Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(87,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.g (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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(70\) |
Relative dimension: | \(35\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 87.15 | ||
Character | \(\chi\) | \(=\) | 403.87 |
Dual form | 403.2.g.a.315.15 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.351546 | + | 0.608895i | −0.248580 | + | 0.430554i | −0.963132 | − | 0.269029i | \(-0.913297\pi\) |
0.714552 | + | 0.699583i | \(0.246631\pi\) | |||||||
\(3\) | −3.24498 | −1.87349 | −0.936746 | − | 0.350011i | \(-0.886178\pi\) | ||||
−0.936746 | + | 0.350011i | \(0.886178\pi\) | |||||||
\(4\) | 0.752831 | + | 1.30394i | 0.376416 | + | 0.651971i | ||||
\(5\) | −1.57412 | + | 2.72646i | −0.703969 | + | 1.21931i | 0.263093 | + | 0.964770i | \(0.415257\pi\) |
−0.967062 | + | 0.254540i | \(0.918076\pi\) | |||||||
\(6\) | 1.14076 | − | 1.97585i | 0.465713 | − | 0.806639i | ||||
\(7\) | −2.53334 | + | 4.38787i | −0.957513 | + | 1.65846i | −0.229002 | + | 0.973426i | \(0.573546\pi\) |
−0.728511 | + | 0.685034i | \(0.759787\pi\) | |||||||
\(8\) | −2.46480 | −0.871439 | ||||||||
\(9\) | 7.52991 | 2.50997 | ||||||||
\(10\) | −1.10675 | − | 1.91695i | −0.349986 | − | 0.606193i | ||||
\(11\) | −0.348040 | − | 0.602824i | −0.104938 | − | 0.181758i | 0.808775 | − | 0.588118i | \(-0.200131\pi\) |
−0.913713 | + | 0.406360i | \(0.866798\pi\) | |||||||
\(12\) | −2.44292 | − | 4.23127i | −0.705211 | − | 1.22146i | ||||
\(13\) | 2.77836 | + | 2.29797i | 0.770580 | + | 0.637344i | ||||
\(14\) | −1.78117 | − | 3.08508i | −0.476038 | − | 0.824521i | ||||
\(15\) | 5.10800 | − | 8.84732i | 1.31888 | − | 2.28437i | ||||
\(16\) | −0.639172 | + | 1.10708i | −0.159793 | + | 0.276770i | ||||
\(17\) | −0.646924 | + | 1.12051i | −0.156902 | + | 0.271762i | −0.933750 | − | 0.357926i | \(-0.883484\pi\) |
0.776848 | + | 0.629688i | \(0.216817\pi\) | |||||||
\(18\) | −2.64711 | + | 4.58492i | −0.623929 | + | 1.08068i | ||||
\(19\) | −0.479613 | + | 0.830713i | −0.110031 | + | 0.190579i | −0.915782 | − | 0.401675i | \(-0.868428\pi\) |
0.805752 | + | 0.592253i | \(0.201762\pi\) | |||||||
\(20\) | −4.74020 | −1.05994 | ||||||||
\(21\) | 8.22064 | − | 14.2386i | 1.79389 | − | 3.10711i | ||||
\(22\) | 0.489408 | 0.104342 | ||||||||
\(23\) | −0.0533488 | + | 0.0924029i | −0.0111240 | + | 0.0192673i | −0.871534 | − | 0.490335i | \(-0.836874\pi\) |
0.860410 | + | 0.509603i | \(0.170208\pi\) | |||||||
\(24\) | 7.99824 | 1.63263 | ||||||||
\(25\) | −2.45573 | − | 4.25344i | −0.491145 | − | 0.850689i | ||||
\(26\) | −2.37595 | + | 0.883889i | −0.465962 | + | 0.173345i | ||||
\(27\) | −14.6995 | −2.82892 | ||||||||
\(28\) | −7.62871 | −1.44169 | ||||||||
\(29\) | 3.67126 | − | 6.35880i | 0.681735 | − | 1.18080i | −0.292716 | − | 0.956199i | \(-0.594559\pi\) |
0.974451 | − | 0.224600i | \(-0.0721077\pi\) | |||||||
\(30\) | 3.59139 | + | 6.22047i | 0.655695 | + | 1.13570i | ||||
\(31\) | 0.714886 | + | 5.52168i | 0.128397 | + | 0.991723i | ||||
\(32\) | −2.91420 | − | 5.04754i | −0.515162 | − | 0.892287i | ||||
\(33\) | 1.12938 | + | 1.95615i | 0.196601 | + | 0.340522i | ||||
\(34\) | −0.454847 | − | 0.787818i | −0.0780056 | − | 0.135110i | ||||
\(35\) | −7.97558 | − | 13.8141i | −1.34812 | − | 2.33501i | ||||
\(36\) | 5.66875 | + | 9.81856i | 0.944792 | + | 1.63643i | ||||
\(37\) | 2.34164 | 0.384963 | 0.192482 | − | 0.981301i | \(-0.438346\pi\) | ||||
0.192482 | + | 0.981301i | \(0.438346\pi\) | |||||||
\(38\) | −0.337211 | − | 0.584067i | −0.0547029 | − | 0.0947482i | ||||
\(39\) | −9.01574 | − | 7.45689i | −1.44367 | − | 1.19406i | ||||
\(40\) | 3.87990 | − | 6.72018i | 0.613466 | − | 1.06255i | ||||
\(41\) | 5.37005 | + | 9.30120i | 0.838661 | + | 1.45260i | 0.891015 | + | 0.453975i | \(0.149994\pi\) |
−0.0523538 | + | 0.998629i | \(0.516672\pi\) | |||||||
\(42\) | 5.77986 | + | 10.0110i | 0.891852 | + | 1.54473i | ||||
\(43\) | −0.0653367 | + | 0.113166i | −0.00996375 | + | 0.0172577i | −0.870964 | − | 0.491346i | \(-0.836505\pi\) |
0.861001 | + | 0.508604i | \(0.169838\pi\) | |||||||
\(44\) | 0.524031 | − | 0.907649i | 0.0790007 | − | 0.136833i | ||||
\(45\) | −11.8530 | + | 20.5300i | −1.76694 | + | 3.06043i | ||||
\(46\) | −0.0375091 | − | 0.0649677i | −0.00553042 | − | 0.00957896i | ||||
\(47\) | 8.88289 | 1.29570 | 0.647852 | − | 0.761767i | \(-0.275668\pi\) | ||||
0.647852 | + | 0.761767i | \(0.275668\pi\) | |||||||
\(48\) | 2.07410 | − | 3.59245i | 0.299371 | − | 0.518526i | ||||
\(49\) | −9.33562 | − | 16.1698i | −1.33366 | − | 2.30997i | ||||
\(50\) | 3.45320 | 0.488356 | ||||||||
\(51\) | 2.09926 | − | 3.63602i | 0.293955 | − | 0.509145i | ||||
\(52\) | −0.904786 | + | 5.35281i | −0.125471 | + | 0.742302i | ||||
\(53\) | 0.521349 | − | 0.903004i | 0.0716128 | − | 0.124037i | −0.827995 | − | 0.560735i | \(-0.810519\pi\) |
0.899608 | + | 0.436698i | \(0.143852\pi\) | |||||||
\(54\) | 5.16754 | − | 8.95044i | 0.703213 | − | 1.21800i | ||||
\(55\) | 2.19143 | 0.295493 | ||||||||
\(56\) | 6.24418 | − | 10.8152i | 0.834414 | − | 1.44525i | ||||
\(57\) | 1.55633 | − | 2.69565i | 0.206141 | − | 0.357048i | ||||
\(58\) | 2.58123 | + | 4.47082i | 0.338932 | + | 0.587047i | ||||
\(59\) | 0.0428005 | − | 0.0741326i | 0.00557215 | − | 0.00965124i | −0.863226 | − | 0.504818i | \(-0.831560\pi\) |
0.868798 | + | 0.495167i | \(0.164893\pi\) | |||||||
\(60\) | 15.3819 | 1.98579 | ||||||||
\(61\) | 3.66979 | + | 6.35626i | 0.469868 | + | 0.813836i | 0.999406 | − | 0.0344505i | \(-0.0109681\pi\) |
−0.529538 | + | 0.848286i | \(0.677635\pi\) | |||||||
\(62\) | −3.61344 | − | 1.50583i | −0.458907 | − | 0.191241i | ||||
\(63\) | −19.0758 | + | 33.0403i | −2.40333 | + | 4.16269i | ||||
\(64\) | 1.54121 | 0.192651 | ||||||||
\(65\) | −10.6388 | + | 3.95781i | −1.31958 | + | 0.490906i | ||||
\(66\) | −1.58812 | −0.195484 | ||||||||
\(67\) | 1.13367 | + | 1.96357i | 0.138500 | + | 0.239889i | 0.926929 | − | 0.375237i | \(-0.122439\pi\) |
−0.788429 | + | 0.615126i | \(0.789105\pi\) | |||||||
\(68\) | −1.94810 | −0.236242 | ||||||||
\(69\) | 0.173116 | − | 0.299846i | 0.0208407 | − | 0.0360972i | ||||
\(70\) | 11.2151 | 1.34046 | ||||||||
\(71\) | −3.68268 | −0.437054 | −0.218527 | − | 0.975831i | \(-0.570125\pi\) | ||||
−0.218527 | + | 0.975831i | \(0.570125\pi\) | |||||||
\(72\) | −18.5597 | −2.18729 | ||||||||
\(73\) | −0.537142 | + | 0.930358i | −0.0628678 | + | 0.108890i | −0.895746 | − | 0.444566i | \(-0.853358\pi\) |
0.832878 | + | 0.553456i | \(0.186691\pi\) | |||||||
\(74\) | −0.823194 | + | 1.42581i | −0.0956943 | + | 0.165747i | ||||
\(75\) | 7.96879 | + | 13.8023i | 0.920157 | + | 1.59376i | ||||
\(76\) | −1.44427 | −0.165669 | ||||||||
\(77\) | 3.52682 | 0.401918 | ||||||||
\(78\) | 7.70991 | − | 2.86821i | 0.872975 | − | 0.324760i | ||||
\(79\) | 6.58335 | + | 11.4027i | 0.740685 | + | 1.28290i | 0.952184 | + | 0.305525i | \(0.0988321\pi\) |
−0.211499 | + | 0.977378i | \(0.567835\pi\) | |||||||
\(80\) | −2.01227 | − | 3.48536i | −0.224979 | − | 0.389675i | ||||
\(81\) | 25.1098 | 2.78998 | ||||||||
\(82\) | −7.55127 | −0.833898 | ||||||||
\(83\) | 4.79021 | − | 8.29689i | 0.525794 | − | 0.910702i | −0.473754 | − | 0.880657i | \(-0.657101\pi\) |
0.999549 | − | 0.0300454i | \(-0.00956518\pi\) | |||||||
\(84\) | 24.7550 | 2.70099 | ||||||||
\(85\) | −2.03668 | − | 3.52763i | −0.220909 | − | 0.382625i | ||||
\(86\) | −0.0459377 | − | 0.0795664i | −0.00495359 | − | 0.00857986i | ||||
\(87\) | −11.9132 | + | 20.6342i | −1.27722 | + | 2.21222i | ||||
\(88\) | 0.857850 | + | 1.48584i | 0.0914472 | + | 0.158391i | ||||
\(89\) | −0.0447961 | + | 0.0775891i | −0.00474838 | + | 0.00822443i | −0.868390 | − | 0.495882i | \(-0.834845\pi\) |
0.863641 | + | 0.504107i | \(0.168178\pi\) | |||||||
\(90\) | −8.33375 | − | 14.4345i | −0.878454 | − | 1.52153i | ||||
\(91\) | −17.1218 | + | 6.36956i | −1.79485 | + | 0.667712i | ||||
\(92\) | −0.160651 | −0.0167490 | ||||||||
\(93\) | −2.31979 | − | 17.9177i | −0.240551 | − | 1.85798i | ||||
\(94\) | −3.12274 | + | 5.40875i | −0.322086 | + | 0.557870i | ||||
\(95\) | −1.50994 | − | 2.61529i | −0.154916 | − | 0.268323i | ||||
\(96\) | 9.45652 | + | 16.3792i | 0.965152 | + | 1.67169i | ||||
\(97\) | 4.19399 | + | 7.26421i | 0.425836 | + | 0.737569i | 0.996498 | − | 0.0836159i | \(-0.0266469\pi\) |
−0.570663 | + | 0.821185i | \(0.693314\pi\) | |||||||
\(98\) | 13.1276 | 1.32609 | ||||||||
\(99\) | −2.62071 | − | 4.53921i | −0.263392 | − | 0.456207i | ||||
\(100\) | 3.69750 | − | 6.40425i | 0.369750 | − | 0.640425i | ||||
\(101\) | −2.79393 | + | 4.83923i | −0.278006 | + | 0.481521i | −0.970889 | − | 0.239529i | \(-0.923007\pi\) |
0.692883 | + | 0.721050i | \(0.256340\pi\) | |||||||
\(102\) | 1.47597 | + | 2.55645i | 0.146143 | + | 0.253127i | ||||
\(103\) | −2.15262 | + | 3.72845i | −0.212104 | + | 0.367376i | −0.952373 | − | 0.304936i | \(-0.901365\pi\) |
0.740269 | + | 0.672311i | \(0.234698\pi\) | |||||||
\(104\) | −6.84812 | − | 5.66405i | −0.671513 | − | 0.555406i | ||||
\(105\) | 25.8806 | + | 44.8265i | 2.52569 | + | 4.37462i | ||||
\(106\) | 0.366556 | + | 0.634894i | 0.0356031 | + | 0.0616664i | ||||
\(107\) | −1.70260 | −0.164596 | −0.0822981 | − | 0.996608i | \(-0.526226\pi\) | ||||
−0.0822981 | + | 0.996608i | \(0.526226\pi\) | |||||||
\(108\) | −11.0662 | − | 19.1673i | −1.06485 | − | 1.84437i | ||||
\(109\) | −9.55259 | −0.914972 | −0.457486 | − | 0.889217i | \(-0.651250\pi\) | ||||
−0.457486 | + | 0.889217i | \(0.651250\pi\) | |||||||
\(110\) | −0.770389 | + | 1.33435i | −0.0734537 | + | 0.127226i | ||||
\(111\) | −7.59858 | −0.721225 | ||||||||
\(112\) | −3.23848 | − | 5.60921i | −0.306008 | − | 0.530021i | ||||
\(113\) | −1.85421 | −0.174430 | −0.0872149 | − | 0.996190i | \(-0.527797\pi\) | ||||
−0.0872149 | + | 0.996190i | \(0.527797\pi\) | |||||||
\(114\) | 1.09425 | + | 1.89529i | 0.102485 | + | 0.177510i | ||||
\(115\) | −0.167955 | − | 0.290907i | −0.0156619 | − | 0.0271272i | ||||
\(116\) | 11.0553 | 1.02646 | ||||||||
\(117\) | 20.9208 | + | 17.3035i | 1.93413 | + | 1.59971i | ||||
\(118\) | 0.0300926 | + | 0.0521220i | 0.00277025 | + | 0.00479822i | ||||
\(119\) | −3.27776 | − | 5.67724i | −0.300471 | − | 0.520432i | ||||
\(120\) | −12.5902 | + | 21.8069i | −1.14932 | + | 1.99069i | ||||
\(121\) | 5.25774 | − | 9.10667i | 0.477976 | − | 0.827879i | ||||
\(122\) | −5.16039 | −0.467200 | ||||||||
\(123\) | −17.4257 | − | 30.1822i | −1.57122 | − | 2.72144i | ||||
\(124\) | −6.66176 | + | 5.08906i | −0.598244 | + | 0.457011i | ||||
\(125\) | −0.278765 | −0.0249335 | ||||||||
\(126\) | −13.4120 | − | 23.2303i | −1.19484 | − | 2.06952i | ||||
\(127\) | −4.71961 | −0.418798 | −0.209399 | − | 0.977830i | \(-0.567151\pi\) | ||||
−0.209399 | + | 0.977830i | \(0.567151\pi\) | |||||||
\(128\) | 5.28659 | − | 9.15664i | 0.467273 | − | 0.809341i | ||||
\(129\) | 0.212016 | − | 0.367223i | 0.0186670 | − | 0.0323322i | ||||
\(130\) | 1.33014 | − | 7.86928i | 0.116661 | − | 0.690182i | ||||
\(131\) | −6.46743 | − | 11.2019i | −0.565062 | − | 0.978716i | −0.997044 | − | 0.0768340i | \(-0.975519\pi\) |
0.431982 | − | 0.901882i | \(-0.357814\pi\) | |||||||
\(132\) | −1.70047 | + | 2.94530i | −0.148007 | + | 0.256356i | ||||
\(133\) | −2.43004 | − | 4.20896i | −0.210711 | − | 0.364963i | ||||
\(134\) | −1.59415 | −0.137713 | ||||||||
\(135\) | 23.1388 | − | 40.0775i | 1.99147 | − | 3.44933i | ||||
\(136\) | 1.59454 | − | 2.76182i | 0.136731 | − | 0.236824i | ||||
\(137\) | −16.1109 | −1.37645 | −0.688224 | − | 0.725498i | \(-0.741609\pi\) | ||||
−0.688224 | + | 0.725498i | \(0.741609\pi\) | |||||||
\(138\) | 0.121716 | + | 0.210819i | 0.0103612 | + | 0.0179461i | ||||
\(139\) | −8.07781 | − | 13.9912i | −0.685151 | − | 1.18672i | −0.973389 | − | 0.229158i | \(-0.926403\pi\) |
0.288238 | − | 0.957559i | \(-0.406931\pi\) | |||||||
\(140\) | 12.0085 | − | 20.7994i | 1.01491 | − | 1.75787i | ||||
\(141\) | −28.8248 | −2.42749 | ||||||||
\(142\) | 1.29463 | − | 2.24237i | 0.108643 | − | 0.188175i | ||||
\(143\) | 0.418290 | − | 2.47465i | 0.0349792 | − | 0.206941i | ||||
\(144\) | −4.81291 | + | 8.33620i | −0.401076 | + | 0.694683i | ||||
\(145\) | 11.5580 | + | 20.0191i | 0.959841 | + | 1.66249i | ||||
\(146\) | −0.377660 | − | 0.654127i | −0.0312554 | − | 0.0541359i | ||||
\(147\) | 30.2939 | + | 52.4706i | 2.49860 | + | 4.32770i | ||||
\(148\) | 1.76286 | + | 3.05336i | 0.144906 | + | 0.250985i | ||||
\(149\) | 5.46698 | − | 9.46910i | 0.447873 | − | 0.775738i | −0.550375 | − | 0.834918i | \(-0.685515\pi\) |
0.998247 | + | 0.0591794i | \(0.0188484\pi\) | |||||||
\(150\) | −11.2056 | −0.914932 | ||||||||
\(151\) | 3.87728 | 0.315528 | 0.157764 | − | 0.987477i | \(-0.449571\pi\) | ||||
0.157764 | + | 0.987477i | \(0.449571\pi\) | |||||||
\(152\) | 1.18215 | − | 2.04754i | 0.0958850 | − | 0.166078i | ||||
\(153\) | −4.87128 | + | 8.43730i | −0.393820 | + | 0.682116i | ||||
\(154\) | −1.23984 | + | 2.14746i | −0.0999090 | + | 0.173047i | ||||
\(155\) | −16.1800 | − | 6.74269i | −1.29961 | − | 0.541586i | ||||
\(156\) | 2.93601 | − | 17.3698i | 0.235069 | − | 1.39070i | ||||
\(157\) | 6.26211 | 0.499771 | 0.249885 | − | 0.968275i | \(-0.419607\pi\) | ||||
0.249885 | + | 0.968275i | \(0.419607\pi\) | |||||||
\(158\) | −9.25739 | −0.736479 | ||||||||
\(159\) | −1.69177 | + | 2.93023i | −0.134166 | + | 0.232382i | ||||
\(160\) | 18.3492 | 1.45063 | ||||||||
\(161\) | −0.270302 | − | 0.468176i | −0.0213027 | − | 0.0368974i | ||||
\(162\) | −8.82725 | + | 15.2892i | −0.693534 | + | 1.20124i | ||||
\(163\) | −0.143956 | − | 0.249340i | −0.0112755 | − | 0.0195298i | 0.860333 | − | 0.509733i | \(-0.170256\pi\) |
−0.871608 | + | 0.490203i | \(0.836923\pi\) | |||||||
\(164\) | −8.08548 | + | 14.0045i | −0.631370 | + | 1.09356i | ||||
\(165\) | −7.11116 | −0.553603 | ||||||||
\(166\) | 3.36796 | + | 5.83348i | 0.261404 | + | 0.452766i | ||||
\(167\) | −4.03843 | −0.312503 | −0.156252 | − | 0.987717i | \(-0.549941\pi\) | ||||
−0.156252 | + | 0.987717i | \(0.549941\pi\) | |||||||
\(168\) | −20.2623 | + | 35.0952i | −1.56327 | + | 2.70766i | ||||
\(169\) | 2.43862 | + | 12.7692i | 0.187586 | + | 0.982248i | ||||
\(170\) | 2.86394 | 0.219654 | ||||||||
\(171\) | −3.61144 | + | 6.25520i | −0.276174 | + | 0.478347i | ||||
\(172\) | −0.196750 | −0.0150020 | ||||||||
\(173\) | 9.55708 | 0.726612 | 0.363306 | − | 0.931670i | \(-0.381648\pi\) | ||||
0.363306 | + | 0.931670i | \(0.381648\pi\) | |||||||
\(174\) | −8.37604 | − | 14.5077i | −0.634986 | − | 1.09983i | ||||
\(175\) | 24.8848 | 1.88111 | ||||||||
\(176\) | 0.889831 | 0.0670735 | ||||||||
\(177\) | −0.138887 | + | 0.240559i | −0.0104394 | + | 0.0180815i | ||||
\(178\) | −0.0314958 | − | 0.0545523i | −0.00236071 | − | 0.00408886i | ||||
\(179\) | −7.56308 | −0.565291 | −0.282645 | − | 0.959224i | \(-0.591212\pi\) | ||||
−0.282645 | + | 0.959224i | \(0.591212\pi\) | |||||||
\(180\) | −35.6932 | −2.66042 | ||||||||
\(181\) | 6.95906 | − | 12.0534i | 0.517263 | − | 0.895925i | −0.482536 | − | 0.875876i | \(-0.660284\pi\) |
0.999799 | − | 0.0200493i | \(-0.00638231\pi\) | |||||||
\(182\) | 2.14069 | − | 12.6646i | 0.158678 | − | 0.938759i | ||||
\(183\) | −11.9084 | − | 20.6259i | −0.880294 | − | 1.52471i | ||||
\(184\) | 0.131494 | − | 0.227755i | 0.00969389 | − | 0.0167903i | ||||
\(185\) | −3.68603 | + | 6.38439i | −0.271002 | + | 0.469390i | ||||
\(186\) | 11.7255 | + | 4.88640i | 0.859758 | + | 0.358288i | ||||
\(187\) | 0.900623 | 0.0658601 | ||||||||
\(188\) | 6.68732 | + | 11.5828i | 0.487723 | + | 0.844761i | ||||
\(189\) | 37.2388 | − | 64.4994i | 2.70872 | − | 4.69164i | ||||
\(190\) | 2.12325 | 0.154037 | ||||||||
\(191\) | 13.2529 | 0.958947 | 0.479474 | − | 0.877556i | \(-0.340828\pi\) | ||||
0.479474 | + | 0.877556i | \(0.340828\pi\) | |||||||
\(192\) | −5.00119 | −0.360930 | ||||||||
\(193\) | 12.8753 | 0.926787 | 0.463394 | − | 0.886153i | \(-0.346632\pi\) | ||||
0.463394 | + | 0.886153i | \(0.346632\pi\) | |||||||
\(194\) | −5.89752 | −0.423417 | ||||||||
\(195\) | 34.5228 | − | 12.8430i | 2.47223 | − | 0.919708i | ||||
\(196\) | 14.0563 | − | 24.3462i | 1.00402 | − | 1.73902i | ||||
\(197\) | 5.19363 | + | 8.99564i | 0.370031 | + | 0.640912i | 0.989570 | − | 0.144053i | \(-0.0460137\pi\) |
−0.619539 | + | 0.784966i | \(0.712680\pi\) | |||||||
\(198\) | 3.68520 | 0.261896 | ||||||||
\(199\) | −8.60982 | −0.610334 | −0.305167 | − | 0.952299i | \(-0.598712\pi\) | ||||
−0.305167 | + | 0.952299i | \(0.598712\pi\) | |||||||
\(200\) | 6.05288 | + | 10.4839i | 0.428003 | + | 0.741323i | ||||
\(201\) | −3.67874 | − | 6.37176i | −0.259478 | − | 0.449429i | ||||
\(202\) | −1.96439 | − | 3.40242i | −0.138214 | − | 0.239393i | ||||
\(203\) | 18.6011 | + | 32.2180i | 1.30554 | + | 2.26126i | ||||
\(204\) | 6.32154 | 0.442597 | ||||||||
\(205\) | −33.8125 | −2.36157 | ||||||||
\(206\) | −1.51349 | − | 2.62144i | −0.105450 | − | 0.182645i | ||||
\(207\) | −0.401712 | + | 0.695786i | −0.0279209 | + | 0.0483604i | ||||
\(208\) | −4.31989 | + | 1.60707i | −0.299531 | + | 0.111430i | ||||
\(209\) | 0.667698 | 0.0461856 | ||||||||
\(210\) | −36.3929 | −2.51135 | ||||||||
\(211\) | 20.5389 | 1.41395 | 0.706977 | − | 0.707237i | \(-0.250058\pi\) | ||||
0.706977 | + | 0.707237i | \(0.250058\pi\) | |||||||
\(212\) | 1.56995 | 0.107825 | ||||||||
\(213\) | 11.9502 | 0.818817 | ||||||||
\(214\) | 0.598540 | − | 1.03670i | 0.0409154 | − | 0.0708675i | ||||
\(215\) | −0.205696 | − | 0.356276i | −0.0140283 | − | 0.0242978i | ||||
\(216\) | 36.2313 | 2.46523 | ||||||||
\(217\) | −26.0395 | − | 10.8515i | −1.76767 | − | 0.736645i | ||||
\(218\) | 3.35817 | − | 5.81652i | 0.227444 | − | 0.393945i | ||||
\(219\) | 1.74302 | − | 3.01899i | 0.117782 | − | 0.204005i | ||||
\(220\) | 1.64978 | + | 2.85750i | 0.111228 | + | 0.192653i | ||||
\(221\) | −4.37228 | + | 1.62656i | −0.294112 | + | 0.109414i | ||||
\(222\) | 2.67125 | − | 4.62674i | 0.179282 | − | 0.310526i | ||||
\(223\) | 18.0402 | 1.20806 | 0.604031 | − | 0.796961i | \(-0.293560\pi\) | ||||
0.604031 | + | 0.796961i | \(0.293560\pi\) | |||||||
\(224\) | 29.5306 | 1.97310 | ||||||||
\(225\) | −18.4914 | − | 32.0280i | −1.23276 | − | 2.13520i | ||||
\(226\) | 0.651841 | − | 1.12902i | 0.0433598 | − | 0.0751014i | ||||
\(227\) | −21.3706 | −1.41841 | −0.709207 | − | 0.705000i | \(-0.750947\pi\) | ||||
−0.709207 | + | 0.705000i | \(0.750947\pi\) | |||||||
\(228\) | 4.68663 | 0.310380 | ||||||||
\(229\) | −12.5388 | − | 21.7178i | −0.828586 | − | 1.43515i | −0.899148 | − | 0.437645i | \(-0.855813\pi\) |
0.0705621 | − | 0.997507i | \(-0.477521\pi\) | |||||||
\(230\) | 0.236176 | 0.0155730 | ||||||||
\(231\) | −11.4445 | −0.752990 | ||||||||
\(232\) | −9.04892 | + | 15.6732i | −0.594090 | + | 1.02899i | ||||
\(233\) | −16.7542 | −1.09761 | −0.548803 | − | 0.835951i | \(-0.684916\pi\) | ||||
−0.548803 | + | 0.835951i | \(0.684916\pi\) | |||||||
\(234\) | −17.8907 | + | 6.65561i | −1.16955 | + | 0.435091i | ||||
\(235\) | −13.9828 | + | 24.2189i | −0.912135 | + | 1.57986i | ||||
\(236\) | 0.128886 | 0.00838977 | ||||||||
\(237\) | −21.3629 | − | 37.0015i | −1.38767 | − | 2.40351i | ||||
\(238\) | 4.60913 | 0.298765 | ||||||||
\(239\) | 1.70582 | − | 2.95456i | 0.110340 | − | 0.191115i | −0.805567 | − | 0.592504i | \(-0.798139\pi\) |
0.915907 | + | 0.401390i | \(0.131473\pi\) | |||||||
\(240\) | 6.52978 | + | 11.3099i | 0.421496 | + | 0.730052i | ||||
\(241\) | −14.1082 | + | 24.4362i | −0.908791 | + | 1.57407i | −0.0930447 | + | 0.995662i | \(0.529660\pi\) |
−0.815746 | + | 0.578410i | \(0.803673\pi\) | |||||||
\(242\) | 3.69667 | + | 6.40282i | 0.237631 | + | 0.411589i | ||||
\(243\) | −37.3825 | −2.39809 | ||||||||
\(244\) | −5.52546 | + | 9.57038i | −0.353731 | + | 0.612681i | ||||
\(245\) | 58.7817 | 3.75542 | ||||||||
\(246\) | 24.5037 | 1.56230 | ||||||||
\(247\) | −3.24150 | + | 1.20589i | −0.206252 | + | 0.0767288i | ||||
\(248\) | −1.76205 | − | 13.6098i | −0.111890 | − | 0.864226i | ||||
\(249\) | −15.5442 | + | 26.9233i | −0.985071 | + | 1.70619i | ||||
\(250\) | 0.0979985 | − | 0.169738i | 0.00619797 | − | 0.0107352i | ||||
\(251\) | −10.7452 | + | 18.6112i | −0.678231 | + | 1.17473i | 0.297282 | + | 0.954790i | \(0.403920\pi\) |
−0.975513 | + | 0.219941i | \(0.929414\pi\) | |||||||
\(252\) | −57.4435 | −3.61860 | ||||||||
\(253\) | 0.0742702 | 0.00466933 | ||||||||
\(254\) | 1.65916 | − | 2.87375i | 0.104105 | − | 0.180315i | ||||
\(255\) | 6.60898 | + | 11.4471i | 0.413870 | + | 0.716844i | ||||
\(256\) | 5.25816 | + | 9.10741i | 0.328635 | + | 0.569213i | ||||
\(257\) | 6.91930 | + | 11.9846i | 0.431614 | + | 0.747577i | 0.997012 | − | 0.0772405i | \(-0.0246109\pi\) |
−0.565398 | + | 0.824818i | \(0.691278\pi\) | |||||||
\(258\) | 0.149067 | + | 0.258191i | 0.00928050 | + | 0.0160743i | ||||
\(259\) | −5.93217 | + | 10.2748i | −0.368607 | + | 0.638446i | ||||
\(260\) | −13.1700 | − | 10.8929i | −0.816768 | − | 0.675546i | ||||
\(261\) | 27.6442 | − | 47.8812i | 1.71113 | − | 2.96377i | ||||
\(262\) | 9.09439 | 0.561853 | ||||||||
\(263\) | 5.24819 | − | 9.09014i | 0.323617 | − | 0.560522i | −0.657614 | − | 0.753355i | \(-0.728434\pi\) |
0.981232 | + | 0.192833i | \(0.0617676\pi\) | |||||||
\(264\) | −2.78371 | − | 4.82153i | −0.171325 | − | 0.296744i | ||||
\(265\) | 1.64134 | + | 2.84288i | 0.100826 | + | 0.174637i | ||||
\(266\) | 3.41709 | 0.209515 | ||||||||
\(267\) | 0.145363 | − | 0.251775i | 0.00889605 | − | 0.0154084i | ||||
\(268\) | −1.70692 | + | 2.95648i | −0.104267 | + | 0.180596i | ||||
\(269\) | 7.04900 | 0.429785 | 0.214892 | − | 0.976638i | \(-0.431060\pi\) | ||||
0.214892 | + | 0.976638i | \(0.431060\pi\) | |||||||
\(270\) | 16.2687 | + | 28.1782i | 0.990080 | + | 1.71487i | ||||
\(271\) | 0.0515000 | − | 0.0892005i | 0.00312840 | − | 0.00541855i | −0.864457 | − | 0.502707i | \(-0.832338\pi\) |
0.867585 | + | 0.497288i | \(0.165671\pi\) | |||||||
\(272\) | −0.826992 | − | 1.43239i | −0.0501437 | − | 0.0868515i | ||||
\(273\) | 55.5598 | − | 20.6691i | 3.36263 | − | 1.25095i | ||||
\(274\) | 5.66372 | − | 9.80985i | 0.342158 | − | 0.592635i | ||||
\(275\) | −1.70938 | + | 2.96074i | −0.103080 | + | 0.178539i | ||||
\(276\) | 0.521309 | 0.0313791 | ||||||||
\(277\) | −3.87075 | − | 6.70434i | −0.232571 | − | 0.402825i | 0.725993 | − | 0.687702i | \(-0.241380\pi\) |
−0.958564 | + | 0.284877i | \(0.908047\pi\) | |||||||
\(278\) | 11.3589 | 0.681261 | ||||||||
\(279\) | 5.38303 | + | 41.5777i | 0.322274 | + | 2.48919i | ||||
\(280\) | 19.6582 | + | 34.0490i | 1.17480 | + | 2.03482i | ||||
\(281\) | −28.6031 | −1.70632 | −0.853160 | − | 0.521649i | \(-0.825317\pi\) | ||||
−0.853160 | + | 0.521649i | \(0.825317\pi\) | |||||||
\(282\) | 10.1332 | − | 17.5513i | 0.603426 | − | 1.04516i | ||||
\(283\) | −2.68044 | + | 4.64266i | −0.159336 | + | 0.275977i | −0.934629 | − | 0.355624i | \(-0.884269\pi\) |
0.775294 | + | 0.631601i | \(0.217602\pi\) | |||||||
\(284\) | −2.77244 | − | 4.80201i | −0.164514 | − | 0.284947i | ||||
\(285\) | 4.89972 | + | 8.48657i | 0.290235 | + | 0.502701i | ||||
\(286\) | 1.35976 | + | 1.12465i | 0.0804040 | + | 0.0665018i | ||||
\(287\) | −54.4166 | −3.21211 | ||||||||
\(288\) | −21.9436 | − | 38.0075i | −1.29304 | − | 2.23961i | ||||
\(289\) | 7.66298 | + | 13.2727i | 0.450763 | + | 0.780745i | ||||
\(290\) | −16.2527 | −0.954391 | ||||||||
\(291\) | −13.6094 | − | 23.5722i | −0.797799 | − | 1.38183i | ||||
\(292\) | −1.61751 | −0.0946576 | ||||||||
\(293\) | 8.86195 | − | 15.3493i | 0.517721 | − | 0.896718i | −0.482068 | − | 0.876134i | \(-0.660114\pi\) |
0.999788 | − | 0.0205843i | \(-0.00655266\pi\) | |||||||
\(294\) | −42.5988 | −2.48441 | ||||||||
\(295\) | 0.134746 | + | 0.233388i | 0.00784524 | + | 0.0135884i | ||||
\(296\) | −5.77168 | −0.335472 | ||||||||
\(297\) | 5.11601 | + | 8.86119i | 0.296861 | + | 0.514178i | ||||
\(298\) | 3.84379 | + | 6.65764i | 0.222665 | + | 0.385667i | ||||
\(299\) | −0.360562 | + | 0.134135i | −0.0208518 | + | 0.00775721i | ||||
\(300\) | −11.9983 | + | 20.7817i | −0.692723 | + | 1.19983i | ||||
\(301\) | −0.331040 | − | 0.573378i | −0.0190808 | − | 0.0330490i | ||||
\(302\) | −1.36304 | + | 2.36085i | −0.0784341 | + | 0.135852i | ||||
\(303\) | 9.06625 | − | 15.7032i | 0.520842 | − | 0.902125i | ||||
\(304\) | −0.613110 | − | 1.06194i | −0.0351643 | − | 0.0609063i | ||||
\(305\) | −23.1068 | −1.32309 | ||||||||
\(306\) | −3.42495 | − | 5.93220i | −0.195792 | − | 0.339121i | ||||
\(307\) | −1.34436 | − | 2.32849i | −0.0767265 | − | 0.132894i | 0.825109 | − | 0.564973i | \(-0.191113\pi\) |
−0.901836 | + | 0.432079i | \(0.857780\pi\) | |||||||
\(308\) | 2.65510 | + | 4.59877i | 0.151288 | + | 0.262039i | ||||
\(309\) | 6.98523 | − | 12.0988i | 0.397376 | − | 0.688275i | ||||
\(310\) | 9.79359 | − | 7.48153i | 0.556238 | − | 0.424923i | ||||
\(311\) | 1.56118 | 0.0885265 | 0.0442633 | − | 0.999020i | \(-0.485906\pi\) | ||||
0.0442633 | + | 0.999020i | \(0.485906\pi\) | |||||||
\(312\) | 22.2220 | + | 18.3797i | 1.25807 | + | 1.04055i | ||||
\(313\) | −9.82704 | − | 17.0209i | −0.555457 | − | 0.962080i | −0.997868 | − | 0.0652677i | \(-0.979210\pi\) |
0.442410 | − | 0.896813i | \(-0.354123\pi\) | |||||||
\(314\) | −2.20142 | + | 3.81297i | −0.124233 | + | 0.215178i | ||||
\(315\) | −60.0554 | − | 104.019i | −3.38374 | − | 5.86080i | ||||
\(316\) | −9.91230 | + | 17.1686i | −0.557611 | + | 0.965810i | ||||
\(317\) | 6.99545 | + | 12.1165i | 0.392904 | + | 0.680529i | 0.992831 | − | 0.119525i | \(-0.0381372\pi\) |
−0.599927 | + | 0.800054i | \(0.704804\pi\) | |||||||
\(318\) | −1.18947 | − | 2.06022i | −0.0667021 | − | 0.115531i | ||||
\(319\) | −5.11098 | −0.286160 | ||||||||
\(320\) | −2.42605 | + | 4.20204i | −0.135620 | + | 0.234901i | ||||
\(321\) | 5.52489 | 0.308370 | ||||||||
\(322\) | 0.380093 | 0.0211818 | ||||||||
\(323\) | −0.620546 | − | 1.07482i | −0.0345281 | − | 0.0598044i | ||||
\(324\) | 18.9034 | + | 32.7417i | 1.05019 | + | 1.81899i | ||||
\(325\) | 2.95140 | − | 17.4608i | 0.163714 | − | 0.968552i | ||||
\(326\) | 0.202429 | 0.0112115 | ||||||||
\(327\) | 30.9980 | 1.71419 | ||||||||
\(328\) | −13.2361 | − | 22.9256i | −0.730842 | − | 1.26585i | ||||
\(329\) | −22.5034 | + | 38.9770i | −1.24065 | + | 2.14887i | ||||
\(330\) | 2.49990 | − | 4.32995i | 0.137615 | − | 0.238356i | ||||
\(331\) | 24.2327 | 1.33195 | 0.665975 | − | 0.745974i | \(-0.268016\pi\) | ||||
0.665975 | + | 0.745974i | \(0.268016\pi\) | |||||||
\(332\) | 14.4249 | 0.791669 | ||||||||
\(333\) | 17.6323 | 0.966246 | ||||||||
\(334\) | 1.41969 | − | 2.45898i | 0.0776821 | − | 0.134549i | ||||
\(335\) | −7.13814 | −0.389998 | ||||||||
\(336\) | 10.5088 | + | 18.2018i | 0.573303 | + | 0.992989i | ||||
\(337\) | 34.6356 | 1.88672 | 0.943359 | − | 0.331773i | \(-0.107647\pi\) | ||||
0.943359 | + | 0.331773i | \(0.107647\pi\) | |||||||
\(338\) | −8.63241 | − | 3.00410i | −0.469541 | − | 0.163402i | ||||
\(339\) | 6.01689 | 0.326793 | ||||||||
\(340\) | 3.06655 | − | 5.31141i | 0.166307 | − | 0.288052i | ||||
\(341\) | 3.07979 | − | 2.35272i | 0.166780 | − | 0.127407i | ||||
\(342\) | −2.53917 | − | 4.39797i | −0.137303 | − | 0.237815i | ||||
\(343\) | 59.1345 | 3.19296 | ||||||||
\(344\) | 0.161042 | − | 0.278933i | 0.00868280 | − | 0.0150390i | ||||
\(345\) | 0.545012 | + | 0.943988i | 0.0293425 | + | 0.0508226i | ||||
\(346\) | −3.35975 | + | 5.81926i | −0.180621 | + | 0.312845i | ||||
\(347\) | 6.13438 | − | 10.6251i | 0.329311 | − | 0.570383i | −0.653064 | − | 0.757302i | \(-0.726517\pi\) |
0.982375 | + | 0.186919i | \(0.0598502\pi\) | |||||||
\(348\) | −35.8744 | −1.92307 | ||||||||
\(349\) | −15.2206 | + | 26.3629i | −0.814740 | + | 1.41117i | 0.0947745 | + | 0.995499i | \(0.469787\pi\) |
−0.909514 | + | 0.415672i | \(0.863546\pi\) | |||||||
\(350\) | −8.74813 | + | 15.1522i | −0.467607 | + | 0.809920i | ||||
\(351\) | −40.8405 | − | 33.7790i | −2.17990 | − | 1.80299i | ||||
\(352\) | −2.02852 | + | 3.51349i | −0.108120 | + | 0.187270i | ||||
\(353\) | 6.41247 | 0.341301 | 0.170651 | − | 0.985332i | \(-0.445413\pi\) | ||||
0.170651 | + | 0.985332i | \(0.445413\pi\) | |||||||
\(354\) | −0.0976501 | − | 0.169135i | −0.00519004 | − | 0.00898942i | ||||
\(355\) | 5.79700 | − | 10.0407i | 0.307673 | − | 0.532905i | ||||
\(356\) | −0.134896 | −0.00714945 | ||||||||
\(357\) | 10.6363 | + | 18.4225i | 0.562931 | + | 0.975025i | ||||
\(358\) | 2.65877 | − | 4.60512i | 0.140520 | − | 0.243388i | ||||
\(359\) | 6.48885 | − | 11.2390i | 0.342468 | − | 0.593172i | −0.642422 | − | 0.766351i | \(-0.722070\pi\) |
0.984890 | + | 0.173179i | \(0.0554038\pi\) | |||||||
\(360\) | 29.2153 | − | 50.6024i | 1.53978 | − | 2.66698i | ||||
\(361\) | 9.03994 | + | 15.6576i | 0.475787 | + | 0.824086i | ||||
\(362\) | 4.89285 | + | 8.47467i | 0.257163 | + | 0.445419i | ||||
\(363\) | −17.0613 | + | 29.5510i | −0.895484 | + | 1.55102i | ||||
\(364\) | −21.1953 | − | 17.5306i | −1.11094 | − | 0.918852i | ||||
\(365\) | −1.69106 | − | 2.92900i | −0.0885139 | − | 0.153311i | ||||
\(366\) | 16.7454 | 0.875295 | ||||||||
\(367\) | −6.21277 | − | 10.7608i | −0.324304 | − | 0.561711i | 0.657067 | − | 0.753832i | \(-0.271797\pi\) |
−0.981371 | + | 0.192121i | \(0.938463\pi\) | |||||||
\(368\) | −0.0681982 | − | 0.118123i | −0.00355508 | − | 0.00615757i | ||||
\(369\) | 40.4360 | + | 70.0372i | 2.10501 | + | 3.64599i | ||||
\(370\) | −2.59162 | − | 4.48881i | −0.134732 | − | 0.233362i | ||||
\(371\) | 2.64151 | + | 4.57523i | 0.137140 | + | 0.237534i | ||||
\(372\) | 21.6173 | − | 16.5139i | 1.12080 | − | 0.856207i | ||||
\(373\) | −10.8988 | − | 18.8773i | −0.564319 | − | 0.977430i | −0.997113 | − | 0.0759364i | \(-0.975805\pi\) |
0.432793 | − | 0.901493i | \(-0.357528\pi\) | |||||||
\(374\) | −0.316610 | + | 0.548385i | −0.0163715 | + | 0.0283563i | ||||
\(375\) | 0.904586 | 0.0467126 | ||||||||
\(376\) | −21.8946 | −1.12913 | ||||||||
\(377\) | 24.8125 | − | 9.23062i | 1.27791 | − | 0.475401i | ||||
\(378\) | 26.1823 | + | 45.3490i | 1.34667 | + | 2.33250i | ||||
\(379\) | 20.2131 | 1.03828 | 0.519138 | − | 0.854691i | \(-0.326253\pi\) | ||||
0.519138 | + | 0.854691i | \(0.326253\pi\) | |||||||
\(380\) | 2.27346 | − | 3.93774i | 0.116626 | − | 0.202002i | ||||
\(381\) | 15.3151 | 0.784614 | ||||||||
\(382\) | −4.65901 | + | 8.06963i | −0.238375 | + | 0.412878i | ||||
\(383\) | 21.6200 | 1.10473 | 0.552366 | − | 0.833602i | \(-0.313725\pi\) | ||||
0.552366 | + | 0.833602i | \(0.313725\pi\) | |||||||
\(384\) | −17.1549 | + | 29.7131i | −0.875432 | + | 1.51629i | ||||
\(385\) | −5.55165 | + | 9.61573i | −0.282938 | + | 0.490063i | ||||
\(386\) | −4.52627 | + | 7.83973i | −0.230381 | + | 0.399032i | ||||
\(387\) | −0.491979 | + | 0.852133i | −0.0250087 | + | 0.0433164i | ||||
\(388\) | −6.31474 | + | 10.9374i | −0.320582 | + | 0.555265i | ||||
\(389\) | 4.59022 | + | 7.95050i | 0.232733 | + | 0.403106i | 0.958612 | − | 0.284717i | \(-0.0918997\pi\) |
−0.725878 | + | 0.687823i | \(0.758566\pi\) | |||||||
\(390\) | −4.31629 | + | 25.5357i | −0.218564 | + | 1.29305i | ||||
\(391\) | −0.0690253 | − | 0.119555i | −0.00349076 | − | 0.00604617i | ||||
\(392\) | 23.0105 | + | 39.8553i | 1.16220 | + | 2.01300i | ||||
\(393\) | 20.9867 | + | 36.3500i | 1.05864 | + | 1.83362i | ||||
\(394\) | −7.30320 | −0.367930 | ||||||||
\(395\) | −41.4520 | −2.08568 | ||||||||
\(396\) | 3.94591 | − | 6.83451i | 0.198289 | − | 0.343447i | ||||
\(397\) | 1.04103 | − | 1.80311i | 0.0522476 | − | 0.0904955i | −0.838719 | − | 0.544565i | \(-0.816695\pi\) |
0.890966 | + | 0.454069i | \(0.150028\pi\) | |||||||
\(398\) | 3.02675 | − | 5.24248i | 0.151717 | − | 0.262782i | ||||
\(399\) | 7.88545 | + | 13.6580i | 0.394766 | + | 0.683755i | ||||
\(400\) | 6.27853 | 0.313926 | ||||||||
\(401\) | −3.86201 | + | 6.68919i | −0.192859 | + | 0.334042i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) |
0.753337 | + | 0.657634i | \(0.228443\pi\) | |||||||
\(402\) | 5.17298 | 0.258005 | ||||||||
\(403\) | −10.7025 | + | 16.9840i | −0.533128 | + | 0.846035i | ||||
\(404\) | −8.41343 | −0.418584 | ||||||||
\(405\) | −39.5259 | + | 68.4609i | −1.96406 | + | 3.40185i | ||||
\(406\) | −26.1565 | −1.29813 | ||||||||
\(407\) | −0.814985 | − | 1.41160i | −0.0403973 | − | 0.0699702i | ||||
\(408\) | −5.17425 | + | 8.96207i | −0.256164 | + | 0.443688i | ||||
\(409\) | 3.01195 | − | 5.21684i | 0.148931 | − | 0.257956i | −0.781902 | − | 0.623402i | \(-0.785750\pi\) |
0.930833 | + | 0.365446i | \(0.119083\pi\) | |||||||
\(410\) | 11.8866 | − | 20.5882i | 0.587039 | − | 1.01678i | ||||
\(411\) | 52.2796 | 2.57876 | ||||||||
\(412\) | −6.48225 | −0.319358 | ||||||||
\(413\) | 0.216856 | + | 0.375606i | 0.0106708 | + | 0.0184824i | ||||
\(414\) | −0.282440 | − | 0.489201i | −0.0138812 | − | 0.0240429i | ||||
\(415\) | 15.0808 | + | 26.1207i | 0.740286 | + | 1.28221i | ||||
\(416\) | 3.50241 | − | 20.7207i | 0.171720 | − | 1.01591i | ||||
\(417\) | 26.2124 | + | 45.4011i | 1.28363 | + | 2.22330i | ||||
\(418\) | −0.234726 | + | 0.406558i | −0.0114808 | + | 0.0198854i | ||||
\(419\) | −0.146218 | + | 0.253256i | −0.00714320 | + | 0.0123724i | −0.869575 | − | 0.493801i | \(-0.835607\pi\) |
0.862432 | + | 0.506173i | \(0.168940\pi\) | |||||||
\(420\) | −38.9675 | + | 67.4936i | −1.90142 | + | 3.29335i | ||||
\(421\) | −12.2268 | + | 21.1775i | −0.595899 | + | 1.03213i | 0.397520 | + | 0.917593i | \(0.369871\pi\) |
−0.993419 | + | 0.114534i | \(0.963462\pi\) | |||||||
\(422\) | −7.22035 | + | 12.5060i | −0.351481 | + | 0.608783i | ||||
\(423\) | 66.8874 | 3.25218 | ||||||||
\(424\) | −1.28502 | + | 2.22572i | −0.0624062 | + | 0.108091i | ||||
\(425\) | 6.35468 | 0.308247 | ||||||||
\(426\) | −4.20106 | + | 7.27644i | −0.203542 | + | 0.352545i | ||||
\(427\) | −37.1873 | −1.79962 | ||||||||
\(428\) | −1.28177 | − | 2.22009i | −0.0619566 | − | 0.107312i | ||||
\(429\) | −1.35734 | + | 8.03020i | −0.0655332 | + | 0.387702i | ||||
\(430\) | 0.289246 | 0.0139487 | ||||||||
\(431\) | −19.0391 | −0.917079 | −0.458539 | − | 0.888674i | \(-0.651627\pi\) | ||||
−0.458539 | + | 0.888674i | \(0.651627\pi\) | |||||||
\(432\) | 9.39549 | − | 16.2735i | 0.452041 | − | 0.782958i | ||||
\(433\) | −5.60518 | − | 9.70845i | −0.269368 | − | 0.466558i | 0.699331 | − | 0.714798i | \(-0.253481\pi\) |
−0.968699 | + | 0.248240i | \(0.920148\pi\) | |||||||
\(434\) | 15.7615 | − | 12.0405i | 0.756575 | − | 0.577964i | ||||
\(435\) | −37.5056 | − | 64.9615i | −1.79825 | − | 3.11467i | ||||
\(436\) | −7.19149 | − | 12.4560i | −0.344410 | − | 0.596535i | ||||
\(437\) | −0.0511736 | − | 0.0886352i | −0.00244796 | − | 0.00424000i | ||||
\(438\) | 1.22550 | + | 2.12263i | 0.0585567 | + | 0.101423i | ||||
\(439\) | 5.49864 | + | 9.52393i | 0.262436 | + | 0.454552i | 0.966889 | − | 0.255199i | \(-0.0821409\pi\) |
−0.704453 | + | 0.709751i | \(0.748808\pi\) | |||||||
\(440\) | −5.40145 | −0.257504 | ||||||||
\(441\) | −70.2964 | − | 121.757i | −3.34745 | − | 5.79795i | ||||
\(442\) | 0.546655 | − | 3.23407i | 0.0260017 | − | 0.153829i | ||||
\(443\) | 4.03510 | − | 6.98900i | 0.191713 | − | 0.332057i | −0.754105 | − | 0.656754i | \(-0.771929\pi\) |
0.945818 | + | 0.324697i | \(0.105262\pi\) | |||||||
\(444\) | −5.72045 | − | 9.90811i | −0.271481 | − | 0.470218i | ||||
\(445\) | −0.141029 | − | 0.244270i | −0.00668542 | − | 0.0115795i | ||||
\(446\) | −6.34196 | + | 10.9846i | −0.300301 | + | 0.520136i | ||||
\(447\) | −17.7403 | + | 30.7270i | −0.839086 | + | 1.45334i | ||||
\(448\) | −3.90440 | + | 6.76262i | −0.184466 | + | 0.319504i | ||||
\(449\) | 18.6990 | + | 32.3875i | 0.882458 | + | 1.52846i | 0.848599 | + | 0.529036i | \(0.177446\pi\) |
0.0338591 | + | 0.999427i | \(0.489220\pi\) | |||||||
\(450\) | 26.0023 | 1.22576 | ||||||||
\(451\) | 3.73799 | − | 6.47439i | 0.176015 | − | 0.304867i | ||||
\(452\) | −1.39591 | − | 2.41779i | −0.0656581 | − | 0.113723i | ||||
\(453\) | −12.5817 | −0.591139 | ||||||||
\(454\) | 7.51273 | − | 13.0124i | 0.352590 | − | 0.610704i | ||||
\(455\) | 9.58540 | − | 56.7083i | 0.449371 | − | 2.65853i | ||||
\(456\) | −3.83605 | + | 6.64424i | −0.179640 | + | 0.311145i | ||||
\(457\) | 19.9401 | − | 34.5372i | 0.932757 | − | 1.61558i | 0.154172 | − | 0.988044i | \(-0.450729\pi\) |
0.778586 | − | 0.627538i | \(-0.215938\pi\) | |||||||
\(458\) | 17.6318 | 0.823881 | ||||||||
\(459\) | 9.50944 | − | 16.4708i | 0.443863 | − | 0.768793i | ||||
\(460\) | 0.252884 | − | 0.438008i | 0.0117908 | − | 0.0204222i | ||||
\(461\) | −15.0884 | − | 26.1339i | −0.702739 | − | 1.21718i | −0.967501 | − | 0.252865i | \(-0.918627\pi\) |
0.264763 | − | 0.964314i | \(-0.414706\pi\) | |||||||
\(462\) | 4.02325 | − | 6.96848i | 0.187179 | − | 0.324203i | ||||
\(463\) | 17.1859 | 0.798695 | 0.399347 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399347 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(464\) | 4.69313 | + | 8.12874i | 0.217873 | + | 0.377367i | ||||
\(465\) | 52.5037 | + | 21.8799i | 2.43480 | + | 1.01466i | ||||
\(466\) | 5.88988 | − | 10.2016i | 0.272843 | − | 0.472579i | ||||
\(467\) | −15.7431 | −0.728504 | −0.364252 | − | 0.931300i | \(-0.618675\pi\) | ||||
−0.364252 | + | 0.931300i | \(0.618675\pi\) | |||||||
\(468\) | −6.81296 | + | 40.3062i | −0.314929 | + | 1.86315i | ||||
\(469\) | −11.4879 | −0.530461 | ||||||||
\(470\) | −9.83116 | − | 17.0281i | −0.453478 | − | 0.785447i | ||||
\(471\) | −20.3204 | −0.936316 | ||||||||
\(472\) | −0.105495 | + | 0.182722i | −0.00485578 | + | 0.00841047i | ||||
\(473\) | 0.0909592 | 0.00418231 | ||||||||
\(474\) | 30.0401 | 1.37979 | ||||||||
\(475\) | 4.71119 | 0.216164 | ||||||||
\(476\) | 4.93520 | − | 8.54801i | 0.226204 | − | 0.391797i | ||||
\(477\) | 3.92571 | − | 6.79954i | 0.179746 | − | 0.311329i | ||||
\(478\) | 1.19934 | + | 2.07733i | 0.0548567 | + | 0.0950146i | ||||
\(479\) | 17.9862 | 0.821811 | 0.410906 | − | 0.911678i | \(-0.365213\pi\) | ||||
0.410906 | + | 0.911678i | \(0.365213\pi\) | |||||||
\(480\) | −59.5429 | −2.71775 | ||||||||
\(481\) | 6.50593 | + | 5.38103i | 0.296645 | + | 0.245354i | ||||
\(482\) | −9.91937 | − | 17.1809i | −0.451815 | − | 0.782567i | ||||
\(483\) | 0.877124 | + | 1.51922i | 0.0399105 | + | 0.0691270i | ||||
\(484\) | 15.8328 | 0.719670 | ||||||||
\(485\) | −26.4074 | −1.19910 | ||||||||
\(486\) | 13.1416 | − | 22.7620i | 0.596117 | − | 1.03250i | ||||
\(487\) | −14.7501 | −0.668389 | −0.334194 | − | 0.942504i | \(-0.608464\pi\) | ||||
−0.334194 | + | 0.942504i | \(0.608464\pi\) | |||||||
\(488\) | −9.04530 | − | 15.6669i | −0.409461 | − | 0.709208i | ||||
\(489\) | 0.467135 | + | 0.809102i | 0.0211246 | + | 0.0365889i | ||||
\(490\) | −20.6644 | + | 35.7919i | −0.933525 | + | 1.61691i | ||||
\(491\) | 15.8445 | + | 27.4435i | 0.715052 | + | 1.23851i | 0.962939 | + | 0.269718i | \(0.0869304\pi\) |
−0.247887 | + | 0.968789i | \(0.579736\pi\) | |||||||
\(492\) | 26.2372 | − | 45.4442i | 1.18287 | − | 2.04878i | ||||
\(493\) | 4.75005 | + | 8.22732i | 0.213931 | + | 0.370540i | ||||
\(494\) | 0.405276 | − | 2.39766i | 0.0182342 | − | 0.107876i | ||||
\(495\) | 16.5013 | 0.741678 | ||||||||
\(496\) | −6.56987 | − | 2.73787i | −0.294996 | − | 0.122934i | ||||
\(497\) | 9.32949 | − | 16.1592i | 0.418485 | − | 0.724837i | ||||
\(498\) | −10.9290 | − | 18.9295i | −0.489739 | − | 0.848252i | ||||
\(499\) | −0.266771 | − | 0.462061i | −0.0119423 | − | 0.0206847i | 0.859992 | − | 0.510307i | \(-0.170468\pi\) |
−0.871935 | + | 0.489622i | \(0.837135\pi\) | |||||||
\(500\) | −0.209863 | − | 0.363493i | −0.00938534 | − | 0.0162559i | ||||
\(501\) | 13.1046 | 0.585472 | ||||||||
\(502\) | −7.55486 | − | 13.0854i | −0.337190 | − | 0.584030i | ||||
\(503\) | −14.2583 | + | 24.6961i | −0.635745 | + | 1.10114i | 0.350612 | + | 0.936521i | \(0.385974\pi\) |
−0.986357 | + | 0.164622i | \(0.947360\pi\) | |||||||
\(504\) | 47.0181 | − | 81.4377i | 2.09435 | − | 3.62753i | ||||
\(505\) | −8.79598 | − | 15.2351i | −0.391416 | − | 0.677952i | ||||
\(506\) | −0.0261094 | + | 0.0452228i | −0.00116070 | + | 0.00201040i | ||||
\(507\) | −7.91329 | − | 41.4359i | −0.351441 | − | 1.84023i | ||||
\(508\) | −3.55307 | − | 6.15410i | −0.157642 | − | 0.273044i | ||||
\(509\) | −0.345521 | − | 0.598459i | −0.0153149 | − | 0.0265262i | 0.858266 | − | 0.513204i | \(-0.171542\pi\) |
−0.873581 | + | 0.486678i | \(0.838208\pi\) | |||||||
\(510\) | −9.29343 | −0.411520 | ||||||||
\(511\) | −2.72153 | − | 4.71383i | −0.120393 | − | 0.208527i | ||||
\(512\) | 13.7524 | 0.607777 | ||||||||
\(513\) | 7.05005 | − | 12.2110i | 0.311267 | − | 0.539131i | ||||
\(514\) | −9.72980 | −0.429163 | ||||||||
\(515\) | −6.77699 | − | 11.7381i | −0.298630 | − | 0.517242i | ||||
\(516\) | 0.638450 | 0.0281062 | ||||||||
\(517\) | −3.09161 | − | 5.35482i | −0.135969 | − | 0.235505i | ||||
\(518\) | −4.17086 | − | 7.22414i | −0.183257 | − | 0.317410i | ||||
\(519\) | −31.0126 | −1.36130 | ||||||||
\(520\) | 26.2226 | − | 9.75521i | 1.14994 | − | 0.427794i | ||||
\(521\) | −15.4391 | − | 26.7413i | −0.676400 | − | 1.17156i | −0.976058 | − | 0.217512i | \(-0.930206\pi\) |
0.299658 | − | 0.954047i | \(-0.403127\pi\) | |||||||
\(522\) | 19.4364 | + | 33.6649i | 0.850709 | + | 1.47347i | ||||
\(523\) | −0.339900 | + | 0.588724i | −0.0148628 | + | 0.0257431i | −0.873361 | − | 0.487073i | \(-0.838064\pi\) |
0.858498 | + | 0.512816i | \(0.171398\pi\) | |||||||
\(524\) | 9.73777 | − | 16.8663i | 0.425396 | − | 0.736808i | ||||
\(525\) | −80.7506 | −3.52425 | ||||||||
\(526\) | 3.68996 | + | 6.39120i | 0.160890 | + | 0.278669i | ||||
\(527\) | −6.64955 | − | 2.77107i | −0.289659 | − | 0.120710i | ||||
\(528\) | −2.88748 | −0.125662 | ||||||||
\(529\) | 11.4943 | + | 19.9087i | 0.499753 | + | 0.865597i | ||||
\(530\) | −2.30802 | −0.100254 | ||||||||
\(531\) | 0.322284 | − | 0.558212i | 0.0139859 | − | 0.0242243i | ||||
\(532\) | 3.65882 | − | 6.33727i | 0.158630 | − | 0.274756i | ||||
\(533\) | −6.45396 | + | 38.1824i | −0.279552 | + | 1.65386i | ||||
\(534\) | 0.102203 | + | 0.177021i | 0.00442276 | + | 0.00766045i | ||||
\(535\) | 2.68010 | − | 4.64206i | 0.115871 | − | 0.200694i | ||||
\(536\) | −2.79427 | − | 4.83982i | −0.120694 | − | 0.209048i | ||||
\(537\) | 24.5420 | 1.05907 | ||||||||
\(538\) | −2.47804 | + | 4.29210i | −0.106836 | + | 0.185046i | ||||
\(539\) | −6.49835 | + | 11.2555i | −0.279904 | + | 0.484807i | ||||
\(540\) | 69.6784 | 2.99848 | ||||||||
\(541\) | −2.13486 | − | 3.69769i | −0.0917848 | − | 0.158976i | 0.816477 | − | 0.577377i | \(-0.195924\pi\) |
−0.908262 | + | 0.418401i | \(0.862591\pi\) | |||||||
\(542\) | 0.0362092 | + | 0.0627161i | 0.00155532 | + | 0.00269389i | ||||
\(543\) | −22.5820 | + | 39.1132i | −0.969087 | + | 1.67851i | ||||
\(544\) | 7.54106 | 0.323320 | ||||||||
\(545\) | 15.0370 | − | 26.0448i | 0.644112 | − | 1.11564i | ||||
\(546\) | −6.94650 | + | 41.0962i | −0.297283 | + | 1.75876i | ||||
\(547\) | 16.2298 | − | 28.1108i | 0.693936 | − | 1.20193i | −0.276602 | − | 0.960985i | \(-0.589208\pi\) |
0.970538 | − | 0.240948i | \(-0.0774583\pi\) | |||||||
\(548\) | −12.1288 | − | 21.0077i | −0.518116 | − | 0.897404i | ||||
\(549\) | 27.6332 | + | 47.8621i | 1.17935 | + | 2.04270i | ||||
\(550\) | −1.20185 | − | 2.08167i | −0.0512472 | − | 0.0887628i | ||||
\(551\) | 3.52156 | + | 6.09952i | 0.150024 | + | 0.259848i | ||||
\(552\) | −0.426697 | + | 0.739060i | −0.0181614 | + | 0.0314565i | ||||
\(553\) | −66.7115 | −2.83686 | ||||||||
\(554\) | 5.44298 | 0.231250 | ||||||||
\(555\) | 11.9611 | − | 20.7172i | 0.507721 | − | 0.879398i | ||||
\(556\) | 12.1625 | − | 21.0660i | 0.515803 | − | 0.893397i | ||||
\(557\) | 0.626683 | − | 1.08545i | 0.0265534 | − | 0.0459918i | −0.852443 | − | 0.522820i | \(-0.824880\pi\) |
0.878997 | + | 0.476828i | \(0.158213\pi\) | |||||||
\(558\) | −27.2089 | − | 11.3388i | −1.15184 | − | 0.480009i | ||||
\(559\) | −0.441583 | + | 0.164276i | −0.0186770 | + | 0.00694812i | ||||
\(560\) | 20.3911 | 0.861680 | ||||||||
\(561\) | −2.92250 | −0.123388 | ||||||||
\(562\) | 10.0553 | − | 17.4163i | 0.424158 | − | 0.734663i | ||||
\(563\) | −15.3460 | −0.646757 | −0.323378 | − | 0.946270i | \(-0.604819\pi\) | ||||
−0.323378 | + | 0.946270i | \(0.604819\pi\) | |||||||
\(564\) | −21.7002 | − | 37.5859i | −0.913745 | − | 1.58265i | ||||
\(565\) | 2.91876 | − | 5.05544i | 0.122793 | − | 0.212684i | ||||
\(566\) | −1.88459 | − | 3.26421i | −0.0792154 | − | 0.137205i | ||||
\(567\) | −63.6117 | + | 110.179i | −2.67144 | + | 4.62707i | ||||
\(568\) | 9.07708 | 0.380866 | ||||||||
\(569\) | 4.52705 | + | 7.84108i | 0.189784 | + | 0.328715i | 0.945178 | − | 0.326555i | \(-0.105888\pi\) |
−0.755394 | + | 0.655271i | \(0.772555\pi\) | |||||||
\(570\) | −6.88991 | −0.288586 | ||||||||
\(571\) | 5.05545 | − | 8.75629i | 0.211564 | − | 0.366439i | −0.740640 | − | 0.671902i | \(-0.765478\pi\) |
0.952204 | + | 0.305462i | \(0.0988110\pi\) | |||||||
\(572\) | 3.54170 | − | 1.31757i | 0.148086 | − | 0.0550903i | ||||
\(573\) | −43.0055 | −1.79658 | ||||||||
\(574\) | 19.1299 | − | 33.1340i | 0.798468 | − | 1.38299i | ||||
\(575\) | 0.524041 | 0.0218540 | ||||||||
\(576\) | 11.6051 | 0.483548 | ||||||||
\(577\) | −17.8614 | − | 30.9368i | −0.743579 | − | 1.28792i | −0.950856 | − | 0.309635i | \(-0.899793\pi\) |
0.207276 | − | 0.978282i | \(-0.433540\pi\) | |||||||
\(578\) | −10.7755 | −0.448204 | ||||||||
\(579\) | −41.7803 | −1.73633 | ||||||||
\(580\) | −17.4025 | + | 30.1420i | −0.722598 | + | 1.25158i | ||||
\(581\) | 24.2705 | + | 42.0377i | 1.00691 | + | 1.74402i | ||||
\(582\) | 19.1374 | 0.793269 | ||||||||
\(583\) | −0.725803 | −0.0300597 | ||||||||
\(584\) | 1.32395 | − | 2.29315i | 0.0547854 | − | 0.0948911i | ||||
\(585\) | −80.1094 | + | 29.8019i | −3.31212 | + | 1.23216i | ||||
\(586\) | 6.23076 | + | 10.7920i | 0.257390 | + | 0.445813i | ||||
\(587\) | −13.3553 | + | 23.1321i | −0.551234 | + | 0.954765i | 0.446952 | + | 0.894558i | \(0.352509\pi\) |
−0.998186 | + | 0.0602070i | \(0.980824\pi\) | |||||||
\(588\) | −45.6124 | + | 79.0031i | −1.88103 | + | 3.25803i | ||||
\(589\) | −4.92980 | − | 2.05440i | −0.203129 | − | 0.0846501i | ||||
\(590\) | −0.189478 | −0.00780069 | ||||||||
\(591\) | −16.8532 | − | 29.1907i | −0.693250 | − | 1.20074i | ||||
\(592\) | −1.49671 | + | 2.59238i | −0.0615144 | + | 0.106546i | ||||
\(593\) | 25.7939 | 1.05923 | 0.529615 | − | 0.848238i | \(-0.322337\pi\) | ||||
0.529615 | + | 0.848238i | \(0.322337\pi\) | |||||||
\(594\) | −7.19405 | −0.295175 | ||||||||
\(595\) | 20.6384 | 0.846091 | ||||||||
\(596\) | 16.4629 | 0.674345 | ||||||||
\(597\) | 27.9387 | 1.14346 | ||||||||
\(598\) | 0.0450801 | − | 0.266699i | 0.00184346 | − | 0.0109061i | ||||
\(599\) | 10.8558 | − | 18.8028i | 0.443556 | − | 0.768262i | −0.554394 | − | 0.832254i | \(-0.687050\pi\) |
0.997950 | + | 0.0639920i | \(0.0203832\pi\) | |||||||
\(600\) | −19.6415 | − | 34.0200i | −0.801860 | − | 1.38886i | ||||
\(601\) | −11.7433 | −0.479020 | −0.239510 | − | 0.970894i | \(-0.576987\pi\) | ||||
−0.239510 | + | 0.970894i | \(0.576987\pi\) | |||||||
\(602\) | 0.465503 | 0.0189725 | ||||||||
\(603\) | 8.53643 | + | 14.7855i | 0.347630 | + | 0.602113i | ||||
\(604\) | 2.91893 | + | 5.05574i | 0.118770 | + | 0.205715i | ||||
\(605\) | 16.5526 | + | 28.6700i | 0.672961 | + | 1.16560i | ||||
\(606\) | 6.37440 | + | 11.0408i | 0.258942 | + | 0.448501i | ||||
\(607\) | 23.5508 | 0.955896 | 0.477948 | − | 0.878388i | \(-0.341381\pi\) | ||||
0.477948 | + | 0.878388i | \(0.341381\pi\) | |||||||
\(608\) | 5.59074 | 0.226735 | ||||||||
\(609\) | −60.3602 | − | 104.547i | −2.44592 | − | 4.23645i | ||||
\(610\) | 8.12309 | − | 14.0696i | 0.328894 | − | 0.569662i | ||||
\(611\) | 24.6799 | + | 20.4127i | 0.998443 | + | 0.825808i | ||||
\(612\) | −14.6690 | −0.592959 | ||||||||
\(613\) | −20.8995 | −0.844122 | −0.422061 | − | 0.906567i | \(-0.638693\pi\) | ||||
−0.422061 | + | 0.906567i | \(0.638693\pi\) | |||||||
\(614\) | 1.89041 | 0.0762908 | ||||||||
\(615\) | 109.721 | 4.42437 | ||||||||
\(616\) | −8.69291 | −0.350247 | ||||||||
\(617\) | −10.7771 | + | 18.6664i | −0.433869 | + | 0.751482i | −0.997203 | − | 0.0747469i | \(-0.976185\pi\) |
0.563334 | + | 0.826229i | \(0.309518\pi\) | |||||||
\(618\) | 4.91125 | + | 8.50654i | 0.197560 | + | 0.342183i | ||||
\(619\) | −28.0171 | −1.12610 | −0.563051 | − | 0.826422i | \(-0.690373\pi\) | ||||
−0.563051 | + | 0.826422i | \(0.690373\pi\) | |||||||
\(620\) | −3.38870 | − | 26.1738i | −0.136094 | − | 1.05117i | ||||
\(621\) | 0.784200 | − | 1.35827i | 0.0314689 | − | 0.0545057i | ||||
\(622\) | −0.548827 | + | 0.950596i | −0.0220059 | + | 0.0381154i | ||||
\(623\) | −0.226968 | − | 0.393119i | −0.00909326 | − | 0.0157500i | ||||
\(624\) | 14.0180 | − | 5.21490i | 0.561168 | − | 0.208763i | ||||
\(625\) | 12.7174 | − | 22.0273i | 0.508698 | − | 0.881090i | ||||
\(626\) | 13.8186 | 0.552303 | ||||||||
\(627\) | −2.16667 | −0.0865284 | ||||||||
\(628\) | 4.71431 | + | 8.16542i | 0.188121 | + | 0.325836i | ||||
\(629\) | −1.51486 | + | 2.62382i | −0.0604016 | + | 0.104619i | ||||
\(630\) | 84.4488 | 3.36452 | ||||||||
\(631\) | 27.3706 | 1.08961 | 0.544803 | − | 0.838564i | \(-0.316604\pi\) | ||||
0.544803 | + | 0.838564i | \(0.316604\pi\) | |||||||
\(632\) | −16.2266 | − | 28.1054i | −0.645461 | − | 1.11797i | ||||
\(633\) | −66.6483 | −2.64903 | ||||||||
\(634\) | −9.83688 | −0.390673 | ||||||||
\(635\) | 7.42925 | − | 12.8678i | 0.294821 | − | 0.510645i | ||||
\(636\) | −5.09447 | −0.202009 | ||||||||
\(637\) | 11.2200 | − | 66.3786i | 0.444551 | − | 2.63001i | ||||
\(638\) | 1.79674 | − | 3.11205i | 0.0711338 | − | 0.123207i | ||||
\(639\) | −27.7303 | −1.09699 | ||||||||
\(640\) | 16.6435 | + | 28.8274i | 0.657892 | + | 1.13950i | ||||
\(641\) | −34.1374 | −1.34835 | −0.674173 | − | 0.738573i | \(-0.735500\pi\) | ||||
−0.674173 | + | 0.738573i | \(0.735500\pi\) | |||||||
\(642\) | −1.94225 | + | 3.36408i | −0.0766546 | + | 0.132770i | ||||
\(643\) | −1.21221 | − | 2.09961i | −0.0478050 | − | 0.0828006i | 0.841133 | − | 0.540829i | \(-0.181889\pi\) |
−0.888938 | + | 0.458028i | \(0.848556\pi\) | |||||||
\(644\) | 0.406983 | − | 0.704915i | 0.0160374 | − | 0.0277775i | ||||
\(645\) | 0.667480 | + | 1.15611i | 0.0262820 | + | 0.0455217i | ||||
\(646\) | 0.872601 | 0.0343320 | ||||||||
\(647\) | −2.37725 | + | 4.11752i | −0.0934593 | + | 0.161876i | −0.908965 | − | 0.416873i | \(-0.863126\pi\) |
0.815505 | + | 0.578750i | \(0.196459\pi\) | |||||||
\(648\) | −61.8907 | −2.43130 | ||||||||
\(649\) | −0.0595852 | −0.00233892 | ||||||||
\(650\) | 9.59425 | + | 7.93537i | 0.376318 | + | 0.311251i | ||||
\(651\) | 84.4976 | + | 35.2128i | 3.31172 | + | 1.38010i | ||||
\(652\) | 0.216750 | − | 0.375421i | 0.00848857 | − | 0.0147026i | ||||
\(653\) | 5.61578 | − | 9.72682i | 0.219763 | − | 0.380640i | −0.734973 | − | 0.678097i | \(-0.762805\pi\) |
0.954735 | + | 0.297457i | \(0.0961384\pi\) | |||||||
\(654\) | −10.8972 | + | 18.8745i | −0.426115 | + | 0.738052i | ||||
\(655\) | 40.7221 | 1.59115 | ||||||||
\(656\) | −13.7295 | −0.536049 | ||||||||
\(657\) | −4.04463 | + | 7.00551i | −0.157796 | + | 0.273311i | ||||
\(658\) | −15.8219 | − | 27.4044i | −0.616803 | − | 1.06833i | ||||
\(659\) | 16.1670 | + | 28.0021i | 0.629778 | + | 1.09081i | 0.987596 | + | 0.157016i | \(0.0501873\pi\) |
−0.357819 | + | 0.933791i | \(0.616479\pi\) | |||||||
\(660\) | −5.35351 | − | 9.27254i | −0.208385 | − | 0.360933i | ||||
\(661\) | −1.82616 | − | 3.16301i | −0.0710296 | − | 0.123027i | 0.828323 | − | 0.560251i | \(-0.189295\pi\) |
−0.899353 | + | 0.437224i | \(0.855962\pi\) | |||||||
\(662\) | −8.51890 | + | 14.7552i | −0.331097 | + | 0.573476i | ||||
\(663\) | 14.1880 | − | 5.27815i | 0.551016 | − | 0.204986i | ||||
\(664\) | −11.8069 | + | 20.4502i | −0.458198 | + | 0.793622i | ||||
\(665\) | 15.3007 | 0.593338 | ||||||||
\(666\) | −6.19857 | + | 10.7362i | −0.240190 | + | 0.416021i | ||||
\(667\) | 0.391715 | + | 0.678470i | 0.0151672 | + | 0.0262704i | ||||
\(668\) | −3.04026 | − | 5.26588i | −0.117631 | − | 0.203743i | ||||
\(669\) | −58.5402 | −2.26330 | ||||||||
\(670\) | 2.50938 | − | 4.34638i | 0.0969459 | − | 0.167915i | ||||
\(671\) | 2.55447 | − | 4.42447i | 0.0986142 | − | 0.170805i | ||||
\(672\) | −95.8263 | −3.69658 | ||||||||
\(673\) | −14.1942 | − | 24.5851i | −0.547146 | − | 0.947685i | −0.998468 | − | 0.0553236i | \(-0.982381\pi\) |
0.451323 | − | 0.892361i | \(-0.350952\pi\) | |||||||
\(674\) | −12.1760 | + | 21.0894i | −0.469001 | + | 0.812334i | ||||
\(675\) | 36.0979 | + | 62.5234i | 1.38941 | + | 2.40653i | ||||
\(676\) | −14.8145 | + | 12.7929i | −0.569787 | + | 0.492034i | ||||
\(677\) | −22.8075 | + | 39.5037i | −0.876563 | + | 1.51825i | −0.0214749 | + | 0.999769i | \(0.506836\pi\) |
−0.855088 | + | 0.518482i | \(0.826497\pi\) | |||||||
\(678\) | −2.11521 | + | 3.66366i | −0.0812342 | + | 0.140702i | ||||
\(679\) | −42.4992 | −1.63097 | ||||||||
\(680\) | 5.02000 | + | 8.69490i | 0.192508 | + | 0.333434i | ||||
\(681\) | 69.3471 | 2.65739 | ||||||||
\(682\) | 0.349871 | + | 2.70236i | 0.0133973 | + | 0.103479i | ||||
\(683\) | 7.61262 | + | 13.1854i | 0.291289 | + | 0.504527i | 0.974115 | − | 0.226054i | \(-0.0725826\pi\) |
−0.682826 | + | 0.730581i | \(0.739249\pi\) | |||||||
\(684\) | −10.8752 | −0.415824 | ||||||||
\(685\) | 25.3606 | − | 43.9258i | 0.968977 | − | 1.67832i | ||||
\(686\) | −20.7885 | + | 36.0067i | −0.793707 | + | 1.37474i | ||||
\(687\) | 40.6881 | + | 70.4739i | 1.55235 | + | 2.68875i | ||||
\(688\) | −0.0835228 | − | 0.144666i | −0.00318428 | − | 0.00551533i | ||||
\(689\) | 3.52358 | − | 1.31083i | 0.134238 | − | 0.0499385i | ||||
\(690\) | −0.766387 | −0.0291758 | ||||||||
\(691\) | −15.4058 | − | 26.6836i | −0.586064 | − | 1.01509i | −0.994742 | − | 0.102414i | \(-0.967343\pi\) |
0.408678 | − | 0.912679i | \(-0.365990\pi\) | |||||||
\(692\) | 7.19487 | + | 12.4619i | 0.273508 | + | 0.473730i | ||||
\(693\) | 26.5566 | 1.00880 | ||||||||
\(694\) | 4.31303 | + | 7.47039i | 0.163720 | + | 0.283572i | ||||
\(695\) | 50.8619 | 1.92930 | ||||||||
\(696\) | 29.3636 | − | 50.8592i | 1.11302 | − | 1.92781i | ||||
\(697\) | −13.8961 | −0.526351 | ||||||||
\(698\) | −10.7015 | − | 18.5355i | −0.405057 | − | 0.701579i | ||||
\(699\) | 54.3672 | 2.05636 | ||||||||
\(700\) | 18.7340 | + | 32.4483i | 0.708080 | + | 1.22643i | ||||
\(701\) | 3.56472 | + | 6.17427i | 0.134638 | + | 0.233199i | 0.925459 | − | 0.378848i | \(-0.123680\pi\) |
−0.790821 | + | 0.612047i | \(0.790346\pi\) | |||||||
\(702\) | 34.9252 | − | 12.9927i | 1.31817 | − | 0.490378i | ||||
\(703\) | −1.12308 | + | 1.94523i | −0.0423578 | + | 0.0733658i | ||||
\(704\) | −0.536402 | − | 0.929076i | −0.0202164 | − | 0.0350159i | ||||
\(705\) | 45.3738 | − | 78.5898i | 1.70888 | − | 2.95986i | ||||
\(706\) | −2.25427 | + | 3.90452i | −0.0848408 | + | 0.146948i | ||||
\(707\) | −14.1559 | − | 24.5188i | −0.532389 | − | 0.922125i | ||||
\(708\) | −0.418233 | −0.0157182 | ||||||||
\(709\) | −16.6833 | − | 28.8964i | −0.626556 | − | 1.08523i | −0.988238 | − | 0.152925i | \(-0.951131\pi\) |
0.361682 | − | 0.932302i | \(-0.382203\pi\) | |||||||
\(710\) | 4.07582 | + | 7.05953i | 0.152963 | + | 0.264939i | ||||
\(711\) | 49.5720 | + | 85.8613i | 1.85910 | + | 3.22005i | ||||
\(712\) | 0.110414 | − | 0.191242i | 0.00413792 | − | 0.00716709i | ||||
\(713\) | −0.548358 | − | 0.228518i | −0.0205362 | − | 0.00855805i | ||||
\(714\) | −14.9565 | −0.559734 | ||||||||
\(715\) | 6.08860 | + | 5.03586i | 0.227701 | + | 0.188330i | ||||
\(716\) | −5.69372 | − | 9.86181i | −0.212784 | − | 0.368553i | ||||
\(717\) | −5.53534 | + | 9.58749i | −0.206721 | + | 0.358051i | ||||
\(718\) | 4.56225 | + | 7.90205i | 0.170262 | + | 0.294902i | ||||
\(719\) | 9.47992 | − | 16.4197i | 0.353542 | − | 0.612352i | −0.633326 | − | 0.773885i | \(-0.718311\pi\) |
0.986867 | + | 0.161533i | \(0.0516440\pi\) | |||||||
\(720\) | −15.1522 | − | 26.2444i | −0.564690 | − | 0.978072i | ||||
\(721\) | −10.9067 | − | 18.8909i | −0.406185 | − | 0.703533i | ||||
\(722\) | −12.7118 | −0.473085 | ||||||||
\(723\) | 45.7809 | − | 79.2949i | 1.70261 | − | 2.94901i | ||||
\(724\) | 20.9560 | 0.778823 | ||||||||
\(725\) | −36.0624 | −1.33932 | ||||||||
\(726\) | −11.9956 | − | 20.7770i | −0.445199 | − | 0.771108i | ||||
\(727\) | −13.4607 | − | 23.3146i | −0.499229 | − | 0.864691i | 0.500770 | − | 0.865580i | \(-0.333050\pi\) |
−1.00000 | 0.000889681i | \(0.999717\pi\) | ||||||||
\(728\) | 42.2018 | − | 15.6997i | 1.56410 | − | 0.581870i | ||||
\(729\) | 45.9760 | 1.70281 | ||||||||
\(730\) | 2.37793 | 0.0880113 | ||||||||
\(731\) | −0.0845357 | − | 0.146420i | −0.00312667 | − | 0.00541555i | ||||
\(732\) | 17.9300 | − | 31.0557i | 0.662713 | − | 1.14785i | ||||
\(733\) | −1.30574 | + | 2.26161i | −0.0482287 | + | 0.0835345i | −0.889132 | − | 0.457651i | \(-0.848691\pi\) |
0.840903 | + | 0.541185i | \(0.182024\pi\) | |||||||
\(734\) | 8.73629 | 0.322462 | ||||||||
\(735\) | −190.746 | −7.03575 | ||||||||
\(736\) | 0.621876 | 0.0229227 | ||||||||
\(737\) | 0.789125 | − | 1.36680i | 0.0290678 | − | 0.0503469i | ||||
\(738\) | −56.8604 | −2.09306 | ||||||||
\(739\) | 13.2612 | + | 22.9691i | 0.487823 | + | 0.844934i | 0.999902 | − | 0.0140045i | \(-0.00445791\pi\) |
−0.512079 | + | 0.858938i | \(0.671125\pi\) | |||||||
\(740\) | −11.0998 | −0.408038 | ||||||||
\(741\) | 10.5186 | − | 3.91308i | 0.386410 | − | 0.143751i | ||||
\(742\) | −3.71445 | −0.136362 | ||||||||
\(743\) | 14.1900 | − | 24.5779i | 0.520582 | − | 0.901674i | −0.479132 | − | 0.877743i | \(-0.659048\pi\) |
0.999714 | − | 0.0239310i | \(-0.00761822\pi\) | |||||||
\(744\) | 5.71783 | + | 44.1637i | 0.209626 | + | 1.61912i | ||||
\(745\) | 17.2114 | + | 29.8110i | 0.630577 | + | 1.09219i | ||||
\(746\) | 15.3257 | 0.561115 | ||||||||
\(747\) | 36.0699 | − | 62.4749i | 1.31973 | − | 2.28584i | ||||
\(748\) | 0.678017 | + | 1.17436i | 0.0247908 | + | 0.0429388i | ||||
\(749\) | 4.31326 | − | 7.47078i | 0.157603 | − | 0.272976i | ||||
\(750\) | −0.318003 | + | 0.550798i | −0.0116118 | + | 0.0201123i | ||||
\(751\) | −36.5681 | −1.33439 | −0.667194 | − | 0.744884i | \(-0.732505\pi\) | ||||
−0.667194 | + | 0.744884i | \(0.732505\pi\) | |||||||
\(752\) | −5.67770 | + | 9.83406i | −0.207044 | + | 0.358611i | ||||
\(753\) | 34.8680 | − | 60.3931i | 1.27066 | − | 2.20085i | ||||
\(754\) | −3.10224 | + | 18.3532i | −0.112977 | + | 0.668383i | ||||
\(755\) | −6.10331 | + | 10.5712i | −0.222122 | + | 0.384727i | ||||
\(756\) | 112.138 | 4.07842 | ||||||||
\(757\) | 17.4917 | + | 30.2965i | 0.635747 | + | 1.10115i | 0.986356 | + | 0.164625i | \(0.0526413\pi\) |
−0.350609 | + | 0.936522i | \(0.614025\pi\) | |||||||
\(758\) | −7.10581 | + | 12.3076i | −0.258095 | + | 0.447033i | ||||
\(759\) | −0.241006 | −0.00874795 | ||||||||
\(760\) | 3.72170 | + | 6.44617i | 0.135000 | + | 0.233827i | ||||
\(761\) | −26.1786 | + | 45.3427i | −0.948975 | + | 1.64367i | −0.201385 | + | 0.979512i | \(0.564544\pi\) |
−0.747590 | + | 0.664161i | \(0.768789\pi\) | |||||||
\(762\) | −5.38394 | + | 9.32526i | −0.195040 | + | 0.337819i | ||||
\(763\) | 24.2000 | − | 41.9156i | 0.876097 | − | 1.51745i | ||||
\(764\) | 9.97721 | + | 17.2810i | 0.360963 | + | 0.625206i | ||||
\(765\) | −15.3360 | − | 26.5627i | −0.554474 | − | 0.960377i | ||||
\(766\) | −7.60043 | + | 13.1643i | −0.274615 | + | 0.475647i | ||||
\(767\) | 0.289270 | − | 0.107613i | 0.0104449 | − | 0.00388568i | ||||
\(768\) | −17.0626 | − | 29.5534i | −0.615695 | − | 1.06642i | ||||
\(769\) | −13.7061 | −0.494255 | −0.247128 | − | 0.968983i | \(-0.579487\pi\) | ||||
−0.247128 | + | 0.968983i | \(0.579487\pi\) | |||||||
\(770\) | −3.90331 | − | 6.76074i | −0.140666 | − | 0.243640i | ||||
\(771\) | −22.4530 | − | 38.8897i | −0.808625 | − | 1.40058i | ||||
\(772\) | 9.69296 | + | 16.7887i | 0.348857 | + | 0.604238i | ||||
\(773\) | 18.1591 | + | 31.4525i | 0.653138 | + | 1.13127i | 0.982357 | + | 0.187014i | \(0.0598810\pi\) |
−0.329220 | + | 0.944253i | \(0.606786\pi\) | |||||||
\(774\) | −0.345906 | − | 0.599128i | −0.0124333 | − | 0.0215352i | ||||
\(775\) | 21.7306 | − | 16.6005i | 0.780586 | − | 0.596306i | ||||
\(776\) | −10.3374 | − | 17.9048i | −0.371090 | − | 0.642746i | ||||
\(777\) | 19.2498 | − | 33.3416i | 0.690582 | − | 1.19612i | ||||
\(778\) | −6.45469 | −0.231412 | ||||||||
\(779\) | −10.3022 | −0.369114 | ||||||||
\(780\) | 42.7364 | + | 35.3471i | 1.53021 | + | 1.26563i | ||||
\(781\) | 1.28172 | + | 2.22001i | 0.0458636 | + | 0.0794382i | ||||
\(782\) | 0.0970622 | 0.00347094 | ||||||||
\(783\) | −53.9655 | + | 93.4711i | −1.92857 | + | 3.34038i | ||||
\(784\) | 23.8683 | 0.852439 | ||||||||
\(785\) | −9.85733 | + | 17.0734i | −0.351823 | + | 0.609375i | ||||
\(786\) | −29.5111 | −1.05263 | ||||||||
\(787\) | −2.33952 | + | 4.05216i | −0.0833947 | + | 0.144444i | −0.904706 | − | 0.426036i | \(-0.859910\pi\) |
0.821311 | + | 0.570480i | \(0.193243\pi\) | |||||||
\(788\) | −7.81986 | + | 13.5444i | −0.278571 | + | 0.482499i | ||||
\(789\) | −17.0303 | + | 29.4973i | −0.606294 | + | 1.05013i | ||||
\(790\) | 14.5723 | − | 25.2399i | 0.518458 | − | 0.897996i | ||||
\(791\) | 4.69735 | − | 8.13606i | 0.167019 | − | 0.289285i | ||||
\(792\) | 6.45954 | + | 11.1882i | 0.229530 | + | 0.397557i | ||||
\(793\) | −4.41051 | + | 26.0931i | −0.156622 | + | 0.926593i | ||||
\(794\) | 0.731937 | + | 1.26775i | 0.0259755 | + | 0.0449908i | ||||
\(795\) | −5.32611 | − | 9.22509i | −0.188898 | − | 0.327180i | ||||
\(796\) | −6.48174 | − | 11.2267i | −0.229739 | − | 0.397920i | ||||
\(797\) | −39.3312 | −1.39318 | −0.696592 | − | 0.717468i | \(-0.745301\pi\) | ||||
−0.696592 | + | 0.717468i | \(0.745301\pi\) | |||||||
\(798\) | −11.0884 | −0.392524 | ||||||||
\(799\) | −5.74656 | + | 9.95333i | −0.203299 | + | 0.352123i | ||||
\(800\) | −14.3129 | + | 24.7908i | −0.506039 | + | 0.876485i | ||||
\(801\) | −0.337311 | + | 0.584239i | −0.0119183 | + | 0.0206431i | ||||
\(802\) | −2.71534 | − | 4.70311i | −0.0958821 | − | 0.166073i | ||||
\(803\) | 0.747789 | 0.0263889 | ||||||||
\(804\) | 5.53893 | − | 9.59372i | 0.195343 | − | 0.338344i | ||||
\(805\) | 1.70195 | 0.0599859 | ||||||||
\(806\) | −6.57909 | − | 12.4873i | −0.231738 | − | 0.439848i | ||||
\(807\) | −22.8739 | −0.805198 | ||||||||
\(808\) | 6.88648 | − | 11.9277i | 0.242265 | − | 0.419616i | ||||
\(809\) | −44.4152 | −1.56155 | −0.780777 | − | 0.624810i | \(-0.785177\pi\) | ||||
−0.780777 | + | 0.624810i | \(0.785177\pi\) | |||||||
\(810\) | −27.7903 | − | 48.1343i | −0.976453 | − | 1.69127i | ||||
\(811\) | −12.1811 | + | 21.0983i | −0.427736 | + | 0.740860i | −0.996672 | − | 0.0815219i | \(-0.974022\pi\) |
0.568936 | + | 0.822382i | \(0.307355\pi\) | |||||||
\(812\) | −28.0069 | + | 48.5095i | −0.982851 | + | 1.70235i | ||||
\(813\) | −0.167116 | + | 0.289454i | −0.00586103 | + | 0.0101516i | ||||
\(814\) | 1.14602 | 0.0401679 | ||||||||
\(815\) | 0.906419 | 0.0317505 | ||||||||
\(816\) | 2.68357 | + | 4.64808i | 0.0939438 | + | 0.162716i | ||||
\(817\) | −0.0626726 | − | 0.108552i | −0.00219264 | − | 0.00379776i | ||||
\(818\) | 2.11767 | + | 3.66792i | 0.0740427 | + | 0.128246i | ||||
\(819\) | −128.925 | + | 47.9622i | −4.50502 | + | 1.67594i | ||||
\(820\) | −25.4551 | − | 44.0895i | −0.888930 | − | 1.53967i | ||||
\(821\) | 9.95642 | − | 17.2450i | 0.347481 | − | 0.601856i | −0.638320 | − | 0.769771i | \(-0.720370\pi\) |
0.985801 | + | 0.167916i | \(0.0537036\pi\) | |||||||
\(822\) | −18.3787 | + | 31.8328i | −0.641030 | + | 1.11030i | ||||
\(823\) | −14.6126 | + | 25.3098i | −0.509364 | + | 0.882245i | 0.490577 | + | 0.871398i | \(0.336786\pi\) |
−0.999941 | + | 0.0108471i | \(0.996547\pi\) | |||||||
\(824\) | 5.30579 | − | 9.18990i | 0.184836 | − | 0.320145i | ||||
\(825\) | 5.54692 | − | 9.60755i | 0.193119 | − | 0.334492i | ||||
\(826\) | −0.304940 | −0.0106102 | ||||||||
\(827\) | −6.75502 | + | 11.7000i | −0.234895 | + | 0.406850i | −0.959242 | − | 0.282585i | \(-0.908808\pi\) |
0.724347 | + | 0.689435i | \(0.242141\pi\) | |||||||
\(828\) | −1.20969 | −0.0420395 | ||||||||
\(829\) | 14.5004 | − | 25.1154i | 0.503620 | − | 0.872295i | −0.496371 | − | 0.868110i | \(-0.665335\pi\) |
0.999991 | − | 0.00418494i | \(-0.00133211\pi\) | |||||||
\(830\) | −21.2063 | −0.736082 | ||||||||
\(831\) | 12.5605 | + | 21.7555i | 0.435719 | + | 0.754688i | ||||
\(832\) | 4.28203 | + | 3.54165i | 0.148453 | + | 0.122785i | ||||
\(833\) | 24.1578 | 0.837017 | ||||||||
\(834\) | −36.8594 | −1.27634 | ||||||||
\(835\) | 6.35699 | − | 11.0106i | 0.219993 | − | 0.381038i | ||||
\(836\) | 0.502664 | + | 0.870640i | 0.0173850 | + | 0.0301117i | ||||
\(837\) | −10.5085 | − | 81.1658i | −0.363225 | − | 2.80550i | ||||
\(838\) | −0.102804 | − | 0.178062i | −0.00355132 | − | 0.00615106i | ||||
\(839\) | 17.4176 | + | 30.1682i | 0.601324 | + | 1.04152i | 0.992621 | + | 0.121259i | \(0.0386930\pi\) |
−0.391297 | + | 0.920264i | \(0.627974\pi\) | |||||||
\(840\) | −63.7906 | − | 110.488i | −2.20098 | − | 3.81221i | ||||
\(841\) | −12.4562 | − | 21.5748i | −0.429526 | − | 0.743960i | ||||
\(842\) | −8.59658 | − | 14.8897i | −0.296258 | − | 0.513133i | ||||
\(843\) | 92.8167 | 3.19678 | ||||||||
\(844\) | 15.4623 | + | 26.7815i | 0.532234 | + | 0.921857i | ||||
\(845\) | −38.6535 | − | 13.4515i | −1.32972 | − | 0.462746i | ||||
\(846\) | −23.5140 | + | 40.7274i | −0.808427 | + | 1.40024i | ||||
\(847\) | 26.6393 | + | 46.1406i | 0.915336 | + | 1.58541i | ||||
\(848\) | 0.666464 | + | 1.15435i | 0.0228865 | + | 0.0396405i | ||||
\(849\) | 8.69798 | − | 15.0653i | 0.298514 | − | 0.517041i | ||||
\(850\) | −2.23396 | + | 3.86933i | −0.0766242 | + | 0.132717i | ||||
\(851\) | −0.124924 | + | 0.216374i | −0.00428233 | + | 0.00741722i | ||||
\(852\) | 8.99652 | + | 15.5824i | 0.308216 | + | 0.533845i | ||||
\(853\) | −23.6132 | −0.808501 | −0.404251 | − | 0.914648i | \(-0.632468\pi\) | ||||
−0.404251 | + | 0.914648i | \(0.632468\pi\) | |||||||
\(854\) | 13.0730 | − | 22.6432i | 0.447350 | − | 0.774833i | ||||
\(855\) | −11.3697 | − | 19.6929i | −0.388836 | − | 0.673483i | ||||
\(856\) | 4.19656 | 0.143436 | ||||||||
\(857\) | −18.3797 | + | 31.8345i | −0.627837 | + | 1.08745i | 0.360148 | + | 0.932895i | \(0.382726\pi\) |
−0.987985 | + | 0.154551i | \(0.950607\pi\) | |||||||
\(858\) | −4.41238 | − | 3.64946i | −0.150636 | − | 0.124591i | ||||
\(859\) | 11.0527 | − | 19.1438i | 0.377112 | − | 0.653177i | −0.613529 | − | 0.789672i | \(-0.710251\pi\) |
0.990641 | + | 0.136495i | \(0.0435839\pi\) | |||||||
\(860\) | 0.309709 | − | 0.536431i | 0.0105610 | − | 0.0182922i | ||||
\(861\) | 176.581 | 6.01787 | ||||||||
\(862\) | 6.69310 | − | 11.5928i | 0.227968 | − | 0.394852i | ||||
\(863\) | 1.94339 | − | 3.36605i | 0.0661537 | − | 0.114582i | −0.831051 | − | 0.556196i | \(-0.812261\pi\) |
0.897205 | + | 0.441614i | \(0.145594\pi\) | |||||||
\(864\) | 42.8372 | + | 74.1962i | 1.45735 | + | 2.52420i | ||||
\(865\) | −15.0440 | + | 26.0570i | −0.511512 | + | 0.885965i | ||||
\(866\) | 7.88190 | 0.267838 | ||||||||
\(867\) | −24.8662 | − | 43.0696i | −0.844501 | − | 1.46272i | ||||
\(868\) | −5.45366 | − | 42.1233i | −0.185109 | − | 1.42976i | ||||
\(869\) | 4.58254 | − | 7.93720i | 0.155452 | − | 0.269251i | ||||
\(870\) | 52.7397 | 1.78804 | ||||||||
\(871\) | −1.36249 | + | 8.06066i | −0.0461663 | + | 0.273125i | ||||
\(872\) | 23.5452 | 0.797342 | ||||||||
\(873\) | 31.5804 | + | 54.6988i | 1.06883 | + | 1.85128i | ||||
\(874\) | 0.0719594 | 0.00243406 | ||||||||
\(875\) | 0.706205 | − | 1.22318i | 0.0238741 | − | 0.0413512i | ||||
\(876\) | 5.24879 | 0.177340 | ||||||||
\(877\) | −55.0667 | −1.85947 | −0.929736 | − | 0.368228i | \(-0.879965\pi\) | ||||
−0.929736 | + | 0.368228i | \(0.879965\pi\) | |||||||
\(878\) | −7.73209 | −0.260946 | ||||||||
\(879\) | −28.7569 | + | 49.8084i | −0.969945 | + | 1.67999i | ||||
\(880\) | −1.40070 | + | 2.42609i | −0.0472177 | + | 0.0817834i | ||||
\(881\) | 14.8061 | + | 25.6449i | 0.498830 | + | 0.864000i | 0.999999 | − | 0.00135007i | \(-0.000429739\pi\) |
−0.501169 | + | 0.865350i | \(0.667096\pi\) | |||||||
\(882\) | 98.8496 | 3.32844 | ||||||||
\(883\) | 35.1274 | 1.18213 | 0.591065 | − | 0.806624i | \(-0.298708\pi\) | ||||
0.591065 | + | 0.806624i | \(0.298708\pi\) | |||||||
\(884\) | −5.41253 | − | 4.47668i | −0.182043 | − | 0.150567i | ||||
\(885\) | −0.437250 | − | 0.757339i | −0.0146980 | − | 0.0254577i | ||||
\(886\) | 2.83704 | + | 4.91390i | 0.0953124 | + | 0.165086i | ||||
\(887\) | −55.0133 | −1.84716 | −0.923582 | − | 0.383400i | \(-0.874753\pi\) | ||||
−0.923582 | + | 0.383400i | \(0.874753\pi\) | |||||||
\(888\) | 18.7290 | 0.628504 | ||||||||
\(889\) | 11.9564 | − | 20.7091i | 0.401004 | − | 0.694560i | ||||
\(890\) | 0.198313 | 0.00664746 | ||||||||
\(891\) | −8.73923 | − | 15.1368i | −0.292775 | − | 0.507101i | ||||
\(892\) | 13.5812 | + | 23.5234i | 0.454734 | + | 0.787622i | ||||
\(893\) | −4.26035 | + | 7.37914i | −0.142567 | + | 0.246933i | ||||
\(894\) | −12.4730 | − | 21.6039i | −0.417161 | − | 0.722543i | ||||
\(895\) | 11.9052 | − | 20.6204i | 0.397947 | − | 0.689265i | ||||
\(896\) | 26.7855 | + | 46.3938i | 0.894840 | + | 1.54991i | ||||
\(897\) | 1.17002 | − | 0.435265i | 0.0390658 | − | 0.0145331i | ||||
\(898\) | −26.2942 | −0.877447 | ||||||||
\(899\) | 37.7358 | + | 15.7257i | 1.25856 | + | 0.524481i | ||||
\(900\) | 27.8418 | − | 48.2234i | 0.928060 | − | 1.60745i | ||||
\(901\) | 0.674547 | + | 1.16835i | 0.0224724 | + | 0.0389234i | ||||
\(902\) | 2.62815 | + | 4.55208i | 0.0875077 | + | 0.151568i | ||||
\(903\) | 1.07422 | + | 1.86060i | 0.0357478 | + | 0.0619170i | ||||
\(904\) | 4.57027 | 0.152005 | ||||||||
\(905\) | 21.9088 | + | 37.9472i | 0.728274 | + | 1.26141i | ||||
\(906\) | 4.42304 | − | 7.66093i | 0.146946 | − | 0.254517i | ||||
\(907\) | −18.8061 | + | 32.5730i | −0.624445 | + | 1.08157i | 0.364203 | + | 0.931320i | \(0.381341\pi\) |
−0.988648 | + | 0.150251i | \(0.951992\pi\) | |||||||
\(908\) | −16.0884 | − | 27.8660i | −0.533913 | − | 0.924765i | ||||
\(909\) | −21.0380 | + | 36.4389i | −0.697787 | + | 1.20860i | ||||
\(910\) | 31.1597 | + | 25.7721i | 1.03293 | + | 0.854336i | ||||
\(911\) | −16.4257 | − | 28.4502i | −0.544209 | − | 0.942597i | −0.998656 | − | 0.0518237i | \(-0.983497\pi\) |
0.454447 | − | 0.890774i | \(-0.349837\pi\) | |||||||
\(912\) | 1.98953 | + | 3.44597i | 0.0658799 | + | 0.114107i | ||||
\(913\) | −6.66875 | −0.220703 | ||||||||
\(914\) | 14.0197 | + | 24.2828i | 0.463730 | + | 0.803204i | ||||
\(915\) | 74.9811 | 2.47880 | ||||||||
\(916\) | 18.8792 | − | 32.6997i | 0.623785 | − | 1.08043i | ||||
\(917\) | 65.5368 | 2.16422 | ||||||||
\(918\) | 6.68601 | + | 11.5805i | 0.220671 | + | 0.382214i | ||||
\(919\) | −40.6474 | −1.34083 | −0.670416 | − | 0.741985i | \(-0.733885\pi\) | ||||
−0.670416 | + | 0.741985i | \(0.733885\pi\) | |||||||
\(920\) | 0.413976 | + | 0.717028i | 0.0136484 | + | 0.0236397i | ||||
\(921\) | 4.36241 | + | 7.55592i | 0.143746 | + | 0.248976i | ||||
\(922\) | 21.2171 | 0.698748 | ||||||||
\(923\) | −10.2318 | − | 8.46272i | −0.336785 | − | 0.278554i | ||||
\(924\) | −8.61575 | − | 14.9229i | −0.283437 | − | 0.490928i | ||||
\(925\) | −5.75043 | − | 9.96004i | −0.189073 | − | 0.327484i | ||||
\(926\) | −6.04162 | + | 10.4644i | −0.198540 | + | 0.343881i | ||||
\(927\) | −16.2091 | + | 28.0749i | −0.532376 | + | 0.922102i | ||||
\(928\) | −42.7951 | −1.40482 | ||||||||
\(929\) | −3.43047 | − | 5.94174i | −0.112550 | − | 0.194942i | 0.804248 | − | 0.594294i | \(-0.202568\pi\) |
−0.916798 | + | 0.399352i | \(0.869235\pi\) | |||||||
\(930\) | −31.7800 | + | 24.2774i | −1.04211 | + | 0.796089i | ||||
\(931\) | 17.9099 | 0.586974 | ||||||||
\(932\) | −12.6131 | − | 21.8466i | −0.413156 | − | 0.715608i | ||||
\(933\) | −5.06601 | −0.165854 | ||||||||
\(934\) | 5.53442 | − | 9.58590i | 0.181092 | − | 0.313660i | ||||
\(935\) | −1.41769 | + | 2.45551i | −0.0463635 | + | 0.0803039i | ||||
\(936\) | −51.5657 | − | 42.6498i | −1.68548 | − | 1.39405i | ||||
\(937\) | −0.765487 | − | 1.32586i | −0.0250074 | − | 0.0433141i | 0.853251 | − | 0.521501i | \(-0.174628\pi\) |
−0.878258 | + | 0.478187i | \(0.841294\pi\) | |||||||
\(938\) | 4.03851 | − | 6.99491i | 0.131862 | − | 0.228392i | ||||
\(939\) | 31.8886 | + | 55.2326i | 1.04064 | + | 1.80245i | ||||
\(940\) | −42.1067 | −1.37337 | ||||||||
\(941\) | 8.75241 | − | 15.1596i | 0.285321 | − | 0.494190i | −0.687366 | − | 0.726311i | \(-0.741233\pi\) |
0.972687 | + | 0.232121i | \(0.0745666\pi\) | |||||||
\(942\) | 7.14356 | − | 12.3730i | 0.232750 | − | 0.403134i | ||||
\(943\) | −1.14594 | −0.0373171 | ||||||||
\(944\) | 0.0547137 | + | 0.0947669i | 0.00178078 | + | 0.00308440i | ||||
\(945\) | 117.237 | + | 203.060i | 3.81371 | + | 6.60555i | ||||
\(946\) | −0.0319763 | + | 0.0553846i | −0.00103964 | + | 0.00180071i | ||||
\(947\) | 30.5337 | 0.992211 | 0.496106 | − | 0.868262i | \(-0.334763\pi\) | ||||
0.496106 | + | 0.868262i | \(0.334763\pi\) | |||||||
\(948\) | 32.1652 | − | 55.7118i | 1.04468 | − | 1.80944i | ||||
\(949\) | −3.63032 | + | 1.35053i | −0.117845 | + | 0.0438402i | ||||
\(950\) | −1.65620 | + | 2.86862i | −0.0537342 | + | 0.0930703i | ||||
\(951\) | −22.7001 | − | 39.3178i | −0.736102 | − | 1.27497i | ||||
\(952\) | 8.07902 | + | 13.9933i | 0.261843 | + | 0.453525i | ||||
\(953\) | 5.40468 | + | 9.36117i | 0.175075 | + | 0.303238i | 0.940187 | − | 0.340658i | \(-0.110650\pi\) |
−0.765112 | + | 0.643897i | \(0.777317\pi\) | |||||||
\(954\) | 2.76014 | + | 4.78070i | 0.0893627 | + | 0.154781i | ||||
\(955\) | −20.8617 | + | 36.1336i | −0.675069 | + | 1.16925i | ||||
\(956\) | 5.13676 | 0.166135 | ||||||||
\(957\) | 16.5850 | 0.536118 | ||||||||
\(958\) | −6.32298 | + | 10.9517i | −0.204286 | + | 0.353834i | ||||
\(959\) | 40.8144 | − | 70.6926i | 1.31797 | − | 2.28278i | ||||
\(960\) | 7.87249 | − | 13.6355i | 0.254083 | − | 0.440085i | ||||
\(961\) | −29.9779 | + | 7.89474i | −0.967028 | + | 0.254669i | ||||
\(962\) | −5.56362 | + | 2.06975i | −0.179378 | + | 0.0667315i | ||||
\(963\) | −12.8204 | −0.413131 | ||||||||
\(964\) | −42.4845 | −1.36833 | ||||||||
\(965\) | −20.2674 | + | 35.1041i | −0.652430 | + | 1.13004i | ||||
\(966\) | −1.23340 | −0.0396839 | ||||||||
\(967\) | −1.94762 | − | 3.37338i | −0.0626313 | − | 0.108481i | 0.833010 | − | 0.553259i | \(-0.186616\pi\) |
−0.895641 | + | 0.444778i | \(0.853283\pi\) | |||||||
\(968\) | −12.9593 | + | 22.4461i | −0.416527 | + | 0.721446i | ||||
\(969\) | 2.01366 | + | 3.48776i | 0.0646881 | + | 0.112043i | ||||
\(970\) | 9.28343 | − | 16.0794i | 0.298073 | − | 0.516277i | ||||
\(971\) | 32.9719 | 1.05812 | 0.529059 | − | 0.848585i | \(-0.322545\pi\) | ||||
0.529059 | + | 0.848585i | \(0.322545\pi\) | |||||||
\(972\) | −28.1427 | − | 48.7445i | −0.902677 | − | 1.56348i | ||||
\(973\) | 81.8554 | 2.62416 | ||||||||
\(974\) | 5.18532 | − | 8.98124i | 0.166148 | − | 0.287777i | ||||
\(975\) | −9.57725 | + | 56.6600i | −0.306717 | + | 1.81457i | ||||
\(976\) | −9.38250 | −0.300327 | ||||||||
\(977\) | 21.1583 | − | 36.6472i | 0.676913 | − | 1.17245i | −0.298993 | − | 0.954255i | \(-0.596651\pi\) |
0.975906 | − | 0.218193i | \(-0.0700161\pi\) | |||||||
\(978\) | −0.656878 | −0.0210046 | ||||||||
\(979\) | 0.0623634 | 0.00199314 | ||||||||
\(980\) | 44.2527 | + | 76.6479i | 1.41360 | + | 2.44843i | ||||
\(981\) | −71.9301 | −2.29655 | ||||||||
\(982\) | −22.2803 | −0.710992 | ||||||||
\(983\) | 24.6411 | − | 42.6796i | 0.785929 | − | 1.36127i | −0.142514 | − | 0.989793i | \(-0.545519\pi\) |
0.928443 | − | 0.371476i | \(-0.121148\pi\) | |||||||
\(984\) | 42.9509 | + | 74.3932i | 1.36923 | + | 2.37157i | ||||
\(985\) | −32.7017 | −1.04196 | ||||||||
\(986\) | −6.67944 | −0.212717 | ||||||||
\(987\) | 73.0231 | − | 126.480i | 2.32435 | − | 4.02589i | ||||
\(988\) | −4.01271 | − | 3.31889i | −0.127661 | − | 0.105588i | ||||
\(989\) | −0.00697127 | − | 0.0120746i | −0.000221674 | − | 0.000383950i | ||||
\(990\) | −5.80096 | + | 10.0476i | −0.184367 | + | 0.319332i | ||||
\(991\) | 28.5787 | − | 49.4998i | 0.907833 | − | 1.57241i | 0.0907640 | − | 0.995872i | \(-0.471069\pi\) |
0.817069 | − | 0.576540i | \(-0.195598\pi\) | |||||||
\(992\) | 25.7876 | − | 19.6997i | 0.818756 | − | 0.625465i | ||||
\(993\) | −78.6347 | −2.49540 | ||||||||
\(994\) | 6.55949 | + | 11.3614i | 0.208054 | + | 0.360361i | ||||
\(995\) | 13.5529 | − | 23.4743i | 0.429656 | − | 0.744187i | ||||
\(996\) | −46.8085 | −1.48318 | ||||||||
\(997\) | −6.10206 | −0.193254 | −0.0966271 | − | 0.995321i | \(-0.530805\pi\) | ||||
−0.0966271 | + | 0.995321i | \(0.530805\pi\) | |||||||
\(998\) | 0.375128 | 0.0118745 | ||||||||
\(999\) | −34.4209 | −1.08903 |
(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 | 403.2.g.a.87.15 | yes | 70 | |
13.3 | even | 3 | 403.2.e.a.211.15 | yes | 70 | ||
31.5 | even | 3 | 403.2.e.a.191.15 | ✓ | 70 | ||
403.315 | even | 3 | inner | 403.2.g.a.315.15 | yes | 70 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.e.a.191.15 | ✓ | 70 | 31.5 | even | 3 | ||
403.2.e.a.211.15 | yes | 70 | 13.3 | even | 3 | ||
403.2.g.a.87.15 | yes | 70 | 1.1 | even | 1 | trivial | |
403.2.g.a.315.15 | yes | 70 | 403.315 | even | 3 | inner |