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 | 161.15 | ||
Character | \(\chi\) | \(=\) | 930.161 |
Dual form | 930.2.o.e.491.5 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.346599 | − | 1.69702i | −0.200109 | − | 0.979774i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | 1.69702 | − | 0.346599i | 0.692805 | − | 0.141498i | ||||
\(7\) | 1.71736 | + | 2.97455i | 0.649100 | + | 1.12427i | 0.983338 | + | 0.181786i | \(0.0581877\pi\) |
−0.334238 | + | 0.942489i | \(0.608479\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −2.75974 | + | 1.17637i | −0.919913 | + | 0.392123i | ||||
\(10\) | 0.500000 | − | 0.866025i | 0.158114 | − | 0.273861i | ||||
\(11\) | −0.402897 | + | 0.697837i | −0.121478 | + | 0.210406i | −0.920351 | − | 0.391094i | \(-0.872097\pi\) |
0.798873 | + | 0.601500i | \(0.205430\pi\) | |||||||
\(12\) | 0.346599 | + | 1.69702i | 0.100054 | + | 0.489887i | ||||
\(13\) | −2.61618 | − | 1.51045i | −0.725599 | − | 0.418925i | 0.0912110 | − | 0.995832i | \(-0.470926\pi\) |
−0.816810 | + | 0.576907i | \(0.804260\pi\) | |||||||
\(14\) | −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 | \(-0.322870\pi\) |
−0.999460 | + | 0.0328666i | \(0.989536\pi\) | |||||||
\(18\) | −1.17637 | − | 2.75974i | −0.277273 | − | 0.650477i | ||||
\(19\) | −1.37995 | − | 2.39014i | −0.316581 | − | 0.548335i | 0.663191 | − | 0.748450i | \(-0.269202\pi\) |
−0.979772 | + | 0.200115i | \(0.935868\pi\) | |||||||
\(20\) | 0.866025 | + | 0.500000i | 0.193649 | + | 0.111803i | ||||
\(21\) | 4.45263 | − | 3.94536i | 0.971644 | − | 0.860948i | ||||
\(22\) | −0.697837 | − | 0.402897i | −0.148779 | − | 0.0858978i | ||||
\(23\) | 0.142267 | 0.0296648 | 0.0148324 | − | 0.999890i | \(-0.495279\pi\) | ||||
0.0148324 | + | 0.999890i | \(0.495279\pi\) | |||||||
\(24\) | −1.69702 | + | 0.346599i | −0.346402 | + | 0.0707492i | ||||
\(25\) | 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 | \(-0.733119\pi\) | ||||
−0.668631 | + | 0.743595i | \(0.733119\pi\) | |||||||
\(30\) | −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 | ||||||
\(36\) | 2.75974 | − | 1.17637i | 0.459956 | − | 0.196061i | ||||
\(37\) | −9.28550 | + | 5.36099i | −1.52653 | + | 0.881341i | −0.527024 | + | 0.849851i | \(0.676692\pi\) |
−0.999504 | + | 0.0314905i | \(0.989975\pi\) | |||||||
\(38\) | 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 | \(-0.315115\pi\) |
−0.449641 | + | 0.893209i | \(0.648448\pi\) | |||||||
\(42\) | 3.94536 | + | 4.45263i | 0.608783 | + | 0.687056i | ||||
\(43\) | −0.711673 | + | 0.410885i | −0.108529 | + | 0.0626594i | −0.553282 | − | 0.832994i | \(-0.686625\pi\) |
0.444753 | + | 0.895653i | \(0.353291\pi\) | |||||||
\(44\) | 0.402897 | − | 0.697837i | 0.0607389 | − | 0.105203i | ||||
\(45\) | 2.97819 | + | 0.361105i | 0.443962 | + | 0.0538303i | ||||
\(46\) | 0.142267i | 0.0209761i | ||||||||
\(47\) | − | 4.88227i | − | 0.712152i | −0.934457 | − | 0.356076i | \(-0.884114\pi\) | ||
0.934457 | − | 0.356076i | \(-0.115886\pi\) | |||||||
\(48\) | −0.346599 | − | 1.69702i | −0.0500272 | − | 0.244943i | ||||
\(49\) | −2.39863 | + | 4.15456i | −0.342662 | + | 0.593508i | ||||
\(50\) | −0.866025 | + | 0.500000i | −0.122474 | + | 0.0707107i | ||||
\(51\) | −5.03787 | + | 4.46393i | −0.705443 | + | 0.625075i | ||||
\(52\) | 2.61618 | + | 1.51045i | 0.362799 | + | 0.209462i | ||||
\(53\) | −6.79605 | + | 11.7711i | −0.933509 | + | 1.61688i | −0.156237 | + | 0.987720i | \(0.549936\pi\) |
−0.777272 | + | 0.629165i | \(0.783397\pi\) | |||||||
\(54\) | −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 | ||||
\(57\) | −3.57782 | + | 3.17021i | −0.473894 | + | 0.419905i | ||||
\(58\) | − | 7.20137i | − | 0.945587i | ||||||
\(59\) | −11.5957 | + | 6.69476i | −1.50963 | + | 0.871584i | −0.509690 | + | 0.860358i | \(0.670240\pi\) |
−0.999937 | + | 0.0112259i | \(0.996427\pi\) | |||||||
\(60\) | 0.548346 | − | 1.64296i | 0.0707911 | − | 0.212105i | ||||
\(61\) | − | 10.6269i | − | 1.36064i | −0.732916 | − | 0.680319i | \(-0.761841\pi\) | ||
0.732916 | − | 0.680319i | \(-0.238159\pi\) | |||||||
\(62\) | −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 | −0.886208 | − | 0.463287i | \(-0.846670\pi\) |
0.844323 | + | 0.535835i | \(0.180003\pi\) | |||||||
\(68\) | 1.94308 | + | 3.36552i | 0.235633 | + | 0.408129i | ||||
\(69\) | −0.0493096 | − | 0.241430i | −0.00593618 | − | 0.0290647i | ||||
\(70\) | 3.43472 | 0.410527 | ||||||||
\(71\) | −9.83676 | − | 5.67926i | −1.16741 | − | 0.674004i | −0.214340 | − | 0.976759i | \(-0.568760\pi\) |
−0.953068 | + | 0.302755i | \(0.902094\pi\) | |||||||
\(72\) | 1.17637 | + | 2.75974i | 0.138636 | + | 0.325238i | ||||
\(73\) | 0.721718 | + | 0.416684i | 0.0844707 | + | 0.0487692i | 0.541640 | − | 0.840610i | \(-0.317803\pi\) |
−0.457170 | + | 0.889380i | \(0.651137\pi\) | |||||||
\(74\) | −5.36099 | − | 9.28550i | −0.623202 | − | 1.07942i | ||||
\(75\) | 1.29636 | − | 1.14867i | 0.149691 | − | 0.132637i | ||||
\(76\) | 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 | −0.333074 | − | 0.942901i | \(-0.608086\pi\) |
0.650039 | + | 0.759901i | \(0.274752\pi\) | |||||||
\(80\) | −0.866025 | − | 0.500000i | −0.0968246 | − | 0.0559017i | ||||
\(81\) | 6.23232 | − | 6.49294i | 0.692480 | − | 0.721438i | ||||
\(82\) | −0.366287 | + | 0.634427i | −0.0404496 | + | 0.0700608i | ||||
\(83\) | −0.934238 | + | 1.61815i | −0.102546 | + | 0.177615i | −0.912733 | − | 0.408557i | \(-0.866032\pi\) |
0.810187 | + | 0.586172i | \(0.199366\pi\) | |||||||
\(84\) | −4.45263 | + | 3.94536i | −0.485822 | + | 0.430474i | ||||
\(85\) | 3.88616i | 0.421514i | ||||||||
\(86\) | −0.410885 | − | 0.711673i | −0.0443069 | − | 0.0767417i | ||||
\(87\) | 2.49599 | + | 12.2209i | 0.267598 | + | 1.31021i | ||||
\(88\) | 0.697837 | + | 0.402897i | 0.0743897 | + | 0.0429489i | ||||
\(89\) | 7.24740 | 0.768222 | 0.384111 | − | 0.923287i | \(-0.374508\pi\) | ||||
0.384111 | + | 0.923287i | \(0.374508\pi\) | |||||||
\(90\) | −0.361105 | + | 2.97819i | −0.0380638 | + | 0.313929i | ||||
\(91\) | − | 10.3760i | − | 1.08770i | ||||||
\(92\) | −0.142267 | −0.0148324 | ||||||||
\(93\) | 9.51724 | + | 1.55631i | 0.986892 | + | 0.161382i | ||||
\(94\) | 4.88227 | 0.503567 | ||||||||
\(95\) | 2.75989i | 0.283159i | ||||||||
\(96\) | 1.69702 | − | 0.346599i | 0.173201 | − | 0.0353746i | ||||
\(97\) | 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 | ||||
\(99\) | 0.290976 | − | 2.39980i | 0.0292442 | − | 0.241189i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | − | 3.07118i | − | 0.305594i | −0.988258 | − | 0.152797i | \(-0.951172\pi\) | ||
0.988258 | − | 0.152797i | \(-0.0488281\pi\) | |||||||
\(102\) | −4.46393 | − | 5.03787i | −0.441995 | − | 0.498824i | ||||
\(103\) | −0.368713 | + | 0.638630i | −0.0363304 | + | 0.0629261i | −0.883619 | − | 0.468207i | \(-0.844900\pi\) |
0.847288 | + | 0.531133i | \(0.178234\pi\) | |||||||
\(104\) | −1.51045 | + | 2.61618i | −0.148112 | + | 0.256538i | ||||
\(105\) | −5.82877 | + | 1.19047i | −0.568830 | + | 0.116178i | ||||
\(106\) | −11.7711 | − | 6.79605i | −1.14331 | − | 0.660090i | ||||
\(107\) | 1.85660 | − | 1.07191i | 0.179484 | − | 0.103625i | −0.407566 | − | 0.913176i | \(-0.633622\pi\) |
0.587050 | + | 0.809551i | \(0.300289\pi\) | |||||||
\(108\) | −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 | ||||
\(111\) | 12.3160 | + | 13.8996i | 1.16899 | + | 1.31929i | ||||
\(112\) | 1.71736 | + | 2.97455i | 0.162275 | + | 0.281069i | ||||
\(113\) | 13.2560 | + | 7.65337i | 1.24702 | + | 0.719968i | 0.970514 | − | 0.241043i | \(-0.0774896\pi\) |
0.276508 | + | 0.961012i | \(0.410823\pi\) | |||||||
\(114\) | −3.17021 | − | 3.57782i | −0.296918 | − | 0.335093i | ||||
\(115\) | −0.123207 | − | 0.0711336i | −0.0114891 | − | 0.00663324i | ||||
\(116\) | 7.20137 | 0.668631 | ||||||||
\(117\) | 8.99684 | + | 1.09086i | 0.831758 | + | 0.100850i | ||||
\(118\) | −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 | −0.0432935 | − | 0.999062i | \(-0.513785\pi\) |
0.843567 | + | 0.537024i | \(0.180452\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0.943944 | + | 1.06531i | 0.0831096 | + | 0.0937953i | ||||
\(130\) | −2.61618 | + | 1.51045i | −0.229455 | + | 0.132476i | ||||
\(131\) | −14.0976 | + | 8.13923i | −1.23171 | + | 0.711128i | −0.967386 | − | 0.253307i | \(-0.918482\pi\) |
−0.264323 | + | 0.964434i | \(0.585148\pi\) | |||||||
\(132\) | −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 | ||||
\(135\) | −0.419435 | − | 5.17920i | −0.0360992 | − | 0.445754i | ||||
\(136\) | −3.36552 | + | 1.94308i | −0.288591 | + | 0.166618i | ||||
\(137\) | −3.25803 | + | 5.64307i | −0.278352 | + | 0.482120i | −0.970975 | − | 0.239180i | \(-0.923121\pi\) |
0.692623 | + | 0.721299i | \(0.256455\pi\) | |||||||
\(138\) | 0.241430 | − | 0.0493096i | 0.0205519 | − | 0.00419751i | ||||
\(139\) | − | 16.3232i | − | 1.38452i | −0.721648 | − | 0.692260i | \(-0.756615\pi\) | ||
0.721648 | − | 0.692260i | \(-0.243385\pi\) | |||||||
\(140\) | 3.43472i | 0.290286i | ||||||||
\(141\) | −8.28529 | + | 1.69219i | −0.697747 | + | 0.142508i | ||||
\(142\) | 5.67926 | − | 9.83676i | 0.476593 | − | 0.825483i | ||||
\(143\) | 2.10810 | − | 1.21711i | 0.176288 | − | 0.101780i | ||||
\(144\) | −2.75974 | + | 1.17637i | −0.229978 | + | 0.0980307i | ||||
\(145\) | 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 | \(-0.626080\pi\) |
0.606067 | + | 0.795414i | \(0.292747\pi\) | |||||||
\(150\) | 1.14867 | + | 1.29636i | 0.0937887 | + | 0.105847i | ||||
\(151\) | − | 19.8572i | − | 1.61596i | −0.589212 | − | 0.807979i | \(-0.700562\pi\) | ||
0.589212 | − | 0.807979i | \(-0.299438\pi\) | |||||||
\(152\) | −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 | ||||
\(162\) | 6.49294 | + | 6.23232i | 0.510133 | + | 0.489657i | ||||
\(163\) | 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 | ||||
\(165\) | −0.925592 | − | 1.04460i | −0.0720572 | − | 0.0813219i | ||||
\(166\) | −1.61815 | − | 0.934238i | −0.125593 | − | 0.0725109i | ||||
\(167\) | −11.5431 | − | 19.9933i | −0.893235 | − | 1.54713i | −0.835974 | − | 0.548768i | \(-0.815097\pi\) |
−0.0572603 | − | 0.998359i | \(-0.518236\pi\) | |||||||
\(168\) | −3.94536 | − | 4.45263i | −0.304391 | − | 0.343528i | ||||
\(169\) | −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 | \(-0.160509\pi\) |
0.0193444 | + | 0.999813i | \(0.493842\pi\) | |||||||
\(174\) | −12.2209 | + | 2.49599i | −0.926461 | + | 0.189220i | ||||
\(175\) | −1.71736 | + | 2.97455i | −0.129820 | + | 0.224855i | ||||
\(176\) | −0.402897 | + | 0.697837i | −0.0303695 | + | 0.0526015i | ||||
\(177\) | 15.3802 | + | 17.3577i | 1.15604 | + | 1.30468i | ||||
\(178\) | 7.24740i | 0.543215i | ||||||||
\(179\) | 1.61838 | + | 2.80311i | 0.120963 | + | 0.209514i | 0.920148 | − | 0.391571i | \(-0.128068\pi\) |
−0.799185 | + | 0.601086i | \(0.794735\pi\) | |||||||
\(180\) | −2.97819 | − | 0.361105i | −0.221981 | − | 0.0269152i | ||||
\(181\) | −14.2426 | − | 8.22298i | −1.05865 | − | 0.611209i | −0.133588 | − | 0.991037i | \(-0.542650\pi\) |
−0.925057 | + | 0.379827i | \(0.875983\pi\) | |||||||
\(182\) | 10.3760 | 0.769118 | ||||||||
\(183\) | −18.0341 | + | 3.68328i | −1.33312 | + | 0.272276i | ||||
\(184\) | − | 0.142267i | − | 0.0104881i | ||||||
\(185\) | 10.7220 | 0.788295 | ||||||||
\(186\) | −1.55631 | + | 9.51724i | −0.114114 | + | 0.697838i | ||||
\(187\) | 3.13144 | 0.228994 | ||||||||
\(188\) | 4.88227i | 0.356076i | ||||||||
\(189\) | −7.64690 | + | 16.1261i | −0.556230 | + | 1.17300i | ||||
\(190\) | −2.75989 | −0.200224 | ||||||||
\(191\) | 11.6288 | + | 6.71391i | 0.841433 | + | 0.485802i | 0.857751 | − | 0.514065i | \(-0.171861\pi\) |
−0.0163179 | + | 0.999867i | \(0.505194\pi\) | |||||||
\(192\) | 0.346599 | + | 1.69702i | 0.0250136 | + | 0.122472i | ||||
\(193\) | 7.75886 | + | 13.4387i | 0.558495 | + | 0.967341i | 0.997622 | + | 0.0689165i | \(0.0219542\pi\) |
−0.439128 | + | 0.898425i | \(0.644712\pi\) | |||||||
\(194\) | 16.1867i | 1.16214i | ||||||||
\(195\) | 3.91619 | − | 3.47003i | 0.280444 | − | 0.248494i | ||||
\(196\) | 2.39863 | − | 4.15456i | 0.171331 | − | 0.296754i | ||||
\(197\) | −2.76263 | + | 4.78502i | −0.196829 | + | 0.340918i | −0.947499 | − | 0.319760i | \(-0.896398\pi\) |
0.750669 | + | 0.660678i | \(0.229731\pi\) | |||||||
\(198\) | 2.39980 | + | 0.290976i | 0.170547 | + | 0.0206787i | ||||
\(199\) | −13.6901 | − | 7.90400i | −0.970467 | − | 0.560299i | −0.0710885 | − | 0.997470i | \(-0.522647\pi\) |
−0.899379 | + | 0.437171i | \(0.855981\pi\) | |||||||
\(200\) | 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 | ||||
\(204\) | 5.03787 | − | 4.46393i | 0.352722 | − | 0.312537i | ||||
\(205\) | −0.366287 | − | 0.634427i | −0.0255826 | − | 0.0443103i | ||||
\(206\) | −0.638630 | − | 0.368713i | −0.0444954 | − | 0.0256895i | ||||
\(207\) | −0.392620 | + | 0.167359i | −0.0272890 | + | 0.0116322i | ||||
\(208\) | −2.61618 | − | 1.51045i | −0.181400 | − | 0.104731i | ||||
\(209\) | 2.22390 | 0.153831 | ||||||||
\(210\) | −1.19047 | − | 5.82877i | −0.0821501 | − | 0.402224i | ||||
\(211\) | −8.66050 | − | 15.0004i | −0.596214 | − | 1.03267i | −0.993374 | − | 0.114923i | \(-0.963338\pi\) |
0.397161 | − | 0.917749i | \(-0.369996\pi\) | |||||||
\(212\) | 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 | ||||||||
\(222\) | −13.8996 | + | 12.3160i | −0.932877 | + | 0.826598i | ||||
\(223\) | 0.150848 | − | 0.0870923i | 0.0101016 | − | 0.00583213i | −0.494941 | − | 0.868927i | \(-0.664810\pi\) |
0.505042 | + | 0.863095i | \(0.331477\pi\) | |||||||
\(224\) | −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 | \(-0.0617811\pi\) |
0.323577 | + | 0.946202i | \(0.395114\pi\) | |||||||
\(228\) | 3.57782 | − | 3.17021i | 0.236947 | − | 0.209952i | ||||
\(229\) | 4.32320 | − | 2.49600i | 0.285685 | − | 0.164940i | −0.350309 | − | 0.936634i | \(-0.613924\pi\) |
0.635994 | + | 0.771694i | \(0.280590\pi\) | |||||||
\(230\) | 0.0711336 | − | 0.123207i | 0.00469041 | − | 0.00812403i | ||||
\(231\) | 0.959271 | + | 4.69678i | 0.0631154 | + | 0.309026i | ||||
\(232\) | 7.20137i | 0.472793i | ||||||||
\(233\) | 2.46821i | 0.161698i | 0.996726 | + | 0.0808491i | \(0.0257632\pi\) | ||||
−0.996726 | + | 0.0808491i | \(0.974237\pi\) | |||||||
\(234\) | −1.09086 | + | 8.99684i | −0.0713120 | + | 0.588142i | ||||
\(235\) | −2.44113 | + | 4.22817i | −0.159242 | + | 0.275815i | ||||
\(236\) | 11.5957 | − | 6.69476i | 0.754814 | − | 0.435792i | ||||
\(237\) | −3.73672 | − | 4.21717i | −0.242726 | − | 0.273935i | ||||
\(238\) | 11.5596 | + | 6.67393i | 0.749297 | + | 0.432607i | ||||
\(239\) | 6.74918 | − | 11.6899i | 0.436568 | − | 0.756158i | −0.560854 | − | 0.827915i | \(-0.689527\pi\) |
0.997422 | + | 0.0717566i | \(0.0228605\pi\) | |||||||
\(240\) | −0.548346 | + | 1.64296i | −0.0353956 | + | 0.106053i | ||||
\(241\) | −6.84964 | + | 3.95464i | −0.441224 | + | 0.254741i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.262892 | + | 0.964825i | \(0.415324\pi\) | |||||||
\(242\) | −8.96397 | + | 5.17535i | −0.576226 | + | 0.332684i | ||||
\(243\) | −13.1787 | − | 8.32591i | −0.845417 | − | 0.534107i | ||||
\(244\) | 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 | 0.992675 | + | 0.120813i | \(0.0385501\pi\) |
−0.391711 | + | 0.920089i | \(0.628117\pi\) | |||||||
\(252\) | 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 | ||||
\(255\) | 6.59489 | − | 1.34694i | 0.412988 | − | 0.0843486i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.10579 | + | 1.79313i | 0.193734 | + | 0.111852i | 0.593729 | − | 0.804665i | \(-0.297655\pi\) |
−0.399995 | + | 0.916517i | \(0.630988\pi\) | |||||||
\(258\) | −1.06531 | + | 0.943944i | −0.0663233 | + | 0.0587674i | ||||
\(259\) | −31.8931 | − | 18.4135i | −1.98174 | − | 1.14416i | ||||
\(260\) | −1.51045 | − | 2.61618i | −0.0936744 | − | 0.162249i | ||||
\(261\) | 19.8739 | − | 8.47147i | 1.23016 | − | 0.524371i | ||||
\(262\) | −8.13923 | − | 14.0976i | −0.502843 | − | 0.870950i | ||||
\(263\) | −16.7103 | −1.03040 | −0.515200 | − | 0.857070i | \(-0.672282\pi\) | ||||
−0.515200 | + | 0.857070i | \(0.672282\pi\) | |||||||
\(264\) | 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 | ||||
\(267\) | −2.51194 | − | 12.2990i | −0.153728 | − | 0.752684i | ||||
\(268\) | 0.342847 | − | 0.593829i | 0.0209427 | − | 0.0362739i | ||||
\(269\) | 9.69936 | − | 16.7998i | 0.591381 | − | 1.02430i | −0.402666 | − | 0.915347i | \(-0.631916\pi\) |
0.994047 | − | 0.108954i | \(-0.0347502\pi\) | |||||||
\(270\) | 5.17920 | − | 0.419435i | 0.315196 | − | 0.0255260i | ||||
\(271\) | 4.62368i | 0.280869i | 0.990090 | + | 0.140434i | \(0.0448499\pi\) | ||||
−0.990090 | + | 0.140434i | \(0.955150\pi\) | |||||||
\(272\) | −1.94308 | − | 3.36552i | −0.117817 | − | 0.204064i | ||||
\(273\) | −17.6082 | + | 3.59630i | −1.06570 | + | 0.217658i | ||||
\(274\) | −5.64307 | − | 3.25803i | −0.340910 | − | 0.196825i | ||||
\(275\) | −0.805793 | −0.0485911 | ||||||||
\(276\) | 0.0493096 | + | 0.241430i | 0.00296809 | + | 0.0145324i | ||||
\(277\) | 23.9855i | 1.44115i | 0.693377 | + | 0.720575i | \(0.256122\pi\) | ||||
−0.693377 | + | 0.720575i | \(0.743878\pi\) | |||||||
\(278\) | 16.3232 | 0.979003 | ||||||||
\(279\) | −0.657583 | − | 16.6903i | −0.0393685 | − | 0.999225i | ||||
\(280\) | −3.43472 | −0.205263 | ||||||||
\(281\) | 9.55099i | 0.569764i | 0.958563 | + | 0.284882i | \(0.0919544\pi\) | ||||
−0.958563 | + | 0.284882i | \(0.908046\pi\) | |||||||
\(282\) | −1.69219 | − | 8.28529i | −0.100768 | − | 0.493382i | ||||
\(283\) | 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 | ||||
\(285\) | 4.68359 | − | 0.956575i | 0.277432 | − | 0.0566626i | ||||
\(286\) | 1.21711 | + | 2.10810i | 0.0719695 | + | 0.124655i | ||||
\(287\) | 2.51618i | 0.148525i | ||||||||
\(288\) | −1.17637 | − | 2.75974i | −0.0693182 | − | 0.162619i | ||||
\(289\) | 0.948867 | − | 1.64349i | 0.0558157 | − | 0.0966757i | ||||
\(290\) | −3.60069 | + | 6.23657i | −0.211440 | + | 0.366224i | ||||
\(291\) | −5.61029 | − | 27.4691i | −0.328881 | − | 1.61027i | ||||
\(292\) | −0.721718 | − | 0.416684i | −0.0422354 | − | 0.0243846i | ||||
\(293\) | −14.6795 | + | 8.47522i | −0.857586 | + | 0.495128i | −0.863203 | − | 0.504857i | \(-0.831545\pi\) |
0.00561696 | + | 0.999984i | \(0.498212\pi\) | |||||||
\(294\) | −2.63056 | + | 7.88172i | −0.153417 | + | 0.459671i | ||||
\(295\) | 13.3895 | 0.779568 | ||||||||
\(296\) | 5.36099 | + | 9.28550i | 0.311601 | + | 0.539709i | ||||
\(297\) | −4.17336 | + | 0.337978i | −0.242163 | + | 0.0196115i | ||||
\(298\) | 1.55221 | + | 2.68851i | 0.0899171 | + | 0.155741i | ||||
\(299\) | −0.372197 | − | 0.214888i | −0.0215247 | − | 0.0124273i | ||||
\(300\) | −1.29636 | + | 1.14867i | −0.0748454 | + | 0.0663186i | ||||
\(301\) | −2.44440 | − | 1.41127i | −0.140893 | − | 0.0813444i | ||||
\(302\) | 19.8572 | 1.14265 | ||||||||
\(303\) | −5.21185 | + | 1.06447i | −0.299413 | + | 0.0611521i | ||||
\(304\) | −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 | 0.990641 | + | 0.136493i | \(0.0435831\pi\) |
−0.377114 | + | 0.926167i | \(0.623084\pi\) | |||||||
\(308\) | 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 | −0.820752 | − | 0.571284i | \(-0.806445\pi\) |
0.0843707 | + | 0.996434i | \(0.473112\pi\) | |||||||
\(314\) | 1.70330i | 0.0961226i | ||||||||
\(315\) | 4.04049 | + | 9.47892i | 0.227656 | + | 0.534076i | ||||
\(316\) | −2.81725 | + | 1.62654i | −0.158483 | + | 0.0915001i | ||||
\(317\) | 8.13168 | − | 4.69483i | 0.456721 | − | 0.263688i | −0.253944 | − | 0.967219i | \(-0.581728\pi\) |
0.710664 | + | 0.703531i | \(0.248394\pi\) | |||||||
\(318\) | −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 | ||||
\(321\) | −2.46254 | − | 2.77915i | −0.137445 | − | 0.155117i | ||||
\(322\) | −0.423181 | + | 0.244324i | −0.0235829 | + | 0.0136156i | ||||
\(323\) | −5.36270 | + | 9.28847i | −0.298389 | + | 0.516824i | ||||
\(324\) | −6.23232 | + | 6.49294i | −0.346240 | + | 0.360719i | ||||
\(325\) | − | 3.02091i | − | 0.167570i | ||||||
\(326\) | 2.96548i | 0.164243i | ||||||||
\(327\) | 4.95230 | + | 24.2474i | 0.273863 | + | 1.34089i | ||||
\(328\) | 0.366287 | − | 0.634427i | 0.0202248 | − | 0.0350304i | ||||
\(329\) | 14.5225 | − | 8.38460i | 0.800654 | − | 0.462258i | ||||
\(330\) | 1.04460 | − | 0.925592i | 0.0575033 | − | 0.0509522i | ||||
\(331\) | 19.1463 | + | 11.0541i | 1.05238 | + | 0.607591i | 0.923314 | − | 0.384045i | \(-0.125469\pi\) |
0.129064 | + | 0.991636i | \(0.458803\pi\) | |||||||
\(332\) | 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 | ||||
\(336\) | 4.45263 | − | 3.94536i | 0.242911 | − | 0.215237i | ||||
\(337\) | 1.64170i | 0.0894289i | 0.999000 | + | 0.0447145i | \(0.0142378\pi\) | ||||
−0.999000 | + | 0.0447145i | \(0.985762\pi\) | |||||||
\(338\) | 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 | \(-0.236433\pi\) |
−0.954020 | + | 0.299743i | \(0.903099\pi\) | |||||||
\(348\) | −2.49599 | − | 12.2209i | −0.133799 | − | 0.655107i | ||||
\(349\) | 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 | ||||
\(351\) | −1.26707 | − | 15.6459i | −0.0676315 | − | 0.835115i | ||||
\(352\) | −0.697837 | − | 0.402897i | −0.0371948 | − | 0.0214745i | ||||
\(353\) | 2.18441 | + | 3.78351i | 0.116265 | + | 0.201376i | 0.918285 | − | 0.395921i | \(-0.129575\pi\) |
−0.802020 | + | 0.597297i | \(0.796241\pi\) | |||||||
\(354\) | −17.3577 | + | 15.3802i | −0.922549 | + | 0.817447i | ||||
\(355\) | 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 | \(-0.277019\pi\) |
−0.339778 | + | 0.940506i | \(0.610352\pi\) | |||||||
\(360\) | 0.361105 | − | 2.97819i | 0.0190319 | − | 0.156964i | ||||
\(361\) | 5.69149 | − | 9.85796i | 0.299552 | − | 0.518840i | ||||
\(362\) | 8.22298 | − | 14.2426i | 0.432190 | − | 0.748576i | ||||
\(363\) | 13.4182 | − | 11.8896i | 0.704275 | − | 0.624040i | ||||
\(364\) | 10.3760i | 0.543848i | ||||||||
\(365\) | −0.416684 | − | 0.721718i | −0.0218103 | − | 0.0377765i | ||||
\(366\) | −3.68328 | − | 18.0341i | −0.192528 | − | 0.942657i | ||||
\(367\) | 12.6325 | + | 7.29338i | 0.659411 | + | 0.380711i | 0.792053 | − | 0.610453i | \(-0.209013\pi\) |
−0.132642 | + | 0.991164i | \(0.542346\pi\) | |||||||
\(368\) | 0.142267 | 0.00741619 | ||||||||
\(369\) | −2.18174 | − | 0.264536i | −0.113577 | − | 0.0137712i | ||||
\(370\) | 10.7220i | 0.557409i | ||||||||
\(371\) | −46.6850 | −2.42376 | ||||||||
\(372\) | −9.51724 | − | 1.55631i | −0.493446 | − | 0.0806908i | ||||
\(373\) | −21.3294 | −1.10439 | −0.552197 | − | 0.833714i | \(-0.686210\pi\) | ||||
−0.552197 | + | 0.833714i | \(0.686210\pi\) | |||||||
\(374\) | 3.13144i | 0.161923i | ||||||||
\(375\) | −1.69702 | + | 0.346599i | −0.0876336 | + | 0.0178983i | ||||
\(376\) | −4.88227 | −0.251784 | ||||||||
\(377\) | 18.8401 | + | 10.8773i | 0.970316 | + | 0.560212i | ||||
\(378\) | −16.1261 | − | 7.64690i | −0.829437 | − | 0.393314i | ||||
\(379\) | −15.6454 | − | 27.0986i | −0.803650 | − | 1.39196i | −0.917199 | − | 0.398430i | \(-0.869555\pi\) |
0.113549 | − | 0.993532i | \(-0.463778\pi\) | |||||||
\(380\) | − | 2.75989i | − | 0.141580i | ||||||
\(381\) | −11.9620 | − | 13.5001i | −0.612834 | − | 0.691629i | ||||
\(382\) | −6.71391 | + | 11.6288i | −0.343514 | + | 0.594983i | ||||
\(383\) | −11.8065 | + | 20.4494i | −0.603282 | + | 1.04491i | 0.389039 | + | 0.921221i | \(0.372807\pi\) |
−0.992320 | + | 0.123693i | \(0.960526\pi\) | |||||||
\(384\) | −1.69702 | + | 0.346599i | −0.0866006 | + | 0.0176873i | ||||
\(385\) | 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 | −0.983832 | − | 0.179096i | \(-0.942683\pi\) |
0.336814 | − | 0.941571i | \(-0.390651\pi\) | |||||||
\(390\) | 3.47003 | + | 3.91619i | 0.175712 | + | 0.198304i | ||||
\(391\) | −0.276437 | − | 0.478802i | −0.0139800 | − | 0.0242141i | ||||
\(392\) | 4.15456 | + | 2.39863i | 0.209837 | + | 0.121149i | ||||
\(393\) | 18.6986 | + | 21.1028i | 0.943220 | + | 1.06449i | ||||
\(394\) | −4.78502 | − | 2.76263i | −0.241066 | − | 0.139179i | ||||
\(395\) | −3.25308 | −0.163680 | ||||||||
\(396\) | −0.290976 | + | 2.39980i | −0.0146221 | + | 0.120595i | ||||
\(397\) | 10.1941 | + | 17.6566i | 0.511625 | + | 0.886161i | 0.999909 | + | 0.0134762i | \(0.00428974\pi\) |
−0.488284 | + | 0.872685i | \(0.662377\pi\) | |||||||
\(398\) | 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 | \(-0.557148\pi\) | ||||
−0.178572 | + | 0.983927i | \(0.557148\pi\) | |||||||
\(402\) | −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 | ||||||
\(408\) | 4.46393 | + | 5.03787i | 0.220997 | + | 0.249412i | ||||
\(409\) | −4.97254 | + | 2.87090i | −0.245876 | + | 0.141957i | −0.617875 | − | 0.786277i | \(-0.712006\pi\) |
0.371998 | + | 0.928233i | \(0.378673\pi\) | |||||||
\(410\) | 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 | ||||
\(414\) | −0.167359 | − | 0.392620i | −0.00822522 | − | 0.0192962i | ||||
\(415\) | 1.61815 | − | 0.934238i | 0.0794318 | − | 0.0458599i | ||||
\(416\) | 1.51045 | − | 2.61618i | 0.0740561 | − | 0.128269i | ||||
\(417\) | −27.7008 | + | 5.65762i | −1.35652 | + | 0.277055i | ||||
\(418\) | 2.22390i | 0.108775i | ||||||||
\(419\) | − | 9.62101i | − | 0.470017i | −0.971993 | − | 0.235008i | \(-0.924488\pi\) | ||
0.971993 | − | 0.235008i | \(-0.0755118\pi\) | |||||||
\(420\) | 5.82877 | − | 1.19047i | 0.284415 | − | 0.0580889i | ||||
\(421\) | −17.3075 | + | 29.9775i | −0.843516 | + | 1.46101i | 0.0433873 | + | 0.999058i | \(0.486185\pi\) |
−0.886904 | + | 0.461955i | \(0.847148\pi\) | |||||||
\(422\) | 15.0004 | − | 8.66050i | 0.730209 | − | 0.421587i | ||||
\(423\) | 5.74334 | + | 13.4738i | 0.279251 | + | 0.655118i | ||||
\(424\) | 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 | ||||
\(429\) | −2.79613 | − | 3.15564i | −0.134998 | − | 0.152356i | ||||
\(430\) | 0.821770i | 0.0396293i | ||||||||
\(431\) | −32.5014 | + | 18.7647i | −1.56554 | + | 0.903864i | −0.568860 | + | 0.822434i | \(0.692615\pi\) |
−0.996679 | + | 0.0814300i | \(0.974051\pi\) | |||||||
\(432\) | 2.95284 | + | 4.27560i | 0.142069 | + | 0.205710i | ||||
\(433\) | 0.00668506i | 0.000321263i | 1.00000 | 0.000160632i | \(5.11307e-5\pi\) | |||||
−1.00000 | 0.000160632i | \(0.999949\pi\) | ||||||||
\(434\) | −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 | −0.999998 | − | 0.00202667i | \(-0.999355\pi\) |
0.501754 | + | 0.865010i | \(0.332688\pi\) | |||||||
\(440\) | −0.402897 | − | 0.697837i | −0.0192073 | − | 0.0332681i | ||||
\(441\) | 1.73232 | − | 14.2872i | 0.0824912 | − | 0.680341i | ||||
\(442\) | −11.7397 | −0.558403 | ||||||||
\(443\) | −23.3341 | − | 13.4719i | −1.10864 | − | 0.640071i | −0.170160 | − | 0.985416i | \(-0.554429\pi\) |
−0.938476 | + | 0.345345i | \(0.887762\pi\) | |||||||
\(444\) | −12.3160 | − | 13.8996i | −0.584493 | − | 0.659644i | ||||
\(445\) | −6.27643 | − | 3.62370i | −0.297531 | − | 0.171780i | ||||
\(446\) | 0.0870923 | + | 0.150848i | 0.00412394 | + | 0.00714288i | ||||
\(447\) | −3.56596 | − | 4.02445i | −0.168664 | − | 0.190350i | ||||
\(448\) | −1.71736 | − | 2.97455i | −0.0811375 | − | 0.140534i | ||||
\(449\) | 22.2082 | 1.04807 | 0.524035 | − | 0.851697i | \(-0.324426\pi\) | ||||
0.524035 | + | 0.851697i | \(0.324426\pi\) | |||||||
\(450\) | 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 | ||||
\(453\) | −33.6981 | + | 6.88249i | −1.58327 | + | 0.323367i | ||||
\(454\) | −11.3500 | + | 19.6588i | −0.532683 | + | 0.922633i | ||||
\(455\) | −5.18798 | + | 8.98585i | −0.243216 | + | 0.421263i | ||||
\(456\) | 3.17021 | + | 3.57782i | 0.148459 | + | 0.167547i | ||||
\(457\) | − | 35.8276i | − | 1.67594i | −0.545714 | − | 0.837972i | \(-0.683741\pi\) | ||
0.545714 | − | 0.837972i | \(-0.316259\pi\) | |||||||
\(458\) | 2.49600 | + | 4.32320i | 0.116630 | + | 0.202010i | ||||
\(459\) | 8.65199 | − | 18.2457i | 0.403840 | − | 0.851635i | ||||
\(460\) | 0.123207 | + | 0.0711336i | 0.00574455 | + | 0.00331662i | ||||
\(461\) | 11.0236 | 0.513419 | 0.256710 | − | 0.966489i | \(-0.417362\pi\) | ||||
0.256710 | + | 0.966489i | \(0.417362\pi\) | |||||||
\(462\) | −4.69678 | + | 0.959271i | −0.218514 | + | 0.0446293i | ||||
\(463\) | 6.77239i | 0.314740i | 0.987540 | + | 0.157370i | \(0.0503015\pi\) | ||||
−0.987540 | + | 0.157370i | \(0.949699\pi\) | |||||||
\(464\) | −7.20137 | −0.334315 | ||||||||
\(465\) | −7.46402 | − | 6.10642i | −0.346136 | − | 0.283179i | ||||
\(466\) | −2.46821 | −0.114338 | ||||||||
\(467\) | − | 19.9229i | − | 0.921923i | −0.887420 | − | 0.460962i | \(-0.847505\pi\) | ||
0.887420 | − | 0.460962i | \(-0.152495\pi\) | |||||||
\(468\) | −8.99684 | − | 1.09086i | −0.415879 | − | 0.0504252i | ||||
\(469\) | −2.35516 | −0.108751 | ||||||||
\(470\) | −4.22817 | − | 2.44113i | −0.195031 | − | 0.112601i | ||||
\(471\) | −0.590361 | − | 2.89053i | −0.0272024 | − | 0.133188i | ||||
\(472\) | 6.69476 | + | 11.5957i | 0.308151 | + | 0.533734i | ||||
\(473\) | − | 0.662176i | − | 0.0304469i | ||||||
\(474\) | 4.21717 | − | 3.73672i | 0.193701 | − | 0.171633i | ||||
\(475\) | 1.37995 | − | 2.39014i | 0.0633163 | − | 0.109667i | ||||
\(476\) | −6.67393 | + | 11.5596i | −0.305899 | + | 0.529833i | ||||
\(477\) | 4.90817 | − | 40.4798i | 0.224730 | − | 1.85344i | ||||
\(478\) | 11.6899 | + | 6.74918i | 0.534684 | + | 0.308700i | ||||
\(479\) | −10.4505 | + | 6.03362i | −0.477497 | + | 0.275683i | −0.719373 | − | 0.694624i | \(-0.755571\pi\) |
0.241876 | + | 0.970307i | \(0.422237\pi\) | |||||||
\(480\) | −1.64296 | − | 0.548346i | −0.0749905 | − | 0.0250284i | ||||
\(481\) | 32.3901 | 1.47686 | ||||||||
\(482\) | −3.95464 | − | 6.84964i | −0.180129 | − | 0.311993i | ||||
\(483\) | 0.633463 | − | 0.561295i | 0.0288236 | − | 0.0255398i | ||||
\(484\) | −5.17535 | − | 8.96397i | −0.235243 | − | 0.407453i | ||||
\(485\) | −14.0181 | − | 8.09335i | −0.636528 | − | 0.367500i | ||||
\(486\) | 8.32591 | − | 13.1787i | 0.377671 | − | 0.597800i | ||||
\(487\) | −25.6391 | − | 14.8027i | −1.16182 | − | 0.670776i | −0.210079 | − | 0.977684i | \(-0.567372\pi\) |
−0.951739 | + | 0.306909i | \(0.900705\pi\) | |||||||
\(488\) | −10.6269 | −0.481058 | ||||||||
\(489\) | −1.02783 | − | 5.03247i | −0.0464802 | − | 0.227576i | ||||
\(490\) | 2.39863 | + | 4.15456i | 0.108359 | + | 0.187684i | ||||
\(491\) | −16.7692 | + | 29.0451i | −0.756784 | + | 1.31079i | 0.187698 | + | 0.982227i | \(0.439897\pi\) |
−0.944482 | + | 0.328562i | \(0.893436\pi\) | |||||||
\(492\) | −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 | 0.478195 | − | 0.878254i | \(-0.341291\pi\) |
0.999688 | + | 0.0249976i | \(0.00795783\pi\) | |||||||
\(500\) | 1.00000i | 0.0447214i | ||||||||
\(501\) | −29.9281 | + | 26.5186i | −1.33709 | + | 1.18476i | ||||
\(502\) | −16.4910 | + | 9.52107i | −0.736029 | + | 0.424946i | ||||
\(503\) | 23.7159 | − | 13.6924i | 1.05744 | − | 0.610513i | 0.132716 | − | 0.991154i | \(-0.457630\pi\) |
0.924723 | + | 0.380642i | \(0.124297\pi\) | |||||||
\(504\) | −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 | ||||
\(507\) | −5.02224 | + | 4.45008i | −0.223046 | + | 0.197635i | ||||
\(508\) | −9.01862 | + | 5.20690i | −0.400137 | + | 0.231019i | ||||
\(509\) | −8.81251 | + | 15.2637i | −0.390608 | + | 0.676552i | −0.992530 | − | 0.122002i | \(-0.961068\pi\) |
0.601922 | + | 0.798555i | \(0.294402\pi\) | |||||||
\(510\) | 1.34694 | + | 6.59489i | 0.0596435 | + | 0.292027i | ||||
\(511\) | 2.86238i | 0.126624i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 6.14451 | − | 12.9578i | 0.271287 | − | 0.572100i | ||||
\(514\) | −1.79313 | + | 3.10579i | −0.0790915 | + | 0.136991i | ||||
\(515\) | 0.638630 | − | 0.368713i | 0.0281414 | − | 0.0162474i | ||||
\(516\) | −0.943944 | − | 1.06531i | −0.0415548 | − | 0.0468977i | ||||
\(517\) | 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 | \(-0.586170\pi\) |
0.700776 | + | 0.713381i | \(0.252837\pi\) | |||||||
\(522\) | 8.47147 | + | 19.8739i | 0.370786 | + | 0.869857i | ||||
\(523\) | − | 39.2997i | − | 1.71846i | −0.511592 | − | 0.859229i | \(-0.670944\pi\) | ||
0.511592 | − | 0.859229i | \(-0.329056\pi\) | |||||||
\(524\) | 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 | ||||
\(534\) | 12.2990 | − | 2.51194i | 0.532228 | − | 0.108702i | ||||
\(535\) | −2.14381 | −0.0926850 | ||||||||
\(536\) | 0.593829 | + | 0.342847i | 0.0256495 | + | 0.0148087i | ||||
\(537\) | 4.19600 | − | 3.71797i | 0.181071 | − | 0.160442i | ||||
\(538\) | 16.7998 | + | 9.69936i | 0.724290 | + | 0.418169i | ||||
\(539\) | −1.93280 | − | 3.34771i | −0.0832517 | − | 0.144196i | ||||
\(540\) | 0.419435 | + | 5.17920i | 0.0180496 | + | 0.222877i | ||||
\(541\) | 0.345486 | + | 0.598400i | 0.0148536 | + | 0.0257272i | 0.873357 | − | 0.487081i | \(-0.161938\pi\) |
−0.858503 | + | 0.512808i | \(0.828605\pi\) | |||||||
\(542\) | −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 | ||||
\(546\) | −3.59630 | − | 17.6082i | −0.153907 | − | 0.753561i | ||||
\(547\) | −7.88536 | + | 13.6578i | −0.337153 | + | 0.583967i | −0.983896 | − | 0.178741i | \(-0.942797\pi\) |
0.646743 | + | 0.762708i | \(0.276131\pi\) | |||||||
\(548\) | 3.25803 | − | 5.64307i | 0.139176 | − | 0.241060i | ||||
\(549\) | 12.5012 | + | 29.3275i | 0.533537 | + | 1.25167i | ||||
\(550\) | − | 0.805793i | − | 0.0343591i | ||||||
\(551\) | 9.93751 | + | 17.2123i | 0.423352 | + | 0.733268i | ||||
\(552\) | −0.241430 | + | 0.0493096i | −0.0102759 | + | 0.00209876i | ||||
\(553\) | 9.67646 | + | 5.58671i | 0.411485 | + | 0.237571i | ||||
\(554\) | −23.9855 | −1.01905 | ||||||||
\(555\) | −3.71622 | − | 18.1954i | −0.157745 | − | 0.772351i | ||||
\(556\) | 16.3232i | 0.692260i | ||||||||
\(557\) | −30.0547 | −1.27346 | −0.636729 | − | 0.771088i | \(-0.719713\pi\) | ||||
−0.636729 | + | 0.771088i | \(0.719713\pi\) | |||||||
\(558\) | 16.6903 | − | 0.657583i | 0.706559 | − | 0.0278377i | ||||
\(559\) | 2.48249 | 0.104998 | ||||||||
\(560\) | − | 3.43472i | − | 0.145143i | ||||||
\(561\) | −1.08535 | − | 5.31412i | −0.0458237 | − | 0.224362i | ||||
\(562\) | −9.55099 | −0.402884 | ||||||||
\(563\) | −20.8367 | − | 12.0301i | −0.878162 | − | 0.507007i | −0.00811024 | − | 0.999967i | \(-0.502582\pi\) |
−0.870052 | + | 0.492960i | \(0.835915\pi\) | |||||||
\(564\) | 8.28529 | − | 1.69219i | 0.348874 | − | 0.0712539i | ||||
\(565\) | −7.65337 | − | 13.2560i | −0.321980 | − | 0.557685i | ||||
\(566\) | 12.9772i | 0.545473i | ||||||||
\(567\) | 30.0167 | + | 7.38764i | 1.26058 | + | 0.310252i | ||||
\(568\) | −5.67926 | + | 9.83676i | −0.238296 | + | 0.412741i | ||||
\(569\) | 1.61547 | − | 2.79807i | 0.0677239 | − | 0.117301i | −0.830175 | − | 0.557503i | \(-0.811760\pi\) |
0.897899 | + | 0.440201i | \(0.145093\pi\) | |||||||
\(570\) | 0.956575 | + | 4.68359i | 0.0400665 | + | 0.196174i | ||||
\(571\) | 16.0871 | + | 9.28786i | 0.673222 | + | 0.388685i | 0.797296 | − | 0.603588i | \(-0.206263\pi\) |
−0.124074 | + | 0.992273i | \(0.539596\pi\) | |||||||
\(572\) | −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 | ||||
\(576\) | 2.75974 | − | 1.17637i | 0.114989 | − | 0.0490153i | ||||
\(577\) | 11.7194 | + | 20.2986i | 0.487886 | + | 0.845043i | 0.999903 | − | 0.0139325i | \(-0.00443500\pi\) |
−0.512017 | + | 0.858975i | \(0.671102\pi\) | |||||||
\(578\) | 1.64349 | + | 0.948867i | 0.0683600 | + | 0.0394677i | ||||
\(579\) | 20.1166 | − | 17.8248i | 0.836016 | − | 0.740772i | ||||
\(580\) | −6.23657 | − | 3.60069i | −0.258960 | − | 0.149510i | ||||
\(581\) | −6.41768 | −0.266250 | ||||||||
\(582\) | 27.4691 | − | 5.61029i | 1.13863 | − | 0.232554i | ||||
\(583\) | −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 | \(-0.411698\pi\) | ||||
0.273866 | + | 0.961768i | \(0.411698\pi\) | |||||||
\(588\) | −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 | \(-0.199716\pi\) | |||||||
\(594\) | −0.337978 | − | 4.17336i | −0.0138674 | − | 0.171235i | ||||
\(595\) | −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 | \(-0.514713\pi\) |
−0.888203 | + | 0.459450i | \(0.848046\pi\) | |||||||
\(600\) | −1.14867 | − | 1.29636i | −0.0468943 | − | 0.0529237i | ||||
\(601\) | −32.0608 | + | 18.5103i | −1.30779 | + | 0.755051i | −0.981726 | − | 0.190298i | \(-0.939055\pi\) |
−0.326060 | + | 0.945349i | \(0.605721\pi\) | |||||||
\(602\) | 1.41127 | − | 2.44440i | 0.0575192 | − | 0.0996261i | ||||
\(603\) | 0.247607 | − | 2.04213i | 0.0100834 | − | 0.0831618i | ||||
\(604\) | 19.8572i | 0.807979i | ||||||||
\(605\) | − | 10.3507i | − | 0.420816i | ||||||
\(606\) | −1.06447 | − | 5.21185i | −0.0432410 | − | 0.211717i | ||||
\(607\) | −1.23539 | + | 2.13976i | −0.0501429 | + | 0.0868500i | −0.890007 | − | 0.455946i | \(-0.849301\pi\) |
0.839865 | + | 0.542796i | \(0.182634\pi\) | |||||||
\(608\) | 2.39014 | − | 1.37995i | 0.0969329 | − | 0.0559642i | ||||
\(609\) | −32.0651 | + | 28.4120i | −1.29934 | + | 1.15131i | ||||
\(610\) | −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 | −0.857271 | − | 0.514865i | \(-0.827842\pi\) |
0.0172504 | + | 0.999851i | \(0.494509\pi\) | |||||||
\(614\) | −18.6193 | + | 10.7499i | −0.751414 | + | 0.433829i | ||||
\(615\) | −0.949680 | + | 0.841487i | −0.0382948 | + | 0.0339320i | ||||
\(616\) | 2.76767i | 0.111513i | ||||||||
\(617\) | −20.4157 | + | 11.7870i | −0.821903 | + | 0.474526i | −0.851072 | − | 0.525048i | \(-0.824047\pi\) |
0.0291690 | + | 0.999574i | \(0.490714\pi\) | |||||||
\(618\) | −0.404364 | + | 1.21156i | −0.0162659 | + | 0.0487362i | ||||
\(619\) | − | 4.54430i | − | 0.182651i | −0.995821 | − | 0.0913255i | \(-0.970890\pi\) | ||
0.995821 | − | 0.0913255i | \(-0.0291104\pi\) | |||||||
\(620\) | −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 | ||||
\(627\) | −0.770802 | − | 3.77400i | −0.0307829 | − | 0.150719i | ||||
\(628\) | −1.70330 | −0.0679690 | ||||||||
\(629\) | 36.0850 | + | 20.8337i | 1.43880 | + | 0.830693i | ||||
\(630\) | −9.47892 | + | 4.04049i | −0.377649 | + | 0.160977i | ||||
\(631\) | −37.2561 | − | 21.5098i | −1.48314 | − | 0.856293i | −0.483326 | − | 0.875440i | \(-0.660572\pi\) |
−0.999817 | + | 0.0191471i | \(0.993905\pi\) | |||||||
\(632\) | −1.62654 | − | 2.81725i | −0.0647003 | − | 0.112064i | ||||
\(633\) | −22.4543 | + | 19.8962i | −0.892477 | + | 0.790801i | ||||
\(634\) | 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 | ||||
\(639\) | 33.8278 | + | 4.10161i | 1.33821 | + | 0.162257i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −16.6839 | + | 28.8974i | −0.658976 | + | 1.14138i | 0.321906 | + | 0.946772i | \(0.395677\pi\) |
−0.980881 | + | 0.194608i | \(0.937657\pi\) | |||||||
\(642\) | 2.77915 | − | 2.46254i | 0.109684 | − | 0.0971886i | ||||
\(643\) | 24.1854i | 0.953778i | 0.878963 | + | 0.476889i | \(0.158236\pi\) | ||||
−0.878963 | + | 0.476889i | \(0.841764\pi\) | |||||||
\(644\) | −0.244324 | − | 0.423181i | −0.00962770 | − | 0.0166757i | ||||
\(645\) | −0.284824 | − | 1.39456i | −0.0112149 | − | 0.0549107i | ||||
\(646\) | −9.28847 | − | 5.36270i | −0.365450 | − | 0.210993i | ||||
\(647\) | −23.9342 | −0.940952 | −0.470476 | − | 0.882413i | \(-0.655918\pi\) | ||||
−0.470476 | + | 0.882413i | \(0.655918\pi\) | |||||||
\(648\) | −6.49294 | − | 6.23232i | −0.255067 | − | 0.244828i | ||||
\(649\) | − | 10.7892i | − | 0.423513i | ||||||
\(650\) | 3.02091 | 0.118490 | ||||||||
\(651\) | 11.7152 | + | 30.9823i | 0.459155 | + | 1.21429i | ||||
\(652\) | −2.96548 | −0.116137 | ||||||||
\(653\) | 21.4538i | 0.839554i | 0.907627 | + | 0.419777i | \(0.137892\pi\) | ||||
−0.907627 | + | 0.419777i | \(0.862108\pi\) | |||||||
\(654\) | −24.2474 | + | 4.95230i | −0.948150 | + | 0.193650i | ||||
\(655\) | 16.2785 | 0.636052 | ||||||||
\(656\) | 0.634427 | + | 0.366287i | 0.0247702 | + | 0.0143011i | ||||
\(657\) | −2.48193 | − | 0.300933i | −0.0968292 | − | 0.0117405i | ||||
\(658\) | 8.38460 | + | 14.5225i | 0.326866 | + | 0.566148i | ||||
\(659\) | 9.57650i | 0.373047i | 0.982450 | + | 0.186524i | \(0.0597221\pi\) | ||||
−0.982450 | + | 0.186524i | \(0.940278\pi\) | |||||||
\(660\) | 0.925592 | + | 1.04460i | 0.0360286 | + | 0.0406610i | ||||
\(661\) | −14.2276 | + | 24.6429i | −0.553390 | + | 0.958499i | 0.444637 | + | 0.895711i | \(0.353333\pi\) |
−0.998027 | + | 0.0627884i | \(0.980001\pi\) | |||||||
\(662\) | −11.0541 | + | 19.1463i | −0.429632 | + | 0.744144i | ||||
\(663\) | 19.9226 | − | 4.06898i | 0.773728 | − | 0.158026i | ||||
\(664\) | 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 | ||||
\(669\) | −0.200081 | − | 0.225806i | −0.00773558 | − | 0.00873017i | ||||
\(670\) | 0.342847 | + | 0.593829i | 0.0132453 | + | 0.0229416i | ||||
\(671\) | 7.41586 | + | 4.28155i | 0.286286 | + | 0.165287i | ||||
\(672\) | 3.94536 | + | 4.45263i | 0.152196 | + | 0.171764i | ||||
\(673\) | −22.2226 | − | 12.8302i | −0.856618 | − | 0.494569i | 0.00626006 | − | 0.999980i | \(-0.498007\pi\) |
−0.862878 | + | 0.505412i | \(0.831341\pi\) | |||||||
\(674\) | −1.64170 | −0.0632358 | ||||||||
\(675\) | −2.22636 | + | 4.69503i | −0.0856925 | + | 0.180712i | ||||
\(676\) | 1.93705 | + | 3.35507i | 0.0745020 | + | 0.129041i | ||||
\(677\) | 23.9003 | − | 41.3965i | 0.918563 | − | 1.59100i | 0.116964 | − | 0.993136i | \(-0.462684\pi\) |
0.801599 | − | 0.597862i | \(-0.203983\pi\) | |||||||
\(678\) | 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 | ||||||||
\(687\) | −5.73417 | − | 6.47144i | −0.218772 | − | 0.246901i | ||||
\(688\) | −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 | 0.276895 | + | 0.960900i | \(0.410695\pi\) |
−0.970611 | + | 0.240652i | \(0.922639\pi\) | |||||||
\(692\) | −11.7703 | − | 6.79559i | −0.447440 | − | 0.258330i | ||||
\(693\) | 7.63804 | − | 3.25580i | 0.290145 | − | 0.123678i | ||||
\(694\) | 7.01513 | − | 4.05019i | 0.266291 | − | 0.153743i | ||||
\(695\) | −8.16162 | + | 14.1363i | −0.309588 | + | 0.536222i | ||||
\(696\) | 12.2209 | − | 2.49599i | 0.463230 | − | 0.0946101i | ||||
\(697\) | − | 2.84690i | − | 0.107834i | ||||||
\(698\) | 10.2078i | 0.386370i | ||||||||
\(699\) | 4.18860 | − | 0.855480i | 0.158428 | − | 0.0323572i | ||||
\(700\) | 1.71736 | − | 2.97455i | 0.0649100 | − | 0.112427i | ||||
\(701\) | 31.1895 | − | 18.0073i | 1.17801 | − | 0.680126i | 0.222459 | − | 0.974942i | \(-0.428592\pi\) |
0.955554 | + | 0.294816i | \(0.0952583\pi\) | |||||||
\(702\) | 15.6459 | − | 1.26707i | 0.590516 | − | 0.0478227i | ||||
\(703\) | 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 | ||||
\(708\) | −15.3802 | − | 17.3577i | −0.578022 | − | 0.652341i | ||||
\(709\) | 45.8983i | 1.72375i | 0.507122 | + | 0.861874i | \(0.330709\pi\) | ||||
−0.507122 | + | 0.861874i | \(0.669291\pi\) | |||||||
\(710\) | −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 | \(-0.113830\pi\) |
−0.771507 | + | 0.636221i | \(0.780497\pi\) | |||||||
\(720\) | 2.97819 | + | 0.361105i | 0.110991 | + | 0.0134576i | ||||
\(721\) | −2.53285 | −0.0943282 | ||||||||
\(722\) | 9.85796 | + | 5.69149i | 0.366875 | + | 0.211815i | ||||
\(723\) | 9.08518 | + | 10.2533i | 0.337881 | + | 0.381324i | ||||
\(724\) | 14.2426 | + | 8.22298i | 0.529323 | + | 0.305605i | ||||
\(725\) | −3.60069 | − | 6.23657i | −0.133726 | − | 0.231620i | ||||
\(726\) | 11.8896 | + | 13.4182i | 0.441263 | + | 0.497998i | ||||
\(727\) | −4.07367 | − | 7.05581i | −0.151084 | − | 0.261685i | 0.780542 | − | 0.625103i | \(-0.214943\pi\) |
−0.931626 | + | 0.363418i | \(0.881610\pi\) | |||||||
\(728\) | −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 | ||||
\(732\) | 18.0341 | − | 3.68328i | 0.666559 | − | 0.136138i | ||||
\(733\) | −8.01155 | + | 13.8764i | −0.295913 | + | 0.512537i | −0.975197 | − | 0.221339i | \(-0.928957\pi\) |
0.679284 | + | 0.733876i | \(0.262291\pi\) | |||||||
\(734\) | −7.29338 | + | 12.6325i | −0.269203 | + | 0.466274i | ||||
\(735\) | −5.51049 | − | 6.21899i | −0.203257 | − | 0.229391i | ||||
\(736\) | 0.142267i | 0.00524404i | ||||||||
\(737\) | −0.276264 | − | 0.478503i | −0.0101763 | − | 0.0176259i | ||||
\(738\) | 0.264536 | − | 2.18174i | 0.00973769 | − | 0.0803110i | ||||
\(739\) | 26.4217 | + | 15.2546i | 0.971938 | + | 0.561149i | 0.899827 | − | 0.436248i | \(-0.143693\pi\) |
0.0721115 | + | 0.997397i | \(0.477026\pi\) | |||||||
\(740\) | −10.7220 | −0.394148 | ||||||||
\(741\) | 14.1487 | − | 2.88973i | 0.519765 | − | 0.106157i | ||||
\(742\) | − | 46.6850i | − | 1.71386i | ||||||
\(743\) | −1.95284 | −0.0716426 | −0.0358213 | − | 0.999358i | \(-0.511405\pi\) | ||||
−0.0358213 | + | 0.999358i | \(0.511405\pi\) | |||||||
\(744\) | 1.55631 | − | 9.51724i | 0.0570570 | − | 0.348919i | ||||
\(745\) | −3.10442 | −0.113737 | ||||||||
\(746\) | − | 21.3294i | − | 0.780924i | ||||||
\(747\) | 0.674716 | − | 5.56467i | 0.0246865 | − | 0.203601i | ||||
\(748\) | −3.13144 | −0.114497 | ||||||||
\(749\) | 6.37688 | + | 3.68169i | 0.233006 | + | 0.134526i | ||||
\(750\) | −0.346599 | − | 1.69702i | −0.0126560 | − | 0.0619663i | ||||
\(751\) | 20.1487 | + | 34.8986i | 0.735238 | + | 1.27347i | 0.954619 | + | 0.297830i | \(0.0962628\pi\) |
−0.219381 | + | 0.975639i | \(0.570404\pi\) | |||||||
\(752\) | − | 4.88227i | − | 0.178038i | ||||||
\(753\) | 24.6855 | − | 21.8732i | 0.899590 | − | 0.797103i | ||||
\(754\) | −10.8773 | + | 18.8401i | −0.396130 | + | 0.686117i | ||||
\(755\) | −9.92861 | + | 17.1969i | −0.361339 | + | 0.625858i | ||||
\(756\) | 7.64690 | − | 16.1261i | 0.278115 | − | 0.586501i | ||||
\(757\) | −41.1044 | − | 23.7316i | −1.49396 | − | 0.862540i | −0.493987 | − | 0.869469i | \(-0.664461\pi\) |
−0.999976 | + | 0.00692880i | \(0.997794\pi\) | |||||||
\(758\) | 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 | \(-0.256711\pi\) |
−0.971167 | + | 0.238398i | \(0.923378\pi\) | |||||||
\(762\) | 13.5001 | − | 11.9620i | 0.489055 | − | 0.433339i | ||||
\(763\) | −24.5381 | − | 42.5012i | −0.888338 | − | 1.53865i | ||||
\(764\) | −11.6288 | − | 6.71391i | −0.420717 | − | 0.242901i | ||||
\(765\) | −4.57156 | − | 10.7248i | −0.165285 | − | 0.387756i | ||||
\(766\) | −20.4494 | − | 11.8065i | −0.738866 | − | 0.426585i | ||||
\(767\) | 40.4485 | 1.46051 | ||||||||
\(768\) | −0.346599 | − | 1.69702i | −0.0125068 | − | 0.0612359i | ||||
\(769\) | −3.29403 | − | 5.70542i | −0.118786 | − | 0.205743i | 0.800501 | − | 0.599331i | \(-0.204567\pi\) |
−0.919287 | + | 0.393589i | \(0.871233\pi\) | |||||||
\(770\) | −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 | \(-0.354436\pi\) | ||||
0.441529 | + | 0.897247i | \(0.354436\pi\) | |||||||
\(774\) | 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 | ||||||
\(780\) | −3.91619 | + | 3.47003i | −0.140222 | + | 0.124247i | ||||
\(781\) | 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 | ||||
\(786\) | −21.1028 | + | 18.6986i | −0.752710 | + | 0.666957i | ||||
\(787\) | 34.3021 | − | 19.8044i | 1.22274 | − | 0.705949i | 0.257238 | − | 0.966348i | \(-0.417187\pi\) |
0.965501 | + | 0.260399i | \(0.0838542\pi\) | |||||||
\(788\) | 2.76263 | − | 4.78502i | 0.0984147 | − | 0.170459i | ||||
\(789\) | 5.79176 | + | 28.3576i | 0.206192 | + | 1.00956i | ||||
\(790\) | − | 3.25308i | − | 0.115739i | ||||||
\(791\) | 52.5743i | 1.86933i | ||||||||
\(792\) | −2.39980 | − | 0.290976i | −0.0852733 | − | 0.0103394i | ||||
\(793\) | −16.0515 | + | 27.8020i | −0.570005 | + | 0.987278i | ||||
\(794\) | −17.6566 | + | 10.1941i | −0.626610 | + | 0.361774i | ||||
\(795\) | −15.6129 | − | 17.6203i | −0.553731 | − | 0.624926i | ||||
\(796\) | 13.6901 | + | 7.90400i | 0.485234 | + | 0.280150i | ||||
\(797\) | 4.95554 | − | 8.58324i | 0.175534 | − | 0.304034i | −0.764812 | − | 0.644254i | \(-0.777168\pi\) |
0.940346 | + | 0.340220i | \(0.110501\pi\) | |||||||
\(798\) | 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 | ||||
\(801\) | −20.0009 | + | 8.52561i | −0.706698 | + | 0.301237i | ||||
\(802\) | − | 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 | \(-0.131509\pi\) |
−0.805635 | + | 0.592412i | \(0.798176\pi\) | |||||||
\(810\) | −2.50689 | − | 8.64381i | −0.0880832 | − | 0.303713i | ||||
\(811\) | −0.848524 | + | 1.46969i | −0.0297957 | + | 0.0516077i | −0.880539 | − | 0.473974i | \(-0.842819\pi\) |
0.850743 | + | 0.525582i | \(0.176152\pi\) | |||||||
\(812\) | 12.3673 | + | 21.4208i | 0.434008 | + | 0.751724i | ||||
\(813\) | 7.84647 | − | 1.60256i | 0.275188 | − | 0.0562043i | ||||
\(814\) | 8.63969 | 0.302821 | ||||||||
\(815\) | −2.56818 | − | 1.48274i | −0.0899595 | − | 0.0519381i | ||||
\(816\) | −5.03787 | + | 4.46393i | −0.176361 | + | 0.156269i | ||||
\(817\) | 1.96414 | + | 1.13400i | 0.0687167 | + | 0.0396736i | ||||
\(818\) | −2.87090 | − | 4.97254i | −0.100379 | − | 0.173861i | ||||
\(819\) | 12.2060 | + | 28.6349i | 0.426511 | + | 1.00059i | ||||
\(820\) | 0.366287 | + | 0.634427i | 0.0127913 | + | 0.0221552i | ||||
\(821\) | 52.5361 | 1.83352 | 0.916761 | − | 0.399436i | \(-0.130794\pi\) | ||||
0.916761 | + | 0.399436i | \(0.130794\pi\) | |||||||
\(822\) | −3.57305 | + | 10.7056i | −0.124624 | + | 0.373401i | ||||
\(823\) | 20.3950 | − | 11.7751i | 0.710926 | − | 0.410453i | −0.100478 | − | 0.994939i | \(-0.532037\pi\) |
0.811404 | + | 0.584486i | \(0.198704\pi\) | |||||||
\(824\) | 0.638630 | + | 0.368713i | 0.0222477 | + | 0.0128447i | ||||
\(825\) | 0.279287 | + | 1.36745i | 0.00972352 | + | 0.0476083i | ||||
\(826\) | 22.9946 | − | 39.8278i | 0.800084 | − | 1.38579i | ||||
\(827\) | −4.50704 | + | 7.80642i | −0.156725 | + | 0.271456i | −0.933686 | − | 0.358093i | \(-0.883427\pi\) |
0.776961 | + | 0.629549i | \(0.216760\pi\) | |||||||
\(828\) | 0.392620 | − | 0.167359i | 0.0136445 | − | 0.00581611i | ||||
\(829\) | − | 3.12929i | − | 0.108685i | −0.998522 | − | 0.0543424i | \(-0.982694\pi\) | ||
0.998522 | − | 0.0543424i | \(-0.0173062\pi\) | |||||||
\(830\) | 0.934238 | + | 1.61815i | 0.0324279 | + | 0.0561667i | ||||
\(831\) | 40.7039 | − | 8.31335i | 1.41200 | − | 0.288387i | ||||
\(832\) | 2.61618 | + | 1.51045i | 0.0906999 | + | 0.0523656i | ||||
\(833\) | 18.6430 | 0.645941 | ||||||||
\(834\) | −5.65762 | − | 27.7008i | −0.195907 | − | 0.959202i | ||||
\(835\) | 23.0863i | 0.798933i | ||||||||
\(836\) | −2.22390 | −0.0769153 | ||||||||
\(837\) | −28.0959 | + | 6.90078i | −0.971136 | + | 0.238526i | ||||
\(838\) | 9.62101 | 0.332352 | ||||||||
\(839\) | − | 13.4727i | − | 0.465128i | −0.972581 | − | 0.232564i | \(-0.925289\pi\) | ||
0.972581 | − | 0.232564i | \(-0.0747115\pi\) | |||||||
\(840\) | 1.19047 | + | 5.82877i | 0.0410750 | + | 0.201112i | ||||
\(841\) | 22.8598 | 0.788268 | ||||||||
\(842\) | −29.9775 | − | 17.3075i | −1.03309 | − | 0.596456i | ||||
\(843\) | 16.2082 | − | 3.31036i | 0.558240 | − | 0.114015i | ||||
\(844\) | 8.66050 | + | 15.0004i | 0.298107 | + | 0.516336i | ||||
\(845\) | 3.87411i | 0.133273i | ||||||||
\(846\) | −13.4738 | + | 5.74334i | −0.463238 | + | 0.197460i | ||||
\(847\) | −17.7758 | + | 30.7887i | −0.610785 | + | 1.05791i | ||||
\(848\) | −6.79605 | + | 11.7711i | −0.233377 | + | 0.404221i | ||||
\(849\) | −4.49788 | − | 22.0226i | −0.154367 | − | 0.755812i | ||||
\(850\) | 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 | ||||
\(855\) | −3.24665 | − | 7.61658i | −0.111033 | − | 0.260482i | ||||
\(856\) | −1.07191 | − | 1.85660i | −0.0366370 | − | 0.0634571i | ||||
\(857\) | 6.41770 | + | 3.70526i | 0.219225 | + | 0.126569i | 0.605591 | − | 0.795776i | \(-0.292937\pi\) |
−0.386367 | + | 0.922345i | \(0.626270\pi\) | |||||||
\(858\) | 3.15564 | − | 2.79613i | 0.107732 | − | 0.0954583i | ||||
\(859\) | −27.1800 | − | 15.6924i | −0.927371 | − | 0.535418i | −0.0413920 | − | 0.999143i | \(-0.513179\pi\) |
−0.885979 | + | 0.463725i | \(0.846513\pi\) | |||||||
\(860\) | −0.821770 | −0.0280221 | ||||||||
\(861\) | 4.27000 | − | 0.872105i | 0.145521 | − | 0.0297213i | ||||
\(862\) | −18.7647 | − | 32.5014i | −0.639129 | − | 1.10700i | ||||
\(863\) | 21.9466 | − | 38.0126i | 0.747071 | − | 1.29396i | −0.202150 | − | 0.979355i | \(-0.564793\pi\) |
0.949221 | − | 0.314610i | \(-0.101874\pi\) | |||||||
\(864\) | −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 | ||||||||
\(873\) | −44.6710 | + | 19.0415i | −1.51189 | + | 0.644457i | ||||
\(874\) | 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 | −0.813252 | − | 0.581911i | \(-0.802305\pi\) |
0.910576 | + | 0.413342i | \(0.135639\pi\) | |||||||
\(878\) | −18.0815 | − | 10.4394i | −0.610222 | − | 0.352312i | ||||
\(879\) | 19.4705 | + | 21.9739i | 0.656724 | + | 0.741161i | ||||
\(880\) | 0.697837 | − | 0.402897i | 0.0235241 | − | 0.0135816i | ||||
\(881\) | 13.5530 | − | 23.4746i | 0.456614 | − | 0.790878i | −0.542166 | − | 0.840272i | \(-0.682395\pi\) |
0.998779 | + | 0.0493933i | \(0.0157288\pi\) | |||||||
\(882\) | 14.2872 | + | 1.73232i | 0.481074 | + | 0.0583301i | ||||
\(883\) | − | 35.9403i | − | 1.20949i | −0.796421 | − | 0.604743i | \(-0.793276\pi\) | ||
0.796421 | − | 0.604743i | \(-0.206724\pi\) | |||||||
\(884\) | − | 11.7397i | − | 0.394850i | ||||||
\(885\) | −4.64079 | − | 22.7223i | −0.155998 | − | 0.763800i | ||||
\(886\) | 13.4719 | − | 23.3341i | 0.452599 | − | 0.783924i | ||||
\(887\) | 25.1393 | − | 14.5142i | 0.844095 | − | 0.487339i | −0.0145588 | − | 0.999894i | \(-0.504634\pi\) |
0.858654 | + | 0.512555i | \(0.171301\pi\) | |||||||
\(888\) | 13.8996 | − | 12.3160i | 0.466439 | − | 0.413299i | ||||
\(889\) | 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 | ||||
\(894\) | 4.02445 | − | 3.56596i | 0.134598 | − | 0.119264i | ||||
\(895\) | − | 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 | ||||
\(906\) | −6.88249 | − | 33.6981i | −0.228655 | − | 1.11954i | ||||
\(907\) | 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 | ||||
\(909\) | 3.61284 | + | 8.47566i | 0.119830 | + | 0.281120i | ||||
\(910\) | −8.98585 | − | 5.18798i | −0.297878 | − | 0.171980i | ||||
\(911\) | −14.1404 | − | 24.4918i | −0.468491 | − | 0.811450i | 0.530860 | − | 0.847459i | \(-0.321869\pi\) |
−0.999351 | + | 0.0360090i | \(0.988535\pi\) | |||||||
\(912\) | −3.57782 | + | 3.17021i | −0.118473 | + | 0.104976i | ||||
\(913\) | −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 | ||||
\(918\) | 18.2457 | + | 8.65199i | 0.602197 | + | 0.285558i | ||||
\(919\) | −27.9372 | + | 48.3886i | −0.921563 | + | 1.59619i | −0.124565 | + | 0.992211i | \(0.539754\pi\) |
−0.796998 | + | 0.603983i | \(0.793580\pi\) | |||||||
\(920\) | −0.0711336 | + | 0.123207i | −0.00234520 | + | 0.00406201i | ||||
\(921\) | 27.8714 | − | 24.6961i | 0.918394 | − | 0.813765i | ||||
\(922\) | 11.0236i | 0.363042i | ||||||||
\(923\) | 17.1565 | + | 29.7160i | 0.564714 | + | 0.978113i | ||||
\(924\) | −0.959271 | − | 4.69678i | −0.0315577 | − | 0.154513i | ||||
\(925\) | −9.28550 | − | 5.36099i | −0.305306 | − | 0.176268i | ||||
\(926\) | −6.77239 | −0.222555 | ||||||||
\(927\) | 0.266288 | − | 2.19619i | 0.00874605 | − | 0.0721325i | ||||
\(928\) | − | 7.20137i | − | 0.236397i | ||||||
\(929\) | −49.7364 | −1.63180 | −0.815900 | − | 0.578193i | \(-0.803758\pi\) | ||||
−0.815900 | + | 0.578193i | \(0.803758\pi\) | |||||||
\(930\) | 6.10642 | − | 7.46402i | 0.200237 | − | 0.244755i | ||||
\(931\) | 13.2399 | 0.433922 | ||||||||
\(932\) | − | 2.46821i | − | 0.0808491i | ||||||
\(933\) | 0.848608 | − | 0.173320i | 0.0277822 | − | 0.00567423i | ||||
\(934\) | 19.9229 | 0.651898 | ||||||||
\(935\) | −2.71191 | − | 1.56572i | −0.0886889 | − | 0.0512046i | ||||
\(936\) | 1.09086 | − | 8.99684i | 0.0356560 | − | 0.294071i | ||||
\(937\) | −4.69392 | − | 8.13010i | −0.153344 | − | 0.265599i | 0.779111 | − | 0.626886i | \(-0.215671\pi\) |
−0.932455 | + | 0.361287i | \(0.882337\pi\) | |||||||
\(938\) | − | 2.35516i | − | 0.0768988i | ||||||
\(939\) | 17.2799 | + | 19.5016i | 0.563907 | + | 0.636411i | ||||
\(940\) | 2.44113 | − | 4.22817i | 0.0796210 | − | 0.137908i | ||||
\(941\) | −29.2702 | + | 50.6975i | −0.954182 | + | 1.65269i | −0.217952 | + | 0.975959i | \(0.569938\pi\) |
−0.736229 | + | 0.676732i | \(0.763396\pi\) | |||||||
\(942\) | 2.89053 | − | 0.590361i | 0.0941784 | − | 0.0192350i | ||||
\(943\) | 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 | \(-0.120827\pi\) |
−0.785305 | + | 0.619109i | \(0.787494\pi\) | |||||||
\(948\) | 3.73672 | + | 4.21717i | 0.121363 | + | 0.136967i | ||||
\(949\) | −1.25877 | − | 2.18025i | −0.0408613 | − | 0.0707738i | ||||
\(950\) | 2.39014 | + | 1.37995i | 0.0775463 | + | 0.0447714i | ||||
\(951\) | −10.7856 | − | 12.1724i | −0.349748 | − | 0.394717i | ||||
\(952\) | −11.5596 | − | 6.67393i | −0.374648 | − | 0.216303i | ||||
\(953\) | 35.8201 | 1.16033 | 0.580164 | − | 0.814500i | \(-0.302989\pi\) | ||||
0.580164 | + | 0.814500i | \(0.302989\pi\) | |||||||
\(954\) | 40.4798 | + | 4.90817i | 1.31058 | + | 0.158908i | ||||
\(955\) | −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 | ||||||
\(966\) | 0.561295 | + | 0.633463i | 0.0180594 | + | 0.0203813i | ||||
\(967\) | −17.9304 | + | 10.3521i | −0.576603 | + | 0.332902i | −0.759782 | − | 0.650178i | \(-0.774695\pi\) |
0.183179 | + | 0.983080i | \(0.441361\pi\) | |||||||
\(968\) | 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 | \(-0.556316\pi\) |
−0.940507 | + | 0.339775i | \(0.889649\pi\) | |||||||
\(972\) | 13.1787 | + | 8.32591i | 0.422708 | + | 0.267054i | ||||
\(973\) | 48.5543 | − | 28.0329i | 1.55658 | − | 0.898692i | ||||
\(974\) | 14.8027 | − | 25.6391i | 0.474310 | − | 0.821529i | ||||
\(975\) | −5.12654 | + | 1.04704i | −0.164181 | + | 0.0335322i | ||||
\(976\) | − | 10.6269i | − | 0.340160i | ||||||
\(977\) | 48.8853i | 1.56398i | 0.623292 | + | 0.781989i | \(0.285795\pi\) | ||||
−0.623292 | + | 0.781989i | \(0.714205\pi\) | |||||||
\(978\) | 5.03247 | − | 1.02783i | 0.160921 | − | 0.0328664i | ||||
\(979\) | −2.91995 | + | 5.05750i | −0.0933220 | + | 0.161638i | ||||
\(980\) | −4.15456 | + | 2.39863i | −0.132712 | + | 0.0766216i | ||||
\(981\) | 39.4319 | − | 16.8083i | 1.25896 | − | 0.536647i | ||||
\(982\) | −29.0451 | − | 16.7692i | −0.926868 | − | 0.535127i | ||||
\(983\) | −15.0761 | + | 26.1125i | −0.480851 | + | 0.832859i | −0.999759 | − | 0.0219715i | \(-0.993006\pi\) |
0.518907 | + | 0.854831i | \(0.326339\pi\) | |||||||
\(984\) | −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 | ||||
\(987\) | −19.2623 | − | 21.7389i | −0.613126 | − | 0.691958i | ||||
\(988\) | − | 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 | \(-0.722765\pi\) | ||
0.644094 | − | 0.764947i | \(-0.277235\pi\) | |||||||
\(992\) | −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 | −0.907003 | − | 0.421123i | \(-0.861636\pi\) |
0.818205 | + | 0.574926i | \(0.194969\pi\) | |||||||
\(998\) | 19.0603 | + | 33.0134i | 0.603343 | + | 1.04502i | ||||
\(999\) | −50.3400 | − | 23.8709i | −1.59269 | − | 0.755243i |
(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.161.15 | yes | 40 | |
3.2 | odd | 2 | inner | 930.2.o.e.161.8 | ✓ | 40 | |
31.26 | odd | 6 | inner | 930.2.o.e.491.18 | yes | 40 | |
93.26 | even | 6 | inner | 930.2.o.e.491.5 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.o.e.161.8 | ✓ | 40 | 3.2 | odd | 2 | inner | |
930.2.o.e.161.15 | yes | 40 | 1.1 | even | 1 | trivial | |
930.2.o.e.491.5 | yes | 40 | 93.26 | even | 6 | inner | |
930.2.o.e.491.18 | yes | 40 | 31.26 | odd | 6 | inner |