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: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 649.2 | ||
Root | \(0.675970 - 0.675970i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.649 |
Dual form | 2025.2.b.m.649.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2025\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(1702\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.08613i | − 1.47512i | −0.675283 | − | 0.737558i | \(-0.735979\pi\) | ||||
0.675283 | − | 0.737558i | \(-0.264021\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.35194 | −1.17597 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 4.08613i | − 1.54441i | −0.635372 | − | 0.772206i | \(-0.719153\pi\) | ||||
0.635372 | − | 0.772206i | \(-0.280847\pi\) | |||||||
\(8\) | 0.734191i | 0.259576i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.35194 | 0.407625 | 0.203813 | − | 0.979010i | \(-0.434667\pi\) | ||||
0.203813 | + | 0.979010i | \(0.434667\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.648061i | 0.179740i | 0.995954 | + | 0.0898699i | \(0.0286451\pi\) | ||||
−0.995954 | + | 0.0898699i | \(0.971355\pi\) | |||||||
\(14\) | −8.52420 | −2.27819 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.17226 | −0.793065 | ||||||||
\(17\) | − 1.35194i | − 0.327893i | −0.986469 | − | 0.163947i | \(-0.947577\pi\) | ||||
0.986469 | − | 0.163947i | \(-0.0524225\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.648061 | −0.148675 | −0.0743377 | − | 0.997233i | \(-0.523684\pi\) | ||||
−0.0743377 | + | 0.997233i | \(0.523684\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 2.82032i | − 0.601294i | ||||||||
\(23\) | − 4.79001i | − 0.998786i | −0.866376 | − | 0.499393i | \(-0.833556\pi\) | ||||
0.866376 | − | 0.499393i | \(-0.166444\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.35194 | 0.265137 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.61033i | 1.81618i | ||||||||
\(29\) | 3.87614 | 0.719781 | 0.359890 | − | 0.932995i | \(-0.382814\pi\) | ||||
0.359890 | + | 0.932995i | \(0.382814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.69646 | −1.38233 | −0.691163 | − | 0.722699i | \(-0.742901\pi\) | ||||
−0.691163 | + | 0.722699i | \(0.742901\pi\) | |||||||
\(32\) | 8.08613i | 1.42944i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.82032 | −0.483681 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.52420i | − 1.23697i | −0.785796 | − | 0.618485i | \(-0.787747\pi\) | ||||
0.785796 | − | 0.618485i | \(-0.212253\pi\) | |||||||
\(38\) | 1.35194i | 0.219313i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.179679 | 0.0280611 | 0.0140306 | − | 0.999902i | \(-0.495534\pi\) | ||||
0.0140306 | + | 0.999902i | \(0.495534\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.820321i | − 0.125098i | −0.998042 | − | 0.0625489i | \(-0.980077\pi\) | ||||
0.998042 | − | 0.0625489i | \(-0.0199229\pi\) | |||||||
\(44\) | −3.17968 | −0.479355 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.99258 | −1.47333 | ||||||||
\(47\) | 10.9065i | 1.59087i | 0.606039 | + | 0.795435i | \(0.292757\pi\) | ||||
−0.606039 | + | 0.795435i | \(0.707243\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.69646 | −1.38521 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 1.52420i | − 0.211368i | ||||||||
\(53\) | − 4.17226i | − 0.573104i | −0.958065 | − | 0.286552i | \(-0.907491\pi\) | ||||
0.958065 | − | 0.286552i | \(-0.0925091\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − 8.08613i | − 1.06176i | ||||||||
\(59\) | 4.17226 | 0.543182 | 0.271591 | − | 0.962413i | \(-0.412450\pi\) | ||||
0.271591 | + | 0.962413i | \(0.412450\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.82032 | −0.489142 | −0.244571 | − | 0.969631i | \(-0.578647\pi\) | ||||
−0.244571 | + | 0.969631i | \(0.578647\pi\) | |||||||
\(62\) | 16.0558i | 2.03909i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 10.5242 | 1.31552 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.14195i | − 0.994697i | −0.867551 | − | 0.497349i | \(-0.834307\pi\) | ||||
0.867551 | − | 0.497349i | \(-0.165693\pi\) | |||||||
\(68\) | 3.17968i | 0.385593i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.11644 | 0.725888 | 0.362944 | − | 0.931811i | \(-0.381772\pi\) | ||||
0.362944 | + | 0.931811i | \(0.381772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 12.3445i | − 1.44482i | −0.691467 | − | 0.722408i | \(-0.743035\pi\) | ||||
0.691467 | − | 0.722408i | \(-0.256965\pi\) | |||||||
\(74\) | −15.6965 | −1.82468 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.52420 | 0.174838 | ||||||||
\(77\) | − 5.52420i | − 0.629541i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.3445 | −1.16385 | −0.581925 | − | 0.813243i | \(-0.697700\pi\) | ||||
−0.581925 | + | 0.813243i | \(0.697700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 0.374833i | − 0.0413934i | ||||||||
\(83\) | 12.2584i | 1.34553i | 0.739855 | + | 0.672767i | \(0.234894\pi\) | ||||
−0.739855 | + | 0.672767i | \(0.765106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.71130 | −0.184534 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.992582i | 0.105810i | ||||||||
\(89\) | −3.00000 | −0.317999 | −0.159000 | − | 0.987279i | \(-0.550827\pi\) | ||||
−0.159000 | + | 0.987279i | \(0.550827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.64806 | 0.277592 | ||||||||
\(92\) | 11.2658i | 1.17454i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 22.7523 | 2.34672 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5800i | 1.37884i | 0.724361 | + | 0.689421i | \(0.242135\pi\) | ||||
−0.724361 | + | 0.689421i | \(0.757865\pi\) | |||||||
\(98\) | 20.2281i | 2.04334i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.46838 | 0.146109 | 0.0730547 | − | 0.997328i | \(-0.476725\pi\) | ||||
0.0730547 | + | 0.997328i | \(0.476725\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.52420i | 0.741381i | 0.928756 | + | 0.370691i | \(0.120879\pi\) | ||||
−0.928756 | + | 0.370691i | \(0.879121\pi\) | |||||||
\(104\) | −0.475800 | −0.0466561 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.70388 | −0.845395 | ||||||||
\(107\) | 1.20999i | 0.116974i | 0.998288 | + | 0.0584871i | \(0.0186277\pi\) | ||||
−0.998288 | + | 0.0584871i | \(0.981372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.1042 | −1.35094 | −0.675469 | − | 0.737388i | \(-0.736059\pi\) | ||||
−0.675469 | + | 0.737388i | \(0.736059\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.9623i | 1.22482i | ||||||||
\(113\) | 11.9245i | 1.12177i | 0.827895 | + | 0.560883i | \(0.189538\pi\) | ||||
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.11644 | −0.846440 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 8.70388i | − 0.801257i | ||||||||
\(119\) | −5.52420 | −0.506403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.17226 | −0.833842 | ||||||||
\(122\) | 7.96969i | 0.721542i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.1016 | 1.62557 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.07871i | 0.628134i | 0.949401 | + | 0.314067i | \(0.101692\pi\) | ||||
−0.949401 | + | 0.314067i | \(0.898308\pi\) | |||||||
\(128\) | − 5.78259i | − 0.511114i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.00000 | 0.524222 | 0.262111 | − | 0.965038i | \(-0.415581\pi\) | ||||
0.262111 | + | 0.965038i | \(0.415581\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.64806i | 0.229616i | ||||||||
\(134\) | −16.9852 | −1.46729 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.992582 | 0.0851132 | ||||||||
\(137\) | − 7.46838i | − 0.638067i | −0.947743 | − | 0.319033i | \(-0.896642\pi\) | ||||
0.947743 | − | 0.319033i | \(-0.103358\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 12.7597i | − 1.07077i | ||||||||
\(143\) | 0.876139i | 0.0732664i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −25.7523 | −2.13127 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.6965i | 1.45464i | ||||||||
\(149\) | −10.5848 | −0.867143 | −0.433571 | − | 0.901119i | \(-0.642747\pi\) | ||||
−0.433571 | + | 0.901119i | \(0.642747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.6965 | 1.44012 | 0.720059 | − | 0.693913i | \(-0.244115\pi\) | ||||
0.720059 | + | 0.693913i | \(0.244115\pi\) | |||||||
\(152\) | − 0.475800i | − 0.0385925i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.5242 | −0.928646 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.53162i | 0.202045i | 0.994884 | + | 0.101023i | \(0.0322114\pi\) | ||||
−0.994884 | + | 0.101023i | \(0.967789\pi\) | |||||||
\(158\) | 21.5800i | 1.71681i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.5726 | −1.54254 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.47580i | 0.663876i | 0.943301 | + | 0.331938i | \(0.107702\pi\) | ||||
−0.943301 | + | 0.331938i | \(0.892298\pi\) | |||||||
\(164\) | −0.422594 | −0.0329990 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 25.5726 | 1.98482 | ||||||||
\(167\) | 12.7342i | 0.985401i | 0.870199 | + | 0.492701i | \(0.163990\pi\) | ||||
−0.870199 | + | 0.492701i | \(0.836010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.5800 | 0.967694 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.92935i | 0.147111i | ||||||||
\(173\) | − 23.0484i | − 1.75234i | −0.482005 | − | 0.876169i | \(-0.660091\pi\) | ||||
0.482005 | − | 0.876169i | \(-0.339909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.28870 | −0.323273 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.25839i | 0.469086i | ||||||||
\(179\) | 2.22808 | 0.166534 | 0.0832672 | − | 0.996527i | \(-0.473465\pi\) | ||||
0.0832672 | + | 0.996527i | \(0.473465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.468382 | 0.0348146 | 0.0174073 | − | 0.999848i | \(-0.494459\pi\) | ||||
0.0174073 | + | 0.999848i | \(0.494459\pi\) | |||||||
\(182\) | − 5.52420i | − 0.409481i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.51678 | 0.259261 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.82774i | − 0.133658i | ||||||||
\(188\) | − 25.6513i | − 1.87081i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.2281 | 1.46365 | 0.731826 | − | 0.681491i | \(-0.238668\pi\) | ||||
0.731826 | + | 0.681491i | \(0.238668\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 19.9293i | − 1.43455i | −0.696792 | − | 0.717273i | \(-0.745390\pi\) | ||||
0.696792 | − | 0.717273i | \(-0.254610\pi\) | |||||||
\(194\) | 28.3297 | 2.03395 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.8055 | 1.62896 | ||||||||
\(197\) | − 15.5800i | − 1.11003i | −0.831840 | − | 0.555015i | \(-0.812712\pi\) | ||||
0.831840 | − | 0.555015i | \(-0.187288\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.58482 | −0.254121 | −0.127061 | − | 0.991895i | \(-0.540554\pi\) | ||||
−0.127061 | + | 0.991895i | \(0.540554\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 3.06324i | − 0.215529i | ||||||||
\(203\) | − 15.8384i | − 1.11164i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 15.6965 | 1.09362 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 2.05582i | − 0.142545i | ||||||||
\(209\) | −0.876139 | −0.0606038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.9926 | 1.03213 | 0.516066 | − | 0.856549i | \(-0.327396\pi\) | ||||
0.516066 | + | 0.856549i | \(0.327396\pi\) | |||||||
\(212\) | 9.81290i | 0.673953i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.52420 | 0.172551 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.4487i | 2.13488i | ||||||||
\(218\) | 29.4232i | 1.99279i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.876139 | 0.0589355 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 26.8310i | − 1.79674i | −0.439244 | − | 0.898368i | \(-0.644754\pi\) | ||||
0.439244 | − | 0.898368i | \(-0.355246\pi\) | |||||||
\(224\) | 33.0410 | 2.20764 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 24.8761 | 1.65474 | ||||||||
\(227\) | 1.35194i | 0.0897314i | 0.998993 | + | 0.0448657i | \(0.0142860\pi\) | ||||
−0.998993 | + | 0.0448657i | \(0.985714\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.23550 | 0.544217 | 0.272108 | − | 0.962267i | \(-0.412279\pi\) | ||||
0.272108 | + | 0.962267i | \(0.412279\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.84583i | 0.186838i | ||||||||
\(233\) | − 8.58744i | − 0.562582i | −0.959623 | − | 0.281291i | \(-0.909237\pi\) | ||||
0.959623 | − | 0.281291i | \(-0.0907626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −9.81290 | −0.638766 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 11.5242i | 0.747003i | ||||||||
\(239\) | −23.9245 | −1.54755 | −0.773775 | − | 0.633461i | \(-0.781634\pi\) | ||||
−0.773775 | + | 0.633461i | \(0.781634\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.24030 | −0.401973 | −0.200987 | − | 0.979594i | \(-0.564415\pi\) | ||||
−0.200987 | + | 0.979594i | \(0.564415\pi\) | |||||||
\(242\) | 19.1345i | 1.23001i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.98516 | 0.575216 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.419983i | − 0.0267229i | ||||||||
\(248\) | − 5.65067i | − 0.358818i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.5726 | 1.80349 | 0.901743 | − | 0.432272i | \(-0.142288\pi\) | ||||
0.901743 | + | 0.432272i | \(0.142288\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.47580i | − 0.407130i | ||||||||
\(254\) | 14.7671 | 0.926571 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.98516 | 0.561573 | ||||||||
\(257\) | − 18.0000i | − 1.12281i | −0.827541 | − | 0.561405i | \(-0.810261\pi\) | ||||
0.827541 | − | 0.561405i | \(-0.189739\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −30.7449 | −1.91039 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 12.5168i | − 0.773289i | ||||||||
\(263\) | − 31.8687i | − 1.96511i | −0.185974 | − | 0.982555i | \(-0.559544\pi\) | ||||
0.185974 | − | 0.982555i | \(-0.440456\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.52420 | 0.338710 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 19.1494i | 1.16973i | ||||||||
\(269\) | −31.4971 | −1.92041 | −0.960207 | − | 0.279289i | \(-0.909901\pi\) | ||||
−0.960207 | + | 0.279289i | \(0.909901\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.24030 | −0.196834 | −0.0984172 | − | 0.995145i | \(-0.531378\pi\) | ||||
−0.0984172 | + | 0.995145i | \(0.531378\pi\) | |||||||
\(272\) | 4.28870i | 0.260041i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −15.5800 | −0.941223 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.58482i | 0.335560i | 0.985824 | + | 0.167780i | \(0.0536598\pi\) | ||||
−0.985824 | + | 0.167780i | \(0.946340\pi\) | |||||||
\(278\) | 16.6890i | 1.00094i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.1042 | 1.43794 | 0.718969 | − | 0.695043i | \(-0.244615\pi\) | ||||
0.718969 | + | 0.695043i | \(0.244615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 10.5423i | − 0.626674i | −0.949642 | − | 0.313337i | \(-0.898553\pi\) | ||||
0.949642 | − | 0.313337i | \(-0.101447\pi\) | |||||||
\(284\) | −14.3855 | −0.853622 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.82774 | 0.108077 | ||||||||
\(287\) | − 0.734191i | − 0.0433379i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.1723 | 0.892486 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 29.0336i | 1.69906i | ||||||||
\(293\) | − 18.9926i | − 1.10956i | −0.831998 | − | 0.554779i | \(-0.812803\pi\) | ||||
0.831998 | − | 0.554779i | \(-0.187197\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5.52420 | 0.321088 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.0813i | 1.27914i | ||||||||
\(299\) | 3.10422 | 0.179521 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.35194 | −0.193203 | ||||||||
\(302\) | − 36.9171i | − 2.12434i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.05582 | 0.117909 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 29.4791i | − 1.68246i | −0.540679 | − | 0.841229i | \(-0.681833\pi\) | ||||
0.540679 | − | 0.841229i | \(-0.318167\pi\) | |||||||
\(308\) | 12.9926i | 0.740321i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.41256 | 0.533738 | 0.266869 | − | 0.963733i | \(-0.414011\pi\) | ||||
0.266869 | + | 0.963733i | \(0.414011\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6210i | 0.656858i | 0.944529 | + | 0.328429i | \(0.106519\pi\) | ||||
−0.944529 | + | 0.328429i | \(0.893481\pi\) | |||||||
\(314\) | 5.28128 | 0.298040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.3297 | 1.36865 | ||||||||
\(317\) | − 9.17968i | − 0.515582i | −0.966201 | − | 0.257791i | \(-0.917005\pi\) | ||||
0.966201 | − | 0.257791i | \(-0.0829946\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.24030 | 0.293401 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 40.8310i | 2.27542i | ||||||||
\(323\) | 0.876139i | 0.0487497i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 17.6816 | 0.979295 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.131919i | 0.00728398i | ||||||||
\(329\) | 44.5652 | 2.45696 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.22066 | −0.396883 | −0.198442 | − | 0.980113i | \(-0.563588\pi\) | ||||
−0.198442 | + | 0.980113i | \(0.563588\pi\) | |||||||
\(332\) | − 28.8310i | − 1.58231i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.5652 | 1.45358 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 2.28390i | − 0.124412i | −0.998063 | − | 0.0622059i | \(-0.980186\pi\) | ||||
0.998063 | − | 0.0622059i | \(-0.0198135\pi\) | |||||||
\(338\) | − 26.2436i | − 1.42746i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.4051 | −0.563470 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0181i | 0.594921i | ||||||||
\(344\) | 0.602272 | 0.0324724 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −48.0820 | −2.58490 | ||||||||
\(347\) | − 0.708686i | − 0.0380443i | −0.999819 | − | 0.0190221i | \(-0.993945\pi\) | ||||
0.999819 | − | 0.0190221i | \(-0.00605530\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3445 | 1.14255 | 0.571273 | − | 0.820760i | \(-0.306450\pi\) | ||||
0.571273 | + | 0.820760i | \(0.306450\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.9320i | 0.582675i | ||||||||
\(353\) | 10.0968i | 0.537398i | 0.963224 | + | 0.268699i | \(0.0865937\pi\) | ||||
−0.963224 | + | 0.268699i | \(0.913406\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.05582 | 0.373958 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 4.64806i | − 0.245658i | ||||||||
\(359\) | 30.5578 | 1.61278 | 0.806388 | − | 0.591386i | \(-0.201419\pi\) | ||||
0.806388 | + | 0.591386i | \(0.201419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5800 | −0.977896 | ||||||||
\(362\) | − 0.977106i | − 0.0513555i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −6.22808 | −0.326440 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.17968i | 0.374776i | 0.982286 | + | 0.187388i | \(0.0600022\pi\) | ||||
−0.982286 | + | 0.187388i | \(0.939998\pi\) | |||||||
\(368\) | 15.1952i | 0.792102i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.0484 | −0.885109 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 21.9245i | − 1.13521i | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
0.823301 | − | 0.567605i | \(-0.192130\pi\) | |||||||
\(374\) | −3.81290 | −0.197161 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.00742 | −0.412951 | ||||||||
\(377\) | 2.51197i | 0.129373i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.3929 | 0.893414 | 0.446707 | − | 0.894680i | \(-0.352597\pi\) | ||||
0.446707 | + | 0.894680i | \(0.352597\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 42.1984i | − 2.15906i | ||||||||
\(383\) | − 0.475800i | − 0.0243123i | −0.999926 | − | 0.0121561i | \(-0.996130\pi\) | ||||
0.999926 | − | 0.0121561i | \(-0.00386951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −41.5752 | −2.11612 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 31.9394i | − 1.62148i | ||||||||
\(389\) | −5.58744 | −0.283294 | −0.141647 | − | 0.989917i | \(-0.545240\pi\) | ||||
−0.141647 | + | 0.989917i | \(0.545240\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.47580 | −0.327495 | ||||||||
\(392\) | − 7.11905i | − 0.359567i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −32.5019 | −1.63742 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 3.75228i | − 0.188321i | −0.995557 | − | 0.0941607i | \(-0.969983\pi\) | ||||
0.995557 | − | 0.0941607i | \(-0.0300168\pi\) | |||||||
\(398\) | 7.47841i | 0.374859i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.5652 | −1.17679 | −0.588394 | − | 0.808574i | \(-0.700240\pi\) | ||||
−0.588394 | + | 0.808574i | \(0.700240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 4.98777i | − 0.248459i | ||||||||
\(404\) | −3.45355 | −0.171820 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −33.0410 | −1.63980 | ||||||||
\(407\) | − 10.1723i | − 0.504220i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.04840 | −0.0518400 | −0.0259200 | − | 0.999664i | \(-0.508252\pi\) | ||||
−0.0259200 | + | 0.999664i | \(0.508252\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 17.6965i | − 0.871842i | ||||||||
\(413\) | − 17.0484i | − 0.838897i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.24030 | −0.256927 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.82774i | 0.0893977i | ||||||||
\(419\) | −25.9197 | −1.26626 | −0.633131 | − | 0.774045i | \(-0.718231\pi\) | ||||
−0.633131 | + | 0.774045i | \(0.718231\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.64064 | 0.372382 | 0.186191 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186191 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(422\) | − 31.2765i | − 1.52252i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.06324 | 0.148764 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.6103i | 0.755437i | ||||||||
\(428\) | − 2.84583i | − 0.137558i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.98516 | −0.384632 | −0.192316 | − | 0.981333i | \(-0.561600\pi\) | ||||
−0.192316 | + | 0.981333i | \(0.561600\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 12.5120i | − 0.601287i | −0.953737 | − | 0.300644i | \(-0.902799\pi\) | ||||
0.953737 | − | 0.300644i | \(-0.0972014\pi\) | |||||||
\(434\) | 65.6062 | 3.14920 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.1723 | 1.58866 | ||||||||
\(437\) | 3.10422i | 0.148495i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.76450 | 0.418307 | 0.209153 | − | 0.977883i | \(-0.432929\pi\) | ||||
0.209153 | + | 0.977883i | \(0.432929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 1.82774i | − 0.0869367i | ||||||||
\(443\) | − 3.67095i | − 0.174412i | −0.996190 | − | 0.0872062i | \(-0.972206\pi\) | ||||
0.996190 | − | 0.0872062i | \(-0.0277939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −55.9729 | −2.65040 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − 43.0032i | − 2.03171i | ||||||||
\(449\) | 28.1723 | 1.32953 | 0.664766 | − | 0.747052i | \(-0.268531\pi\) | ||||
0.664766 | + | 0.747052i | \(0.268531\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.242915 | 0.0114384 | ||||||||
\(452\) | − 28.0458i | − 1.31916i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.82032 | 0.132364 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 35.2616i | − 1.64947i | −0.565519 | − | 0.824735i | \(-0.691324\pi\) | ||||
0.565519 | − | 0.824735i | \(-0.308676\pi\) | |||||||
\(458\) | − 17.1803i | − 0.802784i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.6768 | −1.61506 | −0.807530 | − | 0.589826i | \(-0.799196\pi\) | ||||
−0.807530 | + | 0.589826i | \(0.799196\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.44874i | 0.346172i | 0.984907 | + | 0.173086i | \(0.0553739\pi\) | ||||
−0.984907 | + | 0.173086i | \(0.944626\pi\) | |||||||
\(464\) | −12.2961 | −0.570833 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −17.9145 | −0.829874 | ||||||||
\(467\) | 29.9655i | 1.38664i | 0.720630 | + | 0.693319i | \(0.243852\pi\) | ||||
−0.720630 | + | 0.693319i | \(0.756148\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.2691 | −1.53622 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.06324i | 0.140997i | ||||||||
\(473\) | − 1.10902i | − 0.0509930i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12.9926 | 0.595514 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 49.9097i | 2.28282i | ||||||||
\(479\) | −7.98516 | −0.364851 | −0.182426 | − | 0.983220i | \(-0.558395\pi\) | ||||
−0.182426 | + | 0.983220i | \(0.558395\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.87614 | 0.222333 | ||||||||
\(482\) | 13.0181i | 0.592958i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.5726 | 0.980573 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9442i | 0.541243i | 0.962686 | + | 0.270621i | \(0.0872291\pi\) | ||||
−0.962686 | + | 0.270621i | \(0.912771\pi\) | |||||||
\(488\) | − 2.80485i | − 0.126969i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.22066 | 0.416123 | 0.208061 | − | 0.978116i | \(-0.433285\pi\) | ||||
0.208061 | + | 0.978116i | \(0.433285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 5.24030i | − 0.236011i | ||||||||
\(494\) | −0.876139 | −0.0394193 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 24.4152 | 1.09627 | ||||||||
\(497\) | − 24.9926i | − 1.12107i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.1723 | −1.35070 | −0.675348 | − | 0.737499i | \(-0.736007\pi\) | ||||
−0.675348 | + | 0.737499i | \(0.736007\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 59.6062i | − 2.66035i | ||||||||
\(503\) | 10.5981i | 0.472546i | 0.971687 | + | 0.236273i | \(0.0759260\pi\) | ||||
−0.971687 | + | 0.236273i | \(0.924074\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −13.5094 | −0.600564 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | − 16.6487i | − 0.738667i | ||||||||
\(509\) | 28.7523 | 1.27442 | 0.637211 | − | 0.770689i | \(-0.280088\pi\) | ||||
0.637211 | + | 0.770689i | \(0.280088\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −50.4413 | −2.23139 | ||||||||
\(512\) | − 30.3094i | − 1.33950i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −37.5503 | −1.65627 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7449i | 0.648478i | ||||||||
\(518\) | 64.1378i | 2.81805i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.0942 | 1.58132 | 0.790658 | − | 0.612259i | \(-0.209739\pi\) | ||||
0.790658 | + | 0.612259i | \(0.209739\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1297i | 0.486669i | 0.969942 | + | 0.243334i | \(0.0782412\pi\) | ||||
−0.969942 | + | 0.243334i | \(0.921759\pi\) | |||||||
\(524\) | −14.1116 | −0.616470 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −66.4823 | −2.89877 | ||||||||
\(527\) | 10.4051i | 0.453255i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0558176 | 0.00242685 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 6.22808i | − 0.270021i | ||||||||
\(533\) | 0.116443i | 0.00504370i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.97774 | 0.258199 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 65.7071i | 2.83284i | ||||||||
\(539\) | −13.1090 | −0.564646 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7374 | −1.49348 | −0.746740 | − | 0.665116i | \(-0.768382\pi\) | ||||
−0.746740 | + | 0.665116i | \(0.768382\pi\) | |||||||
\(542\) | 6.75970i | 0.290354i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.9320 | 0.468704 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.71455i | 0.116066i | 0.998315 | + | 0.0580328i | \(0.0184828\pi\) | ||||
−0.998315 | + | 0.0580328i | \(0.981517\pi\) | |||||||
\(548\) | 17.5652i | 0.750347i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.51197 | −0.107014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 42.2691i | 1.79746i | ||||||||
\(554\) | 11.6507 | 0.494990 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.8155 | 0.797956 | ||||||||
\(557\) | − 8.93676i | − 0.378663i | −0.981913 | − | 0.189331i | \(-0.939368\pi\) | ||||
0.981913 | − | 0.189331i | \(-0.0606321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.531618 | 0.0224850 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − 50.2845i | − 2.12113i | ||||||||
\(563\) | 9.36261i | 0.394587i | 0.980344 | + | 0.197293i | \(0.0632152\pi\) | ||||
−0.980344 | + | 0.197293i | \(0.936785\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −21.9926 | −0.924417 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.49064i | 0.188423i | ||||||||
\(569\) | 35.8735 | 1.50390 | 0.751948 | − | 0.659222i | \(-0.229114\pi\) | ||||
0.751948 | + | 0.659222i | \(0.229114\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.0000 | 0.836974 | 0.418487 | − | 0.908223i | \(-0.362561\pi\) | ||||
0.418487 | + | 0.908223i | \(0.362561\pi\) | |||||||
\(572\) | − 2.06063i | − 0.0861591i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.53162 | −0.0639285 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 1.35675i | − 0.0564821i | −0.999601 | − | 0.0282411i | \(-0.991009\pi\) | ||||
0.999601 | − | 0.0282411i | \(-0.00899060\pi\) | |||||||
\(578\) | − 31.6513i | − 1.31652i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 50.0894 | 2.07806 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 5.64064i | − 0.233612i | ||||||||
\(584\) | 9.06324 | 0.375039 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −39.6210 | −1.63673 | ||||||||
\(587\) | 28.7900i | 1.18829i | 0.804358 | + | 0.594145i | \(0.202510\pi\) | ||||
−0.804358 | + | 0.594145i | \(0.797490\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.98777 | 0.205518 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.8687i | 0.980998i | ||||||||
\(593\) | − 30.9171i | − 1.26961i | −0.772671 | − | 0.634807i | \(-0.781080\pi\) | ||||
0.772671 | − | 0.634807i | \(-0.218920\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 24.8949 | 1.01973 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 6.47580i | − 0.264815i | ||||||||
\(599\) | 1.39292 | 0.0569132 | 0.0284566 | − | 0.999595i | \(-0.490941\pi\) | ||||
0.0284566 | + | 0.999595i | \(0.490941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.82513 | 0.359985 | 0.179992 | − | 0.983668i | \(-0.442393\pi\) | ||||
0.179992 | + | 0.983668i | \(0.442393\pi\) | |||||||
\(602\) | 6.99258i | 0.284996i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −41.6210 | −1.69353 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.15678i | 0.0875412i | 0.999042 | + | 0.0437706i | \(0.0139371\pi\) | ||||
−0.999042 | + | 0.0437706i | \(0.986063\pi\) | |||||||
\(608\) | − 5.24030i | − 0.212522i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.06804 | −0.285942 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 9.57521i | − 0.386739i | −0.981126 | − | 0.193370i | \(-0.938058\pi\) | ||||
0.981126 | − | 0.193370i | \(-0.0619416\pi\) | |||||||
\(614\) | −61.4971 | −2.48182 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.05582 | 0.163414 | ||||||||
\(617\) | − 37.6768i | − 1.51681i | −0.651783 | − | 0.758406i | \(-0.725979\pi\) | ||||
0.651783 | − | 0.758406i | \(-0.274021\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.1042 | −0.687477 | −0.343738 | − | 0.939065i | \(-0.611693\pi\) | ||||
−0.343738 | + | 0.939065i | \(0.611693\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 19.6358i | − 0.787325i | ||||||||
\(623\) | 12.2584i | 0.491122i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 24.2429 | 0.968942 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 5.95421i | − 0.237599i | ||||||||
\(629\) | −10.1723 | −0.405595 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1090 | 1.31805 | 0.659025 | − | 0.752121i | \(-0.270969\pi\) | ||||
0.659025 | + | 0.752121i | \(0.270969\pi\) | |||||||
\(632\) | − 7.59485i | − 0.302107i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19.1500 | −0.760544 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.28390i | − 0.248977i | ||||||||
\(638\) | − 10.9320i | − 0.432800i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.1526 | 0.914473 | 0.457237 | − | 0.889345i | \(-0.348839\pi\) | ||||
0.457237 | + | 0.889345i | \(0.348839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 43.0639i | 1.69827i | 0.528173 | + | 0.849137i | \(0.322877\pi\) | ||||
−0.528173 | + | 0.849137i | \(0.677123\pi\) | |||||||
\(644\) | 46.0336 | 1.81398 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.82774 | 0.0719115 | ||||||||
\(647\) | − 20.6439i | − 0.811595i | −0.913963 | − | 0.405798i | \(-0.866994\pi\) | ||||
0.913963 | − | 0.405798i | \(-0.133006\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.64064 | 0.221415 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 19.9346i | − 0.780698i | ||||||||
\(653\) | − 6.83516i | − 0.267480i | −0.991016 | − | 0.133740i | \(-0.957301\pi\) | ||||
0.991016 | − | 0.133740i | \(-0.0426988\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.569988 | −0.0222543 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 92.9688i | − 3.62430i | ||||||||
\(659\) | −26.8613 | −1.04637 | −0.523184 | − | 0.852220i | \(-0.675256\pi\) | ||||
−0.523184 | + | 0.852220i | \(0.675256\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.12125 | −0.0825071 | −0.0412535 | − | 0.999149i | \(-0.513135\pi\) | ||||
−0.0412535 | + | 0.999149i | \(0.513135\pi\) | |||||||
\(662\) | 15.0632i | 0.585449i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.00000 | −0.349268 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 18.5667i | − 0.718907i | ||||||||
\(668\) | − 29.9500i | − 1.15880i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.16484 | −0.199387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.8203i | 1.34222i | 0.741356 | + | 0.671112i | \(0.234183\pi\) | ||||
−0.741356 | + | 0.671112i | \(0.765817\pi\) | |||||||
\(674\) | −4.76450 | −0.183522 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −29.5874 | −1.13798 | ||||||||
\(677\) | − 24.6842i | − 0.948692i | −0.880338 | − | 0.474346i | \(-0.842685\pi\) | ||||
0.880338 | − | 0.474346i | \(-0.157315\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 55.4897 | 2.12950 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 21.7065i | 0.831184i | ||||||||
\(683\) | 38.4610i | 1.47167i | 0.677162 | + | 0.735834i | \(0.263210\pi\) | ||||
−0.677162 | + | 0.735834i | \(0.736790\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 22.9852 | 0.877578 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.60227i | 0.0992107i | ||||||||
\(689\) | 2.70388 | 0.103010 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.480608 | 0.0182832 | 0.00914159 | − | 0.999958i | \(-0.497090\pi\) | ||||
0.00914159 | + | 0.999958i | \(0.497090\pi\) | |||||||
\(692\) | 54.2084i | 2.06070i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.47841 | −0.0561197 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 0.242915i | − 0.00920105i | ||||||||
\(698\) | − 44.5274i | − 1.68539i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1797 | 0.686637 | 0.343318 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343318 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.87614i | 0.183907i | ||||||||
\(704\) | 14.2281 | 0.536241 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.0632 | 0.792725 | ||||||||
\(707\) | − 6.00000i | − 0.225653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.18710 | −0.269917 | −0.134959 | − | 0.990851i | \(-0.543090\pi\) | ||||
−0.134959 | + | 0.990851i | \(0.543090\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 2.20257i | − 0.0825449i | ||||||||
\(713\) | 36.8661i | 1.38065i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.24030 | −0.195839 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 63.7475i | − 2.37903i | ||||||||
\(719\) | 12.5168 | 0.466797 | 0.233399 | − | 0.972381i | \(-0.425015\pi\) | ||||
0.233399 | + | 0.972381i | \(0.425015\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.7449 | 1.14500 | ||||||||
\(722\) | 38.7603i | 1.44251i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.10161 | −0.0409409 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.42584i | − 0.312497i | −0.987718 | − | 0.156249i | \(-0.950060\pi\) | ||||
0.987718 | − | 0.156249i | \(-0.0499401\pi\) | |||||||
\(728\) | 1.94418i | 0.0720562i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.10902 | −0.0410187 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 22.0000i | − 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | 14.9777 | 0.552839 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 38.7326 | 1.42770 | ||||||||
\(737\) | − 11.0074i | − 0.405463i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81290 | 0.0666887 | 0.0333444 | − | 0.999444i | \(-0.489384\pi\) | ||||
0.0333444 | + | 0.999444i | \(0.489384\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 35.5652i | 1.30564i | ||||||||
\(743\) | − 20.1371i | − 0.738760i | −0.929278 | − | 0.369380i | \(-0.879570\pi\) | ||||
0.929278 | − | 0.369380i | \(-0.120430\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −45.7374 | −1.67457 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.29873i | 0.157177i | ||||||||
\(749\) | 4.94418 | 0.180656 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.2132 | 0.445668 | 0.222834 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222834 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(752\) | − 34.5981i | − 1.26166i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.24030 | 0.190841 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 52.9533i | − 1.92462i | −0.271955 | − | 0.962310i | \(-0.587670\pi\) | ||||
0.271955 | − | 0.962310i | \(-0.412330\pi\) | |||||||
\(758\) | − 36.2839i | − 1.31789i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.4535 | 0.668940 | 0.334470 | − | 0.942406i | \(-0.391443\pi\) | ||||
0.334470 | + | 0.942406i | \(0.391443\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 57.6317i | 2.08641i | ||||||||
\(764\) | −47.5752 | −1.72121 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.992582 | −0.0358634 | ||||||||
\(767\) | 2.70388i | 0.0976314i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.45355 | 0.160599 | 0.0802995 | − | 0.996771i | \(-0.474412\pi\) | ||||
0.0802995 | + | 0.996771i | \(0.474412\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 46.8726i | 1.68698i | ||||||||
\(773\) | − 38.9368i | − 1.40046i | −0.713918 | − | 0.700229i | \(-0.753081\pi\) | ||||
0.713918 | − | 0.700229i | \(-0.246919\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −9.97033 | −0.357914 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.6561i | 0.417892i | ||||||||
\(779\) | −0.116443 | −0.00417200 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.26906 | 0.295890 | ||||||||
\(782\) | 13.5094i | 0.483094i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 30.7597 | 1.09856 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.2281i | − 1.22010i | −0.792363 | − | 0.610050i | \(-0.791150\pi\) | ||||
0.792363 | − | 0.610050i | \(-0.208850\pi\) | |||||||
\(788\) | 36.6433i | 1.30536i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 48.7252 | 1.73247 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 2.47580i | − 0.0879183i | ||||||||
\(794\) | −7.82774 | −0.277796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.43129 | 0.298839 | ||||||||
\(797\) | 23.9655i | 0.848902i | 0.905451 | + | 0.424451i | \(0.139533\pi\) | ||||
−0.905451 | + | 0.424451i | \(0.860467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 14.7449 | 0.521636 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49.1600i | 1.73590i | ||||||||
\(803\) | − 16.6890i | − 0.588943i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −10.4051 | −0.366506 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.07807i | 0.0379265i | ||||||||
\(809\) | −0.283896 | −0.00998124 | −0.00499062 | − | 0.999988i | \(-0.501589\pi\) | ||||
−0.00499062 | + | 0.999988i | \(0.501589\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.4413 | 1.13917 | 0.569584 | − | 0.821933i | \(-0.307104\pi\) | ||||
0.569584 | + | 0.821933i | \(0.307104\pi\) | |||||||
\(812\) | 37.2510i | 1.30725i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −21.2207 | −0.743784 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.531618i | 0.0185990i | ||||||||
\(818\) | 2.18710i | 0.0764701i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.6694 | −1.45427 | −0.727136 | − | 0.686493i | \(-0.759149\pi\) | ||||
−0.727136 | + | 0.686493i | \(0.759149\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 19.3626i | − 0.674938i | −0.941337 | − | 0.337469i | \(-0.890429\pi\) | ||||
0.941337 | − | 0.337469i | \(-0.109571\pi\) | |||||||
\(824\) | −5.52420 | −0.192445 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.5652 | −1.23747 | ||||||||
\(827\) | 18.8097i | 0.654076i | 0.945011 | + | 0.327038i | \(0.106050\pi\) | ||||
−0.945011 | + | 0.327038i | \(0.893950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.1016 | 1.14967 | 0.574833 | − | 0.818271i | \(-0.305067\pi\) | ||||
0.574833 | + | 0.818271i | \(0.305067\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.82032i | 0.236452i | ||||||||
\(833\) | 13.1090i | 0.454201i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.06063 | 0.0712682 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 54.0719i | 1.86788i | ||||||||
\(839\) | −39.6965 | −1.37047 | −0.685237 | − | 0.728320i | \(-0.740301\pi\) | ||||
−0.685237 | + | 0.728320i | \(0.740301\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9755 | −0.481915 | ||||||||
\(842\) | − 15.9394i | − 0.549307i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.2616 | −1.21376 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 37.4791i | 1.28780i | ||||||||
\(848\) | 13.2355i | 0.454509i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.0410 | −1.23547 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 4.11644i | − 0.140944i | −0.997514 | − | 0.0704722i | \(-0.977549\pi\) | ||||
0.997514 | − | 0.0704722i | \(-0.0224506\pi\) | |||||||
\(854\) | 32.5652 | 1.11436 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.888365 | −0.0303637 | ||||||||
\(857\) | 14.7449i | 0.503675i | 0.967770 | + | 0.251837i | \(0.0810348\pi\) | ||||
−0.967770 | + | 0.251837i | \(0.918965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.8539 | 1.29156 | 0.645779 | − | 0.763524i | \(-0.276533\pi\) | ||||
0.645779 | + | 0.763524i | \(0.276533\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 16.6581i | 0.567377i | ||||||||
\(863\) | − 26.7704i | − 0.911274i | −0.890166 | − | 0.455637i | \(-0.849412\pi\) | ||||
0.890166 | − | 0.455637i | \(-0.150588\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −26.1016 | −0.886969 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 73.9655i | − 2.51055i | ||||||||
\(869\) | −13.9852 | −0.474414 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.27648 | 0.178787 | ||||||||
\(872\) | − 10.3552i | − 0.350671i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.47580 | 0.219047 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 46.9681i | 1.58600i | 0.609221 | + | 0.793001i | \(0.291482\pi\) | ||||
−0.609221 | + | 0.793001i | \(0.708518\pi\) | |||||||
\(878\) | − 18.2839i | − 0.617052i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.8055 | 0.667264 | 0.333632 | − | 0.942703i | \(-0.391726\pi\) | ||||
0.333632 | + | 0.942703i | \(0.391726\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.20257i | − 0.208733i | −0.994539 | − | 0.104367i | \(-0.966718\pi\) | ||||
0.994539 | − | 0.104367i | \(-0.0332815\pi\) | |||||||
\(884\) | −2.06063 | −0.0693063 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.65809 | −0.257279 | ||||||||
\(887\) | 13.4274i | 0.450848i | 0.974261 | + | 0.225424i | \(0.0723767\pi\) | ||||
−0.974261 | + | 0.225424i | \(0.927623\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.9245 | 0.970098 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 63.1049i | 2.11291i | ||||||||
\(893\) | − 7.06804i | − 0.236523i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −23.6284 | −0.789370 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − 58.7710i | − 1.96121i | ||||||||
\(899\) | −29.8325 | −0.994971 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.64064 | −0.187917 | ||||||||
\(902\) | − 0.506752i | − 0.0168730i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8.75489 | −0.291183 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 0.673566i | − 0.0223654i | −0.999937 | − | 0.0111827i | \(-0.996440\pi\) | ||||
0.999937 | − | 0.0111827i | \(-0.00355964\pi\) | |||||||
\(908\) | − 3.17968i | − 0.105521i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.90970 | 0.262060 | 0.131030 | − | 0.991378i | \(-0.458172\pi\) | ||||
0.131030 | + | 0.991378i | \(0.458172\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 16.5726i | 0.548473i | ||||||||
\(914\) | −73.5604 | −2.43316 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.3694 | −0.639983 | ||||||||
\(917\) | − 24.5168i | − 0.809615i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.58263 | 0.283115 | 0.141557 | − | 0.989930i | \(-0.454789\pi\) | ||||
0.141557 | + | 0.989930i | \(0.454789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 72.3404i | 2.38240i | ||||||||
\(923\) | 3.96383i | 0.130471i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 15.5390 | 0.510644 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 31.3430i | 1.02888i | ||||||||
\(929\) | 29.6162 | 0.971676 | 0.485838 | − | 0.874049i | \(-0.338515\pi\) | ||||
0.485838 | + | 0.874049i | \(0.338515\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.28390 | 0.205946 | ||||||||
\(932\) | 20.1971i | 0.661579i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 62.5120 | 2.04545 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.2058i | 0.496753i | 0.968664 | + | 0.248376i | \(0.0798969\pi\) | ||||
−0.968664 | + | 0.248376i | \(0.920103\pi\) | |||||||
\(938\) | 69.4036i | 2.26611i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.65287 | −0.184278 | −0.0921391 | − | 0.995746i | \(-0.529370\pi\) | ||||
−0.0921391 | + | 0.995746i | \(0.529370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.860663i | − 0.0280270i | ||||||||
\(944\) | −13.2355 | −0.430779 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.31357 | −0.0752206 | ||||||||
\(947\) | − 40.3962i | − 1.31270i | −0.754457 | − | 0.656350i | \(-0.772100\pi\) | ||||
0.754457 | − | 0.656350i | \(-0.227900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.00000 | 0.259691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − 4.05582i | − 0.131450i | ||||||||
\(953\) | 22.9320i | 0.742839i | 0.928465 | + | 0.371419i | \(0.121129\pi\) | ||||
−0.928465 | + | 0.371419i | \(0.878871\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 56.2691 | 1.81987 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 16.6581i | 0.538198i | ||||||||
\(959\) | −30.5168 | −0.985438 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.2355 | 0.910822 | ||||||||
\(962\) | − 10.1723i | − 0.327967i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.6768 | 0.472708 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 10.3700i | − 0.333478i | −0.986001 | − | 0.166739i | \(-0.946676\pi\) | ||||
0.986001 | − | 0.166739i | \(-0.0533237\pi\) | |||||||
\(968\) | − 6.73419i | − 0.216445i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −48.0410 | −1.54171 | −0.770854 | − | 0.637012i | \(-0.780170\pi\) | ||||
−0.770854 | + | 0.637012i | \(0.780170\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.6890i | 1.04796i | ||||||||
\(974\) | 24.9171 | 0.798396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.1191 | 0.387921 | ||||||||
\(977\) | 27.0532i | 0.865509i | 0.901512 | + | 0.432754i | \(0.142458\pi\) | ||||
−0.901512 | + | 0.432754i | \(0.857542\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.05582 | −0.129624 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 19.2355i | − 0.613829i | ||||||||
\(983\) | 22.4817i | 0.717054i | 0.933519 | + | 0.358527i | \(0.116721\pi\) | ||||
−0.933519 | + | 0.358527i | \(0.883279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.9320 | −0.348144 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.987774i | 0.0314253i | ||||||||
\(989\) | −3.92935 | −0.124946 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.5316 | −0.842805 | −0.421402 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421402 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(992\) | − 62.2346i | − 1.97595i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −52.1378 | −1.65371 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.3659i | 0.898356i | 0.893442 | + | 0.449178i | \(0.148283\pi\) | ||||
−0.893442 | + | 0.449178i | \(0.851717\pi\) | |||||||
\(998\) | 62.9433i | 1.99243i | ||||||||
\(999\) | 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.m.649.2 | 6 | ||
3.2 | odd | 2 | 2025.2.b.l.649.5 | 6 | |||
5.2 | odd | 4 | 405.2.a.i.1.3 | 3 | |||
5.3 | odd | 4 | 2025.2.a.o.1.1 | 3 | |||
5.4 | even | 2 | inner | 2025.2.b.m.649.5 | 6 | ||
9.2 | odd | 6 | 225.2.k.b.49.5 | 12 | |||
9.4 | even | 3 | 675.2.k.b.424.5 | 12 | |||
9.5 | odd | 6 | 225.2.k.b.124.2 | 12 | |||
9.7 | even | 3 | 675.2.k.b.199.2 | 12 | |||
15.2 | even | 4 | 405.2.a.j.1.1 | 3 | |||
15.8 | even | 4 | 2025.2.a.n.1.3 | 3 | |||
15.14 | odd | 2 | 2025.2.b.l.649.2 | 6 | |||
20.7 | even | 4 | 6480.2.a.bs.1.1 | 3 | |||
45.2 | even | 12 | 45.2.e.b.31.3 | yes | 6 | ||
45.4 | even | 6 | 675.2.k.b.424.2 | 12 | |||
45.7 | odd | 12 | 135.2.e.b.91.1 | 6 | |||
45.13 | odd | 12 | 675.2.e.b.451.3 | 6 | |||
45.14 | odd | 6 | 225.2.k.b.124.5 | 12 | |||
45.22 | odd | 12 | 135.2.e.b.46.1 | 6 | |||
45.23 | even | 12 | 225.2.e.b.151.1 | 6 | |||
45.29 | odd | 6 | 225.2.k.b.49.2 | 12 | |||
45.32 | even | 12 | 45.2.e.b.16.3 | ✓ | 6 | ||
45.34 | even | 6 | 675.2.k.b.199.5 | 12 | |||
45.38 | even | 12 | 225.2.e.b.76.1 | 6 | |||
45.43 | odd | 12 | 675.2.e.b.226.3 | 6 | |||
60.47 | odd | 4 | 6480.2.a.bv.1.1 | 3 | |||
180.7 | even | 12 | 2160.2.q.k.1441.3 | 6 | |||
180.47 | odd | 12 | 720.2.q.i.481.3 | 6 | |||
180.67 | even | 12 | 2160.2.q.k.721.3 | 6 | |||
180.167 | odd | 12 | 720.2.q.i.241.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.2.e.b.16.3 | ✓ | 6 | 45.32 | even | 12 | ||
45.2.e.b.31.3 | yes | 6 | 45.2 | even | 12 | ||
135.2.e.b.46.1 | 6 | 45.22 | odd | 12 | |||
135.2.e.b.91.1 | 6 | 45.7 | odd | 12 | |||
225.2.e.b.76.1 | 6 | 45.38 | even | 12 | |||
225.2.e.b.151.1 | 6 | 45.23 | even | 12 | |||
225.2.k.b.49.2 | 12 | 45.29 | odd | 6 | |||
225.2.k.b.49.5 | 12 | 9.2 | odd | 6 | |||
225.2.k.b.124.2 | 12 | 9.5 | odd | 6 | |||
225.2.k.b.124.5 | 12 | 45.14 | odd | 6 | |||
405.2.a.i.1.3 | 3 | 5.2 | odd | 4 | |||
405.2.a.j.1.1 | 3 | 15.2 | even | 4 | |||
675.2.e.b.226.3 | 6 | 45.43 | odd | 12 | |||
675.2.e.b.451.3 | 6 | 45.13 | odd | 12 | |||
675.2.k.b.199.2 | 12 | 9.7 | even | 3 | |||
675.2.k.b.199.5 | 12 | 45.34 | even | 6 | |||
675.2.k.b.424.2 | 12 | 45.4 | even | 6 | |||
675.2.k.b.424.5 | 12 | 9.4 | even | 3 | |||
720.2.q.i.241.3 | 6 | 180.167 | odd | 12 | |||
720.2.q.i.481.3 | 6 | 180.47 | odd | 12 | |||
2025.2.a.n.1.3 | 3 | 15.8 | even | 4 | |||
2025.2.a.o.1.1 | 3 | 5.3 | odd | 4 | |||
2025.2.b.l.649.2 | 6 | 15.14 | odd | 2 | |||
2025.2.b.l.649.5 | 6 | 3.2 | odd | 2 | |||
2025.2.b.m.649.2 | 6 | 1.1 | even | 1 | trivial | ||
2025.2.b.m.649.5 | 6 | 5.4 | even | 2 | inner | ||
2160.2.q.k.721.3 | 6 | 180.67 | even | 12 | |||
2160.2.q.k.1441.3 | 6 | 180.7 | even | 12 | |||
6480.2.a.bs.1.1 | 3 | 20.7 | even | 4 | |||
6480.2.a.bv.1.1 | 3 | 60.47 | odd | 4 |