Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(97,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.j (of order \(4\), degree \(2\), not 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: | \(3.06625543762\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(0.500000 + 2.10607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.289 |
Dual form | 384.2.j.a.97.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.27133 | + | 1.27133i | −0.568556 | + | 0.568556i | −0.931724 | − | 0.363168i | \(-0.881695\pi\) |
0.363168 | + | 0.931724i | \(0.381695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.158942i | − | 0.0600743i | −0.999549 | − | 0.0300371i | \(-0.990437\pi\) | ||
0.999549 | − | 0.0300371i | \(-0.00956256\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.79793 | + | 3.79793i | −1.14512 | + | 1.14512i | −0.157620 | + | 0.987500i | \(0.550382\pi\) |
−0.987500 | + | 0.157620i | \(0.949618\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.21215 | + | 4.21215i | 1.16824 | + | 1.16824i | 0.982622 | + | 0.185617i | \(0.0594284\pi\) |
0.185617 | + | 0.982622i | \(0.440572\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.79793 | −0.464224 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.05320 | 0.740511 | 0.370255 | − | 0.928930i | \(-0.379270\pi\) | ||||
0.370255 | + | 0.928930i | \(0.379270\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.15894 | − | 2.15894i | −0.495295 | − | 0.495295i | 0.414675 | − | 0.909970i | \(-0.363895\pi\) |
−0.909970 | + | 0.414675i | \(0.863895\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.112389 | − | 0.112389i | 0.0245252 | − | 0.0245252i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.76744i | 0.353488i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.09976 | − | 2.09976i | −0.389915 | − | 0.389915i | 0.484742 | − | 0.874657i | \(-0.338913\pi\) |
−0.874657 | + | 0.484742i | \(0.838913\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.15894 | −0.746968 | −0.373484 | − | 0.927637i | \(-0.621837\pi\) | ||||
−0.373484 | + | 0.927637i | \(0.621837\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.37109 | −0.934986 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.202067 | + | 0.202067i | 0.0341556 | + | 0.0341556i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.98737 | − | 5.98737i | 0.984317 | − | 0.984317i | −0.0155615 | − | 0.999879i | \(-0.504954\pi\) |
0.999879 | + | 0.0155615i | \(0.00495359\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.95687i | 0.953863i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 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 | −0.115686 | − | 0.993286i | \(-0.536907\pi\) |
0.993286 | + | 0.115686i | \(0.0369066\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.27133 | − | 1.27133i | −0.189519 | − | 0.189519i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 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 | 0 | ||||||||
\(51\) | 2.15894 | + | 2.15894i | 0.302312 | + | 0.302312i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.55710 | + | 3.55710i | −0.488605 | + | 0.488605i | −0.907866 | − | 0.419261i | \(-0.862289\pi\) |
0.419261 | + | 0.907866i | \(0.362289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 9.65685i | − | 1.30213i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.05320i | − | 0.404407i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.00000 | − | 4.00000i | 0.520756 | − | 0.520756i | −0.397044 | − | 0.917800i | \(-0.629964\pi\) |
0.917800 | + | 0.397044i | \(0.129964\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.66949 | − | 3.66949i | −0.469829 | − | 0.469829i | 0.432030 | − | 0.901859i | \(-0.357798\pi\) |
−0.901859 | + | 0.432030i | \(0.857798\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.158942 | 0.0200248 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.7101 | −1.32842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.767438 | + | 0.767438i | 0.0937575 | + | 0.0937575i | 0.752430 | − | 0.658672i | \(-0.228882\pi\) |
−0.658672 | + | 0.752430i | \(0.728882\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | + | 2.00000i | −0.240772 | + | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.317883i | 0.0377258i | 0.999822 | + | 0.0188629i | \(0.00600460\pi\) | ||||
−0.999822 | + | 0.0188629i | \(0.993995\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.33897i | 0.156715i | 0.996925 | + | 0.0783573i | \(0.0249675\pi\) | ||||
−0.996925 | + | 0.0783573i | \(0.975032\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.24977 | + | 1.24977i | −0.144311 | + | 0.144311i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.603650 | + | 0.603650i | 0.0687923 | + | 0.0687923i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.69382 | 1.09064 | 0.545320 | − | 0.838228i | \(-0.316408\pi\) | ||||
0.545320 | + | 0.838228i | \(0.316408\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.115816 | + | 0.115816i | 0.0127125 | + | 0.0127125i | 0.713434 | − | 0.700722i | \(-0.247139\pi\) |
−0.700722 | + | 0.713434i | \(0.747139\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.88163 | + | 3.88163i | −0.421022 | + | 0.421022i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.96951i | − | 0.318364i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.94082 | − | 2.94082i | −0.304948 | − | 0.304948i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.48946 | 0.563206 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.571533 | −0.0580304 | −0.0290152 | − | 0.999579i | \(-0.509237\pi\) | ||||
−0.0290152 | + | 0.999579i | \(0.509237\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.79793 | − | 3.79793i | −0.381707 | − | 0.381707i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.15296 | − | 7.15296i | 0.711746 | − | 0.711746i | −0.255154 | − | 0.966900i | \(-0.582126\pi\) |
0.966900 | + | 0.255154i | \(0.0821262\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 11.3507i | − | 1.11841i | −0.829028 | − | 0.559207i | \(-0.811106\pi\) | ||
0.829028 | − | 0.559207i | \(-0.188894\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.285766i | 0.0278879i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.722018 | + | 0.722018i | −0.0698001 | + | 0.0698001i | −0.741145 | − | 0.671345i | \(-0.765717\pi\) |
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.44471 | + | 1.44471i | 0.138378 | + | 0.138378i | 0.772903 | − | 0.634525i | \(-0.218804\pi\) |
−0.634525 | + | 0.772903i | \(0.718804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.46742 | 0.803692 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.53488 | −0.332533 | −0.166267 | − | 0.986081i | \(-0.553171\pi\) | ||||
−0.166267 | + | 0.986081i | \(0.553171\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.59587 | − | 3.59587i | −0.335316 | − | 0.335316i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.21215 | + | 4.21215i | −0.389413 | + | 0.389413i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 0.485281i | − | 0.0444857i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 17.8486i | − | 1.62260i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.84106 | + | 1.84106i | −0.166003 | + | 0.166003i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.60365 | − | 8.60365i | −0.769534 | − | 0.769534i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.49791 | 0.132918 | 0.0664591 | − | 0.997789i | \(-0.478830\pi\) | ||||
0.0664591 | + | 0.997789i | \(0.478830\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.13853 | 0.716557 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.4243 | + | 10.4243i | 0.910775 | + | 0.910775i | 0.996333 | − | 0.0855585i | \(-0.0272675\pi\) |
−0.0855585 | + | 0.996333i | \(0.527267\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.343146 | + | 0.343146i | −0.0297545 | + | 0.0297545i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 1.79793i | − | 0.154741i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 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 | −0.802405 | − | 0.596779i | \(-0.796447\pi\) |
0.596779 | + | 0.802405i | \(0.296447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | + | 2.00000i | 0.168430 | + | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −31.9949 | −2.67555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.33897 | 0.443377 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.93188 | + | 4.93188i | 0.406775 | + | 0.406775i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.92818 | + | 2.92818i | −0.239886 | + | 0.239886i | −0.816803 | − | 0.576917i | \(-0.804256\pi\) |
0.576917 | + | 0.816803i | \(0.304256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.6644i | 1.84440i | 0.386712 | + | 0.922201i | \(0.373611\pi\) | ||||
−0.386712 | + | 0.922201i | \(0.626389\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.05320i | 0.246837i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.28739 | − | 5.28739i | 0.424693 | − | 0.424693i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.78007 | + | 2.78007i | 0.221874 | + | 0.221874i | 0.809287 | − | 0.587413i | \(-0.199854\pi\) |
−0.587413 | + | 0.809287i | \(0.699854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.03049 | −0.398944 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.449555 | 0.0354299 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.43692 | − | 5.43692i | −0.425853 | − | 0.425853i | 0.461360 | − | 0.887213i | \(-0.347362\pi\) |
−0.887213 | + | 0.461360i | \(0.847362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.82843 | − | 6.82843i | 0.531592 | − | 0.531592i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.95458i | − | 0.306015i | −0.988225 | − | 0.153007i | \(-0.951104\pi\) | ||
0.988225 | − | 0.153007i | \(-0.0488958\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 22.4844i | 1.72957i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.15894 | − | 2.15894i | 0.165098 | − | 0.165098i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.9814 | + | 15.9814i | 1.21504 | + | 1.21504i | 0.969347 | + | 0.245695i | \(0.0790163\pi\) |
0.245695 | + | 0.969347i | \(0.420984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.280920 | 0.0212355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.65685 | 0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.2316 | − | 12.2316i | −0.914235 | − | 0.914235i | 0.0823670 | − | 0.996602i | \(-0.473752\pi\) |
−0.996602 | + | 0.0823670i | \(0.973752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.76259 | + | 5.76259i | −0.428330 | + | 0.428330i | −0.888059 | − | 0.459729i | \(-0.847946\pi\) |
0.459729 | + | 0.888059i | \(0.347946\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.18944i | − | 0.383614i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.2238i | 1.11928i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.5959 | + | 11.5959i | −0.847974 | + | 0.847974i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.112389 | + | 0.112389i | 0.00817508 | + | 0.00817508i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 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 | 0 | ||||||||
\(195\) | −7.57316 | − | 7.57316i | −0.542325 | − | 0.542325i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.2993 | − | 14.2993i | 1.01878 | − | 1.01878i | 0.0189608 | − | 0.999820i | \(-0.493964\pi\) |
0.999820 | − | 0.0189608i | \(-0.00603576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.0075i | 1.77274i | 0.462981 | + | 0.886368i | \(0.346780\pi\) | ||||
−0.462981 | + | 0.886368i | \(0.653220\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.08532i | 0.0765527i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.333739 | + | 0.333739i | −0.0234239 | + | 0.0234239i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.31010 | − | 3.31010i | −0.231187 | − | 0.231187i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.3990 | 1.13434 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.4243 | + | 18.4243i | 1.26838 | + | 1.26838i | 0.946924 | + | 0.321456i | \(0.104172\pi\) |
0.321456 | + | 0.946924i | \(0.395828\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.224777 | + | 0.224777i | −0.0154015 | + | 0.0154015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.6325i | 0.997930i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.661029i | 0.0448736i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.946795 | + | 0.946795i | −0.0639785 | + | 0.0639785i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.8605 | + | 12.8605i | 0.865094 | + | 0.865094i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −18.3465 | −1.22857 | −0.614286 | − | 0.789083i | \(-0.710556\pi\) | ||||
−0.614286 | + | 0.789083i | \(0.710556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.76744 | −0.117829 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.115816 | − | 0.115816i | −0.00768697 | − | 0.00768697i | 0.703253 | − | 0.710940i | \(-0.251730\pi\) |
−0.710940 | + | 0.703253i | \(0.751730\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.84791 | + | 2.84791i | −0.188195 | + | 0.188195i | −0.794916 | − | 0.606720i | \(-0.792485\pi\) |
0.606720 | + | 0.794916i | \(0.292485\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.853690i | 0.0561687i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 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 | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.85456 | + | 6.85456i | 0.445252 | + | 0.445252i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 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 | \(0.478129\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.86720 | + | 8.86720i | −0.566504 | + | 0.566504i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 18.1876i | − | 1.15725i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.163788i | 0.0103797i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.43370 | + | 4.43370i | −0.279853 | + | 0.279853i | −0.833050 | − | 0.553198i | \(-0.813407\pi\) |
0.553198 | + | 0.833050i | \(0.313407\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.7422 | − | 10.7422i | −0.675355 | − | 0.675355i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.48946 | −0.343763 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.0853 | 0.940997 | 0.470498 | − | 0.882401i | \(-0.344074\pi\) | ||||
0.470498 | + | 0.882401i | \(0.344074\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.951642 | − | 0.951642i | −0.0591322 | − | 0.0591322i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.09976 | − | 2.09976i | 0.129972 | − | 0.129972i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 26.1706i | − | 1.61375i | −0.590722 | − | 0.806875i | \(-0.701157\pi\) | ||
0.590722 | − | 0.806875i | \(-0.298843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.04449i | − | 0.555599i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.1817 | − | 10.1817i | 0.623107 | − | 0.623107i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.59700 | − | 8.59700i | −0.524168 | − | 0.524168i | 0.394659 | − | 0.918828i | \(-0.370863\pi\) |
−0.918828 | + | 0.394659i | \(0.870863\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.6644 | −0.647815 | −0.323907 | − | 0.946089i | \(-0.604997\pi\) | ||||
−0.323907 | + | 0.946089i | \(0.604997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.946795 | 0.0573027 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.71261 | − | 6.71261i | −0.404786 | − | 0.404786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.66170 | − | 2.66170i | 0.159926 | − | 0.159926i | −0.622608 | − | 0.782534i | \(-0.713927\pi\) |
0.782534 | + | 0.622608i | \(0.213927\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 4.15894i | − | 0.248989i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 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 | −0.972996 | − | 0.230823i | \(-0.925858\pi\) |
0.230823 | + | 0.972996i | \(0.425858\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.88163 | + | 3.88163i | 0.229928 | + | 0.229928i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.413828 | 0.0244275 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.67794 | −0.451644 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.404135 | − | 0.404135i | −0.0236908 | − | 0.0236908i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.7410 | + | 21.7410i | −1.27013 | + | 1.27013i | −0.324104 | + | 0.946022i | \(0.605063\pi\) |
−0.946022 | + | 0.324104i | \(0.894937\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.1706i | 0.592158i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.37109i | − | 0.311662i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.9137 | + | 11.9137i | −0.688990 | + | 0.688990i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.914679 | − | 0.914679i | −0.0527212 | − | 0.0527212i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 10.1158 | 0.581138 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.33026 | 0.534249 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.0601 | + | 15.0601i | 0.859523 | + | 0.859523i | 0.991282 | − | 0.131759i | \(-0.0420624\pi\) |
−0.131759 | + | 0.991282i | \(0.542062\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.02614 | − | 8.02614i | 0.456591 | − | 0.456591i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.77883i | − | 0.100868i | −0.998727 | − | 0.0504342i | \(-0.983939\pi\) | ||
0.998727 | − | 0.0504342i | \(-0.0160605\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.70320i | 0.152794i | 0.997077 | + | 0.0763971i | \(0.0243417\pi\) | ||||
−0.997077 | + | 0.0763971i | \(0.975658\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.202067 | + | 0.202067i | −0.0113852 | + | 0.0113852i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −15.6025 | − | 15.6025i | −0.876325 | − | 0.876325i | 0.116828 | − | 0.993152i | \(-0.462728\pi\) |
−0.993152 | + | 0.116828i | \(0.962728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.9495 | 0.892999 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.02109 | −0.0569916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.59169 | − | 6.59169i | −0.366771 | − | 0.366771i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.44471 | + | 7.44471i | −0.412958 | + | 0.412958i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.04313i | 0.112985i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 0.449555i | − | 0.0247848i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.4454 | − | 15.4454i | 0.848955 | − | 0.848955i | −0.141048 | − | 0.990003i | \(-0.545047\pi\) |
0.990003 | + | 0.141048i | \(0.0450472\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.98737 | + | 5.98737i | 0.328106 | + | 0.328106i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.95133 | −0.106613 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.8738 | −1.02812 | −0.514062 | − | 0.857753i | \(-0.671860\pi\) | ||||
−0.514062 | + | 0.857753i | \(0.671860\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.49954 | − | 2.49954i | −0.135756 | − | 0.135756i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.7954 | − | 15.7954i | 0.855368 | − | 0.855368i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.22117i | − | 0.119932i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 5.08532i | − | 0.273785i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.8337 | − | 19.8337i | 1.06473 | − | 1.06473i | 0.0669717 | − | 0.997755i | \(-0.478666\pi\) |
0.997755 | − | 0.0669717i | \(-0.0213337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.9718 | − | 11.9718i | −0.640836 | − | 0.640836i | 0.309925 | − | 0.950761i | \(-0.399696\pi\) |
−0.950761 | + | 0.309925i | \(0.899696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.95687 | −0.317954 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.6202 | −0.671705 | −0.335853 | − | 0.941915i | \(-0.609024\pi\) | ||||
−0.335853 | + | 0.941915i | \(0.609024\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.404135 | − | 0.404135i | −0.0214492 | − | 0.0214492i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.343146 | − | 0.343146i | 0.0181612 | − | 0.0181612i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 27.0867i | − | 1.42958i | −0.699339 | − | 0.714790i | \(-0.746522\pi\) | ||
0.699339 | − | 0.714790i | \(-0.253478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 9.67794i | − | 0.509365i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.6209 | − | 12.6209i | 0.662423 | − | 0.662423i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.70227 | − | 1.70227i | −0.0891011 | − | 0.0891011i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.4937 | 1.06976 | 0.534882 | − | 0.844927i | \(-0.320356\pi\) | ||||
0.534882 | + | 0.844927i | \(0.320356\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.60365 | −0.135541 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.565371 | + | 0.565371i | 0.0293526 | + | 0.0293526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.03372 | + | 1.03372i | −0.0535239 | + | 0.0535239i | −0.733362 | − | 0.679838i | \(-0.762050\pi\) |
0.679838 | + | 0.733362i | \(0.262050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 12.1674i | − | 0.628322i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17.6890i | − | 0.911028i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.6686 | − | 17.6686i | 0.907573 | − | 0.907573i | −0.0885032 | − | 0.996076i | \(-0.528208\pi\) |
0.996076 | + | 0.0885032i | \(0.0282083\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.05918 | + | 1.05918i | 0.0542636 | + | 0.0542636i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 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 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.75481 | + | 5.75481i | 0.292533 | + | 0.292533i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.56127 | − | 2.56127i | 0.129862 | − | 0.129862i | −0.639188 | − | 0.769050i | \(-0.720730\pi\) |
0.769050 | + | 0.639188i | \(0.220730\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.63577i | 0.436729i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.7422i | 0.743644i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −12.3240 | + | 12.3240i | −0.620090 | + | 0.620090i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.09795 | + | 5.09795i | 0.255859 | + | 0.255859i | 0.823367 | − | 0.567509i | \(-0.192093\pi\) |
−0.567509 | + | 0.823367i | \(0.692093\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.485281 | −0.0242945 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.2660 | −0.762349 | −0.381174 | − | 0.924503i | \(-0.624480\pi\) | ||||
−0.381174 | + | 0.924503i | \(0.624480\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5181 | − | 17.5181i | −0.872637 | − | 0.872637i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.27133 | − | 1.27133i | 0.0631729 | − | 0.0631729i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.4792i | 2.25432i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.3779i | 0.562603i | 0.959619 | + | 0.281302i | \(0.0907661\pi\) | ||||
−0.959619 | + | 0.281302i | \(0.909234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.75481 | + | 9.75481i | −0.481169 | + | 0.481169i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.635767 | − | 0.635767i | −0.0312840 | − | 0.0312840i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.294481 | −0.0144555 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.42847 | −0.167893 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.3075 | + | 23.3075i | 1.13865 | + | 1.13865i | 0.988693 | + | 0.149955i | \(0.0479130\pi\) |
0.149955 | + | 0.988693i | \(0.452087\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.6154 | − | 17.6154i | 0.858520 | − | 0.858520i | −0.132644 | − | 0.991164i | \(-0.542347\pi\) |
0.991164 | + | 0.132644i | \(0.0423467\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843i | 0.137523i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.39635i | 0.261761i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.583234 | + | 0.583234i | −0.0282247 | + | 0.0282247i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.6238 | − | 22.6238i | −1.09229 | − | 1.09229i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −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 | 0 | ||||||||
\(435\) | 3.77522 | + | 3.77522i | 0.181008 | + | 0.181008i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 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 | \(-0.181080\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.97474i | 0.332130i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.7117 | − | 23.7117i | 1.12658 | − | 1.12658i | 0.135846 | − | 0.990730i | \(-0.456625\pi\) |
0.990730 | − | 0.135846i | \(-0.0433752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.3059 | + | 18.3059i | 0.867784 | + | 0.867784i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.14108 | −0.195866 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.75506 | −0.0828266 | −0.0414133 | − | 0.999142i | \(-0.513186\pi\) | ||||
−0.0414133 | + | 0.999142i | \(0.513186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.88849 | − | 9.88849i | −0.465631 | − | 0.465631i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.0261 | + | 16.0261i | −0.752974 | + | 0.752974i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.70227i | 0.0798039i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 26.7422i | − | 1.25095i | −0.780246 | − | 0.625473i | \(-0.784906\pi\) | ||
0.780246 | − | 0.625473i | \(-0.215094\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.15894 | + | 2.15894i | −0.100771 | + | 0.100771i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.23921 | − | 9.23921i | −0.430313 | − | 0.430313i | 0.458422 | − | 0.888735i | \(-0.348415\pi\) |
−0.888735 | + | 0.458422i | \(0.848415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.4474 | −1.36854 | −0.684268 | − | 0.729231i | \(-0.739878\pi\) | ||||
−0.684268 | + | 0.729231i | \(0.739878\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7.47750 | 0.346761 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.5897 | − | 19.5897i | −0.906503 | − | 0.906503i | 0.0894848 | − | 0.995988i | \(-0.471478\pi\) |
−0.995988 | + | 0.0894848i | \(0.971478\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.121978 | − | 0.121978i | 0.00563242 | − | 0.00563242i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.93161i | 0.181159i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.7127i | 2.00991i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.81580 | − | 3.81580i | 0.175081 | − | 0.175081i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.55710 | − | 3.55710i | −0.162868 | − | 0.162868i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −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 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.317883 | + | 0.317883i | 0.0144642 | + | 0.0144642i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 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 | \(0.928238\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 7.68897i | − | 0.347707i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.449555 | + | 0.449555i | −0.0202881 | + | 0.0202881i | −0.717178 | − | 0.696890i | \(-0.754567\pi\) |
0.696890 | + | 0.717178i | \(0.254567\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.41099 | − | 6.41099i | −0.288736 | − | 0.288736i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.65685 | 0.434043 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0505249 | 0.00226635 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.70645 | + | 2.70645i | 0.121157 | + | 0.121157i | 0.765086 | − | 0.643928i | \(-0.222697\pi\) |
−0.643928 | + | 0.765086i | \(0.722697\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.79631 | − | 2.79631i | 0.124930 | − | 0.124930i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 23.6719i | − | 1.05548i | −0.849407 | − | 0.527739i | \(-0.823040\pi\) | ||
0.849407 | − | 0.527739i | \(-0.176960\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.1876i | 0.809336i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −15.8988 | + | 15.8988i | −0.706092 | + | 0.706092i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.6052 | + | 24.6052i | 1.09061 | + | 1.09061i | 0.995464 | + | 0.0951425i | \(0.0303307\pi\) |
0.0951425 | + | 0.995464i | \(0.469669\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.212818 | 0.00941453 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.05320 | 0.134802 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.4305 | + | 14.4305i | 0.635882 | + | 0.635882i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.7422 | + | 10.7422i | −0.472440 | + | 0.472440i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22.6011i | 0.992078i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 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 | −0.990451 | − | 0.137867i | \(-0.955975\pi\) |
0.137867 | + | 0.990451i | \(0.455975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.198640 | + | 0.198640i | 0.00866937 | + | 0.00866937i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.6981 | −0.553138 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | + | 4.00000i | 0.173585 | + | 0.173585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.9670 | + | 10.9670i | −0.475031 | + | 0.475031i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.83585i | − | 0.0793706i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 17.2981i | − | 0.746470i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −26.4896 | + | 26.4896i | −1.14099 | + | 1.14099i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.0396 | + | 10.0396i | 0.431638 | + | 0.431638i | 0.889185 | − | 0.457547i | \(-0.151272\pi\) |
−0.457547 | + | 0.889185i | \(0.651272\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.14953 | −0.349730 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.67340 | −0.157351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.19884 | − | 7.19884i | −0.307800 | − | 0.307800i | 0.536255 | − | 0.844056i | \(-0.319838\pi\) |
−0.844056 | + | 0.536255i | \(0.819838\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.66949 | − | 3.66949i | 0.156610 | − | 0.156610i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.06651i | 0.386246i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1.54075i | − | 0.0655194i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.7649 | + | 10.7649i | −0.456944 | + | 0.456944i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.02129 | − | 1.02129i | −0.0432735 | − | 0.0432735i | 0.685139 | − | 0.728412i | \(-0.259741\pi\) |
−0.728412 | + | 0.685139i | \(0.759741\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.4802 | 2.05049 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.3990 | −0.692368 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.70751 | + | 6.70751i | 0.282688 | + | 0.282688i | 0.834180 | − | 0.551492i | \(-0.185941\pi\) |
−0.551492 | + | 0.834180i | \(0.685941\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.49400 | − | 4.49400i | 0.189064 | − | 0.189064i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.158942i | 0.00667492i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 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 | −0.872476 | − | 0.488657i | \(-0.837487\pi\) |
0.488657 | + | 0.872476i | \(0.337487\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11.4321 | + | 11.4321i | 0.477582 | + | 0.477582i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.99907 | −0.208476 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.5013 | 1.22815 | 0.614077 | − | 0.789246i | \(-0.289528\pi\) | ||||
0.614077 | + | 0.789246i | \(0.289528\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −15.6591 | − | 15.6591i | −0.650772 | − | 0.650772i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.0184080 | − | 0.0184080i | 0.000763692 | − | 0.000763692i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 27.0192i | − | 1.11902i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 10.7101i | − | 0.442806i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.82425 | − | 1.82425i | 0.0752950 | − | 0.0752950i | −0.668456 | − | 0.743751i | \(-0.733045\pi\) |
0.743751 | + | 0.668456i | \(0.233045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.97891 | + | 8.97891i | 0.369970 | + | 0.369970i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 20.2222 | 0.831831 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −35.4338 | −1.45509 | −0.727546 | − | 0.686058i | \(-0.759339\pi\) | ||||
−0.727546 | + | 0.686058i | \(0.759339\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.616953 | + | 0.616953i | 0.0252926 | + | 0.0252926i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −17.6830 | + | 17.6830i | −0.723717 | + | 0.723717i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.1632i | 1.10986i | 0.831897 | + | 0.554930i | \(0.187255\pi\) | ||||
−0.831897 | + | 0.554930i | \(0.812745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.33897i | 0.217781i | 0.994054 | + | 0.108891i | \(0.0347298\pi\) | ||||
−0.994054 | + | 0.108891i | \(0.965270\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.767438 | + | 0.767438i | −0.0312525 | + | 0.0312525i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.6914 | + | 22.6914i | 0.922539 | + | 0.922539i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1084 | −0.653820 | −0.326910 | − | 0.945055i | \(-0.606007\pi\) | ||||
−0.326910 | + | 0.945055i | \(0.606007\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.471978 | −0.0191255 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.9137 | + | 11.9137i | 0.481979 | + | 0.481979i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.436924 | + | 0.436924i | −0.0176472 | + | 0.0176472i | −0.715875 | − | 0.698228i | \(-0.753972\pi\) |
0.698228 | + | 0.715875i | \(0.253972\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.68119i | − | 0.188764i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 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 | −0.667270 | − | 0.744816i | \(-0.732537\pi\) |
0.744816 | + | 0.667270i | \(0.232537\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 2.00000i | −0.0802572 | − | 0.0802572i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.28861 | −0.0916910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13.0390 | 0.521559 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 11.5959 | + | 11.5959i | 0.463094 | + | 0.463094i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 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 | \(-0.280759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 26.0559i | 1.03563i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.90434 | + | 1.90434i | −0.0755715 | + | 0.0755715i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.3786 | + | 29.3786i | 1.16402 | + | 1.16402i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.317883 | −0.0125753 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 33.1091 | 1.30773 | 0.653865 | − | 0.756611i | \(-0.273146\pi\) | ||||
0.653865 | + | 0.756611i | \(0.273146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2897 | − | 19.2897i | −0.760711 | − | 0.760711i | 0.215740 | − | 0.976451i | \(-0.430784\pi\) |
−0.976451 | + | 0.215740i | \(0.930784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.3468 | + | 10.3468i | −0.407403 | + | 0.407403i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.8477i | 1.64520i | 0.568620 | + | 0.822601i | \(0.307478\pi\) | ||||
−0.568620 | + | 0.822601i | \(0.692522\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.3835i | 1.19266i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.467418 | + | 0.467418i | −0.0183196 | + | 0.0183196i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14.7741 | − | 14.7741i | −0.578155 | − | 0.578155i | 0.356240 | − | 0.934395i | \(-0.384059\pi\) |
−0.934395 | + | 0.356240i | \(0.884059\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.5054 | −1.03565 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.33897 | −0.0522382 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.22839 | − | 2.22839i | −0.0868056 | − | 0.0868056i | 0.662371 | − | 0.749176i | \(-0.269550\pi\) |
−0.749176 | + | 0.662371i | \(0.769550\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.0685 | − | 18.0685i | 0.702784 | − | 0.702784i | −0.262223 | − | 0.965007i | \(-0.584456\pi\) |
0.965007 | + | 0.262223i | \(0.0844557\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.1876i | 0.706346i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.872503i | − | 0.0338342i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.93901 | − | 5.93901i | 0.229959 | − | 0.229959i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.9729 | − | 12.9729i | −0.501563 | − | 0.501563i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 27.8729 | 1.07602 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7981 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.24977 | − | 1.24977i | −0.0481036 | − | 0.0481036i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −29.0213 | + | 29.0213i | −1.11538 | + | 1.11538i | −0.122968 | + | 0.992411i | \(0.539241\pi\) |
−0.992411 | + | 0.122968i | \(0.960759\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0908404i | 0.00348613i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 0.163788i | − | 0.00627639i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.7938 | + | 18.7938i | −0.719123 | + | 0.719123i | −0.968426 | − | 0.249303i | \(-0.919799\pi\) |
0.249303 | + | 0.968426i | \(0.419799\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.5385 | − | 17.5385i | −0.670111 | − | 0.670111i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.02756 | −0.153661 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.9660 | −1.14161 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.4580 | + | 10.4580i | 0.397841 | + | 0.397841i | 0.877471 | − | 0.479630i | \(-0.159229\pi\) |
−0.479630 | + | 0.877471i | \(0.659229\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.603650 | + | 0.603650i | −0.0229308 | + | 0.0229308i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.16415i | − | 0.233820i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.94948i | 0.301108i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.28806 | − | 8.28806i | 0.313483 | − | 0.313483i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.3314 | − | 18.3314i | −0.692367 | − | 0.692367i | 0.270385 | − | 0.962752i | \(-0.412849\pi\) |
−0.962752 | + | 0.270385i | \(0.912849\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −25.8528 | −0.975055 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.08532 | −0.191524 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.13690 | − | 1.13690i | −0.0427577 | − | 0.0427577i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −14.5722 | + | 14.5722i | −0.547271 | + | 0.547271i | −0.925650 | − | 0.378380i | \(-0.876481\pi\) |
0.378380 | + | 0.925650i | \(0.376481\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.69382i | 0.363547i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 11.7633i | − | 0.440538i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 40.6761 | − | 40.6761i | 1.52120 | − | 1.52120i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.65324 | + | 9.65324i | 0.360507 | + | 0.360507i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.50732 | + | 1.50732i | 0.0560578 | + | 0.0560578i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 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 | \(0.945221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.5706 | − | 17.5706i | 0.649872 | − | 0.649872i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2764 | − | 18.2764i | −0.675053 | − | 0.675053i | 0.283823 | − | 0.958877i | \(-0.408397\pi\) |
−0.958877 | + | 0.283823i | \(0.908397\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −12.5401 | −0.462549 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.82936 | −0.214727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9991 | + | 16.9991i | 0.625321 | + | 0.625321i | 0.946887 | − | 0.321566i | \(-0.104209\pi\) |
−0.321566 | + | 0.946887i | \(0.604209\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.8605 | − | 12.8605i | 0.472444 | − | 0.472444i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.8748i | − | 0.655762i | −0.944719 | − | 0.327881i | \(-0.893665\pi\) | ||
0.944719 | − | 0.327881i | \(-0.106335\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 7.44538i | − | 0.272778i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.115816 | + | 0.115816i | −0.00423748 | + | 0.00423748i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.114759 | + | 0.114759i | 0.00419319 | + | 0.00419319i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.0731 | 1.27984 | 0.639918 | − | 0.768443i | \(-0.278968\pi\) | ||||
0.639918 | + | 0.768443i | \(0.278968\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.27020 | −0.228499 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.8139 | − | 28.8139i | −1.04865 | − | 1.04865i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.8071 | − | 32.8071i | 1.19239 | − | 1.19239i | 0.216000 | − | 0.976393i | \(-0.430699\pi\) |
0.976393 | − | 0.216000i | \(-0.0693012\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 15.1917i | − | 0.551425i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 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 | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.88163 | − | 3.88163i | −0.140341 | − | 0.140341i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 33.6972 | 1.21673 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −35.2068 | −1.26959 | −0.634795 | − | 0.772681i | \(-0.718915\pi\) | ||||
−0.634795 | + | 0.772681i | \(0.718915\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.6669 | + | 10.6669i | 0.384160 | + | 0.384160i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.3897 | − | 19.3897i | 0.697399 | − | 0.697399i | −0.266450 | − | 0.963849i | \(-0.585851\pi\) |
0.963849 | + | 0.266450i | \(0.0858507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.35067i | − | 0.264044i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 1.34583i | − | 0.0482812i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.62113 | − | 5.62113i | 0.201398 | − | 0.201398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.20730 | − | 1.20730i | −0.0432006 | − | 0.0432006i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.96951 | 0.106121 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.06877 | −0.252295 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.68964 | − | 6.68964i | −0.238460 | − | 0.238460i | 0.577752 | − | 0.816212i | \(-0.303930\pi\) |
−0.816212 | + | 0.577752i | \(0.803930\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 18.5054 | − | 18.5054i | 0.658811 | − | 0.658811i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.561839i | 0.0199767i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 30.9128i | − | 1.09775i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.39542 | − | 6.39542i | 0.226822 | − | 0.226822i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.5617 | − | 13.5617i | −0.480380 | − | 0.480380i | 0.424873 | − | 0.905253i | \(-0.360319\pi\) |
−0.905253 | + | 0.424873i | \(0.860319\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.63577 | 0.305511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.3990 | 0.508765 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.08532 | − | 5.08532i | −0.179457 | − | 0.179457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.571533 | + | 0.571533i | −0.0201439 | + | 0.0201439i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 12.1580i | − | 0.427982i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 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 | −0.657358 | − | 0.753578i | \(-0.728326\pi\) |
0.753578 | + | 0.657358i | \(0.228326\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.54086 | − | 7.54086i | −0.264469 | − | 0.264469i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.8243 | 0.484242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.8486 | −0.869342 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.669485 | + | 0.669485i | 0.0233937 | + | 0.0233937i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.97453 | + | 3.97453i | −0.138712 | + | 0.138712i | −0.773053 | − | 0.634341i | \(-0.781271\pi\) |
0.634341 | + | 0.773053i | \(0.281271\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5255i | 1.34291i | 0.741043 | + | 0.671457i | \(0.234331\pi\) | ||||
−0.741043 | + | 0.671457i | \(0.765669\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 9.49307i | − | 0.330506i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.99583 | − | 2.99583i | 0.104175 | − | 0.104175i | −0.653098 | − | 0.757273i | \(-0.726531\pi\) |
0.757273 | + | 0.653098i | \(0.226531\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.9699 | + | 24.9699i | 0.867240 | + | 0.867240i | 0.992166 | − | 0.124926i | \(-0.0398693\pi\) |
−0.124926 | + | 0.992166i | \(0.539869\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.76421 | 0.130579 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 21.2953 | 0.737838 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.02758 | + | 5.02758i | 0.173986 | + | 0.173986i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.94082 | − | 2.94082i | 0.101649 | − | 0.101649i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 39.6005i | − | 1.36716i | −0.729876 | − | 0.683580i | \(-0.760422\pi\) | ||
0.729876 | − | 0.683580i | \(-0.239578\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 20.1820i | − | 0.695932i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.38895 | − | 7.38895i | 0.254489 | − | 0.254489i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −28.5850 | − | 28.5850i | −0.983355 | − | 0.983355i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.83688 | −0.0974765 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.6569 | −0.605982 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 16.9348 | + | 16.9348i | 0.580519 | + | 0.580519i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.68505 | + | 7.68505i | −0.263131 | + | 0.263131i | −0.826325 | − | 0.563194i | \(-0.809572\pi\) |
0.563194 | + | 0.826325i | \(0.309572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.48946i | 0.187735i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 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 | −0.532718 | − | 0.846293i | \(-0.678829\pi\) |
0.846293 | + | 0.532718i | \(0.178829\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.292621 | + | 0.292621i | 0.00997249 | + | 0.00997249i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 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 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.42912 | − | 5.42912i | −0.184383 | − | 0.184383i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36.8165 | + | 36.8165i | −1.24891 | + | 1.24891i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.46512i | 0.219062i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 0.571533i | − | 0.0193435i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.36748 | + | 1.36748i | −0.0462292 | + | 0.0462292i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.9718 | − | 31.9718i | −1.07961 | − | 1.07961i | −0.996544 | − | 0.0830670i | \(-0.973528\pi\) |
−0.0830670 | − | 0.996544i | \(-0.526472\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.7465 | −1.03705 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.7403 | 1.17043 | 0.585215 | − | 0.810878i | \(-0.301010\pi\) | ||||
0.585215 | + | 0.810878i | \(0.301010\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34.6034 | − | 34.6034i | −1.16450 | − | 1.16450i | −0.983480 | − | 0.181017i | \(-0.942061\pi\) |
−0.181017 | − | 0.983480i | \(-0.557939\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.19173 | + | 7.19173i | −0.241747 | + | 0.241747i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 22.9284i | − | 0.769860i | −0.922946 | − | 0.384930i | \(-0.874226\pi\) | ||
0.922946 | − | 0.384930i | \(-0.125774\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 0.238081i | − | 0.00798497i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.79793 | − | 3.79793i | 0.127236 | − | 0.127236i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.10641 | − | 6.10641i | −0.204343 | − | 0.204343i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.1009 | 1.03959 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.8486 | −0.562558 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.73277 | + | 8.73277i | 0.291254 | + | 0.291254i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10.8605 | + | 10.8605i | −0.361817 | + | 0.361817i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1.29355i | − | 0.0430467i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 14.6523i | − | 0.487059i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −16.3822 | + | 16.3822i | −0.543963 | + | 0.543963i | −0.924688 | − | 0.380725i | \(-0.875674\pi\) |
0.380725 | + | 0.924688i | \(0.375674\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.15296 | + | 7.15296i | 0.237249 | + | 0.237249i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 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 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.59749 | + | 6.59749i | 0.218106 | + | 0.218106i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 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 | \(0.963906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21.2981i | 0.701798i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.33897 | + | 1.33897i | −0.0440728 | + | 0.0440728i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.5823 | + | 10.5823i | 0.347944 | + | 0.347944i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 11.3507 | 0.372805 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.1385 | 0.529488 | 0.264744 | − | 0.964319i | \(-0.414713\pi\) | ||||
0.264744 | + | 0.964319i | \(0.414713\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0581 | − | 15.0581i | −0.493508 | − | 0.493508i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.25782 | − | 1.25782i | 0.0411793 | − | 0.0411793i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 29.4844i | − | 0.964241i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 34.7669i | − | 1.13579i | −0.823102 | − | 0.567893i | \(-0.807759\pi\) | ||
0.823102 | − | 0.567893i | \(-0.192241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.91145 | + | 1.91145i | −0.0623779 | + | 0.0623779i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.2662 | + | 37.2662i | 1.21484 | + | 1.21484i | 0.969414 | + | 0.245430i | \(0.0789291\pi\) |
0.245430 | + | 0.969414i | \(0.421071\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.36423 | −0.239812 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.285766 | −0.00929598 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.5243 | + | 18.5243i | 0.601957 | + | 0.601957i | 0.940832 | − | 0.338874i | \(-0.110046\pi\) |
−0.338874 | + | 0.940832i | \(0.610046\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.63994 | + | 5.63994i | −0.183080 | + | 0.183080i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 22.0653i | − | 0.715516i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.2780 | + | 11.2780i | 0.364565 | + | 0.364565i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.19266 | 0.0708047 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.7032 | −0.442039 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.722018 | − | 0.722018i | −0.0232667 | − | 0.0232667i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 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 | \(-0.0662195\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 9.32206i | − | 0.299468i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.94517 | − | 5.94517i | 0.190790 | − | 0.190790i | −0.605248 | − | 0.796037i | \(-0.706926\pi\) |
0.796037 | + | 0.605248i | \(0.206926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.385321 | + | 0.385321i | 0.0123528 | + | 0.0123528i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.5284 | −0.337179 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.4156 | 1.29301 | 0.646504 | − | 0.762910i | \(-0.276230\pi\) | ||||
0.646504 | + | 0.762910i | \(0.276230\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.6865 | + | 54.6865i | 1.74779 | + | 1.74779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.44471 | + | 1.44471i | −0.0461260 | + | 0.0461260i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.9202i | 0.443985i | 0.975048 | + | 0.221993i | \(0.0712561\pi\) | ||||
−0.975048 | + | 0.221993i | \(0.928744\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.3582i | 1.15847i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.317883 | − | 0.317883i | 0.0101183 | − | 0.0101183i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 16.2771 | + | 16.2771i | 0.517580 | + | 0.517580i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0309 | −1.30339 | −0.651695 | − | 0.758481i | \(-0.725942\pi\) | ||||
−0.651695 | + | 0.758481i | \(0.725942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 21.8431 | 0.693169 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.7928 | − | 31.7928i | −1.00790 | − | 1.00790i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −27.3245 | + | 27.3245i | −0.865375 | + | 0.865375i | −0.991956 | − | 0.126581i | \(-0.959600\pi\) |
0.126581 | + | 0.991956i | \(0.459600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.46742i | 0.267897i |
(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 | 384.2.j.a.289.3 | 8 | ||
3.2 | odd | 2 | 1152.2.k.f.289.3 | 8 | |||
4.3 | odd | 2 | 384.2.j.b.289.1 | 8 | |||
8.3 | odd | 2 | 48.2.j.a.13.1 | ✓ | 8 | ||
8.5 | even | 2 | 192.2.j.a.145.2 | 8 | |||
12.11 | even | 2 | 1152.2.k.c.289.3 | 8 | |||
16.3 | odd | 4 | 48.2.j.a.37.1 | yes | 8 | ||
16.5 | even | 4 | inner | 384.2.j.a.97.3 | 8 | ||
16.11 | odd | 4 | 384.2.j.b.97.1 | 8 | |||
16.13 | even | 4 | 192.2.j.a.49.2 | 8 | |||
24.5 | odd | 2 | 576.2.k.b.145.2 | 8 | |||
24.11 | even | 2 | 144.2.k.b.109.4 | 8 | |||
32.3 | odd | 8 | 3072.2.d.f.1537.1 | 8 | |||
32.5 | even | 8 | 3072.2.a.n.1.1 | 4 | |||
32.11 | odd | 8 | 3072.2.a.i.1.4 | 4 | |||
32.13 | even | 8 | 3072.2.d.i.1537.4 | 8 | |||
32.19 | odd | 8 | 3072.2.d.f.1537.8 | 8 | |||
32.21 | even | 8 | 3072.2.a.o.1.4 | 4 | |||
32.27 | odd | 8 | 3072.2.a.t.1.1 | 4 | |||
32.29 | even | 8 | 3072.2.d.i.1537.5 | 8 | |||
48.5 | odd | 4 | 1152.2.k.f.865.3 | 8 | |||
48.11 | even | 4 | 1152.2.k.c.865.3 | 8 | |||
48.29 | odd | 4 | 576.2.k.b.433.2 | 8 | |||
48.35 | even | 4 | 144.2.k.b.37.4 | 8 | |||
96.5 | odd | 8 | 9216.2.a.x.1.4 | 4 | |||
96.11 | even | 8 | 9216.2.a.bo.1.1 | 4 | |||
96.53 | odd | 8 | 9216.2.a.bn.1.1 | 4 | |||
96.59 | even | 8 | 9216.2.a.y.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.1 | ✓ | 8 | 8.3 | odd | 2 | ||
48.2.j.a.37.1 | yes | 8 | 16.3 | odd | 4 | ||
144.2.k.b.37.4 | 8 | 48.35 | even | 4 | |||
144.2.k.b.109.4 | 8 | 24.11 | even | 2 | |||
192.2.j.a.49.2 | 8 | 16.13 | even | 4 | |||
192.2.j.a.145.2 | 8 | 8.5 | even | 2 | |||
384.2.j.a.97.3 | 8 | 16.5 | even | 4 | inner | ||
384.2.j.a.289.3 | 8 | 1.1 | even | 1 | trivial | ||
384.2.j.b.97.1 | 8 | 16.11 | odd | 4 | |||
384.2.j.b.289.1 | 8 | 4.3 | odd | 2 | |||
576.2.k.b.145.2 | 8 | 24.5 | odd | 2 | |||
576.2.k.b.433.2 | 8 | 48.29 | odd | 4 | |||
1152.2.k.c.289.3 | 8 | 12.11 | even | 2 | |||
1152.2.k.c.865.3 | 8 | 48.11 | even | 4 | |||
1152.2.k.f.289.3 | 8 | 3.2 | odd | 2 | |||
1152.2.k.f.865.3 | 8 | 48.5 | odd | 4 | |||
3072.2.a.i.1.4 | 4 | 32.11 | odd | 8 | |||
3072.2.a.n.1.1 | 4 | 32.5 | even | 8 | |||
3072.2.a.o.1.4 | 4 | 32.21 | even | 8 | |||
3072.2.a.t.1.1 | 4 | 32.27 | odd | 8 | |||
3072.2.d.f.1537.1 | 8 | 32.3 | odd | 8 | |||
3072.2.d.f.1537.8 | 8 | 32.19 | odd | 8 | |||
3072.2.d.i.1537.4 | 8 | 32.13 | even | 8 | |||
3072.2.d.i.1537.5 | 8 | 32.29 | even | 8 | |||
9216.2.a.x.1.4 | 4 | 96.5 | odd | 8 | |||
9216.2.a.y.1.4 | 4 | 96.59 | even | 8 | |||
9216.2.a.bn.1.1 | 4 | 96.53 | odd | 8 | |||
9216.2.a.bo.1.1 | 4 | 96.11 | even | 8 |