540i | 0.546116 | + | 0.173048i | ||||
\(409\) | 33.8549i | 1.67402i | 0.547190 | + | 0.837009i | \(0.315698\pi\) | ||||
−0.547190 | + | 0.837009i | \(0.684302\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.1298i | 0.696970i | ||||||||
\(412\) | 0.840208 | + | 14.6665i | 0.0413941 | + | 0.722566i | ||||
\(413\) | −5.09939 | − | 5.09939i | −0.250924 | − | 0.250924i | ||||
\(414\) | 2.48225 | + | 0.945925i | 0.121996 | + | 0.0464897i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.31825 | + | 20.8596i | −0.260749 | + | 1.02273i | ||||
\(417\) | −13.6891 | + | 13.6891i | −0.670358 | + | 0.670358i | ||||
\(418\) | 2.34258 | + | 5.22726i | 0.114579 | + | 0.255673i | ||||
\(419\) | 3.80167 | 0.185724 | 0.0928619 | − | 0.995679i | \(-0.470398\pi\) | ||||
0.0928619 | + | 0.995679i | \(0.470398\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.5662 | −0.758648 | −0.379324 | − | 0.925264i | \(-0.623843\pi\) | ||||
−0.379324 | + | 0.925264i | \(0.623843\pi\) | |||||||
\(422\) | 2.48230 | + | 5.53904i | 0.120837 | + | 0.269636i | ||||
\(423\) | −1.86707 | + | 1.86707i | −0.0907801 | + | 0.0907801i | ||||
\(424\) | 32.8337 | − | 17.0326i | 1.59455 | − | 0.827175i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −27.6128 | − | 10.5226i | −1.33785 | − | 0.509820i | ||||
\(427\) | 3.69253 | + | 3.69253i | 0.178694 | + | 0.178694i | ||||
\(428\) | 24.4740 | − | 1.40206i | 1.18299 | − | 0.0677709i | ||||
\(429\) | − | 23.0753i | − | 1.11408i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1.56818i | − | 0.0755367i | −0.999287 | − | 0.0377684i | \(-0.987975\pi\) | ||
0.999287 | − | 0.0377684i | \(-0.0120249\pi\) | |||||||
\(432\) | 12.3397 | − | 15.5451i | 0.593692 | − | 0.747913i | ||||
\(433\) | −5.56380 | − | 5.56380i | −0.267379 | − | 0.267379i | 0.560664 | − | 0.828043i | \(-0.310546\pi\) |
−0.828043 | + | 0.560664i | \(0.810546\pi\) | |||||||
\(434\) | 2.12500 | − | 5.57633i | 0.102003 | − | 0.267672i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.9719 | + | 15.1327i | 0.812809 | + | 0.724727i | ||||
\(437\) | 6.49885 | − | 6.49885i | 0.310882 | − | 0.310882i | ||||
\(438\) | −33.6781 | + | 15.0927i | −1.60920 | + | 0.721159i | ||||
\(439\) | 3.73785 | 0.178398 | 0.0891990 | − | 0.996014i | \(-0.471569\pi\) | ||||
0.0891990 | + | 0.996014i | \(0.471569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.245954 | 0.0117121 | ||||||||
\(442\) | −11.1521 | + | 4.99775i | −0.530449 | + | 0.237719i | ||||
\(443\) | 0.224928 | − | 0.224928i | 0.0106866 | − | 0.0106866i | −0.701743 | − | 0.712430i | \(-0.747595\pi\) |
0.712430 | + | 0.701743i | \(0.247595\pi\) | |||||||
\(444\) | 7.58506 | + | 6.76309i | 0.359971 | + | 0.320962i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 12.3239 | − | 32.3398i | 0.583554 | − | 1.53133i | ||||
\(447\) | 22.6229 | + | 22.6229i | 1.07003 | + | 1.07003i | ||||
\(448\) | 1.36666 | + | 7.88240i | 0.0645688 | + | 0.372408i | ||||
\(449\) | 18.9314i | 0.893428i | 0.894677 | + | 0.446714i | \(0.147406\pi\) | ||||
−0.894677 | + | 0.446714i | \(0.852594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.04946i | 0.426122i | ||||||||
\(452\) | −6.28747 | + | 0.360194i | −0.295738 | + | 0.0169421i | ||||
\(453\) | −4.55989 | − | 4.55989i | −0.214242 | − | 0.214242i | ||||
\(454\) | −3.85416 | − | 1.46872i | −0.180884 | − | 0.0689307i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.82396 | + | 5.44375i | 0.132244 | + | 0.254927i | ||||
\(457\) | −24.5750 | + | 24.5750i | −1.14957 | + | 1.14957i | −0.162934 | + | 0.986637i | \(0.552096\pi\) |
−0.986637 | + | 0.162934i | \(0.947904\pi\) | |||||||
\(458\) | 2.22810 | + | 4.97180i | 0.104112 | + | 0.232317i | ||||
\(459\) | 11.2673 | 0.525910 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.3095 | 1.36508 | 0.682541 | − | 0.730848i | \(-0.260875\pi\) | ||||
0.682541 | + | 0.730848i | \(0.260875\pi\) | |||||||
\(462\) | −3.50699 | − | 7.82554i | −0.163160 | − | 0.364077i | ||||
\(463\) | −10.7432 | + | 10.7432i | −0.499280 | + | 0.499280i | −0.911214 | − | 0.411934i | \(-0.864853\pi\) |
0.411934 | + | 0.911214i | \(0.364853\pi\) | |||||||
\(464\) | −25.9615 | + | 2.98433i | −1.20523 | + | 0.138544i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.92953 | − | 1.49745i | −0.182032 | − | 0.0693680i | ||||
\(467\) | 15.6434 | + | 15.6434i | 0.723890 | + | 0.723890i | 0.969395 | − | 0.245505i | \(-0.0789538\pi\) |
−0.245505 | + | 0.969395i | \(0.578954\pi\) | |||||||
\(468\) | −0.107063 | − | 1.86887i | −0.00494898 | − | 0.0863884i | ||||
\(469\) | − | 0.350479i | − | 0.0161836i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.15356i | 0.283541i | ||||||||
\(472\) | −6.16145 | + | 19.4447i | −0.283604 | + | 0.895015i | ||||
\(473\) | 6.39893 | + | 6.39893i | 0.294223 | + | 0.294223i | ||||
\(474\) | −7.35465 | + | 19.2997i | −0.337810 | + | 0.886465i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.02245 | + | 3.38979i | −0.138534 | + | 0.155371i | ||||
\(477\) | −2.27438 | + | 2.27438i | −0.104137 | + | 0.104137i | ||||
\(478\) | 16.0931 | − | 7.21205i | 0.736080 | − | 0.329872i | ||||
\(479\) | 0.447947 | 0.0204672 | 0.0102336 | − | 0.999948i | \(-0.496742\pi\) | ||||
0.0102336 | + | 0.999948i | \(0.496742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.7324 | −0.489356 | ||||||||
\(482\) | −15.5459 | + | 6.96682i | −0.708094 | + | 0.317330i | ||||
\(483\) | −9.72920 | + | 9.72920i | −0.442694 | + | 0.442694i | ||||
\(484\) | −0.436112 | + | 0.489116i | −0.0198233 | + | 0.0222325i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.28405 | + | 3.36953i | −0.0582455 | + | 0.152845i | ||||
\(487\) | −23.7240 | − | 23.7240i | −1.07504 | − | 1.07504i | −0.996946 | − | 0.0780899i | \(-0.975118\pi\) |
−0.0780899 | − | 0.996946i | \(-0.524882\pi\) | |||||||
\(488\) | 4.46158 | − | 14.0802i | 0.201966 | − | 0.637378i | ||||
\(489\) | 1.21204i | 0.0548104i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.3824i | − | 0.829587i | −0.909916 | − | 0.414793i | \(-0.863854\pi\) | ||
0.909916 | − | 0.414793i | \(-0.136146\pi\) | |||||||
\(492\) | 0.554119 | + | 9.67258i | 0.0249816 | + | 0.436074i | ||||
\(493\) | −10.4901 | − | 10.4901i | −0.472451 | − | 0.472451i | ||||
\(494\) | −6.05211 | − | 2.30631i | −0.272298 | − | 0.103766i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.7682 | + | 1.92755i | −0.752915 | + | 0.0865494i | ||||
\(497\) | 8.20075 | − | 8.20075i | 0.367854 | − | 0.367854i | ||||
\(498\) | 16.8518 | + | 37.6032i | 0.755146 | + | 1.68504i | ||||
\(499\) | −37.0968 | −1.66068 | −0.830340 | − | 0.557257i | \(-0.811854\pi\) | ||||
−0.830340 | + | 0.557257i | \(0.811854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.3033 | −0.817732 | ||||||||
\(502\) | 5.58430 | + | 12.4609i | 0.249240 | + | 0.556156i | ||||
\(503\) | −3.17576 | + | 3.17576i | −0.141600 | + | 0.141600i | −0.774353 | − | 0.632753i | \(-0.781925\pi\) |
0.632753 | + | 0.774353i | \(0.281925\pi\) | |||||||
\(504\) | −0.320339 | − | 0.617519i | −0.0142691 | − | 0.0275065i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 33.9673 | + | 12.9441i | 1.51003 | + | 0.575437i | ||||
\(507\) | 1.88729 | + | 1.88729i | 0.0838175 | + | 0.0838175i | ||||
\(508\) | 6.76316 | − | 0.387445i | 0.300067 | − | 0.0171901i | ||||
\(509\) | 24.5955i | 1.09018i | 0.838379 | + | 0.545088i | \(0.183504\pi\) | ||||
−0.838379 | + | 0.545088i | \(0.816496\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.4845i | − | 0.640756i | ||||||
\(512\) | 18.0104 | − | 13.6976i | 0.795956 | − | 0.605355i | ||||
\(513\) | 4.22239 | + | 4.22239i | 0.186423 | + | 0.186423i | ||||
\(514\) | 2.74631 | − | 7.20673i | 0.121135 | − | 0.317875i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.23137 | + | 6.44773i | 0.318343 | + | 0.283845i | ||||
\(517\) | −25.5492 | + | 25.5492i | −1.12365 | + | 1.12365i | ||||
\(518\) | −3.63969 | + | 1.63112i | −0.159919 | + | 0.0716671i | ||||
\(519\) | −3.09037 | −0.135652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.9594 | 0.523951 | 0.261976 | − | 0.965075i | \(-0.415626\pi\) | ||||
0.261976 | + | 0.965075i | \(0.415626\pi\) | |||||||
\(522\) | 2.07370 | − | 0.929324i | 0.0907636 | − | 0.0406754i | ||||
\(523\) | −8.87100 | + | 8.87100i | −0.387902 | + | 0.387902i | −0.873938 | − | 0.486037i | \(-0.838442\pi\) |
0.486037 | + | 0.873938i | \(0.338442\pi\) | |||||||
\(524\) | −12.1735 | − | 10.8543i | −0.531802 | − | 0.474172i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.82956 | − | 23.1701i | 0.384987 | − | 1.01026i | ||||
\(527\) | −6.77545 | − | 6.77545i | −0.295143 | − | 0.295143i | ||||
\(528\) | −15.0800 | + | 18.9973i | −0.656274 | + | 0.826751i | ||||
\(529\) | − | 35.3233i | − | 1.53579i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.77373i | − | 0.0769732i | ||||||
\(532\) | −2.40297 | + | 0.137661i | −0.104182 | + | 0.00596834i | ||||
\(533\) | −7.23508 | − | 7.23508i | −0.313386 | − | 0.313386i | ||||
\(534\) | −17.9911 | − | 6.85598i | −0.778552 | − | 0.296687i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.879950 | + | 0.456476i | −0.0380080 | + | 0.0197168i | ||||
\(537\) | −14.6779 | + | 14.6779i | −0.633396 | + | 0.633396i | ||||
\(538\) | 3.35741 | + | 7.49177i | 0.144748 | + | 0.322993i | ||||
\(539\) | 3.36566 | 0.144969 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.7774 | −1.02227 | −0.511136 | − | 0.859500i | \(-0.670775\pi\) | ||||
−0.511136 | + | 0.859500i | \(0.670775\pi\) | |||||||
\(542\) | −8.04233 | − | 17.9458i | −0.345448 | − | 0.770836i | ||||
\(543\) | 27.3844 | − | 27.3844i | 1.17518 | − | 1.17518i | ||||
\(544\) | 12.4473 | + | 3.17350i | 0.533674 | + | 0.136063i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 9.06041 | + | 3.45270i | 0.387750 | + | 0.147762i | ||||
\(547\) | −19.2873 | − | 19.2873i | −0.824667 | − | 0.824667i | 0.162106 | − | 0.986773i | \(-0.448171\pi\) |
−0.986773 | + | 0.162106i | \(0.948171\pi\) | |||||||
\(548\) | 0.897104 | + | 15.6597i | 0.0383224 | + | 0.668947i | ||||
\(549\) | 1.28438i | 0.0548159i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 7.86231i | − | 0.334946i | ||||||
\(552\) | 37.0988 | + | 11.7555i | 1.57903 | + | 0.500349i | ||||
\(553\) | −5.73184 | − | 5.73184i | −0.243742 | − | 0.243742i | ||||
\(554\) | −7.19536 | + | 18.8817i | −0.305702 | + | 0.802207i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.3022 | + | 16.0404i | −0.606547 | + | 0.680265i | ||||
\(557\) | 24.6576 | − | 24.6576i | 1.04478 | − | 1.04478i | 0.0458256 | − | 0.998949i | \(-0.485408\pi\) |
0.998949 | − | 0.0458256i | \(-0.0145918\pi\) | |||||||
\(558\) | 1.33938 | − | 0.600240i | 0.0567006 | − | 0.0254102i | ||||
\(559\) | −10.2319 | −0.432765 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.7695 | −0.581347 | ||||||||
\(562\) | 0.742464 | − | 0.332733i | 0.0313190 | − | 0.0140355i | ||||
\(563\) | 8.25606 | − | 8.25606i | 0.347952 | − | 0.347952i | −0.511394 | − | 0.859346i | \(-0.670871\pi\) |
0.859346 | + | 0.511394i | \(0.170871\pi\) | |||||||
\(564\) | −25.7440 | + | 28.8728i | −1.08402 | + | 1.21577i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.86626 | − | 4.89735i | 0.0784447 | − | 0.205851i | ||||
\(567\) | −6.84293 | − | 6.84293i | −0.287376 | − | 0.287376i | ||||
\(568\) | −31.2707 | − | 9.90875i | −1.31209 | − | 0.415762i | ||||
\(569\) | − | 0.397613i | − | 0.0166688i | −0.999965 | − | 0.00833440i | \(-0.997347\pi\) | ||
0.999965 | − | 0.00833440i | \(-0.00265295\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.7372i | 0.742278i | 0.928577 | + | 0.371139i | \(0.121033\pi\) | ||||
−0.928577 | + | 0.371139i | \(0.878967\pi\) | |||||||
\(572\) | −1.46506 | − | 25.5737i | −0.0612571 | − | 1.06929i | ||||
\(573\) | 28.3225 | + | 28.3225i | 1.18319 | + | 1.18319i | ||||
\(574\) | −3.55323 | − | 1.35405i | −0.148309 | − | 0.0565169i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.13319 | + | 1.60856i | −0.0472162 | + | 0.0670233i | ||||
\(577\) | 10.2591 | − | 10.2591i | 0.427092 | − | 0.427092i | −0.460545 | − | 0.887637i | \(-0.652346\pi\) |
0.887637 | + | 0.460545i | \(0.152346\pi\) | |||||||
\(578\) | −6.84976 | − | 15.2846i | −0.284912 | − | 0.635757i | ||||
\(579\) | 35.3004 | 1.46704 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −16.1726 | −0.670954 | ||||||||
\(582\) | −0.0247011 | − | 0.0551184i | −0.00102389 | − | 0.00228473i | ||||
\(583\) | −31.1228 | + | 31.1228i | −1.28898 | + | 1.28898i | ||||
\(584\) | −36.3664 | + | 18.8651i | −1.50485 | + | 0.780645i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.5451 | − | 10.1157i | −1.09657 | − | 0.417875i | ||||
\(587\) | −24.8170 | − | 24.8170i | −1.02431 | − | 1.02431i | −0.999697 | − | 0.0246102i | \(-0.992166\pi\) |
−0.0246102 | − | 0.999697i | \(-0.507834\pi\) | |||||||
\(588\) | 3.59741 | − | 0.206087i | 0.148355 | − | 0.00849888i | ||||
\(589\) | − | 5.07818i | − | 0.209243i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 41.3868i | 1.70243i | ||||||||
\(592\) | 8.83572 | + | 7.01378i | 0.363146 | + | 0.288265i | ||||
\(593\) | 3.67231 | + | 3.67231i | 0.150804 | + | 0.150804i | 0.778477 | − | 0.627673i | \(-0.215993\pi\) |
−0.627673 | + | 0.778477i | \(0.715993\pi\) | |||||||
\(594\) | −8.40997 | + | 22.0690i | −0.345065 | + | 0.905503i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 26.5087 | + | 23.6361i | 1.08584 | + | 0.968171i | ||||
\(597\) | −4.84228 | + | 4.84228i | −0.198181 | + | 0.198181i | ||||
\(598\) | −37.5059 | + | 16.8082i | −1.53373 | + | 0.687337i | ||||
\(599\) | −30.7130 | −1.25490 | −0.627449 | − | 0.778658i | \(-0.715901\pi\) | ||||
−0.627449 | + | 0.778658i | \(0.715901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.5093 | 0.795800 | 0.397900 | − | 0.917429i | \(-0.369739\pi\) | ||||
0.397900 | + | 0.917429i | \(0.369739\pi\) | |||||||
\(602\) | −3.46997 | + | 1.55506i | −0.141425 | + | 0.0633793i | ||||
\(603\) | 0.0609538 | − | 0.0609538i | 0.00248223 | − | 0.00248223i | ||||
\(604\) | −5.34312 | − | 4.76410i | −0.217408 | − | 0.193848i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.12144 | + | 5.56699i | −0.0861778 | + | 0.226144i | ||||
\(607\) | −3.15281 | − | 3.15281i | −0.127969 | − | 0.127969i | 0.640222 | − | 0.768190i | \(-0.278843\pi\) |
−0.768190 | + | 0.640222i | \(0.778843\pi\) | |||||||
\(608\) | 3.47535 | + | 5.85387i | 0.140944 | + | 0.237406i | ||||
\(609\) | 11.7704i | 0.476960i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 40.8533i | − | 1.65275i | ||||||
\(612\) | −1.11519 | + | 0.0638864i | −0.0450788 | + | 0.00258246i | ||||
\(613\) | 24.5054 | + | 24.5054i | 0.989762 | + | 0.989762i | 0.999948 | − | 0.0101859i | \(-0.00324232\pi\) |
−0.0101859 | + | 0.999948i | \(0.503242\pi\) | |||||||
\(614\) | −3.09309 | − | 1.17870i | −0.124827 | − | 0.0475685i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.38355 | − | 8.45019i | −0.176618 | − | 0.340468i | ||||
\(617\) | −29.0478 | + | 29.0478i | −1.16942 | + | 1.16942i | −0.187076 | + | 0.982345i | \(0.559901\pi\) |
−0.982345 | + | 0.187076i | \(0.940099\pi\) | |||||||
\(618\) | −7.65371 | − | 17.0786i | −0.307878 | − | 0.687002i | ||||
\(619\) | 44.8275 | 1.80177 | 0.900885 | − | 0.434059i | \(-0.142919\pi\) | ||||
0.900885 | + | 0.434059i | \(0.142919\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 37.8934 | 1.52061 | ||||||||
\(622\) | 18.8436 | + | 42.0479i | 0.755561 | + | 1.68597i | ||||
\(623\) | 5.34320 | − | 5.34320i | 0.214071 | − | 0.214071i | ||||
\(624\) | −3.13188 | − | 27.2450i | −0.125375 | − | 1.09067i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −25.4818 | − | 9.71049i | −1.01846 | − | 0.388109i | ||||
\(627\) | −5.16008 | − | 5.16008i | −0.206074 | − | 0.206074i | ||||
\(628\) | 0.390692 | + | 6.81983i | 0.0155903 | + | 0.272141i | ||||
\(629\) | 6.40423i | 0.255353i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.6696i | − | 1.18113i | −0.806991 | − | 0.590564i | \(-0.798905\pi\) | ||
0.806991 | − | 0.590564i | \(-0.201095\pi\) | |||||||
\(632\) | −6.92562 | + | 21.8563i | −0.275486 | + | 0.869398i | ||||
\(633\) | −5.46786 | − | 5.46786i | −0.217328 | − | 0.217328i | ||||
\(634\) | −1.19050 | + | 3.12406i | −0.0472809 | + | 0.124072i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −31.3601 | + | 35.1716i | −1.24351 | + | 1.39464i | ||||
\(637\) | −2.69086 | + | 2.69086i | −0.106616 | + | 0.106616i | ||||
\(638\) | 28.3768 | − | 12.7170i | 1.12345 | − | 0.503469i | ||||
\(639\) | 2.85248 | 0.112842 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.4006 | 1.35874 | 0.679372 | − | 0.733794i | \(-0.262252\pi\) | ||||
0.679372 | + | 0.733794i | \(0.262252\pi\) | |||||||
\(642\) | −28.4991 | + | 12.7718i | −1.12477 | + | 0.504061i | ||||
\(643\) | 33.2995 | − | 33.2995i | 1.31321 | − | 1.31321i | 0.394167 | − | 0.919039i | \(-0.371033\pi\) |
0.919039 | − | 0.394167i | \(-0.128967\pi\) | |||||||
\(644\) | −10.1649 | + | 11.4003i | −0.400554 | + | 0.449236i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.37622 | + | 3.61141i | −0.0541467 | + | 0.142089i | ||||
\(647\) | 14.9070 | + | 14.9070i | 0.586055 | + | 0.586055i | 0.936561 | − | 0.350505i | \(-0.113990\pi\) |
−0.350505 | + | 0.936561i | \(0.613990\pi\) | |||||||
\(648\) | −8.26813 | + | 26.0931i | −0.324803 | + | 1.02503i | ||||
\(649\) | − | 24.2718i | − | 0.952753i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.60237i | 0.297960i | ||||||||
\(652\) | 0.0769530 | + | 1.34327i | 0.00301371 | + | 0.0526067i | ||||
\(653\) | −2.33344 | − | 2.33344i | −0.0913146 | − | 0.0913146i | 0.659974 | − | 0.751289i | \(-0.270567\pi\) |
−0.751289 | + | 0.659974i | \(0.770567\pi\) | |||||||
\(654\) | −27.0693 | − | 10.3154i | −1.05849 | − | 0.403366i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.22823 | + | 10.6847i | 0.0479544 | + | 0.417167i | ||||
\(657\) | 2.51908 | − | 2.51908i | 0.0982788 | − | 0.0982788i | ||||
\(658\) | −6.20891 | − | 13.8546i | −0.242048 | − | 0.540110i | ||||
\(659\) | 26.8019 | 1.04405 | 0.522027 | − | 0.852929i | \(-0.325176\pi\) | ||||
0.522027 | + | 0.852929i | \(0.325176\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.38663 | −0.170620 | −0.0853101 | − | 0.996354i | \(-0.527188\pi\) | ||||
−0.0853101 | + | 0.996354i | \(0.527188\pi\) | |||||||
\(662\) | −2.25810 | − | 5.03876i | −0.0877636 | − | 0.195837i | ||||
\(663\) | 11.0087 | − | 11.0087i | 0.427544 | − | 0.427544i | ||||
\(664\) | 21.0638 | + | 40.6048i | 0.817435 | + | 1.57577i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.916677 | − | 0.349323i | −0.0355205 | − | 0.0135360i | ||||
\(667\) | −35.2798 | − | 35.2798i | −1.36604 | − | 1.36604i | ||||
\(668\) | −20.2851 | + | 1.16208i | −0.784854 | + | 0.0449624i | ||||
\(669\) | 44.0897i | 1.70461i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.5756i | 0.678497i | ||||||||
\(672\) | −5.20282 | − | 8.76363i | −0.200703 | − | 0.338064i | ||||
\(673\) | 14.1769 | + | 14.1769i | 0.546479 | + | 0.546479i | 0.925421 | − | 0.378942i | \(-0.123712\pi\) |
−0.378942 | + | 0.925421i | \(0.623712\pi\) | |||||||
\(674\) | −7.47185 | + | 19.6073i | −0.287805 | + | 0.755244i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.21146 | + | 1.97181i | 0.0850562 | + | 0.0758389i | ||||
\(677\) | 17.4009 | − | 17.4009i | 0.668772 | − | 0.668772i | −0.288660 | − | 0.957432i | \(-0.593210\pi\) |
0.957432 | + | 0.288660i | \(0.0932097\pi\) | |||||||
\(678\) | 7.32153 | − | 3.28112i | 0.281182 | − | 0.126011i | ||||
\(679\) | 0.0237057 | 0.000909740 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.25448 | 0.201352 | ||||||||
\(682\) | 18.3282 | − | 8.21374i | 0.701825 | − | 0.314520i | ||||
\(683\) | −15.5454 | + | 15.5454i | −0.594828 | + | 0.594828i | −0.938932 | − | 0.344103i | \(-0.888183\pi\) |
0.344103 | + | 0.938932i | \(0.388183\pi\) | |||||||
\(684\) | −0.441856 | − | 0.393974i | −0.0168948 | − | 0.0150640i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.503596 | + | 1.32151i | −0.0192274 | + | 0.0504555i | ||||
\(687\) | −4.90791 | − | 4.90791i | −0.187249 | − | 0.187249i | ||||
\(688\) | 8.42371 | + | 6.68673i | 0.321151 | + | 0.254929i | ||||
\(689\) | − | 49.7657i | − | 1.89592i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 12.6703i | − | 0.481999i | −0.970525 | − | 0.241000i | \(-0.922525\pi\) | ||
0.970525 | − | 0.241000i | \(-0.0774753\pi\) | |||||||
\(692\) | −3.42498 | + | 0.196209i | −0.130198 | + | 0.00745873i | ||||
\(693\) | 0.585341 | + | 0.585341i | 0.0222353 | + | 0.0222353i | ||||
\(694\) | −23.0291 | − | 8.77583i | −0.874173 | − | 0.333126i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 29.5520 | − | 15.3302i | 1.12017 | − | 0.581089i | ||||
\(697\) | −4.31731 | + | 4.31731i | −0.163530 | + | 0.163530i | ||||
\(698\) | 9.41997 | + | 21.0198i | 0.356551 | + | 0.795613i | ||||
\(699\) | 5.35725 | 0.202630 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.4415 | 0.885373 | 0.442686 | − | 0.896677i | \(-0.354026\pi\) | ||||
0.442686 | + | 0.896677i | \(0.354026\pi\) | |||||||
\(702\) | −10.9205 | − | 24.3681i | −0.412167 | − | 0.919714i | ||||
\(703\) | −2.39998 | + | 2.39998i | −0.0905168 | + | 0.0905168i | ||||
\(704\) | −15.5067 | + | 22.0117i | −0.584429 | + | 0.829596i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9262 | + | 6.45016i | 0.637025 | + | 0.242755i | ||||
\(707\) | −1.65335 | − | 1.65335i | −0.0621804 | − | 0.0621804i | ||||
\(708\) | −1.48622 | − | 25.9431i | −0.0558556 | − | 0.975003i | ||||
\(709\) | 19.6258i | 0.737063i | 0.929615 | + | 0.368531i | \(0.120139\pi\) | ||||
−0.929615 | + | 0.368531i | \(0.879861\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.99371i | − | 0.0747701i | ||||||
\(712\) | −20.3744 | − | 6.45605i | −0.763563 | − | 0.241951i | ||||
\(713\) | −22.7868 | − | 22.7868i | −0.853373 | − | 0.853373i | ||||
\(714\) | 2.06029 | − | 5.40652i | 0.0771045 | − | 0.202334i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.3352 | + | 17.1990i | −0.573103 | + | 0.642757i | ||||
\(717\) | −15.8863 | + | 15.8863i | −0.593283 | + | 0.593283i | ||||
\(718\) | 20.0739 | − | 8.99605i | 0.749151 | − | 0.335730i | ||||
\(719\) | 11.1079 | 0.414254 | 0.207127 | − | 0.978314i | \(-0.433589\pi\) | ||||
0.207127 | + | 0.978314i | \(0.433589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.34527 | 0.273552 | ||||||||
\(722\) | 22.6513 | − | 10.1511i | 0.842992 | − | 0.377784i | ||||
\(723\) | 15.3461 | − | 15.3461i | 0.570727 | − | 0.570727i | ||||
\(724\) | 28.6108 | − | 32.0881i | 1.06331 | − | 1.19254i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.297282 | − | 0.780112i | 0.0110332 | − | 0.0289527i | ||||
\(727\) | −30.5258 | − | 30.5258i | −1.13214 | − | 1.13214i | −0.989821 | − | 0.142320i | \(-0.954544\pi\) |
−0.142320 | − | 0.989821i | \(-0.545456\pi\) | |||||||
\(728\) | 10.2606 | + | 3.25129i | 0.380284 | + | 0.120501i | ||||
\(729\) | 24.4383i | 0.905123i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.10560i | 0.225824i | ||||||||
\(732\) | 1.07619 | + | 18.7858i | 0.0397771 | + | 0.694342i | ||||
\(733\) | −29.8413 | − | 29.8413i | −1.10221 | − | 1.10221i | −0.994143 | − | 0.108069i | \(-0.965533\pi\) |
−0.108069 | − | 0.994143i | \(-0.534467\pi\) | |||||||
\(734\) | 25.3653 | + | 9.66610i | 0.936250 | + | 0.356782i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 41.8621 | + | 10.6729i | 1.54306 | + | 0.393410i | ||||
\(737\) | 0.834097 | − | 0.834097i | 0.0307244 | − | 0.0307244i | ||||
\(738\) | −0.382472 | − | 0.853453i | −0.0140790 | − | 0.0314161i | ||||
\(739\) | 23.6530 | 0.870091 | 0.435046 | − | 0.900408i | \(-0.356732\pi\) | ||||
0.435046 | + | 0.900408i | \(0.356732\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.25102 | 0.303109 | ||||||||
\(742\) | −7.56341 | − | 16.8771i | −0.277661 | − | 0.619577i | ||||
\(743\) | 12.8370 | − | 12.8370i | 0.470945 | − | 0.470945i | −0.431275 | − | 0.902220i | \(-0.641936\pi\) |
0.902220 | + | 0.431275i | \(0.141936\pi\) | |||||||
\(744\) | 19.0873 | − | 9.90160i | 0.699776 | − | 0.363010i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.47585 | + | 2.46779i | 0.237098 | + | 0.0903521i | ||||
\(747\) | −2.81268 | − | 2.81268i | −0.102910 | − | 0.102910i | ||||
\(748\) | −15.2603 | + | 0.874228i | −0.557973 | + | 0.0319649i | ||||
\(749\) | − | 12.2571i | − | 0.447863i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5499i | 0.567426i | 0.958909 | + | 0.283713i | \(0.0915662\pi\) | ||||
−0.958909 | + | 0.283713i | \(0.908434\pi\) | |||||||
\(752\) | −26.6982 | + | 33.6335i | −0.973585 | + | 1.22649i | ||||
\(753\) | −12.3008 | − | 12.3008i | −0.448264 | − | 0.448264i | ||||
\(754\) | −12.5201 | + | 32.8546i | −0.455955 | + | 1.19649i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −7.40694 | − | 6.60427i | −0.269388 | − | 0.240195i | ||||
\(757\) | 1.06506 | − | 1.06506i | 0.0387104 | − | 0.0387104i | −0.687487 | − | 0.726197i | \(-0.741286\pi\) |
0.726197 | + | 0.687487i | \(0.241286\pi\) | |||||||
\(758\) | −18.1214 | + | 8.12106i | −0.658200 | + | 0.294970i | ||||
\(759\) | −46.3086 | −1.68090 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −33.7471 | −1.22333 | −0.611665 | − | 0.791117i | \(-0.709500\pi\) | ||||
−0.611665 | + | 0.791117i | \(0.709500\pi\) | |||||||
\(762\) | −7.87546 | + | 3.52936i | −0.285298 | + | 0.127855i | ||||
\(763\) | 8.03933 | − | 8.03933i | 0.291043 | − | 0.291043i | ||||
\(764\) | 33.1874 | + | 29.5909i | 1.20068 | + | 1.07056i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.12673 | + | 5.58086i | −0.0768419 | + | 0.201645i | ||||
\(767\) | 19.4054 | + | 19.4054i | 0.700690 | + | 0.700690i | ||||
\(768\) | −15.2266 | + | 24.4768i | −0.549442 | + | 0.883232i | ||||
\(769\) | − | 25.8245i | − | 0.931254i | −0.884981 | − | 0.465627i | \(-0.845829\pi\) | ||
0.884981 | − | 0.465627i | \(-0.154171\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.82514i | 0.353844i | ||||||||
\(772\) | 39.1226 | − | 2.24124i | 1.40805 | − | 0.0806639i | ||||
\(773\) | 17.2373 | + | 17.2373i | 0.619981 | + | 0.619981i | 0.945526 | − | 0.325545i | \(-0.105548\pi\) |
−0.325545 | + | 0.945526i | \(0.605548\pi\) | |||||||
\(774\) | −0.873931 | − | 0.333034i | −0.0314128 | − | 0.0119707i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −0.0308751 | − | 0.0595180i | −0.00110835 | − | 0.00213657i | ||||
\(777\) | 3.59292 | − | 3.59292i | 0.128895 | − | 0.128895i | ||||
\(778\) | 8.57846 | + | 19.1421i | 0.307553 | + | 0.686277i | ||||
\(779\) | −3.23581 | −0.115935 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.0336 | 1.39673 | ||||||||
\(782\) | 10.0297 | + | 22.3805i | 0.358663 | + | 0.800325i | ||||
\(783\) | 22.9217 | − | 22.9217i | 0.819155 | − | 0.819155i | ||||
\(784\) | 3.97383 | − | 0.456801i | 0.141923 | − | 0.0163143i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 19.4161 | + | 7.39898i | 0.692548 | + | 0.263913i | ||||
\(787\) | 21.5133 | + | 21.5133i | 0.766866 | + | 0.766866i | 0.977553 | − | 0.210688i | \(-0.0675703\pi\) |
−0.210688 | + | 0.977553i | \(0.567570\pi\) | |||||||
\(788\) | 2.62766 | + | 45.8679i | 0.0936066 | + | 1.63398i | ||||
\(789\) | 31.5884i | 1.12458i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.14889i | 0.111962i | ||||||||
\(792\) | 0.707252 | − | 2.23199i | 0.0251311 | − | 0.0793103i | ||||
\(793\) | −14.0517 | − | 14.0517i | −0.498992 | − | 0.498992i | ||||
\(794\) | −1.20785 | + | 3.16959i | −0.0428651 | + | 0.112485i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.05913 | + | 5.67401i | −0.179316 | + | 0.201110i | ||||
\(797\) | 35.0680 | − | 35.0680i | 1.24217 | − | 1.24217i | 0.283074 | − | 0.959098i | \(-0.408646\pi\) |
0.959098 | − | 0.283074i | \(-0.0913540\pi\) | |||||||
\(798\) | 2.79818 | − | 1.25399i | 0.0990543 | − | 0.0443909i | ||||
\(799\) | −24.3780 | −0.862430 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.85853 | 0.0656681 | ||||||||
\(802\) | 35.7265 | − | 16.0107i | 1.26155 | − | 0.565358i | ||||
\(803\) | 34.4714 | − | 34.4714i | 1.21647 | − | 1.21647i | ||||
\(804\) | 0.840457 | − | 0.942604i | 0.0296406 | − | 0.0332431i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.08659 | + | 21.2204i | −0.284838 | + | 0.747458i | ||||
\(807\) | −7.39549 | − | 7.39549i | −0.260334 | − | 0.260334i | ||||
\(808\) | −1.99769 | + | 6.30445i | −0.0702786 | + | 0.221790i | ||||
\(809\) | − | 24.0099i | − | 0.844143i | −0.906563 | − | 0.422072i | \(-0.861303\pi\) | ||
0.906563 | − | 0.422072i | \(-0.138697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 52.4070i | − | 1.84026i | −0.391615 | − | 0.920129i | \(-0.628084\pi\) | ||
0.391615 | − | 0.920129i | \(-0.371916\pi\) | |||||||
\(812\) | 0.747306 | + | 13.0448i | 0.0262253 | + | 0.457784i | ||||
\(813\) | 17.7151 | + | 17.7151i | 0.621297 | + | 0.621297i | ||||
\(814\) | −12.5439 | − | 4.78017i | −0.439663 | − | 0.167545i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −16.2576 | + | 1.86885i | −0.569130 | + | 0.0654228i | ||||
\(817\) | −2.28806 | + | 2.28806i | −0.0800492 | + | 0.0800492i | ||||
\(818\) | −19.5801 | − | 43.6913i | −0.684602 | − | 1.52763i | ||||
\(819\) | −0.935965 | −0.0327053 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.1519 | −0.668406 | −0.334203 | − | 0.942501i | \(-0.608467\pi\) | ||||
−0.334203 | + | 0.942501i | \(0.608467\pi\) | |||||||
\(822\) | −8.17200 | − | 18.2351i | −0.285031 | − | 0.636022i | ||||
\(823\) | 8.97203 | − | 8.97203i | 0.312745 | − | 0.312745i | −0.533227 | − | 0.845972i | \(-0.679021\pi\) |
0.845972 | + | 0.533227i | \(0.179021\pi\) | |||||||
\(824\) | −9.56674 | − | 18.4418i | −0.333273 | − | 0.642452i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 9.53024 | + | 3.63174i | 0.331599 | + | 0.126364i | ||||
\(827\) | 26.1556 | + | 26.1556i | 0.909520 | + | 0.909520i | 0.996233 | − | 0.0867129i | \(-0.0276363\pi\) |
−0.0867129 | + | 0.996233i | \(0.527636\pi\) | |||||||
\(828\) | −3.75054 | + | 0.214859i | −0.130340 | + | 0.00746687i | ||||
\(829\) | − | 31.1844i | − | 1.08308i | −0.840675 | − | 0.541540i | \(-0.817842\pi\) | ||
0.840675 | − | 0.541540i | \(-0.182158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 25.7420i | − | 0.892979i | ||||||
\(832\) | −5.20077 | − | 29.9961i | −0.180304 | − | 1.03993i | ||||
\(833\) | 1.60569 | + | 1.60569i | 0.0556337 | + | 0.0556337i | ||||
\(834\) | 9.74927 | − | 25.5835i | 0.337589 | − | 0.885886i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.04640 | − | 5.39117i | −0.209119 | − | 0.186458i | ||||
\(837\) | 14.8049 | − | 14.8049i | 0.511732 | − | 0.511732i | ||||
\(838\) | −4.90623 | + | 2.19871i | −0.169483 | + | 0.0759532i | ||||
\(839\) | −8.19874 | −0.283052 | −0.141526 | − | 0.989935i | \(-0.545201\pi\) | ||||
−0.141526 | + | 0.989935i | \(0.545201\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.6815 | −0.471775 | ||||||||
\(842\) | 20.0888 | − | 9.00274i | 0.692307 | − | 0.310255i | ||||
\(843\) | −0.732923 | + | 0.732923i | −0.0252432 | + | 0.0252432i | ||||
\(844\) | −6.40705 | − | 5.71274i | −0.220540 | − | 0.196641i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.32971 | − | 3.48937i | 0.0457164 | − | 0.119967i | ||||
\(847\) | 0.231686 | + | 0.231686i | 0.00796083 | + | 0.00796083i | ||||
\(848\) | −32.5226 | + | 40.9708i | −1.11683 | + | 1.40694i | ||||
\(849\) | 6.67669i | 0.229143i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.5383i | 0.738325i | ||||||||
\(852\) | 41.7214 | − | 2.39012i | 1.42935 | − | 0.0818840i | ||||
\(853\) | 28.0841 | + | 28.0841i | 0.961580 | + | 0.961580i | 0.999289 | − | 0.0377085i | \(-0.0120058\pi\) |
−0.0377085 | + | 0.999289i | \(0.512006\pi\) | |||||||
\(854\) | −6.90096 | − | 2.62979i | −0.236146 | − | 0.0899895i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.7739 | + | 15.9640i | −1.05183 | + | 0.545639i | ||||
\(857\) | −17.0185 | + | 17.0185i | −0.581342 | + | 0.581342i | −0.935272 | − | 0.353930i | \(-0.884845\pi\) |
0.353930 | + | 0.935272i | \(0.384845\pi\) | |||||||
\(858\) | 13.3457 | + | 29.7797i | 0.455614 | + | 1.01666i | ||||
\(859\) | −53.0951 | −1.81158 | −0.905790 | − | 0.423726i | \(-0.860722\pi\) | ||||
−0.905790 | + | 0.423726i | \(0.860722\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.84422 | 0.165091 | ||||||||
\(862\) | 0.906964 | + | 2.02381i | 0.0308913 | + | 0.0689313i | ||||
\(863\) | −36.5447 | + | 36.5447i | −1.24399 | + | 1.24399i | −0.285665 | + | 0.958329i | \(0.592215\pi\) |
−0.958329 | + | 0.285665i | \(0.907785\pi\) | |||||||
\(864\) | −6.93434 | + | 27.1983i | −0.235911 | + | 0.925306i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.3982 | + | 3.96249i | 0.353345 | + | 0.134651i | ||||
\(867\) | 15.0882 | + | 15.0882i | 0.512423 | + | 0.512423i | ||||
\(868\) | 0.482677 | + | 8.42551i | 0.0163831 | + | 0.285980i | ||||
\(869\) | − | 27.2822i | − | 0.925484i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.33373i | 0.0451917i | ||||||||
\(872\) | −30.6551 | − | 9.71371i | −1.03811 | − | 0.328948i | ||||
\(873\) | 0.00412279 | + | 0.00412279i | 0.000139535 | + | 0.000139535i | ||||
\(874\) | −4.62843 | + | 12.1457i | −0.156559 | + | 0.410834i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 34.7342 | − | 38.9557i | 1.17356 | − | 1.31619i | ||||
\(877\) | 3.12021 | − | 3.12021i | 0.105362 | − | 0.105362i | −0.652461 | − | 0.757823i | \(-0.726263\pi\) |
0.757823 | + | 0.652461i | \(0.226263\pi\) | |||||||
\(878\) | −4.82387 | + | 2.16180i | −0.162798 | + | 0.0729573i | ||||
\(879\) | 36.1897 | 1.22065 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.4751 | −1.22888 | −0.614439 | − | 0.788964i | \(-0.710618\pi\) | ||||
−0.614439 | + | 0.788964i | \(0.710618\pi\) | |||||||
\(882\) | −0.317415 | + | 0.142248i | −0.0106879 | + | 0.00478975i | ||||
\(883\) | 10.3357 | − | 10.3357i | 0.347823 | − | 0.347823i | −0.511475 | − | 0.859298i | \(-0.670901\pi\) |
0.859298 | + | 0.511475i | \(0.170901\pi\) | |||||||
\(884\) | 11.5018 | − | 12.8997i | 0.386846 | − | 0.433862i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.160192 | + | 0.420367i | −0.00538175 | + | 0.0141225i | ||||
\(887\) | −4.14097 | − | 4.14097i | −0.139040 | − | 0.139040i | 0.634161 | − | 0.773201i | \(-0.281346\pi\) |
−0.773201 | + | 0.634161i | \(0.781346\pi\) | |||||||
\(888\) | −13.7003 | − | 4.34123i | −0.459753 | − | 0.145682i | ||||
\(889\) | − | 3.38713i | − | 0.113601i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 32.5707i | − | 1.09116i | ||||||
\(892\) | 2.79927 | + | 48.8635i | 0.0937266 | + | 1.63607i | ||||
\(893\) | −9.13560 | − | 9.13560i | −0.305711 | − | 0.305711i | ||||
\(894\) | −42.2800 | − | 16.1119i | −1.41405 | − | 0.538861i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.32256 | − | 9.38218i | −0.211222 | − | 0.313437i | ||||
\(897\) | 37.0240 | − | 37.0240i | 1.23619 | − | 1.23619i | ||||
\(898\) | −10.9490 | − | 24.4318i | −0.365374 | − | 0.815300i | ||||
\(899\) | −27.5675 | −0.919428 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.6961 | −0.989321 | ||||||||
\(902\) | −5.23379 | − | 11.6787i | −0.174266 | − | 0.388859i | ||||
\(903\) | 3.42538 | − | 3.42538i | 0.113990 | − | 0.113990i | ||||
\(904\) | 7.90595 | − | 4.10123i | 0.262948 | − | 0.136405i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.52197 | + | 3.24751i | 0.283123 | + | 0.107891i | ||||
\(907\) | 22.9113 | + | 22.9113i | 0.760758 | + | 0.760758i | 0.976459 | − | 0.215702i | \(-0.0692039\pi\) |
−0.215702 | + | 0.976459i | \(0.569204\pi\) | |||||||
\(908\) | 5.82340 | − | 0.333609i | 0.193256 | − | 0.0110712i | ||||
\(909\) | − | 0.575086i | − | 0.0190744i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.7663i | 1.18499i | 0.805574 | + | 0.592496i | \(0.201857\pi\) | ||||
−0.805574 | + | 0.592496i | \(0.798143\pi\) | |||||||
\(912\) | −6.79286 | − | 5.39216i | −0.224934 | − | 0.178552i | ||||
\(913\) | −38.4889 | − | 38.4889i | −1.27380 | − | 1.27380i | ||||
\(914\) | 17.5021 | − | 45.9282i | 0.578919 | − | 1.51917i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.75092 | − | 5.12771i | −0.190016 | − | 0.169424i | ||||
\(917\) | −5.76639 | + | 5.76639i | −0.190423 | + | 0.190423i | ||||
\(918\) | −14.5409 | + | 6.51646i | −0.479921 | + | 0.215075i | ||||
\(919\) | 32.6970 | 1.07857 | 0.539287 | − | 0.842122i | \(-0.318694\pi\) | ||||
0.539287 | + | 0.842122i | \(0.318694\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.21690 | 0.138952 | ||||||||
\(922\) | −37.8253 | + | 16.9513i | −1.24571 | + | 0.558261i | ||||
\(923\) | −31.2075 | + | 31.2075i | −1.02721 | + | 1.02721i | ||||
\(924\) | 9.05186 | + | 8.07094i | 0.297784 | + | 0.265514i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.65124 | − | 20.0780i | 0.251435 | − | 0.659804i | ||||
\(927\) | 1.27746 | + | 1.27746i | 0.0419572 | + | 0.0419572i | ||||
\(928\) | 31.7784 | − | 18.8663i | 1.04318 | − | 0.619317i | ||||
\(929\) | 1.91098i | 0.0626971i | 0.999509 | + | 0.0313485i | \(0.00998019\pi\) | ||||
−0.999509 | + | 0.0313485i | \(0.990020\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.20346i | 0.0394417i | ||||||||
\(932\) | 5.93730 | − | 0.340133i | 0.194483 | − | 0.0111414i | ||||
\(933\) | −41.5076 | − | 41.5076i | −1.35890 | − | 1.35890i | ||||
\(934\) | −29.2359 | − | 11.1411i | −0.956629 | − | 0.364548i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.21903 | + | 2.34994i | 0.0398454 | + | 0.0768101i | ||||
\(937\) | −16.4547 | + | 16.4547i | −0.537553 | + | 0.537553i | −0.922810 | − | 0.385256i | \(-0.874113\pi\) |
0.385256 | + | 0.922810i | \(0.374113\pi\) | |||||||
\(938\) | 0.202701 | + | 0.452309i | 0.00661841 | + | 0.0147684i | ||||
\(939\) | 34.7400 | 1.13370 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.06433 | 0.197691 | 0.0988457 | − | 0.995103i | \(-0.468485\pi\) | ||||
0.0988457 | + | 0.995103i | \(0.468485\pi\) | |||||||
\(942\) | −3.55893 | − | 7.94145i | −0.115956 | − | 0.258746i | ||||
\(943\) | −14.5197 | + | 14.5197i | −0.472827 | + | 0.472827i | ||||
\(944\) | −3.29428 | − | 28.6578i | −0.107220 | − | 0.932731i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −11.9590 | − | 4.55727i | −0.388819 | − | 0.148170i | ||||
\(947\) | −7.66311 | − | 7.66311i | −0.249018 | − | 0.249018i | 0.571550 | − | 0.820567i | \(-0.306342\pi\) |
−0.820567 | + | 0.571550i | \(0.806342\pi\) | |||||||
\(948\) | −1.67055 | − | 29.1607i | −0.0542569 | − | 0.947096i | ||||
\(949\) | 55.1200i | 1.78927i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.25912i | − | 0.138111i | ||||||
\(952\) | 1.94011 | − | 6.12271i | 0.0628792 | − | 0.198438i | ||||
\(953\) | 4.85409 | + | 4.85409i | 0.157239 | + | 0.157239i | 0.781342 | − | 0.624103i | \(-0.214535\pi\) |
−0.624103 | + | 0.781342i | \(0.714535\pi\) | |||||||
\(954\) | 1.61979 | − | 4.25059i | 0.0524428 | − | 0.137618i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −16.5977 | + | 18.6150i | −0.536808 | + | 0.602051i | ||||
\(957\) | −28.0121 | + | 28.0121i | −0.905503 | + | 0.905503i | ||||
\(958\) | −0.578096 | + | 0.259072i | −0.0186774 | + | 0.00837023i | ||||
\(959\) | 7.84267 | 0.253253 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.1945 | 0.425627 | ||||||||
\(962\) | 13.8507 | − | 6.20713i | 0.446563 | − | 0.200126i | ||||
\(963\) | 2.13170 | − | 2.13170i | 0.0686929 | − | 0.0686929i | ||||
\(964\) | 16.0333 | − | 17.9820i | 0.516399 | − | 0.579161i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 6.92906 | − | 18.1829i | 0.222939 | − | 0.585025i | ||||
\(967\) | −37.2034 | − | 37.2034i | −1.19638 | − | 1.19638i | −0.975242 | − | 0.221139i | \(-0.929022\pi\) |
−0.221139 | − | 0.975242i | \(-0.570978\pi\) | |||||||
\(968\) | 0.279940 | − | 0.883453i | 0.00899761 | − | 0.0283952i | ||||
\(969\) | − | 4.92354i | − | 0.158167i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.1866i | 1.38592i | 0.720974 | + | 0.692962i | \(0.243695\pi\) | ||||
−0.720974 | + | 0.692962i | \(0.756305\pi\) | |||||||
\(972\) | −0.291660 | − | 5.09116i | −0.00935501 | − | 0.163299i | ||||
\(973\) | 7.59808 | + | 7.59808i | 0.243583 | + | 0.243583i | ||||
\(974\) | 44.3377 | + | 16.8960i | 1.42067 | + | 0.541384i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.38543 | + | 20.7514i | 0.0763557 | + | 0.664238i | ||||
\(977\) | −13.0089 | + | 13.0089i | −0.416191 | + | 0.416191i | −0.883888 | − | 0.467698i | \(-0.845084\pi\) |
0.467698 | + | 0.883888i | \(0.345084\pi\) | |||||||
\(978\) | −0.700989 | − | 1.56419i | −0.0224151 | − | 0.0500174i | ||||
\(979\) | 25.4323 | 0.812821 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.79633 | 0.0892800 | ||||||||
\(982\) | 10.6315 | + | 23.7233i | 0.339266 | + | 0.757042i | ||||
\(983\) | 9.22607 | − | 9.22607i | 0.294266 | − | 0.294266i | −0.544497 | − | 0.838763i | \(-0.683279\pi\) |
0.838763 | + | 0.544497i | \(0.183279\pi\) | |||||||
\(984\) | −6.30929 | − | 12.1624i | −0.201133 | − | 0.387724i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19.6050 | + | 7.47098i | 0.624349 | + | 0.237924i | ||||
\(987\) | 13.6766 | + | 13.6766i | 0.435331 | + | 0.435331i | ||||
\(988\) | 9.14439 | − | 0.523860i | 0.290922 | − | 0.0166662i | ||||
\(989\) | 20.5340i | 0.652943i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38.4314i | − | 1.22081i | −0.792088 | − | 0.610407i | \(-0.791006\pi\) | ||
0.792088 | − | 0.610407i | \(-0.208994\pi\) | |||||||
\(992\) | 20.5253 | − | 12.1855i | 0.651680 | − | 0.386892i | ||||
\(993\) | 4.97401 | + | 4.97401i | 0.157845 | + | 0.157845i | ||||
\(994\) | −5.84051 | + | 15.3264i | −0.185250 | + | 0.486123i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −43.4959 | − | 38.7824i | −1.37822 | − | 1.22887i | ||||
\(997\) | −15.2830 | + | 15.2830i | −0.484017 | + | 0.484017i | −0.906412 | − | 0.422395i | \(-0.861189\pi\) |
0.422395 | + | 0.906412i | \(0.361189\pi\) | |||||||
\(998\) | 47.8751 | − | 21.4551i | 1.51546 | − | 0.679148i | ||||
\(999\) | −13.9937 | −0.442742 |
(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 | 700.2.k.b.43.3 | 36 | ||
4.3 | odd | 2 | inner | 700.2.k.b.43.7 | 36 | ||
5.2 | odd | 4 | inner | 700.2.k.b.407.7 | 36 | ||
5.3 | odd | 4 | 140.2.k.a.127.12 | yes | 36 | ||
5.4 | even | 2 | 140.2.k.a.43.16 | yes | 36 | ||
20.3 | even | 4 | 140.2.k.a.127.16 | yes | 36 | ||
20.7 | even | 4 | inner | 700.2.k.b.407.3 | 36 | ||
20.19 | odd | 2 | 140.2.k.a.43.12 | ✓ | 36 | ||
35.3 | even | 12 | 980.2.x.l.667.1 | 72 | |||
35.4 | even | 6 | 980.2.x.k.863.9 | 72 | |||
35.9 | even | 6 | 980.2.x.k.263.3 | 72 | |||
35.13 | even | 4 | 980.2.k.l.687.12 | 36 | |||
35.18 | odd | 12 | 980.2.x.k.667.1 | 72 | |||
35.19 | odd | 6 | 980.2.x.l.263.3 | 72 | |||
35.23 | odd | 12 | 980.2.x.k.67.12 | 72 | |||
35.24 | odd | 6 | 980.2.x.l.863.9 | 72 | |||
35.33 | even | 12 | 980.2.x.l.67.12 | 72 | |||
35.34 | odd | 2 | 980.2.k.l.883.16 | 36 | |||
140.3 | odd | 12 | 980.2.x.l.667.3 | 72 | |||
140.19 | even | 6 | 980.2.x.l.263.1 | 72 | |||
140.23 | even | 12 | 980.2.x.k.67.9 | 72 | |||
140.39 | odd | 6 | 980.2.x.k.863.12 | 72 | |||
140.59 | even | 6 | 980.2.x.l.863.12 | 72 | |||
140.79 | odd | 6 | 980.2.x.k.263.1 | 72 | |||
140.83 | odd | 4 | 980.2.k.l.687.16 | 36 | |||
140.103 | odd | 12 | 980.2.x.l.67.9 | 72 | |||
140.123 | even | 12 | 980.2.x.k.667.3 | 72 | |||
140.139 | even | 2 | 980.2.k.l.883.12 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
140.2.k.a.43.12 | ✓ | 36 | 20.19 | odd | 2 | ||
140.2.k.a.43.16 | yes | 36 | 5.4 | even | 2 | ||
140.2.k.a.127.12 | yes | 36 | 5.3 | odd | 4 | ||
140.2.k.a.127.16 | yes | 36 | 20.3 | even | 4 | ||
700.2.k.b.43.3 | 36 | 1.1 | even | 1 | trivial | ||
700.2.k.b.43.7 | 36 | 4.3 | odd | 2 | inner | ||
700.2.k.b.407.3 | 36 | 20.7 | even | 4 | inner | ||
700.2.k.b.407.7 | 36 | 5.2 | odd | 4 | inner | ||
980.2.k.l.687.12 | 36 | 35.13 | even | 4 | |||
980.2.k.l.687.16 | 36 | 140.83 | odd | 4 | |||
980.2.k.l.883.12 | 36 | 140.139 | even | 2 | |||
980.2.k.l.883.16 | 36 | 35.34 | odd | 2 | |||
980.2.x.k.67.9 | 72 | 140.23 | even | 12 | |||
980.2.x.k.67.12 | 72 | 35.23 | odd | 12 | |||
980.2.x.k.263.1 | 72 | 140.79 | odd | 6 | |||
980.2.x.k.263.3 | 72 | 35.9 | even | 6 | |||
980.2.x.k.667.1 | 72 | 35.18 | odd | 12 | |||
980.2.x.k.667.3 | 72 | 140.123 | even | 12 | |||
980.2.x.k.863.9 | 72 | 35.4 | even | 6 | |||
980.2.x.k.863.12 | 72 | 140.39 | odd | 6 | |||
980.2.x.l.67.9 | 72 | 140.103 | odd | 12 | |||
980.2.x.l.67.12 | 72 | 35.33 | even | 12 | |||
980.2.x.l.263.1 | 72 | 140.19 | even | 6 | |||
980.2.x.l.263.3 | 72 | 35.19 | odd | 6 | |||
980.2.x.l.667.1 | 72 | 35.3 | even | 12 | |||
980.2.x.l.667.3 | 72 | 140.3 | odd | 12 | |||
980.2.x.l.863.9 | 72 | 35.24 | odd | 6 | |||
980.2.x.l.863.12 | 72 | 140.59 | even | 6 |