Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,2,Mod(37,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.k (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: | \(1.14984578911\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(0.500000 - 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.37 |
Dual form | 144.2.k.b.109.4 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34277 | − | 0.443806i | 0.949483 | − | 0.313818i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.60607 | − | 1.19186i | 0.803037 | − | 0.595930i | ||||
\(5\) | −1.27133 | − | 1.27133i | −0.568556 | − | 0.568556i | 0.363168 | − | 0.931724i | \(-0.381695\pi\) |
−0.931724 | + | 0.363168i | \(0.881695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.158942i | − | 0.0600743i | −0.999549 | − | 0.0300371i | \(-0.990437\pi\) | ||
0.999549 | − | 0.0300371i | \(-0.00956256\pi\) | |||||||
\(8\) | 1.62764 | − | 2.31318i | 0.575456 | − | 0.817833i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.27133 | − | 1.14288i | −0.718258 | − | 0.361411i | ||||
\(11\) | 3.79793 | + | 3.79793i | 1.14512 | + | 1.14512i | 0.987500 | + | 0.157620i | \(0.0503821\pi\) |
0.157620 | + | 0.987500i | \(0.449618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.21215 | + | 4.21215i | −1.16824 | + | 1.16824i | −0.185617 | + | 0.982622i | \(0.559428\pi\) |
−0.982622 | + | 0.185617i | \(0.940572\pi\) | |||||||
\(14\) | −0.0705392 | − | 0.213422i | −0.0188524 | − | 0.0570395i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.15894 | − | 3.82843i | 0.289735 | − | 0.957107i | ||||
\(17\) | −3.05320 | −0.740511 | −0.370255 | − | 0.928930i | \(-0.620730\pi\) | ||||
−0.370255 | + | 0.928930i | \(0.620730\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.15894 | + | 2.15894i | −0.495295 | + | 0.495295i | −0.909970 | − | 0.414675i | \(-0.863895\pi\) |
0.414675 | + | 0.909970i | \(0.363895\pi\) | |||||||
\(20\) | −3.55710 | − | 0.526602i | −0.795391 | − | 0.117752i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.78530 | + | 3.41421i | 1.44663 | + | 0.727913i | ||||
\(23\) | − | 2.82843i | − | 0.589768i | −0.955533 | − | 0.294884i | \(-0.904719\pi\) | ||
0.955533 | − | 0.294884i | \(-0.0952810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.76744i | − | 0.353488i | ||||||
\(26\) | −3.78658 | + | 7.52533i | −0.742609 | + | 1.47584i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.189436 | − | 0.255272i | −0.0358001 | − | 0.0482419i | ||||
\(29\) | −2.09976 | + | 2.09976i | −0.389915 | + | 0.389915i | −0.874657 | − | 0.484742i | \(-0.838913\pi\) |
0.484742 | + | 0.874657i | \(0.338913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.15894 | 0.746968 | 0.373484 | − | 0.927637i | \(-0.378163\pi\) | ||||
0.373484 | + | 0.927637i | \(0.378163\pi\) | |||||||
\(32\) | −0.142883 | − | 5.65505i | −0.0252584 | − | 0.999681i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.09976 | + | 1.35503i | −0.703103 | + | 0.232386i | ||||
\(35\) | −0.202067 | + | 0.202067i | −0.0341556 | + | 0.0341556i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.98737 | − | 5.98737i | −0.984317 | − | 0.984317i | 0.0155615 | − | 0.999879i | \(-0.495046\pi\) |
−0.999879 | + | 0.0155615i | \(0.995046\pi\) | |||||||
\(38\) | −1.94082 | + | 3.85712i | −0.314842 | + | 0.625707i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.01008 | + | 0.871553i | −0.792163 | + | 0.137805i | ||||
\(41\) | 2.60365i | 0.406622i | 0.979114 | + | 0.203311i | \(0.0651702\pi\) | ||||
−0.979114 | + | 0.203311i | \(0.934830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.75481 | + | 5.75481i | 0.877600 | + | 0.877600i | 0.993286 | − | 0.115686i | \(-0.0369066\pi\) |
−0.115686 | + | 0.993286i | \(0.536907\pi\) | |||||||
\(44\) | 10.6264 | + | 1.57316i | 1.60198 | + | 0.237162i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.25527 | − | 3.79793i | −0.185080 | − | 0.559975i | ||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.97474 | 0.996391 | ||||||||
\(50\) | −0.784399 | − | 2.37327i | −0.110931 | − | 0.335631i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.74473 | + | 11.7853i | −0.241950 | + | 1.63433i | ||||
\(53\) | −3.55710 | − | 3.55710i | −0.488605 | − | 0.488605i | 0.419261 | − | 0.907866i | \(-0.362289\pi\) |
−0.907866 | + | 0.419261i | \(0.862289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.65685i | − | 1.30213i | ||||||
\(56\) | −0.367661 | − | 0.258699i | −0.0491307 | − | 0.0345701i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.88761 | + | 3.75138i | −0.247856 | + | 0.492580i | ||||
\(59\) | −4.00000 | − | 4.00000i | −0.520756 | − | 0.520756i | 0.397044 | − | 0.917800i | \(-0.370036\pi\) |
−0.917800 | + | 0.397044i | \(0.870036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.66949 | − | 3.66949i | 0.469829 | − | 0.469829i | −0.432030 | − | 0.901859i | \(-0.642202\pi\) |
0.901859 | + | 0.432030i | \(0.142202\pi\) | |||||||
\(62\) | 5.58451 | − | 1.84576i | 0.709234 | − | 0.234412i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.70160 | − | 7.53003i | −0.337700 | − | 0.941254i | ||||
\(65\) | 10.7101 | 1.32842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.767438 | − | 0.767438i | 0.0937575 | − | 0.0937575i | −0.658672 | − | 0.752430i | \(-0.728882\pi\) |
0.752430 | + | 0.658672i | \(0.228882\pi\) | |||||||
\(68\) | −4.90367 | + | 3.63899i | −0.594657 | + | 0.441292i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.181652 | + | 0.361009i | −0.0217115 | + | 0.0431488i | ||||
\(71\) | − | 0.317883i | − | 0.0377258i | −0.999822 | − | 0.0188629i | \(-0.993995\pi\) | ||
0.999822 | − | 0.0188629i | \(-0.00600460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.33897i | − | 0.156715i | −0.996925 | − | 0.0783573i | \(-0.975032\pi\) | ||
0.996925 | − | 0.0783573i | \(-0.0249675\pi\) | |||||||
\(74\) | −10.6969 | − | 5.38244i | −1.24349 | − | 0.625696i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.894263 | + | 6.04057i | −0.102579 | + | 0.692901i | ||||
\(77\) | 0.603650 | − | 0.603650i | 0.0687923 | − | 0.0687923i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.69382 | −1.09064 | −0.545320 | − | 0.838228i | \(-0.683592\pi\) | ||||
−0.545320 | + | 0.838228i | \(0.683592\pi\) | |||||||
\(80\) | −6.34059 | + | 3.39380i | −0.708900 | + | 0.379438i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.15551 | + | 3.49611i | 0.127605 | + | 0.386081i | ||||
\(83\) | −0.115816 | + | 0.115816i | −0.0127125 | + | 0.0127125i | −0.713434 | − | 0.700722i | \(-0.752861\pi\) |
0.700722 | + | 0.713434i | \(0.252861\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.88163 | + | 3.88163i | 0.421022 | + | 0.421022i | ||||
\(86\) | 10.2814 | + | 5.17338i | 1.10867 | + | 0.557860i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 14.9670 | − | 2.60365i | 1.59548 | − | 0.277550i | ||||
\(89\) | − | 14.3990i | − | 1.52629i | −0.646225 | − | 0.763147i | \(-0.723653\pi\) | ||
0.646225 | − | 0.763147i | \(-0.276347\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.669485 | + | 0.669485i | 0.0701811 | + | 0.0701811i | ||||
\(92\) | −3.37109 | − | 4.54266i | −0.351460 | − | 0.473605i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.79793 | − | 1.25527i | 0.391727 | − | 0.129471i | ||||
\(95\) | 5.48946 | 0.563206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.571533 | −0.0580304 | −0.0290152 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290152 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(98\) | 9.36548 | − | 3.09543i | 0.946057 | − | 0.312685i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.10654 | − | 2.83863i | −0.210654 | − | 0.283863i | ||||
\(101\) | 7.15296 | + | 7.15296i | 0.711746 | + | 0.711746i | 0.966900 | − | 0.255154i | \(-0.0821262\pi\) |
−0.255154 | + | 0.966900i | \(0.582126\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.3507i | − | 1.11841i | −0.829028 | − | 0.559207i | \(-0.811106\pi\) | ||
0.829028 | − | 0.559207i | \(-0.188894\pi\) | |||||||
\(104\) | 2.88761 | + | 16.5993i | 0.283154 | + | 1.62769i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.35503 | − | 3.19771i | −0.617255 | − | 0.310589i | ||||
\(107\) | 0.722018 | + | 0.722018i | 0.0698001 | + | 0.0698001i | 0.741145 | − | 0.671345i | \(-0.234283\pi\) |
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.44471 | + | 1.44471i | −0.138378 | + | 0.138378i | −0.772903 | − | 0.634525i | \(-0.781196\pi\) |
0.634525 | + | 0.772903i | \(0.281196\pi\) | |||||||
\(110\) | −4.28577 | − | 12.9670i | −0.408632 | − | 1.23635i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.608497 | − | 0.184204i | −0.0574975 | − | 0.0174057i | ||||
\(113\) | 3.53488 | 0.332533 | 0.166267 | − | 0.986081i | \(-0.446829\pi\) | ||||
0.166267 | + | 0.986081i | \(0.446829\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59587 | + | 3.59587i | −0.335316 | + | 0.335316i | ||||
\(116\) | −0.869748 | + | 5.87498i | −0.0807541 | + | 0.545478i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −7.14631 | − | 3.59587i | −0.657871 | − | 0.331026i | ||||
\(119\) | 0.485281i | 0.0444857i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.8486i | 1.62260i | ||||||||
\(122\) | 3.29874 | − | 6.55582i | 0.298654 | − | 0.593536i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.67956 | − | 4.95687i | 0.599843 | − | 0.445140i | ||||
\(125\) | −8.60365 | + | 8.60365i | −0.769534 | + | 0.769534i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.49791 | −0.132918 | −0.0664591 | − | 0.997789i | \(-0.521170\pi\) | ||||
−0.0664591 | + | 0.997789i | \(0.521170\pi\) | |||||||
\(128\) | −6.96951 | − | 8.91213i | −0.616023 | − | 0.787728i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 14.3812 | − | 4.75318i | 1.26131 | − | 0.416882i | ||||
\(131\) | −10.4243 | + | 10.4243i | −0.910775 | + | 0.910775i | −0.996333 | − | 0.0855585i | \(-0.972733\pi\) |
0.0855585 | + | 0.996333i | \(0.472733\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.343146 | + | 0.343146i | 0.0297545 | + | 0.0297545i | ||||
\(134\) | 0.689901 | − | 1.37109i | 0.0595984 | − | 0.118444i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.96951 | + | 7.06261i | −0.426132 | + | 0.605614i | ||||
\(137\) | 13.7954i | 1.17862i | 0.807907 | + | 0.589309i | \(0.200600\pi\) | ||||
−0.807907 | + | 0.589309i | \(0.799400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.42429 | − | 2.42429i | −0.205626 | − | 0.205626i | 0.596779 | − | 0.802405i | \(-0.296447\pi\) |
−0.802405 | + | 0.596779i | \(0.796447\pi\) | |||||||
\(140\) | −0.0836990 | + | 0.565371i | −0.00707386 | + | 0.0477826i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.141078 | − | 0.426845i | −0.0118390 | − | 0.0358200i | ||||
\(143\) | −31.9949 | −2.67555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.33897 | 0.443377 | ||||||||
\(146\) | −0.594243 | − | 1.79793i | −0.0491799 | − | 0.148798i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −16.7523 | − | 2.48005i | −1.37703 | − | 0.203859i | ||||
\(149\) | −2.92818 | − | 2.92818i | −0.239886 | − | 0.239886i | 0.576917 | − | 0.816803i | \(-0.304256\pi\) |
−0.816803 | + | 0.576917i | \(0.804256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6644i | 1.84440i | 0.386712 | + | 0.922201i | \(0.373611\pi\) | ||||
−0.386712 | + | 0.922201i | \(0.626389\pi\) | |||||||
\(152\) | 1.48005 | + | 8.50799i | 0.120048 | + | 0.690089i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.542661 | − | 1.07847i | 0.0437288 | − | 0.0869053i | ||||
\(155\) | −5.28739 | − | 5.28739i | −0.424693 | − | 0.424693i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.78007 | + | 2.78007i | −0.221874 | + | 0.221874i | −0.809287 | − | 0.587413i | \(-0.800146\pi\) |
0.587413 | + | 0.809287i | \(0.300146\pi\) | |||||||
\(158\) | −13.0166 | + | 4.30217i | −1.03554 | + | 0.342262i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.00778 | + | 7.37109i | −0.554014 | + | 0.582736i | ||||
\(161\) | −0.449555 | −0.0354299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.43692 | + | 5.43692i | −0.425853 | + | 0.425853i | −0.887213 | − | 0.461360i | \(-0.847362\pi\) |
0.461360 | + | 0.887213i | \(0.347362\pi\) | |||||||
\(164\) | 3.10318 | + | 4.18165i | 0.242318 | + | 0.326532i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.104115 | + | 0.206914i | −0.00808086 | + | 0.0160597i | ||||
\(167\) | 3.95458i | 0.306015i | 0.988225 | + | 0.153007i | \(0.0488958\pi\) | ||||
−0.988225 | + | 0.153007i | \(0.951104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 22.4844i | − | 1.72957i | ||||||
\(170\) | 6.93484 | + | 3.48946i | 0.531878 | + | 0.267629i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.1016 | + | 2.38372i | 1.22773 | + | 0.181757i | ||||
\(173\) | 15.9814 | − | 15.9814i | 1.21504 | − | 1.21504i | 0.245695 | − | 0.969347i | \(-0.420984\pi\) |
0.969347 | − | 0.245695i | \(-0.0790163\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.280920 | −0.0212355 | ||||||||
\(176\) | 18.9417 | − | 10.1385i | 1.42778 | − | 0.764220i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.39037 | − | 19.3346i | −0.478979 | − | 1.44919i | ||||
\(179\) | 12.2316 | − | 12.2316i | 0.914235 | − | 0.914235i | −0.0823670 | − | 0.996602i | \(-0.526248\pi\) |
0.996602 | + | 0.0823670i | \(0.0262480\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.76259 | + | 5.76259i | 0.428330 | + | 0.428330i | 0.888059 | − | 0.459729i | \(-0.152054\pi\) |
−0.459729 | + | 0.888059i | \(0.652054\pi\) | |||||||
\(182\) | 1.19609 | + | 0.601845i | 0.0886599 | + | 0.0446117i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.54266 | − | 4.60365i | −0.482331 | − | 0.339386i | ||||
\(185\) | 15.2238i | 1.11928i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5959 | − | 11.5959i | −0.847974 | − | 0.847974i | ||||
\(188\) | 4.54266 | − | 3.37109i | 0.331308 | − | 0.245862i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.37109 | − | 2.43625i | 0.534755 | − | 0.176744i | ||||
\(191\) | 16.1674 | 1.16983 | 0.584916 | − | 0.811094i | \(-0.301127\pi\) | ||||
0.584916 | + | 0.811094i | \(0.301127\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.1454 | −1.59406 | −0.797030 | − | 0.603940i | \(-0.793597\pi\) | ||||
−0.797030 | + | 0.603940i | \(0.793597\pi\) | |||||||
\(194\) | −0.767438 | + | 0.253649i | −0.0550989 | + | 0.0182110i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.2019 | − | 8.31291i | 0.800138 | − | 0.593779i | ||||
\(197\) | 14.2993 | + | 14.2993i | 1.01878 | + | 1.01878i | 0.999820 | + | 0.0189608i | \(0.00603576\pi\) |
0.0189608 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0075i | 1.77274i | 0.462981 | + | 0.886368i | \(0.346780\pi\) | ||||
−0.462981 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(200\) | −4.08840 | − | 2.87675i | −0.289094 | − | 0.203417i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.7793 | + | 6.43027i | 0.899150 | + | 0.452432i | ||||
\(203\) | 0.333739 | + | 0.333739i | 0.0234239 | + | 0.0234239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.31010 | − | 3.31010i | 0.231187 | − | 0.231187i | ||||
\(206\) | −5.03749 | − | 15.2414i | −0.350979 | − | 1.06192i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.2443 | + | 21.0075i | 0.779649 | + | 1.45661i | ||||
\(209\) | −16.3990 | −1.13434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4243 | − | 18.4243i | 1.26838 | − | 1.26838i | 0.321456 | − | 0.946924i | \(-0.395828\pi\) |
0.946924 | − | 0.321456i | \(-0.104172\pi\) | |||||||
\(212\) | −9.95252 | − | 1.47340i | −0.683542 | − | 0.101193i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.28994 | + | 0.649070i | 0.0881786 | + | 0.0443695i | ||||
\(215\) | − | 14.6325i | − | 0.997930i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 0.661029i | − | 0.0448736i | ||||||
\(218\) | −1.29874 | + | 2.58108i | −0.0879620 | + | 0.174813i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −11.5096 | − | 15.5096i | −0.775978 | − | 1.04566i | ||||
\(221\) | 12.8605 | − | 12.8605i | 0.865094 | − | 0.865094i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.3465 | 1.22857 | 0.614286 | − | 0.789083i | \(-0.289444\pi\) | ||||
0.614286 | + | 0.789083i | \(0.289444\pi\) | |||||||
\(224\) | −0.898823 | + | 0.0227101i | −0.0600551 | + | 0.00151738i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.74653 | − | 1.56880i | 0.315735 | − | 0.104355i | ||||
\(227\) | 0.115816 | − | 0.115816i | 0.00768697 | − | 0.00768697i | −0.703253 | − | 0.710940i | \(-0.748270\pi\) |
0.710940 | + | 0.703253i | \(0.248270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.84791 | + | 2.84791i | 0.188195 | + | 0.188195i | 0.794916 | − | 0.606720i | \(-0.207515\pi\) |
−0.606720 | + | 0.794916i | \(0.707515\pi\) | |||||||
\(230\) | −3.23256 | + | 6.42429i | −0.213149 | + | 0.423605i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.43948 | + | 8.27476i | 0.0945062 | + | 0.543264i | ||||
\(233\) | − | 11.7211i | − | 0.767874i | −0.923359 | − | 0.383937i | \(-0.874568\pi\) | ||
0.923359 | − | 0.383937i | \(-0.125432\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.59587 | − | 3.59587i | −0.234568 | − | 0.234568i | ||||
\(236\) | −11.1917 | − | 1.65685i | −0.728520 | − | 0.107852i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.215371 | + | 0.651622i | 0.0139604 | + | 0.0422384i | ||||
\(239\) | 13.6517 | 0.883058 | 0.441529 | − | 0.897247i | \(-0.354436\pi\) | ||||
0.441529 | + | 0.897247i | \(0.354436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.13167 | 0.137313 | 0.0686565 | − | 0.997640i | \(-0.478129\pi\) | ||||
0.0686565 | + | 0.997640i | \(0.478129\pi\) | |||||||
\(242\) | 7.92130 | + | 23.9666i | 0.509201 | + | 1.54063i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.51995 | − | 10.2670i | 0.0973049 | − | 0.657276i | ||||
\(245\) | −8.86720 | − | 8.86720i | −0.566504 | − | 0.566504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.1876i | − | 1.15725i | ||||||
\(248\) | 6.76924 | − | 9.62038i | 0.429847 | − | 0.610895i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −7.73439 | + | 15.3711i | −0.489166 | + | 0.972153i | ||||
\(251\) | 4.43370 | + | 4.43370i | 0.279853 | + | 0.279853i | 0.833050 | − | 0.553198i | \(-0.186593\pi\) |
−0.553198 | + | 0.833050i | \(0.686593\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7422 | − | 10.7422i | 0.675355 | − | 0.675355i | ||||
\(254\) | −2.01136 | + | 0.664782i | −0.126204 | + | 0.0417121i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.3137 | − | 8.87385i | −0.832107 | − | 0.554615i | ||||
\(257\) | −15.0853 | −0.940997 | −0.470498 | − | 0.882401i | \(-0.655926\pi\) | ||||
−0.470498 | + | 0.882401i | \(0.655926\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.951642 | + | 0.951642i | −0.0591322 | + | 0.0591322i | ||||
\(260\) | 17.2011 | − | 12.7649i | 1.06677 | − | 0.791645i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.37109 | + | 18.6238i | −0.578948 | + | 1.15058i | ||||
\(263\) | 26.1706i | 1.61375i | 0.590722 | + | 0.806875i | \(0.298843\pi\) | ||||
−0.590722 | + | 0.806875i | \(0.701157\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.04449i | 0.555599i | ||||||||
\(266\) | 0.613057 | + | 0.308476i | 0.0375889 | + | 0.0189139i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.317883 | − | 2.14724i | 0.0194178 | − | 0.131164i | ||||
\(269\) | −8.59700 | + | 8.59700i | −0.524168 | + | 0.524168i | −0.918828 | − | 0.394659i | \(-0.870863\pi\) |
0.394659 | + | 0.918828i | \(0.370863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.6644 | 0.647815 | 0.323907 | − | 0.946089i | \(-0.395003\pi\) | ||||
0.323907 | + | 0.946089i | \(0.395003\pi\) | |||||||
\(272\) | −3.53849 | + | 11.6890i | −0.214552 | + | 0.708748i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.12247 | + | 18.5240i | 0.369872 | + | 1.11908i | ||||
\(275\) | 6.71261 | − | 6.71261i | 0.404786 | − | 0.404786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.66170 | − | 2.66170i | −0.159926 | − | 0.159926i | 0.622608 | − | 0.782534i | \(-0.286073\pi\) |
−0.782534 | + | 0.622608i | \(0.786073\pi\) | |||||||
\(278\) | −4.33119 | − | 2.17936i | −0.259767 | − | 0.130709i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.138526 | + | 0.796310i | 0.00827851 | + | 0.0475886i | ||||
\(281\) | − | 10.4496i | − | 0.623368i | −0.950186 | − | 0.311684i | \(-0.899107\pi\) | ||
0.950186 | − | 0.311684i | \(-0.100893\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.4853 | − | 12.4853i | −0.742173 | − | 0.742173i | 0.230823 | − | 0.972996i | \(-0.425858\pi\) |
−0.972996 | + | 0.230823i | \(0.925858\pi\) | |||||||
\(284\) | −0.378872 | − | 0.510544i | −0.0224819 | − | 0.0302952i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −42.9618 | + | 14.1995i | −2.54039 | + | 0.839635i | ||||
\(287\) | 0.413828 | 0.0244275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.67794 | −0.451644 | ||||||||
\(290\) | 7.16902 | − | 2.36947i | 0.420979 | − | 0.139140i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.59587 | − | 2.15049i | −0.0933910 | − | 0.125848i | ||||
\(293\) | −21.7410 | − | 21.7410i | −1.27013 | − | 1.27013i | −0.946022 | − | 0.324104i | \(-0.894937\pi\) |
−0.324104 | − | 0.946022i | \(-0.605063\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1706i | 0.592158i | ||||||||
\(296\) | −23.5951 | + | 4.10460i | −1.37144 | + | 0.238575i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.23143 | − | 2.63234i | −0.303049 | − | 0.152487i | ||||
\(299\) | 11.9137 | + | 11.9137i | 0.688990 | + | 0.688990i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.914679 | − | 0.914679i | 0.0527212 | − | 0.0527212i | ||||
\(302\) | 10.0586 | + | 30.4331i | 0.578806 | + | 1.75123i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.76326 | + | 10.7674i | 0.330546 | + | 0.617555i | ||||
\(305\) | −9.33026 | −0.534249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0601 | − | 15.0601i | 0.859523 | − | 0.859523i | −0.131759 | − | 0.991282i | \(-0.542062\pi\) |
0.991282 | + | 0.131759i | \(0.0420624\pi\) | |||||||
\(308\) | 0.250040 | − | 1.68897i | 0.0142473 | − | 0.0962381i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.44633 | − | 4.75318i | −0.536516 | − | 0.269963i | ||||
\(311\) | 1.77883i | 0.100868i | 0.998727 | + | 0.0504342i | \(0.0160605\pi\) | ||||
−0.998727 | + | 0.0504342i | \(0.983939\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.70320i | − | 0.152794i | −0.997077 | − | 0.0763971i | \(-0.975658\pi\) | ||
0.997077 | − | 0.0763971i | \(-0.0243417\pi\) | |||||||
\(314\) | −2.49919 | + | 4.96681i | −0.141037 | + | 0.280293i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5690 | + | 11.5537i | −0.875824 | + | 0.649945i | ||||
\(317\) | −15.6025 | + | 15.6025i | −0.876325 | + | 0.876325i | −0.993152 | − | 0.116828i | \(-0.962728\pi\) |
0.116828 | + | 0.993152i | \(0.462728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.9495 | −0.892999 | ||||||||
\(320\) | −6.13853 | + | 13.0078i | −0.343154 | + | 0.727157i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.603650 | + | 0.199515i | −0.0336401 | + | 0.0111185i | ||||
\(323\) | 6.59169 | − | 6.59169i | 0.366771 | − | 0.366771i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.44471 | + | 7.44471i | 0.412958 | + | 0.412958i | ||||
\(326\) | −4.88761 | + | 9.71349i | −0.270700 | + | 0.537980i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 6.02271 | + | 4.23779i | 0.332549 | + | 0.233993i | ||||
\(329\) | − | 0.449555i | − | 0.0247848i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4454 | + | 15.4454i | 0.848955 | + | 0.848955i | 0.990003 | − | 0.141048i | \(-0.0450472\pi\) |
−0.141048 | + | 0.990003i | \(0.545047\pi\) | |||||||
\(332\) | −0.0479725 | + | 0.324045i | −0.00263284 | + | 0.0177843i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.75506 | + | 5.31010i | 0.0960329 | + | 0.290556i | ||||
\(335\) | −1.95133 | −0.106613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8738 | −1.02812 | −0.514062 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514062 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(338\) | −9.97868 | − | 30.1914i | −0.542769 | − | 1.64219i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.8605 | + | 1.60782i | 0.588996 | + | 0.0871965i | ||||
\(341\) | 15.7954 | + | 15.7954i | 0.855368 | + | 0.855368i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.22117i | − | 0.119932i | ||||||
\(344\) | 22.6786 | − | 3.94517i | 1.22275 | − | 0.212709i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3667 | − | 28.5520i | 0.772360 | − | 1.53496i | ||||
\(347\) | −19.8337 | − | 19.8337i | −1.06473 | − | 1.06473i | −0.997755 | − | 0.0669717i | \(-0.978666\pi\) |
−0.0669717 | − | 0.997755i | \(-0.521334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.9718 | − | 11.9718i | 0.640836 | − | 0.640836i | −0.309925 | − | 0.950761i | \(-0.600304\pi\) |
0.950761 | + | 0.309925i | \(0.100304\pi\) | |||||||
\(350\) | −0.377211 | + | 0.124674i | −0.0201628 | + | 0.00666409i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 20.9348 | − | 22.0202i | 1.11583 | − | 1.17368i | ||||
\(353\) | 12.6202 | 0.671705 | 0.335853 | − | 0.941915i | \(-0.390976\pi\) | ||||
0.335853 | + | 0.941915i | \(0.390976\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.404135 | + | 0.404135i | −0.0214492 | + | 0.0214492i | ||||
\(356\) | −17.1616 | − | 23.1259i | −0.909564 | − | 1.22567i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.9958 | − | 21.8528i | 0.581147 | − | 1.15495i | ||||
\(359\) | 27.0867i | 1.42958i | 0.699339 | + | 0.714790i | \(0.253478\pi\) | ||||
−0.699339 | + | 0.714790i | \(0.746522\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.67794i | 0.509365i | ||||||||
\(362\) | 10.2953 | + | 5.18038i | 0.541110 | + | 0.272274i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.87318 | + | 0.277310i | 0.0981811 | + | 0.0145350i | ||||
\(365\) | −1.70227 | + | 1.70227i | −0.0891011 | + | 0.0891011i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.4937 | −1.06976 | −0.534882 | − | 0.844927i | \(-0.679644\pi\) | ||||
−0.534882 | + | 0.844927i | \(0.679644\pi\) | |||||||
\(368\) | −10.8284 | − | 3.27798i | −0.564471 | − | 0.170877i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.75643 | + | 20.4422i | 0.351250 | + | 1.06274i | ||||
\(371\) | −0.565371 | + | 0.565371i | −0.0293526 | + | 0.0293526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.03372 | + | 1.03372i | 0.0535239 | + | 0.0535239i | 0.733362 | − | 0.679838i | \(-0.237950\pi\) |
−0.679838 | + | 0.733362i | \(0.737950\pi\) | |||||||
\(374\) | −20.7169 | − | 10.4243i | −1.07125 | − | 0.539027i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.60365 | − | 6.54266i | 0.237415 | − | 0.337412i | ||||
\(377\) | − | 17.6890i | − | 0.911028i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6686 | + | 17.6686i | 0.907573 | + | 0.907573i | 0.996076 | − | 0.0885032i | \(-0.0282083\pi\) |
−0.0885032 | + | 0.996076i | \(0.528208\pi\) | |||||||
\(380\) | 8.81647 | − | 6.54266i | 0.452275 | − | 0.335631i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.7091 | − | 7.17518i | 1.11074 | − | 0.367114i | ||||
\(383\) | 31.0958 | 1.58892 | 0.794460 | − | 0.607316i | \(-0.207754\pi\) | ||||
0.794460 | + | 0.607316i | \(0.207754\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.53488 | −0.0782245 | ||||||||
\(386\) | −29.7362 | + | 9.82824i | −1.51353 | + | 0.500244i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.917923 | + | 0.681187i | −0.0466005 | + | 0.0345820i | ||||
\(389\) | 2.56127 | + | 2.56127i | 0.129862 | + | 0.129862i | 0.769050 | − | 0.639188i | \(-0.220730\pi\) |
−0.639188 | + | 0.769050i | \(0.720730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.63577i | 0.436729i | ||||||||
\(392\) | 11.3523 | − | 16.1338i | 0.573379 | − | 0.814881i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.5468 | + | 12.8546i | 1.28703 | + | 0.647604i | ||||
\(395\) | 12.3240 | + | 12.3240i | 0.620090 | + | 0.620090i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.09795 | + | 5.09795i | −0.255859 | + | 0.255859i | −0.823367 | − | 0.567509i | \(-0.807907\pi\) |
0.567509 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(398\) | 11.0985 | + | 33.5794i | 0.556317 | + | 1.68318i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.76651 | − | 2.04836i | −0.338325 | − | 0.102418i | ||||
\(401\) | 15.2660 | 0.762349 | 0.381174 | − | 0.924503i | \(-0.375520\pi\) | ||||
0.381174 | + | 0.924503i | \(0.375520\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5181 | + | 17.5181i | −0.872637 | + | 0.872637i | ||||
\(404\) | 20.0135 | + | 2.96285i | 0.995709 | + | 0.147407i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.596250 | + | 0.300020i | 0.0295914 | + | 0.0148897i | ||||
\(407\) | − | 45.4792i | − | 2.25432i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 11.3779i | − | 0.562603i | −0.959619 | − | 0.281302i | \(-0.909234\pi\) | ||
0.959619 | − | 0.281302i | \(-0.0907661\pi\) | |||||||
\(410\) | 2.97567 | − | 5.91375i | 0.146958 | − | 0.292059i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −13.5284 | − | 18.2300i | −0.666497 | − | 0.898128i | ||||
\(413\) | −0.635767 | + | 0.635767i | −0.0312840 | + | 0.0312840i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.294481 | 0.0144555 | ||||||||
\(416\) | 24.4217 | + | 23.2181i | 1.19737 | + | 1.13836i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.0202 | + | 7.27798i | −1.07704 | + | 0.355978i | ||||
\(419\) | −23.3075 | + | 23.3075i | −1.13865 | + | 1.13865i | −0.149955 | + | 0.988693i | \(0.547913\pi\) |
−0.988693 | + | 0.149955i | \(0.952087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6154 | − | 17.6154i | −0.858520 | − | 0.858520i | 0.132644 | − | 0.991164i | \(-0.457653\pi\) |
−0.991164 | + | 0.132644i | \(0.957653\pi\) | |||||||
\(422\) | 16.5628 | − | 32.9164i | 0.806265 | − | 1.60235i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −14.0179 | + | 2.43855i | −0.680768 | + | 0.118426i | ||||
\(425\) | 5.39635i | 0.261761i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.583234 | − | 0.583234i | −0.0282247 | − | 0.0282247i | ||||
\(428\) | 2.02016 | + | 0.299070i | 0.0976480 | + | 0.0144561i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.49400 | − | 19.6481i | −0.313168 | − | 0.947517i | ||||
\(431\) | −10.3211 | −0.497151 | −0.248576 | − | 0.968612i | \(-0.579962\pi\) | ||||
−0.248576 | + | 0.968612i | \(0.579962\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15.3137 | −0.735930 | −0.367965 | − | 0.929840i | \(-0.619945\pi\) | ||||
−0.367965 | + | 0.929840i | \(0.619945\pi\) | |||||||
\(434\) | −0.293368 | − | 0.887611i | −0.0140821 | − | 0.0426067i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.598418 | + | 4.04220i | −0.0286590 | + | 0.193586i | ||||
\(437\) | 6.10641 | + | 6.10641i | 0.292109 | + | 0.292109i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 22.5735i | − | 1.07738i | −0.842505 | − | 0.538688i | \(-0.818920\pi\) | ||
0.842505 | − | 0.538688i | \(-0.181080\pi\) | |||||||
\(440\) | −22.3380 | − | 15.7178i | −1.06492 | − | 0.749319i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.5612 | − | 22.9764i | 0.549910 | − | 1.09287i | ||||
\(443\) | −23.7117 | − | 23.7117i | −1.12658 | − | 1.12658i | −0.990730 | − | 0.135846i | \(-0.956625\pi\) |
−0.135846 | − | 0.990730i | \(-0.543375\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.3059 | + | 18.3059i | −0.867784 | + | 0.867784i | ||||
\(446\) | 24.6352 | − | 8.14228i | 1.16651 | − | 0.385548i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.19684 | + | 0.429397i | −0.0565452 | + | 0.0202871i | ||||
\(449\) | 1.75506 | 0.0828266 | 0.0414133 | − | 0.999142i | \(-0.486814\pi\) | ||||
0.0414133 | + | 0.999142i | \(0.486814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.88849 | + | 9.88849i | −0.465631 | + | 0.465631i | ||||
\(452\) | 5.67727 | − | 4.21308i | 0.267036 | − | 0.198166i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.104115 | − | 0.206914i | 0.00488634 | − | 0.00971096i | ||||
\(455\) | − | 1.70227i | − | 0.0798039i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7422i | 1.25095i | 0.780246 | + | 0.625473i | \(0.215094\pi\) | ||||
−0.780246 | + | 0.625473i | \(0.784906\pi\) | |||||||
\(458\) | 5.08802 | + | 2.56018i | 0.237747 | + | 0.119629i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.48946 | + | 10.0610i | −0.0694463 | + | 0.469096i | ||||
\(461\) | −9.23921 | + | 9.23921i | −0.430313 | + | 0.430313i | −0.888735 | − | 0.458422i | \(-0.848415\pi\) |
0.458422 | + | 0.888735i | \(0.348415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 29.4474 | 1.36854 | 0.684268 | − | 0.729231i | \(-0.260122\pi\) | ||||
0.684268 | + | 0.729231i | \(0.260122\pi\) | |||||||
\(464\) | 5.60527 | + | 10.4723i | 0.260218 | + | 0.486163i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.20189 | − | 15.7387i | −0.240973 | − | 0.729083i | ||||
\(467\) | 19.5897 | − | 19.5897i | 0.906503 | − | 0.906503i | −0.0894848 | − | 0.995988i | \(-0.528522\pi\) |
0.995988 | + | 0.0894848i | \(0.0285221\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.121978 | − | 0.121978i | −0.00563242 | − | 0.00563242i | ||||
\(470\) | −6.42429 | − | 3.23256i | −0.296331 | − | 0.149107i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.7633 | + | 2.74218i | −0.725563 | + | 0.126219i | ||||
\(473\) | 43.7127i | 2.00991i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.81580 | + | 3.81580i | 0.175081 | + | 0.175081i | ||||
\(476\) | 0.578387 | + | 0.779397i | 0.0265103 | + | 0.0357236i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.3312 | − | 6.05872i | 0.838449 | − | 0.277120i | ||||
\(479\) | −35.5499 | −1.62432 | −0.812159 | − | 0.583436i | \(-0.801708\pi\) | ||||
−0.812159 | + | 0.583436i | \(0.801708\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 50.4393 | 2.29984 | ||||||||
\(482\) | 2.86235 | − | 0.946048i | 0.130376 | − | 0.0430913i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.2730 | + | 28.6661i | 0.966955 | + | 1.30301i | ||||
\(485\) | 0.726607 | + | 0.726607i | 0.0329935 | + | 0.0329935i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.86632i | 0.447086i | 0.974694 | + | 0.223543i | \(0.0717623\pi\) | ||||
−0.974694 | + | 0.223543i | \(0.928238\pi\) | |||||||
\(488\) | −2.51559 | − | 14.4608i | −0.113876 | − | 0.654608i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −15.8419 | − | 7.97131i | −0.715666 | − | 0.360107i | ||||
\(491\) | 0.449555 | + | 0.449555i | 0.0202881 | + | 0.0202881i | 0.717178 | − | 0.696890i | \(-0.245433\pi\) |
−0.696890 | + | 0.717178i | \(0.745433\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.41099 | − | 6.41099i | 0.288736 | − | 0.288736i | ||||
\(494\) | −8.07174 | − | 24.4217i | −0.363165 | − | 1.09879i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.81997 | − | 15.9222i | 0.216423 | − | 0.714928i | ||||
\(497\) | −0.0505249 | −0.00226635 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.70645 | − | 2.70645i | 0.121157 | − | 0.121157i | −0.643928 | − | 0.765086i | \(-0.722697\pi\) |
0.765086 | + | 0.643928i | \(0.222697\pi\) | |||||||
\(500\) | −3.56375 | + | 24.0724i | −0.159376 | + | 1.07655i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.92115 | + | 3.98575i | 0.353538 | + | 0.177893i | ||||
\(503\) | 23.6719i | 1.05548i | 0.849407 | + | 0.527739i | \(0.176960\pi\) | ||||
−0.849407 | + | 0.527739i | \(0.823040\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 18.1876i | − | 0.809336i | ||||||
\(506\) | 9.65685 | − | 19.1917i | 0.429300 | − | 0.853176i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.40576 | + | 1.78530i | −0.106738 | + | 0.0792099i | ||||
\(509\) | 24.6052 | − | 24.6052i | 1.09061 | − | 1.09061i | 0.0951425 | − | 0.995464i | \(-0.469669\pi\) |
0.995464 | − | 0.0951425i | \(-0.0303307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.212818 | −0.00941453 | ||||||||
\(512\) | −21.8155 | − | 6.00685i | −0.964120 | − | 0.265468i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −20.2561 | + | 6.69495i | −0.893460 | + | 0.295302i | ||||
\(515\) | −14.4305 | + | 14.4305i | −0.635882 | + | 0.635882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7422 | + | 10.7422i | 0.472440 | + | 0.472440i | ||||
\(518\) | −0.855494 | + | 1.70018i | −0.0375883 | + | 0.0747017i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 17.4321 | − | 24.7743i | 0.764447 | − | 1.08642i | ||||
\(521\) | − | 14.4889i | − | 0.634770i | −0.948297 | − | 0.317385i | \(-0.897195\pi\) | ||
0.948297 | − | 0.317385i | \(-0.102805\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.4979 | − | 19.4979i | −0.852584 | − | 0.852584i | 0.137867 | − | 0.990451i | \(-0.455975\pi\) |
−0.990451 | + | 0.137867i | \(0.955975\pi\) | |||||||
\(524\) | −4.31788 | + | 29.1665i | −0.188628 | + | 1.27414i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.6147 | + | 35.1412i | 0.506424 | + | 1.53223i | ||||
\(527\) | −12.6981 | −0.553138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 4.01400 | + | 12.1447i | 0.174357 | + | 0.527532i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.960099 | + | 0.142136i | 0.0416256 | + | 0.00616236i | ||||
\(533\) | −10.9670 | − | 10.9670i | −0.475031 | − | 0.475031i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.83585i | − | 0.0793706i | ||||||
\(536\) | −0.526113 | − | 3.02433i | −0.0227246 | − | 0.130631i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.72841 | + | 15.3592i | −0.333195 | + | 0.662182i | ||||
\(539\) | 26.4896 | + | 26.4896i | 1.14099 | + | 1.14099i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0396 | + | 10.0396i | −0.431638 | + | 0.431638i | −0.889185 | − | 0.457547i | \(-0.848728\pi\) |
0.457547 | + | 0.889185i | \(0.348728\pi\) | |||||||
\(542\) | 14.3198 | − | 4.73291i | 0.615089 | − | 0.203296i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.436252 | + | 17.2660i | 0.0187041 | + | 0.740275i | ||||
\(545\) | 3.67340 | 0.157351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.19884 | + | 7.19884i | −0.307800 | + | 0.307800i | −0.844056 | − | 0.536255i | \(-0.819838\pi\) |
0.536255 | + | 0.844056i | \(0.319838\pi\) | |||||||
\(548\) | 16.4422 | + | 22.1564i | 0.702374 | + | 0.946474i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.03441 | − | 11.9926i | 0.257308 | − | 0.511366i | ||||
\(551\) | − | 9.06651i | − | 0.386246i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54075i | 0.0655194i | ||||||||
\(554\) | −4.75534 | − | 2.39278i | −0.202035 | − | 0.101659i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.78301 | − | 1.00417i | −0.287664 | − | 0.0425865i | ||||
\(557\) | −1.02129 | + | 1.02129i | −0.0432735 | + | 0.0432735i | −0.728412 | − | 0.685139i | \(-0.759741\pi\) |
0.685139 | + | 0.728412i | \(0.259741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.4802 | −2.05049 | ||||||||
\(560\) | 0.539416 | + | 1.00778i | 0.0227945 | + | 0.0425867i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.63757 | − | 14.0314i | −0.195624 | − | 0.591878i | ||||
\(563\) | −6.70751 | + | 6.70751i | −0.282688 | + | 0.282688i | −0.834180 | − | 0.551492i | \(-0.814059\pi\) |
0.551492 | + | 0.834180i | \(0.314059\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.49400 | − | 4.49400i | −0.189064 | − | 0.189064i | ||||
\(566\) | −22.3059 | − | 11.2238i | −0.937588 | − | 0.471774i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.735321 | − | 0.517398i | −0.0308534 | − | 0.0217096i | ||||
\(569\) | − | 8.98711i | − | 0.376759i | −0.982096 | − | 0.188380i | \(-0.939676\pi\) | ||
0.982096 | − | 0.188380i | \(-0.0603235\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.17157 | − | 9.17157i | −0.383818 | − | 0.383818i | 0.488657 | − | 0.872476i | \(-0.337487\pi\) |
−0.872476 | + | 0.488657i | \(0.837487\pi\) | |||||||
\(572\) | −51.3861 | + | 38.1334i | −2.14856 | + | 1.59444i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.555677 | − | 0.183659i | 0.0231935 | − | 0.00766579i | ||||
\(575\) | −4.99907 | −0.208476 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5013 | 1.22815 | 0.614077 | − | 0.789246i | \(-0.289528\pi\) | ||||
0.614077 | + | 0.789246i | \(0.289528\pi\) | |||||||
\(578\) | −10.3097 | + | 3.40751i | −0.428828 | + | 0.141734i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.57478 | − | 6.36330i | 0.356048 | − | 0.264222i | ||||
\(581\) | 0.0184080 | + | 0.0184080i | 0.000763692 | + | 0.000763692i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.0192i | − | 1.11902i | ||||||
\(584\) | −3.09728 | − | 2.17936i | −0.128166 | − | 0.0901824i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −38.8421 | − | 19.5445i | −1.60455 | − | 0.807374i | ||||
\(587\) | −1.82425 | − | 1.82425i | −0.0752950 | − | 0.0752950i | 0.668456 | − | 0.743751i | \(-0.266955\pi\) |
−0.743751 | + | 0.668456i | \(0.766955\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.97891 | + | 8.97891i | −0.369970 | + | 0.369970i | ||||
\(590\) | 4.51379 | + | 13.6569i | 0.185830 | + | 0.562244i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −29.8612 | + | 15.9832i | −1.22729 | + | 0.656905i | ||||
\(593\) | 35.4338 | 1.45509 | 0.727546 | − | 0.686058i | \(-0.240661\pi\) | ||||
0.727546 | + | 0.686058i | \(0.240661\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.616953 | − | 0.616953i | 0.0252926 | − | 0.0252926i | ||||
\(596\) | −8.19286 | − | 1.21289i | −0.335593 | − | 0.0496821i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.2848 | + | 10.7101i | 0.870402 | + | 0.437967i | ||||
\(599\) | − | 27.1632i | − | 1.10986i | −0.831897 | − | 0.554930i | \(-0.812745\pi\) | ||
0.831897 | − | 0.554930i | \(-0.187255\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5.33897i | − | 0.217781i | −0.994054 | − | 0.108891i | \(-0.965270\pi\) | ||
0.994054 | − | 0.108891i | \(-0.0347298\pi\) | |||||||
\(602\) | 0.822265 | − | 1.63414i | 0.0335130 | − | 0.0666027i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 27.0128 | + | 36.4007i | 1.09913 | + | 1.48112i | ||||
\(605\) | 22.6914 | − | 22.6914i | 0.922539 | − | 0.922539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.1084 | 0.653820 | 0.326910 | − | 0.945055i | \(-0.393993\pi\) | ||||
0.326910 | + | 0.945055i | \(0.393993\pi\) | |||||||
\(608\) | 12.5174 | + | 11.9004i | 0.507648 | + | 0.482627i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.5284 | + | 4.14082i | −0.507260 | + | 0.167657i | ||||
\(611\) | −11.9137 | + | 11.9137i | −0.481979 | + | 0.481979i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.436924 | + | 0.436924i | 0.0176472 | + | 0.0176472i | 0.715875 | − | 0.698228i | \(-0.246028\pi\) |
−0.698228 | + | 0.715875i | \(0.746028\pi\) | |||||||
\(614\) | 13.5385 | − | 26.9060i | 0.546369 | − | 1.08584i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.413828 | − | 2.37887i | −0.0166736 | − | 0.0958475i | ||||
\(617\) | 8.80641i | 0.354533i | 0.984163 | + | 0.177266i | \(0.0567254\pi\) | ||||
−0.984163 | + | 0.177266i | \(0.943275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.92932 | + | 1.92932i | 0.0775458 | + | 0.0775458i | 0.744816 | − | 0.667270i | \(-0.232537\pi\) |
−0.667270 | + | 0.744816i | \(0.732537\pi\) | |||||||
\(620\) | −14.7938 | − | 2.19011i | −0.594132 | − | 0.0879569i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.789456 | + | 2.38857i | 0.0316543 | + | 0.0957728i | ||||
\(623\) | −2.28861 | −0.0916910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0390 | 0.521559 | ||||||||
\(626\) | −1.19970 | − | 3.62979i | −0.0479495 | − | 0.145075i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.15154 | + | 7.77845i | −0.0459515 | + | 0.310394i | ||||
\(629\) | 18.2807 | + | 18.2807i | 0.728898 | + | 0.728898i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 38.7864i | − | 1.54406i | −0.635586 | − | 0.772030i | \(-0.719241\pi\) | ||
0.635586 | − | 0.772030i | \(-0.280759\pi\) | |||||||
\(632\) | −15.7780 | + | 22.4235i | −0.627615 | + | 0.891961i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.0261 | + | 27.8751i | −0.557049 | + | 1.10706i | ||||
\(635\) | 1.90434 | + | 1.90434i | 0.0755715 | + | 0.0755715i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −29.3786 | + | 29.3786i | −1.16402 | + | 1.16402i | ||||
\(638\) | −21.4165 | + | 7.07847i | −0.847888 | + | 0.280239i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.46971 | + | 20.1908i | −0.0976240 | + | 0.798111i | ||||
\(641\) | −33.1091 | −1.30773 | −0.653865 | − | 0.756611i | \(-0.726854\pi\) | ||||
−0.653865 | + | 0.756611i | \(0.726854\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2897 | + | 19.2897i | −0.760711 | + | 0.760711i | −0.976451 | − | 0.215740i | \(-0.930784\pi\) |
0.215740 | + | 0.976451i | \(0.430784\pi\) | |||||||
\(644\) | −0.722018 | + | 0.535806i | −0.0284515 | + | 0.0211137i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.92571 | − | 11.7766i | 0.233144 | − | 0.463343i | ||||
\(647\) | − | 41.8477i | − | 1.64520i | −0.568620 | − | 0.822601i | \(-0.692522\pi\) | ||
0.568620 | − | 0.822601i | \(-0.307478\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.3835i | − | 1.19266i | ||||||
\(650\) | 13.3005 | + | 6.69254i | 0.521690 | + | 0.262503i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.25205 | + | 15.2121i | −0.0881970 | + | 0.595754i | ||||
\(653\) | −14.7741 | + | 14.7741i | −0.578155 | + | 0.578155i | −0.934395 | − | 0.356240i | \(-0.884059\pi\) |
0.356240 | + | 0.934395i | \(0.384059\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.5054 | 1.03565 | ||||||||
\(656\) | 9.96788 | + | 3.01748i | 0.389180 | + | 0.117813i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.199515 | − | 0.603650i | −0.00777790 | − | 0.0235327i | ||||
\(659\) | 2.22839 | − | 2.22839i | 0.0868056 | − | 0.0868056i | −0.662371 | − | 0.749176i | \(-0.730450\pi\) |
0.749176 | + | 0.662371i | \(0.230450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0685 | − | 18.0685i | −0.702784 | − | 0.702784i | 0.262223 | − | 0.965007i | \(-0.415544\pi\) |
−0.965007 | + | 0.262223i | \(0.915544\pi\) | |||||||
\(662\) | 27.5944 | + | 13.8849i | 1.07249 | + | 0.539651i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.0793969 | + | 0.456409i | 0.00308120 | + | 0.0177121i | ||||
\(665\) | − | 0.872503i | − | 0.0338342i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.93901 | + | 5.93901i | 0.229959 | + | 0.229959i | ||||
\(668\) | 4.71330 | + | 6.35134i | 0.182363 | + | 0.245741i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.62020 | + | 0.866013i | −0.101227 | + | 0.0334570i | ||||
\(671\) | 27.8729 | 1.07602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7981 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(674\) | −25.3433 | + | 8.37632i | −0.976186 | + | 0.322644i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −26.7982 | − | 36.1115i | −1.03070 | − | 1.38890i | ||||
\(677\) | −29.0213 | − | 29.0213i | −1.11538 | − | 1.11538i | −0.992411 | − | 0.122968i | \(-0.960759\pi\) |
−0.122968 | − | 0.992411i | \(-0.539241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0908404i | 0.00348613i | ||||||||
\(680\) | 15.2968 | − | 2.66103i | 0.586605 | − | 0.102046i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 28.2197 | + | 14.1995i | 1.08059 | + | 0.543728i | ||||
\(683\) | 18.7938 | + | 18.7938i | 0.719123 | + | 0.719123i | 0.968426 | − | 0.249303i | \(-0.0802013\pi\) |
−0.249303 | + | 0.968426i | \(0.580201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.5385 | − | 17.5385i | 0.670111 | − | 0.670111i | ||||
\(686\) | −0.985767 | − | 2.98252i | −0.0376368 | − | 0.113873i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 28.7013 | − | 15.3624i | 1.09423 | − | 0.585685i | ||||
\(689\) | 29.9660 | 1.14161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4580 | − | 10.4580i | 0.397841 | − | 0.397841i | −0.479630 | − | 0.877471i | \(-0.659229\pi\) |
0.877471 | + | 0.479630i | \(0.159229\pi\) | |||||||
\(692\) | 6.61971 | − | 44.7149i | 0.251644 | − | 1.69980i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −35.4344 | − | 17.8298i | −1.34507 | − | 0.676810i | ||||
\(695\) | 6.16415i | 0.233820i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 7.94948i | − | 0.301108i | ||||||
\(698\) | 10.7622 | − | 21.3885i | 0.407357 | − | 0.809569i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.451177 | + | 0.334817i | −0.0170529 | + | 0.0126549i | ||||
\(701\) | −18.3314 | + | 18.3314i | −0.692367 | + | 0.692367i | −0.962752 | − | 0.270385i | \(-0.912849\pi\) |
0.270385 | + | 0.962752i | \(0.412849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 25.8528 | 0.975055 | ||||||||
\(704\) | 18.3380 | − | 38.8590i | 0.691141 | − | 1.46456i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.9460 | − | 5.60091i | 0.637773 | − | 0.210793i | ||||
\(707\) | 1.13690 | − | 1.13690i | 0.0427577 | − | 0.0427577i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.5722 | + | 14.5722i | 0.547271 | + | 0.547271i | 0.925650 | − | 0.378380i | \(-0.123519\pi\) |
−0.378380 | + | 0.925650i | \(0.623519\pi\) | |||||||
\(710\) | −0.363303 | + | 0.722018i | −0.0136345 | + | 0.0270969i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −33.3075 | − | 23.4364i | −1.24825 | − | 0.878315i | ||||
\(713\) | − | 11.7633i | − | 0.440538i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.6761 | + | 40.6761i | 1.52120 | + | 1.52120i | ||||
\(716\) | 5.06651 | − | 34.2233i | 0.189344 | − | 1.27898i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12.0212 | + | 36.3712i | 0.448628 | + | 1.35736i | ||||
\(719\) | −44.0949 | −1.64446 | −0.822230 | − | 0.569155i | \(-0.807270\pi\) | ||||
−0.822230 | + | 0.569155i | \(0.807270\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.80409 | −0.0671880 | ||||||||
\(722\) | 4.29513 | + | 12.9953i | 0.159848 | + | 0.483634i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16.1233 | + | 2.38694i | 0.599219 | + | 0.0887101i | ||||
\(725\) | 3.71119 | + | 3.71119i | 0.137830 | + | 0.137830i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.23457i | 0.342491i | 0.985228 | + | 0.171246i | \(0.0547792\pi\) | ||||
−0.985228 | + | 0.171246i | \(0.945221\pi\) | |||||||
\(728\) | 2.63832 | − | 0.458962i | 0.0977826 | − | 0.0170103i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.53029 | + | 3.04125i | −0.0566385 | + | 0.112562i | ||||
\(731\) | −17.5706 | − | 17.5706i | −0.649872 | − | 0.649872i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.2764 | − | 18.2764i | 0.675053 | − | 0.675053i | −0.283823 | − | 0.958877i | \(-0.591603\pi\) |
0.958877 | + | 0.283823i | \(0.0916029\pi\) | |||||||
\(734\) | −27.5184 | + | 9.09524i | −1.01572 | + | 0.335711i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −15.9949 | + | 0.404135i | −0.589580 | + | 0.0148966i | ||||
\(737\) | 5.82936 | 0.214727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9991 | − | 16.9991i | 0.625321 | − | 0.625321i | −0.321566 | − | 0.946887i | \(-0.604209\pi\) |
0.946887 | + | 0.321566i | \(0.104209\pi\) | |||||||
\(740\) | 18.1447 | + | 24.4506i | 0.667012 | + | 0.898822i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.508249 | + | 1.01008i | −0.0186584 | + | 0.0370812i | ||||
\(743\) | 17.8748i | 0.655762i | 0.944719 | + | 0.327881i | \(0.106335\pi\) | ||||
−0.944719 | + | 0.327881i | \(0.893665\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.44538i | 0.272778i | ||||||||
\(746\) | 1.84682 | + | 0.929278i | 0.0676168 | + | 0.0340233i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −32.4445 | − | 4.80316i | −1.18629 | − | 0.175621i | ||||
\(749\) | 0.114759 | − | 0.114759i | 0.00419319 | − | 0.00419319i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.0731 | −1.27984 | −0.639918 | − | 0.768443i | \(-0.721032\pi\) | ||||
−0.639918 | + | 0.768443i | \(0.721032\pi\) | |||||||
\(752\) | 3.27798 | − | 10.8284i | 0.119536 | − | 0.394872i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.85047 | − | 23.7523i | −0.285897 | − | 0.865006i | ||||
\(755\) | 28.8139 | − | 28.8139i | 1.04865 | − | 1.04865i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.8071 | − | 32.8071i | −1.19239 | − | 1.19239i | −0.976393 | − | 0.216000i | \(-0.930699\pi\) |
−0.216000 | − | 0.976393i | \(-0.569301\pi\) | |||||||
\(758\) | 31.5662 | + | 15.8834i | 1.14654 | + | 0.576912i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.93484 | − | 12.6981i | 0.324101 | − | 0.460608i | ||||
\(761\) | 10.5531i | 0.382550i | 0.981536 | + | 0.191275i | \(0.0612623\pi\) | ||||
−0.981536 | + | 0.191275i | \(0.938738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.229624 | + | 0.229624i | 0.00831296 | + | 0.00831296i | ||||
\(764\) | 25.9660 | − | 19.2693i | 0.939418 | − | 0.697138i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.7545 | − | 13.8005i | 1.50865 | − | 0.498632i | ||||
\(767\) | 33.6972 | 1.21673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2068 | −1.26959 | −0.634795 | − | 0.772681i | \(-0.718915\pi\) | ||||
−0.634795 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(770\) | −2.06099 | + | 0.681187i | −0.0742729 | + | 0.0245483i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −35.5671 | + | 26.3942i | −1.28009 | + | 0.949947i | ||||
\(773\) | 19.3897 | + | 19.3897i | 0.697399 | + | 0.697399i | 0.963849 | − | 0.266450i | \(-0.0858507\pi\) |
−0.266450 | + | 0.963849i | \(0.585851\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.35067i | − | 0.264044i | ||||||
\(776\) | −0.930247 | + | 1.32206i | −0.0333939 | + | 0.0474591i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.57591 | + | 2.30250i | 0.164054 | + | 0.0825485i | ||||
\(779\) | −5.62113 | − | 5.62113i | −0.201398 | − | 0.201398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.20730 | − | 1.20730i | 0.0432006 | − | 0.0432006i | ||||
\(782\) | 3.83260 | + | 11.5959i | 0.137054 | + | 0.414667i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.08331 | − | 26.7023i | 0.288690 | − | 0.953653i | ||||
\(785\) | 7.06877 | 0.252295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.68964 | + | 6.68964i | −0.238460 | + | 0.238460i | −0.816212 | − | 0.577752i | \(-0.803930\pi\) |
0.577752 | + | 0.816212i | \(0.303930\pi\) | |||||||
\(788\) | 40.0084 | + | 5.92295i | 1.42524 | + | 0.210996i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.0179 | + | 11.0789i | 0.783360 | + | 0.394170i | ||||
\(791\) | − | 0.561839i | − | 0.0199767i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.9128i | 1.09775i | ||||||||
\(794\) | −4.58289 | + | 9.10789i | −0.162641 | + | 0.323227i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29.8055 | + | 40.1639i | 1.05643 | + | 1.42357i | ||||
\(797\) | −13.5617 | + | 13.5617i | −0.480380 | + | 0.480380i | −0.905253 | − | 0.424873i | \(-0.860319\pi\) |
0.424873 | + | 0.905253i | \(0.360319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.63577 | −0.305511 | ||||||||
\(800\) | −9.99495 | + | 0.252537i | −0.353375 | + | 0.00892854i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 20.4988 | − | 6.77515i | 0.723837 | − | 0.239239i | ||||
\(803\) | 5.08532 | − | 5.08532i | 0.179457 | − | 0.179457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.571533 | + | 0.571533i | 0.0201439 | + | 0.0201439i | ||||
\(806\) | −15.7482 | + | 31.2974i | −0.554705 | + | 1.10240i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 28.1885 | − | 4.90367i | 0.991668 | − | 0.172510i | ||||
\(809\) | − | 43.1578i | − | 1.51735i | −0.651472 | − | 0.758673i | \(-0.725848\pi\) | ||
0.651472 | − | 0.758673i | \(-0.274152\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.74017 | + | 2.74017i | 0.0962203 | + | 0.0962203i | 0.753578 | − | 0.657358i | \(-0.228326\pi\) |
−0.657358 | + | 0.753578i | \(0.728326\pi\) | |||||||
\(812\) | 0.933779 | + | 0.138239i | 0.0327692 | + | 0.00485124i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.1839 | − | 61.0683i | −0.707447 | − | 2.14044i | ||||
\(815\) | 13.8243 | 0.484242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.8486 | −0.869342 | ||||||||
\(818\) | −5.04959 | − | 15.2780i | −0.176555 | − | 0.534182i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.37109 | − | 9.26143i | 0.0478805 | − | 0.323423i | ||||
\(821\) | −3.97453 | − | 3.97453i | −0.138712 | − | 0.138712i | 0.634341 | − | 0.773053i | \(-0.281271\pi\) |
−0.773053 | + | 0.634341i | \(0.781271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5255i | 1.34291i | 0.741043 | + | 0.671457i | \(0.234331\pi\) | ||||
−0.741043 | + | 0.671457i | \(0.765669\pi\) | |||||||
\(824\) | −26.2561 | − | 18.4748i | −0.914676 | − | 0.643599i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −0.571533 | + | 1.13585i | −0.0198862 | + | 0.0395212i | ||||
\(827\) | −2.99583 | − | 2.99583i | −0.104175 | − | 0.104175i | 0.653098 | − | 0.757273i | \(-0.273469\pi\) |
−0.757273 | + | 0.653098i | \(0.773469\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.9699 | + | 24.9699i | −0.867240 | + | 0.867240i | −0.992166 | − | 0.124926i | \(-0.960131\pi\) |
0.124926 | + | 0.992166i | \(0.460131\pi\) | |||||||
\(830\) | 0.395420 | − | 0.130692i | 0.0137252 | − | 0.00453639i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 43.0971 | + | 20.3380i | 1.49412 | + | 0.705095i | ||||
\(833\) | −21.2953 | −0.737838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.02758 | − | 5.02758i | 0.173986 | − | 0.173986i | ||||
\(836\) | −26.3380 | + | 19.5453i | −0.910920 | + | 0.675990i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −20.9527 | + | 41.6407i | −0.723799 | + | 1.43846i | ||||
\(839\) | 39.6005i | 1.36716i | 0.729876 | + | 0.683580i | \(0.239578\pi\) | ||||
−0.729876 | + | 0.683580i | \(0.760422\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.1820i | 0.695932i | ||||||||
\(842\) | −31.4712 | − | 15.8356i | −1.08457 | − | 0.545731i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 7.63159 | − | 51.5499i | 0.262690 | − | 1.77442i | ||||
\(845\) | −28.5850 | + | 28.5850i | −0.983355 | + | 0.983355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.83688 | 0.0974765 | ||||||||
\(848\) | −17.7406 | + | 9.49562i | −0.609213 | + | 0.326081i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.39493 | + | 7.24607i | 0.0821454 | + | 0.248538i | ||||
\(851\) | −16.9348 | + | 16.9348i | −0.580519 | + | 0.580519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.68505 | + | 7.68505i | 0.263131 | + | 0.263131i | 0.826325 | − | 0.563194i | \(-0.190428\pi\) |
−0.563194 | + | 0.826325i | \(0.690428\pi\) | |||||||
\(854\) | −1.04199 | − | 0.524308i | −0.0356563 | − | 0.0179414i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.84534 | − | 0.494975i | 0.0972517 | − | 0.0169179i | ||||
\(857\) | 34.0082i | 1.16170i | 0.814011 | + | 0.580849i | \(0.197279\pi\) | ||||
−0.814011 | + | 0.580849i | \(0.802721\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.19049 | + | 9.19049i | 0.313576 | + | 0.313576i | 0.846293 | − | 0.532718i | \(-0.178829\pi\) |
−0.532718 | + | 0.846293i | \(0.678829\pi\) | |||||||
\(860\) | −17.4399 | − | 23.5009i | −0.594696 | − | 0.801374i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.8589 | + | 4.58057i | −0.472037 | + | 0.156015i | ||||
\(863\) | 25.8307 | 0.879289 | 0.439644 | − | 0.898172i | \(-0.355104\pi\) | ||||
0.439644 | + | 0.898172i | \(0.355104\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −40.6353 | −1.38164 | ||||||||
\(866\) | −20.5628 | + | 6.79631i | −0.698753 | + | 0.230948i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.787854 | − | 1.06166i | −0.0267415 | − | 0.0360351i | ||||
\(869\) | −36.8165 | − | 36.8165i | −1.24891 | − | 1.24891i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.46512i | 0.219062i | ||||||||
\(872\) | 0.990411 | + | 5.69333i | 0.0335395 | + | 0.192800i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 10.9096 | + | 5.48946i | 0.369022 | + | 0.185684i | ||||
\(875\) | 1.36748 | + | 1.36748i | 0.0462292 | + | 0.0462292i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.9718 | − | 31.9718i | 1.07961 | − | 1.07961i | 0.0830670 | − | 0.996544i | \(-0.473528\pi\) |
0.996544 | − | 0.0830670i | \(-0.0264716\pi\) | |||||||
\(878\) | −10.0183 | − | 30.3111i | −0.338100 | − | 1.02295i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −36.9706 | − | 11.1917i | −1.24628 | − | 0.377273i | ||||
\(881\) | −34.7403 | −1.17043 | −0.585215 | − | 0.810878i | \(-0.698990\pi\) | ||||
−0.585215 | + | 0.810878i | \(0.698990\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6034 | + | 34.6034i | −1.16450 | + | 1.16450i | −0.181017 | + | 0.983480i | \(0.557939\pi\) |
−0.983480 | + | 0.181017i | \(0.942061\pi\) | |||||||
\(884\) | 5.32701 | − | 35.9829i | 0.179167 | − | 1.21024i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −42.3628 | − | 21.3160i | −1.42320 | − | 0.716125i | ||||
\(887\) | 22.9284i | 0.769860i | 0.922946 | + | 0.384930i | \(0.125774\pi\) | ||||
−0.922946 | + | 0.384930i | \(0.874226\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.238081i | 0.00798497i | ||||||||
\(890\) | −16.4564 | + | 32.7050i | −0.551620 | + | 1.09627i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 29.4658 | − | 21.8664i | 0.986588 | − | 0.732143i | ||||
\(893\) | −6.10641 | + | 6.10641i | −0.204343 | + | 0.204343i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.1009 | −1.03959 | ||||||||
\(896\) | −1.41651 | + | 1.10774i | −0.0473222 | + | 0.0370072i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.35665 | − | 0.778908i | 0.0786425 | − | 0.0259925i | ||||
\(899\) | −8.73277 | + | 8.73277i | −0.291254 | + | 0.291254i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.8605 | + | 10.8605i | 0.361817 | + | 0.361817i | ||||
\(902\) | −8.88942 | + | 17.6665i | −0.295985 | + | 0.588232i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.75349 | − | 8.17680i | 0.191358 | − | 0.271956i | ||||
\(905\) | − | 14.6523i | − | 0.487059i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3822 | − | 16.3822i | −0.543963 | − | 0.543963i | 0.380725 | − | 0.924688i | \(-0.375674\pi\) |
−0.924688 | + | 0.380725i | \(0.875674\pi\) | |||||||
\(908\) | 0.0479725 | − | 0.324045i | 0.00159202 | − | 0.0107538i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.755479 | − | 2.28577i | −0.0250439 | − | 0.0757724i | ||||
\(911\) | 29.4078 | 0.974324 | 0.487162 | − | 0.873312i | \(-0.338032\pi\) | ||||
0.487162 | + | 0.873312i | \(0.338032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.879722 | −0.0291146 | ||||||||
\(914\) | 11.8683 | + | 35.9086i | 0.392569 | + | 1.18775i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.96827 | + | 1.17964i | 0.263279 | + | 0.0389765i | ||||
\(917\) | 1.65685 | + | 1.65685i | 0.0547141 | + | 0.0547141i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.86029i | 0.226300i | 0.993578 | + | 0.113150i | \(0.0360941\pi\) | ||||
−0.993578 | + | 0.113150i | \(0.963906\pi\) | |||||||
\(920\) | 2.46512 | + | 14.1706i | 0.0812727 | + | 0.467192i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.30574 | + | 16.5066i | −0.273535 | + | 0.543615i | ||||
\(923\) | 1.33897 | + | 1.33897i | 0.0440728 | + | 0.0440728i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.5823 | + | 10.5823i | −0.347944 | + | 0.347944i | ||||
\(926\) | 39.5411 | − | 13.0689i | 1.29940 | − | 0.429471i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 12.1743 | + | 11.5742i | 0.399639 | + | 0.379942i | ||||
\(929\) | −16.1385 | −0.529488 | −0.264744 | − | 0.964319i | \(-0.585287\pi\) | ||||
−0.264744 | + | 0.964319i | \(0.585287\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0581 | + | 15.0581i | −0.493508 | + | 0.493508i | ||||
\(932\) | −13.9699 | − | 18.8249i | −0.457599 | − | 0.616631i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.6105 | − | 34.9985i | 0.576233 | − | 1.14519i | ||||
\(935\) | 29.4844i | 0.964241i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7669i | 1.13579i | 0.823102 | + | 0.567893i | \(0.192241\pi\) | ||||
−0.823102 | + | 0.567893i | \(0.807759\pi\) | |||||||
\(938\) | −0.217923 | − | 0.109654i | −0.00711544 | − | 0.00358033i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.0610 | − | 1.48946i | −0.328153 | − | 0.0485807i | ||||
\(941\) | 37.2662 | − | 37.2662i | 1.21484 | − | 1.21484i | 0.245430 | − | 0.969414i | \(-0.421071\pi\) |
0.969414 | − | 0.245430i | \(-0.0789291\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.36423 | 0.239812 | ||||||||
\(944\) | −19.9495 | + | 10.6779i | −0.649300 | + | 0.347537i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 19.4000 | + | 58.6962i | 0.630747 | + | 1.90838i | ||||
\(947\) | −18.5243 | + | 18.5243i | −0.601957 | + | 0.601957i | −0.940832 | − | 0.338874i | \(-0.889954\pi\) |
0.338874 | + | 0.940832i | \(0.389954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.63994 | + | 5.63994i | 0.183080 | + | 0.183080i | ||||
\(950\) | 6.81722 | + | 3.43027i | 0.221180 | + | 0.111293i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.12254 | + | 0.789861i | 0.0363818 | + | 0.0255996i | ||||
\(953\) | 11.1752i | 0.362000i | 0.983483 | + | 0.181000i | \(0.0579333\pi\) | ||||
−0.983483 | + | 0.181000i | \(0.942067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20.5541 | − | 20.5541i | −0.665115 | − | 0.665115i | ||||
\(956\) | 21.9257 | − | 16.2710i | 0.709128 | − | 0.526241i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −47.7354 | + | 15.7773i | −1.54226 | + | 0.509740i | ||||
\(959\) | 2.19266 | 0.0708047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7032 | −0.442039 | ||||||||
\(962\) | 67.7285 | − | 22.3853i | 2.18366 | − | 0.721730i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.42362 | − | 2.54065i | 0.110267 | − | 0.0818289i | ||||
\(965\) | 28.1541 | + | 28.1541i | 0.906312 | + | 0.906312i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 12.8452i | − | 0.413075i | −0.978439 | − | 0.206537i | \(-0.933780\pi\) | ||
0.978439 | − | 0.206537i | \(-0.0662195\pi\) | |||||||
\(968\) | 41.2870 | + | 29.0510i | 1.32701 | + | 0.933734i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.29814 | + | 0.653195i | 0.0416808 | + | 0.0209728i | ||||
\(971\) | −5.94517 | − | 5.94517i | −0.190790 | − | 0.190790i | 0.605248 | − | 0.796037i | \(-0.293074\pi\) |
−0.796037 | + | 0.605248i | \(0.793074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.385321 | + | 0.385321i | −0.0123528 | + | 0.0123528i | ||||
\(974\) | 4.37873 | + | 13.2482i | 0.140304 | + | 0.424500i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −9.79564 | − | 18.3011i | −0.313551 | − | 0.585803i | ||||
\(977\) | −40.4156 | −1.29301 | −0.646504 | − | 0.762910i | \(-0.723770\pi\) | ||||
−0.646504 | + | 0.762910i | \(0.723770\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.6865 | − | 54.6865i | 1.74779 | − | 1.74779i | ||||
\(980\) | −24.8098 | − | 3.67291i | −0.792521 | − | 0.117327i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.803165 | + | 0.404135i | 0.0256300 | + | 0.0128965i | ||||
\(983\) | − | 13.9202i | − | 0.443985i | −0.975048 | − | 0.221993i | \(-0.928744\pi\) | ||
0.975048 | − | 0.221993i | \(-0.0712561\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 36.3582i | − | 1.15847i | ||||||
\(986\) | 5.76326 | − | 11.4537i | 0.183540 | − | 0.364761i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.6770 | − | 29.2105i | −0.689638 | − | 0.929311i | ||||
\(989\) | 16.2771 | − | 16.2771i | 0.517580 | − | 0.517580i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.0309 | 1.30339 | 0.651695 | − | 0.758481i | \(-0.274058\pi\) | ||||
0.651695 | + | 0.758481i | \(0.274058\pi\) | |||||||
\(992\) | −0.594243 | − | 23.5190i | −0.0188672 | − | 0.746730i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.0678434 | + | 0.0224232i | −0.00215186 | + | 0.000711222i | ||||
\(995\) | 31.7928 | − | 31.7928i | 1.00790 | − | 1.00790i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.3245 | + | 27.3245i | 0.865375 | + | 0.865375i | 0.991956 | − | 0.126581i | \(-0.0404005\pi\) |
−0.126581 | + | 0.991956i | \(0.540400\pi\) | |||||||
\(998\) | 2.43301 | − | 4.83528i | 0.0770155 | − | 0.153058i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 144.2.k.b.37.4 | 8 | ||
3.2 | odd | 2 | 48.2.j.a.37.1 | yes | 8 | ||
4.3 | odd | 2 | 576.2.k.b.433.2 | 8 | |||
8.3 | odd | 2 | 1152.2.k.f.865.3 | 8 | |||
8.5 | even | 2 | 1152.2.k.c.865.3 | 8 | |||
12.11 | even | 2 | 192.2.j.a.49.2 | 8 | |||
16.3 | odd | 4 | 576.2.k.b.145.2 | 8 | |||
16.5 | even | 4 | 1152.2.k.c.289.3 | 8 | |||
16.11 | odd | 4 | 1152.2.k.f.289.3 | 8 | |||
16.13 | even | 4 | inner | 144.2.k.b.109.4 | 8 | ||
24.5 | odd | 2 | 384.2.j.b.97.1 | 8 | |||
24.11 | even | 2 | 384.2.j.a.97.3 | 8 | |||
32.3 | odd | 8 | 9216.2.a.x.1.4 | 4 | |||
32.13 | even | 8 | 9216.2.a.bo.1.1 | 4 | |||
32.19 | odd | 8 | 9216.2.a.bn.1.1 | 4 | |||
32.29 | even | 8 | 9216.2.a.y.1.4 | 4 | |||
48.5 | odd | 4 | 384.2.j.b.289.1 | 8 | |||
48.11 | even | 4 | 384.2.j.a.289.3 | 8 | |||
48.29 | odd | 4 | 48.2.j.a.13.1 | ✓ | 8 | ||
48.35 | even | 4 | 192.2.j.a.145.2 | 8 | |||
96.5 | odd | 8 | 3072.2.d.f.1537.8 | 8 | |||
96.11 | even | 8 | 3072.2.d.i.1537.5 | 8 | |||
96.29 | odd | 8 | 3072.2.a.t.1.1 | 4 | |||
96.35 | even | 8 | 3072.2.a.n.1.1 | 4 | |||
96.53 | odd | 8 | 3072.2.d.f.1537.1 | 8 | |||
96.59 | even | 8 | 3072.2.d.i.1537.4 | 8 | |||
96.77 | odd | 8 | 3072.2.a.i.1.4 | 4 | |||
96.83 | even | 8 | 3072.2.a.o.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.1 | ✓ | 8 | 48.29 | odd | 4 | ||
48.2.j.a.37.1 | yes | 8 | 3.2 | odd | 2 | ||
144.2.k.b.37.4 | 8 | 1.1 | even | 1 | trivial | ||
144.2.k.b.109.4 | 8 | 16.13 | even | 4 | inner | ||
192.2.j.a.49.2 | 8 | 12.11 | even | 2 | |||
192.2.j.a.145.2 | 8 | 48.35 | even | 4 | |||
384.2.j.a.97.3 | 8 | 24.11 | even | 2 | |||
384.2.j.a.289.3 | 8 | 48.11 | even | 4 | |||
384.2.j.b.97.1 | 8 | 24.5 | odd | 2 | |||
384.2.j.b.289.1 | 8 | 48.5 | odd | 4 | |||
576.2.k.b.145.2 | 8 | 16.3 | odd | 4 | |||
576.2.k.b.433.2 | 8 | 4.3 | odd | 2 | |||
1152.2.k.c.289.3 | 8 | 16.5 | even | 4 | |||
1152.2.k.c.865.3 | 8 | 8.5 | even | 2 | |||
1152.2.k.f.289.3 | 8 | 16.11 | odd | 4 | |||
1152.2.k.f.865.3 | 8 | 8.3 | odd | 2 | |||
3072.2.a.i.1.4 | 4 | 96.77 | odd | 8 | |||
3072.2.a.n.1.1 | 4 | 96.35 | even | 8 | |||
3072.2.a.o.1.4 | 4 | 96.83 | even | 8 | |||
3072.2.a.t.1.1 | 4 | 96.29 | odd | 8 | |||
3072.2.d.f.1537.1 | 8 | 96.53 | odd | 8 | |||
3072.2.d.f.1537.8 | 8 | 96.5 | odd | 8 | |||
3072.2.d.i.1537.4 | 8 | 96.59 | even | 8 | |||
3072.2.d.i.1537.5 | 8 | 96.11 | even | 8 | |||
9216.2.a.x.1.4 | 4 | 32.3 | odd | 8 | |||
9216.2.a.y.1.4 | 4 | 32.29 | even | 8 | |||
9216.2.a.bn.1.1 | 4 | 32.19 | odd | 8 | |||
9216.2.a.bo.1.1 | 4 | 32.13 | even | 8 |