Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1575,2,Mod(1268,1575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1575, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1575.1268");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1575 = 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1575.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: | \(12.5764383184\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1457.3 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1575.1457 |
Dual form | 1575.2.m.a.1268.3 |
$q$-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 \(\left(\mathbb{Z}/1575\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(1226\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 0.366025i | 0.258819 | − | 0.258819i | −0.565755 | − | 0.824574i | \(-0.691415\pi\) |
0.824574 | + | 0.565755i | \(0.191415\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73205i | 0.866025i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.707107 | − | 0.707107i | −0.267261 | − | 0.267261i | ||||
\(8\) | 1.36603 | + | 1.36603i | 0.482963 | + | 0.482963i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.44949i | − | 0.738549i | −0.929320 | − | 0.369274i | \(-0.879606\pi\) | ||
0.929320 | − | 0.369274i | \(-0.120394\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.86370 | + | 3.86370i | −1.07160 | + | 1.07160i | −0.0743676 | + | 0.997231i | \(0.523694\pi\) |
−0.997231 | + | 0.0743676i | \(0.976306\pi\) | |||||||
\(14\) | −0.517638 | −0.138345 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.46410 | −0.616025 | ||||||||
\(17\) | −2.00000 | + | 2.00000i | −0.485071 | + | 0.485071i | −0.906747 | − | 0.421676i | \(-0.861442\pi\) |
0.421676 | + | 0.906747i | \(0.361442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.00000i | − | 0.458831i | −0.973329 | − | 0.229416i | \(-0.926318\pi\) | ||
0.973329 | − | 0.229416i | \(-0.0736815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.896575 | − | 0.896575i | −0.191151 | − | 0.191151i | ||||
\(23\) | 6.46410 | + | 6.46410i | 1.34786 | + | 1.34786i | 0.887984 | + | 0.459874i | \(0.152106\pi\) |
0.459874 | + | 0.887984i | \(0.347894\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.82843i | 0.554700i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.22474 | − | 1.22474i | 0.231455 | − | 0.231455i | ||||
\(29\) | −6.31319 | −1.17233 | −0.586165 | − | 0.810192i | \(-0.699363\pi\) | ||||
−0.586165 | + | 0.810192i | \(0.699363\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.92820 | −0.885131 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(32\) | −3.63397 | + | 3.63397i | −0.642402 | + | 0.642402i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.46410i | 0.251091i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.378937 | − | 0.378937i | −0.0622969 | − | 0.0622969i | 0.675272 | − | 0.737569i | \(-0.264026\pi\) |
−0.737569 | + | 0.675272i | \(0.764026\pi\) | |||||||
\(38\) | −0.732051 | − | 0.732051i | −0.118754 | − | 0.118754i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.07055i | − | 0.323366i | −0.986843 | − | 0.161683i | \(-0.948308\pi\) | ||
0.986843 | − | 0.161683i | \(-0.0516922\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.82843 | + | 2.82843i | −0.431331 | + | 0.431331i | −0.889081 | − | 0.457750i | \(-0.848656\pi\) |
0.457750 | + | 0.889081i | \(0.348656\pi\) | |||||||
\(44\) | 4.24264 | 0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.73205 | 0.697703 | ||||||||
\(47\) | −7.46410 | + | 7.46410i | −1.08875 | + | 1.08875i | −0.0930938 | + | 0.995657i | \(0.529676\pi\) |
−0.995657 | + | 0.0930938i | \(0.970324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.69213 | − | 6.69213i | −0.928032 | − | 0.928032i | ||||
\(53\) | 2.26795 | + | 2.26795i | 0.311527 | + | 0.311527i | 0.845501 | − | 0.533974i | \(-0.179302\pi\) |
−0.533974 | + | 0.845501i | \(0.679302\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 1.93185i | − | 0.258155i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.31079 | + | 2.31079i | −0.303421 | + | 0.303421i | ||||
\(59\) | 12.6264 | 1.64382 | 0.821908 | − | 0.569621i | \(-0.192910\pi\) | ||||
0.821908 | + | 0.569621i | \(0.192910\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.92820 | −1.14314 | −0.571570 | − | 0.820554i | \(-0.693665\pi\) | ||||
−0.571570 | + | 0.820554i | \(0.693665\pi\) | |||||||
\(62\) | −1.80385 | + | 1.80385i | −0.229089 | + | 0.229089i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 2.26795i | − | 0.283494i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.31319 | − | 6.31319i | −0.771279 | − | 0.771279i | 0.207051 | − | 0.978330i | \(-0.433613\pi\) |
−0.978330 | + | 0.207051i | \(0.933613\pi\) | |||||||
\(68\) | −3.46410 | − | 3.46410i | −0.420084 | − | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 4.52004i | − | 0.536430i | −0.963359 | − | 0.268215i | \(-0.913566\pi\) | ||
0.963359 | − | 0.268215i | \(-0.0864338\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.03528 | − | 1.03528i | 0.121170 | − | 0.121170i | −0.643922 | − | 0.765091i | \(-0.722694\pi\) |
0.765091 | + | 0.643922i | \(0.222694\pi\) | |||||||
\(74\) | −0.277401 | −0.0322473 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.46410 | 0.397360 | ||||||||
\(77\) | −1.73205 | + | 1.73205i | −0.197386 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.757875 | − | 0.757875i | −0.0836933 | − | 0.0836933i | ||||
\(83\) | 4.53590 | + | 4.53590i | 0.497880 | + | 0.497880i | 0.910777 | − | 0.412898i | \(-0.135483\pi\) |
−0.412898 | + | 0.910777i | \(0.635483\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.07055i | 0.223273i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.34607 | − | 3.34607i | 0.356692 | − | 0.356692i | ||||
\(89\) | −14.1421 | −1.49906 | −0.749532 | − | 0.661968i | \(-0.769721\pi\) | ||||
−0.749532 | + | 0.661968i | \(0.769721\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | −11.1962 | + | 11.1962i | −1.16728 | + | 1.16728i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.46410i | 0.563579i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.8332 | − | 10.8332i | −1.09995 | − | 1.09995i | −0.994416 | − | 0.105533i | \(-0.966345\pi\) |
−0.105533 | − | 0.994416i | \(-0.533655\pi\) | |||||||
\(98\) | 0.366025 | + | 0.366025i | 0.0369741 | + | 0.0369741i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.8685i | 1.18096i | 0.807052 | + | 0.590481i | \(0.201062\pi\) | ||||
−0.807052 | + | 0.590481i | \(0.798938\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.48528 | + | 8.48528i | −0.836080 | + | 0.836080i | −0.988340 | − | 0.152261i | \(-0.951345\pi\) |
0.152261 | + | 0.988340i | \(0.451345\pi\) | |||||||
\(104\) | −10.5558 | −1.03508 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.66025 | 0.161258 | ||||||||
\(107\) | −7.92820 | + | 7.92820i | −0.766448 | + | 0.766448i | −0.977479 | − | 0.211031i | \(-0.932318\pi\) |
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.07180i | 0.102660i | 0.998682 | + | 0.0513298i | \(0.0163460\pi\) | ||||
−0.998682 | + | 0.0513298i | \(0.983654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.74238 | + | 1.74238i | 0.164640 | + | 0.164640i | ||||
\(113\) | 0.267949 | + | 0.267949i | 0.0252065 | + | 0.0252065i | 0.719598 | − | 0.694391i | \(-0.244326\pi\) |
−0.694391 | + | 0.719598i | \(0.744326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 10.9348i | − | 1.01527i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.62158 | − | 4.62158i | 0.425451 | − | 0.425451i | ||||
\(119\) | 2.82843 | 0.259281 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | −3.26795 | + | 3.26795i | −0.295866 | + | 0.295866i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 8.53590i | − | 0.766546i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.55532 | + | 5.55532i | 0.492955 | + | 0.492955i | 0.909236 | − | 0.416281i | \(-0.136667\pi\) |
−0.416281 | + | 0.909236i | \(0.636667\pi\) | |||||||
\(128\) | −8.09808 | − | 8.09808i | −0.715776 | − | 0.715776i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3843i | 1.16939i | 0.811254 | + | 0.584694i | \(0.198785\pi\) | ||||
−0.811254 | + | 0.584694i | \(0.801215\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.41421 | + | 1.41421i | −0.122628 | + | 0.122628i | ||||
\(134\) | −4.62158 | −0.399244 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.46410 | −0.468543 | ||||||||
\(137\) | 7.19615 | − | 7.19615i | 0.614809 | − | 0.614809i | −0.329386 | − | 0.944195i | \(-0.606842\pi\) |
0.944195 | + | 0.329386i | \(0.106842\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.8564i | − | 1.00565i | −0.864389 | − | 0.502824i | \(-0.832295\pi\) | ||
0.864389 | − | 0.502824i | \(-0.167705\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.65445 | − | 1.65445i | −0.138838 | − | 0.138838i | ||||
\(143\) | 9.46410 | + | 9.46410i | 0.791428 | + | 0.791428i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 0.757875i | − | 0.0627222i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.656339 | − | 0.656339i | 0.0539507 | − | 0.0539507i | ||||
\(149\) | 18.9396 | 1.55159 | 0.775795 | − | 0.630985i | \(-0.217349\pi\) | ||||
0.775795 | + | 0.630985i | \(0.217349\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.3923 | 0.845714 | 0.422857 | − | 0.906196i | \(-0.361027\pi\) | ||||
0.422857 | + | 0.906196i | \(0.361027\pi\) | |||||||
\(152\) | 2.73205 | − | 2.73205i | 0.221599 | − | 0.221599i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.26795i | 0.102174i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.45001 | + | 7.45001i | 0.594575 | + | 0.594575i | 0.938864 | − | 0.344289i | \(-0.111880\pi\) |
−0.344289 | + | 0.938864i | \(0.611880\pi\) | |||||||
\(158\) | 1.46410 | + | 1.46410i | 0.116478 | + | 0.116478i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 9.14162i | − | 0.720461i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.38375 | − | 8.38375i | 0.656666 | − | 0.656666i | −0.297924 | − | 0.954590i | \(-0.596294\pi\) |
0.954590 | + | 0.297924i | \(0.0962942\pi\) | |||||||
\(164\) | 3.58630 | 0.280043 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.32051 | 0.257721 | ||||||||
\(167\) | 2.92820 | − | 2.92820i | 0.226591 | − | 0.226591i | −0.584676 | − | 0.811267i | \(-0.698778\pi\) |
0.811267 | + | 0.584676i | \(0.198778\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 16.8564i | − | 1.29665i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.89898 | − | 4.89898i | −0.373544 | − | 0.373544i | ||||
\(173\) | 14.3923 | + | 14.3923i | 1.09423 | + | 1.09423i | 0.995072 | + | 0.0991546i | \(0.0316138\pi\) |
0.0991546 | + | 0.995072i | \(0.468386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.03579i | 0.454965i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.17638 | + | 5.17638i | −0.387986 | + | 0.387986i | ||||
\(179\) | 18.6622 | 1.39488 | 0.697438 | − | 0.716645i | \(-0.254323\pi\) | ||||
0.697438 | + | 0.716645i | \(0.254323\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 2.00000 | − | 2.00000i | 0.148250 | − | 0.148250i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 17.6603i | 1.30193i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.89898 | + | 4.89898i | 0.358249 | + | 0.358249i | ||||
\(188\) | −12.9282 | − | 12.9282i | −0.942886 | − | 0.942886i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 6.79367i | − | 0.491572i | −0.969324 | − | 0.245786i | \(-0.920954\pi\) | ||
0.969324 | − | 0.245786i | \(-0.0790461\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.9043 | + | 17.9043i | −1.28878 | + | 1.28878i | −0.353252 | + | 0.935528i | \(0.614924\pi\) |
−0.935528 | + | 0.353252i | \(0.885076\pi\) | |||||||
\(194\) | −7.93048 | −0.569375 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.73205 | −0.123718 | ||||||||
\(197\) | 10.2679 | − | 10.2679i | 0.731561 | − | 0.731561i | −0.239368 | − | 0.970929i | \(-0.576940\pi\) |
0.970929 | + | 0.239368i | \(0.0769402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.9282i | 1.48356i | 0.670643 | + | 0.741780i | \(0.266018\pi\) | ||||
−0.670643 | + | 0.741780i | \(0.733982\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.34418 | + | 4.34418i | 0.305655 | + | 0.305655i | ||||
\(203\) | 4.46410 | + | 4.46410i | 0.313319 | + | 0.313319i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.21166i | 0.432787i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.52056 | − | 9.52056i | 0.660132 | − | 0.660132i | ||||
\(209\) | −4.89898 | −0.338869 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.535898 | −0.0368928 | −0.0184464 | − | 0.999830i | \(-0.505872\pi\) | ||||
−0.0184464 | + | 0.999830i | \(0.505872\pi\) | |||||||
\(212\) | −3.92820 | + | 3.92820i | −0.269790 | + | 0.269790i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.80385i | 0.396743i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.48477 | + | 3.48477i | 0.236561 | + | 0.236561i | ||||
\(218\) | 0.392305 | + | 0.392305i | 0.0265702 | + | 0.0265702i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.4548i | − | 1.03960i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.8685 | + | 11.8685i | −0.794774 | + | 0.794774i | −0.982266 | − | 0.187492i | \(-0.939964\pi\) |
0.187492 | + | 0.982266i | \(0.439964\pi\) | |||||||
\(224\) | 5.13922 | 0.343378 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.196152 | 0.0130479 | ||||||||
\(227\) | 16.3923 | − | 16.3923i | 1.08800 | − | 1.08800i | 0.0922606 | − | 0.995735i | \(-0.470591\pi\) |
0.995735 | − | 0.0922606i | \(-0.0294093\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 24.9282i | − | 1.64730i | −0.567097 | − | 0.823651i | \(-0.691934\pi\) | ||
0.567097 | − | 0.823651i | \(-0.308066\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.62398 | − | 8.62398i | −0.566192 | − | 0.566192i | ||||
\(233\) | −0.267949 | − | 0.267949i | −0.0175539 | − | 0.0175539i | 0.698275 | − | 0.715829i | \(-0.253951\pi\) |
−0.715829 | + | 0.698275i | \(0.753951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 21.8695i | 1.42359i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.03528 | − | 1.03528i | 0.0671070 | − | 0.0671070i | ||||
\(239\) | −17.3495 | −1.12225 | −0.561123 | − | 0.827732i | \(-0.689631\pi\) | ||||
−0.561123 | + | 0.827732i | \(0.689631\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9282 | 0.832779 | 0.416389 | − | 0.909186i | \(-0.363295\pi\) | ||||
0.416389 | + | 0.909186i | \(0.363295\pi\) | |||||||
\(242\) | 1.83013 | − | 1.83013i | 0.117645 | − | 0.117645i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 15.4641i | − | 0.989988i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.72741 | + | 7.72741i | 0.491683 | + | 0.491683i | ||||
\(248\) | −6.73205 | − | 6.73205i | −0.427486 | − | 0.427486i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.1421i | 0.892644i | 0.894873 | + | 0.446322i | \(0.147266\pi\) | ||||
−0.894873 | + | 0.446322i | \(0.852734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.8338 | − | 15.8338i | 0.995459 | − | 0.995459i | ||||
\(254\) | 4.06678 | 0.255172 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.39230 | −0.0870191 | ||||||||
\(257\) | 14.5359 | − | 14.5359i | 0.906724 | − | 0.906724i | −0.0892820 | − | 0.996006i | \(-0.528457\pi\) |
0.996006 | + | 0.0892820i | \(0.0284572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.535898i | 0.0332991i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.89898 | + | 4.89898i | 0.302660 | + | 0.302660i | ||||
\(263\) | −7.39230 | − | 7.39230i | −0.455829 | − | 0.455829i | 0.441455 | − | 0.897284i | \(-0.354463\pi\) |
−0.897284 | + | 0.441455i | \(0.854463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.03528i | 0.0634769i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.9348 | − | 10.9348i | 0.667947 | − | 0.667947i | ||||
\(269\) | 10.5558 | 0.643601 | 0.321800 | − | 0.946808i | \(-0.395712\pi\) | ||||
0.321800 | + | 0.946808i | \(0.395712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.8564 | −1.44917 | −0.724587 | − | 0.689184i | \(-0.757969\pi\) | ||||
−0.724587 | + | 0.689184i | \(0.757969\pi\) | |||||||
\(272\) | 4.92820 | − | 4.92820i | 0.298816 | − | 0.298816i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 5.26795i | − | 0.318248i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.8695 | + | 21.8695i | 1.31401 | + | 1.31401i | 0.918430 | + | 0.395583i | \(0.129458\pi\) |
0.395583 | + | 0.918430i | \(0.370542\pi\) | |||||||
\(278\) | −4.33975 | − | 4.33975i | −0.260281 | − | 0.260281i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.41421i | − | 0.0843649i | −0.999110 | − | 0.0421825i | \(-0.986569\pi\) | ||
0.999110 | − | 0.0421825i | \(-0.0134311\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.24316 | + | 9.24316i | −0.549449 | + | 0.549449i | −0.926281 | − | 0.376833i | \(-0.877013\pi\) |
0.376833 | + | 0.926281i | \(0.377013\pi\) | |||||||
\(284\) | 7.82894 | 0.464562 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.92820 | 0.409673 | ||||||||
\(287\) | −1.46410 | + | 1.46410i | −0.0864232 | + | 0.0864232i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.00000i | 0.529412i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.79315 | + | 1.79315i | 0.104936 | + | 0.104936i | ||||
\(293\) | −8.39230 | − | 8.39230i | −0.490284 | − | 0.490284i | 0.418112 | − | 0.908396i | \(-0.362692\pi\) |
−0.908396 | + | 0.418112i | \(0.862692\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 1.03528i | − | 0.0601742i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.93237 | − | 6.93237i | 0.401581 | − | 0.401581i | ||||
\(299\) | −49.9507 | −2.88873 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 3.80385 | − | 3.80385i | 0.218887 | − | 0.218887i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.92820i | 0.282652i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.31268 | − | 1.31268i | −0.0749185 | − | 0.0749185i | 0.668655 | − | 0.743573i | \(-0.266870\pi\) |
−0.743573 | + | 0.668655i | \(0.766870\pi\) | |||||||
\(308\) | −3.00000 | − | 3.00000i | −0.170941 | − | 0.170941i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 17.5254i | − | 0.993772i | −0.867816 | − | 0.496886i | \(-0.834477\pi\) | ||
0.867816 | − | 0.496886i | \(-0.165523\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.3185 | − | 19.3185i | 1.09195 | − | 1.09195i | 0.0966264 | − | 0.995321i | \(-0.469195\pi\) |
0.995321 | − | 0.0966264i | \(-0.0308052\pi\) | |||||||
\(314\) | 5.45378 | 0.307775 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.92820 | −0.389742 | ||||||||
\(317\) | 14.2679 | − | 14.2679i | 0.801368 | − | 0.801368i | −0.181941 | − | 0.983309i | \(-0.558238\pi\) |
0.983309 | + | 0.181941i | \(0.0582381\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.4641i | 0.865823i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.34607 | − | 3.34607i | −0.186469 | − | 0.186469i | ||||
\(323\) | 4.00000 | + | 4.00000i | 0.222566 | + | 0.222566i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 6.13733i | − | 0.339915i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.82843 | − | 2.82843i | 0.156174 | − | 0.156174i | ||||
\(329\) | 10.5558 | 0.581962 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.5359 | 0.908895 | 0.454448 | − | 0.890773i | \(-0.349837\pi\) | ||||
0.454448 | + | 0.890773i | \(0.349837\pi\) | |||||||
\(332\) | −7.85641 | + | 7.85641i | −0.431176 | + | 0.431176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 2.14359i | − | 0.117292i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.5612 | + | 23.5612i | 1.28346 | + | 1.28346i | 0.938687 | + | 0.344771i | \(0.112044\pi\) |
0.344771 | + | 0.938687i | \(0.387956\pi\) | |||||||
\(338\) | −6.16987 | − | 6.16987i | −0.335597 | − | 0.335597i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0716i | 0.653713i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.707107 | − | 0.707107i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | −7.72741 | −0.416634 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5359 | 0.566413 | ||||||||
\(347\) | 1.00000 | − | 1.00000i | 0.0536828 | − | 0.0536828i | −0.679756 | − | 0.733439i | \(-0.737914\pi\) |
0.733439 | + | 0.679756i | \(0.237914\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.7128i | 1.59049i | 0.606288 | + | 0.795245i | \(0.292658\pi\) | ||||
−0.606288 | + | 0.795245i | \(0.707342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.90138 | + | 8.90138i | 0.474445 | + | 0.474445i | ||||
\(353\) | −18.9282 | − | 18.9282i | −1.00745 | − | 1.00745i | −0.999972 | − | 0.00747454i | \(-0.997621\pi\) |
−0.00747454 | − | 0.999972i | \(-0.502379\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 24.4949i | − | 1.29823i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.83083 | − | 6.83083i | 0.361021 | − | 0.361021i | ||||
\(359\) | 11.6926 | 0.617114 | 0.308557 | − | 0.951206i | \(-0.400154\pi\) | ||||
0.308557 | + | 0.951206i | \(0.400154\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | −2.19615 | + | 2.19615i | −0.115427 | + | 0.115427i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.46410i | 0.496054i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −14.6969 | − | 14.6969i | −0.767174 | − | 0.767174i | 0.210434 | − | 0.977608i | \(-0.432512\pi\) |
−0.977608 | + | 0.210434i | \(0.932512\pi\) | |||||||
\(368\) | −15.9282 | − | 15.9282i | −0.830315 | − | 0.830315i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.20736i | − | 0.166518i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7990 | + | 19.7990i | −1.02515 | + | 1.02515i | −0.0254774 | + | 0.999675i | \(0.508111\pi\) |
−0.999675 | + | 0.0254774i | \(0.991889\pi\) | |||||||
\(374\) | 3.58630 | 0.185443 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −20.3923 | −1.05165 | ||||||||
\(377\) | 24.3923 | − | 24.3923i | 1.25627 | − | 1.25627i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.6077i | − | 0.698980i | −0.936940 | − | 0.349490i | \(-0.886355\pi\) | ||
0.936940 | − | 0.349490i | \(-0.113645\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.48665 | − | 2.48665i | −0.127228 | − | 0.127228i | ||||
\(383\) | −7.85641 | − | 7.85641i | −0.401444 | − | 0.401444i | 0.477298 | − | 0.878742i | \(-0.341616\pi\) |
−0.878742 | + | 0.477298i | \(0.841616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 13.1069i | 0.667122i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 18.7637 | − | 18.7637i | 0.952583 | − | 0.952583i | ||||
\(389\) | 34.5975 | 1.75416 | 0.877081 | − | 0.480343i | \(-0.159488\pi\) | ||||
0.877081 | + | 0.480343i | \(0.159488\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.8564 | −1.30761 | ||||||||
\(392\) | −1.36603 | + | 1.36603i | −0.0689947 | + | 0.0689947i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 7.51666i | − | 0.378684i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.03528 | − | 1.03528i | −0.0519590 | − | 0.0519590i | 0.680650 | − | 0.732609i | \(-0.261698\pi\) |
−0.732609 | + | 0.680650i | \(0.761698\pi\) | |||||||
\(398\) | 7.66025 | + | 7.66025i | 0.383974 | + | 0.383974i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 22.5259i | − | 1.12489i | −0.826835 | − | 0.562444i | \(-0.809861\pi\) | ||
0.826835 | − | 0.562444i | \(-0.190139\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 19.0411 | − | 19.0411i | 0.948506 | − | 0.948506i | ||||
\(404\) | −20.5569 | −1.02274 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.26795 | 0.162186 | ||||||||
\(407\) | −0.928203 | + | 0.928203i | −0.0460093 | + | 0.0460093i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 8.92820i | − | 0.441471i | −0.975334 | − | 0.220736i | \(-0.929154\pi\) | ||
0.975334 | − | 0.220736i | \(-0.0708458\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.6969 | − | 14.6969i | −0.724066 | − | 0.724066i | ||||
\(413\) | −8.92820 | − | 8.92820i | −0.439328 | − | 0.439328i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 28.0812i | − | 1.37679i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.79315 | + | 1.79315i | −0.0877059 | + | 0.0877059i | ||||
\(419\) | −5.65685 | −0.276355 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.7128 | −1.44811 | −0.724057 | − | 0.689740i | \(-0.757725\pi\) | ||||
−0.724057 | + | 0.689740i | \(0.757725\pi\) | |||||||
\(422\) | −0.196152 | + | 0.196152i | −0.00954855 | + | 0.00954855i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.19615i | 0.300912i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.31319 | + | 6.31319i | 0.305517 | + | 0.305517i | ||||
\(428\) | −13.7321 | − | 13.7321i | −0.663764 | − | 0.663764i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.27792i | 0.254228i | 0.991888 | + | 0.127114i | \(0.0405715\pi\) | ||||
−0.991888 | + | 0.127114i | \(0.959429\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.2784 | − | 10.2784i | 0.493950 | − | 0.493950i | −0.415598 | − | 0.909548i | \(-0.636428\pi\) |
0.909548 | + | 0.415598i | \(0.136428\pi\) | |||||||
\(434\) | 2.55103 | 0.122453 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.85641 | −0.0889057 | ||||||||
\(437\) | 12.9282 | − | 12.9282i | 0.618440 | − | 0.618440i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 39.8564i | − | 1.90224i | −0.308818 | − | 0.951121i | \(-0.599933\pi\) | ||
0.308818 | − | 0.951121i | \(-0.400067\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.65685 | − | 5.65685i | −0.269069 | − | 0.269069i | ||||
\(443\) | 11.9282 | + | 11.9282i | 0.566726 | + | 0.566726i | 0.931210 | − | 0.364484i | \(-0.118755\pi\) |
−0.364484 | + | 0.931210i | \(0.618755\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.68835i | 0.411405i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.60368 | + | 1.60368i | −0.0757669 | + | 0.0757669i | ||||
\(449\) | −22.5259 | −1.06306 | −0.531531 | − | 0.847039i | \(-0.678383\pi\) | ||||
−0.531531 | + | 0.847039i | \(0.678383\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.07180 | −0.238822 | ||||||||
\(452\) | −0.464102 | + | 0.464102i | −0.0218295 | + | 0.0218295i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 12.0000i | − | 0.563188i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4906 | + | 21.4906i | 1.00529 | + | 1.00529i | 0.999986 | + | 0.00530215i | \(0.00168773\pi\) |
0.00530215 | + | 0.999986i | \(0.498312\pi\) | |||||||
\(458\) | −9.12436 | − | 9.12436i | −0.426353 | − | 0.426353i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.3949i | 1.83480i | 0.397962 | + | 0.917402i | \(0.369718\pi\) | ||||
−0.397962 | + | 0.917402i | \(0.630282\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.3543 | + | 25.3543i | −1.17831 | + | 1.17831i | −0.198141 | + | 0.980174i | \(0.563490\pi\) |
−0.980174 | + | 0.198141i | \(0.936510\pi\) | |||||||
\(464\) | 15.5563 | 0.722185 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.196152 | −0.00908659 | ||||||||
\(467\) | −6.53590 | + | 6.53590i | −0.302445 | + | 0.302445i | −0.841970 | − | 0.539525i | \(-0.818604\pi\) |
0.539525 | + | 0.841970i | \(0.318604\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.92820i | 0.412266i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 17.2480 | + | 17.2480i | 0.793902 | + | 0.793902i | ||||
\(473\) | 6.92820 | + | 6.92820i | 0.318559 | + | 0.318559i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.89898i | 0.224544i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.35036 | + | 6.35036i | −0.290459 | + | 0.290459i | ||||
\(479\) | 10.7589 | 0.491587 | 0.245793 | − | 0.969322i | \(-0.420951\pi\) | ||||
0.245793 | + | 0.969322i | \(0.420951\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.92820 | 0.133515 | ||||||||
\(482\) | 4.73205 | − | 4.73205i | 0.215539 | − | 0.215539i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.66025i | 0.393648i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.0411 | − | 19.0411i | −0.862835 | − | 0.862835i | 0.128831 | − | 0.991667i | \(-0.458877\pi\) |
−0.991667 | + | 0.128831i | \(0.958877\pi\) | |||||||
\(488\) | −12.1962 | − | 12.1962i | −0.552094 | − | 0.552094i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.6012i | 1.47127i | 0.677376 | + | 0.735637i | \(0.263117\pi\) | ||||
−0.677376 | + | 0.735637i | \(0.736883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.6264 | − | 12.6264i | 0.568664 | − | 0.568664i | ||||
\(494\) | 5.65685 | 0.254514 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.1436 | 0.545263 | ||||||||
\(497\) | −3.19615 | + | 3.19615i | −0.143367 | + | 0.143367i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3205i | 0.775372i | 0.921791 | + | 0.387686i | \(0.126726\pi\) | ||||
−0.921791 | + | 0.387686i | \(0.873274\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.17638 | + | 5.17638i | 0.231033 | + | 0.231033i | ||||
\(503\) | 12.9282 | + | 12.9282i | 0.576440 | + | 0.576440i | 0.933921 | − | 0.357481i | \(-0.116364\pi\) |
−0.357481 | + | 0.933921i | \(0.616364\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 11.5911i | − | 0.515288i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −9.62209 | + | 9.62209i | −0.426911 | + | 0.426911i | ||||
\(509\) | −38.8401 | −1.72156 | −0.860779 | − | 0.508979i | \(-0.830023\pi\) | ||||
−0.860779 | + | 0.508979i | \(0.830023\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.46410 | −0.0647680 | ||||||||
\(512\) | 15.6865 | − | 15.6865i | 0.693253 | − | 0.693253i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 10.6410i | − | 0.469355i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.2832 | + | 18.2832i | 0.804096 | + | 0.804096i | ||||
\(518\) | 0.196152 | + | 0.196152i | 0.00861844 | + | 0.00861844i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 28.6360i | − | 1.25457i | −0.778791 | − | 0.627283i | \(-0.784167\pi\) | ||
0.778791 | − | 0.627283i | \(-0.215833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.82843 | + | 2.82843i | −0.123678 | + | 0.123678i | −0.766237 | − | 0.642558i | \(-0.777873\pi\) |
0.642558 | + | 0.766237i | \(0.277873\pi\) | |||||||
\(524\) | −23.1822 | −1.01272 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.41154 | −0.235954 | ||||||||
\(527\) | 9.85641 | − | 9.85641i | 0.429352 | − | 0.429352i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 60.5692i | 2.63344i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.44949 | − | 2.44949i | −0.106199 | − | 0.106199i | ||||
\(533\) | 8.00000 | + | 8.00000i | 0.346518 | + | 0.346518i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 17.2480i | − | 0.744999i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.86370 | − | 3.86370i | 0.166576 | − | 0.166576i | ||||
\(539\) | 2.44949 | 0.105507 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.8564 | 0.509747 | 0.254873 | − | 0.966974i | \(-0.417966\pi\) | ||||
0.254873 | + | 0.966974i | \(0.417966\pi\) | |||||||
\(542\) | −8.73205 | + | 8.73205i | −0.375074 | + | 0.375074i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 14.5359i | − | 0.623222i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00052 | − | 5.00052i | −0.213807 | − | 0.213807i | 0.592076 | − | 0.805882i | \(-0.298309\pi\) |
−0.805882 | + | 0.592076i | \(0.798309\pi\) | |||||||
\(548\) | 12.4641 | + | 12.4641i | 0.532440 | + | 0.532440i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.6264i | 0.537902i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.82843 | − | 2.82843i | 0.120277 | − | 0.120277i | ||||
\(554\) | 16.0096 | 0.680183 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 20.5359 | 0.870916 | ||||||||
\(557\) | 14.2679 | − | 14.2679i | 0.604552 | − | 0.604552i | −0.336965 | − | 0.941517i | \(-0.609400\pi\) |
0.941517 | + | 0.336965i | \(0.109400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 21.8564i | − | 0.924427i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.517638 | − | 0.517638i | −0.0218352 | − | 0.0218352i | ||||
\(563\) | 22.7846 | + | 22.7846i | 0.960257 | + | 0.960257i | 0.999240 | − | 0.0389831i | \(-0.0124118\pi\) |
−0.0389831 | + | 0.999240i | \(0.512412\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.76646i | 0.284416i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 6.17449 | − | 6.17449i | 0.259076 | − | 0.259076i | ||||
\(569\) | 9.89949 | 0.415008 | 0.207504 | − | 0.978234i | \(-0.433466\pi\) | ||||
0.207504 | + | 0.978234i | \(0.433466\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17.8564 | −0.747267 | −0.373634 | − | 0.927576i | \(-0.621888\pi\) | ||||
−0.373634 | + | 0.927576i | \(0.621888\pi\) | |||||||
\(572\) | −16.3923 | + | 16.3923i | −0.685397 | + | 0.685397i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.07180i | 0.0447359i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.8332 | − | 10.8332i | −0.450993 | − | 0.450993i | 0.444691 | − | 0.895684i | \(-0.353314\pi\) |
−0.895684 | + | 0.444691i | \(0.853314\pi\) | |||||||
\(578\) | 3.29423 | + | 3.29423i | 0.137022 | + | 0.137022i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 6.41473i | − | 0.266128i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.55532 | − | 5.55532i | 0.230078 | − | 0.230078i | ||||
\(584\) | 2.82843 | 0.117041 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.14359 | −0.253790 | ||||||||
\(587\) | −14.0000 | + | 14.0000i | −0.577842 | + | 0.577842i | −0.934308 | − | 0.356466i | \(-0.883981\pi\) |
0.356466 | + | 0.934308i | \(0.383981\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.85641i | 0.406126i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.933740 | + | 0.933740i | 0.0383765 | + | 0.0383765i | ||||
\(593\) | 5.85641 | + | 5.85641i | 0.240494 | + | 0.240494i | 0.817054 | − | 0.576561i | \(-0.195606\pi\) |
−0.576561 | + | 0.817054i | \(0.695606\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 32.8043i | 1.34372i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −18.2832 | + | 18.2832i | −0.747657 | + | 0.747657i | ||||
\(599\) | 32.0464 | 1.30938 | 0.654691 | − | 0.755897i | \(-0.272799\pi\) | ||||
0.654691 | + | 0.755897i | \(0.272799\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.21539 | −0.212740 | −0.106370 | − | 0.994327i | \(-0.533923\pi\) | ||||
−0.106370 | + | 0.994327i | \(0.533923\pi\) | |||||||
\(602\) | 1.46410 | − | 1.46410i | 0.0596723 | − | 0.0596723i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.0000i | 0.732410i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.82843 | + | 2.82843i | 0.114802 | + | 0.114802i | 0.762174 | − | 0.647372i | \(-0.224132\pi\) |
−0.647372 | + | 0.762174i | \(0.724132\pi\) | |||||||
\(608\) | 7.26795 | + | 7.26795i | 0.294754 | + | 0.294754i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 57.6781i | − | 2.33341i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.04008 | + | 9.04008i | −0.365126 | + | 0.365126i | −0.865696 | − | 0.500570i | \(-0.833124\pi\) |
0.500570 | + | 0.865696i | \(0.333124\pi\) | |||||||
\(614\) | −0.960947 | −0.0387807 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.73205 | −0.190660 | ||||||||
\(617\) | −29.0526 | + | 29.0526i | −1.16961 | + | 1.16961i | −0.187311 | + | 0.982301i | \(0.559977\pi\) |
−0.982301 | + | 0.187311i | \(0.940023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.928203i | − | 0.0373076i | −0.999826 | − | 0.0186538i | \(-0.994062\pi\) | ||
0.999826 | − | 0.0186538i | \(-0.00593804\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.41473 | − | 6.41473i | −0.257207 | − | 0.257207i | ||||
\(623\) | 10.0000 | + | 10.0000i | 0.400642 | + | 0.400642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 14.1421i | − | 0.565233i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −12.9038 | + | 12.9038i | −0.514917 | + | 0.514917i | ||||
\(629\) | 1.51575 | 0.0604369 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.8564 | 1.02933 | 0.514664 | − | 0.857392i | \(-0.327917\pi\) | ||||
0.514664 | + | 0.857392i | \(0.327917\pi\) | |||||||
\(632\) | −5.46410 | + | 5.46410i | −0.217350 | + | 0.217350i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 10.4449i | − | 0.414819i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.86370 | − | 3.86370i | −0.153085 | − | 0.153085i | ||||
\(638\) | 5.66025 | + | 5.66025i | 0.224092 | + | 0.224092i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.8375i | 0.546549i | 0.961936 | + | 0.273275i | \(0.0881068\pi\) | ||||
−0.961936 | + | 0.273275i | \(0.911893\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −27.5264 | + | 27.5264i | −1.08554 | + | 1.08554i | −0.0895531 | + | 0.995982i | \(0.528544\pi\) |
−0.995982 | + | 0.0895531i | \(0.971456\pi\) | |||||||
\(644\) | 15.8338 | 0.623937 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.92820 | 0.115209 | ||||||||
\(647\) | −20.0000 | + | 20.0000i | −0.786281 | + | 0.786281i | −0.980882 | − | 0.194601i | \(-0.937659\pi\) |
0.194601 | + | 0.980882i | \(0.437659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 30.9282i | − | 1.21404i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.5211 | + | 14.5211i | 0.568689 | + | 0.568689i | ||||
\(653\) | −3.33975 | − | 3.33975i | −0.130694 | − | 0.130694i | 0.638734 | − | 0.769428i | \(-0.279459\pi\) |
−0.769428 | + | 0.638734i | \(0.779459\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.10205i | 0.199202i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.86370 | − | 3.86370i | 0.150623 | − | 0.150623i | ||||
\(659\) | −25.0769 | −0.976858 | −0.488429 | − | 0.872604i | \(-0.662430\pi\) | ||||
−0.488429 | + | 0.872604i | \(0.662430\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.7846 | 0.730637 | 0.365318 | − | 0.930883i | \(-0.380960\pi\) | ||||
0.365318 | + | 0.930883i | \(0.380960\pi\) | |||||||
\(662\) | 6.05256 | − | 6.05256i | 0.235239 | − | 0.235239i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.3923i | 0.480915i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −40.8091 | − | 40.8091i | −1.58014 | − | 1.58014i | ||||
\(668\) | 5.07180 | + | 5.07180i | 0.196234 | + | 0.196234i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.8695i | 0.844264i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.89469 | − | 1.89469i | 0.0730348 | − | 0.0730348i | −0.669646 | − | 0.742681i | \(-0.733554\pi\) |
0.742681 | + | 0.669646i | \(0.233554\pi\) | |||||||
\(674\) | 17.2480 | 0.664367 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 29.1962 | 1.12293 | ||||||||
\(677\) | 27.3205 | − | 27.3205i | 1.05001 | − | 1.05001i | 0.0513307 | − | 0.998682i | \(-0.483654\pi\) |
0.998682 | − | 0.0513307i | \(-0.0163463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3205i | 0.587947i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 4.41851 | + | 4.41851i | 0.169193 | + | 0.169193i | ||||
\(683\) | 5.14359 | + | 5.14359i | 0.196814 | + | 0.196814i | 0.798633 | − | 0.601819i | \(-0.205557\pi\) |
−0.601819 | + | 0.798633i | \(0.705557\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 0.517638i | − | 0.0197635i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.96953 | − | 6.96953i | 0.265711 | − | 0.265711i | ||||
\(689\) | −17.5254 | −0.667663 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.7846 | 0.410266 | 0.205133 | − | 0.978734i | \(-0.434237\pi\) | ||||
0.205133 | + | 0.978734i | \(0.434237\pi\) | |||||||
\(692\) | −24.9282 | + | 24.9282i | −0.947628 | + | 0.947628i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 0.732051i | − | 0.0277883i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.14110 | + | 4.14110i | 0.156856 | + | 0.156856i | ||||
\(698\) | 10.8756 | + | 10.8756i | 0.411649 | + | 0.411649i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.96902i | 0.0743687i | 0.999308 | + | 0.0371844i | \(0.0118389\pi\) | ||||
−0.999308 | + | 0.0371844i | \(0.988161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.757875 | + | 0.757875i | −0.0285838 | + | 0.0285838i | ||||
\(704\) | −5.55532 | −0.209374 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13.8564 | −0.521493 | ||||||||
\(707\) | 8.39230 | − | 8.39230i | 0.315625 | − | 0.315625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 24.7846i | − | 0.930806i | −0.885099 | − | 0.465403i | \(-0.845909\pi\) | ||
0.885099 | − | 0.465403i | \(-0.154091\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19.3185 | − | 19.3185i | −0.723992 | − | 0.723992i | ||||
\(713\) | −31.8564 | − | 31.8564i | −1.19303 | − | 1.19303i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.3238i | 1.20800i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.27981 | − | 4.27981i | 0.159721 | − | 0.159721i | ||||
\(719\) | −29.5969 | −1.10378 | −0.551890 | − | 0.833917i | \(-0.686093\pi\) | ||||
−0.551890 | + | 0.833917i | \(0.686093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 5.49038 | − | 5.49038i | 0.204331 | − | 0.204331i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.3923i | − | 0.386227i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.28221 | + | 8.28221i | 0.307170 | + | 0.307170i | 0.843811 | − | 0.536641i | \(-0.180307\pi\) |
−0.536641 | + | 0.843811i | \(0.680307\pi\) | |||||||
\(728\) | 7.46410 | + | 7.46410i | 0.276638 | + | 0.276638i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 11.3137i | − | 0.418453i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −28.5617 | + | 28.5617i | −1.05495 | + | 1.05495i | −0.0565497 | + | 0.998400i | \(0.518010\pi\) |
−0.998400 | + | 0.0565497i | \(0.981990\pi\) | |||||||
\(734\) | −10.7589 | −0.397118 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −46.9808 | −1.73173 | ||||||||
\(737\) | −15.4641 | + | 15.4641i | −0.569628 | + | 0.569628i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 9.85641i | − | 0.362574i | −0.983430 | − | 0.181287i | \(-0.941974\pi\) | ||
0.983430 | − | 0.181287i | \(-0.0580263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.17398 | − | 1.17398i | −0.0430980 | − | 0.0430980i | ||||
\(743\) | 8.60770 | + | 8.60770i | 0.315786 | + | 0.315786i | 0.847146 | − | 0.531360i | \(-0.178319\pi\) |
−0.531360 | + | 0.847146i | \(0.678319\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 14.4939i | 0.530658i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.48528 | + | 8.48528i | −0.310253 | + | 0.310253i | ||||
\(749\) | 11.2122 | 0.409684 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 50.1051 | 1.82836 | 0.914181 | − | 0.405307i | \(-0.132835\pi\) | ||||
0.914181 | + | 0.405307i | \(0.132835\pi\) | |||||||
\(752\) | 18.3923 | − | 18.3923i | 0.670698 | − | 0.670698i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 17.8564i | − | 0.650292i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.7023 | − | 27.7023i | −1.00686 | − | 1.00686i | −0.999976 | − | 0.00687950i | \(-0.997810\pi\) |
−0.00687950 | − | 0.999976i | \(-0.502190\pi\) | |||||||
\(758\) | −4.98076 | − | 4.98076i | −0.180909 | − | 0.180909i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26.5654i | 0.962997i | 0.876447 | + | 0.481498i | \(0.159907\pi\) | ||||
−0.876447 | + | 0.481498i | \(0.840093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.757875 | − | 0.757875i | 0.0274369 | − | 0.0274369i | ||||
\(764\) | 11.7670 | 0.425714 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.75129 | −0.207803 | ||||||||
\(767\) | −48.7846 | + | 48.7846i | −1.76151 | + | 1.76151i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10.7846i | − | 0.388903i | −0.980912 | − | 0.194451i | \(-0.937707\pi\) | ||
0.980912 | − | 0.194451i | \(-0.0622927\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −31.0112 | − | 31.0112i | −1.11612 | − | 1.11612i | ||||
\(773\) | 21.3205 | + | 21.3205i | 0.766845 | + | 0.766845i | 0.977550 | − | 0.210704i | \(-0.0675758\pi\) |
−0.210704 | + | 0.977550i | \(0.567576\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 29.5969i | − | 1.06247i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.6636 | − | 12.6636i | 0.454010 | − | 0.454010i | ||||
\(779\) | −4.14110 | −0.148370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.0718 | −0.396180 | ||||||||
\(782\) | −9.46410 | + | 9.46410i | −0.338436 | + | 0.338436i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 2.46410i | − | 0.0880036i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.41473 | − | 6.41473i | −0.228660 | − | 0.228660i | 0.583473 | − | 0.812133i | \(-0.301694\pi\) |
−0.812133 | + | 0.583473i | \(0.801694\pi\) | |||||||
\(788\) | 17.7846 | + | 17.7846i | 0.633550 | + | 0.633550i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 0.378937i | − | 0.0134735i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 34.4959 | − | 34.4959i | 1.22499 | − | 1.22499i | ||||
\(794\) | −0.757875 | −0.0268960 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −36.2487 | −1.28480 | ||||||||
\(797\) | −27.1769 | + | 27.1769i | −0.962656 | + | 0.962656i | −0.999327 | − | 0.0366717i | \(-0.988324\pi\) |
0.0366717 | + | 0.999327i | \(0.488324\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 29.8564i | − | 1.05624i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.24504 | − | 8.24504i | −0.291143 | − | 0.291143i | ||||
\(803\) | −2.53590 | − | 2.53590i | −0.0894899 | − | 0.0894899i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 13.9391i | − | 0.490983i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −16.2127 | + | 16.2127i | −0.570360 | + | 0.570360i | ||||
\(809\) | 24.0416 | 0.845259 | 0.422629 | − | 0.906303i | \(-0.361107\pi\) | ||||
0.422629 | + | 0.906303i | \(0.361107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.9282 | −0.875348 | −0.437674 | − | 0.899134i | \(-0.644198\pi\) | ||||
−0.437674 | + | 0.899134i | \(0.644198\pi\) | |||||||
\(812\) | −7.73205 | + | 7.73205i | −0.271342 | + | 0.271342i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.679492i | 0.0238162i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.65685 | + | 5.65685i | 0.197908 | + | 0.197908i | ||||
\(818\) | −3.26795 | − | 3.26795i | −0.114261 | − | 0.114261i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 11.9700i | − | 0.417758i | −0.977942 | − | 0.208879i | \(-0.933019\pi\) | ||
0.977942 | − | 0.208879i | \(-0.0669814\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −15.5563 | + | 15.5563i | −0.542260 | + | 0.542260i | −0.924191 | − | 0.381931i | \(-0.875259\pi\) |
0.381931 | + | 0.924191i | \(0.375259\pi\) | |||||||
\(824\) | −23.1822 | −0.807591 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.53590 | −0.227413 | ||||||||
\(827\) | −21.0000 | + | 21.0000i | −0.730242 | + | 0.730242i | −0.970667 | − | 0.240426i | \(-0.922713\pi\) |
0.240426 | + | 0.970667i | \(0.422713\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.7846i | 1.06919i | 0.845107 | + | 0.534597i | \(0.179537\pi\) | ||||
−0.845107 | + | 0.534597i | \(0.820463\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 8.76268 | + | 8.76268i | 0.303791 | + | 0.303791i | ||||
\(833\) | −2.00000 | − | 2.00000i | −0.0692959 | − | 0.0692959i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 8.48528i | − | 0.293470i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.07055 | + | 2.07055i | −0.0715260 | + | 0.0715260i | ||||
\(839\) | 35.8086 | 1.23625 | 0.618125 | − | 0.786080i | \(-0.287892\pi\) | ||||
0.618125 | + | 0.786080i | \(0.287892\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.8564 | 0.374359 | ||||||||
\(842\) | −10.8756 | + | 10.8756i | −0.374799 | + | 0.374799i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 0.928203i | − | 0.0319501i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.53553 | − | 3.53553i | −0.121482 | − | 0.121482i | ||||
\(848\) | −5.58846 | − | 5.58846i | −0.191908 | − | 0.191908i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 4.89898i | − | 0.167935i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0459 | − | 27.0459i | 0.926035 | − | 0.926035i | −0.0714121 | − | 0.997447i | \(-0.522751\pi\) |
0.997447 | + | 0.0714121i | \(0.0227505\pi\) | |||||||
\(854\) | 4.62158 | 0.158147 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.6603 | −0.740332 | ||||||||
\(857\) | −10.3923 | + | 10.3923i | −0.354994 | + | 0.354994i | −0.861964 | − | 0.506970i | \(-0.830766\pi\) |
0.506970 | + | 0.861964i | \(0.330766\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.7846i | 0.640923i | 0.947262 | + | 0.320461i | \(0.103838\pi\) | ||||
−0.947262 | + | 0.320461i | \(0.896162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.93185 | + | 1.93185i | 0.0657991 | + | 0.0657991i | ||||
\(863\) | −23.2487 | − | 23.2487i | −0.791395 | − | 0.791395i | 0.190326 | − | 0.981721i | \(-0.439046\pi\) |
−0.981721 | + | 0.190326i | \(0.939046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 7.52433i | − | 0.255687i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.03579 | + | 6.03579i | −0.204868 | + | 0.204868i | ||||
\(869\) | 9.79796 | 0.332373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 48.7846 | 1.65300 | ||||||||
\(872\) | −1.46410 | + | 1.46410i | −0.0495807 | + | 0.0495807i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 9.46410i | − | 0.320128i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.27362 | + | 2.27362i | 0.0767748 | + | 0.0767748i | 0.744451 | − | 0.667677i | \(-0.232711\pi\) |
−0.667677 | + | 0.744451i | \(0.732711\pi\) | |||||||
\(878\) | −14.5885 | − | 14.5885i | −0.492337 | − | 0.492337i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.9411i | 1.14351i | 0.820426 | + | 0.571753i | \(0.193736\pi\) | ||||
−0.820426 | + | 0.571753i | \(0.806264\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.4949 | + | 24.4949i | −0.824319 | + | 0.824319i | −0.986724 | − | 0.162405i | \(-0.948075\pi\) |
0.162405 | + | 0.986724i | \(0.448075\pi\) | |||||||
\(884\) | 26.7685 | 0.900323 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.73205 | 0.293359 | ||||||||
\(887\) | −41.3205 | + | 41.3205i | −1.38741 | + | 1.38741i | −0.556680 | + | 0.830727i | \(0.687925\pi\) |
−0.830727 | + | 0.556680i | \(0.812075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 7.85641i | − | 0.263495i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.5569 | − | 20.5569i | −0.688295 | − | 0.688295i | ||||
\(893\) | 14.9282 | + | 14.9282i | 0.499553 | + | 0.499553i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 11.4524i | 0.382598i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.24504 | + | 8.24504i | −0.275141 | + | 0.275141i | ||||
\(899\) | 31.1127 | 1.03767 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.07180 | −0.302225 | ||||||||
\(902\) | −1.85641 | + | 1.85641i | −0.0618116 | + | 0.0618116i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.732051i | 0.0243476i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.0716 | − | 12.0716i | −0.400830 | − | 0.400830i | 0.477695 | − | 0.878526i | \(-0.341472\pi\) |
−0.878526 | + | 0.477695i | \(0.841472\pi\) | |||||||
\(908\) | 28.3923 | + | 28.3923i | 0.942232 | + | 0.942232i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 7.55154i | − | 0.250194i | −0.992145 | − | 0.125097i | \(-0.960076\pi\) | ||
0.992145 | − | 0.125097i | \(-0.0399242\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1106 | − | 11.1106i | 0.367708 | − | 0.367708i | ||||
\(914\) | 15.7322 | 0.520375 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 43.1769 | 1.42661 | ||||||||
\(917\) | 9.46410 | − | 9.46410i | 0.312532 | − | 0.312532i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 51.1769i | 1.68817i | 0.536209 | + | 0.844085i | \(0.319856\pi\) | ||||
−0.536209 | + | 0.844085i | \(0.680144\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 14.4195 | + | 14.4195i | 0.474882 | + | 0.474882i | ||||
\(923\) | 17.4641 | + | 17.4641i | 0.574838 | + | 0.574838i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.5606i | 0.609941i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.9420 | − | 22.9420i | 0.753107 | − | 0.753107i | ||||
\(929\) | −23.9401 | −0.785449 | −0.392725 | − | 0.919656i | \(-0.628467\pi\) | ||||
−0.392725 | + | 0.919656i | \(0.628467\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.00000 | 0.0655474 | ||||||||
\(932\) | 0.464102 | − | 0.464102i | 0.0152022 | − | 0.0152022i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.78461i | 0.156557i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.3500 | − | 22.3500i | −0.730143 | − | 0.730143i | 0.240505 | − | 0.970648i | \(-0.422687\pi\) |
−0.970648 | + | 0.240505i | \(0.922687\pi\) | |||||||
\(938\) | 3.26795 | + | 3.26795i | 0.106702 | + | 0.106702i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.1117i | 0.688221i | 0.938929 | + | 0.344110i | \(0.111819\pi\) | ||||
−0.938929 | + | 0.344110i | \(0.888181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3843 | − | 13.3843i | 0.435852 | − | 0.435852i | ||||
\(944\) | −31.1127 | −1.01263 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.07180 | 0.164898 | ||||||||
\(947\) | −31.0000 | + | 31.0000i | −1.00736 | + | 1.00736i | −0.00739197 | + | 0.999973i | \(0.502353\pi\) |
−0.999973 | + | 0.00739197i | \(0.997647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000i | 0.259691i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.86370 | + | 3.86370i | 0.125223 | + | 0.125223i | ||||
\(953\) | −38.6603 | − | 38.6603i | −1.25233 | − | 1.25233i | −0.954674 | − | 0.297655i | \(-0.903796\pi\) |
−0.297655 | − | 0.954674i | \(-0.596204\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 30.0502i | − | 0.971893i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.93803 | − | 3.93803i | 0.127232 | − | 0.127232i | ||||
\(959\) | −10.1769 | −0.328629 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.71281 | −0.216542 | ||||||||
\(962\) | 1.07180 | − | 1.07180i | 0.0345561 | − | 0.0345561i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 22.3923i | 0.721208i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −38.7386 | − | 38.7386i | −1.24575 | − | 1.24575i | −0.957580 | − | 0.288169i | \(-0.906954\pi\) |
−0.288169 | − | 0.957580i | \(-0.593046\pi\) | |||||||
\(968\) | 6.83013 | + | 6.83013i | 0.219529 | + | 0.219529i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.5558i | 0.338753i | 0.985551 | + | 0.169376i | \(0.0541754\pi\) | ||||
−0.985551 | + | 0.169376i | \(0.945825\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8.38375 | + | 8.38375i | −0.268771 | + | 0.268771i | ||||
\(974\) | −13.9391 | −0.446636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 22.0000 | 0.704203 | ||||||||
\(977\) | 15.7321 | − | 15.7321i | 0.503313 | − | 0.503313i | −0.409153 | − | 0.912466i | \(-0.634176\pi\) |
0.912466 | + | 0.409153i | \(0.134176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 34.6410i | 1.10713i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.9329 | + | 11.9329i | 0.380794 | + | 0.380794i | ||||
\(983\) | 23.3205 | + | 23.3205i | 0.743809 | + | 0.743809i | 0.973309 | − | 0.229500i | \(-0.0737091\pi\) |
−0.229500 | + | 0.973309i | \(0.573709\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 9.24316i | − | 0.294362i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.3843 | + | 13.3843i | −0.425810 | + | 0.425810i | ||||
\(989\) | −36.5665 | −1.16275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.3205 | −0.423140 | −0.211570 | − | 0.977363i | \(-0.567858\pi\) | ||||
−0.211570 | + | 0.977363i | \(0.567858\pi\) | |||||||
\(992\) | 17.9090 | − | 17.9090i | 0.568610 | − | 0.568610i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.33975i | 0.0742122i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.8647 | + | 13.8647i | 0.439101 | + | 0.439101i | 0.891709 | − | 0.452609i | \(-0.149507\pi\) |
−0.452609 | + | 0.891709i | \(0.649507\pi\) | |||||||
\(998\) | 6.33975 | + | 6.33975i | 0.200681 | + | 0.200681i | ||||
\(999\) | 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 | 1575.2.m.a.1457.3 | yes | 8 | |
3.2 | odd | 2 | 1575.2.m.b.1457.1 | yes | 8 | ||
5.2 | odd | 4 | inner | 1575.2.m.a.1268.4 | yes | 8 | |
5.3 | odd | 4 | 1575.2.m.b.1268.1 | yes | 8 | ||
5.4 | even | 2 | 1575.2.m.b.1457.2 | yes | 8 | ||
15.2 | even | 4 | 1575.2.m.b.1268.2 | yes | 8 | ||
15.8 | even | 4 | inner | 1575.2.m.a.1268.3 | ✓ | 8 | |
15.14 | odd | 2 | inner | 1575.2.m.a.1457.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1575.2.m.a.1268.3 | ✓ | 8 | 15.8 | even | 4 | inner | |
1575.2.m.a.1268.4 | yes | 8 | 5.2 | odd | 4 | inner | |
1575.2.m.a.1457.3 | yes | 8 | 1.1 | even | 1 | trivial | |
1575.2.m.a.1457.4 | yes | 8 | 15.14 | odd | 2 | inner | |
1575.2.m.b.1268.1 | yes | 8 | 5.3 | odd | 4 | ||
1575.2.m.b.1268.2 | yes | 8 | 15.2 | even | 4 | ||
1575.2.m.b.1457.1 | yes | 8 | 3.2 | odd | 2 | ||
1575.2.m.b.1457.2 | yes | 8 | 5.4 | even | 2 |