Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(1457,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("3150.1457");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2843.2 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.2843 |
Dual form | 3150.2.m.g.1457.2 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.41421i | − | 1.02942i | −0.857363 | − | 0.514712i | \(-0.827899\pi\) | ||
0.857363 | − | 0.514712i | \(-0.172101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.43916 | + | 1.43916i | 0.399150 | + | 0.399150i | 0.877933 | − | 0.478783i | \(-0.158922\pi\) |
−0.478783 | + | 0.877933i | \(0.658922\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.54258 | − | 1.54258i | −0.374131 | − | 0.374131i | 0.494848 | − | 0.868979i | \(-0.335224\pi\) |
−0.868979 | + | 0.494848i | \(0.835224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.04989i | − | 0.470277i | −0.971962 | − | 0.235138i | \(-0.924446\pi\) | ||
0.971962 | − | 0.235138i | \(-0.0755543\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.41421 | + | 2.41421i | −0.514712 | + | 0.514712i | ||||
\(23\) | −1.15660 | + | 1.15660i | −0.241167 | + | 0.241167i | −0.817333 | − | 0.576166i | \(-0.804548\pi\) |
0.576166 | + | 0.817333i | \(0.304548\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 2.03528i | − | 0.399150i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | −8.04524 | −1.49396 | −0.746982 | − | 0.664844i | \(-0.768498\pi\) | ||||
−0.746982 | + | 0.664844i | \(0.768498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.37429 | −1.14486 | −0.572428 | − | 0.819955i | \(-0.693999\pi\) | ||||
−0.572428 | + | 0.819955i | \(0.693999\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.18154i | 0.374131i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.0498881 | + | 0.0498881i | −0.00820155 | + | 0.00820155i | −0.711196 | − | 0.702994i | \(-0.751846\pi\) |
0.702994 | + | 0.711196i | \(0.251846\pi\) | |||||||
\(38\) | −1.44949 | + | 1.44949i | −0.235138 | + | 0.235138i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.94887i | − | 1.24140i | −0.784046 | − | 0.620702i | \(-0.786848\pi\) | ||
0.784046 | − | 0.620702i | \(-0.213152\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.65357 | + | 4.65357i | 0.709663 | + | 0.709663i | 0.966464 | − | 0.256801i | \(-0.0826686\pi\) |
−0.256801 | + | 0.966464i | \(0.582669\pi\) | |||||||
\(44\) | 3.41421 | 0.514712 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.63567 | 0.241167 | ||||||||
\(47\) | −1.39960 | − | 1.39960i | −0.204153 | − | 0.204153i | 0.597624 | − | 0.801777i | \(-0.296112\pi\) |
−0.801777 | + | 0.597624i | \(0.796112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.43916 | + | 1.43916i | −0.199575 | + | 0.199575i | ||||
\(53\) | 2.97506 | − | 2.97506i | 0.408655 | − | 0.408655i | −0.472614 | − | 0.881269i | \(-0.656690\pi\) |
0.881269 | + | 0.472614i | \(0.156690\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.68885 | + | 5.68885i | 0.746982 | + | 0.746982i | ||||
\(59\) | 4.25725 | 0.554247 | 0.277124 | − | 0.960834i | \(-0.410619\pi\) | ||||
0.277124 | + | 0.960834i | \(0.410619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.88953 | −0.882114 | −0.441057 | − | 0.897479i | \(-0.645396\pi\) | ||||
−0.441057 | + | 0.897479i | \(0.645396\pi\) | |||||||
\(62\) | 4.50731 | + | 4.50731i | 0.572428 | + | 0.572428i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.84304 | + | 5.84304i | −0.713841 | + | 0.713841i | −0.967337 | − | 0.253496i | \(-0.918420\pi\) |
0.253496 | + | 0.967337i | \(0.418420\pi\) | |||||||
\(68\) | 1.54258 | − | 1.54258i | 0.187066 | − | 0.187066i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.92820i | 0.347514i | 0.984789 | + | 0.173757i | \(0.0555907\pi\) | ||||
−0.984789 | + | 0.173757i | \(0.944409\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.97469 | + | 5.97469i | 0.699285 | + | 0.699285i | 0.964256 | − | 0.264971i | \(-0.0853626\pi\) |
−0.264971 | + | 0.964256i | \(0.585363\pi\) | |||||||
\(74\) | 0.0705524 | 0.00820155 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.04989 | 0.235138 | ||||||||
\(77\) | −2.41421 | − | 2.41421i | −0.275125 | − | 0.275125i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.6410i | − | 1.30971i | −0.755753 | − | 0.654857i | \(-0.772729\pi\) | ||
0.755753 | − | 0.654857i | \(-0.227271\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.62070 | + | 5.62070i | −0.620702 | + | 0.620702i | ||||
\(83\) | −1.52797 | + | 1.52797i | −0.167717 | + | 0.167717i | −0.785975 | − | 0.618258i | \(-0.787839\pi\) |
0.618258 | + | 0.785975i | \(0.287839\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 6.58114i | − | 0.709663i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.41421 | − | 2.41421i | −0.257356 | − | 0.257356i | ||||
\(89\) | −5.72741 | −0.607104 | −0.303552 | − | 0.952815i | \(-0.598173\pi\) | ||||
−0.303552 | + | 0.952815i | \(0.598173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.03528 | 0.213355 | ||||||||
\(92\) | −1.15660 | − | 1.15660i | −0.120584 | − | 0.120584i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.97934i | 0.204153i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.64564 | + | 9.64564i | −0.979367 | + | 0.979367i | −0.999791 | − | 0.0204248i | \(-0.993498\pi\) |
0.0204248 | + | 0.999791i | \(0.493498\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 16.7420i | − | 1.66589i | −0.553353 | − | 0.832947i | \(-0.686652\pi\) | ||
0.553353 | − | 0.832947i | \(-0.313348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.65597 | + | 8.65597i | 0.852898 | + | 0.852898i | 0.990489 | − | 0.137591i | \(-0.0439359\pi\) |
−0.137591 | + | 0.990489i | \(0.543936\pi\) | |||||||
\(104\) | 2.03528 | 0.199575 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.20736 | −0.408655 | ||||||||
\(107\) | −10.9489 | − | 10.9489i | −1.05847 | − | 1.05847i | −0.998181 | − | 0.0602858i | \(-0.980799\pi\) |
−0.0602858 | − | 0.998181i | \(-0.519201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.23659i | − | 0.501574i | −0.968042 | − | 0.250787i | \(-0.919311\pi\) | ||
0.968042 | − | 0.250787i | \(-0.0806894\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.707107 | + | 0.707107i | −0.0668153 | + | 0.0668153i | ||||
\(113\) | −1.59575 | + | 1.59575i | −0.150116 | + | 0.150116i | −0.778170 | − | 0.628054i | \(-0.783852\pi\) |
0.628054 | + | 0.778170i | \(0.283852\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 8.04524i | − | 0.746982i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.01033 | − | 3.01033i | −0.277124 | − | 0.277124i | ||||
\(119\) | −2.18154 | −0.199981 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.656854 | −0.0597140 | ||||||||
\(122\) | 4.87163 | + | 4.87163i | 0.441057 | + | 0.441057i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 6.37429i | − | 0.572428i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.72084 | + | 7.72084i | −0.685114 | + | 0.685114i | −0.961148 | − | 0.276034i | \(-0.910980\pi\) |
0.276034 | + | 0.961148i | \(0.410980\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.38426i | 0.645166i | 0.946541 | + | 0.322583i | \(0.104551\pi\) | ||||
−0.946541 | + | 0.322583i | \(0.895449\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.44949 | − | 1.44949i | −0.125687 | − | 0.125687i | ||||
\(134\) | 8.26330 | 0.713841 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.18154 | −0.187066 | ||||||||
\(137\) | −12.2268 | − | 12.2268i | −1.04460 | − | 1.04460i | −0.998958 | − | 0.0456471i | \(-0.985465\pi\) |
−0.0456471 | − | 0.998958i | \(-0.514535\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2621i | 1.29451i | 0.762273 | + | 0.647256i | \(0.224083\pi\) | ||||
−0.762273 | + | 0.647256i | \(0.775917\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.07055 | − | 2.07055i | 0.173757 | − | 0.173757i | ||||
\(143\) | 4.91359 | − | 4.91359i | 0.410895 | − | 0.410895i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 8.44949i | − | 0.699285i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.0498881 | − | 0.0498881i | −0.00410077 | − | 0.00410077i | ||||
\(149\) | −6.01602 | −0.492852 | −0.246426 | − | 0.969162i | \(-0.579256\pi\) | ||||
−0.246426 | + | 0.969162i | \(0.579256\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.12096 | −0.416737 | −0.208369 | − | 0.978050i | \(-0.566815\pi\) | ||||
−0.208369 | + | 0.978050i | \(0.566815\pi\) | |||||||
\(152\) | −1.44949 | − | 1.44949i | −0.117569 | − | 0.117569i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.41421i | 0.275125i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.79920 | − | 8.79920i | 0.702253 | − | 0.702253i | −0.262641 | − | 0.964894i | \(-0.584593\pi\) |
0.964894 | + | 0.262641i | \(0.0845934\pi\) | |||||||
\(158\) | −8.23143 | + | 8.23143i | −0.654857 | + | 0.654857i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.63567i | 0.128909i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.73998 | + | 2.73998i | 0.214612 | + | 0.214612i | 0.806223 | − | 0.591611i | \(-0.201508\pi\) |
−0.591611 | + | 0.806223i | \(0.701508\pi\) | |||||||
\(164\) | 7.94887 | 0.620702 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.16088 | 0.167717 | ||||||||
\(167\) | −6.48477 | − | 6.48477i | −0.501806 | − | 0.501806i | 0.410193 | − | 0.911999i | \(-0.365461\pi\) |
−0.911999 | + | 0.410193i | \(0.865461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 8.85765i | − | 0.681358i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.65357 | + | 4.65357i | −0.354831 | + | 0.354831i | ||||
\(173\) | 1.11563 | − | 1.11563i | 0.0848200 | − | 0.0848200i | −0.663424 | − | 0.748244i | \(-0.730897\pi\) |
0.748244 | + | 0.663424i | \(0.230897\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.41421i | 0.257356i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.04989 | + | 4.04989i | 0.303552 | + | 0.303552i | ||||
\(179\) | 1.00124 | 0.0748365 | 0.0374183 | − | 0.999300i | \(-0.488087\pi\) | ||||
0.0374183 | + | 0.999300i | \(0.488087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0411 | −1.71263 | −0.856316 | − | 0.516452i | \(-0.827253\pi\) | ||||
−0.856316 | + | 0.516452i | \(0.827253\pi\) | |||||||
\(182\) | −1.43916 | − | 1.43916i | −0.106677 | − | 0.106677i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.63567i | 0.120584i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.26670 | + | 5.26670i | −0.385140 | + | 0.385140i | ||||
\(188\) | 1.39960 | − | 1.39960i | 0.102076 | − | 0.102076i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.59095i | − | 0.259832i | −0.991525 | − | 0.129916i | \(-0.958529\pi\) | ||
0.991525 | − | 0.129916i | \(-0.0414707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.98539 | − | 4.98539i | −0.358856 | − | 0.358856i | 0.504535 | − | 0.863391i | \(-0.331664\pi\) |
−0.863391 | + | 0.504535i | \(0.831664\pi\) | |||||||
\(194\) | 13.6410 | 0.979367 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −10.0169 | − | 10.0169i | −0.713675 | − | 0.713675i | 0.253627 | − | 0.967302i | \(-0.418376\pi\) |
−0.967302 | + | 0.253627i | \(0.918376\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 27.2820i | − | 1.93397i | −0.254834 | − | 0.966985i | \(-0.582021\pi\) | ||
0.254834 | − | 0.966985i | \(-0.417979\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.8384 | + | 11.8384i | −0.832947 | + | 0.832947i | ||||
\(203\) | −5.68885 | + | 5.68885i | −0.399279 | + | 0.399279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 12.2414i | − | 0.852898i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.43916 | − | 1.43916i | −0.0997876 | − | 0.0997876i | ||||
\(209\) | −6.99876 | −0.484114 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.70193 | −0.599066 | −0.299533 | − | 0.954086i | \(-0.596831\pi\) | ||||
−0.299533 | + | 0.954086i | \(0.596831\pi\) | |||||||
\(212\) | 2.97506 | + | 2.97506i | 0.204328 | + | 0.204328i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 15.4840i | 1.05847i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.50731 | + | 4.50731i | −0.305976 | + | 0.305976i | ||||
\(218\) | −3.70283 | + | 3.70283i | −0.250787 | + | 0.250787i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.44004i | − | 0.298669i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.80813 | − | 2.80813i | −0.188046 | − | 0.188046i | 0.606805 | − | 0.794851i | \(-0.292451\pi\) |
−0.794851 | + | 0.606805i | \(0.792451\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.25674 | 0.150116 | ||||||||
\(227\) | −2.88573 | − | 2.88573i | −0.191532 | − | 0.191532i | 0.604826 | − | 0.796358i | \(-0.293243\pi\) |
−0.796358 | + | 0.604826i | \(0.793243\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.16228i | − | 0.605461i | −0.953076 | − | 0.302730i | \(-0.902102\pi\) | ||
0.953076 | − | 0.302730i | \(-0.0978982\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.68885 | + | 5.68885i | −0.373491 | + | 0.373491i | ||||
\(233\) | −4.67611 | + | 4.67611i | −0.306342 | + | 0.306342i | −0.843489 | − | 0.537147i | \(-0.819502\pi\) |
0.537147 | + | 0.843489i | \(0.319502\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.25725i | 0.277124i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.54258 | + | 1.54258i | 0.0999907 | + | 0.0999907i | ||||
\(239\) | −16.4853 | −1.06634 | −0.533172 | − | 0.846007i | \(-0.679000\pi\) | ||||
−0.533172 | + | 0.846007i | \(0.679000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.50419 | −0.547803 | −0.273901 | − | 0.961758i | \(-0.588314\pi\) | ||||
−0.273901 | + | 0.961758i | \(0.588314\pi\) | |||||||
\(242\) | 0.464466 | + | 0.464466i | 0.0298570 | + | 0.0298570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 6.88953i | − | 0.441057i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.95011 | − | 2.95011i | 0.187711 | − | 0.187711i | ||||
\(248\) | −4.50731 | + | 4.50731i | −0.286214 | + | 0.286214i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.9250i | 1.19453i | 0.802043 | + | 0.597267i | \(0.203747\pi\) | ||||
−0.802043 | + | 0.597267i | \(0.796253\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.94887 | + | 3.94887i | 0.248263 | + | 0.248263i | ||||
\(254\) | 10.9189 | 0.685114 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 16.8697 | + | 16.8697i | 1.05230 | + | 1.05230i | 0.998555 | + | 0.0537457i | \(0.0171160\pi\) |
0.0537457 | + | 0.998555i | \(0.482884\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.0705524i | 0.00438391i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 5.22146 | − | 5.22146i | 0.322583 | − | 0.322583i | ||||
\(263\) | −8.32817 | + | 8.32817i | −0.513537 | + | 0.513537i | −0.915608 | − | 0.402071i | \(-0.868290\pi\) |
0.402071 | + | 0.915608i | \(0.368290\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.04989i | 0.125687i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.84304 | − | 5.84304i | −0.356920 | − | 0.356920i | ||||
\(269\) | 16.3218 | 0.995155 | 0.497577 | − | 0.867420i | \(-0.334223\pi\) | ||||
0.497577 | + | 0.867420i | \(0.334223\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.3911 | −1.66389 | −0.831944 | − | 0.554859i | \(-0.812772\pi\) | ||||
−0.831944 | + | 0.554859i | \(0.812772\pi\) | |||||||
\(272\) | 1.54258 | + | 1.54258i | 0.0935328 | + | 0.0935328i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.2913i | 1.04460i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.564607 | + | 0.564607i | −0.0339239 | + | 0.0339239i | −0.723865 | − | 0.689941i | \(-0.757636\pi\) |
0.689941 | + | 0.723865i | \(0.257636\pi\) | |||||||
\(278\) | 10.7919 | − | 10.7919i | 0.647256 | − | 0.647256i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.14214i | 0.366409i | 0.983075 | + | 0.183205i | \(0.0586471\pi\) | ||||
−0.983075 | + | 0.183205i | \(0.941353\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.9959 | − | 10.9959i | −0.653637 | − | 0.653637i | 0.300230 | − | 0.953867i | \(-0.402937\pi\) |
−0.953867 | + | 0.300230i | \(0.902937\pi\) | |||||||
\(284\) | −2.92820 | −0.173757 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.94887 | −0.410895 | ||||||||
\(287\) | −5.62070 | − | 5.62070i | −0.331779 | − | 0.331779i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.2409i | − | 0.720052i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.97469 | + | 5.97469i | −0.349642 | + | 0.349642i | ||||
\(293\) | 17.4135 | − | 17.4135i | 1.01731 | − | 1.01731i | 0.0174591 | − | 0.999848i | \(-0.494442\pi\) |
0.999848 | − | 0.0174591i | \(-0.00555767\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0.0705524i | 0.00410077i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.25397 | + | 4.25397i | 0.246426 | + | 0.246426i | ||||
\(299\) | −3.32905 | −0.192524 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.58114 | 0.379331 | ||||||||
\(302\) | 3.62106 | + | 3.62106i | 0.208369 | + | 0.208369i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.04989i | 0.117569i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.2979 | − | 17.2979i | 0.987241 | − | 0.987241i | −0.0126790 | − | 0.999920i | \(-0.504036\pi\) |
0.999920 | + | 0.0126790i | \(0.00403597\pi\) | |||||||
\(308\) | 2.41421 | − | 2.41421i | 0.137563 | − | 0.137563i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3046i | 0.697732i | 0.937173 | + | 0.348866i | \(0.113433\pi\) | ||||
−0.937173 | + | 0.348866i | \(0.886567\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.8031 | + | 16.8031i | 0.949768 | + | 0.949768i | 0.998797 | − | 0.0490289i | \(-0.0156127\pi\) |
−0.0490289 | + | 0.998797i | \(0.515613\pi\) | |||||||
\(314\) | −12.4440 | −0.702253 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.6410 | 0.654857 | ||||||||
\(317\) | 3.16781 | + | 3.16781i | 0.177922 | + | 0.177922i | 0.790449 | − | 0.612527i | \(-0.209847\pi\) |
−0.612527 | + | 0.790449i | \(0.709847\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.4682i | 1.53792i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.15660 | − | 1.15660i | 0.0644546 | − | 0.0644546i | ||||
\(323\) | −3.16212 | + | 3.16212i | −0.175945 | + | 0.175945i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 3.87492i | − | 0.214612i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.62070 | − | 5.62070i | −0.310351 | − | 0.310351i | ||||
\(329\) | −1.97934 | −0.109124 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4986 | −0.741953 | −0.370976 | − | 0.928642i | \(-0.620977\pi\) | ||||
−0.370976 | + | 0.928642i | \(0.620977\pi\) | |||||||
\(332\) | −1.52797 | − | 1.52797i | −0.0838583 | − | 0.0838583i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.17084i | 0.501806i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.1303 | + | 18.1303i | −0.987620 | + | 0.987620i | −0.999924 | − | 0.0123043i | \(-0.996083\pi\) |
0.0123043 | + | 0.999924i | \(0.496083\pi\) | |||||||
\(338\) | −6.26330 | + | 6.26330i | −0.340679 | + | 0.340679i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.7632i | 1.17854i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | 6.58114 | 0.354831 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.57774 | −0.0848200 | ||||||||
\(347\) | −18.2259 | − | 18.2259i | −0.978417 | − | 0.978417i | 0.0213548 | − | 0.999772i | \(-0.493202\pi\) |
−0.999772 | + | 0.0213548i | \(0.993202\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.538551i | 0.0288280i | 0.999896 | + | 0.0144140i | \(0.00458827\pi\) | ||||
−0.999896 | + | 0.0144140i | \(0.995412\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.41421 | − | 2.41421i | 0.128678 | − | 0.128678i | ||||
\(353\) | −16.3830 | + | 16.3830i | −0.871980 | + | 0.871980i | −0.992688 | − | 0.120708i | \(-0.961484\pi\) |
0.120708 | + | 0.992688i | \(0.461484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.72741i | − | 0.303552i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.707987 | − | 0.707987i | −0.0374183 | − | 0.0374183i | ||||
\(359\) | 31.9223 | 1.68480 | 0.842398 | − | 0.538856i | \(-0.181143\pi\) | ||||
0.842398 | + | 0.538856i | \(0.181143\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.7980 | 0.778840 | ||||||||
\(362\) | 16.2925 | + | 16.2925i | 0.856316 | + | 0.856316i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.03528i | 0.106677i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.5854 | − | 24.5854i | 1.28335 | − | 1.28335i | 0.344598 | − | 0.938750i | \(-0.388015\pi\) |
0.938750 | − | 0.344598i | \(-0.111985\pi\) | |||||||
\(368\) | 1.15660 | − | 1.15660i | 0.0602918 | − | 0.0602918i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4.20736i | − | 0.218435i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.79796 | − | 2.79796i | −0.144873 | − | 0.144873i | 0.630950 | − | 0.775823i | \(-0.282665\pi\) |
−0.775823 | + | 0.630950i | \(0.782665\pi\) | |||||||
\(374\) | 7.44825 | 0.385140 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.97934 | −0.102076 | ||||||||
\(377\) | −11.5784 | − | 11.5784i | −0.596317 | − | 0.596317i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.4390i | 1.35808i | 0.734102 | + | 0.679039i | \(0.237603\pi\) | ||||
−0.734102 | + | 0.679039i | \(0.762397\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.53918 | + | 2.53918i | −0.129916 | + | 0.129916i | ||||
\(383\) | −17.2280 | + | 17.2280i | −0.880311 | + | 0.880311i | −0.993566 | − | 0.113255i | \(-0.963872\pi\) |
0.113255 | + | 0.993566i | \(0.463872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 7.05040i | 0.358856i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.64564 | − | 9.64564i | −0.489683 | − | 0.489683i | ||||
\(389\) | −32.8766 | −1.66691 | −0.833454 | − | 0.552589i | \(-0.813640\pi\) | ||||
−0.833454 | + | 0.552589i | \(0.813640\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.56829 | 0.180456 | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.1660i | 0.713675i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.39783 | − | 5.39783i | 0.270909 | − | 0.270909i | −0.558557 | − | 0.829466i | \(-0.688645\pi\) |
0.829466 | + | 0.558557i | \(0.188645\pi\) | |||||||
\(398\) | −19.2913 | + | 19.2913i | −0.966985 | + | 0.966985i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 14.4760i | − | 0.722897i | −0.932392 | − | 0.361448i | \(-0.882282\pi\) | ||
0.932392 | − | 0.361448i | \(-0.117718\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.17361 | − | 9.17361i | −0.456970 | − | 0.456970i | ||||
\(404\) | 16.7420 | 0.832947 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.04524 | 0.399279 | ||||||||
\(407\) | 0.170328 | + | 0.170328i | 0.00844287 | + | 0.00844287i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 16.5156i | − | 0.816642i | −0.912838 | − | 0.408321i | \(-0.866114\pi\) | ||
0.912838 | − | 0.408321i | \(-0.133886\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.65597 | + | 8.65597i | −0.426449 | + | 0.426449i | ||||
\(413\) | 3.01033 | − | 3.01033i | 0.148129 | − | 0.148129i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.03528i | 0.0997876i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.94887 | + | 4.94887i | 0.242057 | + | 0.242057i | ||||
\(419\) | −12.0421 | −0.588294 | −0.294147 | − | 0.955760i | \(-0.595036\pi\) | ||||
−0.294147 | + | 0.955760i | \(0.595036\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.4894 | 1.58343 | 0.791717 | − | 0.610888i | \(-0.209187\pi\) | ||||
0.791717 | + | 0.610888i | \(0.209187\pi\) | |||||||
\(422\) | 6.15320 | + | 6.15320i | 0.299533 | + | 0.299533i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 4.20736i | − | 0.204328i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.87163 | + | 4.87163i | −0.235755 | + | 0.235755i | ||||
\(428\) | 10.9489 | − | 10.9489i | 0.529233 | − | 0.529233i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.50883i | 0.409856i | 0.978777 | + | 0.204928i | \(0.0656960\pi\) | ||||
−0.978777 | + | 0.204928i | \(0.934304\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.55532 | + | 3.55532i | 0.170858 | + | 0.170858i | 0.787356 | − | 0.616498i | \(-0.211449\pi\) |
−0.616498 | + | 0.787356i | \(0.711449\pi\) | |||||||
\(434\) | 6.37429 | 0.305976 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.23659 | 0.250787 | ||||||||
\(437\) | 2.37089 | + | 2.37089i | 0.113415 | + | 0.113415i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.2309i | − | 0.631477i | −0.948846 | − | 0.315739i | \(-0.897748\pi\) | ||
0.948846 | − | 0.315739i | \(-0.102252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.13958 | + | 3.13958i | −0.149335 | + | 0.149335i | ||||
\(443\) | −23.9223 | + | 23.9223i | −1.13658 | + | 1.13658i | −0.147525 | + | 0.989058i | \(0.547131\pi\) |
−0.989058 | + | 0.147525i | \(0.952869\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.97129i | 0.188046i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | −4.09905 | −0.193446 | −0.0967230 | − | 0.995311i | \(-0.530836\pi\) | ||||
−0.0967230 | + | 0.995311i | \(0.530836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.1391 | −1.27793 | ||||||||
\(452\) | −1.59575 | − | 1.59575i | −0.0750580 | − | 0.0750580i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.08104i | 0.191532i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.4150 | − | 23.4150i | 1.09531 | − | 1.09531i | 0.100356 | − | 0.994952i | \(-0.468002\pi\) |
0.994952 | − | 0.100356i | \(-0.0319983\pi\) | |||||||
\(458\) | −6.47871 | + | 6.47871i | −0.302730 | + | 0.302730i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.4974i | 0.908085i | 0.890980 | + | 0.454042i | \(0.150019\pi\) | ||||
−0.890980 | + | 0.454042i | \(0.849981\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.62033 | − | 9.62033i | −0.447095 | − | 0.447095i | 0.447293 | − | 0.894388i | \(-0.352388\pi\) |
−0.894388 | + | 0.447293i | \(0.852388\pi\) | |||||||
\(464\) | 8.04524 | 0.373491 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.61302 | 0.306342 | ||||||||
\(467\) | 14.8643 | + | 14.8643i | 0.687839 | + | 0.687839i | 0.961754 | − | 0.273915i | \(-0.0883186\pi\) |
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.26330i | 0.381564i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.01033 | − | 3.01033i | 0.138562 | − | 0.138562i | ||||
\(473\) | 15.8883 | − | 15.8883i | 0.730544 | − | 0.730544i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 2.18154i | − | 0.0999907i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.6569 | + | 11.6569i | 0.533172 | + | 0.533172i | ||||
\(479\) | 11.6065 | 0.530313 | 0.265157 | − | 0.964205i | \(-0.414576\pi\) | ||||
0.265157 | + | 0.964205i | \(0.414576\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.143594 | −0.00654730 | ||||||||
\(482\) | 6.01337 | + | 6.01337i | 0.273901 | + | 0.273901i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 0.656854i | − | 0.0298570i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.5745 | − | 26.5745i | 1.20421 | − | 1.20421i | 0.231332 | − | 0.972875i | \(-0.425692\pi\) |
0.972875 | − | 0.231332i | \(-0.0743083\pi\) | |||||||
\(488\) | −4.87163 | + | 4.87163i | −0.220528 | + | 0.220528i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.5029i | 1.51197i | 0.654591 | + | 0.755983i | \(0.272841\pi\) | ||||
−0.654591 | + | 0.755983i | \(0.727159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.4104 | + | 12.4104i | 0.558939 | + | 0.558939i | ||||
\(494\) | −4.17209 | −0.187711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.37429 | 0.286214 | ||||||||
\(497\) | 2.07055 | + | 2.07055i | 0.0928770 | + | 0.0928770i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.58504i | − | 0.294787i | −0.989078 | − | 0.147393i | \(-0.952912\pi\) | ||
0.989078 | − | 0.147393i | \(-0.0470883\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.3820 | − | 13.3820i | 0.597267 | − | 0.597267i | ||||
\(503\) | 26.4682 | − | 26.4682i | 1.18016 | − | 1.18016i | 0.200455 | − | 0.979703i | \(-0.435758\pi\) |
0.979703 | − | 0.200455i | \(-0.0642420\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 5.58454i | − | 0.248263i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.72084 | − | 7.72084i | −0.342557 | − | 0.342557i | ||||
\(509\) | −11.6050 | −0.514381 | −0.257191 | − | 0.966361i | \(-0.582797\pi\) | ||||
−0.257191 | + | 0.966361i | \(0.582797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.44949 | 0.373783 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 23.8573i | − | 1.05230i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.77854 | + | 4.77854i | −0.210160 | + | 0.210160i | ||||
\(518\) | 0.0498881 | − | 0.0498881i | 0.00219196 | − | 0.00219196i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 27.9474i | − | 1.22440i | −0.790704 | − | 0.612199i | \(-0.790285\pi\) | ||
0.790704 | − | 0.612199i | \(-0.209715\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.4247 | − | 21.4247i | −0.936837 | − | 0.936837i | 0.0612838 | − | 0.998120i | \(-0.480481\pi\) |
−0.998120 | + | 0.0612838i | \(0.980481\pi\) | |||||||
\(524\) | −7.38426 | −0.322583 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 11.7778 | 0.513537 | ||||||||
\(527\) | 9.83287 | + | 9.83287i | 0.428327 | + | 0.428327i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.3246i | 0.883677i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.44949 | − | 1.44949i | 0.0628434 | − | 0.0628434i | ||||
\(533\) | 11.4397 | − | 11.4397i | 0.495507 | − | 0.495507i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.26330i | 0.356920i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.5412 | − | 11.5412i | −0.497577 | − | 0.497577i | ||||
\(539\) | −3.41421 | −0.147061 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.4705 | 1.39601 | 0.698007 | − | 0.716091i | \(-0.254070\pi\) | ||||
0.698007 | + | 0.716091i | \(0.254070\pi\) | |||||||
\(542\) | 19.3684 | + | 19.3684i | 0.831944 | + | 0.831944i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.18154i | − | 0.0935328i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.60441 | + | 6.60441i | −0.282384 | + | 0.282384i | −0.834059 | − | 0.551675i | \(-0.813989\pi\) |
0.551675 | + | 0.834059i | \(0.313989\pi\) | |||||||
\(548\) | 12.2268 | − | 12.2268i | 0.522302 | − | 0.522302i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 16.4918i | 0.702576i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.23143 | − | 8.23143i | −0.350036 | − | 0.350036i | ||||
\(554\) | 0.798474 | 0.0339239 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15.2621 | −0.647256 | ||||||||
\(557\) | −25.2207 | − | 25.2207i | −1.06864 | − | 1.06864i | −0.997464 | − | 0.0711727i | \(-0.977326\pi\) |
−0.0711727 | − | 0.997464i | \(-0.522674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.3944i | 0.566525i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.34315 | − | 4.34315i | 0.183205 | − | 0.183205i | ||||
\(563\) | −0.0225400 | + | 0.0225400i | −0.000949948 | + | 0.000949948i | −0.707582 | − | 0.706632i | \(-0.750214\pi\) |
0.706632 | + | 0.707582i | \(0.250214\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.5505i | 0.653637i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.07055 | + | 2.07055i | 0.0868784 | + | 0.0868784i | ||||
\(569\) | −16.4767 | −0.690740 | −0.345370 | − | 0.938467i | \(-0.612247\pi\) | ||||
−0.345370 | + | 0.938467i | \(0.612247\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9560 | 1.21177 | 0.605884 | − | 0.795553i | \(-0.292819\pi\) | ||||
0.605884 | + | 0.795553i | \(0.292819\pi\) | |||||||
\(572\) | 4.91359 | + | 4.91359i | 0.205448 | + | 0.205448i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 7.94887i | 0.331779i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.3424 | − | 30.3424i | 1.26317 | − | 1.26317i | 0.313624 | − | 0.949547i | \(-0.398457\pi\) |
0.949547 | − | 0.313624i | \(-0.101543\pi\) | |||||||
\(578\) | −8.65561 | + | 8.65561i | −0.360026 | + | 0.360026i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.16088i | 0.0896483i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.1575 | − | 10.1575i | −0.420680 | − | 0.420680i | ||||
\(584\) | 8.44949 | 0.349642 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.6264 | −1.01731 | ||||||||
\(587\) | −5.98778 | − | 5.98778i | −0.247142 | − | 0.247142i | 0.572655 | − | 0.819797i | \(-0.305914\pi\) |
−0.819797 | + | 0.572655i | \(0.805914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13.0666i | 0.538399i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.0498881 | − | 0.0498881i | 0.00205039 | − | 0.00205039i | ||||
\(593\) | 33.1306 | − | 33.1306i | 1.36051 | − | 1.36051i | 0.487243 | − | 0.873266i | \(-0.338003\pi\) |
0.873266 | − | 0.487243i | \(-0.161997\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.01602i | − | 0.246426i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.35399 | + | 2.35399i | 0.0962619 | + | 0.0962619i | ||||
\(599\) | −0.303973 | −0.0124200 | −0.00620999 | − | 0.999981i | \(-0.501977\pi\) | ||||
−0.00620999 | + | 0.999981i | \(0.501977\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2813 | 0.704918 | 0.352459 | − | 0.935827i | \(-0.385346\pi\) | ||||
0.352459 | + | 0.935827i | \(0.385346\pi\) | |||||||
\(602\) | −4.65357 | − | 4.65357i | −0.189665 | − | 0.189665i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 5.12096i | − | 0.208369i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.4243 | + | 16.4243i | −0.666644 | + | 0.666644i | −0.956938 | − | 0.290294i | \(-0.906247\pi\) |
0.290294 | + | 0.956938i | \(0.406247\pi\) | |||||||
\(608\) | 1.44949 | − | 1.44949i | 0.0587846 | − | 0.0587846i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.02849i | − | 0.162975i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6330 | + | 14.6330i | 0.591019 | + | 0.591019i | 0.937907 | − | 0.346887i | \(-0.112761\pi\) |
−0.346887 | + | 0.937907i | \(0.612761\pi\) | |||||||
\(614\) | −24.4629 | −0.987241 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.41421 | −0.137563 | ||||||||
\(617\) | 32.8831 | + | 32.8831i | 1.32382 | + | 1.32382i | 0.910653 | + | 0.413171i | \(0.135579\pi\) |
0.413171 | + | 0.910653i | \(0.364421\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.1001i | − | 1.12944i | −0.825283 | − | 0.564719i | \(-0.808984\pi\) | ||
0.825283 | − | 0.564719i | \(-0.191016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.70069 | − | 8.70069i | 0.348866 | − | 0.348866i | ||||
\(623\) | −4.04989 | + | 4.04989i | −0.162255 | + | 0.162255i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 23.7632i | − | 0.949768i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.79920 | + | 8.79920i | 0.351126 | + | 0.351126i | ||||
\(629\) | 0.153913 | 0.00613691 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.9867 | −0.676228 | −0.338114 | − | 0.941105i | \(-0.609789\pi\) | ||||
−0.338114 | + | 0.941105i | \(0.609789\pi\) | |||||||
\(632\) | −8.23143 | − | 8.23143i | −0.327429 | − | 0.327429i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 4.47996i | − | 0.177922i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.43916 | − | 1.43916i | 0.0570215 | − | 0.0570215i | ||||
\(638\) | 19.4229 | − | 19.4229i | 0.768961 | − | 0.768961i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.1607i | 0.480319i | 0.970733 | + | 0.240160i | \(0.0771998\pi\) | ||||
−0.970733 | + | 0.240160i | \(0.922800\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.93285 | − | 2.93285i | −0.115660 | − | 0.115660i | 0.646908 | − | 0.762568i | \(-0.276062\pi\) |
−0.762568 | + | 0.646908i | \(0.776062\pi\) | |||||||
\(644\) | −1.63567 | −0.0644546 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.47191 | 0.175945 | ||||||||
\(647\) | 29.4705 | + | 29.4705i | 1.15860 | + | 1.15860i | 0.984776 | + | 0.173827i | \(0.0556133\pi\) |
0.173827 | + | 0.984776i | \(0.444387\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.5352i | − | 0.570555i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.73998 | + | 2.73998i | −0.107306 | + | 0.107306i | ||||
\(653\) | −7.46337 | + | 7.46337i | −0.292064 | + | 0.292064i | −0.837895 | − | 0.545831i | \(-0.816214\pi\) |
0.545831 | + | 0.837895i | \(0.316214\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.94887i | 0.310351i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.39960 | + | 1.39960i | 0.0545622 | + | 0.0545622i | ||||
\(659\) | −24.7639 | −0.964666 | −0.482333 | − | 0.875988i | \(-0.660211\pi\) | ||||
−0.482333 | + | 0.875988i | \(0.660211\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.3827 | 0.403840 | 0.201920 | − | 0.979402i | \(-0.435282\pi\) | ||||
0.201920 | + | 0.979402i | \(0.435282\pi\) | |||||||
\(662\) | 9.54499 | + | 9.54499i | 0.370976 | + | 0.370976i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.16088i | 0.0838583i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.30510 | − | 9.30510i | 0.360295 | − | 0.360295i | ||||
\(668\) | 6.48477 | − | 6.48477i | 0.250903 | − | 0.250903i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 23.5223i | 0.908069i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.8380 | − | 11.8380i | −0.456321 | − | 0.456321i | 0.441125 | − | 0.897446i | \(-0.354580\pi\) |
−0.897446 | + | 0.441125i | \(0.854580\pi\) | |||||||
\(674\) | 25.6401 | 0.987620 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.85765 | 0.340679 | ||||||||
\(677\) | 12.7408 | + | 12.7408i | 0.489668 | + | 0.489668i | 0.908201 | − | 0.418534i | \(-0.137456\pi\) |
−0.418534 | + | 0.908201i | \(0.637456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6410i | 0.523493i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.3889 | − | 15.3889i | 0.589272 | − | 0.589272i | ||||
\(683\) | 5.61177 | − | 5.61177i | 0.214729 | − | 0.214729i | −0.591544 | − | 0.806273i | \(-0.701481\pi\) |
0.806273 | + | 0.591544i | \(0.201481\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.65357 | − | 4.65357i | −0.177416 | − | 0.177416i | ||||
\(689\) | 8.56315 | 0.326230 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.6347 | 1.20344 | 0.601721 | − | 0.798706i | \(-0.294482\pi\) | ||||
0.601721 | + | 0.798706i | \(0.294482\pi\) | |||||||
\(692\) | 1.11563 | + | 1.11563i | 0.0424100 | + | 0.0424100i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.7753i | 0.978417i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2618 | + | 12.2618i | −0.464448 | + | 0.464448i | ||||
\(698\) | 0.380813 | − | 0.380813i | 0.0144140 | − | 0.0144140i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.7205i | 1.23583i | 0.786243 | + | 0.617917i | \(0.212023\pi\) | ||||
−0.786243 | + | 0.617917i | \(0.787977\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.102265 | + | 0.102265i | 0.00385699 | + | 0.00385699i | ||||
\(704\) | −3.41421 | −0.128678 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 23.1691 | 0.871980 | ||||||||
\(707\) | −11.8384 | − | 11.8384i | −0.445229 | − | 0.445229i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 47.0878i | − | 1.76842i | −0.467091 | − | 0.884209i | \(-0.654698\pi\) | ||
0.467091 | − | 0.884209i | \(-0.345302\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.04989 | + | 4.04989i | −0.151776 | + | 0.151776i | ||||
\(713\) | 7.37249 | − | 7.37249i | 0.276102 | − | 0.276102i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.00124i | 0.0374183i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −22.5725 | − | 22.5725i | −0.842398 | − | 0.842398i | ||||
\(719\) | 13.9350 | 0.519687 | 0.259844 | − | 0.965651i | \(-0.416329\pi\) | ||||
0.259844 | + | 0.965651i | \(0.416329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.2414 | 0.455893 | ||||||||
\(722\) | −10.4637 | − | 10.4637i | −0.389420 | − | 0.389420i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 23.0411i | − | 0.856316i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.199188 | − | 0.199188i | 0.00738746 | − | 0.00738746i | −0.703403 | − | 0.710791i | \(-0.748337\pi\) |
0.710791 | + | 0.703403i | \(0.248337\pi\) | |||||||
\(728\) | 1.43916 | − | 1.43916i | 0.0533387 | − | 0.0533387i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 14.3570i | − | 0.531014i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.2245 | − | 10.2245i | −0.377650 | − | 0.377650i | 0.492603 | − | 0.870254i | \(-0.336045\pi\) |
−0.870254 | + | 0.492603i | \(0.836045\pi\) | |||||||
\(734\) | −34.7690 | −1.28335 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.63567 | −0.0602918 | ||||||||
\(737\) | 19.9494 | + | 19.9494i | 0.734845 | + | 0.734845i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.1993i | 1.29483i | 0.762139 | + | 0.647414i | \(0.224149\pi\) | ||||
−0.762139 | + | 0.647414i | \(0.775851\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.97506 | + | 2.97506i | −0.109218 | + | 0.109218i | ||||
\(743\) | −12.2052 | + | 12.2052i | −0.447767 | + | 0.447767i | −0.894612 | − | 0.446845i | \(-0.852548\pi\) |
0.446845 | + | 0.894612i | \(0.352548\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.95691i | 0.144873i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.26670 | − | 5.26670i | −0.192570 | − | 0.192570i | ||||
\(749\) | −15.4840 | −0.565774 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.73294 | −0.136217 | −0.0681085 | − | 0.997678i | \(-0.521696\pi\) | ||||
−0.0681085 | + | 0.997678i | \(0.521696\pi\) | |||||||
\(752\) | 1.39960 | + | 1.39960i | 0.0510382 | + | 0.0510382i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 16.3743i | 0.596317i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.363597 | − | 0.363597i | 0.0132151 | − | 0.0132151i | −0.700468 | − | 0.713683i | \(-0.747026\pi\) |
0.713683 | + | 0.700468i | \(0.247026\pi\) | |||||||
\(758\) | 18.6952 | − | 18.6952i | 0.679039 | − | 0.679039i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 26.1799i | − | 0.949022i | −0.880250 | − | 0.474511i | \(-0.842625\pi\) | ||
0.880250 | − | 0.474511i | \(-0.157375\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.70283 | − | 3.70283i | −0.134051 | − | 0.134051i | ||||
\(764\) | 3.59095 | 0.129916 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 24.3641 | 0.880311 | ||||||||
\(767\) | 6.12686 | + | 6.12686i | 0.221228 | + | 0.221228i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 28.9756i | 1.04489i | 0.852674 | + | 0.522443i | \(0.174979\pi\) | ||||
−0.852674 | + | 0.522443i | \(0.825021\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.98539 | − | 4.98539i | 0.179428 | − | 0.179428i | ||||
\(773\) | 27.3745 | − | 27.3745i | 0.984591 | − | 0.984591i | −0.0152923 | − | 0.999883i | \(-0.504868\pi\) |
0.999883 | + | 0.0152923i | \(0.00486787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 13.6410i | 0.489683i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 23.2472 | + | 23.2472i | 0.833454 | + | 0.833454i | ||||
\(779\) | −16.2943 | −0.583803 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.99751 | 0.357739 | ||||||||
\(782\) | −2.52316 | − | 2.52316i | −0.0902281 | − | 0.0902281i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8559 | − | 26.8559i | 0.957309 | − | 0.957309i | −0.0418162 | − | 0.999125i | \(-0.513314\pi\) |
0.999125 | + | 0.0418162i | \(0.0133144\pi\) | |||||||
\(788\) | 10.0169 | − | 10.0169i | 0.356837 | − | 0.356837i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.25674i | 0.0802403i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.91512 | − | 9.91512i | −0.352096 | − | 0.352096i | ||||
\(794\) | −7.63368 | −0.270909 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.2820 | 0.966985 | ||||||||
\(797\) | −5.58506 | − | 5.58506i | −0.197833 | − | 0.197833i | 0.601237 | − | 0.799070i | \(-0.294675\pi\) |
−0.799070 | + | 0.601237i | \(0.794675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.31800i | 0.152760i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.2361 | + | 10.2361i | −0.361448 | + | 0.361448i | ||||
\(803\) | 20.3989 | − | 20.3989i | 0.719861 | − | 0.719861i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.9734i | 0.456970i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −11.8384 | − | 11.8384i | −0.416473 | − | 0.416473i | ||||
\(809\) | 35.7067 | 1.25538 | 0.627691 | − | 0.778463i | \(-0.284000\pi\) | ||||
0.627691 | + | 0.778463i | \(0.284000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5685 | 0.757371 | 0.378685 | − | 0.925525i | \(-0.376376\pi\) | ||||
0.378685 | + | 0.925525i | \(0.376376\pi\) | |||||||
\(812\) | −5.68885 | − | 5.68885i | −0.199639 | − | 0.199639i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 0.240881i | − | 0.00844287i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.53930 | − | 9.53930i | 0.333738 | − | 0.333738i | ||||
\(818\) | −11.6783 | + | 11.6783i | −0.408321 | + | 0.408321i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 45.6237i | − | 1.59228i | −0.605114 | − | 0.796139i | \(-0.706873\pi\) | ||
0.605114 | − | 0.796139i | \(-0.293127\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.0562 | − | 24.0562i | −0.838548 | − | 0.838548i | 0.150120 | − | 0.988668i | \(-0.452034\pi\) |
−0.988668 | + | 0.150120i | \(0.952034\pi\) | |||||||
\(824\) | 12.2414 | 0.426449 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.25725 | −0.148129 | ||||||||
\(827\) | −30.4601 | − | 30.4601i | −1.05920 | − | 1.05920i | −0.998134 | − | 0.0610692i | \(-0.980549\pi\) |
−0.0610692 | − | 0.998134i | \(-0.519451\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 51.5031i | − | 1.78878i | −0.447291 | − | 0.894388i | \(-0.647611\pi\) | ||
0.447291 | − | 0.894388i | \(-0.352389\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.43916 | − | 1.43916i | 0.0498938 | − | 0.0498938i | ||||
\(833\) | −1.54258 | + | 1.54258i | −0.0534473 | + | 0.0534473i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 6.99876i | − | 0.242057i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 8.51503 | + | 8.51503i | 0.294147 | + | 0.294147i | ||||
\(839\) | 26.7154 | 0.922319 | 0.461159 | − | 0.887317i | \(-0.347434\pi\) | ||||
0.461159 | + | 0.887317i | \(0.347434\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.7259 | 1.23193 | ||||||||
\(842\) | −22.9734 | − | 22.9734i | −0.791717 | − | 0.791717i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 8.70193i | − | 0.299533i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.464466 | + | 0.464466i | −0.0159592 | + | 0.0159592i | ||||
\(848\) | −2.97506 | + | 2.97506i | −0.102164 | + | 0.102164i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 0.115401i | − | 0.00395588i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.4710 | + | 36.4710i | 1.24874 | + | 1.24874i | 0.956276 | + | 0.292467i | \(0.0944762\pi\) |
0.292467 | + | 0.956276i | \(0.405524\pi\) | |||||||
\(854\) | 6.88953 | 0.235755 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −15.4840 | −0.529233 | ||||||||
\(857\) | 22.0837 | + | 22.0837i | 0.754364 | + | 0.754364i | 0.975291 | − | 0.220926i | \(-0.0709080\pi\) |
−0.220926 | + | 0.975291i | \(0.570908\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 8.42683i | − | 0.287520i | −0.989613 | − | 0.143760i | \(-0.954081\pi\) | ||
0.989613 | − | 0.143760i | \(-0.0459193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.01665 | − | 6.01665i | 0.204928 | − | 0.204928i | ||||
\(863\) | 9.78940 | − | 9.78940i | 0.333235 | − | 0.333235i | −0.520579 | − | 0.853814i | \(-0.674284\pi\) |
0.853814 | + | 0.520579i | \(0.174284\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 5.02798i | − | 0.170858i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.50731 | − | 4.50731i | −0.152988 | − | 0.152988i | ||||
\(869\) | −39.7449 | −1.34825 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −16.8181 | −0.569860 | ||||||||
\(872\) | −3.70283 | − | 3.70283i | −0.125394 | − | 0.125394i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 3.35295i | − | 0.113415i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.7554 | − | 32.7554i | 1.10607 | − | 1.10607i | 0.112409 | − | 0.993662i | \(-0.464143\pi\) |
0.993662 | − | 0.112409i | \(-0.0358566\pi\) | |||||||
\(878\) | −9.35567 | + | 9.35567i | −0.315739 | + | 0.315739i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 38.0422i | − | 1.28167i | −0.767677 | − | 0.640837i | \(-0.778588\pi\) | ||
0.767677 | − | 0.640837i | \(-0.221412\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.6735 | − | 22.6735i | −0.763024 | − | 0.763024i | 0.213844 | − | 0.976868i | \(-0.431402\pi\) |
−0.976868 | + | 0.213844i | \(0.931402\pi\) | |||||||
\(884\) | 4.44004 | 0.149335 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 33.8313 | 1.13658 | ||||||||
\(887\) | 26.7254 | + | 26.7254i | 0.897352 | + | 0.897352i | 0.995201 | − | 0.0978490i | \(-0.0311962\pi\) |
−0.0978490 | + | 0.995201i | \(0.531196\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.9189i | 0.366209i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.80813 | − | 2.80813i | 0.0940231 | − | 0.0940231i | ||||
\(893\) | −2.86903 | + | 2.86903i | −0.0960083 | + | 0.0960083i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000i | 0.0334077i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.89846 | + | 2.89846i | 0.0967230 | + | 0.0967230i | ||||
\(899\) | 51.2827 | 1.71038 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.17854 | −0.305781 | ||||||||
\(902\) | 19.1903 | + | 19.1903i | 0.638966 | + | 0.638966i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.25674i | 0.0750580i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20.9527 | + | 20.9527i | −0.695722 | + | 0.695722i | −0.963485 | − | 0.267763i | \(-0.913716\pi\) |
0.267763 | + | 0.963485i | \(0.413716\pi\) | |||||||
\(908\) | 2.88573 | − | 2.88573i | 0.0957662 | − | 0.0957662i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.95403i | − | 0.263529i | −0.991281 | − | 0.131764i | \(-0.957936\pi\) | ||
0.991281 | − | 0.131764i | \(-0.0420642\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.21682 | + | 5.21682i | 0.172651 | + | 0.172651i | ||||
\(914\) | −33.1138 | −1.09531 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.16228 | 0.302730 | ||||||||
\(917\) | 5.22146 | + | 5.22146i | 0.172428 | + | 0.172428i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 22.4684i | − | 0.741164i | −0.928800 | − | 0.370582i | \(-0.879158\pi\) | ||
0.928800 | − | 0.370582i | \(-0.120842\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 13.7867 | − | 13.7867i | 0.454042 | − | 0.454042i | ||||
\(923\) | −4.21415 | + | 4.21415i | −0.138710 | + | 0.138710i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.6052i | 0.447095i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.68885 | − | 5.68885i | −0.186746 | − | 0.186746i | ||||
\(929\) | −13.2519 | −0.434782 | −0.217391 | − | 0.976085i | \(-0.569755\pi\) | ||||
−0.217391 | + | 0.976085i | \(0.569755\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.04989 | −0.0671824 | ||||||||
\(932\) | −4.67611 | − | 4.67611i | −0.153171 | − | 0.153171i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 21.0213i | − | 0.687839i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.0638 | + | 29.0638i | −0.949472 | + | 0.949472i | −0.998783 | − | 0.0493114i | \(-0.984297\pi\) |
0.0493114 | + | 0.998783i | \(0.484297\pi\) | |||||||
\(938\) | 5.84304 | − | 5.84304i | 0.190782 | − | 0.190782i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 19.1092i | − | 0.622941i | −0.950256 | − | 0.311471i | \(-0.899178\pi\) | ||
0.950256 | − | 0.311471i | \(-0.100822\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.19363 | + | 9.19363i | 0.299386 | + | 0.299386i | ||||
\(944\) | −4.25725 | −0.138562 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.4694 | −0.730544 | ||||||||
\(947\) | 32.1010 | + | 32.1010i | 1.04314 | + | 1.04314i | 0.999026 | + | 0.0441149i | \(0.0140468\pi\) |
0.0441149 | + | 0.999026i | \(0.485953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.1970i | 0.558240i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.54258 | + | 1.54258i | −0.0499954 | + | 0.0499954i | ||||
\(953\) | 31.8179 | − | 31.8179i | 1.03068 | − | 1.03068i | 0.0311686 | − | 0.999514i | \(-0.490077\pi\) |
0.999514 | − | 0.0311686i | \(-0.00992287\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 16.4853i | − | 0.533172i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.20701 | − | 8.20701i | −0.265157 | − | 0.265157i | ||||
\(959\) | −17.2913 | −0.558365 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.63161 | 0.310697 | ||||||||
\(962\) | 0.101536 | + | 0.101536i | 0.00327365 | + | 0.00327365i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 8.50419i | − | 0.273901i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −32.9608 | + | 32.9608i | −1.05995 | + | 1.05995i | −0.0618618 | + | 0.998085i | \(0.519704\pi\) |
−0.998085 | + | 0.0618618i | \(0.980296\pi\) | |||||||
\(968\) | −0.464466 | + | 0.464466i | −0.0149285 | + | 0.0149285i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 36.4536i | 1.16985i | 0.811087 | + | 0.584925i | \(0.198876\pi\) | ||||
−0.811087 | + | 0.584925i | \(0.801124\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.7919 | + | 10.7919i | 0.345973 | + | 0.345973i | ||||
\(974\) | −37.5821 | −1.20421 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.88953 | 0.220528 | ||||||||
\(977\) | −2.66218 | − | 2.66218i | −0.0851706 | − | 0.0851706i | 0.663238 | − | 0.748409i | \(-0.269182\pi\) |
−0.748409 | + | 0.663238i | \(0.769182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.5546i | 0.624967i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 23.6902 | − | 23.6902i | 0.755983 | − | 0.755983i | ||||
\(983\) | −40.9827 | + | 40.9827i | −1.30714 | + | 1.30714i | −0.383677 | + | 0.923468i | \(0.625342\pi\) |
−0.923468 | + | 0.383677i | \(0.874658\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 17.5510i | − | 0.558939i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.95011 | + | 2.95011i | 0.0938556 | + | 0.0938556i | ||||
\(989\) | −10.7646 | −0.342295 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.8845 | 1.42580 | 0.712901 | − | 0.701264i | \(-0.247381\pi\) | ||||
0.712901 | + | 0.701264i | \(0.247381\pi\) | |||||||
\(992\) | −4.50731 | − | 4.50731i | −0.143107 | − | 0.143107i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 2.92820i | − | 0.0928770i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.9695 | − | 32.9695i | 1.04416 | − | 1.04416i | 0.0451765 | − | 0.998979i | \(-0.485615\pi\) |
0.998979 | − | 0.0451765i | \(-0.0143850\pi\) | |||||||
\(998\) | −4.65633 | + | 4.65633i | −0.147393 | + | 0.147393i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3150.2.m.g.2843.2 | yes | 8 | |
3.2 | odd | 2 | 3150.2.m.h.2843.4 | yes | 8 | ||
5.2 | odd | 4 | 3150.2.m.h.1457.4 | yes | 8 | ||
5.3 | odd | 4 | 3150.2.m.l.1457.1 | yes | 8 | ||
5.4 | even | 2 | 3150.2.m.k.2843.3 | yes | 8 | ||
15.2 | even | 4 | inner | 3150.2.m.g.1457.2 | ✓ | 8 | |
15.8 | even | 4 | 3150.2.m.k.1457.3 | yes | 8 | ||
15.14 | odd | 2 | 3150.2.m.l.2843.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.m.g.1457.2 | ✓ | 8 | 15.2 | even | 4 | inner | |
3150.2.m.g.2843.2 | yes | 8 | 1.1 | even | 1 | trivial | |
3150.2.m.h.1457.4 | yes | 8 | 5.2 | odd | 4 | ||
3150.2.m.h.2843.4 | yes | 8 | 3.2 | odd | 2 | ||
3150.2.m.k.1457.3 | yes | 8 | 15.8 | even | 4 | ||
3150.2.m.k.2843.3 | yes | 8 | 5.4 | even | 2 | ||
3150.2.m.l.1457.1 | yes | 8 | 5.3 | odd | 4 | ||
3150.2.m.l.2843.1 | yes | 8 | 15.14 | odd | 2 |