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 | 1249.1 | ||
Root | \(-2.68704i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.f.1249.12 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.68704i | − 1.90003i | −0.312211 | − | 0.950013i | \(-0.601069\pi\) | ||||
0.312211 | − | 0.950013i | \(-0.398931\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −5.22020 | −2.61010 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.68704 | 1.09698 | ||||||||
\(7\) | 1.68704i | 0.637642i | 0.947815 | + | 0.318821i | \(0.103287\pi\) | ||||
−0.947815 | + | 0.318821i | \(0.896713\pi\) | |||||||
\(8\) | 8.65280i | 3.05923i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.07882 | 0.325276 | 0.162638 | − | 0.986686i | \(-0.448000\pi\) | ||||
0.162638 | + | 0.986686i | \(0.448000\pi\) | |||||||
\(12\) | − 5.22020i | − 1.50694i | ||||||||
\(13\) | − 2.67723i | − 0.742531i | −0.928527 | − | 0.371265i | \(-0.878924\pi\) | ||||
0.928527 | − | 0.371265i | \(-0.121076\pi\) | |||||||
\(14\) | 4.53315 | 1.21154 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 12.8101 | 3.20251 | ||||||||
\(17\) | − 3.93167i | − 0.953570i | −0.879020 | − | 0.476785i | \(-0.841802\pi\) | ||||
0.879020 | − | 0.476785i | \(-0.158198\pi\) | |||||||
\(18\) | 2.68704i | 0.633342i | ||||||||
\(19\) | 1.17755 | 0.270148 | 0.135074 | − | 0.990836i | \(-0.456873\pi\) | ||||
0.135074 | + | 0.990836i | \(0.456873\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.68704 | −0.368143 | ||||||||
\(22\) | − 2.89883i | − 0.618032i | ||||||||
\(23\) | 4.06295i | 0.847183i | 0.905853 | + | 0.423591i | \(0.139231\pi\) | ||||
−0.905853 | + | 0.423591i | \(0.860769\pi\) | |||||||
\(24\) | −8.65280 | −1.76625 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.19384 | −1.41083 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | − 8.80669i | − 1.66431i | ||||||||
\(29\) | −5.95595 | −1.10599 | −0.552996 | − | 0.833184i | \(-0.686516\pi\) | ||||
−0.552996 | + | 0.833184i | \(0.686516\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.10310 | −1.27575 | −0.637877 | − | 0.770138i | \(-0.720187\pi\) | ||||
−0.637877 | + | 0.770138i | \(0.720187\pi\) | |||||||
\(32\) | − 17.1155i | − 3.02563i | ||||||||
\(33\) | 1.07882i | 0.187798i | ||||||||
\(34\) | −10.5646 | −1.81181 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.22020 | 0.870033 | ||||||||
\(37\) | − 4.58187i | − 0.753254i | −0.926365 | − | 0.376627i | \(-0.877084\pi\) | ||||
0.926365 | − | 0.376627i | \(-0.122916\pi\) | |||||||
\(38\) | − 3.16412i | − 0.513287i | ||||||||
\(39\) | 2.67723 | 0.428700 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −11.2614 | −1.75874 | −0.879371 | − | 0.476137i | \(-0.842037\pi\) | ||||
−0.879371 | + | 0.476137i | \(0.842037\pi\) | |||||||
\(42\) | 4.53315i | 0.699481i | ||||||||
\(43\) | − 2.58587i | − 0.394342i | −0.980369 | − | 0.197171i | \(-0.936825\pi\) | ||||
0.980369 | − | 0.197171i | \(-0.0631754\pi\) | |||||||
\(44\) | −5.63164 | −0.849002 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.9173 | 1.60967 | ||||||||
\(47\) | − 1.91782i | − 0.279743i | −0.990170 | − | 0.139871i | \(-0.955331\pi\) | ||||
0.990170 | − | 0.139871i | \(-0.0446689\pi\) | |||||||
\(48\) | 12.8101i | 1.84897i | ||||||||
\(49\) | 4.15389 | 0.593413 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.93167 | 0.550544 | ||||||||
\(52\) | 13.9757i | 1.93808i | ||||||||
\(53\) | 2.54861i | 0.350078i | 0.984561 | + | 0.175039i | \(0.0560052\pi\) | ||||
−0.984561 | + | 0.175039i | \(0.943995\pi\) | |||||||
\(54\) | −2.68704 | −0.365660 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −14.5976 | −1.95069 | ||||||||
\(57\) | 1.17755i | 0.155970i | ||||||||
\(58\) | 16.0039i | 2.10141i | ||||||||
\(59\) | −1.33599 | −0.173931 | −0.0869654 | − | 0.996211i | \(-0.527717\pi\) | ||||
−0.0869654 | + | 0.996211i | \(0.527717\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.28106 | −0.932245 | −0.466122 | − | 0.884720i | \(-0.654349\pi\) | ||||
−0.466122 | + | 0.884720i | \(0.654349\pi\) | |||||||
\(62\) | 19.0863i | 2.42397i | ||||||||
\(63\) | − 1.68704i | − 0.212547i | ||||||||
\(64\) | −20.3701 | −2.54626 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.89883 | 0.356821 | ||||||||
\(67\) | 12.4451i | 1.52041i | 0.649686 | + | 0.760203i | \(0.274900\pi\) | ||||
−0.649686 | + | 0.760203i | \(0.725100\pi\) | |||||||
\(68\) | 20.5241i | 2.48891i | ||||||||
\(69\) | −4.06295 | −0.489121 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.98480 | −0.710266 | −0.355133 | − | 0.934816i | \(-0.615564\pi\) | ||||
−0.355133 | + | 0.934816i | \(0.615564\pi\) | |||||||
\(72\) | − 8.65280i | − 1.01974i | ||||||||
\(73\) | 3.30065i | 0.386312i | 0.981168 | + | 0.193156i | \(0.0618724\pi\) | ||||
−0.981168 | + | 0.193156i | \(0.938128\pi\) | |||||||
\(74\) | −12.3117 | −1.43120 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.14702 | −0.705112 | ||||||||
\(77\) | 1.82001i | 0.207410i | ||||||||
\(78\) | − 7.19384i | − 0.814542i | ||||||||
\(79\) | 4.00404 | 0.450490 | 0.225245 | − | 0.974302i | \(-0.427682\pi\) | ||||
0.225245 | + | 0.974302i | \(0.427682\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 30.2600i | 3.34166i | ||||||||
\(83\) | − 8.87482i | − 0.974138i | −0.873364 | − | 0.487069i | \(-0.838066\pi\) | ||||
0.873364 | − | 0.487069i | \(-0.161934\pi\) | |||||||
\(84\) | 8.80669 | 0.960889 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.94834 | −0.749259 | ||||||||
\(87\) | − 5.95595i | − 0.638545i | ||||||||
\(88\) | 9.33480i | 0.995093i | ||||||||
\(89\) | −15.4436 | −1.63702 | −0.818509 | − | 0.574493i | \(-0.805199\pi\) | ||||
−0.818509 | + | 0.574493i | \(0.805199\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.51660 | 0.473469 | ||||||||
\(92\) | − 21.2094i | − 2.21123i | ||||||||
\(93\) | − 7.10310i | − 0.736557i | ||||||||
\(94\) | −5.15327 | −0.531519 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 17.1155 | 1.74685 | ||||||||
\(97\) | 10.7682i | 1.09335i | 0.837346 | + | 0.546673i | \(0.184106\pi\) | ||||
−0.837346 | + | 0.546673i | \(0.815894\pi\) | |||||||
\(98\) | − 11.1617i | − 1.12750i | ||||||||
\(99\) | −1.07882 | −0.108425 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5654 | −1.34981 | −0.674905 | − | 0.737905i | \(-0.735815\pi\) | ||||
−0.674905 | + | 0.737905i | \(0.735815\pi\) | |||||||
\(102\) | − 10.5646i | − 1.04605i | ||||||||
\(103\) | − 1.36904i | − 0.134895i | −0.997723 | − | 0.0674476i | \(-0.978514\pi\) | ||||
0.997723 | − | 0.0674476i | \(-0.0214856\pi\) | |||||||
\(104\) | 23.1656 | 2.27157 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.84822 | 0.665158 | ||||||||
\(107\) | 11.0115i | 1.06452i | 0.846579 | + | 0.532262i | \(0.178658\pi\) | ||||
−0.846579 | + | 0.532262i | \(0.821342\pi\) | |||||||
\(108\) | 5.22020i | 0.502314i | ||||||||
\(109\) | −3.44890 | −0.330344 | −0.165172 | − | 0.986265i | \(-0.552818\pi\) | ||||
−0.165172 | + | 0.986265i | \(0.552818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.58187 | 0.434891 | ||||||||
\(112\) | 21.6111i | 2.04206i | ||||||||
\(113\) | − 6.05194i | − 0.569319i | −0.958629 | − | 0.284660i | \(-0.908119\pi\) | ||||
0.958629 | − | 0.284660i | \(-0.0918805\pi\) | |||||||
\(114\) | 3.16412 | 0.296347 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 31.0912 | 2.88675 | ||||||||
\(117\) | 2.67723i | 0.247510i | ||||||||
\(118\) | 3.58986i | 0.330473i | ||||||||
\(119\) | 6.63289 | 0.608036 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.83615 | −0.894196 | ||||||||
\(122\) | 19.5645i | 1.77129i | ||||||||
\(123\) | − 11.2614i | − 1.01541i | ||||||||
\(124\) | 37.0796 | 3.32984 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −4.53315 | −0.403845 | ||||||||
\(127\) | − 20.2362i | − 1.79567i | −0.440332 | − | 0.897835i | \(-0.645139\pi\) | ||||
0.440332 | − | 0.897835i | \(-0.354861\pi\) | |||||||
\(128\) | 20.5042i | 1.81233i | ||||||||
\(129\) | 2.58587 | 0.227673 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.05011 | −0.266490 | −0.133245 | − | 0.991083i | \(-0.542540\pi\) | ||||
−0.133245 | + | 0.991083i | \(0.542540\pi\) | |||||||
\(132\) | − 5.63164i | − 0.490171i | ||||||||
\(133\) | 1.98657i | 0.172257i | ||||||||
\(134\) | 33.4404 | 2.88881 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 34.0200 | 2.91719 | ||||||||
\(137\) | − 20.5100i | − 1.75229i | −0.482048 | − | 0.876145i | \(-0.660107\pi\) | ||||
0.482048 | − | 0.876145i | \(-0.339893\pi\) | |||||||
\(138\) | 10.9173i | 0.929343i | ||||||||
\(139\) | −18.3184 | −1.55374 | −0.776871 | − | 0.629659i | \(-0.783194\pi\) | ||||
−0.776871 | + | 0.629659i | \(0.783194\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.91782 | 0.161510 | ||||||||
\(142\) | 16.0814i | 1.34952i | ||||||||
\(143\) | − 2.88825i | − 0.241527i | ||||||||
\(144\) | −12.8101 | −1.06750 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.86899 | 0.734003 | ||||||||
\(147\) | 4.15389i | 0.342607i | ||||||||
\(148\) | 23.9182i | 1.96607i | ||||||||
\(149\) | −0.705938 | −0.0578327 | −0.0289163 | − | 0.999582i | \(-0.509206\pi\) | ||||
−0.0289163 | + | 0.999582i | \(0.509206\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.04538 | 0.573345 | 0.286673 | − | 0.958029i | \(-0.407451\pi\) | ||||
0.286673 | + | 0.958029i | \(0.407451\pi\) | |||||||
\(152\) | 10.1891i | 0.826443i | ||||||||
\(153\) | 3.93167i | 0.317857i | ||||||||
\(154\) | 4.89045 | 0.394083 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13.9757 | −1.11895 | ||||||||
\(157\) | − 5.12880i | − 0.409323i | −0.978833 | − | 0.204662i | \(-0.934391\pi\) | ||||
0.978833 | − | 0.204662i | \(-0.0656094\pi\) | |||||||
\(158\) | − 10.7590i | − 0.855942i | ||||||||
\(159\) | −2.54861 | −0.202118 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.85436 | −0.540199 | ||||||||
\(162\) | − 2.68704i | − 0.211114i | ||||||||
\(163\) | 24.2613i | 1.90029i | 0.311806 | + | 0.950146i | \(0.399066\pi\) | ||||
−0.311806 | + | 0.950146i | \(0.600934\pi\) | |||||||
\(164\) | 58.7869 | 4.59049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −23.8470 | −1.85089 | ||||||||
\(167\) | 4.54890i | 0.352004i | 0.984390 | + | 0.176002i | \(0.0563165\pi\) | ||||
−0.984390 | + | 0.176002i | \(0.943683\pi\) | |||||||
\(168\) | − 14.5976i | − 1.12623i | ||||||||
\(169\) | 5.83243 | 0.448648 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.17755 | −0.0900492 | ||||||||
\(172\) | 13.4988i | 1.02927i | ||||||||
\(173\) | 2.67729i | 0.203550i | 0.994807 | + | 0.101775i | \(0.0324522\pi\) | ||||
−0.994807 | + | 0.101775i | \(0.967548\pi\) | |||||||
\(174\) | −16.0039 | −1.21325 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 13.8197 | 1.04170 | ||||||||
\(177\) | − 1.33599i | − 0.100419i | ||||||||
\(178\) | 41.4976i | 3.11038i | ||||||||
\(179\) | 15.6266 | 1.16799 | 0.583995 | − | 0.811757i | \(-0.301489\pi\) | ||||
0.583995 | + | 0.811757i | \(0.301489\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.202843 | 0.0150772 | 0.00753859 | − | 0.999972i | \(-0.497600\pi\) | ||||
0.00753859 | + | 0.999972i | \(0.497600\pi\) | |||||||
\(182\) | − 12.1363i | − 0.899603i | ||||||||
\(183\) | − 7.28106i | − 0.538232i | ||||||||
\(184\) | −35.1559 | −2.59172 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −19.0863 | −1.39948 | ||||||||
\(187\) | − 4.24155i | − 0.310173i | ||||||||
\(188\) | 10.0114i | 0.730156i | ||||||||
\(189\) | 1.68704 | 0.122714 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.91975 | −0.573053 | −0.286526 | − | 0.958072i | \(-0.592501\pi\) | ||||
−0.286526 | + | 0.958072i | \(0.592501\pi\) | |||||||
\(192\) | − 20.3701i | − 1.47008i | ||||||||
\(193\) | 16.4269i | 1.18243i | 0.806513 | + | 0.591216i | \(0.201352\pi\) | ||||
−0.806513 | + | 0.591216i | \(0.798648\pi\) | |||||||
\(194\) | 28.9346 | 2.07738 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −21.6841 | −1.54887 | ||||||||
\(197\) | − 17.1369i | − 1.22095i | −0.792035 | − | 0.610475i | \(-0.790978\pi\) | ||||
0.792035 | − | 0.610475i | \(-0.209022\pi\) | |||||||
\(198\) | 2.89883i | 0.206011i | ||||||||
\(199\) | 2.01848 | 0.143086 | 0.0715430 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715430 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.4451 | −0.877806 | ||||||||
\(202\) | 36.4509i | 2.56467i | ||||||||
\(203\) | − 10.0479i | − 0.705227i | ||||||||
\(204\) | −20.5241 | −1.43697 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.67866 | −0.256304 | ||||||||
\(207\) | − 4.06295i | − 0.282394i | ||||||||
\(208\) | − 34.2955i | − 2.37796i | ||||||||
\(209\) | 1.27036 | 0.0878725 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8213 | −1.63993 | −0.819963 | − | 0.572416i | \(-0.806006\pi\) | ||||
−0.819963 | + | 0.572416i | \(0.806006\pi\) | |||||||
\(212\) | − 13.3042i | − 0.913738i | ||||||||
\(213\) | − 5.98480i | − 0.410072i | ||||||||
\(214\) | 29.5884 | 2.02262 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.65280 | 0.588749 | ||||||||
\(217\) | − 11.9832i | − 0.813475i | ||||||||
\(218\) | 9.26733i | 0.627663i | ||||||||
\(219\) | −3.30065 | −0.223037 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.5260 | −0.708055 | ||||||||
\(222\) | − 12.3117i | − 0.826305i | ||||||||
\(223\) | − 13.1112i | − 0.877989i | −0.898490 | − | 0.438995i | \(-0.855335\pi\) | ||||
0.898490 | − | 0.438995i | \(-0.144665\pi\) | |||||||
\(224\) | 28.8746 | 1.92927 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.2618 | −1.08172 | ||||||||
\(227\) | − 26.2807i | − 1.74431i | −0.489229 | − | 0.872155i | \(-0.662722\pi\) | ||||
0.489229 | − | 0.872155i | \(-0.337278\pi\) | |||||||
\(228\) | − 6.14702i | − 0.407096i | ||||||||
\(229\) | −1.99605 | −0.131903 | −0.0659513 | − | 0.997823i | \(-0.521008\pi\) | ||||
−0.0659513 | + | 0.997823i | \(0.521008\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.82001 | −0.119748 | ||||||||
\(232\) | − 51.5357i | − 3.38348i | ||||||||
\(233\) | 0.525548i | 0.0344298i | 0.999852 | + | 0.0172149i | \(0.00547995\pi\) | ||||
−0.999852 | + | 0.0172149i | \(0.994520\pi\) | |||||||
\(234\) | 7.19384 | 0.470276 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.97412 | 0.453976 | ||||||||
\(237\) | 4.00404i | 0.260090i | ||||||||
\(238\) | − 17.8229i | − 1.15528i | ||||||||
\(239\) | 7.00971 | 0.453421 | 0.226710 | − | 0.973962i | \(-0.427203\pi\) | ||||
0.226710 | + | 0.973962i | \(0.427203\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.31554 | 0.149157 | 0.0745786 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745786 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(242\) | 26.4302i | 1.69899i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 38.0086 | 2.43325 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −30.2600 | −1.92931 | ||||||||
\(247\) | − 3.15257i | − 0.200593i | ||||||||
\(248\) | − 61.4617i | − 3.90282i | ||||||||
\(249\) | 8.87482 | 0.562419 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.17885 | −0.390005 | −0.195003 | − | 0.980803i | \(-0.562472\pi\) | ||||
−0.195003 | + | 0.980803i | \(0.562472\pi\) | |||||||
\(252\) | 8.80669i | 0.554769i | ||||||||
\(253\) | 4.38318i | 0.275568i | ||||||||
\(254\) | −54.3755 | −3.41182 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.3555 | 0.897217 | ||||||||
\(257\) | 13.2239i | 0.824882i | 0.910984 | + | 0.412441i | \(0.135324\pi\) | ||||
−0.910984 | + | 0.412441i | \(0.864676\pi\) | |||||||
\(258\) | − 6.94834i | − 0.432585i | ||||||||
\(259\) | 7.72980 | 0.480306 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.95595 | 0.368664 | ||||||||
\(262\) | 8.19578i | 0.506337i | ||||||||
\(263\) | 6.97643i | 0.430185i | 0.976594 | + | 0.215092i | \(0.0690053\pi\) | ||||
−0.976594 | + | 0.215092i | \(0.930995\pi\) | |||||||
\(264\) | −9.33480 | −0.574517 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.33800 | 0.327294 | ||||||||
\(267\) | − 15.4436i | − 0.945133i | ||||||||
\(268\) | − 64.9656i | − 3.96841i | ||||||||
\(269\) | −23.7199 | −1.44623 | −0.723113 | − | 0.690730i | \(-0.757289\pi\) | ||||
−0.723113 | + | 0.690730i | \(0.757289\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.9910 | 1.76108 | 0.880539 | − | 0.473975i | \(-0.157181\pi\) | ||||
0.880539 | + | 0.473975i | \(0.157181\pi\) | |||||||
\(272\) | − 50.3649i | − 3.05382i | ||||||||
\(273\) | 4.51660i | 0.273357i | ||||||||
\(274\) | −55.1113 | −3.32940 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 21.2094 | 1.27665 | ||||||||
\(277\) | − 8.58667i | − 0.515923i | −0.966155 | − | 0.257962i | \(-0.916949\pi\) | ||||
0.966155 | − | 0.257962i | \(-0.0830508\pi\) | |||||||
\(278\) | 49.2222i | 2.95215i | ||||||||
\(279\) | 7.10310 | 0.425251 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.1661 | 1.02405 | 0.512023 | − | 0.858972i | \(-0.328896\pi\) | ||||
0.512023 | + | 0.858972i | \(0.328896\pi\) | |||||||
\(282\) | − 5.15327i | − 0.306872i | ||||||||
\(283\) | 9.62005i | 0.571853i | 0.958252 | + | 0.285926i | \(0.0923012\pi\) | ||||
−0.958252 | + | 0.285926i | \(0.907699\pi\) | |||||||
\(284\) | 31.2419 | 1.85386 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.76084 | −0.458908 | ||||||||
\(287\) | − 18.9985i | − 1.12145i | ||||||||
\(288\) | 17.1155i | 1.00854i | ||||||||
\(289\) | 1.54198 | 0.0907048 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −10.7682 | −0.631243 | ||||||||
\(292\) | − 17.2301i | − 1.00831i | ||||||||
\(293\) | − 16.8202i | − 0.982649i | −0.870977 | − | 0.491324i | \(-0.836513\pi\) | ||||
0.870977 | − | 0.491324i | \(-0.163487\pi\) | |||||||
\(294\) | 11.1617 | 0.650962 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 39.6460 | 2.30438 | ||||||||
\(297\) | − 1.07882i | − 0.0625994i | ||||||||
\(298\) | 1.89688i | 0.109884i | ||||||||
\(299\) | 10.8775 | 0.629059 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.36247 | 0.251449 | ||||||||
\(302\) | − 18.9312i | − 1.08937i | ||||||||
\(303\) | − 13.5654i | − 0.779313i | ||||||||
\(304\) | 15.0844 | 0.865151 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.5646 | 0.603936 | ||||||||
\(307\) | 11.3212i | 0.646134i | 0.946376 | + | 0.323067i | \(0.104714\pi\) | ||||
−0.946376 | + | 0.323067i | \(0.895286\pi\) | |||||||
\(308\) | − 9.50081i | − 0.541359i | ||||||||
\(309\) | 1.36904 | 0.0778818 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.5635 | 1.05264 | 0.526318 | − | 0.850288i | \(-0.323572\pi\) | ||||
0.526318 | + | 0.850288i | \(0.323572\pi\) | |||||||
\(312\) | 23.1656i | 1.31149i | ||||||||
\(313\) | 9.69951i | 0.548249i | 0.961694 | + | 0.274124i | \(0.0883880\pi\) | ||||
−0.961694 | + | 0.274124i | \(0.911612\pi\) | |||||||
\(314\) | −13.7813 | −0.777724 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.9019 | −1.17582 | ||||||||
\(317\) | 7.47647i | 0.419920i | 0.977710 | + | 0.209960i | \(0.0673334\pi\) | ||||
−0.977710 | + | 0.209960i | \(0.932667\pi\) | |||||||
\(318\) | 6.84822i | 0.384029i | ||||||||
\(319\) | −6.42538 | −0.359752 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −11.0115 | −0.614604 | ||||||||
\(322\) | 18.4180i | 1.02639i | ||||||||
\(323\) | − 4.62972i | − 0.257605i | ||||||||
\(324\) | −5.22020 | −0.290011 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 65.1911 | 3.61060 | ||||||||
\(327\) | − 3.44890i | − 0.190724i | ||||||||
\(328\) | − 97.4430i | − 5.38039i | ||||||||
\(329\) | 3.23544 | 0.178376 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.2570 | −1.38825 | −0.694125 | − | 0.719854i | \(-0.744209\pi\) | ||||
−0.694125 | + | 0.719854i | \(0.744209\pi\) | |||||||
\(332\) | 46.3283i | 2.54259i | ||||||||
\(333\) | 4.58187i | 0.251085i | ||||||||
\(334\) | 12.2231 | 0.668817 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −21.6111 | −1.17898 | ||||||||
\(337\) | − 13.0240i | − 0.709463i | −0.934968 | − | 0.354731i | \(-0.884572\pi\) | ||||
0.934968 | − | 0.354731i | \(-0.115428\pi\) | |||||||
\(338\) | − 15.6720i | − 0.852443i | ||||||||
\(339\) | 6.05194 | 0.328697 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.66295 | −0.414972 | ||||||||
\(342\) | 3.16412i | 0.171096i | ||||||||
\(343\) | 18.8171i | 1.01603i | ||||||||
\(344\) | 22.3750 | 1.20638 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.19398 | 0.386751 | ||||||||
\(347\) | − 6.00149i | − 0.322177i | −0.986940 | − | 0.161089i | \(-0.948500\pi\) | ||||
0.986940 | − | 0.161089i | \(-0.0515005\pi\) | |||||||
\(348\) | 31.0912i | 1.66666i | ||||||||
\(349\) | 22.7183 | 1.21608 | 0.608042 | − | 0.793905i | \(-0.291955\pi\) | ||||
0.608042 | + | 0.793905i | \(0.291955\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.67723 | −0.142900 | ||||||||
\(352\) | − 18.4646i | − 0.984164i | ||||||||
\(353\) | 4.85493i | 0.258402i | 0.991618 | + | 0.129201i | \(0.0412413\pi\) | ||||
−0.991618 | + | 0.129201i | \(0.958759\pi\) | |||||||
\(354\) | −3.58986 | −0.190799 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 80.6186 | 4.27278 | ||||||||
\(357\) | 6.63289i | 0.351050i | ||||||||
\(358\) | − 41.9895i | − 2.21921i | ||||||||
\(359\) | −28.8910 | −1.52481 | −0.762403 | − | 0.647102i | \(-0.775981\pi\) | ||||
−0.762403 | + | 0.647102i | \(0.775981\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.6134 | −0.927020 | ||||||||
\(362\) | − 0.545047i | − 0.0286470i | ||||||||
\(363\) | − 9.83615i | − 0.516264i | ||||||||
\(364\) | −23.5776 | −1.23580 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −19.5645 | −1.02265 | ||||||||
\(367\) | − 14.7089i | − 0.767800i | −0.923375 | − | 0.383900i | \(-0.874581\pi\) | ||||
0.923375 | − | 0.383900i | \(-0.125419\pi\) | |||||||
\(368\) | 52.0465i | 2.71311i | ||||||||
\(369\) | 11.2614 | 0.586247 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.29961 | −0.223225 | ||||||||
\(372\) | 37.0796i | 1.92249i | ||||||||
\(373\) | 33.0391i | 1.71070i | 0.518051 | + | 0.855350i | \(0.326658\pi\) | ||||
−0.518051 | + | 0.855350i | \(0.673342\pi\) | |||||||
\(374\) | −11.3972 | −0.589337 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 16.5945 | 0.855797 | ||||||||
\(377\) | 15.9455i | 0.821233i | ||||||||
\(378\) | − 4.53315i | − 0.233160i | ||||||||
\(379\) | 15.1556 | 0.778493 | 0.389247 | − | 0.921134i | \(-0.372735\pi\) | ||||
0.389247 | + | 0.921134i | \(0.372735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.2362 | 1.03673 | ||||||||
\(382\) | 21.2807i | 1.08882i | ||||||||
\(383\) | 8.00811i | 0.409195i | 0.978846 | + | 0.204598i | \(0.0655886\pi\) | ||||
−0.978846 | + | 0.204598i | \(0.934411\pi\) | |||||||
\(384\) | −20.5042 | −1.04635 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 44.1397 | 2.24665 | ||||||||
\(387\) | 2.58587i | 0.131447i | ||||||||
\(388\) | − 56.2121i | − 2.85374i | ||||||||
\(389\) | −1.07463 | −0.0544858 | −0.0272429 | − | 0.999629i | \(-0.508673\pi\) | ||||
−0.0272429 | + | 0.999629i | \(0.508673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.9742 | 0.807848 | ||||||||
\(392\) | 35.9428i | 1.81538i | ||||||||
\(393\) | − 3.05011i | − 0.153858i | ||||||||
\(394\) | −46.0475 | −2.31984 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5.63164 | 0.283001 | ||||||||
\(397\) | − 24.2139i | − 1.21526i | −0.794220 | − | 0.607630i | \(-0.792120\pi\) | ||||
0.794220 | − | 0.607630i | \(-0.207880\pi\) | |||||||
\(398\) | − 5.42373i | − 0.271867i | ||||||||
\(399\) | −1.98657 | −0.0994529 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.99317 | −0.0995340 | −0.0497670 | − | 0.998761i | \(-0.515848\pi\) | ||||
−0.0497670 | + | 0.998761i | \(0.515848\pi\) | |||||||
\(402\) | 33.4404i | 1.66785i | ||||||||
\(403\) | 19.0166i | 0.947287i | ||||||||
\(404\) | 70.8142 | 3.52314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26.9992 | −1.33995 | ||||||||
\(407\) | − 4.94300i | − 0.245015i | ||||||||
\(408\) | 34.0200i | 1.68424i | ||||||||
\(409\) | −6.66478 | −0.329552 | −0.164776 | − | 0.986331i | \(-0.552690\pi\) | ||||
−0.164776 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 20.5100 | 1.01168 | ||||||||
\(412\) | 7.14664i | 0.352090i | ||||||||
\(413\) | − 2.25387i | − 0.110906i | ||||||||
\(414\) | −10.9173 | −0.536556 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −45.8223 | −2.24662 | ||||||||
\(417\) | − 18.3184i | − 0.897054i | ||||||||
\(418\) | − 3.41351i | − 0.166960i | ||||||||
\(419\) | −21.3540 | −1.04321 | −0.521606 | − | 0.853186i | \(-0.674667\pi\) | ||||
−0.521606 | + | 0.853186i | \(0.674667\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.3367 | 1.08863 | 0.544313 | − | 0.838882i | \(-0.316790\pi\) | ||||
0.544313 | + | 0.838882i | \(0.316790\pi\) | |||||||
\(422\) | 64.0088i | 3.11590i | ||||||||
\(423\) | 1.91782i | 0.0932476i | ||||||||
\(424\) | −22.0526 | −1.07097 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.0814 | −0.779147 | ||||||||
\(427\) | − 12.2835i | − 0.594438i | ||||||||
\(428\) | − 57.4823i | − 2.77851i | ||||||||
\(429\) | 2.88825 | 0.139446 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.4129 | −1.46494 | −0.732469 | − | 0.680800i | \(-0.761632\pi\) | ||||
−0.732469 | + | 0.680800i | \(0.761632\pi\) | |||||||
\(432\) | − 12.8101i | − 0.616324i | ||||||||
\(433\) | − 0.576639i | − 0.0277115i | −0.999904 | − | 0.0138558i | \(-0.995589\pi\) | ||||
0.999904 | − | 0.0138558i | \(-0.00441057\pi\) | |||||||
\(434\) | −32.1994 | −1.54562 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0039 | 0.862231 | ||||||||
\(437\) | 4.78431i | 0.228864i | ||||||||
\(438\) | 8.86899i | 0.423777i | ||||||||
\(439\) | −12.8045 | −0.611125 | −0.305563 | − | 0.952172i | \(-0.598845\pi\) | ||||
−0.305563 | + | 0.952172i | \(0.598845\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.15389 | −0.197804 | ||||||||
\(442\) | 28.2838i | 1.34532i | ||||||||
\(443\) | − 14.3147i | − 0.680110i | −0.940405 | − | 0.340055i | \(-0.889554\pi\) | ||||
0.940405 | − | 0.340055i | \(-0.110446\pi\) | |||||||
\(444\) | −23.9182 | −1.13511 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −35.2303 | −1.66820 | ||||||||
\(447\) | − 0.705938i | − 0.0333897i | ||||||||
\(448\) | − 34.3652i | − 1.62360i | ||||||||
\(449\) | 11.9663 | 0.564724 | 0.282362 | − | 0.959308i | \(-0.408882\pi\) | ||||
0.282362 | + | 0.959308i | \(0.408882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.1490 | −0.572076 | ||||||||
\(452\) | 31.5923i | 1.48598i | ||||||||
\(453\) | 7.04538i | 0.331021i | ||||||||
\(454\) | −70.6173 | −3.31424 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.1891 | −0.477147 | ||||||||
\(457\) | − 8.22154i | − 0.384587i | −0.981337 | − | 0.192294i | \(-0.938407\pi\) | ||||
0.981337 | − | 0.192294i | \(-0.0615926\pi\) | |||||||
\(458\) | 5.36346i | 0.250618i | ||||||||
\(459\) | −3.93167 | −0.183515 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.27216 | 0.0592505 | 0.0296253 | − | 0.999561i | \(-0.490569\pi\) | ||||
0.0296253 | + | 0.999561i | \(0.490569\pi\) | |||||||
\(462\) | 4.89045i | 0.227524i | ||||||||
\(463\) | − 32.6764i | − 1.51860i | −0.650740 | − | 0.759300i | \(-0.725541\pi\) | ||||
0.650740 | − | 0.759300i | \(-0.274459\pi\) | |||||||
\(464\) | −76.2960 | −3.54195 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.41217 | 0.0654175 | ||||||||
\(467\) | 14.4347i | 0.667958i | 0.942581 | + | 0.333979i | \(0.108391\pi\) | ||||
−0.942581 | + | 0.333979i | \(0.891609\pi\) | |||||||
\(468\) | − 13.9757i | − 0.646026i | ||||||||
\(469\) | −20.9953 | −0.969474 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.12880 | 0.236323 | ||||||||
\(472\) | − 11.5600i | − 0.532094i | ||||||||
\(473\) | − 2.78968i | − 0.128270i | ||||||||
\(474\) | 10.7590 | 0.494178 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −34.6250 | −1.58703 | ||||||||
\(477\) | − 2.54861i | − 0.116693i | ||||||||
\(478\) | − 18.8354i | − 0.861511i | ||||||||
\(479\) | 16.8618 | 0.770436 | 0.385218 | − | 0.922826i | \(-0.374126\pi\) | ||||
0.385218 | + | 0.922826i | \(0.374126\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.2667 | −0.559314 | ||||||||
\(482\) | − 6.22196i | − 0.283403i | ||||||||
\(483\) | − 6.85436i | − 0.311884i | ||||||||
\(484\) | 51.3466 | 2.33394 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.68704 | 0.121887 | ||||||||
\(487\) | 39.8235i | 1.80457i | 0.431135 | + | 0.902287i | \(0.358113\pi\) | ||||
−0.431135 | + | 0.902287i | \(0.641887\pi\) | |||||||
\(488\) | − 63.0016i | − 2.85195i | ||||||||
\(489\) | −24.2613 | −1.09713 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.0255 | 0.632961 | 0.316480 | − | 0.948599i | \(-0.397499\pi\) | ||||
0.316480 | + | 0.948599i | \(0.397499\pi\) | |||||||
\(492\) | 58.7869i | 2.65032i | ||||||||
\(493\) | 23.4168i | 1.05464i | ||||||||
\(494\) | −8.47108 | −0.381132 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −90.9911 | −4.08562 | ||||||||
\(497\) | − 10.0966i | − 0.452895i | ||||||||
\(498\) | − 23.8470i | − 1.06861i | ||||||||
\(499\) | −15.2315 | −0.681857 | −0.340929 | − | 0.940089i | \(-0.610741\pi\) | ||||
−0.340929 | + | 0.940089i | \(0.610741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.54890 | −0.203230 | ||||||||
\(502\) | 16.6028i | 0.741020i | ||||||||
\(503\) | − 23.7330i | − 1.05820i | −0.848559 | − | 0.529101i | \(-0.822529\pi\) | ||||
0.848559 | − | 0.529101i | \(-0.177471\pi\) | |||||||
\(504\) | 14.5976 | 0.650231 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 11.7778 | 0.523586 | ||||||||
\(507\) | 5.83243i | 0.259027i | ||||||||
\(508\) | 105.637i | 4.68688i | ||||||||
\(509\) | 12.5097 | 0.554482 | 0.277241 | − | 0.960800i | \(-0.410580\pi\) | ||||
0.277241 | + | 0.960800i | \(0.410580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.56834 | −0.246329 | ||||||||
\(512\) | 2.43464i | 0.107597i | ||||||||
\(513\) | − 1.17755i | − 0.0519899i | ||||||||
\(514\) | 35.5331 | 1.56730 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −13.4988 | −0.594249 | ||||||||
\(517\) | − 2.06898i | − 0.0909936i | ||||||||
\(518\) | − 20.7703i | − 0.912595i | ||||||||
\(519\) | −2.67729 | −0.117520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.9638 | −1.22512 | −0.612559 | − | 0.790425i | \(-0.709860\pi\) | ||||
−0.612559 | + | 0.790425i | \(0.709860\pi\) | |||||||
\(522\) | − 16.0039i | − 0.700471i | ||||||||
\(523\) | − 15.7013i | − 0.686569i | −0.939231 | − | 0.343285i | \(-0.888460\pi\) | ||||
0.939231 | − | 0.343285i | \(-0.111540\pi\) | |||||||
\(524\) | 15.9222 | 0.695564 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7460 | 0.817362 | ||||||||
\(527\) | 27.9270i | 1.21652i | ||||||||
\(528\) | 13.8197i | 0.601426i | ||||||||
\(529\) | 6.49247 | 0.282281 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.33599 | 0.0579769 | ||||||||
\(532\) | − 10.3703i | − 0.449609i | ||||||||
\(533\) | 30.1495i | 1.30592i | ||||||||
\(534\) | −41.4976 | −1.79578 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −107.685 | −4.65127 | ||||||||
\(537\) | 15.6266i | 0.674340i | ||||||||
\(538\) | 63.7363i | 2.74787i | ||||||||
\(539\) | 4.48129 | 0.193023 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.9783 | −1.03091 | −0.515455 | − | 0.856917i | \(-0.672377\pi\) | ||||
−0.515455 | + | 0.856917i | \(0.672377\pi\) | |||||||
\(542\) | − 77.9000i | − 3.34609i | ||||||||
\(543\) | 0.202843i | 0.00870482i | ||||||||
\(544\) | −67.2927 | −2.88515 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.1363 | 0.519386 | ||||||||
\(547\) | − 5.62681i | − 0.240585i | −0.992738 | − | 0.120293i | \(-0.961617\pi\) | ||||
0.992738 | − | 0.120293i | \(-0.0383833\pi\) | |||||||
\(548\) | 107.066i | 4.57365i | ||||||||
\(549\) | 7.28106 | 0.310748 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.01341 | −0.298781 | ||||||||
\(552\) | − 35.1559i | − 1.49633i | ||||||||
\(553\) | 6.75498i | 0.287251i | ||||||||
\(554\) | −23.0728 | −0.980268 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 95.6254 | 4.05542 | ||||||||
\(557\) | − 42.4247i | − 1.79759i | −0.438366 | − | 0.898796i | \(-0.644443\pi\) | ||||
0.438366 | − | 0.898796i | \(-0.355557\pi\) | |||||||
\(558\) | − 19.0863i | − 0.807989i | ||||||||
\(559\) | −6.92298 | −0.292811 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.24155 | 0.179079 | ||||||||
\(562\) | − 46.1261i | − 1.94571i | ||||||||
\(563\) | − 5.78597i | − 0.243850i | −0.992539 | − | 0.121925i | \(-0.961093\pi\) | ||||
0.992539 | − | 0.121925i | \(-0.0389067\pi\) | |||||||
\(564\) | −10.0114 | −0.421556 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 25.8495 | 1.08653 | ||||||||
\(567\) | 1.68704i | 0.0708491i | ||||||||
\(568\) | − 51.7853i | − 2.17286i | ||||||||
\(569\) | 22.0056 | 0.922522 | 0.461261 | − | 0.887265i | \(-0.347397\pi\) | ||||
0.461261 | + | 0.887265i | \(0.347397\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.6143 | 1.40672 | 0.703358 | − | 0.710835i | \(-0.251683\pi\) | ||||
0.703358 | + | 0.710835i | \(0.251683\pi\) | |||||||
\(572\) | 15.0772i | 0.630410i | ||||||||
\(573\) | − 7.91975i | − 0.330852i | ||||||||
\(574\) | −51.0499 | −2.13078 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.3701 | 0.848754 | ||||||||
\(577\) | 40.2350i | 1.67501i | 0.546433 | + | 0.837503i | \(0.315985\pi\) | ||||
−0.546433 | + | 0.837503i | \(0.684015\pi\) | |||||||
\(578\) | − 4.14337i | − 0.172341i | ||||||||
\(579\) | −16.4269 | −0.682677 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.9722 | 0.621151 | ||||||||
\(582\) | 28.9346i | 1.19938i | ||||||||
\(583\) | 2.74948i | 0.113872i | ||||||||
\(584\) | −28.5599 | −1.18182 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −45.1967 | −1.86706 | ||||||||
\(587\) | − 2.82299i | − 0.116517i | −0.998302 | − | 0.0582587i | \(-0.981445\pi\) | ||||
0.998302 | − | 0.0582587i | \(-0.0185548\pi\) | |||||||
\(588\) | − 21.6841i | − 0.894238i | ||||||||
\(589\) | −8.36423 | −0.344642 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.1369 | 0.704916 | ||||||||
\(592\) | − 58.6939i | − 2.41231i | ||||||||
\(593\) | 24.6805i | 1.01351i | 0.862091 | + | 0.506754i | \(0.169155\pi\) | ||||
−0.862091 | + | 0.506754i | \(0.830845\pi\) | |||||||
\(594\) | −2.89883 | −0.118940 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.68513 | 0.150949 | ||||||||
\(597\) | 2.01848i | 0.0826108i | ||||||||
\(598\) | − 29.2282i | − 1.19523i | ||||||||
\(599\) | 7.71547 | 0.315245 | 0.157623 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157623 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.6506 | 0.923938 | 0.461969 | − | 0.886896i | \(-0.347143\pi\) | ||||
0.461969 | + | 0.886896i | \(0.347143\pi\) | |||||||
\(602\) | − 11.7222i | − 0.477759i | ||||||||
\(603\) | − 12.4451i | − 0.506802i | ||||||||
\(604\) | −36.7783 | −1.49649 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −36.4509 | −1.48072 | ||||||||
\(607\) | − 24.6423i | − 1.00020i | −0.865968 | − | 0.500099i | \(-0.833297\pi\) | ||||
0.865968 | − | 0.500099i | \(-0.166703\pi\) | |||||||
\(608\) | − 20.1543i | − 0.817367i | ||||||||
\(609\) | 10.0479 | 0.407163 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.13445 | −0.207718 | ||||||||
\(612\) | − 20.5241i | − 0.829637i | ||||||||
\(613\) | 41.8034i | 1.68842i | 0.536011 | + | 0.844211i | \(0.319931\pi\) | ||||
−0.536011 | + | 0.844211i | \(0.680069\pi\) | |||||||
\(614\) | 30.4205 | 1.22767 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15.7482 | −0.634513 | ||||||||
\(617\) | 15.9390i | 0.641680i | 0.947133 | + | 0.320840i | \(0.103965\pi\) | ||||
−0.947133 | + | 0.320840i | \(0.896035\pi\) | |||||||
\(618\) | − 3.67866i | − 0.147977i | ||||||||
\(619\) | 47.1700 | 1.89592 | 0.947961 | − | 0.318385i | \(-0.103141\pi\) | ||||
0.947961 | + | 0.318385i | \(0.103141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.06295 | 0.163040 | ||||||||
\(622\) | − 49.8808i | − 2.00004i | ||||||||
\(623\) | − 26.0540i | − 1.04383i | ||||||||
\(624\) | 34.2955 | 1.37292 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 26.0630 | 1.04169 | ||||||||
\(627\) | 1.27036i | 0.0507332i | ||||||||
\(628\) | 26.7734i | 1.06837i | ||||||||
\(629\) | −18.0144 | −0.718280 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.3634 | 1.28836 | 0.644182 | − | 0.764872i | \(-0.277198\pi\) | ||||
0.644182 | + | 0.764872i | \(0.277198\pi\) | |||||||
\(632\) | 34.6462i | 1.37815i | ||||||||
\(633\) | − 23.8213i | − 0.946812i | ||||||||
\(634\) | 20.0896 | 0.797859 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.3042 | 0.527547 | ||||||||
\(637\) | − 11.1209i | − 0.440627i | ||||||||
\(638\) | 17.2653i | 0.683539i | ||||||||
\(639\) | 5.98480 | 0.236755 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0042 | 0.711122 | 0.355561 | − | 0.934653i | \(-0.384290\pi\) | ||||
0.355561 | + | 0.934653i | \(0.384290\pi\) | |||||||
\(642\) | 29.5884i | 1.16776i | ||||||||
\(643\) | − 21.8891i | − 0.863224i | −0.902059 | − | 0.431612i | \(-0.857945\pi\) | ||||
0.902059 | − | 0.431612i | \(-0.142055\pi\) | |||||||
\(644\) | 35.7811 | 1.40997 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.4403 | −0.489455 | ||||||||
\(647\) | 19.0263i | 0.748003i | 0.927428 | + | 0.374001i | \(0.122015\pi\) | ||||
−0.927428 | + | 0.374001i | \(0.877985\pi\) | |||||||
\(648\) | 8.65280i | 0.339914i | ||||||||
\(649\) | −1.44129 | −0.0565755 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.9832 | 0.469660 | ||||||||
\(652\) | − 126.649i | − 4.95995i | ||||||||
\(653\) | 2.31971i | 0.0907774i | 0.998969 | + | 0.0453887i | \(0.0144526\pi\) | ||||
−0.998969 | + | 0.0453887i | \(0.985547\pi\) | |||||||
\(654\) | −9.26733 | −0.362381 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −144.260 | −5.63239 | ||||||||
\(657\) | − 3.30065i | − 0.128771i | ||||||||
\(658\) | − 8.69378i | − 0.338919i | ||||||||
\(659\) | −7.19180 | −0.280153 | −0.140076 | − | 0.990141i | \(-0.544735\pi\) | ||||
−0.140076 | + | 0.990141i | \(0.544735\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.0214 | 1.67334 | 0.836669 | − | 0.547709i | \(-0.184500\pi\) | ||||
0.836669 | + | 0.547709i | \(0.184500\pi\) | |||||||
\(662\) | 67.8666i | 2.63771i | ||||||||
\(663\) | − 10.5260i | − 0.408796i | ||||||||
\(664\) | 76.7920 | 2.98011 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3117 | 0.477067 | ||||||||
\(667\) | − 24.1987i | − 0.936977i | ||||||||
\(668\) | − 23.7461i | − 0.918765i | ||||||||
\(669\) | 13.1112 | 0.506907 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.85494 | −0.303237 | ||||||||
\(672\) | 28.8746i | 1.11386i | ||||||||
\(673\) | 29.8031i | 1.14882i | 0.818566 | + | 0.574412i | \(0.194769\pi\) | ||||
−0.818566 | + | 0.574412i | \(0.805231\pi\) | |||||||
\(674\) | −34.9961 | −1.34800 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −30.4464 | −1.17102 | ||||||||
\(677\) | − 26.7346i | − 1.02749i | −0.857942 | − | 0.513746i | \(-0.828257\pi\) | ||||
0.857942 | − | 0.513746i | \(-0.171743\pi\) | |||||||
\(678\) | − 16.2618i | − 0.624532i | ||||||||
\(679\) | −18.1664 | −0.697163 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.2807 | 1.00708 | ||||||||
\(682\) | 20.5907i | 0.788457i | ||||||||
\(683\) | − 28.4950i | − 1.09033i | −0.838329 | − | 0.545165i | \(-0.816467\pi\) | ||||
0.838329 | − | 0.545165i | \(-0.183533\pi\) | |||||||
\(684\) | 6.14702 | 0.235037 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 50.5623 | 1.93048 | ||||||||
\(687\) | − 1.99605i | − 0.0761540i | ||||||||
\(688\) | − 33.1251i | − 1.26288i | ||||||||
\(689\) | 6.82321 | 0.259944 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 34.6469 | 1.31803 | 0.659015 | − | 0.752130i | \(-0.270973\pi\) | ||||
0.659015 | + | 0.752130i | \(0.270973\pi\) | |||||||
\(692\) | − 13.9760i | − 0.531286i | ||||||||
\(693\) | − 1.82001i | − 0.0691365i | ||||||||
\(694\) | −16.1263 | −0.612145 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 51.5357 | 1.95345 | ||||||||
\(697\) | 44.2763i | 1.67708i | ||||||||
\(698\) | − 61.0451i | − 2.31059i | ||||||||
\(699\) | −0.525548 | −0.0198781 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.973305 | 0.0367612 | 0.0183806 | − | 0.999831i | \(-0.494149\pi\) | ||||
0.0183806 | + | 0.999831i | \(0.494149\pi\) | |||||||
\(702\) | 7.19384i | 0.271514i | ||||||||
\(703\) | − 5.39536i | − 0.203490i | ||||||||
\(704\) | −21.9756 | −0.828237 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.0454 | 0.490971 | ||||||||
\(707\) | − 22.8854i | − 0.860696i | ||||||||
\(708\) | 6.97412i | 0.262103i | ||||||||
\(709\) | 11.3242 | 0.425291 | 0.212645 | − | 0.977129i | \(-0.431792\pi\) | ||||
0.212645 | + | 0.977129i | \(0.431792\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00404 | −0.150163 | ||||||||
\(712\) | − 133.630i | − 5.00801i | ||||||||
\(713\) | − 28.8595i | − 1.08080i | ||||||||
\(714\) | 17.8229 | 0.667004 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −81.5742 | −3.04857 | ||||||||
\(717\) | 7.00971i | 0.261783i | ||||||||
\(718\) | 77.6312i | 2.89717i | ||||||||
\(719\) | 30.7320 | 1.14611 | 0.573056 | − | 0.819516i | \(-0.305758\pi\) | ||||
0.573056 | + | 0.819516i | \(0.305758\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.30962 | 0.0860149 | ||||||||
\(722\) | 47.3279i | 1.76136i | ||||||||
\(723\) | 2.31554i | 0.0861159i | ||||||||
\(724\) | −1.05888 | −0.0393529 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −26.4302 | −0.980915 | ||||||||
\(727\) | − 6.56836i | − 0.243607i | −0.992554 | − | 0.121803i | \(-0.961132\pi\) | ||||
0.992554 | − | 0.121803i | \(-0.0388678\pi\) | |||||||
\(728\) | 39.0813i | 1.44845i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.1668 | −0.376032 | ||||||||
\(732\) | 38.0086i | 1.40484i | ||||||||
\(733\) | 31.9276i | 1.17927i | 0.807669 | + | 0.589636i | \(0.200729\pi\) | ||||
−0.807669 | + | 0.589636i | \(0.799271\pi\) | |||||||
\(734\) | −39.5235 | −1.45884 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 69.5395 | 2.56326 | ||||||||
\(737\) | 13.4259i | 0.494551i | ||||||||
\(738\) | − 30.2600i | − 1.11389i | ||||||||
\(739\) | 15.3072 | 0.563083 | 0.281542 | − | 0.959549i | \(-0.409154\pi\) | ||||
0.281542 | + | 0.959549i | \(0.409154\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.15257 | 0.115812 | ||||||||
\(742\) | 11.5532i | 0.424132i | ||||||||
\(743\) | − 16.5455i | − 0.606995i | −0.952832 | − | 0.303498i | \(-0.901846\pi\) | ||||
0.952832 | − | 0.303498i | \(-0.0981545\pi\) | |||||||
\(744\) | 61.4617 | 2.25330 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 88.7774 | 3.25037 | ||||||||
\(747\) | 8.87482i | 0.324713i | ||||||||
\(748\) | 22.1417i | 0.809582i | ||||||||
\(749\) | −18.5769 | −0.678786 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.0279 | 1.67958 | 0.839791 | − | 0.542911i | \(-0.182678\pi\) | ||||
0.839791 | + | 0.542911i | \(0.182678\pi\) | |||||||
\(752\) | − 24.5674i | − 0.895880i | ||||||||
\(753\) | − 6.17885i | − 0.225170i | ||||||||
\(754\) | 42.8461 | 1.56036 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.80669 | −0.320296 | ||||||||
\(757\) | − 26.5282i | − 0.964184i | −0.876121 | − | 0.482092i | \(-0.839877\pi\) | ||||
0.876121 | − | 0.482092i | \(-0.160123\pi\) | |||||||
\(758\) | − 40.7239i | − 1.47916i | ||||||||
\(759\) | −4.38318 | −0.159099 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.4241 | −1.03037 | −0.515187 | − | 0.857078i | \(-0.672277\pi\) | ||||
−0.515187 | + | 0.857078i | \(0.672277\pi\) | |||||||
\(762\) | − 54.3755i | − 1.96982i | ||||||||
\(763\) | − 5.81843i | − 0.210641i | ||||||||
\(764\) | 41.3426 | 1.49572 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.5181 | 0.777481 | ||||||||
\(767\) | 3.57675i | 0.129149i | ||||||||
\(768\) | 14.3555i | 0.518009i | ||||||||
\(769\) | 8.95952 | 0.323089 | 0.161544 | − | 0.986865i | \(-0.448353\pi\) | ||||
0.161544 | + | 0.986865i | \(0.448353\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −13.2239 | −0.476246 | ||||||||
\(772\) | − 85.7515i | − 3.08626i | ||||||||
\(773\) | − 23.1042i | − 0.831001i | −0.909593 | − | 0.415500i | \(-0.863607\pi\) | ||||
0.909593 | − | 0.415500i | \(-0.136393\pi\) | |||||||
\(774\) | 6.94834 | 0.249753 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −93.1752 | −3.34479 | ||||||||
\(777\) | 7.72980i | 0.277305i | ||||||||
\(778\) | 2.88757i | 0.103524i | ||||||||
\(779\) | −13.2609 | −0.475120 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.45651 | −0.231032 | ||||||||
\(782\) | − 42.9232i | − 1.53493i | ||||||||
\(783\) | 5.95595i | 0.212848i | ||||||||
\(784\) | 53.2115 | 1.90041 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.19578 | −0.292334 | ||||||||
\(787\) | − 2.03390i | − 0.0725009i | −0.999343 | − | 0.0362504i | \(-0.988459\pi\) | ||||
0.999343 | − | 0.0362504i | \(-0.0115414\pi\) | |||||||
\(788\) | 89.4578i | 3.18680i | ||||||||
\(789\) | −6.97643 | −0.248367 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 10.2099 | 0.363022 | ||||||||
\(792\) | − 9.33480i | − 0.331698i | ||||||||
\(793\) | 19.4931i | 0.692220i | ||||||||
\(794\) | −65.0637 | −2.30902 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −10.5368 | −0.373469 | ||||||||
\(797\) | − 12.1923i | − 0.431874i | −0.976407 | − | 0.215937i | \(-0.930719\pi\) | ||||
0.976407 | − | 0.215937i | \(-0.0692806\pi\) | |||||||
\(798\) | 5.33800i | 0.188963i | ||||||||
\(799\) | −7.54024 | −0.266754 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.4436 | 0.545673 | ||||||||
\(802\) | 5.35572i | 0.189117i | ||||||||
\(803\) | 3.56080i | 0.125658i | ||||||||
\(804\) | 64.9656 | 2.29116 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.0985 | 1.79987 | ||||||||
\(807\) | − 23.7199i | − 0.834979i | ||||||||
\(808\) | − 117.379i | − 4.12938i | ||||||||
\(809\) | −8.83355 | −0.310571 | −0.155286 | − | 0.987870i | \(-0.549630\pi\) | ||||
−0.155286 | + | 0.987870i | \(0.549630\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.9184 | −0.488741 | −0.244370 | − | 0.969682i | \(-0.578581\pi\) | ||||
−0.244370 | + | 0.969682i | \(0.578581\pi\) | |||||||
\(812\) | 52.4522i | 1.84071i | ||||||||
\(813\) | 28.9910i | 1.01676i | ||||||||
\(814\) | −13.2820 | −0.465535 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 50.3649 | 1.76312 | ||||||||
\(817\) | − 3.04498i | − 0.106530i | ||||||||
\(818\) | 17.9085i | 0.626158i | ||||||||
\(819\) | −4.51660 | −0.157823 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.4930 | −1.02931 | −0.514656 | − | 0.857397i | \(-0.672080\pi\) | ||||
−0.514656 | + | 0.857397i | \(0.672080\pi\) | |||||||
\(822\) | − 55.1113i | − 1.92223i | ||||||||
\(823\) | 41.9661i | 1.46285i | 0.681924 | + | 0.731423i | \(0.261143\pi\) | ||||
−0.681924 | + | 0.731423i | \(0.738857\pi\) | |||||||
\(824\) | 11.8460 | 0.412675 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.05624 | −0.210724 | ||||||||
\(827\) | 37.4674i | 1.30287i | 0.758704 | + | 0.651435i | \(0.225833\pi\) | ||||
−0.758704 | + | 0.651435i | \(0.774167\pi\) | |||||||
\(828\) | 21.2094i | 0.737077i | ||||||||
\(829\) | 9.55614 | 0.331899 | 0.165949 | − | 0.986134i | \(-0.446931\pi\) | ||||
0.165949 | + | 0.986134i | \(0.446931\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.58667 | 0.297868 | ||||||||
\(832\) | 54.5355i | 1.89068i | ||||||||
\(833\) | − 16.3317i | − 0.565860i | ||||||||
\(834\) | −49.2222 | −1.70443 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.63152 | −0.229356 | ||||||||
\(837\) | 7.10310i | 0.245519i | ||||||||
\(838\) | 57.3792i | 1.98213i | ||||||||
\(839\) | −54.7310 | −1.88952 | −0.944761 | − | 0.327759i | \(-0.893707\pi\) | ||||
−0.944761 | + | 0.327759i | \(0.893707\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.47334 | 0.223219 | ||||||||
\(842\) | − 60.0197i | − 2.06842i | ||||||||
\(843\) | 17.1661i | 0.591233i | ||||||||
\(844\) | 124.352 | 4.28037 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.15327 | 0.177173 | ||||||||
\(847\) | − 16.5940i | − 0.570177i | ||||||||
\(848\) | 32.6478i | 1.12113i | ||||||||
\(849\) | −9.62005 | −0.330159 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 18.6159 | 0.638144 | ||||||||
\(852\) | 31.2419i | 1.07033i | ||||||||
\(853\) | 15.3067i | 0.524092i | 0.965055 | + | 0.262046i | \(0.0843972\pi\) | ||||
−0.965055 | + | 0.262046i | \(0.915603\pi\) | |||||||
\(854\) | −33.0062 | −1.12945 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −95.2806 | −3.25662 | ||||||||
\(857\) | − 8.66910i | − 0.296131i | −0.988978 | − | 0.148065i | \(-0.952695\pi\) | ||||
0.988978 | − | 0.148065i | \(-0.0473046\pi\) | |||||||
\(858\) | − 7.76084i | − 0.264951i | ||||||||
\(859\) | 30.4078 | 1.03750 | 0.518750 | − | 0.854926i | \(-0.326397\pi\) | ||||
0.518750 | + | 0.854926i | \(0.326397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.9985 | 0.647468 | ||||||||
\(862\) | 81.7208i | 2.78342i | ||||||||
\(863\) | 18.0425i | 0.614175i | 0.951681 | + | 0.307088i | \(0.0993545\pi\) | ||||
−0.951681 | + | 0.307088i | \(0.900646\pi\) | |||||||
\(864\) | −17.1155 | −0.582283 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.54945 | −0.0526526 | ||||||||
\(867\) | 1.54198i | 0.0523684i | ||||||||
\(868\) | 62.5548i | 2.12325i | ||||||||
\(869\) | 4.31963 | 0.146533 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.3183 | 1.12895 | ||||||||
\(872\) | − 29.8426i | − 1.01060i | ||||||||
\(873\) | − 10.7682i | − 0.364449i | ||||||||
\(874\) | 12.8556 | 0.434848 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.2301 | 0.582149 | ||||||||
\(877\) | 22.3057i | 0.753211i | 0.926374 | + | 0.376605i | \(0.122909\pi\) | ||||
−0.926374 | + | 0.376605i | \(0.877091\pi\) | |||||||
\(878\) | 34.4062i | 1.16115i | ||||||||
\(879\) | 16.8202 | 0.567332 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.75956 | 0.261426 | 0.130713 | − | 0.991420i | \(-0.458273\pi\) | ||||
0.130713 | + | 0.991420i | \(0.458273\pi\) | |||||||
\(882\) | 11.1617i | 0.375833i | ||||||||
\(883\) | 19.9527i | 0.671462i | 0.941958 | + | 0.335731i | \(0.108983\pi\) | ||||
−0.941958 | + | 0.335731i | \(0.891017\pi\) | |||||||
\(884\) | 54.9477 | 1.84809 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −38.4641 | −1.29223 | ||||||||
\(887\) | 8.60289i | 0.288857i | 0.989515 | + | 0.144428i | \(0.0461343\pi\) | ||||
−0.989515 | + | 0.144428i | \(0.953866\pi\) | |||||||
\(888\) | 39.6460i | 1.33043i | ||||||||
\(889\) | 34.1393 | 1.14499 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.07882 | 0.0361418 | ||||||||
\(892\) | 68.4429i | 2.29164i | ||||||||
\(893\) | − 2.25832i | − 0.0755719i | ||||||||
\(894\) | −1.89688 | −0.0634413 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −34.5915 | −1.15562 | ||||||||
\(897\) | 10.8775i | 0.363187i | ||||||||
\(898\) | − 32.1539i | − 1.07299i | ||||||||
\(899\) | 42.3057 | 1.41097 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.0203 | 0.333824 | ||||||||
\(902\) | 32.6450i | 1.08696i | ||||||||
\(903\) | 4.36247i | 0.145174i | ||||||||
\(904\) | 52.3663 | 1.74168 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.9312 | 0.628948 | ||||||||
\(907\) | 6.26125i | 0.207902i | 0.994582 | + | 0.103951i | \(0.0331484\pi\) | ||||
−0.994582 | + | 0.103951i | \(0.966852\pi\) | |||||||
\(908\) | 137.190i | 4.55282i | ||||||||
\(909\) | 13.5654 | 0.449937 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0.905575 | 0.0300030 | 0.0150015 | − | 0.999887i | \(-0.495225\pi\) | ||||
0.0150015 | + | 0.999887i | \(0.495225\pi\) | |||||||
\(912\) | 15.0844i | 0.499495i | ||||||||
\(913\) | − 9.57431i | − 0.316863i | ||||||||
\(914\) | −22.0916 | −0.730726 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.4198 | 0.344279 | ||||||||
\(917\) | − 5.14567i | − 0.169925i | ||||||||
\(918\) | 10.5646i | 0.348682i | ||||||||
\(919\) | −43.9933 | −1.45120 | −0.725602 | − | 0.688114i | \(-0.758439\pi\) | ||||
−0.725602 | + | 0.688114i | \(0.758439\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.3212 | −0.373046 | ||||||||
\(922\) | − 3.41836i | − 0.112578i | ||||||||
\(923\) | 16.0227i | 0.527394i | ||||||||
\(924\) | 9.50081 | 0.312554 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −87.8029 | −2.88538 | ||||||||
\(927\) | 1.36904i | 0.0449651i | ||||||||
\(928\) | 101.939i | 3.34632i | ||||||||
\(929\) | 36.7447 | 1.20555 | 0.602777 | − | 0.797910i | \(-0.294061\pi\) | ||||
0.602777 | + | 0.797910i | \(0.294061\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.89140 | 0.160309 | ||||||||
\(932\) | − 2.74347i | − 0.0898652i | ||||||||
\(933\) | 18.5635i | 0.607740i | ||||||||
\(934\) | 38.7866 | 1.26914 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −23.1656 | −0.757190 | ||||||||
\(937\) | 24.6490i | 0.805248i | 0.915366 | + | 0.402624i | \(0.131902\pi\) | ||||
−0.915366 | + | 0.402624i | \(0.868098\pi\) | |||||||
\(938\) | 56.4153i | 1.84203i | ||||||||
\(939\) | −9.69951 | −0.316532 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.1479 | −1.92817 | −0.964083 | − | 0.265602i | \(-0.914429\pi\) | ||||
−0.964083 | + | 0.265602i | \(0.914429\pi\) | |||||||
\(942\) | − 13.7813i | − 0.449019i | ||||||||
\(943\) | − 45.7546i | − 1.48998i | ||||||||
\(944\) | −17.1141 | −0.557016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.49600 | −0.243716 | ||||||||
\(947\) | − 30.0960i | − 0.977989i | −0.872287 | − | 0.488995i | \(-0.837364\pi\) | ||||
0.872287 | − | 0.488995i | \(-0.162636\pi\) | |||||||
\(948\) | − 20.9019i | − 0.678861i | ||||||||
\(949\) | 8.83661 | 0.286849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.47647 | −0.242441 | ||||||||
\(952\) | 57.3931i | 1.86012i | ||||||||
\(953\) | 20.6393i | 0.668572i | 0.942472 | + | 0.334286i | \(0.108495\pi\) | ||||
−0.942472 | + | 0.334286i | \(0.891505\pi\) | |||||||
\(954\) | −6.84822 | −0.221719 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −36.5921 | −1.18347 | ||||||||
\(957\) | − 6.42538i | − 0.207703i | ||||||||
\(958\) | − 45.3084i | − 1.46385i | ||||||||
\(959\) | 34.6013 | 1.11733 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 19.4540 | 0.627549 | ||||||||
\(962\) | 32.9612i | 1.06271i | ||||||||
\(963\) | − 11.0115i | − 0.354842i | ||||||||
\(964\) | −12.0876 | −0.389315 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −18.4180 | −0.592588 | ||||||||
\(967\) | − 22.6016i | − 0.726817i | −0.931630 | − | 0.363408i | \(-0.881613\pi\) | ||||
0.931630 | − | 0.363408i | \(-0.118387\pi\) | |||||||
\(968\) | − 85.1103i | − 2.73555i | ||||||||
\(969\) | 4.62972 | 0.148728 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 24.1381 | 0.774628 | 0.387314 | − | 0.921948i | \(-0.373403\pi\) | ||||
0.387314 | + | 0.921948i | \(0.373403\pi\) | |||||||
\(972\) | − 5.22020i | − 0.167438i | ||||||||
\(973\) | − 30.9038i | − 0.990732i | ||||||||
\(974\) | 107.007 | 3.42874 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −93.2708 | −2.98553 | ||||||||
\(977\) | 23.0506i | 0.737454i | 0.929538 | + | 0.368727i | \(0.120206\pi\) | ||||
−0.929538 | + | 0.368727i | \(0.879794\pi\) | |||||||
\(978\) | 65.1911i | 2.08458i | ||||||||
\(979\) | −16.6608 | −0.532483 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.44890 | 0.110115 | ||||||||
\(982\) | − 37.6870i | − 1.20264i | ||||||||
\(983\) | − 29.8713i | − 0.952745i | −0.879243 | − | 0.476373i | \(-0.841951\pi\) | ||||
0.879243 | − | 0.476373i | \(-0.158049\pi\) | |||||||
\(984\) | 97.4430 | 3.10637 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 62.9220 | 2.00384 | ||||||||
\(987\) | 3.23544i | 0.102985i | ||||||||
\(988\) | 16.4570i | 0.523567i | ||||||||
\(989\) | 10.5063 | 0.334079 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.6560 | 0.529096 | 0.264548 | − | 0.964372i | \(-0.414777\pi\) | ||||
0.264548 | + | 0.964372i | \(0.414777\pi\) | |||||||
\(992\) | 121.573i | 3.85996i | ||||||||
\(993\) | − 25.2570i | − 0.801507i | ||||||||
\(994\) | −27.1300 | −0.860513 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −46.3283 | −1.46797 | ||||||||
\(997\) | 12.4934i | 0.395669i | 0.980235 | + | 0.197835i | \(0.0633909\pi\) | ||||
−0.980235 | + | 0.197835i | \(0.936609\pi\) | |||||||
\(998\) | 40.9278i | 1.29555i | ||||||||
\(999\) | −4.58187 | −0.144964 |
(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.1249.1 | 12 | ||
5.2 | odd | 4 | 1875.2.a.k.1.6 | 6 | |||
5.3 | odd | 4 | 1875.2.a.j.1.1 | 6 | |||
5.4 | even | 2 | inner | 1875.2.b.f.1249.12 | 12 | ||
15.2 | even | 4 | 5625.2.a.q.1.1 | 6 | |||
15.8 | even | 4 | 5625.2.a.p.1.6 | 6 | |||
25.2 | odd | 20 | 375.2.g.c.226.3 | 12 | |||
25.9 | even | 10 | 375.2.i.d.349.1 | 24 | |||
25.11 | even | 5 | 375.2.i.d.274.1 | 24 | |||
25.12 | odd | 20 | 375.2.g.c.151.3 | 12 | |||
25.13 | odd | 20 | 75.2.g.c.31.1 | ✓ | 12 | ||
25.14 | even | 10 | 375.2.i.d.274.6 | 24 | |||
25.16 | even | 5 | 375.2.i.d.349.6 | 24 | |||
25.23 | odd | 20 | 75.2.g.c.46.1 | yes | 12 | ||
75.23 | even | 20 | 225.2.h.d.46.3 | 12 | |||
75.38 | even | 20 | 225.2.h.d.181.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.g.c.31.1 | ✓ | 12 | 25.13 | odd | 20 | ||
75.2.g.c.46.1 | yes | 12 | 25.23 | odd | 20 | ||
225.2.h.d.46.3 | 12 | 75.23 | even | 20 | |||
225.2.h.d.181.3 | 12 | 75.38 | even | 20 | |||
375.2.g.c.151.3 | 12 | 25.12 | odd | 20 | |||
375.2.g.c.226.3 | 12 | 25.2 | odd | 20 | |||
375.2.i.d.274.1 | 24 | 25.11 | even | 5 | |||
375.2.i.d.274.6 | 24 | 25.14 | even | 10 | |||
375.2.i.d.349.1 | 24 | 25.9 | even | 10 | |||
375.2.i.d.349.6 | 24 | 25.16 | even | 5 | |||
1875.2.a.j.1.1 | 6 | 5.3 | odd | 4 | |||
1875.2.a.k.1.6 | 6 | 5.2 | odd | 4 | |||
1875.2.b.f.1249.1 | 12 | 1.1 | even | 1 | trivial | ||
1875.2.b.f.1249.12 | 12 | 5.4 | even | 2 | inner | ||
5625.2.a.p.1.6 | 6 | 15.8 | even | 4 | |||
5625.2.a.q.1.1 | 6 | 15.2 | even | 4 |