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 | 993.6 | ||
Character | \(\chi\) | \(=\) | 1400.993 |
Dual form | 1400.2.x.c.657.5 |
$q$-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 | −0.921446 | − | 0.388507i | \(-0.872991\pi\) |
0.388507 | + | 0.921446i | \(0.372991\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.48246 | − | 0.915096i | −0.938281 | − | 0.345874i | ||||
\(8\) | 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 | −0.831634 | − | 0.555323i | \(-0.812594\pi\) |
0.555323 | + | 0.831634i | \(0.312594\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.567852 | − | 0.567852i | −0.137724 | − | 0.137724i | 0.634883 | − | 0.772608i | \(-0.281048\pi\) |
−0.772608 | + | 0.634883i | \(0.781048\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.103488 | −0.0237418 | −0.0118709 | − | 0.999930i | \(-0.503779\pi\) | ||||
−0.0118709 | + | 0.999930i | \(0.503779\pi\) | |||||||
\(20\) | 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 | \(-0.872204\pi\) | ||
0.920482 | − | 0.390784i | \(-0.127796\pi\) | |||||||
\(32\) | 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 | \(-0.813958\pi\) | ||
0.834005 | − | 0.551757i | \(-0.186042\pi\) | |||||||
\(42\) | 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 | \(-0.981800\pi\) |
−0.0571445 | − | 0.998366i | \(-0.518200\pi\) | |||||||
\(48\) | 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 | \(-0.681335\pi\) | ||||
−0.539362 | + | 0.842074i | \(0.681335\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.0630i | − | 1.28844i | −0.764842 | − | 0.644218i | \(-0.777183\pi\) | ||
0.764842 | − | 0.644218i | \(-0.222817\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.18584 | − | 3.21692i | 0.149401 | − | 0.405294i | ||||
\(64\) | 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 | \(0.639087\pi\) |
−0.906044 | + | 0.423183i | \(0.860913\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.02012 | − | 1.11329i | −0.344175 | − | 0.126871i | ||||
\(78\) | 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 | −0.913482 | − | 0.406878i | \(-0.866617\pi\) |
0.406878 | + | 0.913482i | \(0.366617\pi\) | |||||||
\(84\) | 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 | \(-0.253499\pi\) | ||||
0.699291 | + | 0.714837i | \(0.253499\pi\) | |||||||
\(90\) | 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 | 0.818426 | − | 0.574611i | \(-0.194847\pi\) |
−0.574611 | + | 0.818426i | \(0.694847\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.57652i | 0.158446i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.77555i | − | 0.873200i | −0.899656 | − | 0.436600i | \(-0.856183\pi\) | ||
0.899656 | − | 0.436600i | \(-0.143817\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.710448 | − | 0.710448i | 0.0700025 | − | 0.0700025i | −0.671239 | − | 0.741241i | \(-0.734237\pi\) |
0.741241 | + | 0.671239i | \(0.234237\pi\) | |||||||
\(104\) | 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 | \(0.0862684\pi\) | ||||
−0.963498 | + | 0.267714i | \(0.913732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.256905 | + | 0.0947017i | 0.0222765 | + | 0.00821168i | ||||
\(134\) | 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 | \(-0.623996\pi\) | ||||
−0.379768 | + | 0.925082i | \(0.623996\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | −9.10945 | + | 0.721680i | −0.751335 | + | 0.0595232i | ||||
\(148\) | 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 | \(0.0210292\pi\) |
0.0660171 | + | 0.997818i | \(0.478971\pi\) | |||||||
\(158\) | 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 | 0.546839 | − | 0.837238i | \(-0.315831\pi\) |
−0.837238 | + | 0.546839i | \(0.815831\pi\) | |||||||
\(168\) | 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 | \(-0.481752\pi\) |
0.998357 | − | 0.0572975i | \(-0.0182484\pi\) | |||||||
\(174\) | 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 | \(-0.802768\pi\) | ||
0.814097 | − | 0.580728i | \(-0.197232\pi\) | |||||||
\(182\) | 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 | \(-0.837398\pi\) | ||||
−0.872339 | + | 0.488901i | \(0.837398\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 13.0601i | 0.921188i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.55402 | − | 12.3541i | 0.319629 | − | 0.867085i | ||||
\(204\) | 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 | ||||||||
\(217\) | −3.98213 | + | 10.8026i | −0.270324 | + | 0.733331i | ||||
\(218\) | 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 | −0.920005 | − | 0.391907i | \(-0.871816\pi\) |
0.391907 | + | 0.920005i | \(0.371816\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.54162 | + | 6.54162i | 0.434182 | + | 0.434182i | 0.890048 | − | 0.455866i | \(-0.150670\pi\) |
−0.455866 | + | 0.890048i | \(0.650670\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.01657 | −0.397586 | −0.198793 | − | 0.980041i | \(-0.563702\pi\) | ||||
−0.198793 | + | 0.980041i | \(0.563702\pi\) | |||||||
\(230\) | 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 | \(0.264002\pi\) | ||||
−0.675328 | + | 0.737518i | \(0.735998\pi\) | |||||||
\(242\) | 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 | \(0.282060\pi\) | ||||
−0.632423 | + | 0.774623i | \(0.717940\pi\) | |||||||
\(252\) | 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 | 0.895670 | − | 0.444718i | \(-0.146696\pi\) |
−0.444718 | + | 0.895670i | \(0.646696\pi\) | |||||||
\(258\) | 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 | \(-0.504181\pi\) | ||||
−0.0131351 | + | 0.999914i | \(0.504181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.1612i | 0.617248i | 0.951184 | + | 0.308624i | \(0.0998685\pi\) | ||||
−0.951184 | + | 0.308624i | \(0.900132\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.68308 | + | 4.56583i | −0.101865 | + | 0.276336i | ||||
\(274\) | 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 | −0.622840 | − | 0.782349i | \(-0.714021\pi\) |
0.782349 | + | 0.622840i | \(0.214021\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.46601 | + | 17.5409i | −0.381677 | + | 1.03541i | ||||
\(288\) | 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 | \(-0.420434\pi\) |
0.968921 | − | 0.247368i | \(-0.0795658\pi\) | |||||||
\(294\) | 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 | 0.933129 | − | 0.359541i | \(-0.117067\pi\) |
−0.359541 | + | 0.933129i | \(0.617067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.31160i | 0.0746141i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.48676i | 0.367830i | 0.982942 | + | 0.183915i | \(0.0588771\pi\) | ||||
−0.982942 | + | 0.183915i | \(0.941123\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7441 | + | 11.7441i | −0.663814 | + | 0.663814i | −0.956277 | − | 0.292463i | \(-0.905525\pi\) |
0.292463 | + | 0.956277i | \(0.405525\pi\) | |||||||
\(314\) | 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 | ||||||||
\(343\) | −9.06195 | − | 16.1518i | −0.489299 | − | 0.872116i | ||||
\(344\) | 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 | \(-0.761225\pi\) | ||||
−0.731598 | + | 0.681736i | \(0.761225\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.90110 | 0.421730 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.42987 | − | 3.42987i | 0.182553 | − | 0.182553i | −0.609914 | − | 0.792468i | \(-0.708796\pi\) |
0.792468 | + | 0.609914i | \(0.208796\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.60247 | − | 0.959334i | −0.137737 | − | 0.0507734i | ||||
\(358\) | 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 | 0.997019 | − | 0.0771629i | \(-0.0245861\pi\) |
−0.0771629 | + | 0.997019i | \(0.524586\pi\) | |||||||
\(368\) | 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 | −0.747137 | − | 0.664670i | \(-0.768572\pi\) |
0.664670 | + | 0.747137i | \(0.268572\pi\) | |||||||
\(384\) | 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 | 0.814719 | − | 0.579856i | \(-0.196891\pi\) |
−0.579856 | + | 0.814719i | \(0.696891\pi\) | |||||||
\(398\) | 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 | \(-0.625377\pi\) | ||||
−0.383777 | + | 0.923426i | \(0.625377\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 4.98411i | − | 0.245848i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 20.5693 | + | 7.58234i | 1.01215 | + | 0.373103i | ||||
\(414\) | 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 | \(-0.248731\pi\) | ||||
0.709920 | + | 0.704282i | \(0.248731\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | −9.20863 | + | 24.9810i | −0.445637 | + | 1.20892i | ||||
\(428\) | 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 | −0.939968 | − | 0.341262i | \(-0.889146\pi\) |
0.341262 | + | 0.939968i | \(0.389146\pi\) | |||||||
\(434\) | 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 | \(-0.632875\pi\) | ||||
−0.405421 | + | 0.914130i | \(0.632875\pi\) | |||||||
\(440\) | 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 | \(-0.720900\pi\) | ||
0.639599 | − | 0.768709i | \(-0.279100\pi\) | |||||||
\(462\) | 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 | 0.865950 | − | 0.500131i | \(-0.166715\pi\) |
−0.500131 | + | 0.865950i | \(0.666715\pi\) | |||||||
\(468\) | 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 | \(-0.139632\pi\) | ||||
0.905319 | + | 0.424733i | \(0.139632\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.06469i | 0.230930i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.57179 | − | 2.42253i | −0.299027 | − | 0.110229i | ||||
\(484\) | 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 | ||||||||
\(497\) | −0.816742 | − | 0.301072i | −0.0366359 | − | 0.0135049i | ||||
\(498\) | 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 | −0.844753 | − | 0.535157i | \(-0.820252\pi\) |
0.535157 | + | 0.844753i | \(0.320252\pi\) | |||||||
\(504\) | 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 | \(-0.830733\pi\) | ||||
−0.861911 | + | 0.507059i | \(0.830733\pi\) | |||||||
\(510\) | 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 | \(0.239405\pi\) | ||||
−0.730246 | + | 0.683184i | \(0.760595\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.0273 | + | 19.0273i | −0.832007 | + | 0.832007i | −0.987791 | − | 0.155784i | \(-0.950210\pi\) |
0.155784 | + | 0.987791i | \(0.450210\pi\) | |||||||
\(524\) | 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 | ||||||||
\(553\) | −12.5260 | + | 33.9803i | −0.532659 | + | 1.44499i | ||||
\(554\) | 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 | −0.540685 | − | 0.841225i | \(-0.681835\pi\) |
0.841225 | + | 0.540685i | \(0.181835\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.52270 | − | 3.14168i | −0.357920 | − | 0.131938i | ||||
\(568\) | 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 | 0.0710620 | − | 0.997472i | \(-0.477361\pi\) |
−0.997472 | + | 0.0710620i | \(0.977361\pi\) | |||||||
\(578\) | 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 | 0.273512 | − | 0.961869i | \(-0.411815\pi\) |
−0.961869 | + | 0.273512i | \(0.911815\pi\) | |||||||
\(588\) | 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 | −0.828907 | − | 0.559386i | \(-0.811037\pi\) |
0.559386 | + | 0.828907i | \(0.311037\pi\) | |||||||
\(594\) | 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 | \(0.135092\pi\) | ||||
−0.911285 | + | 0.411777i | \(0.864908\pi\) | |||||||
\(602\) | 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 | 0.873962 | − | 0.485993i | \(-0.161542\pi\) |
−0.485993 | + | 0.873962i | \(0.661542\pi\) | |||||||
\(608\) | 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 | \(-0.480853\pi\) | ||||
0.0601145 | + | 0.998191i | \(0.480853\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 11.3724i | 0.456358i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.7540 | − | 12.0740i | −1.31226 | − | 0.483733i | ||||
\(624\) | 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 | ||||||||
\(637\) | −9.83160 | + | 0.778891i | −0.389542 | + | 0.0308608i | ||||
\(638\) | 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 | −0.983860 | − | 0.178939i | \(-0.942733\pi\) |
0.178939 | + | 0.983860i | \(0.442733\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.2719 | − | 18.2719i | −0.718342 | − | 0.718342i | 0.249924 | − | 0.968265i | \(-0.419594\pi\) |
−0.968265 | + | 0.249924i | \(0.919594\pi\) | |||||||
\(648\) | 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 | \(-0.798206\pi\) | ||
0.805692 | − | 0.592335i | \(-0.201794\pi\) | |||||||
\(662\) | 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 | 0.0873819 | − | 0.996175i | \(-0.472150\pi\) |
−0.996175 | + | 0.0873819i | \(0.972150\pi\) | |||||||
\(678\) | 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 | \(-0.719466\pi\) | ||
0.636131 | − | 0.771581i | \(-0.280534\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.44267 | − | 3.91365i | 0.0548025 | − | 0.148667i | ||||
\(694\) | 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 | ||||||||
\(707\) | −8.03048 | + | 21.7849i | −0.302017 | + | 0.819307i | ||||
\(708\) | 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 | \(-0.293368\pi\) | ||||
0.604512 | + | 0.796596i | \(0.293368\pi\) | |||||||
\(720\) | 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 | 0.666291 | − | 0.745692i | \(-0.267881\pi\) |
−0.745692 | + | 0.666291i | \(0.767881\pi\) | |||||||
\(728\) | 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 | −0.957930 | − | 0.287001i | \(-0.907342\pi\) |
0.287001 | + | 0.957930i | \(0.407342\pi\) | |||||||
\(734\) | 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 | \(-0.767825\pi\) | ||
0.745575 | − | 0.666422i | \(-0.232175\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.53133 | + | 17.7181i | −0.236450 | + | 0.641437i | ||||
\(764\) | 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 | \(-0.502136\pi\) | ||||
−0.00671098 | + | 0.999977i | \(0.502136\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.3464 | −0.480659 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 28.1925 | − | 28.1925i | 1.01402 | − | 1.01402i | 0.0141148 | − | 0.999900i | \(-0.495507\pi\) |
0.999900 | − | 0.0141148i | \(-0.00449302\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.29425 | − | 11.6494i | 0.154055 | − | 0.417919i | ||||
\(778\) | 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 | 0.752211 | − | 0.658922i | \(-0.228987\pi\) |
−0.658922 | + | 0.752211i | \(0.728987\pi\) | |||||||
\(788\) | 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 | 0.433180 | − | 0.901307i | \(-0.357391\pi\) |
−0.901307 | + | 0.433180i | \(0.857391\pi\) | |||||||
\(798\) | 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 | \(-0.736201\pi\) | ||
0.675797 | − | 0.737088i | \(-0.263799\pi\) | |||||||
\(812\) | 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 | \(-0.340274\pi\) | ||||
0.481000 | + | 0.876720i | \(0.340274\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 22.0344i | − | 0.764365i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.443959 | − | 5.60389i | −0.0153823 | − | 0.194163i | ||||
\(834\) | 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 | \(-0.402748\pi\) | ||||
0.300796 | + | 0.953689i | \(0.402748\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 23.6328 | + | 8.71165i | 0.812033 | + | 0.299336i | ||||
\(848\) | 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 | −0.963264 | − | 0.268555i | \(-0.913454\pi\) |
0.268555 | + | 0.963264i | \(0.413454\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.9133 | − | 18.9133i | −0.646066 | − | 0.646066i | 0.305974 | − | 0.952040i | \(-0.401018\pi\) |
−0.952040 | + | 0.305974i | \(0.901018\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.6031 | −1.62420 | −0.812098 | − | 0.583520i | \(-0.801675\pi\) | ||||
−0.812098 | + | 0.583520i | \(0.801675\pi\) | |||||||
\(860\) | 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 | \(-0.955957\pi\) | ||
0.990443 | − | 0.137925i | \(-0.0440432\pi\) | |||||||
\(882\) | 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 | 0.397291 | − | 0.917693i | \(-0.369950\pi\) |
−0.917693 | + | 0.397291i | \(0.869950\pi\) | |||||||
\(888\) | 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 | ||||||||
\(903\) | −14.2688 | − | 5.25984i | −0.474836 | − | 0.175037i | ||||
\(904\) | 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 | ||||||||
\(917\) | 5.60795 | − | 15.2132i | 0.185191 | − | 0.502383i | ||||
\(918\) | 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 | \(-0.294218\pi\) | ||||
0.602382 | + | 0.798208i | \(0.294218\pi\) | |||||||
\(930\) | 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 | 0.543226 | − | 0.839586i | \(-0.317202\pi\) |
−0.839586 | + | 0.543226i | \(0.817202\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 21.6813i | − | 0.707544i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 28.6996i | − | 0.935580i | −0.883840 | − | 0.467790i | \(-0.845050\pi\) | ||
0.883840 | − | 0.467790i | \(-0.154950\pi\) | |||||||
\(942\) | 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 | \(0.388285\pi\) | ||||
−0.343803 | + | 0.939042i | \(0.611715\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.2299 | + | 8.19450i | 0.712658 | + | 0.262704i | ||||
\(974\) | 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 | −0.705889 | − | 0.708323i | \(-0.749452\pi\) |
0.708323 | + | 0.705889i | \(0.249452\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −33.1636 | − | 12.2249i | −1.05561 | − | 0.389123i | ||||
\(988\) | 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 | \(0.0525056\pi\) |
0.164204 | + | 0.986426i | \(0.447494\pi\) | |||||||
\(998\) | 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.993.6 | yes | 32 | |
5.2 | odd | 4 | inner | 1400.2.x.c.657.11 | yes | 32 | |
5.3 | odd | 4 | inner | 1400.2.x.c.657.6 | yes | 32 | |
5.4 | even | 2 | inner | 1400.2.x.c.993.12 | yes | 32 | |
7.6 | odd | 2 | inner | 1400.2.x.c.993.11 | yes | 32 | |
35.13 | even | 4 | inner | 1400.2.x.c.657.12 | yes | 32 | |
35.27 | even | 4 | inner | 1400.2.x.c.657.5 | ✓ | 32 | |
35.34 | odd | 2 | inner | 1400.2.x.c.993.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1400.2.x.c.657.5 | ✓ | 32 | 35.27 | even | 4 | inner | |
1400.2.x.c.657.6 | yes | 32 | 5.3 | odd | 4 | inner | |
1400.2.x.c.657.11 | yes | 32 | 5.2 | odd | 4 | inner | |
1400.2.x.c.657.12 | yes | 32 | 35.13 | even | 4 | inner | |
1400.2.x.c.993.5 | yes | 32 | 35.34 | odd | 2 | inner | |
1400.2.x.c.993.6 | yes | 32 | 1.1 | even | 1 | trivial | |
1400.2.x.c.993.11 | yes | 32 | 7.6 | odd | 2 | inner | |
1400.2.x.c.993.12 | yes | 32 | 5.4 | even | 2 | inner |