Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [348,3,Mod(133,348)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(348, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("348.133");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 348 = 2^{2} \cdot 3 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 348.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.48231319974\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} + 8 x^{18} + 480 x^{17} + 8664 x^{16} - 4140 x^{15} + 62448 x^{14} + 2397840 x^{13} + \cdots + 1236544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 157.9 | ||
Root | \(0.531346 - 0.531346i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 348.157 |
Dual form | 348.3.j.a.133.7 |
$q$-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 \(\left(\mathbb{Z}/348\mathbb{Z}\right)^\times\).
\(n\) | \(175\) | \(205\) | \(233\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.22474 | + | 1.22474i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.22487i | 1.24497i | 0.782630 | + | 0.622487i | \(0.213878\pi\) | ||||
−0.782630 | + | 0.622487i | \(0.786122\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.38632 | −1.19805 | −0.599023 | − | 0.800732i | \(-0.704444\pi\) | ||||
−0.599023 | + | 0.800732i | \(0.704444\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −11.2596 | − | 11.2596i | −1.02360 | − | 1.02360i | −0.999715 | − | 0.0238844i | \(-0.992397\pi\) |
−0.0238844 | − | 0.999715i | \(-0.507603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.5547i | 0.965750i | 0.875689 | + | 0.482875i | \(0.160407\pi\) | ||||
−0.875689 | + | 0.482875i | \(0.839593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.62388 | + | 7.62388i | −0.508259 | + | 0.508259i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.97621 | − | 2.97621i | −0.175071 | − | 0.175071i | 0.614132 | − | 0.789203i | \(-0.289506\pi\) |
−0.789203 | + | 0.614132i | \(0.789506\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0514 | − | 19.0514i | −1.00270 | − | 1.00270i | −0.999996 | − | 0.00270834i | \(-0.999138\pi\) |
−0.00270834 | − | 0.999996i | \(-0.500862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.2711 | − | 10.2711i | −0.489100 | − | 0.489100i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.990288 | −0.0430560 | −0.0215280 | − | 0.999768i | \(-0.506853\pi\) | ||||
−0.0215280 | + | 0.999768i | \(0.506853\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −13.7491 | −0.549962 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.67423 | + | 3.67423i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.7707 | − | 16.6118i | 0.819680 | − | 0.572822i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.11485 | + | 9.11485i | 0.294027 | + | 0.294027i | 0.838669 | − | 0.544642i | \(-0.183334\pi\) |
−0.544642 | + | 0.838669i | \(0.683334\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 27.5803i | − | 0.835765i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 52.2038i | − | 1.49154i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41.7531 | + | 41.7531i | −1.12846 | + | 1.12846i | −0.138035 | + | 0.990427i | \(0.544079\pi\) |
−0.990427 | + | 0.138035i | \(0.955921\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.3764 | + | 15.3764i | −0.394266 | + | 0.394266i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.0867 | + | 18.0867i | −0.441138 | + | 0.441138i | −0.892394 | − | 0.451256i | \(-0.850976\pi\) |
0.451256 | + | 0.892394i | \(0.350976\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.0423 | + | 50.0423i | 1.16378 | + | 1.16378i | 0.983642 | + | 0.180133i | \(0.0576529\pi\) |
0.180133 | + | 0.983642i | \(0.442347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.6746 | −0.414992 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −53.3333 | + | 53.3333i | −1.13475 | + | 1.13475i | −0.145375 | + | 0.989377i | \(0.546439\pi\) |
−0.989377 | + | 0.145375i | \(0.953561\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.3304 | 0.435315 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 7.29020i | − | 0.142945i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −42.5439 | −0.802715 | −0.401358 | − | 0.915921i | \(-0.631462\pi\) | ||||
−0.401358 | + | 0.915921i | \(0.631462\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 70.0895 | − | 70.0895i | 1.27436 | − | 1.27436i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 46.6662i | − | 0.818705i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −61.9343 | −1.04973 | −0.524867 | − | 0.851184i | \(-0.675885\pi\) | ||||
−0.524867 | + | 0.851184i | \(0.675885\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.0094 | + | 36.0094i | 0.590318 | + | 0.590318i | 0.937717 | − | 0.347399i | \(-0.112935\pi\) |
−0.347399 | + | 0.937717i | \(0.612935\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 25.1590i | − | 0.399349i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −78.1517 | −1.20233 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.8704i | 0.998066i | 0.866583 | + | 0.499033i | \(0.166311\pi\) | ||||
−0.866583 | + | 0.499033i | \(0.833689\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.21285 | − | 1.21285i | −0.0175775 | − | 0.0175775i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 89.1659i | − | 1.25586i | −0.778271 | − | 0.627929i | \(-0.783903\pi\) | ||
0.778271 | − | 0.627929i | \(-0.216097\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.0513 | − | 16.0513i | 0.219881 | − | 0.219881i | −0.588567 | − | 0.808448i | \(-0.700308\pi\) |
0.808448 | + | 0.588567i | \(0.200308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.8391 | − | 16.8391i | −0.224521 | − | 0.224521i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 94.4266 | + | 94.4266i | 1.22632 | + | 1.22632i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.3011 | + | 74.3011i | 0.940521 | + | 0.940521i | 0.998328 | − | 0.0578072i | \(-0.0184109\pi\) |
−0.0578072 | + | 0.998328i | \(0.518411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −80.2278 | −0.966601 | −0.483300 | − | 0.875455i | \(-0.660562\pi\) | ||||
−0.483300 | + | 0.875455i | \(0.660562\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.5265 | − | 18.5265i | 0.217959 | − | 0.217959i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 49.4583 | + | 8.76782i | 0.568486 | + | 0.100779i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.67823 | + | 3.67823i | 0.0413285 | + | 0.0413285i | 0.727469 | − | 0.686141i | \(-0.240697\pi\) |
−0.686141 | + | 0.727469i | \(0.740697\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 105.288i | − | 1.15701i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.3267i | 0.240072i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 118.592 | − | 118.592i | 1.24834 | − | 1.24834i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −101.725 | + | 101.725i | −1.04871 | + | 1.04871i | −0.0499585 | + | 0.998751i | \(0.515909\pi\) |
−0.998751 | + | 0.0499585i | \(0.984091\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 33.7788 | − | 33.7788i | 0.341200 | − | 0.341200i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 78.5057 | + | 78.5057i | 0.777284 | + | 0.777284i | 0.979368 | − | 0.202084i | \(-0.0647715\pi\) |
−0.202084 | + | 0.979368i | \(0.564772\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 167.789 | 1.62902 | 0.814510 | − | 0.580149i | \(-0.197006\pi\) | ||||
0.814510 | + | 0.580149i | \(0.197006\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 63.9363 | − | 63.9363i | 0.608918 | − | 0.608918i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 41.6570 | 0.389317 | 0.194659 | − | 0.980871i | \(-0.437640\pi\) | ||||
0.194659 | + | 0.980871i | \(0.437640\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.95402i | 0.0179267i | 0.999960 | + | 0.00896337i | \(0.00285317\pi\) | ||||
−0.999960 | + | 0.00896337i | \(0.997147\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −102.274 | −0.921386 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 128.633 | − | 128.633i | 1.13835 | − | 1.13835i | 0.149603 | − | 0.988746i | \(-0.452200\pi\) |
0.988746 | − | 0.149603i | \(-0.0477996\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.16442i | − | 0.0536036i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.6642 | −0.321917 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 24.9595 | + | 24.9595i | 0.209744 | + | 0.209744i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 132.557i | 1.09551i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −44.3031 | −0.360188 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 70.0357i | 0.560286i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −61.7993 | − | 61.7993i | −0.486608 | − | 0.486608i | 0.420626 | − | 0.907234i | \(-0.361811\pi\) |
−0.907234 | + | 0.420626i | \(0.861811\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 122.578i | 0.950219i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −61.6928 | + | 61.6928i | −0.470937 | + | 0.470937i | −0.902218 | − | 0.431280i | \(-0.858062\pi\) |
0.431280 | + | 0.902218i | \(0.358062\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 159.771 | + | 159.771i | 1.20129 | + | 1.20129i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −22.8716 | − | 22.8716i | −0.169420 | − | 0.169420i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −43.1336 | − | 43.1336i | −0.314844 | − | 0.314844i | 0.531939 | − | 0.846783i | \(-0.321464\pi\) |
−0.846783 | + | 0.531939i | \(0.821464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 122.071 | 0.878208 | 0.439104 | − | 0.898436i | \(-0.355296\pi\) | ||||
0.439104 | + | 0.898436i | \(0.355296\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −130.639 | −0.926521 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 141.361 | − | 141.361i | 0.988540 | − | 0.988540i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 103.407 | + | 147.970i | 0.713149 | + | 1.02048i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 26.1243 | + | 26.1243i | 0.177717 | + | 0.177717i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 91.8081i | − | 0.616161i | −0.951360 | − | 0.308081i | \(-0.900313\pi\) | ||
0.951360 | − | 0.308081i | \(-0.0996867\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 189.682i | − | 1.25617i | −0.778144 | − | 0.628087i | \(-0.783838\pi\) | ||
0.778144 | − | 0.628087i | \(-0.216162\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 8.92864 | − | 8.92864i | 0.0583571 | − | 0.0583571i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −56.7388 | + | 56.7388i | −0.366057 | + | 0.366057i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −26.2750 | + | 26.2750i | −0.167357 | + | 0.167357i | −0.785816 | − | 0.618460i | \(-0.787757\pi\) |
0.618460 | + | 0.785816i | \(0.287757\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −52.1054 | − | 52.1054i | −0.327707 | − | 0.327707i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.30488 | 0.0515831 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 69.9956 | − | 69.9956i | 0.429421 | − | 0.429421i | −0.459010 | − | 0.888431i | \(-0.651796\pi\) |
0.888431 | + | 0.459010i | \(0.151796\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 171.684 | 1.04051 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 165.548i | − | 0.991306i | −0.868521 | − | 0.495653i | \(-0.834929\pi\) | ||
0.868521 | − | 0.495653i | \(-0.165071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3784 | 0.0673277 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 57.1542 | − | 57.1542i | 0.334235 | − | 0.334235i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 77.5776i | 0.448426i | 0.974540 | + | 0.224213i | \(0.0719811\pi\) | ||||
−0.974540 | + | 0.224213i | \(0.928019\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 115.304 | 0.658880 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −75.8538 | − | 75.8538i | −0.428552 | − | 0.428552i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 50.7547i | − | 0.283546i | −0.989899 | − | 0.141773i | \(-0.954720\pi\) | ||
0.989899 | − | 0.141773i | \(-0.0452803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −83.8733 | −0.463388 | −0.231694 | − | 0.972789i | \(-0.574427\pi\) | ||||
−0.231694 | + | 0.972789i | \(0.574427\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 88.2047i | 0.481993i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −259.908 | − | 259.908i | −1.40491 | − | 1.40491i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 67.0219i | 0.358406i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 30.8133 | − | 30.8133i | 0.163033 | − | 0.163033i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −132.202 | − | 132.202i | −0.692157 | − | 0.692157i | 0.270549 | − | 0.962706i | \(-0.412795\pi\) |
−0.962706 | + | 0.270549i | \(0.912795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 150.453 | + | 150.453i | 0.779552 | + | 0.779552i | 0.979754 | − | 0.200203i | \(-0.0641601\pi\) |
−0.200203 | + | 0.979754i | \(0.564160\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −95.7159 | − | 95.7159i | −0.490851 | − | 0.490851i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 360.216 | 1.82851 | 0.914253 | − | 0.405143i | \(-0.132778\pi\) | ||||
0.914253 | + | 0.405143i | \(0.132778\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −338.298 | −1.69999 | −0.849995 | − | 0.526791i | \(-0.823395\pi\) | ||||
−0.849995 | + | 0.526791i | \(0.823395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −81.8992 | + | 81.8992i | −0.407459 | + | 0.407459i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −199.349 | + | 139.312i | −0.982015 | + | 0.686267i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −112.587 | − | 112.587i | −0.549206 | − | 0.549206i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 2.97086i | − | 0.0143520i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 429.022i | 2.05274i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −256.472 | + | 256.472i | −1.21551 | + | 1.21551i | −0.246319 | + | 0.969189i | \(0.579221\pi\) |
−0.969189 | + | 0.246319i | \(0.920779\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 109.205 | − | 109.205i | 0.512702 | − | 0.512702i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −311.507 | + | 311.507i | −1.44887 | + | 1.44887i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −76.4401 | − | 76.4401i | −0.352258 | − | 0.352258i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 39.3176 | 0.179532 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 37.3656 | − | 37.3656i | 0.169075 | − | 0.169075i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −154.108 | −0.691067 | −0.345533 | − | 0.938406i | \(-0.612302\pi\) | ||||
−0.345533 | + | 0.938406i | \(0.612302\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 41.2472i | − | 0.183321i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −136.424 | −0.600987 | −0.300493 | − | 0.953784i | \(-0.597151\pi\) | ||||
−0.300493 | + | 0.953784i | \(0.597151\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −125.468 | + | 125.468i | −0.547896 | + | 0.547896i | −0.925832 | − | 0.377936i | \(-0.876634\pi\) |
0.377936 | + | 0.925832i | \(0.376634\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 231.297i | 1.00129i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −448.242 | −1.92378 | −0.961892 | − | 0.273430i | \(-0.911842\pi\) | ||||
−0.961892 | + | 0.273430i | \(0.911842\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −331.993 | − | 331.993i | −1.41274 | − | 1.41274i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 182.000i | 0.767932i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 289.674 | 1.21202 | 0.606012 | − | 0.795456i | \(-0.292768\pi\) | ||||
0.606012 | + | 0.795456i | \(0.292768\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 42.2795i | − | 0.175434i | −0.996145 | − | 0.0877169i | \(-0.972043\pi\) | ||
0.996145 | − | 0.0877169i | \(-0.0279571\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.0227 | − | 11.0227i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 132.779i | 0.541956i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 239.185 | − | 239.185i | 0.968362 | − | 0.968362i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −98.2586 | − | 98.2586i | −0.394613 | − | 0.394613i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 154.680 | + | 154.680i | 0.616256 | + | 0.616256i | 0.944569 | − | 0.328313i | \(-0.106480\pi\) |
−0.328313 | + | 0.944569i | \(0.606480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 11.1502 | + | 11.1502i | 0.0440721 | + | 0.0440721i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 45.3806 | 0.177963 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.2375 | 0.0631809 | 0.0315905 | − | 0.999501i | \(-0.489943\pi\) | ||||
0.0315905 | + | 0.999501i | \(0.489943\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 350.155 | − | 350.155i | 1.35195 | − | 1.35195i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.8355 | + | 71.3122i | 0.190941 | + | 0.273227i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 53.6604 | + | 53.6604i | 0.204032 | + | 0.204032i | 0.801725 | − | 0.597693i | \(-0.203916\pi\) |
−0.597693 | + | 0.801725i | \(0.703916\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 264.830i | − | 0.999360i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00979i | 0.0337446i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 183.535 | − | 183.535i | 0.682288 | − | 0.682288i | −0.278227 | − | 0.960515i | \(-0.589747\pi\) |
0.960515 | + | 0.278227i | \(0.0897469\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −351.496 | + | 351.496i | −1.29703 | + | 1.29703i | −0.366693 | + | 0.930342i | \(0.619510\pi\) |
−0.930342 | + | 0.366693i | \(0.880490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 128.951 | − | 128.951i | 0.472348 | − | 0.472348i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 154.809 | + | 154.809i | 0.562941 | + | 0.562941i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −185.886 | −0.671069 | −0.335534 | − | 0.942028i | \(-0.608917\pi\) | ||||
−0.335534 | + | 0.942028i | \(0.608917\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −27.3445 | + | 27.3445i | −0.0980091 | + | 0.0980091i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −357.621 | −1.27267 | −0.636336 | − | 0.771412i | \(-0.719551\pi\) | ||||
−0.636336 | + | 0.771412i | \(0.719551\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 12.9326i | − | 0.0456983i | −0.999739 | − | 0.0228492i | \(-0.992726\pi\) | ||
0.999739 | − | 0.0228492i | \(-0.00727374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 290.491 | 1.01927 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 151.681 | − | 151.681i | 0.528504 | − | 0.528504i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 271.284i | − | 0.938700i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −249.174 | −0.856268 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −92.7504 | − | 92.7504i | −0.316554 | − | 0.316554i | 0.530888 | − | 0.847442i | \(-0.321859\pi\) |
−0.847442 | + | 0.530888i | \(0.821859\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 385.533i | − | 1.30689i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 82.7408 | 0.278588 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 12.4328i | − | 0.0415813i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −419.671 | − | 419.671i | −1.39426 | − | 1.39426i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 192.299i | 0.634650i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −224.154 | + | 224.154i | −0.734931 | + | 0.734931i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 417.035 | + | 417.035i | 1.35842 | + | 1.35842i | 0.875867 | + | 0.482552i | \(0.160290\pi\) |
0.482552 | + | 0.875867i | \(0.339710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 205.499 | + | 205.499i | 0.665045 | + | 0.665045i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 297.022 | + | 297.022i | 0.955055 | + | 0.955055i | 0.999033 | − | 0.0439779i | \(-0.0140031\pi\) |
−0.0439779 | + | 0.999033i | \(0.514003\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −395.782 | −1.26448 | −0.632239 | − | 0.774773i | \(-0.717864\pi\) | ||||
−0.632239 | + | 0.774773i | \(0.717864\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 156.611 | 0.497179 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −35.4067 | + | 35.4067i | −0.111693 | + | 0.111693i | −0.760744 | − | 0.649052i | \(-0.775166\pi\) |
0.649052 | + | 0.760744i | \(0.275166\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −454.691 | − | 80.6062i | −1.42536 | − | 0.252684i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 51.0192 | + | 51.0192i | 0.158938 | + | 0.158938i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 113.402i | 0.351090i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 172.616i | − | 0.531126i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.39317 | + | 2.39317i | −0.00731856 | + | 0.00731856i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 447.271 | − | 447.271i | 1.35949 | − | 1.35949i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 337.771 | − | 337.771i | 1.02046 | − | 1.02046i | 0.0206709 | − | 0.999786i | \(-0.493420\pi\) |
0.999786 | − | 0.0206709i | \(-0.00658023\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −125.259 | − | 125.259i | −0.376154 | − | 0.376154i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −416.260 | −1.24257 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −367.977 | + | 367.977i | −1.09192 | + | 1.09192i | −0.0965967 | + | 0.995324i | \(0.530796\pi\) |
−0.995324 | + | 0.0965967i | \(0.969204\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 315.086 | 0.929458 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 205.259i | − | 0.601932i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 232.046 | 0.676519 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.54984 | − | 7.54984i | 0.0218836 | − | 0.0218836i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 191.746i | − | 0.552581i | −0.961074 | − | 0.276290i | \(-0.910895\pi\) | ||
0.961074 | − | 0.276290i | \(-0.0891052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −94.2770 | −0.270135 | −0.135067 | − | 0.990836i | \(-0.543125\pi\) | ||||
−0.135067 | + | 0.990836i | \(0.543125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −46.1291 | − | 46.1291i | −0.131422 | − | 0.131422i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 420.448i | − | 1.19107i | −0.803329 | − | 0.595536i | \(-0.796940\pi\) | ||
0.803329 | − | 0.595536i | \(-0.203060\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 555.046 | 1.56351 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 61.1380i | 0.171255i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 186.902 | + | 186.902i | 0.520619 | + | 0.520619i | 0.917758 | − | 0.397139i | \(-0.129997\pi\) |
−0.397139 | + | 0.917758i | \(0.629997\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 364.911i | 1.01083i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −162.348 | + | 162.348i | −0.447240 | + | 0.447240i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 99.9176 | + | 99.9176i | 0.273747 | + | 0.273747i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 148.125 | + | 148.125i | 0.403610 | + | 0.403610i | 0.879503 | − | 0.475893i | \(-0.157875\pi\) |
−0.475893 | + | 0.879503i | \(0.657875\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −54.2600 | − | 54.2600i | −0.147046 | − | 0.147046i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 356.787 | 0.961690 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 372.127 | 0.997659 | 0.498830 | − | 0.866700i | \(-0.333763\pi\) | ||||
0.498830 | + | 0.866700i | \(0.333763\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −85.7759 | + | 85.7759i | −0.228736 | + | 0.228736i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 208.557 | + | 298.435i | 0.553202 | + | 0.791606i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −94.3069 | − | 94.3069i | −0.248831 | − | 0.248831i | 0.571660 | − | 0.820491i | \(-0.306300\pi\) |
−0.820491 | + | 0.571660i | \(0.806300\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 151.377i | − | 0.397314i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 305.251i | 0.797000i | 0.917168 | + | 0.398500i | \(0.130469\pi\) | ||||
−0.917168 | + | 0.398500i | \(0.869531\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −587.794 | + | 587.794i | −1.52674 | + | 1.52674i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −150.127 | + | 150.127i | −0.387925 | + | 0.387925i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 499.186 | − | 499.186i | 1.28325 | − | 1.28325i | 0.344450 | − | 0.938805i | \(-0.388065\pi\) |
0.938805 | − | 0.344450i | \(-0.111935\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.94731 | + | 2.94731i | 0.00753787 | + | 0.00753787i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −151.116 | −0.384519 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −462.515 | + | 462.515i | −1.17092 | + | 1.17092i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 140.405 | 0.353666 | 0.176833 | − | 0.984241i | \(-0.443415\pi\) | ||||
0.176833 | + | 0.984241i | \(0.443415\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 391.358i | 0.980846i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 178.555 | 0.445274 | 0.222637 | − | 0.974901i | \(-0.428534\pi\) | ||||
0.222637 | + | 0.974901i | \(0.428534\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −114.435 | + | 114.435i | −0.283957 | + | 0.283957i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 56.0239i | − | 0.138331i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 940.246 | 2.31019 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 265.947 | + | 265.947i | 0.650237 | + | 0.650237i | 0.953050 | − | 0.302813i | \(-0.0979258\pi\) |
−0.302813 | + | 0.953050i | \(0.597926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 105.655i | − | 0.257069i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 519.402 | 1.25763 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 499.408i | − | 1.20339i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 149.506 | + | 149.506i | 0.358527 | + | 0.358527i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 152.135i | 0.363090i | 0.983383 | + | 0.181545i | \(0.0581098\pi\) | ||||
−0.983383 | + | 0.181545i | \(0.941890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 98.1758 | − | 98.1758i | 0.233197 | − | 0.233197i | −0.580829 | − | 0.814026i | \(-0.697272\pi\) |
0.814026 | + | 0.580829i | \(0.197272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −160.000 | − | 160.000i | −0.378251 | − | 0.378251i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 40.9201 | + | 40.9201i | 0.0962826 | + | 0.0962826i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −301.987 | − | 301.987i | −0.707228 | − | 0.707228i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 346.263 | 0.807140 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −727.779 | −1.68858 | −0.844291 | − | 0.535885i | \(-0.819978\pi\) | ||||
−0.844291 | + | 0.535885i | \(0.819978\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −112.939 | + | 112.939i | −0.260829 | + | 0.260829i | −0.825391 | − | 0.564562i | \(-0.809045\pi\) |
0.564562 | + | 0.825391i | \(0.309045\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −54.5785 | + | 307.872i | −0.125468 | + | 0.707751i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 18.8664 | + | 18.8664i | 0.0431725 | + | 0.0431725i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 405.711i | − | 0.924170i | −0.886836 | − | 0.462085i | \(-0.847101\pi\) | ||
0.886836 | − | 0.462085i | \(-0.152899\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 63.9913i | 0.145105i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −129.892 | + | 129.892i | −0.293210 | + | 0.293210i | −0.838347 | − | 0.545137i | \(-0.816478\pi\) |
0.545137 | + | 0.838347i | \(0.316478\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −22.8965 | + | 22.8965i | −0.0514529 | + | 0.0514529i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 112.441 | − | 112.441i | 0.251547 | − | 0.251547i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 435.307 | + | 435.307i | 0.969503 | + | 0.969503i | 0.999549 | − | 0.0300457i | \(-0.00956527\pi\) |
−0.0300457 | + | 0.999549i | \(0.509565\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 407.297 | 0.903097 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 232.312 | − | 232.312i | 0.512830 | − | 0.512830i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 655.406 | 1.44045 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 632.050i | − | 1.38304i | −0.722357 | − | 0.691521i | \(-0.756941\pi\) | ||
0.722357 | − | 0.691521i | \(-0.243059\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.8706 | 0.0476484 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 271.189 | − | 271.189i | 0.588263 | − | 0.588263i | −0.348898 | − | 0.937161i | \(-0.613444\pi\) |
0.937161 | + | 0.348898i | \(0.113444\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 439.080i | 0.948336i | 0.880434 | + | 0.474168i | \(0.157251\pi\) | ||||
−0.880434 | + | 0.474168i | \(0.842749\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −138.981 | −0.298884 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −356.789 | − | 356.789i | −0.764003 | − | 0.764003i | 0.213041 | − | 0.977043i | \(-0.431663\pi\) |
−0.977043 | + | 0.213041i | \(0.931663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 560.797i | − | 1.19573i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −64.3604 | −0.136646 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 1126.91i | − | 2.38248i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 261.939 | + | 261.939i | 0.551450 | + | 0.551450i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 127.632i | − | 0.267572i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −228.554 | + | 228.554i | −0.477149 | + | 0.477149i | −0.904219 | − | 0.427070i | \(-0.859546\pi\) |
0.427070 | + | 0.904219i | \(0.359546\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −524.200 | − | 524.200i | −1.08981 | − | 1.08981i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.1714 | + | 10.1714i | 0.0210587 | + | 0.0210587i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −633.224 | − | 633.224i | −1.30562 | − | 1.30562i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 228.487 | 0.469172 | 0.234586 | − | 0.972095i | \(-0.424627\pi\) | ||||
0.234586 | + | 0.972095i | \(0.424627\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 171.453 | 0.350621 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −330.119 | + | 330.119i | −0.672340 | + | 0.672340i | −0.958255 | − | 0.285915i | \(-0.907702\pi\) |
0.285915 | + | 0.958255i | \(0.407702\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −120.187 | − | 21.3064i | −0.243787 | − | 0.0432178i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 210.269 | + | 210.269i | 0.424785 | + | 0.424785i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 747.774i | 1.50458i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 739.860i | − | 1.48268i | −0.671127 | − | 0.741342i | \(-0.734189\pi\) | ||
0.671127 | − | 0.741342i | \(-0.265811\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 202.754 | − | 202.754i | 0.404699 | − | 0.404699i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −201.129 | + | 201.129i | −0.399859 | + | 0.399859i | −0.878183 | − | 0.478324i | \(-0.841244\pi\) |
0.478324 | + | 0.878183i | \(0.341244\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −488.688 | + | 488.688i | −0.967699 | + | 0.967699i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.9356 | + | 13.9356i | 0.0274864 | + | 0.0274864i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.0139 | −0.0196736 | −0.00983682 | − | 0.999952i | \(-0.503131\pi\) | ||||
−0.00983682 | + | 0.999952i | \(0.503131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −134.612 | + | 134.612i | −0.263428 | + | 0.263428i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 139.999 | 0.272902 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1044.47i | 2.02809i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1201.02 | 2.32306 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −95.0128 | + | 95.0128i | −0.183069 | + | 0.183069i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 199.135i | − | 0.382216i | −0.981569 | − | 0.191108i | \(-0.938792\pi\) | ||
0.981569 | − | 0.191108i | \(-0.0612081\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 277.854 | 0.531269 | 0.265635 | − | 0.964074i | \(-0.414419\pi\) | ||||
0.265635 | + | 0.964074i | \(0.414419\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 141.218 | + | 141.218i | 0.268987 | + | 0.268987i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 54.2555i | − | 0.102952i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −528.019 | −0.998146 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 185.803i | − | 0.349912i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −227.074 | − | 227.074i | −0.426029 | − | 0.426029i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 259.309i | 0.484690i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 62.1615 | − | 62.1615i | 0.115757 | − | 0.115757i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −240.172 | − | 240.172i | −0.445588 | − | 0.445588i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 327.619 | + | 327.619i | 0.605580 | + | 0.605580i | 0.941788 | − | 0.336208i | \(-0.109144\pi\) |
−0.336208 | + | 0.941788i | \(0.609144\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −102.723 | − | 102.723i | −0.189178 | − | 0.189178i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12.1635 | −0.0223183 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 536.401 | 0.980623 | 0.490311 | − | 0.871547i | \(-0.336883\pi\) | ||||
0.490311 | + | 0.871547i | \(0.336883\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −108.028 | + | 108.028i | −0.196773 | + | 0.196773i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −769.344 | − | 136.387i | −1.39627 | − | 0.247526i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −623.113 | − | 623.113i | −1.12679 | − | 1.12679i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 636.642i | − | 1.14710i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1108.07i | 1.98934i | 0.103087 | + | 0.994672i | \(0.467128\pi\) | ||||
−0.103087 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −628.269 | + | 628.269i | −1.12392 | + | 1.12392i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −82.0847 | + | 82.0847i | −0.146319 | + | 0.146319i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 323.646 | − | 323.646i | 0.574860 | − | 0.574860i | −0.358622 | − | 0.933483i | \(-0.616753\pi\) |
0.933483 | + | 0.358622i | \(0.116753\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 800.727 | + | 800.727i | 1.41722 | + | 1.41722i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 75.4769 | 0.133116 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −534.525 | + | 534.525i | −0.939412 | + | 0.939412i | −0.998267 | − | 0.0588546i | \(-0.981255\pi\) |
0.0588546 | + | 0.998267i | \(0.481255\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −707.131 | −1.23841 | −0.619204 | − | 0.785230i | \(-0.712545\pi\) | ||||
−0.619204 | + | 0.785230i | \(0.712545\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 323.827i | − | 0.565144i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 13.6155 | 0.0236792 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 569.533 | − | 569.533i | 0.987059 | − | 0.987059i | −0.0128581 | − | 0.999917i | \(-0.504093\pi\) |
0.999917 | + | 0.0128581i | \(0.00409298\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 368.534i | 0.636501i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 672.817 | 1.15803 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 479.027 | + | 479.027i | 0.821659 | + | 0.821659i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 234.455i | − | 0.400778i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −453.981 | −0.773392 | −0.386696 | − | 0.922207i | \(-0.626384\pi\) | ||||
−0.386696 | + | 0.922207i | \(0.626384\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 347.301i | − | 0.589645i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 441.172 | + | 441.172i | 0.746485 | + | 0.746485i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 118.602i | − | 0.200004i | −0.994987 | − | 0.100002i | \(-0.968115\pi\) | ||
0.994987 | − | 0.100002i | \(-0.0318849\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −155.370 | + | 155.370i | −0.261125 | + | 0.261125i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −414.329 | − | 414.329i | −0.694018 | − | 0.694018i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −169.686 | − | 169.686i | −0.283282 | − | 0.283282i | 0.551134 | − | 0.834416i | \(-0.314195\pi\) |
−0.834416 | + | 0.551134i | \(0.814195\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −118.429 | − | 118.429i | −0.197052 | − | 0.197052i | 0.601683 | − | 0.798735i | \(-0.294497\pi\) |
−0.798735 | + | 0.601683i | \(0.794497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −200.611 | −0.332689 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −825.149 | −1.36388 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −479.221 | + | 479.221i | −0.789491 | + | 0.789491i | −0.981411 | − | 0.191920i | \(-0.938529\pi\) |
0.191920 | + | 0.981411i | \(0.438529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −414.774 | − | 73.5297i | −0.681073 | − | 0.120739i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −669.586 | − | 669.586i | −1.09589 | − | 1.09589i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 419.425i | 0.684217i | 0.939660 | + | 0.342109i | \(0.111141\pi\) | ||||
−0.939660 | + | 0.342109i | \(0.888859\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 275.781i | − | 0.448425i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 707.633 | − | 707.633i | 1.14689 | − | 1.14689i | 0.159733 | − | 0.987160i | \(-0.448937\pi\) |
0.987160 | − | 0.159733i | \(-0.0510633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −579.890 | + | 579.890i | −0.936818 | + | 0.936818i | −0.998119 | − | 0.0613011i | \(-0.980475\pi\) |
0.0613011 | + | 0.998119i | \(0.480475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.63855 | − | 3.63855i | 0.00585918 | − | 0.00585918i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.8469 | − | 30.8469i | −0.0495134 | − | 0.0495134i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −779.690 | −1.24750 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −525.442 | + | 525.442i | −0.838026 | + | 0.838026i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 248.532 | 0.395123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 600.538i | − | 0.951725i | −0.879520 | − | 0.475863i | \(-0.842136\pi\) | ||
0.879520 | − | 0.475863i | \(-0.157864\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −628.226 | −0.992458 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 384.693 | − | 384.693i | 0.605815 | − | 0.605815i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 267.798i | 0.420405i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 267.498 | 0.418619 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 152.928 | + | 152.928i | 0.238578 | + | 0.238578i | 0.816261 | − | 0.577683i | \(-0.196043\pi\) |
−0.577683 | + | 0.816261i | \(0.696043\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 472.606i | 0.735001i | 0.930023 | + | 0.367500i | \(0.119786\pi\) | ||||
−0.930023 | + | 0.367500i | \(0.880214\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −763.034 | −1.18300 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 436.764i | − | 0.675060i | −0.941315 | − | 0.337530i | \(-0.890409\pi\) | ||
0.941315 | − | 0.337530i | \(-0.109591\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 697.355 | + | 697.355i | 1.07451 | + | 1.07451i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 187.239i | − | 0.287618i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 40.4261 | − | 40.4261i | 0.0619083 | − | 0.0619083i | −0.675475 | − | 0.737383i | \(-0.736061\pi\) |
0.737383 | + | 0.675475i | \(0.236061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −384.030 | − | 384.030i | −0.586305 | − | 0.586305i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 48.1540 | + | 48.1540i | 0.0732938 | + | 0.0732938i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −282.795 | − | 282.795i | −0.429127 | − | 0.429127i | 0.459204 | − | 0.888331i | \(-0.348135\pi\) |
−0.888331 | + | 0.459204i | \(0.848135\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −896.310 | −1.35599 | −0.677996 | − | 0.735066i | \(-0.737151\pi\) | ||||
−0.677996 | + | 0.735066i | \(0.737151\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 91.5266 | 0.138049 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −994.555 | + | 994.555i | −1.49557 | + | 1.49557i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.5399 | + | 16.4505i | −0.0352921 | + | 0.0246634i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −188.743 | − | 188.743i | −0.282127 | − | 0.282127i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 810.902i | − | 1.20850i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 499.060i | 0.741545i | 0.928724 | + | 0.370772i | \(0.120907\pi\) | ||||
−0.928724 | + | 0.370772i | \(0.879093\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 50.5172 | − | 50.5172i | 0.0748404 | − | 0.0748404i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −630.278 | + | 630.278i | −0.930987 | + | 0.930987i | −0.997768 | − | 0.0667803i | \(-0.978727\pi\) |
0.0667803 | + | 0.997768i | \(0.478727\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 853.098 | − | 853.098i | 1.25640 | − | 1.25640i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −167.085 | − | 167.085i | −0.245352 | − | 0.245352i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −561.416 | −0.821985 | −0.410993 | − | 0.911639i | \(-0.634818\pi\) | ||||
−0.410993 | + | 0.911639i | \(0.634818\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 268.501 | − | 268.501i | 0.391973 | − | 0.391973i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −307.333 | −0.447355 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 534.128i | − | 0.775222i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 360.414 | 0.521583 | 0.260792 | − | 0.965395i | \(-0.416016\pi\) | ||||
0.260792 | + | 0.965395i | \(0.416016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −283.280 | + | 283.280i | −0.408773 | + | 0.408773i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 759.876i | 1.09335i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 107.660 | 0.154461 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −548.982 | − | 548.982i | −0.785382 | − | 0.785382i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 741.677i | − | 1.05803i | −0.848613 | − | 0.529013i | \(-0.822562\pi\) | ||
0.848613 | − | 0.529013i | \(-0.177438\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1590.91 | 2.26303 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 813.214i | − | 1.15350i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −658.374 | − | 658.374i | −0.931222 | − | 0.931222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1207.44i | 1.70301i | 0.524344 | + | 0.851506i | \(0.324310\pi\) | ||||
−0.524344 | + | 0.851506i | \(0.675690\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −222.903 | + | 222.903i | −0.313507 | + | 0.313507i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −9.02633 | − | 9.02633i | −0.0126596 | − | 0.0126596i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 879.956 | + | 879.956i | 1.23071 | + | 1.23071i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 354.776 | + | 354.776i | 0.494806 | + | 0.494806i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1289.31 | 1.79320 | 0.896602 | − | 0.442838i | \(-0.146028\pi\) | ||||
0.896602 | + | 0.442838i | \(0.146028\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1407.13 | −1.95164 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.7816 | − | 51.7816i | 0.0716205 | − | 0.0716205i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −326.825 | + | 228.397i | −0.450793 | + | 0.315030i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −492.316 | − | 492.316i | −0.677188 | − | 0.677188i | 0.282175 | − | 0.959363i | \(-0.408944\pi\) |
−0.959363 | + | 0.282175i | \(0.908944\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 297.873i | − | 0.407487i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 713.708 | − | 713.708i | 0.973680 | − | 0.973680i | −0.0259822 | − | 0.999662i | \(-0.508271\pi\) |
0.999662 | + | 0.0259822i | \(0.00827132\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −162.621 | + | 162.621i | −0.221253 | + | 0.221253i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 752.934 | − | 752.934i | 1.02162 | − | 1.02162i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 686.867 | + | 686.867i | 0.929455 | + | 0.929455i | 0.997671 | − | 0.0682158i | \(-0.0217306\pi\) |
−0.0682158 | + | 0.997671i | \(0.521731\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 585.882 | 0.790664 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 799.060 | − | 799.060i | 1.07545 | − | 1.07545i | 0.0785399 | − | 0.996911i | \(-0.474974\pi\) |
0.996911 | − | 0.0785399i | \(-0.0250258\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 571.494 | 0.767105 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 240.684i | − | 0.322200i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −349.349 | −0.466420 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −892.272 | + | 892.272i | −1.18811 | + | 1.18811i | −0.210522 | + | 0.977589i | \(0.567516\pi\) |
−0.977589 | + | 0.210522i | \(0.932484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 378.887i | 0.503171i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1180.75 | 1.56390 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 748.084 | + | 748.084i | 0.988222 | + | 0.988222i | 0.999931 | − | 0.0117098i | \(-0.00372742\pi\) |
−0.0117098 | + | 0.999931i | \(0.503727\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 27.3124i | 0.0359847i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −910.116 | −1.19595 | −0.597974 | − | 0.801516i | \(-0.704027\pi\) | ||||
−0.597974 | + | 0.801516i | \(0.704027\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 16.3870i | − | 0.0214771i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 55.5796 | + | 55.5796i | 0.0726531 | + | 0.0726531i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 777.570i | − | 1.01378i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 791.847 | − | 791.847i | 1.02971 | − | 1.02971i | 0.0301653 | − | 0.999545i | \(-0.490397\pi\) |
0.999545 | − | 0.0301653i | \(-0.00960338\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.8868 | + | 19.8868i | 0.0257935 | + | 0.0257935i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 361.424 | + | 361.424i | 0.467561 | + | 0.467561i | 0.901123 | − | 0.433563i | \(-0.142744\pi\) |
−0.433563 | + | 0.901123i | \(0.642744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −125.321 | − | 125.321i | −0.161704 | − | 0.161704i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 857.702 | 1.10386 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 689.152 | 0.884663 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1003.97 | + | 1003.97i | −1.28550 | + | 1.28550i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.3034 | + | 148.375i | −0.0335932 | + | 0.189495i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −163.559 | − | 163.559i | −0.208355 | − | 0.208355i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 868.958i | 1.10414i | 0.833798 | + | 0.552070i | \(0.186162\pi\) | ||||
−0.833798 | + | 0.552070i | \(0.813838\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 131.441i | 0.166591i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1078.76 | + | 1078.76i | −1.36380 | + | 1.36380i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −452.089 | + | 452.089i | −0.570099 | + | 0.570099i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 324.350 | − | 324.350i | 0.407987 | − | 0.407987i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 702.869 | + | 702.869i | 0.881893 | + | 0.881893i | 0.993727 | − | 0.111834i | \(-0.0356724\pi\) |
−0.111834 | + | 0.993727i | \(0.535672\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 317.463 | 0.397325 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.0347 | + | 11.0347i | −0.0137762 | + | 0.0137762i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −361.463 | −0.450141 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 51.6968i | 0.0642196i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 449.568 | 0.557086 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −475.902 | + | 475.902i | −0.588259 | + | 0.588259i | −0.937160 | − | 0.348901i | \(-0.886555\pi\) |
0.348901 | + | 0.937160i | \(0.386555\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 160.098i | − | 0.197408i | −0.995117 | − | 0.0987040i | \(-0.968530\pi\) | ||
0.995117 | − | 0.0987040i | \(-0.0314697\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −860.987 | −1.05902 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 435.714 | + | 435.714i | 0.534618 | + | 0.534618i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1906.75i | − | 2.33385i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 315.864 | 0.385671 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 417.838i | 0.508937i | 0.967081 | + | 0.254469i | \(0.0819006\pi\) | ||||
−0.967081 | + | 0.254469i | \(0.918099\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −881.681 | − | 881.681i | −1.07130 | − | 1.07130i | −0.997255 | − | 0.0740470i | \(-0.976409\pi\) |
−0.0740470 | − | 0.997255i | \(-0.523591\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 379.202i | 0.459639i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 980.281 | − | 980.281i | 1.18535 | − | 1.18535i | 0.207006 | − | 0.978340i | \(-0.433628\pi\) |
0.978340 | − | 0.207006i | \(-0.0663719\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 712.861 | + | 712.861i | 0.859905 | + | 0.859905i | 0.991327 | − | 0.131422i | \(-0.0419542\pi\) |
−0.131422 | + | 0.991327i | \(0.541954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −227.663 | − | 227.663i | −0.273963 | − | 0.273963i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −63.4839 | − | 63.4839i | −0.0762112 | − | 0.0762112i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1030.52 | 1.23415 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −66.9802 | −0.0800241 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −981.031 | + | 981.031i | −1.16929 | + | 1.16929i | −0.186909 | + | 0.982377i | \(0.559847\pi\) |
−0.982377 | + | 0.186909i | \(0.940153\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 289.094 | − | 789.750i | 0.343751 | − | 0.939061i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −437.994 | − | 437.994i | −0.519566 | − | 0.519566i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 70.8290i | 0.0838213i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1111.66i | − | 1.31247i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.8392 | − | 15.8392i | 0.0186563 | − | 0.0186563i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 41.3476 | − | 41.3476i | 0.0485871 | − | 0.0485871i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 289.400 | − | 289.400i | 0.339273 | − | 0.339273i | −0.516821 | − | 0.856094i | \(-0.672885\pi\) |
0.856094 | + | 0.516821i | \(0.172885\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 355.777 | + | 355.777i | 0.416114 | + | 0.416114i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 74.3861 | 0.0867982 | 0.0433991 | − | 0.999058i | \(-0.486181\pi\) | ||||
0.0433991 | + | 0.999058i | \(0.486181\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −224.397 | + | 224.397i | −0.261230 | + | 0.261230i | −0.825554 | − | 0.564324i | \(-0.809137\pi\) |
0.564324 | + | 0.825554i | \(0.309137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 371.540 | 0.431522 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1041.69i | 1.20705i | 0.797343 | + | 0.603526i | \(0.206238\pi\) | ||||
−0.797343 | + | 0.603526i | \(0.793762\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −482.911 | −0.558279 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 332.254 | − | 332.254i | 0.383223 | − | 0.383223i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1673.20i | − | 1.92543i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −839.541 | −0.963882 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −305.175 | − | 305.175i | −0.349570 | − | 0.349570i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 587.342i | − | 0.671248i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1346.71 | 1.53559 | 0.767796 | − | 0.640695i | \(-0.221354\pi\) | ||||
0.767796 | + | 0.640695i | \(0.221354\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 227.191i | − | 0.258466i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −450.862 | − | 450.862i | −0.511762 | − | 0.511762i | 0.403304 | − | 0.915066i | \(-0.367862\pi\) |
−0.915066 | + | 0.403304i | \(0.867862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1155.28i | 1.30836i | 0.756339 | + | 0.654180i | \(0.226986\pi\) | ||||
−0.756339 | + | 0.654180i | \(0.773014\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 472.180 | − | 472.180i | 0.533537 | − | 0.533537i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 154.986 | + | 154.986i | 0.174731 | + | 0.174731i | 0.789054 | − | 0.614323i | \(-0.210571\pi\) |
−0.614323 | + | 0.789054i | \(0.710571\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 518.269 | + | 518.269i | 0.582980 | + | 0.582980i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 101.336 | + | 101.336i | 0.113733 | + | 0.113733i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2032.15 | 2.27564 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 315.942 | 0.353007 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 15.2270 | − | 15.2270i | 0.0169755 | − | 0.0169755i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 368.081 | + | 65.2522i | 0.409434 | + | 0.0725831i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 126.620 | + | 126.620i | 0.140532 | + | 0.140532i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 1027.98i | − | 1.13841i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 522.101i | − | 0.576907i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 543.696 | − | 543.696i | 0.599444 | − | 0.599444i | −0.340721 | − | 0.940165i | \(-0.610671\pi\) |
0.940165 | + | 0.340721i | \(0.110671\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −235.517 | + | 235.517i | −0.259095 | + | 0.259095i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1196.69 | + | 1196.69i | −1.31360 | + | 1.31360i | −0.394861 | + | 0.918741i | \(0.629207\pi\) |
−0.918741 | + | 0.394861i | \(0.870793\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 903.333 | + | 903.333i | 0.989412 | + | 0.989412i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −549.063 | −0.600069 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 517.376 | − | 517.376i | 0.564205 | − | 0.564205i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 446.342 | 0.485682 | 0.242841 | − | 0.970066i | \(-0.421921\pi\) | ||||
0.242841 | + | 0.970066i | \(0.421921\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1021.52i | 1.10914i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1119.46 | 1.21284 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 574.066 | − | 574.066i | 0.620612 | − | 0.620612i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 503.367i | 0.543007i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1017.18 | −1.09492 | −0.547458 | − | 0.836833i | \(-0.684405\pi\) | ||||
−0.547458 | + | 0.836833i | \(0.684405\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −406.375 | − | 406.375i | −0.436492 | − | 0.436492i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 727.552i | 0.779799i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −417.203 | −0.446206 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 504.667i | − | 0.538598i | −0.963057 | − | 0.269299i | \(-0.913208\pi\) | ||
0.963057 | − | 0.269299i | \(-0.0867920\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −484.732 | − | 484.732i | −0.516221 | − | 0.516221i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1144.29i | 1.21604i | 0.793921 | + | 0.608021i | \(0.208036\pi\) | ||||
−0.793921 | + | 0.608021i | \(0.791964\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.9110 | − | 17.9110i | 0.0189936 | − | 0.0189936i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 191.809 | + | 191.809i | 0.202973 | + | 0.202973i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 458.125 | + | 458.125i | 0.483764 | + | 0.483764i | 0.906332 | − | 0.422567i | \(-0.138871\pi\) |
−0.422567 | + | 0.906332i | \(0.638871\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 201.521 | + | 201.521i | 0.212350 | + | 0.212350i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −86.7283 | −0.0911969 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1072.75 | 1.12565 | 0.562827 | − | 0.826575i | \(-0.309714\pi\) | ||||
0.562827 | + | 0.826575i | \(0.309714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 822.940 | − | 822.940i | 0.861718 | − | 0.861718i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −458.158 | − | 655.602i | −0.478744 | − | 0.685060i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 361.733 | + | 361.733i | 0.377198 | + | 0.377198i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 794.839i | − | 0.827096i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 124.971i | 0.129772i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −936.554 | + | 936.554i | −0.970522 | + | 0.970522i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 108.375 | − | 108.375i | 0.112074 | − | 0.112074i | −0.648846 | − | 0.760920i | \(-0.724748\pi\) |
0.760920 | + | 0.648846i | \(0.224748\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −138.888 | + | 138.888i | −0.143332 | + | 0.143332i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −602.558 | − | 602.558i | −0.620555 | − | 0.620555i | 0.325119 | − | 0.945673i | \(-0.394596\pi\) |
−0.945673 | + | 0.325119i | \(0.894596\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1023.73 | −1.05213 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 211.410 | − | 211.410i | 0.216831 | − | 0.216831i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −272.492 | −0.278907 | −0.139453 | − | 0.990229i | \(-0.544535\pi\) | ||||
−0.139453 | + | 0.990229i | \(0.544535\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 82.8308i | − | 0.0846076i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.86205 | −0.00597558 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 79.4702 | − | 79.4702i | 0.0808445 | − | 0.0808445i | −0.665528 | − | 0.746373i | \(-0.731794\pi\) |
0.746373 | + | 0.665528i | \(0.231794\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2242.30i | 2.27644i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1095.58 | 1.11002 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −49.5563 | − | 49.5563i | −0.0501075 | − | 0.0501075i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 267.139i | 0.269565i | 0.990875 | + | 0.134782i | \(0.0430335\pi\) | ||||
−0.990875 | + | 0.134782i | \(0.956966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 827.367 | 0.833200 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 2105.86i | − | 2.11644i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 164.885 | + | 164.885i | 0.165381 | + | 0.165381i | 0.784946 | − | 0.619565i | \(-0.212691\pi\) |
−0.619565 | + | 0.784946i | \(0.712691\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 306.821i | − | 0.307129i |
(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 | 348.3.j.a.157.9 | yes | 20 | |
3.2 | odd | 2 | 1044.3.k.b.505.2 | 20 | |||
29.17 | odd | 4 | inner | 348.3.j.a.133.7 | ✓ | 20 | |
87.17 | even | 4 | 1044.3.k.b.829.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
348.3.j.a.133.7 | ✓ | 20 | 29.17 | odd | 4 | inner | |
348.3.j.a.157.9 | yes | 20 | 1.1 | even | 1 | trivial | |
1044.3.k.b.505.2 | 20 | 3.2 | odd | 2 | |||
1044.3.k.b.829.9 | 20 | 87.17 | even | 4 |