Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.173309020416.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 5x^{6} - 28x^{5} - 4x^{4} + 70x^{3} + 51x^{2} + 406x + 841 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.4 | ||
Root | \(-1.75834 - 0.512349i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.n.415.4 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.44864 | + | 2.50912i | 0.647851 | + | 1.12211i | 0.983635 | + | 0.180172i | \(0.0576655\pi\) |
−0.335784 | + | 0.941939i | \(0.609001\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −1.32288 | + | 2.29129i | −0.500000 | + | 0.866025i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −1.44864 | + | 2.50912i | −0.458100 | + | 0.793452i | ||||
\(11\) | −0.809697 | + | 1.40244i | −0.244133 | + | 0.422851i | −0.961887 | − | 0.273446i | \(-0.911837\pi\) |
0.717755 | + | 0.696296i | \(0.245170\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −3.02636 | −0.839360 | −0.419680 | − | 0.907672i | \(-0.637858\pi\) | ||||
−0.419680 | + | 0.907672i | \(0.637858\pi\) | |||||||
\(14\) | −2.64575 | −0.707107 | ||||||||
\(15\) | 2.89728 | 0.748074 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −2.77152 | + | 4.80040i | −0.672191 | + | 1.16427i | 0.305090 | + | 0.952323i | \(0.401313\pi\) |
−0.977281 | + | 0.211946i | \(0.932020\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | −1.38410 | − | 2.39733i | −0.317534 | − | 0.549986i | 0.662439 | − | 0.749116i | \(-0.269522\pi\) |
−0.979973 | + | 0.199131i | \(0.936188\pi\) | |||||||
\(20\) | −2.89728 | −0.647851 | ||||||||
\(21\) | 1.32288 | + | 2.29129i | 0.288675 | + | 0.500000i | ||||
\(22\) | −1.61939 | −0.345256 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | ||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −1.69711 | + | 2.93948i | −0.339422 | + | 0.587897i | ||||
\(26\) | −1.51318 | − | 2.62090i | −0.296759 | − | 0.514001i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.32288 | − | 2.29129i | −0.250000 | − | 0.433013i | ||||
\(29\) | 1.76820 | 0.328347 | 0.164173 | − | 0.986432i | \(-0.447504\pi\) | ||||
0.164173 | + | 0.986432i | \(0.447504\pi\) | |||||||
\(30\) | 1.44864 | + | 2.50912i | 0.264484 | + | 0.458100i | ||||
\(31\) | 0.802888 | − | 1.39064i | 0.144203 | − | 0.249767i | −0.784872 | − | 0.619657i | \(-0.787272\pi\) |
0.929075 | + | 0.369891i | \(0.120605\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0.809697 | + | 1.40244i | 0.140950 | + | 0.244133i | ||||
\(34\) | −5.54303 | −0.950622 | ||||||||
\(35\) | −7.66548 | −1.29570 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 0.513179 | + | 0.888851i | 0.0843660 | + | 0.146126i | 0.905121 | − | 0.425154i | \(-0.139780\pi\) |
−0.820755 | + | 0.571281i | \(0.806447\pi\) | |||||||
\(38\) | 1.38410 | − | 2.39733i | 0.224531 | − | 0.388899i | ||||
\(39\) | −1.51318 | + | 2.62090i | −0.242302 | + | 0.419680i | ||||
\(40\) | −1.44864 | − | 2.50912i | −0.229050 | − | 0.396726i | ||||
\(41\) | 6.76820 | 1.05702 | 0.528508 | − | 0.848929i | \(-0.322752\pi\) | ||||
0.528508 | + | 0.848929i | \(0.322752\pi\) | |||||||
\(42\) | −1.32288 | + | 2.29129i | −0.204124 | + | 0.353553i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | −0.809697 | − | 1.40244i | −0.122066 | − | 0.211425i | ||||
\(45\) | 1.44864 | − | 2.50912i | 0.215950 | − | 0.374037i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | 2.07772 | + | 3.59871i | 0.303066 | + | 0.524926i | 0.976829 | − | 0.214022i | \(-0.0686563\pi\) |
−0.673763 | + | 0.738948i | \(0.735323\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | −3.39422 | −0.480016 | ||||||||
\(51\) | 2.77152 | + | 4.80040i | 0.388090 | + | 0.672191i | ||||
\(52\) | 1.51318 | − | 2.62090i | 0.209840 | − | 0.363454i | ||||
\(53\) | −2.44864 | + | 4.24117i | −0.336346 | + | 0.582569i | −0.983743 | − | 0.179585i | \(-0.942525\pi\) |
0.647396 | + | 0.762154i | \(0.275858\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −4.69184 | −0.632647 | ||||||||
\(56\) | 1.32288 | − | 2.29129i | 0.176777 | − | 0.306186i | ||||
\(57\) | −2.76820 | −0.366657 | ||||||||
\(58\) | 0.884100 | + | 1.53131i | 0.116088 | + | 0.201070i | ||||
\(59\) | 3.47849 | − | 6.02492i | 0.452861 | − | 0.784378i | −0.545701 | − | 0.837980i | \(-0.683737\pi\) |
0.998562 | + | 0.0536015i | \(0.0170701\pi\) | |||||||
\(60\) | −1.44864 | + | 2.50912i | −0.187019 | + | 0.323926i | ||||
\(61\) | 6.89728 | + | 11.9464i | 0.883106 | + | 1.52958i | 0.847869 | + | 0.530206i | \(0.177885\pi\) |
0.0352369 | + | 0.999379i | \(0.488781\pi\) | |||||||
\(62\) | 1.60578 | 0.203934 | ||||||||
\(63\) | 2.64575 | 0.333333 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.38410 | − | 7.59348i | −0.543781 | − | 0.941856i | ||||
\(66\) | −0.809697 | + | 1.40244i | −0.0996668 | + | 0.172628i | ||||
\(67\) | −3.61939 | + | 6.26897i | −0.442179 | + | 0.765877i | −0.997851 | − | 0.0655248i | \(-0.979128\pi\) |
0.555672 | + | 0.831402i | \(0.312461\pi\) | |||||||
\(68\) | −2.77152 | − | 4.80040i | −0.336096 | − | 0.582135i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −3.83274 | − | 6.63850i | −0.458100 | − | 0.793452i | ||||
\(71\) | 4.87092 | 0.578072 | 0.289036 | − | 0.957318i | \(-0.406665\pi\) | ||||
0.289036 | + | 0.957318i | \(0.406665\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −2.56803 | + | 4.44796i | −0.300566 | + | 0.520595i | −0.976264 | − | 0.216583i | \(-0.930509\pi\) |
0.675699 | + | 0.737178i | \(0.263842\pi\) | |||||||
\(74\) | −0.513179 | + | 0.888851i | −0.0596558 | + | 0.103327i | ||||
\(75\) | 1.69711 | + | 2.93948i | 0.195966 | + | 0.339422i | ||||
\(76\) | 2.76820 | 0.317534 | ||||||||
\(77\) | −2.14226 | − | 3.71050i | −0.244133 | − | 0.422851i | ||||
\(78\) | −3.02636 | −0.342667 | ||||||||
\(79\) | 3.44532 | + | 5.96748i | 0.387629 | + | 0.671394i | 0.992130 | − | 0.125211i | \(-0.0399607\pi\) |
−0.604501 | + | 0.796604i | \(0.706627\pi\) | |||||||
\(80\) | 1.44864 | − | 2.50912i | 0.161963 | − | 0.280528i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 3.38410 | + | 5.86143i | 0.373711 | + | 0.647287i | ||||
\(83\) | 5.15544 | 0.565883 | 0.282941 | − | 0.959137i | \(-0.408690\pi\) | ||||
0.282941 | + | 0.959137i | \(0.408690\pi\) | |||||||
\(84\) | −2.64575 | −0.288675 | ||||||||
\(85\) | −16.0597 | −1.74192 | ||||||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | 0.884100 | − | 1.53131i | 0.0947855 | − | 0.164173i | ||||
\(88\) | 0.809697 | − | 1.40244i | 0.0863140 | − | 0.149500i | ||||
\(89\) | 7.28138 | + | 12.6117i | 0.771825 | + | 1.33684i | 0.936562 | + | 0.350502i | \(0.113989\pi\) |
−0.164737 | + | 0.986337i | \(0.552678\pi\) | |||||||
\(90\) | 2.89728 | 0.305400 | ||||||||
\(91\) | 4.00349 | − | 6.93426i | 0.419680 | − | 0.726907i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −0.802888 | − | 1.39064i | −0.0832556 | − | 0.144203i | ||||
\(94\) | −2.07772 | + | 3.59871i | −0.214300 | + | 0.371179i | ||||
\(95\) | 4.01012 | − | 6.94574i | 0.411430 | − | 0.712618i | ||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | −14.6988 | −1.49244 | −0.746220 | − | 0.665700i | \(-0.768133\pi\) | ||||
−0.746220 | + | 0.665700i | \(0.768133\pi\) | |||||||
\(98\) | 3.50000 | − | 6.06218i | 0.353553 | − | 0.612372i | ||||
\(99\) | 1.61939 | 0.162755 | ||||||||
\(100\) | −1.69711 | − | 2.93948i | −0.169711 | − | 0.293948i | ||||
\(101\) | 1.69711 | − | 2.93948i | 0.168869 | − | 0.292490i | −0.769154 | − | 0.639064i | \(-0.779322\pi\) |
0.938022 | + | 0.346574i | \(0.112655\pi\) | |||||||
\(102\) | −2.77152 | + | 4.80040i | −0.274421 | + | 0.475311i | ||||
\(103\) | 5.50986 | + | 9.54336i | 0.542903 | + | 0.940336i | 0.998736 | + | 0.0502701i | \(0.0160082\pi\) |
−0.455833 | + | 0.890066i | \(0.650658\pi\) | |||||||
\(104\) | 3.02636 | 0.296759 | ||||||||
\(105\) | −3.83274 | + | 6.63850i | −0.374037 | + | 0.647851i | ||||
\(106\) | −4.89728 | −0.475666 | ||||||||
\(107\) | −4.57772 | − | 7.92884i | −0.442545 | − | 0.766510i | 0.555333 | − | 0.831628i | \(-0.312591\pi\) |
−0.997878 | + | 0.0651183i | \(0.979258\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −5.28469 | + | 9.15336i | −0.506182 | + | 0.876733i | 0.493793 | + | 0.869580i | \(0.335610\pi\) |
−0.999974 | + | 0.00715295i | \(0.997723\pi\) | |||||||
\(110\) | −2.34592 | − | 4.06325i | −0.223675 | − | 0.387416i | ||||
\(111\) | 1.02636 | 0.0974175 | ||||||||
\(112\) | 2.64575 | 0.250000 | ||||||||
\(113\) | 3.76209 | 0.353908 | 0.176954 | − | 0.984219i | \(-0.443376\pi\) | ||||
0.176954 | + | 0.984219i | \(0.443376\pi\) | |||||||
\(114\) | −1.38410 | − | 2.39733i | −0.129633 | − | 0.224531i | ||||
\(115\) | 1.44864 | − | 2.50912i | 0.135086 | − | 0.233976i | ||||
\(116\) | −0.884100 | + | 1.53131i | −0.0820866 | + | 0.142178i | ||||
\(117\) | 1.51318 | + | 2.62090i | 0.139893 | + | 0.242302i | ||||
\(118\) | 6.95698 | 0.640442 | ||||||||
\(119\) | −7.33274 | − | 12.7007i | −0.672191 | − | 1.16427i | ||||
\(120\) | −2.89728 | −0.264484 | ||||||||
\(121\) | 4.18878 | + | 7.25518i | 0.380798 | + | 0.659562i | ||||
\(122\) | −6.89728 | + | 11.9464i | −0.624450 | + | 1.08158i | ||||
\(123\) | 3.38410 | − | 5.86143i | 0.305134 | − | 0.528508i | ||||
\(124\) | 0.802888 | + | 1.39064i | 0.0721015 | + | 0.124883i | ||||
\(125\) | 4.65238 | 0.416122 | ||||||||
\(126\) | 1.32288 | + | 2.29129i | 0.117851 | + | 0.204124i | ||||
\(127\) | 13.7252 | 1.21791 | 0.608956 | − | 0.793204i | \(-0.291588\pi\) | ||||
0.608956 | + | 0.793204i | \(0.291588\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | 4.38410 | − | 7.59348i | 0.384511 | − | 0.665993i | ||||
\(131\) | −1.45876 | − | 2.52665i | −0.127453 | − | 0.220755i | 0.795236 | − | 0.606300i | \(-0.207347\pi\) |
−0.922689 | + | 0.385545i | \(0.874013\pi\) | |||||||
\(132\) | −1.61939 | −0.140950 | ||||||||
\(133\) | 7.32397 | 0.635069 | ||||||||
\(134\) | −7.23879 | −0.625336 | ||||||||
\(135\) | −1.44864 | − | 2.50912i | −0.124679 | − | 0.215950i | ||||
\(136\) | 2.77152 | − | 4.80040i | 0.237655 | − | 0.411631i | ||||
\(137\) | 5.80137 | − | 10.0483i | 0.495644 | − | 0.858481i | −0.504343 | − | 0.863503i | \(-0.668265\pi\) |
0.999987 | + | 0.00502238i | \(0.00159868\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | −0.155436 | −0.0131839 | −0.00659194 | − | 0.999978i | \(-0.502098\pi\) | ||||
−0.00659194 | + | 0.999978i | \(0.502098\pi\) | |||||||
\(140\) | 3.83274 | − | 6.63850i | 0.323926 | − | 0.561056i | ||||
\(141\) | 4.15544 | 0.349951 | ||||||||
\(142\) | 2.43546 | + | 4.21834i | 0.204379 | + | 0.353995i | ||||
\(143\) | 2.45043 | − | 4.24427i | 0.204915 | − | 0.354924i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 2.56148 | + | 4.43662i | 0.212720 | + | 0.368441i | ||||
\(146\) | −5.13607 | −0.425064 | ||||||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | −1.02636 | −0.0843660 | ||||||||
\(149\) | −8.31786 | − | 14.4070i | −0.681426 | − | 1.18026i | −0.974546 | − | 0.224188i | \(-0.928027\pi\) |
0.293120 | − | 0.956076i | \(-0.405306\pi\) | |||||||
\(150\) | −1.69711 | + | 2.93948i | −0.138569 | + | 0.240008i | ||||
\(151\) | 9.86259 | − | 17.0825i | 0.802606 | − | 1.39015i | −0.115289 | − | 0.993332i | \(-0.536779\pi\) |
0.917895 | − | 0.396823i | \(-0.129887\pi\) | |||||||
\(152\) | 1.38410 | + | 2.39733i | 0.112265 | + | 0.194449i | ||||
\(153\) | 5.54303 | 0.448127 | ||||||||
\(154\) | 2.14226 | − | 3.71050i | 0.172628 | − | 0.299000i | ||||
\(155\) | 4.65238 | 0.373688 | ||||||||
\(156\) | −1.51318 | − | 2.62090i | −0.121151 | − | 0.209840i | ||||
\(157\) | −0.900593 | + | 1.55987i | −0.0718752 | + | 0.124491i | −0.899723 | − | 0.436461i | \(-0.856232\pi\) |
0.827848 | + | 0.560953i | \(0.189565\pi\) | |||||||
\(158\) | −3.44532 | + | 5.96748i | −0.274095 | + | 0.474747i | ||||
\(159\) | 2.44864 | + | 4.24117i | 0.194190 | + | 0.336346i | ||||
\(160\) | 2.89728 | 0.229050 | ||||||||
\(161\) | 2.64575 | 0.208514 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −4.43546 | − | 7.68244i | −0.347412 | − | 0.601735i | 0.638377 | − | 0.769724i | \(-0.279606\pi\) |
−0.985789 | + | 0.167989i | \(0.946273\pi\) | |||||||
\(164\) | −3.38410 | + | 5.86143i | −0.264254 | + | 0.457701i | ||||
\(165\) | −2.34592 | + | 4.06325i | −0.182629 | + | 0.316324i | ||||
\(166\) | 2.57772 | + | 4.46474i | 0.200070 | + | 0.346531i | ||||
\(167\) | −1.26427 | −0.0978319 | −0.0489159 | − | 0.998803i | \(-0.515577\pi\) | ||||
−0.0489159 | + | 0.998803i | \(0.515577\pi\) | |||||||
\(168\) | −1.32288 | − | 2.29129i | −0.102062 | − | 0.176777i | ||||
\(169\) | −3.84116 | −0.295474 | ||||||||
\(170\) | −8.02985 | − | 13.9081i | −0.615861 | − | 1.06670i | ||||
\(171\) | −1.38410 | + | 2.39733i | −0.105845 | + | 0.183329i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | 0.431967 | + | 0.748188i | 0.0328418 | + | 0.0568837i | 0.881979 | − | 0.471288i | \(-0.156211\pi\) |
−0.849137 | + | 0.528172i | \(0.822878\pi\) | |||||||
\(174\) | 1.76820 | 0.134047 | ||||||||
\(175\) | −4.49014 | − | 7.77714i | −0.339422 | − | 0.587897i | ||||
\(176\) | 1.61939 | 0.122066 | ||||||||
\(177\) | −3.47849 | − | 6.02492i | −0.261459 | − | 0.452861i | ||||
\(178\) | −7.28138 | + | 12.6117i | −0.545762 | + | 0.945288i | ||||
\(179\) | 8.93062 | − | 15.4683i | 0.667506 | − | 1.15615i | −0.311093 | − | 0.950379i | \(-0.600695\pi\) |
0.978599 | − | 0.205775i | \(-0.0659716\pi\) | |||||||
\(180\) | 1.44864 | + | 2.50912i | 0.107975 | + | 0.187019i | ||||
\(181\) | 5.30512 | 0.394327 | 0.197163 | − | 0.980371i | \(-0.436827\pi\) | ||||
0.197163 | + | 0.980371i | \(0.436827\pi\) | |||||||
\(182\) | 8.00699 | 0.593517 | ||||||||
\(183\) | 13.7946 | 1.01972 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −1.48682 | + | 2.57525i | −0.109313 | + | 0.189336i | ||||
\(186\) | 0.802888 | − | 1.39064i | 0.0588706 | − | 0.101967i | ||||
\(187\) | −4.48818 | − | 7.77375i | −0.328208 | − | 0.568473i | ||||
\(188\) | −4.15544 | −0.303066 | ||||||||
\(189\) | 1.32288 | − | 2.29129i | 0.0962250 | − | 0.166667i | ||||
\(190\) | 8.02025 | 0.581850 | ||||||||
\(191\) | −9.15230 | − | 15.8522i | −0.662237 | − | 1.14703i | −0.980026 | − | 0.198867i | \(-0.936274\pi\) |
0.317789 | − | 0.948161i | \(-0.397060\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −0.170755 | + | 0.295756i | −0.0122912 | + | 0.0212890i | −0.872106 | − | 0.489318i | \(-0.837246\pi\) |
0.859814 | + | 0.510607i | \(0.170579\pi\) | |||||||
\(194\) | −7.34941 | − | 12.7296i | −0.527657 | − | 0.913929i | ||||
\(195\) | −8.76820 | −0.627904 | ||||||||
\(196\) | 7.00000 | 0.500000 | ||||||||
\(197\) | 20.2476 | 1.44258 | 0.721291 | − | 0.692632i | \(-0.243549\pi\) | ||||
0.721291 | + | 0.692632i | \(0.243549\pi\) | |||||||
\(198\) | 0.809697 | + | 1.40244i | 0.0575427 | + | 0.0996668i | ||||
\(199\) | 13.4471 | − | 23.2911i | 0.953241 | − | 1.65106i | 0.214898 | − | 0.976637i | \(-0.431058\pi\) |
0.738343 | − | 0.674425i | \(-0.235608\pi\) | |||||||
\(200\) | 1.69711 | − | 2.93948i | 0.120004 | − | 0.207853i | ||||
\(201\) | 3.61939 | + | 6.26897i | 0.255292 | + | 0.442179i | ||||
\(202\) | 3.39422 | 0.238817 | ||||||||
\(203\) | −2.33911 | + | 4.05146i | −0.164173 | + | 0.284356i | ||||
\(204\) | −5.54303 | −0.388090 | ||||||||
\(205\) | 9.80468 | + | 16.9822i | 0.684789 | + | 1.18609i | ||||
\(206\) | −5.50986 | + | 9.54336i | −0.383890 | + | 0.664918i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 1.51318 | + | 2.62090i | 0.104920 | + | 0.181727i | ||||
\(209\) | 4.48281 | 0.310082 | ||||||||
\(210\) | −7.66548 | −0.528968 | ||||||||
\(211\) | 6.41359 | 0.441530 | 0.220765 | − | 0.975327i | \(-0.429145\pi\) | ||||
0.220765 | + | 0.975327i | \(0.429145\pi\) | |||||||
\(212\) | −2.44864 | − | 4.24117i | −0.168173 | − | 0.291285i | ||||
\(213\) | 2.43546 | − | 4.21834i | 0.166875 | − | 0.289036i | ||||
\(214\) | 4.57772 | − | 7.92884i | 0.312926 | − | 0.542004i | ||||
\(215\) | 2.89728 | + | 5.01823i | 0.197593 | + | 0.342241i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.12424 | + | 3.67930i | 0.144203 | + | 0.249767i | ||||
\(218\) | −10.5694 | −0.715849 | ||||||||
\(219\) | 2.56803 | + | 4.44796i | 0.173532 | + | 0.300566i | ||||
\(220\) | 2.34592 | − | 4.06325i | 0.158162 | − | 0.273944i | ||||
\(221\) | 8.38759 | − | 14.5277i | 0.564211 | − | 0.977242i | ||||
\(222\) | 0.513179 | + | 0.888851i | 0.0344423 | + | 0.0596558i | ||||
\(223\) | −16.1888 | −1.08408 | −0.542040 | − | 0.840352i | \(-0.682348\pi\) | ||||
−0.542040 | + | 0.840352i | \(0.682348\pi\) | |||||||
\(224\) | 1.32288 | + | 2.29129i | 0.0883883 | + | 0.153093i | ||||
\(225\) | 3.39422 | 0.226282 | ||||||||
\(226\) | 1.88105 | + | 3.25807i | 0.125125 | + | 0.216723i | ||||
\(227\) | −11.4554 | + | 19.8414i | −0.760325 | + | 1.31692i | 0.182358 | + | 0.983232i | \(0.441627\pi\) |
−0.942683 | + | 0.333689i | \(0.891706\pi\) | |||||||
\(228\) | 1.38410 | − | 2.39733i | 0.0916643 | − | 0.158767i | ||||
\(229\) | 2.58273 | + | 4.47343i | 0.170672 | + | 0.295612i | 0.938655 | − | 0.344858i | \(-0.112073\pi\) |
−0.767983 | + | 0.640470i | \(0.778740\pi\) | |||||||
\(230\) | 2.89728 | 0.191041 | ||||||||
\(231\) | −4.28451 | −0.281900 | ||||||||
\(232\) | −1.76820 | −0.116088 | ||||||||
\(233\) | −5.54652 | − | 9.60686i | −0.363365 | − | 0.629366i | 0.625147 | − | 0.780507i | \(-0.285039\pi\) |
−0.988512 | + | 0.151140i | \(0.951705\pi\) | |||||||
\(234\) | −1.51318 | + | 2.62090i | −0.0989196 | + | 0.171334i | ||||
\(235\) | −6.01973 | + | 10.4265i | −0.392684 | + | 0.680148i | ||||
\(236\) | 3.47849 | + | 6.02492i | 0.226430 | + | 0.392189i | ||||
\(237\) | 6.89065 | 0.447596 | ||||||||
\(238\) | 7.33274 | − | 12.7007i | 0.475311 | − | 0.823263i | ||||
\(239\) | −5.63912 | −0.364764 | −0.182382 | − | 0.983228i | \(-0.558381\pi\) | ||||
−0.182382 | + | 0.983228i | \(0.558381\pi\) | |||||||
\(240\) | −1.44864 | − | 2.50912i | −0.0935093 | − | 0.161963i | ||||
\(241\) | −12.0479 | + | 20.8675i | −0.776072 | + | 1.34420i | 0.158118 | + | 0.987420i | \(0.449457\pi\) |
−0.934190 | + | 0.356776i | \(0.883876\pi\) | |||||||
\(242\) | −4.18878 | + | 7.25518i | −0.269265 | + | 0.466381i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −13.7946 | −0.883106 | ||||||||
\(245\) | 10.1405 | − | 17.5638i | 0.647851 | − | 1.12211i | ||||
\(246\) | 6.76820 | 0.431525 | ||||||||
\(247\) | 4.18878 | + | 7.25518i | 0.266526 | + | 0.461636i | ||||
\(248\) | −0.802888 | + | 1.39064i | −0.0509834 | + | 0.0883059i | ||||
\(249\) | 2.57772 | − | 4.46474i | 0.163356 | − | 0.282941i | ||||
\(250\) | 2.32619 | + | 4.02908i | 0.147121 | + | 0.254821i | ||||
\(251\) | 17.9970 | 1.13596 | 0.567979 | − | 0.823043i | \(-0.307726\pi\) | ||||
0.567979 | + | 0.823043i | \(0.307726\pi\) | |||||||
\(252\) | −1.32288 | + | 2.29129i | −0.0833333 | + | 0.144338i | ||||
\(253\) | 1.61939 | 0.101810 | ||||||||
\(254\) | 6.86259 | + | 11.8864i | 0.430597 | + | 0.745816i | ||||
\(255\) | −8.02985 | + | 13.9081i | −0.502849 | + | 0.870960i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.635628 | − | 1.10094i | −0.0396494 | − | 0.0686747i | 0.845520 | − | 0.533944i | \(-0.179291\pi\) |
−0.885169 | + | 0.465269i | \(0.845957\pi\) | |||||||
\(258\) | 2.00000 | 0.124515 | ||||||||
\(259\) | −2.71549 | −0.168732 | ||||||||
\(260\) | 8.76820 | 0.543781 | ||||||||
\(261\) | −0.884100 | − | 1.53131i | −0.0547244 | − | 0.0947855i | ||||
\(262\) | 1.45876 | − | 2.52665i | 0.0901227 | − | 0.156097i | ||||
\(263\) | 13.3639 | − | 23.1470i | 0.824056 | − | 1.42731i | −0.0785824 | − | 0.996908i | \(-0.525039\pi\) |
0.902639 | − | 0.430399i | \(-0.141627\pi\) | |||||||
\(264\) | −0.809697 | − | 1.40244i | −0.0498334 | − | 0.0863140i | ||||
\(265\) | −14.1888 | −0.871610 | ||||||||
\(266\) | 3.66198 | + | 6.34274i | 0.224531 | + | 0.388899i | ||||
\(267\) | 14.5628 | 0.891226 | ||||||||
\(268\) | −3.61939 | − | 6.26897i | −0.221090 | − | 0.382939i | ||||
\(269\) | −12.5759 | + | 21.7822i | −0.766768 | + | 1.32808i | 0.172538 | + | 0.985003i | \(0.444803\pi\) |
−0.939307 | + | 0.343079i | \(0.888530\pi\) | |||||||
\(270\) | 1.44864 | − | 2.50912i | 0.0881614 | − | 0.152700i | ||||
\(271\) | 10.8429 | + | 18.7804i | 0.658657 | + | 1.14083i | 0.980964 | + | 0.194192i | \(0.0622085\pi\) |
−0.322306 | + | 0.946635i | \(0.604458\pi\) | |||||||
\(272\) | 5.54303 | 0.336096 | ||||||||
\(273\) | −4.00349 | − | 6.93426i | −0.242302 | − | 0.419680i | ||||
\(274\) | 11.6027 | 0.700947 | ||||||||
\(275\) | −2.74829 | − | 4.76018i | −0.165728 | − | 0.287050i | ||||
\(276\) | 0.500000 | − | 0.866025i | 0.0300965 | − | 0.0521286i | ||||
\(277\) | −4.88454 | + | 8.46027i | −0.293484 | + | 0.508328i | −0.974631 | − | 0.223818i | \(-0.928148\pi\) |
0.681147 | + | 0.732146i | \(0.261481\pi\) | |||||||
\(278\) | −0.0777178 | − | 0.134611i | −0.00466121 | − | 0.00807345i | ||||
\(279\) | −1.60578 | −0.0961353 | ||||||||
\(280\) | 7.66548 | 0.458100 | ||||||||
\(281\) | −2.80730 | −0.167469 | −0.0837346 | − | 0.996488i | \(-0.526685\pi\) | ||||
−0.0837346 | + | 0.996488i | \(0.526685\pi\) | |||||||
\(282\) | 2.07772 | + | 3.59871i | 0.123726 | + | 0.214300i | ||||
\(283\) | −12.9570 | + | 22.4422i | −0.770213 | + | 1.33405i | 0.167234 | + | 0.985917i | \(0.446517\pi\) |
−0.937446 | + | 0.348130i | \(0.886817\pi\) | |||||||
\(284\) | −2.43546 | + | 4.21834i | −0.144518 | + | 0.250313i | ||||
\(285\) | −4.01012 | − | 6.94574i | −0.237539 | − | 0.411430i | ||||
\(286\) | 4.90087 | 0.289794 | ||||||||
\(287\) | −8.95349 | + | 15.5079i | −0.528508 | + | 0.915402i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −6.86259 | − | 11.8864i | −0.403682 | − | 0.699197i | ||||
\(290\) | −2.56148 | + | 4.43662i | −0.150416 | + | 0.260527i | ||||
\(291\) | −7.34941 | + | 12.7296i | −0.430830 | + | 0.746220i | ||||
\(292\) | −2.56803 | − | 4.44796i | −0.150283 | − | 0.260297i | ||||
\(293\) | 31.3143 | 1.82940 | 0.914700 | − | 0.404133i | \(-0.132427\pi\) | ||||
0.914700 | + | 0.404133i | \(0.132427\pi\) | |||||||
\(294\) | −3.50000 | − | 6.06218i | −0.204124 | − | 0.353553i | ||||
\(295\) | 20.1563 | 1.17355 | ||||||||
\(296\) | −0.513179 | − | 0.888851i | −0.0298279 | − | 0.0516634i | ||||
\(297\) | 0.809697 | − | 1.40244i | 0.0469834 | − | 0.0813776i | ||||
\(298\) | 8.31786 | − | 14.4070i | 0.481841 | − | 0.834573i | ||||
\(299\) | 1.51318 | + | 2.62090i | 0.0875094 | + | 0.151571i | ||||
\(300\) | −3.39422 | −0.195966 | ||||||||
\(301\) | −2.64575 | + | 4.58258i | −0.152499 | + | 0.264135i | ||||
\(302\) | 19.7252 | 1.13506 | ||||||||
\(303\) | −1.69711 | − | 2.93948i | −0.0974965 | − | 0.168869i | ||||
\(304\) | −1.38410 | + | 2.39733i | −0.0793836 | + | 0.137496i | ||||
\(305\) | −19.9833 | + | 34.6122i | −1.14424 | + | 1.98189i | ||||
\(306\) | 2.77152 | + | 4.80040i | 0.158437 | + | 0.274421i | ||||
\(307\) | −13.6067 | −0.776573 | −0.388286 | − | 0.921539i | \(-0.626933\pi\) | ||||
−0.388286 | + | 0.921539i | \(0.626933\pi\) | |||||||
\(308\) | 4.28451 | 0.244133 | ||||||||
\(309\) | 11.0197 | 0.626890 | ||||||||
\(310\) | 2.32619 | + | 4.02908i | 0.132119 | + | 0.228836i | ||||
\(311\) | 7.38545 | − | 12.7920i | 0.418791 | − | 0.725367i | −0.577027 | − | 0.816725i | \(-0.695787\pi\) |
0.995818 | + | 0.0913580i | \(0.0291208\pi\) | |||||||
\(312\) | 1.51318 | − | 2.62090i | 0.0856669 | − | 0.148379i | ||||
\(313\) | −1.34242 | − | 2.32515i | −0.0758783 | − | 0.131425i | 0.825590 | − | 0.564271i | \(-0.190843\pi\) |
−0.901468 | + | 0.432846i | \(0.857509\pi\) | |||||||
\(314\) | −1.80119 | −0.101647 | ||||||||
\(315\) | 3.83274 | + | 6.63850i | 0.215950 | + | 0.374037i | ||||
\(316\) | −6.89065 | −0.387629 | ||||||||
\(317\) | −5.52151 | − | 9.56353i | −0.310119 | − | 0.537142i | 0.668269 | − | 0.743920i | \(-0.267036\pi\) |
−0.978388 | + | 0.206778i | \(0.933702\pi\) | |||||||
\(318\) | −2.44864 | + | 4.24117i | −0.137313 | + | 0.237833i | ||||
\(319\) | −1.43171 | + | 2.47979i | −0.0801602 | + | 0.138841i | ||||
\(320\) | 1.44864 | + | 2.50912i | 0.0809814 | + | 0.140264i | ||||
\(321\) | −9.15544 | −0.511007 | ||||||||
\(322\) | 1.32288 | + | 2.29129i | 0.0737210 | + | 0.127688i | ||||
\(323\) | 15.3442 | 0.853775 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 5.13607 | − | 8.89593i | 0.284898 | − | 0.493457i | ||||
\(326\) | 4.43546 | − | 7.68244i | 0.245657 | − | 0.425491i | ||||
\(327\) | 5.28469 | + | 9.15336i | 0.292244 | + | 0.506182i | ||||
\(328\) | −6.76820 | −0.373711 | ||||||||
\(329\) | −10.9942 | −0.606133 | ||||||||
\(330\) | −4.69184 | −0.258277 | ||||||||
\(331\) | −4.14619 | − | 7.18141i | −0.227895 | − | 0.394726i | 0.729289 | − | 0.684206i | \(-0.239851\pi\) |
−0.957184 | + | 0.289480i | \(0.906518\pi\) | |||||||
\(332\) | −2.57772 | + | 4.46474i | −0.141471 | + | 0.245034i | ||||
\(333\) | 0.513179 | − | 0.888851i | 0.0281220 | − | 0.0487088i | ||||
\(334\) | −0.632133 | − | 1.09489i | −0.0345888 | − | 0.0599095i | ||||
\(335\) | −20.9728 | −1.14587 | ||||||||
\(336\) | 1.32288 | − | 2.29129i | 0.0721688 | − | 0.125000i | ||||
\(337\) | −25.0624 | −1.36524 | −0.682618 | − | 0.730775i | \(-0.739159\pi\) | ||||
−0.682618 | + | 0.730775i | \(0.739159\pi\) | |||||||
\(338\) | −1.92058 | − | 3.32654i | −0.104466 | − | 0.180940i | ||||
\(339\) | 1.88105 | − | 3.25807i | 0.102164 | − | 0.176954i | ||||
\(340\) | 8.02985 | − | 13.9081i | 0.435480 | − | 0.754273i | ||||
\(341\) | 1.30019 | + | 2.25200i | 0.0704094 | + | 0.121953i | ||||
\(342\) | −2.76820 | −0.149687 | ||||||||
\(343\) | 18.5203 | 1.00000 | ||||||||
\(344\) | −2.00000 | −0.107833 | ||||||||
\(345\) | −1.44864 | − | 2.50912i | −0.0779921 | − | 0.135086i | ||||
\(346\) | −0.431967 | + | 0.748188i | −0.0232227 | + | 0.0402228i | ||||
\(347\) | −3.39422 | + | 5.87897i | −0.182211 | + | 0.315600i | −0.942633 | − | 0.333830i | \(-0.891659\pi\) |
0.760422 | + | 0.649429i | \(0.224992\pi\) | |||||||
\(348\) | 0.884100 | + | 1.53131i | 0.0473927 | + | 0.0820866i | ||||
\(349\) | 12.0070 | 0.642719 | 0.321360 | − | 0.946957i | \(-0.395860\pi\) | ||||
0.321360 | + | 0.946957i | \(0.395860\pi\) | |||||||
\(350\) | 4.49014 | − | 7.77714i | 0.240008 | − | 0.415706i | ||||
\(351\) | 3.02636 | 0.161535 | ||||||||
\(352\) | 0.809697 | + | 1.40244i | 0.0431570 | + | 0.0747501i | ||||
\(353\) | −10.4632 | + | 18.1227i | −0.556898 | + | 0.964576i | 0.440855 | + | 0.897578i | \(0.354675\pi\) |
−0.997753 | + | 0.0669979i | \(0.978658\pi\) | |||||||
\(354\) | 3.47849 | − | 6.02492i | 0.184880 | − | 0.320221i | ||||
\(355\) | 7.05621 | + | 12.2217i | 0.374505 | + | 0.648661i | ||||
\(356\) | −14.5628 | −0.771825 | ||||||||
\(357\) | −14.6655 | −0.776179 | ||||||||
\(358\) | 17.8612 | 0.943996 | ||||||||
\(359\) | 5.01362 | + | 8.68384i | 0.264609 | + | 0.458316i | 0.967461 | − | 0.253020i | \(-0.0814239\pi\) |
−0.702852 | + | 0.711336i | \(0.748091\pi\) | |||||||
\(360\) | −1.44864 | + | 2.50912i | −0.0763500 | + | 0.132242i | ||||
\(361\) | 5.66853 | − | 9.81819i | 0.298344 | − | 0.516747i | ||||
\(362\) | 2.65256 | + | 4.59437i | 0.139415 | + | 0.241475i | ||||
\(363\) | 8.37756 | 0.439708 | ||||||||
\(364\) | 4.00349 | + | 6.93426i | 0.209840 | + | 0.363454i | ||||
\(365\) | −14.8806 | −0.778887 | ||||||||
\(366\) | 6.89728 | + | 11.9464i | 0.360527 | + | 0.624450i | ||||
\(367\) | 12.1242 | − | 20.9998i | 0.632880 | − | 1.09618i | −0.354080 | − | 0.935215i | \(-0.615206\pi\) |
0.986960 | − | 0.160966i | \(-0.0514608\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | −3.38410 | − | 5.86143i | −0.176169 | − | 0.305134i | ||||
\(370\) | −2.97364 | −0.154592 | ||||||||
\(371\) | −6.47849 | − | 11.2211i | −0.336346 | − | 0.582569i | ||||
\(372\) | 1.60578 | 0.0832556 | ||||||||
\(373\) | −17.4599 | − | 30.2414i | −0.904037 | − | 1.56584i | −0.822205 | − | 0.569192i | \(-0.807256\pi\) |
−0.0818326 | − | 0.996646i | \(-0.526077\pi\) | |||||||
\(374\) | 4.48818 | − | 7.77375i | 0.232078 | − | 0.401971i | ||||
\(375\) | 2.32619 | − | 4.02908i | 0.120124 | − | 0.208061i | ||||
\(376\) | −2.07772 | − | 3.59871i | −0.107150 | − | 0.185589i | ||||
\(377\) | −5.35121 | −0.275601 | ||||||||
\(378\) | 2.64575 | 0.136083 | ||||||||
\(379\) | 3.76732 | 0.193514 | 0.0967571 | − | 0.995308i | \(-0.469153\pi\) | ||||
0.0967571 | + | 0.995308i | \(0.469153\pi\) | |||||||
\(380\) | 4.01012 | + | 6.94574i | 0.205715 | + | 0.356309i | ||||
\(381\) | 6.86259 | − | 11.8864i | 0.351581 | − | 0.608956i | ||||
\(382\) | 9.15230 | − | 15.8522i | 0.468272 | − | 0.811072i | ||||
\(383\) | −16.6826 | − | 28.8951i | −0.852441 | − | 1.47647i | −0.878999 | − | 0.476823i | \(-0.841788\pi\) |
0.0265587 | − | 0.999647i | \(-0.491545\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 6.20672 | − | 10.7503i | 0.316324 | − | 0.547888i | ||||
\(386\) | −0.341510 | −0.0173824 | ||||||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 7.34941 | − | 12.7296i | 0.373110 | − | 0.646245i | ||||
\(389\) | 13.1752 | − | 22.8201i | 0.668007 | − | 1.15702i | −0.310453 | − | 0.950589i | \(-0.600481\pi\) |
0.978461 | − | 0.206434i | \(-0.0661858\pi\) | |||||||
\(390\) | −4.38410 | − | 7.59348i | −0.221998 | − | 0.384511i | ||||
\(391\) | 5.54303 | 0.280323 | ||||||||
\(392\) | 3.50000 | + | 6.06218i | 0.176777 | + | 0.306186i | ||||
\(393\) | −2.91753 | −0.147170 | ||||||||
\(394\) | 10.1238 | + | 17.5349i | 0.510030 | + | 0.883398i | ||||
\(395\) | −9.98207 | + | 17.2894i | −0.502252 | + | 0.869926i | ||||
\(396\) | −0.809697 | + | 1.40244i | −0.0406888 | + | 0.0704751i | ||||
\(397\) | 6.39073 | + | 11.0691i | 0.320742 | + | 0.555541i | 0.980641 | − | 0.195813i | \(-0.0627346\pi\) |
−0.659900 | + | 0.751354i | \(0.729401\pi\) | |||||||
\(398\) | 26.8942 | 1.34809 | ||||||||
\(399\) | 3.66198 | − | 6.34274i | 0.183329 | − | 0.317534i | ||||
\(400\) | 3.39422 | 0.169711 | ||||||||
\(401\) | −3.61957 | − | 6.26929i | −0.180753 | − | 0.313073i | 0.761384 | − | 0.648301i | \(-0.224520\pi\) |
−0.942137 | + | 0.335228i | \(0.891187\pi\) | |||||||
\(402\) | −3.61939 | + | 6.26897i | −0.180519 | + | 0.312668i | ||||
\(403\) | −2.42983 | + | 4.20858i | −0.121038 | + | 0.209644i | ||||
\(404\) | 1.69711 | + | 2.93948i | 0.0844345 | + | 0.146245i | ||||
\(405\) | −2.89728 | −0.143967 | ||||||||
\(406\) | −4.67822 | −0.232176 | ||||||||
\(407\) | −1.66208 | −0.0823861 | ||||||||
\(408\) | −2.77152 | − | 4.80040i | −0.137210 | − | 0.237655i | ||||
\(409\) | −14.1988 | + | 24.5931i | −0.702087 | + | 1.21605i | 0.265646 | + | 0.964071i | \(0.414415\pi\) |
−0.967733 | + | 0.251979i | \(0.918919\pi\) | |||||||
\(410\) | −9.80468 | + | 16.9822i | −0.484219 | + | 0.838691i | ||||
\(411\) | −5.80137 | − | 10.0483i | −0.286160 | − | 0.495644i | ||||
\(412\) | −11.0197 | −0.542903 | ||||||||
\(413\) | 9.20322 | + | 15.9404i | 0.452861 | + | 0.784378i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 7.46837 | + | 12.9356i | 0.366608 | + | 0.634983i | ||||
\(416\) | −1.51318 | + | 2.62090i | −0.0741897 | + | 0.128500i | ||||
\(417\) | −0.0777178 | + | 0.134611i | −0.00380586 | + | 0.00659194i | ||||
\(418\) | 2.24140 | + | 3.88222i | 0.109631 | + | 0.189886i | ||||
\(419\) | 16.3112 | 0.796856 | 0.398428 | − | 0.917200i | \(-0.369556\pi\) | ||||
0.398428 | + | 0.917200i | \(0.369556\pi\) | |||||||
\(420\) | −3.83274 | − | 6.63850i | −0.187019 | − | 0.323926i | ||||
\(421\) | −35.7221 | −1.74099 | −0.870495 | − | 0.492177i | \(-0.836201\pi\) | ||||
−0.870495 | + | 0.492177i | \(0.836201\pi\) | |||||||
\(422\) | 3.20680 | + | 5.55433i | 0.156104 | + | 0.270381i | ||||
\(423\) | 2.07772 | − | 3.59871i | 0.101022 | − | 0.174975i | ||||
\(424\) | 2.44864 | − | 4.24117i | 0.118916 | − | 0.205969i | ||||
\(425\) | −9.40714 | − | 16.2936i | −0.456313 | − | 0.790358i | ||||
\(426\) | 4.87092 | 0.235997 | ||||||||
\(427\) | −36.4970 | −1.76621 | ||||||||
\(428\) | 9.15544 | 0.442545 | ||||||||
\(429\) | −2.45043 | − | 4.24427i | −0.118308 | − | 0.204915i | ||||
\(430\) | −2.89728 | + | 5.01823i | −0.139719 | + | 0.242001i | ||||
\(431\) | −12.7252 | + | 22.0407i | −0.612950 | + | 1.06166i | 0.377790 | + | 0.925891i | \(0.376684\pi\) |
−0.990740 | + | 0.135770i | \(0.956649\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 35.4496 | 1.70360 | 0.851801 | − | 0.523866i | \(-0.175511\pi\) | ||||
0.851801 | + | 0.523866i | \(0.175511\pi\) | |||||||
\(434\) | −2.12424 | + | 3.67930i | −0.101967 | + | 0.176612i | ||||
\(435\) | 5.12297 | 0.245628 | ||||||||
\(436\) | −5.28469 | − | 9.15336i | −0.253091 | − | 0.438366i | ||||
\(437\) | −1.38410 | + | 2.39733i | −0.0662105 | + | 0.114680i | ||||
\(438\) | −2.56803 | + | 4.44796i | −0.122705 | + | 0.212532i | ||||
\(439\) | −8.66378 | − | 15.0061i | −0.413500 | − | 0.716202i | 0.581770 | − | 0.813353i | \(-0.302360\pi\) |
−0.995270 | + | 0.0971510i | \(0.969027\pi\) | |||||||
\(440\) | 4.69184 | 0.223675 | ||||||||
\(441\) | −3.50000 | + | 6.06218i | −0.166667 | + | 0.288675i | ||||
\(442\) | 16.7752 | 0.797914 | ||||||||
\(443\) | 11.8924 | + | 20.5983i | 0.565027 | + | 0.978655i | 0.997047 | + | 0.0767915i | \(0.0244676\pi\) |
−0.432020 | + | 0.901864i | \(0.642199\pi\) | |||||||
\(444\) | −0.513179 | + | 0.888851i | −0.0243544 | + | 0.0421830i | ||||
\(445\) | −21.0962 | + | 36.5397i | −1.00006 | + | 1.73215i | ||||
\(446\) | −8.09439 | − | 14.0199i | −0.383281 | − | 0.663861i | ||||
\(447\) | −16.6357 | −0.786843 | ||||||||
\(448\) | −1.32288 | + | 2.29129i | −0.0625000 | + | 0.108253i | ||||
\(449\) | −30.3846 | −1.43394 | −0.716968 | − | 0.697106i | \(-0.754471\pi\) | ||||
−0.716968 | + | 0.697106i | \(0.754471\pi\) | |||||||
\(450\) | 1.69711 | + | 2.93948i | 0.0800026 | + | 0.138569i | ||||
\(451\) | −5.48019 | + | 9.49197i | −0.258052 | + | 0.446959i | ||||
\(452\) | −1.88105 | + | 3.25807i | −0.0884769 | + | 0.153247i | ||||
\(453\) | −9.86259 | − | 17.0825i | −0.463385 | − | 0.802606i | ||||
\(454\) | −22.9109 | −1.07526 | ||||||||
\(455\) | 23.1985 | 1.08756 | ||||||||
\(456\) | 2.76820 | 0.129633 | ||||||||
\(457\) | −10.7103 | − | 18.5508i | −0.501006 | − | 0.867768i | −0.999999 | − | 0.00116232i | \(-0.999630\pi\) |
0.498993 | − | 0.866606i | \(-0.333703\pi\) | |||||||
\(458\) | −2.58273 | + | 4.47343i | −0.120683 | + | 0.209029i | ||||
\(459\) | 2.77152 | − | 4.80040i | 0.129363 | − | 0.224064i | ||||
\(460\) | 1.44864 | + | 2.50912i | 0.0675432 | + | 0.116988i | ||||
\(461\) | −19.1660 | −0.892650 | −0.446325 | − | 0.894871i | \(-0.647267\pi\) | ||||
−0.446325 | + | 0.894871i | \(0.647267\pi\) | |||||||
\(462\) | −2.14226 | − | 3.71050i | −0.0996668 | − | 0.172628i | ||||
\(463\) | 7.72787 | 0.359144 | 0.179572 | − | 0.983745i | \(-0.442529\pi\) | ||||
0.179572 | + | 0.983745i | \(0.442529\pi\) | |||||||
\(464\) | −0.884100 | − | 1.53131i | −0.0410433 | − | 0.0710891i | ||||
\(465\) | 2.32619 | − | 4.02908i | 0.107874 | − | 0.186844i | ||||
\(466\) | 5.54652 | − | 9.60686i | 0.256938 | − | 0.445029i | ||||
\(467\) | −2.61259 | − | 4.52513i | −0.120896 | − | 0.209398i | 0.799225 | − | 0.601032i | \(-0.205243\pi\) |
−0.920121 | + | 0.391634i | \(0.871910\pi\) | |||||||
\(468\) | −3.02636 | −0.139893 | ||||||||
\(469\) | −9.57602 | − | 16.5861i | −0.442179 | − | 0.765877i | ||||
\(470\) | −12.0395 | −0.555339 | ||||||||
\(471\) | 0.900593 | + | 1.55987i | 0.0414972 | + | 0.0718752i | ||||
\(472\) | −3.47849 | + | 6.02492i | −0.160111 | + | 0.277320i | ||||
\(473\) | −1.61939 | + | 2.80487i | −0.0744598 | + | 0.128968i | ||||
\(474\) | 3.44532 | + | 5.96748i | 0.158249 | + | 0.274095i | ||||
\(475\) | 9.39589 | 0.431113 | ||||||||
\(476\) | 14.6655 | 0.672191 | ||||||||
\(477\) | 4.89728 | 0.224231 | ||||||||
\(478\) | −2.81956 | − | 4.88362i | −0.128964 | − | 0.223372i | ||||
\(479\) | −7.38410 | + | 12.7896i | −0.337388 | + | 0.584373i | −0.983941 | − | 0.178496i | \(-0.942877\pi\) |
0.646552 | + | 0.762870i | \(0.276210\pi\) | |||||||
\(480\) | 1.44864 | − | 2.50912i | 0.0661210 | − | 0.114525i | ||||
\(481\) | −1.55306 | − | 2.68998i | −0.0708135 | − | 0.122653i | ||||
\(482\) | −24.0958 | −1.09753 | ||||||||
\(483\) | 1.32288 | − | 2.29129i | 0.0601929 | − | 0.104257i | ||||
\(484\) | −8.37756 | −0.380798 | ||||||||
\(485\) | −21.2933 | − | 36.8811i | −0.966879 | − | 1.67468i | ||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −5.08077 | + | 8.80016i | −0.230232 | + | 0.398773i | −0.957876 | − | 0.287181i | \(-0.907282\pi\) |
0.727644 | + | 0.685954i | \(0.240615\pi\) | |||||||
\(488\) | −6.89728 | − | 11.9464i | −0.312225 | − | 0.540790i | ||||
\(489\) | −8.87092 | −0.401157 | ||||||||
\(490\) | 20.2810 | 0.916200 | ||||||||
\(491\) | 7.02976 | 0.317249 | 0.158624 | − | 0.987339i | \(-0.449294\pi\) | ||||
0.158624 | + | 0.987339i | \(0.449294\pi\) | |||||||
\(492\) | 3.38410 | + | 5.86143i | 0.152567 | + | 0.264254i | ||||
\(493\) | −4.90059 | + | 8.48808i | −0.220712 | + | 0.382284i | ||||
\(494\) | −4.18878 | + | 7.25518i | −0.188462 | + | 0.326426i | ||||
\(495\) | 2.34592 | + | 4.06325i | 0.105441 | + | 0.182629i | ||||
\(496\) | −1.60578 | −0.0721015 | ||||||||
\(497\) | −6.44362 | + | 11.1607i | −0.289036 | + | 0.500625i | ||||
\(498\) | 5.15544 | 0.231021 | ||||||||
\(499\) | −19.8293 | − | 34.3453i | −0.887679 | − | 1.53751i | −0.842611 | − | 0.538522i | \(-0.818983\pi\) |
−0.0450680 | − | 0.998984i | \(-0.514350\pi\) | |||||||
\(500\) | −2.32619 | + | 4.02908i | −0.104030 | + | 0.180186i | ||||
\(501\) | −0.632133 | + | 1.09489i | −0.0282416 | + | 0.0489159i | ||||
\(502\) | 8.99848 | + | 15.5858i | 0.401622 | + | 0.695629i | ||||
\(503\) | 26.6752 | 1.18939 | 0.594694 | − | 0.803952i | \(-0.297273\pi\) | ||||
0.594694 | + | 0.803952i | \(0.297273\pi\) | |||||||
\(504\) | −2.64575 | −0.117851 | ||||||||
\(505\) | 9.83401 | 0.437608 | ||||||||
\(506\) | 0.809697 | + | 1.40244i | 0.0359954 | + | 0.0623459i | ||||
\(507\) | −1.92058 | + | 3.32654i | −0.0852960 | + | 0.147737i | ||||
\(508\) | −6.86259 | + | 11.8864i | −0.304478 | + | 0.527372i | ||||
\(509\) | −18.3644 | − | 31.8080i | −0.813987 | − | 1.40987i | −0.910053 | − | 0.414492i | \(-0.863959\pi\) |
0.0960660 | − | 0.995375i | \(-0.469374\pi\) | |||||||
\(510\) | −16.0597 | −0.711136 | ||||||||
\(511\) | −6.79438 | − | 11.7682i | −0.300566 | − | 0.520595i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.38410 | + | 2.39733i | 0.0611095 | + | 0.105845i | ||||
\(514\) | 0.635628 | − | 1.10094i | 0.0280363 | − | 0.0485603i | ||||
\(515\) | −15.9636 | + | 27.6498i | −0.703441 | + | 1.21840i | ||||
\(516\) | 1.00000 | + | 1.73205i | 0.0440225 | + | 0.0762493i | ||||
\(517\) | −6.72929 | −0.295954 | ||||||||
\(518\) | −1.35774 | − | 2.35168i | −0.0596558 | − | 0.103327i | ||||
\(519\) | 0.863933 | 0.0379225 | ||||||||
\(520\) | 4.38410 | + | 7.59348i | 0.192256 | + | 0.332996i | ||||
\(521\) | −4.39422 | + | 7.61102i | −0.192514 | + | 0.333445i | −0.946083 | − | 0.323925i | \(-0.894998\pi\) |
0.753568 | + | 0.657369i | \(0.228331\pi\) | |||||||
\(522\) | 0.884100 | − | 1.53131i | 0.0386960 | − | 0.0670235i | ||||
\(523\) | −19.2415 | − | 33.3272i | −0.841372 | − | 1.45730i | −0.888735 | − | 0.458421i | \(-0.848415\pi\) |
0.0473633 | − | 0.998878i | \(-0.484918\pi\) | |||||||
\(524\) | 2.91753 | 0.127453 | ||||||||
\(525\) | −8.98027 | −0.391931 | ||||||||
\(526\) | 26.7279 | 1.16539 | ||||||||
\(527\) | 4.45043 | + | 7.70838i | 0.193864 | + | 0.335782i | ||||
\(528\) | 0.809697 | − | 1.40244i | 0.0352375 | − | 0.0610332i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −7.09439 | − | 12.2878i | −0.308161 | − | 0.533750i | ||||
\(531\) | −6.95698 | −0.301907 | ||||||||
\(532\) | −3.66198 | + | 6.34274i | −0.158767 | + | 0.274993i | ||||
\(533\) | −20.4830 | −0.887217 | ||||||||
\(534\) | 7.28138 | + | 12.6117i | 0.315096 | + | 0.545762i | ||||
\(535\) | 13.2629 | − | 22.9721i | 0.573406 | − | 0.993169i | ||||
\(536\) | 3.61939 | − | 6.26897i | 0.156334 | − | 0.270778i | ||||
\(537\) | −8.93062 | − | 15.4683i | −0.385385 | − | 0.667506i | ||||
\(538\) | −25.1519 | −1.08437 | ||||||||
\(539\) | 11.3358 | 0.488266 | ||||||||
\(540\) | 2.89728 | 0.124679 | ||||||||
\(541\) | 9.98988 | + | 17.3030i | 0.429498 | + | 0.743913i | 0.996829 | − | 0.0795774i | \(-0.0253571\pi\) |
−0.567330 | + | 0.823490i | \(0.692024\pi\) | |||||||
\(542\) | −10.8429 | + | 18.7804i | −0.465741 | + | 0.806687i | ||||
\(543\) | 2.65256 | − | 4.59437i | 0.113832 | − | 0.197163i | ||||
\(544\) | 2.77152 | + | 4.80040i | 0.118828 | + | 0.205816i | ||||
\(545\) | −30.6225 | −1.31172 | ||||||||
\(546\) | 4.00349 | − | 6.93426i | 0.171334 | − | 0.296759i | ||||
\(547\) | 15.3485 | 0.656254 | 0.328127 | − | 0.944634i | \(-0.393583\pi\) | ||||
0.328127 | + | 0.944634i | \(0.393583\pi\) | |||||||
\(548\) | 5.80137 | + | 10.0483i | 0.247822 | + | 0.429240i | ||||
\(549\) | 6.89728 | − | 11.9464i | 0.294369 | − | 0.509862i | ||||
\(550\) | 2.74829 | − | 4.76018i | 0.117188 | − | 0.202975i | ||||
\(551\) | −2.44737 | − | 4.23896i | −0.104261 | − | 0.180586i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −18.2309 | −0.775259 | ||||||||
\(554\) | −9.76908 | −0.415048 | ||||||||
\(555\) | 1.48682 | + | 2.57525i | 0.0631121 | + | 0.109313i | ||||
\(556\) | 0.0777178 | − | 0.134611i | 0.00329597 | − | 0.00570879i | ||||
\(557\) | 10.4320 | − | 18.0687i | 0.442017 | − | 0.765596i | −0.555822 | − | 0.831301i | \(-0.687596\pi\) |
0.997839 | + | 0.0657053i | \(0.0209297\pi\) | |||||||
\(558\) | −0.802888 | − | 1.39064i | −0.0339890 | − | 0.0588706i | ||||
\(559\) | −6.05271 | −0.256003 | ||||||||
\(560\) | 3.83274 | + | 6.63850i | 0.161963 | + | 0.280528i | ||||
\(561\) | −8.97635 | −0.378982 | ||||||||
\(562\) | −1.40365 | − | 2.43119i | −0.0592093 | − | 0.102554i | ||||
\(563\) | −7.31938 | + | 12.6775i | −0.308475 | + | 0.534295i | −0.978029 | − | 0.208469i | \(-0.933152\pi\) |
0.669554 | + | 0.742764i | \(0.266485\pi\) | |||||||
\(564\) | −2.07772 | + | 3.59871i | −0.0874877 | + | 0.151533i | ||||
\(565\) | 5.44991 | + | 9.43953i | 0.229280 | + | 0.397124i | ||||
\(566\) | −25.9140 | −1.08925 | ||||||||
\(567\) | −1.32288 | − | 2.29129i | −0.0555556 | − | 0.0962250i | ||||
\(568\) | −4.87092 | −0.204379 | ||||||||
\(569\) | 19.3512 | + | 33.5173i | 0.811245 | + | 1.40512i | 0.911993 | + | 0.410205i | \(0.134543\pi\) |
−0.100749 | + | 0.994912i | \(0.532124\pi\) | |||||||
\(570\) | 4.01012 | − | 6.94574i | 0.167966 | − | 0.290925i | ||||
\(571\) | −6.47320 | + | 11.2119i | −0.270895 | + | 0.469204i | −0.969091 | − | 0.246702i | \(-0.920653\pi\) |
0.698196 | + | 0.715906i | \(0.253986\pi\) | |||||||
\(572\) | 2.45043 | + | 4.24427i | 0.102458 | + | 0.177462i | ||||
\(573\) | −18.3046 | −0.764686 | ||||||||
\(574\) | −17.9070 | −0.747423 | ||||||||
\(575\) | 3.39422 | 0.141549 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −3.92757 | + | 6.80275i | −0.163507 | + | 0.283202i | −0.936124 | − | 0.351670i | \(-0.885614\pi\) |
0.772617 | + | 0.634872i | \(0.218947\pi\) | |||||||
\(578\) | 6.86259 | − | 11.8864i | 0.285446 | − | 0.494407i | ||||
\(579\) | 0.170755 | + | 0.295756i | 0.00709633 | + | 0.0122912i | ||||
\(580\) | −5.12297 | −0.212720 | ||||||||
\(581\) | −6.82000 | + | 11.8126i | −0.282941 | + | 0.490069i | ||||
\(582\) | −14.6988 | −0.609286 | ||||||||
\(583\) | −3.96531 | − | 6.86812i | −0.164226 | − | 0.284449i | ||||
\(584\) | 2.56803 | − | 4.44796i | 0.106266 | − | 0.184058i | ||||
\(585\) | −4.38410 | + | 7.59348i | −0.181260 | + | 0.313952i | ||||
\(586\) | 15.6571 | + | 27.1190i | 0.646791 | + | 1.12027i | ||||
\(587\) | 39.8243 | 1.64373 | 0.821863 | − | 0.569685i | \(-0.192935\pi\) | ||||
0.821863 | + | 0.569685i | \(0.192935\pi\) | |||||||
\(588\) | 3.50000 | − | 6.06218i | 0.144338 | − | 0.250000i | ||||
\(589\) | −4.44511 | −0.183158 | ||||||||
\(590\) | 10.0782 | + | 17.4559i | 0.414911 | + | 0.718647i | ||||
\(591\) | 10.1238 | − | 17.5349i | 0.416438 | − | 0.721291i | ||||
\(592\) | 0.513179 | − | 0.888851i | 0.0210915 | − | 0.0365316i | ||||
\(593\) | 13.0470 | + | 22.5980i | 0.535775 | + | 0.927989i | 0.999125 | + | 0.0418139i | \(0.0133137\pi\) |
−0.463351 | + | 0.886175i | \(0.653353\pi\) | |||||||
\(594\) | 1.61939 | 0.0664445 | ||||||||
\(595\) | 21.2450 | − | 36.7974i | 0.870960 | − | 1.50855i | ||||
\(596\) | 16.6357 | 0.681426 | ||||||||
\(597\) | −13.4471 | − | 23.2911i | −0.550354 | − | 0.953241i | ||||
\(598\) | −1.51318 | + | 2.62090i | −0.0618785 | + | 0.107177i | ||||
\(599\) | −18.9482 | + | 32.8193i | −0.774203 | + | 1.34096i | 0.161038 | + | 0.986948i | \(0.448516\pi\) |
−0.935241 | + | 0.354011i | \(0.884818\pi\) | |||||||
\(600\) | −1.69711 | − | 2.93948i | −0.0692843 | − | 0.120004i | ||||
\(601\) | 3.65849 | 0.149233 | 0.0746165 | − | 0.997212i | \(-0.476227\pi\) | ||||
0.0746165 | + | 0.997212i | \(0.476227\pi\) | |||||||
\(602\) | −5.29150 | −0.215666 | ||||||||
\(603\) | 7.23879 | 0.294786 | ||||||||
\(604\) | 9.86259 | + | 17.0825i | 0.401303 | + | 0.695077i | ||||
\(605\) | −12.1361 | + | 21.0203i | −0.493401 | + | 0.854596i | ||||
\(606\) | 1.69711 | − | 2.93948i | 0.0689405 | − | 0.119408i | ||||
\(607\) | 10.3323 | + | 17.8961i | 0.419375 | + | 0.726379i | 0.995877 | − | 0.0907170i | \(-0.0289159\pi\) |
−0.576502 | + | 0.817096i | \(0.695583\pi\) | |||||||
\(608\) | −2.76820 | −0.112265 | ||||||||
\(609\) | 2.33911 | + | 4.05146i | 0.0947855 | + | 0.164173i | ||||
\(610\) | −39.9667 | −1.61820 | ||||||||
\(611\) | −6.28792 | − | 10.8910i | −0.254382 | − | 0.440602i | ||||
\(612\) | −2.77152 | + | 4.80040i | −0.112032 | + | 0.194045i | ||||
\(613\) | −14.4269 | + | 24.9881i | −0.582696 | + | 1.00926i | 0.412463 | + | 0.910975i | \(0.364669\pi\) |
−0.995158 | + | 0.0982842i | \(0.968665\pi\) | |||||||
\(614\) | −6.80333 | − | 11.7837i | −0.274560 | − | 0.475552i | ||||
\(615\) | 19.6094 | 0.790726 | ||||||||
\(616\) | 2.14226 | + | 3.71050i | 0.0863140 | + | 0.149500i | ||||
\(617\) | 21.1524 | 0.851563 | 0.425782 | − | 0.904826i | \(-0.359999\pi\) | ||||
0.425782 | + | 0.904826i | \(0.359999\pi\) | |||||||
\(618\) | 5.50986 | + | 9.54336i | 0.221639 | + | 0.383890i | ||||
\(619\) | 10.6492 | − | 18.4450i | 0.428029 | − | 0.741369i | −0.568669 | − | 0.822567i | \(-0.692541\pi\) |
0.996698 | + | 0.0811982i | \(0.0258747\pi\) | |||||||
\(620\) | −2.32619 | + | 4.02908i | −0.0934221 | + | 0.161812i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | 14.7709 | 0.592259 | ||||||||
\(623\) | −38.5294 | −1.54365 | ||||||||
\(624\) | 3.02636 | 0.121151 | ||||||||
\(625\) | 15.2252 | + | 26.3708i | 0.609007 | + | 1.05483i | ||||
\(626\) | 1.34242 | − | 2.32515i | 0.0536540 | − | 0.0929315i | ||||
\(627\) | 2.24140 | − | 3.88222i | 0.0895130 | − | 0.155041i | ||||
\(628\) | −0.900593 | − | 1.55987i | −0.0359376 | − | 0.0622457i | ||||
\(629\) | −5.68913 | −0.226840 | ||||||||
\(630\) | −3.83274 | + | 6.63850i | −0.152700 | + | 0.264484i | ||||
\(631\) | 41.4808 | 1.65133 | 0.825663 | − | 0.564164i | \(-0.190801\pi\) | ||||
0.825663 | + | 0.564164i | \(0.190801\pi\) | |||||||
\(632\) | −3.44532 | − | 5.96748i | −0.137048 | − | 0.237373i | ||||
\(633\) | 3.20680 | − | 5.55433i | 0.127459 | − | 0.220765i | ||||
\(634\) | 5.52151 | − | 9.56353i | 0.219287 | − | 0.379816i | ||||
\(635\) | 19.8828 | + | 34.4381i | 0.789026 | + | 1.36663i | ||||
\(636\) | −4.89728 | −0.194190 | ||||||||
\(637\) | 10.5923 | + | 18.3463i | 0.419680 | + | 0.726907i | ||||
\(638\) | −2.86341 | −0.113364 | ||||||||
\(639\) | −2.43546 | − | 4.21834i | −0.0963453 | − | 0.166875i | ||||
\(640\) | −1.44864 | + | 2.50912i | −0.0572625 | + | 0.0991816i | ||||
\(641\) | 1.60246 | − | 2.77554i | 0.0632934 | − | 0.109627i | −0.832642 | − | 0.553811i | \(-0.813173\pi\) |
0.895936 | + | 0.444184i | \(0.146506\pi\) | |||||||
\(642\) | −4.57772 | − | 7.92884i | −0.180668 | − | 0.312926i | ||||
\(643\) | −34.0131 | −1.34135 | −0.670673 | − | 0.741753i | \(-0.733995\pi\) | ||||
−0.670673 | + | 0.741753i | \(0.733995\pi\) | |||||||
\(644\) | −1.32288 | + | 2.29129i | −0.0521286 | + | 0.0902894i | ||||
\(645\) | 5.79456 | 0.228160 | ||||||||
\(646\) | 7.67211 | + | 13.2885i | 0.301855 | + | 0.522828i | ||||
\(647\) | −5.75986 | + | 9.97637i | −0.226443 | + | 0.392211i | −0.956752 | − | 0.290906i | \(-0.906043\pi\) |
0.730308 | + | 0.683118i | \(0.239376\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 5.63305 | + | 9.75672i | 0.221116 | + | 0.382985i | ||||
\(650\) | 10.2721 | 0.402906 | ||||||||
\(651\) | 4.24848 | 0.166511 | ||||||||
\(652\) | 8.87092 | 0.347412 | ||||||||
\(653\) | 6.17560 | + | 10.6965i | 0.241670 | + | 0.418585i | 0.961190 | − | 0.275887i | \(-0.0889715\pi\) |
−0.719520 | + | 0.694472i | \(0.755638\pi\) | |||||||
\(654\) | −5.28469 | + | 9.15336i | −0.206648 | + | 0.357925i | ||||
\(655\) | 4.22644 | − | 7.32041i | 0.165141 | − | 0.286032i | ||||
\(656\) | −3.38410 | − | 5.86143i | −0.132127 | − | 0.228851i | ||||
\(657\) | 5.13607 | 0.200377 | ||||||||
\(658\) | −5.49712 | − | 9.52130i | −0.214300 | − | 0.371179i | ||||
\(659\) | −4.82754 | −0.188054 | −0.0940272 | − | 0.995570i | \(-0.529974\pi\) | ||||
−0.0940272 | + | 0.995570i | \(0.529974\pi\) | |||||||
\(660\) | −2.34592 | − | 4.06325i | −0.0913147 | − | 0.158162i | ||||
\(661\) | 7.73503 | − | 13.3975i | 0.300858 | − | 0.521101i | −0.675473 | − | 0.737385i | \(-0.736060\pi\) |
0.976331 | + | 0.216284i | \(0.0693937\pi\) | |||||||
\(662\) | 4.14619 | − | 7.18141i | 0.161146 | − | 0.279114i | ||||
\(663\) | −8.38759 | − | 14.5277i | −0.325747 | − | 0.564211i | ||||
\(664\) | −5.15544 | −0.200070 | ||||||||
\(665\) | 10.6098 | + | 18.3767i | 0.411430 | + | 0.712618i | ||||
\(666\) | 1.02636 | 0.0397705 | ||||||||
\(667\) | −0.884100 | − | 1.53131i | −0.0342325 | − | 0.0592924i | ||||
\(668\) | 0.632133 | − | 1.09489i | 0.0244580 | − | 0.0423624i | ||||
\(669\) | −8.09439 | + | 14.0199i | −0.312947 | + | 0.542040i | ||||
\(670\) | −10.4864 | − | 18.1630i | −0.405125 | − | 0.701697i | ||||
\(671\) | −22.3388 | −0.862381 | ||||||||
\(672\) | 2.64575 | 0.102062 | ||||||||
\(673\) | 15.3248 | 0.590729 | 0.295365 | − | 0.955385i | \(-0.404559\pi\) | ||||
0.295365 | + | 0.955385i | \(0.404559\pi\) | |||||||
\(674\) | −12.5312 | − | 21.7047i | −0.482684 | − | 0.836033i | ||||
\(675\) | 1.69711 | − | 2.93948i | 0.0653219 | − | 0.113141i | ||||
\(676\) | 1.92058 | − | 3.32654i | 0.0738685 | − | 0.127944i | ||||
\(677\) | 23.8126 | + | 41.2446i | 0.915192 | + | 1.58516i | 0.806620 | + | 0.591070i | \(0.201294\pi\) |
0.108572 | + | 0.994089i | \(0.465372\pi\) | |||||||
\(678\) | 3.76209 | 0.144482 | ||||||||
\(679\) | 19.4447 | − | 33.6792i | 0.746220 | − | 1.29249i | ||||
\(680\) | 16.0597 | 0.615861 | ||||||||
\(681\) | 11.4554 | + | 19.8414i | 0.438974 | + | 0.760325i | ||||
\(682\) | −1.30019 | + | 2.25200i | −0.0497869 | + | 0.0862335i | ||||
\(683\) | 13.8091 | − | 23.9180i | 0.528390 | − | 0.915199i | −0.471062 | − | 0.882100i | \(-0.656129\pi\) |
0.999452 | − | 0.0330984i | \(-0.0105375\pi\) | |||||||
\(684\) | −1.38410 | − | 2.39733i | −0.0529224 | − | 0.0916643i | ||||
\(685\) | 33.6164 | 1.28441 | ||||||||
\(686\) | 9.26013 | + | 16.0390i | 0.353553 | + | 0.612372i | ||||
\(687\) | 5.16547 | 0.197075 | ||||||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | 7.41046 | − | 12.8353i | 0.282316 | − | 0.488986i | ||||
\(690\) | 1.44864 | − | 2.50912i | 0.0551488 | − | 0.0955205i | ||||
\(691\) | −1.96487 | − | 3.40326i | −0.0747473 | − | 0.129466i | 0.826229 | − | 0.563334i | \(-0.190482\pi\) |
−0.900976 | + | 0.433868i | \(0.857148\pi\) | |||||||
\(692\) | −0.863933 | −0.0328418 | ||||||||
\(693\) | −2.14226 | + | 3.71050i | −0.0813776 | + | 0.140950i | ||||
\(694\) | −6.78845 | −0.257686 | ||||||||
\(695\) | −0.225170 | − | 0.390006i | −0.00854119 | − | 0.0147938i | ||||
\(696\) | −0.884100 | + | 1.53131i | −0.0335117 | + | 0.0580440i | ||||
\(697\) | −18.7582 | + | 32.4901i | −0.710516 | + | 1.23065i | ||||
\(698\) | 6.00349 | + | 10.3984i | 0.227236 | + | 0.393584i | ||||
\(699\) | −11.0930 | −0.419578 | ||||||||
\(700\) | 8.98027 | 0.339422 | ||||||||
\(701\) | 13.5725 | 0.512624 | 0.256312 | − | 0.966594i | \(-0.417492\pi\) | ||||
0.256312 | + | 0.966594i | \(0.417492\pi\) | |||||||
\(702\) | 1.51318 | + | 2.62090i | 0.0571112 | + | 0.0989196i | ||||
\(703\) | 1.42058 | − | 2.46052i | 0.0535782 | − | 0.0928002i | ||||
\(704\) | −0.809697 | + | 1.40244i | −0.0305166 | + | 0.0528563i | ||||
\(705\) | 6.01973 | + | 10.4265i | 0.226716 | + | 0.392684i | ||||
\(706\) | −20.9263 | −0.787573 | ||||||||
\(707\) | 4.49014 | + | 7.77714i | 0.168869 | + | 0.292490i | ||||
\(708\) | 6.95698 | 0.261459 | ||||||||
\(709\) | −6.24821 | − | 10.8222i | −0.234657 | − | 0.406437i | 0.724516 | − | 0.689258i | \(-0.242063\pi\) |
−0.959173 | + | 0.282821i | \(0.908730\pi\) | |||||||
\(710\) | −7.05621 | + | 12.2217i | −0.264815 | + | 0.458673i | ||||
\(711\) | 3.44532 | − | 5.96748i | 0.129210 | − | 0.223798i | ||||
\(712\) | −7.28138 | − | 12.6117i | −0.272881 | − | 0.472644i | ||||
\(713\) | −1.60578 | −0.0601368 | ||||||||
\(714\) | −7.33274 | − | 12.7007i | −0.274421 | − | 0.475311i | ||||
\(715\) | 14.1992 | 0.531019 | ||||||||
\(716\) | 8.93062 | + | 15.4683i | 0.333753 | + | 0.578077i | ||||
\(717\) | −2.81956 | + | 4.88362i | −0.105298 | + | 0.182382i | ||||
\(718\) | −5.01362 | + | 8.68384i | −0.187107 | + | 0.324078i | ||||
\(719\) | 25.7981 | + | 44.6837i | 0.962108 | + | 1.66642i | 0.717191 | + | 0.696877i | \(0.245428\pi\) |
0.244917 | + | 0.969544i | \(0.421239\pi\) | |||||||
\(720\) | −2.89728 | −0.107975 | ||||||||
\(721\) | −29.1555 | −1.08581 | ||||||||
\(722\) | 11.3371 | 0.421922 | ||||||||
\(723\) | 12.0479 | + | 20.8675i | 0.448065 | + | 0.776072i | ||||
\(724\) | −2.65256 | + | 4.59437i | −0.0985816 | + | 0.170748i | ||||
\(725\) | −3.00083 | + | 5.19760i | −0.111448 | + | 0.193034i | ||||
\(726\) | 4.18878 | + | 7.25518i | 0.155460 | + | 0.269265i | ||||
\(727\) | −41.3991 | −1.53541 | −0.767704 | − | 0.640804i | \(-0.778601\pi\) | ||||
−0.767704 | + | 0.640804i | \(0.778601\pi\) | |||||||
\(728\) | −4.00349 | + | 6.93426i | −0.148379 | + | 0.257001i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −7.44031 | − | 12.8870i | −0.275378 | − | 0.476969i | ||||
\(731\) | −5.54303 | + | 9.60081i | −0.205016 | + | 0.355099i | ||||
\(732\) | −6.89728 | + | 11.9464i | −0.254931 | + | 0.441553i | ||||
\(733\) | −12.0494 | − | 20.8702i | −0.445055 | − | 0.770857i | 0.553001 | − | 0.833180i | \(-0.313482\pi\) |
−0.998056 | + | 0.0623230i | \(0.980149\pi\) | |||||||
\(734\) | 24.2485 | 0.895028 | ||||||||
\(735\) | −10.1405 | − | 17.5638i | −0.374037 | − | 0.647851i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −5.86123 | − | 10.1519i | −0.215901 | − | 0.373952i | ||||
\(738\) | 3.38410 | − | 5.86143i | 0.124570 | − | 0.215762i | ||||
\(739\) | −7.79931 | + | 13.5088i | −0.286902 | + | 0.496929i | −0.973069 | − | 0.230515i | \(-0.925959\pi\) |
0.686166 | + | 0.727445i | \(0.259292\pi\) | |||||||
\(740\) | −1.48682 | − | 2.57525i | −0.0546566 | − | 0.0946681i | ||||
\(741\) | 8.37756 | 0.307757 | ||||||||
\(742\) | 6.47849 | − | 11.2211i | 0.237833 | − | 0.411939i | ||||
\(743\) | 25.7488 | 0.944633 | 0.472317 | − | 0.881429i | \(-0.343418\pi\) | ||||
0.472317 | + | 0.881429i | \(0.343418\pi\) | |||||||
\(744\) | 0.802888 | + | 1.39064i | 0.0294353 | + | 0.0509834i | ||||
\(745\) | 24.0992 | − | 41.7410i | 0.882925 | − | 1.52927i | ||||
\(746\) | 17.4599 | − | 30.2414i | 0.639251 | − | 1.10721i | ||||
\(747\) | −2.57772 | − | 4.46474i | −0.0943138 | − | 0.163356i | ||||
\(748\) | 8.97635 | 0.328208 | ||||||||
\(749\) | 24.2230 | 0.885089 | ||||||||
\(750\) | 4.65238 | 0.169881 | ||||||||
\(751\) | −11.2867 | − | 19.5491i | −0.411856 | − | 0.713356i | 0.583236 | − | 0.812302i | \(-0.301786\pi\) |
−0.995093 | + | 0.0989464i | \(0.968453\pi\) | |||||||
\(752\) | 2.07772 | − | 3.59871i | 0.0757666 | − | 0.131232i | ||||
\(753\) | 8.99848 | − | 15.5858i | 0.327923 | − | 0.567979i | ||||
\(754\) | −2.67560 | − | 4.63428i | −0.0974397 | − | 0.168771i | ||||
\(755\) | 57.1493 | 2.07988 | ||||||||
\(756\) | 1.32288 | + | 2.29129i | 0.0481125 | + | 0.0833333i | ||||
\(757\) | 15.4706 | 0.562289 | 0.281144 | − | 0.959665i | \(-0.409286\pi\) | ||||
0.281144 | + | 0.959665i | \(0.409286\pi\) | |||||||
\(758\) | 1.88366 | + | 3.26260i | 0.0684176 | + | 0.118503i | ||||
\(759\) | 0.809697 | − | 1.40244i | 0.0293901 | − | 0.0509052i | ||||
\(760\) | −4.01012 | + | 6.94574i | −0.145462 | + | 0.251948i | ||||
\(761\) | −19.2520 | − | 33.3454i | −0.697884 | − | 1.20877i | −0.969199 | − | 0.246279i | \(-0.920792\pi\) |
0.271315 | − | 0.962491i | \(-0.412541\pi\) | |||||||
\(762\) | 13.7252 | 0.497211 | ||||||||
\(763\) | −13.9820 | − | 24.2175i | −0.506182 | − | 0.876733i | ||||
\(764\) | 18.3046 | 0.662237 | ||||||||
\(765\) | 8.02985 | + | 13.9081i | 0.290320 | + | 0.502849i | ||||
\(766\) | 16.6826 | − | 28.8951i | 0.602767 | − | 1.04402i | ||||
\(767\) | −10.5272 | + | 18.2336i | −0.380114 | + | 0.658376i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 10.9842 | 0.396101 | 0.198051 | − | 0.980192i | \(-0.436539\pi\) | ||||
0.198051 | + | 0.980192i | \(0.436539\pi\) | |||||||
\(770\) | 12.4134 | 0.447349 | ||||||||
\(771\) | −1.27126 | −0.0457831 | ||||||||
\(772\) | −0.170755 | − | 0.295756i | −0.00614560 | − | 0.0106445i | ||||
\(773\) | 9.53640 | − | 16.5175i | 0.343000 | − | 0.594094i | −0.641988 | − | 0.766715i | \(-0.721890\pi\) |
0.984988 | + | 0.172620i | \(0.0552234\pi\) | |||||||
\(774\) | 1.00000 | − | 1.73205i | 0.0359443 | − | 0.0622573i | ||||
\(775\) | 2.72518 | + | 4.72015i | 0.0978914 | + | 0.169553i | ||||
\(776\) | 14.6988 | 0.527657 | ||||||||
\(777\) | −1.35774 | + | 2.35168i | −0.0487088 | + | 0.0843660i | ||||
\(778\) | 26.3503 | 0.944705 | ||||||||
\(779\) | −9.36787 | − | 16.2256i | −0.335639 | − | 0.581343i | ||||
\(780\) | 4.38410 | − | 7.59348i | 0.156976 | − | 0.271890i | ||||
\(781\) | −3.94397 | + | 6.83116i | −0.141126 | + | 0.244438i | ||||
\(782\) | 2.77152 | + | 4.80040i | 0.0991092 | + | 0.171662i | ||||
\(783\) | −1.76820 | −0.0631903 | ||||||||
\(784\) | −3.50000 | + | 6.06218i | −0.125000 | + | 0.216506i | ||||
\(785\) | −5.21854 | −0.186258 | ||||||||
\(786\) | −1.45876 | − | 2.52665i | −0.0520324 | − | 0.0901227i | ||||
\(787\) | −7.05934 | + | 12.2271i | −0.251638 | + | 0.435851i | −0.963977 | − | 0.265985i | \(-0.914303\pi\) |
0.712339 | + | 0.701836i | \(0.247636\pi\) | |||||||
\(788\) | −10.1238 | + | 17.5349i | −0.360646 | + | 0.624656i | ||||
\(789\) | −13.3639 | − | 23.1470i | −0.475769 | − | 0.824056i | ||||
\(790\) | −19.9641 | −0.710292 | ||||||||
\(791\) | −4.97678 | + | 8.62003i | −0.176954 | + | 0.306493i | ||||
\(792\) | −1.61939 | −0.0575427 | ||||||||
\(793\) | −20.8736 | − | 36.1542i | −0.741244 | − | 1.28387i | ||||
\(794\) | −6.39073 | + | 11.0691i | −0.226799 | + | 0.392827i | ||||
\(795\) | −7.09439 | + | 12.2878i | −0.251612 | + | 0.435805i | ||||
\(796\) | 13.4471 | + | 23.2911i | 0.476620 | + | 0.825531i | ||||
\(797\) | −23.3670 | −0.827702 | −0.413851 | − | 0.910345i | \(-0.635817\pi\) | ||||
−0.413851 | + | 0.910345i | \(0.635817\pi\) | |||||||
\(798\) | 7.32397 | 0.259266 | ||||||||
\(799\) | −23.0337 | −0.814874 | ||||||||
\(800\) | 1.69711 | + | 2.93948i | 0.0600020 | + | 0.103926i | ||||
\(801\) | 7.28138 | − | 12.6117i | 0.257275 | − | 0.445613i | ||||
\(802\) | 3.61957 | − | 6.26929i | 0.127812 | − | 0.221376i | ||||
\(803\) | −4.15866 | − | 7.20301i | −0.146756 | − | 0.254189i | ||||
\(804\) | −7.23879 | −0.255292 | ||||||||
\(805\) | 3.83274 | + | 6.63850i | 0.135086 | + | 0.233976i | ||||
\(806\) | −4.85965 | −0.171174 | ||||||||
\(807\) | 12.5759 | + | 21.7822i | 0.442694 | + | 0.766768i | ||||
\(808\) | −1.69711 | + | 2.93948i | −0.0597042 | + | 0.103411i | ||||
\(809\) | −1.19891 | + | 2.07656i | −0.0421513 | + | 0.0730081i | −0.886331 | − | 0.463052i | \(-0.846754\pi\) |
0.844180 | + | 0.536060i | \(0.180088\pi\) | |||||||
\(810\) | −1.44864 | − | 2.50912i | −0.0509000 | − | 0.0881614i | ||||
\(811\) | 11.8990 | 0.417832 | 0.208916 | − | 0.977934i | \(-0.433007\pi\) | ||||
0.208916 | + | 0.977934i | \(0.433007\pi\) | |||||||
\(812\) | −2.33911 | − | 4.05146i | −0.0820866 | − | 0.142178i | ||||
\(813\) | 21.6857 | 0.760552 | ||||||||
\(814\) | −0.831038 | − | 1.43940i | −0.0291279 | − | 0.0504510i | ||||
\(815\) | 12.8508 | − | 22.2582i | 0.450143 | − | 0.779670i | ||||
\(816\) | 2.77152 | − | 4.80040i | 0.0970224 | − | 0.168048i | ||||
\(817\) | −2.76820 | − | 4.79466i | −0.0968471 | − | 0.167744i | ||||
\(818\) | −28.3976 | −0.992901 | ||||||||
\(819\) | −8.00699 | −0.279787 | ||||||||
\(820\) | −19.6094 | −0.684789 | ||||||||
\(821\) | 15.4732 | + | 26.8004i | 0.540019 | + | 0.935340i | 0.998902 | + | 0.0468437i | \(0.0149163\pi\) |
−0.458883 | + | 0.888497i | \(0.651750\pi\) | |||||||
\(822\) | 5.80137 | − | 10.0483i | 0.202346 | − | 0.350473i | ||||
\(823\) | −25.0997 | + | 43.4739i | −0.874920 | + | 1.51541i | −0.0180716 | + | 0.999837i | \(0.505753\pi\) |
−0.856848 | + | 0.515569i | \(0.827581\pi\) | |||||||
\(824\) | −5.50986 | − | 9.54336i | −0.191945 | − | 0.332459i | ||||
\(825\) | −5.49659 | −0.191367 | ||||||||
\(826\) | −9.20322 | + | 15.9404i | −0.320221 | + | 0.554639i | ||||
\(827\) | −9.46738 | −0.329213 | −0.164607 | − | 0.986359i | \(-0.552635\pi\) | ||||
−0.164607 | + | 0.986359i | \(0.552635\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | 26.7454 | − | 46.3244i | 0.928907 | − | 1.60891i | 0.143753 | − | 0.989614i | \(-0.454083\pi\) |
0.785154 | − | 0.619301i | \(-0.212584\pi\) | |||||||
\(830\) | −7.46837 | + | 12.9356i | −0.259231 | + | 0.449001i | ||||
\(831\) | 4.88454 | + | 8.46027i | 0.169443 | + | 0.293484i | ||||
\(832\) | −3.02636 | −0.104920 | ||||||||
\(833\) | 38.8012 | 1.34438 | ||||||||
\(834\) | −0.155436 | −0.00538230 | ||||||||
\(835\) | −1.83147 | − | 3.17219i | −0.0633805 | − | 0.109778i | ||||
\(836\) | −2.24140 | + | 3.88222i | −0.0775206 | + | 0.134270i | ||||
\(837\) | −0.802888 | + | 1.39064i | −0.0277519 | + | 0.0480676i | ||||
\(838\) | 8.15562 | + | 14.1259i | 0.281731 | + | 0.487972i | ||||
\(839\) | 35.3512 | 1.22046 | 0.610230 | − | 0.792225i | \(-0.291077\pi\) | ||||
0.610230 | + | 0.792225i | \(0.291077\pi\) | |||||||
\(840\) | 3.83274 | − | 6.63850i | 0.132242 | − | 0.229050i | ||||
\(841\) | −25.8735 | −0.892189 | ||||||||
\(842\) | −17.8611 | − | 30.9363i | −0.615533 | − | 1.06613i | ||||
\(843\) | −1.40365 | + | 2.43119i | −0.0483442 | + | 0.0837346i | ||||
\(844\) | −3.20680 | + | 5.55433i | −0.110382 | + | 0.191188i | ||||
\(845\) | −5.56446 | − | 9.63793i | −0.191423 | − | 0.331555i | ||||
\(846\) | 4.15544 | 0.142867 | ||||||||
\(847\) | −22.1649 | −0.761597 | ||||||||
\(848\) | 4.89728 | 0.168173 | ||||||||
\(849\) | 12.9570 | + | 22.4422i | 0.444682 | + | 0.770213i | ||||
\(850\) | 9.40714 | − | 16.2936i | 0.322662 | − | 0.558868i | ||||
\(851\) | 0.513179 | − | 0.888851i | 0.0175915 | − | 0.0304694i | ||||
\(852\) | 2.43546 | + | 4.21834i | 0.0834375 | + | 0.144518i | ||||
\(853\) | −7.76908 | −0.266008 | −0.133004 | − | 0.991115i | \(-0.542462\pi\) | ||||
−0.133004 | + | 0.991115i | \(0.542462\pi\) | |||||||
\(854\) | −18.2485 | − | 31.6073i | −0.624450 | − | 1.08158i | ||||
\(855\) | −8.02025 | −0.274287 | ||||||||
\(856\) | 4.57772 | + | 7.92884i | 0.156463 | + | 0.271002i | ||||
\(857\) | −3.66897 | + | 6.35485i | −0.125330 | + | 0.217077i | −0.921862 | − | 0.387519i | \(-0.873332\pi\) |
0.796532 | + | 0.604596i | \(0.206666\pi\) | |||||||
\(858\) | 2.45043 | − | 4.24427i | 0.0836564 | − | 0.144897i | ||||
\(859\) | −22.0255 | − | 38.1492i | −0.751499 | − | 1.30163i | −0.947096 | − | 0.320950i | \(-0.895998\pi\) |
0.195597 | − | 0.980684i | \(-0.437335\pi\) | |||||||
\(860\) | −5.79456 | −0.197593 | ||||||||
\(861\) | 8.95349 | + | 15.5079i | 0.305134 | + | 0.528508i | ||||
\(862\) | −25.4504 | −0.866843 | ||||||||
\(863\) | −21.2766 | − | 36.8522i | −0.724265 | − | 1.25446i | −0.959276 | − | 0.282471i | \(-0.908846\pi\) |
0.235011 | − | 0.971993i | \(-0.424487\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −1.25153 | + | 2.16771i | −0.0425532 | + | 0.0737043i | ||||
\(866\) | 17.7248 | + | 30.7003i | 0.602314 | + | 1.04324i | ||||
\(867\) | −13.7252 | −0.466132 | ||||||||
\(868\) | −4.24848 | −0.144203 | ||||||||
\(869\) | −11.1587 | −0.378532 | ||||||||
\(870\) | 2.56148 | + | 4.43662i | 0.0868425 | + | 0.150416i | ||||
\(871\) | 10.9536 | − | 18.9722i | 0.371148 | − | 0.642847i | ||||
\(872\) | 5.28469 | − | 9.15336i | 0.178962 | − | 0.309972i | ||||
\(873\) | 7.34941 | + | 12.7296i | 0.248740 | + | 0.430830i | ||||
\(874\) | −2.76820 | −0.0936358 | ||||||||
\(875\) | −6.15452 | + | 10.6599i | −0.208061 | + | 0.360372i | ||||
\(876\) | −5.13607 | −0.173532 | ||||||||
\(877\) | −1.46317 | − | 2.53429i | −0.0494078 | − | 0.0855768i | 0.840264 | − | 0.542178i | \(-0.182400\pi\) |
−0.889672 | + | 0.456601i | \(0.849067\pi\) | |||||||
\(878\) | 8.66378 | − | 15.0061i | 0.292388 | − | 0.506431i | ||||
\(879\) | 15.6571 | − | 27.1190i | 0.528103 | − | 0.914700i | ||||
\(880\) | 2.34592 | + | 4.06325i | 0.0790809 | + | 0.136972i | ||||
\(881\) | 14.9670 | 0.504251 | 0.252126 | − | 0.967694i | \(-0.418870\pi\) | ||||
0.252126 | + | 0.967694i | \(0.418870\pi\) | |||||||
\(882\) | −7.00000 | −0.235702 | ||||||||
\(883\) | 1.77431 | 0.0597103 | 0.0298551 | − | 0.999554i | \(-0.490495\pi\) | ||||
0.0298551 | + | 0.999554i | \(0.490495\pi\) | |||||||
\(884\) | 8.38759 | + | 14.5277i | 0.282105 | + | 0.488621i | ||||
\(885\) | 10.0782 | − | 17.4559i | 0.338774 | − | 0.586773i | ||||
\(886\) | −11.8924 | + | 20.5983i | −0.399534 | + | 0.692014i | ||||
\(887\) | 12.6414 | + | 21.8955i | 0.424455 | + | 0.735178i | 0.996369 | − | 0.0851356i | \(-0.0271323\pi\) |
−0.571914 | + | 0.820313i | \(0.693799\pi\) | |||||||
\(888\) | −1.02636 | −0.0344423 | ||||||||
\(889\) | −18.1567 | + | 31.4483i | −0.608956 | + | 1.05474i | ||||
\(890\) | −42.1924 | −1.41429 | ||||||||
\(891\) | −0.809697 | − | 1.40244i | −0.0271259 | − | 0.0469834i | ||||
\(892\) | 8.09439 | − | 14.0199i | 0.271020 | − | 0.469421i | ||||
\(893\) | 5.75154 | − | 9.96196i | 0.192468 | − | 0.333364i | ||||
\(894\) | −8.31786 | − | 14.4070i | −0.278191 | − | 0.481841i | ||||
\(895\) | 51.7490 | 1.72978 | ||||||||
\(896\) | −2.64575 | −0.0883883 | ||||||||
\(897\) | 3.02636 | 0.101047 | ||||||||
\(898\) | −15.1923 | − | 26.3138i | −0.506973 | − | 0.878103i | ||||
\(899\) | 1.41967 | − | 2.45894i | 0.0473485 | − | 0.0820101i | ||||
\(900\) | −1.69711 | + | 2.93948i | −0.0565704 | + | 0.0979828i | ||||
\(901\) | −13.5729 | − | 23.5089i | −0.452178 | − | 0.783196i | ||||
\(902\) | −10.9604 | −0.364941 | ||||||||
\(903\) | 2.64575 | + | 4.58258i | 0.0880451 | + | 0.152499i | ||||
\(904\) | −3.76209 | −0.125125 | ||||||||
\(905\) | 7.68521 | + | 13.3112i | 0.255465 | + | 0.442478i | ||||
\(906\) | 9.86259 | − | 17.0825i | 0.327663 | − | 0.567528i | ||||
\(907\) | −13.5535 | + | 23.4754i | −0.450037 | + | 0.779487i | −0.998388 | − | 0.0567615i | \(-0.981923\pi\) |
0.548351 | + | 0.836248i | \(0.315256\pi\) | |||||||
\(908\) | −11.4554 | − | 19.8414i | −0.380162 | − | 0.658461i | ||||
\(909\) | −3.39422 | −0.112579 | ||||||||
\(910\) | 11.5992 | + | 20.0905i | 0.384511 | + | 0.665993i | ||||
\(911\) | −6.10001 | −0.202102 | −0.101051 | − | 0.994881i | \(-0.532221\pi\) | ||||
−0.101051 | + | 0.994881i | \(0.532221\pi\) | |||||||
\(912\) | 1.38410 | + | 2.39733i | 0.0458321 | + | 0.0793836i | ||||
\(913\) | −4.17434 | + | 7.23017i | −0.138151 | + | 0.239284i | ||||
\(914\) | 10.7103 | − | 18.5508i | 0.354265 | − | 0.613605i | ||||
\(915\) | 19.9833 | + | 34.6122i | 0.660629 | + | 1.14424i | ||||
\(916\) | −5.16547 | −0.170672 | ||||||||
\(917\) | 7.71905 | 0.254905 | ||||||||
\(918\) | 5.54303 | 0.182947 | ||||||||
\(919\) | −27.3711 | − | 47.4082i | −0.902890 | − | 1.56385i | −0.823725 | − | 0.566989i | \(-0.808108\pi\) |
−0.0791645 | − | 0.996862i | \(-0.525225\pi\) | |||||||
\(920\) | −1.44864 | + | 2.50912i | −0.0477602 | + | 0.0827231i | ||||
\(921\) | −6.80333 | + | 11.7837i | −0.224177 | + | 0.388286i | ||||
\(922\) | −9.58301 | − | 16.5983i | −0.315599 | − | 0.546634i | ||||
\(923\) | −14.7411 | −0.485211 | ||||||||
\(924\) | 2.14226 | − | 3.71050i | 0.0704751 | − | 0.122066i | ||||
\(925\) | −3.48369 | −0.114543 | ||||||||
\(926\) | 3.86393 | + | 6.69253i | 0.126977 | + | 0.219930i | ||||
\(927\) | 5.50986 | − | 9.54336i | 0.180968 | − | 0.313445i | ||||
\(928\) | 0.884100 | − | 1.53131i | 0.0290220 | − | 0.0502676i | ||||
\(929\) | 18.9078 | + | 32.7492i | 0.620344 | + | 1.07447i | 0.989422 | + | 0.145068i | \(0.0463401\pi\) |
−0.369078 | + | 0.929398i | \(0.620327\pi\) | |||||||
\(930\) | 4.65238 | 0.152558 | ||||||||
\(931\) | −9.68870 | + | 16.7813i | −0.317534 | + | 0.549986i | ||||
\(932\) | 11.0930 | 0.363365 | ||||||||
\(933\) | −7.38545 | − | 12.7920i | −0.241789 | − | 0.418791i | ||||
\(934\) | 2.61259 | − | 4.52513i | 0.0854864 | − | 0.148067i | ||||
\(935\) | 13.0035 | − | 22.5227i | 0.425260 | − | 0.736571i | ||||
\(936\) | −1.51318 | − | 2.62090i | −0.0494598 | − | 0.0856669i | ||||
\(937\) | 50.2019 | 1.64002 | 0.820012 | − | 0.572346i | \(-0.193967\pi\) | ||||
0.820012 | + | 0.572346i | \(0.193967\pi\) | |||||||
\(938\) | 9.57602 | − | 16.5861i | 0.312668 | − | 0.541557i | ||||
\(939\) | −2.68485 | −0.0876167 | ||||||||
\(940\) | −6.01973 | − | 10.4265i | −0.196342 | − | 0.340074i | ||||
\(941\) | −16.6502 | + | 28.8389i | −0.542780 | + | 0.940122i | 0.455963 | + | 0.889999i | \(0.349295\pi\) |
−0.998743 | + | 0.0501235i | \(0.984039\pi\) | |||||||
\(942\) | −0.900593 | + | 1.55987i | −0.0293429 | + | 0.0508234i | ||||
\(943\) | −3.38410 | − | 5.86143i | −0.110201 | − | 0.190875i | ||||
\(944\) | −6.95698 | −0.226430 | ||||||||
\(945\) | 7.66548 | 0.249358 | ||||||||
\(946\) | −3.23879 | −0.105302 | ||||||||
\(947\) | −5.30153 | − | 9.18253i | −0.172277 | − | 0.298392i | 0.766939 | − | 0.641720i | \(-0.221779\pi\) |
−0.939215 | + | 0.343328i | \(0.888446\pi\) | |||||||
\(948\) | −3.44532 | + | 5.96748i | −0.111899 | + | 0.193815i | ||||
\(949\) | 7.77179 | − | 13.4611i | 0.252283 | − | 0.436967i | ||||
\(950\) | 4.69795 | + | 8.13708i | 0.152421 | + | 0.264002i | ||||
\(951\) | −11.0430 | −0.358094 | ||||||||
\(952\) | 7.33274 | + | 12.7007i | 0.237655 | + | 0.411631i | ||||
\(953\) | 10.0671 | 0.326104 | 0.163052 | − | 0.986617i | \(-0.447866\pi\) | ||||
0.163052 | + | 0.986617i | \(0.447866\pi\) | |||||||
\(954\) | 2.44864 | + | 4.24117i | 0.0792776 | + | 0.137313i | ||||
\(955\) | 26.5168 | − | 45.9284i | 0.858062 | − | 1.48621i | ||||
\(956\) | 2.81956 | − | 4.88362i | 0.0911911 | − | 0.157948i | ||||
\(957\) | 1.43171 | + | 2.47979i | 0.0462805 | + | 0.0801602i | ||||
\(958\) | −14.7682 | −0.477139 | ||||||||
\(959\) | 15.3490 | + | 26.5852i | 0.495644 | + | 0.858481i | ||||
\(960\) | 2.89728 | 0.0935093 | ||||||||
\(961\) | 14.2107 | + | 24.6137i | 0.458411 | + | 0.793991i | ||||
\(962\) | 1.55306 | − | 2.68998i | 0.0500727 | − | 0.0867285i | ||||
\(963\) | −4.57772 | + | 7.92884i | −0.147515 | + | 0.255503i | ||||
\(964\) | −12.0479 | − | 20.8675i | −0.388036 | − | 0.672098i | ||||
\(965\) | −0.989448 | −0.0318515 | ||||||||
\(966\) | 2.64575 | 0.0851257 | ||||||||
\(967\) | 13.1809 | 0.423870 | 0.211935 | − | 0.977284i | \(-0.432024\pi\) | ||||
0.211935 | + | 0.977284i | \(0.432024\pi\) | |||||||
\(968\) | −4.18878 | − | 7.25518i | −0.134633 | − | 0.233190i | ||||
\(969\) | 7.67211 | − | 13.2885i | 0.246464 | − | 0.426888i | ||||
\(970\) | 21.2933 | − | 36.8811i | 0.683687 | − | 1.18418i | ||||
\(971\) | −9.76005 | − | 16.9049i | −0.313215 | − | 0.542504i | 0.665842 | − | 0.746093i | \(-0.268073\pi\) |
−0.979056 | + | 0.203589i | \(0.934739\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 0.205622 | − | 0.356148i | 0.00659194 | − | 0.0114176i | ||||
\(974\) | −10.1615 | −0.325597 | ||||||||
\(975\) | −5.13607 | − | 8.89593i | −0.164486 | − | 0.284898i | ||||
\(976\) | 6.89728 | − | 11.9464i | 0.220777 | − | 0.382396i | ||||
\(977\) | 23.7779 | − | 41.1845i | 0.760722 | − | 1.31761i | −0.181756 | − | 0.983344i | \(-0.558178\pi\) |
0.942479 | − | 0.334266i | \(-0.108488\pi\) | |||||||
\(978\) | −4.43546 | − | 7.68244i | −0.141830 | − | 0.245657i | ||||
\(979\) | −23.5828 | −0.753711 | ||||||||
\(980\) | 10.1405 | + | 17.5638i | 0.323926 | + | 0.561056i | ||||
\(981\) | 10.5694 | 0.337455 | ||||||||
\(982\) | 3.51488 | + | 6.08795i | 0.112164 | + | 0.194274i | ||||
\(983\) | −23.6123 | + | 40.8978i | −0.753117 | + | 1.30444i | 0.193189 | + | 0.981162i | \(0.438117\pi\) |
−0.946305 | + | 0.323275i | \(0.895216\pi\) | |||||||
\(984\) | −3.38410 | + | 5.86143i | −0.107881 | + | 0.186856i | ||||
\(985\) | 29.3315 | + | 50.8036i | 0.934579 | + | 1.61874i | ||||
\(986\) | −9.80119 | −0.312133 | ||||||||
\(987\) | −5.49712 | + | 9.52130i | −0.174975 | + | 0.303066i | ||||
\(988\) | −8.37756 | −0.266526 | ||||||||
\(989\) | −1.00000 | − | 1.73205i | −0.0317982 | − | 0.0550760i | ||||
\(990\) | −2.34592 | + | 4.06325i | −0.0745582 | + | 0.129139i | ||||
\(991\) | 8.05189 | − | 13.9463i | 0.255777 | − | 0.443018i | −0.709329 | − | 0.704877i | \(-0.751002\pi\) |
0.965106 | + | 0.261859i | \(0.0843355\pi\) | |||||||
\(992\) | −0.802888 | − | 1.39064i | −0.0254917 | − | 0.0441530i | ||||
\(993\) | −8.29238 | −0.263151 | ||||||||
\(994\) | −12.8872 | −0.408759 | ||||||||
\(995\) | 77.9201 | 2.47023 | ||||||||
\(996\) | 2.57772 | + | 4.46474i | 0.0816781 | + | 0.141471i | ||||
\(997\) | −4.76506 | + | 8.25333i | −0.150911 | + | 0.261386i | −0.931563 | − | 0.363581i | \(-0.881554\pi\) |
0.780652 | + | 0.624967i | \(0.214887\pi\) | |||||||
\(998\) | 19.8293 | − | 34.3453i | 0.627684 | − | 1.08718i | ||||
\(999\) | −0.513179 | − | 0.888851i | −0.0162363 | − | 0.0281220i |
(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 | 966.2.i.n.277.4 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.n.415.4 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.ch.1.4 | 4 | |||
7.4 | even | 3 | 6762.2.a.cg.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.n.277.4 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.n.415.4 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cg.1.1 | 4 | 7.4 | even | 3 | |||
6762.2.a.ch.1.4 | 4 | 7.3 | odd | 6 |