Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(265,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.265");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.o (of order \(4\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.4 | ||
Root | \(-0.916813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.307 |
Dual form | 546.2.o.a.265.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.27220 | − | 2.27220i | 1.01616 | − | 1.01616i | 0.0162935 | − | 0.999867i | \(-0.494813\pi\) |
0.999867 | − | 0.0162935i | \(-0.00518663\pi\) | |||||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 1.35539 | + | 2.27220i | 0.512290 | + | 0.858813i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 3.21338 | 1.01616 | ||||||||
\(11\) | 0.355392 | − | 0.355392i | 0.107155 | − | 0.107155i | −0.651497 | − | 0.758651i | \(-0.725859\pi\) |
0.758651 | + | 0.651497i | \(0.225859\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.00000 | + | 3.00000i | 0.554700 | + | 0.832050i | ||||
\(14\) | −0.648285 | + | 2.56510i | −0.173261 | + | 0.685551i | ||||
\(15\) | −2.27220 | − | 2.27220i | −0.586681 | − | 0.586681i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −4.32583 | −1.04917 | −0.524584 | − | 0.851359i | \(-0.675779\pi\) | ||||
−0.524584 | + | 0.851359i | \(0.675779\pi\) | |||||||
\(18\) | −0.707107 | − | 0.707107i | −0.166667 | − | 0.166667i | ||||
\(19\) | 5.98299 | − | 5.98299i | 1.37259 | − | 1.37259i | 0.516007 | − | 0.856584i | \(-0.327418\pi\) |
0.856584 | − | 0.516007i | \(-0.172582\pi\) | |||||||
\(20\) | 2.27220 | + | 2.27220i | 0.508080 | + | 0.508080i | ||||
\(21\) | 2.27220 | − | 1.35539i | 0.495836 | − | 0.295771i | ||||
\(22\) | 0.502600 | 0.107155 | ||||||||
\(23\) | − | 2.38496i | − | 0.497298i | −0.968594 | − | 0.248649i | \(-0.920014\pi\) | ||
0.968594 | − | 0.248649i | \(-0.0799865\pi\) | |||||||
\(24\) | 0.707107 | + | 0.707107i | 0.144338 | + | 0.144338i | ||||
\(25\) | − | 5.32583i | − | 1.06517i | ||||||
\(26\) | −0.707107 | + | 3.53553i | −0.138675 | + | 0.693375i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.27220 | + | 1.35539i | −0.429406 | + | 0.256145i | ||||
\(29\) | 1.09574 | 0.203474 | 0.101737 | − | 0.994811i | \(-0.467560\pi\) | ||||
0.101737 | + | 0.994811i | \(0.467560\pi\) | |||||||
\(30\) | − | 3.21338i | − | 0.586681i | ||||||
\(31\) | 1.08319 | − | 1.08319i | 0.194546 | − | 0.194546i | −0.603111 | − | 0.797657i | \(-0.706072\pi\) |
0.797657 | + | 0.603111i | \(0.206072\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −0.355392 | − | 0.355392i | −0.0618657 | − | 0.0618657i | ||||
\(34\) | −3.05882 | − | 3.05882i | −0.524584 | − | 0.524584i | ||||
\(35\) | 8.24264 | + | 2.08319i | 1.39326 | + | 0.352123i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | −5.18902 | + | 5.18902i | −0.853069 | + | 0.853069i | −0.990510 | − | 0.137441i | \(-0.956112\pi\) |
0.137441 | + | 0.990510i | \(0.456112\pi\) | |||||||
\(38\) | 8.46122 | 1.37259 | ||||||||
\(39\) | 3.00000 | − | 2.00000i | 0.480384 | − | 0.320256i | ||||
\(40\) | 3.21338i | 0.508080i | ||||||||
\(41\) | 3.53186 | − | 3.53186i | 0.551583 | − | 0.551583i | −0.375314 | − | 0.926898i | \(-0.622465\pi\) |
0.926898 | + | 0.375314i | \(0.122465\pi\) | |||||||
\(42\) | 2.56510 | + | 0.648285i | 0.395803 | + | 0.100033i | ||||
\(43\) | 7.44867i | 1.13591i | 0.823059 | + | 0.567956i | \(0.192266\pi\) | ||||
−0.823059 | + | 0.567956i | \(0.807734\pi\) | |||||||
\(44\) | 0.355392 | + | 0.355392i | 0.0535773 | + | 0.0535773i | ||||
\(45\) | −2.27220 | + | 2.27220i | −0.338720 | + | 0.338720i | ||||
\(46\) | 1.68642 | − | 1.68642i | 0.248649 | − | 0.248649i | ||||
\(47\) | −4.71078 | − | 4.71078i | −0.687138 | − | 0.687138i | 0.274460 | − | 0.961598i | \(-0.411501\pi\) |
−0.961598 | + | 0.274460i | \(0.911501\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −3.32583 | + | 6.15945i | −0.475118 | + | 0.879922i | ||||
\(50\) | 3.76593 | − | 3.76593i | 0.532583 | − | 0.532583i | ||||
\(51\) | 4.32583i | 0.605737i | ||||||||
\(52\) | −3.00000 | + | 2.00000i | −0.416025 | + | 0.277350i | ||||
\(53\) | −11.2552 | −1.54602 | −0.773010 | − | 0.634394i | \(-0.781250\pi\) | ||||
−0.773010 | + | 0.634394i | \(0.781250\pi\) | |||||||
\(54\) | −0.707107 | + | 0.707107i | −0.0962250 | + | 0.0962250i | ||||
\(55\) | − | 1.61504i | − | 0.217773i | ||||||
\(56\) | −2.56510 | − | 0.648285i | −0.342776 | − | 0.0866307i | ||||
\(57\) | −5.98299 | − | 5.98299i | −0.792466 | − | 0.792466i | ||||
\(58\) | 0.774804 | + | 0.774804i | 0.101737 | + | 0.101737i | ||||
\(59\) | 3.61504 | + | 3.61504i | 0.470639 | + | 0.470639i | 0.902121 | − | 0.431483i | \(-0.142009\pi\) |
−0.431483 | + | 0.902121i | \(0.642009\pi\) | |||||||
\(60\) | 2.27220 | − | 2.27220i | 0.293340 | − | 0.293340i | ||||
\(61\) | 4.32583i | 0.553865i | 0.960889 | + | 0.276933i | \(0.0893179\pi\) | ||||
−0.960889 | + | 0.276933i | \(0.910682\pi\) | |||||||
\(62\) | 1.53186 | 0.194546 | ||||||||
\(63\) | −1.35539 | − | 2.27220i | −0.170763 | − | 0.286271i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 11.3610 | + | 2.27220i | 1.40916 | + | 0.281832i | ||||
\(66\) | − | 0.502600i | − | 0.0618657i | ||||||
\(67\) | −0.531858 | − | 0.531858i | −0.0649768 | − | 0.0649768i | 0.673872 | − | 0.738848i | \(-0.264630\pi\) |
−0.738848 | + | 0.673872i | \(0.764630\pi\) | |||||||
\(68\) | − | 4.32583i | − | 0.524584i | ||||||
\(69\) | −2.38496 | −0.287115 | ||||||||
\(70\) | 4.35539 | + | 7.30146i | 0.520569 | + | 0.872692i | ||||
\(71\) | 6.38496 | + | 6.38496i | 0.757755 | + | 0.757755i | 0.975913 | − | 0.218159i | \(-0.0700050\pi\) |
−0.218159 | + | 0.975913i | \(0.570005\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −5.18902 | − | 5.18902i | −0.607329 | − | 0.607329i | 0.334919 | − | 0.942247i | \(-0.391291\pi\) |
−0.942247 | + | 0.334919i | \(0.891291\pi\) | |||||||
\(74\) | −7.33838 | −0.853069 | ||||||||
\(75\) | −5.32583 | −0.614974 | ||||||||
\(76\) | 5.98299 | + | 5.98299i | 0.686296 | + | 0.686296i | ||||
\(77\) | 1.28922 | + | 0.325828i | 0.146920 | + | 0.0371315i | ||||
\(78\) | 3.53553 | + | 0.707107i | 0.400320 | + | 0.0800641i | ||||
\(79\) | −11.3143 | −1.27296 | −0.636480 | − | 0.771293i | \(-0.719610\pi\) | ||||
−0.636480 | + | 0.771293i | \(0.719610\pi\) | |||||||
\(80\) | −2.27220 | + | 2.27220i | −0.254040 | + | 0.254040i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.99480 | 0.551583 | ||||||||
\(83\) | 6.71078 | − | 6.71078i | 0.736604 | − | 0.736604i | −0.235315 | − | 0.971919i | \(-0.575612\pi\) |
0.971919 | + | 0.235315i | \(0.0756122\pi\) | |||||||
\(84\) | 1.35539 | + | 2.27220i | 0.147885 | + | 0.247918i | ||||
\(85\) | −9.82917 | + | 9.82917i | −1.06612 | + | 1.06612i | ||||
\(86\) | −5.26701 | + | 5.26701i | −0.567956 | + | 0.567956i | ||||
\(87\) | − | 1.09574i | − | 0.117475i | ||||||
\(88\) | 0.502600i | 0.0535773i | ||||||||
\(89\) | −3.75044 | − | 3.75044i | −0.397546 | − | 0.397546i | 0.479821 | − | 0.877367i | \(-0.340702\pi\) |
−0.877367 | + | 0.479821i | \(0.840702\pi\) | |||||||
\(90\) | −3.21338 | −0.338720 | ||||||||
\(91\) | −4.10583 | + | 8.61058i | −0.430408 | + | 0.902634i | ||||
\(92\) | 2.38496 | 0.248649 | ||||||||
\(93\) | −1.08319 | − | 1.08319i | −0.112321 | − | 0.112321i | ||||
\(94\) | − | 6.66205i | − | 0.687138i | ||||||
\(95\) | − | 27.1891i | − | 2.78955i | ||||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | −12.9931 | + | 12.9931i | −1.31925 | + | 1.31925i | −0.404876 | + | 0.914372i | \(0.632685\pi\) |
−0.914372 | + | 0.404876i | \(0.867315\pi\) | |||||||
\(98\) | −6.70711 | + | 2.00368i | −0.677520 | + | 0.202402i | ||||
\(99\) | −0.355392 | + | 0.355392i | −0.0357182 | + | 0.0357182i | ||||
\(100\) | 5.32583 | 0.532583 | ||||||||
\(101\) | −19.7996 | −1.97013 | −0.985067 | − | 0.172171i | \(-0.944922\pi\) | ||||
−0.985067 | + | 0.172171i | \(0.944922\pi\) | |||||||
\(102\) | −3.05882 | + | 3.05882i | −0.302869 | + | 0.302869i | ||||
\(103\) | 2.70386 | 0.266420 | 0.133210 | − | 0.991088i | \(-0.457472\pi\) | ||||
0.133210 | + | 0.991088i | \(0.457472\pi\) | |||||||
\(104\) | −3.53553 | − | 0.707107i | −0.346688 | − | 0.0693375i | ||||
\(105\) | 2.08319 | − | 8.24264i | 0.203298 | − | 0.804399i | ||||
\(106\) | −7.95862 | − | 7.95862i | −0.773010 | − | 0.773010i | ||||
\(107\) | −11.6673 | −1.12792 | −0.563958 | − | 0.825804i | \(-0.690722\pi\) | ||||
−0.563958 | + | 0.825804i | \(0.690722\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −5.29626 | − | 5.29626i | −0.507290 | − | 0.507290i | 0.406404 | − | 0.913694i | \(-0.366783\pi\) |
−0.913694 | + | 0.406404i | \(0.866783\pi\) | |||||||
\(110\) | 1.14201 | − | 1.14201i | 0.108886 | − | 0.108886i | ||||
\(111\) | 5.18902 | + | 5.18902i | 0.492520 | + | 0.492520i | ||||
\(112\) | −1.35539 | − | 2.27220i | −0.128072 | − | 0.214703i | ||||
\(113\) | 20.3440 | 1.91380 | 0.956902 | − | 0.290412i | \(-0.0937923\pi\) | ||||
0.956902 | + | 0.290412i | \(0.0937923\pi\) | |||||||
\(114\) | − | 8.46122i | − | 0.792466i | ||||||
\(115\) | −5.41911 | − | 5.41911i | −0.505334 | − | 0.505334i | ||||
\(116\) | 1.09574i | 0.101737i | ||||||||
\(117\) | −2.00000 | − | 3.00000i | −0.184900 | − | 0.277350i | ||||
\(118\) | 5.11245i | 0.470639i | ||||||||
\(119\) | −5.86319 | − | 9.82917i | −0.537478 | − | 0.901038i | ||||
\(120\) | 3.21338 | 0.293340 | ||||||||
\(121\) | 10.7474i | 0.977036i | ||||||||
\(122\) | −3.05882 | + | 3.05882i | −0.276933 | + | 0.276933i | ||||
\(123\) | −3.53186 | − | 3.53186i | −0.318457 | − | 0.318457i | ||||
\(124\) | 1.08319 | + | 1.08319i | 0.0972731 | + | 0.0972731i | ||||
\(125\) | −0.740347 | − | 0.740347i | −0.0662186 | − | 0.0662186i | ||||
\(126\) | 0.648285 | − | 2.56510i | 0.0577538 | − | 0.228517i | ||||
\(127\) | − | 7.60812i | − | 0.675112i | −0.941305 | − | 0.337556i | \(-0.890400\pi\) | ||
0.941305 | − | 0.337556i | \(-0.109600\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 7.44867 | 0.655819 | ||||||||
\(130\) | 6.42677 | + | 9.64015i | 0.563665 | + | 0.845497i | ||||
\(131\) | 6.87024i | 0.600255i | 0.953899 | + | 0.300128i | \(0.0970293\pi\) | ||||
−0.953899 | + | 0.300128i | \(0.902971\pi\) | |||||||
\(132\) | 0.355392 | − | 0.355392i | 0.0309329 | − | 0.0309329i | ||||
\(133\) | 21.7039 | + | 5.48528i | 1.88196 | + | 0.475634i | ||||
\(134\) | − | 0.752160i | − | 0.0649768i | ||||||
\(135\) | 2.27220 | + | 2.27220i | 0.195560 | + | 0.195560i | ||||
\(136\) | 3.05882 | − | 3.05882i | 0.262292 | − | 0.262292i | ||||
\(137\) | −0.272205 | + | 0.272205i | −0.0232560 | + | 0.0232560i | −0.718639 | − | 0.695383i | \(-0.755235\pi\) |
0.695383 | + | 0.718639i | \(0.255235\pi\) | |||||||
\(138\) | −1.68642 | − | 1.68642i | −0.143557 | − | 0.143557i | ||||
\(139\) | − | 20.3440i | − | 1.72556i | −0.505583 | − | 0.862778i | \(-0.668722\pi\) | ||
0.505583 | − | 0.862778i | \(-0.331278\pi\) | |||||||
\(140\) | −2.08319 | + | 8.24264i | −0.176061 | + | 0.696630i | ||||
\(141\) | −4.71078 | + | 4.71078i | −0.396720 | + | 0.396720i | ||||
\(142\) | 9.02969i | 0.757755i | ||||||||
\(143\) | 1.77696 | + | 0.355392i | 0.148597 | + | 0.0297193i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.48974 | − | 2.48974i | 0.206762 | − | 0.206762i | ||||
\(146\) | − | 7.33838i | − | 0.607329i | ||||||
\(147\) | 6.15945 | + | 3.32583i | 0.508023 | + | 0.274310i | ||||
\(148\) | −5.18902 | − | 5.18902i | −0.426535 | − | 0.426535i | ||||
\(149\) | 10.5685 | + | 10.5685i | 0.865803 | + | 0.865803i | 0.992005 | − | 0.126202i | \(-0.0402787\pi\) |
−0.126202 | + | 0.992005i | \(0.540279\pi\) | |||||||
\(150\) | −3.76593 | − | 3.76593i | −0.307487 | − | 0.307487i | ||||
\(151\) | −0.149362 | + | 0.149362i | −0.0121549 | + | 0.0121549i | −0.713158 | − | 0.701003i | \(-0.752736\pi\) |
0.701003 | + | 0.713158i | \(0.252736\pi\) | |||||||
\(152\) | 8.46122i | 0.686296i | ||||||||
\(153\) | 4.32583 | 0.349722 | ||||||||
\(154\) | 0.681219 | + | 1.14201i | 0.0548942 | + | 0.0920257i | ||||
\(155\) | − | 4.92244i | − | 0.395380i | ||||||
\(156\) | 2.00000 | + | 3.00000i | 0.160128 | + | 0.240192i | ||||
\(157\) | 10.7630i | 0.858980i | 0.903072 | + | 0.429490i | \(0.141307\pi\) | ||||
−0.903072 | + | 0.429490i | \(0.858693\pi\) | |||||||
\(158\) | −8.00043 | − | 8.00043i | −0.636480 | − | 0.636480i | ||||
\(159\) | 11.2552i | 0.892595i | ||||||||
\(160\) | −3.21338 | −0.254040 | ||||||||
\(161\) | 5.41911 | − | 3.23255i | 0.427085 | − | 0.254761i | ||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | −3.40901 | + | 3.40901i | −0.267015 | + | 0.267015i | −0.827896 | − | 0.560881i | \(-0.810462\pi\) |
0.560881 | + | 0.827896i | \(0.310462\pi\) | |||||||
\(164\) | 3.53186 | + | 3.53186i | 0.275792 | + | 0.275792i | ||||
\(165\) | −1.61504 | −0.125731 | ||||||||
\(166\) | 9.49048 | 0.736604 | ||||||||
\(167\) | −10.0226 | − | 10.0226i | −0.775575 | − | 0.775575i | 0.203500 | − | 0.979075i | \(-0.434768\pi\) |
−0.979075 | + | 0.203500i | \(0.934768\pi\) | |||||||
\(168\) | −0.648285 | + | 2.56510i | −0.0500163 | + | 0.197902i | ||||
\(169\) | −5.00000 | + | 12.0000i | −0.384615 | + | 0.923077i | ||||
\(170\) | −13.9005 | −1.06612 | ||||||||
\(171\) | −5.98299 | + | 5.98299i | −0.457531 | + | 0.457531i | ||||
\(172\) | −7.44867 | −0.567956 | ||||||||
\(173\) | −19.7405 | −1.50084 | −0.750420 | − | 0.660961i | \(-0.770149\pi\) | ||||
−0.750420 | + | 0.660961i | \(0.770149\pi\) | |||||||
\(174\) | 0.774804 | − | 0.774804i | 0.0587377 | − | 0.0587377i | ||||
\(175\) | 12.1014 | − | 7.21858i | 0.914778 | − | 0.545673i | ||||
\(176\) | −0.355392 | + | 0.355392i | −0.0267886 | + | 0.0267886i | ||||
\(177\) | 3.61504 | − | 3.61504i | 0.271723 | − | 0.271723i | ||||
\(178\) | − | 5.30392i | − | 0.397546i | ||||||
\(179\) | − | 9.79960i | − | 0.732457i | −0.930525 | − | 0.366228i | \(-0.880649\pi\) | ||
0.930525 | − | 0.366228i | \(-0.119351\pi\) | |||||||
\(180\) | −2.27220 | − | 2.27220i | −0.169360 | − | 0.169360i | ||||
\(181\) | 10.4372 | 0.775788 | 0.387894 | − | 0.921704i | \(-0.373203\pi\) | ||||
0.387894 | + | 0.921704i | \(0.373203\pi\) | |||||||
\(182\) | −8.99186 | + | 3.18534i | −0.666521 | + | 0.236113i | ||||
\(183\) | 4.32583 | 0.319774 | ||||||||
\(184\) | 1.68642 | + | 1.68642i | 0.124324 | + | 0.124324i | ||||
\(185\) | 23.5810i | 1.73371i | ||||||||
\(186\) | − | 1.53186i | − | 0.112321i | ||||||
\(187\) | −1.53736 | + | 1.53736i | −0.112423 | + | 0.112423i | ||||
\(188\) | 4.71078 | − | 4.71078i | 0.343569 | − | 0.343569i | ||||
\(189\) | −2.27220 | + | 1.35539i | −0.165279 | + | 0.0985902i | ||||
\(190\) | 19.2256 | − | 19.2256i | 1.39477 | − | 1.39477i | ||||
\(191\) | 11.1410 | 0.806136 | 0.403068 | − | 0.915170i | \(-0.367944\pi\) | ||||
0.403068 | + | 0.915170i | \(0.367944\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 4.03661 | − | 4.03661i | 0.290562 | − | 0.290562i | −0.546741 | − | 0.837302i | \(-0.684132\pi\) |
0.837302 | + | 0.546741i | \(0.184132\pi\) | |||||||
\(194\) | −18.3750 | −1.31925 | ||||||||
\(195\) | 2.27220 | − | 11.3610i | 0.162716 | − | 0.813580i | ||||
\(196\) | −6.15945 | − | 3.32583i | −0.439961 | − | 0.237559i | ||||
\(197\) | 0.627596 | + | 0.627596i | 0.0447144 | + | 0.0447144i | 0.729110 | − | 0.684396i | \(-0.239934\pi\) |
−0.684396 | + | 0.729110i | \(0.739934\pi\) | |||||||
\(198\) | −0.502600 | −0.0357182 | ||||||||
\(199\) | 16.5375 | 1.17231 | 0.586156 | − | 0.810198i | \(-0.300641\pi\) | ||||
0.586156 | + | 0.810198i | \(0.300641\pi\) | |||||||
\(200\) | 3.76593 | + | 3.76593i | 0.266291 | + | 0.266291i | ||||
\(201\) | −0.531858 | + | 0.531858i | −0.0375143 | + | 0.0375143i | ||||
\(202\) | −14.0004 | − | 14.0004i | −0.985067 | − | 0.985067i | ||||
\(203\) | 1.48515 | + | 2.48974i | 0.104237 | + | 0.174746i | ||||
\(204\) | −4.32583 | −0.302869 | ||||||||
\(205\) | − | 16.0502i | − | 1.12100i | ||||||
\(206\) | 1.91192 | + | 1.91192i | 0.133210 | + | 0.133210i | ||||
\(207\) | 2.38496i | 0.165766i | ||||||||
\(208\) | −2.00000 | − | 3.00000i | −0.138675 | − | 0.208013i | ||||
\(209\) | − | 4.25261i | − | 0.294159i | ||||||
\(210\) | 7.30146 | − | 4.35539i | 0.503849 | − | 0.300551i | ||||
\(211\) | −0.551329 | −0.0379551 | −0.0189775 | − | 0.999820i | \(-0.506041\pi\) | ||||
−0.0189775 | + | 0.999820i | \(0.506041\pi\) | |||||||
\(212\) | − | 11.2552i | − | 0.773010i | ||||||
\(213\) | 6.38496 | − | 6.38496i | 0.437490 | − | 0.437490i | ||||
\(214\) | −8.24999 | − | 8.24999i | −0.563958 | − | 0.563958i | ||||
\(215\) | 16.9249 | + | 16.9249i | 1.15427 | + | 1.15427i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 3.92936 | + | 0.993080i | 0.266743 | + | 0.0674147i | ||||
\(218\) | − | 7.49005i | − | 0.507290i | ||||||
\(219\) | −5.18902 | + | 5.18902i | −0.350641 | + | 0.350641i | ||||
\(220\) | 1.61504 | 0.108886 | ||||||||
\(221\) | −8.65166 | − | 12.9775i | −0.581973 | − | 0.872960i | ||||
\(222\) | 7.33838i | 0.492520i | ||||||||
\(223\) | −9.89430 | + | 9.89430i | −0.662571 | + | 0.662571i | −0.955985 | − | 0.293414i | \(-0.905208\pi\) |
0.293414 | + | 0.955985i | \(0.405208\pi\) | |||||||
\(224\) | 0.648285 | − | 2.56510i | 0.0433153 | − | 0.171388i | ||||
\(225\) | 5.32583i | 0.355055i | ||||||||
\(226\) | 14.3854 | + | 14.3854i | 0.956902 | + | 0.956902i | ||||
\(227\) | −1.67417 | + | 1.67417i | −0.111119 | + | 0.111119i | −0.760480 | − | 0.649361i | \(-0.775036\pi\) |
0.649361 | + | 0.760480i | \(0.275036\pi\) | |||||||
\(228\) | 5.98299 | − | 5.98299i | 0.396233 | − | 0.396233i | ||||
\(229\) | 1.32583 | + | 1.32583i | 0.0876132 | + | 0.0876132i | 0.749555 | − | 0.661942i | \(-0.230267\pi\) |
−0.661942 | + | 0.749555i | \(0.730267\pi\) | |||||||
\(230\) | − | 7.66377i | − | 0.505334i | ||||||
\(231\) | 0.325828 | − | 1.28922i | 0.0214379 | − | 0.0848242i | ||||
\(232\) | −0.774804 | + | 0.774804i | −0.0508684 | + | 0.0508684i | ||||
\(233\) | 10.2117i | 0.668988i | 0.942398 | + | 0.334494i | \(0.108565\pi\) | ||||
−0.942398 | + | 0.334494i | \(0.891435\pi\) | |||||||
\(234\) | 0.707107 | − | 3.53553i | 0.0462250 | − | 0.231125i | ||||
\(235\) | −21.4077 | −1.39649 | ||||||||
\(236\) | −3.61504 | + | 3.61504i | −0.235319 | + | 0.235319i | ||||
\(237\) | 11.3143i | 0.734944i | ||||||||
\(238\) | 2.80437 | − | 11.0962i | 0.181780 | − | 0.719258i | ||||
\(239\) | −15.2212 | − | 15.2212i | −0.984575 | − | 0.984575i | 0.0153074 | − | 0.999883i | \(-0.495127\pi\) |
−0.999883 | + | 0.0153074i | \(0.995127\pi\) | |||||||
\(240\) | 2.27220 | + | 2.27220i | 0.146670 | + | 0.146670i | ||||
\(241\) | −3.38496 | − | 3.38496i | −0.218044 | − | 0.218044i | 0.589630 | − | 0.807674i | \(-0.299274\pi\) |
−0.807674 | + | 0.589630i | \(0.799274\pi\) | |||||||
\(242\) | −7.59955 | + | 7.59955i | −0.488518 | + | 0.488518i | ||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −4.32583 | −0.276933 | ||||||||
\(245\) | 6.43858 | + | 21.5525i | 0.411346 | + | 1.37694i | ||||
\(246\) | − | 4.99480i | − | 0.318457i | ||||||
\(247\) | 29.9149 | + | 5.98299i | 1.90344 | + | 0.380688i | ||||
\(248\) | 1.53186i | 0.0972731i | ||||||||
\(249\) | −6.71078 | − | 6.71078i | −0.425279 | − | 0.425279i | ||||
\(250\) | − | 1.04701i | − | 0.0662186i | ||||||
\(251\) | 17.2281 | 1.08743 | 0.543714 | − | 0.839271i | \(-0.317018\pi\) | ||||
0.543714 | + | 0.839271i | \(0.317018\pi\) | |||||||
\(252\) | 2.27220 | − | 1.35539i | 0.143135 | − | 0.0853816i | ||||
\(253\) | −0.847593 | − | 0.847593i | −0.0532877 | − | 0.0532877i | ||||
\(254\) | 5.37976 | − | 5.37976i | 0.337556 | − | 0.337556i | ||||
\(255\) | 9.82917 | + | 9.82917i | 0.615526 | + | 0.615526i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.32324 | 0.207298 | 0.103649 | − | 0.994614i | \(-0.466948\pi\) | ||||
0.103649 | + | 0.994614i | \(0.466948\pi\) | |||||||
\(258\) | 5.26701 | + | 5.26701i | 0.327909 | + | 0.327909i | ||||
\(259\) | −18.8237 | − | 4.75736i | −1.16965 | − | 0.295608i | ||||
\(260\) | −2.27220 | + | 11.3610i | −0.140916 | + | 0.704581i | ||||
\(261\) | −1.09574 | −0.0678245 | ||||||||
\(262\) | −4.85799 | + | 4.85799i | −0.300128 | + | 0.300128i | ||||
\(263\) | −0.818029 | −0.0504418 | −0.0252209 | − | 0.999682i | \(-0.508029\pi\) | ||||
−0.0252209 | + | 0.999682i | \(0.508029\pi\) | |||||||
\(264\) | 0.502600 | 0.0309329 | ||||||||
\(265\) | −25.5741 | + | 25.5741i | −1.57100 | + | 1.57100i | ||||
\(266\) | 11.4683 | + | 19.2256i | 0.703165 | + | 1.17880i | ||||
\(267\) | −3.75044 | + | 3.75044i | −0.229523 | + | 0.229523i | ||||
\(268\) | 0.531858 | − | 0.531858i | 0.0324884 | − | 0.0324884i | ||||
\(269\) | − | 21.6081i | − | 1.31747i | −0.752375 | − | 0.658735i | \(-0.771092\pi\) | ||
0.752375 | − | 0.658735i | \(-0.228908\pi\) | |||||||
\(270\) | 3.21338i | 0.195560i | ||||||||
\(271\) | 15.0422 | + | 15.0422i | 0.913751 | + | 0.913751i | 0.996565 | − | 0.0828139i | \(-0.0263907\pi\) |
−0.0828139 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(272\) | 4.32583 | 0.262292 | ||||||||
\(273\) | 8.61058 | + | 4.10583i | 0.521136 | + | 0.248496i | ||||
\(274\) | −0.384955 | −0.0232560 | ||||||||
\(275\) | −1.89275 | − | 1.89275i | −0.114137 | − | 0.114137i | ||||
\(276\) | − | 2.38496i | − | 0.143557i | ||||||
\(277\) | − | 17.7996i | − | 1.06947i | −0.845018 | − | 0.534737i | \(-0.820411\pi\) | ||
0.845018 | − | 0.534737i | \(-0.179589\pi\) | |||||||
\(278\) | 14.3854 | − | 14.3854i | 0.862778 | − | 0.862778i | ||||
\(279\) | −1.08319 | + | 1.08319i | −0.0648487 | + | 0.0648487i | ||||
\(280\) | −7.30146 | + | 4.35539i | −0.436346 | + | 0.260284i | ||||
\(281\) | 6.20862 | − | 6.20862i | 0.370375 | − | 0.370375i | −0.497239 | − | 0.867614i | \(-0.665653\pi\) |
0.867614 | + | 0.497239i | \(0.165653\pi\) | |||||||
\(282\) | −6.66205 | −0.396720 | ||||||||
\(283\) | 25.1090 | 1.49258 | 0.746288 | − | 0.665624i | \(-0.231834\pi\) | ||||
0.746288 | + | 0.665624i | \(0.231834\pi\) | |||||||
\(284\) | −6.38496 | + | 6.38496i | −0.378877 | + | 0.378877i | ||||
\(285\) | −27.1891 | −1.61055 | ||||||||
\(286\) | 1.00520 | + | 1.50780i | 0.0594387 | + | 0.0891580i | ||||
\(287\) | 12.8122 | + | 3.23805i | 0.756277 | + | 0.191136i | ||||
\(288\) | 0.707107 | + | 0.707107i | 0.0416667 | + | 0.0416667i | ||||
\(289\) | 1.71278 | 0.100752 | ||||||||
\(290\) | 3.52103 | 0.206762 | ||||||||
\(291\) | 12.9931 | + | 12.9931i | 0.761668 | + | 0.761668i | ||||
\(292\) | 5.18902 | − | 5.18902i | 0.303664 | − | 0.303664i | ||||
\(293\) | 8.51343 | + | 8.51343i | 0.497360 | + | 0.497360i | 0.910615 | − | 0.413255i | \(-0.135608\pi\) |
−0.413255 | + | 0.910615i | \(0.635608\pi\) | |||||||
\(294\) | 2.00368 | + | 6.70711i | 0.116857 | + | 0.391166i | ||||
\(295\) | 16.4282 | 0.956489 | ||||||||
\(296\) | − | 7.33838i | − | 0.426535i | ||||||
\(297\) | 0.355392 | + | 0.355392i | 0.0206219 | + | 0.0206219i | ||||
\(298\) | 14.9461i | 0.865803i | ||||||||
\(299\) | 7.15487 | − | 4.76991i | 0.413777 | − | 0.275851i | ||||
\(300\) | − | 5.32583i | − | 0.307487i | ||||||
\(301\) | −16.9249 | + | 10.0959i | −0.975535 | + | 0.581916i | ||||
\(302\) | −0.211229 | −0.0121549 | ||||||||
\(303\) | 19.7996i | 1.13746i | ||||||||
\(304\) | −5.98299 | + | 5.98299i | −0.343148 | + | 0.343148i | ||||
\(305\) | 9.82917 | + | 9.82917i | 0.562816 | + | 0.562816i | ||||
\(306\) | 3.05882 | + | 3.05882i | 0.174861 | + | 0.174861i | ||||
\(307\) | 10.0397 | + | 10.0397i | 0.572993 | + | 0.572993i | 0.932964 | − | 0.359970i | \(-0.117213\pi\) |
−0.359970 | + | 0.932964i | \(0.617213\pi\) | |||||||
\(308\) | −0.325828 | + | 1.28922i | −0.0185658 | + | 0.0734600i | ||||
\(309\) | − | 2.70386i | − | 0.153817i | ||||||
\(310\) | 3.48069 | − | 3.48069i | 0.197690 | − | 0.197690i | ||||
\(311\) | 15.7064 | 0.890631 | 0.445316 | − | 0.895374i | \(-0.353092\pi\) | ||||
0.445316 | + | 0.895374i | \(0.353092\pi\) | |||||||
\(312\) | −0.707107 | + | 3.53553i | −0.0400320 | + | 0.200160i | ||||
\(313\) | − | 20.7702i | − | 1.17400i | −0.809587 | − | 0.587000i | \(-0.800309\pi\) | ||
0.809587 | − | 0.587000i | \(-0.199691\pi\) | |||||||
\(314\) | −7.61058 | + | 7.61058i | −0.429490 | + | 0.429490i | ||||
\(315\) | −8.24264 | − | 2.08319i | −0.464420 | − | 0.117374i | ||||
\(316\) | − | 11.3143i | − | 0.636480i | ||||||
\(317\) | 19.0126 | + | 19.0126i | 1.06785 | + | 1.06785i | 0.997524 | + | 0.0703273i | \(0.0224044\pi\) |
0.0703273 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(318\) | −7.95862 | + | 7.95862i | −0.446297 | + | 0.446297i | ||||
\(319\) | 0.389416 | − | 0.389416i | 0.0218031 | − | 0.0218031i | ||||
\(320\) | −2.27220 | − | 2.27220i | −0.127020 | − | 0.127020i | ||||
\(321\) | 11.6673i | 0.651203i | ||||||||
\(322\) | 6.11764 | + | 1.54613i | 0.340923 | + | 0.0861625i | ||||
\(323\) | −25.8814 | + | 25.8814i | −1.44008 | + | 1.44008i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | 15.9775 | − | 10.6517i | 0.886271 | − | 0.590848i | ||||
\(326\) | −4.82107 | −0.267015 | ||||||||
\(327\) | −5.29626 | + | 5.29626i | −0.292884 | + | 0.292884i | ||||
\(328\) | 4.99480i | 0.275792i | ||||||||
\(329\) | 4.31891 | − | 17.0888i | 0.238109 | − | 0.942137i | ||||
\(330\) | −1.14201 | − | 1.14201i | −0.0628655 | − | 0.0628655i | ||||
\(331\) | −13.9785 | − | 13.9785i | −0.768329 | − | 0.768329i | 0.209483 | − | 0.977812i | \(-0.432822\pi\) |
−0.977812 | + | 0.209483i | \(0.932822\pi\) | |||||||
\(332\) | 6.71078 | + | 6.71078i | 0.368302 | + | 0.368302i | ||||
\(333\) | 5.18902 | − | 5.18902i | 0.284356 | − | 0.284356i | ||||
\(334\) | − | 14.1742i | − | 0.775575i | ||||||
\(335\) | −2.41698 | −0.132054 | ||||||||
\(336\) | −2.27220 | + | 1.35539i | −0.123959 | + | 0.0739427i | ||||
\(337\) | − | 1.09574i | − | 0.0596887i | −0.999555 | − | 0.0298443i | \(-0.990499\pi\) | ||
0.999555 | − | 0.0298443i | \(-0.00950116\pi\) | |||||||
\(338\) | −12.0208 | + | 4.94975i | −0.653846 | + | 0.269231i | ||||
\(339\) | − | 20.3440i | − | 1.10493i | ||||||
\(340\) | −9.82917 | − | 9.82917i | −0.533061 | − | 0.533061i | ||||
\(341\) | − | 0.769911i | − | 0.0416930i | ||||||
\(342\) | −8.46122 | −0.457531 | ||||||||
\(343\) | −18.5033 | + | 0.791511i | −0.999086 | + | 0.0427376i | ||||
\(344\) | −5.26701 | − | 5.26701i | −0.283978 | − | 0.283978i | ||||
\(345\) | −5.41911 | + | 5.41911i | −0.291755 | + | 0.291755i | ||||
\(346\) | −13.9586 | − | 13.9586i | −0.750420 | − | 0.750420i | ||||
\(347\) | 32.0983 | 1.72313 | 0.861564 | − | 0.507649i | \(-0.169485\pi\) | ||||
0.861564 | + | 0.507649i | \(0.169485\pi\) | |||||||
\(348\) | 1.09574 | 0.0587377 | ||||||||
\(349\) | 18.9660 | + | 18.9660i | 1.01523 | + | 1.01523i | 0.999882 | + | 0.0153431i | \(0.00488405\pi\) |
0.0153431 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(350\) | 13.6613 | + | 3.45265i | 0.730226 | + | 0.184552i | ||||
\(351\) | −3.00000 | + | 2.00000i | −0.160128 | + | 0.106752i | ||||
\(352\) | −0.502600 | −0.0267886 | ||||||||
\(353\) | 15.5500 | − | 15.5500i | 0.827645 | − | 0.827645i | −0.159545 | − | 0.987191i | \(-0.551003\pi\) |
0.987191 | + | 0.159545i | \(0.0510028\pi\) | |||||||
\(354\) | 5.11245 | 0.271723 | ||||||||
\(355\) | 29.0159 | 1.54000 | ||||||||
\(356\) | 3.75044 | − | 3.75044i | 0.198773 | − | 0.198773i | ||||
\(357\) | −9.82917 | + | 5.86319i | −0.520215 | + | 0.310313i | ||||
\(358\) | 6.92936 | − | 6.92936i | 0.366228 | − | 0.366228i | ||||
\(359\) | −14.1846 | + | 14.1846i | −0.748632 | + | 0.748632i | −0.974222 | − | 0.225590i | \(-0.927569\pi\) |
0.225590 | + | 0.974222i | \(0.427569\pi\) | |||||||
\(360\) | − | 3.21338i | − | 0.169360i | ||||||
\(361\) | − | 52.5923i | − | 2.76801i | ||||||
\(362\) | 7.38019 | + | 7.38019i | 0.387894 | + | 0.387894i | ||||
\(363\) | 10.7474 | 0.564092 | ||||||||
\(364\) | −8.61058 | − | 4.10583i | −0.451317 | − | 0.215204i | ||||
\(365\) | −23.5810 | −1.23429 | ||||||||
\(366\) | 3.05882 | + | 3.05882i | 0.159887 | + | 0.159887i | ||||
\(367\) | − | 11.2552i | − | 0.587516i | −0.955880 | − | 0.293758i | \(-0.905094\pi\) | ||
0.955880 | − | 0.293758i | \(-0.0949060\pi\) | |||||||
\(368\) | 2.38496i | 0.124324i | ||||||||
\(369\) | −3.53186 | + | 3.53186i | −0.183861 | + | 0.183861i | ||||
\(370\) | −16.6743 | + | 16.6743i | −0.866856 | + | 0.866856i | ||||
\(371\) | −15.2552 | − | 25.5741i | −0.792010 | − | 1.32774i | ||||
\(372\) | 1.08319 | − | 1.08319i | 0.0561606 | − | 0.0561606i | ||||
\(373\) | 17.1479 | 0.887887 | 0.443944 | − | 0.896055i | \(-0.353579\pi\) | ||||
0.443944 | + | 0.896055i | \(0.353579\pi\) | |||||||
\(374\) | −2.17416 | −0.112423 | ||||||||
\(375\) | −0.740347 | + | 0.740347i | −0.0382314 | + | 0.0382314i | ||||
\(376\) | 6.66205 | 0.343569 | ||||||||
\(377\) | 2.19148 | + | 3.28722i | 0.112867 | + | 0.169300i | ||||
\(378\) | −2.56510 | − | 0.648285i | −0.131934 | − | 0.0333442i | ||||
\(379\) | 11.5685 | + | 11.5685i | 0.594232 | + | 0.594232i | 0.938772 | − | 0.344540i | \(-0.111965\pi\) |
−0.344540 | + | 0.938772i | \(0.611965\pi\) | |||||||
\(380\) | 27.1891 | 1.39477 | ||||||||
\(381\) | −7.60812 | −0.389776 | ||||||||
\(382\) | 7.87790 | + | 7.87790i | 0.403068 | + | 0.403068i | ||||
\(383\) | 1.26657 | − | 1.26657i | 0.0647189 | − | 0.0647189i | −0.674007 | − | 0.738725i | \(-0.735428\pi\) |
0.738725 | + | 0.674007i | \(0.235428\pi\) | |||||||
\(384\) | −0.707107 | − | 0.707107i | −0.0360844 | − | 0.0360844i | ||||
\(385\) | 3.66971 | − | 2.18902i | 0.187026 | − | 0.111563i | ||||
\(386\) | 5.70863 | 0.290562 | ||||||||
\(387\) | − | 7.44867i | − | 0.378637i | ||||||
\(388\) | −12.9931 | − | 12.9931i | −0.659624 | − | 0.659624i | ||||
\(389\) | 7.90685i | 0.400893i | 0.979705 | + | 0.200447i | \(0.0642393\pi\) | ||||
−0.979705 | + | 0.200447i | \(0.935761\pi\) | |||||||
\(390\) | 9.64015 | − | 6.42677i | 0.488148 | − | 0.325432i | ||||
\(391\) | 10.3169i | 0.521748i | ||||||||
\(392\) | −2.00368 | − | 6.70711i | −0.101201 | − | 0.338760i | ||||
\(393\) | 6.87024 | 0.346558 | ||||||||
\(394\) | 0.887555i | 0.0447144i | ||||||||
\(395\) | −25.7085 | + | 25.7085i | −1.29353 | + | 1.29353i | ||||
\(396\) | −0.355392 | − | 0.355392i | −0.0178591 | − | 0.0178591i | ||||
\(397\) | −16.4467 | − | 16.4467i | −0.825435 | − | 0.825435i | 0.161447 | − | 0.986881i | \(-0.448384\pi\) |
−0.986881 | + | 0.161447i | \(0.948384\pi\) | |||||||
\(398\) | 11.6938 | + | 11.6938i | 0.586156 | + | 0.586156i | ||||
\(399\) | 5.48528 | − | 21.7039i | 0.274608 | − | 1.08655i | ||||
\(400\) | 5.32583i | 0.266291i | ||||||||
\(401\) | 15.0126 | − | 15.0126i | 0.749691 | − | 0.749691i | −0.224730 | − | 0.974421i | \(-0.572150\pi\) |
0.974421 | + | 0.224730i | \(0.0721500\pi\) | |||||||
\(402\) | −0.752160 | −0.0375143 | ||||||||
\(403\) | 5.41593 | + | 1.08319i | 0.269787 | + | 0.0539574i | ||||
\(404\) | − | 19.7996i | − | 0.985067i | ||||||
\(405\) | 2.27220 | − | 2.27220i | 0.112907 | − | 0.112907i | ||||
\(406\) | −0.710351 | + | 2.81068i | −0.0352541 | + | 0.139492i | ||||
\(407\) | 3.68827i | 0.182821i | ||||||||
\(408\) | −3.05882 | − | 3.05882i | −0.151434 | − | 0.151434i | ||||
\(409\) | 19.0477 | − | 19.0477i | 0.941850 | − | 0.941850i | −0.0565493 | − | 0.998400i | \(-0.518010\pi\) |
0.998400 | + | 0.0565493i | \(0.0180098\pi\) | |||||||
\(410\) | 11.3492 | − | 11.3492i | 0.560498 | − | 0.560498i | ||||
\(411\) | 0.272205 | + | 0.272205i | 0.0134269 | + | 0.0134269i | ||||
\(412\) | 2.70386i | 0.133210i | ||||||||
\(413\) | −3.31432 | + | 13.1139i | −0.163087 | + | 0.645294i | ||||
\(414\) | −1.68642 | + | 1.68642i | −0.0828829 | + | 0.0828829i | ||||
\(415\) | − | 30.4965i | − | 1.49702i | ||||||
\(416\) | 0.707107 | − | 3.53553i | 0.0346688 | − | 0.173344i | ||||
\(417\) | −20.3440 | −0.996250 | ||||||||
\(418\) | 3.00705 | − | 3.00705i | 0.147079 | − | 0.147079i | ||||
\(419\) | − | 38.8022i | − | 1.89561i | −0.318849 | − | 0.947805i | \(-0.603296\pi\) | ||
0.318849 | − | 0.947805i | \(-0.396704\pi\) | |||||||
\(420\) | 8.24264 | + | 2.08319i | 0.402200 | + | 0.101649i | ||||
\(421\) | −19.5375 | − | 19.5375i | −0.952199 | − | 0.952199i | 0.0467096 | − | 0.998909i | \(-0.485126\pi\) |
−0.998909 | + | 0.0467096i | \(0.985126\pi\) | |||||||
\(422\) | −0.389849 | − | 0.389849i | −0.0189775 | − | 0.0189775i | ||||
\(423\) | 4.71078 | + | 4.71078i | 0.229046 | + | 0.229046i | ||||
\(424\) | 7.95862 | − | 7.95862i | 0.386505 | − | 0.386505i | ||||
\(425\) | 23.0386i | 1.11754i | ||||||||
\(426\) | 9.02969 | 0.437490 | ||||||||
\(427\) | −9.82917 | + | 5.86319i | −0.475667 | + | 0.283740i | ||||
\(428\) | − | 11.6673i | − | 0.563958i | ||||||
\(429\) | 0.355392 | − | 1.77696i | 0.0171585 | − | 0.0857923i | ||||
\(430\) | 23.9354i | 1.15427i | ||||||||
\(431\) | 1.45559 | + | 1.45559i | 0.0701133 | + | 0.0701133i | 0.741294 | − | 0.671181i | \(-0.234212\pi\) |
−0.671181 | + | 0.741294i | \(0.734212\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | −35.8137 | −1.72110 | −0.860548 | − | 0.509369i | \(-0.829879\pi\) | ||||
−0.860548 | + | 0.509369i | \(0.829879\pi\) | |||||||
\(434\) | 2.07627 | + | 3.48069i | 0.0996640 | + | 0.167079i | ||||
\(435\) | −2.48974 | − | 2.48974i | −0.119374 | − | 0.119374i | ||||
\(436\) | 5.29626 | − | 5.29626i | 0.253645 | − | 0.253645i | ||||
\(437\) | −14.2692 | − | 14.2692i | −0.682586 | − | 0.682586i | ||||
\(438\) | −7.33838 | −0.350641 | ||||||||
\(439\) | 14.2667 | 0.680912 | 0.340456 | − | 0.940260i | \(-0.389418\pi\) | ||||
0.340456 | + | 0.940260i | \(0.389418\pi\) | |||||||
\(440\) | 1.14201 | + | 1.14201i | 0.0544431 | + | 0.0544431i | ||||
\(441\) | 3.32583 | − | 6.15945i | 0.158373 | − | 0.293307i | ||||
\(442\) | 3.05882 | − | 15.2941i | 0.145493 | − | 0.727467i | ||||
\(443\) | −20.7019 | −0.983575 | −0.491788 | − | 0.870715i | \(-0.663656\pi\) | ||||
−0.491788 | + | 0.870715i | \(0.663656\pi\) | |||||||
\(444\) | −5.18902 | + | 5.18902i | −0.246260 | + | 0.246260i | ||||
\(445\) | −17.0435 | −0.807941 | ||||||||
\(446\) | −13.9926 | −0.662571 | ||||||||
\(447\) | 10.5685 | − | 10.5685i | 0.499871 | − | 0.499871i | ||||
\(448\) | 2.27220 | − | 1.35539i | 0.107352 | − | 0.0640362i | ||||
\(449\) | −20.2382 | + | 20.2382i | −0.955099 | + | 0.955099i | −0.999034 | − | 0.0439356i | \(-0.986010\pi\) |
0.0439356 | + | 0.999034i | \(0.486010\pi\) | |||||||
\(450\) | −3.76593 | + | 3.76593i | −0.177528 | + | 0.177528i | ||||
\(451\) | − | 2.51038i | − | 0.118209i | ||||||
\(452\) | 20.3440i | 0.956902i | ||||||||
\(453\) | 0.149362 | + | 0.149362i | 0.00701762 | + | 0.00701762i | ||||
\(454\) | −2.36764 | −0.111119 | ||||||||
\(455\) | 10.2357 | + | 28.8943i | 0.479858 | + | 1.35459i | ||||
\(456\) | 8.46122 | 0.396233 | ||||||||
\(457\) | −18.1891 | − | 18.1891i | −0.850852 | − | 0.850852i | 0.139386 | − | 0.990238i | \(-0.455487\pi\) |
−0.990238 | + | 0.139386i | \(0.955487\pi\) | |||||||
\(458\) | 1.87500i | 0.0876132i | ||||||||
\(459\) | − | 4.32583i | − | 0.201912i | ||||||
\(460\) | 5.41911 | − | 5.41911i | 0.252667 | − | 0.252667i | ||||
\(461\) | −1.18339 | + | 1.18339i | −0.0551158 | + | 0.0551158i | −0.734127 | − | 0.679012i | \(-0.762409\pi\) |
0.679012 | + | 0.734127i | \(0.262409\pi\) | |||||||
\(462\) | 1.14201 | − | 0.681219i | 0.0531311 | − | 0.0316932i | ||||
\(463\) | 4.93946 | − | 4.93946i | 0.229556 | − | 0.229556i | −0.582951 | − | 0.812507i | \(-0.698102\pi\) |
0.812507 | + | 0.582951i | \(0.198102\pi\) | |||||||
\(464\) | −1.09574 | −0.0508684 | ||||||||
\(465\) | −4.92244 | −0.228273 | ||||||||
\(466\) | −7.22074 | + | 7.22074i | −0.334494 | + | 0.334494i | ||||
\(467\) | −26.6900 | −1.23507 | −0.617533 | − | 0.786545i | \(-0.711868\pi\) | ||||
−0.617533 | + | 0.786545i | \(0.711868\pi\) | |||||||
\(468\) | 3.00000 | − | 2.00000i | 0.138675 | − | 0.0924500i | ||||
\(469\) | 0.487614 | − | 1.92936i | 0.0225159 | − | 0.0890898i | ||||
\(470\) | −15.1375 | − | 15.1375i | −0.698243 | − | 0.698243i | ||||
\(471\) | 10.7630 | 0.495932 | ||||||||
\(472\) | −5.11245 | −0.235319 | ||||||||
\(473\) | 2.64719 | + | 2.64719i | 0.121718 | + | 0.121718i | ||||
\(474\) | −8.00043 | + | 8.00043i | −0.367472 | + | 0.367472i | ||||
\(475\) | −31.8644 | − | 31.8644i | −1.46204 | − | 1.46204i | ||||
\(476\) | 9.82917 | − | 5.86319i | 0.450519 | − | 0.268739i | ||||
\(477\) | 11.2552 | 0.515340 | ||||||||
\(478\) | − | 21.5260i | − | 0.984575i | ||||||
\(479\) | −7.35998 | − | 7.35998i | −0.336286 | − | 0.336286i | 0.518682 | − | 0.854968i | \(-0.326423\pi\) |
−0.854968 | + | 0.518682i | \(0.826423\pi\) | |||||||
\(480\) | 3.21338i | 0.146670i | ||||||||
\(481\) | −25.9451 | − | 5.18902i | −1.18299 | − | 0.236599i | ||||
\(482\) | − | 4.78705i | − | 0.218044i | ||||||
\(483\) | −3.23255 | − | 5.41911i | −0.147086 | − | 0.246578i | ||||
\(484\) | −10.7474 | −0.488518 | ||||||||
\(485\) | 59.0459i | 2.68113i | ||||||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | 25.1766 | + | 25.1766i | 1.14086 | + | 1.14086i | 0.988293 | + | 0.152567i | \(0.0487541\pi\) |
0.152567 | + | 0.988293i | \(0.451246\pi\) | |||||||
\(488\) | −3.05882 | − | 3.05882i | −0.138466 | − | 0.138466i | ||||
\(489\) | 3.40901 | + | 3.40901i | 0.154161 | + | 0.154161i | ||||
\(490\) | −10.6872 | + | 19.7927i | −0.482797 | + | 0.894142i | ||||
\(491\) | 7.77450i | 0.350858i | 0.984492 | + | 0.175429i | \(0.0561313\pi\) | ||||
−0.984492 | + | 0.175429i | \(0.943869\pi\) | |||||||
\(492\) | 3.53186 | − | 3.53186i | 0.159228 | − | 0.159228i | ||||
\(493\) | −4.73998 | −0.213478 | ||||||||
\(494\) | 16.9224 | + | 25.3837i | 0.761377 | + | 1.14207i | ||||
\(495\) | 1.61504i | 0.0725909i | ||||||||
\(496\) | −1.08319 | + | 1.08319i | −0.0486365 | + | 0.0486365i | ||||
\(497\) | −5.85381 | + | 23.1620i | −0.262579 | + | 1.03896i | ||||
\(498\) | − | 9.49048i | − | 0.425279i | ||||||
\(499\) | 23.4592 | + | 23.4592i | 1.05018 | + | 1.05018i | 0.998673 | + | 0.0515063i | \(0.0164022\pi\) |
0.0515063 | + | 0.998673i | \(0.483598\pi\) | |||||||
\(500\) | 0.740347 | − | 0.740347i | 0.0331093 | − | 0.0331093i | ||||
\(501\) | −10.0226 | + | 10.0226i | −0.447779 | + | 0.447779i | ||||
\(502\) | 12.1821 | + | 12.1821i | 0.543714 | + | 0.543714i | ||||
\(503\) | − | 12.0000i | − | 0.535054i | −0.963550 | − | 0.267527i | \(-0.913794\pi\) | ||
0.963550 | − | 0.267527i | \(-0.0862064\pi\) | |||||||
\(504\) | 2.56510 | + | 0.648285i | 0.114259 | + | 0.0288769i | ||||
\(505\) | −44.9887 | + | 44.9887i | −2.00197 | + | 2.00197i | ||||
\(506\) | − | 1.19868i | − | 0.0532877i | ||||||
\(507\) | 12.0000 | + | 5.00000i | 0.532939 | + | 0.222058i | ||||
\(508\) | 7.60812 | 0.337556 | ||||||||
\(509\) | 11.0283 | − | 11.0283i | 0.488820 | − | 0.488820i | −0.419114 | − | 0.907934i | \(-0.637659\pi\) |
0.907934 | + | 0.419114i | \(0.137659\pi\) | |||||||
\(510\) | 13.9005i | 0.615526i | ||||||||
\(511\) | 4.75736 | − | 18.8237i | 0.210453 | − | 0.832710i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.98299 | + | 5.98299i | 0.264155 | + | 0.264155i | ||||
\(514\) | 2.34989 | + | 2.34989i | 0.103649 | + | 0.103649i | ||||
\(515\) | 6.14373 | − | 6.14373i | 0.270725 | − | 0.270725i | ||||
\(516\) | 7.44867i | 0.327909i | ||||||||
\(517\) | −3.34834 | −0.147260 | ||||||||
\(518\) | −9.94638 | − | 16.6743i | −0.437019 | − | 0.732627i | ||||
\(519\) | 19.7405i | 0.866511i | ||||||||
\(520\) | −9.64015 | + | 6.42677i | −0.422748 | + | 0.281832i | ||||
\(521\) | 18.5654i | 0.813366i | 0.913569 | + | 0.406683i | \(0.133315\pi\) | ||||
−0.913569 | + | 0.406683i | \(0.866685\pi\) | |||||||
\(522\) | −0.774804 | − | 0.774804i | −0.0339123 | − | 0.0339123i | ||||
\(523\) | − | 27.5741i | − | 1.20573i | −0.797843 | − | 0.602866i | \(-0.794026\pi\) | ||
0.797843 | − | 0.602866i | \(-0.205974\pi\) | |||||||
\(524\) | −6.87024 | −0.300128 | ||||||||
\(525\) | −7.21858 | − | 12.1014i | −0.315045 | − | 0.528147i | ||||
\(526\) | −0.578434 | − | 0.578434i | −0.0252209 | − | 0.0252209i | ||||
\(527\) | −4.68568 | + | 4.68568i | −0.204111 | + | 0.204111i | ||||
\(528\) | 0.355392 | + | 0.355392i | 0.0154664 | + | 0.0154664i | ||||
\(529\) | 17.3120 | 0.752695 | ||||||||
\(530\) | −36.1672 | −1.57100 | ||||||||
\(531\) | −3.61504 | − | 3.61504i | −0.156880 | − | 0.156880i | ||||
\(532\) | −5.48528 | + | 21.7039i | −0.237817 | + | 0.940982i | ||||
\(533\) | 17.6593 | + | 3.53186i | 0.764909 | + | 0.152982i | ||||
\(534\) | −5.30392 | −0.229523 | ||||||||
\(535\) | −26.5104 | + | 26.5104i | −1.14614 | + | 1.14614i | ||||
\(536\) | 0.752160 | 0.0324884 | ||||||||
\(537\) | −9.79960 | −0.422884 | ||||||||
\(538\) | 15.2793 | − | 15.2793i | 0.658735 | − | 0.658735i | ||||
\(539\) | 1.00705 | + | 3.37099i | 0.0433766 | + | 0.145199i | ||||
\(540\) | −2.27220 | + | 2.27220i | −0.0977801 | + | 0.0977801i | ||||
\(541\) | −25.5330 | + | 25.5330i | −1.09775 | + | 1.09775i | −0.103077 | + | 0.994673i | \(0.532869\pi\) |
−0.994673 | + | 0.103077i | \(0.967131\pi\) | |||||||
\(542\) | 21.2729i | 0.913751i | ||||||||
\(543\) | − | 10.4372i | − | 0.447902i | ||||||
\(544\) | 3.05882 | + | 3.05882i | 0.131146 | + | 0.131146i | ||||
\(545\) | −24.0684 | −1.03098 | ||||||||
\(546\) | 3.18534 | + | 8.99186i | 0.136320 | + | 0.384816i | ||||
\(547\) | 44.1966 | 1.88971 | 0.944856 | − | 0.327486i | \(-0.106201\pi\) | ||||
0.944856 | + | 0.327486i | \(0.106201\pi\) | |||||||
\(548\) | −0.272205 | − | 0.272205i | −0.0116280 | − | 0.0116280i | ||||
\(549\) | − | 4.32583i | − | 0.184622i | ||||||
\(550\) | − | 2.67676i | − | 0.114137i | ||||||
\(551\) | 6.55579 | − | 6.55579i | 0.279286 | − | 0.279286i | ||||
\(552\) | 1.68642 | − | 1.68642i | 0.0717787 | − | 0.0717787i | ||||
\(553\) | −15.3353 | − | 25.7085i | −0.652125 | − | 1.09323i | ||||
\(554\) | 12.5862 | − | 12.5862i | 0.534737 | − | 0.534737i | ||||
\(555\) | 23.5810 | 1.00096 | ||||||||
\(556\) | 20.3440 | 0.862778 | ||||||||
\(557\) | −11.7755 | + | 11.7755i | −0.498946 | + | 0.498946i | −0.911110 | − | 0.412164i | \(-0.864773\pi\) |
0.412164 | + | 0.911110i | \(0.364773\pi\) | |||||||
\(558\) | −1.53186 | −0.0648487 | ||||||||
\(559\) | −22.3460 | + | 14.8973i | −0.945136 | + | 0.630090i | ||||
\(560\) | −8.24264 | − | 2.08319i | −0.348315 | − | 0.0880307i | ||||
\(561\) | 1.53736 | + | 1.53736i | 0.0649075 | + | 0.0649075i | ||||
\(562\) | 8.78031 | 0.370375 | ||||||||
\(563\) | −45.7636 | −1.92870 | −0.964352 | − | 0.264621i | \(-0.914753\pi\) | ||||
−0.964352 | + | 0.264621i | \(0.914753\pi\) | |||||||
\(564\) | −4.71078 | − | 4.71078i | −0.198360 | − | 0.198360i | ||||
\(565\) | 46.2258 | − | 46.2258i | 1.94473 | − | 1.94473i | ||||
\(566\) | 17.7547 | + | 17.7547i | 0.746288 | + | 0.746288i | ||||
\(567\) | 1.35539 | + | 2.27220i | 0.0569211 | + | 0.0954236i | ||||
\(568\) | −9.02969 | −0.378877 | ||||||||
\(569\) | − | 39.5061i | − | 1.65618i | −0.560595 | − | 0.828090i | \(-0.689428\pi\) | ||
0.560595 | − | 0.828090i | \(-0.310572\pi\) | |||||||
\(570\) | −19.2256 | − | 19.2256i | −0.805273 | − | 0.805273i | ||||
\(571\) | − | 19.1620i | − | 0.801906i | −0.916099 | − | 0.400953i | \(-0.868679\pi\) | ||
0.916099 | − | 0.400953i | \(-0.131321\pi\) | |||||||
\(572\) | −0.355392 | + | 1.77696i | −0.0148597 | + | 0.0742983i | ||||
\(573\) | − | 11.1410i | − | 0.465423i | ||||||
\(574\) | 6.76991 | + | 11.3492i | 0.282571 | + | 0.473707i | ||||
\(575\) | −12.7019 | −0.529704 | ||||||||
\(576\) | 1.00000i | 0.0416667i | ||||||||
\(577\) | −3.53749 | + | 3.53749i | −0.147268 | + | 0.147268i | −0.776896 | − | 0.629629i | \(-0.783207\pi\) |
0.629629 | + | 0.776896i | \(0.283207\pi\) | |||||||
\(578\) | 1.21112 | + | 1.21112i | 0.0503760 | + | 0.0503760i | ||||
\(579\) | −4.03661 | − | 4.03661i | −0.167756 | − | 0.167756i | ||||
\(580\) | 2.48974 | + | 2.48974i | 0.103381 | + | 0.103381i | ||||
\(581\) | 24.3440 | + | 6.15253i | 1.00996 | + | 0.255250i | ||||
\(582\) | 18.3750i | 0.761668i | ||||||||
\(583\) | −4.00000 | + | 4.00000i | −0.165663 | + | 0.165663i | ||||
\(584\) | 7.33838 | 0.303664 | ||||||||
\(585\) | −11.3610 | − | 2.27220i | −0.469720 | − | 0.0939441i | ||||
\(586\) | 12.0398i | 0.497360i | ||||||||
\(587\) | −4.98849 | + | 4.98849i | −0.205897 | + | 0.205897i | −0.802521 | − | 0.596624i | \(-0.796508\pi\) |
0.596624 | + | 0.802521i | \(0.296508\pi\) | |||||||
\(588\) | −3.32583 | + | 6.15945i | −0.137155 | + | 0.254012i | ||||
\(589\) | − | 12.9614i | − | 0.534065i | ||||||
\(590\) | 11.6165 | + | 11.6165i | 0.478245 | + | 0.478245i | ||||
\(591\) | 0.627596 | − | 0.627596i | 0.0258159 | − | 0.0258159i | ||||
\(592\) | 5.18902 | − | 5.18902i | 0.213267 | − | 0.213267i | ||||
\(593\) | −3.14690 | − | 3.14690i | −0.129228 | − | 0.129228i | 0.639535 | − | 0.768762i | \(-0.279127\pi\) |
−0.768762 | + | 0.639535i | \(0.779127\pi\) | |||||||
\(594\) | 0.502600i | 0.0206219i | ||||||||
\(595\) | −35.6562 | − | 9.01151i | −1.46176 | − | 0.369436i | ||||
\(596\) | −10.5685 | + | 10.5685i | −0.432901 | + | 0.432901i | ||||
\(597\) | − | 16.5375i | − | 0.676834i | ||||||
\(598\) | 8.43209 | + | 1.68642i | 0.344814 | + | 0.0689628i | ||||
\(599\) | 14.9244 | 0.609796 | 0.304898 | − | 0.952385i | \(-0.401378\pi\) | ||||
0.304898 | + | 0.952385i | \(0.401378\pi\) | |||||||
\(600\) | 3.76593 | − | 3.76593i | 0.153743 | − | 0.153743i | ||||
\(601\) | − | 14.3189i | − | 0.584080i | −0.956406 | − | 0.292040i | \(-0.905666\pi\) | ||
0.956406 | − | 0.292040i | \(-0.0943341\pi\) | |||||||
\(602\) | −19.1066 | − | 4.82886i | −0.778726 | − | 0.196810i | ||||
\(603\) | 0.531858 | + | 0.531858i | 0.0216589 | + | 0.0216589i | ||||
\(604\) | −0.149362 | − | 0.149362i | −0.00607743 | − | 0.00607743i | ||||
\(605\) | 24.4203 | + | 24.4203i | 0.992825 | + | 0.992825i | ||||
\(606\) | −14.0004 | + | 14.0004i | −0.568729 | + | 0.568729i | ||||
\(607\) | 17.3212i | 0.703047i | 0.936179 | + | 0.351524i | \(0.114336\pi\) | ||||
−0.936179 | + | 0.351524i | \(0.885664\pi\) | |||||||
\(608\) | −8.46122 | −0.343148 | ||||||||
\(609\) | 2.48974 | − | 1.48515i | 0.100889 | − | 0.0601815i | ||||
\(610\) | 13.9005i | 0.562816i | ||||||||
\(611\) | 4.71078 | − | 23.5539i | 0.190578 | − | 0.952889i | ||||
\(612\) | 4.32583i | 0.174861i | ||||||||
\(613\) | 28.6700 | + | 28.6700i | 1.15797 | + | 1.15797i | 0.984912 | + | 0.173057i | \(0.0553646\pi\) |
0.173057 | + | 0.984912i | \(0.444635\pi\) | |||||||
\(614\) | 14.1982i | 0.572993i | ||||||||
\(615\) | −16.0502 | −0.647207 | ||||||||
\(616\) | −1.14201 | + | 0.681219i | −0.0460129 | + | 0.0274471i | ||||
\(617\) | −9.91435 | − | 9.91435i | −0.399137 | − | 0.399137i | 0.478792 | − | 0.877929i | \(-0.341075\pi\) |
−0.877929 | + | 0.478792i | \(0.841075\pi\) | |||||||
\(618\) | 1.91192 | − | 1.91192i | 0.0769087 | − | 0.0769087i | ||||
\(619\) | −3.87574 | − | 3.87574i | −0.155779 | − | 0.155779i | 0.624914 | − | 0.780693i | \(-0.285134\pi\) |
−0.780693 | + | 0.624914i | \(0.785134\pi\) | |||||||
\(620\) | 4.92244 | 0.197690 | ||||||||
\(621\) | 2.38496 | 0.0957050 | ||||||||
\(622\) | 11.1061 | + | 11.1061i | 0.445316 | + | 0.445316i | ||||
\(623\) | 3.43845 | − | 13.6051i | 0.137759 | − | 0.545076i | ||||
\(624\) | −3.00000 | + | 2.00000i | −0.120096 | + | 0.0800641i | ||||
\(625\) | 23.2647 | 0.930588 | ||||||||
\(626\) | 14.6867 | − | 14.6867i | 0.587000 | − | 0.587000i | ||||
\(627\) | −4.25261 | −0.169833 | ||||||||
\(628\) | −10.7630 | −0.429490 | ||||||||
\(629\) | 22.4468 | − | 22.4468i | 0.895012 | − | 0.895012i | ||||
\(630\) | −4.35539 | − | 7.30146i | −0.173523 | − | 0.290897i | ||||
\(631\) | −21.5709 | + | 21.5709i | −0.858725 | + | 0.858725i | −0.991188 | − | 0.132463i | \(-0.957711\pi\) |
0.132463 | + | 0.991188i | \(0.457711\pi\) | |||||||
\(632\) | 8.00043 | − | 8.00043i | 0.318240 | − | 0.318240i | ||||
\(633\) | 0.551329i | 0.0219134i | ||||||||
\(634\) | 26.8878i | 1.06785i | ||||||||
\(635\) | −17.2872 | − | 17.2872i | −0.686022 | − | 0.686022i | ||||
\(636\) | −11.2552 | −0.446297 | ||||||||
\(637\) | −25.1300 | + | 2.34142i | −0.995688 | + | 0.0927706i | ||||
\(638\) | 0.550718 | 0.0218031 | ||||||||
\(639\) | −6.38496 | − | 6.38496i | −0.252585 | − | 0.252585i | ||||
\(640\) | − | 3.21338i | − | 0.127020i | ||||||
\(641\) | 25.8728i | 1.02192i | 0.859606 | + | 0.510958i | \(0.170709\pi\) | ||||
−0.859606 | + | 0.510958i | \(0.829291\pi\) | |||||||
\(642\) | −8.24999 | + | 8.24999i | −0.325601 | + | 0.325601i | ||||
\(643\) | −3.32032 | + | 3.32032i | −0.130941 | + | 0.130941i | −0.769540 | − | 0.638599i | \(-0.779514\pi\) |
0.638599 | + | 0.769540i | \(0.279514\pi\) | |||||||
\(644\) | 3.23255 | + | 5.41911i | 0.127380 | + | 0.213543i | ||||
\(645\) | 16.9249 | − | 16.9249i | 0.666417 | − | 0.666417i | ||||
\(646\) | −36.6018 | −1.44008 | ||||||||
\(647\) | −28.6969 | −1.12819 | −0.564097 | − | 0.825709i | \(-0.690775\pi\) | ||||
−0.564097 | + | 0.825709i | \(0.690775\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 2.56951 | 0.100862 | ||||||||
\(650\) | 18.8296 | + | 3.76593i | 0.738559 | + | 0.147712i | ||||
\(651\) | 0.993080 | − | 3.92936i | 0.0389219 | − | 0.154004i | ||||
\(652\) | −3.40901 | − | 3.40901i | −0.133507 | − | 0.133507i | ||||
\(653\) | −27.9250 | −1.09279 | −0.546395 | − | 0.837527i | \(-0.684000\pi\) | ||||
−0.546395 | + | 0.837527i | \(0.684000\pi\) | |||||||
\(654\) | −7.49005 | −0.292884 | ||||||||
\(655\) | 15.6106 | + | 15.6106i | 0.609956 | + | 0.609956i | ||||
\(656\) | −3.53186 | + | 3.53186i | −0.137896 | + | 0.137896i | ||||
\(657\) | 5.18902 | + | 5.18902i | 0.202443 | + | 0.202443i | ||||
\(658\) | 15.1375 | − | 9.02969i | 0.590123 | − | 0.352014i | ||||
\(659\) | −38.2258 | −1.48906 | −0.744532 | − | 0.667587i | \(-0.767327\pi\) | ||||
−0.744532 | + | 0.667587i | \(0.767327\pi\) | |||||||
\(660\) | − | 1.61504i | − | 0.0628655i | ||||||
\(661\) | −4.52189 | − | 4.52189i | −0.175881 | − | 0.175881i | 0.613676 | − | 0.789558i | \(-0.289690\pi\) |
−0.789558 | + | 0.613676i | \(0.789690\pi\) | |||||||
\(662\) | − | 19.7686i | − | 0.768329i | ||||||
\(663\) | −12.9775 | + | 8.65166i | −0.504004 | + | 0.336002i | ||||
\(664\) | 9.49048i | 0.368302i | ||||||||
\(665\) | 61.7793 | − | 36.8519i | 2.39570 | − | 1.42906i | ||||
\(666\) | 7.33838 | 0.284356 | ||||||||
\(667\) | − | 2.61329i | − | 0.101187i | ||||||
\(668\) | 10.0226 | − | 10.0226i | 0.387788 | − | 0.387788i | ||||
\(669\) | 9.89430 | + | 9.89430i | 0.382536 | + | 0.382536i | ||||
\(670\) | −1.70906 | − | 1.70906i | −0.0660268 | − | 0.0660268i | ||||
\(671\) | 1.53736 | + | 1.53736i | 0.0593492 | + | 0.0593492i | ||||
\(672\) | −2.56510 | − | 0.648285i | −0.0989508 | − | 0.0250081i | ||||
\(673\) | − | 16.7180i | − | 0.644430i | −0.946667 | − | 0.322215i | \(-0.895573\pi\) | ||
0.946667 | − | 0.322215i | \(-0.104427\pi\) | |||||||
\(674\) | 0.774804 | − | 0.774804i | 0.0298443 | − | 0.0298443i | ||||
\(675\) | 5.32583 | 0.204991 | ||||||||
\(676\) | −12.0000 | − | 5.00000i | −0.461538 | − | 0.192308i | ||||
\(677\) | 37.8247i | 1.45372i | 0.686785 | + | 0.726861i | \(0.259021\pi\) | ||||
−0.686785 | + | 0.726861i | \(0.740979\pi\) | |||||||
\(678\) | 14.3854 | − | 14.3854i | 0.552467 | − | 0.552467i | ||||
\(679\) | −47.1336 | − | 11.9122i | −1.80882 | − | 0.457149i | ||||
\(680\) | − | 13.9005i | − | 0.533061i | ||||||
\(681\) | 1.67417 | + | 1.67417i | 0.0641544 | + | 0.0641544i | ||||
\(682\) | 0.544409 | − | 0.544409i | 0.0208465 | − | 0.0208465i | ||||
\(683\) | 3.10020 | − | 3.10020i | 0.118626 | − | 0.118626i | −0.645302 | − | 0.763928i | \(-0.723268\pi\) |
0.763928 | + | 0.645302i | \(0.223268\pi\) | |||||||
\(684\) | −5.98299 | − | 5.98299i | −0.228765 | − | 0.228765i | ||||
\(685\) | 1.23701i | 0.0472637i | ||||||||
\(686\) | −13.6435 | − | 12.5242i | −0.520912 | − | 0.478174i | ||||
\(687\) | 1.32583 | − | 1.32583i | 0.0505835 | − | 0.0505835i | ||||
\(688\) | − | 7.44867i | − | 0.283978i | ||||||
\(689\) | −22.5104 | − | 33.7656i | −0.857577 | − | 1.28637i | ||||
\(690\) | −7.66377 | −0.291755 | ||||||||
\(691\) | −11.1083 | + | 11.1083i | −0.422579 | + | 0.422579i | −0.886091 | − | 0.463512i | \(-0.846589\pi\) |
0.463512 | + | 0.886091i | \(0.346589\pi\) | |||||||
\(692\) | − | 19.7405i | − | 0.750420i | ||||||
\(693\) | −1.28922 | − | 0.325828i | −0.0489733 | − | 0.0123772i | ||||
\(694\) | 22.6969 | + | 22.6969i | 0.861564 | + | 0.861564i | ||||
\(695\) | −46.2258 | − | 46.2258i | −1.75344 | − | 1.75344i | ||||
\(696\) | 0.774804 | + | 0.774804i | 0.0293689 | + | 0.0293689i | ||||
\(697\) | −15.2782 | + | 15.2782i | −0.578703 | + | 0.578703i | ||||
\(698\) | 26.8219i | 1.01523i | ||||||||
\(699\) | 10.2117 | 0.386241 | ||||||||
\(700\) | 7.21858 | + | 12.1014i | 0.272837 | + | 0.457389i | ||||
\(701\) | − | 2.49912i | − | 0.0943905i | −0.998886 | − | 0.0471953i | \(-0.984972\pi\) | ||
0.998886 | − | 0.0471953i | \(-0.0150283\pi\) | |||||||
\(702\) | −3.53553 | − | 0.707107i | −0.133440 | − | 0.0266880i | ||||
\(703\) | 62.0917i | 2.34183i | ||||||||
\(704\) | −0.355392 | − | 0.355392i | −0.0133943 | − | 0.0133943i | ||||
\(705\) | 21.4077i | 0.806262i | ||||||||
\(706\) | 21.9911 | 0.827645 | ||||||||
\(707\) | −26.8362 | − | 44.9887i | −1.00928 | − | 1.69198i | ||||
\(708\) | 3.61504 | + | 3.61504i | 0.135862 | + | 0.135862i | ||||
\(709\) | 25.3601 | − | 25.3601i | 0.952419 | − | 0.952419i | −0.0464996 | − | 0.998918i | \(-0.514807\pi\) |
0.998918 | + | 0.0464996i | \(0.0148066\pi\) | |||||||
\(710\) | 20.5173 | + | 20.5173i | 0.770001 | + | 0.770001i | ||||
\(711\) | 11.3143 | 0.424320 | ||||||||
\(712\) | 5.30392 | 0.198773 | ||||||||
\(713\) | −2.58335 | − | 2.58335i | −0.0967473 | − | 0.0967473i | ||||
\(714\) | −11.0962 | − | 2.80437i | −0.415264 | − | 0.104951i | ||||
\(715\) | 4.84513 | − | 3.23009i | 0.181198 | − | 0.120798i | ||||
\(716\) | 9.79960 | 0.366228 | ||||||||
\(717\) | −15.2212 | + | 15.2212i | −0.568445 | + | 0.568445i | ||||
\(718\) | −20.0600 | −0.748632 | ||||||||
\(719\) | 41.5150 | 1.54825 | 0.774124 | − | 0.633034i | \(-0.218191\pi\) | ||||
0.774124 | + | 0.633034i | \(0.218191\pi\) | |||||||
\(720\) | 2.27220 | − | 2.27220i | 0.0846801 | − | 0.0846801i | ||||
\(721\) | 3.66479 | + | 6.14373i | 0.136484 | + | 0.228804i | ||||
\(722\) | 37.1884 | − | 37.1884i | 1.38401 | − | 1.38401i | ||||
\(723\) | −3.38496 | + | 3.38496i | −0.125888 | + | 0.125888i | ||||
\(724\) | 10.4372i | 0.387894i | ||||||||
\(725\) | − | 5.83571i | − | 0.216733i | ||||||
\(726\) | 7.59955 | + | 7.59955i | 0.282046 | + | 0.282046i | ||||
\(727\) | 48.1505 | 1.78580 | 0.892902 | − | 0.450251i | \(-0.148665\pi\) | ||||
0.892902 | + | 0.450251i | \(0.148665\pi\) | |||||||
\(728\) | −3.18534 | − | 8.99186i | −0.118057 | − | 0.333261i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −16.6743 | − | 16.6743i | −0.617143 | − | 0.617143i | ||||
\(731\) | − | 32.2217i | − | 1.19176i | ||||||
\(732\) | 4.32583i | 0.159887i | ||||||||
\(733\) | 7.58561 | − | 7.58561i | 0.280181 | − | 0.280181i | −0.553000 | − | 0.833181i | \(-0.686517\pi\) |
0.833181 | + | 0.553000i | \(0.186517\pi\) | |||||||
\(734\) | 7.95862 | − | 7.95862i | 0.293758 | − | 0.293758i | ||||
\(735\) | 21.5525 | − | 6.43858i | 0.794976 | − | 0.237491i | ||||
\(736\) | −1.68642 | + | 1.68642i | −0.0621622 | + | 0.0621622i | ||||
\(737\) | −0.378035 | −0.0139251 | ||||||||
\(738\) | −4.99480 | −0.183861 | ||||||||
\(739\) | 0.923733 | − | 0.923733i | 0.0339801 | − | 0.0339801i | −0.689913 | − | 0.723893i | \(-0.742351\pi\) |
0.723893 | + | 0.689913i | \(0.242351\pi\) | |||||||
\(740\) | −23.5810 | −0.866856 | ||||||||
\(741\) | 5.98299 | − | 29.9149i | 0.219791 | − | 1.09895i | ||||
\(742\) | 7.29657 | − | 28.8707i | 0.267865 | − | 1.05988i | ||||
\(743\) | −7.95906 | − | 7.95906i | −0.291989 | − | 0.291989i | 0.545876 | − | 0.837866i | \(-0.316197\pi\) |
−0.837866 | + | 0.545876i | \(0.816197\pi\) | |||||||
\(744\) | 1.53186 | 0.0561606 | ||||||||
\(745\) | 48.0274 | 1.75959 | ||||||||
\(746\) | 12.1254 | + | 12.1254i | 0.443944 | + | 0.443944i | ||||
\(747\) | −6.71078 | + | 6.71078i | −0.245535 | + | 0.245535i | ||||
\(748\) | −1.53736 | − | 1.53736i | −0.0562115 | − | 0.0562115i | ||||
\(749\) | −15.8137 | − | 26.5104i | −0.577820 | − | 0.968668i | ||||
\(750\) | −1.04701 | −0.0382314 | ||||||||
\(751\) | 48.2119i | 1.75928i | 0.475642 | + | 0.879639i | \(0.342216\pi\) | ||||
−0.475642 | + | 0.879639i | \(0.657784\pi\) | |||||||
\(752\) | 4.71078 | + | 4.71078i | 0.171785 | + | 0.171785i | ||||
\(753\) | − | 17.2281i | − | 0.627826i | ||||||
\(754\) | −0.774804 | + | 3.87402i | −0.0282167 | + | 0.141084i | ||||
\(755\) | 0.678760i | 0.0247026i | ||||||||
\(756\) | −1.35539 | − | 2.27220i | −0.0492951 | − | 0.0826393i | ||||
\(757\) | 47.8137 | 1.73782 | 0.868909 | − | 0.494972i | \(-0.164822\pi\) | ||||
0.868909 | + | 0.494972i | \(0.164822\pi\) | |||||||
\(758\) | 16.3603i | 0.594232i | ||||||||
\(759\) | −0.847593 | + | 0.847593i | −0.0307657 | + | 0.0307657i | ||||
\(760\) | 19.2256 | + | 19.2256i | 0.697387 | + | 0.697387i | ||||
\(761\) | 14.6867 | + | 14.6867i | 0.532393 | + | 0.532393i | 0.921284 | − | 0.388891i | \(-0.127142\pi\) |
−0.388891 | + | 0.921284i | \(0.627142\pi\) | |||||||
\(762\) | −5.37976 | − | 5.37976i | −0.194888 | − | 0.194888i | ||||
\(763\) | 4.85568 | − | 19.2127i | 0.175788 | − | 0.695547i | ||||
\(764\) | 11.1410i | 0.403068i | ||||||||
\(765\) | 9.82917 | − | 9.82917i | 0.355374 | − | 0.355374i | ||||
\(766\) | 1.79120 | 0.0647189 | ||||||||
\(767\) | −3.61504 | + | 18.0752i | −0.130532 | + | 0.652658i | ||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 34.5766 | − | 34.5766i | 1.24686 | − | 1.24686i | 0.289765 | − | 0.957098i | \(-0.406423\pi\) |
0.957098 | − | 0.289765i | \(-0.0935771\pi\) | |||||||
\(770\) | 4.14275 | + | 1.04701i | 0.149294 | + | 0.0377316i | ||||
\(771\) | − | 3.32324i | − | 0.119684i | ||||||
\(772\) | 4.03661 | + | 4.03661i | 0.145281 | + | 0.145281i | ||||
\(773\) | −3.88033 | + | 3.88033i | −0.139566 | + | 0.139566i | −0.773438 | − | 0.633872i | \(-0.781465\pi\) |
0.633872 | + | 0.773438i | \(0.281465\pi\) | |||||||
\(774\) | 5.26701 | − | 5.26701i | 0.189319 | − | 0.189319i | ||||
\(775\) | −5.76887 | − | 5.76887i | −0.207224 | − | 0.207224i | ||||
\(776\) | − | 18.3750i | − | 0.659624i | ||||||
\(777\) | −4.75736 | + | 18.8237i | −0.170669 | + | 0.675295i | ||||
\(778\) | −5.59099 | + | 5.59099i | −0.200447 | + | 0.200447i | ||||
\(779\) | − | 42.2621i | − | 1.51420i | ||||||
\(780\) | 11.3610 | + | 2.27220i | 0.406790 | + | 0.0813580i | ||||
\(781\) | 4.53832 | 0.162394 | ||||||||
\(782\) | −7.29515 | + | 7.29515i | −0.260874 | + | 0.260874i | ||||
\(783\) | 1.09574i | 0.0391585i | ||||||||
\(784\) | 3.32583 | − | 6.15945i | 0.118780 | − | 0.219980i | ||||
\(785\) | 24.4557 | + | 24.4557i | 0.872862 | + | 0.872862i | ||||
\(786\) | 4.85799 | + | 4.85799i | 0.173279 | + | 0.173279i | ||||
\(787\) | 7.06054 | + | 7.06054i | 0.251681 | + | 0.251681i | 0.821660 | − | 0.569978i | \(-0.193048\pi\) |
−0.569978 | + | 0.821660i | \(0.693048\pi\) | |||||||
\(788\) | −0.627596 | + | 0.627596i | −0.0223572 | + | 0.0223572i | ||||
\(789\) | 0.818029i | 0.0291226i | ||||||||
\(790\) | −36.3572 | −1.29353 | ||||||||
\(791\) | 27.5741 | + | 46.2258i | 0.980422 | + | 1.64360i | ||||
\(792\) | − | 0.502600i | − | 0.0178591i | ||||||
\(793\) | −12.9775 | + | 8.65166i | −0.460844 | + | 0.307229i | ||||
\(794\) | − | 23.2591i | − | 0.825435i | ||||||
\(795\) | 25.5741 | + | 25.5741i | 0.907020 | + | 0.907020i | ||||
\(796\) | 16.5375i | 0.586156i | ||||||||
\(797\) | 31.7376 | 1.12421 | 0.562103 | − | 0.827068i | \(-0.309993\pi\) | ||||
0.562103 | + | 0.827068i | \(0.309993\pi\) | |||||||
\(798\) | 19.2256 | − | 11.4683i | 0.680580 | − | 0.405972i | ||||
\(799\) | 20.3780 | + | 20.3780i | 0.720923 | + | 0.720923i | ||||
\(800\) | −3.76593 | + | 3.76593i | −0.133146 | + | 0.133146i | ||||
\(801\) | 3.75044 | + | 3.75044i | 0.132515 | + | 0.132515i | ||||
\(802\) | 21.2310 | 0.749691 | ||||||||
\(803\) | −3.68827 | −0.130156 | ||||||||
\(804\) | −0.531858 | − | 0.531858i | −0.0187572 | − | 0.0187572i | ||||
\(805\) | 4.96831 | − | 19.6583i | 0.175110 | − | 0.692865i | ||||
\(806\) | 3.06372 | + | 4.59557i | 0.107915 | + | 0.161872i | ||||
\(807\) | −21.6081 | −0.760642 | ||||||||
\(808\) | 14.0004 | − | 14.0004i | 0.492533 | − | 0.492533i | ||||
\(809\) | 5.38754 | 0.189416 | 0.0947079 | − | 0.995505i | \(-0.469808\pi\) | ||||
0.0947079 | + | 0.995505i | \(0.469808\pi\) | |||||||
\(810\) | 3.21338 | 0.112907 | ||||||||
\(811\) | −24.4934 | + | 24.4934i | −0.860079 | + | 0.860079i | −0.991347 | − | 0.131268i | \(-0.958095\pi\) |
0.131268 | + | 0.991347i | \(0.458095\pi\) | |||||||
\(812\) | −2.48974 | + | 1.48515i | −0.0873728 | + | 0.0521187i | ||||
\(813\) | 15.0422 | − | 15.0422i | 0.527554 | − | 0.527554i | ||||
\(814\) | −2.60800 | + | 2.60800i | −0.0914103 | + | 0.0914103i | ||||
\(815\) | 15.4920i | 0.542660i | ||||||||
\(816\) | − | 4.32583i | − | 0.151434i | ||||||
\(817\) | 44.5653 | + | 44.5653i | 1.55914 | + | 1.55914i | ||||
\(818\) | 26.9376 | 0.941850 | ||||||||
\(819\) | 4.10583 | − | 8.61058i | 0.143469 | − | 0.300878i | ||||
\(820\) | 16.0502 | 0.560498 | ||||||||
\(821\) | −14.8664 | − | 14.8664i | −0.518840 | − | 0.518840i | 0.398381 | − | 0.917220i | \(-0.369572\pi\) |
−0.917220 | + | 0.398381i | \(0.869572\pi\) | |||||||
\(822\) | 0.384955i | 0.0134269i | ||||||||
\(823\) | 46.5078i | 1.62116i | 0.585628 | + | 0.810580i | \(0.300848\pi\) | ||||
−0.585628 | + | 0.810580i | \(0.699152\pi\) | |||||||
\(824\) | −1.91192 | + | 1.91192i | −0.0666049 | + | 0.0666049i | ||||
\(825\) | −1.89275 | + | 1.89275i | −0.0658972 | + | 0.0658972i | ||||
\(826\) | −11.6165 | + | 6.92936i | −0.404190 | + | 0.241103i | ||||
\(827\) | −2.43470 | + | 2.43470i | −0.0846630 | + | 0.0846630i | −0.748170 | − | 0.663507i | \(-0.769067\pi\) |
0.663507 | + | 0.748170i | \(0.269067\pi\) | |||||||
\(828\) | −2.38496 | −0.0828829 | ||||||||
\(829\) | −5.61013 | −0.194848 | −0.0974239 | − | 0.995243i | \(-0.531060\pi\) | ||||
−0.0974239 | + | 0.995243i | \(0.531060\pi\) | |||||||
\(830\) | 21.5643 | − | 21.5643i | 0.748508 | − | 0.748508i | ||||
\(831\) | −17.7996 | −0.617461 | ||||||||
\(832\) | 3.00000 | − | 2.00000i | 0.104006 | − | 0.0693375i | ||||
\(833\) | 14.3870 | − | 26.6447i | 0.498479 | − | 0.923185i | ||||
\(834\) | −14.3854 | − | 14.3854i | −0.498125 | − | 0.498125i | ||||
\(835\) | −45.5470 | −1.57622 | ||||||||
\(836\) | 4.25261 | 0.147079 | ||||||||
\(837\) | 1.08319 | + | 1.08319i | 0.0374404 | + | 0.0374404i | ||||
\(838\) | 27.4373 | − | 27.4373i | 0.947805 | − | 0.947805i | ||||
\(839\) | 35.6724 | + | 35.6724i | 1.23155 | + | 1.23155i | 0.963369 | + | 0.268180i | \(0.0864222\pi\) |
0.268180 | + | 0.963369i | \(0.413578\pi\) | |||||||
\(840\) | 4.35539 | + | 7.30146i | 0.150275 | + | 0.251924i | ||||
\(841\) | −27.7994 | −0.958599 | ||||||||
\(842\) | − | 27.6302i | − | 0.952199i | ||||||
\(843\) | −6.20862 | − | 6.20862i | −0.213836 | − | 0.213836i | ||||
\(844\) | − | 0.551329i | − | 0.0189775i | ||||||
\(845\) | 15.9054 | + | 38.6275i | 0.547164 | + | 1.32883i | ||||
\(846\) | 6.66205i | 0.229046i | ||||||||
\(847\) | −24.4203 | + | 14.5669i | −0.839091 | + | 0.500526i | ||||
\(848\) | 11.2552 | 0.386505 | ||||||||
\(849\) | − | 25.1090i | − | 0.861739i | ||||||
\(850\) | −16.2908 | + | 16.2908i | −0.558768 | + | 0.558768i | ||||
\(851\) | 12.3756 | + | 12.3756i | 0.424229 | + | 0.424229i | ||||
\(852\) | 6.38496 | + | 6.38496i | 0.218745 | + | 0.218745i | ||||
\(853\) | 9.68368 | + | 9.68368i | 0.331563 | + | 0.331563i | 0.853180 | − | 0.521617i | \(-0.174671\pi\) |
−0.521617 | + | 0.853180i | \(0.674671\pi\) | |||||||
\(854\) | −11.0962 | − | 2.80437i | −0.379703 | − | 0.0959635i | ||||
\(855\) | 27.1891i | 0.929849i | ||||||||
\(856\) | 8.24999 | − | 8.24999i | 0.281979 | − | 0.281979i | ||||
\(857\) | 10.6859 | 0.365025 | 0.182512 | − | 0.983204i | \(-0.441577\pi\) | ||||
0.182512 | + | 0.983204i | \(0.441577\pi\) | |||||||
\(858\) | 1.50780 | − | 1.00520i | 0.0514754 | − | 0.0343169i | ||||
\(859\) | − | 15.4218i | − | 0.526186i | −0.964771 | − | 0.263093i | \(-0.915257\pi\) | ||
0.964771 | − | 0.263093i | \(-0.0847426\pi\) | |||||||
\(860\) | −16.9249 | + | 16.9249i | −0.577134 | + | 0.577134i | ||||
\(861\) | 3.23805 | − | 12.8122i | 0.110353 | − | 0.436637i | ||||
\(862\) | 2.05852i | 0.0701133i | ||||||||
\(863\) | −13.8546 | − | 13.8546i | −0.471617 | − | 0.471617i | 0.430820 | − | 0.902438i | \(-0.358224\pi\) |
−0.902438 | + | 0.430820i | \(0.858224\pi\) | |||||||
\(864\) | 0.707107 | − | 0.707107i | 0.0240563 | − | 0.0240563i | ||||
\(865\) | −44.8544 | + | 44.8544i | −1.52510 | + | 1.52510i | ||||
\(866\) | −25.3241 | − | 25.3241i | −0.860548 | − | 0.860548i | ||||
\(867\) | − | 1.71278i | − | 0.0581692i | ||||||
\(868\) | −0.993080 | + | 3.92936i | −0.0337073 | + | 0.133371i | ||||
\(869\) | −4.02101 | + | 4.02101i | −0.136404 | + | 0.136404i | ||||
\(870\) | − | 3.52103i | − | 0.119374i | ||||||
\(871\) | 0.531858 | − | 2.65929i | 0.0180213 | − | 0.0901065i | ||||
\(872\) | 7.49005 | 0.253645 | ||||||||
\(873\) | 12.9931 | − | 12.9931i | 0.439749 | − | 0.439749i | ||||
\(874\) | − | 20.1796i | − | 0.682586i | ||||||
\(875\) | 0.678760 | − | 2.68568i | 0.0229463 | − | 0.0907926i | ||||
\(876\) | −5.18902 | − | 5.18902i | −0.175321 | − | 0.175321i | ||||
\(877\) | 6.59203 | + | 6.59203i | 0.222597 | + | 0.222597i | 0.809591 | − | 0.586994i | \(-0.199689\pi\) |
−0.586994 | + | 0.809591i | \(0.699689\pi\) | |||||||
\(878\) | 10.0881 | + | 10.0881i | 0.340456 | + | 0.340456i | ||||
\(879\) | 8.51343 | − | 8.51343i | 0.287151 | − | 0.287151i | ||||
\(880\) | 1.61504i | 0.0544431i | ||||||||
\(881\) | −4.21366 | −0.141962 | −0.0709810 | − | 0.997478i | \(-0.522613\pi\) | ||||
−0.0709810 | + | 0.997478i | \(0.522613\pi\) | |||||||
\(882\) | 6.70711 | − | 2.00368i | 0.225840 | − | 0.0674673i | ||||
\(883\) | − | 22.3169i | − | 0.751024i | −0.926818 | − | 0.375512i | \(-0.877467\pi\) | ||
0.926818 | − | 0.375512i | \(-0.122533\pi\) | |||||||
\(884\) | 12.9775 | − | 8.65166i | 0.436480 | − | 0.290987i | ||||
\(885\) | − | 16.4282i | − | 0.552229i | ||||||
\(886\) | −14.6384 | − | 14.6384i | −0.491788 | − | 0.491788i | ||||
\(887\) | 22.4573i | 0.754044i | 0.926204 | + | 0.377022i | \(0.123052\pi\) | ||||
−0.926204 | + | 0.377022i | \(0.876948\pi\) | |||||||
\(888\) | −7.33838 | −0.246260 | ||||||||
\(889\) | 17.2872 | − | 10.3120i | 0.579795 | − | 0.345853i | ||||
\(890\) | −12.0516 | − | 12.0516i | −0.403970 | − | 0.403970i | ||||
\(891\) | 0.355392 | − | 0.355392i | 0.0119061 | − | 0.0119061i | ||||
\(892\) | −9.89430 | − | 9.89430i | −0.331286 | − | 0.331286i | ||||
\(893\) | −56.3691 | −1.88632 | ||||||||
\(894\) | 14.9461 | 0.499871 | ||||||||
\(895\) | −22.2667 | − | 22.2667i | −0.744294 | − | 0.744294i | ||||
\(896\) | 2.56510 | + | 0.648285i | 0.0856939 | + | 0.0216577i | ||||
\(897\) | −4.76991 | − | 7.15487i | −0.159263 | − | 0.238894i | ||||
\(898\) | −28.6211 | −0.955099 | ||||||||
\(899\) | 1.18689 | − | 1.18689i | 0.0395850 | − | 0.0395850i | ||||
\(900\) | −5.32583 | −0.177528 | ||||||||
\(901\) | 48.6880 | 1.62203 | ||||||||
\(902\) | 1.77511 | − | 1.77511i | 0.0591047 | − | 0.0591047i | ||||
\(903\) | 10.0959 | + | 16.9249i | 0.335969 | + | 0.563226i | ||||
\(904\) | −14.3854 | + | 14.3854i | −0.478451 | + | 0.478451i | ||||
\(905\) | 23.7154 | − | 23.7154i | 0.788326 | − | 0.788326i | ||||
\(906\) | 0.211229i | 0.00701762i | ||||||||
\(907\) | 27.5490i | 0.914749i | 0.889274 | + | 0.457375i | \(0.151210\pi\) | ||||
−0.889274 | + | 0.457375i | \(0.848790\pi\) | |||||||
\(908\) | −1.67417 | − | 1.67417i | −0.0555594 | − | 0.0555594i | ||||
\(909\) | 19.7996 | 0.656711 | ||||||||
\(910\) | −13.1936 | + | 27.6691i | −0.437364 | + | 0.917222i | ||||
\(911\) | 50.9409 | 1.68775 | 0.843873 | − | 0.536542i | \(-0.180270\pi\) | ||||
0.843873 | + | 0.536542i | \(0.180270\pi\) | |||||||
\(912\) | 5.98299 | + | 5.98299i | 0.198117 | + | 0.198117i | ||||
\(913\) | − | 4.76991i | − | 0.157861i | ||||||
\(914\) | − | 25.7233i | − | 0.850852i | ||||||
\(915\) | 9.82917 | − | 9.82917i | 0.324942 | − | 0.324942i | ||||
\(916\) | −1.32583 | + | 1.32583i | −0.0438066 | + | 0.0438066i | ||||
\(917\) | −15.6106 | + | 9.31186i | −0.515507 | + | 0.307505i | ||||
\(918\) | 3.05882 | − | 3.05882i | 0.100956 | − | 0.100956i | ||||
\(919\) | −7.00433 | −0.231052 | −0.115526 | − | 0.993304i | \(-0.536855\pi\) | ||||
−0.115526 | + | 0.993304i | \(0.536855\pi\) | |||||||
\(920\) | 7.66377 | 0.252667 | ||||||||
\(921\) | 10.0397 | − | 10.0397i | 0.330818 | − | 0.330818i | ||||
\(922\) | −1.67356 | −0.0551158 | ||||||||
\(923\) | −6.38496 | + | 31.9248i | −0.210163 | + | 1.05082i | ||||
\(924\) | 1.28922 | + | 0.325828i | 0.0424121 | + | 0.0107189i | ||||
\(925\) | 27.6358 | + | 27.6358i | 0.908660 | + | 0.908660i | ||||
\(926\) | 6.98545 | 0.229556 | ||||||||
\(927\) | −2.70386 | −0.0888065 | ||||||||
\(928\) | −0.774804 | − | 0.774804i | −0.0254342 | − | 0.0254342i | ||||
\(929\) | −7.38650 | + | 7.38650i | −0.242343 | + | 0.242343i | −0.817819 | − | 0.575476i | \(-0.804817\pi\) |
0.575476 | + | 0.817819i | \(0.304817\pi\) | |||||||
\(930\) | −3.48069 | − | 3.48069i | −0.114136 | − | 0.114136i | ||||
\(931\) | 16.9536 | + | 56.7503i | 0.555630 | + | 1.85992i | ||||
\(932\) | −10.2117 | −0.334494 | ||||||||
\(933\) | − | 15.7064i | − | 0.514206i | ||||||
\(934\) | −18.8727 | − | 18.8727i | −0.617533 | − | 0.617533i | ||||
\(935\) | 6.98640i | 0.228480i | ||||||||
\(936\) | 3.53553 | + | 0.707107i | 0.115563 | + | 0.0231125i | ||||
\(937\) | 47.1203i | 1.53935i | 0.638435 | + | 0.769676i | \(0.279582\pi\) | ||||
−0.638435 | + | 0.769676i | \(0.720418\pi\) | |||||||
\(938\) | 1.70906 | − | 1.01947i | 0.0558029 | − | 0.0332869i | ||||
\(939\) | −20.7702 | −0.677809 | ||||||||
\(940\) | − | 21.4077i | − | 0.698243i | ||||||
\(941\) | −18.1495 | + | 18.1495i | −0.591656 | + | 0.591656i | −0.938079 | − | 0.346422i | \(-0.887396\pi\) |
0.346422 | + | 0.938079i | \(0.387396\pi\) | |||||||
\(942\) | 7.61058 | + | 7.61058i | 0.247966 | + | 0.247966i | ||||
\(943\) | −8.42332 | − | 8.42332i | −0.274301 | − | 0.274301i | ||||
\(944\) | −3.61504 | − | 3.61504i | −0.117660 | − | 0.117660i | ||||
\(945\) | −2.08319 | + | 8.24264i | −0.0677661 | + | 0.268133i | ||||
\(946\) | 3.74370i | 0.121718i | ||||||||
\(947\) | −2.89980 | + | 2.89980i | −0.0942309 | + | 0.0942309i | −0.752651 | − | 0.658420i | \(-0.771225\pi\) |
0.658420 | + | 0.752651i | \(0.271225\pi\) | |||||||
\(948\) | −11.3143 | −0.367472 | ||||||||
\(949\) | 5.18902 | − | 25.9451i | 0.168443 | − | 0.842213i | ||||
\(950\) | − | 45.0630i | − | 1.46204i | ||||||
\(951\) | 19.0126 | − | 19.0126i | 0.616524 | − | 0.616524i | ||||
\(952\) | 11.0962 | + | 2.80437i | 0.359629 | + | 0.0908901i | ||||
\(953\) | 39.8477i | 1.29079i | 0.763847 | + | 0.645397i | \(0.223308\pi\) | ||||
−0.763847 | + | 0.645397i | \(0.776692\pi\) | |||||||
\(954\) | 7.95862 | + | 7.95862i | 0.257670 | + | 0.257670i | ||||
\(955\) | 25.3147 | − | 25.3147i | 0.819164 | − | 0.819164i | ||||
\(956\) | 15.2212 | − | 15.2212i | 0.492288 | − | 0.492288i | ||||
\(957\) | −0.389416 | − | 0.389416i | −0.0125880 | − | 0.0125880i | ||||
\(958\) | − | 10.4086i | − | 0.336286i | ||||||
\(959\) | −0.987448 | − | 0.249561i | −0.0318864 | − | 0.00805874i | ||||
\(960\) | −2.27220 | + | 2.27220i | −0.0733351 | + | 0.0733351i | ||||
\(961\) | 28.6534i | 0.924304i | ||||||||
\(962\) | −14.6768 | − | 22.0151i | −0.473198 | − | 0.709797i | ||||
\(963\) | 11.6673 | 0.375972 | ||||||||
\(964\) | 3.38496 | − | 3.38496i | 0.109022 | − | 0.109022i | ||||
\(965\) | − | 18.3440i | − | 0.590515i | ||||||
\(966\) | 1.54613 | − | 6.11764i | 0.0497459 | − | 0.196832i | ||||
\(967\) | −19.7373 | − | 19.7373i | −0.634709 | − | 0.634709i | 0.314537 | − | 0.949245i | \(-0.398151\pi\) |
−0.949245 | + | 0.314537i | \(0.898151\pi\) | |||||||
\(968\) | −7.59955 | − | 7.59955i | −0.244259 | − | 0.244259i | ||||
\(969\) | 25.8814 | + | 25.8814i | 0.831429 | + | 0.831429i | ||||
\(970\) | −41.7517 | + | 41.7517i | −1.34057 | + | 1.34057i | ||||
\(971\) | − | 12.5416i | − | 0.402478i | −0.979542 | − | 0.201239i | \(-0.935503\pi\) | ||
0.979542 | − | 0.201239i | \(-0.0644969\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 46.2258 | − | 27.5741i | 1.48193 | − | 0.883985i | ||||
\(974\) | 35.6051i | 1.14086i | ||||||||
\(975\) | −10.6517 | − | 15.9775i | −0.341126 | − | 0.511689i | ||||
\(976\) | − | 4.32583i | − | 0.138466i | ||||||
\(977\) | 13.8123 | + | 13.8123i | 0.441894 | + | 0.441894i | 0.892648 | − | 0.450754i | \(-0.148845\pi\) |
−0.450754 | + | 0.892648i | \(0.648845\pi\) | |||||||
\(978\) | 4.82107i | 0.154161i | ||||||||
\(979\) | −2.66575 | −0.0851977 | ||||||||
\(980\) | −21.5525 | + | 6.43858i | −0.688469 | + | 0.205673i | ||||
\(981\) | 5.29626 | + | 5.29626i | 0.169097 | + | 0.169097i | ||||
\(982\) | −5.49740 | + | 5.49740i | −0.175429 | + | 0.175429i | ||||
\(983\) | −26.1069 | − | 26.1069i | −0.832680 | − | 0.832680i | 0.155203 | − | 0.987883i | \(-0.450397\pi\) |
−0.987883 | + | 0.155203i | \(0.950397\pi\) | |||||||
\(984\) | 4.99480 | 0.159228 | ||||||||
\(985\) | 2.85205 | 0.0908740 | ||||||||
\(986\) | −3.35167 | − | 3.35167i | −0.106739 | − | 0.106739i | ||||
\(987\) | −17.0888 | − | 4.31891i | −0.543943 | − | 0.137472i | ||||
\(988\) | −5.98299 | + | 29.9149i | −0.190344 | + | 0.951721i | ||||
\(989\) | 17.7647 | 0.564886 | ||||||||
\(990\) | −1.14201 | + | 1.14201i | −0.0362954 | + | 0.0362954i | ||||
\(991\) | 7.35727 | 0.233711 | 0.116856 | − | 0.993149i | \(-0.462719\pi\) | ||||
0.116856 | + | 0.993149i | \(0.462719\pi\) | |||||||
\(992\) | −1.53186 | −0.0486365 | ||||||||
\(993\) | −13.9785 | + | 13.9785i | −0.443595 | + | 0.443595i | ||||
\(994\) | −20.5173 | + | 12.2388i | −0.650769 | + | 0.388190i | ||||
\(995\) | 37.5766 | − | 37.5766i | 1.19126 | − | 1.19126i | ||||
\(996\) | 6.71078 | − | 6.71078i | 0.212639 | − | 0.212639i | ||||
\(997\) | − | 14.1274i | − | 0.447420i | −0.974656 | − | 0.223710i | \(-0.928183\pi\) | ||
0.974656 | − | 0.223710i | \(-0.0718169\pi\) | |||||||
\(998\) | 33.1763i | 1.05018i | ||||||||
\(999\) | −5.18902 | − | 5.18902i | −0.164173 | − | 0.164173i |
(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 | 546.2.o.a.307.4 | yes | 8 | |
3.2 | odd | 2 | 1638.2.x.d.307.1 | 8 | |||
7.6 | odd | 2 | 546.2.o.d.307.3 | yes | 8 | ||
13.5 | odd | 4 | 546.2.o.d.265.3 | yes | 8 | ||
21.20 | even | 2 | 1638.2.x.b.307.2 | 8 | |||
39.5 | even | 4 | 1638.2.x.b.811.2 | 8 | |||
91.83 | even | 4 | inner | 546.2.o.a.265.4 | ✓ | 8 | |
273.83 | odd | 4 | 1638.2.x.d.811.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.o.a.265.4 | ✓ | 8 | 91.83 | even | 4 | inner | |
546.2.o.a.307.4 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.o.d.265.3 | yes | 8 | 13.5 | odd | 4 | ||
546.2.o.d.307.3 | yes | 8 | 7.6 | odd | 2 | ||
1638.2.x.b.307.2 | 8 | 21.20 | even | 2 | |||
1638.2.x.b.811.2 | 8 | 39.5 | even | 4 | |||
1638.2.x.d.307.1 | 8 | 3.2 | odd | 2 | |||
1638.2.x.d.811.1 | 8 | 273.83 | odd | 4 |