Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(25,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.4 | ||
Root | \(-2.17587 - 1.25624i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.25 |
Dual form | 273.2.bj.d.142.4 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.504542 | + | 0.291297i | −0.356765 | + | 0.205978i | −0.667661 | − | 0.744466i | \(-0.732704\pi\) |
0.310896 | + | 0.950444i | \(0.399371\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.830292 | + | 1.43811i | −0.415146 | + | 0.719054i | ||||
\(5\) | −1.26176 | + | 0.728479i | −0.564277 | + | 0.325786i | −0.754861 | − | 0.655885i | \(-0.772295\pi\) |
0.190583 | + | 0.981671i | \(0.438962\pi\) | |||||||
\(6\) | 0.582595i | 0.237843i | ||||||||
\(7\) | −2.46845 | + | 0.952230i | −0.932987 | + | 0.359909i | ||||
\(8\) | − | 2.13264i | − | 0.754001i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.424408 | − | 0.735096i | 0.134210 | − | 0.232458i | ||||
\(11\) | −2.68042 | − | 1.54754i | −0.808176 | − | 0.466601i | 0.0381460 | − | 0.999272i | \(-0.487855\pi\) |
−0.846322 | + | 0.532671i | \(0.821188\pi\) | |||||||
\(12\) | 0.830292 | + | 1.43811i | 0.239685 | + | 0.415146i | ||||
\(13\) | −3.54446 | + | 0.660933i | −0.983055 | + | 0.183310i | ||||
\(14\) | 0.968055 | − | 1.19949i | 0.258724 | − | 0.320578i | ||||
\(15\) | 1.45696i | 0.376185i | ||||||||
\(16\) | −1.03935 | − | 1.80021i | −0.259838 | − | 0.450053i | ||||
\(17\) | 1.75040 | − | 3.03179i | 0.424535 | − | 0.735317i | −0.571842 | − | 0.820364i | \(-0.693771\pi\) |
0.996377 | + | 0.0850472i | \(0.0271041\pi\) | |||||||
\(18\) | 0.504542 | + | 0.291297i | 0.118922 | + | 0.0686594i | ||||
\(19\) | −3.96420 | + | 2.28873i | −0.909450 | + | 0.525071i | −0.880254 | − | 0.474502i | \(-0.842628\pi\) |
−0.0291959 | + | 0.999574i | \(0.509295\pi\) | |||||||
\(20\) | − | 2.41940i | − | 0.540994i | ||||||
\(21\) | −0.409571 | + | 2.61386i | −0.0893756 | + | 0.570391i | ||||
\(22\) | 1.80318 | 0.384439 | ||||||||
\(23\) | 3.01852 | + | 5.22824i | 0.629406 | + | 1.09016i | 0.987671 | + | 0.156543i | \(0.0500350\pi\) |
−0.358265 | + | 0.933620i | \(0.616632\pi\) | |||||||
\(24\) | −1.84692 | − | 1.06632i | −0.377000 | − | 0.217661i | ||||
\(25\) | −1.43864 | + | 2.49179i | −0.287727 | + | 0.498358i | ||||
\(26\) | 1.59580 | − | 1.36596i | 0.312962 | − | 0.267887i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.680126 | − | 4.34053i | 0.128532 | − | 0.820283i | ||||
\(29\) | −5.81338 | −1.07952 | −0.539759 | − | 0.841819i | \(-0.681485\pi\) | ||||
−0.539759 | + | 0.841819i | \(0.681485\pi\) | |||||||
\(30\) | −0.424408 | − | 0.735096i | −0.0774859 | − | 0.134210i | ||||
\(31\) | 7.82929 | + | 4.52024i | 1.40618 | + | 0.811859i | 0.995017 | − | 0.0997023i | \(-0.0317890\pi\) |
0.411164 | + | 0.911561i | \(0.365122\pi\) | |||||||
\(32\) | 4.74263 | + | 2.73816i | 0.838386 | + | 0.484042i | ||||
\(33\) | −2.68042 | + | 1.54754i | −0.466601 | + | 0.269392i | ||||
\(34\) | 2.03955i | 0.349780i | ||||||||
\(35\) | 2.42092 | − | 2.99970i | 0.409210 | − | 0.507043i | ||||
\(36\) | 1.66058 | 0.276764 | ||||||||
\(37\) | −4.72494 | + | 2.72795i | −0.776775 | + | 0.448472i | −0.835286 | − | 0.549815i | \(-0.814698\pi\) |
0.0585108 | + | 0.998287i | \(0.481365\pi\) | |||||||
\(38\) | 1.33340 | − | 2.30952i | 0.216307 | − | 0.374654i | ||||
\(39\) | −1.19984 | + | 3.40006i | −0.192129 | + | 0.544445i | ||||
\(40\) | 1.55358 | + | 2.69088i | 0.245643 | + | 0.425466i | ||||
\(41\) | − | 8.30215i | − | 1.29658i | −0.761394 | − | 0.648289i | \(-0.775485\pi\) | ||
0.761394 | − | 0.648289i | \(-0.224515\pi\) | |||||||
\(42\) | −0.554764 | − | 1.43811i | −0.0856020 | − | 0.221905i | ||||
\(43\) | −8.12434 | −1.23895 | −0.619475 | − | 0.785016i | \(-0.712655\pi\) | ||||
−0.619475 | + | 0.785016i | \(0.712655\pi\) | |||||||
\(44\) | 4.45106 | − | 2.56982i | 0.671022 | − | 0.387415i | ||||
\(45\) | 1.26176 | + | 0.728479i | 0.188092 | + | 0.108595i | ||||
\(46\) | −3.04594 | − | 1.75858i | −0.449100 | − | 0.259288i | ||||
\(47\) | 9.47860 | − | 5.47247i | 1.38260 | − | 0.798242i | 0.390129 | − | 0.920760i | \(-0.372430\pi\) |
0.992466 | + | 0.122518i | \(0.0390970\pi\) | |||||||
\(48\) | −2.07870 | −0.300035 | ||||||||
\(49\) | 5.18651 | − | 4.70107i | 0.740931 | − | 0.671581i | ||||
\(50\) | − | 1.67628i | − | 0.237062i | ||||||
\(51\) | −1.75040 | − | 3.03179i | −0.245106 | − | 0.424535i | ||||
\(52\) | 1.99244 | − | 5.64608i | 0.276302 | − | 0.782970i | ||||
\(53\) | −3.62864 | + | 6.28499i | −0.498432 | + | 0.863309i | −0.999998 | − | 0.00180978i | \(-0.999424\pi\) |
0.501566 | + | 0.865119i | \(0.332757\pi\) | |||||||
\(54\) | 0.504542 | − | 0.291297i | 0.0686594 | − | 0.0396406i | ||||
\(55\) | 4.50940 | 0.608047 | ||||||||
\(56\) | 2.03076 | + | 5.26431i | 0.271372 | + | 0.703473i | ||||
\(57\) | 4.57747i | 0.606300i | ||||||||
\(58\) | 2.93310 | − | 1.69342i | 0.385134 | − | 0.222357i | ||||
\(59\) | −3.86508 | − | 2.23151i | −0.503191 | − | 0.290518i | 0.226839 | − | 0.973932i | \(-0.427161\pi\) |
−0.730030 | + | 0.683415i | \(0.760494\pi\) | |||||||
\(60\) | −2.09526 | − | 1.20970i | −0.270497 | − | 0.156172i | ||||
\(61\) | 3.83770 | + | 6.64709i | 0.491367 | + | 0.851073i | 0.999951 | − | 0.00994000i | \(-0.00316405\pi\) |
−0.508584 | + | 0.861013i | \(0.669831\pi\) | |||||||
\(62\) | −5.26694 | −0.668902 | ||||||||
\(63\) | 2.05888 | + | 1.66163i | 0.259395 | + | 0.209345i | ||||
\(64\) | 0.966935 | 0.120867 | ||||||||
\(65\) | 3.99079 | − | 3.41600i | 0.494996 | − | 0.423703i | ||||
\(66\) | 0.901588 | − | 1.56160i | 0.110978 | − | 0.192219i | ||||
\(67\) | 10.9344 | + | 6.31301i | 1.33586 | + | 0.771256i | 0.986190 | − | 0.165618i | \(-0.0529619\pi\) |
0.349665 | + | 0.936875i | \(0.386295\pi\) | |||||||
\(68\) | 2.90669 | + | 5.03454i | 0.352488 | + | 0.610527i | ||||
\(69\) | 6.03705 | 0.726775 | ||||||||
\(70\) | −0.347650 | + | 2.21868i | −0.0415521 | + | 0.265183i | ||||
\(71\) | − | 1.67628i | − | 0.198938i | −0.995041 | − | 0.0994692i | \(-0.968286\pi\) | ||
0.995041 | − | 0.0994692i | \(-0.0317145\pi\) | |||||||
\(72\) | −1.84692 | + | 1.06632i | −0.217661 | + | 0.125667i | ||||
\(73\) | −1.45937 | − | 0.842567i | −0.170806 | − | 0.0986150i | 0.412160 | − | 0.911112i | \(-0.364775\pi\) |
−0.582966 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(74\) | 1.58929 | − | 2.75273i | 0.184751 | − | 0.319998i | ||||
\(75\) | 1.43864 | + | 2.49179i | 0.166119 | + | 0.287727i | ||||
\(76\) | − | 7.60126i | − | 0.871925i | ||||||
\(77\) | 8.09010 | + | 1.26765i | 0.921952 | + | 0.144463i | ||||
\(78\) | −0.385056 | − | 2.06498i | −0.0435990 | − | 0.233813i | ||||
\(79\) | −6.05987 | − | 10.4960i | −0.681788 | − | 1.18089i | −0.974435 | − | 0.224671i | \(-0.927869\pi\) |
0.292646 | − | 0.956221i | \(-0.405464\pi\) | |||||||
\(80\) | 2.62283 | + | 1.51429i | 0.293241 | + | 0.169303i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 2.41839 | + | 4.18878i | 0.267067 | + | 0.462574i | ||||
\(83\) | 6.48599i | 0.711930i | 0.934499 | + | 0.355965i | \(0.115848\pi\) | ||||
−0.934499 | + | 0.355965i | \(0.884152\pi\) | |||||||
\(84\) | −3.41894 | − | 2.75927i | −0.373037 | − | 0.301061i | ||||
\(85\) | 5.10053i | 0.553230i | ||||||||
\(86\) | 4.09907 | − | 2.36660i | 0.442014 | − | 0.255197i | ||||
\(87\) | −2.90669 | + | 5.03454i | −0.311630 | + | 0.539759i | ||||
\(88\) | −3.30034 | + | 5.71635i | −0.351817 | + | 0.609365i | ||||
\(89\) | −13.1681 | + | 7.60260i | −1.39582 | + | 0.805874i | −0.993951 | − | 0.109825i | \(-0.964971\pi\) |
−0.401865 | + | 0.915699i | \(0.631638\pi\) | |||||||
\(90\) | −0.848816 | −0.0894731 | ||||||||
\(91\) | 8.11996 | − | 5.00662i | 0.851203 | − | 0.524836i | ||||
\(92\) | −10.0250 | −1.04518 | ||||||||
\(93\) | 7.82929 | − | 4.52024i | 0.811859 | − | 0.468727i | ||||
\(94\) | −3.18823 | + | 5.52218i | −0.328841 | + | 0.569569i | ||||
\(95\) | 3.33459 | − | 5.77567i | 0.342121 | − | 0.592572i | ||||
\(96\) | 4.74263 | − | 2.73816i | 0.484042 | − | 0.279462i | ||||
\(97\) | 1.56662i | 0.159066i | 0.996832 | + | 0.0795331i | \(0.0253430\pi\) | ||||
−0.996832 | + | 0.0795331i | \(0.974657\pi\) | |||||||
\(98\) | −1.24740 | + | 3.88270i | −0.126007 | + | 0.392212i | ||||
\(99\) | 3.09508i | 0.311067i | ||||||||
\(100\) | −2.38898 | − | 4.13783i | −0.238898 | − | 0.413783i | ||||
\(101\) | 5.72587 | − | 9.91749i | 0.569745 | − | 0.986827i | −0.426846 | − | 0.904324i | \(-0.640375\pi\) |
0.996591 | − | 0.0825029i | \(-0.0262914\pi\) | |||||||
\(102\) | 1.76630 | + | 1.01978i | 0.174890 | + | 0.100973i | ||||
\(103\) | 1.53705 | + | 2.66225i | 0.151450 | + | 0.262319i | 0.931761 | − | 0.363073i | \(-0.118272\pi\) |
−0.780311 | + | 0.625392i | \(0.784939\pi\) | |||||||
\(104\) | 1.40953 | + | 7.55904i | 0.138216 | + | 0.741224i | ||||
\(105\) | −1.38736 | − | 3.59643i | −0.135392 | − | 0.350976i | ||||
\(106\) | − | 4.22805i | − | 0.410665i | ||||||
\(107\) | 4.10582 | + | 7.11149i | 0.396925 | + | 0.687493i | 0.993345 | − | 0.115179i | \(-0.0367441\pi\) |
−0.596420 | + | 0.802672i | \(0.703411\pi\) | |||||||
\(108\) | 0.830292 | − | 1.43811i | 0.0798949 | − | 0.138382i | ||||
\(109\) | −4.41034 | − | 2.54631i | −0.422434 | − | 0.243892i | 0.273684 | − | 0.961820i | \(-0.411758\pi\) |
−0.696118 | + | 0.717927i | \(0.745091\pi\) | |||||||
\(110\) | −2.27518 | + | 1.31358i | −0.216930 | + | 0.125245i | ||||
\(111\) | 5.45589i | 0.517850i | ||||||||
\(112\) | 4.27981 | + | 3.45403i | 0.404404 | + | 0.326375i | ||||
\(113\) | −16.6085 | −1.56240 | −0.781199 | − | 0.624282i | \(-0.785392\pi\) | ||||
−0.781199 | + | 0.624282i | \(0.785392\pi\) | |||||||
\(114\) | −1.33340 | − | 2.30952i | −0.124885 | − | 0.216307i | ||||
\(115\) | −7.61732 | − | 4.39786i | −0.710319 | − | 0.410103i | ||||
\(116\) | 4.82680 | − | 8.36027i | 0.448158 | − | 0.776232i | ||||
\(117\) | 2.34461 | + | 2.73912i | 0.216760 | + | 0.253232i | ||||
\(118\) | 2.60013 | 0.239361 | ||||||||
\(119\) | −1.43383 | + | 9.15062i | −0.131439 | + | 0.838836i | ||||
\(120\) | 3.10716 | 0.283644 | ||||||||
\(121\) | −0.710244 | − | 1.23018i | −0.0645676 | − | 0.111834i | ||||
\(122\) | −3.87256 | − | 2.23582i | −0.350605 | − | 0.202422i | ||||
\(123\) | −7.18987 | − | 4.15108i | −0.648289 | − | 0.374290i | ||||
\(124\) | −13.0012 | + | 7.50624i | −1.16754 | + | 0.674080i | ||||
\(125\) | − | 11.4769i | − | 1.02652i | ||||||
\(126\) | −1.52282 | − | 0.238614i | −0.135664 | − | 0.0212574i | ||||
\(127\) | −0.904114 | −0.0802272 | −0.0401136 | − | 0.999195i | \(-0.512772\pi\) | ||||
−0.0401136 | + | 0.999195i | \(0.512772\pi\) | |||||||
\(128\) | −9.97312 | + | 5.75798i | −0.881507 | + | 0.508938i | ||||
\(129\) | −4.06217 | + | 7.03589i | −0.357654 | + | 0.619475i | ||||
\(130\) | −1.01845 | + | 2.88602i | −0.0893236 | + | 0.253121i | ||||
\(131\) | −1.93864 | − | 3.35782i | −0.169379 | − | 0.293374i | 0.768822 | − | 0.639462i | \(-0.220843\pi\) |
−0.938202 | + | 0.346089i | \(0.887510\pi\) | |||||||
\(132\) | − | 5.13964i | − | 0.447348i | ||||||
\(133\) | 7.60604 | − | 9.42446i | 0.659527 | − | 0.817204i | ||||
\(134\) | −7.35585 | −0.635449 | ||||||||
\(135\) | 1.26176 | − | 0.728479i | 0.108595 | − | 0.0626975i | ||||
\(136\) | −6.46570 | − | 3.73298i | −0.554430 | − | 0.320100i | ||||
\(137\) | −16.1496 | − | 9.32396i | −1.37975 | − | 0.796600i | −0.387622 | − | 0.921818i | \(-0.626703\pi\) |
−0.992129 | + | 0.125219i | \(0.960037\pi\) | |||||||
\(138\) | −3.04594 | + | 1.75858i | −0.259288 | + | 0.149700i | ||||
\(139\) | 1.90068 | 0.161214 | 0.0806068 | − | 0.996746i | \(-0.474314\pi\) | ||||
0.0806068 | + | 0.996746i | \(0.474314\pi\) | |||||||
\(140\) | 2.30383 | + | 5.97217i | 0.194709 | + | 0.504741i | ||||
\(141\) | − | 10.9449i | − | 0.921730i | ||||||
\(142\) | 0.488297 | + | 0.845756i | 0.0409770 | + | 0.0709742i | ||||
\(143\) | 10.5234 | + | 3.71361i | 0.880014 | + | 0.310548i | ||||
\(144\) | −1.03935 | + | 1.80021i | −0.0866127 | + | 0.150018i | ||||
\(145\) | 7.33511 | − | 4.23493i | 0.609148 | − | 0.351692i | ||||
\(146\) | 0.981750 | 0.0812502 | ||||||||
\(147\) | −1.47799 | − | 6.84219i | −0.121902 | − | 0.564334i | ||||
\(148\) | − | 9.05996i | − | 0.744724i | ||||||
\(149\) | −18.9572 | + | 10.9449i | −1.55303 | + | 0.896645i | −0.555141 | + | 0.831756i | \(0.687336\pi\) |
−0.997893 | + | 0.0648885i | \(0.979331\pi\) | |||||||
\(150\) | −1.45170 | − | 0.838142i | −0.118531 | − | 0.0684340i | ||||
\(151\) | −1.93837 | − | 1.11912i | −0.157742 | − | 0.0910726i | 0.419051 | − | 0.907963i | \(-0.362363\pi\) |
−0.576793 | + | 0.816890i | \(0.695696\pi\) | |||||||
\(152\) | 4.88104 | + | 8.45420i | 0.395904 | + | 0.685726i | ||||
\(153\) | −3.50081 | −0.283024 | ||||||||
\(154\) | −4.45106 | + | 1.71704i | −0.358676 | + | 0.138363i | ||||
\(155\) | −13.1716 | −1.05797 | ||||||||
\(156\) | −3.89342 | − | 4.54854i | −0.311723 | − | 0.364175i | ||||
\(157\) | −0.522820 | + | 0.905550i | −0.0417256 | + | 0.0722708i | −0.886134 | − | 0.463429i | \(-0.846619\pi\) |
0.844408 | + | 0.535700i | \(0.179952\pi\) | |||||||
\(158\) | 6.11491 | + | 3.53045i | 0.486476 | + | 0.280867i | ||||
\(159\) | 3.62864 | + | 6.28499i | 0.287770 | + | 0.498432i | ||||
\(160\) | −7.97876 | −0.630776 | ||||||||
\(161\) | −12.4296 | − | 10.0313i | −0.979587 | − | 0.790579i | ||||
\(162\) | − | 0.582595i | − | 0.0457730i | ||||||
\(163\) | −6.08149 | + | 3.51115i | −0.476339 | + | 0.275014i | −0.718889 | − | 0.695124i | \(-0.755349\pi\) |
0.242551 | + | 0.970139i | \(0.422016\pi\) | |||||||
\(164\) | 11.9394 | + | 6.89321i | 0.932309 | + | 0.538269i | ||||
\(165\) | 2.25470 | − | 3.90525i | 0.175528 | − | 0.304024i | ||||
\(166\) | −1.88935 | − | 3.27245i | −0.146642 | − | 0.253992i | ||||
\(167\) | 11.9623i | 0.925671i | 0.886444 | + | 0.462835i | \(0.153168\pi\) | ||||
−0.886444 | + | 0.462835i | \(0.846832\pi\) | |||||||
\(168\) | 5.57441 | + | 0.873465i | 0.430075 | + | 0.0673893i | ||||
\(169\) | 12.1263 | − | 4.68530i | 0.932795 | − | 0.360407i | ||||
\(170\) | −1.48577 | − | 2.57343i | −0.113953 | − | 0.197373i | ||||
\(171\) | 3.96420 | + | 2.28873i | 0.303150 | + | 0.175024i | ||||
\(172\) | 6.74557 | − | 11.6837i | 0.514345 | − | 0.890872i | ||||
\(173\) | −0.667991 | − | 1.15699i | −0.0507864 | − | 0.0879646i | 0.839515 | − | 0.543337i | \(-0.182839\pi\) |
−0.890301 | + | 0.455372i | \(0.849506\pi\) | |||||||
\(174\) | − | 3.38685i | − | 0.256756i | ||||||
\(175\) | 1.17845 | − | 7.52078i | 0.0890822 | − | 0.568518i | ||||
\(176\) | 6.43375i | 0.484962i | ||||||||
\(177\) | −3.86508 | + | 2.23151i | −0.290518 | + | 0.167730i | ||||
\(178\) | 4.42924 | − | 7.67166i | 0.331985 | − | 0.575016i | ||||
\(179\) | −1.16370 | + | 2.01558i | −0.0869787 | + | 0.150651i | −0.906233 | − | 0.422779i | \(-0.861055\pi\) |
0.819254 | + | 0.573431i | \(0.194388\pi\) | |||||||
\(180\) | −2.09526 | + | 1.20970i | −0.156172 | + | 0.0901657i | ||||
\(181\) | −2.31096 | −0.171772 | −0.0858861 | − | 0.996305i | \(-0.527372\pi\) | ||||
−0.0858861 | + | 0.996305i | \(0.527372\pi\) | |||||||
\(182\) | −2.63844 | + | 4.89137i | −0.195575 | + | 0.362573i | ||||
\(183\) | 7.67540 | 0.567382 | ||||||||
\(184\) | 11.1499 | − | 6.43742i | 0.821984 | − | 0.474573i | ||||
\(185\) | 3.97450 | − | 6.88404i | 0.292211 | − | 0.506125i | ||||
\(186\) | −2.63347 | + | 4.56130i | −0.193095 | + | 0.334451i | ||||
\(187\) | −9.38363 | + | 5.41764i | −0.686199 | + | 0.396177i | ||||
\(188\) | 18.1750i | 1.32555i | ||||||||
\(189\) | 2.46845 | − | 0.952230i | 0.179553 | − | 0.0692646i | ||||
\(190\) | 3.88543i | 0.281878i | ||||||||
\(191\) | 4.63857 | + | 8.03424i | 0.335635 | + | 0.581337i | 0.983607 | − | 0.180327i | \(-0.0577157\pi\) |
−0.647971 | + | 0.761665i | \(0.724382\pi\) | |||||||
\(192\) | 0.483468 | − | 0.837391i | 0.0348913 | − | 0.0604335i | ||||
\(193\) | 5.85868 | + | 3.38251i | 0.421717 | + | 0.243478i | 0.695812 | − | 0.718224i | \(-0.255045\pi\) |
−0.274095 | + | 0.961703i | \(0.588378\pi\) | |||||||
\(194\) | −0.456353 | − | 0.790426i | −0.0327642 | − | 0.0567493i | ||||
\(195\) | −0.962951 | − | 5.16412i | −0.0689584 | − | 0.369811i | ||||
\(196\) | 2.45432 | + | 11.3620i | 0.175309 | + | 0.811573i | ||||
\(197\) | 10.5817i | 0.753913i | 0.926231 | + | 0.376957i | \(0.123029\pi\) | ||||
−0.926231 | + | 0.376957i | \(0.876971\pi\) | |||||||
\(198\) | −0.901588 | − | 1.56160i | −0.0640731 | − | 0.110978i | ||||
\(199\) | −4.73698 | + | 8.20470i | −0.335796 | + | 0.581616i | −0.983637 | − | 0.180160i | \(-0.942339\pi\) |
0.647842 | + | 0.761775i | \(0.275672\pi\) | |||||||
\(200\) | 5.31409 | + | 3.06809i | 0.375763 | + | 0.216947i | ||||
\(201\) | 10.9344 | − | 6.31301i | 0.771256 | − | 0.445285i | ||||
\(202\) | 6.67172i | 0.469421i | ||||||||
\(203\) | 14.3501 | − | 5.53568i | 1.00718 | − | 0.388529i | ||||
\(204\) | 5.81338 | 0.407018 | ||||||||
\(205\) | 6.04794 | + | 10.4753i | 0.422407 | + | 0.731630i | ||||
\(206\) | −1.55101 | − | 0.895476i | −0.108064 | − | 0.0623908i | ||||
\(207\) | 3.01852 | − | 5.22824i | 0.209802 | − | 0.363388i | ||||
\(208\) | 4.87376 | + | 5.69382i | 0.337934 | + | 0.394796i | ||||
\(209\) | 14.1676 | 0.979994 | ||||||||
\(210\) | 1.74761 | + | 1.41042i | 0.120597 | + | 0.0973279i | ||||
\(211\) | −1.26188 | −0.0868717 | −0.0434358 | − | 0.999056i | \(-0.513830\pi\) | ||||
−0.0434358 | + | 0.999056i | \(0.513830\pi\) | |||||||
\(212\) | −6.02566 | − | 10.4367i | −0.413844 | − | 0.716799i | ||||
\(213\) | −1.45170 | − | 0.838142i | −0.0994692 | − | 0.0574286i | ||||
\(214\) | −4.14311 | − | 2.39203i | −0.283218 | − | 0.163516i | ||||
\(215\) | 10.2510 | − | 5.91841i | 0.699112 | − | 0.403632i | ||||
\(216\) | 2.13264i | 0.145108i | ||||||||
\(217\) | −23.6305 | − | 3.70272i | −1.60414 | − | 0.251357i | ||||
\(218\) | 2.96694 | 0.200946 | ||||||||
\(219\) | −1.45937 | + | 0.842567i | −0.0986150 | + | 0.0569354i | ||||
\(220\) | −3.74412 | + | 6.48500i | −0.252428 | + | 0.437219i | ||||
\(221\) | −4.20042 | + | 11.9029i | −0.282551 | + | 0.800679i | ||||
\(222\) | −1.58929 | − | 2.75273i | −0.106666 | − | 0.184751i | ||||
\(223\) | 3.46335i | 0.231923i | 0.993254 | + | 0.115962i | \(0.0369950\pi\) | ||||
−0.993254 | + | 0.115962i | \(0.963005\pi\) | |||||||
\(224\) | −14.3143 | − | 2.24294i | −0.956415 | − | 0.149863i | ||||
\(225\) | 2.87727 | 0.191818 | ||||||||
\(226\) | 8.37969 | − | 4.83802i | 0.557409 | − | 0.321820i | ||||
\(227\) | 1.24307 | + | 0.717687i | 0.0825055 | + | 0.0476345i | 0.540685 | − | 0.841225i | \(-0.318165\pi\) |
−0.458180 | + | 0.888860i | \(0.651498\pi\) | |||||||
\(228\) | −6.58289 | − | 3.80063i | −0.435962 | − | 0.251703i | ||||
\(229\) | 20.6692 | − | 11.9334i | 1.36586 | − | 0.788581i | 0.375465 | − | 0.926836i | \(-0.377483\pi\) |
0.990397 | + | 0.138256i | \(0.0441496\pi\) | |||||||
\(230\) | 5.12434 | 0.337889 | ||||||||
\(231\) | 5.14287 | − | 6.37240i | 0.338376 | − | 0.419273i | ||||
\(232\) | 12.3978i | 0.813958i | ||||||||
\(233\) | 6.80227 | + | 11.7819i | 0.445631 | + | 0.771856i | 0.998096 | − | 0.0616802i | \(-0.0196459\pi\) |
−0.552465 | + | 0.833536i | \(0.686313\pi\) | |||||||
\(234\) | −1.98085 | − | 0.699022i | −0.129492 | − | 0.0456965i | ||||
\(235\) | −7.97316 | + | 13.8099i | −0.520112 | + | 0.900860i | ||||
\(236\) | 6.41830 | − | 3.70560i | 0.417795 | − | 0.241214i | ||||
\(237\) | −12.1197 | −0.787261 | ||||||||
\(238\) | −1.94212 | − | 5.03454i | −0.125889 | − | 0.326341i | ||||
\(239\) | − | 11.9280i | − | 0.771560i | −0.922591 | − | 0.385780i | \(-0.873932\pi\) | ||
0.922591 | − | 0.385780i | \(-0.126068\pi\) | |||||||
\(240\) | 2.62283 | − | 1.51429i | 0.169303 | − | 0.0977471i | ||||
\(241\) | −8.59672 | − | 4.96332i | −0.553763 | − | 0.319715i | 0.196875 | − | 0.980429i | \(-0.436921\pi\) |
−0.750639 | + | 0.660713i | \(0.770254\pi\) | |||||||
\(242\) | 0.716695 | + | 0.413784i | 0.0460709 | + | 0.0265991i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −12.7456 | −0.815956 | ||||||||
\(245\) | −3.11952 | + | 9.70990i | −0.199299 | + | 0.620343i | ||||
\(246\) | 4.83679 | 0.308382 | ||||||||
\(247\) | 12.5382 | − | 10.7324i | 0.797789 | − | 0.682885i | ||||
\(248\) | 9.64003 | − | 16.6970i | 0.612143 | − | 1.06026i | ||||
\(249\) | 5.61703 | + | 3.24299i | 0.355965 | + | 0.205516i | ||||
\(250\) | 3.34318 | + | 5.79055i | 0.211441 | + | 0.366227i | ||||
\(251\) | 18.9920 | 1.19876 | 0.599381 | − | 0.800464i | \(-0.295414\pi\) | ||||
0.599381 | + | 0.800464i | \(0.295414\pi\) | |||||||
\(252\) | −4.09907 | + | 1.58126i | −0.258217 | + | 0.0996099i | ||||
\(253\) | − | 18.6851i | − | 1.17472i | ||||||
\(254\) | 0.456164 | − | 0.263366i | 0.0286222 | − | 0.0165251i | ||||
\(255\) | 4.41719 | + | 2.55027i | 0.276615 | + | 0.159704i | ||||
\(256\) | 2.38763 | − | 4.13550i | 0.149227 | − | 0.258469i | ||||
\(257\) | −9.98567 | − | 17.2957i | −0.622889 | − | 1.07888i | −0.988945 | − | 0.148283i | \(-0.952625\pi\) |
0.366056 | − | 0.930593i | \(-0.380708\pi\) | |||||||
\(258\) | − | 4.73320i | − | 0.294676i | ||||||
\(259\) | 9.06566 | − | 11.2330i | 0.563313 | − | 0.697987i | ||||
\(260\) | 1.59906 | + | 8.57546i | 0.0991696 | + | 0.531827i | ||||
\(261\) | 2.90669 | + | 5.03454i | 0.179920 | + | 0.311630i | ||||
\(262\) | 1.95625 | + | 1.12944i | 0.120857 | + | 0.0697770i | ||||
\(263\) | −1.65452 | + | 2.86571i | −0.102022 | + | 0.176707i | −0.912518 | − | 0.409037i | \(-0.865865\pi\) |
0.810496 | + | 0.585745i | \(0.199198\pi\) | |||||||
\(264\) | 3.30034 | + | 5.71635i | 0.203122 | + | 0.351817i | ||||
\(265\) | − | 10.5735i | − | 0.649528i | ||||||
\(266\) | −1.09225 | + | 6.97065i | −0.0669699 | + | 0.427398i | ||||
\(267\) | 15.2052i | 0.930544i | ||||||||
\(268\) | −18.1576 | + | 10.4833i | −1.10915 | + | 0.640368i | ||||
\(269\) | 11.9326 | − | 20.6679i | 0.727545 | − | 1.26014i | −0.230373 | − | 0.973102i | \(-0.573995\pi\) |
0.957918 | − | 0.287042i | \(-0.0926720\pi\) | |||||||
\(270\) | −0.424408 | + | 0.735096i | −0.0258286 | + | 0.0447365i | ||||
\(271\) | 1.44819 | − | 0.836111i | 0.0879711 | − | 0.0507901i | −0.455369 | − | 0.890303i | \(-0.650493\pi\) |
0.543340 | + | 0.839513i | \(0.317159\pi\) | |||||||
\(272\) | −7.27714 | −0.441242 | ||||||||
\(273\) | −0.275880 | − | 9.53540i | −0.0166970 | − | 0.577109i | ||||
\(274\) | 10.8642 | 0.656329 | ||||||||
\(275\) | 7.71229 | − | 4.45269i | 0.465069 | − | 0.268508i | ||||
\(276\) | −5.01251 | + | 8.68192i | −0.301718 | + | 0.522590i | ||||
\(277\) | −2.74960 | + | 4.76244i | −0.165207 | + | 0.286147i | −0.936729 | − | 0.350056i | \(-0.886163\pi\) |
0.771522 | + | 0.636203i | \(0.219496\pi\) | |||||||
\(278\) | −0.958972 | + | 0.553663i | −0.0575153 | + | 0.0332065i | ||||
\(279\) | − | 9.04048i | − | 0.541239i | ||||||
\(280\) | −6.39728 | − | 5.16294i | −0.382311 | − | 0.308545i | ||||
\(281\) | − | 32.5989i | − | 1.94469i | −0.233552 | − | 0.972344i | \(-0.575035\pi\) | ||
0.233552 | − | 0.972344i | \(-0.424965\pi\) | |||||||
\(282\) | 3.18823 | + | 5.52218i | 0.189856 | + | 0.328841i | ||||
\(283\) | −8.82509 | + | 15.2855i | −0.524597 | + | 0.908629i | 0.474993 | + | 0.879990i | \(0.342451\pi\) |
−0.999590 | + | 0.0286390i | \(0.990883\pi\) | |||||||
\(284\) | 2.41068 | + | 1.39181i | 0.143047 | + | 0.0825884i | ||||
\(285\) | −3.33459 | − | 5.77567i | −0.197524 | − | 0.342121i | ||||
\(286\) | −6.39128 | + | 1.19178i | −0.377924 | + | 0.0704714i | ||||
\(287\) | 7.90556 | + | 20.4935i | 0.466650 | + | 1.20969i | ||||
\(288\) | − | 5.47632i | − | 0.322695i | ||||||
\(289\) | 2.37217 | + | 4.10872i | 0.139539 | + | 0.241689i | ||||
\(290\) | −2.46725 | + | 4.27340i | −0.144882 | + | 0.250943i | ||||
\(291\) | 1.35673 | + | 0.783311i | 0.0795331 | + | 0.0459185i | ||||
\(292\) | 2.42340 | − | 1.39915i | 0.141819 | − | 0.0818792i | ||||
\(293\) | − | 6.86489i | − | 0.401051i | −0.979688 | − | 0.200526i | \(-0.935735\pi\) | ||
0.979688 | − | 0.200526i | \(-0.0642650\pi\) | |||||||
\(294\) | 2.73882 | + | 3.02164i | 0.159731 | + | 0.176225i | ||||
\(295\) | 6.50243 | 0.378586 | ||||||||
\(296\) | 5.81772 | + | 10.0766i | 0.338148 | + | 0.585689i | ||||
\(297\) | 2.68042 | + | 1.54754i | 0.155534 | + | 0.0897973i | ||||
\(298\) | 6.37647 | − | 11.0444i | 0.369379 | − | 0.639783i | ||||
\(299\) | −14.1545 | − | 16.5362i | −0.818578 | − | 0.956314i | ||||
\(300\) | −4.77795 | −0.275855 | ||||||||
\(301\) | 20.0546 | − | 7.73625i | 1.15593 | − | 0.445910i | ||||
\(302\) | 1.30399 | 0.0750359 | ||||||||
\(303\) | −5.72587 | − | 9.91749i | −0.328942 | − | 0.569745i | ||||
\(304\) | 8.24040 | + | 4.75760i | 0.472619 | + | 0.272867i | ||||
\(305\) | −9.68453 | − | 5.59137i | −0.554535 | − | 0.320161i | ||||
\(306\) | 1.76630 | − | 1.01978i | 0.100973 | − | 0.0582967i | ||||
\(307\) | 28.3680i | 1.61905i | 0.587089 | + | 0.809523i | \(0.300274\pi\) | ||||
−0.587089 | + | 0.809523i | \(0.699726\pi\) | |||||||
\(308\) | −8.54016 | + | 10.5819i | −0.486621 | + | 0.602960i | ||||
\(309\) | 3.07410 | 0.174879 | ||||||||
\(310\) | 6.64562 | − | 3.83685i | 0.377446 | − | 0.217919i | ||||
\(311\) | −9.08499 | + | 15.7357i | −0.515163 | + | 0.892288i | 0.484683 | + | 0.874690i | \(0.338935\pi\) |
−0.999845 | + | 0.0175977i | \(0.994398\pi\) | |||||||
\(312\) | 7.25108 | + | 2.55883i | 0.410512 | + | 0.144865i | ||||
\(313\) | −6.49909 | − | 11.2568i | −0.367350 | − | 0.636269i | 0.621800 | − | 0.783176i | \(-0.286402\pi\) |
−0.989150 | + | 0.146907i | \(0.953068\pi\) | |||||||
\(314\) | − | 0.609184i | − | 0.0343782i | ||||||
\(315\) | −3.80828 | − | 0.596727i | −0.214572 | − | 0.0336218i | ||||
\(316\) | 20.1258 | 1.13217 | ||||||||
\(317\) | −6.87879 | + | 3.97147i | −0.386352 | + | 0.223060i | −0.680578 | − | 0.732676i | \(-0.738271\pi\) |
0.294227 | + | 0.955736i | \(0.404938\pi\) | |||||||
\(318\) | −3.66160 | − | 2.11403i | −0.205332 | − | 0.118549i | ||||
\(319\) | 15.5823 | + | 8.99644i | 0.872441 | + | 0.503704i | ||||
\(320\) | −1.22004 | + | 0.704392i | −0.0682025 | + | 0.0393767i | ||||
\(321\) | 8.21164 | 0.458329 | ||||||||
\(322\) | 9.19334 | + | 1.44052i | 0.512325 | + | 0.0802772i | ||||
\(323\) | 16.0248i | 0.891645i | ||||||||
\(324\) | −0.830292 | − | 1.43811i | −0.0461273 | − | 0.0798949i | ||||
\(325\) | 3.45228 | − | 9.78289i | 0.191498 | − | 0.542657i | ||||
\(326\) | 2.04558 | − | 3.54304i | 0.113294 | − | 0.196231i | ||||
\(327\) | −4.41034 | + | 2.54631i | −0.243892 | + | 0.140811i | ||||
\(328\) | −17.7055 | −0.977621 | ||||||||
\(329\) | −18.1864 | + | 22.5343i | −1.00265 | + | 1.24236i | ||||
\(330\) | 2.62715i | 0.144620i | ||||||||
\(331\) | −4.21336 | + | 2.43259i | −0.231587 | + | 0.133707i | −0.611304 | − | 0.791396i | \(-0.709355\pi\) |
0.379717 | + | 0.925103i | \(0.376021\pi\) | |||||||
\(332\) | −9.32755 | − | 5.38526i | −0.511916 | − | 0.295555i | ||||
\(333\) | 4.72494 | + | 2.72795i | 0.258925 | + | 0.149491i | ||||
\(334\) | −3.48459 | − | 6.03548i | −0.190668 | − | 0.330247i | ||||
\(335\) | −18.3956 | −1.00506 | ||||||||
\(336\) | 5.13118 | − | 1.97940i | 0.279929 | − | 0.107985i | ||||
\(337\) | 7.89831 | 0.430248 | 0.215124 | − | 0.976587i | \(-0.430984\pi\) | ||||
0.215124 | + | 0.976587i | \(0.430984\pi\) | |||||||
\(338\) | −4.75343 | + | 5.89630i | −0.258552 | + | 0.320716i | ||||
\(339\) | −8.30426 | + | 14.3834i | −0.451025 | + | 0.781199i | ||||
\(340\) | −7.33511 | − | 4.23493i | −0.397802 | − | 0.229671i | ||||
\(341\) | −13.9905 | − | 24.2323i | −0.757628 | − | 1.31225i | ||||
\(342\) | −2.66681 | −0.144204 | ||||||||
\(343\) | −8.32616 | + | 16.5431i | −0.449571 | + | 0.893245i | ||||
\(344\) | 17.3263i | 0.934170i | ||||||||
\(345\) | −7.61732 | + | 4.39786i | −0.410103 | + | 0.236773i | ||||
\(346\) | 0.674059 | + | 0.389168i | 0.0362376 | + | 0.0209218i | ||||
\(347\) | 2.00510 | − | 3.47294i | 0.107640 | − | 0.186437i | −0.807174 | − | 0.590314i | \(-0.799004\pi\) |
0.914814 | + | 0.403876i | \(0.132337\pi\) | |||||||
\(348\) | −4.82680 | − | 8.36027i | −0.258744 | − | 0.448158i | ||||
\(349\) | − | 14.1849i | − | 0.759300i | −0.925130 | − | 0.379650i | \(-0.876044\pi\) | ||
0.925130 | − | 0.379650i | \(-0.123956\pi\) | |||||||
\(350\) | 1.59621 | + | 4.13783i | 0.0853210 | + | 0.221176i | ||||
\(351\) | 3.54446 | − | 0.660933i | 0.189189 | − | 0.0352780i | ||||
\(352\) | −8.47481 | − | 14.6788i | −0.451709 | − | 0.782383i | ||||
\(353\) | −0.540295 | − | 0.311940i | −0.0287570 | − | 0.0166029i | 0.485553 | − | 0.874207i | \(-0.338618\pi\) |
−0.514310 | + | 0.857605i | \(0.671952\pi\) | |||||||
\(354\) | 1.30006 | − | 2.25178i | 0.0690977 | − | 0.119681i | ||||
\(355\) | 1.22114 | + | 2.11507i | 0.0648113 | + | 0.112256i | ||||
\(356\) | − | 25.2495i | − | 1.33822i | ||||||
\(357\) | 7.20775 | + | 5.81704i | 0.381475 | + | 0.307870i | ||||
\(358\) | − | 1.35593i | − | 0.0716629i | ||||||
\(359\) | 18.1864 | − | 10.4999i | 0.959843 | − | 0.554166i | 0.0637184 | − | 0.997968i | \(-0.479704\pi\) |
0.896125 | + | 0.443802i | \(0.146371\pi\) | |||||||
\(360\) | 1.55358 | − | 2.69088i | 0.0818809 | − | 0.141822i | ||||
\(361\) | 0.976595 | − | 1.69151i | 0.0513997 | − | 0.0890269i | ||||
\(362\) | 1.16598 | − | 0.673176i | 0.0612823 | − | 0.0353814i | ||||
\(363\) | −1.42049 | −0.0745563 | ||||||||
\(364\) | 0.458121 | + | 15.8343i | 0.0240121 | + | 0.829944i | ||||
\(365\) | 2.45517 | 0.128509 | ||||||||
\(366\) | −3.87256 | + | 2.23582i | −0.202422 | + | 0.116868i | ||||
\(367\) | −1.78938 | + | 3.09930i | −0.0934049 | + | 0.161782i | −0.908942 | − | 0.416923i | \(-0.863108\pi\) |
0.815537 | + | 0.578705i | \(0.196442\pi\) | |||||||
\(368\) | 6.27462 | − | 10.8680i | 0.327087 | − | 0.566531i | ||||
\(369\) | −7.18987 | + | 4.15108i | −0.374290 | + | 0.216096i | ||||
\(370\) | 4.63105i | 0.240757i | ||||||||
\(371\) | 2.97237 | − | 18.9695i | 0.154318 | − | 0.984847i | ||||
\(372\) | 15.0125i | 0.778360i | ||||||||
\(373\) | 11.8376 | + | 20.5033i | 0.612928 | + | 1.06162i | 0.990744 | + | 0.135741i | \(0.0433416\pi\) |
−0.377817 | + | 0.925880i | \(0.623325\pi\) | |||||||
\(374\) | 3.15629 | − | 5.46685i | 0.163208 | − | 0.282684i | ||||
\(375\) | −9.93925 | − | 5.73843i | −0.513261 | − | 0.296331i | ||||
\(376\) | −11.6708 | − | 20.2144i | −0.601875 | − | 1.04248i | ||||
\(377\) | 20.6053 | − | 3.84226i | 1.06123 | − | 0.197886i | ||||
\(378\) | −0.968055 | + | 1.19949i | −0.0497914 | + | 0.0616953i | ||||
\(379\) | 20.5212i | 1.05410i | 0.849833 | + | 0.527052i | \(0.176703\pi\) | ||||
−0.849833 | + | 0.527052i | \(0.823297\pi\) | |||||||
\(380\) | 5.53736 | + | 9.59099i | 0.284061 | + | 0.492007i | ||||
\(381\) | −0.452057 | + | 0.782986i | −0.0231596 | + | 0.0401136i | ||||
\(382\) | −4.68071 | − | 2.70241i | −0.239486 | − | 0.138267i | ||||
\(383\) | 2.53122 | − | 1.46140i | 0.129340 | − | 0.0746742i | −0.433934 | − | 0.900945i | \(-0.642875\pi\) |
0.563274 | + | 0.826270i | \(0.309542\pi\) | |||||||
\(384\) | 11.5160i | 0.587671i | ||||||||
\(385\) | −11.1312 | + | 4.29399i | −0.567300 | + | 0.218842i | ||||
\(386\) | −3.94127 | −0.200605 | ||||||||
\(387\) | 4.06217 | + | 7.03589i | 0.206492 | + | 0.357654i | ||||
\(388\) | −2.25297 | − | 1.30075i | −0.114377 | − | 0.0660357i | ||||
\(389\) | −6.44084 | + | 11.1559i | −0.326564 | + | 0.565625i | −0.981828 | − | 0.189775i | \(-0.939224\pi\) |
0.655264 | + | 0.755400i | \(0.272557\pi\) | |||||||
\(390\) | 1.99014 | + | 2.32501i | 0.100775 | + | 0.117732i | ||||
\(391\) | 21.1346 | 1.06882 | ||||||||
\(392\) | −10.0257 | − | 11.0610i | −0.506373 | − | 0.558662i | ||||
\(393\) | −3.87727 | −0.195583 | ||||||||
\(394\) | −3.08241 | − | 5.33890i | −0.155290 | − | 0.268970i | ||||
\(395\) | 15.2922 | + | 8.82897i | 0.769436 | + | 0.444234i | ||||
\(396\) | −4.45106 | − | 2.56982i | −0.223674 | − | 0.129138i | ||||
\(397\) | −28.6326 | + | 16.5310i | −1.43703 | + | 0.829669i | −0.997642 | − | 0.0686298i | \(-0.978137\pi\) |
−0.439386 | + | 0.898298i | \(0.644804\pi\) | |||||||
\(398\) | − | 5.51948i | − | 0.276667i | ||||||
\(399\) | −4.35880 | − | 11.2993i | −0.218213 | − | 0.565670i | ||||
\(400\) | 5.98100 | 0.299050 | ||||||||
\(401\) | −0.355349 | + | 0.205161i | −0.0177453 | + | 0.0102453i | −0.508846 | − | 0.860857i | \(-0.669928\pi\) |
0.491101 | + | 0.871103i | \(0.336595\pi\) | |||||||
\(402\) | −3.67792 | + | 6.37035i | −0.183438 | + | 0.317724i | ||||
\(403\) | −30.7381 | − | 10.8472i | −1.53118 | − | 0.540336i | ||||
\(404\) | 9.50828 | + | 16.4688i | 0.473055 | + | 0.819355i | ||||
\(405\) | − | 1.45696i | − | 0.0723968i | ||||||
\(406\) | −5.62768 | + | 6.97312i | −0.279297 | + | 0.346070i | ||||
\(407\) | 16.8864 | 0.837028 | ||||||||
\(408\) | −6.46570 | + | 3.73298i | −0.320100 | + | 0.184810i | ||||
\(409\) | −0.741857 | − | 0.428312i | −0.0366825 | − | 0.0211786i | 0.481547 | − | 0.876420i | \(-0.340075\pi\) |
−0.518229 | + | 0.855242i | \(0.673409\pi\) | |||||||
\(410\) | −6.10288 | − | 3.52350i | −0.301400 | − | 0.174013i | ||||
\(411\) | −16.1496 | + | 9.32396i | −0.796600 | + | 0.459917i | ||||
\(412\) | −5.10479 | −0.251495 | ||||||||
\(413\) | 11.6657 | + | 1.82792i | 0.574031 | + | 0.0899461i | ||||
\(414\) | 3.51715i | 0.172859i | ||||||||
\(415\) | −4.72491 | − | 8.18378i | −0.231937 | − | 0.401726i | ||||
\(416\) | −18.6198 | − | 6.57072i | −0.912910 | − | 0.322156i | ||||
\(417\) | 0.950340 | − | 1.64604i | 0.0465383 | − | 0.0806068i | ||||
\(418\) | −7.14815 | + | 4.12699i | −0.349628 | + | 0.201858i | ||||
\(419\) | 27.0368 | 1.32084 | 0.660418 | − | 0.750898i | \(-0.270379\pi\) | ||||
0.660418 | + | 0.750898i | \(0.270379\pi\) | |||||||
\(420\) | 6.32397 | + | 0.990915i | 0.308578 | + | 0.0483517i | ||||
\(421\) | 17.1867i | 0.837628i | 0.908072 | + | 0.418814i | \(0.137554\pi\) | ||||
−0.908072 | + | 0.418814i | \(0.862446\pi\) | |||||||
\(422\) | 0.636673 | − | 0.367584i | 0.0309928 | − | 0.0178937i | ||||
\(423\) | −9.47860 | − | 5.47247i | −0.460865 | − | 0.266081i | ||||
\(424\) | 13.4036 | + | 7.73857i | 0.650936 | + | 0.375818i | ||||
\(425\) | 5.03639 | + | 8.72329i | 0.244301 | + | 0.423142i | ||||
\(426\) | 0.976595 | 0.0473162 | ||||||||
\(427\) | −15.8027 | − | 12.7537i | −0.764748 | − | 0.617192i | ||||
\(428\) | −13.6361 | −0.659126 | ||||||||
\(429\) | 8.47780 | − | 7.25676i | 0.409312 | − | 0.350360i | ||||
\(430\) | −3.44804 | + | 5.97217i | −0.166279 | + | 0.288004i | ||||
\(431\) | −2.12084 | − | 1.22447i | −0.102157 | − | 0.0589805i | 0.448051 | − | 0.894008i | \(-0.352118\pi\) |
−0.550208 | + | 0.835028i | \(0.685452\pi\) | |||||||
\(432\) | 1.03935 | + | 1.80021i | 0.0500058 | + | 0.0866127i | ||||
\(433\) | 40.8612 | 1.96366 | 0.981832 | − | 0.189754i | \(-0.0607689\pi\) | ||||
0.981832 | + | 0.189754i | \(0.0607689\pi\) | |||||||
\(434\) | 13.0012 | − | 5.01534i | 0.624077 | − | 0.240744i | ||||
\(435\) | − | 8.46986i | − | 0.406099i | ||||||
\(436\) | 7.32374 | − | 4.22836i | 0.350743 | − | 0.202502i | ||||
\(437\) | −23.9321 | − | 13.8172i | −1.14483 | − | 0.660966i | ||||
\(438\) | 0.490875 | − | 0.850221i | 0.0234549 | − | 0.0406251i | ||||
\(439\) | −15.7826 | − | 27.3363i | −0.753264 | − | 1.30469i | −0.946233 | − | 0.323486i | \(-0.895145\pi\) |
0.192969 | − | 0.981205i | \(-0.438188\pi\) | |||||||
\(440\) | − | 9.61691i | − | 0.458468i | ||||||
\(441\) | −6.66450 | − | 2.14112i | −0.317357 | − | 0.101958i | ||||
\(442\) | −1.34801 | − | 7.22910i | −0.0641182 | − | 0.343853i | ||||
\(443\) | −19.2093 | − | 33.2715i | −0.912663 | − | 1.58078i | −0.810287 | − | 0.586033i | \(-0.800689\pi\) |
−0.102376 | − | 0.994746i | \(-0.532644\pi\) | |||||||
\(444\) | −7.84616 | − | 4.52998i | −0.372362 | − | 0.214983i | ||||
\(445\) | 11.0767 | − | 19.1854i | 0.525085 | − | 0.909473i | ||||
\(446\) | −1.00887 | − | 1.74741i | −0.0477712 | − | 0.0827421i | ||||
\(447\) | 21.8899i | 1.03536i | ||||||||
\(448\) | −2.38683 | + | 0.920745i | −0.112767 | + | 0.0435011i | ||||
\(449\) | − | 24.0362i | − | 1.13434i | −0.823602 | − | 0.567168i | \(-0.808039\pi\) | ||
0.823602 | − | 0.567168i | \(-0.191961\pi\) | |||||||
\(450\) | −1.45170 | + | 0.838142i | −0.0684340 | + | 0.0395104i | ||||
\(451\) | −12.8479 | + | 22.2532i | −0.604984 | + | 1.04786i | ||||
\(452\) | 13.7899 | − | 23.8848i | 0.648623 | − | 1.12345i | ||||
\(453\) | −1.93837 | + | 1.11912i | −0.0910726 | + | 0.0525808i | ||||
\(454\) | −0.836241 | −0.0392467 | ||||||||
\(455\) | −6.59824 | + | 12.2324i | −0.309330 | + | 0.573463i | ||||
\(456\) | 9.76207 | 0.457151 | ||||||||
\(457\) | −31.0833 | + | 17.9460i | −1.45402 | + | 0.839477i | −0.998706 | − | 0.0508547i | \(-0.983805\pi\) |
−0.455312 | + | 0.890332i | \(0.650472\pi\) | |||||||
\(458\) | −6.95233 | + | 12.0418i | −0.324861 | + | 0.562676i | ||||
\(459\) | −1.75040 | + | 3.03179i | −0.0817019 | + | 0.141512i | ||||
\(460\) | 12.6492 | − | 7.30302i | 0.589772 | − | 0.340505i | ||||
\(461\) | 19.9043i | 0.927036i | 0.886087 | + | 0.463518i | \(0.153413\pi\) | ||||
−0.886087 | + | 0.463518i | \(0.846587\pi\) | |||||||
\(462\) | −0.738528 | + | 4.71325i | −0.0343594 | + | 0.219280i | ||||
\(463\) | − | 2.71044i | − | 0.125965i | −0.998015 | − | 0.0629825i | \(-0.979939\pi\) | ||
0.998015 | − | 0.0629825i | \(-0.0200612\pi\) | |||||||
\(464\) | 6.04215 | + | 10.4653i | 0.280500 | + | 0.485840i | ||||
\(465\) | −6.58580 | + | 11.4069i | −0.305409 | + | 0.528984i | ||||
\(466\) | −6.86406 | − | 3.96297i | −0.317971 | − | 0.183581i | ||||
\(467\) | −16.3733 | − | 28.3593i | −0.757664 | − | 1.31231i | −0.944039 | − | 0.329834i | \(-0.893007\pi\) |
0.186375 | − | 0.982479i | \(-0.440326\pi\) | |||||||
\(468\) | −5.88586 | + | 1.09753i | −0.272074 | + | 0.0507335i | ||||
\(469\) | −33.0026 | − | 5.17124i | −1.52392 | − | 0.238786i | ||||
\(470\) | − | 9.29024i | − | 0.428527i | ||||||
\(471\) | 0.522820 | + | 0.905550i | 0.0240903 | + | 0.0417256i | ||||
\(472\) | −4.75900 | + | 8.24282i | −0.219051 | + | 0.379407i | ||||
\(473\) | 21.7766 | + | 12.5727i | 1.00129 | + | 0.578095i | ||||
\(474\) | 6.11491 | − | 3.53045i | 0.280867 | − | 0.162159i | ||||
\(475\) | − | 13.1706i | − | 0.604310i | ||||||
\(476\) | −11.9691 | − | 9.65968i | −0.548602 | − | 0.442751i | ||||
\(477\) | 7.25728 | 0.332288 | ||||||||
\(478\) | 3.47460 | + | 6.01819i | 0.158925 | + | 0.275266i | ||||
\(479\) | 11.5460 | + | 6.66606i | 0.527548 | + | 0.304580i | 0.740018 | − | 0.672588i | \(-0.234817\pi\) |
−0.212469 | + | 0.977168i | \(0.568151\pi\) | |||||||
\(480\) | −3.98938 | + | 6.90981i | −0.182089 | + | 0.315388i | ||||
\(481\) | 14.9444 | − | 12.7920i | 0.681404 | − | 0.583263i | ||||
\(482\) | 5.78321 | 0.263418 | ||||||||
\(483\) | −14.9022 | + | 5.74866i | −0.678072 | + | 0.261573i | ||||
\(484\) | 2.35884 | 0.107220 | ||||||||
\(485\) | −1.14125 | − | 1.97670i | −0.0518215 | − | 0.0897575i | ||||
\(486\) | −0.504542 | − | 0.291297i | −0.0228865 | − | 0.0132135i | ||||
\(487\) | 32.3489 | + | 18.6767i | 1.46587 | + | 0.846320i | 0.999272 | − | 0.0381500i | \(-0.0121465\pi\) |
0.466597 | + | 0.884470i | \(0.345480\pi\) | |||||||
\(488\) | 14.1758 | − | 8.18442i | 0.641710 | − | 0.370491i | ||||
\(489\) | 7.02229i | 0.317559i | ||||||||
\(490\) | −1.25454 | − | 5.80776i | −0.0566744 | − | 0.262368i | ||||
\(491\) | 4.41544 | 0.199266 | 0.0996329 | − | 0.995024i | \(-0.468233\pi\) | ||||
0.0996329 | + | 0.995024i | \(0.468233\pi\) | |||||||
\(492\) | 11.9394 | − | 6.89321i | 0.538269 | − | 0.310770i | ||||
\(493\) | −10.1758 | + | 17.6250i | −0.458294 | + | 0.793788i | ||||
\(494\) | −3.19975 | + | 9.06729i | −0.143964 | + | 0.407957i | ||||
\(495\) | −2.25470 | − | 3.90525i | −0.101341 | − | 0.175528i | ||||
\(496\) | − | 18.7925i | − | 0.843807i | ||||||
\(497\) | 1.59621 | + | 4.13783i | 0.0715998 | + | 0.185607i | ||||
\(498\) | −3.77870 | −0.169328 | ||||||||
\(499\) | −24.6507 | + | 14.2321i | −1.10352 | + | 0.637116i | −0.937142 | − | 0.348947i | \(-0.886539\pi\) |
−0.166374 | + | 0.986063i | \(0.553206\pi\) | |||||||
\(500\) | 16.5050 | + | 9.52914i | 0.738124 | + | 0.426156i | ||||
\(501\) | 10.3597 | + | 5.98115i | 0.462835 | + | 0.267218i | ||||
\(502\) | −9.58224 | + | 5.53231i | −0.427676 | + | 0.246919i | ||||
\(503\) | −22.6474 | −1.00980 | −0.504899 | − | 0.863179i | \(-0.668470\pi\) | ||||
−0.504899 | + | 0.863179i | \(0.668470\pi\) | |||||||
\(504\) | 3.54365 | − | 4.39085i | 0.157847 | − | 0.195584i | ||||
\(505\) | 16.6847i | 0.742459i | ||||||||
\(506\) | 5.44293 | + | 9.42744i | 0.241968 | + | 0.419101i | ||||
\(507\) | 2.00558 | − | 12.8444i | 0.0890711 | − | 0.570438i | ||||
\(508\) | 0.750679 | − | 1.30021i | 0.0333060 | − | 0.0576877i | ||||
\(509\) | −15.5392 | + | 8.97157i | −0.688764 | + | 0.397658i | −0.803149 | − | 0.595779i | \(-0.796844\pi\) |
0.114385 | + | 0.993436i | \(0.463510\pi\) | |||||||
\(510\) | −2.97154 | −0.131582 | ||||||||
\(511\) | 4.40470 | + | 0.690181i | 0.194852 | + | 0.0305318i | ||||
\(512\) | − | 20.2499i | − | 0.894927i | ||||||
\(513\) | 3.96420 | − | 2.28873i | 0.175024 | − | 0.101050i | ||||
\(514\) | 10.0764 | + | 5.81760i | 0.444450 | + | 0.256603i | ||||
\(515\) | −3.87878 | − | 2.23942i | −0.170919 | − | 0.0986804i | ||||
\(516\) | −6.74557 | − | 11.6837i | −0.296957 | − | 0.514345i | ||||
\(517\) | −33.8755 | −1.48984 | ||||||||
\(518\) | −1.30185 | + | 8.30834i | −0.0572000 | + | 0.365047i | ||||
\(519\) | −1.33598 | −0.0586431 | ||||||||
\(520\) | −7.28509 | − | 8.51090i | −0.319472 | − | 0.373227i | ||||
\(521\) | 3.28321 | − | 5.68668i | 0.143840 | − | 0.249138i | −0.785100 | − | 0.619370i | \(-0.787388\pi\) |
0.928940 | + | 0.370231i | \(0.120722\pi\) | |||||||
\(522\) | −2.93310 | − | 1.69342i | −0.128378 | − | 0.0741191i | ||||
\(523\) | 8.80679 | + | 15.2538i | 0.385094 | + | 0.667002i | 0.991782 | − | 0.127938i | \(-0.0408357\pi\) |
−0.606688 | + | 0.794940i | \(0.707502\pi\) | |||||||
\(524\) | 6.43854 | 0.281269 | ||||||||
\(525\) | −5.92397 | − | 4.78096i | −0.258543 | − | 0.208658i | ||||
\(526\) | − | 1.92783i | − | 0.0840573i | ||||||
\(527\) | 27.4088 | − | 15.8245i | 1.19395 | − | 0.689326i | ||||
\(528\) | 5.57179 | + | 3.21688i | 0.242481 | + | 0.139997i | ||||
\(529\) | −6.72298 | + | 11.6445i | −0.292303 | + | 0.506284i | ||||
\(530\) | 3.08005 | + | 5.33480i | 0.133789 | + | 0.231729i | ||||
\(531\) | 4.46302i | 0.193678i | ||||||||
\(532\) | 7.23815 | + | 18.7634i | 0.313814 | + | 0.813495i | ||||
\(533\) | 5.48717 | + | 29.4266i | 0.237676 | + | 1.27461i | ||||
\(534\) | −4.42924 | − | 7.67166i | −0.191672 | − | 0.331985i | ||||
\(535\) | −10.3611 | − | 5.98201i | −0.447951 | − | 0.258625i | ||||
\(536\) | 13.4633 | − | 23.3192i | 0.581528 | − | 1.00724i | ||||
\(537\) | 1.16370 | + | 2.01558i | 0.0502172 | + | 0.0869787i | ||||
\(538\) | 13.9038i | 0.599434i | ||||||||
\(539\) | −21.1771 | + | 4.57449i | −0.912163 | + | 0.197037i | ||||
\(540\) | 2.41940i | 0.104114i | ||||||||
\(541\) | 13.0409 | − | 7.52918i | 0.560673 | − | 0.323705i | −0.192742 | − | 0.981249i | \(-0.561738\pi\) |
0.753416 | + | 0.657545i | \(0.228405\pi\) | |||||||
\(542\) | −0.487114 | + | 0.843706i | −0.0209233 | + | 0.0362403i | ||||
\(543\) | −1.15548 | + | 2.00135i | −0.0495864 | + | 0.0858861i | ||||
\(544\) | 16.6030 | − | 9.58577i | 0.711849 | − | 0.410986i | ||||
\(545\) | 7.41974 | 0.317827 | ||||||||
\(546\) | 2.91683 | + | 4.73065i | 0.124829 | + | 0.202453i | ||||
\(547\) | 32.9549 | 1.40905 | 0.704525 | − | 0.709679i | \(-0.251160\pi\) | ||||
0.704525 | + | 0.709679i | \(0.251160\pi\) | |||||||
\(548\) | 26.8177 | − | 15.4832i | 1.14560 | − | 0.661410i | ||||
\(549\) | 3.83770 | − | 6.64709i | 0.163789 | − | 0.283691i | ||||
\(550\) | −2.59412 | + | 4.49314i | −0.110613 | + | 0.191588i | ||||
\(551\) | 23.0454 | − | 13.3053i | 0.981768 | − | 0.566824i | ||||
\(552\) | − | 12.8748i | − | 0.547989i | ||||||
\(553\) | 24.9531 | + | 20.1385i | 1.06111 | + | 0.856376i | ||||
\(554\) | − | 3.20380i | − | 0.136116i | ||||||
\(555\) | −3.97450 | − | 6.88404i | −0.168708 | − | 0.292211i | ||||
\(556\) | −1.57812 | + | 2.73338i | −0.0669271 | + | 0.115921i | ||||
\(557\) | 10.1984 | + | 5.88807i | 0.432121 | + | 0.249485i | 0.700250 | − | 0.713898i | \(-0.253072\pi\) |
−0.268129 | + | 0.963383i | \(0.586405\pi\) | |||||||
\(558\) | 2.63347 | + | 4.56130i | 0.111484 | + | 0.193095i | ||||
\(559\) | 28.7964 | − | 5.36965i | 1.21796 | − | 0.227112i | ||||
\(560\) | −7.91629 | − | 1.24042i | −0.334524 | − | 0.0524173i | ||||
\(561\) | 10.8353i | 0.457466i | ||||||||
\(562\) | 9.49598 | + | 16.4475i | 0.400564 | + | 0.693797i | ||||
\(563\) | −2.39918 | + | 4.15551i | −0.101114 | + | 0.175134i | −0.912144 | − | 0.409871i | \(-0.865574\pi\) |
0.811030 | + | 0.585004i | \(0.198907\pi\) | |||||||
\(564\) | 15.7400 | + | 9.08749i | 0.662774 | + | 0.382653i | ||||
\(565\) | 20.9560 | − | 12.0990i | 0.881626 | − | 0.509007i | ||||
\(566\) | − | 10.2829i | − | 0.432222i | ||||||
\(567\) | 0.409571 | − | 2.61386i | 0.0172003 | − | 0.109772i | ||||
\(568\) | −3.57491 | −0.150000 | ||||||||
\(569\) | 15.8171 | + | 27.3961i | 0.663089 | + | 1.14850i | 0.979800 | + | 0.199982i | \(0.0640884\pi\) |
−0.316710 | + | 0.948522i | \(0.602578\pi\) | |||||||
\(570\) | 3.36488 | + | 1.94271i | 0.140939 | + | 0.0813713i | ||||
\(571\) | 18.6468 | − | 32.2972i | 0.780344 | − | 1.35160i | −0.151398 | − | 0.988473i | \(-0.548377\pi\) |
0.931742 | − | 0.363122i | \(-0.118289\pi\) | |||||||
\(572\) | −14.0781 | + | 12.0505i | −0.588635 | + | 0.503855i | ||||
\(573\) | 9.27714 | 0.387558 | ||||||||
\(574\) | −9.95838 | − | 8.03694i | −0.415655 | − | 0.335456i | ||||
\(575\) | −17.3702 | −0.724389 | ||||||||
\(576\) | −0.483468 | − | 0.837391i | −0.0201445 | − | 0.0348913i | ||||
\(577\) | 4.77775 | + | 2.75844i | 0.198901 | + | 0.114835i | 0.596143 | − | 0.802879i | \(-0.296699\pi\) |
−0.397242 | + | 0.917714i | \(0.630033\pi\) | |||||||
\(578\) | −2.39372 | − | 1.38201i | −0.0995655 | − | 0.0574842i | ||||
\(579\) | 5.85868 | − | 3.38251i | 0.243478 | − | 0.140572i | ||||
\(580\) | 14.0649i | 0.584013i | ||||||||
\(581\) | −6.17615 | − | 16.0104i | −0.256230 | − | 0.664221i | ||||
\(582\) | −0.912705 | −0.0378329 | ||||||||
\(583\) | 19.4525 | − | 11.2309i | 0.805641 | − | 0.465137i | ||||
\(584\) | −1.79689 | + | 3.11230i | −0.0743558 | + | 0.128788i | ||||
\(585\) | −4.95374 | − | 1.74812i | −0.204812 | − | 0.0722759i | ||||
\(586\) | 1.99973 | + | 3.46363i | 0.0826079 | + | 0.143081i | ||||
\(587\) | 4.46413i | 0.184255i | 0.995747 | + | 0.0921273i | \(0.0293667\pi\) | ||||
−0.995747 | + | 0.0921273i | \(0.970633\pi\) | |||||||
\(588\) | 11.0670 | + | 3.55551i | 0.456394 | + | 0.146627i | ||||
\(589\) | −41.3825 | −1.70514 | ||||||||
\(590\) | −3.28075 | + | 1.89414i | −0.135066 | + | 0.0779805i | ||||
\(591\) | 9.16400 | + | 5.29084i | 0.376957 | + | 0.217636i | ||||
\(592\) | 9.82175 | + | 5.67059i | 0.403672 | + | 0.233060i | ||||
\(593\) | 2.71683 | − | 1.56856i | 0.111567 | − | 0.0644132i | −0.443178 | − | 0.896434i | \(-0.646149\pi\) |
0.554745 | + | 0.832020i | \(0.312816\pi\) | |||||||
\(594\) | −1.80318 | −0.0739852 | ||||||||
\(595\) | −4.85688 | − | 12.5904i | −0.199113 | − | 0.516157i | ||||
\(596\) | − | 36.3500i | − | 1.48895i | ||||||
\(597\) | 4.73698 | + | 8.20470i | 0.193872 | + | 0.335796i | ||||
\(598\) | 11.9585 | + | 4.22003i | 0.489020 | + | 0.172570i | ||||
\(599\) | −23.6009 | + | 40.8779i | −0.964306 | + | 1.67023i | −0.252838 | + | 0.967509i | \(0.581364\pi\) |
−0.711468 | + | 0.702719i | \(0.751969\pi\) | |||||||
\(600\) | 5.31409 | − | 3.06809i | 0.216947 | − | 0.125254i | ||||
\(601\) | −25.2066 | −1.02820 | −0.514099 | − | 0.857731i | \(-0.671874\pi\) | ||||
−0.514099 | + | 0.857731i | \(0.671874\pi\) | |||||||
\(602\) | −7.86481 | + | 9.74510i | −0.320546 | + | 0.397181i | ||||
\(603\) | − | 12.6260i | − | 0.514171i | ||||||
\(604\) | 3.21883 | − | 1.85839i | 0.130972 | − | 0.0756168i | ||||
\(605\) | 1.79232 | + | 1.03480i | 0.0728681 | + | 0.0420704i | ||||
\(606\) | 5.77788 | + | 3.33586i | 0.234710 | + | 0.135510i | ||||
\(607\) | 2.01193 | + | 3.48476i | 0.0816615 | + | 0.141442i | 0.903964 | − | 0.427609i | \(-0.140644\pi\) |
−0.822302 | + | 0.569051i | \(0.807311\pi\) | |||||||
\(608\) | −25.0676 | −1.01663 | ||||||||
\(609\) | 2.38099 | − | 15.1954i | 0.0964826 | − | 0.615747i | ||||
\(610\) | 6.51500 | 0.263785 | ||||||||
\(611\) | −29.9795 | + | 25.6616i | −1.21284 | + | 1.03816i | ||||
\(612\) | 2.90669 | − | 5.03454i | 0.117496 | − | 0.203509i | ||||
\(613\) | −22.8690 | − | 13.2034i | −0.923671 | − | 0.533282i | −0.0388668 | − | 0.999244i | \(-0.512375\pi\) |
−0.884804 | + | 0.465963i | \(0.845708\pi\) | |||||||
\(614\) | −8.26351 | − | 14.3128i | −0.333488 | − | 0.577619i | ||||
\(615\) | 12.0959 | 0.487753 | ||||||||
\(616\) | 2.70344 | − | 17.2532i | 0.108925 | − | 0.695153i | ||||
\(617\) | 20.2789i | 0.816396i | 0.912893 | + | 0.408198i | \(0.133843\pi\) | ||||
−0.912893 | + | 0.408198i | \(0.866157\pi\) | |||||||
\(618\) | −1.55101 | + | 0.895476i | −0.0623908 | + | 0.0360213i | ||||
\(619\) | −12.2471 | − | 7.07089i | −0.492254 | − | 0.284203i | 0.233255 | − | 0.972416i | \(-0.425062\pi\) |
−0.725509 | + | 0.688213i | \(0.758396\pi\) | |||||||
\(620\) | 10.9363 | − | 18.9422i | 0.439211 | − | 0.760736i | ||||
\(621\) | −3.01852 | − | 5.22824i | −0.121129 | − | 0.209802i | ||||
\(622\) | − | 10.5857i | − | 0.424449i | ||||||
\(623\) | 25.2654 | − | 31.3057i | 1.01224 | − | 1.25424i | ||||
\(624\) | 7.36787 | − | 1.37388i | 0.294951 | − | 0.0549994i | ||||
\(625\) | 1.16746 | + | 2.02211i | 0.0466985 | + | 0.0808842i | ||||
\(626\) | 6.55813 | + | 3.78634i | 0.262115 | + | 0.151332i | ||||
\(627\) | 7.08381 | − | 12.2695i | 0.282900 | − | 0.489997i | ||||
\(628\) | −0.868186 | − | 1.50374i | −0.0346444 | − | 0.0600058i | ||||
\(629\) | 19.1000i | 0.761568i | ||||||||
\(630\) | 2.09526 | − | 0.808268i | 0.0834772 | − | 0.0322022i | ||||
\(631\) | 10.6582i | 0.424295i | 0.977238 | + | 0.212148i | \(0.0680458\pi\) | ||||
−0.977238 | + | 0.212148i | \(0.931954\pi\) | |||||||
\(632\) | −22.3842 | + | 12.9235i | −0.890394 | + | 0.514069i | ||||
\(633\) | −0.630942 | + | 1.09282i | −0.0250777 | + | 0.0434358i | ||||
\(634\) | 2.31376 | − | 4.00755i | 0.0918911 | − | 0.159160i | ||||
\(635\) | 1.14078 | − | 0.658628i | 0.0452704 | − | 0.0261369i | ||||
\(636\) | −12.0513 | −0.477866 | ||||||||
\(637\) | −15.2763 | + | 20.0907i | −0.605268 | + | 0.796022i | ||||
\(638\) | −10.4826 | −0.415008 | ||||||||
\(639\) | −1.45170 | + | 0.838142i | −0.0574286 | + | 0.0331564i | ||||
\(640\) | 8.38914 | − | 14.5304i | 0.331610 | − | 0.574365i | ||||
\(641\) | 3.86852 | − | 6.70048i | 0.152798 | − | 0.264653i | −0.779457 | − | 0.626455i | \(-0.784505\pi\) |
0.932255 | + | 0.361802i | \(0.117838\pi\) | |||||||
\(642\) | −4.14311 | + | 2.39203i | −0.163516 | + | 0.0944058i | ||||
\(643\) | − | 45.0898i | − | 1.77817i | −0.457744 | − | 0.889084i | \(-0.651342\pi\) | ||
0.457744 | − | 0.889084i | \(-0.348658\pi\) | |||||||
\(644\) | 24.7463 | − | 9.54613i | 0.975140 | − | 0.376170i | ||||
\(645\) | − | 11.8368i | − | 0.466075i | ||||||
\(646\) | −4.66799 | − | 8.08520i | −0.183660 | − | 0.318108i | ||||
\(647\) | −10.3836 | + | 17.9850i | −0.408223 | + | 0.707064i | −0.994691 | − | 0.102909i | \(-0.967185\pi\) |
0.586467 | + | 0.809973i | \(0.300518\pi\) | |||||||
\(648\) | 1.84692 | + | 1.06632i | 0.0725538 | + | 0.0418889i | ||||
\(649\) | 6.90669 | + | 11.9627i | 0.271111 | + | 0.469579i | ||||
\(650\) | 1.10791 | + | 5.94152i | 0.0434559 | + | 0.233045i | ||||
\(651\) | −15.0219 | + | 18.6133i | −0.588755 | + | 0.729512i | ||||
\(652\) | − | 11.6611i | − | 0.456684i | ||||||
\(653\) | 10.8366 | + | 18.7695i | 0.424068 | + | 0.734508i | 0.996333 | − | 0.0855614i | \(-0.0272684\pi\) |
−0.572265 | + | 0.820069i | \(0.693935\pi\) | |||||||
\(654\) | 1.48347 | − | 2.56944i | 0.0580082 | − | 0.100473i | ||||
\(655\) | 4.89220 | + | 2.82451i | 0.191154 | + | 0.110363i | ||||
\(656\) | −14.9456 | + | 8.62886i | −0.583528 | + | 0.336900i | ||||
\(657\) | 1.68513i | 0.0657433i | ||||||||
\(658\) | 2.61161 | − | 16.6672i | 0.101811 | − | 0.649754i | ||||
\(659\) | 23.6665 | 0.921916 | 0.460958 | − | 0.887422i | \(-0.347506\pi\) | ||||
0.460958 | + | 0.887422i | \(0.347506\pi\) | |||||||
\(660\) | 3.74412 | + | 6.48500i | 0.145740 | + | 0.252428i | ||||
\(661\) | 30.0061 | + | 17.3240i | 1.16710 | + | 0.673827i | 0.952996 | − | 0.302983i | \(-0.0979826\pi\) |
0.214107 | + | 0.976810i | \(0.431316\pi\) | |||||||
\(662\) | 1.41721 | − | 2.45468i | 0.0550815 | − | 0.0954039i | ||||
\(663\) | 8.20804 | + | 9.58914i | 0.318774 | + | 0.372411i | ||||
\(664\) | 13.8323 | 0.536796 | ||||||||
\(665\) | −2.73150 | + | 17.4323i | −0.105923 | + | 0.675995i | ||||
\(666\) | −3.17857 | −0.123167 | ||||||||
\(667\) | −17.5478 | − | 30.3938i | −0.679455 | − | 1.17685i | ||||
\(668\) | −17.2031 | − | 9.93220i | −0.665607 | − | 0.384288i | ||||
\(669\) | 2.99935 | + | 1.73168i | 0.115962 | + | 0.0669505i | ||||
\(670\) | 9.28133 | − | 5.35858i | 0.358569 | − | 0.207020i | ||||
\(671\) | − | 23.7560i | − | 0.917089i | ||||||
\(672\) | −9.09960 | + | 11.2751i | −0.351025 | + | 0.434946i | ||||
\(673\) | 4.43176 | 0.170832 | 0.0854160 | − | 0.996345i | \(-0.472778\pi\) | ||||
0.0854160 | + | 0.996345i | \(0.472778\pi\) | |||||||
\(674\) | −3.98503 | + | 2.30076i | −0.153498 | + | 0.0886219i | ||||
\(675\) | 1.43864 | − | 2.49179i | 0.0553732 | − | 0.0959091i | ||||
\(676\) | −3.33044 | + | 21.3291i | −0.128094 | + | 0.820351i | ||||
\(677\) | 13.3513 | + | 23.1251i | 0.513132 | + | 0.888770i | 0.999884 | + | 0.0152304i | \(0.00484816\pi\) |
−0.486752 | + | 0.873540i | \(0.661819\pi\) | |||||||
\(678\) | − | 9.67604i | − | 0.371606i | ||||||
\(679\) | −1.49178 | − | 3.86713i | −0.0572494 | − | 0.148407i | ||||
\(680\) | 10.8776 | 0.417136 | ||||||||
\(681\) | 1.24307 | − | 0.717687i | 0.0476345 | − | 0.0275018i | ||||
\(682\) | 14.1176 | + | 8.15079i | 0.540590 | + | 0.312110i | ||||
\(683\) | 34.2170 | + | 19.7552i | 1.30928 | + | 0.755912i | 0.981976 | − | 0.189007i | \(-0.0605270\pi\) |
0.327303 | + | 0.944920i | \(0.393860\pi\) | |||||||
\(684\) | −6.58289 | + | 3.80063i | −0.251703 | + | 0.145321i | ||||
\(685\) | 27.1692 | 1.03808 | ||||||||
\(686\) | −0.618071 | − | 10.7721i | −0.0235980 | − | 0.411280i | ||||
\(687\) | − | 23.8668i | − | 0.910575i | ||||||
\(688\) | 8.44405 | + | 14.6255i | 0.321926 | + | 0.557593i | ||||
\(689\) | 8.70760 | − | 24.6751i | 0.331733 | − | 0.940048i | ||||
\(690\) | 2.56217 | − | 4.43781i | 0.0975402 | − | 0.168945i | ||||
\(691\) | −27.1777 | + | 15.6911i | −1.03389 | + | 0.596917i | −0.918097 | − | 0.396357i | \(-0.870274\pi\) |
−0.115793 | + | 0.993273i | \(0.536941\pi\) | |||||||
\(692\) | 2.21851 | 0.0843350 | ||||||||
\(693\) | −2.94723 | − | 7.64005i | −0.111956 | − | 0.290222i | ||||
\(694\) | 2.33633i | 0.0886857i | ||||||||
\(695\) | −2.39821 | + | 1.38460i | −0.0909691 | + | 0.0525211i | ||||
\(696\) | 10.7368 | + | 6.19892i | 0.406979 | + | 0.234969i | ||||
\(697\) | −25.1704 | − | 14.5321i | −0.953396 | − | 0.550443i | ||||
\(698\) | 4.13203 | + | 7.15688i | 0.156399 | + | 0.270892i | ||||
\(699\) | 13.6045 | 0.514571 | ||||||||
\(700\) | 9.83724 | + | 7.93918i | 0.371813 | + | 0.300073i | ||||
\(701\) | −6.25790 | −0.236358 | −0.118179 | − | 0.992992i | \(-0.537706\pi\) | ||||
−0.118179 | + | 0.992992i | \(0.537706\pi\) | |||||||
\(702\) | −1.59580 | + | 1.36596i | −0.0602295 | + | 0.0515548i | ||||
\(703\) | 12.4871 | − | 21.6283i | 0.470959 | − | 0.815725i | ||||
\(704\) | −2.59179 | − | 1.49637i | −0.0976818 | − | 0.0563966i | ||||
\(705\) | 7.97316 | + | 13.8099i | 0.300287 | + | 0.520112i | ||||
\(706\) | 0.363469 | 0.0136793 | ||||||||
\(707\) | −4.69029 | + | 29.9332i | −0.176397 | + | 1.12575i | ||||
\(708\) | − | 7.41121i | − | 0.278530i | ||||||
\(709\) | 26.5406 | − | 15.3233i | 0.996755 | − | 0.575477i | 0.0894685 | − | 0.995990i | \(-0.471483\pi\) |
0.907287 | + | 0.420513i | \(0.138150\pi\) | |||||||
\(710\) | −1.23223 | − | 0.711429i | −0.0462448 | − | 0.0266994i | ||||
\(711\) | −6.05987 | + | 10.4960i | −0.227263 | + | 0.393631i | ||||
\(712\) | 16.2136 | + | 28.0828i | 0.607630 | + | 1.05245i | ||||
\(713\) | 54.5778i | 2.04396i | ||||||||
\(714\) | −5.33110 | − | 0.835341i | −0.199511 | − | 0.0312618i | ||||
\(715\) | −15.9834 | + | 2.98041i | −0.597744 | + | 0.111461i | ||||
\(716\) | −1.93241 | − | 3.34704i | −0.0722177 | − | 0.125085i | ||||
\(717\) | −10.3300 | − | 5.96401i | −0.385780 | − | 0.222730i | ||||
\(718\) | −6.11721 | + | 10.5953i | −0.228292 | + | 0.395414i | ||||
\(719\) | −10.8125 | − | 18.7278i | −0.403237 | − | 0.698427i | 0.590877 | − | 0.806761i | \(-0.298782\pi\) |
−0.994115 | + | 0.108334i | \(0.965448\pi\) | |||||||
\(720\) | − | 3.02858i | − | 0.112869i | ||||||
\(721\) | −6.32920 | − | 5.10800i | −0.235712 | − | 0.190232i | ||||
\(722\) | 1.13792i | 0.0423489i | ||||||||
\(723\) | −8.59672 | + | 4.96332i | −0.319715 | + | 0.184588i | ||||
\(724\) | 1.91877 | − | 3.32341i | 0.0713105 | − | 0.123513i | ||||
\(725\) | 8.36335 | − | 14.4857i | 0.310607 | − | 0.537987i | ||||
\(726\) | 0.716695 | − | 0.413784i | 0.0265991 | − | 0.0153570i | ||||
\(727\) | −23.1806 | −0.859722 | −0.429861 | − | 0.902895i | \(-0.641437\pi\) | ||||
−0.429861 | + | 0.902895i | \(0.641437\pi\) | |||||||
\(728\) | −10.6773 | − | 17.3169i | −0.395727 | − | 0.641808i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.23874 | + | 0.715184i | −0.0458477 | + | 0.0264702i | ||||
\(731\) | −14.2209 | + | 24.6313i | −0.525978 | + | 0.911021i | ||||
\(732\) | −6.37282 | + | 11.0380i | −0.235546 | + | 0.407978i | ||||
\(733\) | −6.25915 | + | 3.61372i | −0.231187 | + | 0.133476i | −0.611119 | − | 0.791538i | \(-0.709281\pi\) |
0.379933 | + | 0.925014i | \(0.375947\pi\) | |||||||
\(734\) | − | 2.08497i | − | 0.0769576i | ||||||
\(735\) | 6.84926 | + | 7.55653i | 0.252639 | + | 0.278727i | ||||
\(736\) | 33.0608i | 1.21864i | ||||||||
\(737\) | −19.5393 | − | 33.8430i | −0.719738 | − | 1.24662i | ||||
\(738\) | 2.41839 | − | 4.18878i | 0.0890223 | − | 0.154191i | ||||
\(739\) | −40.2868 | − | 23.2596i | −1.48197 | − | 0.855618i | −0.482183 | − | 0.876070i | \(-0.660156\pi\) |
−0.999791 | + | 0.0204525i | \(0.993489\pi\) | |||||||
\(740\) | 6.59999 | + | 11.4315i | 0.242621 | + | 0.420231i | ||||
\(741\) | −3.02540 | − | 16.2246i | −0.111141 | − | 0.596026i | ||||
\(742\) | 4.02608 | + | 10.4367i | 0.147802 | + | 0.383145i | ||||
\(743\) | 27.0715i | 0.993157i | 0.867992 | + | 0.496578i | \(0.165410\pi\) | ||||
−0.867992 | + | 0.496578i | \(0.834590\pi\) | |||||||
\(744\) | −9.64003 | − | 16.6970i | −0.353421 | − | 0.612143i | ||||
\(745\) | 15.9463 | − | 27.6198i | 0.584228 | − | 1.01191i | ||||
\(746\) | −11.9451 | − | 6.89652i | −0.437342 | − | 0.252500i | ||||
\(747\) | 5.61703 | − | 3.24299i | 0.205516 | − | 0.118655i | ||||
\(748\) | − | 17.9929i | − | 0.657885i | ||||||
\(749\) | −16.9068 | − | 13.6447i | −0.617761 | − | 0.498566i | ||||
\(750\) | 6.68636 | 0.244151 | ||||||||
\(751\) | 24.0464 | + | 41.6497i | 0.877467 | + | 1.51982i | 0.854111 | + | 0.520091i | \(0.174102\pi\) |
0.0233564 | + | 0.999727i | \(0.492565\pi\) | |||||||
\(752\) | −19.7032 | − | 11.3756i | −0.718502 | − | 0.414827i | ||||
\(753\) | 9.49598 | − | 16.4475i | 0.346053 | − | 0.599381i | ||||
\(754\) | −9.27699 | + | 7.94084i | −0.337848 | + | 0.289189i | ||||
\(755\) | 3.26102 | 0.118681 | ||||||||
\(756\) | −0.680126 | + | 4.34053i | −0.0247359 | + | 0.157863i | ||||
\(757\) | −5.24707 | −0.190708 | −0.0953540 | − | 0.995443i | \(-0.530398\pi\) | ||||
−0.0953540 | + | 0.995443i | \(0.530398\pi\) | |||||||
\(758\) | −5.97778 | − | 10.3538i | −0.217123 | − | 0.376068i | ||||
\(759\) | −16.1818 | − | 9.34257i | −0.587362 | − | 0.339114i | ||||
\(760\) | −12.3174 | − | 7.11146i | −0.446800 | − | 0.257960i | ||||
\(761\) | −2.29268 | + | 1.32368i | −0.0831095 | + | 0.0479833i | −0.540979 | − | 0.841036i | \(-0.681946\pi\) |
0.457869 | + | 0.889020i | \(0.348613\pi\) | |||||||
\(762\) | − | 0.526732i | − | 0.0190815i | ||||||
\(763\) | 13.3114 | + | 2.08579i | 0.481905 | + | 0.0755106i | ||||
\(764\) | −15.4055 | −0.557350 | ||||||||
\(765\) | 4.41719 | − | 2.55027i | 0.159704 | − | 0.0922050i | ||||
\(766\) | −0.851406 | + | 1.47468i | −0.0307625 | + | 0.0532823i | ||||
\(767\) | 15.1745 | + | 5.35492i | 0.547919 | + | 0.193355i | ||||
\(768\) | −2.38763 | − | 4.13550i | −0.0861563 | − | 0.149227i | ||||
\(769\) | 39.4880i | 1.42397i | 0.702193 | + | 0.711987i | \(0.252204\pi\) | ||||
−0.702193 | + | 0.711987i | \(0.747796\pi\) | |||||||
\(770\) | 4.36535 | − | 5.40900i | 0.157316 | − | 0.194927i | ||||
\(771\) | −19.9713 | −0.719250 | ||||||||
\(772\) | −9.72883 | + | 5.61694i | −0.350148 | + | 0.202158i | ||||
\(773\) | 22.6299 | + | 13.0654i | 0.813939 | + | 0.469928i | 0.848322 | − | 0.529481i | \(-0.177613\pi\) |
−0.0343826 | + | 0.999409i | \(0.510946\pi\) | |||||||
\(774\) | −4.09907 | − | 2.36660i | −0.147338 | − | 0.0850657i | ||||
\(775\) | −22.5270 | + | 13.0060i | −0.809194 | + | 0.467188i | ||||
\(776\) | 3.34103 | 0.119936 | ||||||||
\(777\) | −5.19526 | − | 13.4676i | −0.186379 | − | 0.483148i | ||||
\(778\) | − | 7.50480i | − | 0.269060i | ||||||
\(779\) | 19.0014 | + | 32.9114i | 0.680796 | + | 1.17917i | ||||
\(780\) | 8.22609 | + | 2.90290i | 0.294541 | + | 0.103941i | ||||
\(781\) | −2.59412 | + | 4.49314i | −0.0928248 | + | 0.160777i | ||||
\(782\) | −10.6633 | + | 6.15644i | −0.381318 | + | 0.220154i | ||||
\(783\) | 5.81338 | 0.207753 | ||||||||
\(784\) | −13.8535 | − | 4.45075i | −0.494769 | − | 0.158955i | ||||
\(785\) | − | 1.52345i | − | 0.0543744i | ||||||
\(786\) | 1.95625 | − | 1.12944i | 0.0697770 | − | 0.0402858i | ||||
\(787\) | 3.17249 | + | 1.83164i | 0.113087 | + | 0.0652908i | 0.555477 | − | 0.831532i | \(-0.312536\pi\) |
−0.442390 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(788\) | −15.2176 | − | 8.78588i | −0.542104 | − | 0.312984i | ||||
\(789\) | 1.65452 | + | 2.86571i | 0.0589024 | + | 0.102022i | ||||
\(790\) | −10.2874 | −0.366010 | ||||||||
\(791\) | 40.9973 | − | 15.8151i | 1.45770 | − | 0.562321i | ||||
\(792\) | 6.60068 | 0.234545 | ||||||||
\(793\) | −17.9958 | − | 21.0239i | −0.639051 | − | 0.746579i | ||||
\(794\) | 9.63089 | − | 16.6812i | 0.341788 | − | 0.591993i | ||||
\(795\) | −9.15696 | − | 5.28677i | −0.324764 | − | 0.187503i | ||||
\(796\) | −7.86616 | − | 13.6246i | −0.278809 | − | 0.482911i | ||||
\(797\) | −53.7046 | −1.90232 | −0.951158 | − | 0.308704i | \(-0.900105\pi\) | ||||
−0.951158 | + | 0.308704i | \(0.900105\pi\) | |||||||
\(798\) | 5.49064 | + | 4.43124i | 0.194367 | + | 0.156864i | ||||
\(799\) | − | 38.3161i | − | 1.35553i | ||||||
\(800\) | −13.6458 | + | 7.87843i | −0.482453 | + | 0.278545i | ||||
\(801\) | 13.1681 | + | 7.60260i | 0.465272 | + | 0.268625i | ||||
\(802\) | 0.119526 | − | 0.207025i | 0.00422060 | − | 0.00731030i | ||||
\(803\) | 2.60781 | + | 4.51686i | 0.0920277 | + | 0.159397i | ||||
\(804\) | 20.9665i | 0.739433i | ||||||||
\(805\) | 22.9908 | + | 3.60247i | 0.810318 | + | 0.126970i | ||||
\(806\) | 18.6684 | − | 3.48109i | 0.657567 | − | 0.122616i | ||||
\(807\) | −11.9326 | − | 20.6679i | −0.420048 | − | 0.727545i | ||||
\(808\) | −21.1504 | − | 12.2112i | −0.744069 | − | 0.429588i | ||||
\(809\) | −18.6379 | + | 32.2819i | −0.655275 | + | 1.13497i | 0.326550 | + | 0.945180i | \(0.394114\pi\) |
−0.981825 | + | 0.189790i | \(0.939219\pi\) | |||||||
\(810\) | 0.424408 | + | 0.735096i | 0.0149122 | + | 0.0258286i | ||||
\(811\) | − | 2.11417i | − | 0.0742387i | −0.999311 | − | 0.0371193i | \(-0.988182\pi\) | ||
0.999311 | − | 0.0371193i | \(-0.0118182\pi\) | |||||||
\(812\) | −3.95383 | + | 25.2332i | −0.138752 | + | 0.885510i | ||||
\(813\) | − | 1.67222i | − | 0.0586474i | ||||||
\(814\) | −8.51990 | + | 4.91897i | −0.298622 | + | 0.172410i | ||||
\(815\) | 5.11559 | − | 8.86047i | 0.179191 | − | 0.310369i | ||||
\(816\) | −3.63857 | + | 6.30219i | −0.127376 | + | 0.220621i | ||||
\(817\) | 32.2065 | − | 18.5945i | 1.12676 | − | 0.650537i | ||||
\(818\) | 0.499064 | 0.0174494 | ||||||||
\(819\) | −8.39584 | − | 4.52878i | −0.293374 | − | 0.158248i | ||||
\(820\) | −20.0862 | −0.701441 | ||||||||
\(821\) | −28.9900 | + | 16.7374i | −1.01176 | + | 0.584138i | −0.911706 | − | 0.410844i | \(-0.865234\pi\) |
−0.100051 | + | 0.994982i | \(0.531901\pi\) | |||||||
\(822\) | 5.43209 | − | 9.40866i | 0.189466 | − | 0.328165i | ||||
\(823\) | −16.9290 | + | 29.3218i | −0.590107 | + | 1.02210i | 0.404110 | + | 0.914710i | \(0.367581\pi\) |
−0.994217 | + | 0.107385i | \(0.965752\pi\) | |||||||
\(824\) | 5.67760 | − | 3.27797i | 0.197789 | − | 0.114193i | ||||
\(825\) | − | 8.90539i | − | 0.310046i | ||||||
\(826\) | −6.41830 | + | 2.47592i | −0.223321 | + | 0.0861483i | ||||
\(827\) | − | 2.13815i | − | 0.0743506i | −0.999309 | − | 0.0371753i | \(-0.988164\pi\) | ||
0.999309 | − | 0.0371753i | \(-0.0118360\pi\) | |||||||
\(828\) | 5.01251 | + | 8.68192i | 0.174197 | + | 0.301718i | ||||
\(829\) | 13.1393 | − | 22.7579i | 0.456346 | − | 0.790415i | −0.542418 | − | 0.840108i | \(-0.682491\pi\) |
0.998764 | + | 0.0496939i | \(0.0158246\pi\) | |||||||
\(830\) | 4.76783 | + | 2.75271i | 0.165494 | + | 0.0955478i | ||||
\(831\) | 2.74960 | + | 4.76244i | 0.0953824 | + | 0.165207i | ||||
\(832\) | −3.42726 | + | 0.639079i | −0.118819 | + | 0.0221561i | ||||
\(833\) | −5.17416 | − | 23.9532i | −0.179274 | − | 0.829929i | ||||
\(834\) | 1.10733i | 0.0383436i | ||||||||
\(835\) | −8.71429 | − | 15.0936i | −0.301570 | − | 0.522335i | ||||
\(836\) | −11.7633 | + | 20.3746i | −0.406841 | + | 0.704669i | ||||
\(837\) | −7.82929 | − | 4.52024i | −0.270620 | − | 0.156242i | ||||
\(838\) | −13.6412 | + | 7.87576i | −0.471228 | + | 0.272064i | ||||
\(839\) | − | 9.33965i | − | 0.322441i | −0.986918 | − | 0.161220i | \(-0.948457\pi\) | ||
0.986918 | − | 0.161220i | \(-0.0515430\pi\) | |||||||
\(840\) | −7.66988 | + | 2.95873i | −0.264636 | + | 0.102086i | ||||
\(841\) | 4.79544 | 0.165360 | ||||||||
\(842\) | −5.00643 | − | 8.67140i | −0.172533 | − | 0.298836i | ||||
\(843\) | −28.2315 | − | 16.2995i | −0.972344 | − | 0.561383i | ||||
\(844\) | 1.04773 | − | 1.81473i | 0.0360644 | − | 0.0624654i | ||||
\(845\) | −11.8874 | + | 14.7455i | −0.408940 | + | 0.507261i | ||||
\(846\) | 6.37647 | 0.219227 | ||||||||
\(847\) | 2.92462 | + | 2.36032i | 0.100491 | + | 0.0811016i | ||||
\(848\) | 15.0857 | 0.518046 | ||||||||
\(849\) | 8.82509 | + | 15.2855i | 0.302876 | + | 0.524597i | ||||
\(850\) | −5.08214 | − | 2.93418i | −0.174316 | − | 0.100641i | ||||
\(851\) | −28.5247 | − | 16.4687i | −0.977814 | − | 0.564541i | ||||
\(852\) | 2.41068 | − | 1.39181i | 0.0825884 | − | 0.0476825i | ||||
\(853\) | − | 5.14425i | − | 0.176136i | −0.996114 | − | 0.0880678i | \(-0.971931\pi\) | ||
0.996114 | − | 0.0880678i | \(-0.0280692\pi\) | |||||||
\(854\) | 11.6882 | + | 1.83145i | 0.399964 | + | 0.0626711i | ||||
\(855\) | −6.66917 | −0.228081 | ||||||||
\(856\) | 15.1662 | − | 8.75622i | 0.518371 | − | 0.299281i | ||||
\(857\) | 7.81827 | − | 13.5416i | 0.267067 | − | 0.462573i | −0.701036 | − | 0.713126i | \(-0.747279\pi\) |
0.968103 | + | 0.250552i | \(0.0806122\pi\) | |||||||
\(858\) | −2.16353 | + | 6.13090i | −0.0738617 | + | 0.209305i | ||||
\(859\) | 7.15629 | + | 12.3951i | 0.244169 | + | 0.422914i | 0.961898 | − | 0.273409i | \(-0.0881514\pi\) |
−0.717728 | + | 0.696323i | \(0.754818\pi\) | |||||||
\(860\) | 19.6560i | 0.670265i | ||||||||
\(861\) | 21.7006 | + | 3.40032i | 0.739556 | + | 0.115883i | ||||
\(862\) | 1.42674 | 0.0485948 | ||||||||
\(863\) | 8.02067 | − | 4.63074i | 0.273027 | − | 0.157632i | −0.357236 | − | 0.934014i | \(-0.616281\pi\) |
0.630262 | + | 0.776382i | \(0.282947\pi\) | |||||||
\(864\) | −4.74263 | − | 2.73816i | −0.161347 | − | 0.0931540i | ||||
\(865\) | 1.68569 | + | 0.973234i | 0.0573152 | + | 0.0330910i | ||||
\(866\) | −20.6162 | + | 11.9028i | −0.700566 | + | 0.404472i | ||||
\(867\) | 4.74434 | 0.161126 | ||||||||
\(868\) | 24.9451 | − | 30.9089i | 0.846693 | − | 1.04912i | ||||
\(869\) | 37.5115i | 1.27249i | ||||||||
\(870\) | 2.46725 | + | 4.27340i | 0.0836475 | + | 0.144882i | ||||
\(871\) | −42.9291 | − | 15.1492i | −1.45460 | − | 0.513312i | ||||
\(872\) | −5.43036 | + | 9.40565i | −0.183895 | + | 0.318516i | ||||
\(873\) | 1.35673 | − | 0.783311i | 0.0459185 | − | 0.0265110i | ||||
\(874\) | 16.0996 | 0.544579 | ||||||||
\(875\) | 10.9286 | + | 28.3301i | 0.369454 | + | 0.957731i | ||||
\(876\) | − | 2.79831i | − | 0.0945460i | ||||||
\(877\) | 22.3441 | − | 12.9003i | 0.754505 | − | 0.435614i | −0.0728142 | − | 0.997346i | \(-0.523198\pi\) |
0.827319 | + | 0.561732i | \(0.189865\pi\) | |||||||
\(878\) | 15.9260 | + | 9.19487i | 0.537476 | + | 0.310312i | ||||
\(879\) | −5.94517 | − | 3.43245i | −0.200526 | − | 0.115774i | ||||
\(880\) | −4.68685 | − | 8.11787i | −0.157994 | − | 0.273653i | ||||
\(881\) | −50.1659 | −1.69013 | −0.845066 | − | 0.534661i | \(-0.820439\pi\) | ||||
−0.845066 | + | 0.534661i | \(0.820439\pi\) | |||||||
\(882\) | 3.98622 | − | 0.861069i | 0.134223 | − | 0.0289937i | ||||
\(883\) | −42.9847 | −1.44655 | −0.723275 | − | 0.690560i | \(-0.757364\pi\) | ||||
−0.723275 | + | 0.690560i | \(0.757364\pi\) | |||||||
\(884\) | −13.6301 | − | 15.9236i | −0.458431 | − | 0.535568i | ||||
\(885\) | 3.25121 | − | 5.63127i | 0.109288 | − | 0.189293i | ||||
\(886\) | 19.3838 | + | 11.1913i | 0.651212 | + | 0.375978i | ||||
\(887\) | −5.40363 | − | 9.35937i | −0.181436 | − | 0.314257i | 0.760934 | − | 0.648830i | \(-0.224741\pi\) |
−0.942370 | + | 0.334573i | \(0.891408\pi\) | |||||||
\(888\) | 11.6354 | 0.390460 | ||||||||
\(889\) | 2.23176 | − | 0.860925i | 0.0748509 | − | 0.0288745i | ||||
\(890\) | 12.9064i | 0.432624i | ||||||||
\(891\) | 2.68042 | − | 1.54754i | 0.0897973 | − | 0.0518445i | ||||
\(892\) | −4.98067 | − | 2.87559i | −0.166765 | − | 0.0962819i | ||||
\(893\) | −25.0500 | + | 43.3880i | −0.838268 | + | 1.45192i | ||||
\(894\) | −6.37647 | − | 11.0444i | −0.213261 | − | 0.369379i | ||||
\(895\) | − | 3.39091i | − | 0.113346i | ||||||
\(896\) | 19.1352 | − | 23.7100i | 0.639263 | − | 0.792096i | ||||
\(897\) | −21.3981 | + | 3.99008i | −0.714460 | + | 0.133225i | ||||
\(898\) | 7.00167 | + | 12.1272i | 0.233649 | + | 0.404691i | ||||
\(899\) | −45.5147 | − | 26.2779i | −1.51800 | − | 0.876417i | ||||
\(900\) | −2.38898 | + | 4.13783i | −0.0796325 | + | 0.137928i | ||||
\(901\) | 12.7032 | + | 22.0025i | 0.423204 | + | 0.733011i | ||||
\(902\) | − | 14.9702i | − | 0.498455i | ||||||
\(903\) | 3.32749 | − | 21.2359i | 0.110732 | − | 0.706686i | ||||
\(904\) | 35.4199i | 1.17805i | ||||||||
\(905\) | 2.91588 | − | 1.68348i | 0.0969272 | − | 0.0559609i | ||||
\(906\) | 0.651993 | − | 1.12928i | 0.0216610 | − | 0.0375180i | ||||
\(907\) | 16.4957 | − | 28.5713i | 0.547729 | − | 0.948695i | −0.450700 | − | 0.892675i | \(-0.648826\pi\) |
0.998430 | − | 0.0560196i | \(-0.0178409\pi\) | |||||||
\(908\) | −2.06422 | + | 1.19178i | −0.0685036 | + | 0.0395506i | ||||
\(909\) | −11.4517 | −0.379830 | ||||||||
\(910\) | −0.234171 | − | 8.09380i | −0.00776269 | − | 0.268307i | ||||
\(911\) | −17.6639 | −0.585232 | −0.292616 | − | 0.956230i | \(-0.594526\pi\) | ||||
−0.292616 | + | 0.956230i | \(0.594526\pi\) | |||||||
\(912\) | 8.24040 | − | 4.75760i | 0.272867 | − | 0.157540i | ||||
\(913\) | 10.0373 | − | 17.3852i | 0.332187 | − | 0.575365i | ||||
\(914\) | 10.4552 | − | 18.1090i | 0.345828 | − | 0.598992i | ||||
\(915\) | −9.68453 | + | 5.59137i | −0.320161 | + | 0.184845i | ||||
\(916\) | 39.6328i | 1.30950i | ||||||||
\(917\) | 7.98285 | + | 6.44258i | 0.263617 | + | 0.212753i | ||||
\(918\) | − | 2.03955i | − | 0.0673153i | ||||||
\(919\) | −16.9325 | − | 29.3280i | −0.558552 | − | 0.967441i | −0.997618 | − | 0.0689860i | \(-0.978024\pi\) |
0.439065 | − | 0.898455i | \(-0.355310\pi\) | |||||||
\(920\) | −9.37904 | + | 16.2450i | −0.309218 | + | 0.535581i | ||||
\(921\) | 24.5674 | + | 14.1840i | 0.809523 | + | 0.467378i | ||||
\(922\) | −5.79807 | − | 10.0426i | −0.190949 | − | 0.330734i | ||||
\(923\) | 1.10791 | + | 5.94152i | 0.0364674 | + | 0.195567i | ||||
\(924\) | 4.89412 | + | 12.6869i | 0.161005 | + | 0.417370i | ||||
\(925\) | − | 15.6981i | − | 0.516150i | ||||||
\(926\) | 0.789545 | + | 1.36753i | 0.0259461 | + | 0.0449399i | ||||
\(927\) | 1.53705 | − | 2.66225i | 0.0504833 | − | 0.0874396i | ||||
\(928\) | −27.5707 | − | 15.9180i | −0.905053 | − | 0.522533i | ||||
\(929\) | 1.59169 | − | 0.918962i | 0.0522216 | − | 0.0301502i | −0.473662 | − | 0.880707i | \(-0.657068\pi\) |
0.525884 | + | 0.850557i | \(0.323735\pi\) | |||||||
\(930\) | − | 7.67370i | − | 0.251631i | ||||||
\(931\) | −9.80090 | + | 30.5065i | −0.321211 | + | 0.999811i | ||||
\(932\) | −22.5915 | −0.740008 | ||||||||
\(933\) | 9.08499 | + | 15.7357i | 0.297429 | + | 0.515163i | ||||
\(934\) | 16.5220 | + | 9.53897i | 0.540616 | + | 0.312125i | ||||
\(935\) | 7.89327 | − | 13.6715i | 0.258138 | − | 0.447107i | ||||
\(936\) | 5.84155 | − | 5.00021i | 0.190937 | − | 0.163437i | ||||
\(937\) | −6.63406 | −0.216725 | −0.108363 | − | 0.994111i | \(-0.534561\pi\) | ||||
−0.108363 | + | 0.994111i | \(0.534561\pi\) | |||||||
\(938\) | 18.1576 | − | 7.00446i | 0.592865 | − | 0.228704i | ||||
\(939\) | −12.9982 | −0.424180 | ||||||||
\(940\) | −13.2401 | − | 22.9325i | −0.431844 | − | 0.747976i | ||||
\(941\) | −1.92634 | − | 1.11217i | −0.0627968 | − | 0.0362557i | 0.468273 | − | 0.883584i | \(-0.344876\pi\) |
−0.531070 | + | 0.847328i | \(0.678210\pi\) | |||||||
\(942\) | −0.527569 | − | 0.304592i | −0.0171891 | − | 0.00992414i | ||||
\(943\) | 43.4056 | − | 25.0602i | 1.41348 | − | 0.816074i | ||||
\(944\) | 9.27729i | 0.301950i | ||||||||
\(945\) | −2.42092 | + | 2.99970i | −0.0787526 | + | 0.0975804i | ||||
\(946\) | −14.6496 | −0.476300 | ||||||||
\(947\) | 24.5852 | − | 14.1943i | 0.798912 | − | 0.461252i | −0.0441784 | − | 0.999024i | \(-0.514067\pi\) |
0.843091 | + | 0.537771i | \(0.180734\pi\) | |||||||
\(948\) | 10.0629 | − | 17.4295i | 0.326828 | − | 0.566083i | ||||
\(949\) | 5.72955 | + | 2.02190i | 0.185989 | + | 0.0656335i | ||||
\(950\) | 3.83657 | + | 6.64513i | 0.124475 | + | 0.215596i | ||||
\(951\) | 7.94295i | 0.257568i | ||||||||
\(952\) | 19.5149 | + | 3.05783i | 0.632483 | + | 0.0991050i | ||||
\(953\) | 54.5711 | 1.76773 | 0.883865 | − | 0.467742i | \(-0.154932\pi\) | ||||
0.883865 | + | 0.467742i | \(0.154932\pi\) | |||||||
\(954\) | −3.66160 | + | 2.11403i | −0.118549 | + | 0.0684441i | ||||
\(955\) | −11.7056 | − | 6.75820i | −0.378783 | − | 0.218690i | ||||
\(956\) | 17.1538 | + | 9.90374i | 0.554793 | + | 0.320310i | ||||
\(957\) | 15.5823 | − | 8.99644i | 0.503704 | − | 0.290814i | ||||
\(958\) | −7.76723 | −0.250948 | ||||||||
\(959\) | 48.7430 | + | 7.63764i | 1.57399 | + | 0.246632i | ||||
\(960\) | 1.40878i | 0.0454683i | ||||||||
\(961\) | 25.3651 | + | 43.9337i | 0.818231 | + | 1.41722i | ||||
\(962\) | −3.81379 | + | 10.8073i | −0.122962 | + | 0.348442i | ||||
\(963\) | 4.10582 | − | 7.11149i | 0.132308 | − | 0.229164i | ||||
\(964\) | 14.2756 | − | 8.24200i | 0.459785 | − | 0.265457i | ||||
\(965\) | −9.85635 | −0.317287 | ||||||||
\(966\) | 5.84420 | − | 7.24140i | 0.188034 | − | 0.232988i | ||||
\(967\) | − | 36.7255i | − | 1.18101i | −0.807033 | − | 0.590507i | \(-0.798928\pi\) | ||
0.807033 | − | 0.590507i | \(-0.201072\pi\) | |||||||
\(968\) | −2.62352 | + | 1.51469i | −0.0843232 | + | 0.0486840i | ||||
\(969\) | 13.8779 | + | 8.01241i | 0.445823 | + | 0.257396i | ||||
\(970\) | 1.15162 | + | 0.664887i | 0.0369762 | + | 0.0213482i | ||||
\(971\) | 22.4374 | + | 38.8626i | 0.720049 | + | 1.24716i | 0.960980 | + | 0.276619i | \(0.0892140\pi\) |
−0.240931 | + | 0.970542i | \(0.577453\pi\) | |||||||
\(972\) | −1.66058 | −0.0532632 | ||||||||
\(973\) | −4.69174 | + | 1.80988i | −0.150410 | + | 0.0580222i | ||||
\(974\) | −21.7618 | −0.697294 | ||||||||
\(975\) | −6.74609 | − | 7.88120i | −0.216048 | − | 0.252401i | ||||
\(976\) | 7.97744 | − | 13.8173i | 0.255352 | − | 0.442282i | ||||
\(977\) | −22.1420 | − | 12.7837i | −0.708385 | − | 0.408986i | 0.102078 | − | 0.994776i | \(-0.467451\pi\) |
−0.810463 | + | 0.585790i | \(0.800784\pi\) | |||||||
\(978\) | −2.04558 | − | 3.54304i | −0.0654103 | − | 0.113294i | ||||
\(979\) | 47.0613 | 1.50409 | ||||||||
\(980\) | −11.3738 | − | 12.5483i | −0.363322 | − | 0.400839i | ||||
\(981\) | 5.09262i | 0.162595i | ||||||||
\(982\) | −2.22777 | + | 1.28620i | −0.0710911 | + | 0.0410444i | ||||
\(983\) | 41.0816 | + | 23.7185i | 1.31030 | + | 0.756502i | 0.982146 | − | 0.188122i | \(-0.0602400\pi\) |
0.328155 | + | 0.944624i | \(0.393573\pi\) | |||||||
\(984\) | −8.85274 | + | 15.3334i | −0.282215 | + | 0.488811i | ||||
\(985\) | −7.70853 | − | 13.3516i | −0.245614 | − | 0.425416i | ||||
\(986\) | − | 11.8567i | − | 0.377594i | ||||||
\(987\) | 10.4221 | + | 27.0171i | 0.331739 | + | 0.859963i | ||||
\(988\) | 5.02392 | + | 26.9423i | 0.159832 | + | 0.857150i | ||||
\(989\) | −24.5235 | − | 42.4760i | −0.779803 | − | 1.35066i | ||||
\(990\) | 2.27518 | + | 1.31358i | 0.0723100 | + | 0.0417482i | ||||
\(991\) | −7.21288 | + | 12.4931i | −0.229125 | + | 0.396856i | −0.957549 | − | 0.288271i | \(-0.906920\pi\) |
0.728424 | + | 0.685126i | \(0.240253\pi\) | |||||||
\(992\) | 24.7543 | + | 42.8756i | 0.785949 | + | 1.36130i | ||||
\(993\) | 4.86517i | 0.154392i | ||||||||
\(994\) | −2.01069 | − | 1.62274i | −0.0637753 | − | 0.0514701i | ||||
\(995\) | − | 13.8032i | − | 0.437590i | ||||||
\(996\) | −9.32755 | + | 5.38526i | −0.295555 | + | 0.170639i | ||||
\(997\) | 12.1208 | − | 20.9938i | 0.383868 | − | 0.664879i | −0.607743 | − | 0.794134i | \(-0.707925\pi\) |
0.991611 | + | 0.129254i | \(0.0412584\pi\) | |||||||
\(998\) | 8.29154 | − | 14.3614i | 0.262464 | − | 0.454601i | ||||
\(999\) | 4.72494 | − | 2.72795i | 0.149491 | − | 0.0863084i |
(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 | 273.2.bj.d.25.4 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.dl.g.298.5 | 16 | |||
7.2 | even | 3 | inner | 273.2.bj.d.142.5 | yes | 16 | |
7.3 | odd | 6 | 1911.2.c.m.883.4 | 8 | |||
7.4 | even | 3 | 1911.2.c.j.883.4 | 8 | |||
13.12 | even | 2 | inner | 273.2.bj.d.25.5 | yes | 16 | |
21.2 | odd | 6 | 819.2.dl.g.415.4 | 16 | |||
39.38 | odd | 2 | 819.2.dl.g.298.4 | 16 | |||
91.25 | even | 6 | 1911.2.c.j.883.5 | 8 | |||
91.38 | odd | 6 | 1911.2.c.m.883.5 | 8 | |||
91.51 | even | 6 | inner | 273.2.bj.d.142.4 | yes | 16 | |
273.233 | odd | 6 | 819.2.dl.g.415.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bj.d.25.4 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.bj.d.25.5 | yes | 16 | 13.12 | even | 2 | inner | |
273.2.bj.d.142.4 | yes | 16 | 91.51 | even | 6 | inner | |
273.2.bj.d.142.5 | yes | 16 | 7.2 | even | 3 | inner | |
819.2.dl.g.298.4 | 16 | 39.38 | odd | 2 | |||
819.2.dl.g.298.5 | 16 | 3.2 | odd | 2 | |||
819.2.dl.g.415.4 | 16 | 21.2 | odd | 6 | |||
819.2.dl.g.415.5 | 16 | 273.233 | odd | 6 | |||
1911.2.c.j.883.4 | 8 | 7.4 | even | 3 | |||
1911.2.c.j.883.5 | 8 | 91.25 | even | 6 | |||
1911.2.c.m.883.4 | 8 | 7.3 | odd | 6 | |||
1911.2.c.m.883.5 | 8 | 91.38 | odd | 6 |