Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
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: | yes |
Analytic conductor: | \(6.58765816676\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.148.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.311108\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.311108 | −0.219986 | −0.109993 | − | 0.993932i | \(-0.535083\pi\) | ||||
−0.109993 | + | 0.993932i | \(0.535083\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.90321 | −0.951606 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.311108 | 0.127009 | ||||||||
\(7\) | 0.903212 | 0.341382 | 0.170691 | − | 0.985325i | \(-0.445400\pi\) | ||||
0.170691 | + | 0.985325i | \(0.445400\pi\) | |||||||
\(8\) | 1.21432 | 0.429327 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.90321 | 0.549410 | ||||||||
\(13\) | −2.90321 | −0.805206 | −0.402603 | − | 0.915375i | \(-0.631894\pi\) | ||||
−0.402603 | + | 0.915375i | \(0.631894\pi\) | |||||||
\(14\) | −0.280996 | −0.0750994 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.42864 | 0.857160 | ||||||||
\(17\) | −2.28100 | −0.553223 | −0.276611 | − | 0.960982i | \(-0.589211\pi\) | ||||
−0.276611 | + | 0.960982i | \(0.589211\pi\) | |||||||
\(18\) | −0.311108 | −0.0733288 | ||||||||
\(19\) | 2.42864 | 0.557168 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.903212 | −0.197097 | ||||||||
\(22\) | −0.311108 | −0.0663284 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | −1.21432 | −0.247872 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.903212 | 0.177134 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.71900 | −0.324861 | ||||||||
\(29\) | 7.05086 | 1.30931 | 0.654655 | − | 0.755927i | \(-0.272814\pi\) | ||||
0.654655 | + | 0.755927i | \(0.272814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62222 | −0.470964 | −0.235482 | − | 0.971879i | \(-0.575667\pi\) | ||||
−0.235482 | + | 0.971879i | \(0.575667\pi\) | |||||||
\(32\) | −3.49532 | −0.617890 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.709636 | 0.121702 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.90321 | −0.317202 | ||||||||
\(37\) | −5.80642 | −0.954570 | −0.477285 | − | 0.878749i | \(-0.658379\pi\) | ||||
−0.477285 | + | 0.878749i | \(0.658379\pi\) | |||||||
\(38\) | −0.755569 | −0.122569 | ||||||||
\(39\) | 2.90321 | 0.464886 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.6637 | −1.66539 | −0.832695 | − | 0.553731i | \(-0.813203\pi\) | ||||
−0.832695 | + | 0.553731i | \(0.813203\pi\) | |||||||
\(42\) | 0.280996 | 0.0433587 | ||||||||
\(43\) | −10.7096 | −1.63320 | −0.816602 | − | 0.577201i | \(-0.804145\pi\) | ||||
−0.816602 | + | 0.577201i | \(0.804145\pi\) | |||||||
\(44\) | −1.90321 | −0.286920 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.24443 | 0.183481 | ||||||||
\(47\) | −0.949145 | −0.138447 | −0.0692235 | − | 0.997601i | \(-0.522052\pi\) | ||||
−0.0692235 | + | 0.997601i | \(0.522052\pi\) | |||||||
\(48\) | −3.42864 | −0.494881 | ||||||||
\(49\) | −6.18421 | −0.883458 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.28100 | 0.319403 | ||||||||
\(52\) | 5.52543 | 0.766239 | ||||||||
\(53\) | −0.815792 | −0.112058 | −0.0560288 | − | 0.998429i | \(-0.517844\pi\) | ||||
−0.0560288 | + | 0.998429i | \(0.517844\pi\) | |||||||
\(54\) | 0.311108 | 0.0423364 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.09679 | 0.146564 | ||||||||
\(57\) | −2.42864 | −0.321681 | ||||||||
\(58\) | −2.19358 | −0.288031 | ||||||||
\(59\) | −1.67307 | −0.217815 | −0.108908 | − | 0.994052i | \(-0.534735\pi\) | ||||
−0.108908 | + | 0.994052i | \(0.534735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.24443 | −0.927554 | −0.463777 | − | 0.885952i | \(-0.653506\pi\) | ||||
−0.463777 | + | 0.885952i | \(0.653506\pi\) | |||||||
\(62\) | 0.815792 | 0.103606 | ||||||||
\(63\) | 0.903212 | 0.113794 | ||||||||
\(64\) | −5.76986 | −0.721232 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.311108 | 0.0382947 | ||||||||
\(67\) | −12.8573 | −1.57077 | −0.785383 | − | 0.619010i | \(-0.787534\pi\) | ||||
−0.785383 | + | 0.619010i | \(0.787534\pi\) | |||||||
\(68\) | 4.34122 | 0.526450 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.28592 | 1.10204 | 0.551018 | − | 0.834493i | \(-0.314240\pi\) | ||||
0.551018 | + | 0.834493i | \(0.314240\pi\) | |||||||
\(72\) | 1.21432 | 0.143109 | ||||||||
\(73\) | 5.65878 | 0.662310 | 0.331155 | − | 0.943576i | \(-0.392562\pi\) | ||||
0.331155 | + | 0.943576i | \(0.392562\pi\) | |||||||
\(74\) | 1.80642 | 0.209993 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.62222 | −0.530204 | ||||||||
\(77\) | 0.903212 | 0.102931 | ||||||||
\(78\) | −0.903212 | −0.102269 | ||||||||
\(79\) | −16.5303 | −1.85981 | −0.929905 | − | 0.367800i | \(-0.880111\pi\) | ||||
−0.929905 | + | 0.367800i | \(0.880111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.31756 | 0.366363 | ||||||||
\(83\) | −7.76049 | −0.851825 | −0.425912 | − | 0.904764i | \(-0.640047\pi\) | ||||
−0.425912 | + | 0.904764i | \(0.640047\pi\) | |||||||
\(84\) | 1.71900 | 0.187559 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.33185 | 0.359283 | ||||||||
\(87\) | −7.05086 | −0.755931 | ||||||||
\(88\) | 1.21432 | 0.129447 | ||||||||
\(89\) | 6.13335 | 0.650134 | 0.325067 | − | 0.945691i | \(-0.394613\pi\) | ||||
0.325067 | + | 0.945691i | \(0.394613\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.62222 | −0.274883 | ||||||||
\(92\) | 7.61285 | 0.793694 | ||||||||
\(93\) | 2.62222 | 0.271911 | ||||||||
\(94\) | 0.295286 | 0.0304565 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.49532 | 0.356739 | ||||||||
\(97\) | 12.4701 | 1.26615 | 0.633075 | − | 0.774091i | \(-0.281793\pi\) | ||||
0.633075 | + | 0.774091i | \(0.281793\pi\) | |||||||
\(98\) | 1.92396 | 0.194349 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.1748 | 1.60946 | 0.804728 | − | 0.593643i | \(-0.202311\pi\) | ||||
0.804728 | + | 0.593643i | \(0.202311\pi\) | |||||||
\(102\) | −0.709636 | −0.0702644 | ||||||||
\(103\) | 17.1526 | 1.69009 | 0.845046 | − | 0.534693i | \(-0.179573\pi\) | ||||
0.845046 | + | 0.534693i | \(0.179573\pi\) | |||||||
\(104\) | −3.52543 | −0.345697 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.253799 | 0.0246512 | ||||||||
\(107\) | 13.5669 | 1.31156 | 0.655782 | − | 0.754951i | \(-0.272339\pi\) | ||||
0.655782 | + | 0.754951i | \(0.272339\pi\) | |||||||
\(108\) | 1.90321 | 0.183137 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.80642 | 0.551121 | ||||||||
\(112\) | 3.09679 | 0.292619 | ||||||||
\(113\) | −14.2351 | −1.33912 | −0.669561 | − | 0.742757i | \(-0.733518\pi\) | ||||
−0.669561 | + | 0.742757i | \(0.733518\pi\) | |||||||
\(114\) | 0.755569 | 0.0707655 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −13.4193 | −1.24595 | ||||||||
\(117\) | −2.90321 | −0.268402 | ||||||||
\(118\) | 0.520505 | 0.0479164 | ||||||||
\(119\) | −2.06022 | −0.188860 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.25380 | 0.204049 | ||||||||
\(123\) | 10.6637 | 0.961514 | ||||||||
\(124\) | 4.99063 | 0.448172 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.280996 | −0.0250331 | ||||||||
\(127\) | −11.0049 | −0.976529 | −0.488264 | − | 0.872696i | \(-0.662370\pi\) | ||||
−0.488264 | + | 0.872696i | \(0.662370\pi\) | |||||||
\(128\) | 8.78568 | 0.776552 | ||||||||
\(129\) | 10.7096 | 0.942931 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.24443 | 0.108726 | 0.0543632 | − | 0.998521i | \(-0.482687\pi\) | ||||
0.0543632 | + | 0.998521i | \(0.482687\pi\) | |||||||
\(132\) | 1.90321 | 0.165653 | ||||||||
\(133\) | 2.19358 | 0.190207 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.76986 | −0.237513 | ||||||||
\(137\) | 4.42864 | 0.378364 | 0.189182 | − | 0.981942i | \(-0.439416\pi\) | ||||
0.189182 | + | 0.981942i | \(0.439416\pi\) | |||||||
\(138\) | −1.24443 | −0.105933 | ||||||||
\(139\) | 0.917502 | 0.0778215 | 0.0389108 | − | 0.999243i | \(-0.487611\pi\) | ||||
0.0389108 | + | 0.999243i | \(0.487611\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.949145 | 0.0799324 | ||||||||
\(142\) | −2.88892 | −0.242433 | ||||||||
\(143\) | −2.90321 | −0.242779 | ||||||||
\(144\) | 3.42864 | 0.285720 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1.76049 | −0.145699 | ||||||||
\(147\) | 6.18421 | 0.510065 | ||||||||
\(148\) | 11.0509 | 0.908375 | ||||||||
\(149\) | 2.19358 | 0.179705 | 0.0898524 | − | 0.995955i | \(-0.471360\pi\) | ||||
0.0898524 | + | 0.995955i | \(0.471360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.4286 | −0.848671 | −0.424335 | − | 0.905505i | \(-0.639492\pi\) | ||||
−0.424335 | + | 0.905505i | \(0.639492\pi\) | |||||||
\(152\) | 2.94914 | 0.239207 | ||||||||
\(153\) | −2.28100 | −0.184408 | ||||||||
\(154\) | −0.280996 | −0.0226433 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −5.52543 | −0.442388 | ||||||||
\(157\) | −5.80642 | −0.463403 | −0.231702 | − | 0.972787i | \(-0.574429\pi\) | ||||
−0.231702 | + | 0.972787i | \(0.574429\pi\) | |||||||
\(158\) | 5.14272 | 0.409133 | ||||||||
\(159\) | 0.815792 | 0.0646965 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.61285 | −0.284732 | ||||||||
\(162\) | −0.311108 | −0.0244429 | ||||||||
\(163\) | −11.0509 | −0.865570 | −0.432785 | − | 0.901497i | \(-0.642469\pi\) | ||||
−0.432785 | + | 0.901497i | \(0.642469\pi\) | |||||||
\(164\) | 20.2953 | 1.58480 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.41435 | 0.187390 | ||||||||
\(167\) | −13.9541 | −1.07980 | −0.539899 | − | 0.841730i | \(-0.681538\pi\) | ||||
−0.539899 | + | 0.841730i | \(0.681538\pi\) | |||||||
\(168\) | −1.09679 | −0.0846190 | ||||||||
\(169\) | −4.57136 | −0.351643 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.42864 | 0.185723 | ||||||||
\(172\) | 20.3827 | 1.55417 | ||||||||
\(173\) | 18.8430 | 1.43261 | 0.716303 | − | 0.697789i | \(-0.245833\pi\) | ||||
0.716303 | + | 0.697789i | \(0.245833\pi\) | |||||||
\(174\) | 2.19358 | 0.166295 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.42864 | 0.258443 | ||||||||
\(177\) | 1.67307 | 0.125756 | ||||||||
\(178\) | −1.90813 | −0.143021 | ||||||||
\(179\) | 4.85728 | 0.363050 | 0.181525 | − | 0.983386i | \(-0.441897\pi\) | ||||
0.181525 | + | 0.983386i | \(0.441897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7971 | −1.24852 | −0.624258 | − | 0.781219i | \(-0.714598\pi\) | ||||
−0.624258 | + | 0.781219i | \(0.714598\pi\) | |||||||
\(182\) | 0.815792 | 0.0604705 | ||||||||
\(183\) | 7.24443 | 0.535524 | ||||||||
\(184\) | −4.85728 | −0.358083 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.815792 | −0.0598168 | ||||||||
\(187\) | −2.28100 | −0.166803 | ||||||||
\(188\) | 1.80642 | 0.131747 | ||||||||
\(189\) | −0.903212 | −0.0656990 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.8573 | 1.21975 | 0.609875 | − | 0.792498i | \(-0.291220\pi\) | ||||
0.609875 | + | 0.792498i | \(0.291220\pi\) | |||||||
\(192\) | 5.76986 | 0.416404 | ||||||||
\(193\) | 24.6178 | 1.77203 | 0.886013 | − | 0.463661i | \(-0.153464\pi\) | ||||
0.886013 | + | 0.463661i | \(0.153464\pi\) | |||||||
\(194\) | −3.87955 | −0.278536 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.7699 | 0.840704 | ||||||||
\(197\) | −14.8716 | −1.05956 | −0.529778 | − | 0.848137i | \(-0.677725\pi\) | ||||
−0.529778 | + | 0.848137i | \(0.677725\pi\) | |||||||
\(198\) | −0.311108 | −0.0221095 | ||||||||
\(199\) | −11.2257 | −0.795768 | −0.397884 | − | 0.917436i | \(-0.630255\pi\) | ||||
−0.397884 | + | 0.917436i | \(0.630255\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 12.8573 | 0.906883 | ||||||||
\(202\) | −5.03212 | −0.354059 | ||||||||
\(203\) | 6.36842 | 0.446975 | ||||||||
\(204\) | −4.34122 | −0.303946 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.33630 | −0.371797 | ||||||||
\(207\) | −4.00000 | −0.278019 | ||||||||
\(208\) | −9.95407 | −0.690190 | ||||||||
\(209\) | 2.42864 | 0.167993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9398 | −0.821968 | −0.410984 | − | 0.911643i | \(-0.634815\pi\) | ||||
−0.410984 | + | 0.911643i | \(0.634815\pi\) | |||||||
\(212\) | 1.55262 | 0.106635 | ||||||||
\(213\) | −9.28592 | −0.636261 | ||||||||
\(214\) | −4.22077 | −0.288526 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.21432 | −0.0826240 | ||||||||
\(217\) | −2.36842 | −0.160779 | ||||||||
\(218\) | 3.11108 | 0.210709 | ||||||||
\(219\) | −5.65878 | −0.382385 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.62222 | 0.445458 | ||||||||
\(222\) | −1.80642 | −0.121239 | ||||||||
\(223\) | −21.8064 | −1.46027 | −0.730133 | − | 0.683305i | \(-0.760542\pi\) | ||||
−0.730133 | + | 0.683305i | \(0.760542\pi\) | |||||||
\(224\) | −3.15701 | −0.210937 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.42864 | 0.294589 | ||||||||
\(227\) | −3.19850 | −0.212292 | −0.106146 | − | 0.994351i | \(-0.533851\pi\) | ||||
−0.106146 | + | 0.994351i | \(0.533851\pi\) | |||||||
\(228\) | 4.62222 | 0.306114 | ||||||||
\(229\) | 7.12399 | 0.470766 | 0.235383 | − | 0.971903i | \(-0.424366\pi\) | ||||
0.235383 | + | 0.971903i | \(0.424366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.903212 | −0.0594270 | ||||||||
\(232\) | 8.56199 | 0.562122 | ||||||||
\(233\) | 19.5254 | 1.27915 | 0.639577 | − | 0.768727i | \(-0.279110\pi\) | ||||
0.639577 | + | 0.768727i | \(0.279110\pi\) | |||||||
\(234\) | 0.903212 | 0.0590448 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.18421 | 0.207274 | ||||||||
\(237\) | 16.5303 | 1.07376 | ||||||||
\(238\) | 0.640951 | 0.0415467 | ||||||||
\(239\) | −21.9813 | −1.42185 | −0.710925 | − | 0.703268i | \(-0.751723\pi\) | ||||
−0.710925 | + | 0.703268i | \(0.751723\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.34614 | 0.344375 | 0.172188 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172188 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(242\) | −0.311108 | −0.0199988 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 13.7877 | 0.882666 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.31756 | −0.211520 | ||||||||
\(247\) | −7.05086 | −0.448635 | ||||||||
\(248\) | −3.18421 | −0.202197 | ||||||||
\(249\) | 7.76049 | 0.491801 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.7748 | −1.50065 | −0.750325 | − | 0.661069i | \(-0.770103\pi\) | ||||
−0.750325 | + | 0.661069i | \(0.770103\pi\) | |||||||
\(252\) | −1.71900 | −0.108287 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 3.42372 | 0.214823 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.80642 | 0.550401 | ||||||||
\(257\) | 8.13335 | 0.507345 | 0.253672 | − | 0.967290i | \(-0.418362\pi\) | ||||
0.253672 | + | 0.967290i | \(0.418362\pi\) | |||||||
\(258\) | −3.33185 | −0.207432 | ||||||||
\(259\) | −5.24443 | −0.325873 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.05086 | 0.436437 | ||||||||
\(262\) | −0.387152 | −0.0239183 | ||||||||
\(263\) | −22.9032 | −1.41227 | −0.706136 | − | 0.708076i | \(-0.749563\pi\) | ||||
−0.706136 | + | 0.708076i | \(0.749563\pi\) | |||||||
\(264\) | −1.21432 | −0.0747362 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −0.682439 | −0.0418430 | ||||||||
\(267\) | −6.13335 | −0.375355 | ||||||||
\(268\) | 24.4701 | 1.49475 | ||||||||
\(269\) | 11.8350 | 0.721593 | 0.360796 | − | 0.932645i | \(-0.382505\pi\) | ||||
0.360796 | + | 0.932645i | \(0.382505\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.8988 | 0.905036 | 0.452518 | − | 0.891755i | \(-0.350526\pi\) | ||||
0.452518 | + | 0.891755i | \(0.350526\pi\) | |||||||
\(272\) | −7.82071 | −0.474200 | ||||||||
\(273\) | 2.62222 | 0.158704 | ||||||||
\(274\) | −1.37778 | −0.0832350 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −7.61285 | −0.458240 | ||||||||
\(277\) | 27.6686 | 1.66245 | 0.831223 | − | 0.555939i | \(-0.187641\pi\) | ||||
0.831223 | + | 0.555939i | \(0.187641\pi\) | |||||||
\(278\) | −0.285442 | −0.0171197 | ||||||||
\(279\) | −2.62222 | −0.156988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.80642 | 0.585002 | 0.292501 | − | 0.956265i | \(-0.405512\pi\) | ||||
0.292501 | + | 0.956265i | \(0.405512\pi\) | |||||||
\(282\) | −0.295286 | −0.0175840 | ||||||||
\(283\) | 19.0049 | 1.12973 | 0.564863 | − | 0.825185i | \(-0.308929\pi\) | ||||
0.564863 | + | 0.825185i | \(0.308929\pi\) | |||||||
\(284\) | −17.6731 | −1.04870 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.903212 | 0.0534080 | ||||||||
\(287\) | −9.63158 | −0.568534 | ||||||||
\(288\) | −3.49532 | −0.205963 | ||||||||
\(289\) | −11.7971 | −0.693944 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.4701 | −0.731012 | ||||||||
\(292\) | −10.7699 | −0.630258 | ||||||||
\(293\) | 30.7511 | 1.79650 | 0.898250 | − | 0.439485i | \(-0.144839\pi\) | ||||
0.898250 | + | 0.439485i | \(0.144839\pi\) | |||||||
\(294\) | −1.92396 | −0.112207 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.05086 | −0.409823 | ||||||||
\(297\) | −1.00000 | −0.0580259 | ||||||||
\(298\) | −0.682439 | −0.0395326 | ||||||||
\(299\) | 11.6128 | 0.671588 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.67307 | −0.557547 | ||||||||
\(302\) | 3.24443 | 0.186696 | ||||||||
\(303\) | −16.1748 | −0.929220 | ||||||||
\(304\) | 8.32693 | 0.477582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.709636 | 0.0405672 | ||||||||
\(307\) | 13.4938 | 0.770131 | 0.385065 | − | 0.922889i | \(-0.374179\pi\) | ||||
0.385065 | + | 0.922889i | \(0.374179\pi\) | |||||||
\(308\) | −1.71900 | −0.0979493 | ||||||||
\(309\) | −17.1526 | −0.975775 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.5526 | −0.995318 | −0.497659 | − | 0.867373i | \(-0.665807\pi\) | ||||
−0.497659 | + | 0.867373i | \(0.665807\pi\) | |||||||
\(312\) | 3.52543 | 0.199588 | ||||||||
\(313\) | −14.3970 | −0.813766 | −0.406883 | − | 0.913480i | \(-0.633384\pi\) | ||||
−0.406883 | + | 0.913480i | \(0.633384\pi\) | |||||||
\(314\) | 1.80642 | 0.101942 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 31.4608 | 1.76981 | ||||||||
\(317\) | −29.4608 | −1.65468 | −0.827341 | − | 0.561701i | \(-0.810147\pi\) | ||||
−0.827341 | + | 0.561701i | \(0.810147\pi\) | |||||||
\(318\) | −0.253799 | −0.0142324 | ||||||||
\(319\) | 7.05086 | 0.394772 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −13.5669 | −0.757231 | ||||||||
\(322\) | 1.12399 | 0.0626372 | ||||||||
\(323\) | −5.53972 | −0.308238 | ||||||||
\(324\) | −1.90321 | −0.105734 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.43801 | 0.190414 | ||||||||
\(327\) | 10.0000 | 0.553001 | ||||||||
\(328\) | −12.9491 | −0.714997 | ||||||||
\(329\) | −0.857279 | −0.0472633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.62222 | −0.144130 | −0.0720650 | − | 0.997400i | \(-0.522959\pi\) | ||||
−0.0720650 | + | 0.997400i | \(0.522959\pi\) | |||||||
\(332\) | 14.7699 | 0.810601 | ||||||||
\(333\) | −5.80642 | −0.318190 | ||||||||
\(334\) | 4.34122 | 0.237541 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.09679 | −0.168944 | ||||||||
\(337\) | 5.00492 | 0.272635 | 0.136318 | − | 0.990665i | \(-0.456473\pi\) | ||||
0.136318 | + | 0.990665i | \(0.456473\pi\) | |||||||
\(338\) | 1.42219 | 0.0773567 | ||||||||
\(339\) | 14.2351 | 0.773143 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.62222 | −0.142001 | ||||||||
\(342\) | −0.755569 | −0.0408565 | ||||||||
\(343\) | −11.9081 | −0.642979 | ||||||||
\(344\) | −13.0049 | −0.701178 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.86220 | −0.315154 | ||||||||
\(347\) | 22.8113 | 1.22458 | 0.612289 | − | 0.790634i | \(-0.290249\pi\) | ||||
0.612289 | + | 0.790634i | \(0.290249\pi\) | |||||||
\(348\) | 13.4193 | 0.719348 | ||||||||
\(349\) | 21.2257 | 1.13619 | 0.568093 | − | 0.822965i | \(-0.307681\pi\) | ||||
0.568093 | + | 0.822965i | \(0.307681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.90321 | 0.154962 | ||||||||
\(352\) | −3.49532 | −0.186301 | ||||||||
\(353\) | −7.18421 | −0.382377 | −0.191188 | − | 0.981553i | \(-0.561234\pi\) | ||||
−0.191188 | + | 0.981553i | \(0.561234\pi\) | |||||||
\(354\) | −0.520505 | −0.0276645 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −11.6731 | −0.618672 | ||||||||
\(357\) | 2.06022 | 0.109039 | ||||||||
\(358\) | −1.51114 | −0.0798661 | ||||||||
\(359\) | −14.1017 | −0.744260 | −0.372130 | − | 0.928181i | \(-0.621372\pi\) | ||||
−0.372130 | + | 0.928181i | \(0.621372\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1017 | −0.689564 | ||||||||
\(362\) | 5.22570 | 0.274656 | ||||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 4.99063 | 0.261580 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.25380 | −0.117808 | ||||||||
\(367\) | 3.90813 | 0.204003 | 0.102001 | − | 0.994784i | \(-0.467475\pi\) | ||||
0.102001 | + | 0.994784i | \(0.467475\pi\) | |||||||
\(368\) | −13.7146 | −0.714921 | ||||||||
\(369\) | −10.6637 | −0.555130 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.736833 | −0.0382545 | ||||||||
\(372\) | −4.99063 | −0.258752 | ||||||||
\(373\) | −12.9763 | −0.671890 | −0.335945 | − | 0.941882i | \(-0.609056\pi\) | ||||
−0.335945 | + | 0.941882i | \(0.609056\pi\) | |||||||
\(374\) | 0.709636 | 0.0366944 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.15257 | −0.0594390 | ||||||||
\(377\) | −20.4701 | −1.05427 | ||||||||
\(378\) | 0.280996 | 0.0144529 | ||||||||
\(379\) | 36.0830 | 1.85346 | 0.926729 | − | 0.375731i | \(-0.122608\pi\) | ||||
0.926729 | + | 0.375731i | \(0.122608\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0049 | 0.563799 | ||||||||
\(382\) | −5.24443 | −0.268328 | ||||||||
\(383\) | −20.2953 | −1.03704 | −0.518520 | − | 0.855065i | \(-0.673517\pi\) | ||||
−0.518520 | + | 0.855065i | \(0.673517\pi\) | |||||||
\(384\) | −8.78568 | −0.448342 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.65878 | −0.389822 | ||||||||
\(387\) | −10.7096 | −0.544401 | ||||||||
\(388\) | −23.7333 | −1.20488 | ||||||||
\(389\) | 30.4701 | 1.54490 | 0.772448 | − | 0.635078i | \(-0.219032\pi\) | ||||
0.772448 | + | 0.635078i | \(0.219032\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.12399 | 0.461420 | ||||||||
\(392\) | −7.50961 | −0.379292 | ||||||||
\(393\) | −1.24443 | −0.0627733 | ||||||||
\(394\) | 4.62666 | 0.233088 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.90321 | −0.0956400 | ||||||||
\(397\) | −4.97773 | −0.249825 | −0.124912 | − | 0.992168i | \(-0.539865\pi\) | ||||
−0.124912 | + | 0.992168i | \(0.539865\pi\) | |||||||
\(398\) | 3.49240 | 0.175058 | ||||||||
\(399\) | −2.19358 | −0.109816 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.86665 | −0.0932159 | −0.0466079 | − | 0.998913i | \(-0.514841\pi\) | ||||
−0.0466079 | + | 0.998913i | \(0.514841\pi\) | |||||||
\(402\) | −4.00000 | −0.199502 | ||||||||
\(403\) | 7.61285 | 0.379223 | ||||||||
\(404\) | −30.7841 | −1.53157 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.98126 | −0.0983285 | ||||||||
\(407\) | −5.80642 | −0.287814 | ||||||||
\(408\) | 2.76986 | 0.137128 | ||||||||
\(409\) | −3.63158 | −0.179570 | −0.0897851 | − | 0.995961i | \(-0.528618\pi\) | ||||
−0.0897851 | + | 0.995961i | \(0.528618\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.42864 | −0.218449 | ||||||||
\(412\) | −32.6450 | −1.60830 | ||||||||
\(413\) | −1.51114 | −0.0743582 | ||||||||
\(414\) | 1.24443 | 0.0611605 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.1476 | 0.497529 | ||||||||
\(417\) | −0.917502 | −0.0449303 | ||||||||
\(418\) | −0.755569 | −0.0369561 | ||||||||
\(419\) | 4.85728 | 0.237294 | 0.118647 | − | 0.992937i | \(-0.462144\pi\) | ||||
0.118647 | + | 0.992937i | \(0.462144\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.6321 | 1.10302 | 0.551510 | − | 0.834169i | \(-0.314052\pi\) | ||||
0.551510 | + | 0.834169i | \(0.314052\pi\) | |||||||
\(422\) | 3.71456 | 0.180822 | ||||||||
\(423\) | −0.949145 | −0.0461490 | ||||||||
\(424\) | −0.990632 | −0.0481093 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.88892 | 0.139969 | ||||||||
\(427\) | −6.54326 | −0.316650 | ||||||||
\(428\) | −25.8207 | −1.24809 | ||||||||
\(429\) | 2.90321 | 0.140168 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.24443 | 0.0599421 | 0.0299711 | − | 0.999551i | \(-0.490458\pi\) | ||||
0.0299711 | + | 0.999551i | \(0.490458\pi\) | |||||||
\(432\) | −3.42864 | −0.164960 | ||||||||
\(433\) | 16.0000 | 0.768911 | 0.384455 | − | 0.923144i | \(-0.374389\pi\) | ||||
0.384455 | + | 0.923144i | \(0.374389\pi\) | |||||||
\(434\) | 0.736833 | 0.0353691 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.0321 | 0.911473 | ||||||||
\(437\) | −9.71456 | −0.464710 | ||||||||
\(438\) | 1.76049 | 0.0841195 | ||||||||
\(439\) | −2.42864 | −0.115913 | −0.0579563 | − | 0.998319i | \(-0.518458\pi\) | ||||
−0.0579563 | + | 0.998319i | \(0.518458\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.18421 | −0.294486 | ||||||||
\(442\) | −2.06022 | −0.0979948 | ||||||||
\(443\) | −31.0509 | −1.47527 | −0.737635 | − | 0.675199i | \(-0.764058\pi\) | ||||
−0.737635 | + | 0.675199i | \(0.764058\pi\) | |||||||
\(444\) | −11.0509 | −0.524450 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.78415 | 0.321239 | ||||||||
\(447\) | −2.19358 | −0.103753 | ||||||||
\(448\) | −5.21141 | −0.246216 | ||||||||
\(449\) | −37.3590 | −1.76308 | −0.881541 | − | 0.472107i | \(-0.843494\pi\) | ||||
−0.881541 | + | 0.472107i | \(0.843494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.6637 | −0.502134 | ||||||||
\(452\) | 27.0923 | 1.27432 | ||||||||
\(453\) | 10.4286 | 0.489980 | ||||||||
\(454\) | 0.995078 | 0.0467013 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.94914 | −0.138106 | ||||||||
\(457\) | −8.73822 | −0.408757 | −0.204378 | − | 0.978892i | \(-0.565517\pi\) | ||||
−0.204378 | + | 0.978892i | \(0.565517\pi\) | |||||||
\(458\) | −2.21633 | −0.103562 | ||||||||
\(459\) | 2.28100 | 0.106468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.7877 | 1.48050 | 0.740250 | − | 0.672332i | \(-0.234707\pi\) | ||||
0.740250 | + | 0.672332i | \(0.234707\pi\) | |||||||
\(462\) | 0.280996 | 0.0130731 | ||||||||
\(463\) | −12.0919 | −0.561957 | −0.280978 | − | 0.959714i | \(-0.590659\pi\) | ||||
−0.280978 | + | 0.959714i | \(0.590659\pi\) | |||||||
\(464\) | 24.1748 | 1.12229 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.07451 | −0.281396 | ||||||||
\(467\) | 15.3461 | 0.710135 | 0.355067 | − | 0.934841i | \(-0.384458\pi\) | ||||
0.355067 | + | 0.934841i | \(0.384458\pi\) | |||||||
\(468\) | 5.52543 | 0.255413 | ||||||||
\(469\) | −11.6128 | −0.536231 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.80642 | 0.267546 | ||||||||
\(472\) | −2.03164 | −0.0935139 | ||||||||
\(473\) | −10.7096 | −0.492430 | ||||||||
\(474\) | −5.14272 | −0.236213 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.92104 | 0.179721 | ||||||||
\(477\) | −0.815792 | −0.0373525 | ||||||||
\(478\) | 6.83854 | 0.312788 | ||||||||
\(479\) | 5.89829 | 0.269500 | 0.134750 | − | 0.990880i | \(-0.456977\pi\) | ||||
0.134750 | + | 0.990880i | \(0.456977\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.8573 | 0.768626 | ||||||||
\(482\) | −1.66323 | −0.0757579 | ||||||||
\(483\) | 3.61285 | 0.164390 | ||||||||
\(484\) | −1.90321 | −0.0865096 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.311108 | 0.0141121 | ||||||||
\(487\) | −31.3461 | −1.42043 | −0.710215 | − | 0.703985i | \(-0.751402\pi\) | ||||
−0.710215 | + | 0.703985i | \(0.751402\pi\) | |||||||
\(488\) | −8.79706 | −0.398224 | ||||||||
\(489\) | 11.0509 | 0.499737 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.00000 | −0.361035 | −0.180517 | − | 0.983572i | \(-0.557777\pi\) | ||||
−0.180517 | + | 0.983572i | \(0.557777\pi\) | |||||||
\(492\) | −20.2953 | −0.914982 | ||||||||
\(493\) | −16.0830 | −0.724341 | ||||||||
\(494\) | 2.19358 | 0.0986937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.99063 | −0.403691 | ||||||||
\(497\) | 8.38715 | 0.376215 | ||||||||
\(498\) | −2.41435 | −0.108190 | ||||||||
\(499\) | 15.1427 | 0.677881 | 0.338941 | − | 0.940808i | \(-0.389931\pi\) | ||||
0.338941 | + | 0.940808i | \(0.389931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9541 | 0.623422 | ||||||||
\(502\) | 7.39652 | 0.330123 | ||||||||
\(503\) | −26.0370 | −1.16093 | −0.580467 | − | 0.814284i | \(-0.697130\pi\) | ||||
−0.580467 | + | 0.814284i | \(0.697130\pi\) | |||||||
\(504\) | 1.09679 | 0.0488548 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.24443 | 0.0553217 | ||||||||
\(507\) | 4.57136 | 0.203021 | ||||||||
\(508\) | 20.9447 | 0.929271 | ||||||||
\(509\) | −24.5718 | −1.08913 | −0.544564 | − | 0.838719i | \(-0.683305\pi\) | ||||
−0.544564 | + | 0.838719i | \(0.683305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.11108 | 0.226101 | ||||||||
\(512\) | −20.3111 | −0.897633 | ||||||||
\(513\) | −2.42864 | −0.107227 | ||||||||
\(514\) | −2.53035 | −0.111609 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −20.3827 | −0.897299 | ||||||||
\(517\) | −0.949145 | −0.0417433 | ||||||||
\(518\) | 1.63158 | 0.0716877 | ||||||||
\(519\) | −18.8430 | −0.827115 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.88892 | −0.214188 | −0.107094 | − | 0.994249i | \(-0.534155\pi\) | ||||
−0.107094 | + | 0.994249i | \(0.534155\pi\) | |||||||
\(522\) | −2.19358 | −0.0960102 | ||||||||
\(523\) | 4.22077 | 0.184562 | 0.0922808 | − | 0.995733i | \(-0.470584\pi\) | ||||
0.0922808 | + | 0.995733i | \(0.470584\pi\) | |||||||
\(524\) | −2.36842 | −0.103465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.12537 | 0.310681 | ||||||||
\(527\) | 5.98126 | 0.260548 | ||||||||
\(528\) | −3.42864 | −0.149212 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.67307 | −0.0726051 | ||||||||
\(532\) | −4.17484 | −0.181002 | ||||||||
\(533\) | 30.9590 | 1.34098 | ||||||||
\(534\) | 1.90813 | 0.0825730 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −15.6128 | −0.674372 | ||||||||
\(537\) | −4.85728 | −0.209607 | ||||||||
\(538\) | −3.68196 | −0.158741 | ||||||||
\(539\) | −6.18421 | −0.266373 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.6128 | −0.585262 | −0.292631 | − | 0.956225i | \(-0.594531\pi\) | ||||
−0.292631 | + | 0.956225i | \(0.594531\pi\) | |||||||
\(542\) | −4.63512 | −0.199096 | ||||||||
\(543\) | 16.7971 | 0.720831 | ||||||||
\(544\) | 7.97280 | 0.341831 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.815792 | −0.0349127 | ||||||||
\(547\) | 7.48394 | 0.319990 | 0.159995 | − | 0.987118i | \(-0.448852\pi\) | ||||
0.159995 | + | 0.987118i | \(0.448852\pi\) | |||||||
\(548\) | −8.42864 | −0.360054 | ||||||||
\(549\) | −7.24443 | −0.309185 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.1240 | 0.729506 | ||||||||
\(552\) | 4.85728 | 0.206740 | ||||||||
\(553\) | −14.9304 | −0.634906 | ||||||||
\(554\) | −8.60793 | −0.365716 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.74620 | −0.0740554 | ||||||||
\(557\) | 32.2908 | 1.36821 | 0.684103 | − | 0.729385i | \(-0.260194\pi\) | ||||
0.684103 | + | 0.729385i | \(0.260194\pi\) | |||||||
\(558\) | 0.815792 | 0.0345352 | ||||||||
\(559\) | 31.0923 | 1.31507 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.28100 | 0.0963037 | ||||||||
\(562\) | −3.05086 | −0.128693 | ||||||||
\(563\) | 7.49378 | 0.315825 | 0.157913 | − | 0.987453i | \(-0.449524\pi\) | ||||
0.157913 | + | 0.987453i | \(0.449524\pi\) | |||||||
\(564\) | −1.80642 | −0.0760642 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.91258 | −0.248524 | ||||||||
\(567\) | 0.903212 | 0.0379313 | ||||||||
\(568\) | 11.2761 | 0.473134 | ||||||||
\(569\) | −12.9491 | −0.542856 | −0.271428 | − | 0.962459i | \(-0.587496\pi\) | ||||
−0.271428 | + | 0.962459i | \(0.587496\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.2859 | −0.639696 | −0.319848 | − | 0.947469i | \(-0.603632\pi\) | ||||
−0.319848 | + | 0.947469i | \(0.603632\pi\) | |||||||
\(572\) | 5.52543 | 0.231030 | ||||||||
\(573\) | −16.8573 | −0.704223 | ||||||||
\(574\) | 2.99646 | 0.125070 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.76986 | −0.240411 | ||||||||
\(577\) | 28.4415 | 1.18404 | 0.592019 | − | 0.805924i | \(-0.298331\pi\) | ||||
0.592019 | + | 0.805924i | \(0.298331\pi\) | |||||||
\(578\) | 3.67016 | 0.152658 | ||||||||
\(579\) | −24.6178 | −1.02308 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.00937 | −0.290798 | ||||||||
\(582\) | 3.87955 | 0.160813 | ||||||||
\(583\) | −0.815792 | −0.0337866 | ||||||||
\(584\) | 6.87157 | 0.284348 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.56691 | −0.395206 | ||||||||
\(587\) | −8.47013 | −0.349600 | −0.174800 | − | 0.984604i | \(-0.555928\pi\) | ||||
−0.174800 | + | 0.984604i | \(0.555928\pi\) | |||||||
\(588\) | −11.7699 | −0.485381 | ||||||||
\(589\) | −6.36842 | −0.262406 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.8716 | 0.611735 | ||||||||
\(592\) | −19.9081 | −0.818219 | ||||||||
\(593\) | 26.5763 | 1.09136 | 0.545679 | − | 0.837995i | \(-0.316272\pi\) | ||||
0.545679 | + | 0.837995i | \(0.316272\pi\) | |||||||
\(594\) | 0.311108 | 0.0127649 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.17484 | −0.171008 | ||||||||
\(597\) | 11.2257 | 0.459437 | ||||||||
\(598\) | −3.61285 | −0.147740 | ||||||||
\(599\) | −8.77430 | −0.358508 | −0.179254 | − | 0.983803i | \(-0.557368\pi\) | ||||
−0.179254 | + | 0.983803i | \(0.557368\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −41.8163 | −1.70572 | −0.852861 | − | 0.522139i | \(-0.825134\pi\) | ||||
−0.852861 | + | 0.522139i | \(0.825134\pi\) | |||||||
\(602\) | 3.00937 | 0.122653 | ||||||||
\(603\) | −12.8573 | −0.523589 | ||||||||
\(604\) | 19.8479 | 0.807600 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5.03212 | 0.204416 | ||||||||
\(607\) | 29.9353 | 1.21504 | 0.607519 | − | 0.794305i | \(-0.292165\pi\) | ||||
0.607519 | + | 0.794305i | \(0.292165\pi\) | |||||||
\(608\) | −8.48886 | −0.344269 | ||||||||
\(609\) | −6.36842 | −0.258061 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.75557 | 0.111478 | ||||||||
\(612\) | 4.34122 | 0.175483 | ||||||||
\(613\) | 26.1289 | 1.05534 | 0.527668 | − | 0.849450i | \(-0.323066\pi\) | ||||
0.527668 | + | 0.849450i | \(0.323066\pi\) | |||||||
\(614\) | −4.19802 | −0.169418 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.09679 | 0.0441909 | ||||||||
\(617\) | −3.66323 | −0.147476 | −0.0737380 | − | 0.997278i | \(-0.523493\pi\) | ||||
−0.0737380 | + | 0.997278i | \(0.523493\pi\) | |||||||
\(618\) | 5.33630 | 0.214657 | ||||||||
\(619\) | 43.2958 | 1.74020 | 0.870102 | − | 0.492872i | \(-0.164053\pi\) | ||||
0.870102 | + | 0.492872i | \(0.164053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.00000 | 0.160514 | ||||||||
\(622\) | 5.46076 | 0.218956 | ||||||||
\(623\) | 5.53972 | 0.221944 | ||||||||
\(624\) | 9.95407 | 0.398482 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.47902 | 0.179018 | ||||||||
\(627\) | −2.42864 | −0.0969905 | ||||||||
\(628\) | 11.0509 | 0.440977 | ||||||||
\(629\) | 13.2444 | 0.528090 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.97773 | 0.357398 | 0.178699 | − | 0.983904i | \(-0.442811\pi\) | ||||
0.178699 | + | 0.983904i | \(0.442811\pi\) | |||||||
\(632\) | −20.0731 | −0.798466 | ||||||||
\(633\) | 11.9398 | 0.474564 | ||||||||
\(634\) | 9.16547 | 0.364007 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.55262 | −0.0615656 | ||||||||
\(637\) | 17.9541 | 0.711366 | ||||||||
\(638\) | −2.19358 | −0.0868445 | ||||||||
\(639\) | 9.28592 | 0.367345 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.21279 | 0.363883 | 0.181942 | − | 0.983309i | \(-0.441762\pi\) | ||||
0.181942 | + | 0.983309i | \(0.441762\pi\) | |||||||
\(642\) | 4.22077 | 0.166581 | ||||||||
\(643\) | −16.3783 | −0.645896 | −0.322948 | − | 0.946417i | \(-0.604674\pi\) | ||||
−0.322948 | + | 0.946417i | \(0.604674\pi\) | |||||||
\(644\) | 6.87601 | 0.270953 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.72345 | 0.0678082 | ||||||||
\(647\) | 9.80642 | 0.385530 | 0.192765 | − | 0.981245i | \(-0.438254\pi\) | ||||
0.192765 | + | 0.981245i | \(0.438254\pi\) | |||||||
\(648\) | 1.21432 | 0.0477030 | ||||||||
\(649\) | −1.67307 | −0.0656738 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.36842 | 0.0928256 | ||||||||
\(652\) | 21.0321 | 0.823681 | ||||||||
\(653\) | 33.0736 | 1.29427 | 0.647135 | − | 0.762375i | \(-0.275967\pi\) | ||||
0.647135 | + | 0.762375i | \(0.275967\pi\) | |||||||
\(654\) | −3.11108 | −0.121653 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.5620 | −1.42751 | ||||||||
\(657\) | 5.65878 | 0.220770 | ||||||||
\(658\) | 0.266706 | 0.0103973 | ||||||||
\(659\) | 34.1017 | 1.32841 | 0.664207 | − | 0.747549i | \(-0.268769\pi\) | ||||
0.664207 | + | 0.747549i | \(0.268769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.40943 | −0.210402 | −0.105201 | − | 0.994451i | \(-0.533549\pi\) | ||||
−0.105201 | + | 0.994451i | \(0.533549\pi\) | |||||||
\(662\) | 0.815792 | 0.0317066 | ||||||||
\(663\) | −6.62222 | −0.257186 | ||||||||
\(664\) | −9.42372 | −0.365711 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.80642 | 0.0699975 | ||||||||
\(667\) | −28.2034 | −1.09204 | ||||||||
\(668\) | 26.5575 | 1.02754 | ||||||||
\(669\) | 21.8064 | 0.843085 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.24443 | −0.279668 | ||||||||
\(672\) | 3.15701 | 0.121784 | ||||||||
\(673\) | 24.1476 | 0.930823 | 0.465412 | − | 0.885094i | \(-0.345906\pi\) | ||||
0.465412 | + | 0.885094i | \(0.345906\pi\) | |||||||
\(674\) | −1.55707 | −0.0599761 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.70027 | 0.334626 | ||||||||
\(677\) | 26.2810 | 1.01006 | 0.505030 | − | 0.863102i | \(-0.331481\pi\) | ||||
0.505030 | + | 0.863102i | \(0.331481\pi\) | |||||||
\(678\) | −4.42864 | −0.170081 | ||||||||
\(679\) | 11.2632 | 0.432241 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.19850 | 0.122567 | ||||||||
\(682\) | 0.815792 | 0.0312383 | ||||||||
\(683\) | 15.3176 | 0.586110 | 0.293055 | − | 0.956096i | \(-0.405328\pi\) | ||||
0.293055 | + | 0.956096i | \(0.405328\pi\) | |||||||
\(684\) | −4.62222 | −0.176735 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.70471 | 0.141447 | ||||||||
\(687\) | −7.12399 | −0.271797 | ||||||||
\(688\) | −36.7195 | −1.39992 | ||||||||
\(689\) | 2.36842 | 0.0902295 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0223 | 0.571474 | 0.285737 | − | 0.958308i | \(-0.407762\pi\) | ||||
0.285737 | + | 0.958308i | \(0.407762\pi\) | |||||||
\(692\) | −35.8622 | −1.36328 | ||||||||
\(693\) | 0.903212 | 0.0343102 | ||||||||
\(694\) | −7.09679 | −0.269390 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −8.56199 | −0.324541 | ||||||||
\(697\) | 24.3239 | 0.921332 | ||||||||
\(698\) | −6.60348 | −0.249945 | ||||||||
\(699\) | −19.5254 | −0.738519 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.9081 | −0.751920 | −0.375960 | − | 0.926636i | \(-0.622687\pi\) | ||||
−0.375960 | + | 0.926636i | \(0.622687\pi\) | |||||||
\(702\) | −0.903212 | −0.0340895 | ||||||||
\(703\) | −14.1017 | −0.531856 | ||||||||
\(704\) | −5.76986 | −0.217460 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.23506 | 0.0841177 | ||||||||
\(707\) | 14.6093 | 0.549440 | ||||||||
\(708\) | −3.18421 | −0.119670 | ||||||||
\(709\) | −13.5081 | −0.507306 | −0.253653 | − | 0.967295i | \(-0.581632\pi\) | ||||
−0.253653 | + | 0.967295i | \(0.581632\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.5303 | −0.619937 | ||||||||
\(712\) | 7.44785 | 0.279120 | ||||||||
\(713\) | 10.4889 | 0.392811 | ||||||||
\(714\) | −0.640951 | −0.0239870 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −9.24443 | −0.345481 | ||||||||
\(717\) | 21.9813 | 0.820905 | ||||||||
\(718\) | 4.38715 | 0.163727 | ||||||||
\(719\) | −16.0830 | −0.599794 | −0.299897 | − | 0.953972i | \(-0.596952\pi\) | ||||
−0.299897 | + | 0.953972i | \(0.596952\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.4924 | 0.576967 | ||||||||
\(722\) | 4.07604 | 0.151695 | ||||||||
\(723\) | −5.34614 | −0.198825 | ||||||||
\(724\) | 31.9684 | 1.18809 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.311108 | 0.0115463 | ||||||||
\(727\) | −23.6128 | −0.875752 | −0.437876 | − | 0.899035i | \(-0.644269\pi\) | ||||
−0.437876 | + | 0.899035i | \(0.644269\pi\) | |||||||
\(728\) | −3.18421 | −0.118015 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.4286 | 0.903526 | ||||||||
\(732\) | −13.7877 | −0.509608 | ||||||||
\(733\) | 30.0459 | 1.10977 | 0.554886 | − | 0.831926i | \(-0.312762\pi\) | ||||
0.554886 | + | 0.831926i | \(0.312762\pi\) | |||||||
\(734\) | −1.21585 | −0.0448779 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 13.9813 | 0.515356 | ||||||||
\(737\) | −12.8573 | −0.473604 | ||||||||
\(738\) | 3.31756 | 0.122121 | ||||||||
\(739\) | −24.4099 | −0.897933 | −0.448966 | − | 0.893549i | \(-0.648208\pi\) | ||||
−0.448966 | + | 0.893549i | \(0.648208\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.05086 | 0.259020 | ||||||||
\(742\) | 0.229234 | 0.00841546 | ||||||||
\(743\) | 33.1798 | 1.21725 | 0.608624 | − | 0.793459i | \(-0.291722\pi\) | ||||
0.608624 | + | 0.793459i | \(0.291722\pi\) | |||||||
\(744\) | 3.18421 | 0.116739 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.03704 | 0.147807 | ||||||||
\(747\) | −7.76049 | −0.283942 | ||||||||
\(748\) | 4.34122 | 0.158731 | ||||||||
\(749\) | 12.2538 | 0.447744 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22.5718 | −0.823658 | −0.411829 | − | 0.911261i | \(-0.635110\pi\) | ||||
−0.411829 | + | 0.911261i | \(0.635110\pi\) | |||||||
\(752\) | −3.25428 | −0.118671 | ||||||||
\(753\) | 23.7748 | 0.866401 | ||||||||
\(754\) | 6.36842 | 0.231924 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.71900 | 0.0625196 | ||||||||
\(757\) | 4.94914 | 0.179880 | 0.0899399 | − | 0.995947i | \(-0.471333\pi\) | ||||
0.0899399 | + | 0.995947i | \(0.471333\pi\) | |||||||
\(758\) | −11.2257 | −0.407736 | ||||||||
\(759\) | 4.00000 | 0.145191 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.6637 | 0.531559 | 0.265779 | − | 0.964034i | \(-0.414371\pi\) | ||||
0.265779 | + | 0.964034i | \(0.414371\pi\) | |||||||
\(762\) | −3.42372 | −0.124028 | ||||||||
\(763\) | −9.03212 | −0.326985 | ||||||||
\(764\) | −32.0830 | −1.16072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6.31402 | 0.228135 | ||||||||
\(767\) | 4.85728 | 0.175386 | ||||||||
\(768\) | −8.80642 | −0.317774 | ||||||||
\(769\) | −44.5718 | −1.60730 | −0.803651 | − | 0.595101i | \(-0.797112\pi\) | ||||
−0.803651 | + | 0.595101i | \(0.797112\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.13335 | −0.292916 | ||||||||
\(772\) | −46.8528 | −1.68627 | ||||||||
\(773\) | 17.3145 | 0.622759 | 0.311380 | − | 0.950286i | \(-0.399209\pi\) | ||||
0.311380 | + | 0.950286i | \(0.399209\pi\) | |||||||
\(774\) | 3.33185 | 0.119761 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.1427 | 0.543592 | ||||||||
\(777\) | 5.24443 | 0.188143 | ||||||||
\(778\) | −9.47949 | −0.339856 | ||||||||
\(779\) | −25.8983 | −0.927903 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.28592 | 0.332276 | ||||||||
\(782\) | −2.83854 | −0.101506 | ||||||||
\(783\) | −7.05086 | −0.251977 | ||||||||
\(784\) | −21.2034 | −0.757265 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.387152 | 0.0138093 | ||||||||
\(787\) | 36.5161 | 1.30166 | 0.650828 | − | 0.759225i | \(-0.274422\pi\) | ||||
0.650828 | + | 0.759225i | \(0.274422\pi\) | |||||||
\(788\) | 28.3037 | 1.00828 | ||||||||
\(789\) | 22.9032 | 0.815376 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.8573 | −0.457152 | ||||||||
\(792\) | 1.21432 | 0.0431490 | ||||||||
\(793\) | 21.0321 | 0.746872 | ||||||||
\(794\) | 1.54861 | 0.0549581 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.3649 | 0.757258 | ||||||||
\(797\) | −14.3180 | −0.507171 | −0.253585 | − | 0.967313i | \(-0.581610\pi\) | ||||
−0.253585 | + | 0.967313i | \(0.581610\pi\) | |||||||
\(798\) | 0.682439 | 0.0241581 | ||||||||
\(799\) | 2.16500 | 0.0765921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.13335 | 0.216711 | ||||||||
\(802\) | 0.580728 | 0.0205062 | ||||||||
\(803\) | 5.65878 | 0.199694 | ||||||||
\(804\) | −24.4701 | −0.862995 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −2.36842 | −0.0834239 | ||||||||
\(807\) | −11.8350 | −0.416612 | ||||||||
\(808\) | 19.6414 | 0.690983 | ||||||||
\(809\) | 32.0544 | 1.12697 | 0.563486 | − | 0.826125i | \(-0.309460\pi\) | ||||
0.563486 | + | 0.826125i | \(0.309460\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.44738 | −0.296627 | −0.148314 | − | 0.988940i | \(-0.547385\pi\) | ||||
−0.148314 | + | 0.988940i | \(0.547385\pi\) | |||||||
\(812\) | −12.1204 | −0.425344 | ||||||||
\(813\) | −14.8988 | −0.522523 | ||||||||
\(814\) | 1.80642 | 0.0633151 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 7.82071 | 0.273780 | ||||||||
\(817\) | −26.0098 | −0.909969 | ||||||||
\(818\) | 1.12981 | 0.0395030 | ||||||||
\(819\) | −2.62222 | −0.0916276 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.2159 | 0.600837 | 0.300419 | − | 0.953807i | \(-0.402874\pi\) | ||||
0.300419 | + | 0.953807i | \(0.402874\pi\) | |||||||
\(822\) | 1.37778 | 0.0480557 | ||||||||
\(823\) | 12.7654 | 0.444974 | 0.222487 | − | 0.974936i | \(-0.428582\pi\) | ||||
0.222487 | + | 0.974936i | \(0.428582\pi\) | |||||||
\(824\) | 20.8287 | 0.725602 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.470127 | 0.0163578 | ||||||||
\(827\) | 8.70964 | 0.302864 | 0.151432 | − | 0.988468i | \(-0.451612\pi\) | ||||
0.151432 | + | 0.988468i | \(0.451612\pi\) | |||||||
\(828\) | 7.61285 | 0.264565 | ||||||||
\(829\) | −8.32693 | −0.289206 | −0.144603 | − | 0.989490i | \(-0.546191\pi\) | ||||
−0.144603 | + | 0.989490i | \(0.546191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −27.6686 | −0.959814 | ||||||||
\(832\) | 16.7511 | 0.580741 | ||||||||
\(833\) | 14.1062 | 0.488749 | ||||||||
\(834\) | 0.285442 | 0.00988405 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −4.62222 | −0.159863 | ||||||||
\(837\) | 2.62222 | 0.0906370 | ||||||||
\(838\) | −1.51114 | −0.0522014 | ||||||||
\(839\) | 12.8988 | 0.445315 | 0.222657 | − | 0.974897i | \(-0.428527\pi\) | ||||
0.222657 | + | 0.974897i | \(0.428527\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.7146 | 0.714295 | ||||||||
\(842\) | −7.04101 | −0.242649 | ||||||||
\(843\) | −9.80642 | −0.337751 | ||||||||
\(844\) | 22.7239 | 0.782190 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0.295286 | 0.0101522 | ||||||||
\(847\) | 0.903212 | 0.0310347 | ||||||||
\(848\) | −2.79706 | −0.0960513 | ||||||||
\(849\) | −19.0049 | −0.652247 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23.2257 | 0.796167 | ||||||||
\(852\) | 17.6731 | 0.605469 | ||||||||
\(853\) | −19.6686 | −0.673441 | −0.336720 | − | 0.941605i | \(-0.609318\pi\) | ||||
−0.336720 | + | 0.941605i | \(0.609318\pi\) | |||||||
\(854\) | 2.03566 | 0.0696588 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 16.4746 | 0.563089 | ||||||||
\(857\) | 31.8207 | 1.08697 | 0.543487 | − | 0.839417i | \(-0.317104\pi\) | ||||
0.543487 | + | 0.839417i | \(0.317104\pi\) | |||||||
\(858\) | −0.903212 | −0.0308351 | ||||||||
\(859\) | 27.8292 | 0.949519 | 0.474760 | − | 0.880116i | \(-0.342535\pi\) | ||||
0.474760 | + | 0.880116i | \(0.342535\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.63158 | 0.328243 | ||||||||
\(862\) | −0.387152 | −0.0131865 | ||||||||
\(863\) | −4.82870 | −0.164371 | −0.0821854 | − | 0.996617i | \(-0.526190\pi\) | ||||
−0.0821854 | + | 0.996617i | \(0.526190\pi\) | |||||||
\(864\) | 3.49532 | 0.118913 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −4.97773 | −0.169150 | ||||||||
\(867\) | 11.7971 | 0.400649 | ||||||||
\(868\) | 4.50760 | 0.152998 | ||||||||
\(869\) | −16.5303 | −0.560754 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 37.3274 | 1.26479 | ||||||||
\(872\) | −12.1432 | −0.411221 | ||||||||
\(873\) | 12.4701 | 0.422050 | ||||||||
\(874\) | 3.02227 | 0.102230 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.7699 | 0.363880 | ||||||||
\(877\) | 21.9826 | 0.742301 | 0.371151 | − | 0.928573i | \(-0.378963\pi\) | ||||
0.371151 | + | 0.928573i | \(0.378963\pi\) | |||||||
\(878\) | 0.755569 | 0.0254992 | ||||||||
\(879\) | −30.7511 | −1.03721 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.1017 | −0.407717 | −0.203858 | − | 0.979000i | \(-0.565348\pi\) | ||||
−0.203858 | + | 0.979000i | \(0.565348\pi\) | |||||||
\(882\) | 1.92396 | 0.0647830 | ||||||||
\(883\) | 8.73683 | 0.294018 | 0.147009 | − | 0.989135i | \(-0.453035\pi\) | ||||
0.147009 | + | 0.989135i | \(0.453035\pi\) | |||||||
\(884\) | −12.6035 | −0.423901 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.66016 | 0.324540 | ||||||||
\(887\) | −19.8524 | −0.666577 | −0.333288 | − | 0.942825i | \(-0.608158\pi\) | ||||
−0.333288 | + | 0.942825i | \(0.608158\pi\) | |||||||
\(888\) | 7.05086 | 0.236611 | ||||||||
\(889\) | −9.93978 | −0.333369 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 41.5022 | 1.38960 | ||||||||
\(893\) | −2.30513 | −0.0771383 | ||||||||
\(894\) | 0.682439 | 0.0228242 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 7.93533 | 0.265101 | ||||||||
\(897\) | −11.6128 | −0.387742 | ||||||||
\(898\) | 11.6227 | 0.387854 | ||||||||
\(899\) | −18.4889 | −0.616638 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.86082 | 0.0619928 | ||||||||
\(902\) | 3.31756 | 0.110463 | ||||||||
\(903\) | 9.67307 | 0.321900 | ||||||||
\(904\) | −17.2859 | −0.574921 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.24443 | −0.107789 | ||||||||
\(907\) | 32.8287 | 1.09006 | 0.545030 | − | 0.838417i | \(-0.316518\pi\) | ||||
0.545030 | + | 0.838417i | \(0.316518\pi\) | |||||||
\(908\) | 6.08742 | 0.202018 | ||||||||
\(909\) | 16.1748 | 0.536486 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.3497 | −0.541689 | −0.270845 | − | 0.962623i | \(-0.587303\pi\) | ||||
−0.270845 | + | 0.962623i | \(0.587303\pi\) | |||||||
\(912\) | −8.32693 | −0.275732 | ||||||||
\(913\) | −7.76049 | −0.256835 | ||||||||
\(914\) | 2.71853 | 0.0899209 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.5585 | −0.447984 | ||||||||
\(917\) | 1.12399 | 0.0371173 | ||||||||
\(918\) | −0.709636 | −0.0234215 | ||||||||
\(919\) | 20.0228 | 0.660490 | 0.330245 | − | 0.943895i | \(-0.392869\pi\) | ||||
0.330245 | + | 0.943895i | \(0.392869\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −13.4938 | −0.444635 | ||||||||
\(922\) | −9.88940 | −0.325690 | ||||||||
\(923\) | −26.9590 | −0.887366 | ||||||||
\(924\) | 1.71900 | 0.0565511 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.76187 | 0.123623 | ||||||||
\(927\) | 17.1526 | 0.563364 | ||||||||
\(928\) | −24.6450 | −0.809011 | ||||||||
\(929\) | −43.5308 | −1.42820 | −0.714100 | − | 0.700044i | \(-0.753164\pi\) | ||||
−0.714100 | + | 0.700044i | \(0.753164\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0192 | −0.492235 | ||||||||
\(932\) | −37.1610 | −1.21725 | ||||||||
\(933\) | 17.5526 | 0.574647 | ||||||||
\(934\) | −4.77430 | −0.156220 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.52543 | −0.115232 | ||||||||
\(937\) | −43.4563 | −1.41966 | −0.709828 | − | 0.704375i | \(-0.751227\pi\) | ||||
−0.709828 | + | 0.704375i | \(0.751227\pi\) | |||||||
\(938\) | 3.61285 | 0.117964 | ||||||||
\(939\) | 14.3970 | 0.469828 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.7244 | −0.773393 | −0.386697 | − | 0.922207i | \(-0.626384\pi\) | ||||
−0.386697 | + | 0.922207i | \(0.626384\pi\) | |||||||
\(942\) | −1.80642 | −0.0588565 | ||||||||
\(943\) | 42.6548 | 1.38903 | ||||||||
\(944\) | −5.73636 | −0.186703 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.33185 | 0.108328 | ||||||||
\(947\) | −11.7047 | −0.380352 | −0.190176 | − | 0.981750i | \(-0.560906\pi\) | ||||
−0.190176 | + | 0.981750i | \(0.560906\pi\) | |||||||
\(948\) | −31.4608 | −1.02180 | ||||||||
\(949\) | −16.4286 | −0.533296 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.4608 | 0.955331 | ||||||||
\(952\) | −2.50177 | −0.0810828 | ||||||||
\(953\) | −46.1258 | −1.49416 | −0.747081 | − | 0.664733i | \(-0.768545\pi\) | ||||
−0.747081 | + | 0.664733i | \(0.768545\pi\) | |||||||
\(954\) | 0.253799 | 0.00821705 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 41.8350 | 1.35304 | ||||||||
\(957\) | −7.05086 | −0.227922 | ||||||||
\(958\) | −1.83500 | −0.0592863 | ||||||||
\(959\) | 4.00000 | 0.129167 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1240 | −0.778193 | ||||||||
\(962\) | −5.24443 | −0.169087 | ||||||||
\(963\) | 13.5669 | 0.437188 | ||||||||
\(964\) | −10.1748 | −0.327710 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.12399 | −0.0361636 | ||||||||
\(967\) | −17.0495 | −0.548274 | −0.274137 | − | 0.961691i | \(-0.588392\pi\) | ||||
−0.274137 | + | 0.961691i | \(0.588392\pi\) | |||||||
\(968\) | 1.21432 | 0.0390297 | ||||||||
\(969\) | 5.53972 | 0.177961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −58.1847 | −1.86724 | −0.933618 | − | 0.358271i | \(-0.883366\pi\) | ||||
−0.933618 | + | 0.358271i | \(0.883366\pi\) | |||||||
\(972\) | 1.90321 | 0.0610456 | ||||||||
\(973\) | 0.828699 | 0.0265669 | ||||||||
\(974\) | 9.75203 | 0.312475 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.8385 | −0.795062 | ||||||||
\(977\) | 51.7373 | 1.65522 | 0.827612 | − | 0.561301i | \(-0.189699\pi\) | ||||
0.827612 | + | 0.561301i | \(0.189699\pi\) | |||||||
\(978\) | −3.43801 | −0.109935 | ||||||||
\(979\) | 6.13335 | 0.196023 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 2.48886 | 0.0794228 | ||||||||
\(983\) | 26.3970 | 0.841933 | 0.420967 | − | 0.907076i | \(-0.361691\pi\) | ||||
0.420967 | + | 0.907076i | \(0.361691\pi\) | |||||||
\(984\) | 12.9491 | 0.412804 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 5.00354 | 0.159345 | ||||||||
\(987\) | 0.857279 | 0.0272875 | ||||||||
\(988\) | 13.4193 | 0.426924 | ||||||||
\(989\) | 42.8385 | 1.36219 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.0923 | −0.733552 | −0.366776 | − | 0.930309i | \(-0.619539\pi\) | ||||
−0.366776 | + | 0.930309i | \(0.619539\pi\) | |||||||
\(992\) | 9.16547 | 0.291004 | ||||||||
\(993\) | 2.62222 | 0.0832135 | ||||||||
\(994\) | −2.60931 | −0.0827622 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.7699 | −0.468001 | ||||||||
\(997\) | −12.9131 | −0.408961 | −0.204480 | − | 0.978871i | \(-0.565550\pi\) | ||||
−0.204480 | + | 0.978871i | \(0.565550\pi\) | |||||||
\(998\) | −4.71102 | −0.149125 | ||||||||
\(999\) | 5.80642 | 0.183707 |
(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 | 825.2.a.j.1.2 | 3 | ||
3.2 | odd | 2 | 2475.2.a.bc.1.2 | 3 | |||
5.2 | odd | 4 | 165.2.c.b.34.3 | ✓ | 6 | ||
5.3 | odd | 4 | 165.2.c.b.34.4 | yes | 6 | ||
5.4 | even | 2 | 825.2.a.l.1.2 | 3 | |||
11.10 | odd | 2 | 9075.2.a.ch.1.2 | 3 | |||
15.2 | even | 4 | 495.2.c.e.199.4 | 6 | |||
15.8 | even | 4 | 495.2.c.e.199.3 | 6 | |||
15.14 | odd | 2 | 2475.2.a.ba.1.2 | 3 | |||
20.3 | even | 4 | 2640.2.d.h.529.5 | 6 | |||
20.7 | even | 4 | 2640.2.d.h.529.2 | 6 | |||
55.32 | even | 4 | 1815.2.c.e.364.4 | 6 | |||
55.43 | even | 4 | 1815.2.c.e.364.3 | 6 | |||
55.54 | odd | 2 | 9075.2.a.cg.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.c.b.34.3 | ✓ | 6 | 5.2 | odd | 4 | ||
165.2.c.b.34.4 | yes | 6 | 5.3 | odd | 4 | ||
495.2.c.e.199.3 | 6 | 15.8 | even | 4 | |||
495.2.c.e.199.4 | 6 | 15.2 | even | 4 | |||
825.2.a.j.1.2 | 3 | 1.1 | even | 1 | trivial | ||
825.2.a.l.1.2 | 3 | 5.4 | even | 2 | |||
1815.2.c.e.364.3 | 6 | 55.43 | even | 4 | |||
1815.2.c.e.364.4 | 6 | 55.32 | even | 4 | |||
2475.2.a.ba.1.2 | 3 | 15.14 | odd | 2 | |||
2475.2.a.bc.1.2 | 3 | 3.2 | odd | 2 | |||
2640.2.d.h.529.2 | 6 | 20.7 | even | 4 | |||
2640.2.d.h.529.5 | 6 | 20.3 | even | 4 | |||
9075.2.a.cg.1.2 | 3 | 55.54 | odd | 2 | |||
9075.2.a.ch.1.2 | 3 | 11.10 | odd | 2 |