Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,4,Mod(13,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 8]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.13");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.i (of order \(9\), degree \(6\), 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: | \(6.37220628062\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 25.1 | ||
Character | \(\chi\) | \(=\) | 108.25 |
Dual form | 108.4.i.a.13.1 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(e\left(\frac{5}{9}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −4.52704 | − | 2.55067i | −0.871229 | − | 0.490877i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.73722 | + | 1.45770i | −0.155381 | + | 0.130381i | −0.717164 | − | 0.696904i | \(-0.754560\pi\) |
0.561783 | + | 0.827285i | \(0.310116\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.32680 | + | 1.93880i | −0.287620 | + | 0.104685i | −0.481801 | − | 0.876281i | \(-0.660017\pi\) |
0.194181 | + | 0.980966i | \(0.437795\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 13.9881 | + | 23.0940i | 0.518079 | + | 0.855333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.5694 | + | 16.4207i | 0.536399 | + | 0.450092i | 0.870304 | − | 0.492514i | \(-0.163922\pi\) |
−0.333905 | + | 0.942607i | \(0.608367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.38352 | + | 36.2027i | 0.136190 | + | 0.772372i | 0.974024 | + | 0.226446i | \(0.0727108\pi\) |
−0.837834 | + | 0.545926i | \(0.816178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 11.5826 | − | 2.16798i | 0.199374 | − | 0.0373180i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 49.6174 | + | 85.9398i | 0.707881 | + | 1.22609i | 0.965642 | + | 0.259877i | \(0.0836821\pi\) |
−0.257761 | + | 0.966209i | \(0.582985\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −15.2603 | + | 26.4317i | −0.184261 | + | 0.319150i | −0.943327 | − | 0.331864i | \(-0.892323\pi\) |
0.759066 | + | 0.651014i | \(0.225656\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 29.0598 | + | 4.80992i | 0.301970 | + | 0.0499814i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 55.1467 | + | 20.0717i | 0.499951 | + | 0.181967i | 0.579672 | − | 0.814850i | \(-0.303181\pi\) |
−0.0797209 | + | 0.996817i | \(0.525403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.8130 | + | 118.036i | −0.166504 | + | 0.944290i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.41958 | − | 140.226i | −0.0315018 | − | 0.999504i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.73992 | + | 21.2102i | −0.0239478 | + | 0.135815i | −0.994438 | − | 0.105327i | \(-0.966411\pi\) |
0.970490 | + | 0.241142i | \(0.0775220\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −226.385 | − | 82.3974i | −1.31161 | − | 0.477387i | −0.410850 | − | 0.911703i | \(-0.634768\pi\) |
−0.900761 | + | 0.434316i | \(0.856990\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −46.7076 | − | 124.252i | −0.246386 | − | 0.655440i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.42762 | − | 11.1330i | 0.0310419 | − | 0.0537662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −23.8246 | − | 41.2654i | −0.105858 | − | 0.183351i | 0.808230 | − | 0.588866i | \(-0.200426\pi\) |
−0.914088 | + | 0.405515i | \(0.867092\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 63.4429 | − | 180.173i | 0.260487 | − | 0.739765i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16.7572 | + | 95.0347i | 0.0638300 | + | 0.361998i | 0.999947 | + | 0.0103090i | \(0.00328150\pi\) |
−0.936117 | + | 0.351689i | \(0.885607\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −124.156 | − | 104.179i | −0.440315 | − | 0.369468i | 0.395512 | − | 0.918461i | \(-0.370567\pi\) |
−0.835827 | + | 0.548993i | \(0.815011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −57.9645 | − | 19.7288i | −0.192019 | − | 0.0653555i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 323.003 | − | 117.563i | 1.00244 | − | 0.364859i | 0.211916 | − | 0.977288i | \(-0.432030\pi\) |
0.790526 | + | 0.612429i | \(0.209807\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −238.137 | + | 199.821i | −0.694278 | + | 0.582569i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.41531 | − | 515.610i | −0.0148685 | − | 1.41568i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 343.554 | 0.890391 | 0.445196 | − | 0.895433i | \(-0.353134\pi\) | ||||
0.445196 | + | 0.895433i | \(0.353134\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −57.9326 | −0.142030 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 136.503 | − | 80.7331i | 0.317197 | − | 0.187603i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −212.363 | + | 178.194i | −0.468598 | + | 0.393201i | −0.846283 | − | 0.532734i | \(-0.821165\pi\) |
0.377685 | + | 0.925934i | \(0.376720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −327.611 | + | 119.241i | −0.687643 | + | 0.250282i | −0.662126 | − | 0.749393i | \(-0.730346\pi\) |
−0.0255176 | + | 0.999674i | \(0.508123\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −119.286 | − | 95.8968i | −0.238550 | − | 0.191776i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −63.8622 | − | 53.5868i | −0.121864 | − | 0.102256i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −78.4747 | − | 445.052i | −0.143093 | − | 0.811519i | −0.968879 | − | 0.247536i | \(-0.920379\pi\) |
0.825786 | − | 0.563983i | \(-0.190732\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −198.455 | − | 231.527i | −0.346248 | − | 0.403950i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 407.568 | + | 705.928i | 0.681259 | + | 1.17998i | 0.974597 | + | 0.223967i | \(0.0719007\pi\) |
−0.293338 | + | 0.956009i | \(0.594766\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 71.6513 | − | 124.104i | 0.114879 | − | 0.198976i | −0.802852 | − | 0.596178i | \(-0.796685\pi\) |
0.917731 | + | 0.397202i | \(0.130019\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 395.293 | − | 481.268i | 0.608594 | − | 0.740960i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −136.078 | − | 49.5285i | −0.201397 | − | 0.0733025i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −156.000 | + | 884.718i | −0.222169 | + | 1.25998i | 0.645855 | + | 0.763460i | \(0.276501\pi\) |
−0.868024 | + | 0.496522i | \(0.834610\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −337.664 | + | 646.083i | −0.463188 | + | 0.886260i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 81.0870 | − | 459.867i | 0.107234 | − | 0.608157i | −0.883070 | − | 0.469241i | \(-0.844527\pi\) |
0.990304 | − | 0.138915i | \(-0.0443615\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −211.470 | − | 76.9690i | −0.269849 | − | 0.0982171i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 71.0310 | − | 86.4799i | 0.0875324 | − | 0.106570i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −218.426 | + | 378.326i | −0.260148 | + | 0.450589i | −0.966281 | − | 0.257490i | \(-0.917105\pi\) |
0.706133 | + | 0.708079i | \(0.250438\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −104.193 | − | 180.468i | −0.120027 | − | 0.207892i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 814.684 | + | 950.450i | 0.908374 | + | 1.05975i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.0189 | − | 68.1626i | −0.0129801 | − | 0.0736140i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1103.50 | + | 925.949i | 1.15509 | + | 0.969236i | 0.999826 | − | 0.0186370i | \(-0.00593269\pi\) |
0.155264 | + | 0.987873i | \(0.450377\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −105.479 | + | 681.629i | −0.107082 | + | 0.691983i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 405.014 | − | 147.413i | 0.399014 | − | 0.145229i | −0.134716 | − | 0.990884i | \(-0.543012\pi\) |
0.533730 | + | 0.845655i | \(0.320790\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −422.424 | + | 354.456i | −0.404104 | + | 0.339083i | −0.822077 | − | 0.569376i | \(-0.807185\pi\) |
0.417973 | + | 0.908459i | \(0.362741\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −57.4947 | + | 34.0046i | −0.0534372 | + | 0.0316049i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 860.291 | 0.777266 | 0.388633 | − | 0.921393i | \(-0.372947\pi\) | ||||
0.388633 | + | 0.921393i | \(0.372947\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2113.40 | 1.85713 | 0.928563 | − | 0.371176i | \(-0.121045\pi\) | ||||
0.928563 | + | 0.371176i | \(0.121045\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.60025 | + | 247.579i | 0.00222347 | + | 0.211704i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1627.93 | + | 1366.00i | −1.35525 | + | 1.13719i | −0.377829 | + | 0.925875i | \(0.623329\pi\) |
−0.977419 | + | 0.211313i | \(0.932226\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −125.060 | + | 45.5182i | −0.101408 | + | 0.0369095i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −746.772 | + | 653.830i | −0.590078 | + | 0.516637i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −430.921 | − | 361.586i | −0.331954 | − | 0.278542i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.803 | − | 668.095i | −0.0885072 | − | 0.501949i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 166.542 | − | 472.968i | 0.122086 | − | 0.346716i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −277.641 | − | 480.888i | −0.198663 | − | 0.344095i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1062.08 | − | 1839.58i | 0.742083 | − | 1.28533i | −0.209462 | − | 0.977817i | \(-0.567171\pi\) |
0.951545 | − | 0.307509i | \(-0.0994954\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 296.330 | + | 788.302i | 0.202251 | + | 0.538032i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1522.41 | − | 554.114i | −1.01537 | − | 0.369566i | −0.219880 | − | 0.975527i | \(-0.570566\pi\) |
−0.795494 | + | 0.605961i | \(0.792789\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.0431 | − | 170.383i | 0.0195870 | − | 0.111083i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 212.086 | + | 237.161i | 0.135211 | + | 0.151197i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 498.807 | − | 2828.87i | 0.311065 | − | 1.76414i | −0.282418 | − | 0.959291i | \(-0.591136\pi\) |
0.593483 | − | 0.804847i | \(-0.297752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2332.30 | − | 848.889i | −1.42319 | − | 0.517999i | −0.488218 | − | 0.872722i | \(-0.662353\pi\) |
−0.934971 | + | 0.354723i | \(0.884575\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1762.11 | − | 291.661i | −1.05246 | − | 0.174200i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −469.551 | + | 813.287i | −0.274586 | + | 0.475598i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −24.4210 | − | 42.2983i | −0.0139866 | − | 0.0242254i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1587.74 | − | 297.186i | 0.890845 | − | 0.166745i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −553.705 | − | 3140.22i | −0.304438 | − | 1.72655i | −0.626138 | − | 0.779712i | \(-0.715365\pi\) |
0.321700 | − | 0.946842i | \(-0.395746\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 950.851 | + | 797.859i | 0.512445 | + | 0.429992i | 0.861989 | − | 0.506928i | \(-0.169219\pi\) |
−0.349544 | + | 0.936920i | \(0.613663\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1290.64 | + | 2348.00i | −0.681973 | + | 1.24068i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 513.390 | − | 186.859i | 0.266042 | − | 0.0968313i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1992.20 | − | 1671.65i | 1.01271 | − | 0.849761i | 0.0240121 | − | 0.999712i | \(-0.492356\pi\) |
0.988693 | + | 0.149951i | \(0.0479115\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1555.28 | − | 876.293i | −0.775734 | − | 0.437073i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −332.670 | −0.162845 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1268.83 | 0.609708 | 0.304854 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304854 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 262.263 | + | 147.767i | 0.123740 | + | 0.0697192i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1848.70 | + | 1551.25i | −0.856628 | + | 0.718796i | −0.961239 | − | 0.275717i | \(-0.911085\pi\) |
0.104611 | + | 0.994513i | \(0.466640\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 794.616 | − | 289.216i | 0.361682 | − | 0.131642i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −823.877 | + | 17.3078i | −0.368441 | + | 0.00774012i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2855.25 | − | 2395.84i | −1.25480 | − | 1.05290i | −0.996216 | − | 0.0869166i | \(-0.972299\pi\) |
−0.258587 | − | 0.965988i | \(-0.583257\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −117.982 | − | 669.107i | −0.0509633 | − | 0.289027i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1415.89 | − | 265.021i | 0.601270 | − | 0.112543i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1808.10 | + | 3131.73i | 0.754995 | + | 1.30769i | 0.945377 | + | 0.325979i | \(0.105694\pi\) |
−0.190382 | + | 0.981710i | \(0.560973\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1109.38 | − | 1921.50i | 0.455577 | − | 0.789083i | −0.543144 | − | 0.839640i | \(-0.682766\pi\) |
0.998721 | + | 0.0505564i | \(0.0160995\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1787.25 | + | 295.822i | 0.721952 | + | 0.119496i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 101.541 | + | 36.9579i | 0.0403538 | + | 0.0146876i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −440.207 | + | 2496.54i | −0.172145 | + | 0.976283i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 295.413 | + | 738.389i | 0.113694 | + | 0.284179i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 113.936 | − | 646.162i | 0.0431628 | − | 0.244789i | −0.955591 | − | 0.294696i | \(-0.904782\pi\) |
0.998754 | + | 0.0499076i | \(0.0158927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 377.376 | + | 137.354i | 0.140747 | + | 0.0512276i | 0.411433 | − | 0.911440i | \(-0.365028\pi\) |
−0.270686 | + | 0.962668i | \(0.587251\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 152.424 | + | 405.481i | 0.0559761 | + | 0.148908i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1359.16 | − | 2354.14i | 0.491555 | − | 0.851398i | −0.508398 | − | 0.861122i | \(-0.669762\pi\) |
0.999953 | + | 0.00972432i | \(0.00309540\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 262.797 | + | 455.177i | 0.0936138 | + | 0.162144i | 0.909029 | − | 0.416732i | \(-0.136825\pi\) |
−0.815415 | + | 0.578876i | \(0.803491\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −779.925 | + | 2214.93i | −0.273690 | + | 0.777260i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −21.2004 | − | 120.233i | −0.00732992 | − | 0.0415700i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −167.643 | − | 140.669i | −0.0571155 | − | 0.0479256i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 307.862 | + | 1554.32i | 0.103372 | + | 0.521898i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −732.662 | + | 266.667i | −0.242484 | + | 0.0882571i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3546.31 | + | 2975.70i | −1.15705 | + | 0.970881i | −0.999861 | − | 0.0166873i | \(-0.994688\pi\) |
−0.157190 | + | 0.987568i | \(0.550244\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −44.4825 | − | 4235.34i | −0.0143094 | − | 1.36244i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 367.546 | 0.116588 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1365.66 | 0.427221 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −640.916 | + | 379.063i | −0.197759 | + | 0.116962i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2794.52 | + | 2344.88i | −0.850588 | + | 0.713728i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1359.00 | + | 494.635i | −0.408096 | + | 0.148535i | −0.537907 | − | 0.843004i | \(-0.680785\pi\) |
0.129812 | + | 0.991539i | \(0.458563\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3017.06 | + | 1170.45i | −0.893945 | + | 0.346801i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4668.86 | + | 3917.63i | 1.36512 | + | 1.14547i | 0.974363 | + | 0.224981i | \(0.0722319\pi\) |
0.390759 | + | 0.920493i | \(0.372212\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −184.191 | − | 1044.60i | −0.0531514 | − | 0.301437i | 0.946630 | − | 0.322321i | \(-0.104463\pi\) |
−0.999782 | + | 0.0208842i | \(0.993352\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 489.701 | + | 571.309i | 0.139480 | + | 0.162725i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 444.253 | + | 769.468i | 0.124910 | + | 0.216350i | 0.921698 | − | 0.387909i | \(-0.126803\pi\) |
−0.796788 | + | 0.604259i | \(0.793469\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −389.754 | + | 675.074i | −0.108190 | + | 0.187391i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2962.84 | − | 3607.25i | 0.812057 | − | 0.988675i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4785.72 | + | 1741.86i | 1.29524 | + | 0.471429i | 0.895444 | − | 0.445175i | \(-0.146858\pi\) |
0.399797 | + | 0.916604i | \(0.369081\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −401.648 | + | 2277.86i | −0.107354 | + | 0.608837i | 0.882899 | + | 0.469562i | \(0.155588\pi\) |
−0.990254 | + | 0.139275i | \(0.955523\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3176.57 | − | 2063.57i | 0.838588 | − | 0.544766i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 122.418 | − | 694.265i | 0.0319224 | − | 0.181041i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1054.31 | − | 383.739i | −0.271597 | − | 0.0988532i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1540.06 | + | 1875.01i | −0.391956 | + | 0.477204i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2065.57 | + | 3577.67i | −0.519433 | + | 0.899684i | 0.480312 | + | 0.877098i | \(0.340524\pi\) |
−0.999745 | + | 0.0225867i | \(0.992810\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 749.595 | + | 1298.34i | 0.186271 | + | 0.322631i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 761.012 | + | 887.833i | 0.186888 | + | 0.218032i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −88.6207 | − | 502.593i | −0.0215098 | − | 0.121988i | 0.972162 | − | 0.234309i | \(-0.0752827\pi\) |
−0.993672 | + | 0.112321i | \(0.964172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 206.914 | + | 173.622i | 0.0496410 | + | 0.0416537i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −542.142 | + | 210.321i | −0.128574 | + | 0.0498794i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2625.90 | − | 955.748i | 0.615664 | − | 0.224083i | −0.0153157 | − | 0.999883i | \(-0.504875\pi\) |
0.630980 | + | 0.775799i | \(0.282653\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −596.828 | + | 500.798i | −0.138350 | + | 0.116090i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1953.81 | − | 1155.56i | 0.447832 | − | 0.264866i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4160.31 | 0.942968 | 0.471484 | − | 0.881875i | \(-0.343719\pi\) | ||||
0.471484 | + | 0.881875i | \(0.343719\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5111.90 | −1.14585 | −0.572926 | − | 0.819607i | \(-0.694192\pi\) | ||||
−0.572926 | + | 0.819607i | \(0.694192\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.3718 | + | 1082.75i | 0.00252107 | + | 0.240040i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2345.53 | + | 1968.13i | −0.514330 | + | 0.431574i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 411.220 | − | 149.672i | 0.0891980 | − | 0.0324654i | −0.297036 | − | 0.954866i | \(-0.595998\pi\) |
0.386234 | + | 0.922401i | \(0.373776\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1263.82 | − | 6380.71i | −0.271193 | − | 1.36919i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −533.382 | − | 447.561i | −0.113235 | − | 0.0950151i | 0.584412 | − | 0.811457i | \(-0.301325\pi\) |
−0.697647 | + | 0.716442i | \(0.745770\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −205.873 | − | 1167.56i | −0.0432433 | − | 0.245245i | 0.955522 | − | 0.294919i | \(-0.0952928\pi\) |
−0.998765 | + | 0.0496742i | \(0.984182\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −119.450 | + | 339.231i | −0.0248268 | + | 0.0705063i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −273.515 | − | 473.742i | −0.0562546 | − | 0.0974358i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2467.27 | + | 4273.43i | −0.502191 | + | 0.869821i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2633.81 | − | 7006.48i | −0.530572 | − | 1.41143i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6216.76 | + | 2262.72i | 1.23955 | + | 0.451158i | 0.876857 | − | 0.480752i | \(-0.159636\pi\) |
0.362690 | + | 0.931910i | \(0.381858\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 109.168 | − | 619.122i | 0.0215458 | − | 0.122192i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2216.12 | − | 2816.72i | 0.432971 | − | 0.550312i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −374.622 | + | 2124.59i | −0.0724581 | + | 0.410930i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 863.333 | + | 314.227i | 0.165321 | + | 0.0601720i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2209.52 | − | 365.714i | −0.418922 | − | 0.0693390i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 395.314 | − | 684.704i | 0.0742152 | − | 0.128544i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2737.00 | − | 4740.62i | −0.508823 | − | 0.881308i | −0.999948 | − | 0.0102185i | \(-0.996747\pi\) |
0.491124 | − | 0.871089i | \(-0.336586\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2816.43 | − | 527.169i | 0.518515 | − | 0.0970538i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1849.24 | − | 10487.6i | −0.337173 | − | 1.91220i | −0.404628 | − | 0.914482i | \(-0.632599\pi\) |
0.0674546 | − | 0.997722i | \(-0.478512\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5515.11 | − | 4627.73i | −0.995950 | − | 0.835701i | −0.00953196 | − | 0.999955i | \(-0.503034\pi\) |
−0.986418 | + | 0.164253i | \(0.947479\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 347.015 | − | 7.29001i | 0.0620701 | − | 0.00130395i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 82.0633 | − | 29.8686i | 0.0145398 | − | 0.00529207i | −0.334740 | − | 0.942311i | \(-0.608648\pi\) |
0.349280 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −421.473 | + | 353.658i | −0.0739748 | + | 0.0620722i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3894.57 | − | 2194.32i | −0.677176 | − | 0.381542i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3028.71 | −0.521740 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4406.10 | −0.752019 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9567.42 | − | 5390.58i | −1.61798 | − | 0.911621i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1492.64 | + | 1252.47i | −0.250127 | + | 0.209882i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3752.27 | + | 1365.71i | −0.623091 | + | 0.226787i | −0.634221 | − | 0.773151i | \(-0.718679\pi\) |
0.0111304 | + | 0.999938i | \(0.496457\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 619.722 | − | 1127.43i | 0.101984 | − | 0.185534i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 785.079 | + | 658.760i | 0.128040 | + | 0.107438i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1144.62 | + | 6491.47i | 0.185019 | + | 1.04930i | 0.925931 | + | 0.377694i | \(0.123283\pi\) |
−0.740911 | + | 0.671603i | \(0.765606\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10853.9 | − | 2031.60i | 1.73895 | − | 0.325490i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3077.19 | − | 5329.85i | −0.488678 | − | 0.846416i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1853.27 | − | 3209.96i | 0.291741 | − | 0.505311i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 682.255 | + | 112.925i | 0.106468 | + | 0.0176223i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9057.25 | + | 3296.57i | 1.40121 | + | 0.509997i | 0.928536 | − | 0.371242i | \(-0.121068\pi\) |
0.472670 | + | 0.881240i | \(0.343290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1123.06 | − | 6369.21i | 0.172253 | − | 0.976895i | −0.769014 | − | 0.639232i | \(-0.779253\pi\) |
0.941267 | − | 0.337663i | \(-0.109636\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5048.37 | − | 1055.14i | 0.767698 | − | 0.160453i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1919.44 | + | 10885.7i | −0.289410 | + | 1.64133i | 0.399683 | + | 0.916653i | \(0.369120\pi\) |
−0.689093 | + | 0.724673i | \(0.741991\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1737.06 | − | 632.240i | −0.259701 | − | 0.0945234i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1028.51 | + | 2736.05i | 0.152478 | + | 0.405622i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1362.21 | − | 2359.42i | 0.200264 | − | 0.346868i | −0.748349 | − | 0.663305i | \(-0.769153\pi\) |
0.948614 | + | 0.316437i | \(0.102487\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2963.74 | + | 5133.35i | 0.432096 | + | 0.748411i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1170.79 | + | 3324.97i | −0.169286 | + | 0.480759i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 56.4319 | + | 320.041i | 0.00809255 | + | 0.0458951i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4765.13 | + | 3998.42i | 0.677760 | + | 0.568708i | 0.915351 | − | 0.402657i | \(-0.131913\pi\) |
−0.237591 | + | 0.971365i | \(0.576358\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1960.33 | + | 1716.35i | −0.276560 | + | 0.242140i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1830.04 | + | 666.080i | −0.256094 | + | 0.0932107i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6859.41 | − | 5755.73i | 0.952190 | − | 0.798982i | −0.0274753 | − | 0.999622i | \(-0.508747\pi\) |
0.979665 | + | 0.200641i | \(0.0643023\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 30.3021 | + | 2885.17i | 0.00417278 | + | 0.397305i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −791.740 | −0.108161 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 569.718 | 0.0772148 | 0.0386074 | − | 0.999254i | \(-0.487708\pi\) | ||||
0.0386074 | + | 0.999254i | \(0.487708\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9500.26 | + | 5618.82i | −1.27746 | + | 0.755541i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1839.24 | + | 1543.30i | −0.245380 | + | 0.205898i | −0.757180 | − | 0.653206i | \(-0.773423\pi\) |
0.511800 | + | 0.859105i | \(0.328979\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 308.595 | − | 112.320i | 0.0408506 | − | 0.0148684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 669.201 | − | 4324.51i | 0.0879003 | − | 0.568029i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2278.94 | − | 1912.26i | −0.297036 | − | 0.249243i | 0.482073 | − | 0.876131i | \(-0.339884\pi\) |
−0.779109 | + | 0.626888i | \(0.784328\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1011.27 | + | 5735.20i | 0.130798 | + | 0.741794i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 5478.66 | + | 6391.67i | 0.703211 | + | 0.820400i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1018.65 | − | 1764.35i | −0.129756 | − | 0.224744i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5487.38 | + | 9504.43i | −0.693713 | + | 1.20155i | 0.276900 | + | 0.960899i | \(0.410693\pi\) |
−0.970613 | + | 0.240647i | \(0.922640\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −570.598 | + | 694.700i | −0.0715930 | + | 0.0871641i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12728.6 | + | 4632.81i | 1.58512 | + | 0.576937i | 0.976310 | − | 0.216378i | \(-0.0694244\pi\) |
0.608811 | + | 0.793315i | \(0.291647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1537.88 | − | 8721.74i | 0.190092 | − | 1.07807i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −355.198 | − | 1614.60i | −0.0435801 | − | 0.198099i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 211.373 | − | 1198.76i | 0.0257429 | − | 0.145995i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11812.0 | + | 4299.21i | 1.42803 | + | 0.519761i | 0.936367 | − | 0.351023i | \(-0.114166\pi\) |
0.491665 | + | 0.870784i | \(0.336388\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9473.65 | + | 11534.1i | −1.13698 | + | 1.38427i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 785.733 | − | 1360.93i | 0.0936160 | − | 0.162148i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 529.482 | + | 917.090i | 0.0626295 | + | 0.108478i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8393.18 | + | 9791.89i | 0.985650 | + | 1.14991i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2394.23 | − | 13578.3i | −0.279154 | − | 1.58316i | −0.725448 | − | 0.688277i | \(-0.758368\pi\) |
0.446294 | − | 0.894886i | \(-0.352744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3826.83 | − | 3211.09i | −0.443013 | − | 0.371732i | 0.393823 | − | 0.919186i | \(-0.371152\pi\) |
−0.836835 | + | 0.547455i | \(0.815597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7233.21 | + | 5814.93i | 0.831420 | + | 0.668396i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11176.7 | + | 4067.99i | −1.27565 | + | 0.464297i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1513.93 | − | 1270.34i | 0.171579 | − | 0.143972i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4200.11 | − | 2484.11i | 0.472688 | − | 0.279566i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13508.3 | −1.50968 | −0.754838 | − | 0.655912i | \(-0.772284\pi\) | ||||
−0.754838 | + | 0.655912i | \(0.772284\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6126.85 | −0.679994 | −0.339997 | − | 0.940427i | \(-0.610426\pi\) | ||||
−0.339997 | + | 0.940427i | \(0.610426\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.66534 | + | 253.776i | 0.000293777 | + | 0.0279716i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1372.09 | + | 1151.32i | −0.150196 | + | 0.126030i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13612.4 | − | 4954.50i | 1.47992 | − | 0.538646i | 0.529144 | − | 0.848532i | \(-0.322513\pi\) |
0.950774 | + | 0.309886i | \(0.100291\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7945.76 | − | 2704.42i | −0.857981 | − | 0.292022i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3551.99 | + | 2980.47i | 0.380948 | + | 0.319653i | 0.813074 | − | 0.582160i | \(-0.197792\pi\) |
−0.432126 | + | 0.901813i | \(0.642237\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −172.031 | − | 975.633i | −0.0183259 | − | 0.103931i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5503.02 | + | 15628.2i | −0.582291 | + | 1.65367i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4160.46 | − | 7206.13i | −0.437292 | − | 0.757412i | 0.560187 | − | 0.828366i | \(-0.310729\pi\) |
−0.997480 | + | 0.0709535i | \(0.977396\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1232.60 | + | 2134.93i | −0.128694 | + | 0.222905i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2269.46 | − | 6037.25i | −0.235383 | − | 0.626169i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 444.075 | + | 161.630i | 0.0457551 | + | 0.0166535i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1535.70 | − | 8709.37i | 0.157192 | − | 0.891482i | −0.799562 | − | 0.600584i | \(-0.794935\pi\) |
0.956754 | − | 0.290898i | \(-0.0939541\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 11831.7 | − | 7337.49i | 1.20318 | − | 0.746154i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −890.872 | + | 5052.38i | −0.0900044 | + | 0.510440i | 0.906160 | + | 0.422936i | \(0.139000\pi\) |
−0.996164 | + | 0.0875046i | \(0.972111\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11339.2 | + | 4127.13i | 1.13818 | + | 0.414264i | 0.841256 | − | 0.540637i | \(-0.181817\pi\) |
0.296925 | + | 0.954901i | \(0.404039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2800.75 | − | 463.574i | −0.279316 | − | 0.0462317i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 92.2875 | − | 159.847i | 0.00914466 | − | 0.0158390i | −0.861417 | − | 0.507899i | \(-0.830422\pi\) |
0.870562 | + | 0.492060i | \(0.163756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1280.88 | + | 2218.56i | 0.126110 | + | 0.218429i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13282.6 | + | 2486.19i | −1.29943 | + | 0.243222i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −718.961 | − | 4077.43i | −0.0698898 | − | 0.396365i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2802.29 | − | 2351.40i | −0.270690 | − | 0.227136i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4805.67 | + | 7934.03i | 0.461293 | + | 0.761581i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 85.0550 | − | 30.9575i | 0.00811329 | − | 0.00295299i | −0.337960 | − | 0.941160i | \(-0.609737\pi\) |
0.346074 | + | 0.938207i | \(0.387515\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1341.84 | − | 1125.94i | 0.127199 | − | 0.106732i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1506.01 | + | 848.533i | 0.141875 | + | 0.0799370i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3266.78 | −0.305849 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12807.1 | 1.19167 | 0.595835 | − | 0.803107i | \(-0.296821\pi\) | ||||
0.595835 | + | 0.803107i | \(0.296821\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −5744.04 | − | 3236.37i | −0.531195 | − | 0.299292i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4314.38 | + | 3620.19i | −0.396548 | + | 0.332743i | −0.819158 | − | 0.573568i | \(-0.805559\pi\) |
0.422609 | + | 0.906312i | \(0.361114\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2008.36 | + | 730.984i | −0.183473 | + | 0.0667786i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −810.369 | − | 1337.90i | −0.0735826 | − | 0.121483i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3539.68 | − | 2970.15i | −0.319470 | − | 0.268067i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −401.541 | − | 2277.25i | −0.0360229 | − | 0.204296i | 0.961484 | − | 0.274860i | \(-0.0886314\pi\) |
−0.997507 | + | 0.0705635i | \(0.977520\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 12325.9 | − | 2307.11i | 1.09916 | − | 0.205737i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7235.56 | − | 12532.4i | −0.641387 | − | 1.11092i | −0.985123 | − | 0.171849i | \(-0.945026\pi\) |
0.343736 | − | 0.939066i | \(-0.388308\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −488.714 | + | 846.477i | −0.0430643 | + | 0.0745896i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4334.95 | − | 717.511i | −0.379728 | − | 0.0628517i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12136.9 | + | 4417.47i | 1.05689 | + | 0.384678i | 0.811261 | − | 0.584685i | \(-0.198782\pi\) |
0.245633 | + | 0.969363i | \(0.421004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −141.060 | + | 799.993i | −0.0122116 | + | 0.0692556i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3773.87 | + | 2023.09i | 0.324796 | + | 0.174116i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 217.153 | − | 1231.53i | 0.0185804 | − | 0.105375i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8251.43 | + | 3003.28i | 0.701929 | + | 0.255481i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6814.83 | + | 18128.9i | 0.576373 | + | 1.53327i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5815.68 | − | 10073.0i | 0.489039 | − | 0.847041i | −0.510881 | − | 0.859651i | \(-0.670681\pi\) |
0.999920 | + | 0.0126104i | \(0.00401413\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7100.15 | − | 12297.8i | −0.593629 | − | 1.02820i | −0.993739 | − | 0.111728i | \(-0.964361\pi\) |
0.400110 | − | 0.916467i | \(-0.368972\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1172.57 | + | 3330.01i | −0.0974762 | + | 0.276826i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4151.41 | − | 23543.8i | −0.343147 | − | 1.94608i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6682.18 | − | 5607.02i | −0.549205 | − | 0.460838i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7085.76 | − | 2411.71i | −0.579088 | − | 0.197099i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3333.55 | + | 1213.31i | −0.270904 | + | 0.0986011i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1494.51 | + | 1254.04i | −0.120773 | + | 0.101340i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −197.339 | − | 18789.3i | −0.0158581 | − | 1.50991i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7941.40 | −0.634620 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14803.9 | −1.17647 | −0.588235 | − | 0.808690i | \(-0.700177\pi\) | ||||
−0.588235 | + | 0.808690i | \(0.700177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9923.32 | + | 5869.04i | −0.784255 | + | 0.463839i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3671.43 | + | 3080.69i | −0.288563 | + | 0.242133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8475.32 | − | 3084.76i | 0.662483 | − | 0.241124i | 0.0111752 | − | 0.999938i | \(-0.496443\pi\) |
0.651308 | + | 0.758813i | \(0.274221\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7336.40 | − | 5897.88i | −0.570328 | − | 0.458498i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −503.548 | − | 422.527i | −0.0389326 | − | 0.0326683i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −884.309 | − | 5015.17i | −0.0680012 | − | 0.385654i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −365.413 | − | 426.308i | −0.0279476 | − | 0.0326050i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2010.86 | + | 3482.91i | 0.152967 | + | 0.264947i | 0.932317 | − | 0.361642i | \(-0.117784\pi\) |
−0.779350 | + | 0.626589i | \(0.784450\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2979.01 | − | 5159.80i | 0.225400 | − | 0.390405i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8360.69 | − | 10179.1i | 0.629213 | − | 0.766064i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2100.11 | + | 764.377i | 0.157210 | + | 0.0572196i | 0.419426 | − | 0.907789i | \(-0.362231\pi\) |
−0.262217 | + | 0.965009i | \(0.584454\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 836.860 | − | 4746.07i | 0.0623132 | − | 0.353396i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 546.046 | − | 4096.22i | 0.0404440 | − | 0.303395i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1240.71 | + | 7036.41i | −0.0914117 | + | 0.518421i | 0.904376 | + | 0.426736i | \(0.140337\pi\) |
−0.995788 | + | 0.0916855i | \(0.970775\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5058.44 | − | 1841.12i | −0.370734 | − | 0.134936i | 0.149932 | − | 0.988696i | \(-0.452094\pi\) |
−0.520667 | + | 0.853760i | \(0.674317\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2163.94 | + | 2634.59i | −0.157766 | + | 0.192079i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3516.96 | + | 6091.56i | −0.255074 | + | 0.441801i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −869.206 | − | 1505.51i | −0.0627132 | − | 0.108622i | 0.832964 | − | 0.553327i | \(-0.186642\pi\) |
−0.895677 | + | 0.444705i | \(0.853309\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1358.05 | − | 1584.37i | −0.0974761 | − | 0.113720i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 459.655 | + | 2606.83i | 0.0328222 | + | 0.186144i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6723.13 | + | 5641.38i | 0.477605 | + | 0.400758i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 344.219 | − | 2224.41i | 0.0243277 | − | 0.157211i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3342.33 | + | 1216.51i | −0.235013 | + | 0.0855379i | −0.456842 | − | 0.889548i | \(-0.651020\pi\) |
0.221829 | + | 0.975086i | \(0.428797\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5632.61 | − | 4726.32i | 0.394037 | − | 0.330636i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12157.6 | + | 7190.49i | −0.846189 | + | 0.500469i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1926.38 | 0.133402 | 0.0667008 | − | 0.997773i | \(-0.478753\pi\) | ||||
0.0667008 | + | 0.997773i | \(0.478753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1275.69 | 0.0878959 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −28.6820 | − | 2730.91i | −0.00196629 | − | 0.187217i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2265.90 | − | 1901.31i | 0.154561 | − | 0.129692i | −0.562228 | − | 0.826982i | \(-0.690056\pi\) |
0.716789 | + | 0.697290i | \(0.245611\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9704.79 | + | 3532.26i | −0.658680 | + | 0.239740i | −0.649666 | − | 0.760219i | \(-0.725091\pi\) |
−0.00901370 | + | 0.999959i | \(0.502869\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9180.31 | − | 8037.74i | 0.619986 | − | 0.542823i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1178.53 | + | 988.904i | 0.0791968 | + | 0.0664540i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1586.82 | + | 8999.33i | 0.106107 | + | 0.601765i | 0.990772 | + | 0.135537i | \(0.0432761\pi\) |
−0.884665 | + | 0.466228i | \(0.845613\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −210.701 | + | 598.375i | −0.0140197 | + | 0.0398151i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6318.01 | + | 10943.1i | 0.418329 | + | 0.724568i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7350.25 | + | 12731.0i | −0.484296 | + | 0.838826i | −0.999837 | − | 0.0180389i | \(-0.994258\pi\) |
0.515541 | + | 0.856865i | \(0.327591\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 400.124 | + | 1064.42i | 0.0262351 | + | 0.0697909i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27125.0 | + | 9872.69i | 1.76987 | + | 0.644181i | 0.999982 | + | 0.00600359i | \(0.00191101\pi\) |
0.769890 | + | 0.638177i | \(0.220311\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4390.06 | + | 24897.3i | −0.285059 | + | 1.61665i | 0.420015 | + | 0.907517i | \(0.362025\pi\) |
−0.705074 | + | 0.709133i | \(0.749086\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2570.87 | − | 7821.73i | 0.166128 | − | 0.505435i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 430.017 | − | 2438.75i | 0.0276537 | − | 0.156832i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12895.3 | − | 4693.51i | −0.825299 | − | 0.300384i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3996.97 | + | 661.569i | 0.254583 | + | 0.0421380i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2364.23 | − | 4094.96i | 0.149870 | − | 0.259582i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8143.24 | + | 14104.5i | 0.513752 | + | 0.889844i | 0.999873 | + | 0.0159525i | \(0.00507807\pi\) |
−0.486121 | + | 0.873891i | \(0.661589\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 23644.3 | − | 4425.65i | 1.48464 | − | 0.277889i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 836.486 | + | 4743.95i | 0.0522755 | + | 0.296469i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8754.22 | − | 7345.67i | −0.544513 | − | 0.456901i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10601.6 | + | 19287.0i | −0.656326 | + | 1.19402i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13181.2 | − | 4797.57i | 0.812211 | − | 0.295621i | 0.0976741 | − | 0.995218i | \(-0.468860\pi\) |
0.714537 | + | 0.699598i | \(0.246637\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6177.76 | + | 5183.75i | −0.378891 | + | 0.317927i | −0.812267 | − | 0.583286i | \(-0.801767\pi\) |
0.433376 | + | 0.901213i | \(0.357322\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1663.90 | − | 937.491i | −0.101575 | − | 0.0572305i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18799.9 | 1.14235 | 0.571175 | − | 0.820828i | \(-0.306488\pi\) | ||||
0.571175 | + | 0.820828i | \(0.306488\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7081.87 | −0.428332 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6182.38 | − | 3483.35i | −0.372207 | − | 0.209713i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −22715.5 | + | 19060.6i | −1.36130 | + | 1.14226i | −0.385718 | + | 0.922617i | \(0.626046\pi\) |
−0.975579 | + | 0.219648i | \(0.929509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3452.50 | − | 1256.61i | 0.205954 | − | 0.0749613i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3868.32 | − | 81.2647i | 0.229707 | − | 0.00482563i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24740.9 | + | 20760.1i | 1.46247 | + | 1.22716i | 0.922795 | + | 0.385291i | \(0.125899\pi\) |
0.539679 | + | 0.841871i | \(0.318546\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2315.53 | + | 13132.0i | 0.136254 | + | 0.772732i | 0.973979 | + | 0.226640i | \(0.0727741\pi\) |
−0.837725 | + | 0.546092i | \(0.816115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18631.9 | − | 3487.46i | 1.09141 | − | 0.204286i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 196.176 | + | 339.786i | 0.0114396 | + | 0.0198140i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −631.969 | + | 1094.60i | −0.0366866 | + | 0.0635430i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7413.89 | + | 1227.13i | 0.428457 | + | 0.0709172i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8369.15 | − | 3046.12i | −0.481501 | − | 0.175252i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2027.20 | − | 11496.8i | 0.116111 | − | 0.658500i | −0.870083 | − | 0.492906i | \(-0.835935\pi\) |
0.986194 | − | 0.165594i | \(-0.0529542\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16643.8 | + | 2396.86i | 0.949067 | + | 0.136674i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 789.566 | − | 4477.85i | 0.0448235 | − | 0.254206i | −0.954159 | − | 0.299299i | \(-0.903247\pi\) |
0.998983 | + | 0.0450926i | \(0.0143583\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7673.36 | − | 2792.88i | −0.433692 | − | 0.157851i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11143.5 | − | 29644.0i | −0.627047 | − | 1.66808i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16526.3 | + | 28624.4i | −0.925859 | + | 1.60364i | −0.135686 | + | 0.990752i | \(0.543324\pi\) |
−0.790173 | + | 0.612884i | \(0.790009\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3257.11 | + | 5641.48i | 0.181675 | + | 0.314671i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1830.59 | + | 5198.74i | −0.101661 | + | 0.288711i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2193.08 | + | 12437.6i | 0.121262 | + | 0.687713i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4182.26 | + | 3509.33i | 0.230247 | + | 0.193200i | 0.750611 | − | 0.660745i | \(-0.229759\pi\) |
−0.520364 | + | 0.853944i | \(0.674204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −759.672 | − | 3835.40i | −0.0416415 | − | 0.210238i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5289.14 | − | 1925.09i | 0.288674 | − | 0.105069i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7335.81 | + | 6155.48i | −0.398657 | + | 0.334513i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −48.4863 | − | 4616.55i | −0.00262364 | − | 0.249806i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27349.1 | 1.47355 | 0.736776 | − | 0.676136i | \(-0.236347\pi\) | ||||
0.736776 | + | 0.676136i | \(0.236347\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1454.29 | 0.0780220 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3486.32 | − | 2061.95i | 0.186245 | − | 0.110152i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1871.62 | + | 1570.48i | −0.0995610 | + | 0.0835416i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −24616.2 | + | 8959.56i | −1.30392 | + | 0.474589i | −0.898272 | − | 0.439440i | \(-0.855177\pi\) |
−0.405649 | + | 0.914029i | \(0.632955\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22613.8 | + | 8772.90i | −1.19281 | + | 0.462742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10830.5 | − | 9087.88i | −0.568872 | − | 0.477340i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −369.814 | − | 2097.32i | −0.0193430 | − | 0.109700i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17222.2 | − | 20092.3i | −0.897037 | − | 1.04653i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −356.549 | − | 617.561i | −0.0184938 | − | 0.0320322i | 0.856630 | − | 0.515931i | \(-0.172554\pi\) |
−0.875124 | + | 0.483898i | \(0.839220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1562.95 | − | 2707.11i | 0.0807314 | − | 0.139831i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7628.35 | − | 9287.48i | 0.392395 | − | 0.477738i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2425.73 | − | 882.893i | −0.124261 | − | 0.0452274i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1496.29 | + | 8485.89i | −0.0763334 | + | 0.432908i | 0.922559 | + | 0.385856i | \(0.126094\pi\) |
−0.998892 | + | 0.0470521i | \(0.985017\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19643.9 | + | 1239.48i | −0.998015 | + | 0.0629723i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2792.84 | − | 15839.0i | 0.141309 | − | 0.801403i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14280.8 | − | 5197.80i | −0.719611 | − | 0.261917i | −0.0438506 | − | 0.999038i | \(-0.513963\pi\) |
−0.675761 | + | 0.737121i | \(0.736185\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2325.03 | + | 2830.72i | −0.116680 | + | 0.142058i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5772.35 | − | 9998.00i | 0.288504 | − | 0.499703i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8197.80 | − | 14199.0i | −0.408066 | − | 0.706792i | 0.586607 | − | 0.809872i | \(-0.300463\pi\) |
−0.994673 | + | 0.103080i | \(0.967130\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3794.13 | + | 4426.41i | 0.188098 | + | 0.219444i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2634.69 | − | 14942.1i | −0.130091 | − | 0.737781i | −0.978153 | − | 0.207885i | \(-0.933342\pi\) |
0.848063 | − | 0.529896i | \(-0.177769\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5539.39 | + | 4648.10i | 0.272413 | + | 0.228582i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11754.4 | − | 4560.06i | 0.575732 | − | 0.223352i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4582.59 | + | 1667.93i | −0.223557 | + | 0.0813682i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5652.00 | + | 4742.59i | −0.274626 | + | 0.230439i | −0.769690 | − | 0.638418i | \(-0.779589\pi\) |
0.495064 | + | 0.868857i | \(0.335145\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 18476.4 | − | 10927.7i | 0.894180 | − | 0.528853i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2814.87 | −0.135687 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23826.1 | 1.14395 | 0.571977 | − | 0.820270i | \(-0.306177\pi\) | ||||
0.571977 | + | 0.820270i | \(0.306177\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −81.8118 | − | 7789.59i | −0.00391249 | − | 0.372522i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7406.28 | − | 6214.60i | 0.352795 | − | 0.296030i | −0.449116 | − | 0.893473i | \(-0.648261\pi\) |
0.801911 | + | 0.597443i | \(0.203817\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11257.6 | + | 4097.44i | −0.534146 | + | 0.194413i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1180.56 | − | 5960.35i | −0.0557949 | − | 0.281695i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −7806.72 | − | 6550.62i | −0.367515 | − | 0.308382i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4584.14 | − | 25997.9i | −0.214965 | − | 1.21913i | −0.880967 | − | 0.473178i | \(-0.843107\pi\) |
0.666002 | − | 0.745950i | \(-0.268004\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −880.761 | + | 2501.30i | −0.0411412 | + | 0.116838i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18402.1 | + | 31873.4i | 0.856247 | + | 1.48306i | 0.875484 | + | 0.483248i | \(0.160543\pi\) |
−0.0192370 | + | 0.999815i | \(0.506124\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14437.6 | − | 25006.7i | 0.669180 | − | 1.15905i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −493.856 | − | 1313.76i | −0.0228018 | − | 0.0606576i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2767.65 | − | 1007.34i | −0.127293 | − | 0.0463309i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3615.96 | + | 20507.1i | −0.165671 | + | 0.939567i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2990.76 | + | 430.696i | 0.136502 | + | 0.0196575i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1024.12 | + | 5808.05i | −0.0465634 | + | 0.264074i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23907.0 | − | 8701.45i | −1.08284 | − | 0.394121i | −0.261875 | − | 0.965102i | \(-0.584341\pi\) |
−0.820963 | + | 0.570981i | \(0.806563\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14325.3 | − | 2371.10i | −0.646382 | − | 0.106988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6023.28 | − | 10432.6i | 0.270750 | − | 0.468952i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6408.14 | − | 11099.2i | −0.286961 | − | 0.497031i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3979.23 | − | 744.818i | 0.177521 | − | 0.0332276i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 561.233 | + | 3182.91i | 0.0249434 | + | 0.141461i | 0.994736 | − | 0.102469i | \(-0.0326743\pi\) |
−0.969793 | + | 0.243930i | \(0.921563\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26129.9 | + | 21925.6i | 1.15696 | + | 0.970803i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11792.4 | + | 247.732i | −0.520181 | + | 0.0109278i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3440.04 | − | 1252.07i | 0.151178 | − | 0.0550245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 577.920 | − | 484.933i | 0.0253031 | − | 0.0212318i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18833.9 | − | 10611.6i | −0.821541 | − | 0.462882i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5166.02 | −0.224509 | −0.112254 | − | 0.993680i | \(-0.535807\pi\) | ||||
−0.112254 | + | 0.993680i | \(0.535807\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4953.82 | −0.214491 | −0.107246 | − | 0.994233i | \(-0.534203\pi\) | ||||
−0.107246 | + | 0.994233i | \(0.534203\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23141.8 | + | 13038.8i | 0.998299 | + | 0.562473i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2204.23 | + | 1849.57i | −0.0947373 | + | 0.0794940i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4648.28 | − | 1691.84i | 0.199049 | − | 0.0724478i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2710.26 | − | 4930.66i | 0.115634 | − | 0.210368i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20677.3 | − | 17350.3i | −0.878981 | − | 0.737553i | 0.0869882 | − | 0.996209i | \(-0.472276\pi\) |
−0.965969 | + | 0.258657i | \(0.916720\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4878.12 | − | 27665.2i | −0.206611 | − | 1.17175i | −0.894885 | − | 0.446297i | \(-0.852742\pi\) |
0.688274 | − | 0.725451i | \(-0.258369\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 15638.4 | − | 2927.13i | 0.659949 | − | 0.123527i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10084.8 | + | 17467.4i | 0.424044 | + | 0.734465i | 0.996331 | − | 0.0855883i | \(-0.0272770\pi\) |
−0.572287 | + | 0.820053i | \(0.693944\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2596.43 | − | 4497.14i | 0.108779 | − | 0.188410i | −0.806497 | − | 0.591238i | \(-0.798639\pi\) |
0.915276 | + | 0.402828i | \(0.131973\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2243.37 | − | 371.318i | −0.0936484 | − | 0.0155005i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28988.3 | − | 10550.9i | −1.20575 | − | 0.438855i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 950.350 | − | 5389.70i | 0.0393871 | − | 0.223375i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10553.8 | + | 32109.3i | −0.435832 | + | 1.32600i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6796.07 | − | 38542.4i | 0.279650 | − | 1.58597i | −0.444142 | − | 0.895956i | \(-0.646491\pi\) |
0.723792 | − | 0.690018i | \(-0.242397\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22482.3 | + | 8182.88i | 0.921820 | + | 0.335515i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1273.06 | + | 3386.61i | 0.0520125 | + | 0.138364i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −958.830 | + | 1660.74i | −0.0390352 | + | 0.0676110i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1922.81 | + | 3330.41i | 0.0780031 | + | 0.135105i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2046.08 | + | 5810.71i | −0.0827105 | + | 0.234892i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −485.579 | − | 2753.85i | −0.0195598 | − | 0.110929i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10381.3 | − | 8710.96i | −0.416705 | − | 0.349657i | 0.410203 | − | 0.911994i | \(-0.365458\pi\) |
−0.826908 | + | 0.562337i | \(0.809902\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1406.02 | − | 1231.03i | 0.0562398 | − | 0.0492402i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28911.2 | − | 10522.8i | 1.15238 | − | 0.419432i | 0.306010 | − | 0.952028i | \(-0.401006\pi\) |
0.846369 | + | 0.532596i | \(0.178784\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20278.2 | + | 17015.4i | −0.805453 | + | 0.675855i | −0.949518 | − | 0.313713i | \(-0.898427\pi\) |
0.144065 | + | 0.989568i | \(0.453982\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 29.8518 | + | 2842.29i | 0.00118159 | + | 0.112503i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19823.5 | −0.781925 | −0.390963 | − | 0.920407i | \(-0.627858\pi\) | ||||
−0.390963 | + | 0.920407i | \(0.627858\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8452.61 | 0.332251 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 22069.5 | − | 13052.8i | 0.864499 | − | 0.511299i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17580.5 | + | 14751.8i | −0.686280 | + | 0.575857i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15611.2 | − | 5682.00i | 0.607307 | − | 0.221042i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5947.91 | + | 38436.6i | −0.230591 | + | 1.49013i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2411.28 | + | 2023.30i | 0.0931612 | + | 0.0781716i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 798.489 | + | 4528.46i | 0.0307446 | + | 0.174362i | 0.996314 | − | 0.0857856i | \(-0.0273400\pi\) |
−0.965569 | + | 0.260147i | \(0.916229\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22372.1 | − | 26100.3i | −0.858466 | − | 1.00153i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3156.51 | − | 5467.23i | −0.120710 | − | 0.209076i | 0.799338 | − | 0.600882i | \(-0.205184\pi\) |
−0.920048 | + | 0.391806i | \(0.871850\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18774.4 | − | 32518.3i | 0.715527 | − | 1.23933i | −0.247229 | − | 0.968957i | \(-0.579520\pi\) |
0.962756 | − | 0.270372i | \(-0.0871467\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2073.39 | + | 2524.34i | −0.0787527 | + | 0.0958810i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −42624.1 | − | 15513.9i | −1.61350 | − | 0.587267i | −0.631375 | − | 0.775478i | \(-0.717509\pi\) |
−0.982129 | + | 0.188211i | \(0.939731\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2090.93 | + | 11858.2i | −0.0788835 | + | 0.447370i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17217.0 | + | 7098.78i | −0.647353 | + | 0.266911i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1821.73 | + | 10331.6i | −0.0682665 | + | 0.387159i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7706.19 | − | 2804.82i | −0.287809 | − | 0.104754i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7115.06 | − | 8662.55i | 0.264844 | − | 0.322446i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2594.32 | − | 4493.50i | 0.0962464 | − | 0.166704i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17046.2 | + | 29524.9i | 0.630291 | + | 1.09170i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3106.85 | − | 3624.60i | −0.114495 | − | 0.133576i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 873.737 | + | 4955.21i | 0.0320928 | + | 0.182007i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9498.53 | + | 7970.21i | 0.347732 | + | 0.291782i | 0.799879 | − | 0.600162i | \(-0.204897\pi\) |
−0.452146 | + | 0.891944i | \(0.649342\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 9069.74 | + | 7291.36i | 0.330940 | + | 0.266050i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14823.9 | − | 5395.44i | 0.539118 | − | 0.196223i | −0.0580872 | − | 0.998312i | \(-0.518500\pi\) |
0.597205 | + | 0.802089i | \(0.296278\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9138.15 | − | 7667.82i | 0.331247 | − | 0.277949i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3536.06 | + | 2091.36i | −0.127758 | + | 0.0755611i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9183.90 | 0.330730 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43295.1 | 1.55405 | 0.777025 | − | 0.629469i | \(-0.216728\pi\) | ||||
0.777025 | + | 0.629469i | \(0.216728\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 298.720 | + | 28442.2i | 0.0106875 | + | 1.01759i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22954.8 | + | 19261.4i | −0.818599 | + | 0.686886i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5366.68 | − | 1953.31i | 0.190763 | − | 0.0694319i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14094.7 | − | 4797.28i | −0.499387 | − | 0.169971i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −18194.5 | − | 15267.0i | −0.642564 | − | 0.539176i | 0.262240 | − | 0.965003i | \(-0.415539\pi\) |
−0.904805 | + | 0.425827i | \(0.859983\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1647.55 | − | 9343.71i | −0.0579981 | − | 0.328924i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18378.8 | + | 52194.4i | −0.644903 | + | 1.83148i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2874.47 | − | 4978.72i | −0.100540 | − | 0.174141i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1751.71 | − | 3034.06i | 0.0610737 | − | 0.105783i | −0.833872 | − | 0.551958i | \(-0.813881\pi\) |
0.894946 | + | 0.446175i | \(0.147214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13163.3 | + | 35017.1i | 0.457474 | + | 1.21698i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12581.4 | − | 4579.25i | −0.435857 | − | 0.158639i | 0.114767 | − | 0.993392i | \(-0.463388\pi\) |
−0.550624 | + | 0.834754i | \(0.685610\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −983.409 | + | 5577.19i | −0.0339599 | + | 0.192596i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1589.54 | − | 852.120i | −0.0547174 | − | 0.0293328i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2575.71 | − | 14607.6i | 0.0883837 | − | 0.501249i | −0.908191 | − | 0.418555i | \(-0.862537\pi\) |
0.996575 | − | 0.0826937i | \(-0.0263523\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4950.28 | + | 1801.76i | 0.169329 | + | 0.0616306i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −447.688 | − | 74.1004i | −0.0152653 | − | 0.00252668i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11115.8 | + | 19253.1i | −0.377835 | + | 0.654429i | −0.990747 | − | 0.135722i | \(-0.956665\pi\) |
0.612912 | + | 0.790151i | \(0.289998\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 743.978 | + | 1288.61i | 0.0252090 | + | 0.0436632i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2810.09 | − | 525.982i | 0.0949188 | − | 0.0177665i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2827.56 | + | 16035.9i | 0.0952104 | + | 0.539965i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21639.6 | + | 18157.7i | 0.726379 | + | 0.609504i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 12033.9 | + | 19867.5i | 0.402685 | + | 0.664821i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −855.804 | + | 311.487i | −0.0285485 | + | 0.0103908i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13514.4 | − | 11339.9i | 0.449425 | − | 0.377112i | −0.389798 | − | 0.920901i | \(-0.627455\pi\) |
0.839222 | + | 0.543788i | \(0.183011\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13711.1 | + | 7725.26i | 0.454555 | + | 0.256110i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24718.4 | 0.816944 | 0.408472 | − | 0.912771i | \(-0.366062\pi\) | ||||
0.408472 | + | 0.912771i | \(0.366062\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14069.5 | 0.463564 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 19946.6 | + | 11238.5i | 0.655181 | + | 0.369149i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14888.2 | − | 12492.7i | 0.487528 | − | 0.409085i | −0.365611 | − | 0.930768i | \(-0.619140\pi\) |
0.853139 | + | 0.521683i | \(0.174696\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10486.8 | + | 3816.89i | −0.342350 | + | 0.124605i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29562.5 | + | 48806.7i | 0.962138 | + | 1.58846i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11737.0 | + | 9848.53i | 0.380827 | + | 0.319552i | 0.813027 | − | 0.582226i | \(-0.197818\pi\) |
−0.432200 | + | 0.901778i | \(0.642263\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1070.46 | + | 6070.90i | 0.0346272 | + | 0.196381i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9951.88 | − | 1862.76i | 0.320944 | − | 0.0600731i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4755.71 | − | 8237.13i | −0.152905 | − | 0.264839i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2778.99 | − | 4813.35i | 0.0890793 | − | 0.154290i | −0.818043 | − | 0.575157i | \(-0.804941\pi\) |
0.907122 | + | 0.420867i | \(0.138274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 20470.1 | + | 3388.17i | 0.654179 | + | 0.108278i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1120.05 | − | 407.663i | −0.0356863 | − | 0.0129887i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4994.75 | + | 28326.6i | −0.158661 | + | 0.899812i | 0.796701 | + | 0.604374i | \(0.206577\pi\) |
−0.955362 | + | 0.295438i | \(0.904534\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5681.21 | + | 3523.22i | −0.179926 | + | 0.111581i |
(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 | 108.4.i.a.25.1 | yes | 54 | |
3.2 | odd | 2 | 324.4.i.a.73.5 | 54 | |||
27.13 | even | 9 | inner | 108.4.i.a.13.1 | ✓ | 54 | |
27.14 | odd | 18 | 324.4.i.a.253.5 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.1 | ✓ | 54 | 27.13 | even | 9 | inner | |
108.4.i.a.25.1 | yes | 54 | 1.1 | even | 1 | trivial | |
324.4.i.a.73.5 | 54 | 3.2 | odd | 2 | |||
324.4.i.a.253.5 | 54 | 27.14 | odd | 18 |