Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(148,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.f (of order \(3\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 148.4 | ||
Character | \(\chi\) | \(=\) | 441.148 |
Dual form | 441.2.f.h.295.4 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.649936 | − | 1.12572i | −0.459574 | − | 0.796006i | 0.539364 | − | 0.842073i | \(-0.318665\pi\) |
−0.998938 | + | 0.0460668i | \(0.985331\pi\) | |||||||
\(3\) | 0.0514049 | + | 1.73129i | 0.0296787 | + | 0.999559i | ||||
\(4\) | 0.155166 | − | 0.268756i | 0.0775831 | − | 0.134378i | ||||
\(5\) | −1.76292 | + | 3.05347i | −0.788402 | + | 1.36555i | 0.138543 | + | 0.990356i | \(0.455758\pi\) |
−0.926945 | + | 0.375196i | \(0.877575\pi\) | |||||||
\(6\) | 1.91554 | − | 1.18309i | 0.782016 | − | 0.482996i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −3.00314 | −1.06177 | ||||||||
\(9\) | −2.99472 | + | 0.177994i | −0.998238 | + | 0.0593312i | ||||
\(10\) | 4.58314 | 1.44932 | ||||||||
\(11\) | −0.589267 | − | 1.02064i | −0.177671 | − | 0.307735i | 0.763412 | − | 0.645912i | \(-0.223523\pi\) |
−0.941082 | + | 0.338178i | \(0.890190\pi\) | |||||||
\(12\) | 0.473270 | + | 0.254822i | 0.136621 | + | 0.0735608i | ||||
\(13\) | 1.61030 | − | 2.78913i | 0.446618 | − | 0.773564i | −0.551546 | − | 0.834145i | \(-0.685962\pi\) |
0.998163 | + | 0.0605803i | \(0.0192951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.37706 | − | 2.89516i | −1.38835 | − | 0.747527i | ||||
\(16\) | 1.64151 | + | 2.84319i | 0.410379 | + | 0.710797i | ||||
\(17\) | −4.90317 | −1.18919 | −0.594597 | − | 0.804024i | \(-0.702688\pi\) | ||||
−0.594597 | + | 0.804024i | \(0.702688\pi\) | |||||||
\(18\) | 2.14674 | + | 3.25553i | 0.505993 | + | 0.767336i | ||||
\(19\) | −6.86637 | −1.57525 | −0.787627 | − | 0.616153i | \(-0.788690\pi\) | ||||
−0.787627 | + | 0.616153i | \(0.788690\pi\) | |||||||
\(20\) | 0.547092 | + | 0.947591i | 0.122333 | + | 0.211888i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.765972 | + | 1.32670i | −0.163306 | + | 0.282854i | ||||
\(23\) | 2.14994 | − | 3.72380i | 0.448293 | − | 0.776466i | −0.549982 | − | 0.835176i | \(-0.685366\pi\) |
0.998275 | + | 0.0587106i | \(0.0186989\pi\) | |||||||
\(24\) | −0.154376 | − | 5.19929i | −0.0315119 | − | 1.06130i | ||||
\(25\) | −3.71578 | − | 6.43592i | −0.743156 | − | 1.28718i | ||||
\(26\) | −4.18637 | −0.821016 | ||||||||
\(27\) | −0.462101 | − | 5.17556i | −0.0889314 | − | 0.996038i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.36140 | + | 2.35802i | 0.252806 | + | 0.437873i | 0.964297 | − | 0.264822i | \(-0.0853131\pi\) |
−0.711491 | + | 0.702695i | \(0.751980\pi\) | |||||||
\(30\) | 0.235596 | + | 7.93474i | 0.0430138 | + | 1.44868i | ||||
\(31\) | 0.960401 | − | 1.66346i | 0.172493 | − | 0.298767i | −0.766798 | − | 0.641889i | \(-0.778151\pi\) |
0.939291 | + | 0.343122i | \(0.111484\pi\) | |||||||
\(32\) | −0.869378 | + | 1.50581i | −0.153686 | + | 0.266192i | ||||
\(33\) | 1.73673 | − | 1.07266i | 0.302326 | − | 0.186726i | ||||
\(34\) | 3.18675 | + | 5.51961i | 0.546523 | + | 0.946606i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.416842 | + | 0.832466i | −0.0694737 | + | 0.138744i | ||||
\(37\) | −9.76457 | −1.60529 | −0.802643 | − | 0.596460i | \(-0.796573\pi\) | ||||
−0.802643 | + | 0.596460i | \(0.796573\pi\) | |||||||
\(38\) | 4.46270 | + | 7.72962i | 0.723946 | + | 1.25391i | ||||
\(39\) | 4.91156 | + | 2.64452i | 0.786479 | + | 0.423462i | ||||
\(40\) | 5.29429 | − | 9.16998i | 0.837101 | − | 1.44990i | ||||
\(41\) | −3.32673 | + | 5.76206i | −0.519547 | + | 0.899883i | 0.480194 | + | 0.877162i | \(0.340566\pi\) |
−0.999742 | + | 0.0227205i | \(0.992767\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.83441 | + | 8.37344i | 0.737240 | + | 1.27694i | 0.953734 | + | 0.300653i | \(0.0972047\pi\) |
−0.216493 | + | 0.976284i | \(0.569462\pi\) | |||||||
\(44\) | −0.365738 | −0.0551370 | ||||||||
\(45\) | 4.73595 | − | 9.45806i | 0.705993 | − | 1.40992i | ||||
\(46\) | −5.58928 | −0.824095 | ||||||||
\(47\) | −0.316609 | − | 0.548383i | −0.0461822 | − | 0.0799899i | 0.842010 | − | 0.539461i | \(-0.181372\pi\) |
−0.888192 | + | 0.459472i | \(0.848039\pi\) | |||||||
\(48\) | −4.83799 | + | 2.98809i | −0.698304 | + | 0.431293i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −4.83004 | + | 8.36587i | −0.683071 | + | 1.18311i | ||||
\(51\) | −0.252047 | − | 8.48880i | −0.0352937 | − | 1.18867i | ||||
\(52\) | −0.499729 | − | 0.865557i | −0.0693000 | − | 0.120031i | ||||
\(53\) | −2.22756 | −0.305978 | −0.152989 | − | 0.988228i | \(-0.548890\pi\) | ||||
−0.152989 | + | 0.988228i | \(0.548890\pi\) | |||||||
\(54\) | −5.52591 | + | 3.88398i | −0.751981 | + | 0.528543i | ||||
\(55\) | 4.15533 | 0.560304 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.352965 | − | 11.8877i | −0.0467514 | − | 1.57456i | ||||
\(58\) | 1.76965 | − | 3.06512i | 0.232366 | − | 0.402471i | ||||
\(59\) | −4.10652 | + | 7.11270i | −0.534623 | + | 0.925995i | 0.464558 | + | 0.885543i | \(0.346213\pi\) |
−0.999181 | + | 0.0404521i | \(0.987120\pi\) | |||||||
\(60\) | −1.61243 | + | 0.995884i | −0.208164 | + | 0.128568i | ||||
\(61\) | 4.82958 | + | 8.36508i | 0.618364 | + | 1.07104i | 0.989784 | + | 0.142573i | \(0.0455376\pi\) |
−0.371420 | + | 0.928465i | \(0.621129\pi\) | |||||||
\(62\) | −2.49680 | −0.317093 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.82622 | 1.10328 | ||||||||
\(65\) | 5.67767 | + | 9.83402i | 0.704229 | + | 1.21976i | ||||
\(66\) | −2.33628 | − | 1.25792i | −0.287576 | − | 0.154839i | ||||
\(67\) | −2.66651 | + | 4.61852i | −0.325766 | + | 0.564242i | −0.981667 | − | 0.190604i | \(-0.938955\pi\) |
0.655901 | + | 0.754847i | \(0.272289\pi\) | |||||||
\(68\) | −0.760807 | + | 1.31776i | −0.0922614 | + | 0.159801i | ||||
\(69\) | 6.55748 | + | 3.53074i | 0.789428 | + | 0.425051i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.27719 | −0.388931 | −0.194466 | − | 0.980909i | \(-0.562297\pi\) | ||||
−0.194466 | + | 0.980909i | \(0.562297\pi\) | |||||||
\(72\) | 8.99354 | − | 0.534539i | 1.05990 | − | 0.0629960i | ||||
\(73\) | 1.03807 | 0.121497 | 0.0607486 | − | 0.998153i | \(-0.480651\pi\) | ||||
0.0607486 | + | 0.998153i | \(0.480651\pi\) | |||||||
\(74\) | 6.34635 | + | 10.9922i | 0.737748 | + | 1.27782i | ||||
\(75\) | 10.9514 | − | 6.76392i | 1.26456 | − | 0.781031i | ||||
\(76\) | −1.06543 | + | 1.84538i | −0.122213 | + | 0.211679i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.215200 | − | 7.24782i | −0.0243666 | − | 0.820654i | ||||
\(79\) | −0.502039 | − | 0.869557i | −0.0564838 | − | 0.0978328i | 0.836401 | − | 0.548118i | \(-0.184656\pi\) |
−0.892885 | + | 0.450285i | \(0.851322\pi\) | |||||||
\(80\) | −11.5754 | −1.29417 | ||||||||
\(81\) | 8.93664 | − | 1.06608i | 0.992960 | − | 0.118453i | ||||
\(82\) | 8.64864 | 0.955082 | ||||||||
\(83\) | −3.65598 | − | 6.33234i | −0.401296 | − | 0.695064i | 0.592587 | − | 0.805506i | \(-0.298107\pi\) |
−0.993883 | + | 0.110442i | \(0.964773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.64391 | − | 14.9717i | 0.937563 | − | 1.62391i | ||||
\(86\) | 6.28411 | − | 10.8844i | 0.677633 | − | 1.17369i | ||||
\(87\) | −4.01243 | + | 2.47820i | −0.430177 | + | 0.265690i | ||||
\(88\) | 1.76965 | + | 3.06512i | 0.188645 | + | 0.326743i | ||||
\(89\) | 12.0429 | 1.27654 | 0.638271 | − | 0.769812i | \(-0.279650\pi\) | ||||
0.638271 | + | 0.769812i | \(0.279650\pi\) | |||||||
\(90\) | −13.7252 | + | 0.815770i | −1.44676 | + | 0.0859897i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.667195 | − | 1.15562i | −0.0695599 | − | 0.120481i | ||||
\(93\) | 2.92930 | + | 1.57722i | 0.303755 | + | 0.163550i | ||||
\(94\) | −0.411551 | + | 0.712828i | −0.0424483 | + | 0.0735226i | ||||
\(95\) | 12.1049 | − | 20.9662i | 1.24193 | − | 2.15109i | ||||
\(96\) | −2.65168 | − | 1.42774i | −0.270636 | − | 0.145718i | ||||
\(97\) | −5.46454 | − | 9.46487i | −0.554840 | − | 0.961012i | −0.997916 | − | 0.0645275i | \(-0.979446\pi\) |
0.443076 | − | 0.896484i | \(-0.353887\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.94636 | + | 2.95164i | 0.195616 | + | 0.296651i | ||||
\(100\) | −2.30626 | −0.230626 | ||||||||
\(101\) | 0.797546 | + | 1.38139i | 0.0793588 | + | 0.137453i | 0.902973 | − | 0.429696i | \(-0.141379\pi\) |
−0.823615 | + | 0.567150i | \(0.808046\pi\) | |||||||
\(102\) | −9.39222 | + | 5.80092i | −0.929969 | + | 0.574376i | ||||
\(103\) | −1.16778 | + | 2.02265i | −0.115065 | + | 0.199298i | −0.917806 | − | 0.397030i | \(-0.870041\pi\) |
0.802741 | + | 0.596328i | \(0.203374\pi\) | |||||||
\(104\) | −4.83596 | + | 8.37613i | −0.474205 | + | 0.821347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.44777 | + | 2.50761i | 0.140620 | + | 0.243561i | ||||
\(107\) | −2.22362 | −0.214966 | −0.107483 | − | 0.994207i | \(-0.534279\pi\) | ||||
−0.107483 | + | 0.994207i | \(0.534279\pi\) | |||||||
\(108\) | −1.46267 | − | 0.678881i | −0.140745 | − | 0.0653253i | ||||
\(109\) | −0.919564 | −0.0880782 | −0.0440391 | − | 0.999030i | \(-0.514023\pi\) | ||||
−0.0440391 | + | 0.999030i | \(0.514023\pi\) | |||||||
\(110\) | −2.70070 | − | 4.67774i | −0.257501 | − | 0.446005i | ||||
\(111\) | −0.501947 | − | 16.9053i | −0.0476427 | − | 1.60458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.19327 | − | 2.06681i | 0.112254 | − | 0.194429i | −0.804425 | − | 0.594054i | \(-0.797526\pi\) |
0.916679 | + | 0.399625i | \(0.130860\pi\) | |||||||
\(114\) | −13.1528 | + | 8.12356i | −1.23187 | + | 0.760841i | ||||
\(115\) | 7.58033 | + | 13.1295i | 0.706870 | + | 1.22433i | ||||
\(116\) | 0.844976 | 0.0784540 | ||||||||
\(117\) | −4.32595 | + | 8.63926i | −0.399934 | + | 0.798700i | ||||
\(118\) | 10.6759 | 0.982796 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 16.1480 | + | 8.69456i | 1.47411 | + | 0.793701i | ||||
\(121\) | 4.80553 | − | 8.32342i | 0.436866 | − | 0.756674i | ||||
\(122\) | 6.27783 | − | 10.8735i | 0.568368 | − | 0.984443i | ||||
\(123\) | −10.1468 | − | 5.46332i | −0.914906 | − | 0.492611i | ||||
\(124\) | −0.298044 | − | 0.516227i | −0.0267651 | − | 0.0463585i | ||||
\(125\) | 8.57330 | 0.766819 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.04170 | −0.269907 | −0.134954 | − | 0.990852i | \(-0.543089\pi\) | ||||
−0.134954 | + | 0.990852i | \(0.543089\pi\) | |||||||
\(128\) | −3.99772 | − | 6.92426i | −0.353352 | − | 0.612024i | ||||
\(129\) | −14.2483 | + | 8.80019i | −1.25449 | + | 0.774813i | ||||
\(130\) | 7.38025 | − | 12.7830i | 0.647291 | − | 1.12114i | ||||
\(131\) | 1.63088 | − | 2.82476i | 0.142490 | − | 0.246801i | −0.785943 | − | 0.618298i | \(-0.787822\pi\) |
0.928434 | + | 0.371498i | \(0.121156\pi\) | |||||||
\(132\) | −0.0188007 | − | 0.633197i | −0.00163639 | − | 0.0551127i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 6.93223 | 0.598854 | ||||||||
\(135\) | 16.6181 | + | 7.71310i | 1.43026 | + | 0.663838i | ||||
\(136\) | 14.7249 | 1.26265 | ||||||||
\(137\) | −10.4669 | − | 18.1292i | −0.894246 | − | 1.54888i | −0.834734 | − | 0.550653i | \(-0.814379\pi\) |
−0.0595120 | − | 0.998228i | \(-0.518954\pi\) | |||||||
\(138\) | −0.287317 | − | 9.67666i | −0.0244580 | − | 0.823732i | ||||
\(139\) | −8.31195 | + | 14.3967i | −0.705010 | + | 1.22111i | 0.261677 | + | 0.965155i | \(0.415724\pi\) |
−0.966688 | + | 0.255958i | \(0.917609\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.933134 | − | 0.576331i | 0.0785840 | − | 0.0485358i | ||||
\(142\) | 2.12997 | + | 3.68921i | 0.178743 | + | 0.309592i | ||||
\(143\) | −3.79559 | −0.317404 | ||||||||
\(144\) | −5.42194 | − | 8.22235i | −0.451828 | − | 0.685196i | ||||
\(145\) | −9.60019 | −0.797252 | ||||||||
\(146\) | −0.674681 | − | 1.16858i | −0.0558370 | − | 0.0967124i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.51513 | + | 2.62429i | −0.124543 | + | 0.215715i | ||||
\(149\) | −0.564221 | + | 0.977260i | −0.0462228 | + | 0.0800602i | −0.888211 | − | 0.459435i | \(-0.848052\pi\) |
0.841988 | + | 0.539496i | \(0.181385\pi\) | |||||||
\(150\) | −14.7320 | − | 7.93214i | −1.20286 | − | 0.647657i | ||||
\(151\) | 9.81476 | + | 16.9997i | 0.798714 | + | 1.38341i | 0.920454 | + | 0.390851i | \(0.127819\pi\) |
−0.121740 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(152\) | 20.6206 | 1.67256 | ||||||||
\(153\) | 14.6836 | − | 0.872733i | 1.18710 | − | 0.0705563i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.38622 | + | 5.86511i | 0.271988 | + | 0.471097i | ||||
\(156\) | 1.47284 | − | 0.909669i | 0.117921 | − | 0.0728318i | ||||
\(157\) | −4.66619 | + | 8.08207i | −0.372402 | + | 0.645020i | −0.989935 | − | 0.141526i | \(-0.954799\pi\) |
0.617532 | + | 0.786545i | \(0.288132\pi\) | |||||||
\(158\) | −0.652586 | + | 1.13031i | −0.0519170 | + | 0.0899228i | ||||
\(159\) | −0.114507 | − | 3.85654i | −0.00908103 | − | 0.305844i | ||||
\(160\) | −3.06529 | − | 5.30924i | −0.242332 | − | 0.419732i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −7.00835 | − | 9.36729i | −0.550628 | − | 0.735964i | ||||
\(163\) | 16.9011 | 1.32380 | 0.661899 | − | 0.749593i | \(-0.269751\pi\) | ||||
0.661899 | + | 0.749593i | \(0.269751\pi\) | |||||||
\(164\) | 1.03239 | + | 1.78815i | 0.0806162 | + | 0.139631i | ||||
\(165\) | 0.213604 | + | 7.19407i | 0.0166291 | + | 0.560057i | ||||
\(166\) | −4.75230 | + | 8.23123i | −0.368850 | + | 0.638867i | ||||
\(167\) | 2.57319 | − | 4.45689i | 0.199119 | − | 0.344885i | −0.749124 | − | 0.662430i | \(-0.769525\pi\) |
0.948243 | + | 0.317545i | \(0.102859\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.31385 | + | 2.27566i | 0.101066 | + | 0.175051i | ||||
\(170\) | −22.4719 | −1.72352 | ||||||||
\(171\) | 20.5628 | − | 1.22217i | 1.57248 | − | 0.0934616i | ||||
\(172\) | 3.00055 | 0.228790 | ||||||||
\(173\) | −4.86834 | − | 8.43222i | −0.370133 | − | 0.641090i | 0.619453 | − | 0.785034i | \(-0.287355\pi\) |
−0.989586 | + | 0.143945i | \(0.954021\pi\) | |||||||
\(174\) | 5.39758 | + | 2.90621i | 0.409190 | + | 0.220319i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.93458 | − | 3.35079i | 0.145825 | − | 0.252576i | ||||
\(177\) | −12.5252 | − | 6.74394i | −0.941454 | − | 0.506905i | ||||
\(178\) | −7.82710 | − | 13.5569i | −0.586666 | − | 1.01613i | ||||
\(179\) | 1.37598 | 0.102846 | 0.0514228 | − | 0.998677i | \(-0.483624\pi\) | ||||
0.0514228 | + | 0.998677i | \(0.483624\pi\) | |||||||
\(180\) | −1.80705 | − | 2.74039i | −0.134689 | − | 0.204256i | ||||
\(181\) | −5.66560 | −0.421120 | −0.210560 | − | 0.977581i | \(-0.567529\pi\) | ||||
−0.210560 | + | 0.977581i | \(0.567529\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −14.2341 | + | 8.79140i | −1.05221 | + | 0.649879i | ||||
\(184\) | −6.45655 | + | 11.1831i | −0.475983 | + | 0.824427i | ||||
\(185\) | 17.2142 | − | 29.8158i | 1.26561 | − | 2.19210i | ||||
\(186\) | −0.128348 | − | 4.32267i | −0.00941091 | − | 0.316954i | ||||
\(187\) | 2.88928 | + | 5.00438i | 0.211285 | + | 0.365956i | ||||
\(188\) | −0.196508 | −0.0143318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −31.4696 | −2.28304 | ||||||||
\(191\) | 12.5065 | + | 21.6618i | 0.904936 | + | 1.56740i | 0.821003 | + | 0.570925i | \(0.193415\pi\) |
0.0839339 | + | 0.996471i | \(0.473252\pi\) | |||||||
\(192\) | 0.453711 | + | 15.2807i | 0.0327438 | + | 1.10279i | ||||
\(193\) | −8.76688 | + | 15.1847i | −0.631054 | + | 1.09302i | 0.356282 | + | 0.934378i | \(0.384044\pi\) |
−0.987337 | + | 0.158640i | \(0.949289\pi\) | |||||||
\(194\) | −7.10321 | + | 12.3031i | −0.509981 | + | 0.883312i | ||||
\(195\) | −16.7337 | + | 10.3352i | −1.19832 | + | 0.740119i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7540 | −1.40741 | −0.703707 | − | 0.710490i | \(-0.748473\pi\) | ||||
−0.703707 | + | 0.710490i | \(0.748473\pi\) | |||||||
\(198\) | 2.05772 | − | 4.10943i | 0.146236 | − | 0.292045i | ||||
\(199\) | −19.0222 | −1.34845 | −0.674224 | − | 0.738527i | \(-0.735522\pi\) | ||||
−0.674224 | + | 0.738527i | \(0.735522\pi\) | |||||||
\(200\) | 11.1590 | + | 19.3279i | 0.789060 | + | 1.36669i | ||||
\(201\) | −8.13307 | − | 4.37907i | −0.573662 | − | 0.308876i | ||||
\(202\) | 1.03671 | − | 1.79563i | 0.0729425 | − | 0.126340i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.32053 | − | 1.24944i | −0.162469 | − | 0.0874781i | ||||
\(205\) | −11.7295 | − | 20.3161i | −0.819225 | − | 1.41894i | ||||
\(206\) | 3.03593 | 0.211523 | ||||||||
\(207\) | −5.77563 | + | 11.5344i | −0.401434 | + | 0.801696i | ||||
\(208\) | 10.5733 | 0.733129 | ||||||||
\(209\) | 4.04613 | + | 7.00810i | 0.279876 | + | 0.484760i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.71809 | − | 6.43993i | 0.255964 | − | 0.443343i | −0.709193 | − | 0.705015i | \(-0.750940\pi\) |
0.965157 | + | 0.261672i | \(0.0842738\pi\) | |||||||
\(212\) | −0.345642 | + | 0.598669i | −0.0237388 | + | 0.0411168i | ||||
\(213\) | −0.168464 | − | 5.67376i | −0.0115430 | − | 0.388760i | ||||
\(214\) | 1.44521 | + | 2.50318i | 0.0987927 | + | 0.171114i | ||||
\(215\) | −34.0907 | −2.32497 | ||||||||
\(216\) | 1.38775 | + | 15.5429i | 0.0944246 | + | 1.05756i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.597658 | + | 1.03517i | 0.0404785 | + | 0.0701108i | ||||
\(219\) | 0.0533620 | + | 1.79720i | 0.00360587 | + | 0.121444i | ||||
\(220\) | 0.644767 | − | 1.11677i | 0.0434702 | − | 0.0752925i | ||||
\(221\) | −7.89559 | + | 13.6756i | −0.531115 | + | 0.919918i | ||||
\(222\) | −18.7044 | + | 11.5524i | −1.25536 | + | 0.775347i | ||||
\(223\) | 1.64565 | + | 2.85034i | 0.110201 | + | 0.190873i | 0.915851 | − | 0.401518i | \(-0.131517\pi\) |
−0.805650 | + | 0.592391i | \(0.798184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.2733 | + | 18.6124i | 0.818217 | + | 1.24082i | ||||
\(226\) | −3.10221 | −0.206356 | ||||||||
\(227\) | 9.00847 | + | 15.6031i | 0.597913 | + | 1.03562i | 0.993129 | + | 0.117028i | \(0.0373366\pi\) |
−0.395215 | + | 0.918589i | \(0.629330\pi\) | |||||||
\(228\) | −3.24965 | − | 1.74970i | −0.215213 | − | 0.115877i | ||||
\(229\) | −2.12746 | + | 3.68486i | −0.140586 | + | 0.243503i | −0.927718 | − | 0.373283i | \(-0.878232\pi\) |
0.787131 | + | 0.616785i | \(0.211565\pi\) | |||||||
\(230\) | 9.85347 | − | 17.0667i | 0.649718 | − | 1.12535i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.08848 | − | 7.08146i | −0.268422 | − | 0.464920i | ||||
\(233\) | −14.7055 | −0.963390 | −0.481695 | − | 0.876339i | \(-0.659979\pi\) | ||||
−0.481695 | + | 0.876339i | \(0.659979\pi\) | |||||||
\(234\) | 12.5370 | − | 0.745148i | 0.819569 | − | 0.0487118i | ||||
\(235\) | 2.23263 | 0.145641 | ||||||||
\(236\) | 1.27439 | + | 2.20730i | 0.0829555 | + | 0.143683i | ||||
\(237\) | 1.47965 | − | 0.913873i | 0.0961133 | − | 0.0593624i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.08187 | − | 12.2662i | 0.458088 | − | 0.793432i | −0.540772 | − | 0.841169i | \(-0.681868\pi\) |
0.998860 | + | 0.0477377i | \(0.0152011\pi\) | |||||||
\(240\) | −0.595035 | − | 20.0404i | −0.0384093 | − | 1.29360i | ||||
\(241\) | −3.96752 | − | 6.87194i | −0.255570 | − | 0.442661i | 0.709480 | − | 0.704726i | \(-0.248930\pi\) |
−0.965050 | + | 0.262065i | \(0.915597\pi\) | |||||||
\(242\) | −12.4931 | −0.803090 | ||||||||
\(243\) | 2.30508 | + | 15.4171i | 0.147871 | + | 0.989007i | ||||
\(244\) | 2.99755 | 0.191899 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.444583 | + | 14.9733i | 0.0283456 | + | 0.954662i | ||||
\(247\) | −11.0569 | + | 19.1512i | −0.703536 | + | 1.21856i | ||||
\(248\) | −2.88422 | + | 4.99561i | −0.183148 | + | 0.317221i | ||||
\(249\) | 10.7752 | − | 6.65506i | 0.682848 | − | 0.421747i | ||||
\(250\) | −5.57210 | − | 9.65115i | −0.352410 | − | 0.610392i | ||||
\(251\) | 8.05097 | 0.508173 | 0.254087 | − | 0.967181i | \(-0.418225\pi\) | ||||
0.254087 | + | 0.967181i | \(0.418225\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06755 | −0.318594 | ||||||||
\(254\) | 1.97691 | + | 3.42411i | 0.124042 | + | 0.214848i | ||||
\(255\) | 26.3646 | + | 14.1955i | 1.65102 | + | 0.888955i | ||||
\(256\) | 3.62969 | − | 6.28681i | 0.226856 | − | 0.392926i | ||||
\(257\) | 8.77687 | − | 15.2020i | 0.547486 | − | 0.948273i | −0.450960 | − | 0.892544i | \(-0.648918\pi\) |
0.998446 | − | 0.0557293i | \(-0.0177484\pi\) | |||||||
\(258\) | 19.1671 | + | 10.3201i | 1.19329 | + | 0.642501i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.52393 | 0.218545 | ||||||||
\(261\) | −4.49673 | − | 6.81928i | −0.278340 | − | 0.422103i | ||||
\(262\) | −4.23986 | −0.261940 | ||||||||
\(263\) | 11.6743 | + | 20.2205i | 0.719867 | + | 1.24685i | 0.961052 | + | 0.276367i | \(0.0891306\pi\) |
−0.241185 | + | 0.970479i | \(0.577536\pi\) | |||||||
\(264\) | −5.21564 | + | 3.22134i | −0.321001 | + | 0.198260i | ||||
\(265\) | 3.92701 | − | 6.80177i | 0.241234 | − | 0.417830i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.619063 | + | 20.8497i | 0.0378861 | + | 1.27598i | ||||
\(268\) | 0.827504 | + | 1.43328i | 0.0505478 | + | 0.0875514i | ||||
\(269\) | 0.538488 | 0.0328322 | 0.0164161 | − | 0.999865i | \(-0.494774\pi\) | ||||
0.0164161 | + | 0.999865i | \(0.494774\pi\) | |||||||
\(270\) | −2.11788 | − | 23.7204i | −0.128890 | − | 1.44357i | ||||
\(271\) | −14.4150 | −0.875648 | −0.437824 | − | 0.899061i | \(-0.644251\pi\) | ||||
−0.437824 | + | 0.899061i | \(0.644251\pi\) | |||||||
\(272\) | −8.04863 | − | 13.9406i | −0.488020 | − | 0.845275i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.6056 | + | 23.5656i | −0.821945 | + | 1.42365i | ||||
\(275\) | −4.37918 | + | 7.58495i | −0.264074 | + | 0.457390i | ||||
\(276\) | 1.96641 | − | 1.21451i | 0.118364 | − | 0.0731050i | ||||
\(277\) | −10.9533 | − | 18.9717i | −0.658121 | − | 1.13990i | −0.981101 | − | 0.193494i | \(-0.938018\pi\) |
0.322980 | − | 0.946406i | \(-0.395315\pi\) | |||||||
\(278\) | 21.6089 | 1.29602 | ||||||||
\(279\) | −2.58004 | + | 5.15254i | −0.154463 | + | 0.308475i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.776622 | − | 1.34515i | −0.0463294 | − | 0.0802449i | 0.841931 | − | 0.539586i | \(-0.181419\pi\) |
−0.888260 | + | 0.459341i | \(0.848086\pi\) | |||||||
\(282\) | −1.25527 | − | 0.675871i | −0.0747500 | − | 0.0402475i | ||||
\(283\) | 1.32571 | − | 2.29619i | 0.0788051 | − | 0.136495i | −0.823930 | − | 0.566692i | \(-0.808223\pi\) |
0.902735 | + | 0.430198i | \(0.141556\pi\) | |||||||
\(284\) | −0.508510 | + | 0.880765i | −0.0301745 | + | 0.0522638i | ||||
\(285\) | 36.9208 | + | 19.8792i | 2.18700 | + | 1.17754i | ||||
\(286\) | 2.46689 | + | 4.27279i | 0.145870 | + | 0.252655i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.33552 | − | 4.66421i | 0.137622 | − | 0.274841i | ||||
\(289\) | 7.04111 | 0.414183 | ||||||||
\(290\) | 6.23951 | + | 10.8071i | 0.366396 | + | 0.634617i | ||||
\(291\) | 16.1055 | − | 9.94724i | 0.944121 | − | 0.583118i | ||||
\(292\) | 0.161074 | − | 0.278988i | 0.00942613 | − | 0.0163265i | ||||
\(293\) | −5.19314 | + | 8.99478i | −0.303386 | + | 0.525481i | −0.976901 | − | 0.213694i | \(-0.931451\pi\) |
0.673514 | + | 0.739174i | \(0.264784\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4789 | − | 25.0783i | −0.842996 | − | 1.46011i | ||||
\(296\) | 29.3243 | 1.70444 | ||||||||
\(297\) | −5.01009 | + | 3.52143i | −0.290715 | + | 0.204334i | ||||
\(298\) | 1.46683 | 0.0849712 | ||||||||
\(299\) | −6.92409 | − | 11.9929i | −0.400431 | − | 0.693566i | ||||
\(300\) | −0.118553 | − | 3.99279i | −0.00684466 | − | 0.230524i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.7579 | − | 22.0974i | 0.734137 | − | 1.27156i | ||||
\(303\) | −2.35059 | + | 1.45179i | −0.135038 | + | 0.0834033i | ||||
\(304\) | −11.2712 | − | 19.5224i | −0.646450 | − | 1.11968i | ||||
\(305\) | −34.0567 | −1.95008 | ||||||||
\(306\) | −10.5259 | − | 15.9624i | −0.601723 | − | 0.912512i | ||||
\(307\) | −10.6425 | −0.607400 | −0.303700 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303700 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.56182 | − | 1.91779i | −0.202625 | − | 0.109099i | ||||
\(310\) | 4.40165 | − | 7.62389i | 0.249997 | − | 0.433008i | ||||
\(311\) | 6.85479 | − | 11.8728i | 0.388699 | − | 0.673247i | −0.603576 | − | 0.797306i | \(-0.706258\pi\) |
0.992275 | + | 0.124059i | \(0.0395912\pi\) | |||||||
\(312\) | −14.7501 | − | 7.94186i | −0.835059 | − | 0.449619i | ||||
\(313\) | −10.6090 | − | 18.3752i | −0.599653 | − | 1.03863i | −0.992872 | − | 0.119185i | \(-0.961972\pi\) |
0.393219 | − | 0.919445i | \(-0.371362\pi\) | |||||||
\(314\) | 12.1309 | 0.684586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.311598 | −0.0175288 | ||||||||
\(317\) | −1.78521 | − | 3.09208i | −0.100268 | − | 0.173669i | 0.811527 | − | 0.584315i | \(-0.198637\pi\) |
−0.911795 | + | 0.410646i | \(0.865303\pi\) | |||||||
\(318\) | −4.26697 | + | 2.63541i | −0.239280 | + | 0.147786i | ||||
\(319\) | 1.60446 | − | 2.77901i | 0.0898326 | − | 0.155595i | ||||
\(320\) | −15.5599 | + | 26.9506i | −0.869826 | + | 1.50658i | ||||
\(321\) | −0.114305 | − | 3.84973i | −0.00637989 | − | 0.214871i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.6670 | 1.87328 | ||||||||
\(324\) | 1.10015 | − | 2.56719i | 0.0611194 | − | 0.142622i | ||||
\(325\) | −23.9341 | −1.32763 | ||||||||
\(326\) | −10.9846 | − | 19.0260i | −0.608383 | − | 1.05375i | ||||
\(327\) | −0.0472701 | − | 1.59203i | −0.00261404 | − | 0.0880394i | ||||
\(328\) | 9.99062 | − | 17.3043i | 0.551639 | − | 0.955468i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 7.95969 | − | 4.91614i | 0.438167 | − | 0.270625i | ||||
\(331\) | 11.9728 | + | 20.7375i | 0.658085 | + | 1.13984i | 0.981111 | + | 0.193446i | \(0.0619666\pi\) |
−0.323026 | + | 0.946390i | \(0.604700\pi\) | |||||||
\(332\) | −2.26914 | −0.124535 | ||||||||
\(333\) | 29.2421 | − | 1.73803i | 1.60246 | − | 0.0952435i | ||||
\(334\) | −6.68963 | −0.366040 | ||||||||
\(335\) | −9.40168 | − | 16.2842i | −0.513669 | − | 0.889700i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.7468 | + | 23.8102i | −0.748838 | + | 1.29703i | 0.199542 | + | 0.979889i | \(0.436055\pi\) |
−0.948380 | + | 0.317137i | \(0.897279\pi\) | |||||||
\(338\) | 1.70784 | − | 2.95806i | 0.0928942 | − | 0.160897i | ||||
\(339\) | 3.63959 | + | 1.95966i | 0.197675 | + | 0.106434i | ||||
\(340\) | −2.68249 | − | 4.64620i | −0.145478 | − | 0.251976i | ||||
\(341\) | −2.26373 | −0.122588 | ||||||||
\(342\) | −14.7403 | − | 22.3537i | −0.797066 | − | 1.20875i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −14.5184 | − | 25.1466i | −0.782779 | − | 1.35581i | ||||
\(345\) | −22.3413 | + | 13.7987i | −1.20282 | + | 0.742895i | ||||
\(346\) | −6.32822 | + | 10.9608i | −0.340207 | + | 0.589256i | ||||
\(347\) | 2.56412 | − | 4.44119i | 0.137649 | − | 0.238416i | −0.788957 | − | 0.614448i | \(-0.789379\pi\) |
0.926606 | + | 0.376033i | \(0.122712\pi\) | |||||||
\(348\) | 0.0434359 | + | 1.46290i | 0.00232841 | + | 0.0784195i | ||||
\(349\) | −7.56980 | − | 13.1113i | −0.405202 | − | 0.701830i | 0.589143 | − | 0.808029i | \(-0.299465\pi\) |
−0.994345 | + | 0.106198i | \(0.966132\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −15.1794 | − | 7.04537i | −0.810218 | − | 0.376054i | ||||
\(352\) | 2.04918 | 0.109222 | ||||||||
\(353\) | −16.4878 | − | 28.5578i | −0.877559 | − | 1.51998i | −0.854011 | − | 0.520254i | \(-0.825837\pi\) |
−0.0235477 | − | 0.999723i | \(-0.507496\pi\) | |||||||
\(354\) | 0.548794 | + | 18.4831i | 0.0291681 | + | 0.982363i | ||||
\(355\) | 5.77743 | − | 10.0068i | 0.306634 | − | 0.531106i | ||||
\(356\) | 1.86865 | − | 3.23659i | 0.0990381 | − | 0.171539i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.894299 | − | 1.54897i | −0.0472651 | − | 0.0818656i | ||||
\(359\) | −24.0355 | −1.26855 | −0.634274 | − | 0.773109i | \(-0.718701\pi\) | ||||
−0.634274 | + | 0.773109i | \(0.718701\pi\) | |||||||
\(360\) | −14.2227 | + | 28.4038i | −0.749602 | + | 1.49701i | ||||
\(361\) | 28.1470 | 1.48142 | ||||||||
\(362\) | 3.68227 | + | 6.37789i | 0.193536 | + | 0.335214i | ||||
\(363\) | 14.6573 | + | 7.89189i | 0.769307 | + | 0.414217i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.83004 | + | 3.16972i | −0.0957886 | + | 0.165911i | ||||
\(366\) | 19.1479 | + | 10.3098i | 1.00088 | + | 0.538901i | ||||
\(367\) | 1.32751 | + | 2.29931i | 0.0692952 | + | 0.120023i | 0.898591 | − | 0.438787i | \(-0.144592\pi\) |
−0.829296 | + | 0.558810i | \(0.811258\pi\) | |||||||
\(368\) | 14.1166 | 0.735879 | ||||||||
\(369\) | 8.93699 | − | 17.8479i | 0.465241 | − | 0.929123i | ||||
\(370\) | −44.7524 | −2.32657 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.878416 | − | 0.542536i | 0.0455438 | − | 0.0281292i | ||||
\(373\) | 15.9592 | − | 27.6421i | 0.826334 | − | 1.43125i | −0.0745621 | − | 0.997216i | \(-0.523756\pi\) |
0.900896 | − | 0.434036i | \(-0.142911\pi\) | |||||||
\(374\) | 3.75569 | − | 6.50505i | 0.194202 | − | 0.336368i | ||||
\(375\) | 0.440710 | + | 14.8428i | 0.0227582 | + | 0.766481i | ||||
\(376\) | 0.950821 | + | 1.64687i | 0.0490348 | + | 0.0849308i | ||||
\(377\) | 8.76909 | 0.451631 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.2681 | 1.55477 | 0.777384 | − | 0.629027i | \(-0.216546\pi\) | ||||
0.777384 | + | 0.629027i | \(0.216546\pi\) | |||||||
\(380\) | −3.75653 | − | 6.50651i | −0.192706 | − | 0.333777i | ||||
\(381\) | −0.156358 | − | 5.26606i | −0.00801048 | − | 0.269788i | ||||
\(382\) | 16.2568 | − | 28.1576i | 0.831771 | − | 1.44067i | ||||
\(383\) | −0.866526 | + | 1.50087i | −0.0442774 | + | 0.0766907i | −0.887315 | − | 0.461164i | \(-0.847432\pi\) |
0.843037 | + | 0.537855i | \(0.180765\pi\) | |||||||
\(384\) | 11.7824 | − | 7.27715i | 0.601267 | − | 0.371360i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 22.7917 | 1.16006 | ||||||||
\(387\) | −15.9681 | − | 24.2156i | −0.811704 | − | 1.23095i | ||||
\(388\) | −3.39165 | −0.172185 | ||||||||
\(389\) | 5.54175 | + | 9.59859i | 0.280978 | + | 0.486668i | 0.971626 | − | 0.236523i | \(-0.0760079\pi\) |
−0.690648 | + | 0.723191i | \(0.742675\pi\) | |||||||
\(390\) | 22.5104 | + | 12.1202i | 1.13986 | + | 0.613731i | ||||
\(391\) | −10.5415 | + | 18.2584i | −0.533107 | + | 0.923368i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.97431 | + | 2.67831i | 0.250921 | + | 0.135103i | ||||
\(394\) | 12.8388 | + | 22.2375i | 0.646811 | + | 1.12031i | ||||
\(395\) | 3.54022 | 0.178128 | ||||||||
\(396\) | 1.09528 | − | 0.0650989i | 0.0550399 | − | 0.00327134i | ||||
\(397\) | 25.3391 | 1.27173 | 0.635867 | − | 0.771799i | \(-0.280643\pi\) | ||||
0.635867 | + | 0.771799i | \(0.280643\pi\) | |||||||
\(398\) | 12.3632 | + | 21.4137i | 0.619712 | + | 1.07337i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.1990 | − | 21.1293i | 0.609951 | − | 1.05647i | ||||
\(401\) | 17.4122 | − | 30.1588i | 0.869524 | − | 1.50606i | 0.00704089 | − | 0.999975i | \(-0.497759\pi\) |
0.862483 | − | 0.506085i | \(-0.168908\pi\) | |||||||
\(402\) | 0.356351 | + | 12.0017i | 0.0177732 | + | 0.598590i | ||||
\(403\) | −3.09307 | − | 5.35736i | −0.154077 | − | 0.266869i | ||||
\(404\) | 0.495009 | 0.0246276 | ||||||||
\(405\) | −12.4993 | + | 29.1672i | −0.621097 | + | 1.44933i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.75394 | + | 9.96612i | 0.285212 | + | 0.494002i | ||||
\(408\) | 0.756933 | + | 25.4930i | 0.0374738 | + | 1.26209i | ||||
\(409\) | 9.12308 | − | 15.8016i | 0.451107 | − | 0.781341i | −0.547348 | − | 0.836905i | \(-0.684362\pi\) |
0.998455 | + | 0.0555643i | \(0.0176958\pi\) | |||||||
\(410\) | −15.2469 | + | 26.4083i | −0.752989 | + | 1.30422i | ||||
\(411\) | 30.8488 | − | 19.0531i | 1.52166 | − | 0.939821i | ||||
\(412\) | 0.362400 | + | 0.627695i | 0.0178541 | + | 0.0309243i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 16.7383 | − | 0.994856i | 0.822643 | − | 0.0488945i | ||||
\(415\) | 25.7808 | 1.26553 | ||||||||
\(416\) | 2.79992 | + | 4.84961i | 0.137278 | + | 0.237772i | ||||
\(417\) | −25.3521 | − | 13.6503i | −1.24150 | − | 0.668459i | ||||
\(418\) | 5.25945 | − | 9.10963i | 0.257248 | − | 0.445567i | ||||
\(419\) | −4.20719 | + | 7.28708i | −0.205535 | + | 0.355997i | −0.950303 | − | 0.311326i | \(-0.899227\pi\) |
0.744768 | + | 0.667323i | \(0.232560\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.144291 | + | 0.249919i | 0.00703230 | + | 0.0121803i | 0.869520 | − | 0.493897i | \(-0.164428\pi\) |
−0.862488 | + | 0.506078i | \(0.831095\pi\) | |||||||
\(422\) | −9.66609 | −0.470538 | ||||||||
\(423\) | 1.04576 | + | 1.58590i | 0.0508467 | + | 0.0771090i | ||||
\(424\) | 6.68966 | 0.324878 | ||||||||
\(425\) | 18.2191 | + | 31.5564i | 0.883757 | + | 1.53071i | ||||
\(426\) | −6.27759 | + | 3.87723i | −0.304150 | + | 0.187852i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.345031 | + | 0.597612i | −0.0166777 | + | 0.0288866i | ||||
\(429\) | −0.195112 | − | 6.57127i | −0.00942011 | − | 0.317264i | ||||
\(430\) | 22.1568 | + | 38.3767i | 1.06849 | + | 1.85069i | ||||
\(431\) | −13.4959 | −0.650075 | −0.325037 | − | 0.945701i | \(-0.605377\pi\) | ||||
−0.325037 | + | 0.945701i | \(0.605377\pi\) | |||||||
\(432\) | 13.9565 | − | 9.80960i | 0.671485 | − | 0.471965i | ||||
\(433\) | −4.85211 | −0.233177 | −0.116589 | − | 0.993180i | \(-0.537196\pi\) | ||||
−0.116589 | + | 0.993180i | \(0.537196\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.493497 | − | 16.6207i | −0.0236614 | − | 0.796901i | ||||
\(436\) | −0.142685 | + | 0.247138i | −0.00683339 | + | 0.0118358i | ||||
\(437\) | −14.7623 | + | 25.5690i | −0.706174 | + | 1.22313i | ||||
\(438\) | 1.98847 | − | 1.22814i | 0.0950127 | − | 0.0586827i | ||||
\(439\) | −1.27397 | − | 2.20657i | −0.0608031 | − | 0.105314i | 0.834022 | − | 0.551732i | \(-0.186033\pi\) |
−0.894825 | + | 0.446418i | \(0.852699\pi\) | |||||||
\(440\) | −12.4790 | −0.594914 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.5265 | 0.976347 | ||||||||
\(443\) | 0.322753 | + | 0.559025i | 0.0153345 | + | 0.0265601i | 0.873591 | − | 0.486661i | \(-0.161785\pi\) |
−0.858256 | + | 0.513221i | \(0.828452\pi\) | |||||||
\(444\) | −4.62128 | − | 2.48823i | −0.219316 | − | 0.118086i | ||||
\(445\) | −21.2306 | + | 36.7725i | −1.00643 | + | 1.74319i | ||||
\(446\) | 2.13913 | − | 3.70508i | 0.101291 | − | 0.175441i | ||||
\(447\) | −1.72092 | − | 0.926593i | −0.0813968 | − | 0.0438264i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.22658 | −0.246658 | −0.123329 | − | 0.992366i | \(-0.539357\pi\) | ||||
−0.123329 | + | 0.992366i | \(0.539357\pi\) | |||||||
\(450\) | 12.9755 | − | 25.9131i | 0.611672 | − | 1.22156i | ||||
\(451\) | 7.84133 | 0.369234 | ||||||||
\(452\) | −0.370312 | − | 0.641399i | −0.0174180 | − | 0.0301689i | ||||
\(453\) | −28.9268 | + | 17.8660i | −1.35910 | + | 0.839420i | ||||
\(454\) | 11.7099 | − | 20.2821i | 0.549571 | − | 0.951885i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.06000 | + | 35.7003i | 0.0496392 | + | 1.67182i | ||||
\(457\) | 1.43037 | + | 2.47748i | 0.0669101 | + | 0.115892i | 0.897540 | − | 0.440934i | \(-0.145353\pi\) |
−0.830630 | + | 0.556825i | \(0.812019\pi\) | |||||||
\(458\) | 5.53084 | 0.258439 | ||||||||
\(459\) | 2.26576 | + | 25.3767i | 0.105757 | + | 1.18448i | ||||
\(460\) | 4.70485 | 0.219365 | ||||||||
\(461\) | 1.82624 | + | 3.16314i | 0.0850566 | + | 0.147322i | 0.905415 | − | 0.424527i | \(-0.139560\pi\) |
−0.820359 | + | 0.571849i | \(0.806226\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.4052 | + | 26.6825i | −0.715939 | + | 1.24004i | 0.246657 | + | 0.969103i | \(0.420668\pi\) |
−0.962596 | + | 0.270940i | \(0.912666\pi\) | |||||||
\(464\) | −4.46953 | + | 7.74145i | −0.207493 | + | 0.359388i | ||||
\(465\) | −9.98012 | + | 6.16402i | −0.462817 | + | 0.285850i | ||||
\(466\) | 9.55764 | + | 16.5543i | 0.442749 | + | 0.766864i | ||||
\(467\) | 20.5770 | 0.952191 | 0.476096 | − | 0.879393i | \(-0.342052\pi\) | ||||
0.476096 | + | 0.879393i | \(0.342052\pi\) | |||||||
\(468\) | 1.65061 | + | 2.50315i | 0.0762995 | + | 0.115708i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.45107 | − | 2.51332i | −0.0669327 | − | 0.115931i | ||||
\(471\) | −14.2323 | − | 7.66305i | −0.655788 | − | 0.353095i | ||||
\(472\) | 12.3324 | − | 21.3604i | 0.567647 | − | 0.983193i | ||||
\(473\) | 5.69752 | − | 9.86839i | 0.261972 | − | 0.453749i | ||||
\(474\) | −1.99044 | − | 1.07171i | −0.0914240 | − | 0.0492253i | ||||
\(475\) | 25.5139 | + | 44.1914i | 1.17066 | + | 2.02764i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.67090 | − | 0.396491i | 0.305439 | − | 0.0181541i | ||||
\(478\) | −18.4110 | −0.842102 | ||||||||
\(479\) | −12.5916 | − | 21.8093i | −0.575325 | − | 0.996492i | −0.996006 | − | 0.0892833i | \(-0.971542\pi\) |
0.420682 | − | 0.907208i | \(-0.361791\pi\) | |||||||
\(480\) | 9.03425 | − | 5.57982i | 0.412355 | − | 0.254683i | ||||
\(481\) | −15.7239 | + | 27.2346i | −0.716949 | + | 1.24179i | ||||
\(482\) | −5.15726 | + | 8.93264i | −0.234907 | + | 0.406871i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.49131 | − | 2.58303i | −0.0677869 | − | 0.117410i | ||||
\(485\) | 38.5342 | 1.74975 | ||||||||
\(486\) | 15.8572 | − | 12.6150i | 0.719297 | − | 0.572228i | ||||
\(487\) | −32.7615 | −1.48456 | −0.742282 | − | 0.670088i | \(-0.766256\pi\) | ||||
−0.742282 | + | 0.670088i | \(0.766256\pi\) | |||||||
\(488\) | −14.5039 | − | 25.1215i | −0.656560 | − | 1.13720i | ||||
\(489\) | 0.868801 | + | 29.2607i | 0.0392886 | + | 1.32321i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.76000 | − | 3.04841i | 0.0794278 | − | 0.137573i | −0.823575 | − | 0.567207i | \(-0.808024\pi\) |
0.903003 | + | 0.429634i | \(0.141357\pi\) | |||||||
\(492\) | −3.04274 | + | 1.87929i | −0.137177 | + | 0.0847248i | ||||
\(493\) | −6.67520 | − | 11.5618i | −0.300636 | − | 0.520716i | ||||
\(494\) | 28.7452 | 1.29331 | ||||||||
\(495\) | −12.4440 | + | 0.739621i | −0.559317 | + | 0.0332435i | ||||
\(496\) | 6.30605 | 0.283150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −14.4949 | − | 7.80448i | −0.649533 | − | 0.349727i | ||||
\(499\) | −7.82082 | + | 13.5461i | −0.350108 | + | 0.606405i | −0.986268 | − | 0.165152i | \(-0.947188\pi\) |
0.636160 | + | 0.771557i | \(0.280522\pi\) | |||||||
\(500\) | 1.33029 | − | 2.30412i | 0.0594922 | − | 0.103044i | ||||
\(501\) | 7.84844 | + | 4.22582i | 0.350642 | + | 0.188796i | ||||
\(502\) | −5.23262 | − | 9.06316i | −0.233543 | − | 0.404509i | ||||
\(503\) | −36.5427 | −1.62936 | −0.814678 | − | 0.579913i | \(-0.803086\pi\) | ||||
−0.814678 | + | 0.579913i | \(0.803086\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.62404 | −0.250267 | ||||||||
\(506\) | 3.29358 | + | 5.70465i | 0.146418 | + | 0.253603i | ||||
\(507\) | −3.87228 | + | 2.39164i | −0.171974 | + | 0.106216i | ||||
\(508\) | −0.471969 | + | 0.817474i | −0.0209402 | + | 0.0362696i | ||||
\(509\) | 18.8229 | − | 32.6023i | 0.834311 | − | 1.44507i | −0.0602789 | − | 0.998182i | \(-0.519199\pi\) |
0.894590 | − | 0.446888i | \(-0.147468\pi\) | |||||||
\(510\) | −1.15517 | − | 38.9054i | −0.0511518 | − | 1.72276i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −25.4272 | −1.12373 | ||||||||
\(513\) | 3.17296 | + | 35.5373i | 0.140089 | + | 1.56901i | ||||
\(514\) | −22.8176 | −1.00644 | ||||||||
\(515\) | −4.11740 | − | 7.13155i | −0.181434 | − | 0.314254i | ||||
\(516\) | 0.154243 | + | 5.19481i | 0.00679017 | + | 0.228689i | ||||
\(517\) | −0.373135 | + | 0.646289i | −0.0164105 | + | 0.0284237i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.3483 | − | 8.86196i | 0.629822 | − | 0.388997i | ||||
\(520\) | −17.0508 | − | 29.5329i | −0.747728 | − | 1.29510i | ||||
\(521\) | −14.3423 | −0.628347 | −0.314174 | − | 0.949366i | \(-0.601727\pi\) | ||||
−0.314174 | + | 0.949366i | \(0.601727\pi\) | |||||||
\(522\) | −4.75403 | + | 9.49416i | −0.208078 | + | 0.415548i | ||||
\(523\) | 10.4844 | 0.458453 | 0.229226 | − | 0.973373i | \(-0.426380\pi\) | ||||
0.229226 | + | 0.973373i | \(0.426380\pi\) | |||||||
\(524\) | −0.506114 | − | 0.876616i | −0.0221097 | − | 0.0382951i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.1751 | − | 26.2840i | 0.661665 | − | 1.14604i | ||||
\(527\) | −4.70901 | + | 8.15625i | −0.205128 | + | 0.355292i | ||||
\(528\) | 5.90063 | + | 3.17707i | 0.256792 | + | 0.138264i | ||||
\(529\) | 2.25555 | + | 3.90673i | 0.0980674 | + | 0.169858i | ||||
\(530\) | −10.2092 | −0.443460 | ||||||||
\(531\) | 11.0318 | − | 22.0314i | 0.478741 | − | 0.956083i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.7141 | + | 18.5573i | 0.464078 | + | 0.803807i | ||||
\(534\) | 23.0686 | − | 14.2479i | 0.998276 | − | 0.616565i | ||||
\(535\) | 3.92007 | − | 6.78976i | 0.169479 | − | 0.293547i | ||||
\(536\) | 8.00788 | − | 13.8701i | 0.345888 | − | 0.599095i | ||||
\(537\) | 0.0707321 | + | 2.38222i | 0.00305232 | + | 0.102800i | ||||
\(538\) | −0.349983 | − | 0.606188i | −0.0150888 | − | 0.0261346i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.65150 | − | 3.26939i | 0.200169 | − | 0.140692i | ||||
\(541\) | −46.0922 | −1.98166 | −0.990830 | − | 0.135118i | \(-0.956859\pi\) | ||||
−0.990830 | + | 0.135118i | \(0.956859\pi\) | |||||||
\(542\) | 9.36882 | + | 16.2273i | 0.402425 | + | 0.697021i | ||||
\(543\) | −0.291240 | − | 9.80878i | −0.0124983 | − | 0.420935i | ||||
\(544\) | 4.26271 | − | 7.38323i | 0.182762 | − | 0.316554i | ||||
\(545\) | 1.62112 | − | 2.80786i | 0.0694411 | − | 0.120275i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.1793 | − | 21.0951i | −0.520747 | − | 0.901961i | −0.999709 | − | 0.0241250i | \(-0.992320\pi\) |
0.478962 | − | 0.877836i | \(-0.341013\pi\) | |||||||
\(548\) | −6.49643 | −0.277514 | ||||||||
\(549\) | −15.9521 | − | 24.1914i | −0.680821 | − | 1.03246i | ||||
\(550\) | 11.3847 | 0.485447 | ||||||||
\(551\) | −9.34790 | − | 16.1910i | −0.398234 | − | 0.689761i | ||||
\(552\) | −19.6930 | − | 10.6033i | −0.838191 | − | 0.451306i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −14.2379 | + | 24.6608i | −0.604911 | + | 1.04774i | ||||
\(555\) | 52.5046 | + | 28.2700i | 2.22870 | + | 1.19999i | ||||
\(556\) | 2.57947 | + | 4.46777i | 0.109394 | + | 0.189476i | ||||
\(557\) | 30.5775 | 1.29561 | 0.647806 | − | 0.761805i | \(-0.275687\pi\) | ||||
0.647806 | + | 0.761805i | \(0.275687\pi\) | |||||||
\(558\) | 7.47719 | − | 0.444414i | 0.316535 | − | 0.0188135i | ||||
\(559\) | 31.1394 | 1.31706 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.51550 | + | 5.25943i | −0.359525 | + | 0.222053i | ||||
\(562\) | −1.00951 | + | 1.74852i | −0.0425836 | + | 0.0737570i | ||||
\(563\) | −4.41357 | + | 7.64452i | −0.186010 | + | 0.322178i | −0.943916 | − | 0.330185i | \(-0.892889\pi\) |
0.757907 | + | 0.652363i | \(0.226222\pi\) | |||||||
\(564\) | −0.0101015 | − | 0.340212i | −0.000425350 | − | 0.0143255i | ||||
\(565\) | 4.20730 | + | 7.28725i | 0.177002 | + | 0.306577i | ||||
\(566\) | −3.44650 | −0.144867 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.84186 | 0.412955 | ||||||||
\(569\) | −3.56027 | − | 6.16658i | −0.149254 | − | 0.258516i | 0.781698 | − | 0.623658i | \(-0.214354\pi\) |
−0.930952 | + | 0.365141i | \(0.881021\pi\) | |||||||
\(570\) | −1.61769 | − | 54.4829i | −0.0677576 | − | 2.28204i | ||||
\(571\) | −3.33181 | + | 5.77086i | −0.139432 | + | 0.241503i | −0.927282 | − | 0.374364i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(572\) | −0.588948 | + | 1.02009i | −0.0246252 | + | 0.0426520i | ||||
\(573\) | −36.8600 | + | 22.7658i | −1.53985 | + | 0.951056i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.9548 | −1.33261 | ||||||||
\(576\) | −26.4320 | + | 1.57101i | −1.10133 | + | 0.0654587i | ||||
\(577\) | 7.91259 | 0.329405 | 0.164703 | − | 0.986343i | \(-0.447334\pi\) | ||||
0.164703 | + | 0.986343i | \(0.447334\pi\) | |||||||
\(578\) | −4.57627 | − | 7.92633i | −0.190348 | − | 0.329692i | ||||
\(579\) | −26.7397 | − | 14.3974i | −1.11127 | − | 0.598337i | ||||
\(580\) | −1.48963 | + | 2.58011i | −0.0618533 | + | 0.107133i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −21.6654 | − | 11.6653i | −0.898059 | − | 0.483540i | ||||
\(583\) | 1.31263 | + | 2.27354i | 0.0543634 | + | 0.0941602i | ||||
\(584\) | −3.11747 | −0.129002 | ||||||||
\(585\) | −18.7534 | − | 28.4395i | −0.775358 | − | 1.17583i | ||||
\(586\) | 13.5008 | 0.557714 | ||||||||
\(587\) | −9.13891 | − | 15.8291i | −0.377203 | − | 0.653335i | 0.613451 | − | 0.789733i | \(-0.289781\pi\) |
−0.990654 | + | 0.136398i | \(0.956447\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.59447 | + | 11.4220i | −0.271720 | + | 0.470633i | ||||
\(590\) | −18.8208 | + | 32.5985i | −0.774839 | + | 1.34206i | ||||
\(591\) | −1.01545 | − | 34.1999i | −0.0417702 | − | 1.40679i | ||||
\(592\) | −16.0287 | − | 27.7625i | −0.658775 | − | 1.14103i | ||||
\(593\) | −28.3816 | −1.16549 | −0.582745 | − | 0.812655i | \(-0.698022\pi\) | ||||
−0.582745 | + | 0.812655i | \(0.698022\pi\) | |||||||
\(594\) | 7.22039 | + | 3.35127i | 0.296256 | + | 0.137504i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.175096 | + | 0.303275i | 0.00717222 | + | 0.0124226i | ||||
\(597\) | −0.977835 | − | 32.9329i | −0.0400201 | − | 1.34785i | ||||
\(598\) | −9.00044 | + | 15.5892i | −0.368055 | + | 0.637490i | ||||
\(599\) | −4.69451 | + | 8.13113i | −0.191813 | + | 0.332229i | −0.945851 | − | 0.324601i | \(-0.894770\pi\) |
0.754038 | + | 0.656830i | \(0.228103\pi\) | |||||||
\(600\) | −32.8886 | + | 20.3130i | −1.34267 | + | 0.829274i | ||||
\(601\) | −6.31432 | − | 10.9367i | −0.257566 | − | 0.446118i | 0.708023 | − | 0.706189i | \(-0.249587\pi\) |
−0.965589 | + | 0.260071i | \(0.916254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.16336 | − | 14.3058i | 0.291714 | − | 0.582577i | ||||
\(604\) | 6.09168 | 0.247867 | ||||||||
\(605\) | 16.9435 | + | 29.3471i | 0.688853 | + | 1.19313i | ||||
\(606\) | 3.16205 | + | 1.70254i | 0.128449 | + | 0.0691608i | ||||
\(607\) | −12.0133 | + | 20.8076i | −0.487604 | + | 0.844554i | −0.999898 | − | 0.0142555i | \(-0.995462\pi\) |
0.512295 | + | 0.858810i | \(0.328796\pi\) | |||||||
\(608\) | 5.96947 | − | 10.3394i | 0.242094 | − | 0.419319i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 22.1347 | + | 38.3383i | 0.896206 | + | 1.55227i | ||||
\(611\) | −2.03935 | −0.0825031 | ||||||||
\(612\) | 2.04385 | − | 4.08172i | 0.0826177 | − | 0.164994i | ||||
\(613\) | −28.5415 | −1.15278 | −0.576390 | − | 0.817175i | \(-0.695539\pi\) | ||||
−0.576390 | + | 0.817175i | \(0.695539\pi\) | |||||||
\(614\) | 6.91695 | + | 11.9805i | 0.279145 | + | 0.483494i | ||||
\(615\) | 34.5701 | − | 21.3515i | 1.39400 | − | 0.860976i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.05549 | + | 10.4884i | −0.243785 | + | 0.422248i | −0.961789 | − | 0.273791i | \(-0.911722\pi\) |
0.718004 | + | 0.696039i | \(0.245056\pi\) | |||||||
\(618\) | 0.156062 | + | 5.25606i | 0.00627772 | + | 0.211430i | ||||
\(619\) | 13.2870 | + | 23.0137i | 0.534048 | + | 0.924998i | 0.999209 | + | 0.0397721i | \(0.0126632\pi\) |
−0.465161 | + | 0.885226i | \(0.654003\pi\) | |||||||
\(620\) | 2.10171 | 0.0844067 | ||||||||
\(621\) | −20.2662 | − | 9.40636i | −0.813256 | − | 0.377464i | ||||
\(622\) | −17.8207 | −0.714545 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.543522 | + | 18.3055i | 0.0217583 | + | 0.732806i | ||||
\(625\) | 3.46486 | − | 6.00131i | 0.138594 | − | 0.240052i | ||||
\(626\) | −13.7903 | + | 23.8855i | −0.551170 | + | 0.954655i | ||||
\(627\) | −11.9250 | + | 7.36526i | −0.476240 | + | 0.294140i | ||||
\(628\) | 1.44807 | + | 2.50813i | 0.0577843 | + | 0.100085i | ||||
\(629\) | 47.8774 | 1.90900 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.30962 | 0.131754 | 0.0658770 | − | 0.997828i | \(-0.479015\pi\) | ||||
0.0658770 | + | 0.997828i | \(0.479015\pi\) | |||||||
\(632\) | 1.50769 | + | 2.61140i | 0.0599727 | + | 0.103876i | ||||
\(633\) | 11.3405 | + | 6.10604i | 0.450744 | + | 0.242693i | ||||
\(634\) | −2.32055 | + | 4.01931i | −0.0921608 | + | 0.159627i | ||||
\(635\) | 5.36227 | − | 9.28773i | 0.212795 | − | 0.368572i | ||||
\(636\) | −1.05424 | − | 0.567631i | −0.0418032 | − | 0.0225080i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −4.17119 | −0.165139 | ||||||||
\(639\) | 9.81426 | − | 0.583319i | 0.388246 | − | 0.0230757i | ||||
\(640\) | 28.1907 | 1.11433 | ||||||||
\(641\) | −16.2922 | − | 28.2189i | −0.643503 | − | 1.11458i | −0.984645 | − | 0.174568i | \(-0.944147\pi\) |
0.341142 | − | 0.940012i | \(-0.389186\pi\) | |||||||
\(642\) | −4.25944 | + | 2.63075i | −0.168107 | + | 0.103828i | ||||
\(643\) | 21.5327 | − | 37.2957i | 0.849166 | − | 1.47080i | −0.0327873 | − | 0.999462i | \(-0.510438\pi\) |
0.881953 | − | 0.471337i | \(-0.156228\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.75243 | − | 59.0208i | −0.0690019 | − | 2.32394i | ||||
\(646\) | −21.8814 | − | 37.8997i | −0.860912 | − | 1.49114i | ||||
\(647\) | 46.1975 | 1.81621 | 0.908106 | − | 0.418739i | \(-0.137528\pi\) | ||||
0.908106 | + | 0.418739i | \(0.137528\pi\) | |||||||
\(648\) | −26.8379 | + | 3.20158i | −1.05429 | + | 0.125770i | ||||
\(649\) | 9.67935 | 0.379948 | ||||||||
\(650\) | 15.5556 | + | 26.9432i | 0.610143 | + | 1.05680i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.62248 | − | 4.54228i | 0.102704 | − | 0.177889i | ||||
\(653\) | −16.0002 | + | 27.7132i | −0.626138 | + | 1.08450i | 0.362182 | + | 0.932107i | \(0.382032\pi\) |
−0.988320 | + | 0.152395i | \(0.951301\pi\) | |||||||
\(654\) | −1.76146 | + | 1.08793i | −0.0688786 | + | 0.0425414i | ||||
\(655\) | 5.75022 | + | 9.95967i | 0.224680 | + | 0.389156i | ||||
\(656\) | −21.8435 | −0.852845 | ||||||||
\(657\) | −3.10873 | + | 0.184770i | −0.121283 | + | 0.00720857i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2070 | + | 33.2674i | 0.748197 | + | 1.29591i | 0.948686 | + | 0.316219i | \(0.102413\pi\) |
−0.200490 | + | 0.979696i | \(0.564253\pi\) | |||||||
\(660\) | 1.96659 | + | 1.05887i | 0.0765495 | + | 0.0412164i | ||||
\(661\) | −14.0130 | + | 24.2712i | −0.545043 | + | 0.944042i | 0.453561 | + | 0.891225i | \(0.350153\pi\) |
−0.998604 | + | 0.0528170i | \(0.983180\pi\) | |||||||
\(662\) | 15.5631 | − | 26.9561i | 0.604878 | − | 1.04768i | ||||
\(663\) | −24.0822 | − | 12.9666i | −0.935276 | − | 0.503579i | ||||
\(664\) | 10.9794 | + | 19.0169i | 0.426083 | + | 0.737998i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.9620 | − | 31.7889i | −0.812263 | − | 1.23179i | ||||
\(667\) | 11.7077 | 0.453325 | ||||||||
\(668\) | −0.798544 | − | 1.38312i | −0.0308966 | − | 0.0535145i | ||||
\(669\) | −4.85017 | + | 2.99561i | −0.187518 | + | 0.115817i | ||||
\(670\) | −12.2210 | + | 21.1674i | −0.472138 | + | 0.817766i | ||||
\(671\) | 5.69183 | − | 9.85853i | 0.219730 | − | 0.380584i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.796281 | + | 1.37920i | 0.0306944 | + | 0.0531642i | 0.880965 | − | 0.473182i | \(-0.156895\pi\) |
−0.850270 | + | 0.526347i | \(0.823561\pi\) | |||||||
\(674\) | 35.7383 | 1.37659 | ||||||||
\(675\) | −31.5925 | + | 22.2053i | −1.21599 | + | 0.854683i | ||||
\(676\) | 0.815462 | 0.0313639 | ||||||||
\(677\) | 21.0167 | + | 36.4020i | 0.807737 | + | 1.39904i | 0.914428 | + | 0.404749i | \(0.132641\pi\) |
−0.106691 | + | 0.994292i | \(0.534025\pi\) | |||||||
\(678\) | −0.159469 | − | 5.37082i | −0.00612437 | − | 0.206265i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −25.9588 | + | 44.9620i | −0.995476 | + | 1.72421i | ||||
\(681\) | −26.5504 | + | 16.3983i | −1.01741 | + | 0.628386i | ||||
\(682\) | 1.47128 | + | 2.54833i | 0.0563382 | + | 0.0975807i | ||||
\(683\) | 35.7289 | 1.36713 | 0.683565 | − | 0.729890i | \(-0.260429\pi\) | ||||
0.683565 | + | 0.729890i | \(0.260429\pi\) | |||||||
\(684\) | 2.86219 | − | 5.71602i | 0.109439 | − | 0.218557i | ||||
\(685\) | 73.8092 | 2.82010 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −6.48892 | − | 3.49382i | −0.247568 | − | 0.133298i | ||||
\(688\) | −15.8715 | + | 27.4902i | −0.605095 | + | 1.04806i | ||||
\(689\) | −3.58704 | + | 6.21294i | −0.136655 | + | 0.236694i | ||||
\(690\) | 30.0539 | + | 16.1819i | 1.14413 | + | 0.616033i | ||||
\(691\) | 25.5675 | + | 44.2841i | 0.972632 | + | 1.68465i | 0.687538 | + | 0.726149i | \(0.258692\pi\) |
0.285094 | + | 0.958499i | \(0.407975\pi\) | |||||||
\(692\) | −3.02161 | −0.114864 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.66606 | −0.253040 | ||||||||
\(695\) | −29.3066 | − | 50.7606i | −1.11166 | − | 1.92546i | ||||
\(696\) | 12.0499 | − | 7.44236i | 0.456749 | − | 0.282102i | ||||
\(697\) | 16.3115 | − | 28.2524i | 0.617843 | − | 1.07014i | ||||
\(698\) | −9.83977 | + | 17.0430i | −0.372441 | + | 0.645086i | ||||
\(699\) | −0.755936 | − | 25.4595i | −0.0285921 | − | 0.962965i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5761 | −0.928226 | −0.464113 | − | 0.885776i | \(-0.653627\pi\) | ||||
−0.464113 | + | 0.885776i | \(0.653627\pi\) | |||||||
\(702\) | 1.93453 | + | 21.6668i | 0.0730141 | + | 0.817763i | ||||
\(703\) | 67.0472 | 2.52873 | ||||||||
\(704\) | −5.20100 | − | 9.00840i | −0.196020 | − | 0.339517i | ||||
\(705\) | 0.114768 | + | 3.86532i | 0.00432242 | + | 0.145576i | ||||
\(706\) | −21.4321 | + | 37.1215i | −0.806607 | + | 1.39708i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.75597 | + | 2.31980i | −0.141158 | + | 0.0871833i | ||||
\(709\) | −15.4488 | − | 26.7581i | −0.580192 | − | 1.00492i | −0.995456 | − | 0.0952206i | \(-0.969644\pi\) |
0.415265 | − | 0.909701i | \(-0.363689\pi\) | |||||||
\(710\) | −15.0198 | −0.563685 | ||||||||
\(711\) | 1.65824 | + | 2.51471i | 0.0621888 | + | 0.0943092i | ||||
\(712\) | −36.1664 | −1.35539 | ||||||||
\(713\) | −4.12960 | − | 7.15268i | −0.154655 | − | 0.267870i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.69133 | − | 11.5897i | 0.250242 | − | 0.433431i | ||||
\(716\) | 0.213506 | − | 0.369803i | 0.00797908 | − | 0.0138202i | ||||
\(717\) | 21.6003 | + | 11.6302i | 0.806677 | + | 0.434338i | ||||
\(718\) | 15.6216 | + | 27.0573i | 0.582992 | + | 1.00977i | ||||
\(719\) | −6.11380 | −0.228006 | −0.114003 | − | 0.993480i | \(-0.536367\pi\) | ||||
−0.114003 | + | 0.993480i | \(0.536367\pi\) | |||||||
\(720\) | 34.6651 | − | 2.06035i | 1.29189 | − | 0.0767848i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.2938 | − | 31.6857i | −0.680823 | − | 1.17922i | ||||
\(723\) | 11.6934 | − | 7.22216i | 0.434881 | − | 0.268595i | ||||
\(724\) | −0.879109 | + | 1.52266i | −0.0326718 | + | 0.0565893i | ||||
\(725\) | 10.1174 | − | 17.5238i | 0.375749 | − | 0.650816i | ||||
\(726\) | −0.642209 | − | 21.6292i | −0.0238346 | − | 0.802736i | ||||
\(727\) | −22.2492 | − | 38.5367i | −0.825176 | − | 1.42925i | −0.901785 | − | 0.432186i | \(-0.857743\pi\) |
0.0766087 | − | 0.997061i | \(-0.475591\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.5729 | + | 4.78327i | −0.984182 | + | 0.177158i | ||||
\(730\) | 4.75763 | 0.176088 | ||||||||
\(731\) | −23.7039 | − | 41.0564i | −0.876722 | − | 1.51853i | ||||
\(732\) | 0.154089 | + | 5.18962i | 0.00569529 | + | 0.191814i | ||||
\(733\) | 4.91854 | − | 8.51916i | 0.181670 | − | 0.314662i | −0.760779 | − | 0.649011i | \(-0.775183\pi\) |
0.942449 | + | 0.334349i | \(0.108516\pi\) | |||||||
\(734\) | 1.72559 | − | 2.98881i | 0.0636926 | − | 0.110319i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.73821 | + | 6.47478i | 0.137792 | + | 0.238663i | ||||
\(737\) | 6.28514 | 0.231516 | ||||||||
\(738\) | −25.9002 | + | 1.53940i | −0.953400 | + | 0.0566662i | ||||
\(739\) | 14.8493 | 0.546239 | 0.273120 | − | 0.961980i | \(-0.411944\pi\) | ||||
0.273120 | + | 0.961980i | \(0.411944\pi\) | |||||||
\(740\) | −5.34212 | − | 9.25282i | −0.196380 | − | 0.340140i | ||||
\(741\) | −33.7246 | − | 18.1583i | −1.23890 | − | 0.667061i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.04201 | + | 5.26892i | −0.111601 | + | 0.193298i | −0.916416 | − | 0.400228i | \(-0.868931\pi\) |
0.804815 | + | 0.593525i | \(0.202264\pi\) | |||||||
\(744\) | −8.79710 | − | 4.73661i | −0.322517 | − | 0.173652i | ||||
\(745\) | −1.98935 | − | 3.44566i | −0.0728843 | − | 0.126239i | ||||
\(746\) | −41.4897 | −1.51905 | ||||||||
\(747\) | 12.0757 | + | 18.3128i | 0.441828 | + | 0.670031i | ||||
\(748\) | 1.79328 | 0.0655686 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16.4225 | − | 10.1430i | 0.599665 | − | 0.370371i | ||||
\(751\) | −11.1005 | + | 19.2266i | −0.405063 | + | 0.701590i | −0.994329 | − | 0.106349i | \(-0.966084\pi\) |
0.589266 | + | 0.807939i | \(0.299417\pi\) | |||||||
\(752\) | 1.03944 | − | 1.80036i | 0.0379044 | − | 0.0656523i | ||||
\(753\) | 0.413860 | + | 13.9386i | 0.0150819 | + | 0.507949i | ||||
\(754\) | −5.69934 | − | 9.87156i | −0.207558 | − | 0.359501i | ||||
\(755\) | −69.2106 | −2.51883 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.0464 | 0.910329 | 0.455164 | − | 0.890407i | \(-0.349581\pi\) | ||||
0.455164 | + | 0.890407i | \(0.349581\pi\) | |||||||
\(758\) | −19.6723 | − | 34.0735i | −0.714531 | − | 1.23760i | ||||
\(759\) | −0.260497 | − | 8.77338i | −0.00945544 | − | 0.318454i | ||||
\(760\) | −36.3526 | + | 62.9645i | −1.31865 | + | 2.28396i | ||||
\(761\) | 3.37632 | − | 5.84796i | 0.122392 | − | 0.211988i | −0.798319 | − | 0.602235i | \(-0.794277\pi\) |
0.920710 | + | 0.390247i | \(0.127610\pi\) | |||||||
\(762\) | −5.82649 | + | 3.59862i | −0.211072 | + | 0.130364i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 7.76233 | 0.280831 | ||||||||
\(765\) | −23.2212 | + | 46.3745i | −0.839563 | + | 1.67667i | ||||
\(766\) | 2.25275 | 0.0813950 | ||||||||
\(767\) | 13.2255 | + | 22.9072i | 0.477544 | + | 0.827131i | ||||
\(768\) | 11.0709 | + | 5.96087i | 0.399485 | + | 0.215094i | ||||
\(769\) | −21.0805 | + | 36.5125i | −0.760182 | + | 1.31667i | 0.182575 | + | 0.983192i | \(0.441557\pi\) |
−0.942757 | + | 0.333482i | \(0.891776\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 26.7702 | + | 14.4138i | 0.964104 | + | 0.519101i | ||||
\(772\) | 2.72065 | + | 4.71230i | 0.0979183 | + | 0.169600i | ||||
\(773\) | −3.29852 | −0.118639 | −0.0593197 | − | 0.998239i | \(-0.518893\pi\) | ||||
−0.0593197 | + | 0.998239i | \(0.518893\pi\) | |||||||
\(774\) | −16.8818 | + | 33.7142i | −0.606803 | + | 1.21183i | ||||
\(775\) | −14.2746 | −0.512757 | ||||||||
\(776\) | 16.4108 | + | 28.4243i | 0.589112 | + | 1.02037i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.20356 | − | 12.4769i | 0.258260 | − | 0.447320i | ||||
\(779\) | 22.8425 | − | 39.5644i | 0.818419 | − | 1.41754i | ||||
\(780\) | 0.181148 | + | 6.10094i | 0.00648612 | + | 0.218449i | ||||
\(781\) | 1.93114 | + | 3.34484i | 0.0691017 | + | 0.119688i | ||||
\(782\) | 27.4052 | 0.980009 | ||||||||
\(783\) | 11.5750 | − | 8.13567i | 0.413656 | − | 0.290745i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.4522 | − | 28.4961i | −0.587205 | − | 1.01707i | ||||
\(786\) | −0.217950 | − | 7.34043i | −0.00777402 | − | 0.261824i | ||||
\(787\) | 3.36455 | − | 5.82757i | 0.119933 | − | 0.207731i | −0.799808 | − | 0.600256i | \(-0.795065\pi\) |
0.919741 | + | 0.392526i | \(0.128399\pi\) | |||||||
\(788\) | −3.06515 | + | 5.30900i | −0.109192 | + | 0.189125i | ||||
\(789\) | −34.4073 | + | 21.2510i | −1.22493 | + | 0.756555i | ||||
\(790\) | −2.30092 | − | 3.98530i | −0.0818629 | − | 0.141791i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −5.84517 | − | 8.86419i | −0.207699 | − | 0.314975i | ||||
\(793\) | 31.1083 | 1.10469 | ||||||||
\(794\) | −16.4688 | − | 28.5248i | −0.584456 | − | 1.01231i | ||||
\(795\) | 11.9777 | + | 6.44913i | 0.424805 | + | 0.228727i | ||||
\(796\) | −2.95160 | + | 5.11233i | −0.104617 | + | 0.181202i | ||||
\(797\) | −8.86302 | + | 15.3512i | −0.313944 | + | 0.543767i | −0.979213 | − | 0.202837i | \(-0.934984\pi\) |
0.665268 | + | 0.746604i | \(0.268317\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.55239 | + | 2.68882i | 0.0549196 | + | 0.0951235i | ||||
\(800\) | 12.9217 | 0.456850 | ||||||||
\(801\) | −36.0650 | + | 2.14355i | −1.27429 | + | 0.0757387i | ||||
\(802\) | −45.2673 | −1.59844 | ||||||||
\(803\) | −0.611702 | − | 1.05950i | −0.0215865 | − | 0.0373889i | ||||
\(804\) | −2.43888 | + | 1.50632i | −0.0860126 | + | 0.0531240i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −4.02060 | + | 6.96388i | −0.141620 | + | 0.245292i | ||||
\(807\) | 0.0276809 | + | 0.932277i | 0.000974415 | + | 0.0328177i | ||||
\(808\) | −2.39514 | − | 4.14850i | −0.0842607 | − | 0.145944i | ||||
\(809\) | 39.0857 | 1.37418 | 0.687089 | − | 0.726573i | \(-0.258888\pi\) | ||||
0.687089 | + | 0.726573i | \(0.258888\pi\) | |||||||
\(810\) | 40.9579 | − | 4.88600i | 1.43911 | − | 0.171676i | ||||
\(811\) | −13.9559 | −0.490058 | −0.245029 | − | 0.969516i | \(-0.578797\pi\) | ||||
−0.245029 | + | 0.969516i | \(0.578797\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −0.741002 | − | 24.9565i | −0.0259881 | − | 0.875263i | ||||
\(814\) | 7.47939 | − | 12.9547i | 0.262152 | − | 0.454061i | ||||
\(815\) | −29.7953 | + | 51.6070i | −1.04369 | + | 1.80772i | ||||
\(816\) | 23.7215 | − | 14.6511i | 0.830419 | − | 0.512892i | ||||
\(817\) | −33.1948 | − | 57.4951i | −1.16134 | − | 2.01150i | ||||
\(818\) | −23.7177 | −0.829269 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.28010 | −0.254232 | ||||||||
\(821\) | 22.4983 | + | 38.9682i | 0.785196 | + | 1.36000i | 0.928882 | + | 0.370376i | \(0.120771\pi\) |
−0.143685 | + | 0.989623i | \(0.545895\pi\) | |||||||
\(822\) | −41.4983 | − | 22.3438i | −1.44742 | − | 0.779331i | ||||
\(823\) | 27.6232 | − | 47.8449i | 0.962886 | − | 1.66777i | 0.247694 | − | 0.968838i | \(-0.420327\pi\) |
0.715191 | − | 0.698929i | \(-0.246340\pi\) | |||||||
\(824\) | 3.50700 | − | 6.07430i | 0.122172 | − | 0.211608i | ||||
\(825\) | −13.3569 | − | 7.19171i | −0.465026 | − | 0.250383i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.8901 | −0.483005 | −0.241502 | − | 0.970400i | \(-0.577640\pi\) | ||||
−0.241502 | + | 0.970400i | \(0.577640\pi\) | |||||||
\(828\) | 2.20375 | + | 3.34198i | 0.0765857 | + | 0.116142i | ||||
\(829\) | 38.9792 | 1.35381 | 0.676903 | − | 0.736073i | \(-0.263322\pi\) | ||||
0.676903 | + | 0.736073i | \(0.263322\pi\) | |||||||
\(830\) | −16.7559 | − | 29.0220i | −0.581605 | − | 1.00737i | ||||
\(831\) | 32.2824 | − | 19.9386i | 1.11987 | − | 0.691662i | ||||
\(832\) | 14.2129 | − | 24.6174i | 0.492743 | − | 0.853456i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.11081 | + | 37.4113i | 0.0384641 | + | 1.29545i | ||||
\(835\) | 9.07266 | + | 15.7143i | 0.313972 | + | 0.543816i | ||||
\(836\) | 2.51129 | 0.0868548 | ||||||||
\(837\) | −9.05316 | − | 4.20193i | −0.312923 | − | 0.145240i | ||||
\(838\) | 10.9376 | 0.377834 | ||||||||
\(839\) | 19.4708 | + | 33.7244i | 0.672206 | + | 1.16429i | 0.977277 | + | 0.211965i | \(0.0679862\pi\) |
−0.305072 | + | 0.952329i | \(0.598680\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.7932 | − | 18.6943i | 0.372178 | − | 0.644631i | ||||
\(842\) | 0.187560 | − | 0.324863i | 0.00646373 | − | 0.0111955i | ||||
\(843\) | 2.28892 | − | 1.41370i | 0.0788345 | − | 0.0486906i | ||||
\(844\) | −1.15385 | − | 1.99852i | −0.0397170 | − | 0.0687918i | ||||
\(845\) | −9.26487 | −0.318721 | ||||||||
\(846\) | 1.10560 | − | 2.20797i | 0.0380113 | − | 0.0759116i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.65657 | − | 6.33336i | −0.125567 | − | 0.217488i | ||||
\(849\) | 4.04352 | + | 2.17715i | 0.138773 | + | 0.0747194i | ||||
\(850\) | 23.6825 | − | 41.0193i | 0.812304 | − | 1.40695i | ||||
\(851\) | −20.9932 | + | 36.3613i | −0.719638 | + | 1.24645i | ||||
\(852\) | −1.55100 | − | 0.835101i | −0.0531363 | − | 0.0286101i | ||||
\(853\) | 3.83890 | + | 6.64916i | 0.131441 | + | 0.227663i | 0.924232 | − | 0.381830i | \(-0.124706\pi\) |
−0.792791 | + | 0.609493i | \(0.791373\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −32.5188 | + | 64.9425i | −1.11212 | + | 2.22099i | ||||
\(856\) | 6.67784 | 0.228244 | ||||||||
\(857\) | −7.98194 | − | 13.8251i | −0.272658 | − | 0.472258i | 0.696884 | − | 0.717184i | \(-0.254569\pi\) |
−0.969542 | + | 0.244927i | \(0.921236\pi\) | |||||||
\(858\) | −7.27061 | + | 4.49055i | −0.248215 | + | 0.153305i | ||||
\(859\) | 24.1645 | − | 41.8542i | 0.824483 | − | 1.42805i | −0.0778308 | − | 0.996967i | \(-0.524799\pi\) |
0.902314 | − | 0.431080i | \(-0.141867\pi\) | |||||||
\(860\) | −5.28973 | + | 9.16208i | −0.180378 | + | 0.312424i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.77148 | + | 15.1926i | 0.298758 | + | 0.517463i | ||||
\(863\) | −34.3052 | −1.16776 | −0.583881 | − | 0.811839i | \(-0.698467\pi\) | ||||
−0.583881 | + | 0.811839i | \(0.698467\pi\) | |||||||
\(864\) | 8.19514 | + | 3.80369i | 0.278804 | + | 0.129404i | ||||
\(865\) | 34.3300 | 1.16726 | ||||||||
\(866\) | 3.15356 | + | 5.46212i | 0.107162 | + | 0.185611i | ||||
\(867\) | 0.361948 | + | 12.1902i | 0.0122924 | + | 0.414001i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.591670 | + | 1.02480i | −0.0200710 | + | 0.0347640i | ||||
\(870\) | −18.3895 | + | 11.3579i | −0.623464 | + | 0.385070i | ||||
\(871\) | 8.58776 | + | 14.8744i | 0.290985 | + | 0.504001i | ||||
\(872\) | 2.76158 | 0.0935188 | ||||||||
\(873\) | 18.0494 | + | 27.3719i | 0.610881 | + | 0.926399i | ||||
\(874\) | 38.3781 | 1.29816 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.491288 | + | 0.264524i | 0.0165991 | + | 0.00893743i | ||||
\(877\) | −7.09076 | + | 12.2816i | −0.239438 | + | 0.414719i | −0.960553 | − | 0.278097i | \(-0.910296\pi\) |
0.721115 | + | 0.692815i | \(0.243630\pi\) | |||||||
\(878\) | −1.65599 | + | 2.86826i | −0.0558870 | + | 0.0967992i | ||||
\(879\) | −15.8395 | − | 8.52844i | −0.534253 | − | 0.287657i | ||||
\(880\) | 6.82103 | + | 11.8144i | 0.229937 | + | 0.398262i | ||||
\(881\) | 46.2822 | 1.55929 | 0.779643 | − | 0.626224i | \(-0.215400\pi\) | ||||
0.779643 | + | 0.626224i | \(0.215400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.37483 | −0.147225 | −0.0736124 | − | 0.997287i | \(-0.523453\pi\) | ||||
−0.0736124 | + | 0.997287i | \(0.523453\pi\) | |||||||
\(884\) | 2.45026 | + | 4.24397i | 0.0824111 | + | 0.142740i | ||||
\(885\) | 42.6734 | − | 26.3564i | 1.43445 | − | 0.885959i | ||||
\(886\) | 0.419538 | − | 0.726661i | 0.0140946 | − | 0.0244126i | ||||
\(887\) | −9.57208 | + | 16.5793i | −0.321399 | + | 0.556679i | −0.980777 | − | 0.195132i | \(-0.937486\pi\) |
0.659378 | + | 0.751812i | \(0.270820\pi\) | |||||||
\(888\) | 1.50742 | + | 50.7689i | 0.0505856 | + | 1.70369i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 55.1942 | 1.85011 | ||||||||
\(891\) | −6.35415 | − | 8.49289i | −0.212872 | − | 0.284523i | ||||
\(892\) | 1.02139 | 0.0341988 | ||||||||
\(893\) | 2.17396 | + | 3.76540i | 0.0727486 | + | 0.126004i | ||||
\(894\) | 0.0754024 | + | 2.53951i | 0.00252183 | + | 0.0849338i | ||||
\(895\) | −2.42574 | + | 4.20151i | −0.0810836 | + | 0.140441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 20.4072 | − | 12.6041i | 0.681377 | − | 0.420838i | ||||
\(898\) | 3.39694 | + | 5.88368i | 0.113358 | + | 0.196341i | ||||
\(899\) | 5.22997 | 0.174429 | ||||||||
\(900\) | 6.90658 | − | 0.410498i | 0.230219 | − | 0.0136833i | ||||
\(901\) | 10.9221 | 0.363868 | ||||||||
\(902\) | −5.09636 | − | 8.82715i | −0.169690 | − | 0.293912i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.58357 | + | 6.20692i | −0.119188 | + | 0.206439i | ||||
\(905\) | 9.98800 | − | 17.2997i | 0.332012 | − | 0.575062i | ||||
\(906\) | 38.9128 | + | 20.9517i | 1.29279 | + | 0.696075i | ||||
\(907\) | −19.9225 | − | 34.5068i | −0.661515 | − | 1.14578i | −0.980218 | − | 0.197923i | \(-0.936580\pi\) |
0.318702 | − | 0.947855i | \(-0.396753\pi\) | |||||||
\(908\) | 5.59124 | 0.185552 | ||||||||
\(909\) | −2.63430 | − | 3.99491i | −0.0873743 | − | 0.132503i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.3727 | + | 24.8942i | 0.476189 | + | 0.824783i | 0.999628 | − | 0.0272803i | \(-0.00868466\pi\) |
−0.523439 | + | 0.852063i | \(0.675351\pi\) | |||||||
\(912\) | 33.2194 | − | 20.5173i | 1.10001 | − | 0.679396i | ||||
\(913\) | −4.30870 | + | 7.46288i | −0.142597 | + | 0.246985i | ||||
\(914\) | 1.85930 | − | 3.22041i | 0.0615003 | − | 0.106522i | ||||
\(915\) | −1.75068 | − | 58.9619i | −0.0578757 | − | 1.94922i | ||||
\(916\) | 0.660219 | + | 1.14353i | 0.0218142 | + | 0.0377834i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 27.0945 | − | 19.0438i | 0.894252 | − | 0.628540i | ||||
\(919\) | −16.0269 | −0.528680 | −0.264340 | − | 0.964430i | \(-0.585154\pi\) | ||||
−0.264340 | + | 0.964430i | \(0.585154\pi\) | |||||||
\(920\) | −22.7648 | − | 39.4298i | −0.750533 | − | 1.29996i | ||||
\(921\) | −0.547078 | − | 18.4252i | −0.0180268 | − | 0.607133i | ||||
\(922\) | 2.37388 | − | 4.11168i | 0.0781796 | − | 0.135411i | ||||
\(923\) | −5.27727 | + | 9.14050i | −0.173704 | + | 0.300863i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.2830 | + | 62.8440i | 1.19298 | + | 2.06630i | ||||
\(926\) | 40.0495 | 1.31611 | ||||||||
\(927\) | 3.13714 | − | 6.26512i | 0.103037 | − | 0.205774i | ||||
\(928\) | −4.73430 | −0.155411 | ||||||||
\(929\) | 7.00796 | + | 12.1381i | 0.229924 | + | 0.398239i | 0.957785 | − | 0.287485i | \(-0.0928190\pi\) |
−0.727862 | + | 0.685724i | \(0.759486\pi\) | |||||||
\(930\) | 13.4254 | + | 7.22863i | 0.440237 | + | 0.237036i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −2.28180 | + | 3.95219i | −0.0747428 | + | 0.129458i | ||||
\(933\) | 20.9077 | + | 11.2573i | 0.684486 | + | 0.368547i | ||||
\(934\) | −13.3738 | − | 23.1640i | −0.437603 | − | 0.757950i | ||||
\(935\) | −20.3743 | −0.666310 | ||||||||
\(936\) | 12.9914 | − | 25.9449i | 0.424638 | − | 0.848035i | ||||
\(937\) | −51.5307 | −1.68344 | −0.841718 | − | 0.539918i | \(-0.818455\pi\) | ||||
−0.841718 | + | 0.539918i | \(0.818455\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 31.2675 | − | 19.3117i | 1.02038 | − | 0.630214i | ||||
\(940\) | 0.346429 | − | 0.600032i | 0.0112993 | − | 0.0195709i | ||||
\(941\) | −23.1564 | + | 40.1081i | −0.754877 | + | 1.30749i | 0.190558 | + | 0.981676i | \(0.438970\pi\) |
−0.945435 | + | 0.325809i | \(0.894363\pi\) | |||||||
\(942\) | 0.623588 | + | 21.0021i | 0.0203176 | + | 0.684284i | ||||
\(943\) | 14.3045 | + | 24.7761i | 0.465819 | + | 0.806821i | ||||
\(944\) | −26.9636 | −0.877592 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.8121 | −0.481582 | ||||||||
\(947\) | −10.0041 | − | 17.3277i | −0.325091 | − | 0.563073i | 0.656440 | − | 0.754378i | \(-0.272061\pi\) |
−0.981531 | + | 0.191305i | \(0.938728\pi\) | |||||||
\(948\) | −0.0160177 | − | 0.539466i | −0.000520230 | − | 0.0175210i | ||||
\(949\) | 1.67161 | − | 2.89531i | 0.0542628 | − | 0.0939859i | ||||
\(950\) | 33.1648 | − | 57.4432i | 1.07601 | − | 1.86370i | ||||
\(951\) | 5.26152 | − | 3.24967i | 0.170616 | − | 0.105378i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30.0109 | 0.972148 | 0.486074 | − | 0.873918i | \(-0.338429\pi\) | ||||
0.486074 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(954\) | −4.78200 | − | 7.25188i | −0.154823 | − | 0.234788i | ||||
\(955\) | −88.1917 | −2.85382 | ||||||||
\(956\) | −2.19773 | − | 3.80659i | −0.0710798 | − | 0.123114i | ||||
\(957\) | 4.89374 | + | 2.63493i | 0.158192 | + | 0.0851752i | ||||
\(958\) | −16.3675 | + | 28.3493i | −0.528809 | + | 0.915924i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −47.4591 | − | 25.5533i | −1.53173 | − | 0.824730i | ||||
\(961\) | 13.6553 | + | 23.6516i | 0.440492 | + | 0.762955i | ||||
\(962\) | 40.8782 | 1.31796 | ||||||||
\(963\) | 6.65912 | − | 0.395790i | 0.214587 | − | 0.0127542i | ||||
\(964\) | −2.46250 | −0.0793117 | ||||||||
\(965\) | −30.9106 | − | 53.5388i | −0.995049 | − | 1.72348i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5721 | − | 28.7037i | 0.532923 | − | 0.923050i | −0.466338 | − | 0.884607i | \(-0.654427\pi\) |
0.999261 | − | 0.0384431i | \(-0.0122398\pi\) | |||||||
\(968\) | −14.4317 | + | 24.9964i | −0.463851 | + | 0.803414i | ||||
\(969\) | 1.73065 | + | 58.2873i | 0.0555965 | + | 1.87246i | ||||
\(970\) | −25.0448 | − | 43.3788i | −0.804140 | − | 1.39281i | ||||
\(971\) | −41.6469 | −1.33651 | −0.668256 | − | 0.743932i | \(-0.732959\pi\) | ||||
−0.668256 | + | 0.743932i | \(0.732959\pi\) | |||||||
\(972\) | 4.50110 | + | 1.77271i | 0.144373 | + | 0.0568597i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 21.2928 | + | 36.8803i | 0.682267 | + | 1.18172i | ||||
\(975\) | −1.23033 | − | 41.4369i | −0.0394022 | − | 1.32704i | ||||
\(976\) | −15.8556 | + | 27.4628i | −0.507527 | + | 0.879062i | ||||
\(977\) | −18.7590 | + | 32.4916i | −0.600154 | + | 1.03950i | 0.392643 | + | 0.919691i | \(0.371561\pi\) |
−0.992797 | + | 0.119807i | \(0.961772\pi\) | |||||||
\(978\) | 32.3748 | − | 19.9956i | 1.03523 | − | 0.639389i | ||||
\(979\) | −7.09647 | − | 12.2914i | −0.226804 | − | 0.392836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.75383 | − | 0.163676i | 0.0879231 | − | 0.00522578i | ||||
\(982\) | −4.57556 | −0.146012 | ||||||||
\(983\) | 24.0379 | + | 41.6349i | 0.766690 | + | 1.32795i | 0.939348 | + | 0.342964i | \(0.111431\pi\) |
−0.172658 | + | 0.984982i | \(0.555236\pi\) | |||||||
\(984\) | 30.4722 | + | 16.4071i | 0.971419 | + | 0.523039i | ||||
\(985\) | 34.8247 | − | 60.3182i | 1.10961 | − | 1.92190i | ||||
\(986\) | −8.67690 | + | 15.0288i | −0.276329 | + | 0.478616i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.43133 | + | 5.94323i | 0.109165 | + | 0.189079i | ||||
\(989\) | 41.5747 | 1.32200 | ||||||||
\(990\) | 8.92042 | + | 13.5278i | 0.283510 | + | 0.429942i | ||||
\(991\) | −34.1286 | −1.08413 | −0.542065 | − | 0.840337i | \(-0.682357\pi\) | ||||
−0.542065 | + | 0.840337i | \(0.682357\pi\) | |||||||
\(992\) | 1.66990 | + | 2.89236i | 0.0530195 | + | 0.0918324i | ||||
\(993\) | −35.2871 | + | 21.7944i | −1.11980 | + | 0.691624i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 33.5346 | − | 58.0837i | 1.06312 | − | 1.84138i | ||||
\(996\) | −0.116645 | − | 3.92853i | −0.00369603 | − | 0.124480i | ||||
\(997\) | −22.0413 | − | 38.1767i | −0.698056 | − | 1.20907i | −0.969140 | − | 0.246512i | \(-0.920715\pi\) |
0.271084 | − | 0.962556i | \(-0.412618\pi\) | |||||||
\(998\) | 20.3321 | 0.643602 | ||||||||
\(999\) | 4.51222 | + | 50.5372i | 0.142760 | + | 1.59893i |
(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 | 441.2.f.h.148.4 | yes | 24 | |
3.2 | odd | 2 | 1323.2.f.h.442.10 | 24 | |||
7.2 | even | 3 | 441.2.g.h.67.3 | 24 | |||
7.3 | odd | 6 | 441.2.h.h.373.9 | 24 | |||
7.4 | even | 3 | 441.2.h.h.373.10 | 24 | |||
7.5 | odd | 6 | 441.2.g.h.67.4 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.148.3 | ✓ | 24 | |
9.2 | odd | 6 | 1323.2.f.h.883.10 | 24 | |||
9.4 | even | 3 | 3969.2.a.bh.1.10 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bi.1.3 | 12 | |||
9.7 | even | 3 | inner | 441.2.f.h.295.4 | yes | 24 | |
21.2 | odd | 6 | 1323.2.g.h.361.10 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.361.9 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.226.3 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.226.4 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.442.9 | 24 | |||
63.2 | odd | 6 | 1323.2.h.h.802.3 | 24 | |||
63.11 | odd | 6 | 1323.2.g.h.667.10 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bh.1.9 | 12 | |||
63.16 | even | 3 | 441.2.h.h.214.10 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.883.9 | 24 | |||
63.25 | even | 3 | 441.2.g.h.79.3 | 24 | |||
63.34 | odd | 6 | inner | 441.2.f.h.295.3 | yes | 24 | |
63.38 | even | 6 | 1323.2.g.h.667.9 | 24 | |||
63.41 | even | 6 | 3969.2.a.bi.1.4 | 12 | |||
63.47 | even | 6 | 1323.2.h.h.802.4 | 24 | |||
63.52 | odd | 6 | 441.2.g.h.79.4 | 24 | |||
63.61 | odd | 6 | 441.2.h.h.214.9 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.3 | ✓ | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.148.4 | yes | 24 | 1.1 | even | 1 | trivial | |
441.2.f.h.295.3 | yes | 24 | 63.34 | odd | 6 | inner | |
441.2.f.h.295.4 | yes | 24 | 9.7 | even | 3 | inner | |
441.2.g.h.67.3 | 24 | 7.2 | even | 3 | |||
441.2.g.h.67.4 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.79.3 | 24 | 63.25 | even | 3 | |||
441.2.g.h.79.4 | 24 | 63.52 | odd | 6 | |||
441.2.h.h.214.9 | 24 | 63.61 | odd | 6 | |||
441.2.h.h.214.10 | 24 | 63.16 | even | 3 | |||
441.2.h.h.373.9 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.10 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.9 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.10 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.883.9 | 24 | 63.20 | even | 6 | |||
1323.2.f.h.883.10 | 24 | 9.2 | odd | 6 | |||
1323.2.g.h.361.9 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.361.10 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.667.9 | 24 | 63.38 | even | 6 | |||
1323.2.g.h.667.10 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.226.3 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.226.4 | 24 | 21.17 | even | 6 | |||
1323.2.h.h.802.3 | 24 | 63.2 | odd | 6 | |||
1323.2.h.h.802.4 | 24 | 63.47 | even | 6 | |||
3969.2.a.bh.1.9 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bh.1.10 | 12 | 9.4 | even | 3 | |||
3969.2.a.bi.1.3 | 12 | 9.5 | odd | 6 | |||
3969.2.a.bi.1.4 | 12 | 63.41 | even | 6 |