Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.1 | ||
Root | \(-0.309017 + 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.j.372.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.809017 | + | 2.48990i | 0.572061 | + | 1.76062i | 0.645974 | + | 0.763359i | \(0.276451\pi\) |
−0.0739128 | + | 0.997265i | \(0.523549\pi\) | |||||||
\(3\) | −0.500000 | − | 0.363271i | −0.288675 | − | 0.209735i | 0.434017 | − | 0.900905i | \(-0.357096\pi\) |
−0.722692 | + | 0.691170i | \(0.757096\pi\) | |||||||
\(4\) | −3.92705 | + | 2.85317i | −1.96353 | + | 1.42658i | ||||
\(5\) | 0.309017 | − | 0.951057i | 0.138197 | − | 0.425325i | −0.857877 | − | 0.513855i | \(-0.828217\pi\) |
0.996074 | + | 0.0885298i | \(0.0282169\pi\) | |||||||
\(6\) | 0.500000 | − | 1.53884i | 0.204124 | − | 0.628230i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | −6.04508 | − | 4.39201i | −2.13726 | − | 1.55281i | ||||
\(9\) | −0.809017 | − | 2.48990i | −0.269672 | − | 0.829966i | ||||
\(10\) | 2.61803 | 0.827895 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.00000 | 0.866025 | ||||||||
\(13\) | −1.00000 | − | 3.07768i | −0.277350 | − | 0.853596i | −0.988588 | − | 0.150644i | \(-0.951865\pi\) |
0.711238 | − | 0.702951i | \(-0.248135\pi\) | |||||||
\(14\) | 2.11803 | + | 1.53884i | 0.566068 | + | 0.411273i | ||||
\(15\) | −0.500000 | + | 0.363271i | −0.129099 | + | 0.0937962i | ||||
\(16\) | 3.04508 | − | 9.37181i | 0.761271 | − | 2.34295i | ||||
\(17\) | 2.50000 | − | 7.69421i | 0.606339 | − | 1.86612i | 0.119029 | − | 0.992891i | \(-0.462022\pi\) |
0.487310 | − | 0.873229i | \(-0.337978\pi\) | |||||||
\(18\) | 5.54508 | − | 4.02874i | 1.30699 | − | 0.949583i | ||||
\(19\) | −5.04508 | − | 3.66547i | −1.15742 | − | 0.840916i | −0.167972 | − | 0.985792i | \(-0.553722\pi\) |
−0.989450 | + | 0.144876i | \(0.953722\pi\) | |||||||
\(20\) | 1.50000 | + | 4.61653i | 0.335410 | + | 1.03229i | ||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.09017 | −1.26989 | −0.634944 | − | 0.772558i | \(-0.718977\pi\) | ||||
−0.634944 | + | 0.772558i | \(0.718977\pi\) | |||||||
\(24\) | 1.42705 | + | 4.39201i | 0.291296 | + | 0.896516i | ||||
\(25\) | 3.23607 | + | 2.35114i | 0.647214 | + | 0.470228i | ||||
\(26\) | 6.85410 | − | 4.97980i | 1.34420 | − | 0.976618i | ||||
\(27\) | −1.07295 | + | 3.30220i | −0.206489 | + | 0.635508i | ||||
\(28\) | −1.50000 | + | 4.61653i | −0.283473 | + | 0.872441i | ||||
\(29\) | −1.92705 | + | 1.40008i | −0.357844 | + | 0.259989i | −0.752152 | − | 0.658989i | \(-0.770984\pi\) |
0.394308 | + | 0.918978i | \(0.370984\pi\) | |||||||
\(30\) | −1.30902 | − | 0.951057i | −0.238993 | − | 0.173638i | ||||
\(31\) | 0.0729490 | + | 0.224514i | 0.0131020 | + | 0.0403239i | 0.957394 | − | 0.288786i | \(-0.0932515\pi\) |
−0.944292 | + | 0.329109i | \(0.893251\pi\) | |||||||
\(32\) | 10.8541 | 1.91875 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 21.1803 | 3.63240 | ||||||||
\(35\) | −0.309017 | − | 0.951057i | −0.0522334 | − | 0.160758i | ||||
\(36\) | 10.2812 | + | 7.46969i | 1.71353 | + | 1.24495i | ||||
\(37\) | 2.00000 | − | 1.45309i | 0.328798 | − | 0.238886i | −0.411122 | − | 0.911580i | \(-0.634863\pi\) |
0.739920 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(38\) | 5.04508 | − | 15.5272i | 0.818421 | − | 2.51884i | ||||
\(39\) | −0.618034 | + | 1.90211i | −0.0989646 | + | 0.304582i | ||||
\(40\) | −6.04508 | + | 4.39201i | −0.955812 | + | 0.694438i | ||||
\(41\) | 9.04508 | + | 6.57164i | 1.41260 | + | 1.02632i | 0.992937 | + | 0.118640i | \(0.0378533\pi\) |
0.419668 | + | 0.907678i | \(0.362147\pi\) | |||||||
\(42\) | −0.500000 | − | 1.53884i | −0.0771517 | − | 0.237448i | ||||
\(43\) | −7.56231 | −1.15324 | −0.576620 | − | 0.817012i | \(-0.695629\pi\) | ||||
−0.576620 | + | 0.817012i | \(0.695629\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.61803 | −0.390273 | ||||||||
\(46\) | −4.92705 | − | 15.1639i | −0.726454 | − | 2.23580i | ||||
\(47\) | 3.54508 | + | 2.57565i | 0.517104 | + | 0.375698i | 0.815512 | − | 0.578741i | \(-0.196456\pi\) |
−0.298408 | + | 0.954438i | \(0.596456\pi\) | |||||||
\(48\) | −4.92705 | + | 3.57971i | −0.711159 | + | 0.516687i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | −3.23607 | + | 9.95959i | −0.457649 | + | 1.40850i | ||||
\(51\) | −4.04508 | + | 2.93893i | −0.566425 | + | 0.411532i | ||||
\(52\) | 12.7082 | + | 9.23305i | 1.76231 | + | 1.28039i | ||||
\(53\) | −1.42705 | − | 4.39201i | −0.196021 | − | 0.603289i | −0.999963 | − | 0.00858231i | \(-0.997268\pi\) |
0.803943 | − | 0.594707i | \(-0.202732\pi\) | |||||||
\(54\) | −9.09017 | −1.23702 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.47214 | −0.998506 | ||||||||
\(57\) | 1.19098 | + | 3.66547i | 0.157750 | + | 0.485503i | ||||
\(58\) | −5.04508 | − | 3.66547i | −0.662452 | − | 0.481300i | ||||
\(59\) | 0.0729490 | − | 0.0530006i | 0.00949715 | − | 0.00690009i | −0.583027 | − | 0.812453i | \(-0.698132\pi\) |
0.592524 | + | 0.805553i | \(0.298132\pi\) | |||||||
\(60\) | 0.927051 | − | 2.85317i | 0.119682 | − | 0.368343i | ||||
\(61\) | 1.66312 | − | 5.11855i | 0.212941 | − | 0.655364i | −0.786353 | − | 0.617778i | \(-0.788033\pi\) |
0.999293 | − | 0.0375860i | \(-0.0119668\pi\) | |||||||
\(62\) | −0.500000 | + | 0.363271i | −0.0635001 | + | 0.0461355i | ||||
\(63\) | −2.11803 | − | 1.53884i | −0.266847 | − | 0.193876i | ||||
\(64\) | 2.69098 | + | 8.28199i | 0.336373 | + | 1.03525i | ||||
\(65\) | −3.23607 | −0.401385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.32624 | 0.895042 | 0.447521 | − | 0.894273i | \(-0.352307\pi\) | ||||
0.447521 | + | 0.894273i | \(0.352307\pi\) | |||||||
\(68\) | 12.1353 | + | 37.3485i | 1.47162 | + | 4.52917i | ||||
\(69\) | 3.04508 | + | 2.21238i | 0.366585 | + | 0.266340i | ||||
\(70\) | 2.11803 | − | 1.53884i | 0.253153 | − | 0.183927i | ||||
\(71\) | −1.51722 | + | 4.66953i | −0.180061 | + | 0.554171i | −0.999828 | − | 0.0185259i | \(-0.994103\pi\) |
0.819767 | + | 0.572697i | \(0.194103\pi\) | |||||||
\(72\) | −6.04508 | + | 18.6049i | −0.712420 | + | 2.19260i | ||||
\(73\) | −7.89919 | + | 5.73910i | −0.924530 | + | 0.671710i | −0.944647 | − | 0.328087i | \(-0.893596\pi\) |
0.0201175 | + | 0.999798i | \(0.493596\pi\) | |||||||
\(74\) | 5.23607 | + | 3.80423i | 0.608681 | + | 0.442232i | ||||
\(75\) | −0.763932 | − | 2.35114i | −0.0882113 | − | 0.271486i | ||||
\(76\) | 30.2705 | 3.47227 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.23607 | −0.592868 | ||||||||
\(79\) | −2.66312 | − | 8.19624i | −0.299624 | − | 0.922149i | −0.981629 | − | 0.190801i | \(-0.938892\pi\) |
0.682004 | − | 0.731348i | \(-0.261108\pi\) | |||||||
\(80\) | −7.97214 | − | 5.79210i | −0.891312 | − | 0.647576i | ||||
\(81\) | −4.61803 | + | 3.35520i | −0.513115 | + | 0.372800i | ||||
\(82\) | −9.04508 | + | 27.8379i | −0.998863 | + | 3.07418i | ||||
\(83\) | 3.30902 | − | 10.1841i | 0.363212 | − | 1.11785i | −0.587881 | − | 0.808947i | \(-0.700038\pi\) |
0.951093 | − | 0.308904i | \(-0.0999621\pi\) | |||||||
\(84\) | 2.42705 | − | 1.76336i | 0.264813 | − | 0.192398i | ||||
\(85\) | −6.54508 | − | 4.75528i | −0.709914 | − | 0.515783i | ||||
\(86\) | −6.11803 | − | 18.8294i | −0.659725 | − | 2.03042i | ||||
\(87\) | 1.47214 | 0.157830 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.145898 | 0.0154652 | 0.00773258 | − | 0.999970i | \(-0.497539\pi\) | ||||
0.00773258 | + | 0.999970i | \(0.497539\pi\) | |||||||
\(90\) | −2.11803 | − | 6.51864i | −0.223260 | − | 0.687125i | ||||
\(91\) | −2.61803 | − | 1.90211i | −0.274445 | − | 0.199396i | ||||
\(92\) | 23.9164 | − | 17.3763i | 2.49346 | − | 1.81160i | ||||
\(93\) | 0.0450850 | − | 0.138757i | 0.00467509 | − | 0.0143885i | ||||
\(94\) | −3.54508 | + | 10.9106i | −0.365648 | + | 1.12535i | ||||
\(95\) | −5.04508 | + | 3.66547i | −0.517615 | + | 0.376069i | ||||
\(96\) | −5.42705 | − | 3.94298i | −0.553896 | − | 0.402429i | ||||
\(97\) | 2.16312 | + | 6.65740i | 0.219631 | + | 0.675956i | 0.998792 | + | 0.0491321i | \(0.0156455\pi\) |
−0.779161 | + | 0.626824i | \(0.784354\pi\) | |||||||
\(98\) | 2.61803 | 0.264461 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −19.4164 | −1.94164 | ||||||||
\(101\) | −3.02786 | − | 9.31881i | −0.301284 | − | 0.927256i | −0.981038 | − | 0.193816i | \(-0.937914\pi\) |
0.679754 | − | 0.733440i | \(-0.262086\pi\) | |||||||
\(102\) | −10.5902 | − | 7.69421i | −1.04858 | − | 0.761840i | ||||
\(103\) | −1.73607 | + | 1.26133i | −0.171060 | + | 0.124282i | −0.670021 | − | 0.742342i | \(-0.733715\pi\) |
0.498961 | + | 0.866624i | \(0.333715\pi\) | |||||||
\(104\) | −7.47214 | + | 22.9969i | −0.732703 | + | 2.25503i | ||||
\(105\) | −0.190983 | + | 0.587785i | −0.0186380 | + | 0.0573620i | ||||
\(106\) | 9.78115 | − | 7.10642i | 0.950030 | − | 0.690237i | ||||
\(107\) | −8.66312 | − | 6.29412i | −0.837495 | − | 0.608476i | 0.0841746 | − | 0.996451i | \(-0.473175\pi\) |
−0.921670 | + | 0.387975i | \(0.873175\pi\) | |||||||
\(108\) | −5.20820 | − | 16.0292i | −0.501160 | − | 1.54241i | ||||
\(109\) | 10.4721 | 1.00305 | 0.501524 | − | 0.865144i | \(-0.332773\pi\) | ||||
0.501524 | + | 0.865144i | \(0.332773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.52786 | −0.145018 | ||||||||
\(112\) | −3.04508 | − | 9.37181i | −0.287733 | − | 0.885553i | ||||
\(113\) | −5.54508 | − | 4.02874i | −0.521638 | − | 0.378992i | 0.295583 | − | 0.955317i | \(-0.404486\pi\) |
−0.817220 | + | 0.576325i | \(0.804486\pi\) | |||||||
\(114\) | −8.16312 | + | 5.93085i | −0.764546 | + | 0.555475i | ||||
\(115\) | −1.88197 | + | 5.79210i | −0.175494 | + | 0.540116i | ||||
\(116\) | 3.57295 | − | 10.9964i | 0.331740 | − | 1.02099i | ||||
\(117\) | −6.85410 | + | 4.97980i | −0.633662 | + | 0.460382i | ||||
\(118\) | 0.190983 | + | 0.138757i | 0.0175814 | + | 0.0127736i | ||||
\(119\) | −2.50000 | − | 7.69421i | −0.229175 | − | 0.705327i | ||||
\(120\) | 4.61803 | 0.421567 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 14.0902 | 1.27566 | ||||||||
\(123\) | −2.13525 | − | 6.57164i | −0.192529 | − | 0.592545i | ||||
\(124\) | −0.927051 | − | 0.673542i | −0.0832516 | − | 0.0604859i | ||||
\(125\) | 7.28115 | − | 5.29007i | 0.651246 | − | 0.473158i | ||||
\(126\) | 2.11803 | − | 6.51864i | 0.188689 | − | 0.580726i | ||||
\(127\) | 4.61803 | − | 14.2128i | 0.409784 | − | 1.26119i | −0.507049 | − | 0.861917i | \(-0.669264\pi\) |
0.916834 | − | 0.399269i | \(-0.130736\pi\) | |||||||
\(128\) | −0.881966 | + | 0.640786i | −0.0779555 | + | 0.0566380i | ||||
\(129\) | 3.78115 | + | 2.74717i | 0.332912 | + | 0.241875i | ||||
\(130\) | −2.61803 | − | 8.05748i | −0.229617 | − | 0.706688i | ||||
\(131\) | −1.05573 | −0.0922394 | −0.0461197 | − | 0.998936i | \(-0.514686\pi\) | ||||
−0.0461197 | + | 0.998936i | \(0.514686\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.23607 | −0.540736 | ||||||||
\(134\) | 5.92705 | + | 18.2416i | 0.512019 | + | 1.57583i | ||||
\(135\) | 2.80902 | + | 2.04087i | 0.241762 | + | 0.175650i | ||||
\(136\) | −48.9058 | + | 35.5321i | −4.19363 | + | 3.04685i | ||||
\(137\) | 0.100813 | − | 0.310271i | 0.00861304 | − | 0.0265082i | −0.946658 | − | 0.322241i | \(-0.895564\pi\) |
0.955271 | + | 0.295733i | \(0.0955638\pi\) | |||||||
\(138\) | −3.04508 | + | 9.37181i | −0.259215 | + | 0.797781i | ||||
\(139\) | −4.80902 | + | 3.49396i | −0.407895 | + | 0.296353i | −0.772749 | − | 0.634711i | \(-0.781119\pi\) |
0.364854 | + | 0.931065i | \(0.381119\pi\) | |||||||
\(140\) | 3.92705 | + | 2.85317i | 0.331896 | + | 0.241137i | ||||
\(141\) | −0.836881 | − | 2.57565i | −0.0704781 | − | 0.216909i | ||||
\(142\) | −12.8541 | −1.07869 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −25.7984 | −2.14986 | ||||||||
\(145\) | 0.736068 | + | 2.26538i | 0.0611271 | + | 0.188130i | ||||
\(146\) | −20.6803 | − | 15.0251i | −1.71152 | − | 1.24349i | ||||
\(147\) | −0.500000 | + | 0.363271i | −0.0412393 | + | 0.0299621i | ||||
\(148\) | −3.70820 | + | 11.4127i | −0.304812 | + | 0.938116i | ||||
\(149\) | 0.663119 | − | 2.04087i | 0.0543248 | − | 0.167195i | −0.920213 | − | 0.391418i | \(-0.871985\pi\) |
0.974538 | + | 0.224224i | \(0.0719846\pi\) | |||||||
\(150\) | 5.23607 | − | 3.80423i | 0.427523 | − | 0.310614i | ||||
\(151\) | 14.5172 | + | 10.5474i | 1.18139 | + | 0.858333i | 0.992328 | − | 0.123631i | \(-0.0394539\pi\) |
0.189066 | + | 0.981964i | \(0.439454\pi\) | |||||||
\(152\) | 14.3992 | + | 44.3161i | 1.16793 | + | 3.59451i | ||||
\(153\) | −21.1803 | −1.71233 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.236068 | 0.0189614 | ||||||||
\(156\) | −3.00000 | − | 9.23305i | −0.240192 | − | 0.739236i | ||||
\(157\) | 12.8541 | + | 9.33905i | 1.02587 | + | 0.745337i | 0.967478 | − | 0.252956i | \(-0.0814029\pi\) |
0.0583913 | + | 0.998294i | \(0.481403\pi\) | |||||||
\(158\) | 18.2533 | − | 13.2618i | 1.45215 | − | 1.05505i | ||||
\(159\) | −0.881966 | + | 2.71441i | −0.0699445 | + | 0.215267i | ||||
\(160\) | 3.35410 | − | 10.3229i | 0.265165 | − | 0.816094i | ||||
\(161\) | −4.92705 | + | 3.57971i | −0.388306 | + | 0.282121i | ||||
\(162\) | −12.0902 | − | 8.78402i | −0.949893 | − | 0.690138i | ||||
\(163\) | 1.45492 | + | 4.47777i | 0.113958 | + | 0.350726i | 0.991728 | − | 0.128356i | \(-0.0409699\pi\) |
−0.877770 | + | 0.479081i | \(0.840970\pi\) | |||||||
\(164\) | −54.2705 | −4.23781 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 28.0344 | 2.17589 | ||||||||
\(167\) | 0.763932 | + | 2.35114i | 0.0591148 | + | 0.181937i | 0.976253 | − | 0.216632i | \(-0.0695071\pi\) |
−0.917139 | + | 0.398569i | \(0.869507\pi\) | |||||||
\(168\) | 3.73607 | + | 2.71441i | 0.288244 | + | 0.209421i | ||||
\(169\) | 2.04508 | − | 1.48584i | 0.157314 | − | 0.114295i | ||||
\(170\) | 6.54508 | − | 20.1437i | 0.501985 | − | 1.54495i | ||||
\(171\) | −5.04508 | + | 15.5272i | −0.385807 | + | 1.18739i | ||||
\(172\) | 29.6976 | − | 21.5765i | 2.26442 | − | 1.64520i | ||||
\(173\) | −14.2533 | − | 10.3556i | −1.08366 | − | 0.787323i | −0.105340 | − | 0.994436i | \(-0.533593\pi\) |
−0.978317 | + | 0.207113i | \(0.933593\pi\) | |||||||
\(174\) | 1.19098 | + | 3.66547i | 0.0902882 | + | 0.277878i | ||||
\(175\) | 4.00000 | 0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.0557281 | −0.00418878 | ||||||||
\(178\) | 0.118034 | + | 0.363271i | 0.00884702 | + | 0.0272283i | ||||
\(179\) | 6.66312 | + | 4.84104i | 0.498025 | + | 0.361836i | 0.808262 | − | 0.588823i | \(-0.200408\pi\) |
−0.310237 | + | 0.950659i | \(0.600408\pi\) | |||||||
\(180\) | 10.2812 | − | 7.46969i | 0.766312 | − | 0.556758i | ||||
\(181\) | 6.00000 | − | 18.4661i | 0.445976 | − | 1.37257i | −0.435433 | − | 0.900221i | \(-0.643405\pi\) |
0.881409 | − | 0.472353i | \(-0.156595\pi\) | |||||||
\(182\) | 2.61803 | − | 8.05748i | 0.194062 | − | 0.597260i | ||||
\(183\) | −2.69098 | + | 1.95511i | −0.198923 | + | 0.144526i | ||||
\(184\) | 36.8156 | + | 26.7481i | 2.71408 | + | 1.97190i | ||||
\(185\) | −0.763932 | − | 2.35114i | −0.0561654 | − | 0.172859i | ||||
\(186\) | 0.381966 | 0.0280071 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −21.2705 | −1.55131 | ||||||||
\(189\) | 1.07295 | + | 3.30220i | 0.0780456 | + | 0.240200i | ||||
\(190\) | −13.2082 | − | 9.59632i | −0.958224 | − | 0.696190i | ||||
\(191\) | −16.3713 | + | 11.8945i | −1.18459 | + | 0.860653i | −0.992682 | − | 0.120760i | \(-0.961467\pi\) |
−0.191906 | + | 0.981413i | \(0.561467\pi\) | |||||||
\(192\) | 1.66312 | − | 5.11855i | 0.120025 | − | 0.369400i | ||||
\(193\) | −0.100813 | + | 0.310271i | −0.00725668 | + | 0.0223338i | −0.954619 | − | 0.297829i | \(-0.903738\pi\) |
0.947363 | + | 0.320163i | \(0.103738\pi\) | |||||||
\(194\) | −14.8262 | + | 10.7719i | −1.06446 | + | 0.773377i | ||||
\(195\) | 1.61803 | + | 1.17557i | 0.115870 | + | 0.0841844i | ||||
\(196\) | 1.50000 | + | 4.61653i | 0.107143 | + | 0.329752i | ||||
\(197\) | 17.7082 | 1.26166 | 0.630829 | − | 0.775922i | \(-0.282715\pi\) | ||||
0.630829 | + | 0.775922i | \(0.282715\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.76393 | −0.266818 | −0.133409 | − | 0.991061i | \(-0.542592\pi\) | ||||
−0.133409 | + | 0.991061i | \(0.542592\pi\) | |||||||
\(200\) | −9.23607 | − | 28.4257i | −0.653089 | − | 2.01000i | ||||
\(201\) | −3.66312 | − | 2.66141i | −0.258376 | − | 0.187722i | ||||
\(202\) | 20.7533 | − | 15.0781i | 1.46020 | − | 1.06089i | ||||
\(203\) | −0.736068 | + | 2.26538i | −0.0516618 | + | 0.158999i | ||||
\(204\) | 7.50000 | − | 23.0826i | 0.525105 | − | 1.61611i | ||||
\(205\) | 9.04508 | − | 6.57164i | 0.631736 | − | 0.458983i | ||||
\(206\) | −4.54508 | − | 3.30220i | −0.316671 | − | 0.230075i | ||||
\(207\) | 4.92705 | + | 15.1639i | 0.342454 | + | 1.05396i | ||||
\(208\) | −31.8885 | −2.21107 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −1.61803 | −0.111655 | ||||||||
\(211\) | −4.13525 | − | 12.7270i | −0.284683 | − | 0.876163i | −0.986494 | − | 0.163800i | \(-0.947625\pi\) |
0.701811 | − | 0.712363i | \(-0.252375\pi\) | |||||||
\(212\) | 18.1353 | + | 13.1760i | 1.24553 | + | 0.904934i | ||||
\(213\) | 2.45492 | − | 1.78360i | 0.168208 | − | 0.122210i | ||||
\(214\) | 8.66312 | − | 26.6623i | 0.592199 | − | 1.82260i | ||||
\(215\) | −2.33688 | + | 7.19218i | −0.159374 | + | 0.490503i | ||||
\(216\) | 20.9894 | − | 15.2497i | 1.42814 | − | 1.03761i | ||||
\(217\) | 0.190983 | + | 0.138757i | 0.0129648 | + | 0.00941946i | ||||
\(218\) | 8.47214 | + | 26.0746i | 0.573805 | + | 1.76599i | ||||
\(219\) | 6.03444 | 0.407770 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −26.1803 | −1.76108 | ||||||||
\(222\) | −1.23607 | − | 3.80423i | −0.0829595 | − | 0.255323i | ||||
\(223\) | 21.8713 | + | 15.8904i | 1.46461 | + | 1.06410i | 0.982131 | + | 0.188196i | \(0.0602641\pi\) |
0.482481 | + | 0.875907i | \(0.339736\pi\) | |||||||
\(224\) | 8.78115 | − | 6.37988i | 0.586715 | − | 0.426274i | ||||
\(225\) | 3.23607 | − | 9.95959i | 0.215738 | − | 0.663973i | ||||
\(226\) | 5.54508 | − | 17.0660i | 0.368854 | − | 1.13521i | ||||
\(227\) | 10.5451 | − | 7.66145i | 0.699902 | − | 0.508508i | −0.179998 | − | 0.983667i | \(-0.557609\pi\) |
0.879900 | + | 0.475158i | \(0.157609\pi\) | |||||||
\(228\) | −15.1353 | − | 10.9964i | −1.00236 | − | 0.728255i | ||||
\(229\) | 3.47214 | + | 10.6861i | 0.229445 | + | 0.706160i | 0.997810 | + | 0.0661474i | \(0.0210708\pi\) |
−0.768365 | + | 0.640012i | \(0.778929\pi\) | |||||||
\(230\) | −15.9443 | −1.05133 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 17.7984 | 1.16852 | ||||||||
\(233\) | 0.798374 | + | 2.45714i | 0.0523032 | + | 0.160973i | 0.973796 | − | 0.227422i | \(-0.0730297\pi\) |
−0.921493 | + | 0.388395i | \(0.873030\pi\) | |||||||
\(234\) | −17.9443 | − | 13.0373i | −1.17305 | − | 0.852273i | ||||
\(235\) | 3.54508 | − | 2.57565i | 0.231256 | − | 0.168017i | ||||
\(236\) | −0.135255 | + | 0.416272i | −0.00880435 | + | 0.0270970i | ||||
\(237\) | −1.64590 | + | 5.06555i | −0.106913 | + | 0.329043i | ||||
\(238\) | 17.1353 | − | 12.4495i | 1.11071 | − | 0.806981i | ||||
\(239\) | −4.78115 | − | 3.47371i | −0.309267 | − | 0.224696i | 0.422315 | − | 0.906449i | \(-0.361218\pi\) |
−0.731582 | + | 0.681754i | \(0.761218\pi\) | |||||||
\(240\) | 1.88197 | + | 5.79210i | 0.121480 | + | 0.373878i | ||||
\(241\) | 17.2705 | 1.11249 | 0.556246 | − | 0.831018i | \(-0.312241\pi\) | ||||
0.556246 | + | 0.831018i | \(0.312241\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 8.07295 | + | 24.8460i | 0.516818 | + | 1.59060i | ||||
\(245\) | −0.809017 | − | 0.587785i | −0.0516862 | − | 0.0375522i | ||||
\(246\) | 14.6353 | − | 10.6331i | 0.933110 | − | 0.677944i | ||||
\(247\) | −6.23607 | + | 19.1926i | −0.396792 | + | 1.22120i | ||||
\(248\) | 0.545085 | − | 1.67760i | 0.0346129 | − | 0.106528i | ||||
\(249\) | −5.35410 | + | 3.88998i | −0.339302 | + | 0.246518i | ||||
\(250\) | 19.0623 | + | 13.8496i | 1.20561 | + | 0.875924i | ||||
\(251\) | 7.10739 | + | 21.8743i | 0.448615 | + | 1.38069i | 0.878471 | + | 0.477796i | \(0.158564\pi\) |
−0.429856 | + | 0.902897i | \(0.641436\pi\) | |||||||
\(252\) | 12.7082 | 0.800542 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 39.1246 | 2.45490 | ||||||||
\(255\) | 1.54508 | + | 4.75528i | 0.0967570 | + | 0.297787i | ||||
\(256\) | 11.7812 | + | 8.55951i | 0.736322 | + | 0.534969i | ||||
\(257\) | −9.35410 | + | 6.79615i | −0.583493 | + | 0.423932i | −0.839982 | − | 0.542615i | \(-0.817434\pi\) |
0.256489 | + | 0.966547i | \(0.417434\pi\) | |||||||
\(258\) | −3.78115 | + | 11.6372i | −0.235404 | + | 0.724500i | ||||
\(259\) | 0.763932 | − | 2.35114i | 0.0474684 | − | 0.146093i | ||||
\(260\) | 12.7082 | − | 9.23305i | 0.788129 | − | 0.572609i | ||||
\(261\) | 5.04508 | + | 3.66547i | 0.312283 | + | 0.226887i | ||||
\(262\) | −0.854102 | − | 2.62866i | −0.0527666 | − | 0.162399i | ||||
\(263\) | −23.1246 | −1.42592 | −0.712962 | − | 0.701202i | \(-0.752647\pi\) | ||||
−0.712962 | + | 0.701202i | \(0.752647\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.61803 | −0.283684 | ||||||||
\(266\) | −5.04508 | − | 15.5272i | −0.309334 | − | 0.952032i | ||||
\(267\) | −0.0729490 | − | 0.0530006i | −0.00446441 | − | 0.00324358i | ||||
\(268\) | −28.7705 | + | 20.9030i | −1.75744 | + | 1.27685i | ||||
\(269\) | 3.13525 | − | 9.64932i | 0.191160 | − | 0.588330i | −0.808840 | − | 0.588029i | \(-0.799904\pi\) |
1.00000 | 0.000300908i | \(-9.57819e-5\pi\) | ||||||||
\(270\) | −2.80902 | + | 8.64527i | −0.170951 | + | 0.526134i | ||||
\(271\) | 16.0172 | − | 11.6372i | 0.972977 | − | 0.706909i | 0.0168488 | − | 0.999858i | \(-0.494637\pi\) |
0.956128 | + | 0.292949i | \(0.0946366\pi\) | |||||||
\(272\) | −64.4959 | − | 46.8590i | −3.91064 | − | 2.84125i | ||||
\(273\) | 0.618034 | + | 1.90211i | 0.0374051 | + | 0.115121i | ||||
\(274\) | 0.854102 | 0.0515982 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −18.2705 | −1.09976 | ||||||||
\(277\) | 1.86475 | + | 5.73910i | 0.112042 | + | 0.344829i | 0.991319 | − | 0.131482i | \(-0.0419736\pi\) |
−0.879277 | + | 0.476311i | \(0.841974\pi\) | |||||||
\(278\) | −12.5902 | − | 9.14729i | −0.755108 | − | 0.548618i | ||||
\(279\) | 0.500000 | − | 0.363271i | 0.0299342 | − | 0.0217485i | ||||
\(280\) | −2.30902 | + | 7.10642i | −0.137990 | + | 0.424690i | ||||
\(281\) | 0.871323 | − | 2.68166i | 0.0519788 | − | 0.159974i | −0.921698 | − | 0.387909i | \(-0.873197\pi\) |
0.973676 | + | 0.227935i | \(0.0731974\pi\) | |||||||
\(282\) | 5.73607 | − | 4.16750i | 0.341578 | − | 0.248171i | ||||
\(283\) | −4.80902 | − | 3.49396i | −0.285866 | − | 0.207694i | 0.435606 | − | 0.900138i | \(-0.356534\pi\) |
−0.721472 | + | 0.692443i | \(0.756534\pi\) | |||||||
\(284\) | −7.36475 | − | 22.6664i | −0.437017 | − | 1.34500i | ||||
\(285\) | 3.85410 | 0.228297 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.1803 | 0.659955 | ||||||||
\(288\) | −8.78115 | − | 27.0256i | −0.517434 | − | 1.59250i | ||||
\(289\) | −39.1976 | − | 28.4787i | −2.30574 | − | 1.67522i | ||||
\(290\) | −5.04508 | + | 3.66547i | −0.296258 | + | 0.215244i | ||||
\(291\) | 1.33688 | − | 4.11450i | 0.0783694 | − | 0.241196i | ||||
\(292\) | 14.6459 | − | 45.0754i | 0.857086 | − | 2.63784i | ||||
\(293\) | −8.89919 | + | 6.46564i | −0.519896 | + | 0.377727i | −0.816565 | − | 0.577254i | \(-0.804124\pi\) |
0.296669 | + | 0.954980i | \(0.404124\pi\) | |||||||
\(294\) | −1.30902 | − | 0.951057i | −0.0763434 | − | 0.0554667i | ||||
\(295\) | −0.0278640 | − | 0.0857567i | −0.00162231 | − | 0.00499295i | ||||
\(296\) | −18.4721 | −1.07367 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.61803 | 0.325444 | ||||||||
\(299\) | 6.09017 | + | 18.7436i | 0.352204 | + | 1.08397i | ||||
\(300\) | 9.70820 | + | 7.05342i | 0.560503 | + | 0.407230i | ||||
\(301\) | −6.11803 | + | 4.44501i | −0.352638 | + | 0.256206i | ||||
\(302\) | −14.5172 | + | 44.6794i | −0.835372 | + | 2.57101i | ||||
\(303\) | −1.87132 | + | 5.75934i | −0.107505 | + | 0.330865i | ||||
\(304\) | −49.7148 | + | 36.1199i | −2.85134 | + | 2.07162i | ||||
\(305\) | −4.35410 | − | 3.16344i | −0.249315 | − | 0.181138i | ||||
\(306\) | −17.1353 | − | 52.7369i | −0.979557 | − | 3.01477i | ||||
\(307\) | 0.819660 | 0.0467805 | 0.0233902 | − | 0.999726i | \(-0.492554\pi\) | ||||
0.0233902 | + | 0.999726i | \(0.492554\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.32624 | 0.0754470 | ||||||||
\(310\) | 0.190983 | + | 0.587785i | 0.0108471 | + | 0.0333840i | ||||
\(311\) | −7.28115 | − | 5.29007i | −0.412876 | − | 0.299972i | 0.361889 | − | 0.932221i | \(-0.382132\pi\) |
−0.774765 | + | 0.632249i | \(0.782132\pi\) | |||||||
\(312\) | 12.0902 | − | 8.78402i | 0.684471 | − | 0.497297i | ||||
\(313\) | 0.826238 | − | 2.54290i | 0.0467017 | − | 0.143733i | −0.924986 | − | 0.380000i | \(-0.875924\pi\) |
0.971688 | + | 0.236267i | \(0.0759240\pi\) | |||||||
\(314\) | −12.8541 | + | 39.5609i | −0.725399 | + | 2.23255i | ||||
\(315\) | −2.11803 | + | 1.53884i | −0.119338 | + | 0.0867039i | ||||
\(316\) | 33.8435 | + | 24.5887i | 1.90384 | + | 1.38322i | ||||
\(317\) | −7.59017 | − | 23.3601i | −0.426306 | − | 1.31204i | −0.901738 | − | 0.432283i | \(-0.857708\pi\) |
0.475431 | − | 0.879753i | \(-0.342292\pi\) | |||||||
\(318\) | −7.47214 | −0.419017 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 8.70820 | 0.486803 | ||||||||
\(321\) | 2.04508 | + | 6.29412i | 0.114146 | + | 0.351304i | ||||
\(322\) | −12.8992 | − | 9.37181i | −0.718844 | − | 0.522270i | ||||
\(323\) | −40.8156 | + | 29.6543i | −2.27104 | + | 1.65001i | ||||
\(324\) | 8.56231 | − | 26.3521i | 0.475684 | − | 1.46400i | ||||
\(325\) | 4.00000 | − | 12.3107i | 0.221880 | − | 0.682877i | ||||
\(326\) | −9.97214 | + | 7.24518i | −0.552306 | + | 0.401273i | ||||
\(327\) | −5.23607 | − | 3.80423i | −0.289555 | − | 0.210374i | ||||
\(328\) | −25.8156 | − | 79.4522i | −1.42543 | − | 4.38702i | ||||
\(329\) | 4.38197 | 0.241586 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.1803 | −0.889352 | −0.444676 | − | 0.895692i | \(-0.646681\pi\) | ||||
−0.444676 | + | 0.895692i | \(0.646681\pi\) | |||||||
\(332\) | 16.0623 | + | 49.4347i | 0.881534 | + | 2.71308i | ||||
\(333\) | −5.23607 | − | 3.80423i | −0.286935 | − | 0.208470i | ||||
\(334\) | −5.23607 | + | 3.80423i | −0.286505 | + | 0.208158i | ||||
\(335\) | 2.26393 | − | 6.96767i | 0.123692 | − | 0.380684i | ||||
\(336\) | −1.88197 | + | 5.79210i | −0.102670 | + | 0.315985i | ||||
\(337\) | 6.51722 | − | 4.73504i | 0.355016 | − | 0.257934i | −0.395954 | − | 0.918270i | \(-0.629586\pi\) |
0.750970 | + | 0.660336i | \(0.229586\pi\) | |||||||
\(338\) | 5.35410 | + | 3.88998i | 0.291225 | + | 0.211587i | ||||
\(339\) | 1.30902 | + | 4.02874i | 0.0710960 | + | 0.218811i | ||||
\(340\) | 39.2705 | 2.12974 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −42.7426 | −2.31126 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | 45.7148 | + | 33.2137i | 2.46478 | + | 1.79076i | ||||
\(345\) | 3.04508 | − | 2.21238i | 0.163942 | − | 0.119111i | ||||
\(346\) | 14.2533 | − | 43.8671i | 0.766262 | − | 2.35831i | ||||
\(347\) | −10.3992 | + | 32.0054i | −0.558258 | + | 1.71814i | 0.128924 | + | 0.991654i | \(0.458848\pi\) |
−0.687182 | + | 0.726486i | \(0.741152\pi\) | |||||||
\(348\) | −5.78115 | + | 4.20025i | −0.309902 | + | 0.225157i | ||||
\(349\) | 6.63525 | + | 4.82079i | 0.355177 | + | 0.258051i | 0.751038 | − | 0.660259i | \(-0.229554\pi\) |
−0.395861 | + | 0.918311i | \(0.629554\pi\) | |||||||
\(350\) | 3.23607 | + | 9.95959i | 0.172975 | + | 0.532363i | ||||
\(351\) | 11.2361 | 0.599737 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.9098 | 0.687121 | 0.343560 | − | 0.939131i | \(-0.388367\pi\) | ||||
0.343560 | + | 0.939131i | \(0.388367\pi\) | |||||||
\(354\) | −0.0450850 | − | 0.138757i | −0.00239624 | − | 0.00737487i | ||||
\(355\) | 3.97214 | + | 2.88593i | 0.210819 | + | 0.153169i | ||||
\(356\) | −0.572949 | + | 0.416272i | −0.0303662 | + | 0.0220624i | ||||
\(357\) | −1.54508 | + | 4.75528i | −0.0817746 | + | 0.251676i | ||||
\(358\) | −6.66312 | + | 20.5070i | −0.352157 | + | 1.08383i | ||||
\(359\) | −10.8262 | + | 7.86572i | −0.571387 | + | 0.415137i | −0.835609 | − | 0.549325i | \(-0.814885\pi\) |
0.264222 | + | 0.964462i | \(0.414885\pi\) | |||||||
\(360\) | 15.8262 | + | 11.4984i | 0.834116 | + | 0.606021i | ||||
\(361\) | 6.14590 | + | 18.9151i | 0.323468 | + | 0.995533i | ||||
\(362\) | 50.8328 | 2.67171 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.7082 | 0.823334 | ||||||||
\(365\) | 3.01722 | + | 9.28605i | 0.157929 | + | 0.486054i | ||||
\(366\) | −7.04508 | − | 5.11855i | −0.368252 | − | 0.267551i | ||||
\(367\) | 16.8541 | − | 12.2452i | 0.879777 | − | 0.639195i | −0.0534155 | − | 0.998572i | \(-0.517011\pi\) |
0.933192 | + | 0.359377i | \(0.117011\pi\) | |||||||
\(368\) | −18.5451 | + | 57.0759i | −0.966729 | + | 2.97529i | ||||
\(369\) | 9.04508 | − | 27.8379i | 0.470868 | − | 1.44918i | ||||
\(370\) | 5.23607 | − | 3.80423i | 0.272210 | − | 0.197772i | ||||
\(371\) | −3.73607 | − | 2.71441i | −0.193967 | − | 0.140925i | ||||
\(372\) | 0.218847 | + | 0.673542i | 0.0113467 | + | 0.0349215i | ||||
\(373\) | 35.5623 | 1.84135 | 0.920673 | − | 0.390334i | \(-0.127641\pi\) | ||||
0.920673 | + | 0.390334i | \(0.127641\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.56231 | −0.287236 | ||||||||
\(376\) | −10.1180 | − | 31.1401i | −0.521798 | − | 1.60593i | ||||
\(377\) | 6.23607 | + | 4.53077i | 0.321174 | + | 0.233346i | ||||
\(378\) | −7.35410 | + | 5.34307i | −0.378254 | + | 0.274818i | ||||
\(379\) | −8.05573 | + | 24.7930i | −0.413795 | + | 1.27353i | 0.499529 | + | 0.866297i | \(0.333506\pi\) |
−0.913324 | + | 0.407233i | \(0.866494\pi\) | |||||||
\(380\) | 9.35410 | − | 28.7890i | 0.479855 | − | 1.47684i | ||||
\(381\) | −7.47214 | + | 5.42882i | −0.382809 | + | 0.278127i | ||||
\(382\) | −42.8607 | − | 31.1401i | −2.19294 | − | 1.59327i | ||||
\(383\) | 4.51064 | + | 13.8823i | 0.230483 | + | 0.709354i | 0.997689 | + | 0.0679526i | \(0.0216467\pi\) |
−0.767205 | + | 0.641401i | \(0.778353\pi\) | |||||||
\(384\) | 0.673762 | 0.0343828 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −0.854102 | −0.0434726 | ||||||||
\(387\) | 6.11803 | + | 18.8294i | 0.310997 | + | 0.957151i | ||||
\(388\) | −27.4894 | − | 19.9722i | −1.39556 | − | 1.01393i | ||||
\(389\) | 9.56231 | − | 6.94742i | 0.484828 | − | 0.352248i | −0.318364 | − | 0.947969i | \(-0.603133\pi\) |
0.803192 | + | 0.595720i | \(0.203133\pi\) | |||||||
\(390\) | −1.61803 | + | 4.97980i | −0.0819323 | + | 0.252162i | ||||
\(391\) | −15.2254 | + | 46.8590i | −0.769983 | + | 2.36976i | ||||
\(392\) | −6.04508 | + | 4.39201i | −0.305323 | + | 0.221830i | ||||
\(393\) | 0.527864 | + | 0.383516i | 0.0266272 | + | 0.0193458i | ||||
\(394\) | 14.3262 | + | 44.0916i | 0.721745 | + | 2.22130i | ||||
\(395\) | −8.61803 | −0.433620 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.1803 | −1.16339 | −0.581694 | − | 0.813408i | \(-0.697610\pi\) | ||||
−0.581694 | + | 0.813408i | \(0.697610\pi\) | |||||||
\(398\) | −3.04508 | − | 9.37181i | −0.152636 | − | 0.469766i | ||||
\(399\) | 3.11803 | + | 2.26538i | 0.156097 | + | 0.113411i | ||||
\(400\) | 31.8885 | − | 23.1684i | 1.59443 | − | 1.15842i | ||||
\(401\) | −8.18034 | + | 25.1765i | −0.408507 | + | 1.25725i | 0.509425 | + | 0.860515i | \(0.329858\pi\) |
−0.917931 | + | 0.396739i | \(0.870142\pi\) | |||||||
\(402\) | 3.66312 | − | 11.2739i | 0.182700 | − | 0.562292i | ||||
\(403\) | 0.618034 | − | 0.449028i | 0.0307865 | − | 0.0223677i | ||||
\(404\) | 38.4787 | + | 27.9564i | 1.91439 | + | 1.39088i | ||||
\(405\) | 1.76393 | + | 5.42882i | 0.0876505 | + | 0.269760i | ||||
\(406\) | −6.23607 | −0.309491 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 37.3607 | 1.84963 | ||||||||
\(409\) | 1.32624 | + | 4.08174i | 0.0655782 | + | 0.201829i | 0.978477 | − | 0.206358i | \(-0.0661611\pi\) |
−0.912898 | + | 0.408187i | \(0.866161\pi\) | |||||||
\(410\) | 23.6803 | + | 17.2048i | 1.16949 | + | 0.849683i | ||||
\(411\) | −0.163119 | + | 0.118513i | −0.00804606 | + | 0.00584581i | ||||
\(412\) | 3.21885 | − | 9.90659i | 0.158581 | − | 0.488063i | ||||
\(413\) | 0.0278640 | − | 0.0857567i | 0.00137110 | − | 0.00421981i | ||||
\(414\) | −33.7705 | + | 24.5357i | −1.65973 | + | 1.20586i | ||||
\(415\) | −8.66312 | − | 6.29412i | −0.425256 | − | 0.308966i | ||||
\(416\) | −10.8541 | − | 33.4055i | −0.532166 | − | 1.63784i | ||||
\(417\) | 3.67376 | 0.179905 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.88854 | −0.287674 | −0.143837 | − | 0.989601i | \(-0.545944\pi\) | ||||
−0.143837 | + | 0.989601i | \(0.545944\pi\) | |||||||
\(420\) | −0.927051 | − | 2.85317i | −0.0452355 | − | 0.139220i | ||||
\(421\) | −4.23607 | − | 3.07768i | −0.206453 | − | 0.149997i | 0.479754 | − | 0.877403i | \(-0.340726\pi\) |
−0.686208 | + | 0.727406i | \(0.740726\pi\) | |||||||
\(422\) | 28.3435 | − | 20.5927i | 1.37974 | − | 1.00244i | ||||
\(423\) | 3.54508 | − | 10.9106i | 0.172368 | − | 0.530494i | ||||
\(424\) | −10.6631 | + | 32.8177i | −0.517847 | + | 1.59377i | ||||
\(425\) | 26.1803 | − | 19.0211i | 1.26993 | − | 0.922660i | ||||
\(426\) | 6.42705 | + | 4.66953i | 0.311392 | + | 0.226239i | ||||
\(427\) | −1.66312 | − | 5.11855i | −0.0804840 | − | 0.247704i | ||||
\(428\) | 51.9787 | 2.51249 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −19.7984 | −0.954762 | ||||||||
\(431\) | 2.20820 | + | 6.79615i | 0.106365 | + | 0.327359i | 0.990049 | − | 0.140727i | \(-0.0449438\pi\) |
−0.883683 | + | 0.468086i | \(0.844944\pi\) | |||||||
\(432\) | 27.6803 | + | 20.1109i | 1.33177 | + | 0.967588i | ||||
\(433\) | 30.7705 | − | 22.3561i | 1.47874 | − | 1.07436i | 0.500775 | − | 0.865577i | \(-0.333048\pi\) |
0.977961 | − | 0.208788i | \(-0.0669517\pi\) | |||||||
\(434\) | −0.190983 | + | 0.587785i | −0.00916748 | + | 0.0282146i | ||||
\(435\) | 0.454915 | − | 1.40008i | 0.0218115 | − | 0.0671289i | ||||
\(436\) | −41.1246 | + | 29.8788i | −1.96951 | + | 1.43093i | ||||
\(437\) | 30.7254 | + | 22.3233i | 1.46980 | + | 1.06787i | ||||
\(438\) | 4.88197 | + | 15.0251i | 0.233269 | + | 0.717929i | ||||
\(439\) | −5.61803 | −0.268134 | −0.134067 | − | 0.990972i | \(-0.542804\pi\) | ||||
−0.134067 | + | 0.990972i | \(0.542804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | −21.1803 | − | 65.1864i | −1.00745 | − | 3.10060i | ||||
\(443\) | 6.54508 | + | 4.75528i | 0.310966 | + | 0.225930i | 0.732311 | − | 0.680970i | \(-0.238442\pi\) |
−0.421345 | + | 0.906901i | \(0.638442\pi\) | |||||||
\(444\) | 6.00000 | − | 4.35926i | 0.284747 | − | 0.206881i | ||||
\(445\) | 0.0450850 | − | 0.138757i | 0.00213723 | − | 0.00657773i | ||||
\(446\) | −21.8713 | + | 67.3130i | −1.03564 | + | 3.18736i | ||||
\(447\) | −1.07295 | + | 0.779543i | −0.0507487 | + | 0.0368711i | ||||
\(448\) | 7.04508 | + | 5.11855i | 0.332849 | + | 0.241829i | ||||
\(449\) | −1.02786 | − | 3.16344i | −0.0485079 | − | 0.149292i | 0.923869 | − | 0.382710i | \(-0.125009\pi\) |
−0.972377 | + | 0.233418i | \(0.925009\pi\) | |||||||
\(450\) | 27.4164 | 1.29242 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 33.2705 | 1.56491 | ||||||||
\(453\) | −3.42705 | − | 10.5474i | −0.161017 | − | 0.495559i | ||||
\(454\) | 27.6074 | + | 20.0579i | 1.29568 | + | 0.941366i | ||||
\(455\) | −2.61803 | + | 1.90211i | −0.122735 | + | 0.0891724i | ||||
\(456\) | 8.89919 | − | 27.3889i | 0.416743 | − | 1.28260i | ||||
\(457\) | 2.11803 | − | 6.51864i | 0.0990775 | − | 0.304929i | −0.889217 | − | 0.457485i | \(-0.848750\pi\) |
0.988295 | + | 0.152556i | \(0.0487504\pi\) | |||||||
\(458\) | −23.7984 | + | 17.2905i | −1.11202 | + | 0.807933i | ||||
\(459\) | 22.7254 | + | 16.5110i | 1.06073 | + | 0.770667i | ||||
\(460\) | −9.13525 | − | 28.1154i | −0.425933 | − | 1.31089i | ||||
\(461\) | −19.5066 | −0.908512 | −0.454256 | − | 0.890871i | \(-0.650095\pi\) | ||||
−0.454256 | + | 0.890871i | \(0.650095\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17.7639 | 0.825560 | 0.412780 | − | 0.910831i | \(-0.364558\pi\) | ||||
0.412780 | + | 0.910831i | \(0.364558\pi\) | |||||||
\(464\) | 7.25329 | + | 22.3233i | 0.336725 | + | 1.03633i | ||||
\(465\) | −0.118034 | − | 0.0857567i | −0.00547370 | − | 0.00397687i | ||||
\(466\) | −5.47214 | + | 3.97574i | −0.253492 | + | 0.184173i | ||||
\(467\) | 10.3541 | − | 31.8666i | 0.479131 | − | 1.47461i | −0.361174 | − | 0.932498i | \(-0.617624\pi\) |
0.840305 | − | 0.542114i | \(-0.182376\pi\) | |||||||
\(468\) | 12.7082 | − | 39.1118i | 0.587437 | − | 1.80794i | ||||
\(469\) | 5.92705 | − | 4.30625i | 0.273686 | − | 0.198844i | ||||
\(470\) | 9.28115 | + | 6.74315i | 0.428108 | + | 0.311038i | ||||
\(471\) | −3.03444 | − | 9.33905i | −0.139820 | − | 0.430321i | ||||
\(472\) | −0.673762 | −0.0310124 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −13.9443 | −0.640482 | ||||||||
\(475\) | −7.70820 | − | 23.7234i | −0.353677 | − | 1.08850i | ||||
\(476\) | 31.7705 | + | 23.0826i | 1.45620 | + | 1.05799i | ||||
\(477\) | −9.78115 | + | 7.10642i | −0.447848 | + | 0.325381i | ||||
\(478\) | 4.78115 | − | 14.7149i | 0.218685 | − | 0.673043i | ||||
\(479\) | −8.10739 | + | 24.9520i | −0.370436 | + | 1.14009i | 0.576070 | + | 0.817400i | \(0.304585\pi\) |
−0.946506 | + | 0.322685i | \(0.895415\pi\) | |||||||
\(480\) | −5.42705 | + | 3.94298i | −0.247710 | + | 0.179972i | ||||
\(481\) | −6.47214 | − | 4.70228i | −0.295104 | − | 0.214406i | ||||
\(482\) | 13.9721 | + | 43.0018i | 0.636413 | + | 1.95868i | ||||
\(483\) | 3.76393 | 0.171265 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.00000 | 0.317854 | ||||||||
\(486\) | 11.2812 | + | 34.7198i | 0.511723 | + | 1.57492i | ||||
\(487\) | −13.4271 | − | 9.75532i | −0.608438 | − | 0.442056i | 0.240426 | − | 0.970667i | \(-0.422713\pi\) |
−0.848864 | + | 0.528612i | \(0.822713\pi\) | |||||||
\(488\) | −32.5344 | + | 23.6377i | −1.47276 | + | 1.07003i | ||||
\(489\) | 0.899187 | − | 2.76741i | 0.0406626 | − | 0.125147i | ||||
\(490\) | 0.809017 | − | 2.48990i | 0.0365477 | − | 0.112482i | ||||
\(491\) | 23.3435 | − | 16.9600i | 1.05348 | − | 0.765395i | 0.0806053 | − | 0.996746i | \(-0.474315\pi\) |
0.972870 | + | 0.231351i | \(0.0743147\pi\) | |||||||
\(492\) | 27.1353 | + | 19.7149i | 1.22335 | + | 0.888817i | ||||
\(493\) | 5.95492 | + | 18.3273i | 0.268196 | + | 0.825422i | ||||
\(494\) | −52.8328 | −2.37706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.32624 | 0.104451 | ||||||||
\(497\) | 1.51722 | + | 4.66953i | 0.0680567 | + | 0.209457i | ||||
\(498\) | −14.0172 | − | 10.1841i | −0.628127 | − | 0.456361i | ||||
\(499\) | −0.881966 | + | 0.640786i | −0.0394822 | + | 0.0286855i | −0.607351 | − | 0.794433i | \(-0.707768\pi\) |
0.567869 | + | 0.823119i | \(0.307768\pi\) | |||||||
\(500\) | −13.5000 | + | 41.5487i | −0.603738 | + | 1.85812i | ||||
\(501\) | 0.472136 | − | 1.45309i | 0.0210935 | − | 0.0649191i | ||||
\(502\) | −48.7148 | + | 35.3934i | −2.17425 | + | 1.57968i | ||||
\(503\) | 15.2361 | + | 11.0697i | 0.679343 | + | 0.493571i | 0.873140 | − | 0.487470i | \(-0.162080\pi\) |
−0.193797 | + | 0.981042i | \(0.562080\pi\) | |||||||
\(504\) | 6.04508 | + | 18.6049i | 0.269269 | + | 0.828726i | ||||
\(505\) | −9.79837 | −0.436022 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.56231 | −0.0693844 | ||||||||
\(508\) | 22.4164 | + | 68.9906i | 0.994567 | + | 3.06096i | ||||
\(509\) | −25.6803 | − | 18.6579i | −1.13826 | − | 0.826995i | −0.151385 | − | 0.988475i | \(-0.548373\pi\) |
−0.986876 | + | 0.161480i | \(0.948373\pi\) | |||||||
\(510\) | −10.5902 | + | 7.69421i | −0.468941 | + | 0.340705i | ||||
\(511\) | −3.01722 | + | 9.28605i | −0.133474 | + | 0.410791i | ||||
\(512\) | −12.4549 | + | 38.3323i | −0.550435 | + | 1.69406i | ||||
\(513\) | 17.5172 | − | 12.7270i | 0.773404 | − | 0.561911i | ||||
\(514\) | −24.4894 | − | 17.7926i | −1.08018 | − | 0.784796i | ||||
\(515\) | 0.663119 | + | 2.04087i | 0.0292205 | + | 0.0899315i | ||||
\(516\) | −22.6869 | −0.998736 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 6.47214 | 0.284369 | ||||||||
\(519\) | 3.36475 | + | 10.3556i | 0.147696 | + | 0.454561i | ||||
\(520\) | 19.5623 | + | 14.2128i | 0.857864 | + | 0.623275i | ||||
\(521\) | 6.28115 | − | 4.56352i | 0.275182 | − | 0.199932i | −0.441631 | − | 0.897197i | \(-0.645600\pi\) |
0.716813 | + | 0.697265i | \(0.245600\pi\) | |||||||
\(522\) | −5.04508 | + | 15.5272i | −0.220817 | + | 0.679606i | ||||
\(523\) | 1.10081 | − | 3.38795i | 0.0481352 | − | 0.148145i | −0.924100 | − | 0.382151i | \(-0.875183\pi\) |
0.972235 | + | 0.234006i | \(0.0751835\pi\) | |||||||
\(524\) | 4.14590 | − | 3.01217i | 0.181114 | − | 0.131587i | ||||
\(525\) | −2.00000 | − | 1.45309i | −0.0872872 | − | 0.0634178i | ||||
\(526\) | −18.7082 | − | 57.5779i | −0.815716 | − | 2.51052i | ||||
\(527\) | 1.90983 | 0.0831935 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.0902 | 0.612616 | ||||||||
\(530\) | −3.73607 | − | 11.4984i | −0.162284 | − | 0.499460i | ||||
\(531\) | −0.190983 | − | 0.138757i | −0.00828796 | − | 0.00602155i | ||||
\(532\) | 24.4894 | − | 17.7926i | 1.06175 | − | 0.771405i | ||||
\(533\) | 11.1803 | − | 34.4095i | 0.484274 | − | 1.49044i | ||||
\(534\) | 0.0729490 | − | 0.224514i | 0.00315681 | − | 0.00971567i | ||||
\(535\) | −8.66312 | + | 6.29412i | −0.374539 | + | 0.272119i | ||||
\(536\) | −44.2877 | − | 32.1769i | −1.91294 | − | 1.38983i | ||||
\(537\) | −1.57295 | − | 4.84104i | −0.0678778 | − | 0.208906i | ||||
\(538\) | 26.5623 | 1.14518 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −16.8541 | −0.725285 | ||||||||
\(541\) | 3.92705 | + | 12.0862i | 0.168837 | + | 0.519627i | 0.999299 | − | 0.0374489i | \(-0.0119232\pi\) |
−0.830461 | + | 0.557076i | \(0.811923\pi\) | |||||||
\(542\) | 41.9336 | + | 30.4666i | 1.80120 | + | 1.30865i | ||||
\(543\) | −9.70820 | + | 7.05342i | −0.416619 | + | 0.302691i | ||||
\(544\) | 27.1353 | − | 83.5137i | 1.16341 | − | 3.58062i | ||||
\(545\) | 3.23607 | − | 9.95959i | 0.138618 | − | 0.426622i | ||||
\(546\) | −4.23607 | + | 3.07768i | −0.181287 | + | 0.131713i | ||||
\(547\) | −28.5344 | − | 20.7315i | −1.22004 | − | 0.886414i | −0.223941 | − | 0.974603i | \(-0.571892\pi\) |
−0.996104 | + | 0.0881884i | \(0.971892\pi\) | |||||||
\(548\) | 0.489357 | + | 1.50609i | 0.0209043 | + | 0.0643368i | ||||
\(549\) | −14.0902 | −0.601354 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 14.8541 | 0.632806 | ||||||||
\(552\) | −8.69098 | − | 26.7481i | −0.369913 | − | 1.13847i | ||||
\(553\) | −6.97214 | − | 5.06555i | −0.296485 | − | 0.215409i | ||||
\(554\) | −12.7812 | + | 9.28605i | −0.543019 | + | 0.394527i | ||||
\(555\) | −0.472136 | + | 1.45309i | −0.0200411 | + | 0.0616800i | ||||
\(556\) | 8.91641 | − | 27.4419i | 0.378140 | − | 1.16380i | ||||
\(557\) | −11.5172 | + | 8.36775i | −0.488000 | + | 0.354553i | −0.804415 | − | 0.594068i | \(-0.797521\pi\) |
0.316414 | + | 0.948621i | \(0.397521\pi\) | |||||||
\(558\) | 1.30902 | + | 0.951057i | 0.0554151 | + | 0.0402614i | ||||
\(559\) | 7.56231 | + | 23.2744i | 0.319851 | + | 0.984402i | ||||
\(560\) | −9.85410 | −0.416412 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.38197 | 0.311389 | ||||||||
\(563\) | −4.62868 | − | 14.2456i | −0.195075 | − | 0.600381i | −0.999976 | − | 0.00697043i | \(-0.997781\pi\) |
0.804900 | − | 0.593410i | \(-0.202219\pi\) | |||||||
\(564\) | 10.6353 | + | 7.72696i | 0.447825 | + | 0.325364i | ||||
\(565\) | −5.54508 | + | 4.02874i | −0.233283 | + | 0.169490i | ||||
\(566\) | 4.80902 | − | 14.8006i | 0.202138 | − | 0.622117i | ||||
\(567\) | −1.76393 | + | 5.42882i | −0.0740782 | + | 0.227989i | ||||
\(568\) | 29.6803 | − | 21.5640i | 1.24536 | − | 0.904807i | ||||
\(569\) | −20.4721 | − | 14.8739i | −0.858237 | − | 0.623545i | 0.0691681 | − | 0.997605i | \(-0.477966\pi\) |
−0.927405 | + | 0.374060i | \(0.877966\pi\) | |||||||
\(570\) | 3.11803 | + | 9.59632i | 0.130600 | + | 0.401946i | ||||
\(571\) | 28.3050 | 1.18453 | 0.592263 | − | 0.805745i | \(-0.298235\pi\) | ||||
0.592263 | + | 0.805745i | \(0.298235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.5066 | 0.522470 | ||||||||
\(574\) | 9.04508 | + | 27.8379i | 0.377535 | + | 1.16193i | ||||
\(575\) | −19.7082 | − | 14.3188i | −0.821889 | − | 0.597137i | ||||
\(576\) | 18.4443 | − | 13.4005i | 0.768511 | − | 0.558356i | ||||
\(577\) | −6.69098 | + | 20.5927i | −0.278549 | + | 0.857286i | 0.709709 | + | 0.704495i | \(0.248826\pi\) |
−0.988258 | + | 0.152792i | \(0.951174\pi\) | |||||||
\(578\) | 39.1976 | − | 120.638i | 1.63040 | − | 5.01787i | ||||
\(579\) | 0.163119 | − | 0.118513i | 0.00677899 | − | 0.00492523i | ||||
\(580\) | −9.35410 | − | 6.79615i | −0.388408 | − | 0.282195i | ||||
\(581\) | −3.30902 | − | 10.1841i | −0.137281 | − | 0.422508i | ||||
\(582\) | 11.3262 | 0.469488 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 72.9574 | 3.01900 | ||||||||
\(585\) | 2.61803 | + | 8.05748i | 0.108242 | + | 0.333136i | ||||
\(586\) | −23.2984 | − | 16.9273i | −0.962447 | − | 0.699259i | ||||
\(587\) | −0.809017 | + | 0.587785i | −0.0333917 | + | 0.0242605i | −0.604356 | − | 0.796714i | \(-0.706569\pi\) |
0.570964 | + | 0.820975i | \(0.306569\pi\) | |||||||
\(588\) | 0.927051 | − | 2.85317i | 0.0382309 | − | 0.117663i | ||||
\(589\) | 0.454915 | − | 1.40008i | 0.0187444 | − | 0.0576895i | ||||
\(590\) | 0.190983 | − | 0.138757i | 0.00786265 | − | 0.00571255i | ||||
\(591\) | −8.85410 | − | 6.43288i | −0.364209 | − | 0.264613i | ||||
\(592\) | −7.52786 | − | 23.1684i | −0.309393 | − | 0.952215i | ||||
\(593\) | 29.1246 | 1.19600 | 0.598002 | − | 0.801494i | \(-0.295961\pi\) | ||||
0.598002 | + | 0.801494i | \(0.295961\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.09017 | −0.331665 | ||||||||
\(596\) | 3.21885 | + | 9.90659i | 0.131849 | + | 0.405790i | ||||
\(597\) | 1.88197 | + | 1.36733i | 0.0770237 | + | 0.0559610i | ||||
\(598\) | −41.7426 | + | 30.3278i | −1.70698 | + | 1.24020i | ||||
\(599\) | −4.94427 | + | 15.2169i | −0.202017 | + | 0.621746i | 0.797805 | + | 0.602915i | \(0.205994\pi\) |
−0.999823 | + | 0.0188306i | \(0.994006\pi\) | |||||||
\(600\) | −5.70820 | + | 17.5680i | −0.233036 | + | 0.717212i | ||||
\(601\) | 0.236068 | − | 0.171513i | 0.00962941 | − | 0.00699618i | −0.582960 | − | 0.812501i | \(-0.698106\pi\) |
0.592590 | + | 0.805505i | \(0.298106\pi\) | |||||||
\(602\) | −16.0172 | − | 11.6372i | −0.652813 | − | 0.474297i | ||||
\(603\) | −5.92705 | − | 18.2416i | −0.241368 | − | 0.742855i | ||||
\(604\) | −87.1033 | −3.54418 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.8541 | −0.644029 | ||||||||
\(607\) | −13.8435 | − | 42.6058i | −0.561889 | − | 1.72932i | −0.677019 | − | 0.735965i | \(-0.736729\pi\) |
0.115131 | − | 0.993350i | \(-0.463271\pi\) | |||||||
\(608\) | −54.7599 | − | 39.7854i | −2.22081 | − | 1.61351i | ||||
\(609\) | 1.19098 | − | 0.865300i | 0.0482611 | − | 0.0350637i | ||||
\(610\) | 4.35410 | − | 13.4005i | 0.176292 | − | 0.542572i | ||||
\(611\) | 4.38197 | − | 13.4863i | 0.177275 | − | 0.545597i | ||||
\(612\) | 83.1763 | − | 60.4311i | 3.36220 | − | 2.44278i | ||||
\(613\) | 28.2254 | + | 20.5070i | 1.14001 | + | 0.828269i | 0.987121 | − | 0.159974i | \(-0.0511410\pi\) |
0.152893 | + | 0.988243i | \(0.451141\pi\) | |||||||
\(614\) | 0.663119 | + | 2.04087i | 0.0267613 | + | 0.0823628i | ||||
\(615\) | −6.90983 | −0.278631 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.4164 | −0.701158 | −0.350579 | − | 0.936533i | \(-0.614015\pi\) | ||||
−0.350579 | + | 0.936533i | \(0.614015\pi\) | |||||||
\(618\) | 1.07295 | + | 3.30220i | 0.0431603 | + | 0.132834i | ||||
\(619\) | 21.2705 | + | 15.4539i | 0.854934 | + | 0.621146i | 0.926502 | − | 0.376290i | \(-0.122800\pi\) |
−0.0715680 | + | 0.997436i | \(0.522800\pi\) | |||||||
\(620\) | −0.927051 | + | 0.673542i | −0.0372313 | + | 0.0270501i | ||||
\(621\) | 6.53444 | − | 20.1109i | 0.262218 | − | 0.807024i | ||||
\(622\) | 7.28115 | − | 22.4091i | 0.291948 | − | 0.898522i | ||||
\(623\) | 0.118034 | − | 0.0857567i | 0.00472893 | − | 0.00343577i | ||||
\(624\) | 15.9443 | + | 11.5842i | 0.638282 | + | 0.463739i | ||||
\(625\) | 3.39919 | + | 10.4616i | 0.135967 | + | 0.418465i | ||||
\(626\) | 7.00000 | 0.279776 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −77.1246 | −3.07761 | ||||||||
\(629\) | −6.18034 | − | 19.0211i | −0.246426 | − | 0.758422i | ||||
\(630\) | −5.54508 | − | 4.02874i | −0.220921 | − | 0.160509i | ||||
\(631\) | 28.9894 | − | 21.0620i | 1.15405 | − | 0.838465i | 0.165034 | − | 0.986288i | \(-0.447227\pi\) |
0.989014 | + | 0.147823i | \(0.0472265\pi\) | |||||||
\(632\) | −19.8992 | + | 61.2434i | −0.791547 | + | 2.43613i | ||||
\(633\) | −2.55573 | + | 7.86572i | −0.101581 | + | 0.312634i | ||||
\(634\) | 52.0238 | − | 37.7975i | 2.06613 | − | 1.50113i | ||||
\(635\) | −12.0902 | − | 8.78402i | −0.479784 | − | 0.348583i | ||||
\(636\) | −4.28115 | − | 13.1760i | −0.169759 | − | 0.522464i | ||||
\(637\) | −3.23607 | −0.128218 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 12.8541 | 0.508500 | ||||||||
\(640\) | 0.336881 | + | 1.03681i | 0.0133164 | + | 0.0409836i | ||||
\(641\) | −0.281153 | − | 0.204270i | −0.0111049 | − | 0.00806816i | 0.582219 | − | 0.813032i | \(-0.302185\pi\) |
−0.593324 | + | 0.804964i | \(0.702185\pi\) | |||||||
\(642\) | −14.0172 | + | 10.1841i | −0.553216 | + | 0.401935i | ||||
\(643\) | 8.78115 | − | 27.0256i | 0.346295 | − | 1.06579i | −0.614592 | − | 0.788845i | \(-0.710679\pi\) |
0.960887 | − | 0.276941i | \(-0.0893206\pi\) | |||||||
\(644\) | 9.13525 | − | 28.1154i | 0.359979 | − | 1.10790i | ||||
\(645\) | 3.78115 | − | 2.74717i | 0.148883 | − | 0.108170i | ||||
\(646\) | −106.857 | − | 77.6359i | −4.20422 | − | 3.05454i | ||||
\(647\) | −5.00000 | − | 15.3884i | −0.196570 | − | 0.604981i | −0.999955 | − | 0.00952037i | \(-0.996970\pi\) |
0.803384 | − | 0.595461i | \(-0.203030\pi\) | |||||||
\(648\) | 42.6525 | 1.67555 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 33.8885 | 1.32922 | ||||||||
\(651\) | −0.0450850 | − | 0.138757i | −0.00176702 | − | 0.00543833i | ||||
\(652\) | −18.4894 | − | 13.4333i | −0.724099 | − | 0.526089i | ||||
\(653\) | −11.1353 | + | 8.09024i | −0.435756 | + | 0.316595i | −0.783946 | − | 0.620828i | \(-0.786796\pi\) |
0.348190 | + | 0.937424i | \(0.386796\pi\) | |||||||
\(654\) | 5.23607 | − | 16.1150i | 0.204746 | − | 0.630145i | ||||
\(655\) | −0.326238 | + | 1.00406i | −0.0127472 | + | 0.0392318i | ||||
\(656\) | 89.1312 | − | 64.7576i | 3.47999 | − | 2.52836i | ||||
\(657\) | 20.6803 | + | 15.0251i | 0.806817 | + | 0.586187i | ||||
\(658\) | 3.54508 | + | 10.9106i | 0.138202 | + | 0.425341i | ||||
\(659\) | −22.5279 | −0.877561 | −0.438780 | − | 0.898594i | \(-0.644589\pi\) | ||||
−0.438780 | + | 0.898594i | \(0.644589\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.4377 | −0.561561 | −0.280781 | − | 0.959772i | \(-0.590593\pi\) | ||||
−0.280781 | + | 0.959772i | \(0.590593\pi\) | |||||||
\(662\) | −13.0902 | − | 40.2874i | −0.508764 | − | 1.56581i | ||||
\(663\) | 13.0902 | + | 9.51057i | 0.508380 | + | 0.369360i | ||||
\(664\) | −64.7320 | + | 47.0306i | −2.51209 | + | 1.82514i | ||||
\(665\) | −1.92705 | + | 5.93085i | −0.0747278 | + | 0.229989i | ||||
\(666\) | 5.23607 | − | 16.1150i | 0.202894 | − | 0.624442i | ||||
\(667\) | 11.7361 | − | 8.52675i | 0.454422 | − | 0.330157i | ||||
\(668\) | −9.70820 | − | 7.05342i | −0.375622 | − | 0.272905i | ||||
\(669\) | −5.16312 | − | 15.8904i | −0.199618 | − | 0.614360i | ||||
\(670\) | 19.1803 | 0.741001 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −6.70820 | −0.258775 | ||||||||
\(673\) | 10.3262 | + | 31.7809i | 0.398047 | + | 1.22506i | 0.926563 | + | 0.376140i | \(0.122749\pi\) |
−0.528516 | + | 0.848924i | \(0.677251\pi\) | |||||||
\(674\) | 17.0623 | + | 12.3965i | 0.657215 | + | 0.477495i | ||||
\(675\) | −11.2361 | + | 8.16348i | −0.432476 | + | 0.314213i | ||||
\(676\) | −3.79180 | + | 11.6699i | −0.145838 | + | 0.448844i | ||||
\(677\) | 0.843459 | − | 2.59590i | 0.0324168 | − | 0.0997685i | −0.933539 | − | 0.358476i | \(-0.883297\pi\) |
0.965956 | + | 0.258707i | \(0.0832965\pi\) | |||||||
\(678\) | −8.97214 | + | 6.51864i | −0.344573 | + | 0.250347i | ||||
\(679\) | 5.66312 | + | 4.11450i | 0.217331 | + | 0.157900i | ||||
\(680\) | 18.6803 | + | 57.4922i | 0.716358 | + | 2.20472i | ||||
\(681\) | −8.05573 | −0.308696 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.5066 | 1.47341 | 0.736707 | − | 0.676213i | \(-0.236380\pi\) | ||||
0.736707 | + | 0.676213i | \(0.236380\pi\) | |||||||
\(684\) | −24.4894 | − | 75.3705i | −0.936374 | − | 2.88186i | ||||
\(685\) | −0.263932 | − | 0.191758i | −0.0100843 | − | 0.00732669i | ||||
\(686\) | 2.11803 | − | 1.53884i | 0.0808669 | − | 0.0587533i | ||||
\(687\) | 2.14590 | − | 6.60440i | 0.0818711 | − | 0.251973i | ||||
\(688\) | −23.0279 | + | 70.8725i | −0.877929 | + | 2.70199i | ||||
\(689\) | −12.0902 | + | 8.78402i | −0.460599 | + | 0.334645i | ||||
\(690\) | 7.97214 | + | 5.79210i | 0.303494 | + | 0.220501i | ||||
\(691\) | −15.0000 | − | 46.1653i | −0.570627 | − | 1.75621i | −0.650609 | − | 0.759413i | \(-0.725486\pi\) |
0.0799823 | − | 0.996796i | \(-0.474514\pi\) | |||||||
\(692\) | 85.5197 | 3.25097 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −88.1033 | −3.34436 | ||||||||
\(695\) | 1.83688 | + | 5.65334i | 0.0696769 | + | 0.214443i | ||||
\(696\) | −8.89919 | − | 6.46564i | −0.337323 | − | 0.245079i | ||||
\(697\) | 73.1763 | − | 53.1657i | 2.77175 | − | 2.01379i | ||||
\(698\) | −6.63525 | + | 20.4212i | −0.251148 | + | 0.772954i | ||||
\(699\) | 0.493422 | − | 1.51860i | 0.0186629 | − | 0.0574386i | ||||
\(700\) | −15.7082 | + | 11.4127i | −0.593714 | + | 0.431359i | ||||
\(701\) | −15.7812 | − | 11.4657i | −0.596046 | − | 0.433053i | 0.248427 | − | 0.968651i | \(-0.420086\pi\) |
−0.844473 | + | 0.535598i | \(0.820086\pi\) | |||||||
\(702\) | 9.09017 | + | 27.9767i | 0.343086 | + | 1.05591i | ||||
\(703\) | −15.4164 | −0.581441 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.70820 | −0.101997 | ||||||||
\(706\) | 10.4443 | + | 32.1442i | 0.393075 | + | 1.20976i | ||||
\(707\) | −7.92705 | − | 5.75934i | −0.298127 | − | 0.216602i | ||||
\(708\) | 0.218847 | − | 0.159002i | 0.00822478 | − | 0.00597565i | ||||
\(709\) | 6.80902 | − | 20.9560i | 0.255718 | − | 0.787019i | −0.737969 | − | 0.674834i | \(-0.764215\pi\) |
0.993687 | − | 0.112185i | \(-0.0357849\pi\) | |||||||
\(710\) | −3.97214 | + | 12.2250i | −0.149072 | + | 0.458795i | ||||
\(711\) | −18.2533 | + | 13.2618i | −0.684552 | + | 0.497356i | ||||
\(712\) | −0.881966 | − | 0.640786i | −0.0330531 | − | 0.0240145i | ||||
\(713\) | −0.444272 | − | 1.36733i | −0.0166381 | − | 0.0512068i | ||||
\(714\) | −13.0902 | −0.489887 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −39.9787 | −1.49407 | ||||||||
\(717\) | 1.12868 | + | 3.47371i | 0.0421512 | + | 0.129728i | ||||
\(718\) | −28.3435 | − | 20.5927i | −1.05777 | − | 0.768514i | ||||
\(719\) | −26.6074 | + | 19.3314i | −0.992288 | + | 0.720940i | −0.960421 | − | 0.278553i | \(-0.910145\pi\) |
−0.0318672 | + | 0.999492i | \(0.510145\pi\) | |||||||
\(720\) | −7.97214 | + | 24.5357i | −0.297104 | + | 0.914392i | ||||
\(721\) | −0.663119 | + | 2.04087i | −0.0246958 | + | 0.0760060i | ||||
\(722\) | −42.1246 | + | 30.6053i | −1.56772 | + | 1.13901i | ||||
\(723\) | −8.63525 | − | 6.27388i | −0.321149 | − | 0.233328i | ||||
\(724\) | 29.1246 | + | 89.6363i | 1.08241 | + | 3.33131i | ||||
\(725\) | −9.52786 | −0.353856 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.4508 | 1.61150 | 0.805751 | − | 0.592254i | \(-0.201762\pi\) | ||||
0.805751 | + | 0.592254i | \(0.201762\pi\) | |||||||
\(728\) | 7.47214 | + | 22.9969i | 0.276936 | + | 0.852321i | ||||
\(729\) | 6.88197 | + | 5.00004i | 0.254888 | + | 0.185187i | ||||
\(730\) | −20.6803 | + | 15.0251i | −0.765414 | + | 0.556106i | ||||
\(731\) | −18.9058 | + | 58.1860i | −0.699255 | + | 2.15209i | ||||
\(732\) | 4.98936 | − | 15.3557i | 0.184412 | − | 0.567562i | ||||
\(733\) | 28.3607 | − | 20.6052i | 1.04753 | − | 0.761072i | 0.0757852 | − | 0.997124i | \(-0.475854\pi\) |
0.971740 | + | 0.236052i | \(0.0758537\pi\) | |||||||
\(734\) | 44.1246 | + | 32.0584i | 1.62867 | + | 1.18330i | ||||
\(735\) | 0.190983 | + | 0.587785i | 0.00704451 | + | 0.0216808i | ||||
\(736\) | −66.1033 | −2.43660 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 76.6312 | 2.82083 | ||||||||
\(739\) | 4.20820 | + | 12.9515i | 0.154801 | + | 0.476429i | 0.998141 | − | 0.0609519i | \(-0.0194136\pi\) |
−0.843339 | + | 0.537381i | \(0.819414\pi\) | |||||||
\(740\) | 9.70820 | + | 7.05342i | 0.356881 | + | 0.259289i | ||||
\(741\) | 10.0902 | − | 7.33094i | 0.370672 | − | 0.269309i | ||||
\(742\) | 3.73607 | − | 11.4984i | 0.137155 | − | 0.422121i | ||||
\(743\) | 8.06231 | − | 24.8132i | 0.295777 | − | 0.910309i | −0.687182 | − | 0.726485i | \(-0.741152\pi\) |
0.982959 | − | 0.183824i | \(-0.0588475\pi\) | |||||||
\(744\) | −0.881966 | + | 0.640786i | −0.0323344 | + | 0.0234923i | ||||
\(745\) | −1.73607 | − | 1.26133i | −0.0636046 | − | 0.0462115i | ||||
\(746\) | 28.7705 | + | 88.5465i | 1.05336 | + | 3.24192i | ||||
\(747\) | −28.0344 | −1.02573 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.7082 | −0.391269 | ||||||||
\(750\) | −4.50000 | − | 13.8496i | −0.164317 | − | 0.505715i | ||||
\(751\) | 17.2361 | + | 12.5227i | 0.628953 | + | 0.456961i | 0.856037 | − | 0.516914i | \(-0.172919\pi\) |
−0.227084 | + | 0.973875i | \(0.572919\pi\) | |||||||
\(752\) | 34.9336 | − | 25.3808i | 1.27390 | − | 0.925541i | ||||
\(753\) | 4.39261 | − | 13.5191i | 0.160076 | − | 0.492662i | ||||
\(754\) | −6.23607 | + | 19.1926i | −0.227104 | + | 0.698955i | ||||
\(755\) | 14.5172 | − | 10.5474i | 0.528336 | − | 0.383858i | ||||
\(756\) | −13.6353 | − | 9.90659i | −0.495909 | − | 0.360299i | ||||
\(757\) | −5.94427 | − | 18.2946i | −0.216048 | − | 0.664928i | −0.999078 | − | 0.0429433i | \(-0.986327\pi\) |
0.783029 | − | 0.621985i | \(-0.213673\pi\) | |||||||
\(758\) | −68.2492 | −2.47892 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 46.5967 | 1.69024 | ||||||||
\(761\) | 14.6180 | + | 44.9897i | 0.529903 | + | 1.63087i | 0.754411 | + | 0.656402i | \(0.227923\pi\) |
−0.224508 | + | 0.974472i | \(0.572077\pi\) | |||||||
\(762\) | −19.5623 | − | 14.2128i | −0.708668 | − | 0.514877i | ||||
\(763\) | 8.47214 | − | 6.15537i | 0.306712 | − | 0.222839i | ||||
\(764\) | 30.3541 | − | 93.4203i | 1.09817 | − | 3.37983i | ||||
\(765\) | −6.54508 | + | 20.1437i | −0.236638 | + | 0.728297i | ||||
\(766\) | −30.9164 | + | 22.4621i | −1.11706 | + | 0.811588i | ||||
\(767\) | −0.236068 | − | 0.171513i | −0.00852392 | − | 0.00619299i | ||||
\(768\) | −2.78115 | − | 8.55951i | −0.100356 | − | 0.308865i | ||||
\(769\) | −28.4377 | −1.02549 | −0.512745 | − | 0.858541i | \(-0.671371\pi\) | ||||
−0.512745 | + | 0.858541i | \(0.671371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.14590 | 0.257353 | ||||||||
\(772\) | −0.489357 | − | 1.50609i | −0.0176123 | − | 0.0542052i | ||||
\(773\) | −28.9336 | − | 21.0215i | −1.04067 | − | 0.756091i | −0.0702540 | − | 0.997529i | \(-0.522381\pi\) |
−0.970416 | + | 0.241438i | \(0.922381\pi\) | |||||||
\(774\) | −41.9336 | + | 30.4666i | −1.50727 | + | 1.09510i | ||||
\(775\) | −0.291796 | + | 0.898056i | −0.0104816 | + | 0.0322591i | ||||
\(776\) | 16.1631 | − | 49.7450i | 0.580222 | − | 1.78574i | ||||
\(777\) | −1.23607 | + | 0.898056i | −0.0443437 | + | 0.0322176i | ||||
\(778\) | 25.0344 | + | 18.1886i | 0.897528 | + | 0.652092i | ||||
\(779\) | −21.5451 | − | 66.3090i | −0.771933 | − | 2.37576i | ||||
\(780\) | −9.70820 | −0.347609 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −128.992 | −4.61274 | ||||||||
\(783\) | −2.55573 | − | 7.86572i | −0.0913343 | − | 0.281098i | ||||
\(784\) | −7.97214 | − | 5.79210i | −0.284719 | − | 0.206861i | ||||
\(785\) | 12.8541 | − | 9.33905i | 0.458783 | − | 0.333325i | ||||
\(786\) | −0.527864 | + | 1.62460i | −0.0188283 | + | 0.0579475i | ||||
\(787\) | −0.135255 | + | 0.416272i | −0.00482132 | + | 0.0148385i | −0.953438 | − | 0.301588i | \(-0.902483\pi\) |
0.948617 | + | 0.316427i | \(0.102483\pi\) | |||||||
\(788\) | −69.5410 | + | 50.5245i | −2.47730 | + | 1.79986i | ||||
\(789\) | 11.5623 | + | 8.40051i | 0.411629 | + | 0.299066i | ||||
\(790\) | −6.97214 | − | 21.4580i | −0.248057 | − | 0.763442i | ||||
\(791\) | −6.85410 | −0.243704 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.4164 | −0.618475 | ||||||||
\(794\) | −18.7533 | − | 57.7167i | −0.665529 | − | 2.04829i | ||||
\(795\) | 2.30902 | + | 1.67760i | 0.0818924 | + | 0.0594983i | ||||
\(796\) | 14.7812 | − | 10.7391i | 0.523904 | − | 0.380639i | ||||
\(797\) | 8.57953 | − | 26.4051i | 0.303902 | − | 0.935316i | −0.676182 | − | 0.736735i | \(-0.736367\pi\) |
0.980084 | − | 0.198581i | \(-0.0636333\pi\) | |||||||
\(798\) | −3.11803 | + | 9.59632i | −0.110377 | + | 0.339706i | ||||
\(799\) | 28.6803 | − | 20.8375i | 1.01464 | − | 0.737177i | ||||
\(800\) | 35.1246 | + | 25.5195i | 1.24184 | + | 0.902251i | ||||
\(801\) | −0.118034 | − | 0.363271i | −0.00417053 | − | 0.0128356i | ||||
\(802\) | −69.3050 | −2.44724 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 21.9787 | 0.775129 | ||||||||
\(805\) | 1.88197 | + | 5.79210i | 0.0663306 | + | 0.204145i | ||||
\(806\) | 1.61803 | + | 1.17557i | 0.0569928 | + | 0.0414077i | ||||
\(807\) | −5.07295 | + | 3.68571i | −0.178576 | + | 0.129743i | ||||
\(808\) | −22.6246 | + | 69.6314i | −0.795931 | + | 2.44962i | ||||
\(809\) | 1.70163 | − | 5.23707i | 0.0598260 | − | 0.184125i | −0.916677 | − | 0.399629i | \(-0.869139\pi\) |
0.976503 | + | 0.215503i | \(0.0691391\pi\) | |||||||
\(810\) | −12.0902 | + | 8.78402i | −0.424805 | + | 0.308639i | ||||
\(811\) | 44.3607 | + | 32.2299i | 1.55771 | + | 1.13175i | 0.937852 | + | 0.347035i | \(0.112811\pi\) |
0.619862 | + | 0.784711i | \(0.287189\pi\) | |||||||
\(812\) | −3.57295 | − | 10.9964i | −0.125386 | − | 0.385898i | ||||
\(813\) | −12.2361 | −0.429138 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.70820 | 0.164921 | ||||||||
\(816\) | 15.2254 | + | 46.8590i | 0.532996 | + | 1.64039i | ||||
\(817\) | 38.1525 | + | 27.7194i | 1.33479 | + | 0.969779i | ||||
\(818\) | −9.09017 | + | 6.60440i | −0.317830 | + | 0.230917i | ||||
\(819\) | −2.61803 | + | 8.05748i | −0.0914815 | + | 0.281551i | ||||
\(820\) | −16.7705 | + | 51.6143i | −0.585652 | + | 1.80245i | ||||
\(821\) | −40.9894 | + | 29.7805i | −1.43054 | + | 1.03935i | −0.440622 | + | 0.897693i | \(0.645242\pi\) |
−0.989916 | + | 0.141654i | \(0.954758\pi\) | |||||||
\(822\) | −0.427051 | − | 0.310271i | −0.0148951 | − | 0.0108219i | ||||
\(823\) | 1.20163 | + | 3.69822i | 0.0418861 | + | 0.128912i | 0.969813 | − | 0.243850i | \(-0.0784106\pi\) |
−0.927927 | + | 0.372762i | \(0.878411\pi\) | |||||||
\(824\) | 16.0344 | 0.558586 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.236068 | 0.00821386 | ||||||||
\(827\) | −9.14590 | − | 28.1482i | −0.318034 | − | 0.978808i | −0.974488 | − | 0.224442i | \(-0.927944\pi\) |
0.656453 | − | 0.754366i | \(-0.272056\pi\) | |||||||
\(828\) | −62.6140 | − | 45.4917i | −2.17599 | − | 1.58095i | ||||
\(829\) | 0.826238 | − | 0.600297i | 0.0286964 | − | 0.0208492i | −0.573345 | − | 0.819314i | \(-0.694354\pi\) |
0.602041 | + | 0.798465i | \(0.294354\pi\) | |||||||
\(830\) | 8.66312 | − | 26.6623i | 0.300701 | − | 0.925463i | ||||
\(831\) | 1.15248 | − | 3.54696i | 0.0399789 | − | 0.123043i | ||||
\(832\) | 22.7984 | − | 16.5640i | 0.790391 | − | 0.574253i | ||||
\(833\) | −6.54508 | − | 4.75528i | −0.226774 | − | 0.164761i | ||||
\(834\) | 2.97214 | + | 9.14729i | 0.102917 | + | 0.316745i | ||||
\(835\) | 2.47214 | 0.0855518 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.819660 | −0.0283316 | ||||||||
\(838\) | −4.76393 | − | 14.6619i | −0.164567 | − | 0.506486i | ||||
\(839\) | 15.0451 | + | 10.9309i | 0.519414 | + | 0.377376i | 0.816383 | − | 0.577511i | \(-0.195976\pi\) |
−0.296969 | + | 0.954887i | \(0.595976\pi\) | |||||||
\(840\) | 3.73607 | − | 2.71441i | 0.128907 | − | 0.0936561i | ||||
\(841\) | −7.20820 | + | 22.1846i | −0.248559 | + | 0.764985i | ||||
\(842\) | 4.23607 | − | 13.0373i | 0.145985 | − | 0.449294i | ||||
\(843\) | −1.40983 | + | 1.02430i | −0.0485571 | + | 0.0352788i | ||||
\(844\) | 52.5517 | + | 38.1810i | 1.80890 | + | 1.31424i | ||||
\(845\) | −0.781153 | − | 2.40414i | −0.0268725 | − | 0.0827050i | ||||
\(846\) | 30.0344 | 1.03261 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −45.5066 | −1.56270 | ||||||||
\(849\) | 1.13525 | + | 3.49396i | 0.0389618 | + | 0.119912i | ||||
\(850\) | 68.5410 | + | 49.7980i | 2.35094 | + | 1.70806i | ||||
\(851\) | −12.1803 | + | 8.84953i | −0.417537 | + | 0.303358i | ||||
\(852\) | −4.55166 | + | 14.0086i | −0.155937 | + | 0.479926i | ||||
\(853\) | 14.2426 | − | 43.8344i | 0.487659 | − | 1.50086i | −0.340434 | − | 0.940269i | \(-0.610574\pi\) |
0.828093 | − | 0.560591i | \(-0.189426\pi\) | |||||||
\(854\) | 11.3992 | − | 8.28199i | 0.390072 | − | 0.283404i | ||||
\(855\) | 13.2082 | + | 9.59632i | 0.451711 | + | 0.328187i | ||||
\(856\) | 24.7254 | + | 76.0970i | 0.845098 | + | 2.60094i | ||||
\(857\) | 3.90983 | 0.133557 | 0.0667786 | − | 0.997768i | \(-0.478728\pi\) | ||||
0.0667786 | + | 0.997768i | \(0.478728\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.43769 | 0.0490535 | 0.0245267 | − | 0.999699i | \(-0.492192\pi\) | ||||
0.0245267 | + | 0.999699i | \(0.492192\pi\) | |||||||
\(860\) | −11.3435 | − | 34.9116i | −0.386809 | − | 1.19047i | ||||
\(861\) | −5.59017 | − | 4.06150i | −0.190512 | − | 0.138415i | ||||
\(862\) | −15.1353 | + | 10.9964i | −0.515509 | + | 0.374539i | ||||
\(863\) | −9.28773 | + | 28.5847i | −0.316158 | + | 0.973034i | 0.659117 | + | 0.752040i | \(0.270930\pi\) |
−0.975275 | + | 0.220994i | \(0.929070\pi\) | |||||||
\(864\) | −11.6459 | + | 35.8424i | −0.396201 | + | 1.21938i | ||||
\(865\) | −14.2533 | + | 10.3556i | −0.484626 | + | 0.352102i | ||||
\(866\) | 80.5582 | + | 58.5290i | 2.73748 | + | 1.98890i | ||||
\(867\) | 9.25329 | + | 28.4787i | 0.314258 | + | 0.967187i | ||||
\(868\) | −1.14590 | −0.0388943 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 3.85410 | 0.130666 | ||||||||
\(871\) | −7.32624 | − | 22.5478i | −0.248240 | − | 0.764004i | ||||
\(872\) | −63.3050 | − | 45.9937i | −2.14378 | − | 1.55754i | ||||
\(873\) | 14.8262 | − | 10.7719i | 0.501792 | − | 0.364573i | ||||
\(874\) | −30.7254 | + | 94.5631i | −1.03930 | + | 3.19865i | ||||
\(875\) | 2.78115 | − | 8.55951i | 0.0940201 | − | 0.289364i | ||||
\(876\) | −23.6976 | + | 17.2173i | −0.800666 | + | 0.581718i | ||||
\(877\) | 10.5172 | + | 7.64121i | 0.355141 | + | 0.258025i | 0.751023 | − | 0.660276i | \(-0.229561\pi\) |
−0.395881 | + | 0.918302i | \(0.629561\pi\) | |||||||
\(878\) | −4.54508 | − | 13.9883i | −0.153389 | − | 0.472083i | ||||
\(879\) | 6.79837 | 0.229303 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 20.8541 | 0.702593 | 0.351296 | − | 0.936264i | \(-0.385741\pi\) | ||||
0.351296 | + | 0.936264i | \(0.385741\pi\) | |||||||
\(882\) | −2.11803 | − | 6.51864i | −0.0713179 | − | 0.219494i | ||||
\(883\) | 37.7254 | + | 27.4091i | 1.26956 | + | 0.922391i | 0.999185 | − | 0.0403641i | \(-0.0128518\pi\) |
0.270377 | + | 0.962755i | \(0.412852\pi\) | |||||||
\(884\) | 102.812 | − | 74.6969i | 3.45793 | − | 2.51233i | ||||
\(885\) | −0.0172209 | + | 0.0530006i | −0.000578875 | + | 0.00178159i | ||||
\(886\) | −6.54508 | + | 20.1437i | −0.219886 | + | 0.676741i | ||||
\(887\) | 4.68034 | − | 3.40047i | 0.157150 | − | 0.114176i | −0.506431 | − | 0.862280i | \(-0.669036\pi\) |
0.663582 | + | 0.748104i | \(0.269036\pi\) | |||||||
\(888\) | 9.23607 | + | 6.71040i | 0.309942 | + | 0.225186i | ||||
\(889\) | −4.61803 | − | 14.2128i | −0.154884 | − | 0.476684i | ||||
\(890\) | 0.381966 | 0.0128035 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −131.228 | −4.39384 | ||||||||
\(893\) | −8.44427 | − | 25.9888i | −0.282577 | − | 0.869682i | ||||
\(894\) | −2.80902 | − | 2.04087i | −0.0939476 | − | 0.0682569i | ||||
\(895\) | 6.66312 | − | 4.84104i | 0.222724 | − | 0.161818i | ||||
\(896\) | −0.336881 | + | 1.03681i | −0.0112544 | + | 0.0346375i | ||||
\(897\) | 3.76393 | − | 11.5842i | 0.125674 | − | 0.386785i | ||||
\(898\) | 7.04508 | − | 5.11855i | 0.235098 | − | 0.170808i | ||||
\(899\) | −0.454915 | − | 0.330515i | −0.0151723 | − | 0.0110233i | ||||
\(900\) | 15.7082 | + | 48.3449i | 0.523607 | + | 1.61150i | ||||
\(901\) | −37.3607 | −1.24466 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.67376 | 0.155533 | ||||||||
\(904\) | 15.8262 | + | 48.7082i | 0.526373 | + | 1.62001i | ||||
\(905\) | −15.7082 | − | 11.4127i | −0.522158 | − | 0.379370i | ||||
\(906\) | 23.4894 | − | 17.0660i | 0.780382 | − | 0.566980i | ||||
\(907\) | −6.25329 | + | 19.2456i | −0.207637 | + | 0.639041i | 0.791958 | + | 0.610576i | \(0.209062\pi\) |
−0.999595 | + | 0.0284652i | \(0.990938\pi\) | |||||||
\(908\) | −19.5517 | + | 60.1738i | −0.648845 | + | 1.99694i | ||||
\(909\) | −20.7533 | + | 15.0781i | −0.688343 | + | 0.500111i | ||||
\(910\) | −6.85410 | − | 4.97980i | −0.227211 | − | 0.165079i | ||||
\(911\) | −7.05166 | − | 21.7028i | −0.233632 | − | 0.719045i | −0.997300 | − | 0.0734361i | \(-0.976603\pi\) |
0.763668 | − | 0.645609i | \(-0.223397\pi\) | |||||||
\(912\) | 37.9787 | 1.25760 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.9443 | 0.593544 | ||||||||
\(915\) | 1.02786 | + | 3.16344i | 0.0339801 | + | 0.104580i | ||||
\(916\) | −44.1246 | − | 32.0584i | −1.45792 | − | 1.05924i | ||||
\(917\) | −0.854102 | + | 0.620541i | −0.0282049 | + | 0.0204921i | ||||
\(918\) | −22.7254 | + | 69.9417i | −0.750051 | + | 2.30842i | ||||
\(919\) | −6.45492 | + | 19.8662i | −0.212928 | + | 0.655325i | 0.786366 | + | 0.617761i | \(0.211960\pi\) |
−0.999294 | + | 0.0375644i | \(0.988040\pi\) | |||||||
\(920\) | 36.8156 | − | 26.7481i | 1.21377 | − | 0.881859i | ||||
\(921\) | −0.409830 | − | 0.297759i | −0.0135044 | − | 0.00981149i | ||||
\(922\) | −15.7812 | − | 48.5694i | −0.519725 | − | 1.59955i | ||||
\(923\) | 15.8885 | 0.522978 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.88854 | 0.325133 | ||||||||
\(926\) | 14.3713 | + | 44.2304i | 0.472271 | + | 1.45350i | ||||
\(927\) | 4.54508 | + | 3.30220i | 0.149280 | + | 0.108458i | ||||
\(928\) | −20.9164 | + | 15.1967i | −0.686615 | + | 0.498855i | ||||
\(929\) | 7.41641 | − | 22.8254i | 0.243324 | − | 0.748876i | −0.752583 | − | 0.658497i | \(-0.771192\pi\) |
0.995908 | − | 0.0903783i | \(-0.0288076\pi\) | |||||||
\(930\) | 0.118034 | − | 0.363271i | 0.00387049 | − | 0.0119121i | ||||
\(931\) | −5.04508 | + | 3.66547i | −0.165346 | + | 0.120131i | ||||
\(932\) | −10.1459 | − | 7.37143i | −0.332340 | − | 0.241459i | ||||
\(933\) | 1.71885 | + | 5.29007i | 0.0562725 | + | 0.173189i | ||||
\(934\) | 87.7214 | 2.87033 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 63.3050 | 2.06919 | ||||||||
\(937\) | −11.6565 | − | 35.8751i | −0.380803 | − | 1.17199i | −0.939480 | − | 0.342605i | \(-0.888691\pi\) |
0.558677 | − | 0.829385i | \(-0.311309\pi\) | |||||||
\(938\) | 15.5172 | + | 11.2739i | 0.506655 | + | 0.368107i | ||||
\(939\) | −1.33688 | + | 0.971301i | −0.0436275 | + | 0.0316972i | ||||
\(940\) | −6.57295 | + | 20.2295i | −0.214386 | + | 0.659812i | ||||
\(941\) | 9.60081 | − | 29.5483i | 0.312978 | − | 0.963246i | −0.663601 | − | 0.748086i | \(-0.730973\pi\) |
0.976579 | − | 0.215160i | \(-0.0690271\pi\) | |||||||
\(942\) | 20.7984 | − | 15.1109i | 0.677648 | − | 0.492340i | ||||
\(943\) | −55.0861 | − | 40.0224i | −1.79385 | − | 1.30331i | ||||
\(944\) | −0.274575 | − | 0.845055i | −0.00893666 | − | 0.0275042i | ||||
\(945\) | 3.47214 | 0.112949 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 19.7082 | 0.640431 | 0.320215 | − | 0.947345i | \(-0.396245\pi\) | ||||
0.320215 | + | 0.947345i | \(0.396245\pi\) | |||||||
\(948\) | −7.98936 | − | 24.5887i | −0.259482 | − | 0.798604i | ||||
\(949\) | 25.5623 | + | 18.5721i | 0.829788 | + | 0.602876i | ||||
\(950\) | 52.8328 | − | 38.3853i | 1.71412 | − | 1.24538i | ||||
\(951\) | −4.69098 | + | 14.4374i | −0.152116 | + | 0.468164i | ||||
\(952\) | −18.6803 | + | 57.4922i | −0.605433 | + | 1.86333i | ||||
\(953\) | −1.42705 | + | 1.03681i | −0.0462267 | + | 0.0335857i | −0.610659 | − | 0.791894i | \(-0.709095\pi\) |
0.564432 | + | 0.825480i | \(0.309095\pi\) | |||||||
\(954\) | −25.6074 | − | 18.6049i | −0.829070 | − | 0.602355i | ||||
\(955\) | 6.25329 | + | 19.2456i | 0.202352 | + | 0.622774i | ||||
\(956\) | 28.6869 | 0.927801 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −68.6869 | −2.21917 | ||||||||
\(959\) | −0.100813 | − | 0.310271i | −0.00325542 | − | 0.0100192i | ||||
\(960\) | −4.35410 | − | 3.16344i | −0.140528 | − | 0.102100i | ||||
\(961\) | 25.0344 | − | 18.1886i | 0.807563 | − | 0.586729i | ||||
\(962\) | 6.47214 | − | 19.9192i | 0.208670 | − | 0.642220i | ||||
\(963\) | −8.66312 | + | 26.6623i | −0.279165 | + | 0.859182i | ||||
\(964\) | −67.8222 | + | 49.2757i | −2.18441 | + | 1.58706i | ||||
\(965\) | 0.263932 | + | 0.191758i | 0.00849627 | + | 0.00617290i | ||||
\(966\) | 3.04508 | + | 9.37181i | 0.0979740 | + | 0.301533i | ||||
\(967\) | 28.4508 | 0.914918 | 0.457459 | − | 0.889231i | \(-0.348760\pi\) | ||||
0.457459 | + | 0.889231i | \(0.348760\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 31.1803 | 1.00166 | ||||||||
\(970\) | 5.66312 | + | 17.4293i | 0.181832 | + | 0.559621i | ||||
\(971\) | −42.2705 | − | 30.7113i | −1.35653 | − | 0.985573i | −0.998657 | − | 0.0518010i | \(-0.983504\pi\) |
−0.357868 | − | 0.933772i | \(-0.616496\pi\) | |||||||
\(972\) | −54.7599 | + | 39.7854i | −1.75642 | + | 1.27612i | ||||
\(973\) | −1.83688 | + | 5.65334i | −0.0588877 | + | 0.181238i | ||||
\(974\) | 13.4271 | − | 41.3242i | 0.430230 | − | 1.32411i | ||||
\(975\) | −6.47214 | + | 4.70228i | −0.207274 | + | 0.150594i | ||||
\(976\) | −42.9058 | − | 31.1729i | −1.37338 | − | 0.997819i | ||||
\(977\) | −10.2533 | − | 31.5564i | −0.328032 | − | 1.00958i | −0.970053 | − | 0.242892i | \(-0.921904\pi\) |
0.642022 | − | 0.766686i | \(-0.278096\pi\) | |||||||
\(978\) | 7.61803 | 0.243598 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.85410 | 0.155059 | ||||||||
\(981\) | −8.47214 | − | 26.0746i | −0.270494 | − | 0.832496i | ||||
\(982\) | 61.1140 | + | 44.4019i | 1.95023 | + | 1.41692i | ||||
\(983\) | 11.8262 | − | 8.59226i | 0.377198 | − | 0.274051i | −0.382991 | − | 0.923752i | \(-0.625106\pi\) |
0.760190 | + | 0.649701i | \(0.225106\pi\) | |||||||
\(984\) | −15.9549 | + | 49.1042i | −0.508624 | + | 1.56538i | ||||
\(985\) | 5.47214 | − | 16.8415i | 0.174357 | − | 0.536615i | ||||
\(986\) | −40.8156 | + | 29.6543i | −1.29983 | + | 0.944384i | ||||
\(987\) | −2.19098 | − | 1.59184i | −0.0697398 | − | 0.0506689i | ||||
\(988\) | −30.2705 | − | 93.1630i | −0.963033 | − | 2.96391i | ||||
\(989\) | 46.0557 | 1.46449 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.2705 | −1.08864 | −0.544319 | − | 0.838878i | \(-0.683212\pi\) | ||||
−0.544319 | + | 0.838878i | \(0.683212\pi\) | |||||||
\(992\) | 0.791796 | + | 2.43690i | 0.0251396 | + | 0.0773716i | ||||
\(993\) | 8.09017 | + | 5.87785i | 0.256734 | + | 0.186528i | ||||
\(994\) | −10.3992 | + | 7.55545i | −0.329842 | + | 0.239644i | ||||
\(995\) | −1.16312 | + | 3.57971i | −0.0368733 | + | 0.113485i | ||||
\(996\) | 9.92705 | − | 30.5523i | 0.314551 | − | 0.968087i | ||||
\(997\) | 21.7361 | − | 15.7922i | 0.688388 | − | 0.500143i | −0.187742 | − | 0.982218i | \(-0.560117\pi\) |
0.876130 | + | 0.482075i | \(0.160117\pi\) | |||||||
\(998\) | −2.30902 | − | 1.67760i | −0.0730907 | − | 0.0531035i | ||||
\(999\) | 2.65248 | + | 8.16348i | 0.0839206 | + | 0.258281i |
(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 | 847.2.f.j.148.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.d.372.1 | 4 | |||
11.3 | even | 5 | 847.2.a.h.1.2 | yes | 2 | ||
11.4 | even | 5 | 847.2.f.c.729.1 | 4 | |||
11.5 | even | 5 | 847.2.f.c.323.1 | 4 | |||
11.6 | odd | 10 | 847.2.f.l.323.1 | 4 | |||
11.7 | odd | 10 | 847.2.f.l.729.1 | 4 | |||
11.8 | odd | 10 | 847.2.a.d.1.1 | ✓ | 2 | ||
11.9 | even | 5 | inner | 847.2.f.j.372.1 | 4 | ||
11.10 | odd | 2 | 847.2.f.d.148.1 | 4 | |||
33.8 | even | 10 | 7623.2.a.bx.1.2 | 2 | |||
33.14 | odd | 10 | 7623.2.a.t.1.1 | 2 | |||
77.41 | even | 10 | 5929.2.a.i.1.1 | 2 | |||
77.69 | odd | 10 | 5929.2.a.s.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.d.1.1 | ✓ | 2 | 11.8 | odd | 10 | ||
847.2.a.h.1.2 | yes | 2 | 11.3 | even | 5 | ||
847.2.f.c.323.1 | 4 | 11.5 | even | 5 | |||
847.2.f.c.729.1 | 4 | 11.4 | even | 5 | |||
847.2.f.d.148.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.d.372.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.j.148.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.j.372.1 | 4 | 11.9 | even | 5 | inner | ||
847.2.f.l.323.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.l.729.1 | 4 | 11.7 | odd | 10 | |||
5929.2.a.i.1.1 | 2 | 77.41 | even | 10 | |||
5929.2.a.s.1.2 | 2 | 77.69 | odd | 10 | |||
7623.2.a.t.1.1 | 2 | 33.14 | odd | 10 | |||
7623.2.a.bx.1.2 | 2 | 33.8 | even | 10 |