Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(649,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.34810603776.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 12x^{6} + 42x^{4} + 49x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.3 | ||
Root | \(-1.47325i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.649 |
Dual form | 2025.2.b.o.649.6 |
$q$-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 \(\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(1702\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.47325i | − 1.04175i | −0.853633 | − | 0.520874i | \(-0.825606\pi\) | ||||
0.853633 | − | 0.520874i | \(-0.174394\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.170479 | −0.0852394 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.86583i | 1.46115i | 0.682835 | + | 0.730573i | \(0.260747\pi\) | ||||
−0.682835 | + | 0.730573i | \(0.739253\pi\) | |||||||
\(8\) | − 2.69535i | − 0.952950i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.260278 | −0.0784767 | −0.0392384 | − | 0.999230i | \(-0.512493\pi\) | ||||
−0.0392384 | + | 0.999230i | \(0.512493\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.07881i | 1.13126i | 0.824660 | + | 0.565629i | \(0.191366\pi\) | ||||
−0.824660 | + | 0.565629i | \(0.808634\pi\) | |||||||
\(14\) | 5.69535 | 1.52215 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.31189 | −1.07797 | ||||||||
\(17\) | − 3.26028i | − 0.790734i | −0.918523 | − | 0.395367i | \(-0.870617\pi\) | ||||
0.918523 | − | 0.395367i | \(-0.129383\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.24928 | −0.974853 | −0.487426 | − | 0.873164i | \(-0.662064\pi\) | ||||
−0.487426 | + | 0.873164i | \(0.662064\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.383456i | 0.0817530i | ||||||||
\(23\) | 8.69535i | 1.81311i | 0.422092 | + | 0.906553i | \(0.361296\pi\) | ||||
−0.422092 | + | 0.906553i | \(0.638704\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00912 | 1.17849 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 0.659042i | − 0.124547i | ||||||||
\(29\) | 4.22210 | 0.784023 | 0.392012 | − | 0.919960i | \(-0.371779\pi\) | ||||
0.392012 | + | 0.919960i | \(0.371779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.65285 | 0.476466 | 0.238233 | − | 0.971208i | \(-0.423432\pi\) | ||||
0.238233 | + | 0.971208i | \(0.423432\pi\) | |||||||
\(32\) | 0.961818i | 0.170027i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.80322 | −0.823745 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.27559i | − 0.374104i | −0.982350 | − | 0.187052i | \(-0.940107\pi\) | ||||
0.982350 | − | 0.187052i | \(-0.0598933\pi\) | |||||||
\(38\) | 6.26028i | 1.01555i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.64186 | −0.881110 | −0.440555 | − | 0.897726i | \(-0.645218\pi\) | ||||
−0.440555 | + | 0.897726i | \(0.645218\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.07262i | 1.38356i | 0.722108 | + | 0.691780i | \(0.243173\pi\) | ||||
−0.722108 | + | 0.691780i | \(0.756827\pi\) | |||||||
\(44\) | 0.0443719 | 0.00668931 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 12.8105 | 1.88880 | ||||||||
\(47\) | 1.42888i | 0.208424i | 0.994555 | + | 0.104212i | \(0.0332320\pi\) | ||||
−0.994555 | + | 0.104212i | \(0.966768\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.94463 | −1.13495 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 0.695350i | − 0.0964277i | ||||||||
\(53\) | 11.3816i | 1.56338i | 0.623667 | + | 0.781690i | \(0.285642\pi\) | ||||
−0.623667 | + | 0.781690i | \(0.714358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 10.4198 | 1.39240 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 6.22022i | − 0.816755i | ||||||||
\(59\) | −7.12423 | −0.927496 | −0.463748 | − | 0.885967i | \(-0.653496\pi\) | ||||
−0.463748 | + | 0.885967i | \(0.653496\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.52487 | 0.323277 | 0.161638 | − | 0.986850i | \(-0.448322\pi\) | ||||
0.161638 | + | 0.986850i | \(0.448322\pi\) | |||||||
\(62\) | − 3.90833i | − 0.496358i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.20679 | −0.900848 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.2856i | 1.37875i | 0.724402 | + | 0.689377i | \(0.242116\pi\) | ||||
−0.724402 | + | 0.689377i | \(0.757884\pi\) | |||||||
\(68\) | 0.555809i | 0.0674017i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.38158 | 0.994711 | 0.497355 | − | 0.867547i | \(-0.334305\pi\) | ||||
0.497355 | + | 0.867547i | \(0.334305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.403568i | − 0.0472340i | −0.999721 | − | 0.0236170i | \(-0.992482\pi\) | ||||
0.999721 | − | 0.0236170i | \(-0.00751823\pi\) | |||||||
\(74\) | −3.35252 | −0.389722 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.724413 | 0.0830959 | ||||||||
\(77\) | − 1.00619i | − 0.114666i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.04250 | 0.342308 | 0.171154 | − | 0.985244i | \(-0.445250\pi\) | ||||
0.171154 | + | 0.985244i | \(0.445250\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.31189i | 0.917895i | ||||||||
\(83\) | 4.58024i | 0.502746i | 0.967890 | + | 0.251373i | \(0.0808821\pi\) | ||||
−0.967890 | + | 0.251373i | \(0.919118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 13.3663 | 1.44132 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.701540i | 0.0747844i | ||||||||
\(89\) | 7.17772 | 0.760837 | 0.380419 | − | 0.924814i | \(-0.375780\pi\) | ||||
0.380419 | + | 0.924814i | \(0.375780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.7680 | −1.65293 | ||||||||
\(92\) | − 1.48237i | − 0.154548i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.10511 | 0.217125 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.11511i | 0.316292i | 0.987416 | + | 0.158146i | \(0.0505516\pi\) | ||||
−0.987416 | + | 0.158146i | \(0.949448\pi\) | |||||||
\(98\) | 11.7045i | 1.18233i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.84572 | −0.382663 | −0.191332 | − | 0.981525i | \(-0.561281\pi\) | ||||
−0.191332 | + | 0.981525i | \(0.561281\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.20679i | 0.414507i | 0.978287 | + | 0.207254i | \(0.0664525\pi\) | ||||
−0.978287 | + | 0.207254i | \(0.933548\pi\) | |||||||
\(104\) | 10.9938 | 1.07803 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.7680 | 1.62865 | ||||||||
\(107\) | 1.62655i | 0.157245i | 0.996904 | + | 0.0786223i | \(0.0250521\pi\) | ||||
−0.996904 | + | 0.0786223i | \(0.974948\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.9021 | 1.23580 | 0.617900 | − | 0.786256i | \(-0.287984\pi\) | ||||
0.617900 | + | 0.786256i | \(0.287984\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 16.6690i | − 1.57508i | ||||||||
\(113\) | 1.32908i | 0.125029i | 0.998044 | + | 0.0625146i | \(0.0199120\pi\) | ||||
−0.998044 | + | 0.0625146i | \(0.980088\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.719778 | −0.0668297 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10.4958i | 0.966217i | ||||||||
\(119\) | 12.6037 | 1.15538 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9323 | −0.993841 | ||||||||
\(122\) | − 3.71978i | − 0.336773i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.452255 | −0.0406137 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 1.65285i | − 0.146667i | −0.997307 | − | 0.0733335i | \(-0.976636\pi\) | ||||
0.997307 | − | 0.0733335i | \(-0.0233637\pi\) | |||||||
\(128\) | 12.5411i | 1.10848i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.1777 | 1.15134 | 0.575672 | − | 0.817681i | \(-0.304741\pi\) | ||||
0.575672 | + | 0.817681i | \(0.304741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 16.4270i | − 1.42440i | ||||||||
\(134\) | 16.6266 | 1.43632 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.78759 | −0.753530 | ||||||||
\(137\) | − 20.2928i | − 1.73373i | −0.498539 | − | 0.866867i | \(-0.666130\pi\) | ||||
0.498539 | − | 0.866867i | \(-0.333870\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.06880 | −0.260292 | −0.130146 | − | 0.991495i | \(-0.541545\pi\) | ||||
−0.130146 | + | 0.991495i | \(0.541545\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 12.3482i | − 1.03624i | ||||||||
\(143\) | − 1.06162i | − 0.0887774i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −0.594558 | −0.0492060 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.387939i | 0.0318884i | ||||||||
\(149\) | 4.06162 | 0.332741 | 0.166371 | − | 0.986063i | \(-0.446795\pi\) | ||||
0.166371 | + | 0.986063i | \(0.446795\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6199 | −1.10837 | −0.554185 | − | 0.832394i | \(-0.686970\pi\) | ||||
−0.554185 | + | 0.832394i | \(0.686970\pi\) | |||||||
\(152\) | 11.4533i | 0.928986i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.48237 | −0.119453 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.06261i | 0.164614i | 0.996607 | + | 0.0823071i | \(0.0262288\pi\) | ||||
−0.996607 | + | 0.0823071i | \(0.973771\pi\) | |||||||
\(158\) | − 4.48237i | − 0.356598i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −33.6147 | −2.64921 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.50525i | 0.274552i | 0.990533 | + | 0.137276i | \(0.0438347\pi\) | ||||
−0.990533 | + | 0.137276i | \(0.956165\pi\) | |||||||
\(164\) | 0.961818 | 0.0751054 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.74785 | 0.523735 | ||||||||
\(167\) | − 20.5349i | − 1.58904i | −0.607240 | − | 0.794518i | \(-0.707723\pi\) | ||||
0.607240 | − | 0.794518i | \(-0.292277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.63666 | −0.279743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 1.54669i | − 0.117934i | ||||||||
\(173\) | − 7.75177i | − 0.589356i | −0.955597 | − | 0.294678i | \(-0.904788\pi\) | ||||
0.955597 | − | 0.294678i | \(-0.0952124\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.12229 | 0.0845958 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 10.5746i | − 0.792601i | ||||||||
\(179\) | −10.7632 | −0.804477 | −0.402238 | − | 0.915535i | \(-0.631768\pi\) | ||||
−0.402238 | + | 0.915535i | \(0.631768\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.84572 | −0.583168 | −0.291584 | − | 0.956545i | \(-0.594182\pi\) | ||||
−0.291584 | + | 0.956545i | \(0.594182\pi\) | |||||||
\(182\) | 23.2302i | 1.72194i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 23.4370 | 1.72780 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.848578i | 0.0620542i | ||||||||
\(188\) | − 0.243594i | − 0.0177659i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.73255 | 0.414792 | 0.207396 | − | 0.978257i | \(-0.433501\pi\) | ||||
0.207396 | + | 0.978257i | \(0.433501\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48237i | 0.610575i | 0.952260 | + | 0.305287i | \(0.0987525\pi\) | ||||
−0.952260 | + | 0.305287i | \(0.901248\pi\) | |||||||
\(194\) | 4.58936 | 0.329497 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.35439 | 0.0967423 | ||||||||
\(197\) | − 10.6266i | − 0.757110i | −0.925579 | − | 0.378555i | \(-0.876421\pi\) | ||||
0.925579 | − | 0.378555i | \(-0.123579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.5784 | 1.31699 | 0.658495 | − | 0.752585i | \(-0.271193\pi\) | ||||
0.658495 | + | 0.752585i | \(0.271193\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.66572i | 0.398639i | ||||||||
\(203\) | 16.3219i | 1.14557i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.19767 | 0.431812 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 17.5874i | − 1.21947i | ||||||||
\(209\) | 1.10599 | 0.0765033 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.4533 | 0.719636 | 0.359818 | − | 0.933023i | \(-0.382839\pi\) | ||||
0.359818 | + | 0.933023i | \(0.382839\pi\) | |||||||
\(212\) | − 1.94032i | − 0.133262i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.39632 | 0.163809 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.2555i | 0.696187i | ||||||||
\(218\) | − 19.0081i | − 1.28739i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.2980 | 0.894523 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 3.93120i | − 0.263253i | −0.991299 | − | 0.131626i | \(-0.957980\pi\) | ||||
0.991299 | − | 0.131626i | \(-0.0420199\pi\) | |||||||
\(224\) | −3.71822 | −0.248434 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.95807 | 0.130249 | ||||||||
\(227\) | − 4.83140i | − 0.320671i | −0.987063 | − | 0.160335i | \(-0.948742\pi\) | ||||
0.987063 | − | 0.160335i | \(-0.0512576\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.8530 | 1.24584 | 0.622919 | − | 0.782286i | \(-0.285946\pi\) | ||||
0.622919 | + | 0.782286i | \(0.285946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 11.3800i | − 0.747135i | ||||||||
\(233\) | − 11.9021i | − 0.779735i | −0.920871 | − | 0.389867i | \(-0.872521\pi\) | ||||
0.920871 | − | 0.389867i | \(-0.127479\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.21453 | 0.0790593 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − 18.5684i | − 1.20361i | ||||||||
\(239\) | −21.6295 | −1.39909 | −0.699547 | − | 0.714586i | \(-0.746615\pi\) | ||||
−0.699547 | + | 0.714586i | \(0.746615\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.89832 | 0.251113 | 0.125556 | − | 0.992086i | \(-0.459928\pi\) | ||||
0.125556 | + | 0.992086i | \(0.459928\pi\) | |||||||
\(242\) | 16.1060i | 1.03533i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.430437 | −0.0275559 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 17.3320i | − 1.10281i | ||||||||
\(248\) | − 7.15037i | − 0.454049i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 30.1033 | 1.90010 | 0.950052 | − | 0.312092i | \(-0.101030\pi\) | ||||
0.950052 | + | 0.312092i | \(0.101030\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 2.26321i | − 0.142287i | ||||||||
\(254\) | −2.43507 | −0.152790 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.06261 | 0.253913 | ||||||||
\(257\) | 16.4141i | 1.02389i | 0.859019 | + | 0.511943i | \(0.171074\pi\) | ||||
−0.859019 | + | 0.511943i | \(0.828926\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.79703 | 0.546621 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 19.4141i | − 1.19941i | ||||||||
\(263\) | 25.8072i | 1.59134i | 0.605730 | + | 0.795670i | \(0.292881\pi\) | ||||
−0.605730 | + | 0.795670i | \(0.707119\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −24.2012 | −1.48387 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 1.92396i | − 0.117524i | ||||||||
\(269\) | −12.5206 | −0.763392 | −0.381696 | − | 0.924288i | \(-0.624660\pi\) | ||||
−0.381696 | + | 0.924288i | \(0.624660\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.6462 | 1.19342 | 0.596710 | − | 0.802457i | \(-0.296474\pi\) | ||||
0.596710 | + | 0.802457i | \(0.296474\pi\) | |||||||
\(272\) | 14.0580i | 0.852390i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −29.8965 | −1.80611 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 20.8301i | − 1.25156i | −0.780000 | − | 0.625779i | \(-0.784781\pi\) | ||||
0.780000 | − | 0.625779i | \(-0.215219\pi\) | |||||||
\(278\) | 4.52112i | 0.271159i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.72441 | −0.281835 | −0.140917 | − | 0.990021i | \(-0.545005\pi\) | ||||
−0.140917 | + | 0.990021i | \(0.545005\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.1525i | − 1.37627i | −0.725582 | − | 0.688136i | \(-0.758429\pi\) | ||||
0.725582 | − | 0.688136i | \(-0.241571\pi\) | |||||||
\(284\) | −1.42888 | −0.0847886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.56404 | −0.0924837 | ||||||||
\(287\) | − 21.8105i | − 1.28743i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.37059 | 0.374740 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.0687998i | 0.00402620i | ||||||||
\(293\) | − 16.8793i | − 0.986097i | −0.870002 | − | 0.493049i | \(-0.835882\pi\) | ||||
0.870002 | − | 0.493049i | \(-0.164118\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.13350 | −0.356503 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 5.98380i | − 0.346632i | ||||||||
\(299\) | −35.4666 | −2.05109 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.0732 | −2.02158 | ||||||||
\(302\) | 20.0655i | 1.15464i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 18.3225 | 1.05087 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 22.7177i | − 1.29657i | −0.761398 | − | 0.648285i | \(-0.775487\pi\) | ||||
0.761398 | − | 0.648285i | \(-0.224513\pi\) | |||||||
\(308\) | 0.171534i | 0.00977406i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.5936 | −1.79151 | −0.895754 | − | 0.444551i | \(-0.853363\pi\) | ||||
−0.895754 | + | 0.444551i | \(0.853363\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30.4996i | 1.72394i | 0.506959 | + | 0.861970i | \(0.330770\pi\) | ||||
−0.506959 | + | 0.861970i | \(0.669230\pi\) | |||||||
\(314\) | 3.03875 | 0.171487 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.518682 | −0.0291781 | ||||||||
\(317\) | − 22.0890i | − 1.24064i | −0.784349 | − | 0.620320i | \(-0.787003\pi\) | ||||
0.784349 | − | 0.620320i | \(-0.212997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.09892 | −0.0615276 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 49.5231i | 2.75981i | ||||||||
\(323\) | 13.8538i | 0.770849i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.16412 | 0.286014 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.2068i | 0.839654i | ||||||||
\(329\) | −5.52382 | −0.304538 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.6047 | −1.62722 | −0.813612 | − | 0.581409i | \(-0.802502\pi\) | ||||
−0.813612 | + | 0.581409i | \(0.802502\pi\) | |||||||
\(332\) | − 0.780834i | − 0.0428538i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.2531 | −1.65538 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.5311i | 0.682610i | 0.939953 | + | 0.341305i | \(0.110869\pi\) | ||||
−0.939953 | + | 0.341305i | \(0.889131\pi\) | |||||||
\(338\) | 5.35772i | 0.291422i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.690479 | −0.0373915 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 3.65180i | − 0.197179i | ||||||||
\(344\) | 24.4539 | 1.31846 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.4203 | −0.613961 | ||||||||
\(347\) | 17.0974i | 0.917839i | 0.888478 | + | 0.458919i | \(0.151763\pi\) | ||||
−0.888478 | + | 0.458919i | \(0.848237\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.4046 | 0.985177 | 0.492588 | − | 0.870262i | \(-0.336051\pi\) | ||||
0.492588 | + | 0.870262i | \(0.336051\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 0.250340i | − 0.0133432i | ||||||||
\(353\) | − 31.7188i | − 1.68822i | −0.536169 | − | 0.844110i | \(-0.680129\pi\) | ||||
0.536169 | − | 0.844110i | \(-0.319871\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.22365 | −0.0648533 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 15.8569i | 0.838062i | ||||||||
\(359\) | −11.4533 | −0.604483 | −0.302241 | − | 0.953231i | \(-0.597735\pi\) | ||||
−0.302241 | + | 0.953231i | \(0.597735\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.943580 | −0.0496621 | ||||||||
\(362\) | 11.5587i | 0.607514i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.68811 | 0.140895 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.49238i | 0.130101i | 0.997882 | + | 0.0650506i | \(0.0207209\pi\) | ||||
−0.997882 | + | 0.0650506i | \(0.979279\pi\) | |||||||
\(368\) | − 37.4934i | − 1.95448i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −43.9992 | −2.28433 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.0374i | 0.778605i | 0.921110 | + | 0.389303i | \(0.127284\pi\) | ||||
−0.921110 | + | 0.389303i | \(0.872716\pi\) | |||||||
\(374\) | 1.25017 | 0.0646448 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.85134 | 0.198618 | ||||||||
\(377\) | 17.2211i | 0.886932i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.27273 | −0.322208 | −0.161104 | − | 0.986937i | \(-0.551505\pi\) | ||||
−0.161104 | + | 0.986937i | \(0.551505\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 8.44550i | − 0.432109i | ||||||||
\(383\) | − 22.1888i | − 1.13379i | −0.823789 | − | 0.566897i | \(-0.808144\pi\) | ||||
0.823789 | − | 0.566897i | \(-0.191856\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.4967 | 0.636065 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 0.531061i | − 0.0269605i | ||||||||
\(389\) | −30.0922 | −1.52574 | −0.762869 | − | 0.646554i | \(-0.776210\pi\) | ||||
−0.762869 | + | 0.646554i | \(0.776210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.3493 | 1.43368 | ||||||||
\(392\) | 21.4136i | 1.08155i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −15.6556 | −0.788718 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.2313i | 1.46708i | 0.679648 | + | 0.733538i | \(0.262132\pi\) | ||||
−0.679648 | + | 0.733538i | \(0.737868\pi\) | |||||||
\(398\) | − 27.3708i | − 1.37197i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.2341 | −1.21020 | −0.605098 | − | 0.796151i | \(-0.706866\pi\) | ||||
−0.605098 | + | 0.796151i | \(0.706866\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.8205i | 0.539006i | ||||||||
\(404\) | 0.655614 | 0.0326180 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 24.0463 | 1.19340 | ||||||||
\(407\) | 0.592285i | 0.0293585i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.33990 | −0.115701 | −0.0578504 | − | 0.998325i | \(-0.518425\pi\) | ||||
−0.0578504 | + | 0.998325i | \(0.518425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 0.717168i | − 0.0353323i | ||||||||
\(413\) | − 27.5411i | − 1.35521i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.92307 | −0.192344 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 1.62941i | − 0.0796971i | ||||||||
\(419\) | 22.8425 | 1.11593 | 0.557964 | − | 0.829865i | \(-0.311583\pi\) | ||||
0.557964 | + | 0.829865i | \(0.311583\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11.8758 | 0.578793 | 0.289396 | − | 0.957209i | \(-0.406545\pi\) | ||||
0.289396 | + | 0.957209i | \(0.406545\pi\) | |||||||
\(422\) | − 15.4004i | − 0.749679i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 30.6773 | 1.48982 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.76072i | 0.472354i | ||||||||
\(428\) | − 0.277293i | − 0.0134034i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.86916 | −0.427212 | −0.213606 | − | 0.976920i | \(-0.568521\pi\) | ||||
−0.213606 | + | 0.976920i | \(0.568521\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 9.37059i | − 0.450322i | −0.974322 | − | 0.225161i | \(-0.927709\pi\) | ||||
0.974322 | − | 0.225161i | \(-0.0722908\pi\) | |||||||
\(434\) | 15.1089 | 0.725252 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.19954 | −0.105339 | ||||||||
\(437\) | − 36.9490i | − 1.76751i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4231 | −0.927014 | −0.463507 | − | 0.886093i | \(-0.653409\pi\) | ||||
−0.463507 | + | 0.886093i | \(0.653409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 19.5914i | − 0.931868i | ||||||||
\(443\) | 10.8793i | 0.516889i | 0.966026 | + | 0.258445i | \(0.0832100\pi\) | ||||
−0.966026 | + | 0.258445i | \(0.916790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.79166 | −0.274243 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 27.8602i | − 1.31627i | ||||||||
\(449\) | 1.34014 | 0.0632451 | 0.0316225 | − | 0.999500i | \(-0.489933\pi\) | ||||
0.0316225 | + | 0.999500i | \(0.489933\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.46845 | 0.0691467 | ||||||||
\(452\) | − 0.226580i | − 0.0106574i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.11787 | −0.334058 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1113i | 0.940767i | 0.882462 | + | 0.470383i | \(0.155884\pi\) | ||||
−0.882462 | + | 0.470383i | \(0.844116\pi\) | |||||||
\(458\) | − 27.7752i | − 1.29785i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 33.7533 | 1.57205 | 0.786024 | − | 0.618196i | \(-0.212136\pi\) | ||||
0.786024 | + | 0.618196i | \(0.212136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.24537i | 0.243773i | 0.992544 | + | 0.121886i | \(0.0388944\pi\) | ||||
−0.992544 | + | 0.121886i | \(0.961106\pi\) | |||||||
\(464\) | −18.2052 | −0.845157 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.5349 | −0.812288 | ||||||||
\(467\) | − 14.2120i | − 0.657652i | −0.944390 | − | 0.328826i | \(-0.893347\pi\) | ||||
0.944390 | − | 0.328826i | \(-0.106653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −43.6282 | −2.01456 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.2023i | 0.883858i | ||||||||
\(473\) | − 2.36140i | − 0.108577i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.14866 | −0.0984837 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 31.8657i | 1.45750i | ||||||||
\(479\) | 20.4833 | 0.935907 | 0.467954 | − | 0.883753i | \(-0.344991\pi\) | ||||
0.467954 | + | 0.883753i | \(0.344991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.28168 | 0.423208 | ||||||||
\(482\) | − 5.74322i | − 0.261596i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.86372 | 0.0847145 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 31.3554i | 1.42085i | 0.703772 | + | 0.710425i | \(0.251497\pi\) | ||||
−0.703772 | + | 0.710425i | \(0.748503\pi\) | |||||||
\(488\) | − 6.80541i | − 0.308067i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.3921 | 0.468988 | 0.234494 | − | 0.972118i | \(-0.424657\pi\) | ||||
0.234494 | + | 0.972118i | \(0.424657\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13.7652i | − 0.619954i | ||||||||
\(494\) | −25.5345 | −1.14885 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.4388 | −0.513618 | ||||||||
\(497\) | 32.4018i | 1.45342i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.82570 | 0.171262 | 0.0856310 | − | 0.996327i | \(-0.472709\pi\) | ||||
0.0856310 | + | 0.996327i | \(0.472709\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 44.3498i | − 1.97943i | ||||||||
\(503\) | 1.00236i | 0.0446931i | 0.999750 | + | 0.0223466i | \(0.00711372\pi\) | ||||
−0.999750 | + | 0.0223466i | \(0.992886\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.33428 | −0.148227 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.281776i | 0.0125018i | ||||||||
\(509\) | 4.56322 | 0.202261 | 0.101131 | − | 0.994873i | \(-0.467754\pi\) | ||||
0.101131 | + | 0.994873i | \(0.467754\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.56012 | 0.0690158 | ||||||||
\(512\) | 19.0969i | 0.843971i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 24.1822 | 1.06663 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.371907i | − 0.0163564i | ||||||||
\(518\) | − 12.9603i | − 0.569441i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −39.3708 | −1.72486 | −0.862432 | − | 0.506173i | \(-0.831060\pi\) | ||||
−0.862432 | + | 0.506173i | \(0.831060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.3998i | 0.454749i | 0.973807 | + | 0.227375i | \(0.0730142\pi\) | ||||
−0.973807 | + | 0.227375i | \(0.926986\pi\) | |||||||
\(524\) | −2.24652 | −0.0981398 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 38.0206 | 1.65778 | ||||||||
\(527\) | − 8.64904i | − 0.376758i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −52.6091 | −2.28735 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.80046i | 0.121415i | ||||||||
\(533\) | − 23.0120i | − 0.996762i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 30.4186 | 1.31388 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.4460i | 0.795262i | ||||||||
\(539\) | 2.06781 | 0.0890670 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.7093 | 0.589408 | 0.294704 | − | 0.955589i | \(-0.404779\pi\) | ||||
0.294704 | + | 0.955589i | \(0.404779\pi\) | |||||||
\(542\) | − 28.9438i | − 1.24324i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.13579 | 0.134446 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.7847i | 0.974205i | 0.873345 | + | 0.487102i | \(0.161946\pi\) | ||||
−0.873345 | + | 0.487102i | \(0.838054\pi\) | |||||||
\(548\) | 3.45950i | 0.147783i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.9409 | −0.764307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.7618i | 0.500162i | ||||||||
\(554\) | −30.6880 | −1.30381 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.523166 | 0.0221872 | ||||||||
\(557\) | 18.2341i | 0.772605i | 0.922372 | + | 0.386303i | \(0.126248\pi\) | ||||
−0.922372 | + | 0.386303i | \(0.873752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.0054 | −1.56516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.96026i | 0.293601i | ||||||||
\(563\) | 24.1112i | 1.01617i | 0.861308 | + | 0.508083i | \(0.169646\pi\) | ||||
−0.861308 | + | 0.508083i | \(0.830354\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −34.1095 | −1.43373 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 22.5913i | − 0.947910i | ||||||||
\(569\) | −32.0049 | −1.34171 | −0.670857 | − | 0.741587i | \(-0.734074\pi\) | ||||
−0.670857 | + | 0.741587i | \(0.734074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.7808 | −0.827802 | −0.413901 | − | 0.910322i | \(-0.635834\pi\) | ||||
−0.413901 | + | 0.910322i | \(0.635834\pi\) | |||||||
\(572\) | 0.180984i | 0.00756733i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −32.1324 | −1.34118 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 35.4119i | − 1.47422i | −0.675775 | − | 0.737108i | \(-0.736191\pi\) | ||||
0.675775 | − | 0.737108i | \(-0.263809\pi\) | |||||||
\(578\) | − 9.38550i | − 0.390385i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.7064 | −0.734586 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.96237i | − 0.122689i | ||||||||
\(584\) | −1.08776 | −0.0450117 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24.8675 | −1.02726 | ||||||||
\(587\) | 32.3851i | 1.33668i | 0.743858 | + | 0.668338i | \(0.232994\pi\) | ||||
−0.743858 | + | 0.668338i | \(0.767006\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.2727 | −0.464485 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.81209i | 0.403274i | ||||||||
\(593\) | 29.2504i | 1.20117i | 0.799561 | + | 0.600585i | \(0.205066\pi\) | ||||
−0.799561 | + | 0.600585i | \(0.794934\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.692421 | −0.0283627 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 52.2514i | 2.13672i | ||||||||
\(599\) | 4.06162 | 0.165953 | 0.0829767 | − | 0.996551i | \(-0.473557\pi\) | ||||
0.0829767 | + | 0.996551i | \(0.473557\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.9076 | 1.91340 | 0.956700 | − | 0.291076i | \(-0.0940132\pi\) | ||||
0.956700 | + | 0.291076i | \(0.0940132\pi\) | |||||||
\(602\) | 51.6717i | 2.10598i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.32190 | 0.0944768 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 40.9466i | − 1.66197i | −0.556293 | − | 0.830987i | \(-0.687777\pi\) | ||||
0.556293 | − | 0.830987i | \(-0.312223\pi\) | |||||||
\(608\) | − 4.08704i | − 0.165751i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.82813 | −0.235781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.3827i | 1.34831i | 0.738588 | + | 0.674157i | \(0.235493\pi\) | ||||
−0.738588 | + | 0.674157i | \(0.764507\pi\) | |||||||
\(614\) | −33.4690 | −1.35070 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.71203 | −0.109271 | ||||||||
\(617\) | − 2.24880i | − 0.0905332i | −0.998975 | − | 0.0452666i | \(-0.985586\pi\) | ||||
0.998975 | − | 0.0452666i | \(-0.0144137\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 34.2934 | 1.37837 | 0.689184 | − | 0.724586i | \(-0.257969\pi\) | ||||
0.689184 | + | 0.724586i | \(0.257969\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 46.5454i | 1.86630i | ||||||||
\(623\) | 27.7479i | 1.11169i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 44.9337 | 1.79591 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 0.351631i | − 0.0140316i | ||||||||
\(629\) | −7.41904 | −0.295817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.7552 | −0.746633 | −0.373316 | − | 0.927704i | \(-0.621779\pi\) | ||||
−0.373316 | + | 0.927704i | \(0.621779\pi\) | |||||||
\(632\) | − 8.20060i | − 0.326202i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −32.5427 | −1.29244 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 32.4046i | − 1.28392i | ||||||||
\(638\) | 1.61899i | 0.0640963i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.6350 | −0.815034 | −0.407517 | − | 0.913198i | \(-0.633605\pi\) | ||||
−0.407517 | + | 0.913198i | \(0.633605\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 27.1939i | − 1.07242i | −0.844084 | − | 0.536212i | \(-0.819855\pi\) | ||||
0.844084 | − | 0.536212i | \(-0.180145\pi\) | |||||||
\(644\) | 5.73060 | 0.225817 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.4102 | 0.803030 | ||||||||
\(647\) | − 16.7316i | − 0.657787i | −0.944367 | − | 0.328893i | \(-0.893324\pi\) | ||||
0.944367 | − | 0.328893i | \(-0.106676\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.85428 | 0.0727869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 0.597571i | − 0.0234027i | ||||||||
\(653\) | − 45.7331i | − 1.78967i | −0.446392 | − | 0.894837i | \(-0.647291\pi\) | ||||
0.446392 | − | 0.894837i | \(-0.352709\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 24.3271 | 0.949814 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.13799i | 0.317252i | ||||||||
\(659\) | 18.6109 | 0.724976 | 0.362488 | − | 0.931988i | \(-0.381927\pi\) | ||||
0.362488 | + | 0.931988i | \(0.381927\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7960 | 0.653288 | 0.326644 | − | 0.945148i | \(-0.394082\pi\) | ||||
0.326644 | + | 0.945148i | \(0.394082\pi\) | |||||||
\(662\) | 43.6153i | 1.69516i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.3453 | 0.479092 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.7126i | 1.42152i | ||||||||
\(668\) | 3.50076i | 0.135449i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.657168 | −0.0253697 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 49.9480i | − 1.92535i | −0.270656 | − | 0.962676i | \(-0.587240\pi\) | ||||
0.270656 | − | 0.962676i | \(-0.412760\pi\) | |||||||
\(674\) | 18.4614 | 0.711108 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.619973 | 0.0238451 | ||||||||
\(677\) | − 10.8311i | − 0.416272i | −0.978100 | − | 0.208136i | \(-0.933260\pi\) | ||||
0.978100 | − | 0.208136i | \(-0.0667396\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.0425 | −0.462149 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.01725i | 0.0389526i | ||||||||
\(683\) | 0.429870i | 0.0164485i | 0.999966 | + | 0.00822426i | \(0.00261789\pi\) | ||||
−0.999966 | + | 0.00822426i | \(0.997382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5.38003 | −0.205410 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 39.1202i | − 1.49144i | ||||||||
\(689\) | −46.4233 | −1.76859 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.7036 | 1.32019 | 0.660093 | − | 0.751184i | \(-0.270517\pi\) | ||||
0.660093 | + | 0.751184i | \(0.270517\pi\) | |||||||
\(692\) | 1.32151i | 0.0502364i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.1889 | 0.956157 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.3940i | 0.696724i | ||||||||
\(698\) | − 27.1147i | − 1.02631i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.84808 | −0.0698010 | −0.0349005 | − | 0.999391i | \(-0.511111\pi\) | ||||
−0.0349005 | + | 0.999391i | \(0.511111\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.66962i | 0.364696i | ||||||||
\(704\) | 1.87577 | 0.0706956 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −46.7299 | −1.75870 | ||||||||
\(707\) | − 14.8669i | − 0.559127i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.30676 | 0.236855 | 0.118428 | − | 0.992963i | \(-0.462215\pi\) | ||||
0.118428 | + | 0.992963i | \(0.462215\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 19.3465i | − 0.725040i | ||||||||
\(713\) | 23.0675i | 0.863884i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.83489 | 0.0685731 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.8736i | 0.629719i | ||||||||
\(719\) | 18.0129 | 0.671770 | 0.335885 | − | 0.941903i | \(-0.390965\pi\) | ||||
0.335885 | + | 0.941903i | \(0.390965\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.2627 | −0.605655 | ||||||||
\(722\) | 1.39013i | 0.0517354i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.33753 | 0.0497089 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.2823i | 0.974758i | 0.873190 | + | 0.487379i | \(0.162047\pi\) | ||||
−0.873190 | + | 0.487379i | \(0.837953\pi\) | |||||||
\(728\) | 42.5002i | 1.57516i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.5792 | 1.09403 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 47.6633i | − 1.76049i | −0.474524 | − | 0.880243i | \(-0.657380\pi\) | ||||
0.474524 | − | 0.880243i | \(-0.342620\pi\) | |||||||
\(734\) | 3.67191 | 0.135533 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.36334 | −0.308277 | ||||||||
\(737\) | − 2.93739i | − 0.108200i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.0273 | 0.368859 | 0.184429 | − | 0.982846i | \(-0.440956\pi\) | ||||
0.184429 | + | 0.982846i | \(0.440956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 64.8221i | 2.37969i | ||||||||
\(743\) | 8.27266i | 0.303494i | 0.988419 | + | 0.151747i | \(0.0484900\pi\) | ||||
−0.988419 | + | 0.151747i | \(0.951510\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.1539 | 0.811111 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 0.144665i | − 0.00528946i | ||||||||
\(749\) | −6.28797 | −0.229757 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.79760 | −0.211557 | −0.105779 | − | 0.994390i | \(-0.533734\pi\) | ||||
−0.105779 | + | 0.994390i | \(0.533734\pi\) | |||||||
\(752\) | − 6.16119i | − 0.224676i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 25.3711 | 0.923960 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 25.2804i | − 0.918830i | −0.888222 | − | 0.459415i | \(-0.848059\pi\) | ||||
0.888222 | − | 0.459415i | \(-0.151941\pi\) | |||||||
\(758\) | 9.24132i | 0.335660i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.4638 | −0.705562 | −0.352781 | − | 0.935706i | \(-0.614764\pi\) | ||||
−0.352781 | + | 0.935706i | \(0.614764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 49.8775i | 1.80569i | ||||||||
\(764\) | −0.977278 | −0.0353567 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −32.6897 | −1.18113 | ||||||||
\(767\) | − 29.0584i | − 1.04924i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 49.3431 | 1.77936 | 0.889678 | − | 0.456588i | \(-0.150929\pi\) | ||||
0.889678 | + | 0.456588i | \(0.150929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 1.44607i | − 0.0520450i | ||||||||
\(773\) | 20.8502i | 0.749930i | 0.927039 | + | 0.374965i | \(0.122345\pi\) | ||||
−0.927039 | + | 0.374965i | \(0.877655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.39632 | 0.301410 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.3335i | 1.58943i | ||||||||
\(779\) | 23.9739 | 0.858953 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.18154 | −0.0780616 | ||||||||
\(782\) | − 41.7657i | − 1.49354i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 34.2564 | 1.22344 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 44.1883i | − 1.57514i | −0.616223 | − | 0.787571i | \(-0.711338\pi\) | ||||
0.616223 | − | 0.787571i | \(-0.288662\pi\) | |||||||
\(788\) | 1.81160i | 0.0645357i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.13799 | −0.182686 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.2985i | 0.365709i | ||||||||
\(794\) | 43.0651 | 1.52832 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.16723 | −0.112259 | ||||||||
\(797\) | − 31.0374i | − 1.09940i | −0.835361 | − | 0.549701i | \(-0.814742\pi\) | ||||
0.835361 | − | 0.549701i | \(-0.185258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.65855 | 0.164808 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.7031i | 1.26072i | ||||||||
\(803\) | 0.105040i | 0.00370677i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 15.9413 | 0.561509 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3656i | 0.364659i | ||||||||
\(809\) | 14.6229 | 0.514114 | 0.257057 | − | 0.966396i | \(-0.417247\pi\) | ||||
0.257057 | + | 0.966396i | \(0.417247\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.7177 | 0.938187 | 0.469093 | − | 0.883149i | \(-0.344581\pi\) | ||||
0.469093 | + | 0.883149i | \(0.344581\pi\) | |||||||
\(812\) | − 2.78254i | − 0.0976480i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.872586 | 0.0305841 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 38.5521i | − 1.34877i | ||||||||
\(818\) | 3.44727i | 0.120531i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5981 | 0.649077 | 0.324538 | − | 0.945873i | \(-0.394791\pi\) | ||||
0.324538 | + | 0.945873i | \(0.394791\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.06204i | 0.106736i | 0.998575 | + | 0.0533680i | \(0.0169957\pi\) | ||||
−0.998575 | + | 0.0533680i | \(0.983004\pi\) | |||||||
\(824\) | 11.3388 | 0.395005 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −40.5750 | −1.41178 | ||||||||
\(827\) | − 7.27526i | − 0.252985i | −0.991968 | − | 0.126493i | \(-0.959628\pi\) | ||||
0.991968 | − | 0.126493i | \(-0.0403720\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.5211 | −0.365411 | −0.182706 | − | 0.983168i | \(-0.558486\pi\) | ||||
−0.182706 | + | 0.983168i | \(0.558486\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 29.3951i | − 1.01909i | ||||||||
\(833\) | 25.9017i | 0.897441i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.188549 | −0.00652109 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 33.6528i | − 1.16252i | ||||||||
\(839\) | 15.1807 | 0.524094 | 0.262047 | − | 0.965055i | \(-0.415602\pi\) | ||||
0.262047 | + | 0.965055i | \(0.415602\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.1739 | −0.385307 | ||||||||
\(842\) | − 17.4961i | − 0.602956i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.78207 | −0.0613413 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 42.2622i | − 1.45215i | ||||||||
\(848\) | − 49.0762i | − 1.68528i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 19.7870 | 0.678290 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 10.4862i | − 0.359040i | −0.983754 | − | 0.179520i | \(-0.942545\pi\) | ||||
0.983754 | − | 0.179520i | \(-0.0574545\pi\) | |||||||
\(854\) | 14.3800 | 0.492074 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.38412 | 0.149846 | ||||||||
\(857\) | 8.84075i | 0.301994i | 0.988534 | + | 0.150997i | \(0.0482484\pi\) | ||||
−0.988534 | + | 0.150997i | \(0.951752\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.06831 | 0.0705699 | 0.0352849 | − | 0.999377i | \(-0.488766\pi\) | ||||
0.0352849 | + | 0.999377i | \(0.488766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.0665i | 0.445048i | ||||||||
\(863\) | − 22.4434i | − 0.763984i | −0.924166 | − | 0.381992i | \(-0.875238\pi\) | ||||
0.924166 | − | 0.381992i | \(-0.124762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.8053 | −0.469122 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1.74834i | − 0.0593426i | ||||||||
\(869\) | −0.791895 | −0.0268632 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −46.0317 | −1.55973 | ||||||||
\(872\) | − 34.7758i | − 1.17766i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −54.4353 | −1.84130 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.8932i | 0.941886i | 0.882164 | + | 0.470943i | \(0.156086\pi\) | ||||
−0.882164 | + | 0.470943i | \(0.843914\pi\) | |||||||
\(878\) | 28.6152i | 0.965715i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.22153 | 0.310681 | 0.155341 | − | 0.987861i | \(-0.450353\pi\) | ||||
0.155341 | + | 0.987861i | \(0.450353\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 49.2436i | − 1.65718i | −0.559858 | − | 0.828589i | \(-0.689144\pi\) | ||||
0.559858 | − | 0.828589i | \(-0.310856\pi\) | |||||||
\(884\) | −2.26704 | −0.0762486 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.0279 | 0.538469 | ||||||||
\(887\) | − 10.7681i | − 0.361556i | −0.983524 | − | 0.180778i | \(-0.942138\pi\) | ||||
0.983524 | − | 0.180778i | \(-0.0578616\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.38965 | 0.214302 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.670187i | 0.0224395i | ||||||||
\(893\) | − 6.07173i | − 0.203183i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −48.4816 | −1.61966 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 1.97437i | − 0.0658854i | ||||||||
\(899\) | 11.2006 | 0.373561 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.1071 | 1.23622 | ||||||||
\(902\) | − 2.16340i | − 0.0720334i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.58233 | 0.119147 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 31.9703i | − 1.06156i | −0.847510 | − | 0.530779i | \(-0.821899\pi\) | ||||
0.847510 | − | 0.530779i | \(-0.178101\pi\) | |||||||
\(908\) | 0.823651i | 0.0273338i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.0802 | 0.333972 | 0.166986 | − | 0.985959i | \(-0.446597\pi\) | ||||
0.166986 | + | 0.985959i | \(0.446597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 1.19213i | − 0.0394539i | ||||||||
\(914\) | 29.6291 | 0.980042 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.21403 | −0.106195 | ||||||||
\(917\) | 50.9428i | 1.68228i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.7976 | 0.982932 | 0.491466 | − | 0.870897i | \(-0.336461\pi\) | ||||
0.491466 | + | 0.870897i | \(0.336461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 49.7272i | − 1.63768i | ||||||||
\(923\) | 34.1868i | 1.12527i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7.72776 | 0.253950 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.06089i | 0.133305i | ||||||||
\(929\) | −12.3855 | −0.406355 | −0.203178 | − | 0.979142i | \(-0.565127\pi\) | ||||
−0.203178 | + | 0.979142i | \(0.565127\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.7590 | 1.10641 | ||||||||
\(932\) | 2.02906i | 0.0664642i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.9379 | −0.685108 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 44.4280i | − 1.45140i | −0.688012 | − | 0.725699i | \(-0.741516\pi\) | ||||
0.688012 | − | 0.725699i | \(-0.258484\pi\) | |||||||
\(938\) | 64.2754i | 2.09867i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.3323 | −0.499820 | −0.249910 | − | 0.968269i | \(-0.580401\pi\) | ||||
−0.249910 | + | 0.968269i | \(0.580401\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 49.0579i | − 1.59755i | ||||||||
\(944\) | 30.7189 | 0.999816 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.47894 | −0.113110 | ||||||||
\(947\) | 21.6997i | 0.705144i | 0.935785 | + | 0.352572i | \(0.114693\pi\) | ||||
−0.935785 | + | 0.352572i | \(0.885307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.64607 | 0.0534338 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 33.9713i | − 1.10102i | ||||||||
\(953\) | − 36.9099i | − 1.19563i | −0.801634 | − | 0.597815i | \(-0.796036\pi\) | ||||
0.801634 | − | 0.597815i | \(-0.203964\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.68737 | 0.119258 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 30.1772i | − 0.974980i | ||||||||
\(959\) | 78.4486 | 2.53324 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9624 | −0.772980 | ||||||||
\(962\) | − 13.6743i | − 0.440876i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.664581 | −0.0214047 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.3382i | 0.686190i | 0.939301 | + | 0.343095i | \(0.111475\pi\) | ||||
−0.939301 | + | 0.343095i | \(0.888525\pi\) | |||||||
\(968\) | 29.4663i | 0.947081i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5851 | 1.36662 | 0.683311 | − | 0.730128i | \(-0.260540\pi\) | ||||
0.683311 | + | 0.730128i | \(0.260540\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 11.8635i | − 0.380325i | ||||||||
\(974\) | 46.1946 | 1.48017 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8870 | −0.348484 | ||||||||
\(977\) | 48.9392i | 1.56570i | 0.622209 | + | 0.782852i | \(0.286236\pi\) | ||||
−0.622209 | + | 0.782852i | \(0.713764\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.86820 | −0.0597080 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 15.3102i | − 0.488567i | ||||||||
\(983\) | 36.1089i | 1.15170i | 0.817557 | + | 0.575848i | \(0.195328\pi\) | ||||
−0.817557 | + | 0.575848i | \(0.804672\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −20.2797 | −0.645836 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.95474i | 0.0940028i | ||||||||
\(989\) | −78.8896 | −2.50854 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0054 | 1.01669 | 0.508343 | − | 0.861155i | \(-0.330258\pi\) | ||||
0.508343 | + | 0.861155i | \(0.330258\pi\) | |||||||
\(992\) | 2.55156i | 0.0810121i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 47.7360 | 1.51410 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 51.7680i | 1.63951i | 0.572716 | + | 0.819754i | \(0.305890\pi\) | ||||
−0.572716 | + | 0.819754i | \(0.694110\pi\) | |||||||
\(998\) | − 5.63624i | − 0.178412i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2025.2.b.o.649.3 | 8 | ||
3.2 | odd | 2 | 2025.2.b.n.649.6 | 8 | |||
5.2 | odd | 4 | 2025.2.a.z.1.3 | 4 | |||
5.3 | odd | 4 | 2025.2.a.p.1.2 | 4 | |||
5.4 | even | 2 | inner | 2025.2.b.o.649.6 | 8 | ||
9.2 | odd | 6 | 225.2.k.c.49.6 | 16 | |||
9.4 | even | 3 | 675.2.k.c.424.6 | 16 | |||
9.5 | odd | 6 | 225.2.k.c.124.3 | 16 | |||
9.7 | even | 3 | 675.2.k.c.199.3 | 16 | |||
15.2 | even | 4 | 2025.2.a.q.1.2 | 4 | |||
15.8 | even | 4 | 2025.2.a.y.1.3 | 4 | |||
15.14 | odd | 2 | 2025.2.b.n.649.3 | 8 | |||
45.2 | even | 12 | 225.2.e.e.76.3 | yes | 8 | ||
45.4 | even | 6 | 675.2.k.c.424.3 | 16 | |||
45.7 | odd | 12 | 675.2.e.c.226.2 | 8 | |||
45.13 | odd | 12 | 675.2.e.e.451.3 | 8 | |||
45.14 | odd | 6 | 225.2.k.c.124.6 | 16 | |||
45.22 | odd | 12 | 675.2.e.c.451.2 | 8 | |||
45.23 | even | 12 | 225.2.e.c.151.2 | yes | 8 | ||
45.29 | odd | 6 | 225.2.k.c.49.3 | 16 | |||
45.32 | even | 12 | 225.2.e.e.151.3 | yes | 8 | ||
45.34 | even | 6 | 675.2.k.c.199.6 | 16 | |||
45.38 | even | 12 | 225.2.e.c.76.2 | ✓ | 8 | ||
45.43 | odd | 12 | 675.2.e.e.226.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.2 | ✓ | 8 | 45.38 | even | 12 | ||
225.2.e.c.151.2 | yes | 8 | 45.23 | even | 12 | ||
225.2.e.e.76.3 | yes | 8 | 45.2 | even | 12 | ||
225.2.e.e.151.3 | yes | 8 | 45.32 | even | 12 | ||
225.2.k.c.49.3 | 16 | 45.29 | odd | 6 | |||
225.2.k.c.49.6 | 16 | 9.2 | odd | 6 | |||
225.2.k.c.124.3 | 16 | 9.5 | odd | 6 | |||
225.2.k.c.124.6 | 16 | 45.14 | odd | 6 | |||
675.2.e.c.226.2 | 8 | 45.7 | odd | 12 | |||
675.2.e.c.451.2 | 8 | 45.22 | odd | 12 | |||
675.2.e.e.226.3 | 8 | 45.43 | odd | 12 | |||
675.2.e.e.451.3 | 8 | 45.13 | odd | 12 | |||
675.2.k.c.199.3 | 16 | 9.7 | even | 3 | |||
675.2.k.c.199.6 | 16 | 45.34 | even | 6 | |||
675.2.k.c.424.3 | 16 | 45.4 | even | 6 | |||
675.2.k.c.424.6 | 16 | 9.4 | even | 3 | |||
2025.2.a.p.1.2 | 4 | 5.3 | odd | 4 | |||
2025.2.a.q.1.2 | 4 | 15.2 | even | 4 | |||
2025.2.a.y.1.3 | 4 | 15.8 | even | 4 | |||
2025.2.a.z.1.3 | 4 | 5.2 | odd | 4 | |||
2025.2.b.n.649.3 | 8 | 15.14 | odd | 2 | |||
2025.2.b.n.649.6 | 8 | 3.2 | odd | 2 | |||
2025.2.b.o.649.3 | 8 | 1.1 | even | 1 | trivial | ||
2025.2.b.o.649.6 | 8 | 5.4 | even | 2 | inner |