Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.2 | ||
Root | \(-1.32288 + 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.2.i.i.121.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 2.64575 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 4.29150 | 1.29394 | 0.646968 | − | 0.762517i | \(-0.276037\pi\) | ||||
0.646968 | + | 0.762517i | \(0.276037\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(14\) | 1.32288 | − | 2.29129i | 0.353553 | − | 0.612372i | ||||
\(15\) | −0.500000 | − | 0.866025i | −0.129099 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.177124 | − | 0.306788i | 0.0429590 | − | 0.0744071i | −0.843746 | − | 0.536742i | \(-0.819655\pi\) |
0.886705 | + | 0.462335i | \(0.152988\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −4.32288 | + | 0.559237i | −0.991736 | + | 0.128298i | ||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.32288 | − | 2.29129i | 0.288675 | − | 0.500000i | ||||
\(22\) | 2.14575 | − | 3.71655i | 0.457476 | − | 0.792371i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.32288 | − | 2.29129i | −0.250000 | − | 0.433013i | ||||
\(29\) | −0.822876 | − | 1.42526i | −0.152804 | − | 0.264665i | 0.779453 | − | 0.626461i | \(-0.215497\pi\) |
−0.932257 | + | 0.361796i | \(0.882164\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | −3.29150 | −0.591171 | −0.295586 | − | 0.955316i | \(-0.595515\pi\) | ||||
−0.295586 | + | 0.955316i | \(0.595515\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.14575 | − | 3.71655i | 0.373527 | − | 0.646968i | ||||
\(34\) | −0.177124 | − | 0.306788i | −0.0303766 | − | 0.0526138i | ||||
\(35\) | 1.32288 | − | 2.29129i | 0.223607 | − | 0.387298i | ||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −2.29150 | −0.376721 | −0.188360 | − | 0.982100i | \(-0.560317\pi\) | ||||
−0.188360 | + | 0.982100i | \(0.560317\pi\) | |||||||
\(38\) | −1.67712 | + | 4.02334i | −0.272065 | + | 0.652672i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 1.67712 | − | 2.90486i | 0.261923 | − | 0.453664i | −0.704830 | − | 0.709376i | \(-0.748977\pi\) |
0.966753 | + | 0.255713i | \(0.0823101\pi\) | |||||||
\(42\) | −1.32288 | − | 2.29129i | −0.204124 | − | 0.353553i | ||||
\(43\) | −3.00000 | + | 5.19615i | −0.457496 | + | 0.792406i | −0.998828 | − | 0.0484030i | \(-0.984587\pi\) |
0.541332 | + | 0.840809i | \(0.317920\pi\) | |||||||
\(44\) | −2.14575 | − | 3.71655i | −0.323484 | − | 0.560291i | ||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.29150 | + | 7.43310i | 0.625980 | + | 1.08423i | 0.988350 | + | 0.152195i | \(0.0486342\pi\) |
−0.362370 | + | 0.932034i | \(0.618032\pi\) | |||||||
\(48\) | 0.500000 | + | 0.866025i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −0.177124 | − | 0.306788i | −0.0248024 | − | 0.0429590i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.322876 | − | 0.559237i | −0.0443504 | − | 0.0768171i | 0.842998 | − | 0.537917i | \(-0.180788\pi\) |
−0.887348 | + | 0.461099i | \(0.847455\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 2.14575 | − | 3.71655i | 0.289333 | − | 0.501140i | ||||
\(56\) | −2.64575 | −0.353553 | ||||||||
\(57\) | −1.67712 | + | 4.02334i | −0.222141 | + | 0.532904i | ||||
\(58\) | −1.64575 | −0.216098 | ||||||||
\(59\) | 2.64575 | − | 4.58258i | 0.344447 | − | 0.596601i | −0.640806 | − | 0.767703i | \(-0.721400\pi\) |
0.985253 | + | 0.171103i | \(0.0547329\pi\) | |||||||
\(60\) | −0.500000 | + | 0.866025i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 4.46863 | + | 7.73989i | 0.572149 | + | 0.990991i | 0.996345 | + | 0.0854208i | \(0.0272235\pi\) |
−0.424196 | + | 0.905570i | \(0.639443\pi\) | |||||||
\(62\) | −1.64575 | + | 2.85052i | −0.209011 | + | 0.362017i | ||||
\(63\) | −1.32288 | − | 2.29129i | −0.166667 | − | 0.288675i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.14575 | − | 3.71655i | −0.264124 | − | 0.457476i | ||||
\(67\) | 2.17712 | + | 3.77089i | 0.265978 | + | 0.460688i | 0.967819 | − | 0.251646i | \(-0.0809718\pi\) |
−0.701841 | + | 0.712333i | \(0.747638\pi\) | |||||||
\(68\) | −0.354249 | −0.0429590 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | −1.32288 | − | 2.29129i | −0.158114 | − | 0.273861i | ||||
\(71\) | 4.17712 | − | 7.23499i | 0.495733 | − | 0.858636i | −0.504254 | − | 0.863555i | \(-0.668233\pi\) |
0.999988 | + | 0.00491959i | \(0.00156596\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −4.17712 | + | 7.23499i | −0.488895 | + | 0.846792i | −0.999918 | − | 0.0127753i | \(-0.995933\pi\) |
0.511023 | + | 0.859567i | \(0.329267\pi\) | |||||||
\(74\) | −1.14575 | + | 1.98450i | −0.133191 | + | 0.230693i | ||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | 2.64575 | + | 3.46410i | 0.303488 | + | 0.397360i | ||||
\(77\) | 11.3542 | 1.29394 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.64575 | − | 4.58258i | 0.297670 | − | 0.515580i | −0.677932 | − | 0.735124i | \(-0.737124\pi\) |
0.975603 | + | 0.219544i | \(0.0704571\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.67712 | − | 2.90486i | −0.185207 | − | 0.320789i | ||||
\(83\) | −4.58301 | −0.503050 | −0.251525 | − | 0.967851i | \(-0.580932\pi\) | ||||
−0.251525 | + | 0.967851i | \(0.580932\pi\) | |||||||
\(84\) | −2.64575 | −0.288675 | ||||||||
\(85\) | −0.177124 | − | 0.306788i | −0.0192118 | − | 0.0332759i | ||||
\(86\) | 3.00000 | + | 5.19615i | 0.323498 | + | 0.560316i | ||||
\(87\) | −1.64575 | −0.176443 | ||||||||
\(88\) | −4.29150 | −0.457476 | ||||||||
\(89\) | 6.61438 | + | 11.4564i | 0.701123 | + | 1.21438i | 0.968073 | + | 0.250670i | \(0.0806508\pi\) |
−0.266950 | + | 0.963710i | \(0.586016\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | −1.64575 | + | 2.85052i | −0.170656 | + | 0.295586i | ||||
\(94\) | 8.58301 | 0.885269 | ||||||||
\(95\) | −1.67712 | + | 4.02334i | −0.172069 | + | 0.412786i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −1.82288 | + | 3.15731i | −0.185085 | + | 0.320577i | −0.943605 | − | 0.331073i | \(-0.892589\pi\) |
0.758520 | + | 0.651650i | \(0.225923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.14575 | − | 3.71655i | −0.215656 | − | 0.373527i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 9.93725 | + | 17.2118i | 0.988794 | + | 1.71264i | 0.623684 | + | 0.781676i | \(0.285635\pi\) |
0.365109 | + | 0.930965i | \(0.381032\pi\) | |||||||
\(102\) | −0.354249 | −0.0350758 | ||||||||
\(103\) | −13.9373 | −1.37328 | −0.686639 | − | 0.726998i | \(-0.740915\pi\) | ||||
−0.686639 | + | 0.726998i | \(0.740915\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.32288 | − | 2.29129i | −0.129099 | − | 0.223607i | ||||
\(106\) | −0.645751 | −0.0627209 | ||||||||
\(107\) | 9.64575 | 0.932490 | 0.466245 | − | 0.884656i | \(-0.345607\pi\) | ||||
0.466245 | + | 0.884656i | \(0.345607\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 2.82288 | − | 4.88936i | 0.270382 | − | 0.468316i | −0.698577 | − | 0.715535i | \(-0.746183\pi\) |
0.968960 | + | 0.247218i | \(0.0795165\pi\) | |||||||
\(110\) | −2.14575 | − | 3.71655i | −0.204589 | − | 0.354359i | ||||
\(111\) | −1.14575 | + | 1.98450i | −0.108750 | + | 0.188360i | ||||
\(112\) | −1.32288 | + | 2.29129i | −0.125000 | + | 0.216506i | ||||
\(113\) | −0.354249 | −0.0333249 | −0.0166625 | − | 0.999861i | \(-0.505304\pi\) | ||||
−0.0166625 | + | 0.999861i | \(0.505304\pi\) | |||||||
\(114\) | 2.64575 | + | 3.46410i | 0.247797 | + | 0.324443i | ||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | −0.822876 | + | 1.42526i | −0.0764021 | + | 0.132332i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.64575 | − | 4.58258i | −0.243561 | − | 0.421860i | ||||
\(119\) | 0.468627 | − | 0.811686i | 0.0429590 | − | 0.0744071i | ||||
\(120\) | 0.500000 | + | 0.866025i | 0.0456435 | + | 0.0790569i | ||||
\(121\) | 7.41699 | 0.674272 | ||||||||
\(122\) | 8.93725 | 0.809141 | ||||||||
\(123\) | −1.67712 | − | 2.90486i | −0.151221 | − | 0.261923i | ||||
\(124\) | 1.64575 | + | 2.85052i | 0.147793 | + | 0.255985i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −2.64575 | −0.235702 | ||||||||
\(127\) | −7.61438 | − | 13.1885i | −0.675667 | − | 1.17029i | −0.976274 | − | 0.216541i | \(-0.930522\pi\) |
0.300607 | − | 0.953748i | \(-0.402811\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.00000 | + | 5.19615i | 0.264135 | + | 0.457496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.14575 | − | 15.8409i | 0.799068 | − | 1.38403i | −0.121156 | − | 0.992634i | \(-0.538660\pi\) |
0.920224 | − | 0.391393i | \(-0.128007\pi\) | |||||||
\(132\) | −4.29150 | −0.373527 | ||||||||
\(133\) | −11.4373 | + | 1.47960i | −0.991736 | + | 0.128298i | ||||
\(134\) | 4.35425 | 0.376150 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −0.177124 | + | 0.306788i | −0.0151883 | + | 0.0263069i | ||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | 3.64575 | + | 6.31463i | 0.309229 | + | 0.535600i | 0.978194 | − | 0.207694i | \(-0.0665958\pi\) |
−0.668965 | + | 0.743294i | \(0.733263\pi\) | |||||||
\(140\) | −2.64575 | −0.223607 | ||||||||
\(141\) | 8.58301 | 0.722819 | ||||||||
\(142\) | −4.17712 | − | 7.23499i | −0.350536 | − | 0.607147i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.64575 | −0.136672 | ||||||||
\(146\) | 4.17712 | + | 7.23499i | 0.345701 | + | 0.598772i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.14575 | + | 1.98450i | 0.0941802 | + | 0.163125i | ||||
\(149\) | −5.11438 | + | 8.85836i | −0.418986 | + | 0.725705i | −0.995838 | − | 0.0911436i | \(-0.970948\pi\) |
0.576852 | + | 0.816849i | \(0.304281\pi\) | |||||||
\(150\) | −0.500000 | + | 0.866025i | −0.0408248 | + | 0.0707107i | ||||
\(151\) | 6.22876 | 0.506889 | 0.253445 | − | 0.967350i | \(-0.418436\pi\) | ||||
0.253445 | + | 0.967350i | \(0.418436\pi\) | |||||||
\(152\) | 4.32288 | − | 0.559237i | 0.350632 | − | 0.0453601i | ||||
\(153\) | −0.354249 | −0.0286393 | ||||||||
\(154\) | 5.67712 | − | 9.83307i | 0.457476 | − | 0.792371i | ||||
\(155\) | −1.64575 | + | 2.85052i | −0.132190 | + | 0.228960i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.43725 | + | 16.3458i | −0.753175 | + | 1.30454i | 0.193102 | + | 0.981179i | \(0.438145\pi\) |
−0.946277 | + | 0.323358i | \(0.895188\pi\) | |||||||
\(158\) | −2.64575 | − | 4.58258i | −0.210485 | − | 0.364570i | ||||
\(159\) | −0.645751 | −0.0512114 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.32288 | − | 2.29129i | −0.104257 | − | 0.180579i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | −13.2915 | −1.04107 | −0.520535 | − | 0.853840i | \(-0.674268\pi\) | ||||
−0.520535 | + | 0.853840i | \(0.674268\pi\) | |||||||
\(164\) | −3.35425 | −0.261923 | ||||||||
\(165\) | −2.14575 | − | 3.71655i | −0.167047 | − | 0.289333i | ||||
\(166\) | −2.29150 | + | 3.96900i | −0.177855 | + | 0.308054i | ||||
\(167\) | 1.79150 | + | 3.10297i | 0.138631 | + | 0.240115i | 0.926979 | − | 0.375114i | \(-0.122397\pi\) |
−0.788348 | + | 0.615230i | \(0.789063\pi\) | |||||||
\(168\) | −1.32288 | + | 2.29129i | −0.102062 | + | 0.176777i | ||||
\(169\) | 6.50000 | − | 11.2583i | 0.500000 | − | 0.866025i | ||||
\(170\) | −0.354249 | −0.0271696 | ||||||||
\(171\) | 2.64575 | + | 3.46410i | 0.202326 | + | 0.264906i | ||||
\(172\) | 6.00000 | 0.457496 | ||||||||
\(173\) | 3.96863 | − | 6.87386i | 0.301729 | − | 0.522610i | −0.674799 | − | 0.738002i | \(-0.735770\pi\) |
0.976528 | + | 0.215392i | \(0.0691028\pi\) | |||||||
\(174\) | −0.822876 | + | 1.42526i | −0.0623820 | + | 0.108049i | ||||
\(175\) | −1.32288 | − | 2.29129i | −0.100000 | − | 0.173205i | ||||
\(176\) | −2.14575 | + | 3.71655i | −0.161742 | + | 0.280146i | ||||
\(177\) | −2.64575 | − | 4.58258i | −0.198867 | − | 0.344447i | ||||
\(178\) | 13.2288 | 0.991537 | ||||||||
\(179\) | −17.5830 | −1.31422 | −0.657108 | − | 0.753797i | \(-0.728220\pi\) | ||||
−0.657108 | + | 0.753797i | \(0.728220\pi\) | |||||||
\(180\) | 0.500000 | + | 0.866025i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 9.82288 | + | 17.0137i | 0.730129 | + | 1.26462i | 0.956828 | + | 0.290655i | \(0.0938732\pi\) |
−0.226699 | + | 0.973965i | \(0.572793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.93725 | 0.660661 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | −1.14575 | + | 1.98450i | −0.0842373 | + | 0.145903i | ||||
\(186\) | 1.64575 | + | 2.85052i | 0.120672 | + | 0.209011i | ||||
\(187\) | 0.760130 | − | 1.31658i | 0.0555862 | − | 0.0962781i | ||||
\(188\) | 4.29150 | − | 7.43310i | 0.312990 | − | 0.542115i | ||||
\(189\) | −2.64575 | −0.192450 | ||||||||
\(190\) | 2.64575 | + | 3.46410i | 0.191943 | + | 0.251312i | ||||
\(191\) | 16.5830 | 1.19990 | 0.599952 | − | 0.800036i | \(-0.295186\pi\) | ||||
0.599952 | + | 0.800036i | \(0.295186\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −3.17712 | + | 5.50294i | −0.228694 | + | 0.396110i | −0.957421 | − | 0.288694i | \(-0.906779\pi\) |
0.728727 | + | 0.684804i | \(0.240112\pi\) | |||||||
\(194\) | 1.82288 | + | 3.15731i | 0.130875 | + | 0.226682i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.64575 | 0.188502 | 0.0942510 | − | 0.995548i | \(-0.469954\pi\) | ||||
0.0942510 | + | 0.995548i | \(0.469954\pi\) | |||||||
\(198\) | −4.29150 | −0.304984 | ||||||||
\(199\) | −9.46863 | − | 16.4001i | −0.671213 | − | 1.16258i | −0.977560 | − | 0.210655i | \(-0.932440\pi\) |
0.306347 | − | 0.951920i | \(-0.400893\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 4.35425 | 0.307125 | ||||||||
\(202\) | 19.8745 | 1.39837 | ||||||||
\(203\) | −2.17712 | − | 3.77089i | −0.152804 | − | 0.264665i | ||||
\(204\) | −0.177124 | + | 0.306788i | −0.0124012 | + | 0.0214795i | ||||
\(205\) | −1.67712 | − | 2.90486i | −0.117135 | − | 0.202885i | ||||
\(206\) | −6.96863 | + | 12.0700i | −0.485527 | + | 0.840958i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −18.5516 | + | 2.39997i | −1.28324 | + | 0.166009i | ||||
\(210\) | −2.64575 | −0.182574 | ||||||||
\(211\) | −9.26013 | + | 16.0390i | −0.637494 | + | 1.10417i | 0.348487 | + | 0.937313i | \(0.386695\pi\) |
−0.985981 | + | 0.166858i | \(0.946638\pi\) | |||||||
\(212\) | −0.322876 | + | 0.559237i | −0.0221752 | + | 0.0384086i | ||||
\(213\) | −4.17712 | − | 7.23499i | −0.286212 | − | 0.495733i | ||||
\(214\) | 4.82288 | − | 8.35347i | 0.329685 | − | 0.571031i | ||||
\(215\) | 3.00000 | + | 5.19615i | 0.204598 | + | 0.354375i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −8.70850 | −0.591171 | ||||||||
\(218\) | −2.82288 | − | 4.88936i | −0.191189 | − | 0.331150i | ||||
\(219\) | 4.17712 | + | 7.23499i | 0.282264 | + | 0.488895i | ||||
\(220\) | −4.29150 | −0.289333 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.14575 | + | 1.98450i | 0.0768978 | + | 0.133191i | ||||
\(223\) | −0.677124 | + | 1.17281i | −0.0453436 | + | 0.0785374i | −0.887806 | − | 0.460217i | \(-0.847772\pi\) |
0.842463 | + | 0.538754i | \(0.181105\pi\) | |||||||
\(224\) | 1.32288 | + | 2.29129i | 0.0883883 | + | 0.153093i | ||||
\(225\) | −0.500000 | + | 0.866025i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | −0.177124 | + | 0.306788i | −0.0117821 | + | 0.0204073i | ||||
\(227\) | −24.8118 | −1.64681 | −0.823407 | − | 0.567451i | \(-0.807930\pi\) | ||||
−0.823407 | + | 0.567451i | \(0.807930\pi\) | |||||||
\(228\) | 4.32288 | − | 0.559237i | 0.286289 | − | 0.0370364i | ||||
\(229\) | 25.2915 | 1.67131 | 0.835655 | − | 0.549255i | \(-0.185088\pi\) | ||||
0.835655 | + | 0.549255i | \(0.185088\pi\) | |||||||
\(230\) | −0.500000 | + | 0.866025i | −0.0329690 | + | 0.0571040i | ||||
\(231\) | 5.67712 | − | 9.83307i | 0.373527 | − | 0.646968i | ||||
\(232\) | 0.822876 | + | 1.42526i | 0.0540244 | + | 0.0935731i | ||||
\(233\) | 0.291503 | − | 0.504897i | 0.0190970 | − | 0.0330769i | −0.856319 | − | 0.516447i | \(-0.827254\pi\) |
0.875416 | + | 0.483370i | \(0.160588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.58301 | 0.559894 | ||||||||
\(236\) | −5.29150 | −0.344447 | ||||||||
\(237\) | −2.64575 | − | 4.58258i | −0.171860 | − | 0.297670i | ||||
\(238\) | −0.468627 | − | 0.811686i | −0.0303766 | − | 0.0526138i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −11.2915 | − | 19.5575i | −0.727350 | − | 1.25981i | −0.958000 | − | 0.286770i | \(-0.907419\pi\) |
0.230650 | − | 0.973037i | \(-0.425915\pi\) | |||||||
\(242\) | 3.70850 | − | 6.42331i | 0.238391 | − | 0.412906i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 4.46863 | − | 7.73989i | 0.286075 | − | 0.495496i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.35425 | −0.213859 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 3.29150 | 0.209011 | ||||||||
\(249\) | −2.29150 | + | 3.96900i | −0.145218 | + | 0.251525i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −9.29150 | − | 16.0934i | −0.586474 | − | 1.01580i | −0.994690 | − | 0.102918i | \(-0.967182\pi\) |
0.408215 | − | 0.912886i | \(-0.366151\pi\) | |||||||
\(252\) | −1.32288 | + | 2.29129i | −0.0833333 | + | 0.144338i | ||||
\(253\) | −2.14575 | − | 3.71655i | −0.134902 | − | 0.233658i | ||||
\(254\) | −15.2288 | −0.955537 | ||||||||
\(255\) | −0.354249 | −0.0221839 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.00000 | − | 5.19615i | −0.187135 | − | 0.324127i | 0.757159 | − | 0.653231i | \(-0.226587\pi\) |
−0.944294 | + | 0.329104i | \(0.893253\pi\) | |||||||
\(258\) | 6.00000 | 0.373544 | ||||||||
\(259\) | −6.06275 | −0.376721 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.822876 | + | 1.42526i | −0.0509347 | + | 0.0882215i | ||||
\(262\) | −9.14575 | − | 15.8409i | −0.565026 | − | 0.978654i | ||||
\(263\) | 3.14575 | − | 5.44860i | 0.193975 | − | 0.335975i | −0.752589 | − | 0.658491i | \(-0.771195\pi\) |
0.946564 | + | 0.322516i | \(0.104528\pi\) | |||||||
\(264\) | −2.14575 | + | 3.71655i | −0.132062 | + | 0.228738i | ||||
\(265\) | −0.645751 | −0.0396682 | ||||||||
\(266\) | −4.43725 | + | 10.6448i | −0.272065 | + | 0.652672i | ||||
\(267\) | 13.2288 | 0.809587 | ||||||||
\(268\) | 2.17712 | − | 3.77089i | 0.132989 | − | 0.230344i | ||||
\(269\) | 1.46863 | − | 2.54374i | 0.0895438 | − | 0.155094i | −0.817775 | − | 0.575539i | \(-0.804792\pi\) |
0.907318 | + | 0.420444i | \(0.138126\pi\) | |||||||
\(270\) | 0.500000 | + | 0.866025i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 9.93725 | − | 17.2118i | 0.603645 | − | 1.04554i | −0.388619 | − | 0.921399i | \(-0.627048\pi\) |
0.992264 | − | 0.124146i | \(-0.0396190\pi\) | |||||||
\(272\) | 0.177124 | + | 0.306788i | 0.0107397 | + | 0.0186018i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.0000 | 0.724947 | ||||||||
\(275\) | −2.14575 | − | 3.71655i | −0.129394 | − | 0.224116i | ||||
\(276\) | 0.500000 | + | 0.866025i | 0.0300965 | + | 0.0521286i | ||||
\(277\) | −8.00000 | −0.480673 | −0.240337 | − | 0.970690i | \(-0.577258\pi\) | ||||
−0.240337 | + | 0.970690i | \(0.577258\pi\) | |||||||
\(278\) | 7.29150 | 0.437315 | ||||||||
\(279\) | 1.64575 | + | 2.85052i | 0.0985286 | + | 0.170656i | ||||
\(280\) | −1.32288 | + | 2.29129i | −0.0790569 | + | 0.136931i | ||||
\(281\) | −13.9059 | − | 24.0857i | −0.829555 | − | 1.43683i | −0.898388 | − | 0.439204i | \(-0.855261\pi\) |
0.0688322 | − | 0.997628i | \(-0.478073\pi\) | |||||||
\(282\) | 4.29150 | − | 7.43310i | 0.255555 | − | 0.442635i | ||||
\(283\) | 5.93725 | − | 10.2836i | 0.352933 | − | 0.611298i | −0.633829 | − | 0.773473i | \(-0.718518\pi\) |
0.986762 | + | 0.162175i | \(0.0518510\pi\) | |||||||
\(284\) | −8.35425 | −0.495733 | ||||||||
\(285\) | 2.64575 | + | 3.46410i | 0.156721 | + | 0.205196i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.43725 | − | 7.68555i | 0.261923 | − | 0.453664i | ||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.43725 | + | 14.6138i | 0.496309 | + | 0.859632i | ||||
\(290\) | −0.822876 | + | 1.42526i | −0.0483209 | + | 0.0836943i | ||||
\(291\) | 1.82288 | + | 3.15731i | 0.106859 | + | 0.185085i | ||||
\(292\) | 8.35425 | 0.488895 | ||||||||
\(293\) | −14.6458 | −0.855614 | −0.427807 | − | 0.903870i | \(-0.640714\pi\) | ||||
−0.427807 | + | 0.903870i | \(0.640714\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.64575 | − | 4.58258i | −0.154042 | − | 0.266808i | ||||
\(296\) | 2.29150 | 0.133191 | ||||||||
\(297\) | −4.29150 | −0.249018 | ||||||||
\(298\) | 5.11438 | + | 8.85836i | 0.296268 | + | 0.513151i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.500000 | + | 0.866025i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | −7.93725 | + | 13.7477i | −0.457496 | + | 0.792406i | ||||
\(302\) | 3.11438 | − | 5.39426i | 0.179212 | − | 0.310405i | ||||
\(303\) | 19.8745 | 1.14176 | ||||||||
\(304\) | 1.67712 | − | 4.02334i | 0.0961897 | − | 0.230754i | ||||
\(305\) | 8.93725 | 0.511746 | ||||||||
\(306\) | −0.177124 | + | 0.306788i | −0.0101255 | + | 0.0175379i | ||||
\(307\) | −5.76013 | + | 9.97684i | −0.328748 | + | 0.569408i | −0.982264 | − | 0.187505i | \(-0.939960\pi\) |
0.653516 | + | 0.756913i | \(0.273293\pi\) | |||||||
\(308\) | −5.67712 | − | 9.83307i | −0.323484 | − | 0.560291i | ||||
\(309\) | −6.96863 | + | 12.0700i | −0.396431 | + | 0.686639i | ||||
\(310\) | 1.64575 | + | 2.85052i | 0.0934724 | + | 0.161899i | ||||
\(311\) | 17.1660 | 0.973395 | 0.486698 | − | 0.873571i | \(-0.338201\pi\) | ||||
0.486698 | + | 0.873571i | \(0.338201\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.29150 | − | 16.0934i | −0.525187 | − | 0.909650i | −0.999570 | − | 0.0293316i | \(-0.990662\pi\) |
0.474383 | − | 0.880319i | \(-0.342671\pi\) | |||||||
\(314\) | 9.43725 | + | 16.3458i | 0.532575 | + | 0.922447i | ||||
\(315\) | −2.64575 | −0.149071 | ||||||||
\(316\) | −5.29150 | −0.297670 | ||||||||
\(317\) | −9.96863 | − | 17.2662i | −0.559894 | − | 0.969765i | −0.997505 | − | 0.0706001i | \(-0.977509\pi\) |
0.437611 | − | 0.899164i | \(-0.355825\pi\) | |||||||
\(318\) | −0.322876 | + | 0.559237i | −0.0181060 | + | 0.0313605i | ||||
\(319\) | −3.53137 | − | 6.11652i | −0.197719 | − | 0.342459i | ||||
\(320\) | 0.500000 | − | 0.866025i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 4.82288 | − | 8.35347i | 0.269187 | − | 0.466245i | ||||
\(322\) | −2.64575 | −0.147442 | ||||||||
\(323\) | −0.594119 | + | 1.42526i | −0.0330577 | + | 0.0793037i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.64575 | + | 11.5108i | −0.368074 | + | 0.637523i | ||||
\(327\) | −2.82288 | − | 4.88936i | −0.156105 | − | 0.270382i | ||||
\(328\) | −1.67712 | + | 2.90486i | −0.0926037 | + | 0.160394i | ||||
\(329\) | 11.3542 | + | 19.6661i | 0.625980 | + | 1.08423i | ||||
\(330\) | −4.29150 | −0.236239 | ||||||||
\(331\) | −13.3542 | −0.734016 | −0.367008 | − | 0.930218i | \(-0.619618\pi\) | ||||
−0.367008 | + | 0.930218i | \(0.619618\pi\) | |||||||
\(332\) | 2.29150 | + | 3.96900i | 0.125763 | + | 0.217827i | ||||
\(333\) | 1.14575 | + | 1.98450i | 0.0627868 | + | 0.108750i | ||||
\(334\) | 3.58301 | 0.196053 | ||||||||
\(335\) | 4.35425 | 0.237898 | ||||||||
\(336\) | 1.32288 | + | 2.29129i | 0.0721688 | + | 0.125000i | ||||
\(337\) | −8.64575 | + | 14.9749i | −0.470964 | + | 0.815734i | −0.999448 | − | 0.0332093i | \(-0.989427\pi\) |
0.528484 | + | 0.848943i | \(0.322761\pi\) | |||||||
\(338\) | −6.50000 | − | 11.2583i | −0.353553 | − | 0.612372i | ||||
\(339\) | −0.177124 | + | 0.306788i | −0.00962007 | + | 0.0166625i | ||||
\(340\) | −0.177124 | + | 0.306788i | −0.00960592 | + | 0.0166379i | ||||
\(341\) | −14.1255 | −0.764938 | ||||||||
\(342\) | 4.32288 | − | 0.559237i | 0.233754 | − | 0.0302401i | ||||
\(343\) | −18.5203 | −1.00000 | ||||||||
\(344\) | 3.00000 | − | 5.19615i | 0.161749 | − | 0.280158i | ||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | −3.96863 | − | 6.87386i | −0.213355 | − | 0.369541i | ||||
\(347\) | 4.29150 | − | 7.43310i | 0.230380 | − | 0.399030i | −0.727540 | − | 0.686065i | \(-0.759336\pi\) |
0.957920 | + | 0.287036i | \(0.0926698\pi\) | |||||||
\(348\) | 0.822876 | + | 1.42526i | 0.0441108 | + | 0.0764021i | ||||
\(349\) | 32.9373 | 1.76309 | 0.881545 | − | 0.472099i | \(-0.156504\pi\) | ||||
0.881545 | + | 0.472099i | \(0.156504\pi\) | |||||||
\(350\) | −2.64575 | −0.141421 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.14575 | + | 3.71655i | 0.114369 | + | 0.198093i | ||||
\(353\) | −22.9373 | −1.22083 | −0.610413 | − | 0.792083i | \(-0.708997\pi\) | ||||
−0.610413 | + | 0.792083i | \(0.708997\pi\) | |||||||
\(354\) | −5.29150 | −0.281240 | ||||||||
\(355\) | −4.17712 | − | 7.23499i | −0.221699 | − | 0.383993i | ||||
\(356\) | 6.61438 | − | 11.4564i | 0.350561 | − | 0.607190i | ||||
\(357\) | −0.468627 | − | 0.811686i | −0.0248024 | − | 0.0429590i | ||||
\(358\) | −8.79150 | + | 15.2273i | −0.464645 | + | 0.804789i | ||||
\(359\) | 5.46863 | − | 9.47194i | 0.288623 | − | 0.499910i | −0.684858 | − | 0.728676i | \(-0.740136\pi\) |
0.973481 | + | 0.228766i | \(0.0734692\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 18.3745 | − | 4.83502i | 0.967079 | − | 0.254475i | ||||
\(362\) | 19.6458 | 1.03256 | ||||||||
\(363\) | 3.70850 | − | 6.42331i | 0.194646 | − | 0.337136i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.17712 | + | 7.23499i | 0.218641 | + | 0.378697i | ||||
\(366\) | 4.46863 | − | 7.73989i | 0.233579 | − | 0.404570i | ||||
\(367\) | −14.9373 | − | 25.8721i | −0.779718 | − | 1.35051i | −0.932104 | − | 0.362191i | \(-0.882029\pi\) |
0.152386 | − | 0.988321i | \(-0.451304\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −3.35425 | −0.174615 | ||||||||
\(370\) | 1.14575 | + | 1.98450i | 0.0595648 | + | 0.103169i | ||||
\(371\) | −0.854249 | − | 1.47960i | −0.0443504 | − | 0.0768171i | ||||
\(372\) | 3.29150 | 0.170656 | ||||||||
\(373\) | 7.70850 | 0.399131 | 0.199565 | − | 0.979885i | \(-0.436047\pi\) | ||||
0.199565 | + | 0.979885i | \(0.436047\pi\) | |||||||
\(374\) | −0.760130 | − | 1.31658i | −0.0393054 | − | 0.0680789i | ||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −4.29150 | − | 7.43310i | −0.221317 | − | 0.383333i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −1.32288 | + | 2.29129i | −0.0680414 | + | 0.117851i | ||||
\(379\) | −13.8745 | −0.712686 | −0.356343 | − | 0.934355i | \(-0.615976\pi\) | ||||
−0.356343 | + | 0.934355i | \(0.615976\pi\) | |||||||
\(380\) | 4.32288 | − | 0.559237i | 0.221759 | − | 0.0286883i | ||||
\(381\) | −15.2288 | −0.780193 | ||||||||
\(382\) | 8.29150 | − | 14.3613i | 0.424230 | − | 0.734788i | ||||
\(383\) | 7.70850 | − | 13.3515i | 0.393886 | − | 0.682230i | −0.599072 | − | 0.800695i | \(-0.704464\pi\) |
0.992958 | + | 0.118465i | \(0.0377972\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 5.67712 | − | 9.83307i | 0.289333 | − | 0.501140i | ||||
\(386\) | 3.17712 | + | 5.50294i | 0.161711 | + | 0.280092i | ||||
\(387\) | 6.00000 | 0.304997 | ||||||||
\(388\) | 3.64575 | 0.185085 | ||||||||
\(389\) | −9.76013 | − | 16.9050i | −0.494858 | − | 0.857120i | 0.505124 | − | 0.863047i | \(-0.331447\pi\) |
−0.999982 | + | 0.00592708i | \(0.998113\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.354249 | −0.0179151 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.14575 | − | 15.8409i | −0.461342 | − | 0.799068i | ||||
\(394\) | 1.32288 | − | 2.29129i | 0.0666455 | − | 0.115433i | ||||
\(395\) | −2.64575 | − | 4.58258i | −0.133122 | − | 0.230574i | ||||
\(396\) | −2.14575 | + | 3.71655i | −0.107828 | + | 0.186764i | ||||
\(397\) | −12.7288 | + | 22.0469i | −0.638838 | + | 1.10650i | 0.346850 | + | 0.937921i | \(0.387251\pi\) |
−0.985688 | + | 0.168579i | \(0.946082\pi\) | |||||||
\(398\) | −18.9373 | −0.949239 | ||||||||
\(399\) | −4.43725 | + | 10.6448i | −0.222141 | + | 0.532904i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −3.00000 | + | 5.19615i | −0.149813 | + | 0.259483i | −0.931158 | − | 0.364615i | \(-0.881200\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(402\) | 2.17712 | − | 3.77089i | 0.108585 | − | 0.188075i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 9.93725 | − | 17.2118i | 0.494397 | − | 0.856320i | ||||
\(405\) | 0.500000 | + | 0.866025i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | −4.35425 | −0.216098 | ||||||||
\(407\) | −9.83399 | −0.487453 | ||||||||
\(408\) | 0.177124 | + | 0.306788i | 0.00876896 | + | 0.0151883i | ||||
\(409\) | 19.7915 | + | 34.2799i | 0.978627 | + | 1.69503i | 0.667407 | + | 0.744694i | \(0.267404\pi\) |
0.311220 | + | 0.950338i | \(0.399262\pi\) | |||||||
\(410\) | −3.35425 | −0.165655 | ||||||||
\(411\) | 12.0000 | 0.591916 | ||||||||
\(412\) | 6.96863 | + | 12.0700i | 0.343320 | + | 0.594647i | ||||
\(413\) | 7.00000 | − | 12.1244i | 0.344447 | − | 0.596601i | ||||
\(414\) | 0.500000 | + | 0.866025i | 0.0245737 | + | 0.0425628i | ||||
\(415\) | −2.29150 | + | 3.96900i | −0.112485 | + | 0.194830i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.29150 | 0.357066 | ||||||||
\(418\) | −7.19738 | + | 17.2662i | −0.352036 | + | 0.844516i | ||||
\(419\) | −4.16601 | −0.203523 | −0.101761 | − | 0.994809i | \(-0.532448\pi\) | ||||
−0.101761 | + | 0.994809i | \(0.532448\pi\) | |||||||
\(420\) | −1.32288 | + | 2.29129i | −0.0645497 | + | 0.111803i | ||||
\(421\) | 1.53137 | − | 2.65242i | 0.0746346 | − | 0.129271i | −0.826293 | − | 0.563241i | \(-0.809554\pi\) |
0.900927 | + | 0.433970i | \(0.142888\pi\) | |||||||
\(422\) | 9.26013 | + | 16.0390i | 0.450776 | + | 0.780767i | ||||
\(423\) | 4.29150 | − | 7.43310i | 0.208660 | − | 0.361410i | ||||
\(424\) | 0.322876 | + | 0.559237i | 0.0156802 | + | 0.0271590i | ||||
\(425\) | −0.354249 | −0.0171836 | ||||||||
\(426\) | −8.35425 | −0.404765 | ||||||||
\(427\) | 11.8229 | + | 20.4778i | 0.572149 | + | 0.990991i | ||||
\(428\) | −4.82288 | − | 8.35347i | −0.233122 | − | 0.403780i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.00000 | 0.289346 | ||||||||
\(431\) | −16.8229 | − | 29.1381i | −0.810329 | − | 1.40353i | −0.912634 | − | 0.408779i | \(-0.865955\pi\) |
0.102304 | − | 0.994753i | \(-0.467378\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 5.46863 | + | 9.47194i | 0.262805 | + | 0.455192i | 0.966986 | − | 0.254828i | \(-0.0820189\pi\) |
−0.704181 | + | 0.710021i | \(0.748686\pi\) | |||||||
\(434\) | −4.35425 | + | 7.54178i | −0.209011 | + | 0.362017i | ||||
\(435\) | −0.822876 | + | 1.42526i | −0.0394539 | + | 0.0683361i | ||||
\(436\) | −5.64575 | −0.270382 | ||||||||
\(437\) | 2.64575 | + | 3.46410i | 0.126563 | + | 0.165710i | ||||
\(438\) | 8.35425 | 0.399181 | ||||||||
\(439\) | 9.46863 | − | 16.4001i | 0.451913 | − | 0.782736i | −0.546592 | − | 0.837399i | \(-0.684075\pi\) |
0.998505 | + | 0.0546630i | \(0.0174084\pi\) | |||||||
\(440\) | −2.14575 | + | 3.71655i | −0.102295 | + | 0.177180i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.4686 | + | 35.4527i | 0.972494 | + | 1.68441i | 0.687969 | + | 0.725740i | \(0.258502\pi\) |
0.284525 | + | 0.958669i | \(0.408164\pi\) | |||||||
\(444\) | 2.29150 | 0.108750 | ||||||||
\(445\) | 13.2288 | 0.627103 | ||||||||
\(446\) | 0.677124 | + | 1.17281i | 0.0320628 | + | 0.0555343i | ||||
\(447\) | 5.11438 | + | 8.85836i | 0.241902 | + | 0.418986i | ||||
\(448\) | 2.64575 | 0.125000 | ||||||||
\(449\) | −22.6458 | −1.06872 | −0.534360 | − | 0.845257i | \(-0.679447\pi\) | ||||
−0.534360 | + | 0.845257i | \(0.679447\pi\) | |||||||
\(450\) | 0.500000 | + | 0.866025i | 0.0235702 | + | 0.0408248i | ||||
\(451\) | 7.19738 | − | 12.4662i | 0.338912 | − | 0.587012i | ||||
\(452\) | 0.177124 | + | 0.306788i | 0.00833123 | + | 0.0144301i | ||||
\(453\) | 3.11438 | − | 5.39426i | 0.146326 | − | 0.253445i | ||||
\(454\) | −12.4059 | + | 21.4876i | −0.582237 | + | 1.00846i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.67712 | − | 4.02334i | 0.0785385 | − | 0.188410i | ||||
\(457\) | 28.2288 | 1.32049 | 0.660243 | − | 0.751052i | \(-0.270453\pi\) | ||||
0.660243 | + | 0.751052i | \(0.270453\pi\) | |||||||
\(458\) | 12.6458 | − | 21.9031i | 0.590897 | − | 1.02346i | ||||
\(459\) | −0.177124 | + | 0.306788i | −0.00826746 | + | 0.0143197i | ||||
\(460\) | 0.500000 | + | 0.866025i | 0.0233126 | + | 0.0403786i | ||||
\(461\) | −3.58301 | + | 6.20595i | −0.166877 | + | 0.289040i | −0.937320 | − | 0.348469i | \(-0.886702\pi\) |
0.770443 | + | 0.637509i | \(0.220035\pi\) | |||||||
\(462\) | −5.67712 | − | 9.83307i | −0.264124 | − | 0.457476i | ||||
\(463\) | 34.6458 | 1.61012 | 0.805062 | − | 0.593190i | \(-0.202132\pi\) | ||||
0.805062 | + | 0.593190i | \(0.202132\pi\) | |||||||
\(464\) | 1.64575 | 0.0764021 | ||||||||
\(465\) | 1.64575 | + | 2.85052i | 0.0763199 | + | 0.132190i | ||||
\(466\) | −0.291503 | − | 0.504897i | −0.0135036 | − | 0.0233889i | ||||
\(467\) | −21.5203 | −0.995839 | −0.497919 | − | 0.867223i | \(-0.665902\pi\) | ||||
−0.497919 | + | 0.867223i | \(0.665902\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.76013 | + | 9.97684i | 0.265978 | + | 0.460688i | ||||
\(470\) | 4.29150 | − | 7.43310i | 0.197952 | − | 0.342863i | ||||
\(471\) | 9.43725 | + | 16.3458i | 0.434846 | + | 0.753175i | ||||
\(472\) | −2.64575 | + | 4.58258i | −0.121781 | + | 0.210930i | ||||
\(473\) | −12.8745 | + | 22.2993i | −0.591971 | + | 1.02532i | ||||
\(474\) | −5.29150 | −0.243047 | ||||||||
\(475\) | 2.64575 | + | 3.46410i | 0.121395 | + | 0.158944i | ||||
\(476\) | −0.937254 | −0.0429590 | ||||||||
\(477\) | −0.322876 | + | 0.559237i | −0.0147835 | + | 0.0256057i | ||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | 5.46863 | + | 9.47194i | 0.249868 | + | 0.432784i | 0.963489 | − | 0.267748i | \(-0.0862795\pi\) |
−0.713621 | + | 0.700532i | \(0.752946\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −22.5830 | −1.02863 | ||||||||
\(483\) | −2.64575 | −0.120386 | ||||||||
\(484\) | −3.70850 | − | 6.42331i | −0.168568 | − | 0.291968i | ||||
\(485\) | 1.82288 | + | 3.15731i | 0.0827725 | + | 0.143366i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 15.3542 | 0.695767 | 0.347884 | − | 0.937538i | \(-0.386900\pi\) | ||||
0.347884 | + | 0.937538i | \(0.386900\pi\) | |||||||
\(488\) | −4.46863 | − | 7.73989i | −0.202285 | − | 0.350368i | ||||
\(489\) | −6.64575 | + | 11.5108i | −0.300531 | + | 0.520535i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.72876 | − | 11.6545i | 0.303665 | − | 0.525962i | −0.673299 | − | 0.739371i | \(-0.735123\pi\) |
0.976963 | + | 0.213408i | \(0.0684565\pi\) | |||||||
\(492\) | −1.67712 | + | 2.90486i | −0.0756106 | + | 0.130961i | ||||
\(493\) | −0.583005 | −0.0262572 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.29150 | −0.192889 | ||||||||
\(496\) | 1.64575 | − | 2.85052i | 0.0738964 | − | 0.127992i | ||||
\(497\) | 11.0516 | − | 19.1420i | 0.495733 | − | 0.858636i | ||||
\(498\) | 2.29150 | + | 3.96900i | 0.102685 | + | 0.177855i | ||||
\(499\) | −6.32288 | + | 10.9515i | −0.283051 | + | 0.490258i | −0.972135 | − | 0.234423i | \(-0.924680\pi\) |
0.689084 | + | 0.724682i | \(0.258013\pi\) | |||||||
\(500\) | 0.500000 | + | 0.866025i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 3.58301 | 0.160077 | ||||||||
\(502\) | −18.5830 | −0.829400 | ||||||||
\(503\) | 18.3745 | + | 31.8256i | 0.819279 | + | 1.41903i | 0.906214 | + | 0.422819i | \(0.138959\pi\) |
−0.0869355 | + | 0.996214i | \(0.527707\pi\) | |||||||
\(504\) | 1.32288 | + | 2.29129i | 0.0589256 | + | 0.102062i | ||||
\(505\) | 19.8745 | 0.884404 | ||||||||
\(506\) | −4.29150 | −0.190781 | ||||||||
\(507\) | −6.50000 | − | 11.2583i | −0.288675 | − | 0.500000i | ||||
\(508\) | −7.61438 | + | 13.1885i | −0.337833 | + | 0.585145i | ||||
\(509\) | 6.64575 | + | 11.5108i | 0.294568 | + | 0.510206i | 0.974884 | − | 0.222712i | \(-0.0714910\pi\) |
−0.680317 | + | 0.732918i | \(0.738158\pi\) | |||||||
\(510\) | −0.177124 | + | 0.306788i | −0.00784320 | + | 0.0135848i | ||||
\(511\) | −11.0516 | + | 19.1420i | −0.488895 | + | 0.846792i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.32288 | − | 0.559237i | 0.190860 | − | 0.0246909i | ||||
\(514\) | −6.00000 | −0.264649 | ||||||||
\(515\) | −6.96863 | + | 12.0700i | −0.307074 | + | 0.531868i | ||||
\(516\) | 3.00000 | − | 5.19615i | 0.132068 | − | 0.228748i | ||||
\(517\) | 18.4170 | + | 31.8992i | 0.809979 | + | 1.40292i | ||||
\(518\) | −3.03137 | + | 5.25049i | −0.133191 | + | 0.230693i | ||||
\(519\) | −3.96863 | − | 6.87386i | −0.174203 | − | 0.301729i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.4575 | −1.33437 | −0.667184 | − | 0.744893i | \(-0.732501\pi\) | ||||
−0.667184 | + | 0.744893i | \(0.732501\pi\) | |||||||
\(522\) | 0.822876 | + | 1.42526i | 0.0360163 | + | 0.0623820i | ||||
\(523\) | 20.1144 | + | 34.8391i | 0.879540 | + | 1.52341i | 0.851846 | + | 0.523792i | \(0.175483\pi\) |
0.0276942 | + | 0.999616i | \(0.491184\pi\) | |||||||
\(524\) | −18.2915 | −0.799068 | ||||||||
\(525\) | −2.64575 | −0.115470 | ||||||||
\(526\) | −3.14575 | − | 5.44860i | −0.137161 | − | 0.237570i | ||||
\(527\) | −0.583005 | + | 1.00979i | −0.0253961 | + | 0.0439873i | ||||
\(528\) | 2.14575 | + | 3.71655i | 0.0933818 | + | 0.161742i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | −0.322876 | + | 0.559237i | −0.0140248 | + | 0.0242917i | ||||
\(531\) | −5.29150 | −0.229632 | ||||||||
\(532\) | 7.00000 | + | 9.16515i | 0.303488 | + | 0.397360i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 6.61438 | − | 11.4564i | 0.286232 | − | 0.495769i | ||||
\(535\) | 4.82288 | − | 8.35347i | 0.208511 | − | 0.361152i | ||||
\(536\) | −2.17712 | − | 3.77089i | −0.0940374 | − | 0.162878i | ||||
\(537\) | −8.79150 | + | 15.2273i | −0.379381 | + | 0.657108i | ||||
\(538\) | −1.46863 | − | 2.54374i | −0.0633170 | − | 0.109668i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 6.93725 | + | 12.0157i | 0.298256 | + | 0.516594i | 0.975737 | − | 0.218946i | \(-0.0702618\pi\) |
−0.677481 | + | 0.735540i | \(0.736928\pi\) | |||||||
\(542\) | −9.93725 | − | 17.2118i | −0.426842 | − | 0.739311i | ||||
\(543\) | 19.6458 | 0.843080 | ||||||||
\(544\) | 0.354249 | 0.0151883 | ||||||||
\(545\) | −2.82288 | − | 4.88936i | −0.120919 | − | 0.209437i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.6458 | − | 25.3672i | −0.626207 | − | 1.08462i | −0.988306 | − | 0.152483i | \(-0.951273\pi\) |
0.362099 | − | 0.932140i | \(-0.382060\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | 4.46863 | − | 7.73989i | 0.190716 | − | 0.330330i | ||||
\(550\) | −4.29150 | −0.182990 | ||||||||
\(551\) | 4.35425 | + | 5.70105i | 0.185497 | + | 0.242873i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 7.00000 | − | 12.1244i | 0.297670 | − | 0.515580i | ||||
\(554\) | −4.00000 | + | 6.92820i | −0.169944 | + | 0.294351i | ||||
\(555\) | 1.14575 | + | 1.98450i | 0.0486344 | + | 0.0842373i | ||||
\(556\) | 3.64575 | − | 6.31463i | 0.154614 | − | 0.267800i | ||||
\(557\) | −6.26013 | − | 10.8429i | −0.265250 | − | 0.459427i | 0.702379 | − | 0.711803i | \(-0.252121\pi\) |
−0.967629 | + | 0.252376i | \(0.918788\pi\) | |||||||
\(558\) | 3.29150 | 0.139340 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.32288 | + | 2.29129i | 0.0559017 | + | 0.0968246i | ||||
\(561\) | −0.760130 | − | 1.31658i | −0.0320927 | − | 0.0555862i | ||||
\(562\) | −27.8118 | −1.17317 | ||||||||
\(563\) | 42.5830 | 1.79466 | 0.897330 | − | 0.441361i | \(-0.145504\pi\) | ||||
0.897330 | + | 0.441361i | \(0.145504\pi\) | |||||||
\(564\) | −4.29150 | − | 7.43310i | −0.180705 | − | 0.312990i | ||||
\(565\) | −0.177124 | + | 0.306788i | −0.00745168 | + | 0.0129067i | ||||
\(566\) | −5.93725 | − | 10.2836i | −0.249561 | − | 0.432253i | ||||
\(567\) | −1.32288 | + | 2.29129i | −0.0555556 | + | 0.0962250i | ||||
\(568\) | −4.17712 | + | 7.23499i | −0.175268 | + | 0.303574i | ||||
\(569\) | 10.6458 | 0.446293 | 0.223147 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223147 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(570\) | 4.32288 | − | 0.559237i | 0.181065 | − | 0.0234239i | ||||
\(571\) | −26.4575 | −1.10721 | −0.553606 | − | 0.832779i | \(-0.686749\pi\) | ||||
−0.553606 | + | 0.832779i | \(0.686749\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8.29150 | − | 14.3613i | 0.346382 | − | 0.599952i | ||||
\(574\) | −4.43725 | − | 7.68555i | −0.185207 | − | 0.320789i | ||||
\(575\) | −0.500000 | + | 0.866025i | −0.0208514 | + | 0.0361158i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −12.9373 | −0.538585 | −0.269292 | − | 0.963058i | \(-0.586790\pi\) | ||||
−0.269292 | + | 0.963058i | \(0.586790\pi\) | |||||||
\(578\) | 16.8745 | 0.701887 | ||||||||
\(579\) | 3.17712 | + | 5.50294i | 0.132037 | + | 0.228694i | ||||
\(580\) | 0.822876 | + | 1.42526i | 0.0341681 | + | 0.0591808i | ||||
\(581\) | −12.1255 | −0.503050 | ||||||||
\(582\) | 3.64575 | 0.151121 | ||||||||
\(583\) | −1.38562 | − | 2.39997i | −0.0573866 | − | 0.0993965i | ||||
\(584\) | 4.17712 | − | 7.23499i | 0.172851 | − | 0.299386i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.32288 | + | 12.6836i | −0.302505 | + | 0.523954i | ||||
\(587\) | −21.6458 | + | 37.4915i | −0.893416 | + | 1.54744i | −0.0576626 | + | 0.998336i | \(0.518365\pi\) |
−0.835753 | + | 0.549105i | \(0.814969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.2288 | − | 1.84073i | 0.586286 | − | 0.0758460i | ||||
\(590\) | −5.29150 | −0.217848 | ||||||||
\(591\) | 1.32288 | − | 2.29129i | 0.0544158 | − | 0.0942510i | ||||
\(592\) | 1.14575 | − | 1.98450i | 0.0470901 | − | 0.0815624i | ||||
\(593\) | 15.1771 | + | 26.2876i | 0.623250 | + | 1.07950i | 0.988877 | + | 0.148739i | \(0.0475213\pi\) |
−0.365627 | + | 0.930762i | \(0.619145\pi\) | |||||||
\(594\) | −2.14575 | + | 3.71655i | −0.0880412 | + | 0.152492i | ||||
\(595\) | −0.468627 | − | 0.811686i | −0.0192118 | − | 0.0332759i | ||||
\(596\) | 10.2288 | 0.418986 | ||||||||
\(597\) | −18.9373 | −0.775050 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.76013 | − | 16.9050i | −0.398788 | − | 0.690721i | 0.594789 | − | 0.803882i | \(-0.297236\pi\) |
−0.993577 | + | 0.113161i | \(0.963902\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −5.70850 | −0.232854 | −0.116427 | − | 0.993199i | \(-0.537144\pi\) | ||||
−0.116427 | + | 0.993199i | \(0.537144\pi\) | |||||||
\(602\) | 7.93725 | + | 13.7477i | 0.323498 | + | 0.560316i | ||||
\(603\) | 2.17712 | − | 3.77089i | 0.0886594 | − | 0.153563i | ||||
\(604\) | −3.11438 | − | 5.39426i | −0.126722 | − | 0.219489i | ||||
\(605\) | 3.70850 | − | 6.42331i | 0.150772 | − | 0.261145i | ||||
\(606\) | 9.93725 | − | 17.2118i | 0.403673 | − | 0.699183i | ||||
\(607\) | 19.2288 | 0.780471 | 0.390236 | − | 0.920715i | \(-0.372394\pi\) | ||||
0.390236 | + | 0.920715i | \(0.372394\pi\) | |||||||
\(608\) | −2.64575 | − | 3.46410i | −0.107299 | − | 0.140488i | ||||
\(609\) | −4.35425 | −0.176443 | ||||||||
\(610\) | 4.46863 | − | 7.73989i | 0.180929 | − | 0.313379i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0.177124 | + | 0.306788i | 0.00715983 | + | 0.0124012i | ||||
\(613\) | −1.43725 | + | 2.48940i | −0.0580501 | + | 0.100546i | −0.893590 | − | 0.448884i | \(-0.851822\pi\) |
0.835540 | + | 0.549430i | \(0.185155\pi\) | |||||||
\(614\) | 5.76013 | + | 9.97684i | 0.232460 | + | 0.402632i | ||||
\(615\) | −3.35425 | −0.135256 | ||||||||
\(616\) | −11.3542 | −0.457476 | ||||||||
\(617\) | −9.29150 | − | 16.0934i | −0.374062 | − | 0.647894i | 0.616124 | − | 0.787649i | \(-0.288702\pi\) |
−0.990186 | + | 0.139755i | \(0.955369\pi\) | |||||||
\(618\) | 6.96863 | + | 12.0700i | 0.280319 | + | 0.485527i | ||||
\(619\) | −33.9373 | −1.36405 | −0.682027 | − | 0.731327i | \(-0.738901\pi\) | ||||
−0.682027 | + | 0.731327i | \(0.738901\pi\) | |||||||
\(620\) | 3.29150 | 0.132190 | ||||||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | 8.58301 | − | 14.8662i | 0.344147 | − | 0.596080i | ||||
\(623\) | 17.5000 | + | 30.3109i | 0.701123 | + | 1.21438i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −18.5830 | −0.742726 | ||||||||
\(627\) | −7.19738 | + | 17.2662i | −0.287436 | + | 0.689544i | ||||
\(628\) | 18.8745 | 0.753175 | ||||||||
\(629\) | −0.405881 | + | 0.703006i | −0.0161835 | + | 0.0280307i | ||||
\(630\) | −1.32288 | + | 2.29129i | −0.0527046 | + | 0.0912871i | ||||
\(631\) | −10.8229 | − | 18.7458i | −0.430852 | − | 0.746257i | 0.566095 | − | 0.824340i | \(-0.308454\pi\) |
−0.996947 | + | 0.0780827i | \(0.975120\pi\) | |||||||
\(632\) | −2.64575 | + | 4.58258i | −0.105242 | + | 0.182285i | ||||
\(633\) | 9.26013 | + | 16.0390i | 0.368057 | + | 0.637494i | ||||
\(634\) | −19.9373 | −0.791810 | ||||||||
\(635\) | −15.2288 | −0.604335 | ||||||||
\(636\) | 0.322876 | + | 0.559237i | 0.0128029 | + | 0.0221752i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −7.06275 | −0.279617 | ||||||||
\(639\) | −8.35425 | −0.330489 | ||||||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 5.35425 | − | 9.27383i | 0.211480 | − | 0.366294i | −0.740698 | − | 0.671838i | \(-0.765505\pi\) |
0.952178 | + | 0.305544i | \(0.0988383\pi\) | |||||||
\(642\) | −4.82288 | − | 8.35347i | −0.190344 | − | 0.329685i | ||||
\(643\) | −24.4059 | + | 42.2722i | −0.962474 | + | 1.66705i | −0.246220 | + | 0.969214i | \(0.579189\pi\) |
−0.716254 | + | 0.697840i | \(0.754145\pi\) | |||||||
\(644\) | −1.32288 | + | 2.29129i | −0.0521286 | + | 0.0902894i | ||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0.937254 | + | 1.22715i | 0.0368758 | + | 0.0482817i | ||||
\(647\) | 5.12549 | 0.201504 | 0.100752 | − | 0.994912i | \(-0.467875\pi\) | ||||
0.100752 | + | 0.994912i | \(0.467875\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 11.3542 | − | 19.6661i | 0.445693 | − | 0.771963i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.35425 | + | 7.54178i | −0.170656 | + | 0.295586i | ||||
\(652\) | 6.64575 | + | 11.5108i | 0.260268 | + | 0.450797i | ||||
\(653\) | 10.0627 | 0.393786 | 0.196893 | − | 0.980425i | \(-0.436915\pi\) | ||||
0.196893 | + | 0.980425i | \(0.436915\pi\) | |||||||
\(654\) | −5.64575 | −0.220766 | ||||||||
\(655\) | −9.14575 | − | 15.8409i | −0.357354 | − | 0.618955i | ||||
\(656\) | 1.67712 | + | 2.90486i | 0.0654807 | + | 0.113416i | ||||
\(657\) | 8.35425 | 0.325930 | ||||||||
\(658\) | 22.7085 | 0.885269 | ||||||||
\(659\) | 5.79150 | + | 10.0312i | 0.225605 | + | 0.390759i | 0.956501 | − | 0.291730i | \(-0.0942308\pi\) |
−0.730896 | + | 0.682489i | \(0.760897\pi\) | |||||||
\(660\) | −2.14575 | + | 3.71655i | −0.0835233 | + | 0.144667i | ||||
\(661\) | 6.70850 | + | 11.6195i | 0.260930 | + | 0.451945i | 0.966489 | − | 0.256707i | \(-0.0826374\pi\) |
−0.705559 | + | 0.708651i | \(0.749304\pi\) | |||||||
\(662\) | −6.67712 | + | 11.5651i | −0.259514 | + | 0.449491i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.58301 | 0.177855 | ||||||||
\(665\) | −4.43725 | + | 10.6448i | −0.172069 | + | 0.412786i | ||||
\(666\) | 2.29150 | 0.0887939 | ||||||||
\(667\) | −0.822876 | + | 1.42526i | −0.0318619 | + | 0.0551864i | ||||
\(668\) | 1.79150 | − | 3.10297i | 0.0693153 | − | 0.120058i | ||||
\(669\) | 0.677124 | + | 1.17281i | 0.0261791 | + | 0.0453436i | ||||
\(670\) | 2.17712 | − | 3.77089i | 0.0841097 | − | 0.145682i | ||||
\(671\) | 19.1771 | + | 33.2158i | 0.740325 | + | 1.28228i | ||||
\(672\) | 2.64575 | 0.102062 | ||||||||
\(673\) | −6.12549 | −0.236120 | −0.118060 | − | 0.993006i | \(-0.537668\pi\) | ||||
−0.118060 | + | 0.993006i | \(0.537668\pi\) | |||||||
\(674\) | 8.64575 | + | 14.9749i | 0.333022 | + | 0.576811i | ||||
\(675\) | 0.500000 | + | 0.866025i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −13.0000 | −0.500000 | ||||||||
\(677\) | −41.2288 | −1.58455 | −0.792275 | − | 0.610164i | \(-0.791103\pi\) | ||||
−0.792275 | + | 0.610164i | \(0.791103\pi\) | |||||||
\(678\) | 0.177124 | + | 0.306788i | 0.00680242 | + | 0.0117821i | ||||
\(679\) | −4.82288 | + | 8.35347i | −0.185085 | + | 0.320577i | ||||
\(680\) | 0.177124 | + | 0.306788i | 0.00679241 | + | 0.0117648i | ||||
\(681\) | −12.4059 | + | 21.4876i | −0.475394 | + | 0.823407i | ||||
\(682\) | −7.06275 | + | 12.2330i | −0.270447 | + | 0.468427i | ||||
\(683\) | 28.9373 | 1.10725 | 0.553627 | − | 0.832765i | \(-0.313243\pi\) | ||||
0.553627 | + | 0.832765i | \(0.313243\pi\) | |||||||
\(684\) | 1.67712 | − | 4.02334i | 0.0641265 | − | 0.153836i | ||||
\(685\) | 12.0000 | 0.458496 | ||||||||
\(686\) | −9.26013 | + | 16.0390i | −0.353553 | + | 0.612372i | ||||
\(687\) | 12.6458 | − | 21.9031i | 0.482466 | − | 0.835655i | ||||
\(688\) | −3.00000 | − | 5.19615i | −0.114374 | − | 0.198101i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.500000 | + | 0.866025i | 0.0190347 | + | 0.0329690i | ||||
\(691\) | −13.8118 | −0.525424 | −0.262712 | − | 0.964874i | \(-0.584617\pi\) | ||||
−0.262712 | + | 0.964874i | \(0.584617\pi\) | |||||||
\(692\) | −7.93725 | −0.301729 | ||||||||
\(693\) | −5.67712 | − | 9.83307i | −0.215656 | − | 0.373527i | ||||
\(694\) | −4.29150 | − | 7.43310i | −0.162903 | − | 0.282157i | ||||
\(695\) | 7.29150 | 0.276582 | ||||||||
\(696\) | 1.64575 | 0.0623820 | ||||||||
\(697\) | −0.594119 | − | 1.02904i | −0.0225039 | − | 0.0389778i | ||||
\(698\) | 16.4686 | − | 28.5245i | 0.623347 | − | 1.07967i | ||||
\(699\) | −0.291503 | − | 0.504897i | −0.0110256 | − | 0.0190970i | ||||
\(700\) | −1.32288 | + | 2.29129i | −0.0500000 | + | 0.0866025i | ||||
\(701\) | 20.1660 | − | 34.9286i | 0.761660 | − | 1.31923i | −0.180335 | − | 0.983605i | \(-0.557718\pi\) |
0.941995 | − | 0.335628i | \(-0.108949\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.90588 | − | 1.28149i | 0.373607 | − | 0.0483324i | ||||
\(704\) | 4.29150 | 0.161742 | ||||||||
\(705\) | 4.29150 | − | 7.43310i | 0.161627 | − | 0.279947i | ||||
\(706\) | −11.4686 | + | 19.8642i | −0.431627 | + | 0.747601i | ||||
\(707\) | 26.2915 | + | 45.5382i | 0.988794 | + | 1.71264i | ||||
\(708\) | −2.64575 | + | 4.58258i | −0.0994334 | + | 0.172224i | ||||
\(709\) | −12.4686 | − | 21.5963i | −0.468269 | − | 0.811066i | 0.531073 | − | 0.847326i | \(-0.321789\pi\) |
−0.999342 | + | 0.0362600i | \(0.988456\pi\) | |||||||
\(710\) | −8.35425 | −0.313529 | ||||||||
\(711\) | −5.29150 | −0.198447 | ||||||||
\(712\) | −6.61438 | − | 11.4564i | −0.247884 | − | 0.429348i | ||||
\(713\) | 1.64575 | + | 2.85052i | 0.0616339 | + | 0.106753i | ||||
\(714\) | −0.937254 | −0.0350758 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.79150 | + | 15.2273i | 0.328554 | + | 0.569072i | ||||
\(717\) | −12.0000 | + | 20.7846i | −0.448148 | + | 0.776215i | ||||
\(718\) | −5.46863 | − | 9.47194i | −0.204087 | − | 0.353490i | ||||
\(719\) | 11.6458 | − | 20.1710i | 0.434313 | − | 0.752253i | −0.562926 | − | 0.826507i | \(-0.690324\pi\) |
0.997239 | + | 0.0742547i | \(0.0236578\pi\) | |||||||
\(720\) | 0.500000 | − | 0.866025i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | −36.8745 | −1.37328 | ||||||||
\(722\) | 5.00000 | − | 18.3303i | 0.186081 | − | 0.682183i | ||||
\(723\) | −22.5830 | −0.839871 | ||||||||
\(724\) | 9.82288 | − | 17.0137i | 0.365064 | − | 0.632310i | ||||
\(725\) | −0.822876 | + | 1.42526i | −0.0305608 | + | 0.0529329i | ||||
\(726\) | −3.70850 | − | 6.42331i | −0.137635 | − | 0.238391i | ||||
\(727\) | 9.93725 | − | 17.2118i | 0.368552 | − | 0.638351i | −0.620787 | − | 0.783979i | \(-0.713187\pi\) |
0.989339 | + | 0.145628i | \(0.0465202\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 8.35425 | 0.309205 | ||||||||
\(731\) | 1.06275 | + | 1.84073i | 0.0393071 | + | 0.0680819i | ||||
\(732\) | −4.46863 | − | 7.73989i | −0.165165 | − | 0.286075i | ||||
\(733\) | −1.70850 | −0.0631048 | −0.0315524 | − | 0.999502i | \(-0.510045\pi\) | ||||
−0.0315524 | + | 0.999502i | \(0.510045\pi\) | |||||||
\(734\) | −29.8745 | −1.10269 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | 9.34313 | + | 16.1828i | 0.344159 | + | 0.596101i | ||||
\(738\) | −1.67712 | + | 2.90486i | −0.0617358 | + | 0.106930i | ||||
\(739\) | 25.4889 | − | 44.1480i | 0.937624 | − | 1.62401i | 0.167737 | − | 0.985832i | \(-0.446354\pi\) |
0.769887 | − | 0.638180i | \(-0.220313\pi\) | |||||||
\(740\) | 2.29150 | 0.0842373 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.70850 | −0.0627209 | ||||||||
\(743\) | 10.2085 | − | 17.6816i | 0.374513 | − | 0.648676i | −0.615741 | − | 0.787949i | \(-0.711143\pi\) |
0.990254 | + | 0.139273i | \(0.0444764\pi\) | |||||||
\(744\) | 1.64575 | − | 2.85052i | 0.0603362 | − | 0.104505i | ||||
\(745\) | 5.11438 | + | 8.85836i | 0.187376 | + | 0.324545i | ||||
\(746\) | 3.85425 | − | 6.67575i | 0.141114 | − | 0.244417i | ||||
\(747\) | 2.29150 | + | 3.96900i | 0.0838417 | + | 0.145218i | ||||
\(748\) | −1.52026 | −0.0555862 | ||||||||
\(749\) | 25.5203 | 0.932490 | ||||||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | 22.0000 | + | 38.1051i | 0.802791 | + | 1.39048i | 0.917772 | + | 0.397108i | \(0.129986\pi\) |
−0.114981 | + | 0.993368i | \(0.536681\pi\) | |||||||
\(752\) | −8.58301 | −0.312990 | ||||||||
\(753\) | −18.5830 | −0.677202 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.11438 | − | 5.39426i | 0.113344 | − | 0.196317i | ||||
\(756\) | 1.32288 | + | 2.29129i | 0.0481125 | + | 0.0833333i | ||||
\(757\) | 14.7288 | − | 25.5110i | 0.535326 | − | 0.927211i | −0.463822 | − | 0.885929i | \(-0.653522\pi\) |
0.999147 | − | 0.0412829i | \(-0.0131445\pi\) | |||||||
\(758\) | −6.93725 | + | 12.0157i | −0.251972 | + | 0.436429i | ||||
\(759\) | −4.29150 | −0.155772 | ||||||||
\(760\) | 1.67712 | − | 4.02334i | 0.0608357 | − | 0.145942i | ||||
\(761\) | 16.5203 | 0.598859 | 0.299429 | − | 0.954118i | \(-0.403204\pi\) | ||||
0.299429 | + | 0.954118i | \(0.403204\pi\) | |||||||
\(762\) | −7.61438 | + | 13.1885i | −0.275840 | + | 0.477769i | ||||
\(763\) | 7.46863 | − | 12.9360i | 0.270382 | − | 0.468316i | ||||
\(764\) | −8.29150 | − | 14.3613i | −0.299976 | − | 0.519574i | ||||
\(765\) | −0.177124 | + | 0.306788i | −0.00640394 | + | 0.0110920i | ||||
\(766\) | −7.70850 | − | 13.3515i | −0.278519 | − | 0.482410i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −4.35425 | − | 7.54178i | −0.157018 | − | 0.271964i | 0.776774 | − | 0.629780i | \(-0.216855\pi\) |
−0.933792 | + | 0.357816i | \(0.883521\pi\) | |||||||
\(770\) | −5.67712 | − | 9.83307i | −0.204589 | − | 0.354359i | ||||
\(771\) | −6.00000 | −0.216085 | ||||||||
\(772\) | 6.35425 | 0.228694 | ||||||||
\(773\) | −6.96863 | − | 12.0700i | −0.250644 | − | 0.434128i | 0.713059 | − | 0.701104i | \(-0.247309\pi\) |
−0.963703 | + | 0.266976i | \(0.913976\pi\) | |||||||
\(774\) | 3.00000 | − | 5.19615i | 0.107833 | − | 0.186772i | ||||
\(775\) | 1.64575 | + | 2.85052i | 0.0591171 | + | 0.102394i | ||||
\(776\) | 1.82288 | − | 3.15731i | 0.0654374 | − | 0.113341i | ||||
\(777\) | −3.03137 | + | 5.25049i | −0.108750 | + | 0.188360i | ||||
\(778\) | −19.5203 | −0.699835 | ||||||||
\(779\) | −5.62549 | + | 13.4953i | −0.201554 | + | 0.483519i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.9261 | − | 31.0490i | 0.641448 | − | 1.11102i | ||||
\(782\) | −0.177124 | + | 0.306788i | −0.00633395 | + | 0.0109707i | ||||
\(783\) | 0.822876 | + | 1.42526i | 0.0294072 | + | 0.0509347i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.43725 | + | 16.3458i | 0.336830 | + | 0.583407i | ||||
\(786\) | −18.2915 | −0.652436 | ||||||||
\(787\) | −50.1033 | −1.78599 | −0.892994 | − | 0.450068i | \(-0.851400\pi\) | ||||
−0.892994 | + | 0.450068i | \(0.851400\pi\) | |||||||
\(788\) | −1.32288 | − | 2.29129i | −0.0471255 | − | 0.0816237i | ||||
\(789\) | −3.14575 | − | 5.44860i | −0.111992 | − | 0.193975i | ||||
\(790\) | −5.29150 | −0.188263 | ||||||||
\(791\) | −0.937254 | −0.0333249 | ||||||||
\(792\) | 2.14575 | + | 3.71655i | 0.0762460 | + | 0.132062i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 12.7288 | + | 22.0469i | 0.451727 | + | 0.782414i | ||||
\(795\) | −0.322876 | + | 0.559237i | −0.0114512 | + | 0.0198341i | ||||
\(796\) | −9.46863 | + | 16.4001i | −0.335607 | + | 0.581288i | ||||
\(797\) | 41.6863 | 1.47660 | 0.738302 | − | 0.674471i | \(-0.235628\pi\) | ||||
0.738302 | + | 0.674471i | \(0.235628\pi\) | |||||||
\(798\) | 7.00000 | + | 9.16515i | 0.247797 | + | 0.324443i | ||||
\(799\) | 3.04052 | 0.107566 | ||||||||
\(800\) | 0.500000 | − | 0.866025i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | 6.61438 | − | 11.4564i | 0.233708 | − | 0.404793i | ||||
\(802\) | 3.00000 | + | 5.19615i | 0.105934 | + | 0.183483i | ||||
\(803\) | −17.9261 | + | 31.0490i | −0.632600 | + | 1.09569i | ||||
\(804\) | −2.17712 | − | 3.77089i | −0.0767813 | − | 0.132989i | ||||
\(805\) | −2.64575 | −0.0932505 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.46863 | − | 2.54374i | −0.0516981 | − | 0.0895438i | ||||
\(808\) | −9.93725 | − | 17.2118i | −0.349591 | − | 0.605510i | ||||
\(809\) | −24.0000 | −0.843795 | −0.421898 | − | 0.906644i | \(-0.638636\pi\) | ||||
−0.421898 | + | 0.906644i | \(0.638636\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −16.3229 | − | 28.2720i | −0.573174 | − | 0.992766i | −0.996237 | − | 0.0866660i | \(-0.972379\pi\) |
0.423064 | − | 0.906100i | \(-0.360955\pi\) | |||||||
\(812\) | −2.17712 | + | 3.77089i | −0.0764021 | + | 0.132332i | ||||
\(813\) | −9.93725 | − | 17.2118i | −0.348515 | − | 0.603645i | ||||
\(814\) | −4.91699 | + | 8.51648i | −0.172341 | + | 0.298503i | ||||
\(815\) | −6.64575 | + | 11.5108i | −0.232791 | + | 0.403205i | ||||
\(816\) | 0.354249 | 0.0124012 | ||||||||
\(817\) | 10.0627 | − | 24.1400i | 0.352051 | − | 0.844553i | ||||
\(818\) | 39.5830 | 1.38399 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.67712 | + | 2.90486i | −0.0585677 | + | 0.101442i | ||||
\(821\) | −0.291503 | − | 0.504897i | −0.0101735 | − | 0.0176210i | 0.860894 | − | 0.508785i | \(-0.169905\pi\) |
−0.871067 | + | 0.491164i | \(0.836572\pi\) | |||||||
\(822\) | 6.00000 | − | 10.3923i | 0.209274 | − | 0.362473i | ||||
\(823\) | −2.38562 | − | 4.13202i | −0.0831575 | − | 0.144033i | 0.821447 | − | 0.570285i | \(-0.193167\pi\) |
−0.904605 | + | 0.426252i | \(0.859834\pi\) | |||||||
\(824\) | 13.9373 | 0.485527 | ||||||||
\(825\) | −4.29150 | −0.149411 | ||||||||
\(826\) | −7.00000 | − | 12.1244i | −0.243561 | − | 0.421860i | ||||
\(827\) | −23.4686 | − | 40.6489i | −0.816084 | − | 1.41350i | −0.908547 | − | 0.417783i | \(-0.862807\pi\) |
0.0924627 | − | 0.995716i | \(-0.470526\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 0.457513 | 0.0158901 | 0.00794504 | − | 0.999968i | \(-0.497471\pi\) | ||||
0.00794504 | + | 0.999968i | \(0.497471\pi\) | |||||||
\(830\) | 2.29150 | + | 3.96900i | 0.0795392 | + | 0.137766i | ||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.64575 | − | 6.31463i | 0.126242 | − | 0.218658i | ||||
\(835\) | 3.58301 | 0.123995 | ||||||||
\(836\) | 11.3542 | + | 14.8662i | 0.392695 | + | 0.514158i | ||||
\(837\) | 3.29150 | 0.113771 | ||||||||
\(838\) | −2.08301 | + | 3.60787i | −0.0719562 | + | 0.124632i | ||||
\(839\) | 7.93725 | − | 13.7477i | 0.274024 | − | 0.474624i | −0.695864 | − | 0.718173i | \(-0.744978\pi\) |
0.969889 | + | 0.243549i | \(0.0783117\pi\) | |||||||
\(840\) | 1.32288 | + | 2.29129i | 0.0456435 | + | 0.0790569i | ||||
\(841\) | 13.1458 | − | 22.7691i | 0.453302 | − | 0.785142i | ||||
\(842\) | −1.53137 | − | 2.65242i | −0.0527746 | − | 0.0914083i | ||||
\(843\) | −27.8118 | −0.957888 | ||||||||
\(844\) | 18.5203 | 0.637494 | ||||||||
\(845\) | −6.50000 | − | 11.2583i | −0.223607 | − | 0.387298i | ||||
\(846\) | −4.29150 | − | 7.43310i | −0.147545 | − | 0.255555i | ||||
\(847\) | 19.6235 | 0.674272 | ||||||||
\(848\) | 0.645751 | 0.0221752 | ||||||||
\(849\) | −5.93725 | − | 10.2836i | −0.203766 | − | 0.352933i | ||||
\(850\) | −0.177124 | + | 0.306788i | −0.00607531 | + | 0.0105228i | ||||
\(851\) | 1.14575 | + | 1.98450i | 0.0392758 | + | 0.0680278i | ||||
\(852\) | −4.17712 | + | 7.23499i | −0.143106 | + | 0.247867i | ||||
\(853\) | 18.2915 | − | 31.6818i | 0.626289 | − | 1.08476i | −0.362001 | − | 0.932178i | \(-0.617906\pi\) |
0.988290 | − | 0.152587i | \(-0.0487604\pi\) | |||||||
\(854\) | 23.6458 | 0.809141 | ||||||||
\(855\) | 4.32288 | − | 0.559237i | 0.147839 | − | 0.0191255i | ||||
\(856\) | −9.64575 | −0.329685 | ||||||||
\(857\) | 6.00000 | − | 10.3923i | 0.204956 | − | 0.354994i | −0.745163 | − | 0.666883i | \(-0.767628\pi\) |
0.950119 | + | 0.311888i | \(0.100962\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.2601 | − | 21.2352i | −0.418310 | − | 0.724535i | 0.577459 | − | 0.816419i | \(-0.304044\pi\) |
−0.995770 | + | 0.0918848i | \(0.970711\pi\) | |||||||
\(860\) | 3.00000 | − | 5.19615i | 0.102299 | − | 0.177187i | ||||
\(861\) | −4.43725 | − | 7.68555i | −0.151221 | − | 0.261923i | ||||
\(862\) | −33.6458 | −1.14598 | ||||||||
\(863\) | 41.5830 | 1.41550 | 0.707751 | − | 0.706462i | \(-0.249710\pi\) | ||||
0.707751 | + | 0.706462i | \(0.249710\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −3.96863 | − | 6.87386i | −0.134937 | − | 0.233718i | ||||
\(866\) | 10.9373 | 0.371663 | ||||||||
\(867\) | 16.8745 | 0.573088 | ||||||||
\(868\) | 4.35425 | + | 7.54178i | 0.147793 | + | 0.255985i | ||||
\(869\) | 11.3542 | − | 19.6661i | 0.385167 | − | 0.667128i | ||||
\(870\) | 0.822876 | + | 1.42526i | 0.0278981 | + | 0.0483209i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −2.82288 | + | 4.88936i | −0.0955946 | + | 0.165575i | ||||
\(873\) | 3.64575 | 0.123390 | ||||||||
\(874\) | 4.32288 | − | 0.559237i | 0.146223 | − | 0.0189165i | ||||
\(875\) | −2.64575 | −0.0894427 | ||||||||
\(876\) | 4.17712 | − | 7.23499i | 0.141132 | − | 0.244448i | ||||
\(877\) | 16.8542 | − | 29.1924i | 0.569128 | − | 0.985758i | −0.427525 | − | 0.904004i | \(-0.640614\pi\) |
0.996653 | − | 0.0817543i | \(-0.0260523\pi\) | |||||||
\(878\) | −9.46863 | − | 16.4001i | −0.319551 | − | 0.553478i | ||||
\(879\) | −7.32288 | + | 12.6836i | −0.246994 | + | 0.427807i | ||||
\(880\) | 2.14575 | + | 3.71655i | 0.0723333 | + | 0.125285i | ||||
\(881\) | −40.6458 | −1.36939 | −0.684695 | − | 0.728830i | \(-0.740065\pi\) | ||||
−0.684695 | + | 0.728830i | \(0.740065\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.05163 | − | 10.4817i | −0.203654 | − | 0.352738i | 0.746049 | − | 0.665891i | \(-0.231948\pi\) |
−0.949703 | + | 0.313152i | \(0.898615\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.29150 | −0.177872 | ||||||||
\(886\) | 40.9373 | 1.37531 | ||||||||
\(887\) | −23.2288 | − | 40.2334i | −0.779945 | − | 1.35090i | −0.931973 | − | 0.362529i | \(-0.881914\pi\) |
0.152027 | − | 0.988376i | \(-0.451420\pi\) | |||||||
\(888\) | 1.14575 | − | 1.98450i | 0.0384489 | − | 0.0665954i | ||||
\(889\) | −20.1458 | − | 34.8935i | −0.675667 | − | 1.17029i | ||||
\(890\) | 6.61438 | − | 11.4564i | 0.221714 | − | 0.384021i | ||||
\(891\) | −2.14575 | + | 3.71655i | −0.0718854 | + | 0.124509i | ||||
\(892\) | 1.35425 | 0.0453436 | ||||||||
\(893\) | −22.7085 | − | 29.7324i | −0.759911 | − | 0.994957i | ||||
\(894\) | 10.2288 | 0.342101 | ||||||||
\(895\) | −8.79150 | + | 15.2273i | −0.293868 | + | 0.508993i | ||||
\(896\) | 1.32288 | − | 2.29129i | 0.0441942 | − | 0.0765466i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −11.3229 | + | 19.6118i | −0.377849 | + | 0.654454i | ||||
\(899\) | 2.70850 | + | 4.69126i | 0.0903334 | + | 0.156462i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −0.228757 | −0.00762099 | ||||||||
\(902\) | −7.19738 | − | 12.4662i | −0.239647 | − | 0.415080i | ||||
\(903\) | 7.93725 | + | 13.7477i | 0.264135 | + | 0.457496i | ||||
\(904\) | 0.354249 | 0.0117821 | ||||||||
\(905\) | 19.6458 | 0.653047 | ||||||||
\(906\) | −3.11438 | − | 5.39426i | −0.103468 | − | 0.179212i | ||||
\(907\) | −2.29150 | + | 3.96900i | −0.0760881 | + | 0.131788i | −0.901559 | − | 0.432656i | \(-0.857576\pi\) |
0.825471 | + | 0.564445i | \(0.190910\pi\) | |||||||
\(908\) | 12.4059 | + | 21.4876i | 0.411704 | + | 0.713092i | ||||
\(909\) | 9.93725 | − | 17.2118i | 0.329598 | − | 0.570880i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.70850 | 0.0897365 | 0.0448683 | − | 0.998993i | \(-0.485713\pi\) | ||||
0.0448683 | + | 0.998993i | \(0.485713\pi\) | |||||||
\(912\) | −2.64575 | − | 3.46410i | −0.0876096 | − | 0.114708i | ||||
\(913\) | −19.6680 | −0.650915 | ||||||||
\(914\) | 14.1144 | − | 24.4468i | 0.466862 | − | 0.808629i | ||||
\(915\) | 4.46863 | − | 7.73989i | 0.147728 | − | 0.255873i | ||||
\(916\) | −12.6458 | − | 21.9031i | −0.417827 | − | 0.723698i | ||||
\(917\) | 24.1974 | − | 41.9111i | 0.799068 | − | 1.38403i | ||||
\(918\) | 0.177124 | + | 0.306788i | 0.00584597 | + | 0.0101255i | ||||
\(919\) | −16.2288 | −0.535337 | −0.267669 | − | 0.963511i | \(-0.586253\pi\) | ||||
−0.267669 | + | 0.963511i | \(0.586253\pi\) | |||||||
\(920\) | 1.00000 | 0.0329690 | ||||||||
\(921\) | 5.76013 | + | 9.97684i | 0.189803 | + | 0.328748i | ||||
\(922\) | 3.58301 | + | 6.20595i | 0.118000 | + | 0.204382i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −11.3542 | −0.373527 | ||||||||
\(925\) | 1.14575 | + | 1.98450i | 0.0376721 | + | 0.0652499i | ||||
\(926\) | 17.3229 | − | 30.0041i | 0.569265 | − | 0.985996i | ||||
\(927\) | 6.96863 | + | 12.0700i | 0.228880 | + | 0.396431i | ||||
\(928\) | 0.822876 | − | 1.42526i | 0.0270122 | − | 0.0467865i | ||||
\(929\) | 8.03137 | − | 13.9107i | 0.263501 | − | 0.456397i | −0.703669 | − | 0.710528i | \(-0.748456\pi\) |
0.967170 | + | 0.254131i | \(0.0817895\pi\) | |||||||
\(930\) | 3.29150 | 0.107933 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.583005 | −0.0190970 | ||||||||
\(933\) | 8.58301 | − | 14.8662i | 0.280995 | − | 0.486698i | ||||
\(934\) | −10.7601 | + | 18.6371i | −0.352082 | + | 0.609824i | ||||
\(935\) | −0.760130 | − | 1.31658i | −0.0248589 | − | 0.0430569i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −10.5314 | − | 18.2409i | −0.344045 | − | 0.595903i | 0.641135 | − | 0.767428i | \(-0.278464\pi\) |
−0.985180 | + | 0.171525i | \(0.945131\pi\) | |||||||
\(938\) | 11.5203 | 0.376150 | ||||||||
\(939\) | −18.5830 | −0.606433 | ||||||||
\(940\) | −4.29150 | − | 7.43310i | −0.139973 | − | 0.242441i | ||||
\(941\) | −9.88562 | − | 17.1224i | −0.322262 | − | 0.558174i | 0.658692 | − | 0.752412i | \(-0.271110\pi\) |
−0.980954 | + | 0.194238i | \(0.937777\pi\) | |||||||
\(942\) | 18.8745 | 0.614965 | ||||||||
\(943\) | −3.35425 | −0.109229 | ||||||||
\(944\) | 2.64575 | + | 4.58258i | 0.0861119 | + | 0.149150i | ||||
\(945\) | −1.32288 | + | 2.29129i | −0.0430331 | + | 0.0745356i | ||||
\(946\) | 12.8745 | + | 22.2993i | 0.418586 | + | 0.725013i | ||||
\(947\) | −12.6974 | + | 21.9925i | −0.412610 | + | 0.714661i | −0.995174 | − | 0.0981237i | \(-0.968716\pi\) |
0.582565 | + | 0.812784i | \(0.302049\pi\) | |||||||
\(948\) | −2.64575 | + | 4.58258i | −0.0859300 | + | 0.148835i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 4.32288 | − | 0.559237i | 0.140253 | − | 0.0181440i | ||||
\(951\) | −19.9373 | −0.646510 | ||||||||
\(952\) | −0.468627 | + | 0.811686i | −0.0151883 | + | 0.0263069i | ||||
\(953\) | −6.58301 | + | 11.4021i | −0.213244 | + | 0.369350i | −0.952728 | − | 0.303824i | \(-0.901736\pi\) |
0.739484 | + | 0.673175i | \(0.235070\pi\) | |||||||
\(954\) | 0.322876 | + | 0.559237i | 0.0104535 | + | 0.0181060i | ||||
\(955\) | 8.29150 | − | 14.3613i | 0.268307 | − | 0.464721i | ||||
\(956\) | 12.0000 | + | 20.7846i | 0.388108 | + | 0.672222i | ||||
\(957\) | −7.06275 | −0.228306 | ||||||||
\(958\) | 10.9373 | 0.353367 | ||||||||
\(959\) | 15.8745 | + | 27.4955i | 0.512615 | + | 0.887875i | ||||
\(960\) | −0.500000 | − | 0.866025i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | −20.1660 | −0.650516 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.82288 | − | 8.35347i | −0.155415 | − | 0.269187i | ||||
\(964\) | −11.2915 | + | 19.5575i | −0.363675 | + | 0.629903i | ||||
\(965\) | 3.17712 | + | 5.50294i | 0.102275 | + | 0.177146i | ||||
\(966\) | −1.32288 | + | 2.29129i | −0.0425628 | + | 0.0737210i | ||||
\(967\) | −1.06275 | + | 1.84073i | −0.0341756 | + | 0.0591939i | −0.882607 | − | 0.470111i | \(-0.844214\pi\) |
0.848432 | + | 0.529305i | \(0.177547\pi\) | |||||||
\(968\) | −7.41699 | −0.238391 | ||||||||
\(969\) | 0.937254 | + | 1.22715i | 0.0301089 | + | 0.0394218i | ||||
\(970\) | 3.64575 | 0.117058 | ||||||||
\(971\) | −30.8745 | + | 53.4762i | −0.990810 | + | 1.71613i | −0.378266 | + | 0.925697i | \(0.623480\pi\) |
−0.612544 | + | 0.790437i | \(0.709854\pi\) | |||||||
\(972\) | 0.500000 | − | 0.866025i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | 9.64575 | + | 16.7069i | 0.309229 | + | 0.535600i | ||||
\(974\) | 7.67712 | − | 13.2972i | 0.245991 | − | 0.426069i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.93725 | −0.286075 | ||||||||
\(977\) | −16.9373 | −0.541871 | −0.270935 | − | 0.962598i | \(-0.587333\pi\) | ||||
−0.270935 | + | 0.962598i | \(0.587333\pi\) | |||||||
\(978\) | 6.64575 | + | 11.5108i | 0.212508 | + | 0.368074i | ||||
\(979\) | 28.3856 | + | 49.1653i | 0.907208 | + | 1.57133i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.64575 | −0.180255 | ||||||||
\(982\) | −6.72876 | − | 11.6545i | −0.214723 | − | 0.371912i | ||||
\(983\) | 8.56275 | − | 14.8311i | 0.273109 | − | 0.473039i | −0.696547 | − | 0.717511i | \(-0.745281\pi\) |
0.969656 | + | 0.244472i | \(0.0786146\pi\) | |||||||
\(984\) | 1.67712 | + | 2.90486i | 0.0534648 | + | 0.0926037i | ||||
\(985\) | 1.32288 | − | 2.29129i | 0.0421503 | − | 0.0730065i | ||||
\(986\) | −0.291503 | + | 0.504897i | −0.00928333 | + | 0.0160792i | ||||
\(987\) | 22.7085 | 0.722819 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.00000 | 0.190789 | ||||||||
\(990\) | −2.14575 | + | 3.71655i | −0.0681965 | + | 0.118120i | ||||
\(991\) | 3.17712 | − | 5.50294i | 0.100925 | − | 0.174807i | −0.811141 | − | 0.584850i | \(-0.801153\pi\) |
0.912066 | + | 0.410044i | \(0.134487\pi\) | |||||||
\(992\) | −1.64575 | − | 2.85052i | −0.0522527 | − | 0.0905043i | ||||
\(993\) | −6.67712 | + | 11.5651i | −0.211892 | + | 0.367008i | ||||
\(994\) | −11.0516 | − | 19.1420i | −0.350536 | − | 0.607147i | ||||
\(995\) | −18.9373 | −0.600351 | ||||||||
\(996\) | 4.58301 | 0.145218 | ||||||||
\(997\) | −5.50000 | − | 9.52628i | −0.174187 | − | 0.301700i | 0.765693 | − | 0.643206i | \(-0.222396\pi\) |
−0.939880 | + | 0.341506i | \(0.889063\pi\) | |||||||
\(998\) | 6.32288 | + | 10.9515i | 0.200147 | + | 0.346665i | ||||
\(999\) | 2.29150 | 0.0724999 |
(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 | 570.2.i.i.391.2 | yes | 4 | |
3.2 | odd | 2 | 1710.2.l.j.1531.2 | 4 | |||
19.7 | even | 3 | inner | 570.2.i.i.121.2 | ✓ | 4 | |
57.26 | odd | 6 | 1710.2.l.j.1261.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.i.i.121.2 | ✓ | 4 | 19.7 | even | 3 | inner | |
570.2.i.i.391.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1710.2.l.j.1261.2 | 4 | 57.26 | odd | 6 | |||
1710.2.l.j.1531.2 | 4 | 3.2 | odd | 2 |