Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(37,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.y (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(18\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 37.12 | ||
Character | \(\chi\) | \(=\) | 432.37 |
Dual form | 432.2.y.e.397.12 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.751042 | − | 1.19831i | 0.531067 | − | 0.847330i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.871873 | − | 1.79995i | −0.435936 | − | 0.899977i | ||||
\(5\) | 1.60558 | − | 0.430214i | 0.718037 | − | 0.192397i | 0.118741 | − | 0.992925i | \(-0.462114\pi\) |
0.599296 | + | 0.800528i | \(0.295447\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.62762 | − | 2.09441i | 1.37111 | − | 0.791611i | 0.380043 | − | 0.924969i | \(-0.375909\pi\) |
0.991068 | + | 0.133358i | \(0.0425759\pi\) | |||||||
\(8\) | −2.81171 | − | 0.307071i | −0.994089 | − | 0.108566i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.690330 | − | 2.24708i | 0.218301 | − | 0.710590i | ||||
\(11\) | −1.24125 | + | 4.63241i | −0.374251 | + | 1.39673i | 0.480184 | + | 0.877168i | \(0.340570\pi\) |
−0.854436 | + | 0.519557i | \(0.826097\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.879738 | − | 3.28323i | −0.243995 | − | 0.910603i | −0.973886 | − | 0.227039i | \(-0.927096\pi\) |
0.729890 | − | 0.683564i | \(-0.239571\pi\) | |||||||
\(14\) | 0.214754 | − | 5.91998i | 0.0573953 | − | 1.58218i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.47968 | + | 3.13866i | −0.619919 | + | 0.784666i | ||||
\(17\) | 2.14142 | 0.519370 | 0.259685 | − | 0.965693i | \(-0.416381\pi\) | ||||
0.259685 | + | 0.965693i | \(0.416381\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03156 | − | 1.03156i | 0.236656 | − | 0.236656i | −0.578808 | − | 0.815464i | \(-0.696482\pi\) |
0.815464 | + | 0.578808i | \(0.196482\pi\) | |||||||
\(20\) | −2.17423 | − | 2.51488i | −0.486172 | − | 0.562344i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.61882 | + | 4.96653i | 0.984735 | + | 1.05887i | ||||
\(23\) | 0.405884 | + | 0.234337i | 0.0846327 | + | 0.0488627i | 0.541719 | − | 0.840560i | \(-0.317774\pi\) |
−0.457086 | + | 0.889422i | \(0.651107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.93733 | + | 1.11852i | −0.387465 | + | 0.223703i | ||||
\(26\) | −4.59503 | − | 1.41164i | −0.901159 | − | 0.276846i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.93266 | − | 4.70349i | −1.31015 | − | 0.888877i | ||||
\(29\) | −6.55186 | − | 1.75557i | −1.21665 | − | 0.326000i | −0.407282 | − | 0.913302i | \(-0.633523\pi\) |
−0.809368 | + | 0.587302i | \(0.800190\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.18054 | − | 5.50886i | 0.571242 | − | 0.989421i | −0.425196 | − | 0.905101i | \(-0.639795\pi\) |
0.996439 | − | 0.0843198i | \(-0.0268717\pi\) | |||||||
\(32\) | 1.89874 | + | 5.32868i | 0.335653 | + | 0.941986i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.60829 | − | 2.56607i | 0.275820 | − | 0.440078i | ||||
\(35\) | 4.92339 | − | 4.92339i | 0.832204 | − | 0.832204i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.728237 | − | 0.728237i | −0.119721 | − | 0.119721i | 0.644708 | − | 0.764429i | \(-0.276979\pi\) |
−0.764429 | + | 0.644708i | \(0.776979\pi\) | |||||||
\(38\) | −0.461380 | − | 2.01087i | −0.0748456 | − | 0.326206i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.64653 | + | 0.716609i | −0.734681 | + | 0.113306i | ||||
\(41\) | −2.52351 | − | 1.45695i | −0.394105 | − | 0.227537i | 0.289832 | − | 0.957078i | \(-0.406401\pi\) |
−0.683937 | + | 0.729541i | \(0.739734\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.84802 | + | 10.6289i | −0.434318 | + | 1.62090i | 0.308374 | + | 0.951265i | \(0.400215\pi\) |
−0.742692 | + | 0.669633i | \(0.766451\pi\) | |||||||
\(44\) | 9.42035 | − | 1.80468i | 1.42017 | − | 0.272066i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.585644 | − | 0.310376i | 0.0863485 | − | 0.0457625i | ||||
\(47\) | 4.61716 | + | 7.99715i | 0.673482 | + | 1.16650i | 0.976910 | + | 0.213650i | \(0.0685352\pi\) |
−0.303429 | + | 0.952854i | \(0.598131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.27308 | − | 9.13324i | 0.753297 | − | 1.30475i | ||||
\(50\) | −0.114689 | + | 3.16156i | −0.0162195 | + | 0.447112i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.14264 | + | 4.44604i | −0.713156 | + | 0.616555i | ||||
\(53\) | −1.17892 | − | 1.17892i | −0.161937 | − | 0.161937i | 0.621487 | − | 0.783424i | \(-0.286529\pi\) |
−0.783424 | + | 0.621487i | \(0.786529\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.97171i | 1.07491i | ||||||||
\(56\) | −10.8429 | + | 4.77492i | −1.44895 | + | 0.638076i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.02443 | + | 6.53263i | −0.922352 | + | 0.857776i | ||||
\(59\) | 1.48185 | − | 0.397061i | 0.192921 | − | 0.0516930i | −0.161065 | − | 0.986944i | \(-0.551493\pi\) |
0.353986 | + | 0.935251i | \(0.384826\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.53224 | + | 2.01826i | 0.964404 | + | 0.258411i | 0.706464 | − | 0.707749i | \(-0.250289\pi\) |
0.257941 | + | 0.966161i | \(0.416956\pi\) | |||||||
\(62\) | −4.21258 | − | 7.94865i | −0.534998 | − | 1.00948i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.81141 | + | 1.72679i | 0.976427 | + | 0.215849i | ||||
\(65\) | −2.82498 | − | 4.89300i | −0.350395 | − | 0.606902i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.63252 | + | 9.82470i | 0.321614 | + | 1.20028i | 0.917673 | + | 0.397338i | \(0.130066\pi\) |
−0.596059 | + | 0.802941i | \(0.703268\pi\) | |||||||
\(68\) | −1.86704 | − | 3.85445i | −0.226412 | − | 0.467421i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.20205 | − | 9.59739i | −0.263196 | − | 1.14711i | ||||
\(71\) | 8.27863i | 0.982493i | 0.871021 | + | 0.491246i | \(0.163458\pi\) | ||||
−0.871021 | + | 0.491246i | \(0.836542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.16641i | 0.955806i | 0.878413 | + | 0.477903i | \(0.158603\pi\) | ||||
−0.878413 | + | 0.477903i | \(0.841397\pi\) | |||||||
\(74\) | −1.41959 | + | 0.325714i | −0.165024 | + | 0.0378635i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.75615 | − | 0.957372i | −0.316152 | − | 0.109818i | ||||
\(77\) | 5.19937 | + | 19.4043i | 0.592523 | + | 2.21133i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.63065 | + | 6.28847i | 0.408480 | + | 0.707508i | 0.994720 | − | 0.102630i | \(-0.0327257\pi\) |
−0.586240 | + | 0.810138i | \(0.699392\pi\) | |||||||
\(80\) | −2.63102 | + | 6.10616i | −0.294157 | + | 0.682690i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.64113 | + | 1.92970i | −0.402095 | + | 0.213100i | ||||
\(83\) | 7.59149 | + | 2.03413i | 0.833274 | + | 0.223275i | 0.650142 | − | 0.759813i | \(-0.274710\pi\) |
0.183133 | + | 0.983088i | \(0.441376\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.43821 | − | 0.921267i | 0.372927 | − | 0.0999254i | ||||
\(86\) | 10.5977 | + | 11.3956i | 1.14278 | + | 1.22882i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.91252 | − | 12.6438i | 0.523676 | − | 1.34784i | ||||
\(89\) | − | 11.1968i | − | 1.18686i | −0.804886 | − | 0.593429i | \(-0.797774\pi\) | ||
0.804886 | − | 0.593429i | \(-0.202226\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0678 | − | 10.0678i | −1.05539 | − | 1.05539i | ||||
\(92\) | 0.0679173 | − | 0.934886i | 0.00708087 | − | 0.0974686i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.0507 | + | 0.473428i | 1.34608 | + | 0.0488304i | ||||
\(95\) | 1.21246 | − | 2.10004i | 0.124396 | − | 0.215460i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.67759 | − | 9.83387i | −0.576472 | − | 0.998479i | −0.995880 | − | 0.0906808i | \(-0.971096\pi\) |
0.419408 | − | 0.907798i | \(-0.362238\pi\) | |||||||
\(98\) | −6.98411 | − | 13.1782i | −0.705501 | − | 1.33120i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.70238 | + | 2.51190i | 0.370238 | + | 0.251190i | ||||
\(101\) | −0.777558 | + | 2.90189i | −0.0773699 | + | 0.288749i | −0.993760 | − | 0.111537i | \(-0.964423\pi\) |
0.916390 | + | 0.400286i | \(0.131089\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.24824 | − | 0.720669i | −0.122992 | − | 0.0710096i | 0.437242 | − | 0.899344i | \(-0.355955\pi\) |
−0.560234 | + | 0.828334i | \(0.689289\pi\) | |||||||
\(104\) | 1.46538 | + | 9.50162i | 0.143693 | + | 0.931710i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.29812 | + | 0.527287i | −0.223213 | + | 0.0512146i | ||||
\(107\) | −5.85602 | − | 5.85602i | −0.566123 | − | 0.566123i | 0.364917 | − | 0.931040i | \(-0.381097\pi\) |
−0.931040 | + | 0.364917i | \(0.881097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.05249 | + | 2.05249i | −0.196593 | + | 0.196593i | −0.798538 | − | 0.601945i | \(-0.794393\pi\) |
0.601945 | + | 0.798538i | \(0.294393\pi\) | |||||||
\(110\) | 9.55255 | + | 5.98709i | 0.910799 | + | 0.570846i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.42168 | + | 16.5793i | −0.228827 | + | 1.56660i | ||||
\(113\) | 4.12726 | − | 7.14862i | 0.388260 | − | 0.672486i | −0.603956 | − | 0.797018i | \(-0.706410\pi\) |
0.992216 | + | 0.124532i | \(0.0397430\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.752495 | + | 0.201630i | 0.0701705 | + | 0.0188021i | ||||
\(116\) | 2.55245 | + | 13.3237i | 0.236989 | + | 1.23707i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.637132 | − | 2.07392i | 0.0586528 | − | 0.190920i | ||||
\(119\) | 7.76824 | − | 4.48500i | 0.712114 | − | 0.411139i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3923 | − | 5.99998i | −0.944752 | − | 0.545453i | ||||
\(122\) | 8.07551 | − | 7.51013i | 0.731123 | − | 0.679935i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.6887 | − | 0.921808i | −1.13948 | − | 0.0827808i | ||||
\(125\) | −8.50616 | + | 8.50616i | −0.760814 | + | 0.760814i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.68483 | −0.149504 | −0.0747521 | − | 0.997202i | \(-0.523817\pi\) | ||||
−0.0747521 | + | 0.997202i | \(0.523817\pi\) | |||||||
\(128\) | 7.93592 | − | 8.06357i | 0.701443 | − | 0.712726i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.98499 | − | 0.289664i | −0.700330 | − | 0.0254052i | ||||
\(131\) | −1.97334 | − | 7.36461i | −0.172412 | − | 0.643449i | −0.996978 | − | 0.0776838i | \(-0.975248\pi\) |
0.824566 | − | 0.565765i | \(-0.191419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.58160 | − | 5.90261i | 0.137142 | − | 0.511821i | ||||
\(134\) | 13.7501 | + | 4.22420i | 1.18783 | + | 0.364915i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.02104 | − | 0.657567i | −0.516300 | − | 0.0563859i | ||||
\(137\) | −8.26806 | + | 4.77357i | −0.706388 | + | 0.407833i | −0.809722 | − | 0.586813i | \(-0.800382\pi\) |
0.103334 | + | 0.994647i | \(0.467049\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.9684 | + | 3.74281i | −1.18478 | + | 0.317461i | −0.796821 | − | 0.604215i | \(-0.793487\pi\) |
−0.387960 | + | 0.921676i | \(0.626820\pi\) | |||||||
\(140\) | −13.1544 | − | 4.56931i | −1.11175 | − | 0.386177i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 9.92033 | + | 6.21760i | 0.832495 | + | 0.521769i | ||||
\(143\) | 16.3012 | 1.36318 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2748 | −0.936321 | ||||||||
\(146\) | 9.78586 | + | 6.13331i | 0.809883 | + | 0.507597i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.675864 | + | 1.94572i | −0.0555557 | + | 0.159938i | ||||
\(149\) | 1.66249 | − | 0.445462i | 0.136196 | − | 0.0364937i | −0.190077 | − | 0.981769i | \(-0.560874\pi\) |
0.326273 | + | 0.945276i | \(0.394207\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.5071 | − | 10.6851i | 1.50609 | − | 0.869542i | 0.506115 | − | 0.862466i | \(-0.331081\pi\) |
0.999975 | − | 0.00707596i | \(-0.00225237\pi\) | |||||||
\(152\) | −3.21721 | + | 2.58368i | −0.260950 | + | 0.209564i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 27.1572 | + | 8.34301i | 2.18839 | + | 0.672299i | ||||
\(155\) | 2.73663 | − | 10.2132i | 0.219811 | − | 0.820346i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.74550 | + | 10.2463i | 0.219114 | + | 0.817746i | 0.984677 | + | 0.174385i | \(0.0557938\pi\) |
−0.765563 | + | 0.643361i | \(0.777539\pi\) | |||||||
\(158\) | 10.2623 | + | 0.372275i | 0.816422 | + | 0.0296166i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.34104 | + | 7.73875i | 0.422247 | + | 0.611802i | ||||
\(161\) | 1.96319 | 0.154721 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.47621 | + | 3.47621i | −0.272278 | + | 0.272278i | −0.830017 | − | 0.557739i | \(-0.811669\pi\) |
0.557739 | + | 0.830017i | \(0.311669\pi\) | |||||||
\(164\) | −0.422263 | + | 5.81247i | −0.0329732 | + | 0.453878i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.13904 | − | 7.56920i | 0.631712 | − | 0.587484i | ||||
\(167\) | −0.277442 | − | 0.160181i | −0.0214691 | − | 0.0123952i | 0.489227 | − | 0.872156i | \(-0.337279\pi\) |
−0.510696 | + | 0.859761i | \(0.670612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.25270 | − | 0.723245i | 0.0963613 | − | 0.0556342i | ||||
\(170\) | 1.47828 | − | 4.81194i | 0.113379 | − | 0.369059i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 21.6147 | − | 4.14078i | 1.64811 | − | 0.315732i | ||||
\(173\) | −11.6901 | − | 3.13236i | −0.888784 | − | 0.238149i | −0.214591 | − | 0.976704i | \(-0.568842\pi\) |
−0.674193 | + | 0.738555i | \(0.735509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.68525 | + | 8.11510i | −0.354172 | + | 0.613444i | ||||
\(176\) | −11.4617 | − | 15.3828i | −0.863957 | − | 1.15952i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −13.4172 | − | 8.40926i | −1.00566 | − | 0.630301i | ||||
\(179\) | −18.6780 | + | 18.6780i | −1.39606 | + | 1.39606i | −0.585104 | + | 0.810958i | \(0.698946\pi\) |
−0.810958 | + | 0.585104i | \(0.801054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.10527 | + | 4.10527i | 0.305143 | + | 0.305143i | 0.843022 | − | 0.537879i | \(-0.180774\pi\) |
−0.537879 | + | 0.843022i | \(0.680774\pi\) | |||||||
\(182\) | −19.6256 | + | 4.50295i | −1.45474 | + | 0.333781i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.06927 | − | 0.783524i | −0.0788277 | − | 0.0577622i | ||||
\(185\) | −1.48254 | − | 0.855945i | −0.108998 | − | 0.0629303i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.65804 | + | 9.91993i | −0.194375 | + | 0.725417i | ||||
\(188\) | 10.3689 | − | 15.2832i | 0.756232 | − | 1.11464i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.60588 | − | 3.03012i | −0.116503 | − | 0.219828i | ||||
\(191\) | −8.60099 | − | 14.8974i | −0.622346 | − | 1.07793i | −0.989048 | − | 0.147596i | \(-0.952846\pi\) |
0.366702 | − | 0.930338i | \(-0.380487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.17459 | − | 15.8909i | 0.660402 | − | 1.14385i | −0.320108 | − | 0.947381i | \(-0.603719\pi\) |
0.980510 | − | 0.196468i | \(-0.0629473\pi\) | |||||||
\(194\) | −16.0481 | − | 0.582162i | −1.15219 | − | 0.0417968i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.0369 | − | 1.52828i | −1.50263 | − | 0.109163i | ||||
\(197\) | −8.80431 | − | 8.80431i | −0.627281 | − | 0.627281i | 0.320102 | − | 0.947383i | \(-0.396283\pi\) |
−0.947383 | + | 0.320102i | \(0.896283\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.0277i | 0.710847i | 0.934705 | + | 0.355423i | \(0.115663\pi\) | ||||
−0.934705 | + | 0.355423i | \(0.884337\pi\) | |||||||
\(200\) | 5.79066 | − | 2.55004i | 0.409462 | − | 0.180315i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.89337 | + | 3.11119i | 0.203577 | + | 0.218903i | ||||
\(203\) | −27.4445 | + | 7.35374i | −1.92623 | + | 0.516131i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.67849 | − | 1.25360i | −0.326760 | − | 0.0875550i | ||||
\(206\) | −1.80106 | + | 0.954515i | −0.125486 | + | 0.0665042i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 12.4864 | + | 5.38014i | 0.865776 | + | 0.373045i | ||||
\(209\) | 3.49819 | + | 6.05904i | 0.241975 | + | 0.419112i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.14678 | − | 19.2080i | −0.354319 | − | 1.32234i | −0.881340 | − | 0.472483i | \(-0.843358\pi\) |
0.527021 | − | 0.849852i | \(-0.323309\pi\) | |||||||
\(212\) | −1.09413 | + | 3.14986i | −0.0751452 | + | 0.216333i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −11.4154 | + | 2.61919i | −0.780342 | + | 0.179044i | ||||
\(215\) | 18.2909i | 1.24743i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 26.6454i | − | 1.80881i | ||||||
\(218\) | 0.918005 | + | 4.00102i | 0.0621751 | + | 0.270983i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 14.3487 | − | 6.95032i | 0.967390 | − | 0.468590i | ||||
\(221\) | −1.88389 | − | 7.03076i | −0.126724 | − | 0.472940i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.96587 | − | 12.0652i | −0.466469 | − | 0.807948i | 0.532797 | − | 0.846243i | \(-0.321141\pi\) |
−0.999266 | + | 0.0382947i | \(0.987807\pi\) | |||||||
\(224\) | 18.0483 | + | 15.3537i | 1.20590 | + | 1.02586i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.46649 | − | 10.3146i | −0.363625 | − | 0.686119i | ||||
\(227\) | 7.32092 | + | 1.96164i | 0.485907 | + | 0.130198i | 0.493452 | − | 0.869773i | \(-0.335735\pi\) |
−0.00754492 | + | 0.999972i | \(0.502402\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.4637 | + | 4.94734i | −1.22012 | + | 0.326930i | −0.810724 | − | 0.585428i | \(-0.800926\pi\) |
−0.409394 | + | 0.912358i | \(0.634260\pi\) | |||||||
\(230\) | 0.806770 | − | 0.750286i | 0.0531968 | − | 0.0494724i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.8828 | + | 6.94803i | 1.17407 | + | 0.456160i | ||||
\(233\) | − | 10.7647i | − | 0.705216i | −0.935771 | − | 0.352608i | \(-0.885295\pi\) | ||
0.935771 | − | 0.352608i | \(-0.114705\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.8537 | + | 10.8537i | 0.708017 | + | 0.708017i | ||||
\(236\) | −2.00668 | − | 2.32108i | −0.130624 | − | 0.151089i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.459877 | − | 12.6771i | 0.0298094 | − | 0.821738i | ||||
\(239\) | 11.1429 | − | 19.3001i | 0.720774 | − | 1.24842i | −0.239916 | − | 0.970794i | \(-0.577120\pi\) |
0.960690 | − | 0.277624i | \(-0.0895469\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7285 | + | 23.7785i | 0.884332 | + | 1.53171i | 0.846478 | + | 0.532424i | \(0.178719\pi\) |
0.0378540 | + | 0.999283i | \(0.487948\pi\) | |||||||
\(242\) | −14.9948 | + | 7.94688i | −0.963905 | + | 0.510845i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.93438 | − | 15.3174i | −0.187855 | − | 0.980593i | ||||
\(245\) | 4.53710 | − | 16.9327i | 0.289865 | − | 1.08179i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.29435 | − | 2.47934i | −0.273243 | − | 0.157757i | ||||
\(248\) | −10.6344 | + | 14.5127i | −0.675284 | + | 0.921555i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.80450 | + | 16.5815i | 0.240618 | + | 1.04870i | ||||
\(251\) | −11.4125 | − | 11.4125i | −0.720350 | − | 0.720350i | 0.248326 | − | 0.968676i | \(-0.420119\pi\) |
−0.968676 | + | 0.248326i | \(0.920119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.58935 | + | 1.58935i | −0.0999217 | + | 0.0999217i | ||||
\(254\) | −1.26538 | + | 2.01894i | −0.0793967 | + | 0.126679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.70242 | − | 15.5657i | −0.231401 | − | 0.972858i | ||||
\(257\) | 0.930384 | − | 1.61147i | 0.0580357 | − | 0.100521i | −0.835548 | − | 0.549418i | \(-0.814850\pi\) |
0.893584 | + | 0.448897i | \(0.148183\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.16699 | − | 1.11654i | −0.258924 | − | 0.0693785i | ||||
\(260\) | −6.34417 | + | 9.35091i | −0.393449 | + | 0.579919i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.3071 | − | 3.16646i | −0.636776 | − | 0.195625i | ||||
\(263\) | −0.0414842 | + | 0.0239509i | −0.00255802 | + | 0.00147687i | −0.501278 | − | 0.865286i | \(-0.667137\pi\) |
0.498720 | + | 0.866763i | \(0.333803\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.40003 | − | 1.38566i | −0.147433 | − | 0.0851203i | ||||
\(266\) | −5.88528 | − | 6.32835i | −0.360850 | − | 0.388016i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.3888 | − | 13.3043i | 0.940020 | − | 0.812690i | ||||
\(269\) | 14.5681 | − | 14.5681i | 0.888235 | − | 0.888235i | −0.106118 | − | 0.994354i | \(-0.533842\pi\) |
0.994354 | + | 0.106118i | \(0.0338421\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.7807 | −0.958607 | −0.479304 | − | 0.877649i | \(-0.659111\pi\) | ||||
−0.479304 | + | 0.877649i | \(0.659111\pi\) | |||||||
\(272\) | −5.31002 | + | 6.72119i | −0.321967 | + | 0.407532i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.489466 | + | 13.4928i | −0.0295697 | + | 0.815131i | ||||
\(275\) | −2.77672 | − | 10.3629i | −0.167442 | − | 0.624904i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.93294 | + | 7.21383i | −0.116139 | + | 0.433437i | −0.999370 | − | 0.0355022i | \(-0.988697\pi\) |
0.883231 | + | 0.468939i | \(0.155364\pi\) | |||||||
\(278\) | −6.00579 | + | 19.5494i | −0.360203 | + | 1.17249i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −15.3550 | + | 12.3313i | −0.917634 | + | 0.736936i | ||||
\(281\) | 5.84440 | − | 3.37427i | 0.348648 | − | 0.201292i | −0.315442 | − | 0.948945i | \(-0.602153\pi\) |
0.664089 | + | 0.747653i | \(0.268819\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.4414 | − | 3.33366i | 0.739563 | − | 0.198165i | 0.130679 | − | 0.991425i | \(-0.458284\pi\) |
0.608884 | + | 0.793259i | \(0.291617\pi\) | |||||||
\(284\) | 14.9012 | − | 7.21791i | 0.884221 | − | 0.428304i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.2429 | − | 19.5339i | 0.723938 | − | 1.15506i | ||||
\(287\) | −12.2058 | −0.720483 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.4143 | −0.730255 | ||||||||
\(290\) | −8.46785 | + | 13.5107i | −0.497249 | + | 0.793373i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.6992 | − | 7.12007i | 0.860204 | − | 0.416671i | ||||
\(293\) | −13.8785 | + | 3.71874i | −0.810792 | + | 0.217251i | −0.640317 | − | 0.768111i | \(-0.721197\pi\) |
−0.170475 | + | 0.985362i | \(0.554530\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.20841 | − | 1.27503i | 0.128579 | − | 0.0742349i | ||||
\(296\) | 1.82397 | + | 2.27121i | 0.106016 | + | 0.132011i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.714797 | − | 2.32673i | 0.0414071 | − | 0.134784i | ||||
\(299\) | 0.412311 | − | 1.53877i | 0.0238446 | − | 0.0889891i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9298 | + | 44.5226i | 0.687622 | + | 2.56624i | ||||
\(302\) | 1.09562 | − | 30.2022i | 0.0630456 | − | 1.73794i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.679785 | + | 5.79565i | 0.0389884 | + | 0.332404i | ||||
\(305\) | 12.9619 | 0.742196 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.2394 | − | 12.2394i | 0.698539 | − | 0.698539i | −0.265556 | − | 0.964095i | \(-0.585556\pi\) |
0.964095 | + | 0.265556i | \(0.0855556\pi\) | |||||||
\(308\) | 30.3937 | − | 26.2767i | 1.73184 | − | 1.49726i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.1832 | − | 10.9499i | −0.578370 | − | 0.621911i | ||||
\(311\) | 0.742777 | + | 0.428842i | 0.0421190 | + | 0.0243174i | 0.520912 | − | 0.853611i | \(-0.325592\pi\) |
−0.478793 | + | 0.877928i | \(0.658925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −15.8984 | + | 9.17895i | −0.898631 | + | 0.518825i | −0.876756 | − | 0.480936i | \(-0.840297\pi\) |
−0.0218755 | + | 0.999761i | \(0.506964\pi\) | |||||||
\(314\) | 14.3402 | + | 4.40548i | 0.809265 | + | 0.248616i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.15349 | − | 12.0177i | 0.458670 | − | 0.676051i | ||||
\(317\) | 4.02641 | + | 1.07887i | 0.226146 | + | 0.0605956i | 0.370112 | − | 0.928987i | \(-0.379319\pi\) |
−0.143967 | + | 0.989583i | \(0.545986\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.2650 | − | 28.1718i | 0.910666 | − | 1.57732i | ||||
\(320\) | 13.2847 | − | 0.588080i | 0.742639 | − | 0.0328747i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.47444 | − | 2.35250i | 0.0821673 | − | 0.131100i | ||||
\(323\) | 2.20900 | − | 2.20900i | 0.122912 | − | 0.122912i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.37668 | + | 5.37668i | 0.298244 | + | 0.298244i | ||||
\(326\) | 1.55478 | + | 6.77634i | 0.0861115 | + | 0.375307i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.64798 | + | 4.87141i | 0.367073 | + | 0.268978i | ||||
\(329\) | 33.4986 | + | 19.3404i | 1.84684 | + | 1.06627i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.33734 | − | 4.99103i | 0.0735070 | − | 0.274332i | −0.919384 | − | 0.393362i | \(-0.871312\pi\) |
0.992891 | + | 0.119030i | \(0.0379785\pi\) | |||||||
\(332\) | −2.95746 | − | 15.4378i | −0.162312 | − | 0.847262i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.400317 | + | 0.212158i | −0.0219044 | + | 0.0116088i | ||||
\(335\) | 8.45344 | + | 14.6418i | 0.461861 | + | 0.799966i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.94762 | − | 3.37338i | 0.106094 | − | 0.183760i | −0.808091 | − | 0.589058i | \(-0.799499\pi\) |
0.914185 | + | 0.405298i | \(0.132832\pi\) | |||||||
\(338\) | 0.0741592 | − | 2.04430i | 0.00403373 | − | 0.111195i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.65592 | − | 5.38540i | −0.252503 | − | 0.292065i | ||||
\(341\) | 21.5715 | + | 21.5715i | 1.16816 | + | 1.16816i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 14.8542i | − | 0.802049i | ||||||
\(344\) | 11.2716 | − | 29.0109i | 0.607726 | − | 1.56417i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.5333 | + | 11.6558i | −0.673795 | + | 0.626621i | ||||
\(347\) | 3.04812 | − | 0.816741i | 0.163632 | − | 0.0438449i | −0.176073 | − | 0.984377i | \(-0.556340\pi\) |
0.339705 | + | 0.940532i | \(0.389673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.39893 | + | 0.374843i | 0.0748831 | + | 0.0200649i | 0.296066 | − | 0.955167i | \(-0.404325\pi\) |
−0.221183 | + | 0.975232i | \(0.570992\pi\) | |||||||
\(350\) | 6.20554 | + | 11.7091i | 0.331700 | + | 0.625880i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −27.0414 | + | 2.18151i | −1.44131 | + | 0.116275i | ||||
\(353\) | −7.73892 | − | 13.4042i | −0.411901 | − | 0.713434i | 0.583196 | − | 0.812331i | \(-0.301802\pi\) |
−0.995098 | + | 0.0988971i | \(0.968469\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.56158 | + | 13.2920i | 0.189029 | + | 0.705466i | ||||
\(356\) | −20.1537 | + | 9.76218i | −1.06815 | + | 0.517395i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.35401 | + | 36.4100i | 0.441523 | + | 1.92433i | ||||
\(359\) | − | 4.78775i | − | 0.252688i | −0.991987 | − | 0.126344i | \(-0.959676\pi\) | ||
0.991987 | − | 0.126344i | \(-0.0403242\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.8718i | 0.887988i | ||||||||
\(362\) | 8.00261 | − | 1.83614i | 0.420608 | − | 0.0965054i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.34371 | + | 26.8993i | −0.489743 | + | 1.40991i | ||||
\(365\) | 3.51330 | + | 13.1118i | 0.183895 | + | 0.686304i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.93807 | − | 17.2133i | −0.518763 | − | 0.898524i | −0.999762 | − | 0.0218032i | \(-0.993059\pi\) |
0.480999 | − | 0.876721i | \(-0.340274\pi\) | |||||||
\(368\) | −1.74197 | + | 0.692854i | −0.0908064 | + | 0.0361175i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.13913 | + | 1.13369i | −0.111208 | + | 0.0589375i | ||||
\(371\) | −6.74579 | − | 1.80753i | −0.350224 | − | 0.0938422i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.427591 | + | 0.114573i | −0.0221398 | + | 0.00593235i | −0.269872 | − | 0.962896i | \(-0.586981\pi\) |
0.247732 | + | 0.968829i | \(0.420315\pi\) | |||||||
\(374\) | 9.89081 | + | 10.6354i | 0.511442 | + | 0.549944i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.5264 | − | 23.9035i | −0.542858 | − | 1.23273i | ||||
\(377\) | 23.0557i | 1.18743i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.18132 | − | 6.18132i | −0.317513 | − | 0.317513i | 0.530298 | − | 0.847811i | \(-0.322080\pi\) |
−0.847811 | + | 0.530298i | \(0.822080\pi\) | |||||||
\(380\) | −4.83709 | − | 0.351404i | −0.248138 | − | 0.0180266i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.3113 | − | 0.881917i | −1.24387 | − | 0.0451228i | ||||
\(383\) | −6.46708 | + | 11.2013i | −0.330452 | + | 0.572360i | −0.982601 | − | 0.185731i | \(-0.940535\pi\) |
0.652148 | + | 0.758091i | \(0.273868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 16.6960 | + | 28.9183i | 0.850907 | + | 1.47381i | ||||
\(386\) | −12.1516 | − | 22.9287i | −0.618501 | − | 1.16704i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −12.7504 | + | 18.7933i | −0.647303 | + | 0.954085i | ||||
\(389\) | −7.08096 | + | 26.4265i | −0.359019 | + | 1.33988i | 0.516331 | + | 0.856389i | \(0.327297\pi\) |
−0.875351 | + | 0.483489i | \(0.839369\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.869168 | + | 0.501814i | 0.0439557 | + | 0.0253778i | ||||
\(392\) | −17.6309 | + | 24.0608i | −0.890495 | + | 1.21525i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −17.1627 | + | 3.93785i | −0.864642 | + | 0.198386i | ||||
\(395\) | 8.53468 | + | 8.53468i | 0.429426 | + | 0.429426i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.9741 | − | 21.9741i | 1.10285 | − | 1.10285i | 0.108781 | − | 0.994066i | \(-0.465305\pi\) |
0.994066 | − | 0.108781i | \(-0.0346948\pi\) | |||||||
\(398\) | 12.0163 | + | 7.53124i | 0.602322 | + | 0.377507i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.29330 | − | 8.85417i | 0.0646648 | − | 0.442709i | ||||
\(401\) | −13.4970 | + | 23.3775i | −0.674009 | + | 1.16742i | 0.302749 | + | 0.953070i | \(0.402096\pi\) |
−0.976758 | + | 0.214347i | \(0.931238\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −20.8849 | − | 5.59609i | −1.04035 | − | 0.278761i | ||||
\(404\) | 5.90120 | − | 1.13051i | 0.293596 | − | 0.0562448i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −11.8000 | + | 38.4099i | −0.585622 | + | 1.90625i | ||||
\(407\) | 4.27742 | − | 2.46957i | 0.212024 | − | 0.122412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.1537 | + | 6.43957i | 0.551513 | + | 0.318416i | 0.749732 | − | 0.661741i | \(-0.230182\pi\) |
−0.198219 | + | 0.980158i | \(0.563516\pi\) | |||||||
\(410\) | −5.01593 | + | 4.66475i | −0.247719 | + | 0.230376i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.208869 | + | 2.87510i | −0.0102903 | + | 0.141646i | ||||
\(413\) | 4.54399 | − | 4.54399i | 0.223595 | − | 0.223595i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.0638 | 0.641279 | ||||||||
\(416\) | 15.8249 | − | 10.9218i | 0.775877 | − | 0.535486i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.88786 | + | 0.358693i | 0.483631 | + | 0.0175442i | ||||
\(419\) | 0.0545100 | + | 0.203434i | 0.00266299 | + | 0.00993841i | 0.967245 | − | 0.253846i | \(-0.0816958\pi\) |
−0.964582 | + | 0.263785i | \(0.915029\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.17194 | − | 34.2301i | 0.447013 | − | 1.66827i | −0.263554 | − | 0.964645i | \(-0.584895\pi\) |
0.710567 | − | 0.703630i | \(-0.248439\pi\) | |||||||
\(422\) | −26.8825 | − | 8.25862i | −1.30862 | − | 0.402023i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.95276 | + | 3.67678i | 0.143399 | + | 0.178560i | ||||
\(425\) | −4.14862 | + | 2.39521i | −0.201238 | + | 0.116185i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 31.5511 | − | 8.45410i | 1.52687 | − | 0.409123i | ||||
\(428\) | −5.43487 | + | 15.6463i | −0.262704 | + | 0.756292i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.9180 | + | 13.7372i | 1.05698 | + | 0.662467i | ||||
\(431\) | −33.5339 | −1.61527 | −0.807635 | − | 0.589683i | \(-0.799253\pi\) | ||||
−0.807635 | + | 0.589683i | \(0.799253\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.9691 | −1.39217 | −0.696083 | − | 0.717962i | \(-0.745075\pi\) | ||||
−0.696083 | + | 0.717962i | \(0.745075\pi\) | |||||||
\(434\) | −31.9293 | − | 20.0118i | −1.53266 | − | 0.960597i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.48390 | + | 1.90488i | 0.262631 | + | 0.0912272i | ||||
\(437\) | 0.660427 | − | 0.176961i | 0.0315925 | − | 0.00846519i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.6656 | + | 8.46718i | −0.699950 | + | 0.404116i | −0.807329 | − | 0.590102i | \(-0.799088\pi\) |
0.107379 | + | 0.994218i | \(0.465754\pi\) | |||||||
\(440\) | 2.44788 | − | 22.4141i | 0.116698 | − | 1.06855i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.83987 | − | 3.02292i | −0.468035 | − | 0.143786i | ||||
\(443\) | −0.826654 | + | 3.08511i | −0.0392755 | + | 0.146578i | −0.982779 | − | 0.184784i | \(-0.940841\pi\) |
0.943504 | + | 0.331362i | \(0.107508\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.81702 | − | 17.9773i | −0.228348 | − | 0.852208i | ||||
\(446\) | −19.6895 | − | 0.714257i | −0.932325 | − | 0.0338211i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 31.9534 | − | 10.0961i | 1.50966 | − | 0.476998i | ||||
\(449\) | 41.9192 | 1.97829 | 0.989145 | − | 0.146944i | \(-0.0469436\pi\) | ||||
0.989145 | + | 0.146944i | \(0.0469436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.88149 | − | 9.88149i | 0.465301 | − | 0.465301i | ||||
\(452\) | −16.4656 | − | 1.19619i | −0.774478 | − | 0.0562641i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.84896 | − | 7.29943i | 0.368370 | − | 0.342579i | ||||
\(455\) | −20.4959 | − | 11.8333i | −0.960862 | − | 0.554754i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.93980 | − | 2.85199i | 0.231074 | − | 0.133411i | −0.379993 | − | 0.924989i | \(-0.624074\pi\) |
0.611067 | + | 0.791579i | \(0.290740\pi\) | |||||||
\(458\) | −7.93860 | + | 25.8409i | −0.370947 | + | 1.20746i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.293154 | − | 1.53025i | −0.0136684 | − | 0.0713484i | ||||
\(461\) | 38.3338 | + | 10.2715i | 1.78538 | + | 0.478392i | 0.991548 | − | 0.129743i | \(-0.0414153\pi\) |
0.793834 | + | 0.608135i | \(0.208082\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.28293 | + | 10.8824i | −0.291992 | + | 0.505746i | −0.974281 | − | 0.225337i | \(-0.927652\pi\) |
0.682288 | + | 0.731083i | \(0.260985\pi\) | |||||||
\(464\) | 21.7566 | − | 16.2109i | 1.01003 | − | 0.752570i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.8993 | − | 8.08471i | −0.597551 | − | 0.374517i | ||||
\(467\) | −12.1784 | + | 12.1784i | −0.563550 | + | 0.563550i | −0.930314 | − | 0.366764i | \(-0.880466\pi\) |
0.366764 | + | 0.930314i | \(0.380466\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.1267 | + | 30.1267i | 1.39112 | + | 1.39112i | ||||
\(470\) | 21.1576 | − | 4.85447i | 0.975928 | − | 0.223920i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.28846 | + | 0.661386i | −0.197393 | + | 0.0304428i | ||||
\(473\) | −45.7025 | − | 26.3864i | −2.10140 | − | 1.21325i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.844652 | + | 3.15228i | −0.0387553 | + | 0.144637i | ||||
\(476\) | −14.8457 | − | 10.0721i | −0.680452 | − | 0.461656i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14.7586 | − | 27.8478i | −0.675043 | − | 1.27373i | ||||
\(479\) | 10.6864 | + | 18.5094i | 0.488275 | + | 0.845717i | 0.999909 | − | 0.0134862i | \(-0.00429292\pi\) |
−0.511634 | + | 0.859204i | \(0.670960\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.75031 | + | 3.03162i | −0.0798072 | + | 0.138230i | ||||
\(482\) | 38.8046 | + | 1.40768i | 1.76750 | + | 0.0641180i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.73896 | + | 23.9368i | −0.0790435 | + | 1.08804i | ||||
\(485\) | −13.3465 | − | 13.3465i | −0.606033 | − | 0.606033i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.3716i | 1.78410i | 0.451939 | + | 0.892049i | \(0.350732\pi\) | ||||
−0.451939 | + | 0.892049i | \(0.649268\pi\) | |||||||
\(488\) | −20.5587 | − | 7.98769i | −0.930649 | − | 0.361586i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.8830 | − | 18.1540i | −0.762695 | − | 0.820113i | ||||
\(491\) | 33.8903 | − | 9.08087i | 1.52945 | − | 0.409814i | 0.606608 | − | 0.795001i | \(-0.292530\pi\) |
0.922839 | + | 0.385187i | \(0.125863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.0303 | − | 3.75940i | −0.631891 | − | 0.169315i | ||||
\(494\) | −6.19624 | + | 3.28385i | −0.278782 | + | 0.147747i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.40375 | + | 23.6428i | 0.422241 | + | 1.06160i | ||||
\(497\) | 17.3388 | + | 30.0317i | 0.777752 | + | 1.34711i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.38889 | + | 12.6475i | 0.151708 | + | 0.566181i | 0.999365 | + | 0.0356364i | \(0.0113458\pi\) |
−0.847657 | + | 0.530544i | \(0.821988\pi\) | |||||||
\(500\) | 22.7270 | + | 7.89441i | 1.01638 | + | 0.353049i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.2469 | + | 5.10440i | −0.992928 | + | 0.227820i | ||||
\(503\) | 2.93881i | 0.131035i | 0.997851 | + | 0.0655175i | \(0.0208698\pi\) | ||||
−0.997851 | + | 0.0655175i | \(0.979130\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.99373i | 0.222218i | ||||||||
\(506\) | 0.710860 | + | 3.09820i | 0.0316016 | + | 0.137732i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.46896 | + | 3.03261i | 0.0651744 | + | 0.134550i | ||||
\(509\) | −4.11461 | − | 15.3559i | −0.182377 | − | 0.680640i | −0.995177 | − | 0.0980972i | \(-0.968724\pi\) |
0.812800 | − | 0.582543i | \(-0.197942\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.1038 | + | 29.6246i | 0.756627 | + | 1.31052i | ||||
\(512\) | −21.4332 | − | 7.25389i | −0.947222 | − | 0.320580i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.23228 | − | 2.32517i | −0.0543535 | − | 0.102559i | ||||
\(515\) | −2.31418 | − | 0.620083i | −0.101975 | − | 0.0273241i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.7772 | + | 11.4621i | −1.88134 | + | 0.504103i | ||||
\(518\) | −4.46754 | + | 4.15476i | −0.196293 | + | 0.182550i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.44051 | + | 14.6252i | 0.282435 | + | 0.641356i | ||||
\(521\) | − | 19.2119i | − | 0.841689i | −0.907133 | − | 0.420844i | \(-0.861734\pi\) | ||
0.907133 | − | 0.420844i | \(-0.138266\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.0495 | − | 10.0495i | −0.439436 | − | 0.439436i | 0.452386 | − | 0.891822i | \(-0.350573\pi\) |
−0.891822 | + | 0.452386i | \(0.850573\pi\) | |||||||
\(524\) | −11.5355 | + | 9.97293i | −0.503929 | + | 0.435669i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.00245585 | + | 0.0676988i | −0.000107080 | + | 0.00295181i | ||||
\(527\) | 6.81087 | − | 11.7968i | 0.296686 | − | 0.513875i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3902 | − | 19.7284i | −0.495225 | − | 0.857755i | ||||
\(530\) | −3.46296 | + | 1.83528i | −0.150422 | + | 0.0797196i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0034 | + | 2.29952i | −0.520413 | + | 0.0996967i | ||||
\(533\) | −2.56346 | + | 9.56697i | −0.111036 | + | 0.414392i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.9217 | − | 6.88297i | −0.515418 | − | 0.297577i | ||||
\(536\) | −4.38500 | − | 28.4326i | −0.189403 | − | 1.22810i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.51581 | − | 28.3984i | −0.280916 | − | 1.22434i | ||||
\(539\) | 35.7637 | + | 35.7637i | 1.54045 | + | 1.54045i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.3802 | − | 15.3802i | 0.661246 | − | 0.661246i | −0.294428 | − | 0.955674i | \(-0.595129\pi\) |
0.955674 | + | 0.294428i | \(0.0951290\pi\) | |||||||
\(542\) | −11.8519 | + | 18.9101i | −0.509084 | + | 0.812257i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.06599 | + | 11.4109i | 0.174328 | + | 0.489239i | ||||
\(545\) | −2.41243 | + | 4.17844i | −0.103337 | + | 0.178985i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.1362 | − | 6.19933i | −0.989233 | − | 0.265064i | −0.272304 | − | 0.962211i | \(-0.587786\pi\) |
−0.716928 | + | 0.697147i | \(0.754452\pi\) | |||||||
\(548\) | 15.8009 | + | 10.7202i | 0.674981 | + | 0.457944i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.5033 | − | 4.45558i | −0.618423 | − | 0.189986i | ||||
\(551\) | −8.56961 | + | 4.94767i | −0.365078 | + | 0.210778i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.3412 | + | 15.2081i | 1.12014 | + | 0.646714i | ||||
\(554\) | 7.19265 | + | 7.73414i | 0.305587 | + | 0.328592i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.9155 | + | 21.8792i | 0.802197 | + | 0.927883i | ||||
\(557\) | −0.932077 | + | 0.932077i | −0.0394934 | + | 0.0394934i | −0.726578 | − | 0.687084i | \(-0.758890\pi\) |
0.687084 | + | 0.726578i | \(0.258890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 37.4027 | 1.58197 | ||||||||
\(560\) | 3.24445 | + | 27.6613i | 0.137103 | + | 1.16890i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.345986 | − | 9.53759i | 0.0145945 | − | 0.402319i | ||||
\(563\) | 1.71390 | + | 6.39635i | 0.0722321 | + | 0.269574i | 0.992591 | − | 0.121500i | \(-0.0387704\pi\) |
−0.920359 | + | 0.391074i | \(0.872104\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.55121 | − | 13.2533i | 0.149400 | − | 0.557570i | ||||
\(566\) | 5.34926 | − | 17.4123i | 0.224846 | − | 0.731893i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.54213 | − | 23.2771i | 0.106665 | − | 0.976685i | ||||
\(569\) | −7.84553 | + | 4.52962i | −0.328902 | + | 0.189892i | −0.655353 | − | 0.755322i | \(-0.727480\pi\) |
0.326452 | + | 0.945214i | \(0.394147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.9078 | + | 4.79838i | −0.749417 | + | 0.200806i | −0.613260 | − | 0.789881i | \(-0.710142\pi\) |
−0.136158 | + | 0.990687i | \(0.543475\pi\) | |||||||
\(572\) | −14.2126 | − | 29.3415i | −0.594259 | − | 1.22683i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.16703 | + | 14.6262i | −0.382625 | + | 0.610487i | ||||
\(575\) | −1.04844 | −0.0437230 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 43.3455 | 1.80450 | 0.902248 | − | 0.431217i | \(-0.141916\pi\) | ||||
0.902248 | + | 0.431217i | \(0.141916\pi\) | |||||||
\(578\) | −9.32368 | + | 14.8762i | −0.387814 | + | 0.618767i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.83019 | + | 20.2941i | 0.408177 | + | 0.842668i | ||||
\(581\) | 31.7993 | − | 8.52060i | 1.31926 | − | 0.353494i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.92456 | − | 3.99790i | 0.286786 | − | 0.165576i | ||||
\(584\) | 2.50767 | − | 22.9616i | 0.103768 | − | 0.950156i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.96717 | + | 19.4236i | −0.246501 | + | 0.802383i | ||||
\(587\) | 6.81553 | − | 25.4359i | 0.281307 | − | 1.04985i | −0.670189 | − | 0.742191i | \(-0.733787\pi\) |
0.951496 | − | 0.307662i | \(-0.0995465\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.40180 | − | 8.96364i | −0.0989645 | − | 0.369341i | ||||
\(590\) | 0.130737 | − | 3.60395i | 0.00538236 | − | 0.148372i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.09148 | − | 0.479899i | 0.168159 | − | 0.0197237i | ||||
\(593\) | −41.9274 | −1.72175 | −0.860876 | − | 0.508814i | \(-0.830084\pi\) | ||||
−0.860876 | + | 0.508814i | \(0.830084\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5430 | − | 10.5430i | 0.432222 | − | 0.432222i | ||||
\(596\) | −2.25129 | − | 2.60402i | −0.0922164 | − | 0.106665i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.53425 | − | 1.64975i | −0.0627401 | − | 0.0674634i | ||||
\(599\) | 21.1742 | + | 12.2249i | 0.865154 | + | 0.499497i | 0.865735 | − | 0.500503i | \(-0.166852\pi\) |
−0.000580933 | 1.00000i | \(0.500185\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.7521 | − | 14.2906i | 1.00966 | − | 0.582928i | 0.0985682 | − | 0.995130i | \(-0.468574\pi\) |
0.911092 | + | 0.412203i | \(0.135240\pi\) | |||||||
\(602\) | 62.3115 | + | 19.1428i | 2.53963 | + | 0.780202i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −35.3686 | − | 23.9960i | −1.43913 | − | 0.976383i | ||||
\(605\) | −19.2669 | − | 5.16255i | −0.783310 | − | 0.209887i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.32245 | + | 16.1470i | −0.378387 | + | 0.655385i | −0.990828 | − | 0.135131i | \(-0.956854\pi\) |
0.612441 | + | 0.790516i | \(0.290188\pi\) | |||||||
\(608\) | 7.45551 | + | 3.53819i | 0.302361 | + | 0.143492i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9.73492 | − | 15.5323i | 0.394155 | − | 0.628885i | ||||
\(611\) | 22.1946 | − | 22.1946i | 0.897896 | − | 0.897896i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −13.3177 | − | 13.3177i | −0.537896 | − | 0.537896i | 0.385014 | − | 0.922911i | \(-0.374196\pi\) |
−0.922911 | + | 0.385014i | \(0.874196\pi\) | |||||||
\(614\) | −5.47424 | − | 23.8588i | −0.220922 | − | 0.962864i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.66061 | − | 56.1559i | −0.348946 | − | 2.26258i | ||||
\(617\) | 15.1035 | + | 8.72003i | 0.608045 | + | 0.351055i | 0.772200 | − | 0.635379i | \(-0.219156\pi\) |
−0.164155 | + | 0.986435i | \(0.552490\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.84959 | − | 21.8310i | 0.235115 | − | 0.877461i | −0.742982 | − | 0.669311i | \(-0.766589\pi\) |
0.978097 | − | 0.208150i | \(-0.0667441\pi\) | |||||||
\(620\) | −20.7693 | + | 3.97883i | −0.834117 | + | 0.159794i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.07174 | − | 0.567995i | 0.0429729 | − | 0.0227745i | ||||
\(623\) | −23.4506 | − | 40.6177i | −0.939530 | − | 1.62731i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.40527 | + | 7.63015i | −0.176211 | + | 0.305206i | ||||
\(626\) | −0.941180 | + | 25.9449i | −0.0376171 | + | 1.03697i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.0492 | − | 13.8753i | 0.640433 | − | 0.553683i | ||||
\(629\) | −1.55946 | − | 1.55946i | −0.0621797 | − | 0.0621797i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.8510i | − | 0.790254i | −0.918627 | − | 0.395127i | \(-0.870701\pi\) | ||
0.918627 | − | 0.395127i | \(-0.129299\pi\) | |||||||
\(632\) | −8.27732 | − | 18.7962i | −0.329254 | − | 0.747673i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.31682 | − | 4.01459i | 0.171443 | − | 0.159440i | ||||
\(635\) | −2.70512 | + | 0.724836i | −0.107350 | + | 0.0287642i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −34.6254 | − | 9.27785i | −1.37191 | − | 0.367602i | ||||
\(638\) | −21.5428 | − | 40.6487i | −0.852886 | − | 1.60930i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 9.27269 | − | 16.3608i | 0.366535 | − | 0.646719i | ||||
\(641\) | −20.5842 | − | 35.6529i | −0.813026 | − | 1.40820i | −0.910736 | − | 0.412988i | \(-0.864485\pi\) |
0.0977099 | − | 0.995215i | \(-0.468848\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.73128 | + | 25.1215i | 0.265456 | + | 0.990694i | 0.961971 | + | 0.273152i | \(0.0880662\pi\) |
−0.696515 | + | 0.717542i | \(0.745267\pi\) | |||||||
\(644\) | −1.71165 | − | 3.53366i | −0.0674486 | − | 0.139246i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.988006 | − | 4.30611i | −0.0388726 | − | 0.169422i | ||||
\(647\) | − | 40.3426i | − | 1.58603i | −0.609201 | − | 0.793016i | \(-0.708510\pi\) | ||
0.609201 | − | 0.793016i | \(-0.291490\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.35741i | 0.288803i | ||||||||
\(650\) | 10.4810 | − | 2.40479i | 0.411099 | − | 0.0943238i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.28783 | + | 3.22621i | 0.363740 | + | 0.126348i | ||||
\(653\) | −1.68547 | − | 6.29024i | −0.0659574 | − | 0.246156i | 0.925074 | − | 0.379787i | \(-0.124003\pi\) |
−0.991031 | + | 0.133631i | \(0.957336\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.33671 | − | 10.9755i | −0.247596 | − | 0.428849i | ||||
\(656\) | 10.8303 | − | 4.30768i | 0.422854 | − | 0.168187i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 48.3345 | − | 25.6161i | 1.88428 | − | 0.998618i | ||||
\(659\) | −0.0887093 | − | 0.0237696i | −0.00345562 | − | 0.000925932i | 0.257091 | − | 0.966387i | \(-0.417236\pi\) |
−0.260546 | + | 0.965461i | \(0.583903\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.0157 | − | 7.23883i | 1.05079 | − | 0.281558i | 0.308211 | − | 0.951318i | \(-0.400270\pi\) |
0.742578 | + | 0.669760i | \(0.233603\pi\) | |||||||
\(662\) | −4.97638 | − | 5.35102i | −0.193413 | − | 0.207973i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.7204 | − | 8.05052i | −0.804109 | − | 0.312421i | ||||
\(665\) | − | 10.1575i | − | 0.393892i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.24790 | − | 2.24790i | −0.0870392 | − | 0.0870392i | ||||
\(668\) | −0.0464249 | + | 0.639041i | −0.00179623 | + | 0.0247253i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23.8942 | + | 0.866788i | 0.923114 | + | 0.0334870i | ||||
\(671\) | −18.6988 | + | 32.3873i | −0.721859 | + | 1.25030i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.48158 | + | 4.29822i | 0.0956578 | + | 0.165684i | 0.909883 | − | 0.414865i | \(-0.136171\pi\) |
−0.814225 | + | 0.580549i | \(0.802838\pi\) | |||||||
\(674\) | −2.57959 | − | 4.86739i | −0.0993622 | − | 0.187485i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.39400 | − | 1.62422i | −0.0920769 | − | 0.0624700i | ||||
\(677\) | −1.77876 | + | 6.63841i | −0.0683632 | + | 0.255135i | −0.991647 | − | 0.128985i | \(-0.958828\pi\) |
0.923283 | + | 0.384119i | \(0.125495\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −41.1923 | − | 23.7824i | −1.58081 | − | 0.912683i | ||||
\(680\) | −9.95015 | + | 1.53456i | −0.381571 | + | 0.0588476i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42.0503 | − | 9.64814i | 1.61019 | − | 0.369447i | ||||
\(683\) | −20.7192 | − | 20.7192i | −0.792797 | − | 0.792797i | 0.189151 | − | 0.981948i | \(-0.439426\pi\) |
−0.981948 | + | 0.189151i | \(0.939426\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.2214 | + | 11.2214i | −0.428747 | + | 0.428747i | ||||
\(686\) | −17.7998 | − | 11.1561i | −0.679601 | − | 0.425942i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.2985 | − | 35.2953i | −1.00262 | − | 1.34562i | ||||
\(689\) | −2.83351 | + | 4.90779i | −0.107948 | + | 0.186972i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.31450 | − | 1.42402i | −0.202173 | − | 0.0541721i | 0.156311 | − | 0.987708i | \(-0.450040\pi\) |
−0.358484 | + | 0.933536i | \(0.616706\pi\) | |||||||
\(692\) | 4.55420 | + | 23.7727i | 0.173125 | + | 0.903704i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.31056 | − | 4.26598i | 0.0497481 | − | 0.161934i | ||||
\(695\) | −20.8171 | + | 12.0188i | −0.789638 | + | 0.455898i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.40388 | − | 3.11993i | −0.204687 | − | 0.118176i | ||||
\(698\) | 1.49983 | − | 1.39483i | 0.0567695 | − | 0.0527949i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 18.6918 | + | 1.35791i | 0.706482 | + | 0.0513243i | ||||
\(701\) | 1.06232 | − | 1.06232i | 0.0401233 | − | 0.0401233i | −0.686760 | − | 0.726884i | \(-0.740968\pi\) |
0.726884 | + | 0.686760i | \(0.240968\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.50244 | −0.0566656 | ||||||||
\(704\) | −17.6951 | + | 34.0423i | −0.666910 | + | 1.28302i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −21.8746 | − | 0.793524i | −0.823261 | − | 0.0298647i | ||||
\(707\) | 3.25705 | + | 12.1555i | 0.122494 | + | 0.457153i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.50159 | + | 35.4604i | −0.356840 | + | 1.33174i | 0.521314 | + | 0.853365i | \(0.325442\pi\) |
−0.878153 | + | 0.478379i | \(0.841224\pi\) | |||||||
\(710\) | 18.6028 | + | 5.71498i | 0.698149 | + | 0.214479i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.43821 | + | 31.4821i | −0.128853 | + | 1.17984i | ||||
\(713\) | 2.58187 | − | 1.49064i | 0.0966916 | − | 0.0558249i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 26.1729 | − | 7.01301i | 0.978812 | − | 0.262272i | ||||
\(716\) | 49.9045 | + | 17.3348i | 1.86502 | + | 0.647830i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.73718 | − | 3.59580i | −0.214110 | − | 0.134194i | ||||
\(719\) | 7.37513 | 0.275046 | 0.137523 | − | 0.990499i | \(-0.456086\pi\) | ||||
0.137523 | + | 0.990499i | \(0.456086\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.03749 | −0.224848 | ||||||||
\(722\) | 20.2175 | + | 12.6714i | 0.752419 | + | 0.471581i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.81003 | − | 10.9686i | 0.141599 | − | 0.407644i | ||||
\(725\) | 14.6567 | − | 3.92726i | 0.544337 | − | 0.145855i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.80127 | − | 3.34936i | 0.215157 | − | 0.124221i | −0.388549 | − | 0.921428i | \(-0.627023\pi\) |
0.603706 | + | 0.797207i | \(0.293690\pi\) | |||||||
\(728\) | 25.2161 | + | 31.3991i | 0.934571 | + | 1.16373i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.3506 | + | 5.63751i | 0.679186 | + | 0.208654i | ||||
\(731\) | −6.09879 | + | 22.7610i | −0.225572 | + | 0.841846i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.28281 | − | 34.6439i | −0.342868 | − | 1.27960i | −0.895083 | − | 0.445900i | \(-0.852884\pi\) |
0.552214 | − | 0.833702i | \(-0.313783\pi\) | |||||||
\(734\) | −28.0906 | − | 1.01902i | −1.03684 | − | 0.0376126i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.478040 | + | 2.60777i | −0.0176208 | + | 0.0961238i | ||||
\(737\) | −48.7797 | −1.79682 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.01107 | − | 4.01107i | 0.147549 | − | 0.147549i | −0.629473 | − | 0.777022i | \(-0.716729\pi\) |
0.777022 | + | 0.629473i | \(0.216729\pi\) | |||||||
\(740\) | −0.248076 | + | 3.41478i | −0.00911945 | + | 0.125530i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.23234 | + | 6.72599i | −0.265508 | + | 0.246919i | ||||
\(743\) | −19.1551 | − | 11.0592i | −0.702734 | − | 0.405724i | 0.105631 | − | 0.994405i | \(-0.466314\pi\) |
−0.808365 | + | 0.588682i | \(0.799647\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.47761 | − | 1.43045i | 0.0907726 | − | 0.0524076i | ||||
\(746\) | −0.183846 | + | 0.598434i | −0.00673107 | + | 0.0219102i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 20.1729 | − | 3.86457i | 0.737594 | − | 0.141303i | ||||
\(749\) | −33.5083 | − | 8.97853i | −1.22437 | − | 0.328068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.05672 | + | 10.4905i | −0.221013 | + | 0.382805i | −0.955116 | − | 0.296233i | \(-0.904270\pi\) |
0.734103 | + | 0.679038i | \(0.237603\pi\) | |||||||
\(752\) | −36.5494 | − | 5.33864i | −1.33282 | − | 0.194680i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 27.6278 | + | 17.3158i | 1.00614 | + | 0.630603i | ||||
\(755\) | 25.1178 | − | 25.1178i | 0.914131 | − | 0.914131i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.9365 | − | 19.9365i | −0.724604 | − | 0.724604i | 0.244935 | − | 0.969539i | \(-0.421233\pi\) |
−0.969539 | + | 0.244935i | \(0.921233\pi\) | |||||||
\(758\) | −12.0495 | + | 2.76468i | −0.437659 | + | 0.100418i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.05395 | + | 5.53240i | −0.147052 | + | 0.200681i | ||||
\(761\) | 37.1681 | + | 21.4590i | 1.34734 | + | 0.777889i | 0.987873 | − | 0.155267i | \(-0.0496237\pi\) |
0.359471 | + | 0.933156i | \(0.382957\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.14690 | + | 11.7444i | −0.113925 | + | 0.425176i | ||||
\(764\) | −19.3156 | + | 28.4700i | −0.698814 | + | 1.03001i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.56555 | + | 16.1622i | 0.309486 | + | 0.583964i | ||||
\(767\) | −2.60728 | − | 4.51595i | −0.0941435 | − | 0.163061i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.7618 | + | 23.8361i | −0.496263 | + | 0.859553i | −0.999991 | − | 0.00430961i | \(-0.998628\pi\) |
0.503728 | + | 0.863863i | \(0.331962\pi\) | |||||||
\(770\) | 47.1924 | + | 1.71195i | 1.70070 | + | 0.0616945i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −36.6019 | − | 2.65905i | −1.31733 | − | 0.0957011i | ||||
\(773\) | 11.4688 | + | 11.4688i | 0.412504 | + | 0.412504i | 0.882610 | − | 0.470106i | \(-0.155784\pi\) |
−0.470106 | + | 0.882610i | \(0.655784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.2300i | 0.511155i | ||||||||
\(776\) | 12.9440 | + | 29.3934i | 0.464664 | + | 1.05516i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.3489 | + | 28.3326i | 0.944655 | + | 1.01577i | ||||
\(779\) | −4.10608 | + | 1.10022i | −0.147115 | + | 0.0394195i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −38.3500 | − | 10.2759i | −1.37227 | − | 0.367699i | ||||
\(782\) | 1.25411 | − | 0.664645i | 0.0448468 | − | 0.0237677i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.5906 | + | 39.1979i | 0.556808 | + | 1.39992i | ||||
\(785\) | 8.81622 | + | 15.2701i | 0.314664 | + | 0.545015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4753 | + | 42.8263i | 0.409049 | + | 1.52659i | 0.796463 | + | 0.604687i | \(0.206702\pi\) |
−0.387414 | + | 0.921906i | \(0.626632\pi\) | |||||||
\(788\) | −8.17112 | + | 23.5236i | −0.291084 | + | 0.837993i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 16.6370 | − | 3.81725i | 0.591920 | − | 0.135812i | ||||
\(791\) | − | 34.5766i | − | 1.22940i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 26.5056i | − | 0.941241i | ||||||
\(794\) | −9.82821 | − | 42.8351i | −0.348790 | − | 1.52016i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.0495 | − | 8.74290i | 0.639746 | − | 0.309884i | ||||
\(797\) | −7.68647 | − | 28.6863i | −0.272269 | − | 1.01612i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) |
0.685381 | − | 0.728185i | \(-0.259636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.88726 | + | 17.1252i | 0.349786 | + | 0.605847i | ||||
\(800\) | −9.63868 | − | 8.19961i | −0.340779 | − | 0.289900i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 17.8766 | + | 33.7310i | 0.631244 | + | 1.19108i | ||||
\(803\) | −37.8302 | − | 10.1366i | −1.33500 | − | 0.357712i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.15206 | − | 0.844592i | 0.111096 | − | 0.0297679i | ||||
\(806\) | −22.3912 | + | 20.8236i | −0.788698 | + | 0.733479i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.07735 | − | 7.92049i | 0.108261 | − | 0.278642i | ||||
\(809\) | 16.7474i | 0.588806i | 0.955681 | + | 0.294403i | \(0.0951209\pi\) | ||||
−0.955681 | + | 0.294403i | \(0.904879\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.60619 | − | 7.60619i | −0.267090 | − | 0.267090i | 0.560837 | − | 0.827926i | \(-0.310480\pi\) |
−0.827926 | + | 0.560837i | \(0.810480\pi\) | |||||||
\(812\) | 37.1645 | + | 42.9874i | 1.30422 | + | 1.50856i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.253222 | − | 6.98041i | 0.00887541 | − | 0.244663i | ||||
\(815\) | −4.08582 | + | 7.07684i | −0.143120 | + | 0.247891i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.02649 | + | 13.9023i | 0.280811 | + | 0.486379i | ||||
\(818\) | 16.0934 | − | 8.52912i | 0.562694 | − | 0.298214i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.82263 | + | 9.51404i | 0.0636489 | + | 0.332245i | ||||
\(821\) | 9.99074 | − | 37.2860i | 0.348679 | − | 1.30129i | −0.539575 | − | 0.841937i | \(-0.681415\pi\) |
0.888255 | − | 0.459351i | \(-0.151918\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −23.9783 | − | 13.8439i | −0.835831 | − | 0.482567i | 0.0200141 | − | 0.999800i | \(-0.493629\pi\) |
−0.855845 | + | 0.517233i | \(0.826962\pi\) | |||||||
\(824\) | 3.28838 | + | 2.40961i | 0.114556 | + | 0.0839427i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.03236 | − | 8.85781i | −0.0707149 | − | 0.308203i | ||||
\(827\) | 27.6025 | + | 27.6025i | 0.959833 | + | 0.959833i | 0.999224 | − | 0.0393907i | \(-0.0125417\pi\) |
−0.0393907 | + | 0.999224i | \(0.512542\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8542 | − | 14.8542i | 0.515908 | − | 0.515908i | −0.400423 | − | 0.916330i | \(-0.631137\pi\) |
0.916330 | + | 0.400423i | \(0.131137\pi\) | |||||||
\(830\) | 9.81150 | − | 15.6545i | 0.340562 | − | 0.543375i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.20256 | − | 27.1658i | −0.0416911 | − | 0.941803i | ||||
\(833\) | 11.2919 | − | 19.5581i | 0.391240 | − | 0.677647i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.514368 | − | 0.137824i | −0.0178004 | − | 0.00476961i | ||||
\(836\) | 7.85602 | − | 11.5793i | 0.271706 | − | 0.400478i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.284716 | + | 0.0874679i | 0.00983534 | + | 0.00302153i | ||||
\(839\) | 44.0413 | − | 25.4272i | 1.52047 | − | 0.877846i | 0.520766 | − | 0.853700i | \(-0.325647\pi\) |
0.999708 | − | 0.0241463i | \(-0.00768676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.7301 | + | 8.50445i | 0.507936 | + | 0.293257i | ||||
\(842\) | −34.1297 | − | 36.6990i | −1.17619 | − | 1.26473i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.0863 | + | 26.0109i | −1.03561 | + | 0.895333i | ||||
\(845\) | 1.70015 | − | 1.70015i | 0.0584871 | − | 0.0584871i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.2656 | −1.72715 | ||||||||
\(848\) | 6.62355 | − | 0.776891i | 0.227454 | − | 0.0266786i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.245597 | + | 6.77022i | −0.00842390 | + | 0.232217i | ||||
\(851\) | −0.124927 | − | 0.466233i | −0.00428244 | − | 0.0159823i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.65390 | − | 13.6365i | 0.125107 | − | 0.466906i | −0.874736 | − | 0.484599i | \(-0.838966\pi\) |
0.999843 | + | 0.0176931i | \(0.00563219\pi\) | |||||||
\(854\) | 13.5656 | − | 44.1573i | 0.464206 | − | 1.51103i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.6672 | + | 18.2637i | 0.501315 | + | 0.624239i | ||||
\(857\) | −14.7618 | + | 8.52275i | −0.504255 | + | 0.291132i | −0.730469 | − | 0.682946i | \(-0.760698\pi\) |
0.226214 | + | 0.974078i | \(0.427365\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.9255 | − | 6.67877i | 0.850448 | − | 0.227877i | 0.192833 | − | 0.981232i | \(-0.438232\pi\) |
0.657614 | + | 0.753355i | \(0.271566\pi\) | |||||||
\(860\) | 32.9227 | − | 15.9473i | 1.12266 | − | 0.543798i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −25.1853 | + | 40.1838i | −0.857816 | + | 1.36867i | ||||
\(863\) | 18.8217 | 0.640698 | 0.320349 | − | 0.947300i | \(-0.396200\pi\) | ||||
0.320349 | + | 0.947300i | \(0.396200\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.1170 | −0.683999 | ||||||||
\(866\) | −21.7570 | + | 34.7138i | −0.739333 | + | 1.17962i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −47.9605 | + | 23.2314i | −1.62789 | + | 0.788525i | ||||
\(869\) | −33.6373 | + | 9.01309i | −1.14107 | + | 0.305748i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 29.9408 | − | 17.2863i | 1.01450 | − | 0.585725i | ||||
\(872\) | 6.40126 | − | 5.14074i | 0.216774 | − | 0.174088i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.283955 | − | 0.924299i | 0.00960492 | − | 0.0312649i | ||||
\(875\) | −13.0417 | + | 48.6724i | −0.440891 | + | 1.64543i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.80014 | + | 10.4503i | 0.0945540 | + | 0.352880i | 0.996951 | − | 0.0780244i | \(-0.0248612\pi\) |
−0.902397 | + | 0.430905i | \(0.858195\pi\) | |||||||
\(878\) | −0.868197 | + | 23.9330i | −0.0293002 | + | 0.807701i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −25.0205 | − | 19.7673i | −0.843441 | − | 0.666354i | ||||
\(881\) | −40.1658 | −1.35322 | −0.676610 | − | 0.736342i | \(-0.736552\pi\) | ||||
−0.676610 | + | 0.736342i | \(0.736552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5617 | + | 16.5617i | −0.557346 | + | 0.557346i | −0.928551 | − | 0.371205i | \(-0.878945\pi\) |
0.371205 | + | 0.928551i | \(0.378945\pi\) | |||||||
\(884\) | −11.0125 | + | 9.52083i | −0.370392 | + | 0.320220i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.07606 | + | 3.30763i | 0.103342 | + | 0.111122i | ||||
\(887\) | 13.1259 | + | 7.57822i | 0.440723 | + | 0.254452i | 0.703904 | − | 0.710295i | \(-0.251438\pi\) |
−0.263181 | + | 0.964746i | \(0.584772\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.11191 | + | 3.52871i | −0.204987 | + | 0.118349i | ||||
\(890\) | −25.1601 | − | 7.72948i | −0.843370 | − | 0.259093i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −15.6435 | + | 23.0576i | −0.523784 | + | 0.772026i | ||||
\(893\) | 13.0124 | + | 3.48667i | 0.435444 | + | 0.116677i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21.9535 | + | 38.0246i | −0.733826 | + | 1.27102i | ||||
\(896\) | 11.9001 | − | 45.8726i | 0.397554 | − | 1.53250i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.4831 | − | 50.2320i | 1.05060 | − | 1.67626i | ||||
\(899\) | −30.5097 | + | 30.5097i | −1.01755 | + | 1.01755i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.52455 | − | 2.52455i | −0.0841050 | − | 0.0841050i | ||||
\(902\) | −4.41963 | − | 19.2624i | −0.147158 | − | 0.641369i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.7998 | + | 18.8325i | −0.458974 | + | 0.626359i | ||||
\(905\) | 8.35749 | + | 4.82520i | 0.277812 | + | 0.160395i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.61434 | + | 9.75684i | −0.0868077 | + | 0.323971i | −0.995650 | − | 0.0931683i | \(-0.970301\pi\) |
0.908843 | + | 0.417139i | \(0.136967\pi\) | |||||||
\(908\) | −2.85206 | − | 14.8876i | −0.0946489 | − | 0.494063i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −29.5732 | + | 15.6730i | −0.980341 | + | 0.519556i | ||||
\(911\) | 25.2358 | + | 43.7097i | 0.836099 | + | 1.44817i | 0.893132 | + | 0.449794i | \(0.148503\pi\) |
−0.0570332 | + | 0.998372i | \(0.518164\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.8459 | + | 32.6420i | −0.623708 | + | 1.08029i | ||||
\(914\) | 0.292434 | − | 8.06136i | 0.00967286 | − | 0.266646i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 25.0030 | + | 28.9204i | 0.826123 | + | 0.955558i | ||||
\(917\) | −22.5830 | − | 22.5830i | −0.745757 | − | 0.745757i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.7422i | 0.552274i | 0.961118 | + | 0.276137i | \(0.0890544\pi\) | ||||
−0.961118 | + | 0.276137i | \(0.910946\pi\) | |||||||
\(920\) | −2.05388 | − | 0.797995i | −0.0677145 | − | 0.0263091i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 41.0987 | − | 38.2212i | 1.35351 | − | 1.25875i | ||||
\(923\) | 27.1806 | − | 7.28302i | 0.894661 | − | 0.239724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.22538 | + | 0.596288i | 0.0731699 | + | 0.0196058i | ||||
\(926\) | 8.32164 | + | 15.7020i | 0.273466 | + | 0.515999i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.08543 | − | 38.2461i | −0.101284 | − | 1.25549i | ||||
\(929\) | −9.92665 | − | 17.1935i | −0.325683 | − | 0.564099i | 0.655967 | − | 0.754789i | \(-0.272261\pi\) |
−0.981650 | + | 0.190690i | \(0.938927\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.98199 | − | 14.8610i | −0.130504 | − | 0.487049i | ||||
\(932\) | −19.3759 | + | 9.38541i | −0.634679 | + | 0.307429i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.44696 | + | 23.7400i | 0.178230 | + | 0.776795i | ||||
\(935\) | 17.0708i | 0.558273i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.05876i | 0.0999253i | 0.998751 | + | 0.0499626i | \(0.0159102\pi\) | ||||
−0.998751 | + | 0.0499626i | \(0.984090\pi\) | |||||||
\(938\) | 58.7274 | − | 13.4746i | 1.91752 | − | 0.439961i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.0731 | − | 28.9992i | 0.328549 | − | 0.945850i | ||||
\(941\) | −3.07424 | − | 11.4732i | −0.100217 | − | 0.374016i | 0.897541 | − | 0.440930i | \(-0.145351\pi\) |
−0.997759 | + | 0.0669140i | \(0.978685\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.682835 | − | 1.18270i | −0.0222362 | − | 0.0385141i | ||||
\(944\) | −2.42827 | + | 5.63562i | −0.0790335 | + | 0.183424i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −65.9434 | + | 34.9483i | −2.14401 | + | 1.13627i | ||||
\(947\) | 55.6732 | + | 14.9176i | 1.80914 | + | 0.484757i | 0.995343 | − | 0.0963965i | \(-0.0307317\pi\) |
0.813794 | + | 0.581153i | \(0.197398\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26.8122 | − | 7.18430i | 0.870360 | − | 0.233212i | ||||
\(950\) | 3.14303 | + | 3.37965i | 0.101973 | + | 0.109650i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −23.2193 | + | 10.2251i | −0.752540 | + | 0.331397i | ||||
\(953\) | 44.2546i | 1.43355i | 0.697306 | + | 0.716774i | \(0.254382\pi\) | ||||
−0.697306 | + | 0.716774i | \(0.745618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.2186 | − | 20.2186i | −0.654259 | − | 0.654259i | ||||
\(956\) | −44.4544 | − | 3.22951i | −1.43776 | − | 0.104450i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 30.2059 | + | 1.09575i | 0.975908 | + | 0.0354021i | ||||
\(959\) | −19.9956 | + | 34.6334i | −0.645691 | + | 1.11837i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.73171 | − | 8.19557i | −0.152636 | − | 0.264373i | ||||
\(962\) | 2.31826 | + | 4.37428i | 0.0747436 | + | 0.141032i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 30.8307 | − | 45.4425i | 0.992990 | − | 1.46361i | ||||
\(965\) | 7.89407 | − | 29.4611i | 0.254119 | − | 0.948386i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.7930 | + | 21.2424i | 1.18318 | + | 0.683110i | 0.956748 | − | 0.290916i | \(-0.0939602\pi\) |
0.226433 | + | 0.974027i | \(0.427294\pi\) | |||||||
\(968\) | 27.3776 | + | 20.0614i | 0.879950 | + | 0.644797i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −26.0169 | + | 5.96940i | −0.835354 | + | 0.191666i | ||||
\(971\) | −11.1469 | − | 11.1469i | −0.357720 | − | 0.357720i | 0.505252 | − | 0.862972i | \(-0.331400\pi\) |
−0.862972 | + | 0.505252i | \(0.831400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −42.8329 | + | 42.8329i | −1.37316 | + | 1.37316i | ||||
\(974\) | 47.1792 | + | 29.5697i | 1.51172 | + | 0.947475i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −25.0121 | + | 18.6365i | −0.800619 | + | 0.596541i | ||||
\(977\) | 2.47430 | − | 4.28561i | 0.0791598 | − | 0.137109i | −0.823728 | − | 0.566985i | \(-0.808110\pi\) |
0.902888 | + | 0.429877i | \(0.141443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 51.8682 | + | 13.8980i | 1.65771 | + | 0.444183i | ||||
\(980\) | −34.4338 | + | 6.59657i | −1.09995 | + | 0.210720i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.5714 | − | 47.4310i | 0.464991 | − | 1.51359i | ||||
\(983\) | −41.6831 | + | 24.0658i | −1.32948 | + | 0.767578i | −0.985220 | − | 0.171294i | \(-0.945205\pi\) |
−0.344265 | + | 0.938873i | \(0.611872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −17.9237 | − | 10.3483i | −0.571098 | − | 0.329724i | ||||
\(986\) | −15.0422 | + | 13.9891i | −0.479042 | + | 0.445503i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.718580 | + | 9.89130i | −0.0228611 | + | 0.314684i | ||||
\(989\) | −3.64672 | + | 3.64672i | −0.115959 | + | 0.115959i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.90020 | −0.282724 | −0.141362 | − | 0.989958i | \(-0.545148\pi\) | ||||
−0.141362 | + | 0.989958i | \(0.545148\pi\) | |||||||
\(992\) | 35.3940 | + | 6.48820i | 1.12376 | + | 0.206001i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 49.0093 | + | 1.77787i | 1.55448 | + | 0.0563905i | ||||
\(995\) | 4.31407 | + | 16.1003i | 0.136765 | + | 0.510414i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.66586 | − | 24.8773i | 0.211110 | − | 0.787873i | −0.776390 | − | 0.630253i | \(-0.782951\pi\) |
0.987500 | − | 0.157620i | \(-0.0503822\pi\) | |||||||
\(998\) | 17.7008 | + | 5.43789i | 0.560309 | + | 0.172133i | ||||
\(999\) | 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 | 432.2.y.e.37.12 | 72 | ||
3.2 | odd | 2 | 144.2.x.e.85.7 | yes | 72 | ||
4.3 | odd | 2 | 1728.2.bc.e.1009.13 | 72 | |||
9.2 | odd | 6 | 144.2.x.e.133.18 | yes | 72 | ||
9.7 | even | 3 | inner | 432.2.y.e.181.1 | 72 | ||
12.11 | even | 2 | 576.2.bb.e.49.16 | 72 | |||
16.3 | odd | 4 | 1728.2.bc.e.145.6 | 72 | |||
16.13 | even | 4 | inner | 432.2.y.e.253.1 | 72 | ||
36.7 | odd | 6 | 1728.2.bc.e.1585.6 | 72 | |||
36.11 | even | 6 | 576.2.bb.e.241.8 | 72 | |||
48.29 | odd | 4 | 144.2.x.e.13.18 | ✓ | 72 | ||
48.35 | even | 4 | 576.2.bb.e.337.8 | 72 | |||
144.29 | odd | 12 | 144.2.x.e.61.7 | yes | 72 | ||
144.61 | even | 12 | inner | 432.2.y.e.397.12 | 72 | ||
144.83 | even | 12 | 576.2.bb.e.529.16 | 72 | |||
144.115 | odd | 12 | 1728.2.bc.e.721.13 | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.2.x.e.13.18 | ✓ | 72 | 48.29 | odd | 4 | ||
144.2.x.e.61.7 | yes | 72 | 144.29 | odd | 12 | ||
144.2.x.e.85.7 | yes | 72 | 3.2 | odd | 2 | ||
144.2.x.e.133.18 | yes | 72 | 9.2 | odd | 6 | ||
432.2.y.e.37.12 | 72 | 1.1 | even | 1 | trivial | ||
432.2.y.e.181.1 | 72 | 9.7 | even | 3 | inner | ||
432.2.y.e.253.1 | 72 | 16.13 | even | 4 | inner | ||
432.2.y.e.397.12 | 72 | 144.61 | even | 12 | inner | ||
576.2.bb.e.49.16 | 72 | 12.11 | even | 2 | |||
576.2.bb.e.241.8 | 72 | 36.11 | even | 6 | |||
576.2.bb.e.337.8 | 72 | 48.35 | even | 4 | |||
576.2.bb.e.529.16 | 72 | 144.83 | even | 12 | |||
1728.2.bc.e.145.6 | 72 | 16.3 | odd | 4 | |||
1728.2.bc.e.721.13 | 72 | 144.115 | odd | 12 | |||
1728.2.bc.e.1009.13 | 72 | 4.3 | odd | 2 | |||
1728.2.bc.e.1585.6 | 72 | 36.7 | odd | 6 |