Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [130,2,Mod(101,130)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(130, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("130.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 130 = 2 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 130.l (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: | \(1.03805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 130.121 |
Dual form | 130.2.l.a.101.1 |
$q$-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 \(\left(\mathbb{Z}/130\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(41\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −0.366025 | + | 0.633975i | −0.211325 | + | 0.366025i | −0.952129 | − | 0.305695i | \(-0.901111\pi\) |
0.740805 | + | 0.671721i | \(0.234444\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.633975 | − | 0.366025i | 0.258819 | − | 0.149429i | ||||
\(7\) | 2.59808 | − | 1.50000i | 0.981981 | − | 0.566947i | 0.0791130 | − | 0.996866i | \(-0.474791\pi\) |
0.902867 | + | 0.429919i | \(0.141458\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.23205 | + | 2.13397i | 0.410684 | + | 0.711325i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 2.59808 | + | 1.50000i | 0.783349 | + | 0.452267i | 0.837616 | − | 0.546259i | \(-0.183949\pi\) |
−0.0542666 | + | 0.998526i | \(0.517282\pi\) | |||||||
\(12\) | −0.732051 | −0.211325 | ||||||||
\(13\) | 3.50000 | − | 0.866025i | 0.970725 | − | 0.240192i | ||||
\(14\) | −3.00000 | −0.801784 | ||||||||
\(15\) | 0.633975 | + | 0.366025i | 0.163692 | + | 0.0945074i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −4.09808 | − | 7.09808i | −0.993929 | − | 1.72154i | −0.592244 | − | 0.805759i | \(-0.701758\pi\) |
−0.401685 | − | 0.915778i | \(-0.631575\pi\) | |||||||
\(18\) | − | 2.46410i | − | 0.580794i | ||||||
\(19\) | −0.401924 | + | 0.232051i | −0.0922076 | + | 0.0532361i | −0.545395 | − | 0.838179i | \(-0.683620\pi\) |
0.453187 | + | 0.891415i | \(0.350287\pi\) | |||||||
\(20\) | 0.866025 | − | 0.500000i | 0.193649 | − | 0.111803i | ||||
\(21\) | 2.19615i | 0.479240i | ||||||||
\(22\) | −1.50000 | − | 2.59808i | −0.319801 | − | 0.553912i | ||||
\(23\) | −4.73205 | + | 8.19615i | −0.986701 | + | 1.70902i | −0.352581 | + | 0.935781i | \(0.614696\pi\) |
−0.634120 | + | 0.773234i | \(0.718638\pi\) | |||||||
\(24\) | 0.633975 | + | 0.366025i | 0.129410 | + | 0.0747146i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.46410 | − | 1.00000i | −0.679366 | − | 0.196116i | ||||
\(27\) | −4.00000 | −0.769800 | ||||||||
\(28\) | 2.59808 | + | 1.50000i | 0.490990 | + | 0.283473i | ||||
\(29\) | 1.26795 | − | 2.19615i | 0.235452 | − | 0.407815i | −0.723952 | − | 0.689851i | \(-0.757676\pi\) |
0.959404 | + | 0.282035i | \(0.0910095\pi\) | |||||||
\(30\) | −0.366025 | − | 0.633975i | −0.0668268 | − | 0.115747i | ||||
\(31\) | 4.73205i | 0.849901i | 0.905216 | + | 0.424951i | \(0.139709\pi\) | ||||
−0.905216 | + | 0.424951i | \(0.860291\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | −1.90192 | + | 1.09808i | −0.331082 | + | 0.191151i | ||||
\(34\) | 8.19615i | 1.40563i | ||||||||
\(35\) | −1.50000 | − | 2.59808i | −0.253546 | − | 0.439155i | ||||
\(36\) | −1.23205 | + | 2.13397i | −0.205342 | + | 0.355662i | ||||
\(37\) | −0.696152 | − | 0.401924i | −0.114447 | − | 0.0660759i | 0.441684 | − | 0.897171i | \(-0.354381\pi\) |
−0.556131 | + | 0.831095i | \(0.687715\pi\) | |||||||
\(38\) | 0.464102 | 0.0752872 | ||||||||
\(39\) | −0.732051 | + | 2.53590i | −0.117222 | + | 0.406069i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −9.00000 | − | 5.19615i | −1.40556 | − | 0.811503i | −0.410608 | − | 0.911812i | \(-0.634683\pi\) |
−0.994956 | + | 0.100309i | \(0.968017\pi\) | |||||||
\(42\) | 1.09808 | − | 1.90192i | 0.169437 | − | 0.293473i | ||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 3.00000i | 0.452267i | ||||||||
\(45\) | 2.13397 | − | 1.23205i | 0.318114 | − | 0.183663i | ||||
\(46\) | 8.19615 | − | 4.73205i | 1.20846 | − | 0.697703i | ||||
\(47\) | 3.00000i | 0.437595i | 0.975770 | + | 0.218797i | \(0.0702134\pi\) | ||||
−0.975770 | + | 0.218797i | \(0.929787\pi\) | |||||||
\(48\) | −0.366025 | − | 0.633975i | −0.0528312 | − | 0.0915064i | ||||
\(49\) | 1.00000 | − | 1.73205i | 0.142857 | − | 0.247436i | ||||
\(50\) | 0.866025 | + | 0.500000i | 0.122474 | + | 0.0707107i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | 2.50000 | + | 2.59808i | 0.346688 | + | 0.360288i | ||||
\(53\) | 0.464102 | 0.0637493 | 0.0318746 | − | 0.999492i | \(-0.489852\pi\) | ||||
0.0318746 | + | 0.999492i | \(0.489852\pi\) | |||||||
\(54\) | 3.46410 | + | 2.00000i | 0.471405 | + | 0.272166i | ||||
\(55\) | 1.50000 | − | 2.59808i | 0.202260 | − | 0.350325i | ||||
\(56\) | −1.50000 | − | 2.59808i | −0.200446 | − | 0.347183i | ||||
\(57\) | − | 0.339746i | − | 0.0450005i | ||||||
\(58\) | −2.19615 | + | 1.26795i | −0.288369 | + | 0.166490i | ||||
\(59\) | 9.00000 | − | 5.19615i | 1.17170 | − | 0.676481i | 0.217620 | − | 0.976034i | \(-0.430171\pi\) |
0.954080 | + | 0.299552i | \(0.0968372\pi\) | |||||||
\(60\) | 0.732051i | 0.0945074i | ||||||||
\(61\) | −3.09808 | − | 5.36603i | −0.396668 | − | 0.687049i | 0.596645 | − | 0.802506i | \(-0.296500\pi\) |
−0.993313 | + | 0.115456i | \(0.963167\pi\) | |||||||
\(62\) | 2.36603 | − | 4.09808i | 0.300486 | − | 0.520456i | ||||
\(63\) | 6.40192 | + | 3.69615i | 0.806567 | + | 0.465671i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.866025 | − | 3.50000i | −0.107417 | − | 0.434122i | ||||
\(66\) | 2.19615 | 0.270328 | ||||||||
\(67\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(68\) | 4.09808 | − | 7.09808i | 0.496965 | − | 0.860768i | ||||
\(69\) | −3.46410 | − | 6.00000i | −0.417029 | − | 0.722315i | ||||
\(70\) | 3.00000i | 0.358569i | ||||||||
\(71\) | −5.19615 | + | 3.00000i | −0.616670 | + | 0.356034i | −0.775571 | − | 0.631260i | \(-0.782538\pi\) |
0.158901 | + | 0.987294i | \(0.449205\pi\) | |||||||
\(72\) | 2.13397 | − | 1.23205i | 0.251491 | − | 0.145199i | ||||
\(73\) | 11.6603i | 1.36473i | 0.731012 | + | 0.682365i | \(0.239048\pi\) | ||||
−0.731012 | + | 0.682365i | \(0.760952\pi\) | |||||||
\(74\) | 0.401924 | + | 0.696152i | 0.0467227 | + | 0.0809261i | ||||
\(75\) | 0.366025 | − | 0.633975i | 0.0422650 | − | 0.0732051i | ||||
\(76\) | −0.401924 | − | 0.232051i | −0.0461038 | − | 0.0266181i | ||||
\(77\) | 9.00000 | 1.02565 | ||||||||
\(78\) | 1.90192 | − | 1.83013i | 0.215350 | − | 0.207221i | ||||
\(79\) | −4.19615 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(80\) | 0.866025 | + | 0.500000i | 0.0968246 | + | 0.0559017i | ||||
\(81\) | −2.23205 | + | 3.86603i | −0.248006 | + | 0.429558i | ||||
\(82\) | 5.19615 | + | 9.00000i | 0.573819 | + | 0.993884i | ||||
\(83\) | − | 8.19615i | − | 0.899645i | −0.893118 | − | 0.449822i | \(-0.851487\pi\) | ||
0.893118 | − | 0.449822i | \(-0.148513\pi\) | |||||||
\(84\) | −1.90192 | + | 1.09808i | −0.207517 | + | 0.119810i | ||||
\(85\) | −7.09808 | + | 4.09808i | −0.769894 | + | 0.444499i | ||||
\(86\) | 2.00000i | 0.215666i | ||||||||
\(87\) | 0.928203 | + | 1.60770i | 0.0995138 | + | 0.172363i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | 5.89230 | + | 3.40192i | 0.624583 | + | 0.360603i | 0.778651 | − | 0.627457i | \(-0.215904\pi\) |
−0.154068 | + | 0.988060i | \(0.549238\pi\) | |||||||
\(90\) | −2.46410 | −0.259739 | ||||||||
\(91\) | 7.79423 | − | 7.50000i | 0.817057 | − | 0.786214i | ||||
\(92\) | −9.46410 | −0.986701 | ||||||||
\(93\) | −3.00000 | − | 1.73205i | −0.311086 | − | 0.179605i | ||||
\(94\) | 1.50000 | − | 2.59808i | 0.154713 | − | 0.267971i | ||||
\(95\) | 0.232051 | + | 0.401924i | 0.0238079 | + | 0.0412365i | ||||
\(96\) | 0.732051i | 0.0747146i | ||||||||
\(97\) | 7.90192 | − | 4.56218i | 0.802319 | − | 0.463219i | −0.0419625 | − | 0.999119i | \(-0.513361\pi\) |
0.844281 | + | 0.535900i | \(0.180028\pi\) | |||||||
\(98\) | −1.73205 | + | 1.00000i | −0.174964 | + | 0.101015i | ||||
\(99\) | 7.39230i | 0.742955i | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | −5.36603 | + | 9.29423i | −0.533939 | + | 0.924810i | 0.465274 | + | 0.885167i | \(0.345956\pi\) |
−0.999214 | + | 0.0396438i | \(0.987378\pi\) | |||||||
\(102\) | −5.19615 | − | 3.00000i | −0.514496 | − | 0.297044i | ||||
\(103\) | −9.19615 | −0.906124 | −0.453062 | − | 0.891479i | \(-0.649668\pi\) | ||||
−0.453062 | + | 0.891479i | \(0.649668\pi\) | |||||||
\(104\) | −0.866025 | − | 3.50000i | −0.0849208 | − | 0.343203i | ||||
\(105\) | 2.19615 | 0.214323 | ||||||||
\(106\) | −0.401924 | − | 0.232051i | −0.0390383 | − | 0.0225388i | ||||
\(107\) | −8.83013 | + | 15.2942i | −0.853641 | + | 1.47855i | 0.0242598 | + | 0.999706i | \(0.492277\pi\) |
−0.877900 | + | 0.478843i | \(0.841056\pi\) | |||||||
\(108\) | −2.00000 | − | 3.46410i | −0.192450 | − | 0.333333i | ||||
\(109\) | − | 8.53590i | − | 0.817591i | −0.912626 | − | 0.408795i | \(-0.865949\pi\) | ||
0.912626 | − | 0.408795i | \(-0.134051\pi\) | |||||||
\(110\) | −2.59808 | + | 1.50000i | −0.247717 | + | 0.143019i | ||||
\(111\) | 0.509619 | − | 0.294229i | 0.0483709 | − | 0.0279269i | ||||
\(112\) | 3.00000i | 0.283473i | ||||||||
\(113\) | −3.46410 | − | 6.00000i | −0.325875 | − | 0.564433i | 0.655814 | − | 0.754923i | \(-0.272326\pi\) |
−0.981689 | + | 0.190490i | \(0.938992\pi\) | |||||||
\(114\) | −0.169873 | + | 0.294229i | −0.0159101 | + | 0.0275570i | ||||
\(115\) | 8.19615 | + | 4.73205i | 0.764295 | + | 0.441266i | ||||
\(116\) | 2.53590 | 0.235452 | ||||||||
\(117\) | 6.16025 | + | 6.40192i | 0.569516 | + | 0.591858i | ||||
\(118\) | −10.3923 | −0.956689 | ||||||||
\(119\) | −21.2942 | − | 12.2942i | −1.95204 | − | 1.12701i | ||||
\(120\) | 0.366025 | − | 0.633975i | 0.0334134 | − | 0.0578737i | ||||
\(121\) | −1.00000 | − | 1.73205i | −0.0909091 | − | 0.157459i | ||||
\(122\) | 6.19615i | 0.560973i | ||||||||
\(123\) | 6.58846 | − | 3.80385i | 0.594061 | − | 0.342981i | ||||
\(124\) | −4.09808 | + | 2.36603i | −0.368018 | + | 0.212475i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −3.69615 | − | 6.40192i | −0.329279 | − | 0.570329i | ||||
\(127\) | −5.40192 | + | 9.35641i | −0.479343 | + | 0.830247i | −0.999719 | − | 0.0236904i | \(-0.992458\pi\) |
0.520376 | + | 0.853937i | \(0.325792\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 1.46410 | 0.128907 | ||||||||
\(130\) | −1.00000 | + | 3.46410i | −0.0877058 | + | 0.303822i | ||||
\(131\) | 6.12436 | 0.535087 | 0.267544 | − | 0.963546i | \(-0.413788\pi\) | ||||
0.267544 | + | 0.963546i | \(0.413788\pi\) | |||||||
\(132\) | −1.90192 | − | 1.09808i | −0.165541 | − | 0.0955753i | ||||
\(133\) | −0.696152 | + | 1.20577i | −0.0603641 | + | 0.104554i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.00000i | 0.344265i | ||||||||
\(136\) | −7.09808 | + | 4.09808i | −0.608655 | + | 0.351407i | ||||
\(137\) | 1.90192 | − | 1.09808i | 0.162492 | − | 0.0938150i | −0.416549 | − | 0.909113i | \(-0.636760\pi\) |
0.579041 | + | 0.815298i | \(0.303427\pi\) | |||||||
\(138\) | 6.92820i | 0.589768i | ||||||||
\(139\) | −0.598076 | − | 1.03590i | −0.0507282 | − | 0.0878638i | 0.839546 | − | 0.543288i | \(-0.182821\pi\) |
−0.890274 | + | 0.455424i | \(0.849488\pi\) | |||||||
\(140\) | 1.50000 | − | 2.59808i | 0.126773 | − | 0.219578i | ||||
\(141\) | −1.90192 | − | 1.09808i | −0.160171 | − | 0.0924747i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | 10.3923 | + | 3.00000i | 0.869048 | + | 0.250873i | ||||
\(144\) | −2.46410 | −0.205342 | ||||||||
\(145\) | −2.19615 | − | 1.26795i | −0.182381 | − | 0.105297i | ||||
\(146\) | 5.83013 | − | 10.0981i | 0.482505 | − | 0.835723i | ||||
\(147\) | 0.732051 | + | 1.26795i | 0.0603785 | + | 0.104579i | ||||
\(148\) | − | 0.803848i | − | 0.0660759i | ||||||
\(149\) | 5.19615 | − | 3.00000i | 0.425685 | − | 0.245770i | −0.271821 | − | 0.962348i | \(-0.587626\pi\) |
0.697507 | + | 0.716578i | \(0.254293\pi\) | |||||||
\(150\) | −0.633975 | + | 0.366025i | −0.0517638 | + | 0.0298858i | ||||
\(151\) | − | 23.6603i | − | 1.92544i | −0.270492 | − | 0.962722i | \(-0.587187\pi\) | ||
0.270492 | − | 0.962722i | \(-0.412813\pi\) | |||||||
\(152\) | 0.232051 | + | 0.401924i | 0.0188218 | + | 0.0326003i | ||||
\(153\) | 10.0981 | − | 17.4904i | 0.816381 | − | 1.41401i | ||||
\(154\) | −7.79423 | − | 4.50000i | −0.628077 | − | 0.362620i | ||||
\(155\) | 4.73205 | 0.380087 | ||||||||
\(156\) | −2.56218 | + | 0.633975i | −0.205138 | + | 0.0507586i | ||||
\(157\) | −13.0000 | −1.03751 | −0.518756 | − | 0.854922i | \(-0.673605\pi\) | ||||
−0.518756 | + | 0.854922i | \(0.673605\pi\) | |||||||
\(158\) | 3.63397 | + | 2.09808i | 0.289103 | + | 0.166914i | ||||
\(159\) | −0.169873 | + | 0.294229i | −0.0134718 | + | 0.0233338i | ||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 28.3923i | 2.23763i | ||||||||
\(162\) | 3.86603 | − | 2.23205i | 0.303744 | − | 0.175366i | ||||
\(163\) | −9.29423 | + | 5.36603i | −0.727980 | + | 0.420300i | −0.817683 | − | 0.575669i | \(-0.804742\pi\) |
0.0897026 | + | 0.995969i | \(0.471408\pi\) | |||||||
\(164\) | − | 10.3923i | − | 0.811503i | ||||||
\(165\) | 1.09808 | + | 1.90192i | 0.0854851 | + | 0.148065i | ||||
\(166\) | −4.09808 | + | 7.09808i | −0.318072 | + | 0.550918i | ||||
\(167\) | 2.59808 | + | 1.50000i | 0.201045 | + | 0.116073i | 0.597143 | − | 0.802135i | \(-0.296303\pi\) |
−0.396098 | + | 0.918208i | \(0.629636\pi\) | |||||||
\(168\) | 2.19615 | 0.169437 | ||||||||
\(169\) | 11.5000 | − | 6.06218i | 0.884615 | − | 0.466321i | ||||
\(170\) | 8.19615 | 0.628616 | ||||||||
\(171\) | −0.990381 | − | 0.571797i | −0.0757363 | − | 0.0437264i | ||||
\(172\) | 1.00000 | − | 1.73205i | 0.0762493 | − | 0.132068i | ||||
\(173\) | 7.50000 | + | 12.9904i | 0.570214 | + | 0.987640i | 0.996544 | + | 0.0830722i | \(0.0264732\pi\) |
−0.426329 | + | 0.904568i | \(0.640193\pi\) | |||||||
\(174\) | − | 1.85641i | − | 0.140734i | ||||||
\(175\) | −2.59808 | + | 1.50000i | −0.196396 | + | 0.113389i | ||||
\(176\) | −2.59808 | + | 1.50000i | −0.195837 | + | 0.113067i | ||||
\(177\) | 7.60770i | 0.571829i | ||||||||
\(178\) | −3.40192 | − | 5.89230i | −0.254985 | − | 0.441647i | ||||
\(179\) | 4.73205 | − | 8.19615i | 0.353690 | − | 0.612609i | −0.633203 | − | 0.773986i | \(-0.718260\pi\) |
0.986893 | + | 0.161377i | \(0.0515934\pi\) | |||||||
\(180\) | 2.13397 | + | 1.23205i | 0.159057 | + | 0.0918316i | ||||
\(181\) | 14.5885 | 1.08435 | 0.542176 | − | 0.840265i | \(-0.317601\pi\) | ||||
0.542176 | + | 0.840265i | \(0.317601\pi\) | |||||||
\(182\) | −10.5000 | + | 2.59808i | −0.778312 | + | 0.192582i | ||||
\(183\) | 4.53590 | 0.335303 | ||||||||
\(184\) | 8.19615 | + | 4.73205i | 0.604228 | + | 0.348851i | ||||
\(185\) | −0.401924 | + | 0.696152i | −0.0295500 | + | 0.0511821i | ||||
\(186\) | 1.73205 | + | 3.00000i | 0.127000 | + | 0.219971i | ||||
\(187\) | − | 24.5885i | − | 1.79809i | ||||||
\(188\) | −2.59808 | + | 1.50000i | −0.189484 | + | 0.109399i | ||||
\(189\) | −10.3923 | + | 6.00000i | −0.755929 | + | 0.436436i | ||||
\(190\) | − | 0.464102i | − | 0.0336695i | ||||||
\(191\) | 11.3660 | + | 19.6865i | 0.822417 | + | 1.42447i | 0.903878 | + | 0.427791i | \(0.140708\pi\) |
−0.0814609 | + | 0.996677i | \(0.525959\pi\) | |||||||
\(192\) | 0.366025 | − | 0.633975i | 0.0264156 | − | 0.0457532i | ||||
\(193\) | −14.1962 | − | 8.19615i | −1.02186 | − | 0.589972i | −0.107219 | − | 0.994235i | \(-0.534195\pi\) |
−0.914643 | + | 0.404263i | \(0.867528\pi\) | |||||||
\(194\) | −9.12436 | −0.655091 | ||||||||
\(195\) | 2.53590 | + | 0.732051i | 0.181599 | + | 0.0524232i | ||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 18.6962 | + | 10.7942i | 1.33205 | + | 0.769057i | 0.985613 | − | 0.169018i | \(-0.0540596\pi\) |
0.346433 | + | 0.938075i | \(0.387393\pi\) | |||||||
\(198\) | 3.69615 | − | 6.40192i | 0.262674 | − | 0.454965i | ||||
\(199\) | 3.19615 | + | 5.53590i | 0.226569 | + | 0.392429i | 0.956789 | − | 0.290783i | \(-0.0939157\pi\) |
−0.730220 | + | 0.683212i | \(0.760582\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.29423 | − | 5.36603i | 0.653940 | − | 0.377552i | ||||
\(203\) | − | 7.60770i | − | 0.533956i | ||||||
\(204\) | 3.00000 | + | 5.19615i | 0.210042 | + | 0.363803i | ||||
\(205\) | −5.19615 | + | 9.00000i | −0.362915 | + | 0.628587i | ||||
\(206\) | 7.96410 | + | 4.59808i | 0.554885 | + | 0.320363i | ||||
\(207\) | −23.3205 | −1.62089 | ||||||||
\(208\) | −1.00000 | + | 3.46410i | −0.0693375 | + | 0.240192i | ||||
\(209\) | −1.39230 | −0.0963077 | ||||||||
\(210\) | −1.90192 | − | 1.09808i | −0.131245 | − | 0.0757745i | ||||
\(211\) | 8.79423 | − | 15.2321i | 0.605420 | − | 1.04862i | −0.386565 | − | 0.922262i | \(-0.626339\pi\) |
0.991985 | − | 0.126356i | \(-0.0403280\pi\) | |||||||
\(212\) | 0.232051 | + | 0.401924i | 0.0159373 | + | 0.0276042i | ||||
\(213\) | − | 4.39230i | − | 0.300956i | ||||||
\(214\) | 15.2942 | − | 8.83013i | 1.04549 | − | 0.603615i | ||||
\(215\) | −1.73205 | + | 1.00000i | −0.118125 | + | 0.0681994i | ||||
\(216\) | 4.00000i | 0.272166i | ||||||||
\(217\) | 7.09808 | + | 12.2942i | 0.481849 | + | 0.834587i | ||||
\(218\) | −4.26795 | + | 7.39230i | −0.289062 | + | 0.500670i | ||||
\(219\) | −7.39230 | − | 4.26795i | −0.499526 | − | 0.288401i | ||||
\(220\) | 3.00000 | 0.202260 | ||||||||
\(221\) | −20.4904 | − | 21.2942i | −1.37833 | − | 1.43240i | ||||
\(222\) | −0.588457 | −0.0394947 | ||||||||
\(223\) | −5.59808 | − | 3.23205i | −0.374875 | − | 0.216434i | 0.300711 | − | 0.953715i | \(-0.402776\pi\) |
−0.675586 | + | 0.737281i | \(0.736109\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | −1.23205 | − | 2.13397i | −0.0821367 | − | 0.142265i | ||||
\(226\) | 6.92820i | 0.460857i | ||||||||
\(227\) | 14.1962 | − | 8.19615i | 0.942232 | − | 0.543998i | 0.0515725 | − | 0.998669i | \(-0.483577\pi\) |
0.890659 | + | 0.454672i | \(0.150243\pi\) | |||||||
\(228\) | 0.294229 | − | 0.169873i | 0.0194858 | − | 0.0112501i | ||||
\(229\) | − | 1.26795i | − | 0.0837884i | −0.999122 | − | 0.0418942i | \(-0.986661\pi\) | ||
0.999122 | − | 0.0418942i | \(-0.0133392\pi\) | |||||||
\(230\) | −4.73205 | − | 8.19615i | −0.312022 | − | 0.540438i | ||||
\(231\) | −3.29423 | + | 5.70577i | −0.216744 | + | 0.375412i | ||||
\(232\) | −2.19615 | − | 1.26795i | −0.144184 | − | 0.0832449i | ||||
\(233\) | 4.73205 | 0.310007 | 0.155003 | − | 0.987914i | \(-0.450461\pi\) | ||||
0.155003 | + | 0.987914i | \(0.450461\pi\) | |||||||
\(234\) | −2.13397 | − | 8.62436i | −0.139502 | − | 0.563792i | ||||
\(235\) | 3.00000 | 0.195698 | ||||||||
\(236\) | 9.00000 | + | 5.19615i | 0.585850 | + | 0.338241i | ||||
\(237\) | 1.53590 | − | 2.66025i | 0.0997673 | − | 0.172802i | ||||
\(238\) | 12.2942 | + | 21.2942i | 0.796916 | + | 1.38030i | ||||
\(239\) | 2.19615i | 0.142057i | 0.997474 | + | 0.0710286i | \(0.0226282\pi\) | ||||
−0.997474 | + | 0.0710286i | \(0.977372\pi\) | |||||||
\(240\) | −0.633975 | + | 0.366025i | −0.0409229 | + | 0.0236268i | ||||
\(241\) | −7.50000 | + | 4.33013i | −0.483117 | + | 0.278928i | −0.721715 | − | 0.692191i | \(-0.756646\pi\) |
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(242\) | 2.00000i | 0.128565i | ||||||||
\(243\) | −7.63397 | − | 13.2224i | −0.489720 | − | 0.848219i | ||||
\(244\) | 3.09808 | − | 5.36603i | 0.198334 | − | 0.343525i | ||||
\(245\) | −1.73205 | − | 1.00000i | −0.110657 | − | 0.0638877i | ||||
\(246\) | −7.60770 | −0.485049 | ||||||||
\(247\) | −1.20577 | + | 1.16025i | −0.0767214 | + | 0.0738252i | ||||
\(248\) | 4.73205 | 0.300486 | ||||||||
\(249\) | 5.19615 | + | 3.00000i | 0.329293 | + | 0.190117i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −8.59808 | − | 14.8923i | −0.542706 | − | 0.939994i | −0.998747 | − | 0.0500355i | \(-0.984067\pi\) |
0.456042 | − | 0.889958i | \(-0.349267\pi\) | |||||||
\(252\) | 7.39230i | 0.465671i | ||||||||
\(253\) | −24.5885 | + | 14.1962i | −1.54586 | + | 0.892504i | ||||
\(254\) | 9.35641 | − | 5.40192i | 0.587073 | − | 0.338947i | ||||
\(255\) | − | 6.00000i | − | 0.375735i | ||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.92820 | − | 12.0000i | 0.432169 | − | 0.748539i | −0.564890 | − | 0.825166i | \(-0.691082\pi\) |
0.997060 | + | 0.0766265i | \(0.0244149\pi\) | |||||||
\(258\) | −1.26795 | − | 0.732051i | −0.0789391 | − | 0.0455755i | ||||
\(259\) | −2.41154 | −0.149846 | ||||||||
\(260\) | 2.59808 | − | 2.50000i | 0.161126 | − | 0.155043i | ||||
\(261\) | 6.24871 | 0.386786 | ||||||||
\(262\) | −5.30385 | − | 3.06218i | −0.327673 | − | 0.189182i | ||||
\(263\) | −1.79423 | + | 3.10770i | −0.110637 | + | 0.191629i | −0.916027 | − | 0.401116i | \(-0.868622\pi\) |
0.805390 | + | 0.592745i | \(0.201956\pi\) | |||||||
\(264\) | 1.09808 | + | 1.90192i | 0.0675819 | + | 0.117055i | ||||
\(265\) | − | 0.464102i | − | 0.0285095i | ||||||
\(266\) | 1.20577 | − | 0.696152i | 0.0739306 | − | 0.0426838i | ||||
\(267\) | −4.31347 | + | 2.49038i | −0.263980 | + | 0.152409i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.5622 | + | 23.4904i | 0.826901 | + | 1.43223i | 0.900458 | + | 0.434943i | \(0.143231\pi\) |
−0.0735575 | + | 0.997291i | \(0.523435\pi\) | |||||||
\(270\) | 2.00000 | − | 3.46410i | 0.121716 | − | 0.210819i | ||||
\(271\) | 8.19615 | + | 4.73205i | 0.497881 | + | 0.287452i | 0.727838 | − | 0.685749i | \(-0.240525\pi\) |
−0.229957 | + | 0.973201i | \(0.573859\pi\) | |||||||
\(272\) | 8.19615 | 0.496965 | ||||||||
\(273\) | 1.90192 | + | 7.68653i | 0.115110 | + | 0.465210i | ||||
\(274\) | −2.19615 | −0.132674 | ||||||||
\(275\) | −2.59808 | − | 1.50000i | −0.156670 | − | 0.0904534i | ||||
\(276\) | 3.46410 | − | 6.00000i | 0.208514 | − | 0.361158i | ||||
\(277\) | 0.500000 | + | 0.866025i | 0.0300421 | + | 0.0520344i | 0.880656 | − | 0.473757i | \(-0.157103\pi\) |
−0.850613 | + | 0.525792i | \(0.823769\pi\) | |||||||
\(278\) | 1.19615i | 0.0717405i | ||||||||
\(279\) | −10.0981 | + | 5.83013i | −0.604556 | + | 0.349041i | ||||
\(280\) | −2.59808 | + | 1.50000i | −0.155265 | + | 0.0896421i | ||||
\(281\) | − | 10.3923i | − | 0.619953i | −0.950744 | − | 0.309976i | \(-0.899679\pi\) | ||
0.950744 | − | 0.309976i | \(-0.100321\pi\) | |||||||
\(282\) | 1.09808 | + | 1.90192i | 0.0653895 | + | 0.113258i | ||||
\(283\) | 4.80385 | − | 8.32051i | 0.285559 | − | 0.494603i | −0.687186 | − | 0.726482i | \(-0.741154\pi\) |
0.972745 | + | 0.231879i | \(0.0744874\pi\) | |||||||
\(284\) | −5.19615 | − | 3.00000i | −0.308335 | − | 0.178017i | ||||
\(285\) | −0.339746 | −0.0201248 | ||||||||
\(286\) | −7.50000 | − | 7.79423i | −0.443484 | − | 0.460882i | ||||
\(287\) | −31.1769 | −1.84032 | ||||||||
\(288\) | 2.13397 | + | 1.23205i | 0.125746 | + | 0.0725993i | ||||
\(289\) | −25.0885 | + | 43.4545i | −1.47579 | + | 2.55615i | ||||
\(290\) | 1.26795 | + | 2.19615i | 0.0744565 | + | 0.128963i | ||||
\(291\) | 6.67949i | 0.391559i | ||||||||
\(292\) | −10.0981 | + | 5.83013i | −0.590945 | + | 0.341182i | ||||
\(293\) | 9.69615 | − | 5.59808i | 0.566455 | − | 0.327043i | −0.189277 | − | 0.981924i | \(-0.560614\pi\) |
0.755732 | + | 0.654881i | \(0.227281\pi\) | |||||||
\(294\) | − | 1.46410i | − | 0.0853881i | ||||||
\(295\) | −5.19615 | − | 9.00000i | −0.302532 | − | 0.524000i | ||||
\(296\) | −0.401924 | + | 0.696152i | −0.0233613 | + | 0.0404630i | ||||
\(297\) | −10.3923 | − | 6.00000i | −0.603023 | − | 0.348155i | ||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −9.46410 | + | 32.7846i | −0.547323 | + | 1.89598i | ||||
\(300\) | 0.732051 | 0.0422650 | ||||||||
\(301\) | −5.19615 | − | 3.00000i | −0.299501 | − | 0.172917i | ||||
\(302\) | −11.8301 | + | 20.4904i | −0.680747 | + | 1.17909i | ||||
\(303\) | −3.92820 | − | 6.80385i | −0.225669 | − | 0.390871i | ||||
\(304\) | − | 0.464102i | − | 0.0266181i | ||||||
\(305\) | −5.36603 | + | 3.09808i | −0.307258 | + | 0.177395i | ||||
\(306\) | −17.4904 | + | 10.0981i | −0.999859 | + | 0.577269i | ||||
\(307\) | − | 27.4641i | − | 1.56746i | −0.621102 | − | 0.783730i | \(-0.713315\pi\) | ||
0.621102 | − | 0.783730i | \(-0.286685\pi\) | |||||||
\(308\) | 4.50000 | + | 7.79423i | 0.256411 | + | 0.444117i | ||||
\(309\) | 3.36603 | − | 5.83013i | 0.191486 | − | 0.331664i | ||||
\(310\) | −4.09808 | − | 2.36603i | −0.232755 | − | 0.134381i | ||||
\(311\) | −9.12436 | −0.517395 | −0.258697 | − | 0.965958i | \(-0.583293\pi\) | ||||
−0.258697 | + | 0.965958i | \(0.583293\pi\) | |||||||
\(312\) | 2.53590 | + | 0.732051i | 0.143567 | + | 0.0414442i | ||||
\(313\) | 26.3923 | 1.49178 | 0.745891 | − | 0.666068i | \(-0.232024\pi\) | ||||
0.745891 | + | 0.666068i | \(0.232024\pi\) | |||||||
\(314\) | 11.2583 | + | 6.50000i | 0.635344 | + | 0.366816i | ||||
\(315\) | 3.69615 | − | 6.40192i | 0.208255 | − | 0.360708i | ||||
\(316\) | −2.09808 | − | 3.63397i | −0.118026 | − | 0.204427i | ||||
\(317\) | − | 23.1962i | − | 1.30283i | −0.758723 | − | 0.651413i | \(-0.774177\pi\) | ||
0.758723 | − | 0.651413i | \(-0.225823\pi\) | |||||||
\(318\) | 0.294229 | − | 0.169873i | 0.0164995 | − | 0.00952600i | ||||
\(319\) | 6.58846 | − | 3.80385i | 0.368883 | − | 0.212975i | ||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | −6.46410 | − | 11.1962i | −0.360791 | − | 0.624908i | ||||
\(322\) | 14.1962 | − | 24.5885i | 0.791121 | − | 1.37026i | ||||
\(323\) | 3.29423 | + | 1.90192i | 0.183296 | + | 0.105826i | ||||
\(324\) | −4.46410 | −0.248006 | ||||||||
\(325\) | −3.50000 | + | 0.866025i | −0.194145 | + | 0.0480384i | ||||
\(326\) | 10.7321 | 0.594393 | ||||||||
\(327\) | 5.41154 | + | 3.12436i | 0.299259 | + | 0.172777i | ||||
\(328\) | −5.19615 | + | 9.00000i | −0.286910 | + | 0.496942i | ||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | − | 2.19615i | − | 0.120894i | ||||||
\(331\) | 11.1962 | − | 6.46410i | 0.615396 | − | 0.355299i | −0.159678 | − | 0.987169i | \(-0.551046\pi\) |
0.775074 | + | 0.631870i | \(0.217712\pi\) | |||||||
\(332\) | 7.09808 | − | 4.09808i | 0.389558 | − | 0.224911i | ||||
\(333\) | − | 1.98076i | − | 0.108545i | ||||||
\(334\) | −1.50000 | − | 2.59808i | −0.0820763 | − | 0.142160i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.90192 | − | 1.09808i | −0.103758 | − | 0.0599050i | ||||
\(337\) | 6.19615 | 0.337526 | 0.168763 | − | 0.985657i | \(-0.446023\pi\) | ||||
0.168763 | + | 0.985657i | \(0.446023\pi\) | |||||||
\(338\) | −12.9904 | − | 0.500000i | −0.706584 | − | 0.0271964i | ||||
\(339\) | 5.07180 | 0.275462 | ||||||||
\(340\) | −7.09808 | − | 4.09808i | −0.384947 | − | 0.222249i | ||||
\(341\) | −7.09808 | + | 12.2942i | −0.384382 | + | 0.665770i | ||||
\(342\) | 0.571797 | + | 0.990381i | 0.0309192 | + | 0.0535537i | ||||
\(343\) | 15.0000i | 0.809924i | ||||||||
\(344\) | −1.73205 | + | 1.00000i | −0.0933859 | + | 0.0539164i | ||||
\(345\) | −6.00000 | + | 3.46410i | −0.323029 | + | 0.186501i | ||||
\(346\) | − | 15.0000i | − | 0.806405i | ||||||
\(347\) | 14.3660 | + | 24.8827i | 0.771209 | + | 1.33577i | 0.936901 | + | 0.349595i | \(0.113681\pi\) |
−0.165692 | + | 0.986178i | \(0.552986\pi\) | |||||||
\(348\) | −0.928203 | + | 1.60770i | −0.0497569 | + | 0.0861815i | ||||
\(349\) | −3.50962 | − | 2.02628i | −0.187866 | − | 0.108464i | 0.403117 | − | 0.915148i | \(-0.367927\pi\) |
−0.590983 | + | 0.806684i | \(0.701260\pi\) | |||||||
\(350\) | 3.00000 | 0.160357 | ||||||||
\(351\) | −14.0000 | + | 3.46410i | −0.747265 | + | 0.184900i | ||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | 8.49038 | + | 4.90192i | 0.451897 | + | 0.260903i | 0.708631 | − | 0.705579i | \(-0.249313\pi\) |
−0.256734 | + | 0.966482i | \(0.582646\pi\) | |||||||
\(354\) | 3.80385 | − | 6.58846i | 0.202172 | − | 0.350173i | ||||
\(355\) | 3.00000 | + | 5.19615i | 0.159223 | + | 0.275783i | ||||
\(356\) | 6.80385i | 0.360603i | ||||||||
\(357\) | 15.5885 | − | 9.00000i | 0.825029 | − | 0.476331i | ||||
\(358\) | −8.19615 | + | 4.73205i | −0.433180 | + | 0.250097i | ||||
\(359\) | 1.60770i | 0.0848509i | 0.999100 | + | 0.0424255i | \(0.0135085\pi\) | ||||
−0.999100 | + | 0.0424255i | \(0.986492\pi\) | |||||||
\(360\) | −1.23205 | − | 2.13397i | −0.0649348 | − | 0.112470i | ||||
\(361\) | −9.39230 | + | 16.2679i | −0.494332 | + | 0.856208i | ||||
\(362\) | −12.6340 | − | 7.29423i | −0.664027 | − | 0.383376i | ||||
\(363\) | 1.46410 | 0.0768454 | ||||||||
\(364\) | 10.3923 | + | 3.00000i | 0.544705 | + | 0.157243i | ||||
\(365\) | 11.6603 | 0.610326 | ||||||||
\(366\) | −3.92820 | − | 2.26795i | −0.205330 | − | 0.118548i | ||||
\(367\) | 2.80385 | − | 4.85641i | 0.146360 | − | 0.253502i | −0.783520 | − | 0.621367i | \(-0.786578\pi\) |
0.929879 | + | 0.367865i | \(0.119911\pi\) | |||||||
\(368\) | −4.73205 | − | 8.19615i | −0.246675 | − | 0.427254i | ||||
\(369\) | − | 25.6077i | − | 1.33308i | ||||||
\(370\) | 0.696152 | − | 0.401924i | 0.0361912 | − | 0.0208950i | ||||
\(371\) | 1.20577 | − | 0.696152i | 0.0626005 | − | 0.0361424i | ||||
\(372\) | − | 3.46410i | − | 0.179605i | ||||||
\(373\) | 0.196152 | + | 0.339746i | 0.0101564 | + | 0.0175914i | 0.871059 | − | 0.491179i | \(-0.163434\pi\) |
−0.860903 | + | 0.508770i | \(0.830100\pi\) | |||||||
\(374\) | −12.2942 | + | 21.2942i | −0.635719 | + | 1.10110i | ||||
\(375\) | −0.633975 | − | 0.366025i | −0.0327383 | − | 0.0189015i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 2.53590 | − | 8.78461i | 0.130605 | − | 0.452430i | ||||
\(378\) | 12.0000 | 0.617213 | ||||||||
\(379\) | 25.7942 | + | 14.8923i | 1.32496 | + | 0.764966i | 0.984515 | − | 0.175298i | \(-0.0560889\pi\) |
0.340445 | + | 0.940264i | \(0.389422\pi\) | |||||||
\(380\) | −0.232051 | + | 0.401924i | −0.0119040 | + | 0.0206183i | ||||
\(381\) | −3.95448 | − | 6.84936i | −0.202594 | − | 0.350904i | ||||
\(382\) | − | 22.7321i | − | 1.16307i | ||||||
\(383\) | 19.3923 | − | 11.1962i | 0.990900 | − | 0.572097i | 0.0853571 | − | 0.996350i | \(-0.472797\pi\) |
0.905543 | + | 0.424254i | \(0.139464\pi\) | |||||||
\(384\) | −0.633975 | + | 0.366025i | −0.0323524 | + | 0.0186787i | ||||
\(385\) | − | 9.00000i | − | 0.458682i | ||||||
\(386\) | 8.19615 | + | 14.1962i | 0.417173 | + | 0.722565i | ||||
\(387\) | 2.46410 | − | 4.26795i | 0.125257 | − | 0.216952i | ||||
\(388\) | 7.90192 | + | 4.56218i | 0.401159 | + | 0.231609i | ||||
\(389\) | 22.7321 | 1.15256 | 0.576280 | − | 0.817252i | \(-0.304504\pi\) | ||||
0.576280 | + | 0.817252i | \(0.304504\pi\) | |||||||
\(390\) | −1.83013 | − | 1.90192i | −0.0926721 | − | 0.0963077i | ||||
\(391\) | 77.5692 | 3.92284 | ||||||||
\(392\) | −1.73205 | − | 1.00000i | −0.0874818 | − | 0.0505076i | ||||
\(393\) | −2.24167 | + | 3.88269i | −0.113077 | + | 0.195856i | ||||
\(394\) | −10.7942 | − | 18.6962i | −0.543805 | − | 0.941899i | ||||
\(395\) | 4.19615i | 0.211131i | ||||||||
\(396\) | −6.40192 | + | 3.69615i | −0.321709 | + | 0.185739i | ||||
\(397\) | −9.69615 | + | 5.59808i | −0.486636 | + | 0.280959i | −0.723178 | − | 0.690662i | \(-0.757319\pi\) |
0.236542 | + | 0.971621i | \(0.423986\pi\) | |||||||
\(398\) | − | 6.39230i | − | 0.320417i | ||||||
\(399\) | −0.509619 | − | 0.882686i | −0.0255129 | − | 0.0441896i | ||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | −4.50000 | − | 2.59808i | −0.224719 | − | 0.129742i | 0.383414 | − | 0.923576i | \(-0.374748\pi\) |
−0.608134 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.09808 | + | 16.5622i | 0.204140 | + | 0.825021i | ||||
\(404\) | −10.7321 | −0.533939 | ||||||||
\(405\) | 3.86603 | + | 2.23205i | 0.192104 | + | 0.110911i | ||||
\(406\) | −3.80385 | + | 6.58846i | −0.188782 | + | 0.326980i | ||||
\(407\) | −1.20577 | − | 2.08846i | −0.0597679 | − | 0.103521i | ||||
\(408\) | − | 6.00000i | − | 0.297044i | ||||||
\(409\) | −14.0885 | + | 8.13397i | −0.696629 | + | 0.402199i | −0.806091 | − | 0.591792i | \(-0.798421\pi\) |
0.109461 | + | 0.993991i | \(0.465087\pi\) | |||||||
\(410\) | 9.00000 | − | 5.19615i | 0.444478 | − | 0.256620i | ||||
\(411\) | 1.60770i | 0.0793018i | ||||||||
\(412\) | −4.59808 | − | 7.96410i | −0.226531 | − | 0.392363i | ||||
\(413\) | 15.5885 | − | 27.0000i | 0.767058 | − | 1.32858i | ||||
\(414\) | 20.1962 | + | 11.6603i | 0.992587 | + | 0.573070i | ||||
\(415\) | −8.19615 | −0.402333 | ||||||||
\(416\) | 2.59808 | − | 2.50000i | 0.127381 | − | 0.122573i | ||||
\(417\) | 0.875644 | 0.0428805 | ||||||||
\(418\) | 1.20577 | + | 0.696152i | 0.0589762 | + | 0.0340499i | ||||
\(419\) | 8.66025 | − | 15.0000i | 0.423081 | − | 0.732798i | −0.573158 | − | 0.819445i | \(-0.694282\pi\) |
0.996239 | + | 0.0866469i | \(0.0276152\pi\) | |||||||
\(420\) | 1.09808 | + | 1.90192i | 0.0535806 | + | 0.0928044i | ||||
\(421\) | 2.87564i | 0.140150i | 0.997542 | + | 0.0700752i | \(0.0223239\pi\) | ||||
−0.997542 | + | 0.0700752i | \(0.977676\pi\) | |||||||
\(422\) | −15.2321 | + | 8.79423i | −0.741485 | + | 0.428096i | ||||
\(423\) | −6.40192 | + | 3.69615i | −0.311272 | + | 0.179713i | ||||
\(424\) | − | 0.464102i | − | 0.0225388i | ||||||
\(425\) | 4.09808 | + | 7.09808i | 0.198786 | + | 0.344307i | ||||
\(426\) | −2.19615 | + | 3.80385i | −0.106404 | + | 0.184297i | ||||
\(427\) | −16.0981 | − | 9.29423i | −0.779041 | − | 0.449779i | ||||
\(428\) | −17.6603 | −0.853641 | ||||||||
\(429\) | −5.70577 | + | 5.49038i | −0.275477 | + | 0.265078i | ||||
\(430\) | 2.00000 | 0.0964486 | ||||||||
\(431\) | −7.09808 | − | 4.09808i | −0.341902 | − | 0.197397i | 0.319211 | − | 0.947684i | \(-0.396582\pi\) |
−0.661113 | + | 0.750286i | \(0.729916\pi\) | |||||||
\(432\) | 2.00000 | − | 3.46410i | 0.0962250 | − | 0.166667i | ||||
\(433\) | −4.19615 | − | 7.26795i | −0.201654 | − | 0.349275i | 0.747407 | − | 0.664366i | \(-0.231298\pi\) |
−0.949062 | + | 0.315091i | \(0.897965\pi\) | |||||||
\(434\) | − | 14.1962i | − | 0.681437i | ||||||
\(435\) | 1.60770 | − | 0.928203i | 0.0770831 | − | 0.0445039i | ||||
\(436\) | 7.39230 | − | 4.26795i | 0.354027 | − | 0.204398i | ||||
\(437\) | − | 4.39230i | − | 0.210112i | ||||||
\(438\) | 4.26795 | + | 7.39230i | 0.203931 | + | 0.353218i | ||||
\(439\) | 1.70577 | − | 2.95448i | 0.0814120 | − | 0.141010i | −0.822445 | − | 0.568845i | \(-0.807390\pi\) |
0.903857 | + | 0.427835i | \(0.140724\pi\) | |||||||
\(440\) | −2.59808 | − | 1.50000i | −0.123858 | − | 0.0715097i | ||||
\(441\) | 4.92820 | 0.234676 | ||||||||
\(442\) | 7.09808 | + | 28.6865i | 0.337621 | + | 1.36448i | ||||
\(443\) | −22.3923 | −1.06389 | −0.531945 | − | 0.846779i | \(-0.678539\pi\) | ||||
−0.531945 | + | 0.846779i | \(0.678539\pi\) | |||||||
\(444\) | 0.509619 | + | 0.294229i | 0.0241854 | + | 0.0139635i | ||||
\(445\) | 3.40192 | − | 5.89230i | 0.161267 | − | 0.279322i | ||||
\(446\) | 3.23205 | + | 5.59808i | 0.153042 | + | 0.265077i | ||||
\(447\) | 4.39230i | 0.207749i | ||||||||
\(448\) | −2.59808 | + | 1.50000i | −0.122748 | + | 0.0708683i | ||||
\(449\) | 13.5000 | − | 7.79423i | 0.637104 | − | 0.367832i | −0.146394 | − | 0.989226i | \(-0.546767\pi\) |
0.783498 | + | 0.621394i | \(0.213433\pi\) | |||||||
\(450\) | 2.46410i | 0.116159i | ||||||||
\(451\) | −15.5885 | − | 27.0000i | −0.734032 | − | 1.27138i | ||||
\(452\) | 3.46410 | − | 6.00000i | 0.162938 | − | 0.282216i | ||||
\(453\) | 15.0000 | + | 8.66025i | 0.704761 | + | 0.406894i | ||||
\(454\) | −16.3923 | −0.769329 | ||||||||
\(455\) | −7.50000 | − | 7.79423i | −0.351605 | − | 0.365399i | ||||
\(456\) | −0.339746 | −0.0159101 | ||||||||
\(457\) | 15.8827 | + | 9.16987i | 0.742961 | + | 0.428949i | 0.823145 | − | 0.567832i | \(-0.192217\pi\) |
−0.0801841 | + | 0.996780i | \(0.525551\pi\) | |||||||
\(458\) | −0.633975 | + | 1.09808i | −0.0296237 | + | 0.0513097i | ||||
\(459\) | 16.3923 | + | 28.3923i | 0.765127 | + | 1.32524i | ||||
\(460\) | 9.46410i | 0.441266i | ||||||||
\(461\) | −26.4904 | + | 15.2942i | −1.23378 | + | 0.712323i | −0.967816 | − | 0.251660i | \(-0.919024\pi\) |
−0.265964 | + | 0.963983i | \(0.585690\pi\) | |||||||
\(462\) | 5.70577 | − | 3.29423i | 0.265457 | − | 0.153261i | ||||
\(463\) | 12.9282i | 0.600825i | 0.953809 | + | 0.300412i | \(0.0971243\pi\) | ||||
−0.953809 | + | 0.300412i | \(0.902876\pi\) | |||||||
\(464\) | 1.26795 | + | 2.19615i | 0.0588631 | + | 0.101954i | ||||
\(465\) | −1.73205 | + | 3.00000i | −0.0803219 | + | 0.139122i | ||||
\(466\) | −4.09808 | − | 2.36603i | −0.189840 | − | 0.109604i | ||||
\(467\) | −37.8564 | −1.75179 | −0.875893 | − | 0.482506i | \(-0.839727\pi\) | ||||
−0.875893 | + | 0.482506i | \(0.839727\pi\) | |||||||
\(468\) | −2.46410 | + | 8.53590i | −0.113903 | + | 0.394572i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −2.59808 | − | 1.50000i | −0.119840 | − | 0.0691898i | ||||
\(471\) | 4.75833 | − | 8.24167i | 0.219252 | − | 0.379756i | ||||
\(472\) | −5.19615 | − | 9.00000i | −0.239172 | − | 0.414259i | ||||
\(473\) | − | 6.00000i | − | 0.275880i | ||||||
\(474\) | −2.66025 | + | 1.53590i | −0.122190 | + | 0.0705461i | ||||
\(475\) | 0.401924 | − | 0.232051i | 0.0184415 | − | 0.0106472i | ||||
\(476\) | − | 24.5885i | − | 1.12701i | ||||||
\(477\) | 0.571797 | + | 0.990381i | 0.0261808 | + | 0.0453464i | ||||
\(478\) | 1.09808 | − | 1.90192i | 0.0502248 | − | 0.0869920i | ||||
\(479\) | −35.4904 | − | 20.4904i | −1.62160 | − | 0.936229i | −0.986493 | − | 0.163803i | \(-0.947624\pi\) |
−0.635104 | − | 0.772427i | \(-0.719043\pi\) | |||||||
\(480\) | 0.732051 | 0.0334134 | ||||||||
\(481\) | −2.78461 | − | 0.803848i | −0.126967 | − | 0.0366523i | ||||
\(482\) | 8.66025 | 0.394464 | ||||||||
\(483\) | −18.0000 | − | 10.3923i | −0.819028 | − | 0.472866i | ||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | −4.56218 | − | 7.90192i | −0.207158 | − | 0.358808i | ||||
\(486\) | 15.2679i | 0.692568i | ||||||||
\(487\) | −13.2058 | + | 7.62436i | −0.598411 | + | 0.345493i | −0.768416 | − | 0.639951i | \(-0.778955\pi\) |
0.170005 | + | 0.985443i | \(0.445621\pi\) | |||||||
\(488\) | −5.36603 | + | 3.09808i | −0.242909 | + | 0.140243i | ||||
\(489\) | − | 7.85641i | − | 0.355279i | ||||||
\(490\) | 1.00000 | + | 1.73205i | 0.0451754 | + | 0.0782461i | ||||
\(491\) | −10.3301 | + | 17.8923i | −0.466192 | + | 0.807468i | −0.999254 | − | 0.0386076i | \(-0.987708\pi\) |
0.533062 | + | 0.846076i | \(0.321041\pi\) | |||||||
\(492\) | 6.58846 | + | 3.80385i | 0.297031 | + | 0.171491i | ||||
\(493\) | −20.7846 | −0.936092 | ||||||||
\(494\) | 1.62436 | − | 0.401924i | 0.0730832 | − | 0.0180834i | ||||
\(495\) | 7.39230 | 0.332259 | ||||||||
\(496\) | −4.09808 | − | 2.36603i | −0.184009 | − | 0.106238i | ||||
\(497\) | −9.00000 | + | 15.5885i | −0.403705 | + | 0.699238i | ||||
\(498\) | −3.00000 | − | 5.19615i | −0.134433 | − | 0.232845i | ||||
\(499\) | 25.8564i | 1.15749i | 0.815508 | + | 0.578746i | \(0.196458\pi\) | ||||
−0.815508 | + | 0.578746i | \(0.803542\pi\) | |||||||
\(500\) | −0.866025 | + | 0.500000i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | −1.90192 | + | 1.09808i | −0.0849717 | + | 0.0490584i | ||||
\(502\) | 17.1962i | 0.767502i | ||||||||
\(503\) | 13.3301 | + | 23.0885i | 0.594361 | + | 1.02946i | 0.993637 | + | 0.112633i | \(0.0359283\pi\) |
−0.399276 | + | 0.916831i | \(0.630738\pi\) | |||||||
\(504\) | 3.69615 | − | 6.40192i | 0.164640 | − | 0.285164i | ||||
\(505\) | 9.29423 | + | 5.36603i | 0.413588 | + | 0.238785i | ||||
\(506\) | 28.3923 | 1.26219 | ||||||||
\(507\) | −0.366025 | + | 9.50962i | −0.0162558 | + | 0.422337i | ||||
\(508\) | −10.8038 | −0.479343 | ||||||||
\(509\) | −19.3923 | − | 11.1962i | −0.859549 | − | 0.496261i | 0.00431237 | − | 0.999991i | \(-0.498627\pi\) |
−0.863861 | + | 0.503730i | \(0.831961\pi\) | |||||||
\(510\) | −3.00000 | + | 5.19615i | −0.132842 | + | 0.230089i | ||||
\(511\) | 17.4904 | + | 30.2942i | 0.773729 | + | 1.34014i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.60770 | − | 0.928203i | 0.0709815 | − | 0.0409812i | ||||
\(514\) | −12.0000 | + | 6.92820i | −0.529297 | + | 0.305590i | ||||
\(515\) | 9.19615i | 0.405231i | ||||||||
\(516\) | 0.732051 | + | 1.26795i | 0.0322267 | + | 0.0558184i | ||||
\(517\) | −4.50000 | + | 7.79423i | −0.197910 | + | 0.342790i | ||||
\(518\) | 2.08846 | + | 1.20577i | 0.0917615 | + | 0.0529786i | ||||
\(519\) | −10.9808 | −0.482002 | ||||||||
\(520\) | −3.50000 | + | 0.866025i | −0.153485 | + | 0.0379777i | ||||
\(521\) | 6.46410 | 0.283197 | 0.141599 | − | 0.989924i | \(-0.454776\pi\) | ||||
0.141599 | + | 0.989924i | \(0.454776\pi\) | |||||||
\(522\) | −5.41154 | − | 3.12436i | −0.236857 | − | 0.136749i | ||||
\(523\) | 1.19615 | − | 2.07180i | 0.0523041 | − | 0.0905933i | −0.838688 | − | 0.544612i | \(-0.816677\pi\) |
0.890992 | + | 0.454019i | \(0.150010\pi\) | |||||||
\(524\) | 3.06218 | + | 5.30385i | 0.133772 | + | 0.231700i | ||||
\(525\) | − | 2.19615i | − | 0.0958479i | ||||||
\(526\) | 3.10770 | − | 1.79423i | 0.135502 | − | 0.0782321i | ||||
\(527\) | 33.5885 | − | 19.3923i | 1.46314 | − | 0.844742i | ||||
\(528\) | − | 2.19615i | − | 0.0955753i | ||||||
\(529\) | −33.2846 | − | 57.6506i | −1.44716 | − | 2.50655i | ||||
\(530\) | −0.232051 | + | 0.401924i | −0.0100796 | + | 0.0174585i | ||||
\(531\) | 22.1769 | + | 12.8038i | 0.962396 | + | 0.555640i | ||||
\(532\) | −1.39230 | −0.0603641 | ||||||||
\(533\) | −36.0000 | − | 10.3923i | −1.55933 | − | 0.450141i | ||||
\(534\) | 4.98076 | 0.215539 | ||||||||
\(535\) | 15.2942 | + | 8.83013i | 0.661227 | + | 0.381760i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.46410 | + | 6.00000i | 0.149487 | + | 0.258919i | ||||
\(538\) | − | 27.1244i | − | 1.16941i | ||||||
\(539\) | 5.19615 | − | 3.00000i | 0.223814 | − | 0.129219i | ||||
\(540\) | −3.46410 | + | 2.00000i | −0.149071 | + | 0.0860663i | ||||
\(541\) | 22.0526i | 0.948114i | 0.880494 | + | 0.474057i | \(0.157211\pi\) | ||||
−0.880494 | + | 0.474057i | \(0.842789\pi\) | |||||||
\(542\) | −4.73205 | − | 8.19615i | −0.203259 | − | 0.352055i | ||||
\(543\) | −5.33975 | + | 9.24871i | −0.229150 | + | 0.396900i | ||||
\(544\) | −7.09808 | − | 4.09808i | −0.304328 | − | 0.175704i | ||||
\(545\) | −8.53590 | −0.365638 | ||||||||
\(546\) | 2.19615 | − | 7.60770i | 0.0939866 | − | 0.325579i | ||||
\(547\) | −6.78461 | −0.290089 | −0.145044 | − | 0.989425i | \(-0.546333\pi\) | ||||
−0.145044 | + | 0.989425i | \(0.546333\pi\) | |||||||
\(548\) | 1.90192 | + | 1.09808i | 0.0812462 | + | 0.0469075i | ||||
\(549\) | 7.63397 | − | 13.2224i | 0.325810 | − | 0.564320i | ||||
\(550\) | 1.50000 | + | 2.59808i | 0.0639602 | + | 0.110782i | ||||
\(551\) | 1.17691i | 0.0501382i | ||||||||
\(552\) | −6.00000 | + | 3.46410i | −0.255377 | + | 0.147442i | ||||
\(553\) | −10.9019 | + | 6.29423i | −0.463597 | + | 0.267658i | ||||
\(554\) | − | 1.00000i | − | 0.0424859i | ||||||
\(555\) | −0.294229 | − | 0.509619i | −0.0124893 | − | 0.0216321i | ||||
\(556\) | 0.598076 | − | 1.03590i | 0.0253641 | − | 0.0439319i | ||||
\(557\) | −5.89230 | − | 3.40192i | −0.249665 | − | 0.144144i | 0.369946 | − | 0.929053i | \(-0.379376\pi\) |
−0.619611 | + | 0.784909i | \(0.712710\pi\) | |||||||
\(558\) | 11.6603 | 0.493618 | ||||||||
\(559\) | −5.00000 | − | 5.19615i | −0.211477 | − | 0.219774i | ||||
\(560\) | 3.00000 | 0.126773 | ||||||||
\(561\) | 15.5885 | + | 9.00000i | 0.658145 | + | 0.379980i | ||||
\(562\) | −5.19615 | + | 9.00000i | −0.219186 | + | 0.379642i | ||||
\(563\) | −7.26795 | − | 12.5885i | −0.306308 | − | 0.530540i | 0.671244 | − | 0.741236i | \(-0.265760\pi\) |
−0.977552 | + | 0.210696i | \(0.932427\pi\) | |||||||
\(564\) | − | 2.19615i | − | 0.0924747i | ||||||
\(565\) | −6.00000 | + | 3.46410i | −0.252422 | + | 0.145736i | ||||
\(566\) | −8.32051 | + | 4.80385i | −0.349737 | + | 0.201921i | ||||
\(567\) | 13.3923i | 0.562424i | ||||||||
\(568\) | 3.00000 | + | 5.19615i | 0.125877 | + | 0.218026i | ||||
\(569\) | 13.6244 | − | 23.5981i | 0.571163 | − | 0.989283i | −0.425284 | − | 0.905060i | \(-0.639826\pi\) |
0.996447 | − | 0.0842230i | \(-0.0268408\pi\) | |||||||
\(570\) | 0.294229 | + | 0.169873i | 0.0123239 | + | 0.00711520i | ||||
\(571\) | −38.3731 | −1.60586 | −0.802931 | − | 0.596071i | \(-0.796728\pi\) | ||||
−0.802931 | + | 0.596071i | \(0.796728\pi\) | |||||||
\(572\) | 2.59808 | + | 10.5000i | 0.108631 | + | 0.439027i | ||||
\(573\) | −16.6410 | −0.695188 | ||||||||
\(574\) | 27.0000 | + | 15.5885i | 1.12696 | + | 0.650650i | ||||
\(575\) | 4.73205 | − | 8.19615i | 0.197340 | − | 0.341803i | ||||
\(576\) | −1.23205 | − | 2.13397i | −0.0513355 | − | 0.0889156i | ||||
\(577\) | − | 26.4449i | − | 1.10091i | −0.834863 | − | 0.550457i | \(-0.814453\pi\) | ||
0.834863 | − | 0.550457i | \(-0.185547\pi\) | |||||||
\(578\) | 43.4545 | − | 25.0885i | 1.80747 | − | 1.04354i | ||||
\(579\) | 10.3923 | − | 6.00000i | 0.431889 | − | 0.249351i | ||||
\(580\) | − | 2.53590i | − | 0.105297i | ||||||
\(581\) | −12.2942 | − | 21.2942i | −0.510051 | − | 0.883433i | ||||
\(582\) | 3.33975 | − | 5.78461i | 0.138437 | − | 0.239780i | ||||
\(583\) | 1.20577 | + | 0.696152i | 0.0499379 | + | 0.0288317i | ||||
\(584\) | 11.6603 | 0.482505 | ||||||||
\(585\) | 6.40192 | − | 6.16025i | 0.264687 | − | 0.254695i | ||||
\(586\) | −11.1962 | −0.462509 | ||||||||
\(587\) | 25.9808 | + | 15.0000i | 1.07234 | + | 0.619116i | 0.928820 | − | 0.370531i | \(-0.120824\pi\) |
0.143521 | + | 0.989647i | \(0.454158\pi\) | |||||||
\(588\) | −0.732051 | + | 1.26795i | −0.0301893 | + | 0.0522893i | ||||
\(589\) | −1.09808 | − | 1.90192i | −0.0452454 | − | 0.0783674i | ||||
\(590\) | 10.3923i | 0.427844i | ||||||||
\(591\) | −13.6865 | + | 7.90192i | −0.562989 | + | 0.325042i | ||||
\(592\) | 0.696152 | − | 0.401924i | 0.0286117 | − | 0.0165190i | ||||
\(593\) | − | 20.7846i | − | 0.853522i | −0.904365 | − | 0.426761i | \(-0.859655\pi\) | ||
0.904365 | − | 0.426761i | \(-0.140345\pi\) | |||||||
\(594\) | 6.00000 | + | 10.3923i | 0.246183 | + | 0.426401i | ||||
\(595\) | −12.2942 | + | 21.2942i | −0.504014 | + | 0.872978i | ||||
\(596\) | 5.19615 | + | 3.00000i | 0.212843 | + | 0.122885i | ||||
\(597\) | −4.67949 | −0.191519 | ||||||||
\(598\) | 24.5885 | − | 23.6603i | 1.00550 | − | 0.967540i | ||||
\(599\) | −19.8564 | −0.811311 | −0.405655 | − | 0.914026i | \(-0.632957\pi\) | ||||
−0.405655 | + | 0.914026i | \(0.632957\pi\) | |||||||
\(600\) | −0.633975 | − | 0.366025i | −0.0258819 | − | 0.0149429i | ||||
\(601\) | 18.8923 | − | 32.7224i | 0.770633 | − | 1.33478i | −0.166583 | − | 0.986027i | \(-0.553273\pi\) |
0.937216 | − | 0.348748i | \(-0.113393\pi\) | |||||||
\(602\) | 3.00000 | + | 5.19615i | 0.122271 | + | 0.211779i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 20.4904 | − | 11.8301i | 0.833742 | − | 0.481361i | ||||
\(605\) | −1.73205 | + | 1.00000i | −0.0704179 | + | 0.0406558i | ||||
\(606\) | 7.85641i | 0.319145i | ||||||||
\(607\) | 18.7942 | + | 32.5526i | 0.762834 | + | 1.32127i | 0.941384 | + | 0.337337i | \(0.109526\pi\) |
−0.178550 | + | 0.983931i | \(0.557141\pi\) | |||||||
\(608\) | −0.232051 | + | 0.401924i | −0.00941090 | + | 0.0163002i | ||||
\(609\) | 4.82309 | + | 2.78461i | 0.195441 | + | 0.112838i | ||||
\(610\) | 6.19615 | 0.250875 | ||||||||
\(611\) | 2.59808 | + | 10.5000i | 0.105107 | + | 0.424785i | ||||
\(612\) | 20.1962 | 0.816381 | ||||||||
\(613\) | 33.6962 | + | 19.4545i | 1.36097 | + | 0.785759i | 0.989754 | − | 0.142785i | \(-0.0456059\pi\) |
0.371221 | + | 0.928545i | \(0.378939\pi\) | |||||||
\(614\) | −13.7321 | + | 23.7846i | −0.554180 | + | 0.959869i | ||||
\(615\) | −3.80385 | − | 6.58846i | −0.153386 | − | 0.265672i | ||||
\(616\) | − | 9.00000i | − | 0.362620i | ||||||
\(617\) | 15.5885 | − | 9.00000i | 0.627568 | − | 0.362326i | −0.152242 | − | 0.988343i | \(-0.548649\pi\) |
0.779809 | + | 0.626017i | \(0.215316\pi\) | |||||||
\(618\) | −5.83013 | + | 3.36603i | −0.234522 | + | 0.135401i | ||||
\(619\) | − | 31.3923i | − | 1.26176i | −0.775879 | − | 0.630882i | \(-0.782693\pi\) | ||
0.775879 | − | 0.630882i | \(-0.217307\pi\) | |||||||
\(620\) | 2.36603 | + | 4.09808i | 0.0950219 | + | 0.164583i | ||||
\(621\) | 18.9282 | − | 32.7846i | 0.759563 | − | 1.31560i | ||||
\(622\) | 7.90192 | + | 4.56218i | 0.316838 | + | 0.182927i | ||||
\(623\) | 20.4115 | 0.817771 | ||||||||
\(624\) | −1.83013 | − | 1.90192i | −0.0732637 | − | 0.0761379i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −22.8564 | − | 13.1962i | −0.913526 | − | 0.527424i | ||||
\(627\) | 0.509619 | − | 0.882686i | 0.0203522 | − | 0.0352511i | ||||
\(628\) | −6.50000 | − | 11.2583i | −0.259378 | − | 0.449256i | ||||
\(629\) | 6.58846i | 0.262699i | ||||||||
\(630\) | −6.40192 | + | 3.69615i | −0.255059 | + | 0.147258i | ||||
\(631\) | −18.0000 | + | 10.3923i | −0.716569 | + | 0.413711i | −0.813488 | − | 0.581581i | \(-0.802434\pi\) |
0.0969198 | + | 0.995292i | \(0.469101\pi\) | |||||||
\(632\) | 4.19615i | 0.166914i | ||||||||
\(633\) | 6.43782 | + | 11.1506i | 0.255880 | + | 0.443198i | ||||
\(634\) | −11.5981 | + | 20.0885i | −0.460618 | + | 0.797815i | ||||
\(635\) | 9.35641 | + | 5.40192i | 0.371298 | + | 0.214369i | ||||
\(636\) | −0.339746 | −0.0134718 | ||||||||
\(637\) | 2.00000 | − | 6.92820i | 0.0792429 | − | 0.274505i | ||||
\(638\) | −7.60770 | −0.301192 | ||||||||
\(639\) | −12.8038 | − | 7.39230i | −0.506512 | − | 0.292435i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −16.0359 | − | 27.7750i | −0.633380 | − | 1.09705i | −0.986856 | − | 0.161603i | \(-0.948334\pi\) |
0.353476 | − | 0.935444i | \(-0.385000\pi\) | |||||||
\(642\) | 12.9282i | 0.510235i | ||||||||
\(643\) | −9.29423 | + | 5.36603i | −0.366529 | + | 0.211615i | −0.671941 | − | 0.740605i | \(-0.734539\pi\) |
0.305412 | + | 0.952220i | \(0.401206\pi\) | |||||||
\(644\) | −24.5885 | + | 14.1962i | −0.968921 | + | 0.559407i | ||||
\(645\) | − | 1.46410i | − | 0.0576489i | ||||||
\(646\) | −1.90192 | − | 3.29423i | −0.0748302 | − | 0.129610i | ||||
\(647\) | 0.401924 | − | 0.696152i | 0.0158013 | − | 0.0273686i | −0.858017 | − | 0.513622i | \(-0.828303\pi\) |
0.873818 | + | 0.486253i | \(0.161637\pi\) | |||||||
\(648\) | 3.86603 | + | 2.23205i | 0.151872 | + | 0.0876832i | ||||
\(649\) | 31.1769 | 1.22380 | ||||||||
\(650\) | 3.46410 | + | 1.00000i | 0.135873 | + | 0.0392232i | ||||
\(651\) | −10.3923 | −0.407307 | ||||||||
\(652\) | −9.29423 | − | 5.36603i | −0.363990 | − | 0.210150i | ||||
\(653\) | −0.696152 | + | 1.20577i | −0.0272425 | + | 0.0471855i | −0.879325 | − | 0.476222i | \(-0.842006\pi\) |
0.852083 | + | 0.523407i | \(0.175339\pi\) | |||||||
\(654\) | −3.12436 | − | 5.41154i | −0.122172 | − | 0.211608i | ||||
\(655\) | − | 6.12436i | − | 0.239298i | ||||||
\(656\) | 9.00000 | − | 5.19615i | 0.351391 | − | 0.202876i | ||||
\(657\) | −24.8827 | + | 14.3660i | −0.970766 | + | 0.560472i | ||||
\(658\) | − | 9.00000i | − | 0.350857i | ||||||
\(659\) | 2.66025 | + | 4.60770i | 0.103629 | + | 0.179490i | 0.913177 | − | 0.407563i | \(-0.133621\pi\) |
−0.809548 | + | 0.587053i | \(0.800288\pi\) | |||||||
\(660\) | −1.09808 | + | 1.90192i | −0.0427426 | + | 0.0740323i | ||||
\(661\) | 31.0981 | + | 17.9545i | 1.20957 | + | 0.698348i | 0.962666 | − | 0.270690i | \(-0.0872520\pi\) |
0.246909 | + | 0.969039i | \(0.420585\pi\) | |||||||
\(662\) | −12.9282 | −0.502469 | ||||||||
\(663\) | 21.0000 | − | 5.19615i | 0.815572 | − | 0.201802i | ||||
\(664\) | −8.19615 | −0.318072 | ||||||||
\(665\) | 1.20577 | + | 0.696152i | 0.0467578 | + | 0.0269956i | ||||
\(666\) | −0.990381 | + | 1.71539i | −0.0383765 | + | 0.0664700i | ||||
\(667\) | 12.0000 | + | 20.7846i | 0.464642 | + | 0.804783i | ||||
\(668\) | 3.00000i | 0.116073i | ||||||||
\(669\) | 4.09808 | − | 2.36603i | 0.158441 | − | 0.0914758i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 18.5885i | − | 0.717599i | ||||||
\(672\) | 1.09808 | + | 1.90192i | 0.0423592 | + | 0.0733683i | ||||
\(673\) | −12.1962 | + | 21.1244i | −0.470127 | + | 0.814284i | −0.999416 | − | 0.0341573i | \(-0.989125\pi\) |
0.529289 | + | 0.848441i | \(0.322459\pi\) | |||||||
\(674\) | −5.36603 | − | 3.09808i | −0.206692 | − | 0.119333i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 11.0000 | + | 6.92820i | 0.423077 | + | 0.266469i | ||||
\(677\) | −25.8564 | −0.993742 | −0.496871 | − | 0.867824i | \(-0.665518\pi\) | ||||
−0.496871 | + | 0.867824i | \(0.665518\pi\) | |||||||
\(678\) | −4.39230 | − | 2.53590i | −0.168685 | − | 0.0973906i | ||||
\(679\) | 13.6865 | − | 23.7058i | 0.525241 | − | 0.909744i | ||||
\(680\) | 4.09808 | + | 7.09808i | 0.157154 | + | 0.272199i | ||||
\(681\) | 12.0000i | 0.459841i | ||||||||
\(682\) | 12.2942 | − | 7.09808i | 0.470770 | − | 0.271799i | ||||
\(683\) | 27.0000 | − | 15.5885i | 1.03313 | − | 0.596476i | 0.115248 | − | 0.993337i | \(-0.463234\pi\) |
0.917879 | + | 0.396861i | \(0.129901\pi\) | |||||||
\(684\) | − | 1.14359i | − | 0.0437264i | ||||||
\(685\) | −1.09808 | − | 1.90192i | −0.0419553 | − | 0.0726688i | ||||
\(686\) | 7.50000 | − | 12.9904i | 0.286351 | − | 0.495975i | ||||
\(687\) | 0.803848 | + | 0.464102i | 0.0306687 | + | 0.0177066i | ||||
\(688\) | 2.00000 | 0.0762493 | ||||||||
\(689\) | 1.62436 | − | 0.401924i | 0.0618830 | − | 0.0153121i | ||||
\(690\) | 6.92820 | 0.263752 | ||||||||
\(691\) | −31.7942 | − | 18.3564i | −1.20951 | − | 0.698311i | −0.246857 | − | 0.969052i | \(-0.579398\pi\) |
−0.962652 | + | 0.270741i | \(0.912731\pi\) | |||||||
\(692\) | −7.50000 | + | 12.9904i | −0.285107 | + | 0.493820i | ||||
\(693\) | 11.0885 | + | 19.2058i | 0.421216 | + | 0.729567i | ||||
\(694\) | − | 28.7321i | − | 1.09065i | ||||||
\(695\) | −1.03590 | + | 0.598076i | −0.0392939 | + | 0.0226863i | ||||
\(696\) | 1.60770 | − | 0.928203i | 0.0609395 | − | 0.0351835i | ||||
\(697\) | 85.1769i | 3.22631i | ||||||||
\(698\) | 2.02628 | + | 3.50962i | 0.0766958 | + | 0.132841i | ||||
\(699\) | −1.73205 | + | 3.00000i | −0.0655122 | + | 0.113470i | ||||
\(700\) | −2.59808 | − | 1.50000i | −0.0981981 | − | 0.0566947i | ||||
\(701\) | 35.9090 | 1.35626 | 0.678131 | − | 0.734941i | \(-0.262790\pi\) | ||||
0.678131 | + | 0.734941i | \(0.262790\pi\) | |||||||
\(702\) | 13.8564 | + | 4.00000i | 0.522976 | + | 0.150970i | ||||
\(703\) | 0.373067 | 0.0140705 | ||||||||
\(704\) | −2.59808 | − | 1.50000i | −0.0979187 | − | 0.0565334i | ||||
\(705\) | −1.09808 | + | 1.90192i | −0.0413559 | + | 0.0716306i | ||||
\(706\) | −4.90192 | − | 8.49038i | −0.184486 | − | 0.319540i | ||||
\(707\) | 32.1962i | 1.21086i | ||||||||
\(708\) | −6.58846 | + | 3.80385i | −0.247609 | + | 0.142957i | ||||
\(709\) | 9.50962 | − | 5.49038i | 0.357141 | − | 0.206196i | −0.310685 | − | 0.950513i | \(-0.600558\pi\) |
0.667826 | + | 0.744317i | \(0.267225\pi\) | |||||||
\(710\) | − | 6.00000i | − | 0.225176i | ||||||
\(711\) | −5.16987 | − | 8.95448i | −0.193885 | − | 0.335819i | ||||
\(712\) | 3.40192 | − | 5.89230i | 0.127492 | − | 0.220823i | ||||
\(713\) | −38.7846 | − | 22.3923i | −1.45250 | − | 0.838598i | ||||
\(714\) | −18.0000 | −0.673633 | ||||||||
\(715\) | 3.00000 | − | 10.3923i | 0.112194 | − | 0.388650i | ||||
\(716\) | 9.46410 | 0.353690 | ||||||||
\(717\) | −1.39230 | − | 0.803848i | −0.0519966 | − | 0.0300202i | ||||
\(718\) | 0.803848 | − | 1.39230i | 0.0299993 | − | 0.0519604i | ||||
\(719\) | −12.9282 | − | 22.3923i | −0.482141 | − | 0.835092i | 0.517649 | − | 0.855593i | \(-0.326807\pi\) |
−0.999790 | + | 0.0205009i | \(0.993474\pi\) | |||||||
\(720\) | 2.46410i | 0.0918316i | ||||||||
\(721\) | −23.8923 | + | 13.7942i | −0.889796 | + | 0.513724i | ||||
\(722\) | 16.2679 | − | 9.39230i | 0.605430 | − | 0.349545i | ||||
\(723\) | − | 6.33975i | − | 0.235778i | ||||||
\(724\) | 7.29423 | + | 12.6340i | 0.271088 | + | 0.469538i | ||||
\(725\) | −1.26795 | + | 2.19615i | −0.0470905 | + | 0.0815631i | ||||
\(726\) | −1.26795 | − | 0.732051i | −0.0470580 | − | 0.0271690i | ||||
\(727\) | 34.3731 | 1.27483 | 0.637413 | − | 0.770522i | \(-0.280004\pi\) | ||||
0.637413 | + | 0.770522i | \(0.280004\pi\) | |||||||
\(728\) | −7.50000 | − | 7.79423i | −0.277968 | − | 0.288873i | ||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | −10.0981 | − | 5.83013i | −0.373747 | − | 0.215783i | ||||
\(731\) | −8.19615 | + | 14.1962i | −0.303146 | + | 0.525064i | ||||
\(732\) | 2.26795 | + | 3.92820i | 0.0838258 | + | 0.145191i | ||||
\(733\) | 14.9090i | 0.550675i | 0.961348 | + | 0.275338i | \(0.0887896\pi\) | ||||
−0.961348 | + | 0.275338i | \(0.911210\pi\) | |||||||
\(734\) | −4.85641 | + | 2.80385i | −0.179253 | + | 0.103492i | ||||
\(735\) | 1.26795 | − | 0.732051i | 0.0467690 | − | 0.0270021i | ||||
\(736\) | 9.46410i | 0.348851i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −12.8038 | + | 22.1769i | −0.471316 | + | 0.816344i | ||||
\(739\) | 28.2058 | + | 16.2846i | 1.03757 | + | 0.599039i | 0.919143 | − | 0.393924i | \(-0.128883\pi\) |
0.118423 | + | 0.992963i | \(0.462216\pi\) | |||||||
\(740\) | −0.803848 | −0.0295500 | ||||||||
\(741\) | −0.294229 | − | 1.18911i | −0.0108088 | − | 0.0436831i | ||||
\(742\) | −1.39230 | −0.0511131 | ||||||||
\(743\) | −11.7846 | − | 6.80385i | −0.432335 | − | 0.249609i | 0.268006 | − | 0.963417i | \(-0.413635\pi\) |
−0.700341 | + | 0.713808i | \(0.746969\pi\) | |||||||
\(744\) | −1.73205 | + | 3.00000i | −0.0635001 | + | 0.109985i | ||||
\(745\) | −3.00000 | − | 5.19615i | −0.109911 | − | 0.190372i | ||||
\(746\) | − | 0.392305i | − | 0.0143633i | ||||||
\(747\) | 17.4904 | − | 10.0981i | 0.639940 | − | 0.369469i | ||||
\(748\) | 21.2942 | − | 12.2942i | 0.778594 | − | 0.449522i | ||||
\(749\) | 52.9808i | 1.93587i | ||||||||
\(750\) | 0.366025 | + | 0.633975i | 0.0133654 | + | 0.0231495i | ||||
\(751\) | 10.1962 | − | 17.6603i | 0.372063 | − | 0.644432i | −0.617820 | − | 0.786320i | \(-0.711984\pi\) |
0.989883 | + | 0.141888i | \(0.0453172\pi\) | |||||||
\(752\) | −2.59808 | − | 1.50000i | −0.0947421 | − | 0.0546994i | ||||
\(753\) | 12.5885 | 0.458749 | ||||||||
\(754\) | −6.58846 | + | 6.33975i | −0.239937 | + | 0.230880i | ||||
\(755\) | −23.6603 | −0.861085 | ||||||||
\(756\) | −10.3923 | − | 6.00000i | −0.377964 | − | 0.218218i | ||||
\(757\) | 18.8923 | − | 32.7224i | 0.686652 | − | 1.18932i | −0.286262 | − | 0.958151i | \(-0.592413\pi\) |
0.972914 | − | 0.231166i | \(-0.0742539\pi\) | |||||||
\(758\) | −14.8923 | − | 25.7942i | −0.540913 | − | 0.936889i | ||||
\(759\) | − | 20.7846i | − | 0.754434i | ||||||
\(760\) | 0.401924 | − | 0.232051i | 0.0145793 | − | 0.00841737i | ||||
\(761\) | 16.2846 | − | 9.40192i | 0.590317 | − | 0.340819i | −0.174906 | − | 0.984585i | \(-0.555962\pi\) |
0.765223 | + | 0.643766i | \(0.222629\pi\) | |||||||
\(762\) | 7.90897i | 0.286512i | ||||||||
\(763\) | −12.8038 | − | 22.1769i | −0.463530 | − | 0.802858i | ||||
\(764\) | −11.3660 | + | 19.6865i | −0.411208 | + | 0.712234i | ||||
\(765\) | −17.4904 | − | 10.0981i | −0.632366 | − | 0.365097i | ||||
\(766\) | −22.3923 | −0.809067 | ||||||||
\(767\) | 27.0000 | − | 25.9808i | 0.974913 | − | 0.938111i | ||||
\(768\) | 0.732051 | 0.0264156 | ||||||||
\(769\) | −33.0000 | − | 19.0526i | −1.19001 | − | 0.687053i | −0.231701 | − | 0.972787i | \(-0.574429\pi\) |
−0.958309 | + | 0.285734i | \(0.907763\pi\) | |||||||
\(770\) | −4.50000 | + | 7.79423i | −0.162169 | + | 0.280885i | ||||
\(771\) | 5.07180 | + | 8.78461i | 0.182656 | + | 0.316370i | ||||
\(772\) | − | 16.3923i | − | 0.589972i | ||||||
\(773\) | 2.08846 | − | 1.20577i | 0.0751166 | − | 0.0433686i | −0.461971 | − | 0.886895i | \(-0.652858\pi\) |
0.537088 | + | 0.843526i | \(0.319524\pi\) | |||||||
\(774\) | −4.26795 | + | 2.46410i | −0.153408 | + | 0.0885703i | ||||
\(775\) | − | 4.73205i | − | 0.169980i | ||||||
\(776\) | −4.56218 | − | 7.90192i | −0.163773 | − | 0.283663i | ||||
\(777\) | 0.882686 | − | 1.52886i | 0.0316662 | − | 0.0548474i | ||||
\(778\) | −19.6865 | − | 11.3660i | −0.705796 | − | 0.407492i | ||||
\(779\) | 4.82309 | 0.172805 | ||||||||
\(780\) | 0.633975 | + | 2.56218i | 0.0226999 | + | 0.0917407i | ||||
\(781\) | −18.0000 | −0.644091 | ||||||||
\(782\) | −67.1769 | − | 38.7846i | −2.40224 | − | 1.38693i | ||||
\(783\) | −5.07180 | + | 8.78461i | −0.181251 | + | 0.313936i | ||||
\(784\) | 1.00000 | + | 1.73205i | 0.0357143 | + | 0.0618590i | ||||
\(785\) | 13.0000i | 0.463990i | ||||||||
\(786\) | 3.88269 | − | 2.24167i | 0.138491 | − | 0.0799577i | ||||
\(787\) | −37.0981 | + | 21.4186i | −1.32240 | + | 0.763490i | −0.984112 | − | 0.177551i | \(-0.943182\pi\) |
−0.338292 | + | 0.941041i | \(0.609849\pi\) | |||||||
\(788\) | 21.5885i | 0.769057i | ||||||||
\(789\) | −1.31347 | − | 2.27499i | −0.0467606 | − | 0.0809918i | ||||
\(790\) | 2.09808 | − | 3.63397i | 0.0746462 | − | 0.129291i | ||||
\(791\) | −18.0000 | − | 10.3923i | −0.640006 | − | 0.369508i | ||||
\(792\) | 7.39230 | 0.262674 | ||||||||
\(793\) | −15.4904 | − | 16.0981i | −0.550080 | − | 0.571659i | ||||
\(794\) | 11.1962 | 0.397337 | ||||||||
\(795\) | 0.294229 | + | 0.169873i | 0.0104352 | + | 0.00602477i | ||||
\(796\) | −3.19615 | + | 5.53590i | −0.113285 | + | 0.196215i | ||||
\(797\) | 6.46410 | + | 11.1962i | 0.228970 | + | 0.396588i | 0.957503 | − | 0.288423i | \(-0.0931308\pi\) |
−0.728533 | + | 0.685011i | \(0.759797\pi\) | |||||||
\(798\) | 1.01924i | 0.0360806i | ||||||||
\(799\) | 21.2942 | − | 12.2942i | 0.753336 | − | 0.434939i | ||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 16.7654i | 0.592375i | ||||||||
\(802\) | 2.59808 | + | 4.50000i | 0.0917413 | + | 0.158901i | ||||
\(803\) | −17.4904 | + | 30.2942i | −0.617222 | + | 1.06906i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 28.3923 | 1.00070 | ||||||||
\(806\) | 4.73205 | − | 16.3923i | 0.166679 | − | 0.577394i | ||||
\(807\) | −19.8564 | −0.698979 | ||||||||
\(808\) | 9.29423 | + | 5.36603i | 0.326970 | + | 0.188776i | ||||
\(809\) | −12.0000 | + | 20.7846i | −0.421898 | + | 0.730748i | −0.996125 | − | 0.0879478i | \(-0.971969\pi\) |
0.574228 | + | 0.818696i | \(0.305302\pi\) | |||||||
\(810\) | −2.23205 | − | 3.86603i | −0.0784263 | − | 0.135838i | ||||
\(811\) | 43.3923i | 1.52371i | 0.647748 | + | 0.761855i | \(0.275711\pi\) | ||||
−0.647748 | + | 0.761855i | \(0.724289\pi\) | |||||||
\(812\) | 6.58846 | − | 3.80385i | 0.231210 | − | 0.133489i | ||||
\(813\) | −6.00000 | + | 3.46410i | −0.210429 | + | 0.121491i | ||||
\(814\) | 2.41154i | 0.0845245i | ||||||||
\(815\) | 5.36603 | + | 9.29423i | 0.187964 | + | 0.325563i | ||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 0.803848 | + | 0.464102i | 0.0281231 | + | 0.0162369i | ||||
\(818\) | 16.2679 | 0.568796 | ||||||||
\(819\) | 25.6077 | + | 7.39230i | 0.894805 | + | 0.258308i | ||||
\(820\) | −10.3923 | −0.362915 | ||||||||
\(821\) | 17.4904 | + | 10.0981i | 0.610419 | + | 0.352425i | 0.773129 | − | 0.634249i | \(-0.218690\pi\) |
−0.162711 | + | 0.986674i | \(0.552024\pi\) | |||||||
\(822\) | 0.803848 | − | 1.39230i | 0.0280374 | − | 0.0485622i | ||||
\(823\) | 13.5981 | + | 23.5526i | 0.473999 | + | 0.820991i | 0.999557 | − | 0.0297674i | \(-0.00947664\pi\) |
−0.525558 | + | 0.850758i | \(0.676143\pi\) | |||||||
\(824\) | 9.19615i | 0.320363i | ||||||||
\(825\) | 1.90192 | − | 1.09808i | 0.0662165 | − | 0.0382301i | ||||
\(826\) | −27.0000 | + | 15.5885i | −0.939450 | + | 0.542392i | ||||
\(827\) | − | 42.5885i | − | 1.48095i | −0.672086 | − | 0.740473i | \(-0.734602\pi\) | ||
0.672086 | − | 0.740473i | \(-0.265398\pi\) | |||||||
\(828\) | −11.6603 | − | 20.1962i | −0.405222 | − | 0.701865i | ||||
\(829\) | 10.0000 | − | 17.3205i | 0.347314 | − | 0.601566i | −0.638457 | − | 0.769657i | \(-0.720427\pi\) |
0.985771 | + | 0.168091i | \(0.0537604\pi\) | |||||||
\(830\) | 7.09808 | + | 4.09808i | 0.246378 | + | 0.142246i | ||||
\(831\) | −0.732051 | −0.0253946 | ||||||||
\(832\) | −3.50000 | + | 0.866025i | −0.121341 | + | 0.0300240i | ||||
\(833\) | −16.3923 | −0.567960 | ||||||||
\(834\) | −0.758330 | − | 0.437822i | −0.0262588 | − | 0.0151605i | ||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | −0.696152 | − | 1.20577i | −0.0240769 | − | 0.0417025i | ||||
\(837\) | − | 18.9282i | − | 0.654254i | ||||||
\(838\) | −15.0000 | + | 8.66025i | −0.518166 | + | 0.299164i | ||||
\(839\) | 18.8827 | − | 10.9019i | 0.651903 | − | 0.376376i | −0.137282 | − | 0.990532i | \(-0.543837\pi\) |
0.789185 | + | 0.614156i | \(0.210503\pi\) | |||||||
\(840\) | − | 2.19615i | − | 0.0757745i | ||||||
\(841\) | 11.2846 | + | 19.5455i | 0.389124 | + | 0.673983i | ||||
\(842\) | 1.43782 | − | 2.49038i | 0.0495506 | − | 0.0858242i | ||||
\(843\) | 6.58846 | + | 3.80385i | 0.226919 | + | 0.131011i | ||||
\(844\) | 17.5885 | 0.605420 | ||||||||
\(845\) | −6.06218 | − | 11.5000i | −0.208545 | − | 0.395612i | ||||
\(846\) | 7.39230 | 0.254153 | ||||||||
\(847\) | −5.19615 | − | 3.00000i | −0.178542 | − | 0.103081i | ||||
\(848\) | −0.232051 | + | 0.401924i | −0.00796866 | + | 0.0138021i | ||||
\(849\) | 3.51666 | + | 6.09103i | 0.120691 | + | 0.209044i | ||||
\(850\) | − | 8.19615i | − | 0.281126i | ||||||
\(851\) | 6.58846 | − | 3.80385i | 0.225849 | − | 0.130394i | ||||
\(852\) | 3.80385 | − | 2.19615i | 0.130318 | − | 0.0752389i | ||||
\(853\) | 13.8564i | 0.474434i | 0.971457 | + | 0.237217i | \(0.0762353\pi\) | ||||
−0.971457 | + | 0.237217i | \(0.923765\pi\) | |||||||
\(854\) | 9.29423 | + | 16.0981i | 0.318042 | + | 0.550865i | ||||
\(855\) | −0.571797 | + | 0.990381i | −0.0195550 | + | 0.0338703i | ||||
\(856\) | 15.2942 | + | 8.83013i | 0.522746 | + | 0.301808i | ||||
\(857\) | −16.7321 | −0.571556 | −0.285778 | − | 0.958296i | \(-0.592252\pi\) | ||||
−0.285778 | + | 0.958296i | \(0.592252\pi\) | |||||||
\(858\) | 7.68653 | − | 1.90192i | 0.262414 | − | 0.0649306i | ||||
\(859\) | −20.3731 | −0.695120 | −0.347560 | − | 0.937658i | \(-0.612990\pi\) | ||||
−0.347560 | + | 0.937658i | \(0.612990\pi\) | |||||||
\(860\) | −1.73205 | − | 1.00000i | −0.0590624 | − | 0.0340997i | ||||
\(861\) | 11.4115 | − | 19.7654i | 0.388904 | − | 0.673602i | ||||
\(862\) | 4.09808 | + | 7.09808i | 0.139581 | + | 0.241761i | ||||
\(863\) | 43.1769i | 1.46976i | 0.678198 | + | 0.734880i | \(0.262761\pi\) | ||||
−0.678198 | + | 0.734880i | \(0.737239\pi\) | |||||||
\(864\) | −3.46410 | + | 2.00000i | −0.117851 | + | 0.0680414i | ||||
\(865\) | 12.9904 | − | 7.50000i | 0.441686 | − | 0.255008i | ||||
\(866\) | 8.39230i | 0.285182i | ||||||||
\(867\) | −18.3660 | − | 31.8109i | −0.623743 | − | 1.08035i | ||||
\(868\) | −7.09808 | + | 12.2942i | −0.240924 | + | 0.417293i | ||||
\(869\) | −10.9019 | − | 6.29423i | −0.369822 | − | 0.213517i | ||||
\(870\) | −1.85641 | −0.0629381 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −8.53590 | −0.289062 | ||||||||
\(873\) | 19.4711 | + | 11.2417i | 0.658998 | + | 0.380473i | ||||
\(874\) | −2.19615 | + | 3.80385i | −0.0742860 | + | 0.128667i | ||||
\(875\) | 1.50000 | + | 2.59808i | 0.0507093 | + | 0.0878310i | ||||
\(876\) | − | 8.53590i | − | 0.288401i | ||||||
\(877\) | −23.7846 | + | 13.7321i | −0.803149 | + | 0.463698i | −0.844571 | − | 0.535443i | \(-0.820145\pi\) |
0.0414220 | + | 0.999142i | \(0.486811\pi\) | |||||||
\(878\) | −2.95448 | + | 1.70577i | −0.0997090 | + | 0.0575670i | ||||
\(879\) | 8.19615i | 0.276449i | ||||||||
\(880\) | 1.50000 | + | 2.59808i | 0.0505650 | + | 0.0875811i | ||||
\(881\) | −13.1603 | + | 22.7942i | −0.443380 | + | 0.767957i | −0.997938 | − | 0.0641883i | \(-0.979554\pi\) |
0.554558 | + | 0.832145i | \(0.312888\pi\) | |||||||
\(882\) | −4.26795 | − | 2.46410i | −0.143709 | − | 0.0829706i | ||||
\(883\) | 4.58846 | 0.154414 | 0.0772069 | − | 0.997015i | \(-0.475400\pi\) | ||||
0.0772069 | + | 0.997015i | \(0.475400\pi\) | |||||||
\(884\) | 8.19615 | − | 28.3923i | 0.275666 | − | 0.954937i | ||||
\(885\) | 7.60770 | 0.255730 | ||||||||
\(886\) | 19.3923 | + | 11.1962i | 0.651497 | + | 0.376142i | ||||
\(887\) | 20.3827 | − | 35.3038i | 0.684384 | − | 1.18539i | −0.289246 | − | 0.957255i | \(-0.593405\pi\) |
0.973630 | − | 0.228133i | \(-0.0732620\pi\) | |||||||
\(888\) | −0.294229 | − | 0.509619i | −0.00987367 | − | 0.0171017i | ||||
\(889\) | 32.4115i | 1.08705i | ||||||||
\(890\) | −5.89230 | + | 3.40192i | −0.197511 | + | 0.114033i | ||||
\(891\) | −11.5981 | + | 6.69615i | −0.388550 | + | 0.224330i | ||||
\(892\) | − | 6.46410i | − | 0.216434i | ||||||
\(893\) | −0.696152 | − | 1.20577i | −0.0232959 | − | 0.0403496i | ||||
\(894\) | 2.19615 | − | 3.80385i | 0.0734503 | − | 0.127220i | ||||
\(895\) | −8.19615 | − | 4.73205i | −0.273967 | − | 0.158175i | ||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | −17.3205 | − | 18.0000i | −0.578315 | − | 0.601003i | ||||
\(898\) | −15.5885 | −0.520194 | ||||||||
\(899\) | 10.3923 | + | 6.00000i | 0.346603 | + | 0.200111i | ||||
\(900\) | 1.23205 | − | 2.13397i | 0.0410684 | − | 0.0711325i | ||||
\(901\) | −1.90192 | − | 3.29423i | −0.0633623 | − | 0.109747i | ||||
\(902\) | 31.1769i | 1.03808i | ||||||||
\(903\) | 3.80385 | − | 2.19615i | 0.126584 | − | 0.0730834i | ||||
\(904\) | −6.00000 | + | 3.46410i | −0.199557 | + | 0.115214i | ||||
\(905\) | − | 14.5885i | − | 0.484937i | ||||||
\(906\) | −8.66025 | − | 15.0000i | −0.287718 | − | 0.498342i | ||||
\(907\) | −2.29423 | + | 3.97372i | −0.0761786 | + | 0.131945i | −0.901598 | − | 0.432574i | \(-0.857605\pi\) |
0.825420 | + | 0.564520i | \(0.190939\pi\) | |||||||
\(908\) | 14.1962 | + | 8.19615i | 0.471116 | + | 0.271999i | ||||
\(909\) | −26.4449 | −0.877121 | ||||||||
\(910\) | 2.59808 | + | 10.5000i | 0.0861254 | + | 0.348072i | ||||
\(911\) | −21.4641 | −0.711137 | −0.355569 | − | 0.934650i | \(-0.615713\pi\) | ||||
−0.355569 | + | 0.934650i | \(0.615713\pi\) | |||||||
\(912\) | 0.294229 | + | 0.169873i | 0.00974288 | + | 0.00562506i | ||||
\(913\) | 12.2942 | − | 21.2942i | 0.406880 | − | 0.704736i | ||||
\(914\) | −9.16987 | − | 15.8827i | −0.303312 | − | 0.525353i | ||||
\(915\) | − | 4.53590i | − | 0.149952i | ||||||
\(916\) | 1.09808 | − | 0.633975i | 0.0362815 | − | 0.0209471i | ||||
\(917\) | 15.9115 | − | 9.18653i | 0.525445 | − | 0.303366i | ||||
\(918\) | − | 32.7846i | − | 1.08205i | ||||||
\(919\) | −15.3923 | − | 26.6603i | −0.507745 | − | 0.879441i | −0.999960 | − | 0.00896670i | \(-0.997146\pi\) |
0.492215 | − | 0.870474i | \(-0.336188\pi\) | |||||||
\(920\) | 4.73205 | − | 8.19615i | 0.156011 | − | 0.270219i | ||||
\(921\) | 17.4115 | + | 10.0526i | 0.573730 | + | 0.331243i | ||||
\(922\) | 30.5885 | 1.00738 | ||||||||
\(923\) | −15.5885 | + | 15.0000i | −0.513100 | + | 0.493731i | ||||
\(924\) | −6.58846 | −0.216744 | ||||||||
\(925\) | 0.696152 | + | 0.401924i | 0.0228894 | + | 0.0132152i | ||||
\(926\) | 6.46410 | − | 11.1962i | 0.212424 | − | 0.367928i | ||||
\(927\) | −11.3301 | − | 19.6244i | −0.372130 | − | 0.644548i | ||||
\(928\) | − | 2.53590i | − | 0.0832449i | ||||||
\(929\) | −2.78461 | + | 1.60770i | −0.0913601 | + | 0.0527468i | −0.544984 | − | 0.838446i | \(-0.683464\pi\) |
0.453624 | + | 0.891193i | \(0.350131\pi\) | |||||||
\(930\) | 3.00000 | − | 1.73205i | 0.0983739 | − | 0.0567962i | ||||
\(931\) | 0.928203i | 0.0304206i | ||||||||
\(932\) | 2.36603 | + | 4.09808i | 0.0775017 | + | 0.134237i | ||||
\(933\) | 3.33975 | − | 5.78461i | 0.109338 | − | 0.189380i | ||||
\(934\) | 32.7846 | + | 18.9282i | 1.07275 | + | 0.619350i | ||||
\(935\) | −24.5885 | −0.804129 | ||||||||
\(936\) | 6.40192 | − | 6.16025i | 0.209253 | − | 0.201354i | ||||
\(937\) | −9.60770 | −0.313870 | −0.156935 | − | 0.987609i | \(-0.550161\pi\) | ||||
−0.156935 | + | 0.987609i | \(0.550161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.66025 | + | 16.7321i | −0.315250 | + | 0.546030i | ||||
\(940\) | 1.50000 | + | 2.59808i | 0.0489246 | + | 0.0847399i | ||||
\(941\) | 3.21539i | 0.104819i | 0.998626 | + | 0.0524094i | \(0.0166901\pi\) | ||||
−0.998626 | + | 0.0524094i | \(0.983310\pi\) | |||||||
\(942\) | −8.24167 | + | 4.75833i | −0.268528 | + | 0.155035i | ||||
\(943\) | 85.1769 | − | 49.1769i | 2.77374 | − | 1.60142i | ||||
\(944\) | 10.3923i | 0.338241i | ||||||||
\(945\) | 6.00000 | + | 10.3923i | 0.195180 | + | 0.338062i | ||||
\(946\) | −3.00000 | + | 5.19615i | −0.0975384 | + | 0.168941i | ||||
\(947\) | 13.3135 | + | 7.68653i | 0.432630 | + | 0.249779i | 0.700466 | − | 0.713686i | \(-0.252975\pi\) |
−0.267837 | + | 0.963464i | \(0.586309\pi\) | |||||||
\(948\) | 3.07180 | 0.0997673 | ||||||||
\(949\) | 10.0981 | + | 40.8109i | 0.327797 | + | 1.32478i | ||||
\(950\) | −0.464102 | −0.0150574 | ||||||||
\(951\) | 14.7058 | + | 8.49038i | 0.476867 | + | 0.275319i | ||||
\(952\) | −12.2942 | + | 21.2942i | −0.398458 | + | 0.690150i | ||||
\(953\) | 3.29423 | + | 5.70577i | 0.106711 | + | 0.184828i | 0.914436 | − | 0.404731i | \(-0.132635\pi\) |
−0.807725 | + | 0.589559i | \(0.799302\pi\) | |||||||
\(954\) | − | 1.14359i | − | 0.0370252i | ||||||
\(955\) | 19.6865 | − | 11.3660i | 0.637041 | − | 0.367796i | ||||
\(956\) | −1.90192 | + | 1.09808i | −0.0615126 | + | 0.0355143i | ||||
\(957\) | 5.56922i | 0.180027i | ||||||||
\(958\) | 20.4904 | + | 35.4904i | 0.662014 | + | 1.14664i | ||||
\(959\) | 3.29423 | − | 5.70577i | 0.106376 | − | 0.184249i | ||||
\(960\) | −0.633975 | − | 0.366025i | −0.0204614 | − | 0.0118134i | ||||
\(961\) | 8.60770 | 0.277668 | ||||||||
\(962\) | 2.00962 | + | 2.08846i | 0.0647927 | + | 0.0673346i | ||||
\(963\) | −43.5167 | −1.40230 | ||||||||
\(964\) | −7.50000 | − | 4.33013i | −0.241559 | − | 0.139464i | ||||
\(965\) | −8.19615 | + | 14.1962i | −0.263843 | + | 0.456990i | ||||
\(966\) | 10.3923 | + | 18.0000i | 0.334367 | + | 0.579141i | ||||
\(967\) | − | 44.5692i | − | 1.43325i | −0.697459 | − | 0.716625i | \(-0.745686\pi\) | ||
0.697459 | − | 0.716625i | \(-0.254314\pi\) | |||||||
\(968\) | −1.73205 | + | 1.00000i | −0.0556702 | + | 0.0321412i | ||||
\(969\) | −2.41154 | + | 1.39230i | −0.0774699 | + | 0.0447273i | ||||
\(970\) | 9.12436i | 0.292965i | ||||||||
\(971\) | −23.3827 | − | 40.5000i | −0.750386 | − | 1.29971i | −0.947636 | − | 0.319354i | \(-0.896534\pi\) |
0.197250 | − | 0.980353i | \(-0.436799\pi\) | |||||||
\(972\) | 7.63397 | − | 13.2224i | 0.244860 | − | 0.424110i | ||||
\(973\) | −3.10770 | − | 1.79423i | −0.0996281 | − | 0.0575203i | ||||
\(974\) | 15.2487 | 0.488600 | ||||||||
\(975\) | 0.732051 | − | 2.53590i | 0.0234444 | − | 0.0812137i | ||||
\(976\) | 6.19615 | 0.198334 | ||||||||
\(977\) | 14.1962 | + | 8.19615i | 0.454175 | + | 0.262218i | 0.709592 | − | 0.704613i | \(-0.248879\pi\) |
−0.255417 | + | 0.966831i | \(0.582213\pi\) | |||||||
\(978\) | −3.92820 | + | 6.80385i | −0.125610 | + | 0.217563i | ||||
\(979\) | 10.2058 | + | 17.6769i | 0.326178 | + | 0.564957i | ||||
\(980\) | − | 2.00000i | − | 0.0638877i | ||||||
\(981\) | 18.2154 | − | 10.5167i | 0.581573 | − | 0.335771i | ||||
\(982\) | 17.8923 | − | 10.3301i | 0.570966 | − | 0.329648i | ||||
\(983\) | 44.5692i | 1.42154i | 0.703426 | + | 0.710769i | \(0.251653\pi\) | ||||
−0.703426 | + | 0.710769i | \(0.748347\pi\) | |||||||
\(984\) | −3.80385 | − | 6.58846i | −0.121262 | − | 0.210032i | ||||
\(985\) | 10.7942 | − | 18.6962i | 0.343933 | − | 0.595709i | ||||
\(986\) | 18.0000 | + | 10.3923i | 0.573237 | + | 0.330958i | ||||
\(987\) | −6.58846 | −0.209713 | ||||||||
\(988\) | −1.60770 | − | 0.464102i | −0.0511476 | − | 0.0147650i | ||||
\(989\) | 18.9282 | 0.601882 | ||||||||
\(990\) | −6.40192 | − | 3.69615i | −0.203466 | − | 0.117471i | ||||
\(991\) | 5.58846 | − | 9.67949i | 0.177523 | − | 0.307479i | −0.763508 | − | 0.645798i | \(-0.776525\pi\) |
0.941032 | + | 0.338319i | \(0.109858\pi\) | |||||||
\(992\) | 2.36603 | + | 4.09808i | 0.0751214 | + | 0.130114i | ||||
\(993\) | 9.46410i | 0.300334i | ||||||||
\(994\) | 15.5885 | − | 9.00000i | 0.494436 | − | 0.285463i | ||||
\(995\) | 5.53590 | − | 3.19615i | 0.175500 | − | 0.101325i | ||||
\(996\) | 6.00000i | 0.190117i | ||||||||
\(997\) | −20.2846 | − | 35.1340i | −0.642420 | − | 1.11270i | −0.984891 | − | 0.173176i | \(-0.944597\pi\) |
0.342471 | − | 0.939528i | \(-0.388736\pi\) | |||||||
\(998\) | 12.9282 | − | 22.3923i | 0.409235 | − | 0.708816i | ||||
\(999\) | 2.78461 | + | 1.60770i | 0.0881012 | + | 0.0508652i |
(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 | 130.2.l.a.121.1 | yes | 4 | |
3.2 | odd | 2 | 1170.2.bs.c.901.2 | 4 | |||
4.3 | odd | 2 | 1040.2.da.a.641.2 | 4 | |||
5.2 | odd | 4 | 650.2.n.b.199.1 | 4 | |||
5.3 | odd | 4 | 650.2.n.a.199.2 | 4 | |||
5.4 | even | 2 | 650.2.m.a.251.2 | 4 | |||
13.2 | odd | 12 | 1690.2.e.l.991.1 | 4 | |||
13.3 | even | 3 | 1690.2.l.g.361.2 | 4 | |||
13.4 | even | 6 | 1690.2.d.f.1351.2 | 4 | |||
13.5 | odd | 4 | 1690.2.e.l.191.1 | 4 | |||
13.6 | odd | 12 | 1690.2.a.m.1.2 | 2 | |||
13.7 | odd | 12 | 1690.2.a.j.1.2 | 2 | |||
13.8 | odd | 4 | 1690.2.e.n.191.1 | 4 | |||
13.9 | even | 3 | 1690.2.d.f.1351.4 | 4 | |||
13.10 | even | 6 | inner | 130.2.l.a.101.1 | ✓ | 4 | |
13.11 | odd | 12 | 1690.2.e.n.991.1 | 4 | |||
13.12 | even | 2 | 1690.2.l.g.1161.2 | 4 | |||
39.23 | odd | 6 | 1170.2.bs.c.361.2 | 4 | |||
52.23 | odd | 6 | 1040.2.da.a.881.2 | 4 | |||
65.19 | odd | 12 | 8450.2.a.bf.1.1 | 2 | |||
65.23 | odd | 12 | 650.2.n.b.49.1 | 4 | |||
65.49 | even | 6 | 650.2.m.a.101.2 | 4 | |||
65.59 | odd | 12 | 8450.2.a.bm.1.1 | 2 | |||
65.62 | odd | 12 | 650.2.n.a.49.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
130.2.l.a.101.1 | ✓ | 4 | 13.10 | even | 6 | inner | |
130.2.l.a.121.1 | yes | 4 | 1.1 | even | 1 | trivial | |
650.2.m.a.101.2 | 4 | 65.49 | even | 6 | |||
650.2.m.a.251.2 | 4 | 5.4 | even | 2 | |||
650.2.n.a.49.2 | 4 | 65.62 | odd | 12 | |||
650.2.n.a.199.2 | 4 | 5.3 | odd | 4 | |||
650.2.n.b.49.1 | 4 | 65.23 | odd | 12 | |||
650.2.n.b.199.1 | 4 | 5.2 | odd | 4 | |||
1040.2.da.a.641.2 | 4 | 4.3 | odd | 2 | |||
1040.2.da.a.881.2 | 4 | 52.23 | odd | 6 | |||
1170.2.bs.c.361.2 | 4 | 39.23 | odd | 6 | |||
1170.2.bs.c.901.2 | 4 | 3.2 | odd | 2 | |||
1690.2.a.j.1.2 | 2 | 13.7 | odd | 12 | |||
1690.2.a.m.1.2 | 2 | 13.6 | odd | 12 | |||
1690.2.d.f.1351.2 | 4 | 13.4 | even | 6 | |||
1690.2.d.f.1351.4 | 4 | 13.9 | even | 3 | |||
1690.2.e.l.191.1 | 4 | 13.5 | odd | 4 | |||
1690.2.e.l.991.1 | 4 | 13.2 | odd | 12 | |||
1690.2.e.n.191.1 | 4 | 13.8 | odd | 4 | |||
1690.2.e.n.991.1 | 4 | 13.11 | odd | 12 | |||
1690.2.l.g.361.2 | 4 | 13.3 | even | 3 | |||
1690.2.l.g.1161.2 | 4 | 13.12 | even | 2 | |||
8450.2.a.bf.1.1 | 2 | 65.19 | odd | 12 | |||
8450.2.a.bm.1.1 | 2 | 65.59 | odd | 12 |