Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1400,2,Mod(657,1400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1400, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1400.657");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1400.x (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: | \(11.1790562830\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 993.11 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.c.657.11 |
$q$-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 \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).
\(n\) | \(351\) | \(701\) | \(801\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.923076 | − | 0.923076i | 0.532938 | − | 0.532938i | −0.388507 | − | 0.921446i | \(-0.627009\pi\) |
0.921446 | + | 0.388507i | \(0.127009\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.915096 | + | 2.48246i | 0.345874 | + | 0.938281i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.29586i | 0.431953i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.21658 | 0.366814 | 0.183407 | − | 0.983037i | \(-0.441287\pi\) | ||||
0.183407 | + | 0.983037i | \(0.441287\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.996254 | − | 0.996254i | 0.276311 | − | 0.276311i | −0.555323 | − | 0.831634i | \(-0.687406\pi\) |
0.831634 | + | 0.555323i | \(0.187406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.567852 | + | 0.567852i | 0.137724 | + | 0.137724i | 0.772608 | − | 0.634883i | \(-0.218952\pi\) |
−0.634883 | + | 0.772608i | \(0.718952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.103488 | 0.0237418 | 0.0118709 | − | 0.999930i | \(-0.496221\pi\) | ||||
0.0118709 | + | 0.999930i | \(0.496221\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.13620 | + | 1.44679i | 0.684376 | + | 0.315717i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.43395 | − | 1.43395i | −0.298999 | − | 0.298999i | 0.541623 | − | 0.840622i | \(-0.317810\pi\) |
−0.840622 | + | 0.541623i | \(0.817810\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.96541 | + | 3.96541i | 0.763143 | + | 0.763143i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.97655i | 0.924121i | 0.886848 | + | 0.462061i | \(0.152890\pi\) | ||||
−0.886848 | + | 0.462061i | \(0.847110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.35159i | 0.781569i | 0.920482 | + | 0.390784i | \(0.127796\pi\) | ||||
−0.920482 | + | 0.390784i | \(0.872204\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.12300 | − | 1.12300i | 0.195489 | − | 0.195489i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.54187 | − | 2.54187i | 0.417880 | − | 0.417880i | −0.466592 | − | 0.884473i | \(-0.654518\pi\) |
0.884473 | + | 0.466592i | \(0.154518\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 1.83924i | − | 0.294514i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.06593i | 1.10351i | 0.834005 | + | 0.551757i | \(0.186042\pi\) | ||||
−0.834005 | + | 0.551757i | \(0.813958\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.11342 | − | 3.11342i | −0.474793 | − | 0.474793i | 0.428669 | − | 0.903462i | \(-0.358983\pi\) |
−0.903462 | + | 0.428669i | \(0.858983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.23621 | + | 7.23621i | 1.05551 | + | 1.05551i | 0.998366 | + | 0.0571445i | \(0.0181996\pi\) |
0.0571445 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.32520 | + | 4.54338i | −0.760742 | + | 0.649054i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.04834 | 0.146797 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.882128 | − | 0.882128i | −0.121170 | − | 0.121170i | 0.643922 | − | 0.765091i | \(-0.277306\pi\) |
−0.765091 | + | 0.643922i | \(0.777306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0955275 | − | 0.0955275i | 0.0126529 | − | 0.0126529i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.28584 | 1.07872 | 0.539362 | − | 0.842074i | \(-0.318665\pi\) | ||||
0.539362 | + | 0.842074i | \(0.318665\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0630i | 1.28844i | 0.764842 | + | 0.644218i | \(0.222817\pi\) | ||||
−0.764842 | + | 0.644218i | \(0.777183\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.21692 | + | 1.18584i | −0.405294 | + | 0.149401i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.07422 | − | 7.07422i | 0.864253 | − | 0.864253i | −0.127575 | − | 0.991829i | \(-0.540720\pi\) |
0.991829 | + | 0.127575i | \(0.0407195\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.64729 | −0.318696 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.329005 | 0.0390457 | 0.0195229 | − | 0.999809i | \(-0.493785\pi\) | ||||
0.0195229 | + | 0.999809i | \(0.493785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.3569 | − | 11.3569i | 1.32923 | − | 1.32923i | 0.423183 | − | 0.906044i | \(-0.360913\pi\) |
0.906044 | − | 0.423183i | \(-0.139087\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.11329 | + | 3.02012i | 0.126871 | + | 0.344175i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.6882i | − | 1.54004i | −0.638020 | − | 0.770019i | \(-0.720246\pi\) | ||
0.638020 | − | 0.770019i | \(-0.279754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.43317 | 0.381463 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.61538 | − | 4.61538i | 0.506604 | − | 0.506604i | −0.406878 | − | 0.913482i | \(-0.633383\pi\) |
0.913482 | + | 0.406878i | \(0.133383\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.59373 | + | 4.59373i | 0.492500 | + | 0.492500i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.1942 | −1.39858 | −0.699291 | − | 0.714837i | \(-0.746501\pi\) | ||||
−0.699291 | + | 0.714837i | \(0.746501\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.38483 | + | 1.56149i | 0.354826 | + | 0.163689i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.01685 | + | 4.01685i | 0.416528 | + | 0.416528i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.40130 | − | 2.40130i | −0.243815 | − | 0.243815i | 0.574611 | − | 0.818426i | \(-0.305153\pi\) |
−0.818426 | + | 0.574611i | \(0.805153\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.57652i | 0.158446i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.77555i | 0.873200i | 0.899656 | + | 0.436600i | \(0.143817\pi\) | ||||
−0.899656 | + | 0.436600i | \(0.856183\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.710448 | + | 0.710448i | −0.0700025 | + | 0.0700025i | −0.741241 | − | 0.671239i | \(-0.765763\pi\) |
0.671239 | + | 0.741241i | \(0.265763\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.2829 | − | 13.2829i | 1.28411 | − | 1.28411i | 0.345796 | − | 0.938310i | \(-0.387609\pi\) |
0.938310 | − | 0.345796i | \(-0.112391\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.13731i | − | 0.683630i | −0.939767 | − | 0.341815i | \(-0.888958\pi\) | ||
0.939767 | − | 0.341815i | \(-0.111042\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.69267i | − | 0.445409i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.35947 | − | 4.35947i | −0.410104 | − | 0.410104i | 0.471671 | − | 0.881775i | \(-0.343651\pi\) |
−0.881775 | + | 0.471671i | \(0.843651\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.29100 | + | 1.29100i | 0.119353 | + | 0.119353i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.890030 | + | 1.92931i | −0.0815889 | + | 0.176860i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.51992 | −0.865448 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.52240 | + | 6.52240i | 0.588105 | + | 0.588105i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.07395 | + | 3.07395i | −0.272769 | + | 0.272769i | −0.830214 | − | 0.557445i | \(-0.811782\pi\) |
0.557445 | + | 0.830214i | \(0.311782\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.74786 | −0.506070 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.12826i | − | 0.535429i | −0.963498 | − | 0.267714i | \(-0.913732\pi\) | ||
0.963498 | − | 0.267714i | \(-0.0862684\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0947017 | + | 0.256905i | 0.00821168 | + | 0.0222765i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.69973 | + | 2.69973i | −0.230654 | + | 0.230654i | −0.812965 | − | 0.582312i | \(-0.802148\pi\) |
0.582312 | + | 0.812965i | \(0.302148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.95480 | 0.759536 | 0.379768 | − | 0.925082i | \(-0.376004\pi\) | ||||
0.379768 | + | 0.925082i | \(0.376004\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.3592 | 1.12504 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.21203 | − | 1.21203i | 0.101355 | − | 0.101355i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.721680 | + | 9.10945i | −0.0595232 | + | 0.751335i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 9.15227i | − | 0.749783i | −0.927069 | − | 0.374891i | \(-0.877680\pi\) | ||
0.927069 | − | 0.374891i | \(-0.122320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4406 | −0.849648 | −0.424824 | − | 0.905276i | \(-0.639664\pi\) | ||||
−0.424824 | + | 0.905276i | \(0.639664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.735857 | + | 0.735857i | −0.0594905 | + | 0.0594905i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3298 | − | 13.3298i | −1.06384 | − | 1.06384i | −0.997818 | − | 0.0660171i | \(-0.978971\pi\) |
−0.0660171 | − | 0.997818i | \(-0.521029\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.62854 | −0.129152 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.24752 | − | 4.87192i | 0.177129 | − | 0.383961i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.31503 | − | 3.31503i | −0.259653 | − | 0.259653i | 0.565260 | − | 0.824913i | \(-0.308776\pi\) |
−0.824913 | + | 0.565260i | \(0.808776\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.75278 | + | 3.75278i | 0.290399 | + | 0.290399i | 0.837238 | − | 0.546839i | \(-0.184169\pi\) |
−0.546839 | + | 0.837238i | \(0.684169\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0150i | 0.847304i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.134106i | 0.0102554i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.8850 | + | 13.8850i | −1.05565 | + | 1.05565i | −0.0572975 | + | 0.998357i | \(0.518248\pi\) |
−0.998357 | + | 0.0572975i | \(0.981752\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.64846 | − | 7.64846i | 0.574894 | − | 0.574894i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.64006i | 0.720532i | 0.932850 | + | 0.360266i | \(0.117314\pi\) | ||||
−0.932850 | + | 0.360266i | \(0.882686\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6258i | 1.16146i | 0.814097 | + | 0.580728i | \(0.197232\pi\) | ||||
−0.814097 | + | 0.580728i | \(0.802768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.28893 | + | 9.28893i | 0.686657 | + | 0.686657i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.690840 | + | 0.690840i | 0.0505192 | + | 0.0505192i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.21523 | + | 13.4727i | −0.452091 | + | 0.979994i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.4481 | −1.33486 | −0.667430 | − | 0.744673i | \(-0.732606\pi\) | ||||
−0.667430 | + | 0.744673i | \(0.732606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.3732 | − | 15.3732i | −1.10659 | − | 1.10659i | −0.993596 | − | 0.112990i | \(-0.963957\pi\) |
−0.112990 | − | 0.993596i | \(-0.536043\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.7687 | + | 15.7687i | −1.12347 | + | 1.12347i | −0.132258 | + | 0.991215i | \(0.542223\pi\) |
−0.991215 | + | 0.132258i | \(0.957777\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.6117 | 1.74468 | 0.872339 | − | 0.488901i | \(-0.162602\pi\) | ||||
0.872339 | + | 0.488901i | \(0.162602\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 13.0601i | − | 0.921188i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.3541 | + | 4.55402i | −0.867085 | + | 0.319629i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.85820 | − | 1.85820i | 0.129154 | − | 0.129154i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.125902 | 0.00870883 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.49647 | 0.516078 | 0.258039 | − | 0.966134i | \(-0.416924\pi\) | ||||
0.258039 | + | 0.966134i | \(0.416924\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.303697 | − | 0.303697i | 0.0208090 | − | 0.0208090i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8026 | + | 3.98213i | −0.733331 | + | 0.270324i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 20.9666i | − | 1.41679i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.13145 | 0.0761096 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.88619 | − | 7.88619i | 0.528098 | − | 0.528098i | −0.391907 | − | 0.920005i | \(-0.628184\pi\) |
0.920005 | + | 0.391907i | \(0.128184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.54162 | − | 6.54162i | −0.434182 | − | 0.434182i | 0.455866 | − | 0.890048i | \(-0.349330\pi\) |
−0.890048 | + | 0.455866i | \(0.849330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.01657 | 0.397586 | 0.198793 | − | 0.980041i | \(-0.436298\pi\) | ||||
0.198793 | + | 0.980041i | \(0.436298\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.81545 | + | 1.76015i | 0.251039 | + | 0.115809i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.74138 | + | 8.74138i | 0.572667 | + | 0.572667i | 0.932873 | − | 0.360206i | \(-0.117294\pi\) |
−0.360206 | + | 0.932873i | \(0.617294\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.6352 | − | 12.6352i | −0.820746 | − | 0.820746i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.0398i | 1.49032i | 0.666884 | + | 0.745162i | \(0.267628\pi\) | ||||
−0.666884 | + | 0.745162i | \(0.732372\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 22.8987i | − | 1.47504i | −0.675328 | − | 0.737518i | \(-0.735998\pi\) | ||
0.675328 | − | 0.737518i | \(-0.264002\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.72714 | + | 8.72714i | −0.559847 | + | 0.559847i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.103101 | − | 0.103101i | 0.00656013 | − | 0.00656013i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 8.52070i | − | 0.539978i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 24.5447i | − | 1.54925i | −0.632423 | − | 0.774623i | \(-0.717940\pi\) | ||
0.632423 | − | 0.774623i | \(-0.282060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.74452 | − | 1.74452i | −0.109677 | − | 0.109677i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.22931 | − | 7.22931i | −0.450952 | − | 0.450952i | 0.444718 | − | 0.895670i | \(-0.353304\pi\) |
−0.895670 | + | 0.444718i | \(0.853304\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.63613 | + | 3.98402i | 0.536623 | + | 0.247555i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.44890 | −0.399177 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0746 | + | 12.0746i | 0.744550 | + | 0.744550i | 0.973450 | − | 0.228900i | \(-0.0735130\pi\) |
−0.228900 | + | 0.973450i | \(0.573513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.1793 | + | 12.1793i | −0.745358 | + | 0.745358i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.430862 | 0.0262701 | 0.0131351 | − | 0.999914i | \(-0.495819\pi\) | ||||
0.0131351 | + | 0.999914i | \(0.495819\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 10.1612i | − | 0.617248i | −0.951184 | − | 0.308624i | \(-0.900132\pi\) | ||
0.951184 | − | 0.308624i | \(-0.0998685\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.56583 | − | 1.68308i | 0.276336 | − | 0.101865i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.9353 | + | 11.9353i | −0.717123 | + | 0.717123i | −0.968015 | − | 0.250892i | \(-0.919276\pi\) |
0.250892 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.63905 | −0.337601 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.47379 | 0.0879191 | 0.0439596 | − | 0.999033i | \(-0.486003\pi\) | ||||
0.0439596 | + | 0.999033i | \(0.486003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.68335 | + | 2.68335i | −0.159508 | + | 0.159508i | −0.782349 | − | 0.622840i | \(-0.785979\pi\) |
0.622840 | + | 0.782349i | \(0.285979\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.5409 | + | 6.46601i | −1.03541 | + | 0.381677i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 16.3551i | − | 0.962064i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.43317 | −0.259877 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.8195 | + | 20.8195i | −1.21629 | + | 1.21629i | −0.247368 | + | 0.968921i | \(0.579566\pi\) |
−0.968921 | + | 0.247368i | \(0.920434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.82425 | + | 4.82425i | 0.279931 | + | 0.279931i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.85715 | −0.165234 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.87986 | − | 10.5780i | 0.281271 | − | 0.609707i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.10050 | + | 8.10050i | 0.465362 | + | 0.465362i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −10.0501 | − | 10.0501i | −0.573588 | − | 0.573588i | 0.359541 | − | 0.933129i | \(-0.382933\pi\) |
−0.933129 | + | 0.359541i | \(0.882933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.31160i | 0.0746141i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.48676i | − | 0.367830i | −0.982942 | − | 0.183915i | \(-0.941123\pi\) | ||
0.982942 | − | 0.183915i | \(-0.0588771\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.7441 | − | 11.7441i | 0.663814 | − | 0.663814i | −0.292463 | − | 0.956277i | \(-0.594475\pi\) |
0.956277 | + | 0.292463i | \(0.0944748\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.1787 | − | 18.1787i | 1.02102 | − | 1.02102i | 0.0212445 | − | 0.999774i | \(-0.493237\pi\) |
0.999774 | − | 0.0212445i | \(-0.00676284\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.05439i | 0.338981i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 24.5223i | − | 1.36870i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.0587660 | + | 0.0587660i | 0.00326983 | + | 0.00326983i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −6.58828 | − | 6.58828i | −0.364333 | − | 0.364333i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.3418 | + | 24.5854i | −0.625292 | + | 1.35544i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.57796 | −0.141697 | −0.0708486 | − | 0.997487i | \(-0.522571\pi\) | ||||
−0.0708486 | + | 0.997487i | \(0.522571\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.29390 | + | 3.29390i | 0.180505 | + | 0.180505i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.8387 | + | 16.8387i | −0.917264 | + | 0.917264i | −0.996830 | − | 0.0795652i | \(-0.974647\pi\) |
0.0795652 | + | 0.996830i | \(0.474647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.04825 | −0.437121 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.29408i | 0.286690i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.1518 | − | 9.06195i | −0.872116 | − | 0.489299i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.2400 | − | 12.2400i | 0.657079 | − | 0.657079i | −0.297609 | − | 0.954688i | \(-0.596189\pi\) |
0.954688 | + | 0.297609i | \(0.0961892\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.3348 | 1.46320 | 0.731598 | − | 0.681736i | \(-0.238775\pi\) | ||||
0.731598 | + | 0.681736i | \(0.238775\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.90110 | 0.421730 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.42987 | + | 3.42987i | −0.182553 | + | 0.182553i | −0.792468 | − | 0.609914i | \(-0.791204\pi\) |
0.609914 | + | 0.792468i | \(0.291204\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.959334 | + | 2.60247i | 0.0507734 | + | 0.137737i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 30.4578i | − | 1.60750i | −0.594966 | − | 0.803751i | \(-0.702834\pi\) | ||
0.594966 | − | 0.803751i | \(-0.297166\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9893 | −0.999436 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.78762 | + | 8.78762i | −0.461230 | + | 0.461230i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.6219 | − | 17.6219i | −0.919856 | − | 0.919856i | 0.0771629 | − | 0.997019i | \(-0.475414\pi\) |
−0.997019 | + | 0.0771629i | \(0.975414\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.15646 | −0.476666 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.38261 | − | 2.99708i | 0.0717817 | − | 0.155601i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1403 | + | 13.1403i | 0.680379 | + | 0.680379i | 0.960086 | − | 0.279707i | \(-0.0902372\pi\) |
−0.279707 | + | 0.960086i | \(0.590237\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.95790 | + | 4.95790i | 0.255345 | + | 0.255345i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.88955i | 0.507992i | 0.967205 | + | 0.253996i | \(0.0817450\pi\) | ||||
−0.967205 | + | 0.253996i | \(0.918255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.67499i | 0.290738i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.61392 | − | 1.61392i | 0.0824673 | − | 0.0824673i | −0.664670 | − | 0.747137i | \(-0.731428\pi\) |
0.747137 | + | 0.664670i | \(0.231428\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.03456 | − | 4.03456i | 0.205088 | − | 0.205088i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 33.9003i | − | 1.71881i | −0.511292 | − | 0.859407i | \(-0.670833\pi\) | ||
0.511292 | − | 0.859407i | \(-0.329167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.62854i | − | 0.0823590i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.65685 | − | 5.65685i | −0.285351 | − | 0.285351i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.67961 | − | 4.67961i | −0.234863 | − | 0.234863i | 0.579856 | − | 0.814719i | \(-0.303109\pi\) |
−0.814719 | + | 0.579856i | \(0.803109\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.324560 | + | 0.149726i | 0.0162483 | + | 0.00749569i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −31.2427 | −1.56018 | −0.780092 | − | 0.625665i | \(-0.784828\pi\) | ||||
−0.780092 | + | 0.625665i | \(0.784828\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.33529 | + | 4.33529i | 0.215956 | + | 0.215956i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.09239 | − | 3.09239i | 0.153284 | − | 0.153284i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.5228 | 0.767554 | 0.383777 | − | 0.923426i | \(-0.374623\pi\) | ||||
0.383777 | + | 0.923426i | \(0.374623\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.98411i | 0.245848i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.58234 | + | 20.5693i | 0.373103 | + | 1.01215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.26596 | − | 8.26596i | 0.404786 | − | 0.404786i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0634 | −1.41984 | −0.709920 | − | 0.704282i | \(-0.751269\pi\) | ||||
−0.709920 | + | 0.704282i | \(0.751269\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.76601 | 0.134807 | 0.0674034 | − | 0.997726i | \(-0.478529\pi\) | ||||
0.0674034 | + | 0.997726i | \(0.478529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.37712 | + | 9.37712i | −0.455931 | + | 0.455931i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.9810 | + | 9.20863i | −1.20892 | + | 0.445637i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.23759i | − | 0.108032i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.31931 | −0.304391 | −0.152195 | − | 0.988350i | \(-0.548634\pi\) | ||||
−0.152195 | + | 0.988350i | \(0.548634\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.4583 | − | 12.4583i | 0.598706 | − | 0.598706i | −0.341262 | − | 0.939968i | \(-0.610854\pi\) |
0.939968 | + | 0.341262i | \(0.110854\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.148397 | − | 0.148397i | −0.00709878 | − | 0.00709878i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.9890 | 0.810842 | 0.405421 | − | 0.914130i | \(-0.367125\pi\) | ||||
0.405421 | + | 0.914130i | \(0.367125\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.88758 | − | 6.90071i | −0.280361 | − | 0.328605i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.8935 | − | 16.8935i | −0.802633 | − | 0.802633i | 0.180873 | − | 0.983506i | \(-0.442108\pi\) |
−0.983506 | + | 0.180873i | \(0.942108\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.44824 | − | 8.44824i | −0.399588 | − | 0.399588i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.85641i | 0.229188i | 0.993412 | + | 0.114594i | \(0.0365567\pi\) | ||||
−0.993412 | + | 0.114594i | \(0.963443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.59630i | 0.404784i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.63752 | + | 9.63752i | −0.452810 | + | 0.452810i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.2995 | − | 27.2995i | 1.27702 | − | 1.27702i | 0.334686 | − | 0.942330i | \(-0.391370\pi\) |
0.942330 | − | 0.334686i | \(-0.108630\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.50353i | 0.210207i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.0098i | 1.53742i | 0.639599 | + | 0.768709i | \(0.279100\pi\) | ||||
−0.639599 | + | 0.768709i | \(0.720900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.5774 | − | 11.5774i | −0.538048 | − | 0.538048i | 0.384908 | − | 0.922955i | \(-0.374233\pi\) |
−0.922955 | + | 0.384908i | \(0.874233\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.90541 | − | 7.90541i | −0.365819 | − | 0.365819i | 0.500131 | − | 0.865950i | \(-0.333285\pi\) |
−0.865950 | + | 0.500131i | \(0.833285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0350 | + | 11.0879i | 1.10984 | + | 0.511990i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.6089 | −1.13392 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.78774 | − | 3.78774i | −0.174161 | − | 0.174161i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.14311 | − | 1.14311i | 0.0523396 | − | 0.0523396i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.6277 | −1.81064 | −0.905319 | − | 0.424733i | \(-0.860368\pi\) | ||||
−0.905319 | + | 0.424733i | \(0.860368\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5.06469i | − | 0.230930i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.42253 | − | 6.57179i | −0.110229 | − | 0.299027i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.44241 | − | 7.44241i | 0.337248 | − | 0.337248i | −0.518083 | − | 0.855331i | \(-0.673354\pi\) |
0.855331 | + | 0.518083i | \(0.173354\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.12006 | −0.276759 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.423477 | −0.0191113 | −0.00955563 | − | 0.999954i | \(-0.503042\pi\) | ||||
−0.00955563 | + | 0.999954i | \(0.503042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.82594 | + | 2.82594i | −0.127274 | + | 0.127274i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.301072 | + | 0.816742i | 0.0135049 | + | 0.0366359i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 42.5173i | − | 1.90334i | −0.307130 | − | 0.951668i | \(-0.599369\pi\) | ||
0.307130 | − | 0.951668i | \(-0.400631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.92820 | 0.309529 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.94351 | − | 6.94351i | 0.309596 | − | 0.309596i | −0.535157 | − | 0.844753i | \(-0.679748\pi\) |
0.844753 | + | 0.535157i | \(0.179748\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.1676 | + | 10.1676i | 0.451561 | + | 0.451561i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 38.8912 | 1.72382 | 0.861911 | − | 0.507059i | \(-0.169267\pi\) | ||||
0.861911 | + | 0.507059i | \(0.169267\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 38.5858 | + | 17.8004i | 1.70693 | + | 0.787444i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.410373 | + | 0.410373i | 0.0181184 | + | 0.0181184i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.80347 | + | 8.80347i | 0.387176 | + | 0.387176i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.6338i | 1.12520i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 31.1879i | − | 1.36637i | −0.730246 | − | 0.683184i | \(-0.760595\pi\) | ||
0.730246 | − | 0.683184i | \(-0.239405\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 19.0273 | − | 19.0273i | 0.832007 | − | 0.832007i | −0.155784 | − | 0.987791i | \(-0.549790\pi\) |
0.987791 | + | 0.155784i | \(0.0497903\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.47106 | + | 2.47106i | −0.107641 | + | 0.107641i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 18.8876i | − | 0.821199i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7373i | 0.465959i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.03946 | + | 7.03946i | 0.304913 | + | 0.304913i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.89851 | + | 8.89851i | 0.383999 | + | 0.383999i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.47855 | + | 5.52740i | −0.279051 | + | 0.238082i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.48151 | 0.106688 | 0.0533442 | − | 0.998576i | \(-0.483012\pi\) | ||||
0.0533442 | + | 0.998576i | \(0.483012\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.4238 | + | 14.4238i | 0.618985 | + | 0.618985i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.6132 | + | 20.6132i | −0.881356 | + | 0.881356i | −0.993673 | − | 0.112316i | \(-0.964173\pi\) |
0.112316 | + | 0.993673i | \(0.464173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.0403 | −0.556544 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.515014i | 0.0219403i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 33.9803 | − | 12.5260i | 1.44499 | − | 0.532659i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.10076 | − | 5.10076i | 0.216126 | − | 0.216126i | −0.590738 | − | 0.806864i | \(-0.701163\pi\) |
0.806864 | + | 0.590738i | \(0.201163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.20352 | −0.262381 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.27540 | 0.0538473 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.13112 | + | 7.13112i | −0.300541 | + | 0.300541i | −0.841225 | − | 0.540685i | \(-0.818165\pi\) |
0.540685 | + | 0.841225i | \(0.318165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.14168 | + | 8.52270i | 0.131938 | + | 0.357920i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.16848i | 0.342441i | 0.985233 | + | 0.171220i | \(0.0547710\pi\) | ||||
−0.985233 | + | 0.171220i | \(0.945229\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.66328 | −0.278849 | −0.139425 | − | 0.990233i | \(-0.544525\pi\) | ||||
−0.139425 | + | 0.990233i | \(0.544525\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.0290 | + | 17.0290i | −0.711398 | + | 0.711398i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.2531 | + | 22.2531i | 0.926410 | + | 0.926410i | 0.997472 | − | 0.0710620i | \(-0.0226388\pi\) |
−0.0710620 | + | 0.997472i | \(0.522639\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −28.3812 | −1.17948 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.6810 | + | 7.23397i | 0.650558 | + | 0.300116i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.07318 | − | 1.07318i | −0.0444467 | − | 0.0444467i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.6776 | + | 16.6776i | 0.688357 | + | 0.688357i | 0.961869 | − | 0.273512i | \(-0.0881853\pi\) |
−0.273512 | + | 0.961869i | \(0.588185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.450338i | 0.0185559i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 29.1114i | 1.19748i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.56327 | − | 6.56327i | 0.269521 | − | 0.269521i | −0.559386 | − | 0.828907i | \(-0.688963\pi\) |
0.828907 | + | 0.559386i | \(0.188963\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 22.7185 | − | 22.7185i | 0.929806 | − | 0.929806i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.55935i | 0.390585i | 0.980745 | + | 0.195292i | \(0.0625655\pi\) | ||||
−0.980745 | + | 0.195292i | \(0.937434\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 20.1897i | − | 0.823555i | −0.911285 | − | 0.411777i | \(-0.864908\pi\) | ||
0.911285 | − | 0.411777i | \(-0.135092\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 9.16719 | + | 9.16719i | 0.373317 | + | 0.373317i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.55854 | − | 9.55854i | −0.387969 | − | 0.387969i | 0.485993 | − | 0.873962i | \(-0.338458\pi\) |
−0.873962 | + | 0.485993i | \(0.838458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.20004 | + | 15.6075i | −0.291760 | + | 0.632446i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.4182 | 0.583298 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.0641 | − | 27.0641i | −1.09311 | − | 1.09311i | −0.995195 | − | 0.0979135i | \(-0.968783\pi\) |
−0.0979135 | − | 0.995195i | \(-0.531217\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.331871 | + | 0.331871i | −0.0133606 | + | 0.0133606i | −0.713756 | − | 0.700395i | \(-0.753007\pi\) |
0.700395 | + | 0.713756i | \(0.253007\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.99126 | −0.120229 | −0.0601145 | − | 0.998191i | \(-0.519147\pi\) | ||||
−0.0601145 | + | 0.998191i | \(0.519147\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 11.3724i | − | 0.456358i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −12.0740 | − | 32.7540i | −0.483733 | − | 1.31226i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.116217 | − | 0.116217i | 0.00464127 | − | 0.00464127i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.88681 | 0.115105 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0573 | 1.11694 | 0.558471 | − | 0.829524i | \(-0.311388\pi\) | ||||
0.558471 | + | 0.829524i | \(0.311388\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.91981 | − | 6.91981i | 0.275038 | − | 0.275038i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.778891 | + | 9.83160i | −0.0308608 | + | 0.389542i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.426345i | 0.0168659i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26.1153 | 1.03149 | 0.515746 | − | 0.856742i | \(-0.327515\pi\) | ||||
0.515746 | + | 0.856742i | \(0.327515\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.4107 | − | 20.4107i | 0.804921 | − | 0.804921i | −0.178939 | − | 0.983860i | \(-0.557267\pi\) |
0.983860 | + | 0.178939i | \(0.0572666\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.2719 | + | 18.2719i | 0.718342 | + | 0.718342i | 0.968265 | − | 0.249924i | \(-0.0804056\pi\) |
−0.249924 | + | 0.968265i | \(0.580406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0804 | 0.395691 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.29586 | + | 13.6475i | −0.246754 | + | 0.534887i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 24.0558 | + | 24.0558i | 0.941376 | + | 0.941376i | 0.998374 | − | 0.0569981i | \(-0.0181529\pi\) |
−0.0569981 | + | 0.998374i | \(0.518153\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.7170 | + | 14.7170i | 0.574164 | + | 0.574164i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.6949i | 1.19570i | 0.801607 | + | 0.597851i | \(0.203979\pi\) | ||||
−0.801607 | + | 0.597851i | \(0.796021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.4577i | 1.18467i | 0.805692 | + | 0.592335i | \(0.201794\pi\) | ||||
−0.805692 | + | 0.592335i | \(0.798206\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.04441 | − | 1.04441i | 0.0405617 | − | 0.0405617i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.13611 | − | 7.13611i | 0.276311 | − | 0.276311i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 14.5591i | − | 0.562888i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.2425i | 0.472617i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.7437 | − | 24.7437i | −0.953801 | − | 0.953801i | 0.0451778 | − | 0.998979i | \(-0.485615\pi\) |
−0.998979 | + | 0.0451778i | \(0.985615\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 23.6461 | + | 23.6461i | 0.908793 | + | 0.908793i | 0.996175 | − | 0.0873819i | \(-0.0278500\pi\) |
−0.0873819 | + | 0.996175i | \(0.527850\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.76371 | − | 8.15855i | 0.144438 | − | 0.313096i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0768 | −0.462785 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.8548 | + | 25.8548i | 0.989307 | + | 0.989307i | 0.999943 | − | 0.0106366i | \(-0.00338580\pi\) |
−0.0106366 | + | 0.999943i | \(0.503386\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.55375 | − | 5.55375i | 0.211889 | − | 0.211889i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.75765 | −0.0669610 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 40.5649i | 1.54316i | 0.636131 | + | 0.771581i | \(0.280534\pi\) | ||||
−0.636131 | + | 0.771581i | \(0.719466\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.91365 | + | 1.44267i | −0.148667 | + | 0.0548025i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.01241 | + | 4.01241i | −0.151981 | + | 0.151981i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.1379 | 0.610393 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.4481 | 0.470159 | 0.235080 | − | 0.971976i | \(-0.424465\pi\) | ||||
0.235080 | + | 0.971976i | \(0.424465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.263053 | − | 0.263053i | 0.00992124 | − | 0.00992124i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.7849 | + | 8.03048i | −0.819307 | + | 0.302017i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 23.9211i | − | 0.898377i | −0.893437 | − | 0.449189i | \(-0.851713\pi\) | ||
0.893437 | − | 0.449189i | \(-0.148287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.7379 | 0.665225 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.23996 | − | 6.23996i | 0.233688 | − | 0.233688i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.2675 | + | 21.2675i | 0.794251 | + | 0.794251i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.4190 | −1.20902 | −0.604512 | − | 0.796596i | \(-0.706632\pi\) | ||||
−0.604512 | + | 0.796596i | \(0.706632\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.41379 | − | 1.11353i | −0.0898941 | − | 0.0414700i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −21.1373 | − | 21.1373i | −0.786103 | − | 0.786103i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.14090 | + | 2.14090i | 0.0794017 | + | 0.0794017i | 0.745692 | − | 0.666291i | \(-0.232119\pi\) |
−0.666291 | + | 0.745692i | \(0.732119\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 26.4111i | 0.978191i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 3.53593i | − | 0.130781i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.1647 | − | 18.1647i | 0.670930 | − | 0.670930i | −0.287001 | − | 0.957930i | \(-0.592658\pi\) |
0.957930 | + | 0.287001i | \(0.0926582\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 8.60638 | − | 8.60638i | 0.317020 | − | 0.317020i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.7086i | 1.57106i | 0.618822 | + | 0.785531i | \(0.287610\pi\) | ||||
−0.618822 | + | 0.785531i | \(0.712390\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.190339i | − | 0.00699229i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.2579 | − | 15.2579i | −0.559759 | − | 0.559759i | 0.369480 | − | 0.929239i | \(-0.379536\pi\) |
−0.929239 | + | 0.369480i | \(0.879536\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.98089 | + | 5.98089i | 0.218829 | + | 0.218829i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.1294 | + | 20.8191i | 1.64899 | + | 0.760713i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.87908 | 0.324002 | 0.162001 | − | 0.986791i | \(-0.448205\pi\) | ||||
0.162001 | + | 0.986791i | \(0.448205\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.6566 | − | 22.6566i | −0.825653 | − | 0.825653i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.15917 | + | 7.15917i | −0.260204 | + | 0.260204i | −0.825137 | − | 0.564933i | \(-0.808902\pi\) |
0.564933 | + | 0.825137i | \(0.308902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.22065 | −0.116902 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.7681i | 1.33284i | 0.745575 | + | 0.666422i | \(0.232175\pi\) | ||||
−0.745575 | + | 0.666422i | \(0.767825\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.7181 | − | 6.53133i | 0.641437 | − | 0.236450i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.25480 | − | 8.25480i | 0.298064 | − | 0.298064i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.372202 | 0.0134220 | 0.00671098 | − | 0.999977i | \(-0.497864\pi\) | ||||
0.00671098 | + | 0.999977i | \(0.497864\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3464 | −0.480659 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.1925 | + | 28.1925i | −1.01402 | + | 1.01402i | −0.0141148 | + | 0.999900i | \(0.504493\pi\) |
−0.999900 | + | 0.0141148i | \(0.995507\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6494 | − | 4.29425i | 0.417919 | − | 0.154055i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.731241i | 0.0261994i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.400263 | 0.0143225 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.7340 | + | 19.7340i | −0.705237 | + | 0.705237i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.61707 | − | 2.61707i | −0.0932886 | − | 0.0932886i | 0.658922 | − | 0.752211i | \(-0.271013\pi\) |
−0.752211 | + | 0.658922i | \(0.771013\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 22.2915 | 0.793598 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.83286 | − | 14.8115i | 0.242949 | − | 0.526637i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.0253 | + | 10.0253i | 0.356009 | + | 0.356009i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.2158 | + | 13.2158i | 0.468127 | + | 0.468127i | 0.901307 | − | 0.433180i | \(-0.142609\pi\) |
−0.433180 | + | 0.901307i | \(0.642609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.21820i | 0.290739i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 17.0978i | − | 0.604122i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.8167 | − | 13.8167i | 0.487579 | − | 0.487579i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.397719 | − | 0.397719i | 0.0140004 | − | 0.0140004i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 35.0904i | − | 1.23371i | −0.787076 | − | 0.616856i | \(-0.788406\pi\) | ||
0.787076 | − | 0.616856i | \(-0.211594\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 41.9817i | 1.47418i | 0.675797 | + | 0.737088i | \(0.263799\pi\) | ||||
−0.675797 | + | 0.737088i | \(0.736201\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.37955 | − | 9.37955i | −0.328955 | − | 0.328955i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.322203 | − | 0.322203i | −0.0112724 | − | 0.0112724i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.02347 | + | 4.38626i | −0.0707058 | + | 0.153268i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.93042 | −0.241873 | −0.120937 | − | 0.992660i | \(-0.538590\pi\) | ||||
−0.120937 | + | 0.992660i | \(0.538590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.193913 | − | 0.193913i | −0.00675937 | − | 0.00675937i | 0.703719 | − | 0.710478i | \(-0.251521\pi\) |
−0.710478 | + | 0.703719i | \(0.751521\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.94789 | + | 1.94789i | −0.0677346 | + | 0.0677346i | −0.740163 | − | 0.672428i | \(-0.765251\pi\) |
0.672428 | + | 0.740163i | \(0.265251\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −27.6983 | −0.962001 | −0.481000 | − | 0.876720i | \(-0.659726\pi\) | ||||
−0.481000 | + | 0.876720i | \(0.659726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 22.0344i | 0.764365i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.60389 | − | 0.443959i | −0.194163 | − | 0.0153823i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.2558 | + | 17.2558i | −0.596449 | + | 0.596449i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.4254 | −0.601591 | −0.300796 | − | 0.953689i | \(-0.597252\pi\) | ||||
−0.300796 | + | 0.953689i | \(0.597252\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.23399 | 0.146000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.36042 | − | 1.36042i | 0.0468555 | − | 0.0468555i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.71165 | − | 23.6328i | −0.299336 | − | 0.812033i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.95387i | 0.170016i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.28981 | −0.249892 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.2898 | − | 20.2898i | 0.694709 | − | 0.694709i | −0.268555 | − | 0.963264i | \(-0.586546\pi\) |
0.963264 | + | 0.268555i | \(0.0865461\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 18.9133 | + | 18.9133i | 0.646066 | + | 0.646066i | 0.952040 | − | 0.305974i | \(-0.0989821\pi\) |
−0.305974 | + | 0.952040i | \(0.598982\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 47.6031 | 1.62420 | 0.812098 | − | 0.583520i | \(-0.198325\pi\) | ||||
0.812098 | + | 0.583520i | \(0.198325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10.2230 | + | 22.1602i | −0.348397 | + | 0.755218i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.74024 | − | 8.74024i | −0.297521 | − | 0.297521i | 0.542521 | − | 0.840042i | \(-0.317470\pi\) |
−0.840042 | + | 0.542521i | \(0.817470\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −15.0970 | − | 15.0970i | −0.512721 | − | 0.512721i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 16.6528i | − | 0.564908i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.0954i | − | 0.477606i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.11175 | − | 3.11175i | 0.105317 | − | 0.105317i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.95163 | − | 7.95163i | 0.268508 | − | 0.268508i | −0.559991 | − | 0.828499i | \(-0.689195\pi\) |
0.828499 | + | 0.559991i | \(0.189195\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 38.4360i | 1.29642i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 8.18767i | 0.275850i | 0.990443 | + | 0.137925i | \(0.0440432\pi\) | ||||
−0.990443 | + | 0.137925i | \(0.955957\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.3047 | + | 21.3047i | 0.716961 | + | 0.716961i | 0.967982 | − | 0.251021i | \(-0.0807662\pi\) |
−0.251021 | + | 0.967982i | \(0.580766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.4989 | + | 15.4989i | 0.520402 | + | 0.520402i | 0.917693 | − | 0.397291i | \(-0.130050\pi\) |
−0.397291 | + | 0.917693i | \(0.630050\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.4439 | − | 4.81799i | −0.350278 | − | 0.161590i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.17674 | 0.139926 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.748863 | + | 0.748863i | 0.0250597 | + | 0.0250597i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.63737 | + | 2.63737i | −0.0880593 | + | 0.0880593i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.6559 | −0.722264 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.00184i | − | 0.0333760i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.25984 | − | 14.2688i | −0.175037 | − | 0.474836i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.3564 | − | 26.3564i | 0.875150 | − | 0.875150i | −0.117878 | − | 0.993028i | \(-0.537609\pi\) |
0.993028 | + | 0.117878i | \(0.0376091\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.3719 | −0.377182 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 41.4208 | 1.37233 | 0.686167 | − | 0.727444i | \(-0.259292\pi\) | ||||
0.686167 | + | 0.727444i | \(0.259292\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.61500 | − | 5.61500i | 0.185829 | − | 0.185829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 15.2132 | − | 5.60795i | 0.502383 | − | 0.185191i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.8247i | − | 1.47863i | −0.673360 | − | 0.739315i | \(-0.735149\pi\) | ||
0.673360 | − | 0.739315i | \(-0.264851\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.5540 | −0.611374 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.327773 | − | 0.327773i | 0.0107888 | − | 0.0107888i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.920641 | − | 0.920641i | −0.0302378 | − | 0.0302378i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −36.7206 | −1.20476 | −0.602382 | − | 0.798208i | \(-0.705782\pi\) | ||||
−0.602382 | + | 0.798208i | \(0.705782\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.551095 | + | 0.470186i | −0.0180614 | + | 0.0154097i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.98777 | − | 5.98777i | −0.196031 | − | 0.196031i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.07171 | + | 9.07171i | 0.296360 | + | 0.296360i | 0.839586 | − | 0.543226i | \(-0.182798\pi\) |
−0.543226 | + | 0.839586i | \(0.682798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 21.6813i | − | 0.707544i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6996i | 0.935580i | 0.883840 | + | 0.467790i | \(0.154950\pi\) | ||||
−0.883840 | + | 0.467790i | \(0.845050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.1322 | − | 10.1322i | 0.329950 | − | 0.329950i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.9306 | − | 14.9306i | 0.485179 | − | 0.485179i | −0.421602 | − | 0.906781i | \(-0.638532\pi\) |
0.906781 | + | 0.421602i | \(0.138532\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 22.6288i | − | 0.734560i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 33.5607i | − | 1.08828i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 20.5690 | + | 20.5690i | 0.666296 | + | 0.666296i | 0.956857 | − | 0.290560i | \(-0.0938417\pi\) |
−0.290560 | + | 0.956857i | \(0.593842\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.58866 | + | 5.58866i | 0.180656 | + | 0.180656i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.17248 | − | 4.23145i | −0.296195 | − | 0.136641i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.0637 | 0.389150 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 17.2128 | + | 17.2128i | 0.554674 | + | 0.554674i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.2690 | − | 20.2690i | 0.651807 | − | 0.651807i | −0.301621 | − | 0.953428i | \(-0.597528\pi\) |
0.953428 | + | 0.301621i | \(0.0975276\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.108491 | 0.00348524 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 58.5227i | − | 1.87808i | −0.343803 | − | 0.939042i | \(-0.611715\pi\) | ||
0.343803 | − | 0.939042i | \(-0.388285\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.19450 | + | 22.2299i | 0.262704 | + | 0.712658i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −17.0405 | + | 17.0405i | −0.545174 | + | 0.545174i | −0.925041 | − | 0.379867i | \(-0.875970\pi\) |
0.379867 | + | 0.925041i | \(0.375970\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.0519 | −0.513019 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.24895 | 0.295296 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.0763218 | + | 0.0763218i | −0.00243429 | + | 0.00243429i | −0.708323 | − | 0.705889i | \(-0.750548\pi\) |
0.705889 | + | 0.708323i | \(0.250548\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.2249 | + | 33.1636i | 0.389123 | + | 1.05561i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.92898i | 0.283925i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.8932 | −0.727226 | −0.363613 | − | 0.931550i | \(-0.618457\pi\) | ||||
−0.363613 | + | 0.931550i | \(0.618457\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.37965 | + | 2.37965i | −0.0755159 | + | 0.0755159i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36.3315 | − | 36.3315i | −1.15063 | − | 1.15063i | −0.986426 | − | 0.164204i | \(-0.947494\pi\) |
−0.164204 | − | 0.986426i | \(-0.552506\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.1591 | 0.637805 |
(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 | 1400.2.x.c.993.11 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.657.5 | ✓ | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.657.12 | yes | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.993.5 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.993.6 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.657.6 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.657.11 | yes | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.993.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.5 | ✓ | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.657.6 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.657.11 | yes | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.657.12 | yes | 32 | 5.3 | odd | 4 | inner | |
1400.2.x.c.993.5 | yes | 32 | 5.4 | even | 2 | inner | |
1400.2.x.c.993.6 | yes | 32 | 7.6 | odd | 2 | inner | |
1400.2.x.c.993.11 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.993.12 | yes | 32 | 35.34 | odd | 2 | inner |