Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [351,2,Mod(64,351)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(351, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("351.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 351 = 3^{3} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 351.t (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.80274911095\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 6x^{16} + 9x^{14} + 54x^{12} + 81x^{10} + 486x^{8} + 729x^{6} - 4374x^{4} + 59049 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{9} \) |
Twist minimal: | no (minimal twist has level 117) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 64.2 | ||
Root | \(-1.23798 - 1.21137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 351.64 |
Dual form | 351.2.t.c.181.2 |
$q$-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 \(\left(\mathbb{Z}/351\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97712 | + | 1.14149i | −1.39803 | + | 0.807156i | −0.994187 | − | 0.107670i | \(-0.965661\pi\) |
−0.403848 | + | 0.914826i | \(0.632328\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.60600 | − | 2.78168i | 0.803001 | − | 1.39084i | ||||
\(5\) | 2.78501 | + | 1.60793i | 1.24550 | + | 0.719088i | 0.970208 | − | 0.242274i | \(-0.0778933\pi\) |
0.275289 | + | 0.961362i | \(0.411227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.09815 | + | 1.21137i | −0.793025 | + | 0.457853i | −0.841026 | − | 0.540994i | \(-0.818048\pi\) |
0.0480013 | + | 0.998847i | \(0.484715\pi\) | |||||||
\(8\) | 2.76698i | 0.978274i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.34174 | −2.32166 | ||||||||
\(11\) | −1.27730 | + | 0.737448i | −0.385119 | + | 0.222349i | −0.680043 | − | 0.733172i | \(-0.738039\pi\) |
0.294924 | + | 0.955521i | \(0.404706\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.56557 | + | 0.535475i | 0.988910 | + | 0.148514i | ||||
\(14\) | 2.76553 | − | 4.79003i | 0.739118 | − | 1.28019i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0535232 | + | 0.0927049i | 0.0133808 | + | 0.0231762i | ||||
\(17\) | 5.12974 | 1.24414 | 0.622072 | − | 0.782960i | \(-0.286291\pi\) | ||||
0.622072 | + | 0.782960i | \(0.286291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.13065i | − | 0.259389i | −0.991554 | − | 0.129694i | \(-0.958600\pi\) | ||
0.991554 | − | 0.129694i | \(-0.0413996\pi\) | |||||||
\(20\) | 8.94547 | − | 5.16467i | 2.00027 | − | 1.15486i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.68358 | − | 2.91604i | 0.358940 | − | 0.621703i | ||||
\(23\) | −4.61735 | + | 7.99748i | −0.962784 | + | 1.66759i | −0.247328 | + | 0.968932i | \(0.579553\pi\) |
−0.715455 | + | 0.698658i | \(0.753781\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.67087 | + | 4.62608i | 0.534174 | + | 0.925217i | ||||
\(26\) | −7.66079 | + | 3.01136i | −1.50240 | + | 0.590577i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 7.78182i | 1.47063i | ||||||||
\(29\) | 0.487293 | + | 0.844016i | 0.0904880 | + | 0.156730i | 0.907717 | − | 0.419584i | \(-0.137824\pi\) |
−0.817229 | + | 0.576314i | \(0.804491\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.16380 | − | 1.82662i | −0.568235 | − | 0.328071i | 0.188209 | − | 0.982129i | \(-0.439732\pi\) |
−0.756444 | + | 0.654058i | \(0.773065\pi\) | |||||||
\(32\) | −5.00419 | − | 2.88917i | −0.884624 | − | 0.510738i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −10.1421 | + | 5.85555i | −1.73936 | + | 1.00422i | ||||
\(35\) | −7.79116 | −1.31695 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.22691i | 0.694900i | 0.937698 | + | 0.347450i | \(0.112952\pi\) | ||||
−0.937698 | + | 0.347450i | \(0.887048\pi\) | |||||||
\(38\) | 1.29063 | + | 2.23543i | 0.209367 | + | 0.362634i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.44910 | + | 7.70607i | −0.703465 | + | 1.21844i | ||||
\(41\) | −3.47188 | − | 2.00449i | −0.542217 | − | 0.313049i | 0.203760 | − | 0.979021i | \(-0.434684\pi\) |
−0.745977 | + | 0.665972i | \(0.768017\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.33040 | + | 7.50047i | 0.660379 | + | 1.14381i | 0.980516 | + | 0.196439i | \(0.0629377\pi\) |
−0.320137 | + | 0.947371i | \(0.603729\pi\) | |||||||
\(44\) | 4.73737i | 0.714185i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 21.0826i | − | 3.10847i | ||||||
\(47\) | −1.33337 | + | 0.769820i | −0.194492 | + | 0.112290i | −0.594084 | − | 0.804403i | \(-0.702485\pi\) |
0.399592 | + | 0.916693i | \(0.369152\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.565185 | + | 0.978929i | −0.0807407 | + | 0.139847i | ||||
\(50\) | −10.5613 | − | 6.09755i | −1.49359 | − | 0.862324i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.21582 | − | 9.05828i | 1.00065 | − | 1.25616i | ||||
\(53\) | −0.739889 | −0.101632 | −0.0508158 | − | 0.998708i | \(-0.516182\pi\) | ||||
−0.0508158 | + | 0.998708i | \(0.516182\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.74305 | −0.639553 | ||||||||
\(56\) | −3.35182 | − | 5.80553i | −0.447906 | − | 0.775796i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.92687 | − | 1.11248i | −0.253011 | − | 0.146076i | ||||
\(59\) | 6.72630 | + | 3.88343i | 0.875689 | + | 0.505580i | 0.869235 | − | 0.494400i | \(-0.164612\pi\) |
0.00645471 | + | 0.999979i | \(0.497945\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.06781 | − | 7.04566i | −0.520830 | − | 0.902104i | −0.999707 | − | 0.0242218i | \(-0.992289\pi\) |
0.478877 | − | 0.877882i | \(-0.341044\pi\) | |||||||
\(62\) | 8.34028 | 1.05922 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.9777 | 1.62222 | ||||||||
\(65\) | 9.06915 | + | 7.22448i | 1.12489 | + | 0.896087i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.669411 | − | 0.386485i | −0.0817816 | − | 0.0472166i | 0.458552 | − | 0.888668i | \(-0.348368\pi\) |
−0.540333 | + | 0.841451i | \(0.681702\pi\) | |||||||
\(68\) | 8.23837 | − | 14.2693i | 0.999049 | − | 1.73040i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 15.4041 | − | 8.89354i | 1.84114 | − | 1.06298i | ||||
\(71\) | 3.01136i | 0.357383i | 0.983905 | + | 0.178692i | \(0.0571864\pi\) | ||||
−0.983905 | + | 0.178692i | \(0.942814\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.21010i | 1.07796i | 0.842318 | + | 0.538980i | \(0.181190\pi\) | ||||
−0.842318 | + | 0.538980i | \(0.818810\pi\) | |||||||
\(74\) | −4.82498 | − | 8.35711i | −0.560893 | − | 0.971495i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.14510 | − | 1.81582i | −0.360768 | − | 0.208289i | ||||
\(77\) | 1.78664 | − | 3.09455i | 0.203606 | − | 0.352656i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.86858 | − | 3.23648i | −0.210232 | − | 0.364133i | 0.741555 | − | 0.670892i | \(-0.234089\pi\) |
−0.951787 | + | 0.306759i | \(0.900755\pi\) | |||||||
\(80\) | 0.344246i | 0.0384879i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.15243 | 1.01072 | ||||||||
\(83\) | 12.3640 | − | 7.13838i | 1.35713 | − | 0.783539i | 0.367893 | − | 0.929868i | \(-0.380079\pi\) |
0.989236 | + | 0.146329i | \(0.0467460\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.2864 | + | 8.24826i | 1.54958 | + | 0.894649i | ||||
\(86\) | −17.1234 | − | 9.88621i | −1.84647 | − | 1.06606i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.04050 | − | 3.53425i | −0.217518 | − | 0.376752i | ||||
\(89\) | − | 8.21257i | − | 0.870531i | −0.900302 | − | 0.435265i | \(-0.856655\pi\) | ||
0.900302 | − | 0.435265i | \(-0.143345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.12974 | + | 3.19570i | −0.852228 | + | 0.335000i | ||||
\(92\) | 14.8309 | + | 25.6879i | 1.54623 | + | 2.67815i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.75748 | − | 3.04405i | 0.181271 | − | 0.313970i | ||||
\(95\) | 1.81800 | − | 3.14887i | 0.186523 | − | 0.323068i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.1880 | − | 7.61407i | 1.33903 | − | 0.773092i | 0.352370 | − | 0.935861i | \(-0.385376\pi\) |
0.986664 | + | 0.162769i | \(0.0520425\pi\) | |||||||
\(98\) | − | 2.58061i | − | 0.260681i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 17.1577 | 1.71577 | ||||||||
\(101\) | −7.45316 | − | 12.9092i | −0.741617 | − | 1.28452i | −0.951759 | − | 0.306847i | \(-0.900726\pi\) |
0.210142 | − | 0.977671i | \(-0.432607\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.26553 | − | 5.65606i | 0.321762 | − | 0.557308i | −0.659090 | − | 0.752064i | \(-0.729058\pi\) |
0.980852 | + | 0.194756i | \(0.0623916\pi\) | |||||||
\(104\) | −1.48165 | + | 9.86584i | −0.145287 | + | 0.967426i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.46285 | − | 0.844576i | 0.142084 | − | 0.0820325i | ||||
\(107\) | 9.37527 | 0.906341 | 0.453171 | − | 0.891424i | \(-0.350293\pi\) | ||||
0.453171 | + | 0.891424i | \(0.350293\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.5859i | − | 1.39707i | −0.715574 | − | 0.698537i | \(-0.753835\pi\) | ||
0.715574 | − | 0.698537i | \(-0.246165\pi\) | |||||||
\(110\) | 9.37758 | − | 5.41415i | 0.894117 | − | 0.516219i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.224599 | − | 0.129672i | −0.0212226 | − | 0.0122529i | ||||
\(113\) | 1.53382 | − | 2.65665i | 0.144290 | − | 0.249917i | −0.784818 | − | 0.619726i | \(-0.787244\pi\) |
0.929108 | + | 0.369809i | \(0.120577\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −25.7188 | + | 14.8487i | −2.39829 | + | 1.38465i | ||||
\(116\) | 3.13037 | 0.290648 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −17.7316 | −1.63233 | ||||||||
\(119\) | −10.7630 | + | 6.21399i | −0.986638 | + | 0.569636i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.41234 | + | 7.64240i | −0.401122 | + | 0.694764i | ||||
\(122\) | 16.0851 | + | 9.28674i | 1.45628 | + | 0.840782i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.1621 | + | 5.86711i | −0.912587 | + | 0.526882i | ||||
\(125\) | 1.09900i | 0.0982972i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.163893 | 0.0145432 | 0.00727160 | − | 0.999974i | \(-0.497685\pi\) | ||||
0.00727160 | + | 0.999974i | \(0.497685\pi\) | |||||||
\(128\) | −15.6502 | + | 9.03564i | −1.38329 | + | 0.798645i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −26.1775 | − | 3.93132i | −2.29592 | − | 0.344799i | ||||
\(131\) | 3.26584 | − | 5.65660i | 0.285338 | − | 0.494220i | −0.687353 | − | 0.726323i | \(-0.741228\pi\) |
0.972691 | + | 0.232104i | \(0.0745609\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.36963 | + | 2.37227i | 0.118762 | + | 0.205702i | ||||
\(134\) | 1.76467 | 0.152445 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14.1939i | 1.21712i | ||||||||
\(137\) | −12.0632 | + | 6.96467i | −1.03063 | + | 0.595032i | −0.917164 | − | 0.398511i | \(-0.869527\pi\) |
−0.113462 | + | 0.993542i | \(0.536194\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.09082 | − | 12.2817i | 0.601436 | − | 1.04172i | −0.391168 | − | 0.920319i | \(-0.627929\pi\) |
0.992604 | − | 0.121398i | \(-0.0387377\pi\) | |||||||
\(140\) | −12.5126 | + | 21.6725i | −1.05751 | + | 1.83166i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.43744 | − | 5.95382i | −0.288464 | − | 0.499634i | ||||
\(143\) | −4.94917 | + | 1.94546i | −0.413870 | + | 0.162687i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.13413i | 0.260275i | ||||||||
\(146\) | −10.5132 | − | 18.2095i | −0.870082 | − | 1.50703i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.7579 | + | 6.78843i | 0.966493 | + | 0.558005i | ||||
\(149\) | 16.0882 | + | 9.28851i | 1.31799 | + | 0.760945i | 0.983406 | − | 0.181419i | \(-0.0580691\pi\) |
0.334589 | + | 0.942364i | \(0.391402\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2989 | − | 5.94609i | 0.838115 | − | 0.483886i | −0.0185081 | − | 0.999829i | \(-0.505892\pi\) |
0.856623 | + | 0.515943i | \(0.172558\pi\) | |||||||
\(152\) | 3.12848 | 0.253753 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.15772i | 0.657368i | ||||||||
\(155\) | −5.87415 | − | 10.1743i | −0.471823 | − | 0.817222i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.99459 | + | 3.45472i | −0.159185 | + | 0.275717i | −0.934575 | − | 0.355766i | \(-0.884220\pi\) |
0.775390 | + | 0.631483i | \(0.217553\pi\) | |||||||
\(158\) | 7.38883 | + | 4.26594i | 0.587824 | + | 0.339380i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.29116 | − | 16.0928i | −0.734531 | − | 1.27224i | ||||
\(161\) | − | 22.3732i | − | 1.76325i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 5.18096i | − | 0.405804i | −0.979199 | − | 0.202902i | \(-0.934963\pi\) | ||
0.979199 | − | 0.202902i | \(-0.0650373\pi\) | |||||||
\(164\) | −11.1517 | + | 6.43843i | −0.870801 | + | 0.502757i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.2968 | + | 28.2268i | −1.26488 | + | 2.19083i | ||||
\(167\) | −0.706703 | − | 0.408015i | −0.0546863 | − | 0.0315732i | 0.472408 | − | 0.881380i | \(-0.343385\pi\) |
−0.527094 | + | 0.849807i | \(0.676718\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.4265 | + | 3.81854i | 0.955887 | + | 0.293734i | ||||
\(170\) | −37.6612 | −2.88848 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 27.8185 | 2.12114 | ||||||||
\(173\) | 0.261538 | + | 0.452997i | 0.0198844 | + | 0.0344407i | 0.875796 | − | 0.482681i | \(-0.160337\pi\) |
−0.855912 | + | 0.517122i | \(0.827004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.2078 | − | 6.47081i | −0.847227 | − | 0.489147i | ||||
\(176\) | −0.136730 | − | 0.0789411i | −0.0103064 | − | 0.00595041i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.37457 | + | 16.2372i | 0.702654 | + | 1.21703i | ||||
\(179\) | 14.1750 | 1.05949 | 0.529746 | − | 0.848156i | \(-0.322287\pi\) | ||||
0.529746 | + | 0.848156i | \(0.322287\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.9757 | −1.33612 | −0.668060 | − | 0.744107i | \(-0.732875\pi\) | ||||
−0.668060 | + | 0.744107i | \(0.732875\pi\) | |||||||
\(182\) | 12.4256 | − | 15.5983i | 0.921047 | − | 1.15622i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −22.1289 | − | 12.7761i | −1.63136 | − | 0.941867i | ||||
\(185\) | −6.79658 | + | 11.7720i | −0.499694 | + | 0.865496i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.55220 | + | 3.78291i | −0.479144 | + | 0.276634i | ||||
\(188\) | 4.94532i | 0.360675i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.30093i | 0.602213i | ||||||||
\(191\) | 4.64755 | + | 8.04979i | 0.336285 | + | 0.582462i | 0.983731 | − | 0.179649i | \(-0.0574962\pi\) |
−0.647446 | + | 0.762111i | \(0.724163\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.93585 | + | 5.73646i | 0.715198 | + | 0.412920i | 0.812983 | − | 0.582288i | \(-0.197842\pi\) |
−0.0977848 | + | 0.995208i | \(0.531176\pi\) | |||||||
\(194\) | −17.3828 | + | 30.1079i | −1.24801 | + | 2.16162i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.81538 | + | 3.14432i | 0.129670 | + | 0.224595i | ||||
\(197\) | − | 11.0296i | − | 0.785828i | −0.919575 | − | 0.392914i | \(-0.871467\pi\) | ||
0.919575 | − | 0.392914i | \(-0.128533\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.38397 | −0.0981068 | −0.0490534 | − | 0.998796i | \(-0.515620\pi\) | ||||
−0.0490534 | + | 0.998796i | \(0.515620\pi\) | |||||||
\(200\) | −12.8003 | + | 7.39024i | −0.905116 | + | 0.522569i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 29.4716 | + | 17.0154i | 2.07361 | + | 1.19720i | ||||
\(203\) | −2.04482 | − | 1.18058i | −0.143518 | − | 0.0828604i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.44616 | − | 11.1651i | −0.450219 | − | 0.779803i | ||||
\(206\) | 14.9103i | 1.03885i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.141199 | + | 0.359206i | 0.00979042 | + | 0.0249064i | ||||
\(209\) | 0.833794 | + | 1.44417i | 0.0576748 | + | 0.0998956i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.59187 | − | 7.95335i | 0.316117 | − | 0.547531i | −0.663557 | − | 0.748126i | \(-0.730954\pi\) |
0.979674 | + | 0.200595i | \(0.0642874\pi\) | |||||||
\(212\) | −1.18826 | + | 2.05813i | −0.0816102 | + | 0.141353i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.5360 | + | 10.7018i | −1.26710 | + | 0.731558i | ||||
\(215\) | 27.8519i | 1.89948i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.85083 | 0.600833 | ||||||||
\(218\) | 16.6496 | + | 28.8380i | 1.12766 | + | 1.95316i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.61735 | + | 13.1936i | −0.513562 | + | 0.889515i | ||||
\(221\) | 18.2904 | + | 2.74685i | 1.23035 | + | 0.184773i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.51495 | − | 3.18406i | 0.369308 | − | 0.213220i | −0.303848 | − | 0.952721i | \(-0.598271\pi\) |
0.673156 | + | 0.739500i | \(0.264938\pi\) | |||||||
\(224\) | 13.9994 | 0.935372 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 7.00336i | 0.465857i | ||||||||
\(227\) | −8.83052 | + | 5.09830i | −0.586102 | + | 0.338386i | −0.763555 | − | 0.645743i | \(-0.776548\pi\) |
0.177453 | + | 0.984129i | \(0.443214\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.02980 | − | 4.05866i | −0.464542 | − | 0.268204i | 0.249410 | − | 0.968398i | \(-0.419763\pi\) |
−0.713952 | + | 0.700194i | \(0.753097\pi\) | |||||||
\(230\) | 33.8994 | − | 58.7155i | 2.23526 | − | 3.87158i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.33537 | + | 1.34833i | −0.153325 | + | 0.0885221i | ||||
\(233\) | −8.37795 | −0.548858 | −0.274429 | − | 0.961607i | \(-0.588489\pi\) | ||||
−0.274429 | + | 0.961607i | \(0.588489\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.95126 | −0.322985 | ||||||||
\(236\) | 21.6049 | − | 12.4736i | 1.40636 | − | 0.811961i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.1864 | − | 24.5716i | 0.919570 | − | 1.59274i | ||||
\(239\) | −3.99453 | − | 2.30624i | −0.258385 | − | 0.149178i | 0.365213 | − | 0.930924i | \(-0.380996\pi\) |
−0.623598 | + | 0.781746i | \(0.714330\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.95910 | + | 4.01784i | −0.448275 | + | 0.258812i | −0.707101 | − | 0.707112i | \(-0.749998\pi\) |
0.258826 | + | 0.965924i | \(0.416664\pi\) | |||||||
\(242\) | − | 20.1466i | − | 1.29507i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −26.1316 | −1.67291 | ||||||||
\(245\) | −3.14810 | + | 1.81756i | −0.201125 | + | 0.116119i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.605434 | − | 4.03140i | 0.0385228 | − | 0.256512i | ||||
\(248\) | 5.05422 | − | 8.75417i | 0.320943 | − | 0.555890i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.25449 | − | 2.17285i | −0.0793411 | − | 0.137423i | ||||
\(251\) | −17.1127 | −1.08015 | −0.540073 | − | 0.841618i | \(-0.681604\pi\) | ||||
−0.540073 | + | 0.841618i | \(0.681604\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 13.6202i | − | 0.856295i | ||||||
\(254\) | −0.324037 | + | 0.187083i | −0.0203319 | + | 0.0117386i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 7.65044 | − | 13.2509i | 0.478152 | − | 0.828184i | ||||
\(257\) | −4.75712 | + | 8.23957i | −0.296741 | + | 0.513971i | −0.975388 | − | 0.220494i | \(-0.929233\pi\) |
0.678647 | + | 0.734464i | \(0.262566\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.12034 | − | 8.86869i | −0.318162 | − | 0.551073i | ||||
\(260\) | 34.6612 | − | 13.6249i | 2.14960 | − | 0.844981i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.9117i | 0.921248i | ||||||||
\(263\) | −13.9945 | − | 24.2392i | −0.862937 | − | 1.49465i | −0.869081 | − | 0.494670i | \(-0.835289\pi\) |
0.00614342 | − | 0.999981i | \(-0.498044\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.06060 | − | 1.18969i | −0.126582 | − | 0.0730820i | ||||
\(266\) | −5.41584 | − | 3.12684i | −0.332067 | − | 0.191719i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.15015 | + | 1.24139i | −0.131341 | + | 0.0758299i | ||||
\(269\) | 11.4199 | 0.696285 | 0.348143 | − | 0.937442i | \(-0.386812\pi\) | ||||
0.348143 | + | 0.937442i | \(0.386812\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 13.2786i | − | 0.806620i | −0.915064 | − | 0.403310i | \(-0.867860\pi\) | ||
0.915064 | − | 0.403310i | \(-0.132140\pi\) | |||||||
\(272\) | 0.274560 | + | 0.475552i | 0.0166477 | + | 0.0288346i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 15.9002 | − | 27.5400i | 0.960567 | − | 1.66375i | ||||
\(275\) | −6.82299 | − | 3.93925i | −0.411442 | − | 0.237546i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.900995 | − | 1.56057i | −0.0541356 | − | 0.0937655i | 0.837688 | − | 0.546150i | \(-0.183907\pi\) |
−0.891823 | + | 0.452384i | \(0.850574\pi\) | |||||||
\(278\) | 32.3764i | 1.94181i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 21.5580i | − | 1.28834i | ||||||
\(281\) | 9.94035 | − | 5.73906i | 0.592991 | − | 0.342364i | −0.173288 | − | 0.984871i | \(-0.555439\pi\) |
0.766279 | + | 0.642507i | \(0.222106\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3277 | − | 19.6201i | 0.673360 | − | 1.16629i | −0.303585 | − | 0.952804i | \(-0.598184\pi\) |
0.976945 | − | 0.213490i | \(-0.0684831\pi\) | |||||||
\(284\) | 8.37663 | + | 4.83625i | 0.497062 | + | 0.286979i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 7.56438 | − | 9.49583i | 0.447291 | − | 0.561500i | ||||
\(287\) | 9.71269 | 0.573322 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.31424 | 0.547896 | ||||||||
\(290\) | −3.57758 | − | 6.19655i | −0.210083 | − | 0.363874i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 25.6195 | + | 14.7914i | 1.49927 | + | 0.865603i | ||||
\(293\) | −14.1753 | − | 8.18413i | −0.828132 | − | 0.478122i | 0.0250809 | − | 0.999685i | \(-0.492016\pi\) |
−0.853213 | + | 0.521563i | \(0.825349\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4886 | + | 21.6308i | 0.727112 | + | 1.25940i | ||||
\(296\) | −11.6958 | −0.679803 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −42.4110 | −2.45680 | ||||||||
\(299\) | −20.7459 | + | 26.0431i | −1.19977 | + | 1.50611i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.1716 | − | 10.4914i | −1.04739 | − | 0.604714i | ||||
\(302\) | −13.5748 | + | 23.5123i | −0.781142 | + | 1.35298i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.104817 | − | 0.0605160i | 0.00601165 | − | 0.00347083i | ||||
\(305\) | − | 26.1630i | − | 1.49809i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.6786i | − | 0.951898i | −0.879473 | − | 0.475949i | \(-0.842105\pi\) | ||
0.879473 | − | 0.475949i | \(-0.157895\pi\) | |||||||
\(308\) | −5.73868 | − | 9.93969i | −0.326992 | − | 0.566367i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 23.2278 | + | 13.4106i | 1.31925 | + | 0.761670i | ||||
\(311\) | 4.05615 | − | 7.02546i | 0.230003 | − | 0.398377i | −0.727806 | − | 0.685784i | \(-0.759460\pi\) |
0.957809 | + | 0.287406i | \(0.0927930\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.0021 | + | 19.0562i | 0.621877 | + | 1.07712i | 0.989136 | + | 0.147003i | \(0.0469628\pi\) |
−0.367260 | + | 0.930119i | \(0.619704\pi\) | |||||||
\(314\) | − | 9.10720i | − | 0.513949i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.0038 | −0.675266 | ||||||||
\(317\) | 5.82742 | − | 3.36446i | 0.327301 | − | 0.188967i | −0.327341 | − | 0.944906i | \(-0.606153\pi\) |
0.654642 | + | 0.755939i | \(0.272819\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.24483 | − | 0.718706i | −0.0696974 | − | 0.0402398i | ||||
\(320\) | 36.1432 | + | 20.8673i | 2.02047 | + | 1.16652i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 25.5388 | + | 44.2345i | 1.42322 | + | 2.46509i | ||||
\(323\) | − | 5.79994i | − | 0.322717i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.04602 | + | 17.9248i | 0.390843 | + | 0.994289i | ||||
\(326\) | 5.91402 | + | 10.2434i | 0.327547 | + | 0.567328i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.54639 | − | 9.60662i | 0.306248 | − | 0.530437i | ||||
\(329\) | 1.86507 | − | 3.23039i | 0.102824 | − | 0.178097i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.226288 | + | 0.130648i | −0.0124379 | + | 0.00718104i | −0.506206 | − | 0.862413i | \(-0.668952\pi\) |
0.493768 | + | 0.869594i | \(0.335619\pi\) | |||||||
\(332\) | − | 45.8570i | − | 2.51673i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.86298 | 0.101938 | ||||||||
\(335\) | −1.24288 | − | 2.15273i | −0.0679058 | − | 0.117616i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.94402 | + | 5.09920i | −0.160371 | + | 0.277771i | −0.935002 | − | 0.354643i | \(-0.884602\pi\) |
0.774631 | + | 0.632414i | \(0.217936\pi\) | |||||||
\(338\) | −28.9276 | + | 6.63505i | −1.57345 | + | 0.360899i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 45.8880 | − | 26.4934i | 2.48862 | − | 1.43681i | ||||
\(341\) | 5.38815 | 0.291785 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 19.6977i | − | 1.06358i | ||||||
\(344\) | −20.7536 | + | 11.9821i | −1.11896 | + | 0.646032i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.03418 | − | 0.597086i | −0.0555980 | − | 0.0320995i | ||||
\(347\) | 1.59900 | − | 2.76956i | 0.0858391 | − | 0.148678i | −0.819909 | − | 0.572493i | \(-0.805976\pi\) |
0.905748 | + | 0.423816i | \(0.139310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0677 | − | 6.96727i | 0.645967 | − | 0.372949i | −0.140942 | − | 0.990018i | \(-0.545013\pi\) |
0.786909 | + | 0.617069i | \(0.211680\pi\) | |||||||
\(350\) | 29.5454 | 1.57927 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.52245 | 0.454248 | ||||||||
\(353\) | −13.5867 | + | 7.84426i | −0.723145 | + | 0.417508i | −0.815909 | − | 0.578180i | \(-0.803763\pi\) |
0.0927643 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.84206 | + | 8.38669i | −0.256990 | + | 0.445119i | ||||
\(356\) | −22.8447 | − | 13.1894i | −1.21077 | − | 0.699036i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −28.0257 | + | 16.1807i | −1.48121 | + | 0.855175i | ||||
\(359\) | 5.86486i | 0.309535i | 0.987951 | + | 0.154768i | \(0.0494629\pi\) | ||||
−0.987951 | + | 0.154768i | \(0.950537\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7216 | 0.932718 | ||||||||
\(362\) | 35.5400 | − | 20.5190i | 1.86794 | − | 1.07846i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.16697 | + | 27.7466i | −0.218409 | + | 1.45432i | ||||
\(365\) | −14.8092 | + | 25.6503i | −0.775148 | + | 1.34260i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.66786 | − | 2.88882i | −0.0870617 | − | 0.150795i | 0.819206 | − | 0.573499i | \(-0.194414\pi\) |
−0.906268 | + | 0.422704i | \(0.861081\pi\) | |||||||
\(368\) | −0.988541 | −0.0515313 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 31.0329i | − | 1.61332i | ||||||
\(371\) | 1.55240 | − | 0.896277i | 0.0805964 | − | 0.0465324i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.3206 | + | 23.0720i | −0.689716 | + | 1.19462i | 0.282214 | + | 0.959352i | \(0.408931\pi\) |
−0.971930 | + | 0.235272i | \(0.924402\pi\) | |||||||
\(374\) | 8.63632 | − | 14.9585i | 0.446574 | − | 0.773488i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.13007 | − | 3.68940i | −0.109850 | − | 0.190266i | ||||
\(377\) | 1.28553 | + | 3.27033i | 0.0662079 | + | 0.168430i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.4926i | 1.56630i | 0.621832 | + | 0.783150i | \(0.286389\pi\) | ||||
−0.621832 | + | 0.783150i | \(0.713611\pi\) | |||||||
\(380\) | −5.83943 | − | 10.1142i | −0.299556 | − | 0.518847i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.3775 | − | 10.6103i | −0.940275 | − | 0.542868i | ||||
\(383\) | −21.6814 | − | 12.5178i | −1.10787 | − | 0.639628i | −0.169592 | − | 0.985514i | \(-0.554245\pi\) |
−0.938276 | + | 0.345886i | \(0.887578\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.95162 | − | 5.74557i | 0.507182 | − | 0.292821i | ||||
\(386\) | −26.1925 | −1.33316 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 48.9128i | − | 2.48317i | ||||||
\(389\) | −1.05615 | − | 1.82931i | −0.0535490 | − | 0.0927495i | 0.838008 | − | 0.545657i | \(-0.183720\pi\) |
−0.891557 | + | 0.452908i | \(0.850387\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.6858 | + | 41.0250i | −1.19784 | + | 2.07472i | ||||
\(392\) | −2.70868 | − | 1.56385i | −0.136809 | − | 0.0789866i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5902 | + | 21.8069i | 0.634286 | + | 1.09861i | ||||
\(395\) | − | 12.0182i | − | 0.604701i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.7853i | 1.44469i | 0.691533 | + | 0.722345i | \(0.256936\pi\) | ||||
−0.691533 | + | 0.722345i | \(0.743064\pi\) | |||||||
\(398\) | 2.73627 | − | 1.57979i | 0.137157 | − | 0.0791875i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.285907 | + | 0.495206i | −0.0142954 | + | 0.0247603i | ||||
\(401\) | 9.86207 | + | 5.69387i | 0.492488 | + | 0.284338i | 0.725606 | − | 0.688110i | \(-0.241560\pi\) |
−0.233118 | + | 0.972448i | \(0.574893\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.3026 | − | 8.20707i | −0.513211 | − | 0.408824i | ||||
\(404\) | −47.8791 | −2.38208 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.39048 | 0.267525 | ||||||||
\(407\) | −3.11713 | − | 5.39902i | −0.154510 | − | 0.267620i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.90604 | − | 1.67780i | −0.143695 | − | 0.0829621i | 0.426429 | − | 0.904521i | \(-0.359771\pi\) |
−0.570124 | + | 0.821559i | \(0.693105\pi\) | |||||||
\(410\) | 25.4897 | + | 14.7165i | 1.25884 | + | 0.726794i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.4889 | − | 18.1673i | −0.516750 | − | 0.895037i | ||||
\(413\) | −18.8170 | −0.925925 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 45.9120 | 2.25373 | ||||||||
\(416\) | −16.2957 | − | 12.9811i | −0.798962 | − | 0.636453i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.29702 | − | 1.90354i | −0.161263 | − | 0.0931050i | ||||
\(419\) | 1.03279 | − | 1.78885i | 0.0504552 | − | 0.0873910i | −0.839695 | − | 0.543059i | \(-0.817266\pi\) |
0.890150 | + | 0.455668i | \(0.150599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −29.3605 | + | 16.9513i | −1.43094 | + | 0.826156i | −0.997193 | − | 0.0748758i | \(-0.976144\pi\) |
−0.433752 | + | 0.901032i | \(0.642811\pi\) | |||||||
\(422\) | 20.9663i | 1.02062i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 2.04726i | − | 0.0994236i | ||||||
\(425\) | 13.7009 | + | 23.7306i | 0.664590 | + | 1.15110i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.0697 | + | 9.85522i | 0.826063 | + | 0.476927i | ||||
\(428\) | 15.0567 | − | 26.0789i | 0.727792 | − | 1.26057i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −31.7927 | − | 55.0665i | −1.53318 | − | 2.65554i | ||||
\(431\) | 30.6212i | 1.47497i | 0.675364 | + | 0.737485i | \(0.263987\pi\) | ||||
−0.675364 | + | 0.737485i | \(0.736013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.63597 | 0.415018 | 0.207509 | − | 0.978233i | \(-0.433464\pi\) | ||||
0.207509 | + | 0.978233i | \(0.433464\pi\) | |||||||
\(434\) | −17.4991 | + | 10.1031i | −0.839986 | + | 0.484966i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −40.5732 | − | 23.4249i | −1.94310 | − | 1.12185i | ||||
\(437\) | 9.04234 | + | 5.22060i | 0.432554 | + | 0.249735i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7827 | − | 25.6043i | −0.705538 | − | 1.22203i | −0.966497 | − | 0.256678i | \(-0.917372\pi\) |
0.260959 | − | 0.965350i | \(-0.415961\pi\) | |||||||
\(440\) | − | 13.1239i | − | 0.625658i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −39.2979 | + | 15.4475i | −1.86921 | + | 0.734763i | ||||
\(443\) | 15.6331 | + | 27.0773i | 0.742751 | + | 1.28648i | 0.951238 | + | 0.308457i | \(0.0998127\pi\) |
−0.208487 | + | 0.978025i | \(0.566854\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.2052 | − | 22.8721i | 0.625988 | − | 1.08424i | ||||
\(446\) | −7.26915 | + | 12.5905i | −0.344204 | + | 0.596179i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −27.2292 | + | 15.7208i | −1.28646 | + | 0.742738i | ||||
\(449\) | − | 10.8346i | − | 0.511316i | −0.966767 | − | 0.255658i | \(-0.917708\pi\) | ||
0.966767 | − | 0.255658i | \(-0.0822922\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.91283 | 0.278424 | ||||||||
\(452\) | −4.92663 | − | 8.53318i | −0.231729 | − | 0.401367i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.6393 | − | 20.1599i | 0.546261 | − | 0.946152i | ||||
\(455\) | −27.7799 | − | 4.17197i | −1.30234 | − | 0.195585i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.8936 | − | 8.02147i | 0.649915 | − | 0.375229i | −0.138509 | − | 0.990361i | \(-0.544231\pi\) |
0.788424 | + | 0.615133i | \(0.210898\pi\) | |||||||
\(458\) | 18.5317 | 0.865929 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 95.3883i | 4.44750i | ||||||||
\(461\) | 22.1953 | − | 12.8145i | 1.03374 | − | 0.596830i | 0.115686 | − | 0.993286i | \(-0.463093\pi\) |
0.918054 | + | 0.396456i | \(0.129760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.1926 | − | 16.2770i | −1.31022 | − | 0.756457i | −0.328090 | − | 0.944647i | \(-0.606405\pi\) |
−0.982133 | + | 0.188189i | \(0.939738\pi\) | |||||||
\(464\) | −0.0521629 | + | 0.0903488i | −0.00242160 | + | 0.00419434i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 16.5642 | − | 9.56335i | 0.767322 | − | 0.443014i | ||||
\(467\) | −16.2179 | −0.750474 | −0.375237 | − | 0.926929i | \(-0.622439\pi\) | ||||
−0.375237 | + | 0.926929i | \(0.622439\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.87270 | 0.0864731 | ||||||||
\(470\) | 9.78924 | − | 5.65182i | 0.451544 | − | 0.260699i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.7454 | + | 18.6115i | −0.494596 | + | 0.856665i | ||||
\(473\) | −11.0624 | − | 6.38688i | −0.508650 | − | 0.293669i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.23048 | − | 3.01982i | 0.239991 | − | 0.138559i | ||||
\(476\) | 39.9187i | 1.82967i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 10.5302 | 0.481641 | ||||||||
\(479\) | −8.86463 | + | 5.11800i | −0.405035 | + | 0.233847i | −0.688654 | − | 0.725090i | \(-0.741798\pi\) |
0.283619 | + | 0.958937i | \(0.408465\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.26341 | + | 15.0713i | −0.103202 | + | 0.687194i | ||||
\(482\) | 9.17265 | − | 15.8875i | 0.417803 | − | 0.723655i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.1725 | + | 24.5474i | 0.644202 | + | 1.11579i | ||||
\(485\) | 48.9715 | 2.22368 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.0863i | 0.728940i | 0.931215 | + | 0.364470i | \(0.118750\pi\) | ||||
−0.931215 | + | 0.364470i | \(0.881250\pi\) | |||||||
\(488\) | 19.4952 | − | 11.2555i | 0.882505 | − | 0.509515i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.14944 | − | 7.18705i | 0.187453 | − | 0.324678i | ||||
\(491\) | 2.20943 | − | 3.82684i | 0.0997101 | − | 0.172703i | −0.811855 | − | 0.583860i | \(-0.801542\pi\) |
0.911565 | + | 0.411157i | \(0.134875\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.49969 | + | 4.32958i | 0.112580 | + | 0.194995i | ||||
\(494\) | 3.40479 | + | 8.66167i | 0.153189 | + | 0.389707i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 0.391066i | − | 0.0175594i | ||||||
\(497\) | −3.64786 | − | 6.31828i | −0.163629 | − | 0.283414i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.39369 | − | 3.69140i | −0.286221 | − | 0.165250i | 0.350015 | − | 0.936744i | \(-0.386176\pi\) |
−0.636236 | + | 0.771494i | \(0.719510\pi\) | |||||||
\(500\) | 3.05705 | + | 1.76499i | 0.136715 | + | 0.0789327i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 33.8339 | − | 19.5340i | 1.51008 | − | 0.871847i | ||||
\(503\) | −5.65418 | −0.252107 | −0.126054 | − | 0.992023i | \(-0.540231\pi\) | ||||
−0.126054 | + | 0.992023i | \(0.540231\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 47.9366i | − | 2.13315i | ||||||
\(506\) | 15.5473 | + | 26.9288i | 0.691163 | + | 1.19713i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.263213 | − | 0.455898i | 0.0116782 | − | 0.0202272i | ||||
\(509\) | 23.2192 | + | 13.4056i | 1.02917 | + | 0.594193i | 0.916747 | − | 0.399467i | \(-0.130805\pi\) |
0.112425 | + | 0.993660i | \(0.464138\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1568 | − | 19.3242i | −0.493548 | − | 0.854850i | ||||
\(512\) | − | 1.21094i | − | 0.0535165i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 21.7208i | − | 0.958065i | ||||||
\(515\) | 18.1891 | − | 10.5015i | 0.801506 | − | 0.462750i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.13540 | − | 1.96658i | 0.0499350 | − | 0.0864899i | ||||
\(518\) | 20.2470 | + | 11.6896i | 0.889604 | + | 0.513613i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −19.9900 | + | 25.0941i | −0.876619 | + | 1.10045i | ||||
\(521\) | 20.3407 | 0.891143 | 0.445572 | − | 0.895246i | \(-0.353000\pi\) | ||||
0.445572 | + | 0.895246i | \(0.353000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.74660 | 0.251281 | 0.125641 | − | 0.992076i | \(-0.459901\pi\) | ||||
0.125641 | + | 0.992076i | \(0.459901\pi\) | |||||||
\(524\) | −10.4899 | − | 18.1690i | −0.458253 | − | 0.793717i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 55.3376 | + | 31.9492i | 2.41283 | + | 1.39305i | ||||
\(527\) | −16.2295 | − | 9.37009i | −0.706967 | − | 0.408168i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.1398 | − | 53.9357i | −1.35390 | − | 2.34503i | ||||
\(530\) | 5.43208 | 0.235954 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8.79851 | 0.381464 | ||||||||
\(533\) | −11.3059 | − | 9.00626i | −0.489712 | − | 0.390104i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.1103 | + | 15.0748i | 1.12884 | + | 0.651739i | ||||
\(536\) | 1.06939 | − | 1.85225i | 0.0461908 | − | 0.0800048i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.5786 | + | 13.0357i | −0.973431 | + | 0.562011i | ||||
\(539\) | − | 1.66718i | − | 0.0718104i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.0286i | 1.84994i | 0.380036 | + | 0.924972i | \(0.375912\pi\) | ||||
−0.380036 | + | 0.924972i | \(0.624088\pi\) | |||||||
\(542\) | 15.1574 | + | 26.2534i | 0.651068 | + | 1.12768i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −25.6702 | − | 14.8207i | −1.10060 | − | 0.635432i | ||||
\(545\) | 23.4531 | − | 40.6219i | 1.00462 | − | 1.74005i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.1581 | + | 19.3265i | 0.477088 | + | 0.826340i | 0.999655 | − | 0.0262576i | \(-0.00835902\pi\) |
−0.522567 | + | 0.852598i | \(0.675026\pi\) | |||||||
\(548\) | 44.7411i | 1.91124i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 17.9865 | 0.766946 | ||||||||
\(551\) | 0.954285 | − | 0.550957i | 0.0406539 | − | 0.0234716i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.84113 | + | 4.52708i | 0.333439 | + | 0.192511i | ||||
\(554\) | 3.56275 | + | 2.05696i | 0.151367 | + | 0.0873917i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −22.7757 | − | 39.4487i | −0.965906 | − | 1.67300i | ||||
\(557\) | 28.7460i | 1.21801i | 0.793168 | + | 0.609003i | \(0.208430\pi\) | ||||
−0.793168 | + | 0.609003i | \(0.791570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.4240 | + | 29.0622i | 0.483184 | + | 1.22920i | ||||
\(560\) | −0.417008 | − | 0.722279i | −0.0176218 | − | 0.0305219i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13.1022 | + | 22.6936i | −0.552682 | + | 0.957273i | ||||
\(563\) | −5.91647 | + | 10.2476i | −0.249350 | + | 0.431886i | −0.963346 | − | 0.268264i | \(-0.913550\pi\) |
0.713996 | + | 0.700150i | \(0.246883\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.54342 | − | 4.93255i | 0.359424 | − | 0.207514i | ||||
\(566\) | 51.7217i | 2.17403i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.33237 | −0.349619 | ||||||||
\(569\) | −4.39661 | − | 7.61515i | −0.184315 | − | 0.319244i | 0.759030 | − | 0.651055i | \(-0.225673\pi\) |
−0.943346 | + | 0.331812i | \(0.892340\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −15.6380 | + | 27.0858i | −0.654430 | + | 1.13351i | 0.327606 | + | 0.944814i | \(0.393758\pi\) |
−0.982036 | + | 0.188692i | \(0.939575\pi\) | |||||||
\(572\) | −2.53674 | + | 16.8914i | −0.106066 | + | 0.706265i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.2032 | + | 11.0869i | −0.801524 | + | 0.462760i | ||||
\(575\) | −49.3294 | −2.05718 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 45.2450i | − | 1.88357i | −0.336210 | − | 0.941787i | \(-0.609145\pi\) | ||
0.336210 | − | 0.941787i | \(-0.390855\pi\) | |||||||
\(578\) | −18.4154 | + | 10.6321i | −0.765978 | + | 0.442238i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.71813 | + | 5.03341i | 0.362001 | + | 0.209001i | ||||
\(581\) | −17.2944 | + | 29.9547i | −0.717492 | + | 1.24273i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.945058 | − | 0.545629i | 0.0391403 | − | 0.0225977i | ||||
\(584\) | −25.4841 | −1.05454 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 37.3684 | 1.54368 | ||||||||
\(587\) | 25.1277 | − | 14.5075i | 1.03713 | − | 0.598788i | 0.118112 | − | 0.993000i | \(-0.462316\pi\) |
0.919020 | + | 0.394212i | \(0.128982\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.06527 | + | 3.57715i | −0.0850978 | + | 0.147394i | ||||
\(590\) | −49.3828 | − | 28.5111i | −2.03306 | − | 1.17379i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.391856 | + | 0.226238i | −0.0161052 | + | 0.00929832i | ||||
\(593\) | − | 25.7497i | − | 1.05741i | −0.848805 | − | 0.528707i | \(-0.822677\pi\) | ||
0.848805 | − | 0.528707i | \(-0.177323\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.9666 | −1.63847 | ||||||||
\(596\) | 51.6753 | − | 29.8347i | 2.11670 | − | 1.22208i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 11.2892 | − | 75.1715i | 0.461651 | − | 3.07399i | ||||
\(599\) | 18.8670 | − | 32.6786i | 0.770885 | − | 1.33521i | −0.166194 | − | 0.986093i | \(-0.553148\pi\) |
0.937079 | − | 0.349118i | \(-0.113519\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.46451 | − | 14.6610i | −0.345274 | − | 0.598033i | 0.640129 | − | 0.768267i | \(-0.278881\pi\) |
−0.985404 | + | 0.170235i | \(0.945547\pi\) | |||||||
\(602\) | 47.9033 | 1.95239 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 38.1977i | − | 1.55424i | ||||||
\(605\) | −24.5769 | + | 14.1895i | −0.999192 | + | 0.576884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.13946 | − | 10.6339i | 0.249193 | − | 0.431615i | −0.714109 | − | 0.700034i | \(-0.753168\pi\) |
0.963302 | + | 0.268420i | \(0.0865014\pi\) | |||||||
\(608\) | −3.26664 | + | 5.65798i | −0.132480 | + | 0.229461i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 29.8648 | + | 51.7274i | 1.20919 | + | 2.09438i | ||||
\(611\) | −5.16643 | + | 2.03086i | −0.209011 | + | 0.0821598i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.84764i | 0.155405i | 0.996977 | + | 0.0777023i | \(0.0247584\pi\) | ||||
−0.996977 | + | 0.0777023i | \(0.975242\pi\) | |||||||
\(614\) | 19.0385 | + | 32.9756i | 0.768330 | + | 1.33079i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.56254 | + | 4.94359i | 0.344995 | + | 0.199183i | ||||
\(617\) | 29.7198 | + | 17.1587i | 1.19647 | + | 0.690785i | 0.959767 | − | 0.280796i | \(-0.0905986\pi\) |
0.236707 | + | 0.971581i | \(0.423932\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.7880 | − | 21.2396i | 1.47864 | − | 0.853691i | 0.478928 | − | 0.877854i | \(-0.341025\pi\) |
0.999708 | + | 0.0241630i | \(0.00769205\pi\) | |||||||
\(620\) | −37.7356 | −1.51550 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 18.5202i | 0.742594i | ||||||||
\(623\) | 9.94843 | + | 17.2312i | 0.398575 | + | 0.690353i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 11.5872 | − | 20.0697i | 0.463490 | − | 0.802788i | ||||
\(626\) | −43.5050 | − | 25.1176i | −1.73881 | − | 1.00390i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.40661 | + | 11.0966i | 0.255652 | + | 0.442802i | ||||
\(629\) | 21.6830i | 0.864557i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9430i | 0.714300i | 0.934047 | + | 0.357150i | \(0.116252\pi\) | ||||
−0.934047 | + | 0.357150i | \(0.883748\pi\) | |||||||
\(632\) | 8.95528 | − | 5.17033i | 0.356222 | − | 0.205665i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7.68100 | + | 13.3039i | −0.305052 | + | 0.528365i | ||||
\(635\) | 0.456446 | + | 0.263529i | 0.0181135 | + | 0.0104578i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.53940 | + | 3.18780i | −0.100615 | + | 0.126305i | ||||
\(638\) | 3.28158 | 0.129919 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −58.1146 | −2.29718 | ||||||||
\(641\) | −8.43114 | − | 14.6032i | −0.333010 | − | 0.576790i | 0.650090 | − | 0.759857i | \(-0.274731\pi\) |
−0.983101 | + | 0.183066i | \(0.941398\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.2179 | − | 24.9519i | −1.70435 | − | 0.984006i | −0.941242 | − | 0.337732i | \(-0.890340\pi\) |
−0.763105 | − | 0.646274i | \(-0.776326\pi\) | |||||||
\(644\) | −62.2350 | − | 35.9314i | −2.45240 | − | 1.41589i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.62057 | + | 11.4672i | 0.260483 | + | 0.451170i | ||||
\(647\) | −28.5920 | −1.12407 | −0.562034 | − | 0.827114i | \(-0.689981\pi\) | ||||
−0.562034 | + | 0.827114i | \(0.689981\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.4553 | −0.449660 | ||||||||
\(650\) | −34.3918 | − | 27.3965i | −1.34896 | − | 1.07458i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −14.4118 | − | 8.32063i | −0.564408 | − | 0.325861i | ||||
\(653\) | 13.2734 | − | 22.9902i | 0.519429 | − | 0.899677i | −0.480316 | − | 0.877095i | \(-0.659478\pi\) |
0.999745 | − | 0.0225814i | \(-0.00718849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1908 | − | 10.5025i | 0.710774 | − | 0.410366i | ||||
\(656\) | − | 0.429147i | − | 0.0167554i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.51582i | 0.331981i | ||||||||
\(659\) | −21.7318 | − | 37.6406i | −0.846552 | − | 1.46627i | −0.884266 | − | 0.466983i | \(-0.845341\pi\) |
0.0377144 | − | 0.999289i | \(-0.487992\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.6716 | + | 7.89332i | 0.531765 | + | 0.307015i | 0.741735 | − | 0.670693i | \(-0.234003\pi\) |
−0.209970 | + | 0.977708i | \(0.567337\pi\) | |||||||
\(662\) | 0.298266 | − | 0.516612i | 0.0115924 | − | 0.0200787i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 19.7517 | + | 34.2110i | 0.766516 | + | 1.32764i | ||||
\(665\) | 8.80907i | 0.341601i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | −0.348481 | ||||||||
\(668\) | −2.26993 | + | 1.31055i | −0.0878263 | + | 0.0507065i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 4.91464 | + | 2.83747i | 0.189869 | + | 0.109621i | ||||
\(671\) | 10.3916 | + | 5.99960i | 0.401163 | + | 0.231612i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.76355 | + | 15.1789i | 0.337810 | + | 0.585104i | 0.984021 | − | 0.178055i | \(-0.0569805\pi\) |
−0.646210 | + | 0.763159i | \(0.723647\pi\) | |||||||
\(674\) | − | 13.4423i | − | 0.517778i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 30.5790 | − | 28.4340i | 1.17611 | − | 1.09362i | ||||
\(677\) | −9.25036 | − | 16.0221i | −0.355520 | − | 0.615779i | 0.631687 | − | 0.775224i | \(-0.282363\pi\) |
−0.987207 | + | 0.159445i | \(0.949030\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.4469 | + | 31.9509i | −0.707925 | + | 1.22616i | ||||
\(680\) | −22.8227 | + | 39.5302i | −0.875212 | + | 1.51591i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −10.6530 | + | 6.15052i | −0.407925 | + | 0.235516i | ||||
\(683\) | − | 4.68607i | − | 0.179307i | −0.995973 | − | 0.0896537i | \(-0.971424\pi\) | ||
0.995973 | − | 0.0896537i | \(-0.0285760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −44.7948 | −1.71152 | ||||||||
\(686\) | 22.4847 | + | 38.9447i | 0.858472 | + | 1.48692i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.463553 | + | 0.802898i | −0.0176728 | + | 0.0306102i | ||||
\(689\) | −2.63812 | − | 0.396192i | −0.100505 | − | 0.0150937i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.3398 | + | 21.5581i | −1.42047 | + | 0.820110i | −0.996339 | − | 0.0854897i | \(-0.972755\pi\) |
−0.424133 | + | 0.905600i | \(0.639421\pi\) | |||||||
\(692\) | 1.68012 | 0.0638686 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.30099i | 0.277142i | ||||||||
\(695\) | 39.4961 | − | 22.8031i | 1.49817 | − | 0.864970i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.8099 | − | 10.2825i | −0.674596 | − | 0.389478i | ||||
\(698\) | −15.9061 | + | 27.5502i | −0.602056 | + | 1.04279i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −35.9994 | + | 20.7842i | −1.36065 | + | 0.785570i | ||||
\(701\) | −35.9226 | −1.35678 | −0.678389 | − | 0.734703i | \(-0.737322\pi\) | ||||
−0.678389 | + | 0.734703i | \(0.737322\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.77915 | 0.180249 | ||||||||
\(704\) | −16.5764 | + | 9.57041i | −0.624748 | + | 0.360698i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 17.9083 | − | 31.0181i | 0.673988 | − | 1.16738i | ||||
\(707\) | 31.2756 | + | 18.0570i | 1.17624 | + | 0.679104i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.9125 | + | 12.0738i | −0.785384 | + | 0.453442i | −0.838335 | − | 0.545156i | \(-0.816471\pi\) |
0.0529511 | + | 0.998597i | \(0.483137\pi\) | |||||||
\(710\) | − | 22.1087i | − | 0.829723i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 22.7240 | 0.851618 | ||||||||
\(713\) | 29.2167 | − | 16.8683i | 1.09418 | − | 0.631722i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −16.9117 | − | 2.53979i | −0.632461 | − | 0.0949826i | ||||
\(716\) | 22.7651 | − | 39.4303i | 0.850772 | − | 1.47358i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.69468 | − | 11.5955i | −0.249843 | − | 0.432741i | ||||
\(719\) | 32.3717 | 1.20726 | 0.603630 | − | 0.797265i | \(-0.293720\pi\) | ||||
0.603630 | + | 0.797265i | \(0.293720\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8230i | 0.589279i | ||||||||
\(722\) | −35.0378 | + | 20.2291i | −1.30397 | + | 0.752848i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −28.8689 | + | 50.0024i | −1.07291 | + | 1.85833i | ||||
\(725\) | −2.60299 | + | 4.50851i | −0.0966727 | + | 0.167442i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.76910 | − | 16.9206i | −0.362316 | − | 0.627549i | 0.626026 | − | 0.779802i | \(-0.284680\pi\) |
−0.988342 | + | 0.152253i | \(0.951347\pi\) | |||||||
\(728\) | −8.84243 | − | 22.4948i | −0.327722 | − | 0.833713i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 67.6182i | − | 2.50266i | ||||||
\(731\) | 22.2138 | + | 38.4754i | 0.821607 | + | 1.42307i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.7224 | + | 20.6243i | 1.31944 | + | 0.761777i | 0.983638 | − | 0.180157i | \(-0.0576605\pi\) |
0.335799 | + | 0.941934i | \(0.390994\pi\) | |||||||
\(734\) | 6.59513 | + | 3.80770i | 0.243431 | + | 0.140545i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 46.2122 | − | 26.6806i | 1.70340 | − | 0.983460i | ||||
\(737\) | 1.14005 | 0.0419942 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 12.6677i | − | 0.465988i | −0.972478 | − | 0.232994i | \(-0.925148\pi\) | ||
0.972478 | − | 0.232994i | \(-0.0748523\pi\) | |||||||
\(740\) | 21.8306 | + | 37.8117i | 0.802509 | + | 1.38999i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.04618 | + | 3.54409i | −0.0751177 | + | 0.130108i | ||||
\(743\) | 10.3523 | + | 5.97690i | 0.379789 | + | 0.219271i | 0.677726 | − | 0.735314i | \(-0.262965\pi\) |
−0.297938 | + | 0.954585i | \(0.596299\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.8705 | + | 51.7373i | 1.09437 | + | 1.89551i | ||||
\(746\) | − | 60.8215i | − | 2.22683i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.3015i | 0.888549i | ||||||||
\(749\) | −19.6707 | + | 11.3569i | −0.718751 | + | 0.414971i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.59296 | − | 11.4193i | 0.240581 | − | 0.416698i | −0.720299 | − | 0.693663i | \(-0.755996\pi\) |
0.960880 | + | 0.276966i | \(0.0893289\pi\) | |||||||
\(752\) | −0.142732 | − | 0.0824064i | −0.00520490 | − | 0.00300505i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −6.27469 | − | 4.99841i | −0.228511 | − | 0.182031i | ||||
\(755\) | 38.2436 | 1.39183 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.1835 | −0.951657 | −0.475829 | − | 0.879538i | \(-0.657852\pi\) | ||||
−0.475829 | + | 0.879538i | \(0.657852\pi\) | |||||||
\(758\) | −34.8070 | − | 60.2876i | −1.26425 | − | 2.18974i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.71286 | + | 5.03037i | 0.316049 | + | 0.182471i | ||||
\(761\) | 6.00320 | + | 3.46595i | 0.217616 | + | 0.125640i | 0.604846 | − | 0.796343i | \(-0.293235\pi\) |
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17.6688 | + | 30.6033i | 0.639655 | + | 1.10792i | ||||
\(764\) | 29.8559 | 1.08015 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 57.1557 | 2.06512 | ||||||||
\(767\) | 21.9036 | + | 17.4484i | 0.790893 | + | 0.630025i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 33.4083 | + | 19.2883i | 1.20473 | + | 0.695553i | 0.961604 | − | 0.274441i | \(-0.0884927\pi\) |
0.243129 | + | 0.969994i | \(0.421826\pi\) | |||||||
\(770\) | −13.1170 | + | 22.7194i | −0.472705 | + | 0.818749i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 31.9140 | − | 18.4255i | 1.14861 | − | 0.663149i | ||||
\(773\) | − | 34.7210i | − | 1.24883i | −0.781093 | − | 0.624415i | \(-0.785338\pi\) | ||
0.781093 | − | 0.624415i | \(-0.214662\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 19.5147i | − | 0.700988i | ||||||
\(776\) | 21.0680 | + | 36.4908i | 0.756296 | + | 1.30994i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.17627 | + | 2.41117i | 0.149727 | + | 0.0864447i | ||||
\(779\) | −2.26638 | + | 3.92548i | −0.0812014 | + | 0.140645i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.22072 | − | 3.84640i | −0.0794637 | − | 0.137635i | ||||
\(782\) | − | 108.148i | − | 3.86738i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.121002 | −0.00432150 | ||||||||
\(785\) | −11.1099 | + | 6.41430i | −0.396529 | + | 0.228936i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.0375 | + | 17.9195i | 1.10637 | + | 0.638761i | 0.937886 | − | 0.346944i | \(-0.112781\pi\) |
0.168480 | + | 0.985705i | \(0.446114\pi\) | |||||||
\(788\) | −30.6808 | − | 17.7136i | −1.09296 | − | 0.631020i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.7187 | + | 23.7614i | 0.488088 | + | 0.845394i | ||||
\(791\) | 7.43207i | 0.264254i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −10.7313 | − | 27.3000i | −0.381079 | − | 0.969451i | ||||
\(794\) | −32.8581 | − | 56.9119i | −1.16609 | − | 2.01973i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.22265 | + | 3.84975i | −0.0787798 | + | 0.136451i | ||||
\(797\) | −19.4271 | + | 33.6487i | −0.688144 | + | 1.19190i | 0.284294 | + | 0.958737i | \(0.408241\pi\) |
−0.972438 | + | 0.233163i | \(0.925093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.83983 | + | 3.94898i | −0.241976 | + | 0.139705i | ||||
\(800\) | − | 30.8664i | − | 1.09129i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −25.9980 | −0.918020 | ||||||||
\(803\) | −6.79197 | − | 11.7640i | −0.239683 | − | 0.415144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35.9745 | − | 62.3097i | 1.26793 | − | 2.19613i | ||||
\(806\) | 29.7378 | + | 4.46601i | 1.04747 | + | 0.157309i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 35.7196 | − | 20.6227i | 1.25661 | − | 0.725505i | ||||
\(809\) | 12.2765 | 0.431619 | 0.215809 | − | 0.976435i | \(-0.430761\pi\) | ||||
0.215809 | + | 0.976435i | \(0.430761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.8855i | 0.487585i | 0.969827 | + | 0.243792i | \(0.0783915\pi\) | ||||
−0.969827 | + | 0.243792i | \(0.921608\pi\) | |||||||
\(812\) | −6.56798 | + | 3.79202i | −0.230491 | + | 0.133074i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 12.3259 | + | 7.11634i | 0.432021 | + | 0.249428i | ||||
\(815\) | 8.33062 | − | 14.4291i | 0.291809 | − | 0.505428i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.48039 | − | 4.89616i | 0.296691 | − | 0.171295i | ||||
\(818\) | 7.66079 | 0.267853 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −41.4102 | −1.44611 | ||||||||
\(821\) | −7.91360 | + | 4.56892i | −0.276187 | + | 0.159456i | −0.631696 | − | 0.775216i | \(-0.717641\pi\) |
0.355509 | + | 0.934673i | \(0.384307\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.95741 | + | 3.39033i | −0.0682310 | + | 0.118180i | −0.898123 | − | 0.439745i | \(-0.855069\pi\) |
0.829892 | + | 0.557925i | \(0.188402\pi\) | |||||||
\(824\) | 15.6502 | + | 9.03564i | 0.545200 | + | 0.314771i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.2035 | − | 21.4794i | 1.29448 | − | 0.747366i | ||||
\(827\) | 18.1786i | 0.632131i | 0.948737 | + | 0.316065i | \(0.102362\pi\) | ||||
−0.948737 | + | 0.316065i | \(0.897638\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0468 | 1.32142 | 0.660711 | − | 0.750641i | \(-0.270255\pi\) | ||||
0.660711 | + | 0.750641i | \(0.270255\pi\) | |||||||
\(830\) | −90.7735 | + | 52.4081i | −3.15080 | + | 1.81911i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 46.2730 | + | 6.94926i | 1.60423 | + | 0.240922i | ||||
\(833\) | −2.89925 | + | 5.02165i | −0.100453 | + | 0.173990i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.31212 | − | 2.27266i | −0.0454077 | − | 0.0786485i | ||||
\(836\) | 5.35630 | 0.185251 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.71569i | 0.162901i | ||||||||
\(839\) | 24.7704 | − | 14.3012i | 0.855171 | − | 0.493733i | −0.00722153 | − | 0.999974i | \(-0.502299\pi\) |
0.862392 | + | 0.506241i | \(0.168965\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0251 | − | 24.2922i | 0.483624 | − | 0.837661i | ||||
\(842\) | 38.6995 | − | 67.0295i | 1.33367 | − | 2.30999i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −14.7491 | − | 25.5462i | −0.507684 | − | 0.879335i | ||||
\(845\) | 28.4681 | + | 30.6157i | 0.979334 | + | 1.05321i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 21.3798i | − | 0.734620i | ||||||
\(848\) | −0.0396012 | − | 0.0685914i | −0.00135991 | − | 0.00235544i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −54.1765 | − | 31.2788i | −1.85824 | − | 1.07286i | ||||
\(851\) | −33.8047 | − | 19.5171i | −1.15881 | − | 0.669039i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −26.0272 | + | 15.0268i | −0.891154 | + | 0.514508i | −0.874320 | − | 0.485350i | \(-0.838692\pi\) |
−0.0168345 | + | 0.999858i | \(0.505359\pi\) | |||||||
\(854\) | −44.9986 | −1.53982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.9412i | 0.886650i | ||||||||
\(857\) | −0.668881 | − | 1.15854i | −0.0228485 | − | 0.0395748i | 0.854375 | − | 0.519657i | \(-0.173940\pi\) |
−0.877224 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.6362 | − | 35.7429i | 0.704097 | − | 1.21953i | −0.262920 | − | 0.964818i | \(-0.584685\pi\) |
0.967017 | − | 0.254714i | \(-0.0819812\pi\) | |||||||
\(860\) | 77.4749 | + | 44.7301i | 2.64187 | + | 1.52529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −34.9538 | − | 60.5417i | −1.19053 | − | 2.06206i | ||||
\(863\) | 37.3326i | 1.27082i | 0.772176 | + | 0.635408i | \(0.219168\pi\) | ||||
−0.772176 | + | 0.635408i | \(0.780832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.68214i | 0.0571944i | ||||||||
\(866\) | −17.0743 | + | 9.85788i | −0.580210 | + | 0.334984i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.2144 | − | 24.6201i | 0.482469 | − | 0.835661i | ||||
\(869\) | 4.77347 | + | 2.75597i | 0.161929 | + | 0.0934897i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.17988 | − | 1.73649i | −0.0738623 | − | 0.0588387i | ||||
\(872\) | 40.3588 | 1.36672 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −23.8371 | −0.806301 | ||||||||
\(875\) | −1.33129 | − | 2.30586i | −0.0450057 | − | 0.0779521i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.8042 | − | 20.0942i | −1.17526 | − | 0.678534i | −0.220343 | − | 0.975422i | \(-0.570718\pi\) |
−0.954912 | + | 0.296889i | \(0.904051\pi\) | |||||||
\(878\) | 58.4542 | + | 33.7485i | 1.97273 | + | 1.13896i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.253863 | − | 0.439704i | −0.00855773 | − | 0.0148224i | ||||
\(881\) | −13.8402 | −0.466289 | −0.233144 | − | 0.972442i | \(-0.574901\pi\) | ||||
−0.233144 | + | 0.972442i | \(0.574901\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.1280 | −0.980235 | −0.490118 | − | 0.871656i | \(-0.663046\pi\) | ||||
−0.490118 | + | 0.871656i | \(0.663046\pi\) | |||||||
\(884\) | 37.0153 | − | 46.4666i | 1.24496 | − | 1.56284i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −61.8170 | − | 35.6901i | −2.07678 | − | 1.19903i | ||||
\(887\) | 9.07561 | − | 15.7194i | 0.304729 | − | 0.527806i | −0.672472 | − | 0.740123i | \(-0.734767\pi\) |
0.977201 | + | 0.212316i | \(0.0681008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.343873 | + | 0.198535i | −0.0115331 | + | 0.00665865i | ||||
\(890\) | 60.2946i | 2.02108i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 20.4544i | − | 0.684864i | ||||||
\(893\) | 0.870396 | + | 1.50757i | 0.0291267 | + | 0.0504489i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 39.4777 | + | 22.7924i | 1.31959 | + | 0.761867i | ||||
\(896\) | 21.8909 | − | 37.9162i | 0.731324 | − | 1.26669i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.3676 | + | 21.4213i | 0.412712 | + | 0.714838i | ||||
\(899\) | − | 3.56040i | − | 0.118746i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.79544 | −0.126444 | ||||||||
\(902\) | −11.6904 | + | 6.74944i | −0.389247 | + | 0.224732i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.35090 | + | 4.24404i | 0.244487 | + | 0.141155i | ||||
\(905\) | −50.0625 | − | 28.9036i | −1.66413 | − | 0.960788i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.55936 | − | 4.43293i | −0.0849820 | − | 0.147193i | 0.820402 | − | 0.571788i | \(-0.193750\pi\) |
−0.905384 | + | 0.424595i | \(0.860417\pi\) | |||||||
\(908\) | 32.7515i | 1.08690i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 59.6865 | − | 23.4620i | 1.97859 | − | 0.777758i | ||||
\(911\) | 21.1217 | + | 36.5839i | 0.699794 | + | 1.21208i | 0.968538 | + | 0.248867i | \(0.0800582\pi\) |
−0.268744 | + | 0.963212i | \(0.586608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −10.5284 | + | 18.2356i | −0.348438 | + | 0.603512i | ||||
\(914\) | −18.3129 | + | 31.7188i | −0.605736 | + | 1.04916i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.5797 | + | 13.0364i | −0.746056 | + | 0.430735i | ||||
\(917\) | 15.8245i | 0.522571i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.2207 | 1.22780 | 0.613899 | − | 0.789384i | \(-0.289600\pi\) | ||||
0.613899 | + | 0.789384i | \(0.289600\pi\) | |||||||
\(920\) | −41.0861 | − | 71.1633i | −1.35457 | − | 2.34618i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.2552 | + | 50.6715i | −0.963469 | + | 1.66878i | ||||
\(923\) | −1.61251 | + | 10.7372i | −0.0530764 | + | 0.353420i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19.5541 | + | 11.2895i | −0.642933 | + | 0.371198i | ||||
\(926\) | 74.3202 | 2.44231 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 5.63149i | − | 0.184863i | ||||||
\(929\) | −18.3982 | + | 10.6222i | −0.603624 | + | 0.348502i | −0.770466 | − | 0.637481i | \(-0.779976\pi\) |
0.166842 | + | 0.985984i | \(0.446643\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.10683 | + | 0.639026i | 0.0362747 | + | 0.0209432i | ||||
\(932\) | −13.4550 | + | 23.3047i | −0.440733 | + | 0.763372i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 32.0647 | − | 18.5126i | 1.04919 | − | 0.605750i | ||||
\(935\) | −24.3306 | −0.795697 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −55.6976 | −1.81956 | −0.909781 | − | 0.415089i | \(-0.863750\pi\) | ||||
−0.909781 | + | 0.415089i | \(0.863750\pi\) | |||||||
\(938\) | −3.70255 | + | 2.13767i | −0.120892 | + | 0.0697973i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −7.95173 | + | 13.7728i | −0.259357 | + | 0.449219i | ||||
\(941\) | −17.2655 | − | 9.96821i | −0.562838 | − | 0.324954i | 0.191446 | − | 0.981503i | \(-0.438682\pi\) |
−0.754284 | + | 0.656549i | \(0.772016\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0618 | − | 18.5109i | 1.04408 | − | 0.602797i | ||||
\(944\) | 0.831414i | 0.0270602i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 29.1622 | 0.948146 | ||||||||
\(947\) | −28.2364 | + | 16.3023i | −0.917560 | + | 0.529754i | −0.882856 | − | 0.469644i | \(-0.844382\pi\) |
−0.0347045 | + | 0.999398i | \(0.511049\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.93178 | + | 32.8392i | −0.160092 | + | 1.06601i | ||||
\(950\) | −6.89419 | + | 11.9411i | −0.223677 | + | 0.387420i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.1940 | − | 29.7808i | −0.557260 | − | 0.965203i | ||||
\(953\) | 15.6146 | 0.505808 | 0.252904 | − | 0.967491i | \(-0.418614\pi\) | ||||
0.252904 | + | 0.967491i | \(0.418614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.8917i | 0.967273i | ||||||||
\(956\) | −12.8304 | + | 7.40766i | −0.414966 | + | 0.239581i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.6843 | − | 20.2378i | 0.377502 | − | 0.653853i | ||||
\(959\) | 16.8735 | − | 29.2258i | 0.544875 | − | 0.943750i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.82691 | − | 15.2887i | −0.284739 | − | 0.493183i | ||||
\(962\) | −12.7288 | − | 32.3815i | −0.410392 | − | 1.04402i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.8106i | 0.831304i | ||||||||
\(965\) | 18.4477 | + | 31.9523i | 0.593851 | + | 1.02858i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.47716 | + | 2.00754i | 0.111818 | + | 0.0645581i | 0.554866 | − | 0.831940i | \(-0.312770\pi\) |
−0.443048 | + | 0.896498i | \(0.646103\pi\) | |||||||
\(968\) | −21.1464 | − | 12.2089i | −0.679670 | − | 0.392407i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −96.8226 | + | 55.9006i | −3.10879 | + | 1.79486i | ||||
\(971\) | 27.3969 | 0.879209 | 0.439604 | − | 0.898192i | \(-0.355119\pi\) | ||||
0.439604 | + | 0.898192i | \(0.355119\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.3583i | 1.10148i | ||||||||
\(974\) | −18.3624 | − | 31.8045i | −0.588368 | − | 1.01908i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.435445 | − | 0.754212i | 0.0139382 | − | 0.0241417i | ||||
\(977\) | −33.3866 | − | 19.2758i | −1.06813 | − | 0.616687i | −0.140462 | − | 0.990086i | \(-0.544859\pi\) |
−0.927671 | + | 0.373399i | \(0.878192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.05634 | + | 10.4899i | 0.193561 | + | 0.335258i | ||||
\(980\) | 11.6760i | 0.372976i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.0882i | 0.321926i | ||||||||
\(983\) | 40.2933 | − | 23.2633i | 1.28516 | − | 0.741986i | 0.307370 | − | 0.951590i | \(-0.400551\pi\) |
0.977786 | + | 0.209604i | \(0.0672176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.7349 | − | 30.7177i | 0.565079 | − | 0.978746i | ||||
\(986\) | −9.88435 | − | 5.70673i | −0.314782 | − | 0.181739i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −10.2417 | − | 8.15856i | −0.325833 | − | 0.259558i | ||||
\(989\) | −79.9798 | −2.54321 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.1031 | 1.30568 | 0.652841 | − | 0.757495i | \(-0.273577\pi\) | ||||
0.652841 | + | 0.757495i | \(0.273577\pi\) | |||||||
\(992\) | 10.5548 | + | 18.2815i | 0.335116 | + | 0.580439i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 14.4245 | + | 8.32800i | 0.457518 | + | 0.264148i | ||||
\(995\) | −3.85437 | − | 2.22532i | −0.122192 | − | 0.0705474i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8886 | + | 48.3045i | 0.883241 | + | 1.52982i | 0.847716 | + | 0.530450i | \(0.177977\pi\) |
0.0355252 | + | 0.999369i | \(0.488690\pi\) | |||||||
\(998\) | 16.8548 | 0.533529 | ||||||||
\(999\) | 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 | 351.2.t.c.64.2 | 20 | ||
3.2 | odd | 2 | 117.2.t.c.103.9 | yes | 20 | ||
9.2 | odd | 6 | 117.2.t.c.25.2 | ✓ | 20 | ||
9.4 | even | 3 | 1053.2.b.i.649.2 | 10 | |||
9.5 | odd | 6 | 1053.2.b.j.649.9 | 10 | |||
9.7 | even | 3 | inner | 351.2.t.c.181.9 | 20 | ||
13.12 | even | 2 | inner | 351.2.t.c.64.9 | 20 | ||
39.38 | odd | 2 | 117.2.t.c.103.2 | yes | 20 | ||
117.25 | even | 6 | inner | 351.2.t.c.181.2 | 20 | ||
117.38 | odd | 6 | 117.2.t.c.25.9 | yes | 20 | ||
117.77 | odd | 6 | 1053.2.b.j.649.2 | 10 | |||
117.103 | even | 6 | 1053.2.b.i.649.9 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
117.2.t.c.25.2 | ✓ | 20 | 9.2 | odd | 6 | ||
117.2.t.c.25.9 | yes | 20 | 117.38 | odd | 6 | ||
117.2.t.c.103.2 | yes | 20 | 39.38 | odd | 2 | ||
117.2.t.c.103.9 | yes | 20 | 3.2 | odd | 2 | ||
351.2.t.c.64.2 | 20 | 1.1 | even | 1 | trivial | ||
351.2.t.c.64.9 | 20 | 13.12 | even | 2 | inner | ||
351.2.t.c.181.2 | 20 | 117.25 | even | 6 | inner | ||
351.2.t.c.181.9 | 20 | 9.7 | even | 3 | inner | ||
1053.2.b.i.649.2 | 10 | 9.4 | even | 3 | |||
1053.2.b.i.649.9 | 10 | 117.103 | even | 6 | |||
1053.2.b.j.649.2 | 10 | 117.77 | odd | 6 | |||
1053.2.b.j.649.9 | 10 | 9.5 | odd | 6 |