Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (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: | \(9.22272143346\) |
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: | \( x^{16} + x^{14} - 4x^{12} - 49x^{10} + 11x^{8} + 395x^{6} + 900x^{4} + 1125x^{2} + 625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.10 | ||
Root | \(0.917186 + 1.66637i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.c.76.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.474903i | 0.335807i | 0.985803 | + | 0.167904i | \(0.0536997\pi\) | ||||
−0.985803 | + | 0.167904i | \(0.946300\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.77447 | 0.887234 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −0.474903 | −0.193878 | ||||||||
\(7\) | 0.474903 | + | 2.60278i | 0.179496 | + | 0.983759i | ||||
\(8\) | 1.79251i | 0.633746i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0.474903 | 0.150177 | ||||||||
\(11\) | 3.23607 | + | 0.726543i | 0.975711 | + | 0.219061i | ||||
\(12\) | 1.77447i | 0.512245i | ||||||||
\(13\) | −0.814323 | −0.225853 | −0.112926 | − | 0.993603i | \(-0.536022\pi\) | ||||
−0.112926 | + | 0.993603i | \(0.536022\pi\) | |||||||
\(14\) | −1.23607 | + | 0.225533i | −0.330353 | + | 0.0602762i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.69767 | 0.674417 | ||||||||
\(17\) | 6.40701 | 1.55393 | 0.776964 | − | 0.629545i | \(-0.216759\pi\) | ||||
0.776964 | + | 0.629545i | \(0.216759\pi\) | |||||||
\(18\) | − | 0.474903i | − | 0.111936i | ||||||
\(19\) | −4.95392 | −1.13651 | −0.568254 | − | 0.822853i | \(-0.692381\pi\) | ||||
−0.568254 | + | 0.822853i | \(0.692381\pi\) | |||||||
\(20\) | − | 1.77447i | − | 0.396783i | ||||||
\(21\) | −2.60278 | + | 0.474903i | −0.567973 | + | 0.103632i | ||||
\(22\) | −0.345037 | + | 1.53682i | −0.0735622 | + | 0.327651i | ||||
\(23\) | −0.774467 | −0.161488 | −0.0807438 | − | 0.996735i | \(-0.525730\pi\) | ||||
−0.0807438 | + | 0.996735i | \(0.525730\pi\) | |||||||
\(24\) | −1.79251 | −0.365894 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | − | 0.386724i | − | 0.0758429i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0.842700 | + | 4.61855i | 0.159255 | + | 0.872824i | ||||
\(29\) | 2.51905i | 0.467775i | 0.972264 | + | 0.233888i | \(0.0751448\pi\) | ||||
−0.972264 | + | 0.233888i | \(0.924855\pi\) | |||||||
\(30\) | 0.474903i | 0.0867050i | ||||||||
\(31\) | − | 5.42943i | − | 0.975154i | −0.873080 | − | 0.487577i | \(-0.837881\pi\) | ||
0.873080 | − | 0.487577i | \(-0.162119\pi\) | |||||||
\(32\) | 4.86614i | 0.860220i | ||||||||
\(33\) | −0.726543 | + | 3.23607i | −0.126475 | + | 0.563327i | ||||
\(34\) | 3.04271i | 0.521820i | ||||||||
\(35\) | 2.60278 | − | 0.474903i | 0.439950 | − | 0.0802732i | ||||
\(36\) | −1.77447 | −0.295745 | ||||||||
\(37\) | −5.42943 | −0.892593 | −0.446296 | − | 0.894885i | \(-0.647257\pi\) | ||||
−0.446296 | + | 0.894885i | \(0.647257\pi\) | |||||||
\(38\) | − | 2.35263i | − | 0.381647i | ||||||
\(39\) | − | 0.814323i | − | 0.130396i | ||||||
\(40\) | 1.79251 | 0.283420 | ||||||||
\(41\) | 2.77069 | 0.432709 | 0.216354 | − | 0.976315i | \(-0.430583\pi\) | ||||
0.216354 | + | 0.976315i | \(0.430583\pi\) | |||||||
\(42\) | −0.225533 | − | 1.23607i | −0.0348005 | − | 0.190729i | ||||
\(43\) | 6.55058i | 0.998955i | 0.866327 | + | 0.499477i | \(0.166475\pi\) | ||||
−0.866327 | + | 0.499477i | \(0.833525\pi\) | |||||||
\(44\) | 5.74230 | + | 1.28923i | 0.865684 | + | 0.194358i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − | 0.367797i | − | 0.0542287i | ||||||
\(47\) | 4.57057i | 0.666686i | 0.942806 | + | 0.333343i | \(0.108177\pi\) | ||||
−0.942806 | + | 0.333343i | \(0.891823\pi\) | |||||||
\(48\) | 2.69767i | 0.389375i | ||||||||
\(49\) | −6.54893 | + | 2.47214i | −0.935562 | + | 0.353162i | ||||
\(50\) | − | 0.474903i | − | 0.0671614i | ||||||
\(51\) | 6.40701i | 0.897160i | ||||||||
\(52\) | −1.44499 | −0.200384 | ||||||||
\(53\) | 9.63333 | 1.32324 | 0.661620 | − | 0.749840i | \(-0.269869\pi\) | ||||
0.661620 | + | 0.749840i | \(0.269869\pi\) | |||||||
\(54\) | 0.474903 | 0.0646261 | ||||||||
\(55\) | 0.726543 | − | 3.23607i | 0.0979670 | − | 0.436351i | ||||
\(56\) | −4.66550 | + | 0.851266i | −0.623453 | + | 0.113755i | ||||
\(57\) | − | 4.95392i | − | 0.656163i | ||||||
\(58\) | −1.19630 | −0.157082 | ||||||||
\(59\) | − | 3.34504i | − | 0.435487i | −0.976006 | − | 0.217743i | \(-0.930130\pi\) | ||
0.976006 | − | 0.217743i | \(-0.0698696\pi\) | |||||||
\(60\) | 1.77447 | 0.229083 | ||||||||
\(61\) | −8.03565 | −1.02886 | −0.514430 | − | 0.857532i | \(-0.671996\pi\) | ||||
−0.514430 | + | 0.857532i | \(0.671996\pi\) | |||||||
\(62\) | 2.57845 | 0.327464 | ||||||||
\(63\) | −0.474903 | − | 2.60278i | −0.0598321 | − | 0.327920i | ||||
\(64\) | 3.08439 | 0.385549 | ||||||||
\(65\) | 0.814323i | 0.101004i | ||||||||
\(66\) | −1.53682 | − | 0.345037i | −0.189169 | − | 0.0424711i | ||||
\(67\) | 16.0211 | 1.95729 | 0.978643 | − | 0.205569i | \(-0.0659045\pi\) | ||||
0.978643 | + | 0.205569i | \(0.0659045\pi\) | |||||||
\(68\) | 11.3690 | 1.37870 | ||||||||
\(69\) | − | 0.774467i | − | 0.0932349i | ||||||
\(70\) | 0.225533 | + | 1.23607i | 0.0269563 | + | 0.147738i | ||||
\(71\) | −3.04271 | −0.361103 | −0.180551 | − | 0.983566i | \(-0.557788\pi\) | ||||
−0.180551 | + | 0.983566i | \(0.557788\pi\) | |||||||
\(72\) | − | 1.79251i | − | 0.211249i | ||||||
\(73\) | −9.23710 | −1.08112 | −0.540560 | − | 0.841305i | \(-0.681788\pi\) | ||||
−0.540560 | + | 0.841305i | \(0.681788\pi\) | |||||||
\(74\) | − | 2.57845i | − | 0.299739i | ||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −8.79057 | −1.00835 | ||||||||
\(77\) | −0.354213 | + | 8.76781i | −0.0403663 | + | 0.999185i | ||||
\(78\) | 0.386724 | 0.0437879 | ||||||||
\(79\) | − | 7.97625i | − | 0.897398i | −0.893683 | − | 0.448699i | \(-0.851888\pi\) | ||
0.893683 | − | 0.448699i | \(-0.148112\pi\) | |||||||
\(80\) | − | 2.69767i | − | 0.301609i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.31581i | 0.145307i | ||||||||
\(83\) | 6.58257 | 0.722531 | 0.361265 | − | 0.932463i | \(-0.382345\pi\) | ||||
0.361265 | + | 0.932463i | \(0.382345\pi\) | |||||||
\(84\) | −4.61855 | + | 0.842700i | −0.503925 | + | 0.0919461i | ||||
\(85\) | − | 6.40701i | − | 0.694937i | ||||||
\(86\) | −3.11089 | −0.335456 | ||||||||
\(87\) | −2.51905 | −0.270070 | ||||||||
\(88\) | −1.30233 | + | 5.80067i | −0.138829 | + | 0.618353i | ||||
\(89\) | 1.12710i | 0.119472i | 0.998214 | + | 0.0597361i | \(0.0190259\pi\) | ||||
−0.998214 | + | 0.0597361i | \(0.980974\pi\) | |||||||
\(90\) | −0.474903 | −0.0500592 | ||||||||
\(91\) | −0.386724 | − | 2.11950i | −0.0405397 | − | 0.222184i | ||||
\(92\) | −1.37427 | −0.143277 | ||||||||
\(93\) | 5.42943 | 0.563006 | ||||||||
\(94\) | −2.17058 | −0.223878 | ||||||||
\(95\) | 4.95392i | 0.508262i | ||||||||
\(96\) | −4.86614 | −0.496648 | ||||||||
\(97\) | 12.2039i | 1.23912i | 0.784950 | + | 0.619559i | \(0.212689\pi\) | ||||
−0.784950 | + | 0.619559i | \(0.787311\pi\) | |||||||
\(98\) | −1.17402 | − | 3.11011i | −0.118594 | − | 0.314168i | ||||
\(99\) | −3.23607 | − | 0.726543i | −0.325237 | − | 0.0730203i | ||||
\(100\) | −1.77447 | −0.177447 | ||||||||
\(101\) | −6.15537 | −0.612482 | −0.306241 | − | 0.951954i | \(-0.599071\pi\) | ||||
−0.306241 | + | 0.951954i | \(0.599071\pi\) | |||||||
\(102\) | −3.04271 | −0.301273 | ||||||||
\(103\) | 1.57816i | 0.155501i | 0.996973 | + | 0.0777506i | \(0.0247738\pi\) | ||||
−0.996973 | + | 0.0777506i | \(0.975226\pi\) | |||||||
\(104\) | − | 1.45968i | − | 0.143133i | ||||||
\(105\) | 0.474903 | + | 2.60278i | 0.0463458 | + | 0.254005i | ||||
\(106\) | 4.57489i | 0.444353i | ||||||||
\(107\) | − | 6.29895i | − | 0.608942i | −0.952522 | − | 0.304471i | \(-0.901520\pi\) | ||
0.952522 | − | 0.304471i | \(-0.0984797\pi\) | |||||||
\(108\) | − | 1.77447i | − | 0.170748i | ||||||
\(109\) | − | 8.92605i | − | 0.854961i | −0.904025 | − | 0.427480i | \(-0.859401\pi\) | ||
0.904025 | − | 0.427480i | \(-0.140599\pi\) | |||||||
\(110\) | 1.53682 | + | 0.345037i | 0.146530 | + | 0.0328980i | ||||
\(111\) | − | 5.42943i | − | 0.515339i | ||||||
\(112\) | 1.28113 | + | 7.02144i | 0.121055 | + | 0.663464i | ||||
\(113\) | −9.46454 | −0.890349 | −0.445175 | − | 0.895444i | \(-0.646858\pi\) | ||||
−0.445175 | + | 0.895444i | \(0.646858\pi\) | |||||||
\(114\) | 2.35263 | 0.220344 | ||||||||
\(115\) | 0.774467i | 0.0722194i | ||||||||
\(116\) | 4.46997i | 0.415026i | ||||||||
\(117\) | 0.814323 | 0.0752842 | ||||||||
\(118\) | 1.58857 | 0.146240 | ||||||||
\(119\) | 3.04271 | + | 16.6760i | 0.278924 | + | 1.52869i | ||||
\(120\) | 1.79251i | 0.163633i | ||||||||
\(121\) | 9.94427 | + | 4.70228i | 0.904025 | + | 0.427480i | ||||
\(122\) | − | 3.81615i | − | 0.345498i | ||||||
\(123\) | 2.77069i | 0.249824i | ||||||||
\(124\) | − | 9.63435i | − | 0.865190i | ||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 1.23607 | − | 0.225533i | 0.110118 | − | 0.0200921i | ||||
\(127\) | − | 1.51249i | − | 0.134212i | −0.997746 | − | 0.0671059i | \(-0.978623\pi\) | ||
0.997746 | − | 0.0671059i | \(-0.0213765\pi\) | |||||||
\(128\) | 11.1971i | 0.989690i | ||||||||
\(129\) | −6.55058 | −0.576747 | ||||||||
\(130\) | −0.386724 | −0.0339180 | ||||||||
\(131\) | 9.19702 | 0.803547 | 0.401774 | − | 0.915739i | \(-0.368394\pi\) | ||||
0.401774 | + | 0.915739i | \(0.368394\pi\) | |||||||
\(132\) | −1.28923 | + | 5.74230i | −0.112213 | + | 0.499803i | ||||
\(133\) | −2.35263 | − | 12.8940i | −0.203999 | − | 1.11805i | ||||
\(134\) | 7.60845i | 0.657270i | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | 11.4846i | 0.984796i | ||||||||
\(137\) | −12.7263 | −1.08728 | −0.543642 | − | 0.839317i | \(-0.682955\pi\) | ||||
−0.543642 | + | 0.839317i | \(0.682955\pi\) | |||||||
\(138\) | 0.367797 | 0.0313089 | ||||||||
\(139\) | −10.6902 | −0.906730 | −0.453365 | − | 0.891325i | \(-0.649776\pi\) | ||||
−0.453365 | + | 0.891325i | \(0.649776\pi\) | |||||||
\(140\) | 4.61855 | − | 0.842700i | 0.390339 | − | 0.0712211i | ||||
\(141\) | −4.57057 | −0.384911 | ||||||||
\(142\) | − | 1.44499i | − | 0.121261i | ||||||
\(143\) | −2.63520 | − | 0.591640i | −0.220367 | − | 0.0494755i | ||||
\(144\) | −2.69767 | −0.224806 | ||||||||
\(145\) | 2.51905 | 0.209196 | ||||||||
\(146\) | − | 4.38672i | − | 0.363048i | ||||||
\(147\) | −2.47214 | − | 6.54893i | −0.203898 | − | 0.540147i | ||||
\(148\) | −9.63435 | −0.791938 | ||||||||
\(149\) | − | 3.07364i | − | 0.251802i | −0.992043 | − | 0.125901i | \(-0.959818\pi\) | ||
0.992043 | − | 0.125901i | \(-0.0401822\pi\) | |||||||
\(150\) | 0.474903 | 0.0387757 | ||||||||
\(151\) | − | 9.28384i | − | 0.755509i | −0.925906 | − | 0.377754i | \(-0.876696\pi\) | ||
0.925906 | − | 0.377754i | \(-0.123304\pi\) | |||||||
\(152\) | − | 8.87993i | − | 0.720257i | ||||||
\(153\) | −6.40701 | −0.517976 | ||||||||
\(154\) | −4.16386 | − | 0.168217i | −0.335533 | − | 0.0135553i | ||||
\(155\) | −5.42943 | −0.436102 | ||||||||
\(156\) | − | 1.44499i | − | 0.115692i | ||||||
\(157\) | − | 22.6971i | − | 1.81143i | −0.423891 | − | 0.905713i | \(-0.639336\pi\) | ||
0.423891 | − | 0.905713i | \(-0.360664\pi\) | |||||||
\(158\) | 3.78794 | 0.301353 | ||||||||
\(159\) | 9.63333i | 0.763973i | ||||||||
\(160\) | 4.86614 | 0.384702 | ||||||||
\(161\) | −0.367797 | − | 2.01577i | −0.0289864 | − | 0.158865i | ||||
\(162\) | 0.474903i | 0.0373119i | ||||||||
\(163\) | 1.19630 | 0.0937017 | 0.0468508 | − | 0.998902i | \(-0.485081\pi\) | ||||
0.0468508 | + | 0.998902i | \(0.485081\pi\) | |||||||
\(164\) | 4.91649 | 0.383914 | ||||||||
\(165\) | 3.23607 | + | 0.726543i | 0.251928 | + | 0.0565613i | ||||
\(166\) | 3.12608i | 0.242631i | ||||||||
\(167\) | 20.0947 | 1.55498 | 0.777489 | − | 0.628896i | \(-0.216493\pi\) | ||||
0.777489 | + | 0.628896i | \(0.216493\pi\) | |||||||
\(168\) | −0.851266 | − | 4.66550i | −0.0656766 | − | 0.359951i | ||||
\(169\) | −12.3369 | −0.948991 | ||||||||
\(170\) | 3.04271 | 0.233365 | ||||||||
\(171\) | 4.95392 | 0.378836 | ||||||||
\(172\) | 11.6238i | 0.886306i | ||||||||
\(173\) | −14.0429 | −1.06766 | −0.533830 | − | 0.845592i | \(-0.679248\pi\) | ||||
−0.533830 | + | 0.845592i | \(0.679248\pi\) | |||||||
\(174\) | − | 1.19630i | − | 0.0906915i | ||||||
\(175\) | −0.474903 | − | 2.60278i | −0.0358993 | − | 0.196752i | ||||
\(176\) | 8.72984 | + | 1.95997i | 0.658036 | + | 0.147738i | ||||
\(177\) | 3.34504 | 0.251428 | ||||||||
\(178\) | −0.535262 | −0.0401196 | ||||||||
\(179\) | 3.88638 | 0.290481 | 0.145241 | − | 0.989396i | \(-0.453604\pi\) | ||||
0.145241 | + | 0.989396i | \(0.453604\pi\) | |||||||
\(180\) | 1.77447i | 0.132261i | ||||||||
\(181\) | − | 4.60466i | − | 0.342262i | −0.985248 | − | 0.171131i | \(-0.945258\pi\) | ||
0.985248 | − | 0.171131i | \(-0.0547421\pi\) | |||||||
\(182\) | 1.00656 | − | 0.183657i | 0.0746111 | − | 0.0136135i | ||||
\(183\) | − | 8.03565i | − | 0.594013i | ||||||
\(184\) | − | 1.38824i | − | 0.102342i | ||||||
\(185\) | 5.42943i | 0.399180i | ||||||||
\(186\) | 2.57845i | 0.189061i | ||||||||
\(187\) | 20.7335 | + | 4.65496i | 1.51618 | + | 0.340405i | ||||
\(188\) | 8.11033i | 0.591506i | ||||||||
\(189\) | 2.60278 | − | 0.474903i | 0.189324 | − | 0.0345441i | ||||
\(190\) | −2.35263 | −0.170678 | ||||||||
\(191\) | 14.1747 | 1.02564 | 0.512821 | − | 0.858495i | \(-0.328600\pi\) | ||||
0.512821 | + | 0.858495i | \(0.328600\pi\) | |||||||
\(192\) | 3.08439i | 0.222597i | ||||||||
\(193\) | − | 0.949806i | − | 0.0683685i | −0.999416 | − | 0.0341843i | \(-0.989117\pi\) | ||
0.999416 | − | 0.0341843i | \(-0.0108833\pi\) | |||||||
\(194\) | −5.79567 | −0.416105 | ||||||||
\(195\) | −0.814323 | −0.0583149 | ||||||||
\(196\) | −11.6209 | + | 4.38672i | −0.830062 | + | 0.313337i | ||||
\(197\) | − | 14.1068i | − | 1.00507i | −0.864557 | − | 0.502536i | \(-0.832401\pi\) | ||
0.864557 | − | 0.502536i | \(-0.167599\pi\) | |||||||
\(198\) | 0.345037 | − | 1.53682i | 0.0245207 | − | 0.109217i | ||||
\(199\) | − | 3.30993i | − | 0.234634i | −0.993094 | − | 0.117317i | \(-0.962571\pi\) | ||
0.993094 | − | 0.117317i | \(-0.0374294\pi\) | |||||||
\(200\) | − | 1.79251i | − | 0.126749i | ||||||
\(201\) | 16.0211i | 1.13004i | ||||||||
\(202\) | − | 2.92320i | − | 0.205676i | ||||||
\(203\) | −6.55653 | + | 1.19630i | −0.460178 | + | 0.0839640i | ||||
\(204\) | 11.3690i | 0.795991i | ||||||||
\(205\) | − | 2.77069i | − | 0.193513i | ||||||
\(206\) | −0.749475 | −0.0522184 | ||||||||
\(207\) | 0.774467 | 0.0538292 | ||||||||
\(208\) | −2.19677 | −0.152319 | ||||||||
\(209\) | −16.0312 | − | 3.59923i | −1.10890 | − | 0.248964i | ||||
\(210\) | −1.23607 | + | 0.225533i | −0.0852968 | + | 0.0155632i | ||||
\(211\) | − | 26.5392i | − | 1.82703i | −0.406802 | − | 0.913516i | \(-0.633356\pi\) | ||
0.406802 | − | 0.913516i | \(-0.366644\pi\) | |||||||
\(212\) | 17.0940 | 1.17402 | ||||||||
\(213\) | − | 3.04271i | − | 0.208483i | ||||||
\(214\) | 2.99139 | 0.204487 | ||||||||
\(215\) | 6.55058 | 0.446746 | ||||||||
\(216\) | 1.79251 | 0.121965 | ||||||||
\(217\) | 14.1316 | − | 2.57845i | 0.959317 | − | 0.175037i | ||||
\(218\) | 4.23901 | 0.287102 | ||||||||
\(219\) | − | 9.23710i | − | 0.624185i | ||||||
\(220\) | 1.28923 | − | 5.74230i | 0.0869196 | − | 0.387146i | ||||
\(221\) | −5.21737 | −0.350959 | ||||||||
\(222\) | 2.57845 | 0.173054 | ||||||||
\(223\) | 12.6760i | 0.848850i | 0.905463 | + | 0.424425i | \(0.139524\pi\) | ||||
−0.905463 | + | 0.424425i | \(0.860476\pi\) | |||||||
\(224\) | −12.6655 | + | 2.31094i | −0.846249 | + | 0.154406i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | − | 4.49474i | − | 0.298986i | ||||||
\(227\) | 22.8060 | 1.51369 | 0.756845 | − | 0.653595i | \(-0.226740\pi\) | ||||
0.756845 | + | 0.653595i | \(0.226740\pi\) | |||||||
\(228\) | − | 8.79057i | − | 0.582170i | ||||||
\(229\) | 15.2326i | 1.00660i | 0.864113 | + | 0.503298i | \(0.167880\pi\) | ||||
−0.864113 | + | 0.503298i | \(0.832120\pi\) | |||||||
\(230\) | −0.367797 | −0.0242518 | ||||||||
\(231\) | −8.76781 | − | 0.354213i | −0.576880 | − | 0.0233055i | ||||
\(232\) | −4.51541 | −0.296451 | ||||||||
\(233\) | − | 19.5595i | − | 1.28138i | −0.767798 | − | 0.640692i | \(-0.778647\pi\) | ||
0.767798 | − | 0.640692i | \(-0.221353\pi\) | |||||||
\(234\) | 0.386724i | 0.0252810i | ||||||||
\(235\) | 4.57057 | 0.298151 | ||||||||
\(236\) | − | 5.93566i | − | 0.386378i | ||||||
\(237\) | 7.97625 | 0.518113 | ||||||||
\(238\) | −7.91950 | + | 1.44499i | −0.513345 | + | 0.0936648i | ||||
\(239\) | − | 23.6204i | − | 1.52787i | −0.645291 | − | 0.763937i | \(-0.723264\pi\) | ||
0.645291 | − | 0.763937i | \(-0.276736\pi\) | |||||||
\(240\) | 2.69767 | 0.174134 | ||||||||
\(241\) | 27.7113 | 1.78504 | 0.892521 | − | 0.451006i | \(-0.148935\pi\) | ||||
0.892521 | + | 0.451006i | \(0.148935\pi\) | |||||||
\(242\) | −2.23313 | + | 4.72256i | −0.143551 | + | 0.303578i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −14.2590 | −0.912839 | ||||||||
\(245\) | 2.47214 | + | 6.54893i | 0.157939 | + | 0.418396i | ||||
\(246\) | −1.31581 | −0.0838928 | ||||||||
\(247\) | 4.03409 | 0.256683 | ||||||||
\(248\) | 9.73228 | 0.618001 | ||||||||
\(249\) | 6.58257i | 0.417153i | ||||||||
\(250\) | −0.474903 | −0.0300355 | ||||||||
\(251\) | − | 20.4289i | − | 1.28946i | −0.764411 | − | 0.644729i | \(-0.776970\pi\) | ||
0.764411 | − | 0.644729i | \(-0.223030\pi\) | |||||||
\(252\) | −0.842700 | − | 4.61855i | −0.0530851 | − | 0.290941i | ||||
\(253\) | −2.50623 | − | 0.562683i | −0.157565 | − | 0.0353756i | ||||
\(254\) | 0.718285 | 0.0450692 | ||||||||
\(255\) | 6.40701 | 0.401222 | ||||||||
\(256\) | 0.851266 | 0.0532041 | ||||||||
\(257\) | − | 20.2883i | − | 1.26555i | −0.774336 | − | 0.632774i | \(-0.781916\pi\) | ||
0.774336 | − | 0.632774i | \(-0.218084\pi\) | |||||||
\(258\) | − | 3.11089i | − | 0.193676i | ||||||
\(259\) | −2.57845 | − | 14.1316i | −0.160217 | − | 0.878096i | ||||
\(260\) | 1.44499i | 0.0896145i | ||||||||
\(261\) | − | 2.51905i | − | 0.155925i | ||||||
\(262\) | 4.36769i | 0.269837i | ||||||||
\(263\) | − | 25.6361i | − | 1.58079i | −0.612597 | − | 0.790396i | \(-0.709875\pi\) | ||
0.612597 | − | 0.790396i | \(-0.290125\pi\) | |||||||
\(264\) | −5.80067 | − | 1.30233i | −0.357006 | − | 0.0801530i | ||||
\(265\) | − | 9.63333i | − | 0.591771i | ||||||
\(266\) | 6.12338 | − | 1.11727i | 0.375449 | − | 0.0685043i | ||||
\(267\) | −1.12710 | −0.0689773 | ||||||||
\(268\) | 28.4289 | 1.73657 | ||||||||
\(269\) | − | 15.5197i | − | 0.946253i | −0.880994 | − | 0.473127i | \(-0.843125\pi\) | ||
0.880994 | − | 0.473127i | \(-0.156875\pi\) | |||||||
\(270\) | − | 0.474903i | − | 0.0289017i | ||||||
\(271\) | 1.42566 | 0.0866029 | 0.0433015 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433015 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(272\) | 17.2840 | 1.04800 | ||||||||
\(273\) | 2.11950 | − | 0.386724i | 0.128278 | − | 0.0234056i | ||||
\(274\) | − | 6.04377i | − | 0.365118i | ||||||
\(275\) | −3.23607 | − | 0.726543i | −0.195142 | − | 0.0438122i | ||||
\(276\) | − | 1.37427i | − | 0.0827211i | ||||||
\(277\) | − | 3.29785i | − | 0.198149i | −0.995080 | − | 0.0990744i | \(-0.968412\pi\) | ||
0.995080 | − | 0.0990744i | \(-0.0315882\pi\) | |||||||
\(278\) | − | 5.07680i | − | 0.304486i | ||||||
\(279\) | 5.42943i | 0.325051i | ||||||||
\(280\) | 0.851266 | + | 4.66550i | 0.0508729 | + | 0.278817i | ||||
\(281\) | 6.26696i | 0.373856i | 0.982374 | + | 0.186928i | \(0.0598530\pi\) | ||||
−0.982374 | + | 0.186928i | \(0.940147\pi\) | |||||||
\(282\) | − | 2.17058i | − | 0.129256i | ||||||
\(283\) | −25.9472 | −1.54240 | −0.771199 | − | 0.636594i | \(-0.780343\pi\) | ||||
−0.771199 | + | 0.636594i | \(0.780343\pi\) | |||||||
\(284\) | −5.39918 | −0.320383 | ||||||||
\(285\) | −4.95392 | −0.293445 | ||||||||
\(286\) | 0.280972 | − | 1.25147i | 0.0166142 | − | 0.0740008i | ||||
\(287\) | 1.31581 | + | 7.21149i | 0.0776697 | + | 0.425681i | ||||
\(288\) | − | 4.86614i | − | 0.286740i | ||||||
\(289\) | 24.0497 | 1.41469 | ||||||||
\(290\) | 1.19630i | 0.0702493i | ||||||||
\(291\) | −12.2039 | −0.715405 | ||||||||
\(292\) | −16.3909 | −0.959207 | ||||||||
\(293\) | −25.6554 | −1.49881 | −0.749404 | − | 0.662113i | \(-0.769660\pi\) | ||||
−0.749404 | + | 0.662113i | \(0.769660\pi\) | |||||||
\(294\) | 3.11011 | − | 1.17402i | 0.181385 | − | 0.0684705i | ||||
\(295\) | −3.34504 | −0.194756 | ||||||||
\(296\) | − | 9.73228i | − | 0.565677i | ||||||
\(297\) | 0.726543 | − | 3.23607i | 0.0421583 | − | 0.187776i | ||||
\(298\) | 1.45968 | 0.0845569 | ||||||||
\(299\) | 0.630667 | 0.0364724 | ||||||||
\(300\) | − | 1.77447i | − | 0.102449i | ||||||
\(301\) | −17.0497 | + | 3.11089i | −0.982730 | + | 0.179309i | ||||
\(302\) | 4.40892 | 0.253705 | ||||||||
\(303\) | − | 6.15537i | − | 0.353617i | ||||||
\(304\) | −13.3640 | −0.766480 | ||||||||
\(305\) | 8.03565i | 0.460120i | ||||||||
\(306\) | − | 3.04271i | − | 0.173940i | ||||||
\(307\) | 17.7954 | 1.01563 | 0.507817 | − | 0.861465i | \(-0.330452\pi\) | ||||
0.507817 | + | 0.861465i | \(0.330452\pi\) | |||||||
\(308\) | −0.628539 | + | 15.5582i | −0.0358143 | + | 0.886510i | ||||
\(309\) | −1.57816 | −0.0897786 | ||||||||
\(310\) | − | 2.57845i | − | 0.146446i | ||||||
\(311\) | 27.2195i | 1.54348i | 0.635939 | + | 0.771739i | \(0.280613\pi\) | ||||
−0.635939 | + | 0.771739i | \(0.719387\pi\) | |||||||
\(312\) | 1.45968 | 0.0826380 | ||||||||
\(313\) | 10.4581i | 0.591126i | 0.955323 | + | 0.295563i | \(0.0955073\pi\) | ||||
−0.955323 | + | 0.295563i | \(0.904493\pi\) | |||||||
\(314\) | 10.7789 | 0.608290 | ||||||||
\(315\) | −2.60278 | + | 0.474903i | −0.146650 | + | 0.0267577i | ||||
\(316\) | − | 14.1536i | − | 0.796202i | ||||||
\(317\) | 11.7821 | 0.661747 | 0.330873 | − | 0.943675i | \(-0.392657\pi\) | ||||
0.330873 | + | 0.943675i | \(0.392657\pi\) | |||||||
\(318\) | −4.57489 | −0.256547 | ||||||||
\(319\) | −1.83020 | + | 8.15181i | −0.102471 | + | 0.456414i | ||||
\(320\) | − | 3.08439i | − | 0.172423i | ||||||
\(321\) | 6.29895 | 0.351573 | ||||||||
\(322\) | 0.957294 | − | 0.174668i | 0.0533479 | − | 0.00973385i | ||||
\(323\) | −31.7398 | −1.76605 | ||||||||
\(324\) | 1.77447 | 0.0985815 | ||||||||
\(325\) | 0.814323 | 0.0451705 | ||||||||
\(326\) | 0.568128i | 0.0314657i | ||||||||
\(327\) | 8.92605 | 0.493612 | ||||||||
\(328\) | 4.96647i | 0.274228i | ||||||||
\(329\) | −11.8962 | + | 2.17058i | −0.655858 | + | 0.119668i | ||||
\(330\) | −0.345037 | + | 1.53682i | −0.0189937 | + | 0.0845990i | ||||
\(331\) | −18.5987 | −1.02228 | −0.511138 | − | 0.859499i | \(-0.670776\pi\) | ||||
−0.511138 | + | 0.859499i | \(0.670776\pi\) | |||||||
\(332\) | 11.6806 | 0.641054 | ||||||||
\(333\) | 5.42943 | 0.297531 | ||||||||
\(334\) | 9.54305i | 0.522173i | ||||||||
\(335\) | − | 16.0211i | − | 0.875325i | ||||||
\(336\) | −7.02144 | + | 1.28113i | −0.383051 | + | 0.0698914i | ||||
\(337\) | 16.6826i | 0.908762i | 0.890808 | + | 0.454381i | \(0.150139\pi\) | ||||
−0.890808 | + | 0.454381i | \(0.849861\pi\) | |||||||
\(338\) | − | 5.85882i | − | 0.318678i | ||||||
\(339\) | − | 9.46454i | − | 0.514043i | ||||||
\(340\) | − | 11.3690i | − | 0.616572i | ||||||
\(341\) | 3.94471 | − | 17.5700i | 0.213618 | − | 0.951469i | ||||
\(342\) | 2.35263i | 0.127216i | ||||||||
\(343\) | −9.54454 | − | 15.8714i | −0.515356 | − | 0.856976i | ||||
\(344\) | −11.7420 | −0.633084 | ||||||||
\(345\) | −0.774467 | −0.0416959 | ||||||||
\(346\) | − | 6.66900i | − | 0.358528i | ||||||
\(347\) | − | 26.9136i | − | 1.44480i | −0.691475 | − | 0.722400i | \(-0.743039\pi\) | ||
0.691475 | − | 0.722400i | \(-0.256961\pi\) | |||||||
\(348\) | −4.46997 | −0.239615 | ||||||||
\(349\) | −5.84889 | −0.313084 | −0.156542 | − | 0.987671i | \(-0.550035\pi\) | ||||
−0.156542 | + | 0.987671i | \(0.550035\pi\) | |||||||
\(350\) | 1.23607 | − | 0.225533i | 0.0660706 | − | 0.0120552i | ||||
\(351\) | 0.814323i | 0.0434654i | ||||||||
\(352\) | −3.53546 | + | 15.7472i | −0.188441 | + | 0.839327i | ||||
\(353\) | 32.0573i | 1.70624i | 0.521715 | + | 0.853120i | \(0.325292\pi\) | ||||
−0.521715 | + | 0.853120i | \(0.674708\pi\) | |||||||
\(354\) | 1.58857i | 0.0844314i | ||||||||
\(355\) | 3.04271i | 0.161490i | ||||||||
\(356\) | 2.00000i | 0.106000i | ||||||||
\(357\) | −16.6760 | + | 3.04271i | −0.882589 | + | 0.161037i | ||||
\(358\) | 1.84565i | 0.0975457i | ||||||||
\(359\) | 8.34861i | 0.440623i | 0.975430 | + | 0.220311i | \(0.0707073\pi\) | ||||
−0.975430 | + | 0.220311i | \(0.929293\pi\) | |||||||
\(360\) | −1.79251 | −0.0944733 | ||||||||
\(361\) | 5.54134 | 0.291649 | ||||||||
\(362\) | 2.18677 | 0.114934 | ||||||||
\(363\) | −4.70228 | + | 9.94427i | −0.246806 | + | 0.521939i | ||||
\(364\) | −0.686230 | − | 3.76099i | −0.0359682 | − | 0.197130i | ||||
\(365\) | 9.23710i | 0.483492i | ||||||||
\(366\) | 3.81615 | 0.199474 | ||||||||
\(367\) | 9.51970i | 0.496925i | 0.968642 | + | 0.248462i | \(0.0799252\pi\) | ||||
−0.968642 | + | 0.248462i | \(0.920075\pi\) | |||||||
\(368\) | −2.08926 | −0.108910 | ||||||||
\(369\) | −2.77069 | −0.144236 | ||||||||
\(370\) | −2.57845 | −0.134047 | ||||||||
\(371\) | 4.57489 | + | 25.0734i | 0.237517 | + | 1.30175i | ||||
\(372\) | 9.63435 | 0.499518 | ||||||||
\(373\) | − | 3.36535i | − | 0.174251i | −0.996197 | − | 0.0871257i | \(-0.972232\pi\) | ||
0.996197 | − | 0.0871257i | \(-0.0277682\pi\) | |||||||
\(374\) | −2.21066 | + | 9.84640i | −0.114310 | + | 0.509145i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −8.19277 | −0.422510 | ||||||||
\(377\) | − | 2.05132i | − | 0.105648i | ||||||
\(378\) | 0.225533 | + | 1.23607i | 0.0116002 | + | 0.0635765i | ||||
\(379\) | −16.2742 | −0.835952 | −0.417976 | − | 0.908458i | \(-0.637260\pi\) | ||||
−0.417976 | + | 0.908458i | \(0.637260\pi\) | |||||||
\(380\) | 8.79057i | 0.450947i | ||||||||
\(381\) | 1.51249 | 0.0774872 | ||||||||
\(382\) | 6.73159i | 0.344418i | ||||||||
\(383\) | − | 28.6127i | − | 1.46204i | −0.682355 | − | 0.731021i | \(-0.739044\pi\) | ||
0.682355 | − | 0.731021i | \(-0.260956\pi\) | |||||||
\(384\) | −11.1971 | −0.571398 | ||||||||
\(385\) | 8.76781 | + | 0.354213i | 0.446849 | + | 0.0180524i | ||||
\(386\) | 0.451065 | 0.0229586 | ||||||||
\(387\) | − | 6.55058i | − | 0.332985i | ||||||
\(388\) | 21.6554i | 1.09939i | ||||||||
\(389\) | 28.6279 | 1.45149 | 0.725746 | − | 0.687963i | \(-0.241495\pi\) | ||||
0.725746 | + | 0.687963i | \(0.241495\pi\) | |||||||
\(390\) | − | 0.386724i | − | 0.0195825i | ||||||
\(391\) | −4.96202 | −0.250940 | ||||||||
\(392\) | −4.43132 | − | 11.7390i | −0.223815 | − | 0.592909i | ||||
\(393\) | 9.19702i | 0.463928i | ||||||||
\(394\) | 6.69938 | 0.337510 | ||||||||
\(395\) | −7.97625 | −0.401329 | ||||||||
\(396\) | −5.74230 | − | 1.28923i | −0.288561 | − | 0.0647860i | ||||
\(397\) | 8.00588i | 0.401804i | 0.979611 | + | 0.200902i | \(0.0643872\pi\) | ||||
−0.979611 | + | 0.200902i | \(0.935613\pi\) | |||||||
\(398\) | 1.57189 | 0.0787919 | ||||||||
\(399\) | 12.8940 | − | 2.35263i | 0.645506 | − | 0.117779i | ||||
\(400\) | −2.69767 | −0.134883 | ||||||||
\(401\) | 29.7106 | 1.48368 | 0.741838 | − | 0.670579i | \(-0.233954\pi\) | ||||
0.741838 | + | 0.670579i | \(0.233954\pi\) | |||||||
\(402\) | −7.60845 | −0.379475 | ||||||||
\(403\) | 4.42131i | 0.220241i | ||||||||
\(404\) | −10.9225 | −0.543415 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | −0.568128 | − | 3.11371i | −0.0281957 | − | 0.154531i | ||||
\(407\) | −17.5700 | − | 3.94471i | −0.870913 | − | 0.195532i | ||||
\(408\) | −11.4846 | −0.568572 | ||||||||
\(409\) | −25.5245 | −1.26211 | −0.631053 | − | 0.775739i | \(-0.717377\pi\) | ||||
−0.631053 | + | 0.775739i | \(0.717377\pi\) | |||||||
\(410\) | 1.31581 | 0.0649831 | ||||||||
\(411\) | − | 12.7263i | − | 0.627744i | ||||||
\(412\) | 2.80040i | 0.137966i | ||||||||
\(413\) | 8.70640 | − | 1.58857i | 0.428414 | − | 0.0781683i | ||||
\(414\) | 0.367797i | 0.0180762i | ||||||||
\(415\) | − | 6.58257i | − | 0.323126i | ||||||
\(416\) | − | 3.96261i | − | 0.194283i | ||||||
\(417\) | − | 10.6902i | − | 0.523501i | ||||||
\(418\) | 1.70929 | − | 7.61328i | 0.0836040 | − | 0.372377i | ||||
\(419\) | − | 9.79610i | − | 0.478571i | −0.970949 | − | 0.239285i | \(-0.923087\pi\) | ||
0.970949 | − | 0.239285i | \(-0.0769132\pi\) | |||||||
\(420\) | 0.842700 | + | 4.61855i | 0.0411195 | + | 0.225362i | ||||
\(421\) | −3.20446 | −0.156176 | −0.0780880 | − | 0.996946i | \(-0.524882\pi\) | ||||
−0.0780880 | + | 0.996946i | \(0.524882\pi\) | |||||||
\(422\) | 12.6035 | 0.613530 | ||||||||
\(423\) | − | 4.57057i | − | 0.222229i | ||||||
\(424\) | 17.2678i | 0.838598i | ||||||||
\(425\) | −6.40701 | −0.310785 | ||||||||
\(426\) | 1.44499 | 0.0700100 | ||||||||
\(427\) | −3.81615 | − | 20.9150i | −0.184677 | − | 1.01215i | ||||
\(428\) | − | 11.1773i | − | 0.540274i | ||||||
\(429\) | 0.591640 | − | 2.63520i | 0.0285647 | − | 0.127229i | ||||
\(430\) | 3.11089i | 0.150021i | ||||||||
\(431\) | − | 13.2057i | − | 0.636096i | −0.948075 | − | 0.318048i | \(-0.896973\pi\) | ||
0.948075 | − | 0.318048i | \(-0.103027\pi\) | |||||||
\(432\) | − | 2.69767i | − | 0.129792i | ||||||
\(433\) | − | 18.1217i | − | 0.870872i | −0.900220 | − | 0.435436i | \(-0.856594\pi\) | ||
0.900220 | − | 0.435436i | \(-0.143406\pi\) | |||||||
\(434\) | 1.22451 | + | 6.71114i | 0.0587786 | + | 0.322145i | ||||
\(435\) | 2.51905i | 0.120779i | ||||||||
\(436\) | − | 15.8390i | − | 0.758550i | ||||||
\(437\) | 3.83665 | 0.183532 | ||||||||
\(438\) | 4.38672 | 0.209606 | ||||||||
\(439\) | 28.9147 | 1.38002 | 0.690011 | − | 0.723799i | \(-0.257606\pi\) | ||||
0.690011 | + | 0.723799i | \(0.257606\pi\) | |||||||
\(440\) | 5.80067 | + | 1.30233i | 0.276536 | + | 0.0620862i | ||||
\(441\) | 6.54893 | − | 2.47214i | 0.311854 | − | 0.117721i | ||||
\(442\) | − | 2.47775i | − | 0.117854i | ||||||
\(443\) | 8.10648 | 0.385151 | 0.192575 | − | 0.981282i | \(-0.438316\pi\) | ||||
0.192575 | + | 0.981282i | \(0.438316\pi\) | |||||||
\(444\) | − | 9.63435i | − | 0.457226i | ||||||
\(445\) | 1.12710 | 0.0534296 | ||||||||
\(446\) | −6.01988 | −0.285050 | ||||||||
\(447\) | 3.07364 | 0.145378 | ||||||||
\(448\) | 1.46479 | + | 8.02800i | 0.0692047 | + | 0.379287i | ||||
\(449\) | −10.6127 | −0.500845 | −0.250422 | − | 0.968137i | \(-0.580569\pi\) | ||||
−0.250422 | + | 0.968137i | \(0.580569\pi\) | |||||||
\(450\) | 0.474903i | 0.0223871i | ||||||||
\(451\) | 8.96613 | + | 2.01302i | 0.422199 | + | 0.0947895i | ||||
\(452\) | −16.7945 | −0.789948 | ||||||||
\(453\) | 9.28384 | 0.436193 | ||||||||
\(454\) | 10.8306i | 0.508308i | ||||||||
\(455\) | −2.11950 | + | 0.386724i | −0.0993639 | + | 0.0181299i | ||||
\(456\) | 8.87993 | 0.415841 | ||||||||
\(457\) | 39.1722i | 1.83240i | 0.400724 | + | 0.916199i | \(0.368759\pi\) | ||||
−0.400724 | + | 0.916199i | \(0.631241\pi\) | |||||||
\(458\) | −7.23399 | −0.338022 | ||||||||
\(459\) | − | 6.40701i | − | 0.299053i | ||||||
\(460\) | 1.37427i | 0.0640755i | ||||||||
\(461\) | −6.71349 | −0.312678 | −0.156339 | − | 0.987703i | \(-0.549969\pi\) | ||||
−0.156339 | + | 0.987703i | \(0.549969\pi\) | |||||||
\(462\) | 0.168217 | − | 4.16386i | 0.00782615 | − | 0.193720i | ||||
\(463\) | −19.4164 | −0.902357 | −0.451178 | − | 0.892434i | \(-0.648996\pi\) | ||||
−0.451178 | + | 0.892434i | \(0.648996\pi\) | |||||||
\(464\) | 6.79556i | 0.315476i | ||||||||
\(465\) | − | 5.42943i | − | 0.251784i | ||||||
\(466\) | 9.28886 | 0.430298 | ||||||||
\(467\) | 21.2515i | 0.983401i | 0.870765 | + | 0.491700i | \(0.163624\pi\) | ||||
−0.870765 | + | 0.491700i | \(0.836376\pi\) | |||||||
\(468\) | 1.44499 | 0.0667947 | ||||||||
\(469\) | 7.60845 | + | 41.6993i | 0.351326 | + | 1.92550i | ||||
\(470\) | 2.17058i | 0.100121i | ||||||||
\(471\) | 22.6971 | 1.04583 | ||||||||
\(472\) | 5.99600 | 0.275988 | ||||||||
\(473\) | −4.75928 | + | 21.1981i | −0.218832 | + | 0.974691i | ||||
\(474\) | 3.78794i | 0.173986i | ||||||||
\(475\) | 4.95392 | 0.227302 | ||||||||
\(476\) | 5.39918 | + | 29.5911i | 0.247471 | + | 1.35630i | ||||
\(477\) | −9.63333 | −0.441080 | ||||||||
\(478\) | 11.2174 | 0.513071 | ||||||||
\(479\) | −6.81032 | −0.311171 | −0.155586 | − | 0.987822i | \(-0.549726\pi\) | ||||
−0.155586 | + | 0.987822i | \(0.549726\pi\) | |||||||
\(480\) | 4.86614i | 0.222108i | ||||||||
\(481\) | 4.42131 | 0.201594 | ||||||||
\(482\) | 13.1602i | 0.599429i | ||||||||
\(483\) | 2.01577 | − | 0.367797i | 0.0917206 | − | 0.0167353i | ||||
\(484\) | 17.6458 | + | 8.34405i | 0.802081 | + | 0.379275i | ||||
\(485\) | 12.2039 | 0.554150 | ||||||||
\(486\) | −0.474903 | −0.0215420 | ||||||||
\(487\) | 5.26281 | 0.238481 | 0.119240 | − | 0.992865i | \(-0.461954\pi\) | ||||
0.119240 | + | 0.992865i | \(0.461954\pi\) | |||||||
\(488\) | − | 14.4040i | − | 0.652036i | ||||||
\(489\) | 1.19630i | 0.0540987i | ||||||||
\(490\) | −3.11011 | + | 1.17402i | −0.140500 | + | 0.0530370i | ||||
\(491\) | 42.5430i | 1.91994i | 0.280106 | + | 0.959969i | \(0.409630\pi\) | ||||
−0.280106 | + | 0.959969i | \(0.590370\pi\) | |||||||
\(492\) | 4.91649i | 0.221653i | ||||||||
\(493\) | 16.1396i | 0.726889i | ||||||||
\(494\) | 1.91580i | 0.0861960i | ||||||||
\(495\) | −0.726543 | + | 3.23607i | −0.0326557 | + | 0.145450i | ||||
\(496\) | − | 14.6468i | − | 0.657661i | ||||||
\(497\) | −1.44499 | − | 7.91950i | −0.0648166 | − | 0.355238i | ||||
\(498\) | −3.12608 | −0.140083 | ||||||||
\(499\) | 7.33201 | 0.328226 | 0.164113 | − | 0.986442i | \(-0.447524\pi\) | ||||
0.164113 | + | 0.986442i | \(0.447524\pi\) | |||||||
\(500\) | 1.77447i | 0.0793566i | ||||||||
\(501\) | 20.0947i | 0.897767i | ||||||||
\(502\) | 9.70173 | 0.433009 | ||||||||
\(503\) | −8.59569 | −0.383263 | −0.191631 | − | 0.981467i | \(-0.561378\pi\) | ||||
−0.191631 | + | 0.981467i | \(0.561378\pi\) | |||||||
\(504\) | 4.66550 | − | 0.851266i | 0.207818 | − | 0.0379184i | ||||
\(505\) | 6.15537i | 0.273910i | ||||||||
\(506\) | 0.267220 | − | 1.19022i | 0.0118794 | − | 0.0529115i | ||||
\(507\) | − | 12.3369i | − | 0.547900i | ||||||
\(508\) | − | 2.68386i | − | 0.119077i | ||||||
\(509\) | − | 8.12437i | − | 0.360106i | −0.983657 | − | 0.180053i | \(-0.942373\pi\) | ||
0.983657 | − | 0.180053i | \(-0.0576270\pi\) | |||||||
\(510\) | 3.04271i | 0.134733i | ||||||||
\(511\) | −4.38672 | − | 24.0421i | −0.194057 | − | 1.06356i | ||||
\(512\) | 22.7984i | 1.00756i | ||||||||
\(513\) | 4.95392i | 0.218721i | ||||||||
\(514\) | 9.63497 | 0.424980 | ||||||||
\(515\) | 1.57816 | 0.0695422 | ||||||||
\(516\) | −11.6238 | −0.511709 | ||||||||
\(517\) | −3.32071 | + | 14.7907i | −0.146045 | + | 0.650493i | ||||
\(518\) | 6.71114 | − | 1.22451i | 0.294871 | − | 0.0538021i | ||||
\(519\) | − | 14.0429i | − | 0.616414i | ||||||
\(520\) | −1.45968 | −0.0640111 | ||||||||
\(521\) | 33.4082i | 1.46364i | 0.681497 | + | 0.731821i | \(0.261329\pi\) | ||||
−0.681497 | + | 0.731821i | \(0.738671\pi\) | |||||||
\(522\) | 1.19630 | 0.0523608 | ||||||||
\(523\) | 23.4555 | 1.02564 | 0.512820 | − | 0.858496i | \(-0.328601\pi\) | ||||
0.512820 | + | 0.858496i | \(0.328601\pi\) | |||||||
\(524\) | 16.3198 | 0.712934 | ||||||||
\(525\) | 2.60278 | − | 0.474903i | 0.113595 | − | 0.0207265i | ||||
\(526\) | 12.1747 | 0.530841 | ||||||||
\(527\) | − | 34.7864i | − | 1.51532i | ||||||
\(528\) | −1.95997 | + | 8.72984i | −0.0852968 | + | 0.379917i | ||||
\(529\) | −22.4002 | −0.973922 | ||||||||
\(530\) | 4.57489 | 0.198721 | ||||||||
\(531\) | 3.34504i | 0.145162i | ||||||||
\(532\) | −4.17467 | − | 22.8799i | −0.180995 | − | 0.991971i | ||||
\(533\) | −2.25623 | −0.0977284 | ||||||||
\(534\) | − | 0.535262i | − | 0.0231631i | ||||||
\(535\) | −6.29895 | −0.272327 | ||||||||
\(536\) | 28.7179i | 1.24042i | ||||||||
\(537\) | 3.88638i | 0.167710i | ||||||||
\(538\) | 7.37035 | 0.317758 | ||||||||
\(539\) | −22.9889 | + | 3.24192i | −0.990202 | + | 0.139639i | ||||
\(540\) | −1.77447 | −0.0763609 | ||||||||
\(541\) | − | 22.0272i | − | 0.947024i | −0.880787 | − | 0.473512i | \(-0.842986\pi\) | ||
0.880787 | − | 0.473512i | \(-0.157014\pi\) | |||||||
\(542\) | 0.677052i | 0.0290819i | ||||||||
\(543\) | 4.60466 | 0.197605 | ||||||||
\(544\) | 31.1774i | 1.33672i | ||||||||
\(545\) | −8.92605 | −0.382350 | ||||||||
\(546\) | 0.183657 | + | 1.00656i | 0.00785977 | + | 0.0430767i | ||||
\(547\) | 45.2889i | 1.93641i | 0.250151 | + | 0.968207i | \(0.419520\pi\) | ||||
−0.250151 | + | 0.968207i | \(0.580480\pi\) | |||||||
\(548\) | −22.5825 | −0.964675 | ||||||||
\(549\) | 8.03565 | 0.342953 | ||||||||
\(550\) | 0.345037 | − | 1.53682i | 0.0147124 | − | 0.0655301i | ||||
\(551\) | − | 12.4792i | − | 0.531630i | ||||||
\(552\) | 1.38824 | 0.0590873 | ||||||||
\(553\) | 20.7604 | − | 3.78794i | 0.882823 | − | 0.161080i | ||||
\(554\) | 1.56616 | 0.0665398 | ||||||||
\(555\) | −5.42943 | −0.230466 | ||||||||
\(556\) | −18.9694 | −0.804481 | ||||||||
\(557\) | 31.9590i | 1.35414i | 0.735917 | + | 0.677072i | \(0.236752\pi\) | ||||
−0.735917 | + | 0.677072i | \(0.763248\pi\) | |||||||
\(558\) | −2.57845 | −0.109155 | ||||||||
\(559\) | − | 5.33429i | − | 0.225617i | ||||||
\(560\) | 7.02144 | − | 1.28113i | 0.296710 | − | 0.0541376i | ||||
\(561\) | −4.65496 | + | 20.7335i | −0.196533 | + | 0.875369i | ||||
\(562\) | −2.97620 | −0.125543 | ||||||||
\(563\) | −7.22589 | −0.304535 | −0.152268 | − | 0.988339i | \(-0.548658\pi\) | ||||
−0.152268 | + | 0.988339i | \(0.548658\pi\) | |||||||
\(564\) | −8.11033 | −0.341506 | ||||||||
\(565\) | 9.46454i | 0.398176i | ||||||||
\(566\) | − | 12.3224i | − | 0.517948i | ||||||
\(567\) | 0.474903 | + | 2.60278i | 0.0199440 | + | 0.109307i | ||||
\(568\) | − | 5.45407i | − | 0.228848i | ||||||
\(569\) | 14.1104i | 0.591538i | 0.955260 | + | 0.295769i | \(0.0955758\pi\) | ||||
−0.955260 | + | 0.295769i | \(0.904424\pi\) | |||||||
\(570\) | − | 2.35263i | − | 0.0985409i | ||||||
\(571\) | − | 33.9554i | − | 1.42099i | −0.703703 | − | 0.710495i | \(-0.748471\pi\) | ||
0.703703 | − | 0.710495i | \(-0.251529\pi\) | |||||||
\(572\) | −4.67608 | − | 1.04985i | −0.195517 | − | 0.0438963i | ||||
\(573\) | 14.1747i | 0.592155i | ||||||||
\(574\) | −3.42476 | + | 0.624881i | −0.142947 | + | 0.0260820i | ||||
\(575\) | 0.774467 | 0.0322975 | ||||||||
\(576\) | −3.08439 | −0.128516 | ||||||||
\(577\) | − | 12.8097i | − | 0.533275i | −0.963797 | − | 0.266638i | \(-0.914087\pi\) | ||
0.963797 | − | 0.266638i | \(-0.0859127\pi\) | |||||||
\(578\) | 11.4213i | 0.475063i | ||||||||
\(579\) | 0.949806 | 0.0394726 | ||||||||
\(580\) | 4.46997 | 0.185605 | ||||||||
\(581\) | 3.12608 | + | 17.1330i | 0.129692 | + | 0.710796i | ||||
\(582\) | − | 5.79567i | − | 0.240238i | ||||||
\(583\) | 31.1741 | + | 6.99902i | 1.29110 | + | 0.289870i | ||||
\(584\) | − | 16.5575i | − | 0.685156i | ||||||
\(585\) | − | 0.814323i | − | 0.0336681i | ||||||
\(586\) | − | 12.1838i | − | 0.503310i | ||||||
\(587\) | − | 3.45751i | − | 0.142707i | −0.997451 | − | 0.0713534i | \(-0.977268\pi\) | ||
0.997451 | − | 0.0713534i | \(-0.0227318\pi\) | |||||||
\(588\) | −4.38672 | − | 11.6209i | −0.180905 | − | 0.479237i | ||||
\(589\) | 26.8970i | 1.10827i | ||||||||
\(590\) | − | 1.58857i | − | 0.0654003i | ||||||
\(591\) | 14.1068 | 0.580278 | ||||||||
\(592\) | −14.6468 | −0.601980 | ||||||||
\(593\) | −16.9490 | −0.696014 | −0.348007 | − | 0.937492i | \(-0.613141\pi\) | ||||
−0.348007 | + | 0.937492i | \(0.613141\pi\) | |||||||
\(594\) | 1.53682 | + | 0.345037i | 0.0630564 | + | 0.0141570i | ||||
\(595\) | 16.6760 | − | 3.04271i | 0.683651 | − | 0.124739i | ||||
\(596\) | − | 5.45407i | − | 0.223407i | ||||||
\(597\) | 3.30993 | 0.135466 | ||||||||
\(598\) | 0.299505i | 0.0122477i | ||||||||
\(599\) | 0.684193 | 0.0279554 | 0.0139777 | − | 0.999902i | \(-0.495551\pi\) | ||||
0.0139777 | + | 0.999902i | \(0.495551\pi\) | |||||||
\(600\) | 1.79251 | 0.0731787 | ||||||||
\(601\) | 24.6102 | 1.00387 | 0.501936 | − | 0.864905i | \(-0.332621\pi\) | ||||
0.501936 | + | 0.864905i | \(0.332621\pi\) | |||||||
\(602\) | −1.47737 | − | 8.09697i | −0.0602132 | − | 0.330008i | ||||
\(603\) | −16.0211 | −0.652428 | ||||||||
\(604\) | − | 16.4739i | − | 0.670313i | ||||||
\(605\) | 4.70228 | − | 9.94427i | 0.191175 | − | 0.404292i | ||||
\(606\) | 2.92320 | 0.118747 | ||||||||
\(607\) | −11.5771 | −0.469898 | −0.234949 | − | 0.972008i | \(-0.575492\pi\) | ||||
−0.234949 | + | 0.972008i | \(0.575492\pi\) | |||||||
\(608\) | − | 24.1065i | − | 0.977647i | ||||||
\(609\) | −1.19630 | − | 6.55653i | −0.0484766 | − | 0.265684i | ||||
\(610\) | −3.81615 | −0.154512 | ||||||||
\(611\) | − | 3.72192i | − | 0.150573i | ||||||
\(612\) | −11.3690 | −0.459566 | ||||||||
\(613\) | − | 4.12694i | − | 0.166686i | −0.996521 | − | 0.0833428i | \(-0.973440\pi\) | ||
0.996521 | − | 0.0833428i | \(-0.0265596\pi\) | |||||||
\(614\) | 8.45107i | 0.341057i | ||||||||
\(615\) | 2.77069 | 0.111725 | ||||||||
\(616\) | −15.7163 | − | 0.634929i | −0.633230 | − | 0.0255820i | ||||
\(617\) | 0.965342 | 0.0388632 | 0.0194316 | − | 0.999811i | \(-0.493814\pi\) | ||||
0.0194316 | + | 0.999811i | \(0.493814\pi\) | |||||||
\(618\) | − | 0.749475i | − | 0.0301483i | ||||||
\(619\) | − | 46.5505i | − | 1.87102i | −0.353295 | − | 0.935512i | \(-0.614939\pi\) | ||
0.353295 | − | 0.935512i | \(-0.385061\pi\) | |||||||
\(620\) | −9.63435 | −0.386925 | ||||||||
\(621\) | 0.774467i | 0.0310783i | ||||||||
\(622\) | −12.9266 | −0.518311 | ||||||||
\(623\) | −2.93359 | + | 0.535262i | −0.117532 | + | 0.0214448i | ||||
\(624\) | − | 2.19677i | − | 0.0879413i | ||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.96658 | −0.198504 | ||||||||
\(627\) | 3.59923 | − | 16.0312i | 0.143740 | − | 0.640226i | ||||
\(628\) | − | 40.2753i | − | 1.60716i | ||||||
\(629\) | −34.7864 | −1.38702 | ||||||||
\(630\) | −0.225533 | − | 1.23607i | −0.00898544 | − | 0.0492461i | ||||
\(631\) | −41.6284 | −1.65720 | −0.828599 | − | 0.559842i | \(-0.810862\pi\) | ||||
−0.828599 | + | 0.559842i | \(0.810862\pi\) | |||||||
\(632\) | 14.2975 | 0.568723 | ||||||||
\(633\) | 26.5392 | 1.05484 | ||||||||
\(634\) | 5.59533i | 0.222219i | ||||||||
\(635\) | −1.51249 | −0.0600213 | ||||||||
\(636\) | 17.0940i | 0.677822i | ||||||||
\(637\) | 5.33295 | − | 2.01312i | 0.211299 | − | 0.0797626i | ||||
\(638\) | −3.87132 | − | 0.869165i | −0.153267 | − | 0.0344106i | ||||
\(639\) | 3.04271 | 0.120368 | ||||||||
\(640\) | 11.1971 | 0.442603 | ||||||||
\(641\) | −22.0702 | −0.871721 | −0.435861 | − | 0.900014i | \(-0.643556\pi\) | ||||
−0.435861 | + | 0.900014i | \(0.643556\pi\) | |||||||
\(642\) | 2.99139i | 0.118061i | ||||||||
\(643\) | 31.7057i | 1.25035i | 0.780484 | + | 0.625176i | \(0.214973\pi\) | ||||
−0.780484 | + | 0.625176i | \(0.785027\pi\) | |||||||
\(644\) | −0.652643 | − | 3.57692i | −0.0257177 | − | 0.140950i | ||||
\(645\) | 6.55058i | 0.257929i | ||||||||
\(646\) | − | 15.0733i | − | 0.593052i | ||||||
\(647\) | − | 8.53648i | − | 0.335604i | −0.985821 | − | 0.167802i | \(-0.946333\pi\) | ||
0.985821 | − | 0.167802i | \(-0.0536669\pi\) | |||||||
\(648\) | 1.79251i | 0.0704163i | ||||||||
\(649\) | 2.43031 | − | 10.8248i | 0.0953981 | − | 0.424909i | ||||
\(650\) | 0.386724i | 0.0151686i | ||||||||
\(651\) | 2.57845 | + | 14.1316i | 0.101057 | + | 0.553862i | ||||
\(652\) | 2.12280 | 0.0831353 | ||||||||
\(653\) | −13.4224 | −0.525259 | −0.262630 | − | 0.964897i | \(-0.584590\pi\) | ||||
−0.262630 | + | 0.964897i | \(0.584590\pi\) | |||||||
\(654\) | 4.23901i | 0.165758i | ||||||||
\(655\) | − | 9.19702i | − | 0.359357i | ||||||
\(656\) | 7.47440 | 0.291826 | ||||||||
\(657\) | 9.23710 | 0.360374 | ||||||||
\(658\) | −1.03081 | − | 5.64954i | −0.0401853 | − | 0.220242i | ||||
\(659\) | − | 26.5905i | − | 1.03582i | −0.855436 | − | 0.517909i | \(-0.826710\pi\) | ||
0.855436 | − | 0.517909i | \(-0.173290\pi\) | |||||||
\(660\) | 5.74230 | + | 1.28923i | 0.223519 | + | 0.0501831i | ||||
\(661\) | 47.0053i | 1.82829i | 0.405382 | + | 0.914147i | \(0.367139\pi\) | ||||
−0.405382 | + | 0.914147i | \(0.632861\pi\) | |||||||
\(662\) | − | 8.83256i | − | 0.343287i | ||||||
\(663\) | − | 5.21737i | − | 0.202626i | ||||||
\(664\) | 11.7993i | 0.457901i | ||||||||
\(665\) | −12.8940 | + | 2.35263i | −0.500007 | + | 0.0912311i | ||||
\(666\) | 2.57845i | 0.0999130i | ||||||||
\(667\) | − | 1.95092i | − | 0.0755399i | ||||||
\(668\) | 35.6575 | 1.37963 | ||||||||
\(669\) | −12.6760 | −0.490084 | ||||||||
\(670\) | 7.60845 | 0.293940 | ||||||||
\(671\) | −26.0039 | − | 5.83824i | −1.00387 | − | 0.225383i | ||||
\(672\) | −2.31094 | − | 12.6655i | −0.0891466 | − | 0.488582i | ||||
\(673\) | − | 15.6212i | − | 0.602155i | −0.953600 | − | 0.301077i | \(-0.902654\pi\) | ||
0.953600 | − | 0.301077i | \(-0.0973463\pi\) | |||||||
\(674\) | −7.92264 | −0.305169 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | −21.8914 | −0.841976 | ||||||||
\(677\) | −36.8022 | −1.41442 | −0.707211 | − | 0.707003i | \(-0.750047\pi\) | ||||
−0.707211 | + | 0.707003i | \(0.750047\pi\) | |||||||
\(678\) | 4.49474 | 0.172619 | ||||||||
\(679\) | −31.7641 | + | 5.79567i | −1.21899 | + | 0.222417i | ||||
\(680\) | 11.4846 | 0.440414 | ||||||||
\(681\) | 22.8060i | 0.873929i | ||||||||
\(682\) | 8.34405 | + | 1.87335i | 0.319510 | + | 0.0717345i | ||||
\(683\) | 21.6534 | 0.828544 | 0.414272 | − | 0.910153i | \(-0.364036\pi\) | ||||
0.414272 | + | 0.910153i | \(0.364036\pi\) | |||||||
\(684\) | 8.79057 | 0.336116 | ||||||||
\(685\) | 12.7263i | 0.486248i | ||||||||
\(686\) | 7.53738 | − | 4.53273i | 0.287779 | − | 0.173060i | ||||
\(687\) | −15.2326 | −0.581159 | ||||||||
\(688\) | 17.6713i | 0.673712i | ||||||||
\(689\) | −7.84464 | −0.298857 | ||||||||
\(690\) | − | 0.367797i | − | 0.0140018i | ||||||
\(691\) | − | 0.111456i | − | 0.00423999i | −0.999998 | − | 0.00212000i | \(-0.999325\pi\) | ||
0.999998 | − | 0.00212000i | \(-0.000674816\pi\) | |||||||
\(692\) | −24.9186 | −0.947264 | ||||||||
\(693\) | 0.354213 | − | 8.76781i | 0.0134554 | − | 0.333062i | ||||
\(694\) | 12.7814 | 0.485174 | ||||||||
\(695\) | 10.6902i | 0.405502i | ||||||||
\(696\) | − | 4.51541i | − | 0.171156i | ||||||
\(697\) | 17.7518 | 0.672398 | ||||||||
\(698\) | − | 2.77765i | − | 0.105136i | ||||||
\(699\) | 19.5595 | 0.739808 | ||||||||
\(700\) | −0.842700 | − | 4.61855i | −0.0318511 | − | 0.174565i | ||||
\(701\) | − | 11.9236i | − | 0.450349i | −0.974318 | − | 0.225174i | \(-0.927705\pi\) | ||
0.974318 | − | 0.225174i | \(-0.0722952\pi\) | |||||||
\(702\) | −0.386724 | −0.0145960 | ||||||||
\(703\) | 26.8970 | 1.01444 | ||||||||
\(704\) | 9.98131 | + | 2.24094i | 0.376185 | + | 0.0844587i | ||||
\(705\) | 4.57057i | 0.172138i | ||||||||
\(706\) | −15.2241 | −0.572967 | ||||||||
\(707\) | −2.92320 | − | 16.0211i | −0.109938 | − | 0.602534i | ||||
\(708\) | 5.93566 | 0.223076 | ||||||||
\(709\) | 19.5862 | 0.735576 | 0.367788 | − | 0.929910i | \(-0.380115\pi\) | ||||
0.367788 | + | 0.929910i | \(0.380115\pi\) | |||||||
\(710\) | −1.44499 | −0.0542295 | ||||||||
\(711\) | 7.97625i | 0.299133i | ||||||||
\(712\) | −2.02033 | −0.0757151 | ||||||||
\(713\) | 4.20492i | 0.157475i | ||||||||
\(714\) | −1.44499 | − | 7.91950i | −0.0540774 | − | 0.296380i | ||||
\(715\) | −0.591640 | + | 2.63520i | −0.0221261 | + | 0.0985511i | ||||
\(716\) | 6.89625 | 0.257725 | ||||||||
\(717\) | 23.6204 | 0.882118 | ||||||||
\(718\) | −3.96478 | −0.147964 | ||||||||
\(719\) | 37.2055i | 1.38753i | 0.720201 | + | 0.693765i | \(0.244050\pi\) | ||||
−0.720201 | + | 0.693765i | \(0.755950\pi\) | |||||||
\(720\) | 2.69767i | 0.100536i | ||||||||
\(721\) | −4.10762 | + | 0.749475i | −0.152976 | + | 0.0279119i | ||||
\(722\) | 2.63160i | 0.0979379i | ||||||||
\(723\) | 27.7113i | 1.03059i | ||||||||
\(724\) | − | 8.17082i | − | 0.303666i | ||||||
\(725\) | − | 2.51905i | − | 0.0935551i | ||||||
\(726\) | −4.72256 | − | 2.23313i | −0.175271 | − | 0.0828791i | ||||
\(727\) | 5.74695i | 0.213143i | 0.994305 | + | 0.106571i | \(0.0339872\pi\) | ||||
−0.994305 | + | 0.106571i | \(0.966013\pi\) | |||||||
\(728\) | 3.79922 | − | 0.693205i | 0.140809 | − | 0.0256919i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −4.38672 | −0.162360 | ||||||||
\(731\) | 41.9696i | 1.55230i | ||||||||
\(732\) | − | 14.2590i | − | 0.527028i | ||||||
\(733\) | −21.6027 | −0.797913 | −0.398956 | − | 0.916970i | \(-0.630628\pi\) | ||||
−0.398956 | + | 0.916970i | \(0.630628\pi\) | |||||||
\(734\) | −4.52094 | −0.166871 | ||||||||
\(735\) | −6.54893 | + | 2.47214i | −0.241561 | + | 0.0911861i | ||||
\(736\) | − | 3.76867i | − | 0.138915i | ||||||
\(737\) | 51.8453 | + | 11.6400i | 1.90975 | + | 0.428765i | ||||
\(738\) | − | 1.31581i | − | 0.0484355i | ||||||
\(739\) | 43.4396i | 1.59795i | 0.601364 | + | 0.798975i | \(0.294624\pi\) | ||||
−0.601364 | + | 0.798975i | \(0.705376\pi\) | |||||||
\(740\) | 9.63435i | 0.354166i | ||||||||
\(741\) | 4.03409i | 0.148196i | ||||||||
\(742\) | −11.9074 | + | 2.17263i | −0.437136 | + | 0.0797598i | ||||
\(743\) | 39.7439i | 1.45806i | 0.684481 | + | 0.729030i | \(0.260029\pi\) | ||||
−0.684481 | + | 0.729030i | \(0.739971\pi\) | |||||||
\(744\) | 9.73228i | 0.356803i | ||||||||
\(745\) | −3.07364 | −0.112609 | ||||||||
\(746\) | 1.59822 | 0.0585149 | ||||||||
\(747\) | −6.58257 | −0.240844 | ||||||||
\(748\) | 36.7909 | + | 8.26008i | 1.34521 | + | 0.302018i | ||||
\(749\) | 16.3948 | − | 2.99139i | 0.599052 | − | 0.109303i | ||||
\(750\) | − | 0.474903i | − | 0.0173410i | ||||||
\(751\) | −10.9222 | −0.398556 | −0.199278 | − | 0.979943i | \(-0.563860\pi\) | ||||
−0.199278 | + | 0.979943i | \(0.563860\pi\) | |||||||
\(752\) | 12.3299i | 0.449625i | ||||||||
\(753\) | 20.4289 | 0.744469 | ||||||||
\(754\) | 0.974177 | 0.0354774 | ||||||||
\(755\) | −9.28384 | −0.337874 | ||||||||
\(756\) | 4.61855 | − | 0.842700i | 0.167975 | − | 0.0306487i | ||||
\(757\) | 32.6738 | 1.18755 | 0.593774 | − | 0.804632i | \(-0.297637\pi\) | ||||
0.593774 | + | 0.804632i | \(0.297637\pi\) | |||||||
\(758\) | − | 7.72869i | − | 0.280719i | ||||||
\(759\) | 0.562683 | − | 2.50623i | 0.0204241 | − | 0.0909703i | ||||
\(760\) | −8.87993 | −0.322109 | ||||||||
\(761\) | −41.0691 | −1.48876 | −0.744378 | − | 0.667759i | \(-0.767254\pi\) | ||||
−0.744378 | + | 0.667759i | \(0.767254\pi\) | |||||||
\(762\) | 0.718285i | 0.0260207i | ||||||||
\(763\) | 23.2326 | − | 4.23901i | 0.841075 | − | 0.153462i | ||||
\(764\) | 25.1525 | 0.909985 | ||||||||
\(765\) | 6.40701i | 0.231646i | ||||||||
\(766\) | 13.5883 | 0.490964 | ||||||||
\(767\) | 2.72394i | 0.0983558i | ||||||||
\(768\) | 0.851266i | 0.0307174i | ||||||||
\(769\) | 37.8727 | 1.36572 | 0.682862 | − | 0.730547i | \(-0.260735\pi\) | ||||
0.682862 | + | 0.730547i | \(0.260735\pi\) | |||||||
\(770\) | −0.168217 | + | 4.16386i | −0.00606211 | + | 0.150055i | ||||
\(771\) | 20.2883 | 0.730665 | ||||||||
\(772\) | − | 1.68540i | − | 0.0606588i | ||||||
\(773\) | 14.2694i | 0.513234i | 0.966513 | + | 0.256617i | \(0.0826079\pi\) | ||||
−0.966513 | + | 0.256617i | \(0.917392\pi\) | |||||||
\(774\) | 3.11089 | 0.111819 | ||||||||
\(775\) | 5.42943i | 0.195031i | ||||||||
\(776\) | −21.8756 | −0.785287 | ||||||||
\(777\) | 14.1316 | − | 2.57845i | 0.506969 | − | 0.0925014i | ||||
\(778\) | 13.5955i | 0.487421i | ||||||||
\(779\) | −13.7258 | −0.491777 | ||||||||
\(780\) | −1.44499 | −0.0517389 | ||||||||
\(781\) | −9.84640 | − | 2.21066i | −0.352332 | − | 0.0791035i | ||||
\(782\) | − | 2.35648i | − | 0.0842674i | ||||||
\(783\) | 2.51905 | 0.0900234 | ||||||||
\(784\) | −17.6669 | + | 6.66900i | −0.630959 | + | 0.238179i | ||||
\(785\) | −22.6971 | −0.810094 | ||||||||
\(786\) | −4.36769 | −0.155790 | ||||||||
\(787\) | −55.7594 | −1.98761 | −0.993805 | − | 0.111142i | \(-0.964549\pi\) | ||||
−0.993805 | + | 0.111142i | \(0.964549\pi\) | |||||||
\(788\) | − | 25.0321i | − | 0.891733i | ||||||
\(789\) | 25.6361 | 0.912670 | ||||||||
\(790\) | − | 3.78794i | − | 0.134769i | ||||||
\(791\) | −4.49474 | − | 24.6341i | −0.159814 | − | 0.875889i | ||||
\(792\) | 1.30233 | − | 5.80067i | 0.0462763 | − | 0.206118i | ||||
\(793\) | 6.54362 | 0.232371 | ||||||||
\(794\) | −3.80202 | −0.134929 | ||||||||
\(795\) | 9.63333 | 0.341659 | ||||||||
\(796\) | − | 5.87335i | − | 0.208176i | ||||||
\(797\) | − | 37.1400i | − | 1.31557i | −0.753207 | − | 0.657783i | \(-0.771494\pi\) | ||
0.753207 | − | 0.657783i | \(-0.228506\pi\) | |||||||
\(798\) | 1.11727 | + | 6.12338i | 0.0395510 | + | 0.216765i | ||||
\(799\) | 29.2837i | 1.03598i | ||||||||
\(800\) | − | 4.86614i | − | 0.172044i | ||||||
\(801\) | − | 1.12710i | − | 0.0398241i | ||||||
\(802\) | 14.1096i | 0.498229i | ||||||||
\(803\) | −29.8919 | − | 6.71114i | −1.05486 | − | 0.236831i | ||||
\(804\) | 28.4289i | 1.00261i | ||||||||
\(805\) | −2.01577 | + | 0.367797i | −0.0710465 | + | 0.0129631i | ||||
\(806\) | −2.09969 | −0.0739585 | ||||||||
\(807\) | 15.5197 | 0.546319 | ||||||||
\(808\) | − | 11.0335i | − | 0.388158i | ||||||
\(809\) | 20.4773i | 0.719944i | 0.932963 | + | 0.359972i | \(0.117214\pi\) | ||||
−0.932963 | + | 0.359972i | \(0.882786\pi\) | |||||||
\(810\) | 0.474903 | 0.0166864 | ||||||||
\(811\) | 11.2321 | 0.394413 | 0.197206 | − | 0.980362i | \(-0.436813\pi\) | ||||
0.197206 | + | 0.980362i | \(0.436813\pi\) | |||||||
\(812\) | −11.6343 | + | 2.12280i | −0.408286 | + | 0.0744957i | ||||
\(813\) | 1.42566i | 0.0500002i | ||||||||
\(814\) | 1.87335 | − | 8.34405i | 0.0656611 | − | 0.292459i | ||||
\(815\) | − | 1.19630i | − | 0.0419047i | ||||||
\(816\) | 17.2840i | 0.605060i | ||||||||
\(817\) | − | 32.4511i | − | 1.13532i | ||||||
\(818\) | − | 12.1217i | − | 0.423824i | ||||||
\(819\) | 0.386724 | + | 2.11950i | 0.0135132 | + | 0.0740615i | ||||
\(820\) | − | 4.91649i | − | 0.171691i | ||||||
\(821\) | 36.1005i | 1.25991i | 0.776630 | + | 0.629957i | \(0.216928\pi\) | ||||
−0.776630 | + | 0.629957i | \(0.783072\pi\) | |||||||
\(822\) | 6.04377 | 0.210801 | ||||||||
\(823\) | −7.42012 | −0.258649 | −0.129325 | − | 0.991602i | \(-0.541281\pi\) | ||||
−0.129325 | + | 0.991602i | \(0.541281\pi\) | |||||||
\(824\) | −2.82887 | −0.0985483 | ||||||||
\(825\) | 0.726543 | − | 3.23607i | 0.0252950 | − | 0.112665i | ||||
\(826\) | 0.754415 | + | 4.13469i | 0.0262495 | + | 0.143864i | ||||
\(827\) | − | 8.28729i | − | 0.288177i | −0.989565 | − | 0.144089i | \(-0.953975\pi\) | ||
0.989565 | − | 0.144089i | \(-0.0460251\pi\) | |||||||
\(828\) | 1.37427 | 0.0477591 | ||||||||
\(829\) | − | 39.1704i | − | 1.36044i | −0.733006 | − | 0.680222i | \(-0.761883\pi\) | ||
0.733006 | − | 0.680222i | \(-0.238117\pi\) | |||||||
\(830\) | 3.12608 | 0.108508 | ||||||||
\(831\) | 3.29785 | 0.114401 | ||||||||
\(832\) | −2.51169 | −0.0870773 | ||||||||
\(833\) | −41.9591 | + | 15.8390i | −1.45380 | + | 0.548789i | ||||
\(834\) | 5.07680 | 0.175795 | ||||||||
\(835\) | − | 20.0947i | − | 0.695407i | ||||||
\(836\) | −28.4469 | − | 6.38672i | −0.983856 | − | 0.220889i | ||||
\(837\) | −5.42943 | −0.187669 | ||||||||
\(838\) | 4.65220 | 0.160707 | ||||||||
\(839\) | 2.69823i | 0.0931534i | 0.998915 | + | 0.0465767i | \(0.0148312\pi\) | ||||
−0.998915 | + | 0.0465767i | \(0.985169\pi\) | |||||||
\(840\) | −4.66550 | + | 0.851266i | −0.160975 | + | 0.0293715i | ||||
\(841\) | 22.6544 | 0.781186 | ||||||||
\(842\) | − | 1.52181i | − | 0.0524450i | ||||||
\(843\) | −6.26696 | −0.215846 | ||||||||
\(844\) | − | 47.0929i | − | 1.62100i | ||||||
\(845\) | 12.3369i | 0.424402i | ||||||||
\(846\) | 2.17058 | 0.0746260 | ||||||||
\(847\) | −7.51645 | + | 28.1159i | −0.258268 | + | 0.966073i | ||||
\(848\) | 25.9875 | 0.892415 | ||||||||
\(849\) | − | 25.9472i | − | 0.890504i | ||||||
\(850\) | − | 3.04271i | − | 0.104364i | ||||||
\(851\) | 4.20492 | 0.144143 | ||||||||
\(852\) | − | 5.39918i | − | 0.184973i | ||||||
\(853\) | −13.5735 | −0.464748 | −0.232374 | − | 0.972627i | \(-0.574649\pi\) | ||||
−0.232374 | + | 0.972627i | \(0.574649\pi\) | |||||||
\(854\) | 9.93261 | − | 1.81230i | 0.339887 | − | 0.0620157i | ||||
\(855\) | − | 4.95392i | − | 0.169421i | ||||||
\(856\) | 11.2909 | 0.385915 | ||||||||
\(857\) | −43.4406 | −1.48390 | −0.741951 | − | 0.670454i | \(-0.766099\pi\) | ||||
−0.741951 | + | 0.670454i | \(0.766099\pi\) | |||||||
\(858\) | 1.25147 | + | 0.280972i | 0.0427244 | + | 0.00959222i | ||||
\(859\) | 22.6431i | 0.772572i | 0.922379 | + | 0.386286i | \(0.126242\pi\) | ||||
−0.922379 | + | 0.386286i | \(0.873758\pi\) | |||||||
\(860\) | 11.6238 | 0.396368 | ||||||||
\(861\) | −7.21149 | + | 1.31581i | −0.245767 | + | 0.0448426i | ||||
\(862\) | 6.27142 | 0.213606 | ||||||||
\(863\) | −15.8723 | −0.540301 | −0.270150 | − | 0.962818i | \(-0.587073\pi\) | ||||
−0.270150 | + | 0.962818i | \(0.587073\pi\) | |||||||
\(864\) | 4.86614 | 0.165549 | ||||||||
\(865\) | 14.0429i | 0.477472i | ||||||||
\(866\) | 8.60603 | 0.292445 | ||||||||
\(867\) | 24.0497i | 0.816772i | ||||||||
\(868\) | 25.0761 | − | 4.57538i | 0.851138 | − | 0.155298i | ||||
\(869\) | 5.79508 | − | 25.8117i | 0.196585 | − | 0.875601i | ||||
\(870\) | −1.19630 | −0.0405585 | ||||||||
\(871\) | −13.0463 | −0.442058 | ||||||||
\(872\) | 16.0000 | 0.541828 | ||||||||
\(873\) | − | 12.2039i | − | 0.413039i | ||||||
\(874\) | 1.82204i | 0.0616313i | ||||||||
\(875\) | −2.60278 | + | 0.474903i | −0.0879900 | + | 0.0160546i | ||||
\(876\) | − | 16.3909i | − | 0.553798i | ||||||
\(877\) | 2.06252i | 0.0696462i | 0.999393 | + | 0.0348231i | \(0.0110868\pi\) | ||||
−0.999393 | + | 0.0348231i | \(0.988913\pi\) | |||||||
\(878\) | 13.7317i | 0.463421i | ||||||||
\(879\) | − | 25.6554i | − | 0.865337i | ||||||
\(880\) | 1.95997 | − | 8.72984i | 0.0660706 | − | 0.294283i | ||||
\(881\) | − | 23.7891i | − | 0.801475i | −0.916193 | − | 0.400737i | \(-0.868754\pi\) | ||
0.916193 | − | 0.400737i | \(-0.131246\pi\) | |||||||
\(882\) | 1.17402 | + | 3.11011i | 0.0395315 | + | 0.104723i | ||||
\(883\) | −24.7263 | −0.832107 | −0.416054 | − | 0.909340i | \(-0.636587\pi\) | ||||
−0.416054 | + | 0.909340i | \(0.636587\pi\) | |||||||
\(884\) | −9.25806 | −0.311382 | ||||||||
\(885\) | − | 3.34504i | − | 0.112442i | ||||||
\(886\) | 3.84979i | 0.129336i | ||||||||
\(887\) | −51.4590 | −1.72783 | −0.863913 | − | 0.503642i | \(-0.831993\pi\) | ||||
−0.863913 | + | 0.503642i | \(0.831993\pi\) | |||||||
\(888\) | 9.73228 | 0.326594 | ||||||||
\(889\) | 3.93668 | − | 0.718285i | 0.132032 | − | 0.0240905i | ||||
\(890\) | 0.535262i | 0.0179420i | ||||||||
\(891\) | 3.23607 | + | 0.726543i | 0.108412 | + | 0.0243401i | ||||
\(892\) | 22.4932i | 0.753128i | ||||||||
\(893\) | − | 22.6422i | − | 0.757694i | ||||||
\(894\) | 1.45968i | 0.0488189i | ||||||||
\(895\) | − | 3.88638i | − | 0.129907i | ||||||
\(896\) | −29.1435 | + | 5.31752i | −0.973617 | + | 0.177646i | ||||
\(897\) | 0.630667i | 0.0210573i | ||||||||
\(898\) | − | 5.04001i | − | 0.168187i | ||||||
\(899\) | 13.6770 | 0.456153 | ||||||||
\(900\) | 1.77447 | 0.0591489 | ||||||||
\(901\) | 61.7208 | 2.05622 | ||||||||
\(902\) | −0.955990 | + | 4.25804i | −0.0318310 | + | 0.141777i | ||||
\(903\) | −3.11089 | − | 17.0497i | −0.103524 | − | 0.567380i | ||||
\(904\) | − | 16.9652i | − | 0.564256i | ||||||
\(905\) | −4.60466 | −0.153064 | ||||||||
\(906\) | 4.40892i | 0.146477i | ||||||||
\(907\) | 16.6220 | 0.551925 | 0.275963 | − | 0.961168i | \(-0.411003\pi\) | ||||
0.275963 | + | 0.961168i | \(0.411003\pi\) | |||||||
\(908\) | 40.4686 | 1.34300 | ||||||||
\(909\) | 6.15537 | 0.204161 | ||||||||
\(910\) | −0.183657 | − | 1.00656i | −0.00608815 | − | 0.0333671i | ||||
\(911\) | 33.6402 | 1.11455 | 0.557275 | − | 0.830328i | \(-0.311847\pi\) | ||||
0.557275 | + | 0.830328i | \(0.311847\pi\) | |||||||
\(912\) | − | 13.3640i | − | 0.442528i | ||||||
\(913\) | 21.3016 | + | 4.78252i | 0.704981 | + | 0.158278i | ||||
\(914\) | −18.6030 | −0.615332 | ||||||||
\(915\) | −8.03565 | −0.265650 | ||||||||
\(916\) | 27.0297i | 0.893086i | ||||||||
\(917\) | 4.36769 | + | 23.9378i | 0.144234 | + | 0.790497i | ||||
\(918\) | 3.04271 | 0.100424 | ||||||||
\(919\) | 16.0146i | 0.528271i | 0.964486 | + | 0.264136i | \(0.0850867\pi\) | ||||
−0.964486 | + | 0.264136i | \(0.914913\pi\) | |||||||
\(920\) | −1.38824 | −0.0457688 | ||||||||
\(921\) | 17.7954i | 0.586377i | ||||||||
\(922\) | − | 3.18825i | − | 0.105000i | ||||||
\(923\) | 2.47775 | 0.0815560 | ||||||||
\(924\) | −15.5582 | − | 0.628539i | −0.511827 | − | 0.0206774i | ||||
\(925\) | 5.42943 | 0.178519 | ||||||||
\(926\) | − | 9.22091i | − | 0.303018i | ||||||
\(927\) | − | 1.57816i | − | 0.0518337i | ||||||
\(928\) | −12.2580 | −0.402390 | ||||||||
\(929\) | − | 1.93181i | − | 0.0633808i | −0.999498 | − | 0.0316904i | \(-0.989911\pi\) | ||
0.999498 | − | 0.0316904i | \(-0.0100891\pi\) | |||||||
\(930\) | 2.57845 | 0.0845508 | ||||||||
\(931\) | 32.4429 | − | 12.2468i | 1.06327 | − | 0.401372i | ||||
\(932\) | − | 34.7077i | − | 1.13689i | ||||||
\(933\) | −27.2195 | −0.891128 | ||||||||
\(934\) | −10.0924 | −0.330233 | ||||||||
\(935\) | 4.65496 | − | 20.7335i | 0.152234 | − | 0.678058i | ||||
\(936\) | 1.45968i | 0.0477111i | ||||||||
\(937\) | 44.3331 | 1.44830 | 0.724150 | − | 0.689643i | \(-0.242232\pi\) | ||||
0.724150 | + | 0.689643i | \(0.242232\pi\) | |||||||
\(938\) | −19.8031 | + | 3.61328i | −0.646595 | + | 0.117978i | ||||
\(939\) | −10.4581 | −0.341287 | ||||||||
\(940\) | 8.11033 | 0.264530 | ||||||||
\(941\) | 0.677413 | 0.0220830 | 0.0110415 | − | 0.999939i | \(-0.496485\pi\) | ||||
0.0110415 | + | 0.999939i | \(0.496485\pi\) | |||||||
\(942\) | 10.7789i | 0.351196i | ||||||||
\(943\) | −2.14581 | −0.0698771 | ||||||||
\(944\) | − | 9.02380i | − | 0.293700i | ||||||
\(945\) | −0.474903 | − | 2.60278i | −0.0154486 | − | 0.0846685i | ||||
\(946\) | −10.0671 | − | 2.26019i | −0.327308 | − | 0.0734853i | ||||
\(947\) | −49.5219 | −1.60924 | −0.804622 | − | 0.593787i | \(-0.797632\pi\) | ||||
−0.804622 | + | 0.593787i | \(0.797632\pi\) | |||||||
\(948\) | 14.1536 | 0.459687 | ||||||||
\(949\) | 7.52198 | 0.244174 | ||||||||
\(950\) | 2.35263i | 0.0763294i | ||||||||
\(951\) | 11.7821i | 0.382060i | ||||||||
\(952\) | −29.8919 | + | 5.45407i | −0.968801 | + | 0.176767i | ||||
\(953\) | 32.2848i | 1.04581i | 0.852392 | + | 0.522903i | \(0.175151\pi\) | ||||
−0.852392 | + | 0.522903i | \(0.824849\pi\) | |||||||
\(954\) | − | 4.57489i | − | 0.148118i | ||||||
\(955\) | − | 14.1747i | − | 0.458681i | ||||||
\(956\) | − | 41.9135i | − | 1.35558i | ||||||
\(957\) | −8.15181 | − | 1.83020i | −0.263511 | − | 0.0591618i | ||||
\(958\) | − | 3.23424i | − | 0.104494i | ||||||
\(959\) | −6.04377 | − | 33.1239i | −0.195164 | − | 1.06963i | ||||
\(960\) | 3.08439 | 0.0995484 | ||||||||
\(961\) | 1.52129 | 0.0490738 | ||||||||
\(962\) | 2.09969i | 0.0676968i | ||||||||
\(963\) | 6.29895i | 0.202981i | ||||||||
\(964\) | 49.1728 | 1.58375 | ||||||||
\(965\) | −0.949806 | −0.0305753 | ||||||||
\(966\) | 0.174668 | + | 0.957294i | 0.00561984 | + | 0.0308004i | ||||
\(967\) | − | 16.1326i | − | 0.518790i | −0.965771 | − | 0.259395i | \(-0.916477\pi\) | ||
0.965771 | − | 0.259395i | \(-0.0835232\pi\) | |||||||
\(968\) | −8.42887 | + | 17.8252i | −0.270914 | + | 0.572922i | ||||
\(969\) | − | 31.7398i | − | 1.01963i | ||||||
\(970\) | 5.79567i | 0.186088i | ||||||||
\(971\) | 11.9237i | 0.382648i | 0.981527 | + | 0.191324i | \(0.0612782\pi\) | ||||
−0.981527 | + | 0.191324i | \(0.938722\pi\) | |||||||
\(972\) | 1.77447i | 0.0569161i | ||||||||
\(973\) | −5.07680 | − | 27.8242i | −0.162755 | − | 0.892003i | ||||
\(974\) | 2.49932i | 0.0800835i | ||||||||
\(975\) | 0.814323i | 0.0260792i | ||||||||
\(976\) | −21.6775 | −0.693881 | ||||||||
\(977\) | −10.6478 | −0.340654 | −0.170327 | − | 0.985388i | \(-0.554482\pi\) | ||||
−0.170327 | + | 0.985388i | \(0.554482\pi\) | |||||||
\(978\) | −0.568128 | −0.0181667 | ||||||||
\(979\) | −0.818885 | + | 3.64737i | −0.0261717 | + | 0.116570i | ||||
\(980\) | 4.38672 | + | 11.6209i | 0.140129 | + | 0.371215i | ||||
\(981\) | 8.92605i | 0.284987i | ||||||||
\(982\) | −20.2038 | −0.644729 | ||||||||
\(983\) | 59.3412i | 1.89269i | 0.323157 | + | 0.946345i | \(0.395256\pi\) | ||||
−0.323157 | + | 0.946345i | \(0.604744\pi\) | |||||||
\(984\) | −4.96647 | −0.158325 | ||||||||
\(985\) | −14.1068 | −0.449481 | ||||||||
\(986\) | −7.66472 | −0.244094 | ||||||||
\(987\) | −2.17058 | − | 11.8962i | −0.0690902 | − | 0.378660i | ||||
\(988\) | 7.15837 | 0.227738 | ||||||||
\(989\) | − | 5.07321i | − | 0.161319i | ||||||
\(990\) | −1.53682 | − | 0.345037i | −0.0488433 | − | 0.0109660i | ||||
\(991\) | 39.7659 | 1.26320 | 0.631602 | − | 0.775293i | \(-0.282398\pi\) | ||||
0.631602 | + | 0.775293i | \(0.282398\pi\) | |||||||
\(992\) | 26.4204 | 0.838848 | ||||||||
\(993\) | − | 18.5987i | − | 0.590211i | ||||||
\(994\) | 3.76099 | − | 0.686230i | 0.119291 | − | 0.0217659i | ||||
\(995\) | −3.30993 | −0.104932 | ||||||||
\(996\) | 11.6806i | 0.370112i | ||||||||
\(997\) | −7.48964 | −0.237199 | −0.118600 | − | 0.992942i | \(-0.537841\pi\) | ||||
−0.118600 | + | 0.992942i | \(0.537841\pi\) | |||||||
\(998\) | 3.48199i | 0.110221i | ||||||||
\(999\) | 5.42943i | 0.171780i |
(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 | 1155.2.i.c.76.10 | yes | 16 | |
7.6 | odd | 2 | inner | 1155.2.i.c.76.9 | yes | 16 | |
11.10 | odd | 2 | inner | 1155.2.i.c.76.8 | yes | 16 | |
77.76 | even | 2 | inner | 1155.2.i.c.76.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.c.76.7 | ✓ | 16 | 77.76 | even | 2 | inner | |
1155.2.i.c.76.8 | yes | 16 | 11.10 | odd | 2 | inner | |
1155.2.i.c.76.9 | yes | 16 | 7.6 | odd | 2 | inner | |
1155.2.i.c.76.10 | yes | 16 | 1.1 | even | 1 | trivial |