Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(239,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.p (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.45474709504.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 38x^{6} + 481x^{4} + 2112x^{2} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 281.3 | ||
Root | \(3.49421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.281 |
Dual form | 546.2.p.b.239.3 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.41421 | + | 1.00000i | 0.816497 | + | 0.577350i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.47078 | + | 2.47078i | −1.10497 | + | 1.10497i | −0.111164 | + | 0.993802i | \(0.535458\pi\) |
−0.993802 | + | 0.111164i | \(0.964542\pi\) | |||||||
\(6\) | 1.70711 | − | 0.292893i | 0.696923 | − | 0.119573i | ||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000 | + | 2.82843i | 0.333333 | + | 0.942809i | ||||
\(10\) | 3.49421i | 1.10497i | ||||||||
\(11\) | 0.976570 | + | 0.976570i | 0.294447 | + | 0.294447i | 0.838834 | − | 0.544387i | \(-0.183238\pi\) |
−0.544387 | + | 0.838834i | \(0.683238\pi\) | |||||||
\(12\) | 1.00000 | − | 1.41421i | 0.288675 | − | 0.408248i | ||||
\(13\) | 1.76367 | + | 3.14475i | 0.489155 | + | 0.872197i | ||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | −5.96499 | + | 1.02343i | −1.54015 | + | 0.264249i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.49421 | −1.33254 | −0.666271 | − | 0.745710i | \(-0.732111\pi\) | ||||
−0.666271 | + | 0.745710i | \(0.732111\pi\) | |||||||
\(18\) | 2.70711 | + | 1.29289i | 0.638071 | + | 0.304738i | ||||
\(19\) | 0.470780 | + | 0.470780i | 0.108004 | + | 0.108004i | 0.759044 | − | 0.651040i | \(-0.225667\pi\) |
−0.651040 | + | 0.759044i | \(0.725667\pi\) | |||||||
\(20\) | 2.47078 | + | 2.47078i | 0.552483 | + | 0.552483i | ||||
\(21\) | −1.70711 | + | 0.292893i | −0.372521 | + | 0.0639145i | ||||
\(22\) | 1.38108 | 0.294447 | ||||||||
\(23\) | 8.97470 | 1.87135 | 0.935677 | − | 0.352859i | \(-0.114790\pi\) | ||||
0.935677 | + | 0.352859i | \(0.114790\pi\) | |||||||
\(24\) | −0.292893 | − | 1.70711i | −0.0597866 | − | 0.348462i | ||||
\(25\) | − | 7.20950i | − | 1.44190i | ||||||
\(26\) | 3.47078 | + | 0.976570i | 0.680676 | + | 0.191521i | ||||
\(27\) | −1.41421 | + | 5.00000i | −0.272166 | + | 0.962250i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 2.03314i | 0.377544i | 0.982021 | + | 0.188772i | \(0.0604507\pi\) | ||||
−0.982021 | + | 0.188772i | \(0.939549\pi\) | |||||||
\(30\) | −3.49421 | + | 4.94156i | −0.637953 | + | 0.902201i | ||||
\(31\) | 0.585786 | + | 0.585786i | 0.105210 | + | 0.105210i | 0.757752 | − | 0.652542i | \(-0.226297\pi\) |
−0.652542 | + | 0.757752i | \(0.726297\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0.404508 | + | 2.35765i | 0.0704159 | + | 0.410414i | ||||
\(34\) | −3.88499 | + | 3.88499i | −0.666271 | + | 0.666271i | ||||
\(35\) | − | 3.49421i | − | 0.590629i | ||||||
\(36\) | 2.82843 | − | 1.00000i | 0.471405 | − | 0.166667i | ||||
\(37\) | −1.56236 | + | 1.56236i | −0.256850 | + | 0.256850i | −0.823772 | − | 0.566922i | \(-0.808134\pi\) |
0.566922 | + | 0.823772i | \(0.308134\pi\) | |||||||
\(38\) | 0.665783 | 0.108004 | ||||||||
\(39\) | −0.650541 | + | 6.21102i | −0.104170 | + | 0.994560i | ||||
\(40\) | 3.49421 | 0.552483 | ||||||||
\(41\) | 0.966864 | − | 0.966864i | 0.150999 | − | 0.150999i | −0.627565 | − | 0.778564i | \(-0.715948\pi\) |
0.778564 | + | 0.627565i | \(0.215948\pi\) | |||||||
\(42\) | −1.00000 | + | 1.41421i | −0.154303 | + | 0.218218i | ||||
\(43\) | − | 10.3889i | − | 1.58429i | −0.610331 | − | 0.792147i | \(-0.708963\pi\) | ||
0.610331 | − | 0.792147i | \(-0.291037\pi\) | |||||||
\(44\) | 0.976570 | − | 0.976570i | 0.147223 | − | 0.147223i | ||||
\(45\) | −9.45920 | − | 4.51764i | −1.41009 | − | 0.673450i | ||||
\(46\) | 6.34607 | − | 6.34607i | 0.935677 | − | 0.935677i | ||||
\(47\) | 4.24264 | + | 4.24264i | 0.618853 | + | 0.618853i | 0.945237 | − | 0.326384i | \(-0.105830\pi\) |
−0.326384 | + | 0.945237i | \(0.605830\pi\) | |||||||
\(48\) | −1.41421 | − | 1.00000i | −0.204124 | − | 0.144338i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −5.09789 | − | 5.09789i | −0.720950 | − | 0.720950i | ||||
\(51\) | −7.76999 | − | 5.49421i | −1.08802 | − | 0.769343i | ||||
\(52\) | 3.14475 | − | 1.76367i | 0.436098 | − | 0.244577i | ||||
\(53\) | − | 13.9464i | − | 1.91568i | −0.287303 | − | 0.957840i | \(-0.592759\pi\) | ||
0.287303 | − | 0.957840i | \(-0.407241\pi\) | |||||||
\(54\) | 2.53553 | + | 4.53553i | 0.345042 | + | 0.617208i | ||||
\(55\) | −4.82578 | −0.650708 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0.195003 | + | 1.13656i | 0.0258288 | + | 0.150541i | ||||
\(58\) | 1.43764 | + | 1.43764i | 0.188772 | + | 0.188772i | ||||
\(59\) | −8.81685 | − | 8.81685i | −1.14786 | − | 1.14786i | −0.986974 | − | 0.160882i | \(-0.948566\pi\) |
−0.160882 | − | 0.986974i | \(-0.551434\pi\) | |||||||
\(60\) | 1.02343 | + | 5.96499i | 0.132124 | + | 0.770077i | ||||
\(61\) | 13.1347 | 1.68172 | 0.840862 | − | 0.541249i | \(-0.182048\pi\) | ||||
0.840862 | + | 0.541249i | \(0.182048\pi\) | |||||||
\(62\) | 0.828427 | 0.105210 | ||||||||
\(63\) | −2.70711 | − | 1.29289i | −0.341063 | − | 0.162889i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −12.1276 | − | 3.41234i | −1.50425 | − | 0.423249i | ||||
\(66\) | 1.95314 | + | 1.38108i | 0.240415 | + | 0.169999i | ||||
\(67\) | 4.36735 | + | 4.36735i | 0.533557 | + | 0.533557i | 0.921629 | − | 0.388072i | \(-0.126859\pi\) |
−0.388072 | + | 0.921629i | \(0.626859\pi\) | |||||||
\(68\) | 5.49421i | 0.666271i | ||||||||
\(69\) | 12.6921 | + | 8.97470i | 1.52795 | + | 1.08043i | ||||
\(70\) | −2.47078 | − | 2.47078i | −0.295315 | − | 0.295315i | ||||
\(71\) | 0.908424 | − | 0.908424i | 0.107810 | − | 0.107810i | −0.651144 | − | 0.758954i | \(-0.725711\pi\) |
0.758954 | + | 0.651144i | \(0.225711\pi\) | |||||||
\(72\) | 1.29289 | − | 2.70711i | 0.152369 | − | 0.319036i | ||||
\(73\) | −11.0361 | + | 11.0361i | −1.29167 | + | 1.29167i | −0.357921 | + | 0.933752i | \(0.616514\pi\) |
−0.933752 | + | 0.357921i | \(0.883486\pi\) | |||||||
\(74\) | 2.20950i | 0.256850i | ||||||||
\(75\) | 7.20950 | − | 10.1958i | 0.832482 | − | 1.17731i | ||||
\(76\) | 0.470780 | − | 0.470780i | 0.0540021 | − | 0.0540021i | ||||
\(77\) | −1.38108 | −0.157388 | ||||||||
\(78\) | 3.93185 | + | 4.85186i | 0.445195 | + | 0.549365i | ||||
\(79\) | 6.11313 | 0.687781 | 0.343891 | − | 0.939010i | \(-0.388255\pi\) | ||||
0.343891 | + | 0.939010i | \(0.388255\pi\) | |||||||
\(80\) | 2.47078 | − | 2.47078i | 0.276242 | − | 0.276242i | ||||
\(81\) | −7.00000 | + | 5.65685i | −0.777778 | + | 0.628539i | ||||
\(82\) | − | 1.36735i | − | 0.150999i | ||||||
\(83\) | 6.49421 | − | 6.49421i | 0.712832 | − | 0.712832i | −0.254295 | − | 0.967127i | \(-0.581843\pi\) |
0.967127 | + | 0.254295i | \(0.0818433\pi\) | |||||||
\(84\) | 0.292893 | + | 1.70711i | 0.0319573 | + | 0.186261i | ||||
\(85\) | 13.5750 | − | 13.5750i | 1.47241 | − | 1.47241i | ||||
\(86\) | −7.34607 | − | 7.34607i | −0.792147 | − | 0.792147i | ||||
\(87\) | −2.03314 | + | 2.87529i | −0.217975 | + | 0.308263i | ||||
\(88\) | − | 1.38108i | − | 0.147223i | ||||||
\(89\) | 1.74578 | + | 1.74578i | 0.185052 | + | 0.185052i | 0.793553 | − | 0.608501i | \(-0.208229\pi\) |
−0.608501 | + | 0.793553i | \(0.708229\pi\) | |||||||
\(90\) | −9.88312 | + | 3.49421i | −1.04177 | + | 0.368322i | ||||
\(91\) | −3.47078 | − | 0.976570i | −0.363837 | − | 0.102372i | ||||
\(92\) | − | 8.97470i | − | 0.935677i | ||||||
\(93\) | 0.242641 | + | 1.41421i | 0.0251607 | + | 0.146647i | ||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −2.32639 | −0.238682 | ||||||||
\(96\) | −1.70711 | + | 0.292893i | −0.174231 | + | 0.0298933i | ||||
\(97\) | 5.41421 | + | 5.41421i | 0.549730 | + | 0.549730i | 0.926363 | − | 0.376633i | \(-0.122918\pi\) |
−0.376633 | + | 0.926363i | \(0.622918\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | −1.78559 | + | 3.73873i | −0.179458 | + | 0.375756i | ||||
\(100\) | −7.20950 | −0.720950 | ||||||||
\(101\) | 8.53214 | 0.848980 | 0.424490 | − | 0.905433i | \(-0.360453\pi\) | ||||
0.424490 | + | 0.905433i | \(0.360453\pi\) | |||||||
\(102\) | −9.37920 | + | 1.60922i | −0.928680 | + | 0.159336i | ||||
\(103\) | − | 11.7563i | − | 1.15838i | −0.815193 | − | 0.579189i | \(-0.803369\pi\) | ||
0.815193 | − | 0.579189i | \(-0.196631\pi\) | |||||||
\(104\) | 0.976570 | − | 3.47078i | 0.0957605 | − | 0.340338i | ||||
\(105\) | 3.49421 | − | 4.94156i | 0.341000 | − | 0.482247i | ||||
\(106\) | −9.86156 | − | 9.86156i | −0.957840 | − | 0.957840i | ||||
\(107\) | 0.828427i | 0.0800871i | 0.999198 | + | 0.0400435i | \(0.0127497\pi\) | ||||
−0.999198 | + | 0.0400435i | \(0.987250\pi\) | |||||||
\(108\) | 5.00000 | + | 1.41421i | 0.481125 | + | 0.136083i | ||||
\(109\) | 1.62863 | + | 1.62863i | 0.155994 | + | 0.155994i | 0.780789 | − | 0.624795i | \(-0.214817\pi\) |
−0.624795 | + | 0.780789i | \(0.714817\pi\) | |||||||
\(110\) | −3.41234 | + | 3.41234i | −0.325354 | + | 0.325354i | ||||
\(111\) | −3.77186 | + | 0.647149i | −0.358009 | + | 0.0614247i | ||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | 4.48528i | 0.421940i | 0.977493 | + | 0.210970i | \(0.0676622\pi\) | ||||
−0.977493 | + | 0.210970i | \(0.932338\pi\) | |||||||
\(114\) | 0.941559 | + | 0.665783i | 0.0881851 | + | 0.0623563i | ||||
\(115\) | −22.1745 | + | 22.1745i | −2.06778 | + | 2.06778i | ||||
\(116\) | 2.03314 | 0.188772 | ||||||||
\(117\) | −7.13103 | + | 8.13317i | −0.659264 | + | 0.751912i | ||||
\(118\) | −12.4689 | −1.14786 | ||||||||
\(119\) | 3.88499 | − | 3.88499i | 0.356137 | − | 0.356137i | ||||
\(120\) | 4.94156 | + | 3.49421i | 0.451101 | + | 0.318976i | ||||
\(121\) | − | 9.09262i | − | 0.826602i | ||||||
\(122\) | 9.28763 | − | 9.28763i | 0.840862 | − | 0.840862i | ||||
\(123\) | 2.33422 | − | 0.400488i | 0.210469 | − | 0.0361108i | ||||
\(124\) | 0.585786 | − | 0.585786i | 0.0526052 | − | 0.0526052i | ||||
\(125\) | 5.45920 | + | 5.45920i | 0.488286 | + | 0.488286i | ||||
\(126\) | −2.82843 | + | 1.00000i | −0.251976 | + | 0.0890871i | ||||
\(127\) | 19.2437i | 1.70760i | 0.520600 | + | 0.853801i | \(0.325708\pi\) | ||||
−0.520600 | + | 0.853801i | \(0.674292\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 10.3889 | − | 14.6921i | 0.914692 | − | 1.29357i | ||||
\(130\) | −10.9884 | + | 6.16264i | −0.963748 | + | 0.540500i | ||||
\(131\) | 0.778915i | 0.0680542i | 0.999421 | + | 0.0340271i | \(0.0108332\pi\) | ||||
−0.999421 | + | 0.0340271i | \(0.989167\pi\) | |||||||
\(132\) | 2.35765 | − | 0.404508i | 0.205207 | − | 0.0352079i | ||||
\(133\) | −0.665783 | −0.0577307 | ||||||||
\(134\) | 6.17637 | 0.533557 | ||||||||
\(135\) | −8.85969 | − | 15.8481i | −0.762521 | − | 1.36399i | ||||
\(136\) | 3.88499 | + | 3.88499i | 0.333135 | + | 0.333135i | ||||
\(137\) | −4.82655 | − | 4.82655i | −0.412360 | − | 0.412360i | 0.470200 | − | 0.882560i | \(-0.344182\pi\) |
−0.882560 | + | 0.470200i | \(0.844182\pi\) | |||||||
\(138\) | 15.3208 | − | 2.62863i | 1.30419 | − | 0.223764i | ||||
\(139\) | 2.18315 | 0.185173 | 0.0925863 | − | 0.995705i | \(-0.470487\pi\) | ||||
0.0925863 | + | 0.995705i | \(0.470487\pi\) | |||||||
\(140\) | −3.49421 | −0.295315 | ||||||||
\(141\) | 1.75736 | + | 10.2426i | 0.147996 | + | 0.862586i | ||||
\(142\) | − | 1.28471i | − | 0.107810i | ||||||
\(143\) | −1.34872 | + | 4.79342i | −0.112786 | + | 0.400846i | ||||
\(144\) | −1.00000 | − | 2.82843i | −0.0833333 | − | 0.235702i | ||||
\(145\) | −5.02343 | − | 5.02343i | −0.417173 | − | 0.417173i | ||||
\(146\) | 15.6073i | 1.29167i | ||||||||
\(147\) | 1.00000 | − | 1.41421i | 0.0824786 | − | 0.116642i | ||||
\(148\) | 1.56236 | + | 1.56236i | 0.128425 | + | 0.128425i | ||||
\(149\) | 10.5020 | − | 10.5020i | 0.860361 | − | 0.860361i | −0.131019 | − | 0.991380i | \(-0.541825\pi\) |
0.991380 | + | 0.131019i | \(0.0418249\pi\) | |||||||
\(150\) | −2.11162 | − | 12.3074i | −0.172413 | − | 1.00489i | ||||
\(151\) | −8.12763 | + | 8.12763i | −0.661417 | + | 0.661417i | −0.955714 | − | 0.294297i | \(-0.904915\pi\) |
0.294297 | + | 0.955714i | \(0.404915\pi\) | |||||||
\(152\) | − | 0.665783i | − | 0.0540021i | ||||||
\(153\) | −5.49421 | − | 15.5400i | −0.444181 | − | 1.25633i | ||||
\(154\) | −0.976570 | + | 0.976570i | −0.0786942 | + | 0.0786942i | ||||
\(155\) | −2.89470 | −0.232508 | ||||||||
\(156\) | 6.21102 | + | 0.650541i | 0.497280 | + | 0.0520849i | ||||
\(157\) | −3.22412 | −0.257313 | −0.128656 | − | 0.991689i | \(-0.541066\pi\) | ||||
−0.128656 | + | 0.991689i | \(0.541066\pi\) | |||||||
\(158\) | 4.32264 | − | 4.32264i | 0.343891 | − | 0.343891i | ||||
\(159\) | 13.9464 | − | 19.7231i | 1.10602 | − | 1.56415i | ||||
\(160\) | − | 3.49421i | − | 0.276242i | ||||||
\(161\) | −6.34607 | + | 6.34607i | −0.500140 | + | 0.500140i | ||||
\(162\) | −0.949747 | + | 8.94975i | −0.0746192 | + | 0.703159i | ||||
\(163\) | −14.2973 | + | 14.2973i | −1.11985 | + | 1.11985i | −0.128091 | + | 0.991762i | \(0.540885\pi\) |
−0.991762 | + | 0.128091i | \(0.959115\pi\) | |||||||
\(164\) | −0.966864 | − | 0.966864i | −0.0754994 | − | 0.0754994i | ||||
\(165\) | −6.82468 | − | 4.82578i | −0.531300 | − | 0.375686i | ||||
\(166\) | − | 9.18420i | − | 0.712832i | ||||||
\(167\) | −8.20763 | − | 8.20763i | −0.635126 | − | 0.635126i | 0.314224 | − | 0.949349i | \(-0.398256\pi\) |
−0.949349 | + | 0.314224i | \(0.898256\pi\) | |||||||
\(168\) | 1.41421 | + | 1.00000i | 0.109109 | + | 0.0771517i | ||||
\(169\) | −6.77892 | + | 11.0926i | −0.521455 | + | 0.853279i | ||||
\(170\) | − | 19.1979i | − | 1.47241i | ||||||
\(171\) | −0.860786 | + | 1.80235i | −0.0658260 | + | 0.137829i | ||||
\(172\) | −10.3889 | −0.792147 | ||||||||
\(173\) | 1.08744 | 0.0826768 | 0.0413384 | − | 0.999145i | \(-0.486838\pi\) | ||||
0.0413384 | + | 0.999145i | \(0.486838\pi\) | |||||||
\(174\) | 0.595492 | + | 3.47078i | 0.0451441 | + | 0.263119i | ||||
\(175\) | 5.09789 | + | 5.09789i | 0.385364 | + | 0.385364i | ||||
\(176\) | −0.976570 | − | 0.976570i | −0.0736117 | − | 0.0736117i | ||||
\(177\) | −3.65206 | − | 21.2858i | −0.274505 | − | 1.59994i | ||||
\(178\) | 2.46891 | 0.185052 | ||||||||
\(179\) | 5.12471 | 0.383039 | 0.191519 | − | 0.981489i | \(-0.438658\pi\) | ||||
0.191519 | + | 0.981489i | \(0.438658\pi\) | |||||||
\(180\) | −4.51764 | + | 9.45920i | −0.336725 | + | 0.705047i | ||||
\(181\) | − | 14.2895i | − | 1.06213i | −0.847331 | − | 0.531065i | \(-0.821792\pi\) | ||
0.847331 | − | 0.531065i | \(-0.178208\pi\) | |||||||
\(182\) | −3.14475 | + | 1.76367i | −0.233104 | + | 0.130732i | ||||
\(183\) | 18.5753 | + | 13.1347i | 1.37312 | + | 0.970944i | ||||
\(184\) | −6.34607 | − | 6.34607i | −0.467838 | − | 0.467838i | ||||
\(185\) | − | 7.72047i | − | 0.567621i | ||||||
\(186\) | 1.17157 | + | 0.828427i | 0.0859039 | + | 0.0607432i | ||||
\(187\) | −5.36548 | − | 5.36548i | −0.392363 | − | 0.392363i | ||||
\(188\) | 4.24264 | − | 4.24264i | 0.309426 | − | 0.309426i | ||||
\(189\) | −2.53553 | − | 4.53553i | −0.184433 | − | 0.329912i | ||||
\(190\) | −1.64500 | + | 1.64500i | −0.119341 | + | 0.119341i | ||||
\(191\) | 17.6200i | 1.27494i | 0.770477 | + | 0.637468i | \(0.220018\pi\) | ||||
−0.770477 | + | 0.637468i | \(0.779982\pi\) | |||||||
\(192\) | −1.00000 | + | 1.41421i | −0.0721688 | + | 0.102062i | ||||
\(193\) | 15.2058 | − | 15.2058i | 1.09453 | − | 1.09453i | 0.0994964 | − | 0.995038i | \(-0.468277\pi\) |
0.995038 | − | 0.0994964i | \(-0.0317232\pi\) | |||||||
\(194\) | 7.65685 | 0.549730 | ||||||||
\(195\) | −13.7387 | − | 16.9534i | −0.983851 | − | 1.21406i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 11.3111 | − | 11.3111i | 0.805879 | − | 0.805879i | −0.178128 | − | 0.984007i | \(-0.557004\pi\) |
0.984007 | + | 0.178128i | \(0.0570041\pi\) | |||||||
\(198\) | 1.38108 | + | 3.90628i | 0.0981489 | + | 0.277607i | ||||
\(199\) | 13.9394i | 0.988139i | 0.869422 | + | 0.494069i | \(0.164491\pi\) | ||||
−0.869422 | + | 0.494069i | \(0.835509\pi\) | |||||||
\(200\) | −5.09789 | + | 5.09789i | −0.360475 | + | 0.360475i | ||||
\(201\) | 1.80902 | + | 10.5437i | 0.127598 | + | 0.743697i | ||||
\(202\) | 6.03314 | − | 6.03314i | 0.424490 | − | 0.424490i | ||||
\(203\) | −1.43764 | − | 1.43764i | −0.100903 | − | 0.100903i | ||||
\(204\) | −5.49421 | + | 7.76999i | −0.384672 | + | 0.544008i | ||||
\(205\) | 4.77782i | 0.333697i | ||||||||
\(206\) | −8.31293 | − | 8.31293i | −0.579189 | − | 0.579189i | ||||
\(207\) | 8.97470 | + | 25.3843i | 0.623784 | + | 1.76433i | ||||
\(208\) | −1.76367 | − | 3.14475i | −0.122289 | − | 0.218049i | ||||
\(209\) | 0.919498i | 0.0636030i | ||||||||
\(210\) | −1.02343 | − | 5.96499i | −0.0706234 | − | 0.411623i | ||||
\(211\) | −8.09637 | −0.557377 | −0.278689 | − | 0.960382i | \(-0.589900\pi\) | ||||
−0.278689 | + | 0.960382i | \(0.589900\pi\) | |||||||
\(212\) | −13.9464 | −0.957840 | ||||||||
\(213\) | 2.19313 | − | 0.376281i | 0.150271 | − | 0.0257824i | ||||
\(214\) | 0.585786 | + | 0.585786i | 0.0400435 | + | 0.0400435i | ||||
\(215\) | 25.6687 | + | 25.6687i | 1.75059 | + | 1.75059i | ||||
\(216\) | 4.53553 | − | 2.53553i | 0.308604 | − | 0.172521i | ||||
\(217\) | −0.828427 | −0.0562373 | ||||||||
\(218\) | 2.30323 | 0.155994 | ||||||||
\(219\) | −26.6434 | + | 4.57128i | −1.80039 | + | 0.308899i | ||||
\(220\) | 4.82578i | 0.325354i | ||||||||
\(221\) | −9.68999 | − | 17.2779i | −0.651819 | − | 1.16224i | ||||
\(222\) | −2.20950 | + | 3.12471i | −0.148292 | + | 0.209717i | ||||
\(223\) | 8.52949 | + | 8.52949i | 0.571177 | + | 0.571177i | 0.932457 | − | 0.361280i | \(-0.117660\pi\) |
−0.361280 | + | 0.932457i | \(0.617660\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 20.3916 | − | 7.20950i | 1.35944 | − | 0.480634i | ||||
\(226\) | 3.17157 | + | 3.17157i | 0.210970 | + | 0.210970i | ||||
\(227\) | −16.8831 | + | 16.8831i | −1.12057 | + | 1.12057i | −0.128917 | + | 0.991655i | \(0.541150\pi\) |
−0.991655 | + | 0.128917i | \(0.958850\pi\) | |||||||
\(228\) | 1.13656 | − | 0.195003i | 0.0752707 | − | 0.0129144i | ||||
\(229\) | 0.715295 | − | 0.715295i | 0.0472680 | − | 0.0472680i | −0.683078 | − | 0.730346i | \(-0.739359\pi\) |
0.730346 | + | 0.683078i | \(0.239359\pi\) | |||||||
\(230\) | 31.3595i | 2.06778i | ||||||||
\(231\) | −1.95314 | − | 1.38108i | −0.128507 | − | 0.0908683i | ||||
\(232\) | 1.43764 | − | 1.43764i | 0.0943860 | − | 0.0943860i | ||||
\(233\) | −16.8753 | −1.10554 | −0.552768 | − | 0.833335i | \(-0.686429\pi\) | ||||
−0.552768 | + | 0.833335i | \(0.686429\pi\) | |||||||
\(234\) | 0.708624 | + | 10.7934i | 0.0463242 | + | 0.705588i | ||||
\(235\) | −20.9653 | −1.36762 | ||||||||
\(236\) | −8.81685 | + | 8.81685i | −0.573928 | + | 0.573928i | ||||
\(237\) | 8.64527 | + | 6.11313i | 0.561571 | + | 0.397091i | ||||
\(238\) | − | 5.49421i | − | 0.356137i | ||||||
\(239\) | −13.8168 | + | 13.8168i | −0.893738 | + | 0.893738i | −0.994873 | − | 0.101135i | \(-0.967753\pi\) |
0.101135 | + | 0.994873i | \(0.467753\pi\) | |||||||
\(240\) | 5.96499 | − | 1.02343i | 0.385038 | − | 0.0660622i | ||||
\(241\) | 6.95794 | − | 6.95794i | 0.448200 | − | 0.448200i | −0.446556 | − | 0.894756i | \(-0.647350\pi\) |
0.894756 | + | 0.446556i | \(0.147350\pi\) | |||||||
\(242\) | −6.42946 | − | 6.42946i | −0.413301 | − | 0.413301i | ||||
\(243\) | −15.5563 | + | 1.00000i | −0.997940 | + | 0.0641500i | ||||
\(244\) | − | 13.1347i | − | 0.840862i | ||||||
\(245\) | 2.47078 | + | 2.47078i | 0.157852 | + | 0.157852i | ||||
\(246\) | 1.36735 | − | 1.93373i | 0.0871792 | − | 0.123290i | ||||
\(247\) | −0.650183 | + | 2.31079i | −0.0413702 | + | 0.147032i | ||||
\(248\) | − | 0.828427i | − | 0.0526052i | ||||||
\(249\) | 15.6784 | − | 2.68999i | 0.993579 | − | 0.170471i | ||||
\(250\) | 7.72047 | 0.488286 | ||||||||
\(251\) | 22.7611 | 1.43667 | 0.718333 | − | 0.695700i | \(-0.244906\pi\) | ||||
0.718333 | + | 0.695700i | \(0.244906\pi\) | |||||||
\(252\) | −1.29289 | + | 2.70711i | −0.0814446 | + | 0.170532i | ||||
\(253\) | 8.76441 | + | 8.76441i | 0.551014 | + | 0.551014i | ||||
\(254\) | 13.6073 | + | 13.6073i | 0.853801 | + | 0.853801i | ||||
\(255\) | 32.7729 | − | 5.62294i | 2.05232 | − | 0.352122i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.59058 | 0.348731 | 0.174365 | − | 0.984681i | \(-0.444213\pi\) | ||||
0.174365 | + | 0.984681i | \(0.444213\pi\) | |||||||
\(258\) | −3.04284 | − | 17.7350i | −0.189439 | − | 1.10413i | ||||
\(259\) | − | 2.20950i | − | 0.137292i | ||||||
\(260\) | −3.41234 | + | 12.1276i | −0.211624 | + | 0.752124i | ||||
\(261\) | −5.75058 | + | 2.03314i | −0.355952 | + | 0.125848i | ||||
\(262\) | 0.550776 | + | 0.550776i | 0.0340271 | + | 0.0340271i | ||||
\(263\) | − | 12.6052i | − | 0.777270i | −0.921392 | − | 0.388635i | \(-0.872947\pi\) | ||
0.921392 | − | 0.388635i | \(-0.127053\pi\) | |||||||
\(264\) | 1.38108 | − | 1.95314i | 0.0849995 | − | 0.120207i | ||||
\(265\) | 34.4584 | + | 34.4584i | 2.11676 | + | 2.11676i | ||||
\(266\) | −0.470780 | + | 0.470780i | −0.0288654 | + | 0.0288654i | ||||
\(267\) | 0.723126 | + | 4.21469i | 0.0442546 | + | 0.257935i | ||||
\(268\) | 4.36735 | − | 4.36735i | 0.266779 | − | 0.266779i | ||||
\(269\) | 2.87529i | 0.175309i | 0.996151 | + | 0.0876547i | \(0.0279372\pi\) | ||||
−0.996151 | + | 0.0876547i | \(0.972063\pi\) | |||||||
\(270\) | −17.4711 | − | 4.94156i | −1.06325 | − | 0.300734i | ||||
\(271\) | −0.505790 | + | 0.505790i | −0.0307245 | + | 0.0307245i | −0.722302 | − | 0.691578i | \(-0.756916\pi\) |
0.691578 | + | 0.722302i | \(0.256916\pi\) | |||||||
\(272\) | 5.49421 | 0.333135 | ||||||||
\(273\) | −3.93185 | − | 4.85186i | −0.237967 | − | 0.293648i | ||||
\(274\) | −6.82578 | −0.412360 | ||||||||
\(275\) | 7.04058 | − | 7.04058i | 0.424563 | − | 0.424563i | ||||
\(276\) | 8.97470 | − | 12.6921i | 0.540213 | − | 0.763977i | ||||
\(277\) | 7.68056i | 0.461480i | 0.973015 | + | 0.230740i | \(0.0741147\pi\) | ||||
−0.973015 | + | 0.230740i | \(0.925885\pi\) | |||||||
\(278\) | 1.54372 | − | 1.54372i | 0.0925863 | − | 0.0925863i | ||||
\(279\) | −1.07107 | + | 2.24264i | −0.0641232 | + | 0.134263i | ||||
\(280\) | −2.47078 | + | 2.47078i | −0.147657 | + | 0.147657i | ||||
\(281\) | −2.76519 | − | 2.76519i | −0.164957 | − | 0.164957i | 0.619801 | − | 0.784759i | \(-0.287213\pi\) |
−0.784759 | + | 0.619801i | \(0.787213\pi\) | |||||||
\(282\) | 8.48528 | + | 6.00000i | 0.505291 | + | 0.357295i | ||||
\(283\) | − | 32.2500i | − | 1.91706i | −0.284989 | − | 0.958531i | \(-0.591990\pi\) | ||
0.284989 | − | 0.958531i | \(-0.408010\pi\) | |||||||
\(284\) | −0.908424 | − | 0.908424i | −0.0539050 | − | 0.0539050i | ||||
\(285\) | −3.29001 | − | 2.32639i | −0.194883 | − | 0.137803i | ||||
\(286\) | 2.43577 | + | 4.34315i | 0.144030 | + | 0.256816i | ||||
\(287\) | 1.36735i | 0.0807123i | ||||||||
\(288\) | −2.70711 | − | 1.29289i | −0.159518 | − | 0.0761845i | ||||
\(289\) | 13.1863 | 0.775667 | ||||||||
\(290\) | −7.10420 | −0.417173 | ||||||||
\(291\) | 2.24264 | + | 13.0711i | 0.131466 | + | 0.766240i | ||||
\(292\) | 11.0361 | + | 11.0361i | 0.645836 | + | 0.645836i | ||||
\(293\) | 3.19098 | + | 3.19098i | 0.186419 | + | 0.186419i | 0.794146 | − | 0.607727i | \(-0.207918\pi\) |
−0.607727 | + | 0.794146i | \(0.707918\pi\) | |||||||
\(294\) | −0.292893 | − | 1.70711i | −0.0170819 | − | 0.0995605i | ||||
\(295\) | 43.5690 | 2.53668 | ||||||||
\(296\) | 2.20950 | 0.128425 | ||||||||
\(297\) | −6.26393 | + | 3.50177i | −0.363470 | + | 0.203193i | ||||
\(298\) | − | 14.8521i | − | 0.860361i | ||||||
\(299\) | 15.8284 | + | 28.2232i | 0.915382 | + | 1.63219i | ||||
\(300\) | −10.1958 | − | 7.20950i | −0.588654 | − | 0.416241i | ||||
\(301\) | 7.34607 | + | 7.34607i | 0.423420 | + | 0.423420i | ||||
\(302\) | 11.4942i | 0.661417i | ||||||||
\(303\) | 12.0663 | + | 8.53214i | 0.693189 | + | 0.490159i | ||||
\(304\) | −0.470780 | − | 0.470780i | −0.0270011 | − | 0.0270011i | ||||
\(305\) | −32.4529 | + | 32.4529i | −1.85825 | + | 1.85825i | ||||
\(306\) | −14.8734 | − | 7.10343i | −0.850256 | − | 0.406076i | ||||
\(307\) | 7.47745 | − | 7.47745i | 0.426761 | − | 0.426761i | −0.460763 | − | 0.887523i | \(-0.652424\pi\) |
0.887523 | + | 0.460763i | \(0.152424\pi\) | |||||||
\(308\) | 1.38108i | 0.0786942i | ||||||||
\(309\) | 11.7563 | − | 16.6259i | 0.668790 | − | 0.945812i | ||||
\(310\) | −2.04686 | + | 2.04686i | −0.116254 | + | 0.116254i | ||||
\(311\) | 8.80902 | 0.499514 | 0.249757 | − | 0.968309i | \(-0.419649\pi\) | ||||
0.249757 | + | 0.968309i | \(0.419649\pi\) | |||||||
\(312\) | 4.85186 | − | 3.93185i | 0.274682 | − | 0.222597i | ||||
\(313\) | 24.7310 | 1.39788 | 0.698938 | − | 0.715182i | \(-0.253656\pi\) | ||||
0.698938 | + | 0.715182i | \(0.253656\pi\) | |||||||
\(314\) | −2.27980 | + | 2.27980i | −0.128656 | + | 0.128656i | ||||
\(315\) | 9.88312 | − | 3.49421i | 0.556851 | − | 0.196876i | ||||
\(316\) | − | 6.11313i | − | 0.343891i | ||||||
\(317\) | −2.05949 | + | 2.05949i | −0.115672 | + | 0.115672i | −0.762574 | − | 0.646901i | \(-0.776065\pi\) |
0.646901 | + | 0.762574i | \(0.276065\pi\) | |||||||
\(318\) | −4.08479 | − | 23.8079i | −0.229064 | − | 1.33508i | ||||
\(319\) | −1.98550 | + | 1.98550i | −0.111167 | + | 0.111167i | ||||
\(320\) | −2.47078 | − | 2.47078i | −0.138121 | − | 0.138121i | ||||
\(321\) | −0.828427 | + | 1.17157i | −0.0462383 | + | 0.0653908i | ||||
\(322\) | 8.97470i | 0.500140i | ||||||||
\(323\) | −2.58656 | − | 2.58656i | −0.143920 | − | 0.143920i | ||||
\(324\) | 5.65685 | + | 7.00000i | 0.314270 | + | 0.388889i | ||||
\(325\) | 22.6721 | − | 12.7152i | 1.25762 | − | 0.705313i | ||||
\(326\) | 20.2195i | 1.11985i | ||||||||
\(327\) | 0.674600 | + | 3.93185i | 0.0373054 | + | 0.217432i | ||||
\(328\) | −1.36735 | −0.0754994 | ||||||||
\(329\) | −6.00000 | −0.330791 | ||||||||
\(330\) | −8.23812 | + | 1.41344i | −0.453493 | + | 0.0778072i | ||||
\(331\) | 2.48048 | + | 2.48048i | 0.136340 | + | 0.136340i | 0.771983 | − | 0.635643i | \(-0.219265\pi\) |
−0.635643 | + | 0.771983i | \(0.719265\pi\) | |||||||
\(332\) | −6.49421 | − | 6.49421i | −0.356416 | − | 0.356416i | ||||
\(333\) | −5.98137 | − | 2.85665i | −0.327777 | − | 0.156544i | ||||
\(334\) | −11.6073 | −0.635126 | ||||||||
\(335\) | −21.5815 | −1.17913 | ||||||||
\(336\) | 1.70711 | − | 0.292893i | 0.0931303 | − | 0.0159786i | ||||
\(337\) | − | 4.80207i | − | 0.261586i | −0.991410 | − | 0.130793i | \(-0.958248\pi\) | ||
0.991410 | − | 0.130793i | \(-0.0417523\pi\) | |||||||
\(338\) | 3.05025 | + | 12.6371i | 0.165912 | + | 0.687367i | ||||
\(339\) | −4.48528 | + | 6.34315i | −0.243607 | + | 0.344512i | ||||
\(340\) | −13.5750 | − | 13.5750i | −0.736207 | − | 0.736207i | ||||
\(341\) | 1.14412i | 0.0619577i | ||||||||
\(342\) | 0.665783 | + | 1.88312i | 0.0360014 | + | 0.101827i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | −7.34607 | + | 7.34607i | −0.396073 | + | 0.396073i | ||||
\(345\) | −53.5340 | + | 9.18498i | −2.88217 | + | 0.494503i | ||||
\(346\) | 0.768939 | − | 0.768939i | 0.0413384 | − | 0.0413384i | ||||
\(347\) | − | 14.6453i | − | 0.786200i | −0.919496 | − | 0.393100i | \(-0.871403\pi\) | ||
0.919496 | − | 0.393100i | \(-0.128597\pi\) | |||||||
\(348\) | 2.87529 | + | 2.03314i | 0.154132 | + | 0.108988i | ||||
\(349\) | 5.21734 | − | 5.21734i | 0.279278 | − | 0.279278i | −0.553543 | − | 0.832821i | \(-0.686725\pi\) |
0.832821 | + | 0.553543i | \(0.186725\pi\) | |||||||
\(350\) | 7.20950 | 0.385364 | ||||||||
\(351\) | −18.2180 | + | 4.37102i | −0.972403 | + | 0.233308i | ||||
\(352\) | −1.38108 | −0.0736117 | ||||||||
\(353\) | 8.13734 | − | 8.13734i | 0.433107 | − | 0.433107i | −0.456577 | − | 0.889684i | \(-0.650925\pi\) |
0.889684 | + | 0.456577i | \(0.150925\pi\) | |||||||
\(354\) | −17.6337 | − | 12.4689i | −0.937220 | − | 0.662715i | ||||
\(355\) | 4.48903i | 0.238253i | ||||||||
\(356\) | 1.74578 | − | 1.74578i | 0.0925261 | − | 0.0925261i | ||||
\(357\) | 9.37920 | − | 1.60922i | 0.496400 | − | 0.0851688i | ||||
\(358\) | 3.62372 | − | 3.62372i | 0.191519 | − | 0.191519i | ||||
\(359\) | 13.4600 | + | 13.4600i | 0.710390 | + | 0.710390i | 0.966617 | − | 0.256226i | \(-0.0824793\pi\) |
−0.256226 | + | 0.966617i | \(0.582479\pi\) | |||||||
\(360\) | 3.49421 | + | 9.88312i | 0.184161 | + | 0.520886i | ||||
\(361\) | − | 18.5567i | − | 0.976670i | ||||||
\(362\) | −10.1042 | − | 10.1042i | −0.531065 | − | 0.531065i | ||||
\(363\) | 9.09262 | − | 12.8589i | 0.477239 | − | 0.674918i | ||||
\(364\) | −0.976570 | + | 3.47078i | −0.0511862 | + | 0.181918i | ||||
\(365\) | − | 54.5353i | − | 2.85451i | ||||||
\(366\) | 22.4223 | − | 3.84706i | 1.17203 | − | 0.201089i | ||||
\(367\) | −28.1220 | −1.46796 | −0.733979 | − | 0.679173i | \(-0.762339\pi\) | ||||
−0.733979 | + | 0.679173i | \(0.762339\pi\) | |||||||
\(368\) | −8.97470 | −0.467838 | ||||||||
\(369\) | 3.70157 | + | 1.76784i | 0.192696 | + | 0.0920301i | ||||
\(370\) | −5.45920 | − | 5.45920i | −0.283810 | − | 0.283810i | ||||
\(371\) | 9.86156 | + | 9.86156i | 0.511987 | + | 0.511987i | ||||
\(372\) | 1.41421 | − | 0.242641i | 0.0733236 | − | 0.0125803i | ||||
\(373\) | −1.28471 | −0.0665195 | −0.0332598 | − | 0.999447i | \(-0.510589\pi\) | ||||
−0.0332598 | + | 0.999447i | \(0.510589\pi\) | |||||||
\(374\) | −7.58793 | −0.392363 | ||||||||
\(375\) | 2.26127 | + | 13.1797i | 0.116772 | + | 0.680595i | ||||
\(376\) | − | 6.00000i | − | 0.309426i | ||||||
\(377\) | −6.39371 | + | 3.58579i | −0.329293 | + | 0.184677i | ||||
\(378\) | −5.00000 | − | 1.41421i | −0.257172 | − | 0.0727393i | ||||
\(379\) | 7.53627 | + | 7.53627i | 0.387112 | + | 0.387112i | 0.873656 | − | 0.486544i | \(-0.161743\pi\) |
−0.486544 | + | 0.873656i | \(0.661743\pi\) | |||||||
\(380\) | 2.32639i | 0.119341i | ||||||||
\(381\) | −19.2437 | + | 27.2147i | −0.985884 | + | 1.39425i | ||||
\(382\) | 12.4592 | + | 12.4592i | 0.637468 | + | 0.637468i | ||||
\(383\) | −2.37137 | + | 2.37137i | −0.121171 | + | 0.121171i | −0.765092 | − | 0.643921i | \(-0.777307\pi\) |
0.643921 | + | 0.765092i | \(0.277307\pi\) | |||||||
\(384\) | 0.292893 | + | 1.70711i | 0.0149466 | + | 0.0871154i | ||||
\(385\) | 3.41234 | − | 3.41234i | 0.173909 | − | 0.173909i | ||||
\(386\) | − | 21.5042i | − | 1.09453i | ||||||
\(387\) | 29.3843 | − | 10.3889i | 1.49369 | − | 0.528098i | ||||
\(388\) | 5.41421 | − | 5.41421i | 0.274865 | − | 0.274865i | ||||
\(389\) | −19.0189 | −0.964297 | −0.482148 | − | 0.876090i | \(-0.660143\pi\) | ||||
−0.482148 | + | 0.876090i | \(0.660143\pi\) | |||||||
\(390\) | −21.7026 | − | 2.27313i | −1.09895 | − | 0.115104i | ||||
\(391\) | −49.3089 | −2.49366 | ||||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −0.778915 | + | 1.10155i | −0.0392911 | + | 0.0555660i | ||||
\(394\) | − | 15.9963i | − | 0.805879i | ||||||
\(395\) | −15.1042 | + | 15.1042i | −0.759975 | + | 0.759975i | ||||
\(396\) | 3.73873 | + | 1.78559i | 0.187878 | + | 0.0897291i | ||||
\(397\) | −20.6121 | + | 20.6121i | −1.03449 | + | 1.03449i | −0.0351102 | + | 0.999383i | \(0.511178\pi\) |
−0.999383 | + | 0.0351102i | \(0.988822\pi\) | |||||||
\(398\) | 9.85665 | + | 9.85665i | 0.494069 | + | 0.494069i | ||||
\(399\) | −0.941559 | − | 0.665783i | −0.0471369 | − | 0.0333308i | ||||
\(400\) | 7.20950i | 0.360475i | ||||||||
\(401\) | 26.4689 | + | 26.4689i | 1.32179 | + | 1.32179i | 0.912323 | + | 0.409471i | \(0.134287\pi\) |
0.409471 | + | 0.912323i | \(0.365713\pi\) | |||||||
\(402\) | 8.73471 | + | 6.17637i | 0.435648 | + | 0.308049i | ||||
\(403\) | −0.809017 | + | 2.87529i | −0.0403000 | + | 0.143228i | ||||
\(404\) | − | 8.53214i | − | 0.424490i | ||||||
\(405\) | 3.31862 | − | 31.2723i | 0.164903 | − | 1.55393i | ||||
\(406\) | −2.03314 | −0.100903 | ||||||||
\(407\) | −3.05150 | −0.151257 | ||||||||
\(408\) | 1.60922 | + | 9.37920i | 0.0796681 | + | 0.464340i | ||||
\(409\) | −20.0008 | − | 20.0008i | −0.988975 | − | 0.988975i | 0.0109651 | − | 0.999940i | \(-0.496510\pi\) |
−0.999940 | + | 0.0109651i | \(0.996510\pi\) | |||||||
\(410\) | 3.37843 | + | 3.37843i | 0.166849 | + | 0.166849i | ||||
\(411\) | −1.99922 | − | 11.6523i | −0.0986144 | − | 0.574767i | ||||
\(412\) | −11.7563 | −0.579189 | ||||||||
\(413\) | 12.4689 | 0.613555 | ||||||||
\(414\) | 24.2955 | + | 11.6033i | 1.19406 | + | 0.570272i | ||||
\(415\) | 32.0915i | 1.57531i | ||||||||
\(416\) | −3.47078 | − | 0.976570i | −0.170169 | − | 0.0478803i | ||||
\(417\) | 3.08744 | + | 2.18315i | 0.151193 | + | 0.106909i | ||||
\(418\) | 0.650183 | + | 0.650183i | 0.0318015 | + | 0.0318015i | ||||
\(419\) | 9.86636i | 0.482003i | 0.970525 | + | 0.241002i | \(0.0774759\pi\) | ||||
−0.970525 | + | 0.241002i | \(0.922524\pi\) | |||||||
\(420\) | −4.94156 | − | 3.49421i | −0.241123 | − | 0.170500i | ||||
\(421\) | −17.4767 | − | 17.4767i | −0.851764 | − | 0.851764i | 0.138586 | − | 0.990350i | \(-0.455744\pi\) |
−0.990350 | + | 0.138586i | \(0.955744\pi\) | |||||||
\(422\) | −5.72500 | + | 5.72500i | −0.278689 | + | 0.278689i | ||||
\(423\) | −7.75736 | + | 16.2426i | −0.377176 | + | 0.789744i | ||||
\(424\) | −9.86156 | + | 9.86156i | −0.478920 | + | 0.478920i | ||||
\(425\) | 39.6105i | 1.92139i | ||||||||
\(426\) | 1.28471 | − | 1.81685i | 0.0622442 | − | 0.0880266i | ||||
\(427\) | −9.28763 | + | 9.28763i | −0.449460 | + | 0.449460i | ||||
\(428\) | 0.828427 | 0.0400435 | ||||||||
\(429\) | −6.70079 | + | 5.43020i | −0.323517 | + | 0.262172i | ||||
\(430\) | 36.3010 | 1.75059 | ||||||||
\(431\) | 23.5563 | − | 23.5563i | 1.13467 | − | 1.13467i | 0.145279 | − | 0.989391i | \(-0.453592\pi\) |
0.989391 | − | 0.145279i | \(-0.0464079\pi\) | |||||||
\(432\) | 1.41421 | − | 5.00000i | 0.0680414 | − | 0.240563i | ||||
\(433\) | − | 14.0000i | − | 0.672797i | −0.941720 | − | 0.336399i | \(-0.890791\pi\) | ||
0.941720 | − | 0.336399i | \(-0.109209\pi\) | |||||||
\(434\) | −0.585786 | + | 0.585786i | −0.0281186 | + | 0.0281186i | ||||
\(435\) | −2.08077 | − | 12.1276i | −0.0997654 | − | 0.581476i | ||||
\(436\) | 1.62863 | − | 1.62863i | 0.0779971 | − | 0.0779971i | ||||
\(437\) | 4.22510 | + | 4.22510i | 0.202114 | + | 0.202114i | ||||
\(438\) | −15.6073 | + | 22.0721i | −0.745748 | + | 1.05465i | ||||
\(439\) | 3.38996i | 0.161794i | 0.996722 | + | 0.0808969i | \(0.0257785\pi\) | ||||
−0.996722 | + | 0.0808969i | \(0.974222\pi\) | |||||||
\(440\) | 3.41234 | + | 3.41234i | 0.162677 | + | 0.162677i | ||||
\(441\) | 2.82843 | − | 1.00000i | 0.134687 | − | 0.0476190i | ||||
\(442\) | −19.0692 | − | 5.36548i | −0.907029 | − | 0.255210i | ||||
\(443\) | − | 13.2810i | − | 0.630997i | −0.948926 | − | 0.315499i | \(-0.897828\pi\) | ||
0.948926 | − | 0.315499i | \(-0.102172\pi\) | |||||||
\(444\) | 0.647149 | + | 3.77186i | 0.0307123 | + | 0.179005i | ||||
\(445\) | −8.62687 | −0.408953 | ||||||||
\(446\) | 12.0625 | 0.571177 | ||||||||
\(447\) | 25.3542 | − | 4.35009i | 1.19921 | − | 0.205752i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 5.79556 | + | 5.79556i | 0.273510 | + | 0.273510i | 0.830511 | − | 0.557002i | \(-0.188048\pi\) |
−0.557002 | + | 0.830511i | \(0.688048\pi\) | |||||||
\(450\) | 9.32112 | − | 19.5169i | 0.439402 | − | 0.920035i | ||||
\(451\) | 1.88842 | 0.0889222 | ||||||||
\(452\) | 4.48528 | 0.210970 | ||||||||
\(453\) | −19.6218 | + | 3.36658i | −0.921915 | + | 0.158176i | ||||
\(454\) | 23.8763i | 1.12057i | ||||||||
\(455\) | 10.9884 | − | 6.16264i | 0.515145 | − | 0.288909i | ||||
\(456\) | 0.665783 | − | 0.941559i | 0.0311781 | − | 0.0440926i | ||||
\(457\) | −17.9211 | − | 17.9211i | −0.838311 | − | 0.838311i | 0.150325 | − | 0.988637i | \(-0.451968\pi\) |
−0.988637 | + | 0.150325i | \(0.951968\pi\) | |||||||
\(458\) | − | 1.01158i | − | 0.0472680i | ||||||
\(459\) | 7.76999 | − | 27.4711i | 0.362672 | − | 1.28224i | ||||
\(460\) | 22.1745 | + | 22.1745i | 1.03389 | + | 1.03389i | ||||
\(461\) | −8.77291 | + | 8.77291i | −0.408595 | + | 0.408595i | −0.881248 | − | 0.472653i | \(-0.843296\pi\) |
0.472653 | + | 0.881248i | \(0.343296\pi\) | |||||||
\(462\) | −2.35765 | + | 0.404508i | −0.109688 | + | 0.0188194i | ||||
\(463\) | −1.52922 | + | 1.52922i | −0.0710689 | + | 0.0710689i | −0.741748 | − | 0.670679i | \(-0.766003\pi\) |
0.670679 | + | 0.741748i | \(0.266003\pi\) | |||||||
\(464\) | − | 2.03314i | − | 0.0943860i | ||||||
\(465\) | −4.09372 | − | 2.89470i | −0.189842 | − | 0.134238i | ||||
\(466\) | −11.9326 | + | 11.9326i | −0.552768 | + | 0.552768i | ||||
\(467\) | −15.8432 | −0.733136 | −0.366568 | − | 0.930391i | \(-0.619467\pi\) | ||||
−0.366568 | + | 0.930391i | \(0.619467\pi\) | |||||||
\(468\) | 8.13317 | + | 7.13103i | 0.375956 | + | 0.329632i | ||||
\(469\) | −6.17637 | −0.285198 | ||||||||
\(470\) | −14.8247 | + | 14.8247i | −0.683811 | + | 0.683811i | ||||
\(471\) | −4.55959 | − | 3.22412i | −0.210095 | − | 0.148560i | ||||
\(472\) | 12.4689i | 0.573928i | ||||||||
\(473\) | 10.1455 | − | 10.1455i | 0.466490 | − | 0.466490i | ||||
\(474\) | 10.4358 | − | 1.79050i | 0.479331 | − | 0.0822402i | ||||
\(475\) | 3.39409 | − | 3.39409i | 0.155731 | − | 0.155731i | ||||
\(476\) | −3.88499 | − | 3.88499i | −0.178068 | − | 0.178068i | ||||
\(477\) | 39.4463 | − | 13.9464i | 1.80612 | − | 0.638560i | ||||
\(478\) | 19.5400i | 0.893738i | ||||||||
\(479\) | −27.1217 | − | 27.1217i | −1.23922 | − | 1.23922i | −0.960319 | − | 0.278905i | \(-0.910028\pi\) |
−0.278905 | − | 0.960319i | \(-0.589972\pi\) | |||||||
\(480\) | 3.49421 | − | 4.94156i | 0.159488 | − | 0.225550i | ||||
\(481\) | −7.66871 | − | 2.15774i | −0.349663 | − | 0.0983843i | ||||
\(482\) | − | 9.84001i | − | 0.448200i | ||||||
\(483\) | −15.3208 | + | 2.62863i | −0.697119 | + | 0.119607i | ||||
\(484\) | −9.09262 | −0.413301 | ||||||||
\(485\) | −26.7547 | −1.21487 | ||||||||
\(486\) | −10.2929 | + | 11.7071i | −0.466895 | + | 0.531045i | ||||
\(487\) | 9.05844 | + | 9.05844i | 0.410477 | + | 0.410477i | 0.881905 | − | 0.471428i | \(-0.156261\pi\) |
−0.471428 | + | 0.881905i | \(0.656261\pi\) | |||||||
\(488\) | −9.28763 | − | 9.28763i | −0.420431 | − | 0.420431i | ||||
\(489\) | −34.5168 | + | 5.92215i | −1.56090 | + | 0.267809i | ||||
\(490\) | 3.49421 | 0.157852 | ||||||||
\(491\) | −21.6100 | −0.975245 | −0.487623 | − | 0.873054i | \(-0.662136\pi\) | ||||
−0.487623 | + | 0.873054i | \(0.662136\pi\) | |||||||
\(492\) | −0.400488 | − | 2.33422i | −0.0180554 | − | 0.105235i | ||||
\(493\) | − | 11.1705i | − | 0.503093i | ||||||
\(494\) | 1.17422 | + | 2.09372i | 0.0528308 | + | 0.0942010i | ||||
\(495\) | −4.82578 | − | 13.6494i | −0.216903 | − | 0.613493i | ||||
\(496\) | −0.585786 | − | 0.585786i | −0.0263026 | − | 0.0263026i | ||||
\(497\) | 1.28471i | 0.0576269i | ||||||||
\(498\) | 9.18420 | − | 12.9884i | 0.411554 | − | 0.582025i | ||||
\(499\) | −22.2779 | − | 22.2779i | −0.997297 | − | 0.997297i | 0.00269960 | − | 0.999996i | \(-0.499141\pi\) |
−0.999996 | + | 0.00269960i | \(0.999141\pi\) | |||||||
\(500\) | 5.45920 | − | 5.45920i | 0.244143 | − | 0.244143i | ||||
\(501\) | −3.39971 | − | 19.8150i | −0.151888 | − | 0.885268i | ||||
\(502\) | 16.0945 | − | 16.0945i | 0.718333 | − | 0.718333i | ||||
\(503\) | − | 0.485281i | − | 0.0216376i | −0.999941 | − | 0.0108188i | \(-0.996556\pi\) | ||
0.999941 | − | 0.0108188i | \(-0.00344380\pi\) | |||||||
\(504\) | 1.00000 | + | 2.82843i | 0.0445435 | + | 0.125988i | ||||
\(505\) | −21.0810 | + | 21.0810i | −0.938094 | + | 0.938094i | ||||
\(506\) | 12.3948 | 0.551014 | ||||||||
\(507\) | −20.6795 | + | 8.90842i | −0.918407 | + | 0.395637i | ||||
\(508\) | 19.2437 | 0.853801 | ||||||||
\(509\) | 22.2876 | − | 22.2876i | 0.987882 | − | 0.987882i | −0.0120457 | − | 0.999927i | \(-0.503834\pi\) |
0.999927 | + | 0.0120457i | \(0.00383437\pi\) | |||||||
\(510\) | 19.1979 | − | 27.1500i | 0.850098 | − | 1.20222i | ||||
\(511\) | − | 15.6073i | − | 0.690428i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −3.01968 | + | 1.68812i | −0.133322 | + | 0.0745321i | ||||
\(514\) | 3.95314 | − | 3.95314i | 0.174365 | − | 0.174365i | ||||
\(515\) | 29.0471 | + | 29.0471i | 1.27997 | + | 1.27997i | ||||
\(516\) | −14.6921 | − | 10.3889i | −0.646785 | − | 0.457346i | ||||
\(517\) | 8.28647i | 0.364438i | ||||||||
\(518\) | −1.56236 | − | 1.56236i | −0.0686460 | − | 0.0686460i | ||||
\(519\) | 1.53788 | + | 1.08744i | 0.0675053 | + | 0.0477335i | ||||
\(520\) | 6.16264 | + | 10.9884i | 0.270250 | + | 0.481874i | ||||
\(521\) | − | 11.5174i | − | 0.504585i | −0.967651 | − | 0.252293i | \(-0.918815\pi\) | ||
0.967651 | − | 0.252293i | \(-0.0811845\pi\) | |||||||
\(522\) | −2.62863 | + | 5.50392i | −0.115052 | + | 0.240900i | ||||
\(523\) | −18.5611 | −0.811622 | −0.405811 | − | 0.913957i | \(-0.633011\pi\) | ||||
−0.405811 | + | 0.913957i | \(0.633011\pi\) | |||||||
\(524\) | 0.778915 | 0.0340271 | ||||||||
\(525\) | 2.11162 | + | 12.3074i | 0.0921584 | + | 0.537139i | ||||
\(526\) | −8.91322 | − | 8.91322i | −0.388635 | − | 0.388635i | ||||
\(527\) | −3.21843 | − | 3.21843i | −0.140197 | − | 0.140197i | ||||
\(528\) | −0.404508 | − | 2.35765i | −0.0176040 | − | 0.102603i | ||||
\(529\) | 57.5452 | 2.50196 | ||||||||
\(530\) | 48.7315 | 2.11676 | ||||||||
\(531\) | 16.1210 | − | 33.7547i | 0.699590 | − | 1.46483i | ||||
\(532\) | 0.665783i | 0.0288654i | ||||||||
\(533\) | 4.74578 | + | 1.33531i | 0.205563 | + | 0.0578389i | ||||
\(534\) | 3.49156 | + | 2.46891i | 0.151095 | + | 0.106840i | ||||
\(535\) | −2.04686 | − | 2.04686i | −0.0884935 | − | 0.0884935i | ||||
\(536\) | − | 6.17637i | − | 0.266779i | ||||||
\(537\) | 7.24744 | + | 5.12471i | 0.312750 | + | 0.221148i | ||||
\(538\) | 2.03314 | + | 2.03314i | 0.0876547 | + | 0.0876547i | ||||
\(539\) | 0.976570 | − | 0.976570i | 0.0420638 | − | 0.0420638i | ||||
\(540\) | −15.8481 | + | 8.85969i | −0.681994 | + | 0.381260i | ||||
\(541\) | 24.9854 | − | 24.9854i | 1.07421 | − | 1.07421i | 0.0771921 | − | 0.997016i | \(-0.475405\pi\) |
0.997016 | − | 0.0771921i | \(-0.0245955\pi\) | |||||||
\(542\) | 0.715295i | 0.0307245i | ||||||||
\(543\) | 14.2895 | − | 20.2084i | 0.613221 | − | 0.867226i | ||||
\(544\) | 3.88499 | − | 3.88499i | 0.166568 | − | 0.166568i | ||||
\(545\) | −8.04796 | −0.344737 | ||||||||
\(546\) | −6.21102 | − | 0.650541i | −0.265807 | − | 0.0278406i | ||||
\(547\) | −0.0506097 | −0.00216391 | −0.00108196 | − | 0.999999i | \(-0.500344\pi\) | ||||
−0.00108196 | + | 0.999999i | \(0.500344\pi\) | |||||||
\(548\) | −4.82655 | + | 4.82655i | −0.206180 | + | 0.206180i | ||||
\(549\) | 13.1347 | + | 37.1505i | 0.560575 | + | 1.58555i | ||||
\(550\) | − | 9.95689i | − | 0.424563i | ||||||
\(551\) | −0.957159 | + | 0.957159i | −0.0407763 | + | 0.0407763i | ||||
\(552\) | −2.62863 | − | 15.3208i | −0.111882 | − | 0.652095i | ||||
\(553\) | −4.32264 | + | 4.32264i | −0.183817 | + | 0.183817i | ||||
\(554\) | 5.43097 | + | 5.43097i | 0.230740 | + | 0.230740i | ||||
\(555\) | 7.72047 | − | 10.9184i | 0.327716 | − | 0.463460i | ||||
\(556\) | − | 2.18315i | − | 0.0925863i | ||||||
\(557\) | −26.0100 | − | 26.0100i | −1.10208 | − | 1.10208i | −0.994160 | − | 0.107918i | \(-0.965582\pi\) |
−0.107918 | − | 0.994160i | \(-0.534418\pi\) | |||||||
\(558\) | 0.828427 | + | 2.34315i | 0.0350701 | + | 0.0991933i | ||||
\(559\) | 32.6705 | − | 18.3226i | 1.38182 | − | 0.774965i | ||||
\(560\) | 3.49421i | 0.147657i | ||||||||
\(561\) | −2.22245 | − | 12.9534i | −0.0938321 | − | 0.546893i | ||||
\(562\) | −3.91057 | −0.164957 | ||||||||
\(563\) | −12.5758 | −0.530007 | −0.265004 | − | 0.964247i | \(-0.585373\pi\) | ||||
−0.265004 | + | 0.964247i | \(0.585373\pi\) | |||||||
\(564\) | 10.2426 | − | 1.75736i | 0.431293 | − | 0.0739982i | ||||
\(565\) | −11.0821 | − | 11.0821i | −0.466229 | − | 0.466229i | ||||
\(566\) | −22.8042 | − | 22.8042i | −0.958531 | − | 0.958531i | ||||
\(567\) | 0.949747 | − | 8.94975i | 0.0398856 | − | 0.375854i | ||||
\(568\) | −1.28471 | −0.0539050 | ||||||||
\(569\) | 0.972759 | 0.0407802 | 0.0203901 | − | 0.999792i | \(-0.493509\pi\) | ||||
0.0203901 | + | 0.999792i | \(0.493509\pi\) | |||||||
\(570\) | −3.97139 | + | 0.681383i | −0.166343 | + | 0.0285400i | ||||
\(571\) | − | 18.5790i | − | 0.777507i | −0.921342 | − | 0.388754i | \(-0.872906\pi\) | ||
0.921342 | − | 0.388754i | \(-0.127094\pi\) | |||||||
\(572\) | 4.79342 | + | 1.34872i | 0.200423 | + | 0.0563928i | ||||
\(573\) | −17.6200 | + | 24.9184i | −0.736085 | + | 1.04098i | ||||
\(574\) | 0.966864 | + | 0.966864i | 0.0403561 | + | 0.0403561i | ||||
\(575\) | − | 64.7031i | − | 2.69831i | ||||||
\(576\) | −2.82843 | + | 1.00000i | −0.117851 | + | 0.0416667i | ||||
\(577\) | −18.8589 | − | 18.8589i | −0.785107 | − | 0.785107i | 0.195581 | − | 0.980688i | \(-0.437341\pi\) |
−0.980688 | + | 0.195581i | \(0.937341\pi\) | |||||||
\(578\) | 9.32415 | − | 9.32415i | 0.387834 | − | 0.387834i | ||||
\(579\) | 36.7099 | − | 6.29843i | 1.52561 | − | 0.261754i | ||||
\(580\) | −5.02343 | + | 5.02343i | −0.208587 | + | 0.208587i | ||||
\(581\) | 9.18420i | 0.381025i | ||||||||
\(582\) | 10.8284 | + | 7.65685i | 0.448853 | + | 0.317387i | ||||
\(583\) | 13.6196 | − | 13.6196i | 0.564066 | − | 0.564066i | ||||
\(584\) | 15.6073 | 0.645836 | ||||||||
\(585\) | −2.47608 | − | 37.7145i | −0.102373 | − | 1.55930i | ||||
\(586\) | 4.51273 | 0.186419 | ||||||||
\(587\) | −24.3800 | + | 24.3800i | −1.00627 | + | 1.00627i | −0.00628924 | + | 0.999980i | \(0.502002\pi\) |
−0.999980 | + | 0.00628924i | \(0.997998\pi\) | |||||||
\(588\) | −1.41421 | − | 1.00000i | −0.0583212 | − | 0.0412393i | ||||
\(589\) | 0.551553i | 0.0227263i | ||||||||
\(590\) | 30.8079 | − | 30.8079i | 1.26834 | − | 1.26834i | ||||
\(591\) | 27.3073 | − | 4.68519i | 1.12327 | − | 0.192723i | ||||
\(592\) | 1.56236 | − | 1.56236i | 0.0642124 | − | 0.0642124i | ||||
\(593\) | 0.273631 | + | 0.273631i | 0.0112367 | + | 0.0112367i | 0.712703 | − | 0.701466i | \(-0.247471\pi\) |
−0.701466 | + | 0.712703i | \(0.747471\pi\) | |||||||
\(594\) | −1.95314 | + | 6.90539i | −0.0801383 | + | 0.283332i | ||||
\(595\) | 19.1979i | 0.787038i | ||||||||
\(596\) | −10.5020 | − | 10.5020i | −0.430180 | − | 0.430180i | ||||
\(597\) | −13.9394 | + | 19.7133i | −0.570502 | + | 0.806812i | ||||
\(598\) | 31.1492 | + | 8.76441i | 1.27379 | + | 0.358404i | ||||
\(599\) | 14.6590i | 0.598950i | 0.954104 | + | 0.299475i | \(0.0968116\pi\) | ||||
−0.954104 | + | 0.299475i | \(0.903188\pi\) | |||||||
\(600\) | −12.3074 | + | 2.11162i | −0.502447 | + | 0.0862063i | ||||
\(601\) | −35.7758 | −1.45933 | −0.729663 | − | 0.683807i | \(-0.760323\pi\) | ||||
−0.729663 | + | 0.683807i | \(0.760323\pi\) | |||||||
\(602\) | 10.3889 | 0.423420 | ||||||||
\(603\) | −7.98539 | + | 16.7201i | −0.325190 | + | 0.680895i | ||||
\(604\) | 8.12763 | + | 8.12763i | 0.330709 | + | 0.330709i | ||||
\(605\) | 22.4659 | + | 22.4659i | 0.913368 | + | 0.913368i | ||||
\(606\) | 14.5653 | − | 2.49901i | 0.591674 | − | 0.101515i | ||||
\(607\) | −9.06038 | −0.367749 | −0.183875 | − | 0.982950i | \(-0.558864\pi\) | ||||
−0.183875 | + | 0.982950i | \(0.558864\pi\) | |||||||
\(608\) | −0.665783 | −0.0270011 | ||||||||
\(609\) | −0.595492 | − | 3.47078i | −0.0241305 | − | 0.140643i | ||||
\(610\) | 45.8954i | 1.85825i | ||||||||
\(611\) | −5.85942 | + | 20.8247i | −0.237047 | + | 0.842476i | ||||
\(612\) | −15.5400 | + | 5.49421i | −0.628166 | + | 0.222090i | ||||
\(613\) | −19.8823 | − | 19.8823i | −0.803040 | − | 0.803040i | 0.180529 | − | 0.983570i | \(-0.442219\pi\) |
−0.983570 | + | 0.180529i | \(0.942219\pi\) | |||||||
\(614\) | − | 10.5747i | − | 0.426761i | ||||||
\(615\) | −4.77782 | + | 6.75685i | −0.192660 | + | 0.272463i | ||||
\(616\) | 0.976570 | + | 0.976570i | 0.0393471 | + | 0.0393471i | ||||
\(617\) | −10.5728 | + | 10.5728i | −0.425646 | + | 0.425646i | −0.887142 | − | 0.461496i | \(-0.847313\pi\) |
0.461496 | + | 0.887142i | \(0.347313\pi\) | |||||||
\(618\) | −3.44333 | − | 20.0692i | −0.138511 | − | 0.807301i | ||||
\(619\) | 13.7555 | − | 13.7555i | 0.552880 | − | 0.552880i | −0.374391 | − | 0.927271i | \(-0.622148\pi\) |
0.927271 | + | 0.374391i | \(0.122148\pi\) | |||||||
\(620\) | 2.89470i | 0.116254i | ||||||||
\(621\) | −12.6921 | + | 44.8735i | −0.509318 | + | 1.80071i | ||||
\(622\) | 6.22892 | − | 6.22892i | 0.249757 | − | 0.249757i | ||||
\(623\) | −2.46891 | −0.0989146 | ||||||||
\(624\) | 0.650541 | − | 6.21102i | 0.0260425 | − | 0.248640i | ||||
\(625\) | 9.07056 | 0.362823 | ||||||||
\(626\) | 17.4874 | − | 17.4874i | 0.698938 | − | 0.698938i | ||||
\(627\) | −0.919498 | + | 1.30037i | −0.0367212 | + | 0.0519317i | ||||
\(628\) | 3.22412i | 0.128656i | ||||||||
\(629\) | 8.58391 | − | 8.58391i | 0.342263 | − | 0.342263i | ||||
\(630\) | 4.51764 | − | 9.45920i | 0.179987 | − | 0.376864i | ||||
\(631\) | −8.67334 | + | 8.67334i | −0.345280 | + | 0.345280i | −0.858348 | − | 0.513068i | \(-0.828509\pi\) |
0.513068 | + | 0.858348i | \(0.328509\pi\) | |||||||
\(632\) | −4.32264 | − | 4.32264i | −0.171945 | − | 0.171945i | ||||
\(633\) | −11.4500 | − | 8.09637i | −0.455097 | − | 0.321802i | ||||
\(634\) | 2.91256i | 0.115672i | ||||||||
\(635\) | −47.5469 | − | 47.5469i | −1.88684 | − | 1.88684i | ||||
\(636\) | −19.7231 | − | 13.9464i | −0.782073 | − | 0.553009i | ||||
\(637\) | 3.14475 | − | 1.76367i | 0.124600 | − | 0.0698793i | ||||
\(638\) | 2.80792i | 0.111167i | ||||||||
\(639\) | 3.47783 | + | 1.66099i | 0.137581 | + | 0.0657076i | ||||
\(640\) | −3.49421 | −0.138121 | ||||||||
\(641\) | 15.0449 | 0.594237 | 0.297118 | − | 0.954841i | \(-0.403974\pi\) | ||||
0.297118 | + | 0.954841i | \(0.403974\pi\) | |||||||
\(642\) | 0.242641 | + | 1.41421i | 0.00957626 | + | 0.0558146i | ||||
\(643\) | 2.63452 | + | 2.63452i | 0.103895 | + | 0.103895i | 0.757144 | − | 0.653248i | \(-0.226594\pi\) |
−0.653248 | + | 0.757144i | \(0.726594\pi\) | |||||||
\(644\) | 6.34607 | + | 6.34607i | 0.250070 | + | 0.250070i | ||||
\(645\) | 10.6323 | + | 61.9697i | 0.418647 | + | 2.44006i | ||||
\(646\) | −3.65795 | −0.143920 | ||||||||
\(647\) | −9.79315 | −0.385008 | −0.192504 | − | 0.981296i | \(-0.561661\pi\) | ||||
−0.192504 | + | 0.981296i | \(0.561661\pi\) | |||||||
\(648\) | 8.94975 | + | 0.949747i | 0.351579 | + | 0.0373096i | ||||
\(649\) | − | 17.2205i | − | 0.675965i | ||||||
\(650\) | 7.04058 | − | 25.0226i | 0.276154 | − | 0.981467i | ||||
\(651\) | −1.17157 | − | 0.828427i | −0.0459176 | − | 0.0324686i | ||||
\(652\) | 14.2973 | + | 14.2973i | 0.559927 | + | 0.559927i | ||||
\(653\) | 39.9825i | 1.56464i | 0.622879 | + | 0.782319i | \(0.285963\pi\) | ||||
−0.622879 | + | 0.782319i | \(0.714037\pi\) | |||||||
\(654\) | 3.25725 | + | 2.30323i | 0.127369 | + | 0.0900633i | ||||
\(655\) | −1.92453 | − | 1.92453i | −0.0751975 | − | 0.0751975i | ||||
\(656\) | −0.966864 | + | 0.966864i | −0.0377497 | + | 0.0377497i | ||||
\(657\) | −42.2507 | − | 20.1786i | −1.64836 | − | 0.787243i | ||||
\(658\) | −4.24264 | + | 4.24264i | −0.165395 | + | 0.165395i | ||||
\(659\) | − | 12.7294i | − | 0.495867i | −0.968777 | − | 0.247934i | \(-0.920249\pi\) | ||
0.968777 | − | 0.247934i | \(-0.0797515\pi\) | |||||||
\(660\) | −4.82578 | + | 6.82468i | −0.187843 | + | 0.265650i | ||||
\(661\) | −23.2601 | + | 23.2601i | −0.904712 | + | 0.904712i | −0.995839 | − | 0.0911276i | \(-0.970953\pi\) |
0.0911276 | + | 0.995839i | \(0.470953\pi\) | |||||||
\(662\) | 3.50794 | 0.136340 | ||||||||
\(663\) | 3.57421 | − | 34.1247i | 0.138811 | − | 1.32529i | ||||
\(664\) | −9.18420 | −0.356416 | ||||||||
\(665\) | 1.64500 | − | 1.64500i | 0.0637905 | − | 0.0637905i | ||||
\(666\) | −6.24942 | + | 2.20950i | −0.242160 | + | 0.0856166i | ||||
\(667\) | 18.2468i | 0.706518i | ||||||||
\(668\) | −8.20763 | + | 8.20763i | −0.317563 | + | 0.317563i | ||||
\(669\) | 3.53303 | + | 20.5920i | 0.136595 | + | 0.796133i | ||||
\(670\) | −15.2604 | + | 15.2604i | −0.589563 | + | 0.589563i | ||||
\(671\) | 12.8269 | + | 12.8269i | 0.495178 | + | 0.495178i | ||||
\(672\) | 1.00000 | − | 1.41421i | 0.0385758 | − | 0.0545545i | ||||
\(673\) | 49.5336i | 1.90938i | 0.297604 | + | 0.954689i | \(0.403813\pi\) | ||||
−0.297604 | + | 0.954689i | \(0.596187\pi\) | |||||||
\(674\) | −3.39558 | − | 3.39558i | −0.130793 | − | 0.130793i | ||||
\(675\) | 36.0475 | + | 10.1958i | 1.38747 | + | 0.392436i | ||||
\(676\) | 11.0926 | + | 6.77892i | 0.426639 | + | 0.260728i | ||||
\(677\) | 40.2984i | 1.54879i | 0.632701 | + | 0.774396i | \(0.281946\pi\) | ||||
−0.632701 | + | 0.774396i | \(0.718054\pi\) | |||||||
\(678\) | 1.31371 | + | 7.65685i | 0.0504527 | + | 0.294060i | ||||
\(679\) | −7.65685 | −0.293843 | ||||||||
\(680\) | −19.1979 | −0.736207 | ||||||||
\(681\) | −40.7595 | + | 6.99322i | −1.56191 | + | 0.267981i | ||||
\(682\) | 0.809017 | + | 0.809017i | 0.0309788 | + | 0.0309788i | ||||
\(683\) | 23.5944 | + | 23.5944i | 0.902814 | + | 0.902814i | 0.995679 | − | 0.0928644i | \(-0.0296023\pi\) |
−0.0928644 | + | 0.995679i | \(0.529602\pi\) | |||||||
\(684\) | 1.80235 | + | 0.860786i | 0.0689144 | + | 0.0329130i | ||||
\(685\) | 23.8507 | 0.911288 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 1.72687 | − | 0.296285i | 0.0658844 | − | 0.0113040i | ||||
\(688\) | 10.3889i | 0.396073i | ||||||||
\(689\) | 43.8578 | − | 24.5968i | 1.67085 | − | 0.937064i | ||||
\(690\) | −31.3595 | + | 44.3490i | −1.19383 | + | 1.68834i | ||||
\(691\) | −29.6768 | − | 29.6768i | −1.12896 | − | 1.12896i | −0.990347 | − | 0.138612i | \(-0.955736\pi\) |
−0.138612 | − | 0.990347i | \(-0.544264\pi\) | |||||||
\(692\) | − | 1.08744i | − | 0.0413384i | ||||||
\(693\) | −1.38108 | − | 3.90628i | −0.0524628 | − | 0.148387i | ||||
\(694\) | −10.3558 | − | 10.3558i | −0.393100 | − | 0.393100i | ||||
\(695\) | −5.39409 | + | 5.39409i | −0.204609 | + | 0.204609i | ||||
\(696\) | 3.47078 | − | 0.595492i | 0.131560 | − | 0.0225721i | ||||
\(697\) | −5.31216 | + | 5.31216i | −0.201212 | + | 0.201212i | ||||
\(698\) | − | 7.37843i | − | 0.279278i | ||||||
\(699\) | −23.8653 | − | 16.8753i | −0.902667 | − | 0.638282i | ||||
\(700\) | 5.09789 | − | 5.09789i | 0.192682 | − | 0.192682i | ||||
\(701\) | 6.49261 | 0.245222 | 0.122611 | − | 0.992455i | \(-0.460873\pi\) | ||||
0.122611 | + | 0.992455i | \(0.460873\pi\) | |||||||
\(702\) | −9.79127 | + | 15.9728i | −0.369548 | + | 0.602855i | ||||
\(703\) | −1.47105 | −0.0554817 | ||||||||
\(704\) | −0.976570 | + | 0.976570i | −0.0368058 | + | 0.0368058i | ||||
\(705\) | −29.6494 | − | 20.9653i | −1.11666 | − | 0.789597i | ||||
\(706\) | − | 11.5079i | − | 0.433107i | ||||||
\(707\) | −6.03314 | + | 6.03314i | −0.226899 | + | 0.226899i | ||||
\(708\) | −21.2858 | + | 3.65206i | −0.799968 | + | 0.137253i | ||||
\(709\) | 32.3795 | − | 32.3795i | 1.21604 | − | 1.21604i | 0.247028 | − | 0.969008i | \(-0.420546\pi\) |
0.969008 | − | 0.247028i | \(-0.0794541\pi\) | |||||||
\(710\) | 3.17422 | + | 3.17422i | 0.119126 | + | 0.119126i | ||||
\(711\) | 6.11313 | + | 17.2905i | 0.229260 | + | 0.648446i | ||||
\(712\) | − | 2.46891i | − | 0.0925261i | ||||||
\(713\) | 5.25725 | + | 5.25725i | 0.196886 | + | 0.196886i | ||||
\(714\) | 5.49421 | − | 7.76999i | 0.205616 | − | 0.290784i | ||||
\(715\) | −8.51109 | − | 15.1759i | −0.318297 | − | 0.567545i | ||||
\(716\) | − | 5.12471i | − | 0.191519i | ||||||
\(717\) | −33.3568 | + | 5.72313i | −1.24573 | + | 0.213734i | ||||
\(718\) | 19.0353 | 0.710390 | ||||||||
\(719\) | −36.7955 | −1.37224 | −0.686119 | − | 0.727489i | \(-0.740687\pi\) | ||||
−0.686119 | + | 0.727489i | \(0.740687\pi\) | |||||||
\(720\) | 9.45920 | + | 4.51764i | 0.352524 | + | 0.168363i | ||||
\(721\) | 8.31293 | + | 8.31293i | 0.309590 | + | 0.309590i | ||||
\(722\) | −13.1216 | − | 13.1216i | −0.488335 | − | 0.488335i | ||||
\(723\) | 16.7979 | − | 2.88207i | 0.624722 | − | 0.107185i | ||||
\(724\) | −14.2895 | −0.531065 | ||||||||
\(725\) | 14.6579 | 0.544381 | ||||||||
\(726\) | −2.66317 | − | 15.5221i | −0.0988394 | − | 0.576078i | ||||
\(727\) | 26.1269i | 0.968992i | 0.874794 | + | 0.484496i | \(0.160997\pi\) | ||||
−0.874794 | + | 0.484496i | \(0.839003\pi\) | |||||||
\(728\) | 1.76367 | + | 3.14475i | 0.0653661 | + | 0.116552i | ||||
\(729\) | −23.0000 | − | 14.1421i | −0.851852 | − | 0.523783i | ||||
\(730\) | −38.5623 | − | 38.5623i | −1.42725 | − | 1.42725i | ||||
\(731\) | 57.0788i | 2.11114i | ||||||||
\(732\) | 13.1347 | − | 18.5753i | 0.485472 | − | 0.686561i | ||||
\(733\) | −27.3747 | − | 27.3747i | −1.01111 | − | 1.01111i | −0.999938 | − | 0.0111692i | \(-0.996445\pi\) |
−0.0111692 | − | 0.999938i | \(-0.503555\pi\) | |||||||
\(734\) | −19.8853 | + | 19.8853i | −0.733979 | + | 0.733979i | ||||
\(735\) | 1.02343 | + | 5.96499i | 0.0377498 | + | 0.220022i | ||||
\(736\) | −6.34607 | + | 6.34607i | −0.233919 | + | 0.233919i | ||||
\(737\) | 8.53005i | 0.314208i | ||||||||
\(738\) | 3.86746 | − | 1.36735i | 0.142363 | − | 0.0503329i | ||||
\(739\) | 21.0363 | − | 21.0363i | 0.773834 | − | 0.773834i | −0.204941 | − | 0.978774i | \(-0.565700\pi\) |
0.978774 | + | 0.204941i | \(0.0657001\pi\) | |||||||
\(740\) | −7.72047 | −0.283810 | ||||||||
\(741\) | −3.23028 | + | 2.61776i | −0.118667 | + | 0.0961659i | ||||
\(742\) | 13.9464 | 0.511987 | ||||||||
\(743\) | 11.0752 | − | 11.0752i | 0.406310 | − | 0.406310i | −0.474140 | − | 0.880450i | \(-0.657241\pi\) |
0.880450 | + | 0.474140i | \(0.157241\pi\) | |||||||
\(744\) | 0.828427 | − | 1.17157i | 0.0303716 | − | 0.0429519i | ||||
\(745\) | 51.8965i | 1.90134i | ||||||||
\(746\) | −0.908424 | + | 0.908424i | −0.0332598 | + | 0.0332598i | ||||
\(747\) | 24.8626 | + | 11.8742i | 0.909675 | + | 0.434454i | ||||
\(748\) | −5.36548 | + | 5.36548i | −0.196181 | + | 0.196181i | ||||
\(749\) | −0.585786 | − | 0.585786i | −0.0214042 | − | 0.0214042i | ||||
\(750\) | 10.9184 | + | 7.72047i | 0.398684 | + | 0.281912i | ||||
\(751\) | − | 14.5694i | − | 0.531645i | −0.964022 | − | 0.265823i | \(-0.914356\pi\) | ||
0.964022 | − | 0.265823i | \(-0.0856436\pi\) | |||||||
\(752\) | −4.24264 | − | 4.24264i | −0.154713 | − | 0.154713i | ||||
\(753\) | 32.1890 | + | 22.7611i | 1.17303 | + | 0.829459i | ||||
\(754\) | −1.98550 | + | 7.05657i | −0.0723076 | + | 0.256985i | ||||
\(755\) | − | 40.1632i | − | 1.46169i | ||||||
\(756\) | −4.53553 | + | 2.53553i | −0.164956 | + | 0.0922165i | ||||
\(757\) | 21.8653 | 0.794706 | 0.397353 | − | 0.917666i | \(-0.369929\pi\) | ||||
0.397353 | + | 0.917666i | \(0.369929\pi\) | |||||||
\(758\) | 10.6579 | 0.387112 | ||||||||
\(759\) | 3.63034 | + | 21.1592i | 0.131773 | + | 0.768029i | ||||
\(760\) | 1.64500 | + | 1.64500i | 0.0596705 | + | 0.0596705i | ||||
\(761\) | 10.1083 | + | 10.1083i | 0.366427 | + | 0.366427i | 0.866172 | − | 0.499745i | \(-0.166573\pi\) |
−0.499745 | + | 0.866172i | \(0.666573\pi\) | |||||||
\(762\) | 5.63635 | + | 32.8510i | 0.204183 | + | 1.19007i | ||||
\(763\) | −2.30323 | −0.0833824 | ||||||||
\(764\) | 17.6200 | 0.637468 | ||||||||
\(765\) | 51.9708 | + | 24.8209i | 1.87901 | + | 0.897400i | ||||
\(766\) | 3.35363i | 0.121171i | ||||||||
\(767\) | 12.1768 | − | 43.2768i | 0.439677 | − | 1.56264i | ||||
\(768\) | 1.41421 | + | 1.00000i | 0.0510310 | + | 0.0360844i | ||||
\(769\) | −15.6851 | − | 15.6851i | −0.565618 | − | 0.565618i | 0.365279 | − | 0.930898i | \(-0.380973\pi\) |
−0.930898 | + | 0.365279i | \(0.880973\pi\) | |||||||
\(770\) | − | 4.82578i | − | 0.173909i | ||||||
\(771\) | 7.90628 | + | 5.59058i | 0.284738 | + | 0.201340i | ||||
\(772\) | −15.2058 | − | 15.2058i | −0.547267 | − | 0.547267i | ||||
\(773\) | 20.2229 | − | 20.2229i | 0.727367 | − | 0.727367i | −0.242727 | − | 0.970095i | \(-0.578042\pi\) |
0.970095 | + | 0.242727i | \(0.0780420\pi\) | |||||||
\(774\) | 13.4317 | − | 28.1239i | 0.482794 | − | 1.01089i | ||||
\(775\) | 4.22323 | − | 4.22323i | 0.151703 | − | 0.151703i | ||||
\(776\) | − | 7.65685i | − | 0.274865i | ||||||
\(777\) | 2.20950 | − | 3.12471i | 0.0792656 | − | 0.112098i | ||||
\(778\) | −13.4484 | + | 13.4484i | −0.482148 | + | 0.482148i | ||||
\(779\) | 0.910360 | 0.0326170 | ||||||||
\(780\) | −16.9534 | + | 13.7387i | −0.607029 | + | 0.491925i | ||||
\(781\) | 1.77428 | 0.0634887 | ||||||||
\(782\) | −34.8666 | + | 34.8666i | −1.24683 | + | 1.24683i | ||||
\(783\) | −10.1657 | − | 2.87529i | −0.363292 | − | 0.102754i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 7.96609 | − | 7.96609i | 0.284322 | − | 0.284322i | ||||
\(786\) | 0.228139 | + | 1.32969i | 0.00813745 | + | 0.0474285i | ||||
\(787\) | 16.0851 | − | 16.0851i | 0.573371 | − | 0.573371i | −0.359698 | − | 0.933069i | \(-0.617120\pi\) |
0.933069 | + | 0.359698i | \(0.117120\pi\) | |||||||
\(788\) | −11.3111 | − | 11.3111i | −0.402940 | − | 0.402940i | ||||
\(789\) | 12.6052 | − | 17.8264i | 0.448757 | − | 0.634638i | ||||
\(790\) | 21.3606i | 0.759975i | ||||||||
\(791\) | −3.17157 | − | 3.17157i | −0.112768 | − | 0.112768i | ||||
\(792\) | 3.90628 | − | 1.38108i | 0.138804 | − | 0.0490745i | ||||
\(793\) | 23.1653 | + | 41.3053i | 0.822624 | + | 1.46680i | ||||
\(794\) | 29.1500i | 1.03449i | ||||||||
\(795\) | 14.2731 | + | 83.1899i | 0.506216 | + | 2.95044i | ||||
\(796\) | 13.9394 | 0.494069 | ||||||||
\(797\) | 12.5984 | 0.446259 | 0.223129 | − | 0.974789i | \(-0.428373\pi\) | ||||
0.223129 | + | 0.974789i | \(0.428373\pi\) | |||||||
\(798\) | −1.13656 | + | 0.195003i | −0.0402339 | + | 0.00690304i | ||||
\(799\) | −23.3100 | − | 23.3100i | −0.824647 | − | 0.824647i | ||||
\(800\) | 5.09789 | + | 5.09789i | 0.180238 | + | 0.180238i | ||||
\(801\) | −3.19203 | + | 6.68359i | −0.112785 | + | 0.236153i | ||||
\(802\) | 37.4327 | 1.32179 | ||||||||
\(803\) | −21.5550 | −0.760658 | ||||||||
\(804\) | 10.5437 | − | 1.80902i | 0.371848 | − | 0.0637991i | ||||
\(805\) | − | 31.3595i | − | 1.10528i | ||||||
\(806\) | 1.46107 | + | 2.60520i | 0.0514642 | + | 0.0917641i | ||||
\(807\) | −2.87529 | + | 4.06627i | −0.101215 | + | 0.143140i | ||||
\(808\) | −6.03314 | − | 6.03314i | −0.212245 | − | 0.212245i | ||||
\(809\) | 49.7721i | 1.74989i | 0.484219 | + | 0.874947i | \(0.339104\pi\) | ||||
−0.484219 | + | 0.874947i | \(0.660896\pi\) | |||||||
\(810\) | −19.7662 | − | 24.4595i | −0.694515 | − | 0.859418i | ||||
\(811\) | −11.7129 | − | 11.7129i | −0.411296 | − | 0.411296i | 0.470894 | − | 0.882190i | \(-0.343931\pi\) |
−0.882190 | + | 0.470894i | \(0.843931\pi\) | |||||||
\(812\) | −1.43764 | + | 1.43764i | −0.0504514 | + | 0.0504514i | ||||
\(813\) | −1.22108 | + | 0.209505i | −0.0428253 | + | 0.00734766i | ||||
\(814\) | −2.15774 | + | 2.15774i | −0.0756286 | + | 0.0756286i | ||||
\(815\) | − | 70.6511i | − | 2.47480i | ||||||
\(816\) | 7.76999 | + | 5.49421i | 0.272004 | + | 0.192336i | ||||
\(817\) | 4.89089 | − | 4.89089i | 0.171111 | − | 0.171111i | ||||
\(818\) | −28.2854 | −0.988975 | ||||||||
\(819\) | −0.708624 | − | 10.7934i | −0.0247613 | − | 0.377153i | ||||
\(820\) | 4.77782 | 0.166849 | ||||||||
\(821\) | 12.3789 | − | 12.3789i | 0.432028 | − | 0.432028i | −0.457290 | − | 0.889318i | \(-0.651180\pi\) |
0.889318 | + | 0.457290i | \(0.151180\pi\) | |||||||
\(822\) | −9.65311 | − | 6.82578i | −0.336691 | − | 0.238076i | ||||
\(823\) | 45.0293i | 1.56962i | 0.619734 | + | 0.784812i | \(0.287241\pi\) | ||||
−0.619734 | + | 0.784812i | \(0.712759\pi\) | |||||||
\(824\) | −8.31293 | + | 8.31293i | −0.289595 | + | 0.289595i | ||||
\(825\) | 16.9975 | − | 2.91630i | 0.591776 | − | 0.101533i | ||||
\(826\) | 8.81685 | − | 8.81685i | 0.306777 | − | 0.306777i | ||||
\(827\) | −39.0724 | − | 39.0724i | −1.35868 | − | 1.35868i | −0.875547 | − | 0.483133i | \(-0.839499\pi\) |
−0.483133 | − | 0.875547i | \(-0.660501\pi\) | |||||||
\(828\) | 25.3843 | − | 8.97470i | 0.882164 | − | 0.311892i | ||||
\(829\) | − | 36.4537i | − | 1.26609i | −0.774115 | − | 0.633045i | \(-0.781805\pi\) | ||
0.774115 | − | 0.633045i | \(-0.218195\pi\) | |||||||
\(830\) | 22.6921 | + | 22.6921i | 0.787656 | + | 0.787656i | ||||
\(831\) | −7.68056 | + | 10.8619i | −0.266436 | + | 0.376797i | ||||
\(832\) | −3.14475 | + | 1.76367i | −0.109025 | + | 0.0611444i | ||||
\(833\) | 5.49421i | 0.190363i | ||||||||
\(834\) | 3.72687 | − | 0.639431i | 0.129051 | − | 0.0221417i | ||||
\(835\) | 40.5585 | 1.40358 | ||||||||
\(836\) | 0.919498 | 0.0318015 | ||||||||
\(837\) | −3.75736 | + | 2.10051i | −0.129873 | + | 0.0726041i | ||||
\(838\) | 6.97657 | + | 6.97657i | 0.241002 | + | 0.241002i | ||||
\(839\) | 26.3654 | + | 26.3654i | 0.910234 | + | 0.910234i | 0.996290 | − | 0.0860567i | \(-0.0274266\pi\) |
−0.0860567 | + | 0.996290i | \(0.527427\pi\) | |||||||
\(840\) | −5.96499 | + | 1.02343i | −0.205812 | + | 0.0353117i | ||||
\(841\) | 24.8664 | 0.857461 | ||||||||
\(842\) | −24.7158 | −0.851764 | ||||||||
\(843\) | −1.14538 | − | 6.67576i | −0.0394490 | − | 0.229925i | ||||
\(844\) | 8.09637i | 0.278689i | ||||||||
\(845\) | −10.6582 | − | 44.1566i | −0.366654 | − | 1.51903i | ||||
\(846\) | 6.00000 | + | 16.9706i | 0.206284 | + | 0.583460i | ||||
\(847\) | 6.42946 | + | 6.42946i | 0.220919 | + | 0.220919i | ||||
\(848\) | 13.9464i | 0.478920i | ||||||||
\(849\) | 32.2500 | − | 45.6083i | 1.10682 | − | 1.56527i | ||||
\(850\) | 28.0089 | + | 28.0089i | 0.960697 | + | 0.960697i | ||||
\(851\) | −14.0217 | + | 14.0217i | −0.480657 | + | 0.480657i | ||||
\(852\) | −0.376281 | − | 2.19313i | −0.0128912 | − | 0.0751354i | ||||
\(853\) | −19.6599 | + | 19.6599i | −0.673142 | + | 0.673142i | −0.958439 | − | 0.285297i | \(-0.907908\pi\) |
0.285297 | + | 0.958439i | \(0.407908\pi\) | |||||||
\(854\) | 13.1347i | 0.449460i | ||||||||
\(855\) | −2.32639 | − | 6.58001i | −0.0795607 | − | 0.225032i | ||||
\(856\) | 0.585786 | − | 0.585786i | 0.0200218 | − | 0.0200218i | ||||
\(857\) | −46.4642 | −1.58719 | −0.793594 | − | 0.608448i | \(-0.791792\pi\) | ||||
−0.793594 | + | 0.608448i | \(0.791792\pi\) | |||||||
\(858\) | −0.898447 | + | 8.57791i | −0.0306725 | + | 0.292845i | ||||
\(859\) | −4.98788 | −0.170184 | −0.0850921 | − | 0.996373i | \(-0.527118\pi\) | ||||
−0.0850921 | + | 0.996373i | \(0.527118\pi\) | |||||||
\(860\) | 25.6687 | − | 25.6687i | 0.875296 | − | 0.875296i | ||||
\(861\) | −1.36735 | + | 1.93373i | −0.0465993 | + | 0.0659013i | ||||
\(862\) | − | 33.3137i | − | 1.13467i | ||||||
\(863\) | −17.3237 | + | 17.3237i | −0.589705 | + | 0.589705i | −0.937552 | − | 0.347846i | \(-0.886913\pi\) |
0.347846 | + | 0.937552i | \(0.386913\pi\) | |||||||
\(864\) | −2.53553 | − | 4.53553i | −0.0862606 | − | 0.154302i | ||||
\(865\) | −2.68683 | + | 2.68683i | −0.0913551 | + | 0.0913551i | ||||
\(866\) | −9.89949 | − | 9.89949i | −0.336399 | − | 0.336399i | ||||
\(867\) | 18.6483 | + | 13.1863i | 0.633330 | + | 0.447832i | ||||
\(868\) | 0.828427i | 0.0281186i | ||||||||
\(869\) | 5.96990 | + | 5.96990i | 0.202515 | + | 0.202515i | ||||
\(870\) | −10.0469 | − | 7.10420i | −0.340620 | − | 0.240855i | ||||
\(871\) | −6.03165 | + | 21.4368i | −0.204375 | + | 0.726359i | ||||
\(872\) | − | 2.30323i | − | 0.0779971i | ||||||
\(873\) | −9.89949 | + | 20.7279i | −0.335047 | + | 0.701534i | ||||
\(874\) | 5.97520 | 0.202114 | ||||||||
\(875\) | −7.72047 | −0.261000 | ||||||||
\(876\) | 4.57128 | + | 26.6434i | 0.154449 | + | 0.900197i | ||||
\(877\) | −21.2736 | − | 21.2736i | −0.718359 | − | 0.718359i | 0.249910 | − | 0.968269i | \(-0.419599\pi\) |
−0.968269 | + | 0.249910i | \(0.919599\pi\) | |||||||
\(878\) | 2.39706 | + | 2.39706i | 0.0808969 | + | 0.0808969i | ||||
\(879\) | 1.32175 | + | 7.70372i | 0.0445815 | + | 0.259840i | ||||
\(880\) | 4.82578 | 0.162677 | ||||||||
\(881\) | 48.7163 | 1.64129 | 0.820647 | − | 0.571436i | \(-0.193613\pi\) | ||||
0.820647 | + | 0.571436i | \(0.193613\pi\) | |||||||
\(882\) | 1.29289 | − | 2.70711i | 0.0435340 | − | 0.0911530i | ||||
\(883\) | 13.5195i | 0.454966i | 0.973782 | + | 0.227483i | \(0.0730496\pi\) | ||||
−0.973782 | + | 0.227483i | \(0.926950\pi\) | |||||||
\(884\) | −17.2779 | + | 9.68999i | −0.581119 | + | 0.325910i | ||||
\(885\) | 61.6158 | + | 43.5690i | 2.07119 | + | 1.46456i | ||||
\(886\) | −9.39105 | − | 9.39105i | −0.315499 | − | 0.315499i | ||||
\(887\) | − | 55.2689i | − | 1.85575i | −0.372892 | − | 0.927875i | \(-0.621634\pi\) | ||
0.372892 | − | 0.927875i | \(-0.378366\pi\) | |||||||
\(888\) | 3.12471 | + | 2.20950i | 0.104858 | + | 0.0741461i | ||||
\(889\) | −13.6073 | − | 13.6073i | −0.456376 | − | 0.456376i | ||||
\(890\) | −6.10012 | + | 6.10012i | −0.204477 | + | 0.204477i | ||||
\(891\) | −12.3603 | − | 1.31168i | −0.414086 | − | 0.0439428i | ||||
\(892\) | 8.52949 | − | 8.52949i | 0.285589 | − | 0.285589i | ||||
\(893\) | 3.99470i | 0.133677i | ||||||||
\(894\) | 14.8521 | − | 21.0041i | 0.496729 | − | 0.702482i | ||||
\(895\) | −12.6620 | + | 12.6620i | −0.423245 | + | 0.423245i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −5.83840 | + | 55.7420i | −0.194939 | + | 1.86117i | ||||
\(898\) | 8.19616 | 0.273510 | ||||||||
\(899\) | −1.19098 | + | 1.19098i | −0.0397215 | + | 0.0397215i | ||||
\(900\) | −7.20950 | − | 20.3916i | −0.240317 | − | 0.679719i | ||||
\(901\) | 76.6242i | 2.55272i | ||||||||
\(902\) | 1.33531 | − | 1.33531i | 0.0444611 | − | 0.0444611i | ||||
\(903\) | 3.04284 | + | 17.7350i | 0.101259 | + | 0.590183i | ||||
\(904\) | 3.17157 | − | 3.17157i | 0.105485 | − | 0.105485i | ||||
\(905\) | 35.3062 | + | 35.3062i | 1.17362 | + | 1.17362i | ||||
\(906\) | −11.4942 | + | 16.2553i | −0.381870 | + | 0.540045i | ||||
\(907\) | 38.8537i | 1.29012i | 0.764134 | + | 0.645058i | \(0.223167\pi\) | ||||
−0.764134 | + | 0.645058i | \(0.776833\pi\) | |||||||
\(908\) | 16.8831 | + | 16.8831i | 0.560286 | + | 0.560286i | ||||
\(909\) | 8.53214 | + | 24.1325i | 0.282993 | + | 0.800426i | ||||
\(910\) | 3.41234 | − | 12.1276i | 0.113118 | − | 0.402027i | ||||
\(911\) | − | 3.45038i | − | 0.114316i | −0.998365 | − | 0.0571582i | \(-0.981796\pi\) | ||
0.998365 | − | 0.0571582i | \(-0.0182039\pi\) | |||||||
\(912\) | −0.195003 | − | 1.13656i | −0.00645721 | − | 0.0376354i | ||||
\(913\) | 12.6841 | 0.419782 | ||||||||
\(914\) | −25.3442 | −0.838311 | ||||||||
\(915\) | −78.3483 | + | 13.4424i | −2.59011 | + | 0.444393i | ||||
\(916\) | −0.715295 | − | 0.715295i | −0.0236340 | − | 0.0236340i | ||||
\(917\) | −0.550776 | − | 0.550776i | −0.0181882 | − | 0.0181882i | ||||
\(918\) | −13.9308 | − | 24.9192i | −0.459783 | − | 0.822455i | ||||
\(919\) | 4.34744 | 0.143409 | 0.0717044 | − | 0.997426i | \(-0.477156\pi\) | ||||
0.0717044 | + | 0.997426i | \(0.477156\pi\) | |||||||
\(920\) | 31.3595 | 1.03389 | ||||||||
\(921\) | 18.0522 | − | 3.09726i | 0.594839 | − | 0.102058i | ||||
\(922\) | 12.4068i | 0.408595i | ||||||||
\(923\) | 4.45893 | + | 1.25460i | 0.146767 | + | 0.0412958i | ||||
\(924\) | −1.38108 | + | 1.95314i | −0.0454341 | + | 0.0642536i | ||||
\(925\) | 11.2638 | + | 11.2638i | 0.370352 | + | 0.370352i | ||||
\(926\) | 2.16264i | 0.0710689i | ||||||||
\(927\) | 33.2517 | − | 11.7563i | 1.09213 | − | 0.386126i | ||||
\(928\) | −1.43764 | − | 1.43764i | −0.0471930 | − | 0.0471930i | ||||
\(929\) | 30.9194 | − | 30.9194i | 1.01443 | − | 1.01443i | 0.0145399 | − | 0.999894i | \(-0.495372\pi\) |
0.999894 | − | 0.0145399i | \(-0.00462835\pi\) | |||||||
\(930\) | −4.94156 | + | 0.847838i | −0.162040 | + | 0.0278017i | ||||
\(931\) | 0.470780 | − | 0.470780i | 0.0154292 | − | 0.0154292i | ||||
\(932\) | 16.8753i | 0.552768i | ||||||||
\(933\) | 12.4578 | + | 8.80902i | 0.407851 | + | 0.288394i | ||||
\(934\) | −11.2028 | + | 11.2028i | −0.366568 | + | 0.366568i | ||||
\(935\) | 26.5138 | 0.867095 | ||||||||
\(936\) | 10.7934 | − | 0.708624i | 0.352794 | − | 0.0231621i | ||||
\(937\) | 22.8867 | 0.747675 | 0.373837 | − | 0.927494i | \(-0.378042\pi\) | ||||
0.373837 | + | 0.927494i | \(0.378042\pi\) | |||||||
\(938\) | −4.36735 | + | 4.36735i | −0.142599 | + | 0.142599i | ||||
\(939\) | 34.9749 | + | 24.7310i | 1.14136 | + | 0.807064i | ||||
\(940\) | 20.9653i | 0.683811i | ||||||||
\(941\) | 0.532142 | − | 0.532142i | 0.0173473 | − | 0.0173473i | −0.698380 | − | 0.715727i | \(-0.746095\pi\) |
0.715727 | + | 0.698380i | \(0.246095\pi\) | |||||||
\(942\) | −5.50392 | + | 0.944323i | −0.179327 | + | 0.0307677i | ||||
\(943\) | 8.67731 | − | 8.67731i | 0.282572 | − | 0.282572i | ||||
\(944\) | 8.81685 | + | 8.81685i | 0.286964 | + | 0.286964i | ||||
\(945\) | 17.4711 | + | 4.94156i | 0.568333 | + | 0.160749i | ||||
\(946\) | − | 14.3479i | − | 0.466490i | ||||||
\(947\) | 16.5909 | + | 16.5909i | 0.539130 | + | 0.539130i | 0.923274 | − | 0.384143i | \(-0.125503\pi\) |
−0.384143 | + | 0.923274i | \(0.625503\pi\) | |||||||
\(948\) | 6.11313 | − | 8.64527i | 0.198545 | − | 0.280785i | ||||
\(949\) | −54.1696 | − | 15.2417i | −1.75842 | − | 0.494765i | ||||
\(950\) | − | 4.79997i | − | 0.155731i | ||||||
\(951\) | −4.97204 | + | 0.853068i | −0.161230 | + | 0.0276626i | ||||
\(952\) | −5.49421 | −0.178068 | ||||||||
\(953\) | −33.1817 | −1.07486 | −0.537430 | − | 0.843308i | \(-0.680605\pi\) | ||||
−0.537430 | + | 0.843308i | \(0.680605\pi\) | |||||||
\(954\) | 18.0311 | − | 37.7543i | 0.583780 | − | 1.22234i | ||||
\(955\) | −43.5351 | − | 43.5351i | −1.40876 | − | 1.40876i | ||||
\(956\) | 13.8168 | + | 13.8168i | 0.446869 | + | 0.446869i | ||||
\(957\) | −4.79342 | + | 0.822420i | −0.154949 | + | 0.0265851i | ||||
\(958\) | −38.3559 | −1.23922 | ||||||||
\(959\) | 6.82578 | 0.220416 | ||||||||
\(960\) | −1.02343 | − | 5.96499i | −0.0330311 | − | 0.192519i | ||||
\(961\) | − | 30.3137i | − | 0.977862i | ||||||
\(962\) | −6.94834 | + | 3.89684i | −0.224024 | + | 0.125639i | ||||
\(963\) | −2.34315 | + | 0.828427i | −0.0755068 | + | 0.0266957i | ||||
\(964\) | −6.95794 | − | 6.95794i | −0.224100 | − | 0.224100i | ||||
\(965\) | 75.1401i | 2.41885i | ||||||||
\(966\) | −8.97470 | + | 12.6921i | −0.288756 | + | 0.408363i | ||||
\(967\) | −8.88979 | − | 8.88979i | −0.285876 | − | 0.285876i | 0.549571 | − | 0.835447i | \(-0.314791\pi\) |
−0.835447 | + | 0.549571i | \(0.814791\pi\) | |||||||
\(968\) | −6.42946 | + | 6.42946i | −0.206651 | + | 0.206651i | ||||
\(969\) | −1.07139 | − | 6.24452i | −0.0344180 | − | 0.200603i | ||||
\(970\) | −18.9184 | + | 18.9184i | −0.607433 | + | 0.607433i | ||||
\(971\) | − | 25.1915i | − | 0.808435i | −0.914663 | − | 0.404217i | \(-0.867544\pi\) | ||
0.914663 | − | 0.404217i | \(-0.132456\pi\) | |||||||
\(972\) | 1.00000 | + | 15.5563i | 0.0320750 | + | 0.498970i | ||||
\(973\) | −1.54372 | + | 1.54372i | −0.0494895 | + | 0.0494895i | ||||
\(974\) | 12.8106 | 0.410477 | ||||||||
\(975\) | 44.7784 | + | 4.69008i | 1.43406 | + | 0.150203i | ||||
\(976\) | −13.1347 | −0.420431 | ||||||||
\(977\) | −27.5046 | + | 27.5046i | −0.879949 | + | 0.879949i | −0.993529 | − | 0.113579i | \(-0.963768\pi\) |
0.113579 | + | 0.993529i | \(0.463768\pi\) | |||||||
\(978\) | −20.2195 | + | 28.5947i | −0.646548 | + | 0.914357i | ||||
\(979\) | 3.40975i | 0.108976i | ||||||||
\(980\) | 2.47078 | − | 2.47078i | 0.0789262 | − | 0.0789262i | ||||
\(981\) | −2.97783 | + | 6.23508i | −0.0950747 | + | 0.199071i | ||||
\(982\) | −15.2806 | + | 15.2806i | −0.487623 | + | 0.487623i | ||||
\(983\) | 2.11820 | + | 2.11820i | 0.0675601 | + | 0.0675601i | 0.740079 | − | 0.672519i | \(-0.234788\pi\) |
−0.672519 | + | 0.740079i | \(0.734788\pi\) | |||||||
\(984\) | −1.93373 | − | 1.36735i | −0.0616450 | − | 0.0435896i | ||||
\(985\) | 55.8943i | 1.78094i | ||||||||
\(986\) | −7.89872 | − | 7.89872i | −0.251546 | − | 0.251546i | ||||
\(987\) | −8.48528 | − | 6.00000i | −0.270089 | − | 0.190982i | ||||
\(988\) | 2.31079 | + | 0.650183i | 0.0735159 | + | 0.0206851i | ||||
\(989\) | − | 93.2373i | − | 2.96477i | ||||||
\(990\) | −13.0639 | − | 6.23921i | −0.415198 | − | 0.198295i | ||||
\(991\) | 38.9900 | 1.23856 | 0.619279 | − | 0.785171i | \(-0.287425\pi\) | ||||
0.619279 | + | 0.785171i | \(0.287425\pi\) | |||||||
\(992\) | −0.828427 | −0.0263026 | ||||||||
\(993\) | 1.02745 | + | 5.98842i | 0.0326052 | + | 0.190037i | ||||
\(994\) | 0.908424 | + | 0.908424i | 0.0288135 | + | 0.0288135i | ||||
\(995\) | −34.4412 | − | 34.4412i | −1.09186 | − | 1.09186i | ||||
\(996\) | −2.68999 | − | 15.6784i | −0.0852356 | − | 0.496789i | ||||
\(997\) | −40.2114 | −1.27351 | −0.636755 | − | 0.771067i | \(-0.719724\pi\) | ||||
−0.636755 | + | 0.771067i | \(0.719724\pi\) | |||||||
\(998\) | −31.5057 | −0.997297 | ||||||||
\(999\) | −5.60227 | − | 10.0213i | −0.177248 | − | 0.317059i |
(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 | 546.2.p.b.281.3 | yes | 8 | |
3.2 | odd | 2 | 546.2.p.a.281.2 | yes | 8 | ||
13.5 | odd | 4 | 546.2.p.a.239.2 | ✓ | 8 | ||
39.5 | even | 4 | inner | 546.2.p.b.239.3 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.p.a.239.2 | ✓ | 8 | 13.5 | odd | 4 | ||
546.2.p.a.281.2 | yes | 8 | 3.2 | odd | 2 | ||
546.2.p.b.239.3 | yes | 8 | 39.5 | even | 4 | inner | |
546.2.p.b.281.3 | yes | 8 | 1.1 | even | 1 | trivial |