Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [169,4,Mod(22,169)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(169, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("169.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 169 = 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 169.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.97132279097\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 13) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 146.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 169.146 |
Dual form | 169.4.c.i.22.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | + | 3.00000i | 0.612372 | + | 1.06066i | 0.990839 | + | 0.135045i | \(0.0431180\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(3\) | 3.50000 | + | 6.06218i | 0.673575 | + | 1.16667i | 0.976883 | + | 0.213774i | \(0.0685756\pi\) |
−0.303308 | + | 0.952893i | \(0.598091\pi\) | |||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | −13.8564 | −1.23935 | −0.619677 | − | 0.784857i | \(-0.712737\pi\) | ||||
−0.619677 | + | 0.784857i | \(0.712737\pi\) | |||||||
\(6\) | −12.1244 | + | 21.0000i | −0.824958 | + | 1.42887i | ||||
\(7\) | −11.2583 | + | 19.5000i | −0.607893 | + | 1.05290i | 0.383694 | + | 0.923460i | \(0.374652\pi\) |
−0.991587 | + | 0.129441i | \(0.958682\pi\) | |||||||
\(8\) | 13.8564 | 0.612372 | ||||||||
\(9\) | −11.0000 | + | 19.0526i | −0.407407 | + | 0.705650i | ||||
\(10\) | −24.0000 | − | 41.5692i | −0.758947 | − | 1.31453i | ||||
\(11\) | −11.2583 | − | 19.5000i | −0.308592 | − | 0.534497i | 0.669462 | − | 0.742846i | \(-0.266525\pi\) |
−0.978055 | + | 0.208349i | \(0.933191\pi\) | |||||||
\(12\) | −28.0000 | −0.673575 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −78.0000 | −1.48903 | ||||||||
\(15\) | −48.4974 | − | 84.0000i | −0.834799 | − | 1.44591i | ||||
\(16\) | 40.0000 | + | 69.2820i | 0.625000 | + | 1.08253i | ||||
\(17\) | 13.5000 | − | 23.3827i | 0.192602 | − | 0.333596i | −0.753510 | − | 0.657437i | \(-0.771641\pi\) |
0.946112 | + | 0.323840i | \(0.104974\pi\) | |||||||
\(18\) | −76.2102 | −0.997940 | ||||||||
\(19\) | −44.1673 | + | 76.5000i | −0.533299 | + | 0.923700i | 0.465945 | + | 0.884814i | \(0.345714\pi\) |
−0.999244 | + | 0.0388865i | \(0.987619\pi\) | |||||||
\(20\) | 27.7128 | − | 48.0000i | 0.309839 | − | 0.536656i | ||||
\(21\) | −157.617 | −1.63785 | ||||||||
\(22\) | 39.0000 | − | 67.5500i | 0.377947 | − | 0.654623i | ||||
\(23\) | 28.5000 | + | 49.3634i | 0.258377 | + | 0.447521i | 0.965807 | − | 0.259261i | \(-0.0834791\pi\) |
−0.707431 | + | 0.706783i | \(0.750146\pi\) | |||||||
\(24\) | 48.4974 | + | 84.0000i | 0.412479 | + | 0.714435i | ||||
\(25\) | 67.0000 | 0.536000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 35.0000 | 0.249472 | ||||||||
\(28\) | −45.0333 | − | 78.0000i | −0.303946 | − | 0.526451i | ||||
\(29\) | 34.5000 | + | 59.7558i | 0.220913 | + | 0.382633i | 0.955086 | − | 0.296330i | \(-0.0957628\pi\) |
−0.734172 | + | 0.678963i | \(0.762430\pi\) | |||||||
\(30\) | 168.000 | − | 290.985i | 1.02242 | − | 1.77088i | ||||
\(31\) | 72.7461 | 0.421471 | 0.210735 | − | 0.977543i | \(-0.432414\pi\) | ||||
0.210735 | + | 0.977543i | \(0.432414\pi\) | |||||||
\(32\) | −83.1384 | + | 144.000i | −0.459279 | + | 0.795495i | ||||
\(33\) | 78.8083 | − | 136.500i | 0.415720 | − | 0.720048i | ||||
\(34\) | 93.5307 | 0.471776 | ||||||||
\(35\) | 156.000 | − | 270.200i | 0.753395 | − | 1.30492i | ||||
\(36\) | −44.0000 | − | 76.2102i | −0.203704 | − | 0.352825i | ||||
\(37\) | −19.9186 | − | 34.5000i | −0.0885026 | − | 0.153291i | 0.818376 | − | 0.574683i | \(-0.194875\pi\) |
−0.906878 | + | 0.421393i | \(0.861541\pi\) | |||||||
\(38\) | −306.000 | −1.30631 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −192.000 | −0.758947 | ||||||||
\(41\) | 196.588 | + | 340.500i | 0.748826 | + | 1.29700i | 0.948386 | + | 0.317118i | \(0.102715\pi\) |
−0.199560 | + | 0.979886i | \(0.563951\pi\) | |||||||
\(42\) | −273.000 | − | 472.850i | −1.00297 | − | 1.73720i | ||||
\(43\) | −42.5000 | + | 73.6122i | −0.150725 | + | 0.261064i | −0.931494 | − | 0.363756i | \(-0.881494\pi\) |
0.780769 | + | 0.624820i | \(0.214828\pi\) | |||||||
\(44\) | 90.0666 | 0.308592 | ||||||||
\(45\) | 152.420 | − | 264.000i | 0.504922 | − | 0.874551i | ||||
\(46\) | −98.7269 | + | 171.000i | −0.316445 | + | 0.548099i | ||||
\(47\) | −342.946 | −1.06434 | −0.532168 | − | 0.846639i | \(-0.678623\pi\) | ||||
−0.532168 | + | 0.846639i | \(0.678623\pi\) | |||||||
\(48\) | −280.000 | + | 484.974i | −0.841969 | + | 1.45833i | ||||
\(49\) | −82.0000 | − | 142.028i | −0.239067 | − | 0.414076i | ||||
\(50\) | 116.047 | + | 201.000i | 0.328232 | + | 0.568514i | ||||
\(51\) | 189.000 | 0.518927 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 426.000 | 1.10407 | 0.552034 | − | 0.833822i | \(-0.313852\pi\) | ||||
0.552034 | + | 0.833822i | \(0.313852\pi\) | |||||||
\(54\) | 60.6218 | + | 105.000i | 0.152770 | + | 0.264605i | ||||
\(55\) | 156.000 | + | 270.200i | 0.382455 | + | 0.662432i | ||||
\(56\) | −156.000 | + | 270.200i | −0.372257 | + | 0.644768i | ||||
\(57\) | −618.342 | −1.43687 | ||||||||
\(58\) | −119.512 | + | 207.000i | −0.270563 | + | 0.468628i | ||||
\(59\) | 9.52628 | − | 16.5000i | 0.0210206 | − | 0.0364088i | −0.855324 | − | 0.518094i | \(-0.826642\pi\) |
0.876344 | + | 0.481685i | \(0.159975\pi\) | |||||||
\(60\) | 387.979 | 0.834799 | ||||||||
\(61\) | 8.50000 | − | 14.7224i | 0.0178412 | − | 0.0309019i | −0.856967 | − | 0.515371i | \(-0.827654\pi\) |
0.874808 | + | 0.484469i | \(0.160987\pi\) | |||||||
\(62\) | 126.000 | + | 218.238i | 0.258097 | + | 0.447037i | ||||
\(63\) | −247.683 | − | 429.000i | −0.495320 | − | 0.857919i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 546.000 | 1.01830 | ||||||||
\(67\) | −82.2724 | − | 142.500i | −0.150018 | − | 0.259838i | 0.781216 | − | 0.624261i | \(-0.214600\pi\) |
−0.931234 | + | 0.364423i | \(0.881266\pi\) | |||||||
\(68\) | 54.0000 | + | 93.5307i | 0.0963009 | + | 0.166798i | ||||
\(69\) | −199.500 | + | 345.544i | −0.348072 | + | 0.602879i | ||||
\(70\) | 1080.80 | 1.84543 | ||||||||
\(71\) | 291.851 | − | 505.500i | 0.487835 | − | 0.844955i | −0.512067 | − | 0.858945i | \(-0.671120\pi\) |
0.999902 | + | 0.0139904i | \(0.00445341\pi\) | |||||||
\(72\) | −152.420 | + | 264.000i | −0.249485 | + | 0.432121i | ||||
\(73\) | 1004.59 | 1.61066 | 0.805331 | − | 0.592826i | \(-0.201988\pi\) | ||||
0.805331 | + | 0.592826i | \(0.201988\pi\) | |||||||
\(74\) | 69.0000 | − | 119.512i | 0.108393 | − | 0.187742i | ||||
\(75\) | 234.500 | + | 406.166i | 0.361036 | + | 0.625333i | ||||
\(76\) | −176.669 | − | 306.000i | −0.266649 | − | 0.461850i | ||||
\(77\) | 507.000 | 0.750364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1244.00 | −1.77166 | −0.885829 | − | 0.464012i | \(-0.846409\pi\) | ||||
−0.885829 | + | 0.464012i | \(0.846409\pi\) | |||||||
\(80\) | −554.256 | − | 960.000i | −0.774597 | − | 1.34164i | ||||
\(81\) | 419.500 | + | 726.595i | 0.575446 | + | 0.996701i | ||||
\(82\) | −681.000 | + | 1179.53i | −0.917120 | + | 1.58850i | ||||
\(83\) | 426.084 | 0.563480 | 0.281740 | − | 0.959491i | \(-0.409088\pi\) | ||||
0.281740 | + | 0.959491i | \(0.409088\pi\) | |||||||
\(84\) | 315.233 | − | 546.000i | 0.409462 | − | 0.709208i | ||||
\(85\) | −187.061 | + | 324.000i | −0.238702 | + | 0.413444i | ||||
\(86\) | −294.449 | −0.369200 | ||||||||
\(87\) | −241.500 | + | 418.290i | −0.297604 | + | 0.515465i | ||||
\(88\) | −156.000 | − | 270.200i | −0.188973 | − | 0.327311i | ||||
\(89\) | 153.286 | + | 265.500i | 0.182566 | + | 0.316213i | 0.942753 | − | 0.333490i | \(-0.108226\pi\) |
−0.760188 | + | 0.649703i | \(0.774893\pi\) | |||||||
\(90\) | 1056.00 | 1.23680 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −228.000 | −0.258377 | ||||||||
\(93\) | 254.611 | + | 441.000i | 0.283892 | + | 0.491716i | ||||
\(94\) | −594.000 | − | 1028.84i | −0.651770 | − | 1.12890i | ||||
\(95\) | 612.000 | − | 1060.02i | 0.660946 | − | 1.14479i | ||||
\(96\) | −1163.94 | −1.23744 | ||||||||
\(97\) | 617.476 | − | 1069.50i | 0.646342 | − | 1.11950i | −0.337647 | − | 0.941273i | \(-0.609631\pi\) |
0.983990 | − | 0.178225i | \(-0.0570355\pi\) | |||||||
\(98\) | 284.056 | − | 492.000i | 0.292796 | − | 0.507138i | ||||
\(99\) | 495.367 | 0.502891 | ||||||||
\(100\) | −134.000 | + | 232.095i | −0.134000 | + | 0.232095i | ||||
\(101\) | 979.500 | + | 1696.54i | 0.964989 | + | 1.67141i | 0.709645 | + | 0.704560i | \(0.248856\pi\) |
0.255345 | + | 0.966850i | \(0.417811\pi\) | |||||||
\(102\) | 327.358 | + | 567.000i | 0.317777 | + | 0.550406i | ||||
\(103\) | −1856.00 | −1.77551 | −0.887753 | − | 0.460320i | \(-0.847735\pi\) | ||||
−0.887753 | + | 0.460320i | \(0.847735\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2184.00 | 2.02987 | ||||||||
\(106\) | 737.854 | + | 1278.00i | 0.676101 | + | 1.17104i | ||||
\(107\) | 127.500 | + | 220.836i | 0.115195 | + | 0.199524i | 0.917858 | − | 0.396909i | \(-0.129917\pi\) |
−0.802663 | + | 0.596433i | \(0.796584\pi\) | |||||||
\(108\) | −70.0000 | + | 121.244i | −0.0623681 | + | 0.108025i | ||||
\(109\) | 609.682 | 0.535752 | 0.267876 | − | 0.963453i | \(-0.413678\pi\) | ||||
0.267876 | + | 0.963453i | \(0.413678\pi\) | |||||||
\(110\) | −540.400 | + | 936.000i | −0.468410 | + | 0.811310i | ||||
\(111\) | 139.430 | − | 241.500i | 0.119226 | − | 0.206506i | ||||
\(112\) | −1801.33 | −1.51973 | ||||||||
\(113\) | −205.500 | + | 355.936i | −0.171078 | + | 0.296316i | −0.938797 | − | 0.344471i | \(-0.888058\pi\) |
0.767719 | + | 0.640787i | \(0.221392\pi\) | |||||||
\(114\) | −1071.00 | − | 1855.03i | −0.879898 | − | 1.52403i | ||||
\(115\) | −394.908 | − | 684.000i | −0.320220 | − | 0.554638i | ||||
\(116\) | −276.000 | −0.220913 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 66.0000 | 0.0514898 | ||||||||
\(119\) | 303.975 | + | 526.500i | 0.234162 | + | 0.405581i | ||||
\(120\) | −672.000 | − | 1163.94i | −0.511208 | − | 0.885438i | ||||
\(121\) | 412.000 | − | 713.605i | 0.309542 | − | 0.536142i | ||||
\(122\) | 58.8897 | 0.0437018 | ||||||||
\(123\) | −1376.11 | + | 2383.50i | −1.00878 | + | 1.74726i | ||||
\(124\) | −145.492 | + | 252.000i | −0.105368 | + | 0.182502i | ||||
\(125\) | 803.672 | 0.575061 | ||||||||
\(126\) | 858.000 | − | 1486.10i | 0.606641 | − | 1.05073i | ||||
\(127\) | −1121.50 | − | 1942.49i | −0.783599 | − | 1.35723i | −0.929833 | − | 0.367983i | \(-0.880049\pi\) |
0.146234 | − | 0.989250i | \(-0.453285\pi\) | |||||||
\(128\) | 775.959 | + | 1344.00i | 0.535826 | + | 0.928078i | ||||
\(129\) | −595.000 | −0.406099 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −372.000 | −0.248105 | −0.124053 | − | 0.992276i | \(-0.539589\pi\) | ||||
−0.124053 | + | 0.992276i | \(0.539589\pi\) | |||||||
\(132\) | 315.233 | + | 546.000i | 0.207860 | + | 0.360024i | ||||
\(133\) | −994.500 | − | 1722.52i | −0.648377 | − | 1.12302i | ||||
\(134\) | 285.000 | − | 493.634i | 0.183733 | − | 0.318235i | ||||
\(135\) | −484.974 | −0.309185 | ||||||||
\(136\) | 187.061 | − | 324.000i | 0.117944 | − | 0.204285i | ||||
\(137\) | 594.959 | − | 1030.50i | 0.371028 | − | 0.642639i | −0.618696 | − | 0.785630i | \(-0.712339\pi\) |
0.989724 | + | 0.142991i | \(0.0456721\pi\) | |||||||
\(138\) | −1382.18 | −0.852599 | ||||||||
\(139\) | 1272.50 | − | 2204.03i | 0.776490 | − | 1.34492i | −0.157464 | − | 0.987525i | \(-0.550332\pi\) |
0.933953 | − | 0.357395i | \(-0.116335\pi\) | |||||||
\(140\) | 624.000 | + | 1080.80i | 0.376697 | + | 0.652459i | ||||
\(141\) | −1200.31 | − | 2079.00i | −0.716911 | − | 1.24173i | ||||
\(142\) | 2022.00 | 1.19495 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1760.00 | −1.01852 | ||||||||
\(145\) | −478.046 | − | 828.000i | −0.273790 | − | 0.474218i | ||||
\(146\) | 1740.00 | + | 3013.77i | 0.986325 | + | 1.70836i | ||||
\(147\) | 574.000 | − | 994.197i | 0.322059 | − | 0.557823i | ||||
\(148\) | 159.349 | 0.0885026 | ||||||||
\(149\) | 652.117 | − | 1129.50i | 0.358547 | − | 0.621022i | −0.629171 | − | 0.777267i | \(-0.716606\pi\) |
0.987718 | + | 0.156245i | \(0.0499389\pi\) | |||||||
\(150\) | −812.332 | + | 1407.00i | −0.442177 | + | 0.765874i | ||||
\(151\) | −86.6025 | −0.0466729 | −0.0233365 | − | 0.999728i | \(-0.507429\pi\) | ||||
−0.0233365 | + | 0.999728i | \(0.507429\pi\) | |||||||
\(152\) | −612.000 | + | 1060.02i | −0.326577 | + | 0.565649i | ||||
\(153\) | 297.000 | + | 514.419i | 0.156935 | + | 0.271819i | ||||
\(154\) | 878.150 | + | 1521.00i | 0.459502 | + | 0.795881i | ||||
\(155\) | −1008.00 | −0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1534.00 | −0.779787 | −0.389893 | − | 0.920860i | \(-0.627488\pi\) | ||||
−0.389893 | + | 0.920860i | \(0.627488\pi\) | |||||||
\(158\) | −2154.67 | − | 3732.00i | −1.08491 | − | 1.87913i | ||||
\(159\) | 1491.00 | + | 2582.49i | 0.743673 | + | 1.28808i | ||||
\(160\) | 1152.00 | − | 1995.32i | 0.569210 | − | 0.985901i | ||||
\(161\) | −1283.45 | −0.628261 | ||||||||
\(162\) | −1453.19 | + | 2517.00i | −0.704774 | + | 1.22070i | ||||
\(163\) | 816.662 | − | 1414.50i | 0.392429 | − | 0.679707i | −0.600340 | − | 0.799745i | \(-0.704968\pi\) |
0.992769 | + | 0.120038i | \(0.0383016\pi\) | |||||||
\(164\) | −1572.70 | −0.748826 | ||||||||
\(165\) | −1092.00 | + | 1891.40i | −0.515225 | + | 0.892395i | ||||
\(166\) | 738.000 | + | 1278.25i | 0.345060 | + | 0.597661i | ||||
\(167\) | 813.198 | + | 1408.50i | 0.376809 | + | 0.652653i | 0.990596 | − | 0.136819i | \(-0.0436879\pi\) |
−0.613787 | + | 0.789472i | \(0.710355\pi\) | |||||||
\(168\) | −2184.00 | −1.00297 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −1296.00 | −0.584698 | ||||||||
\(171\) | −971.681 | − | 1683.00i | −0.434540 | − | 0.752645i | ||||
\(172\) | −170.000 | − | 294.449i | −0.0753627 | − | 0.130532i | ||||
\(173\) | −436.500 | + | 756.040i | −0.191829 | + | 0.332258i | −0.945857 | − | 0.324585i | \(-0.894775\pi\) |
0.754027 | + | 0.656843i | \(0.228109\pi\) | |||||||
\(174\) | −1673.16 | −0.728977 | ||||||||
\(175\) | −754.308 | + | 1306.50i | −0.325830 | + | 0.564355i | ||||
\(176\) | 900.666 | − | 1560.00i | 0.385740 | − | 0.668122i | ||||
\(177\) | 133.368 | 0.0566359 | ||||||||
\(178\) | −531.000 | + | 919.719i | −0.223596 | + | 0.387280i | ||||
\(179\) | −643.500 | − | 1114.57i | −0.268701 | − | 0.465403i | 0.699826 | − | 0.714314i | \(-0.253261\pi\) |
−0.968527 | + | 0.248910i | \(0.919928\pi\) | |||||||
\(180\) | 609.682 | + | 1056.00i | 0.252461 | + | 0.437276i | ||||
\(181\) | −2.00000 | −0.000821319 | −0.000410660 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000410660 | 1.00000i | \(0.500131\pi\) | ||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 119.000 | 0.0480696 | ||||||||
\(184\) | 394.908 | + | 684.000i | 0.158223 | + | 0.274050i | ||||
\(185\) | 276.000 | + | 478.046i | 0.109686 | + | 0.189982i | ||||
\(186\) | −882.000 | + | 1527.67i | −0.347696 | + | 0.602226i | ||||
\(187\) | −607.950 | −0.237742 | ||||||||
\(188\) | 685.892 | − | 1188.00i | 0.266084 | − | 0.460871i | ||||
\(189\) | −394.042 | + | 682.500i | −0.151652 | + | 0.262670i | ||||
\(190\) | 4240.06 | 1.61898 | ||||||||
\(191\) | 1420.50 | − | 2460.38i | 0.538135 | − | 0.932077i | −0.460870 | − | 0.887468i | \(-0.652462\pi\) |
0.999005 | − | 0.0446092i | \(-0.0142043\pi\) | |||||||
\(192\) | 224.000 | + | 387.979i | 0.0841969 | + | 0.145833i | ||||
\(193\) | −2122.63 | − | 3676.50i | −0.791659 | − | 1.37119i | −0.924939 | − | 0.380115i | \(-0.875885\pi\) |
0.133281 | − | 0.991078i | \(-0.457449\pi\) | |||||||
\(194\) | 4278.00 | 1.58321 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 656.000 | 0.239067 | ||||||||
\(197\) | −1376.11 | − | 2383.50i | −0.497686 | − | 0.862017i | 0.502311 | − | 0.864687i | \(-0.332483\pi\) |
−0.999996 | + | 0.00267023i | \(0.999150\pi\) | |||||||
\(198\) | 858.000 | + | 1486.10i | 0.307957 | + | 0.533396i | ||||
\(199\) | −842.500 | + | 1459.25i | −0.300117 | + | 0.519818i | −0.976162 | − | 0.217042i | \(-0.930359\pi\) |
0.676045 | + | 0.736860i | \(0.263692\pi\) | |||||||
\(200\) | 928.379 | 0.328232 | ||||||||
\(201\) | 575.907 | − | 997.500i | 0.202096 | − | 0.350041i | ||||
\(202\) | −3393.09 | + | 5877.00i | −1.18187 | + | 2.04705i | ||||
\(203\) | −1553.65 | −0.537167 | ||||||||
\(204\) | −378.000 | + | 654.715i | −0.129732 | + | 0.224702i | ||||
\(205\) | −2724.00 | − | 4718.11i | −0.928061 | − | 1.60745i | ||||
\(206\) | −3214.69 | − | 5568.00i | −1.08727 | − | 1.88321i | ||||
\(207\) | −1254.00 | −0.421058 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1989.00 | 0.658287 | ||||||||
\(210\) | 3782.80 | + | 6552.00i | 1.24304 | + | 2.15300i | ||||
\(211\) | −840.500 | − | 1455.79i | −0.274229 | − | 0.474979i | 0.695711 | − | 0.718322i | \(-0.255089\pi\) |
−0.969940 | + | 0.243343i | \(0.921756\pi\) | |||||||
\(212\) | −852.000 | + | 1475.71i | −0.276017 | + | 0.478075i | ||||
\(213\) | 4085.91 | 1.31437 | ||||||||
\(214\) | −441.673 | + | 765.000i | −0.141085 | + | 0.244366i | ||||
\(215\) | 588.897 | − | 1020.00i | 0.186802 | − | 0.323551i | ||||
\(216\) | 484.974 | 0.152770 | ||||||||
\(217\) | −819.000 | + | 1418.55i | −0.256209 | + | 0.443767i | ||||
\(218\) | 1056.00 | + | 1829.05i | 0.328080 | + | 0.568250i | ||||
\(219\) | 3516.06 | + | 6090.00i | 1.08490 | + | 1.87911i | ||||
\(220\) | −1248.00 | −0.382455 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 966.000 | 0.292044 | ||||||||
\(223\) | 2048.15 | + | 3547.50i | 0.615042 | + | 1.06528i | 0.990377 | + | 0.138394i | \(0.0441941\pi\) |
−0.375336 | + | 0.926889i | \(0.622473\pi\) | |||||||
\(224\) | −1872.00 | − | 3242.40i | −0.558385 | − | 0.967151i | ||||
\(225\) | −737.000 | + | 1276.52i | −0.218370 | + | 0.378229i | ||||
\(226\) | −1423.75 | −0.419054 | ||||||||
\(227\) | 219.104 | − | 379.500i | 0.0640638 | − | 0.110962i | −0.832215 | − | 0.554454i | \(-0.812927\pi\) |
0.896278 | + | 0.443492i | \(0.146261\pi\) | |||||||
\(228\) | 1236.68 | − | 2142.00i | 0.359217 | − | 0.622182i | ||||
\(229\) | 180.133 | 0.0519805 | 0.0259903 | − | 0.999662i | \(-0.491726\pi\) | ||||
0.0259903 | + | 0.999662i | \(0.491726\pi\) | |||||||
\(230\) | 1368.00 | − | 2369.45i | 0.392188 | − | 0.679290i | ||||
\(231\) | 1774.50 | + | 3073.52i | 0.505427 | + | 0.875424i | ||||
\(232\) | 478.046 | + | 828.000i | 0.135281 | + | 0.234314i | ||||
\(233\) | 5778.00 | 1.62459 | 0.812295 | − | 0.583247i | \(-0.198218\pi\) | ||||
0.812295 | + | 0.583247i | \(0.198218\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4752.00 | 1.31909 | ||||||||
\(236\) | 38.1051 | + | 66.0000i | 0.0105103 | + | 0.0182044i | ||||
\(237\) | −4354.00 | − | 7541.35i | −1.19334 | − | 2.06693i | ||||
\(238\) | −1053.00 | + | 1823.85i | −0.286789 | + | 0.496734i | ||||
\(239\) | 1860.22 | 0.503464 | 0.251732 | − | 0.967797i | \(-0.419000\pi\) | ||||
0.251732 | + | 0.967797i | \(0.419000\pi\) | |||||||
\(240\) | 3879.79 | − | 6720.00i | 1.04350 | − | 1.80739i | ||||
\(241\) | −1029.70 | + | 1783.50i | −0.275224 | + | 0.476703i | −0.970192 | − | 0.242339i | \(-0.922085\pi\) |
0.694967 | + | 0.719041i | \(0.255419\pi\) | |||||||
\(242\) | 2854.42 | 0.758219 | ||||||||
\(243\) | −2464.00 | + | 4267.77i | −0.650476 | + | 1.12666i | ||||
\(244\) | 34.0000 | + | 58.8897i | 0.00892060 | + | 0.0154509i | ||||
\(245\) | 1136.23 | + | 1968.00i | 0.296289 | + | 0.513187i | ||||
\(246\) | −9534.00 | −2.47100 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 1008.00 | 0.258097 | ||||||||
\(249\) | 1491.30 | + | 2583.00i | 0.379546 | + | 0.657393i | ||||
\(250\) | 1392.00 | + | 2411.01i | 0.352151 | + | 0.609944i | ||||
\(251\) | 2245.50 | − | 3889.32i | 0.564680 | − | 0.978055i | −0.432399 | − | 0.901682i | \(-0.642333\pi\) |
0.997079 | − | 0.0763724i | \(-0.0243338\pi\) | |||||||
\(252\) | 1981.47 | 0.495320 | ||||||||
\(253\) | 641.725 | − | 1111.50i | 0.159466 | − | 0.276203i | ||||
\(254\) | 3884.99 | − | 6729.00i | 0.959708 | − | 1.66226i | ||||
\(255\) | −2618.86 | −0.643135 | ||||||||
\(256\) | −2432.00 | + | 4212.35i | −0.593750 | + | 1.02841i | ||||
\(257\) | 2725.50 | + | 4720.70i | 0.661525 | + | 1.14580i | 0.980215 | + | 0.197936i | \(0.0634239\pi\) |
−0.318690 | + | 0.947859i | \(0.603243\pi\) | |||||||
\(258\) | −1030.57 | − | 1785.00i | −0.248684 | − | 0.430734i | ||||
\(259\) | 897.000 | 0.215200 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1518.00 | −0.360007 | ||||||||
\(262\) | −644.323 | − | 1116.00i | −0.151933 | − | 0.263155i | ||||
\(263\) | 391.500 | + | 678.098i | 0.0917906 | + | 0.158986i | 0.908265 | − | 0.418396i | \(-0.137408\pi\) |
−0.816474 | + | 0.577382i | \(0.804074\pi\) | |||||||
\(264\) | 1092.00 | − | 1891.40i | 0.254576 | − | 0.440938i | ||||
\(265\) | −5902.83 | −1.36833 | ||||||||
\(266\) | 3445.05 | − | 5967.00i | 0.794096 | − | 1.37541i | ||||
\(267\) | −1073.01 | + | 1858.50i | −0.245943 | + | 0.425986i | ||||
\(268\) | 658.179 | 0.150018 | ||||||||
\(269\) | 2542.50 | − | 4403.74i | 0.576279 | − | 0.998144i | −0.419623 | − | 0.907699i | \(-0.637838\pi\) |
0.995901 | − | 0.0904453i | \(-0.0288290\pi\) | |||||||
\(270\) | −840.000 | − | 1454.92i | −0.189336 | − | 0.327940i | ||||
\(271\) | −662.509 | − | 1147.50i | −0.148504 | − | 0.257216i | 0.782171 | − | 0.623064i | \(-0.214112\pi\) |
−0.930675 | + | 0.365848i | \(0.880779\pi\) | |||||||
\(272\) | 2160.00 | 0.481505 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4122.00 | 0.908829 | ||||||||
\(275\) | −754.308 | − | 1306.50i | −0.165405 | − | 0.286491i | ||||
\(276\) | −798.000 | − | 1382.18i | −0.174036 | − | 0.301439i | ||||
\(277\) | −1710.50 | + | 2962.67i | −0.371025 | + | 0.642635i | −0.989724 | − | 0.142994i | \(-0.954327\pi\) |
0.618698 | + | 0.785629i | \(0.287660\pi\) | |||||||
\(278\) | 8816.14 | 1.90200 | ||||||||
\(279\) | −800.207 | + | 1386.00i | −0.171710 | + | 0.297411i | ||||
\(280\) | 2161.60 | − | 3744.00i | 0.461358 | − | 0.799096i | ||||
\(281\) | 810.600 | 0.172087 | 0.0860433 | − | 0.996291i | \(-0.472578\pi\) | ||||
0.0860433 | + | 0.996291i | \(0.472578\pi\) | |||||||
\(282\) | 4158.00 | − | 7201.87i | 0.878033 | − | 1.52080i | ||||
\(283\) | 3588.50 | + | 6215.46i | 0.753760 | + | 1.30555i | 0.945988 | + | 0.324201i | \(0.105095\pi\) |
−0.192228 | + | 0.981350i | \(0.561571\pi\) | |||||||
\(284\) | 1167.40 | + | 2022.00i | 0.243918 | + | 0.422478i | ||||
\(285\) | 8568.00 | 1.78079 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8853.00 | −1.82082 | ||||||||
\(288\) | −1829.05 | − | 3168.00i | −0.374228 | − | 0.648181i | ||||
\(289\) | 2092.00 | + | 3623.45i | 0.425809 | + | 0.737523i | ||||
\(290\) | 1656.00 | − | 2868.28i | 0.335323 | − | 0.580796i | ||||
\(291\) | 8644.67 | 1.74144 | ||||||||
\(292\) | −2009.18 | + | 3480.00i | −0.402665 | + | 0.697437i | ||||
\(293\) | −4656.62 | + | 8065.50i | −0.928473 | + | 1.60816i | −0.142595 | + | 0.989781i | \(0.545544\pi\) |
−0.785878 | + | 0.618381i | \(0.787789\pi\) | |||||||
\(294\) | 3976.79 | 0.788881 | ||||||||
\(295\) | −132.000 | + | 228.631i | −0.0260520 | + | 0.0451234i | ||||
\(296\) | −276.000 | − | 478.046i | −0.0541965 | − | 0.0938712i | ||||
\(297\) | −394.042 | − | 682.500i | −0.0769852 | − | 0.133342i | ||||
\(298\) | 4518.00 | 0.878257 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1876.00 | −0.361036 | ||||||||
\(301\) | −956.958 | − | 1657.50i | −0.183250 | − | 0.317398i | ||||
\(302\) | −150.000 | − | 259.808i | −0.0285812 | − | 0.0495041i | ||||
\(303\) | −6856.50 | + | 11875.8i | −1.29999 | + | 2.25164i | ||||
\(304\) | −7066.77 | −1.33325 | ||||||||
\(305\) | −117.779 | + | 204.000i | −0.0221116 | + | 0.0382984i | ||||
\(306\) | −1028.84 | + | 1782.00i | −0.192205 | + | 0.332909i | ||||
\(307\) | −4777.00 | −0.888070 | −0.444035 | − | 0.896009i | \(-0.646453\pi\) | ||||
−0.444035 | + | 0.896009i | \(0.646453\pi\) | |||||||
\(308\) | −1014.00 | + | 1756.30i | −0.187591 | + | 0.324917i | ||||
\(309\) | −6496.00 | − | 11251.4i | −1.19594 | − | 2.07142i | ||||
\(310\) | −1745.91 | − | 3024.00i | −0.319874 | − | 0.554038i | ||||
\(311\) | −6192.00 | −1.12899 | −0.564495 | − | 0.825436i | \(-0.690929\pi\) | ||||
−0.564495 | + | 0.825436i | \(0.690929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −770.000 | −0.139051 | −0.0695255 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695255 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(314\) | −2656.97 | − | 4602.00i | −0.477520 | − | 0.827089i | ||||
\(315\) | 3432.00 | + | 5944.40i | 0.613877 | + | 1.06327i | ||||
\(316\) | 2488.00 | − | 4309.34i | 0.442914 | − | 0.767150i | ||||
\(317\) | −8057.50 | −1.42762 | −0.713808 | − | 0.700341i | \(-0.753031\pi\) | ||||
−0.713808 | + | 0.700341i | \(0.753031\pi\) | |||||||
\(318\) | −5164.98 | + | 8946.00i | −0.910810 | + | 1.57757i | ||||
\(319\) | 776.825 | − | 1345.50i | 0.136344 | − | 0.236155i | ||||
\(320\) | −886.810 | −0.154919 | ||||||||
\(321\) | −892.500 | + | 1545.86i | −0.155185 | + | 0.268789i | ||||
\(322\) | −2223.00 | − | 3850.35i | −0.384730 | − | 0.666371i | ||||
\(323\) | 1192.52 | + | 2065.50i | 0.205429 | + | 0.355813i | ||||
\(324\) | −3356.00 | −0.575446 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5658.00 | 0.961250 | ||||||||
\(327\) | 2133.89 | + | 3696.00i | 0.360869 | + | 0.625044i | ||||
\(328\) | 2724.00 | + | 4718.11i | 0.458560 | + | 0.794250i | ||||
\(329\) | 3861.00 | − | 6687.45i | 0.647002 | − | 1.12064i | ||||
\(330\) | −7565.60 | −1.26204 | ||||||||
\(331\) | −2638.78 | + | 4570.50i | −0.438189 | + | 0.758965i | −0.997550 | − | 0.0699590i | \(-0.977713\pi\) |
0.559361 | + | 0.828924i | \(0.311046\pi\) | |||||||
\(332\) | −852.169 | + | 1476.00i | −0.140870 | + | 0.243994i | ||||
\(333\) | 876.418 | 0.144226 | ||||||||
\(334\) | −2817.00 | + | 4879.19i | −0.461495 | + | 0.799333i | ||||
\(335\) | 1140.00 | + | 1974.54i | 0.185925 | + | 0.322031i | ||||
\(336\) | −6304.66 | − | 10920.0i | −1.02365 | − | 1.77302i | ||||
\(337\) | −8278.00 | −1.33808 | −0.669038 | − | 0.743228i | \(-0.733294\pi\) | ||||
−0.669038 | + | 0.743228i | \(0.733294\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2877.00 | −0.460936 | ||||||||
\(340\) | −748.246 | − | 1296.00i | −0.119351 | − | 0.206722i | ||||
\(341\) | −819.000 | − | 1418.55i | −0.130063 | − | 0.225275i | ||||
\(342\) | 3366.00 | − | 5830.08i | 0.532200 | − | 0.921798i | ||||
\(343\) | −4030.48 | −0.634477 | ||||||||
\(344\) | −588.897 | + | 1020.00i | −0.0923000 | + | 0.159868i | ||||
\(345\) | 2764.35 | − | 4788.00i | 0.431385 | − | 0.747180i | ||||
\(346\) | −3024.16 | −0.469884 | ||||||||
\(347\) | −3433.50 | + | 5947.00i | −0.531181 | + | 0.920033i | 0.468156 | + | 0.883646i | \(0.344918\pi\) |
−0.999338 | + | 0.0363875i | \(0.988415\pi\) | |||||||
\(348\) | −966.000 | − | 1673.16i | −0.148802 | − | 0.257732i | ||||
\(349\) | 6076.90 | + | 10525.5i | 0.932060 | + | 1.61438i | 0.779794 | + | 0.626036i | \(0.215324\pi\) |
0.152266 | + | 0.988340i | \(0.451343\pi\) | |||||||
\(350\) | −5226.00 | −0.798118 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3744.00 | 0.566920 | ||||||||
\(353\) | −2903.78 | − | 5029.50i | −0.437827 | − | 0.758338i | 0.559695 | − | 0.828699i | \(-0.310918\pi\) |
−0.997522 | + | 0.0703608i | \(0.977585\pi\) | |||||||
\(354\) | 231.000 | + | 400.104i | 0.0346822 | + | 0.0600714i | ||||
\(355\) | −4044.00 | + | 7004.41i | −0.604601 | + | 1.04720i | ||||
\(356\) | −1226.29 | −0.182566 | ||||||||
\(357\) | −2127.82 | + | 3685.50i | −0.315452 | + | 0.546379i | ||||
\(358\) | 2229.15 | − | 3861.00i | 0.329090 | − | 0.570001i | ||||
\(359\) | 1340.61 | 0.197088 | 0.0985439 | − | 0.995133i | \(-0.468581\pi\) | ||||
0.0985439 | + | 0.995133i | \(0.468581\pi\) | |||||||
\(360\) | 2112.00 | − | 3658.09i | 0.309200 | − | 0.535551i | ||||
\(361\) | −472.000 | − | 817.528i | −0.0688147 | − | 0.119191i | ||||
\(362\) | −3.46410 | − | 6.00000i | −0.000502953 | − | 0.000871141i | ||||
\(363\) | 5768.00 | 0.833999 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13920.0 | −1.99618 | ||||||||
\(366\) | 206.114 | + | 357.000i | 0.0294365 | + | 0.0509855i | ||||
\(367\) | −1832.50 | − | 3173.98i | −0.260642 | − | 0.451446i | 0.705770 | − | 0.708441i | \(-0.250601\pi\) |
−0.966413 | + | 0.256995i | \(0.917268\pi\) | |||||||
\(368\) | −2280.00 | + | 3949.08i | −0.322971 | + | 0.559402i | ||||
\(369\) | −8649.86 | −1.22031 | ||||||||
\(370\) | −956.092 | + | 1656.00i | −0.134337 | + | 0.232679i | ||||
\(371\) | −4796.05 | + | 8307.00i | −0.671155 | + | 1.16247i | ||||
\(372\) | −2036.89 | −0.283892 | ||||||||
\(373\) | −2685.50 | + | 4651.42i | −0.372788 | + | 0.645688i | −0.989993 | − | 0.141114i | \(-0.954931\pi\) |
0.617205 | + | 0.786802i | \(0.288265\pi\) | |||||||
\(374\) | −1053.00 | − | 1823.85i | −0.145586 | − | 0.252163i | ||||
\(375\) | 2812.85 | + | 4872.00i | 0.387347 | + | 0.670904i | ||||
\(376\) | −4752.00 | −0.651770 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2730.00 | −0.371471 | ||||||||
\(379\) | 5754.74 | + | 9967.50i | 0.779950 | + | 1.35091i | 0.931970 | + | 0.362536i | \(0.118089\pi\) |
−0.152020 | + | 0.988377i | \(0.548578\pi\) | |||||||
\(380\) | 2448.00 | + | 4240.06i | 0.330473 | + | 0.572396i | ||||
\(381\) | 7850.50 | − | 13597.5i | 1.05563 | − | 1.82840i | ||||
\(382\) | 9841.51 | 1.31816 | ||||||||
\(383\) | 1209.84 | − | 2095.50i | 0.161409 | − | 0.279569i | −0.773965 | − | 0.633228i | \(-0.781729\pi\) |
0.935374 | + | 0.353659i | \(0.115063\pi\) | |||||||
\(384\) | −5431.71 | + | 9408.00i | −0.721838 | + | 1.25026i | ||||
\(385\) | −7025.20 | −0.929967 | ||||||||
\(386\) | 7353.00 | − | 12735.8i | 0.969580 | − | 1.67936i | ||||
\(387\) | −935.000 | − | 1619.47i | −0.122813 | − | 0.212719i | ||||
\(388\) | 2469.90 | + | 4278.00i | 0.323171 | + | 0.559749i | ||||
\(389\) | 9858.00 | 1.28489 | 0.642443 | − | 0.766334i | \(-0.277921\pi\) | ||||
0.642443 | + | 0.766334i | \(0.277921\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1539.00 | 0.199055 | ||||||||
\(392\) | −1136.23 | − | 1968.00i | −0.146398 | − | 0.253569i | ||||
\(393\) | −1302.00 | − | 2255.13i | −0.167118 | − | 0.289456i | ||||
\(394\) | 4767.00 | − | 8256.69i | 0.609538 | − | 1.05575i | ||||
\(395\) | 17237.4 | 2.19571 | ||||||||
\(396\) | −990.733 | + | 1716.00i | −0.125723 | + | 0.217758i | ||||
\(397\) | 4360.44 | − | 7552.50i | 0.551245 | − | 0.954784i | −0.446941 | − | 0.894564i | \(-0.647486\pi\) |
0.998185 | − | 0.0602200i | \(-0.0191802\pi\) | |||||||
\(398\) | −5837.01 | −0.735133 | ||||||||
\(399\) | 6961.50 | − | 12057.7i | 0.873461 | − | 1.51288i | ||||
\(400\) | 2680.00 | + | 4641.90i | 0.335000 | + | 0.580237i | ||||
\(401\) | −3792.33 | − | 6568.50i | −0.472269 | − | 0.817993i | 0.527228 | − | 0.849724i | \(-0.323231\pi\) |
−0.999496 | + | 0.0317308i | \(0.989898\pi\) | |||||||
\(402\) | 3990.00 | 0.495033 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −7836.00 | −0.964989 | ||||||||
\(405\) | −5812.76 | − | 10068.0i | −0.713181 | − | 1.23527i | ||||
\(406\) | −2691.00 | − | 4660.95i | −0.328946 | − | 0.569751i | ||||
\(407\) | −448.500 | + | 776.825i | −0.0546224 | + | 0.0946088i | ||||
\(408\) | 2618.86 | 0.317777 | ||||||||
\(409\) | 2152.07 | − | 3727.50i | 0.260179 | − | 0.450643i | −0.706110 | − | 0.708102i | \(-0.749552\pi\) |
0.966289 | + | 0.257459i | \(0.0828851\pi\) | |||||||
\(410\) | 9436.21 | − | 16344.0i | 1.13664 | − | 1.96871i | ||||
\(411\) | 8329.43 | 0.999661 | ||||||||
\(412\) | 3712.00 | − | 6429.37i | 0.443876 | − | 0.768817i | ||||
\(413\) | 214.500 | + | 371.525i | 0.0255565 | + | 0.0442652i | ||||
\(414\) | −2171.99 | − | 3762.00i | −0.257844 | − | 0.446600i | ||||
\(415\) | −5904.00 | −0.698352 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17815.0 | 2.09210 | ||||||||
\(418\) | 3445.05 | + | 5967.00i | 0.403117 | + | 0.698219i | ||||
\(419\) | −2698.50 | − | 4673.94i | −0.314631 | − | 0.544957i | 0.664728 | − | 0.747085i | \(-0.268547\pi\) |
−0.979359 | + | 0.202129i | \(0.935214\pi\) | |||||||
\(420\) | −4368.00 | + | 7565.60i | −0.507468 | + | 0.878960i | ||||
\(421\) | −7260.76 | −0.840541 | −0.420270 | − | 0.907399i | \(-0.638065\pi\) | ||||
−0.420270 | + | 0.907399i | \(0.638065\pi\) | |||||||
\(422\) | 2911.58 | − | 5043.00i | 0.335861 | − | 0.581728i | ||||
\(423\) | 3772.41 | − | 6534.00i | 0.433619 | − | 0.751050i | ||||
\(424\) | 5902.83 | 0.676101 | ||||||||
\(425\) | 904.500 | − | 1566.64i | 0.103235 | − | 0.178808i | ||||
\(426\) | 7077.00 | + | 12257.7i | 0.804887 | + | 1.39410i | ||||
\(427\) | 191.392 | + | 331.500i | 0.0216911 | + | 0.0375700i | ||||
\(428\) | −1020.00 | −0.115195 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4080.00 | 0.457570 | ||||||||
\(431\) | 243.353 | + | 421.500i | 0.0271970 | + | 0.0471066i | 0.879304 | − | 0.476262i | \(-0.158009\pi\) |
−0.852107 | + | 0.523368i | \(0.824675\pi\) | |||||||
\(432\) | 1400.00 | + | 2424.87i | 0.155920 | + | 0.270062i | ||||
\(433\) | 6069.50 | − | 10512.7i | 0.673629 | − | 1.16676i | −0.303238 | − | 0.952915i | \(-0.598068\pi\) |
0.976867 | − | 0.213846i | \(-0.0685989\pi\) | |||||||
\(434\) | −5674.20 | −0.627581 | ||||||||
\(435\) | 3346.32 | − | 5796.00i | 0.368836 | − | 0.638844i | ||||
\(436\) | −1219.36 | + | 2112.00i | −0.133938 | + | 0.231987i | ||||
\(437\) | −5035.07 | −0.551167 | ||||||||
\(438\) | −12180.0 | + | 21096.4i | −1.32873 | + | 2.30142i | ||||
\(439\) | 230.500 | + | 399.238i | 0.0250596 | + | 0.0434045i | 0.878283 | − | 0.478141i | \(-0.158689\pi\) |
−0.853224 | + | 0.521545i | \(0.825356\pi\) | |||||||
\(440\) | 2161.60 | + | 3744.00i | 0.234205 | + | 0.405655i | ||||
\(441\) | 3608.00 | 0.389591 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12156.0 | 1.30372 | 0.651861 | − | 0.758338i | \(-0.273988\pi\) | ||||
0.651861 | + | 0.758338i | \(0.273988\pi\) | |||||||
\(444\) | 557.720 | + | 966.000i | 0.0596131 | + | 0.103253i | ||||
\(445\) | −2124.00 | − | 3678.88i | −0.226263 | − | 0.391900i | ||||
\(446\) | −7095.00 | + | 12288.9i | −0.753269 | + | 1.30470i | ||||
\(447\) | 9129.64 | 0.966034 | ||||||||
\(448\) | −720.533 | + | 1248.00i | −0.0759866 | + | 0.131613i | ||||
\(449\) | 148.090 | − | 256.500i | 0.0155653 | − | 0.0269599i | −0.858138 | − | 0.513419i | \(-0.828379\pi\) |
0.873703 | + | 0.486459i | \(0.161712\pi\) | |||||||
\(450\) | −5106.09 | −0.534896 | ||||||||
\(451\) | 4426.50 | − | 7666.92i | 0.462164 | − | 0.800491i | ||||
\(452\) | −822.000 | − | 1423.75i | −0.0855390 | − | 0.148158i | ||||
\(453\) | −303.109 | − | 525.000i | −0.0314377 | − | 0.0544518i | ||||
\(454\) | 1518.00 | 0.156924 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8568.00 | −0.879898 | ||||||||
\(457\) | −305.707 | − | 529.500i | −0.0312918 | − | 0.0541990i | 0.849955 | − | 0.526855i | \(-0.176629\pi\) |
−0.881247 | + | 0.472656i | \(0.843295\pi\) | |||||||
\(458\) | 312.000 | + | 540.400i | 0.0318314 | + | 0.0551337i | ||||
\(459\) | 472.500 | − | 818.394i | 0.0480488 | − | 0.0832230i | ||||
\(460\) | 3159.26 | 0.320220 | ||||||||
\(461\) | −6563.61 | + | 11368.5i | −0.663119 | + | 1.14855i | 0.316673 | + | 0.948535i | \(0.397434\pi\) |
−0.979792 | + | 0.200020i | \(0.935899\pi\) | |||||||
\(462\) | −6147.05 | + | 10647.0i | −0.619019 | + | 1.07217i | ||||
\(463\) | −834.848 | −0.0837985 | −0.0418992 | − | 0.999122i | \(-0.513341\pi\) | ||||
−0.0418992 | + | 0.999122i | \(0.513341\pi\) | |||||||
\(464\) | −2760.00 | + | 4780.46i | −0.276142 | + | 0.478292i | ||||
\(465\) | −3528.00 | − | 6110.68i | −0.351843 | − | 0.609410i | ||||
\(466\) | 10007.8 | + | 17334.0i | 0.994854 | + | 1.72314i | ||||
\(467\) | −14496.0 | −1.43639 | −0.718196 | − | 0.695841i | \(-0.755032\pi\) | ||||
−0.718196 | + | 0.695841i | \(0.755032\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3705.00 | 0.364778 | ||||||||
\(470\) | 8230.71 | + | 14256.0i | 0.807775 | + | 1.39911i | ||||
\(471\) | −5369.00 | − | 9299.38i | −0.525245 | − | 0.909751i | ||||
\(472\) | 132.000 | − | 228.631i | 0.0128724 | − | 0.0222957i | ||||
\(473\) | 1913.92 | 0.186051 | ||||||||
\(474\) | 15082.7 | − | 26124.0i | 1.46154 | − | 2.53147i | ||||
\(475\) | −2959.21 | + | 5125.50i | −0.285848 | + | 0.495103i | ||||
\(476\) | −2431.80 | −0.234162 | ||||||||
\(477\) | −4686.00 | + | 8116.39i | −0.449805 | + | 0.779086i | ||||
\(478\) | 3222.00 | + | 5580.67i | 0.308307 | + | 0.534004i | ||||
\(479\) | −4448.77 | − | 7705.50i | −0.424362 | − | 0.735017i | 0.571998 | − | 0.820255i | \(-0.306168\pi\) |
−0.996361 | + | 0.0852376i | \(0.972835\pi\) | |||||||
\(480\) | 16128.0 | 1.53362 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −7134.00 | −0.674159 | ||||||||
\(483\) | −4492.07 | − | 7780.50i | −0.423181 | − | 0.732971i | ||||
\(484\) | 1648.00 | + | 2854.42i | 0.154771 | + | 0.268071i | ||||
\(485\) | −8556.00 | + | 14819.4i | −0.801047 | + | 1.38745i | ||||
\(486\) | −17071.1 | −1.59333 | ||||||||
\(487\) | 2377.24 | − | 4117.50i | 0.221197 | − | 0.383125i | −0.733975 | − | 0.679177i | \(-0.762337\pi\) |
0.955172 | + | 0.296052i | \(0.0956702\pi\) | |||||||
\(488\) | 117.779 | − | 204.000i | 0.0109255 | − | 0.0189235i | ||||
\(489\) | 11433.3 | 1.05732 | ||||||||
\(490\) | −3936.00 | + | 6817.35i | −0.362878 | + | 0.628524i | ||||
\(491\) | −817.500 | − | 1415.95i | −0.0751390 | − | 0.130145i | 0.826008 | − | 0.563659i | \(-0.190607\pi\) |
−0.901147 | + | 0.433514i | \(0.857273\pi\) | |||||||
\(492\) | −5504.46 | − | 9534.00i | −0.504390 | − | 0.873630i | ||||
\(493\) | 1863.00 | 0.170193 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6864.00 | −0.623260 | ||||||||
\(496\) | 2909.85 | + | 5040.00i | 0.263419 | + | 0.456255i | ||||
\(497\) | 6571.50 | + | 11382.2i | 0.593103 | + | 1.02728i | ||||
\(498\) | −5166.00 | + | 8947.77i | −0.464847 | + | 0.805139i | ||||
\(499\) | 14434.9 | 1.29498 | 0.647490 | − | 0.762074i | \(-0.275819\pi\) | ||||
0.647490 | + | 0.762074i | \(0.275819\pi\) | |||||||
\(500\) | −1607.34 | + | 2784.00i | −0.143765 | + | 0.249009i | ||||
\(501\) | −5692.38 | + | 9859.50i | −0.507619 | + | 0.879222i | ||||
\(502\) | 15557.3 | 1.38318 | ||||||||
\(503\) | −6343.50 | + | 10987.3i | −0.562312 | + | 0.973952i | 0.434983 | + | 0.900439i | \(0.356754\pi\) |
−0.997294 | + | 0.0735133i | \(0.976579\pi\) | |||||||
\(504\) | −3432.00 | − | 5944.40i | −0.303320 | − | 0.525366i | ||||
\(505\) | −13572.4 | − | 23508.0i | −1.19596 | − | 2.07147i | ||||
\(506\) | 4446.00 | 0.390610 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8972.00 | 0.783599 | ||||||||
\(509\) | 2874.34 | + | 4978.50i | 0.250300 | + | 0.433533i | 0.963608 | − | 0.267318i | \(-0.0861373\pi\) |
−0.713308 | + | 0.700850i | \(0.752804\pi\) | |||||||
\(510\) | −4536.00 | − | 7856.58i | −0.393838 | − | 0.682148i | ||||
\(511\) | −11310.0 | + | 19589.5i | −0.979109 | + | 1.69587i | ||||
\(512\) | −4434.05 | −0.382733 | ||||||||
\(513\) | −1545.86 | + | 2677.50i | −0.133043 | + | 0.230438i | ||||
\(514\) | −9441.41 | + | 16353.0i | −0.810200 | + | 1.40331i | ||||
\(515\) | 25717.5 | 2.20048 | ||||||||
\(516\) | 1190.00 | − | 2061.14i | 0.101525 | − | 0.175846i | ||||
\(517\) | 3861.00 | + | 6687.45i | 0.328446 | + | 0.568885i | ||||
\(518\) | 1553.65 | + | 2691.00i | 0.131783 | + | 0.228254i | ||||
\(519\) | −6111.00 | −0.516846 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6054.00 | 0.509080 | 0.254540 | − | 0.967062i | \(-0.418076\pi\) | ||||
0.254540 | + | 0.967062i | \(0.418076\pi\) | |||||||
\(522\) | −2629.25 | − | 4554.00i | −0.220458 | − | 0.381845i | ||||
\(523\) | 7401.50 | + | 12819.8i | 0.618824 | + | 1.07183i | 0.989701 | + | 0.143153i | \(0.0457240\pi\) |
−0.370877 | + | 0.928682i | \(0.620943\pi\) | |||||||
\(524\) | 744.000 | − | 1288.65i | 0.0620263 | − | 0.107433i | ||||
\(525\) | −10560.3 | −0.877885 | ||||||||
\(526\) | −1356.20 | + | 2349.00i | −0.112420 | + | 0.194717i | ||||
\(527\) | 982.073 | − | 1701.00i | 0.0811760 | − | 0.140601i | ||||
\(528\) | 12609.3 | 1.03930 | ||||||||
\(529\) | 4459.00 | − | 7723.21i | 0.366483 | − | 0.634767i | ||||
\(530\) | −10224.0 | − | 17708.5i | −0.837929 | − | 1.45133i | ||||
\(531\) | 209.578 | + | 363.000i | 0.0171279 | + | 0.0296664i | ||||
\(532\) | 7956.00 | 0.648377 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −7434.00 | −0.602436 | ||||||||
\(535\) | −1766.69 | − | 3060.00i | −0.142768 | − | 0.247281i | ||||
\(536\) | −1140.00 | − | 1974.54i | −0.0918666 | − | 0.159118i | ||||
\(537\) | 4504.50 | − | 7802.02i | 0.361980 | − | 0.626969i | ||||
\(538\) | 17615.0 | 1.41159 | ||||||||
\(539\) | −1846.37 | + | 3198.00i | −0.147548 | + | 0.255561i | ||||
\(540\) | 969.948 | − | 1680.00i | 0.0772962 | − | 0.133881i | ||||
\(541\) | −21470.5 | −1.70626 | −0.853132 | − | 0.521695i | \(-0.825300\pi\) | ||||
−0.853132 | + | 0.521695i | \(0.825300\pi\) | |||||||
\(542\) | 2295.00 | − | 3975.06i | 0.181880 | − | 0.315025i | ||||
\(543\) | −7.00000 | − | 12.1244i | −0.000553221 | − | 0.000958206i | ||||
\(544\) | 2244.74 | + | 3888.00i | 0.176916 | + | 0.306428i | ||||
\(545\) | −8448.00 | −0.663986 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13516.0 | −1.05649 | −0.528247 | − | 0.849091i | \(-0.677151\pi\) | ||||
−0.528247 | + | 0.849091i | \(0.677151\pi\) | |||||||
\(548\) | 2379.84 | + | 4122.00i | 0.185514 | + | 0.321320i | ||||
\(549\) | 187.000 | + | 323.894i | 0.0145373 | + | 0.0251793i | ||||
\(550\) | 2613.00 | − | 4525.85i | 0.202579 | − | 0.350878i | ||||
\(551\) | −6095.09 | −0.471251 | ||||||||
\(552\) | −2764.35 | + | 4788.00i | −0.213150 | + | 0.369186i | ||||
\(553\) | 14005.4 | − | 24258.0i | 1.07698 | − | 1.86538i | ||||
\(554\) | −11850.7 | −0.908822 | ||||||||
\(555\) | −1932.00 | + | 3346.32i | −0.147764 | + | 0.255934i | ||||
\(556\) | 5090.00 | + | 8816.14i | 0.388245 | + | 0.672460i | ||||
\(557\) | 1445.40 | + | 2503.50i | 0.109952 | + | 0.190443i | 0.915751 | − | 0.401747i | \(-0.131597\pi\) |
−0.805798 | + | 0.592190i | \(0.798264\pi\) | |||||||
\(558\) | −5544.00 | −0.420603 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 24960.0 | 1.88349 | ||||||||
\(561\) | −2127.82 | − | 3685.50i | −0.160137 | − | 0.277365i | ||||
\(562\) | 1404.00 | + | 2431.80i | 0.105381 | + | 0.182525i | ||||
\(563\) | 5791.50 | − | 10031.2i | 0.433539 | − | 0.750912i | −0.563636 | − | 0.826023i | \(-0.690598\pi\) |
0.997175 | + | 0.0751113i | \(0.0239312\pi\) | |||||||
\(564\) | 9602.49 | 0.716911 | ||||||||
\(565\) | 2847.49 | − | 4932.00i | 0.212026 | − | 0.367240i | ||||
\(566\) | −12430.9 | + | 21531.0i | −0.923164 | + | 1.59897i | ||||
\(567\) | −18891.5 | −1.39924 | ||||||||
\(568\) | 4044.00 | − | 7004.41i | 0.298737 | − | 0.517427i | ||||
\(569\) | 6439.50 | + | 11153.5i | 0.474443 | + | 0.821759i | 0.999572 | − | 0.0292638i | \(-0.00931628\pi\) |
−0.525129 | + | 0.851023i | \(0.675983\pi\) | |||||||
\(570\) | 14840.2 | + | 25704.0i | 1.09051 | + | 1.88881i | ||||
\(571\) | 11636.0 | 0.852805 | 0.426402 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426402 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 19887.0 | 1.44990 | ||||||||
\(574\) | −15333.8 | − | 26559.0i | −1.11502 | − | 1.93127i | ||||
\(575\) | 1909.50 | + | 3307.35i | 0.138490 | + | 0.239871i | ||||
\(576\) | −704.000 | + | 1219.36i | −0.0509259 | + | 0.0882063i | ||||
\(577\) | −12311.4 | −0.888269 | −0.444134 | − | 0.895960i | \(-0.646489\pi\) | ||||
−0.444134 | + | 0.895960i | \(0.646489\pi\) | |||||||
\(578\) | −7246.90 | + | 12552.0i | −0.521507 | + | 0.903277i | ||||
\(579\) | 14858.4 | − | 25735.5i | 1.06648 | − | 1.84720i | ||||
\(580\) | 3824.37 | 0.273790 | ||||||||
\(581\) | −4797.00 | + | 8308.65i | −0.342535 | + | 0.593289i | ||||
\(582\) | 14973.0 | + | 25934.0i | 1.06641 | + | 1.84708i | ||||
\(583\) | −4796.05 | − | 8307.00i | −0.340707 | − | 0.590121i | ||||
\(584\) | 13920.0 | 0.986325 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −32262.0 | −2.27428 | ||||||||
\(587\) | 7822.81 | + | 13549.5i | 0.550054 | + | 0.952722i | 0.998270 | + | 0.0587964i | \(0.0187263\pi\) |
−0.448216 | + | 0.893925i | \(0.647940\pi\) | |||||||
\(588\) | 2296.00 | + | 3976.79i | 0.161030 | + | 0.278912i | ||||
\(589\) | −3213.00 | + | 5565.08i | −0.224770 | + | 0.389313i | ||||
\(590\) | −914.523 | −0.0638141 | ||||||||
\(591\) | 9632.80 | − | 16684.5i | 0.670458 | − | 1.16127i | ||||
\(592\) | 1593.49 | − | 2760.00i | 0.110628 | − | 0.191614i | ||||
\(593\) | 25821.4 | 1.78813 | 0.894063 | − | 0.447942i | \(-0.147843\pi\) | ||||
0.894063 | + | 0.447942i | \(0.147843\pi\) | |||||||
\(594\) | 1365.00 | − | 2364.25i | 0.0942873 | − | 0.163310i | ||||
\(595\) | −4212.00 | − | 7295.40i | −0.290210 | − | 0.502659i | ||||
\(596\) | 2608.47 | + | 4518.00i | 0.179274 | + | 0.310511i | ||||
\(597\) | −11795.0 | −0.808605 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1668.00 | 0.113777 | 0.0568887 | − | 0.998381i | \(-0.481882\pi\) | ||||
0.0568887 | + | 0.998381i | \(0.481882\pi\) | |||||||
\(600\) | 3249.33 | + | 5628.00i | 0.221089 | + | 0.382937i | ||||
\(601\) | −6849.50 | − | 11863.7i | −0.464887 | − | 0.805207i | 0.534310 | − | 0.845289i | \(-0.320572\pi\) |
−0.999196 | + | 0.0400813i | \(0.987238\pi\) | |||||||
\(602\) | 3315.00 | − | 5741.75i | 0.224434 | − | 0.388731i | ||||
\(603\) | 3619.99 | 0.244473 | ||||||||
\(604\) | 173.205 | − | 300.000i | 0.0116682 | − | 0.0202100i | ||||
\(605\) | −5708.84 | + | 9888.00i | −0.383632 | + | 0.664470i | ||||
\(606\) | −47503.2 | −3.18430 | ||||||||
\(607\) | 11586.5 | − | 20068.4i | 0.774764 | − | 1.34193i | −0.160164 | − | 0.987090i | \(-0.551202\pi\) |
0.934927 | − | 0.354839i | \(-0.115464\pi\) | |||||||
\(608\) | −7344.00 | − | 12720.2i | −0.489866 | − | 0.848473i | ||||
\(609\) | −5437.77 | − | 9418.50i | −0.361822 | − | 0.626694i | ||||
\(610\) | −816.000 | −0.0541621 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −2376.00 | −0.156935 | ||||||||
\(613\) | −8307.78 | − | 14389.5i | −0.547387 | − | 0.948102i | −0.998453 | − | 0.0556111i | \(-0.982289\pi\) |
0.451066 | − | 0.892491i | \(-0.351044\pi\) | |||||||
\(614\) | −8274.00 | − | 14331.0i | −0.543830 | − | 0.941941i | ||||
\(615\) | 19068.0 | − | 33026.7i | 1.25024 | − | 2.16547i | ||||
\(616\) | 7025.20 | 0.459502 | ||||||||
\(617\) | 14196.8 | − | 24589.5i | 0.926321 | − | 1.60443i | 0.136897 | − | 0.990585i | \(-0.456287\pi\) |
0.789423 | − | 0.613849i | \(-0.210380\pi\) | |||||||
\(618\) | 22502.8 | − | 38976.0i | 1.46472 | − | 2.53697i | ||||
\(619\) | −6245.78 | −0.405556 | −0.202778 | − | 0.979225i | \(-0.564997\pi\) | ||||
−0.202778 | + | 0.979225i | \(0.564997\pi\) | |||||||
\(620\) | 2016.00 | − | 3491.81i | 0.130588 | − | 0.226185i | ||||
\(621\) | 997.500 | + | 1727.72i | 0.0644578 | + | 0.111644i | ||||
\(622\) | −10724.9 | − | 18576.0i | −0.691363 | − | 1.19748i | ||||
\(623\) | −6903.00 | −0.443921 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19511.0 | −1.24870 | ||||||||
\(626\) | −1333.68 | − | 2310.00i | −0.0851510 | − | 0.147486i | ||||
\(627\) | 6961.50 | + | 12057.7i | 0.443406 | + | 0.768002i | ||||
\(628\) | 3068.00 | − | 5313.93i | 0.194947 | − | 0.337658i | ||||
\(629\) | −1075.60 | −0.0681830 | ||||||||
\(630\) | −11888.8 | + | 20592.0i | −0.751843 | + | 1.30223i | ||||
\(631\) | −11189.9 | + | 19381.5i | −0.705964 | + | 1.22277i | 0.260378 | + | 0.965507i | \(0.416153\pi\) |
−0.966342 | + | 0.257259i | \(0.917181\pi\) | |||||||
\(632\) | −17237.4 | −1.08491 | ||||||||
\(633\) | 5883.50 | − | 10190.5i | 0.369428 | − | 0.639869i | ||||
\(634\) | −13956.0 | − | 24172.5i | −0.874233 | − | 1.51422i | ||||
\(635\) | 15540.0 | + | 26916.0i | 0.971157 | + | 1.68209i | ||||
\(636\) | −11928.0 | −0.743673 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5382.00 | 0.333974 | ||||||||
\(639\) | 6420.71 | + | 11121.0i | 0.397495 | + | 0.688482i | ||||
\(640\) | −10752.0 | − | 18623.0i | −0.664078 | − | 1.15022i | ||||
\(641\) | 9913.50 | − | 17170.7i | 0.610858 | − | 1.05804i | −0.380239 | − | 0.924888i | \(-0.624158\pi\) |
0.991096 | − | 0.133148i | \(-0.0425085\pi\) | |||||||
\(642\) | −6183.42 | −0.380125 | ||||||||
\(643\) | −4225.34 | + | 7318.50i | −0.259146 | + | 0.448855i | −0.966013 | − | 0.258492i | \(-0.916775\pi\) |
0.706867 | + | 0.707346i | \(0.250108\pi\) | |||||||
\(644\) | 2566.90 | − | 4446.00i | 0.157065 | − | 0.272045i | ||||
\(645\) | 8244.56 | 0.503301 | ||||||||
\(646\) | −4131.00 | + | 7155.10i | −0.251598 | + | 0.435780i | ||||
\(647\) | 1474.50 | + | 2553.91i | 0.0895959 | + | 0.155185i | 0.907340 | − | 0.420397i | \(-0.138109\pi\) |
−0.817744 | + | 0.575581i | \(0.804776\pi\) | |||||||
\(648\) | 5812.76 | + | 10068.0i | 0.352387 | + | 0.610352i | ||||
\(649\) | −429.000 | −0.0259472 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11466.0 | −0.690304 | ||||||||
\(652\) | 3266.65 | + | 5658.00i | 0.196214 | + | 0.339853i | ||||
\(653\) | −6019.50 | − | 10426.1i | −0.360737 | − | 0.624815i | 0.627345 | − | 0.778741i | \(-0.284141\pi\) |
−0.988082 | + | 0.153926i | \(0.950808\pi\) | |||||||
\(654\) | −7392.00 | + | 12803.3i | −0.441973 | + | 0.765519i | ||||
\(655\) | 5154.58 | 0.307490 | ||||||||
\(656\) | −15727.0 | + | 27240.0i | −0.936032 | + | 1.62126i | ||||
\(657\) | −11050.5 | + | 19140.0i | −0.656196 | + | 1.13656i | ||||
\(658\) | 26749.8 | 1.58483 | ||||||||
\(659\) | −1681.50 | + | 2912.44i | −0.0993960 | + | 0.172159i | −0.911435 | − | 0.411445i | \(-0.865024\pi\) |
0.812039 | + | 0.583603i | \(0.198358\pi\) | |||||||
\(660\) | −4368.00 | − | 7565.60i | −0.257612 | − | 0.446198i | ||||
\(661\) | 5079.24 | + | 8797.50i | 0.298880 | + | 0.517675i | 0.975880 | − | 0.218308i | \(-0.0700537\pi\) |
−0.677000 | + | 0.735983i | \(0.736720\pi\) | |||||||
\(662\) | −18282.0 | −1.07334 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5904.00 | 0.345060 | ||||||||
\(665\) | 13780.2 | + | 23868.0i | 0.803569 | + | 1.39182i | ||||
\(666\) | 1518.00 | + | 2629.25i | 0.0883203 | + | 0.152975i | ||||
\(667\) | −1966.50 | + | 3406.08i | −0.114158 | + | 0.197727i | ||||
\(668\) | −6505.58 | −0.376809 | ||||||||
\(669\) | −14337.1 | + | 24832.5i | −0.828554 | + | 1.43510i | ||||
\(670\) | −3949.08 | + | 6840.00i | −0.227711 | + | 0.394406i | ||||
\(671\) | −382.783 | −0.0220226 | ||||||||
\(672\) | 13104.0 | − | 22696.8i | 0.752229 | − | 1.30290i | ||||
\(673\) | −9084.50 | − | 15734.8i | −0.520329 | − | 0.901237i | −0.999721 | − | 0.0236358i | \(-0.992476\pi\) |
0.479391 | − | 0.877601i | \(-0.340858\pi\) | |||||||
\(674\) | −14337.9 | − | 24834.0i | −0.819400 | − | 1.41924i | ||||
\(675\) | 2345.00 | 0.133717 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9042.00 | 0.513312 | 0.256656 | − | 0.966503i | \(-0.417379\pi\) | ||||
0.256656 | + | 0.966503i | \(0.417379\pi\) | |||||||
\(678\) | −4983.11 | − | 8631.00i | −0.282264 | − | 0.488896i | ||||
\(679\) | 13903.5 | + | 24081.6i | 0.785813 | + | 1.36107i | ||||
\(680\) | −2592.00 | + | 4489.48i | −0.146175 | + | 0.253182i | ||||
\(681\) | 3067.46 | 0.172607 | ||||||||
\(682\) | 2837.10 | − | 4914.00i | 0.159293 | − | 0.275904i | ||||
\(683\) | 6231.05 | − | 10792.5i | 0.349084 | − | 0.604632i | −0.637003 | − | 0.770862i | \(-0.719826\pi\) |
0.986087 | + | 0.166230i | \(0.0531593\pi\) | |||||||
\(684\) | 7773.44 | 0.434540 | ||||||||
\(685\) | −8244.00 | + | 14279.0i | −0.459835 | + | 0.796458i | ||||
\(686\) | −6981.00 | − | 12091.4i | −0.388536 | − | 0.672964i | ||||
\(687\) | 630.466 | + | 1092.00i | 0.0350128 | + | 0.0606440i | ||||
\(688\) | −6800.00 | −0.376813 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 19152.0 | 1.05667 | ||||||||
\(691\) | 2159.00 | + | 3739.50i | 0.118860 | + | 0.205872i | 0.919316 | − | 0.393520i | \(-0.128743\pi\) |
−0.800456 | + | 0.599391i | \(0.795409\pi\) | |||||||
\(692\) | −1746.00 | − | 3024.16i | −0.0959147 | − | 0.166129i | ||||
\(693\) | −5577.00 | + | 9659.65i | −0.305704 | + | 0.529494i | ||||
\(694\) | −23788.0 | −1.30112 | ||||||||
\(695\) | −17632.3 | + | 30540.0i | −0.962346 | + | 1.66683i | ||||
\(696\) | −3346.32 | + | 5796.00i | −0.182244 | + | 0.315656i | ||||
\(697\) | 10615.7 | 0.576901 | ||||||||
\(698\) | −21051.0 | + | 36461.4i | −1.14154 | + | 1.97720i | ||||
\(699\) | 20223.0 | + | 35027.3i | 1.09428 | + | 1.89535i | ||||
\(700\) | −3017.23 | − | 5226.00i | −0.162915 | − | 0.282177i | ||||
\(701\) | 18270.0 | 0.984377 | 0.492189 | − | 0.870489i | \(-0.336197\pi\) | ||||
0.492189 | + | 0.870489i | \(0.336197\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3519.00 | 0.188793 | ||||||||
\(704\) | −720.533 | − | 1248.00i | −0.0385740 | − | 0.0668122i | ||||
\(705\) | 16632.0 | + | 28807.5i | 0.888507 | + | 1.53894i | ||||
\(706\) | 10059.0 | − | 17422.7i | 0.536226 | − | 0.928770i | ||||
\(707\) | −44110.1 | −2.34644 | ||||||||
\(708\) | −266.736 | + | 462.000i | −0.0141590 | + | 0.0245240i | ||||
\(709\) | −814.930 | + | 1411.50i | −0.0431669 | + | 0.0747673i | −0.886802 | − | 0.462150i | \(-0.847078\pi\) |
0.843635 | + | 0.536918i | \(0.180411\pi\) | |||||||
\(710\) | −28017.7 | −1.48096 | ||||||||
\(711\) | 13684.0 | − | 23701.4i | 0.721786 | − | 1.25017i | ||||
\(712\) | 2124.00 | + | 3678.88i | 0.111798 | + | 0.193640i | ||||
\(713\) | 2073.26 | + | 3591.00i | 0.108898 | + | 0.188617i | ||||
\(714\) | −14742.0 | −0.772697 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5148.00 | 0.268701 | ||||||||
\(717\) | 6510.78 | + | 11277.0i | 0.339121 | + | 0.587374i | ||||
\(718\) | 2322.00 | + | 4021.82i | 0.120691 | + | 0.209043i | ||||
\(719\) | 4915.50 | − | 8513.90i | 0.254961 | − | 0.441606i | −0.709924 | − | 0.704279i | \(-0.751271\pi\) |
0.964885 | + | 0.262673i | \(0.0846039\pi\) | |||||||
\(720\) | 24387.3 | 1.26231 | ||||||||
\(721\) | 20895.5 | − | 36192.0i | 1.07932 | − | 1.86943i | ||||
\(722\) | 1635.06 | − | 2832.00i | 0.0842804 | − | 0.145978i | ||||
\(723\) | −14415.9 | −0.741537 | ||||||||
\(724\) | 4.00000 | − | 6.92820i | 0.000205330 | − | 0.000355642i | ||||
\(725\) | 2311.50 | + | 4003.64i | 0.118410 | + | 0.205091i | ||||
\(726\) | 9990.47 | + | 17304.0i | 0.510718 | + | 0.884589i | ||||
\(727\) | 15464.0 | 0.788897 | 0.394448 | − | 0.918918i | \(-0.370936\pi\) | ||||
0.394448 | + | 0.918918i | \(0.370936\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11843.0 | −0.601687 | ||||||||
\(730\) | −24110.1 | − | 41760.0i | −1.22241 | − | 2.11727i | ||||
\(731\) | 1147.50 | + | 1987.53i | 0.0580599 | + | 0.100563i | ||||
\(732\) | −238.000 | + | 412.228i | −0.0120174 | + | 0.0208147i | ||||
\(733\) | 12616.3 | 0.635733 | 0.317866 | − | 0.948136i | \(-0.397034\pi\) | ||||
0.317866 | + | 0.948136i | \(0.397034\pi\) | |||||||
\(734\) | 6347.97 | − | 10995.0i | 0.319220 | − | 0.552906i | ||||
\(735\) | −7953.58 | + | 13776.0i | −0.399146 | + | 0.691341i | ||||
\(736\) | −9477.78 | −0.474668 | ||||||||
\(737\) | −1852.50 | + | 3208.62i | −0.0925885 | + | 0.160368i | ||||
\(738\) | −14982.0 | − | 25949.6i | −0.747283 | − | 1.29433i | ||||
\(739\) | −8141.50 | − | 14101.5i | −0.405264 | − | 0.701938i | 0.589088 | − | 0.808069i | \(-0.299487\pi\) |
−0.994352 | + | 0.106131i | \(0.966154\pi\) | |||||||
\(740\) | −2208.00 | −0.109686 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −33228.0 | −1.64399 | ||||||||
\(743\) | −5403.13 | − | 9358.50i | −0.266786 | − | 0.462086i | 0.701244 | − | 0.712921i | \(-0.252628\pi\) |
−0.968030 | + | 0.250835i | \(0.919295\pi\) | |||||||
\(744\) | 3528.00 | + | 6110.68i | 0.173848 | + | 0.301113i | ||||
\(745\) | −9036.00 | + | 15650.8i | −0.444367 | + | 0.769666i | ||||
\(746\) | −18605.7 | −0.913140 | ||||||||
\(747\) | −4686.93 | + | 8118.00i | −0.229566 | + | 0.397620i | ||||
\(748\) | 1215.90 | − | 2106.00i | 0.0594354 | − | 0.102945i | ||||
\(749\) | −5741.75 | −0.280105 | ||||||||
\(750\) | −9744.00 | + | 16877.1i | −0.474401 | + | 0.821686i | ||||
\(751\) | −6807.50 | − | 11790.9i | −0.330771 | − | 0.572913i | 0.651892 | − | 0.758312i | \(-0.273976\pi\) |
−0.982663 | + | 0.185399i | \(0.940642\pi\) | |||||||
\(752\) | −13717.8 | − | 23760.0i | −0.665210 | − | 1.15218i | ||||
\(753\) | 31437.0 | 1.52142 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1200.00 | 0.0578443 | ||||||||
\(756\) | −1576.17 | − | 2730.00i | −0.0758262 | − | 0.131335i | ||||
\(757\) | −2775.50 | − | 4807.31i | −0.133259 | − | 0.230812i | 0.791672 | − | 0.610947i | \(-0.209211\pi\) |
−0.924931 | + | 0.380135i | \(0.875878\pi\) | |||||||
\(758\) | −19935.0 | + | 34528.4i | −0.955240 | + | 1.65452i | ||||
\(759\) | 8984.15 | 0.429649 | ||||||||
\(760\) | 8480.12 | − | 14688.0i | 0.404745 | − | 0.701039i | ||||
\(761\) | −5041.13 | + | 8731.50i | −0.240133 | + | 0.415922i | −0.960752 | − | 0.277409i | \(-0.910524\pi\) |
0.720619 | + | 0.693331i | \(0.243858\pi\) | |||||||
\(762\) | 54389.9 | 2.58574 | ||||||||
\(763\) | −6864.00 | + | 11888.8i | −0.325680 | + | 0.564093i | ||||
\(764\) | 5682.00 | + | 9841.51i | 0.269067 | + | 0.466039i | ||||
\(765\) | −4115.35 | − | 7128.00i | −0.194498 | − | 0.336880i | ||||
\(766\) | 8382.00 | 0.395371 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −34048.0 | −1.59974 | ||||||||
\(769\) | −14879.2 | − | 25771.5i | −0.697733 | − | 1.20851i | −0.969250 | − | 0.246076i | \(-0.920859\pi\) |
0.271517 | − | 0.962434i | \(-0.412475\pi\) | |||||||
\(770\) | −12168.0 | − | 21075.6i | −0.569486 | − | 0.986379i | ||||
\(771\) | −19078.5 | + | 33044.9i | −0.891174 | + | 1.54356i | ||||
\(772\) | 16981.0 | 0.791659 | ||||||||
\(773\) | 13867.7 | − | 24019.5i | 0.645259 | − | 1.11762i | −0.338983 | − | 0.940793i | \(-0.610083\pi\) |
0.984242 | − | 0.176829i | \(-0.0565839\pi\) | |||||||
\(774\) | 3238.94 | − | 5610.00i | 0.150415 | − | 0.260526i | ||||
\(775\) | 4873.99 | 0.225908 | ||||||||
\(776\) | 8556.00 | − | 14819.4i | 0.395802 | − | 0.685550i | ||||
\(777\) | 3139.50 | + | 5437.77i | 0.144954 | + | 0.251067i | ||||
\(778\) | 17074.6 | + | 29574.0i | 0.786828 | + | 1.36283i | ||||
\(779\) | −34731.0 | −1.59739 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13143.0 | −0.602168 | ||||||||
\(782\) | 2665.63 | + | 4617.00i | 0.121896 | + | 0.211130i | ||||
\(783\) | 1207.50 | + | 2091.45i | 0.0551118 | + | 0.0954564i | ||||
\(784\) | 6560.00 | − | 11362.3i | 0.298834 | − | 0.517595i | ||||
\(785\) | 21255.7 | 0.966432 | ||||||||
\(786\) | 4510.26 | − | 7812.00i | 0.204676 | − | 0.354510i | ||||
\(787\) | 15774.7 | − | 27322.5i | 0.714493 | − | 1.23754i | −0.248662 | − | 0.968590i | \(-0.579991\pi\) |
0.963155 | − | 0.268947i | \(-0.0866757\pi\) | |||||||
\(788\) | 11008.9 | 0.497686 | ||||||||
\(789\) | −2740.50 | + | 4746.69i | −0.123656 | + | 0.214178i | ||||
\(790\) | 29856.0 | + | 51712.1i | 1.34459 | + | 2.32890i | ||||
\(791\) | −4627.17 | − | 8014.50i | −0.207994 | − | 0.360256i | ||||
\(792\) | 6864.00 | 0.307957 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 30210.0 | 1.35027 | ||||||||
\(795\) | −20659.9 | − | 35784.0i | −0.921674 | − | 1.59639i | ||||
\(796\) | −3370.00 | − | 5837.01i | −0.150058 | − | 0.259909i | ||||
\(797\) | 727.500 | − | 1260.07i | 0.0323330 | − | 0.0560023i | −0.849406 | − | 0.527740i | \(-0.823040\pi\) |
0.881739 | + | 0.471737i | \(0.156373\pi\) | |||||||
\(798\) | 48230.7 | 2.13953 | ||||||||
\(799\) | −4629.77 | + | 8019.00i | −0.204993 | + | 0.355059i | ||||
\(800\) | −5570.28 | + | 9648.00i | −0.246174 | + | 0.426385i | ||||
\(801\) | −6744.61 | −0.297514 | ||||||||
\(802\) | 13137.0 | − | 22754.0i | 0.578408 | − | 1.00183i | ||||
\(803\) | −11310.0 | − | 19589.5i | −0.497038 | − | 0.860894i | ||||
\(804\) | 2303.63 | + | 3990.00i | 0.101048 | + | 0.175020i | ||||
\(805\) | 17784.0 | 0.778638 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 35595.0 | 1.55267 | ||||||||
\(808\) | 13572.4 | + | 23508.0i | 0.590933 | + | 1.02353i | ||||
\(809\) | −829.500 | − | 1436.74i | −0.0360490 | − | 0.0624388i | 0.847438 | − | 0.530894i | \(-0.178144\pi\) |
−0.883487 | + | 0.468456i | \(0.844811\pi\) | |||||||
\(810\) | 20136.0 | − | 34876.6i | 0.873465 | − | 1.51289i | ||||
\(811\) | −4402.87 | −0.190636 | −0.0953180 | − | 0.995447i | \(-0.530387\pi\) | ||||
−0.0953180 | + | 0.995447i | \(0.530387\pi\) | |||||||
\(812\) | 3107.30 | − | 5382.00i | 0.134292 | − | 0.232600i | ||||
\(813\) | 4637.57 | − | 8032.50i | 0.200057 | − | 0.346509i | ||||
\(814\) | −3107.30 | −0.133797 | ||||||||
\(815\) | −11316.0 | + | 19599.9i | −0.486359 | + | 0.842398i | ||||
\(816\) | 7560.00 | + | 13094.3i | 0.324330 | + | 0.561755i | ||||
\(817\) | −3754.22 | − | 6502.50i | −0.160763 | − | 0.278450i | ||||
\(818\) | 14910.0 | 0.637306 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 21792.0 | 0.928061 | ||||||||
\(821\) | 14350.9 | + | 24856.5i | 0.610049 | + | 1.05664i | 0.991232 | + | 0.132136i | \(0.0421835\pi\) |
−0.381183 | + | 0.924500i | \(0.624483\pi\) | |||||||
\(822\) | 14427.0 | + | 24988.3i | 0.612165 | + | 1.06030i | ||||
\(823\) | 7889.50 | − | 13665.0i | 0.334156 | − | 0.578776i | −0.649166 | − | 0.760647i | \(-0.724882\pi\) |
0.983322 | + | 0.181871i | \(0.0582153\pi\) | |||||||
\(824\) | −25717.5 | −1.08727 | ||||||||
\(825\) | 5280.16 | − | 9145.50i | 0.222826 | − | 0.385946i | ||||
\(826\) | −743.050 | + | 1287.00i | −0.0313003 | + | 0.0542136i | ||||
\(827\) | −7354.29 | −0.309231 | −0.154615 | − | 0.987975i | \(-0.549414\pi\) | ||||
−0.154615 | + | 0.987975i | \(0.549414\pi\) | |||||||
\(828\) | 2508.00 | − | 4343.98i | 0.105265 | − | 0.182324i | ||||
\(829\) | 8685.50 | + | 15043.7i | 0.363884 | + | 0.630266i | 0.988596 | − | 0.150589i | \(-0.0481171\pi\) |
−0.624712 | + | 0.780855i | \(0.714784\pi\) | |||||||
\(830\) | −10226.0 | − | 17712.0i | −0.427651 | − | 0.740714i | ||||
\(831\) | −23947.0 | −0.999654 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4428.00 | −0.184179 | ||||||||
\(834\) | 30856.5 | + | 53445.0i | 1.28114 | + | 2.21900i | ||||
\(835\) | −11268.0 | − | 19516.7i | −0.467000 | − | 0.808868i | ||||
\(836\) | −3978.00 | + | 6890.10i | −0.164572 | + | 0.285047i | ||||
\(837\) | 2546.11 | 0.105145 | ||||||||
\(838\) | 9347.88 | − | 16191.0i | 0.385343 | − | 0.667433i | ||||
\(839\) | −14737.2 | + | 25525.5i | −0.606416 | + | 1.05034i | 0.385410 | + | 0.922745i | \(0.374060\pi\) |
−0.991826 | + | 0.127598i | \(0.959273\pi\) | |||||||
\(840\) | 30262.4 | 1.24304 | ||||||||
\(841\) | 9814.00 | − | 16998.3i | 0.402395 | − | 0.696968i | ||||
\(842\) | −12576.0 | − | 21782.3i | −0.514724 | − | 0.891528i | ||||
\(843\) | 2837.10 | + | 4914.00i | 0.115913 | + | 0.200768i | ||||
\(844\) | 6724.00 | 0.274229 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 26136.0 | 1.06214 | ||||||||
\(847\) | 9276.86 | + | 16068.0i | 0.376336 | + | 0.651834i | ||||
\(848\) | 17040.0 | + | 29514.1i | 0.690042 | + | 1.19519i | ||||
\(849\) | −25119.5 | + | 43508.3i | −1.01543 | + | 1.75877i | ||||
\(850\) | 6266.56 | 0.252872 | ||||||||
\(851\) | 1135.36 | − | 1966.50i | 0.0457340 | − | 0.0792136i | ||||
\(852\) | −8171.82 | + | 14154.0i | −0.328594 | + | 0.569141i | ||||
\(853\) | 2909.85 | 0.116801 | 0.0584005 | − | 0.998293i | \(-0.481400\pi\) | ||||
0.0584005 | + | 0.998293i | \(0.481400\pi\) | |||||||
\(854\) | −663.000 | + | 1148.35i | −0.0265660 | + | 0.0460137i | ||||
\(855\) | 13464.0 | + | 23320.3i | 0.538549 | + | 0.932794i | ||||
\(856\) | 1766.69 | + | 3060.00i | 0.0705424 | + | 0.122183i | ||||
\(857\) | 5346.00 | 0.213087 | 0.106544 | − | 0.994308i | \(-0.466022\pi\) | ||||
0.106544 | + | 0.994308i | \(0.466022\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24244.0 | 0.962974 | 0.481487 | − | 0.876453i | \(-0.340097\pi\) | ||||
0.481487 | + | 0.876453i | \(0.340097\pi\) | |||||||
\(860\) | 2355.59 | + | 4080.00i | 0.0934011 | + | 0.161775i | ||||
\(861\) | −30985.5 | − | 53668.5i | −1.22646 | − | 2.12429i | ||||
\(862\) | −843.000 | + | 1460.12i | −0.0333094 | + | 0.0576936i | ||||
\(863\) | −32780.8 | −1.29301 | −0.646507 | − | 0.762908i | \(-0.723771\pi\) | ||||
−0.646507 | + | 0.762908i | \(0.723771\pi\) | |||||||
\(864\) | −2909.85 | + | 5040.00i | −0.114577 | + | 0.198454i | ||||
\(865\) | 6048.32 | − | 10476.0i | 0.237745 | − | 0.411786i | ||||
\(866\) | 42050.7 | 1.65005 | ||||||||
\(867\) | −14644.0 | + | 25364.2i | −0.573629 | + | 0.993555i | ||||
\(868\) | −3276.00 | − | 5674.20i | −0.128104 | − | 0.221883i | ||||
\(869\) | 14005.4 | + | 24258.0i | 0.546720 | + | 0.946946i | ||||
\(870\) | 23184.0 | 0.903461 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 8448.00 | 0.328080 | ||||||||
\(873\) | 13584.5 | + | 23529.0i | 0.526649 | + | 0.912183i | ||||
\(874\) | −8721.00 | − | 15105.2i | −0.337520 | − | 0.584601i | ||||
\(875\) | −9048.00 | + | 15671.6i | −0.349575 | + | 0.605482i | ||||
\(876\) | −28128.5 | −1.08490 | ||||||||
\(877\) | −2271.58 | + | 3934.50i | −0.0874640 | + | 0.151492i | −0.906439 | − | 0.422338i | \(-0.861210\pi\) |
0.818974 | + | 0.573830i | \(0.194543\pi\) | |||||||
\(878\) | −798.475 | + | 1383.00i | −0.0306916 | + | 0.0531594i | ||||
\(879\) | −65192.7 | −2.50159 | ||||||||
\(880\) | −12480.0 | + | 21616.0i | −0.478069 | + | 0.828040i | ||||
\(881\) | −10258.5 | − | 17768.2i | −0.392302 | − | 0.679486i | 0.600451 | − | 0.799661i | \(-0.294988\pi\) |
−0.992753 | + | 0.120175i | \(0.961654\pi\) | |||||||
\(882\) | 6249.24 | + | 10824.0i | 0.238575 | + | 0.413223i | ||||
\(883\) | 23852.0 | 0.909042 | 0.454521 | − | 0.890736i | \(-0.349811\pi\) | ||||
0.454521 | + | 0.890736i | \(0.349811\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1848.00 | −0.0701919 | ||||||||
\(886\) | 21054.8 | + | 36468.0i | 0.798364 | + | 1.38281i | ||||
\(887\) | −19378.5 | − | 33564.5i | −0.733558 | − | 1.27056i | −0.955353 | − | 0.295467i | \(-0.904525\pi\) |
0.221794 | − | 0.975093i | \(-0.428809\pi\) | |||||||
\(888\) | 1932.00 | − | 3346.32i | 0.0730109 | − | 0.126459i | ||||
\(889\) | 50504.9 | 1.90538 | ||||||||
\(890\) | 7357.75 | − | 12744.0i | 0.277115 | − | 0.479977i | ||||
\(891\) | 9445.74 | − | 16360.5i | 0.355156 | − | 0.615149i | ||||
\(892\) | −16385.2 | −0.615042 | ||||||||
\(893\) | 15147.0 | − | 26235.4i | 0.567609 | − | 0.983128i | ||||
\(894\) | 15813.0 | + | 27388.9i | 0.591573 | + | 1.02463i | ||||
\(895\) | 8916.60 | + | 15444.0i | 0.333016 | + | 0.576800i | ||||
\(896\) | −34944.0 | −1.30290 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1026.00 | 0.0381270 | ||||||||
\(899\) | 2509.74 | + | 4347.00i | 0.0931085 | + | 0.161269i | ||||
\(900\) | −2948.00 | − | 5106.09i | −0.109185 | − | 0.189114i | ||||
\(901\) | 5751.00 | − | 9961.02i | 0.212645 | − | 0.368313i | ||||
\(902\) | 30667.7 | 1.13206 | ||||||||
\(903\) | 6698.71 | − | 11602.5i | 0.246865 | − | 0.427583i | ||||
\(904\) | −2847.49 | + | 4932.00i | −0.104763 | + | 0.181456i | ||||
\(905\) | 27.7128 | 0.00101791 | ||||||||
\(906\) | 1050.00 | − | 1818.65i | 0.0385032 | − | 0.0666895i | ||||
\(907\) | −19535.5 | − | 33836.5i | −0.715177 | − | 1.23872i | −0.962891 | − | 0.269890i | \(-0.913013\pi\) |
0.247714 | − | 0.968833i | \(-0.420321\pi\) | |||||||
\(908\) | 876.418 | + | 1518.00i | 0.0320319 | + | 0.0554808i | ||||
\(909\) | −43098.0 | −1.57257 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −53040.0 | −1.92897 | −0.964486 | − | 0.264134i | \(-0.914914\pi\) | ||||
−0.964486 | + | 0.264134i | \(0.914914\pi\) | |||||||
\(912\) | −24733.7 | − | 42840.0i | −0.898042 | − | 1.55545i | ||||
\(913\) | −4797.00 | − | 8308.65i | −0.173886 | − | 0.301179i | ||||
\(914\) | 1059.00 | − | 1834.24i | 0.0383245 | − | 0.0663800i | ||||
\(915\) | −1648.91 | −0.0595753 | ||||||||
\(916\) | −360.267 | + | 624.000i | −0.0129951 | + | 0.0225082i | ||||
\(917\) | 4188.10 | − | 7254.00i | 0.150821 | − | 0.261230i | ||||
\(918\) | 3273.58 | 0.117695 | ||||||||
\(919\) | −183.500 | + | 317.831i | −0.00658662 | + | 0.0114084i | −0.869300 | − | 0.494285i | \(-0.835430\pi\) |
0.862713 | + | 0.505693i | \(0.168763\pi\) | |||||||
\(920\) | −5472.00 | − | 9477.78i | −0.196094 | − | 0.339645i | ||||
\(921\) | −16719.5 | − | 28959.0i | −0.598182 | − | 1.03608i | ||||
\(922\) | −45474.0 | −1.62430 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −14196.0 | −0.505427 | ||||||||
\(925\) | −1334.55 | − | 2311.50i | −0.0474374 | − | 0.0821639i | ||||
\(926\) | −1446.00 | − | 2504.55i | −0.0513159 | − | 0.0888817i | ||||
\(927\) | 20416.0 | − | 35361.5i | 0.723354 | − | 1.25289i | ||||
\(928\) | −11473.1 | −0.405844 | ||||||||
\(929\) | −14967.5 | + | 25924.5i | −0.528599 | + | 0.915560i | 0.470845 | + | 0.882216i | \(0.343949\pi\) |
−0.999444 | + | 0.0333441i | \(0.989384\pi\) | |||||||
\(930\) | 12221.4 | − | 21168.0i | 0.430918 | − | 0.746372i | ||||
\(931\) | 14486.9 | 0.509976 | ||||||||
\(932\) | −11556.0 | + | 20015.6i | −0.406147 | + | 0.703468i | ||||
\(933\) | −21672.0 | − | 37537.0i | −0.760460 | − | 1.31716i | ||||
\(934\) | −25107.8 | − | 43488.0i | −0.879607 | − | 1.52352i | ||||
\(935\) | 8424.00 | 0.294646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42166.0 | 1.47012 | 0.735060 | − | 0.678002i | \(-0.237154\pi\) | ||||
0.735060 | + | 0.678002i | \(0.237154\pi\) | |||||||
\(938\) | 6417.25 | + | 11115.0i | 0.223380 | + | 0.386906i | ||||
\(939\) | −2695.00 | − | 4667.88i | −0.0936613 | − | 0.162226i | ||||
\(940\) | −9504.00 | + | 16461.4i | −0.329773 | + | 0.571183i | ||||
\(941\) | 35022.1 | 1.21327 | 0.606635 | − | 0.794981i | \(-0.292519\pi\) | ||||
0.606635 | + | 0.794981i | \(0.292519\pi\) | |||||||
\(942\) | 18598.8 | − | 32214.0i | 0.643291 | − | 1.11421i | ||||
\(943\) | −11205.5 | + | 19408.5i | −0.386958 | + | 0.670231i | ||||
\(944\) | 1524.20 | 0.0525515 | ||||||||
\(945\) | 5460.00 | − | 9457.00i | 0.187951 | − | 0.325541i | ||||
\(946\) | 3315.00 | + | 5741.75i | 0.113932 | + | 0.197337i | ||||
\(947\) | −1299.90 | − | 2251.50i | −0.0446053 | − | 0.0772586i | 0.842861 | − | 0.538132i | \(-0.180870\pi\) |
−0.887466 | + | 0.460873i | \(0.847536\pi\) | |||||||
\(948\) | 34832.0 | 1.19334 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −20502.0 | −0.700182 | ||||||||
\(951\) | −28201.3 | − | 48846.0i | −0.961607 | − | 1.66555i | ||||
\(952\) | 4212.00 | + | 7295.40i | 0.143395 | + | 0.248367i | ||||
\(953\) | 5311.50 | − | 9199.79i | 0.180542 | − | 0.312708i | −0.761523 | − | 0.648137i | \(-0.775548\pi\) |
0.942065 | + | 0.335430i | \(0.108882\pi\) | |||||||
\(954\) | −32465.6 | −1.10179 | ||||||||
\(955\) | −19683.0 | + | 34092.0i | −0.666940 | + | 1.15517i | ||||
\(956\) | −3720.45 | + | 6444.00i | −0.125866 | + | 0.218006i | ||||
\(957\) | 10875.5 | 0.367353 | ||||||||
\(958\) | 15411.0 | − | 26692.6i | 0.519736 | − | 0.900209i | ||||
\(959\) | 13396.5 | + | 23203.4i | 0.451090 | + | 0.781311i | ||||
\(960\) | −3103.84 | − | 5376.00i | −0.104350 | − | 0.180739i | ||||
\(961\) | −24499.0 | −0.822362 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5610.00 | −0.187726 | ||||||||
\(964\) | −4118.82 | − | 7134.00i | −0.137612 | − | 0.238351i | ||||
\(965\) | 29412.0 | + | 50943.1i | 0.981146 | + | 1.69939i | ||||
\(966\) | 15561.0 | − | 26952.4i | 0.518289 | − | 0.897703i | ||||
\(967\) | −20199.2 | −0.671729 | −0.335864 | − | 0.941910i | \(-0.609028\pi\) | ||||
−0.335864 | + | 0.941910i | \(0.609028\pi\) | |||||||
\(968\) | 5708.84 | − | 9888.00i | 0.189555 | − | 0.328319i | ||||
\(969\) | −8347.62 | + | 14458.5i | −0.276743 | + | 0.479333i | ||||
\(970\) | −59277.7 | −1.96216 | ||||||||
\(971\) | 1162.50 | − | 2013.51i | 0.0384206 | − | 0.0665464i | −0.846176 | − | 0.532904i | \(-0.821101\pi\) |
0.884596 | + | 0.466358i | \(0.154434\pi\) | |||||||
\(972\) | −9856.00 | − | 17071.1i | −0.325238 | − | 0.563329i | ||||
\(973\) | 28652.5 | + | 49627.5i | 0.944045 | + | 1.63513i | ||||
\(974\) | 16470.0 | 0.541820 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1360.00 | 0.0446030 | ||||||||
\(977\) | −16469.2 | − | 28525.5i | −0.539300 | − | 0.934096i | −0.998942 | − | 0.0459912i | \(-0.985355\pi\) |
0.459641 | − | 0.888105i | \(-0.347978\pi\) | |||||||
\(978\) | 19803.0 | + | 34299.8i | 0.647475 | + | 1.12146i | ||||
\(979\) | 3451.50 | − | 5978.17i | 0.112677 | − | 0.195162i | ||||
\(980\) | −9089.80 | −0.296289 | ||||||||
\(981\) | −6706.50 | + | 11616.0i | −0.218269 | + | 0.378053i | ||||
\(982\) | 2831.90 | − | 4905.00i | 0.0920261 | − | 0.159394i | ||||
\(983\) | 42702.0 | 1.38554 | 0.692768 | − | 0.721161i | \(-0.256391\pi\) | ||||
0.692768 | + | 0.721161i | \(0.256391\pi\) | |||||||
\(984\) | −19068.0 | + | 33026.7i | −0.617750 | + | 1.06997i | ||||
\(985\) | 19068.0 | + | 33026.7i | 0.616809 | + | 1.06834i | ||||
\(986\) | 3226.81 | + | 5589.00i | 0.104222 | + | 0.180517i | ||||
\(987\) | 54054.0 | 1.74322 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4845.00 | −0.155776 | ||||||||
\(990\) | −11888.8 | − | 20592.0i | −0.381667 | − | 0.661067i | ||||
\(991\) | 2421.50 | + | 4194.16i | 0.0776201 | + | 0.134442i | 0.902223 | − | 0.431271i | \(-0.141935\pi\) |
−0.824603 | + | 0.565712i | \(0.808601\pi\) | |||||||
\(992\) | −6048.00 | + | 10475.4i | −0.193573 | + | 0.335278i | ||||
\(993\) | −36942.9 | −1.18061 | ||||||||
\(994\) | −22764.3 | + | 39429.0i | −0.726400 | + | 1.25816i | ||||
\(995\) | 11674.0 | − | 20220.0i | 0.371951 | − | 0.644238i | ||||
\(996\) | −11930.4 | −0.379546 | ||||||||
\(997\) | −5471.50 | + | 9476.92i | −0.173806 | + | 0.301040i | −0.939747 | − | 0.341870i | \(-0.888940\pi\) |
0.765942 | + | 0.642910i | \(0.222273\pi\) | |||||||
\(998\) | 25002.0 | + | 43304.7i | 0.793011 | + | 1.37353i | ||||
\(999\) | −697.150 | − | 1207.50i | −0.0220789 | − | 0.0382419i |
(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 | 169.4.c.i.146.2 | 4 | ||
13.2 | odd | 12 | 169.4.b.b.168.2 | 2 | |||
13.3 | even | 3 | 169.4.a.h.1.1 | 2 | |||
13.4 | even | 6 | inner | 169.4.c.i.22.1 | 4 | ||
13.5 | odd | 4 | 169.4.e.b.23.1 | 2 | |||
13.6 | odd | 12 | 13.4.e.a.4.1 | ✓ | 2 | ||
13.7 | odd | 12 | 169.4.e.b.147.1 | 2 | |||
13.8 | odd | 4 | 13.4.e.a.10.1 | yes | 2 | ||
13.9 | even | 3 | inner | 169.4.c.i.22.2 | 4 | ||
13.10 | even | 6 | 169.4.a.h.1.2 | 2 | |||
13.11 | odd | 12 | 169.4.b.b.168.1 | 2 | |||
13.12 | even | 2 | inner | 169.4.c.i.146.1 | 4 | ||
39.8 | even | 4 | 117.4.q.c.10.1 | 2 | |||
39.23 | odd | 6 | 1521.4.a.q.1.1 | 2 | |||
39.29 | odd | 6 | 1521.4.a.q.1.2 | 2 | |||
39.32 | even | 12 | 117.4.q.c.82.1 | 2 | |||
52.19 | even | 12 | 208.4.w.a.17.1 | 2 | |||
52.47 | even | 4 | 208.4.w.a.49.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.4.e.a.4.1 | ✓ | 2 | 13.6 | odd | 12 | ||
13.4.e.a.10.1 | yes | 2 | 13.8 | odd | 4 | ||
117.4.q.c.10.1 | 2 | 39.8 | even | 4 | |||
117.4.q.c.82.1 | 2 | 39.32 | even | 12 | |||
169.4.a.h.1.1 | 2 | 13.3 | even | 3 | |||
169.4.a.h.1.2 | 2 | 13.10 | even | 6 | |||
169.4.b.b.168.1 | 2 | 13.11 | odd | 12 | |||
169.4.b.b.168.2 | 2 | 13.2 | odd | 12 | |||
169.4.c.i.22.1 | 4 | 13.4 | even | 6 | inner | ||
169.4.c.i.22.2 | 4 | 13.9 | even | 3 | inner | ||
169.4.c.i.146.1 | 4 | 13.12 | even | 2 | inner | ||
169.4.c.i.146.2 | 4 | 1.1 | even | 1 | trivial | ||
169.4.e.b.23.1 | 2 | 13.5 | odd | 4 | |||
169.4.e.b.147.1 | 2 | 13.7 | odd | 12 | |||
208.4.w.a.17.1 | 2 | 52.19 | even | 12 | |||
208.4.w.a.49.1 | 2 | 52.47 | even | 4 | |||
1521.4.a.q.1.1 | 2 | 39.23 | odd | 6 | |||
1521.4.a.q.1.2 | 2 | 39.29 | odd | 6 |