Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [875,2,Mod(176,875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(875, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("875.176");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 875 = 5^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 875.h (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.98691017686\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{5})\) |
Twist minimal: | no (minimal twist has level 175) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 701.7 | ||
Character | \(\chi\) | \(=\) | 875.701 |
Dual form | 875.2.h.e.176.7 |
$q$-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 \(\left(\mathbb{Z}/875\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(626\) |
\(\chi(n)\) | \(e\left(\frac{1}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.160894 | + | 0.116896i | 0.113769 | + | 0.0826582i | 0.643215 | − | 0.765686i | \(-0.277600\pi\) |
−0.529446 | + | 0.848344i | \(0.677600\pi\) | |||||||
\(3\) | −0.477493 | − | 1.46957i | −0.275681 | − | 0.848458i | −0.989039 | − | 0.147658i | \(-0.952827\pi\) |
0.713358 | − | 0.700800i | \(-0.247173\pi\) | |||||||
\(4\) | −0.605812 | − | 1.86450i | −0.302906 | − | 0.932249i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.0949619 | − | 0.292263i | 0.0387680 | − | 0.119316i | ||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0.243394 | − | 0.749089i | 0.0860526 | − | 0.264843i | ||||
\(9\) | 0.495409 | − | 0.359936i | 0.165136 | − | 0.119979i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.54486 | − | 1.84895i | −0.767305 | − | 0.557480i | 0.133837 | − | 0.991003i | \(-0.457270\pi\) |
−0.901142 | + | 0.433524i | \(0.857270\pi\) | |||||||
\(12\) | −2.45074 | + | 1.78057i | −0.707468 | + | 0.514006i | ||||
\(13\) | 5.25890 | − | 3.82082i | 1.45856 | − | 1.05970i | 0.474822 | − | 0.880082i | \(-0.342512\pi\) |
0.983736 | − | 0.179622i | \(-0.0574875\pi\) | |||||||
\(14\) | 0.160894 | + | 0.116896i | 0.0430008 | + | 0.0312419i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.04535 | + | 2.21257i | −0.761336 | + | 0.553143i | ||||
\(17\) | 0.881886 | − | 2.71417i | 0.213889 | − | 0.658282i | −0.785342 | − | 0.619062i | \(-0.787513\pi\) |
0.999231 | − | 0.0392195i | \(-0.0124872\pi\) | |||||||
\(18\) | 0.121784 | 0.0287047 | ||||||||
\(19\) | −1.06144 | + | 3.26678i | −0.243512 | + | 0.749451i | 0.752366 | + | 0.658745i | \(0.228912\pi\) |
−0.995878 | + | 0.0907063i | \(0.971088\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.477493 | − | 1.46957i | −0.104197 | − | 0.320687i | ||||
\(22\) | −0.193318 | − | 0.594971i | −0.0412155 | − | 0.126848i | ||||
\(23\) | −0.469412 | − | 0.341048i | −0.0978792 | − | 0.0711134i | 0.537769 | − | 0.843092i | \(-0.319267\pi\) |
−0.635648 | + | 0.771979i | \(0.719267\pi\) | |||||||
\(24\) | −1.21706 | −0.248431 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.29277 | 0.253532 | ||||||||
\(27\) | −4.51578 | − | 3.28091i | −0.869063 | − | 0.631411i | ||||
\(28\) | −0.605812 | − | 1.86450i | −0.114488 | − | 0.352357i | ||||
\(29\) | 0.343638 | + | 1.05761i | 0.0638120 | + | 0.196393i | 0.977880 | − | 0.209169i | \(-0.0670758\pi\) |
−0.914068 | + | 0.405562i | \(0.867076\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.595158 | + | 1.83171i | −0.106894 | + | 0.328985i | −0.990170 | − | 0.139868i | \(-0.955332\pi\) |
0.883277 | + | 0.468852i | \(0.155332\pi\) | |||||||
\(32\) | −2.32390 | −0.410811 | ||||||||
\(33\) | −1.50201 | + | 4.62272i | −0.261467 | + | 0.804712i | ||||
\(34\) | 0.459166 | − | 0.333604i | 0.0787464 | − | 0.0572126i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.971225 | − | 0.705636i | −0.161871 | − | 0.117606i | ||||
\(37\) | 2.04235 | − | 1.48385i | 0.335760 | − | 0.243944i | −0.407111 | − | 0.913379i | \(-0.633464\pi\) |
0.742871 | + | 0.669435i | \(0.233464\pi\) | |||||||
\(38\) | −0.552655 | + | 0.401527i | −0.0896525 | + | 0.0651363i | ||||
\(39\) | −8.12605 | − | 5.90392i | −1.30121 | − | 0.945384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.17033 | + | 3.02992i | −0.651296 | + | 0.473194i | −0.863712 | − | 0.503985i | \(-0.831867\pi\) |
0.212417 | + | 0.977179i | \(0.431867\pi\) | |||||||
\(42\) | 0.0949619 | − | 0.292263i | 0.0146529 | − | 0.0450971i | ||||
\(43\) | 3.23994 | 0.494086 | 0.247043 | − | 0.969004i | \(-0.420541\pi\) | ||||
0.247043 | + | 0.969004i | \(0.420541\pi\) | |||||||
\(44\) | −1.90566 | + | 5.86501i | −0.287288 | + | 0.884183i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.0356584 | − | 0.109745i | −0.00525754 | − | 0.0161810i | ||||
\(47\) | −1.09432 | − | 3.36797i | −0.159623 | − | 0.491268i | 0.838977 | − | 0.544167i | \(-0.183154\pi\) |
−0.998600 | + | 0.0528982i | \(0.983154\pi\) | |||||||
\(48\) | 4.70567 | + | 3.41887i | 0.679204 | + | 0.493471i | ||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.40975 | −0.617489 | ||||||||
\(52\) | −10.3098 | − | 7.49052i | −1.42971 | − | 1.03875i | ||||
\(53\) | 0.220620 | + | 0.678998i | 0.0303044 | + | 0.0932675i | 0.965065 | − | 0.262012i | \(-0.0843859\pi\) |
−0.934760 | + | 0.355279i | \(0.884386\pi\) | |||||||
\(54\) | −0.343036 | − | 1.05576i | −0.0466814 | − | 0.143670i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.243394 | − | 0.749089i | 0.0325248 | − | 0.100101i | ||||
\(57\) | 5.30760 | 0.703009 | ||||||||
\(58\) | −0.0683414 | + | 0.210333i | −0.00897366 | + | 0.0276181i | ||||
\(59\) | −8.59038 | + | 6.24127i | −1.11837 | + | 0.812545i | −0.983961 | − | 0.178381i | \(-0.942914\pi\) |
−0.134410 | + | 0.990926i | \(0.542914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.90849 | − | 5.01931i | −0.884541 | − | 0.642657i | 0.0499078 | − | 0.998754i | \(-0.484107\pi\) |
−0.934449 | + | 0.356097i | \(0.884107\pi\) | |||||||
\(62\) | −0.309878 | + | 0.225139i | −0.0393545 | + | 0.0285927i | ||||
\(63\) | 0.495409 | − | 0.359936i | 0.0624157 | − | 0.0453477i | ||||
\(64\) | 5.71679 | + | 4.15349i | 0.714599 | + | 0.519186i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.782044 | + | 0.568189i | −0.0962630 | + | 0.0699392i | ||||
\(67\) | −4.71139 | + | 14.5002i | −0.575587 | + | 1.77148i | 0.0585831 | + | 0.998283i | \(0.481342\pi\) |
−0.634171 | + | 0.773193i | \(0.718658\pi\) | |||||||
\(68\) | −5.59481 | −0.678470 | ||||||||
\(69\) | −0.277053 | + | 0.852682i | −0.0333533 | + | 0.102651i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.64856 | − | 11.2291i | −0.433004 | − | 1.33265i | −0.895118 | − | 0.445829i | \(-0.852909\pi\) |
0.462114 | − | 0.886821i | \(-0.347091\pi\) | |||||||
\(72\) | −0.149044 | − | 0.458712i | −0.0175651 | − | 0.0540597i | ||||
\(73\) | 1.51347 | + | 1.09960i | 0.177138 | + | 0.128698i | 0.672821 | − | 0.739805i | \(-0.265082\pi\) |
−0.495683 | + | 0.868503i | \(0.665082\pi\) | |||||||
\(74\) | 0.502059 | 0.0583631 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.73394 | 0.772436 | ||||||||
\(77\) | −2.54486 | − | 1.84895i | −0.290014 | − | 0.210708i | ||||
\(78\) | −0.617287 | − | 1.89981i | −0.0698940 | − | 0.215111i | ||||
\(79\) | 2.62230 | + | 8.07060i | 0.295031 | + | 0.908013i | 0.983211 | + | 0.182473i | \(0.0584101\pi\) |
−0.688180 | + | 0.725540i | \(0.741590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.09759 | + | 6.45571i | −0.233065 | + | 0.717301i | ||||
\(82\) | −1.02517 | −0.113211 | ||||||||
\(83\) | 3.67741 | − | 11.3179i | 0.403648 | − | 1.24230i | −0.518370 | − | 0.855156i | \(-0.673461\pi\) |
0.922019 | − | 0.387146i | \(-0.126539\pi\) | |||||||
\(84\) | −2.45074 | + | 1.78057i | −0.267398 | + | 0.194276i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.521288 | + | 0.378738i | 0.0562119 | + | 0.0408403i | ||||
\(87\) | 1.39015 | − | 1.01000i | 0.149039 | − | 0.108284i | ||||
\(88\) | −2.00443 | + | 1.45631i | −0.213673 | + | 0.155243i | ||||
\(89\) | −13.5558 | − | 9.84885i | −1.43691 | − | 1.04398i | −0.988677 | − | 0.150060i | \(-0.952053\pi\) |
−0.448233 | − | 0.893917i | \(-0.647947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.25890 | − | 3.82082i | 0.551283 | − | 0.400530i | ||||
\(92\) | −0.351507 | + | 1.08183i | −0.0366472 | + | 0.112788i | ||||
\(93\) | 2.97601 | 0.308598 | ||||||||
\(94\) | 0.217634 | − | 0.669808i | 0.0224472 | − | 0.0690854i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.10964 | + | 3.41513i | 0.113253 | + | 0.348556i | ||||
\(97\) | 3.09402 | + | 9.52242i | 0.314150 | + | 0.966855i | 0.976103 | + | 0.217309i | \(0.0697280\pi\) |
−0.661953 | + | 0.749546i | \(0.730272\pi\) | |||||||
\(98\) | 0.160894 | + | 0.116896i | 0.0162528 | + | 0.0118083i | ||||
\(99\) | −1.92625 | −0.193596 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.6057 | 1.85133 | 0.925667 | − | 0.378339i | \(-0.123505\pi\) | ||||
0.925667 | + | 0.378339i | \(0.123505\pi\) | |||||||
\(102\) | −0.709504 | − | 0.515485i | −0.0702513 | − | 0.0510406i | ||||
\(103\) | −2.10824 | − | 6.48850i | −0.207731 | − | 0.639331i | −0.999590 | − | 0.0286269i | \(-0.990887\pi\) |
0.791859 | − | 0.610704i | \(-0.209113\pi\) | |||||||
\(104\) | −1.58215 | − | 4.86935i | −0.155142 | − | 0.477479i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.0438760 | + | 0.135036i | −0.00426161 | + | 0.0131159i | ||||
\(107\) | 11.2305 | 1.08570 | 0.542848 | − | 0.839831i | \(-0.317346\pi\) | ||||
0.542848 | + | 0.839831i | \(0.317346\pi\) | |||||||
\(108\) | −3.38153 | + | 10.4073i | −0.325388 | + | 1.00144i | ||||
\(109\) | 14.6006 | − | 10.6079i | 1.39848 | − | 1.01606i | 0.403608 | − | 0.914932i | \(-0.367756\pi\) |
0.994874 | − | 0.101124i | \(-0.0322439\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.15583 | − | 2.29285i | −0.299538 | − | 0.217627i | ||||
\(112\) | −3.04535 | + | 2.21257i | −0.287758 | + | 0.209069i | ||||
\(113\) | 8.82526 | − | 6.41192i | 0.830210 | − | 0.603183i | −0.0894084 | − | 0.995995i | \(-0.528498\pi\) |
0.919619 | + | 0.392812i | \(0.128498\pi\) | |||||||
\(114\) | 0.853962 | + | 0.620440i | 0.0799809 | + | 0.0581095i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.76373 | − | 1.28142i | 0.163758 | − | 0.118977i | ||||
\(117\) | 1.23006 | − | 3.78574i | 0.113719 | − | 0.349992i | ||||
\(118\) | −2.11172 | −0.194400 | ||||||||
\(119\) | 0.881886 | − | 2.71417i | 0.0808423 | − | 0.248807i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.341479 | − | 1.05096i | −0.0310436 | − | 0.0955423i | ||||
\(122\) | −0.524796 | − | 1.61515i | −0.0475128 | − | 0.146229i | ||||
\(123\) | 6.44398 | + | 4.68183i | 0.581035 | + | 0.422146i | ||||
\(124\) | 3.77577 | 0.339074 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.121784 | 0.0108494 | ||||||||
\(127\) | 10.0747 | + | 7.31970i | 0.893986 | + | 0.649519i | 0.936914 | − | 0.349559i | \(-0.113669\pi\) |
−0.0429283 | + | 0.999078i | \(0.513669\pi\) | |||||||
\(128\) | 1.87052 | + | 5.75686i | 0.165332 | + | 0.508839i | ||||
\(129\) | −1.54705 | − | 4.76133i | −0.136210 | − | 0.419211i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.769069 | + | 2.36695i | −0.0671939 | + | 0.206802i | −0.979016 | − | 0.203784i | \(-0.934676\pi\) |
0.911822 | + | 0.410586i | \(0.134676\pi\) | |||||||
\(132\) | 9.52899 | 0.829392 | ||||||||
\(133\) | −1.06144 | + | 3.26678i | −0.0920387 | + | 0.283266i | ||||
\(134\) | −2.45305 | + | 1.78225i | −0.211911 | + | 0.153963i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.81851 | − | 1.32122i | −0.155936 | − | 0.113294i | ||||
\(137\) | 8.17703 | − | 5.94096i | 0.698611 | − | 0.507571i | −0.180868 | − | 0.983507i | \(-0.557891\pi\) |
0.879480 | + | 0.475937i | \(0.157891\pi\) | |||||||
\(138\) | −0.144252 | + | 0.104805i | −0.0122795 | + | 0.00892160i | ||||
\(139\) | 14.8897 | + | 10.8180i | 1.26293 | + | 0.917574i | 0.998898 | − | 0.0469397i | \(-0.0149469\pi\) |
0.264034 | + | 0.964513i | \(0.414947\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.42694 | + | 3.21636i | −0.372816 | + | 0.270866i | ||||
\(142\) | 0.725611 | − | 2.23320i | 0.0608919 | − | 0.187406i | ||||
\(143\) | −20.4477 | −1.70992 | ||||||||
\(144\) | −0.712308 | + | 2.19226i | −0.0593590 | + | 0.182688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.114969 | + | 0.353838i | 0.00951490 | + | 0.0292838i | ||||
\(147\) | −0.477493 | − | 1.46957i | −0.0393829 | − | 0.121208i | ||||
\(148\) | −4.00392 | − | 2.90902i | −0.329120 | − | 0.239120i | ||||
\(149\) | 20.1992 | 1.65479 | 0.827393 | − | 0.561623i | \(-0.189823\pi\) | ||||
0.827393 | + | 0.561623i | \(0.189823\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8668 | 0.965706 | 0.482853 | − | 0.875701i | \(-0.339601\pi\) | ||||
0.482853 | + | 0.875701i | \(0.339601\pi\) | |||||||
\(152\) | 2.18876 | + | 1.59023i | 0.177532 | + | 0.128985i | ||||
\(153\) | −0.540031 | − | 1.66205i | −0.0436589 | − | 0.134368i | ||||
\(154\) | −0.193318 | − | 0.594971i | −0.0155780 | − | 0.0479441i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.08499 | + | 18.7277i | −0.487189 | + | 1.49941i | ||||
\(157\) | −16.5799 | −1.32322 | −0.661608 | − | 0.749850i | \(-0.730126\pi\) | ||||
−0.661608 | + | 0.749850i | \(0.730126\pi\) | |||||||
\(158\) | −0.521512 | + | 1.60505i | −0.0414893 | + | 0.127691i | ||||
\(159\) | 0.892491 | − | 0.648433i | 0.0707792 | − | 0.0514241i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.469412 | − | 0.341048i | −0.0369948 | − | 0.0268783i | ||||
\(162\) | −1.09214 | + | 0.793485i | −0.0858065 | + | 0.0623421i | ||||
\(163\) | 15.6328 | − | 11.3579i | 1.22446 | − | 0.889620i | 0.227994 | − | 0.973663i | \(-0.426783\pi\) |
0.996462 | + | 0.0840429i | \(0.0267833\pi\) | |||||||
\(164\) | 8.17571 | + | 5.94000i | 0.638416 | + | 0.463836i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.91470 | − | 1.39111i | 0.148609 | − | 0.107971i | ||||
\(167\) | 0.473525 | − | 1.45736i | 0.0366425 | − | 0.112774i | −0.931062 | − | 0.364860i | \(-0.881117\pi\) |
0.967705 | + | 0.252086i | \(0.0811167\pi\) | |||||||
\(168\) | −1.21706 | −0.0938981 | ||||||||
\(169\) | 9.04020 | − | 27.8229i | 0.695400 | − | 2.14022i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.649984 | + | 2.00045i | 0.0497056 | + | 0.152978i | ||||
\(172\) | −1.96280 | − | 6.04086i | −0.149662 | − | 0.460611i | ||||
\(173\) | −3.74051 | − | 2.71764i | −0.284386 | − | 0.206618i | 0.436442 | − | 0.899732i | \(-0.356238\pi\) |
−0.720828 | + | 0.693114i | \(0.756238\pi\) | |||||||
\(174\) | 0.341732 | 0.0259066 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.8409 | 0.892544 | ||||||||
\(177\) | 13.2738 | + | 9.64401i | 0.997723 | + | 0.724888i | ||||
\(178\) | −1.02975 | − | 3.16924i | −0.0771830 | − | 0.237545i | ||||
\(179\) | 0.568958 | + | 1.75107i | 0.0425259 | + | 0.130881i | 0.970065 | − | 0.242844i | \(-0.0780803\pi\) |
−0.927539 | + | 0.373725i | \(0.878080\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.648662 | + | 1.99638i | −0.0482146 | + | 0.148389i | −0.972265 | − | 0.233881i | \(-0.924858\pi\) |
0.924051 | + | 0.382270i | \(0.124858\pi\) | |||||||
\(182\) | 1.29277 | 0.0958262 | ||||||||
\(183\) | −4.07748 | + | 12.5492i | −0.301416 | + | 0.927664i | ||||
\(184\) | −0.369727 | + | 0.268622i | −0.0272566 | + | 0.0198031i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.478823 | + | 0.347885i | 0.0351090 | + | 0.0255082i | ||||
\(187\) | −7.26264 | + | 5.27662i | −0.531097 | + | 0.385864i | ||||
\(188\) | −5.61661 | + | 4.08071i | −0.409634 | + | 0.297616i | ||||
\(189\) | −4.51578 | − | 3.28091i | −0.328475 | − | 0.238651i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.0257 | + | 12.3699i | −1.23194 | + | 0.895056i | −0.997034 | − | 0.0769630i | \(-0.975478\pi\) |
−0.234904 | + | 0.972019i | \(0.575478\pi\) | |||||||
\(192\) | 3.37413 | − | 10.3845i | 0.243507 | − | 0.749436i | ||||
\(193\) | −22.4099 | −1.61310 | −0.806548 | − | 0.591168i | \(-0.798667\pi\) | ||||
−0.806548 | + | 0.591168i | \(0.798667\pi\) | |||||||
\(194\) | −0.615327 | + | 1.89378i | −0.0441779 | + | 0.135966i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.605812 | − | 1.86450i | −0.0432723 | − | 0.133178i | ||||
\(197\) | −3.83414 | − | 11.8003i | −0.273171 | − | 0.840734i | −0.989697 | − | 0.143174i | \(-0.954269\pi\) |
0.716526 | − | 0.697560i | \(-0.245731\pi\) | |||||||
\(198\) | −0.309923 | − | 0.225172i | −0.0220253 | − | 0.0160023i | ||||
\(199\) | −16.7681 | −1.18866 | −0.594329 | − | 0.804222i | \(-0.702582\pi\) | ||||
−0.594329 | + | 0.804222i | \(0.702582\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.5587 | 1.66170 | ||||||||
\(202\) | 2.99354 | + | 2.17494i | 0.210625 | + | 0.153028i | ||||
\(203\) | 0.343638 | + | 1.05761i | 0.0241187 | + | 0.0742296i | ||||
\(204\) | 2.67148 | + | 8.22198i | 0.187041 | + | 0.575653i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.419279 | − | 1.29041i | 0.0292125 | − | 0.0899069i | ||||
\(207\) | −0.355306 | −0.0246955 | ||||||||
\(208\) | −7.56134 | + | 23.2714i | −0.524285 | + | 1.61358i | ||||
\(209\) | 8.74135 | − | 6.35096i | 0.604652 | − | 0.439305i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.43639 | + | 5.40286i | 0.511943 | + | 0.371948i | 0.813560 | − | 0.581481i | \(-0.197527\pi\) |
−0.301617 | + | 0.953429i | \(0.597527\pi\) | |||||||
\(212\) | 1.13234 | − | 0.822690i | 0.0777691 | − | 0.0565026i | ||||
\(213\) | −14.7598 | + | 10.7236i | −1.01133 | + | 0.734772i | ||||
\(214\) | 1.80693 | + | 1.31281i | 0.123519 | + | 0.0897418i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.55680 | + | 2.58417i | −0.242010 | + | 0.175830i | ||||
\(217\) | −0.595158 | + | 1.83171i | −0.0404020 | + | 0.124344i | ||||
\(218\) | 3.58918 | 0.243090 | ||||||||
\(219\) | 0.893269 | − | 2.74920i | 0.0603616 | − | 0.185774i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.73258 | − | 17.6431i | −0.385615 | − | 1.18680i | ||||
\(222\) | −0.239729 | − | 0.737811i | −0.0160896 | − | 0.0495186i | ||||
\(223\) | 14.8206 | + | 10.7678i | 0.992460 | + | 0.721064i | 0.960458 | − | 0.278423i | \(-0.0898118\pi\) |
0.0320016 | + | 0.999488i | \(0.489812\pi\) | |||||||
\(224\) | −2.32390 | −0.155272 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.16946 | 0.144311 | ||||||||
\(227\) | 13.9235 | + | 10.1160i | 0.924137 | + | 0.671424i | 0.944550 | − | 0.328367i | \(-0.106498\pi\) |
−0.0204137 | + | 0.999792i | \(0.506498\pi\) | |||||||
\(228\) | −3.21541 | − | 9.89601i | −0.212946 | − | 0.655379i | ||||
\(229\) | 0.727716 | + | 2.23968i | 0.0480889 | + | 0.148002i | 0.972218 | − | 0.234079i | \(-0.0752074\pi\) |
−0.924129 | + | 0.382081i | \(0.875207\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.50201 | + | 4.62272i | −0.0988252 | + | 0.304153i | ||||
\(232\) | 0.875882 | 0.0575045 | ||||||||
\(233\) | −0.429855 | + | 1.32296i | −0.0281608 | + | 0.0866699i | −0.964149 | − | 0.265361i | \(-0.914509\pi\) |
0.935988 | + | 0.352031i | \(0.114509\pi\) | |||||||
\(234\) | 0.640449 | − | 0.465313i | 0.0418674 | − | 0.0304185i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 16.8410 | + | 12.2357i | 1.09625 | + | 0.796476i | ||||
\(237\) | 10.6082 | − | 7.70730i | 0.689076 | − | 0.500643i | ||||
\(238\) | 0.459166 | − | 0.333604i | 0.0297633 | − | 0.0216243i | ||||
\(239\) | 8.49728 | + | 6.17364i | 0.549644 | + | 0.399339i | 0.827654 | − | 0.561239i | \(-0.189675\pi\) |
−0.278010 | + | 0.960578i | \(0.589675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 10.3506 | − | 7.52017i | 0.666742 | − | 0.484417i | −0.202191 | − | 0.979346i | \(-0.564806\pi\) |
0.868933 | + | 0.494930i | \(0.164806\pi\) | |||||||
\(242\) | 0.0679120 | − | 0.209012i | 0.00436555 | − | 0.0134358i | ||||
\(243\) | −6.25673 | −0.401370 | ||||||||
\(244\) | −5.17325 | + | 15.9216i | −0.331183 | + | 1.01928i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.489510 | + | 1.50656i | 0.0312100 | + | 0.0960546i | ||||
\(247\) | 6.89976 | + | 21.2353i | 0.439021 | + | 1.35117i | ||||
\(248\) | 1.22725 | + | 0.891652i | 0.0779307 | + | 0.0566200i | ||||
\(249\) | −18.3884 | −1.16532 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7027 | −0.801789 | −0.400894 | − | 0.916124i | \(-0.631301\pi\) | ||||
−0.400894 | + | 0.916124i | \(0.631301\pi\) | |||||||
\(252\) | −0.971225 | − | 0.705636i | −0.0611814 | − | 0.0444509i | ||||
\(253\) | 0.564009 | + | 1.73584i | 0.0354589 | + | 0.109131i | ||||
\(254\) | 0.765314 | + | 2.35539i | 0.0480201 | + | 0.147791i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.99524 | − | 12.2961i | 0.249702 | − | 0.768505i | ||||
\(257\) | −20.2119 | −1.26079 | −0.630393 | − | 0.776276i | \(-0.717106\pi\) | ||||
−0.630393 | + | 0.776276i | \(0.717106\pi\) | |||||||
\(258\) | 0.307671 | − | 0.946914i | 0.0191548 | − | 0.0589523i | ||||
\(259\) | 2.04235 | − | 1.48385i | 0.126905 | − | 0.0922021i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.550913 | + | 0.400262i | 0.0341007 | + | 0.0247756i | ||||
\(262\) | −0.400427 | + | 0.290927i | −0.0247385 | + | 0.0179735i | ||||
\(263\) | −1.29573 | + | 0.941404i | −0.0798983 | + | 0.0580495i | −0.627017 | − | 0.779005i | \(-0.715724\pi\) |
0.547119 | + | 0.837055i | \(0.315724\pi\) | |||||||
\(264\) | 3.09725 | + | 2.25028i | 0.190622 | + | 0.138495i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.552655 | + | 0.401527i | −0.0338855 | + | 0.0246192i | ||||
\(267\) | −8.00081 | + | 24.6239i | −0.489641 | + | 1.50696i | ||||
\(268\) | 29.8897 | 1.82580 | ||||||||
\(269\) | 6.08709 | − | 18.7341i | 0.371136 | − | 1.14224i | −0.574912 | − | 0.818215i | \(-0.694964\pi\) |
0.946049 | − | 0.324025i | \(-0.105036\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.23911 | − | 25.3574i | −0.500490 | − | 1.54035i | −0.808222 | − | 0.588878i | \(-0.799570\pi\) |
0.307732 | − | 0.951473i | \(-0.400430\pi\) | |||||||
\(272\) | 3.31964 | + | 10.2168i | 0.201283 | + | 0.619485i | ||||
\(273\) | −8.12605 | − | 5.90392i | −0.491811 | − | 0.357322i | ||||
\(274\) | 2.01011 | 0.121435 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.75767 | 0.105799 | ||||||||
\(277\) | 2.74918 | + | 1.99739i | 0.165182 | + | 0.120012i | 0.667305 | − | 0.744784i | \(-0.267448\pi\) |
−0.502123 | + | 0.864796i | \(0.667448\pi\) | |||||||
\(278\) | 1.13108 | + | 3.48112i | 0.0678379 | + | 0.208783i | ||||
\(279\) | 0.364451 | + | 1.12166i | 0.0218191 | + | 0.0671523i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.2397 | + | 31.5144i | −0.610847 | + | 1.87999i | −0.160806 | + | 0.986986i | \(0.551409\pi\) |
−0.450041 | + | 0.893008i | \(0.648591\pi\) | |||||||
\(282\) | −1.08825 | −0.0648043 | ||||||||
\(283\) | 2.72669 | − | 8.39189i | 0.162085 | − | 0.498846i | −0.836725 | − | 0.547624i | \(-0.815533\pi\) |
0.998810 | + | 0.0487777i | \(0.0155326\pi\) | |||||||
\(284\) | −18.7263 | + | 13.6055i | −1.11120 | + | 0.807335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.28991 | − | 2.39026i | −0.194537 | − | 0.141339i | ||||
\(287\) | −4.17033 | + | 3.02992i | −0.246167 | + | 0.178850i | ||||
\(288\) | −1.15128 | + | 0.836454i | −0.0678398 | + | 0.0492885i | ||||
\(289\) | 7.16432 | + | 5.20518i | 0.421430 | + | 0.306187i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.5165 | − | 9.09377i | 0.733730 | − | 0.533086i | ||||
\(292\) | 1.13332 | − | 3.48801i | 0.0663227 | − | 0.204120i | ||||
\(293\) | −16.0205 | −0.935929 | −0.467965 | − | 0.883747i | \(-0.655013\pi\) | ||||
−0.467965 | + | 0.883747i | \(0.655013\pi\) | |||||||
\(294\) | 0.0949619 | − | 0.292263i | 0.00553829 | − | 0.0170451i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.614442 | − | 1.89106i | −0.0357137 | − | 0.109916i | ||||
\(297\) | 5.42581 | + | 16.6989i | 0.314837 | + | 0.968970i | ||||
\(298\) | 3.24994 | + | 2.36122i | 0.188264 | + | 0.136782i | ||||
\(299\) | −3.77167 | −0.218122 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.23994 | 0.186747 | ||||||||
\(302\) | 1.90930 | + | 1.38719i | 0.109868 | + | 0.0798236i | ||||
\(303\) | −8.88408 | − | 27.3424i | −0.510377 | − | 1.57078i | ||||
\(304\) | −3.99554 | − | 12.2970i | −0.229160 | − | 0.705281i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.107399 | − | 0.330541i | 0.00613961 | − | 0.0188958i | ||||
\(307\) | 13.9199 | 0.794452 | 0.397226 | − | 0.917721i | \(-0.369973\pi\) | ||||
0.397226 | + | 0.917721i | \(0.369973\pi\) | |||||||
\(308\) | −1.90566 | + | 5.86501i | −0.108585 | + | 0.334190i | ||||
\(309\) | −8.52865 | + | 6.19642i | −0.485178 | + | 0.352502i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1323 | − | 12.4473i | −0.971481 | − | 0.705822i | −0.0156926 | − | 0.999877i | \(-0.504995\pi\) |
−0.955789 | + | 0.294054i | \(0.904995\pi\) | |||||||
\(312\) | −6.40039 | + | 4.65016i | −0.362351 | + | 0.263263i | ||||
\(313\) | 9.62791 | − | 6.99509i | 0.544202 | − | 0.395386i | −0.281441 | − | 0.959578i | \(-0.590812\pi\) |
0.825643 | + | 0.564193i | \(0.190812\pi\) | |||||||
\(314\) | −2.66760 | − | 1.93813i | −0.150541 | − | 0.109375i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4590 | − | 9.77853i | 0.757127 | − | 0.550085i | ||||
\(317\) | 4.88635 | − | 15.0386i | 0.274445 | − | 0.844653i | −0.714921 | − | 0.699205i | \(-0.753537\pi\) |
0.989366 | − | 0.145448i | \(-0.0464625\pi\) | |||||||
\(318\) | 0.219396 | 0.0123031 | ||||||||
\(319\) | 1.08096 | − | 3.32684i | 0.0605219 | − | 0.186267i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.36250 | − | 16.5041i | −0.299305 | − | 0.921167i | ||||
\(322\) | −0.0356584 | − | 0.109745i | −0.00198716 | − | 0.00611586i | ||||
\(323\) | 7.93052 | + | 5.76186i | 0.441266 | + | 0.320598i | ||||
\(324\) | 13.3074 | 0.739300 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.84293 | 0.212840 | ||||||||
\(327\) | −22.5608 | − | 16.3914i | −1.24761 | − | 0.906445i | ||||
\(328\) | 1.25465 | + | 3.86141i | 0.0692763 | + | 0.213211i | ||||
\(329\) | −1.09432 | − | 3.36797i | −0.0603318 | − | 0.185682i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.154570 | − | 0.475716i | 0.00849591 | − | 0.0261477i | −0.946719 | − | 0.322062i | \(-0.895624\pi\) |
0.955215 | + | 0.295914i | \(0.0956242\pi\) | |||||||
\(332\) | −23.3300 | −1.28040 | ||||||||
\(333\) | 0.477706 | − | 1.47023i | 0.0261781 | − | 0.0805680i | ||||
\(334\) | 0.246548 | − | 0.179127i | 0.0134905 | − | 0.00980142i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.70567 | + | 3.41887i | 0.256715 | + | 0.186514i | ||||
\(337\) | 12.9844 | − | 9.43372i | 0.707305 | − | 0.513887i | −0.174998 | − | 0.984569i | \(-0.555992\pi\) |
0.882303 | + | 0.470681i | \(0.155992\pi\) | |||||||
\(338\) | 4.70691 | − | 3.41977i | 0.256022 | − | 0.186011i | ||||
\(339\) | −13.6368 | − | 9.90770i | −0.740648 | − | 0.538112i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.90134 | − | 3.56103i | 0.265422 | − | 0.192841i | ||||
\(342\) | −0.129266 | + | 0.397841i | −0.00698992 | + | 0.0215128i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.788581 | − | 2.42700i | 0.0425175 | − | 0.130855i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.284144 | − | 0.874504i | −0.0152757 | − | 0.0470136i | ||||
\(347\) | −9.18549 | − | 28.2700i | −0.493103 | − | 1.51761i | −0.819893 | − | 0.572517i | \(-0.805967\pi\) |
0.326790 | − | 0.945097i | \(-0.394033\pi\) | |||||||
\(348\) | −2.72531 | − | 1.98006i | −0.146092 | − | 0.106142i | ||||
\(349\) | 4.77252 | 0.255467 | 0.127734 | − | 0.991809i | \(-0.459230\pi\) | ||||
0.127734 | + | 0.991809i | \(0.459230\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.2838 | −1.93669 | ||||||||
\(352\) | 5.91400 | + | 4.29677i | 0.315217 | + | 0.229019i | ||||
\(353\) | 4.59978 | + | 14.1567i | 0.244821 | + | 0.753483i | 0.995666 | + | 0.0930035i | \(0.0296468\pi\) |
−0.750844 | + | 0.660479i | \(0.770353\pi\) | |||||||
\(354\) | 1.00833 | + | 3.10333i | 0.0535923 | + | 0.164940i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.1509 | + | 31.2413i | −0.537997 | + | 1.65578i | ||||
\(357\) | −4.40975 | −0.233389 | ||||||||
\(358\) | −0.113152 | + | 0.348246i | −0.00598028 | + | 0.0184054i | ||||
\(359\) | 1.22879 | − | 0.892771i | 0.0648532 | − | 0.0471186i | −0.554886 | − | 0.831926i | \(-0.687238\pi\) |
0.619740 | + | 0.784808i | \(0.287238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.82611 | + | 4.23292i | 0.306637 | + | 0.222785i | ||||
\(362\) | −0.337735 | + | 0.245379i | −0.0177510 | + | 0.0128968i | ||||
\(363\) | −1.38141 | + | 1.00366i | −0.0725055 | + | 0.0526783i | ||||
\(364\) | −10.3098 | − | 7.49052i | −0.540381 | − | 0.392610i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.12300 | + | 1.54245i | −0.110971 | + | 0.0806251i | ||||
\(367\) | 0.346453 | − | 1.06627i | 0.0180847 | − | 0.0556589i | −0.941607 | − | 0.336714i | \(-0.890684\pi\) |
0.959692 | + | 0.281055i | \(0.0906844\pi\) | |||||||
\(368\) | 2.18411 | 0.113855 | ||||||||
\(369\) | −0.975442 | + | 3.00210i | −0.0507795 | + | 0.156283i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.220620 | + | 0.678998i | 0.0114540 | + | 0.0352518i | ||||
\(372\) | −1.80290 | − | 5.54876i | −0.0934761 | − | 0.287690i | ||||
\(373\) | 16.7488 | + | 12.1687i | 0.867217 | + | 0.630070i | 0.929839 | − | 0.367967i | \(-0.119946\pi\) |
−0.0626214 | + | 0.998037i | \(0.519946\pi\) | |||||||
\(374\) | −1.78533 | −0.0923174 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.78926 | −0.143845 | ||||||||
\(377\) | 5.84809 | + | 4.24889i | 0.301192 | + | 0.218829i | ||||
\(378\) | −0.343036 | − | 1.05576i | −0.0176439 | − | 0.0543023i | ||||
\(379\) | 3.43439 | + | 10.5700i | 0.176413 | + | 0.542942i | 0.999695 | − | 0.0246897i | \(-0.00785978\pi\) |
−0.823283 | + | 0.567632i | \(0.807860\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.94623 | − | 18.3006i | 0.304635 | − | 0.937569i | ||||
\(382\) | −4.18534 | −0.214140 | ||||||||
\(383\) | 6.76503 | − | 20.8206i | 0.345677 | − | 1.06388i | −0.615543 | − | 0.788103i | \(-0.711063\pi\) |
0.961220 | − | 0.275782i | \(-0.0889367\pi\) | |||||||
\(384\) | 7.56696 | − | 5.49772i | 0.386150 | − | 0.280554i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.60561 | − | 2.61963i | −0.183521 | − | 0.133336i | ||||
\(387\) | 1.60510 | − | 1.16617i | 0.0815917 | − | 0.0592798i | ||||
\(388\) | 15.8801 | − | 11.5376i | 0.806191 | − | 0.585732i | ||||
\(389\) | 26.3164 | + | 19.1200i | 1.33429 | + | 0.969422i | 0.999633 | + | 0.0270833i | \(0.00862194\pi\) |
0.334661 | + | 0.942338i | \(0.391378\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.33963 | + | 0.973297i | −0.0677479 | + | 0.0492217i | ||||
\(392\) | 0.243394 | − | 0.749089i | 0.0122932 | − | 0.0378347i | ||||
\(393\) | 3.84563 | 0.193986 | ||||||||
\(394\) | 0.762519 | − | 2.34679i | 0.0384151 | − | 0.118230i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.16695 | + | 3.59149i | 0.0586413 | + | 0.180479i | ||||
\(397\) | 2.57008 | + | 7.90989i | 0.128989 | + | 0.396986i | 0.994607 | − | 0.103719i | \(-0.0330742\pi\) |
−0.865618 | + | 0.500705i | \(0.833074\pi\) | |||||||
\(398\) | −2.69789 | − | 1.96013i | −0.135233 | − | 0.0982524i | ||||
\(399\) | 5.30760 | 0.265712 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.343282 | 0.0171427 | 0.00857134 | − | 0.999963i | \(-0.497272\pi\) | ||||
0.00857134 | + | 0.999963i | \(0.497272\pi\) | |||||||
\(402\) | 3.79045 | + | 2.75392i | 0.189051 | + | 0.137353i | ||||
\(403\) | 3.86874 | + | 11.9068i | 0.192716 | + | 0.593118i | ||||
\(404\) | −11.2715 | − | 34.6902i | −0.560780 | − | 1.72590i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.0683414 | + | 0.210333i | −0.00339173 | + | 0.0104387i | ||||
\(407\) | −7.94107 | −0.393624 | ||||||||
\(408\) | −1.07331 | + | 3.30330i | −0.0531366 | + | 0.163538i | ||||
\(409\) | 13.6719 | − | 9.93319i | 0.676030 | − | 0.491165i | −0.196008 | − | 0.980602i | \(-0.562798\pi\) |
0.872038 | + | 0.489438i | \(0.162798\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.6351 | − | 9.17997i | −0.623246 | − | 0.452815i | ||||
\(412\) | −10.8206 | + | 7.86162i | −0.533092 | + | 0.387314i | ||||
\(413\) | −8.59038 | + | 6.24127i | −0.422705 | + | 0.307113i | ||||
\(414\) | −0.0571667 | − | 0.0415341i | −0.00280959 | − | 0.00204129i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −12.2212 | + | 8.87919i | −0.599191 | + | 0.435338i | ||||
\(417\) | 8.78813 | − | 27.0471i | 0.430357 | − | 1.32450i | ||||
\(418\) | 2.14884 | 0.105103 | ||||||||
\(419\) | −8.47434 | + | 26.0813i | −0.413999 | + | 1.27416i | 0.499145 | + | 0.866519i | \(0.333648\pi\) |
−0.913143 | + | 0.407639i | \(0.866352\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.84570 | + | 11.8358i | 0.187428 | + | 0.576843i | 0.999982 | − | 0.00604268i | \(-0.00192346\pi\) |
−0.812554 | + | 0.582886i | \(0.801923\pi\) | |||||||
\(422\) | 0.564898 | + | 1.73858i | 0.0274988 | + | 0.0846325i | ||||
\(423\) | −1.75439 | − | 1.27464i | −0.0853013 | − | 0.0619750i | ||||
\(424\) | 0.562327 | 0.0273090 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −3.62832 | −0.175793 | ||||||||
\(427\) | −6.90849 | − | 5.01931i | −0.334325 | − | 0.242901i | ||||
\(428\) | −6.80359 | − | 20.9393i | −0.328864 | − | 1.01214i | ||||
\(429\) | 9.76363 | + | 30.0494i | 0.471392 | + | 1.45080i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.58749 | + | 17.1965i | −0.269140 | + | 0.828327i | 0.721571 | + | 0.692341i | \(0.243420\pi\) |
−0.990711 | + | 0.135987i | \(0.956580\pi\) | |||||||
\(432\) | 21.0114 | 1.01091 | ||||||||
\(433\) | 4.90270 | − | 15.0890i | 0.235609 | − | 0.725130i | −0.761431 | − | 0.648246i | \(-0.775503\pi\) |
0.997040 | − | 0.0768839i | \(-0.0244971\pi\) | |||||||
\(434\) | −0.309878 | + | 0.225139i | −0.0148746 | + | 0.0108070i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −28.6237 | − | 20.7963i | −1.37083 | − | 0.995963i | ||||
\(437\) | 1.61238 | − | 1.17146i | 0.0771307 | − | 0.0560387i | ||||
\(438\) | 0.465093 | − | 0.337910i | 0.0222230 | − | 0.0161460i | ||||
\(439\) | −16.8115 | − | 12.2143i | −0.802370 | − | 0.582956i | 0.109238 | − | 0.994016i | \(-0.465159\pi\) |
−0.911609 | + | 0.411059i | \(0.865159\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.495409 | − | 0.359936i | 0.0235909 | − | 0.0171398i | ||||
\(442\) | 1.14007 | − | 3.50878i | 0.0542277 | − | 0.166896i | ||||
\(443\) | 17.1519 | 0.814913 | 0.407456 | − | 0.913225i | \(-0.366416\pi\) | ||||
0.407456 | + | 0.913225i | \(0.366416\pi\) | |||||||
\(444\) | −2.36317 | + | 7.27308i | −0.112151 | + | 0.345165i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.12583 | + | 3.46495i | 0.0533096 | + | 0.164070i | ||||
\(447\) | −9.64499 | − | 29.6842i | −0.456192 | − | 1.40402i | ||||
\(448\) | 5.71679 | + | 4.15349i | 0.270093 | + | 0.196234i | ||||
\(449\) | −40.9515 | −1.93262 | −0.966311 | − | 0.257378i | \(-0.917141\pi\) | ||||
−0.966311 | + | 0.257378i | \(0.917141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.2151 | 0.763538 | ||||||||
\(452\) | −17.3015 | − | 12.5702i | −0.813792 | − | 0.591255i | ||||
\(453\) | −5.66631 | − | 17.4391i | −0.266226 | − | 0.819360i | ||||
\(454\) | 1.05768 | + | 3.25522i | 0.0496396 | + | 0.152775i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.29184 | − | 3.97586i | 0.0604958 | − | 0.186187i | ||||
\(457\) | −2.15047 | −0.100595 | −0.0502974 | − | 0.998734i | \(-0.516017\pi\) | ||||
−0.0502974 | + | 0.998734i | \(0.516017\pi\) | |||||||
\(458\) | −0.144725 | + | 0.445419i | −0.00676257 | + | 0.0208131i | ||||
\(459\) | −12.8873 | + | 9.36320i | −0.601529 | + | 0.437037i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1567 | + | 11.0120i | 0.705919 | + | 0.512880i | 0.881855 | − | 0.471521i | \(-0.156295\pi\) |
−0.175935 | + | 0.984402i | \(0.556295\pi\) | |||||||
\(462\) | −0.782044 | + | 0.568189i | −0.0363840 | + | 0.0264345i | ||||
\(463\) | 7.57799 | − | 5.50573i | 0.352179 | − | 0.255873i | −0.397604 | − | 0.917557i | \(-0.630158\pi\) |
0.749783 | + | 0.661684i | \(0.230158\pi\) | |||||||
\(464\) | −3.38653 | − | 2.46046i | −0.157216 | − | 0.114224i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.223810 | + | 0.162608i | −0.0103678 | + | 0.00753266i | ||||
\(467\) | 5.31635 | − | 16.3621i | 0.246012 | − | 0.757146i | −0.749457 | − | 0.662053i | \(-0.769685\pi\) |
0.995468 | − | 0.0950926i | \(-0.0303147\pi\) | |||||||
\(468\) | −7.80368 | −0.360725 | ||||||||
\(469\) | −4.71139 | + | 14.5002i | −0.217552 | + | 0.669555i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.91676 | + | 24.3653i | 0.364785 | + | 1.12269i | ||||
\(472\) | 2.58442 | + | 7.95404i | 0.118958 | + | 0.366114i | ||||
\(473\) | −8.24521 | − | 5.99049i | −0.379115 | − | 0.275443i | ||||
\(474\) | 2.60775 | 0.119778 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.59481 | −0.256438 | ||||||||
\(477\) | 0.353693 | + | 0.256973i | 0.0161945 | + | 0.0117660i | ||||
\(478\) | 0.645487 | + | 1.98660i | 0.0295239 | + | 0.0908651i | ||||
\(479\) | −0.493255 | − | 1.51808i | −0.0225374 | − | 0.0693630i | 0.939155 | − | 0.343493i | \(-0.111610\pi\) |
−0.961693 | + | 0.274130i | \(0.911610\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.07098 | − | 15.6069i | 0.231217 | − | 0.711612i | ||||
\(482\) | 2.54444 | 0.115896 | ||||||||
\(483\) | −0.277053 | + | 0.852682i | −0.0126064 | + | 0.0387984i | ||||
\(484\) | −1.75265 | + | 1.27337i | −0.0796659 | + | 0.0578806i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00667 | − | 0.731390i | −0.0456635 | − | 0.0331765i | ||||
\(487\) | −29.8809 | + | 21.7097i | −1.35403 | + | 0.983761i | −0.355231 | + | 0.934779i | \(0.615598\pi\) |
−0.998800 | + | 0.0489823i | \(0.984402\pi\) | |||||||
\(488\) | −5.44139 | + | 3.95340i | −0.246320 | + | 0.178962i | ||||
\(489\) | −24.1558 | − | 17.5502i | −1.09236 | − | 0.793648i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.5175 | + | 8.36798i | −0.519779 | + | 0.377642i | −0.816521 | − | 0.577316i | \(-0.804100\pi\) |
0.296742 | + | 0.954958i | \(0.404100\pi\) | |||||||
\(492\) | 4.82541 | − | 14.8511i | 0.217546 | − | 0.669539i | ||||
\(493\) | 3.17358 | 0.142931 | ||||||||
\(494\) | −1.37220 | + | 4.22319i | −0.0617381 | + | 0.190010i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.24033 | − | 6.89502i | −0.100594 | − | 0.309595i | ||||
\(497\) | −3.64856 | − | 11.2291i | −0.163660 | − | 0.503694i | ||||
\(498\) | −2.95859 | − | 2.14954i | −0.132577 | − | 0.0963232i | ||||
\(499\) | 8.62876 | 0.386276 | 0.193138 | − | 0.981172i | \(-0.438133\pi\) | ||||
0.193138 | + | 0.981172i | \(0.438133\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.36780 | −0.105786 | ||||||||
\(502\) | −2.04379 | − | 1.48490i | −0.0912190 | − | 0.0662745i | ||||
\(503\) | 1.73953 | + | 5.35372i | 0.0775618 | + | 0.238711i | 0.982318 | − | 0.187219i | \(-0.0599473\pi\) |
−0.904757 | + | 0.425929i | \(0.859947\pi\) | |||||||
\(504\) | −0.149044 | − | 0.458712i | −0.00663897 | − | 0.0204326i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −0.112168 | + | 0.345217i | −0.00498647 | + | 0.0153468i | ||||
\(507\) | −45.2044 | −2.00760 | ||||||||
\(508\) | 7.54419 | − | 23.2186i | 0.334719 | − | 1.03016i | ||||
\(509\) | −13.1848 | + | 9.57934i | −0.584407 | + | 0.424597i | −0.840310 | − | 0.542106i | \(-0.817627\pi\) |
0.255903 | + | 0.966702i | \(0.417627\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.51347 | + | 1.09960i | 0.0669519 | + | 0.0486434i | ||||
\(512\) | 11.8743 | − | 8.62721i | 0.524776 | − | 0.381272i | ||||
\(513\) | 15.5113 | − | 11.2696i | 0.684839 | − | 0.497565i | ||||
\(514\) | −3.25198 | − | 2.36270i | −0.143439 | − | 0.104214i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −7.94026 | + | 5.76894i | −0.349550 | + | 0.253963i | ||||
\(517\) | −3.44232 | + | 10.5944i | −0.151393 | + | 0.465939i | ||||
\(518\) | 0.502059 | 0.0220592 | ||||||||
\(519\) | −2.20770 | + | 6.79460i | −0.0969072 | + | 0.298250i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.0730238 | + | 0.224744i | 0.00319923 | + | 0.00984623i | 0.952643 | − | 0.304090i | \(-0.0983523\pi\) |
−0.949444 | + | 0.313936i | \(0.898352\pi\) | |||||||
\(522\) | 0.0418495 | + | 0.128800i | 0.00183170 | + | 0.00563740i | ||||
\(523\) | −6.20767 | − | 4.51014i | −0.271443 | − | 0.197215i | 0.443734 | − | 0.896159i | \(-0.353654\pi\) |
−0.715176 | + | 0.698944i | \(0.753654\pi\) | |||||||
\(524\) | 4.87909 | 0.213144 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.318522 | −0.0138882 | ||||||||
\(527\) | 4.44670 | + | 3.23071i | 0.193701 | + | 0.140732i | ||||
\(528\) | −5.65396 | − | 17.4011i | −0.246057 | − | 0.757285i | ||||
\(529\) | −7.00336 | − | 21.5541i | −0.304494 | − | 0.937135i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.00929 | + | 6.18397i | −0.0871959 | + | 0.268361i | ||||
\(532\) | 6.73394 | 0.291953 | ||||||||
\(533\) | −10.3546 | + | 31.8681i | −0.448507 | + | 1.38036i | ||||
\(534\) | −4.16573 | + | 3.02658i | −0.180269 | + | 0.130973i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.71518 | + | 7.05849i | 0.419632 | + | 0.304880i | ||||
\(537\) | 2.30165 | − | 1.67225i | 0.0993237 | − | 0.0721629i | ||||
\(538\) | 3.16933 | − | 2.30265i | 0.136639 | − | 0.0992744i | ||||
\(539\) | −2.54486 | − | 1.84895i | −0.109615 | − | 0.0796400i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.06900 | + | 0.776676i | −0.0459600 | + | 0.0333919i | −0.610528 | − | 0.791995i | \(-0.709043\pi\) |
0.564568 | + | 0.825387i | \(0.309043\pi\) | |||||||
\(542\) | 1.63856 | − | 5.04298i | 0.0703823 | − | 0.216614i | ||||
\(543\) | 3.24355 | 0.139194 | ||||||||
\(544\) | −2.04941 | + | 6.30744i | −0.0878678 | + | 0.270429i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.617287 | − | 1.89981i | −0.0264174 | − | 0.0813045i | ||||
\(547\) | −10.6660 | − | 32.8266i | −0.456046 | − | 1.40357i | −0.869903 | − | 0.493224i | \(-0.835818\pi\) |
0.413856 | − | 0.910342i | \(-0.364182\pi\) | |||||||
\(548\) | −16.0307 | − | 11.6469i | −0.684795 | − | 0.497533i | ||||
\(549\) | −5.22916 | −0.223175 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.81973 | −0.162726 | ||||||||
\(552\) | 0.571302 | + | 0.415075i | 0.0243162 | + | 0.0176668i | ||||
\(553\) | 2.62230 | + | 8.07060i | 0.111511 | + | 0.343197i | ||||
\(554\) | 0.208838 | + | 0.642738i | 0.00887269 | + | 0.0273073i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.1498 | − | 34.3156i | 0.472857 | − | 1.45530i | ||||
\(557\) | 39.5507 | 1.67582 | 0.837909 | − | 0.545810i | \(-0.183778\pi\) | ||||
0.837909 | + | 0.545810i | \(0.183778\pi\) | |||||||
\(558\) | −0.0724805 | + | 0.223072i | −0.00306835 | + | 0.00944340i | ||||
\(559\) | 17.0385 | − | 12.3792i | 0.720654 | − | 0.523585i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11.2222 | + | 8.15342i | 0.473803 | + | 0.344238i | ||||
\(562\) | −5.33143 | + | 3.87351i | −0.224893 | + | 0.163394i | ||||
\(563\) | −3.94887 | + | 2.86902i | −0.166425 | + | 0.120915i | −0.667880 | − | 0.744269i | \(-0.732798\pi\) |
0.501455 | + | 0.865184i | \(0.332798\pi\) | |||||||
\(564\) | 8.67879 | + | 6.30551i | 0.365443 | + | 0.265510i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.41969 | − | 1.03147i | 0.0596740 | − | 0.0433557i | ||||
\(567\) | −2.09759 | + | 6.45571i | −0.0880904 | + | 0.271114i | ||||
\(568\) | −9.29963 | −0.390204 | ||||||||
\(569\) | −3.15196 | + | 9.70074i | −0.132137 | + | 0.406676i | −0.995134 | − | 0.0985334i | \(-0.968585\pi\) |
0.862997 | + | 0.505210i | \(0.168585\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.82386 | + | 11.7686i | 0.160024 | + | 0.492502i | 0.998635 | − | 0.0522276i | \(-0.0166321\pi\) |
−0.838611 | + | 0.544730i | \(0.816632\pi\) | |||||||
\(572\) | 12.3875 | + | 38.1247i | 0.517946 | + | 1.59407i | ||||
\(573\) | 26.3081 | + | 19.1140i | 1.09904 | + | 0.798498i | ||||
\(574\) | −1.02517 | −0.0427897 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.32714 | 0.180298 | ||||||||
\(577\) | 20.4264 | + | 14.8406i | 0.850362 | + | 0.617824i | 0.925246 | − | 0.379368i | \(-0.123859\pi\) |
−0.0748839 | + | 0.997192i | \(0.523859\pi\) | |||||||
\(578\) | 0.544229 | + | 1.67497i | 0.0226370 | + | 0.0696694i | ||||
\(579\) | 10.7005 | + | 32.9329i | 0.444699 | + | 1.36864i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.67741 | − | 11.3179i | 0.152565 | − | 0.469546i | ||||
\(582\) | 3.07686 | 0.127540 | ||||||||
\(583\) | 0.693987 | − | 2.13587i | 0.0287420 | − | 0.0884587i | ||||
\(584\) | 1.19207 | − | 0.866086i | 0.0493280 | − | 0.0358389i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.57761 | − | 1.87274i | −0.106480 | − | 0.0773623i | ||||
\(587\) | −20.5017 | + | 14.8953i | −0.846194 | + | 0.614796i | −0.924094 | − | 0.382165i | \(-0.875179\pi\) |
0.0778996 | + | 0.996961i | \(0.475179\pi\) | |||||||
\(588\) | −2.45074 | + | 1.78057i | −0.101067 | + | 0.0734294i | ||||
\(589\) | −5.35207 | − | 3.88850i | −0.220528 | − | 0.160223i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.5106 | + | 11.2691i | −0.638019 | + | 0.463548i | ||||
\(592\) | −2.93652 | + | 9.03769i | −0.120690 | + | 0.371447i | ||||
\(593\) | 22.4503 | 0.921924 | 0.460962 | − | 0.887420i | \(-0.347505\pi\) | ||||
0.460962 | + | 0.887420i | \(0.347505\pi\) | |||||||
\(594\) | −1.07906 | + | 3.32102i | −0.0442745 | + | 0.136263i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.2369 | − | 37.6614i | −0.501244 | − | 1.54267i | ||||
\(597\) | 8.00664 | + | 24.6419i | 0.327690 | + | 1.00853i | ||||
\(598\) | −0.606840 | − | 0.440895i | −0.0248155 | − | 0.0180295i | ||||
\(599\) | −19.6210 | −0.801691 | −0.400845 | − | 0.916146i | \(-0.631284\pi\) | ||||
−0.400845 | + | 0.916146i | \(0.631284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.6423 | −0.434109 | −0.217055 | − | 0.976159i | \(-0.569645\pi\) | ||||
−0.217055 | + | 0.976159i | \(0.569645\pi\) | |||||||
\(602\) | 0.521288 | + | 0.378738i | 0.0212461 | + | 0.0154362i | ||||
\(603\) | 2.88506 | + | 8.87931i | 0.117489 | + | 0.361593i | ||||
\(604\) | −7.18904 | − | 22.1256i | −0.292518 | − | 0.900278i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.76683 | − | 5.43774i | 0.0717726 | − | 0.220893i | ||||
\(607\) | −0.0394412 | −0.00160087 | −0.000800435 | − | 1.00000i | \(-0.500255\pi\) | ||||
−0.000800435 | 1.00000i | \(0.500255\pi\) | ||||||||
\(608\) | 2.46668 | − | 7.59167i | 0.100037 | − | 0.307883i | ||||
\(609\) | 1.39015 | − | 1.01000i | 0.0563316 | − | 0.0409273i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −18.6233 | − | 13.5306i | −0.753418 | − | 0.547390i | ||||
\(612\) | −2.77172 | + | 2.01377i | −0.112040 | + | 0.0814020i | ||||
\(613\) | −10.9840 | + | 7.98031i | −0.443638 | + | 0.322322i | −0.787079 | − | 0.616853i | \(-0.788407\pi\) |
0.343441 | + | 0.939174i | \(0.388407\pi\) | |||||||
\(614\) | 2.23963 | + | 1.62719i | 0.0903843 | + | 0.0656680i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.00443 | + | 1.45631i | −0.0807609 | + | 0.0586762i | ||||
\(617\) | −13.2111 | + | 40.6595i | −0.531858 | + | 1.63689i | 0.218484 | + | 0.975840i | \(0.429889\pi\) |
−0.750342 | + | 0.661050i | \(0.770111\pi\) | |||||||
\(618\) | −2.09655 | −0.0843356 | ||||||||
\(619\) | −0.536195 | + | 1.65024i | −0.0215515 | + | 0.0663287i | −0.961254 | − | 0.275665i | \(-0.911102\pi\) |
0.939702 | + | 0.341993i | \(0.111102\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00082 | + | 3.08020i | 0.0401614 | + | 0.123604i | ||||
\(622\) | −1.30143 | − | 4.00540i | −0.0521827 | − | 0.160602i | ||||
\(623\) | −13.5558 | − | 9.84885i | −0.543101 | − | 0.394586i | ||||
\(624\) | 37.8095 | 1.51359 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.36678 | 0.0945954 | ||||||||
\(627\) | −13.5071 | − | 9.81350i | −0.539423 | − | 0.391913i | ||||
\(628\) | 10.0443 | + | 30.9131i | 0.400810 | + | 1.23357i | ||||
\(629\) | −2.22630 | − | 6.85186i | −0.0887685 | − | 0.273201i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.77123 | − | 11.6066i | 0.150130 | − | 0.462053i | −0.847505 | − | 0.530788i | \(-0.821896\pi\) |
0.997635 | + | 0.0687345i | \(0.0218961\pi\) | |||||||
\(632\) | 6.68384 | 0.265869 | ||||||||
\(633\) | 4.38906 | − | 13.5081i | 0.174450 | − | 0.536900i | ||||
\(634\) | 2.54415 | − | 1.84843i | 0.101041 | − | 0.0734105i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.74968 | − | 1.27122i | −0.0693795 | − | 0.0504071i | ||||
\(637\) | 5.25890 | − | 3.82082i | 0.208365 | − | 0.151386i | ||||
\(638\) | 0.562815 | − | 0.408909i | 0.0222821 | − | 0.0161889i | ||||
\(639\) | −5.84929 | − | 4.24976i | −0.231394 | − | 0.168118i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.04063 | − | 3.66223i | 0.199093 | − | 0.144650i | −0.483772 | − | 0.875194i | \(-0.660734\pi\) |
0.682865 | + | 0.730544i | \(0.260734\pi\) | |||||||
\(642\) | 1.06647 | − | 3.28226i | 0.0420903 | − | 0.129541i | ||||
\(643\) | 11.8383 | 0.466857 | 0.233429 | − | 0.972374i | \(-0.425005\pi\) | ||||
0.233429 | + | 0.972374i | \(0.425005\pi\) | |||||||
\(644\) | −0.351507 | + | 1.08183i | −0.0138513 | + | 0.0426300i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.602433 | + | 1.85410i | 0.0237024 | + | 0.0729485i | ||||
\(647\) | 1.25127 | + | 3.85100i | 0.0491923 | + | 0.151398i | 0.972635 | − | 0.232337i | \(-0.0746373\pi\) |
−0.923443 | + | 0.383736i | \(0.874637\pi\) | |||||||
\(648\) | 4.32536 | + | 3.14256i | 0.169916 | + | 0.123451i | ||||
\(649\) | 33.4011 | 1.31111 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.97601 | 0.116639 | ||||||||
\(652\) | −30.6473 | − | 22.2666i | −1.20024 | − | 0.872027i | ||||
\(653\) | 6.61410 | + | 20.3561i | 0.258830 | + | 0.796596i | 0.993051 | + | 0.117685i | \(0.0375474\pi\) |
−0.734221 | + | 0.678910i | \(0.762453\pi\) | |||||||
\(654\) | −1.71381 | − | 5.27455i | −0.0670151 | − | 0.206251i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.99617 | − | 18.4543i | 0.234111 | − | 0.720520i | ||||
\(657\) | 1.14557 | 0.0446930 | ||||||||
\(658\) | 0.217634 | − | 0.669808i | 0.00848425 | − | 0.0261118i | ||||
\(659\) | −12.3162 | + | 8.94823i | −0.479770 | + | 0.348573i | −0.801237 | − | 0.598348i | \(-0.795824\pi\) |
0.321467 | + | 0.946921i | \(0.395824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.1057 | + | 7.34222i | 0.393066 | + | 0.285579i | 0.766711 | − | 0.641993i | \(-0.221892\pi\) |
−0.373645 | + | 0.927572i | \(0.621892\pi\) | |||||||
\(662\) | 0.0804788 | − | 0.0584713i | 0.00312790 | − | 0.00227255i | ||||
\(663\) | −23.1905 | + | 16.8489i | −0.900644 | + | 0.654356i | ||||
\(664\) | −7.58306 | − | 5.50941i | −0.294280 | − | 0.213807i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.248725 | − | 0.180709i | 0.00963788 | − | 0.00700233i | ||||
\(667\) | 0.199387 | − | 0.613651i | 0.00772031 | − | 0.0237607i | ||||
\(668\) | −3.00411 | −0.116233 | ||||||||
\(669\) | 8.74731 | − | 26.9215i | 0.338191 | − | 1.04084i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.30070 | + | 25.5469i | 0.320445 | + | 0.986228i | ||||
\(672\) | 1.10964 | + | 3.41513i | 0.0428054 | + | 0.131742i | ||||
\(673\) | −13.2376 | − | 9.61769i | −0.510273 | − | 0.370735i | 0.302654 | − | 0.953100i | \(-0.402127\pi\) |
−0.812927 | + | 0.582366i | \(0.802127\pi\) | |||||||
\(674\) | 3.19188 | 0.122947 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −57.3524 | −2.20586 | ||||||||
\(677\) | −18.0175 | − | 13.0905i | −0.692470 | − | 0.503109i | 0.185001 | − | 0.982738i | \(-0.440771\pi\) |
−0.877471 | + | 0.479630i | \(0.840771\pi\) | |||||||
\(678\) | −1.03590 | − | 3.18818i | −0.0397836 | − | 0.122441i | ||||
\(679\) | 3.09402 | + | 9.52242i | 0.118738 | + | 0.365437i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.21785 | − | 25.2919i | 0.314909 | − | 0.969189i | ||||
\(682\) | 1.20487 | 0.0461368 | ||||||||
\(683\) | −3.12674 | + | 9.62312i | −0.119641 | + | 0.368219i | −0.992887 | − | 0.119062i | \(-0.962011\pi\) |
0.873245 | + | 0.487281i | \(0.162011\pi\) | |||||||
\(684\) | 3.33606 | − | 2.42379i | 0.127557 | − | 0.0926759i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.160894 | + | 0.116896i | 0.00614297 | + | 0.00446313i | ||||
\(687\) | 2.94389 | − | 2.13886i | 0.112316 | − | 0.0816027i | ||||
\(688\) | −9.86674 | + | 7.16861i | −0.376166 | + | 0.273301i | ||||
\(689\) | 3.75454 | + | 2.72784i | 0.143037 | + | 0.103922i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.9145 | + | 7.92983i | −0.415206 | + | 0.301665i | −0.775706 | − | 0.631094i | \(-0.782606\pi\) |
0.360500 | + | 0.932759i | \(0.382606\pi\) | |||||||
\(692\) | −2.80099 | + | 8.62055i | −0.106477 | + | 0.327704i | ||||
\(693\) | −1.92625 | −0.0731723 | ||||||||
\(694\) | 1.82677 | − | 5.62223i | 0.0693434 | − | 0.213417i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.418227 | − | 1.28717i | −0.0158529 | − | 0.0487901i | ||||
\(697\) | 4.54595 | + | 13.9910i | 0.172190 | + | 0.529947i | ||||
\(698\) | 0.767870 | + | 0.557890i | 0.0290643 | + | 0.0211165i | ||||
\(699\) | 2.14944 | 0.0812991 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.7883 | 0.483007 | 0.241503 | − | 0.970400i | \(-0.422360\pi\) | ||||
0.241503 | + | 0.970400i | \(0.422360\pi\) | |||||||
\(702\) | −5.83785 | − | 4.24145i | −0.220336 | − | 0.160083i | ||||
\(703\) | 2.67959 | + | 8.24693i | 0.101063 | + | 0.311039i | ||||
\(704\) | −6.86885 | − | 21.1401i | −0.258879 | − | 0.796749i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −0.914785 | + | 2.81542i | −0.0344284 | + | 0.105960i | ||||
\(707\) | 18.6057 | 0.699739 | ||||||||
\(708\) | 9.93978 | − | 30.5915i | 0.373560 | − | 1.14970i | ||||
\(709\) | 20.2329 | − | 14.7001i | 0.759864 | − | 0.552073i | −0.139005 | − | 0.990292i | \(-0.544390\pi\) |
0.898868 | + | 0.438218i | \(0.144390\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.20401 | + | 3.05439i | 0.157663 | + | 0.114549i | ||||
\(712\) | −10.6771 | + | 7.75733i | −0.400140 | + | 0.290718i | ||||
\(713\) | 0.904074 | − | 0.656848i | 0.0338578 | − | 0.0245992i | ||||
\(714\) | −0.709504 | − | 0.515485i | −0.0265525 | − | 0.0192915i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.92019 | − | 2.12164i | 0.109133 | − | 0.0792895i | ||||
\(717\) | 5.01521 | − | 15.4352i | 0.187297 | − | 0.576439i | ||||
\(718\) | 0.302067 | 0.0112731 | ||||||||
\(719\) | 2.24894 | − | 6.92151i | 0.0838712 | − | 0.258129i | −0.900323 | − | 0.435223i | \(-0.856670\pi\) |
0.984194 | + | 0.177094i | \(0.0566696\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.10824 | − | 6.48850i | −0.0785150 | − | 0.241644i | ||||
\(722\) | 0.442574 | + | 1.36210i | 0.0164709 | + | 0.0506922i | ||||
\(723\) | −15.9938 | − | 11.6202i | −0.594815 | − | 0.432158i | ||||
\(724\) | 4.11520 | 0.152940 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.339585 | −0.0126032 | ||||||||
\(727\) | −18.8077 | − | 13.6646i | −0.697540 | − | 0.506792i | 0.181590 | − | 0.983374i | \(-0.441876\pi\) |
−0.879130 | + | 0.476582i | \(0.841876\pi\) | |||||||
\(728\) | −1.58215 | − | 4.86935i | −0.0586383 | − | 0.180470i | ||||
\(729\) | 9.28031 | + | 28.5618i | 0.343715 | + | 1.05785i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.85726 | − | 8.79374i | 0.105680 | − | 0.325248i | ||||
\(732\) | 25.8681 | 0.956114 | ||||||||
\(733\) | −10.8631 | + | 33.4330i | −0.401236 | + | 1.23488i | 0.522761 | + | 0.852479i | \(0.324902\pi\) |
−0.923997 | + | 0.382399i | \(0.875098\pi\) | |||||||
\(734\) | 0.180386 | − | 0.131058i | 0.00665815 | − | 0.00483743i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.09086 | + | 0.792560i | 0.0402098 | + | 0.0292141i | ||||
\(737\) | 38.7999 | − | 28.1898i | 1.42921 | − | 1.03838i | ||||
\(738\) | −0.507878 | + | 0.368995i | −0.0186952 | + | 0.0135829i | ||||
\(739\) | −14.1676 | − | 10.2934i | −0.521164 | − | 0.378648i | 0.295878 | − | 0.955226i | \(-0.404388\pi\) |
−0.817042 | + | 0.576578i | \(0.804388\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 27.9122 | − | 20.2794i | 1.02538 | − | 0.744982i | ||||
\(742\) | −0.0438760 | + | 0.135036i | −0.00161074 | + | 0.00495734i | ||||
\(743\) | 12.5993 | 0.462223 | 0.231111 | − | 0.972927i | \(-0.425764\pi\) | ||||
0.231111 | + | 0.972927i | \(0.425764\pi\) | |||||||
\(744\) | 0.724342 | − | 2.22930i | 0.0265557 | − | 0.0817299i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.27230 | + | 3.91574i | 0.0465822 | + | 0.143365i | ||||
\(747\) | −2.25190 | − | 6.93063i | −0.0823927 | − | 0.253579i | ||||
\(748\) | 14.2380 | + | 10.3445i | 0.520594 | + | 0.378234i | ||||
\(749\) | 11.2305 | 0.410355 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.86802 | 0.360089 | 0.180045 | − | 0.983658i | \(-0.442376\pi\) | ||||
0.180045 | + | 0.983658i | \(0.442376\pi\) | |||||||
\(752\) | 10.7845 | + | 7.83536i | 0.393269 | + | 0.285726i | ||||
\(753\) | 6.06546 | + | 18.6676i | 0.221038 | + | 0.680284i | ||||
\(754\) | 0.444244 | + | 1.36724i | 0.0161784 | + | 0.0497920i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3.38153 | + | 10.4073i | −0.122985 | + | 0.378509i | ||||
\(757\) | 37.0730 | 1.34744 | 0.673721 | − | 0.738986i | \(-0.264695\pi\) | ||||
0.673721 | + | 0.738986i | \(0.264695\pi\) | |||||||
\(758\) | −0.683017 | + | 2.10211i | −0.0248083 | + | 0.0763521i | ||||
\(759\) | 2.28163 | − | 1.65770i | 0.0828180 | − | 0.0601708i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.8906 | + | 17.3575i | 0.866032 | + | 0.629209i | 0.929519 | − | 0.368774i | \(-0.120222\pi\) |
−0.0634873 | + | 0.997983i | \(0.520222\pi\) | |||||||
\(762\) | 3.09599 | − | 2.24937i | 0.112156 | − | 0.0814860i | ||||
\(763\) | 14.6006 | − | 10.6079i | 0.528576 | − | 0.384033i | ||||
\(764\) | 33.3781 | + | 24.2506i | 1.20758 | + | 0.877355i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.52231 | − | 2.55911i | 0.127266 | − | 0.0924644i | ||||
\(767\) | −21.3292 | + | 65.6445i | −0.770153 | + | 2.37029i | ||||
\(768\) | −19.9777 | −0.720882 | ||||||||
\(769\) | −7.81095 | + | 24.0396i | −0.281670 | + | 0.866891i | 0.705707 | + | 0.708504i | \(0.250629\pi\) |
−0.987377 | + | 0.158387i | \(0.949371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.65105 | + | 29.7029i | 0.347574 | + | 1.06972i | ||||
\(772\) | 13.5762 | + | 41.7831i | 0.488617 | + | 1.50381i | ||||
\(773\) | 3.46722 | + | 2.51909i | 0.124707 | + | 0.0906052i | 0.648391 | − | 0.761308i | \(-0.275442\pi\) |
−0.523683 | + | 0.851913i | \(0.675442\pi\) | |||||||
\(774\) | 0.394572 | 0.0141826 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 7.88620 | 0.283098 | ||||||||
\(777\) | −3.15583 | − | 2.29285i | −0.113215 | − | 0.0822554i | ||||
\(778\) | 1.99910 | + | 6.15259i | 0.0716711 | + | 0.220581i | ||||
\(779\) | −5.47153 | − | 16.8396i | −0.196038 | − | 0.603343i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.4770 | + | 35.3226i | −0.410679 | + | 1.26394i | ||||
\(782\) | −0.329313 | −0.0117762 | ||||||||
\(783\) | 1.91812 | − | 5.90338i | 0.0685482 | − | 0.210970i | ||||
\(784\) | −3.04535 | + | 2.21257i | −0.108762 | + | 0.0790205i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.618739 | + | 0.449540i | 0.0220697 | + | 0.0160346i | ||||
\(787\) | 37.0174 | − | 26.8947i | 1.31953 | − | 0.958693i | 0.319590 | − | 0.947556i | \(-0.396455\pi\) |
0.999938 | − | 0.0111376i | \(-0.00354527\pi\) | |||||||
\(788\) | −19.6788 | + | 14.2975i | −0.701028 | + | 0.509327i | ||||
\(789\) | 2.00216 | + | 1.45466i | 0.0712789 | + | 0.0517872i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.82526 | − | 6.41192i | 0.313790 | − | 0.227982i | ||||
\(792\) | −0.468838 | + | 1.44293i | −0.0166594 | + | 0.0512724i | ||||
\(793\) | −55.5089 | −1.97118 | ||||||||
\(794\) | −0.511127 | + | 1.57309i | −0.0181392 | + | 0.0558268i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.1583 | + | 31.2641i | 0.360052 | + | 1.10813i | ||||
\(797\) | −8.24078 | − | 25.3625i | −0.291903 | − | 0.898386i | −0.984244 | − | 0.176816i | \(-0.943420\pi\) |
0.692341 | − | 0.721571i | \(-0.256580\pi\) | |||||||
\(798\) | 0.853962 | + | 0.620440i | 0.0302299 | + | 0.0219633i | ||||
\(799\) | −10.1063 | −0.357535 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10.2606 | −0.362541 | ||||||||
\(802\) | 0.0552320 | + | 0.0401284i | 0.00195031 | + | 0.00141698i | ||||
\(803\) | −1.81846 | − | 5.59666i | −0.0641722 | − | 0.197502i | ||||
\(804\) | −14.2721 | − | 43.9251i | −0.503339 | − | 1.54912i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.769400 | + | 2.36797i | −0.0271010 | + | 0.0834082i | ||||
\(807\) | −30.4377 | −1.07146 | ||||||||
\(808\) | 4.52850 | − | 13.9373i | 0.159312 | − | 0.490313i | ||||
\(809\) | 7.26466 | − | 5.27808i | 0.255412 | − | 0.185568i | −0.452710 | − | 0.891658i | \(-0.649543\pi\) |
0.708122 | + | 0.706090i | \(0.249543\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.2348 | + | 18.3341i | 0.886113 | + | 0.643799i | 0.934862 | − | 0.355012i | \(-0.115523\pi\) |
−0.0487484 | + | 0.998811i | \(0.515523\pi\) | |||||||
\(812\) | 1.76373 | − | 1.28142i | 0.0618948 | − | 0.0449692i | ||||
\(813\) | −33.3304 | + | 24.2159i | −1.16895 | + | 0.849290i | ||||
\(814\) | −1.27767 | − | 0.928282i | −0.0447823 | − | 0.0325363i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 13.4292 | − | 9.75690i | 0.470117 | − | 0.341560i | ||||
\(817\) | −3.43901 | + | 10.5842i | −0.120316 | + | 0.370294i | ||||
\(818\) | 3.36088 | 0.117510 | ||||||||
\(819\) | 1.23006 | − | 3.78574i | 0.0429818 | − | 0.132284i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.28513 | + | 19.3437i | 0.219353 | + | 0.675098i | 0.998816 | + | 0.0486501i | \(0.0154919\pi\) |
−0.779463 | + | 0.626448i | \(0.784508\pi\) | |||||||
\(822\) | −0.959815 | − | 2.95401i | −0.0334774 | − | 0.103033i | ||||
\(823\) | −11.3083 | − | 8.21599i | −0.394184 | − | 0.286391i | 0.372984 | − | 0.927838i | \(-0.378335\pi\) |
−0.767168 | + | 0.641446i | \(0.778335\pi\) | |||||||
\(824\) | −5.37359 | −0.187198 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.11172 | −0.0734762 | ||||||||
\(827\) | 27.6754 | + | 20.1073i | 0.962367 | + | 0.699200i | 0.953699 | − | 0.300762i | \(-0.0972411\pi\) |
0.00866736 | + | 0.999962i | \(0.497241\pi\) | |||||||
\(828\) | 0.215249 | + | 0.662468i | 0.00748041 | + | 0.0230223i | ||||
\(829\) | 13.7578 | + | 42.3423i | 0.477829 | + | 1.47061i | 0.842103 | + | 0.539316i | \(0.181317\pi\) |
−0.364274 | + | 0.931292i | \(0.618683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.62260 | − | 4.99385i | 0.0562874 | − | 0.173235i | ||||
\(832\) | 45.9338 | 1.59247 | ||||||||
\(833\) | 0.881886 | − | 2.71417i | 0.0305555 | − | 0.0940403i | ||||
\(834\) | 4.57567 | − | 3.32442i | 0.158442 | − | 0.115115i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −17.1370 | − | 12.4507i | −0.592694 | − | 0.430618i | ||||
\(837\) | 8.69727 | − | 6.31894i | 0.300622 | − | 0.218414i | ||||
\(838\) | −4.41229 | + | 3.20572i | −0.152420 | + | 0.110740i | ||||
\(839\) | 28.4507 | + | 20.6706i | 0.982227 | + | 0.713630i | 0.958205 | − | 0.286082i | \(-0.0923529\pi\) |
0.0240218 | + | 0.999711i | \(0.492353\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.4610 | − | 16.3189i | 0.774519 | − | 0.562721i | ||||
\(842\) | −0.764817 | + | 2.35386i | −0.0263573 | + | 0.0811195i | ||||
\(843\) | 51.2021 | 1.76349 | ||||||||
\(844\) | 5.56856 | − | 17.1383i | 0.191678 | − | 0.589923i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −0.133270 | − | 0.410163i | −0.00458192 | − | 0.0141017i | ||||
\(847\) | −0.341479 | − | 1.05096i | −0.0117334 | − | 0.0361116i | ||||
\(848\) | −2.17420 | − | 1.57965i | −0.0746622 | − | 0.0542452i | ||||
\(849\) | −13.6345 | −0.467933 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.46477 | −0.0502116 | ||||||||
\(852\) | 28.9359 | + | 21.0231i | 0.991327 | + | 0.720241i | ||||
\(853\) | −5.60038 | − | 17.2362i | −0.191753 | − | 0.590156i | −0.999999 | − | 0.00131102i | \(-0.999583\pi\) |
0.808246 | − | 0.588845i | \(-0.200417\pi\) | |||||||
\(854\) | −0.524796 | − | 1.61515i | −0.0179581 | − | 0.0552695i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.73344 | − | 8.41266i | 0.0934271 | − | 0.287539i | ||||
\(857\) | −34.1832 | −1.16767 | −0.583837 | − | 0.811871i | \(-0.698449\pi\) | ||||
−0.583837 | + | 0.811871i | \(0.698449\pi\) | |||||||
\(858\) | −1.94175 | + | 5.97610i | −0.0662903 | + | 0.204021i | ||||
\(859\) | 16.6058 | − | 12.0648i | 0.566584 | − | 0.411647i | −0.267279 | − | 0.963619i | \(-0.586125\pi\) |
0.833863 | + | 0.551972i | \(0.186125\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.44398 | + | 4.68183i | 0.219610 | + | 0.159556i | ||||
\(862\) | −2.90921 | + | 2.11366i | −0.0990880 | + | 0.0719916i | ||||
\(863\) | −23.7550 | + | 17.2590i | −0.808630 | + | 0.587504i | −0.913433 | − | 0.406989i | \(-0.866579\pi\) |
0.104803 | + | 0.994493i | \(0.466579\pi\) | |||||||
\(864\) | 10.4942 | + | 7.62449i | 0.357020 | + | 0.259391i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.55266 | − | 1.85462i | 0.0867430 | − | 0.0630225i | ||||
\(867\) | 4.22848 | − | 13.0139i | 0.143607 | − | 0.441976i | ||||
\(868\) | 3.77577 | 0.128158 | ||||||||
\(869\) | 8.24876 | − | 25.3871i | 0.279820 | − | 0.861197i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.6257 | + | 94.2563i | 1.03771 | + | 3.19375i | ||||
\(872\) | −4.39260 | − | 13.5190i | −0.148752 | − | 0.457812i | ||||
\(873\) | 4.96027 | + | 3.60385i | 0.167880 | + | 0.121972i | ||||
\(874\) | 0.396363 | 0.0134072 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.66703 | −0.191471 | ||||||||
\(877\) | −23.4416 | − | 17.0313i | −0.791568 | − | 0.575108i | 0.116861 | − | 0.993148i | \(-0.462717\pi\) |
−0.908428 | + | 0.418041i | \(0.862717\pi\) | |||||||
\(878\) | −1.27707 | − | 3.93041i | −0.0430990 | − | 0.132645i | ||||
\(879\) | 7.64969 | + | 23.5433i | 0.258017 | + | 0.794096i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15.8830 | − | 48.8829i | 0.535112 | − | 1.64691i | −0.208294 | − | 0.978066i | \(-0.566791\pi\) |
0.743407 | − | 0.668840i | \(-0.233209\pi\) | |||||||
\(882\) | 0.121784 | 0.00410067 | ||||||||
\(883\) | 7.65007 | − | 23.5445i | 0.257445 | − | 0.792335i | −0.735893 | − | 0.677098i | \(-0.763237\pi\) |
0.993338 | − | 0.115237i | \(-0.0367627\pi\) | |||||||
\(884\) | −29.4226 | + | 21.3768i | −0.989588 | + | 0.718978i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.75965 | + | 2.00500i | 0.0927121 | + | 0.0673593i | ||||
\(887\) | 20.3908 | − | 14.8148i | 0.684658 | − | 0.497433i | −0.190242 | − | 0.981737i | \(-0.560927\pi\) |
0.874900 | + | 0.484304i | \(0.160927\pi\) | |||||||
\(888\) | −2.48566 | + | 1.80593i | −0.0834131 | + | 0.0606032i | ||||
\(889\) | 10.0747 | + | 7.31970i | 0.337895 | + | 0.245495i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.2744 | − | 12.5506i | 0.578713 | − | 0.420460i | ||||
\(892\) | 11.0980 | − | 34.1562i | 0.371589 | − | 1.14363i | ||||
\(893\) | 12.1640 | 0.407052 | ||||||||
\(894\) | 1.91816 | − | 5.90348i | 0.0641528 | − | 0.197442i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.87052 | + | 5.75686i | 0.0624896 | + | 0.192323i | ||||
\(897\) | 1.80095 | + | 5.54274i | 0.0601319 | + | 0.185067i | ||||
\(898\) | −6.58886 | − | 4.78709i | −0.219873 | − | 0.159747i | ||||
\(899\) | −2.14175 | −0.0714314 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.03747 | 0.0678781 | ||||||||
\(902\) | 2.60891 | + | 1.89549i | 0.0868673 | + | 0.0631128i | ||||
\(903\) | −1.54705 | − | 4.76133i | −0.0514826 | − | 0.158447i | ||||
\(904\) | −2.65509 | − | 8.17152i | −0.0883069 | − | 0.271781i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.12689 | − | 3.46822i | 0.0374385 | − | 0.115224i | ||||
\(907\) | −9.04710 | −0.300404 | −0.150202 | − | 0.988655i | \(-0.547992\pi\) | ||||
−0.150202 | + | 0.988655i | \(0.547992\pi\) | |||||||
\(908\) | 10.4263 | − | 32.0888i | 0.346008 | − | 1.06490i | ||||
\(909\) | 9.21743 | − | 6.69685i | 0.305723 | − | 0.222121i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.94024 | + | 3.58929i | 0.163677 | + | 0.118919i | 0.666609 | − | 0.745408i | \(-0.267745\pi\) |
−0.502931 | + | 0.864326i | \(0.667745\pi\) | |||||||
\(912\) | −16.1635 | + | 11.7435i | −0.535226 | + | 0.388865i | ||||
\(913\) | −30.2848 | + | 22.0032i | −1.00228 | + | 0.728199i | ||||
\(914\) | −0.345998 | − | 0.251382i | −0.0114446 | − | 0.00831498i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.73502 | − | 2.71365i | 0.123409 | − | 0.0896615i | ||||
\(917\) | −0.769069 | + | 2.36695i | −0.0253969 | + | 0.0781636i | ||||
\(918\) | −3.16802 | −0.104560 | ||||||||
\(919\) | −0.955985 | + | 2.94222i | −0.0315350 | + | 0.0970548i | −0.965585 | − | 0.260087i | \(-0.916249\pi\) |
0.934050 | + | 0.357142i | \(0.116249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.64666 | − | 20.4563i | −0.219015 | − | 0.674059i | ||||
\(922\) | 1.15136 | + | 3.54353i | 0.0379182 | + | 0.116700i | ||||
\(923\) | −62.0918 | − | 45.1123i | −2.04378 | − | 1.48489i | ||||
\(924\) | 9.52899 | 0.313481 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.86285 | 0.0612172 | ||||||||
\(927\) | −3.37989 | − | 2.45563i | −0.111010 | − | 0.0806535i | ||||
\(928\) | −0.798579 | − | 2.45777i | −0.0262147 | − | 0.0806804i | ||||
\(929\) | −2.76439 | − | 8.50791i | −0.0906966 | − | 0.279135i | 0.895412 | − | 0.445239i | \(-0.146881\pi\) |
−0.986108 | + | 0.166104i | \(0.946881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06144 | + | 3.26678i | −0.0347874 | + | 0.107064i | ||||
\(932\) | 2.72706 | 0.0893280 | ||||||||
\(933\) | −10.1117 | + | 31.1206i | −0.331042 | + | 1.01884i | ||||
\(934\) | 2.76804 | − | 2.01110i | 0.0905729 | − | 0.0658051i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.53646 | − | 1.84285i | −0.0829069 | − | 0.0602354i | ||||
\(937\) | −14.1455 | + | 10.2773i | −0.462113 | + | 0.335745i | −0.794360 | − | 0.607448i | \(-0.792193\pi\) |
0.332247 | + | 0.943193i | \(0.392193\pi\) | |||||||
\(938\) | −2.45305 | + | 1.78225i | −0.0800949 | + | 0.0581924i | ||||
\(939\) | −14.8770 | − | 10.8088i | −0.485494 | − | 0.352732i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −35.2364 | + | 25.6007i | −1.14867 | + | 0.834561i | −0.988304 | − | 0.152496i | \(-0.951269\pi\) |
−0.160370 | + | 0.987057i | \(0.551269\pi\) | |||||||
\(942\) | −1.57445 | + | 4.84567i | −0.0512985 | + | 0.157880i | ||||
\(943\) | 2.99095 | 0.0973987 | ||||||||
\(944\) | 12.3514 | − | 38.0137i | 0.402003 | − | 1.23724i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.626338 | − | 1.92767i | −0.0203640 | − | 0.0626740i | ||||
\(947\) | −16.0885 | − | 49.5152i | −0.522805 | − | 1.60903i | −0.768616 | − | 0.639711i | \(-0.779054\pi\) |
0.245811 | − | 0.969318i | \(-0.420946\pi\) | |||||||
\(948\) | −20.7968 | − | 15.1098i | −0.675449 | − | 0.490742i | ||||
\(949\) | 12.1606 | 0.394748 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.4335 | −0.792312 | ||||||||
\(952\) | −1.81851 | − | 1.32122i | −0.0589381 | − | 0.0428210i | ||||
\(953\) | 4.33482 | + | 13.3412i | 0.140419 | + | 0.432164i | 0.996393 | − | 0.0848534i | \(-0.0270422\pi\) |
−0.855975 | + | 0.517018i | \(0.827042\pi\) | |||||||
\(954\) | 0.0268679 | + | 0.0826908i | 0.000869880 | + | 0.00267721i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.36297 | − | 19.5832i | 0.205793 | − | 0.633367i | ||||
\(957\) | −5.40518 | −0.174725 | ||||||||
\(958\) | 0.0980967 | − | 0.301911i | 0.00316936 | − | 0.00975429i | ||||
\(959\) | 8.17703 | − | 5.94096i | 0.264050 | − | 0.191844i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.0786 | + | 16.0410i | 0.712212 | + | 0.517453i | ||||
\(962\) | 2.64028 | − | 1.91827i | 0.0851260 | − | 0.0618477i | ||||
\(963\) | 5.56371 | − | 4.04227i | 0.179288 | − | 0.130260i | ||||
\(964\) | −20.2919 | − | 14.7429i | −0.653557 | − | 0.474837i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.144252 | + | 0.104805i | −0.00464122 | + | 0.00337205i | ||||
\(967\) | −5.81641 | + | 17.9011i | −0.187043 | + | 0.575659i | −0.999978 | − | 0.00669587i | \(-0.997869\pi\) |
0.812935 | + | 0.582355i | \(0.197869\pi\) | |||||||
\(968\) | −0.870380 | −0.0279751 | ||||||||
\(969\) | 4.68070 | − | 14.4057i | 0.150366 | − | 0.462778i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.79293 | + | 17.8288i | 0.185904 | + | 0.572153i | 0.999963 | − | 0.00862896i | \(-0.00274672\pi\) |
−0.814059 | + | 0.580782i | \(0.802747\pi\) | |||||||
\(972\) | 3.79040 | + | 11.6657i | 0.121577 | + | 0.374176i | ||||
\(973\) | 14.8897 | + | 10.8180i | 0.477343 | + | 0.346810i | ||||
\(974\) | −7.34544 | −0.235363 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 32.1443 | 1.02891 | ||||||||
\(977\) | 36.8251 | + | 26.7550i | 1.17814 | + | 0.855968i | 0.991960 | − | 0.126548i | \(-0.0403899\pi\) |
0.186178 | + | 0.982516i | \(0.440390\pi\) | |||||||
\(978\) | −1.83497 | − | 5.64745i | −0.0586758 | − | 0.180586i | ||||
\(979\) | 16.2876 | + | 50.1280i | 0.520553 | + | 1.60210i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.41508 | − | 10.5105i | 0.109035 | − | 0.335576i | ||||
\(982\) | −2.83129 | −0.0903501 | ||||||||
\(983\) | −3.52908 | + | 10.8614i | −0.112560 | + | 0.346424i | −0.991430 | − | 0.130637i | \(-0.958298\pi\) |
0.878870 | + | 0.477061i | \(0.158298\pi\) | |||||||
\(984\) | 5.07553 | − | 3.68759i | 0.161802 | − | 0.117556i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.510610 | + | 0.370980i | 0.0162611 | + | 0.0118144i | ||||
\(987\) | −4.42694 | + | 3.21636i | −0.140911 | + | 0.102378i | ||||
\(988\) | 35.4132 | − | 25.7292i | 1.12664 | − | 0.818554i | ||||
\(989\) | −1.52087 | − | 1.10497i | −0.0483608 | − | 0.0351362i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.23921 | + | 5.25959i | −0.229961 | + | 0.167076i | −0.696799 | − | 0.717266i | \(-0.745393\pi\) |
0.466838 | + | 0.884343i | \(0.345393\pi\) | |||||||
\(992\) | 1.38309 | − | 4.25670i | 0.0439130 | − | 0.135150i | ||||
\(993\) | −0.772905 | −0.0245274 | ||||||||
\(994\) | 0.725611 | − | 2.23320i | 0.0230150 | − | 0.0708328i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 11.1399 | + | 34.2851i | 0.352982 | + | 1.08637i | ||||
\(997\) | 11.1261 | + | 34.2425i | 0.352366 | + | 1.08447i | 0.957521 | + | 0.288363i | \(0.0931111\pi\) |
−0.605155 | + | 0.796108i | \(0.706889\pi\) | |||||||
\(998\) | 1.38832 | + | 1.00867i | 0.0439464 | + | 0.0319289i | ||||
\(999\) | −14.0912 | −0.445825 |
(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 | 875.2.h.e.701.7 | 56 | ||
5.2 | odd | 4 | 875.2.n.c.799.7 | 56 | |||
5.3 | odd | 4 | 175.2.n.a.134.8 | yes | 56 | ||
5.4 | even | 2 | 875.2.h.d.701.8 | 56 | |||
25.2 | odd | 20 | 175.2.n.a.64.8 | ✓ | 56 | ||
25.6 | even | 5 | 4375.2.a.o.1.16 | 28 | |||
25.11 | even | 5 | inner | 875.2.h.e.176.7 | 56 | ||
25.14 | even | 10 | 875.2.h.d.176.8 | 56 | |||
25.19 | even | 10 | 4375.2.a.p.1.13 | 28 | |||
25.23 | odd | 20 | 875.2.n.c.449.7 | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
175.2.n.a.64.8 | ✓ | 56 | 25.2 | odd | 20 | ||
175.2.n.a.134.8 | yes | 56 | 5.3 | odd | 4 | ||
875.2.h.d.176.8 | 56 | 25.14 | even | 10 | |||
875.2.h.d.701.8 | 56 | 5.4 | even | 2 | |||
875.2.h.e.176.7 | 56 | 25.11 | even | 5 | inner | ||
875.2.h.e.701.7 | 56 | 1.1 | even | 1 | trivial | ||
875.2.n.c.449.7 | 56 | 25.23 | odd | 20 | |||
875.2.n.c.799.7 | 56 | 5.2 | odd | 4 | |||
4375.2.a.o.1.16 | 28 | 25.6 | even | 5 | |||
4375.2.a.p.1.13 | 28 | 25.19 | even | 10 |