Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1368,2,Mod(379,1368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1368.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1368.e (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: | \(10.9235349965\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 456) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.20 | ||
Character | \(\chi\) | \(=\) | 1368.379 |
Dual form | 1368.2.e.g.379.19 |
$q$-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 \(\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times\).
\(n\) | \(343\) | \(685\) | \(1009\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.134537 | + | 1.40780i | −0.0951320 | + | 0.995465i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.96380 | − | 0.378802i | −0.981900 | − | 0.189401i | ||||
\(5\) | − | 2.61555i | − | 1.16971i | −0.811138 | − | 0.584854i | \(-0.801152\pi\) | ||
0.811138 | − | 0.584854i | \(-0.198848\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.81248i | − | 1.81895i | −0.415763 | − | 0.909473i | \(-0.636485\pi\) | ||
0.415763 | − | 0.909473i | \(-0.363515\pi\) | |||||||
\(8\) | 0.797481 | − | 2.71367i | 0.281952 | − | 0.959428i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.68217 | + | 0.351888i | 1.16440 | + | 0.111277i | ||||
\(11\) | −3.49434 | −1.05358 | −0.526792 | − | 0.849994i | \(-0.676605\pi\) | ||||
−0.526792 | + | 0.849994i | \(0.676605\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.50149 | 0.416438 | 0.208219 | − | 0.978082i | \(-0.433233\pi\) | ||||
0.208219 | + | 0.978082i | \(0.433233\pi\) | |||||||
\(14\) | 6.77501 | + | 0.647456i | 1.81070 | + | 0.173040i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.71302 | + | 1.48778i | 0.928254 | + | 0.371946i | ||||
\(17\) | −5.31012 | −1.28789 | −0.643947 | − | 0.765071i | \(-0.722704\pi\) | ||||
−0.643947 | + | 0.765071i | \(0.722704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.83470 | + | 2.07245i | 0.879742 | + | 0.475452i | ||||
\(20\) | −0.990775 | + | 5.13641i | −0.221544 | + | 1.14854i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.470118 | − | 4.91934i | 0.100230 | − | 1.04881i | ||||
\(23\) | 2.26423i | 0.472125i | 0.971738 | + | 0.236063i | \(0.0758570\pi\) | ||||
−0.971738 | + | 0.236063i | \(0.924143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.84109 | −0.368219 | ||||||||
\(26\) | −0.202006 | + | 2.11379i | −0.0396165 | + | 0.414549i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.82298 | + | 9.45075i | −0.344510 | + | 1.78602i | ||||
\(29\) | −5.12817 | −0.952277 | −0.476139 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476139 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.72573 | 0.309950 | 0.154975 | − | 0.987918i | \(-0.450470\pi\) | ||||
0.154975 | + | 0.987918i | \(0.450470\pi\) | |||||||
\(32\) | −2.59404 | + | 5.02702i | −0.458566 | + | 0.888661i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.714407 | − | 7.47558i | 0.122520 | − | 1.28205i | ||||
\(35\) | −12.5873 | −2.12764 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2996 | −1.69324 | −0.846622 | − | 0.532195i | \(-0.821367\pi\) | ||||
−0.846622 | + | 0.532195i | \(0.821367\pi\) | |||||||
\(38\) | −3.43350 | + | 5.11967i | −0.556987 | + | 0.830521i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.09774 | − | 2.08585i | −1.12225 | − | 0.329802i | ||||
\(41\) | − | 3.90666i | − | 0.610118i | −0.952333 | − | 0.305059i | \(-0.901324\pi\) | ||
0.952333 | − | 0.305059i | \(-0.0986762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.342152 | 0.0521777 | 0.0260888 | − | 0.999660i | \(-0.491695\pi\) | ||||
0.0260888 | + | 0.999660i | \(0.491695\pi\) | |||||||
\(44\) | 6.86219 | + | 1.32366i | 1.03451 | + | 0.199550i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.18759 | − | 0.304623i | −0.469984 | − | 0.0449142i | ||||
\(47\) | 0.679062i | 0.0990514i | 0.998773 | + | 0.0495257i | \(0.0157710\pi\) | ||||
−0.998773 | + | 0.0495257i | \(0.984229\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.1600 | −2.30857 | ||||||||
\(50\) | 0.247695 | − | 2.59189i | 0.0350294 | − | 0.366549i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.94862 | − | 0.568767i | −0.408900 | − | 0.0788737i | ||||
\(53\) | 10.0708 | 1.38333 | 0.691667 | − | 0.722216i | \(-0.256876\pi\) | ||||
0.691667 | + | 0.722216i | \(0.256876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.13962i | 1.23239i | ||||||||
\(56\) | −13.0595 | − | 3.83786i | −1.74515 | − | 0.512856i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.689928 | − | 7.21944i | 0.0905920 | − | 0.947958i | ||||
\(59\) | 9.15071i | 1.19132i | 0.803236 | + | 0.595660i | \(0.203110\pi\) | ||||
−0.803236 | + | 0.595660i | \(0.796890\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.65473i | − | 0.339904i | −0.985452 | − | 0.169952i | \(-0.945639\pi\) | ||
0.985452 | − | 0.169952i | \(-0.0543613\pi\) | |||||||
\(62\) | −0.232175 | + | 2.42948i | −0.0294862 | + | 0.308545i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.72805 | − | 4.32821i | −0.841006 | − | 0.541026i | ||||
\(65\) | − | 3.92721i | − | 0.487111i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.37340i | 0.900804i | 0.892826 | + | 0.450402i | \(0.148719\pi\) | ||||
−0.892826 | + | 0.450402i | \(0.851281\pi\) | |||||||
\(68\) | 10.4280 | + | 2.01148i | 1.26458 | + | 0.243928i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.69345 | − | 17.7204i | 0.202406 | − | 2.11799i | ||||
\(71\) | −9.74773 | −1.15684 | −0.578421 | − | 0.815738i | \(-0.696331\pi\) | ||||
−0.578421 | + | 0.815738i | \(0.696331\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.16085 | −0.838114 | −0.419057 | − | 0.907960i | \(-0.637639\pi\) | ||||
−0.419057 | + | 0.907960i | \(0.637639\pi\) | |||||||
\(74\) | 1.38568 | − | 14.4998i | 0.161082 | − | 1.68556i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.74554 | − | 5.52247i | −0.773767 | − | 0.633470i | ||||
\(77\) | 16.8165i | 1.91641i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.21007 | −0.586178 | −0.293089 | − | 0.956085i | \(-0.594683\pi\) | ||||
−0.293089 | + | 0.956085i | \(0.594683\pi\) | |||||||
\(80\) | 3.89137 | − | 9.71158i | 0.435068 | − | 1.08579i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.49980 | + | 0.525590i | 0.607351 | + | 0.0580417i | ||||
\(83\) | 4.80051 | 0.526925 | 0.263462 | − | 0.964670i | \(-0.415135\pi\) | ||||
0.263462 | + | 0.964670i | \(0.415135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8889i | 1.50646i | ||||||||
\(86\) | −0.0460321 | + | 0.481681i | −0.00496377 | + | 0.0519410i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.78667 | + | 9.48251i | −0.297060 | + | 1.01084i | ||||
\(89\) | − | 14.0944i | − | 1.49400i | −0.664823 | − | 0.747001i | \(-0.731493\pi\) | ||
0.664823 | − | 0.747001i | \(-0.268507\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 7.22588i | − | 0.757478i | ||||||
\(92\) | 0.857696 | − | 4.44650i | 0.0894210 | − | 0.463579i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.955984 | − | 0.0913590i | −0.0986022 | − | 0.00942296i | ||||
\(95\) | 5.42059 | − | 10.0299i | 0.556141 | − | 1.02904i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.2574i | − | 1.34608i | −0.739604 | − | 0.673042i | \(-0.764987\pi\) | ||
0.739604 | − | 0.673042i | \(-0.235013\pi\) | |||||||
\(98\) | 2.17411 | − | 22.7500i | 0.219618 | − | 2.29810i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.61554 | + | 0.697410i | 0.361554 | + | 0.0697410i | ||||
\(101\) | 0.101742i | 0.0101237i | 0.999987 | + | 0.00506187i | \(0.00161125\pi\) | ||||
−0.999987 | + | 0.00506187i | \(0.998389\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.3937 | 1.91092 | 0.955460 | − | 0.295120i | \(-0.0953597\pi\) | ||||
0.955460 | + | 0.295120i | \(0.0953597\pi\) | |||||||
\(104\) | 1.19741 | − | 4.07455i | 0.117415 | − | 0.399542i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.35490 | + | 14.1777i | −0.131599 | + | 1.37706i | ||||
\(107\) | − | 2.03827i | − | 0.197047i | −0.995135 | − | 0.0985235i | \(-0.968588\pi\) | ||
0.995135 | − | 0.0985235i | \(-0.0314120\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0323 | 1.72718 | 0.863589 | − | 0.504197i | \(-0.168212\pi\) | ||||
0.863589 | + | 0.504197i | \(0.168212\pi\) | |||||||
\(110\) | −12.8668 | − | 1.22962i | −1.22680 | − | 0.117239i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 7.15993 | − | 17.8688i | 0.676549 | − | 1.68845i | ||||
\(113\) | 5.54322i | 0.521462i | 0.965412 | + | 0.260731i | \(0.0839635\pi\) | ||||
−0.965412 | + | 0.260731i | \(0.916036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.92221 | 0.552249 | ||||||||
\(116\) | 10.0707 | + | 1.94256i | 0.935041 | + | 0.180362i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.8824 | − | 1.23111i | −1.18592 | − | 0.113333i | ||||
\(119\) | 25.5548i | 2.34261i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.21043 | 0.110039 | ||||||||
\(122\) | 3.73733 | + | 0.357160i | 0.338362 | + | 0.0323357i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.38899 | − | 0.653711i | −0.304340 | − | 0.0587050i | ||||
\(125\) | − | 8.26227i | − | 0.739000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4962 | −1.10886 | −0.554430 | − | 0.832231i | \(-0.687064\pi\) | ||||
−0.554430 | + | 0.832231i | \(0.687064\pi\) | |||||||
\(128\) | 6.99842 | − | 8.88944i | 0.618579 | − | 0.785723i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.52873 | + | 0.528355i | 0.484901 | + | 0.0463398i | ||||
\(131\) | −12.5819 | −1.09928 | −0.549642 | − | 0.835400i | \(-0.685236\pi\) | ||||
−0.549642 | + | 0.835400i | \(0.685236\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.97362 | − | 18.4544i | 0.864822 | − | 1.60020i | ||||
\(134\) | −10.3803 | − | 0.991994i | −0.896718 | − | 0.0856952i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.23472 | + | 14.4099i | −0.363124 | + | 1.23564i | ||||
\(137\) | 1.32093 | 0.112855 | 0.0564273 | − | 0.998407i | \(-0.482029\pi\) | ||||
0.0564273 | + | 0.998407i | \(0.482029\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41682 | 0.120173 | 0.0600864 | − | 0.998193i | \(-0.480862\pi\) | ||||
0.0600864 | + | 0.998193i | \(0.480862\pi\) | |||||||
\(140\) | 24.7189 | + | 4.76809i | 2.08913 | + | 0.402977i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.31143 | − | 13.7229i | 0.110053 | − | 1.15160i | ||||
\(143\) | −5.24671 | −0.438752 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.4130i | 1.11389i | ||||||||
\(146\) | 0.963399 | − | 10.0810i | 0.0797315 | − | 0.834313i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.2264 | + | 3.90151i | 1.66260 | + | 0.320702i | ||||
\(149\) | − | 13.2785i | − | 1.08782i | −0.839144 | − | 0.543909i | \(-0.816943\pi\) | ||
0.839144 | − | 0.543909i | \(-0.183057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.2778 | −1.32467 | −0.662334 | − | 0.749208i | \(-0.730434\pi\) | ||||
−0.662334 | + | 0.749208i | \(0.730434\pi\) | |||||||
\(152\) | 8.68205 | − | 8.75340i | 0.704207 | − | 0.709994i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −23.6742 | − | 2.26243i | −1.90772 | − | 0.182312i | ||||
\(155\) | − | 4.51373i | − | 0.362552i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.3793i | 1.46683i | 0.679783 | + | 0.733413i | \(0.262074\pi\) | ||||
−0.679783 | + | 0.733413i | \(0.737926\pi\) | |||||||
\(158\) | 0.700946 | − | 7.33473i | 0.0557643 | − | 0.583520i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 13.1484 | + | 6.78483i | 1.03947 | + | 0.536388i | ||||
\(161\) | 10.8966 | 0.858770 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.3413 | −0.966649 | −0.483325 | − | 0.875441i | \(-0.660571\pi\) | ||||
−0.483325 | + | 0.875441i | \(0.660571\pi\) | |||||||
\(164\) | −1.47985 | + | 7.67190i | −0.115557 | + | 0.599075i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.645847 | + | 6.75816i | −0.0501274 | + | 0.524535i | ||||
\(167\) | 20.7583 | 1.60632 | 0.803161 | − | 0.595762i | \(-0.203150\pi\) | ||||
0.803161 | + | 0.595762i | \(0.203150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.7455 | −0.826580 | ||||||||
\(170\) | −19.5527 | − | 1.86857i | −1.49963 | − | 0.143313i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.671918 | − | 0.129608i | −0.0512333 | − | 0.00988251i | ||||
\(173\) | 0.684931 | 0.0520743 | 0.0260372 | − | 0.999661i | \(-0.491711\pi\) | ||||
0.0260372 | + | 0.999661i | \(0.491711\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.86022i | 0.669770i | ||||||||
\(176\) | −12.9746 | − | 5.19882i | −0.977994 | − | 0.391876i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 19.8421 | + | 1.89622i | 1.48723 | + | 0.142127i | ||||
\(179\) | 18.7464i | 1.40117i | 0.713568 | + | 0.700586i | \(0.247078\pi\) | ||||
−0.713568 | + | 0.700586i | \(0.752922\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8359 | −0.879758 | −0.439879 | − | 0.898057i | \(-0.644979\pi\) | ||||
−0.439879 | + | 0.898057i | \(0.644979\pi\) | |||||||
\(182\) | 10.1726 | + | 0.972147i | 0.754042 | + | 0.0720604i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.14439 | + | 1.80568i | 0.452970 | + | 0.133117i | ||||
\(185\) | 26.9391i | 1.98060i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.5554 | 1.35690 | ||||||||
\(188\) | 0.257230 | − | 1.33354i | 0.0187604 | − | 0.0972586i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 13.3908 | + | 8.98049i | 0.971468 | + | 0.651513i | ||||
\(191\) | − | 17.4611i | − | 1.26344i | −0.775197 | − | 0.631720i | \(-0.782349\pi\) | ||
0.775197 | − | 0.631720i | \(-0.217651\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 11.0743i | − | 0.797149i | −0.917136 | − | 0.398574i | \(-0.869505\pi\) | ||
0.917136 | − | 0.398574i | \(-0.130495\pi\) | |||||||
\(194\) | 18.6638 | + | 1.78361i | 1.33998 | + | 0.128056i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.7349 | + | 6.12143i | 2.26678 | + | 0.437245i | ||||
\(197\) | − | 20.2434i | − | 1.44228i | −0.692788 | − | 0.721141i | \(-0.743618\pi\) | ||
0.692788 | − | 0.721141i | \(-0.256382\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.1969i | − | 0.864613i | −0.901727 | − | 0.432307i | \(-0.857700\pi\) | ||
0.901727 | − | 0.432307i | \(-0.142300\pi\) | |||||||
\(200\) | −1.46824 | + | 4.99613i | −0.103820 | + | 0.353279i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.143233 | − | 0.0136881i | −0.0100778 | − | 0.000963092i | ||||
\(203\) | 24.6792i | 1.73214i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −10.2181 | −0.713660 | ||||||||
\(206\) | −2.60917 | + | 27.3025i | −0.181790 | + | 1.90225i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.57505 | + | 2.23389i | 0.386560 | + | 0.154892i | ||||
\(209\) | −13.3998 | − | 7.24185i | −0.926882 | − | 0.500929i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2304i | 0.773136i | 0.922261 | + | 0.386568i | \(0.126339\pi\) | ||||
−0.922261 | + | 0.386568i | \(0.873661\pi\) | |||||||
\(212\) | −19.7771 | − | 3.81485i | −1.35830 | − | 0.262005i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.86948 | + | 0.274223i | 0.196153 | + | 0.0187455i | ||||
\(215\) | − | 0.894915i | − | 0.0610327i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.30505i | − | 0.563783i | ||||||
\(218\) | −2.42601 | + | 25.3858i | −0.164310 | + | 1.71934i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.46211 | − | 17.9484i | 0.233415 | − | 1.21008i | ||||
\(221\) | −7.97308 | −0.536327 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.86592 | −0.392811 | −0.196406 | − | 0.980523i | \(-0.562927\pi\) | ||||
−0.196406 | + | 0.980523i | \(0.562927\pi\) | |||||||
\(224\) | 24.1924 | + | 12.4838i | 1.61643 | + | 0.834106i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −7.80374 | − | 0.745767i | −0.519097 | − | 0.0496077i | ||||
\(227\) | 13.7884i | 0.915168i | 0.889166 | + | 0.457584i | \(0.151285\pi\) | ||||
−0.889166 | + | 0.457584i | \(0.848715\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 7.75918i | − | 0.512741i | −0.966579 | − | 0.256371i | \(-0.917473\pi\) | ||
0.966579 | − | 0.256371i | \(-0.0825268\pi\) | |||||||
\(230\) | −0.796756 | + | 8.33728i | −0.0525365 | + | 0.549744i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.08962 | + | 13.9162i | −0.268497 | + | 0.913642i | ||||
\(233\) | −23.5694 | −1.54408 | −0.772041 | − | 0.635573i | \(-0.780764\pi\) | ||||
−0.772041 | + | 0.635573i | \(0.780764\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.77612 | 0.115861 | ||||||||
\(236\) | 3.46631 | − | 17.9702i | 0.225637 | − | 1.16976i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −35.9761 | − | 3.43807i | −2.33198 | − | 0.222857i | ||||
\(239\) | − | 13.3670i | − | 0.864640i | −0.901720 | − | 0.432320i | \(-0.857695\pi\) | ||
0.901720 | − | 0.432320i | \(-0.142305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 19.9602i | − | 1.28575i | −0.765972 | − | 0.642873i | \(-0.777742\pi\) | ||
0.765972 | − | 0.642873i | \(-0.222258\pi\) | |||||||
\(242\) | −0.162848 | + | 1.70405i | −0.0104683 | + | 0.109540i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00562 | + | 5.21337i | −0.0643782 | + | 0.333752i | ||||
\(245\) | 42.2672i | 2.70035i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.75776 | + | 3.11175i | 0.366357 | + | 0.197996i | ||||
\(248\) | 1.37624 | − | 4.68307i | 0.0873912 | − | 0.297375i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.6316 | + | 1.11158i | 0.735649 | + | 0.0703026i | ||||
\(251\) | 29.8620 | 1.88487 | 0.942435 | − | 0.334388i | \(-0.108530\pi\) | ||||
0.942435 | + | 0.334388i | \(0.108530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.91200i | − | 0.497423i | ||||||
\(254\) | 1.68120 | − | 17.5922i | 0.105488 | − | 1.10383i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.5730 | + | 11.0483i | 0.723313 | + | 0.690521i | ||||
\(257\) | − | 0.677951i | − | 0.0422894i | −0.999776 | − | 0.0211447i | \(-0.993269\pi\) | ||
0.999776 | − | 0.0211447i | \(-0.00673108\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 49.5666i | 3.07992i | ||||||||
\(260\) | −1.48764 | + | 7.71226i | −0.0922593 | + | 0.478294i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.69273 | − | 17.7128i | 0.104577 | − | 1.09430i | ||||
\(263\) | 3.00903i | 0.185545i | 0.995687 | + | 0.0927723i | \(0.0295729\pi\) | ||||
−0.995687 | + | 0.0927723i | \(0.970427\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 26.3407i | − | 1.61810i | ||||||
\(266\) | 24.6383 | + | 16.5237i | 1.51067 | + | 1.01313i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 2.79306 | − | 14.4799i | 0.170613 | − | 0.884499i | ||||
\(269\) | −7.04041 | −0.429261 | −0.214631 | − | 0.976695i | \(-0.568855\pi\) | ||||
−0.214631 | + | 0.976695i | \(0.568855\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.8229i | − | 1.38639i | −0.720750 | − | 0.693195i | \(-0.756202\pi\) | ||
0.720750 | − | 0.693195i | \(-0.243798\pi\) | |||||||
\(272\) | −19.7166 | − | 7.90031i | −1.19549 | − | 0.479026i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.177714 | + | 1.85960i | −0.0107361 | + | 0.112343i | ||||
\(275\) | 6.43341 | 0.387949 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 20.9985i | − | 1.26168i | −0.775913 | − | 0.630840i | \(-0.782710\pi\) | ||
0.775913 | − | 0.630840i | \(-0.217290\pi\) | |||||||
\(278\) | −0.190614 | + | 1.99459i | −0.0114323 | + | 0.119628i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.0381 | + | 34.1577i | −0.599892 | + | 2.04132i | ||||
\(281\) | − | 5.03139i | − | 0.300148i | −0.988675 | − | 0.150074i | \(-0.952049\pi\) | ||
0.988675 | − | 0.150074i | \(-0.0479511\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.25113 | −0.0743719 | −0.0371860 | − | 0.999308i | \(-0.511839\pi\) | ||||
−0.0371860 | + | 0.999308i | \(0.511839\pi\) | |||||||
\(284\) | 19.1426 | + | 3.69246i | 1.13590 | + | 0.219107i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.705877 | − | 7.38632i | 0.0417394 | − | 0.436762i | ||||
\(287\) | −18.8007 | −1.10977 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 11.1974 | 0.658668 | ||||||||
\(290\) | −18.8828 | − | 1.80454i | −1.10884 | − | 0.105966i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 14.0625 | + | 2.71255i | 0.822944 | + | 0.158740i | ||||
\(293\) | −18.5789 | −1.08539 | −0.542695 | − | 0.839930i | \(-0.682596\pi\) | ||||
−0.542695 | + | 0.839930i | \(0.682596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 23.9341 | 1.39350 | ||||||||
\(296\) | −8.21374 | + | 27.9498i | −0.477414 | + | 1.62455i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 18.6935 | + | 1.78645i | 1.08289 | + | 0.103486i | ||||
\(299\) | 3.39972i | 0.196611i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.64660i | − | 0.0949084i | ||||||
\(302\) | 2.18997 | − | 22.9159i | 0.126018 | − | 1.31866i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 11.1550 | + | 13.4002i | 0.639782 | + | 0.768557i | ||||
\(305\) | −6.94359 | −0.397589 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10.7076i | − | 0.611115i | −0.952174 | − | 0.305557i | \(-0.901157\pi\) | ||
0.952174 | − | 0.305557i | \(-0.0988428\pi\) | |||||||
\(308\) | 6.37011 | − | 33.0241i | 0.362971 | − | 1.88173i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.35443 | + | 0.607264i | 0.360907 | + | 0.0344903i | ||||
\(311\) | − | 13.2171i | − | 0.749472i | −0.927132 | − | 0.374736i | \(-0.877733\pi\) | ||
0.927132 | − | 0.374736i | \(-0.122267\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.4175 | −1.83235 | −0.916174 | − | 0.400781i | \(-0.868739\pi\) | ||||
−0.916174 | + | 0.400781i | \(0.868739\pi\) | |||||||
\(314\) | −25.8743 | − | 2.47269i | −1.46017 | − | 0.139542i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.2315 | + | 1.97358i | 0.575568 | + | 0.111023i | ||||
\(317\) | 14.4866 | 0.813650 | 0.406825 | − | 0.913506i | \(-0.366636\pi\) | ||||
0.406825 | + | 0.913506i | \(0.366636\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.9196 | 1.00330 | ||||||||
\(320\) | −11.3206 | + | 17.5975i | −0.632843 | + | 0.983732i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.46599 | + | 15.3402i | −0.0816965 | + | 0.854875i | ||||
\(323\) | −20.3627 | − | 11.0049i | −1.13301 | − | 0.612332i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.76438 | −0.153340 | ||||||||
\(326\) | 1.66037 | − | 17.3741i | 0.0919593 | − | 0.962265i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6014 | − | 3.11549i | −0.585364 | − | 0.172024i | ||||
\(329\) | 3.26797 | 0.180169 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 5.22689i | − | 0.287296i | −0.989629 | − | 0.143648i | \(-0.954117\pi\) | ||
0.989629 | − | 0.143648i | \(-0.0458832\pi\) | |||||||
\(332\) | −9.42725 | − | 1.81845i | −0.517387 | − | 0.0998001i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.79275 | + | 29.2235i | −0.152813 | + | 1.59904i | ||||
\(335\) | 19.2855 | 1.05368 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.1981i | 0.991312i | 0.868519 | + | 0.495656i | \(0.165072\pi\) | ||||
−0.868519 | + | 0.495656i | \(0.834928\pi\) | |||||||
\(338\) | 1.44567 | − | 15.1276i | 0.0786342 | − | 0.822831i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.26114 | − | 27.2750i | 0.285325 | − | 1.47919i | ||||
\(341\) | −6.03030 | −0.326559 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.0821i | 2.38021i | ||||||||
\(344\) | 0.272860 | − | 0.928489i | 0.0147116 | − | 0.0500608i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.0921485 | + | 0.964245i | −0.00495393 | + | 0.0518381i | ||||
\(347\) | 16.9154 | 0.908066 | 0.454033 | − | 0.890985i | \(-0.349985\pi\) | ||||
0.454033 | + | 0.890985i | \(0.349985\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 28.3766i | 1.51896i | 0.650528 | + | 0.759482i | \(0.274547\pi\) | ||||
−0.650528 | + | 0.759482i | \(0.725453\pi\) | |||||||
\(350\) | −12.4734 | − | 1.19203i | −0.666732 | − | 0.0637165i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 9.06446 | − | 17.5661i | 0.483137 | − | 0.936279i | ||||
\(353\) | −2.43957 | −0.129845 | −0.0649227 | − | 0.997890i | \(-0.520680\pi\) | ||||
−0.0649227 | + | 0.997890i | \(0.520680\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.4957i | 1.35317i | ||||||||
\(356\) | −5.33899 | + | 27.6786i | −0.282966 | + | 1.46696i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −26.3912 | − | 2.52209i | −1.39482 | − | 0.133296i | ||||
\(359\) | 24.6073i | 1.29872i | 0.760479 | + | 0.649362i | \(0.224964\pi\) | ||||
−0.760479 | + | 0.649362i | \(0.775036\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.4099 | + | 15.8945i | 0.547890 | + | 0.836550i | ||||
\(362\) | 1.59237 | − | 16.6626i | 0.0836931 | − | 0.875768i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.73718 | + | 14.1902i | −0.143467 | + | 0.743767i | ||||
\(365\) | 18.7295i | 0.980349i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 18.9695i | − | 0.990201i | −0.868836 | − | 0.495100i | \(-0.835131\pi\) | ||
0.868836 | − | 0.495100i | \(-0.164869\pi\) | |||||||
\(368\) | −3.36869 | + | 8.40713i | −0.175605 | + | 0.438252i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −37.9249 | − | 3.62431i | −1.97162 | − | 0.188419i | ||||
\(371\) | − | 48.4657i | − | 2.51621i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.4231 | −1.05747 | −0.528734 | − | 0.848788i | \(-0.677333\pi\) | ||||
−0.528734 | + | 0.848788i | \(0.677333\pi\) | |||||||
\(374\) | −2.49638 | + | 26.1223i | −0.129085 | + | 1.35075i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.84275 | + | 0.541540i | 0.0950328 | + | 0.0279278i | ||||
\(377\) | −7.69988 | −0.396564 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0452i | 1.33785i | 0.743330 | + | 0.668925i | \(0.233245\pi\) | ||||
−0.743330 | + | 0.668925i | \(0.766755\pi\) | |||||||
\(380\) | −14.4443 | + | 17.6433i | −0.740976 | + | 0.905082i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 24.5817 | + | 2.34916i | 1.25771 | + | 0.120194i | ||||
\(383\) | 23.1300 | 1.18189 | 0.590944 | − | 0.806712i | \(-0.298755\pi\) | ||||
0.590944 | + | 0.806712i | \(0.298755\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 43.9843 | 2.24165 | ||||||||
\(386\) | 15.5905 | + | 1.48991i | 0.793534 | + | 0.0758344i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.02193 | + | 26.0349i | −0.254950 | + | 1.32172i | ||||
\(389\) | − | 17.1821i | − | 0.871166i | −0.900148 | − | 0.435583i | \(-0.856542\pi\) | ||
0.900148 | − | 0.435583i | \(-0.143458\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0233i | − | 0.608047i | ||||||
\(392\) | −12.8873 | + | 43.8529i | −0.650905 | + | 2.21490i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 28.4986 | + | 2.72349i | 1.43574 | + | 0.137207i | ||||
\(395\) | 13.6272i | 0.685658i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3706i | 1.42388i | 0.702242 | + | 0.711939i | \(0.252183\pi\) | ||||
−0.702242 | + | 0.711939i | \(0.747817\pi\) | |||||||
\(398\) | 17.1708 | + | 1.64093i | 0.860692 | + | 0.0822524i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.83601 | − | 2.73915i | −0.341801 | − | 0.136957i | ||||
\(401\) | 6.28011i | 0.313614i | 0.987629 | + | 0.156807i | \(0.0501200\pi\) | ||||
−0.987629 | + | 0.156807i | \(0.949880\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.59116 | 0.129075 | ||||||||
\(404\) | 0.0385402 | − | 0.199802i | 0.00191745 | − | 0.00994050i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.7434 | − | 3.32027i | −1.72429 | − | 0.164782i | ||||
\(407\) | 35.9903 | 1.78398 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.75238i | 0.136097i | 0.997682 | + | 0.0680483i | \(0.0216772\pi\) | ||||
−0.997682 | + | 0.0680483i | \(0.978323\pi\) | |||||||
\(410\) | 1.37471 | − | 14.3850i | 0.0678919 | − | 0.710424i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −38.0854 | − | 7.34638i | −1.87633 | − | 0.361930i | ||||
\(413\) | 44.0376 | 2.16695 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 12.5560i | − | 0.616349i | ||||||
\(416\) | −3.89492 | + | 7.54801i | −0.190964 | + | 0.370072i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 11.9978 | − | 17.8899i | 0.586833 | − | 0.875024i | ||||
\(419\) | 33.3577 | 1.62963 | 0.814816 | − | 0.579719i | \(-0.196838\pi\) | ||||
0.814816 | + | 0.579719i | \(0.196838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.929028 | 0.0452781 | 0.0226390 | − | 0.999744i | \(-0.492793\pi\) | ||||
0.0226390 | + | 0.999744i | \(0.492793\pi\) | |||||||
\(422\) | −15.8102 | − | 1.51091i | −0.769629 | − | 0.0735499i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.03130 | − | 27.3289i | 0.390034 | − | 1.32721i | ||||
\(425\) | 9.77642 | 0.474226 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.7759 | −0.618267 | ||||||||
\(428\) | −0.772101 | + | 4.00275i | −0.0373209 | + | 0.193480i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.25986 | + | 0.120399i | 0.0607559 | + | 0.00580616i | ||||
\(431\) | −34.4951 | −1.66157 | −0.830786 | − | 0.556592i | \(-0.812109\pi\) | ||||
−0.830786 | + | 0.556592i | \(0.812109\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 24.9055i | − | 1.19688i | −0.801166 | − | 0.598442i | \(-0.795787\pi\) | ||
0.801166 | − | 0.598442i | \(-0.204213\pi\) | |||||||
\(434\) | 11.6918 | + | 1.11734i | 0.561226 | + | 0.0536338i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −35.4117 | − | 6.83066i | −1.69591 | − | 0.327129i | ||||
\(437\) | −4.69250 | + | 8.68266i | −0.224473 | + | 0.415348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −20.5120 | −0.978984 | −0.489492 | − | 0.872008i | \(-0.662818\pi\) | ||||
−0.489492 | + | 0.872008i | \(0.662818\pi\) | |||||||
\(440\) | 24.8020 | + | 7.28868i | 1.18239 | + | 0.347474i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.07267 | − | 11.2245i | 0.0510219 | − | 0.533895i | ||||
\(443\) | −25.9849 | −1.23458 | −0.617289 | − | 0.786736i | \(-0.711769\pi\) | ||||
−0.617289 | + | 0.786736i | \(0.711769\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −36.8646 | −1.74755 | ||||||||
\(446\) | 0.789184 | − | 8.25805i | 0.0373689 | − | 0.391030i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −20.8294 | + | 32.3786i | −0.984097 | + | 1.52974i | ||||
\(449\) | − | 36.4806i | − | 1.72163i | −0.508920 | − | 0.860814i | \(-0.669955\pi\) | ||
0.508920 | − | 0.860814i | \(-0.330045\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.6512i | 0.642810i | ||||||||
\(452\) | 2.09978 | − | 10.8858i | 0.0987654 | − | 0.512023i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −19.4113 | − | 1.85505i | −0.911018 | − | 0.0870618i | ||||
\(455\) | −18.8996 | −0.886028 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2770 | 1.08885 | 0.544425 | − | 0.838809i | \(-0.316748\pi\) | ||||
0.544425 | + | 0.838809i | \(0.316748\pi\) | |||||||
\(458\) | 10.9234 | + | 1.04390i | 0.510416 | + | 0.0487781i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.6300 | − | 2.24335i | −0.542253 | − | 0.104597i | ||||
\(461\) | − | 14.2845i | − | 0.665298i | −0.943051 | − | 0.332649i | \(-0.892058\pi\) | ||
0.943051 | − | 0.332649i | \(-0.107942\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 15.6276i | − | 0.726275i | −0.931736 | − | 0.363137i | \(-0.881706\pi\) | ||
0.931736 | − | 0.363137i | \(-0.118294\pi\) | |||||||
\(464\) | −19.0410 | − | 7.62961i | −0.883956 | − | 0.354196i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.17095 | − | 33.1810i | 0.146892 | − | 1.53708i | ||||
\(467\) | 8.66870 | 0.401140 | 0.200570 | − | 0.979679i | \(-0.435721\pi\) | ||||
0.200570 | + | 0.979679i | \(0.435721\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 35.4843 | 1.63851 | ||||||||
\(470\) | −0.238954 | + | 2.50042i | −0.0110221 | + | 0.115336i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 24.8320 | + | 7.29752i | 1.14299 | + | 0.335895i | ||||
\(473\) | −1.19560 | −0.0549736 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.06005 | − | 3.81557i | −0.323937 | − | 0.175070i | ||||
\(476\) | 9.68023 | − | 50.1846i | 0.443693 | − | 2.30021i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 18.8181 | + | 1.79836i | 0.860719 | + | 0.0822549i | ||||
\(479\) | 3.41248i | 0.155920i | 0.996956 | + | 0.0779602i | \(0.0248407\pi\) | ||||
−0.996956 | + | 0.0779602i | \(0.975159\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.4647 | −0.705130 | ||||||||
\(482\) | 28.0999 | + | 2.68538i | 1.27992 | + | 0.122316i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.37705 | − | 0.458515i | −0.108048 | − | 0.0208416i | ||||
\(485\) | −34.6754 | −1.57453 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 41.8116 | 1.89467 | 0.947333 | − | 0.320250i | \(-0.103767\pi\) | ||||
0.947333 | + | 0.320250i | \(0.103767\pi\) | |||||||
\(488\) | −7.20408 | − | 2.11710i | −0.326114 | − | 0.0958367i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −59.5037 | − | 5.68650i | −2.68810 | − | 0.256890i | ||||
\(491\) | 13.0613 | 0.589448 | 0.294724 | − | 0.955582i | \(-0.404772\pi\) | ||||
0.294724 | + | 0.955582i | \(0.404772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 27.2312 | 1.22643 | ||||||||
\(494\) | −5.15536 | + | 7.68713i | −0.231951 | + | 0.345860i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.40767 | + | 2.56751i | 0.287713 | + | 0.115285i | ||||
\(497\) | 46.9108i | 2.10424i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.12405 | 0.318916 | 0.159458 | − | 0.987205i | \(-0.449025\pi\) | ||||
0.159458 | + | 0.987205i | \(0.449025\pi\) | |||||||
\(500\) | −3.12977 | + | 16.2255i | −0.139967 | + | 0.725624i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.01754 | + | 42.0397i | −0.179312 | + | 1.87632i | ||||
\(503\) | − | 6.92730i | − | 0.308873i | −0.988003 | − | 0.154437i | \(-0.950644\pi\) | ||
0.988003 | − | 0.154437i | \(-0.0493562\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.266112 | 0.0118418 | ||||||||
\(506\) | 11.1385 | + | 1.06446i | 0.495167 | + | 0.0473209i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 24.5400 | + | 4.73359i | 1.08879 | + | 0.210019i | ||||
\(509\) | −5.92205 | −0.262490 | −0.131245 | − | 0.991350i | \(-0.541897\pi\) | ||||
−0.131245 | + | 0.991350i | \(0.541897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 34.4614i | 1.52448i | ||||||||
\(512\) | −17.1108 | + | 14.8061i | −0.756199 | + | 0.654342i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.954420 | + | 0.0912095i | 0.0420977 | + | 0.00402308i | ||||
\(515\) | − | 50.7252i | − | 2.23522i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.37288i | − | 0.104359i | ||||||
\(518\) | −69.7799 | − | 6.66854i | −3.06595 | − | 0.292999i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.6572 | − | 3.13188i | −0.467348 | − | 0.137342i | ||||
\(521\) | 16.9113i | 0.740898i | 0.928853 | + | 0.370449i | \(0.120796\pi\) | ||||
−0.928853 | + | 0.370449i | \(0.879204\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.3406i | − | 0.889434i | −0.895671 | − | 0.444717i | \(-0.853304\pi\) | ||
0.895671 | − | 0.444717i | \(-0.146696\pi\) | |||||||
\(524\) | 24.7083 | + | 4.76604i | 1.07939 | + | 0.208206i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.23611 | − | 0.404826i | −0.184703 | − | 0.0176512i | ||||
\(527\) | −9.16384 | −0.399183 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.8733 | 0.777098 | ||||||||
\(530\) | 37.0825 | + | 3.54380i | 1.61076 | + | 0.153933i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.5768 | + | 32.4628i | −1.15225 | + | 1.40744i | ||||
\(533\) | − | 5.86580i | − | 0.254076i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.33119 | −0.230488 | ||||||||
\(536\) | 20.0090 | + | 5.88014i | 0.864257 | + | 0.253984i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0.947196 | − | 9.91149i | 0.0408365 | − | 0.427315i | ||||
\(539\) | 56.4684 | 2.43227 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.8364i | − | 1.06780i | −0.845548 | − | 0.533900i | \(-0.820726\pi\) | ||
0.845548 | − | 0.533900i | \(-0.179274\pi\) | |||||||
\(542\) | 32.1300 | + | 3.07052i | 1.38010 | + | 0.131890i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.7747 | − | 26.6941i | 0.590583 | − | 1.14450i | ||||
\(545\) | − | 47.1642i | − | 2.02029i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 22.8518i | − | 0.977071i | −0.872544 | − | 0.488535i | \(-0.837531\pi\) | ||
0.872544 | − | 0.488535i | \(-0.162469\pi\) | |||||||
\(548\) | −2.59404 | − | 0.500370i | −0.110812 | − | 0.0213748i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.865532 | + | 9.05695i | −0.0369064 | + | 0.386190i | ||||
\(551\) | −19.6650 | − | 10.6279i | −0.837758 | − | 0.452762i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25.0733i | 1.06623i | ||||||||
\(554\) | 29.5617 | + | 2.82508i | 1.25596 | + | 0.120026i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.78234 | − | 0.536693i | −0.117998 | − | 0.0227609i | ||||
\(557\) | 5.88751i | 0.249462i | 0.992191 | + | 0.124731i | \(0.0398067\pi\) | ||||
−0.992191 | + | 0.124731i | \(0.960193\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.513737 | 0.0217288 | ||||||||
\(560\) | −46.7368 | − | 18.7271i | −1.97499 | − | 0.791366i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.08319 | + | 0.676908i | 0.298786 | + | 0.0285536i | ||||
\(563\) | − | 6.33319i | − | 0.266912i | −0.991055 | − | 0.133456i | \(-0.957393\pi\) | ||
0.991055 | − | 0.133456i | \(-0.0426075\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.4985 | 0.609959 | ||||||||
\(566\) | 0.168323 | − | 1.76134i | 0.00707515 | − | 0.0740346i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.77363 | + | 26.4522i | −0.326174 | + | 1.10991i | ||||
\(569\) | − | 19.8209i | − | 0.830937i | −0.909607 | − | 0.415469i | \(-0.863618\pi\) | ||
0.909607 | − | 0.415469i | \(-0.136382\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.3004 | −1.47728 | −0.738639 | − | 0.674101i | \(-0.764531\pi\) | ||||
−0.738639 | + | 0.674101i | \(0.764531\pi\) | |||||||
\(572\) | 10.3035 | + | 1.98747i | 0.430811 | + | 0.0831001i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.52939 | − | 26.4677i | 0.105575 | − | 1.10474i | ||||
\(575\) | − | 4.16866i | − | 0.173845i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4776 | 1.18554 | 0.592769 | − | 0.805373i | \(-0.298035\pi\) | ||||
0.592769 | + | 0.805373i | \(0.298035\pi\) | |||||||
\(578\) | −1.50646 | + | 15.7636i | −0.0626604 | + | 0.655681i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.08087 | − | 26.3404i | 0.210971 | − | 1.09373i | ||||
\(581\) | − | 23.1024i | − | 0.958448i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.1909 | −1.45746 | ||||||||
\(584\) | −5.71064 | + | 19.4322i | −0.236308 | + | 0.804111i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.49955 | − | 26.1554i | 0.103255 | − | 1.08047i | ||||
\(587\) | −28.0180 | −1.15643 | −0.578214 | − | 0.815885i | \(-0.696250\pi\) | ||||
−0.578214 | + | 0.815885i | \(0.696250\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.61767 | + | 3.57649i | 0.272676 | + | 0.147367i | ||||
\(590\) | −3.22002 | + | 33.6944i | −0.132566 | + | 1.38718i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −38.2426 | − | 15.3236i | −1.57176 | − | 0.629795i | ||||
\(593\) | 45.6450 | 1.87442 | 0.937208 | − | 0.348771i | \(-0.113401\pi\) | ||||
0.937208 | + | 0.348771i | \(0.113401\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 66.8399 | 2.74017 | ||||||||
\(596\) | −5.02993 | + | 26.0764i | −0.206034 | + | 1.06813i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.78612 | − | 0.457387i | −0.195719 | − | 0.0187040i | ||||
\(599\) | 20.9807 | 0.857248 | 0.428624 | − | 0.903483i | \(-0.358998\pi\) | ||||
0.428624 | + | 0.903483i | \(0.358998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.458660i | − | 0.0187091i | −0.999956 | − | 0.00935456i | \(-0.997022\pi\) | ||
0.999956 | − | 0.00935456i | \(-0.00297769\pi\) | |||||||
\(602\) | 2.31808 | + | 0.221528i | 0.0944780 | + | 0.00902883i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 31.9663 | + | 6.16607i | 1.30069 | + | 0.250894i | ||||
\(605\) | − | 3.16595i | − | 0.128714i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.1779 | 1.22488 | 0.612441 | − | 0.790516i | \(-0.290188\pi\) | ||||
0.612441 | + | 0.790516i | \(0.290188\pi\) | |||||||
\(608\) | −20.3656 | + | 13.9011i | −0.825935 | + | 0.563766i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.934169 | − | 9.77518i | 0.0378234 | − | 0.395785i | ||||
\(611\) | 1.01960i | 0.0412487i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 15.1288i | − | 0.611045i | −0.952185 | − | 0.305523i | \(-0.901169\pi\) | ||
0.952185 | − | 0.305523i | \(-0.0988311\pi\) | |||||||
\(614\) | 15.0742 | + | 1.44057i | 0.608343 | + | 0.0581366i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 45.6344 | + | 13.4108i | 1.83866 | + | 0.540337i | ||||
\(617\) | 3.05065 | 0.122815 | 0.0614073 | − | 0.998113i | \(-0.480441\pi\) | ||||
0.0614073 | + | 0.998113i | \(0.480441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14.3298 | −0.575962 | −0.287981 | − | 0.957636i | \(-0.592984\pi\) | ||||
−0.287981 | + | 0.957636i | \(0.592984\pi\) | |||||||
\(620\) | −1.70981 | + | 8.86407i | −0.0686677 | + | 0.355990i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.6070 | + | 1.77819i | 0.746073 | + | 0.0712987i | ||||
\(623\) | −67.8290 | −2.71751 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.8158 | −1.23263 | ||||||||
\(626\) | 4.36136 | − | 45.6374i | 0.174315 | − | 1.82404i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.96211 | − | 36.0932i | 0.277818 | − | 1.44028i | ||||
\(629\) | 54.6921 | 2.18072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.4416i | − | 0.455482i | −0.973722 | − | 0.227741i | \(-0.926866\pi\) | ||
0.973722 | − | 0.227741i | \(-0.0731340\pi\) | |||||||
\(632\) | −4.15493 | + | 14.1384i | −0.165274 | + | 0.562396i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.94899 | + | 20.3943i | −0.0774041 | + | 0.809960i | ||||
\(635\) | 32.6844i | 1.29704i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.2640 | −0.961374 | ||||||||
\(638\) | −2.41085 | + | 25.2272i | −0.0954463 | + | 0.998754i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −23.2508 | − | 18.3047i | −0.919067 | − | 0.723557i | ||||
\(641\) | − | 13.6910i | − | 0.540760i | −0.962754 | − | 0.270380i | \(-0.912851\pi\) | ||
0.962754 | − | 0.270380i | \(-0.0871494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 7.58609 | 0.299166 | 0.149583 | − | 0.988749i | \(-0.452207\pi\) | ||||
0.149583 | + | 0.988749i | \(0.452207\pi\) | |||||||
\(644\) | −21.3987 | − | 4.12764i | −0.843226 | − | 0.162652i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 18.2323 | − | 27.1861i | 0.717340 | − | 1.06962i | ||||
\(647\) | 27.2526i | 1.07141i | 0.844405 | + | 0.535705i | \(0.179954\pi\) | ||||
−0.844405 | + | 0.535705i | \(0.820046\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.9757i | − | 1.25516i | ||||||
\(650\) | 0.371911 | − | 3.89169i | 0.0145875 | − | 0.152645i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.2359 | + | 4.67493i | 0.949153 | + | 0.183084i | ||||
\(653\) | 3.86565i | 0.151274i | 0.997135 | + | 0.0756372i | \(0.0240991\pi\) | ||||
−0.997135 | + | 0.0756372i | \(0.975901\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 32.9085i | 1.28584i | ||||||||
\(656\) | 5.81226 | − | 14.5055i | 0.226931 | − | 0.566345i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.439663 | + | 4.60065i | −0.0171399 | + | 0.179352i | ||||
\(659\) | − | 33.7642i | − | 1.31527i | −0.753338 | − | 0.657633i | \(-0.771558\pi\) | ||
0.753338 | − | 0.657633i | \(-0.228442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.29497 | −0.283741 | −0.141871 | − | 0.989885i | \(-0.545312\pi\) | ||||
−0.141871 | + | 0.989885i | \(0.545312\pi\) | |||||||
\(662\) | 7.35841 | + | 0.703209i | 0.285993 | + | 0.0273310i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.82832 | − | 13.0270i | 0.148568 | − | 0.505547i | ||||
\(665\) | −48.2685 | − | 26.0865i | −1.87177 | − | 1.01159i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.6114i | − | 0.449594i | ||||||
\(668\) | −40.7651 | − | 7.86327i | −1.57725 | − | 0.304239i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.59461 | + | 27.1501i | −0.100238 | + | 1.04890i | ||||
\(671\) | 9.27655i | 0.358117i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.7118i | 0.798380i | 0.916868 | + | 0.399190i | \(0.130709\pi\) | ||||
−0.916868 | + | 0.399190i | \(0.869291\pi\) | |||||||
\(674\) | −25.6192 | − | 2.44831i | −0.986816 | − | 0.0943055i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 21.1021 | + | 4.07043i | 0.811618 | + | 0.156555i | ||||
\(677\) | −22.9317 | −0.881336 | −0.440668 | − | 0.897670i | \(-0.645258\pi\) | ||||
−0.440668 | + | 0.897670i | \(0.645258\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −63.8009 | −2.44846 | ||||||||
\(680\) | 37.6899 | + | 11.0761i | 1.44534 | + | 0.424750i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.811298 | − | 8.48945i | 0.0310662 | − | 0.325078i | ||||
\(683\) | 22.5142i | 0.861483i | 0.902475 | + | 0.430741i | \(0.141748\pi\) | ||||
−0.902475 | + | 0.430741i | \(0.858252\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.45495i | − | 0.132007i | ||||||
\(686\) | −62.0588 | − | 5.93068i | −2.36942 | − | 0.226434i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.27042 | + | 0.509048i | 0.0484342 | + | 0.0194073i | ||||
\(689\) | 15.1212 | 0.576073 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.4002 | −0.509766 | −0.254883 | − | 0.966972i | \(-0.582037\pi\) | ||||
−0.254883 | + | 0.966972i | \(0.582037\pi\) | |||||||
\(692\) | −1.34507 | − | 0.259453i | −0.0511318 | − | 0.00986293i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.27575 | + | 23.8135i | −0.0863861 | + | 0.903948i | ||||
\(695\) | − | 3.70575i | − | 0.140567i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.7448i | 0.785767i | ||||||||
\(698\) | −39.9485 | − | 3.81770i | −1.51207 | − | 0.144502i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.35627 | − | 17.3997i | 0.126855 | − | 0.657647i | ||||
\(701\) | − | 33.0858i | − | 1.24963i | −0.780772 | − | 0.624816i | \(-0.785174\pi\) | ||
0.780772 | − | 0.624816i | \(-0.214826\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −39.4959 | − | 21.3454i | −1.48962 | − | 0.805057i | ||||
\(704\) | 23.5101 | + | 15.1242i | 0.886070 | + | 0.570016i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.328213 | − | 3.43443i | 0.0123525 | − | 0.129257i | ||||
\(707\) | 0.489633 | 0.0184145 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 19.4606i | − | 0.730858i | −0.930839 | − | 0.365429i | \(-0.880922\pi\) | ||
0.930839 | − | 0.365429i | \(-0.119078\pi\) | |||||||
\(710\) | −35.8928 | − | 3.43011i | −1.34703 | − | 0.128730i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.2476 | − | 11.2400i | −1.43339 | − | 0.421237i | ||||
\(713\) | 3.90746i | 0.146335i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.7230i | 0.513212i | ||||||||
\(716\) | 7.10118 | − | 36.8142i | 0.265384 | − | 1.37581i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −34.6422 | − | 3.31059i | −1.29283 | − | 0.123550i | ||||
\(719\) | − | 32.5024i | − | 1.21213i | −0.795414 | − | 0.606067i | \(-0.792746\pi\) | ||
0.795414 | − | 0.606067i | \(-0.207254\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 93.3319i | − | 3.47586i | ||||||
\(722\) | −23.7767 | + | 12.5167i | −0.884878 | + | 0.465823i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.2434 | + | 4.48348i | 0.863834 | + | 0.166627i | ||||
\(725\) | 9.44144 | 0.350646 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.3190i | 0.419800i | 0.977723 | + | 0.209900i | \(0.0673139\pi\) | ||||
−0.977723 | + | 0.209900i | \(0.932686\pi\) | |||||||
\(728\) | −19.6087 | − | 5.76250i | −0.726746 | − | 0.213572i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −26.3675 | − | 2.51982i | −0.975903 | − | 0.0932626i | ||||
\(731\) | −1.81687 | −0.0671993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.7845i | 0.546079i | 0.962003 | + | 0.273040i | \(0.0880290\pi\) | ||||
−0.962003 | + | 0.273040i | \(0.911971\pi\) | |||||||
\(734\) | 26.7053 | + | 2.55210i | 0.985710 | + | 0.0941998i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.3823 | − | 5.87351i | −0.419559 | − | 0.216500i | ||||
\(737\) | − | 25.7652i | − | 0.949072i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.9300 | 1.24813 | 0.624067 | − | 0.781371i | \(-0.285479\pi\) | ||||
0.624067 | + | 0.781371i | \(0.285479\pi\) | |||||||
\(740\) | 10.2046 | − | 52.9030i | 0.375128 | − | 1.94475i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 68.2299 | + | 6.52042i | 2.50480 | + | 0.239372i | ||||
\(743\) | 14.5846 | 0.535056 | 0.267528 | − | 0.963550i | \(-0.413793\pi\) | ||||
0.267528 | + | 0.963550i | \(0.413793\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −34.7306 | −1.27243 | ||||||||
\(746\) | 2.74766 | − | 28.7516i | 0.100599 | − | 1.05267i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −36.4390 | − | 7.02882i | −1.33234 | − | 0.256999i | ||||
\(749\) | −9.80913 | −0.358418 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.8729 | −0.506229 | −0.253114 | − | 0.967436i | \(-0.581455\pi\) | ||||
−0.253114 | + | 0.967436i | \(0.581455\pi\) | |||||||
\(752\) | −1.01030 | + | 2.52137i | −0.0368418 | + | 0.0919449i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.03592 | − | 10.8399i | 0.0377259 | − | 0.394766i | ||||
\(755\) | 42.5754i | 1.54948i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.4956i | − | 0.490506i | −0.969459 | − | 0.245253i | \(-0.921129\pi\) | ||
0.969459 | − | 0.245253i | \(-0.0788710\pi\) | |||||||
\(758\) | −36.6664 | − | 3.50404i | −1.33178 | − | 0.127272i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −22.8949 | − | 22.7083i | −0.830487 | − | 0.823718i | ||||
\(761\) | −19.7088 | −0.714442 | −0.357221 | − | 0.934020i | \(-0.616276\pi\) | ||||
−0.357221 | + | 0.934020i | \(0.616276\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 86.7799i | − | 3.14164i | ||||||
\(764\) | −6.61430 | + | 34.2901i | −0.239297 | + | 1.24057i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.11184 | + | 32.5624i | −0.112435 | + | 1.17653i | ||||
\(767\) | 13.7397i | 0.496111i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8060 | 0.678163 | 0.339081 | − | 0.940757i | \(-0.389884\pi\) | ||||
0.339081 | + | 0.940757i | \(0.389884\pi\) | |||||||
\(770\) | −5.91751 | + | 61.9210i | −0.213252 | + | 2.23148i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.19499 | + | 21.7478i | −0.150981 | + | 0.782720i | ||||
\(773\) | −0.638576 | −0.0229680 | −0.0114840 | − | 0.999934i | \(-0.503656\pi\) | ||||
−0.0114840 | + | 0.999934i | \(0.503656\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.17723 | −0.114130 | ||||||||
\(776\) | −35.9762 | − | 10.5725i | −1.29147 | − | 0.379531i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.1889 | + | 2.31163i | 0.867215 | + | 0.0828758i | ||||
\(779\) | 8.09635 | − | 14.9809i | 0.290082 | − | 0.536746i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 34.0619 | 1.21883 | ||||||||
\(782\) | 16.9265 | + | 1.61758i | 0.605289 | + | 0.0578447i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −60.0022 | − | 24.0425i | −2.14294 | − | 0.858661i | ||||
\(785\) | 48.0719 | 1.71576 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.69613i | − | 0.203045i | −0.994833 | − | 0.101522i | \(-0.967629\pi\) | ||
0.994833 | − | 0.101522i | \(-0.0323714\pi\) | |||||||
\(788\) | −7.66824 | + | 39.7540i | −0.273170 | + | 1.41618i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −19.1843 | − | 1.83336i | −0.682548 | − | 0.0652280i | ||||
\(791\) | 26.6766 | 0.948511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 3.98605i | − | 0.141549i | ||||||
\(794\) | −39.9401 | − | 3.81689i | −1.41742 | − | 0.135456i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4.62020 | + | 23.9522i | −0.163759 | + | 0.848964i | ||||
\(797\) | 0.349816 | 0.0123911 | 0.00619557 | − | 0.999981i | \(-0.498028\pi\) | ||||
0.00619557 | + | 0.999981i | \(0.498028\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.60590i | − | 0.127568i | ||||||
\(800\) | 4.77587 | − | 9.25522i | 0.168852 | − | 0.327221i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.84114 | − | 0.844907i | −0.312191 | − | 0.0298347i | ||||
\(803\) | 25.0225 | 0.883024 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 28.5005i | − | 1.00451i | ||||||
\(806\) | −0.348607 | + | 3.64784i | −0.0122792 | + | 0.128490i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.276096 | + | 0.0811376i | 0.00971301 | + | 0.00285441i | ||||
\(809\) | −11.1848 | −0.393236 | −0.196618 | − | 0.980480i | \(-0.562996\pi\) | ||||
−0.196618 | + | 0.980480i | \(0.562996\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 11.3206i | − | 0.397520i | −0.980048 | − | 0.198760i | \(-0.936309\pi\) | ||
0.980048 | − | 0.198760i | \(-0.0636914\pi\) | |||||||
\(812\) | 9.34854 | − | 48.4650i | 0.328069 | − | 1.70079i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.84203 | + | 50.6672i | −0.169713 | + | 1.77588i | ||||
\(815\) | 32.2794i | 1.13070i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31205 | + | 0.709092i | 0.0459029 | + | 0.0248080i | ||||
\(818\) | −3.87480 | − | 0.370297i | −0.135479 | − | 0.0129471i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 20.0662 | + | 3.87062i | 0.700743 | + | 0.135168i | ||||
\(821\) | − | 16.9782i | − | 0.592542i | −0.955104 | − | 0.296271i | \(-0.904257\pi\) | ||
0.955104 | − | 0.296271i | \(-0.0957432\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 5.17146i | − | 0.180266i | −0.995930 | − | 0.0901329i | \(-0.971271\pi\) | ||
0.995930 | − | 0.0901329i | \(-0.0287292\pi\) | |||||||
\(824\) | 15.4661 | − | 52.6282i | 0.538788 | − | 1.83339i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.92468 | + | 61.9961i | −0.206146 | + | 2.15712i | ||||
\(827\) | − | 0.733529i | − | 0.0255073i | −0.999919 | − | 0.0127536i | \(-0.995940\pi\) | ||
0.999919 | − | 0.0127536i | \(-0.00405972\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.3783 | 0.638304 | 0.319152 | − | 0.947703i | \(-0.396602\pi\) | ||||
0.319152 | + | 0.947703i | \(0.396602\pi\) | |||||||
\(830\) | 17.6763 | + | 1.68924i | 0.613553 | + | 0.0586345i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.1021 | − | 6.49875i | −0.350226 | − | 0.225304i | ||||
\(833\) | 85.8113 | 2.97319 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 54.2942i | − | 1.87893i | ||||||
\(836\) | 23.5712 | + | 19.2974i | 0.815228 | + | 0.667414i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.48785 | + | 46.9610i | −0.155030 | + | 1.62224i | ||||
\(839\) | −37.9165 | −1.30902 | −0.654511 | − | 0.756052i | \(-0.727125\pi\) | ||||
−0.654511 | + | 0.756052i | \(0.727125\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.70187 | −0.0931678 | ||||||||
\(842\) | −0.124989 | + | 1.30789i | −0.00430739 | + | 0.0450727i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.25412 | − | 22.0543i | 0.146433 | − | 0.759142i | ||||
\(845\) | 28.1055i | 0.966858i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 5.82519i | − | 0.200156i | ||||||
\(848\) | 37.3932 | + | 14.9832i | 1.28409 | + | 0.514525i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.31529 | + | 13.7632i | −0.0451141 | + | 0.472075i | ||||
\(851\) | − | 23.3207i | − | 0.799423i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 46.5801i | 1.59487i | 0.603404 | + | 0.797436i | \(0.293811\pi\) | ||||
−0.603404 | + | 0.797436i | \(0.706189\pi\) | |||||||
\(854\) | 1.71883 | − | 17.9858i | 0.0588170 | − | 0.615463i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.53120 | − | 1.62548i | −0.189053 | − | 0.0555578i | ||||
\(857\) | 25.6585i | 0.876477i | 0.898859 | + | 0.438238i | \(0.144397\pi\) | ||||
−0.898859 | + | 0.438238i | \(0.855603\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.5918 | −0.531986 | −0.265993 | − | 0.963975i | \(-0.585700\pi\) | ||||
−0.265993 | + | 0.963975i | \(0.585700\pi\) | |||||||
\(860\) | −0.338996 | + | 1.75743i | −0.0115597 | + | 0.0599280i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.64087 | − | 48.5622i | 0.158069 | − | 1.65404i | ||||
\(863\) | 31.1083 | 1.05894 | 0.529470 | − | 0.848329i | \(-0.322391\pi\) | ||||
0.529470 | + | 0.848329i | \(0.322391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.79147i | − | 0.0609118i | ||||||
\(866\) | 35.0620 | + | 3.35072i | 1.19146 | + | 0.113862i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.14597 | + | 16.3094i | −0.106781 | + | 0.553579i | ||||
\(869\) | 18.2058 | 0.617588 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.0711i | 0.375128i | ||||||||
\(872\) | 14.3804 | − | 48.9337i | 0.486981 | − | 1.65710i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −11.5921 | − | 7.77424i | −0.392110 | − | 0.262968i | ||||
\(875\) | −39.7620 | −1.34420 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.487909 | −0.0164755 | −0.00823776 | − | 0.999966i | \(-0.502622\pi\) | ||||
−0.00823776 | + | 0.999966i | \(0.502622\pi\) | |||||||
\(878\) | 2.75962 | − | 28.8768i | 0.0931327 | − | 0.974544i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.5978 | + | 33.9356i | −0.458381 | + | 1.14397i | ||||
\(881\) | 13.5269 | 0.455732 | 0.227866 | − | 0.973693i | \(-0.426825\pi\) | ||||
0.227866 | + | 0.973693i | \(0.426825\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.7988 | 1.17107 | 0.585537 | − | 0.810646i | \(-0.300884\pi\) | ||||
0.585537 | + | 0.810646i | \(0.300884\pi\) | |||||||
\(884\) | 15.6575 | + | 3.02022i | 0.526619 | + | 0.101581i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.49592 | − | 36.5815i | 0.117448 | − | 1.22898i | ||||
\(887\) | −18.9849 | −0.637449 | −0.318725 | − | 0.947847i | \(-0.603255\pi\) | ||||
−0.318725 | + | 0.947847i | \(0.603255\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 60.1377i | 2.01696i | ||||||||
\(890\) | 4.95965 | − | 51.8979i | 0.166248 | − | 1.73962i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 11.5195 | + | 2.22202i | 0.385701 | + | 0.0743989i | ||||
\(893\) | −1.40732 | + | 2.60400i | −0.0470942 | + | 0.0871397i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 49.0321 | 1.63896 | ||||||||
\(896\) | −42.7802 | − | 33.6798i | −1.42919 | − | 1.12516i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 51.3574 | + | 4.90799i | 1.71382 | + | 0.163782i | ||||
\(899\) | −8.84984 | −0.295159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.4773 | −1.78159 | ||||||||
\(902\) | −19.2182 | − | 1.83659i | −0.639895 | − | 0.0611518i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 15.0425 | + | 4.42061i | 0.500305 | + | 0.147027i | ||||
\(905\) | 30.9574i | 1.02906i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.6905i | 0.687016i | 0.939150 | + | 0.343508i | \(0.111615\pi\) | ||||
−0.939150 | + | 0.343508i | \(0.888385\pi\) | |||||||
\(908\) | 5.22308 | − | 27.0777i | 0.173334 | − | 0.898603i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.54270 | − | 26.6069i | 0.0842896 | − | 0.882010i | ||||
\(911\) | 29.8333 | 0.988420 | 0.494210 | − | 0.869342i | \(-0.335457\pi\) | ||||
0.494210 | + | 0.869342i | \(0.335457\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.7746 | −0.555160 | ||||||||
\(914\) | −3.13161 | + | 32.7693i | −0.103584 | + | 1.08391i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.93920 | + | 15.2375i | −0.0971138 | + | 0.503461i | ||||
\(917\) | 60.5500i | 1.99954i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.6710i | 1.17668i | 0.808615 | + | 0.588338i | \(0.200218\pi\) | ||||
−0.808615 | + | 0.588338i | \(0.799782\pi\) | |||||||
\(920\) | 4.72285 | − | 16.0709i | 0.155708 | − | 0.529843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.1098 | + | 1.92180i | 0.662280 | + | 0.0632911i | ||||
\(923\) | −14.6361 | −0.481753 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.9625 | 0.623484 | ||||||||
\(926\) | 22.0005 | + | 2.10249i | 0.722981 | + | 0.0690920i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 13.3027 | − | 25.7794i | 0.436682 | − | 0.846251i | ||||
\(929\) | 5.05272 | 0.165774 | 0.0828872 | − | 0.996559i | \(-0.473586\pi\) | ||||
0.0828872 | + | 0.996559i | \(0.473586\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −61.9687 | − | 33.4907i | −2.03094 | − | 1.09761i | ||||
\(932\) | 46.2856 | + | 8.92814i | 1.51613 | + | 0.292451i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.16626 | + | 12.2038i | −0.0381612 | + | 0.399320i | ||||
\(935\) | − | 48.5325i | − | 1.58718i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.91078 | 0.193097 | 0.0965484 | − | 0.995328i | \(-0.469220\pi\) | ||||
0.0965484 | + | 0.995328i | \(0.469220\pi\) | |||||||
\(938\) | −4.77395 | + | 49.9548i | −0.155875 | + | 1.63108i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.48794 | − | 0.672798i | −0.113764 | − | 0.0219443i | ||||
\(941\) | 19.2287 | 0.626837 | 0.313418 | − | 0.949615i | \(-0.398526\pi\) | ||||
0.313418 | + | 0.949615i | \(0.398526\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.84559 | 0.288052 | ||||||||
\(944\) | −13.6143 | + | 33.9767i | −0.443107 | + | 1.10585i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.160852 | − | 1.68316i | 0.00522975 | − | 0.0547243i | ||||
\(947\) | −26.5034 | −0.861245 | −0.430623 | − | 0.902532i | \(-0.641706\pi\) | ||||
−0.430623 | + | 0.902532i | \(0.641706\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.7519 | −0.349022 | ||||||||
\(950\) | 6.32140 | − | 9.42580i | 0.205093 | − | 0.305813i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 69.3475 | + | 20.3795i | 2.24757 | + | 0.660504i | ||||
\(953\) | 37.0464i | 1.20005i | 0.799981 | + | 0.600025i | \(0.204843\pi\) | ||||
−0.799981 | + | 0.600025i | \(0.795157\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −45.6703 | −1.47786 | ||||||||
\(956\) | −5.06345 | + | 26.2501i | −0.163764 | + | 0.848990i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −4.80409 | − | 0.459105i | −0.155213 | − | 0.0148330i | ||||
\(959\) | − | 6.35694i | − | 0.205276i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.0219 | −0.903931 | ||||||||
\(962\) | 2.08058 | − | 21.7712i | 0.0670805 | − | 0.701932i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −7.56095 | + | 39.1978i | −0.243522 | + | 1.26247i | ||||
\(965\) | −28.9655 | −0.932432 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.4739i | − | 1.59097i | −0.605970 | − | 0.795487i | \(-0.707215\pi\) | ||
0.605970 | − | 0.795487i | \(-0.292785\pi\) | |||||||
\(968\) | 0.965299 | − | 3.28472i | 0.0310259 | − | 0.105575i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.66512 | − | 48.8159i | 0.149788 | − | 1.56739i | ||||
\(971\) | − | 13.1840i | − | 0.423095i | −0.977368 | − | 0.211548i | \(-0.932150\pi\) | ||
0.977368 | − | 0.211548i | \(-0.0678503\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6.81840i | − | 0.218588i | ||||||
\(974\) | −5.62521 | + | 58.8624i | −0.180243 | + | 1.88607i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.94967 | − | 9.85708i | 0.126426 | − | 0.315517i | ||||
\(977\) | 28.8518i | 0.923049i | 0.887127 | + | 0.461525i | \(0.152697\pi\) | ||||
−0.887127 | + | 0.461525i | \(0.847303\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49.2506i | 1.57406i | ||||||||
\(980\) | 16.0109 | − | 83.0042i | 0.511449 | − | 2.65147i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.75723 | + | 18.3877i | −0.0560754 | + | 0.586775i | ||||
\(983\) | −9.02606 | −0.287887 | −0.143943 | − | 0.989586i | \(-0.545978\pi\) | ||||
−0.143943 | + | 0.989586i | \(0.545978\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −52.9476 | −1.68705 | ||||||||
\(986\) | −3.66360 | + | 38.3361i | −0.116673 | + | 1.22087i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.1283 | − | 8.29191i | −0.322226 | − | 0.263801i | ||||
\(989\) | 0.774712i | 0.0246344i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9609 | −0.411717 | −0.205858 | − | 0.978582i | \(-0.565999\pi\) | ||||
−0.205858 | + | 0.978582i | \(0.565999\pi\) | |||||||
\(992\) | −4.47661 | + | 8.67529i | −0.142133 | + | 0.275441i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −66.0410 | − | 6.31123i | −2.09469 | − | 0.200180i | ||||
\(995\) | −31.9015 | −1.01135 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.01059i | 0.158687i | 0.996847 | + | 0.0793435i | \(0.0252824\pi\) | ||||
−0.996847 | + | 0.0793435i | \(0.974718\pi\) | |||||||
\(998\) | −0.958448 | + | 10.0292i | −0.0303391 | + | 0.317470i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1368.2.e.g.379.20 | 40 | ||
3.2 | odd | 2 | 456.2.e.a.379.21 | yes | 40 | ||
4.3 | odd | 2 | 5472.2.e.g.5167.33 | 40 | |||
8.3 | odd | 2 | inner | 1368.2.e.g.379.22 | 40 | ||
8.5 | even | 2 | 5472.2.e.g.5167.4 | 40 | |||
12.11 | even | 2 | 1824.2.e.a.1519.37 | 40 | |||
19.18 | odd | 2 | inner | 1368.2.e.g.379.21 | 40 | ||
24.5 | odd | 2 | 1824.2.e.a.1519.7 | 40 | |||
24.11 | even | 2 | 456.2.e.a.379.19 | ✓ | 40 | ||
57.56 | even | 2 | 456.2.e.a.379.20 | yes | 40 | ||
76.75 | even | 2 | 5472.2.e.g.5167.3 | 40 | |||
152.37 | odd | 2 | 5472.2.e.g.5167.34 | 40 | |||
152.75 | even | 2 | inner | 1368.2.e.g.379.19 | 40 | ||
228.227 | odd | 2 | 1824.2.e.a.1519.8 | 40 | |||
456.227 | odd | 2 | 456.2.e.a.379.22 | yes | 40 | ||
456.341 | even | 2 | 1824.2.e.a.1519.38 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
456.2.e.a.379.19 | ✓ | 40 | 24.11 | even | 2 | ||
456.2.e.a.379.20 | yes | 40 | 57.56 | even | 2 | ||
456.2.e.a.379.21 | yes | 40 | 3.2 | odd | 2 | ||
456.2.e.a.379.22 | yes | 40 | 456.227 | odd | 2 | ||
1368.2.e.g.379.19 | 40 | 152.75 | even | 2 | inner | ||
1368.2.e.g.379.20 | 40 | 1.1 | even | 1 | trivial | ||
1368.2.e.g.379.21 | 40 | 19.18 | odd | 2 | inner | ||
1368.2.e.g.379.22 | 40 | 8.3 | odd | 2 | inner | ||
1824.2.e.a.1519.7 | 40 | 24.5 | odd | 2 | |||
1824.2.e.a.1519.8 | 40 | 228.227 | odd | 2 | |||
1824.2.e.a.1519.37 | 40 | 12.11 | even | 2 | |||
1824.2.e.a.1519.38 | 40 | 456.341 | even | 2 | |||
5472.2.e.g.5167.3 | 40 | 76.75 | even | 2 | |||
5472.2.e.g.5167.4 | 40 | 8.5 | even | 2 | |||
5472.2.e.g.5167.33 | 40 | 4.3 | odd | 2 | |||
5472.2.e.g.5167.34 | 40 | 152.37 | odd | 2 |