Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,2,Mod(139,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.139");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.u (of order \(4\), degree \(2\), 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: | \(2.68297350792\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 139.19 | ||
Character | \(\chi\) | \(=\) | 336.139 |
Dual form | 336.2.u.a.307.19 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0748365 | − | 1.41223i | 0.0529174 | − | 0.998599i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | −1.98880 | − | 0.211373i | −0.994399 | − | 0.105687i | ||||
\(5\) | −0.353074 | + | 0.353074i | −0.157900 | + | 0.157900i | −0.781635 | − | 0.623736i | \(-0.785614\pi\) |
0.623736 | + | 0.781635i | \(0.285614\pi\) | |||||||
\(6\) | 0.945681 | + | 1.05152i | 0.386073 | + | 0.429280i | ||||
\(7\) | 2.14763 | + | 1.54521i | 0.811729 | + | 0.584035i | ||||
\(8\) | −0.447343 | + | 2.79283i | −0.158160 | + | 0.987414i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.472200 | + | 0.525045i | 0.149323 | + | 0.166034i | ||||
\(11\) | 2.06639 | − | 2.06639i | 0.623041 | − | 0.623041i | −0.323267 | − | 0.946308i | \(-0.604781\pi\) |
0.946308 | + | 0.323267i | \(0.104781\pi\) | |||||||
\(12\) | 1.55576 | − | 1.25683i | 0.449108 | − | 0.362816i | ||||
\(13\) | 2.73784 | + | 2.73784i | 0.759342 | + | 0.759342i | 0.976202 | − | 0.216861i | \(-0.0695818\pi\) |
−0.216861 | + | 0.976202i | \(0.569582\pi\) | |||||||
\(14\) | 2.34292 | − | 2.91732i | 0.626171 | − | 0.779686i | ||||
\(15\) | − | 0.499322i | − | 0.128924i | ||||||
\(16\) | 3.91064 | + | 0.840757i | 0.977661 | + | 0.210189i | ||||
\(17\) | 3.57407i | 0.866840i | 0.901192 | + | 0.433420i | \(0.142693\pi\) | ||||
−0.901192 | + | 0.433420i | \(0.857307\pi\) | |||||||
\(18\) | −1.41223 | − | 0.0748365i | −0.332866 | − | 0.0176391i | ||||
\(19\) | 5.95882 | − | 5.95882i | 1.36705 | − | 1.36705i | 0.502430 | − | 0.864618i | \(-0.332439\pi\) |
0.864618 | − | 0.502430i | \(-0.167561\pi\) | |||||||
\(20\) | 0.776824 | − | 0.627563i | 0.173703 | − | 0.140327i | ||||
\(21\) | −2.61123 | + | 0.425977i | −0.569818 | + | 0.0929558i | ||||
\(22\) | −2.76359 | − | 3.07287i | −0.589199 | − | 0.655138i | ||||
\(23\) | −1.74465 | −0.363786 | −0.181893 | − | 0.983318i | \(-0.558222\pi\) | ||||
−0.181893 | + | 0.983318i | \(0.558222\pi\) | |||||||
\(24\) | −1.65851 | − | 2.29115i | −0.338542 | − | 0.467678i | ||||
\(25\) | 4.75068i | 0.950135i | ||||||||
\(26\) | 4.07136 | − | 3.66158i | 0.798460 | − | 0.718095i | ||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | −3.94459 | − | 3.52706i | −0.745458 | − | 0.666552i | ||||
\(29\) | 4.96403 | − | 4.96403i | 0.921797 | − | 0.921797i | −0.0753590 | − | 0.997156i | \(-0.524010\pi\) |
0.997156 | + | 0.0753590i | \(0.0240103\pi\) | |||||||
\(30\) | −0.705159 | − | 0.0373675i | −0.128744 | − | 0.00682235i | ||||
\(31\) | −3.65022 | −0.655599 | −0.327800 | − | 0.944747i | \(-0.606307\pi\) | ||||
−0.327800 | + | 0.944747i | \(0.606307\pi\) | |||||||
\(32\) | 1.48000 | − | 5.45982i | 0.261630 | − | 0.965168i | ||||
\(33\) | 2.92232i | 0.508711i | ||||||||
\(34\) | 5.04742 | + | 0.267471i | 0.865625 | + | 0.0458709i | ||||
\(35\) | −1.30385 | + | 0.212700i | −0.220390 | + | 0.0359528i | ||||
\(36\) | −0.211373 | + | 1.98880i | −0.0352288 | + | 0.331466i | ||||
\(37\) | 6.34670 | + | 6.34670i | 1.04339 | + | 1.04339i | 0.999015 | + | 0.0443760i | \(0.0141300\pi\) |
0.0443760 | + | 0.999015i | \(0.485870\pi\) | |||||||
\(38\) | −7.96931 | − | 8.86118i | −1.29279 | − | 1.43747i | ||||
\(39\) | −3.87190 | −0.620000 | ||||||||
\(40\) | −0.828130 | − | 1.14402i | −0.130939 | − | 0.180885i | ||||
\(41\) | −6.29768 | −0.983533 | −0.491766 | − | 0.870727i | \(-0.663649\pi\) | ||||
−0.491766 | + | 0.870727i | \(0.663649\pi\) | |||||||
\(42\) | 0.406163 | + | 3.71955i | 0.0626723 | + | 0.573939i | ||||
\(43\) | −4.71295 | + | 4.71295i | −0.718719 | + | 0.718719i | −0.968343 | − | 0.249624i | \(-0.919693\pi\) |
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(44\) | −4.54642 | + | 3.67286i | −0.685399 | + | 0.553705i | ||||
\(45\) | 0.353074 | + | 0.353074i | 0.0526332 | + | 0.0526332i | ||||
\(46\) | −0.130564 | + | 2.46386i | −0.0192506 | + | 0.363276i | ||||
\(47\) | 0.538446 | 0.0785404 | 0.0392702 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392702 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(48\) | −3.35975 | + | 2.17074i | −0.484938 | + | 0.313319i | ||||
\(49\) | 2.22465 | + | 6.63709i | 0.317807 | + | 0.948155i | ||||
\(50\) | 6.70906 | + | 0.355524i | 0.948804 | + | 0.0502787i | ||||
\(51\) | −2.52725 | − | 2.52725i | −0.353886 | − | 0.353886i | ||||
\(52\) | −4.86632 | − | 6.02373i | −0.674837 | − | 0.835341i | ||||
\(53\) | −1.52324 | − | 1.52324i | −0.209233 | − | 0.209233i | 0.594709 | − | 0.803941i | \(-0.297267\pi\) |
−0.803941 | + | 0.594709i | \(0.797267\pi\) | |||||||
\(54\) | 1.05152 | − | 0.945681i | 0.143093 | − | 0.128691i | ||||
\(55\) | 1.45918i | 0.196756i | ||||||||
\(56\) | −5.27623 | + | 5.30673i | −0.705066 | + | 0.709141i | ||||
\(57\) | 8.42705i | 1.11619i | ||||||||
\(58\) | −6.63887 | − | 7.38186i | −0.871727 | − | 0.969285i | ||||
\(59\) | −7.32765 | − | 7.32765i | −0.953979 | − | 0.953979i | 0.0450080 | − | 0.998987i | \(-0.485669\pi\) |
−0.998987 | + | 0.0450080i | \(0.985669\pi\) | |||||||
\(60\) | −0.105543 | + | 0.993051i | −0.0136256 | + | 0.128202i | ||||
\(61\) | 4.15611 | + | 4.15611i | 0.532135 | + | 0.532135i | 0.921207 | − | 0.389072i | \(-0.127204\pi\) |
−0.389072 | + | 0.921207i | \(0.627204\pi\) | |||||||
\(62\) | −0.273170 | + | 5.15496i | −0.0346926 | + | 0.654681i | ||||
\(63\) | 1.54521 | − | 2.14763i | 0.194678 | − | 0.270576i | ||||
\(64\) | −7.59977 | − | 2.49870i | −0.949971 | − | 0.312338i | ||||
\(65\) | −1.93332 | −0.239799 | ||||||||
\(66\) | 4.12700 | + | 0.218697i | 0.507998 | + | 0.0269197i | ||||
\(67\) | −1.75078 | − | 1.75078i | −0.213892 | − | 0.213892i | 0.592026 | − | 0.805919i | \(-0.298328\pi\) |
−0.805919 | + | 0.592026i | \(0.798328\pi\) | |||||||
\(68\) | 0.755463 | − | 7.10811i | 0.0916133 | − | 0.861985i | ||||
\(69\) | 1.23366 | − | 1.23366i | 0.148515 | − | 0.148515i | ||||
\(70\) | 0.202806 | + | 1.85725i | 0.0242400 | + | 0.221984i | ||||
\(71\) | 9.51053 | 1.12869 | 0.564346 | − | 0.825538i | \(-0.309128\pi\) | ||||
0.564346 | + | 0.825538i | \(0.309128\pi\) | |||||||
\(72\) | 2.79283 | + | 0.447343i | 0.329138 | + | 0.0527198i | ||||
\(73\) | −8.67488 | −1.01532 | −0.507659 | − | 0.861558i | \(-0.669489\pi\) | ||||
−0.507659 | + | 0.861558i | \(0.669489\pi\) | |||||||
\(74\) | 9.43798 | − | 8.48805i | 1.09714 | − | 0.986715i | ||||
\(75\) | −3.35924 | − | 3.35924i | −0.387891 | − | 0.387891i | ||||
\(76\) | −13.1104 | + | 10.5914i | −1.50387 | + | 1.21491i | ||||
\(77\) | 7.63087 | − | 1.24484i | 0.869618 | − | 0.141863i | ||||
\(78\) | −0.289759 | + | 5.46802i | −0.0328088 | + | 0.619131i | ||||
\(79\) | 1.66646i | 0.187491i | 0.995596 | + | 0.0937457i | \(0.0298841\pi\) | ||||
−0.995596 | + | 0.0937457i | \(0.970116\pi\) | |||||||
\(80\) | −1.67760 | + | 1.08390i | −0.187561 | + | 0.121183i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −0.471297 | + | 8.89379i | −0.0520460 | + | 0.982155i | ||||
\(83\) | 7.80102 | − | 7.80102i | 0.856273 | − | 0.856273i | −0.134624 | − | 0.990897i | \(-0.542983\pi\) |
0.990897 | + | 0.134624i | \(0.0429825\pi\) | |||||||
\(84\) | 5.28326 | − | 0.295238i | 0.576451 | − | 0.0322131i | ||||
\(85\) | −1.26191 | − | 1.26191i | −0.136874 | − | 0.136874i | ||||
\(86\) | 6.30308 | + | 7.00848i | 0.679679 | + | 0.755744i | ||||
\(87\) | 7.02020i | 0.752645i | ||||||||
\(88\) | 4.84670 | + | 6.69547i | 0.516660 | + | 0.713739i | ||||
\(89\) | −5.38478 | −0.570786 | −0.285393 | − | 0.958411i | \(-0.592124\pi\) | ||||
−0.285393 | + | 0.958411i | \(0.592124\pi\) | |||||||
\(90\) | 0.525045 | − | 0.472200i | 0.0553446 | − | 0.0497742i | ||||
\(91\) | 1.64934 | + | 10.1104i | 0.172898 | + | 1.05986i | ||||
\(92\) | 3.46977 | + | 0.368773i | 0.361748 | + | 0.0384473i | ||||
\(93\) | 2.58110 | − | 2.58110i | 0.267647 | − | 0.267647i | ||||
\(94\) | 0.0402954 | − | 0.760410i | 0.00415615 | − | 0.0784303i | ||||
\(95\) | 4.20781i | 0.431712i | ||||||||
\(96\) | 2.81415 | + | 4.90719i | 0.287218 | + | 0.500838i | ||||
\(97\) | − | 15.5590i | − | 1.57978i | −0.613248 | − | 0.789891i | \(-0.710137\pi\) | ||
0.613248 | − | 0.789891i | \(-0.289863\pi\) | |||||||
\(98\) | 9.53959 | − | 2.64503i | 0.963644 | − | 0.267188i | ||||
\(99\) | −2.06639 | − | 2.06639i | −0.207680 | − | 0.207680i | ||||
\(100\) | 1.00417 | − | 9.44814i | 0.100417 | − | 0.944814i | ||||
\(101\) | −10.8391 | + | 10.8391i | −1.07853 | + | 1.07853i | −0.0818847 | + | 0.996642i | \(0.526094\pi\) |
−0.996642 | + | 0.0818847i | \(0.973906\pi\) | |||||||
\(102\) | −3.75819 | + | 3.37993i | −0.372117 | + | 0.334663i | ||||
\(103\) | − | 8.56545i | − | 0.843978i | −0.906601 | − | 0.421989i | \(-0.861332\pi\) | ||
0.906601 | − | 0.421989i | \(-0.138668\pi\) | |||||||
\(104\) | −8.87108 | + | 6.42157i | −0.869881 | + | 0.629687i | ||||
\(105\) | 0.771558 | − | 1.07236i | 0.0752963 | − | 0.104652i | ||||
\(106\) | −2.26516 | + | 2.03717i | −0.220012 | + | 0.197868i | ||||
\(107\) | −10.4598 | + | 10.4598i | −1.01118 | + | 1.01118i | −0.0112477 | + | 0.999937i | \(0.503580\pi\) |
−0.999937 | + | 0.0112477i | \(0.996420\pi\) | |||||||
\(108\) | −1.25683 | − | 1.55576i | −0.120939 | − | 0.149703i | ||||
\(109\) | 0.746037 | − | 0.746037i | 0.0714574 | − | 0.0714574i | −0.670475 | − | 0.741932i | \(-0.733910\pi\) |
0.741932 | + | 0.670475i | \(0.233910\pi\) | |||||||
\(110\) | 2.06070 | + | 0.109200i | 0.196480 | + | 0.0104118i | ||||
\(111\) | −8.97559 | −0.851925 | ||||||||
\(112\) | 7.09948 | + | 7.84840i | 0.670838 | + | 0.741604i | ||||
\(113\) | −1.23013 | −0.115721 | −0.0578606 | − | 0.998325i | \(-0.518428\pi\) | ||||
−0.0578606 | + | 0.998325i | \(0.518428\pi\) | |||||||
\(114\) | 11.9010 | + | 0.630651i | 1.11463 | + | 0.0590659i | ||||
\(115\) | 0.615992 | − | 0.615992i | 0.0574416 | − | 0.0574416i | ||||
\(116\) | −10.9217 | + | 8.82320i | −1.01406 | + | 0.819213i | ||||
\(117\) | 2.73784 | − | 2.73784i | 0.253114 | − | 0.253114i | ||||
\(118\) | −10.8967 | + | 9.79997i | −1.00312 | + | 0.902160i | ||||
\(119\) | −5.52269 | + | 7.67579i | −0.506264 | + | 0.703639i | ||||
\(120\) | 1.39452 | + | 0.223368i | 0.127302 | + | 0.0203906i | ||||
\(121\) | 2.46003i | 0.223639i | ||||||||
\(122\) | 6.18042 | − | 5.55836i | 0.559549 | − | 0.503230i | ||||
\(123\) | 4.45313 | − | 4.45313i | 0.401526 | − | 0.401526i | ||||
\(124\) | 7.25956 | + | 0.771559i | 0.651928 | + | 0.0692880i | ||||
\(125\) | −3.44271 | − | 3.44271i | −0.307925 | − | 0.307925i | ||||
\(126\) | −2.91732 | − | 2.34292i | −0.259895 | − | 0.208724i | ||||
\(127\) | − | 11.6177i | − | 1.03090i | −0.856919 | − | 0.515451i | \(-0.827624\pi\) | ||
0.856919 | − | 0.515451i | \(-0.172376\pi\) | |||||||
\(128\) | −4.09749 | + | 10.5456i | −0.362170 | + | 0.932112i | ||||
\(129\) | − | 6.66512i | − | 0.586831i | ||||||
\(130\) | −0.144683 | + | 2.73030i | −0.0126896 | + | 0.239463i | ||||
\(131\) | 14.1444 | − | 14.1444i | 1.23580 | − | 1.23580i | 0.274102 | − | 0.961701i | \(-0.411619\pi\) |
0.961701 | − | 0.274102i | \(-0.0883806\pi\) | |||||||
\(132\) | 0.617700 | − | 5.81191i | 0.0537639 | − | 0.505862i | ||||
\(133\) | 22.0050 | − | 3.58973i | 1.90808 | − | 0.311269i | ||||
\(134\) | −2.60353 | + | 2.34149i | −0.224911 | + | 0.202274i | ||||
\(135\) | −0.499322 | −0.0429748 | ||||||||
\(136\) | −9.98177 | − | 1.59883i | −0.855929 | − | 0.137099i | ||||
\(137\) | − | 2.58160i | − | 0.220561i | −0.993901 | − | 0.110281i | \(-0.964825\pi\) | ||
0.993901 | − | 0.110281i | \(-0.0351749\pi\) | |||||||
\(138\) | −1.64989 | − | 1.83453i | −0.140448 | − | 0.156166i | ||||
\(139\) | −10.2454 | − | 10.2454i | −0.869002 | − | 0.869002i | 0.123360 | − | 0.992362i | \(-0.460633\pi\) |
−0.992362 | + | 0.123360i | \(0.960633\pi\) | |||||||
\(140\) | 2.63805 | − | 0.147419i | 0.222956 | − | 0.0124592i | ||||
\(141\) | −0.380739 | + | 0.380739i | −0.0320640 | + | 0.0320640i | ||||
\(142\) | 0.711735 | − | 13.4311i | 0.0597275 | − | 1.12711i | ||||
\(143\) | 11.3149 | 0.946202 | ||||||||
\(144\) | 0.840757 | − | 3.91064i | 0.0700631 | − | 0.325887i | ||||
\(145\) | 3.50534i | 0.291103i | ||||||||
\(146\) | −0.649198 | + | 12.2509i | −0.0537280 | + | 1.01390i | ||||
\(147\) | −6.26620 | − | 3.12006i | −0.516827 | − | 0.257338i | ||||
\(148\) | −11.2808 | − | 13.9638i | −0.927275 | − | 1.14782i | ||||
\(149\) | −16.4288 | − | 16.4288i | −1.34590 | − | 1.34590i | −0.890064 | − | 0.455836i | \(-0.849341\pi\) |
−0.455836 | − | 0.890064i | \(-0.650659\pi\) | |||||||
\(150\) | −4.99541 | + | 4.49263i | −0.407874 | + | 0.366822i | ||||
\(151\) | 10.6869 | 0.869686 | 0.434843 | − | 0.900506i | \(-0.356804\pi\) | ||||
0.434843 | + | 0.900506i | \(0.356804\pi\) | |||||||
\(152\) | 13.9763 | + | 19.3076i | 1.13363 | + | 1.56605i | ||||
\(153\) | 3.57407 | 0.288947 | ||||||||
\(154\) | −1.18694 | − | 10.8697i | −0.0956463 | − | 0.875907i | ||||
\(155\) | 1.28880 | − | 1.28880i | 0.103519 | − | 0.103519i | ||||
\(156\) | 7.70043 | + | 0.818415i | 0.616527 | + | 0.0655256i | ||||
\(157\) | 7.53988 | + | 7.53988i | 0.601748 | + | 0.601748i | 0.940776 | − | 0.339028i | \(-0.110098\pi\) |
−0.339028 | + | 0.940776i | \(0.610098\pi\) | |||||||
\(158\) | 2.35343 | + | 0.124712i | 0.187229 | + | 0.00992156i | ||||
\(159\) | 2.15418 | 0.170838 | ||||||||
\(160\) | 1.40517 | + | 2.45027i | 0.111088 | + | 0.193711i | ||||
\(161\) | −3.74688 | − | 2.69586i | −0.295295 | − | 0.212463i | ||||
\(162\) | −0.0748365 | + | 1.41223i | −0.00587971 | + | 0.110955i | ||||
\(163\) | −10.2545 | − | 10.2545i | −0.803198 | − | 0.803198i | 0.180396 | − | 0.983594i | \(-0.442262\pi\) |
−0.983594 | + | 0.180396i | \(0.942262\pi\) | |||||||
\(164\) | 12.5248 | + | 1.33116i | 0.978025 | + | 0.103946i | ||||
\(165\) | −1.03180 | − | 1.03180i | −0.0803252 | − | 0.0803252i | ||||
\(166\) | −10.4331 | − | 11.6007i | −0.809762 | − | 0.900385i | ||||
\(167\) | 2.17484i | 0.168294i | 0.996453 | + | 0.0841472i | \(0.0268166\pi\) | ||||
−0.996453 | + | 0.0841472i | \(0.973183\pi\) | |||||||
\(168\) | −0.0215640 | − | 7.48328i | −0.00166370 | − | 0.577348i | ||||
\(169\) | 1.99159i | 0.153199i | ||||||||
\(170\) | −1.87655 | + | 1.68768i | −0.143925 | + | 0.129439i | ||||
\(171\) | −5.95882 | − | 5.95882i | −0.455683 | − | 0.455683i | ||||
\(172\) | 10.3693 | − | 8.37692i | 0.790652 | − | 0.638734i | ||||
\(173\) | 5.40669 | + | 5.40669i | 0.411063 | + | 0.411063i | 0.882109 | − | 0.471046i | \(-0.156123\pi\) |
−0.471046 | + | 0.882109i | \(0.656123\pi\) | |||||||
\(174\) | 9.91415 | + | 0.525367i | 0.751590 | + | 0.0398280i | ||||
\(175\) | −7.34079 | + | 10.2027i | −0.554912 | + | 0.771252i | ||||
\(176\) | 9.81827 | − | 6.34359i | 0.740080 | − | 0.478166i | ||||
\(177\) | 10.3629 | 0.778920 | ||||||||
\(178\) | −0.402979 | + | 7.60457i | −0.0302045 | + | 0.569986i | ||||
\(179\) | −1.42198 | − | 1.42198i | −0.106284 | − | 0.106284i | 0.651965 | − | 0.758249i | \(-0.273945\pi\) |
−0.758249 | + | 0.651965i | \(0.773945\pi\) | |||||||
\(180\) | −0.627563 | − | 0.776824i | −0.0467758 | − | 0.0579010i | ||||
\(181\) | 14.2278 | − | 14.2278i | 1.05754 | − | 1.05754i | 0.0593014 | − | 0.998240i | \(-0.481113\pi\) |
0.998240 | − | 0.0593014i | \(-0.0188873\pi\) | |||||||
\(182\) | 14.4017 | − | 1.57262i | 1.06753 | − | 0.116570i | ||||
\(183\) | −5.87762 | −0.434486 | ||||||||
\(184\) | 0.780459 | − | 4.87252i | 0.0575362 | − | 0.359207i | ||||
\(185\) | −4.48171 | −0.329502 | ||||||||
\(186\) | −3.45195 | − | 3.83827i | −0.253109 | − | 0.281435i | ||||
\(187\) | 7.38544 | + | 7.38544i | 0.540077 | + | 0.540077i | ||||
\(188\) | −1.07086 | − | 0.113813i | −0.0781005 | − | 0.00830066i | ||||
\(189\) | 0.425977 | + | 2.61123i | 0.0309853 | + | 0.189939i | ||||
\(190\) | 5.94241 | + | 0.314898i | 0.431108 | + | 0.0228451i | ||||
\(191\) | 11.5354i | 0.834673i | 0.908752 | + | 0.417336i | \(0.137036\pi\) | ||||
−0.908752 | + | 0.417336i | \(0.862964\pi\) | |||||||
\(192\) | 7.14070 | − | 3.60700i | 0.515335 | − | 0.260313i | ||||
\(193\) | −12.7812 | −0.920013 | −0.460006 | − | 0.887916i | \(-0.652153\pi\) | ||||
−0.460006 | + | 0.887916i | \(0.652153\pi\) | |||||||
\(194\) | −21.9730 | − | 1.16438i | −1.57757 | − | 0.0835979i | ||||
\(195\) | 1.36707 | − | 1.36707i | 0.0978977 | − | 0.0978977i | ||||
\(196\) | −3.02148 | − | 13.6701i | −0.215820 | − | 0.976433i | ||||
\(197\) | −11.5499 | − | 11.5499i | −0.822894 | − | 0.822894i | 0.163628 | − | 0.986522i | \(-0.447680\pi\) |
−0.986522 | + | 0.163628i | \(0.947680\pi\) | |||||||
\(198\) | −3.07287 | + | 2.76359i | −0.218379 | + | 0.196400i | ||||
\(199\) | 2.69165i | 0.190806i | 0.995439 | + | 0.0954030i | \(0.0304140\pi\) | ||||
−0.995439 | + | 0.0954030i | \(0.969586\pi\) | |||||||
\(200\) | −13.2678 | − | 2.12518i | −0.938177 | − | 0.150273i | ||||
\(201\) | 2.47598 | 0.174642 | ||||||||
\(202\) | 14.4961 | + | 16.1184i | 1.01994 | + | 1.13409i | ||||
\(203\) | 18.3314 | − | 2.99044i | 1.28661 | − | 0.209888i | ||||
\(204\) | 4.49200 | + | 5.56039i | 0.314503 | + | 0.389305i | ||||
\(205\) | 2.22355 | − | 2.22355i | 0.155299 | − | 0.155299i | ||||
\(206\) | −12.0964 | − | 0.641008i | −0.842796 | − | 0.0446612i | ||||
\(207\) | 1.74465i | 0.121262i | ||||||||
\(208\) | 8.40487 | + | 13.0086i | 0.582773 | + | 0.901984i | ||||
\(209\) | − | 24.6266i | − | 1.70345i | ||||||
\(210\) | −1.45668 | − | 1.16987i | −0.100521 | − | 0.0807287i | ||||
\(211\) | −12.4646 | − | 12.4646i | −0.858099 | − | 0.858099i | 0.133015 | − | 0.991114i | \(-0.457534\pi\) |
−0.991114 | + | 0.133015i | \(0.957534\pi\) | |||||||
\(212\) | 2.70744 | + | 3.35138i | 0.185948 | + | 0.230174i | ||||
\(213\) | −6.72496 | + | 6.72496i | −0.460787 | + | 0.460787i | ||||
\(214\) | 13.9889 | + | 15.5544i | 0.956258 | + | 1.06328i | ||||
\(215\) | − | 3.32804i | − | 0.226971i | ||||||
\(216\) | −2.29115 | + | 1.65851i | −0.155893 | + | 0.112847i | ||||
\(217\) | −7.83934 | − | 5.64036i | −0.532169 | − | 0.382893i | ||||
\(218\) | −0.997747 | − | 1.10941i | −0.0675760 | − | 0.0751386i | ||||
\(219\) | 6.13407 | − | 6.13407i | 0.414502 | − | 0.414502i | ||||
\(220\) | 0.308432 | − | 2.90202i | 0.0207944 | − | 0.195654i | ||||
\(221\) | −9.78525 | + | 9.78525i | −0.658227 | + | 0.658227i | ||||
\(222\) | −0.671702 | + | 12.6756i | −0.0450817 | + | 0.850731i | ||||
\(223\) | 12.7117 | 0.851237 | 0.425618 | − | 0.904903i | \(-0.360057\pi\) | ||||
0.425618 | + | 0.904903i | \(0.360057\pi\) | |||||||
\(224\) | 11.6151 | − | 9.43876i | 0.776064 | − | 0.630654i | ||||
\(225\) | 4.75068 | 0.316712 | ||||||||
\(226\) | −0.0920589 | + | 1.73723i | −0.00612367 | + | 0.115559i | ||||
\(227\) | −10.9992 | + | 10.9992i | −0.730040 | + | 0.730040i | −0.970627 | − | 0.240587i | \(-0.922660\pi\) |
0.240587 | + | 0.970627i | \(0.422660\pi\) | |||||||
\(228\) | 1.78125 | − | 16.7597i | 0.117966 | − | 1.10994i | ||||
\(229\) | 2.73573 | − | 2.73573i | 0.180782 | − | 0.180782i | −0.610914 | − | 0.791697i | \(-0.709198\pi\) |
0.791697 | + | 0.610914i | \(0.209198\pi\) | |||||||
\(230\) | −0.823825 | − | 0.916023i | −0.0543214 | − | 0.0604008i | ||||
\(231\) | −4.51560 | + | 6.27608i | −0.297105 | + | 0.412935i | ||||
\(232\) | 11.6431 | + | 16.0843i | 0.764404 | + | 1.05599i | ||||
\(233\) | 8.97538i | 0.587996i | 0.955806 | + | 0.293998i | \(0.0949860\pi\) | ||||
−0.955806 | + | 0.293998i | \(0.905014\pi\) | |||||||
\(234\) | −3.66158 | − | 4.07136i | −0.239365 | − | 0.266153i | ||||
\(235\) | −0.190111 | + | 0.190111i | −0.0124015 | + | 0.0124015i | ||||
\(236\) | 13.0244 | + | 16.1221i | 0.847813 | + | 1.04946i | ||||
\(237\) | −1.17836 | − | 1.17836i | −0.0765430 | − | 0.0765430i | ||||
\(238\) | 10.4267 | + | 8.37375i | 0.675863 | + | 0.542790i | ||||
\(239\) | 20.5737i | 1.33080i | 0.746487 | + | 0.665400i | \(0.231739\pi\) | ||||
−0.746487 | + | 0.665400i | \(0.768261\pi\) | |||||||
\(240\) | 0.419809 | − | 1.95267i | 0.0270985 | − | 0.126044i | ||||
\(241\) | 2.73898i | 0.176434i | 0.996101 | + | 0.0882168i | \(0.0281168\pi\) | ||||
−0.996101 | + | 0.0882168i | \(0.971883\pi\) | |||||||
\(242\) | 3.47413 | + | 0.184100i | 0.223326 | + | 0.0118344i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | −7.38717 | − | 9.14415i | −0.472915 | − | 0.585394i | ||||
\(245\) | −3.12885 | − | 1.55792i | −0.199895 | − | 0.0995316i | ||||
\(246\) | −5.95560 | − | 6.62212i | −0.379715 | − | 0.422211i | ||||
\(247\) | 32.6287 | 2.07611 | ||||||||
\(248\) | 1.63290 | − | 10.1944i | 0.103689 | − | 0.647348i | ||||
\(249\) | 11.0323i | 0.699144i | ||||||||
\(250\) | −5.11955 | + | 4.60427i | −0.323789 | + | 0.291199i | ||||
\(251\) | 1.27628 | + | 1.27628i | 0.0805580 | + | 0.0805580i | 0.746238 | − | 0.665680i | \(-0.231858\pi\) |
−0.665680 | + | 0.746238i | \(0.731858\pi\) | |||||||
\(252\) | −3.52706 | + | 3.94459i | −0.222184 | + | 0.248486i | ||||
\(253\) | −3.60514 | + | 3.60514i | −0.226654 | + | 0.226654i | ||||
\(254\) | −16.4069 | − | 0.869427i | −1.02946 | − | 0.0545527i | ||||
\(255\) | 1.78461 | 0.111757 | ||||||||
\(256\) | 14.5863 | + | 6.57580i | 0.911641 | + | 0.410988i | ||||
\(257\) | 30.4875i | 1.90176i | 0.309560 | + | 0.950880i | \(0.399818\pi\) | ||||
−0.309560 | + | 0.950880i | \(0.600182\pi\) | |||||||
\(258\) | −9.41270 | − | 0.498795i | −0.586009 | − | 0.0310536i | ||||
\(259\) | 3.82339 | + | 23.4374i | 0.237574 | + | 1.45633i | ||||
\(260\) | 3.84499 | + | 0.408653i | 0.238456 | + | 0.0253436i | ||||
\(261\) | −4.96403 | − | 4.96403i | −0.307266 | − | 0.307266i | ||||
\(262\) | −18.9167 | − | 21.0337i | −1.16868 | − | 1.29947i | ||||
\(263\) | 6.42214 | 0.396006 | 0.198003 | − | 0.980201i | \(-0.436554\pi\) | ||||
0.198003 | + | 0.980201i | \(0.436554\pi\) | |||||||
\(264\) | −8.16154 | − | 1.30728i | −0.502308 | − | 0.0804575i | ||||
\(265\) | 1.07563 | 0.0660755 | ||||||||
\(266\) | −3.42275 | − | 31.3448i | −0.209863 | − | 1.92187i | ||||
\(267\) | 3.80762 | − | 3.80762i | 0.233022 | − | 0.233022i | ||||
\(268\) | 3.11189 | + | 3.85202i | 0.190089 | + | 0.235300i | ||||
\(269\) | 4.61296 | + | 4.61296i | 0.281257 | + | 0.281257i | 0.833610 | − | 0.552353i | \(-0.186270\pi\) |
−0.552353 | + | 0.833610i | \(0.686270\pi\) | |||||||
\(270\) | −0.0373675 | + | 0.705159i | −0.00227412 | + | 0.0429146i | ||||
\(271\) | −19.5070 | −1.18496 | −0.592482 | − | 0.805584i | \(-0.701852\pi\) | ||||
−0.592482 | + | 0.805584i | \(0.701852\pi\) | |||||||
\(272\) | −3.00493 | + | 13.9769i | −0.182200 | + | 0.847475i | ||||
\(273\) | −8.31541 | − | 5.98289i | −0.503272 | − | 0.362101i | ||||
\(274\) | −3.64582 | − | 0.193198i | −0.220252 | − | 0.0116715i | ||||
\(275\) | 9.81677 | + | 9.81677i | 0.591974 | + | 0.591974i | ||||
\(276\) | −2.71426 | + | 2.19273i | −0.163379 | + | 0.131987i | ||||
\(277\) | 6.01010 | + | 6.01010i | 0.361112 | + | 0.361112i | 0.864222 | − | 0.503110i | \(-0.167811\pi\) |
−0.503110 | + | 0.864222i | \(0.667811\pi\) | |||||||
\(278\) | −15.2356 | + | 13.7021i | −0.913770 | + | 0.821799i | ||||
\(279\) | 3.65022i | 0.218533i | ||||||||
\(280\) | −0.0107674 | − | 3.73657i | −0.000643475 | − | 0.223303i | ||||
\(281\) | − | 4.75038i | − | 0.283384i | −0.989911 | − | 0.141692i | \(-0.954746\pi\) | ||
0.989911 | − | 0.141692i | \(-0.0452542\pi\) | |||||||
\(282\) | 0.509198 | + | 0.566184i | 0.0303223 | + | 0.0337158i | ||||
\(283\) | 2.71232 | + | 2.71232i | 0.161231 | + | 0.161231i | 0.783112 | − | 0.621881i | \(-0.213631\pi\) |
−0.621881 | + | 0.783112i | \(0.713631\pi\) | |||||||
\(284\) | −18.9145 | − | 2.01027i | −1.12237 | − | 0.119288i | ||||
\(285\) | −2.97537 | − | 2.97537i | −0.176246 | − | 0.176246i | ||||
\(286\) | 0.846770 | − | 15.9793i | 0.0500706 | − | 0.944877i | ||||
\(287\) | −13.5251 | − | 9.73124i | −0.798362 | − | 0.574417i | ||||
\(288\) | −5.45982 | − | 1.48000i | −0.321723 | − | 0.0872100i | ||||
\(289\) | 4.22601 | 0.248589 | ||||||||
\(290\) | 4.95036 | + | 0.262328i | 0.290695 | + | 0.0154044i | ||||
\(291\) | 11.0019 | + | 11.0019i | 0.644943 | + | 0.644943i | ||||
\(292\) | 17.2526 | + | 1.83364i | 1.00963 | + | 0.107305i | ||||
\(293\) | 12.9786 | − | 12.9786i | 0.758217 | − | 0.758217i | −0.217781 | − | 0.975998i | \(-0.569882\pi\) |
0.975998 | + | 0.217781i | \(0.0698819\pi\) | |||||||
\(294\) | −4.87519 | + | 8.61583i | −0.284327 | + | 0.502485i | ||||
\(295\) | 5.17441 | 0.301266 | ||||||||
\(296\) | −20.5644 | + | 14.8861i | −1.19528 | + | 0.865236i | ||||
\(297\) | 2.92232 | 0.169570 | ||||||||
\(298\) | −24.4307 | + | 21.9718i | −1.41524 | + | 1.27279i | ||||
\(299\) | −4.77659 | − | 4.77659i | −0.276238 | − | 0.276238i | ||||
\(300\) | 5.97079 | + | 7.39090i | 0.344724 | + | 0.426714i | ||||
\(301\) | −17.4042 | + | 2.83919i | −1.00316 | + | 0.163648i | ||||
\(302\) | 0.799769 | − | 15.0924i | 0.0460215 | − | 0.868468i | ||||
\(303\) | − | 15.3287i | − | 0.880613i | ||||||
\(304\) | 28.3128 | − | 18.2929i | 1.62385 | − | 1.04917i | ||||
\(305\) | −2.93483 | −0.168048 | ||||||||
\(306\) | 0.267471 | − | 5.04742i | 0.0152903 | − | 0.288542i | ||||
\(307\) | −13.2165 | + | 13.2165i | −0.754307 | + | 0.754307i | −0.975280 | − | 0.220973i | \(-0.929077\pi\) |
0.220973 | + | 0.975280i | \(0.429077\pi\) | |||||||
\(308\) | −15.4394 | + | 0.862781i | −0.879741 | + | 0.0491615i | ||||
\(309\) | 6.05668 | + | 6.05668i | 0.344553 | + | 0.344553i | ||||
\(310\) | −1.72363 | − | 1.91653i | −0.0978958 | − | 0.108852i | ||||
\(311\) | 23.9389i | 1.35745i | 0.734391 | + | 0.678726i | \(0.237468\pi\) | ||||
−0.734391 | + | 0.678726i | \(0.762532\pi\) | |||||||
\(312\) | 1.73206 | − | 10.8135i | 0.0980589 | − | 0.612196i | ||||
\(313\) | −9.65156 | −0.545539 | −0.272769 | − | 0.962079i | \(-0.587940\pi\) | ||||
−0.272769 | + | 0.962079i | \(0.587940\pi\) | |||||||
\(314\) | 11.2123 | − | 10.0838i | 0.632748 | − | 0.569062i | ||||
\(315\) | 0.212700 | + | 1.30385i | 0.0119843 | + | 0.0734635i | ||||
\(316\) | 0.352245 | − | 3.31425i | 0.0198153 | − | 0.186441i | ||||
\(317\) | 2.04754 | − | 2.04754i | 0.115001 | − | 0.115001i | −0.647264 | − | 0.762266i | \(-0.724087\pi\) |
0.762266 | + | 0.647264i | \(0.224087\pi\) | |||||||
\(318\) | 0.161212 | − | 3.04221i | 0.00904030 | − | 0.170598i | ||||
\(319\) | − | 20.5153i | − | 1.14864i | ||||||
\(320\) | 3.56551 | − | 1.80105i | 0.199318 | − | 0.100682i | ||||
\(321\) | − | 14.7924i | − | 0.825629i | ||||||
\(322\) | −4.08758 | + | 5.08971i | −0.227792 | + | 0.283639i | ||||
\(323\) | 21.2973 | + | 21.2973i | 1.18501 | + | 1.18501i | ||||
\(324\) | 1.98880 | + | 0.211373i | 0.110489 | + | 0.0117429i | ||||
\(325\) | −13.0066 | + | 13.0066i | −0.721477 | + | 0.721477i | ||||
\(326\) | −15.2492 | + | 13.7144i | −0.844575 | + | 0.759569i | ||||
\(327\) | 1.05506i | 0.0583447i | ||||||||
\(328\) | 2.81722 | − | 17.5883i | 0.155555 | − | 0.971154i | ||||
\(329\) | 1.15638 | + | 0.832012i | 0.0637535 | + | 0.0458703i | ||||
\(330\) | −1.53435 | + | 1.37992i | −0.0844633 | + | 0.0759621i | ||||
\(331\) | −4.46464 | + | 4.46464i | −0.245399 | + | 0.245399i | −0.819079 | − | 0.573680i | \(-0.805515\pi\) |
0.573680 | + | 0.819079i | \(0.305515\pi\) | |||||||
\(332\) | −17.1636 | + | 13.8657i | −0.941974 | + | 0.760981i | ||||
\(333\) | 6.34670 | − | 6.34670i | 0.347797 | − | 0.347797i | ||||
\(334\) | 3.07138 | + | 0.162758i | 0.168059 | + | 0.00890570i | ||||
\(335\) | 1.23631 | 0.0675470 | ||||||||
\(336\) | −10.5697 | − | 0.529570i | −0.576627 | − | 0.0288904i | ||||
\(337\) | −11.1195 | −0.605716 | −0.302858 | − | 0.953036i | \(-0.597941\pi\) | ||||
−0.302858 | + | 0.953036i | \(0.597941\pi\) | |||||||
\(338\) | 2.81258 | + | 0.149044i | 0.152984 | + | 0.00810690i | ||||
\(339\) | 0.869835 | − | 0.869835i | 0.0472430 | − | 0.0472430i | ||||
\(340\) | 2.24296 | + | 2.77642i | 0.121641 | + | 0.150573i | ||||
\(341\) | −7.54280 | + | 7.54280i | −0.408465 | + | 0.408465i | ||||
\(342\) | −8.86118 | + | 7.96931i | −0.479158 | + | 0.430931i | ||||
\(343\) | −5.47796 | + | 17.6916i | −0.295782 | + | 0.955255i | ||||
\(344\) | −11.0542 | − | 15.2708i | −0.596000 | − | 0.823345i | ||||
\(345\) | 0.871145i | 0.0469009i | ||||||||
\(346\) | 8.04011 | − | 7.23088i | 0.432239 | − | 0.388734i | ||||
\(347\) | −2.56028 | + | 2.56028i | −0.137443 | + | 0.137443i | −0.772481 | − | 0.635038i | \(-0.780985\pi\) |
0.635038 | + | 0.772481i | \(0.280985\pi\) | |||||||
\(348\) | 1.48388 | − | 13.9618i | 0.0795444 | − | 0.748429i | ||||
\(349\) | −15.4685 | − | 15.4685i | −0.828011 | − | 0.828011i | 0.159231 | − | 0.987241i | \(-0.449099\pi\) |
−0.987241 | + | 0.159231i | \(0.949099\pi\) | |||||||
\(350\) | 13.8592 | + | 11.1304i | 0.740807 | + | 0.594947i | ||||
\(351\) | 3.87190i | 0.206667i | ||||||||
\(352\) | −8.22386 | − | 14.3404i | −0.438333 | − | 0.764346i | ||||
\(353\) | − | 21.5190i | − | 1.14534i | −0.819786 | − | 0.572670i | \(-0.805908\pi\) | ||
0.819786 | − | 0.572670i | \(-0.194092\pi\) | |||||||
\(354\) | 0.775520 | − | 14.6348i | 0.0412184 | − | 0.777829i | ||||
\(355\) | −3.35792 | + | 3.35792i | −0.178220 | + | 0.178220i | ||||
\(356\) | 10.7093 | + | 1.13820i | 0.567589 | + | 0.0603244i | ||||
\(357\) | −1.52247 | − | 9.33274i | −0.0805778 | − | 0.493941i | ||||
\(358\) | −2.11459 | + | 1.90175i | −0.111759 | + | 0.100511i | ||||
\(359\) | −28.9399 | −1.52739 | −0.763696 | − | 0.645576i | \(-0.776617\pi\) | ||||
−0.763696 | + | 0.645576i | \(0.776617\pi\) | |||||||
\(360\) | −1.14402 | + | 0.828130i | −0.0602951 | + | 0.0436463i | ||||
\(361\) | − | 52.0152i | − | 2.73764i | ||||||
\(362\) | −19.0282 | − | 21.1577i | −1.00010 | − | 1.11202i | ||||
\(363\) | −1.73950 | − | 1.73950i | −0.0913002 | − | 0.0913002i | ||||
\(364\) | −1.14313 | − | 20.4562i | −0.0599164 | − | 1.07220i | ||||
\(365\) | 3.06287 | − | 3.06287i | 0.160318 | − | 0.160318i | ||||
\(366\) | −0.439861 | + | 8.30057i | −0.0229919 | + | 0.433878i | ||||
\(367\) | 5.65132 | 0.294996 | 0.147498 | − | 0.989062i | \(-0.452878\pi\) | ||||
0.147498 | + | 0.989062i | \(0.452878\pi\) | |||||||
\(368\) | −6.82272 | − | 1.46683i | −0.355659 | − | 0.0764639i | ||||
\(369\) | 6.29768i | 0.327844i | ||||||||
\(370\) | −0.335396 | + | 6.32921i | −0.0174364 | + | 0.329040i | ||||
\(371\) | −0.917633 | − | 5.62508i | −0.0476411 | − | 0.292039i | ||||
\(372\) | −5.67886 | + | 4.58771i | −0.294435 | + | 0.237862i | ||||
\(373\) | 13.3574 | + | 13.3574i | 0.691618 | + | 0.691618i | 0.962588 | − | 0.270970i | \(-0.0873445\pi\) |
−0.270970 | + | 0.962588i | \(0.587344\pi\) | |||||||
\(374\) | 10.9827 | − | 9.87726i | 0.567900 | − | 0.510741i | ||||
\(375\) | 4.86873 | 0.251420 | ||||||||
\(376\) | −0.240870 | + | 1.50379i | −0.0124219 | + | 0.0775518i | ||||
\(377\) | 27.1815 | 1.39992 | ||||||||
\(378\) | 3.71955 | − | 0.406163i | 0.191313 | − | 0.0208908i | ||||
\(379\) | −12.3344 | + | 12.3344i | −0.633577 | + | 0.633577i | −0.948963 | − | 0.315386i | \(-0.897866\pi\) |
0.315386 | + | 0.948963i | \(0.397866\pi\) | |||||||
\(380\) | 0.889418 | − | 8.36849i | 0.0456262 | − | 0.429295i | ||||
\(381\) | 8.21494 | + | 8.21494i | 0.420864 | + | 0.420864i | ||||
\(382\) | 16.2907 | + | 0.863270i | 0.833503 | + | 0.0441687i | ||||
\(383\) | 4.53694 | 0.231827 | 0.115913 | − | 0.993259i | \(-0.463021\pi\) | ||||
0.115913 | + | 0.993259i | \(0.463021\pi\) | |||||||
\(384\) | −4.55954 | − | 10.3543i | −0.232678 | − | 0.528388i | ||||
\(385\) | −2.25474 | + | 3.13378i | −0.114912 | + | 0.159712i | ||||
\(386\) | −0.956503 | + | 18.0501i | −0.0486847 | + | 0.918724i | ||||
\(387\) | 4.71295 | + | 4.71295i | 0.239573 | + | 0.239573i | ||||
\(388\) | −3.28876 | + | 30.9438i | −0.166962 | + | 1.57093i | ||||
\(389\) | 16.5413 | + | 16.5413i | 0.838679 | + | 0.838679i | 0.988685 | − | 0.150006i | \(-0.0479294\pi\) |
−0.150006 | + | 0.988685i | \(0.547929\pi\) | |||||||
\(390\) | −1.82831 | − | 2.03292i | −0.0925800 | − | 0.102941i | ||||
\(391\) | − | 6.23552i | − | 0.315344i | ||||||
\(392\) | −19.5314 | + | 3.24402i | −0.986486 | + | 0.163848i | ||||
\(393\) | 20.0032i | 1.00903i | ||||||||
\(394\) | −17.1755 | + | 15.4467i | −0.865287 | + | 0.778196i | ||||
\(395\) | −0.588384 | − | 0.588384i | −0.0296048 | − | 0.0296048i | ||||
\(396\) | 3.67286 | + | 4.54642i | 0.184568 | + | 0.228466i | ||||
\(397\) | −2.13420 | − | 2.13420i | −0.107113 | − | 0.107113i | 0.651519 | − | 0.758632i | \(-0.274132\pi\) |
−0.758632 | + | 0.651519i | \(0.774132\pi\) | |||||||
\(398\) | 3.80124 | + | 0.201434i | 0.190539 | + | 0.0100970i | ||||
\(399\) | −13.0216 | + | 18.0982i | −0.651894 | + | 0.906044i | ||||
\(400\) | −3.99417 | + | 18.5782i | −0.199708 | + | 0.928910i | ||||
\(401\) | −8.15672 | −0.407327 | −0.203663 | − | 0.979041i | \(-0.565285\pi\) | ||||
−0.203663 | + | 0.979041i | \(0.565285\pi\) | |||||||
\(402\) | 0.185294 | − | 3.49666i | 0.00924162 | − | 0.174398i | ||||
\(403\) | −9.99374 | − | 9.99374i | −0.497824 | − | 0.497824i | ||||
\(404\) | 23.8478 | − | 19.2656i | 1.18647 | − | 0.958500i | ||||
\(405\) | 0.353074 | − | 0.353074i | 0.0175444 | − | 0.0175444i | ||||
\(406\) | −2.85134 | − | 26.1120i | −0.141510 | − | 1.29592i | ||||
\(407\) | 26.2296 | 1.30015 | ||||||||
\(408\) | 8.18872 | − | 5.92763i | 0.405402 | − | 0.293461i | ||||
\(409\) | 12.5423 | 0.620177 | 0.310089 | − | 0.950708i | \(-0.399641\pi\) | ||||
0.310089 | + | 0.950708i | \(0.399641\pi\) | |||||||
\(410\) | −2.97376 | − | 3.30657i | −0.146864 | − | 0.163300i | ||||
\(411\) | 1.82547 | + | 1.82547i | 0.0900437 | + | 0.0900437i | ||||
\(412\) | −1.81050 | + | 17.0350i | −0.0891972 | + | 0.839252i | ||||
\(413\) | −4.41434 | − | 27.0599i | −0.217216 | − | 1.33153i | ||||
\(414\) | 2.46386 | + | 0.130564i | 0.121092 | + | 0.00641687i | ||||
\(415\) | 5.50868i | 0.270410i | ||||||||
\(416\) | 19.0001 | − | 10.8961i | 0.931559 | − | 0.534226i | ||||
\(417\) | 14.4892 | 0.709537 | ||||||||
\(418\) | −34.7784 | − | 1.84297i | −1.70107 | − | 0.0901424i | ||||
\(419\) | −18.0414 | + | 18.0414i | −0.881378 | + | 0.881378i | −0.993675 | − | 0.112296i | \(-0.964179\pi\) |
0.112296 | + | 0.993675i | \(0.464179\pi\) | |||||||
\(420\) | −1.76114 | + | 1.96962i | −0.0859349 | + | 0.0961078i | ||||
\(421\) | −0.0605701 | − | 0.0605701i | −0.00295201 | − | 0.00295201i | 0.705629 | − | 0.708581i | \(-0.250664\pi\) |
−0.708581 | + | 0.705629i | \(0.750664\pi\) | |||||||
\(422\) | −18.5357 | + | 16.6701i | −0.902305 | + | 0.811488i | ||||
\(423\) | − | 0.538446i | − | 0.0261801i | ||||||
\(424\) | 4.93555 | − | 3.57273i | 0.239691 | − | 0.173507i | ||||
\(425\) | −16.9793 | −0.823615 | ||||||||
\(426\) | 8.99394 | + | 10.0005i | 0.435758 | + | 0.484525i | ||||
\(427\) | 2.50373 | + | 15.3478i | 0.121164 | + | 0.742734i | ||||
\(428\) | 23.0133 | − | 18.5915i | 1.11239 | − | 0.898653i | ||||
\(429\) | −8.00087 | + | 8.00087i | −0.386285 | + | 0.386285i | ||||
\(430\) | −4.69997 | − | 0.249059i | −0.226653 | − | 0.0120107i | ||||
\(431\) | 12.8411i | 0.618532i | 0.950976 | + | 0.309266i | \(0.100083\pi\) | ||||
−0.950976 | + | 0.309266i | \(0.899917\pi\) | |||||||
\(432\) | 2.17074 | + | 3.35975i | 0.104440 | + | 0.161646i | ||||
\(433\) | 8.05085i | 0.386899i | 0.981110 | + | 0.193449i | \(0.0619676\pi\) | ||||
−0.981110 | + | 0.193449i | \(0.938032\pi\) | |||||||
\(434\) | −8.55217 | + | 10.6489i | −0.410517 | + | 0.511162i | ||||
\(435\) | −2.47865 | − | 2.47865i | −0.118842 | − | 0.118842i | ||||
\(436\) | −1.64141 | + | 1.32603i | −0.0786093 | + | 0.0635051i | ||||
\(437\) | −10.3961 | + | 10.3961i | −0.497312 | + | 0.497312i | ||||
\(438\) | −8.20367 | − | 9.12178i | −0.391987 | − | 0.435855i | ||||
\(439\) | − | 36.3698i | − | 1.73584i | −0.496708 | − | 0.867918i | \(-0.665458\pi\) | ||
0.496708 | − | 0.867918i | \(-0.334542\pi\) | |||||||
\(440\) | −4.07524 | − | 0.652754i | −0.194279 | − | 0.0311188i | ||||
\(441\) | 6.63709 | − | 2.22465i | 0.316052 | − | 0.105936i | ||||
\(442\) | 13.0868 | + | 14.5513i | 0.622473 | + | 0.692137i | ||||
\(443\) | 27.1483 | − | 27.1483i | 1.28986 | − | 1.28986i | 0.354984 | − | 0.934873i | \(-0.384486\pi\) |
0.934873 | − | 0.354984i | \(-0.115514\pi\) | |||||||
\(444\) | 17.8506 | + | 1.89720i | 0.847154 | + | 0.0900370i | ||||
\(445\) | 1.90123 | − | 1.90123i | 0.0901268 | − | 0.0901268i | ||||
\(446\) | 0.951298 | − | 17.9518i | 0.0450453 | − | 0.850044i | ||||
\(447\) | 23.2338 | 1.09892 | ||||||||
\(448\) | −12.4605 | − | 17.1095i | −0.588703 | − | 0.808349i | ||||
\(449\) | 6.95274 | 0.328120 | 0.164060 | − | 0.986450i | \(-0.447541\pi\) | ||||
0.164060 | + | 0.986450i | \(0.447541\pi\) | |||||||
\(450\) | 0.355524 | − | 6.70906i | 0.0167596 | − | 0.316268i | ||||
\(451\) | −13.0135 | + | 13.0135i | −0.612782 | + | 0.612782i | ||||
\(452\) | 2.44649 | + | 0.260017i | 0.115073 | + | 0.0122302i | ||||
\(453\) | −7.55677 | + | 7.55677i | −0.355048 | + | 0.355048i | ||||
\(454\) | 14.7102 | + | 16.3565i | 0.690385 | + | 0.767649i | ||||
\(455\) | −4.15207 | − | 2.98739i | −0.194652 | − | 0.140051i | ||||
\(456\) | −23.5353 | − | 3.76978i | −1.10214 | − | 0.176536i | ||||
\(457\) | − | 5.32640i | − | 0.249158i | −0.992210 | − | 0.124579i | \(-0.960242\pi\) | ||
0.992210 | − | 0.124579i | \(-0.0397581\pi\) | |||||||
\(458\) | −3.65876 | − | 4.06822i | −0.170962 | − | 0.190096i | ||||
\(459\) | −2.52725 | + | 2.52725i | −0.117962 | + | 0.117962i | ||||
\(460\) | −1.35529 | + | 1.09488i | −0.0631907 | + | 0.0510491i | ||||
\(461\) | −7.44077 | − | 7.44077i | −0.346551 | − | 0.346551i | 0.512272 | − | 0.858823i | \(-0.328804\pi\) |
−0.858823 | + | 0.512272i | \(0.828804\pi\) | |||||||
\(462\) | 8.52534 | + | 6.84676i | 0.396635 | + | 0.318540i | ||||
\(463\) | − | 35.4707i | − | 1.64846i | −0.566252 | − | 0.824232i | \(-0.691607\pi\) | ||
0.566252 | − | 0.824232i | \(-0.308393\pi\) | |||||||
\(464\) | 23.5861 | − | 15.2390i | 1.09496 | − | 0.707453i | ||||
\(465\) | 1.82264i | 0.0845228i | ||||||||
\(466\) | 12.6753 | + | 0.671686i | 0.587173 | + | 0.0311153i | ||||
\(467\) | 9.30469 | − | 9.30469i | 0.430570 | − | 0.430570i | −0.458252 | − | 0.888822i | \(-0.651524\pi\) |
0.888822 | + | 0.458252i | \(0.151524\pi\) | |||||||
\(468\) | −6.02373 | + | 4.86632i | −0.278447 | + | 0.224946i | ||||
\(469\) | −1.05471 | − | 6.46537i | −0.0487020 | − | 0.298543i | ||||
\(470\) | 0.254254 | + | 0.282708i | 0.0117279 | + | 0.0130404i | ||||
\(471\) | −10.6630 | −0.491325 | ||||||||
\(472\) | 23.7428 | − | 17.1869i | 1.09285 | − | 0.791091i | ||||
\(473\) | 19.4776i | 0.895583i | ||||||||
\(474\) | −1.75231 | + | 1.57594i | −0.0804862 | + | 0.0723853i | ||||
\(475\) | 28.3085 | + | 28.3085i | 1.29888 | + | 1.29888i | ||||
\(476\) | 12.6060 | − | 14.0983i | 0.577794 | − | 0.646193i | ||||
\(477\) | −1.52324 | + | 1.52324i | −0.0697443 | + | 0.0697443i | ||||
\(478\) | 29.0548 | + | 1.53966i | 1.32894 | + | 0.0704225i | ||||
\(479\) | 31.1329 | 1.42250 | 0.711250 | − | 0.702940i | \(-0.248130\pi\) | ||||
0.711250 | + | 0.702940i | \(0.248130\pi\) | |||||||
\(480\) | −2.72621 | − | 0.738998i | −0.124434 | − | 0.0337305i | ||||
\(481\) | 34.7526i | 1.58458i | ||||||||
\(482\) | 3.86808 | + | 0.204976i | 0.176186 | + | 0.00933641i | ||||
\(483\) | 4.55570 | − | 0.743183i | 0.207292 | − | 0.0338160i | ||||
\(484\) | 0.519984 | − | 4.89250i | 0.0236356 | − | 0.222386i | ||||
\(485\) | 5.49349 | + | 5.49349i | 0.249447 | + | 0.249447i | ||||
\(486\) | −0.945681 | − | 1.05152i | −0.0428970 | − | 0.0476977i | ||||
\(487\) | −32.7989 | −1.48626 | −0.743131 | − | 0.669146i | \(-0.766660\pi\) | ||||
−0.743131 | + | 0.669146i | \(0.766660\pi\) | |||||||
\(488\) | −13.4665 | + | 9.74809i | −0.609599 | + | 0.441275i | ||||
\(489\) | 14.5021 | 0.655808 | ||||||||
\(490\) | −2.43429 | + | 4.30207i | −0.109970 | + | 0.194348i | ||||
\(491\) | −6.83946 | + | 6.83946i | −0.308660 | + | 0.308660i | −0.844390 | − | 0.535729i | \(-0.820037\pi\) |
0.535729 | + | 0.844390i | \(0.320037\pi\) | |||||||
\(492\) | −9.79766 | + | 7.91512i | −0.441713 | + | 0.356841i | ||||
\(493\) | 17.7418 | + | 17.7418i | 0.799051 | + | 0.799051i | ||||
\(494\) | 2.44182 | − | 46.0793i | 0.109863 | − | 2.07320i | ||||
\(495\) | 1.45918 | 0.0655853 | ||||||||
\(496\) | −14.2747 | − | 3.06895i | −0.640954 | − | 0.137800i | ||||
\(497\) | 20.4251 | + | 14.6958i | 0.916192 | + | 0.659196i | ||||
\(498\) | 15.5802 | + | 0.825620i | 0.698165 | + | 0.0369969i | ||||
\(499\) | 6.96812 | + | 6.96812i | 0.311936 | + | 0.311936i | 0.845659 | − | 0.533723i | \(-0.179208\pi\) |
−0.533723 | + | 0.845659i | \(0.679208\pi\) | |||||||
\(500\) | 6.11916 | + | 7.57456i | 0.273657 | + | 0.338744i | ||||
\(501\) | −1.53785 | − | 1.53785i | −0.0687059 | − | 0.0687059i | ||||
\(502\) | 1.89791 | − | 1.70689i | 0.0847080 | − | 0.0761822i | ||||
\(503\) | 15.3570i | 0.684735i | 0.939566 | + | 0.342368i | \(0.111229\pi\) | ||||
−0.939566 | + | 0.342368i | \(0.888771\pi\) | |||||||
\(504\) | 5.30673 | + | 5.27623i | 0.236380 | + | 0.235022i | ||||
\(505\) | − | 7.65398i | − | 0.340598i | ||||||
\(506\) | 4.82150 | + | 5.36110i | 0.214342 | + | 0.238330i | ||||
\(507\) | −1.40827 | − | 1.40827i | −0.0625433 | − | 0.0625433i | ||||
\(508\) | −2.45567 | + | 23.1052i | −0.108953 | + | 1.02513i | ||||
\(509\) | −16.6366 | − | 16.6366i | −0.737403 | − | 0.737403i | 0.234672 | − | 0.972075i | \(-0.424598\pi\) |
−0.972075 | + | 0.234672i | \(0.924598\pi\) | |||||||
\(510\) | 0.133554 | − | 2.52029i | 0.00591388 | − | 0.111600i | ||||
\(511\) | −18.6305 | − | 13.4045i | −0.824163 | − | 0.592981i | ||||
\(512\) | 10.3781 | − | 20.1071i | 0.458653 | − | 0.888615i | ||||
\(513\) | 8.42705 | 0.372063 | ||||||||
\(514\) | 43.0555 | + | 2.28158i | 1.89910 | + | 0.100636i | ||||
\(515\) | 3.02424 | + | 3.02424i | 0.133264 | + | 0.133264i | ||||
\(516\) | −1.40883 | + | 13.2556i | −0.0620202 | + | 0.583545i | ||||
\(517\) | 1.11264 | − | 1.11264i | 0.0489339 | − | 0.0489339i | ||||
\(518\) | 33.3851 | − | 3.64555i | 1.46686 | − | 0.160176i | ||||
\(519\) | −7.64621 | −0.335631 | ||||||||
\(520\) | 0.864858 | − | 5.39944i | 0.0379265 | − | 0.236781i | ||||
\(521\) | 44.6141 | 1.95458 | 0.977290 | − | 0.211906i | \(-0.0679672\pi\) | ||||
0.977290 | + | 0.211906i | \(0.0679672\pi\) | |||||||
\(522\) | −7.38186 | + | 6.63887i | −0.323095 | + | 0.290576i | ||||
\(523\) | 9.34118 | + | 9.34118i | 0.408461 | + | 0.408461i | 0.881202 | − | 0.472741i | \(-0.156735\pi\) |
−0.472741 | + | 0.881202i | \(0.656735\pi\) | |||||||
\(524\) | −31.1201 | + | 25.1406i | −1.35949 | + | 1.09827i | ||||
\(525\) | −2.02368 | − | 12.4051i | −0.0883206 | − | 0.541404i | ||||
\(526\) | 0.480611 | − | 9.06956i | 0.0209556 | − | 0.395451i | ||||
\(527\) | − | 13.0462i | − | 0.568300i | ||||||
\(528\) | −2.45696 | + | 11.4282i | −0.106926 | + | 0.497347i | ||||
\(529\) | −19.9562 | −0.867660 | ||||||||
\(530\) | 0.0804965 | − | 1.51904i | 0.00349655 | − | 0.0659829i | ||||
\(531\) | −7.32765 | + | 7.32765i | −0.317993 | + | 0.317993i | ||||
\(532\) | −44.5223 | + | 2.48799i | −1.93029 | + | 0.107868i | ||||
\(533\) | −17.2421 | − | 17.2421i | −0.746837 | − | 0.746837i | ||||
\(534\) | −5.09229 | − | 5.66219i | −0.220365 | − | 0.245027i | ||||
\(535\) | − | 7.38615i | − | 0.319331i | ||||||
\(536\) | 5.67284 | − | 4.10644i | 0.245029 | − | 0.177371i | ||||
\(537\) | 2.01099 | 0.0867805 | ||||||||
\(538\) | 6.85978 | − | 6.16935i | 0.295746 | − | 0.265979i | ||||
\(539\) | 18.3118 | + | 9.11783i | 0.788747 | + | 0.392733i | ||||
\(540\) | 0.993051 | + | 0.105543i | 0.0427341 | + | 0.00454186i | ||||
\(541\) | 11.7558 | − | 11.7558i | 0.505423 | − | 0.505423i | −0.407695 | − | 0.913118i | \(-0.633667\pi\) |
0.913118 | + | 0.407695i | \(0.133667\pi\) | |||||||
\(542\) | −1.45983 | + | 27.5483i | −0.0627052 | + | 1.18330i | ||||
\(543\) | 20.1211i | 0.863479i | ||||||||
\(544\) | 19.5138 | + | 5.28964i | 0.836646 | + | 0.226791i | ||||
\(545\) | 0.526813i | 0.0225662i | ||||||||
\(546\) | −9.07153 | + | 11.2956i | −0.388226 | + | 0.483405i | ||||
\(547\) | 2.81777 | + | 2.81777i | 0.120479 | + | 0.120479i | 0.764776 | − | 0.644297i | \(-0.222850\pi\) |
−0.644297 | + | 0.764776i | \(0.722850\pi\) | |||||||
\(548\) | −0.545681 | + | 5.13428i | −0.0233103 | + | 0.219326i | ||||
\(549\) | 4.15611 | − | 4.15611i | 0.177378 | − | 0.177378i | ||||
\(550\) | 14.5982 | − | 13.1289i | 0.622470 | − | 0.559819i | ||||
\(551\) | − | 59.1596i | − | 2.52028i | ||||||
\(552\) | 2.89352 | + | 3.99726i | 0.123157 | + | 0.170135i | ||||
\(553\) | −2.57503 | + | 3.57894i | −0.109501 | + | 0.152192i | ||||
\(554\) | 8.93744 | − | 8.03789i | 0.379715 | − | 0.341497i | ||||
\(555\) | 3.16905 | − | 3.16905i | 0.134519 | − | 0.134519i | ||||
\(556\) | 18.2104 | + | 22.5416i | 0.772294 | + | 0.955977i | ||||
\(557\) | −4.72518 | + | 4.72518i | −0.200212 | + | 0.200212i | −0.800091 | − | 0.599879i | \(-0.795216\pi\) |
0.599879 | + | 0.800091i | \(0.295216\pi\) | |||||||
\(558\) | 5.15496 | + | 0.273170i | 0.218227 | + | 0.0115642i | ||||
\(559\) | −25.8067 | −1.09151 | ||||||||
\(560\) | −5.27771 | − | 0.264426i | −0.223024 | − | 0.0111740i | ||||
\(561\) | −10.4446 | −0.440971 | ||||||||
\(562\) | −6.70863 | − | 0.355502i | −0.282987 | − | 0.0149959i | ||||
\(563\) | 15.3342 | − | 15.3342i | 0.646258 | − | 0.646258i | −0.305829 | − | 0.952087i | \(-0.598933\pi\) |
0.952087 | + | 0.305829i | \(0.0989335\pi\) | |||||||
\(564\) | 0.837690 | − | 0.676735i | 0.0352731 | − | 0.0284957i | ||||
\(565\) | 0.434328 | − | 0.434328i | 0.0182723 | − | 0.0182723i | ||||
\(566\) | 4.03341 | − | 3.62745i | 0.169537 | − | 0.152473i | ||||
\(567\) | −2.14763 | − | 1.54521i | −0.0901921 | − | 0.0648927i | ||||
\(568\) | −4.25447 | + | 26.5613i | −0.178514 | + | 1.11449i | ||||
\(569\) | − | 23.2208i | − | 0.973465i | −0.873551 | − | 0.486733i | \(-0.838189\pi\) | ||
0.873551 | − | 0.486733i | \(-0.161811\pi\) | |||||||
\(570\) | −4.42458 | + | 3.97925i | −0.185325 | + | 0.166672i | ||||
\(571\) | 8.47744 | − | 8.47744i | 0.354770 | − | 0.354770i | −0.507111 | − | 0.861881i | \(-0.669287\pi\) |
0.861881 | + | 0.507111i | \(0.169287\pi\) | |||||||
\(572\) | −22.5031 | − | 2.39167i | −0.940903 | − | 0.100001i | ||||
\(573\) | −8.15676 | − | 8.15676i | −0.340754 | − | 0.340754i | ||||
\(574\) | −14.7549 | + | 18.3723i | −0.615860 | + | 0.766847i | ||||
\(575\) | − | 8.28829i | − | 0.345646i | ||||||
\(576\) | −2.49870 | + | 7.59977i | −0.104113 | + | 0.316657i | ||||
\(577\) | − | 24.4767i | − | 1.01898i | −0.860477 | − | 0.509489i | \(-0.829834\pi\) | ||
0.860477 | − | 0.509489i | \(-0.170166\pi\) | |||||||
\(578\) | 0.316260 | − | 5.96811i | 0.0131547 | − | 0.248241i | ||||
\(579\) | 9.03769 | − | 9.03769i | 0.375594 | − | 0.375594i | ||||
\(580\) | 0.740935 | − | 6.97142i | 0.0307656 | − | 0.289472i | ||||
\(581\) | 28.8079 | − | 4.69951i | 1.19515 | − | 0.194969i | ||||
\(582\) | 16.3606 | − | 14.7139i | 0.678168 | − | 0.609911i | ||||
\(583\) | −6.29522 | −0.260721 | ||||||||
\(584\) | 3.88064 | − | 24.2274i | 0.160582 | − | 1.00254i | ||||
\(585\) | 1.93332i | 0.0799331i | ||||||||
\(586\) | −17.3575 | − | 19.3000i | −0.717031 | − | 0.797277i | ||||
\(587\) | −23.2347 | − | 23.2347i | −0.958999 | − | 0.958999i | 0.0401932 | − | 0.999192i | \(-0.487203\pi\) |
−0.999192 | + | 0.0401932i | \(0.987203\pi\) | |||||||
\(588\) | 11.8027 | + | 7.52968i | 0.486735 | + | 0.310519i | ||||
\(589\) | −21.7510 | + | 21.7510i | −0.896236 | + | 0.896236i | ||||
\(590\) | 0.387235 | − | 7.30746i | 0.0159422 | − | 0.300843i | ||||
\(591\) | 16.3340 | 0.671890 | ||||||||
\(592\) | 19.4836 | + | 30.1557i | 0.800773 | + | 1.23939i | ||||
\(593\) | 9.36212i | 0.384456i | 0.981350 | + | 0.192228i | \(0.0615714\pi\) | ||||
−0.981350 | + | 0.192228i | \(0.938429\pi\) | |||||||
\(594\) | 0.218697 | − | 4.12700i | 0.00897323 | − | 0.169333i | ||||
\(595\) | −0.760204 | − | 4.66004i | −0.0311653 | − | 0.191043i | ||||
\(596\) | 29.2010 | + | 36.1462i | 1.19612 | + | 1.48061i | ||||
\(597\) | −1.90328 | − | 1.90328i | −0.0778963 | − | 0.0778963i | ||||
\(598\) | −7.10312 | + | 6.38820i | −0.290468 | + | 0.261233i | ||||
\(599\) | −40.1015 | −1.63850 | −0.819251 | − | 0.573435i | \(-0.805611\pi\) | ||||
−0.819251 | + | 0.573435i | \(0.805611\pi\) | |||||||
\(600\) | 10.8845 | − | 7.87904i | 0.444358 | − | 0.321660i | ||||
\(601\) | −6.55291 | −0.267299 | −0.133649 | − | 0.991029i | \(-0.542670\pi\) | ||||
−0.133649 | + | 0.991029i | \(0.542670\pi\) | |||||||
\(602\) | 2.70712 | + | 24.7912i | 0.110334 | + | 1.01042i | ||||
\(603\) | −1.75078 | + | 1.75078i | −0.0712974 | + | 0.0712974i | ||||
\(604\) | −21.2541 | − | 2.25892i | −0.864816 | − | 0.0919141i | ||||
\(605\) | −0.868572 | − | 0.868572i | −0.0353125 | − | 0.0353125i | ||||
\(606\) | −21.6477 | − | 1.14715i | −0.879379 | − | 0.0465998i | ||||
\(607\) | −8.02925 | −0.325897 | −0.162949 | − | 0.986635i | \(-0.552100\pi\) | ||||
−0.162949 | + | 0.986635i | \(0.552100\pi\) | |||||||
\(608\) | −23.7150 | − | 41.3532i | −0.961770 | − | 1.67709i | ||||
\(609\) | −10.8477 | + | 15.0768i | −0.439570 | + | 0.610943i | ||||
\(610\) | −0.219632 | + | 4.14466i | −0.00889265 | + | 0.167812i | ||||
\(611\) | 1.47418 | + | 1.47418i | 0.0596390 | + | 0.0596390i | ||||
\(612\) | −7.10811 | − | 0.755463i | −0.287328 | − | 0.0305378i | ||||
\(613\) | −25.1899 | − | 25.1899i | −1.01741 | − | 1.01741i | −0.999846 | − | 0.0175663i | \(-0.994408\pi\) |
−0.0175663 | − | 0.999846i | \(-0.505592\pi\) | |||||||
\(614\) | 17.6757 | + | 19.6539i | 0.713334 | + | 0.793166i | ||||
\(615\) | 3.14457i | 0.126801i | ||||||||
\(616\) | 0.0630170 | + | 21.8686i | 0.00253903 | + | 0.881110i | ||||
\(617\) | − | 4.23466i | − | 0.170481i | −0.996360 | − | 0.0852406i | \(-0.972834\pi\) | ||
0.996360 | − | 0.0852406i | \(-0.0271659\pi\) | |||||||
\(618\) | 9.00671 | − | 8.10018i | 0.362303 | − | 0.325837i | ||||
\(619\) | −34.1958 | − | 34.1958i | −1.37445 | − | 1.37445i | −0.853730 | − | 0.520716i | \(-0.825665\pi\) |
−0.520716 | − | 0.853730i | \(-0.674335\pi\) | |||||||
\(620\) | −2.83558 | + | 2.29074i | −0.113880 | + | 0.0919985i | ||||
\(621\) | −1.23366 | − | 1.23366i | −0.0495050 | − | 0.0495050i | ||||
\(622\) | 33.8073 | + | 1.79151i | 1.35555 | + | 0.0718329i | ||||
\(623\) | −11.5645 | − | 8.32062i | −0.463324 | − | 0.333359i | ||||
\(624\) | −15.1416 | − | 3.25533i | −0.606149 | − | 0.130317i | ||||
\(625\) | −21.3223 | −0.852893 | ||||||||
\(626\) | −0.722289 | + | 13.6302i | −0.0288685 | + | 0.544774i | ||||
\(627\) | 17.4136 | + | 17.4136i | 0.695433 | + | 0.695433i | ||||
\(628\) | −13.4016 | − | 16.5890i | −0.534781 | − | 0.661975i | ||||
\(629\) | −22.6836 | + | 22.6836i | −0.904453 | + | 0.904453i | ||||
\(630\) | 1.85725 | − | 0.202806i | 0.0739947 | − | 0.00807999i | ||||
\(631\) | −13.8558 | −0.551590 | −0.275795 | − | 0.961216i | \(-0.588941\pi\) | ||||
−0.275795 | + | 0.961216i | \(0.588941\pi\) | |||||||
\(632\) | −4.65413 | − | 0.745478i | −0.185131 | − | 0.0296535i | ||||
\(633\) | 17.6276 | 0.700635 | ||||||||
\(634\) | −2.73837 | − | 3.04483i | −0.108754 | − | 0.120926i | ||||
\(635\) | 4.10190 | + | 4.10190i | 0.162779 | + | 0.162779i | ||||
\(636\) | −4.28424 | − | 0.455336i | −0.169881 | − | 0.0180553i | ||||
\(637\) | −12.0806 | + | 24.2621i | −0.478649 | + | 0.961298i | ||||
\(638\) | −28.9724 | − | 1.53529i | −1.14703 | − | 0.0607828i | ||||
\(639\) | − | 9.51053i | − | 0.376231i | ||||||
\(640\) | −2.27668 | − | 5.17011i | −0.0899936 | − | 0.204367i | ||||
\(641\) | 46.9366 | 1.85388 | 0.926942 | − | 0.375204i | \(-0.122427\pi\) | ||||
0.926942 | + | 0.375204i | \(0.122427\pi\) | |||||||
\(642\) | −20.8902 | − | 1.10701i | −0.824472 | − | 0.0436901i | ||||
\(643\) | 2.57173 | − | 2.57173i | 0.101419 | − | 0.101419i | −0.654577 | − | 0.755996i | \(-0.727153\pi\) |
0.755996 | + | 0.654577i | \(0.227153\pi\) | |||||||
\(644\) | 6.88195 | + | 6.15351i | 0.271187 | + | 0.242482i | ||||
\(645\) | 2.35328 | + | 2.35328i | 0.0926604 | + | 0.0926604i | ||||
\(646\) | 31.6705 | − | 28.4829i | 1.24606 | − | 1.12064i | ||||
\(647\) | − | 43.5484i | − | 1.71206i | −0.516924 | − | 0.856031i | \(-0.672923\pi\) | ||
0.516924 | − | 0.856031i | \(-0.327077\pi\) | |||||||
\(648\) | 0.447343 | − | 2.79283i | 0.0175733 | − | 0.109713i | ||||
\(649\) | −30.2836 | −1.18874 | ||||||||
\(650\) | 17.3950 | + | 19.3417i | 0.682288 | + | 0.758645i | ||||
\(651\) | 9.53158 | − | 1.55491i | 0.373572 | − | 0.0609418i | ||||
\(652\) | 18.2267 | + | 22.5618i | 0.713812 | + | 0.883587i | ||||
\(653\) | −33.5572 | + | 33.5572i | −1.31320 | + | 1.31320i | −0.394150 | + | 0.919046i | \(0.628961\pi\) |
−0.919046 | + | 0.394150i | \(0.871039\pi\) | |||||||
\(654\) | 1.48998 | + | 0.0789567i | 0.0582630 | + | 0.00308745i | ||||
\(655\) | 9.98805i | 0.390265i | ||||||||
\(656\) | −24.6280 | − | 5.29482i | −0.961561 | − | 0.206728i | ||||
\(657\) | 8.67488i | 0.338439i | ||||||||
\(658\) | 1.26153 | − | 1.57082i | 0.0491797 | − | 0.0612368i | ||||
\(659\) | −7.90569 | − | 7.90569i | −0.307962 | − | 0.307962i | 0.536157 | − | 0.844119i | \(-0.319876\pi\) |
−0.844119 | + | 0.536157i | \(0.819876\pi\) | |||||||
\(660\) | 1.83394 | + | 2.27013i | 0.0713861 | + | 0.0883647i | ||||
\(661\) | −17.8307 | + | 17.8307i | −0.693532 | + | 0.693532i | −0.963007 | − | 0.269475i | \(-0.913150\pi\) |
0.269475 | + | 0.963007i | \(0.413150\pi\) | |||||||
\(662\) | 5.97099 | + | 6.63923i | 0.232069 | + | 0.258041i | ||||
\(663\) | − | 13.8384i | − | 0.537440i | ||||||
\(664\) | 18.2972 | + | 25.2766i | 0.710068 | + | 0.980924i | ||||
\(665\) | −6.50195 | + | 9.03684i | −0.252135 | + | 0.350433i | ||||
\(666\) | −8.48805 | − | 9.43798i | −0.328905 | − | 0.365714i | ||||
\(667\) | −8.66052 | + | 8.66052i | −0.335337 | + | 0.335337i | ||||
\(668\) | 0.459703 | − | 4.32532i | 0.0177864 | − | 0.167352i | ||||
\(669\) | −8.98851 | + | 8.98851i | −0.347516 | + | 0.347516i | ||||
\(670\) | 0.0925213 | − | 1.74596i | 0.00357441 | − | 0.0674523i | ||||
\(671\) | 17.1763 | 0.663084 | ||||||||
\(672\) | −1.53888 | + | 14.8873i | −0.0593635 | + | 0.574290i | ||||
\(673\) | 36.1564 | 1.39373 | 0.696864 | − | 0.717203i | \(-0.254578\pi\) | ||||
0.696864 | + | 0.717203i | \(0.254578\pi\) | |||||||
\(674\) | −0.832142 | + | 15.7033i | −0.0320529 | + | 0.604867i | ||||
\(675\) | −3.35924 | + | 3.35924i | −0.129297 | + | 0.129297i | ||||
\(676\) | 0.420968 | − | 3.96087i | 0.0161911 | − | 0.152341i | ||||
\(677\) | 12.4463 | − | 12.4463i | 0.478351 | − | 0.478351i | −0.426253 | − | 0.904604i | \(-0.640167\pi\) |
0.904604 | + | 0.426253i | \(0.140167\pi\) | |||||||
\(678\) | −1.16331 | − | 1.29351i | −0.0446768 | − | 0.0496768i | ||||
\(679\) | 24.0420 | − | 33.4151i | 0.922647 | − | 1.28235i | ||||
\(680\) | 4.08881 | − | 2.95980i | 0.156799 | − | 0.113503i | ||||
\(681\) | − | 15.5552i | − | 0.596075i | ||||||
\(682\) | 10.0877 | + | 11.2167i | 0.386278 | + | 0.429508i | ||||
\(683\) | 6.11759 | − | 6.11759i | 0.234083 | − | 0.234083i | −0.580312 | − | 0.814395i | \(-0.697069\pi\) |
0.814395 | + | 0.580312i | \(0.197069\pi\) | |||||||
\(684\) | 10.5914 | + | 13.1104i | 0.404971 | + | 0.501290i | ||||
\(685\) | 0.911496 | + | 0.911496i | 0.0348265 | + | 0.0348265i | ||||
\(686\) | 24.5747 | + | 9.06013i | 0.938265 | + | 0.345917i | ||||
\(687\) | 3.86891i | 0.147608i | ||||||||
\(688\) | −22.3931 | + | 14.4682i | −0.853730 | + | 0.551596i | ||||
\(689\) | − | 8.34078i | − | 0.317758i | ||||||
\(690\) | 1.23026 | + | 0.0651934i | 0.0468351 | + | 0.00248187i | ||||
\(691\) | 27.1676 | − | 27.1676i | 1.03350 | − | 1.03350i | 0.0340857 | − | 0.999419i | \(-0.489148\pi\) |
0.999419 | − | 0.0340857i | \(-0.0108519\pi\) | |||||||
\(692\) | −9.60998 | − | 11.8956i | −0.365317 | − | 0.452204i | ||||
\(693\) | −1.24484 | − | 7.63087i | −0.0472877 | − | 0.289873i | ||||
\(694\) | 3.42411 | + | 3.80732i | 0.129978 | + | 0.144524i | ||||
\(695\) | 7.23476 | 0.274430 | ||||||||
\(696\) | −19.6062 | − | 3.14044i | −0.743171 | − | 0.119038i | ||||
\(697\) | − | 22.5084i | − | 0.852565i | ||||||
\(698\) | −23.0027 | + | 20.6875i | −0.870667 | + | 0.783034i | ||||
\(699\) | −6.34655 | − | 6.34655i | −0.240049 | − | 0.240049i | ||||
\(700\) | 16.7559 | − | 18.7395i | 0.633315 | − | 0.708286i | ||||
\(701\) | 29.1131 | − | 29.1131i | 1.09959 | − | 1.09959i | 0.105127 | − | 0.994459i | \(-0.466475\pi\) |
0.994459 | − | 0.105127i | \(-0.0335248\pi\) | |||||||
\(702\) | 5.46802 | + | 0.289759i | 0.206377 | + | 0.0109363i | ||||
\(703\) | 75.6377 | 2.85273 | ||||||||
\(704\) | −20.8674 | + | 10.5408i | −0.786471 | + | 0.397272i | ||||
\(705\) | − | 0.268858i | − | 0.0101258i | ||||||
\(706\) | −30.3898 | − | 1.61041i | −1.14373 | − | 0.0606084i | ||||
\(707\) | −40.0269 | + | 6.52969i | −1.50537 | + | 0.245574i | ||||
\(708\) | −20.6096 | − | 2.19043i | −0.774558 | − | 0.0823214i | ||||
\(709\) | 17.0893 | + | 17.0893i | 0.641803 | + | 0.641803i | 0.950998 | − | 0.309196i | \(-0.100060\pi\) |
−0.309196 | + | 0.950998i | \(0.600060\pi\) | |||||||
\(710\) | 4.49087 | + | 4.99346i | 0.168539 | + | 0.187401i | ||||
\(711\) | 1.66646 | 0.0624971 | ||||||||
\(712\) | 2.40884 | − | 15.0388i | 0.0902752 | − | 0.563602i | ||||
\(713\) | 6.36838 | 0.238498 | ||||||||
\(714\) | −13.2939 | + | 1.45166i | −0.497513 | + | 0.0543268i | ||||
\(715\) | −3.99501 | + | 3.99501i | −0.149405 | + | 0.149405i | ||||
\(716\) | 2.52747 | + | 3.12861i | 0.0944560 | + | 0.116922i | ||||
\(717\) | −14.5478 | − | 14.5478i | −0.543297 | − | 0.543297i | ||||
\(718\) | −2.16577 | + | 40.8699i | −0.0808256 | + | 1.52525i | ||||
\(719\) | −41.2461 | −1.53822 | −0.769109 | − | 0.639117i | \(-0.779300\pi\) | ||||
−0.769109 | + | 0.639117i | \(0.779300\pi\) | |||||||
\(720\) | 1.08390 | + | 1.67760i | 0.0403945 | + | 0.0625203i | ||||
\(721\) | 13.2354 | − | 18.3954i | 0.492913 | − | 0.685082i | ||||
\(722\) | −73.4575 | − | 3.89264i | −2.73381 | − | 0.144869i | ||||
\(723\) | −1.93675 | − | 1.93675i | −0.0720287 | − | 0.0720287i | ||||
\(724\) | −31.3035 | + | 25.2888i | −1.16339 | + | 0.939851i | ||||
\(725\) | 23.5825 | + | 23.5825i | 0.875833 | + | 0.875833i | ||||
\(726\) | −2.58676 | + | 2.32640i | −0.0960037 | + | 0.0863409i | ||||
\(727\) | 1.60524i | 0.0595352i | 0.999557 | + | 0.0297676i | \(0.00947672\pi\) | ||||
−0.999557 | + | 0.0297676i | \(0.990523\pi\) | |||||||
\(728\) | −28.9745 | + | 0.0834937i | −1.07387 | + | 0.00309448i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | −4.09628 | − | 4.55471i | −0.151610 | − | 0.168577i | ||||
\(731\) | −16.8444 | − | 16.8444i | −0.623014 | − | 0.623014i | ||||
\(732\) | 11.6894 | + | 1.24237i | 0.432053 | + | 0.0459194i | ||||
\(733\) | −6.18188 | − | 6.18188i | −0.228333 | − | 0.228333i | 0.583663 | − | 0.811996i | \(-0.301619\pi\) |
−0.811996 | + | 0.583663i | \(0.801619\pi\) | |||||||
\(734\) | 0.422925 | − | 7.98097i | 0.0156104 | − | 0.294583i | ||||
\(735\) | 3.31404 | − | 1.11082i | 0.122240 | − | 0.0409731i | ||||
\(736\) | −2.58209 | + | 9.52549i | −0.0951773 | + | 0.351114i | ||||
\(737\) | −7.23562 | −0.266527 | ||||||||
\(738\) | 8.89379 | + | 0.471297i | 0.327385 | + | 0.0173487i | ||||
\(739\) | −8.69821 | − | 8.69821i | −0.319969 | − | 0.319969i | 0.528786 | − | 0.848755i | \(-0.322647\pi\) |
−0.848755 | + | 0.528786i | \(0.822647\pi\) | |||||||
\(740\) | 8.91322 | + | 0.947313i | 0.327656 | + | 0.0348239i | ||||
\(741\) | −23.0720 | + | 23.0720i | −0.847569 | + | 0.847569i | ||||
\(742\) | −8.01259 | + | 0.874949i | −0.294151 | + | 0.0321204i | ||||
\(743\) | −41.3906 | −1.51847 | −0.759236 | − | 0.650815i | \(-0.774427\pi\) | ||||
−0.759236 | + | 0.650815i | \(0.774427\pi\) | |||||||
\(744\) | 6.05392 | + | 8.36319i | 0.221948 | + | 0.306610i | ||||
\(745\) | 11.6012 | 0.425034 | ||||||||
\(746\) | 19.8633 | − | 17.8641i | 0.727247 | − | 0.654050i | ||||
\(747\) | −7.80102 | − | 7.80102i | −0.285424 | − | 0.285424i | ||||
\(748\) | −13.1271 | − | 16.2492i | −0.479973 | − | 0.594131i | ||||
\(749\) | −38.6263 | + | 6.30120i | −1.41137 | + | 0.230241i | ||||
\(750\) | 0.364359 | − | 6.87578i | 0.0133045 | − | 0.251068i | ||||
\(751\) | 37.5813i | 1.37136i | 0.727903 | + | 0.685680i | \(0.240495\pi\) | ||||
−0.727903 | + | 0.685680i | \(0.759505\pi\) | |||||||
\(752\) | 2.10567 | + | 0.452702i | 0.0767858 | + | 0.0165083i | ||||
\(753\) | −1.80493 | −0.0657753 | ||||||||
\(754\) | 2.03417 | − | 38.3866i | 0.0740801 | − | 1.39796i | ||||
\(755\) | −3.77326 | + | 3.77326i | −0.137323 | + | 0.137323i | ||||
\(756\) | −0.295238 | − | 5.28326i | −0.0107377 | − | 0.192150i | ||||
\(757\) | 35.7246 | + | 35.7246i | 1.29843 | + | 1.29843i | 0.929428 | + | 0.369002i | \(0.120301\pi\) |
0.369002 | + | 0.929428i | \(0.379699\pi\) | |||||||
\(758\) | 16.4960 | + | 18.3421i | 0.599162 | + | 0.666216i | ||||
\(759\) | − | 5.09844i | − | 0.185062i | ||||||
\(760\) | −11.7517 | − | 1.88233i | −0.426279 | − | 0.0682794i | ||||
\(761\) | 45.5380 | 1.65075 | 0.825375 | − | 0.564585i | \(-0.190964\pi\) | ||||
0.825375 | + | 0.564585i | \(0.190964\pi\) | |||||||
\(762\) | 12.2162 | − | 10.9866i | 0.442546 | − | 0.398004i | ||||
\(763\) | 2.75500 | − | 0.449430i | 0.0997376 | − | 0.0162704i | ||||
\(764\) | 2.43827 | − | 22.9416i | 0.0882137 | − | 0.829998i | ||||
\(765\) | −1.26191 | + | 1.26191i | −0.0456245 | + | 0.0456245i | ||||
\(766\) | 0.339529 | − | 6.40721i | 0.0122677 | − | 0.231502i | ||||
\(767\) | − | 40.1239i | − | 1.44879i | ||||||
\(768\) | −14.9638 | + | 5.66425i | −0.539961 | + | 0.204391i | ||||
\(769\) | 6.07515i | 0.219075i | 0.993983 | + | 0.109538i | \(0.0349370\pi\) | ||||
−0.993983 | + | 0.109538i | \(0.965063\pi\) | |||||||
\(770\) | 4.25689 | + | 3.41874i | 0.153408 | + | 0.123203i | ||||
\(771\) | −21.5579 | − | 21.5579i | −0.776390 | − | 0.776390i | ||||
\(772\) | 25.4193 | + | 2.70161i | 0.914860 | + | 0.0972330i | ||||
\(773\) | −26.1824 | + | 26.1824i | −0.941716 | + | 0.941716i | −0.998393 | − | 0.0566766i | \(-0.981950\pi\) |
0.0566766 | + | 0.998393i | \(0.481950\pi\) | |||||||
\(774\) | 7.00848 | − | 6.30308i | 0.251915 | − | 0.226560i | ||||
\(775\) | − | 17.3410i | − | 0.622908i | ||||||
\(776\) | 43.4537 | + | 6.96022i | 1.55990 | + | 0.249857i | ||||
\(777\) | −19.2763 | − | 13.8692i | −0.691532 | − | 0.497554i | ||||
\(778\) | 24.5981 | − | 22.1223i | 0.881884 | − | 0.793123i | ||||
\(779\) | −37.5268 | + | 37.5268i | −1.34454 | + | 1.34454i | ||||
\(780\) | −3.00778 | + | 2.42986i | −0.107696 | + | 0.0870029i | ||||
\(781\) | 19.6525 | − | 19.6525i | 0.703222 | − | 0.703222i | ||||
\(782\) | −8.80600 | − | 0.466645i | −0.314902 | − | 0.0166872i | ||||
\(783\) | 7.02020 | 0.250882 | ||||||||
\(784\) | 3.11964 | + | 27.8257i | 0.111416 | + | 0.993774i | ||||
\(785\) | −5.32427 | −0.190031 | ||||||||
\(786\) | 28.2492 | + | 1.49697i | 1.00761 | + | 0.0533952i | ||||
\(787\) | −3.92778 | + | 3.92778i | −0.140010 | + | 0.140010i | −0.773638 | − | 0.633628i | \(-0.781565\pi\) |
0.633628 | + | 0.773638i | \(0.281565\pi\) | |||||||
\(788\) | 20.5290 | + | 25.4117i | 0.731317 | + | 0.905255i | ||||
\(789\) | −4.54114 | + | 4.54114i | −0.161669 | + | 0.161669i | ||||
\(790\) | −0.874967 | + | 0.786902i | −0.0311299 | + | 0.0279967i | ||||
\(791\) | −2.64187 | − | 1.90081i | −0.0939342 | − | 0.0675852i | ||||
\(792\) | 6.69547 | − | 4.84670i | 0.237913 | − | 0.172220i | ||||
\(793\) | 22.7576i | 0.808144i | ||||||||
\(794\) | −3.17371 | + | 2.85427i | −0.112631 | + | 0.101294i | ||||
\(795\) | −0.760586 | + | 0.760586i | −0.0269752 | + | 0.0269752i | ||||
\(796\) | 0.568943 | − | 5.35315i | 0.0201656 | − | 0.189737i | ||||
\(797\) | 34.0489 | + | 34.0489i | 1.20608 | + | 1.20608i | 0.972288 | + | 0.233788i | \(0.0751122\pi\) |
0.233788 | + | 0.972288i | \(0.424888\pi\) | |||||||
\(798\) | 24.5844 | + | 19.7439i | 0.870278 | + | 0.698926i | ||||
\(799\) | 1.92444i | 0.0680819i | ||||||||
\(800\) | 25.9378 | + | 7.03102i | 0.917041 | + | 0.248584i | ||||
\(801\) | 5.38478i | 0.190262i | ||||||||
\(802\) | −0.610420 | + | 11.5192i | −0.0215547 | + | 0.406756i | ||||
\(803\) | −17.9257 | + | 17.9257i | −0.632585 | + | 0.632585i | ||||
\(804\) | −4.92423 | − | 0.523356i | −0.173664 | − | 0.0184573i | ||||
\(805\) | 2.27476 | − | 0.371088i | 0.0801749 | − | 0.0130791i | ||||
\(806\) | −14.8614 | + | 13.3656i | −0.523470 | + | 0.470783i | ||||
\(807\) | −6.52370 | −0.229645 | ||||||||
\(808\) | −25.4228 | − | 35.1204i | −0.894372 | − | 1.23553i | ||||
\(809\) | 53.0107i | 1.86376i | 0.362772 | + | 0.931878i | \(0.381830\pi\) | ||||
−0.362772 | + | 0.931878i | \(0.618170\pi\) | |||||||
\(810\) | −0.472200 | − | 0.525045i | −0.0165914 | − | 0.0184482i | ||||
\(811\) | 12.0779 | + | 12.0779i | 0.424114 | + | 0.424114i | 0.886617 | − | 0.462504i | \(-0.153049\pi\) |
−0.462504 | + | 0.886617i | \(0.653049\pi\) | |||||||
\(812\) | −37.0895 | + | 2.07263i | −1.30159 | + | 0.0727351i | ||||
\(813\) | 13.7935 | − | 13.7935i | 0.483759 | − | 0.483759i | ||||
\(814\) | 1.96293 | − | 37.0422i | 0.0688007 | − | 1.29833i | ||||
\(815\) | 7.24123 | 0.253649 | ||||||||
\(816\) | −7.75837 | − | 12.0080i | −0.271597 | − | 0.420363i | ||||
\(817\) | 56.1673i | 1.96505i | ||||||||
\(818\) | 0.938622 | − | 17.7126i | 0.0328182 | − | 0.619308i | ||||
\(819\) | 10.1104 | − | 1.64934i | 0.353287 | − | 0.0576326i | ||||
\(820\) | −4.89219 | + | 3.95219i | −0.170843 | + | 0.138017i | ||||
\(821\) | −9.63963 | − | 9.63963i | −0.336425 | − | 0.336425i | 0.518595 | − | 0.855020i | \(-0.326455\pi\) |
−0.855020 | + | 0.518595i | \(0.826455\pi\) | |||||||
\(822\) | 2.71460 | − | 2.44137i | 0.0946824 | − | 0.0851526i | ||||
\(823\) | 9.83217 | 0.342728 | 0.171364 | − | 0.985208i | \(-0.445183\pi\) | ||||
0.171364 | + | 0.985208i | \(0.445183\pi\) | |||||||
\(824\) | 23.9218 | + | 3.83169i | 0.833356 | + | 0.133483i | ||||
\(825\) | −13.8830 | −0.483345 | ||||||||
\(826\) | −38.5451 | + | 4.20901i | −1.34116 | + | 0.146450i | ||||
\(827\) | 22.5314 | − | 22.5314i | 0.783492 | − | 0.783492i | −0.196926 | − | 0.980418i | \(-0.563096\pi\) |
0.980418 | + | 0.196926i | \(0.0630959\pi\) | |||||||
\(828\) | 0.368773 | − | 3.46977i | 0.0128158 | − | 0.120583i | ||||
\(829\) | −16.6214 | − | 16.6214i | −0.577286 | − | 0.577286i | 0.356869 | − | 0.934155i | \(-0.383844\pi\) |
−0.934155 | + | 0.356869i | \(0.883844\pi\) | |||||||
\(830\) | 7.77953 | + | 0.412250i | 0.270031 | + | 0.0143094i | ||||
\(831\) | −8.49957 | −0.294847 | ||||||||
\(832\) | −13.9659 | − | 27.6480i | −0.484182 | − | 0.958524i | ||||
\(833\) | −23.7214 | + | 7.95107i | −0.821899 | + | 0.275488i | ||||
\(834\) | 1.08432 | − | 20.4621i | 0.0375469 | − | 0.708543i | ||||
\(835\) | −0.767880 | − | 0.767880i | −0.0265736 | − | 0.0265736i | ||||
\(836\) | −5.20539 | + | 48.9773i | −0.180032 | + | 1.69391i | ||||
\(837\) | −2.58110 | − | 2.58110i | −0.0892158 | − | 0.0892158i | ||||
\(838\) | 24.1284 | + | 26.8287i | 0.833503 | + | 0.926784i | ||||
\(839\) | 32.5829i | 1.12489i | 0.826836 | + | 0.562444i | \(0.190139\pi\) | ||||
−0.826836 | + | 0.562444i | \(0.809861\pi\) | |||||||
\(840\) | 2.64977 | + | 2.63454i | 0.0914256 | + | 0.0909003i | ||||
\(841\) | − | 20.2832i | − | 0.699421i | ||||||
\(842\) | −0.0900719 | + | 0.0810062i | −0.00310408 | + | 0.00279166i | ||||
\(843\) | 3.35902 | + | 3.35902i | 0.115691 | + | 0.115691i | ||||
\(844\) | 22.1549 | + | 27.4243i | 0.762603 | + | 0.943982i | ||||
\(845\) | −0.703178 | − | 0.703178i | −0.0241901 | − | 0.0241901i | ||||
\(846\) | −0.760410 | − | 0.0402954i | −0.0261434 | − | 0.00138538i | ||||
\(847\) | −3.80126 | + | 5.28324i | −0.130613 | + | 0.181534i | ||||
\(848\) | −4.67617 | − | 7.23751i | −0.160580 | − | 0.248537i | ||||
\(849\) | −3.83581 | −0.131645 | ||||||||
\(850\) | −1.27067 | + | 23.9787i | −0.0435836 | + | 0.822461i | ||||
\(851\) | −11.0728 | − | 11.0728i | −0.379571 | − | 0.379571i | ||||
\(852\) | 14.7961 | − | 11.9531i | 0.506905 | − | 0.409507i | ||||
\(853\) | −7.56835 | + | 7.56835i | −0.259135 | + | 0.259135i | −0.824702 | − | 0.565567i | \(-0.808657\pi\) |
0.565567 | + | 0.824702i | \(0.308657\pi\) | |||||||
\(854\) | 21.8621 | − | 2.38727i | 0.748106 | − | 0.0816908i | ||||
\(855\) | 4.20781 | 0.143904 | ||||||||
\(856\) | −24.5332 | − | 33.8914i | −0.838529 | − | 1.15839i | ||||
\(857\) | −31.0643 | −1.06114 | −0.530568 | − | 0.847642i | \(-0.678021\pi\) | ||||
−0.530568 | + | 0.847642i | \(0.678021\pi\) | |||||||
\(858\) | 10.7003 | + | 11.8978i | 0.365303 | + | 0.406185i | ||||
\(859\) | 3.62803 | + | 3.62803i | 0.123787 | + | 0.123787i | 0.766286 | − | 0.642499i | \(-0.222103\pi\) |
−0.642499 | + | 0.766286i | \(0.722103\pi\) | |||||||
\(860\) | −0.703459 | + | 6.61881i | −0.0239877 | + | 0.225699i | ||||
\(861\) | 16.4447 | − | 2.68267i | 0.560435 | − | 0.0914251i | ||||
\(862\) | 18.1345 | + | 0.960980i | 0.617665 | + | 0.0327311i | ||||
\(863\) | − | 41.7045i | − | 1.41964i | −0.704384 | − | 0.709819i | \(-0.748777\pi\) | ||
0.704384 | − | 0.709819i | \(-0.251223\pi\) | |||||||
\(864\) | 4.90719 | − | 2.81415i | 0.166946 | − | 0.0957394i | ||||
\(865\) | −3.81792 | −0.129813 | ||||||||
\(866\) | 11.3697 | + | 0.602497i | 0.386357 | + | 0.0204737i | ||||
\(867\) | −2.98824 | + | 2.98824i | −0.101486 | + | 0.101486i | ||||
\(868\) | 14.3986 | + | 12.8746i | 0.488722 | + | 0.436991i | ||||
\(869\) | 3.44356 | + | 3.44356i | 0.116815 | + | 0.116815i | ||||
\(870\) | −3.68592 | + | 3.31494i | −0.124965 | + | 0.112387i | ||||
\(871\) | − | 9.58675i | − | 0.324835i | ||||||
\(872\) | 1.74982 | + | 2.41729i | 0.0592564 | + | 0.0818597i | ||||
\(873\) | −15.5590 | −0.526594 | ||||||||
\(874\) | 13.9037 | + | 15.4597i | 0.470299 | + | 0.522932i | ||||
\(875\) | −2.07397 | − | 12.7134i | −0.0701129 | − | 0.429791i | ||||
\(876\) | −13.4960 | + | 10.9028i | −0.455988 | + | 0.368373i | ||||
\(877\) | 11.5486 | − | 11.5486i | 0.389968 | − | 0.389968i | −0.484708 | − | 0.874676i | \(-0.661074\pi\) |
0.874676 | + | 0.484708i | \(0.161074\pi\) | |||||||
\(878\) | −51.3626 | − | 2.72179i | −1.73340 | − | 0.0918559i | ||||
\(879\) | 18.3545i | 0.619081i | ||||||||
\(880\) | −1.22682 | + | 5.70633i | −0.0413560 | + | 0.192360i | ||||
\(881\) | − | 13.5809i | − | 0.457551i | −0.973479 | − | 0.228775i | \(-0.926528\pi\) | ||
0.973479 | − | 0.228775i | \(-0.0734721\pi\) | |||||||
\(882\) | −2.64503 | − | 9.53959i | −0.0890627 | − | 0.321215i | ||||
\(883\) | 26.0931 | + | 26.0931i | 0.878104 | + | 0.878104i | 0.993338 | − | 0.115234i | \(-0.0367619\pi\) |
−0.115234 | + | 0.993338i | \(0.536762\pi\) | |||||||
\(884\) | 21.5292 | − | 17.3926i | 0.724107 | − | 0.584975i | ||||
\(885\) | −3.65886 | + | 3.65886i | −0.122991 | + | 0.122991i | ||||
\(886\) | −36.3081 | − | 40.3714i | −1.21979 | − | 1.35630i | ||||
\(887\) | 46.2557i | 1.55312i | 0.630046 | + | 0.776558i | \(0.283036\pi\) | ||||
−0.630046 | + | 0.776558i | \(0.716964\pi\) | |||||||
\(888\) | 4.01516 | − | 25.0673i | 0.134740 | − | 0.841202i | ||||
\(889\) | 17.9518 | − | 24.9505i | 0.602083 | − | 0.836814i | ||||
\(890\) | −2.54269 | − | 2.82726i | −0.0852313 | − | 0.0947698i | ||||
\(891\) | −2.06639 | + | 2.06639i | −0.0692268 | + | 0.0692268i | ||||
\(892\) | −25.2810 | − | 2.68691i | −0.846469 | − | 0.0899643i | ||||
\(893\) | 3.20850 | − | 3.20850i | 0.107368 | − | 0.107368i | ||||
\(894\) | 1.73874 | − | 32.8116i | 0.0581521 | − | 1.09738i | ||||
\(895\) | 1.00413 | 0.0335644 | ||||||||
\(896\) | −25.0951 | + | 16.3167i | −0.838369 | + | 0.545102i | ||||
\(897\) | 6.75512 | 0.225547 | ||||||||
\(898\) | 0.520319 | − | 9.81889i | 0.0173633 | − | 0.327661i | ||||
\(899\) | −18.1198 | + | 18.1198i | −0.604330 | + | 0.604330i | ||||
\(900\) | −9.44814 | − | 1.00417i | −0.314938 | − | 0.0334722i | ||||
\(901\) | 5.44416 | − | 5.44416i | 0.181371 | − | 0.181371i | ||||
\(902\) | 17.4042 | + | 19.3520i | 0.579496 | + | 0.644350i | ||||
\(903\) | 10.2990 | − | 14.3142i | 0.342730 | − | 0.476348i | ||||
\(904\) | 0.550291 | − | 3.43555i | 0.0183024 | − | 0.114265i | ||||
\(905\) | 10.0469i | 0.333971i | ||||||||
\(906\) | 10.1064 | + | 11.2374i | 0.335762 | + | 0.373339i | ||||
\(907\) | −24.3139 | + | 24.3139i | −0.807329 | + | 0.807329i | −0.984229 | − | 0.176900i | \(-0.943393\pi\) |
0.176900 | + | 0.984229i | \(0.443393\pi\) | |||||||
\(908\) | 24.2001 | − | 19.5502i | 0.803107 | − | 0.648796i | ||||
\(909\) | 10.8391 | + | 10.8391i | 0.359509 | + | 0.359509i | ||||
\(910\) | −4.52962 | + | 5.64012i | −0.150155 | + | 0.186968i | ||||
\(911\) | 57.0504i | 1.89017i | 0.326832 | + | 0.945083i | \(0.394019\pi\) | ||||
−0.326832 | + | 0.945083i | \(0.605981\pi\) | |||||||
\(912\) | −7.08510 | + | 32.9552i | −0.234611 | + | 1.09126i | ||||
\(913\) | − | 32.2400i | − | 1.06699i | ||||||
\(914\) | −7.52211 | − | 0.398609i | −0.248809 | − | 0.0131848i | ||||
\(915\) | 2.07524 | − | 2.07524i | 0.0686052 | − | 0.0686052i | ||||
\(916\) | −6.01908 | + | 4.86256i | −0.198876 | + | 0.160664i | ||||
\(917\) | 52.2331 | − | 8.52091i | 1.72489 | − | 0.281385i | ||||
\(918\) | 3.37993 | + | 3.75819i | 0.111554 | + | 0.124039i | ||||
\(919\) | 29.2687 | 0.965487 | 0.482743 | − | 0.875762i | \(-0.339640\pi\) | ||||
0.482743 | + | 0.875762i | \(0.339640\pi\) | |||||||
\(920\) | 1.44480 | + | 1.99592i | 0.0476337 | + | 0.0658035i | ||||
\(921\) | − | 18.6910i | − | 0.615889i | ||||||
\(922\) | −11.0649 | + | 9.95125i | −0.364404 | + | 0.327727i | ||||
\(923\) | 26.0384 | + | 26.0384i | 0.857063 | + | 0.857063i | ||||
\(924\) | 10.3072 | − | 11.5274i | 0.339083 | − | 0.379223i | ||||
\(925\) | −30.1511 | + | 30.1511i | −0.991363 | + | 0.991363i | ||||
\(926\) | −50.0929 | − | 2.65451i | −1.64615 | − | 0.0872325i | ||||
\(927\) | −8.56545 | −0.281326 | ||||||||
\(928\) | −19.7559 | − | 34.4495i | −0.648520 | − | 1.13086i | ||||
\(929\) | 10.5983i | 0.347719i | 0.984770 | + | 0.173860i | \(0.0556239\pi\) | ||||
−0.984770 | + | 0.173860i | \(0.944376\pi\) | |||||||
\(930\) | 2.57399 | + | 0.136400i | 0.0844043 | + | 0.00447273i | ||||
\(931\) | 52.8055 | + | 26.2929i | 1.73063 | + | 0.861716i | ||||
\(932\) | 1.89715 | − | 17.8502i | 0.0621433 | − | 0.584703i | ||||
\(933\) | −16.9274 | − | 16.9274i | −0.554178 | − | 0.554178i | ||||
\(934\) | −12.4441 | − | 13.8367i | −0.407182 | − | 0.452751i | ||||
\(935\) | −5.21522 | −0.170556 | ||||||||
\(936\) | 6.42157 | + | 8.87108i | 0.209896 | + | 0.289960i | ||||
\(937\) | 22.8293 | 0.745801 | 0.372901 | − | 0.927871i | \(-0.378363\pi\) | ||||
0.372901 | + | 0.927871i | \(0.378363\pi\) | |||||||
\(938\) | −9.20953 | + | 1.00565i | −0.300702 | + | 0.0328357i | ||||
\(939\) | 6.82469 | − | 6.82469i | 0.222715 | − | 0.222715i | ||||
\(940\) | 0.418277 | − | 0.337909i | 0.0136427 | − | 0.0110214i | ||||
\(941\) | 34.5257 | + | 34.5257i | 1.12551 | + | 1.12551i | 0.990899 | + | 0.134606i | \(0.0429769\pi\) |
0.134606 | + | 0.990899i | \(0.457023\pi\) | |||||||
\(942\) | −0.797982 | + | 15.0586i | −0.0259997 | + | 0.490637i | ||||
\(943\) | 10.9873 | 0.357795 | ||||||||
\(944\) | −22.4950 | − | 34.8166i | −0.732151 | − | 1.13318i | ||||
\(945\) | −1.07236 | − | 0.771558i | −0.0348839 | − | 0.0250988i | ||||
\(946\) | 27.5069 | + | 1.45764i | 0.894328 | + | 0.0473919i | ||||
\(947\) | −11.7166 | − | 11.7166i | −0.380738 | − | 0.380738i | 0.490630 | − | 0.871368i | \(-0.336767\pi\) |
−0.871368 | + | 0.490630i | \(0.836767\pi\) | |||||||
\(948\) | 2.09446 | + | 2.59260i | 0.0680248 | + | 0.0842039i | ||||
\(949\) | −23.7505 | − | 23.7505i | −0.770973 | − | 0.770973i | ||||
\(950\) | 42.0966 | − | 37.8596i | 1.36579 | − | 1.22833i | ||||
\(951\) | 2.89565i | 0.0938980i | ||||||||
\(952\) | −18.9666 | − | 18.8576i | −0.614712 | − | 0.611179i | ||||
\(953\) | − | 44.2619i | − | 1.43378i | −0.697185 | − | 0.716891i | \(-0.745564\pi\) | ||
0.697185 | − | 0.716891i | \(-0.254436\pi\) | |||||||
\(954\) | 2.03717 | + | 2.26516i | 0.0659559 | + | 0.0733372i | ||||
\(955\) | −4.07285 | − | 4.07285i | −0.131794 | − | 0.131794i | ||||
\(956\) | 4.34872 | − | 40.9169i | 0.140648 | − | 1.32335i | ||||
\(957\) | 14.5065 | + | 14.5065i | 0.468929 | + | 0.468929i | ||||
\(958\) | 2.32988 | − | 43.9669i | 0.0752750 | − | 1.42051i | ||||
\(959\) | 3.98912 | − | 5.54433i | 0.128815 | − | 0.179036i | ||||
\(960\) | −1.24766 | + | 3.79473i | −0.0402680 | + | 0.122474i | ||||
\(961\) | −17.6759 | −0.570190 | ||||||||
\(962\) | 49.0787 | + | 2.60076i | 1.58236 | + | 0.0838519i | ||||
\(963\) | 10.4598 | + | 10.4598i | 0.337061 | + | 0.337061i | ||||
\(964\) | 0.578948 | − | 5.44729i | 0.0186466 | − | 0.175445i | ||||
\(965\) | 4.51272 | − | 4.51272i | 0.145270 | − | 0.145270i | ||||
\(966\) | −0.708614 | − | 6.48933i | −0.0227993 | − | 0.208791i | ||||
\(967\) | −20.2806 | −0.652179 | −0.326089 | − | 0.945339i | \(-0.605731\pi\) | ||||
−0.326089 | + | 0.945339i | \(0.605731\pi\) | |||||||
\(968\) | −6.87043 | − | 1.10048i | −0.220824 | − | 0.0353706i | ||||
\(969\) | −30.1189 | −0.967558 | ||||||||
\(970\) | 8.16920 | − | 7.34697i | 0.262297 | − | 0.235897i | ||||
\(971\) | 22.3463 | + | 22.3463i | 0.717127 | + | 0.717127i | 0.968016 | − | 0.250889i | \(-0.0807230\pi\) |
−0.250889 | + | 0.968016i | \(0.580723\pi\) | |||||||
\(972\) | −1.55576 | + | 1.25683i | −0.0499009 | + | 0.0403128i | ||||
\(973\) | −6.17205 | − | 37.8346i | −0.197867 | − | 1.21292i | ||||
\(974\) | −2.45456 | + | 46.3197i | −0.0786491 | + | 1.48418i | ||||
\(975\) | − | 18.3941i | − | 0.589084i | ||||||
\(976\) | 12.7588 | + | 19.7473i | 0.408398 | + | 0.632097i | ||||
\(977\) | 21.0247 | 0.672638 | 0.336319 | − | 0.941748i | \(-0.390818\pi\) | ||||
0.336319 | + | 0.941748i | \(0.390818\pi\) | |||||||
\(978\) | 1.08529 | − | 20.4803i | 0.0347037 | − | 0.654889i | ||||
\(979\) | −11.1271 | + | 11.1271i | −0.355623 | + | 0.355623i | ||||
\(980\) | 5.89335 | + | 3.75974i | 0.188256 | + | 0.120100i | ||||
\(981\) | −0.746037 | − | 0.746037i | −0.0238191 | − | 0.0238191i | ||||
\(982\) | 9.14706 | + | 10.1707i | 0.291894 | + | 0.324561i | ||||
\(983\) | 18.7833i | 0.599096i | 0.954081 | + | 0.299548i | \(0.0968358\pi\) | ||||
−0.954081 | + | 0.299548i | \(0.903164\pi\) | |||||||
\(984\) | 10.4448 | + | 14.4289i | 0.332967 | + | 0.459977i | ||||
\(985\) | 8.15592 | 0.259869 | ||||||||
\(986\) | 26.3833 | − | 23.7278i | 0.840215 | − | 0.755647i | ||||
\(987\) | −1.40601 | + | 0.229365i | −0.0447537 | + | 0.00730078i | ||||
\(988\) | −64.8919 | − | 6.89682i | −2.06449 | − | 0.219417i | ||||
\(989\) | 8.22248 | − | 8.22248i | 0.261460 | − | 0.261460i | ||||
\(990\) | 0.109200 | − | 2.06070i | 0.00347060 | − | 0.0654934i | ||||
\(991\) | 13.2725i | 0.421614i | 0.977528 | + | 0.210807i | \(0.0676092\pi\) | ||||
−0.977528 | + | 0.210807i | \(0.932391\pi\) | |||||||
\(992\) | −5.40234 | + | 19.9295i | −0.171524 | + | 0.632764i | ||||
\(993\) | − | 6.31395i | − | 0.200367i | ||||||
\(994\) | 22.2824 | − | 27.7452i | 0.706754 | − | 0.880026i | ||||
\(995\) | −0.950352 | − | 0.950352i | −0.0301282 | − | 0.0301282i | ||||
\(996\) | 2.33193 | − | 21.9410i | 0.0738901 | − | 0.695229i | ||||
\(997\) | −6.05815 | + | 6.05815i | −0.191864 | + | 0.191864i | −0.796501 | − | 0.604637i | \(-0.793318\pi\) |
0.604637 | + | 0.796501i | \(0.293318\pi\) | |||||||
\(998\) | 10.3621 | − | 9.31913i | 0.328006 | − | 0.294992i | ||||
\(999\) | 8.97559i | 0.283975i |
(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 | 336.2.u.a.139.19 | ✓ | 64 | |
4.3 | odd | 2 | 1344.2.u.a.1231.23 | 64 | |||
7.6 | odd | 2 | inner | 336.2.u.a.139.20 | yes | 64 | |
16.3 | odd | 4 | inner | 336.2.u.a.307.20 | yes | 64 | |
16.13 | even | 4 | 1344.2.u.a.559.10 | 64 | |||
28.27 | even | 2 | 1344.2.u.a.1231.10 | 64 | |||
112.13 | odd | 4 | 1344.2.u.a.559.23 | 64 | |||
112.83 | even | 4 | inner | 336.2.u.a.307.19 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.2.u.a.139.19 | ✓ | 64 | 1.1 | even | 1 | trivial | |
336.2.u.a.139.20 | yes | 64 | 7.6 | odd | 2 | inner | |
336.2.u.a.307.19 | yes | 64 | 112.83 | even | 4 | inner | |
336.2.u.a.307.20 | yes | 64 | 16.3 | odd | 4 | inner | |
1344.2.u.a.559.10 | 64 | 16.13 | even | 4 | |||
1344.2.u.a.559.23 | 64 | 112.13 | odd | 4 | |||
1344.2.u.a.1231.10 | 64 | 28.27 | even | 2 | |||
1344.2.u.a.1231.23 | 64 | 4.3 | odd | 2 |