Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,2,Mod(101,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.08596546749\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 8x^{14} + 20x^{12} + 36x^{10} + 240x^{8} - 156x^{6} + 268x^{4} + 136x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 101.9 | ||
Root | \(-0.476789 + 2.28924i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 136.101 |
Dual form | 136.2.h.a.101.11 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.288356 | − | 1.38450i | 0.203899 | − | 0.978992i | ||||
\(3\) | −1.14379 | −0.660366 | −0.330183 | − | 0.943917i | \(-0.607110\pi\) | ||||
−0.330183 | + | 0.943917i | \(0.607110\pi\) | |||||||
\(4\) | −1.83370 | − | 0.798461i | −0.916851 | − | 0.399230i | ||||
\(5\) | −3.30694 | −1.47891 | −0.739455 | − | 0.673206i | \(-0.764917\pi\) | ||||
−0.739455 | + | 0.673206i | \(0.764917\pi\) | |||||||
\(6\) | −0.329818 | + | 1.58358i | −0.134648 | + | 0.646493i | ||||
\(7\) | − | 1.93801i | − | 0.732499i | −0.930517 | − | 0.366250i | \(-0.880642\pi\) | ||
0.930517 | − | 0.366250i | \(-0.119358\pi\) | |||||||
\(8\) | −1.63423 | + | 2.30853i | −0.577788 | + | 0.816187i | ||||
\(9\) | −1.69175 | −0.563917 | ||||||||
\(10\) | −0.953577 | + | 4.57847i | −0.301548 | + | 1.44784i | ||||
\(11\) | 3.71058 | 1.11878 | 0.559391 | − | 0.828904i | \(-0.311035\pi\) | ||||
0.559391 | + | 0.828904i | \(0.311035\pi\) | |||||||
\(12\) | 2.09737 | + | 0.913270i | 0.605457 | + | 0.263638i | ||||
\(13\) | − | 5.23680i | − | 1.45243i | −0.687469 | − | 0.726214i | \(-0.741278\pi\) | ||
0.687469 | − | 0.726214i | \(-0.258722\pi\) | |||||||
\(14\) | −2.68318 | − | 0.558837i | −0.717111 | − | 0.149356i | ||||
\(15\) | 3.78244 | 0.976622 | ||||||||
\(16\) | 2.72492 | + | 2.92828i | 0.681230 | + | 0.732069i | ||||
\(17\) | −2.09069 | − | 3.55373i | −0.507067 | − | 0.861907i | ||||
\(18\) | −0.487827 | + | 2.34223i | −0.114982 | + | 0.552070i | ||||
\(19\) | 2.14926i | 0.493073i | 0.969133 | + | 0.246537i | \(0.0792926\pi\) | ||||
−0.969133 | + | 0.246537i | \(0.920707\pi\) | |||||||
\(20\) | 6.06394 | + | 2.64046i | 1.35594 | + | 0.590425i | ||||
\(21\) | 2.21667i | 0.483718i | ||||||||
\(22\) | 1.06997 | − | 5.13731i | 0.228118 | − | 1.09528i | ||||
\(23\) | 3.05569i | 0.637154i | 0.947897 | + | 0.318577i | \(0.103205\pi\) | ||||
−0.947897 | + | 0.318577i | \(0.896795\pi\) | |||||||
\(24\) | 1.86921 | − | 2.64046i | 0.381552 | − | 0.538982i | ||||
\(25\) | 5.93586 | 1.18717 | ||||||||
\(26\) | −7.25037 | − | 1.51006i | −1.42191 | − | 0.296148i | ||||
\(27\) | 5.36637 | 1.03276 | ||||||||
\(28\) | −1.54743 | + | 3.55373i | −0.292436 | + | 0.671592i | ||||
\(29\) | −4.62622 | −0.859067 | −0.429533 | − | 0.903051i | \(-0.641322\pi\) | ||||
−0.429533 | + | 0.903051i | \(0.641322\pi\) | |||||||
\(30\) | 1.09069 | − | 5.23680i | 0.199132 | − | 0.956105i | ||||
\(31\) | − | 10.3861i | − | 1.86540i | −0.360656 | − | 0.932699i | \(-0.617447\pi\) | ||
0.360656 | − | 0.932699i | \(-0.382553\pi\) | |||||||
\(32\) | 4.83996 | − | 2.92828i | 0.855592 | − | 0.517651i | ||||
\(33\) | −4.24412 | −0.738806 | ||||||||
\(34\) | −5.52302 | + | 1.86983i | −0.947190 | + | 0.320673i | ||||
\(35\) | 6.40889i | 1.08330i | ||||||||
\(36\) | 3.10216 | + | 1.35080i | 0.517027 | + | 0.225133i | ||||
\(37\) | −2.79494 | −0.459486 | −0.229743 | − | 0.973251i | \(-0.573789\pi\) | ||||
−0.229743 | + | 0.973251i | \(0.573789\pi\) | |||||||
\(38\) | 2.97565 | + | 0.619751i | 0.482715 | + | 0.100537i | ||||
\(39\) | 5.98979i | 0.959134i | ||||||||
\(40\) | 5.40431 | − | 7.63416i | 0.854496 | − | 1.20707i | ||||
\(41\) | 7.33041i | 1.14482i | 0.819968 | + | 0.572409i | \(0.193991\pi\) | ||||
−0.819968 | + | 0.572409i | \(0.806009\pi\) | |||||||
\(42\) | 3.06899 | + | 0.639191i | 0.473556 | + | 0.0986294i | ||||
\(43\) | − | 6.21397i | − | 0.947622i | −0.880627 | − | 0.473811i | \(-0.842878\pi\) | ||
0.880627 | − | 0.473811i | \(-0.157122\pi\) | |||||||
\(44\) | −6.80409 | − | 2.96275i | −1.02576 | − | 0.446652i | ||||
\(45\) | 5.59452 | 0.833981 | ||||||||
\(46\) | 4.23061 | + | 0.881126i | 0.623769 | + | 0.129915i | ||||
\(47\) | −1.60106 | −0.233539 | −0.116769 | − | 0.993159i | \(-0.537254\pi\) | ||||
−0.116769 | + | 0.993159i | \(0.537254\pi\) | |||||||
\(48\) | −3.11673 | − | 3.34933i | −0.449861 | − | 0.483434i | ||||
\(49\) | 3.24412 | 0.463445 | ||||||||
\(50\) | 1.71164 | − | 8.21823i | 0.242063 | − | 1.16223i | ||||
\(51\) | 2.39131 | + | 4.06472i | 0.334850 | + | 0.569174i | ||||
\(52\) | −4.18138 | + | 9.60273i | −0.579853 | + | 1.33166i | ||||
\(53\) | 0.675957i | 0.0928498i | 0.998922 | + | 0.0464249i | \(0.0147828\pi\) | ||||
−0.998922 | + | 0.0464249i | \(0.985217\pi\) | |||||||
\(54\) | 1.54743 | − | 7.42975i | 0.210578 | − | 1.01106i | ||||
\(55\) | −12.2707 | −1.65458 | ||||||||
\(56\) | 4.47395 | + | 3.16716i | 0.597856 | + | 0.423229i | ||||
\(57\) | − | 2.45829i | − | 0.325609i | ||||||
\(58\) | −1.33400 | + | 6.40501i | −0.175163 | + | 0.841019i | ||||
\(59\) | − | 2.51789i | − | 0.327801i | −0.986477 | − | 0.163900i | \(-0.947592\pi\) | ||
0.986477 | − | 0.163900i | \(-0.0524076\pi\) | |||||||
\(60\) | −6.93586 | − | 3.02013i | −0.895416 | − | 0.389897i | ||||
\(61\) | 0.507368 | 0.0649618 | 0.0324809 | − | 0.999472i | \(-0.489659\pi\) | ||||
0.0324809 | + | 0.999472i | \(0.489659\pi\) | |||||||
\(62\) | −14.3796 | − | 2.99490i | −1.82621 | − | 0.380352i | ||||
\(63\) | 3.27863i | 0.413068i | ||||||||
\(64\) | −2.65858 | − | 7.54533i | −0.332322 | − | 0.943166i | ||||
\(65\) | 17.3178i | 2.14801i | ||||||||
\(66\) | −1.22382 | + | 5.87599i | −0.150641 | + | 0.723285i | ||||
\(67\) | 6.58260i | 0.804193i | 0.915597 | + | 0.402096i | \(0.131718\pi\) | ||||
−0.915597 | + | 0.402096i | \(0.868282\pi\) | |||||||
\(68\) | 0.996186 | + | 8.18582i | 0.120805 | + | 0.992676i | ||||
\(69\) | − | 3.49506i | − | 0.420755i | ||||||
\(70\) | 8.87313 | + | 1.84804i | 1.06054 | + | 0.220883i | ||||
\(71\) | 9.04548i | 1.07350i | 0.843741 | + | 0.536750i | \(0.180348\pi\) | ||||
−0.843741 | + | 0.536750i | \(0.819652\pi\) | |||||||
\(72\) | 2.76471 | − | 3.90545i | 0.325824 | − | 0.460261i | ||||
\(73\) | − | 4.87212i | − | 0.570238i | −0.958492 | − | 0.285119i | \(-0.907967\pi\) | ||
0.958492 | − | 0.285119i | \(-0.0920331\pi\) | |||||||
\(74\) | −0.805939 | + | 3.86961i | −0.0936885 | + | 0.449833i | ||||
\(75\) | −6.78937 | −0.783969 | ||||||||
\(76\) | 1.71610 | − | 3.94109i | 0.196850 | − | 0.452074i | ||||
\(77\) | − | 7.19114i | − | 0.819507i | ||||||
\(78\) | 8.29289 | + | 1.72719i | 0.938985 | + | 0.195566i | ||||
\(79\) | 3.27863i | 0.368875i | 0.982844 | + | 0.184437i | \(0.0590463\pi\) | ||||
−0.982844 | + | 0.184437i | \(0.940954\pi\) | |||||||
\(80\) | −9.01116 | − | 9.68364i | −1.00748 | − | 1.08266i | ||||
\(81\) | −1.06273 | −0.118082 | ||||||||
\(82\) | 10.1490 | + | 2.11377i | 1.12077 | + | 0.233427i | ||||
\(83\) | − | 12.9915i | − | 1.42600i | −0.701163 | − | 0.713001i | \(-0.747336\pi\) | ||
0.701163 | − | 0.713001i | \(-0.252664\pi\) | |||||||
\(84\) | 1.76993 | − | 4.06472i | 0.193115 | − | 0.443497i | ||||
\(85\) | 6.91379 | + | 11.7520i | 0.749906 | + | 1.27468i | ||||
\(86\) | −8.60327 | − | 1.79184i | −0.927714 | − | 0.193219i | ||||
\(87\) | 5.29141 | 0.567299 | ||||||||
\(88\) | −6.06394 | + | 8.56597i | −0.646419 | + | 0.913135i | ||||
\(89\) | −13.8090 | −1.46375 | −0.731875 | − | 0.681439i | \(-0.761355\pi\) | ||||
−0.731875 | + | 0.681439i | \(0.761355\pi\) | |||||||
\(90\) | 1.61321 | − | 7.74563i | 0.170048 | − | 0.816461i | ||||
\(91\) | −10.1490 | −1.06390 | ||||||||
\(92\) | 2.43984 | − | 5.60321i | 0.254371 | − | 0.584175i | ||||
\(93\) | 11.8795i | 1.23185i | ||||||||
\(94\) | −0.461675 | + | 2.21667i | −0.0476182 | + | 0.228632i | ||||
\(95\) | − | 7.10746i | − | 0.729211i | ||||||
\(96\) | −5.53589 | + | 3.34933i | −0.565004 | + | 0.341839i | ||||
\(97\) | − | 10.2103i | − | 1.03670i | −0.855168 | − | 0.518351i | \(-0.826546\pi\) | ||
0.855168 | − | 0.518351i | \(-0.173454\pi\) | |||||||
\(98\) | 0.935461 | − | 4.49149i | 0.0944958 | − | 0.453709i | ||||
\(99\) | −6.27737 | −0.630900 | ||||||||
\(100\) | −10.8846 | − | 4.73955i | −1.08846 | − | 0.473955i | ||||
\(101\) | − | 7.58097i | − | 0.754335i | −0.926145 | − | 0.377168i | \(-0.876898\pi\) | ||
0.926145 | − | 0.377168i | \(-0.123102\pi\) | |||||||
\(102\) | 6.31716 | − | 2.13869i | 0.625492 | − | 0.211761i | ||||
\(103\) | 14.7951 | 1.45780 | 0.728901 | − | 0.684619i | \(-0.240031\pi\) | ||||
0.728901 | + | 0.684619i | \(0.240031\pi\) | |||||||
\(104\) | 12.0893 | + | 8.55814i | 1.18545 | + | 0.839195i | ||||
\(105\) | − | 7.33041i | − | 0.715375i | ||||||
\(106\) | 0.935865 | + | 0.194916i | 0.0908992 | + | 0.0189320i | ||||
\(107\) | 4.15082 | 0.401275 | 0.200638 | − | 0.979666i | \(-0.435699\pi\) | ||||
0.200638 | + | 0.979666i | \(0.435699\pi\) | |||||||
\(108\) | −9.84031 | − | 4.28483i | −0.946884 | − | 0.412308i | ||||
\(109\) | 10.7281 | 1.02757 | 0.513783 | − | 0.857920i | \(-0.328244\pi\) | ||||
0.513783 | + | 0.857920i | \(0.328244\pi\) | |||||||
\(110\) | −3.53832 | + | 16.9888i | −0.337366 | + | 1.61982i | ||||
\(111\) | 3.19682 | 0.303429 | ||||||||
\(112\) | 5.67503 | − | 5.28093i | 0.536240 | − | 0.499001i | ||||
\(113\) | − | 17.3178i | − | 1.62912i | −0.580078 | − | 0.814561i | \(-0.696978\pi\) | ||
0.580078 | − | 0.814561i | \(-0.303022\pi\) | |||||||
\(114\) | −3.40352 | − | 0.708864i | −0.318768 | − | 0.0663912i | ||||
\(115\) | − | 10.1050i | − | 0.942294i | ||||||
\(116\) | 8.48310 | + | 3.69385i | 0.787636 | + | 0.342965i | ||||
\(117\) | 8.85936i | 0.819048i | ||||||||
\(118\) | −3.48602 | − | 0.726048i | −0.320914 | − | 0.0668381i | ||||
\(119\) | −6.88717 | + | 4.05178i | −0.631346 | + | 0.371426i | ||||
\(120\) | −6.18138 | + | 8.73186i | −0.564280 | + | 0.797106i | ||||
\(121\) | 2.76840 | 0.251673 | ||||||||
\(122\) | 0.146303 | − | 0.702452i | 0.0132456 | − | 0.0635971i | ||||
\(123\) | − | 8.38443i | − | 0.755999i | ||||||
\(124\) | −8.29289 | + | 19.0450i | −0.744723 | + | 1.71029i | ||||
\(125\) | −3.09485 | −0.276812 | ||||||||
\(126\) | 4.53927 | + | 0.945413i | 0.404391 | + | 0.0842241i | ||||
\(127\) | 17.7463 | 1.57473 | 0.787363 | − | 0.616490i | \(-0.211446\pi\) | ||||
0.787363 | + | 0.616490i | \(0.211446\pi\) | |||||||
\(128\) | −11.2132 | + | 1.50507i | −0.991112 | + | 0.133031i | ||||
\(129\) | 7.10746i | 0.625777i | ||||||||
\(130\) | 23.9766 | + | 4.99370i | 2.10288 | + | 0.437976i | ||||
\(131\) | 3.78233 | 0.330464 | 0.165232 | − | 0.986255i | \(-0.447163\pi\) | ||||
0.165232 | + | 0.986255i | \(0.447163\pi\) | |||||||
\(132\) | 7.78244 | + | 3.38876i | 0.677374 | + | 0.294954i | ||||
\(133\) | 4.16528 | 0.361176 | ||||||||
\(134\) | 9.11364 | + | 1.89813i | 0.787298 | + | 0.163974i | ||||
\(135\) | −17.7463 | −1.52735 | ||||||||
\(136\) | 11.6206 | + | 0.981209i | 0.996454 | + | 0.0841380i | ||||
\(137\) | 13.0545 | 1.11532 | 0.557661 | − | 0.830069i | \(-0.311699\pi\) | ||||
0.557661 | + | 0.830069i | \(0.311699\pi\) | |||||||
\(138\) | −4.83892 | − | 1.00782i | −0.411916 | − | 0.0857914i | ||||
\(139\) | −4.22258 | −0.358154 | −0.179077 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179077 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(140\) | 5.11725 | − | 11.7520i | 0.432486 | − | 0.993224i | ||||
\(141\) | 1.83127 | 0.154221 | ||||||||
\(142\) | 12.5235 | + | 2.60832i | 1.05095 | + | 0.218885i | ||||
\(143\) | − | 19.4316i | − | 1.62495i | ||||||
\(144\) | −4.60988 | − | 4.95391i | −0.384157 | − | 0.412826i | ||||
\(145\) | 15.2986 | 1.27048 | ||||||||
\(146\) | −6.74546 | − | 1.40490i | −0.558258 | − | 0.116271i | ||||
\(147\) | −3.71058 | −0.306043 | ||||||||
\(148\) | 5.12509 | + | 2.23165i | 0.421280 | + | 0.183441i | ||||
\(149\) | − | 4.29851i | − | 0.352148i | −0.984377 | − | 0.176074i | \(-0.943660\pi\) | ||
0.984377 | − | 0.176074i | \(-0.0563398\pi\) | |||||||
\(150\) | −1.95776 | + | 9.39991i | −0.159850 | + | 0.767499i | ||||
\(151\) | −11.2552 | −0.915938 | −0.457969 | − | 0.888968i | \(-0.651423\pi\) | ||||
−0.457969 | + | 0.888968i | \(0.651423\pi\) | |||||||
\(152\) | −4.96161 | − | 3.51238i | −0.402440 | − | 0.284892i | ||||
\(153\) | 3.53692 | + | 6.01203i | 0.285943 | + | 0.486043i | ||||
\(154\) | −9.95616 | − | 2.07361i | −0.802290 | − | 0.167096i | ||||
\(155\) | 34.3462i | 2.75875i | ||||||||
\(156\) | 4.78261 | − | 10.9835i | 0.382915 | − | 0.879383i | ||||
\(157\) | 10.0102i | 0.798904i | 0.916754 | + | 0.399452i | \(0.130800\pi\) | ||||
−0.916754 | + | 0.399452i | \(0.869200\pi\) | |||||||
\(158\) | 4.53927 | + | 0.945413i | 0.361125 | + | 0.0752130i | ||||
\(159\) | − | 0.773151i | − | 0.0613149i | ||||||
\(160\) | −16.0055 | + | 9.68364i | −1.26534 | + | 0.765559i | ||||
\(161\) | 5.92195 | 0.466715 | ||||||||
\(162\) | −0.306446 | + | 1.47136i | −0.0240767 | + | 0.115601i | ||||
\(163\) | −17.4503 | −1.36682 | −0.683408 | − | 0.730036i | \(-0.739503\pi\) | ||||
−0.683408 | + | 0.730036i | \(0.739503\pi\) | |||||||
\(164\) | 5.85304 | − | 13.4418i | 0.457046 | − | 1.04963i | ||||
\(165\) | 14.0350 | 1.09263 | ||||||||
\(166\) | −17.9868 | − | 3.74618i | −1.39604 | − | 0.290760i | ||||
\(167\) | − | 1.16486i | − | 0.0901395i | −0.998984 | − | 0.0450698i | \(-0.985649\pi\) | ||
0.998984 | − | 0.0450698i | \(-0.0143510\pi\) | |||||||
\(168\) | −5.11725 | − | 3.62256i | −0.394804 | − | 0.279486i | ||||
\(169\) | −14.4241 | −1.10955 | ||||||||
\(170\) | 18.2643 | − | 6.18341i | 1.40081 | − | 0.474246i | ||||
\(171\) | − | 3.63600i | − | 0.278052i | ||||||
\(172\) | −4.96161 | + | 11.3946i | −0.378319 | + | 0.868828i | ||||
\(173\) | 5.88979 | 0.447793 | 0.223896 | − | 0.974613i | \(-0.428122\pi\) | ||||
0.223896 | + | 0.974613i | \(0.428122\pi\) | |||||||
\(174\) | 1.52581 | − | 7.32598i | 0.115671 | − | 0.555381i | ||||
\(175\) | − | 11.5038i | − | 0.869603i | ||||||
\(176\) | 10.1110 | + | 10.8656i | 0.762148 | + | 0.819026i | ||||
\(177\) | 2.87993i | 0.216469i | ||||||||
\(178\) | −3.98191 | + | 19.1186i | −0.298457 | + | 1.43300i | ||||
\(179\) | − | 8.53694i | − | 0.638081i | −0.947741 | − | 0.319040i | \(-0.896639\pi\) | ||
0.947741 | − | 0.319040i | \(-0.103361\pi\) | |||||||
\(180\) | −10.2587 | − | 4.46700i | −0.764636 | − | 0.332951i | ||||
\(181\) | −19.4221 | −1.44363 | −0.721817 | − | 0.692084i | \(-0.756693\pi\) | ||||
−0.721817 | + | 0.692084i | \(0.756693\pi\) | |||||||
\(182\) | −2.92652 | + | 14.0513i | −0.216928 | + | 1.04155i | ||||
\(183\) | −0.580321 | −0.0428986 | ||||||||
\(184\) | −7.05413 | − | 4.99370i | −0.520037 | − | 0.368140i | ||||
\(185\) | 9.24271 | 0.679538 | ||||||||
\(186\) | 16.4472 | + | 3.42552i | 1.20597 | + | 0.251172i | ||||
\(187\) | −7.75767 | − | 13.1864i | −0.567297 | − | 0.964286i | ||||
\(188\) | 2.93586 | + | 1.27838i | 0.214120 | + | 0.0932357i | ||||
\(189\) | − | 10.4001i | − | 0.756494i | ||||||
\(190\) | −9.84031 | − | 2.04948i | −0.713891 | − | 0.148685i | ||||
\(191\) | −2.52441 | −0.182660 | −0.0913300 | − | 0.995821i | \(-0.529112\pi\) | ||||
−0.0913300 | + | 0.995821i | \(0.529112\pi\) | |||||||
\(192\) | 3.04085 | + | 8.63025i | 0.219454 | + | 0.622835i | ||||
\(193\) | − | 0.644577i | − | 0.0463977i | −0.999731 | − | 0.0231988i | \(-0.992615\pi\) | ||
0.999731 | − | 0.0231988i | \(-0.00738508\pi\) | |||||||
\(194\) | −14.1362 | − | 2.94421i | −1.01492 | − | 0.211382i | ||||
\(195\) | − | 19.8079i | − | 1.41847i | ||||||
\(196\) | −5.94874 | − | 2.59030i | −0.424910 | − | 0.185021i | ||||
\(197\) | −4.67265 | −0.332912 | −0.166456 | − | 0.986049i | \(-0.553232\pi\) | ||||
−0.166456 | + | 0.986049i | \(0.553232\pi\) | |||||||
\(198\) | −1.81012 | + | 8.69104i | −0.128640 | + | 0.617646i | ||||
\(199\) | 16.4975i | 1.16947i | 0.811223 | + | 0.584737i | \(0.198802\pi\) | ||||
−0.811223 | + | 0.584737i | \(0.801198\pi\) | |||||||
\(200\) | −9.70057 | + | 13.7031i | −0.685934 | + | 0.968955i | ||||
\(201\) | − | 7.52910i | − | 0.531062i | ||||||
\(202\) | −10.4959 | − | 2.18602i | −0.738488 | − | 0.153808i | ||||
\(203\) | 8.96565i | 0.629266i | ||||||||
\(204\) | −1.13943 | − | 9.36284i | −0.0797757 | − | 0.655530i | ||||
\(205\) | − | 24.2412i | − | 1.69308i | ||||||
\(206\) | 4.26625 | − | 20.4838i | 0.297244 | − | 1.42718i | ||||
\(207\) | − | 5.16945i | − | 0.359302i | ||||||
\(208\) | 15.3348 | − | 14.2699i | 1.06328 | − | 0.989438i | ||||
\(209\) | 7.97499i | 0.551641i | ||||||||
\(210\) | −10.1490 | − | 2.11377i | −0.700346 | − | 0.145864i | ||||
\(211\) | 22.3047 | 1.53552 | 0.767760 | − | 0.640738i | \(-0.221371\pi\) | ||||
0.767760 | + | 0.640738i | \(0.221371\pi\) | |||||||
\(212\) | 0.539725 | − | 1.23950i | 0.0370685 | − | 0.0851294i | ||||
\(213\) | − | 10.3461i | − | 0.708903i | ||||||
\(214\) | 1.19692 | − | 5.74683i | 0.0818195 | − | 0.392845i | ||||
\(215\) | 20.5492i | 1.40145i | ||||||||
\(216\) | −8.76988 | + | 12.3884i | −0.596715 | + | 0.842923i | ||||
\(217\) | −20.1284 | −1.36640 | ||||||||
\(218\) | 3.09351 | − | 14.8531i | 0.209519 | − | 1.00598i | ||||
\(219\) | 5.57267i | 0.376566i | ||||||||
\(220\) | 22.5007 | + | 9.79765i | 1.51700 | + | 0.660557i | ||||
\(221\) | −18.6102 | + | 10.9485i | −1.25186 | + | 0.736478i | ||||
\(222\) | 0.921824 | − | 4.42601i | 0.0618687 | − | 0.297054i | ||||
\(223\) | −8.24259 | −0.551965 | −0.275982 | − | 0.961163i | \(-0.589003\pi\) | ||||
−0.275982 | + | 0.961163i | \(0.589003\pi\) | |||||||
\(224\) | −5.67503 | − | 9.37989i | −0.379179 | − | 0.626720i | ||||
\(225\) | −10.0420 | −0.669466 | ||||||||
\(226\) | −23.9766 | − | 4.99370i | −1.59490 | − | 0.332176i | ||||
\(227\) | 24.8715 | 1.65078 | 0.825390 | − | 0.564563i | \(-0.190955\pi\) | ||||
0.825390 | + | 0.564563i | \(0.190955\pi\) | |||||||
\(228\) | −1.96285 | + | 4.50777i | −0.129993 | + | 0.298535i | ||||
\(229\) | 14.3585i | 0.948836i | 0.880300 | + | 0.474418i | \(0.157341\pi\) | ||||
−0.880300 | + | 0.474418i | \(0.842659\pi\) | |||||||
\(230\) | −13.9904 | − | 2.91383i | −0.922498 | − | 0.192132i | ||||
\(231\) | 8.22514i | 0.541174i | ||||||||
\(232\) | 7.56030 | − | 10.6797i | 0.496358 | − | 0.701159i | ||||
\(233\) | 5.29375i | 0.346805i | 0.984851 | + | 0.173403i | \(0.0554762\pi\) | ||||
−0.984851 | + | 0.173403i | \(0.944524\pi\) | |||||||
\(234\) | 12.2658 | + | 2.55465i | 0.801841 | + | 0.167003i | ||||
\(235\) | 5.29461 | 0.345382 | ||||||||
\(236\) | −2.01043 | + | 4.61705i | −0.130868 | + | 0.300544i | ||||
\(237\) | − | 3.75006i | − | 0.243592i | ||||||
\(238\) | 3.62375 | + | 10.7037i | 0.234893 | + | 0.693816i | ||||
\(239\) | 20.3238 | 1.31464 | 0.657318 | − | 0.753613i | \(-0.271691\pi\) | ||||
0.657318 | + | 0.753613i | \(0.271691\pi\) | |||||||
\(240\) | 10.3069 | + | 11.0760i | 0.665304 | + | 0.714955i | ||||
\(241\) | 0.222943i | 0.0143610i | 0.999974 | + | 0.00718051i | \(0.00228565\pi\) | ||||
−0.999974 | + | 0.00718051i | \(0.997714\pi\) | |||||||
\(242\) | 0.798285 | − | 3.83286i | 0.0513157 | − | 0.246385i | ||||
\(243\) | −14.8836 | −0.954780 | ||||||||
\(244\) | −0.930361 | − | 0.405113i | −0.0595602 | − | 0.0259347i | ||||
\(245\) | −10.7281 | −0.685393 | ||||||||
\(246\) | −11.6083 | − | 2.41770i | −0.740117 | − | 0.154147i | ||||
\(247\) | 11.2552 | 0.716153 | ||||||||
\(248\) | 23.9766 | + | 16.9733i | 1.52251 | + | 1.07780i | ||||
\(249\) | 14.8595i | 0.941683i | ||||||||
\(250\) | −0.892419 | + | 4.28483i | −0.0564416 | + | 0.270997i | ||||
\(251\) | 25.4406i | 1.60580i | 0.596115 | + | 0.802899i | \(0.296710\pi\) | ||||
−0.596115 | + | 0.802899i | \(0.703290\pi\) | |||||||
\(252\) | 2.61786 | − | 6.01203i | 0.164909 | − | 0.378722i | ||||
\(253\) | 11.3384i | 0.712837i | ||||||||
\(254\) | 5.11725 | − | 24.5698i | 0.321085 | − | 1.54164i | ||||
\(255\) | −7.90791 | − | 13.4418i | −0.495212 | − | 0.841757i | ||||
\(256\) | −1.14961 | + | 15.9586i | −0.0718506 | + | 0.997415i | ||||
\(257\) | −29.7213 | −1.85397 | −0.926983 | − | 0.375105i | \(-0.877607\pi\) | ||||
−0.926983 | + | 0.375105i | \(0.877607\pi\) | |||||||
\(258\) | 9.84031 | + | 2.04948i | 0.612631 | + | 0.127595i | ||||
\(259\) | 5.41663i | 0.336573i | ||||||||
\(260\) | 13.8276 | − | 31.7557i | 0.857550 | − | 1.96940i | ||||
\(261\) | 7.82640 | 0.484442 | ||||||||
\(262\) | 1.09066 | − | 5.23666i | 0.0673812 | − | 0.323522i | ||||
\(263\) | −14.7951 | −0.912304 | −0.456152 | − | 0.889902i | \(-0.650773\pi\) | ||||
−0.456152 | + | 0.889902i | \(0.650773\pi\) | |||||||
\(264\) | 6.93586 | − | 9.79765i | 0.426873 | − | 0.603004i | ||||
\(265\) | − | 2.23535i | − | 0.137316i | ||||||
\(266\) | 1.20108 | − | 5.76685i | 0.0736432 | − | 0.353588i | ||||
\(267\) | 15.7946 | 0.966611 | ||||||||
\(268\) | 5.25595 | − | 12.0705i | 0.321058 | − | 0.737325i | ||||
\(269\) | −7.67968 | −0.468239 | −0.234119 | − | 0.972208i | \(-0.575221\pi\) | ||||
−0.234119 | + | 0.972208i | \(0.575221\pi\) | |||||||
\(270\) | −5.11725 | + | 24.5698i | −0.311426 | + | 1.49527i | ||||
\(271\) | 12.3681 | 0.751306 | 0.375653 | − | 0.926760i | \(-0.377418\pi\) | ||||
0.375653 | + | 0.926760i | \(0.377418\pi\) | |||||||
\(272\) | 4.70935 | − | 15.8058i | 0.285546 | − | 0.958365i | ||||
\(273\) | 11.6083 | 0.702565 | ||||||||
\(274\) | 3.76435 | − | 18.0740i | 0.227413 | − | 1.09189i | ||||
\(275\) | 22.0255 | 1.32819 | ||||||||
\(276\) | −2.79066 | + | 6.40889i | −0.167978 | + | 0.385770i | ||||
\(277\) | 15.3033 | 0.919483 | 0.459742 | − | 0.888053i | \(-0.347942\pi\) | ||||
0.459742 | + | 0.888053i | \(0.347942\pi\) | |||||||
\(278\) | −1.21761 | + | 5.84618i | −0.0730272 | + | 0.350630i | ||||
\(279\) | 17.5707i | 1.05193i | ||||||||
\(280\) | −14.7951 | − | 10.4736i | −0.884175 | − | 0.625918i | ||||
\(281\) | 4.47572 | 0.266999 | 0.133499 | − | 0.991049i | \(-0.457379\pi\) | ||||
0.133499 | + | 0.991049i | \(0.457379\pi\) | |||||||
\(282\) | 0.528059 | − | 2.53540i | 0.0314454 | − | 0.150981i | ||||
\(283\) | −8.49319 | −0.504868 | −0.252434 | − | 0.967614i | \(-0.581231\pi\) | ||||
−0.252434 | + | 0.967614i | \(0.581231\pi\) | |||||||
\(284\) | 7.22246 | − | 16.5867i | 0.428574 | − | 0.984240i | ||||
\(285\) | 8.12943i | 0.481546i | ||||||||
\(286\) | −26.9031 | − | 5.60321i | −1.59081 | − | 0.331325i | ||||
\(287\) | 14.2064 | 0.838578 | ||||||||
\(288\) | −8.18800 | + | 4.95391i | −0.482482 | + | 0.291912i | ||||
\(289\) | −8.25803 | + | 14.8595i | −0.485766 | + | 0.874089i | ||||
\(290\) | 4.41145 | − | 21.1810i | 0.259050 | − | 1.24379i | ||||
\(291\) | 11.6785i | 0.684603i | ||||||||
\(292\) | −3.89019 | + | 8.93400i | −0.227656 | + | 0.522823i | ||||
\(293\) | − | 1.74175i | − | 0.101754i | −0.998705 | − | 0.0508770i | \(-0.983798\pi\) | ||
0.998705 | − | 0.0508770i | \(-0.0162016\pi\) | |||||||
\(294\) | −1.06997 | + | 5.13731i | −0.0624018 | + | 0.299614i | ||||
\(295\) | 8.32650i | 0.484788i | ||||||||
\(296\) | 4.56758 | − | 6.45220i | 0.265485 | − | 0.375026i | ||||
\(297\) | 19.9123 | 1.15543 | ||||||||
\(298\) | −5.95131 | − | 1.23950i | −0.344750 | − | 0.0718025i | ||||
\(299\) | 16.0020 | 0.925421 | ||||||||
\(300\) | 12.4497 | + | 5.42104i | 0.718782 | + | 0.312984i | ||||
\(301\) | −12.0427 | −0.694132 | ||||||||
\(302\) | −3.24552 | + | 15.5829i | −0.186758 | + | 0.896695i | ||||
\(303\) | 8.67103i | 0.498137i | ||||||||
\(304\) | −6.29362 | + | 5.85655i | −0.360964 | + | 0.335896i | ||||
\(305\) | −1.67784 | −0.0960726 | ||||||||
\(306\) | 9.34357 | − | 3.16328i | 0.534136 | − | 0.180833i | ||||
\(307\) | 32.4520i | 1.85213i | 0.377363 | + | 0.926065i | \(0.376831\pi\) | ||||
−0.377363 | + | 0.926065i | \(0.623169\pi\) | |||||||
\(308\) | −5.74184 | + | 13.1864i | −0.327172 | + | 0.751365i | ||||
\(309\) | −16.9224 | −0.962684 | ||||||||
\(310\) | 47.5525 | + | 9.90394i | 2.70080 | + | 0.562506i | ||||
\(311\) | − | 10.9091i | − | 0.618598i | −0.950965 | − | 0.309299i | \(-0.899906\pi\) | ||
0.950965 | − | 0.309299i | \(-0.100094\pi\) | |||||||
\(312\) | −13.8276 | − | 9.78870i | −0.782833 | − | 0.554176i | ||||
\(313\) | − | 22.4129i | − | 1.26685i | −0.773804 | − | 0.633425i | \(-0.781649\pi\) | ||
0.773804 | − | 0.633425i | \(-0.218351\pi\) | |||||||
\(314\) | 13.8592 | + | 2.88652i | 0.782121 | + | 0.162895i | ||||
\(315\) | − | 10.8422i | − | 0.610891i | ||||||
\(316\) | 2.61786 | − | 6.01203i | 0.147266 | − | 0.338203i | ||||
\(317\) | 7.16263 | 0.402294 | 0.201147 | − | 0.979561i | \(-0.435533\pi\) | ||||
0.201147 | + | 0.979561i | \(0.435533\pi\) | |||||||
\(318\) | −1.07043 | − | 0.222943i | −0.0600268 | − | 0.0125020i | ||||
\(319\) | −17.1659 | −0.961108 | ||||||||
\(320\) | 8.79176 | + | 24.9520i | 0.491474 | + | 1.39486i | ||||
\(321\) | −4.74766 | −0.264989 | ||||||||
\(322\) | 1.70763 | − | 8.19896i | 0.0951626 | − | 0.456910i | ||||
\(323\) | 7.63788 | − | 4.49343i | 0.424983 | − | 0.250021i | ||||
\(324\) | 1.94874 | + | 0.848552i | 0.108263 | + | 0.0471418i | ||||
\(325\) | − | 31.0849i | − | 1.72428i | ||||||
\(326\) | −5.03192 | + | 24.1601i | −0.278692 | + | 1.33810i | ||||
\(327\) | −12.2707 | −0.678570 | ||||||||
\(328\) | −16.9224 | − | 11.9796i | −0.934385 | − | 0.661462i | ||||
\(329\) | 3.10287i | 0.171067i | ||||||||
\(330\) | 4.04709 | − | 19.4316i | 0.222785 | − | 1.06967i | ||||
\(331\) | − | 26.0219i | − | 1.43029i | −0.698976 | − | 0.715145i | \(-0.746360\pi\) | ||
0.698976 | − | 0.715145i | \(-0.253640\pi\) | |||||||
\(332\) | −10.3732 | + | 23.8225i | −0.569303 | + | 1.30743i | ||||
\(333\) | 4.72834 | 0.259112 | ||||||||
\(334\) | −1.61275 | − | 0.335895i | −0.0882459 | − | 0.0183793i | ||||
\(335\) | − | 21.7683i | − | 1.18933i | ||||||
\(336\) | −6.49103 | + | 6.04026i | −0.354115 | + | 0.329523i | ||||
\(337\) | − | 13.7933i | − | 0.751369i | −0.926748 | − | 0.375684i | \(-0.877408\pi\) | ||
0.926748 | − | 0.375684i | \(-0.122592\pi\) | |||||||
\(338\) | −4.15928 | + | 19.9702i | −0.226235 | + | 1.08624i | ||||
\(339\) | 19.8079i | 1.07582i | ||||||||
\(340\) | −3.29433 | − | 27.0700i | −0.178660 | − | 1.46808i | ||||
\(341\) | − | 38.5384i | − | 2.08697i | ||||||
\(342\) | −5.03406 | − | 1.04846i | −0.272211 | − | 0.0566945i | ||||
\(343\) | − | 19.8532i | − | 1.07197i | ||||||
\(344\) | 14.3451 | + | 10.1551i | 0.773437 | + | 0.547524i | ||||
\(345\) | 11.5579i | 0.622259i | ||||||||
\(346\) | 1.69836 | − | 8.15444i | 0.0913043 | − | 0.438385i | ||||
\(347\) | −18.8750 | −1.01326 | −0.506630 | − | 0.862163i | \(-0.669109\pi\) | ||||
−0.506630 | + | 0.862163i | \(0.669109\pi\) | |||||||
\(348\) | −9.70286 | − | 4.22498i | −0.520128 | − | 0.226483i | ||||
\(349\) | 6.71622i | 0.359511i | 0.983711 | + | 0.179755i | \(0.0575306\pi\) | ||||
−0.983711 | + | 0.179755i | \(0.942469\pi\) | |||||||
\(350\) | −15.9270 | − | 3.31718i | −0.851335 | − | 0.177311i | ||||
\(351\) | − | 28.1026i | − | 1.50001i | ||||||
\(352\) | 17.9590 | − | 10.8656i | 0.957221 | − | 0.579139i | ||||
\(353\) | 19.7029 | 1.04868 | 0.524339 | − | 0.851510i | \(-0.324313\pi\) | ||||
0.524339 | + | 0.851510i | \(0.324313\pi\) | |||||||
\(354\) | 3.98727 | + | 0.830445i | 0.211921 | + | 0.0441377i | ||||
\(355\) | − | 29.9129i | − | 1.58761i | ||||||
\(356\) | 25.3216 | + | 11.0259i | 1.34204 | + | 0.584374i | ||||
\(357\) | 7.87746 | − | 4.63438i | 0.416919 | − | 0.245277i | ||||
\(358\) | −11.8194 | − | 2.46168i | −0.624676 | − | 0.130104i | ||||
\(359\) | −12.4549 | −0.657342 | −0.328671 | − | 0.944444i | \(-0.606601\pi\) | ||||
−0.328671 | + | 0.944444i | \(0.606601\pi\) | |||||||
\(360\) | −9.14273 | + | 12.9151i | −0.481864 | + | 0.680685i | ||||
\(361\) | 14.3807 | 0.756879 | ||||||||
\(362\) | −5.60048 | + | 26.8900i | −0.294355 | + | 1.41331i | ||||
\(363\) | −3.16646 | −0.166196 | ||||||||
\(364\) | 18.6102 | + | 8.10356i | 0.975439 | + | 0.424742i | ||||
\(365\) | 16.1118i | 0.843330i | ||||||||
\(366\) | −0.167339 | + | 0.803457i | −0.00874696 | + | 0.0419973i | ||||
\(367\) | 11.5038i | 0.600492i | 0.953862 | + | 0.300246i | \(0.0970687\pi\) | ||||
−0.953862 | + | 0.300246i | \(0.902931\pi\) | |||||||
\(368\) | −8.94789 | + | 8.32650i | −0.466441 | + | 0.434049i | ||||
\(369\) | − | 12.4012i | − | 0.645581i | ||||||
\(370\) | 2.66519 | − | 12.7966i | 0.138557 | − | 0.665262i | ||||
\(371\) | 1.31001 | 0.0680124 | ||||||||
\(372\) | 9.48530 | − | 21.7834i | 0.491790 | − | 1.12942i | ||||
\(373\) | 8.93289i | 0.462527i | 0.972891 | + | 0.231264i | \(0.0742860\pi\) | ||||
−0.972891 | + | 0.231264i | \(0.925714\pi\) | |||||||
\(374\) | −20.4936 | + | 6.93814i | −1.05970 | + | 0.358763i | ||||
\(375\) | 3.53985 | 0.182797 | ||||||||
\(376\) | 2.61650 | − | 3.69609i | 0.134936 | − | 0.190611i | ||||
\(377\) | 24.2266i | 1.24773i | ||||||||
\(378\) | −14.3989 | − | 2.99893i | −0.740602 | − | 0.154248i | ||||
\(379\) | 26.8799 | 1.38073 | 0.690363 | − | 0.723463i | \(-0.257451\pi\) | ||||
0.690363 | + | 0.723463i | \(0.257451\pi\) | |||||||
\(380\) | −5.67503 | + | 13.0330i | −0.291123 | + | 0.668577i | ||||
\(381\) | −20.2980 | −1.03990 | ||||||||
\(382\) | −0.727930 | + | 3.49506i | −0.0372441 | + | 0.178823i | ||||
\(383\) | 21.2861 | 1.08767 | 0.543835 | − | 0.839192i | \(-0.316972\pi\) | ||||
0.543835 | + | 0.839192i | \(0.316972\pi\) | |||||||
\(384\) | 12.8255 | − | 1.72148i | 0.654497 | − | 0.0878489i | ||||
\(385\) | 23.7807i | 1.21198i | ||||||||
\(386\) | −0.892419 | − | 0.185868i | −0.0454230 | − | 0.00946042i | ||||
\(387\) | 10.5125i | 0.534380i | ||||||||
\(388\) | −8.15255 | + | 18.7227i | −0.413883 | + | 0.950501i | ||||
\(389\) | 20.6113i | 1.04504i | 0.852628 | + | 0.522518i | \(0.175007\pi\) | ||||
−0.852628 | + | 0.522518i | \(0.824993\pi\) | |||||||
\(390\) | −27.4241 | − | 5.71173i | −1.38867 | − | 0.289225i | ||||
\(391\) | 10.8591 | − | 6.38849i | 0.549168 | − | 0.323080i | ||||
\(392\) | −5.30163 | + | 7.48912i | −0.267773 | + | 0.378258i | ||||
\(393\) | −4.32619 | −0.218227 | ||||||||
\(394\) | −1.34739 | + | 6.46930i | −0.0678804 | + | 0.325919i | ||||
\(395\) | − | 10.8422i | − | 0.545532i | ||||||
\(396\) | 11.5108 | + | 5.01223i | 0.578441 | + | 0.251874i | ||||
\(397\) | −26.1970 | −1.31479 | −0.657395 | − | 0.753546i | \(-0.728342\pi\) | ||||
−0.657395 | + | 0.753546i | \(0.728342\pi\) | |||||||
\(398\) | 22.8408 | + | 4.75715i | 1.14491 | + | 0.238454i | ||||
\(399\) | −4.76420 | −0.238508 | ||||||||
\(400\) | 16.1748 | + | 17.3819i | 0.808738 | + | 0.869093i | ||||
\(401\) | − | 36.4048i | − | 1.81797i | −0.416828 | − | 0.908986i | \(-0.636858\pi\) | ||
0.416828 | − | 0.908986i | \(-0.363142\pi\) | |||||||
\(402\) | −10.4241 | − | 2.17106i | −0.519905 | − | 0.108283i | ||||
\(403\) | −54.3899 | −2.70935 | ||||||||
\(404\) | −6.05311 | + | 13.9012i | −0.301153 | + | 0.691613i | ||||
\(405\) | 3.51440 | 0.174632 | ||||||||
\(406\) | 12.4130 | + | 2.58530i | 0.616046 | + | 0.128306i | ||||
\(407\) | −10.3709 | −0.514064 | ||||||||
\(408\) | −13.2914 | − | 1.12229i | −0.658025 | − | 0.0555619i | ||||
\(409\) | −1.23020 | −0.0608295 | −0.0304148 | − | 0.999537i | \(-0.509683\pi\) | ||||
−0.0304148 | + | 0.999537i | \(0.509683\pi\) | |||||||
\(410\) | −33.5621 | − | 6.99011i | −1.65751 | − | 0.345217i | ||||
\(411\) | −14.9316 | −0.736521 | ||||||||
\(412\) | −27.1298 | − | 11.8133i | −1.33659 | − | 0.581999i | ||||
\(413\) | −4.87969 | −0.240114 | ||||||||
\(414\) | −7.15713 | − | 1.49064i | −0.351754 | − | 0.0732612i | ||||
\(415\) | 42.9621i | 2.10893i | ||||||||
\(416\) | −15.3348 | − | 25.3459i | −0.751851 | − | 1.24269i | ||||
\(417\) | 4.82973 | 0.236513 | ||||||||
\(418\) | 11.0414 | + | 2.29964i | 0.540052 | + | 0.112479i | ||||
\(419\) | 13.6985 | 0.669217 | 0.334608 | − | 0.942357i | \(-0.391396\pi\) | ||||
0.334608 | + | 0.942357i | \(0.391396\pi\) | |||||||
\(420\) | −5.85304 | + | 13.4418i | −0.285599 | + | 0.655892i | ||||
\(421\) | − | 12.0143i | − | 0.585542i | −0.956183 | − | 0.292771i | \(-0.905423\pi\) | ||
0.956183 | − | 0.292771i | \(-0.0945774\pi\) | |||||||
\(422\) | 6.43170 | − | 30.8810i | 0.313090 | − | 1.50326i | ||||
\(423\) | 2.70859 | 0.131696 | ||||||||
\(424\) | −1.56046 | − | 1.10467i | −0.0757828 | − | 0.0536475i | ||||
\(425\) | −12.4101 | − | 21.0945i | −0.601976 | − | 1.02323i | ||||
\(426\) | −14.3242 | − | 2.98336i | −0.694011 | − | 0.144544i | ||||
\(427\) | − | 0.983284i | − | 0.0475844i | ||||||
\(428\) | −7.61137 | − | 3.31427i | −0.367909 | − | 0.160201i | ||||
\(429\) | 22.2256i | 1.07306i | ||||||||
\(430\) | 28.4505 | + | 5.92550i | 1.37201 | + | 0.285753i | ||||
\(431\) | − | 9.39000i | − | 0.452300i | −0.974092 | − | 0.226150i | \(-0.927386\pi\) | ||
0.974092 | − | 0.226150i | \(-0.0726140\pi\) | |||||||
\(432\) | 14.6229 | + | 15.7142i | 0.703546 | + | 0.756050i | ||||
\(433\) | −3.13938 | −0.150869 | −0.0754346 | − | 0.997151i | \(-0.524034\pi\) | ||||
−0.0754346 | + | 0.997151i | \(0.524034\pi\) | |||||||
\(434\) | −5.80414 | + | 27.8678i | −0.278608 | + | 1.33770i | ||||
\(435\) | −17.4984 | −0.838983 | ||||||||
\(436\) | −19.6721 | − | 8.56597i | −0.942124 | − | 0.410235i | ||||
\(437\) | −6.56745 | −0.314164 | ||||||||
\(438\) | 7.71538 | + | 1.60691i | 0.368655 | + | 0.0767813i | ||||
\(439\) | 16.0244i | 0.764801i | 0.923997 | + | 0.382401i | \(0.124903\pi\) | ||||
−0.923997 | + | 0.382401i | \(0.875097\pi\) | |||||||
\(440\) | 20.0531 | − | 28.3272i | 0.955994 | − | 1.35044i | ||||
\(441\) | −5.48823 | −0.261344 | ||||||||
\(442\) | 9.79192 | + | 28.9230i | 0.465754 | + | 1.37572i | ||||
\(443\) | − | 7.58709i | − | 0.360473i | −0.983623 | − | 0.180237i | \(-0.942314\pi\) | ||
0.983623 | − | 0.180237i | \(-0.0576864\pi\) | |||||||
\(444\) | −5.86202 | − | 2.55254i | −0.278199 | − | 0.121138i | ||||
\(445\) | 45.6655 | 2.16475 | ||||||||
\(446\) | −2.37680 | + | 11.4119i | −0.112545 | + | 0.540369i | ||||
\(447\) | 4.91659i | 0.232547i | ||||||||
\(448\) | −14.6229 | + | 5.15235i | −0.690868 | + | 0.243426i | ||||
\(449\) | 19.0870i | 0.900773i | 0.892834 | + | 0.450387i | \(0.148714\pi\) | ||||
−0.892834 | + | 0.450387i | \(0.851286\pi\) | |||||||
\(450\) | −2.89567 | + | 13.9032i | −0.136503 | + | 0.655402i | ||||
\(451\) | 27.2001i | 1.28080i | ||||||||
\(452\) | −13.8276 | + | 31.7557i | −0.650395 | + | 1.49366i | ||||
\(453\) | 12.8736 | 0.604854 | ||||||||
\(454\) | 7.17185 | − | 34.4347i | 0.336592 | − | 1.61610i | ||||
\(455\) | 33.5621 | 1.57341 | ||||||||
\(456\) | 5.67503 | + | 4.01742i | 0.265758 | + | 0.188133i | ||||
\(457\) | −8.52288 | −0.398684 | −0.199342 | − | 0.979930i | \(-0.563880\pi\) | ||||
−0.199342 | + | 0.979930i | \(0.563880\pi\) | |||||||
\(458\) | 19.8794 | + | 4.14036i | 0.928903 | + | 0.193466i | ||||
\(459\) | −11.2194 | − | 19.0706i | −0.523677 | − | 0.890141i | ||||
\(460\) | −8.06842 | + | 18.5295i | −0.376192 | + | 0.863943i | ||||
\(461\) | − | 20.7388i | − | 0.965904i | −0.875647 | − | 0.482952i | \(-0.839565\pi\) | ||
0.875647 | − | 0.482952i | \(-0.160435\pi\) | |||||||
\(462\) | 11.3877 | + | 2.37177i | 0.529805 | + | 0.110345i | ||||
\(463\) | −13.7743 | −0.640148 | −0.320074 | − | 0.947393i | \(-0.603708\pi\) | ||||
−0.320074 | + | 0.947393i | \(0.603708\pi\) | |||||||
\(464\) | −12.6061 | − | 13.5468i | −0.585222 | − | 0.628896i | ||||
\(465\) | − | 39.2848i | − | 1.82179i | ||||||
\(466\) | 7.32922 | + | 1.52649i | 0.339519 | + | 0.0707131i | ||||
\(467\) | − | 26.0431i | − | 1.20513i | −0.798070 | − | 0.602565i | \(-0.794146\pi\) | ||
0.798070 | − | 0.602565i | \(-0.205854\pi\) | |||||||
\(468\) | 7.07385 | − | 16.2454i | 0.326989 | − | 0.750945i | ||||
\(469\) | 12.7572 | 0.589071 | ||||||||
\(470\) | 1.52673 | − | 7.33041i | 0.0704230 | − | 0.338127i | ||||
\(471\) | − | 11.4496i | − | 0.527569i | ||||||
\(472\) | 5.81260 | + | 4.11481i | 0.267547 | + | 0.189399i | ||||
\(473\) | − | 23.0574i | − | 1.06018i | ||||||
\(474\) | −5.19197 | − | 1.08135i | −0.238475 | − | 0.0496681i | ||||
\(475\) | 12.7577i | 0.585363i | ||||||||
\(476\) | 15.8642 | − | 1.93062i | 0.727134 | − | 0.0884898i | ||||
\(477\) | − | 1.14355i | − | 0.0523595i | ||||||
\(478\) | 5.86049 | − | 28.1383i | 0.268053 | − | 1.28702i | ||||
\(479\) | − | 17.9152i | − | 0.818566i | −0.912407 | − | 0.409283i | \(-0.865779\pi\) | ||
0.912407 | − | 0.409283i | \(-0.134221\pi\) | |||||||
\(480\) | 18.3069 | − | 11.0760i | 0.835590 | − | 0.505549i | ||||
\(481\) | 14.6366i | 0.667370i | ||||||||
\(482\) | 0.308665 | + | 0.0642870i | 0.0140593 | + | 0.00292819i | ||||
\(483\) | −6.77345 | −0.308203 | ||||||||
\(484\) | −5.07642 | − | 2.21046i | −0.230746 | − | 0.100475i | ||||
\(485\) | 33.7650i | 1.53319i | ||||||||
\(486\) | −4.29177 | + | 20.6063i | −0.194678 | + | 0.934722i | ||||
\(487\) | − | 32.0530i | − | 1.45246i | −0.687451 | − | 0.726230i | \(-0.741271\pi\) | ||
0.687451 | − | 0.726230i | \(-0.258729\pi\) | |||||||
\(488\) | −0.829156 | + | 1.17127i | −0.0375341 | + | 0.0530210i | ||||
\(489\) | 19.9595 | 0.902599 | ||||||||
\(490\) | −3.09351 | + | 14.8531i | −0.139751 | + | 0.670994i | ||||
\(491\) | − | 21.8794i | − | 0.987403i | −0.869631 | − | 0.493701i | \(-0.835644\pi\) | ||
0.869631 | − | 0.493701i | \(-0.164356\pi\) | |||||||
\(492\) | −6.69464 | + | 15.3745i | −0.301818 | + | 0.693138i | ||||
\(493\) | 9.67198 | + | 16.4403i | 0.435604 | + | 0.740435i | ||||
\(494\) | 3.24552 | − | 15.5829i | 0.146023 | − | 0.701108i | ||||
\(495\) | 20.7589 | 0.933043 | ||||||||
\(496\) | 30.4134 | − | 28.3013i | 1.36560 | − | 1.27077i | ||||
\(497\) | 17.5302 | 0.786338 | ||||||||
\(498\) | 20.5730 | + | 4.28483i | 0.921900 | + | 0.192008i | ||||
\(499\) | 10.1185 | 0.452964 | 0.226482 | − | 0.974015i | \(-0.427277\pi\) | ||||
0.226482 | + | 0.974015i | \(0.427277\pi\) | |||||||
\(500\) | 5.67503 | + | 2.47112i | 0.253795 | + | 0.110512i | ||||
\(501\) | 1.33235i | 0.0595251i | ||||||||
\(502\) | 35.2227 | + | 7.33597i | 1.57206 | + | 0.327420i | ||||
\(503\) | 18.0166i | 0.803318i | 0.915789 | + | 0.401659i | \(0.131566\pi\) | ||||
−0.915789 | + | 0.401659i | \(0.868434\pi\) | |||||||
\(504\) | −7.56880 | − | 5.35804i | −0.337141 | − | 0.238666i | ||||
\(505\) | 25.0698i | 1.11559i | ||||||||
\(506\) | 15.6980 | + | 3.26949i | 0.697862 | + | 0.145346i | ||||
\(507\) | 16.4981 | 0.732707 | ||||||||
\(508\) | −32.5413 | − | 14.1697i | −1.44379 | − | 0.628678i | ||||
\(509\) | − | 40.8899i | − | 1.81241i | −0.422834 | − | 0.906207i | \(-0.638965\pi\) | ||
0.422834 | − | 0.906207i | \(-0.361035\pi\) | |||||||
\(510\) | −20.8905 | + | 7.07251i | −0.925046 | + | 0.313176i | ||||
\(511\) | −9.44221 | −0.417699 | ||||||||
\(512\) | 21.7633 | + | 6.19341i | 0.961811 | + | 0.273713i | ||||
\(513\) | 11.5337i | 0.509225i | ||||||||
\(514\) | −8.57033 | + | 41.1493i | −0.378021 | + | 1.81502i | ||||
\(515\) | −48.9265 | −2.15596 | ||||||||
\(516\) | 5.67503 | − | 13.0330i | 0.249829 | − | 0.573744i | ||||
\(517\) | −5.94086 | −0.261279 | ||||||||
\(518\) | 7.49934 | + | 1.56192i | 0.329502 | + | 0.0686268i | ||||
\(519\) | −6.73667 | −0.295707 | ||||||||
\(520\) | −39.9786 | − | 28.3013i | −1.75318 | − | 1.24109i | ||||
\(521\) | − | 13.7933i | − | 0.604295i | −0.953261 | − | 0.302148i | \(-0.902296\pi\) | ||
0.953261 | − | 0.302148i | \(-0.0977036\pi\) | |||||||
\(522\) | 2.25679 | − | 10.8357i | 0.0987770 | − | 0.474265i | ||||
\(523\) | 4.23843i | 0.185334i | 0.995697 | + | 0.0926668i | \(0.0295391\pi\) | ||||
−0.995697 | + | 0.0926668i | \(0.970461\pi\) | |||||||
\(524\) | −6.93567 | − | 3.02005i | −0.302986 | − | 0.131931i | ||||
\(525\) | 13.1579i | 0.574257i | ||||||||
\(526\) | −4.26625 | + | 20.4838i | −0.186018 | + | 0.893138i | ||||
\(527\) | −36.9094 | + | 21.7141i | −1.60780 | + | 0.945881i | ||||
\(528\) | −11.5649 | − | 12.4279i | −0.503297 | − | 0.540857i | ||||
\(529\) | 13.6628 | 0.594034 | ||||||||
\(530\) | −3.09485 | − | 0.644577i | −0.134432 | − | 0.0279986i | ||||
\(531\) | 4.25963i | 0.184852i | ||||||||
\(532\) | −7.63788 | − | 3.32581i | −0.331144 | − | 0.144192i | ||||
\(533\) | 38.3879 | 1.66276 | ||||||||
\(534\) | 4.55446 | − | 21.8676i | 0.197091 | − | 0.946305i | ||||
\(535\) | −13.7265 | −0.593450 | ||||||||
\(536\) | −15.1961 | − | 10.7575i | −0.656372 | − | 0.464653i | ||||
\(537\) | 9.76445i | 0.421367i | ||||||||
\(538\) | −2.21448 | + | 10.6326i | −0.0954732 | + | 0.458402i | ||||
\(539\) | 12.0375 | 0.518494 | ||||||||
\(540\) | 32.5413 | + | 14.1697i | 1.40036 | + | 0.609766i | ||||
\(541\) | 22.8390 | 0.981925 | 0.490963 | − | 0.871181i | \(-0.336645\pi\) | ||||
0.490963 | + | 0.871181i | \(0.336645\pi\) | |||||||
\(542\) | 3.56641 | − | 17.1236i | 0.153190 | − | 0.735523i | ||||
\(543\) | 22.2148 | 0.953327 | ||||||||
\(544\) | −20.5252 | − | 11.0778i | −0.880009 | − | 0.474957i | ||||
\(545\) | −35.4772 | −1.51968 | ||||||||
\(546\) | 3.34732 | − | 16.0717i | 0.143252 | − | 0.687805i | ||||
\(547\) | −7.09391 | −0.303314 | −0.151657 | − | 0.988433i | \(-0.548461\pi\) | ||||
−0.151657 | + | 0.988433i | \(0.548461\pi\) | |||||||
\(548\) | −23.9381 | − | 10.4235i | −1.02258 | − | 0.445270i | ||||
\(549\) | −0.858339 | −0.0366330 | ||||||||
\(550\) | 6.35119 | − | 30.4944i | 0.270816 | − | 1.30028i | ||||
\(551\) | − | 9.94292i | − | 0.423583i | ||||||
\(552\) | 8.06842 | + | 5.71173i | 0.343415 | + | 0.243107i | ||||
\(553\) | 6.35402 | 0.270200 | ||||||||
\(554\) | 4.41279 | − | 21.1874i | 0.187481 | − | 0.900167i | ||||
\(555\) | −10.5717 | −0.448744 | ||||||||
\(556\) | 7.74295 | + | 3.37156i | 0.328374 | + | 0.142986i | ||||
\(557\) | 2.41037i | 0.102131i | 0.998695 | + | 0.0510653i | \(0.0162617\pi\) | ||||
−0.998695 | + | 0.0510653i | \(0.983738\pi\) | |||||||
\(558\) | 24.3267 | + | 5.06661i | 1.02983 | + | 0.214487i | ||||
\(559\) | −32.5413 | −1.37635 | ||||||||
\(560\) | −18.7670 | + | 17.4637i | −0.793050 | + | 0.737977i | ||||
\(561\) | 8.87313 | + | 15.0825i | 0.374624 | + | 0.636782i | ||||
\(562\) | 1.29060 | − | 6.19665i | 0.0544407 | − | 0.261390i | ||||
\(563\) | 7.55366i | 0.318349i | 0.987250 | + | 0.159174i | \(0.0508832\pi\) | ||||
−0.987250 | + | 0.159174i | \(0.949117\pi\) | |||||||
\(564\) | −3.35801 | − | 1.46220i | −0.141398 | − | 0.0615697i | ||||
\(565\) | 57.2690i | 2.40932i | ||||||||
\(566\) | −2.44906 | + | 11.7589i | −0.102942 | + | 0.494262i | ||||
\(567\) | 2.05959i | 0.0864947i | ||||||||
\(568\) | −20.8817 | − | 14.7824i | −0.876177 | − | 0.620256i | ||||
\(569\) | −23.4800 | −0.984333 | −0.492167 | − | 0.870501i | \(-0.663795\pi\) | ||||
−0.492167 | + | 0.870501i | \(0.663795\pi\) | |||||||
\(570\) | 11.2552 | + | 2.34417i | 0.471430 | + | 0.0981866i | ||||
\(571\) | 42.0442 | 1.75950 | 0.879748 | − | 0.475440i | \(-0.157711\pi\) | ||||
0.879748 | + | 0.475440i | \(0.157711\pi\) | |||||||
\(572\) | −15.5153 | + | 35.6317i | −0.648729 | + | 1.48984i | ||||
\(573\) | 2.88739 | 0.120622 | ||||||||
\(574\) | 4.09651 | − | 19.6688i | 0.170985 | − | 0.820961i | ||||
\(575\) | 18.1381i | 0.756413i | ||||||||
\(576\) | 4.49765 | + | 12.7648i | 0.187402 | + | 0.531867i | ||||
\(577\) | −3.67101 | −0.152826 | −0.0764131 | − | 0.997076i | \(-0.524347\pi\) | ||||
−0.0764131 | + | 0.997076i | \(0.524347\pi\) | |||||||
\(578\) | 18.1918 | + | 15.7181i | 0.756679 | + | 0.653787i | ||||
\(579\) | 0.737259i | 0.0306395i | ||||||||
\(580\) | −28.0531 | − | 12.2154i | −1.16484 | − | 0.507215i | ||||
\(581\) | −25.1776 | −1.04454 | ||||||||
\(582\) | 16.1689 | + | 3.36756i | 0.670221 | + | 0.139590i | ||||
\(583\) | 2.50819i | 0.103879i | ||||||||
\(584\) | 11.2474 | + | 7.96216i | 0.465421 | + | 0.329477i | ||||
\(585\) | − | 29.2974i | − | 1.21130i | ||||||
\(586\) | −2.41145 | − | 0.502243i | −0.0996163 | − | 0.0207475i | ||||
\(587\) | 10.0661i | 0.415472i | 0.978185 | + | 0.207736i | \(0.0666095\pi\) | ||||
−0.978185 | + | 0.207736i | \(0.933390\pi\) | |||||||
\(588\) | 6.80409 | + | 2.96275i | 0.280596 | + | 0.122182i | ||||
\(589\) | 22.3224 | 0.919777 | ||||||||
\(590\) | 11.5281 | + | 2.40100i | 0.474603 | + | 0.0988476i | ||||
\(591\) | 5.34452 | 0.219844 | ||||||||
\(592\) | −7.61600 | − | 8.18437i | −0.313016 | − | 0.336375i | ||||
\(593\) | 23.6586 | 0.971542 | 0.485771 | − | 0.874086i | \(-0.338539\pi\) | ||||
0.485771 | + | 0.874086i | \(0.338539\pi\) | |||||||
\(594\) | 5.74184 | − | 27.5687i | 0.235591 | − | 1.13116i | ||||
\(595\) | 22.7755 | − | 13.3990i | 0.933703 | − | 0.549305i | ||||
\(596\) | −3.43219 | + | 7.88219i | −0.140588 | + | 0.322867i | ||||
\(597\) | − | 18.8696i | − | 0.772281i | ||||||
\(598\) | 4.61428 | − | 22.1549i | 0.188692 | − | 0.905979i | ||||
\(599\) | 32.5413 | 1.32960 | 0.664802 | − | 0.747020i | \(-0.268516\pi\) | ||||
0.664802 | + | 0.747020i | \(0.268516\pi\) | |||||||
\(600\) | 11.0954 | − | 15.6734i | 0.452968 | − | 0.639865i | ||||
\(601\) | 44.8459i | 1.82930i | 0.404242 | + | 0.914652i | \(0.367535\pi\) | ||||
−0.404242 | + | 0.914652i | \(0.632465\pi\) | |||||||
\(602\) | −3.47260 | + | 16.6732i | −0.141533 | + | 0.679550i | ||||
\(603\) | − | 11.1361i | − | 0.453498i | ||||||
\(604\) | 20.6387 | + | 8.98686i | 0.839778 | + | 0.365670i | ||||
\(605\) | −9.15493 | −0.372201 | ||||||||
\(606\) | 12.0051 | + | 2.50034i | 0.487673 | + | 0.101570i | ||||
\(607\) | 19.2628i | 0.781853i | 0.920422 | + | 0.390927i | \(0.127845\pi\) | ||||
−0.920422 | + | 0.390927i | \(0.872155\pi\) | |||||||
\(608\) | 6.29362 | + | 10.4023i | 0.255240 | + | 0.421869i | ||||
\(609\) | − | 10.2548i | − | 0.415546i | ||||||
\(610\) | −0.483814 | + | 2.32297i | −0.0195891 | + | 0.0940543i | ||||
\(611\) | 8.38443i | 0.339198i | ||||||||
\(612\) | −1.68530 | − | 13.8484i | −0.0681241 | − | 0.559787i | ||||
\(613\) | 11.2231i | 0.453296i | 0.973977 | + | 0.226648i | \(0.0727768\pi\) | ||||
−0.973977 | + | 0.226648i | \(0.927223\pi\) | |||||||
\(614\) | 44.9298 | + | 9.35772i | 1.81322 | + | 0.377647i | ||||
\(615\) | 27.7268i | 1.11805i | ||||||||
\(616\) | 16.6009 | + | 11.7520i | 0.668871 | + | 0.473501i | ||||
\(617\) | − | 20.1977i | − | 0.813130i | −0.913622 | − | 0.406565i | \(-0.866726\pi\) | ||
0.913622 | − | 0.406565i | \(-0.133274\pi\) | |||||||
\(618\) | −4.87969 | + | 23.4292i | −0.196290 | + | 0.942459i | ||||
\(619\) | −10.7486 | −0.432025 | −0.216012 | − | 0.976391i | \(-0.569305\pi\) | ||||
−0.216012 | + | 0.976391i | \(0.569305\pi\) | |||||||
\(620\) | 27.4241 | − | 62.9807i | 1.10138 | − | 2.52937i | ||||
\(621\) | 16.3979i | 0.658026i | ||||||||
\(622\) | −15.1037 | − | 3.14570i | −0.605602 | − | 0.126131i | ||||
\(623\) | 26.7620i | 1.07220i | ||||||||
\(624\) | −17.5398 | + | 16.3217i | −0.702152 | + | 0.653391i | ||||
\(625\) | −19.4448 | −0.777793 | ||||||||
\(626\) | −31.0307 | − | 6.46289i | −1.24024 | − | 0.258309i | ||||
\(627\) | − | 9.12169i | − | 0.364285i | ||||||
\(628\) | 7.99278 | − | 18.3558i | 0.318947 | − | 0.732476i | ||||
\(629\) | 5.84336 | + | 9.93248i | 0.232990 | + | 0.396034i | ||||
\(630\) | −15.0111 | − | 3.12643i | −0.598057 | − | 0.124560i | ||||
\(631\) | 4.94308 | 0.196781 | 0.0983905 | − | 0.995148i | \(-0.468631\pi\) | ||||
0.0983905 | + | 0.995148i | \(0.468631\pi\) | |||||||
\(632\) | −7.56880 | − | 5.35804i | −0.301071 | − | 0.213131i | ||||
\(633\) | −25.5119 | −1.01401 | ||||||||
\(634\) | 2.06539 | − | 9.91669i | 0.0820271 | − | 0.393842i | ||||
\(635\) | −58.6858 | −2.32888 | ||||||||
\(636\) | −0.617331 | + | 1.41773i | −0.0244788 | + | 0.0562166i | ||||
\(637\) | − | 16.9888i | − | 0.673120i | ||||||
\(638\) | −4.94991 | + | 23.7663i | −0.195969 | + | 0.940917i | ||||
\(639\) | − | 15.3027i | − | 0.605365i | ||||||
\(640\) | 37.0812 | − | 4.97717i | 1.46576 | − | 0.196740i | ||||
\(641\) | 35.8047i | 1.41420i | 0.707112 | + | 0.707101i | \(0.249997\pi\) | ||||
−0.707112 | + | 0.707101i | \(0.750003\pi\) | |||||||
\(642\) | −1.36902 | + | 6.57315i | −0.0540308 | + | 0.259422i | ||||
\(643\) | −5.10986 | −0.201513 | −0.100757 | − | 0.994911i | \(-0.532126\pi\) | ||||
−0.100757 | + | 0.994911i | \(0.532126\pi\) | |||||||
\(644\) | −10.8591 | − | 4.72844i | −0.427908 | − | 0.186327i | ||||
\(645\) | − | 23.5040i | − | 0.925468i | ||||||
\(646\) | −4.01874 | − | 11.8704i | −0.158115 | − | 0.467034i | ||||
\(647\) | −31.5790 | −1.24150 | −0.620749 | − | 0.784009i | \(-0.713172\pi\) | ||||
−0.620749 | + | 0.784009i | \(0.713172\pi\) | |||||||
\(648\) | 1.73675 | − | 2.45335i | 0.0682262 | − | 0.0963767i | ||||
\(649\) | − | 9.34281i | − | 0.366738i | ||||||
\(650\) | −43.0372 | − | 8.96354i | −1.68806 | − | 0.351579i | ||||
\(651\) | 23.0226 | 0.902326 | ||||||||
\(652\) | 31.9987 | + | 13.9334i | 1.25317 | + | 0.545675i | ||||
\(653\) | 32.7138 | 1.28019 | 0.640095 | − | 0.768296i | \(-0.278895\pi\) | ||||
0.640095 | + | 0.768296i | \(0.278895\pi\) | |||||||
\(654\) | −3.53832 | + | 16.9888i | −0.138359 | + | 0.664314i | ||||
\(655\) | −12.5080 | −0.488726 | ||||||||
\(656\) | −21.4655 | + | 19.9748i | −0.838086 | + | 0.779884i | ||||
\(657\) | 8.24240i | 0.321567i | ||||||||
\(658\) | 4.29594 | + | 0.894732i | 0.167473 | + | 0.0348803i | ||||
\(659\) | − | 4.60706i | − | 0.179466i | −0.995966 | − | 0.0897328i | \(-0.971399\pi\) | ||
0.995966 | − | 0.0897328i | \(-0.0286013\pi\) | |||||||
\(660\) | −25.7361 | − | 11.2064i | −1.00178 | − | 0.436210i | ||||
\(661\) | − | 16.3790i | − | 0.637070i | −0.947911 | − | 0.318535i | \(-0.896809\pi\) | ||
0.947911 | − | 0.318535i | \(-0.103191\pi\) | |||||||
\(662\) | −36.0274 | − | 7.50357i | −1.40024 | − | 0.291634i | ||||
\(663\) | 21.2861 | − | 12.5228i | 0.826684 | − | 0.486345i | ||||
\(664\) | 29.9912 | + | 21.2311i | 1.16388 | + | 0.823926i | ||||
\(665\) | −13.7743 | −0.534146 | ||||||||
\(666\) | 1.36345 | − | 6.54641i | 0.0528325 | − | 0.253668i | ||||
\(667\) | − | 14.1363i | − | 0.547358i | ||||||
\(668\) | −0.930094 | + | 2.13600i | −0.0359864 | + | 0.0826445i | ||||
\(669\) | 9.42777 | 0.364499 | ||||||||
\(670\) | −30.1383 | − | 6.27702i | −1.16434 | − | 0.242502i | ||||
\(671\) | 1.88263 | 0.0726780 | ||||||||
\(672\) | 6.49103 | + | 10.7286i | 0.250397 | + | 0.413865i | ||||
\(673\) | 24.0036i | 0.925272i | 0.886548 | + | 0.462636i | \(0.153096\pi\) | ||||
−0.886548 | + | 0.462636i | \(0.846904\pi\) | |||||||
\(674\) | −19.0969 | − | 3.97738i | −0.735584 | − | 0.153203i | ||||
\(675\) | 31.8540 | 1.22606 | ||||||||
\(676\) | 26.4495 | + | 11.5171i | 1.01729 | + | 0.442964i | ||||
\(677\) | −34.3233 | −1.31915 | −0.659576 | − | 0.751638i | \(-0.729264\pi\) | ||||
−0.659576 | + | 0.751638i | \(0.729264\pi\) | |||||||
\(678\) | 27.4241 | + | 5.71173i | 1.05322 | + | 0.219358i | ||||
\(679\) | −19.7877 | −0.759384 | ||||||||
\(680\) | −38.4285 | − | 3.24480i | −1.47367 | − | 0.124432i | ||||
\(681\) | −28.4477 | −1.09012 | ||||||||
\(682\) | −53.3566 | − | 11.1128i | −2.04313 | − | 0.425531i | ||||
\(683\) | −15.4420 | −0.590871 | −0.295436 | − | 0.955363i | \(-0.595465\pi\) | ||||
−0.295436 | + | 0.955363i | \(0.595465\pi\) | |||||||
\(684\) | −2.90321 | + | 6.66734i | −0.111007 | + | 0.254932i | ||||
\(685\) | −43.1705 | −1.64946 | ||||||||
\(686\) | −27.4868 | − | 5.72480i | −1.04945 | − | 0.218574i | ||||
\(687\) | − | 16.4231i | − | 0.626579i | ||||||
\(688\) | 18.1962 | − | 16.9326i | 0.693725 | − | 0.645549i | ||||
\(689\) | 3.53985 | 0.134858 | ||||||||
\(690\) | 16.0020 | + | 3.33281i | 0.609186 | + | 0.126878i | ||||
\(691\) | 7.18318 | 0.273261 | 0.136631 | − | 0.990622i | \(-0.456373\pi\) | ||||
0.136631 | + | 0.990622i | \(0.456373\pi\) | |||||||
\(692\) | −10.8001 | − | 4.70277i | −0.410559 | − | 0.178772i | ||||
\(693\) | 12.1656i | 0.462133i | ||||||||
\(694\) | −5.44271 | + | 26.1324i | −0.206602 | + | 0.991974i | ||||
\(695\) | 13.9638 | 0.529678 | ||||||||
\(696\) | −8.64738 | + | 12.2154i | −0.327778 | + | 0.463022i | ||||
\(697\) | 26.0503 | − | 15.3256i | 0.986726 | − | 0.580499i | ||||
\(698\) | 9.29863 | + | 1.93666i | 0.351958 | + | 0.0733038i | ||||
\(699\) | − | 6.05493i | − | 0.229018i | ||||||
\(700\) | −9.18531 | + | 21.0945i | −0.347172 | + | 0.797296i | ||||
\(701\) | − | 26.6092i | − | 1.00502i | −0.864573 | − | 0.502508i | \(-0.832411\pi\) | ||
0.864573 | − | 0.502508i | \(-0.167589\pi\) | |||||||
\(702\) | −38.9081 | − | 8.10356i | −1.46849 | − | 0.305849i | ||||
\(703\) | − | 6.00705i | − | 0.226560i | ||||||
\(704\) | −9.86486 | − | 27.9975i | −0.371796 | − | 1.05520i | ||||
\(705\) | −6.05591 | −0.228079 | ||||||||
\(706\) | 5.68144 | − | 27.2787i | 0.213824 | − | 1.02665i | ||||
\(707\) | −14.6920 | −0.552550 | ||||||||
\(708\) | 2.29951 | − | 5.28093i | 0.0864208 | − | 0.198469i | ||||
\(709\) | −5.24355 | −0.196926 | −0.0984628 | − | 0.995141i | \(-0.531393\pi\) | ||||
−0.0984628 | + | 0.995141i | \(0.531393\pi\) | |||||||
\(710\) | −41.4145 | − | 8.62556i | −1.55426 | − | 0.323712i | ||||
\(711\) | − | 5.54662i | − | 0.208014i | ||||||
\(712\) | 22.5671 | − | 31.8784i | 0.845737 | − | 1.19469i | ||||
\(713\) | 31.7366 | 1.18855 | ||||||||
\(714\) | −4.14480 | − | 12.2427i | −0.155115 | − | 0.458173i | ||||
\(715\) | 64.2591i | 2.40315i | ||||||||
\(716\) | −6.81641 | + | 15.6542i | −0.254741 | + | 0.585025i | ||||
\(717\) | −23.2461 | −0.868141 | ||||||||
\(718\) | −3.59143 | + | 17.2438i | −0.134031 | + | 0.643532i | ||||
\(719\) | 5.81403i | 0.216827i | 0.994106 | + | 0.108413i | \(0.0345770\pi\) | ||||
−0.994106 | + | 0.108413i | \(0.965423\pi\) | |||||||
\(720\) | 15.2446 | + | 16.3823i | 0.568133 | + | 0.610532i | ||||
\(721\) | − | 28.6730i | − | 1.06784i | ||||||
\(722\) | 4.14676 | − | 19.9101i | 0.154327 | − | 0.740978i | ||||
\(723\) | − | 0.254999i | − | 0.00948353i | ||||||
\(724\) | 35.6143 | + | 15.5078i | 1.32360 | + | 0.576342i | ||||
\(725\) | −27.4606 | −1.01986 | ||||||||
\(726\) | −0.913069 | + | 4.38398i | −0.0338872 | + | 0.162705i | ||||
\(727\) | 25.8384 | 0.958291 | 0.479146 | − | 0.877735i | \(-0.340947\pi\) | ||||
0.479146 | + | 0.877735i | \(0.340947\pi\) | |||||||
\(728\) | 16.5858 | − | 23.4292i | 0.614710 | − | 0.868343i | ||||
\(729\) | 20.2118 | 0.748586 | ||||||||
\(730\) | 22.3069 | + | 4.64594i | 0.825614 | + | 0.171954i | ||||
\(731\) | −22.0828 | + | 12.9915i | −0.816762 | + | 0.480508i | ||||
\(732\) | 1.06414 | + | 0.463363i | 0.0393316 | + | 0.0171264i | ||||
\(733\) | − | 35.4643i | − | 1.30990i | −0.755670 | − | 0.654952i | \(-0.772689\pi\) | ||
0.755670 | − | 0.654952i | \(-0.227311\pi\) | |||||||
\(734\) | 15.9270 | + | 3.31718i | 0.587877 | + | 0.122439i | ||||
\(735\) | 12.2707 | 0.452610 | ||||||||
\(736\) | 8.94789 | + | 14.7894i | 0.329824 | + | 0.545144i | ||||
\(737\) | 24.4253i | 0.899716i | ||||||||
\(738\) | −17.1695 | − | 3.57597i | −0.632019 | − | 0.131633i | ||||
\(739\) | − | 1.54683i | − | 0.0569011i | −0.999595 | − | 0.0284505i | \(-0.990943\pi\) | ||
0.999595 | − | 0.0284505i | \(-0.00905731\pi\) | |||||||
\(740\) | −16.9484 | − | 7.37994i | −0.623035 | − | 0.271292i | ||||
\(741\) | −12.8736 | −0.472923 | ||||||||
\(742\) | 0.377750 | − | 1.81372i | 0.0138676 | − | 0.0665836i | ||||
\(743\) | − | 24.8240i | − | 0.910703i | −0.890312 | − | 0.455352i | \(-0.849514\pi\) | ||
0.890312 | − | 0.455352i | \(-0.150486\pi\) | |||||||
\(744\) | −27.4241 | − | 19.4138i | −1.00542 | − | 0.711745i | ||||
\(745\) | 14.2149i | 0.520795i | ||||||||
\(746\) | 12.3676 | + | 2.57585i | 0.452811 | + | 0.0943087i | ||||
\(747\) | 21.9783i | 0.804146i | ||||||||
\(748\) | 3.69643 | + | 30.3741i | 0.135155 | + | 1.11059i | ||||
\(749\) | − | 8.04434i | − | 0.293934i | ||||||
\(750\) | 1.02074 | − | 4.90094i | 0.0372721 | − | 0.178957i | ||||
\(751\) | 33.0249i | 1.20509i | 0.798083 | + | 0.602547i | \(0.205847\pi\) | ||||
−0.798083 | + | 0.602547i | \(0.794153\pi\) | |||||||
\(752\) | −4.36276 | − | 4.68834i | −0.159094 | − | 0.170966i | ||||
\(753\) | − | 29.0987i | − | 1.06042i | ||||||
\(754\) | 33.5418 | + | 6.98588i | 1.22152 | + | 0.254411i | ||||
\(755\) | 37.2204 | 1.35459 | ||||||||
\(756\) | −8.30405 | + | 19.0706i | −0.302015 | + | 0.693592i | ||||
\(757\) | − | 25.0871i | − | 0.911806i | −0.890029 | − | 0.455903i | \(-0.849316\pi\) | ||
0.890029 | − | 0.455903i | \(-0.150684\pi\) | |||||||
\(758\) | 7.75098 | − | 37.2153i | 0.281528 | − | 1.35172i | ||||
\(759\) | − | 12.9687i | − | 0.470733i | ||||||
\(760\) | 16.4078 | + | 11.6152i | 0.595172 | + | 0.421329i | ||||
\(761\) | 16.5944 | 0.601545 | 0.300773 | − | 0.953696i | \(-0.402755\pi\) | ||||
0.300773 | + | 0.953696i | \(0.402755\pi\) | |||||||
\(762\) | −5.85304 | + | 28.1026i | −0.212033 | + | 1.01805i | ||||
\(763\) | − | 20.7912i | − | 0.752691i | ||||||
\(764\) | 4.62901 | + | 2.01564i | 0.167472 | + | 0.0729234i | ||||
\(765\) | −11.6964 | − | 19.8814i | −0.422884 | − | 0.718814i | ||||
\(766\) | 6.13798 | − | 29.4707i | 0.221774 | − | 1.06482i | ||||
\(767\) | −13.1857 | −0.476107 | ||||||||
\(768\) | 1.31491 | − | 18.2533i | 0.0474477 | − | 0.658659i | ||||
\(769\) | 4.63304 | 0.167072 | 0.0835358 | − | 0.996505i | \(-0.473379\pi\) | ||||
0.0835358 | + | 0.996505i | \(0.473379\pi\) | |||||||
\(770\) | 32.9245 | + | 6.85731i | 1.18651 | + | 0.247120i | ||||
\(771\) | 33.9949 | 1.22430 | ||||||||
\(772\) | −0.514669 | + | 1.18196i | −0.0185234 | + | 0.0425397i | ||||
\(773\) | 51.9898i | 1.86994i | 0.354725 | + | 0.934971i | \(0.384574\pi\) | ||||
−0.354725 | + | 0.934971i | \(0.615426\pi\) | |||||||
\(774\) | 14.5546 | + | 3.03134i | 0.523153 | + | 0.108959i | ||||
\(775\) | − | 61.6504i | − | 2.21455i | ||||||
\(776\) | 23.5708 | + | 16.6860i | 0.846143 | + | 0.598994i | ||||
\(777\) | − | 6.19547i | − | 0.222261i | ||||||
\(778\) | 28.5365 | + | 5.94341i | 1.02308 | + | 0.213082i | ||||
\(779\) | −15.7549 | −0.564479 | ||||||||
\(780\) | −15.8158 | + | 36.3218i | −0.566297 | + | 1.30053i | ||||
\(781\) | 33.5640i | 1.20101i | ||||||||
\(782\) | −5.71360 | − | 16.8766i | −0.204318 | − | 0.603506i | ||||
\(783\) | −24.8260 | −0.887208 | ||||||||
\(784\) | 8.83996 | + | 9.49967i | 0.315713 | + | 0.339274i | ||||
\(785\) | − | 33.1033i | − | 1.18151i | ||||||
\(786\) | −1.24748 | + | 5.98962i | −0.0444963 | + | 0.213643i | ||||
\(787\) | 24.0375 | 0.856843 | 0.428421 | − | 0.903579i | \(-0.359070\pi\) | ||||
0.428421 | + | 0.903579i | \(0.359070\pi\) | |||||||
\(788\) | 8.56824 | + | 3.73093i | 0.305231 | + | 0.132909i | ||||
\(789\) | 16.9224 | 0.602455 | ||||||||
\(790\) | −15.0111 | − | 3.12643i | −0.534071 | − | 0.111233i | ||||
\(791\) | −33.5621 | −1.19333 | ||||||||
\(792\) | 10.2587 | − | 14.4915i | 0.364526 | − | 0.514932i | ||||
\(793\) | − | 2.65698i | − | 0.0943523i | ||||||
\(794\) | −7.55407 | + | 36.2699i | −0.268084 | + | 1.28717i | ||||
\(795\) | 2.55677i | 0.0906791i | ||||||||
\(796\) | 13.1726 | − | 30.2514i | 0.466890 | − | 1.07223i | ||||
\(797\) | 14.9847i | 0.530786i | 0.964140 | + | 0.265393i | \(0.0855016\pi\) | ||||
−0.964140 | + | 0.265393i | \(0.914498\pi\) | |||||||
\(798\) | −1.37379 | + | 6.59605i | −0.0486315 | + | 0.233498i | ||||
\(799\) | 3.34732 | + | 5.68974i | 0.118420 | + | 0.201288i | ||||
\(800\) | 28.7293 | − | 17.3819i | 1.01574 | − | 0.614541i | ||||
\(801\) | 23.3614 | 0.825433 | ||||||||
\(802\) | −50.4026 | − | 10.4976i | −1.77978 | − | 0.370682i | ||||
\(803\) | − | 18.0784i | − | 0.637972i | ||||||
\(804\) | −6.01169 | + | 13.8061i | −0.212016 | + | 0.486904i | ||||
\(805\) | −19.5835 | −0.690229 | ||||||||
\(806\) | −15.6837 | + | 75.3030i | −0.552434 | + | 2.65244i | ||||
\(807\) | 8.78393 | 0.309209 | ||||||||
\(808\) | 17.5009 | + | 12.3891i | 0.615678 | + | 0.435846i | ||||
\(809\) | 14.9040i | 0.523996i | 0.965068 | + | 0.261998i | \(0.0843814\pi\) | ||||
−0.965068 | + | 0.261998i | \(0.915619\pi\) | |||||||
\(810\) | 1.01340 | − | 4.86570i | 0.0356072 | − | 0.170963i | ||||
\(811\) | 36.3701 | 1.27713 | 0.638564 | − | 0.769569i | \(-0.279529\pi\) | ||||
0.638564 | + | 0.769569i | \(0.279529\pi\) | |||||||
\(812\) | 7.15872 | − | 16.4403i | 0.251222 | − | 0.576943i | ||||
\(813\) | −14.1464 | −0.496137 | ||||||||
\(814\) | −2.99050 | + | 14.3585i | −0.104817 | + | 0.503265i | ||||
\(815\) | 57.7073 | 2.02140 | ||||||||
\(816\) | −5.38649 | + | 18.0784i | −0.188565 | + | 0.632872i | ||||
\(817\) | 13.3554 | 0.467247 | ||||||||
\(818\) | −0.354736 | + | 1.70322i | −0.0124031 | + | 0.0595516i | ||||
\(819\) | 17.1695 | 0.599952 | ||||||||
\(820\) | −19.3557 | + | 44.4512i | −0.675929 | + | 1.55230i | ||||
\(821\) | 17.0881 | 0.596378 | 0.298189 | − | 0.954507i | \(-0.403617\pi\) | ||||
0.298189 | + | 0.954507i | \(0.403617\pi\) | |||||||
\(822\) | −4.30562 | + | 20.6728i | −0.150176 | + | 0.721048i | ||||
\(823\) | − | 18.3953i | − | 0.641219i | −0.947211 | − | 0.320610i | \(-0.896112\pi\) | ||
0.947211 | − | 0.320610i | \(-0.103888\pi\) | |||||||
\(824\) | −24.1786 | + | 34.1548i | −0.842301 | + | 1.18984i | ||||
\(825\) | −25.1925 | −0.877090 | ||||||||
\(826\) | −1.40709 | + | 6.75595i | −0.0489589 | + | 0.235069i | ||||
\(827\) | 0.488278 | 0.0169791 | 0.00848955 | − | 0.999964i | \(-0.497298\pi\) | ||||
0.00848955 | + | 0.999964i | \(0.497298\pi\) | |||||||
\(828\) | −4.12761 | + | 9.47924i | −0.143444 | + | 0.329426i | ||||
\(829\) | − | 27.3938i | − | 0.951424i | −0.879601 | − | 0.475712i | \(-0.842190\pi\) | ||
0.879601 | − | 0.475712i | \(-0.157810\pi\) | |||||||
\(830\) | 59.4812 | + | 12.3884i | 2.06462 | + | 0.430007i | ||||
\(831\) | −17.5037 | −0.607196 | ||||||||
\(832\) | −39.5134 | + | 13.9224i | −1.36988 | + | 0.482674i | ||||
\(833\) | −6.78244 | − | 11.5287i | −0.234998 | − | 0.399446i | ||||
\(834\) | 1.39268 | − | 6.68678i | 0.0482247 | − | 0.231544i | ||||
\(835\) | 3.85212i | 0.133308i | ||||||||
\(836\) | 6.36771 | − | 14.6237i | 0.220232 | − | 0.505773i | ||||
\(837\) | − | 55.7356i | − | 1.92650i | ||||||
\(838\) | 3.95006 | − | 18.9657i | 0.136452 | − | 0.655158i | ||||
\(839\) | − | 42.7092i | − | 1.47449i | −0.675627 | − | 0.737243i | \(-0.736127\pi\) | ||
0.675627 | − | 0.737243i | \(-0.263873\pi\) | |||||||
\(840\) | 16.9224 | + | 11.9796i | 0.583879 | + | 0.413335i | ||||
\(841\) | −7.59813 | −0.262005 | ||||||||
\(842\) | −16.6339 | − | 3.46440i | −0.573241 | − | 0.119391i | ||||
\(843\) | −5.11927 | −0.176317 | ||||||||
\(844\) | −40.9002 | − | 17.8094i | −1.40784 | − | 0.613026i | ||||
\(845\) | 47.6996 | 1.64092 | ||||||||
\(846\) | 0.781039 | − | 3.75006i | 0.0268527 | − | 0.128930i | ||||
\(847\) | − | 5.36519i | − | 0.184350i | ||||||
\(848\) | −1.97939 | + | 1.84193i | −0.0679725 | + | 0.0632521i | ||||
\(849\) | 9.71441 | 0.333398 | ||||||||
\(850\) | −32.7839 | + | 11.0990i | −1.12448 | + | 0.380694i | ||||
\(851\) | − | 8.54047i | − | 0.292763i | ||||||
\(852\) | −8.26096 | + | 18.9717i | −0.283016 | + | 0.649959i | ||||
\(853\) | −1.72451 | −0.0590462 | −0.0295231 | − | 0.999564i | \(-0.509399\pi\) | ||||
−0.0295231 | + | 0.999564i | \(0.509399\pi\) | |||||||
\(854\) | −1.36136 | − | 0.283536i | −0.0465848 | − | 0.00970240i | ||||
\(855\) | 12.0241i | 0.411214i | ||||||||
\(856\) | −6.78340 | + | 9.58228i | −0.231852 | + | 0.327516i | ||||
\(857\) | 48.6074i | 1.66040i | 0.557469 | + | 0.830198i | \(0.311773\pi\) | ||||
−0.557469 | + | 0.830198i | \(0.688227\pi\) | |||||||
\(858\) | 30.7714 | + | 6.40889i | 1.05052 | + | 0.218796i | ||||
\(859\) | 30.5330i | 1.04177i | 0.853626 | + | 0.520886i | \(0.174398\pi\) | ||||
−0.853626 | + | 0.520886i | \(0.825602\pi\) | |||||||
\(860\) | 16.4078 | − | 37.6812i | 0.559500 | − | 1.28492i | ||||
\(861\) | −16.2491 | −0.553768 | ||||||||
\(862\) | −13.0005 | − | 2.70767i | −0.442798 | − | 0.0922234i | ||||
\(863\) | −25.2580 | −0.859793 | −0.429897 | − | 0.902878i | \(-0.641450\pi\) | ||||
−0.429897 | + | 0.902878i | \(0.641450\pi\) | |||||||
\(864\) | 25.9730 | − | 15.7142i | 0.883619 | − | 0.534608i | ||||
\(865\) | −19.4772 | −0.662245 | ||||||||
\(866\) | −0.905261 | + | 4.34649i | −0.0307620 | + | 0.147700i | ||||
\(867\) | 9.44543 | − | 16.9961i | 0.320784 | − | 0.577219i | ||||
\(868\) | 36.9094 | + | 16.0717i | 1.25279 | + | 0.545509i | ||||
\(869\) | 12.1656i | 0.412690i | ||||||||
\(870\) | −5.04577 | + | 24.2266i | −0.171068 | + | 0.821358i | ||||
\(871\) | 34.4718 | 1.16803 | ||||||||
\(872\) | −17.5322 | + | 24.7661i | −0.593715 | + | 0.838686i | ||||
\(873\) | 17.2733i | 0.584614i | ||||||||
\(874\) | −1.89377 | + | 9.09266i | −0.0640576 | + | 0.307564i | ||||
\(875\) | 5.99785i | 0.202764i | ||||||||
\(876\) | 4.44955 | − | 10.2186i | 0.150337 | − | 0.345255i | ||||
\(877\) | −30.1870 | −1.01934 | −0.509670 | − | 0.860370i | \(-0.670233\pi\) | ||||
−0.509670 | + | 0.860370i | \(0.670233\pi\) | |||||||
\(878\) | 22.1858 | + | 4.62073i | 0.748734 | + | 0.155942i | ||||
\(879\) | 1.99219i | 0.0671948i | ||||||||
\(880\) | −33.4366 | − | 35.9319i | −1.12715 | − | 1.21126i | ||||
\(881\) | 12.8471i | 0.432830i | 0.976301 | + | 0.216415i | \(0.0694364\pi\) | ||||
−0.976301 | + | 0.216415i | \(0.930564\pi\) | |||||||
\(882\) | −1.58257 | + | 7.59848i | −0.0532878 | + | 0.255854i | ||||
\(883\) | − | 34.6548i | − | 1.16623i | −0.812391 | − | 0.583113i | \(-0.801835\pi\) | ||
0.812391 | − | 0.583113i | \(-0.198165\pi\) | |||||||
\(884\) | 42.8675 | − | 5.21683i | 1.44179 | − | 0.175461i | ||||
\(885\) | − | 9.52375i | − | 0.320137i | ||||||
\(886\) | −10.5044 | − | 2.18778i | −0.352901 | − | 0.0735001i | ||||
\(887\) | − | 30.3609i | − | 1.01942i | −0.860347 | − | 0.509709i | \(-0.829753\pi\) | ||
0.860347 | − | 0.509709i | \(-0.170247\pi\) | |||||||
\(888\) | −5.22435 | + | 7.37994i | −0.175318 | + | 0.247655i | ||||
\(889\) | − | 34.3924i | − | 1.15349i | ||||||
\(890\) | 13.1679 | − | 63.2241i | 0.441391 | − | 2.11928i | ||||
\(891\) | −3.94336 | −0.132108 | ||||||||
\(892\) | 15.1144 | + | 6.58138i | 0.506069 | + | 0.220361i | ||||
\(893\) | − | 3.44109i | − | 0.115152i | ||||||
\(894\) | 6.80703 | + | 1.41773i | 0.227661 | + | 0.0474159i | ||||
\(895\) | 28.2312i | 0.943664i | ||||||||
\(896\) | 2.91684 | + | 21.7312i | 0.0974448 | + | 0.725989i | ||||
\(897\) | −18.3029 | −0.611117 | ||||||||
\(898\) | 26.4261 | + | 5.50387i | 0.881850 | + | 0.183666i | ||||
\(899\) | 48.0483i | 1.60250i | ||||||||
\(900\) | 18.4140 | + | 8.01814i | 0.613801 | + | 0.267271i | ||||
\(901\) | 2.40217 | − | 1.41322i | 0.0800279 | − | 0.0470811i | ||||
\(902\) | 37.6586 | + | 7.84331i | 1.25389 | + | 0.261154i | ||||
\(903\) | 13.7743 | 0.458381 | ||||||||
\(904\) | 39.9786 | + | 28.3013i | 1.32967 | + | 0.941287i | ||||
\(905\) | 64.2278 | 2.13500 | ||||||||
\(906\) | 3.71218 | − | 17.8235i | 0.123329 | − | 0.592147i | ||||
\(907\) | −17.8653 | −0.593206 | −0.296603 | − | 0.955001i | \(-0.595854\pi\) | ||||
−0.296603 | + | 0.955001i | \(0.595854\pi\) | |||||||
\(908\) | −45.6069 | − | 19.8589i | −1.51352 | − | 0.659041i | ||||
\(909\) | 12.8251i | 0.425382i | ||||||||
\(910\) | 9.67784 | − | 46.4668i | 0.320817 | − | 1.54036i | ||||
\(911\) | 15.9542i | 0.528588i | 0.964442 | + | 0.264294i | \(0.0851389\pi\) | ||||
−0.964442 | + | 0.264294i | \(0.914861\pi\) | |||||||
\(912\) | 7.19856 | − | 6.69865i | 0.238368 | − | 0.221815i | ||||
\(913\) | − | 48.2060i | − | 1.59538i | ||||||
\(914\) | −2.45763 | + | 11.8000i | −0.0812911 | + | 0.390308i | ||||
\(915\) | 1.91909 | 0.0634431 | ||||||||
\(916\) | 11.4647 | − | 26.3292i | 0.378804 | − | 0.869941i | ||||
\(917\) | − | 7.33020i | − | 0.242065i | ||||||
\(918\) | −29.6385 | + | 10.0342i | −0.978218 | + | 0.331177i | ||||
\(919\) | 52.4743 | 1.73097 | 0.865483 | − | 0.500938i | \(-0.167011\pi\) | ||||
0.865483 | + | 0.500938i | \(0.167011\pi\) | |||||||
\(920\) | 23.3276 | + | 16.5139i | 0.769088 | + | 0.544446i | ||||
\(921\) | − | 37.1181i | − | 1.22308i | ||||||
\(922\) | −28.7130 | − | 5.98018i | −0.945613 | − | 0.196947i | ||||
\(923\) | 47.3694 | 1.55918 | ||||||||
\(924\) | 6.56745 | − | 15.0825i | 0.216053 | − | 0.496176i | ||||
\(925\) | −16.5904 | −0.545489 | ||||||||
\(926\) | −3.97192 | + | 19.0706i | −0.130525 | + | 0.626700i | ||||
\(927\) | −25.0296 | −0.822079 | ||||||||
\(928\) | −22.3907 | + | 13.5468i | −0.735010 | + | 0.444697i | ||||
\(929\) | − | 42.6106i | − | 1.39801i | −0.715118 | − | 0.699004i | \(-0.753627\pi\) | ||
0.715118 | − | 0.699004i | \(-0.246373\pi\) | |||||||
\(930\) | −54.3899 | − | 11.3280i | −1.78352 | − | 0.371460i | ||||
\(931\) | 6.97243i | 0.228512i | ||||||||
\(932\) | 4.22685 | − | 9.70716i | 0.138455 | − | 0.317968i | ||||
\(933\) | 12.4777i | 0.408501i | ||||||||
\(934\) | −36.0567 | − | 7.50968i | −1.17981 | − | 0.245724i | ||||
\(935\) | 25.6542 | + | 43.6067i | 0.838981 | + | 1.42609i | ||||
\(936\) | −20.4521 | − | 14.4782i | −0.668496 | − | 0.473236i | ||||
\(937\) | −15.8687 | −0.518407 | −0.259204 | − | 0.965823i | \(-0.583460\pi\) | ||||
−0.259204 | + | 0.965823i | \(0.583460\pi\) | |||||||
\(938\) | 3.67860 | − | 17.6623i | 0.120111 | − | 0.576695i | ||||
\(939\) | 25.6356i | 0.836585i | ||||||||
\(940\) | −9.70873 | − | 4.22754i | −0.316664 | − | 0.137887i | ||||
\(941\) | −41.3614 | −1.34834 | −0.674171 | − | 0.738575i | \(-0.735499\pi\) | ||||
−0.674171 | + | 0.738575i | \(0.735499\pi\) | |||||||
\(942\) | −15.8520 | − | 3.30156i | −0.516486 | − | 0.107571i | ||||
\(943\) | −22.3994 | −0.729426 | ||||||||
\(944\) | 7.37307 | − | 6.86104i | 0.239973 | − | 0.223308i | ||||
\(945\) | 34.3924i | 1.11879i | ||||||||
\(946\) | −31.9231 | − | 6.64876i | −1.03791 | − | 0.216170i | ||||
\(947\) | −30.7567 | −0.999457 | −0.499729 | − | 0.866182i | \(-0.666567\pi\) | ||||
−0.499729 | + | 0.866182i | \(0.666567\pi\) | |||||||
\(948\) | −2.99427 | + | 6.87648i | −0.0972494 | + | 0.223338i | ||||
\(949\) | −25.5143 | −0.828229 | ||||||||
\(950\) | 17.6631 | + | 3.67876i | 0.573066 | + | 0.119355i | ||||
\(951\) | −8.19253 | −0.265661 | ||||||||
\(952\) | 1.90159 | − | 22.5208i | 0.0616310 | − | 0.729902i | ||||
\(953\) | −26.0213 | −0.842911 | −0.421456 | − | 0.906849i | \(-0.638481\pi\) | ||||
−0.421456 | + | 0.906849i | \(0.638481\pi\) | |||||||
\(954\) | −1.58325 | − | 0.329750i | −0.0512596 | − | 0.0106760i | ||||
\(955\) | 8.34808 | 0.270137 | ||||||||
\(956\) | −37.2677 | − | 16.2277i | −1.20532 | − | 0.524843i | ||||
\(957\) | 19.6342 | 0.634683 | ||||||||
\(958\) | −24.8037 | − | 5.16596i | −0.801370 | − | 0.166905i | ||||
\(959\) | − | 25.2998i | − | 0.816972i | ||||||
\(960\) | −10.0559 | − | 28.5397i | −0.324553 | − | 0.921116i | ||||
\(961\) | −76.8709 | −2.47971 | ||||||||
\(962\) | 20.2644 | + | 4.22054i | 0.653350 | + | 0.136076i | ||||
\(963\) | −7.02215 | −0.226286 | ||||||||
\(964\) | 0.178011 | − | 0.408811i | 0.00573335 | − | 0.0131669i | ||||
\(965\) | 2.13158i | 0.0686180i | ||||||||
\(966\) | −1.95317 | + | 9.37787i | −0.0628422 | + | 0.301728i | ||||
\(967\) | 31.7101 | 1.01973 | 0.509864 | − | 0.860255i | \(-0.329696\pi\) | ||||
0.509864 | + | 0.860255i | \(0.329696\pi\) | |||||||
\(968\) | −4.52420 | + | 6.39092i | −0.145413 | + | 0.205412i | ||||
\(969\) | −8.73612 | + | 5.13953i | −0.280644 | + | 0.165105i | ||||
\(970\) | 46.7477 | + | 9.73634i | 1.50098 | + | 0.312615i | ||||
\(971\) | 18.1743i | 0.583242i | 0.956534 | + | 0.291621i | \(0.0941946\pi\) | ||||
−0.956534 | + | 0.291621i | \(0.905805\pi\) | |||||||
\(972\) | 27.2920 | + | 11.8839i | 0.875391 | + | 0.381177i | ||||
\(973\) | 8.18340i | 0.262348i | ||||||||
\(974\) | −44.3775 | − | 9.24269i | −1.42195 | − | 0.296155i | ||||
\(975\) | 35.5546i | 1.13866i | ||||||||
\(976\) | 1.38254 | + | 1.48571i | 0.0442539 | + | 0.0475565i | ||||
\(977\) | 8.03754 | 0.257144 | 0.128572 | − | 0.991700i | \(-0.458961\pi\) | ||||
0.128572 | + | 0.991700i | \(0.458961\pi\) | |||||||
\(978\) | 5.75544 | − | 27.6340i | 0.184039 | − | 0.883638i | ||||
\(979\) | −51.2394 | −1.63762 | ||||||||
\(980\) | 19.6721 | + | 8.56597i | 0.628403 | + | 0.273630i | ||||
\(981\) | −18.1493 | −0.579461 | ||||||||
\(982\) | −30.2921 | − | 6.30906i | −0.966659 | − | 0.201330i | ||||
\(983\) | − | 3.10715i | − | 0.0991027i | −0.998772 | − | 0.0495513i | \(-0.984221\pi\) | ||
0.998772 | − | 0.0495513i | \(-0.0157791\pi\) | |||||||
\(984\) | 19.3557 | + | 13.7021i | 0.617036 | + | 0.436807i | ||||
\(985\) | 15.4522 | 0.492347 | ||||||||
\(986\) | 25.5507 | − | 8.65022i | 0.813699 | − | 0.275479i | ||||
\(987\) | − | 3.54902i | − | 0.112967i | ||||||
\(988\) | −20.6387 | − | 8.98686i | −0.656605 | − | 0.285910i | ||||
\(989\) | 18.9879 | 0.603781 | ||||||||
\(990\) | 5.98596 | − | 28.7408i | 0.190246 | − | 0.913442i | ||||
\(991\) | 48.4588i | 1.53935i | 0.638439 | + | 0.769673i | \(0.279581\pi\) | ||||
−0.638439 | + | 0.769673i | \(0.720419\pi\) | |||||||
\(992\) | −30.4134 | − | 50.2683i | −0.965625 | − | 1.59602i | ||||
\(993\) | 29.7635i | 0.944516i | ||||||||
\(994\) | 5.05495 | − | 24.2707i | 0.160333 | − | 0.769819i | ||||
\(995\) | − | 54.5562i | − | 1.72955i | ||||||
\(996\) | 11.8647 | − | 27.2479i | 0.375948 | − | 0.863383i | ||||
\(997\) | −13.7301 | −0.434836 | −0.217418 | − | 0.976079i | \(-0.569763\pi\) | ||||
−0.217418 | + | 0.976079i | \(0.569763\pi\) | |||||||
\(998\) | 2.91772 | − | 14.0090i | 0.0923588 | − | 0.443449i | ||||
\(999\) | −14.9987 | −0.474537 |
(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 | 136.2.h.a.101.9 | ✓ | 16 | |
3.2 | odd | 2 | 1224.2.l.b.1189.8 | 16 | |||
4.3 | odd | 2 | 544.2.h.a.305.12 | 16 | |||
8.3 | odd | 2 | 544.2.h.a.305.6 | 16 | |||
8.5 | even | 2 | inner | 136.2.h.a.101.12 | yes | 16 | |
12.11 | even | 2 | 4896.2.l.b.3025.16 | 16 | |||
17.16 | even | 2 | inner | 136.2.h.a.101.10 | yes | 16 | |
24.5 | odd | 2 | 1224.2.l.b.1189.5 | 16 | |||
24.11 | even | 2 | 4896.2.l.b.3025.2 | 16 | |||
51.50 | odd | 2 | 1224.2.l.b.1189.7 | 16 | |||
68.67 | odd | 2 | 544.2.h.a.305.5 | 16 | |||
136.67 | odd | 2 | 544.2.h.a.305.11 | 16 | |||
136.101 | even | 2 | inner | 136.2.h.a.101.11 | yes | 16 | |
204.203 | even | 2 | 4896.2.l.b.3025.1 | 16 | |||
408.101 | odd | 2 | 1224.2.l.b.1189.6 | 16 | |||
408.203 | even | 2 | 4896.2.l.b.3025.15 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.h.a.101.9 | ✓ | 16 | 1.1 | even | 1 | trivial | |
136.2.h.a.101.10 | yes | 16 | 17.16 | even | 2 | inner | |
136.2.h.a.101.11 | yes | 16 | 136.101 | even | 2 | inner | |
136.2.h.a.101.12 | yes | 16 | 8.5 | even | 2 | inner | |
544.2.h.a.305.5 | 16 | 68.67 | odd | 2 | |||
544.2.h.a.305.6 | 16 | 8.3 | odd | 2 | |||
544.2.h.a.305.11 | 16 | 136.67 | odd | 2 | |||
544.2.h.a.305.12 | 16 | 4.3 | odd | 2 | |||
1224.2.l.b.1189.5 | 16 | 24.5 | odd | 2 | |||
1224.2.l.b.1189.6 | 16 | 408.101 | odd | 2 | |||
1224.2.l.b.1189.7 | 16 | 51.50 | odd | 2 | |||
1224.2.l.b.1189.8 | 16 | 3.2 | odd | 2 | |||
4896.2.l.b.3025.1 | 16 | 204.203 | even | 2 | |||
4896.2.l.b.3025.2 | 16 | 24.11 | even | 2 | |||
4896.2.l.b.3025.15 | 16 | 408.203 | even | 2 | |||
4896.2.l.b.3025.16 | 16 | 12.11 | even | 2 |