Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(3,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([8, 8, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.3");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.s (of order \(16\), degree \(8\), 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: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{16}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(-0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.11 |
Dual form | 136.2.s.b.99.1 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{7}{16}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.30656 | − | 0.541196i | −0.923880 | − | 0.382683i | ||||
\(3\) | 0.675577 | + | 3.39635i | 0.390044 | + | 1.96089i | 0.220942 | + | 0.975287i | \(0.429087\pi\) |
0.169102 | + | 0.985599i | \(0.445913\pi\) | |||||||
\(4\) | 1.41421 | + | 1.41421i | 0.707107 | + | 0.707107i | ||||
\(5\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(6\) | 0.955410 | − | 4.80317i | 0.390044 | − | 1.96089i | ||||
\(7\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(8\) | −1.08239 | − | 2.61313i | −0.382683 | − | 0.923880i | ||||
\(9\) | −8.30717 | + | 3.44094i | −2.76906 | + | 1.14698i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.57273 | + | 0.312835i | 0.474195 | + | 0.0943232i | 0.426401 | − | 0.904534i | \(-0.359781\pi\) |
0.0477934 | + | 0.998857i | \(0.484781\pi\) | |||||||
\(12\) | −3.84776 | + | 5.75858i | −1.11075 | + | 1.66236i | ||||
\(13\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000i | 1.00000i | ||||||||
\(17\) | −1.68925 | − | 3.76118i | −0.409702 | − | 0.912219i | ||||
\(18\) | 12.7161 | 2.99721 | ||||||||
\(19\) | 6.84984 | + | 2.83730i | 1.57146 | + | 0.650921i | 0.987032 | − | 0.160524i | \(-0.0513185\pi\) |
0.584429 | + | 0.811445i | \(0.301318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.88556 | − | 1.25989i | −0.402003 | − | 0.268610i | ||||
\(23\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(24\) | 8.14386 | − | 5.44155i | 1.66236 | − | 1.11075i | ||||
\(25\) | 1.91342 | + | 4.61940i | 0.382683 | + | 0.923880i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −11.5272 | − | 17.2516i | −2.21840 | − | 3.32007i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(32\) | 2.16478 | − | 5.22625i | 0.382683 | − | 0.923880i | ||||
\(33\) | 5.55288i | 0.966632i | ||||||||
\(34\) | 0.171573 | + | 5.82843i | 0.0294245 | + | 0.999567i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −16.6143 | − | 6.88189i | −2.76906 | − | 1.14698i | ||||
\(37\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(38\) | −7.41421 | − | 7.41421i | −1.20274 | − | 1.20274i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.72817 | − | 4.49562i | 1.05076 | − | 0.702098i | 0.0947747 | − | 0.995499i | \(-0.469787\pi\) |
0.955990 | + | 0.293400i | \(0.0947869\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.53553 | − | 2.29289i | 0.844161 | − | 0.349663i | 0.0816682 | − | 0.996660i | \(-0.473975\pi\) |
0.762493 | + | 0.646997i | \(0.223975\pi\) | |||||||
\(44\) | 1.78176 | + | 2.66659i | 0.268610 | + | 0.402003i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(48\) | −13.5854 | + | 2.70231i | −1.96089 | + | 0.390044i | ||||
\(49\) | 2.67878 | − | 6.46716i | 0.382683 | − | 0.923880i | ||||
\(50\) | − | 7.07107i | − | 1.00000i | ||||||
\(51\) | 11.6331 | − | 8.27824i | 1.62896 | − | 1.15919i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(54\) | 5.72445 | + | 28.7788i | 0.778999 | + | 3.91629i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.00887 | + | 25.1813i | −0.663441 | + | 3.33534i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.19239 | + | 10.1213i | 0.545802 | + | 1.31768i | 0.920575 | + | 0.390567i | \(0.127721\pi\) |
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −5.65685 | + | 5.65685i | −0.707107 | + | 0.707107i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00520 | − | 7.25518i | 0.369914 | − | 0.893051i | ||||
\(67\) | − | 2.48181i | − | 0.303201i | −0.988442 | − | 0.151601i | \(-0.951557\pi\) | ||
0.988442 | − | 0.151601i | \(-0.0484428\pi\) | |||||||
\(68\) | 2.93015 | − | 7.70806i | 0.355333 | − | 0.934740i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(72\) | 17.9832 | + | 17.9832i | 2.11934 | + | 2.11934i | ||||
\(73\) | −13.5150 | − | 9.03040i | −1.58181 | − | 1.05693i | −0.962319 | − | 0.271921i | \(-0.912341\pi\) |
−0.619486 | − | 0.785007i | \(-0.712659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −14.3964 | + | 9.61940i | −1.66236 | + | 1.11075i | ||||
\(76\) | 5.67459 | + | 13.6997i | 0.650921 | + | 1.57146i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 31.7310 | − | 31.7310i | 3.52566 | − | 3.52566i | ||||
\(82\) | −11.2238 | + | 2.23255i | −1.23946 | + | 0.246544i | ||||
\(83\) | −3.63604 | + | 8.77817i | −0.399107 | + | 0.963530i | 0.588771 | + | 0.808300i | \(0.299612\pi\) |
−0.987878 | + | 0.155230i | \(0.950388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.47343 | −0.913713 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.884830 | − | 4.44834i | −0.0943232 | − | 0.474195i | ||||
\(89\) | −10.2283 | − | 10.2283i | −1.08420 | − | 1.08420i | −0.996113 | − | 0.0880885i | \(-0.971924\pi\) |
−0.0880885 | − | 0.996113i | \(-0.528076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 19.2127 | + | 3.82164i | 1.96089 | + | 0.390044i | ||||
\(97\) | −0.618707 | + | 0.925961i | −0.0628202 | + | 0.0940171i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) |
0.798730 | + | 0.601690i | \(0.205506\pi\) | |||||||
\(98\) | −7.00000 | + | 7.00000i | −0.707107 | + | 0.707107i | ||||
\(99\) | −14.1414 | + | 2.81289i | −1.42126 | + | 0.282706i | ||||
\(100\) | −3.82683 | + | 9.23880i | −0.382683 | + | 0.923880i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | −19.6795 | + | 4.52027i | −1.94856 | + | 0.447574i | ||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.99789 | − | 3.33948i | −0.483164 | − | 0.322840i | 0.290021 | − | 0.957020i | \(-0.406338\pi\) |
−0.773185 | + | 0.634180i | \(0.781338\pi\) | |||||||
\(108\) | 8.09560 | − | 40.6993i | 0.778999 | − | 3.91629i | ||||
\(109\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.51409 | − | 1.69356i | −0.800938 | − | 0.159317i | −0.222383 | − | 0.974959i | \(-0.571383\pi\) |
−0.578556 | + | 0.815643i | \(0.696383\pi\) | |||||||
\(114\) | 20.1724 | − | 30.1902i | 1.88932 | − | 2.82757i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 15.4930i | − | 1.42625i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.78707 | − | 3.22551i | −0.707916 | − | 0.293228i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19.8141 | + | 19.8141i | 1.78658 | + | 1.78658i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(128\) | 10.4525 | − | 4.32957i | 0.923880 | − | 0.382683i | ||||
\(129\) | 11.5272 | + | 17.2516i | 1.01491 | + | 1.51892i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.27530 | + | 12.3849i | −0.723016 | + | 1.08207i | 0.269858 | + | 0.962900i | \(0.413023\pi\) |
−0.992874 | + | 0.119170i | \(0.961977\pi\) | |||||||
\(132\) | −7.85295 | + | 7.85295i | −0.683512 | + | 0.683512i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.34315 | + | 3.24264i | −0.116030 | + | 0.280121i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.00000 | + | 8.48528i | −0.685994 | + | 0.727607i | ||||
\(137\) | 11.7574 | 1.00450 | 0.502249 | − | 0.864723i | \(-0.332506\pi\) | ||||
0.502249 | + | 0.864723i | \(0.332506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.64897 | − | 13.3173i | −0.224683 | − | 1.12956i | −0.914193 | − | 0.405279i | \(-0.867174\pi\) |
0.689510 | − | 0.724276i | \(-0.257826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −13.7638 | − | 33.2287i | −1.14698 | − | 2.76906i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.7709 | + | 19.1130i | 1.05693 | + | 1.58181i | ||||
\(147\) | 23.7745 | + | 4.72904i | 1.96089 | + | 0.390044i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(150\) | 24.0158 | − | 4.77705i | 1.96089 | − | 0.390044i | ||||
\(151\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(152\) | − | 20.9706i | − | 1.70094i | ||||||
\(153\) | 26.9749 | + | 25.4321i | 2.18079 | + | 2.05607i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −58.6312 | + | 24.2858i | −4.60650 | + | 1.90807i | ||||
\(163\) | −8.78104 | − | 13.1418i | −0.687784 | − | 1.02934i | −0.996928 | − | 0.0783260i | \(-0.975042\pi\) |
0.309144 | − | 0.951015i | \(-0.399958\pi\) | |||||||
\(164\) | 15.8728 | + | 3.15731i | 1.23946 | + | 0.246544i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.50143 | − | 9.50143i | 0.737454 | − | 0.737454i | ||||
\(167\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 13.0000i | − | 1.00000i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −66.6658 | −5.09806 | ||||||||
\(172\) | 11.0711 | + | 4.58579i | 0.844161 | + | 0.349663i | ||||
\(173\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.25134 | + | 6.29090i | −0.0943232 | + | 0.474195i | ||||
\(177\) | −31.5433 | + | 21.0766i | −2.37094 | + | 1.58421i | ||||
\(178\) | 7.82843 | + | 18.8995i | 0.586765 | + | 1.41658i | ||||
\(179\) | −1.17525 | + | 0.486803i | −0.0878421 | + | 0.0363854i | −0.426172 | − | 0.904642i | \(-0.640138\pi\) |
0.338330 | + | 0.941028i | \(0.390138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.48010 | − | 6.44376i | −0.108235 | − | 0.471214i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(192\) | −23.0343 | − | 15.3910i | −1.66236 | − | 1.11075i | ||||
\(193\) | 0.368323 | − | 1.85169i | 0.0265125 | − | 0.133287i | −0.965262 | − | 0.261283i | \(-0.915854\pi\) |
0.991775 | + | 0.127996i | \(0.0408544\pi\) | |||||||
\(194\) | 1.30951 | − | 0.874984i | 0.0940171 | − | 0.0628202i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.9343 | − | 5.35757i | 0.923880 | − | 0.382683i | ||||
\(197\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(198\) | 19.9989 | + | 3.97803i | 1.42126 | + | 0.282706i | ||||
\(199\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(200\) | 10.0000 | − | 10.0000i | 0.707107 | − | 0.707107i | ||||
\(201\) | 8.42910 | − | 1.67665i | 0.594543 | − | 0.118262i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 28.1588 | + | 4.74444i | 1.97151 | + | 0.332177i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.88532 | + | 6.60516i | 0.683782 | + | 0.456888i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0300 | − | 15.3882i | 1.58545 | − | 1.05937i | 0.625112 | − | 0.780535i | \(-0.285053\pi\) |
0.960340 | − | 0.278831i | \(-0.0899469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.72274 | + | 7.06808i | 0.322840 | + | 0.483164i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −32.6037 | + | 48.7949i | −2.21840 | + | 3.32007i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 21.5401 | − | 52.0023i | 1.45554 | − | 3.51399i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −31.7902 | − | 31.7902i | −2.11934 | − | 2.11934i | ||||
\(226\) | 10.2077 | + | 6.82053i | 0.679003 | + | 0.453695i | ||||
\(227\) | −4.55979 | + | 22.9236i | −0.302644 | + | 1.52149i | 0.467714 | + | 0.883880i | \(0.345078\pi\) |
−0.770357 | + | 0.637613i | \(0.779922\pi\) | |||||||
\(228\) | −42.6953 | + | 28.5281i | −2.82757 | + | 1.88932i | ||||
\(229\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.64662 | − | 9.94737i | 0.435435 | − | 0.651674i | −0.547248 | − | 0.836971i | \(-0.684325\pi\) |
0.982683 | + | 0.185296i | \(0.0593245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.38478 | + | 20.2426i | −0.545802 | + | 1.31768i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.62079 | + | 28.2576i | 0.362067 | + | 1.82023i | 0.546585 | + | 0.837404i | \(0.315928\pi\) |
−0.184518 | + | 0.982829i | \(0.559072\pi\) | |||||||
\(242\) | 8.42867 | + | 8.42867i | 0.541815 | + | 0.541815i | ||||
\(243\) | 77.4514 | + | 51.7514i | 4.96851 | + | 3.31985i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.1651 | − | 36.6117i | −0.966890 | − | 2.33428i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −32.2702 | − | 6.41894i | −2.04504 | − | 0.406784i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7018 | + | 18.7018i | −1.18044 | + | 1.18044i | −0.200816 | + | 0.979629i | \(0.564359\pi\) |
−0.979629 | + | 0.200816i | \(0.935641\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.0000 | −1.00000 | ||||||||
\(257\) | 0.949747 | + | 0.393398i | 0.0592436 | + | 0.0245395i | 0.412108 | − | 0.911135i | \(-0.364792\pi\) |
−0.352865 | + | 0.935674i | \(0.614792\pi\) | |||||||
\(258\) | −5.72445 | − | 28.7788i | −0.356389 | − | 1.79169i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.5148 | − | 11.7030i | 1.08207 | − | 0.723016i | ||||
\(263\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(264\) | 14.5104 | − | 6.01039i | 0.893051 | − | 0.369914i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 27.8290 | − | 41.6491i | 1.70311 | − | 2.54888i | ||||
\(268\) | 3.50981 | − | 3.50981i | 0.214396 | − | 0.214396i | ||||
\(269\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 15.0447 | − | 6.75699i | 0.912219 | − | 0.409702i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.3617 | − | 6.36304i | −0.928036 | − | 0.384405i | ||||
\(275\) | 1.56417 | + | 7.86363i | 0.0943232 | + | 0.474195i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(278\) | −3.74621 | + | 18.8335i | −0.224683 | + | 1.12956i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.2367 | − | 12.5244i | 1.80377 | − | 0.747145i | 0.818877 | − | 0.573969i | \(-0.194597\pi\) |
0.984891 | − | 0.173176i | \(-0.0554029\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.0334 | − | 5.17837i | −1.54753 | − | 0.307822i | −0.653882 | − | 0.756596i | \(-0.726861\pi\) |
−0.893645 | + | 0.448774i | \(0.851861\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 50.8643i | 2.99721i | ||||||||
\(289\) | −11.2929 | + | 12.7071i | −0.664288 | + | 0.747477i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.56287 | − | 1.47579i | −0.208859 | − | 0.0865124i | ||||
\(292\) | −6.34211 | − | 31.8840i | −0.371144 | − | 1.86587i | ||||
\(293\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(294\) | −28.5035 | − | 19.0454i | −1.66236 | − | 1.11075i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.7322 | − | 30.7381i | −0.738795 | − | 1.78361i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −33.9635 | − | 6.75577i | −1.96089 | − | 0.390044i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.3492 | + | 27.3994i | −0.650921 | + | 1.57146i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −21.4806 | − | 47.8274i | −1.22796 | − | 2.73411i | ||||
\(307\) | 8.48528 | 0.484281 | 0.242140 | − | 0.970241i | \(-0.422151\pi\) | ||||
0.242140 | + | 0.970241i | \(0.422151\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.8455 | − | 12.5922i | 1.06521 | − | 0.711752i | 0.105979 | − | 0.994368i | \(-0.466202\pi\) |
0.959233 | + | 0.282617i | \(0.0912024\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.96561 | − | 19.2307i | 0.444597 | − | 1.07335i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.899495 | − | 30.5563i | −0.0500492 | − | 1.70020i | ||||
\(324\) | 89.7487 | 4.98604 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.36071 | + | 21.9228i | 0.241518 | + | 1.21419i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.0302 | − | 12.7155i | −1.05076 | − | 0.702098i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.8076 | + | 30.9203i | 0.703970 | + | 1.69953i | 0.714545 | + | 0.699590i | \(0.246634\pi\) |
−0.0105746 | + | 0.999944i | \(0.503366\pi\) | |||||||
\(332\) | −17.5563 | + | 7.27208i | −0.963530 | + | 0.399107i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9113 | + | 5.94972i | −1.62937 | + | 0.324102i | −0.923312 | − | 0.384052i | \(-0.874528\pi\) |
−0.706058 | + | 0.708154i | \(0.749528\pi\) | |||||||
\(338\) | −7.03555 | + | 16.9853i | −0.382683 | + | 0.923880i | ||||
\(339\) | − | 30.0610i | − | 1.63269i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 87.1030 | + | 36.0793i | 4.70999 | + | 1.95094i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.9832 | − | 11.9832i | −0.646093 | − | 0.646093i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.07149 | + | 0.715948i | −0.0575207 | + | 0.0384341i | −0.583998 | − | 0.811755i | \(-0.698512\pi\) |
0.526477 | + | 0.850189i | \(0.323512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.03957 | − | 7.54224i | 0.268610 | − | 0.402003i | ||||
\(353\) | −25.7214 | + | 25.7214i | −1.36901 | + | 1.36901i | −0.507157 | + | 0.861853i | \(0.669304\pi\) |
−0.861853 | + | 0.507157i | \(0.830696\pi\) | |||||||
\(354\) | 52.6199 | − | 10.4667i | 2.79671 | − | 0.556301i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 28.9301i | − | 1.53329i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.79899 | 0.0950796 | ||||||||
\(359\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.4350 | + | 25.4350i | 1.33869 | + | 1.33869i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.69421 | − | 28.6267i | 0.298869 | − | 1.50251i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −40.4229 | + | 60.4972i | −2.10433 | + | 3.14936i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(374\) | −1.55350 | + | 9.22019i | −0.0803294 | + | 0.476765i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.6123 | − | 19.7863i | −1.52108 | − | 1.01636i | −0.985072 | − | 0.172145i | \(-0.944930\pi\) |
−0.536011 | − | 0.844211i | \(-0.680070\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(384\) | 21.7662 | + | 32.5754i | 1.11075 | + | 1.66236i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.48336 | + | 2.22001i | −0.0755012 | + | 0.112995i | ||||
\(387\) | −38.0949 | + | 38.0949i | −1.93647 | + | 1.93647i | ||||
\(388\) | −2.18449 | + | 0.434522i | −0.110901 | + | 0.0220595i | ||||
\(389\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −19.7990 | −1.00000 | ||||||||
\(393\) | −47.6539 | − | 19.7389i | −2.40382 | − | 0.995696i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −23.9769 | − | 16.0209i | −1.20489 | − | 0.805079i | ||||
\(397\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −18.4776 | + | 7.65367i | −0.923880 | + | 0.382683i | ||||
\(401\) | 16.4399 | + | 24.6041i | 0.820971 | + | 1.22867i | 0.970784 | + | 0.239956i | \(0.0771329\pi\) |
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | −11.9206 | − | 2.37115i | −0.594543 | − | 0.118262i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −34.2236 | − | 21.4384i | −1.69432 | − | 1.06136i | ||||
\(409\) | 22.9385 | 1.13423 | 0.567117 | − | 0.823637i | \(-0.308059\pi\) | ||||
0.567117 | + | 0.823637i | \(0.308059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.94300 | + | 39.9321i | 0.391799 | + | 1.96971i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 43.4405 | − | 17.9937i | 2.12729 | − | 0.881153i | ||||
\(418\) | −9.34110 | − | 13.9800i | −0.456888 | − | 0.683782i | ||||
\(419\) | −34.7144 | − | 6.90513i | −1.69591 | − | 0.337338i | −0.749919 | − | 0.661529i | \(-0.769908\pi\) |
−0.945991 | + | 0.324192i | \(0.894908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(422\) | −38.4182 | + | 7.64186i | −1.87017 | + | 0.372000i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 14.1421 | − | 15.0000i | 0.685994 | − | 0.727607i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.34534 | − | 11.7908i | −0.113366 | − | 0.569931i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(432\) | 69.0064 | − | 46.1086i | 3.32007 | − | 2.21840i | ||||
\(433\) | 14.8749 | + | 35.9113i | 0.714843 | + | 1.72578i | 0.687528 | + | 0.726158i | \(0.258696\pi\) |
0.0273152 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −56.2869 | + | 56.2869i | −2.68949 | + | 2.68949i | ||||
\(439\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 62.9413i | 2.99721i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.8853 | 1.89501 | 0.947505 | − | 0.319742i | \(-0.103596\pi\) | ||||
0.947505 | + | 0.319742i | \(0.103596\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.6495 | − | 21.1475i | 1.49363 | − | 0.998012i | 0.502580 | − | 0.864531i | \(-0.332384\pi\) |
0.991051 | − | 0.133482i | \(-0.0426157\pi\) | |||||||
\(450\) | 24.3311 | + | 58.7406i | 1.14698 | + | 2.76906i | ||||
\(451\) | 11.9880 | − | 4.96558i | 0.564491 | − | 0.233820i | ||||
\(452\) | −9.64569 | − | 14.4358i | −0.453695 | − | 0.679003i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.3638 | − | 27.4834i | 0.861856 | − | 1.28986i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 71.2234 | − | 14.1672i | 3.33534 | − | 0.663441i | ||||
\(457\) | −2.14885 | + | 5.18779i | −0.100519 | + | 0.242675i | −0.966137 | − | 0.258031i | \(-0.916926\pi\) |
0.865617 | + | 0.500706i | \(0.166926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −45.4141 | + | 72.4979i | −2.11975 | + | 3.38391i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0677 | + | 9.39974i | −0.651674 | + | 0.435435i | ||||
\(467\) | −16.5370 | − | 39.9238i | −0.765240 | − | 1.84745i | −0.399439 | − | 0.916760i | \(-0.630795\pi\) |
−0.365801 | − | 0.930693i | \(-0.619205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 21.9105 | − | 21.9105i | 1.00851 | − | 1.00851i | ||||
\(473\) | 9.42318 | − | 1.87439i | 0.433278 | − | 0.0861844i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 37.0711i | 1.70094i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 7.94899 | − | 39.9623i | 0.362067 | − | 1.82023i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6.45102 | − | 15.5741i | −0.293228 | − | 0.707916i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −73.1875 | − | 109.533i | −3.31985 | − | 4.96851i | ||||
\(487\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 38.7018 | − | 38.7018i | 1.75015 | − | 1.75015i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.53828 | + | 18.1990i | −0.340198 | + | 0.821311i | 0.657497 | + | 0.753457i | \(0.271615\pi\) |
−0.997695 | + | 0.0678537i | \(0.978385\pi\) | |||||||
\(492\) | 56.0428i | 2.52660i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 38.6891 | + | 25.8513i | 1.73370 | + | 1.15842i | ||||
\(499\) | −4.29354 | + | 21.5851i | −0.192205 | + | 0.966282i | 0.757428 | + | 0.652919i | \(0.226456\pi\) |
−0.949633 | + | 0.313363i | \(0.898544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 34.5563 | − | 14.3137i | 1.54233 | − | 0.638852i | ||||
\(503\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 44.1526 | − | 8.78250i | 1.96089 | − | 0.390044i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 20.9050 | + | 8.65914i | 0.923880 | + | 0.382683i | ||||
\(513\) | −30.0112 | − | 150.877i | −1.32503 | − | 6.66137i | ||||
\(514\) | −1.02800 | − | 1.02800i | −0.0453431 | − | 0.0453431i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.09560 | + | 40.6993i | −0.356389 | + | 1.79169i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −44.6805 | − | 8.88750i | −1.95749 | − | 0.389368i | −0.991325 | − | 0.131432i | \(-0.958042\pi\) |
−0.966162 | − | 0.257936i | \(-0.916958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 31.7130 | − | 31.7130i | 1.38671 | − | 1.38671i | 0.554587 | − | 0.832126i | \(-0.312876\pi\) |
0.832126 | − | 0.554587i | \(-0.187124\pi\) | |||||||
\(524\) | −29.2179 | + | 5.81180i | −1.27639 | + | 0.253889i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −22.2115 | −0.966632 | ||||||||
\(529\) | −21.2492 | − | 8.80172i | −0.923880 | − | 0.382683i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −69.6538 | − | 69.6538i | −3.02272 | − | 3.02272i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −58.9007 | + | 39.3562i | −2.54888 | + | 1.70311i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.48528 | + | 2.68629i | −0.280121 | + | 0.116030i | ||||
\(537\) | −2.44732 | − | 3.66268i | −0.105610 | − | 0.158056i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.23614 | − | 9.33305i | 0.268610 | − | 0.402003i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −23.3137 | + | 0.686292i | −0.999567 | + | 0.0294245i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.38143 | + | 42.1363i | 0.358364 | + | 1.80162i | 0.567104 | + | 0.823646i | \(0.308064\pi\) |
−0.208741 | + | 0.977971i | \(0.566936\pi\) | |||||||
\(548\) | 16.6274 | + | 16.6274i | 0.710288 | + | 0.710288i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.21208 | − | 11.1209i | 0.0943232 | − | 0.474195i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.0872 | − | 22.5797i | 0.639842 | − | 0.957591i | ||||
\(557\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.8854 | − | 9.38018i | 0.881780 | − | 0.396031i | ||||
\(562\) | −46.2843 | −1.95238 | ||||||||
\(563\) | 41.9914 | + | 17.3934i | 1.76973 | + | 0.733044i | 0.994900 | + | 0.100870i | \(0.0321625\pi\) |
0.774826 | + | 0.632175i | \(0.217837\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31.2118 | + | 20.8551i | 1.31193 | + | 0.876604i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.1508 | − | 34.1630i | −0.593231 | − | 1.43219i | −0.880366 | − | 0.474295i | \(-0.842703\pi\) |
0.287135 | − | 0.957890i | \(-0.407297\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.7334 | − | 31.0298i | −0.867668 | − | 1.29856i | −0.953237 | − | 0.302224i | \(-0.902271\pi\) |
0.0855694 | − | 0.996332i | \(-0.472729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 27.5275 | − | 66.4574i | 1.14698 | − | 2.76906i | ||||
\(577\) | 33.9411i | 1.41299i | 0.707719 | + | 0.706494i | \(0.249724\pi\) | ||||
−0.707719 | + | 0.706494i | \(0.750276\pi\) | |||||||
\(578\) | 21.6319 | − | 10.4910i | 0.899769 | − | 0.436367i | ||||
\(579\) | 6.53781 | 0.271702 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.85643 | + | 3.85643i | 0.159854 | + | 0.159854i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −8.96910 | + | 45.0907i | −0.371144 | + | 1.86587i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.54328 | + | 2.29610i | −0.228796 | + | 0.0947702i | −0.494136 | − | 0.869385i | \(-0.664516\pi\) |
0.265341 | + | 0.964155i | \(0.414516\pi\) | |||||||
\(588\) | 26.9343 | + | 40.3100i | 1.11075 | + | 1.66236i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.3640 | − | 32.2635i | 0.548792 | − | 1.32490i | −0.369586 | − | 0.929197i | \(-0.620500\pi\) |
0.918378 | − | 0.395705i | \(-0.129500\pi\) | |||||||
\(594\) | 47.0519i | 1.93056i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(600\) | 40.7193 | + | 27.2078i | 1.66236 | + | 1.11075i | ||||
\(601\) | 7.73860 | − | 38.9046i | 0.315664 | − | 1.58695i | −0.418655 | − | 0.908145i | \(-0.637498\pi\) |
0.734319 | − | 0.678804i | \(-0.237502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.53977 | + | 20.6168i | 0.347766 | + | 0.839582i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(608\) | 29.6569 | − | 29.6569i | 1.20274 | − | 1.20274i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.18173 | + | 74.1147i | 0.0881913 | + | 2.99591i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | −11.0866 | − | 4.59220i | −0.447417 | − | 0.185326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0415 | + | 12.0550i | 0.726325 | + | 0.485315i | 0.862938 | − | 0.505310i | \(-0.168622\pi\) |
−0.136613 | + | 0.990624i | \(0.543622\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.5733 | + | 25.1057i | −1.51020 | + | 1.00908i | −0.522514 | + | 0.852631i | \(0.675006\pi\) |
−0.987685 | + | 0.156452i | \(0.949994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.6777 | + | 17.6777i | −0.707107 | + | 0.707107i | ||||
\(626\) | −31.4377 | + | 6.25335i | −1.25650 | + | 0.249934i | ||||
\(627\) | −15.7552 | + | 38.0363i | −0.629201 | + | 1.51902i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 67.8222 | + | 67.8222i | 2.69569 | + | 2.69569i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.9642 | + | 29.8785i | −0.788538 | + | 1.18013i | 0.191534 | + | 0.981486i | \(0.438654\pi\) |
−0.980072 | + | 0.198645i | \(0.936346\pi\) | |||||||
\(642\) | −20.8151 | + | 20.8151i | −0.821508 | + | 0.821508i | ||||
\(643\) | −17.7294 | + | 3.52660i | −0.699180 | + | 0.139076i | −0.531866 | − | 0.846828i | \(-0.678509\pi\) |
−0.167313 | + | 0.985904i | \(0.553509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −15.3617 | + | 40.4106i | −0.604399 | + | 1.58993i | ||||
\(647\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(648\) | −117.262 | − | 48.5716i | −4.60650 | − | 1.90807i | ||||
\(649\) | 3.42718 | + | 17.2296i | 0.134529 | + | 0.676321i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.16698 | − | 31.0035i | 0.241518 | − | 1.21419i | ||||
\(653\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 17.9825 | + | 26.9127i | 0.702098 | + | 1.05076i | ||||
\(657\) | 143.344 | + | 28.5129i | 5.59239 | + | 1.11240i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.7279 | − | 12.7279i | 0.495809 | − | 0.495809i | −0.414321 | − | 0.910131i | \(-0.635981\pi\) |
0.910131 | + | 0.414321i | \(0.135981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(662\) | − | 47.3308i | − | 1.83956i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.8741 | 1.04292 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9671 | − | 16.4134i | −0.422750 | − | 0.632690i | 0.557564 | − | 0.830134i | \(-0.311736\pi\) |
−0.980314 | + | 0.197444i | \(0.936736\pi\) | |||||||
\(674\) | 42.3009 | + | 8.41417i | 1.62937 | + | 0.324102i | ||||
\(675\) | 57.6358 | − | 86.2580i | 2.21840 | − | 3.32007i | ||||
\(676\) | 18.3848 | − | 18.3848i | 0.707107 | − | 0.707107i | ||||
\(677\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(678\) | −16.2689 | + | 39.2766i | −0.624803 | + | 1.50841i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −80.9371 | −3.10152 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.22051 | − | 46.3546i | −0.352813 | − | 1.77371i | −0.595247 | − | 0.803543i | \(-0.702946\pi\) |
0.242434 | − | 0.970168i | \(-0.422054\pi\) | |||||||
\(684\) | −94.2797 | − | 94.2797i | −3.60487 | − | 3.60487i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.17157 | + | 22.1421i | 0.349663 | + | 0.844161i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.3785 | + | 7.83286i | 1.49803 | + | 0.297976i | 0.874961 | − | 0.484193i | \(-0.160887\pi\) |
0.623066 | + | 0.782169i | \(0.285887\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.78744 | − | 0.355544i | 0.0678503 | − | 0.0134963i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.2744 | − | 17.7116i | −1.07097 | − | 0.670876i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.2751 | + | 15.8541i | 1.44770 | + | 0.599656i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −10.6663 | + | 7.12702i | −0.402003 | + | 0.268610i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 47.5269 | − | 19.6863i | 1.78870 | − | 0.740903i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −74.4157 | − | 14.8022i | −2.79671 | − | 0.556301i | ||||
\(709\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −15.6569 | + | 37.7990i | −0.586765 | + | 1.41658i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.35049 | − | 0.973606i | −0.0878421 | − | 0.0363854i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19.4671 | − | 46.9978i | −0.724491 | − | 1.74908i | ||||
\(723\) | −92.1756 | + | 38.1804i | −3.42805 | + | 1.41994i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.9325 | + | 34.3209i | −0.851106 | + | 1.27377i | ||||
\(727\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −71.9236 | + | 173.639i | −2.66384 | + | 6.43107i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.9749 | − | 16.9469i | −0.664824 | − | 0.626802i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.923880 | − | 0.382683i | \(-0.875000\pi\) | ||||
0.923880 | + | 0.382683i | \(0.125000\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.776396 | − | 3.90321i | 0.0285989 | − | 0.143776i | ||||
\(738\) | 85.5559 | − | 57.1666i | 3.14936 | − | 2.10433i | ||||
\(739\) | 16.2359 | + | 39.1969i | 0.597247 | + | 1.44188i | 0.876376 | + | 0.481627i | \(0.159954\pi\) |
−0.279129 | + | 0.960253i | \(0.590046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.555570 | − | 0.831470i | \(-0.312500\pi\) | ||||
−0.555570 | + | 0.831470i | \(0.687500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 85.4332i | − | 3.12584i | ||||||
\(748\) | 7.01967 | − | 11.2060i | 0.256665 | − | 0.409733i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −76.1523 | − | 50.8833i | −2.77514 | − | 1.85429i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 0.923880 | − | 0.382683i | \(-0.125000\pi\) | ||||
−0.923880 | + | 0.382683i | \(0.875000\pi\) | |||||||
\(758\) | 27.9821 | + | 41.8782i | 1.01636 | + | 1.52108i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.3431 | + | 21.3431i | −0.773688 | + | 0.773688i | −0.978749 | − | 0.205061i | \(-0.934261\pi\) |
0.205061 | + | 0.978749i | \(0.434261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −10.8092 | − | 54.3417i | −0.390044 | − | 1.96089i | ||||
\(769\) | −14.4558 | − | 14.4558i | −0.521291 | − | 0.521291i | 0.396670 | − | 0.917961i | \(-0.370166\pi\) |
−0.917961 | + | 0.396670i | \(0.870166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.694492 | + | 3.49145i | −0.0250115 | + | 0.125741i | ||||
\(772\) | 3.13957 | − | 2.09779i | 0.112995 | − | 0.0755012i | ||||
\(773\) | 0 | 0 | −0.382683 | − | 0.923880i | \(-0.625000\pi\) | ||||
0.382683 | + | 0.923880i | \(0.375000\pi\) | |||||||
\(774\) | 70.3902 | − | 29.1566i | 2.53012 | − | 1.04801i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.08934 | + | 0.614507i | 0.110901 | + | 0.0220595i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 58.8423 | − | 11.7045i | 2.10825 | − | 0.419356i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.8686 | + | 10.7151i | 0.923880 | + | 0.382683i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 51.5803 | + | 51.5803i | 1.83981 | + | 1.83981i | ||||
\(787\) | −5.49830 | − | 3.67385i | −0.195993 | − | 0.130959i | 0.453701 | − | 0.891154i | \(-0.350103\pi\) |
−0.649695 | + | 0.760195i | \(0.725103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 22.6569 | + | 33.9085i | 0.805079 | + | 1.20489i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 28.2843 | 1.00000 | ||||||||
\(801\) | 120.164 | + | 49.7734i | 4.24577 | + | 1.75866i | ||||
\(802\) | −8.16416 | − | 41.0440i | −0.288287 | − | 1.44932i | ||||
\(803\) | −18.4303 | − | 18.4303i | −0.650391 | − | 0.650391i | ||||
\(804\) | 14.2917 | + | 9.54941i | 0.504029 | + | 0.336782i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.9832 | − | 41.8798i | −0.983837 | − | 1.47242i | −0.878363 | − | 0.477994i | \(-0.841364\pi\) |
−0.105474 | − | 0.994422i | \(-0.533636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.86943 | − | 11.7774i | 0.276333 | − | 0.413562i | −0.667180 | − | 0.744896i | \(-0.732499\pi\) |
0.943513 | + | 0.331335i | \(0.107499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 33.1130 | + | 46.5323i | 1.15919 | + | 1.62896i | ||||
\(817\) | 44.4231 | 1.55417 | ||||||||
\(818\) | −29.9706 | − | 12.4142i | −1.04790 | − | 0.434053i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(822\) | 11.2331 | − | 56.4726i | 0.391799 | − | 1.96971i | ||||
\(823\) | 0 | 0 | 0.831470 | − | 0.555570i | \(-0.187500\pi\) | ||||
−0.831470 | + | 0.555570i | \(0.812500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.6509 | + | 10.6250i | −0.893051 | + | 0.369914i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.2784 | − | 2.64124i | −0.461735 | − | 0.0918448i | −0.0412591 | − | 0.999148i | \(-0.513137\pi\) |
−0.420476 | + | 0.907304i | \(0.638137\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −28.8492 | + | 0.849242i | −0.999567 | + | 0.0294245i | ||||
\(834\) | −66.4959 | −2.30256 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.63885 | + | 23.3211i | 0.160438 | + | 0.806576i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 41.6196 | + | 27.8093i | 1.43772 | + | 0.960656i | ||||
\(839\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.0978 | − | 26.7925i | −0.382683 | − | 0.923880i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 62.9646 | + | 94.2332i | 2.16862 | + | 3.24556i | ||||
\(844\) | 54.3315 | + | 10.8072i | 1.87017 | + | 0.372000i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 91.9171i | − | 3.15459i | ||||||
\(850\) | −26.5955 | + | 11.9448i | −0.912219 | + | 0.409702i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.31681 | + | 16.6747i | −0.113366 | + | 0.569931i | ||||
\(857\) | −27.2119 | + | 18.1824i | −0.929542 | + | 0.621100i | −0.925441 | − | 0.378892i | \(-0.876305\pi\) |
−0.00410087 | + | 0.999992i | \(0.501305\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −52.5061 | + | 21.7487i | −1.79148 | + | 0.742057i | −0.802018 | + | 0.597300i | \(0.796240\pi\) |
−0.989467 | + | 0.144757i | \(0.953760\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(864\) | −115.115 | + | 22.8978i | −3.91629 | + | 0.778999i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 54.9706i | − | 1.86798i | ||||||
\(867\) | −50.7870 | − | 29.7700i | −1.72482 | − | 1.01104i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.95353 | − | 9.82105i | 0.0661169 | − | 0.332392i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 104.005 | − | 43.0801i | 3.51399 | − | 1.45554i | ||||
\(877\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −50.9714 | + | 10.1388i | −1.71727 | + | 0.341586i | −0.952921 | − | 0.303218i | \(-0.901939\pi\) |
−0.764348 | + | 0.644804i | \(0.776939\pi\) | |||||||
\(882\) | 34.0636 | − | 82.2368i | 1.14698 | − | 2.76906i | ||||
\(883\) | 20.8825i | 0.702751i | 0.936235 | + | 0.351376i | \(0.114286\pi\) | ||||
−0.936235 | + | 0.351376i | \(0.885714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −52.1127 | − | 21.5858i | −1.75076 | − | 0.725189i | ||||
\(887\) | 0 | 0 | −0.195090 | − | 0.980785i | \(-0.562500\pi\) | ||||
0.195090 | + | 0.980785i | \(0.437500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 59.8307 | − | 39.9776i | 2.00440 | − | 1.33930i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −52.7970 | + | 10.5020i | −1.76186 | + | 0.350455i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | − | 89.9162i | − | 2.99721i | ||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −18.3504 | −0.611001 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.79011 | + | 24.0815i | 0.159317 | + | 0.800938i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11.7457 | + | 59.0497i | −0.390010 | + | 1.96071i | −0.166022 | + | 0.986122i | \(0.553092\pi\) |
−0.223988 | + | 0.974592i | \(0.571908\pi\) | |||||||
\(908\) | −38.8674 | + | 25.9704i | −1.28986 | + | 0.861856i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.555570 | − | 0.831470i | \(-0.687500\pi\) | ||||
0.555570 | + | 0.831470i | \(0.312500\pi\) | |||||||
\(912\) | −100.725 | − | 20.0355i | −3.33534 | − | 0.663441i | ||||
\(913\) | −8.46461 | + | 12.6682i | −0.280138 | + | 0.419256i | ||||
\(914\) | 5.61522 | − | 5.61522i | 0.185735 | − | 0.185735i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 98.5720 | − | 70.1451i | 3.25336 | − | 2.31513i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.73246 | + | 28.8190i | 0.188891 | + | 0.949619i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.4900 | − | 10.4409i | −1.72214 | − | 0.342555i | −0.767666 | − | 0.640850i | \(-0.778582\pi\) |
−0.954474 | + | 0.298295i | \(0.903582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.6985 | − | 36.6985i | 1.20274 | − | 1.20274i | ||||
\(932\) | 23.4675 | − | 4.66797i | 0.768702 | − | 0.152904i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 61.1127i | 1.99967i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −47.0363 | − | 19.4831i | −1.53661 | − | 0.636484i | −0.555775 | − | 0.831333i | \(-0.687578\pi\) |
−0.980833 | + | 0.194849i | \(0.937578\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 55.4991 | + | 55.4991i | 1.81114 | + | 1.81114i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.195090 | − | 0.980785i | \(-0.437500\pi\) | ||||
−0.195090 | + | 0.980785i | \(0.562500\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −40.4853 | + | 16.7696i | −1.31768 | + | 0.545802i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −13.3264 | − | 2.65078i | −0.433278 | − | 0.0861844i | ||||
\(947\) | −15.5649 | + | 23.2946i | −0.505793 | + | 0.756972i | −0.993227 | − | 0.116187i | \(-0.962933\pi\) |
0.487435 | + | 0.873160i | \(0.337933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 20.0627 | − | 48.4357i | 0.650921 | − | 1.57146i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.4847 | 0.695957 | 0.347978 | − | 0.937503i | \(-0.386868\pi\) | ||||
0.347978 | + | 0.937503i | \(0.386868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.6403 | − | 11.8632i | 0.923880 | − | 0.382683i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 53.0093 | + | 10.5442i | 1.70820 | + | 0.339782i | ||||
\(964\) | −32.0133 | + | 47.9113i | −1.03108 | + | 1.54312i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 0.382683 | − | 0.923880i | \(-0.375000\pi\) | ||||
−0.382683 | + | 0.923880i | \(0.625000\pi\) | |||||||
\(968\) | 23.8399i | 0.766242i | ||||||||
\(969\) | 103.172 | − | 23.6982i | 3.31438 | − | 0.761295i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 57.0919 | + | 23.6482i | 1.83217 | + | 0.758908i | 0.965694 | + | 0.259681i | \(0.0836174\pi\) |
0.866471 | + | 0.499227i | \(0.166383\pi\) | |||||||
\(972\) | 36.3453 | + | 182.720i | 1.16578 | + | 5.86076i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 11.2340 | + | 27.1213i | 0.359408 | + | 0.867688i | 0.995383 | + | 0.0959785i | \(0.0305980\pi\) |
−0.635975 | + | 0.771709i | \(0.719402\pi\) | |||||||
\(978\) | −71.5115 | + | 29.6210i | −2.28669 | + | 0.947177i | ||||
\(979\) | −12.8866 | − | 19.2861i | −0.411857 | − | 0.616388i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.6985 | − | 19.6985i | 0.628604 | − | 0.628604i | ||||
\(983\) | 0 | 0 | 0.980785 | − | 0.195090i | \(-0.0625000\pi\) | ||||
−0.980785 | + | 0.195090i | \(0.937500\pi\) | |||||||
\(984\) | 30.3301 | − | 73.2234i | 0.966890 | − | 2.33428i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.831470 | − | 0.555570i | \(-0.812500\pi\) | ||||
0.831470 | + | 0.555570i | \(0.187500\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −96.3638 | + | 64.3882i | −3.05801 | + | 2.04330i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −36.5592 | − | 54.7147i | −1.15842 | − | 1.73370i | ||||
\(997\) | 0 | 0 | −0.980785 | − | 0.195090i | \(-0.937500\pi\) | ||||
0.980785 | + | 0.195090i | \(0.0625000\pi\) | |||||||
\(998\) | 17.2916 | − | 25.8786i | 0.547355 | − | 0.819174i | ||||
\(999\) | 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 | 136.2.s.b.11.1 | ✓ | 8 | |
4.3 | odd | 2 | 544.2.cc.a.79.1 | 8 | |||
8.3 | odd | 2 | CM | 136.2.s.b.11.1 | ✓ | 8 | |
8.5 | even | 2 | 544.2.cc.a.79.1 | 8 | |||
17.14 | odd | 16 | inner | 136.2.s.b.99.1 | yes | 8 | |
68.31 | even | 16 | 544.2.cc.a.303.1 | 8 | |||
136.99 | even | 16 | inner | 136.2.s.b.99.1 | yes | 8 | |
136.133 | odd | 16 | 544.2.cc.a.303.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.s.b.11.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
136.2.s.b.11.1 | ✓ | 8 | 8.3 | odd | 2 | CM | |
136.2.s.b.99.1 | yes | 8 | 17.14 | odd | 16 | inner | |
136.2.s.b.99.1 | yes | 8 | 136.99 | even | 16 | inner | |
544.2.cc.a.79.1 | 8 | 4.3 | odd | 2 | |||
544.2.cc.a.79.1 | 8 | 8.5 | even | 2 | |||
544.2.cc.a.303.1 | 8 | 68.31 | even | 16 | |||
544.2.cc.a.303.1 | 8 | 136.133 | odd | 16 |