Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.d (of order \(2\), degree \(1\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\Q(\zeta_{48})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{14} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.8 | ||
Root | \(-0.793353 + 0.608761i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.f.2645.16 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 3.57981 | 1.60094 | 0.800470 | − | 0.599373i | \(-0.204583\pi\) | ||||
0.800470 | + | 0.599373i | \(0.204583\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 3.57981i | − 1.13204i | ||||||||
\(11\) | 5.52607i | 1.66617i | 0.553144 | + | 0.833086i | \(0.313428\pi\) | ||||
−0.553144 | + | 0.833086i | \(0.686572\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 6.91037i | − 1.91659i | −0.285776 | − | 0.958297i | \(-0.592251\pi\) | ||||
0.285776 | − | 0.958297i | \(-0.407749\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.44949 | 0.594089 | 0.297044 | − | 0.954864i | \(-0.403999\pi\) | ||||
0.297044 | + | 0.954864i | \(0.403999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.16176i | 1.87244i | 0.351418 | + | 0.936219i | \(0.385699\pi\) | ||||
−0.351418 | + | 0.936219i | \(0.614301\pi\) | |||||||
\(20\) | −3.57981 | −0.800470 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.52607 | 1.17816 | ||||||||
\(23\) | 3.08856i | 0.644009i | 0.946738 | + | 0.322005i | \(0.104357\pi\) | ||||
−0.946738 | + | 0.322005i | \(0.895643\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.81504 | 1.56301 | ||||||||
\(26\) | −6.91037 | −1.35524 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 5.66096i | − 1.05121i | −0.850728 | − | 0.525607i | \(-0.823838\pi\) | ||||
0.850728 | − | 0.525607i | \(-0.176162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.400414i | 0.0719164i | 0.999353 | + | 0.0359582i | \(0.0114483\pi\) | ||||
−0.999353 | + | 0.0359582i | \(0.988552\pi\) | |||||||
\(32\) | − 1.00000i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.44949i | − 0.420084i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.79174 | 0.952157 | 0.476078 | − | 0.879403i | \(-0.342058\pi\) | ||||
0.476078 | + | 0.879403i | \(0.342058\pi\) | |||||||
\(38\) | 8.16176 | 1.32401 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.57981i | 0.566018i | ||||||||
\(41\) | 5.49535 | 0.858229 | 0.429115 | − | 0.903250i | \(-0.358826\pi\) | ||||
0.429115 | + | 0.903250i | \(0.358826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.95367 | −0.450430 | −0.225215 | − | 0.974309i | \(-0.572308\pi\) | ||||
−0.225215 | + | 0.974309i | \(0.572308\pi\) | |||||||
\(44\) | − 5.52607i | − 0.833086i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.08856 | 0.455383 | ||||||||
\(47\) | 0.0958559 | 0.0139820 | 0.00699101 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00699101 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 7.81504i | − 1.10521i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.91037i | 0.958297i | ||||||||
\(53\) | 5.17738i | 0.711167i | 0.934644 | + | 0.355584i | \(0.115718\pi\) | ||||
−0.934644 | + | 0.355584i | \(0.884282\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.7823i | 2.66744i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.66096 | −0.743320 | ||||||||
\(59\) | 6.38401 | 0.831127 | 0.415563 | − | 0.909564i | \(-0.363584\pi\) | ||||
0.415563 | + | 0.909564i | \(0.363584\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.06376i | 0.904422i | 0.891911 | + | 0.452211i | \(0.149365\pi\) | ||||
−0.891911 | + | 0.452211i | \(0.850635\pi\) | |||||||
\(62\) | 0.400414 | 0.0508526 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 24.7378i | − 3.06835i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.45090 | −0.177255 | −0.0886276 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886276 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(68\) | −2.44949 | −0.297044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 8.77836i | − 1.04180i | −0.853618 | − | 0.520900i | \(-0.825597\pi\) | ||||
0.853618 | − | 0.520900i | \(-0.174403\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 0.679758i | − 0.0795597i | −0.999208 | − | 0.0397798i | \(-0.987334\pi\) | ||||
0.999208 | − | 0.0397798i | \(-0.0126657\pi\) | |||||||
\(74\) | − 5.79174i | − 0.673277i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 8.16176i | − 0.936219i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.43340 | −0.723815 | −0.361907 | − | 0.932214i | \(-0.617874\pi\) | ||||
−0.361907 | + | 0.932214i | \(0.617874\pi\) | |||||||
\(80\) | 3.57981 | 0.400235 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 5.49535i | − 0.606860i | ||||||||
\(83\) | 1.64156 | 0.180184 | 0.0900921 | − | 0.995933i | \(-0.471284\pi\) | ||||
0.0900921 | + | 0.995933i | \(0.471284\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.76871 | 0.951100 | ||||||||
\(86\) | 2.95367i | 0.318502i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.52607 | −0.589081 | ||||||||
\(89\) | 12.1921 | 1.29236 | 0.646182 | − | 0.763183i | \(-0.276365\pi\) | ||||
0.646182 | + | 0.763183i | \(0.276365\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 3.08856i | − 0.322005i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − 0.0958559i | − 0.00988678i | ||||||||
\(95\) | 29.2176i | 2.99766i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 11.3788i | 1.15535i | 0.816268 | + | 0.577673i | \(0.196039\pi\) | ||||
−0.816268 | + | 0.577673i | \(0.803961\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.81504 | −0.781504 | ||||||||
\(101\) | −1.82679 | −0.181772 | −0.0908862 | − | 0.995861i | \(-0.528970\pi\) | ||||
−0.0908862 | + | 0.995861i | \(0.528970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 5.79030i | − 0.570535i | −0.958448 | − | 0.285268i | \(-0.907917\pi\) | ||||
0.958448 | − | 0.285268i | \(-0.0920825\pi\) | |||||||
\(104\) | 6.91037 | 0.677618 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.17738 | 0.502871 | ||||||||
\(107\) | 5.49867i | 0.531576i | 0.964031 | + | 0.265788i | \(0.0856322\pi\) | ||||
−0.964031 | + | 0.265788i | \(0.914368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4705 | 1.29024 | 0.645118 | − | 0.764083i | \(-0.276808\pi\) | ||||
0.645118 | + | 0.764083i | \(0.276808\pi\) | |||||||
\(110\) | 19.7823 | 1.88617 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.8843i | 1.11798i | 0.829174 | + | 0.558990i | \(0.188811\pi\) | ||||
−0.829174 | + | 0.558990i | \(0.811189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 11.0565i | 1.03102i | ||||||||
\(116\) | 5.66096i | 0.525607i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − 6.38401i | − 0.587695i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.5374 | −1.77613 | ||||||||
\(122\) | 7.06376 | 0.639523 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 0.400414i | − 0.0359582i | ||||||||
\(125\) | 10.0773 | 0.901341 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.09410 | 0.629500 | 0.314750 | − | 0.949175i | \(-0.398079\pi\) | ||||
0.314750 | + | 0.949175i | \(0.398079\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −24.7378 | −2.16965 | ||||||||
\(131\) | −16.0312 | −1.40066 | −0.700328 | − | 0.713821i | \(-0.746963\pi\) | ||||
−0.700328 | + | 0.713821i | \(0.746963\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.45090i | 0.125338i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.44949i | 0.210042i | ||||||||
\(137\) | − 6.94172i | − 0.593071i | −0.955022 | − | 0.296536i | \(-0.904169\pi\) | ||||
0.955022 | − | 0.296536i | \(-0.0958314\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 0.273984i | − 0.0232390i | −0.999932 | − | 0.0116195i | \(-0.996301\pi\) | ||||
0.999932 | − | 0.0116195i | \(-0.00369868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.77836 | −0.736663 | ||||||||
\(143\) | 38.1872 | 3.19337 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 20.2652i | − 1.68293i | ||||||||
\(146\) | −0.679758 | −0.0562572 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.79174 | −0.476078 | ||||||||
\(149\) | − 19.1139i | − 1.56587i | −0.622102 | − | 0.782937i | \(-0.713721\pi\) | ||||
0.622102 | − | 0.782937i | \(-0.286279\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.61463 | −0.701048 | −0.350524 | − | 0.936554i | \(-0.613997\pi\) | ||||
−0.350524 | + | 0.936554i | \(0.613997\pi\) | |||||||
\(152\) | −8.16176 | −0.662006 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.43340i | 0.115134i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5807i | 0.844430i | 0.906496 | + | 0.422215i | \(0.138747\pi\) | ||||
−0.906496 | + | 0.422215i | \(0.861253\pi\) | |||||||
\(158\) | 6.43340i | 0.511814i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 3.57981i | − 0.283009i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.25809 | 0.725150 | 0.362575 | − | 0.931955i | \(-0.381898\pi\) | ||||
0.362575 | + | 0.931955i | \(0.381898\pi\) | |||||||
\(164\) | −5.49535 | −0.429115 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 1.64156i | − 0.127409i | ||||||||
\(167\) | 14.6539 | 1.13395 | 0.566976 | − | 0.823734i | \(-0.308113\pi\) | ||||
0.566976 | + | 0.823734i | \(0.308113\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −34.7533 | −2.67333 | ||||||||
\(170\) | − 8.76871i | − 0.672529i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.95367 | 0.225215 | ||||||||
\(173\) | 7.93301 | 0.603136 | 0.301568 | − | 0.953445i | \(-0.402490\pi\) | ||||
0.301568 | + | 0.953445i | \(0.402490\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.52607i | 0.416543i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 12.1921i | − 0.913839i | ||||||||
\(179\) | − 16.7361i | − 1.25092i | −0.780257 | − | 0.625458i | \(-0.784912\pi\) | ||||
0.780257 | − | 0.625458i | \(-0.215088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.85077i | 0.732202i | 0.930575 | + | 0.366101i | \(0.119308\pi\) | ||||
−0.930575 | + | 0.366101i | \(0.880692\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.08856 | −0.227692 | ||||||||
\(185\) | 20.7333 | 1.52435 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.5360i | 0.989854i | ||||||||
\(188\) | −0.0958559 | −0.00699101 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 29.2176 | 2.11966 | ||||||||
\(191\) | − 17.5738i | − 1.27160i | −0.771854 | − | 0.635799i | \(-0.780671\pi\) | ||||
0.771854 | − | 0.635799i | \(-0.219329\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 19.8534 | 1.42908 | 0.714540 | − | 0.699594i | \(-0.246636\pi\) | ||||
0.714540 | + | 0.699594i | \(0.246636\pi\) | |||||||
\(194\) | 11.3788 | 0.816953 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 21.5007i | − 1.53186i | −0.642922 | − | 0.765932i | \(-0.722278\pi\) | ||||
0.642922 | − | 0.765932i | \(-0.277722\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 13.4805i | − 0.955610i | −0.878466 | − | 0.477805i | \(-0.841433\pi\) | ||||
0.878466 | − | 0.477805i | \(-0.158567\pi\) | |||||||
\(200\) | 7.81504i | 0.552607i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.82679i | 0.128533i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 19.6723 | 1.37397 | ||||||||
\(206\) | −5.79030 | −0.403429 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 6.91037i | − 0.479148i | ||||||||
\(209\) | −45.1025 | −3.11980 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.8575 | −1.64242 | −0.821210 | − | 0.570626i | \(-0.806700\pi\) | ||||
−0.821210 | + | 0.570626i | \(0.806700\pi\) | |||||||
\(212\) | − 5.17738i | − 0.355584i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.49867 | 0.375881 | ||||||||
\(215\) | −10.5736 | −0.721112 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 13.4705i | − 0.912334i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − 19.7823i | − 1.33372i | ||||||||
\(221\) | − 16.9269i | − 1.13863i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 7.75175i | − 0.519095i | −0.965730 | − | 0.259548i | \(-0.916427\pi\) | ||||
0.965730 | − | 0.259548i | \(-0.0835735\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.8843 | 0.790532 | ||||||||
\(227\) | −11.1867 | −0.742484 | −0.371242 | − | 0.928536i | \(-0.621068\pi\) | ||||
−0.371242 | + | 0.928536i | \(0.621068\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.0107i | 1.05802i | 0.848616 | + | 0.529010i | \(0.177437\pi\) | ||||
−0.848616 | + | 0.529010i | \(0.822563\pi\) | |||||||
\(230\) | 11.0565 | 0.729041 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.66096 | 0.371660 | ||||||||
\(233\) | 5.62801i | 0.368703i | 0.982860 | + | 0.184352i | \(0.0590186\pi\) | ||||
−0.982860 | + | 0.184352i | \(0.940981\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.343146 | 0.0223844 | ||||||||
\(236\) | −6.38401 | −0.415563 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 25.9630i | − 1.67941i | −0.543046 | − | 0.839703i | \(-0.682729\pi\) | ||||
0.543046 | − | 0.839703i | \(-0.317271\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 14.5302i | − 0.935970i | −0.883736 | − | 0.467985i | \(-0.844980\pi\) | ||||
0.883736 | − | 0.467985i | \(-0.155020\pi\) | |||||||
\(242\) | 19.5374i | 1.25591i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 7.06376i | − 0.452211i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 56.4008 | 3.58870 | ||||||||
\(248\) | −0.400414 | −0.0254263 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 10.0773i | − 0.637345i | ||||||||
\(251\) | 21.5246 | 1.35862 | 0.679309 | − | 0.733852i | \(-0.262279\pi\) | ||||
0.679309 | + | 0.733852i | \(0.262279\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.0676 | −1.07303 | ||||||||
\(254\) | − 7.09410i | − 0.445124i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.85613 | −0.614809 | −0.307404 | − | 0.951579i | \(-0.599460\pi\) | ||||
−0.307404 | + | 0.951579i | \(0.599460\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 24.7378i | 1.53417i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.0312i | 0.990413i | ||||||||
\(263\) | − 3.29041i | − 0.202896i | −0.994841 | − | 0.101448i | \(-0.967653\pi\) | ||||
0.994841 | − | 0.101448i | \(-0.0323475\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.5340i | 1.13854i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.45090 | 0.0886276 | ||||||||
\(269\) | −18.9670 | −1.15644 | −0.578218 | − | 0.815883i | \(-0.696252\pi\) | ||||
−0.578218 | + | 0.815883i | \(0.696252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4806i | 0.636650i | 0.947982 | + | 0.318325i | \(0.103120\pi\) | ||||
−0.947982 | + | 0.318325i | \(0.896880\pi\) | |||||||
\(272\) | 2.44949 | 0.148522 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.94172 | −0.419365 | ||||||||
\(275\) | 43.1864i | 2.60424i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.37173 | −0.382840 | −0.191420 | − | 0.981508i | \(-0.561309\pi\) | ||||
−0.191420 | + | 0.981508i | \(0.561309\pi\) | |||||||
\(278\) | −0.273984 | −0.0164324 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 1.76520i | − 0.105303i | −0.998613 | − | 0.0526516i | \(-0.983233\pi\) | ||||
0.998613 | − | 0.0526516i | \(-0.0167673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1243i | 1.55293i | 0.630160 | + | 0.776466i | \(0.282989\pi\) | ||||
−0.630160 | + | 0.776466i | \(0.717011\pi\) | |||||||
\(284\) | 8.77836i | 0.520900i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 38.1872i | − 2.25806i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | −20.2652 | −1.19001 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.679758i | 0.0397798i | ||||||||
\(293\) | 12.8799 | 0.752453 | 0.376226 | − | 0.926528i | \(-0.377221\pi\) | ||||
0.376226 | + | 0.926528i | \(0.377221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.8535 | 1.33058 | ||||||||
\(296\) | 5.79174i | 0.336638i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.1139 | −1.10724 | ||||||||
\(299\) | 21.3431 | 1.23430 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 8.61463i | 0.495716i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.16176i | 0.468109i | ||||||||
\(305\) | 25.2869i | 1.44793i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 11.8601i | − 0.676894i | −0.940985 | − | 0.338447i | \(-0.890098\pi\) | ||||
0.940985 | − | 0.338447i | \(-0.109902\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.43340 | 0.0814119 | ||||||||
\(311\) | 9.41692 | 0.533985 | 0.266992 | − | 0.963699i | \(-0.413970\pi\) | ||||
0.266992 | + | 0.963699i | \(0.413970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 5.60415i | − 0.316765i | −0.987378 | − | 0.158383i | \(-0.949372\pi\) | ||||
0.987378 | − | 0.158383i | \(-0.0506279\pi\) | |||||||
\(314\) | 10.5807 | 0.597102 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.43340 | 0.361907 | ||||||||
\(317\) | − 25.8724i | − 1.45314i | −0.687094 | − | 0.726568i | \(-0.741114\pi\) | ||||
0.687094 | − | 0.726568i | \(-0.258886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 31.2828 | 1.75150 | ||||||||
\(320\) | −3.57981 | −0.200117 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 19.9922i | 1.11239i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 54.0048i | − 2.99565i | ||||||||
\(326\) | − 9.25809i | − 0.512758i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.49535i | 0.303430i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.0987 | 0.610041 | 0.305020 | − | 0.952346i | \(-0.401337\pi\) | ||||
0.305020 | + | 0.952346i | \(0.401337\pi\) | |||||||
\(332\) | −1.64156 | −0.0900921 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 14.6539i | − 0.801826i | ||||||||
\(335\) | −5.19393 | −0.283775 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −16.4340 | −0.895218 | −0.447609 | − | 0.894229i | \(-0.647724\pi\) | ||||
−0.447609 | + | 0.894229i | \(0.647724\pi\) | |||||||
\(338\) | 34.7533i | 1.89033i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.76871 | −0.475550 | ||||||||
\(341\) | −2.21271 | −0.119825 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 2.95367i | − 0.159251i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 7.93301i | − 0.426481i | ||||||||
\(347\) | − 6.61282i | − 0.354995i | −0.984121 | − | 0.177497i | \(-0.943200\pi\) | ||||
0.984121 | − | 0.177497i | \(-0.0568001\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.9468i | − 0.960669i | −0.877085 | − | 0.480335i | \(-0.840515\pi\) | ||||
0.877085 | − | 0.480335i | \(-0.159485\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.52607 | 0.294540 | ||||||||
\(353\) | 3.64649 | 0.194083 | 0.0970414 | − | 0.995280i | \(-0.469062\pi\) | ||||
0.0970414 | + | 0.995280i | \(0.469062\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 31.4248i | − 1.66786i | ||||||||
\(356\) | −12.1921 | −0.646182 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.7361 | −0.884532 | ||||||||
\(359\) | 3.05213i | 0.161085i | 0.996751 | + | 0.0805427i | \(0.0256653\pi\) | ||||
−0.996751 | + | 0.0805427i | \(0.974335\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −47.6144 | −2.50602 | ||||||||
\(362\) | 9.85077 | 0.517745 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.43340i | − 0.127370i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.7523i | 1.18766i | 0.804590 | + | 0.593831i | \(0.202385\pi\) | ||||
−0.804590 | + | 0.593831i | \(0.797615\pi\) | |||||||
\(368\) | 3.08856i | 0.161002i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 20.7333i | − 1.07788i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.718273 | −0.0371908 | −0.0185954 | − | 0.999827i | \(-0.505919\pi\) | ||||
−0.0185954 | + | 0.999827i | \(0.505919\pi\) | |||||||
\(374\) | 13.5360 | 0.699932 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.0958559i | 0.00494339i | ||||||||
\(377\) | −39.1193 | −2.01475 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.4935 | 0.744480 | 0.372240 | − | 0.928136i | \(-0.378590\pi\) | ||||
0.372240 | + | 0.928136i | \(0.378590\pi\) | |||||||
\(380\) | − 29.2176i | − 1.49883i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.5738 | −0.899156 | ||||||||
\(383\) | −19.1105 | −0.976503 | −0.488251 | − | 0.872703i | \(-0.662365\pi\) | ||||
−0.488251 | + | 0.872703i | \(0.662365\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 19.8534i | − 1.01051i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 11.3788i | − 0.577673i | ||||||||
\(389\) | 1.90154i | 0.0964117i | 0.998837 | + | 0.0482058i | \(0.0153503\pi\) | ||||
−0.998837 | + | 0.0482058i | \(0.984650\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.56539i | 0.382598i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.5007 | −1.08319 | ||||||||
\(395\) | −23.0304 | −1.15878 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.5802i | 0.781950i | 0.920401 | + | 0.390975i | \(0.127862\pi\) | ||||
−0.920401 | + | 0.390975i | \(0.872138\pi\) | |||||||
\(398\) | −13.4805 | −0.675718 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.81504 | 0.390752 | ||||||||
\(401\) | 34.2752i | 1.71162i | 0.517287 | + | 0.855812i | \(0.326942\pi\) | ||||
−0.517287 | + | 0.855812i | \(0.673058\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.76701 | 0.137834 | ||||||||
\(404\) | 1.82679 | 0.0908862 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 32.0056i | 1.58646i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 4.14858i | − 0.205134i | −0.994726 | − | 0.102567i | \(-0.967294\pi\) | ||||
0.994726 | − | 0.102567i | \(-0.0327056\pi\) | |||||||
\(410\) | − 19.6723i | − 0.971546i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.79030i | 0.285268i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.87646 | 0.288464 | ||||||||
\(416\) | −6.91037 | −0.338809 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 45.1025i | 2.20603i | ||||||||
\(419\) | −16.8972 | −0.825481 | −0.412741 | − | 0.910849i | \(-0.635428\pi\) | ||||
−0.412741 | + | 0.910849i | \(0.635428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.16773 | 0.349334 | 0.174667 | − | 0.984628i | \(-0.444115\pi\) | ||||
0.174667 | + | 0.984628i | \(0.444115\pi\) | |||||||
\(422\) | 23.8575i | 1.16137i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.17738 | −0.251436 | ||||||||
\(425\) | 19.1429 | 0.928565 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 5.49867i | − 0.265788i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 10.5736i | 0.509903i | ||||||||
\(431\) | − 19.6670i | − 0.947327i | −0.880706 | − | 0.473663i | \(-0.842931\pi\) | ||||
0.880706 | − | 0.473663i | \(-0.157069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.1213i | 0.774740i | 0.921924 | + | 0.387370i | \(0.126616\pi\) | ||||
−0.921924 | + | 0.387370i | \(0.873384\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4705 | −0.645118 | ||||||||
\(437\) | −25.2081 | −1.20587 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 26.7007i | − 1.27435i | −0.770718 | − | 0.637177i | \(-0.780102\pi\) | ||||
0.770718 | − | 0.637177i | \(-0.219898\pi\) | |||||||
\(440\) | −19.7823 | −0.943083 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.9269 | −0.805130 | ||||||||
\(443\) | − 19.8643i | − 0.943779i | −0.881658 | − | 0.471890i | \(-0.843572\pi\) | ||||
0.881658 | − | 0.471890i | \(-0.156428\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 43.6455 | 2.06900 | ||||||||
\(446\) | −7.75175 | −0.367056 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0132i | 0.944479i | 0.881470 | + | 0.472240i | \(0.156554\pi\) | ||||
−0.881470 | + | 0.472240i | \(0.843446\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.3677i | 1.42996i | ||||||||
\(452\) | − 11.8843i | − 0.558990i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.1867i | 0.525016i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.9138 | −1.11864 | −0.559319 | − | 0.828952i | \(-0.688937\pi\) | ||||
−0.559319 | + | 0.828952i | \(0.688937\pi\) | |||||||
\(458\) | 16.0107 | 0.748133 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 11.0565i | − 0.515510i | ||||||||
\(461\) | −18.6642 | −0.869279 | −0.434640 | − | 0.900604i | \(-0.643124\pi\) | ||||
−0.434640 | + | 0.900604i | \(0.643124\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.64166 | −0.355138 | −0.177569 | − | 0.984108i | \(-0.556823\pi\) | ||||
−0.177569 | + | 0.984108i | \(0.556823\pi\) | |||||||
\(464\) | − 5.66096i | − 0.262803i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.62801 | 0.260713 | ||||||||
\(467\) | −34.7012 | −1.60578 | −0.802890 | − | 0.596127i | \(-0.796706\pi\) | ||||
−0.802890 | + | 0.596127i | \(0.796706\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 0.343146i | − 0.0158281i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.38401i | 0.293848i | ||||||||
\(473\) | − 16.3222i | − 0.750494i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 63.7845i | 2.92663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −25.9630 | −1.18752 | ||||||||
\(479\) | −26.2363 | −1.19877 | −0.599383 | − | 0.800462i | \(-0.704587\pi\) | ||||
−0.599383 | + | 0.800462i | \(0.704587\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 40.0231i | − 1.82490i | ||||||||
\(482\) | −14.5302 | −0.661831 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 19.5374 | 0.888064 | ||||||||
\(485\) | 40.7341i | 1.84964i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.73022 | −0.350290 | −0.175145 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175145 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(488\) | −7.06376 | −0.319762 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0173i | 1.49005i | 0.667038 | + | 0.745024i | \(0.267562\pi\) | ||||
−0.667038 | + | 0.745024i | \(0.732438\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 13.8665i | − 0.624514i | ||||||||
\(494\) | − 56.4008i | − 2.53759i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.400414i | 0.0179791i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.61078 | −0.340705 | −0.170353 | − | 0.985383i | \(-0.554491\pi\) | ||||
−0.170353 | + | 0.985383i | \(0.554491\pi\) | |||||||
\(500\) | −10.0773 | −0.450671 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 21.5246i | − 0.960688i | ||||||||
\(503\) | 39.9386 | 1.78078 | 0.890388 | − | 0.455203i | \(-0.150433\pi\) | ||||
0.890388 | + | 0.455203i | \(0.150433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.53956 | −0.291007 | ||||||||
\(506\) | 17.0676i | 0.758747i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.09410 | −0.314750 | ||||||||
\(509\) | −25.5868 | −1.13411 | −0.567057 | − | 0.823678i | \(-0.691918\pi\) | ||||
−0.567057 | + | 0.823678i | \(0.691918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 1.00000i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 9.85613i | 0.434735i | ||||||||
\(515\) | − 20.7282i | − 0.913393i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.529706i | 0.0232964i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.7378 | 1.08483 | ||||||||
\(521\) | −14.8838 | −0.652070 | −0.326035 | − | 0.945358i | \(-0.605713\pi\) | ||||
−0.326035 | + | 0.945358i | \(0.605713\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.63492i | 0.333852i | 0.985969 | + | 0.166926i | \(0.0533841\pi\) | ||||
−0.985969 | + | 0.166926i | \(0.946616\pi\) | |||||||
\(524\) | 16.0312 | 0.700328 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.29041 | −0.143469 | ||||||||
\(527\) | 0.980809i | 0.0427247i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.4608 | 0.585252 | ||||||||
\(530\) | 18.5340 | 0.805066 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 37.9749i | − 1.64488i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.6842i | 0.851022i | ||||||||
\(536\) | − 1.45090i | − 0.0626692i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.9670i | 0.817723i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −36.0600 | −1.55034 | −0.775170 | − | 0.631752i | \(-0.782336\pi\) | ||||
−0.775170 | + | 0.631752i | \(0.782336\pi\) | |||||||
\(542\) | 10.4806 | 0.450179 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 2.44949i | − 0.105021i | ||||||||
\(545\) | 48.2217 | 2.06559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.3548 | −1.46890 | −0.734452 | − | 0.678661i | \(-0.762561\pi\) | ||||
−0.734452 | + | 0.678661i | \(0.762561\pi\) | |||||||
\(548\) | 6.94172i | 0.296536i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 43.1864 | 1.84148 | ||||||||
\(551\) | 46.2034 | 1.96833 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.37173i | 0.270709i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.273984i | 0.0116195i | ||||||||
\(557\) | 36.6100i | 1.55122i | 0.631214 | + | 0.775608i | \(0.282557\pi\) | ||||
−0.631214 | + | 0.775608i | \(0.717443\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.4110i | 0.863292i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.76520 | −0.0744606 | ||||||||
\(563\) | −33.0644 | −1.39350 | −0.696749 | − | 0.717315i | \(-0.745371\pi\) | ||||
−0.696749 | + | 0.717315i | \(0.745371\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 42.5435i | 1.78982i | ||||||||
\(566\) | 26.1243 | 1.09809 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 8.77836 | 0.368332 | ||||||||
\(569\) | 44.0195i | 1.84539i | 0.385528 | + | 0.922696i | \(0.374019\pi\) | ||||
−0.385528 | + | 0.922696i | \(0.625981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.7407 | −1.03537 | −0.517684 | − | 0.855572i | \(-0.673206\pi\) | ||||
−0.517684 | + | 0.855572i | \(0.673206\pi\) | |||||||
\(572\) | −38.1872 | −1.59669 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.1372i | 1.00659i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.6883i | 0.861264i | 0.902528 | + | 0.430632i | \(0.141709\pi\) | ||||
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(578\) | 11.0000i | 0.457540i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 20.2652i | 0.841465i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.6105 | −1.18493 | ||||||||
\(584\) | 0.679758 | 0.0281286 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 12.8799i | − 0.532065i | ||||||||
\(587\) | −4.24396 | −0.175167 | −0.0875835 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875835 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.26808 | −0.134659 | ||||||||
\(590\) | − 22.8535i | − 0.940865i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.79174 | 0.238039 | ||||||||
\(593\) | 14.8951 | 0.611669 | 0.305835 | − | 0.952085i | \(-0.401065\pi\) | ||||
0.305835 | + | 0.952085i | \(0.401065\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 19.1139i | 0.782937i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 21.3431i | − 0.872784i | ||||||||
\(599\) | 21.4812i | 0.877697i | 0.898561 | + | 0.438849i | \(0.144614\pi\) | ||||
−0.898561 | + | 0.438849i | \(0.855386\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 37.5607i | − 1.53213i | −0.642761 | − | 0.766067i | \(-0.722211\pi\) | ||||
0.642761 | − | 0.766067i | \(-0.277789\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.61463 | 0.350524 | ||||||||
\(605\) | −69.9402 | −2.84347 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 41.7681i | 1.69532i | 0.530543 | + | 0.847658i | \(0.321988\pi\) | ||||
−0.530543 | + | 0.847658i | \(0.678012\pi\) | |||||||
\(608\) | 8.16176 | 0.331003 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 25.2869 | 1.02384 | ||||||||
\(611\) | − 0.662400i | − 0.0267978i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.5940 | 1.27607 | 0.638035 | − | 0.770007i | \(-0.279747\pi\) | ||||
0.638035 | + | 0.770007i | \(0.279747\pi\) | |||||||
\(614\) | −11.8601 | −0.478636 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 48.9718i | 1.97153i | 0.168127 | + | 0.985765i | \(0.446228\pi\) | ||||
−0.168127 | + | 0.985765i | \(0.553772\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 6.67646i | − 0.268350i | −0.990958 | − | 0.134175i | \(-0.957162\pi\) | ||||
0.990958 | − | 0.134175i | \(-0.0428384\pi\) | |||||||
\(620\) | − 1.43340i | − 0.0575669i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 9.41692i | − 0.377584i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.00036 | −0.120015 | ||||||||
\(626\) | −5.60415 | −0.223987 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 10.5807i | − 0.422215i | ||||||||
\(629\) | 14.1868 | 0.565666 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.503852 | −0.0200580 | −0.0100290 | − | 0.999950i | \(-0.503192\pi\) | ||||
−0.0100290 | + | 0.999950i | \(0.503192\pi\) | |||||||
\(632\) | − 6.43340i | − 0.255907i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −25.8724 | −1.02752 | ||||||||
\(635\) | 25.3955 | 1.00779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − 31.2828i | − 1.23850i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.57981i | 0.141504i | ||||||||
\(641\) | − 20.8631i | − 0.824042i | −0.911174 | − | 0.412021i | \(-0.864823\pi\) | ||||
0.911174 | − | 0.412021i | \(-0.135177\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 33.6322i | − 1.32632i | −0.748476 | − | 0.663162i | \(-0.769214\pi\) | ||||
0.748476 | − | 0.663162i | \(-0.230786\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.9922 | 0.786581 | ||||||||
\(647\) | −17.6878 | −0.695378 | −0.347689 | − | 0.937610i | \(-0.613033\pi\) | ||||
−0.347689 | + | 0.937610i | \(0.613033\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 35.2784i | 1.38480i | ||||||||
\(650\) | −54.0048 | −2.11824 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.25809 | −0.362575 | ||||||||
\(653\) | − 9.80139i | − 0.383558i | −0.981438 | − | 0.191779i | \(-0.938574\pi\) | ||||
0.981438 | − | 0.191779i | \(-0.0614257\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.3888 | −2.24237 | ||||||||
\(656\) | 5.49535 | 0.214557 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 28.9869i | − 1.12917i | −0.825376 | − | 0.564584i | \(-0.809037\pi\) | ||||
0.825376 | − | 0.564584i | \(-0.190963\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 7.41931i | − 0.288578i | −0.989536 | − | 0.144289i | \(-0.953911\pi\) | ||||
0.989536 | − | 0.144289i | \(-0.0460894\pi\) | |||||||
\(662\) | − 11.0987i | − 0.431364i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.64156i | 0.0637047i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.4842 | 0.676991 | ||||||||
\(668\) | −14.6539 | −0.566976 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.19393i | 0.200659i | ||||||||
\(671\) | −39.0348 | −1.50692 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.5802 | 1.06314 | 0.531570 | − | 0.847014i | \(-0.321602\pi\) | ||||
0.531570 | + | 0.847014i | \(0.321602\pi\) | |||||||
\(674\) | 16.4340i | 0.633015i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 34.7533 | 1.33666 | ||||||||
\(677\) | −21.7087 | −0.834334 | −0.417167 | − | 0.908830i | \(-0.636977\pi\) | ||||
−0.417167 | + | 0.908830i | \(0.636977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.76871i | 0.336265i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.21271i | 0.0847291i | ||||||||
\(683\) | − 22.0113i | − 0.842241i | −0.907005 | − | 0.421120i | \(-0.861637\pi\) | ||||
0.907005 | − | 0.421120i | \(-0.138363\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 24.8500i | − 0.949472i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.95367 | −0.112608 | ||||||||
\(689\) | 35.7776 | 1.36302 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.8589i | 0.755470i | 0.925914 | + | 0.377735i | \(0.123297\pi\) | ||||
−0.925914 | + | 0.377735i | \(0.876703\pi\) | |||||||
\(692\) | −7.93301 | −0.301568 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.61282 | −0.251019 | ||||||||
\(695\) | − 0.980809i | − 0.0372042i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.4608 | 0.509864 | ||||||||
\(698\) | −17.9468 | −0.679296 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.8055i | 0.445887i | 0.974831 | + | 0.222944i | \(0.0715666\pi\) | ||||
−0.974831 | + | 0.222944i | \(0.928433\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 47.2709i | 1.78285i | ||||||||
\(704\) | − 5.52607i | − 0.208271i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 3.64649i | − 0.137237i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.33992 | −0.350768 | −0.175384 | − | 0.984500i | \(-0.556117\pi\) | ||||
−0.175384 | + | 0.984500i | \(0.556117\pi\) | |||||||
\(710\) | −31.4248 | −1.17935 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.1921i | 0.456920i | ||||||||
\(713\) | −1.23670 | −0.0463148 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 136.703 | 5.11240 | ||||||||
\(716\) | 16.7361i | 0.625458i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 3.05213 | 0.113905 | ||||||||
\(719\) | 38.6032 | 1.43966 | 0.719828 | − | 0.694152i | \(-0.244220\pi\) | ||||
0.719828 | + | 0.694152i | \(0.244220\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 47.6144i | 1.77202i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 9.85077i | − 0.366101i | ||||||||
\(725\) | − 44.2406i | − 1.64305i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.9640i | 0.554984i | 0.960728 | + | 0.277492i | \(0.0895033\pi\) | ||||
−0.960728 | + | 0.277492i | \(0.910497\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.43340 | −0.0900643 | ||||||||
\(731\) | −7.23498 | −0.267595 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 28.6378i | − 1.05776i | −0.848696 | − | 0.528881i | \(-0.822612\pi\) | ||||
0.848696 | − | 0.528881i | \(-0.177388\pi\) | |||||||
\(734\) | 22.7523 | 0.839804 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.08856 | 0.113846 | ||||||||
\(737\) | − 8.01775i | − 0.295338i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −33.8925 | −1.24676 | −0.623378 | − | 0.781921i | \(-0.714240\pi\) | ||||
−0.623378 | + | 0.781921i | \(0.714240\pi\) | |||||||
\(740\) | −20.7333 | −0.762173 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 29.8058i | − 1.09347i | −0.837307 | − | 0.546734i | \(-0.815871\pi\) | ||||
0.837307 | − | 0.546734i | \(-0.184129\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 68.4242i | − 2.50687i | ||||||||
\(746\) | 0.718273i | 0.0262979i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 13.5360i | − 0.494927i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0036 | −0.729942 | −0.364971 | − | 0.931019i | \(-0.618921\pi\) | ||||
−0.364971 | + | 0.931019i | \(0.618921\pi\) | |||||||
\(752\) | 0.0958559 | 0.00349550 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 39.1193i | 1.42464i | ||||||||
\(755\) | −30.8387 | −1.12234 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.6330 | −1.00434 | −0.502169 | − | 0.864770i | \(-0.667464\pi\) | ||||
−0.502169 | + | 0.864770i | \(0.667464\pi\) | |||||||
\(758\) | − 14.4935i | − 0.526427i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −29.2176 | −1.05983 | ||||||||
\(761\) | 26.3712 | 0.955954 | 0.477977 | − | 0.878372i | \(-0.341370\pi\) | ||||
0.477977 | + | 0.878372i | \(0.341370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.5738i | 0.635799i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.1105i | 0.690492i | ||||||||
\(767\) | − 44.1159i | − 1.59293i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 46.4263i | − 1.67418i | −0.547068 | − | 0.837088i | \(-0.684256\pi\) | ||||
0.547068 | − | 0.837088i | \(-0.315744\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.8534 | −0.714540 | ||||||||
\(773\) | 9.18820 | 0.330477 | 0.165238 | − | 0.986254i | \(-0.447161\pi\) | ||||
0.165238 | + | 0.986254i | \(0.447161\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.12925i | 0.112406i | ||||||||
\(776\) | −11.3788 | −0.408477 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.90154 | 0.0681733 | ||||||||
\(779\) | 44.8517i | 1.60698i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 48.5098 | 1.73582 | ||||||||
\(782\) | 7.56539 | 0.270538 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 37.8768i | 1.35188i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 16.9582i | − 0.604495i | −0.953230 | − | 0.302247i | \(-0.902263\pi\) | ||||
0.953230 | − | 0.302247i | \(-0.0977369\pi\) | |||||||
\(788\) | 21.5007i | 0.765932i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.0304i | 0.819384i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.8133 | 1.73341 | ||||||||
\(794\) | 15.5802 | 0.552922 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 13.4805i | 0.477805i | ||||||||
\(797\) | 28.7507 | 1.01840 | 0.509200 | − | 0.860648i | \(-0.329941\pi\) | ||||
0.509200 | + | 0.860648i | \(0.329941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.234798 | 0.00830655 | ||||||||
\(800\) | − 7.81504i | − 0.276303i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 34.2752 | 1.21030 | ||||||||
\(803\) | 3.75639 | 0.132560 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 2.76701i | − 0.0974637i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 1.82679i | − 0.0642663i | ||||||||
\(809\) | − 20.9726i | − 0.737358i | −0.929557 | − | 0.368679i | \(-0.879810\pi\) | ||||
0.929557 | − | 0.368679i | \(-0.120190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 35.0116i | − 1.22942i | −0.788752 | − | 0.614711i | \(-0.789272\pi\) | ||||
0.788752 | − | 0.614711i | \(-0.210728\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.0056 | 1.12179 | ||||||||
\(815\) | 33.1422 | 1.16092 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 24.1071i | − 0.843402i | ||||||||
\(818\) | −4.14858 | −0.145052 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −19.6723 | −0.686987 | ||||||||
\(821\) | 39.6709i | 1.38452i | 0.721647 | + | 0.692261i | \(0.243385\pi\) | ||||
−0.721647 | + | 0.692261i | \(0.756615\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.17619 | −0.110715 | −0.0553575 | − | 0.998467i | \(-0.517630\pi\) | ||||
−0.0553575 | + | 0.998467i | \(0.517630\pi\) | |||||||
\(824\) | 5.79030 | 0.201715 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.7069i | 0.893918i | 0.894554 | + | 0.446959i | \(0.147493\pi\) | ||||
−0.894554 | + | 0.446959i | \(0.852507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 0.943062i | − 0.0327539i | −0.999866 | − | 0.0163769i | \(-0.994787\pi\) | ||||
0.999866 | − | 0.0163769i | \(-0.00521318\pi\) | |||||||
\(830\) | − 5.87646i | − 0.203975i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.91037i | 0.239574i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 52.4582 | 1.81539 | ||||||||
\(836\) | 45.1025 | 1.55990 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 16.8972i | 0.583704i | ||||||||
\(839\) | −9.97589 | −0.344406 | −0.172203 | − | 0.985061i | \(-0.555089\pi\) | ||||
−0.172203 | + | 0.985061i | \(0.555089\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.04644 | −0.105050 | ||||||||
\(842\) | − 7.16773i | − 0.247016i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 23.8575 | 0.821210 | ||||||||
\(845\) | −124.410 | −4.27984 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 5.17738i | 0.177792i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 19.1429i | − 0.656595i | ||||||||
\(851\) | 17.8881i | 0.613198i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 0.267352i | − 0.00915394i | −0.999990 | − | 0.00457697i | \(-0.998543\pi\) | ||||
0.999990 | − | 0.00457697i | \(-0.00145690\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.49867 | −0.187941 | ||||||||
\(857\) | 36.3969 | 1.24330 | 0.621648 | − | 0.783297i | \(-0.286464\pi\) | ||||
0.621648 | + | 0.783297i | \(0.286464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.12650i | 0.277273i | 0.990343 | + | 0.138636i | \(0.0442719\pi\) | ||||
−0.990343 | + | 0.138636i | \(0.955728\pi\) | |||||||
\(860\) | 10.5736 | 0.360556 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −19.6670 | −0.669861 | ||||||||
\(863\) | − 36.7419i | − 1.25071i | −0.780340 | − | 0.625355i | \(-0.784954\pi\) | ||||
0.780340 | − | 0.625355i | \(-0.215046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 28.3987 | 0.965584 | ||||||||
\(866\) | 16.1213 | 0.547824 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 35.5514i | − 1.20600i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.0262i | 0.339726i | ||||||||
\(872\) | 13.4705i | 0.456167i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.2081i | 0.852676i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −55.2141 | −1.86445 | −0.932224 | − | 0.361883i | \(-0.882134\pi\) | ||||
−0.932224 | + | 0.361883i | \(0.882134\pi\) | |||||||
\(878\) | −26.7007 | −0.901104 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 19.7823i | 0.666860i | ||||||||
\(881\) | −22.0434 | −0.742660 | −0.371330 | − | 0.928501i | \(-0.621098\pi\) | ||||
−0.371330 | + | 0.928501i | \(0.621098\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.7683 | −0.564300 | −0.282150 | − | 0.959370i | \(-0.591048\pi\) | ||||
−0.282150 | + | 0.959370i | \(0.591048\pi\) | |||||||
\(884\) | 16.9269i | 0.569313i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.8643 | −0.667353 | ||||||||
\(887\) | −15.9974 | −0.537139 | −0.268569 | − | 0.963260i | \(-0.586551\pi\) | ||||
−0.268569 | + | 0.963260i | \(0.586551\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 43.6455i | − 1.46300i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.75175i | 0.259548i | ||||||||
\(893\) | 0.782353i | 0.0261804i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 59.9122i | − 2.00264i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.0132 | 0.667848 | ||||||||
\(899\) | 2.26672 | 0.0755995 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6819i | 0.422496i | ||||||||
\(902\) | 30.3677 | 1.01113 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.8843 | −0.395266 | ||||||||
\(905\) | 35.2639i | 1.17221i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.5899 | 0.683676 | 0.341838 | − | 0.939759i | \(-0.388951\pi\) | ||||
0.341838 | + | 0.939759i | \(0.388951\pi\) | |||||||
\(908\) | 11.1867 | 0.371242 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 23.5024i | − 0.778670i | −0.921096 | − | 0.389335i | \(-0.872705\pi\) | ||||
0.921096 | − | 0.389335i | \(-0.127295\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.07135i | 0.300218i | ||||||||
\(914\) | 23.9138i | 0.790997i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 16.0107i | − 0.529010i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8861 | 0.886891 | 0.443445 | − | 0.896301i | \(-0.353756\pi\) | ||||
0.443445 | + | 0.896301i | \(0.353756\pi\) | |||||||
\(920\) | −11.0565 | −0.364521 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 18.6642i | 0.614673i | ||||||||
\(923\) | −60.6617 | −1.99671 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 45.2627 | 1.48823 | ||||||||
\(926\) | 7.64166i | 0.251121i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.66096 | −0.185830 | ||||||||
\(929\) | 10.2186 | 0.335262 | 0.167631 | − | 0.985850i | \(-0.446388\pi\) | ||||
0.167631 | + | 0.985850i | \(0.446388\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 5.62801i | − 0.184352i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.7012i | 1.13546i | ||||||||
\(935\) | 48.4565i | 1.58470i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.9366i | 1.40268i | 0.712829 | + | 0.701338i | \(0.247414\pi\) | ||||
−0.712829 | + | 0.701338i | \(0.752586\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.343146 | −0.0111922 | ||||||||
\(941\) | −9.15254 | −0.298364 | −0.149182 | − | 0.988810i | \(-0.547664\pi\) | ||||
−0.149182 | + | 0.988810i | \(0.547664\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9727i | 0.552708i | ||||||||
\(944\) | 6.38401 | 0.207782 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −16.3222 | −0.530680 | ||||||||
\(947\) | − 40.6714i | − 1.32164i | −0.750543 | − | 0.660821i | \(-0.770208\pi\) | ||||
0.750543 | − | 0.660821i | \(-0.229792\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.69738 | −0.152483 | ||||||||
\(950\) | 63.7845 | 2.06944 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 7.49289i | − 0.242719i | −0.992609 | − | 0.121359i | \(-0.961275\pi\) | ||||
0.992609 | − | 0.121359i | \(-0.0387253\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 62.9110i | − 2.03575i | ||||||||
\(956\) | 25.9630i | 0.839703i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.2363i | 0.847656i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.8397 | 0.994828 | ||||||||
\(962\) | −40.0231 | −1.29040 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.5302i | 0.467985i | ||||||||
\(965\) | 71.0715 | 2.28787 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.71864 | 0.312530 | 0.156265 | − | 0.987715i | \(-0.450055\pi\) | ||||
0.156265 | + | 0.987715i | \(0.450055\pi\) | |||||||
\(968\) | − 19.5374i | − 0.627956i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 40.7341 | 1.30789 | ||||||||
\(971\) | 5.15136 | 0.165315 | 0.0826576 | − | 0.996578i | \(-0.473659\pi\) | ||||
0.0826576 | + | 0.996578i | \(0.473659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 7.73022i | 0.247692i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 7.06376i | 0.226106i | ||||||||
\(977\) | 50.1137i | 1.60328i | 0.597808 | + | 0.801639i | \(0.296039\pi\) | ||||
−0.597808 | + | 0.801639i | \(0.703961\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 67.3746i | 2.15330i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 33.0173 | 1.05362 | ||||||||
\(983\) | −28.5480 | −0.910538 | −0.455269 | − | 0.890354i | \(-0.650457\pi\) | ||||
−0.455269 | + | 0.890354i | \(0.650457\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 76.9685i | − 2.45242i | ||||||||
\(986\) | −13.8665 | −0.441598 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −56.4008 | −1.79435 | ||||||||
\(989\) | − 9.12258i | − 0.290081i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −62.0232 | −1.97023 | −0.985116 | − | 0.171888i | \(-0.945013\pi\) | ||||
−0.985116 | + | 0.171888i | \(0.945013\pi\) | |||||||
\(992\) | 0.400414 | 0.0127131 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 48.2578i | − 1.52987i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 7.05415i | − 0.223407i | −0.993742 | − | 0.111704i | \(-0.964369\pi\) | ||||
0.993742 | − | 0.111704i | \(-0.0356307\pi\) | |||||||
\(998\) | 7.61078i | 0.240915i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2646.2.d.f.2645.8 | yes | 16 | |
3.2 | odd | 2 | inner | 2646.2.d.f.2645.9 | yes | 16 | |
7.6 | odd | 2 | inner | 2646.2.d.f.2645.1 | ✓ | 16 | |
21.20 | even | 2 | inner | 2646.2.d.f.2645.16 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2646.2.d.f.2645.1 | ✓ | 16 | 7.6 | odd | 2 | inner | |
2646.2.d.f.2645.8 | yes | 16 | 1.1 | even | 1 | trivial | |
2646.2.d.f.2645.9 | yes | 16 | 3.2 | odd | 2 | inner | |
2646.2.d.f.2645.16 | yes | 16 | 21.20 | even | 2 | inner |