Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(161,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 491.18 | ||
Character | \(\chi\) | \(=\) | 930.491 |
Dual form | 930.2.o.e.161.8 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.29636 | − | 1.14867i | 0.748454 | − | 0.663186i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.866025 | − | 0.500000i | 0.387298 | − | 0.223607i | ||||
\(6\) | 1.14867 | + | 1.29636i | 0.468943 | + | 0.529237i | ||||
\(7\) | 1.71736 | − | 2.97455i | 0.649100 | − | 1.12427i | −0.334238 | − | 0.942489i | \(-0.608479\pi\) |
0.983338 | − | 0.181786i | \(-0.0581877\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.361105 | − | 2.97819i | 0.120368 | − | 0.992729i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 0.402897 | + | 0.697837i | 0.121478 | + | 0.210406i | 0.920351 | − | 0.391094i | \(-0.127903\pi\) |
−0.798873 | + | 0.601500i | \(0.794570\pi\) | |||||||
\(12\) | −1.29636 | + | 1.14867i | −0.374227 | + | 0.331593i | ||||
\(13\) | −2.61618 | + | 1.51045i | −0.725599 | + | 0.418925i | −0.816810 | − | 0.576907i | \(-0.804260\pi\) |
0.0912110 | + | 0.995832i | \(0.470926\pi\) | |||||||
\(14\) | 2.97455 | + | 1.71736i | 0.794982 | + | 0.458983i | ||||
\(15\) | 0.548346 | − | 1.64296i | 0.141582 | − | 0.424210i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.94308 | − | 3.36552i | 0.471267 | − | 0.816258i | −0.528193 | − | 0.849124i | \(-0.677130\pi\) |
0.999460 | + | 0.0328666i | \(0.0104637\pi\) | |||||||
\(18\) | 2.97819 | + | 0.361105i | 0.701966 | + | 0.0851132i | ||||
\(19\) | −1.37995 | + | 2.39014i | −0.316581 | + | 0.548335i | −0.979772 | − | 0.200115i | \(-0.935868\pi\) |
0.663191 | + | 0.748450i | \(0.269202\pi\) | |||||||
\(20\) | −0.866025 | + | 0.500000i | −0.193649 | + | 0.111803i | ||||
\(21\) | −1.19047 | − | 5.82877i | −0.259781 | − | 1.27194i | ||||
\(22\) | −0.697837 | + | 0.402897i | −0.148779 | + | 0.0858978i | ||||
\(23\) | −0.142267 | −0.0296648 | −0.0148324 | − | 0.999890i | \(-0.504721\pi\) | ||||
−0.0148324 | + | 0.999890i | \(0.504721\pi\) | |||||||
\(24\) | −1.14867 | − | 1.29636i | −0.234472 | − | 0.264619i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −1.51045 | − | 2.61618i | −0.296225 | − | 0.513076i | ||||
\(27\) | −2.95284 | − | 4.27560i | −0.568274 | − | 0.822839i | ||||
\(28\) | −1.71736 | + | 2.97455i | −0.324550 | + | 0.562137i | ||||
\(29\) | 7.20137 | 1.33726 | 0.668631 | − | 0.743595i | \(-0.266881\pi\) | ||||
0.668631 | + | 0.743595i | \(0.266881\pi\) | |||||||
\(30\) | 1.64296 | + | 0.548346i | 0.299962 | + | 0.100114i | ||||
\(31\) | −1.97991 | − | 5.20384i | −0.355603 | − | 0.934637i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 1.32389 | + | 0.441853i | 0.230459 | + | 0.0769168i | ||||
\(34\) | 3.36552 | + | 1.94308i | 0.577181 | + | 0.333236i | ||||
\(35\) | − | 3.43472i | − | 0.580573i | ||||||
\(36\) | −0.361105 | + | 2.97819i | −0.0601841 | + | 0.496365i | ||||
\(37\) | −9.28550 | − | 5.36099i | −1.52653 | − | 0.881341i | −0.999504 | − | 0.0314905i | \(-0.989975\pi\) |
−0.527024 | − | 0.849851i | \(-0.676692\pi\) | |||||||
\(38\) | −2.39014 | − | 1.37995i | −0.387732 | − | 0.223857i | ||||
\(39\) | −1.65650 | + | 4.96323i | −0.265253 | + | 0.794753i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | −0.634427 | + | 0.366287i | −0.0990809 | + | 0.0572044i | −0.548722 | − | 0.836005i | \(-0.684885\pi\) |
0.449641 | + | 0.893209i | \(0.351552\pi\) | |||||||
\(42\) | 5.82877 | − | 1.19047i | 0.899399 | − | 0.183693i | ||||
\(43\) | −0.711673 | − | 0.410885i | −0.108529 | − | 0.0626594i | 0.444753 | − | 0.895653i | \(-0.353291\pi\) |
−0.553282 | + | 0.832994i | \(0.686625\pi\) | |||||||
\(44\) | −0.402897 | − | 0.697837i | −0.0607389 | − | 0.105203i | ||||
\(45\) | −1.17637 | − | 2.75974i | −0.175363 | − | 0.411398i | ||||
\(46\) | − | 0.142267i | − | 0.0209761i | ||||||
\(47\) | − | 4.88227i | − | 0.712152i | −0.934457 | − | 0.356076i | \(-0.884114\pi\) | ||
0.934457 | − | 0.356076i | \(-0.115886\pi\) | |||||||
\(48\) | 1.29636 | − | 1.14867i | 0.187114 | − | 0.165797i | ||||
\(49\) | −2.39863 | − | 4.15456i | −0.342662 | − | 0.593508i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | −1.34694 | − | 6.59489i | −0.188609 | − | 0.923469i | ||||
\(52\) | 2.61618 | − | 1.51045i | 0.362799 | − | 0.209462i | ||||
\(53\) | 6.79605 | + | 11.7711i | 0.933509 | + | 1.61688i | 0.777272 | + | 0.629165i | \(0.216603\pi\) |
0.156237 | + | 0.987720i | \(0.450064\pi\) | |||||||
\(54\) | 4.27560 | − | 2.95284i | 0.581835 | − | 0.401831i | ||||
\(55\) | 0.697837 | + | 0.402897i | 0.0940964 | + | 0.0543266i | ||||
\(56\) | −2.97455 | − | 1.71736i | −0.397491 | − | 0.229492i | ||||
\(57\) | 0.956575 | + | 4.68359i | 0.126701 | + | 0.620356i | ||||
\(58\) | 7.20137i | 0.945587i | ||||||||
\(59\) | 11.5957 | + | 6.69476i | 1.50963 | + | 0.871584i | 0.999937 | + | 0.0112259i | \(0.00357339\pi\) |
0.509690 | + | 0.860358i | \(0.329760\pi\) | |||||||
\(60\) | −0.548346 | + | 1.64296i | −0.0707911 | + | 0.212105i | ||||
\(61\) | 10.6269i | 1.36064i | 0.732916 | + | 0.680319i | \(0.238159\pi\) | ||||
−0.732916 | + | 0.680319i | \(0.761841\pi\) | |||||||
\(62\) | 5.20384 | − | 1.97991i | 0.660888 | − | 0.251449i | ||||
\(63\) | −8.23862 | − | 6.18874i | −1.03797 | − | 0.779708i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.51045 | + | 2.61618i | −0.187349 | + | 0.324498i | ||||
\(66\) | −0.441853 | + | 1.32389i | −0.0543884 | + | 0.162959i | ||||
\(67\) | −0.342847 | − | 0.593829i | −0.0418854 | − | 0.0725477i | 0.844323 | − | 0.535835i | \(-0.180003\pi\) |
−0.886208 | + | 0.463287i | \(0.846670\pi\) | |||||||
\(68\) | −1.94308 | + | 3.36552i | −0.235633 | + | 0.408129i | ||||
\(69\) | −0.184430 | + | 0.163418i | −0.0222027 | + | 0.0196733i | ||||
\(70\) | 3.43472 | 0.410527 | ||||||||
\(71\) | 9.83676 | − | 5.67926i | 1.16741 | − | 0.674004i | 0.214340 | − | 0.976759i | \(-0.431240\pi\) |
0.953068 | + | 0.302755i | \(0.0979065\pi\) | |||||||
\(72\) | −2.97819 | − | 0.361105i | −0.350983 | − | 0.0425566i | ||||
\(73\) | 0.721718 | − | 0.416684i | 0.0844707 | − | 0.0487692i | −0.457170 | − | 0.889380i | \(-0.651137\pi\) |
0.541640 | + | 0.840610i | \(0.317803\pi\) | |||||||
\(74\) | 5.36099 | − | 9.28550i | 0.623202 | − | 1.07942i | ||||
\(75\) | −0.346599 | − | 1.69702i | −0.0400218 | − | 0.195955i | ||||
\(76\) | 1.37995 | − | 2.39014i | 0.158291 | − | 0.274168i | ||||
\(77\) | 2.76767 | 0.315405 | ||||||||
\(78\) | −4.96323 | − | 1.65650i | −0.561975 | − | 0.187562i | ||||
\(79\) | 2.81725 | + | 1.62654i | 0.316966 | + | 0.183000i | 0.650039 | − | 0.759901i | \(-0.274752\pi\) |
−0.333074 | + | 0.942901i | \(0.608086\pi\) | |||||||
\(80\) | 0.866025 | − | 0.500000i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | −8.73921 | − | 2.15088i | −0.971023 | − | 0.238986i | ||||
\(82\) | −0.366287 | − | 0.634427i | −0.0404496 | − | 0.0700608i | ||||
\(83\) | 0.934238 | + | 1.61815i | 0.102546 | + | 0.177615i | 0.912733 | − | 0.408557i | \(-0.133968\pi\) |
−0.810187 | + | 0.586172i | \(0.800634\pi\) | |||||||
\(84\) | 1.19047 | + | 5.82877i | 0.129891 | + | 0.635971i | ||||
\(85\) | − | 3.88616i | − | 0.421514i | ||||||
\(86\) | 0.410885 | − | 0.711673i | 0.0443069 | − | 0.0767417i | ||||
\(87\) | 9.33558 | − | 8.27202i | 1.00088 | − | 0.886853i | ||||
\(88\) | 0.697837 | − | 0.402897i | 0.0743897 | − | 0.0429489i | ||||
\(89\) | −7.24740 | −0.768222 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(90\) | 2.75974 | − | 1.17637i | 0.290902 | − | 0.124000i | ||||
\(91\) | 10.3760i | 1.08770i | ||||||||
\(92\) | 0.142267 | 0.0148324 | ||||||||
\(93\) | −8.54419 | − | 4.47178i | −0.885991 | − | 0.463702i | ||||
\(94\) | 4.88227 | 0.503567 | ||||||||
\(95\) | 2.75989i | 0.283159i | ||||||||
\(96\) | 1.14867 | + | 1.29636i | 0.117236 | + | 0.132309i | ||||
\(97\) | 16.1867 | 1.64351 | 0.821755 | − | 0.569841i | \(-0.192995\pi\) | ||||
0.821755 | + | 0.569841i | \(0.192995\pi\) | |||||||
\(98\) | 4.15456 | − | 2.39863i | 0.419674 | − | 0.242299i | ||||
\(99\) | 2.22378 | − | 0.947909i | 0.223498 | − | 0.0952685i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | − | 3.07118i | − | 0.305594i | −0.988258 | − | 0.152797i | \(-0.951172\pi\) | ||
0.988258 | − | 0.152797i | \(-0.0488281\pi\) | |||||||
\(102\) | 6.59489 | − | 1.34694i | 0.652991 | − | 0.133367i | ||||
\(103\) | −0.368713 | − | 0.638630i | −0.0363304 | − | 0.0629261i | 0.847288 | − | 0.531133i | \(-0.178234\pi\) |
−0.883619 | + | 0.468207i | \(0.844900\pi\) | |||||||
\(104\) | 1.51045 | + | 2.61618i | 0.148112 | + | 0.256538i | ||||
\(105\) | −3.94536 | − | 4.45263i | −0.385028 | − | 0.434532i | ||||
\(106\) | −11.7711 | + | 6.79605i | −1.14331 | + | 0.660090i | ||||
\(107\) | −1.85660 | − | 1.07191i | −0.179484 | − | 0.103625i | 0.407566 | − | 0.913176i | \(-0.366378\pi\) |
−0.587050 | + | 0.809551i | \(0.699711\pi\) | |||||||
\(108\) | 2.95284 | + | 4.27560i | 0.284137 | + | 0.411420i | ||||
\(109\) | −14.2883 | −1.36857 | −0.684284 | − | 0.729216i | \(-0.739885\pi\) | ||||
−0.684284 | + | 0.729216i | \(0.739885\pi\) | |||||||
\(110\) | −0.402897 | + | 0.697837i | −0.0384147 | + | 0.0665362i | ||||
\(111\) | −18.1954 | + | 3.71622i | −1.72703 | + | 0.352728i | ||||
\(112\) | 1.71736 | − | 2.97455i | 0.162275 | − | 0.281069i | ||||
\(113\) | −13.2560 | + | 7.65337i | −1.24702 | + | 0.719968i | −0.970514 | − | 0.241043i | \(-0.922510\pi\) |
−0.276508 | + | 0.961012i | \(0.589177\pi\) | |||||||
\(114\) | −4.68359 | + | 0.956575i | −0.438658 | + | 0.0895915i | ||||
\(115\) | −0.123207 | + | 0.0711336i | −0.0114891 | + | 0.00663324i | ||||
\(116\) | −7.20137 | −0.668631 | ||||||||
\(117\) | 3.55370 | + | 8.33692i | 0.328540 | + | 0.770749i | ||||
\(118\) | −6.69476 | + | 11.5957i | −0.616303 | + | 1.06747i | ||||
\(119\) | −6.67393 | − | 11.5596i | −0.611798 | − | 1.05967i | ||||
\(120\) | −1.64296 | − | 0.548346i | −0.149981 | − | 0.0500569i | ||||
\(121\) | 5.17535 | − | 8.96397i | 0.470486 | − | 0.814906i | ||||
\(122\) | −10.6269 | −0.962117 | ||||||||
\(123\) | −0.401704 | + | 1.20359i | −0.0362204 | + | 0.108524i | ||||
\(124\) | 1.97991 | + | 5.20384i | 0.177802 | + | 0.467319i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 6.18874 | − | 8.23862i | 0.551337 | − | 0.733955i | ||||
\(127\) | 9.01862 | + | 5.20690i | 0.800273 | + | 0.462038i | 0.843567 | − | 0.537024i | \(-0.180452\pi\) |
−0.0432935 | + | 0.999062i | \(0.513785\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −1.39456 | + | 0.284824i | −0.122784 | + | 0.0250774i | ||||
\(130\) | −2.61618 | − | 1.51045i | −0.229455 | − | 0.132476i | ||||
\(131\) | 14.0976 | + | 8.13923i | 1.23171 | + | 0.711128i | 0.967386 | − | 0.253307i | \(-0.0815182\pi\) |
0.264323 | + | 0.964434i | \(0.414852\pi\) | |||||||
\(132\) | −1.32389 | − | 0.441853i | −0.115229 | − | 0.0384584i | ||||
\(133\) | 4.73972 | + | 8.20944i | 0.410986 | + | 0.711849i | ||||
\(134\) | 0.593829 | − | 0.342847i | 0.0512990 | − | 0.0296175i | ||||
\(135\) | −4.69503 | − | 2.22636i | −0.404084 | − | 0.191614i | ||||
\(136\) | −3.36552 | − | 1.94308i | −0.288591 | − | 0.166618i | ||||
\(137\) | 3.25803 | + | 5.64307i | 0.278352 | + | 0.482120i | 0.970975 | − | 0.239180i | \(-0.0768785\pi\) |
−0.692623 | + | 0.721299i | \(0.743545\pi\) | |||||||
\(138\) | −0.163418 | − | 0.184430i | −0.0139111 | − | 0.0156997i | ||||
\(139\) | 16.3232i | 1.38452i | 0.721648 | + | 0.692260i | \(0.243385\pi\) | ||||
−0.721648 | + | 0.692260i | \(0.756615\pi\) | |||||||
\(140\) | 3.43472i | 0.290286i | ||||||||
\(141\) | −5.60812 | − | 6.32918i | −0.472289 | − | 0.533013i | ||||
\(142\) | 5.67926 | + | 9.83676i | 0.476593 | + | 0.825483i | ||||
\(143\) | −2.10810 | − | 1.21711i | −0.176288 | − | 0.101780i | ||||
\(144\) | 0.361105 | − | 2.97819i | 0.0300921 | − | 0.248182i | ||||
\(145\) | 6.23657 | − | 3.60069i | 0.517919 | − | 0.299021i | ||||
\(146\) | 0.416684 | + | 0.721718i | 0.0344850 | + | 0.0597298i | ||||
\(147\) | −7.88172 | − | 2.63056i | −0.650073 | − | 0.216965i | ||||
\(148\) | 9.28550 | + | 5.36099i | 0.763264 | + | 0.440671i | ||||
\(149\) | −2.68851 | − | 1.55221i | −0.220251 | − | 0.127162i | 0.385815 | − | 0.922576i | \(-0.373920\pi\) |
−0.606067 | + | 0.795414i | \(0.707253\pi\) | |||||||
\(150\) | 1.69702 | − | 0.346599i | 0.138561 | − | 0.0282997i | ||||
\(151\) | 19.8572i | 1.61596i | 0.589212 | + | 0.807979i | \(0.299438\pi\) | ||||
−0.589212 | + | 0.807979i | \(0.700562\pi\) | |||||||
\(152\) | 2.39014 | + | 1.37995i | 0.193866 | + | 0.111928i | ||||
\(153\) | −9.32148 | − | 7.00217i | −0.753597 | − | 0.566092i | ||||
\(154\) | 2.76767i | 0.223025i | ||||||||
\(155\) | −4.31658 | − | 3.51670i | −0.346716 | − | 0.282468i | ||||
\(156\) | 1.65650 | − | 4.96323i | 0.132626 | − | 0.397377i | ||||
\(157\) | 1.70330 | 0.135938 | 0.0679690 | − | 0.997687i | \(-0.478348\pi\) | ||||
0.0679690 | + | 0.997687i | \(0.478348\pi\) | |||||||
\(158\) | −1.62654 | + | 2.81725i | −0.129401 | + | 0.224129i | ||||
\(159\) | 22.3313 | + | 7.45317i | 1.77098 | + | 0.591074i | ||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −0.244324 | + | 0.423181i | −0.0192554 | + | 0.0333513i | ||||
\(162\) | 2.15088 | − | 8.73921i | 0.168989 | − | 0.686617i | ||||
\(163\) | 2.96548 | 0.232274 | 0.116137 | − | 0.993233i | \(-0.462949\pi\) | ||||
0.116137 | + | 0.993233i | \(0.462949\pi\) | |||||||
\(164\) | 0.634427 | − | 0.366287i | 0.0495405 | − | 0.0286022i | ||||
\(165\) | 1.36745 | − | 0.279287i | 0.106455 | − | 0.0217424i | ||||
\(166\) | −1.61815 | + | 0.934238i | −0.125593 | + | 0.0725109i | ||||
\(167\) | 11.5431 | − | 19.9933i | 0.893235 | − | 1.54713i | 0.0572603 | − | 0.998359i | \(-0.481764\pi\) |
0.835974 | − | 0.548768i | \(-0.184903\pi\) | |||||||
\(168\) | −5.82877 | + | 1.19047i | −0.449700 | + | 0.0918466i | ||||
\(169\) | −1.93705 | + | 3.35507i | −0.149004 | + | 0.258083i | ||||
\(170\) | 3.88616 | 0.298055 | ||||||||
\(171\) | 6.61997 | + | 4.97283i | 0.506242 | + | 0.380282i | ||||
\(172\) | 0.711673 | + | 0.410885i | 0.0542646 | + | 0.0313297i | ||||
\(173\) | −11.7703 | + | 6.79559i | −0.894880 | + | 0.516659i | −0.875536 | − | 0.483154i | \(-0.839491\pi\) |
−0.0193444 | + | 0.999813i | \(0.506158\pi\) | |||||||
\(174\) | 8.27202 | + | 9.33558i | 0.627100 | + | 0.707729i | ||||
\(175\) | −1.71736 | − | 2.97455i | −0.129820 | − | 0.224855i | ||||
\(176\) | 0.402897 | + | 0.697837i | 0.0303695 | + | 0.0526015i | ||||
\(177\) | 22.7223 | − | 4.64079i | 1.70791 | − | 0.348823i | ||||
\(178\) | − | 7.24740i | − | 0.543215i | ||||||
\(179\) | −1.61838 | + | 2.80311i | −0.120963 | + | 0.209514i | −0.920148 | − | 0.391571i | \(-0.871932\pi\) |
0.799185 | + | 0.601086i | \(0.205265\pi\) | |||||||
\(180\) | 1.17637 | + | 2.75974i | 0.0876813 | + | 0.205699i | ||||
\(181\) | −14.2426 | + | 8.22298i | −1.05865 | + | 0.611209i | −0.925057 | − | 0.379827i | \(-0.875983\pi\) |
−0.133588 | + | 0.991037i | \(0.542650\pi\) | |||||||
\(182\) | −10.3760 | −0.769118 | ||||||||
\(183\) | 12.2069 | + | 13.7763i | 0.902357 | + | 1.01838i | ||||
\(184\) | 0.142267i | 0.0104881i | ||||||||
\(185\) | −10.7220 | −0.788295 | ||||||||
\(186\) | 4.47178 | − | 8.54419i | 0.327887 | − | 0.626490i | ||||
\(187\) | 3.13144 | 0.228994 | ||||||||
\(188\) | 4.88227i | 0.356076i | ||||||||
\(189\) | −17.7891 | + | 1.44064i | −1.29396 | + | 0.104791i | ||||
\(190\) | −2.75989 | −0.200224 | ||||||||
\(191\) | −11.6288 | + | 6.71391i | −0.841433 | + | 0.485802i | −0.857751 | − | 0.514065i | \(-0.828139\pi\) |
0.0163179 | + | 0.999867i | \(0.494806\pi\) | |||||||
\(192\) | −1.29636 | + | 1.14867i | −0.0935568 | + | 0.0828983i | ||||
\(193\) | 7.75886 | − | 13.4387i | 0.558495 | − | 0.967341i | −0.439128 | − | 0.898425i | \(-0.644712\pi\) |
0.997622 | − | 0.0689165i | \(-0.0219542\pi\) | |||||||
\(194\) | 16.1867i | 1.16214i | ||||||||
\(195\) | 1.04704 | + | 5.12654i | 0.0749803 | + | 0.367119i | ||||
\(196\) | 2.39863 | + | 4.15456i | 0.171331 | + | 0.296754i | ||||
\(197\) | 2.76263 | + | 4.78502i | 0.196829 | + | 0.340918i | 0.947499 | − | 0.319760i | \(-0.103602\pi\) |
−0.750669 | + | 0.660678i | \(0.770269\pi\) | |||||||
\(198\) | 0.947909 | + | 2.22378i | 0.0673650 | + | 0.158037i | ||||
\(199\) | −13.6901 | + | 7.90400i | −0.970467 | + | 0.560299i | −0.899379 | − | 0.437171i | \(-0.855981\pi\) |
−0.0710885 | + | 0.997470i | \(0.522647\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | −1.12657 | − | 0.375997i | −0.0794620 | − | 0.0265208i | ||||
\(202\) | 3.07118 | 0.216088 | ||||||||
\(203\) | 12.3673 | − | 21.4208i | 0.868017 | − | 1.50345i | ||||
\(204\) | 1.34694 | + | 6.59489i | 0.0943046 | + | 0.461735i | ||||
\(205\) | −0.366287 | + | 0.634427i | −0.0255826 | + | 0.0443103i | ||||
\(206\) | 0.638630 | − | 0.368713i | 0.0444954 | − | 0.0256895i | ||||
\(207\) | −0.0513733 | + | 0.423698i | −0.00357069 | + | 0.0294491i | ||||
\(208\) | −2.61618 | + | 1.51045i | −0.181400 | + | 0.104731i | ||||
\(209\) | −2.22390 | −0.153831 | ||||||||
\(210\) | 4.45263 | − | 3.94536i | 0.307261 | − | 0.272256i | ||||
\(211\) | −8.66050 | + | 15.0004i | −0.596214 | + | 1.03267i | 0.397161 | + | 0.917749i | \(0.369996\pi\) |
−0.993374 | + | 0.114923i | \(0.963338\pi\) | |||||||
\(212\) | −6.79605 | − | 11.7711i | −0.466754 | − | 0.808442i | ||||
\(213\) | 6.22839 | − | 18.6616i | 0.426762 | − | 1.27867i | ||||
\(214\) | 1.07191 | − | 1.85660i | 0.0732740 | − | 0.126914i | ||||
\(215\) | −0.821770 | −0.0560442 | ||||||||
\(216\) | −4.27560 | + | 2.95284i | −0.290918 | + | 0.200915i | ||||
\(217\) | −18.8793 | − | 3.04750i | −1.28161 | − | 0.206877i | ||||
\(218\) | − | 14.2883i | − | 0.967724i | ||||||
\(219\) | 0.456974 | − | 1.36919i | 0.0308794 | − | 0.0925214i | ||||
\(220\) | −0.697837 | − | 0.402897i | −0.0470482 | − | 0.0271633i | ||||
\(221\) | 11.7397i | 0.789701i | ||||||||
\(222\) | −3.71622 | − | 18.1954i | −0.249417 | − | 1.22119i | ||||
\(223\) | 0.150848 | + | 0.0870923i | 0.0101016 | + | 0.00583213i | 0.505042 | − | 0.863095i | \(-0.331477\pi\) |
−0.494941 | + | 0.868927i | \(0.664810\pi\) | |||||||
\(224\) | 2.97455 | + | 1.71736i | 0.198746 | + | 0.114746i | ||||
\(225\) | −2.39863 | − | 1.80182i | −0.159909 | − | 0.120121i | ||||
\(226\) | −7.65337 | − | 13.2560i | −0.509095 | − | 0.881778i | ||||
\(227\) | −19.6588 | + | 11.3500i | −1.30480 | + | 0.753327i | −0.981223 | − | 0.192875i | \(-0.938219\pi\) |
−0.323577 | + | 0.946202i | \(0.604886\pi\) | |||||||
\(228\) | −0.956575 | − | 4.68359i | −0.0633507 | − | 0.310178i | ||||
\(229\) | 4.32320 | + | 2.49600i | 0.285685 | + | 0.164940i | 0.635994 | − | 0.771694i | \(-0.280590\pi\) |
−0.350309 | + | 0.936634i | \(0.613924\pi\) | |||||||
\(230\) | −0.0711336 | − | 0.123207i | −0.00469041 | − | 0.00812403i | ||||
\(231\) | 3.58790 | − | 3.17914i | 0.236066 | − | 0.209172i | ||||
\(232\) | − | 7.20137i | − | 0.472793i | ||||||
\(233\) | 2.46821i | 0.161698i | 0.996726 | + | 0.0808491i | \(0.0257632\pi\) | ||||
−0.996726 | + | 0.0808491i | \(0.974237\pi\) | |||||||
\(234\) | −8.33692 | + | 3.55370i | −0.545002 | + | 0.232313i | ||||
\(235\) | −2.44113 | − | 4.22817i | −0.159242 | − | 0.275815i | ||||
\(236\) | −11.5957 | − | 6.69476i | −0.754814 | − | 0.435792i | ||||
\(237\) | 5.52054 | − | 1.12751i | 0.358597 | − | 0.0732399i | ||||
\(238\) | 11.5596 | − | 6.67393i | 0.749297 | − | 0.432607i | ||||
\(239\) | −6.74918 | − | 11.6899i | −0.436568 | − | 0.756158i | 0.560854 | − | 0.827915i | \(-0.310473\pi\) |
−0.997422 | + | 0.0717566i | \(0.977140\pi\) | |||||||
\(240\) | 0.548346 | − | 1.64296i | 0.0353956 | − | 0.106053i | ||||
\(241\) | −6.84964 | − | 3.95464i | −0.441224 | − | 0.254741i | 0.262892 | − | 0.964825i | \(-0.415324\pi\) |
−0.704117 | + | 0.710084i | \(0.748657\pi\) | |||||||
\(242\) | 8.96397 | + | 5.17535i | 0.576226 | + | 0.332684i | ||||
\(243\) | −13.7998 | + | 7.25017i | −0.885259 | + | 0.465099i | ||||
\(244\) | − | 10.6269i | − | 0.680319i | ||||||
\(245\) | −4.15456 | − | 2.39863i | −0.265425 | − | 0.153243i | ||||
\(246\) | −1.20359 | − | 0.401704i | −0.0767380 | − | 0.0256117i | ||||
\(247\) | − | 8.33739i | − | 0.530495i | ||||||
\(248\) | −5.20384 | + | 1.97991i | −0.330444 | + | 0.125725i | ||||
\(249\) | 3.06983 | + | 1.02457i | 0.194543 | + | 0.0649295i | ||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −9.52107 | + | 16.4910i | −0.600965 | + | 1.04090i | 0.391711 | + | 0.920089i | \(0.371883\pi\) |
−0.992675 | + | 0.120813i | \(0.961450\pi\) | |||||||
\(252\) | 8.23862 | + | 6.18874i | 0.518985 | + | 0.389854i | ||||
\(253\) | −0.0573189 | − | 0.0992793i | −0.00360361 | − | 0.00624164i | ||||
\(254\) | −5.20690 | + | 9.01862i | −0.326710 | + | 0.565879i | ||||
\(255\) | −4.46393 | − | 5.03787i | −0.279542 | − | 0.315484i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.10579 | + | 1.79313i | −0.193734 | + | 0.111852i | −0.593729 | − | 0.804665i | \(-0.702345\pi\) |
0.399995 | + | 0.916517i | \(0.369012\pi\) | |||||||
\(258\) | −0.284824 | − | 1.39456i | −0.0177324 | − | 0.0868214i | ||||
\(259\) | −31.8931 | + | 18.4135i | −1.98174 | + | 1.14416i | ||||
\(260\) | 1.51045 | − | 2.61618i | 0.0936744 | − | 0.162249i | ||||
\(261\) | 2.60045 | − | 21.4470i | 0.160964 | − | 1.32754i | ||||
\(262\) | −8.13923 | + | 14.0976i | −0.502843 | + | 0.870950i | ||||
\(263\) | 16.7103 | 1.03040 | 0.515200 | − | 0.857070i | \(-0.327718\pi\) | ||||
0.515200 | + | 0.857070i | \(0.327718\pi\) | |||||||
\(264\) | 0.441853 | − | 1.32389i | 0.0271942 | − | 0.0814795i | ||||
\(265\) | 11.7711 | + | 6.79605i | 0.723093 | + | 0.417478i | ||||
\(266\) | −8.20944 | + | 4.73972i | −0.503353 | + | 0.290611i | ||||
\(267\) | −9.39524 | + | 8.32488i | −0.574979 | + | 0.509474i | ||||
\(268\) | 0.342847 | + | 0.593829i | 0.0209427 | + | 0.0362739i | ||||
\(269\) | −9.69936 | − | 16.7998i | −0.591381 | − | 1.02430i | −0.994047 | − | 0.108954i | \(-0.965250\pi\) |
0.402666 | − | 0.915347i | \(-0.368084\pi\) | |||||||
\(270\) | 2.22636 | − | 4.69503i | 0.135492 | − | 0.285731i | ||||
\(271\) | − | 4.62368i | − | 0.280869i | −0.990090 | − | 0.140434i | \(-0.955150\pi\) | ||
0.990090 | − | 0.140434i | \(-0.0448499\pi\) | |||||||
\(272\) | 1.94308 | − | 3.36552i | 0.117817 | − | 0.204064i | ||||
\(273\) | 11.9186 | + | 13.4510i | 0.721345 | + | 0.814091i | ||||
\(274\) | −5.64307 | + | 3.25803i | −0.340910 | + | 0.196825i | ||||
\(275\) | 0.805793 | 0.0485911 | ||||||||
\(276\) | 0.184430 | − | 0.163418i | 0.0111014 | − | 0.00983663i | ||||
\(277\) | − | 23.9855i | − | 1.44115i | −0.693377 | − | 0.720575i | \(-0.743878\pi\) | ||
0.693377 | − | 0.720575i | \(-0.256122\pi\) | |||||||
\(278\) | −16.3232 | −0.979003 | ||||||||
\(279\) | −16.2130 | + | 4.01743i | −0.970645 | + | 0.240517i | ||||
\(280\) | −3.43472 | −0.205263 | ||||||||
\(281\) | 9.55099i | 0.569764i | 0.958563 | + | 0.284882i | \(0.0919544\pi\) | ||||
−0.958563 | + | 0.284882i | \(0.908046\pi\) | |||||||
\(282\) | 6.32918 | − | 5.60812i | 0.376897 | − | 0.333959i | ||||
\(283\) | 12.9772 | 0.771415 | 0.385708 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385708 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(284\) | −9.83676 | + | 5.67926i | −0.583704 | + | 0.337002i | ||||
\(285\) | 3.17021 | + | 3.57782i | 0.187787 | + | 0.211932i | ||||
\(286\) | 1.21711 | − | 2.10810i | 0.0719695 | − | 0.124655i | ||||
\(287\) | 2.51618i | 0.148525i | ||||||||
\(288\) | 2.97819 | + | 0.361105i | 0.175491 | + | 0.0212783i | ||||
\(289\) | 0.948867 | + | 1.64349i | 0.0558157 | + | 0.0966757i | ||||
\(290\) | 3.60069 | + | 6.23657i | 0.211440 | + | 0.366224i | ||||
\(291\) | 20.9838 | − | 18.5932i | 1.23009 | − | 1.08995i | ||||
\(292\) | −0.721718 | + | 0.416684i | −0.0422354 | + | 0.0243846i | ||||
\(293\) | 14.6795 | + | 8.47522i | 0.857586 | + | 0.495128i | 0.863203 | − | 0.504857i | \(-0.168455\pi\) |
−0.00561696 | + | 0.999984i | \(0.501788\pi\) | |||||||
\(294\) | 2.63056 | − | 7.88172i | 0.153417 | − | 0.459671i | ||||
\(295\) | 13.3895 | 0.779568 | ||||||||
\(296\) | −5.36099 | + | 9.28550i | −0.311601 | + | 0.539709i | ||||
\(297\) | 1.79398 | − | 3.78322i | 0.104097 | − | 0.219525i | ||||
\(298\) | 1.55221 | − | 2.68851i | 0.0899171 | − | 0.155741i | ||||
\(299\) | 0.372197 | − | 0.214888i | 0.0215247 | − | 0.0124273i | ||||
\(300\) | 0.346599 | + | 1.69702i | 0.0200109 | + | 0.0979774i | ||||
\(301\) | −2.44440 | + | 1.41127i | −0.140893 | + | 0.0813444i | ||||
\(302\) | −19.8572 | −1.14265 | ||||||||
\(303\) | −3.52778 | − | 3.98136i | −0.202666 | − | 0.228723i | ||||
\(304\) | −1.37995 | + | 2.39014i | −0.0791454 | + | 0.137084i | ||||
\(305\) | 5.31346 | + | 9.20319i | 0.304248 | + | 0.526973i | ||||
\(306\) | 7.00217 | − | 9.32148i | 0.400287 | − | 0.532874i | ||||
\(307\) | 10.7499 | − | 18.6193i | 0.613527 | − | 1.06266i | −0.377114 | − | 0.926167i | \(-0.623084\pi\) |
0.990641 | − | 0.136493i | \(-0.0435831\pi\) | |||||||
\(308\) | −2.76767 | −0.157703 | ||||||||
\(309\) | −1.21156 | − | 0.404364i | −0.0689233 | − | 0.0230035i | ||||
\(310\) | 3.51670 | − | 4.31658i | 0.199735 | − | 0.245165i | ||||
\(311\) | 0.500059i | 0.0283557i | 0.999899 | + | 0.0141779i | \(0.00451310\pi\) | ||||
−0.999899 | + | 0.0141779i | \(0.995487\pi\) | |||||||
\(312\) | 4.96323 | + | 1.65650i | 0.280988 | + | 0.0937810i | ||||
\(313\) | −13.0279 | − | 7.52167i | −0.736381 | − | 0.425150i | 0.0843707 | − | 0.996434i | \(-0.473112\pi\) |
−0.820752 | + | 0.571284i | \(0.806445\pi\) | |||||||
\(314\) | 1.70330i | 0.0961226i | ||||||||
\(315\) | −10.2292 | − | 1.24029i | −0.576352 | − | 0.0698825i | ||||
\(316\) | −2.81725 | − | 1.62654i | −0.158483 | − | 0.0915001i | ||||
\(317\) | −8.13168 | − | 4.69483i | −0.456721 | − | 0.263688i | 0.253944 | − | 0.967219i | \(-0.418272\pi\) |
−0.710664 | + | 0.703531i | \(0.751606\pi\) | |||||||
\(318\) | −7.45317 | + | 22.3313i | −0.417953 | + | 1.25228i | ||||
\(319\) | 2.90141 | + | 5.02539i | 0.162448 | + | 0.281368i | ||||
\(320\) | −0.866025 | + | 0.500000i | −0.0484123 | + | 0.0279508i | ||||
\(321\) | −3.63809 | + | 0.743042i | −0.203058 | + | 0.0414726i | ||||
\(322\) | −0.423181 | − | 0.244324i | −0.0235829 | − | 0.0136156i | ||||
\(323\) | 5.36270 | + | 9.28847i | 0.298389 | + | 0.516824i | ||||
\(324\) | 8.73921 | + | 2.15088i | 0.485511 | + | 0.119493i | ||||
\(325\) | 3.02091i | 0.167570i | ||||||||
\(326\) | 2.96548i | 0.164243i | ||||||||
\(327\) | −18.5228 | + | 16.4125i | −1.02431 | + | 0.907615i | ||||
\(328\) | 0.366287 | + | 0.634427i | 0.0202248 | + | 0.0350304i | ||||
\(329\) | −14.5225 | − | 8.38460i | −0.800654 | − | 0.462258i | ||||
\(330\) | 0.279287 | + | 1.36745i | 0.0153742 | + | 0.0752754i | ||||
\(331\) | 19.1463 | − | 11.0541i | 1.05238 | − | 0.607591i | 0.129064 | − | 0.991636i | \(-0.458803\pi\) |
0.923314 | + | 0.384045i | \(0.125469\pi\) | |||||||
\(332\) | −0.934238 | − | 1.61815i | −0.0512730 | − | 0.0888074i | ||||
\(333\) | −19.3191 | + | 25.7181i | −1.05868 | + | 1.40934i | ||||
\(334\) | 19.9933 | + | 11.5431i | 1.09398 | + | 0.631612i | ||||
\(335\) | −0.593829 | − | 0.342847i | −0.0324443 | − | 0.0187317i | ||||
\(336\) | −1.19047 | − | 5.82877i | −0.0649453 | − | 0.317986i | ||||
\(337\) | − | 1.64170i | − | 0.0894289i | −0.999000 | − | 0.0447145i | \(-0.985762\pi\) | ||
0.999000 | − | 0.0447145i | \(-0.0142378\pi\) | |||||||
\(338\) | −3.35507 | − | 1.93705i | −0.182492 | − | 0.105362i | ||||
\(339\) | −8.39338 | + | 25.1484i | −0.455866 | + | 1.36587i | ||||
\(340\) | 3.88616i | 0.210757i | ||||||||
\(341\) | 2.83373 | − | 3.47827i | 0.153455 | − | 0.188359i | ||||
\(342\) | −4.97283 | + | 6.61997i | −0.268900 | + | 0.357967i | ||||
\(343\) | 7.56576 | 0.408512 | ||||||||
\(344\) | −0.410885 | + | 0.711673i | −0.0221534 | + | 0.0383709i | ||||
\(345\) | −0.0780116 | + | 0.233739i | −0.00420000 | + | 0.0125841i | ||||
\(346\) | −6.79559 | − | 11.7703i | −0.365333 | − | 0.632776i | ||||
\(347\) | 4.05019 | − | 7.01513i | 0.217425 | − | 0.376592i | −0.736595 | − | 0.676334i | \(-0.763567\pi\) |
0.954020 | + | 0.299743i | \(0.0969008\pi\) | |||||||
\(348\) | −9.33558 | + | 8.27202i | −0.500440 | + | 0.443427i | ||||
\(349\) | 10.2078 | 0.546409 | 0.273205 | − | 0.961956i | \(-0.411916\pi\) | ||||
0.273205 | + | 0.961956i | \(0.411916\pi\) | |||||||
\(350\) | 2.97455 | − | 1.71736i | 0.158996 | − | 0.0917966i | ||||
\(351\) | 14.1833 | + | 6.72562i | 0.757047 | + | 0.358987i | ||||
\(352\) | −0.697837 | + | 0.402897i | −0.0371948 | + | 0.0214745i | ||||
\(353\) | −2.18441 | + | 3.78351i | −0.116265 | + | 0.201376i | −0.918285 | − | 0.395921i | \(-0.870425\pi\) |
0.802020 | + | 0.597297i | \(0.203759\pi\) | |||||||
\(354\) | 4.64079 | + | 22.7223i | 0.246655 | + | 1.20767i | ||||
\(355\) | 5.67926 | − | 9.83676i | 0.301424 | − | 0.522081i | ||||
\(356\) | 7.24740 | 0.384111 | ||||||||
\(357\) | −21.9300 | − | 7.31924i | −1.16066 | − | 0.387375i | ||||
\(358\) | −2.80311 | − | 1.61838i | −0.148149 | − | 0.0855339i | ||||
\(359\) | −5.77578 | + | 3.33465i | −0.304834 | + | 0.175996i | −0.644612 | − | 0.764509i | \(-0.722981\pi\) |
0.339778 | + | 0.940506i | \(0.389648\pi\) | |||||||
\(360\) | −2.75974 | + | 1.17637i | −0.145451 | + | 0.0620000i | ||||
\(361\) | 5.69149 | + | 9.85796i | 0.299552 | + | 0.518840i | ||||
\(362\) | −8.22298 | − | 14.2426i | −0.432190 | − | 0.748576i | ||||
\(363\) | −3.58754 | − | 17.5653i | −0.188297 | − | 0.921940i | ||||
\(364\) | − | 10.3760i | − | 0.543848i | ||||||
\(365\) | 0.416684 | − | 0.721718i | 0.0218103 | − | 0.0377765i | ||||
\(366\) | −13.7763 | + | 12.2069i | −0.720100 | + | 0.638062i | ||||
\(367\) | 12.6325 | − | 7.29338i | 0.659411 | − | 0.380711i | −0.132642 | − | 0.991164i | \(-0.542346\pi\) |
0.792053 | + | 0.610453i | \(0.209013\pi\) | |||||||
\(368\) | −0.142267 | −0.00741619 | ||||||||
\(369\) | 0.861776 | + | 2.02171i | 0.0448623 | + | 0.105246i | ||||
\(370\) | − | 10.7220i | − | 0.557409i | ||||||
\(371\) | 46.6850 | 2.42376 | ||||||||
\(372\) | 8.54419 | + | 4.47178i | 0.442996 | + | 0.231851i | ||||
\(373\) | −21.3294 | −1.10439 | −0.552197 | − | 0.833714i | \(-0.686210\pi\) | ||||
−0.552197 | + | 0.833714i | \(0.686210\pi\) | |||||||
\(374\) | 3.13144i | 0.161923i | ||||||||
\(375\) | −1.14867 | − | 1.29636i | −0.0593172 | − | 0.0669438i | ||||
\(376\) | −4.88227 | −0.251784 | ||||||||
\(377\) | −18.8401 | + | 10.8773i | −0.970316 | + | 0.560212i | ||||
\(378\) | −1.44064 | − | 17.7891i | −0.0740985 | − | 0.914971i | ||||
\(379\) | −15.6454 | + | 27.0986i | −0.803650 | + | 1.39196i | 0.113549 | + | 0.993532i | \(0.463778\pi\) |
−0.917199 | + | 0.398430i | \(0.869555\pi\) | |||||||
\(380\) | − | 2.75989i | − | 0.141580i | ||||||
\(381\) | 17.6724 | − | 3.60941i | 0.905385 | − | 0.184916i | ||||
\(382\) | −6.71391 | − | 11.6288i | −0.343514 | − | 0.594983i | ||||
\(383\) | 11.8065 | + | 20.4494i | 0.603282 | + | 1.04491i | 0.992320 | + | 0.123693i | \(0.0394739\pi\) |
−0.389039 | + | 0.921221i | \(0.627193\pi\) | |||||||
\(384\) | −1.14867 | − | 1.29636i | −0.0586179 | − | 0.0661547i | ||||
\(385\) | 2.39687 | − | 1.38383i | 0.122156 | − | 0.0705268i | ||||
\(386\) | 13.4387 | + | 7.75886i | 0.684013 | + | 0.394915i | ||||
\(387\) | −1.48068 | + | 1.97112i | −0.0752672 | + | 0.100198i | ||||
\(388\) | −16.1867 | −0.821755 | ||||||||
\(389\) | 12.7612 | − | 22.1030i | 0.647018 | − | 1.12067i | −0.336814 | − | 0.941571i | \(-0.609349\pi\) |
0.983832 | − | 0.179096i | \(-0.0573173\pi\) | |||||||
\(390\) | −5.12654 | + | 1.04704i | −0.259592 | + | 0.0530191i | ||||
\(391\) | −0.276437 | + | 0.478802i | −0.0139800 | + | 0.0242141i | ||||
\(392\) | −4.15456 | + | 2.39863i | −0.209837 | + | 0.121149i | ||||
\(393\) | 27.6248 | − | 5.64209i | 1.39349 | − | 0.284606i | ||||
\(394\) | −4.78502 | + | 2.76263i | −0.241066 | + | 0.139179i | ||||
\(395\) | 3.25308 | 0.163680 | ||||||||
\(396\) | −2.22378 | + | 0.947909i | −0.111749 | + | 0.0476342i | ||||
\(397\) | 10.1941 | − | 17.6566i | 0.511625 | − | 0.886161i | −0.488284 | − | 0.872685i | \(-0.662377\pi\) |
0.999909 | − | 0.0134762i | \(-0.00428974\pi\) | |||||||
\(398\) | −7.90400 | − | 13.6901i | −0.396192 | − | 0.686224i | ||||
\(399\) | 15.5744 | + | 5.19801i | 0.779693 | + | 0.260226i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 7.15181 | 0.357144 | 0.178572 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178572 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(402\) | 0.375997 | − | 1.12657i | 0.0187531 | − | 0.0561881i | ||||
\(403\) | 13.0400 | + | 10.6236i | 0.649568 | + | 0.529201i | ||||
\(404\) | 3.07118i | 0.152797i | ||||||||
\(405\) | −8.64381 | + | 2.50689i | −0.429515 | + | 0.124568i | ||||
\(406\) | 21.4208 | + | 12.3673i | 1.06310 | + | 0.613780i | ||||
\(407\) | − | 8.63969i | − | 0.428254i | ||||||
\(408\) | −6.59489 | + | 1.34694i | −0.326496 | + | 0.0666834i | ||||
\(409\) | −4.97254 | − | 2.87090i | −0.245876 | − | 0.141957i | 0.371998 | − | 0.928233i | \(-0.378673\pi\) |
−0.617875 | + | 0.786277i | \(0.712006\pi\) | |||||||
\(410\) | −0.634427 | − | 0.366287i | −0.0313321 | − | 0.0180896i | ||||
\(411\) | 10.7056 | + | 3.57305i | 0.528069 | + | 0.176245i | ||||
\(412\) | 0.368713 | + | 0.638630i | 0.0181652 | + | 0.0314630i | ||||
\(413\) | 39.8278 | − | 22.9946i | 1.95980 | − | 1.13149i | ||||
\(414\) | −0.423698 | − | 0.0513733i | −0.0208236 | − | 0.00252486i | ||||
\(415\) | 1.61815 | + | 0.934238i | 0.0794318 | + | 0.0458599i | ||||
\(416\) | −1.51045 | − | 2.61618i | −0.0740561 | − | 0.128269i | ||||
\(417\) | 18.7501 | + | 21.1608i | 0.918194 | + | 1.03625i | ||||
\(418\) | − | 2.22390i | − | 0.108775i | ||||||
\(419\) | − | 9.62101i | − | 0.470017i | −0.971993 | − | 0.235008i | \(-0.924488\pi\) | ||
0.971993 | − | 0.235008i | \(-0.0755118\pi\) | |||||||
\(420\) | 3.94536 | + | 4.45263i | 0.192514 | + | 0.217266i | ||||
\(421\) | −17.3075 | − | 29.9775i | −0.843516 | − | 1.46101i | −0.886904 | − | 0.461955i | \(-0.847148\pi\) |
0.0433873 | − | 0.999058i | \(-0.486185\pi\) | |||||||
\(422\) | −15.0004 | − | 8.66050i | −0.730209 | − | 0.421587i | ||||
\(423\) | −14.5403 | − | 1.76301i | −0.706974 | − | 0.0857204i | ||||
\(424\) | 11.7711 | − | 6.79605i | 0.571655 | − | 0.330045i | ||||
\(425\) | −1.94308 | − | 3.36552i | −0.0942533 | − | 0.163252i | ||||
\(426\) | 18.6616 | + | 6.22839i | 0.904157 | + | 0.301767i | ||||
\(427\) | 31.6103 | + | 18.2502i | 1.52973 | + | 0.883191i | ||||
\(428\) | 1.85660 | + | 1.07191i | 0.0897419 | + | 0.0518125i | ||||
\(429\) | −4.13093 | + | 0.843700i | −0.199443 | + | 0.0407342i | ||||
\(430\) | − | 0.821770i | − | 0.0396293i | ||||||
\(431\) | 32.5014 | + | 18.7647i | 1.56554 | + | 0.903864i | 0.996679 | + | 0.0814300i | \(0.0259487\pi\) |
0.568860 | + | 0.822434i | \(0.307385\pi\) | |||||||
\(432\) | −2.95284 | − | 4.27560i | −0.142069 | − | 0.205710i | ||||
\(433\) | − | 0.00668506i | − | 0.000321263i | −1.00000 | 0.000160632i | \(-0.999949\pi\) | |||
1.00000 | 0.000160632i | \(-5.11307e-5\pi\) | ||||||||
\(434\) | 3.04750 | − | 18.8793i | 0.146284 | − | 0.906236i | ||||
\(435\) | 3.94884 | − | 11.8316i | 0.189332 | − | 0.567280i | ||||
\(436\) | 14.2883 | 0.684284 | ||||||||
\(437\) | 0.196321 | − | 0.340038i | 0.00939131 | − | 0.0162662i | ||||
\(438\) | 1.36919 | + | 0.456974i | 0.0654225 | + | 0.0218351i | ||||
\(439\) | −10.4394 | − | 18.0815i | −0.498244 | − | 0.862984i | 0.501754 | − | 0.865010i | \(-0.332688\pi\) |
−0.999998 | + | 0.00202667i | \(0.999355\pi\) | |||||||
\(440\) | 0.402897 | − | 0.697837i | 0.0192073 | − | 0.0332681i | ||||
\(441\) | −13.2392 | + | 5.64335i | −0.630438 | + | 0.268731i | ||||
\(442\) | −11.7397 | −0.558403 | ||||||||
\(443\) | 23.3341 | − | 13.4719i | 1.10864 | − | 0.640071i | 0.170160 | − | 0.985416i | \(-0.445571\pi\) |
0.938476 | + | 0.345345i | \(0.112238\pi\) | |||||||
\(444\) | 18.1954 | − | 3.71622i | 0.863515 | − | 0.176364i | ||||
\(445\) | −6.27643 | + | 3.62370i | −0.297531 | + | 0.171780i | ||||
\(446\) | −0.0870923 | + | 0.150848i | −0.00412394 | + | 0.00714288i | ||||
\(447\) | −5.26826 | + | 1.07599i | −0.249180 | + | 0.0508925i | ||||
\(448\) | −1.71736 | + | 2.97455i | −0.0811375 | + | 0.140534i | ||||
\(449\) | −22.2082 | −1.04807 | −0.524035 | − | 0.851697i | \(-0.675574\pi\) | ||||
−0.524035 | + | 0.851697i | \(0.675574\pi\) | |||||||
\(450\) | 1.80182 | − | 2.39863i | 0.0849386 | − | 0.113073i | ||||
\(451\) | −0.511217 | − | 0.295151i | −0.0240723 | − | 0.0138981i | ||||
\(452\) | 13.2560 | − | 7.65337i | 0.623511 | − | 0.359984i | ||||
\(453\) | 22.8094 | + | 25.7421i | 1.07168 | + | 1.20947i | ||||
\(454\) | −11.3500 | − | 19.6588i | −0.532683 | − | 0.922633i | ||||
\(455\) | 5.18798 | + | 8.98585i | 0.243216 | + | 0.421263i | ||||
\(456\) | 4.68359 | − | 0.956575i | 0.219329 | − | 0.0447957i | ||||
\(457\) | 35.8276i | 1.67594i | 0.545714 | + | 0.837972i | \(0.316259\pi\) | ||||
−0.545714 | + | 0.837972i | \(0.683741\pi\) | |||||||
\(458\) | −2.49600 | + | 4.32320i | −0.116630 | + | 0.202010i | ||||
\(459\) | −20.1272 | + | 1.62999i | −0.939457 | + | 0.0760815i | ||||
\(460\) | 0.123207 | − | 0.0711336i | 0.00574455 | − | 0.00331662i | ||||
\(461\) | −11.0236 | −0.513419 | −0.256710 | − | 0.966489i | \(-0.582638\pi\) | ||||
−0.256710 | + | 0.966489i | \(0.582638\pi\) | |||||||
\(462\) | 3.17914 | + | 3.58790i | 0.147907 | + | 0.166924i | ||||
\(463\) | − | 6.77239i | − | 0.314740i | −0.987540 | − | 0.157370i | \(-0.949699\pi\) | ||
0.987540 | − | 0.157370i | \(-0.0503015\pi\) | |||||||
\(464\) | 7.20137 | 0.334315 | ||||||||
\(465\) | −9.63538 | + | 0.399418i | −0.446830 | + | 0.0185226i | ||||
\(466\) | −2.46821 | −0.114338 | ||||||||
\(467\) | − | 19.9229i | − | 0.921923i | −0.887420 | − | 0.460962i | \(-0.847505\pi\) | ||
0.887420 | − | 0.460962i | \(-0.152495\pi\) | |||||||
\(468\) | −3.55370 | − | 8.33692i | −0.164270 | − | 0.385374i | ||||
\(469\) | −2.35516 | −0.108751 | ||||||||
\(470\) | 4.22817 | − | 2.44113i | 0.195031 | − | 0.112601i | ||||
\(471\) | 2.20809 | − | 1.95653i | 0.101743 | − | 0.0901522i | ||||
\(472\) | 6.69476 | − | 11.5957i | 0.308151 | − | 0.533734i | ||||
\(473\) | − | 0.662176i | − | 0.0304469i | ||||||
\(474\) | 1.12751 | + | 5.52054i | 0.0517884 | + | 0.253567i | ||||
\(475\) | 1.37995 | + | 2.39014i | 0.0633163 | + | 0.109667i | ||||
\(476\) | 6.67393 | + | 11.5596i | 0.305899 | + | 0.529833i | ||||
\(477\) | 37.5106 | − | 15.9893i | 1.71749 | − | 0.732100i | ||||
\(478\) | 11.6899 | − | 6.74918i | 0.534684 | − | 0.308700i | ||||
\(479\) | 10.4505 | + | 6.03362i | 0.477497 | + | 0.275683i | 0.719373 | − | 0.694624i | \(-0.244429\pi\) |
−0.241876 | + | 0.970307i | \(0.577763\pi\) | |||||||
\(480\) | 1.64296 | + | 0.548346i | 0.0749905 | + | 0.0250284i | ||||
\(481\) | 32.3901 | 1.47686 | ||||||||
\(482\) | 3.95464 | − | 6.84964i | 0.180129 | − | 0.311993i | ||||
\(483\) | 0.169364 | + | 0.829243i | 0.00770635 | + | 0.0377319i | ||||
\(484\) | −5.17535 | + | 8.96397i | −0.235243 | + | 0.407453i | ||||
\(485\) | 14.0181 | − | 8.09335i | 0.636528 | − | 0.367500i | ||||
\(486\) | −7.25017 | − | 13.7998i | −0.328874 | − | 0.625972i | ||||
\(487\) | −25.6391 | + | 14.8027i | −1.16182 | + | 0.670776i | −0.951739 | − | 0.306909i | \(-0.900705\pi\) |
−0.210079 | + | 0.977684i | \(0.567372\pi\) | |||||||
\(488\) | 10.6269 | 0.481058 | ||||||||
\(489\) | 3.84433 | − | 3.40636i | 0.173847 | − | 0.154041i | ||||
\(490\) | 2.39863 | − | 4.15456i | 0.108359 | − | 0.187684i | ||||
\(491\) | 16.7692 | + | 29.0451i | 0.756784 | + | 1.31079i | 0.944482 | + | 0.328562i | \(0.106564\pi\) |
−0.187698 | + | 0.982227i | \(0.560103\pi\) | |||||||
\(492\) | 0.401704 | − | 1.20359i | 0.0181102 | − | 0.0542620i | ||||
\(493\) | 13.9929 | − | 24.2363i | 0.630207 | − | 1.09155i | ||||
\(494\) | 8.33739 | 0.375117 | ||||||||
\(495\) | 1.45189 | − | 1.93280i | 0.0652578 | − | 0.0868730i | ||||
\(496\) | −1.97991 | − | 5.20384i | −0.0889008 | − | 0.233659i | ||||
\(497\) | − | 39.0133i | − | 1.74998i | ||||||
\(498\) | −1.02457 | + | 3.06983i | −0.0459121 | + | 0.137562i | ||||
\(499\) | 33.0134 | + | 19.0603i | 1.47788 | + | 0.853256i | 0.999688 | − | 0.0249976i | \(-0.00795783\pi\) |
0.478195 | + | 0.878254i | \(0.341291\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −8.00167 | − | 39.1778i | −0.357488 | − | 1.75034i | ||||
\(502\) | −16.4910 | − | 9.52107i | −0.736029 | − | 0.424946i | ||||
\(503\) | −23.7159 | − | 13.6924i | −1.05744 | − | 0.610513i | −0.132716 | − | 0.991154i | \(-0.542370\pi\) |
−0.924723 | + | 0.380642i | \(0.875703\pi\) | |||||||
\(504\) | −6.18874 | + | 8.23862i | −0.275668 | + | 0.366978i | ||||
\(505\) | −1.53559 | − | 2.65972i | −0.0683329 | − | 0.118356i | ||||
\(506\) | 0.0992793 | − | 0.0573189i | 0.00441350 | − | 0.00254814i | ||||
\(507\) | 1.34276 | + | 6.57443i | 0.0596341 | + | 0.291981i | ||||
\(508\) | −9.01862 | − | 5.20690i | −0.400137 | − | 0.231019i | ||||
\(509\) | 8.81251 | + | 15.2637i | 0.390608 | + | 0.676552i | 0.992530 | − | 0.122002i | \(-0.0389316\pi\) |
−0.601922 | + | 0.798555i | \(0.705598\pi\) | |||||||
\(510\) | 5.03787 | − | 4.46393i | 0.223081 | − | 0.197666i | ||||
\(511\) | − | 2.86238i | − | 0.126624i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 14.2940 | − | 1.15760i | 0.631097 | − | 0.0511091i | ||||
\(514\) | −1.79313 | − | 3.10579i | −0.0790915 | − | 0.136991i | ||||
\(515\) | −0.638630 | − | 0.368713i | −0.0281414 | − | 0.0162474i | ||||
\(516\) | 1.39456 | − | 0.284824i | 0.0613920 | − | 0.0125387i | ||||
\(517\) | 3.40703 | − | 1.96705i | 0.149841 | − | 0.0865107i | ||||
\(518\) | −18.4135 | − | 31.8931i | −0.809041 | − | 1.40130i | ||||
\(519\) | −7.45267 | + | 22.3298i | −0.327136 | + | 0.980168i | ||||
\(520\) | 2.61618 | + | 1.51045i | 0.114727 | + | 0.0662378i | ||||
\(521\) | −9.89159 | − | 5.71091i | −0.433359 | − | 0.250200i | 0.267418 | − | 0.963581i | \(-0.413830\pi\) |
−0.700776 | + | 0.713381i | \(0.747163\pi\) | |||||||
\(522\) | 21.4470 | + | 2.60045i | 0.938712 | + | 0.113819i | ||||
\(523\) | 39.2997i | 1.71846i | 0.511592 | + | 0.859229i | \(0.329056\pi\) | ||||
−0.511592 | + | 0.859229i | \(0.670944\pi\) | |||||||
\(524\) | −14.0976 | − | 8.13923i | −0.615855 | − | 0.355564i | ||||
\(525\) | −5.64310 | − | 1.88341i | −0.246285 | − | 0.0821988i | ||||
\(526\) | 16.7103i | 0.728602i | ||||||||
\(527\) | −21.3607 | − | 3.44805i | −0.930488 | − | 0.150199i | ||||
\(528\) | 1.32389 | + | 0.441853i | 0.0576147 | + | 0.0192292i | ||||
\(529\) | −22.9798 | −0.999120 | ||||||||
\(530\) | −6.79605 | + | 11.7711i | −0.295201 | + | 0.511304i | ||||
\(531\) | 24.1255 | − | 32.1166i | 1.04696 | − | 1.39374i | ||||
\(532\) | −4.73972 | − | 8.20944i | −0.205493 | − | 0.355924i | ||||
\(533\) | 1.10652 | − | 1.91655i | 0.0479287 | − | 0.0830149i | ||||
\(534\) | −8.32488 | − | 9.39524i | −0.360253 | − | 0.406572i | ||||
\(535\) | −2.14381 | −0.0926850 | ||||||||
\(536\) | −0.593829 | + | 0.342847i | −0.0256495 | + | 0.0148087i | ||||
\(537\) | 1.12186 | + | 5.49283i | 0.0484116 | + | 0.237033i | ||||
\(538\) | 16.7998 | − | 9.69936i | 0.724290 | − | 0.418169i | ||||
\(539\) | 1.93280 | − | 3.34771i | 0.0832517 | − | 0.144196i | ||||
\(540\) | 4.69503 | + | 2.22636i | 0.202042 | + | 0.0958071i | ||||
\(541\) | 0.345486 | − | 0.598400i | 0.0148536 | − | 0.0257272i | −0.858503 | − | 0.512808i | \(-0.828605\pi\) |
0.873357 | + | 0.487081i | \(0.161938\pi\) | |||||||
\(542\) | 4.62368 | 0.198604 | ||||||||
\(543\) | −9.01807 | + | 27.0201i | −0.387003 | + | 1.15954i | ||||
\(544\) | 3.36552 | + | 1.94308i | 0.144295 | + | 0.0833089i | ||||
\(545\) | −12.3740 | + | 7.14414i | −0.530044 | + | 0.306021i | ||||
\(546\) | −13.4510 | + | 11.9186i | −0.575650 | + | 0.510068i | ||||
\(547\) | −7.88536 | − | 13.6578i | −0.337153 | − | 0.583967i | 0.646743 | − | 0.762708i | \(-0.276131\pi\) |
−0.983896 | + | 0.178741i | \(0.942797\pi\) | |||||||
\(548\) | −3.25803 | − | 5.64307i | −0.139176 | − | 0.241060i | ||||
\(549\) | 31.6490 | + | 3.83743i | 1.35075 | + | 0.163778i | ||||
\(550\) | 0.805793i | 0.0343591i | ||||||||
\(551\) | −9.93751 | + | 17.2123i | −0.423352 | + | 0.733268i | ||||
\(552\) | 0.163418 | + | 0.184430i | 0.00695555 | + | 0.00784985i | ||||
\(553\) | 9.67646 | − | 5.58671i | 0.411485 | − | 0.237571i | ||||
\(554\) | 23.9855 | 1.01905 | ||||||||
\(555\) | −13.8996 | + | 12.3160i | −0.590003 | + | 0.522787i | ||||
\(556\) | − | 16.3232i | − | 0.692260i | ||||||
\(557\) | 30.0547 | 1.27346 | 0.636729 | − | 0.771088i | \(-0.280287\pi\) | ||||
0.636729 | + | 0.771088i | \(0.280287\pi\) | |||||||
\(558\) | −4.01743 | − | 16.2130i | −0.170071 | − | 0.686350i | ||||
\(559\) | 2.48249 | 0.104998 | ||||||||
\(560\) | − | 3.43472i | − | 0.145143i | ||||||
\(561\) | 4.05948 | − | 3.59700i | 0.171391 | − | 0.151866i | ||||
\(562\) | −9.55099 | −0.402884 | ||||||||
\(563\) | 20.8367 | − | 12.0301i | 0.878162 | − | 0.507007i | 0.00811024 | − | 0.999967i | \(-0.497418\pi\) |
0.870052 | + | 0.492960i | \(0.164085\pi\) | |||||||
\(564\) | 5.60812 | + | 6.32918i | 0.236145 | + | 0.266507i | ||||
\(565\) | −7.65337 | + | 13.2560i | −0.321980 | + | 0.557685i | ||||
\(566\) | 12.9772i | 0.545473i | ||||||||
\(567\) | −21.4062 | + | 22.3014i | −0.898977 | + | 0.936570i | ||||
\(568\) | −5.67926 | − | 9.83676i | −0.238296 | − | 0.412741i | ||||
\(569\) | −1.61547 | − | 2.79807i | −0.0677239 | − | 0.117301i | 0.830175 | − | 0.557503i | \(-0.188240\pi\) |
−0.897899 | + | 0.440201i | \(0.854907\pi\) | |||||||
\(570\) | −3.57782 | + | 3.17021i | −0.149858 | + | 0.132786i | ||||
\(571\) | 16.0871 | − | 9.28786i | 0.673222 | − | 0.388685i | −0.124074 | − | 0.992273i | \(-0.539596\pi\) |
0.797296 | + | 0.603588i | \(0.206263\pi\) | |||||||
\(572\) | 2.10810 | + | 1.21711i | 0.0881442 | + | 0.0508901i | ||||
\(573\) | −7.36309 | + | 22.0614i | −0.307597 | + | 0.921627i | ||||
\(574\) | −2.51618 | −0.105023 | ||||||||
\(575\) | −0.0711336 | + | 0.123207i | −0.00296648 | + | 0.00513809i | ||||
\(576\) | −0.361105 | + | 2.97819i | −0.0150460 | + | 0.124091i | ||||
\(577\) | 11.7194 | − | 20.2986i | 0.487886 | − | 0.845043i | −0.512017 | − | 0.858975i | \(-0.671102\pi\) |
0.999903 | + | 0.0139325i | \(0.00443500\pi\) | |||||||
\(578\) | −1.64349 | + | 0.948867i | −0.0683600 | + | 0.0394677i | ||||
\(579\) | −5.37842 | − | 26.3338i | −0.223519 | − | 1.09440i | ||||
\(580\) | −6.23657 | + | 3.60069i | −0.258960 | + | 0.149510i | ||||
\(581\) | 6.41768 | 0.266250 | ||||||||
\(582\) | 18.5932 | + | 20.9838i | 0.770713 | + | 0.869806i | ||||
\(583\) | −5.47621 | + | 9.48507i | −0.226801 | + | 0.392831i | ||||
\(584\) | −0.416684 | − | 0.721718i | −0.0172425 | − | 0.0298649i | ||||
\(585\) | 7.24606 | + | 5.44313i | 0.299588 | + | 0.225046i | ||||
\(586\) | −8.47522 | + | 14.6795i | −0.350108 | + | 0.606405i | ||||
\(587\) | −13.2705 | −0.547732 | −0.273866 | − | 0.961768i | \(-0.588302\pi\) | ||||
−0.273866 | + | 0.961768i | \(0.588302\pi\) | |||||||
\(588\) | 7.88172 | + | 2.63056i | 0.325037 | + | 0.108483i | ||||
\(589\) | 15.1701 | + | 2.44875i | 0.625072 | + | 0.100899i | ||||
\(590\) | 13.3895i | 0.551238i | ||||||||
\(591\) | 9.07779 | + | 3.02975i | 0.373410 | + | 0.124627i | ||||
\(592\) | −9.28550 | − | 5.36099i | −0.381632 | − | 0.220335i | ||||
\(593\) | − | 28.5918i | − | 1.17412i | −0.809542 | − | 0.587062i | \(-0.800284\pi\) | ||
0.809542 | − | 0.587062i | \(-0.199716\pi\) | |||||||
\(594\) | 3.78322 | + | 1.79398i | 0.155228 | + | 0.0736080i | ||||
\(595\) | −11.5596 | − | 6.67393i | −0.473897 | − | 0.273605i | ||||
\(596\) | 2.68851 | + | 1.55221i | 0.110126 | + | 0.0635810i | ||||
\(597\) | −8.66824 | + | 25.9719i | −0.354768 | + | 1.06296i | ||||
\(598\) | 0.214888 | + | 0.372197i | 0.00878743 | + | 0.0152203i | ||||
\(599\) | 22.8692 | − | 13.2035i | 0.934410 | − | 0.539482i | 0.0462061 | − | 0.998932i | \(-0.485287\pi\) |
0.888203 | + | 0.459450i | \(0.151954\pi\) | |||||||
\(600\) | −1.69702 | + | 0.346599i | −0.0692805 | + | 0.0141498i | ||||
\(601\) | −32.0608 | − | 18.5103i | −1.30779 | − | 0.755051i | −0.326060 | − | 0.945349i | \(-0.605721\pi\) |
−0.981726 | + | 0.190298i | \(0.939055\pi\) | |||||||
\(602\) | −1.41127 | − | 2.44440i | −0.0575192 | − | 0.0996261i | ||||
\(603\) | −1.89234 | + | 0.806629i | −0.0770619 | + | 0.0328485i | ||||
\(604\) | − | 19.8572i | − | 0.807979i | ||||||
\(605\) | − | 10.3507i | − | 0.420816i | ||||||
\(606\) | 3.98136 | − | 3.52778i | 0.161732 | − | 0.143306i | ||||
\(607\) | −1.23539 | − | 2.13976i | −0.0501429 | − | 0.0868500i | 0.839865 | − | 0.542796i | \(-0.182634\pi\) |
−0.890007 | + | 0.455946i | \(0.849301\pi\) | |||||||
\(608\) | −2.39014 | − | 1.37995i | −0.0969329 | − | 0.0559642i | ||||
\(609\) | −8.57300 | − | 41.9752i | −0.347396 | − | 1.70092i | ||||
\(610\) | −9.20319 | + | 5.31346i | −0.372626 | + | 0.215136i | ||||
\(611\) | 7.37444 | + | 12.7729i | 0.298338 | + | 0.516737i | ||||
\(612\) | 9.32148 | + | 7.00217i | 0.376799 | + | 0.283046i | ||||
\(613\) | −20.7979 | − | 12.0077i | −0.840021 | − | 0.484986i | 0.0172504 | − | 0.999851i | \(-0.494509\pi\) |
−0.857271 | + | 0.514865i | \(0.827842\pi\) | |||||||
\(614\) | 18.6193 | + | 10.7499i | 0.751414 | + | 0.433829i | ||||
\(615\) | 0.253909 | + | 1.24319i | 0.0102386 | + | 0.0501303i | ||||
\(616\) | − | 2.76767i | − | 0.111513i | ||||||
\(617\) | 20.4157 | + | 11.7870i | 0.821903 | + | 0.474526i | 0.851072 | − | 0.525048i | \(-0.175953\pi\) |
−0.0291690 | + | 0.999574i | \(0.509286\pi\) | |||||||
\(618\) | 0.404364 | − | 1.21156i | 0.0162659 | − | 0.0487362i | ||||
\(619\) | 4.54430i | 0.182651i | 0.995821 | + | 0.0913255i | \(0.0291104\pi\) | ||||
−0.995821 | + | 0.0913255i | \(0.970890\pi\) | |||||||
\(620\) | 4.31658 | + | 3.51670i | 0.173358 | + | 0.141234i | ||||
\(621\) | 0.420092 | + | 0.608277i | 0.0168577 | + | 0.0244093i | ||||
\(622\) | −0.500059 | −0.0200505 | ||||||||
\(623\) | −12.4464 | + | 21.5577i | −0.498653 | + | 0.863693i | ||||
\(624\) | −1.65650 | + | 4.96323i | −0.0663132 | + | 0.198688i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 7.52167 | − | 13.0279i | 0.300626 | − | 0.520700i | ||||
\(627\) | −2.88298 | + | 2.55454i | −0.115135 | + | 0.102018i | ||||
\(628\) | −1.70330 | −0.0679690 | ||||||||
\(629\) | −36.0850 | + | 20.8337i | −1.43880 | + | 0.830693i | ||||
\(630\) | 1.24029 | − | 10.2292i | 0.0494144 | − | 0.407542i | ||||
\(631\) | −37.2561 | + | 21.5098i | −1.48314 | + | 0.856293i | −0.999817 | − | 0.0191471i | \(-0.993905\pi\) |
−0.483326 | + | 0.875440i | \(0.660572\pi\) | |||||||
\(632\) | 1.62654 | − | 2.81725i | 0.0647003 | − | 0.112064i | ||||
\(633\) | 6.00344 | + | 29.3941i | 0.238615 | + | 1.16831i | ||||
\(634\) | 4.69483 | − | 8.13168i | 0.186455 | − | 0.322950i | ||||
\(635\) | 10.4138 | 0.413259 | ||||||||
\(636\) | −22.3313 | − | 7.45317i | −0.885492 | − | 0.295537i | ||||
\(637\) | 12.5505 | + | 7.24606i | 0.497270 | + | 0.287099i | ||||
\(638\) | −5.02539 | + | 2.90141i | −0.198957 | + | 0.114868i | ||||
\(639\) | −13.3618 | − | 31.3465i | −0.528584 | − | 1.24005i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 16.6839 | + | 28.8974i | 0.658976 | + | 1.14138i | 0.980881 | + | 0.194608i | \(0.0623433\pi\) |
−0.321906 | + | 0.946772i | \(0.604323\pi\) | |||||||
\(642\) | −0.743042 | − | 3.63809i | −0.0293255 | − | 0.143584i | ||||
\(643\) | − | 24.1854i | − | 0.953778i | −0.878963 | − | 0.476889i | \(-0.841764\pi\) | ||
0.878963 | − | 0.476889i | \(-0.158236\pi\) | |||||||
\(644\) | 0.244324 | − | 0.423181i | 0.00962770 | − | 0.0166757i | ||||
\(645\) | −1.06531 | + | 0.943944i | −0.0419466 | + | 0.0371678i | ||||
\(646\) | −9.28847 | + | 5.36270i | −0.365450 | + | 0.210993i | ||||
\(647\) | 23.9342 | 0.940952 | 0.470476 | − | 0.882413i | \(-0.344082\pi\) | ||||
0.470476 | + | 0.882413i | \(0.344082\pi\) | |||||||
\(648\) | −2.15088 | + | 8.73921i | −0.0844944 | + | 0.343308i | ||||
\(649\) | 10.7892i | 0.423513i | ||||||||
\(650\) | −3.02091 | −0.118490 | ||||||||
\(651\) | −27.9750 | + | 17.7355i | −1.09643 | + | 0.695108i | ||||
\(652\) | −2.96548 | −0.116137 | ||||||||
\(653\) | 21.4538i | 0.839554i | 0.907627 | + | 0.419777i | \(0.137892\pi\) | ||||
−0.907627 | + | 0.419777i | \(0.862108\pi\) | |||||||
\(654\) | −16.4125 | − | 18.5228i | −0.641781 | − | 0.724297i | ||||
\(655\) | 16.2785 | 0.636052 | ||||||||
\(656\) | −0.634427 | + | 0.366287i | −0.0247702 | + | 0.0143011i | ||||
\(657\) | −0.980348 | − | 2.29988i | −0.0382470 | − | 0.0897268i | ||||
\(658\) | 8.38460 | − | 14.5225i | 0.326866 | − | 0.566148i | ||||
\(659\) | 9.57650i | 0.373047i | 0.982450 | + | 0.186524i | \(0.0597221\pi\) | ||||
−0.982450 | + | 0.186524i | \(0.940278\pi\) | |||||||
\(660\) | −1.36745 | + | 0.279287i | −0.0532277 | + | 0.0108712i | ||||
\(661\) | −14.2276 | − | 24.6429i | −0.553390 | − | 0.958499i | −0.998027 | − | 0.0627884i | \(-0.980001\pi\) |
0.444637 | − | 0.895711i | \(-0.353333\pi\) | |||||||
\(662\) | 11.0541 | + | 19.1463i | 0.429632 | + | 0.744144i | ||||
\(663\) | 13.4851 | + | 15.2190i | 0.523719 | + | 0.591055i | ||||
\(664\) | 1.61815 | − | 0.934238i | 0.0627963 | − | 0.0362555i | ||||
\(665\) | 8.20944 | + | 4.73972i | 0.318349 | + | 0.183799i | ||||
\(666\) | −25.7181 | − | 19.3191i | −0.996556 | − | 0.748599i | ||||
\(667\) | −1.02452 | −0.0396695 | ||||||||
\(668\) | −11.5431 | + | 19.9933i | −0.446617 | + | 0.773564i | ||||
\(669\) | 0.295594 | − | 0.0603722i | 0.0114283 | − | 0.00233412i | ||||
\(670\) | 0.342847 | − | 0.593829i | 0.0132453 | − | 0.0229416i | ||||
\(671\) | −7.41586 | + | 4.28155i | −0.286286 | + | 0.165287i | ||||
\(672\) | 5.82877 | − | 1.19047i | 0.224850 | − | 0.0459233i | ||||
\(673\) | −22.2226 | + | 12.8302i | −0.856618 | + | 0.494569i | −0.862878 | − | 0.505412i | \(-0.831341\pi\) |
0.00626006 | + | 0.999980i | \(0.498007\pi\) | |||||||
\(674\) | 1.64170 | 0.0632358 | ||||||||
\(675\) | −5.17920 | + | 0.419435i | −0.199347 | + | 0.0161441i | ||||
\(676\) | 1.93705 | − | 3.35507i | 0.0745020 | − | 0.129041i | ||||
\(677\) | −23.9003 | − | 41.3965i | −0.918563 | − | 1.59100i | −0.801599 | − | 0.597862i | \(-0.796017\pi\) |
−0.116964 | − | 0.993136i | \(-0.537316\pi\) | |||||||
\(678\) | −25.1484 | − | 8.39338i | −0.965817 | − | 0.322346i | ||||
\(679\) | 27.7983 | − | 48.1481i | 1.06680 | − | 1.84776i | ||||
\(680\) | −3.88616 | −0.149028 | ||||||||
\(681\) | −12.4475 | + | 37.2952i | −0.476988 | + | 1.42916i | ||||
\(682\) | 3.47827 | + | 2.83373i | 0.133190 | + | 0.108509i | ||||
\(683\) | 19.5460i | 0.747908i | 0.927447 | + | 0.373954i | \(0.121998\pi\) | ||||
−0.927447 | + | 0.373954i | \(0.878002\pi\) | |||||||
\(684\) | −6.61997 | − | 4.97283i | −0.253121 | − | 0.190141i | ||||
\(685\) | 5.64307 | + | 3.25803i | 0.215610 | + | 0.124483i | ||||
\(686\) | 7.56576i | 0.288862i | ||||||||
\(687\) | 8.47151 | − | 1.73022i | 0.323208 | − | 0.0660120i | ||||
\(688\) | −0.711673 | − | 0.410885i | −0.0271323 | − | 0.0156648i | ||||
\(689\) | −35.5594 | − | 20.5302i | −1.35471 | − | 0.782140i | ||||
\(690\) | −0.233739 | − | 0.0780116i | −0.00889830 | − | 0.00296985i | ||||
\(691\) | −18.2356 | − | 31.5851i | −0.693717 | − | 1.20155i | −0.970611 | − | 0.240652i | \(-0.922639\pi\) |
0.276895 | − | 0.960900i | \(-0.410695\pi\) | |||||||
\(692\) | 11.7703 | − | 6.79559i | 0.447440 | − | 0.258330i | ||||
\(693\) | 0.999418 | − | 8.24264i | 0.0379648 | − | 0.313112i | ||||
\(694\) | 7.01513 | + | 4.05019i | 0.266291 | + | 0.153743i | ||||
\(695\) | 8.16162 | + | 14.1363i | 0.309588 | + | 0.536222i | ||||
\(696\) | −8.27202 | − | 9.33558i | −0.313550 | − | 0.353864i | ||||
\(697\) | 2.84690i | 0.107834i | ||||||||
\(698\) | 10.2078i | 0.386370i | ||||||||
\(699\) | 2.83517 | + | 3.19970i | 0.107236 | + | 0.121024i | ||||
\(700\) | 1.71736 | + | 2.97455i | 0.0649100 | + | 0.112427i | ||||
\(701\) | −31.1895 | − | 18.0073i | −1.17801 | − | 0.680126i | −0.222459 | − | 0.974942i | \(-0.571408\pi\) |
−0.955554 | + | 0.294816i | \(0.904742\pi\) | |||||||
\(702\) | −6.72562 | + | 14.1833i | −0.253842 | + | 0.535313i | ||||
\(703\) | 25.6270 | − | 14.7958i | 0.966541 | − | 0.558033i | ||||
\(704\) | −0.402897 | − | 0.697837i | −0.0151847 | − | 0.0263007i | ||||
\(705\) | −8.02137 | − | 2.67717i | −0.302102 | − | 0.100828i | ||||
\(706\) | −3.78351 | − | 2.18441i | −0.142394 | − | 0.0822114i | ||||
\(707\) | −9.13539 | − | 5.27432i | −0.343572 | − | 0.198361i | ||||
\(708\) | −22.7223 | + | 4.64079i | −0.853955 | + | 0.174412i | ||||
\(709\) | − | 45.8983i | − | 1.72375i | −0.507122 | − | 0.861874i | \(-0.669291\pi\) | ||
0.507122 | − | 0.861874i | \(-0.330709\pi\) | |||||||
\(710\) | 9.83676 | + | 5.67926i | 0.369167 | + | 0.213139i | ||||
\(711\) | 5.86147 | − | 7.80295i | 0.219822 | − | 0.292634i | ||||
\(712\) | 7.24740i | 0.271608i | ||||||||
\(713\) | 0.281677 | + | 0.740335i | 0.0105489 | + | 0.0277258i | ||||
\(714\) | 7.31924 | − | 21.9300i | 0.273916 | − | 0.820710i | ||||
\(715\) | −2.43423 | −0.0910350 | ||||||||
\(716\) | 1.61838 | − | 2.80311i | 0.0604816 | − | 0.104757i | ||||
\(717\) | −22.1773 | − | 7.40176i | −0.828225 | − | 0.276424i | ||||
\(718\) | −3.33465 | − | 5.77578i | −0.124448 | − | 0.215550i | ||||
\(719\) | −4.43050 | + | 7.67386i | −0.165230 | + | 0.286187i | −0.936737 | − | 0.350034i | \(-0.886170\pi\) |
0.771507 | + | 0.636221i | \(0.219503\pi\) | |||||||
\(720\) | −1.17637 | − | 2.75974i | −0.0438407 | − | 0.102849i | ||||
\(721\) | −2.53285 | −0.0943282 | ||||||||
\(722\) | −9.85796 | + | 5.69149i | −0.366875 | + | 0.211815i | ||||
\(723\) | −13.4222 | + | 2.74135i | −0.499177 | + | 0.101952i | ||||
\(724\) | 14.2426 | − | 8.22298i | 0.529323 | − | 0.305605i | ||||
\(725\) | 3.60069 | − | 6.23657i | 0.133726 | − | 0.231620i | ||||
\(726\) | 17.5653 | − | 3.58754i | 0.651910 | − | 0.133146i | ||||
\(727\) | −4.07367 | + | 7.05581i | −0.151084 | + | 0.261685i | −0.931626 | − | 0.363418i | \(-0.881610\pi\) |
0.780542 | + | 0.625103i | \(0.214943\pi\) | |||||||
\(728\) | 10.3760 | 0.384559 | ||||||||
\(729\) | −9.56148 | + | 25.2503i | −0.354129 | + | 0.935197i | ||||
\(730\) | 0.721718 | + | 0.416684i | 0.0267120 | + | 0.0154222i | ||||
\(731\) | −2.76568 | + | 1.59677i | −0.102292 | + | 0.0590585i | ||||
\(732\) | −12.2069 | − | 13.7763i | −0.451178 | − | 0.509188i | ||||
\(733\) | −8.01155 | − | 13.8764i | −0.295913 | − | 0.512537i | 0.679284 | − | 0.733876i | \(-0.262291\pi\) |
−0.975197 | + | 0.221339i | \(0.928957\pi\) | |||||||
\(734\) | 7.29338 | + | 12.6325i | 0.269203 | + | 0.466274i | ||||
\(735\) | −8.14105 | + | 1.66273i | −0.300287 | + | 0.0613306i | ||||
\(736\) | − | 0.142267i | − | 0.00524404i | ||||||
\(737\) | 0.276264 | − | 0.478503i | 0.0101763 | − | 0.0176259i | ||||
\(738\) | −2.02171 | + | 0.861776i | −0.0744202 | + | 0.0317224i | ||||
\(739\) | 26.4217 | − | 15.2546i | 0.971938 | − | 0.561149i | 0.0721115 | − | 0.997397i | \(-0.477026\pi\) |
0.899827 | + | 0.436248i | \(0.143693\pi\) | |||||||
\(740\) | 10.7220 | 0.394148 | ||||||||
\(741\) | −9.57693 | − | 10.8083i | −0.351817 | − | 0.397052i | ||||
\(742\) | 46.6850i | 1.71386i | ||||||||
\(743\) | 1.95284 | 0.0716426 | 0.0358213 | − | 0.999358i | \(-0.488595\pi\) | ||||
0.0358213 | + | 0.999358i | \(0.488595\pi\) | |||||||
\(744\) | −4.47178 | + | 8.54419i | −0.163943 | + | 0.313245i | ||||
\(745\) | −3.10442 | −0.113737 | ||||||||
\(746\) | − | 21.3294i | − | 0.780924i | ||||||
\(747\) | 5.15651 | − | 2.19802i | 0.188667 | − | 0.0804212i | ||||
\(748\) | −3.13144 | −0.114497 | ||||||||
\(749\) | −6.37688 | + | 3.68169i | −0.233006 | + | 0.134526i | ||||
\(750\) | 1.29636 | − | 1.14867i | 0.0473364 | − | 0.0419436i | ||||
\(751\) | 20.1487 | − | 34.8986i | 0.735238 | − | 1.27347i | −0.219381 | − | 0.975639i | \(-0.570404\pi\) |
0.954619 | − | 0.297830i | \(-0.0962628\pi\) | |||||||
\(752\) | − | 4.88227i | − | 0.178038i | ||||||
\(753\) | 6.59998 | + | 32.3149i | 0.240517 | + | 1.17762i | ||||
\(754\) | −10.8773 | − | 18.8401i | −0.396130 | − | 0.686117i | ||||
\(755\) | 9.92861 | + | 17.1969i | 0.361339 | + | 0.625858i | ||||
\(756\) | 17.7891 | − | 1.44064i | 0.646982 | − | 0.0523955i | ||||
\(757\) | −41.1044 | + | 23.7316i | −1.49396 | + | 0.862540i | −0.999976 | − | 0.00692880i | \(-0.997794\pi\) |
−0.493987 | + | 0.869469i | \(0.664461\pi\) | |||||||
\(758\) | −27.0986 | − | 15.6454i | −0.984266 | − | 0.568266i | ||||
\(759\) | −0.188345 | − | 0.0628612i | −0.00683651 | − | 0.00228172i | ||||
\(760\) | 2.75989 | 0.100112 | ||||||||
\(761\) | 7.70000 | − | 13.3368i | 0.279125 | − | 0.483458i | −0.692043 | − | 0.721856i | \(-0.743289\pi\) |
0.971167 | + | 0.238398i | \(0.0766224\pi\) | |||||||
\(762\) | 3.60941 | + | 17.6724i | 0.130755 | + | 0.640204i | ||||
\(763\) | −24.5381 | + | 42.5012i | −0.888338 | + | 1.53865i | ||||
\(764\) | 11.6288 | − | 6.71391i | 0.420717 | − | 0.242901i | ||||
\(765\) | −11.5737 | − | 1.40331i | −0.418449 | − | 0.0507368i | ||||
\(766\) | −20.4494 | + | 11.8065i | −0.738866 | + | 0.426585i | ||||
\(767\) | −40.4485 | −1.46051 | ||||||||
\(768\) | 1.29636 | − | 1.14867i | 0.0467784 | − | 0.0414491i | ||||
\(769\) | −3.29403 | + | 5.70542i | −0.118786 | + | 0.205743i | −0.919287 | − | 0.393589i | \(-0.871233\pi\) |
0.800501 | + | 0.599331i | \(0.204567\pi\) | |||||||
\(770\) | 1.38383 | + | 2.39687i | 0.0498699 | + | 0.0863773i | ||||
\(771\) | −1.96651 | + | 5.89208i | −0.0708221 | + | 0.212198i | ||||
\(772\) | −7.75886 | + | 13.4387i | −0.279247 | + | 0.483671i | ||||
\(773\) | −24.5515 | −0.883057 | −0.441529 | − | 0.897247i | \(-0.645564\pi\) | ||||
−0.441529 | + | 0.897247i | \(0.645564\pi\) | |||||||
\(774\) | −1.97112 | − | 1.48068i | −0.0708506 | − | 0.0532220i | ||||
\(775\) | −5.49661 | − | 0.887263i | −0.197444 | − | 0.0318714i | ||||
\(776\) | − | 16.1867i | − | 0.581068i | ||||||
\(777\) | −20.1939 | + | 60.5052i | −0.724452 | + | 2.17061i | ||||
\(778\) | 22.1030 | + | 12.7612i | 0.792431 | + | 0.457511i | ||||
\(779\) | − | 2.02182i | − | 0.0724394i | ||||||
\(780\) | −1.04704 | − | 5.12654i | −0.0374902 | − | 0.183559i | ||||
\(781\) | 7.92639 | + | 4.57631i | 0.283629 | + | 0.163753i | ||||
\(782\) | −0.478802 | − | 0.276437i | −0.0171219 | − | 0.00988536i | ||||
\(783\) | −21.2645 | − | 30.7902i | −0.759931 | − | 1.10035i | ||||
\(784\) | −2.39863 | − | 4.15456i | −0.0856655 | − | 0.148377i | ||||
\(785\) | 1.47510 | − | 0.851649i | 0.0526485 | − | 0.0303966i | ||||
\(786\) | 5.64209 | + | 27.6248i | 0.201247 | + | 0.985345i | ||||
\(787\) | 34.3021 | + | 19.8044i | 1.22274 | + | 0.705949i | 0.965501 | − | 0.260399i | \(-0.0838542\pi\) |
0.257238 | + | 0.966348i | \(0.417187\pi\) | |||||||
\(788\) | −2.76263 | − | 4.78502i | −0.0984147 | − | 0.170459i | ||||
\(789\) | 21.6625 | − | 19.1946i | 0.771207 | − | 0.683347i | ||||
\(790\) | 3.25308i | 0.115739i | ||||||||
\(791\) | 52.5743i | 1.86933i | ||||||||
\(792\) | −0.947909 | − | 2.22378i | −0.0336825 | − | 0.0790185i | ||||
\(793\) | −16.0515 | − | 27.8020i | −0.570005 | − | 0.987278i | ||||
\(794\) | 17.6566 | + | 10.1941i | 0.626610 | + | 0.361774i | ||||
\(795\) | 23.0660 | − | 4.71100i | 0.818068 | − | 0.167082i | ||||
\(796\) | 13.6901 | − | 7.90400i | 0.485234 | − | 0.280150i | ||||
\(797\) | −4.95554 | − | 8.58324i | −0.175534 | − | 0.304034i | 0.764812 | − | 0.644254i | \(-0.222832\pi\) |
−0.940346 | + | 0.340220i | \(0.889499\pi\) | |||||||
\(798\) | −5.19801 | + | 15.5744i | −0.184008 | + | 0.551326i | ||||
\(799\) | −16.4313 | − | 9.48664i | −0.581299 | − | 0.335613i | ||||
\(800\) | 0.866025 | + | 0.500000i | 0.0306186 | + | 0.0176777i | ||||
\(801\) | −2.61707 | + | 21.5841i | −0.0924696 | + | 0.762637i | ||||
\(802\) | 7.15181i | 0.252539i | ||||||||
\(803\) | 0.581556 | + | 0.335761i | 0.0205227 | + | 0.0118488i | ||||
\(804\) | 1.12657 | + | 0.375997i | 0.0397310 | + | 0.0132604i | ||||
\(805\) | 0.488647i | 0.0172225i | ||||||||
\(806\) | −10.6236 | + | 13.0400i | −0.374201 | + | 0.459314i | ||||
\(807\) | −31.8713 | − | 10.6372i | −1.12192 | − | 0.374447i | ||||
\(808\) | −3.07118 | −0.108044 | ||||||||
\(809\) | −3.13516 | + | 5.43025i | −0.110226 | + | 0.190918i | −0.915861 | − | 0.401495i | \(-0.868491\pi\) |
0.805635 | + | 0.592412i | \(0.201824\pi\) | |||||||
\(810\) | −2.50689 | − | 8.64381i | −0.0880832 | − | 0.303713i | ||||
\(811\) | −0.848524 | − | 1.46969i | −0.0297957 | − | 0.0516077i | 0.850743 | − | 0.525582i | \(-0.176152\pi\) |
−0.880539 | + | 0.473974i | \(0.842819\pi\) | |||||||
\(812\) | −12.3673 | + | 21.4208i | −0.434008 | + | 0.751724i | ||||
\(813\) | −5.31109 | − | 5.99396i | −0.186268 | − | 0.210217i | ||||
\(814\) | 8.63969 | 0.302821 | ||||||||
\(815\) | 2.56818 | − | 1.48274i | 0.0899595 | − | 0.0519381i | ||||
\(816\) | −1.34694 | − | 6.59489i | −0.0471523 | − | 0.230867i | ||||
\(817\) | 1.96414 | − | 1.13400i | 0.0687167 | − | 0.0396736i | ||||
\(818\) | 2.87090 | − | 4.97254i | 0.100379 | − | 0.173861i | ||||
\(819\) | 30.9016 | + | 3.74681i | 1.07979 | + | 0.130924i | ||||
\(820\) | 0.366287 | − | 0.634427i | 0.0127913 | − | 0.0221552i | ||||
\(821\) | −52.5361 | −1.83352 | −0.916761 | − | 0.399436i | \(-0.869206\pi\) | ||||
−0.916761 | + | 0.399436i | \(0.869206\pi\) | |||||||
\(822\) | −3.57305 | + | 10.7056i | −0.124624 | + | 0.373401i | ||||
\(823\) | 20.3950 | + | 11.7751i | 0.710926 | + | 0.410453i | 0.811404 | − | 0.584486i | \(-0.198704\pi\) |
−0.100478 | + | 0.994939i | \(0.532037\pi\) | |||||||
\(824\) | −0.638630 | + | 0.368713i | −0.0222477 | + | 0.0128447i | ||||
\(825\) | 1.04460 | − | 0.925592i | 0.0363683 | − | 0.0322250i | ||||
\(826\) | 22.9946 | + | 39.8278i | 0.800084 | + | 1.38579i | ||||
\(827\) | 4.50704 | + | 7.80642i | 0.156725 | + | 0.271456i | 0.933686 | − | 0.358093i | \(-0.116573\pi\) |
−0.776961 | + | 0.629549i | \(0.783240\pi\) | |||||||
\(828\) | 0.0513733 | − | 0.423698i | 0.00178535 | − | 0.0147245i | ||||
\(829\) | 3.12929i | 0.108685i | 0.998522 | + | 0.0543424i | \(0.0173062\pi\) | ||||
−0.998522 | + | 0.0543424i | \(0.982694\pi\) | |||||||
\(830\) | −0.934238 | + | 1.61815i | −0.0324279 | + | 0.0561667i | ||||
\(831\) | −27.5515 | − | 31.0939i | −0.955751 | − | 1.07864i | ||||
\(832\) | 2.61618 | − | 1.51045i | 0.0906999 | − | 0.0523656i | ||||
\(833\) | −18.6430 | −0.645941 | ||||||||
\(834\) | −21.1608 | + | 18.7501i | −0.732739 | + | 0.649261i | ||||
\(835\) | − | 23.0863i | − | 0.798933i | ||||||
\(836\) | 2.22390 | 0.0769153 | ||||||||
\(837\) | −16.4032 | + | 23.8314i | −0.566976 | + | 0.823734i | ||||
\(838\) | 9.62101 | 0.332352 | ||||||||
\(839\) | − | 13.4727i | − | 0.465128i | −0.972581 | − | 0.232564i | \(-0.925289\pi\) | ||
0.972581 | − | 0.232564i | \(-0.0747115\pi\) | |||||||
\(840\) | −4.45263 | + | 3.94536i | −0.153630 | + | 0.136128i | ||||
\(841\) | 22.8598 | 0.788268 | ||||||||
\(842\) | 29.9775 | − | 17.3075i | 1.03309 | − | 0.596456i | ||||
\(843\) | 10.9710 | + | 12.3815i | 0.377860 | + | 0.426443i | ||||
\(844\) | 8.66050 | − | 15.0004i | 0.298107 | − | 0.516336i | ||||
\(845\) | 3.87411i | 0.133273i | ||||||||
\(846\) | 1.76301 | − | 14.5403i | 0.0606135 | − | 0.499906i | ||||
\(847\) | −17.7758 | − | 30.7887i | −0.610785 | − | 1.05791i | ||||
\(848\) | 6.79605 | + | 11.7711i | 0.233377 | + | 0.404221i | ||||
\(849\) | 16.8232 | − | 14.9066i | 0.577369 | − | 0.511592i | ||||
\(850\) | 3.36552 | − | 1.94308i | 0.115436 | − | 0.0666472i | ||||
\(851\) | 1.32102 | + | 0.762693i | 0.0452841 | + | 0.0261448i | ||||
\(852\) | −6.22839 | + | 18.6616i | −0.213381 | + | 0.639335i | ||||
\(853\) | 21.9362 | 0.751079 | 0.375540 | − | 0.926806i | \(-0.377457\pi\) | ||||
0.375540 | + | 0.926806i | \(0.377457\pi\) | |||||||
\(854\) | −18.2502 | + | 31.6103i | −0.624510 | + | 1.08168i | ||||
\(855\) | 8.21948 | + | 0.996610i | 0.281100 | + | 0.0340834i | ||||
\(856\) | −1.07191 | + | 1.85660i | −0.0366370 | + | 0.0634571i | ||||
\(857\) | −6.41770 | + | 3.70526i | −0.219225 | + | 0.126569i | −0.605591 | − | 0.795776i | \(-0.707063\pi\) |
0.386367 | + | 0.922345i | \(0.373730\pi\) | |||||||
\(858\) | −0.843700 | − | 4.13093i | −0.0288034 | − | 0.141028i | ||||
\(859\) | −27.1800 | + | 15.6924i | −0.927371 | + | 0.535418i | −0.885979 | − | 0.463725i | \(-0.846513\pi\) |
−0.0413920 | + | 0.999143i | \(0.513179\pi\) | |||||||
\(860\) | 0.821770 | 0.0280221 | ||||||||
\(861\) | 2.89027 | + | 3.26188i | 0.0985001 | + | 0.111165i | ||||
\(862\) | −18.7647 | + | 32.5014i | −0.639129 | + | 1.10700i | ||||
\(863\) | −21.9466 | − | 38.0126i | −0.747071 | − | 1.29396i | −0.949221 | − | 0.314610i | \(-0.898126\pi\) |
0.202150 | − | 0.979355i | \(-0.435207\pi\) | |||||||
\(864\) | 4.27560 | − | 2.95284i | 0.145459 | − | 0.100458i | ||||
\(865\) | −6.79559 | + | 11.7703i | −0.231057 | + | 0.400203i | ||||
\(866\) | 0.00668506 | 0.000227168 | ||||||||
\(867\) | 3.11790 | + | 1.04061i | 0.105890 | + | 0.0353411i | ||||
\(868\) | 18.8793 | + | 3.04750i | 0.640805 | + | 0.103439i | ||||
\(869\) | 2.62131i | 0.0889219i | ||||||||
\(870\) | 11.8316 | + | 3.94884i | 0.401128 | + | 0.133878i | ||||
\(871\) | 1.79390 | + | 1.03571i | 0.0607841 | + | 0.0350937i | ||||
\(872\) | 14.2883i | 0.483862i | ||||||||
\(873\) | 5.84509 | − | 48.2070i | 0.197826 | − | 1.63156i | ||||
\(874\) | 0.340038 | + | 0.196321i | 0.0115020 | + | 0.00664066i | ||||
\(875\) | −2.97455 | − | 1.71736i | −0.100558 | − | 0.0580573i | ||||
\(876\) | −0.456974 | + | 1.36919i | −0.0154397 | + | 0.0462607i | ||||
\(877\) | 2.88216 | + | 4.99204i | 0.0973236 | + | 0.168569i | 0.910576 | − | 0.413342i | \(-0.135639\pi\) |
−0.813252 | + | 0.581911i | \(0.802305\pi\) | |||||||
\(878\) | 18.0815 | − | 10.4394i | 0.610222 | − | 0.352312i | ||||
\(879\) | 28.7652 | − | 5.87500i | 0.970226 | − | 0.198159i | ||||
\(880\) | 0.697837 | + | 0.402897i | 0.0235241 | + | 0.0135816i | ||||
\(881\) | −13.5530 | − | 23.4746i | −0.456614 | − | 0.790878i | 0.542166 | − | 0.840272i | \(-0.317605\pi\) |
−0.998779 | + | 0.0493933i | \(0.984271\pi\) | |||||||
\(882\) | −5.64335 | − | 13.2392i | −0.190022 | − | 0.445787i | ||||
\(883\) | 35.9403i | 1.20949i | 0.796421 | + | 0.604743i | \(0.206724\pi\) | ||||
−0.796421 | + | 0.604743i | \(0.793276\pi\) | |||||||
\(884\) | − | 11.7397i | − | 0.394850i | ||||||
\(885\) | 17.3577 | − | 15.3802i | 0.583471 | − | 0.516999i | ||||
\(886\) | 13.4719 | + | 23.3341i | 0.452599 | + | 0.783924i | ||||
\(887\) | −25.1393 | − | 14.5142i | −0.844095 | − | 0.487339i | 0.0145588 | − | 0.999894i | \(-0.495366\pi\) |
−0.858654 | + | 0.512555i | \(0.828699\pi\) | |||||||
\(888\) | 3.71622 | + | 18.1954i | 0.124708 | + | 0.610597i | ||||
\(889\) | 30.9764 | − | 17.8842i | 1.03891 | − | 0.599818i | ||||
\(890\) | −3.62370 | − | 6.27643i | −0.121467 | − | 0.210386i | ||||
\(891\) | −2.02004 | − | 6.96512i | −0.0676737 | − | 0.233340i | ||||
\(892\) | −0.150848 | − | 0.0870923i | −0.00505078 | − | 0.00291607i | ||||
\(893\) | 11.6693 | + | 6.73727i | 0.390498 | + | 0.225454i | ||||
\(894\) | −1.07599 | − | 5.26826i | −0.0359864 | − | 0.176197i | ||||
\(895\) | 3.23676i | 0.108193i | ||||||||
\(896\) | −2.97455 | − | 1.71736i | −0.0993728 | − | 0.0573729i | ||||
\(897\) | 0.235666 | − | 0.706105i | 0.00786866 | − | 0.0235762i | ||||
\(898\) | − | 22.2082i | − | 0.741098i | ||||||
\(899\) | −14.2581 | − | 37.4748i | −0.475534 | − | 1.24985i | ||||
\(900\) | 2.39863 | + | 1.80182i | 0.0799545 | + | 0.0600607i | ||||
\(901\) | 52.8211 | 1.75973 | ||||||||
\(902\) | 0.295151 | − | 0.511217i | 0.00982746 | − | 0.0170217i | ||||
\(903\) | −1.54773 | + | 4.63733i | −0.0515052 | + | 0.154321i | ||||
\(904\) | 7.65337 | + | 13.2560i | 0.254547 | + | 0.440889i | ||||
\(905\) | −8.22298 | + | 14.2426i | −0.273341 | + | 0.473441i | ||||
\(906\) | −25.7421 | + | 22.8094i | −0.855225 | + | 0.757793i | ||||
\(907\) | 11.3469 | 0.376768 | 0.188384 | − | 0.982095i | \(-0.439675\pi\) | ||||
0.188384 | + | 0.982095i | \(0.439675\pi\) | |||||||
\(908\) | 19.6588 | − | 11.3500i | 0.652400 | − | 0.376663i | ||||
\(909\) | −9.14656 | − | 1.10902i | −0.303372 | − | 0.0367838i | ||||
\(910\) | −8.98585 | + | 5.18798i | −0.297878 | + | 0.171980i | ||||
\(911\) | 14.1404 | − | 24.4918i | 0.468491 | − | 0.811450i | −0.530860 | − | 0.847459i | \(-0.678131\pi\) |
0.999351 | + | 0.0360090i | \(0.0114645\pi\) | |||||||
\(912\) | 0.956575 | + | 4.68359i | 0.0316754 | + | 0.155089i | ||||
\(913\) | −0.752803 | + | 1.30389i | −0.0249141 | + | 0.0431525i | ||||
\(914\) | −35.8276 | −1.18507 | ||||||||
\(915\) | 17.4596 | + | 5.82723i | 0.577197 | + | 0.192642i | ||||
\(916\) | −4.32320 | − | 2.49600i | −0.142843 | − | 0.0824702i | ||||
\(917\) | 48.4211 | − | 27.9559i | 1.59901 | − | 0.923186i | ||||
\(918\) | −1.62999 | − | 20.1272i | −0.0537978 | − | 0.664297i | ||||
\(919\) | −27.9372 | − | 48.3886i | −0.921563 | − | 1.59619i | −0.796998 | − | 0.603983i | \(-0.793580\pi\) |
−0.124565 | − | 0.992211i | \(-0.539754\pi\) | |||||||
\(920\) | 0.0711336 | + | 0.123207i | 0.00234520 | + | 0.00406201i | ||||
\(921\) | −7.45177 | − | 36.4854i | −0.245544 | − | 1.20223i | ||||
\(922\) | − | 11.0236i | − | 0.363042i | ||||||
\(923\) | −17.1565 | + | 29.7160i | −0.564714 | + | 0.978113i | ||||
\(924\) | −3.58790 | + | 3.17914i | −0.118033 | + | 0.104586i | ||||
\(925\) | −9.28550 | + | 5.36099i | −0.305306 | + | 0.176268i | ||||
\(926\) | 6.77239 | 0.222555 | ||||||||
\(927\) | −2.03510 | + | 0.867485i | −0.0668416 | + | 0.0284919i | ||||
\(928\) | 7.20137i | 0.236397i | ||||||||
\(929\) | 49.7364 | 1.63180 | 0.815900 | − | 0.578193i | \(-0.196242\pi\) | ||||
0.815900 | + | 0.578193i | \(0.196242\pi\) | |||||||
\(930\) | −0.399418 | − | 9.63538i | −0.0130974 | − | 0.315956i | ||||
\(931\) | 13.2399 | 0.433922 | ||||||||
\(932\) | − | 2.46821i | − | 0.0808491i | ||||||
\(933\) | 0.574403 | + | 0.648257i | 0.0188051 | + | 0.0212230i | ||||
\(934\) | 19.9229 | 0.651898 | ||||||||
\(935\) | 2.71191 | − | 1.56572i | 0.0886889 | − | 0.0512046i | ||||
\(936\) | 8.33692 | − | 3.55370i | 0.272501 | − | 0.116156i | ||||
\(937\) | −4.69392 | + | 8.13010i | −0.153344 | + | 0.265599i | −0.932455 | − | 0.361287i | \(-0.882337\pi\) |
0.779111 | + | 0.626886i | \(0.215671\pi\) | |||||||
\(938\) | − | 2.35516i | − | 0.0768988i | ||||||
\(939\) | −25.5288 | + | 5.21400i | −0.833102 | + | 0.170153i | ||||
\(940\) | 2.44113 | + | 4.22817i | 0.0796210 | + | 0.137908i | ||||
\(941\) | 29.2702 | + | 50.6975i | 0.954182 | + | 1.65269i | 0.736229 | + | 0.676732i | \(0.236604\pi\) |
0.217952 | + | 0.975959i | \(0.430062\pi\) | |||||||
\(942\) | 1.95653 | + | 2.20809i | 0.0637472 | + | 0.0719434i | ||||
\(943\) | 0.0902582 | − | 0.0521106i | 0.00293921 | − | 0.00169695i | ||||
\(944\) | 11.5957 | + | 6.69476i | 0.377407 | + | 0.217896i | ||||
\(945\) | −14.6855 | + | 10.1422i | −0.477718 | + | 0.329925i | ||||
\(946\) | 0.662176 | 0.0215292 | ||||||||
\(947\) | −4.41635 | + | 7.64934i | −0.143512 | + | 0.248570i | −0.928817 | − | 0.370539i | \(-0.879173\pi\) |
0.785305 | + | 0.619109i | \(0.212506\pi\) | |||||||
\(948\) | −5.52054 | + | 1.12751i | −0.179299 | + | 0.0366199i | ||||
\(949\) | −1.25877 | + | 2.18025i | −0.0408613 | + | 0.0707738i | ||||
\(950\) | −2.39014 | + | 1.37995i | −0.0775463 | + | 0.0447714i | ||||
\(951\) | −15.9344 | + | 3.25444i | −0.516709 | + | 0.105533i | ||||
\(952\) | −11.5596 | + | 6.67393i | −0.374648 | + | 0.216303i | ||||
\(953\) | −35.8201 | −1.16033 | −0.580164 | − | 0.814500i | \(-0.697011\pi\) | ||||
−0.580164 | + | 0.814500i | \(0.697011\pi\) | |||||||
\(954\) | 15.9893 | + | 37.5106i | 0.517673 | + | 1.21445i | ||||
\(955\) | −6.71391 | + | 11.6288i | −0.217257 | + | 0.376300i | ||||
\(956\) | 6.74918 | + | 11.6899i | 0.218284 | + | 0.378079i | ||||
\(957\) | 9.53379 | + | 3.18195i | 0.308184 | + | 0.102858i | ||||
\(958\) | −6.03362 | + | 10.4505i | −0.194938 | + | 0.337642i | ||||
\(959\) | 22.3808 | 0.722713 | ||||||||
\(960\) | −0.548346 | + | 1.64296i | −0.0176978 | + | 0.0530263i | ||||
\(961\) | −23.1599 | + | 20.6063i | −0.747093 | + | 0.664720i | ||||
\(962\) | 32.3901i | 1.04430i | ||||||||
\(963\) | −3.86276 | + | 5.14222i | −0.124476 | + | 0.165706i | ||||
\(964\) | 6.84964 | + | 3.95464i | 0.220612 | + | 0.127371i | ||||
\(965\) | − | 15.5177i | − | 0.499533i | ||||||
\(966\) | −0.829243 | + | 0.169364i | −0.0266805 | + | 0.00544921i | ||||
\(967\) | −17.9304 | − | 10.3521i | −0.576603 | − | 0.332902i | 0.183179 | − | 0.983080i | \(-0.441361\pi\) |
−0.759782 | + | 0.650178i | \(0.774695\pi\) | |||||||
\(968\) | −8.96397 | − | 5.17535i | −0.288113 | − | 0.166342i | ||||
\(969\) | 17.6214 | + | 5.88122i | 0.566081 | + | 0.188932i | ||||
\(970\) | 8.09335 | + | 14.0181i | 0.259862 | + | 0.450094i | ||||
\(971\) | 34.7913 | − | 20.0868i | 1.11651 | − | 0.644615i | 0.176000 | − | 0.984390i | \(-0.443684\pi\) |
0.940507 | + | 0.339775i | \(0.110351\pi\) | |||||||
\(972\) | 13.7998 | − | 7.25017i | 0.442629 | − | 0.232549i | ||||
\(973\) | 48.5543 | + | 28.0329i | 1.55658 | + | 0.898692i | ||||
\(974\) | −14.8027 | − | 25.6391i | −0.474310 | − | 0.821529i | ||||
\(975\) | 3.47003 | + | 3.91619i | 0.111130 | + | 0.125418i | ||||
\(976\) | 10.6269i | 0.340160i | ||||||||
\(977\) | 48.8853i | 1.56398i | 0.623292 | + | 0.781989i | \(0.285795\pi\) | ||||
−0.623292 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(978\) | 3.40636 | + | 3.84433i | 0.108924 | + | 0.122928i | ||||
\(979\) | −2.91995 | − | 5.05750i | −0.0933220 | − | 0.161638i | ||||
\(980\) | 4.15456 | + | 2.39863i | 0.132712 | + | 0.0766216i | ||||
\(981\) | −5.15956 | + | 42.5532i | −0.164732 | + | 1.35862i | ||||
\(982\) | −29.0451 | + | 16.7692i | −0.926868 | + | 0.535127i | ||||
\(983\) | 15.0761 | + | 26.1125i | 0.480851 | + | 0.832859i | 0.999759 | − | 0.0219715i | \(-0.00699430\pi\) |
−0.518907 | + | 0.854831i | \(0.673661\pi\) | |||||||
\(984\) | 1.20359 | + | 0.401704i | 0.0383690 | + | 0.0128058i | ||||
\(985\) | 4.78502 | + | 2.76263i | 0.152463 | + | 0.0880248i | ||||
\(986\) | 24.2363 | + | 13.9929i | 0.771842 | + | 0.445623i | ||||
\(987\) | −28.4576 | + | 5.81218i | −0.905816 | + | 0.185004i | ||||
\(988\) | 8.33739i | 0.265248i | ||||||||
\(989\) | 0.101248 | + | 0.0584554i | 0.00321949 | + | 0.00185877i | ||||
\(990\) | 1.93280 | + | 1.45189i | 0.0614285 | + | 0.0461442i | ||||
\(991\) | 48.1613i | 1.52989i | 0.644094 | + | 0.764947i | \(0.277235\pi\) | ||||
−0.644094 | + | 0.764947i | \(0.722765\pi\) | |||||||
\(992\) | 5.20384 | − | 1.97991i | 0.165222 | − | 0.0628624i | ||||
\(993\) | 12.1230 | − | 36.3230i | 0.384711 | − | 1.15268i | ||||
\(994\) | 39.0133 | 1.23743 | ||||||||
\(995\) | −7.90400 | + | 13.6901i | −0.250574 | + | 0.434006i | ||||
\(996\) | −3.06983 | − | 1.02457i | −0.0972713 | − | 0.0324648i | ||||
\(997\) | −2.80383 | − | 4.85637i | −0.0887981 | − | 0.153803i | 0.818205 | − | 0.574926i | \(-0.194969\pi\) |
−0.907003 | + | 0.421123i | \(0.861636\pi\) | |||||||
\(998\) | −19.0603 | + | 33.0134i | −0.603343 | + | 1.04502i | ||||
\(999\) | 4.49717 | + | 55.5312i | 0.142284 | + | 1.75693i |
(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 | 930.2.o.e.491.18 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.491.5 | yes | 40 | |
31.6 | odd | 6 | inner | 930.2.o.e.161.15 | yes | 40 | |
93.68 | even | 6 | inner | 930.2.o.e.161.8 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.8 | ✓ | 40 | 93.68 | even | 6 | inner | |
930.2.o.e.161.15 | yes | 40 | 31.6 | odd | 6 | inner | |
930.2.o.e.491.5 | yes | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.491.18 | yes | 40 | 1.1 | even | 1 | trivial |