Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(19,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.m (of order \(4\), 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: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 91.3 | ||
Root | \(-1.66730 + 1.10459i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.91 |
Dual form | 144.3.m.b.19.3 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.10459 | − | 1.66730i | −0.552295 | − | 0.833649i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.55976 | + | 3.68336i | −0.389940 | + | 0.920840i | ||||
\(5\) | −4.23991 | − | 4.23991i | −0.847982 | − | 0.847982i | 0.141900 | − | 0.989881i | \(-0.454679\pi\) |
−0.989881 | + | 0.141900i | \(0.954679\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.262225 | −0.0374608 | −0.0187304 | − | 0.999825i | \(-0.505962\pi\) | ||||
−0.0187304 | + | 0.999825i | \(0.505962\pi\) | |||||||
\(8\) | 7.86415 | − | 1.46802i | 0.983019 | − | 0.183503i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.38583 | + | 11.7525i | −0.238583 | + | 1.17525i | ||||
\(11\) | −8.60531 | + | 8.60531i | −0.782301 | + | 0.782301i | −0.980219 | − | 0.197917i | \(-0.936582\pi\) |
0.197917 | + | 0.980219i | \(0.436582\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.9957 | + | 15.9957i | −1.23044 | + | 1.23044i | −0.266640 | + | 0.963796i | \(0.585913\pi\) |
−0.963796 | + | 0.266640i | \(0.914087\pi\) | |||||||
\(14\) | 0.289652 | + | 0.437208i | 0.0206894 | + | 0.0312291i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −11.1343 | − | 11.4903i | −0.695893 | − | 0.718145i | ||||
\(17\) | −3.51534 | −0.206785 | −0.103392 | − | 0.994641i | \(-0.532970\pi\) | ||||
−0.103392 | + | 0.994641i | \(0.532970\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.7566 | + | 10.7566i | 0.566138 | + | 0.566138i | 0.931044 | − | 0.364906i | \(-0.118899\pi\) |
−0.364906 | + | 0.931044i | \(0.618899\pi\) | |||||||
\(20\) | 22.2304 | − | 9.00387i | 1.11152 | − | 0.450193i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 23.8530 | + | 4.84227i | 1.08423 | + | 0.220103i | ||||
\(23\) | −16.4968 | −0.717253 | −0.358626 | − | 0.933481i | \(-0.616755\pi\) | ||||
−0.358626 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 10.9536i | 0.438145i | ||||||||
\(26\) | 44.3382 | + | 9.00087i | 1.70532 | + | 0.346187i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.409009 | − | 0.965871i | 0.0146075 | − | 0.0344954i | ||||
\(29\) | −25.9522 | + | 25.9522i | −0.894903 | + | 0.894903i | −0.994980 | − | 0.100077i | \(-0.968091\pi\) |
0.100077 | + | 0.994980i | \(0.468091\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 46.2072i | − | 1.49055i | −0.666755 | − | 0.745277i | \(-0.732317\pi\) | ||
0.666755 | − | 0.745277i | \(-0.267683\pi\) | |||||||
\(32\) | −6.85895 | + | 31.2563i | −0.214342 | + | 0.976759i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.88301 | + | 5.86112i | 0.114206 | + | 0.172386i | ||||
\(35\) | 1.11181 | + | 1.11181i | 0.0317660 | + | 0.0317660i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.99313 | − | 2.99313i | −0.0808955 | − | 0.0808955i | 0.665501 | − | 0.746397i | \(-0.268218\pi\) |
−0.746397 | + | 0.665501i | \(0.768218\pi\) | |||||||
\(38\) | 6.05283 | − | 29.8162i | 0.159285 | − | 0.784636i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −39.5676 | − | 27.1190i | −0.989189 | − | 0.677975i | ||||
\(41\) | 21.9026i | 0.534210i | 0.963667 | + | 0.267105i | \(0.0860670\pi\) | ||||
−0.963667 | + | 0.267105i | \(0.913933\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 48.7016 | − | 48.7016i | 1.13260 | − | 1.13260i | 0.142851 | − | 0.989744i | \(-0.454373\pi\) |
0.989744 | − | 0.142851i | \(-0.0456270\pi\) | |||||||
\(44\) | −18.2742 | − | 45.1187i | −0.415324 | − | 1.02543i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 18.2222 | + | 27.5051i | 0.396135 | + | 0.597937i | ||||
\(47\) | − | 70.7760i | − | 1.50587i | −0.658094 | − | 0.752936i | \(-0.728637\pi\) | ||
0.658094 | − | 0.752936i | \(-0.271363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9312 | −0.998597 | ||||||||
\(50\) | 18.2630 | − | 12.0993i | 0.365259 | − | 0.241986i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −33.9684 | − | 83.8672i | −0.653239 | − | 1.61283i | ||||
\(53\) | −52.8193 | − | 52.8193i | −0.996590 | − | 0.996590i | 0.00340427 | − | 0.999994i | \(-0.498916\pi\) |
−0.999994 | + | 0.00340427i | \(0.998916\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 72.9715 | 1.32675 | ||||||||
\(56\) | −2.06218 | + | 0.384952i | −0.0368247 | + | 0.00687415i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 71.9366 | + | 14.6035i | 1.24029 | + | 0.251784i | ||||
\(59\) | −61.7726 | + | 61.7726i | −1.04699 | + | 1.04699i | −0.0481541 | + | 0.998840i | \(0.515334\pi\) |
−0.998840 | + | 0.0481541i | \(0.984666\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −22.9004 | + | 22.9004i | −0.375416 | + | 0.375416i | −0.869445 | − | 0.494029i | \(-0.835524\pi\) |
0.494029 | + | 0.869445i | \(0.335524\pi\) | |||||||
\(62\) | −77.0411 | + | 51.0400i | −1.24260 | + | 0.823226i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 59.6898 | − | 23.0895i | 0.932654 | − | 0.360773i | ||||
\(65\) | 135.640 | 2.08677 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −54.9939 | − | 54.9939i | −0.820804 | − | 0.820804i | 0.165419 | − | 0.986223i | \(-0.447102\pi\) |
−0.986223 | + | 0.165419i | \(0.947102\pi\) | |||||||
\(68\) | 5.48309 | − | 12.9483i | 0.0806337 | − | 0.190416i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.625624 | − | 3.08182i | 0.00893749 | − | 0.0440260i | ||||
\(71\) | 84.2532 | 1.18666 | 0.593332 | − | 0.804958i | \(-0.297812\pi\) | ||||
0.593332 | + | 0.804958i | \(0.297812\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 78.0341i | 1.06896i | 0.845181 | + | 0.534480i | \(0.179493\pi\) | ||||
−0.845181 | + | 0.534480i | \(0.820507\pi\) | |||||||
\(74\) | −1.68426 | + | 8.29663i | −0.0227602 | + | 0.112117i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −56.3983 | + | 22.8428i | −0.742083 | + | 0.300563i | ||||
\(77\) | 2.25653 | − | 2.25653i | 0.0293056 | − | 0.0293056i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59.2887i | 0.750490i | 0.926926 | + | 0.375245i | \(0.122441\pi\) | ||||
−0.926926 | + | 0.375245i | \(0.877559\pi\) | |||||||
\(80\) | −1.50953 | + | 95.9263i | −0.0188691 | + | 1.19908i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 36.5181 | − | 24.1934i | 0.445343 | − | 0.295041i | ||||
\(83\) | 111.661 | + | 111.661i | 1.34531 | + | 1.34531i | 0.890676 | + | 0.454638i | \(0.150231\pi\) |
0.454638 | + | 0.890676i | \(0.349769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.9047 | + | 14.9047i | 0.175350 | + | 0.175350i | ||||
\(86\) | −134.995 | − | 27.4047i | −1.56971 | − | 0.318660i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −55.0407 | + | 80.3063i | −0.625463 | + | 0.912571i | ||||
\(89\) | − | 34.5426i | − | 0.388119i | −0.980990 | − | 0.194060i | \(-0.937834\pi\) | ||
0.980990 | − | 0.194060i | \(-0.0621655\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.19447 | − | 4.19447i | 0.0460931 | − | 0.0460931i | ||||
\(92\) | 25.7311 | − | 60.7637i | 0.279686 | − | 0.660475i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −118.005 | + | 78.1784i | −1.25537 | + | 0.831686i | ||||
\(95\) | − | 91.2142i | − | 0.960150i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −66.0805 | −0.681242 | −0.340621 | − | 0.940201i | \(-0.610637\pi\) | ||||
−0.340621 | + | 0.940201i | \(0.610637\pi\) | |||||||
\(98\) | 54.0490 | + | 81.5829i | 0.551520 | + | 0.832479i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −40.3462 | − | 17.0850i | −0.403462 | − | 0.170850i | ||||
\(101\) | −25.5254 | − | 25.5254i | −0.252727 | − | 0.252727i | 0.569361 | − | 0.822088i | \(-0.307191\pi\) |
−0.822088 | + | 0.569361i | \(0.807191\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.2072 | −0.137934 | −0.0689670 | − | 0.997619i | \(-0.521970\pi\) | ||||
−0.0689670 | + | 0.997619i | \(0.521970\pi\) | |||||||
\(104\) | −102.310 | + | 149.274i | −0.983754 | + | 1.43533i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −29.7218 | + | 146.409i | −0.280394 | + | 1.38122i | ||||
\(107\) | 21.8489 | − | 21.8489i | 0.204195 | − | 0.204195i | −0.597600 | − | 0.801795i | \(-0.703879\pi\) |
0.801795 | + | 0.597600i | \(0.203879\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.8979 | − | 17.8979i | 0.164201 | − | 0.164201i | −0.620224 | − | 0.784425i | \(-0.712958\pi\) |
0.784425 | + | 0.620224i | \(0.212958\pi\) | |||||||
\(110\) | −80.6036 | − | 121.665i | −0.732760 | − | 1.10605i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.91970 | + | 3.01305i | 0.0260687 | + | 0.0269023i | ||||
\(113\) | 174.546 | 1.54465 | 0.772325 | − | 0.635227i | \(-0.219093\pi\) | ||||
0.772325 | + | 0.635227i | \(0.219093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69.9450 | + | 69.9450i | 0.608217 | + | 0.608217i | ||||
\(116\) | −55.1121 | − | 136.070i | −0.475104 | − | 1.17302i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 171.227 | + | 34.7599i | 1.45107 | + | 0.294575i | ||||
\(119\) | 0.921813 | 0.00774632 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 27.1029i | − | 0.223991i | ||||||
\(122\) | 63.4773 | + | 12.8862i | 0.520306 | + | 0.105625i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 170.198 | + | 72.0722i | 1.37256 | + | 0.581227i | ||||
\(125\) | −59.5553 | + | 59.5553i | −0.476442 | + | 0.476442i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 45.3438i | − | 0.357037i | −0.983937 | − | 0.178519i | \(-0.942869\pi\) | ||
0.983937 | − | 0.178519i | \(-0.0571305\pi\) | |||||||
\(128\) | −104.430 | − | 74.0163i | −0.815858 | − | 0.578252i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −149.827 | − | 226.153i | −1.15252 | − | 1.73964i | ||||
\(131\) | −32.6213 | − | 32.6213i | −0.249017 | − | 0.249017i | 0.571550 | − | 0.820567i | \(-0.306342\pi\) |
−0.820567 | + | 0.571550i | \(0.806342\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.82066 | − | 2.82066i | −0.0212080 | − | 0.0212080i | ||||
\(134\) | −30.9454 | + | 152.437i | −0.230936 | + | 1.13759i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −27.6452 | + | 5.16059i | −0.203274 | + | 0.0379455i | ||||
\(137\) | 115.159i | 0.840577i | 0.907390 | + | 0.420289i | \(0.138071\pi\) | ||||
−0.907390 | + | 0.420289i | \(0.861929\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −122.841 | + | 122.841i | −0.883748 | + | 0.883748i | −0.993913 | − | 0.110165i | \(-0.964862\pi\) |
0.110165 | + | 0.993913i | \(0.464862\pi\) | |||||||
\(140\) | −5.82936 | + | 2.36104i | −0.0416383 | + | 0.0168646i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −93.0652 | − | 140.475i | −0.655389 | − | 0.989261i | ||||
\(143\) | − | 275.296i | − | 1.92514i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 220.070 | 1.51772 | ||||||||
\(146\) | 130.106 | − | 86.1957i | 0.891137 | − | 0.590382i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 15.6934 | − | 6.35622i | 0.106036 | − | 0.0429474i | ||||
\(149\) | −99.9710 | − | 99.9710i | −0.670946 | − | 0.670946i | 0.286988 | − | 0.957934i | \(-0.407346\pi\) |
−0.957934 | + | 0.286988i | \(0.907346\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −222.762 | −1.47525 | −0.737623 | − | 0.675212i | \(-0.764052\pi\) | ||||
−0.737623 | + | 0.675212i | \(0.764052\pi\) | |||||||
\(152\) | 100.383 | + | 68.8008i | 0.660413 | + | 0.452637i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.25485 | − | 1.26977i | −0.0406159 | − | 0.00824524i | ||||
\(155\) | −195.914 | + | 195.914i | −1.26396 | + | 1.26396i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 45.9080 | − | 45.9080i | 0.292408 | − | 0.292408i | −0.545623 | − | 0.838031i | \(-0.683707\pi\) |
0.838031 | + | 0.545623i | \(0.183707\pi\) | |||||||
\(158\) | 98.8519 | − | 65.4898i | 0.625645 | − | 0.414492i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 161.605 | − | 103.442i | 1.01003 | − | 0.646515i | ||||
\(161\) | 4.32588 | 0.0268689 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 37.3289 | + | 37.3289i | 0.229012 | + | 0.229012i | 0.812280 | − | 0.583268i | \(-0.198226\pi\) |
−0.583268 | + | 0.812280i | \(0.698226\pi\) | |||||||
\(164\) | −80.6752 | − | 34.1628i | −0.491922 | − | 0.208310i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 62.8325 | − | 309.512i | 0.378509 | − | 1.86453i | ||||
\(167\) | 71.6232 | 0.428882 | 0.214441 | − | 0.976737i | \(-0.431207\pi\) | ||||
0.214441 | + | 0.976737i | \(0.431207\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 342.723i | − | 2.02795i | ||||||
\(170\) | 8.38700 | − | 41.3142i | 0.0493353 | − | 0.243025i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 103.423 | + | 255.348i | 0.601295 | + | 1.48458i | ||||
\(173\) | −100.398 | + | 100.398i | −0.580334 | + | 0.580334i | −0.934995 | − | 0.354661i | \(-0.884596\pi\) |
0.354661 | + | 0.934995i | \(0.384596\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.87232i | − | 0.0164133i | ||||||
\(176\) | 194.692 | + | 3.06373i | 1.10620 | + | 0.0174076i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −57.5928 | + | 38.1554i | −0.323555 | + | 0.214356i | ||||
\(179\) | 64.4199 | + | 64.4199i | 0.359888 | + | 0.359888i | 0.863771 | − | 0.503884i | \(-0.168096\pi\) |
−0.503884 | + | 0.863771i | \(0.668096\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −79.0033 | − | 79.0033i | −0.436482 | − | 0.436482i | 0.454344 | − | 0.890826i | \(-0.349874\pi\) |
−0.890826 | + | 0.454344i | \(0.849874\pi\) | |||||||
\(182\) | −11.6266 | − | 2.36026i | −0.0638824 | − | 0.0129685i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −129.733 | + | 24.2177i | −0.705073 | + | 0.131618i | ||||
\(185\) | 25.3812i | 0.137196i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 30.2506 | − | 30.2506i | 0.161768 | − | 0.161768i | ||||
\(188\) | 260.693 | + | 110.394i | 1.38667 | + | 0.587200i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −152.081 | + | 100.754i | −0.800427 | + | 0.530286i | ||||
\(191\) | 304.422i | 1.59383i | 0.604089 | + | 0.796917i | \(0.293537\pi\) | ||||
−0.604089 | + | 0.796917i | \(0.706463\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 253.689 | 1.31445 | 0.657225 | − | 0.753695i | \(-0.271730\pi\) | ||||
0.657225 | + | 0.753695i | \(0.271730\pi\) | |||||||
\(194\) | 72.9919 | + | 110.176i | 0.376247 | + | 0.567917i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 76.3210 | − | 180.231i | 0.389393 | − | 0.919548i | ||||
\(197\) | −89.4218 | − | 89.4218i | −0.453918 | − | 0.453918i | 0.442735 | − | 0.896653i | \(-0.354008\pi\) |
−0.896653 | + | 0.442735i | \(0.854008\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 117.278 | 0.589339 | 0.294670 | − | 0.955599i | \(-0.404790\pi\) | ||||
0.294670 | + | 0.955599i | \(0.404790\pi\) | |||||||
\(200\) | 16.0802 | + | 86.1411i | 0.0804008 | + | 0.430705i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −14.3633 | + | 70.7536i | −0.0711056 | + | 0.350265i | ||||
\(203\) | 6.80533 | − | 6.80533i | 0.0335238 | − | 0.0335238i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 92.8650 | − | 92.8650i | 0.453000 | − | 0.453000i | ||||
\(206\) | 15.6931 | + | 23.6876i | 0.0761802 | + | 0.114988i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 361.896 | + | 5.69491i | 1.73988 | + | 0.0273794i | ||||
\(209\) | −185.128 | −0.885781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −80.8941 | − | 80.8941i | −0.383384 | − | 0.383384i | 0.488936 | − | 0.872320i | \(-0.337385\pi\) |
−0.872320 | + | 0.488936i | \(0.837385\pi\) | |||||||
\(212\) | 276.938 | − | 112.167i | 1.30631 | − | 0.529090i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −60.5626 | − | 12.2945i | −0.283003 | − | 0.0574510i | ||||
\(215\) | −412.981 | −1.92084 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 12.1167i | 0.0558373i | ||||||||
\(218\) | −49.6109 | − | 10.0713i | −0.227573 | − | 0.0461984i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −113.818 | + | 268.780i | −0.517355 | + | 1.22173i | ||||
\(221\) | 56.2303 | − | 56.2303i | 0.254436 | − | 0.254436i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 263.109i | 1.17986i | 0.807453 | + | 0.589931i | \(0.200845\pi\) | ||||
−0.807453 | + | 0.589931i | \(0.799155\pi\) | |||||||
\(224\) | 1.79859 | − | 8.19619i | 0.00802943 | − | 0.0365901i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −192.801 | − | 291.019i | −0.853103 | − | 1.28770i | ||||
\(227\) | −112.085 | − | 112.085i | −0.493765 | − | 0.493765i | 0.415725 | − | 0.909490i | \(-0.363528\pi\) |
−0.909490 | + | 0.415725i | \(0.863528\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 100.869 | + | 100.869i | 0.440477 | + | 0.440477i | 0.892172 | − | 0.451695i | \(-0.149180\pi\) |
−0.451695 | + | 0.892172i | \(0.649180\pi\) | |||||||
\(230\) | 39.3585 | − | 193.880i | 0.171124 | − | 0.842955i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −165.994 | + | 242.190i | −0.715490 | + | 1.04392i | ||||
\(233\) | − | 325.669i | − | 1.39772i | −0.715259 | − | 0.698860i | \(-0.753691\pi\) | ||
0.715259 | − | 0.698860i | \(-0.246309\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −300.084 | + | 300.084i | −1.27695 | + | 1.27695i | ||||
\(236\) | −131.180 | − | 323.881i | −0.555849 | − | 1.37238i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.01823 | − | 1.53694i | −0.00427826 | − | 0.00645771i | ||||
\(239\) | 25.2269i | 0.105552i | 0.998606 | + | 0.0527760i | \(0.0168069\pi\) | ||||
−0.998606 | + | 0.0527760i | \(0.983193\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −305.987 | −1.26966 | −0.634828 | − | 0.772653i | \(-0.718929\pi\) | ||||
−0.634828 | + | 0.772653i | \(0.718929\pi\) | |||||||
\(242\) | −45.1885 | + | 29.9376i | −0.186730 | + | 0.123709i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −48.6313 | − | 120.070i | −0.199309 | − | 0.492088i | ||||
\(245\) | 207.464 | + | 207.464i | 0.846792 | + | 0.846792i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −344.119 | −1.39319 | ||||||||
\(248\) | −67.8331 | − | 363.381i | −0.273521 | − | 1.46524i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 165.081 | + | 33.5122i | 0.660322 | + | 0.134049i | ||||
\(251\) | 99.5293 | − | 99.5293i | 0.396531 | − | 0.396531i | −0.480476 | − | 0.877008i | \(-0.659536\pi\) |
0.877008 | + | 0.480476i | \(0.159536\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 141.960 | − | 141.960i | 0.561108 | − | 0.561108i | ||||
\(254\) | −75.6015 | + | 50.0863i | −0.297644 | + | 0.197190i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.05500 | + | 255.873i | −0.0314648 | + | 0.999505i | ||||
\(257\) | −265.635 | −1.03360 | −0.516799 | − | 0.856107i | \(-0.672876\pi\) | ||||
−0.516799 | + | 0.856107i | \(0.672876\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.784876 | + | 0.784876i | 0.00303041 | + | 0.00303041i | ||||
\(260\) | −211.566 | + | 499.612i | −0.813717 | + | 1.92159i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −18.3562 | + | 90.4225i | −0.0700619 | + | 0.345124i | ||||
\(263\) | 206.692 | 0.785901 | 0.392950 | − | 0.919560i | \(-0.371454\pi\) | ||||
0.392950 | + | 0.919560i | \(0.371454\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 447.898i | 1.69018i | ||||||||
\(266\) | −1.58721 | + | 7.81856i | −0.00596694 | + | 0.0293931i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 288.340 | − | 116.785i | 1.07589 | − | 0.435765i | ||||
\(269\) | 8.03470 | − | 8.03470i | 0.0298688 | − | 0.0298688i | −0.692015 | − | 0.721883i | \(-0.743277\pi\) |
0.721883 | + | 0.692015i | \(0.243277\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 216.666i | 0.799507i | 0.916623 | + | 0.399754i | \(0.130904\pi\) | ||||
−0.916623 | + | 0.399754i | \(0.869096\pi\) | |||||||
\(272\) | 39.1409 | + | 40.3924i | 0.143900 | + | 0.148502i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 192.004 | − | 127.204i | 0.700746 | − | 0.464247i | ||||
\(275\) | −94.2595 | − | 94.2595i | −0.342762 | − | 0.342762i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 65.0909 | + | 65.0909i | 0.234985 | + | 0.234985i | 0.814770 | − | 0.579785i | \(-0.196863\pi\) |
−0.579785 | + | 0.814770i | \(0.696863\pi\) | |||||||
\(278\) | 340.502 | + | 69.1235i | 1.22483 | + | 0.248646i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 10.3756 | + | 7.11130i | 0.0370558 | + | 0.0253975i | ||||
\(281\) | 403.952i | 1.43755i | 0.695242 | + | 0.718776i | \(0.255297\pi\) | ||||
−0.695242 | + | 0.718776i | \(0.744703\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 245.705 | − | 245.705i | 0.868214 | − | 0.868214i | −0.124061 | − | 0.992275i | \(-0.539592\pi\) |
0.992275 | + | 0.124061i | \(0.0395917\pi\) | |||||||
\(284\) | −131.415 | + | 310.335i | −0.462728 | + | 1.09273i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −458.999 | + | 304.089i | −1.60489 | + | 1.06325i | ||||
\(287\) | − | 5.74342i | − | 0.0200119i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −276.642 | −0.957240 | ||||||||
\(290\) | −243.087 | − | 366.922i | −0.838231 | − | 1.26525i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −287.428 | − | 121.715i | −0.984342 | − | 0.416831i | ||||
\(293\) | 67.6849 | + | 67.6849i | 0.231007 | + | 0.231007i | 0.813113 | − | 0.582106i | \(-0.197771\pi\) |
−0.582106 | + | 0.813113i | \(0.697771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 523.821 | 1.77566 | ||||||||
\(296\) | −27.9324 | − | 19.1445i | −0.0943664 | − | 0.0646773i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −56.2544 | + | 277.108i | −0.188773 | + | 0.929894i | ||||
\(299\) | 263.878 | − | 263.878i | 0.882534 | − | 0.882534i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.7708 | + | 12.7708i | −0.0424279 | + | 0.0424279i | ||||
\(302\) | 246.061 | + | 371.411i | 0.814772 | + | 1.22984i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.82966 | − | 243.365i | 0.0125976 | − | 0.800541i | ||||
\(305\) | 194.191 | 0.636692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.98162 | − | 4.98162i | −0.0162268 | − | 0.0162268i | 0.698947 | − | 0.715174i | \(-0.253652\pi\) |
−0.715174 | + | 0.698947i | \(0.753652\pi\) | |||||||
\(308\) | 4.79197 | + | 11.8313i | 0.0155584 | + | 0.0384132i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 543.052 | + | 110.242i | 1.75178 | + | 0.355620i | ||||
\(311\) | 380.390 | 1.22312 | 0.611560 | − | 0.791198i | \(-0.290542\pi\) | ||||
0.611560 | + | 0.791198i | \(0.290542\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 145.761i | − | 0.465691i | −0.972514 | − | 0.232845i | \(-0.925196\pi\) | ||
0.972514 | − | 0.232845i | \(-0.0748036\pi\) | |||||||
\(314\) | −127.252 | − | 25.8328i | −0.405261 | − | 0.0822699i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −218.382 | − | 92.4762i | −0.691082 | − | 0.292646i | ||||
\(317\) | 283.175 | − | 283.175i | 0.893295 | − | 0.893295i | −0.101537 | − | 0.994832i | \(-0.532376\pi\) |
0.994832 | + | 0.101537i | \(0.0323759\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 446.654i | − | 1.40017i | ||||||
\(320\) | −350.977 | − | 155.182i | −1.09680 | − | 0.484944i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.77833 | − | 7.21254i | −0.0148395 | − | 0.0223992i | ||||
\(323\) | −37.8132 | − | 37.8132i | −0.117069 | − | 0.117069i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −175.211 | − | 175.211i | −0.539110 | − | 0.539110i | ||||
\(326\) | 21.0052 | − | 103.472i | 0.0644333 | − | 0.317397i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 32.1535 | + | 172.245i | 0.0980288 | + | 0.525139i | ||||
\(329\) | 18.5593i | 0.0564111i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 105.963 | − | 105.963i | 0.320131 | − | 0.320131i | −0.528687 | − | 0.848817i | \(-0.677315\pi\) |
0.848817 | + | 0.528687i | \(0.177315\pi\) | |||||||
\(332\) | −585.453 | + | 237.124i | −1.76341 | + | 0.714227i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −79.1143 | − | 119.417i | −0.236869 | − | 0.357537i | ||||
\(335\) | 466.338i | 1.39205i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 249.581 | 0.740595 | 0.370298 | − | 0.928913i | \(-0.379256\pi\) | ||||
0.370298 | + | 0.928913i | \(0.379256\pi\) | |||||||
\(338\) | −571.421 | + | 378.568i | −1.69059 | + | 1.12002i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −78.1473 | + | 31.6517i | −0.229845 | + | 0.0930932i | ||||
\(341\) | 397.627 | + | 397.627i | 1.16606 | + | 1.16606i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 25.6801 | 0.0748690 | ||||||||
\(344\) | 311.502 | − | 454.492i | 0.905529 | − | 1.32120i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 278.291 | + | 56.4945i | 0.804310 | + | 0.163279i | ||||
\(347\) | 297.586 | − | 297.586i | 0.857597 | − | 0.857597i | −0.133458 | − | 0.991054i | \(-0.542608\pi\) |
0.991054 | + | 0.133458i | \(0.0426081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −288.797 | + | 288.797i | −0.827498 | + | 0.827498i | −0.987170 | − | 0.159672i | \(-0.948956\pi\) |
0.159672 | + | 0.987170i | \(0.448956\pi\) | |||||||
\(350\) | −4.78901 | + | 3.17274i | −0.0136829 | + | 0.00906497i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −209.947 | − | 327.994i | −0.596439 | − | 0.931800i | ||||
\(353\) | −255.362 | −0.723404 | −0.361702 | − | 0.932294i | \(-0.617804\pi\) | ||||
−0.361702 | + | 0.932294i | \(0.617804\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −357.226 | − | 357.226i | −1.00627 | − | 1.00627i | ||||
\(356\) | 127.233 | + | 53.8782i | 0.357396 | + | 0.151343i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 36.2495 | − | 178.565i | 0.101256 | − | 0.498784i | ||||
\(359\) | −381.798 | −1.06350 | −0.531752 | − | 0.846900i | \(-0.678466\pi\) | ||||
−0.531752 | + | 0.846900i | \(0.678466\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 129.590i | − | 0.358975i | ||||||
\(362\) | −44.4557 | + | 218.988i | −0.122806 | + | 0.604940i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.90738 | + | 21.9921i | 0.0244708 | + | 0.0604179i | ||||
\(365\) | 330.857 | − | 330.857i | 0.906459 | − | 0.906459i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.6026i | 0.0506884i | 0.999679 | + | 0.0253442i | \(0.00806817\pi\) | ||||
−0.999679 | + | 0.0253442i | \(0.991932\pi\) | |||||||
\(368\) | 183.680 | + | 189.554i | 0.499131 | + | 0.515092i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 42.3180 | − | 28.0358i | 0.114373 | − | 0.0757726i | ||||
\(371\) | 13.8506 | + | 13.8506i | 0.0373330 | + | 0.0373330i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 150.079 | + | 150.079i | 0.402357 | + | 0.402357i | 0.879063 | − | 0.476706i | \(-0.158169\pi\) |
−0.476706 | + | 0.879063i | \(0.658169\pi\) | |||||||
\(374\) | −83.8514 | − | 17.0222i | −0.224202 | − | 0.0455140i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −103.901 | − | 556.593i | −0.276331 | − | 1.48030i | ||||
\(377\) | − | 830.245i | − | 2.20224i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 379.359 | − | 379.359i | 1.00095 | − | 1.00095i | 0.000948851 | − | 1.00000i | \(-0.499698\pi\) |
1.00000 | 0.000948851i | \(-0.000302029\pi\) | ||||||||
\(380\) | 335.975 | + | 142.272i | 0.884144 | + | 0.374401i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 507.562 | − | 336.262i | 1.32870 | − | 0.880267i | ||||
\(383\) | 427.421i | 1.11598i | 0.829847 | + | 0.557991i | \(0.188428\pi\) | ||||
−0.829847 | + | 0.557991i | \(0.811572\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −19.1350 | −0.0497012 | ||||||||
\(386\) | −280.222 | − | 422.975i | −0.725964 | − | 1.09579i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 103.070 | − | 243.398i | 0.265644 | − | 0.627315i | ||||
\(389\) | 236.247 | + | 236.247i | 0.607318 | + | 0.607318i | 0.942244 | − | 0.334926i | \(-0.108711\pi\) |
−0.334926 | + | 0.942244i | \(0.608711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 57.9920 | 0.148317 | ||||||||
\(392\) | −384.803 | + | 71.8320i | −0.981640 | + | 0.183245i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −50.3183 | + | 247.867i | −0.127711 | + | 0.629105i | ||||
\(395\) | 251.379 | − | 251.379i | 0.636402 | − | 0.636402i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −427.593 | + | 427.593i | −1.07706 | + | 1.07706i | −0.0802895 | + | 0.996772i | \(0.525584\pi\) |
−0.996772 | + | 0.0802895i | \(0.974416\pi\) | |||||||
\(398\) | −129.545 | − | 195.538i | −0.325489 | − | 0.491302i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 125.861 | − | 121.961i | 0.314652 | − | 0.304902i | ||||
\(401\) | −638.396 | −1.59201 | −0.796005 | − | 0.605290i | \(-0.793057\pi\) | ||||
−0.796005 | + | 0.605290i | \(0.793057\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 739.115 | + | 739.115i | 1.83403 | + | 1.83403i | ||||
\(404\) | 133.833 | − | 54.2058i | 0.331270 | − | 0.134173i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −18.8636 | − | 3.82940i | −0.0464621 | − | 0.00943203i | ||||
\(407\) | 51.5137 | 0.126569 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 273.582i | 0.668905i | 0.942413 | + | 0.334453i | \(0.108551\pi\) | ||||
−0.942413 | + | 0.334453i | \(0.891449\pi\) | |||||||
\(410\) | −257.411 | − | 52.2558i | −0.627833 | − | 0.127453i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 22.1598 | − | 52.3302i | 0.0537860 | − | 0.127015i | ||||
\(413\) | 16.1984 | − | 16.1984i | 0.0392212 | − | 0.0392212i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 946.865i | − | 2.28160i | ||||||
\(416\) | −390.252 | − | 609.679i | −0.938105 | − | 1.46557i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 204.491 | + | 308.664i | 0.489213 | + | 0.738430i | ||||
\(419\) | −150.314 | − | 150.314i | −0.358745 | − | 0.358745i | 0.504606 | − | 0.863350i | \(-0.331638\pi\) |
−0.863350 | + | 0.504606i | \(0.831638\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −220.826 | − | 220.826i | −0.524527 | − | 0.524527i | 0.394408 | − | 0.918935i | \(-0.370950\pi\) |
−0.918935 | + | 0.394408i | \(0.870950\pi\) | |||||||
\(422\) | −45.5196 | + | 224.229i | −0.107866 | + | 0.531349i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −492.919 | − | 337.839i | −1.16254 | − | 0.796790i | ||||
\(425\) | − | 38.5058i | − | 0.0906018i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.00507 | − | 6.00507i | 0.0140634 | − | 0.0140634i | ||||
\(428\) | 46.3983 | + | 114.556i | 0.108407 | + | 0.267655i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 456.174 | + | 688.561i | 1.06087 | + | 1.60131i | ||||
\(431\) | 463.722i | 1.07592i | 0.842970 | + | 0.537960i | \(0.180805\pi\) | ||||
−0.842970 | + | 0.537960i | \(0.819195\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −310.114 | −0.716199 | −0.358099 | − | 0.933683i | \(-0.616575\pi\) | ||||
−0.358099 | + | 0.933683i | \(0.616575\pi\) | |||||||
\(434\) | 20.2021 | − | 13.3840i | 0.0465487 | − | 0.0308387i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 38.0079 | + | 93.8407i | 0.0871741 | + | 0.215231i | ||||
\(437\) | −177.450 | − | 177.450i | −0.406064 | − | 0.406064i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 89.9103 | 0.204807 | 0.102404 | − | 0.994743i | \(-0.467347\pi\) | ||||
0.102404 | + | 0.994743i | \(0.467347\pi\) | |||||||
\(440\) | 573.859 | − | 107.124i | 1.30422 | − | 0.243463i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −155.864 | − | 31.6412i | −0.352633 | − | 0.0715864i | ||||
\(443\) | 78.9267 | − | 78.9267i | 0.178164 | − | 0.178164i | −0.612391 | − | 0.790555i | \(-0.709792\pi\) |
0.790555 | + | 0.612391i | \(0.209792\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −146.458 | + | 146.458i | −0.329118 | + | 0.329118i | ||||
\(446\) | 438.682 | − | 290.628i | 0.983591 | − | 0.651632i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −15.6522 | + | 6.05465i | −0.0349379 | + | 0.0135148i | ||||
\(449\) | −187.048 | −0.416587 | −0.208294 | − | 0.978066i | \(-0.566791\pi\) | ||||
−0.208294 | + | 0.978066i | \(0.566791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −188.479 | − | 188.479i | −0.417913 | − | 0.417913i | ||||
\(452\) | −272.249 | + | 642.914i | −0.602321 | + | 1.42238i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −63.0709 | + | 310.686i | −0.138923 | + | 0.684331i | ||||
\(455\) | −35.5683 | −0.0781722 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 153.318i | 0.335489i | 0.985831 | + | 0.167744i | \(0.0536483\pi\) | ||||
−0.985831 | + | 0.167744i | \(0.946352\pi\) | |||||||
\(458\) | 56.7599 | − | 279.598i | 0.123930 | − | 0.610477i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −366.730 | + | 148.535i | −0.797239 | + | 0.322903i | ||||
\(461\) | −99.6025 | + | 99.6025i | −0.216057 | + | 0.216057i | −0.806835 | − | 0.590777i | \(-0.798821\pi\) |
0.590777 | + | 0.806835i | \(0.298821\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 255.682i | 0.552229i | 0.961125 | + | 0.276114i | \(0.0890469\pi\) | ||||
−0.961125 | + | 0.276114i | \(0.910953\pi\) | |||||||
\(464\) | 587.158 | + | 9.23971i | 1.26543 | + | 0.0199132i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −542.986 | + | 359.730i | −1.16521 | + | 0.771954i | ||||
\(467\) | −285.533 | − | 285.533i | −0.611420 | − | 0.611420i | 0.331896 | − | 0.943316i | \(-0.392312\pi\) |
−0.943316 | + | 0.331896i | \(0.892312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.4208 | + | 14.4208i | 0.0307480 | + | 0.0307480i | ||||
\(470\) | 831.798 | + | 168.859i | 1.76978 | + | 0.359275i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −395.106 | + | 576.473i | −0.837089 | + | 1.22134i | ||||
\(473\) | 838.185i | 1.77206i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −117.824 | + | 117.824i | −0.248051 | + | 0.248051i | ||||
\(476\) | −1.43781 | + | 3.39537i | −0.00302060 | + | 0.00713313i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 42.0608 | − | 27.8654i | 0.0879933 | − | 0.0582959i | ||||
\(479\) | − | 418.575i | − | 0.873852i | −0.899498 | − | 0.436926i | \(-0.856067\pi\) | ||
0.899498 | − | 0.436926i | \(-0.143933\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 95.7543 | 0.199073 | ||||||||
\(482\) | 337.991 | + | 510.172i | 0.701225 | + | 1.05845i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 99.8297 | + | 42.2740i | 0.206260 | + | 0.0873430i | ||||
\(485\) | 280.175 | + | 280.175i | 0.577681 | + | 0.577681i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −162.560 | −0.333800 | −0.166900 | − | 0.985974i | \(-0.553376\pi\) | ||||
−0.166900 | + | 0.985974i | \(0.553376\pi\) | |||||||
\(488\) | −146.474 | + | 213.711i | −0.300152 | + | 0.437931i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 116.741 | − | 575.067i | 0.238248 | − | 1.17361i | ||||
\(491\) | −559.393 | + | 559.393i | −1.13929 | + | 1.13929i | −0.150715 | + | 0.988577i | \(0.548158\pi\) |
−0.988577 | + | 0.150715i | \(0.951842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 91.2309 | − | 91.2309i | 0.185052 | − | 0.185052i | ||||
\(494\) | 380.110 | + | 573.748i | 0.769454 | + | 1.16143i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −530.936 | + | 514.485i | −1.07043 | + | 1.03727i | ||||
\(497\) | −22.0933 | −0.0444534 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 247.957 | + | 247.957i | 0.496908 | + | 0.496908i | 0.910474 | − | 0.413566i | \(-0.135717\pi\) |
−0.413566 | + | 0.910474i | \(0.635717\pi\) | |||||||
\(500\) | −126.472 | − | 312.256i | −0.252943 | − | 0.624511i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −275.884 | − | 56.0059i | −0.549570 | − | 0.111565i | ||||
\(503\) | −260.971 | −0.518829 | −0.259415 | − | 0.965766i | \(-0.583530\pi\) | ||||
−0.259415 | + | 0.965766i | \(0.583530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 216.451i | 0.428616i | ||||||||
\(506\) | −393.498 | − | 79.8820i | −0.777664 | − | 0.157870i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 167.017 | + | 70.7254i | 0.328774 | + | 0.139223i | ||||
\(509\) | −149.941 | + | 149.941i | −0.294580 | + | 0.294580i | −0.838886 | − | 0.544306i | \(-0.816793\pi\) |
0.544306 | + | 0.838886i | \(0.316793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 20.4625i | − | 0.0400441i | ||||||
\(512\) | 435.514 | − | 269.205i | 0.850614 | − | 0.525791i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 293.417 | + | 442.892i | 0.570851 | + | 0.861657i | ||||
\(515\) | 60.2372 | + | 60.2372i | 0.116965 | + | 0.116965i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 609.049 | + | 609.049i | 1.17805 | + | 1.17805i | ||||
\(518\) | 0.441655 | − | 2.17559i | 0.000852616 | − | 0.00419998i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1066.70 | − | 199.123i | 2.05134 | − | 0.382928i | ||||
\(521\) | 391.686i | 0.751797i | 0.926661 | + | 0.375899i | \(0.122666\pi\) | ||||
−0.926661 | + | 0.375899i | \(0.877334\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −128.962 | + | 128.962i | −0.246582 | + | 0.246582i | −0.819566 | − | 0.572985i | \(-0.805786\pi\) |
0.572985 | + | 0.819566i | \(0.305786\pi\) | |||||||
\(524\) | 171.037 | − | 69.2745i | 0.326407 | − | 0.132203i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −228.310 | − | 344.617i | −0.434049 | − | 0.655165i | ||||
\(527\) | 162.434i | 0.308224i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −256.855 | −0.485548 | ||||||||
\(530\) | 746.779 | − | 494.743i | 1.40902 | − | 0.933478i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 14.7891 | − | 5.98996i | 0.0277990 | − | 0.0112593i | ||||
\(533\) | −350.347 | − | 350.347i | −0.657311 | − | 0.657311i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −185.274 | −0.346307 | ||||||||
\(536\) | −513.212 | − | 351.748i | −0.957486 | − | 0.656247i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −22.2713 | − | 4.52118i | −0.0413965 | − | 0.00840369i | ||||
\(539\) | 421.069 | − | 421.069i | 0.781204 | − | 0.781204i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 71.0166 | − | 71.0166i | 0.131269 | − | 0.131269i | −0.638420 | − | 0.769689i | \(-0.720411\pi\) |
0.769689 | + | 0.638420i | \(0.220411\pi\) | |||||||
\(542\) | 361.247 | − | 239.328i | 0.666508 | − | 0.441564i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 24.1116 | − | 109.877i | 0.0443227 | − | 0.201979i | ||||
\(545\) | −151.771 | −0.278478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −672.846 | − | 672.846i | −1.23007 | − | 1.23007i | −0.963938 | − | 0.266128i | \(-0.914255\pi\) |
−0.266128 | − | 0.963938i | \(-0.585745\pi\) | |||||||
\(548\) | −424.172 | − | 179.621i | −0.774037 | − | 0.327775i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −53.0405 | + | 261.277i | −0.0964372 | + | 0.475048i | ||||
\(551\) | −558.316 | −1.01328 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 15.5470i | − | 0.0281140i | ||||||
\(554\) | 36.6271 | − | 180.425i | 0.0661139 | − | 0.325676i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −260.865 | − | 644.070i | −0.469182 | − | 1.15840i | ||||
\(557\) | −294.546 | + | 294.546i | −0.528809 | + | 0.528809i | −0.920217 | − | 0.391408i | \(-0.871988\pi\) |
0.391408 | + | 0.920217i | \(0.371988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1558.03i | 2.78717i | ||||||||
\(560\) | 0.395836 | − | 25.1543i | 0.000706850 | − | 0.0449184i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 673.508 | − | 446.201i | 1.19841 | − | 0.793953i | ||||
\(563\) | −613.943 | − | 613.943i | −1.09048 | − | 1.09048i | −0.995477 | − | 0.0950080i | \(-0.969712\pi\) |
−0.0950080 | − | 0.995477i | \(-0.530288\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −740.057 | − | 740.057i | −1.30984 | − | 1.30984i | ||||
\(566\) | −681.065 | − | 138.260i | −1.20330 | − | 0.244275i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 662.580 | − | 123.685i | 1.16651 | − | 0.217756i | ||||
\(569\) | − | 1044.74i | − | 1.83610i | −0.396460 | − | 0.918052i | \(-0.629761\pi\) | ||
0.396460 | − | 0.918052i | \(-0.370239\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 131.781 | − | 131.781i | 0.230789 | − | 0.230789i | −0.582233 | − | 0.813022i | \(-0.697821\pi\) |
0.813022 | + | 0.582233i | \(0.197821\pi\) | |||||||
\(572\) | 1014.01 | + | 429.395i | 1.77275 | + | 0.750691i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −9.57599 | + | 6.34413i | −0.0166829 | + | 0.0110525i | ||||
\(575\) | − | 180.700i | − | 0.314261i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −114.453 | −0.198359 | −0.0991794 | − | 0.995070i | \(-0.531622\pi\) | ||||
−0.0991794 | + | 0.995070i | \(0.531622\pi\) | |||||||
\(578\) | 305.576 | + | 461.245i | 0.528679 | + | 0.798002i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −343.256 | + | 810.596i | −0.591821 | + | 1.39758i | ||||
\(581\) | −29.2804 | − | 29.2804i | −0.0503965 | − | 0.0503965i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 909.053 | 1.55927 | ||||||||
\(584\) | 114.556 | + | 613.672i | 0.196157 | + | 1.05081i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 38.0868 | − | 187.615i | 0.0649945 | − | 0.320162i | ||||
\(587\) | −308.249 | + | 308.249i | −0.525125 | + | 0.525125i | −0.919115 | − | 0.393990i | \(-0.871095\pi\) |
0.393990 | + | 0.919115i | \(0.371095\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 497.034 | − | 497.034i | 0.843860 | − | 0.843860i | ||||
\(590\) | −578.607 | − | 873.365i | −0.980690 | − | 1.48028i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.06564 | + | 67.7185i | −0.00180007 | + | 0.114389i | ||||
\(593\) | −646.173 | −1.08967 | −0.544834 | − | 0.838544i | \(-0.683407\pi\) | ||||
−0.544834 | + | 0.838544i | \(0.683407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.90840 | − | 3.90840i | −0.00656874 | − | 0.00656874i | ||||
\(596\) | 524.160 | − | 212.298i | 0.879463 | − | 0.356205i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −731.439 | − | 148.486i | −1.22314 | − | 0.248304i | ||||
\(599\) | 528.055 | 0.881561 | 0.440780 | − | 0.897615i | \(-0.354702\pi\) | ||||
0.440780 | + | 0.897615i | \(0.354702\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 280.764i | − | 0.467161i | −0.972338 | − | 0.233580i | \(-0.924956\pi\) | ||
0.972338 | − | 0.233580i | \(-0.0750442\pi\) | |||||||
\(602\) | 35.3992 | + | 7.18622i | 0.0588027 | + | 0.0119372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 347.456 | − | 820.514i | 0.575258 | − | 1.35847i | ||||
\(605\) | −114.914 | + | 114.914i | −0.189940 | + | 0.189940i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 662.871i | − | 1.09204i | −0.837771 | − | 0.546022i | \(-0.816141\pi\) | ||
0.837771 | − | 0.546022i | \(-0.183859\pi\) | |||||||
\(608\) | −409.991 | + | 262.433i | −0.674328 | + | 0.431633i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −214.502 | − | 323.774i | −0.351642 | − | 0.530778i | ||||
\(611\) | 1132.11 | + | 1132.11i | 1.85288 | + | 1.85288i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 128.389 | + | 128.389i | 0.209443 | + | 0.209443i | 0.804031 | − | 0.594588i | \(-0.202685\pi\) |
−0.594588 | + | 0.804031i | \(0.702685\pi\) | |||||||
\(614\) | −2.80319 | + | 13.8085i | −0.00456546 | + | 0.0224894i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 14.4331 | − | 21.0584i | 0.0234303 | − | 0.0341856i | ||||
\(617\) | − | 20.8646i | − | 0.0338162i | −0.999857 | − | 0.0169081i | \(-0.994618\pi\) | ||
0.999857 | − | 0.0169081i | \(-0.00538228\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −472.367 | + | 472.367i | −0.763113 | + | 0.763113i | −0.976884 | − | 0.213771i | \(-0.931425\pi\) |
0.213771 | + | 0.976884i | \(0.431425\pi\) | |||||||
\(620\) | −416.044 | − | 1027.20i | −0.671038 | − | 1.65678i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −420.175 | − | 634.224i | −0.675523 | − | 1.01965i | ||||
\(623\) | 9.05795i | 0.0145393i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 778.859 | 1.24617 | ||||||||
\(626\) | −243.027 | + | 161.006i | −0.388222 | + | 0.257199i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 97.4903 | + | 240.701i | 0.155239 | + | 0.383282i | ||||
\(629\) | 10.5219 | + | 10.5219i | 0.0167280 | + | 0.0167280i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −906.653 | −1.43685 | −0.718426 | − | 0.695604i | \(-0.755137\pi\) | ||||
−0.718426 | + | 0.695604i | \(0.755137\pi\) | |||||||
\(632\) | 87.0370 | + | 466.256i | 0.137717 | + | 0.737746i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −784.928 | − | 159.344i | −1.23806 | − | 0.251332i | ||||
\(635\) | −192.253 | + | 192.253i | −0.302761 | + | 0.302761i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 782.688 | − | 782.688i | 1.22871 | − | 1.22871i | ||||
\(638\) | −744.704 | + | 493.369i | −1.16725 | + | 0.773306i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 128.951 | + | 756.595i | 0.201485 | + | 1.18218i | ||||
\(641\) | 1125.11 | 1.75524 | 0.877622 | − | 0.479353i | \(-0.159129\pi\) | ||||
0.877622 | + | 0.479353i | \(0.159129\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −607.794 | − | 607.794i | −0.945247 | − | 0.945247i | 0.0533302 | − | 0.998577i | \(-0.483016\pi\) |
−0.998577 | + | 0.0533302i | \(0.983016\pi\) | |||||||
\(644\) | −6.74734 | + | 15.9338i | −0.0104772 | + | 0.0247419i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −21.2778 | + | 104.814i | −0.0329377 | + | 0.162251i | ||||
\(647\) | −383.377 | −0.592545 | −0.296273 | − | 0.955103i | \(-0.595744\pi\) | ||||
−0.296273 | + | 0.955103i | \(0.595744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1063.15i | − | 1.63813i | ||||||
\(650\) | −98.5923 | + | 485.664i | −0.151680 | + | 0.747176i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −195.720 | + | 79.2717i | −0.300184 | + | 0.121582i | ||||
\(653\) | 755.121 | − | 755.121i | 1.15639 | − | 1.15639i | 0.171141 | − | 0.985246i | \(-0.445254\pi\) |
0.985246 | − | 0.171141i | \(-0.0547455\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 276.622i | 0.422324i | ||||||||
\(656\) | 251.668 | − | 243.870i | 0.383640 | − | 0.371753i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.9438 | − | 20.5004i | 0.0470271 | − | 0.0311556i | ||||
\(659\) | 31.8233 | + | 31.8233i | 0.0482902 | + | 0.0482902i | 0.730840 | − | 0.682549i | \(-0.239129\pi\) |
−0.682549 | + | 0.730840i | \(0.739129\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 579.890 | + | 579.890i | 0.877292 | + | 0.877292i | 0.993254 | − | 0.115961i | \(-0.0369949\pi\) |
−0.115961 | + | 0.993254i | \(0.536995\pi\) | |||||||
\(662\) | −293.718 | − | 59.6263i | −0.443683 | − | 0.0900699i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1042.04 | + | 714.199i | 1.56934 | + | 1.07560i | ||||
\(665\) | 23.9187i | 0.0359680i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 428.129 | − | 428.129i | 0.641872 | − | 0.641872i | ||||
\(668\) | −111.715 | + | 263.814i | −0.167238 | + | 0.394931i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 777.524 | − | 515.112i | 1.16048 | − | 0.768824i | ||||
\(671\) | − | 394.130i | − | 0.587377i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 262.375 | 0.389859 | 0.194930 | − | 0.980817i | \(-0.437552\pi\) | ||||
0.194930 | + | 0.980817i | \(0.437552\pi\) | |||||||
\(674\) | −275.684 | − | 416.125i | −0.409027 | − | 0.617396i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1262.37 | + | 534.566i | 1.86741 | + | 0.790777i | ||||
\(677\) | −574.436 | − | 574.436i | −0.848502 | − | 0.848502i | 0.141444 | − | 0.989946i | \(-0.454825\pi\) |
−0.989946 | + | 0.141444i | \(0.954825\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3280 | 0.0255199 | ||||||||
\(680\) | 139.094 | + | 95.3327i | 0.204549 | + | 0.140195i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 223.748 | − | 1102.18i | 0.328076 | − | 1.61610i | ||||
\(683\) | −253.790 | + | 253.790i | −0.371582 | + | 0.371582i | −0.868053 | − | 0.496471i | \(-0.834629\pi\) |
0.496471 | + | 0.868053i | \(0.334629\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 488.264 | − | 488.264i | 0.712794 | − | 0.712794i | ||||
\(686\) | −28.3659 | − | 42.8163i | −0.0413498 | − | 0.0624144i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1101.85 | − | 17.3391i | −1.60153 | − | 0.0252022i | ||||
\(689\) | 1689.76 | 2.45248 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 734.512 | + | 734.512i | 1.06297 | + | 1.06297i | 0.997879 | + | 0.0650902i | \(0.0207335\pi\) |
0.0650902 | + | 0.997879i | \(0.479266\pi\) | |||||||
\(692\) | −213.205 | − | 526.398i | −0.308099 | − | 0.760690i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −824.875 | − | 167.454i | −1.18858 | − | 0.241288i | ||||
\(695\) | 1041.67 | 1.49880 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 76.9952i | − | 0.110467i | ||||||
\(698\) | 800.513 | + | 162.508i | 1.14687 | + | 0.232820i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 10.5798 | + | 4.48013i | 0.0151140 | + | 0.00640019i | ||||
\(701\) | −745.410 | + | 745.410i | −1.06335 | + | 1.06335i | −0.0655005 | + | 0.997853i | \(0.520864\pi\) |
−0.997853 | + | 0.0655005i | \(0.979136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 64.3920i | − | 0.0915961i | ||||||
\(704\) | −314.958 | + | 712.342i | −0.447383 | + | 1.01185i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 282.070 | + | 425.764i | 0.399533 | + | 0.603065i | ||||
\(707\) | 6.69342 | + | 6.69342i | 0.00946735 | + | 0.00946735i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −809.881 | − | 809.881i | −1.14229 | − | 1.14229i | −0.988031 | − | 0.154255i | \(-0.950702\pi\) |
−0.154255 | − | 0.988031i | \(-0.549298\pi\) | |||||||
\(710\) | −201.013 | + | 990.189i | −0.283117 | + | 1.39463i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −50.7093 | − | 271.648i | −0.0712209 | − | 0.381529i | ||||
\(713\) | 762.272i | 1.06910i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1167.23 | + | 1167.23i | −1.63249 | + | 1.63249i | ||||
\(716\) | −337.761 | + | 136.802i | −0.471734 | + | 0.191064i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 421.730 | + | 636.570i | 0.587368 | + | 0.886588i | ||||
\(719\) | − | 662.400i | − | 0.921280i | −0.887587 | − | 0.460640i | \(-0.847620\pi\) | ||
0.887587 | − | 0.460640i | \(-0.152380\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.72549 | 0.00516711 | ||||||||
\(722\) | −216.065 | + | 143.144i | −0.299259 | + | 0.198260i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 414.224 | − | 167.771i | 0.572132 | − | 0.231728i | ||||
\(725\) | −284.271 | − | 284.271i | −0.392098 | − | 0.392098i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1253.93 | −1.72481 | −0.862403 | − | 0.506222i | \(-0.831042\pi\) | ||||
−0.862403 | + | 0.506222i | \(0.831042\pi\) | |||||||
\(728\) | 26.8284 | − | 39.1435i | 0.0368522 | − | 0.0537686i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −917.100 | − | 186.176i | −1.25630 | − | 0.255035i | ||||
\(731\) | −171.203 | + | 171.203i | −0.234204 | + | 0.234204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −509.300 | + | 509.300i | −0.694816 | + | 0.694816i | −0.963288 | − | 0.268472i | \(-0.913481\pi\) |
0.268472 | + | 0.963288i | \(0.413481\pi\) | |||||||
\(734\) | 31.0161 | − | 20.5483i | 0.0422563 | − | 0.0279949i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 113.151 | − | 515.629i | 0.153738 | − | 0.700583i | ||||
\(737\) | 946.479 | 1.28423 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 818.847 | + | 818.847i | 1.10805 | + | 1.10805i | 0.993407 | + | 0.114640i | \(0.0365716\pi\) |
0.114640 | + | 0.993407i | \(0.463428\pi\) | |||||||
\(740\) | −93.4882 | − | 39.5886i | −0.126335 | − | 0.0534981i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.79381 | − | 38.3922i | 0.0105038 | − | 0.0517415i | ||||
\(743\) | 1110.03 | 1.49398 | 0.746991 | − | 0.664834i | \(-0.231498\pi\) | ||||
0.746991 | + | 0.664834i | \(0.231498\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 847.736i | 1.13790i | ||||||||
\(746\) | 84.4506 | − | 416.002i | 0.113205 | − | 0.557644i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 64.2403 | + | 158.608i | 0.0858827 | + | 0.212042i | ||||
\(749\) | −5.72933 | + | 5.72933i | −0.00764931 | + | 0.00764931i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0597i | 0.0453525i | 0.999743 | + | 0.0226762i | \(0.00721869\pi\) | ||||
−0.999743 | + | 0.0226762i | \(0.992781\pi\) | |||||||
\(752\) | −813.239 | + | 788.040i | −1.08143 | + | 1.04793i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1384.27 | + | 917.081i | −1.83590 | + | 1.21629i | ||||
\(755\) | 944.491 | + | 944.491i | 1.25098 | + | 1.25098i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 398.543 | + | 398.543i | 0.526477 | + | 0.526477i | 0.919520 | − | 0.393043i | \(-0.128578\pi\) |
−0.393043 | + | 0.919520i | \(0.628578\pi\) | |||||||
\(758\) | −1051.54 | − | 213.468i | −1.38726 | − | 0.281620i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −133.904 | − | 717.323i | −0.176190 | − | 0.943845i | ||||
\(761\) | 903.338i | 1.18704i | 0.804819 | + | 0.593520i | \(0.202262\pi\) | ||||
−0.804819 | + | 0.593520i | \(0.797738\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.69328 | + | 4.69328i | −0.00615108 | + | 0.00615108i | ||||
\(764\) | −1121.30 | − | 474.826i | −1.46767 | − | 0.621500i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 712.638 | − | 472.125i | 0.930337 | − | 0.616352i | ||||
\(767\) | − | 1976.19i | − | 2.57652i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −98.9621 | −0.128689 | −0.0643447 | − | 0.997928i | \(-0.520496\pi\) | ||||
−0.0643447 | + | 0.997928i | \(0.520496\pi\) | |||||||
\(770\) | 21.1363 | + | 31.9037i | 0.0274498 | + | 0.0414334i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −395.694 | + | 934.427i | −0.512557 | + | 1.21040i | ||||
\(773\) | 111.945 | + | 111.945i | 0.144818 | + | 0.144818i | 0.775799 | − | 0.630980i | \(-0.217347\pi\) |
−0.630980 | + | 0.775799i | \(0.717347\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 506.137 | 0.653080 | ||||||||
\(776\) | −519.667 | + | 97.0075i | −0.669674 | + | 0.125010i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 132.938 | − | 654.849i | 0.170871 | − | 0.841709i | ||||
\(779\) | −235.598 | + | 235.598i | −0.302437 | + | 0.302437i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −725.025 | + | 725.025i | −0.928329 | + | 0.928329i | ||||
\(782\) | −64.0574 | − | 96.6899i | −0.0819148 | − | 0.123644i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 544.815 | + | 562.236i | 0.694917 | + | 0.717137i | ||||
\(785\) | −389.291 | −0.495913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −163.931 | − | 163.931i | −0.208299 | − | 0.208299i | 0.595245 | − | 0.803544i | \(-0.297055\pi\) |
−0.803544 | + | 0.595245i | \(0.797055\pi\) | |||||||
\(788\) | 468.850 | − | 189.896i | 0.594987 | − | 0.240985i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −696.794 | − | 141.453i | −0.882017 | − | 0.179054i | ||||
\(791\) | −45.7703 | −0.0578638 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 732.614i | − | 0.923852i | ||||||
\(794\) | 1185.24 | + | 240.610i | 1.49275 | + | 0.303035i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −182.926 | + | 431.979i | −0.229807 | + | 0.542687i | ||||
\(797\) | 271.277 | − | 271.277i | 0.340373 | − | 0.340373i | −0.516135 | − | 0.856507i | \(-0.672630\pi\) |
0.856507 | + | 0.516135i | \(0.172630\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 248.802i | 0.311392i | ||||||||
\(800\) | −342.370 | − | 75.1304i | −0.427962 | − | 0.0939130i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 705.166 | + | 1064.40i | 0.879260 | + | 1.32718i | ||||
\(803\) | −671.508 | − | 671.508i | −0.836249 | − | 0.836249i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −18.3414 | − | 18.3414i | −0.0227843 | − | 0.0227843i | ||||
\(806\) | 415.905 | − | 2048.74i | 0.516011 | − | 2.54187i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −238.208 | − | 163.264i | −0.294811 | − | 0.202059i | ||||
\(809\) | − | 1505.90i | − | 1.86144i | −0.365736 | − | 0.930718i | \(-0.619183\pi\) | ||
0.365736 | − | 0.930718i | \(-0.380817\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −492.677 | + | 492.677i | −0.607493 | + | 0.607493i | −0.942290 | − | 0.334797i | \(-0.891332\pi\) |
0.334797 | + | 0.942290i | \(0.391332\pi\) | |||||||
\(812\) | 14.4518 | + | 35.6811i | 0.0177978 | + | 0.0439423i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −56.9015 | − | 85.8887i | −0.0699036 | − | 0.105514i | ||||
\(815\) | − | 316.542i | − | 0.388396i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1047.73 | 1.28241 | ||||||||
\(818\) | 456.143 | − | 302.196i | 0.557632 | − | 0.369433i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 197.208 | + | 486.903i | 0.240498 | + | 0.593784i | ||||
\(821\) | −139.500 | − | 139.500i | −0.169914 | − | 0.169914i | 0.617027 | − | 0.786942i | \(-0.288337\pi\) |
−0.786942 | + | 0.617027i | \(0.788337\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1262.09 | −1.53353 | −0.766763 | − | 0.641931i | \(-0.778134\pi\) | ||||
−0.766763 | + | 0.641931i | \(0.778134\pi\) | |||||||
\(824\) | −111.728 | + | 20.8564i | −0.135592 | + | 0.0253112i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −44.9000 | − | 9.11493i | −0.0543584 | − | 0.0110350i | ||||
\(827\) | 179.936 | − | 179.936i | 0.217577 | − | 0.217577i | −0.589900 | − | 0.807477i | \(-0.700833\pi\) |
0.807477 | + | 0.589900i | \(0.200833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −144.901 | + | 144.901i | −0.174790 | + | 0.174790i | −0.789080 | − | 0.614290i | \(-0.789443\pi\) |
0.614290 | + | 0.789080i | \(0.289443\pi\) | |||||||
\(830\) | −1578.71 | + | 1045.90i | −1.90206 | + | 1.26012i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −585.447 | + | 1324.11i | −0.703663 | + | 1.59148i | ||||
\(833\) | 172.010 | 0.206495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −303.676 | − | 303.676i | −0.363684 | − | 0.363684i | ||||
\(836\) | 288.756 | − | 681.894i | 0.345402 | − | 0.815663i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −84.5827 | + | 416.653i | −0.100934 | + | 0.497200i | ||||
\(839\) | −1006.03 | −1.19908 | −0.599540 | − | 0.800345i | \(-0.704650\pi\) | ||||
−0.599540 | + | 0.800345i | \(0.704650\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 506.033i | − | 0.601703i | ||||||
\(842\) | −124.260 | + | 612.105i | −0.147578 | + | 0.726965i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 424.137 | − | 171.787i | 0.502532 | − | 0.203539i | ||||
\(845\) | −1453.11 | + | 1453.11i | −1.71966 | + | 1.71966i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.10706i | 0.00839087i | ||||||||
\(848\) | −18.8051 | + | 1195.02i | −0.0221759 | + | 1.40922i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −64.2006 | + | 42.5331i | −0.0755301 | + | 0.0500390i | ||||
\(851\) | 49.3772 | + | 49.3772i | 0.0580225 | + | 0.0580225i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 77.4150 | + | 77.4150i | 0.0907561 | + | 0.0907561i | 0.751027 | − | 0.660271i | \(-0.229559\pi\) |
−0.660271 | + | 0.751027i | \(0.729559\pi\) | |||||||
\(854\) | −16.6454 | − | 3.37909i | −0.0194911 | − | 0.00395678i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 139.748 | − | 203.898i | 0.163257 | − | 0.238198i | ||||
\(857\) | 175.567i | 0.204863i | 0.994740 | + | 0.102431i | \(0.0326622\pi\) | ||||
−0.994740 | + | 0.102431i | \(0.967338\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1058.18 | − | 1058.18i | 1.23188 | − | 1.23188i | 0.268634 | − | 0.963242i | \(-0.413428\pi\) |
0.963242 | − | 0.268634i | \(-0.0865722\pi\) | |||||||
\(860\) | 644.151 | − | 1521.16i | 0.749013 | − | 1.76879i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 773.162 | − | 512.222i | 0.896939 | − | 0.594225i | ||||
\(863\) | 569.219i | 0.659581i | 0.944054 | + | 0.329791i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329791i | \(0.893022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 851.355 | 0.984225 | ||||||||
\(866\) | 342.549 | + | 517.052i | 0.395553 | + | 0.597058i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −44.6302 | − | 18.8992i | −0.0514173 | − | 0.0217732i | ||||
\(869\) | −510.198 | − | 510.198i | −0.587110 | − | 0.587110i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1759.33 | 2.01989 | ||||||||
\(872\) | 114.477 | − | 167.026i | 0.131281 | − | 0.191544i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −99.8524 | + | 491.872i | −0.114248 | + | 0.562782i | ||||
\(875\) | 15.6169 | − | 15.6169i | 0.0178479 | − | 0.0178479i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −166.695 | + | 166.695i | −0.190074 | + | 0.190074i | −0.795728 | − | 0.605654i | \(-0.792912\pi\) |
0.605654 | + | 0.795728i | \(0.292912\pi\) | |||||||
\(878\) | −99.3141 | − | 149.907i | −0.113114 | − | 0.170737i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −812.486 | − | 838.466i | −0.923279 | − | 0.952802i | ||||
\(881\) | 1495.53 | 1.69754 | 0.848771 | − | 0.528761i | \(-0.177343\pi\) | ||||
0.848771 | + | 0.528761i | \(0.177343\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 134.367 | + | 134.367i | 0.152171 | + | 0.152171i | 0.779087 | − | 0.626916i | \(-0.215683\pi\) |
−0.626916 | + | 0.779087i | \(0.715683\pi\) | |||||||
\(884\) | 119.411 | + | 294.822i | 0.135080 | + | 0.333509i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −218.776 | − | 44.4126i | −0.246926 | − | 0.0501271i | ||||
\(887\) | −414.255 | −0.467030 | −0.233515 | − | 0.972353i | \(-0.575023\pi\) | ||||
−0.233515 | + | 0.972353i | \(0.575023\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.8903i | 0.0133749i | ||||||||
\(890\) | 405.964 | + | 82.4127i | 0.456139 | + | 0.0925985i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −969.127 | − | 410.388i | −1.08646 | − | 0.460076i | ||||
\(893\) | 761.311 | − | 761.311i | 0.852531 | − | 0.852531i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 546.269i | − | 0.610356i | ||||||
\(896\) | 27.3842 | + | 19.4090i | 0.0305627 | + | 0.0216618i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 206.611 | + | 311.864i | 0.230079 | + | 0.347287i | ||||
\(899\) | 1199.18 | + | 1199.18i | 1.33390 | + | 1.33390i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 185.678 | + | 185.678i | 0.206080 | + | 0.206080i | ||||
\(902\) | −106.058 | + | 522.442i | −0.117581 | + | 0.579204i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1372.65 | − | 256.236i | 1.51842 | − | 0.283447i | ||||
\(905\) | 669.933i | 0.740258i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −312.683 | + | 312.683i | −0.344744 | + | 0.344744i | −0.858148 | − | 0.513403i | \(-0.828385\pi\) |
0.513403 | + | 0.858148i | \(0.328385\pi\) | |||||||
\(908\) | 587.674 | − | 238.023i | 0.647218 | − | 0.262140i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 39.2884 | + | 59.3030i | 0.0431741 | + | 0.0651681i | ||||
\(911\) | 391.366i | 0.429601i | 0.976658 | + | 0.214800i | \(0.0689101\pi\) | ||||
−0.976658 | + | 0.214800i | \(0.931090\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1921.76 | −2.10488 | ||||||||
\(914\) | 255.627 | − | 169.354i | 0.279680 | − | 0.185289i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −528.870 | + | 214.206i | −0.577369 | + | 0.233850i | ||||
\(917\) | 8.55413 | + | 8.55413i | 0.00932838 | + | 0.00932838i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 294.161 | 0.320088 | 0.160044 | − | 0.987110i | \(-0.448836\pi\) | ||||
0.160044 | + | 0.987110i | \(0.448836\pi\) | |||||||
\(920\) | 652.739 | + | 447.377i | 0.709499 | + | 0.486280i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 276.087 | + | 56.0470i | 0.299443 | + | 0.0607885i | ||||
\(923\) | −1347.69 | + | 1347.69i | −1.46011 | + | 1.46011i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 32.7857 | − | 32.7857i | 0.0354440 | − | 0.0354440i | ||||
\(926\) | 426.298 | − | 282.424i | 0.460365 | − | 0.304993i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −633.164 | − | 989.174i | −0.682289 | − | 1.06592i | ||||
\(929\) | −1015.40 | −1.09300 | −0.546501 | − | 0.837458i | \(-0.684041\pi\) | ||||
−0.546501 | + | 0.837458i | \(0.684041\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −526.335 | − | 526.335i | −0.565344 | − | 0.565344i | ||||
\(932\) | 1199.55 | + | 507.965i | 1.28708 | + | 0.545027i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −160.672 | + | 791.466i | −0.172025 | + | 0.847394i | ||||
\(935\) | −256.520 | −0.274353 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1582.09i | 1.68846i | 0.535977 | + | 0.844232i | \(0.319943\pi\) | ||||
−0.535977 | + | 0.844232i | \(0.680057\pi\) | |||||||
\(938\) | 8.11468 | − | 39.9728i | 0.00865105 | − | 0.0426149i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −637.257 | − | 1573.37i | −0.677933 | − | 1.67380i | ||||
\(941\) | −113.842 | + | 113.842i | −0.120980 | + | 0.120980i | −0.765005 | − | 0.644025i | \(-0.777263\pi\) |
0.644025 | + | 0.765005i | \(0.277263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 361.323i | − | 0.383163i | ||||||
\(944\) | 1397.58 | + | 21.9928i | 1.48049 | + | 0.0232974i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1397.50 | − | 925.851i | 1.47728 | − | 0.978701i | ||||
\(947\) | −388.664 | − | 388.664i | −0.410416 | − | 0.410416i | 0.471467 | − | 0.881884i | \(-0.343725\pi\) |
−0.881884 | + | 0.471467i | \(0.843725\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1248.21 | − | 1248.21i | −1.31529 | − | 1.31529i | ||||
\(950\) | 326.595 | + | 66.3005i | 0.343785 | + | 0.0697900i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.24928 | − | 1.35324i | 0.00761479 | − | 0.00142147i | ||||
\(953\) | − | 211.977i | − | 0.222431i | −0.993796 | − | 0.111215i | \(-0.964526\pi\) | ||
0.993796 | − | 0.111215i | \(-0.0354744\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1290.72 | − | 1290.72i | 1.35154 | − | 1.35154i | ||||
\(956\) | −92.9199 | − | 39.3480i | −0.0971966 | − | 0.0411590i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −697.889 | + | 462.354i | −0.728485 | + | 0.482624i | ||||
\(959\) | − | 30.1976i | − | 0.0314887i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1174.11 | −1.22175 | ||||||||
\(962\) | −105.769 | − | 159.651i | −0.109947 | − | 0.165957i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 477.267 | − | 1127.06i | 0.495090 | − | 1.16915i | ||||
\(965\) | −1075.62 | − | 1075.62i | −1.11463 | − | 1.11463i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 516.501 | 0.534127 | 0.267063 | − | 0.963679i | \(-0.413947\pi\) | ||||
0.267063 | + | 0.963679i | \(0.413947\pi\) | |||||||
\(968\) | −39.7876 | − | 213.141i | −0.0411029 | − | 0.220187i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 157.657 | − | 776.614i | 0.162532 | − | 0.800633i | ||||
\(971\) | −795.556 | + | 795.556i | −0.819316 | + | 0.819316i | −0.986009 | − | 0.166693i | \(-0.946691\pi\) |
0.166693 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.2120 | − | 32.2120i | 0.0331059 | − | 0.0331059i | ||||
\(974\) | 179.563 | + | 271.037i | 0.184356 | + | 0.278272i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 518.113 | + | 8.15318i | 0.530853 | + | 0.00835367i | ||||
\(977\) | −512.430 | −0.524493 | −0.262246 | − | 0.965001i | \(-0.584463\pi\) | ||||
−0.262246 | + | 0.965001i | \(0.584463\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 297.250 | + | 297.250i | 0.303626 | + | 0.303626i | ||||
\(980\) | −1087.76 | + | 440.570i | −1.10996 | + | 0.449562i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1550.57 | + | 314.774i | 1.57900 | + | 0.320544i | ||||
\(983\) | 722.200 | 0.734690 | 0.367345 | − | 0.930085i | \(-0.380267\pi\) | ||||
0.367345 | + | 0.930085i | \(0.380267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 758.281i | 0.769828i | ||||||||
\(986\) | −252.882 | − | 51.3363i | −0.256472 | − | 0.0520652i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 536.743 | − | 1267.51i | 0.543262 | − | 1.28291i | ||||
\(989\) | −803.421 | + | 803.421i | −0.812357 | + | 0.812357i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 794.715i | − | 0.801932i | −0.916093 | − | 0.400966i | \(-0.868675\pi\) | ||
0.916093 | − | 0.400966i | \(-0.131325\pi\) | |||||||
\(992\) | 1444.26 | + | 316.933i | 1.45591 | + | 0.319489i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 24.4041 | + | 36.8361i | 0.0245514 | + | 0.0370585i | ||||
\(995\) | −497.250 | − | 497.250i | −0.499749 | − | 0.499749i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1080.18 | + | 1080.18i | 1.08343 | + | 1.08343i | 0.996187 | + | 0.0872401i | \(0.0278047\pi\) |
0.0872401 | + | 0.996187i | \(0.472195\pi\) | |||||||
\(998\) | 139.527 | − | 687.310i | 0.139807 | − | 0.688687i | ||||
\(999\) | 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 | 144.3.m.b.91.3 | yes | 16 | |
3.2 | odd | 2 | inner | 144.3.m.b.91.6 | yes | 16 | |
4.3 | odd | 2 | 576.3.m.b.271.2 | 16 | |||
8.3 | odd | 2 | 1152.3.m.d.415.7 | 16 | |||
8.5 | even | 2 | 1152.3.m.e.415.7 | 16 | |||
12.11 | even | 2 | 576.3.m.b.271.7 | 16 | |||
16.3 | odd | 4 | inner | 144.3.m.b.19.3 | ✓ | 16 | |
16.5 | even | 4 | 1152.3.m.d.991.7 | 16 | |||
16.11 | odd | 4 | 1152.3.m.e.991.7 | 16 | |||
16.13 | even | 4 | 576.3.m.b.559.2 | 16 | |||
24.5 | odd | 2 | 1152.3.m.e.415.2 | 16 | |||
24.11 | even | 2 | 1152.3.m.d.415.2 | 16 | |||
48.5 | odd | 4 | 1152.3.m.d.991.2 | 16 | |||
48.11 | even | 4 | 1152.3.m.e.991.2 | 16 | |||
48.29 | odd | 4 | 576.3.m.b.559.7 | 16 | |||
48.35 | even | 4 | inner | 144.3.m.b.19.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.3 | ✓ | 16 | 16.3 | odd | 4 | inner | |
144.3.m.b.19.6 | yes | 16 | 48.35 | even | 4 | inner | |
144.3.m.b.91.3 | yes | 16 | 1.1 | even | 1 | trivial | |
144.3.m.b.91.6 | yes | 16 | 3.2 | odd | 2 | inner | |
576.3.m.b.271.2 | 16 | 4.3 | odd | 2 | |||
576.3.m.b.271.7 | 16 | 12.11 | even | 2 | |||
576.3.m.b.559.2 | 16 | 16.13 | even | 4 | |||
576.3.m.b.559.7 | 16 | 48.29 | odd | 4 | |||
1152.3.m.d.415.2 | 16 | 24.11 | even | 2 | |||
1152.3.m.d.415.7 | 16 | 8.3 | odd | 2 | |||
1152.3.m.d.991.2 | 16 | 48.5 | odd | 4 | |||
1152.3.m.d.991.7 | 16 | 16.5 | even | 4 | |||
1152.3.m.e.415.2 | 16 | 24.5 | odd | 2 | |||
1152.3.m.e.415.7 | 16 | 8.5 | even | 2 | |||
1152.3.m.e.991.2 | 16 | 48.11 | even | 4 | |||
1152.3.m.e.991.7 | 16 | 16.11 | odd | 4 |