Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,2,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), 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: | \(2.58715302549\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} + 24 x^{16} - 66 x^{15} + 153 x^{14} - 315 x^{13} + 651 x^{12} - 1350 x^{11} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{5} \) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 37.1 | ||
Root | \(1.68668 + 0.393823i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.37 |
Dual form | 324.2.i.a.289.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{7}{9}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.29878 | + | 0.836687i | −1.02805 | + | 0.374178i | −0.800336 | − | 0.599551i | \(-0.795346\pi\) |
−0.227709 | + | 0.973729i | \(0.573124\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.775345 | − | 4.39720i | −0.293053 | − | 1.66199i | −0.675012 | − | 0.737807i | \(-0.735862\pi\) |
0.381959 | − | 0.924179i | \(-0.375250\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.73892 | − | 0.996887i | −0.825816 | − | 0.300573i | −0.105676 | − | 0.994401i | \(-0.533701\pi\) |
−0.720141 | + | 0.693828i | \(0.755923\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.01596 | − | 1.69159i | −0.559127 | − | 0.469163i | 0.318891 | − | 0.947791i | \(-0.396690\pi\) |
−0.878018 | + | 0.478628i | \(0.841134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.67030 | − | 2.89305i | 0.405108 | − | 0.701667i | −0.589226 | − | 0.807968i | \(-0.700567\pi\) |
0.994334 | + | 0.106301i | \(0.0339007\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.02319 | + | 1.77222i | 0.234736 | + | 0.406575i | 0.959196 | − | 0.282742i | \(-0.0912441\pi\) |
−0.724460 | + | 0.689317i | \(0.757911\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.60711 | − | 9.11438i | 0.335106 | − | 1.90048i | −0.0910783 | − | 0.995844i | \(-0.529031\pi\) |
0.426184 | − | 0.904636i | \(-0.359858\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.754121 | − | 0.632782i | 0.150824 | − | 0.126556i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.30671 | + | 4.45286i | −0.985431 | + | 0.826875i | −0.984900 | − | 0.173125i | \(-0.944614\pi\) |
−0.000531132 | 1.00000i | \(0.500169\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.380324 | + | 2.15692i | −0.0683082 | + | 0.387395i | 0.931417 | + | 0.363954i | \(0.118573\pi\) |
−0.999725 | + | 0.0234413i | \(0.992538\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.46143 | + | 9.45948i | 0.923151 | + | 1.59894i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.708571 | − | 1.22728i | 0.116488 | − | 0.201764i | −0.801885 | − | 0.597478i | \(-0.796170\pi\) |
0.918374 | + | 0.395714i | \(0.129503\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.13541 | − | 2.63092i | −0.489669 | − | 0.410881i | 0.364238 | − | 0.931306i | \(-0.381329\pi\) |
−0.853908 | + | 0.520424i | \(0.825774\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.42467 | + | 1.61045i | 0.674755 | + | 0.245591i | 0.656594 | − | 0.754244i | \(-0.271997\pi\) |
0.0181613 | + | 0.999835i | \(0.494219\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.03917 | + | 5.89344i | 0.151579 | + | 0.859647i | 0.961847 | + | 0.273588i | \(0.0882103\pi\) |
−0.810268 | + | 0.586059i | \(0.800679\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −12.1564 | + | 4.42456i | −1.73663 | + | 0.632080i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.97011 | −0.270616 | −0.135308 | − | 0.990804i | \(-0.543202\pi\) | ||||
−0.135308 | + | 0.990804i | \(0.543202\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.13026 | 0.961445 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.20572 | − | 2.25870i | 0.807916 | − | 0.294057i | 0.0951531 | − | 0.995463i | \(-0.469666\pi\) |
0.712763 | + | 0.701405i | \(0.247444\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.25433 | − | 7.11368i | −0.160601 | − | 0.910814i | −0.953485 | − | 0.301441i | \(-0.902532\pi\) |
0.792884 | − | 0.609373i | \(-0.208579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.04958 | + | 2.20187i | 0.750358 | + | 0.273108i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.37884 | + | 1.99608i | 0.290621 | + | 0.243860i | 0.776428 | − | 0.630206i | \(-0.217030\pi\) |
−0.485807 | + | 0.874066i | \(0.661474\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.60947 | − | 11.4479i | 0.784400 | − | 1.35862i | −0.144958 | − | 0.989438i | \(-0.546305\pi\) |
0.929357 | − | 0.369182i | \(-0.120362\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.40266 | + | 11.0897i | 0.749374 | + | 1.29795i | 0.948123 | + | 0.317904i | \(0.102979\pi\) |
−0.198749 | + | 0.980051i | \(0.563688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.25990 | + | 12.8165i | −0.257540 | + | 1.46058i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.57726 | − | 1.32348i | 0.177456 | − | 0.148903i | −0.549733 | − | 0.835340i | \(-0.685271\pi\) |
0.727189 | + | 0.686437i | \(0.240826\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.20111 | − | 1.00785i | 0.131839 | − | 0.110626i | −0.574484 | − | 0.818516i | \(-0.694797\pi\) |
0.706323 | + | 0.707890i | \(0.250353\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.41908 | + | 8.04800i | −0.153921 | + | 0.872928i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.88694 | + | 11.9285i | 0.730014 | + | 1.26442i | 0.956877 | + | 0.290495i | \(0.0938199\pi\) |
−0.226862 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.87520 | + | 10.1761i | −0.615889 | + | 1.06675i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.83488 | − | 3.21785i | −0.393451 | − | 0.330144i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.9332 | − | 5.07127i | −1.41470 | − | 0.514909i | −0.482195 | − | 0.876064i | \(-0.660160\pi\) |
−0.932506 | + | 0.361155i | \(0.882383\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.515693 | − | 2.92464i | −0.0513134 | − | 0.291013i | 0.948342 | − | 0.317249i | \(-0.102759\pi\) |
−0.999656 | + | 0.0262361i | \(0.991648\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.5040 | − | 3.82316i | 1.03499 | − | 0.376707i | 0.232013 | − | 0.972713i | \(-0.425469\pi\) |
0.802980 | + | 0.596006i | \(0.203247\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.88974 | −0.472709 | −0.236355 | − | 0.971667i | \(-0.575953\pi\) | ||||
−0.236355 | + | 0.971667i | \(0.575953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.68231 | −0.352701 | −0.176351 | − | 0.984327i | \(-0.556429\pi\) | ||||
−0.176351 | + | 0.984327i | \(0.556429\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.55548 | − | 2.38600i | 0.616688 | − | 0.224456i | −0.0147393 | − | 0.999891i | \(-0.504692\pi\) |
0.631427 | + | 0.775435i | \(0.282470\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.93149 | + | 22.2966i | 0.366614 | + | 2.07917i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.0164 | − | 5.10154i | −1.28488 | − | 0.467658i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.91857 | − | 1.60987i | −0.174416 | − | 0.146352i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.91166 | − | 8.50724i | 0.439312 | − | 0.760911i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.67931 | − | 16.7651i | −0.858900 | − | 1.48766i | −0.872979 | − | 0.487757i | \(-0.837815\pi\) |
0.0140793 | − | 0.999901i | \(-0.495518\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.481816 | − | 2.73252i | 0.0420965 | − | 0.238741i | −0.956498 | − | 0.291738i | \(-0.905766\pi\) |
0.998595 | + | 0.0529973i | \(0.0168775\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.99947 | − | 5.87326i | 0.606931 | − | 0.509276i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.21498 | − | 4.37589i | 0.445546 | − | 0.373858i | −0.392234 | − | 0.919865i | \(-0.628298\pi\) |
0.837780 | + | 0.546008i | \(0.183853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.23814 | − | 18.3644i | 0.274656 | − | 1.55765i | −0.465398 | − | 0.885102i | \(-0.654089\pi\) |
0.740053 | − | 0.672548i | \(-0.234800\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.83523 | + | 6.64282i | 0.320718 | + | 0.555501i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.47330 | − | 14.6762i | 0.703670 | − | 1.21879i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −0.277361 | − | 0.232733i | −0.0227223 | − | 0.0190662i | 0.631356 | − | 0.775493i | \(-0.282499\pi\) |
−0.654078 | + | 0.756427i | \(0.726943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.32130 | + | 1.20886i | 0.270284 | + | 0.0983752i | 0.473607 | − | 0.880737i | \(-0.342952\pi\) |
−0.203323 | + | 0.979112i | \(0.565174\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.930390 | − | 5.27651i | −0.0747308 | − | 0.423819i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.7131 | − | 4.26323i | 0.934810 | − | 0.340243i | 0.170696 | − | 0.985324i | \(-0.445398\pi\) |
0.764114 | + | 0.645081i | \(0.223176\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −41.3238 | −3.25678 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.1125 | −1.26203 | −0.631016 | − | 0.775770i | \(-0.717362\pi\) | ||||
−0.631016 | + | 0.775770i | \(0.717362\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −16.7783 | + | 6.10681i | −1.29835 | + | 0.472559i | −0.896458 | − | 0.443129i | \(-0.853868\pi\) |
−0.401889 | + | 0.915689i | \(0.631646\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.05481 | − | 5.98214i | −0.0811395 | − | 0.460165i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 13.9855 | + | 5.09032i | 1.06330 | + | 0.387010i | 0.813667 | − | 0.581331i | \(-0.197468\pi\) |
0.249633 | + | 0.968340i | \(0.419690\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.36718 | − | 2.82540i | −0.254535 | − | 0.213580i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.817468 | + | 1.41590i | −0.0611004 | + | 0.105829i | −0.894958 | − | 0.446151i | \(-0.852794\pi\) |
0.833857 | + | 0.551980i | \(0.186128\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.16838 | − | 3.75574i | −0.161174 | − | 0.279162i | 0.774116 | − | 0.633044i | \(-0.218195\pi\) |
−0.935290 | + | 0.353882i | \(0.884861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.601998 | + | 3.41410i | −0.0442598 | + | 0.251010i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.45887 | + | 6.25873i | −0.545447 | + | 0.457684i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.661413 | + | 0.554991i | −0.0478582 | + | 0.0401578i | −0.666403 | − | 0.745592i | \(-0.732167\pi\) |
0.618545 | + | 0.785749i | \(0.287723\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.904508 | + | 5.12972i | −0.0651079 | + | 0.369245i | 0.934793 | + | 0.355192i | \(0.115585\pi\) |
−0.999901 | + | 0.0140533i | \(0.995527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.1550 | − | 22.7852i | −0.937257 | − | 1.62338i | −0.770559 | − | 0.637368i | \(-0.780023\pi\) |
−0.166697 | − | 0.986008i | \(-0.553310\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.38490 | − | 9.32692i | 0.381725 | − | 0.661168i | −0.609584 | − | 0.792722i | \(-0.708663\pi\) |
0.991309 | + | 0.131554i | \(0.0419967\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.6946 | + | 19.8822i | 1.66304 | + | 1.39545i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.40889 | + | 3.42456i | 0.657145 | + | 0.239181i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.03574 | − | 5.87397i | −0.0716436 | − | 0.406311i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.45213 | + | 1.25647i | −0.237654 | + | 0.0864990i | −0.458102 | − | 0.888900i | \(-0.651470\pi\) |
0.220448 | + | 0.975399i | \(0.429248\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.5188 | −0.785574 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.77931 | 0.663863 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.26111 | + | 3.00680i | −0.555703 | + | 0.202259i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.863453 | + | 4.89688i | 0.0578211 | + | 0.327920i | 0.999974 | − | 0.00726484i | \(-0.00231249\pi\) |
−0.942153 | + | 0.335184i | \(0.891201\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.99997 | + | 3.63969i | 0.663721 | + | 0.241575i | 0.651842 | − | 0.758355i | \(-0.273996\pi\) |
0.0118791 | + | 0.999929i | \(0.496219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9102 | + | 9.15476i | 0.720967 | + | 0.604963i | 0.927653 | − | 0.373444i | \(-0.121823\pi\) |
−0.206685 | + | 0.978407i | \(0.566268\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.93762 | − | 13.7484i | 0.520011 | − | 0.900685i | −0.479719 | − | 0.877422i | \(-0.659261\pi\) |
0.999729 | − | 0.0232627i | \(-0.00740541\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.31980 | − | 12.6783i | −0.477491 | − | 0.827039i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.85681 | − | 10.5305i | 0.120107 | − | 0.681160i | −0.863988 | − | 0.503513i | \(-0.832041\pi\) |
0.984094 | − | 0.177646i | \(-0.0568483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.5594 | + | 9.69950i | −0.744607 | + | 0.624800i | −0.934071 | − | 0.357088i | \(-0.883770\pi\) |
0.189463 | + | 0.981888i | \(0.439325\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 24.2429 | − | 20.3422i | 1.54882 | − | 1.29961i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.935157 | − | 5.30354i | 0.0595026 | − | 0.337456i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.07700 | + | 13.9898i | 0.509816 | + | 0.883027i | 0.999935 | + | 0.0113719i | \(0.00361986\pi\) |
−0.490119 | + | 0.871655i | \(0.663047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −13.4878 | + | 23.3615i | −0.847968 | + | 1.46872i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.39647 | + | 1.17178i | 0.0871096 | + | 0.0730936i | 0.685303 | − | 0.728258i | \(-0.259670\pi\) |
−0.598193 | + | 0.801352i | \(0.704114\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.94599 | − | 2.16416i | −0.369466 | − | 0.134475i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.36051 | − | 13.3871i | −0.145556 | − | 0.825487i | −0.966919 | − | 0.255082i | \(-0.917898\pi\) |
0.821364 | − | 0.570405i | \(-0.193214\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.52885 | − | 1.64837i | 0.278205 | − | 0.101258i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.0603 | 0.979212 | 0.489606 | − | 0.871944i | \(-0.337141\pi\) | ||||
0.489606 | + | 0.871944i | \(0.337141\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.0822 | −0.976924 | −0.488462 | − | 0.872585i | \(-0.662442\pi\) | ||||
−0.488462 | + | 0.872585i | \(0.662442\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.69629 | + | 0.981370i | −0.162592 | + | 0.0591788i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.62263 | + | 14.8737i | 0.157578 | + | 0.893672i | 0.956390 | + | 0.292091i | \(0.0943511\pi\) |
−0.798812 | + | 0.601581i | \(0.794538\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.84548 | − | 2.12758i | −0.348712 | − | 0.126921i | 0.161725 | − | 0.986836i | \(-0.448294\pi\) |
−0.510437 | + | 0.859915i | \(0.670516\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.75911 | + | 6.51066i | 0.461231 | + | 0.387019i | 0.843584 | − | 0.536998i | \(-0.180442\pi\) |
−0.382353 | + | 0.924016i | \(0.624886\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −9.13768 | + | 15.8269i | −0.539380 | + | 0.934234i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.92018 | + | 5.05791i | 0.171776 | + | 0.297524i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.02648 | + | 28.5066i | −0.293650 | + | 1.66537i | 0.378989 | + | 0.925401i | \(0.376272\pi\) |
−0.672639 | + | 0.739971i | \(0.734839\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3758 | + | 10.3845i | −0.720544 | + | 0.604609i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.6577 | + | 15.6557i | −1.07900 | + | 0.905390i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.65081 | − | 20.7048i | 0.210429 | − | 1.19340i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.83537 | + | 15.3033i | 0.505912 | + | 0.876265i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.33981 | + | 2.32062i | −0.0764669 | + | 0.132445i | −0.901723 | − | 0.432314i | \(-0.857697\pi\) |
0.825256 | + | 0.564758i | \(0.191031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1610 | + | 9.36520i | 0.632883 | + | 0.531052i | 0.901823 | − | 0.432105i | \(-0.142229\pi\) |
−0.268941 | + | 0.963157i | \(0.586674\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.9660 | + | 9.08687i | 1.41116 | + | 0.513620i | 0.931470 | − | 0.363818i | \(-0.118527\pi\) |
0.479690 | + | 0.877438i | \(0.340749\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.59994 | + | 20.4163i | 0.202193 | + | 1.14669i | 0.901797 | + | 0.432161i | \(0.142249\pi\) |
−0.699604 | + | 0.714531i | \(0.746640\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.9737 | − | 6.90585i | 1.06232 | − | 0.386653i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.83615 | 0.380373 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.59069 | −0.143705 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 25.1089 | − | 9.13890i | 1.38430 | − | 0.503844i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.94118 | − | 11.0090i | −0.106697 | − | 0.605107i | −0.990529 | − | 0.137303i | \(-0.956156\pi\) |
0.883832 | − | 0.467804i | \(-0.154955\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.13851 | − | 2.59821i | −0.390019 | − | 0.141955i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.44752 | + | 5.41011i | 0.351219 | + | 0.294707i | 0.801279 | − | 0.598291i | \(-0.204153\pi\) |
−0.450061 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.19189 | − | 5.52851i | 0.172850 | − | 0.299386i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.2534 | + | 22.9556i | 0.715619 | + | 1.23949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.44612 | − | 8.20137i | 0.0776319 | − | 0.440273i | −0.921073 | − | 0.389391i | \(-0.872686\pi\) |
0.998705 | − | 0.0508820i | \(-0.0162032\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.14276 | + | 1.79799i | −0.114700 | + | 0.0962444i | −0.698334 | − | 0.715772i | \(-0.746075\pi\) |
0.583634 | + | 0.812017i | \(0.301630\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.96097 | − | 6.68005i | 0.423720 | − | 0.355543i | −0.405856 | − | 0.913937i | \(-0.633027\pi\) |
0.829576 | + | 0.558394i | \(0.188582\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.61537 | + | 31.8463i | −0.298033 | + | 1.69023i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.64987 | − | 8.05381i | −0.245411 | − | 0.425064i | 0.716836 | − | 0.697241i | \(-0.245589\pi\) |
−0.962247 | + | 0.272178i | \(0.912256\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.40616 | − | 12.8278i | 0.389798 | − | 0.675150i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.9969 | − | 20.1358i | −1.25606 | − | 1.05396i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.86164 | − | 1.04155i | −0.149376 | − | 0.0543686i | 0.266250 | − | 0.963904i | \(-0.414215\pi\) |
−0.415626 | + | 0.909535i | \(0.636438\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52752 | + | 8.66297i | 0.0793047 | + | 0.449759i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.8374 | + | 6.85625i | −0.975363 | + | 0.355003i | −0.780036 | − | 0.625735i | \(-0.784799\pi\) |
−0.195327 | + | 0.980738i | \(0.562577\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 18.2305 | 0.938920 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.89450 | 0.302780 | 0.151390 | − | 0.988474i | \(-0.451625\pi\) | ||||
0.151390 | + | 0.988474i | \(0.451625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.02364 | − | 1.82846i | 0.256696 | − | 0.0934298i | −0.210467 | − | 0.977601i | \(-0.567498\pi\) |
0.467163 | + | 0.884171i | \(0.345276\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.52842 | − | 31.3532i | −0.281754 | − | 1.59791i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.75979 | + | 1.00448i | 0.139927 | + | 0.0509293i | 0.411034 | − | 0.911620i | \(-0.365168\pi\) |
−0.271107 | + | 0.962549i | \(0.587390\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.6840 | − | 19.8732i | −1.19775 | − | 1.00503i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.51844 | + | 4.36206i | −0.126716 | + | 0.219479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.19815 | − | 12.4676i | −0.361265 | − | 0.625729i | 0.626905 | − | 0.779096i | \(-0.284322\pi\) |
−0.988169 | + | 0.153367i | \(0.950988\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.55499 | + | 14.4901i | −0.127590 | + | 0.723599i | 0.852146 | + | 0.523305i | \(0.175301\pi\) |
−0.979736 | + | 0.200294i | \(0.935810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.41535 | − | 3.70492i | 0.219944 | − | 0.184555i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.16418 | + | 2.65506i | −0.156843 | + | 0.131607i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.83984 | + | 27.4481i | −0.239315 | + | 1.35722i | 0.594018 | + | 0.804451i | \(0.297541\pi\) |
−0.833333 | + | 0.552771i | \(0.813570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.7435 | − | 25.5365i | −0.725481 | − | 1.25657i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.91783 | + | 3.32178i | −0.0941425 | + | 0.163060i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −26.7631 | − | 22.4569i | −1.30746 | − | 1.09709i | −0.988804 | − | 0.149223i | \(-0.952323\pi\) |
−0.318660 | − | 0.947869i | \(-0.603233\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.75763 | − | 3.18752i | −0.426821 | − | 0.155350i | 0.119673 | − | 0.992813i | \(-0.461815\pi\) |
−0.546493 | + | 0.837463i | \(0.684038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.571060 | − | 3.23865i | −0.0277005 | − | 0.157097i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −30.3078 | + | 11.0311i | −1.46670 | + | 0.533833i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.92496 | −0.189058 | −0.0945292 | − | 0.995522i | \(-0.530135\pi\) | ||||
−0.0945292 | + | 0.995522i | \(0.530135\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 40.3617 | 1.93966 | 0.969829 | − | 0.243786i | \(-0.0783894\pi\) | ||||
0.969829 | + | 0.243786i | \(0.0783894\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 17.7971 | − | 6.47760i | 0.851349 | − | 0.309866i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.759264 | − | 4.30600i | −0.0362377 | − | 0.205514i | 0.961313 | − | 0.275457i | \(-0.0888293\pi\) |
−0.997551 | + | 0.0699432i | \(0.977718\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.3212 | + | 9.58012i | 1.25056 | + | 0.455165i | 0.880590 | − | 0.473880i | \(-0.157147\pi\) |
0.369967 | + | 0.929045i | \(0.379369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.8120 | − | 21.6589i | −1.22361 | − | 1.02673i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.0254 | + | 24.2927i | −0.661899 | + | 1.14644i | 0.318217 | + | 0.948018i | \(0.396916\pi\) |
−0.980116 | + | 0.198425i | \(0.936417\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.96493 | + | 10.3316i | 0.280877 | + | 0.486494i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.99154 | − | 28.3084i | 0.234007 | − | 1.32712i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.3932 | − | 21.3074i | 1.18784 | − | 0.996718i | 0.187948 | − | 0.982179i | \(-0.439816\pi\) |
0.999894 | − | 0.0145393i | \(-0.00462816\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.7916 | + | 14.9290i | −0.828639 | + | 0.695311i | −0.954978 | − | 0.296676i | \(-0.904122\pi\) |
0.126339 | + | 0.991987i | \(0.459677\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.87203 | − | 16.2881i | 0.133475 | − | 0.756972i | −0.842435 | − | 0.538798i | \(-0.818879\pi\) |
0.975910 | − | 0.218174i | \(-0.0700102\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.44277 | − | 14.6233i | −0.390685 | − | 0.676686i | 0.601855 | − | 0.798605i | \(-0.294428\pi\) |
−0.992540 | + | 0.121919i | \(0.961095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.93275 | − | 12.0079i | 0.320125 | − | 0.554472i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.5134 | − | 8.82178i | −0.483406 | − | 0.405626i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.89304 | + | 0.689009i | 0.0868585 | + | 0.0316139i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.572645 | − | 3.24763i | −0.0261648 | − | 0.148388i | 0.968927 | − | 0.247349i | \(-0.0795593\pi\) |
−0.995091 | + | 0.0989606i | \(0.968448\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.50451 | + | 1.27554i | −0.159792 | + | 0.0581594i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 36.2724 | 1.64704 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.40222 | −0.380741 | −0.190370 | − | 0.981712i | \(-0.560969\pi\) | ||||
−0.190370 | + | 0.981712i | \(0.560969\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.7943 | + | 11.5722i | −1.43486 | + | 0.522246i | −0.938320 | − | 0.345769i | \(-0.887618\pi\) |
−0.496538 | + | 0.868015i | \(0.665396\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.01852 | + | 22.7902i | 0.180985 | + | 1.02642i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −55.4635 | − | 20.1871i | −2.48788 | − | 0.905513i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.6162 | + | 24.0118i | 1.28103 | + | 1.07492i | 0.993101 | + | 0.117266i | \(0.0374129\pi\) |
0.287934 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.0186236 | − | 0.0322570i | 0.000830385 | − | 0.00143827i | −0.865610 | − | 0.500719i | \(-0.833069\pi\) |
0.866440 | + | 0.499281i | \(0.166402\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.63247 | + | 6.29163i | 0.161643 | + | 0.279974i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.22655 | − | 18.2987i | 0.143014 | − | 0.811074i | −0.825926 | − | 0.563779i | \(-0.809347\pi\) |
0.968940 | − | 0.247295i | \(-0.0795417\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 43.7995 | − | 36.7521i | 1.93758 | − | 1.62582i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −20.9477 | + | 17.5772i | −0.923065 | + | 0.774543i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.02888 | − | 17.1776i | 0.133210 | − | 0.755471i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.96816 | + | 15.5333i | 0.392902 | + | 0.680526i | 0.992831 | − | 0.119527i | \(-0.0381378\pi\) |
−0.599929 | + | 0.800053i | \(0.704804\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.28323 | − | 3.95468i | 0.0998388 | − | 0.172926i | −0.811779 | − | 0.583965i | \(-0.801501\pi\) |
0.911618 | + | 0.411039i | \(0.134834\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.60483 | + | 4.70301i | 0.244150 | + | 0.204866i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −58.8762 | − | 21.4292i | −2.55984 | − | 0.931704i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.87042 | + | 10.6077i | 0.0810169 | + | 0.459470i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 11.2404 | − | 4.09119i | 0.485967 | − | 0.176877i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.7062 | 1.62412 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3230 | −0.572802 | −0.286401 | − | 0.958110i | \(-0.592459\pi\) | ||||
−0.286401 | + | 0.958110i | \(0.592459\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.46481 | − | 3.08094i | 0.362593 | − | 0.131973i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.06345 | − | 28.7162i | −0.216497 | − | 1.22782i | −0.878289 | − | 0.478130i | \(-0.841315\pi\) |
0.661792 | − | 0.749688i | \(-0.269796\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.3212 | − | 4.84852i | −0.567503 | − | 0.206554i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.04253 | − | 5.90938i | −0.299479 | − | 0.251292i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.7045 | + | 28.9330i | −0.707791 | + | 1.22593i | 0.257884 | + | 0.966176i | \(0.416975\pi\) |
−0.965675 | + | 0.259753i | \(0.916359\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.19573 | − | 10.7313i | −0.262051 | − | 0.453886i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.01400 | − | 17.0933i | 0.127025 | − | 0.720395i | −0.853059 | − | 0.521814i | \(-0.825256\pi\) |
0.980084 | − | 0.198581i | \(-0.0636333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.0733 | + | 10.9698i | −0.549996 | + | 0.461502i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.5890 | + | 29.0236i | −1.45004 | + | 1.21673i | −0.517498 | + | 0.855685i | \(0.673136\pi\) |
−0.932547 | + | 0.361047i | \(0.882419\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.85742 | − | 27.5478i | 0.203277 | − | 1.15284i | −0.696851 | − | 0.717215i | \(-0.745416\pi\) |
0.900128 | − | 0.435625i | \(-0.143473\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.55547 | − | 7.89030i | −0.189976 | − | 0.329048i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.9009 | + | 29.2732i | −0.703593 | + | 1.21866i | 0.263603 | + | 0.964631i | \(0.415089\pi\) |
−0.967197 | + | 0.254028i | \(0.918244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.36299 | − | 4.50009i | −0.222494 | − | 0.186695i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.39598 | + | 1.96398i | 0.223479 | + | 0.0813396i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.35230 | − | 7.66925i | −0.0558152 | − | 0.316544i | 0.944099 | − | 0.329663i | \(-0.106935\pi\) |
−0.999914 | + | 0.0131190i | \(0.995824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.21168 | + | 1.53293i | −0.173539 | + | 0.0631632i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.2877 | 0.750986 | 0.375493 | − | 0.926825i | \(-0.377473\pi\) | ||||
0.375493 | + | 0.926825i | \(0.377473\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 36.4890 | 1.49590 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.3587 | + | 7.40994i | −0.831832 | + | 0.302762i | −0.722611 | − | 0.691255i | \(-0.757058\pi\) |
−0.109221 | + | 0.994017i | \(0.534836\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.0948417 | + | 0.537874i | 0.00386867 | + | 0.0219403i | 0.986681 | − | 0.162667i | \(-0.0520097\pi\) |
−0.982812 | + | 0.184608i | \(0.940899\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.75733 | + | 2.09550i | 0.234069 | + | 0.0851941i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.78443 | − | 8.21011i | −0.397138 | − | 0.333238i | 0.422248 | − | 0.906480i | \(-0.361241\pi\) |
−0.819386 | + | 0.573242i | \(0.805685\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.87436 | − | 13.6388i | 0.318563 | − | 0.551767i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.48439 | + | 12.9634i | 0.302292 | + | 0.523585i | 0.976655 | − | 0.214815i | \(-0.0689150\pi\) |
−0.674363 | + | 0.738400i | \(0.735582\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.91960 | − | 22.2292i | 0.157797 | − | 0.894912i | −0.798387 | − | 0.602145i | \(-0.794313\pi\) |
0.956184 | − | 0.292767i | \(-0.0945760\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.0226 | + | 20.1574i | −0.965551 | + | 0.810193i | −0.981847 | − | 0.189674i | \(-0.939257\pi\) |
0.0162965 | + | 0.999867i | \(0.494812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 47.1124 | − | 39.5320i | 1.88752 | − | 1.58382i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.02765 | + | 28.5132i | −0.201106 | + | 1.14053i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.36705 | − | 4.09986i | −0.0943806 | − | 0.163472i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.23348 | − | 5.60055i | 0.128723 | − | 0.222955i | −0.794459 | − | 0.607318i | \(-0.792246\pi\) |
0.923182 | + | 0.384363i | \(0.125579\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 36.2777 | + | 30.4406i | 1.43964 | + | 1.20800i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.9913 | + | 11.6439i | 1.26754 | + | 0.461348i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.29933 | − | 13.0401i | −0.0908180 | − | 0.515055i | −0.995949 | − | 0.0899216i | \(-0.971338\pi\) |
0.905131 | − | 0.425133i | \(-0.139773\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.5304 | + | 5.28864i | −0.573024 | + | 0.208564i | −0.612247 | − | 0.790667i | \(-0.709734\pi\) |
0.0392228 | + | 0.999230i | \(0.487512\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.4105 | 1.70664 | 0.853321 | − | 0.521386i | \(-0.174585\pi\) | ||||
0.853321 | + | 0.521386i | \(0.174585\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.2486 | −0.755576 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −13.3043 | + | 4.84239i | −0.520639 | + | 0.189497i | −0.588954 | − | 0.808167i | \(-0.700460\pi\) |
0.0683146 | + | 0.997664i | \(0.478238\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.17867 | + | 6.68458i | 0.0460545 | + | 0.261188i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.4190 | + | 10.3437i | 1.10705 | + | 0.402933i | 0.829910 | − | 0.557897i | \(-0.188392\pi\) |
0.277138 | + | 0.960830i | \(0.410614\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.2334 | + | 21.1734i | 0.981467 | + | 0.823548i | 0.984310 | − | 0.176448i | \(-0.0564607\pi\) |
−0.00284345 | + | 0.999996i | \(0.500905\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.1762 | + | 19.3577i | −0.433393 | + | 0.750659i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.0566 | + | 55.5236i | 1.24124 | + | 2.14988i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.65601 | + | 20.7343i | −0.141139 | + | 0.800437i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.6823 | − | 20.7109i | 0.951435 | − | 0.798348i | −0.0281040 | − | 0.999605i | \(-0.508947\pi\) |
0.979539 | + | 0.201257i | \(0.0645025\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.7327 | − | 12.3622i | 0.566224 | − | 0.475119i | −0.314166 | − | 0.949368i | \(-0.601725\pi\) |
0.880391 | + | 0.474249i | \(0.157280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.4963 | + | 65.1990i | −0.441189 | + | 2.50211i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.7531 | − | 34.2134i | −0.755832 | − | 1.30914i | −0.944960 | − | 0.327186i | \(-0.893900\pi\) |
0.189128 | − | 0.981952i | \(-0.439434\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.32684 | + | 14.4225i | −0.318152 | + | 0.551056i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.97166 | + | 3.33262i | 0.151308 | + | 0.126963i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10.3604 | − | 3.77088i | −0.394128 | − | 0.143451i | 0.137351 | − | 0.990522i | \(-0.456141\pi\) |
−0.531479 | + | 0.847072i | \(0.678363\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.92150 | + | 44.9251i | 0.300480 | + | 1.70411i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.8485 | + | 4.67646i | −0.486671 | + | 0.177134i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −19.4643 | −0.735157 | −0.367578 | − | 0.929993i | \(-0.619813\pi\) | ||||
−0.367578 | + | 0.929993i | \(0.619813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.90001 | 0.109376 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.4604 | + | 4.53521i | −0.468621 | + | 0.170564i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.68146 | + | 20.8786i | 0.138260 | + | 0.784112i | 0.972534 | + | 0.232761i | \(0.0747761\pi\) |
−0.834274 | + | 0.551350i | \(0.814113\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19.0478 | + | 6.93284i | 0.713346 | + | 0.259637i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3743 | − | 12.0615i | −0.537569 | − | 0.451074i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.7055 | + | 18.5424i | −0.399247 | + | 0.691516i | −0.993633 | − | 0.112664i | \(-0.964062\pi\) |
0.594386 | + | 0.804180i | \(0.297395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −24.9554 | − | 43.2241i | −0.929389 | − | 1.60975i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.18421 | + | 6.71598i | −0.0439804 | + | 0.249425i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19.1435 | + | 16.0633i | −0.709994 | + | 0.595756i | −0.924598 | − | 0.380945i | \(-0.875599\pi\) |
0.214603 | + | 0.976701i | \(0.431154\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0496 | − | 10.1108i | 0.445671 | − | 0.373963i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.39490 | − | 36.2673i | 0.236201 | − | 1.33956i | −0.603869 | − | 0.797084i | \(-0.706375\pi\) |
0.840070 | − | 0.542478i | \(-0.182514\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.52558 | − | 7.83854i | −0.166702 | − | 0.288736i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0508 | − | 41.6573i | 0.884724 | − | 1.53239i | 0.0386947 | − | 0.999251i | \(-0.487680\pi\) |
0.846029 | − | 0.533136i | \(-0.178987\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.1085 | + | 25.2640i | 1.10457 | + | 0.926846i | 0.997724 | − | 0.0674292i | \(-0.0214797\pi\) |
0.106848 | + | 0.994275i | \(0.465924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.832316 | + | 0.302938i | 0.0304937 | + | 0.0110988i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.79124 | + | 21.5012i | 0.138529 | + | 0.785636i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −30.2087 | + | 10.9951i | −1.10233 | + | 0.401215i | −0.828174 | − | 0.560470i | \(-0.810620\pi\) |
−0.274155 | + | 0.961685i | \(0.588398\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.64638 | −0.314674 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.58106 | −0.311884 | −0.155942 | − | 0.987766i | \(-0.549841\pi\) | ||||
−0.155942 | + | 0.987766i | \(0.549841\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.1796 | − | 13.1683i | 1.31151 | − | 0.477350i | 0.410781 | − | 0.911734i | \(-0.365256\pi\) |
0.900728 | + | 0.434384i | \(0.143034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.85506 | + | 16.1918i | 0.103360 | + | 0.586184i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.3313 | − | 5.94410i | −0.589688 | − | 0.214629i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.402488 | − | 0.337727i | −0.0145141 | − | 0.0121788i | 0.635502 | − | 0.772099i | \(-0.280793\pi\) |
−0.650016 | + | 0.759921i | \(0.725238\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.89821 | + | 13.6801i | −0.284079 | + | 0.492039i | −0.972385 | − | 0.233381i | \(-0.925021\pi\) |
0.688307 | + | 0.725420i | \(0.258354\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.07805 | + | 1.86724i | 0.0387248 | + | 0.0670734i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.45445 | − | 8.24858i | 0.0521109 | − | 0.295536i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.5151 | + | 24.7661i | −1.05613 | + | 0.886202i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.3589 | + | 19.6005i | −0.833716 | + | 0.699571i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.719048 | − | 4.07793i | 0.0256313 | − | 0.145362i | −0.969306 | − | 0.245856i | \(-0.920931\pi\) |
0.994938 | + | 0.100493i | \(0.0320421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5745 | − | 26.9758i | −0.553765 | − | 0.959149i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.50476 | + | 16.4627i | −0.337524 | + | 0.584608i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −31.1285 | − | 26.1199i | −1.10263 | − | 0.925215i | −0.105029 | − | 0.994469i | \(-0.533494\pi\) |
−0.997599 | + | 0.0692544i | \(0.977938\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 18.7857 | + | 6.83745i | 0.664592 | + | 0.241892i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.48119 | − | 36.7566i | −0.228716 | − | 1.29711i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 94.9944 | − | 34.5751i | 3.34811 | − | 1.21861i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 18.5974 | 0.653851 | 0.326925 | − | 0.945050i | \(-0.393987\pi\) | ||||
0.326925 | + | 0.945050i | \(0.393987\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.3945 | −0.575690 | −0.287845 | − | 0.957677i | \(-0.592939\pi\) | ||||
−0.287845 | + | 0.957677i | \(0.592939\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 37.0392 | − | 13.4812i | 1.29743 | − | 0.472224i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.67321 | + | 9.48927i | 0.0585383 | + | 0.331987i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 48.0156 | + | 17.4762i | 1.67575 | + | 0.609925i | 0.992718 | − | 0.120459i | \(-0.0384367\pi\) |
0.683037 | + | 0.730384i | \(0.260659\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.2465 | + | 21.1843i | 0.880038 | + | 0.738439i | 0.966187 | − | 0.257843i | \(-0.0830117\pi\) |
−0.0861493 | + | 0.996282i | \(0.527456\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.1025 | + | 22.6941i | −0.455617 | + | 0.789152i | −0.998723 | − | 0.0505118i | \(-0.983915\pi\) |
0.543106 | + | 0.839664i | \(0.317248\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.8984 | − | 37.9291i | −0.760563 | − | 1.31733i | −0.942561 | − | 0.334035i | \(-0.891590\pi\) |
0.181998 | − | 0.983299i | \(-0.441744\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.50436 | + | 42.5593i | −0.260011 | + | 1.47459i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.4602 | − | 28.0764i | 1.15794 | − | 0.971625i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.6982 | − | 9.81599i | 0.403868 | − | 0.338886i | −0.418118 | − | 0.908393i | \(-0.637310\pi\) |
0.821987 | + | 0.569507i | \(0.192866\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.29742 | − | 18.7006i | 0.113704 | − | 0.644848i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.42997 | + | 12.8691i | 0.255599 | + | 0.442710i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.59138 | + | 9.68455i | −0.192122 | + | 0.332765i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0472 | − | 8.43056i | −0.344412 | − | 0.288996i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.5924 | + | 12.2266i | 1.15018 | + | 0.418632i | 0.845581 | − | 0.533848i | \(-0.179254\pi\) |
0.304602 | + | 0.952480i | \(0.401477\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.58863 | − | 48.7086i | −0.293382 | − | 1.66385i | −0.673706 | − | 0.738999i | \(-0.735299\pi\) |
0.380324 | − | 0.924853i | \(-0.375812\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.7052 | − | 10.4479i | 0.979410 | − | 0.356476i | 0.197799 | − | 0.980243i | \(-0.436621\pi\) |
0.781611 | + | 0.623766i | \(0.214398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.4315 | −0.899738 | −0.449869 | − | 0.893095i | \(-0.648529\pi\) | ||||
−0.449869 | + | 0.893095i | \(0.648529\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.4087 | −1.23793 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.63935 | + | 2.05256i | −0.191302 | + | 0.0696282i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.41909 | − | 8.04803i | −0.0480839 | − | 0.272697i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −41.2163 | − | 15.0015i | −1.39337 | − | 0.507144i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.7367 | − | 20.7565i | −0.835298 | − | 0.700898i | 0.121203 | − | 0.992628i | \(-0.461325\pi\) |
−0.956501 | + | 0.291729i | \(0.905769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.59147 | + | 13.1488i | −0.255763 | + | 0.442995i | −0.965103 | − | 0.261872i | \(-0.915660\pi\) |
0.709339 | + | 0.704867i | \(0.248993\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.8015 | − | 49.8856i | −0.969246 | − | 1.67878i | −0.697746 | − | 0.716346i | \(-0.745813\pi\) |
−0.271501 | − | 0.962438i | \(-0.587520\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.36638 | + | 24.7630i | −0.146609 | + | 0.831460i | 0.819453 | + | 0.573147i | \(0.194278\pi\) |
−0.966061 | + | 0.258313i | \(0.916834\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66.2145 | + | 55.5606i | −2.22076 | + | 1.86344i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −9.38119 | + | 7.87175i | −0.313930 | + | 0.263418i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.694517 | − | 3.93880i | 0.0232151 | − | 0.131660i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.58621 | − | 13.1397i | −0.253014 | − | 0.438233i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.29068 | + | 5.69962i | −0.109628 | + | 0.189882i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.12700 | + | 6.81936i | 0.270150 | + | 0.226683i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1517 | + | 4.05888i | 0.370286 | + | 0.134773i | 0.520459 | − | 0.853887i | \(-0.325761\pi\) |
−0.150173 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.83884 | + | 10.4286i | 0.0609234 | + | 0.345514i | 0.999998 | + | 0.00180148i | \(0.000573429\pi\) |
−0.939075 | + | 0.343712i | \(0.888315\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.29446 | + | 1.56305i | −0.142126 | + | 0.0517295i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.3890 | −0.409121 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 56.7884 | 1.87328 | 0.936639 | − | 0.350297i | \(-0.113919\pi\) | ||||
0.936639 | + | 0.350297i | \(0.113919\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32.6896 | + | 11.8981i | −1.07599 | + | 0.391629i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.242254 | − | 1.37389i | −0.00796525 | − | 0.0451732i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.9543 | − | 5.07894i | −0.457825 | − | 0.166635i | 0.102804 | − | 0.994702i | \(-0.467218\pi\) |
−0.560629 | + | 0.828067i | \(0.689441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −20.2796 | − | 17.0166i | −0.664636 | − | 0.557696i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.9097 | − | 20.6282i | 0.389489 | − | 0.674614i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.12589 | + | 5.41420i | 0.102118 | + | 0.176874i | 0.912557 | − | 0.408949i | \(-0.134105\pi\) |
−0.810439 | + | 0.585823i | \(0.800771\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.42421 | + | 42.1048i | −0.242022 | + | 1.37258i | 0.585286 | + | 0.810827i | \(0.300982\pi\) |
−0.827308 | + | 0.561749i | \(0.810129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −29.0182 | + | 24.3492i | −0.944963 | + | 0.792918i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.1099 | − | 29.4607i | 1.14092 | − | 0.957343i | 0.141449 | − | 0.989946i | \(-0.454824\pi\) |
0.999468 | + | 0.0326022i | \(0.0103794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.85179 | − | 33.1871i | 0.189957 | − | 1.07730i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.9742 | − | 25.9361i | −0.485062 | − | 0.840152i | 0.514790 | − | 0.857316i | \(-0.327870\pi\) |
−0.999853 | + | 0.0171636i | \(0.994536\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.05609 | − | 1.82920i | 0.0341742 | − | 0.0591915i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −23.2851 | − | 19.5385i | −0.751915 | − | 0.630931i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.6228 | + | 8.96196i | 0.794284 | + | 0.289096i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.21271 | − | 12.5489i | −0.0712296 | − | 0.403963i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.92520 | − | 1.79262i | 0.158384 | − | 0.0576469i | −0.261612 | − | 0.965173i | \(-0.584254\pi\) |
0.419995 | + | 0.907526i | \(0.362032\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −39.9453 | −1.28191 | −0.640953 | − | 0.767580i | \(-0.721461\pi\) | ||||
−0.640953 | + | 0.767580i | \(0.721461\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −83.2627 | −2.66928 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41.6045 | − | 15.1428i | 1.33105 | − | 0.484462i | 0.424065 | − | 0.905632i | \(-0.360603\pi\) |
0.906982 | + | 0.421170i | \(0.138380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.97141 | − | 39.5368i | −0.222807 | − | 1.26360i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.6361 | + | 7.51093i | 0.658189 | + | 0.239561i | 0.649454 | − | 0.760400i | \(-0.274997\pi\) |
0.00873499 | + | 0.999962i | \(0.497220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 49.3046 | + | 41.3714i | 1.57097 | + | 1.31820i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.7892 | − | 37.7399i | 0.692855 | − | 1.20006i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.6409 | + | 34.0190i | 0.623912 | + | 1.08065i | 0.988750 | + | 0.149577i | \(0.0477911\pi\) |
−0.364838 | + | 0.931071i | \(0.618876\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.57498 | + | 25.9460i | −0.145037 | + | 0.822544i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.1124 | − | 16.8763i | 0.636967 | − | 0.534479i | −0.266118 | − | 0.963940i | \(-0.585741\pi\) |
0.903085 | + | 0.429462i | \(0.141297\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 324.2.i.a.37.1 | 18 | ||
3.2 | odd | 2 | 108.2.i.a.49.1 | ✓ | 18 | ||
9.2 | odd | 6 | 972.2.i.a.433.1 | 18 | |||
9.4 | even | 3 | 972.2.i.b.757.3 | 18 | |||
9.5 | odd | 6 | 972.2.i.c.757.1 | 18 | |||
9.7 | even | 3 | 972.2.i.d.433.3 | 18 | |||
12.11 | even | 2 | 432.2.u.d.49.3 | 18 | |||
27.2 | odd | 18 | 972.2.i.a.541.1 | 18 | |||
27.4 | even | 9 | 2916.2.a.c.1.9 | 9 | |||
27.5 | odd | 18 | 2916.2.e.c.973.9 | 18 | |||
27.7 | even | 9 | 972.2.i.b.217.3 | 18 | |||
27.11 | odd | 18 | 108.2.i.a.97.1 | yes | 18 | ||
27.13 | even | 9 | 2916.2.e.d.1945.1 | 18 | |||
27.14 | odd | 18 | 2916.2.e.c.1945.9 | 18 | |||
27.16 | even | 9 | inner | 324.2.i.a.289.1 | 18 | ||
27.20 | odd | 18 | 972.2.i.c.217.1 | 18 | |||
27.22 | even | 9 | 2916.2.e.d.973.1 | 18 | |||
27.23 | odd | 18 | 2916.2.a.d.1.1 | 9 | |||
27.25 | even | 9 | 972.2.i.d.541.3 | 18 | |||
108.11 | even | 18 | 432.2.u.d.97.3 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.2.i.a.49.1 | ✓ | 18 | 3.2 | odd | 2 | ||
108.2.i.a.97.1 | yes | 18 | 27.11 | odd | 18 | ||
324.2.i.a.37.1 | 18 | 1.1 | even | 1 | trivial | ||
324.2.i.a.289.1 | 18 | 27.16 | even | 9 | inner | ||
432.2.u.d.49.3 | 18 | 12.11 | even | 2 | |||
432.2.u.d.97.3 | 18 | 108.11 | even | 18 | |||
972.2.i.a.433.1 | 18 | 9.2 | odd | 6 | |||
972.2.i.a.541.1 | 18 | 27.2 | odd | 18 | |||
972.2.i.b.217.3 | 18 | 27.7 | even | 9 | |||
972.2.i.b.757.3 | 18 | 9.4 | even | 3 | |||
972.2.i.c.217.1 | 18 | 27.20 | odd | 18 | |||
972.2.i.c.757.1 | 18 | 9.5 | odd | 6 | |||
972.2.i.d.433.3 | 18 | 9.7 | even | 3 | |||
972.2.i.d.541.3 | 18 | 27.25 | even | 9 | |||
2916.2.a.c.1.9 | 9 | 27.4 | even | 9 | |||
2916.2.a.d.1.1 | 9 | 27.23 | odd | 18 | |||
2916.2.e.c.973.9 | 18 | 27.5 | odd | 18 | |||
2916.2.e.c.1945.9 | 18 | 27.14 | odd | 18 | |||
2916.2.e.d.973.1 | 18 | 27.22 | even | 9 | |||
2916.2.e.d.1945.1 | 18 | 27.13 | even | 9 |