Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.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: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 74) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.3 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.i.149.2 |
$q$-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 \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 0.302776i | − 0.174808i | −0.996173 | − | 0.0874038i | \(-0.972143\pi\) | ||||
0.996173 | − | 0.0874038i | \(-0.0278570\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.302776 | 0.123608 | ||||||||
\(7\) | − 4.60555i | − 1.74073i | −0.492403 | − | 0.870367i | \(-0.663881\pi\) | ||||
0.492403 | − | 0.870367i | \(-0.336119\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.90833 | 0.969442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.30278 | 0.392802 | 0.196401 | − | 0.980524i | \(-0.437075\pi\) | ||||
0.196401 | + | 0.980524i | \(0.437075\pi\) | |||||||
\(12\) | 0.302776i | 0.0874038i | ||||||||
\(13\) | − 2.30278i | − 0.638675i | −0.947641 | − | 0.319338i | \(-0.896540\pi\) | ||||
0.947641 | − | 0.319338i | \(-0.103460\pi\) | |||||||
\(14\) | 4.60555 | 1.23089 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000i | 1.45521i | 0.685994 | + | 0.727607i | \(0.259367\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 2.90833i | 0.685499i | ||||||||
\(19\) | −2.00000 | −0.458831 | −0.229416 | − | 0.973329i | \(-0.573682\pi\) | ||||
−0.229416 | + | 0.973329i | \(0.573682\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.39445 | −0.304294 | ||||||||
\(22\) | 1.30278i | 0.277753i | ||||||||
\(23\) | − 6.90833i | − 1.44049i | −0.693722 | − | 0.720243i | \(-0.744030\pi\) | ||||
0.693722 | − | 0.720243i | \(-0.255970\pi\) | |||||||
\(24\) | −0.302776 | −0.0618038 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.30278 | 0.451611 | ||||||||
\(27\) | − 1.78890i | − 0.344273i | ||||||||
\(28\) | 4.60555i | 0.870367i | ||||||||
\(29\) | −6.90833 | −1.28284 | −0.641422 | − | 0.767188i | \(-0.721655\pi\) | ||||
−0.641422 | + | 0.767188i | \(0.721655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.30278 | 0.593196 | 0.296598 | − | 0.955002i | \(-0.404148\pi\) | ||||
0.296598 | + | 0.955002i | \(0.404148\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 0.394449i | − 0.0686647i | ||||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.90833 | −0.484721 | ||||||||
\(37\) | − 1.00000i | − 0.164399i | ||||||||
\(38\) | − 2.00000i | − 0.324443i | ||||||||
\(39\) | −0.697224 | −0.111645 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.908327 | −0.141857 | −0.0709284 | − | 0.997481i | \(-0.522596\pi\) | ||||
−0.0709284 | + | 0.997481i | \(0.522596\pi\) | |||||||
\(42\) | − 1.39445i | − 0.215168i | ||||||||
\(43\) | − 6.60555i | − 1.00734i | −0.863897 | − | 0.503669i | \(-0.831983\pi\) | ||||
0.863897 | − | 0.503669i | \(-0.168017\pi\) | |||||||
\(44\) | −1.30278 | −0.196401 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.90833 | 1.01858 | ||||||||
\(47\) | 2.60555i | 0.380059i | 0.981778 | + | 0.190029i | \(0.0608583\pi\) | ||||
−0.981778 | + | 0.190029i | \(0.939142\pi\) | |||||||
\(48\) | − 0.302776i | − 0.0437019i | ||||||||
\(49\) | −14.2111 | −2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.81665 | 0.254382 | ||||||||
\(52\) | 2.30278i | 0.319338i | ||||||||
\(53\) | − 6.00000i | − 0.824163i | −0.911147 | − | 0.412082i | \(-0.864802\pi\) | ||||
0.911147 | − | 0.412082i | \(-0.135198\pi\) | |||||||
\(54\) | 1.78890 | 0.243438 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.60555 | −0.615443 | ||||||||
\(57\) | 0.605551i | 0.0802072i | ||||||||
\(58\) | − 6.90833i | − 0.907108i | ||||||||
\(59\) | −3.39445 | −0.441920 | −0.220960 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220960 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.5139 | −1.34616 | −0.673082 | − | 0.739568i | \(-0.735030\pi\) | ||||
−0.673082 | + | 0.739568i | \(0.735030\pi\) | |||||||
\(62\) | 3.30278i | 0.419453i | ||||||||
\(63\) | − 13.3944i | − 1.68754i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.394449 | 0.0485533 | ||||||||
\(67\) | − 14.5139i | − 1.77315i | −0.462583 | − | 0.886576i | \(-0.653077\pi\) | ||||
0.462583 | − | 0.886576i | \(-0.346923\pi\) | |||||||
\(68\) | − 6.00000i | − 0.727607i | ||||||||
\(69\) | −2.09167 | −0.251808 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | − 2.90833i | − 0.342750i | ||||||||
\(73\) | − 8.69722i | − 1.01793i | −0.860786 | − | 0.508967i | \(-0.830028\pi\) | ||||
0.860786 | − | 0.508967i | \(-0.169972\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | 0.229416 | ||||||||
\(77\) | − 6.00000i | − 0.683763i | ||||||||
\(78\) | − 0.697224i | − 0.0789451i | ||||||||
\(79\) | 16.1194 | 1.81358 | 0.906789 | − | 0.421585i | \(-0.138526\pi\) | ||||
0.906789 | + | 0.421585i | \(0.138526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | − 0.908327i | − 0.100308i | ||||||||
\(83\) | 17.2111i | 1.88916i | 0.328276 | + | 0.944582i | \(0.393533\pi\) | ||||
−0.328276 | + | 0.944582i | \(0.606467\pi\) | |||||||
\(84\) | 1.39445 | 0.152147 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 6.60555 | 0.712295 | ||||||||
\(87\) | 2.09167i | 0.224251i | ||||||||
\(88\) | − 1.30278i | − 0.138876i | ||||||||
\(89\) | −5.21110 | −0.552376 | −0.276188 | − | 0.961104i | \(-0.589071\pi\) | ||||
−0.276188 | + | 0.961104i | \(0.589071\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.6056 | −1.11176 | ||||||||
\(92\) | 6.90833i | 0.720243i | ||||||||
\(93\) | − 1.00000i | − 0.103695i | ||||||||
\(94\) | −2.60555 | −0.268742 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.302776 | 0.0309019 | ||||||||
\(97\) | − 12.4222i | − 1.26128i | −0.776074 | − | 0.630642i | \(-0.782792\pi\) | ||||
0.776074 | − | 0.630642i | \(-0.217208\pi\) | |||||||
\(98\) | − 14.2111i | − 1.43554i | ||||||||
\(99\) | 3.78890 | 0.380799 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4222 | 1.63407 | 0.817035 | − | 0.576588i | \(-0.195616\pi\) | ||||
0.817035 | + | 0.576588i | \(0.195616\pi\) | |||||||
\(102\) | 1.81665i | 0.179876i | ||||||||
\(103\) | 3.30278i | 0.325432i | 0.986673 | + | 0.162716i | \(0.0520255\pi\) | ||||
−0.986673 | + | 0.162716i | \(0.947975\pi\) | |||||||
\(104\) | −2.30278 | −0.225806 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.00000 | 0.582772 | ||||||||
\(107\) | − 4.30278i | − 0.415965i | −0.978133 | − | 0.207983i | \(-0.933310\pi\) | ||||
0.978133 | − | 0.207983i | \(-0.0666897\pi\) | |||||||
\(108\) | 1.78890i | 0.172137i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.302776 | −0.0287382 | ||||||||
\(112\) | − 4.60555i | − 0.435184i | ||||||||
\(113\) | 11.2111i | 1.05465i | 0.849663 | + | 0.527326i | \(0.176805\pi\) | ||||
−0.849663 | + | 0.527326i | \(0.823195\pi\) | |||||||
\(114\) | −0.605551 | −0.0567151 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.90833 | 0.641422 | ||||||||
\(117\) | − 6.69722i | − 0.619159i | ||||||||
\(118\) | − 3.39445i | − 0.312484i | ||||||||
\(119\) | 27.6333 | 2.53314 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.30278 | −0.845707 | ||||||||
\(122\) | − 10.5139i | − 0.951882i | ||||||||
\(123\) | 0.275019i | 0.0247977i | ||||||||
\(124\) | −3.30278 | −0.296598 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 13.3944 | 1.19327 | ||||||||
\(127\) | 4.78890i | 0.424946i | 0.977167 | + | 0.212473i | \(0.0681517\pi\) | ||||
−0.977167 | + | 0.212473i | \(0.931848\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −2.00000 | −0.176090 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.39445 | 0.296574 | 0.148287 | − | 0.988944i | \(-0.452624\pi\) | ||||
0.148287 | + | 0.988944i | \(0.452624\pi\) | |||||||
\(132\) | 0.394449i | 0.0343324i | ||||||||
\(133\) | 9.21110i | 0.798704i | ||||||||
\(134\) | 14.5139 | 1.25381 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.00000 | 0.514496 | ||||||||
\(137\) | 9.90833i | 0.846525i | 0.906007 | + | 0.423263i | \(0.139115\pi\) | ||||
−0.906007 | + | 0.423263i | \(0.860885\pi\) | |||||||
\(138\) | − 2.09167i | − 0.178055i | ||||||||
\(139\) | −8.90833 | −0.755594 | −0.377797 | − | 0.925888i | \(-0.623318\pi\) | ||||
−0.377797 | + | 0.925888i | \(0.623318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.788897 | 0.0664372 | ||||||||
\(142\) | 6.00000i | 0.503509i | ||||||||
\(143\) | − 3.00000i | − 0.250873i | ||||||||
\(144\) | 2.90833 | 0.242361 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.69722 | 0.719787 | ||||||||
\(147\) | 4.30278i | 0.354887i | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | 1.81665 | 0.148826 | 0.0744130 | − | 0.997228i | \(-0.476292\pi\) | ||||
0.0744130 | + | 0.997228i | \(0.476292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3944 | −1.09002 | −0.545012 | − | 0.838428i | \(-0.683475\pi\) | ||||
−0.545012 | + | 0.838428i | \(0.683475\pi\) | |||||||
\(152\) | 2.00000i | 0.162221i | ||||||||
\(153\) | 17.4500i | 1.41075i | ||||||||
\(154\) | 6.00000 | 0.483494 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.697224 | 0.0558226 | ||||||||
\(157\) | − 7.21110i | − 0.575509i | −0.957704 | − | 0.287754i | \(-0.907091\pi\) | ||||
0.957704 | − | 0.287754i | \(-0.0929087\pi\) | |||||||
\(158\) | 16.1194i | 1.28239i | ||||||||
\(159\) | −1.81665 | −0.144070 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −31.8167 | −2.50750 | ||||||||
\(162\) | 8.18335i | 0.642944i | ||||||||
\(163\) | − 20.4222i | − 1.59959i | −0.600273 | − | 0.799795i | \(-0.704941\pi\) | ||||
0.600273 | − | 0.799795i | \(-0.295059\pi\) | |||||||
\(164\) | 0.908327 | 0.0709284 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −17.2111 | −1.33584 | ||||||||
\(167\) | − 12.5139i | − 0.968353i | −0.874970 | − | 0.484176i | \(-0.839119\pi\) | ||||
0.874970 | − | 0.484176i | \(-0.160881\pi\) | |||||||
\(168\) | 1.39445i | 0.107584i | ||||||||
\(169\) | 7.69722 | 0.592094 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.81665 | −0.444811 | ||||||||
\(172\) | 6.60555i | 0.503669i | ||||||||
\(173\) | − 23.2111i | − 1.76471i | −0.470587 | − | 0.882354i | \(-0.655958\pi\) | ||||
0.470587 | − | 0.882354i | \(-0.344042\pi\) | |||||||
\(174\) | −2.09167 | −0.158569 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.30278 | 0.0982004 | ||||||||
\(177\) | 1.02776i | 0.0772509i | ||||||||
\(178\) | − 5.21110i | − 0.390589i | ||||||||
\(179\) | −7.81665 | −0.584244 | −0.292122 | − | 0.956381i | \(-0.594361\pi\) | ||||
−0.292122 | + | 0.956381i | \(0.594361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | − 10.6056i | − 0.786136i | ||||||||
\(183\) | 3.18335i | 0.235320i | ||||||||
\(184\) | −6.90833 | −0.509289 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 7.81665i | 0.571610i | ||||||||
\(188\) | − 2.60555i | − 0.190029i | ||||||||
\(189\) | −8.23886 | −0.599289 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.5139 | 0.905472 | 0.452736 | − | 0.891644i | \(-0.350448\pi\) | ||||
0.452736 | + | 0.891644i | \(0.350448\pi\) | |||||||
\(192\) | 0.302776i | 0.0218509i | ||||||||
\(193\) | − 4.00000i | − 0.287926i | −0.989583 | − | 0.143963i | \(-0.954015\pi\) | ||||
0.989583 | − | 0.143963i | \(-0.0459847\pi\) | |||||||
\(194\) | 12.4222 | 0.891862 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 14.2111 | 1.01508 | ||||||||
\(197\) | 6.00000i | 0.427482i | 0.976890 | + | 0.213741i | \(0.0685649\pi\) | ||||
−0.976890 | + | 0.213741i | \(0.931435\pi\) | |||||||
\(198\) | 3.78890i | 0.269265i | ||||||||
\(199\) | 2.42221 | 0.171706 | 0.0858528 | − | 0.996308i | \(-0.472639\pi\) | ||||
0.0858528 | + | 0.996308i | \(0.472639\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.39445 | −0.309961 | ||||||||
\(202\) | 16.4222i | 1.15546i | ||||||||
\(203\) | 31.8167i | 2.23309i | ||||||||
\(204\) | −1.81665 | −0.127191 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.30278 | −0.230115 | ||||||||
\(207\) | − 20.0917i | − 1.39647i | ||||||||
\(208\) | − 2.30278i | − 0.159669i | ||||||||
\(209\) | −2.60555 | −0.180230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.69722 | 0.461056 | 0.230528 | − | 0.973066i | \(-0.425955\pi\) | ||||
0.230528 | + | 0.973066i | \(0.425955\pi\) | |||||||
\(212\) | 6.00000i | 0.412082i | ||||||||
\(213\) | − 1.81665i | − 0.124475i | ||||||||
\(214\) | 4.30278 | 0.294132 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.78890 | −0.121719 | ||||||||
\(217\) | − 15.2111i | − 1.03260i | ||||||||
\(218\) | − 2.00000i | − 0.135457i | ||||||||
\(219\) | −2.63331 | −0.177942 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.8167 | 0.929409 | ||||||||
\(222\) | − 0.302776i | − 0.0203210i | ||||||||
\(223\) | 15.8167i | 1.05916i | 0.848260 | + | 0.529581i | \(0.177651\pi\) | ||||
−0.848260 | + | 0.529581i | \(0.822349\pi\) | |||||||
\(224\) | 4.60555 | 0.307721 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.2111 | −0.745751 | ||||||||
\(227\) | 7.81665i | 0.518810i | 0.965769 | + | 0.259405i | \(0.0835264\pi\) | ||||
−0.965769 | + | 0.259405i | \(0.916474\pi\) | |||||||
\(228\) | − 0.605551i | − 0.0401036i | ||||||||
\(229\) | −17.3944 | −1.14946 | −0.574729 | − | 0.818344i | \(-0.694892\pi\) | ||||
−0.574729 | + | 0.818344i | \(0.694892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.81665 | −0.119527 | ||||||||
\(232\) | 6.90833i | 0.453554i | ||||||||
\(233\) | − 9.51388i | − 0.623275i | −0.950201 | − | 0.311637i | \(-0.899123\pi\) | ||||
0.950201 | − | 0.311637i | \(-0.100877\pi\) | |||||||
\(234\) | 6.69722 | 0.437811 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.39445 | 0.220960 | ||||||||
\(237\) | − 4.88057i | − 0.317027i | ||||||||
\(238\) | 27.6333i | 1.79120i | ||||||||
\(239\) | −0.513878 | −0.0332400 | −0.0166200 | − | 0.999862i | \(-0.505291\pi\) | ||||
−0.0166200 | + | 0.999862i | \(0.505291\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.00000 | 0.515325 | 0.257663 | − | 0.966235i | \(-0.417048\pi\) | ||||
0.257663 | + | 0.966235i | \(0.417048\pi\) | |||||||
\(242\) | − 9.30278i | − 0.598005i | ||||||||
\(243\) | − 7.84441i | − 0.503219i | ||||||||
\(244\) | 10.5139 | 0.673082 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −0.275019 | −0.0175346 | ||||||||
\(247\) | 4.60555i | 0.293044i | ||||||||
\(248\) | − 3.30278i | − 0.209726i | ||||||||
\(249\) | 5.21110 | 0.330240 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.78890 | −0.428511 | −0.214256 | − | 0.976778i | \(-0.568733\pi\) | ||||
−0.214256 | + | 0.976778i | \(0.568733\pi\) | |||||||
\(252\) | 13.3944i | 0.843771i | ||||||||
\(253\) | − 9.00000i | − 0.565825i | ||||||||
\(254\) | −4.78890 | −0.300482 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.2111i | 0.699329i | 0.936875 | + | 0.349665i | \(0.113704\pi\) | ||||
−0.936875 | + | 0.349665i | \(0.886296\pi\) | |||||||
\(258\) | − 2.00000i | − 0.124515i | ||||||||
\(259\) | −4.60555 | −0.286175 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −20.0917 | −1.24364 | ||||||||
\(262\) | 3.39445i | 0.209710i | ||||||||
\(263\) | − 7.81665i | − 0.481996i | −0.970526 | − | 0.240998i | \(-0.922525\pi\) | ||||
0.970526 | − | 0.240998i | \(-0.0774746\pi\) | |||||||
\(264\) | −0.394449 | −0.0242766 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −9.21110 | −0.564769 | ||||||||
\(267\) | 1.57779i | 0.0965595i | ||||||||
\(268\) | 14.5139i | 0.886576i | ||||||||
\(269\) | 6.78890 | 0.413926 | 0.206963 | − | 0.978349i | \(-0.433642\pi\) | ||||
0.206963 | + | 0.978349i | \(0.433642\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.42221 | 0.390121 | 0.195061 | − | 0.980791i | \(-0.437510\pi\) | ||||
0.195061 | + | 0.980791i | \(0.437510\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | 3.21110i | 0.194345i | ||||||||
\(274\) | −9.90833 | −0.598584 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.09167 | 0.125904 | ||||||||
\(277\) | 25.1194i | 1.50928i | 0.656139 | + | 0.754640i | \(0.272189\pi\) | ||||
−0.656139 | + | 0.754640i | \(0.727811\pi\) | |||||||
\(278\) | − 8.90833i | − 0.534286i | ||||||||
\(279\) | 9.60555 | 0.575069 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | 0.788897i | 0.0469782i | ||||||||
\(283\) | 17.3944i | 1.03399i | 0.855988 | + | 0.516996i | \(0.172950\pi\) | ||||
−0.855988 | + | 0.516996i | \(0.827050\pi\) | |||||||
\(284\) | −6.00000 | −0.356034 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.00000 | 0.177394 | ||||||||
\(287\) | 4.18335i | 0.246935i | ||||||||
\(288\) | 2.90833i | 0.171375i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.76114 | −0.220482 | ||||||||
\(292\) | 8.69722i | 0.508967i | ||||||||
\(293\) | − 25.0278i | − 1.46214i | −0.682304 | − | 0.731069i | \(-0.739022\pi\) | ||||
0.682304 | − | 0.731069i | \(-0.260978\pi\) | |||||||
\(294\) | −4.30278 | −0.250943 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | − 2.33053i | − 0.135231i | ||||||||
\(298\) | 1.81665i | 0.105236i | ||||||||
\(299\) | −15.9083 | −0.920002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4222 | −1.75351 | ||||||||
\(302\) | − 13.3944i | − 0.770764i | ||||||||
\(303\) | − 4.97224i | − 0.285648i | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −17.4500 | −0.997548 | ||||||||
\(307\) | − 7.09167i | − 0.404743i | −0.979309 | − | 0.202372i | \(-0.935135\pi\) | ||||
0.979309 | − | 0.202372i | \(-0.0648649\pi\) | |||||||
\(308\) | 6.00000i | 0.341882i | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.09167 | 0.288722 | 0.144361 | − | 0.989525i | \(-0.453887\pi\) | ||||
0.144361 | + | 0.989525i | \(0.453887\pi\) | |||||||
\(312\) | 0.697224i | 0.0394726i | ||||||||
\(313\) | 27.0278i | 1.52770i | 0.645394 | + | 0.763850i | \(0.276693\pi\) | ||||
−0.645394 | + | 0.763850i | \(0.723307\pi\) | |||||||
\(314\) | 7.21110 | 0.406946 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.1194 | −0.906789 | ||||||||
\(317\) | 5.21110i | 0.292685i | 0.989234 | + | 0.146342i | \(0.0467501\pi\) | ||||
−0.989234 | + | 0.146342i | \(0.953250\pi\) | |||||||
\(318\) | − 1.81665i | − 0.101873i | ||||||||
\(319\) | −9.00000 | −0.503903 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.30278 | −0.0727138 | ||||||||
\(322\) | − 31.8167i | − 1.77307i | ||||||||
\(323\) | − 12.0000i | − 0.667698i | ||||||||
\(324\) | −8.18335 | −0.454630 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.4222 | 1.13108 | ||||||||
\(327\) | 0.605551i | 0.0334871i | ||||||||
\(328\) | 0.908327i | 0.0501540i | ||||||||
\(329\) | 12.0000 | 0.661581 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.21110 | 0.0665682 | 0.0332841 | − | 0.999446i | \(-0.489403\pi\) | ||||
0.0332841 | + | 0.999446i | \(0.489403\pi\) | |||||||
\(332\) | − 17.2111i | − 0.944582i | ||||||||
\(333\) | − 2.90833i | − 0.159375i | ||||||||
\(334\) | 12.5139 | 0.684729 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.39445 | −0.0760734 | ||||||||
\(337\) | 19.1194i | 1.04150i | 0.853709 | + | 0.520751i | \(0.174348\pi\) | ||||
−0.853709 | + | 0.520751i | \(0.825652\pi\) | |||||||
\(338\) | 7.69722i | 0.418674i | ||||||||
\(339\) | 3.39445 | 0.184361 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.30278 | 0.233008 | ||||||||
\(342\) | − 5.81665i | − 0.314529i | ||||||||
\(343\) | 33.2111i | 1.79323i | ||||||||
\(344\) | −6.60555 | −0.356147 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.2111 | 1.24784 | ||||||||
\(347\) | − 31.8167i | − 1.70801i | −0.520267 | − | 0.854004i | \(-0.674168\pi\) | ||||
0.520267 | − | 0.854004i | \(-0.325832\pi\) | |||||||
\(348\) | − 2.09167i | − 0.112125i | ||||||||
\(349\) | 22.2389 | 1.19042 | 0.595209 | − | 0.803571i | \(-0.297069\pi\) | ||||
0.595209 | + | 0.803571i | \(0.297069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.11943 | −0.219879 | ||||||||
\(352\) | 1.30278i | 0.0694382i | ||||||||
\(353\) | 31.8167i | 1.69343i | 0.532047 | + | 0.846715i | \(0.321423\pi\) | ||||
−0.532047 | + | 0.846715i | \(0.678577\pi\) | |||||||
\(354\) | −1.02776 | −0.0546246 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.21110 | 0.276188 | ||||||||
\(357\) | − 8.36669i | − 0.442812i | ||||||||
\(358\) | − 7.81665i | − 0.413123i | ||||||||
\(359\) | 11.2111 | 0.591699 | 0.295850 | − | 0.955235i | \(-0.404397\pi\) | ||||
0.295850 | + | 0.955235i | \(0.404397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 20.0000i | 1.05118i | ||||||||
\(363\) | 2.81665i | 0.147836i | ||||||||
\(364\) | 10.6056 | 0.555882 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.18335 | −0.166396 | ||||||||
\(367\) | 17.8167i | 0.930022i | 0.885305 | + | 0.465011i | \(0.153950\pi\) | ||||
−0.885305 | + | 0.465011i | \(0.846050\pi\) | |||||||
\(368\) | − 6.90833i | − 0.360121i | ||||||||
\(369\) | −2.64171 | −0.137522 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −27.6333 | −1.43465 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | 3.81665i | 0.197619i | 0.995106 | + | 0.0988094i | \(0.0315034\pi\) | ||||
−0.995106 | + | 0.0988094i | \(0.968497\pi\) | |||||||
\(374\) | −7.81665 | −0.404190 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.60555 | 0.134371 | ||||||||
\(377\) | 15.9083i | 0.819321i | ||||||||
\(378\) | − 8.23886i | − 0.423761i | ||||||||
\(379\) | 15.3305 | 0.787477 | 0.393738 | − | 0.919223i | \(-0.371182\pi\) | ||||
0.393738 | + | 0.919223i | \(0.371182\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.44996 | 0.0742838 | ||||||||
\(382\) | 12.5139i | 0.640266i | ||||||||
\(383\) | 20.8444i | 1.06510i | 0.846399 | + | 0.532550i | \(0.178766\pi\) | ||||
−0.846399 | + | 0.532550i | \(0.821234\pi\) | |||||||
\(384\) | −0.302776 | −0.0154510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.00000 | 0.203595 | ||||||||
\(387\) | − 19.2111i | − 0.976555i | ||||||||
\(388\) | 12.4222i | 0.630642i | ||||||||
\(389\) | 11.8806 | 0.602369 | 0.301184 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301184 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.4500 | 2.09621 | ||||||||
\(392\) | 14.2111i | 0.717769i | ||||||||
\(393\) | − 1.02776i | − 0.0518435i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.78890 | −0.190399 | ||||||||
\(397\) | − 27.8167i | − 1.39608i | −0.716060 | − | 0.698039i | \(-0.754056\pi\) | ||||
0.716060 | − | 0.698039i | \(-0.245944\pi\) | |||||||
\(398\) | 2.42221i | 0.121414i | ||||||||
\(399\) | 2.78890 | 0.139620 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.8167 | 0.689971 | 0.344985 | − | 0.938608i | \(-0.387884\pi\) | ||||
0.344985 | + | 0.938608i | \(0.387884\pi\) | |||||||
\(402\) | − 4.39445i | − 0.219175i | ||||||||
\(403\) | − 7.60555i | − 0.378859i | ||||||||
\(404\) | −16.4222 | −0.817035 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −31.8167 | −1.57903 | ||||||||
\(407\) | − 1.30278i | − 0.0645762i | ||||||||
\(408\) | − 1.81665i | − 0.0899378i | ||||||||
\(409\) | 5.02776 | 0.248607 | 0.124303 | − | 0.992244i | \(-0.460330\pi\) | ||||
0.124303 | + | 0.992244i | \(0.460330\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | − 3.30278i | − 0.162716i | ||||||||
\(413\) | 15.6333i | 0.769265i | ||||||||
\(414\) | 20.0917 | 0.987452 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.30278 | 0.112903 | ||||||||
\(417\) | 2.69722i | 0.132084i | ||||||||
\(418\) | − 2.60555i | − 0.127442i | ||||||||
\(419\) | 25.1472 | 1.22852 | 0.614260 | − | 0.789104i | \(-0.289455\pi\) | ||||
0.614260 | + | 0.789104i | \(0.289455\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.7250 | 1.39997 | 0.699985 | − | 0.714158i | \(-0.253190\pi\) | ||||
0.699985 | + | 0.714158i | \(0.253190\pi\) | |||||||
\(422\) | 6.69722i | 0.326016i | ||||||||
\(423\) | 7.57779i | 0.368445i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.81665 | 0.0880172 | ||||||||
\(427\) | 48.4222i | 2.34331i | ||||||||
\(428\) | 4.30278i | 0.207983i | ||||||||
\(429\) | −0.908327 | −0.0438544 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.21110 | −0.251010 | −0.125505 | − | 0.992093i | \(-0.540055\pi\) | ||||
−0.125505 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(432\) | − 1.78890i | − 0.0860684i | ||||||||
\(433\) | − 11.9361i | − 0.573612i | −0.957989 | − | 0.286806i | \(-0.907407\pi\) | ||||
0.957989 | − | 0.286806i | \(-0.0925934\pi\) | |||||||
\(434\) | 15.2111 | 0.730156 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 13.8167i | 0.660940i | ||||||||
\(438\) | − 2.63331i | − 0.125824i | ||||||||
\(439\) | 9.33053 | 0.445322 | 0.222661 | − | 0.974896i | \(-0.428526\pi\) | ||||
0.222661 | + | 0.974896i | \(0.428526\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −41.3305 | −1.96812 | ||||||||
\(442\) | 13.8167i | 0.657191i | ||||||||
\(443\) | 0.275019i | 0.0130666i | 0.999979 | + | 0.00653328i | \(0.00207962\pi\) | ||||
−0.999979 | + | 0.00653328i | \(0.997920\pi\) | |||||||
\(444\) | 0.302776 | 0.0143691 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.8167 | −0.748940 | ||||||||
\(447\) | − 0.550039i | − 0.0260159i | ||||||||
\(448\) | 4.60555i | 0.217592i | ||||||||
\(449\) | 0.788897 | 0.0372304 | 0.0186152 | − | 0.999827i | \(-0.494074\pi\) | ||||
0.0186152 | + | 0.999827i | \(0.494074\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.18335 | −0.0557216 | ||||||||
\(452\) | − 11.2111i | − 0.527326i | ||||||||
\(453\) | 4.05551i | 0.190545i | ||||||||
\(454\) | −7.81665 | −0.366854 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.605551 | 0.0283575 | ||||||||
\(457\) | − 4.60555i | − 0.215439i | −0.994181 | − | 0.107719i | \(-0.965645\pi\) | ||||
0.994181 | − | 0.107719i | \(-0.0343548\pi\) | |||||||
\(458\) | − 17.3944i | − 0.812789i | ||||||||
\(459\) | 10.7334 | 0.500991 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.4222 | −0.764858 | −0.382429 | − | 0.923985i | \(-0.624912\pi\) | ||||
−0.382429 | + | 0.923985i | \(0.624912\pi\) | |||||||
\(462\) | − 1.81665i | − 0.0845184i | ||||||||
\(463\) | 30.3028i | 1.40829i | 0.710056 | + | 0.704145i | \(0.248669\pi\) | ||||
−0.710056 | + | 0.704145i | \(0.751331\pi\) | |||||||
\(464\) | −6.90833 | −0.320711 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.51388 | 0.440722 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 6.69722i | 0.309579i | ||||||||
\(469\) | −66.8444 | −3.08659 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.18335 | −0.100603 | ||||||||
\(472\) | 3.39445i | 0.156242i | ||||||||
\(473\) | − 8.60555i | − 0.395684i | ||||||||
\(474\) | 4.88057 | 0.224172 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −27.6333 | −1.26657 | ||||||||
\(477\) | − 17.4500i | − 0.798979i | ||||||||
\(478\) | − 0.513878i | − 0.0235042i | ||||||||
\(479\) | −12.1194 | −0.553751 | −0.276875 | − | 0.960906i | \(-0.589299\pi\) | ||||
−0.276875 | + | 0.960906i | \(0.589299\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.30278 | −0.104998 | ||||||||
\(482\) | 8.00000i | 0.364390i | ||||||||
\(483\) | 9.63331i | 0.438331i | ||||||||
\(484\) | 9.30278 | 0.422853 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.84441 | 0.355830 | ||||||||
\(487\) | 22.7889i | 1.03266i | 0.856389 | + | 0.516332i | \(0.172703\pi\) | ||||
−0.856389 | + | 0.516332i | \(0.827297\pi\) | |||||||
\(488\) | 10.5139i | 0.475941i | ||||||||
\(489\) | −6.18335 | −0.279621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −14.7250 | −0.664529 | −0.332265 | − | 0.943186i | \(-0.607813\pi\) | ||||
−0.332265 | + | 0.943186i | \(0.607813\pi\) | |||||||
\(492\) | − 0.275019i | − 0.0123988i | ||||||||
\(493\) | − 41.4500i | − 1.86681i | ||||||||
\(494\) | −4.60555 | −0.207214 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.30278 | 0.148299 | ||||||||
\(497\) | − 27.6333i | − 1.23952i | ||||||||
\(498\) | 5.21110i | 0.233515i | ||||||||
\(499\) | −8.23886 | −0.368822 | −0.184411 | − | 0.982849i | \(-0.559038\pi\) | ||||
−0.184411 | + | 0.982849i | \(0.559038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.78890 | −0.169275 | ||||||||
\(502\) | − 6.78890i | − 0.303003i | ||||||||
\(503\) | − 24.5139i | − 1.09302i | −0.837453 | − | 0.546510i | \(-0.815956\pi\) | ||||
0.837453 | − | 0.546510i | \(-0.184044\pi\) | |||||||
\(504\) | −13.3944 | −0.596636 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 9.00000 | 0.400099 | ||||||||
\(507\) | − 2.33053i | − 0.103503i | ||||||||
\(508\) | − 4.78890i | − 0.212473i | ||||||||
\(509\) | 25.8167 | 1.14430 | 0.572152 | − | 0.820148i | \(-0.306109\pi\) | ||||
0.572152 | + | 0.820148i | \(0.306109\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −40.0555 | −1.77195 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 3.57779i | 0.157964i | ||||||||
\(514\) | −11.2111 | −0.494501 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | 0.0880451 | ||||||||
\(517\) | 3.39445i | 0.149288i | ||||||||
\(518\) | − 4.60555i | − 0.202356i | ||||||||
\(519\) | −7.02776 | −0.308484 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.63331 | −0.422043 | −0.211021 | − | 0.977481i | \(-0.567679\pi\) | ||||
−0.211021 | + | 0.977481i | \(0.567679\pi\) | |||||||
\(522\) | − 20.0917i | − 0.879389i | ||||||||
\(523\) | 32.2389i | 1.40971i | 0.709353 | + | 0.704853i | \(0.248987\pi\) | ||||
−0.709353 | + | 0.704853i | \(0.751013\pi\) | |||||||
\(524\) | −3.39445 | −0.148287 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.81665 | 0.340822 | ||||||||
\(527\) | 19.8167i | 0.863227i | ||||||||
\(528\) | − 0.394449i | − 0.0171662i | ||||||||
\(529\) | −24.7250 | −1.07500 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.87217 | −0.428416 | ||||||||
\(532\) | − 9.21110i | − 0.399352i | ||||||||
\(533\) | 2.09167i | 0.0906004i | ||||||||
\(534\) | −1.57779 | −0.0682779 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −14.5139 | −0.626904 | ||||||||
\(537\) | 2.36669i | 0.102130i | ||||||||
\(538\) | 6.78890i | 0.292690i | ||||||||
\(539\) | −18.5139 | −0.797449 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.9361 | −0.900113 | −0.450056 | − | 0.893000i | \(-0.648596\pi\) | ||||
−0.450056 | + | 0.893000i | \(0.648596\pi\) | |||||||
\(542\) | 6.42221i | 0.275857i | ||||||||
\(543\) | − 6.05551i | − 0.259867i | ||||||||
\(544\) | −6.00000 | −0.257248 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3.21110 | −0.137423 | ||||||||
\(547\) | 13.3944i | 0.572705i | 0.958124 | + | 0.286353i | \(0.0924429\pi\) | ||||
−0.958124 | + | 0.286353i | \(0.907557\pi\) | |||||||
\(548\) | − 9.90833i | − 0.423263i | ||||||||
\(549\) | −30.5778 | −1.30503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 13.8167 | 0.588609 | ||||||||
\(552\) | 2.09167i | 0.0890275i | ||||||||
\(553\) | − 74.2389i | − 3.15696i | ||||||||
\(554\) | −25.1194 | −1.06722 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.90833 | 0.377797 | ||||||||
\(557\) | 6.51388i | 0.276002i | 0.990432 | + | 0.138001i | \(0.0440677\pi\) | ||||
−0.990432 | + | 0.138001i | \(0.955932\pi\) | |||||||
\(558\) | 9.60555i | 0.406635i | ||||||||
\(559\) | −15.2111 | −0.643361 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.36669 | 0.0999218 | ||||||||
\(562\) | − 12.0000i | − 0.506189i | ||||||||
\(563\) | 44.0555i | 1.85672i | 0.371684 | + | 0.928359i | \(0.378780\pi\) | ||||
−0.371684 | + | 0.928359i | \(0.621220\pi\) | |||||||
\(564\) | −0.788897 | −0.0332186 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −17.3944 | −0.731143 | ||||||||
\(567\) | − 37.6888i | − 1.58278i | ||||||||
\(568\) | − 6.00000i | − 0.251754i | ||||||||
\(569\) | 10.4222 | 0.436922 | 0.218461 | − | 0.975846i | \(-0.429896\pi\) | ||||
0.218461 | + | 0.975846i | \(0.429896\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3028 | −0.849645 | −0.424822 | − | 0.905277i | \(-0.639663\pi\) | ||||
−0.424822 | + | 0.905277i | \(0.639663\pi\) | |||||||
\(572\) | 3.00000i | 0.125436i | ||||||||
\(573\) | − 3.78890i | − 0.158283i | ||||||||
\(574\) | −4.18335 | −0.174609 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.90833 | −0.121180 | ||||||||
\(577\) | 28.2389i | 1.17560i | 0.809007 | + | 0.587800i | \(0.200006\pi\) | ||||
−0.809007 | + | 0.587800i | \(0.799994\pi\) | |||||||
\(578\) | − 19.0000i | − 0.790296i | ||||||||
\(579\) | −1.21110 | −0.0503317 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 79.2666 | 3.28853 | ||||||||
\(582\) | − 3.76114i | − 0.155904i | ||||||||
\(583\) | − 7.81665i | − 0.323733i | ||||||||
\(584\) | −8.69722 | −0.359894 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.0278 | 1.03389 | ||||||||
\(587\) | 2.36669i | 0.0976838i | 0.998807 | + | 0.0488419i | \(0.0155531\pi\) | ||||
−0.998807 | + | 0.0488419i | \(0.984447\pi\) | |||||||
\(588\) | − 4.30278i | − 0.177443i | ||||||||
\(589\) | −6.60555 | −0.272177 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.81665 | 0.0747272 | ||||||||
\(592\) | − 1.00000i | − 0.0410997i | ||||||||
\(593\) | 36.5139i | 1.49945i | 0.661752 | + | 0.749723i | \(0.269813\pi\) | ||||
−0.661752 | + | 0.749723i | \(0.730187\pi\) | |||||||
\(594\) | 2.33053 | 0.0956229 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.81665 | −0.0744130 | ||||||||
\(597\) | − 0.733385i | − 0.0300154i | ||||||||
\(598\) | − 15.9083i | − 0.650540i | ||||||||
\(599\) | 35.2111 | 1.43869 | 0.719343 | − | 0.694655i | \(-0.244443\pi\) | ||||
0.719343 | + | 0.694655i | \(0.244443\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.6972 | −0.844257 | −0.422129 | − | 0.906536i | \(-0.638717\pi\) | ||||
−0.422129 | + | 0.906536i | \(0.638717\pi\) | |||||||
\(602\) | − 30.4222i | − 1.23992i | ||||||||
\(603\) | − 42.2111i | − 1.71897i | ||||||||
\(604\) | 13.3944 | 0.545012 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.97224 | 0.201984 | ||||||||
\(607\) | 31.5139i | 1.27911i | 0.768746 | + | 0.639554i | \(0.220881\pi\) | ||||
−0.768746 | + | 0.639554i | \(0.779119\pi\) | |||||||
\(608\) | − 2.00000i | − 0.0811107i | ||||||||
\(609\) | 9.63331 | 0.390361 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.00000 | 0.242734 | ||||||||
\(612\) | − 17.4500i | − 0.705373i | ||||||||
\(613\) | − 8.18335i | − 0.330522i | −0.986250 | − | 0.165261i | \(-0.947153\pi\) | ||||
0.986250 | − | 0.165261i | \(-0.0528467\pi\) | |||||||
\(614\) | 7.09167 | 0.286197 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | − 47.5694i | − 1.91507i | −0.288314 | − | 0.957536i | \(-0.593095\pi\) | ||||
0.288314 | − | 0.957536i | \(-0.406905\pi\) | |||||||
\(618\) | 1.00000i | 0.0402259i | ||||||||
\(619\) | 2.69722 | 0.108411 | 0.0542053 | − | 0.998530i | \(-0.482737\pi\) | ||||
0.0542053 | + | 0.998530i | \(0.482737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −12.3583 | −0.495921 | ||||||||
\(622\) | 5.09167i | 0.204157i | ||||||||
\(623\) | 24.0000i | 0.961540i | ||||||||
\(624\) | −0.697224 | −0.0279113 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −27.0278 | −1.08025 | ||||||||
\(627\) | 0.788897i | 0.0315055i | ||||||||
\(628\) | 7.21110i | 0.287754i | ||||||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.3028 | 0.728622 | 0.364311 | − | 0.931277i | \(-0.381305\pi\) | ||||
0.364311 | + | 0.931277i | \(0.381305\pi\) | |||||||
\(632\) | − 16.1194i | − 0.641196i | ||||||||
\(633\) | − 2.02776i | − 0.0805961i | ||||||||
\(634\) | −5.21110 | −0.206959 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.81665 | 0.0720350 | ||||||||
\(637\) | 32.7250i | 1.29661i | ||||||||
\(638\) | − 9.00000i | − 0.356313i | ||||||||
\(639\) | 17.4500 | 0.690310 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.48612 | −0.0981959 | −0.0490980 | − | 0.998794i | \(-0.515635\pi\) | ||||
−0.0490980 | + | 0.998794i | \(0.515635\pi\) | |||||||
\(642\) | − 1.30278i | − 0.0514165i | ||||||||
\(643\) | − 29.8167i | − 1.17585i | −0.808914 | − | 0.587927i | \(-0.799944\pi\) | ||||
0.808914 | − | 0.587927i | \(-0.200056\pi\) | |||||||
\(644\) | 31.8167 | 1.25375 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 12.0000 | 0.472134 | ||||||||
\(647\) | 25.9361i | 1.01965i | 0.860277 | + | 0.509826i | \(0.170290\pi\) | ||||
−0.860277 | + | 0.509826i | \(0.829710\pi\) | |||||||
\(648\) | − 8.18335i | − 0.321472i | ||||||||
\(649\) | −4.42221 | −0.173587 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.60555 | −0.180506 | ||||||||
\(652\) | 20.4222i | 0.799795i | ||||||||
\(653\) | 6.90833i | 0.270344i | 0.990822 | + | 0.135172i | \(0.0431587\pi\) | ||||
−0.990822 | + | 0.135172i | \(0.956841\pi\) | |||||||
\(654\) | −0.605551 | −0.0236789 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −0.908327 | −0.0354642 | ||||||||
\(657\) | − 25.2944i | − 0.986827i | ||||||||
\(658\) | 12.0000i | 0.467809i | ||||||||
\(659\) | 42.1194 | 1.64074 | 0.820370 | − | 0.571833i | \(-0.193767\pi\) | ||||
0.820370 | + | 0.571833i | \(0.193767\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.4861 | −0.485654 | −0.242827 | − | 0.970070i | \(-0.578075\pi\) | ||||
−0.242827 | + | 0.970070i | \(0.578075\pi\) | |||||||
\(662\) | 1.21110i | 0.0470708i | ||||||||
\(663\) | − 4.18335i | − 0.162468i | ||||||||
\(664\) | 17.2111 | 0.667920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.90833 | 0.112695 | ||||||||
\(667\) | 47.7250i | 1.84792i | ||||||||
\(668\) | 12.5139i | 0.484176i | ||||||||
\(669\) | 4.78890 | 0.185149 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.6972 | −0.528775 | ||||||||
\(672\) | − 1.39445i | − 0.0537920i | ||||||||
\(673\) | 24.3028i | 0.936803i | 0.883516 | + | 0.468402i | \(0.155170\pi\) | ||||
−0.883516 | + | 0.468402i | \(0.844830\pi\) | |||||||
\(674\) | −19.1194 | −0.736453 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.69722 | −0.296047 | ||||||||
\(677\) | 36.2389i | 1.39277i | 0.717667 | + | 0.696386i | \(0.245210\pi\) | ||||
−0.717667 | + | 0.696386i | \(0.754790\pi\) | |||||||
\(678\) | 3.39445i | 0.130363i | ||||||||
\(679\) | −57.2111 | −2.19556 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.36669 | 0.0906918 | ||||||||
\(682\) | 4.30278i | 0.164762i | ||||||||
\(683\) | 12.0000i | 0.459167i | 0.973289 | + | 0.229584i | \(0.0737364\pi\) | ||||
−0.973289 | + | 0.229584i | \(0.926264\pi\) | |||||||
\(684\) | 5.81665 | 0.222405 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −33.2111 | −1.26801 | ||||||||
\(687\) | 5.26662i | 0.200934i | ||||||||
\(688\) | − 6.60555i | − 0.251834i | ||||||||
\(689\) | −13.8167 | −0.526373 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | 23.2111i | 0.882354i | ||||||||
\(693\) | − 17.4500i | − 0.662869i | ||||||||
\(694\) | 31.8167 | 1.20774 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2.09167 | 0.0792847 | ||||||||
\(697\) | − 5.44996i | − 0.206432i | ||||||||
\(698\) | 22.2389i | 0.841753i | ||||||||
\(699\) | −2.88057 | −0.108953 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.8806 | 0.562031 | 0.281016 | − | 0.959703i | \(-0.409329\pi\) | ||||
0.281016 | + | 0.959703i | \(0.409329\pi\) | |||||||
\(702\) | − 4.11943i | − 0.155478i | ||||||||
\(703\) | 2.00000i | 0.0754314i | ||||||||
\(704\) | −1.30278 | −0.0491002 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −31.8167 | −1.19744 | ||||||||
\(707\) | − 75.6333i | − 2.84448i | ||||||||
\(708\) | − 1.02776i | − 0.0386254i | ||||||||
\(709\) | 1.66947 | 0.0626982 | 0.0313491 | − | 0.999508i | \(-0.490020\pi\) | ||||
0.0313491 | + | 0.999508i | \(0.490020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 46.8806 | 1.75816 | ||||||||
\(712\) | 5.21110i | 0.195294i | ||||||||
\(713\) | − 22.8167i | − 0.854490i | ||||||||
\(714\) | 8.36669 | 0.313116 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 7.81665 | 0.292122 | ||||||||
\(717\) | 0.155590i | 0.00581061i | ||||||||
\(718\) | 11.2111i | 0.418395i | ||||||||
\(719\) | 8.36669 | 0.312025 | 0.156012 | − | 0.987755i | \(-0.450136\pi\) | ||||
0.156012 | + | 0.987755i | \(0.450136\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.2111 | 0.566491 | ||||||||
\(722\) | − 15.0000i | − 0.558242i | ||||||||
\(723\) | − 2.42221i | − 0.0900828i | ||||||||
\(724\) | −20.0000 | −0.743294 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.81665 | −0.104536 | ||||||||
\(727\) | − 29.9083i | − 1.10924i | −0.832104 | − | 0.554619i | \(-0.812864\pi\) | ||||
0.832104 | − | 0.554619i | \(-0.187136\pi\) | |||||||
\(728\) | 10.6056i | 0.393068i | ||||||||
\(729\) | 22.1749 | 0.821294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 39.6333 | 1.46589 | ||||||||
\(732\) | − 3.18335i | − 0.117660i | ||||||||
\(733\) | 29.6333i | 1.09453i | 0.836959 | + | 0.547266i | \(0.184331\pi\) | ||||
−0.836959 | + | 0.547266i | \(0.815669\pi\) | |||||||
\(734\) | −17.8167 | −0.657625 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.90833 | 0.254644 | ||||||||
\(737\) | − 18.9083i | − 0.696497i | ||||||||
\(738\) | − 2.64171i | − 0.0972427i | ||||||||
\(739\) | 42.3305 | 1.55715 | 0.778577 | − | 0.627549i | \(-0.215942\pi\) | ||||
0.778577 | + | 0.627549i | \(0.215942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.39445 | 0.0512264 | ||||||||
\(742\) | − 27.6333i | − 1.01445i | ||||||||
\(743\) | 35.4500i | 1.30053i | 0.759706 | + | 0.650266i | \(0.225343\pi\) | ||||
−0.759706 | + | 0.650266i | \(0.774657\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.81665 | −0.139738 | ||||||||
\(747\) | 50.0555i | 1.83144i | ||||||||
\(748\) | − 7.81665i | − 0.285805i | ||||||||
\(749\) | −19.8167 | −0.724085 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.0000 | 0.510867 | 0.255434 | − | 0.966827i | \(-0.417782\pi\) | ||||
0.255434 | + | 0.966827i | \(0.417782\pi\) | |||||||
\(752\) | 2.60555i | 0.0950147i | ||||||||
\(753\) | 2.05551i | 0.0749070i | ||||||||
\(754\) | −15.9083 | −0.579347 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 8.23886 | 0.299644 | ||||||||
\(757\) | − 9.30278i | − 0.338115i | −0.985606 | − | 0.169058i | \(-0.945928\pi\) | ||||
0.985606 | − | 0.169058i | \(-0.0540724\pi\) | |||||||
\(758\) | 15.3305i | 0.556830i | ||||||||
\(759\) | −2.72498 | −0.0989105 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 42.1194 | 1.52683 | 0.763414 | − | 0.645909i | \(-0.223522\pi\) | ||||
0.763414 | + | 0.645909i | \(0.223522\pi\) | |||||||
\(762\) | 1.44996i | 0.0525266i | ||||||||
\(763\) | 9.21110i | 0.333464i | ||||||||
\(764\) | −12.5139 | −0.452736 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −20.8444 | −0.753139 | ||||||||
\(767\) | 7.81665i | 0.282243i | ||||||||
\(768\) | − 0.302776i | − 0.0109255i | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.39445 | 0.122248 | ||||||||
\(772\) | 4.00000i | 0.143963i | ||||||||
\(773\) | − 50.0555i | − 1.80037i | −0.435506 | − | 0.900186i | \(-0.643431\pi\) | ||||
0.435506 | − | 0.900186i | \(-0.356569\pi\) | |||||||
\(774\) | 19.2111 | 0.690529 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.4222 | −0.445931 | ||||||||
\(777\) | 1.39445i | 0.0500256i | ||||||||
\(778\) | 11.8806i | 0.425939i | ||||||||
\(779\) | 1.81665 | 0.0650884 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.81665 | 0.279702 | ||||||||
\(782\) | 41.4500i | 1.48225i | ||||||||
\(783\) | 12.3583i | 0.441649i | ||||||||
\(784\) | −14.2111 | −0.507539 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.02776 | 0.0366589 | ||||||||
\(787\) | − 25.2111i | − 0.898679i | −0.893361 | − | 0.449339i | \(-0.851659\pi\) | ||||
0.893361 | − | 0.449339i | \(-0.148341\pi\) | |||||||
\(788\) | − 6.00000i | − 0.213741i | ||||||||
\(789\) | −2.36669 | −0.0842565 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 51.6333 | 1.83587 | ||||||||
\(792\) | − 3.78890i | − 0.134633i | ||||||||
\(793\) | 24.2111i | 0.859761i | ||||||||
\(794\) | 27.8167 | 0.987176 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.42221 | −0.0858528 | ||||||||
\(797\) | 17.3305i | 0.613879i | 0.951729 | + | 0.306939i | \(0.0993049\pi\) | ||||
−0.951729 | + | 0.306939i | \(0.900695\pi\) | |||||||
\(798\) | 2.78890i | 0.0987259i | ||||||||
\(799\) | −15.6333 | −0.553067 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.1556 | −0.535496 | ||||||||
\(802\) | 13.8167i | 0.487883i | ||||||||
\(803\) | − 11.3305i | − 0.399846i | ||||||||
\(804\) | 4.39445 | 0.154980 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.60555 | 0.267894 | ||||||||
\(807\) | − 2.05551i | − 0.0723575i | ||||||||
\(808\) | − 16.4222i | − 0.577731i | ||||||||
\(809\) | −29.4500 | −1.03541 | −0.517703 | − | 0.855561i | \(-0.673213\pi\) | ||||
−0.517703 | + | 0.855561i | \(0.673213\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.1472 | 1.90136 | 0.950682 | − | 0.310166i | \(-0.100385\pi\) | ||||
0.950682 | + | 0.310166i | \(0.100385\pi\) | |||||||
\(812\) | − 31.8167i | − 1.11655i | ||||||||
\(813\) | − 1.94449i | − 0.0681961i | ||||||||
\(814\) | 1.30278 | 0.0456623 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.81665 | 0.0635956 | ||||||||
\(817\) | 13.2111i | 0.462198i | ||||||||
\(818\) | 5.02776i | 0.175791i | ||||||||
\(819\) | −30.8444 | −1.07779 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.2111 | 0.391270 | 0.195635 | − | 0.980677i | \(-0.437323\pi\) | ||||
0.195635 | + | 0.980677i | \(0.437323\pi\) | |||||||
\(822\) | 3.00000i | 0.104637i | ||||||||
\(823\) | − 12.8444i | − 0.447728i | −0.974620 | − | 0.223864i | \(-0.928133\pi\) | ||||
0.974620 | − | 0.223864i | \(-0.0718671\pi\) | |||||||
\(824\) | 3.30278 | 0.115058 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.6333 | −0.543952 | ||||||||
\(827\) | − 27.3944i | − 0.952598i | −0.879283 | − | 0.476299i | \(-0.841978\pi\) | ||||
0.879283 | − | 0.476299i | \(-0.158022\pi\) | |||||||
\(828\) | 20.0917i | 0.698234i | ||||||||
\(829\) | −4.72498 | −0.164105 | −0.0820527 | − | 0.996628i | \(-0.526148\pi\) | ||||
−0.0820527 | + | 0.996628i | \(0.526148\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.60555 | 0.263834 | ||||||||
\(832\) | 2.30278i | 0.0798344i | ||||||||
\(833\) | − 85.2666i | − 2.95431i | ||||||||
\(834\) | −2.69722 | −0.0933972 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.60555 | 0.0901149 | ||||||||
\(837\) | − 5.90833i | − 0.204222i | ||||||||
\(838\) | 25.1472i | 0.868695i | ||||||||
\(839\) | 49.0278 | 1.69263 | 0.846313 | − | 0.532686i | \(-0.178817\pi\) | ||||
0.846313 | + | 0.532686i | \(0.178817\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.7250 | 0.645689 | ||||||||
\(842\) | 28.7250i | 0.989928i | ||||||||
\(843\) | 3.63331i | 0.125138i | ||||||||
\(844\) | −6.69722 | −0.230528 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.57779 | −0.260530 | ||||||||
\(847\) | 42.8444i | 1.47215i | ||||||||
\(848\) | − 6.00000i | − 0.206041i | ||||||||
\(849\) | 5.26662 | 0.180750 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.90833 | −0.236814 | ||||||||
\(852\) | 1.81665i | 0.0622375i | ||||||||
\(853\) | − 11.5416i | − 0.395178i | −0.980285 | − | 0.197589i | \(-0.936689\pi\) | ||||
0.980285 | − | 0.197589i | \(-0.0633111\pi\) | |||||||
\(854\) | −48.4222 | −1.65697 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.30278 | −0.147066 | ||||||||
\(857\) | 14.8444i | 0.507075i | 0.967326 | + | 0.253538i | \(0.0815942\pi\) | ||||
−0.967326 | + | 0.253538i | \(0.918406\pi\) | |||||||
\(858\) | − 0.908327i | − 0.0310098i | ||||||||
\(859\) | 24.0555 | 0.820764 | 0.410382 | − | 0.911914i | \(-0.365395\pi\) | ||||
0.410382 | + | 0.911914i | \(0.365395\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.26662 | 0.0431661 | ||||||||
\(862\) | − 5.21110i | − 0.177491i | ||||||||
\(863\) | 12.0000i | 0.408485i | 0.978920 | + | 0.204242i | \(0.0654731\pi\) | ||||
−0.978920 | + | 0.204242i | \(0.934527\pi\) | |||||||
\(864\) | 1.78890 | 0.0608595 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.9361 | 0.405605 | ||||||||
\(867\) | 5.75274i | 0.195373i | ||||||||
\(868\) | 15.2111i | 0.516298i | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.4222 | −1.13247 | ||||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | − 36.1278i | − 1.22274i | ||||||||
\(874\) | −13.8167 | −0.467355 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.63331 | 0.0889712 | ||||||||
\(877\) | − 7.21110i | − 0.243502i | −0.992561 | − | 0.121751i | \(-0.961149\pi\) | ||||
0.992561 | − | 0.121751i | \(-0.0388509\pi\) | |||||||
\(878\) | 9.33053i | 0.314890i | ||||||||
\(879\) | −7.57779 | −0.255593 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25.5416 | 0.860520 | 0.430260 | − | 0.902705i | \(-0.358422\pi\) | ||||
0.430260 | + | 0.902705i | \(0.358422\pi\) | |||||||
\(882\) | − 41.3305i | − 1.39167i | ||||||||
\(883\) | − 2.42221i | − 0.0815137i | −0.999169 | − | 0.0407568i | \(-0.987023\pi\) | ||||
0.999169 | − | 0.0407568i | \(-0.0129769\pi\) | |||||||
\(884\) | −13.8167 | −0.464704 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.275019 | −0.00923945 | ||||||||
\(887\) | − 28.4222i | − 0.954324i | −0.878815 | − | 0.477162i | \(-0.841665\pi\) | ||||
0.878815 | − | 0.477162i | \(-0.158335\pi\) | |||||||
\(888\) | 0.302776i | 0.0101605i | ||||||||
\(889\) | 22.0555 | 0.739718 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.6611 | 0.357159 | ||||||||
\(892\) | − 15.8167i | − 0.529581i | ||||||||
\(893\) | − 5.21110i | − 0.174383i | ||||||||
\(894\) | 0.550039 | 0.0183960 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.60555 | −0.153861 | ||||||||
\(897\) | 4.81665i | 0.160823i | ||||||||
\(898\) | 0.788897i | 0.0263258i | ||||||||
\(899\) | −22.8167 | −0.760978 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | − 1.18335i | − 0.0394011i | ||||||||
\(903\) | 9.21110i | 0.306526i | ||||||||
\(904\) | 11.2111 | 0.372876 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.05551 | −0.134735 | ||||||||
\(907\) | − 26.0000i | − 0.863316i | −0.902037 | − | 0.431658i | \(-0.857929\pi\) | ||||
0.902037 | − | 0.431658i | \(-0.142071\pi\) | |||||||
\(908\) | − 7.81665i | − 0.259405i | ||||||||
\(909\) | 47.7611 | 1.58414 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.4222 | −1.53804 | −0.769018 | − | 0.639227i | \(-0.779254\pi\) | ||||
−0.769018 | + | 0.639227i | \(0.779254\pi\) | |||||||
\(912\) | 0.605551i | 0.0200518i | ||||||||
\(913\) | 22.4222i | 0.742067i | ||||||||
\(914\) | 4.60555 | 0.152338 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.3944 | 0.574729 | ||||||||
\(917\) | − 15.6333i | − 0.516257i | ||||||||
\(918\) | 10.7334i | 0.354254i | ||||||||
\(919\) | 38.4222 | 1.26743 | 0.633716 | − | 0.773566i | \(-0.281529\pi\) | ||||
0.633716 | + | 0.773566i | \(0.281529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.14719 | −0.0707522 | ||||||||
\(922\) | − 16.4222i | − 0.540837i | ||||||||
\(923\) | − 13.8167i | − 0.454781i | ||||||||
\(924\) | 1.81665 | 0.0597635 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −30.3028 | −0.995811 | ||||||||
\(927\) | 9.60555i | 0.315488i | ||||||||
\(928\) | − 6.90833i | − 0.226777i | ||||||||
\(929\) | 36.5139 | 1.19798 | 0.598991 | − | 0.800756i | \(-0.295569\pi\) | ||||
0.598991 | + | 0.800756i | \(0.295569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.4222 | 0.931500 | ||||||||
\(932\) | 9.51388i | 0.311637i | ||||||||
\(933\) | − 1.54163i | − 0.0504708i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.69722 | −0.218906 | ||||||||
\(937\) | 28.9083i | 0.944394i | 0.881493 | + | 0.472197i | \(0.156539\pi\) | ||||
−0.881493 | + | 0.472197i | \(0.843461\pi\) | |||||||
\(938\) | − 66.8444i | − 2.18255i | ||||||||
\(939\) | 8.18335 | 0.267053 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.81665 | −0.254816 | −0.127408 | − | 0.991850i | \(-0.540666\pi\) | ||||
−0.127408 | + | 0.991850i | \(0.540666\pi\) | |||||||
\(942\) | − 2.18335i | − 0.0711373i | ||||||||
\(943\) | 6.27502i | 0.204343i | ||||||||
\(944\) | −3.39445 | −0.110480 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.60555 | 0.279791 | ||||||||
\(947\) | − 39.6333i | − 1.28791i | −0.765064 | − | 0.643955i | \(-0.777293\pi\) | ||||
0.765064 | − | 0.643955i | \(-0.222707\pi\) | |||||||
\(948\) | 4.88057i | 0.158514i | ||||||||
\(949\) | −20.0278 | −0.650128 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.57779 | 0.0511635 | ||||||||
\(952\) | − 27.6333i | − 0.895601i | ||||||||
\(953\) | − 18.7527i | − 0.607461i | −0.952758 | − | 0.303730i | \(-0.901768\pi\) | ||||
0.952758 | − | 0.303730i | \(-0.0982322\pi\) | |||||||
\(954\) | 17.4500 | 0.564963 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.513878 | 0.0166200 | ||||||||
\(957\) | 2.72498i | 0.0880861i | ||||||||
\(958\) | − 12.1194i | − 0.391561i | ||||||||
\(959\) | 45.6333 | 1.47358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.0917 | −0.648118 | ||||||||
\(962\) | − 2.30278i | − 0.0742445i | ||||||||
\(963\) | − 12.5139i | − 0.403254i | ||||||||
\(964\) | −8.00000 | −0.257663 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −9.63331 | −0.309947 | ||||||||
\(967\) | − 25.7250i | − 0.827260i | −0.910445 | − | 0.413630i | \(-0.864261\pi\) | ||||
0.910445 | − | 0.413630i | \(-0.135739\pi\) | |||||||
\(968\) | 9.30278i | 0.299003i | ||||||||
\(969\) | −3.63331 | −0.116719 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5416 | 1.01222 | 0.506110 | − | 0.862469i | \(-0.331083\pi\) | ||||
0.506110 | + | 0.862469i | \(0.331083\pi\) | |||||||
\(972\) | 7.84441i | 0.251610i | ||||||||
\(973\) | 41.0278i | 1.31529i | ||||||||
\(974\) | −22.7889 | −0.730203 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.5139 | −0.336541 | ||||||||
\(977\) | − 18.0000i | − 0.575871i | −0.957650 | − | 0.287936i | \(-0.907031\pi\) | ||||
0.957650 | − | 0.287936i | \(-0.0929689\pi\) | |||||||
\(978\) | − 6.18335i | − 0.197722i | ||||||||
\(979\) | −6.78890 | −0.216974 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.81665 | −0.185711 | ||||||||
\(982\) | − 14.7250i | − 0.469893i | ||||||||
\(983\) | − 12.0000i | − 0.382741i | −0.981518 | − | 0.191370i | \(-0.938707\pi\) | ||||
0.981518 | − | 0.191370i | \(-0.0612931\pi\) | |||||||
\(984\) | 0.275019 | 0.00876729 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 41.4500 | 1.32004 | ||||||||
\(987\) | − 3.63331i | − 0.115649i | ||||||||
\(988\) | − 4.60555i | − 0.146522i | ||||||||
\(989\) | −45.6333 | −1.45105 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 54.3028 | 1.72498 | 0.862492 | − | 0.506070i | \(-0.168902\pi\) | ||||
0.862492 | + | 0.506070i | \(0.168902\pi\) | |||||||
\(992\) | 3.30278i | 0.104863i | ||||||||
\(993\) | − 0.366692i | − 0.0116366i | ||||||||
\(994\) | 27.6333 | 0.876475 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.21110 | −0.165120 | ||||||||
\(997\) | 23.5778i | 0.746716i | 0.927687 | + | 0.373358i | \(0.121794\pi\) | ||||
−0.927687 | + | 0.373358i | \(0.878206\pi\) | |||||||
\(998\) | − 8.23886i | − 0.260797i | ||||||||
\(999\) | −1.78890 | −0.0565982 |
(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 | 1850.2.b.i.149.3 | 4 | ||
5.2 | odd | 4 | 74.2.a.a.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1850.2.a.u.1.2 | 2 | |||
5.4 | even | 2 | inner | 1850.2.b.i.149.2 | 4 | ||
15.2 | even | 4 | 666.2.a.j.1.1 | 2 | |||
20.7 | even | 4 | 592.2.a.f.1.2 | 2 | |||
35.27 | even | 4 | 3626.2.a.a.1.2 | 2 | |||
40.27 | even | 4 | 2368.2.a.ba.1.1 | 2 | |||
40.37 | odd | 4 | 2368.2.a.s.1.2 | 2 | |||
55.32 | even | 4 | 8954.2.a.p.1.1 | 2 | |||
60.47 | odd | 4 | 5328.2.a.bf.1.1 | 2 | |||
185.147 | odd | 4 | 2738.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.a.a.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
592.2.a.f.1.2 | 2 | 20.7 | even | 4 | |||
666.2.a.j.1.1 | 2 | 15.2 | even | 4 | |||
1850.2.a.u.1.2 | 2 | 5.3 | odd | 4 | |||
1850.2.b.i.149.2 | 4 | 5.4 | even | 2 | inner | ||
1850.2.b.i.149.3 | 4 | 1.1 | even | 1 | trivial | ||
2368.2.a.s.1.2 | 2 | 40.37 | odd | 4 | |||
2368.2.a.ba.1.1 | 2 | 40.27 | even | 4 | |||
2738.2.a.l.1.1 | 2 | 185.147 | odd | 4 | |||
3626.2.a.a.1.2 | 2 | 35.27 | even | 4 | |||
5328.2.a.bf.1.1 | 2 | 60.47 | odd | 4 | |||
8954.2.a.p.1.1 | 2 | 55.32 | even | 4 |