Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [153,4,Mod(19,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("153.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.l (of order \(8\), degree \(4\), 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: | \(9.02729223088\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 100.3 | ||
Root | \(-3.68604i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 153.100 |
Dual form | 153.4.l.a.127.3 |
$q$-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 \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.89932 | + | 1.89932i | 0.671511 | + | 0.671511i | 0.958064 | − | 0.286553i | \(-0.0925095\pi\) |
−0.286553 | + | 0.958064i | \(0.592510\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 0.785167i | − | 0.0981459i | ||||||
\(5\) | −1.92782 | + | 0.798529i | −0.172429 | + | 0.0714226i | −0.467228 | − | 0.884137i | \(-0.654747\pi\) |
0.294799 | + | 0.955559i | \(0.404747\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 23.0956 | + | 9.56650i | 1.24704 | + | 0.516543i | 0.905909 | − | 0.423472i | \(-0.139189\pi\) |
0.341135 | + | 0.940014i | \(0.389189\pi\) | |||||||
\(8\) | 16.6858 | − | 16.6858i | 0.737417 | − | 0.737417i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −5.17821 | − | 2.14488i | −0.163749 | − | 0.0678272i | ||||
\(11\) | −1.46245 | + | 3.53068i | −0.0400860 | + | 0.0967763i | −0.942655 | − | 0.333770i | \(-0.891679\pi\) |
0.902568 | + | 0.430546i | \(0.141679\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 17.6726i | − | 0.377038i | −0.982070 | − | 0.188519i | \(-0.939631\pi\) | ||
0.982070 | − | 0.188519i | \(-0.0603687\pi\) | |||||||
\(14\) | 25.6960 | + | 62.0357i | 0.490540 | + | 1.18427i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 57.1022 | 0.892221 | ||||||||
\(17\) | 69.7847 | + | 6.56433i | 0.995605 | + | 0.0936520i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 113.784 | + | 113.784i | 1.37388 | + | 1.37388i | 0.854605 | + | 0.519279i | \(0.173799\pi\) |
0.519279 | + | 0.854605i | \(0.326201\pi\) | |||||||
\(20\) | 0.626979 | + | 1.51366i | 0.00700984 | + | 0.0169232i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.48355 | + | 3.92822i | −0.0919046 | + | 0.0380681i | ||||
\(23\) | 38.2560 | − | 92.3581i | 0.346823 | − | 0.837304i | −0.650169 | − | 0.759790i | \(-0.725302\pi\) |
0.996991 | − | 0.0775138i | \(-0.0246982\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −85.3095 | + | 85.3095i | −0.682476 | + | 0.682476i | ||||
\(26\) | 33.5659 | − | 33.5659i | 0.253185 | − | 0.253185i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.51131 | − | 18.1339i | 0.0506966 | − | 0.122392i | ||||
\(29\) | −185.315 | + | 76.7600i | −1.18662 | + | 0.491516i | −0.886655 | − | 0.462432i | \(-0.846977\pi\) |
−0.299970 | + | 0.953949i | \(0.596977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −29.2899 | − | 70.7121i | −0.169697 | − | 0.409686i | 0.816036 | − | 0.578001i | \(-0.196167\pi\) |
−0.985733 | + | 0.168316i | \(0.946167\pi\) | |||||||
\(32\) | −25.0315 | − | 25.0315i | −0.138281 | − | 0.138281i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 120.076 | + | 145.011i | 0.605671 | + | 0.731448i | ||||
\(35\) | −52.1632 | −0.251920 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −93.6650 | − | 226.127i | −0.416174 | − | 1.00473i | −0.983446 | − | 0.181202i | \(-0.942001\pi\) |
0.567272 | − | 0.823531i | \(-0.307999\pi\) | |||||||
\(38\) | 432.224i | 1.84516i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −18.8432 | + | 45.4914i | −0.0744841 | + | 0.179821i | ||||
\(41\) | 49.9941 | + | 20.7082i | 0.190433 | + | 0.0788800i | 0.475862 | − | 0.879520i | \(-0.342136\pi\) |
−0.285429 | + | 0.958400i | \(0.592136\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −100.471 | + | 100.471i | −0.356318 | + | 0.356318i | −0.862454 | − | 0.506136i | \(-0.831073\pi\) |
0.506136 | + | 0.862454i | \(0.331073\pi\) | |||||||
\(44\) | 2.77217 | + | 1.14827i | 0.00949820 | + | 0.00393428i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 248.078 | − | 102.757i | 0.795154 | − | 0.329363i | ||||
\(47\) | − | 468.451i | − | 1.45384i | −0.686721 | − | 0.726921i | \(-0.740951\pi\) | ||
0.686721 | − | 0.726921i | \(-0.259049\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 199.350 | + | 199.350i | 0.581196 | + | 0.581196i | ||||
\(50\) | −324.060 | −0.916580 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.8759 | −0.0370047 | ||||||||
\(53\) | −68.2834 | − | 68.2834i | −0.176971 | − | 0.176971i | 0.613063 | − | 0.790034i | \(-0.289937\pi\) |
−0.790034 | + | 0.613063i | \(0.789937\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.97432i | − | 0.0195501i | ||||||
\(56\) | 544.994 | − | 225.744i | 1.30050 | − | 0.538684i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −497.764 | − | 206.181i | −1.12689 | − | 0.466773i | ||||
\(59\) | −257.729 | + | 257.729i | −0.568703 | + | 0.568703i | −0.931765 | − | 0.363062i | \(-0.881731\pi\) |
0.363062 | + | 0.931765i | \(0.381731\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −653.988 | − | 270.891i | −1.37270 | − | 0.568590i | −0.430179 | − | 0.902743i | \(-0.641550\pi\) |
−0.942519 | + | 0.334153i | \(0.891550\pi\) | |||||||
\(62\) | 78.6740 | − | 189.936i | 0.161155 | − | 0.389062i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 551.903i | − | 1.07794i | ||||||
\(65\) | 14.1121 | + | 34.0695i | 0.0269290 | + | 0.0650124i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 304.454 | 0.555150 | 0.277575 | − | 0.960704i | \(-0.410469\pi\) | ||||
0.277575 | + | 0.960704i | \(0.410469\pi\) | |||||||
\(68\) | 5.15410 | − | 54.7927i | 0.00919156 | − | 0.0977146i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −99.0747 | − | 99.0747i | −0.169167 | − | 0.169167i | ||||
\(71\) | 179.862 | + | 434.226i | 0.300644 | + | 0.725819i | 0.999940 | + | 0.0109864i | \(0.00349716\pi\) |
−0.699296 | + | 0.714833i | \(0.746503\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −131.243 | + | 54.3626i | −0.210422 | + | 0.0871597i | −0.485405 | − | 0.874289i | \(-0.661328\pi\) |
0.274983 | + | 0.961449i | \(0.411328\pi\) | |||||||
\(74\) | 251.588 | − | 607.388i | 0.395224 | − | 0.954155i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 89.3393 | − | 89.3393i | 0.134841 | − | 0.134841i | ||||
\(77\) | −67.5525 | + | 67.5525i | −0.0999781 | + | 0.0999781i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −274.715 | + | 663.221i | −0.391239 | + | 0.944534i | 0.598432 | + | 0.801174i | \(0.295791\pi\) |
−0.989671 | + | 0.143360i | \(0.954209\pi\) | |||||||
\(80\) | −110.083 | + | 45.5977i | −0.153845 | + | 0.0637248i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 55.6232 | + | 134.286i | 0.0749092 | + | 0.180847i | ||||
\(83\) | 259.960 | + | 259.960i | 0.343787 | + | 0.343787i | 0.857789 | − | 0.514002i | \(-0.171838\pi\) |
−0.514002 | + | 0.857789i | \(0.671838\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −139.774 | + | 43.0703i | −0.178360 | + | 0.0549603i | ||||
\(86\) | −381.653 | −0.478542 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 34.5100 | + | 83.3146i | 0.0418043 | + | 0.100925i | ||||
\(89\) | − | 1042.28i | − | 1.24137i | −0.784061 | − | 0.620684i | \(-0.786855\pi\) | ||
0.784061 | − | 0.620684i | \(-0.213145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 169.065 | − | 408.158i | 0.194756 | − | 0.470183i | ||||
\(92\) | −72.5165 | − | 30.0373i | −0.0821780 | − | 0.0340392i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 889.738 | − | 889.738i | 0.976271 | − | 0.976271i | ||||
\(95\) | −310.214 | − | 128.495i | −0.335024 | − | 0.138772i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −834.757 | + | 345.768i | −0.873781 | + | 0.361932i | −0.774082 | − | 0.633086i | \(-0.781788\pi\) |
−0.0996991 | + | 0.995018i | \(0.531788\pi\) | |||||||
\(98\) | 757.260i | 0.780559i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 66.9823 | + | 66.9823i | 0.0669823 | + | 0.0669823i | ||||
\(101\) | 443.233 | 0.436667 | 0.218333 | − | 0.975874i | \(-0.429938\pi\) | ||||
0.218333 | + | 0.975874i | \(0.429938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1396.36 | −1.33580 | −0.667901 | − | 0.744250i | \(-0.732807\pi\) | ||||
−0.667901 | + | 0.744250i | \(0.732807\pi\) | |||||||
\(104\) | −294.882 | − | 294.882i | −0.278034 | − | 0.278034i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 259.384i | − | 0.237676i | ||||||
\(107\) | −1703.54 | + | 705.628i | −1.53913 | + | 0.637529i | −0.981310 | − | 0.192432i | \(-0.938363\pi\) |
−0.557821 | + | 0.829961i | \(0.688363\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 344.570 | + | 142.726i | 0.302788 | + | 0.125419i | 0.528904 | − | 0.848681i | \(-0.322603\pi\) |
−0.226117 | + | 0.974100i | \(0.572603\pi\) | |||||||
\(110\) | 15.1458 | − | 15.1458i | 0.0131281 | − | 0.0131281i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1318.81 | + | 546.268i | 1.11264 | + | 0.460870i | ||||
\(113\) | −680.844 | + | 1643.70i | −0.566800 | + | 1.36838i | 0.337438 | + | 0.941348i | \(0.390440\pi\) |
−0.904238 | + | 0.427029i | \(0.859560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 208.598i | 0.169147i | ||||||||
\(116\) | 60.2694 | + | 145.503i | 0.0482403 | + | 0.116462i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −979.020 | −0.763781 | ||||||||
\(119\) | 1548.92 | + | 819.203i | 1.19319 | + | 0.631061i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 930.832 | + | 930.832i | 0.699348 | + | 0.699348i | ||||
\(122\) | −727.624 | − | 1756.64i | −0.539967 | − | 1.30360i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −55.5208 | + | 22.9975i | −0.0402090 | + | 0.0166551i | ||||
\(125\) | 196.155 | − | 473.561i | 0.140357 | − | 0.338852i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1226.83 | − | 1226.83i | 0.857192 | − | 0.857192i | −0.133814 | − | 0.991006i | \(-0.542723\pi\) |
0.991006 | + | 0.133814i | \(0.0427225\pi\) | |||||||
\(128\) | 847.988 | − | 847.988i | 0.585565 | − | 0.585565i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −37.9056 | + | 91.5123i | −0.0255734 | + | 0.0617397i | ||||
\(131\) | −522.374 | + | 216.374i | −0.348397 | + | 0.144311i | −0.550018 | − | 0.835153i | \(-0.685379\pi\) |
0.201621 | + | 0.979464i | \(0.435379\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1539.39 | + | 3716.42i | 1.00362 | + | 2.42296i | ||||
\(134\) | 578.256 | + | 578.256i | 0.372789 | + | 0.372789i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1273.95 | − | 1054.89i | 0.803237 | − | 0.665116i | ||||
\(137\) | 1150.24 | 0.717314 | 0.358657 | − | 0.933469i | \(-0.383235\pi\) | ||||
0.358657 | + | 0.933469i | \(0.383235\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −376.814 | − | 909.710i | −0.229935 | − | 0.555112i | 0.766234 | − | 0.642562i | \(-0.222128\pi\) |
−0.996169 | + | 0.0874493i | \(0.972128\pi\) | |||||||
\(140\) | 40.9569i | 0.0247249i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −483.118 | + | 1166.35i | −0.285510 | + | 0.689281i | ||||
\(143\) | 62.3962 | + | 25.8453i | 0.0364883 | + | 0.0151140i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 295.959 | − | 295.959i | 0.169504 | − | 0.169504i | ||||
\(146\) | −352.524 | − | 146.020i | −0.199830 | − | 0.0827721i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −177.548 | + | 73.5428i | −0.0986105 | + | 0.0408458i | ||||
\(149\) | 1772.18i | 0.974382i | 0.873295 | + | 0.487191i | \(0.161979\pi\) | ||||
−0.873295 | + | 0.487191i | \(0.838021\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1337.91 | − | 1337.91i | −0.721044 | − | 0.721044i | 0.247774 | − | 0.968818i | \(-0.420301\pi\) |
−0.968818 | + | 0.247774i | \(0.920301\pi\) | |||||||
\(152\) | 3797.16 | 2.02625 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −256.607 | −0.134273 | ||||||||
\(155\) | 112.931 | + | 112.931i | 0.0585216 | + | 0.0585216i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 289.955i | 0.147395i | 0.997281 | + | 0.0736973i | \(0.0234799\pi\) | ||||
−0.997281 | + | 0.0736973i | \(0.976520\pi\) | |||||||
\(158\) | −1781.44 | + | 737.897i | −0.896986 | + | 0.371544i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 68.2445 | + | 28.2678i | 0.0337200 | + | 0.0139673i | ||||
\(161\) | 1767.09 | − | 1767.09i | 0.865006 | − | 0.865006i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1563.14 | + | 647.475i | 0.751134 | + | 0.311130i | 0.725204 | − | 0.688534i | \(-0.241745\pi\) |
0.0259298 | + | 0.999664i | \(0.491745\pi\) | |||||||
\(164\) | 16.2594 | − | 39.2537i | 0.00774175 | − | 0.0186902i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 987.495i | 0.461714i | ||||||||
\(167\) | −480.582 | − | 1160.23i | −0.222686 | − | 0.537612i | 0.772567 | − | 0.634933i | \(-0.218972\pi\) |
−0.995253 | + | 0.0973216i | \(0.968972\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1884.68 | 0.857842 | ||||||||
\(170\) | −347.280 | − | 183.672i | −0.156677 | − | 0.0828645i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 78.8864 | + | 78.8864i | 0.0349711 | + | 0.0349711i | ||||
\(173\) | −153.530 | − | 370.654i | −0.0674720 | − | 0.162892i | 0.886547 | − | 0.462639i | \(-0.153098\pi\) |
−0.954019 | + | 0.299748i | \(0.903098\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2786.39 | + | 1154.16i | −1.20361 | + | 0.498550i | ||||
\(176\) | −83.5093 | + | 201.609i | −0.0357656 | + | 0.0863459i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1979.63 | − | 1979.63i | 0.833593 | − | 0.833593i | ||||
\(179\) | −543.928 | + | 543.928i | −0.227123 | + | 0.227123i | −0.811490 | − | 0.584366i | \(-0.801343\pi\) |
0.584366 | + | 0.811490i | \(0.301343\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1005.65 | + | 2427.86i | −0.412980 | + | 0.997022i | 0.571353 | + | 0.820704i | \(0.306419\pi\) |
−0.984333 | + | 0.176318i | \(0.943581\pi\) | |||||||
\(182\) | 1096.33 | − | 454.115i | 0.446514 | − | 0.184952i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −902.739 | − | 2179.40i | −0.361689 | − | 0.873195i | ||||
\(185\) | 361.139 | + | 361.139i | 0.143521 | + | 0.143521i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −125.233 | + | 236.787i | −0.0489732 | + | 0.0925968i | ||||
\(188\) | −367.812 | −0.142689 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −345.143 | − | 833.249i | −0.131786 | − | 0.318159i | ||||
\(191\) | − | 207.856i | − | 0.0787430i | −0.999225 | − | 0.0393715i | \(-0.987464\pi\) | ||
0.999225 | − | 0.0393715i | \(-0.0125356\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1751.78 | − | 4229.18i | 0.653348 | − | 1.57732i | −0.154541 | − | 0.987986i | \(-0.549390\pi\) |
0.807889 | − | 0.589335i | \(-0.200610\pi\) | |||||||
\(194\) | −2242.19 | − | 928.747i | −0.829795 | − | 0.343712i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 156.523 | − | 156.523i | 0.0570420 | − | 0.0570420i | ||||
\(197\) | 2439.95 | + | 1010.66i | 0.882434 | + | 0.365516i | 0.777440 | − | 0.628957i | \(-0.216518\pi\) |
0.104994 | + | 0.994473i | \(0.466518\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1525.28 | + | 631.793i | −0.543339 | + | 0.225059i | −0.637434 | − | 0.770505i | \(-0.720004\pi\) |
0.0940949 | + | 0.995563i | \(0.470004\pi\) | |||||||
\(200\) | 2846.92i | 1.00654i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 841.842 | + | 841.842i | 0.293227 | + | 0.293227i | ||||
\(203\) | −5014.28 | −1.73366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −112.916 | −0.0384701 | ||||||||
\(206\) | −2652.14 | − | 2652.14i | −0.897006 | − | 0.897006i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1009.14i | − | 0.336401i | ||||||
\(209\) | −568.137 | + | 235.330i | −0.188033 | + | 0.0778858i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1020.47 | − | 422.694i | −0.332949 | − | 0.137912i | 0.209945 | − | 0.977713i | \(-0.432672\pi\) |
−0.542894 | + | 0.839801i | \(0.682672\pi\) | |||||||
\(212\) | −53.6139 | + | 53.6139i | −0.0173690 | + | 0.0173690i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4575.77 | − | 1895.35i | −1.46165 | − | 0.605436i | ||||
\(215\) | 113.461 | − | 273.918i | 0.0359905 | − | 0.0868888i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1913.34i | − | 0.598552i | ||||||
\(218\) | 383.367 | + | 925.531i | 0.119105 | + | 0.287545i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.26117 | −0.00191876 | ||||||||
\(221\) | 116.009 | − | 1233.28i | 0.0353103 | − | 0.375381i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1530.74 | − | 1530.74i | −0.459667 | − | 0.459667i | 0.438879 | − | 0.898546i | \(-0.355376\pi\) |
−0.898546 | + | 0.438879i | \(0.855376\pi\) | |||||||
\(224\) | −338.653 | − | 817.580i | −0.101014 | − | 0.243870i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4415.06 | + | 1828.78i | −1.29949 | + | 0.538267i | ||||
\(227\) | 997.159 | − | 2407.36i | 0.291559 | − | 0.703885i | −0.708440 | − | 0.705771i | \(-0.750601\pi\) |
0.999998 | + | 0.00188682i | \(0.000600593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −798.278 | + | 798.278i | −0.230357 | + | 0.230357i | −0.812842 | − | 0.582485i | \(-0.802081\pi\) |
0.582485 | + | 0.812842i | \(0.302081\pi\) | |||||||
\(230\) | −396.194 | + | 396.194i | −0.113584 | + | 0.113584i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1811.33 | + | 4372.94i | −0.512585 | + | 1.23749i | ||||
\(233\) | −3987.43 | + | 1651.65i | −1.12114 | + | 0.464391i | −0.864760 | − | 0.502185i | \(-0.832530\pi\) |
−0.256379 | + | 0.966576i | \(0.582530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 374.072 | + | 903.089i | 0.103837 | + | 0.250685i | ||||
\(236\) | 202.361 | + | 202.361i | 0.0558159 | + | 0.0558159i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1385.97 | + | 4497.83i | 0.377475 | + | 1.22500i | ||||
\(239\) | −788.197 | −0.213323 | −0.106662 | − | 0.994295i | \(-0.534016\pi\) | ||||
−0.106662 | + | 0.994295i | \(0.534016\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1386.41 | − | 3347.08i | −0.370566 | − | 0.894625i | −0.993655 | − | 0.112474i | \(-0.964123\pi\) |
0.623089 | − | 0.782151i | \(-0.285877\pi\) | |||||||
\(242\) | 3535.90i | 0.939240i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −212.695 | + | 513.490i | −0.0558048 | + | 0.134725i | ||||
\(245\) | −543.498 | − | 225.124i | −0.141726 | − | 0.0587047i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2010.85 | − | 2010.85i | 0.518006 | − | 0.518006i | ||||
\(248\) | −1668.62 | − | 691.164i | −0.427247 | − | 0.176972i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1272.01 | − | 526.882i | 0.321795 | − | 0.133292i | ||||
\(251\) | − | 5974.99i | − | 1.50254i | −0.659994 | − | 0.751271i | \(-0.729441\pi\) | ||
0.659994 | − | 0.751271i | \(-0.270559\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 270.139 | + | 270.139i | 0.0671284 | + | 0.0671284i | ||||
\(254\) | 4660.28 | 1.15123 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1194.02 | −0.291509 | ||||||||
\(257\) | −2652.30 | − | 2652.30i | −0.643758 | − | 0.643758i | 0.307719 | − | 0.951477i | \(-0.400434\pi\) |
−0.951477 | + | 0.307719i | \(0.900434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 6118.59i | − | 1.46792i | ||||||
\(260\) | 26.7503 | − | 11.0803i | 0.00638070 | − | 0.00264297i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1403.12 | − | 581.191i | −0.330859 | − | 0.137046i | ||||
\(263\) | 5350.27 | − | 5350.27i | 1.25442 | − | 1.25442i | 0.300699 | − | 0.953719i | \(-0.402780\pi\) |
0.953719 | − | 0.300699i | \(-0.0972198\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 186.164 | + | 77.1118i | 0.0431547 | + | 0.0178752i | ||||
\(266\) | −4134.87 | + | 9982.46i | −0.953102 | + | 2.30099i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 239.048i | − | 0.0544857i | ||||||
\(269\) | 2675.20 | + | 6458.50i | 0.606356 | + | 1.46387i | 0.866935 | + | 0.498421i | \(0.166087\pi\) |
−0.260579 | + | 0.965453i | \(0.583913\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1356.64 | 0.304097 | 0.152049 | − | 0.988373i | \(-0.451413\pi\) | ||||
0.152049 | + | 0.988373i | \(0.451413\pi\) | |||||||
\(272\) | 3984.86 | + | 374.837i | 0.888300 | + | 0.0835583i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2184.68 | + | 2184.68i | 0.481684 | + | 0.481684i | ||||
\(275\) | −176.439 | − | 425.962i | −0.0386897 | − | 0.0934053i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6628.70 | − | 2745.70i | 1.43783 | − | 0.595570i | 0.478562 | − | 0.878054i | \(-0.341158\pi\) |
0.959272 | + | 0.282484i | \(0.0911583\pi\) | |||||||
\(278\) | 1012.14 | − | 2443.52i | 0.218360 | − | 0.527168i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −870.387 | + | 870.387i | −0.185770 | + | 0.185770i | ||||
\(281\) | 4674.98 | − | 4674.98i | 0.992476 | − | 0.992476i | −0.00749542 | − | 0.999972i | \(-0.502386\pi\) |
0.999972 | + | 0.00749542i | \(0.00238589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −884.335 | + | 2134.97i | −0.185754 | + | 0.448449i | −0.989134 | − | 0.147017i | \(-0.953033\pi\) |
0.803380 | + | 0.595466i | \(0.203033\pi\) | |||||||
\(284\) | 340.940 | − | 141.222i | 0.0712362 | − | 0.0295070i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 69.4217 | + | 167.599i | 0.0143531 | + | 0.0346515i | ||||
\(287\) | 956.537 | + | 956.537i | 0.196734 | + | 0.196734i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4826.82 | + | 916.180i | 0.982459 | + | 0.186481i | ||||
\(290\) | 1124.24 | 0.227647 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 42.6837 | + | 103.048i | 0.00855437 | + | 0.0206521i | ||||
\(293\) | 6445.85i | 1.28522i | 0.766192 | + | 0.642612i | \(0.222149\pi\) | ||||
−0.766192 | + | 0.642612i | \(0.777851\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 291.051 | − | 702.659i | 0.0574429 | − | 0.138679i | ||||
\(296\) | −5336.01 | − | 2210.25i | −1.04780 | − | 0.434013i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3365.94 | + | 3365.94i | −0.654309 | + | 0.654309i | ||||
\(299\) | −1632.20 | − | 676.081i | −0.315695 | − | 0.130765i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3281.59 | + | 1359.28i | −0.628397 | + | 0.260291i | ||||
\(302\) | − | 5082.24i | − | 0.968378i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6497.30 | + | 6497.30i | 1.22581 | + | 1.22581i | ||||
\(305\) | 1477.08 | 0.277304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 221.421 | 0.0411634 | 0.0205817 | − | 0.999788i | \(-0.493448\pi\) | ||||
0.0205817 | + | 0.999788i | \(0.493448\pi\) | |||||||
\(308\) | 53.0400 | + | 53.0400i | 0.00981245 | + | 0.00981245i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 428.985i | 0.0785959i | ||||||||
\(311\) | −1195.38 | + | 495.142i | −0.217954 | + | 0.0902795i | −0.488989 | − | 0.872290i | \(-0.662634\pi\) |
0.271035 | + | 0.962570i | \(0.412634\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −356.107 | − | 147.504i | −0.0643079 | − | 0.0266372i | 0.350298 | − | 0.936638i | \(-0.386080\pi\) |
−0.414606 | + | 0.910001i | \(0.636080\pi\) | |||||||
\(314\) | −550.718 | + | 550.718i | −0.0989772 | + | 0.0989772i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 520.739 | + | 215.697i | 0.0927021 | + | 0.0383985i | ||||
\(317\) | −248.380 | + | 599.641i | −0.0440075 | + | 0.106244i | −0.944355 | − | 0.328929i | \(-0.893312\pi\) |
0.900347 | + | 0.435172i | \(0.143312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 766.545i | − | 0.134540i | ||||||
\(320\) | 440.710 | + | 1063.97i | 0.0769889 | + | 0.185868i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6712.53 | 1.16172 | ||||||||
\(323\) | 7193.46 | + | 8687.29i | 1.23918 | + | 1.49651i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1507.64 | + | 1507.64i | 0.257319 | + | 0.257319i | ||||
\(326\) | 1739.15 | + | 4198.67i | 0.295468 | + | 0.713322i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1179.73 | − | 488.659i | 0.198596 | − | 0.0822612i | ||||
\(329\) | 4481.44 | − | 10819.1i | 0.750972 | − | 1.81301i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1010.96 | − | 1010.96i | 0.167877 | − | 0.167877i | −0.618168 | − | 0.786046i | \(-0.712125\pi\) |
0.786046 | + | 0.618168i | \(0.212125\pi\) | |||||||
\(332\) | 204.112 | − | 204.112i | 0.0337413 | − | 0.0337413i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1290.87 | − | 3116.42i | 0.211476 | − | 0.510548i | ||||
\(335\) | −586.933 | + | 243.116i | −0.0957241 | + | 0.0396502i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 216.355 | + | 522.328i | 0.0349722 | + | 0.0844303i | 0.940401 | − | 0.340069i | \(-0.110450\pi\) |
−0.905428 | + | 0.424499i | \(0.860450\pi\) | |||||||
\(338\) | 3579.61 | + | 3579.61i | 0.576051 | + | 0.576051i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 33.8174 | + | 109.746i | 0.00539413 | + | 0.0175053i | ||||
\(341\) | 292.497 | 0.0464504 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −584.286 | − | 1410.59i | −0.0919780 | − | 0.222055i | ||||
\(344\) | 3352.88i | 0.525509i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 412.388 | − | 995.592i | 0.0640754 | − | 0.154692i | ||||
\(347\) | −3500.32 | − | 1449.88i | −0.541518 | − | 0.224304i | 0.0951212 | − | 0.995466i | \(-0.469676\pi\) |
−0.636640 | + | 0.771161i | \(0.719676\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4516.50 | − | 4516.50i | 0.692730 | − | 0.692730i | −0.270102 | − | 0.962832i | \(-0.587057\pi\) |
0.962832 | + | 0.270102i | \(0.0870573\pi\) | |||||||
\(350\) | −7484.36 | − | 3100.12i | −1.14302 | − | 0.473453i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 124.985 | − | 51.7706i | 0.0189254 | − | 0.00783916i | ||||
\(353\) | 6291.34i | 0.948595i | 0.880365 | + | 0.474298i | \(0.157298\pi\) | ||||
−0.880365 | + | 0.474298i | \(0.842702\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −693.484 | − | 693.484i | −0.103680 | − | 0.103680i | ||||
\(356\) | −818.367 | −0.121835 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2066.19 | −0.305032 | ||||||||
\(359\) | −2382.60 | − | 2382.60i | −0.350275 | − | 0.350275i | 0.509937 | − | 0.860212i | \(-0.329669\pi\) |
−0.860212 | + | 0.509937i | \(0.829669\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19034.5i | 2.77511i | ||||||||
\(362\) | −6521.33 | + | 2701.22i | −0.946832 | + | 0.392191i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −320.473 | − | 132.744i | −0.0461465 | − | 0.0191145i | ||||
\(365\) | 209.602 | − | 209.602i | 0.0300578 | − | 0.0300578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −921.585 | − | 381.733i | −0.131080 | − | 0.0542951i | 0.316179 | − | 0.948699i | \(-0.397600\pi\) |
−0.447259 | + | 0.894404i | \(0.647600\pi\) | |||||||
\(368\) | 2184.50 | − | 5273.85i | 0.309443 | − | 0.747060i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1371.84i | 0.192752i | ||||||||
\(371\) | −923.812 | − | 2230.28i | −0.129277 | − | 0.312103i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3180.59 | −0.441514 | −0.220757 | − | 0.975329i | \(-0.570853\pi\) | ||||
−0.220757 | + | 0.975329i | \(0.570853\pi\) | |||||||
\(374\) | −687.593 | + | 211.876i | −0.0950658 | + | 0.0292938i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −7816.50 | − | 7816.50i | −1.07209 | − | 1.07209i | ||||
\(377\) | 1356.55 | + | 3274.99i | 0.185320 | + | 0.447402i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10009.2 | + | 4145.96i | −1.35657 | + | 0.561910i | −0.938114 | − | 0.346327i | \(-0.887429\pi\) |
−0.418456 | + | 0.908237i | \(0.637429\pi\) | |||||||
\(380\) | −100.890 | + | 243.570i | −0.0136199 | + | 0.0328813i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 394.785 | − | 394.785i | 0.0528768 | − | 0.0528768i | ||||
\(383\) | −5351.33 | + | 5351.33i | −0.713944 | + | 0.713944i | −0.967358 | − | 0.253414i | \(-0.918446\pi\) |
0.253414 | + | 0.967358i | \(0.418446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 76.2863 | − | 184.171i | 0.0100985 | − | 0.0243799i | ||||
\(386\) | 11359.8 | − | 4705.37i | 1.49792 | − | 0.620458i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 271.486 | + | 655.424i | 0.0355221 | + | 0.0857580i | ||||
\(389\) | −6787.77 | − | 6787.77i | −0.884714 | − | 0.884714i | 0.109295 | − | 0.994009i | \(-0.465141\pi\) |
−0.994009 | + | 0.109295i | \(0.965141\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3275.95 | − | 6194.06i | 0.423713 | − | 0.801143i | ||||
\(392\) | 6652.65 | 0.857168 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2714.68 | + | 6553.82i | 0.347116 | + | 0.838013i | ||||
\(395\) | − | 1497.94i | − | 0.190809i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2017.52 | − | 4870.72i | 0.255054 | − | 0.615754i | −0.743545 | − | 0.668686i | \(-0.766857\pi\) |
0.998598 | + | 0.0529327i | \(0.0168569\pi\) | |||||||
\(398\) | −4096.98 | − | 1697.03i | −0.515988 | − | 0.213729i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4871.36 | + | 4871.36i | −0.608920 | + | 0.608920i | ||||
\(401\) | −3326.28 | − | 1377.79i | −0.414231 | − | 0.171580i | 0.165828 | − | 0.986155i | \(-0.446970\pi\) |
−0.580059 | + | 0.814575i | \(0.696970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1249.66 | + | 517.628i | −0.154467 | + | 0.0639824i | ||||
\(404\) | − | 348.012i | − | 0.0428571i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −9523.72 | − | 9523.72i | −1.16417 | − | 1.16417i | ||||
\(407\) | 935.364 | 0.113917 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9516.13 | 1.15047 | 0.575235 | − | 0.817988i | \(-0.304911\pi\) | ||||
0.575235 | + | 0.817988i | \(0.304911\pi\) | |||||||
\(410\) | −214.463 | − | 214.463i | −0.0258331 | − | 0.0258331i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1096.38i | 0.131104i | ||||||||
\(413\) | −8417.97 | + | 3486.84i | −1.00296 | + | 0.415439i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −708.742 | − | 293.570i | −0.0838332 | − | 0.0347248i | ||||
\(416\) | −442.370 | + | 442.370i | −0.0521370 | + | 0.0521370i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1526.04 | − | 632.107i | −0.178567 | − | 0.0739650i | ||||
\(419\) | −2414.93 | + | 5830.16i | −0.281568 | + | 0.679766i | −0.999873 | − | 0.0159630i | \(-0.994919\pi\) |
0.718304 | + | 0.695729i | \(0.244919\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1544.81i | 0.178835i | 0.995994 | + | 0.0894177i | \(0.0285006\pi\) | ||||
−0.995994 | + | 0.0894177i | \(0.971499\pi\) | |||||||
\(422\) | −1135.37 | − | 2741.04i | −0.130970 | − | 0.316188i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2278.73 | −0.261002 | ||||||||
\(425\) | −6513.30 | + | 5393.30i | −0.743392 | + | 0.615561i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12512.8 | − | 12512.8i | −1.41811 | − | 1.41811i | ||||
\(428\) | 554.036 | + | 1337.56i | 0.0625709 | + | 0.151060i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 735.757 | − | 304.761i | 0.0825148 | − | 0.0341787i | ||||
\(431\) | −343.395 | + | 829.029i | −0.0383776 | + | 0.0926518i | −0.941906 | − | 0.335876i | \(-0.890968\pi\) |
0.903529 | + | 0.428528i | \(0.140968\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3462.33 | − | 3462.33i | 0.384270 | − | 0.384270i | −0.488368 | − | 0.872638i | \(-0.662408\pi\) |
0.872638 | + | 0.488368i | \(0.162408\pi\) | |||||||
\(434\) | 3634.04 | − | 3634.04i | 0.401934 | − | 0.401934i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 112.064 | − | 270.545i | 0.0123093 | − | 0.0297174i | ||||
\(437\) | 14861.8 | − | 6155.94i | 1.62685 | − | 0.673864i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 537.292 | + | 1297.14i | 0.0584136 | + | 0.141023i | 0.950392 | − | 0.311056i | \(-0.100683\pi\) |
−0.891978 | + | 0.452079i | \(0.850683\pi\) | |||||||
\(440\) | −133.058 | − | 133.058i | −0.0144166 | − | 0.0144166i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2562.72 | − | 2122.05i | 0.275784 | − | 0.228361i | ||||
\(443\) | 6453.57 | 0.692141 | 0.346070 | − | 0.938209i | \(-0.387516\pi\) | ||||
0.346070 | + | 0.938209i | \(0.387516\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 832.293 | + | 2009.33i | 0.0886617 | + | 0.214048i | ||||
\(446\) | − | 5814.71i | − | 0.617342i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 5279.78 | − | 12746.5i | 0.556799 | − | 1.34423i | ||||
\(449\) | 4073.49 | + | 1687.29i | 0.428151 | + | 0.177346i | 0.586344 | − | 0.810062i | \(-0.300567\pi\) |
−0.158193 | + | 0.987408i | \(0.550567\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −146.228 | + | 146.228i | −0.0152674 | + | 0.0152674i | ||||
\(452\) | 1290.58 | + | 534.577i | 0.134301 | + | 0.0556291i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6466.26 | − | 2678.41i | 0.668451 | − | 0.276881i | ||||
\(455\) | 921.859i | 0.0949833i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8889.44 | + | 8889.44i | 0.909913 | + | 0.909913i | 0.996265 | − | 0.0863515i | \(-0.0275208\pi\) |
−0.0863515 | + | 0.996265i | \(0.527521\pi\) | |||||||
\(458\) | −3032.37 | −0.309374 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 163.784 | 0.0166011 | ||||||||
\(461\) | −3616.85 | − | 3616.85i | −0.365409 | − | 0.365409i | 0.500391 | − | 0.865800i | \(-0.333190\pi\) |
−0.865800 | + | 0.500391i | \(0.833190\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5280.96i | 0.530080i | 0.964237 | + | 0.265040i | \(0.0853852\pi\) | ||||
−0.964237 | + | 0.265040i | \(0.914615\pi\) | |||||||
\(464\) | −10581.9 | + | 4383.16i | −1.05873 | + | 0.438541i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10710.4 | − | 4436.40i | −1.06470 | − | 0.441014i | ||||
\(467\) | 3132.80 | − | 3132.80i | 0.310425 | − | 0.310425i | −0.534649 | − | 0.845074i | \(-0.679556\pi\) |
0.845074 | + | 0.534649i | \(0.179556\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7031.55 | + | 2912.56i | 0.692296 | + | 0.286758i | ||||
\(470\) | −1004.77 | + | 2425.74i | −0.0986100 | + | 0.238066i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8600.86i | 0.838743i | ||||||||
\(473\) | −207.796 | − | 501.664i | −0.0201997 | − | 0.0487665i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19413.7 | −1.87529 | ||||||||
\(476\) | 643.211 | − | 1216.16i | 0.0619360 | − | 0.117107i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1497.04 | − | 1497.04i | −0.143249 | − | 0.143249i | ||||
\(479\) | −3328.23 | − | 8035.07i | −0.317476 | − | 0.766454i | −0.999387 | − | 0.0350190i | \(-0.988851\pi\) |
0.681911 | − | 0.731435i | \(-0.261149\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3996.25 | + | 1655.30i | −0.378822 | + | 0.156913i | ||||
\(482\) | 3723.95 | − | 8990.41i | 0.351911 | − | 0.849589i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 730.859 | − | 730.859i | 0.0686382 | − | 0.0686382i | ||||
\(485\) | 1333.15 | − | 1333.15i | 0.124815 | − | 0.124815i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4986.78 | − | 12039.2i | 0.464010 | − | 1.12022i | −0.502727 | − | 0.864445i | \(-0.667670\pi\) |
0.966737 | − | 0.255773i | \(-0.0823301\pi\) | |||||||
\(488\) | −15432.4 | + | 6392.30i | −1.43154 | + | 0.592963i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −604.694 | − | 1459.86i | −0.0557495 | − | 0.134591i | ||||
\(491\) | 8315.81 | + | 8315.81i | 0.764332 | + | 0.764332i | 0.977102 | − | 0.212770i | \(-0.0682486\pi\) |
−0.212770 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13436.0 | + | 4140.21i | −1.22744 | + | 0.378226i | ||||
\(494\) | 7638.51 | 0.695694 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1672.52 | − | 4037.81i | −0.151408 | − | 0.365531i | ||||
\(497\) | 11749.4i | 1.06042i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4104.11 | + | 9908.19i | −0.368187 | + | 0.888881i | 0.625861 | + | 0.779935i | \(0.284748\pi\) |
−0.994048 | + | 0.108946i | \(0.965252\pi\) | |||||||
\(500\) | −371.825 | − | 154.015i | −0.0332570 | − | 0.0137755i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 11348.4 | − | 11348.4i | 1.00897 | − | 1.00897i | ||||
\(503\) | −3607.71 | − | 1494.36i | −0.319801 | − | 0.132466i | 0.217008 | − | 0.976170i | \(-0.430370\pi\) |
−0.536809 | + | 0.843704i | \(0.680370\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −854.473 | + | 353.934i | −0.0752942 | + | 0.0311879i | ||||
\(506\) | 1026.16i | 0.0901549i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −963.266 | − | 963.266i | −0.0841299 | − | 0.0841299i | ||||
\(509\) | 15132.3 | 1.31774 | 0.658870 | − | 0.752257i | \(-0.271035\pi\) | ||||
0.658870 | + | 0.752257i | \(0.271035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3551.19 | −0.307427 | ||||||||
\(512\) | −9051.73 | − | 9051.73i | −0.781316 | − | 0.781316i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10075.1i | − | 0.864581i | ||||||
\(515\) | 2691.93 | − | 1115.04i | 0.230332 | − | 0.0954065i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1653.95 | + | 685.088i | 0.140697 | + | 0.0582788i | ||||
\(518\) | 11621.2 | − | 11621.2i | 0.985723 | − | 0.985723i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 803.951 | + | 333.007i | 0.0677992 | + | 0.0280833i | ||||
\(521\) | −6327.62 | + | 15276.2i | −0.532088 | + | 1.28457i | 0.398050 | + | 0.917364i | \(0.369687\pi\) |
−0.930138 | + | 0.367210i | \(0.880313\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8724.36i | 0.729426i | 0.931120 | + | 0.364713i | \(0.118833\pi\) | ||||
−0.931120 | + | 0.364713i | \(0.881167\pi\) | |||||||
\(524\) | 169.890 | + | 410.151i | 0.0141635 | + | 0.0341938i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 20323.8 | 1.68471 | ||||||||
\(527\) | −1579.81 | − | 5126.89i | −0.130584 | − | 0.423778i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1536.88 | + | 1536.88i | 0.126315 | + | 0.126315i | ||||
\(530\) | 207.126 | + | 500.046i | 0.0169754 | + | 0.0409822i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2918.01 | − | 1208.68i | 0.237804 | − | 0.0985016i | ||||
\(533\) | 365.968 | − | 883.524i | 0.0297407 | − | 0.0718005i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2720.65 | − | 2720.65i | 0.219858 | − | 0.219858i | ||||
\(536\) | 5080.08 | − | 5080.08i | 0.409377 | − | 0.409377i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7185.70 | + | 17347.8i | −0.575832 | + | 1.39018i | ||||
\(539\) | −995.382 | + | 412.301i | −0.0795438 | + | 0.0329481i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3155.65 | − | 7618.42i | −0.250780 | − | 0.605437i | 0.747487 | − | 0.664276i | \(-0.231260\pi\) |
−0.998267 | + | 0.0588391i | \(0.981260\pi\) | |||||||
\(542\) | 2576.70 | + | 2576.70i | 0.204205 | + | 0.204205i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1582.50 | − | 1911.13i | −0.124723 | − | 0.150623i | ||||
\(545\) | −778.240 | −0.0611672 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9124.03 | + | 22027.4i | 0.713191 | + | 1.72179i | 0.691870 | + | 0.722022i | \(0.256787\pi\) |
0.0213210 | + | 0.999773i | \(0.493213\pi\) | |||||||
\(548\) | − | 903.134i | − | 0.0704014i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 473.923 | − | 1144.15i | 0.0367421 | − | 0.0887032i | ||||
\(551\) | −29819.9 | − | 12351.8i | −2.30557 | − | 0.954999i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12689.4 | + | 12689.4i | −0.975784 | + | 0.975784i | ||||
\(554\) | 17805.0 | + | 7375.06i | 1.36545 | + | 0.565589i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −714.275 | + | 295.862i | −0.0544820 | + | 0.0225672i | ||||
\(557\) | 19341.5i | 1.47132i | 0.677350 | + | 0.735661i | \(0.263128\pi\) | ||||
−0.677350 | + | 0.735661i | \(0.736872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1775.58 | + | 1775.58i | 0.134345 | + | 0.134345i | ||||
\(560\) | −2978.63 | −0.224768 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 17758.6 | 1.33292 | ||||||||
\(563\) | −10048.2 | − | 10048.2i | −0.752189 | − | 0.752189i | 0.222698 | − | 0.974887i | \(-0.428513\pi\) |
−0.974887 | + | 0.222698i | \(0.928513\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 3712.44i | − | 0.276431i | ||||||
\(566\) | −5734.63 | + | 2375.36i | −0.425874 | + | 0.176403i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10246.6 | + | 4244.27i | 0.756932 | + | 0.313531i | ||||
\(569\) | 6771.36 | − | 6771.36i | 0.498893 | − | 0.498893i | −0.412200 | − | 0.911093i | \(-0.635239\pi\) |
0.911093 | + | 0.412200i | \(0.135239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13659.5 | − | 5657.96i | −1.00111 | − | 0.414673i | −0.178905 | − | 0.983866i | \(-0.557255\pi\) |
−0.822203 | + | 0.569194i | \(0.807255\pi\) | |||||||
\(572\) | 20.2929 | − | 48.9914i | 0.00148337 | − | 0.00358118i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3633.54i | 0.264218i | ||||||||
\(575\) | 4615.42 | + | 11142.6i | 0.334742 | + | 0.808138i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11438.5 | 0.825284 | 0.412642 | − | 0.910893i | \(-0.364606\pi\) | ||||
0.412642 | + | 0.910893i | \(0.364606\pi\) | |||||||
\(578\) | 7427.56 | + | 10907.8i | 0.534508 | + | 0.784956i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −232.377 | − | 232.377i | −0.0166361 | − | 0.0166361i | ||||
\(581\) | 3517.02 | + | 8490.84i | 0.251137 | + | 0.606298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 340.948 | − | 141.225i | 0.0242206 | − | 0.0100325i | ||||
\(584\) | −1282.81 | + | 3096.98i | −0.0908958 | + | 0.219442i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12242.7 | + | 12242.7i | −0.863042 | + | 0.863042i | ||||
\(587\) | −5580.55 | + | 5580.55i | −0.392392 | + | 0.392392i | −0.875539 | − | 0.483147i | \(-0.839493\pi\) |
0.483147 | + | 0.875539i | \(0.339493\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4713.17 | − | 11378.6i | 0.329716 | − | 0.796005i | ||||
\(590\) | 1887.37 | − | 781.776i | 0.131698 | − | 0.0545512i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5348.48 | − | 12912.4i | −0.371319 | − | 0.896444i | ||||
\(593\) | −5536.25 | − | 5536.25i | −0.383384 | − | 0.383384i | 0.488936 | − | 0.872320i | \(-0.337385\pi\) |
−0.872320 | + | 0.488936i | \(0.837385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3640.20 | − | 342.416i | −0.250813 | − | 0.0235928i | ||||
\(596\) | 1391.46 | 0.0956317 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1815.98 | − | 4384.17i | −0.124182 | − | 0.299803i | ||||
\(599\) | 18939.7i | 1.29191i | 0.763375 | + | 0.645956i | \(0.223541\pi\) | ||||
−0.763375 | + | 0.645956i | \(0.776459\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6803.11 | + | 16424.1i | −0.461738 | + | 1.11473i | 0.505945 | + | 0.862565i | \(0.331144\pi\) |
−0.967683 | + | 0.252168i | \(0.918856\pi\) | |||||||
\(602\) | −8814.49 | − | 3651.08i | −0.596764 | − | 0.247188i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1050.48 | + | 1050.48i | −0.0707675 | + | 0.0707675i | ||||
\(605\) | −2537.77 | − | 1051.18i | −0.170537 | − | 0.0706389i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16364.9 | − | 6778.57i | 1.09429 | − | 0.453268i | 0.238787 | − | 0.971072i | \(-0.423250\pi\) |
0.855499 | + | 0.517804i | \(0.173250\pi\) | |||||||
\(608\) | − | 5696.35i | − | 0.379963i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2805.46 | + | 2805.46i | 0.186212 | + | 0.186212i | ||||
\(611\) | −8278.74 | −0.548154 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25427.3 | 1.67537 | 0.837683 | − | 0.546156i | \(-0.183910\pi\) | ||||
0.837683 | + | 0.546156i | \(0.183910\pi\) | |||||||
\(614\) | 420.549 | + | 420.549i | 0.0276417 | + | 0.0276417i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2254.34i | 0.147451i | ||||||||
\(617\) | 9265.07 | − | 3837.72i | 0.604534 | − | 0.250406i | −0.0593552 | − | 0.998237i | \(-0.518904\pi\) |
0.663890 | + | 0.747831i | \(0.268904\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4121.37 | − | 1707.13i | −0.267612 | − | 0.110849i | 0.244842 | − | 0.969563i | \(-0.421264\pi\) |
−0.512455 | + | 0.858714i | \(0.671264\pi\) | |||||||
\(620\) | 88.6699 | − | 88.6699i | 0.00574366 | − | 0.00574366i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −3210.84 | − | 1329.97i | −0.206982 | − | 0.0857348i | ||||
\(623\) | 9971.00 | − | 24072.1i | 0.641220 | − | 1.54804i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 14011.2i | − | 0.896714i | ||||||
\(626\) | −396.203 | − | 956.520i | −0.0252963 | − | 0.0610706i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 227.664 | 0.0144662 | ||||||||
\(629\) | −5052.02 | − | 16395.1i | −0.320250 | − | 1.03929i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 776.752 | + | 776.752i | 0.0490048 | + | 0.0490048i | 0.731185 | − | 0.682180i | \(-0.238968\pi\) |
−0.682180 | + | 0.731185i | \(0.738968\pi\) | |||||||
\(632\) | 6482.55 | + | 15650.3i | 0.408009 | + | 0.985021i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1610.66 | + | 667.158i | −0.100895 | + | 0.0417922i | ||||
\(635\) | −1385.45 | + | 3344.76i | −0.0865822 | + | 0.209028i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3523.03 | − | 3523.03i | 0.219133 | − | 0.219133i | ||||
\(638\) | 1455.91 | − | 1455.91i | 0.0903451 | − | 0.0903451i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −957.625 | + | 2311.91i | −0.0591460 | + | 0.142791i | ||||
\(641\) | −982.245 | + | 406.859i | −0.0605247 | + | 0.0250702i | −0.412740 | − | 0.910849i | \(-0.635428\pi\) |
0.352216 | + | 0.935919i | \(0.385428\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2514.71 | + | 6071.06i | 0.154231 | + | 0.372347i | 0.982043 | − | 0.188660i | \(-0.0604143\pi\) |
−0.827811 | + | 0.561006i | \(0.810414\pi\) | |||||||
\(644\) | −1387.46 | − | 1387.46i | −0.0848968 | − | 0.0848968i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2837.26 | + | 30162.6i | −0.172802 | + | 1.83705i | ||||
\(647\) | 14783.1 | 0.898273 | 0.449137 | − | 0.893463i | \(-0.351732\pi\) | ||||
0.449137 | + | 0.893463i | \(0.351732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −533.041 | − | 1286.88i | −0.0322399 | − | 0.0778340i | ||||
\(650\) | 5726.98i | 0.345585i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 508.377 | − | 1227.33i | 0.0305361 | − | 0.0737208i | ||||
\(653\) | 23939.5 | + | 9916.08i | 1.43465 | + | 0.594251i | 0.958495 | − | 0.285110i | \(-0.0920302\pi\) |
0.476155 | + | 0.879362i | \(0.342030\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 834.261 | − | 834.261i | 0.0497668 | − | 0.0497668i | ||||
\(656\) | 2854.77 | + | 1182.48i | 0.169909 | + | 0.0703784i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29060.7 | − | 12037.3i | 1.72174 | − | 0.713168i | ||||
\(659\) | 4302.30i | 0.254315i | 0.991883 | + | 0.127158i | \(0.0405854\pi\) | ||||
−0.991883 | + | 0.127158i | \(0.959415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5280.43 | − | 5280.43i | −0.310719 | − | 0.310719i | 0.534469 | − | 0.845188i | \(-0.320512\pi\) |
−0.845188 | + | 0.534469i | \(0.820512\pi\) | |||||||
\(662\) | 3840.28 | 0.225463 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8675.31 | 0.507029 | ||||||||
\(665\) | −5935.33 | − | 5935.33i | −0.346109 | − | 0.346109i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20051.9i | 1.16403i | ||||||||
\(668\) | −910.974 | + | 377.338i | −0.0527644 | + | 0.0218557i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1576.53 | − | 653.019i | −0.0909054 | − | 0.0376542i | ||||
\(671\) | 1912.85 | − | 1912.85i | 0.110052 | − | 0.110052i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3914.28 | + | 1621.35i | 0.224197 | + | 0.0928654i | 0.491955 | − | 0.870621i | \(-0.336283\pi\) |
−0.267758 | + | 0.963486i | \(0.586283\pi\) | |||||||
\(674\) | −581.140 | + | 1403.00i | −0.0332117 | + | 0.0801801i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 1479.79i | − | 0.0841938i | ||||||
\(677\) | −8851.64 | − | 21369.8i | −0.502506 | − | 1.21316i | −0.948115 | − | 0.317928i | \(-0.897013\pi\) |
0.445609 | − | 0.895228i | \(-0.352987\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22587.0 | −1.27660 | ||||||||
\(680\) | −1613.59 | + | 3050.91i | −0.0909973 | + | 0.172055i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 555.545 | + | 555.545i | 0.0311919 | + | 0.0311919i | ||||
\(683\) | −4391.09 | − | 10601.0i | −0.246004 | − | 0.593905i | 0.751854 | − | 0.659330i | \(-0.229160\pi\) |
−0.997858 | + | 0.0654244i | \(0.979160\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2217.46 | + | 918.503i | −0.123686 | + | 0.0512324i | ||||
\(686\) | 1569.42 | − | 3788.91i | 0.0873478 | − | 0.210876i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5737.10 | + | 5737.10i | −0.317914 | + | 0.317914i | ||||
\(689\) | −1206.74 | + | 1206.74i | −0.0667246 | + | 0.0667246i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5825.05 | − | 14062.9i | 0.320688 | − | 0.774209i | −0.678527 | − | 0.734576i | \(-0.737381\pi\) |
0.999214 | − | 0.0396328i | \(-0.0126188\pi\) | |||||||
\(692\) | −291.025 | + | 120.547i | −0.0159872 | + | 0.00662210i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3894.44 | − | 9402.01i | −0.213013 | − | 0.514258i | ||||
\(695\) | 1452.86 | + | 1452.86i | 0.0792951 | + | 0.0792951i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3352.89 | + | 1773.29i | 0.182209 | + | 0.0963678i | ||||
\(698\) | 17156.6 | 0.930352 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 906.208 | + | 2187.78i | 0.0489306 | + | 0.118129i | ||||
\(701\) | 23996.1i | 1.29289i | 0.762959 | + | 0.646447i | \(0.223746\pi\) | ||||
−0.762959 | + | 0.646447i | \(0.776254\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15072.1 | − | 36387.2i | 0.808612 | − | 1.95216i | ||||
\(704\) | 1948.59 | + | 807.133i | 0.104319 | + | 0.0432102i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −11949.3 | + | 11949.3i | −0.636992 | + | 0.636992i | ||||
\(707\) | 10236.7 | + | 4240.19i | 0.544543 | + | 0.225557i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20645.7 | + | 8551.75i | −1.09361 | + | 0.452987i | −0.855263 | − | 0.518194i | \(-0.826605\pi\) |
−0.238344 | + | 0.971181i | \(0.576605\pi\) | |||||||
\(710\) | − | 2634.30i | − | 0.139244i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −17391.4 | − | 17391.4i | −0.915406 | − | 0.915406i | ||||
\(713\) | −7651.34 | −0.401886 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −140.927 | −0.00737113 | ||||||||
\(716\) | 427.075 | + | 427.075i | 0.0222912 | + | 0.0222912i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 9050.64i | − | 0.470427i | ||||||
\(719\) | 29996.7 | − | 12425.0i | 1.55590 | − | 0.644473i | 0.571525 | − | 0.820584i | \(-0.306352\pi\) |
0.984370 | + | 0.176111i | \(0.0563519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32249.8 | − | 13358.3i | −1.66581 | − | 0.689999i | ||||
\(722\) | −36152.6 | + | 36152.6i | −1.86352 | + | 1.86352i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1906.27 | + | 789.604i | 0.0978537 | + | 0.0405323i | ||||
\(725\) | 9260.77 | − | 22357.5i | 0.474395 | − | 1.14529i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2899.33i | 0.147909i | 0.997262 | + | 0.0739547i | \(0.0235620\pi\) | ||||
−0.997262 | + | 0.0739547i | \(0.976438\pi\) | |||||||
\(728\) | −3989.48 | − | 9631.46i | −0.203104 | − | 0.490337i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 796.204 | 0.0403683 | ||||||||
\(731\) | −7670.86 | + | 6351.81i | −0.388122 | + | 0.321382i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −11596.5 | − | 11596.5i | −0.584346 | − | 0.584346i | 0.351749 | − | 0.936095i | \(-0.385587\pi\) |
−0.936095 | + | 0.351749i | \(0.885587\pi\) | |||||||
\(734\) | −1025.35 | − | 2475.42i | −0.0515619 | − | 0.124481i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3269.46 | + | 1354.25i | −0.163742 | + | 0.0678240i | ||||
\(737\) | −445.251 | + | 1074.93i | −0.0222538 | + | 0.0537253i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4575.44 | − | 4575.44i | 0.227754 | − | 0.227754i | −0.584000 | − | 0.811754i | \(-0.698513\pi\) |
0.811754 | + | 0.584000i | \(0.198513\pi\) | |||||||
\(740\) | 283.554 | − | 283.554i | 0.0140860 | − | 0.0140860i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2481.40 | − | 5990.63i | 0.122770 | − | 0.296392i | ||||
\(743\) | −6947.76 | + | 2877.86i | −0.343053 | + | 0.142097i | −0.547557 | − | 0.836769i | \(-0.684442\pi\) |
0.204504 | + | 0.978866i | \(0.434442\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1415.14 | − | 3416.45i | −0.0695929 | − | 0.168012i | ||||
\(746\) | −6040.96 | − | 6040.96i | −0.296481 | − | 0.296481i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 185.918 | + | 98.3293i | 0.00908800 | + | 0.00480652i | ||||
\(749\) | −46094.6 | −2.24868 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4179.61 | + | 10090.5i | 0.203084 | + | 0.490289i | 0.992305 | − | 0.123821i | \(-0.0395150\pi\) |
−0.789220 | + | 0.614110i | \(0.789515\pi\) | |||||||
\(752\) | − | 26749.6i | − | 1.29715i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3643.74 | + | 8796.78i | −0.175991 | + | 0.424880i | ||||
\(755\) | 3647.61 | + | 1510.89i | 0.175828 | + | 0.0728303i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12100.6 | + | 12100.6i | −0.580984 | + | 0.580984i | −0.935174 | − | 0.354189i | \(-0.884757\pi\) |
0.354189 | + | 0.935174i | \(0.384757\pi\) | |||||||
\(758\) | −26885.3 | − | 11136.2i | −1.28828 | − | 0.533623i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −7320.23 | + | 3032.14i | −0.349385 | + | 0.144720i | ||||
\(761\) | − | 35934.3i | − | 1.71172i | −0.517207 | − | 0.855860i | \(-0.673028\pi\) | ||
0.517207 | − | 0.855860i | \(-0.326972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6592.67 | + | 6592.67i | 0.312805 | + | 0.312805i | ||||
\(764\) | −163.202 | −0.00772831 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20327.8 | −0.958842 | ||||||||
\(767\) | 4554.74 | + | 4554.74i | 0.214423 | + | 0.214423i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29085.3i | 1.36390i | 0.731397 | + | 0.681952i | \(0.238869\pi\) | ||||
−0.731397 | + | 0.681952i | \(0.761131\pi\) | |||||||
\(770\) | 494.693 | − | 204.908i | 0.0231526 | − | 0.00959011i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −3320.61 | − | 1375.44i | −0.154808 | − | 0.0641234i | ||||
\(773\) | 11669.3 | − | 11669.3i | 0.542968 | − | 0.542968i | −0.381430 | − | 0.924398i | \(-0.624568\pi\) |
0.924398 | + | 0.381430i | \(0.124568\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8531.12 | + | 3533.71i | 0.395415 | + | 0.163786i | ||||
\(776\) | −8159.20 | + | 19698.0i | −0.377446 | + | 0.911236i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 25784.3i | − | 1.18819i | ||||||
\(779\) | 3332.25 | + | 8044.77i | 0.153261 | + | 0.370005i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1796.15 | −0.0822937 | ||||||||
\(782\) | 17986.6 | − | 5542.42i | 0.822505 | − | 0.253448i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11383.3 | + | 11383.3i | 0.518556 | + | 0.518556i | ||||
\(785\) | −231.538 | − | 558.982i | −0.0105273 | − | 0.0254152i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25290.4 | − | 10475.6i | 1.14550 | − | 0.474480i | 0.272474 | − | 0.962163i | \(-0.412158\pi\) |
0.873021 | + | 0.487683i | \(0.162158\pi\) | |||||||
\(788\) | 793.539 | − | 1915.77i | 0.0358739 | − | 0.0866073i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2845.06 | − | 2845.06i | 0.128130 | − | 0.128130i | ||||
\(791\) | −31449.0 | + | 31449.0i | −1.41365 | + | 1.41365i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4787.34 | + | 11557.7i | −0.214380 | + | 0.517559i | ||||
\(794\) | 13083.0 | − | 5419.14i | 0.584757 | − | 0.242214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 496.064 | + | 1197.60i | 0.0220886 | + | 0.0533266i | ||||
\(797\) | 22469.1 | + | 22469.1i | 0.998615 | + | 0.998615i | 0.999999 | − | 0.00138359i | \(-0.000440412\pi\) |
−0.00138359 | + | 0.999999i | \(0.500440\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3075.07 | − | 32690.7i | 0.136155 | − | 1.44745i | ||||
\(800\) | 4270.84 | 0.188746 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3700.81 | − | 8934.54i | −0.162943 | − | 0.393379i | ||||
\(803\) | − | 542.879i | − | 0.0238578i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1995.55 | + | 4817.69i | −0.0873715 | + | 0.210933i | ||||
\(806\) | −3356.65 | − | 1390.37i | −0.146691 | − | 0.0607615i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7395.72 | − | 7395.72i | 0.322006 | − | 0.322006i | ||||
\(809\) | −31751.1 | − | 13151.8i | −1.37986 | − | 0.571559i | −0.435420 | − | 0.900228i | \(-0.643400\pi\) |
−0.944445 | + | 0.328669i | \(0.893400\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1216.74 | − | 503.991i | 0.0526826 | − | 0.0218218i | −0.356187 | − | 0.934415i | \(-0.615923\pi\) |
0.408869 | + | 0.912593i | \(0.365923\pi\) | |||||||
\(812\) | 3937.05i | 0.170152i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1776.55 | + | 1776.55i | 0.0764966 | + | 0.0764966i | ||||
\(815\) | −3530.49 | −0.151739 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22863.9 | −0.979078 | ||||||||
\(818\) | 18074.2 | + | 18074.2i | 0.772553 | + | 0.772553i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 88.6577i | 0.00377568i | ||||||||
\(821\) | −30932.5 | + | 12812.7i | −1.31492 | + | 0.544659i | −0.926317 | − | 0.376744i | \(-0.877044\pi\) |
−0.388607 | + | 0.921404i | \(0.627044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10852.6 | + | 4495.29i | 0.459657 | + | 0.190396i | 0.600482 | − | 0.799638i | \(-0.294975\pi\) |
−0.140825 | + | 0.990035i | \(0.544975\pi\) | |||||||
\(824\) | −23299.5 | + | 23299.5i | −0.985044 | + | 0.985044i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −22611.0 | − | 9365.80i | −0.952468 | − | 0.394525i | ||||
\(827\) | −1671.50 | + | 4035.36i | −0.0702827 | + | 0.169678i | −0.955117 | − | 0.296228i | \(-0.904271\pi\) |
0.884835 | + | 0.465905i | \(0.154271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 19994.7i | − | 0.837689i | −0.908058 | − | 0.418844i | \(-0.862435\pi\) | ||
0.908058 | − | 0.418844i | \(-0.137565\pi\) | |||||||
\(830\) | −788.543 | − | 1903.71i | −0.0329768 | − | 0.0796130i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −9753.55 | −0.406422 | ||||||||
\(833\) | 12603.0 | + | 15220.2i | 0.524211 | + | 0.633072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1852.95 | + | 1852.95i | 0.0767952 | + | 0.0767952i | ||||
\(836\) | 184.774 | + | 446.083i | 0.00764417 | + | 0.0184547i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −15660.1 | + | 6486.61i | −0.645547 | + | 0.267394i | ||||
\(839\) | 9824.30 | − | 23718.0i | 0.404258 | − | 0.975965i | −0.582362 | − | 0.812929i | \(-0.697871\pi\) |
0.986620 | − | 0.163036i | \(-0.0521286\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11203.9 | − | 11203.9i | 0.459384 | − | 0.459384i | ||||
\(842\) | −2934.10 | + | 2934.10i | −0.120090 | + | 0.120090i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −331.885 | + | 801.242i | −0.0135355 | + | 0.0326776i | ||||
\(845\) | −3633.32 | + | 1504.97i | −0.147917 | + | 0.0612693i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12593.3 | + | 30402.9i | 0.510875 | + | 1.23336i | ||||
\(848\) | −3899.13 | − | 3899.13i | −0.157897 | − | 0.157897i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −22614.4 | − | 2127.24i | −0.912552 | − | 0.0858395i | ||||
\(851\) | −24467.9 | −0.985605 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5933.37 | − | 14324.4i | −0.238165 | − | 0.574981i | 0.758928 | − | 0.651174i | \(-0.225723\pi\) |
−0.997093 | + | 0.0761933i | \(0.975723\pi\) | |||||||
\(854\) | − | 47531.5i | − | 1.90456i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −16650.9 | + | 40198.9i | −0.664857 | + | 1.60511i | ||||
\(857\) | 33181.2 | + | 13744.1i | 1.32258 | + | 0.547830i | 0.928529 | − | 0.371260i | \(-0.121074\pi\) |
0.394049 | + | 0.919089i | \(0.371074\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25862.4 | − | 25862.4i | 1.02726 | − | 1.02726i | 0.0276409 | − | 0.999618i | \(-0.491201\pi\) |
0.999618 | − | 0.0276409i | \(-0.00879949\pi\) | |||||||
\(860\) | −215.072 | − | 89.0857i | −0.00852778 | − | 0.00353232i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2226.81 | + | 922.374i | −0.0879877 | + | 0.0364457i | ||||
\(863\) | 11402.6i | 0.449768i | 0.974386 | + | 0.224884i | \(0.0722003\pi\) | ||||
−0.974386 | + | 0.224884i | \(0.927800\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 591.955 | + | 591.955i | 0.0232683 | + | 0.0232683i | ||||
\(866\) | 13152.1 | 0.516083 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1502.29 | −0.0587455 | ||||||||
\(869\) | −1939.86 | − | 1939.86i | −0.0757252 | − | 0.0757252i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5380.50i | − | 0.209312i | ||||||
\(872\) | 8130.94 | − | 3367.95i | 0.315767 | − | 0.130795i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 39919.3 | + | 16535.1i | 1.54496 | + | 0.639942i | ||||
\(875\) | 9060.64 | − | 9060.64i | 0.350063 | − | 0.350063i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21641.6 | + | 8964.22i | 0.833276 | + | 0.345154i | 0.758199 | − | 0.652023i | \(-0.226080\pi\) |
0.0750774 | + | 0.997178i | \(0.476080\pi\) | |||||||
\(878\) | −1443.19 | + | 3484.17i | −0.0554731 | + | 0.133924i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 455.351i | − | 0.0174430i | ||||||
\(881\) | 938.538 | + | 2265.83i | 0.0358912 | + | 0.0866490i | 0.940809 | − | 0.338938i | \(-0.110068\pi\) |
−0.904918 | + | 0.425587i | \(0.860068\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3832.99 | −0.146082 | −0.0730409 | − | 0.997329i | \(-0.523270\pi\) | ||||
−0.0730409 | + | 0.997329i | \(0.523270\pi\) | |||||||
\(884\) | −968.328 | − | 91.0862i | −0.0368421 | − | 0.00346557i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12257.4 | + | 12257.4i | 0.464780 | + | 0.464780i | ||||
\(887\) | −5102.84 | − | 12319.3i | −0.193164 | − | 0.466340i | 0.797390 | − | 0.603465i | \(-0.206214\pi\) |
−0.990554 | + | 0.137125i | \(0.956214\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 40070.8 | − | 16597.9i | 1.51173 | − | 0.626180i | ||||
\(890\) | −2235.58 | + | 5397.16i | −0.0841985 | + | 0.203273i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1201.88 | + | 1201.88i | −0.0451144 | + | 0.0451144i | ||||
\(893\) | 53302.1 | − | 53302.1i | 1.99741 | − | 1.99741i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 614.253 | − | 1482.94i | 0.0229410 | − | 0.0553845i | ||||
\(896\) | 27697.1 | − | 11472.5i | 1.03269 | − | 0.427756i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4532.15 | + | 10941.6i | 0.168418 | + | 0.406598i | ||||
\(899\) | 10855.7 | + | 10855.7i | 0.402734 | + | 0.402734i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4316.90 | − | 5213.37i | −0.159619 | − | 0.192767i | ||||
\(902\) | −555.468 | −0.0205045 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16066.1 | + | 38787.0i | 0.591096 | + | 1.42703i | ||||
\(905\) | − | 5483.51i | − | 0.201412i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5523.15 | + | 13334.1i | −0.202198 | + | 0.488148i | −0.992155 | − | 0.125013i | \(-0.960103\pi\) |
0.789957 | + | 0.613162i | \(0.210103\pi\) | |||||||
\(908\) | −1890.18 | − | 782.937i | −0.0690834 | − | 0.0286153i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1750.90 | + | 1750.90i | −0.0637823 | + | 0.0637823i | ||||
\(911\) | 46624.0 | + | 19312.3i | 1.69563 | + | 0.702354i | 0.999873 | − | 0.0159195i | \(-0.00506754\pi\) |
0.695760 | + | 0.718274i | \(0.255068\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1298.01 | + | 537.655i | −0.0470515 | + | 0.0194894i | ||||
\(914\) | 33767.8i | 1.22203i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 626.782 | + | 626.782i | 0.0226086 | + | 0.0226086i | ||||
\(917\) | −14134.5 | −0.509009 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −33955.2 | −1.21880 | −0.609401 | − | 0.792862i | \(-0.708590\pi\) | ||||
−0.609401 | + | 0.792862i | \(0.708590\pi\) | |||||||
\(920\) | 3480.63 | + | 3480.63i | 0.124732 | + | 0.124732i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 13739.1i | − | 0.490753i | ||||||
\(923\) | 7673.90 | − | 3178.63i | 0.273661 | − | 0.113354i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27281.3 | + | 11300.3i | 0.969735 | + | 0.401677i | ||||
\(926\) | −10030.2 | + | 10030.2i | −0.355955 | + | 0.355955i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6560.12 | + | 2717.29i | 0.232054 | + | 0.0961200i | ||||
\(929\) | 5666.65 | − | 13680.5i | 0.200126 | − | 0.483146i | −0.791675 | − | 0.610943i | \(-0.790790\pi\) |
0.991800 | + | 0.127797i | \(0.0407905\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45365.6i | 1.59699i | ||||||||
\(932\) | 1296.82 | + | 3130.80i | 0.0455781 | + | 0.110035i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 11900.4 | 0.416908 | ||||||||
\(935\) | 52.3460 | − | 556.486i | 0.00183091 | − | 0.0194642i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3635.47 | + | 3635.47i | 0.126751 | + | 0.126751i | 0.767637 | − | 0.640885i | \(-0.221433\pi\) |
−0.640885 | + | 0.767637i | \(0.721433\pi\) | |||||||
\(938\) | 7823.28 | + | 18887.1i | 0.272323 | + | 0.657446i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 709.076 | − | 293.709i | 0.0246037 | − | 0.0101912i | ||||
\(941\) | −14908.7 | + | 35992.9i | −0.516484 | + | 1.24690i | 0.423566 | + | 0.905865i | \(0.360778\pi\) |
−0.940050 | + | 0.341037i | \(0.889222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3825.14 | − | 3825.14i | 0.132093 | − | 0.132093i | ||||
\(944\) | −14716.9 | + | 14716.9i | −0.507409 | + | 0.507409i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 558.149 | − | 1347.49i | 0.0191829 | − | 0.0463116i | ||||
\(947\) | −13111.3 | + | 5430.89i | −0.449906 | + | 0.186357i | −0.596119 | − | 0.802896i | \(-0.703291\pi\) |
0.146213 | + | 0.989253i | \(0.453291\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 960.727 | + | 2319.40i | 0.0328625 | + | 0.0793371i | ||||
\(950\) | −36872.8 | − | 36872.8i | −1.25927 | − | 1.25927i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 39514.2 | − | 12176.0i | 1.34523 | − | 0.414523i | ||||
\(953\) | 32646.8 | 1.10969 | 0.554844 | − | 0.831955i | \(-0.312778\pi\) | ||||
0.554844 | + | 0.831955i | \(0.312778\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 165.979 | + | 400.708i | 0.00562403 | + | 0.0135776i | ||||
\(956\) | 618.867i | 0.0209368i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8939.78 | − | 21582.5i | 0.301494 | − | 0.727871i | ||||
\(959\) | 26565.5 | + | 11003.8i | 0.894522 | + | 0.370523i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16923.1 | − | 16923.1i | 0.568061 | − | 0.568061i | ||||
\(962\) | −10734.1 | − | 4446.22i | −0.359752 | − | 0.149014i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2628.02 | + | 1088.56i | −0.0878038 | + | 0.0363695i | ||||
\(965\) | 9551.94i | 0.318640i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11443.7 | − | 11443.7i | −0.380562 | − | 0.380562i | 0.490743 | − | 0.871305i | \(-0.336726\pi\) |
−0.871305 | + | 0.490743i | \(0.836726\pi\) | |||||||
\(968\) | 31063.4 | 1.03142 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5064.18 | 0.167630 | ||||||||
\(971\) | 20370.1 | + | 20370.1i | 0.673233 | + | 0.673233i | 0.958460 | − | 0.285227i | \(-0.0920690\pi\) |
−0.285227 | + | 0.958460i | \(0.592069\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 24615.1i | − | 0.811021i | ||||||
\(974\) | 32337.7 | − | 13394.7i | 1.06383 | − | 0.440651i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37344.1 | − | 15468.4i | −1.22475 | − | 0.507308i | ||||
\(977\) | −2231.39 | + | 2231.39i | −0.0730689 | + | 0.0730689i | −0.742697 | − | 0.669628i | \(-0.766454\pi\) |
0.669628 | + | 0.742697i | \(0.266454\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3679.96 | + | 1524.29i | 0.120135 | + | 0.0497615i | ||||
\(980\) | −176.760 | + | 426.737i | −0.00576163 | + | 0.0139098i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 31588.8i | 1.02651i | ||||||||
\(983\) | −5670.86 | − | 13690.7i | −0.184000 | − | 0.444216i | 0.804784 | − | 0.593568i | \(-0.202281\pi\) |
−0.988784 | + | 0.149352i | \(0.952281\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5510.83 | −0.178264 | ||||||||
\(986\) | −33382.9 | − | 17655.7i | −1.07822 | − | 0.570257i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1578.86 | − | 1578.86i | −0.0508402 | − | 0.0508402i | ||||
\(989\) | 5435.68 | + | 13122.9i | 0.174767 | + | 0.421925i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 820.788 | − | 339.981i | 0.0263100 | − | 0.0108979i | −0.369490 | − | 0.929235i | \(-0.620467\pi\) |
0.395800 | + | 0.918337i | \(0.370467\pi\) | |||||||
\(992\) | −1036.86 | + | 2503.19i | −0.0331857 | + | 0.0801175i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22315.8 | + | 22315.8i | −0.712086 | + | 0.712086i | ||||
\(995\) | 2435.97 | − | 2435.97i | 0.0776134 | − | 0.0776134i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1958.18 | − | 4727.46i | 0.0622027 | − | 0.150171i | −0.889722 | − | 0.456503i | \(-0.849102\pi\) |
0.951925 | + | 0.306332i | \(0.0991018\pi\) | |||||||
\(998\) | −26613.8 | + | 11023.8i | −0.844135 | + | 0.349652i | ||||
\(999\) | 0 | 0 |
(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 | 153.4.l.a.100.3 | 12 | ||
3.2 | odd | 2 | 17.4.d.a.15.1 | yes | 12 | ||
17.8 | even | 8 | inner | 153.4.l.a.127.3 | 12 | ||
51.5 | even | 16 | 289.4.a.g.1.10 | 12 | |||
51.8 | odd | 8 | 17.4.d.a.8.1 | ✓ | 12 | ||
51.14 | even | 16 | 289.4.b.e.288.4 | 12 | |||
51.20 | even | 16 | 289.4.b.e.288.3 | 12 | |||
51.29 | even | 16 | 289.4.a.g.1.9 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.8.1 | ✓ | 12 | 51.8 | odd | 8 | ||
17.4.d.a.15.1 | yes | 12 | 3.2 | odd | 2 | ||
153.4.l.a.100.3 | 12 | 1.1 | even | 1 | trivial | ||
153.4.l.a.127.3 | 12 | 17.8 | even | 8 | inner | ||
289.4.a.g.1.9 | 12 | 51.29 | even | 16 | |||
289.4.a.g.1.10 | 12 | 51.5 | even | 16 | |||
289.4.b.e.288.3 | 12 | 51.20 | even | 16 | |||
289.4.b.e.288.4 | 12 | 51.14 | even | 16 |