Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(251,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.b (of order \(2\), degree \(1\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.2 | ||
Root | \(1.68614 + 0.396143i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.251 |
Dual form | 525.2.b.g.251.3 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.792287i | − | 0.560232i | −0.959966 | − | 0.280116i | \(-0.909627\pi\) | ||
0.959966 | − | 0.280116i | \(-0.0903729\pi\) | |||||||
\(3\) | −1.18614 | + | 1.26217i | −0.684819 | + | 0.728714i | ||||
\(4\) | 1.37228 | 0.686141 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | + | 0.939764i | 0.408248 | + | 0.383657i | ||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | − | 2.67181i | − | 0.944629i | ||||||
\(9\) | −0.186141 | − | 2.99422i | −0.0620469 | − | 0.998073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.52434i | 0.761116i | 0.924757 | + | 0.380558i | \(0.124268\pi\) | ||||
−0.924757 | + | 0.380558i | \(0.875732\pi\) | |||||||
\(12\) | −1.62772 | + | 1.73205i | −0.469882 | + | 0.500000i | ||||
\(13\) | − | 4.10891i | − | 1.13961i | −0.821781 | − | 0.569804i | \(-0.807019\pi\) | ||
0.821781 | − | 0.569804i | \(-0.192981\pi\) | |||||||
\(14\) | 1.37228 | − | 1.58457i | 0.366758 | − | 0.423495i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.627719 | 0.156930 | ||||||||
\(17\) | 4.37228 | 1.06043 | 0.530217 | − | 0.847862i | \(-0.322110\pi\) | ||||
0.530217 | + | 0.847862i | \(0.322110\pi\) | |||||||
\(18\) | −2.37228 | + | 0.147477i | −0.559152 | + | 0.0347606i | ||||
\(19\) | 3.46410i | 0.794719i | 0.917663 | + | 0.397360i | \(0.130073\pi\) | ||||
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.55842 | + | 0.469882i | −0.994729 | + | 0.102537i | ||||
\(22\) | 2.00000 | 0.426401 | ||||||||
\(23\) | 8.51278i | 1.77504i | 0.460772 | + | 0.887518i | \(0.347572\pi\) | ||||
−0.460772 | + | 0.887518i | \(0.652428\pi\) | |||||||
\(24\) | 3.37228 | + | 3.16915i | 0.688364 | + | 0.646900i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.25544 | −0.638444 | ||||||||
\(27\) | 4.00000 | + | 3.31662i | 0.769800 | + | 0.638285i | ||||
\(28\) | 2.74456 | + | 2.37686i | 0.518674 | + | 0.449185i | ||||
\(29\) | − | 0.939764i | − | 0.174510i | −0.996186 | − | 0.0872549i | \(-0.972191\pi\) | ||
0.996186 | − | 0.0872549i | \(-0.0278095\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.46410i | − | 0.622171i | −0.950382 | − | 0.311086i | \(-0.899307\pi\) | ||
0.950382 | − | 0.311086i | \(-0.100693\pi\) | |||||||
\(32\) | − | 5.84096i | − | 1.03255i | ||||||
\(33\) | −3.18614 | − | 2.99422i | −0.554636 | − | 0.521227i | ||||
\(34\) | − | 3.46410i | − | 0.594089i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.255437 | − | 4.10891i | −0.0425729 | − | 0.684819i | ||||
\(37\) | 6.74456 | 1.10880 | 0.554400 | − | 0.832251i | \(-0.312948\pi\) | ||||
0.554400 | + | 0.832251i | \(0.312948\pi\) | |||||||
\(38\) | 2.74456 | 0.445227 | ||||||||
\(39\) | 5.18614 | + | 4.87375i | 0.830447 | + | 0.780424i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0.372281 | + | 3.61158i | 0.0574443 | + | 0.557279i | ||||
\(43\) | −4.74456 | −0.723539 | −0.361770 | − | 0.932268i | \(-0.617827\pi\) | ||||
−0.361770 | + | 0.932268i | \(0.617827\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.74456 | 0.994432 | ||||||||
\(47\) | −1.62772 | −0.237427 | −0.118714 | − | 0.992929i | \(-0.537877\pi\) | ||||
−0.118714 | + | 0.992929i | \(0.537877\pi\) | |||||||
\(48\) | −0.744563 | + | 0.792287i | −0.107468 | + | 0.114357i | ||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.18614 | + | 5.51856i | −0.726205 | + | 0.772753i | ||||
\(52\) | − | 5.63858i | − | 0.781931i | ||||||
\(53\) | − | 1.87953i | − | 0.258173i | −0.991633 | − | 0.129086i | \(-0.958796\pi\) | ||
0.991633 | − | 0.129086i | \(-0.0412045\pi\) | |||||||
\(54\) | 2.62772 | − | 3.16915i | 0.357587 | − | 0.431266i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.62772 | − | 5.34363i | 0.618405 | − | 0.714072i | ||||
\(57\) | −4.37228 | − | 4.10891i | −0.579123 | − | 0.544239i | ||||
\(58\) | −0.744563 | −0.0977659 | ||||||||
\(59\) | 8.74456 | 1.13845 | 0.569223 | − | 0.822183i | \(-0.307244\pi\) | ||||
0.569223 | + | 0.822183i | \(0.307244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.92820i | − | 0.887066i | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | −2.74456 | −0.348560 | ||||||||
\(63\) | 4.81386 | − | 6.31084i | 0.606489 | − | 0.795092i | ||||
\(64\) | −3.37228 | −0.421535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.37228 | + | 2.52434i | −0.292008 | + | 0.310725i | ||||
\(67\) | −4.74456 | −0.579641 | −0.289820 | − | 0.957081i | \(-0.593596\pi\) | ||||
−0.289820 | + | 0.957081i | \(0.593596\pi\) | |||||||
\(68\) | 6.00000 | 0.727607 | ||||||||
\(69\) | −10.7446 | − | 10.0974i | −1.29349 | − | 1.21558i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.294954i | − | 0.0350046i | −0.999847 | − | 0.0175023i | \(-0.994429\pi\) | ||
0.999847 | − | 0.0175023i | \(-0.00557143\pi\) | |||||||
\(72\) | −8.00000 | + | 0.497333i | −0.942809 | + | 0.0586113i | ||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | − | 5.34363i | − | 0.621184i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.75372i | 0.545289i | ||||||||
\(77\) | −4.37228 | + | 5.04868i | −0.498268 | + | 0.575350i | ||||
\(78\) | 3.86141 | − | 4.10891i | 0.437218 | − | 0.465243i | ||||
\(79\) | −2.37228 | −0.266903 | −0.133451 | − | 0.991055i | \(-0.542606\pi\) | ||||
−0.133451 | + | 0.991055i | \(0.542606\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.93070 | + | 1.11469i | −0.992300 | + | 0.123855i | ||||
\(82\) | − | 4.75372i | − | 0.524961i | ||||||
\(83\) | −17.4891 | −1.91968 | −0.959840 | − | 0.280546i | \(-0.909484\pi\) | ||||
−0.959840 | + | 0.280546i | \(0.909484\pi\) | |||||||
\(84\) | −6.25544 | + | 0.644810i | −0.682524 | + | 0.0703546i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.75906i | 0.405349i | ||||||||
\(87\) | 1.18614 | + | 1.11469i | 0.127168 | + | 0.119508i | ||||
\(88\) | 6.74456 | 0.718973 | ||||||||
\(89\) | −14.7446 | −1.56292 | −0.781460 | − | 0.623955i | \(-0.785525\pi\) | ||||
−0.781460 | + | 0.623955i | \(0.785525\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.11684 | − | 8.21782i | 0.746048 | − | 0.861462i | ||||
\(92\) | 11.6819i | 1.21792i | ||||||||
\(93\) | 4.37228 | + | 4.10891i | 0.453384 | + | 0.426074i | ||||
\(94\) | 1.28962i | 0.133014i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.37228 | + | 6.92820i | 0.752430 | + | 0.707107i | ||||
\(97\) | − | 11.0371i | − | 1.12065i | −0.828273 | − | 0.560325i | \(-0.810676\pi\) | ||
0.828273 | − | 0.560325i | \(-0.189324\pi\) | |||||||
\(98\) | 5.48913 | − | 0.792287i | 0.554485 | − | 0.0800331i | ||||
\(99\) | 7.55842 | − | 0.469882i | 0.759650 | − | 0.0472249i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | −0.597022 | −0.298511 | − | 0.954406i | \(-0.596490\pi\) | ||||
−0.298511 | + | 0.954406i | \(0.596490\pi\) | |||||||
\(102\) | 4.37228 | + | 4.10891i | 0.432920 | + | 0.406843i | ||||
\(103\) | − | 6.28339i | − | 0.619121i | −0.950880 | − | 0.309561i | \(-0.899818\pi\) | ||
0.950880 | − | 0.309561i | \(-0.100182\pi\) | |||||||
\(104\) | −10.9783 | −1.07651 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.48913 | −0.144637 | ||||||||
\(107\) | − | 6.63325i | − | 0.641260i | −0.947204 | − | 0.320630i | \(-0.896105\pi\) | ||
0.947204 | − | 0.320630i | \(-0.103895\pi\) | |||||||
\(108\) | 5.48913 | + | 4.55134i | 0.528191 | + | 0.437953i | ||||
\(109\) | −17.1168 | −1.63950 | −0.819748 | − | 0.572724i | \(-0.805887\pi\) | ||||
−0.819748 | + | 0.572724i | \(0.805887\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | + | 8.51278i | −0.759326 | + | 0.807997i | ||||
\(112\) | 1.25544 | + | 1.08724i | 0.118628 | + | 0.102735i | ||||
\(113\) | − | 3.16915i | − | 0.298128i | −0.988828 | − | 0.149064i | \(-0.952374\pi\) | ||
0.988828 | − | 0.149064i | \(-0.0476261\pi\) | |||||||
\(114\) | −3.25544 | + | 3.46410i | −0.304900 | + | 0.324443i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.28962i | − | 0.119738i | ||||||
\(117\) | −12.3030 | + | 0.764836i | −1.13741 | + | 0.0707091i | ||||
\(118\) | − | 6.92820i | − | 0.637793i | ||||||
\(119\) | 8.74456 | + | 7.57301i | 0.801613 | + | 0.694217i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.62772 | 0.420702 | ||||||||
\(122\) | −5.48913 | −0.496962 | ||||||||
\(123\) | −7.11684 | + | 7.57301i | −0.641704 | + | 0.682836i | ||||
\(124\) | − | 4.75372i | − | 0.426897i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5.00000 | − | 3.81396i | −0.445435 | − | 0.339774i | ||||
\(127\) | 0.744563 | 0.0660693 | 0.0330346 | − | 0.999454i | \(-0.489483\pi\) | ||||
0.0330346 | + | 0.999454i | \(0.489483\pi\) | |||||||
\(128\) | − | 9.01011i | − | 0.796389i | ||||||
\(129\) | 5.62772 | − | 5.98844i | 0.495493 | − | 0.527253i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.48913 | −0.479587 | −0.239794 | − | 0.970824i | \(-0.577080\pi\) | ||||
−0.239794 | + | 0.970824i | \(0.577080\pi\) | |||||||
\(132\) | −4.37228 | − | 4.10891i | −0.380558 | − | 0.357635i | ||||
\(133\) | −6.00000 | + | 6.92820i | −0.520266 | + | 0.600751i | ||||
\(134\) | 3.75906i | 0.324733i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 11.6819i | − | 1.00172i | ||||||
\(137\) | 13.2665i | 1.13343i | 0.823913 | + | 0.566717i | \(0.191787\pi\) | ||||
−0.823913 | + | 0.566717i | \(0.808213\pi\) | |||||||
\(138\) | −8.00000 | + | 8.51278i | −0.681005 | + | 0.724656i | ||||
\(139\) | − | 18.6101i | − | 1.57849i | −0.614078 | − | 0.789245i | \(-0.710472\pi\) | ||
0.614078 | − | 0.789245i | \(-0.289528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.93070 | − | 2.05446i | 0.162595 | − | 0.173016i | ||||
\(142\) | −0.233688 | −0.0196107 | ||||||||
\(143\) | 10.3723 | 0.867374 | ||||||||
\(144\) | −0.116844 | − | 1.87953i | −0.00973700 | − | 0.156627i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.48913 | 0.454283 | ||||||||
\(147\) | −9.93070 | − | 6.95565i | −0.819071 | − | 0.573693i | ||||
\(148\) | 9.25544 | 0.760792 | ||||||||
\(149\) | 3.16915i | 0.259627i | 0.991538 | + | 0.129813i | \(0.0414378\pi\) | ||||
−0.991538 | + | 0.129813i | \(0.958562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.37228 | −0.193054 | −0.0965268 | − | 0.995330i | \(-0.530773\pi\) | ||||
−0.0965268 | + | 0.995330i | \(0.530773\pi\) | |||||||
\(152\) | 9.25544 | 0.750715 | ||||||||
\(153\) | −0.813859 | − | 13.0916i | −0.0657966 | − | 1.05839i | ||||
\(154\) | 4.00000 | + | 3.46410i | 0.322329 | + | 0.279145i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 7.11684 | + | 6.68815i | 0.569804 | + | 0.535481i | ||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 1.87953i | 0.149527i | ||||||||
\(159\) | 2.37228 | + | 2.22938i | 0.188134 | + | 0.176802i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −14.7446 | + | 17.0256i | −1.16203 | + | 1.34180i | ||||
\(162\) | 0.883156 | + | 7.07568i | 0.0693873 | + | 0.555918i | ||||
\(163\) | −8.00000 | −0.626608 | −0.313304 | − | 0.949653i | \(-0.601436\pi\) | ||||
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 8.23369 | 0.642943 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.8564i | 1.07547i | ||||||||
\(167\) | −4.88316 | −0.377870 | −0.188935 | − | 0.981990i | \(-0.560504\pi\) | ||||
−0.188935 | + | 0.981990i | \(0.560504\pi\) | |||||||
\(168\) | 1.25544 | + | 12.1793i | 0.0968591 | + | 0.939650i | ||||
\(169\) | −3.88316 | −0.298704 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3723 | − | 0.644810i | 0.793188 | − | 0.0493099i | ||||
\(172\) | −6.51087 | −0.496450 | ||||||||
\(173\) | −1.11684 | −0.0849121 | −0.0424560 | − | 0.999098i | \(-0.513518\pi\) | ||||
−0.0424560 | + | 0.999098i | \(0.513518\pi\) | |||||||
\(174\) | 0.883156 | − | 0.939764i | 0.0669519 | − | 0.0712433i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.58457i | 0.119442i | ||||||||
\(177\) | −10.3723 | + | 11.0371i | −0.779628 | + | 0.829600i | ||||
\(178\) | 11.6819i | 0.875597i | ||||||||
\(179\) | 6.63325i | 0.495792i | 0.968787 | + | 0.247896i | \(0.0797392\pi\) | ||||
−0.968787 | + | 0.247896i | \(0.920261\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.28962i | − | 0.0958567i | −0.998851 | − | 0.0479284i | \(-0.984738\pi\) | ||
0.998851 | − | 0.0479284i | \(-0.0152619\pi\) | |||||||
\(182\) | −6.51087 | − | 5.63858i | −0.482618 | − | 0.417960i | ||||
\(183\) | 8.74456 | + | 8.21782i | 0.646417 | + | 0.607479i | ||||
\(184\) | 22.7446 | 1.67675 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.25544 | − | 3.46410i | 0.238700 | − | 0.254000i | ||||
\(187\) | 11.0371i | 0.807114i | ||||||||
\(188\) | −2.23369 | −0.162908 | ||||||||
\(189\) | 2.25544 | + | 13.5615i | 0.164059 | + | 0.986451i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 20.8395i | − | 1.50789i | −0.656935 | − | 0.753947i | \(-0.728147\pi\) | ||
0.656935 | − | 0.753947i | \(-0.271853\pi\) | |||||||
\(192\) | 4.00000 | − | 4.25639i | 0.288675 | − | 0.307178i | ||||
\(193\) | 12.2337 | 0.880600 | 0.440300 | − | 0.897851i | \(-0.354872\pi\) | ||||
0.440300 | + | 0.897851i | \(0.354872\pi\) | |||||||
\(194\) | −8.74456 | −0.627823 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.37228 | + | 9.50744i | 0.0980201 | + | 0.679103i | ||||
\(197\) | − | 15.7359i | − | 1.12114i | −0.828107 | − | 0.560569i | \(-0.810582\pi\) | ||
0.828107 | − | 0.560569i | \(-0.189418\pi\) | |||||||
\(198\) | −0.372281 | − | 5.98844i | −0.0264569 | − | 0.425580i | ||||
\(199\) | 26.8280i | 1.90178i | 0.309524 | + | 0.950892i | \(0.399830\pi\) | ||||
−0.309524 | + | 0.950892i | \(0.600170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.62772 | − | 5.98844i | 0.396949 | − | 0.422392i | ||||
\(202\) | 4.75372i | 0.334471i | ||||||||
\(203\) | 1.62772 | − | 1.87953i | 0.114243 | − | 0.131917i | ||||
\(204\) | −7.11684 | + | 7.57301i | −0.498279 | + | 0.530217i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.97825 | −0.346851 | ||||||||
\(207\) | 25.4891 | − | 1.58457i | 1.77162 | − | 0.110136i | ||||
\(208\) | − | 2.57924i | − | 0.178838i | ||||||
\(209\) | −8.74456 | −0.604874 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.1168 | −0.765315 | −0.382658 | − | 0.923890i | \(-0.624991\pi\) | ||||
−0.382658 | + | 0.923890i | \(0.624991\pi\) | |||||||
\(212\) | − | 2.57924i | − | 0.177143i | ||||||
\(213\) | 0.372281 | + | 0.349857i | 0.0255083 | + | 0.0239718i | ||||
\(214\) | −5.25544 | −0.359254 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.86141 | − | 10.6873i | 0.602942 | − | 0.727176i | ||||
\(217\) | 6.00000 | − | 6.92820i | 0.407307 | − | 0.470317i | ||||
\(218\) | 13.5615i | 0.918497i | ||||||||
\(219\) | −8.74456 | − | 8.21782i | −0.590903 | − | 0.555309i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 17.9653i | − | 1.20848i | ||||||
\(222\) | 6.74456 | + | 6.33830i | 0.452665 | + | 0.425399i | ||||
\(223\) | − | 8.86263i | − | 0.593486i | −0.954957 | − | 0.296743i | \(-0.904100\pi\) | ||
0.954957 | − | 0.296743i | \(-0.0959004\pi\) | |||||||
\(224\) | 10.1168 | − | 11.6819i | 0.675960 | − | 0.780531i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.51087 | −0.167021 | ||||||||
\(227\) | 24.6060 | 1.63316 | 0.816578 | − | 0.577235i | \(-0.195869\pi\) | ||||
0.816578 | + | 0.577235i | \(0.195869\pi\) | |||||||
\(228\) | −6.00000 | − | 5.63858i | −0.397360 | − | 0.373424i | ||||
\(229\) | − | 15.1460i | − | 1.00088i | −0.865772 | − | 0.500439i | \(-0.833172\pi\) | ||
0.865772 | − | 0.500439i | \(-0.166828\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.18614 | − | 11.5070i | −0.0780423 | − | 0.757105i | ||||
\(232\) | −2.51087 | −0.164847 | ||||||||
\(233\) | − | 17.0256i | − | 1.11538i | −0.830049 | − | 0.557691i | \(-0.811688\pi\) | ||
0.830049 | − | 0.557691i | \(-0.188312\pi\) | |||||||
\(234\) | 0.605969 | + | 9.74749i | 0.0396134 | + | 0.637214i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 2.81386 | − | 2.99422i | 0.182780 | − | 0.194495i | ||||
\(238\) | 6.00000 | − | 6.92820i | 0.388922 | − | 0.449089i | ||||
\(239\) | − | 20.8395i | − | 1.34800i | −0.738733 | − | 0.673998i | \(-0.764576\pi\) | ||
0.738733 | − | 0.673998i | \(-0.235424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.4356i | 1.05871i | 0.848399 | + | 0.529357i | \(0.177567\pi\) | ||||
−0.848399 | + | 0.529357i | \(0.822433\pi\) | |||||||
\(242\) | − | 3.66648i | − | 0.235690i | ||||||
\(243\) | 9.18614 | − | 12.5942i | 0.589291 | − | 0.807921i | ||||
\(244\) | − | 9.50744i | − | 0.608652i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.00000 | + | 5.63858i | 0.382546 | + | 0.359503i | ||||
\(247\) | 14.2337 | 0.905668 | ||||||||
\(248\) | −9.25544 | −0.587721 | ||||||||
\(249\) | 20.7446 | − | 22.0742i | 1.31463 | − | 1.39890i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.48913 | 0.346471 | 0.173235 | − | 0.984880i | \(-0.444578\pi\) | ||||
0.173235 | + | 0.984880i | \(0.444578\pi\) | |||||||
\(252\) | 6.60597 | − | 8.66025i | 0.416137 | − | 0.545545i | ||||
\(253\) | −21.4891 | −1.35101 | ||||||||
\(254\) | − | 0.589907i | − | 0.0370141i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.8832 | −0.867697 | ||||||||
\(257\) | 0.510875 | 0.0318675 | 0.0159337 | − | 0.999873i | \(-0.494928\pi\) | ||||
0.0159337 | + | 0.999873i | \(0.494928\pi\) | |||||||
\(258\) | −4.74456 | − | 4.45877i | −0.295384 | − | 0.277591i | ||||
\(259\) | 13.4891 | + | 11.6819i | 0.838173 | + | 0.725880i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.81386 | + | 0.174928i | −0.174174 | + | 0.0108278i | ||||
\(262\) | 4.34896i | 0.268680i | ||||||||
\(263\) | 0.294954i | 0.0181876i | 0.999959 | + | 0.00909381i | \(0.00289469\pi\) | ||||
−0.999959 | + | 0.00909381i | \(0.997105\pi\) | |||||||
\(264\) | −8.00000 | + | 8.51278i | −0.492366 | + | 0.523925i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.48913 | + | 4.75372i | 0.336560 | + | 0.291469i | ||||
\(267\) | 17.4891 | − | 18.6101i | 1.07032 | − | 1.13892i | ||||
\(268\) | −6.51087 | −0.397715 | ||||||||
\(269\) | −2.74456 | −0.167339 | −0.0836695 | − | 0.996494i | \(-0.526664\pi\) | ||||
−0.0836695 | + | 0.996494i | \(0.526664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.75372i | 0.288768i | 0.989522 | + | 0.144384i | \(0.0461201\pi\) | ||||
−0.989522 | + | 0.144384i | \(0.953880\pi\) | |||||||
\(272\) | 2.74456 | 0.166414 | ||||||||
\(273\) | 1.93070 | + | 18.7302i | 0.116851 | + | 1.13360i | ||||
\(274\) | 10.5109 | 0.634985 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −14.7446 | − | 13.8564i | −0.887518 | − | 0.834058i | ||||
\(277\) | −28.2337 | −1.69640 | −0.848199 | − | 0.529678i | \(-0.822313\pi\) | ||||
−0.848199 | + | 0.529678i | \(0.822313\pi\) | |||||||
\(278\) | −14.7446 | −0.884320 | ||||||||
\(279\) | −10.3723 | + | 0.644810i | −0.620972 | + | 0.0386038i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.0627i | 1.67408i | 0.547143 | + | 0.837039i | \(0.315715\pi\) | ||||
−0.547143 | + | 0.837039i | \(0.684285\pi\) | |||||||
\(282\) | −1.62772 | − | 1.52967i | −0.0969292 | − | 0.0910906i | ||||
\(283\) | 0.644810i | 0.0383300i | 0.999816 | + | 0.0191650i | \(0.00610078\pi\) | ||||
−0.999816 | + | 0.0191650i | \(0.993899\pi\) | |||||||
\(284\) | − | 0.404759i | − | 0.0240181i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 8.21782i | − | 0.485930i | ||||||
\(287\) | 12.0000 | + | 10.3923i | 0.708338 | + | 0.613438i | ||||
\(288\) | −17.4891 | + | 1.08724i | −1.03056 | + | 0.0640663i | ||||
\(289\) | 2.11684 | 0.124520 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.9307 | + | 13.0916i | 0.816632 | + | 0.767441i | ||||
\(292\) | 9.50744i | 0.556381i | ||||||||
\(293\) | −10.8832 | −0.635801 | −0.317900 | − | 0.948124i | \(-0.602978\pi\) | ||||
−0.317900 | + | 0.948124i | \(0.602978\pi\) | |||||||
\(294\) | −5.51087 | + | 7.86797i | −0.321401 | + | 0.458869i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 18.0202i | − | 1.04740i | ||||||
\(297\) | −8.37228 | + | 10.0974i | −0.485809 | + | 0.585908i | ||||
\(298\) | 2.51087 | 0.145451 | ||||||||
\(299\) | 34.9783 | 2.02284 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.48913 | − | 8.21782i | −0.546944 | − | 0.473667i | ||||
\(302\) | 1.87953i | 0.108155i | ||||||||
\(303\) | 7.11684 | − | 7.57301i | 0.408852 | − | 0.435058i | ||||
\(304\) | 2.17448i | 0.124715i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −10.3723 | + | 0.644810i | −0.592944 | + | 0.0368613i | ||||
\(307\) | 22.7190i | 1.29664i | 0.761366 | + | 0.648322i | \(0.224529\pi\) | ||||
−0.761366 | + | 0.648322i | \(0.775471\pi\) | |||||||
\(308\) | −6.00000 | + | 6.92820i | −0.341882 | + | 0.394771i | ||||
\(309\) | 7.93070 | + | 7.45299i | 0.451162 | + | 0.423986i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 14.2337 | 0.807118 | 0.403559 | − | 0.914954i | \(-0.367773\pi\) | ||||
0.403559 | + | 0.914954i | \(0.367773\pi\) | |||||||
\(312\) | 13.0217 | − | 13.8564i | 0.737211 | − | 0.784465i | ||||
\(313\) | 5.39853i | 0.305143i | 0.988292 | + | 0.152572i | \(0.0487554\pi\) | ||||
−0.988292 | + | 0.152572i | \(0.951245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.25544 | −0.183133 | ||||||||
\(317\) | − | 1.87953i | − | 0.105565i | −0.998606 | − | 0.0527824i | \(-0.983191\pi\) | ||
0.998606 | − | 0.0527824i | \(-0.0168090\pi\) | |||||||
\(318\) | 1.76631 | − | 1.87953i | 0.0990499 | − | 0.105399i | ||||
\(319\) | 2.37228 | 0.132822 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.37228 | + | 7.86797i | 0.467295 | + | 0.439147i | ||||
\(322\) | 13.4891 | + | 11.6819i | 0.751720 | + | 0.651008i | ||||
\(323\) | 15.1460i | 0.842747i | ||||||||
\(324\) | −12.2554 | + | 1.52967i | −0.680858 | + | 0.0849817i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.33830i | 0.351046i | ||||||||
\(327\) | 20.3030 | − | 21.6043i | 1.12276 | − | 1.19472i | ||||
\(328\) | − | 16.0309i | − | 0.885158i | ||||||
\(329\) | −3.25544 | − | 2.81929i | −0.179478 | − | 0.155433i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | −24.0000 | −1.31717 | ||||||||
\(333\) | −1.25544 | − | 20.1947i | −0.0687975 | − | 1.10666i | ||||
\(334\) | 3.86886i | 0.211695i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.86141 | + | 0.294954i | −0.156103 | + | 0.0160910i | ||||
\(337\) | −16.2337 | −0.884305 | −0.442153 | − | 0.896940i | \(-0.645785\pi\) | ||||
−0.442153 | + | 0.896940i | \(0.645785\pi\) | |||||||
\(338\) | 3.07657i | 0.167344i | ||||||||
\(339\) | 4.00000 | + | 3.75906i | 0.217250 | + | 0.204164i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.74456 | 0.473545 | ||||||||
\(342\) | −0.510875 | − | 8.21782i | −0.0276249 | − | 0.444369i | ||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 12.6766i | 0.683476i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.884861i | 0.0475704i | ||||||||
\(347\) | − | 14.8511i | − | 0.797247i | −0.917115 | − | 0.398624i | \(-0.869488\pi\) | ||
0.917115 | − | 0.398624i | \(-0.130512\pi\) | |||||||
\(348\) | 1.62772 | + | 1.52967i | 0.0872549 | + | 0.0819990i | ||||
\(349\) | 15.1460i | 0.810748i | 0.914151 | + | 0.405374i | \(0.132859\pi\) | ||||
−0.914151 | + | 0.405374i | \(0.867141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 13.6277 | − | 16.4356i | 0.727394 | − | 0.877270i | ||||
\(352\) | 14.7446 | 0.785888 | ||||||||
\(353\) | 25.1168 | 1.33683 | 0.668417 | − | 0.743786i | \(-0.266972\pi\) | ||||
0.668417 | + | 0.743786i | \(0.266972\pi\) | |||||||
\(354\) | 8.74456 | + | 8.21782i | 0.464768 | + | 0.436772i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −20.2337 | −1.07238 | ||||||||
\(357\) | −19.9307 | + | 2.05446i | −1.05484 | + | 0.108733i | ||||
\(358\) | 5.25544 | 0.277758 | ||||||||
\(359\) | − | 16.7306i | − | 0.883007i | −0.897259 | − | 0.441504i | \(-0.854445\pi\) | ||
0.897259 | − | 0.441504i | \(-0.145555\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.00000 | 0.368421 | ||||||||
\(362\) | −1.02175 | −0.0537020 | ||||||||
\(363\) | −5.48913 | + | 5.84096i | −0.288104 | + | 0.306571i | ||||
\(364\) | 9.76631 | − | 11.2772i | 0.511894 | − | 0.591084i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.51087 | − | 6.92820i | 0.340329 | − | 0.362143i | ||||
\(367\) | 35.2858i | 1.84191i | 0.389675 | + | 0.920953i | \(0.372587\pi\) | ||||
−0.389675 | + | 0.920953i | \(0.627413\pi\) | |||||||
\(368\) | 5.34363i | 0.278556i | ||||||||
\(369\) | −1.11684 | − | 17.9653i | −0.0581406 | − | 0.935237i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.25544 | − | 3.75906i | 0.169014 | − | 0.195160i | ||||
\(372\) | 6.00000 | + | 5.63858i | 0.311086 | + | 0.292347i | ||||
\(373\) | 13.2554 | 0.686341 | 0.343170 | − | 0.939273i | \(-0.388499\pi\) | ||||
0.343170 | + | 0.939273i | \(0.388499\pi\) | |||||||
\(374\) | 8.74456 | 0.452171 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.34896i | 0.224281i | ||||||||
\(377\) | −3.86141 | −0.198873 | ||||||||
\(378\) | 10.7446 | − | 1.78695i | 0.552641 | − | 0.0919110i | ||||
\(379\) | −21.4891 | −1.10382 | −0.551911 | − | 0.833903i | \(-0.686101\pi\) | ||||
−0.551911 | + | 0.833903i | \(0.686101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.883156 | + | 0.939764i | −0.0452455 | + | 0.0481456i | ||||
\(382\) | −16.5109 | −0.844770 | ||||||||
\(383\) | 5.48913 | 0.280481 | 0.140241 | − | 0.990117i | \(-0.455212\pi\) | ||||
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(384\) | 11.3723 | + | 10.6873i | 0.580339 | + | 0.545382i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 9.69259i | − | 0.493340i | ||||||
\(387\) | 0.883156 | + | 14.2063i | 0.0448933 | + | 0.722145i | ||||
\(388\) | − | 15.1460i | − | 0.768923i | ||||||
\(389\) | 29.3523i | 1.48822i | 0.668057 | + | 0.744110i | \(0.267126\pi\) | ||||
−0.668057 | + | 0.744110i | \(0.732874\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.2203i | 1.88231i | ||||||||
\(392\) | 18.5109 | − | 2.67181i | 0.934940 | − | 0.134947i | ||||
\(393\) | 6.51087 | − | 6.92820i | 0.328430 | − | 0.349482i | ||||
\(394\) | −12.4674 | −0.628097 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.3723 | − | 0.644810i | 0.521227 | − | 0.0324029i | ||||
\(397\) | − | 26.1831i | − | 1.31409i | −0.753850 | − | 0.657047i | \(-0.771805\pi\) | ||
0.753850 | − | 0.657047i | \(-0.228195\pi\) | |||||||
\(398\) | 21.2554 | 1.06544 | ||||||||
\(399\) | −1.62772 | − | 15.7908i | −0.0814879 | − | 0.790531i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.98844i | 0.299048i | 0.988758 | + | 0.149524i | \(0.0477742\pi\) | ||||
−0.988758 | + | 0.149524i | \(0.952226\pi\) | |||||||
\(402\) | −4.74456 | − | 4.45877i | −0.236637 | − | 0.222383i | ||||
\(403\) | −14.2337 | −0.709030 | ||||||||
\(404\) | −8.23369 | −0.409641 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.48913 | − | 1.28962i | −0.0739040 | − | 0.0640028i | ||||
\(407\) | 17.0256i | 0.843925i | ||||||||
\(408\) | 14.7446 | + | 13.8564i | 0.729965 | + | 0.685994i | ||||
\(409\) | − | 24.6535i | − | 1.21904i | −0.792772 | − | 0.609518i | \(-0.791363\pi\) | ||
0.792772 | − | 0.609518i | \(-0.208637\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.7446 | − | 15.7359i | −0.825948 | − | 0.776196i | ||||
\(412\) | − | 8.62258i | − | 0.424804i | ||||||
\(413\) | 17.4891 | + | 15.1460i | 0.860584 | + | 0.745287i | ||||
\(414\) | −1.25544 | − | 20.1947i | −0.0617014 | − | 0.992515i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −24.0000 | −1.17670 | ||||||||
\(417\) | 23.4891 | + | 22.0742i | 1.15027 | + | 1.08098i | ||||
\(418\) | 6.92820i | 0.338869i | ||||||||
\(419\) | −8.74456 | −0.427200 | −0.213600 | − | 0.976921i | \(-0.568519\pi\) | ||||
−0.213600 | + | 0.976921i | \(0.568519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.6060 | 0.711851 | 0.355926 | − | 0.934514i | \(-0.384166\pi\) | ||||
0.355926 | + | 0.934514i | \(0.384166\pi\) | |||||||
\(422\) | 8.80773i | 0.428754i | ||||||||
\(423\) | 0.302985 | + | 4.87375i | 0.0147316 | + | 0.236970i | ||||
\(424\) | −5.02175 | −0.243878 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0.277187 | − | 0.294954i | 0.0134297 | − | 0.0142906i | ||||
\(427\) | 12.0000 | − | 13.8564i | 0.580721 | − | 0.670559i | ||||
\(428\) | − | 9.10268i | − | 0.439995i | ||||||
\(429\) | −12.3030 | + | 13.0916i | −0.593994 | + | 0.632067i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.0911i | 0.726914i | 0.931611 | + | 0.363457i | \(0.118404\pi\) | ||||
−0.931611 | + | 0.363457i | \(0.881596\pi\) | |||||||
\(432\) | 2.51087 | + | 2.08191i | 0.120805 | + | 0.100166i | ||||
\(433\) | 37.2203i | 1.78869i | 0.447377 | + | 0.894346i | \(0.352358\pi\) | ||||
−0.447377 | + | 0.894346i | \(0.647642\pi\) | |||||||
\(434\) | −5.48913 | − | 4.75372i | −0.263486 | − | 0.228186i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.4891 | −1.12493 | ||||||||
\(437\) | −29.4891 | −1.41066 | ||||||||
\(438\) | −6.51087 | + | 6.92820i | −0.311102 | + | 0.331042i | ||||
\(439\) | 18.6101i | 0.888213i | 0.895974 | + | 0.444106i | \(0.146479\pi\) | ||||
−0.895974 | + | 0.444106i | \(0.853521\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.5584 | − | 4.28384i | 0.978972 | − | 0.203992i | ||||
\(442\) | −14.2337 | −0.677027 | ||||||||
\(443\) | − | 6.63325i | − | 0.315155i | −0.987507 | − | 0.157578i | \(-0.949632\pi\) | ||
0.987507 | − | 0.157578i | \(-0.0503684\pi\) | |||||||
\(444\) | −10.9783 | + | 11.6819i | −0.521005 | + | 0.554400i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.02175 | −0.332489 | ||||||||
\(447\) | −4.00000 | − | 3.75906i | −0.189194 | − | 0.177797i | ||||
\(448\) | −6.74456 | − | 5.84096i | −0.318651 | − | 0.275960i | ||||
\(449\) | 11.6270i | 0.548713i | 0.961628 | + | 0.274357i | \(0.0884648\pi\) | ||||
−0.961628 | + | 0.274357i | \(0.911535\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.1460i | 0.713199i | ||||||||
\(452\) | − | 4.34896i | − | 0.204558i | ||||||
\(453\) | 2.81386 | − | 2.99422i | 0.132207 | − | 0.140681i | ||||
\(454\) | − | 19.4950i | − | 0.914945i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.9783 | + | 11.6819i | −0.514104 | + | 0.547056i | ||||
\(457\) | −12.9783 | −0.607097 | −0.303548 | − | 0.952816i | \(-0.598171\pi\) | ||||
−0.303548 | + | 0.952816i | \(0.598171\pi\) | |||||||
\(458\) | −12.0000 | −0.560723 | ||||||||
\(459\) | 17.4891 | + | 14.5012i | 0.816322 | + | 0.676859i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.74456 | −0.127827 | −0.0639135 | − | 0.997955i | \(-0.520358\pi\) | ||||
−0.0639135 | + | 0.997955i | \(0.520358\pi\) | |||||||
\(462\) | −9.11684 | + | 0.939764i | −0.424154 | + | 0.0437218i | ||||
\(463\) | 32.4674 | 1.50889 | 0.754443 | − | 0.656365i | \(-0.227907\pi\) | ||||
0.754443 | + | 0.656365i | \(0.227907\pi\) | |||||||
\(464\) | − | 0.589907i | − | 0.0273858i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.4891 | −0.624872 | ||||||||
\(467\) | −31.1168 | −1.43992 | −0.719958 | − | 0.694018i | \(-0.755839\pi\) | ||||
−0.719958 | + | 0.694018i | \(0.755839\pi\) | |||||||
\(468\) | −16.8832 | + | 1.04957i | −0.780424 | + | 0.0485164i | ||||
\(469\) | −9.48913 | − | 8.21782i | −0.438167 | − | 0.379464i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 23.3639i | − | 1.07541i | ||||||
\(473\) | − | 11.9769i | − | 0.550697i | ||||||
\(474\) | −2.37228 | − | 2.22938i | −0.108962 | − | 0.102399i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.0000 | + | 10.3923i | 0.550019 | + | 0.476331i | ||||
\(477\) | −5.62772 | + | 0.349857i | −0.257676 | + | 0.0160188i | ||||
\(478\) | −16.5109 | −0.755190 | ||||||||
\(479\) | −41.4891 | −1.89569 | −0.947843 | − | 0.318737i | \(-0.896741\pi\) | ||||
−0.947843 | + | 0.318737i | \(0.896741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 27.7128i | − | 1.26360i | ||||||
\(482\) | 13.0217 | 0.593124 | ||||||||
\(483\) | −4.00000 | − | 38.8048i | −0.182006 | − | 1.76568i | ||||
\(484\) | 6.35053 | 0.288661 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −9.97825 | − | 7.27806i | −0.452623 | − | 0.330139i | ||||
\(487\) | −37.4891 | −1.69879 | −0.849397 | − | 0.527754i | \(-0.823034\pi\) | ||||
−0.849397 | + | 0.527754i | \(0.823034\pi\) | |||||||
\(488\) | −18.5109 | −0.837948 | ||||||||
\(489\) | 9.48913 | − | 10.0974i | 0.429113 | − | 0.456618i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 5.69349i | − | 0.256943i | −0.991713 | − | 0.128472i | \(-0.958993\pi\) | ||
0.991713 | − | 0.128472i | \(-0.0410072\pi\) | |||||||
\(492\) | −9.76631 | + | 10.3923i | −0.440299 | + | 0.468521i | ||||
\(493\) | − | 4.10891i | − | 0.185056i | ||||||
\(494\) | − | 11.2772i | − | 0.507384i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2.17448i | − | 0.0976371i | ||||||
\(497\) | 0.510875 | − | 0.589907i | 0.0229159 | − | 0.0264610i | ||||
\(498\) | −17.4891 | − | 16.4356i | −0.783706 | − | 0.736499i | ||||
\(499\) | 41.3505 | 1.85110 | 0.925552 | − | 0.378620i | \(-0.123601\pi\) | ||||
0.925552 | + | 0.378620i | \(0.123601\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.79211 | − | 6.16337i | 0.258772 | − | 0.275359i | ||||
\(502\) | − | 4.34896i | − | 0.194104i | ||||||
\(503\) | 12.6060 | 0.562072 | 0.281036 | − | 0.959697i | \(-0.409322\pi\) | ||||
0.281036 | + | 0.959697i | \(0.409322\pi\) | |||||||
\(504\) | −16.8614 | − | 12.8617i | −0.751067 | − | 0.572907i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.0256i | 0.756878i | ||||||||
\(507\) | 4.60597 | − | 4.90120i | 0.204558 | − | 0.217670i | ||||
\(508\) | 1.02175 | 0.0453328 | ||||||||
\(509\) | 3.76631 | 0.166939 | 0.0834694 | − | 0.996510i | \(-0.473400\pi\) | ||||
0.0834694 | + | 0.996510i | \(0.473400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | + | 13.8564i | −0.530849 | + | 0.612971i | ||||
\(512\) | − | 7.02078i | − | 0.310277i | ||||||
\(513\) | −11.4891 | + | 13.8564i | −0.507257 | + | 0.611775i | ||||
\(514\) | − | 0.404759i | − | 0.0178532i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.72281 | − | 8.21782i | 0.339978 | − | 0.361770i | ||||
\(517\) | − | 4.10891i | − | 0.180710i | ||||||
\(518\) | 9.25544 | − | 10.6873i | 0.406661 | − | 0.469571i | ||||
\(519\) | 1.32473 | − | 1.40965i | 0.0581494 | − | 0.0618766i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.4674 | 1.51004 | 0.755022 | − | 0.655700i | \(-0.227626\pi\) | ||||
0.755022 | + | 0.655700i | \(0.227626\pi\) | |||||||
\(522\) | 0.138593 | + | 2.22938i | 0.00606607 | + | 0.0975775i | ||||
\(523\) | 10.3923i | 0.454424i | 0.973845 | + | 0.227212i | \(0.0729610\pi\) | ||||
−0.973845 | + | 0.227212i | \(0.927039\pi\) | |||||||
\(524\) | −7.53262 | −0.329064 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.233688 | 0.0101893 | ||||||||
\(527\) | − | 15.1460i | − | 0.659771i | ||||||
\(528\) | −2.00000 | − | 1.87953i | −0.0870388 | − | 0.0817959i | ||||
\(529\) | −49.4674 | −2.15076 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.62772 | − | 26.1831i | −0.0706370 | − | 1.13625i | ||||
\(532\) | −8.23369 | + | 9.50744i | −0.356976 | + | 0.412200i | ||||
\(533\) | − | 24.6535i | − | 1.06786i | ||||||
\(534\) | −14.7446 | − | 13.8564i | −0.638060 | − | 0.599625i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.6766i | 0.547545i | ||||||||
\(537\) | −8.37228 | − | 7.86797i | −0.361291 | − | 0.339528i | ||||
\(538\) | 2.17448i | 0.0937485i | ||||||||
\(539\) | −17.4891 | + | 2.52434i | −0.753310 | + | 0.108731i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.3723 | 1.04785 | 0.523923 | − | 0.851766i | \(-0.324468\pi\) | ||||
0.523923 | + | 0.851766i | \(0.324468\pi\) | |||||||
\(542\) | 3.76631 | 0.161777 | ||||||||
\(543\) | 1.62772 | + | 1.52967i | 0.0698521 | + | 0.0656445i | ||||
\(544\) | − | 25.5383i | − | 1.09495i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.8397 | − | 1.52967i | 0.635079 | − | 0.0654639i | ||||
\(547\) | 2.97825 | 0.127341 | 0.0636704 | − | 0.997971i | \(-0.479719\pi\) | ||||
0.0636704 | + | 0.997971i | \(0.479719\pi\) | |||||||
\(548\) | 18.2054i | 0.777695i | ||||||||
\(549\) | −20.7446 | + | 1.28962i | −0.885356 | + | 0.0550397i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.25544 | 0.138686 | ||||||||
\(552\) | −26.9783 | + | 28.7075i | −1.14827 | + | 1.22187i | ||||
\(553\) | −4.74456 | − | 4.10891i | −0.201759 | − | 0.174729i | ||||
\(554\) | 22.3692i | 0.950376i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 25.5383i | − | 1.08307i | ||||||
\(557\) | 17.6155i | 0.746391i | 0.927753 | + | 0.373196i | \(0.121738\pi\) | ||||
−0.927753 | + | 0.373196i | \(0.878262\pi\) | |||||||
\(558\) | 0.510875 | + | 8.21782i | 0.0216271 | + | 0.347888i | ||||
\(559\) | 19.4950i | 0.824550i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −13.9307 | − | 13.0916i | −0.588155 | − | 0.552727i | ||||
\(562\) | 22.2337 | 0.937872 | ||||||||
\(563\) | −17.4891 | −0.737079 | −0.368539 | − | 0.929612i | \(-0.620142\pi\) | ||||
−0.368539 | + | 0.929612i | \(0.620142\pi\) | |||||||
\(564\) | 2.64947 | − | 2.81929i | 0.111563 | − | 0.118714i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.510875 | 0.0214737 | ||||||||
\(567\) | −19.7921 | − | 13.2390i | −0.831190 | − | 0.555988i | ||||
\(568\) | −0.788061 | −0.0330663 | ||||||||
\(569\) | 23.9538i | 1.00419i | 0.864811 | + | 0.502097i | \(0.167438\pi\) | ||||
−0.864811 | + | 0.502097i | \(0.832562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.00000 | −0.167395 | −0.0836974 | − | 0.996491i | \(-0.526673\pi\) | ||||
−0.0836974 | + | 0.996491i | \(0.526673\pi\) | |||||||
\(572\) | 14.2337 | 0.595140 | ||||||||
\(573\) | 26.3030 | + | 24.7186i | 1.09882 | + | 1.03263i | ||||
\(574\) | 8.23369 | − | 9.50744i | 0.343667 | − | 0.396833i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.627719 | + | 10.0974i | 0.0261549 | + | 0.420723i | ||||
\(577\) | − | 2.81929i | − | 0.117369i | −0.998277 | − | 0.0586843i | \(-0.981309\pi\) | ||
0.998277 | − | 0.0586843i | \(-0.0186905\pi\) | |||||||
\(578\) | − | 1.67715i | − | 0.0697602i | ||||||
\(579\) | −14.5109 | + | 15.4410i | −0.603051 | + | 0.641705i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −34.9783 | − | 30.2921i | −1.45114 | − | 1.25673i | ||||
\(582\) | 10.3723 | − | 11.0371i | 0.429945 | − | 0.457503i | ||||
\(583\) | 4.74456 | 0.196500 | ||||||||
\(584\) | 18.5109 | 0.765985 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.62258i | 0.356196i | ||||||||
\(587\) | 17.4891 | 0.721853 | 0.360927 | − | 0.932594i | \(-0.382460\pi\) | ||||
0.360927 | + | 0.932594i | \(0.382460\pi\) | |||||||
\(588\) | −13.6277 | − | 9.54511i | −0.561998 | − | 0.393634i | ||||
\(589\) | 12.0000 | 0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.8614 | + | 18.6650i | 0.816989 | + | 0.767777i | ||||
\(592\) | 4.23369 | 0.174004 | ||||||||
\(593\) | 4.37228 | 0.179548 | 0.0897740 | − | 0.995962i | \(-0.471386\pi\) | ||||
0.0897740 | + | 0.995962i | \(0.471386\pi\) | |||||||
\(594\) | 8.00000 | + | 6.63325i | 0.328244 | + | 0.272166i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.34896i | 0.178140i | ||||||||
\(597\) | −33.8614 | − | 31.8217i | −1.38586 | − | 1.30238i | ||||
\(598\) | − | 27.7128i | − | 1.13326i | ||||||
\(599\) | − | 34.6959i | − | 1.41764i | −0.705391 | − | 0.708818i | \(-0.749229\pi\) | ||
0.705391 | − | 0.708818i | \(-0.250771\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 22.0742i | − | 0.900427i | −0.892921 | − | 0.450213i | \(-0.851348\pi\) | ||
0.892921 | − | 0.450213i | \(-0.148652\pi\) | |||||||
\(602\) | −6.51087 | + | 7.51811i | −0.265363 | + | 0.306415i | ||||
\(603\) | 0.883156 | + | 14.2063i | 0.0359649 | + | 0.578524i | ||||
\(604\) | −3.25544 | −0.132462 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.00000 | − | 5.63858i | −0.243733 | − | 0.229052i | ||||
\(607\) | − | 8.86263i | − | 0.359723i | −0.983692 | − | 0.179862i | \(-0.942435\pi\) | ||
0.983692 | − | 0.179862i | \(-0.0575650\pi\) | |||||||
\(608\) | 20.2337 | 0.820584 | ||||||||
\(609\) | 0.441578 | + | 4.28384i | 0.0178936 | + | 0.173590i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.68815i | 0.270574i | ||||||||
\(612\) | −1.11684 | − | 17.9653i | −0.0451457 | − | 0.726205i | ||||
\(613\) | 27.4891 | 1.11028 | 0.555138 | − | 0.831758i | \(-0.312666\pi\) | ||||
0.555138 | + | 0.831758i | \(0.312666\pi\) | |||||||
\(614\) | 18.0000 | 0.726421 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.4891 | + | 11.6819i | 0.543492 | + | 0.470678i | ||||
\(617\) | 24.5437i | 0.988091i | 0.869436 | + | 0.494045i | \(0.164482\pi\) | ||||
−0.869436 | + | 0.494045i | \(0.835518\pi\) | |||||||
\(618\) | 5.90491 | − | 6.28339i | 0.237530 | − | 0.252755i | ||||
\(619\) | − | 18.6101i | − | 0.748004i | −0.927428 | − | 0.374002i | \(-0.877985\pi\) | ||
0.927428 | − | 0.374002i | \(-0.122015\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.2337 | + | 34.0511i | −1.13298 | + | 1.36642i | ||||
\(622\) | − | 11.2772i | − | 0.452173i | ||||||
\(623\) | −29.4891 | − | 25.5383i | −1.18146 | − | 1.02317i | ||||
\(624\) | 3.25544 | + | 3.05934i | 0.130322 | + | 0.122472i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.27719 | 0.170951 | ||||||||
\(627\) | 10.3723 | − | 11.0371i | 0.414229 | − | 0.440780i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.4891 | 1.17581 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.1168 | −0.920267 | −0.460134 | − | 0.887850i | \(-0.652198\pi\) | ||||
−0.460134 | + | 0.887850i | \(0.652198\pi\) | |||||||
\(632\) | 6.33830i | 0.252124i | ||||||||
\(633\) | 13.1861 | − | 14.0313i | 0.524102 | − | 0.557695i | ||||
\(634\) | −1.48913 | −0.0591407 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.25544 | + | 3.05934i | 0.129086 | + | 0.121311i | ||||
\(637\) | 28.4674 | − | 4.10891i | 1.12792 | − | 0.162801i | ||||
\(638\) | − | 1.87953i | − | 0.0744112i | ||||||
\(639\) | −0.883156 | + | 0.0549029i | −0.0349371 | + | 0.00217192i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 36.6303i | − | 1.44681i | −0.690423 | − | 0.723406i | \(-0.742576\pi\) | ||
0.690423 | − | 0.723406i | \(-0.257424\pi\) | |||||||
\(642\) | 6.23369 | − | 6.63325i | 0.246024 | − | 0.261793i | ||||
\(643\) | − | 10.1523i | − | 0.400366i | −0.979759 | − | 0.200183i | \(-0.935846\pi\) | ||
0.979759 | − | 0.200183i | \(-0.0641536\pi\) | |||||||
\(644\) | −20.2337 | + | 23.3639i | −0.797319 | + | 0.920665i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 12.0000 | 0.471769 | 0.235884 | − | 0.971781i | \(-0.424201\pi\) | ||||
0.235884 | + | 0.971781i | \(0.424201\pi\) | |||||||
\(648\) | 2.97825 | + | 23.8612i | 0.116997 | + | 0.937356i | ||||
\(649\) | 22.0742i | 0.866489i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.62772 | + | 15.7908i | 0.0637953 | + | 0.618892i | ||||
\(652\) | −10.9783 | −0.429941 | ||||||||
\(653\) | 39.6897i | 1.55318i | 0.630008 | + | 0.776589i | \(0.283052\pi\) | ||||
−0.630008 | + | 0.776589i | \(0.716948\pi\) | |||||||
\(654\) | −17.1168 | − | 16.0858i | −0.669322 | − | 0.629004i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.76631 | 0.147050 | ||||||||
\(657\) | 20.7446 | − | 1.28962i | 0.809322 | − | 0.0503129i | ||||
\(658\) | −2.23369 | + | 2.57924i | −0.0870782 | + | 0.100549i | ||||
\(659\) | − | 35.9855i | − | 1.40180i | −0.713261 | − | 0.700899i | \(-0.752782\pi\) | ||
0.713261 | − | 0.700899i | \(-0.247218\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.92820i | 0.269476i | 0.990881 | + | 0.134738i | \(0.0430193\pi\) | ||||
−0.990881 | + | 0.134738i | \(0.956981\pi\) | |||||||
\(662\) | 3.16915i | 0.123172i | ||||||||
\(663\) | 22.6753 | + | 21.3094i | 0.880634 | + | 0.827588i | ||||
\(664\) | 46.7277i | 1.81339i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −16.0000 | + | 0.994667i | −0.619987 | + | 0.0385426i | ||||
\(667\) | 8.00000 | 0.309761 | ||||||||
\(668\) | −6.70106 | −0.259272 | ||||||||
\(669\) | 11.1861 | + | 10.5123i | 0.432481 | + | 0.406430i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.4891 | 0.675160 | ||||||||
\(672\) | 2.74456 | + | 26.6256i | 0.105874 | + | 1.02710i | ||||
\(673\) | 12.2337 | 0.471574 | 0.235787 | − | 0.971805i | \(-0.424233\pi\) | ||||
0.235787 | + | 0.971805i | \(0.424233\pi\) | |||||||
\(674\) | 12.8617i | 0.495416i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.32878 | −0.204953 | ||||||||
\(677\) | −18.6060 | −0.715085 | −0.357543 | − | 0.933897i | \(-0.616385\pi\) | ||||
−0.357543 | + | 0.933897i | \(0.616385\pi\) | |||||||
\(678\) | 2.97825 | − | 3.16915i | 0.114379 | − | 0.121710i | ||||
\(679\) | 19.1168 | − | 22.0742i | 0.733637 | − | 0.847131i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.1861 | + | 31.0569i | −1.11842 | + | 1.19010i | ||||
\(682\) | − | 6.92820i | − | 0.265295i | ||||||
\(683\) | 34.4559i | 1.31842i | 0.751960 | + | 0.659209i | \(0.229109\pi\) | ||||
−0.751960 | + | 0.659209i | \(0.770891\pi\) | |||||||
\(684\) | 14.2337 | − | 0.884861i | 0.544239 | − | 0.0338335i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.3505 | + | 7.92287i | 0.471545 | + | 0.302497i | ||||
\(687\) | 19.1168 | + | 17.9653i | 0.729353 | + | 0.685420i | ||||
\(688\) | −2.97825 | −0.113545 | ||||||||
\(689\) | −7.72281 | −0.294216 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 21.1894i | − | 0.806082i | −0.915182 | − | 0.403041i | \(-0.867953\pi\) | ||
0.915182 | − | 0.403041i | \(-0.132047\pi\) | |||||||
\(692\) | −1.53262 | −0.0582616 | ||||||||
\(693\) | 15.9307 | + | 12.1518i | 0.605157 | + | 0.461609i | ||||
\(694\) | −11.7663 | −0.446643 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.97825 | − | 3.16915i | 0.112890 | − | 0.120126i | ||||
\(697\) | 26.2337 | 0.993672 | ||||||||
\(698\) | 12.0000 | 0.454207 | ||||||||
\(699\) | 21.4891 | + | 20.1947i | 0.812793 | + | 0.763834i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 42.5090i | − | 1.60554i | −0.596287 | − | 0.802771i | \(-0.703358\pi\) | ||
0.596287 | − | 0.802771i | \(-0.296642\pi\) | |||||||
\(702\) | −13.0217 | − | 10.7971i | −0.491474 | − | 0.407509i | ||||
\(703\) | 23.3639i | 0.881184i | ||||||||
\(704\) | − | 8.51278i | − | 0.320837i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 19.8997i | − | 0.748937i | ||||||
\(707\) | −12.0000 | − | 10.3923i | −0.451306 | − | 0.390843i | ||||
\(708\) | −14.2337 | + | 15.1460i | −0.534935 | + | 0.569223i | ||||
\(709\) | 6.88316 | 0.258502 | 0.129251 | − | 0.991612i | \(-0.458743\pi\) | ||||
0.129251 | + | 0.991612i | \(0.458743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.441578 | + | 7.10313i | 0.0165605 | + | 0.266388i | ||||
\(712\) | 39.3947i | 1.47638i | ||||||||
\(713\) | 29.4891 | 1.10438 | ||||||||
\(714\) | 1.62772 | + | 15.7908i | 0.0609158 | + | 0.590957i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.10268i | 0.340183i | ||||||||
\(717\) | 26.3030 | + | 24.7186i | 0.982303 | + | 0.923133i | ||||
\(718\) | −13.2554 | −0.494689 | ||||||||
\(719\) | 28.4674 | 1.06165 | 0.530827 | − | 0.847480i | \(-0.321881\pi\) | ||||
0.530827 | + | 0.847480i | \(0.321881\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8832 | − | 12.5668i | 0.405310 | − | 0.468012i | ||||
\(722\) | − | 5.54601i | − | 0.206401i | ||||||
\(723\) | −20.7446 | − | 19.4950i | −0.771499 | − | 0.725026i | ||||
\(724\) | − | 1.76972i | − | 0.0657712i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.62772 | + | 4.34896i | 0.171751 | + | 0.161405i | ||||
\(727\) | 3.46410i | 0.128476i | 0.997935 | + | 0.0642382i | \(0.0204617\pi\) | ||||
−0.997935 | + | 0.0642382i | \(0.979538\pi\) | |||||||
\(728\) | −21.9565 | − | 19.0149i | −0.813762 | − | 0.704739i | ||||
\(729\) | 5.00000 | + | 26.5330i | 0.185185 | + | 0.982704i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.7446 | −0.767265 | ||||||||
\(732\) | 12.0000 | + | 11.2772i | 0.443533 | + | 0.416816i | ||||
\(733\) | − | 40.0395i | − | 1.47889i | −0.673215 | − | 0.739447i | \(-0.735087\pi\) | ||
0.673215 | − | 0.739447i | \(-0.264913\pi\) | |||||||
\(734\) | 27.9565 | 1.03189 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 49.7228 | 1.83281 | ||||||||
\(737\) | − | 11.9769i | − | 0.441174i | ||||||
\(738\) | −14.2337 | + | 0.884861i | −0.523949 | + | 0.0325722i | ||||
\(739\) | −14.3723 | −0.528693 | −0.264346 | − | 0.964428i | \(-0.585156\pi\) | ||||
−0.264346 | + | 0.964428i | \(0.585156\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16.8832 | + | 17.9653i | −0.620218 | + | 0.659972i | ||||
\(742\) | −2.97825 | − | 2.57924i | −0.109335 | − | 0.0946869i | ||||
\(743\) | − | 16.1407i | − | 0.592145i | −0.955166 | − | 0.296072i | \(-0.904323\pi\) | ||
0.955166 | − | 0.296072i | \(-0.0956769\pi\) | |||||||
\(744\) | 10.9783 | − | 11.6819i | 0.402482 | − | 0.428280i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 10.5021i | − | 0.384510i | ||||||
\(747\) | 3.25544 | + | 52.3663i | 0.119110 | + | 1.91598i | ||||
\(748\) | 15.1460i | 0.553794i | ||||||||
\(749\) | 11.4891 | − | 13.2665i | 0.419804 | − | 0.484747i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.3505 | 1.07102 | 0.535508 | − | 0.844530i | \(-0.320120\pi\) | ||||
0.535508 | + | 0.844530i | \(0.320120\pi\) | |||||||
\(752\) | −1.02175 | −0.0372594 | ||||||||
\(753\) | −6.51087 | + | 6.92820i | −0.237269 | + | 0.252478i | ||||
\(754\) | 3.05934i | 0.111415i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.09509 | + | 18.6101i | 0.112568 | + | 0.676844i | ||||
\(757\) | 19.7663 | 0.718419 | 0.359209 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359209 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(758\) | 17.0256i | 0.618396i | ||||||||
\(759\) | 25.4891 | − | 27.1229i | 0.925197 | − | 0.984499i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8.23369 | −0.298471 | −0.149235 | − | 0.988802i | \(-0.547681\pi\) | ||||
−0.149235 | + | 0.988802i | \(0.547681\pi\) | |||||||
\(762\) | 0.744563 | + | 0.699713i | 0.0269727 | + | 0.0253479i | ||||
\(763\) | −34.2337 | − | 29.6472i | −1.23934 | − | 1.07330i | ||||
\(764\) | − | 28.5977i | − | 1.03463i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 4.34896i | − | 0.157134i | ||||||
\(767\) | − | 35.9306i | − | 1.29738i | ||||||
\(768\) | 16.4674 | − | 17.5229i | 0.594215 | − | 0.632303i | ||||
\(769\) | 38.5099i | 1.38870i | 0.719637 | + | 0.694351i | \(0.244308\pi\) | ||||
−0.719637 | + | 0.694351i | \(0.755692\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.605969 | + | 0.644810i | −0.0218234 | + | 0.0232223i | ||||
\(772\) | 16.7881 | 0.604216 | ||||||||
\(773\) | −52.3723 | −1.88370 | −0.941850 | − | 0.336034i | \(-0.890914\pi\) | ||||
−0.941850 | + | 0.336034i | \(0.890914\pi\) | |||||||
\(774\) | 11.2554 | − | 0.699713i | 0.404568 | − | 0.0251507i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29.4891 | −1.05860 | ||||||||
\(777\) | −30.7446 | + | 3.16915i | −1.10296 | + | 0.113693i | ||||
\(778\) | 23.2554 | 0.833748 | ||||||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.744563 | 0.0266425 | ||||||||
\(782\) | 29.4891 | 1.05453 | ||||||||
\(783\) | 3.11684 | − | 3.75906i | 0.111387 | − | 0.134338i | ||||
\(784\) | 0.627719 | + | 4.34896i | 0.0224185 | + | 0.155320i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5.48913 | − | 5.15848i | −0.195791 | − | 0.183997i | ||||
\(787\) | 3.22405i | 0.114925i | 0.998348 | + | 0.0574625i | \(0.0183010\pi\) | ||||
−0.998348 | + | 0.0574625i | \(0.981699\pi\) | |||||||
\(788\) | − | 21.5941i | − | 0.769259i | ||||||
\(789\) | −0.372281 | − | 0.349857i | −0.0132536 | − | 0.0124552i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.48913 | − | 6.33830i | 0.195171 | − | 0.225364i | ||||
\(792\) | −1.25544 | − | 20.1947i | −0.0446100 | − | 0.717588i | ||||
\(793\) | −28.4674 | −1.01091 | ||||||||
\(794\) | −20.7446 | −0.736197 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.8155i | 1.30489i | ||||||||
\(797\) | −14.1386 | −0.500815 | −0.250407 | − | 0.968141i | \(-0.580565\pi\) | ||||
−0.250407 | + | 0.968141i | \(0.580565\pi\) | |||||||
\(798\) | −12.5109 | + | 1.28962i | −0.442880 | + | 0.0456521i | ||||
\(799\) | −7.11684 | −0.251776 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.74456 | + | 44.1485i | 0.0969744 | + | 1.55991i | ||||
\(802\) | 4.74456 | 0.167536 | ||||||||
\(803\) | −17.4891 | −0.617178 | ||||||||
\(804\) | 7.72281 | − | 8.21782i | 0.272363 | − | 0.289820i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 11.2772i | 0.397221i | ||||||||
\(807\) | 3.25544 | − | 3.46410i | 0.114597 | − | 0.121942i | ||||
\(808\) | 16.0309i | 0.563965i | ||||||||
\(809\) | − | 13.5065i | − | 0.474865i | −0.971404 | − | 0.237433i | \(-0.923694\pi\) | ||
0.971404 | − | 0.237433i | \(-0.0763059\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 18.6101i | − | 0.653490i | −0.945113 | − | 0.326745i | \(-0.894048\pi\) | ||
0.945113 | − | 0.326745i | \(-0.105952\pi\) | |||||||
\(812\) | 2.23369 | − | 2.57924i | 0.0783871 | − | 0.0905136i | ||||
\(813\) | −6.00000 | − | 5.63858i | −0.210429 | − | 0.197754i | ||||
\(814\) | 13.4891 | 0.472794 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.25544 | + | 3.46410i | −0.113963 | + | 0.121268i | ||||
\(817\) | − | 16.4356i | − | 0.575011i | ||||||
\(818\) | −19.5326 | −0.682942 | ||||||||
\(819\) | −25.9307 | − | 19.7797i | −0.906092 | − | 0.691159i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 34.9909i | 1.22119i | 0.791943 | + | 0.610595i | \(0.209070\pi\) | ||||
−0.791943 | + | 0.610595i | \(0.790930\pi\) | |||||||
\(822\) | −12.4674 | + | 13.2665i | −0.434850 | + | 0.462722i | ||||
\(823\) | 13.7663 | 0.479863 | 0.239932 | − | 0.970790i | \(-0.422875\pi\) | ||||
0.239932 | + | 0.970790i | \(0.422875\pi\) | |||||||
\(824\) | −16.7881 | −0.584840 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | − | 13.8564i | 0.417533 | − | 0.482126i | ||||
\(827\) | − | 14.8511i | − | 0.516422i | −0.966088 | − | 0.258211i | \(-0.916867\pi\) | ||
0.966088 | − | 0.258211i | \(-0.0831330\pi\) | |||||||
\(828\) | 34.9783 | − | 2.17448i | 1.21558 | − | 0.0755684i | ||||
\(829\) | − | 12.5668i | − | 0.436463i | −0.975897 | − | 0.218231i | \(-0.929971\pi\) | ||
0.975897 | − | 0.218231i | \(-0.0700287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.4891 | − | 35.6357i | 1.16172 | − | 1.23619i | ||||
\(832\) | 13.8564i | 0.480384i | ||||||||
\(833\) | 4.37228 | + | 30.2921i | 0.151491 | + | 1.04956i | ||||
\(834\) | 17.4891 | − | 18.6101i | 0.605599 | − | 0.644416i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −12.0000 | −0.415029 | ||||||||
\(837\) | 11.4891 | − | 13.8564i | 0.397122 | − | 0.478947i | ||||
\(838\) | 6.92820i | 0.239331i | ||||||||
\(839\) | 30.5109 | 1.05335 | 0.526676 | − | 0.850066i | \(-0.323438\pi\) | ||||
0.526676 | + | 0.850066i | \(0.323438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.1168 | 0.969546 | ||||||||
\(842\) | − | 11.5721i | − | 0.398802i | ||||||
\(843\) | −35.4198 | − | 33.2863i | −1.21992 | − | 1.14644i | ||||
\(844\) | −15.2554 | −0.525114 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.86141 | − | 0.240051i | 0.132758 | − | 0.00825312i | ||||
\(847\) | 9.25544 | + | 8.01544i | 0.318021 | + | 0.275414i | ||||
\(848\) | − | 1.17981i | − | 0.0405150i | ||||||
\(849\) | −0.813859 | − | 0.764836i | −0.0279316 | − | 0.0262491i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 57.4150i | 1.96816i | ||||||||
\(852\) | 0.510875 | + | 0.480102i | 0.0175023 | + | 0.0164480i | ||||
\(853\) | 32.8713i | 1.12549i | 0.826630 | + | 0.562746i | \(0.190255\pi\) | ||||
−0.826630 | + | 0.562746i | \(0.809745\pi\) | |||||||
\(854\) | −10.9783 | − | 9.50744i | −0.375668 | − | 0.325338i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −17.7228 | −0.605753 | ||||||||
\(857\) | 46.4674 | 1.58730 | 0.793648 | − | 0.608378i | \(-0.208179\pi\) | ||||
0.793648 | + | 0.608378i | \(0.208179\pi\) | |||||||
\(858\) | 10.3723 | + | 9.74749i | 0.354104 | + | 0.332774i | ||||
\(859\) | 14.2612i | 0.486585i | 0.969953 | + | 0.243292i | \(0.0782274\pi\) | ||||
−0.969953 | + | 0.243292i | \(0.921773\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.3505 | + | 2.81929i | −0.932104 | + | 0.0960812i | ||||
\(862\) | 11.9565 | 0.407240 | ||||||||
\(863\) | − | 41.2743i | − | 1.40499i | −0.711688 | − | 0.702496i | \(-0.752069\pi\) | ||
0.711688 | − | 0.702496i | \(-0.247931\pi\) | |||||||
\(864\) | 19.3723 | − | 23.3639i | 0.659058 | − | 0.794854i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 29.4891 | 1.00208 | ||||||||
\(867\) | −2.51087 | + | 2.67181i | −0.0852738 | + | 0.0907396i | ||||
\(868\) | 8.23369 | − | 9.50744i | 0.279470 | − | 0.322704i | ||||
\(869\) | − | 5.98844i | − | 0.203144i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.4950i | 0.660563i | ||||||||
\(872\) | 45.7330i | 1.54872i | ||||||||
\(873\) | −33.0475 | + | 2.05446i | −1.11849 | + | 0.0695328i | ||||
\(874\) | 23.3639i | 0.790294i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | − | 11.2772i | −0.405442 | − | 0.381020i | ||||
\(877\) | 38.4674 | 1.29895 | 0.649475 | − | 0.760383i | \(-0.274989\pi\) | ||||
0.649475 | + | 0.760383i | \(0.274989\pi\) | |||||||
\(878\) | 14.7446 | 0.497605 | ||||||||
\(879\) | 12.9090 | − | 13.7364i | 0.435408 | − | 0.463317i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −32.2337 | −1.08598 | −0.542990 | − | 0.839739i | \(-0.682708\pi\) | ||||
−0.542990 | + | 0.839739i | \(0.682708\pi\) | |||||||
\(882\) | −3.39403 | − | 16.2882i | −0.114283 | − | 0.548451i | ||||
\(883\) | −49.4891 | −1.66544 | −0.832721 | − | 0.553693i | \(-0.813218\pi\) | ||||
−0.832721 | + | 0.553693i | \(0.813218\pi\) | |||||||
\(884\) | − | 24.6535i | − | 0.829186i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.25544 | −0.176560 | ||||||||
\(887\) | 18.5109 | 0.621534 | 0.310767 | − | 0.950486i | \(-0.399414\pi\) | ||||
0.310767 | + | 0.950486i | \(0.399414\pi\) | |||||||
\(888\) | 22.7446 | + | 21.3745i | 0.763258 | + | 0.717282i | ||||
\(889\) | 1.48913 | + | 1.28962i | 0.0499437 | + | 0.0432525i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.81386 | − | 22.5441i | −0.0942678 | − | 0.755256i | ||||
\(892\) | − | 12.1620i | − | 0.407215i | ||||||
\(893\) | − | 5.63858i | − | 0.188688i | ||||||
\(894\) | −2.97825 | + | 3.16915i | −0.0996076 | + | 0.105992i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 15.6060 | − | 18.0202i | 0.521359 | − | 0.602013i | ||||
\(897\) | −41.4891 | + | 44.1485i | −1.38528 | + | 1.47407i | ||||
\(898\) | 9.21194 | 0.307406 | ||||||||
\(899\) | −3.25544 | −0.108575 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 8.21782i | − | 0.273775i | ||||||
\(902\) | 12.0000 | 0.399556 | ||||||||
\(903\) | 21.6277 | − | 2.22938i | 0.719725 | − | 0.0741893i | ||||
\(904\) | −8.46738 | −0.281621 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2.37228 | − | 2.22938i | −0.0788138 | − | 0.0740663i | ||||
\(907\) | −8.00000 | −0.265636 | −0.132818 | − | 0.991140i | \(-0.542403\pi\) | ||||
−0.132818 | + | 0.991140i | \(0.542403\pi\) | |||||||
\(908\) | 33.7663 | 1.12057 | ||||||||
\(909\) | 1.11684 | + | 17.9653i | 0.0370434 | + | 0.595872i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 2.87419i | − | 0.0952263i | −0.998866 | − | 0.0476132i | \(-0.984839\pi\) | ||
0.998866 | − | 0.0476132i | \(-0.0151615\pi\) | |||||||
\(912\) | −2.74456 | − | 2.57924i | −0.0908816 | − | 0.0854072i | ||||
\(913\) | − | 44.1485i | − | 1.46110i | ||||||
\(914\) | 10.2825i | 0.340115i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 20.7846i | − | 0.686743i | ||||||
\(917\) | −10.9783 | − | 9.50744i | −0.362534 | − | 0.313963i | ||||
\(918\) | 11.4891 | − | 13.8564i | 0.379198 | − | 0.457330i | ||||
\(919\) | −5.62772 | −0.185641 | −0.0928207 | − | 0.995683i | \(-0.529588\pi\) | ||||
−0.0928207 | + | 0.995683i | \(0.529588\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.6753 | − | 26.9480i | −0.944882 | − | 0.887966i | ||||
\(922\) | 2.17448i | 0.0716127i | ||||||||
\(923\) | −1.21194 | −0.0398914 | ||||||||
\(924\) | −1.62772 | − | 15.7908i | −0.0535480 | − | 0.519480i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 25.7235i | − | 0.845326i | ||||||
\(927\) | −18.8139 | + | 1.16959i | −0.617928 | + | 0.0384145i | ||||
\(928\) | −5.48913 | −0.180189 | ||||||||
\(929\) | −52.9783 | −1.73816 | −0.869080 | − | 0.494672i | \(-0.835288\pi\) | ||||
−0.869080 | + | 0.494672i | \(0.835288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.0000 | + | 3.46410i | −0.786568 | + | 0.113531i | ||||
\(932\) | − | 23.3639i | − | 0.765308i | ||||||
\(933\) | −16.8832 | + | 17.9653i | −0.552730 | + | 0.588158i | ||||
\(934\) | 24.6535i | 0.806686i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.04350 | + | 32.8713i | 0.0667938 | + | 1.07443i | ||||
\(937\) | − | 0.240051i | − | 0.00784212i | −0.999992 | − | 0.00392106i | \(-0.998752\pi\) | ||
0.999992 | − | 0.00392106i | \(-0.00124811\pi\) | |||||||
\(938\) | −6.51087 | + | 7.51811i | −0.212588 | + | 0.245475i | ||||
\(939\) | −6.81386 | − | 6.40342i | −0.222362 | − | 0.208968i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.7446 | 1.26304 | 0.631518 | − | 0.775361i | \(-0.282432\pi\) | ||||
0.631518 | + | 0.775361i | \(0.282432\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 51.0767i | 1.66329i | ||||||||
\(944\) | 5.48913 | 0.178656 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.48913 | −0.308518 | ||||||||
\(947\) | 34.9360i | 1.13527i | 0.823282 | + | 0.567633i | \(0.192141\pi\) | ||||
−0.823282 | + | 0.567633i | \(0.807859\pi\) | |||||||
\(948\) | 3.86141 | − | 4.10891i | 0.125413 | − | 0.133451i | ||||
\(949\) | 28.4674 | 0.924090 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.37228 | + | 2.22938i | 0.0769265 | + | 0.0722927i | ||||
\(952\) | 20.2337 | − | 23.3639i | 0.655778 | − | 0.757227i | ||||
\(953\) | 7.62792i | 0.247092i | 0.992339 | + | 0.123546i | \(0.0394267\pi\) | ||||
−0.992339 | + | 0.123546i | \(0.960573\pi\) | |||||||
\(954\) | 0.277187 | + | 4.45877i | 0.00897425 | + | 0.144358i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 28.5977i | − | 0.924915i | ||||||
\(957\) | −2.81386 | + | 2.99422i | −0.0909592 | + | 0.0967894i | ||||
\(958\) | 32.8713i | 1.06202i | ||||||||
\(959\) | −22.9783 | + | 26.5330i | −0.742006 | + | 0.856795i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.0000 | 0.612903 | ||||||||
\(962\) | −21.9565 | −0.707906 | ||||||||
\(963\) | −19.8614 | + | 1.23472i | −0.640025 | + | 0.0397882i | ||||
\(964\) | 22.5543i | 0.726426i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −30.7446 | + | 3.16915i | −0.989190 | + | 0.101966i | ||||
\(967\) | −10.2337 | −0.329093 | −0.164547 | − | 0.986369i | \(-0.552616\pi\) | ||||
−0.164547 | + | 0.986369i | \(0.552616\pi\) | |||||||
\(968\) | − | 12.3644i | − | 0.397407i | ||||||
\(969\) | −19.1168 | − | 17.9653i | −0.614122 | − | 0.577129i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.2119 | −1.19419 | −0.597094 | − | 0.802171i | \(-0.703678\pi\) | ||||
−0.597094 | + | 0.802171i | \(0.703678\pi\) | |||||||
\(972\) | 12.6060 | − | 17.2828i | 0.404337 | − | 0.554347i | ||||
\(973\) | 32.2337 | − | 37.2203i | 1.03336 | − | 1.19323i | ||||
\(974\) | 29.7021i | 0.951718i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.34896i | − | 0.139207i | ||||||
\(977\) | 7.62792i | 0.244039i | 0.992528 | + | 0.122019i | \(0.0389370\pi\) | ||||
−0.992528 | + | 0.122019i | \(0.961063\pi\) | |||||||
\(978\) | −8.00000 | − | 7.51811i | −0.255812 | − | 0.240403i | ||||
\(979\) | − | 37.2203i | − | 1.18956i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.18614 | + | 51.2516i | 0.101726 | + | 1.63634i | ||||
\(982\) | −4.51087 | −0.143948 | ||||||||
\(983\) | 39.8614 | 1.27138 | 0.635691 | − | 0.771944i | \(-0.280715\pi\) | ||||
0.635691 | + | 0.771944i | \(0.280715\pi\) | |||||||
\(984\) | 20.2337 | + | 19.0149i | 0.645026 | + | 0.606172i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.25544 | −0.103674 | ||||||||
\(987\) | 7.41983 | − | 0.764836i | 0.236176 | − | 0.0243450i | ||||
\(988\) | 19.5326 | 0.621416 | ||||||||
\(989\) | − | 40.3894i | − | 1.28431i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25.4891 | 0.809689 | 0.404844 | − | 0.914386i | \(-0.367326\pi\) | ||||
0.404844 | + | 0.914386i | \(0.367326\pi\) | |||||||
\(992\) | −20.2337 | −0.642420 | ||||||||
\(993\) | 4.74456 | − | 5.04868i | 0.150564 | − | 0.160215i | ||||
\(994\) | −0.467376 | − | 0.404759i | −0.0148243 | − | 0.0128382i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 28.4674 | − | 30.2921i | 0.902023 | − | 0.959840i | ||||
\(997\) | − | 31.8217i | − | 1.00780i | −0.863761 | − | 0.503902i | \(-0.831897\pi\) | ||
0.863761 | − | 0.503902i | \(-0.168103\pi\) | |||||||
\(998\) | − | 32.7615i | − | 1.03705i | ||||||
\(999\) | 26.9783 | + | 22.3692i | 0.853554 | + | 0.707730i |
(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 | 525.2.b.g.251.2 | 4 | ||
3.2 | odd | 2 | 525.2.b.e.251.3 | 4 | |||
5.2 | odd | 4 | 525.2.g.e.524.6 | 8 | |||
5.3 | odd | 4 | 525.2.g.e.524.3 | 8 | |||
5.4 | even | 2 | 105.2.b.c.41.3 | yes | 4 | ||
7.6 | odd | 2 | 525.2.b.e.251.2 | 4 | |||
15.2 | even | 4 | 525.2.g.d.524.3 | 8 | |||
15.8 | even | 4 | 525.2.g.d.524.6 | 8 | |||
15.14 | odd | 2 | 105.2.b.d.41.2 | yes | 4 | ||
20.19 | odd | 2 | 1680.2.f.h.881.2 | 4 | |||
21.20 | even | 2 | inner | 525.2.b.g.251.3 | 4 | ||
35.4 | even | 6 | 735.2.s.i.656.1 | 4 | |||
35.9 | even | 6 | 735.2.s.h.521.2 | 4 | |||
35.13 | even | 4 | 525.2.g.d.524.4 | 8 | |||
35.19 | odd | 6 | 735.2.s.g.521.2 | 4 | |||
35.24 | odd | 6 | 735.2.s.j.656.1 | 4 | |||
35.27 | even | 4 | 525.2.g.d.524.5 | 8 | |||
35.34 | odd | 2 | 105.2.b.d.41.3 | yes | 4 | ||
60.59 | even | 2 | 1680.2.f.g.881.4 | 4 | |||
105.44 | odd | 6 | 735.2.s.j.521.1 | 4 | |||
105.59 | even | 6 | 735.2.s.h.656.2 | 4 | |||
105.62 | odd | 4 | 525.2.g.e.524.4 | 8 | |||
105.74 | odd | 6 | 735.2.s.g.656.2 | 4 | |||
105.83 | odd | 4 | 525.2.g.e.524.5 | 8 | |||
105.89 | even | 6 | 735.2.s.i.521.1 | 4 | |||
105.104 | even | 2 | 105.2.b.c.41.2 | ✓ | 4 | ||
140.139 | even | 2 | 1680.2.f.g.881.3 | 4 | |||
420.419 | odd | 2 | 1680.2.f.h.881.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.b.c.41.2 | ✓ | 4 | 105.104 | even | 2 | ||
105.2.b.c.41.3 | yes | 4 | 5.4 | even | 2 | ||
105.2.b.d.41.2 | yes | 4 | 15.14 | odd | 2 | ||
105.2.b.d.41.3 | yes | 4 | 35.34 | odd | 2 | ||
525.2.b.e.251.2 | 4 | 7.6 | odd | 2 | |||
525.2.b.e.251.3 | 4 | 3.2 | odd | 2 | |||
525.2.b.g.251.2 | 4 | 1.1 | even | 1 | trivial | ||
525.2.b.g.251.3 | 4 | 21.20 | even | 2 | inner | ||
525.2.g.d.524.3 | 8 | 15.2 | even | 4 | |||
525.2.g.d.524.4 | 8 | 35.13 | even | 4 | |||
525.2.g.d.524.5 | 8 | 35.27 | even | 4 | |||
525.2.g.d.524.6 | 8 | 15.8 | even | 4 | |||
525.2.g.e.524.3 | 8 | 5.3 | odd | 4 | |||
525.2.g.e.524.4 | 8 | 105.62 | odd | 4 | |||
525.2.g.e.524.5 | 8 | 105.83 | odd | 4 | |||
525.2.g.e.524.6 | 8 | 5.2 | odd | 4 | |||
735.2.s.g.521.2 | 4 | 35.19 | odd | 6 | |||
735.2.s.g.656.2 | 4 | 105.74 | odd | 6 | |||
735.2.s.h.521.2 | 4 | 35.9 | even | 6 | |||
735.2.s.h.656.2 | 4 | 105.59 | even | 6 | |||
735.2.s.i.521.1 | 4 | 105.89 | even | 6 | |||
735.2.s.i.656.1 | 4 | 35.4 | even | 6 | |||
735.2.s.j.521.1 | 4 | 105.44 | odd | 6 | |||
735.2.s.j.656.1 | 4 | 35.24 | odd | 6 | |||
1680.2.f.g.881.3 | 4 | 140.139 | even | 2 | |||
1680.2.f.g.881.4 | 4 | 60.59 | even | 2 | |||
1680.2.f.h.881.1 | 4 | 420.419 | odd | 2 | |||
1680.2.f.h.881.2 | 4 | 20.19 | odd | 2 |