Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [153,4,Mod(19,153)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(153, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("153.19");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 153 = 3^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 153.l (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.02729223088\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 54x^{10} + 1085x^{8} + 9836x^{6} + 38276x^{4} + 49664x^{2} + 16384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 145.1 | ||
Root | \(4.15292i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 153.145 |
Dual form | 153.4.l.a.19.1 |
$q$-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 \(\left(\mathbb{Z}/153\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(137\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.22945 | + | 2.22945i | −0.788229 | + | 0.788229i | −0.981204 | − | 0.192974i | \(-0.938187\pi\) |
0.192974 | + | 0.981204i | \(0.438187\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.94089i | − | 0.242611i | ||||||
\(5\) | 1.91633 | − | 4.62643i | 0.171402 | − | 0.413800i | −0.814713 | − | 0.579864i | \(-0.803106\pi\) |
0.986115 | + | 0.166064i | \(0.0531057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.06584 | + | 2.57316i | 0.0575498 | + | 0.138937i | 0.950039 | − | 0.312131i | \(-0.101043\pi\) |
−0.892489 | + | 0.451069i | \(0.851043\pi\) | |||||||
\(8\) | −13.5085 | − | 13.5085i | −0.596996 | − | 0.596996i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.04203 | + | 14.5867i | 0.191066 | + | 0.461273i | ||||
\(11\) | 25.1714 | − | 10.4263i | 0.689952 | − | 0.285787i | −0.0100284 | − | 0.999950i | \(-0.503192\pi\) |
0.699980 | + | 0.714162i | \(0.253192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 59.7352i | − | 1.27443i | −0.770687 | − | 0.637214i | \(-0.780087\pi\) | ||
0.770687 | − | 0.637214i | \(-0.219913\pi\) | |||||||
\(14\) | −8.11295 | − | 3.36049i | −0.154877 | − | 0.0641521i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 75.7601 | 1.18375 | ||||||||
\(17\) | −70.0883 | + | 0.790881i | −0.999936 | + | 0.0112833i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 23.5187 | − | 23.5187i | 0.283977 | − | 0.283977i | −0.550716 | − | 0.834693i | \(-0.685645\pi\) |
0.834693 | + | 0.550716i | \(0.185645\pi\) | |||||||
\(20\) | −8.97939 | − | 3.71938i | −0.100393 | − | 0.0415840i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −32.8734 | + | 79.3634i | −0.318574 | + | 0.769106i | ||||
\(23\) | 194.831 | − | 80.7017i | 1.76631 | − | 0.731629i | 0.770787 | − | 0.637093i | \(-0.219863\pi\) |
0.995522 | − | 0.0945353i | \(-0.0301365\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 70.6568 | + | 70.6568i | 0.565255 | + | 0.565255i | ||||
\(26\) | 133.177 | + | 133.177i | 1.00454 | + | 1.00454i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.99421 | − | 2.06867i | 0.0337078 | − | 0.0139622i | ||||
\(29\) | −7.67362 | + | 18.5258i | −0.0491364 | + | 0.118626i | −0.946542 | − | 0.322581i | \(-0.895449\pi\) |
0.897405 | + | 0.441207i | \(0.145449\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 123.485 | + | 51.1492i | 0.715438 | + | 0.296344i | 0.710553 | − | 0.703644i | \(-0.248445\pi\) |
0.00488535 | + | 0.999988i | \(0.498445\pi\) | |||||||
\(32\) | −60.8354 | + | 60.8354i | −0.336071 | + | 0.336071i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 154.495 | − | 158.022i | 0.779285 | − | 0.797073i | ||||
\(35\) | 13.9470 | 0.0673565 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 141.143 | + | 58.4634i | 0.627129 | + | 0.259765i | 0.673533 | − | 0.739157i | \(-0.264776\pi\) |
−0.0464037 | + | 0.998923i | \(0.514776\pi\) | |||||||
\(38\) | 104.868i | 0.447678i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −88.3827 | + | 36.6093i | −0.349363 | + | 0.144711i | ||||
\(41\) | 100.202 | + | 241.908i | 0.381680 | + | 0.921456i | 0.991641 | + | 0.129025i | \(0.0411849\pi\) |
−0.609962 | + | 0.792431i | \(0.708815\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −224.025 | − | 224.025i | −0.794501 | − | 0.794501i | 0.187721 | − | 0.982222i | \(-0.439890\pi\) |
−0.982222 | + | 0.187721i | \(0.939890\pi\) | |||||||
\(44\) | −20.2364 | − | 48.8550i | −0.0693352 | − | 0.167390i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −254.446 | + | 614.286i | −0.815565 | + | 1.96895i | ||||
\(47\) | − | 329.443i | − | 1.02243i | −0.859453 | − | 0.511215i | \(-0.829196\pi\) | ||
0.859453 | − | 0.511215i | \(-0.170804\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 237.052 | − | 237.052i | 0.691115 | − | 0.691115i | ||||
\(50\) | −315.052 | −0.891101 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −115.939 | −0.309190 | ||||||||
\(53\) | 219.585 | − | 219.585i | 0.569100 | − | 0.569100i | −0.362776 | − | 0.931876i | \(-0.618171\pi\) |
0.931876 | + | 0.362776i | \(0.118171\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 136.434i | − | 0.334487i | ||||||
\(56\) | 20.3616 | − | 49.1573i | 0.0485881 | − | 0.117302i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24.1943 | − | 58.4102i | −0.0547735 | − | 0.132235i | ||||
\(59\) | −38.7062 | − | 38.7062i | −0.0854087 | − | 0.0854087i | 0.663112 | − | 0.748520i | \(-0.269235\pi\) |
−0.748520 | + | 0.663112i | \(0.769235\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −313.322 | − | 756.427i | −0.657653 | − | 1.58771i | −0.801419 | − | 0.598103i | \(-0.795921\pi\) |
0.143767 | − | 0.989612i | \(-0.454079\pi\) | |||||||
\(62\) | −389.338 | + | 161.269i | −0.797517 | + | 0.330342i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 334.822i | 0.653948i | ||||||||
\(65\) | −276.360 | − | 114.472i | −0.527358 | − | 0.218439i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −731.181 | −1.33325 | −0.666627 | − | 0.745392i | \(-0.732262\pi\) | ||||
−0.666627 | + | 0.745392i | \(0.732262\pi\) | |||||||
\(68\) | 1.53501 | + | 136.034i | 0.00273747 | + | 0.242596i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −31.0942 | + | 31.0942i | −0.0530923 | + | 0.0530923i | ||||
\(71\) | −581.286 | − | 240.777i | −0.971633 | − | 0.402464i | −0.160313 | − | 0.987066i | \(-0.551250\pi\) |
−0.811320 | + | 0.584603i | \(0.801250\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −189.995 | + | 458.689i | −0.304620 | + | 0.735417i | 0.695242 | + | 0.718776i | \(0.255297\pi\) |
−0.999862 | + | 0.0166414i | \(0.994703\pi\) | |||||||
\(74\) | −445.012 | + | 184.330i | −0.699076 | + | 0.289567i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −45.6473 | − | 45.6473i | −0.0688960 | − | 0.0688960i | ||||
\(77\) | 53.6572 | + | 53.6572i | 0.0794131 | + | 0.0794131i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 83.1733 | − | 34.4515i | 0.118452 | − | 0.0490646i | −0.322670 | − | 0.946511i | \(-0.604580\pi\) |
0.441122 | + | 0.897447i | \(0.354580\pi\) | |||||||
\(80\) | 145.181 | − | 350.498i | 0.202897 | − | 0.489836i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −762.717 | − | 315.928i | −1.02717 | − | 0.425468i | ||||
\(83\) | 257.404 | − | 257.404i | 0.340407 | − | 0.340407i | −0.516113 | − | 0.856520i | \(-0.672622\pi\) |
0.856520 | + | 0.516113i | \(0.172622\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −130.653 | + | 325.774i | −0.166722 | + | 0.415708i | ||||
\(86\) | 998.907 | 1.25250 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −480.872 | − | 199.184i | −0.582512 | − | 0.241285i | ||||
\(89\) | − | 192.079i | − | 0.228767i | −0.993437 | − | 0.114384i | \(-0.963511\pi\) | ||
0.993437 | − | 0.114384i | \(-0.0364893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 153.708 | − | 63.6679i | 0.177066 | − | 0.0733430i | ||||
\(92\) | −156.633 | − | 378.146i | −0.177501 | − | 0.428526i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 734.476 | + | 734.476i | 0.805909 | + | 0.805909i | ||||
\(95\) | −63.7380 | − | 153.877i | −0.0688356 | − | 0.166184i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 516.698 | − | 1247.42i | 0.540853 | − | 1.30574i | −0.383268 | − | 0.923637i | \(-0.625202\pi\) |
0.924122 | − | 0.382098i | \(-0.124798\pi\) | |||||||
\(98\) | 1056.99i | 1.08951i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 137.137 | − | 137.137i | 0.137137 | − | 0.137137i | ||||
\(101\) | −304.020 | −0.299516 | −0.149758 | − | 0.988723i | \(-0.547850\pi\) | ||||
−0.149758 | + | 0.988723i | \(0.547850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 988.515 | 0.945643 | 0.472822 | − | 0.881158i | \(-0.343236\pi\) | ||||
0.472822 | + | 0.881158i | \(0.343236\pi\) | |||||||
\(104\) | −806.931 | + | 806.931i | −0.760828 | + | 0.760828i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 979.107i | 0.897163i | ||||||||
\(107\) | −449.658 | + | 1085.57i | −0.406263 | + | 0.980805i | 0.579849 | + | 0.814724i | \(0.303111\pi\) |
−0.986112 | + | 0.166081i | \(0.946889\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 321.020 | + | 775.010i | 0.282093 | + | 0.681032i | 0.999884 | − | 0.0152262i | \(-0.00484683\pi\) |
−0.717791 | + | 0.696258i | \(0.754847\pi\) | |||||||
\(110\) | 304.173 | + | 304.173i | 0.263652 | + | 0.263652i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 80.7478 | + | 194.943i | 0.0681246 | + | 0.164467i | ||||
\(113\) | 1872.53 | − | 775.626i | 1.55887 | − | 0.645706i | 0.573979 | − | 0.818870i | \(-0.305399\pi\) |
0.984893 | + | 0.173164i | \(0.0553992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1056.02i | − | 0.856301i | ||||||
\(116\) | 35.9564 | + | 14.8936i | 0.0287799 | + | 0.0119210i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 172.587 | 0.134643 | ||||||||
\(119\) | −76.7378 | − | 179.505i | −0.0591138 | − | 0.138279i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −416.267 | + | 416.267i | −0.312748 | + | 0.312748i | ||||
\(122\) | 2384.95 | + | 987.880i | 1.76986 | + | 0.733102i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 99.2750 | − | 239.671i | 0.0718964 | − | 0.173573i | ||||
\(125\) | 1040.59 | − | 431.028i | 0.744588 | − | 0.308419i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1131.58 | + | 1131.58i | 0.790645 | + | 0.790645i | 0.981599 | − | 0.190954i | \(-0.0611582\pi\) |
−0.190954 | + | 0.981599i | \(0.561158\pi\) | |||||||
\(128\) | −1233.15 | − | 1233.15i | −0.851533 | − | 0.851533i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 871.342 | − | 360.921i | 0.587859 | − | 0.243499i | ||||
\(131\) | −1000.75 | + | 2416.01i | −0.667447 | + | 1.61136i | 0.118420 | + | 0.992964i | \(0.462217\pi\) |
−0.785867 | + | 0.618396i | \(0.787783\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 85.5845 | + | 35.4502i | 0.0557979 | + | 0.0231122i | ||||
\(134\) | 1630.13 | − | 1630.13i | 1.05091 | − | 1.05091i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 957.470 | + | 936.103i | 0.603694 | + | 0.590222i | ||||
\(137\) | −745.711 | −0.465039 | −0.232520 | − | 0.972592i | \(-0.574697\pi\) | ||||
−0.232520 | + | 0.972592i | \(0.574697\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2339.68 | − | 969.128i | −1.42769 | − | 0.591369i | −0.470912 | − | 0.882180i | \(-0.656075\pi\) |
−0.956781 | + | 0.290811i | \(0.906075\pi\) | |||||||
\(140\) | − | 27.0696i | − | 0.0163414i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1832.75 | − | 759.149i | 1.08310 | − | 0.448636i | ||||
\(143\) | −622.819 | − | 1503.62i | −0.364215 | − | 0.879293i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 71.0029 | + | 71.0029i | 0.0406653 | + | 0.0406653i | ||||
\(146\) | −599.039 | − | 1446.21i | −0.339567 | − | 0.819788i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 113.471 | − | 273.943i | 0.0630220 | − | 0.152149i | ||||
\(149\) | 1816.70i | 0.998858i | 0.866355 | + | 0.499429i | \(0.166457\pi\) | ||||
−0.866355 | + | 0.499429i | \(0.833543\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1499.42 | − | 1499.42i | 0.808085 | − | 0.808085i | −0.176259 | − | 0.984344i | \(-0.556400\pi\) |
0.984344 | + | 0.176259i | \(0.0563996\pi\) | |||||||
\(152\) | −635.404 | −0.339066 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −239.252 | −0.125191 | ||||||||
\(155\) | 473.276 | − | 473.276i | 0.245255 | − | 0.245255i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1607.82i | 0.817314i | 0.912688 | + | 0.408657i | \(0.134003\pi\) | ||||
−0.912688 | + | 0.408657i | \(0.865997\pi\) | |||||||
\(158\) | −108.623 | + | 262.239i | −0.0546935 | + | 0.132042i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 164.870 | + | 398.031i | 0.0814632 | + | 0.196670i | ||||
\(161\) | 415.316 | + | 415.316i | 0.203301 | + | 0.203301i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −871.753 | − | 2104.60i | −0.418902 | − | 1.01132i | −0.982666 | − | 0.185383i | \(-0.940647\pi\) |
0.563765 | − | 0.825936i | \(-0.309353\pi\) | |||||||
\(164\) | 469.517 | − | 194.480i | 0.223556 | − | 0.0925998i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1147.74i | 0.536638i | ||||||||
\(167\) | −1526.36 | − | 632.239i | −0.707265 | − | 0.292959i | −9.26752e−5 | − | 1.00000i | \(-0.500029\pi\) |
−0.707172 | + | 0.707041i | \(0.750029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1371.29 | −0.624165 | ||||||||
\(170\) | −435.012 | − | 1017.58i | −0.196258 | − | 0.459088i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −434.809 | + | 434.809i | −0.192755 | + | 0.192755i | ||||
\(173\) | −2042.54 | − | 846.046i | −0.897637 | − | 0.371813i | −0.114326 | − | 0.993443i | \(-0.536471\pi\) |
−0.783311 | + | 0.621630i | \(0.786471\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −106.502 | + | 257.120i | −0.0460048 | + | 0.111065i | ||||
\(176\) | 1906.99 | − | 789.900i | 0.816731 | − | 0.338301i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 428.230 | + | 428.230i | 0.180321 | + | 0.180321i | ||||
\(179\) | −14.6759 | − | 14.6759i | −0.00612807 | − | 0.00612807i | 0.704036 | − | 0.710164i | \(-0.251379\pi\) |
−0.710164 | + | 0.704036i | \(0.751379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 403.272 | − | 167.041i | 0.165608 | − | 0.0685969i | −0.298340 | − | 0.954460i | \(-0.596433\pi\) |
0.463947 | + | 0.885863i | \(0.346433\pi\) | |||||||
\(182\) | −200.740 | + | 484.629i | −0.0817572 | + | 0.197379i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3722.03 | − | 1541.71i | −1.49126 | − | 0.617700i | ||||
\(185\) | 540.953 | − | 540.953i | 0.214982 | − | 0.214982i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1755.98 | + | 750.673i | −0.686683 | + | 0.293554i | ||||
\(188\) | −639.412 | −0.248053 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 485.162 | + | 200.961i | 0.185249 | + | 0.0767328i | ||||
\(191\) | 787.808i | 0.298449i | 0.988803 | + | 0.149225i | \(0.0476777\pi\) | ||||
−0.988803 | + | 0.149225i | \(0.952322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3443.17 | − | 1426.21i | 1.28417 | − | 0.531921i | 0.366928 | − | 0.930249i | \(-0.380410\pi\) |
0.917243 | + | 0.398329i | \(0.130410\pi\) | |||||||
\(194\) | 1629.11 | + | 3933.01i | 0.602903 | + | 1.45554i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −460.093 | − | 460.093i | −0.167672 | − | 0.167672i | ||||
\(197\) | −172.929 | − | 417.488i | −0.0625415 | − | 0.150989i | 0.889519 | − | 0.456898i | \(-0.151040\pi\) |
−0.952061 | + | 0.305909i | \(0.901040\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1331.80 | + | 3215.25i | −0.474416 | + | 1.14534i | 0.487775 | + | 0.872969i | \(0.337809\pi\) |
−0.962192 | + | 0.272373i | \(0.912191\pi\) | |||||||
\(200\) | − | 1908.93i | − | 0.674910i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 677.798 | − | 677.798i | 0.236088 | − | 0.236088i | ||||
\(203\) | −55.8485 | −0.0193093 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1311.19 | 0.446719 | ||||||||
\(206\) | −2203.84 | + | 2203.84i | −0.745384 | + | 0.745384i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4525.54i | − | 1.50860i | ||||||
\(209\) | 346.785 | − | 837.214i | 0.114773 | − | 0.277088i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 695.912 | + | 1680.08i | 0.227055 | + | 0.548159i | 0.995816 | − | 0.0913768i | \(-0.0291268\pi\) |
−0.768762 | + | 0.639535i | \(0.779127\pi\) | |||||||
\(212\) | −426.190 | − | 426.190i | −0.138070 | − | 0.138070i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1417.74 | − | 3422.72i | −0.452871 | − | 1.09333i | ||||
\(215\) | −1465.74 | + | 607.131i | −0.464944 | + | 0.192586i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 372.263i | 0.116456i | ||||||||
\(218\) | −2443.54 | − | 1012.15i | −0.759163 | − | 0.314456i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −264.803 | −0.0811502 | ||||||||
\(221\) | 47.2434 | + | 4186.74i | 0.0143798 | + | 1.27435i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4601.73 | + | 4601.73i | −1.38186 | + | 1.38186i | −0.540546 | + | 0.841315i | \(0.681782\pi\) |
−0.841315 | + | 0.540546i | \(0.818218\pi\) | |||||||
\(224\) | −221.380 | − | 91.6984i | −0.0660337 | − | 0.0273521i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2445.48 | + | 5903.92i | −0.719784 | + | 1.73771i | ||||
\(227\) | 2242.41 | − | 928.835i | 0.655655 | − | 0.271581i | −0.0299538 | − | 0.999551i | \(-0.509536\pi\) |
0.685609 | + | 0.727970i | \(0.259536\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −463.654 | − | 463.654i | −0.133795 | − | 0.133795i | 0.637037 | − | 0.770833i | \(-0.280160\pi\) |
−0.770833 | + | 0.637037i | \(0.780160\pi\) | |||||||
\(230\) | 2354.35 | + | 2354.35i | 0.674962 | + | 0.674962i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 353.914 | − | 146.596i | 0.100153 | − | 0.0414849i | ||||
\(233\) | 448.391 | − | 1082.51i | 0.126073 | − | 0.304368i | −0.848223 | − | 0.529640i | \(-0.822327\pi\) |
0.974296 | + | 0.225272i | \(0.0723271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1524.14 | − | 631.321i | −0.423081 | − | 0.175246i | ||||
\(236\) | −75.1244 | + | 75.1244i | −0.0207211 | + | 0.0207211i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 571.281 | + | 229.115i | 0.155591 | + | 0.0624005i | ||||
\(239\) | 5281.06 | 1.42930 | 0.714651 | − | 0.699481i | \(-0.246585\pi\) | ||||
0.714651 | + | 0.699481i | \(0.246585\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1226.76 | + | 508.143i | 0.327896 | + | 0.135819i | 0.540558 | − | 0.841307i | \(-0.318213\pi\) |
−0.212662 | + | 0.977126i | \(0.568213\pi\) | |||||||
\(242\) | − | 1856.09i | − | 0.493034i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1468.14 | + | 608.124i | −0.385197 | + | 0.159554i | ||||
\(245\) | −642.436 | − | 1550.98i | −0.167525 | − | 0.404442i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1404.89 | − | 1404.89i | −0.361908 | − | 0.361908i | ||||
\(248\) | −977.148 | − | 2359.04i | −0.250197 | − | 0.604030i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1359.00 | + | 3280.91i | −0.343802 | + | 0.830011i | ||||
\(251\) | 4280.39i | 1.07640i | 0.842818 | + | 0.538198i | \(0.180895\pi\) | ||||
−0.842818 | + | 0.538198i | \(0.819105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4062.75 | − | 4062.75i | 1.00958 | − | 1.00958i | ||||
\(254\) | −5045.62 | −1.24642 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2819.92 | 0.688458 | ||||||||
\(257\) | −171.749 | + | 171.749i | −0.0416865 | + | 0.0416865i | −0.727643 | − | 0.685956i | \(-0.759384\pi\) |
0.685956 | + | 0.727643i | \(0.259384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 425.496i | 0.102081i | ||||||||
\(260\) | −222.178 | + | 536.385i | −0.0529957 | + | 0.127943i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3155.27 | − | 7617.49i | −0.744020 | − | 1.79622i | ||||
\(263\) | −2229.86 | − | 2229.86i | −0.522809 | − | 0.522809i | 0.395609 | − | 0.918419i | \(-0.370533\pi\) |
−0.918419 | + | 0.395609i | \(0.870533\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −595.097 | − | 1436.69i | −0.137949 | − | 0.333038i | ||||
\(266\) | −269.841 | + | 111.772i | −0.0621993 | + | 0.0257638i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1419.14i | 0.323462i | ||||||||
\(269\) | 194.844 | + | 80.7072i | 0.0441631 | + | 0.0182930i | 0.404656 | − | 0.914469i | \(-0.367391\pi\) |
−0.360493 | + | 0.932762i | \(0.617391\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1627.36 | 0.364780 | 0.182390 | − | 0.983226i | \(-0.441617\pi\) | ||||
0.182390 | + | 0.983226i | \(0.441617\pi\) | |||||||
\(272\) | −5309.90 | + | 59.9172i | −1.18368 | + | 0.0133567i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1662.52 | − | 1662.52i | 0.366558 | − | 0.366558i | ||||
\(275\) | 2515.23 | + | 1041.84i | 0.551541 | + | 0.228456i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1770.63 | + | 4274.69i | −0.384069 | + | 0.927224i | 0.607101 | + | 0.794625i | \(0.292332\pi\) |
−0.991170 | + | 0.132599i | \(0.957668\pi\) | |||||||
\(278\) | 7376.82 | − | 3055.58i | 1.59148 | − | 0.659214i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −188.403 | − | 188.403i | −0.0402115 | − | 0.0402115i | ||||
\(281\) | 3589.47 | + | 3589.47i | 0.762029 | + | 0.762029i | 0.976689 | − | 0.214660i | \(-0.0688644\pi\) |
−0.214660 | + | 0.976689i | \(0.568864\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2251.53 | + | 932.616i | −0.472932 | + | 0.195895i | −0.606402 | − | 0.795158i | \(-0.707388\pi\) |
0.133470 | + | 0.991053i | \(0.457388\pi\) | |||||||
\(284\) | −467.321 | + | 1128.21i | −0.0976422 | + | 0.235729i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4740.79 | + | 1963.70i | 0.980170 | + | 0.406000i | ||||
\(287\) | −515.669 | + | 515.669i | −0.106059 | + | 0.106059i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4911.75 | − | 110.863i | 0.999745 | − | 0.0225653i | ||||
\(290\) | −316.595 | −0.0641072 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 890.265 | + | 368.760i | 0.178421 | + | 0.0739042i | ||||
\(293\) | − | 3300.30i | − | 0.658041i | −0.944323 | − | 0.329020i | \(-0.893282\pi\) | ||
0.944323 | − | 0.329020i | \(-0.106718\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −253.245 | + | 104.898i | −0.0499814 | + | 0.0207030i | ||||
\(296\) | −1116.88 | − | 2696.38i | −0.219315 | − | 0.529472i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4050.24 | − | 4050.24i | −0.787329 | − | 0.787329i | ||||
\(299\) | −4820.73 | − | 11638.3i | −0.932408 | − | 2.25103i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 337.678 | − | 815.227i | 0.0646626 | − | 0.156109i | ||||
\(302\) | 6685.75i | 1.27391i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1781.78 | − | 1781.78i | 0.336158 | − | 0.336158i | ||||
\(305\) | −4099.98 | −0.769719 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1186.40 | −0.220558 | −0.110279 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110279 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(308\) | 104.143 | − | 104.143i | 0.0192665 | − | 0.0192665i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2110.29i | 0.386634i | ||||||||
\(311\) | −251.604 | + | 607.425i | −0.0458751 | + | 0.110752i | −0.945156 | − | 0.326619i | \(-0.894091\pi\) |
0.899281 | + | 0.437371i | \(0.144091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2324.29 | + | 5611.33i | 0.419733 | + | 1.01333i | 0.982425 | + | 0.186659i | \(0.0597659\pi\) |
−0.562691 | + | 0.826667i | \(0.690234\pi\) | |||||||
\(314\) | −3584.56 | − | 3584.56i | −0.644231 | − | 0.644231i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −66.8666 | − | 161.430i | −0.0119036 | − | 0.0287379i | ||||
\(317\) | 5315.32 | − | 2201.68i | 0.941761 | − | 0.390090i | 0.141633 | − | 0.989919i | \(-0.454765\pi\) |
0.800128 | + | 0.599829i | \(0.204765\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 546.327i | 0.0958886i | ||||||||
\(320\) | 1549.03 | + | 641.628i | 0.270604 | + | 0.112088i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1851.85 | −0.320496 | ||||||||
\(323\) | −1629.79 | + | 1666.99i | −0.280755 | + | 0.287163i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4220.70 | − | 4220.70i | 0.720376 | − | 0.720376i | ||||
\(326\) | 6635.63 | + | 2748.57i | 1.12734 | + | 0.466960i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1914.24 | − | 4621.38i | 0.322245 | − | 0.777967i | ||||
\(329\) | 847.708 | − | 351.132i | 0.142054 | − | 0.0588406i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 63.5284 | + | 63.5284i | 0.0105493 | + | 0.0105493i | 0.712362 | − | 0.701812i | \(-0.247626\pi\) |
−0.701812 | + | 0.712362i | \(0.747626\pi\) | |||||||
\(332\) | −499.594 | − | 499.594i | −0.0825866 | − | 0.0825866i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 4812.49 | − | 1993.40i | 0.788406 | − | 0.326568i | ||||
\(335\) | −1401.18 | + | 3382.75i | −0.228522 | + | 0.551700i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 782.810 | + | 324.251i | 0.126535 | + | 0.0524126i | 0.445053 | − | 0.895504i | \(-0.353185\pi\) |
−0.318517 | + | 0.947917i | \(0.603185\pi\) | |||||||
\(338\) | 3057.22 | − | 3057.22i | 0.491985 | − | 0.491985i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 632.292 | + | 253.584i | 0.100855 | + | 0.0404486i | ||||
\(341\) | 3641.60 | 0.578309 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1745.23 | + | 722.896i | 0.274733 | + | 0.113798i | ||||
\(344\) | 6052.48i | 0.948628i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6439.95 | − | 2667.51i | 1.00062 | − | 0.414469i | ||||
\(347\) | 225.906 | + | 545.386i | 0.0349490 | + | 0.0843742i | 0.940390 | − | 0.340097i | \(-0.110460\pi\) |
−0.905441 | + | 0.424471i | \(0.860460\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6638.10 | + | 6638.10i | 1.01813 | + | 1.01813i | 0.999832 | + | 0.0183025i | \(0.00582618\pi\) |
0.0183025 | + | 0.999832i | \(0.494174\pi\) | |||||||
\(350\) | −335.794 | − | 810.677i | −0.0512826 | − | 0.123807i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −897.023 | + | 2165.60i | −0.135828 | + | 0.327918i | ||||
\(353\) | 6176.09i | 0.931218i | 0.884990 | + | 0.465609i | \(0.154165\pi\) | ||||
−0.884990 | + | 0.465609i | \(0.845835\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2227.87 | + | 2227.87i | −0.333079 | + | 0.333079i | ||||
\(356\) | −372.804 | −0.0555015 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 65.4382 | 0.00966066 | ||||||||
\(359\) | −5056.62 | + | 5056.62i | −0.743393 | + | 0.743393i | −0.973229 | − | 0.229836i | \(-0.926181\pi\) |
0.229836 | + | 0.973229i | \(0.426181\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5752.74i | 0.838714i | ||||||||
\(362\) | −526.666 | + | 1271.48i | −0.0764667 | + | 0.184607i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −123.572 | − | 298.330i | −0.0177938 | − | 0.0429581i | ||||
\(365\) | 1758.00 | + | 1758.00i | 0.252104 | + | 0.252104i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1285.07 | − | 3102.43i | −0.182780 | − | 0.441269i | 0.805758 | − | 0.592245i | \(-0.201758\pi\) |
−0.988537 | + | 0.150976i | \(0.951758\pi\) | |||||||
\(368\) | 14760.4 | − | 6113.96i | 2.09087 | − | 0.866066i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2412.05i | 0.338910i | ||||||||
\(371\) | 799.068 | + | 330.985i | 0.111821 | + | 0.0463177i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8379.14 | −1.16315 | −0.581576 | − | 0.813492i | \(-0.697564\pi\) | ||||
−0.581576 | + | 0.813492i | \(0.697564\pi\) | |||||||
\(374\) | 2241.27 | − | 5588.45i | 0.309876 | − | 0.772652i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4450.27 | + | 4450.27i | −0.610386 | + | 0.610386i | ||||
\(377\) | 1106.64 | + | 458.385i | 0.151180 | + | 0.0626207i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2447.53 | − | 5908.86i | 0.331718 | − | 0.800839i | −0.666738 | − | 0.745292i | \(-0.732310\pi\) |
0.998456 | − | 0.0555463i | \(-0.0176901\pi\) | |||||||
\(380\) | −298.659 | + | 123.709i | −0.0403181 | + | 0.0167003i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1756.38 | − | 1756.38i | −0.235246 | − | 0.235246i | ||||
\(383\) | 144.736 | + | 144.736i | 0.0193098 | + | 0.0193098i | 0.716696 | − | 0.697386i | \(-0.245654\pi\) |
−0.697386 | + | 0.716696i | \(0.745654\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 351.066 | − | 145.416i | 0.0464727 | − | 0.0192496i | ||||
\(386\) | −4496.72 | + | 10856.0i | −0.592945 | + | 1.43150i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2421.11 | − | 1002.85i | −0.316786 | − | 0.131217i | ||||
\(389\) | 4080.40 | − | 4080.40i | 0.531837 | − | 0.531837i | −0.389282 | − | 0.921119i | \(-0.627277\pi\) |
0.921119 | + | 0.389282i | \(0.127277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13591.6 | + | 5810.33i | −1.75794 | + | 0.751512i | ||||
\(392\) | −6404.44 | −0.825186 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1316.30 | + | 545.231i | 0.168311 | + | 0.0697166i | ||||
\(395\) | − | 450.816i | − | 0.0574253i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6600.54 | − | 2734.03i | 0.834437 | − | 0.345635i | 0.0757795 | − | 0.997125i | \(-0.475855\pi\) |
0.758658 | + | 0.651489i | \(0.225855\pi\) | |||||||
\(398\) | −4199.06 | − | 10137.4i | −0.528844 | − | 1.27674i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5352.97 | + | 5352.97i | 0.669121 | + | 0.669121i | ||||
\(401\) | 2435.60 | + | 5880.05i | 0.303312 | + | 0.732259i | 0.999891 | + | 0.0147789i | \(0.00470446\pi\) |
−0.696579 | + | 0.717480i | \(0.745296\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3055.41 | − | 7376.40i | 0.377669 | − | 0.911774i | ||||
\(404\) | 590.070i | 0.0726660i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 124.511 | − | 124.511i | 0.0152202 | − | 0.0152202i | ||||
\(407\) | 4162.33 | 0.506926 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2997.87 | 0.362433 | 0.181217 | − | 0.983443i | \(-0.441997\pi\) | ||||
0.181217 | + | 0.983443i | \(0.441997\pi\) | |||||||
\(410\) | −2923.23 | + | 2923.23i | −0.352117 | + | 0.352117i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1918.60i | − | 0.229424i | ||||||
\(413\) | 58.3426 | − | 140.852i | 0.00695122 | − | 0.0167817i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −697.591 | − | 1684.13i | −0.0825142 | − | 0.199207i | ||||
\(416\) | 3634.01 | + | 3634.01i | 0.428298 | + | 0.428298i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1093.39 | + | 2639.67i | 0.127941 | + | 0.308876i | ||||
\(419\) | −10853.1 | + | 4495.49i | −1.26541 | + | 0.524150i | −0.911566 | − | 0.411154i | \(-0.865126\pi\) |
−0.353844 | + | 0.935304i | \(0.615126\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8842.15i | 1.02361i | 0.859102 | + | 0.511805i | \(0.171023\pi\) | ||||
−0.859102 | + | 0.511805i | \(0.828977\pi\) | |||||||
\(422\) | −5297.15 | − | 2194.15i | −0.611046 | − | 0.253103i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5932.52 | −0.679501 | ||||||||
\(425\) | −5008.10 | − | 4896.34i | −0.571597 | − | 0.558841i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1612.46 | − | 1612.46i | 0.182745 | − | 0.182745i | ||||
\(428\) | 2106.97 | + | 872.737i | 0.237954 | + | 0.0985639i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1914.23 | − | 4621.37i | 0.214680 | − | 0.518284i | ||||
\(431\) | −2863.45 | + | 1186.08i | −0.320018 | + | 0.132556i | −0.536909 | − | 0.843640i | \(-0.680408\pi\) |
0.216891 | + | 0.976196i | \(0.430408\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7122.55 | − | 7122.55i | −0.790503 | − | 0.790503i | 0.191073 | − | 0.981576i | \(-0.438803\pi\) |
−0.981576 | + | 0.191073i | \(0.938803\pi\) | |||||||
\(434\) | −829.942 | − | 829.942i | −0.0917938 | − | 0.0917938i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1504.21 | − | 623.064i | 0.165226 | − | 0.0684389i | ||||
\(437\) | 2684.18 | − | 6480.18i | 0.293825 | − | 0.709357i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16036.6 | − | 6642.57i | −1.74347 | − | 0.722170i | −0.998481 | − | 0.0550975i | \(-0.982453\pi\) |
−0.744992 | − | 0.667073i | \(-0.767547\pi\) | |||||||
\(440\) | −1843.02 | + | 1843.02i | −0.199687 | + | 0.199687i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9439.45 | − | 9228.79i | −1.01581 | − | 0.993143i | ||||
\(443\) | −6979.90 | −0.748589 | −0.374295 | − | 0.927310i | \(-0.622115\pi\) | ||||
−0.374295 | + | 0.927310i | \(0.622115\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −888.638 | − | 368.086i | −0.0946640 | − | 0.0392111i | ||||
\(446\) | − | 20518.7i | − | 2.17845i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −861.549 | + | 356.865i | −0.0908579 | + | 0.0376346i | ||||
\(449\) | 3532.36 | + | 8527.87i | 0.371275 | + | 0.896336i | 0.993535 | + | 0.113526i | \(0.0362145\pi\) |
−0.622260 | + | 0.782810i | \(0.713785\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5044.44 | + | 5044.44i | 0.526681 | + | 0.526681i | ||||
\(452\) | −1505.40 | − | 3634.37i | −0.156655 | − | 0.378200i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2928.54 | + | 7070.12i | −0.302738 | + | 0.730875i | ||||
\(455\) | − | 833.127i | − | 0.0858409i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8662.49 | + | 8662.49i | −0.886683 | + | 0.886683i | −0.994203 | − | 0.107520i | \(-0.965709\pi\) |
0.107520 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(458\) | 2067.39 | 0.210923 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2049.62 | −0.207748 | ||||||||
\(461\) | −4426.14 | + | 4426.14i | −0.447171 | + | 0.447171i | −0.894413 | − | 0.447242i | \(-0.852406\pi\) |
0.447242 | + | 0.894413i | \(0.352406\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10195.0i | − | 1.02333i | −0.859185 | − | 0.511665i | \(-0.829029\pi\) | ||
0.859185 | − | 0.511665i | \(-0.170971\pi\) | |||||||
\(464\) | −581.354 | + | 1403.51i | −0.0581652 | + | 0.140423i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1413.74 | + | 3413.07i | 0.140537 | + | 0.339286i | ||||
\(467\) | −10453.2 | − | 10453.2i | −1.03579 | − | 1.03579i | −0.999335 | − | 0.0364587i | \(-0.988392\pi\) |
−0.0364587 | − | 0.999335i | \(-0.511608\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −779.319 | − | 1881.44i | −0.0767284 | − | 0.185239i | ||||
\(470\) | 4805.50 | − | 1990.50i | 0.471619 | − | 0.195351i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1045.72i | 0.101977i | ||||||||
\(473\) | −7974.80 | − | 3303.27i | −0.775226 | − | 0.321109i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3323.52 | 0.321039 | ||||||||
\(476\) | −348.400 | + | 148.940i | −0.0335481 | + | 0.0143417i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11773.9 | + | 11773.9i | −1.12662 | + | 1.12662i | ||||
\(479\) | 15123.9 | + | 6264.54i | 1.44265 | + | 0.597566i | 0.960440 | − | 0.278488i | \(-0.0898334\pi\) |
0.482212 | + | 0.876054i | \(0.339833\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3492.32 | − | 8431.20i | 0.331052 | − | 0.799230i | ||||
\(482\) | −3867.89 | + | 1602.13i | −0.365513 | + | 0.151401i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 807.929 | + | 807.929i | 0.0758761 | + | 0.0758761i | ||||
\(485\) | −4780.93 | − | 4780.93i | −0.447610 | − | 0.447610i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3793.74 | − | 1571.42i | 0.352999 | − | 0.146217i | −0.199135 | − | 0.979972i | \(-0.563813\pi\) |
0.552135 | + | 0.833755i | \(0.313813\pi\) | |||||||
\(488\) | −5985.67 | + | 14450.7i | −0.555243 | + | 1.34048i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4890.10 | + | 2025.55i | 0.450841 | + | 0.186745i | ||||
\(491\) | −620.841 | + | 620.841i | −0.0570634 | + | 0.0570634i | −0.735063 | − | 0.677999i | \(-0.762847\pi\) |
0.677999 | + | 0.735063i | \(0.262847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 523.179 | − | 1304.51i | 0.0477948 | − | 0.119173i | ||||
\(494\) | 6264.28 | 0.570533 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9355.24 | + | 3875.07i | 0.846901 | + | 0.350798i | ||||
\(497\) | − | 1752.37i | − | 0.158158i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12767.7 | + | 5288.55i | −1.14541 | + | 0.474445i | −0.872992 | − | 0.487734i | \(-0.837824\pi\) |
−0.272419 | + | 0.962179i | \(0.587824\pi\) | |||||||
\(500\) | −836.578 | − | 2019.68i | −0.0748258 | − | 0.180646i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9542.91 | − | 9542.91i | −0.848448 | − | 0.848448i | ||||
\(503\) | −1806.81 | − | 4362.03i | −0.160163 | − | 0.386667i | 0.823343 | − | 0.567544i | \(-0.192106\pi\) |
−0.983506 | + | 0.180877i | \(0.942106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −582.603 | + | 1406.53i | −0.0513376 | + | 0.123940i | ||||
\(506\) | 18115.4i | 1.59156i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2196.28 | − | 2196.28i | 0.191819 | − | 0.191819i | ||||
\(509\) | −16554.3 | −1.44156 | −0.720782 | − | 0.693161i | \(-0.756217\pi\) | ||||
−0.720782 | + | 0.693161i | \(0.756217\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1382.78 | −0.119708 | ||||||||
\(512\) | 3578.33 | − | 3578.33i | 0.308870 | − | 0.308870i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 765.813i | − | 0.0657171i | ||||||
\(515\) | 1894.32 | − | 4573.29i | 0.162085 | − | 0.391307i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3434.88 | − | 8292.54i | −0.292197 | − | 0.705427i | ||||
\(518\) | −948.621 | − | 948.621i | −0.0804633 | − | 0.0804633i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2186.86 | + | 5279.55i | 0.184424 | + | 0.445238i | ||||
\(521\) | 13632.3 | − | 5646.69i | 1.14634 | − | 0.474829i | 0.273035 | − | 0.962004i | \(-0.411973\pi\) |
0.873304 | + | 0.487175i | \(0.161973\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7800.86i | 0.652214i | 0.945333 | + | 0.326107i | \(0.105737\pi\) | ||||
−0.945333 | + | 0.326107i | \(0.894263\pi\) | |||||||
\(524\) | 4689.22 | + | 1942.34i | 0.390934 | + | 0.161930i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9942.71 | 0.824188 | ||||||||
\(527\) | −8695.32 | − | 3487.30i | −0.718736 | − | 0.288253i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22843.0 | − | 22843.0i | 1.87746 | − | 1.87746i | ||||
\(530\) | 4529.77 | + | 1876.29i | 0.371246 | + | 0.153775i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 68.8050 | − | 166.110i | 0.00560729 | − | 0.0135372i | ||||
\(533\) | 14450.4 | − | 5985.56i | 1.17433 | − | 0.486423i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4160.62 | + | 4160.62i | 0.336223 | + | 0.336223i | ||||
\(536\) | 9877.14 | + | 9877.14i | 0.795947 | + | 0.795947i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −614.329 | + | 254.463i | −0.0492297 | + | 0.0203916i | ||||
\(539\) | 3495.36 | − | 8438.54i | 0.279324 | − | 0.674348i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21275.5 | + | 8812.61i | 1.69077 | + | 0.700339i | 0.999747 | − | 0.0224947i | \(-0.00716090\pi\) |
0.691022 | + | 0.722834i | \(0.257161\pi\) | |||||||
\(542\) | −3628.13 | + | 3628.13i | −0.287530 | + | 0.287530i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4215.74 | − | 4311.97i | 0.332258 | − | 0.339842i | ||||
\(545\) | 4200.71 | 0.330162 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2440.68 | − | 1010.96i | −0.190779 | − | 0.0790232i | 0.285249 | − | 0.958454i | \(-0.407924\pi\) |
−0.476028 | + | 0.879430i | \(0.657924\pi\) | |||||||
\(548\) | 1447.34i | 0.112824i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −7930.30 | + | 3284.84i | −0.614816 | + | 0.254665i | ||||
\(551\) | 255.228 | + | 616.176i | 0.0197334 | + | 0.0476406i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 177.298 | + | 177.298i | 0.0136338 | + | 0.0136338i | ||||
\(554\) | −5582.66 | − | 13477.7i | −0.428131 | − | 1.03360i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1880.97 | + | 4541.06i | −0.143473 | + | 0.346374i | ||||
\(557\) | 19800.8i | 1.50626i | 0.657873 | + | 0.753129i | \(0.271456\pi\) | ||||
−0.657873 | + | 0.753129i | \(0.728544\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13382.2 | + | 13382.2i | −1.01253 | + | 1.01253i | ||||
\(560\) | 1056.63 | 0.0797333 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16005.1 | −1.20131 | ||||||||
\(563\) | 6882.93 | − | 6882.93i | 0.515241 | − | 0.515241i | −0.400886 | − | 0.916128i | \(-0.631298\pi\) |
0.916128 | + | 0.400886i | \(0.131298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10149.5i | − | 0.755736i | ||||||
\(566\) | 2940.46 | − | 7098.90i | 0.218369 | − | 0.527189i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4599.76 | + | 11104.8i | 0.339792 | + | 0.820330i | ||||
\(569\) | 4483.53 | + | 4483.53i | 0.330333 | + | 0.330333i | 0.852713 | − | 0.522380i | \(-0.174956\pi\) |
−0.522380 | + | 0.852713i | \(0.674956\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4736.75 | + | 11435.5i | 0.347157 | + | 0.838112i | 0.996953 | + | 0.0780032i | \(0.0248544\pi\) |
−0.649796 | + | 0.760109i | \(0.725146\pi\) | |||||||
\(572\) | −2918.36 | + | 1208.82i | −0.213326 | + | 0.0883627i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 2299.32i | − | 0.167198i | ||||||
\(575\) | 19468.3 | + | 8064.02i | 1.41197 | + | 0.584857i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.6040 | 0.00264098 | 0.00132049 | − | 0.999999i | \(-0.499580\pi\) | ||||
0.00132049 | + | 0.999999i | \(0.499580\pi\) | |||||||
\(578\) | −10703.3 | + | 11197.7i | −0.770242 | + | 0.805815i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 137.809 | − | 137.809i | 0.00986586 | − | 0.00986586i | ||||
\(581\) | 936.693 | + | 387.991i | 0.0668857 | + | 0.0277049i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3237.80 | − | 7816.73i | 0.230010 | − | 0.555293i | ||||
\(584\) | 8762.74 | − | 3629.64i | 0.620898 | − | 0.257184i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7357.86 | + | 7357.86i | 0.518687 | + | 0.518687i | ||||
\(587\) | 14389.9 | + | 14389.9i | 1.01182 | + | 1.01182i | 0.999929 | + | 0.0118873i | \(0.00378392\pi\) |
0.0118873 | + | 0.999929i | \(0.496216\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4107.18 | − | 1701.25i | 0.287323 | − | 0.119013i | ||||
\(590\) | 330.733 | − | 798.461i | 0.0230781 | − | 0.0557155i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10693.0 | + | 4429.19i | 0.742365 | + | 0.307498i | ||||
\(593\) | −14416.1 | + | 14416.1i | −0.998308 | + | 0.998308i | −0.999999 | − | 0.00169056i | \(-0.999462\pi\) |
0.00169056 | + | 0.999999i | \(0.499462\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −977.523 | + | 11.0304i | −0.0673522 | + | 0.000760006i | ||||
\(596\) | 3526.02 | 0.242334 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 36694.5 | + | 15199.4i | 2.50928 | + | 1.03938i | ||||
\(599\) | 316.417i | 0.0215834i | 0.999942 | + | 0.0107917i | \(0.00343517\pi\) | ||||
−0.999942 | + | 0.0107917i | \(0.996565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1230.47 | − | 509.678i | 0.0835141 | − | 0.0345927i | −0.340535 | − | 0.940232i | \(-0.610608\pi\) |
0.424049 | + | 0.905639i | \(0.360608\pi\) | |||||||
\(602\) | 1064.67 | + | 2570.34i | 0.0720810 | + | 0.174019i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2910.20 | − | 2910.20i | −0.196050 | − | 0.196050i | ||||
\(605\) | 1128.13 | + | 2723.54i | 0.0758096 | + | 0.183021i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5309.03 | − | 12817.1i | 0.355003 | − | 0.857053i | −0.640984 | − | 0.767554i | \(-0.721473\pi\) |
0.995987 | − | 0.0894989i | \(-0.0285266\pi\) | |||||||
\(608\) | 2861.54i | 0.190873i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 9140.71 | − | 9140.71i | 0.606715 | − | 0.606715i | ||||
\(611\) | −19679.3 | −1.30301 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15297.0 | 1.00790 | 0.503948 | − | 0.863734i | \(-0.331880\pi\) | ||||
0.503948 | + | 0.863734i | \(0.331880\pi\) | |||||||
\(614\) | 2645.01 | − | 2645.01i | 0.173850 | − | 0.173850i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 1449.66i | − | 0.0948186i | ||||||
\(617\) | 5784.96 | − | 13966.1i | 0.377461 | − | 0.911272i | −0.614979 | − | 0.788544i | \(-0.710835\pi\) |
0.992440 | − | 0.122729i | \(-0.0391645\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8576.73 | − | 20706.0i | −0.556911 | − | 1.34450i | −0.912200 | − | 0.409745i | \(-0.865618\pi\) |
0.355289 | − | 0.934756i | \(-0.384382\pi\) | |||||||
\(620\) | −918.577 | − | 918.577i | −0.0595015 | − | 0.0595015i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −793.286 | − | 1915.16i | −0.0511381 | − | 0.123458i | ||||
\(623\) | 494.249 | − | 204.724i | 0.0317844 | − | 0.0131655i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6850.26i | 0.438417i | ||||||||
\(626\) | −17692.1 | − | 7328.29i | −1.12958 | − | 0.467887i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3120.61 | 0.198290 | ||||||||
\(629\) | −9938.72 | − | 3985.97i | −0.630020 | − | 0.252673i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3415.99 | + | 3415.99i | −0.215513 | + | 0.215513i | −0.806604 | − | 0.591092i | \(-0.798697\pi\) |
0.591092 | + | 0.806604i | \(0.298697\pi\) | |||||||
\(632\) | −1588.93 | − | 658.158i | −0.100007 | − | 0.0414242i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6941.71 | + | 16758.8i | −0.434843 | + | 1.04980i | ||||
\(635\) | 7403.68 | − | 3066.70i | 0.462687 | − | 0.191651i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14160.4 | − | 14160.4i | −0.880776 | − | 0.880776i | ||||
\(638\) | −1218.01 | − | 1218.01i | −0.0755822 | − | 0.0755822i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8068.21 | + | 3341.96i | −0.498319 | + | 0.206410i | ||||
\(641\) | 8804.50 | − | 21255.9i | 0.542522 | − | 1.30976i | −0.380416 | − | 0.924816i | \(-0.624219\pi\) |
0.922938 | − | 0.384949i | \(-0.125781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5256.78 | − | 2177.43i | −0.322406 | − | 0.133545i | 0.215610 | − | 0.976480i | \(-0.430826\pi\) |
−0.538016 | + | 0.842935i | \(0.680826\pi\) | |||||||
\(644\) | 806.083 | − | 806.083i | 0.0493232 | − | 0.0493232i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −82.9378 | − | 7350.00i | −0.00505131 | − | 0.447650i | ||||
\(647\) | 15949.0 | 0.969122 | 0.484561 | − | 0.874758i | \(-0.338979\pi\) | ||||
0.484561 | + | 0.874758i | \(0.338979\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1377.85 | − | 570.726i | −0.0833366 | − | 0.0345192i | ||||
\(650\) | 18819.7i | 1.13564i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4084.79 | + | 1691.98i | −0.245357 | + | 0.101630i | ||||
\(653\) | −4119.43 | − | 9945.18i | −0.246869 | − | 0.595995i | 0.751066 | − | 0.660228i | \(-0.229540\pi\) |
−0.997935 | + | 0.0642322i | \(0.979540\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9259.75 | + | 9259.75i | 0.552379 | + | 0.552379i | ||||
\(656\) | 7591.28 | + | 18327.0i | 0.451814 | + | 1.09078i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1107.09 | + | 2672.75i | −0.0655910 | + | 0.158351i | ||||
\(659\) | − | 25208.2i | − | 1.49010i | −0.667011 | − | 0.745048i | \(-0.732427\pi\) | ||
0.667011 | − | 0.745048i | \(-0.267573\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10196.1 | + | 10196.1i | −0.599975 | + | 0.599975i | −0.940306 | − | 0.340331i | \(-0.889461\pi\) |
0.340331 | + | 0.940306i | \(0.389461\pi\) | |||||||
\(662\) | −283.267 | −0.0166306 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6954.28 | −0.406444 | ||||||||
\(665\) | 328.016 | − | 328.016i | 0.0191277 | − | 0.0191277i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4228.67i | 0.245479i | ||||||||
\(668\) | −1227.11 | + | 2962.50i | −0.0710751 | + | 0.171590i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4417.81 | − | 10665.5i | −0.254739 | − | 0.614994i | ||||
\(671\) | −15773.5 | − | 15773.5i | −0.907497 | − | 0.907497i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −807.706 | − | 1949.97i | −0.0462627 | − | 0.111688i | 0.899059 | − | 0.437828i | \(-0.144252\pi\) |
−0.945322 | + | 0.326140i | \(0.894252\pi\) | |||||||
\(674\) | −2468.14 | + | 1022.34i | −0.141052 | + | 0.0584256i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2661.52i | 0.151429i | ||||||||
\(677\) | 11035.3 | + | 4570.96i | 0.626470 | + | 0.259493i | 0.673253 | − | 0.739413i | \(-0.264897\pi\) |
−0.0467822 | + | 0.998905i | \(0.514897\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3760.52 | 0.212541 | ||||||||
\(680\) | 6165.64 | − | 2635.79i | 0.347708 | − | 0.148644i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8118.75 | + | 8118.75i | −0.455840 | + | 0.455840i | ||||
\(683\) | −17633.0 | − | 7303.83i | −0.987859 | − | 0.409185i | −0.170528 | − | 0.985353i | \(-0.554547\pi\) |
−0.817331 | + | 0.576168i | \(0.804547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1429.03 | + | 3449.98i | −0.0797085 | + | 0.192433i | ||||
\(686\) | −5502.55 | + | 2279.23i | −0.306251 | + | 0.126853i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16972.2 | − | 16972.2i | −0.940492 | − | 0.940492i | ||||
\(689\) | −13116.9 | − | 13116.9i | −0.725277 | − | 0.725277i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26161.3 | − | 10836.4i | 1.44026 | − | 0.596577i | 0.480402 | − | 0.877048i | \(-0.340491\pi\) |
0.959862 | + | 0.280471i | \(0.0904908\pi\) | |||||||
\(692\) | −1642.08 | + | 3964.34i | −0.0902061 | + | 0.217777i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1719.56 | − | 712.264i | −0.0940540 | − | 0.0389585i | ||||
\(695\) | −8967.20 | + | 8967.20i | −0.489418 | + | 0.489418i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7214.29 | − | 16875.7i | −0.392053 | − | 0.917091i | ||||
\(698\) | −29598.6 | −1.60505 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 499.041 | + | 206.710i | 0.0269457 | + | 0.0111613i | ||||
\(701\) | − | 5916.75i | − | 0.318791i | −0.987215 | − | 0.159396i | \(-0.949045\pi\) | ||
0.987215 | − | 0.159396i | \(-0.0509545\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4694.49 | − | 1944.52i | 0.251858 | − | 0.104323i | ||||
\(704\) | 3490.97 | + | 8427.94i | 0.186890 | + | 0.451193i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −13769.3 | − | 13769.3i | −0.734014 | − | 0.734014i | ||||
\(707\) | −324.036 | − | 782.292i | −0.0172371 | − | 0.0416140i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7079.57 | + | 17091.6i | −0.375005 | + | 0.905343i | 0.617880 | + | 0.786272i | \(0.287992\pi\) |
−0.992886 | + | 0.119071i | \(0.962008\pi\) | |||||||
\(710\) | − | 9933.85i | − | 0.525085i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2594.69 | + | 2594.69i | −0.136573 | + | 0.136573i | ||||
\(713\) | 28186.6 | 1.48050 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8149.91 | −0.426279 | ||||||||
\(716\) | −28.4842 | + | 28.4842i | −0.00148674 | + | 0.00148674i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 22546.9i | − | 1.17193i | ||||||
\(719\) | −8498.05 | + | 20516.1i | −0.440784 | + | 1.06415i | 0.534890 | + | 0.844922i | \(0.320353\pi\) |
−0.975674 | + | 0.219226i | \(0.929647\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1053.60 | + | 2543.60i | 0.0544215 | + | 0.131385i | ||||
\(722\) | −12825.4 | − | 12825.4i | −0.661099 | − | 0.661099i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −324.208 | − | 782.706i | −0.0166424 | − | 0.0401783i | ||||
\(725\) | −1851.16 | + | 766.778i | −0.0948283 | + | 0.0392792i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3777.02i | 0.192685i | 0.995348 | + | 0.0963424i | \(0.0307144\pi\) | ||||
−0.995348 | + | 0.0963424i | \(0.969286\pi\) | |||||||
\(728\) | −2936.42 | − | 1216.30i | −0.149493 | − | 0.0619220i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7838.73 | −0.397431 | ||||||||
\(731\) | 15878.7 | + | 15524.4i | 0.803415 | + | 0.785486i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14111.3 | + | 14111.3i | −0.711068 | + | 0.711068i | −0.966759 | − | 0.255690i | \(-0.917697\pi\) |
0.255690 | + | 0.966759i | \(0.417697\pi\) | |||||||
\(734\) | 9781.72 | + | 4051.72i | 0.491894 | + | 0.203749i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6943.11 | + | 16762.1i | −0.347726 | + | 0.839485i | ||||
\(737\) | −18404.9 | + | 7623.54i | −0.919880 | + | 0.381027i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16453.2 | − | 16453.2i | −0.819001 | − | 0.819001i | 0.166962 | − | 0.985963i | \(-0.446604\pi\) |
−0.985963 | + | 0.166962i | \(0.946604\pi\) | |||||||
\(740\) | −1049.93 | − | 1049.93i | −0.0521570 | − | 0.0521570i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2519.40 | + | 1043.57i | −0.124649 | + | 0.0516315i | ||||
\(743\) | −4816.87 | + | 11629.0i | −0.237838 | + | 0.574193i | −0.997059 | − | 0.0766410i | \(-0.975580\pi\) |
0.759220 | + | 0.650834i | \(0.225580\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8404.83 | + | 3481.39i | 0.413328 | + | 0.171206i | ||||
\(746\) | 18680.9 | − | 18680.9i | 0.916830 | − | 0.916830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1456.97 | + | 3408.16i | 0.0712195 | + | 0.166597i | ||||
\(749\) | −3272.61 | −0.159651 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2460.10 | + | 1019.01i | 0.119534 | + | 0.0495127i | 0.441649 | − | 0.897188i | \(-0.354394\pi\) |
−0.322115 | + | 0.946701i | \(0.604394\pi\) | |||||||
\(752\) | − | 24958.6i | − | 1.21030i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3489.14 | + | 1445.25i | −0.168524 | + | 0.0698049i | ||||
\(755\) | −4063.57 | − | 9810.32i | −0.195879 | − | 0.472893i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18689.0 | + | 18689.0i | 0.897308 | + | 0.897308i | 0.995197 | − | 0.0978891i | \(-0.0312090\pi\) |
−0.0978891 | + | 0.995197i | \(0.531209\pi\) | |||||||
\(758\) | 7716.86 | + | 18630.2i | 0.369775 | + | 0.892715i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1217.64 | + | 2939.65i | −0.0581166 | + | 0.140306i | ||||
\(761\) | 8469.75i | 0.403454i | 0.979442 | + | 0.201727i | \(0.0646553\pi\) | ||||
−0.979442 | + | 0.201727i | \(0.935345\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1652.07 | + | 1652.07i | −0.0783865 | + | 0.0783865i | ||||
\(764\) | 1529.05 | 0.0724071 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −645.361 | −0.0304410 | ||||||||
\(767\) | −2312.12 | + | 2312.12i | −0.108847 | + | 0.108847i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8452.54i | 0.396367i | 0.980165 | + | 0.198184i | \(0.0635043\pi\) | ||||
−0.980165 | + | 0.198184i | \(0.936496\pi\) | |||||||
\(770\) | −458.486 | + | 1106.88i | −0.0214580 | + | 0.0518043i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2768.11 | − | 6682.82i | −0.129050 | − | 0.311554i | ||||
\(773\) | 23996.5 | + | 23996.5i | 1.11655 | + | 1.11655i | 0.992244 | + | 0.124307i | \(0.0396707\pi\) |
0.124307 | + | 0.992244i | \(0.460329\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5111.03 | + | 12339.1i | 0.236895 | + | 0.571915i | ||||
\(776\) | −23830.6 | + | 9870.94i | −1.10241 | + | 0.456632i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18194.1i | 0.838419i | ||||||||
\(779\) | 8045.99 | + | 3332.76i | 0.370061 | + | 0.153284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17142.2 | −0.785399 | ||||||||
\(782\) | 17347.8 | − | 43255.5i | 0.793296 | − | 1.97802i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 17959.1 | − | 17959.1i | 0.818108 | − | 0.818108i | ||||
\(785\) | 7438.48 | + | 3081.12i | 0.338205 | + | 0.140089i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13156.3 | − | 31762.1i | 0.595898 | − | 1.43863i | −0.281829 | − | 0.959465i | \(-0.590941\pi\) |
0.877727 | − | 0.479161i | \(-0.159059\pi\) | |||||||
\(788\) | −810.297 | + | 335.636i | −0.0366315 | + | 0.0151733i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1005.07 | + | 1005.07i | 0.0452643 | + | 0.0452643i | ||||
\(791\) | 3991.61 | + | 3991.61i | 0.179425 | + | 0.179425i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −45185.3 | + | 18716.4i | −2.02343 | + | 0.838131i | ||||
\(794\) | −8620.18 | + | 20811.0i | −0.385288 | + | 0.930168i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6240.45 | + | 2584.88i | 0.277873 | + | 0.115099i | ||||
\(797\) | −2354.14 | + | 2354.14i | −0.104627 | + | 0.104627i | −0.757483 | − | 0.652855i | \(-0.773571\pi\) |
0.652855 | + | 0.757483i | \(0.273571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 260.550 | + | 23090.1i | 0.0115364 | + | 1.02236i | ||||
\(800\) | −8596.87 | −0.379932 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18539.3 | − | 7679.24i | −0.816267 | − | 0.338109i | ||||
\(803\) | 13526.8i | 0.594459i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2717.31 | − | 1125.55i | 0.118972 | − | 0.0492799i | ||||
\(806\) | 9633.45 | + | 23257.2i | 0.420997 | + | 1.01638i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4106.85 | + | 4106.85i | 0.178810 | + | 0.178810i | ||||
\(809\) | 2762.07 | + | 6668.23i | 0.120036 | + | 0.289793i | 0.972464 | − | 0.233051i | \(-0.0748710\pi\) |
−0.852428 | + | 0.522844i | \(0.824871\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13992.5 | − | 33780.9i | 0.605848 | − | 1.46265i | −0.261628 | − | 0.965169i | \(-0.584259\pi\) |
0.867476 | − | 0.497478i | \(-0.165741\pi\) | |||||||
\(812\) | 108.396i | 0.00468466i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9279.70 | + | 9279.70i | −0.399574 | + | 0.399574i | ||||
\(815\) | −11407.3 | −0.490284 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10537.6 | −0.451240 | ||||||||
\(818\) | −6683.60 | + | 6683.60i | −0.285680 | + | 0.285680i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 2544.88i | − | 0.108379i | ||||||
\(821\) | 8855.50 | − | 21379.1i | 0.376442 | − | 0.908812i | −0.616185 | − | 0.787602i | \(-0.711323\pi\) |
0.992627 | − | 0.121210i | \(-0.0386775\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15800.2 | + | 38145.0i | 0.669210 | + | 1.61562i | 0.782935 | + | 0.622103i | \(0.213722\pi\) |
−0.113725 | + | 0.993512i | \(0.536278\pi\) | |||||||
\(824\) | −13353.3 | − | 13353.3i | −0.564545 | − | 0.564545i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 183.949 | + | 444.093i | 0.00774869 | + | 0.0187070i | ||||
\(827\) | −9246.14 | + | 3829.88i | −0.388779 | + | 0.161037i | −0.568506 | − | 0.822679i | \(-0.692478\pi\) |
0.179727 | + | 0.983716i | \(0.442478\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 44643.6i | − | 1.87037i | −0.354159 | − | 0.935185i | \(-0.615233\pi\) | ||
0.354159 | − | 0.935185i | \(-0.384767\pi\) | |||||||
\(830\) | 5309.94 | + | 2199.45i | 0.222061 | + | 0.0919806i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20000.6 | 0.833410 | ||||||||
\(833\) | −16427.1 | + | 16802.1i | −0.683273 | + | 0.698869i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5850.01 | + | 5850.01i | −0.242453 | + | 0.242453i | ||||
\(836\) | −1624.94 | − | 673.072i | −0.0672246 | − | 0.0278453i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 14173.9 | − | 34218.8i | 0.584283 | − | 1.41058i | ||||
\(839\) | −13151.7 | + | 5447.61i | −0.541176 | + | 0.224163i | −0.636490 | − | 0.771285i | \(-0.719614\pi\) |
0.0953141 | + | 0.995447i | \(0.469614\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16961.3 | + | 16961.3i | 0.695449 | + | 0.695449i | ||||
\(842\) | −19713.1 | − | 19713.1i | −0.806840 | − | 0.806840i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3260.85 | − | 1350.69i | 0.132989 | − | 0.0550860i | ||||
\(845\) | −2627.84 | + | 6344.17i | −0.106983 | + | 0.258280i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1514.79 | − | 627.448i | −0.0614509 | − | 0.0254538i | ||||
\(848\) | 16635.8 | − | 16635.8i | 0.673673 | − | 0.673673i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22081.4 | − | 249.168i | 0.891044 | − | 0.0100546i | ||||
\(851\) | 32217.1 | 1.29775 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25618.2 | − | 10611.4i | −1.02831 | − | 0.425942i | −0.196211 | − | 0.980562i | \(-0.562864\pi\) |
−0.832104 | + | 0.554620i | \(0.812864\pi\) | |||||||
\(854\) | 7189.78i | 0.288090i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20738.6 | − | 8590.22i | 0.828074 | − | 0.342999i | ||||
\(857\) | −11970.6 | − | 28899.6i | −0.477138 | − | 1.15191i | −0.960945 | − | 0.276739i | \(-0.910746\pi\) |
0.483807 | − | 0.875175i | \(-0.339254\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39.0952 | − | 39.0952i | −0.00155287 | − | 0.00155287i | 0.706330 | − | 0.707883i | \(-0.250350\pi\) |
−0.707883 | + | 0.706330i | \(0.750350\pi\) | |||||||
\(860\) | 1178.37 | + | 2844.85i | 0.0467235 | + | 0.112801i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3739.62 | − | 9028.23i | 0.147763 | − | 0.356732i | ||||
\(863\) | 22900.4i | 0.903291i | 0.892197 | + | 0.451646i | \(0.149163\pi\) | ||||
−0.892197 | + | 0.451646i | \(0.850837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7828.34 | + | 7828.34i | −0.307713 | + | 0.307713i | ||||
\(866\) | 31758.7 | 1.24620 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 722.522 | 0.0282535 | ||||||||
\(869\) | 1734.39 | − | 1734.39i | 0.0677043 | − | 0.0677043i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 43677.2i | 1.69913i | ||||||||
\(872\) | 6132.72 | − | 14805.7i | 0.238165 | − | 0.574982i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8462.99 | + | 20431.5i | 0.327534 | + | 0.790738i | ||||
\(875\) | 2218.21 | + | 2218.21i | 0.0857018 | + | 0.0857018i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −682.134 | − | 1646.82i | −0.0262646 | − | 0.0634083i | 0.910203 | − | 0.414162i | \(-0.135925\pi\) |
−0.936468 | + | 0.350754i | \(0.885925\pi\) | |||||||
\(878\) | 50562.1 | − | 20943.5i | 1.94349 | − | 0.805021i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 10336.3i | − | 0.395949i | ||||||
\(881\) | −15920.8 | − | 6594.62i | −0.608838 | − | 0.252189i | 0.0568939 | − | 0.998380i | \(-0.481880\pi\) |
−0.665731 | + | 0.746191i | \(0.731880\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10188.2 | −0.388291 | −0.194145 | − | 0.980973i | \(-0.562193\pi\) | ||||
−0.194145 | + | 0.980973i | \(0.562193\pi\) | |||||||
\(884\) | 8126.00 | − | 91.6943i | 0.309171 | − | 0.00348870i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15561.3 | − | 15561.3i | 0.590060 | − | 0.590060i | ||||
\(887\) | 14478.7 | + | 5997.28i | 0.548081 | + | 0.227022i | 0.639501 | − | 0.768790i | \(-0.279141\pi\) |
−0.0914208 | + | 0.995812i | \(0.529141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1705.66 | + | 4117.83i | −0.0643487 | + | 0.155352i | ||||
\(890\) | 2801.80 | − | 1160.54i | 0.105524 | − | 0.0437096i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8931.46 | + | 8931.46i | 0.335255 | + | 0.335255i | ||||
\(893\) | −7748.07 | − | 7748.07i | −0.290347 | − | 0.290347i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −96.0206 | + | 39.7730i | −0.00358616 | + | 0.00148544i | ||||
\(896\) | 1858.75 | − | 4487.43i | 0.0693042 | − | 0.167315i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −26887.7 | − | 11137.2i | −0.999168 | − | 0.413869i | ||||
\(899\) | −1895.16 | + | 1895.16i | −0.0703081 | + | 0.0703081i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15216.7 | + | 15564.0i | −0.562643 | + | 0.575485i | ||||
\(902\) | −22492.6 | −0.830291 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −35772.5 | − | 14817.5i | −1.31612 | − | 0.545156i | ||||
\(905\) | − | 2185.81i | − | 0.0802861i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15621.3 | − | 6470.54i | 0.571881 | − | 0.236881i | −0.0779531 | − | 0.996957i | \(-0.524838\pi\) |
0.649834 | + | 0.760076i | \(0.274838\pi\) | |||||||
\(908\) | −1802.77 | − | 4352.26i | −0.0658887 | − | 0.159069i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1857.42 | + | 1857.42i | 0.0676623 | + | 0.0676623i | ||||
\(911\) | −13815.1 | − | 33352.6i | −0.502431 | − | 1.21298i | −0.948156 | − | 0.317806i | \(-0.897054\pi\) |
0.445724 | − | 0.895170i | \(-0.352946\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3795.45 | − | 9163.02i | 0.137580 | − | 0.332149i | ||||
\(914\) | − | 38625.1i | − | 1.39782i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −899.902 | + | 899.902i | −0.0324603 | + | 0.0324603i | ||||
\(917\) | −7283.41 | −0.262290 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 20016.2 | 0.718470 | 0.359235 | − | 0.933247i | \(-0.383038\pi\) | ||||
0.359235 | + | 0.933247i | \(0.383038\pi\) | |||||||
\(920\) | −14265.3 | + | 14265.3i | −0.511208 | + | 0.511208i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 19735.7i | − | 0.704947i | ||||||
\(923\) | −14382.8 | + | 34723.2i | −0.512911 | + | 1.23828i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5841.88 | + | 14103.6i | 0.207654 | + | 0.501321i | ||||
\(926\) | 22729.2 | + | 22729.2i | 0.806618 | + | 0.806618i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −660.194 | − | 1593.85i | −0.0233534 | − | 0.0563800i | ||||
\(929\) | −28298.7 | + | 11721.7i | −0.999407 | + | 0.413968i | −0.821580 | − | 0.570094i | \(-0.806907\pi\) |
−0.177828 | + | 0.984062i | \(0.556907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 11150.3i | − | 0.392522i | ||||||
\(932\) | −2101.04 | − | 870.278i | −0.0738431 | − | 0.0305868i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 46609.7 | 1.63289 | ||||||||
\(935\) | 107.903 | + | 9562.43i | 0.00377413 | + | 0.334465i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2746.18 | − | 2746.18i | 0.0957458 | − | 0.0957458i | −0.657611 | − | 0.753357i | \(-0.728433\pi\) |
0.753357 | + | 0.657611i | \(0.228433\pi\) | |||||||
\(938\) | 5932.03 | + | 2457.13i | 0.206490 | + | 0.0855310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1225.32 | + | 2958.19i | −0.0425167 | + | 0.102644i | ||||
\(941\) | −20044.5 | + | 8302.68i | −0.694400 | + | 0.287630i | −0.701832 | − | 0.712342i | \(-0.747634\pi\) |
0.00743202 | + | 0.999972i | \(0.497634\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 39044.8 | + | 39044.8i | 1.34833 | + | 1.34833i | ||||
\(944\) | −2932.38 | − | 2932.38i | −0.101103 | − | 0.101103i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25143.9 | − | 10414.9i | 0.864163 | − | 0.357948i | ||||
\(947\) | 6086.52 | − | 14694.2i | 0.208855 | − | 0.504220i | −0.784389 | − | 0.620269i | \(-0.787023\pi\) |
0.993243 | + | 0.116050i | \(0.0370233\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27399.9 | + | 11349.4i | 0.937236 | + | 0.388216i | ||||
\(950\) | −7409.61 | + | 7409.61i | −0.253052 | + | 0.253052i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1388.23 | + | 3461.45i | −0.0472615 | + | 0.117843i | ||||
\(953\) | 81.8493 | 0.00278212 | 0.00139106 | − | 0.999999i | \(-0.499557\pi\) | ||||
0.00139106 | + | 0.999999i | \(0.499557\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3644.74 | + | 1509.70i | 0.123498 | + | 0.0511547i | ||||
\(956\) | − | 10250.0i | − | 0.346765i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −47684.5 | + | 19751.6i | −1.60816 | + | 0.666122i | ||||
\(959\) | −794.806 | − | 1918.83i | −0.0267629 | − | 0.0646113i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8433.08 | − | 8433.08i | −0.283075 | − | 0.283075i | ||||
\(962\) | 11011.0 | + | 26582.9i | 0.369032 | + | 0.890922i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 986.249 | − | 2381.02i | 0.0329512 | − | 0.0795512i | ||||
\(965\) | − | 18662.7i | − | 0.622562i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13632.8 | − | 13632.8i | 0.453363 | − | 0.453363i | −0.443106 | − | 0.896469i | \(-0.646124\pi\) |
0.896469 | + | 0.443106i | \(0.146124\pi\) | |||||||
\(968\) | 11246.3 | 0.373419 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 21317.7 | 0.705639 | ||||||||
\(971\) | 38025.6 | − | 38025.6i | 1.25674 | − | 1.25674i | 0.304107 | − | 0.952638i | \(-0.401642\pi\) |
0.952638 | − | 0.304107i | \(-0.0983579\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 7053.30i | − | 0.232393i | ||||||
\(974\) | −4954.55 | + | 11961.3i | −0.162992 | + | 0.393497i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23737.3 | − | 57307.0i | −0.778497 | − | 1.87946i | ||||
\(977\) | 38705.7 | + | 38705.7i | 1.26746 | + | 1.26746i | 0.947397 | + | 0.320061i | \(0.103703\pi\) |
0.320061 | + | 0.947397i | \(0.396297\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2002.68 | − | 4834.89i | −0.0653788 | − | 0.157838i | ||||
\(980\) | −3010.27 | + | 1246.90i | −0.0981221 | + | 0.0406435i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 2768.27i | − | 0.0899581i | ||||||
\(983\) | 3146.11 | + | 1303.16i | 0.102081 | + | 0.0422832i | 0.433139 | − | 0.901327i | \(-0.357406\pi\) |
−0.331059 | + | 0.943610i | \(0.607406\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2262.86 | −0.0731988 | ||||||||
\(986\) | 1741.93 | + | 4074.74i | 0.0562621 | + | 0.131609i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2726.75 | + | 2726.75i | −0.0878030 | + | 0.0878030i | ||||
\(989\) | −61726.3 | − | 25567.9i | −1.98461 | − | 0.822054i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11452.1 | + | 27647.8i | −0.367091 | + | 0.886237i | 0.627133 | + | 0.778912i | \(0.284228\pi\) |
−0.994224 | + | 0.107324i | \(0.965772\pi\) | |||||||
\(992\) | −10624.0 | + | 4400.58i | −0.340031 | + | 0.140845i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3906.82 | + | 3906.82i | 0.124665 | + | 0.124665i | ||||
\(995\) | 12323.0 | + | 12323.0i | 0.392627 | + | 0.392627i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30224.2 | + | 12519.3i | −0.960092 | + | 0.397683i | −0.807015 | − | 0.590531i | \(-0.798918\pi\) |
−0.153077 | + | 0.988214i | \(0.548918\pi\) | |||||||
\(998\) | 16674.4 | − | 40255.5i | 0.528875 | − | 1.27682i | ||||
\(999\) | 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 | 153.4.l.a.145.1 | 12 | ||
3.2 | odd | 2 | 17.4.d.a.9.3 | yes | 12 | ||
17.2 | even | 8 | inner | 153.4.l.a.19.1 | 12 | ||
51.2 | odd | 8 | 17.4.d.a.2.3 | ✓ | 12 | ||
51.11 | even | 16 | 289.4.a.g.1.12 | 12 | |||
51.23 | even | 16 | 289.4.a.g.1.11 | 12 | |||
51.41 | even | 16 | 289.4.b.e.288.2 | 12 | |||
51.44 | even | 16 | 289.4.b.e.288.1 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.4.d.a.2.3 | ✓ | 12 | 51.2 | odd | 8 | ||
17.4.d.a.9.3 | yes | 12 | 3.2 | odd | 2 | ||
153.4.l.a.19.1 | 12 | 17.2 | even | 8 | inner | ||
153.4.l.a.145.1 | 12 | 1.1 | even | 1 | trivial | ||
289.4.a.g.1.11 | 12 | 51.23 | even | 16 | |||
289.4.a.g.1.12 | 12 | 51.11 | even | 16 | |||
289.4.b.e.288.1 | 12 | 51.44 | even | 16 | |||
289.4.b.e.288.2 | 12 | 51.41 | even | 16 |