Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(107,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.be (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 107.3 | ||
Character | \(\chi\) | \(=\) | 756.107 |
Dual form | 756.2.be.c.431.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.04864 | + | 0.948869i | −0.741501 | + | 0.670952i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.199295 | − | 1.99005i | 0.0996476 | − | 0.995023i | ||||
\(5\) | −0.479813 | − | 0.277020i | −0.214579 | − | 0.123887i | 0.388859 | − | 0.921297i | \(-0.372869\pi\) |
−0.603438 | + | 0.797410i | \(0.706203\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.45883 | − | 0.976797i | 0.929352 | − | 0.369194i | ||||
\(8\) | 1.67930 | + | 2.27595i | 0.593723 | + | 0.804669i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.766008 | − | 0.164785i | 0.242233 | − | 0.0521096i | ||||
\(11\) | −2.96884 | − | 5.14218i | −0.895138 | − | 1.55042i | −0.833634 | − | 0.552317i | \(-0.813744\pi\) |
−0.0615040 | − | 0.998107i | \(-0.519590\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.20224 | 0.888143 | 0.444071 | − | 0.895991i | \(-0.353534\pi\) | ||||
0.444071 | + | 0.895991i | \(0.353534\pi\) | |||||||
\(14\) | −1.65158 | + | 3.35742i | −0.441404 | + | 0.897308i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.92056 | − | 0.793213i | −0.980141 | − | 0.198303i | ||||
\(17\) | −2.48564 | + | 1.43509i | −0.602856 | + | 0.348059i | −0.770164 | − | 0.637845i | \(-0.779826\pi\) |
0.167308 | + | 0.985905i | \(0.446493\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.43890 | − | 1.98545i | −0.788938 | − | 0.455494i | 0.0506503 | − | 0.998716i | \(-0.483871\pi\) |
−0.839589 | + | 0.543223i | \(0.817204\pi\) | |||||||
\(20\) | −0.646908 | + | 0.899641i | −0.144653 | + | 0.201166i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 7.99249 | + | 2.57526i | 1.70401 | + | 0.549047i | ||||
\(23\) | 0.145485 | − | 0.251987i | 0.0303357 | − | 0.0525430i | −0.850459 | − | 0.526041i | \(-0.823676\pi\) |
0.880795 | + | 0.473498i | \(0.157009\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.34652 | − | 4.06429i | −0.469304 | − | 0.812858i | ||||
\(26\) | −3.35800 | + | 3.03851i | −0.658559 | + | 0.595901i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.45384 | − | 5.08786i | −0.274749 | − | 0.961516i | ||||
\(29\) | 4.13555i | 0.767953i | 0.923343 | + | 0.383976i | \(0.125446\pi\) | ||||
−0.923343 | + | 0.383976i | \(0.874554\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.96048 | + | 3.44128i | −1.07053 | + | 0.618073i | −0.928327 | − | 0.371764i | \(-0.878753\pi\) |
−0.142206 | + | 0.989837i | \(0.545420\pi\) | |||||||
\(32\) | 4.86392 | − | 2.88830i | 0.859827 | − | 0.510585i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.24484 | − | 3.86344i | 0.213488 | − | 0.662574i | ||||
\(35\) | −1.45037 | − | 0.212467i | −0.245158 | − | 0.0359135i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.20253 | − | 2.08285i | 0.197695 | − | 0.342418i | −0.750086 | − | 0.661341i | \(-0.769988\pi\) |
0.947781 | + | 0.318923i | \(0.103321\pi\) | |||||||
\(38\) | 5.49011 | − | 1.18104i | 0.890613 | − | 0.191590i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.175268 | − | 1.55723i | −0.0277123 | − | 0.246220i | ||||
\(41\) | − | 2.27815i | − | 0.355787i | −0.984050 | − | 0.177893i | \(-0.943072\pi\) | ||
0.984050 | − | 0.177893i | \(-0.0569282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.31569i | − | 1.26813i | −0.773280 | − | 0.634065i | \(-0.781385\pi\) | ||
0.773280 | − | 0.634065i | \(-0.218615\pi\) | |||||||
\(44\) | −10.8248 | + | 4.88331i | −1.63191 | + | 0.736186i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0865415 | + | 0.402290i | 0.0127598 | + | 0.0593145i | ||||
\(47\) | 6.19284 | − | 10.7263i | 0.903318 | − | 1.56459i | 0.0801597 | − | 0.996782i | \(-0.474457\pi\) |
0.823159 | − | 0.567811i | \(-0.192210\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.09174 | − | 4.80356i | 0.727391 | − | 0.686223i | ||||
\(50\) | 6.31714 | + | 2.03544i | 0.893378 | + | 0.287855i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.638192 | − | 6.37261i | 0.0885013 | − | 0.883722i | ||||
\(53\) | −4.21439 | + | 2.43318i | −0.578892 | + | 0.334223i | −0.760693 | − | 0.649112i | \(-0.775141\pi\) |
0.181801 | + | 0.983335i | \(0.441807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.28971i | 0.443585i | ||||||||
\(56\) | 6.35227 | + | 3.95584i | 0.848858 | + | 0.528622i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.92410 | − | 4.33671i | −0.515259 | − | 0.569438i | ||||
\(59\) | −6.24666 | − | 10.8195i | −0.813246 | − | 1.40858i | −0.910581 | − | 0.413331i | \(-0.864365\pi\) |
0.0973349 | − | 0.995252i | \(-0.468968\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.305765 | + | 0.529601i | −0.0391492 | + | 0.0678085i | −0.884936 | − | 0.465712i | \(-0.845798\pi\) |
0.845787 | + | 0.533521i | \(0.179131\pi\) | |||||||
\(62\) | 2.98507 | − | 9.26438i | 0.379105 | − | 1.17658i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.35988 | + | 7.64402i | −0.294985 | + | 0.955502i | ||||
\(65\) | −1.53648 | − | 0.887087i | −0.190577 | − | 0.110030i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.70186 | − | 2.13727i | 0.452254 | − | 0.261109i | −0.256528 | − | 0.966537i | \(-0.582578\pi\) |
0.708782 | + | 0.705428i | \(0.249245\pi\) | |||||||
\(68\) | 2.36051 | + | 5.23254i | 0.286254 | + | 0.634539i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.72253 | − | 1.15341i | 0.205881 | − | 0.137859i | ||||
\(71\) | 7.00902 | 0.831818 | 0.415909 | − | 0.909406i | \(-0.363464\pi\) | ||||
0.415909 | + | 0.909406i | \(0.363464\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.28996 | + | 10.8945i | 0.736184 | + | 1.27511i | 0.954202 | + | 0.299164i | \(0.0967078\pi\) |
−0.218017 | + | 0.975945i | \(0.569959\pi\) | |||||||
\(74\) | 0.715324 | + | 3.32520i | 0.0831547 | + | 0.386547i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.63650 | + | 6.44788i | −0.531843 | + | 0.739623i | ||||
\(77\) | −12.3227 | − | 9.74381i | −1.40431 | − | 1.11041i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.20851 | − | 3.00714i | −0.586003 | − | 0.338329i | 0.177512 | − | 0.984119i | \(-0.443195\pi\) |
−0.763516 | + | 0.645789i | \(0.776528\pi\) | |||||||
\(80\) | 1.66140 | + | 1.46667i | 0.185750 | + | 0.163979i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.16166 | + | 2.38896i | 0.238716 | + | 0.263816i | ||||
\(83\) | −0.675423 | −0.0741373 | −0.0370686 | − | 0.999313i | \(-0.511802\pi\) | ||||
−0.0370686 | + | 0.999313i | \(0.511802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.59019 | 0.172480 | ||||||||
\(86\) | 7.89050 | + | 8.72017i | 0.850854 | + | 0.940320i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.71775 | − | 15.3922i | 0.716114 | − | 1.64081i | ||||
\(89\) | 11.1545 | + | 6.44005i | 1.18237 | + | 0.682644i | 0.956562 | − | 0.291527i | \(-0.0941635\pi\) |
0.225811 | + | 0.974171i | \(0.427497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.87379 | − | 3.12794i | 0.825397 | − | 0.327897i | ||||
\(92\) | −0.472472 | − | 0.339741i | −0.0492586 | − | 0.0354205i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.68380 | + | 17.1242i | 0.379955 | + | 1.76623i | ||||
\(95\) | 1.10002 | + | 1.90529i | 0.112860 | + | 0.195479i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.00803 | −0.305420 | −0.152710 | − | 0.988271i | \(-0.548800\pi\) | ||||
−0.152710 | + | 0.988271i | \(0.548800\pi\) | |||||||
\(98\) | −0.781450 | + | 9.86860i | −0.0789384 | + | 0.996879i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.55577 | + | 3.85969i | −0.855577 | + | 0.385969i | ||||
\(101\) | 15.3276 | − | 8.84940i | 1.52515 | − | 0.880548i | 0.525598 | − | 0.850733i | \(-0.323842\pi\) |
0.999555 | − | 0.0298150i | \(-0.00949180\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.01639 | + | 2.31886i | 0.395746 | + | 0.228484i | 0.684647 | − | 0.728875i | \(-0.259956\pi\) |
−0.288901 | + | 0.957359i | \(0.593290\pi\) | |||||||
\(104\) | 5.37754 | + | 7.28814i | 0.527311 | + | 0.714661i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.11062 | − | 6.55044i | 0.205001 | − | 0.636235i | ||||
\(107\) | 3.39483 | − | 5.88002i | 0.328191 | − | 0.568443i | −0.653962 | − | 0.756527i | \(-0.726895\pi\) |
0.982153 | + | 0.188084i | \(0.0602279\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.48848 | − | 11.2384i | −0.621483 | − | 1.07644i | −0.989210 | − | 0.146507i | \(-0.953197\pi\) |
0.367726 | − | 0.929934i | \(-0.380136\pi\) | |||||||
\(110\) | −3.12151 | − | 3.44973i | −0.297624 | − | 0.328919i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −10.4148 | + | 1.87921i | −0.984108 | + | 0.177569i | ||||
\(113\) | − | 12.0732i | − | 1.13575i | −0.823115 | − | 0.567875i | \(-0.807766\pi\) | ||
0.823115 | − | 0.567875i | \(-0.192234\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.139611 | + | 0.0806045i | −0.0130188 | + | 0.00751641i | ||||
\(116\) | 8.22994 | + | 0.824196i | 0.764130 | + | 0.0765247i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 16.8168 | + | 5.41854i | 1.54811 | + | 0.498817i | ||||
\(119\) | −4.70999 | + | 5.95660i | −0.431764 | + | 0.546041i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.1280 | + | 21.0063i | −1.10254 | + | 1.90966i | ||||
\(122\) | −0.181884 | − | 0.845493i | −0.0164670 | − | 0.0765473i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.66042 | + | 12.5475i | 0.508320 | + | 1.12679i | ||||
\(125\) | 5.37034i | 0.480338i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 19.0672i | 1.69194i | 0.533233 | + | 0.845968i | \(0.320977\pi\) | ||||
−0.533233 | + | 0.845968i | \(0.679023\pi\) | |||||||
\(128\) | −4.77850 | − | 10.2550i | −0.422364 | − | 0.906426i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.45294 | − | 0.527682i | 0.215137 | − | 0.0462808i | ||||
\(131\) | 0.945219 | − | 1.63717i | 0.0825842 | − | 0.143040i | −0.821775 | − | 0.569812i | \(-0.807016\pi\) |
0.904359 | + | 0.426772i | \(0.140349\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3951 | − | 1.52279i | −0.901367 | − | 0.132042i | ||||
\(134\) | −1.85393 | + | 5.75381i | −0.160155 | + | 0.497053i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.44032 | − | 3.24725i | −0.638002 | − | 0.278449i | ||||
\(137\) | −16.9097 | + | 9.76280i | −1.44469 | + | 0.834092i | −0.998158 | − | 0.0606749i | \(-0.980675\pi\) |
−0.446533 | + | 0.894767i | \(0.647341\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.3163i | 1.38393i | 0.721931 | + | 0.691965i | \(0.243255\pi\) | ||||
−0.721931 | + | 0.691965i | \(0.756745\pi\) | |||||||
\(140\) | −0.711872 | + | 2.84397i | −0.0601642 | + | 0.240359i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.34995 | + | 6.65064i | −0.616794 | + | 0.558110i | ||||
\(143\) | −9.50694 | − | 16.4665i | −0.795010 | − | 1.37700i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.14563 | − | 1.98429i | 0.0951395 | − | 0.164787i | ||||
\(146\) | −16.9334 | − | 5.45610i | −1.40142 | − | 0.451550i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.90530 | − | 2.80819i | −0.321014 | − | 0.230832i | ||||
\(149\) | −11.3984 | − | 6.58089i | −0.933797 | − | 0.539128i | −0.0457864 | − | 0.998951i | \(-0.514579\pi\) |
−0.888010 | + | 0.459823i | \(0.847913\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.8095 | − | 6.81819i | 0.961040 | − | 0.554856i | 0.0645468 | − | 0.997915i | \(-0.479440\pi\) |
0.896493 | + | 0.443058i | \(0.146106\pi\) | |||||||
\(152\) | −1.25618 | − | 11.1609i | −0.101889 | − | 0.905272i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 22.1677 | − | 1.47491i | 1.78633 | − | 0.118851i | ||||
\(155\) | 3.81322 | 0.306285 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.63724 | − | 9.76398i | −0.449900 | − | 0.779250i | 0.548479 | − | 0.836165i | \(-0.315207\pi\) |
−0.998379 | + | 0.0569142i | \(0.981874\pi\) | |||||||
\(158\) | 8.31524 | − | 1.78879i | 0.661525 | − | 0.142308i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.13389 | + | 0.0384429i | −0.247756 | + | 0.00303918i | ||||
\(161\) | 0.111583 | − | 0.761704i | 0.00879397 | − | 0.0600307i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4495 | − | 7.18771i | −0.975118 | − | 0.562985i | −0.0743256 | − | 0.997234i | \(-0.523680\pi\) |
−0.900793 | + | 0.434249i | \(0.857014\pi\) | |||||||
\(164\) | −4.53362 | − | 0.454024i | −0.354016 | − | 0.0354533i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.708276 | − | 0.640888i | 0.0549729 | − | 0.0497425i | ||||
\(167\) | −7.45155 | −0.576618 | −0.288309 | − | 0.957537i | \(-0.593093\pi\) | ||||
−0.288309 | + | 0.957537i | \(0.593093\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.74563 | −0.211203 | ||||||||
\(170\) | −1.66754 | + | 1.50888i | −0.127894 | + | 0.115726i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −16.5486 | − | 1.65728i | −1.26182 | − | 0.126366i | ||||
\(173\) | 12.9948 | + | 7.50257i | 0.987978 | + | 0.570410i | 0.904669 | − | 0.426114i | \(-0.140118\pi\) |
0.0833090 | + | 0.996524i | \(0.473451\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.73969 | − | 7.70135i | −0.736251 | − | 0.582167i | ||||
\(176\) | 7.56067 | + | 22.5151i | 0.569907 | + | 1.69714i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −17.8078 | + | 3.83085i | −1.33475 | + | 0.287135i | ||||
\(179\) | 3.35522 | + | 5.81141i | 0.250781 | + | 0.434365i | 0.963741 | − | 0.266839i | \(-0.0859793\pi\) |
−0.712960 | + | 0.701205i | \(0.752646\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.69773 | 0.423509 | 0.211755 | − | 0.977323i | \(-0.432082\pi\) | ||||
0.211755 | + | 0.977323i | \(0.432082\pi\) | |||||||
\(182\) | −5.28877 | + | 10.7513i | −0.392030 | + | 0.796938i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.817823 | − | 0.0920469i | 0.0602907 | − | 0.00678579i | ||||
\(185\) | −1.15398 | + | 0.666251i | −0.0848424 | + | 0.0489838i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7589 | + | 8.52107i | 1.07928 | + | 0.623122i | ||||
\(188\) | −20.1116 | − | 14.4617i | −1.46679 | − | 1.05473i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.96140 | − | 0.954191i | −0.214842 | − | 0.0692243i | ||||
\(191\) | −2.01847 | + | 3.49609i | −0.146051 | + | 0.252968i | −0.929765 | − | 0.368154i | \(-0.879990\pi\) |
0.783713 | + | 0.621123i | \(0.213323\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.24035 | + | 16.0047i | 0.665135 | + | 1.15205i | 0.979249 | + | 0.202662i | \(0.0649592\pi\) |
−0.314114 | + | 0.949385i | \(0.601707\pi\) | |||||||
\(194\) | 3.15435 | − | 2.85423i | 0.226469 | − | 0.204922i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.54455 | − | 11.0901i | −0.610325 | − | 0.792151i | ||||
\(197\) | 8.91601i | 0.635239i | 0.948218 | + | 0.317620i | \(0.102883\pi\) | ||||
−0.948218 | + | 0.317620i | \(0.897117\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.08418 | − | 3.51270i | 0.431296 | − | 0.249009i | −0.268603 | − | 0.963251i | \(-0.586562\pi\) |
0.699898 | + | 0.714242i | \(0.253229\pi\) | |||||||
\(200\) | 5.30960 | − | 12.1657i | 0.375445 | − | 0.860247i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.67623 | + | 23.8237i | −0.540098 | + | 1.67623i | ||||
\(203\) | 4.03959 | + | 10.1686i | 0.283524 | + | 0.713698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.631093 | + | 1.09309i | −0.0440775 | + | 0.0763444i | ||||
\(206\) | −6.41205 | + | 1.37937i | −0.446748 | + | 0.0961054i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −12.5546 | − | 2.54006i | −0.870505 | − | 0.176122i | ||||
\(209\) | 23.5779i | 1.63092i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.6524i | 0.733339i | 0.930351 | + | 0.366669i | \(0.119502\pi\) | ||||
−0.930351 | + | 0.366669i | \(0.880498\pi\) | |||||||
\(212\) | 4.00223 | + | 8.87176i | 0.274875 | + | 0.609315i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.01941 | + | 9.38727i | 0.138044 | + | 0.641701i | ||||
\(215\) | −2.30361 | + | 3.98998i | −0.157105 | + | 0.272114i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.2944 | + | 14.2837i | −0.766714 | + | 0.969642i | ||||
\(218\) | 17.4678 | + | 5.62830i | 1.18307 | + | 0.381197i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.54668 | + | 0.655624i | 0.441377 | + | 0.0442022i | ||||
\(221\) | −7.95963 | + | 4.59549i | −0.535422 | + | 0.309126i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.485215i | − | 0.0324924i | −0.999868 | − | 0.0162462i | \(-0.994828\pi\) | ||
0.999868 | − | 0.0162462i | \(-0.00517155\pi\) | |||||||
\(224\) | 9.13828 | − | 11.8529i | 0.610577 | − | 0.791957i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.4559 | + | 12.6604i | 0.762033 | + | 0.842159i | ||||
\(227\) | 8.05240 | + | 13.9472i | 0.534456 | + | 0.925705i | 0.999189 | + | 0.0402546i | \(0.0128169\pi\) |
−0.464733 | + | 0.885451i | \(0.653850\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.98446 | − | 12.0974i | 0.461546 | − | 0.799421i | −0.537492 | − | 0.843269i | \(-0.680628\pi\) |
0.999038 | + | 0.0438475i | \(0.0139616\pi\) | |||||||
\(230\) | 0.0699188 | − | 0.216998i | 0.00461031 | − | 0.0143084i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.41230 | + | 6.94485i | −0.617948 | + | 0.455951i | ||||
\(233\) | 18.4130 | + | 10.6308i | 1.20628 | + | 0.696445i | 0.961944 | − | 0.273247i | \(-0.0880975\pi\) |
0.244333 | + | 0.969691i | \(0.421431\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.94281 | + | 3.43108i | −0.387666 | + | 0.223819i | ||||
\(236\) | −22.7763 | + | 10.2749i | −1.48261 | + | 0.668836i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.712945 | − | 10.7155i | −0.0462134 | − | 0.694583i | ||||
\(239\) | −13.8556 | −0.896247 | −0.448123 | − | 0.893972i | \(-0.647907\pi\) | ||||
−0.448123 | + | 0.893972i | \(0.647907\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.31224 | + | 7.46902i | 0.277776 | + | 0.481122i | 0.970832 | − | 0.239762i | \(-0.0770694\pi\) |
−0.693056 | + | 0.720884i | \(0.743736\pi\) | |||||||
\(242\) | −7.21431 | − | 33.5359i | −0.463753 | − | 2.15577i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.992993 | + | 0.714034i | 0.0635698 | + | 0.0457113i | ||||
\(245\) | −3.77377 | + | 0.894299i | −0.241097 | + | 0.0571347i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.0122 | − | 6.35790i | −0.700690 | − | 0.404543i | ||||
\(248\) | −17.8416 | − | 7.78678i | −1.13294 | − | 0.494461i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −5.09575 | − | 5.63156i | −0.322283 | − | 0.356171i | ||||
\(251\) | 10.0174 | 0.632293 | 0.316147 | − | 0.948710i | \(-0.397611\pi\) | ||||
0.316147 | + | 0.948710i | \(0.397611\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.72768 | −0.108619 | ||||||||
\(254\) | −18.0922 | − | 19.9946i | −1.13521 | − | 1.25457i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.7416 | + | 6.21968i | 0.921352 | + | 0.388730i | ||||
\(257\) | −8.40598 | − | 4.85319i | −0.524351 | − | 0.302734i | 0.214362 | − | 0.976754i | \(-0.431233\pi\) |
−0.738713 | + | 0.674020i | \(0.764566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.922309 | − | 6.29600i | 0.0573095 | − | 0.391215i | ||||
\(260\) | −2.07156 | + | 2.88087i | −0.128472 | + | 0.178664i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.562262 | + | 2.61369i | 0.0347367 | + | 0.161474i | ||||
\(263\) | 5.83530 | + | 10.1070i | 0.359820 | + | 0.623226i | 0.987931 | − | 0.154898i | \(-0.0495048\pi\) |
−0.628111 | + | 0.778124i | \(0.716171\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.69616 | 0.165624 | ||||||||
\(266\) | 12.3456 | − | 8.26671i | 0.756959 | − | 0.506864i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.51550 | − | 7.79281i | −0.214743 | − | 0.476022i | ||||
\(269\) | 12.2044 | − | 7.04622i | 0.744116 | − | 0.429616i | −0.0794480 | − | 0.996839i | \(-0.525316\pi\) |
0.823564 | + | 0.567223i | \(0.191982\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.52302 | + | 2.61137i | 0.274754 | + | 0.158629i | 0.631046 | − | 0.775745i | \(-0.282626\pi\) |
−0.356292 | + | 0.934375i | \(0.615959\pi\) | |||||||
\(272\) | 10.8834 | − | 3.65470i | 0.659905 | − | 0.221599i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.46855 | − | 26.2827i | 0.511604 | − | 1.58780i | ||||
\(275\) | −13.9329 | + | 24.1324i | −0.840183 | + | 1.45524i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.09716 | − | 8.82854i | −0.306259 | − | 0.530456i | 0.671282 | − | 0.741202i | \(-0.265744\pi\) |
−0.977541 | + | 0.210746i | \(0.932411\pi\) | |||||||
\(278\) | −15.4820 | − | 17.1099i | −0.928550 | − | 1.02619i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.95205 | − | 3.65777i | −0.116658 | − | 0.218594i | ||||
\(281\) | − | 28.3097i | − | 1.68881i | −0.535702 | − | 0.844407i | \(-0.679953\pi\) | ||
0.535702 | − | 0.844407i | \(-0.320047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.18829 | − | 4.15016i | 0.427300 | − | 0.246702i | −0.270896 | − | 0.962609i | \(-0.587320\pi\) |
0.698196 | + | 0.715907i | \(0.253987\pi\) | |||||||
\(284\) | 1.39686 | − | 13.9483i | 0.0828887 | − | 0.827678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 25.5939 | + | 8.24661i | 1.51340 | + | 0.487632i | ||||
\(287\) | −2.22529 | − | 5.60159i | −0.131355 | − | 0.330651i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.38106 | + | 7.58822i | −0.257710 | + | 0.446366i | ||||
\(290\) | 0.681477 | + | 3.16786i | 0.0400177 | + | 0.186023i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 22.9342 | − | 10.3461i | 1.34212 | − | 0.605459i | ||||
\(293\) | − | 18.3982i | − | 1.07483i | −0.843317 | − | 0.537416i | \(-0.819401\pi\) | ||
0.843317 | − | 0.537416i | \(-0.180599\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.92181i | 0.403003i | ||||||||
\(296\) | 6.75986 | − | 0.760830i | 0.392909 | − | 0.0442224i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.1973 | − | 3.91463i | 1.05414 | − | 0.226769i | ||||
\(299\) | 0.465878 | − | 0.806925i | 0.0269424 | − | 0.0466657i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.12274 | − | 20.4469i | −0.468187 | − | 1.17854i | ||||
\(302\) | −5.91430 | + | 18.3555i | −0.340330 | + | 1.05624i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.9075 | + | 10.5119i | 0.682945 | + | 0.602897i | ||||
\(305\) | 0.293421 | − | 0.169406i | 0.0168012 | − | 0.00970018i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.96914i | 0.340677i | 0.985386 | + | 0.170338i | \(0.0544861\pi\) | ||||
−0.985386 | + | 0.170338i | \(0.945514\pi\) | |||||||
\(308\) | −21.8465 | + | 22.5809i | −1.24482 | + | 1.28667i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.99870 | + | 3.61825i | −0.227111 | + | 0.205503i | ||||
\(311\) | 14.9380 | + | 25.8734i | 0.847058 | + | 1.46715i | 0.883822 | + | 0.467823i | \(0.154962\pi\) |
−0.0367643 | + | 0.999324i | \(0.511705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.862490 | + | 1.49388i | −0.0487508 | + | 0.0844389i | −0.889371 | − | 0.457186i | \(-0.848857\pi\) |
0.840620 | + | 0.541625i | \(0.182191\pi\) | |||||||
\(314\) | 15.1762 | + | 4.88991i | 0.856441 | + | 0.275954i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.02237 | + | 9.76587i | −0.395039 | + | 0.549373i | ||||
\(317\) | −1.24055 | − | 0.716235i | −0.0696765 | − | 0.0402277i | 0.464757 | − | 0.885438i | \(-0.346142\pi\) |
−0.534434 | + | 0.845211i | \(0.679475\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 21.2657 | − | 12.2778i | 1.19065 | − | 0.687423i | ||||
\(320\) | 3.24985 | − | 3.01397i | 0.181672 | − | 0.168486i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.605747 | + | 0.904632i | 0.0337570 | + | 0.0504132i | ||||
\(323\) | 11.3972 | 0.634155 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.51413 | − | 13.0149i | −0.416809 | − | 0.721934i | ||||
\(326\) | 19.8752 | − | 4.27560i | 1.10079 | − | 0.236803i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.18495 | − | 3.82570i | 0.286291 | − | 0.211239i | ||||
\(329\) | 4.74974 | − | 32.4234i | 0.261862 | − | 1.78756i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.0867 | − | 9.86503i | −0.939172 | − | 0.542231i | −0.0494711 | − | 0.998776i | \(-0.515754\pi\) |
−0.889701 | + | 0.456545i | \(0.849087\pi\) | |||||||
\(332\) | −0.134609 | + | 1.34412i | −0.00738760 | + | 0.0737683i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.81400 | − | 7.07054i | 0.427563 | − | 0.386883i | ||||
\(335\) | −2.36827 | −0.129392 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.45266 | 0.188079 | 0.0940393 | − | 0.995568i | \(-0.470022\pi\) | ||||
0.0940393 | + | 0.995568i | \(0.470022\pi\) | |||||||
\(338\) | 2.87918 | − | 2.60525i | 0.156607 | − | 0.141707i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.316917 | − | 3.16455i | 0.0171873 | − | 0.171622i | ||||
\(341\) | 35.3914 | + | 20.4332i | 1.91655 | + | 1.10652i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.82763 | − | 16.7848i | 0.422652 | − | 0.906292i | ||||
\(344\) | 18.9261 | − | 13.9646i | 1.02043 | − | 0.752919i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.7459 | + | 4.46289i | −1.11530 | + | 0.239926i | ||||
\(347\) | 7.69485 | + | 13.3279i | 0.413081 | + | 0.715478i | 0.995225 | − | 0.0976081i | \(-0.0311192\pi\) |
−0.582144 | + | 0.813086i | \(0.697786\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.4402 | 1.89707 | 0.948534 | − | 0.316676i | \(-0.102567\pi\) | ||||
0.948534 | + | 0.316676i | \(0.102567\pi\) | |||||||
\(350\) | 17.5210 | − | 1.16574i | 0.936537 | − | 0.0623115i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −29.2923 | − | 16.4362i | −1.56129 | − | 0.876053i | ||||
\(353\) | 9.96600 | − | 5.75387i | 0.530436 | − | 0.306248i | −0.210758 | − | 0.977538i | \(-0.567593\pi\) |
0.741194 | + | 0.671291i | \(0.234260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.36302 | − | 1.94164i | −0.178491 | − | 0.103052i | ||||
\(356\) | 15.0390 | − | 20.9145i | 0.797067 | − | 1.10846i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.03269 | − | 2.91042i | −0.477392 | − | 0.153820i | ||||
\(359\) | −7.16808 | + | 12.4155i | −0.378317 | + | 0.655264i | −0.990817 | − | 0.135206i | \(-0.956830\pi\) |
0.612501 | + | 0.790470i | \(0.290164\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.61596 | − | 2.79893i | −0.0850508 | − | 0.147312i | ||||
\(362\) | −5.97488 | + | 5.40640i | −0.314033 | + | 0.284154i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.65554 | − | 16.2926i | −0.244016 | − | 0.853963i | ||||
\(365\) | − | 6.96979i | − | 0.364815i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.6088 | + | 15.3626i | −1.38897 | + | 0.801921i | −0.993199 | − | 0.116428i | \(-0.962855\pi\) |
−0.395770 | + | 0.918350i | \(0.629522\pi\) | |||||||
\(368\) | −0.770262 | + | 0.872531i | −0.0401527 | + | 0.0454838i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0.577927 | − | 1.79364i | 0.0300450 | − | 0.0932467i | ||||
\(371\) | −7.98577 | + | 10.0994i | −0.414601 | + | 0.524335i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.94955 | − | 13.7690i | 0.411612 | − | 0.712933i | −0.583454 | − | 0.812146i | \(-0.698299\pi\) |
0.995066 | + | 0.0992132i | \(0.0316326\pi\) | |||||||
\(374\) | −23.5622 | + | 5.06874i | −1.21837 | + | 0.262098i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 34.8122 | − | 3.91815i | 1.79530 | − | 0.202063i | ||||
\(377\) | 13.2430i | 0.682051i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 23.8379i | − | 1.22447i | −0.790675 | − | 0.612236i | \(-0.790270\pi\) | ||
0.790675 | − | 0.612236i | \(-0.209730\pi\) | |||||||
\(380\) | 4.01085 | − | 1.80938i | 0.205752 | − | 0.0928190i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.20068 | − | 5.58141i | −0.0614323 | − | 0.285570i | ||||
\(383\) | 3.63573 | − | 6.29726i | 0.185777 | − | 0.321775i | −0.758061 | − | 0.652184i | \(-0.773853\pi\) |
0.943838 | + | 0.330408i | \(0.107186\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.21338 | + | 8.08886i | 0.163769 | + | 0.412246i | ||||
\(386\) | −24.8762 | − | 8.01536i | −1.26617 | − | 0.407971i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.599487 | + | 5.98613i | −0.0304343 | + | 0.303900i | ||||
\(389\) | −13.6345 | + | 7.87187i | −0.691295 | + | 0.399120i | −0.804097 | − | 0.594498i | \(-0.797351\pi\) |
0.112802 | + | 0.993618i | \(0.464017\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.835133i | 0.0422345i | ||||||||
\(392\) | 19.4832 | + | 3.52189i | 0.984052 | + | 0.177882i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.46012 | − | 9.34969i | −0.426215 | − | 0.471031i | ||||
\(395\) | 1.66608 | + | 2.88573i | 0.0838293 | + | 0.145197i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.93160 | − | 8.54177i | 0.247510 | − | 0.428699i | −0.715325 | − | 0.698792i | \(-0.753721\pi\) |
0.962834 | + | 0.270093i | \(0.0870545\pi\) | |||||||
\(398\) | −3.04702 | + | 9.45665i | −0.152733 | + | 0.474019i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.97583 | + | 17.7956i | 0.298791 | + | 0.889780i | ||||
\(401\) | 22.7516 | + | 13.1357i | 1.13616 | + | 0.655964i | 0.945477 | − | 0.325688i | \(-0.105596\pi\) |
0.190685 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −19.0869 | + | 11.0198i | −0.950786 | + | 0.548937i | ||||
\(404\) | −14.5560 | − | 32.2663i | −0.724187 | − | 1.60531i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.8848 | − | 6.83020i | −0.689090 | − | 0.338977i | ||||
\(407\) | −14.2805 | −0.707857 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.3008 | + | 21.3056i | 0.608234 | + | 1.05349i | 0.991531 | + | 0.129867i | \(0.0414551\pi\) |
−0.383298 | + | 0.923625i | \(0.625212\pi\) | |||||||
\(410\) | −0.375405 | − | 1.74508i | −0.0185399 | − | 0.0861833i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.41509 | − | 7.53066i | 0.266782 | − | 0.371009i | ||||
\(413\) | −25.9280 | − | 20.5017i | −1.27583 | − | 1.00882i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.324077 | + | 0.187106i | 0.0159083 | + | 0.00918466i | ||||
\(416\) | 15.5755 | − | 9.24906i | 0.763649 | − | 0.453472i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.3724 | − | 24.7248i | −1.09427 | − | 1.20933i | ||||
\(419\) | 22.1374 | 1.08148 | 0.540742 | − | 0.841189i | \(-0.318144\pi\) | ||||
0.540742 | + | 0.841189i | \(0.318144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.42567 | 0.313168 | 0.156584 | − | 0.987665i | \(-0.449952\pi\) | ||||
0.156584 | + | 0.987665i | \(0.449952\pi\) | |||||||
\(422\) | −10.1077 | − | 11.1705i | −0.492035 | − | 0.543772i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −12.6150 | − | 5.50569i | −0.612641 | − | 0.267380i | ||||
\(425\) | 11.6652 | + | 6.73491i | 0.565846 | + | 0.326691i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.234514 | + | 1.60087i | −0.0113489 | + | 0.0774716i | ||||
\(428\) | −11.0249 | − | 7.92772i | −0.532910 | − | 0.383201i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.37030 | − | 6.36988i | −0.0660818 | − | 0.307183i | ||||
\(431\) | 14.9953 | + | 25.9727i | 0.722299 | + | 1.25106i | 0.960076 | + | 0.279739i | \(0.0902479\pi\) |
−0.237777 | + | 0.971320i | \(0.576419\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.6049 | 1.61495 | 0.807475 | − | 0.589902i | \(-0.200833\pi\) | ||||
0.807475 | + | 0.589902i | \(0.200833\pi\) | |||||||
\(434\) | −1.70962 | − | 25.6954i | −0.0820643 | − | 1.23342i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.6580 | + | 10.6726i | −1.13301 | + | 0.511125i | ||||
\(437\) | −1.00062 | + | 0.577706i | −0.0478660 | + | 0.0276354i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.83511 | − | 5.67831i | −0.469404 | − | 0.271011i | 0.246586 | − | 0.969121i | \(-0.420691\pi\) |
−0.715990 | + | 0.698110i | \(0.754025\pi\) | |||||||
\(440\) | −7.48721 | + | 5.52442i | −0.356939 | + | 0.263367i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.98627 | − | 12.3717i | 0.189607 | − | 0.588460i | ||||
\(443\) | 14.1468 | − | 24.5029i | 0.672132 | − | 1.16417i | −0.305166 | − | 0.952299i | \(-0.598712\pi\) |
0.977298 | − | 0.211868i | \(-0.0679548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.56805 | − | 6.18004i | −0.169142 | − | 0.292962i | ||||
\(446\) | 0.460406 | + | 0.508816i | 0.0218008 | + | 0.0240932i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.66409 | + | 21.1005i | 0.0786210 | + | 0.996905i | ||||
\(449\) | − | 29.4996i | − | 1.39217i | −0.717959 | − | 0.696086i | \(-0.754923\pi\) | ||
0.717959 | − | 0.696086i | \(-0.245077\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7146 | + | 6.76345i | −0.551621 | + | 0.318478i | ||||
\(452\) | −24.0262 | − | 2.40613i | −1.13010 | − | 0.113175i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −21.6781 | − | 6.98489i | −1.01740 | − | 0.327817i | ||||
\(455\) | −4.64445 | − | 0.680372i | −0.217735 | − | 0.0318963i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.43214 | − | 2.48054i | 0.0669926 | − | 0.116035i | −0.830584 | − | 0.556894i | \(-0.811993\pi\) |
0.897576 | + | 0.440859i | \(0.145326\pi\) | |||||||
\(458\) | 4.15470 | + | 19.3132i | 0.194136 | + | 0.902447i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.132583 | + | 0.293897i | 0.00618171 | + | 0.0137030i | ||||
\(461\) | 21.1377i | 0.984482i | 0.870459 | + | 0.492241i | \(0.163822\pi\) | ||||
−0.870459 | + | 0.492241i | \(0.836178\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 39.2453i | − | 1.82389i | −0.410317 | − | 0.911943i | \(-0.634582\pi\) | ||
0.410317 | − | 0.911943i | \(-0.365418\pi\) | |||||||
\(464\) | 3.28037 | − | 16.2137i | 0.152288 | − | 0.752702i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.3959 | + | 6.32369i | −1.36174 | + | 0.292940i | ||||
\(467\) | −14.6992 | + | 25.4597i | −0.680196 | + | 1.17813i | 0.294725 | + | 0.955582i | \(0.404772\pi\) |
−0.974921 | + | 0.222552i | \(0.928561\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.01458 | − | 8.87115i | 0.323903 | − | 0.409632i | ||||
\(470\) | 2.97623 | − | 9.23693i | 0.137283 | − | 0.426068i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.1347 | − | 32.3863i | 0.650600 | − | 1.49070i | ||||
\(473\) | −42.7607 | + | 24.6879i | −1.96614 | + | 1.13515i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 18.6356i | 0.855060i | ||||||||
\(476\) | 10.9152 | + | 10.5602i | 0.500299 | + | 0.484027i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 14.5296 | − | 13.1472i | 0.664568 | − | 0.601338i | ||||
\(479\) | 9.81732 | + | 17.0041i | 0.448565 | + | 0.776937i | 0.998293 | − | 0.0584067i | \(-0.0186020\pi\) |
−0.549728 | + | 0.835344i | \(0.685269\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.85080 | − | 6.66978i | 0.175581 | − | 0.304116i | ||||
\(482\) | −11.6091 | − | 3.74057i | −0.528781 | − | 0.170378i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 39.3864 | + | 28.3217i | 1.79029 | + | 1.28735i | ||||
\(485\) | 1.44330 | + | 0.833287i | 0.0655367 | + | 0.0378376i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.798307 | + | 0.460903i | −0.0361748 | + | 0.0208855i | −0.517978 | − | 0.855394i | \(-0.673315\pi\) |
0.481804 | + | 0.876279i | \(0.339982\pi\) | |||||||
\(488\) | −1.71882 | + | 0.193455i | −0.0778072 | + | 0.00875729i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.10875 | − | 4.51861i | 0.140439 | − | 0.204130i | ||||
\(491\) | −31.2381 | −1.40976 | −0.704878 | − | 0.709329i | \(-0.748998\pi\) | ||||
−0.704878 | + | 0.709329i | \(0.748998\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.93487 | − | 10.2795i | −0.267293 | − | 0.462965i | ||||
\(494\) | 17.5807 | − | 3.78199i | 0.790991 | − | 0.170160i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.0981 | − | 8.76384i | 1.17184 | − | 0.393508i | ||||
\(497\) | 17.2340 | − | 6.84639i | 0.773052 | − | 0.307103i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.1999 | + | 7.04359i | 0.546141 | + | 0.315314i | 0.747564 | − | 0.664190i | \(-0.231223\pi\) |
−0.201423 | + | 0.979504i | \(0.564557\pi\) | |||||||
\(500\) | 10.6872 | + | 1.07028i | 0.477947 | + | 0.0478645i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.5047 | + | 9.50521i | −0.468846 | + | 0.424238i | ||||
\(503\) | 21.4391 | 0.955922 | 0.477961 | − | 0.878381i | \(-0.341376\pi\) | ||||
0.477961 | + | 0.878381i | \(0.341376\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.80585 | −0.436355 | ||||||||
\(506\) | 1.81172 | − | 1.63935i | 0.0805408 | − | 0.0728778i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 37.9445 | + | 3.79999i | 1.68352 | + | 0.168597i | ||||
\(509\) | 32.8654 | + | 18.9749i | 1.45673 | + | 0.841046i | 0.998849 | − | 0.0479657i | \(-0.0152738\pi\) |
0.457885 | + | 0.889011i | \(0.348607\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.1077 | + | 20.6438i | 1.15494 | + | 0.913230i | ||||
\(512\) | −21.3603 | + | 7.46566i | −0.944002 | + | 0.329938i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.4199 | − | 2.88691i | 0.591926 | − | 0.127336i | ||||
\(515\) | −1.28474 | − | 2.22524i | −0.0566126 | − | 0.0980559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −73.5421 | −3.23438 | ||||||||
\(518\) | 5.00691 | + | 7.47740i | 0.219991 | + | 0.328538i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.561251 | − | 4.98663i | −0.0246125 | − | 0.218678i | ||||
\(521\) | −24.5753 | + | 14.1886i | −1.07666 | + | 0.621613i | −0.929995 | − | 0.367573i | \(-0.880189\pi\) |
−0.146670 | + | 0.989185i | \(0.546856\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.2425 | + | 7.64559i | 0.579056 | + | 0.334318i | 0.760758 | − | 0.649035i | \(-0.224827\pi\) |
−0.181702 | + | 0.983354i | \(0.558161\pi\) | |||||||
\(524\) | −3.06966 | − | 2.20731i | −0.134099 | − | 0.0964267i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.7094 | − | 5.06171i | −0.684961 | − | 0.220701i | ||||
\(527\) | 9.87707 | − | 17.1076i | 0.430252 | − | 0.745218i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4577 | + | 19.8453i | 0.498159 | + | 0.862838i | ||||
\(530\) | −2.82731 | + | 2.55831i | −0.122810 | + | 0.111126i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.10211 | + | 20.3832i | −0.221204 | + | 0.883723i | ||||
\(533\) | − | 7.29518i | − | 0.315990i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.25777 | + | 1.88087i | −0.140846 | + | 0.0813172i | ||||
\(536\) | 11.0809 | + | 4.83611i | 0.478620 | + | 0.208888i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.11210 | + | 18.9693i | −0.263511 | + | 0.817826i | ||||
\(539\) | −39.8173 | − | 11.9216i | −1.71505 | − | 0.513500i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.90969 | − | 8.50383i | 0.211084 | − | 0.365608i | −0.740970 | − | 0.671538i | \(-0.765634\pi\) |
0.952054 | + | 0.305930i | \(0.0989673\pi\) | |||||||
\(542\) | −7.22087 | + | 1.55337i | −0.310163 | + | 0.0667228i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.94499 | + | 14.1594i | −0.340638 | + | 0.607080i | ||||
\(545\) | 7.18976i | 0.307975i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.27148i | 0.0971213i | 0.998820 | + | 0.0485606i | \(0.0154634\pi\) | ||||
−0.998820 | + | 0.0485606i | \(0.984537\pi\) | |||||||
\(548\) | 16.0584 | + | 35.5967i | 0.685981 | + | 1.52062i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.28794 | − | 38.5267i | −0.353399 | − | 1.64278i | ||||
\(551\) | 8.21094 | − | 14.2218i | 0.349798 | − | 0.605867i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.7442 | − | 2.30639i | −0.669513 | − | 0.0980778i | ||||
\(554\) | 13.7222 | + | 4.42143i | 0.583001 | + | 0.187849i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 32.4702 | + | 3.25176i | 1.37704 | + | 0.137905i | ||||
\(557\) | −24.7675 | + | 14.2995i | −1.04943 | + | 0.605890i | −0.922490 | − | 0.386020i | \(-0.873849\pi\) |
−0.126942 | + | 0.991910i | \(0.540516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 26.6289i | − | 1.12628i | ||||||
\(560\) | 5.51775 | + | 1.98345i | 0.233168 | + | 0.0838159i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 26.8622 | + | 29.6867i | 1.13311 | + | 1.25226i | ||||
\(563\) | −16.7025 | − | 28.9296i | −0.703926 | − | 1.21924i | −0.967078 | − | 0.254481i | \(-0.918095\pi\) |
0.263152 | − | 0.964754i | \(-0.415238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.34452 | + | 5.79287i | −0.140705 | + | 0.243708i | ||||
\(566\) | −3.59998 | + | 11.1728i | −0.151318 | + | 0.469627i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.7703 | + | 15.9522i | 0.493870 | + | 0.669338i | ||||
\(569\) | 2.83434 | + | 1.63641i | 0.118822 | + | 0.0686018i | 0.558233 | − | 0.829684i | \(-0.311480\pi\) |
−0.439411 | + | 0.898286i | \(0.644813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.4191 | − | 8.32487i | 0.603420 | − | 0.348385i | −0.166966 | − | 0.985963i | \(-0.553397\pi\) |
0.770386 | + | 0.637578i | \(0.220064\pi\) | |||||||
\(572\) | −34.6638 | + | 15.6375i | −1.44937 | + | 0.653839i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.64870 | + | 3.76255i | 0.319251 | + | 0.157046i | ||||
\(575\) | −1.36553 | −0.0569466 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.61179 | − | 6.25581i | −0.150361 | − | 0.260433i | 0.780999 | − | 0.624532i | \(-0.214710\pi\) |
−0.931360 | + | 0.364099i | \(0.881377\pi\) | |||||||
\(578\) | −2.60607 | − | 12.1144i | −0.108398 | − | 0.503891i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.72051 | − | 2.67532i | −0.154486 | − | 0.111087i | ||||
\(581\) | −1.66075 | + | 0.659751i | −0.0688996 | + | 0.0273711i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 25.0237 | + | 14.4474i | 1.03638 | + | 0.598352i | ||||
\(584\) | −14.2326 | + | 32.6109i | −0.588951 | + | 1.34945i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.4574 | + | 19.2931i | 0.721160 | + | 0.796989i | ||||
\(587\) | −25.0736 | −1.03490 | −0.517448 | − | 0.855714i | \(-0.673118\pi\) | ||||
−0.517448 | + | 0.855714i | \(0.673118\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.3300 | 1.12611 | ||||||||
\(590\) | −6.56789 | − | 7.25849i | −0.270396 | − | 0.298827i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.36674 | + | 7.21206i | −0.261671 | + | 0.296414i | ||||
\(593\) | −10.8437 | − | 6.26064i | −0.445299 | − | 0.257094i | 0.260544 | − | 0.965462i | \(-0.416098\pi\) |
−0.705843 | + | 0.708368i | \(0.749432\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.91002 | − | 1.55329i | 0.160295 | − | 0.0636788i | ||||
\(596\) | −15.3679 | + | 21.3719i | −0.629495 | + | 0.875426i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.277127 | + | 1.28823i | 0.0113326 | + | 0.0526797i | ||||
\(599\) | −9.23709 | − | 15.9991i | −0.377417 | − | 0.653706i | 0.613268 | − | 0.789875i | \(-0.289854\pi\) |
−0.990686 | + | 0.136169i | \(0.956521\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.51523 | 0.0618074 | 0.0309037 | − | 0.999522i | \(-0.490161\pi\) | ||||
0.0309037 | + | 0.999522i | \(0.490161\pi\) | |||||||
\(602\) | 27.9193 | + | 13.7340i | 1.13790 | + | 0.559758i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.2149 | − | 24.8602i | −0.456330 | − | 1.01155i | ||||
\(605\) | 11.6383 | − | 6.71939i | 0.473165 | − | 0.273182i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.1840 | − | 21.4682i | −1.50925 | − | 0.871366i | −0.999942 | − | 0.0107826i | \(-0.996568\pi\) |
−0.509309 | − | 0.860584i | \(-0.670099\pi\) | |||||||
\(608\) | −22.4611 | + | 0.275527i | −0.910919 | + | 0.0111741i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.146948 | + | 0.456064i | −0.00594976 | + | 0.0184655i | ||||
\(611\) | 19.8310 | − | 34.3483i | 0.802276 | − | 1.38958i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.06912 | − | 10.5120i | −0.245130 | − | 0.424577i | 0.717039 | − | 0.697034i | \(-0.245497\pi\) |
−0.962168 | + | 0.272457i | \(0.912164\pi\) | |||||||
\(614\) | −5.66393 | − | 6.25948i | −0.228578 | − | 0.252612i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.48279 | − | 44.4087i | 0.0597433 | − | 1.78928i | ||||
\(617\) | − | 16.9417i | − | 0.682049i | −0.940054 | − | 0.341024i | \(-0.889226\pi\) | ||
0.940054 | − | 0.341024i | \(-0.110774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.94601 | − | 5.74233i | 0.399764 | − | 0.230804i | −0.286618 | − | 0.958045i | \(-0.592531\pi\) |
0.686382 | + | 0.727241i | \(0.259198\pi\) | |||||||
\(620\) | 0.759957 | − | 7.58849i | 0.0305206 | − | 0.304761i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −40.2151 | − | 12.9577i | −1.61248 | − | 0.519556i | ||||
\(623\) | 33.7177 | + | 4.93934i | 1.35087 | + | 0.197891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.2449 | + | 17.7447i | −0.409796 | + | 0.709788i | ||||
\(626\) | −0.513051 | − | 2.38493i | −0.0205056 | − | 0.0953209i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.5542 | + | 9.27244i | −0.820203 | + | 0.370011i | ||||
\(629\) | 6.90294i | 0.275238i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.5485i | 0.977262i | 0.872491 | + | 0.488631i | \(0.162503\pi\) | ||||
−0.872491 | + | 0.488631i | \(0.837497\pi\) | |||||||
\(632\) | −1.90259 | − | 16.9042i | −0.0756808 | − | 0.672413i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.98051 | − | 0.426051i | 0.0786561 | − | 0.0169207i | ||||
\(635\) | 5.28199 | − | 9.14868i | 0.209609 | − | 0.363054i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 16.3050 | − | 15.3822i | 0.646027 | − | 0.609464i | ||||
\(638\) | −10.6501 | + | 33.0534i | −0.421642 | + | 1.30860i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.548067 | + | 6.24425i | −0.0216642 | + | 0.246826i | ||||
\(641\) | −5.19237 | + | 2.99782i | −0.205086 | + | 0.118407i | −0.599026 | − | 0.800730i | \(-0.704445\pi\) |
0.393939 | + | 0.919136i | \(0.371112\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.2008i | 1.34875i | 0.738390 | + | 0.674374i | \(0.235587\pi\) | ||||
−0.738390 | + | 0.674374i | \(0.764413\pi\) | |||||||
\(644\) | −1.49359 | − | 0.373859i | −0.0588556 | − | 0.0147321i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.9515 | + | 10.8144i | −0.470227 | + | 0.425488i | ||||
\(647\) | −15.1478 | − | 26.2367i | −0.595520 | − | 1.03147i | −0.993473 | − | 0.114065i | \(-0.963613\pi\) |
0.397954 | − | 0.917406i | \(-0.369721\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.0906 | + | 64.2428i | −1.45593 | + | 2.52175i | ||||
\(650\) | 20.2290 | + | 6.51798i | 0.793447 | + | 0.255656i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −16.7850 | + | 23.3426i | −0.657351 | + | 0.914165i | ||||
\(653\) | 19.9310 | + | 11.5072i | 0.779959 | + | 0.450310i | 0.836416 | − | 0.548095i | \(-0.184647\pi\) |
−0.0564565 | + | 0.998405i | \(0.517980\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.907057 | + | 0.523690i | −0.0354417 | + | 0.0204623i | ||||
\(656\) | −1.80706 | + | 8.93162i | −0.0705537 | + | 0.348721i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 25.7848 | + | 38.5074i | 1.00519 | + | 1.50117i | ||||
\(659\) | −44.6195 | −1.73813 | −0.869065 | − | 0.494698i | \(-0.835279\pi\) | ||||
−0.869065 | + | 0.494698i | \(0.835279\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.1633 | + | 21.0674i | 0.473097 | + | 0.819428i | 0.999526 | − | 0.0307915i | \(-0.00980277\pi\) |
−0.526429 | + | 0.850219i | \(0.676469\pi\) | |||||||
\(662\) | 27.2785 | − | 5.86820i | 1.06021 | − | 0.228074i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.13424 | − | 1.53723i | −0.0440170 | − | 0.0596560i | ||||
\(665\) | 4.56585 | + | 3.61030i | 0.177056 | + | 0.140001i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.04211 | + | 0.601660i | 0.0403505 | + | 0.0232964i | ||||
\(668\) | −1.48506 | + | 14.8289i | −0.0574586 | + | 0.573748i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.48346 | − | 2.24718i | 0.0959445 | − | 0.0868160i | ||||
\(671\) | 3.63107 | 0.140176 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.06192 | −0.0794813 | −0.0397406 | − | 0.999210i | \(-0.512653\pi\) | ||||
−0.0397406 | + | 0.999210i | \(0.512653\pi\) | |||||||
\(674\) | −3.62060 | + | 3.27612i | −0.139460 | + | 0.126192i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −0.547192 | + | 5.46394i | −0.0210458 | + | 0.210151i | ||||
\(677\) | −38.1309 | − | 22.0149i | −1.46549 | − | 0.846101i | −0.466234 | − | 0.884662i | \(-0.654389\pi\) |
−0.999256 | + | 0.0385604i | \(0.987723\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.39626 | + | 2.93824i | −0.283842 | + | 0.112759i | ||||
\(680\) | 2.67041 | + | 3.61919i | 0.102406 | + | 0.138790i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −56.5013 | + | 12.1547i | −2.16355 | + | 0.465426i | ||||
\(683\) | 8.85834 | + | 15.3431i | 0.338955 | + | 0.587087i | 0.984236 | − | 0.176858i | \(-0.0565933\pi\) |
−0.645282 | + | 0.763945i | \(0.723260\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.8180 | 0.413334 | ||||||||
\(686\) | 7.71816 | + | 25.0286i | 0.294681 | + | 0.955596i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.59611 | + | 32.6022i | −0.251474 | + | 1.24295i | ||||
\(689\) | −13.4955 | + | 7.79164i | −0.514138 | + | 0.296838i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.82540 | − | 3.94065i | −0.259651 | − | 0.149909i | 0.364525 | − | 0.931194i | \(-0.381232\pi\) |
−0.624175 | + | 0.781284i | \(0.714565\pi\) | |||||||
\(692\) | 17.5203 | − | 24.3651i | 0.666020 | − | 0.926221i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.7155 | − | 6.67475i | −0.786351 | − | 0.253370i | ||||
\(695\) | 4.51995 | − | 7.82878i | 0.171451 | − | 0.296962i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.26934 | + | 5.66266i | 0.123835 | + | 0.214488i | ||||
\(698\) | −37.1640 | + | 33.6281i | −1.40668 | + | 1.27284i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −17.2671 | + | 17.8476i | −0.652635 | + | 0.674575i | ||||
\(701\) | − | 42.2417i | − | 1.59545i | −0.603025 | − | 0.797723i | \(-0.706038\pi\) | ||
0.603025 | − | 0.797723i | \(-0.293962\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.27078 | + | 4.77514i | −0.311938 | + | 0.180098i | ||||
\(704\) | 46.3130 | − | 10.5589i | 1.74549 | − | 0.397954i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.99108 | + | 15.4902i | −0.187842 | + | 0.582980i | ||||
\(707\) | 29.0440 | − | 36.7312i | 1.09231 | − | 1.38142i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.75030 | + | 13.4239i | −0.291069 | + | 0.504146i | −0.974063 | − | 0.226278i | \(-0.927344\pi\) |
0.682994 | + | 0.730424i | \(0.260678\pi\) | |||||||
\(710\) | 5.36896 | − | 1.15498i | 0.201494 | − | 0.0433457i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.07456 | + | 36.2018i | 0.152701 | + | 1.35672i | ||||
\(713\) | 2.00262i | 0.0749987i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.5345i | 0.393966i | ||||||||
\(716\) | 12.2337 | − | 5.51885i | 0.457193 | − | 0.206249i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.26392 | − | 19.8209i | −0.159128 | − | 0.739711i | ||||
\(719\) | −19.9952 | + | 34.6327i | −0.745695 | + | 1.29158i | 0.204174 | + | 0.978935i | \(0.434549\pi\) |
−0.949869 | + | 0.312647i | \(0.898784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.1407 | + | 1.77851i | 0.452143 | + | 0.0662350i | ||||
\(722\) | 4.35039 | + | 1.40174i | 0.161905 | + | 0.0521672i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.13553 | − | 11.3388i | 0.0422017 | − | 0.421401i | ||||
\(725\) | 16.8081 | − | 9.70415i | 0.624237 | − | 0.360403i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 4.48716i | − | 0.166420i | −0.996532 | − | 0.0832098i | \(-0.973483\pi\) | ||
0.996532 | − | 0.0832098i | \(-0.0265172\pi\) | |||||||
\(728\) | 20.3415 | + | 12.6676i | 0.753907 | + | 0.469491i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 6.61342 | + | 7.30881i | 0.244774 | + | 0.270511i | ||||
\(731\) | 11.9337 | + | 20.6698i | 0.441385 | + | 0.764500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.0072 | − | 25.9933i | 0.554305 | − | 0.960084i | −0.443653 | − | 0.896199i | \(-0.646318\pi\) |
0.997957 | − | 0.0638849i | \(-0.0203490\pi\) | |||||||
\(734\) | 13.3260 | − | 41.3581i | 0.491871 | − | 1.52656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.0201893 | − | 1.64585i | −0.000744189 | − | 0.0606668i | ||||
\(737\) | −21.9804 | − | 12.6904i | −0.809659 | − | 0.467457i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.53183 | + | 4.34850i | −0.277063 | + | 0.159962i | −0.632093 | − | 0.774893i | \(-0.717804\pi\) |
0.355030 | + | 0.934855i | \(0.384471\pi\) | |||||||
\(740\) | 1.09589 | + | 2.42926i | 0.0402856 | + | 0.0893012i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.20880 | − | 18.1681i | −0.0443763 | − | 0.666972i | ||||
\(743\) | 9.85512 | 0.361549 | 0.180775 | − | 0.983525i | \(-0.442140\pi\) | ||||
0.180775 | + | 0.983525i | \(0.442140\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.64608 | + | 6.31520i | 0.133582 | + | 0.231371i | ||||
\(746\) | 4.72878 | + | 21.9818i | 0.173133 | + | 0.804812i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.8987 | − | 27.6727i | 0.727568 | − | 1.01181i | ||||
\(749\) | 2.60374 | − | 17.7740i | 0.0951387 | − | 0.649450i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.10524 | + | 1.21546i | 0.0768214 | + | 0.0443528i | 0.537919 | − | 0.842997i | \(-0.319211\pi\) |
−0.461097 | + | 0.887350i | \(0.652544\pi\) | |||||||
\(752\) | −32.7877 | + | 37.1409i | −1.19564 | + | 1.35439i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.5659 | − | 13.8872i | −0.457624 | − | 0.505742i | ||||
\(755\) | −7.55511 | −0.274959 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −36.0235 | −1.30929 | −0.654647 | − | 0.755934i | \(-0.727183\pi\) | ||||
−0.654647 | + | 0.755934i | \(0.727183\pi\) | |||||||
\(758\) | 22.6191 | + | 24.9974i | 0.821562 | + | 0.907948i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.48908 | + | 5.70315i | −0.0902883 | + | 0.206875i | ||||
\(761\) | 24.3003 | + | 14.0298i | 0.880884 | + | 0.508578i | 0.870950 | − | 0.491372i | \(-0.163505\pi\) |
0.00993401 | + | 0.999951i | \(0.496838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.9317 | − | 21.2954i | −0.974993 | − | 0.770944i | ||||
\(764\) | 6.55511 | + | 4.71360i | 0.237156 | + | 0.170532i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.16271 | + | 10.0534i | 0.0781418 | + | 0.363244i | ||||
\(767\) | −20.0033 | − | 34.6468i | −0.722278 | − | 1.25102i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.3367 | −1.05791 | −0.528955 | − | 0.848650i | \(-0.677416\pi\) | ||||
−0.528955 | + | 0.848650i | \(0.677416\pi\) | |||||||
\(770\) | −11.0449 | − | 5.43323i | −0.398032 | − | 0.195800i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 33.6917 | − | 15.1990i | 1.21259 | − | 0.547025i | ||||
\(773\) | 2.54413 | − | 1.46885i | 0.0915059 | − | 0.0528310i | −0.453549 | − | 0.891231i | \(-0.649842\pi\) |
0.545055 | + | 0.838400i | \(0.316509\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 27.9728 | + | 16.1501i | 1.00481 | + | 0.580128i | ||||
\(776\) | −5.05140 | − | 6.84613i | −0.181335 | − | 0.245762i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.82830 | − | 21.1921i | 0.244806 | − | 0.759773i | ||||
\(779\) | −4.52315 | + | 7.83433i | −0.162059 | + | 0.280694i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.8086 | − | 36.0416i | −0.744592 | − | 1.28967i | ||||
\(782\) | −0.792432 | − | 0.875754i | −0.0283373 | − | 0.0313169i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −23.7727 | + | 14.7938i | −0.849026 | + | 0.528351i | ||||
\(785\) | 6.24652i | 0.222948i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.7966 | − | 20.0898i | 1.24037 | − | 0.716125i | 0.271197 | − | 0.962524i | \(-0.412581\pi\) |
0.969169 | + | 0.246399i | \(0.0792472\pi\) | |||||||
\(788\) | 17.7433 | + | 1.77692i | 0.632077 | + | 0.0633001i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.48529 | − | 1.44520i | −0.159580 | − | 0.0514181i | ||||
\(791\) | −11.7930 | − | 29.6859i | −0.419312 | − | 1.05551i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.979135 | + | 1.69591i | −0.0347701 | + | 0.0602236i | ||||
\(794\) | 2.93355 | + | 13.6367i | 0.104108 | + | 0.483948i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.77789 | − | 12.8079i | −0.204792 | − | 0.453962i | ||||
\(797\) | 37.9519i | 1.34433i | 0.740403 | + | 0.672164i | \(0.234635\pi\) | ||||
−0.740403 | + | 0.672164i | \(0.765365\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.5490i | 1.25763i | ||||||||
\(800\) | −23.1522 | − | 12.9909i | −0.818553 | − | 0.459298i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −36.3223 | + | 7.81373i | −1.28259 | + | 0.275912i | ||||
\(803\) | 37.3477 | − | 64.6882i | 1.31797 | − | 2.28280i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.264547 | + | 0.334565i | −0.00932404 | + | 0.0117919i | ||||
\(806\) | 9.55893 | − | 29.6668i | 0.336699 | − | 1.04497i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 45.8805 | + | 20.0240i | 1.61407 | + | 0.704442i | ||||
\(809\) | −19.6636 | + | 11.3528i | −0.691337 | + | 0.399144i | −0.804113 | − | 0.594477i | \(-0.797359\pi\) |
0.112776 | + | 0.993620i | \(0.464026\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 49.7833i | − | 1.74813i | −0.485810 | − | 0.874064i | \(-0.661475\pi\) | ||
0.485810 | − | 0.874064i | \(-0.338525\pi\) | |||||||
\(812\) | 21.0411 | − | 6.01241i | 0.738399 | − | 0.210994i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 14.9751 | − | 13.5503i | 0.524877 | − | 0.474938i | ||||
\(815\) | 3.98228 | + | 6.89752i | 0.139493 | + | 0.241609i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −16.5104 | + | 28.5968i | −0.577626 | + | 1.00048i | ||||
\(818\) | −33.1153 | − | 10.6701i | −1.15785 | − | 0.373070i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.04952 | + | 1.47375i | 0.0715722 | + | 0.0514656i | ||||
\(821\) | −18.0237 | − | 10.4060i | −0.629033 | − | 0.363172i | 0.151345 | − | 0.988481i | \(-0.451640\pi\) |
−0.780377 | + | 0.625309i | \(0.784973\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.19964 | + | 3.57936i | −0.216106 | + | 0.124769i | −0.604146 | − | 0.796874i | \(-0.706486\pi\) |
0.388040 | + | 0.921643i | \(0.373152\pi\) | |||||||
\(824\) | 1.46712 | + | 13.0352i | 0.0511096 | + | 0.454102i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 46.6426 | − | 3.10332i | 1.62290 | − | 0.107978i | ||||
\(827\) | 41.7124 | 1.45048 | 0.725241 | − | 0.688495i | \(-0.241728\pi\) | ||||
0.725241 | + | 0.688495i | \(0.241728\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.5508 | − | 28.6668i | −0.574832 | − | 0.995638i | −0.996060 | − | 0.0886830i | \(-0.971734\pi\) |
0.421228 | − | 0.906955i | \(-0.361599\pi\) | |||||||
\(830\) | −0.517379 | + | 0.111300i | −0.0179585 | + | 0.00386327i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −7.55691 | + | 24.4780i | −0.261989 | + | 0.848622i | ||||
\(833\) | −5.76270 | + | 19.2470i | −0.199666 | + | 0.666869i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.57535 | + | 2.06423i | 0.123730 | + | 0.0714356i | ||||
\(836\) | 46.9211 | + | 4.69897i | 1.62280 | + | 0.162517i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −23.2142 | + | 21.0055i | −0.801921 | + | 0.725623i | ||||
\(839\) | −2.73750 | −0.0945091 | −0.0472545 | − | 0.998883i | \(-0.515047\pi\) | ||||
−0.0472545 | + | 0.998883i | \(0.515047\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11.8972 | 0.410249 | ||||||||
\(842\) | −6.73821 | + | 6.09711i | −0.232214 | + | 0.210120i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 21.1987 | + | 2.12297i | 0.729689 | + | 0.0730755i | ||||
\(845\) | 1.31739 | + | 0.760597i | 0.0453197 | + | 0.0261653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.30184 | + | 63.4975i | −0.319615 | + | 2.18180i | ||||
\(848\) | 18.4528 | − | 6.19653i | 0.633673 | − | 0.212790i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −18.6232 | + | 4.00625i | −0.638769 | + | 0.137413i | ||||
\(851\) | −0.349900 | − | 0.606045i | −0.0119944 | − | 0.0207750i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9013 | −0.715647 | −0.357824 | − | 0.933789i | \(-0.616481\pi\) | ||||
−0.357824 | + | 0.933789i | \(0.616481\pi\) | |||||||
\(854\) | −1.27310 | − | 1.90126i | −0.0435645 | − | 0.0650599i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.0836 | − | 2.14788i | 0.652263 | − | 0.0734129i | ||||
\(857\) | 29.1110 | − | 16.8073i | 0.994413 | − | 0.574125i | 0.0878229 | − | 0.996136i | \(-0.472009\pi\) |
0.906591 | + | 0.422011i | \(0.138676\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.3404 | + | 22.1358i | 1.30816 | + | 0.755265i | 0.981788 | − | 0.189978i | \(-0.0608416\pi\) |
0.326369 | + | 0.945243i | \(0.394175\pi\) | |||||||
\(860\) | 7.48114 | + | 5.37948i | 0.255105 | + | 0.183439i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −40.3693 | − | 13.0074i | −1.37499 | − | 0.443033i | ||||
\(863\) | 7.62621 | − | 13.2090i | 0.259599 | − | 0.449639i | −0.706535 | − | 0.707678i | \(-0.749743\pi\) |
0.966135 | + | 0.258039i | \(0.0830763\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.15673 | − | 7.19966i | −0.141333 | − | 0.244796i | ||||
\(866\) | −35.2395 | + | 31.8867i | −1.19749 | + | 1.08355i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 26.1743 | + | 25.3230i | 0.888415 | + | 0.859520i | ||||
\(869\) | 35.7108i | 1.21141i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.8543 | − | 6.84406i | 0.401666 | − | 0.231902i | ||||
\(872\) | 14.6818 | − | 33.6401i | 0.497189 | − | 1.13920i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0.501120 | − | 1.55526i | 0.0169506 | − | 0.0526075i | ||||
\(875\) | 5.24573 | + | 13.2048i | 0.177338 | + | 0.446403i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.3837 | − | 30.1095i | 0.587006 | − | 1.01672i | −0.407616 | − | 0.913153i | \(-0.633640\pi\) |
0.994622 | − | 0.103571i | \(-0.0330269\pi\) | |||||||
\(878\) | 15.7015 | − | 3.37773i | 0.529899 | − | 0.113993i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.60944 | − | 12.8975i | 0.0879643 | − | 0.434775i | ||||
\(881\) | − | 32.5275i | − | 1.09588i | −0.836518 | − | 0.547940i | \(-0.815412\pi\) | ||
0.836518 | − | 0.547940i | \(-0.184588\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 15.6505i | − | 0.526682i | −0.964703 | − | 0.263341i | \(-0.915176\pi\) | ||
0.964703 | − | 0.263341i | \(-0.0848244\pi\) | |||||||
\(884\) | 7.55892 | + | 16.7559i | 0.254234 | + | 0.563561i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.41517 | + | 39.1181i | 0.282713 | + | 1.31420i | ||||
\(887\) | 24.5362 | − | 42.4979i | 0.823844 | − | 1.42694i | −0.0789562 | − | 0.996878i | \(-0.525159\pi\) |
0.902800 | − | 0.430061i | \(-0.141508\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.6247 | + | 46.8830i | 0.624654 | + | 1.57241i | ||||
\(890\) | 9.60565 | + | 3.09503i | 0.321982 | + | 0.103746i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.965600 | − | 0.0967010i | −0.0323307 | − | 0.00323779i | ||||
\(893\) | −42.5931 | + | 24.5912i | −1.42533 | + | 0.822912i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 3.71786i | − | 0.124274i | ||||||
\(896\) | −21.7666 | − | 20.5478i | −0.727172 | − | 0.686455i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.9912 | + | 30.9345i | 0.934080 | + | 1.03230i | ||||
\(899\) | −14.2316 | − | 24.6499i | −0.474651 | − | 0.822119i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.98365 | − | 12.0960i | 0.232659 | − | 0.402977i | ||||
\(902\) | 5.86682 | − | 18.2081i | 0.195344 | − | 0.606263i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.4779 | − | 20.2745i | 0.913902 | − | 0.674321i | ||||
\(905\) | −2.73385 | − | 1.57839i | −0.0908762 | − | 0.0524674i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.3280 | + | 12.3137i | −0.708184 | + | 0.408870i | −0.810388 | − | 0.585893i | \(-0.800744\pi\) |
0.102204 | + | 0.994763i | \(0.467411\pi\) | |||||||
\(908\) | 29.3603 | − | 13.2450i | 0.974355 | − | 0.439552i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.51595 | − | 3.69351i | 0.182852 | − | 0.122439i | ||||
\(911\) | −35.3866 | −1.17241 | −0.586205 | − | 0.810163i | \(-0.699379\pi\) | ||||
−0.586205 | + | 0.810163i | \(0.699379\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00522 | + | 3.47314i | 0.0663631 | + | 0.114944i | ||||
\(914\) | 0.851905 | + | 3.96010i | 0.0281785 | + | 0.130989i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.6825 | − | 16.3104i | −0.749450 | − | 0.538909i | ||||
\(917\) | 0.724958 | − | 4.94881i | 0.0239402 | − | 0.163424i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.4726 | − | 6.04637i | −0.345460 | − | 0.199451i | 0.317224 | − | 0.948351i | \(-0.397249\pi\) |
−0.662684 | + | 0.748899i | \(0.730583\pi\) | |||||||
\(920\) | −0.417901 | − | 0.182388i | −0.0137778 | − | 0.00601316i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.0569 | − | 22.1659i | −0.660540 | − | 0.729994i | ||||
\(923\) | 22.4446 | 0.738773 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.2871 | −0.371116 | ||||||||
\(926\) | 37.2387 | + | 41.1543i | 1.22374 | + | 1.35241i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 11.9447 | + | 20.1150i | 0.392105 | + | 0.660307i | ||||
\(929\) | 11.1624 | + | 6.44460i | 0.366226 | + | 0.211441i | 0.671808 | − | 0.740725i | \(-0.265518\pi\) |
−0.305583 | + | 0.952166i | \(0.598851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −27.0472 | + | 6.40959i | −0.886437 | + | 0.210066i | ||||
\(932\) | 24.8253 | − | 34.5241i | 0.813181 | − | 1.13087i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.74378 | − | 40.6457i | −0.286105 | − | 1.32997i | ||||
\(935\) | −4.72102 | − | 8.17704i | −0.154394 | − | 0.267418i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.49179 | −0.310083 | −0.155042 | − | 0.987908i | \(-0.549551\pi\) | ||||
−0.155042 | + | 0.987908i | \(0.549551\pi\) | |||||||
\(938\) | 1.06179 | + | 15.9586i | 0.0346686 | + | 0.521066i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 5.64364 | + | 12.5103i | 0.184075 | + | 0.408040i | ||||
\(941\) | 22.6714 | − | 13.0893i | 0.739067 | − | 0.426700i | −0.0826632 | − | 0.996578i | \(-0.526343\pi\) |
0.821730 | + | 0.569877i | \(0.193009\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.574064 | − | 0.331436i | −0.0186941 | − | 0.0107930i | ||||
\(944\) | 15.9082 | + | 47.3736i | 0.517769 | + | 1.54188i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.4150 | − | 66.4631i | 0.696263 | − | 2.16090i | ||||
\(947\) | −16.4945 | + | 28.5693i | −0.536000 | + | 0.928379i | 0.463115 | + | 0.886298i | \(0.346732\pi\) |
−0.999114 | + | 0.0420801i | \(0.986602\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 20.1420 | + | 34.8870i | 0.653837 | + | 1.13248i | ||||
\(950\) | −17.6827 | − | 19.5421i | −0.573704 | − | 0.634028i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −21.4664 | − | 0.716756i | −0.695731 | − | 0.0232302i | ||||
\(953\) | − | 35.8953i | − | 1.16276i | −0.813631 | − | 0.581382i | \(-0.802512\pi\) | ||
0.813631 | − | 0.581382i | \(-0.197488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.93698 | − | 1.11831i | 0.0626791 | − | 0.0361878i | ||||
\(956\) | −2.76136 | + | 27.5733i | −0.0893088 | + | 0.891786i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.4295 | − | 8.51584i | −0.853898 | − | 0.275134i | ||||
\(959\) | −32.0418 | + | 40.5224i | −1.03468 | + | 1.30854i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.18487 | − | 14.1766i | 0.264028 | − | 0.457310i | ||||
\(962\) | 2.29064 | + | 10.6481i | 0.0738533 | + | 0.343309i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.7231 | − | 7.09302i | 0.506407 | − | 0.228451i | ||||
\(965\) | − | 10.2391i | − | 0.329607i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.1841i | 0.520444i | 0.965549 | + | 0.260222i | \(0.0837958\pi\) | ||||
−0.965549 | + | 0.260222i | \(0.916204\pi\) | |||||||
\(968\) | −68.1758 | + | 7.67326i | −2.19125 | + | 0.246628i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.30418 | + | 0.495679i | −0.0739827 | + | 0.0159153i | ||||
\(971\) | −10.2868 | + | 17.8172i | −0.330118 | + | 0.571781i | −0.982535 | − | 0.186079i | \(-0.940422\pi\) |
0.652417 | + | 0.757861i | \(0.273755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.9377 | + | 40.1191i | 0.510939 | + | 1.28616i | ||||
\(974\) | 0.399801 | − | 1.24081i | 0.0128105 | − | 0.0397581i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.61886 | − | 1.83380i | 0.0518184 | − | 0.0586984i | ||||
\(977\) | 21.0179 | − | 12.1347i | 0.672421 | − | 0.388222i | −0.124572 | − | 0.992211i | \(-0.539756\pi\) |
0.796993 | + | 0.603988i | \(0.206423\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 76.4778i | − | 2.44424i | ||||||
\(980\) | 1.02760 | + | 7.68820i | 0.0328255 | + | 0.245591i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 32.7575 | − | 29.6409i | 1.04534 | − | 0.945878i | ||||
\(983\) | −7.34094 | − | 12.7149i | −0.234140 | − | 0.405542i | 0.724883 | − | 0.688872i | \(-0.241894\pi\) |
−0.959022 | + | 0.283331i | \(0.908561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.46992 | − | 4.27802i | 0.0786980 | − | 0.136309i | ||||
\(986\) | 15.9774 | + | 5.14808i | 0.508825 | + | 0.163948i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.8472 | + | 20.6477i | −0.472352 | + | 0.656891i | ||||
\(989\) | −2.09545 | − | 1.20981i | −0.0666313 | − | 0.0384696i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.6167 | − | 13.6351i | 0.750209 | − | 0.433133i | −0.0755605 | − | 0.997141i | \(-0.524075\pi\) |
0.825769 | + | 0.564008i | \(0.190741\pi\) | |||||||
\(992\) | −19.0518 | + | 33.9538i | −0.604895 | + | 1.07803i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −11.5760 | + | 23.5322i | −0.367168 | + | 0.746397i | ||||
\(995\) | −3.89236 | −0.123396 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.4820 | − | 23.3515i | −0.426979 | − | 0.739550i | 0.569624 | − | 0.821906i | \(-0.307089\pi\) |
−0.996603 | + | 0.0823557i | \(0.973756\pi\) | |||||||
\(998\) | −19.4767 | + | 4.18987i | −0.616525 | + | 0.132628i | ||||
\(999\) | 0 | 0 |
(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 | 756.2.be.c.107.3 | ✓ | 28 | |
3.2 | odd | 2 | inner | 756.2.be.c.107.12 | yes | 28 | |
4.3 | odd | 2 | 756.2.be.d.107.8 | yes | 28 | ||
7.4 | even | 3 | 756.2.be.d.431.7 | yes | 28 | ||
12.11 | even | 2 | 756.2.be.d.107.7 | yes | 28 | ||
21.11 | odd | 6 | 756.2.be.d.431.8 | yes | 28 | ||
28.11 | odd | 6 | inner | 756.2.be.c.431.12 | yes | 28 | |
84.11 | even | 6 | inner | 756.2.be.c.431.3 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
756.2.be.c.107.3 | ✓ | 28 | 1.1 | even | 1 | trivial | |
756.2.be.c.107.12 | yes | 28 | 3.2 | odd | 2 | inner | |
756.2.be.c.431.3 | yes | 28 | 84.11 | even | 6 | inner | |
756.2.be.c.431.12 | yes | 28 | 28.11 | odd | 6 | inner | |
756.2.be.d.107.7 | yes | 28 | 12.11 | even | 2 | ||
756.2.be.d.107.8 | yes | 28 | 4.3 | odd | 2 | ||
756.2.be.d.431.7 | yes | 28 | 7.4 | even | 3 | ||
756.2.be.d.431.8 | yes | 28 | 21.11 | odd | 6 |