Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(163,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.163");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.w (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 5x^{12} + 28x^{8} + 80x^{4} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.3 | ||
Root | \(1.17431 - 0.788026i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.307 |
Dual form | 360.2.w.d.163.3 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.788026 | − | 1.17431i | −0.557219 | − | 0.830366i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.758030 | + | 1.85078i | −0.379015 | + | 0.925391i | ||||
\(5\) | −0.386289 | − | 2.20245i | −0.172754 | − | 0.984965i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.51606 | + | 1.51606i | −0.573017 | + | 0.573017i | −0.932970 | − | 0.359953i | \(-0.882793\pi\) |
0.359953 | + | 0.932970i | \(0.382793\pi\) | |||||||
\(8\) | 2.77075 | − | 0.568298i | 0.979607 | − | 0.200924i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.28196 | + | 2.18921i | −0.721620 | + | 0.692289i | ||||
\(11\) | −3.92468 | −1.18334 | −0.591668 | − | 0.806182i | \(-0.701530\pi\) | ||||
−0.591668 | + | 0.806182i | \(0.701530\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.56393 | − | 3.56393i | −0.988455 | − | 0.988455i | 0.0114791 | − | 0.999934i | \(-0.496346\pi\) |
−0.999934 | + | 0.0114791i | \(0.996346\pi\) | |||||||
\(14\) | 2.97503 | + | 0.585637i | 0.795109 | + | 0.156518i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.85078 | − | 2.80590i | −0.712695 | − | 0.701474i | ||||
\(17\) | 1.37670 | + | 1.37670i | 0.333900 | + | 0.333900i | 0.854065 | − | 0.520166i | \(-0.174130\pi\) |
−0.520166 | + | 0.854065i | \(0.674130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000i | 0.917663i | 0.888523 | + | 0.458831i | \(0.151732\pi\) | ||||
−0.888523 | + | 0.458831i | \(0.848268\pi\) | |||||||
\(20\) | 4.36907 | + | 0.954587i | 0.976954 | + | 0.213452i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.09275 | + | 4.60881i | 0.659377 | + | 0.982602i | ||||
\(23\) | −5.17748 | − | 5.17748i | −1.07958 | − | 1.07958i | −0.996547 | − | 0.0830312i | \(-0.973540\pi\) |
−0.0830312 | − | 0.996547i | \(-0.526460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.70156 | + | 1.70156i | −0.940312 | + | 0.340312i | ||||
\(26\) | −1.37670 | + | 6.99364i | −0.269994 | + | 1.37156i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.65668 | − | 3.95511i | −0.313082 | − | 0.747446i | ||||
\(29\) | −5.95005 | −1.10490 | −0.552449 | − | 0.833547i | \(-0.686306\pi\) | ||||
−0.552449 | + | 0.833547i | \(0.686306\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.12785i | 1.28020i | 0.768292 | + | 0.640100i | \(0.221107\pi\) | ||||
−0.768292 | + | 0.640100i | \(0.778893\pi\) | |||||||
\(32\) | −1.04851 | + | 5.55883i | −0.185353 | + | 0.982672i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.531805 | − | 2.70156i | 0.0912038 | − | 0.463314i | ||||
\(35\) | 3.92468 | + | 2.75341i | 0.663392 | + | 0.465411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.56393 | − | 3.56393i | 0.585906 | − | 0.585906i | −0.350614 | − | 0.936520i | \(-0.614027\pi\) |
0.936520 | + | 0.350614i | \(0.114027\pi\) | |||||||
\(38\) | 4.69726 | − | 3.15210i | 0.761996 | − | 0.511339i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.32196 | − | 5.88290i | −0.367133 | − | 0.930168i | ||||
\(41\) | −2.75341 | −0.430010 | −0.215005 | − | 0.976613i | \(-0.568977\pi\) | ||||
−0.215005 | + | 0.976613i | \(0.568977\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.40312 | − | 5.40312i | 0.823969 | − | 0.823969i | −0.162706 | − | 0.986675i | \(-0.552022\pi\) |
0.986675 | + | 0.162706i | \(0.0520222\pi\) | |||||||
\(44\) | 2.97503 | − | 7.26373i | 0.448502 | − | 1.09505i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.00000 | + | 10.1600i | −0.294884 | + | 1.49801i | ||||
\(47\) | −1.54515 | + | 1.54515i | −0.225384 | + | 0.225384i | −0.810761 | − | 0.585377i | \(-0.800946\pi\) |
0.585377 | + | 0.810761i | \(0.300946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.40312i | 0.343303i | ||||||||
\(50\) | 5.70312 | + | 4.18024i | 0.806543 | + | 0.591175i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.29761 | − | 3.89448i | 1.28935 | − | 0.540068i | ||||
\(53\) | −1.81616 | − | 1.81616i | −0.249469 | − | 0.249469i | 0.571284 | − | 0.820753i | \(-0.306446\pi\) |
−0.820753 | + | 0.571284i | \(0.806446\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.51606 | + | 8.64391i | 0.204425 | + | 1.16554i | ||||
\(56\) | −3.33904 | + | 5.06219i | −0.446199 | + | 0.676464i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.68880 | + | 6.98723i | 0.615669 | + | 0.917469i | ||||
\(59\) | 3.92468i | 0.510950i | 0.966816 | + | 0.255475i | \(0.0822318\pi\) | ||||
−0.966816 | + | 0.255475i | \(0.917768\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 13.1921i | − | 1.68907i | −0.535497 | − | 0.844537i | \(-0.679876\pi\) | ||
0.535497 | − | 0.844537i | \(-0.320124\pi\) | |||||||
\(62\) | 8.37034 | − | 5.61693i | 1.06303 | − | 0.713351i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.35408 | − | 3.14922i | 0.919259 | − | 0.393652i | ||||
\(65\) | −6.47266 | + | 9.22607i | −0.802835 | + | 1.14435i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.40312 | − | 5.40312i | −0.660097 | − | 0.660097i | 0.295306 | − | 0.955403i | \(-0.404578\pi\) |
−0.955403 | + | 0.295306i | \(0.904578\pi\) | |||||||
\(68\) | −3.59156 | + | 1.50439i | −0.435541 | + | 0.182435i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.140616 | − | 6.77857i | 0.0168068 | − | 0.810194i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | − | 5.00000i | 0.585206 | − | 0.585206i | −0.351123 | − | 0.936329i | \(-0.614200\pi\) |
0.936329 | + | 0.351123i | \(0.114200\pi\) | |||||||
\(74\) | −6.99364 | − | 1.37670i | −0.812994 | − | 0.160039i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.40312 | − | 3.03212i | −0.849197 | − | 0.347808i | ||||
\(77\) | 5.95005 | − | 5.95005i | 0.678071 | − | 0.678071i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.12785 | 0.801946 | 0.400973 | − | 0.916090i | \(-0.368672\pi\) | ||||
0.400973 | + | 0.916090i | \(0.368672\pi\) | |||||||
\(80\) | −5.07862 | + | 7.36259i | −0.567807 | + | 0.823162i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.16976 | + | 3.23337i | 0.239610 | + | 0.357066i | ||||
\(83\) | 6.67809 | − | 6.67809i | 0.733016 | − | 0.733016i | −0.238200 | − | 0.971216i | \(-0.576558\pi\) |
0.971216 | + | 0.238200i | \(0.0765575\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.50031 | − | 3.56393i | 0.271197 | − | 0.386562i | ||||
\(86\) | −10.6028 | − | 2.08717i | −1.14333 | − | 0.225065i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −10.8743 | + | 2.23039i | −1.15920 | + | 0.237760i | ||||
\(89\) | − | 18.4521i | − | 1.95592i | −0.208787 | − | 0.977961i | \(-0.566952\pi\) | ||
0.208787 | − | 0.977961i | \(-0.433048\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.8062 | 1.13280 | ||||||||
\(92\) | 13.5071 | − | 5.65769i | 1.40821 | − | 0.589855i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.03212 | + | 0.596876i | 0.312739 | + | 0.0615630i | ||||
\(95\) | 8.80980 | − | 1.54515i | 0.903866 | − | 0.158530i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.4031 | − | 10.4031i | −1.05628 | − | 1.05628i | −0.998319 | − | 0.0579582i | \(-0.981541\pi\) |
−0.0579582 | − | 0.998319i | \(-0.518459\pi\) | |||||||
\(98\) | 2.82202 | − | 1.89372i | 0.285067 | − | 0.191295i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.414706 | − | 9.99140i | 0.0414706 | − | 0.999140i | ||||
\(101\) | 8.03722i | 0.799733i | 0.916573 | + | 0.399867i | \(0.130944\pi\) | ||||
−0.916573 | + | 0.399867i | \(0.869056\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.61179 | + | 5.61179i | 0.552946 | + | 0.552946i | 0.927290 | − | 0.374344i | \(-0.122132\pi\) |
−0.374344 | + | 0.927290i | \(0.622132\pi\) | |||||||
\(104\) | −11.9001 | − | 7.84936i | −1.16690 | − | 0.769693i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.701562 | + | 3.56393i | −0.0681417 | + | 0.346159i | ||||
\(107\) | −3.92468 | − | 3.92468i | −0.379413 | − | 0.379413i | 0.491477 | − | 0.870890i | \(-0.336457\pi\) |
−0.870890 | + | 0.491477i | \(0.836457\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.06424 | 0.580849 | 0.290424 | − | 0.956898i | \(-0.406204\pi\) | ||||
0.290424 | + | 0.956898i | \(0.406204\pi\) | |||||||
\(110\) | 8.95598 | − | 8.59196i | 0.853919 | − | 0.819211i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8.57586 | − | 0.0680498i | 0.810343 | − | 0.00643010i | ||||
\(113\) | 1.37670 | − | 1.37670i | 0.129509 | − | 0.129509i | −0.639381 | − | 0.768890i | \(-0.720809\pi\) |
0.768890 | + | 0.639381i | \(0.220809\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.40312 | + | 13.4031i | −0.876846 | + | 1.24985i | ||||
\(116\) | 4.51032 | − | 11.0122i | 0.418773 | − | 1.02246i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.60881 | − | 3.09275i | 0.424275 | − | 0.284711i | ||||
\(119\) | −4.17433 | −0.382660 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40312 | 0.400284 | ||||||||
\(122\) | −15.4917 | + | 10.3957i | −1.40255 | + | 0.941183i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.1921 | − | 5.40312i | −1.18468 | − | 0.485215i | ||||
\(125\) | 5.56376 | + | 9.69766i | 0.497638 | + | 0.867385i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.6760 | + | 11.6760i | −1.03608 | + | 1.03608i | −0.0367559 | + | 0.999324i | \(0.511702\pi\) |
−0.999324 | + | 0.0367559i | \(0.988298\pi\) | |||||||
\(128\) | −9.49338 | − | 6.15433i | −0.839104 | − | 0.543971i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.9349 | + | 0.330558i | 1.39759 | + | 0.0289918i | ||||
\(131\) | −17.2809 | −1.50984 | −0.754918 | − | 0.655819i | \(-0.772323\pi\) | ||||
−0.754918 | + | 0.655819i | \(0.772323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.06424 | − | 6.06424i | −0.525836 | − | 0.525836i | ||||
\(134\) | −2.08717 | + | 10.6028i | −0.180304 | + | 0.915940i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.59688 | + | 3.03212i | 0.394179 | + | 0.260002i | ||||
\(137\) | 14.3220 | + | 14.3220i | 1.22361 | + | 1.22361i | 0.966338 | + | 0.257275i | \(0.0828245\pi\) |
0.257275 | + | 0.966338i | \(0.417176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.00000i | − | 0.339276i | −0.985506 | − | 0.169638i | \(-0.945740\pi\) | ||
0.985506 | − | 0.169638i | \(-0.0542598\pi\) | |||||||
\(140\) | −8.07098 | + | 5.17656i | −0.682122 | + | 0.437499i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.9873 | + | 13.9873i | 1.16967 | + | 1.16967i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.29844 | + | 13.1047i | 0.190875 | + | 1.08828i | ||||
\(146\) | −9.81170 | − | 1.93144i | −0.812022 | − | 0.159847i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.89448 | + | 9.29761i | 0.320125 | + | 0.764259i | ||||
\(149\) | 8.03722 | 0.658435 | 0.329217 | − | 0.944254i | \(-0.393215\pi\) | ||||
0.329217 | + | 0.944254i | \(0.393215\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.1600i | − | 0.826807i | −0.910548 | − | 0.413403i | \(-0.864340\pi\) | ||
0.910548 | − | 0.413403i | \(-0.135660\pi\) | |||||||
\(152\) | 2.27319 | + | 11.0830i | 0.184380 | + | 0.898949i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −11.6760 | − | 2.29844i | −0.940881 | − | 0.185213i | ||||
\(155\) | 15.6987 | − | 2.75341i | 1.26095 | − | 0.221159i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.62817 | + | 9.62817i | −0.768411 | + | 0.768411i | −0.977827 | − | 0.209416i | \(-0.932844\pi\) |
0.209416 | + | 0.977827i | \(0.432844\pi\) | |||||||
\(158\) | −5.61693 | − | 8.37034i | −0.446859 | − | 0.665908i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 12.6481 | + | 0.161985i | 0.999918 | + | 0.0128060i | ||||
\(161\) | 15.6987 | 1.23723 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(164\) | 2.08717 | − | 5.09596i | 0.162980 | − | 0.397927i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −13.1047 | − | 2.57967i | −1.01712 | − | 0.200221i | ||||
\(167\) | 1.54515 | − | 1.54515i | 0.119568 | − | 0.119568i | −0.644791 | − | 0.764359i | \(-0.723056\pi\) |
0.764359 | + | 0.644791i | \(0.223056\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4031i | 0.954086i | ||||||||
\(170\) | −6.15548 | − | 0.127691i | −0.472104 | − | 0.00979343i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.90427 | + | 14.0957i | 0.450196 | + | 1.07479i | ||||
\(173\) | 4.13389 | + | 4.13389i | 0.314294 | + | 0.314294i | 0.846571 | − | 0.532277i | \(-0.178663\pi\) |
−0.532277 | + | 0.846571i | \(0.678663\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.54818 | − | 9.70752i | 0.343810 | − | 0.733820i | ||||
\(176\) | 11.1884 | + | 11.0122i | 0.843358 | + | 0.830079i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −21.6686 | + | 14.5408i | −1.62413 | + | 1.08988i | ||||
\(179\) | 14.1166i | 1.05512i | 0.849517 | + | 0.527562i | \(0.176894\pi\) | ||||
−0.849517 | + | 0.527562i | \(0.823106\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.06424i | 0.450751i | 0.974272 | + | 0.225376i | \(0.0723610\pi\) | ||||
−0.974272 | + | 0.225376i | \(0.927639\pi\) | |||||||
\(182\) | −8.51560 | − | 12.6899i | −0.631219 | − | 0.940641i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −17.2878 | − | 11.4031i | −1.27448 | − | 0.840649i | ||||
\(185\) | −9.22607 | − | 6.47266i | −0.678314 | − | 0.475879i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.40312 | − | 5.40312i | −0.395116 | − | 0.395116i | ||||
\(188\) | −1.68847 | − | 4.03102i | −0.123144 | − | 0.293992i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.75685 | − | 9.12785i | −0.635288 | − | 0.662204i | ||||
\(191\) | 23.8002i | 1.72212i | 0.508501 | + | 0.861061i | \(0.330200\pi\) | ||||
−0.508501 | + | 0.861061i | \(0.669800\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.403124 | − | 0.403124i | 0.0290175 | − | 0.0290175i | −0.692449 | − | 0.721467i | \(-0.743468\pi\) |
0.721467 | + | 0.692449i | \(0.243468\pi\) | |||||||
\(194\) | −4.01861 | + | 20.4145i | −0.288519 | + | 1.46567i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.44766 | − | 1.82164i | −0.317690 | − | 0.130117i | ||||
\(197\) | −5.44848 | + | 5.44848i | −0.388188 | + | 0.388188i | −0.874041 | − | 0.485853i | \(-0.838509\pi\) |
0.485853 | + | 0.874041i | \(0.338509\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3514 | −1.30090 | −0.650449 | − | 0.759550i | \(-0.725419\pi\) | ||||
−0.650449 | + | 0.759550i | \(0.725419\pi\) | |||||||
\(200\) | −12.0598 | + | 7.38649i | −0.852760 | + | 0.522303i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.43822 | − | 6.33354i | 0.664071 | − | 0.445626i | ||||
\(203\) | 9.02064 | − | 9.02064i | 0.633125 | − | 0.633125i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.06361 | + | 6.06424i | 0.0742858 | + | 0.423545i | ||||
\(206\) | 2.16777 | − | 11.0122i | 0.151036 | − | 0.767259i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.159970 | + | 20.1600i | 0.0110919 | + | 1.39784i | ||||
\(209\) | − | 15.6987i | − | 1.08590i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 4.73802 | − | 1.98461i | 0.325408 | − | 0.136304i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.51606 | + | 7.70156i | −0.103636 | + | 0.526468i | ||||
\(215\) | −13.9873 | − | 9.81294i | −0.953924 | − | 0.669237i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.8062 | − | 10.8062i | −0.733576 | − | 0.733576i | ||||
\(218\) | −4.77878 | − | 7.12133i | −0.323660 | − | 0.482317i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.1472 | − | 3.74645i | −1.15606 | − | 0.252585i | ||||
\(221\) | − | 9.81294i | − | 0.660090i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.6760 | − | 11.6760i | −0.781885 | − | 0.781885i | 0.198264 | − | 0.980149i | \(-0.436470\pi\) |
−0.980149 | + | 0.198264i | \(0.936470\pi\) | |||||||
\(224\) | −6.83791 | − | 10.0171i | −0.456877 | − | 0.669298i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.70156 | − | 0.531805i | −0.179705 | − | 0.0353752i | ||||
\(227\) | −12.9453 | − | 12.9453i | −0.859211 | − | 0.859211i | 0.132034 | − | 0.991245i | \(-0.457849\pi\) |
−0.991245 | + | 0.132034i | \(0.957849\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.1921 | −0.871758 | −0.435879 | − | 0.900005i | \(-0.643562\pi\) | ||||
−0.435879 | + | 0.900005i | \(0.643562\pi\) | |||||||
\(230\) | 23.1494 | + | 0.480216i | 1.52643 | + | 0.0316645i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −16.4861 | + | 3.38140i | −1.08236 | + | 0.222000i | ||||
\(233\) | −14.3220 | + | 14.3220i | −0.938267 | + | 0.938267i | −0.998202 | − | 0.0599354i | \(-0.980911\pi\) |
0.0599354 | + | 0.998202i | \(0.480911\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | + | 2.80625i | 0.260931 | + | 0.183059i | ||||
\(236\) | −7.26373 | − | 2.97503i | −0.472828 | − | 0.193658i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.28948 | + | 4.90198i | 0.213225 | + | 0.317748i | ||||
\(239\) | 27.9745 | 1.80952 | 0.904761 | − | 0.425919i | \(-0.140049\pi\) | ||||
0.904761 | + | 0.425919i | \(0.140049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.8062 | 1.21142 | 0.605708 | − | 0.795687i | \(-0.292890\pi\) | ||||
0.605708 | + | 0.795687i | \(0.292890\pi\) | |||||||
\(242\) | −3.46978 | − | 5.17065i | −0.223046 | − | 0.332382i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 24.4157 | + | 10.0000i | 1.56305 | + | 0.640184i | ||||
\(245\) | 5.29276 | − | 0.928300i | 0.338142 | − | 0.0593069i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2557 | − | 14.2557i | 0.907068 | − | 0.907068i | ||||
\(248\) | 4.05074 | + | 19.7495i | 0.257222 | + | 1.25409i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.00371 | − | 14.1756i | 0.442953 | − | 0.896545i | ||||
\(251\) | 1.58213 | 0.0998634 | 0.0499317 | − | 0.998753i | \(-0.484100\pi\) | ||||
0.0499317 | + | 0.998753i | \(0.484100\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.3199 | + | 20.3199i | 1.27750 | + | 1.27750i | ||||
\(254\) | 22.9123 | + | 4.51032i | 1.43765 | + | 0.283003i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.253905 | + | 15.9980i | 0.0158691 | + | 0.999874i | ||||
\(257\) | −4.13011 | − | 4.13011i | −0.257629 | − | 0.257629i | 0.566460 | − | 0.824089i | \(-0.308313\pi\) |
−0.824089 | + | 0.566460i | \(0.808313\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 10.8062i | 0.671468i | ||||||||
\(260\) | −12.1690 | − | 18.9731i | −0.754687 | − | 1.17666i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.6178 | + | 20.2932i | 0.841308 | + | 1.25372i | ||||
\(263\) | −19.1647 | − | 19.1647i | −1.18175 | − | 1.18175i | −0.979291 | − | 0.202458i | \(-0.935107\pi\) |
−0.202458 | − | 0.979291i | \(-0.564893\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.29844 | + | 4.70156i | −0.202621 | + | 0.288815i | ||||
\(266\) | −2.34255 | + | 11.9001i | −0.143631 | + | 0.729642i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.0957 | − | 5.90427i | 0.861034 | − | 0.360661i | ||||
\(269\) | −3.86289 | −0.235524 | −0.117762 | − | 0.993042i | \(-0.537572\pi\) | ||||
−0.117762 | + | 0.993042i | \(0.537572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 16.2242i | − | 0.985551i | −0.870157 | − | 0.492775i | \(-0.835982\pi\) | ||
0.870157 | − | 0.492775i | \(-0.164018\pi\) | |||||||
\(272\) | −0.0617947 | − | 7.78757i | −0.00374685 | − | 0.472191i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.53243 | − | 28.1047i | 0.334227 | − | 1.69787i | ||||
\(275\) | 18.4521 | − | 6.67809i | 1.11271 | − | 0.402704i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.6918 | + | 10.6918i | −0.642407 | + | 0.642407i | −0.951146 | − | 0.308740i | \(-0.900093\pi\) |
0.308740 | + | 0.951146i | \(0.400093\pi\) | |||||||
\(278\) | −4.69726 | + | 3.15210i | −0.281723 | + | 0.189051i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 12.4391 | + | 5.39861i | 0.743376 | + | 0.322629i | ||||
\(281\) | 8.26022 | 0.492764 | 0.246382 | − | 0.969173i | \(-0.420758\pi\) | ||||
0.246382 | + | 0.969173i | \(0.420758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.40312 | + | 5.40312i | −0.321182 | + | 0.321182i | −0.849221 | − | 0.528038i | \(-0.822928\pi\) |
0.528038 | + | 0.849221i | \(0.322928\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.40312 | − | 27.4478i | 0.319493 | − | 1.62302i | ||||
\(287\) | 4.17433 | − | 4.17433i | 0.246403 | − | 0.246403i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 13.2094i | − | 0.777022i | ||||||
\(290\) | 13.5778 | − | 13.0259i | 0.797316 | − | 0.764909i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.46376 | + | 13.0441i | 0.319742 | + | 0.763346i | ||||
\(293\) | 1.81616 | + | 1.81616i | 0.106101 | + | 0.106101i | 0.758165 | − | 0.652063i | \(-0.226096\pi\) |
−0.652063 | + | 0.758165i | \(0.726096\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.64391 | − | 1.51606i | 0.503268 | − | 0.0882684i | ||||
\(296\) | 7.84936 | − | 11.9001i | 0.456235 | − | 0.691680i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.33354 | − | 9.43822i | −0.366892 | − | 0.546742i | ||||
\(299\) | 36.9043i | 2.13423i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3829i | 0.944296i | ||||||||
\(302\) | −11.9310 | + | 8.00632i | −0.686552 | + | 0.460712i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.2236 | − | 11.4031i | 0.643716 | − | 0.654014i | ||||
\(305\) | −29.0549 | + | 5.09596i | −1.66368 | + | 0.291794i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | − | 20.0000i | −1.14146 | − | 1.14146i | −0.988183 | − | 0.153277i | \(-0.951017\pi\) |
−0.153277 | − | 0.988183i | \(-0.548983\pi\) | |||||||
\(308\) | 6.50193 | + | 15.5226i | 0.370482 | + | 0.884480i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.6044 | − | 16.2655i | −0.886269 | − | 0.923818i | ||||
\(311\) | − | 27.9745i | − | 1.58629i | −0.609032 | − | 0.793145i | \(-0.708442\pi\) | ||
0.609032 | − | 0.793145i | \(-0.291558\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.80625 | − | 5.80625i | 0.328189 | − | 0.328189i | −0.523709 | − | 0.851897i | \(-0.675452\pi\) |
0.851897 | + | 0.523709i | \(0.175452\pi\) | |||||||
\(314\) | 18.8937 | + | 3.71925i | 1.06624 | + | 0.209889i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.40312 | + | 13.1921i | −0.303949 | + | 0.742113i | ||||
\(317\) | −11.3985 | + | 11.3985i | −0.640205 | + | 0.640205i | −0.950606 | − | 0.310400i | \(-0.899537\pi\) |
0.310400 | + | 0.950606i | \(0.399537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.3521 | 1.30746 | ||||||||
\(320\) | −9.77679 | − | 14.9805i | −0.546539 | − | 0.837434i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.3710 | − | 18.4352i | −0.689409 | − | 1.02736i | ||||
\(323\) | −5.50682 | + | 5.50682i | −0.306407 | + | 0.306407i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.8203 | + | 10.6918i | 1.26584 | + | 0.593073i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.62900 | + | 1.56476i | −0.421241 | + | 0.0863992i | ||||
\(329\) | − | 4.68509i | − | 0.258298i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.8062 | −1.25354 | −0.626772 | − | 0.779202i | \(-0.715624\pi\) | ||||
−0.626772 | + | 0.779202i | \(0.715624\pi\) | |||||||
\(332\) | 7.29749 | + | 17.4219i | 0.400502 | + | 0.956149i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.03212 | − | 0.596876i | −0.165910 | − | 0.0326596i | ||||
\(335\) | −9.81294 | + | 13.9873i | −0.536138 | + | 0.764206i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4031 | + | 10.4031i | 0.566694 | + | 0.566694i | 0.931201 | − | 0.364507i | \(-0.118762\pi\) |
−0.364507 | + | 0.931201i | \(0.618762\pi\) | |||||||
\(338\) | 14.5652 | − | 9.77398i | 0.792241 | − | 0.531635i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.70073 | + | 7.32910i | 0.254933 | + | 0.397476i | ||||
\(341\) | − | 27.9745i | − | 1.51491i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −14.2557 | − | 14.2557i | −0.769735 | − | 0.769735i | ||||
\(344\) | 11.9001 | − | 18.0413i | 0.641611 | − | 0.972720i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.59688 | − | 8.11211i | 0.0858486 | − | 0.436109i | ||||
\(347\) | −18.4521 | − | 18.4521i | −0.990562 | − | 0.990562i | 0.00939345 | − | 0.999956i | \(-0.497010\pi\) |
−0.999956 | + | 0.00939345i | \(0.997010\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1921 | 0.706156 | 0.353078 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353078 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(350\) | −14.9838 | + | 2.30878i | −0.800916 | + | 0.123410i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.11508 | − | 21.8166i | 0.219335 | − | 1.16283i | ||||
\(353\) | −4.13011 | + | 4.13011i | −0.219824 | + | 0.219824i | −0.808424 | − | 0.588600i | \(-0.799679\pi\) |
0.588600 | + | 0.808424i | \(0.299679\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 34.1509 | + | 13.9873i | 1.80999 | + | 0.741324i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 16.5773 | − | 11.1242i | 0.876139 | − | 0.587934i | ||||
\(359\) | −32.1489 | −1.69675 | −0.848376 | − | 0.529394i | \(-0.822419\pi\) | ||||
−0.848376 | + | 0.529394i | \(0.822419\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.00000 | 0.157895 | ||||||||
\(362\) | 7.12133 | − | 4.77878i | 0.374289 | − | 0.251167i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.19146 | + | 20.0000i | −0.429349 | + | 1.04828i | ||||
\(365\) | −12.9437 | − | 9.08080i | −0.677504 | − | 0.475311i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.58030 | − | 7.58030i | 0.395688 | − | 0.395688i | −0.481021 | − | 0.876709i | \(-0.659734\pi\) |
0.876709 | + | 0.481021i | \(0.159734\pi\) | |||||||
\(368\) | 0.232396 | + | 29.2873i | 0.0121145 | + | 1.52671i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −0.330558 | + | 15.9349i | −0.0171849 | + | 0.828418i | ||||
\(371\) | 5.50682 | 0.285900 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.50031 | − | 2.50031i | −0.129461 | − | 0.129461i | 0.639407 | − | 0.768868i | \(-0.279180\pi\) |
−0.768868 | + | 0.639407i | \(0.779180\pi\) | |||||||
\(374\) | −2.08717 | + | 10.6028i | −0.107925 | + | 0.548256i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.40312 | + | 5.15934i | −0.175503 | + | 0.266073i | ||||
\(377\) | 21.2055 | + | 21.2055i | 1.09214 | + | 1.09214i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.80625i | 0.349614i | 0.984603 | + | 0.174807i | \(0.0559301\pi\) | ||||
−0.984603 | + | 0.174807i | \(0.944070\pi\) | |||||||
\(380\) | −3.81835 | + | 17.4763i | −0.195877 | + | 0.896514i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 27.9489 | − | 18.7552i | 1.42999 | − | 0.959599i | ||||
\(383\) | 9.35181 | + | 9.35181i | 0.477855 | + | 0.477855i | 0.904445 | − | 0.426590i | \(-0.140285\pi\) |
−0.426590 | + | 0.904445i | \(0.640285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.4031 | − | 10.8062i | −0.785016 | − | 0.550737i | ||||
\(386\) | −0.791067 | − | 0.155722i | −0.0402643 | − | 0.00792606i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 27.1398 | − | 11.3680i | 1.37781 | − | 0.577124i | ||||
\(389\) | −27.6631 | −1.40257 | −0.701287 | − | 0.712879i | \(-0.747391\pi\) | ||||
−0.701287 | + | 0.712879i | \(0.747391\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.2557i | − | 0.720942i | ||||||
\(392\) | 1.36569 | + | 6.65845i | 0.0689778 | + | 0.336302i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.6918 | + | 2.10469i | 0.538644 | + | 0.106033i | ||||
\(395\) | −2.75341 | − | 15.6987i | −0.138539 | − | 0.789889i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.62754 | − | 4.62754i | 0.232249 | − | 0.232249i | −0.581382 | − | 0.813631i | \(-0.697488\pi\) |
0.813631 | + | 0.581382i | \(0.197488\pi\) | |||||||
\(398\) | 14.4614 | + | 21.5504i | 0.724885 | + | 1.08022i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 18.1775 | + | 8.34131i | 0.908876 | + | 0.417065i | ||||
\(401\) | 31.3975 | 1.56791 | 0.783957 | − | 0.620815i | \(-0.213198\pi\) | ||||
0.783957 | + | 0.620815i | \(0.213198\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 25.4031 | − | 25.4031i | 1.26542 | − | 1.26542i | ||||
\(404\) | −14.8751 | − | 6.09245i | −0.740065 | − | 0.303111i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.7016 | − | 3.48457i | −0.878514 | − | 0.172936i | ||||
\(407\) | −13.9873 | + | 13.9873i | −0.693323 | + | 0.693323i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.40312i | − | 0.464955i | −0.972602 | − | 0.232477i | \(-0.925317\pi\) | ||
0.972602 | − | 0.232477i | \(-0.0746831\pi\) | |||||||
\(410\) | 6.28317 | − | 6.02779i | 0.310304 | − | 0.297691i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −14.6401 | + | 6.13229i | −0.721266 | + | 0.302116i | ||||
\(413\) | −5.95005 | − | 5.95005i | −0.292783 | − | 0.292783i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.2878 | − | 12.1285i | −0.848626 | − | 0.595364i | ||||
\(416\) | 23.5481 | − | 16.0744i | 1.15454 | − | 0.788114i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.4352 | + | 12.3710i | −0.901697 | + | 0.605086i | ||||
\(419\) | 22.7877i | 1.11325i | 0.830764 | + | 0.556625i | \(0.187904\pi\) | ||||
−0.830764 | + | 0.556625i | \(0.812096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3206i | 1.23405i | 0.786944 | + | 0.617025i | \(0.211662\pi\) | ||||
−0.786944 | + | 0.617025i | \(0.788338\pi\) | |||||||
\(422\) | −9.45631 | − | 14.0918i | −0.460326 | − | 0.685977i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.06424 | − | 4.00000i | −0.294506 | − | 0.194257i | ||||
\(425\) | −8.81521 | − | 4.13011i | −0.427600 | − | 0.200340i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.0000 | + | 20.0000i | 0.967868 | + | 0.967868i | ||||
\(428\) | 10.2388 | − | 4.28870i | 0.494909 | − | 0.207302i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.501146 | + | 24.1583i | −0.0241674 | + | 1.16502i | ||||
\(431\) | − | 4.17433i | − | 0.201070i | −0.994933 | − | 0.100535i | \(-0.967944\pi\) | ||
0.994933 | − | 0.100535i | \(-0.0320555\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.403124 | + | 0.403124i | −0.0193729 | + | 0.0193729i | −0.716727 | − | 0.697354i | \(-0.754361\pi\) |
0.697354 | + | 0.716727i | \(0.254361\pi\) | |||||||
\(434\) | −4.17433 | + | 21.2055i | −0.200374 | + | 1.01790i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.59688 | + | 11.2236i | −0.220150 | + | 0.537512i | ||||
\(437\) | 20.7099 | − | 20.7099i | 0.990689 | − | 0.990689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.09573 | 0.195479 | 0.0977393 | − | 0.995212i | \(-0.468839\pi\) | ||||
0.0977393 | + | 0.995212i | \(0.468839\pi\) | |||||||
\(440\) | 9.11293 | + | 23.0885i | 0.434442 | + | 1.10070i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.5235 | + | 7.73285i | −0.548116 | + | 0.367814i | ||||
\(443\) | −12.9453 | + | 12.9453i | −0.615051 | + | 0.615051i | −0.944258 | − | 0.329207i | \(-0.893219\pi\) |
0.329207 | + | 0.944258i | \(0.393219\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −40.6399 | + | 7.12785i | −1.92652 | + | 0.337893i | ||||
\(446\) | −4.51032 | + | 22.9123i | −0.213570 | + | 1.08493i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.37481 | + | 15.9236i | −0.301182 | + | 0.752321i | ||||
\(449\) | − | 15.6987i | − | 0.740869i | −0.928859 | − | 0.370434i | \(-0.879209\pi\) | ||
0.928859 | − | 0.370434i | \(-0.120791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8062 | 0.508846 | ||||||||
\(452\) | 1.50439 | + | 3.59156i | 0.0707608 | + | 0.168933i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −5.00063 | + | 25.4031i | −0.234691 | + | 1.19223i | ||||
\(455\) | −4.17433 | − | 23.8002i | −0.195696 | − | 1.11577i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.8062 | + | 15.8062i | 0.739385 | + | 0.739385i | 0.972459 | − | 0.233074i | \(-0.0748784\pi\) |
−0.233074 | + | 0.972459i | \(0.574878\pi\) | |||||||
\(458\) | 10.3957 | + | 15.4917i | 0.485760 | + | 0.723878i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.6784 | − | 27.5631i | −0.824260 | − | 1.28514i | ||||
\(461\) | 3.86289i | 0.179913i | 0.995946 | + | 0.0899563i | \(0.0286727\pi\) | ||||
−0.995946 | + | 0.0899563i | \(0.971327\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58030 | + | 7.58030i | 0.352286 | + | 0.352286i | 0.860960 | − | 0.508673i | \(-0.169864\pi\) |
−0.508673 | + | 0.860960i | \(0.669864\pi\) | |||||||
\(464\) | 16.9623 | + | 16.6952i | 0.787455 | + | 0.775056i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.1047 | + | 5.53243i | 1.30192 | + | 0.256285i | ||||
\(467\) | 1.17127 | + | 1.17127i | 0.0542001 | + | 0.0542001i | 0.733687 | − | 0.679487i | \(-0.237798\pi\) |
−0.679487 | + | 0.733687i | \(0.737798\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3829 | 0.756493 | ||||||||
\(470\) | 0.143315 | − | 6.90866i | 0.00661062 | − | 0.318673i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.23039 | + | 10.8743i | 0.102662 | + | 0.500530i | ||||
\(473\) | −21.2055 | + | 21.2055i | −0.975032 | + | 0.975032i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.80625 | − | 18.8062i | −0.312292 | − | 0.862890i | ||||
\(476\) | 3.16427 | − | 7.72577i | 0.145034 | − | 0.354110i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −22.0447 | − | 32.8509i | −1.00830 | − | 1.50257i | ||||
\(479\) | 27.9745 | 1.27819 | 0.639095 | − | 0.769128i | \(-0.279309\pi\) | ||||
0.639095 | + | 0.769128i | \(0.279309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.4031 | −1.15828 | ||||||||
\(482\) | −14.8198 | − | 22.0845i | −0.675024 | − | 1.00592i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.33770 | + | 8.14922i | −0.151714 | + | 0.370419i | ||||
\(485\) | −18.8937 | + | 26.9310i | −0.857921 | + | 1.22287i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.64391 | + | 8.64391i | −0.391693 | + | 0.391693i | −0.875290 | − | 0.483598i | \(-0.839330\pi\) |
0.483598 | + | 0.875290i | \(0.339330\pi\) | |||||||
\(488\) | −7.49704 | − | 36.5519i | −0.339375 | − | 1.65463i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.26095 | − | 5.48384i | −0.237665 | − | 0.247735i | ||||
\(491\) | −27.4728 | −1.23983 | −0.619914 | − | 0.784669i | \(-0.712833\pi\) | ||||
−0.619914 | + | 0.784669i | \(0.712833\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.19146 | − | 8.19146i | −0.368925 | − | 0.368925i | ||||
\(494\) | −27.9745 | − | 5.50682i | −1.25863 | − | 0.247763i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 20.0000 | − | 20.3199i | 0.898027 | − | 0.912392i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.80625i | − | 0.304690i | −0.988327 | − | 0.152345i | \(-0.951318\pi\) | ||
0.988327 | − | 0.152345i | \(-0.0486824\pi\) | |||||||
\(500\) | −22.1657 | + | 2.94619i | −0.991282 | + | 0.131758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.24676 | − | 1.85792i | −0.0556458 | − | 0.0829232i | ||||
\(503\) | −8.80980 | − | 8.80980i | −0.392809 | − | 0.392809i | 0.482878 | − | 0.875688i | \(-0.339591\pi\) |
−0.875688 | + | 0.482878i | \(0.839591\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.7016 | − | 3.10469i | 0.787709 | − | 0.138157i | ||||
\(506\) | 7.84936 | − | 39.8746i | 0.348947 | − | 1.77264i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −12.7590 | − | 30.4606i | −0.566089 | − | 1.35147i | ||||
\(509\) | 22.0245 | 0.976218 | 0.488109 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488109 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.1606i | 0.670665i | ||||||||
\(512\) | 18.5866 | − | 12.9050i | 0.821419 | − | 0.570326i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.59542 | + | 8.10469i | −0.0703708 | + | 0.357482i | ||||
\(515\) | 10.1919 | − | 14.5275i | 0.449109 | − | 0.640156i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.06424 | − | 6.06424i | 0.266705 | − | 0.266705i | ||||
\(518\) | 12.6899 | − | 8.51560i | 0.557564 | − | 0.374154i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.6909 | + | 29.2415i | −0.556535 | + | 1.28232i | ||||
\(521\) | 15.6987 | 0.687774 | 0.343887 | − | 0.939011i | \(-0.388256\pi\) | ||||
0.343887 | + | 0.939011i | \(0.388256\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.8062 | + | 30.8062i | −1.34706 | + | 1.34706i | −0.458229 | + | 0.888834i | \(0.651516\pi\) |
−0.888834 | + | 0.458229i | \(0.848484\pi\) | |||||||
\(524\) | 13.0994 | − | 31.9831i | 0.572250 | − | 1.39719i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.40312 | + | 37.6078i | −0.322792 | + | 1.63978i | ||||
\(527\) | −9.81294 | + | 9.81294i | −0.427458 | + | 0.427458i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 30.6125i | 1.33098i | ||||||||
\(530\) | 8.12037 | + | 0.168451i | 0.352726 | + | 0.00731703i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.8205 | − | 6.62670i | 0.685904 | − | 0.287304i | ||||
\(533\) | 9.81294 | + | 9.81294i | 0.425046 | + | 0.425046i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.12785 | + | 10.1600i | −0.308164 | + | 0.439254i | ||||
\(536\) | −18.0413 | − | 11.9001i | −0.779264 | − | 0.514006i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.04406 | + | 4.53624i | 0.131239 | + | 0.195571i | ||||
\(539\) | − | 9.43150i | − | 0.406243i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.5756i | − | 1.48652i | −0.669001 | − | 0.743261i | \(-0.733278\pi\) | ||
0.669001 | − | 0.743261i | \(-0.266722\pi\) | |||||||
\(542\) | −19.0523 | + | 12.7851i | −0.818368 | + | 0.549167i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.09636 | + | 6.20937i | −0.390003 | + | 0.266225i | ||||
\(545\) | −2.34255 | − | 13.3562i | −0.100344 | − | 0.572116i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2094 | + | 16.2094i | 0.693063 | + | 0.693063i | 0.962905 | − | 0.269842i | \(-0.0869714\pi\) |
−0.269842 | + | 0.962905i | \(0.586971\pi\) | |||||||
\(548\) | −37.3634 | + | 15.6504i | −1.59609 | + | 0.668552i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −22.3829 | − | 16.4061i | −0.954412 | − | 0.699559i | ||||
\(551\) | − | 23.8002i | − | 1.01392i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8062 | + | 10.8062i | −0.459528 | + | 0.459528i | ||||
\(554\) | 20.9809 | + | 4.13011i | 0.891393 | + | 0.175472i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 7.40312 | + | 3.03212i | 0.313962 | + | 0.128591i | ||||
\(557\) | 15.2614 | − | 15.2614i | 0.646647 | − | 0.646647i | −0.305534 | − | 0.952181i | \(-0.598835\pi\) |
0.952181 | + | 0.305534i | \(0.0988350\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.5127 | −1.62891 | ||||||||
\(560\) | −3.46263 | − | 18.8616i | −0.146323 | − | 0.797048i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.50927 | − | 9.70010i | −0.274577 | − | 0.409174i | ||||
\(563\) | 18.4521 | − | 18.4521i | 0.777665 | − | 0.777665i | −0.201769 | − | 0.979433i | \(-0.564669\pi\) |
0.979433 | + | 0.201769i | \(0.0646689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.56393 | − | 2.50031i | −0.149935 | − | 0.105189i | ||||
\(566\) | 10.6028 | + | 2.08717i | 0.445668 | + | 0.0877301i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 11.0136i | − | 0.461715i | −0.972988 | − | 0.230858i | \(-0.925847\pi\) | ||
0.972988 | − | 0.230858i | \(-0.0741532\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.6125 | −1.40664 | −0.703320 | − | 0.710874i | \(-0.748300\pi\) | ||||
−0.703320 | + | 0.710874i | \(0.748300\pi\) | |||||||
\(572\) | −36.4901 | + | 15.2846i | −1.52573 | + | 0.639081i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.19146 | − | 1.61250i | −0.341905 | − | 0.0673043i | ||||
\(575\) | 33.1520 | + | 15.5324i | 1.38253 | + | 0.647747i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.403124 | − | 0.403124i | −0.0167823 | − | 0.0167823i | 0.698666 | − | 0.715448i | \(-0.253777\pi\) |
−0.715448 | + | 0.698666i | \(0.753777\pi\) | |||||||
\(578\) | −15.5120 | + | 10.4093i | −0.645212 | + | 0.432971i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −25.9962 | − | 5.67984i | −1.07943 | − | 0.235843i | ||||
\(581\) | 20.2488i | 0.840060i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.12785 | + | 7.12785i | 0.295205 | + | 0.295205i | ||||
\(584\) | 11.0122 | − | 16.6952i | 0.455690 | − | 0.690853i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.701562 | − | 3.56393i | 0.0289813 | − | 0.147224i | ||||
\(587\) | 3.92468 | + | 3.92468i | 0.161989 | + | 0.161989i | 0.783447 | − | 0.621458i | \(-0.213459\pi\) |
−0.621458 | + | 0.783447i | \(0.713459\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −28.5114 | −1.17479 | ||||||||
\(590\) | −8.59196 | − | 8.95598i | −0.353725 | − | 0.368712i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.1600 | + | 0.159970i | −0.828570 | + | 0.00657473i | ||||
\(593\) | −1.37670 | + | 1.37670i | −0.0565345 | + | 0.0565345i | −0.734809 | − | 0.678274i | \(-0.762728\pi\) |
0.678274 | + | 0.734809i | \(0.262728\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.61250 | + | 9.19375i | 0.0661059 | + | 0.376907i | ||||
\(596\) | −6.09245 | + | 14.8751i | −0.249557 | + | 0.609309i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 43.3372 | − | 29.0815i | 1.77219 | − | 1.18923i | ||||
\(599\) | −4.17433 | −0.170559 | −0.0852793 | − | 0.996357i | \(-0.527178\pi\) | ||||
−0.0852793 | + | 0.996357i | \(0.527178\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2094 | −0.742776 | −0.371388 | − | 0.928478i | \(-0.621118\pi\) | ||||
−0.371388 | + | 0.928478i | \(0.621118\pi\) | |||||||
\(602\) | 19.2387 | − | 12.9102i | 0.784111 | − | 0.526179i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18.8039 | + | 7.70156i | 0.765119 | + | 0.313372i | ||||
\(605\) | −1.70088 | − | 9.69766i | −0.0691505 | − | 0.394266i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.70752 | − | 9.70752i | 0.394016 | − | 0.394016i | −0.482100 | − | 0.876116i | \(-0.660126\pi\) |
0.876116 | + | 0.482100i | \(0.160126\pi\) | |||||||
\(608\) | −22.2353 | − | 4.19406i | −0.901762 | − | 0.170091i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 28.8803 | + | 30.1039i | 1.16933 | + | 1.21887i | ||||
\(611\) | 11.0136 | 0.445564 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.62754 | − | 4.62754i | −0.186904 | − | 0.186904i | 0.607452 | − | 0.794356i | \(-0.292192\pi\) |
−0.794356 | + | 0.607452i | \(0.792192\pi\) | |||||||
\(614\) | −7.72577 | + | 39.2468i | −0.311787 | + | 1.58387i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.1047 | − | 19.8675i | 0.528003 | − | 0.800484i | ||||
\(617\) | −19.8288 | − | 19.8288i | −0.798279 | − | 0.798279i | 0.184545 | − | 0.982824i | \(-0.440919\pi\) |
−0.982824 | + | 0.184545i | \(0.940919\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 14.8062i | − | 0.595113i | −0.954704 | − | 0.297557i | \(-0.903828\pi\) | ||
0.954704 | − | 0.297557i | \(-0.0961717\pi\) | |||||||
\(620\) | −6.80415 | + | 31.1421i | −0.273261 | + | 1.25070i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −32.8509 | + | 22.0447i | −1.31720 | + | 0.883911i | ||||
\(623\) | 27.9745 | + | 27.9745i | 1.12078 | + | 1.12078i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.2094 | − | 16.0000i | 0.768375 | − | 0.640000i | ||||
\(626\) | −11.3938 | − | 2.24289i | −0.455389 | − | 0.0896438i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −10.5212 | − | 25.1181i | −0.419841 | − | 1.00232i | ||||
\(629\) | 9.81294 | 0.391268 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.6393i | 1.41878i | 0.704818 | + | 0.709388i | \(0.251029\pi\) | ||||
−0.704818 | + | 0.709388i | \(0.748971\pi\) | |||||||
\(632\) | 19.7495 | − | 4.05074i | 0.785592 | − | 0.161130i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 22.3678 | + | 4.40312i | 0.888339 | + | 0.174870i | ||||
\(635\) | 30.2262 | + | 21.2055i | 1.19949 | + | 0.841516i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.56455 | − | 8.56455i | 0.339340 | − | 0.339340i | ||||
\(638\) | −18.4020 | − | 27.4227i | −0.728543 | − | 1.08567i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.88742 | + | 23.2860i | −0.390834 | + | 0.920461i | ||||
\(641\) | −18.4521 | −0.728815 | −0.364408 | − | 0.931240i | \(-0.618729\pi\) | ||||
−0.364408 | + | 0.931240i | \(0.618729\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(644\) | −11.9001 | + | 29.0549i | −0.468930 | + | 1.14492i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.8062 | + | 2.12722i | 0.425166 | + | 0.0836944i | ||||
\(647\) | −5.71949 | + | 5.71949i | −0.224856 | + | 0.224856i | −0.810540 | − | 0.585684i | \(-0.800826\pi\) |
0.585684 | + | 0.810540i | \(0.300826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 15.4031i | − | 0.604626i | ||||||
\(650\) | −5.42745 | − | 35.2236i | −0.212882 | − | 1.38158i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.67905 | + | 5.67905i | 0.222238 | + | 0.222238i | 0.809440 | − | 0.587202i | \(-0.199771\pi\) |
−0.587202 | + | 0.809440i | \(0.699771\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.67540 | + | 38.0602i | 0.260829 | + | 1.48714i | ||||
\(656\) | 7.84936 | + | 7.72577i | 0.306466 | + | 0.301641i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.50178 | + | 3.69198i | −0.214482 | + | 0.143928i | ||||
\(659\) | 11.7740i | 0.458652i | 0.973350 | + | 0.229326i | \(0.0736521\pi\) | ||||
−0.973350 | + | 0.229326i | \(0.926348\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 15.3193i | − | 0.595852i | −0.954589 | − | 0.297926i | \(-0.903705\pi\) | ||
0.954589 | − | 0.297926i | \(-0.0962949\pi\) | |||||||
\(662\) | 17.9719 | + | 26.7817i | 0.698498 | + | 1.04090i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 14.7082 | − | 22.2984i | 0.570787 | − | 0.865347i | ||||
\(665\) | −11.0136 | + | 15.6987i | −0.427090 | + | 0.608770i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.8062 | + | 30.8062i | 1.19282 | + | 1.19282i | ||||
\(668\) | 1.68847 | + | 4.03102i | 0.0653288 | + | 0.155965i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.1583 | + | 0.501146i | 0.933317 | + | 0.0193609i | ||||
\(671\) | 51.7748i | 1.99874i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.0000 | − | 15.0000i | 0.578208 | − | 0.578208i | −0.356202 | − | 0.934409i | \(-0.615928\pi\) |
0.934409 | + | 0.356202i | \(0.115928\pi\) | |||||||
\(674\) | 4.01861 | − | 20.4145i | 0.154791 | − | 0.786336i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −22.9555 | − | 9.40194i | −0.882903 | − | 0.361613i | ||||
\(677\) | −13.4857 | + | 13.4857i | −0.518298 | + | 0.518298i | −0.917056 | − | 0.398758i | \(-0.869441\pi\) |
0.398758 | + | 0.917056i | \(0.369441\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.5435 | 1.21053 | ||||||||
\(680\) | 4.90237 | − | 11.2957i | 0.187997 | − | 0.433169i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −32.8509 | + | 22.0447i | −1.25793 | + | 0.844134i | ||||
\(683\) | 22.3768 | − | 22.3768i | 0.856225 | − | 0.856225i | −0.134666 | − | 0.990891i | \(-0.542996\pi\) |
0.990891 | + | 0.134666i | \(0.0429962\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.0111 | − | 37.0760i | 0.993833 | − | 1.41660i | ||||
\(686\) | −5.50682 | + | 27.9745i | −0.210251 | + | 1.06807i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −30.5637 | + | 0.242524i | −1.16523 | + | 0.00924616i | ||||
\(689\) | 12.9453i | 0.493177i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | −10.7845 | + | 4.51732i | −0.409967 | + | 0.171723i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.12785 | + | 36.2094i | −0.270569 | + | 1.37449i | ||||
\(695\) | −8.80980 | + | 1.54515i | −0.334175 | + | 0.0586111i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.79063 | − | 3.79063i | −0.143580 | − | 0.143580i | ||||
\(698\) | −10.3957 | − | 15.4917i | −0.393483 | − | 0.586368i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 14.5188 | + | 15.7763i | 0.548761 | + | 0.596287i | ||||
\(701\) | 33.9246i | 1.28131i | 0.767827 | + | 0.640657i | \(0.221338\pi\) | ||||
−0.767827 | + | 0.640657i | \(0.778662\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.2557 | + | 14.2557i | 0.537664 | + | 0.537664i | ||||
\(704\) | −28.8624 | + | 12.3597i | −1.08779 | + | 0.465823i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.10469 | + | 1.59542i | 0.305024 | + | 0.0600443i | ||||
\(707\) | −12.1849 | − | 12.1849i | −0.458261 | − | 0.458261i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3193 | −0.575329 | −0.287664 | − | 0.957731i | \(-0.592879\pi\) | ||||
−0.287664 | + | 0.957731i | \(0.592879\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −10.4863 | − | 51.1262i | −0.392991 | − | 1.91603i | ||||
\(713\) | 36.9043 | − | 36.9043i | 1.38208 | − | 1.38208i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 25.4031 | − | 36.2094i | 0.950023 | − | 1.35415i | ||||
\(716\) | −26.1267 | − | 10.7008i | −0.976401 | − | 0.399908i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 25.3341 | + | 37.7529i | 0.945462 | + | 1.40893i | ||||
\(719\) | 27.9745 | 1.04327 | 0.521637 | − | 0.853167i | \(-0.325321\pi\) | ||||
0.521637 | + | 0.853167i | \(0.325321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.0156 | −0.633695 | ||||||||
\(722\) | −2.36408 | − | 3.52294i | −0.0879819 | − | 0.131110i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.2236 | − | 4.59688i | −0.417121 | − | 0.170842i | ||||
\(725\) | 27.9745 | − | 10.1244i | 1.03895 | − | 0.376010i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.7711 | + | 10.7711i | −0.399479 | + | 0.399479i | −0.878049 | − | 0.478570i | \(-0.841155\pi\) |
0.478570 | + | 0.878049i | \(0.341155\pi\) | |||||||
\(728\) | 29.9414 | − | 6.14117i | 1.10970 | − | 0.227607i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.463755 | + | 22.3559i | −0.0171644 | + | 0.827428i | ||||
\(731\) | 14.8770 | 0.550246 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.56393 | − | 3.56393i | −0.131637 | − | 0.131637i | 0.638219 | − | 0.769855i | \(-0.279672\pi\) |
−0.769855 | + | 0.638219i | \(0.779672\pi\) | |||||||
\(734\) | −14.8751 | − | 2.92818i | −0.549051 | − | 0.108081i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.2094 | − | 23.3521i | 1.26097 | − | 0.860768i | ||||
\(737\) | 21.2055 | + | 21.2055i | 0.781116 | + | 0.781116i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.4187i | − | 1.04540i | −0.852517 | − | 0.522700i | \(-0.824925\pi\) | ||
0.852517 | − | 0.522700i | \(-0.175075\pi\) | |||||||
\(740\) | 18.9731 | − | 12.1690i | 0.697465 | − | 0.447340i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.33951 | − | 6.46673i | −0.159309 | − | 0.237401i | ||||
\(743\) | −22.7971 | − | 22.7971i | −0.836343 | − | 0.836343i | 0.152032 | − | 0.988376i | \(-0.451418\pi\) |
−0.988376 | + | 0.152032i | \(0.951418\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.10469 | − | 17.7016i | −0.113747 | − | 0.648535i | ||||
\(746\) | −0.965843 | + | 4.90647i | −0.0353620 | + | 0.179639i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.0957 | − | 5.90427i | 0.515391 | − | 0.215881i | ||||
\(749\) | 11.9001 | 0.434820 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3836i | 0.780297i | 0.920752 | + | 0.390148i | \(0.127576\pi\) | ||||
−0.920752 | + | 0.390148i | \(0.872424\pi\) | |||||||
\(752\) | 8.74044 | − | 0.0693557i | 0.318731 | − | 0.00252914i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.19146 | − | 41.6125i | 0.298315 | − | 1.51544i | ||||
\(755\) | −22.3768 | + | 3.92468i | −0.814376 | + | 0.142834i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.9481 | − | 29.9481i | 1.08848 | − | 1.08848i | 0.0927974 | − | 0.995685i | \(-0.470419\pi\) |
0.995685 | − | 0.0927974i | \(-0.0295809\pi\) | |||||||
\(758\) | 7.99268 | − | 5.36350i | 0.290307 | − | 0.194811i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 23.5316 | − | 9.28782i | 0.853581 | − | 0.336905i | ||||
\(761\) | 4.68509 | 0.169835 | 0.0849173 | − | 0.996388i | \(-0.472937\pi\) | ||||
0.0849173 | + | 0.996388i | \(0.472937\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.19375 | + | 9.19375i | −0.332836 | + | 0.332836i | ||||
\(764\) | −44.0490 | − | 18.0413i | −1.59364 | − | 0.652710i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.61250 | − | 18.3514i | 0.130525 | − | 0.663064i | ||||
\(767\) | 13.9873 | − | 13.9873i | 0.505051 | − | 0.505051i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 11.4031i | − | 0.411207i | −0.978635 | − | 0.205604i | \(-0.934084\pi\) | ||
0.978635 | − | 0.205604i | \(-0.0659157\pi\) | |||||||
\(770\) | −0.551874 | + | 26.6037i | −0.0198881 | + | 0.958732i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.440514 | + | 1.05167i | 0.0158545 | + | 0.0378506i | ||||
\(773\) | 11.9405 | + | 11.9405i | 0.429472 | + | 0.429472i | 0.888448 | − | 0.458977i | \(-0.151784\pi\) |
−0.458977 | + | 0.888448i | \(0.651784\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −12.1285 | − | 33.5120i | −0.435668 | − | 1.20379i | ||||
\(776\) | −34.7365 | − | 22.9123i | −1.24697 | − | 0.822505i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 21.7992 | + | 32.4852i | 0.781541 | + | 1.16465i | ||||
\(779\) | − | 11.0136i | − | 0.394604i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −16.7407 | + | 11.2339i | −0.598645 | + | 0.401722i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.74291 | − | 6.85078i | 0.240818 | − | 0.244671i | ||||
\(785\) | 24.9248 | + | 17.4863i | 0.889604 | + | 0.624112i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | − | 20.0000i | −0.712923 | − | 0.712923i | 0.254223 | − | 0.967146i | \(-0.418180\pi\) |
−0.967146 | + | 0.254223i | \(0.918180\pi\) | |||||||
\(788\) | −5.95383 | − | 14.2141i | −0.212097 | − | 0.506355i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.2655 | + | 15.6044i | −0.578700 | + | 0.555179i | ||||
\(791\) | 4.17433i | 0.148422i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −47.0156 | + | 47.0156i | −1.66957 | + | 1.66957i | ||||
\(794\) | −9.08080 | − | 1.78756i | −0.322266 | − | 0.0634383i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.9109 | − | 33.9645i | 0.493060 | − | 1.20384i | ||||
\(797\) | −28.4761 | + | 28.4761i | −1.00868 | + | 1.00868i | −0.00871364 | + | 0.999962i | \(0.502774\pi\) |
−0.999962 | + | 0.00871364i | \(0.997226\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.25444 | −0.150511 | ||||||||
\(800\) | −4.52904 | − | 27.9193i | −0.160126 | − | 0.987097i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.7420 | − | 36.8705i | −0.873671 | − | 1.30194i | ||||
\(803\) | −19.6234 | + | 19.6234i | −0.692495 | + | 0.692495i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.06424 | − | 34.5756i | −0.213736 | − | 1.21863i | ||||
\(806\) | −49.8496 | − | 9.81294i | −1.75588 | − | 0.345646i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.56753 | + | 22.2691i | 0.160685 | + | 0.783424i | ||||
\(809\) | − | 18.4521i | − | 0.648742i | −0.945930 | − | 0.324371i | \(-0.894847\pi\) | ||
0.945930 | − | 0.324371i | \(-0.105153\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −17.1938 | −0.603754 | −0.301877 | − | 0.953347i | \(-0.597613\pi\) | ||||
−0.301877 | + | 0.953347i | \(0.597613\pi\) | |||||||
\(812\) | 9.85731 | + | 23.5331i | 0.345924 | + | 0.825851i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.4478 | + | 5.40312i | 0.962045 | + | 0.189379i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21.6125 | + | 21.6125i | 0.756126 | + | 0.756126i | ||||
\(818\) | −11.0422 | + | 7.40991i | −0.386082 | + | 0.259081i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −12.0298 | − | 2.62837i | −0.420100 | − | 0.0917865i | ||||
\(821\) | − | 26.1988i | − | 0.914345i | −0.889378 | − | 0.457173i | \(-0.848862\pi\) | ||
0.889378 | − | 0.457173i | \(-0.151138\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.9960 | + | 31.9960i | 1.11531 | + | 1.11531i | 0.992420 | + | 0.122889i | \(0.0392159\pi\) |
0.122889 | + | 0.992420i | \(0.460784\pi\) | |||||||
\(824\) | 18.7380 | + | 12.3597i | 0.652770 | + | 0.430570i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.29844 | + | 11.6760i | −0.0799729 | + | 0.406261i | ||||
\(827\) | 11.0136 | + | 11.0136i | 0.382981 | + | 0.382981i | 0.872175 | − | 0.489194i | \(-0.162709\pi\) |
−0.489194 | + | 0.872175i | \(0.662709\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.5756 | 1.20086 | 0.600431 | − | 0.799677i | \(-0.294996\pi\) | ||||
0.600431 | + | 0.799677i | \(0.294996\pi\) | |||||||
\(830\) | −0.619400 | + | 29.8589i | −0.0214997 | + | 1.03642i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −37.4330 | − | 14.9858i | −1.29775 | − | 0.519539i | ||||
\(833\) | −3.30839 | + | 3.30839i | −0.114629 | + | 0.114629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.00000 | − | 2.80625i | −0.138426 | − | 0.0971142i | ||||
\(836\) | 29.0549 | + | 11.9001i | 1.00488 | + | 0.411574i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.7599 | − | 17.9573i | 0.924405 | − | 0.620324i | ||||
\(839\) | −4.17433 | −0.144114 | −0.0720570 | − | 0.997401i | \(-0.522956\pi\) | ||||
−0.0720570 | + | 0.997401i | \(0.522956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.40312 | 0.220797 | ||||||||
\(842\) | 29.7343 | − | 19.9533i | 1.02471 | − | 0.687635i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9.09636 | + | 22.2094i | −0.313110 | + | 0.764478i | ||||
\(845\) | 27.3172 | − | 4.79119i | 0.939742 | − | 0.164822i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.67540 | + | 6.67540i | −0.229369 | + | 0.229369i | ||||
\(848\) | 0.0815201 | + | 10.2734i | 0.00279941 | + | 0.352791i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.09656 | + | 13.6065i | 0.0719114 | + | 0.466698i | ||||
\(851\) | −36.9043 | −1.26506 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.50031 | − | 2.50031i | −0.0856091 | − | 0.0856091i | 0.663005 | − | 0.748615i | \(-0.269281\pi\) |
−0.748615 | + | 0.663005i | \(0.769281\pi\) | |||||||
\(854\) | 7.72577 | − | 39.2468i | 0.264371 | − | 1.34300i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −13.1047 | − | 8.64391i | −0.447909 | − | 0.295443i | ||||
\(857\) | −4.13011 | − | 4.13011i | −0.141082 | − | 0.141082i | 0.633038 | − | 0.774120i | \(-0.281807\pi\) |
−0.774120 | + | 0.633038i | \(0.781807\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 25.6125i | − | 0.873887i | −0.899489 | − | 0.436944i | \(-0.856061\pi\) | ||
0.899489 | − | 0.436944i | \(-0.143939\pi\) | |||||||
\(860\) | 28.7644 | − | 18.4489i | 0.980857 | − | 0.629101i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.90198 | + | 3.28948i | −0.166962 | + | 0.112040i | ||||
\(863\) | 4.63546 | + | 4.63546i | 0.157793 | + | 0.157793i | 0.781588 | − | 0.623795i | \(-0.214410\pi\) |
−0.623795 | + | 0.781588i | \(0.714410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.50781 | − | 10.7016i | 0.255273 | − | 0.363864i | ||||
\(866\) | 0.791067 | + | 0.155722i | 0.0268816 | + | 0.00529166i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 28.1915 | − | 11.8085i | 0.956881 | − | 0.400808i | ||||
\(869\) | −27.9745 | −0.948971 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.5127i | 1.30495i | ||||||||
\(872\) | 16.8025 | − | 3.44629i | 0.569004 | − | 0.116706i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −40.6399 | − | 8.00000i | −1.37466 | − | 0.270604i | ||||
\(875\) | −23.1372 | − | 6.26723i | −0.782181 | − | 0.211871i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.50031 | − | 2.50031i | 0.0844296 | − | 0.0844296i | −0.663631 | − | 0.748060i | \(-0.730985\pi\) |
0.748060 | + | 0.663631i | \(0.230985\pi\) | |||||||
\(878\) | −3.22754 | − | 4.80968i | −0.108924 | − | 0.162319i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.9320 | − | 28.8958i | 0.671906 | − | 0.974077i | ||||
\(881\) | −38.8360 | −1.30842 | −0.654208 | − | 0.756314i | \(-0.726998\pi\) | ||||
−0.654208 | + | 0.756314i | \(0.726998\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10.8062 | + | 10.8062i | −0.363659 | + | 0.363659i | −0.865158 | − | 0.501499i | \(-0.832782\pi\) |
0.501499 | + | 0.865158i | \(0.332782\pi\) | |||||||
\(884\) | 18.1616 | + | 7.43850i | 0.610841 | + | 0.250184i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25.4031 | + | 5.00063i | 0.853435 | + | 0.167999i | ||||
\(887\) | 25.3454 | − | 25.3454i | 0.851014 | − | 0.851014i | −0.139244 | − | 0.990258i | \(-0.544467\pi\) |
0.990258 | + | 0.139244i | \(0.0444672\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 35.4031i | − | 1.18738i | ||||||
\(890\) | 40.3956 | + | 42.1071i | 1.35406 | + | 1.41143i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 30.4606 | − | 12.7590i | 1.01989 | − | 0.427203i | ||||
\(893\) | −6.18062 | − | 6.18062i | −0.206827 | − | 0.206827i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 31.0911 | − | 5.45308i | 1.03926 | − | 0.182276i | ||||
\(896\) | 23.7229 | − | 5.06219i | 0.792525 | − | 0.169116i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.4352 | + | 12.3710i | −0.615192 | + | 0.412826i | ||||
\(899\) | − | 42.4111i | − | 1.41449i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.00063i | − | 0.166595i | ||||||
\(902\) | −8.51560 | − | 12.6899i | −0.283539 | − | 0.422529i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.03212 | − | 4.59688i | 0.100847 | − | 0.152890i | ||||
\(905\) | 13.3562 | − | 2.34255i | 0.443974 | − | 0.0778689i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.4031 | + | 25.4031i | 0.843497 | + | 0.843497i | 0.989312 | − | 0.145815i | \(-0.0465804\pi\) |
−0.145815 | + | 0.989312i | \(0.546580\pi\) | |||||||
\(908\) | 33.7719 | − | 14.1460i | 1.12076 | − | 0.469452i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.6595 | + | 23.6572i | −0.817453 | + | 0.784227i | ||||
\(911\) | 4.17433i | 0.138302i | 0.997606 | + | 0.0691509i | \(0.0220290\pi\) | ||||
−0.997606 | + | 0.0691509i | \(0.977971\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −26.2094 | + | 26.2094i | −0.867404 | + | 0.867404i | ||||
\(914\) | 6.10577 | − | 31.0172i | 0.201961 | − | 1.02596i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.0000 | − | 24.4157i | 0.330409 | − | 0.806716i | ||||
\(917\) | 26.1988 | − | 26.1988i | 0.865161 | − | 0.865161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.1291 | −0.565037 | −0.282519 | − | 0.959262i | \(-0.591170\pi\) | ||||
−0.282519 | + | 0.959262i | \(0.591170\pi\) | |||||||
\(920\) | −18.4367 | + | 42.4804i | −0.607840 | + | 1.40054i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.53624 | − | 3.04406i | 0.149393 | − | 0.100251i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6918 | + | 22.8203i | −0.351543 | + | 0.750325i | ||||
\(926\) | 2.92818 | − | 14.8751i | 0.0962261 | − | 0.488827i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.23871 | − | 33.0753i | 0.204796 | − | 1.08575i | ||||
\(929\) | − | 4.68509i | − | 0.153713i | −0.997042 | − | 0.0768565i | \(-0.975512\pi\) | ||
0.997042 | − | 0.0768565i | \(-0.0244883\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.61250 | −0.315037 | ||||||||
\(932\) | −15.6504 | − | 37.3634i | −0.512646 | − | 1.22388i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0.452450 | − | 2.29844i | 0.0148046 | − | 0.0752072i | ||||
\(935\) | −9.81294 | + | 13.9873i | −0.320917 | + | 0.457433i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.59688 | + | 9.59688i | 0.313516 | + | 0.313516i | 0.846270 | − | 0.532754i | \(-0.178843\pi\) |
−0.532754 | + | 0.846270i | \(0.678843\pi\) | |||||||
\(938\) | −12.9102 | − | 19.2387i | −0.421532 | − | 0.628166i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.22587 | + | 5.27590i | −0.268298 | + | 0.172081i | ||||
\(941\) | − | 31.8374i | − | 1.03787i | −0.854814 | − | 0.518935i | \(-0.826329\pi\) | ||
0.854814 | − | 0.518935i | \(-0.173671\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.2557 | + | 14.2557i | 0.464229 | + | 0.464229i | ||||
\(944\) | 11.0122 | − | 11.1884i | 0.358418 | − | 0.364152i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.6125 | + | 8.19146i | 1.35294 | + | 0.266327i | ||||
\(947\) | 5.50682 | + | 5.50682i | 0.178947 | + | 0.178947i | 0.790897 | − | 0.611949i | \(-0.209614\pi\) |
−0.611949 | + | 0.790897i | \(0.709614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.6393 | −1.15690 | ||||||||
\(950\) | −16.7210 | + | 22.8125i | −0.542499 | + | 0.740135i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.5660 | + | 2.37226i | −0.374857 | + | 0.0768855i | ||||
\(953\) | 17.0754 | − | 17.0754i | 0.553127 | − | 0.553127i | −0.374215 | − | 0.927342i | \(-0.622088\pi\) |
0.927342 | + | 0.374215i | \(0.122088\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 52.4187 | − | 9.19375i | 1.69623 | − | 0.297503i | ||||
\(956\) | −21.2055 | + | 51.7748i | −0.685836 | + | 1.67452i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −22.0447 | − | 32.8509i | −0.712231 | − | 1.06136i | ||||
\(959\) | −43.4261 | −1.40230 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.8062 | −0.638911 | ||||||||
\(962\) | 20.0183 | + | 29.8313i | 0.645417 | + | 0.961798i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.2557 | + | 34.8062i | −0.459145 | + | 1.12103i | ||||
\(965\) | −1.04358 | − | 0.732138i | −0.0335941 | − | 0.0235684i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.64391 | + | 8.64391i | −0.277969 | + | 0.277969i | −0.832298 | − | 0.554329i | \(-0.812975\pi\) |
0.554329 | + | 0.832298i | \(0.312975\pi\) | |||||||
\(968\) | 12.1999 | − | 2.50229i | 0.392121 | − | 0.0804265i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 46.5142 | + | 0.964901i | 1.49348 | + | 0.0309811i | ||||
\(971\) | −7.08895 | −0.227495 | −0.113748 | − | 0.993510i | \(-0.536286\pi\) | ||||
−0.113748 | + | 0.993510i | \(0.536286\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.06424 | + | 6.06424i | 0.194411 | + | 0.194411i | ||||
\(974\) | 16.9623 | + | 3.33904i | 0.543507 | + | 0.106990i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37.0156 | + | 37.6078i | −1.18484 | + | 1.20380i | ||||
\(977\) | 19.8288 | + | 19.8288i | 0.634381 | + | 0.634381i | 0.949164 | − | 0.314783i | \(-0.101932\pi\) |
−0.314783 | + | 0.949164i | \(0.601932\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.4187i | 2.31451i | ||||||||
\(980\) | −2.29399 | + | 10.4994i | −0.0732788 | + | 0.335392i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.6493 | + | 32.2617i | 0.690856 | + | 1.02951i | ||||
\(983\) | −22.7971 | − | 22.7971i | −0.727113 | − | 0.727113i | 0.242930 | − | 0.970044i | \(-0.421891\pi\) |
−0.970044 | + | 0.242930i | \(0.921891\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.1047 | + | 9.89531i | 0.449413 | + | 0.315291i | ||||
\(986\) | −3.16427 | + | 16.0744i | −0.100771 | + | 0.511914i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.5779 | + | 37.1904i | 0.495600 | + | 1.18319i | ||||
\(989\) | −55.9491 | −1.77908 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 26.5429i | − | 0.843163i | −0.906791 | − | 0.421581i | \(-0.861475\pi\) | ||
0.906791 | − | 0.421581i | \(-0.138525\pi\) | |||||||
\(992\) | −39.6225 | − | 7.47365i | −1.25802 | − | 0.237289i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.08895 | + | 40.4181i | 0.224735 | + | 1.28134i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.56393 | − | 3.56393i | 0.112871 | − | 0.112871i | −0.648416 | − | 0.761286i | \(-0.724568\pi\) |
0.761286 | + | 0.648416i | \(0.224568\pi\) | |||||||
\(998\) | −7.99268 | + | 5.36350i | −0.253004 | + | 0.169779i | ||||
\(999\) | 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 | 360.2.w.d.307.3 | yes | 16 | |
3.2 | odd | 2 | inner | 360.2.w.d.307.6 | yes | 16 | |
4.3 | odd | 2 | 1440.2.bi.d.847.4 | 16 | |||
5.3 | odd | 4 | inner | 360.2.w.d.163.2 | ✓ | 16 | |
8.3 | odd | 2 | inner | 360.2.w.d.307.2 | yes | 16 | |
8.5 | even | 2 | 1440.2.bi.d.847.5 | 16 | |||
12.11 | even | 2 | 1440.2.bi.d.847.6 | 16 | |||
15.8 | even | 4 | inner | 360.2.w.d.163.7 | yes | 16 | |
20.3 | even | 4 | 1440.2.bi.d.1423.5 | 16 | |||
24.5 | odd | 2 | 1440.2.bi.d.847.3 | 16 | |||
24.11 | even | 2 | inner | 360.2.w.d.307.7 | yes | 16 | |
40.3 | even | 4 | inner | 360.2.w.d.163.3 | yes | 16 | |
40.13 | odd | 4 | 1440.2.bi.d.1423.4 | 16 | |||
60.23 | odd | 4 | 1440.2.bi.d.1423.3 | 16 | |||
120.53 | even | 4 | 1440.2.bi.d.1423.6 | 16 | |||
120.83 | odd | 4 | inner | 360.2.w.d.163.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.w.d.163.2 | ✓ | 16 | 5.3 | odd | 4 | inner | |
360.2.w.d.163.3 | yes | 16 | 40.3 | even | 4 | inner | |
360.2.w.d.163.6 | yes | 16 | 120.83 | odd | 4 | inner | |
360.2.w.d.163.7 | yes | 16 | 15.8 | even | 4 | inner | |
360.2.w.d.307.2 | yes | 16 | 8.3 | odd | 2 | inner | |
360.2.w.d.307.3 | yes | 16 | 1.1 | even | 1 | trivial | |
360.2.w.d.307.6 | yes | 16 | 3.2 | odd | 2 | inner | |
360.2.w.d.307.7 | yes | 16 | 24.11 | even | 2 | inner | |
1440.2.bi.d.847.3 | 16 | 24.5 | odd | 2 | |||
1440.2.bi.d.847.4 | 16 | 4.3 | odd | 2 | |||
1440.2.bi.d.847.5 | 16 | 8.5 | even | 2 | |||
1440.2.bi.d.847.6 | 16 | 12.11 | even | 2 | |||
1440.2.bi.d.1423.3 | 16 | 60.23 | odd | 4 | |||
1440.2.bi.d.1423.4 | 16 | 40.13 | odd | 4 | |||
1440.2.bi.d.1423.5 | 16 | 20.3 | even | 4 | |||
1440.2.bi.d.1423.6 | 16 | 120.53 | even | 4 |