Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, 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("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 22x^{10} + 179x^{8} + 641x^{6} + 869x^{4} + 67x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.6 | ||
Root | \(-0.141689i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.f.1249.7 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.141689i | − 0.100190i | −0.998744 | − | 0.0500948i | \(-0.984048\pi\) | ||||
0.998744 | − | 0.0500948i | \(-0.0159523\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.97992 | 0.989962 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.141689 | 0.0578445 | ||||||||
\(7\) | − 0.858311i | − 0.324411i | −0.986757 | − | 0.162205i | \(-0.948139\pi\) | ||||
0.986757 | − | 0.162205i | \(-0.0518607\pi\) | |||||||
\(8\) | − 0.563913i | − 0.199374i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.67993 | −1.10954 | −0.554770 | − | 0.832004i | \(-0.687194\pi\) | ||||
−0.554770 | + | 0.832004i | \(0.687194\pi\) | |||||||
\(12\) | 1.97992i | 0.571555i | ||||||||
\(13\) | − 4.58134i | − 1.27064i | −0.772251 | − | 0.635318i | \(-0.780869\pi\) | ||||
0.772251 | − | 0.635318i | \(-0.219131\pi\) | |||||||
\(14\) | −0.121614 | −0.0325026 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.87995 | 0.969987 | ||||||||
\(17\) | − 5.30702i | − 1.28714i | −0.765387 | − | 0.643571i | \(-0.777452\pi\) | ||||
0.765387 | − | 0.643571i | \(-0.222548\pi\) | |||||||
\(18\) | 0.141689i | 0.0333965i | ||||||||
\(19\) | −6.36870 | −1.46108 | −0.730540 | − | 0.682870i | \(-0.760732\pi\) | ||||
−0.730540 | + | 0.682870i | \(0.760732\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.858311 | 0.187299 | ||||||||
\(22\) | 0.521407i | 0.111164i | ||||||||
\(23\) | − 3.42379i | − 0.713909i | −0.934122 | − | 0.356954i | \(-0.883815\pi\) | ||||
0.934122 | − | 0.356954i | \(-0.116185\pi\) | |||||||
\(24\) | 0.563913 | 0.115108 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.649128 | −0.127304 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 1.69939i | − 0.321154i | ||||||||
\(29\) | −3.73405 | −0.693396 | −0.346698 | − | 0.937977i | \(-0.612697\pi\) | ||||
−0.346698 | + | 0.937977i | \(0.612697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.25290 | 0.225028 | 0.112514 | − | 0.993650i | \(-0.464110\pi\) | ||||
0.112514 | + | 0.993650i | \(0.464110\pi\) | |||||||
\(32\) | − 1.67757i | − 0.296556i | ||||||||
\(33\) | − 3.67993i | − 0.640593i | ||||||||
\(34\) | −0.751949 | −0.128958 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.97992 | −0.329987 | ||||||||
\(37\) | − 7.45067i | − 1.22488i | −0.790516 | − | 0.612441i | \(-0.790188\pi\) | ||||
0.790516 | − | 0.612441i | \(-0.209812\pi\) | |||||||
\(38\) | 0.902378i | 0.146385i | ||||||||
\(39\) | 4.58134 | 0.733602 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.53168 | −0.395381 | −0.197691 | − | 0.980264i | \(-0.563344\pi\) | ||||
−0.197691 | + | 0.980264i | \(0.563344\pi\) | |||||||
\(42\) | − 0.121614i | − 0.0187654i | ||||||||
\(43\) | 3.37972i | 0.515402i | 0.966225 | + | 0.257701i | \(0.0829650\pi\) | ||||
−0.966225 | + | 0.257701i | \(0.917035\pi\) | |||||||
\(44\) | −7.28598 | −1.09840 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.485114 | −0.0715262 | ||||||||
\(47\) | − 8.49937i | − 1.23976i | −0.784696 | − | 0.619880i | \(-0.787181\pi\) | ||||
0.784696 | − | 0.619880i | \(-0.212819\pi\) | |||||||
\(48\) | 3.87995i | 0.560022i | ||||||||
\(49\) | 6.26330 | 0.894758 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.30702 | 0.743132 | ||||||||
\(52\) | − 9.07071i | − 1.25788i | ||||||||
\(53\) | 2.34827i | 0.322560i | 0.986909 | + | 0.161280i | \(0.0515622\pi\) | ||||
−0.986909 | + | 0.161280i | \(0.948438\pi\) | |||||||
\(54\) | −0.141689 | −0.0192815 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.484013 | −0.0646789 | ||||||||
\(57\) | − 6.36870i | − 0.843555i | ||||||||
\(58\) | 0.529076i | 0.0694710i | ||||||||
\(59\) | −13.1264 | −1.70891 | −0.854455 | − | 0.519525i | \(-0.826109\pi\) | ||||
−0.854455 | + | 0.519525i | \(0.826109\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.3476 | 1.32488 | 0.662439 | − | 0.749116i | \(-0.269521\pi\) | ||||
0.662439 | + | 0.749116i | \(0.269521\pi\) | |||||||
\(62\) | − 0.177523i | − 0.0225454i | ||||||||
\(63\) | 0.858311i | 0.108137i | ||||||||
\(64\) | 7.52220 | 0.940275 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.521407 | −0.0641808 | ||||||||
\(67\) | 3.34649i | 0.408838i | 0.978883 | + | 0.204419i | \(0.0655305\pi\) | ||||
−0.978883 | + | 0.204419i | \(0.934469\pi\) | |||||||
\(68\) | − 10.5075i | − 1.27422i | ||||||||
\(69\) | 3.42379 | 0.412175 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.32289 | −0.513032 | −0.256516 | − | 0.966540i | \(-0.582575\pi\) | ||||
−0.256516 | + | 0.966540i | \(0.582575\pi\) | |||||||
\(72\) | 0.563913i | 0.0664578i | ||||||||
\(73\) | 9.08007i | 1.06274i | 0.847139 | + | 0.531371i | \(0.178323\pi\) | ||||
−0.847139 | + | 0.531371i | \(0.821677\pi\) | |||||||
\(74\) | −1.05568 | −0.122721 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.6095 | −1.44641 | ||||||||
\(77\) | 3.15852i | 0.359947i | ||||||||
\(78\) | − 0.649128i | − 0.0734993i | ||||||||
\(79\) | 3.24730 | 0.365350 | 0.182675 | − | 0.983173i | \(-0.441524\pi\) | ||||
0.182675 | + | 0.983173i | \(0.441524\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.358712i | 0.0396131i | ||||||||
\(83\) | 7.39269i | 0.811453i | 0.913994 | + | 0.405727i | \(0.132981\pi\) | ||||
−0.913994 | + | 0.405727i | \(0.867019\pi\) | |||||||
\(84\) | 1.69939 | 0.185419 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.478870 | 0.0516379 | ||||||||
\(87\) | − 3.73405i | − 0.400332i | ||||||||
\(88\) | 2.07516i | 0.221213i | ||||||||
\(89\) | 15.4975 | 1.64273 | 0.821367 | − | 0.570400i | \(-0.193212\pi\) | ||||
0.821367 | + | 0.570400i | \(0.193212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.93221 | −0.412208 | ||||||||
\(92\) | − 6.77883i | − 0.706742i | ||||||||
\(93\) | 1.25290i | 0.129920i | ||||||||
\(94\) | −1.20427 | −0.124211 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.67757 | 0.171217 | ||||||||
\(97\) | − 10.0386i | − 1.01926i | −0.860393 | − | 0.509631i | \(-0.829782\pi\) | ||||
0.860393 | − | 0.509631i | \(-0.170218\pi\) | |||||||
\(98\) | − 0.887444i | − 0.0896454i | ||||||||
\(99\) | 3.67993 | 0.369847 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.714616 | −0.0711070 | −0.0355535 | − | 0.999368i | \(-0.511319\pi\) | ||||
−0.0355535 | + | 0.999368i | \(0.511319\pi\) | |||||||
\(102\) | − 0.751949i | − 0.0744541i | ||||||||
\(103\) | − 0.780764i | − 0.0769310i | −0.999260 | − | 0.0384655i | \(-0.987753\pi\) | ||||
0.999260 | − | 0.0384655i | \(-0.0122470\pi\) | |||||||
\(104\) | −2.58348 | −0.253331 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.332725 | 0.0323171 | ||||||||
\(107\) | 11.9601i | 1.15623i | 0.815957 | + | 0.578113i | \(0.196211\pi\) | ||||
−0.815957 | + | 0.578113i | \(0.803789\pi\) | |||||||
\(108\) | − 1.97992i | − 0.190518i | ||||||||
\(109\) | −2.43384 | −0.233119 | −0.116560 | − | 0.993184i | \(-0.537187\pi\) | ||||
−0.116560 | + | 0.993184i | \(0.537187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.45067 | 0.707186 | ||||||||
\(112\) | − 3.33020i | − 0.314674i | ||||||||
\(113\) | 16.0354i | 1.50848i | 0.656599 | + | 0.754240i | \(0.271994\pi\) | ||||
−0.656599 | + | 0.754240i | \(0.728006\pi\) | |||||||
\(114\) | −0.902378 | −0.0845154 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.39313 | −0.686435 | ||||||||
\(117\) | 4.58134i | 0.423545i | ||||||||
\(118\) | 1.85987i | 0.171215i | ||||||||
\(119\) | −4.55507 | −0.417563 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.54188 | 0.231080 | ||||||||
\(122\) | − 1.46615i | − 0.132739i | ||||||||
\(123\) | − 2.53168i | − 0.228274i | ||||||||
\(124\) | 2.48065 | 0.222769 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.121614 | 0.0108342 | ||||||||
\(127\) | − 3.83848i | − 0.340610i | −0.985391 | − | 0.170305i | \(-0.945525\pi\) | ||||
0.985391 | − | 0.170305i | \(-0.0544753\pi\) | |||||||
\(128\) | − 4.42097i | − 0.390762i | ||||||||
\(129\) | −3.37972 | −0.297568 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.4495 | −1.08771 | −0.543857 | − | 0.839178i | \(-0.683037\pi\) | ||||
−0.543857 | + | 0.839178i | \(0.683037\pi\) | |||||||
\(132\) | − 7.28598i | − 0.634163i | ||||||||
\(133\) | 5.46632i | 0.473990i | ||||||||
\(134\) | 0.474162 | 0.0409613 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.99270 | −0.256622 | ||||||||
\(137\) | − 11.8589i | − 1.01317i | −0.862189 | − | 0.506587i | \(-0.830907\pi\) | ||||
0.862189 | − | 0.506587i | \(-0.169093\pi\) | |||||||
\(138\) | − 0.485114i | − 0.0412957i | ||||||||
\(139\) | 4.66089 | 0.395332 | 0.197666 | − | 0.980269i | \(-0.436664\pi\) | ||||
0.197666 | + | 0.980269i | \(0.436664\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.49937 | 0.715776 | ||||||||
\(142\) | 0.612508i | 0.0514005i | ||||||||
\(143\) | 16.8590i | 1.40982i | ||||||||
\(144\) | −3.87995 | −0.323329 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.28655 | 0.106476 | ||||||||
\(147\) | 6.26330i | 0.516589i | ||||||||
\(148\) | − 14.7518i | − 1.21259i | ||||||||
\(149\) | 11.5480 | 0.946053 | 0.473026 | − | 0.881048i | \(-0.343162\pi\) | ||||
0.473026 | + | 0.881048i | \(0.343162\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 24.4694 | 1.99129 | 0.995646 | − | 0.0932103i | \(-0.0297129\pi\) | ||||
0.995646 | + | 0.0932103i | \(0.0297129\pi\) | |||||||
\(152\) | 3.59140i | 0.291301i | ||||||||
\(153\) | 5.30702i | 0.429047i | ||||||||
\(154\) | 0.447529 | 0.0360629 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.07071 | 0.726238 | ||||||||
\(157\) | − 22.3660i | − 1.78500i | −0.451045 | − | 0.892501i | \(-0.648948\pi\) | ||||
0.451045 | − | 0.892501i | \(-0.351052\pi\) | |||||||
\(158\) | − 0.460109i | − 0.0366043i | ||||||||
\(159\) | −2.34827 | −0.186230 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.93867 | −0.231600 | ||||||||
\(162\) | − 0.141689i | − 0.0111322i | ||||||||
\(163\) | 0.813450i | 0.0637143i | 0.999492 | + | 0.0318572i | \(0.0101422\pi\) | ||||
−0.999492 | + | 0.0318572i | \(0.989858\pi\) | |||||||
\(164\) | −5.01253 | −0.391413 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.04747 | 0.0812992 | ||||||||
\(167\) | − 25.1660i | − 1.94740i | −0.227833 | − | 0.973700i | \(-0.573164\pi\) | ||||
0.227833 | − | 0.973700i | \(-0.426836\pi\) | |||||||
\(168\) | − 0.484013i | − 0.0373424i | ||||||||
\(169\) | −7.98869 | −0.614515 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.36870 | 0.487027 | ||||||||
\(172\) | 6.69158i | 0.510229i | ||||||||
\(173\) | − 0.410945i | − 0.0312436i | −0.999878 | − | 0.0156218i | \(-0.995027\pi\) | ||||
0.999878 | − | 0.0156218i | \(-0.00497277\pi\) | |||||||
\(174\) | −0.529076 | −0.0401091 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −14.2779 | −1.07624 | ||||||||
\(177\) | − 13.1264i | − 0.986640i | ||||||||
\(178\) | − 2.19584i | − 0.164585i | ||||||||
\(179\) | 14.8502 | 1.10996 | 0.554978 | − | 0.831865i | \(-0.312727\pi\) | ||||
0.554978 | + | 0.831865i | \(0.312727\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.739223 | 0.0549460 | 0.0274730 | − | 0.999623i | \(-0.491254\pi\) | ||||
0.0274730 | + | 0.999623i | \(0.491254\pi\) | |||||||
\(182\) | 0.557153i | 0.0412990i | ||||||||
\(183\) | 10.3476i | 0.764919i | ||||||||
\(184\) | −1.93072 | −0.142334 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0.177523 | 0.0130166 | ||||||||
\(187\) | 19.5295i | 1.42814i | ||||||||
\(188\) | − 16.8281i | − 1.22732i | ||||||||
\(189\) | −0.858311 | −0.0624329 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.72506 | −0.197179 | −0.0985893 | − | 0.995128i | \(-0.531433\pi\) | ||||
−0.0985893 | + | 0.995128i | \(0.531433\pi\) | |||||||
\(192\) | 7.52220i | 0.542868i | ||||||||
\(193\) | − 14.2040i | − 1.02243i | −0.859453 | − | 0.511215i | \(-0.829196\pi\) | ||||
0.859453 | − | 0.511215i | \(-0.170804\pi\) | |||||||
\(194\) | −1.42236 | −0.102120 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4009 | 0.885776 | ||||||||
\(197\) | − 5.54591i | − 0.395130i | −0.980290 | − | 0.197565i | \(-0.936697\pi\) | ||||
0.980290 | − | 0.197565i | \(-0.0633033\pi\) | |||||||
\(198\) | − 0.521407i | − 0.0370548i | ||||||||
\(199\) | −5.96371 | −0.422756 | −0.211378 | − | 0.977404i | \(-0.567795\pi\) | ||||
−0.211378 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.34649 | −0.236043 | ||||||||
\(202\) | 0.101254i | 0.00712418i | ||||||||
\(203\) | 3.20497i | 0.224945i | ||||||||
\(204\) | 10.5075 | 0.735672 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.110626 | −0.00770768 | ||||||||
\(207\) | 3.42379i | 0.237970i | ||||||||
\(208\) | − 17.7754i | − 1.23250i | ||||||||
\(209\) | 23.4364 | 1.62113 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.7183 | −0.944407 | −0.472204 | − | 0.881490i | \(-0.656541\pi\) | ||||
−0.472204 | + | 0.881490i | \(0.656541\pi\) | |||||||
\(212\) | 4.64940i | 0.319322i | ||||||||
\(213\) | − 4.32289i | − 0.296199i | ||||||||
\(214\) | 1.69462 | 0.115842 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −0.563913 | −0.0383694 | ||||||||
\(217\) | − 1.07538i | − 0.0730014i | ||||||||
\(218\) | 0.344849i | 0.0233561i | ||||||||
\(219\) | −9.08007 | −0.613574 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −24.3133 | −1.63549 | ||||||||
\(222\) | − 1.05568i | − 0.0708527i | ||||||||
\(223\) | − 3.24170i | − 0.217081i | −0.994092 | − | 0.108540i | \(-0.965382\pi\) | ||||
0.994092 | − | 0.108540i | \(-0.0346176\pi\) | |||||||
\(224\) | −1.43988 | −0.0962060 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.27204 | 0.151134 | ||||||||
\(227\) | 13.1799i | 0.874779i | 0.899272 | + | 0.437390i | \(0.144097\pi\) | ||||
−0.899272 | + | 0.437390i | \(0.855903\pi\) | |||||||
\(228\) | − 12.6095i | − 0.835087i | ||||||||
\(229\) | −5.83810 | −0.385793 | −0.192896 | − | 0.981219i | \(-0.561788\pi\) | ||||
−0.192896 | + | 0.981219i | \(0.561788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.15852 | −0.207815 | ||||||||
\(232\) | 2.10568i | 0.138245i | ||||||||
\(233\) | − 9.33453i | − 0.611526i | −0.952108 | − | 0.305763i | \(-0.901089\pi\) | ||||
0.952108 | − | 0.305763i | \(-0.0989115\pi\) | |||||||
\(234\) | 0.649128 | 0.0424348 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −25.9893 | −1.69176 | ||||||||
\(237\) | 3.24730i | 0.210935i | ||||||||
\(238\) | 0.645406i | 0.0418354i | ||||||||
\(239\) | −17.1502 | −1.10935 | −0.554676 | − | 0.832066i | \(-0.687158\pi\) | ||||
−0.554676 | + | 0.832066i | \(0.687158\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.22073 | 0.465128 | 0.232564 | − | 0.972581i | \(-0.425289\pi\) | ||||
0.232564 | + | 0.972581i | \(0.425289\pi\) | |||||||
\(242\) | − 0.360157i | − 0.0231518i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 20.4875 | 1.31158 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.358712 | −0.0228706 | ||||||||
\(247\) | 29.1772i | 1.85650i | ||||||||
\(248\) | − 0.706527i | − 0.0448645i | ||||||||
\(249\) | −7.39269 | −0.468493 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.75708 | −0.363383 | −0.181692 | − | 0.983356i | \(-0.558157\pi\) | ||||
−0.181692 | + | 0.983356i | \(0.558157\pi\) | |||||||
\(252\) | 1.69939i | 0.107051i | ||||||||
\(253\) | 12.5993i | 0.792110i | ||||||||
\(254\) | −0.543872 | −0.0341256 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.4180 | 0.901125 | ||||||||
\(257\) | 26.9602i | 1.68173i | 0.541242 | + | 0.840867i | \(0.317954\pi\) | ||||
−0.541242 | + | 0.840867i | \(0.682046\pi\) | |||||||
\(258\) | 0.478870i | 0.0298132i | ||||||||
\(259\) | −6.39499 | −0.397365 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.73405 | 0.231132 | ||||||||
\(262\) | 1.76396i | 0.108978i | ||||||||
\(263\) | − 20.6673i | − 1.27440i | −0.770699 | − | 0.637200i | \(-0.780093\pi\) | ||||
0.770699 | − | 0.637200i | \(-0.219907\pi\) | |||||||
\(264\) | −2.07516 | −0.127717 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.774520 | 0.0474889 | ||||||||
\(267\) | 15.4975i | 0.948433i | ||||||||
\(268\) | 6.62579i | 0.404734i | ||||||||
\(269\) | 13.7435 | 0.837958 | 0.418979 | − | 0.907996i | \(-0.362388\pi\) | ||||
0.418979 | + | 0.907996i | \(0.362388\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.34392 | 0.203128 | 0.101564 | − | 0.994829i | \(-0.467615\pi\) | ||||
0.101564 | + | 0.994829i | \(0.467615\pi\) | |||||||
\(272\) | − 20.5910i | − 1.24851i | ||||||||
\(273\) | − 3.93221i | − 0.237988i | ||||||||
\(274\) | −1.68028 | −0.101510 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.77883 | 0.408038 | ||||||||
\(277\) | 8.90947i | 0.535318i | 0.963514 | + | 0.267659i | \(0.0862500\pi\) | ||||
−0.963514 | + | 0.267659i | \(0.913750\pi\) | |||||||
\(278\) | − 0.660400i | − 0.0396081i | ||||||||
\(279\) | −1.25290 | −0.0750092 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4913 | −1.34172 | −0.670859 | − | 0.741585i | \(-0.734074\pi\) | ||||
−0.670859 | + | 0.741585i | \(0.734074\pi\) | |||||||
\(282\) | − 1.20427i | − 0.0717133i | ||||||||
\(283\) | − 1.30694i | − 0.0776894i | −0.999245 | − | 0.0388447i | \(-0.987632\pi\) | ||||
0.999245 | − | 0.0388447i | \(-0.0123678\pi\) | |||||||
\(284\) | −8.55899 | −0.507883 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.38874 | 0.141249 | ||||||||
\(287\) | 2.17296i | 0.128266i | ||||||||
\(288\) | 1.67757i | 0.0988520i | ||||||||
\(289\) | −11.1645 | −0.656733 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.0386 | 0.588472 | ||||||||
\(292\) | 17.9779i | 1.05207i | ||||||||
\(293\) | − 1.97058i | − 0.115123i | −0.998342 | − | 0.0575613i | \(-0.981668\pi\) | ||||
0.998342 | − | 0.0575613i | \(-0.0183325\pi\) | |||||||
\(294\) | 0.887444 | 0.0517568 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.20153 | −0.244209 | ||||||||
\(297\) | 3.67993i | 0.213531i | ||||||||
\(298\) | − 1.63624i | − 0.0947847i | ||||||||
\(299\) | −15.6855 | −0.907118 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.90085 | 0.167202 | ||||||||
\(302\) | − 3.46706i | − 0.199507i | ||||||||
\(303\) | − 0.714616i | − 0.0410536i | ||||||||
\(304\) | −24.7102 | −1.41723 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.751949 | 0.0429861 | ||||||||
\(307\) | − 15.2544i | − 0.870617i | −0.900281 | − | 0.435308i | \(-0.856639\pi\) | ||||
0.900281 | − | 0.435308i | \(-0.143361\pi\) | |||||||
\(308\) | 6.25363i | 0.356334i | ||||||||
\(309\) | 0.780764 | 0.0444161 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7452 | 1.00624 | 0.503120 | − | 0.864217i | \(-0.332185\pi\) | ||||
0.503120 | + | 0.864217i | \(0.332185\pi\) | |||||||
\(312\) | − 2.58348i | − 0.146261i | ||||||||
\(313\) | 27.3869i | 1.54800i | 0.633187 | + | 0.773999i | \(0.281747\pi\) | ||||
−0.633187 | + | 0.773999i | \(0.718253\pi\) | |||||||
\(314\) | −3.16903 | −0.178839 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.42941 | 0.361683 | ||||||||
\(317\) | 8.64563i | 0.485587i | 0.970078 | + | 0.242793i | \(0.0780637\pi\) | ||||
−0.970078 | + | 0.242793i | \(0.921936\pi\) | |||||||
\(318\) | 0.332725i | 0.0186583i | ||||||||
\(319\) | 13.7410 | 0.769350 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.9601 | −0.667547 | ||||||||
\(322\) | 0.416379i | 0.0232039i | ||||||||
\(323\) | 33.7988i | 1.88062i | ||||||||
\(324\) | 1.97992 | 0.109996 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.115257 | 0.00638351 | ||||||||
\(327\) | − 2.43384i | − 0.134592i | ||||||||
\(328\) | 1.42765i | 0.0788286i | ||||||||
\(329\) | −7.29510 | −0.402192 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.96260 | 0.272769 | 0.136385 | − | 0.990656i | \(-0.456452\pi\) | ||||
0.136385 | + | 0.990656i | \(0.456452\pi\) | |||||||
\(332\) | 14.6370i | 0.803308i | ||||||||
\(333\) | 7.45067i | 0.408294i | ||||||||
\(334\) | −3.56575 | −0.195109 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.33020 | 0.181677 | ||||||||
\(337\) | − 7.30529i | − 0.397945i | −0.980005 | − | 0.198972i | \(-0.936240\pi\) | ||||
0.980005 | − | 0.198972i | \(-0.0637604\pi\) | |||||||
\(338\) | 1.13191i | 0.0615680i | ||||||||
\(339\) | −16.0354 | −0.870921 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.61058 | −0.249677 | ||||||||
\(342\) | − 0.902378i | − 0.0487950i | ||||||||
\(343\) | − 11.3840i | − 0.614680i | ||||||||
\(344\) | 1.90587 | 0.102758 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0582266 | −0.00313028 | ||||||||
\(347\) | 15.9374i | 0.855565i | 0.903882 | + | 0.427783i | \(0.140705\pi\) | ||||
−0.903882 | + | 0.427783i | \(0.859295\pi\) | |||||||
\(348\) | − 7.39313i | − 0.396314i | ||||||||
\(349\) | −16.5844 | −0.887743 | −0.443871 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443871 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.58134 | −0.244534 | ||||||||
\(352\) | 6.17336i | 0.329041i | ||||||||
\(353\) | − 12.9691i | − 0.690277i | −0.938552 | − | 0.345138i | \(-0.887832\pi\) | ||||
0.938552 | − | 0.345138i | \(-0.112168\pi\) | |||||||
\(354\) | −1.85987 | −0.0988511 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 30.6839 | 1.62624 | ||||||||
\(357\) | − 4.55507i | − 0.241080i | ||||||||
\(358\) | − 2.10412i | − 0.111206i | ||||||||
\(359\) | 13.4920 | 0.712082 | 0.356041 | − | 0.934470i | \(-0.384126\pi\) | ||||
0.356041 | + | 0.934470i | \(0.384126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.5603 | 1.13475 | ||||||||
\(362\) | − 0.104740i | − 0.00550502i | ||||||||
\(363\) | 2.54188i | 0.133414i | ||||||||
\(364\) | −7.78549 | −0.408070 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.46615 | 0.0766369 | ||||||||
\(367\) | 4.57463i | 0.238794i | 0.992847 | + | 0.119397i | \(0.0380961\pi\) | ||||
−0.992847 | + | 0.119397i | \(0.961904\pi\) | |||||||
\(368\) | − 13.2841i | − 0.692482i | ||||||||
\(369\) | 2.53168 | 0.131794 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.01555 | 0.104642 | ||||||||
\(372\) | 2.48065i | 0.128616i | ||||||||
\(373\) | 20.7463i | 1.07420i | 0.843518 | + | 0.537101i | \(0.180481\pi\) | ||||
−0.843518 | + | 0.537101i | \(0.819519\pi\) | |||||||
\(374\) | 2.76712 | 0.143084 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.79291 | −0.247175 | ||||||||
\(377\) | 17.1070i | 0.881053i | ||||||||
\(378\) | 0.121614i | 0.00625513i | ||||||||
\(379\) | 5.78163 | 0.296982 | 0.148491 | − | 0.988914i | \(-0.452558\pi\) | ||||
0.148491 | + | 0.988914i | \(0.452558\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.83848 | 0.196651 | ||||||||
\(382\) | 0.386113i | 0.0197553i | ||||||||
\(383\) | − 25.8124i | − 1.31895i | −0.751726 | − | 0.659476i | \(-0.770778\pi\) | ||||
0.751726 | − | 0.659476i | \(-0.229222\pi\) | |||||||
\(384\) | 4.42097 | 0.225606 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.01256 | −0.102437 | ||||||||
\(387\) | − 3.37972i | − 0.171801i | ||||||||
\(388\) | − 19.8756i | − 1.00903i | ||||||||
\(389\) | 15.7046 | 0.796254 | 0.398127 | − | 0.917330i | \(-0.369660\pi\) | ||||
0.398127 | + | 0.917330i | \(0.369660\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.1701 | −0.918901 | ||||||||
\(392\) | − 3.53196i | − 0.178391i | ||||||||
\(393\) | − 12.4495i | − 0.627992i | ||||||||
\(394\) | −0.785797 | −0.0395879 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.28598 | 0.366134 | ||||||||
\(397\) | − 19.6040i | − 0.983895i | −0.870625 | − | 0.491948i | \(-0.836285\pi\) | ||||
0.870625 | − | 0.491948i | \(-0.163715\pi\) | |||||||
\(398\) | 0.844995i | 0.0423558i | ||||||||
\(399\) | −5.46632 | −0.273658 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.4239 | −0.720297 | −0.360148 | − | 0.932895i | \(-0.617274\pi\) | ||||
−0.360148 | + | 0.932895i | \(0.617274\pi\) | |||||||
\(402\) | 0.474162i | 0.0236490i | ||||||||
\(403\) | − 5.73996i | − 0.285928i | ||||||||
\(404\) | −1.41489 | −0.0703932 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.454111 | 0.0225372 | ||||||||
\(407\) | 27.4179i | 1.35906i | ||||||||
\(408\) | − 2.99270i | − 0.148161i | ||||||||
\(409\) | 27.8742 | 1.37829 | 0.689146 | − | 0.724622i | \(-0.257986\pi\) | ||||
0.689146 | + | 0.724622i | \(0.257986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11.8589 | 0.584957 | ||||||||
\(412\) | − 1.54585i | − 0.0761588i | ||||||||
\(413\) | 11.2665i | 0.554389i | ||||||||
\(414\) | 0.485114 | 0.0238421 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −7.68554 | −0.376815 | ||||||||
\(417\) | 4.66089i | 0.228245i | ||||||||
\(418\) | − 3.32069i | − 0.162420i | ||||||||
\(419\) | 36.2881 | 1.77279 | 0.886396 | − | 0.462928i | \(-0.153201\pi\) | ||||
0.886396 | + | 0.462928i | \(0.153201\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.37600 | −0.164536 | −0.0822681 | − | 0.996610i | \(-0.526216\pi\) | ||||
−0.0822681 | + | 0.996610i | \(0.526216\pi\) | |||||||
\(422\) | 1.94374i | 0.0946198i | ||||||||
\(423\) | 8.49937i | 0.413254i | ||||||||
\(424\) | 1.32422 | 0.0643099 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −0.612508 | −0.0296761 | ||||||||
\(427\) | − 8.88148i | − 0.429805i | ||||||||
\(428\) | 23.6801i | 1.14462i | ||||||||
\(429\) | −16.8590 | −0.813961 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.6625 | −1.23612 | −0.618059 | − | 0.786131i | \(-0.712081\pi\) | ||||
−0.618059 | + | 0.786131i | \(0.712081\pi\) | |||||||
\(432\) | − 3.87995i | − 0.186674i | ||||||||
\(433\) | 39.8070i | 1.91300i | 0.291730 | + | 0.956501i | \(0.405769\pi\) | ||||
−0.291730 | + | 0.956501i | \(0.594231\pi\) | |||||||
\(434\) | −0.152370 | −0.00731398 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.81882 | −0.230779 | ||||||||
\(437\) | 21.8051i | 1.04308i | ||||||||
\(438\) | 1.28655i | 0.0614738i | ||||||||
\(439\) | −33.9180 | −1.61882 | −0.809408 | − | 0.587247i | \(-0.800212\pi\) | ||||
−0.809408 | + | 0.587247i | \(0.800212\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.26330 | −0.298253 | ||||||||
\(442\) | 3.44494i | 0.163859i | ||||||||
\(443\) | 28.9300i | 1.37451i | 0.726418 | + | 0.687253i | \(0.241184\pi\) | ||||
−0.726418 | + | 0.687253i | \(0.758816\pi\) | |||||||
\(444\) | 14.7518 | 0.700088 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.459315 | −0.0217492 | ||||||||
\(447\) | 11.5480i | 0.546204i | ||||||||
\(448\) | − 6.45638i | − 0.305035i | ||||||||
\(449\) | 10.2089 | 0.481788 | 0.240894 | − | 0.970551i | \(-0.422559\pi\) | ||||
0.240894 | + | 0.970551i | \(0.422559\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.31639 | 0.438692 | ||||||||
\(452\) | 31.7488i | 1.49334i | ||||||||
\(453\) | 24.4694i | 1.14967i | ||||||||
\(454\) | 1.86745 | 0.0876438 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.59140 | −0.168182 | ||||||||
\(457\) | 32.4952i | 1.52006i | 0.649888 | + | 0.760030i | \(0.274816\pi\) | ||||
−0.649888 | + | 0.760030i | \(0.725184\pi\) | |||||||
\(458\) | 0.827198i | 0.0386524i | ||||||||
\(459\) | −5.30702 | −0.247711 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.700568 | −0.0326287 | −0.0163144 | − | 0.999867i | \(-0.505193\pi\) | ||||
−0.0163144 | + | 0.999867i | \(0.505193\pi\) | |||||||
\(462\) | 0.447529i | 0.0208209i | ||||||||
\(463\) | − 2.17126i | − 0.100907i | −0.998726 | − | 0.0504535i | \(-0.983933\pi\) | ||||
0.998726 | − | 0.0504535i | \(-0.0160667\pi\) | |||||||
\(464\) | −14.4879 | −0.672585 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.32261 | −0.0612685 | ||||||||
\(467\) | − 3.87710i | − 0.179411i | −0.995968 | − | 0.0897053i | \(-0.971407\pi\) | ||||
0.995968 | − | 0.0897053i | \(-0.0285925\pi\) | |||||||
\(468\) | 9.07071i | 0.419294i | ||||||||
\(469\) | 2.87232 | 0.132632 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.3660 | 1.03057 | ||||||||
\(472\) | 7.40215i | 0.340711i | ||||||||
\(473\) | − 12.4371i | − 0.571859i | ||||||||
\(474\) | 0.460109 | 0.0211335 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −9.01870 | −0.413371 | ||||||||
\(477\) | − 2.34827i | − 0.107520i | ||||||||
\(478\) | 2.43000i | 0.111146i | ||||||||
\(479\) | 21.9994 | 1.00518 | 0.502588 | − | 0.864526i | \(-0.332381\pi\) | ||||
0.502588 | + | 0.864526i | \(0.332381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.1341 | −1.55638 | ||||||||
\(482\) | − 1.02310i | − 0.0466010i | ||||||||
\(483\) | − 2.93867i | − 0.133714i | ||||||||
\(484\) | 5.03272 | 0.228760 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.141689 | 0.00642717 | ||||||||
\(487\) | 28.3997i | 1.28692i | 0.765482 | + | 0.643458i | \(0.222501\pi\) | ||||
−0.765482 | + | 0.643458i | \(0.777499\pi\) | |||||||
\(488\) | − 5.83517i | − 0.264146i | ||||||||
\(489\) | −0.813450 | −0.0367855 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.0468 | −0.633925 | −0.316963 | − | 0.948438i | \(-0.602663\pi\) | ||||
−0.316963 | + | 0.948438i | \(0.602663\pi\) | |||||||
\(492\) | − 5.01253i | − 0.225982i | ||||||||
\(493\) | 19.8167i | 0.892498i | ||||||||
\(494\) | 4.13410 | 0.186002 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.86119 | 0.218274 | ||||||||
\(497\) | 3.71038i | 0.166433i | ||||||||
\(498\) | 1.04747i | 0.0469381i | ||||||||
\(499\) | −13.0842 | −0.585731 | −0.292866 | − | 0.956154i | \(-0.594609\pi\) | ||||
−0.292866 | + | 0.956154i | \(0.594609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.1660 | 1.12433 | ||||||||
\(502\) | 0.815717i | 0.0364072i | ||||||||
\(503\) | − 12.3044i | − 0.548625i | −0.961641 | − | 0.274312i | \(-0.911550\pi\) | ||||
0.961641 | − | 0.274312i | \(-0.0884502\pi\) | |||||||
\(504\) | 0.484013 | 0.0215596 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.78519 | 0.0793612 | ||||||||
\(507\) | − 7.98869i | − 0.354790i | ||||||||
\(508\) | − 7.59990i | − 0.337191i | ||||||||
\(509\) | −0.0783897 | −0.00347456 | −0.00173728 | − | 0.999998i | \(-0.500553\pi\) | ||||
−0.00173728 | + | 0.999998i | \(0.500553\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.79352 | 0.344765 | ||||||||
\(512\) | − 10.8848i | − 0.481045i | ||||||||
\(513\) | 6.36870i | 0.281185i | ||||||||
\(514\) | 3.81998 | 0.168492 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.69158 | −0.294581 | ||||||||
\(517\) | 31.2771i | 1.37556i | ||||||||
\(518\) | 0.906103i | 0.0398119i | ||||||||
\(519\) | 0.410945 | 0.0180385 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.1194 | 0.793824 | 0.396912 | − | 0.917857i | \(-0.370082\pi\) | ||||
0.396912 | + | 0.917857i | \(0.370082\pi\) | |||||||
\(522\) | − 0.529076i | − 0.0231570i | ||||||||
\(523\) | − 11.6303i | − 0.508558i | −0.967131 | − | 0.254279i | \(-0.918162\pi\) | ||||
0.967131 | − | 0.254279i | \(-0.0818382\pi\) | |||||||
\(524\) | −24.6490 | −1.07680 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.92834 | −0.127682 | ||||||||
\(527\) | − 6.64917i | − 0.289642i | ||||||||
\(528\) | − 14.2779i | − 0.621367i | ||||||||
\(529\) | 11.2777 | 0.490335 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.1264 | 0.569637 | ||||||||
\(532\) | 10.8229i | 0.469232i | ||||||||
\(533\) | 11.5985i | 0.502386i | ||||||||
\(534\) | 2.19584 | 0.0950231 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.88713 | 0.0815115 | ||||||||
\(537\) | 14.8502i | 0.640833i | ||||||||
\(538\) | − 1.94732i | − 0.0839547i | ||||||||
\(539\) | −23.0485 | −0.992770 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.2716 | 1.25848 | 0.629242 | − | 0.777209i | \(-0.283365\pi\) | ||||
0.629242 | + | 0.777209i | \(0.283365\pi\) | |||||||
\(542\) | − 0.473798i | − 0.0203514i | ||||||||
\(543\) | 0.739223i | 0.0317231i | ||||||||
\(544\) | −8.90292 | −0.381710 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.557153 | −0.0238440 | ||||||||
\(547\) | 12.0675i | 0.515971i | 0.966149 | + | 0.257985i | \(0.0830587\pi\) | ||||
−0.966149 | + | 0.257985i | \(0.916941\pi\) | |||||||
\(548\) | − 23.4797i | − 1.00300i | ||||||||
\(549\) | −10.3476 | −0.441626 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.7810 | 1.01311 | ||||||||
\(552\) | − 1.93072i | − 0.0821768i | ||||||||
\(553\) | − 2.78719i | − 0.118524i | ||||||||
\(554\) | 1.26238 | 0.0536333 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.22821 | 0.391363 | ||||||||
\(557\) | − 41.4154i | − 1.75483i | −0.479737 | − | 0.877413i | \(-0.659268\pi\) | ||||
0.479737 | − | 0.877413i | \(-0.340732\pi\) | |||||||
\(558\) | 0.177523i | 0.00751514i | ||||||||
\(559\) | 15.4836 | 0.654888 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.5295 | −0.824534 | ||||||||
\(562\) | 3.18678i | 0.134426i | ||||||||
\(563\) | 32.1467i | 1.35482i | 0.735604 | + | 0.677411i | \(0.236898\pi\) | ||||
−0.735604 | + | 0.677411i | \(0.763102\pi\) | |||||||
\(564\) | 16.8281 | 0.708591 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −0.185179 | −0.00778367 | ||||||||
\(567\) | − 0.858311i | − 0.0360457i | ||||||||
\(568\) | 2.43773i | 0.102285i | ||||||||
\(569\) | −21.1080 | −0.884893 | −0.442446 | − | 0.896795i | \(-0.645889\pi\) | ||||
−0.442446 | + | 0.896795i | \(0.645889\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7493 | −1.03573 | −0.517863 | − | 0.855464i | \(-0.673272\pi\) | ||||
−0.517863 | + | 0.855464i | \(0.673272\pi\) | |||||||
\(572\) | 33.3796i | 1.39567i | ||||||||
\(573\) | − 2.72506i | − 0.113841i | ||||||||
\(574\) | 0.307886 | 0.0128509 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.52220 | −0.313425 | ||||||||
\(577\) | − 18.7710i | − 0.781448i | −0.920508 | − | 0.390724i | \(-0.872225\pi\) | ||||
0.920508 | − | 0.390724i | \(-0.127775\pi\) | |||||||
\(578\) | 1.58189i | 0.0657979i | ||||||||
\(579\) | 14.2040 | 0.590300 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.34522 | 0.263244 | ||||||||
\(582\) | − 1.42236i | − 0.0589587i | ||||||||
\(583\) | − 8.64147i | − 0.357893i | ||||||||
\(584\) | 5.12037 | 0.211883 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.279211 | −0.0115341 | ||||||||
\(587\) | 14.7572i | 0.609095i | 0.952497 | + | 0.304547i | \(0.0985052\pi\) | ||||
−0.952497 | + | 0.304547i | \(0.901495\pi\) | |||||||
\(588\) | 12.4009i | 0.511403i | ||||||||
\(589\) | −7.97935 | −0.328783 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.54591 | 0.228128 | ||||||||
\(592\) | − 28.9082i | − 1.18812i | ||||||||
\(593\) | − 8.01859i | − 0.329284i | −0.986353 | − | 0.164642i | \(-0.947353\pi\) | ||||
0.986353 | − | 0.164642i | \(-0.0526469\pi\) | |||||||
\(594\) | 0.521407 | 0.0213936 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 22.8643 | 0.936556 | ||||||||
\(597\) | − 5.96371i | − 0.244078i | ||||||||
\(598\) | 2.22247i | 0.0908838i | ||||||||
\(599\) | 1.28951 | 0.0526878 | 0.0263439 | − | 0.999653i | \(-0.491614\pi\) | ||||
0.0263439 | + | 0.999653i | \(0.491614\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.8813 | −0.688603 | −0.344302 | − | 0.938859i | \(-0.611884\pi\) | ||||
−0.344302 | + | 0.938859i | \(0.611884\pi\) | |||||||
\(602\) | − 0.411020i | − 0.0167519i | ||||||||
\(603\) | − 3.34649i | − 0.136279i | ||||||||
\(604\) | 48.4476 | 1.97130 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.101254 | −0.00411315 | ||||||||
\(607\) | − 0.499318i | − 0.0202667i | −0.999949 | − | 0.0101334i | \(-0.996774\pi\) | ||||
0.999949 | − | 0.0101334i | \(-0.00322560\pi\) | |||||||
\(608\) | 10.6840i | 0.433292i | ||||||||
\(609\) | −3.20497 | −0.129872 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −38.9385 | −1.57528 | ||||||||
\(612\) | 10.5075i | 0.424740i | ||||||||
\(613\) | − 27.4241i | − 1.10765i | −0.832633 | − | 0.553825i | \(-0.813168\pi\) | ||||
0.832633 | − | 0.553825i | \(-0.186832\pi\) | |||||||
\(614\) | −2.16139 | −0.0872267 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.78113 | 0.0717639 | ||||||||
\(617\) | − 28.3205i | − 1.14014i | −0.821596 | − | 0.570070i | \(-0.806916\pi\) | ||||
0.821596 | − | 0.570070i | \(-0.193084\pi\) | |||||||
\(618\) | − 0.110626i | − 0.00445003i | ||||||||
\(619\) | 0.371804 | 0.0149440 | 0.00747202 | − | 0.999972i | \(-0.497622\pi\) | ||||
0.00747202 | + | 0.999972i | \(0.497622\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.42379 | −0.137392 | ||||||||
\(622\) | − 2.51431i | − 0.100815i | ||||||||
\(623\) | − 13.3017i | − 0.532921i | ||||||||
\(624\) | 17.7754 | 0.711584 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.88043 | 0.155093 | ||||||||
\(627\) | 23.4364i | 0.935958i | ||||||||
\(628\) | − 44.2830i | − 1.76709i | ||||||||
\(629\) | −39.5409 | −1.57660 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.4507 | 0.654892 | 0.327446 | − | 0.944870i | \(-0.393812\pi\) | ||||
0.327446 | + | 0.944870i | \(0.393812\pi\) | |||||||
\(632\) | − 1.83120i | − 0.0728411i | ||||||||
\(633\) | − 13.7183i | − 0.545254i | ||||||||
\(634\) | 1.22499 | 0.0486508 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.64940 | −0.184361 | ||||||||
\(637\) | − 28.6943i | − 1.13691i | ||||||||
\(638\) | − 1.94696i | − 0.0770809i | ||||||||
\(639\) | 4.32289 | 0.171011 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.02604 | −0.0800239 | −0.0400119 | − | 0.999199i | \(-0.512740\pi\) | ||||
−0.0400119 | + | 0.999199i | \(0.512740\pi\) | |||||||
\(642\) | 1.69462i | 0.0668813i | ||||||||
\(643\) | 33.2034i | 1.30941i | 0.755883 | + | 0.654706i | \(0.227208\pi\) | ||||
−0.755883 | + | 0.654706i | \(0.772792\pi\) | |||||||
\(644\) | −5.81834 | −0.229275 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.78894 | 0.188418 | ||||||||
\(647\) | − 40.5797i | − 1.59535i | −0.603085 | − | 0.797677i | \(-0.706062\pi\) | ||||
0.603085 | − | 0.797677i | \(-0.293938\pi\) | |||||||
\(648\) | − 0.563913i | − 0.0221526i | ||||||||
\(649\) | 48.3042 | 1.89611 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.07538 | 0.0421474 | ||||||||
\(652\) | 1.61057i | 0.0630748i | ||||||||
\(653\) | 9.29712i | 0.363824i | 0.983315 | + | 0.181912i | \(0.0582286\pi\) | ||||
−0.983315 | + | 0.181912i | \(0.941771\pi\) | |||||||
\(654\) | −0.344849 | −0.0134847 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.82277 | −0.383515 | ||||||||
\(657\) | − 9.08007i | − 0.354247i | ||||||||
\(658\) | 1.03364i | 0.0402954i | ||||||||
\(659\) | 3.47563 | 0.135391 | 0.0676957 | − | 0.997706i | \(-0.478435\pi\) | ||||
0.0676957 | + | 0.997706i | \(0.478435\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.07303 | 0.158422 | 0.0792112 | − | 0.996858i | \(-0.474760\pi\) | ||||
0.0792112 | + | 0.996858i | \(0.474760\pi\) | |||||||
\(662\) | − 0.703148i | − 0.0273286i | ||||||||
\(663\) | − 24.3133i | − 0.944249i | ||||||||
\(664\) | 4.16884 | 0.161782 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.05568 | 0.0409068 | ||||||||
\(667\) | 12.7846i | 0.495021i | ||||||||
\(668\) | − 49.8267i | − 1.92785i | ||||||||
\(669\) | 3.24170 | 0.125332 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −38.0785 | −1.47001 | ||||||||
\(672\) | − 1.43988i | − 0.0555446i | ||||||||
\(673\) | − 21.3843i | − 0.824305i | −0.911115 | − | 0.412153i | \(-0.864777\pi\) | ||||
0.911115 | − | 0.412153i | \(-0.135223\pi\) | |||||||
\(674\) | −1.03508 | −0.0398699 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −15.8170 | −0.608346 | ||||||||
\(677\) | − 20.3257i | − 0.781181i | −0.920565 | − | 0.390590i | \(-0.872271\pi\) | ||||
0.920565 | − | 0.390590i | \(-0.127729\pi\) | |||||||
\(678\) | 2.27204i | 0.0872573i | ||||||||
\(679\) | −8.61621 | −0.330660 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.1799 | −0.505054 | ||||||||
\(682\) | 0.653271i | 0.0250150i | ||||||||
\(683\) | 18.9591i | 0.725449i | 0.931896 | + | 0.362725i | \(0.118153\pi\) | ||||
−0.931896 | + | 0.362725i | \(0.881847\pi\) | |||||||
\(684\) | 12.6095 | 0.482138 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.61300 | −0.0615845 | ||||||||
\(687\) | − 5.83810i | − 0.222737i | ||||||||
\(688\) | 13.1131i | 0.499933i | ||||||||
\(689\) | 10.7582 | 0.409856 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.8195 | 0.563762 | 0.281881 | − | 0.959449i | \(-0.409042\pi\) | ||||
0.281881 | + | 0.959449i | \(0.409042\pi\) | |||||||
\(692\) | − 0.813641i | − 0.0309300i | ||||||||
\(693\) | − 3.15852i | − 0.119982i | ||||||||
\(694\) | 2.25816 | 0.0857187 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.10568 | −0.0798156 | ||||||||
\(697\) | 13.4357i | 0.508912i | ||||||||
\(698\) | 2.34984i | 0.0889426i | ||||||||
\(699\) | 9.33453 | 0.353064 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 31.3996 | 1.18595 | 0.592973 | − | 0.805222i | \(-0.297954\pi\) | ||||
0.592973 | + | 0.805222i | \(0.297954\pi\) | |||||||
\(702\) | 0.649128i | 0.0244998i | ||||||||
\(703\) | 47.4511i | 1.78965i | ||||||||
\(704\) | −27.6812 | −1.04327 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.83759 | −0.0691586 | ||||||||
\(707\) | 0.613363i | 0.0230679i | ||||||||
\(708\) | − 25.9893i | − 0.976736i | ||||||||
\(709\) | −25.3324 | −0.951379 | −0.475690 | − | 0.879613i | \(-0.657801\pi\) | ||||
−0.475690 | + | 0.879613i | \(0.657801\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.24730 | −0.121783 | ||||||||
\(712\) | − 8.73926i | − 0.327518i | ||||||||
\(713\) | − 4.28966i | − 0.160649i | ||||||||
\(714\) | −0.645406 | −0.0241537 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 29.4023 | 1.09881 | ||||||||
\(717\) | − 17.1502i | − 0.640485i | ||||||||
\(718\) | − 1.91168i | − 0.0713432i | ||||||||
\(719\) | 4.12711 | 0.153915 | 0.0769575 | − | 0.997034i | \(-0.475479\pi\) | ||||
0.0769575 | + | 0.997034i | \(0.475479\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.670138 | −0.0249572 | ||||||||
\(722\) | − 3.05487i | − 0.113691i | ||||||||
\(723\) | 7.22073i | 0.268542i | ||||||||
\(724\) | 1.46361 | 0.0543945 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.360157 | 0.0133667 | ||||||||
\(727\) | 23.0039i | 0.853168i | 0.904448 | + | 0.426584i | \(0.140283\pi\) | ||||
−0.904448 | + | 0.426584i | \(0.859717\pi\) | |||||||
\(728\) | 2.21743i | 0.0821834i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.9362 | 0.663396 | ||||||||
\(732\) | 20.4875i | 0.757240i | ||||||||
\(733\) | 9.35692i | 0.345606i | 0.984956 | + | 0.172803i | \(0.0552823\pi\) | ||||
−0.984956 | + | 0.172803i | \(0.944718\pi\) | |||||||
\(734\) | 0.648176 | 0.0239246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.74366 | −0.211714 | ||||||||
\(737\) | − 12.3148i | − 0.453623i | ||||||||
\(738\) | − 0.358712i | − 0.0132044i | ||||||||
\(739\) | 47.1754 | 1.73538 | 0.867688 | − | 0.497109i | \(-0.165605\pi\) | ||||
0.867688 | + | 0.497109i | \(0.165605\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −29.1772 | −1.07185 | ||||||||
\(742\) | − 0.285582i | − 0.0104840i | ||||||||
\(743\) | − 2.39450i | − 0.0878455i | −0.999035 | − | 0.0439228i | \(-0.986014\pi\) | ||||
0.999035 | − | 0.0439228i | \(-0.0139855\pi\) | |||||||
\(744\) | 0.706527 | 0.0259025 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.93953 | 0.107624 | ||||||||
\(747\) | − 7.39269i | − 0.270484i | ||||||||
\(748\) | 38.6668i | 1.41380i | ||||||||
\(749\) | 10.2655 | 0.375092 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.21632 | −0.263327 | −0.131664 | − | 0.991294i | \(-0.542032\pi\) | ||||
−0.131664 | + | 0.991294i | \(0.542032\pi\) | |||||||
\(752\) | − 32.9771i | − 1.20255i | ||||||||
\(753\) | − 5.75708i | − 0.209800i | ||||||||
\(754\) | 2.42388 | 0.0882724 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −1.69939 | −0.0618062 | ||||||||
\(757\) | 13.3742i | 0.486094i | 0.970015 | + | 0.243047i | \(0.0781469\pi\) | ||||
−0.970015 | + | 0.243047i | \(0.921853\pi\) | |||||||
\(758\) | − 0.819196i | − 0.0297545i | ||||||||
\(759\) | −12.5993 | −0.457325 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7541 | 0.788584 | 0.394292 | − | 0.918985i | \(-0.370990\pi\) | ||||
0.394292 | + | 0.918985i | \(0.370990\pi\) | |||||||
\(762\) | − 0.543872i | − 0.0197024i | ||||||||
\(763\) | 2.08899i | 0.0756265i | ||||||||
\(764\) | −5.39542 | −0.195199 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.65735 | −0.132145 | ||||||||
\(767\) | 60.1365i | 2.17140i | ||||||||
\(768\) | 14.4180i | 0.520265i | ||||||||
\(769\) | −14.2003 | −0.512077 | −0.256038 | − | 0.966667i | \(-0.582417\pi\) | ||||
−0.256038 | + | 0.966667i | \(0.582417\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.9602 | −0.970949 | ||||||||
\(772\) | − 28.1229i | − 1.01217i | ||||||||
\(773\) | − 22.8365i | − 0.821373i | −0.911777 | − | 0.410687i | \(-0.865289\pi\) | ||||
0.911777 | − | 0.410687i | \(-0.134711\pi\) | |||||||
\(774\) | −0.478870 | −0.0172126 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.66089 | −0.203214 | ||||||||
\(777\) | − 6.39499i | − 0.229419i | ||||||||
\(778\) | − 2.22517i | − 0.0797763i | ||||||||
\(779\) | 16.1235 | 0.577684 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9079 | 0.569230 | ||||||||
\(782\) | 2.57451i | 0.0920644i | ||||||||
\(783\) | 3.73405i | 0.133444i | ||||||||
\(784\) | 24.3013 | 0.867903 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.76396 | −0.0629183 | ||||||||
\(787\) | − 38.4761i | − 1.37153i | −0.727825 | − | 0.685763i | \(-0.759469\pi\) | ||||
0.727825 | − | 0.685763i | \(-0.240531\pi\) | |||||||
\(788\) | − 10.9805i | − 0.391163i | ||||||||
\(789\) | 20.6673 | 0.735775 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.7633 | 0.489367 | ||||||||
\(792\) | − 2.07516i | − 0.0737376i | ||||||||
\(793\) | − 47.4060i | − 1.68344i | ||||||||
\(794\) | −2.77768 | −0.0985760 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8077 | −0.418512 | ||||||||
\(797\) | − 1.86739i | − 0.0661464i | −0.999453 | − | 0.0330732i | \(-0.989471\pi\) | ||||
0.999453 | − | 0.0330732i | \(-0.0105294\pi\) | |||||||
\(798\) | 0.774520i | 0.0274177i | ||||||||
\(799\) | −45.1063 | −1.59575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.4975 | −0.547578 | ||||||||
\(802\) | 2.04372i | 0.0721662i | ||||||||
\(803\) | − 33.4140i | − 1.17916i | ||||||||
\(804\) | −6.62579 | −0.233673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.813293 | −0.0286470 | ||||||||
\(807\) | 13.7435i | 0.483796i | ||||||||
\(808\) | 0.402982i | 0.0141768i | ||||||||
\(809\) | −35.1514 | −1.23586 | −0.617929 | − | 0.786234i | \(-0.712028\pi\) | ||||
−0.617929 | + | 0.786234i | \(0.712028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.59158 | −0.231462 | −0.115731 | − | 0.993281i | \(-0.536921\pi\) | ||||
−0.115731 | + | 0.993281i | \(0.536921\pi\) | |||||||
\(812\) | 6.34561i | 0.222687i | ||||||||
\(813\) | 3.34392i | 0.117276i | ||||||||
\(814\) | 3.88483 | 0.136163 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 20.5910 | 0.720828 | ||||||||
\(817\) | − 21.5244i | − 0.753044i | ||||||||
\(818\) | − 3.94949i | − 0.138091i | ||||||||
\(819\) | 3.93221 | 0.137403 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.25743 | 0.183486 | 0.0917428 | − | 0.995783i | \(-0.470756\pi\) | ||||
0.0917428 | + | 0.995783i | \(0.470756\pi\) | |||||||
\(822\) | − 1.68028i | − 0.0586066i | ||||||||
\(823\) | 22.1919i | 0.773560i | 0.922172 | + | 0.386780i | \(0.126413\pi\) | ||||
−0.922172 | + | 0.386780i | \(0.873587\pi\) | |||||||
\(824\) | −0.440283 | −0.0153380 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.59635 | 0.0555440 | ||||||||
\(827\) | − 6.56256i | − 0.228203i | −0.993469 | − | 0.114101i | \(-0.963601\pi\) | ||||
0.993469 | − | 0.114101i | \(-0.0363988\pi\) | |||||||
\(828\) | 6.77883i | 0.235581i | ||||||||
\(829\) | −25.0574 | −0.870279 | −0.435140 | − | 0.900363i | \(-0.643301\pi\) | ||||
−0.435140 | + | 0.900363i | \(0.643301\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.90947 | −0.309066 | ||||||||
\(832\) | − 34.4618i | − 1.19475i | ||||||||
\(833\) | − 33.2395i | − 1.15168i | ||||||||
\(834\) | 0.660400 | 0.0228678 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 46.4022 | 1.60485 | ||||||||
\(837\) | − 1.25290i | − 0.0433066i | ||||||||
\(838\) | − 5.14165i | − 0.177615i | ||||||||
\(839\) | 42.1485 | 1.45513 | 0.727564 | − | 0.686040i | \(-0.240652\pi\) | ||||
0.727564 | + | 0.686040i | \(0.240652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.0569 | −0.519203 | ||||||||
\(842\) | 0.478344i | 0.0164848i | ||||||||
\(843\) | − 22.4913i | − 0.774641i | ||||||||
\(844\) | −27.1612 | −0.934927 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.20427 | 0.0414037 | ||||||||
\(847\) | − 2.18172i | − 0.0749648i | ||||||||
\(848\) | 9.11117i | 0.312879i | ||||||||
\(849\) | 1.30694 | 0.0448540 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −25.5095 | −0.874454 | ||||||||
\(852\) | − 8.55899i | − 0.293226i | ||||||||
\(853\) | − 43.2473i | − 1.48076i | −0.672189 | − | 0.740379i | \(-0.734646\pi\) | ||||
0.672189 | − | 0.740379i | \(-0.265354\pi\) | |||||||
\(854\) | −1.25841 | −0.0430620 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.74446 | 0.230521 | ||||||||
\(857\) | − 39.2430i | − 1.34052i | −0.742128 | − | 0.670258i | \(-0.766183\pi\) | ||||
0.742128 | − | 0.670258i | \(-0.233817\pi\) | |||||||
\(858\) | 2.38874i | 0.0815504i | ||||||||
\(859\) | −52.6092 | −1.79500 | −0.897501 | − | 0.441013i | \(-0.854619\pi\) | ||||
−0.897501 | + | 0.441013i | \(0.854619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.17296 | −0.0740544 | ||||||||
\(862\) | 3.63611i | 0.123846i | ||||||||
\(863\) | 42.8744i | 1.45946i | 0.683735 | + | 0.729731i | \(0.260355\pi\) | ||||
−0.683735 | + | 0.729731i | \(0.739645\pi\) | |||||||
\(864\) | −1.67757 | −0.0570722 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.64023 | 0.191663 | ||||||||
\(867\) | − 11.1645i | − 0.379165i | ||||||||
\(868\) | − 2.12917i | − 0.0722686i | ||||||||
\(869\) | −11.9498 | −0.405371 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.3314 | 0.519484 | ||||||||
\(872\) | 1.37247i | 0.0464778i | ||||||||
\(873\) | 10.0386i | 0.339754i | ||||||||
\(874\) | 3.08955 | 0.104506 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −17.9779 | −0.607415 | ||||||||
\(877\) | − 0.390314i | − 0.0131800i | −0.999978 | − | 0.00658999i | \(-0.997902\pi\) | ||||
0.999978 | − | 0.00658999i | \(-0.00209767\pi\) | |||||||
\(878\) | 4.80582i | 0.162188i | ||||||||
\(879\) | 1.97058 | 0.0664660 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7002 | 1.50599 | 0.752994 | − | 0.658028i | \(-0.228609\pi\) | ||||
0.752994 | + | 0.658028i | \(0.228609\pi\) | |||||||
\(882\) | 0.887444i | 0.0298818i | ||||||||
\(883\) | − 32.7567i | − 1.10235i | −0.834390 | − | 0.551175i | \(-0.814180\pi\) | ||||
0.834390 | − | 0.551175i | \(-0.185820\pi\) | |||||||
\(884\) | −48.1384 | −1.61907 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.09908 | 0.137711 | ||||||||
\(887\) | − 15.7130i | − 0.527591i | −0.964579 | − | 0.263796i | \(-0.915026\pi\) | ||||
0.964579 | − | 0.263796i | \(-0.0849745\pi\) | |||||||
\(888\) | − 4.20153i | − 0.140994i | ||||||||
\(889\) | −3.29461 | −0.110498 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.67993 | −0.123282 | ||||||||
\(892\) | − 6.41833i | − 0.214902i | ||||||||
\(893\) | 54.1299i | 1.81139i | ||||||||
\(894\) | 1.63624 | 0.0547239 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.79456 | −0.126767 | ||||||||
\(897\) | − 15.6855i | − 0.523725i | ||||||||
\(898\) | − 1.44649i | − 0.0482701i | ||||||||
\(899\) | −4.67839 | −0.156033 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.4623 | 0.415180 | ||||||||
\(902\) | − 1.32003i | − 0.0439523i | ||||||||
\(903\) | 2.90085i | 0.0965342i | ||||||||
\(904\) | 9.04256 | 0.300751 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.46706 | 0.115185 | ||||||||
\(907\) | − 1.50466i | − 0.0499613i | −0.999688 | − | 0.0249806i | \(-0.992048\pi\) | ||||
0.999688 | − | 0.0249806i | \(-0.00795241\pi\) | |||||||
\(908\) | 26.0952i | 0.865998i | ||||||||
\(909\) | 0.714616 | 0.0237023 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.4509 | 0.379386 | 0.189693 | − | 0.981843i | \(-0.439251\pi\) | ||||
0.189693 | + | 0.981843i | \(0.439251\pi\) | |||||||
\(912\) | − 24.7102i | − 0.818237i | ||||||||
\(913\) | − 27.2046i | − 0.900340i | ||||||||
\(914\) | 4.60422 | 0.152294 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.5590 | −0.381920 | ||||||||
\(917\) | 10.6855i | 0.352866i | ||||||||
\(918\) | 0.751949i | 0.0248180i | ||||||||
\(919\) | 21.8001 | 0.719119 | 0.359559 | − | 0.933122i | \(-0.382927\pi\) | ||||
0.359559 | + | 0.933122i | \(0.382927\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.2544 | 0.502651 | ||||||||
\(922\) | 0.0992632i | 0.00326906i | ||||||||
\(923\) | 19.8046i | 0.651877i | ||||||||
\(924\) | −6.25363 | −0.205729 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.307645 | −0.0101098 | ||||||||
\(927\) | 0.780764i | 0.0256437i | ||||||||
\(928\) | 6.26415i | 0.205631i | ||||||||
\(929\) | 30.7507 | 1.00890 | 0.504449 | − | 0.863442i | \(-0.331696\pi\) | ||||
0.504449 | + | 0.863442i | \(0.331696\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.8891 | −1.30731 | ||||||||
\(932\) | − 18.4817i | − 0.605387i | ||||||||
\(933\) | 17.7452i | 0.580953i | ||||||||
\(934\) | −0.549344 | −0.0179751 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.58348 | 0.0844437 | ||||||||
\(937\) | − 3.81060i | − 0.124487i | −0.998061 | − | 0.0622435i | \(-0.980174\pi\) | ||||
0.998061 | − | 0.0622435i | \(-0.0198255\pi\) | |||||||
\(938\) | − 0.406978i | − 0.0132883i | ||||||||
\(939\) | −27.3869 | −0.893737 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.7043 | −0.674939 | −0.337470 | − | 0.941336i | \(-0.609571\pi\) | ||||
−0.337470 | + | 0.941336i | \(0.609571\pi\) | |||||||
\(942\) | − 3.16903i | − 0.103253i | ||||||||
\(943\) | 8.66792i | 0.282266i | ||||||||
\(944\) | −50.9297 | −1.65762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.76221 | −0.0572944 | ||||||||
\(947\) | 15.6833i | 0.509639i | 0.966989 | + | 0.254819i | \(0.0820160\pi\) | ||||
−0.966989 | + | 0.254819i | \(0.917984\pi\) | |||||||
\(948\) | 6.42941i | 0.208818i | ||||||||
\(949\) | 41.5989 | 1.35036 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.64563 | −0.280354 | ||||||||
\(952\) | 2.56867i | 0.0832509i | ||||||||
\(953\) | 7.75207i | 0.251114i | 0.992086 | + | 0.125557i | \(0.0400718\pi\) | ||||
−0.992086 | + | 0.125557i | \(0.959928\pi\) | |||||||
\(954\) | −0.332725 | −0.0107724 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −33.9560 | −1.09822 | ||||||||
\(957\) | 13.7410i | 0.444185i | ||||||||
\(958\) | − 3.11708i | − 0.100708i | ||||||||
\(959\) | −10.1786 | −0.328685 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.4302 | −0.949363 | ||||||||
\(962\) | 4.83644i | 0.155933i | ||||||||
\(963\) | − 11.9601i | − 0.385409i | ||||||||
\(964\) | 14.2965 | 0.460459 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.416379 | −0.0133968 | ||||||||
\(967\) | − 48.4273i | − 1.55732i | −0.627447 | − | 0.778659i | \(-0.715900\pi\) | ||||
0.627447 | − | 0.778659i | \(-0.284100\pi\) | |||||||
\(968\) | − 1.43340i | − 0.0460712i | ||||||||
\(969\) | −33.7988 | −1.08577 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.3350 | 0.813039 | 0.406520 | − | 0.913642i | \(-0.366742\pi\) | ||||
0.406520 | + | 0.913642i | \(0.366742\pi\) | |||||||
\(972\) | 1.97992i | 0.0635061i | ||||||||
\(973\) | − 4.00049i | − 0.128250i | ||||||||
\(974\) | 4.02394 | 0.128936 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 40.1483 | 1.28511 | ||||||||
\(977\) | − 1.16885i | − 0.0373948i | −0.999825 | − | 0.0186974i | \(-0.994048\pi\) | ||||
0.999825 | − | 0.0186974i | \(-0.00595192\pi\) | |||||||
\(978\) | 0.115257i | 0.00368552i | ||||||||
\(979\) | −57.0298 | −1.82268 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.43384 | 0.0777065 | ||||||||
\(982\) | 1.99029i | 0.0635127i | ||||||||
\(983\) | 23.9943i | 0.765299i | 0.923894 | + | 0.382649i | \(0.124988\pi\) | ||||
−0.923894 | + | 0.382649i | \(0.875012\pi\) | |||||||
\(984\) | −1.42765 | −0.0455117 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.80782 | 0.0894190 | ||||||||
\(987\) | − 7.29510i | − 0.232206i | ||||||||
\(988\) | 57.7686i | 1.83786i | ||||||||
\(989\) | 11.5714 | 0.367950 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.6726 | −1.16494 | −0.582472 | − | 0.812851i | \(-0.697914\pi\) | ||||
−0.582472 | + | 0.812851i | \(0.697914\pi\) | |||||||
\(992\) | − 2.10183i | − 0.0667333i | ||||||||
\(993\) | 4.96260i | 0.157483i | ||||||||
\(994\) | 0.525722 | 0.0166749 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −14.6370 | −0.463790 | ||||||||
\(997\) | − 57.0203i | − 1.80585i | −0.429798 | − | 0.902925i | \(-0.641415\pi\) | ||||
0.429798 | − | 0.902925i | \(-0.358585\pi\) | |||||||
\(998\) | 1.85390i | 0.0586842i | ||||||||
\(999\) | −7.45067 | −0.235729 |
(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 | 1875.2.b.f.1249.6 | 12 | ||
5.2 | odd | 4 | 1875.2.a.k.1.4 | 6 | |||
5.3 | odd | 4 | 1875.2.a.j.1.3 | 6 | |||
5.4 | even | 2 | inner | 1875.2.b.f.1249.7 | 12 | ||
15.2 | even | 4 | 5625.2.a.q.1.3 | 6 | |||
15.8 | even | 4 | 5625.2.a.p.1.4 | 6 | |||
25.3 | odd | 20 | 75.2.g.c.16.2 | ✓ | 12 | ||
25.4 | even | 10 | 375.2.i.d.49.4 | 24 | |||
25.6 | even | 5 | 375.2.i.d.199.4 | 24 | |||
25.8 | odd | 20 | 75.2.g.c.61.2 | yes | 12 | ||
25.17 | odd | 20 | 375.2.g.c.301.2 | 12 | |||
25.19 | even | 10 | 375.2.i.d.199.3 | 24 | |||
25.21 | even | 5 | 375.2.i.d.49.3 | 24 | |||
25.22 | odd | 20 | 375.2.g.c.76.2 | 12 | |||
75.8 | even | 20 | 225.2.h.d.136.2 | 12 | |||
75.53 | even | 20 | 225.2.h.d.91.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.16.2 | ✓ | 12 | 25.3 | odd | 20 | ||
75.2.g.c.61.2 | yes | 12 | 25.8 | odd | 20 | ||
225.2.h.d.91.2 | 12 | 75.53 | even | 20 | |||
225.2.h.d.136.2 | 12 | 75.8 | even | 20 | |||
375.2.g.c.76.2 | 12 | 25.22 | odd | 20 | |||
375.2.g.c.301.2 | 12 | 25.17 | odd | 20 | |||
375.2.i.d.49.3 | 24 | 25.21 | even | 5 | |||
375.2.i.d.49.4 | 24 | 25.4 | even | 10 | |||
375.2.i.d.199.3 | 24 | 25.19 | even | 10 | |||
375.2.i.d.199.4 | 24 | 25.6 | even | 5 | |||
1875.2.a.j.1.3 | 6 | 5.3 | odd | 4 | |||
1875.2.a.k.1.4 | 6 | 5.2 | odd | 4 | |||
1875.2.b.f.1249.6 | 12 | 1.1 | even | 1 | trivial | ||
1875.2.b.f.1249.7 | 12 | 5.4 | even | 2 | inner | ||
5625.2.a.p.1.4 | 6 | 15.8 | even | 4 | |||
5625.2.a.q.1.3 | 6 | 15.2 | even | 4 |