Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.15759792.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.1 | ||
Root | \(0.500000 - 2.88506i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.c.151.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.28679 | − | 3.96084i | −0.808502 | − | 1.40037i | −0.913901 | − | 0.405937i | \(-0.866945\pi\) |
0.105398 | − | 0.994430i | \(-0.466388\pi\) | |||||||
\(3\) | −3.36330 | + | 3.96084i | −0.647267 | + | 0.762263i | ||||
\(4\) | −6.45882 | + | 11.1870i | −0.807352 | + | 1.39838i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 23.3794 | + | 4.26387i | 1.59077 | + | 0.290120i | ||||
\(7\) | −10.0573 | − | 17.4197i | −0.543041 | − | 0.940575i | −0.998727 | − | 0.0504348i | \(-0.983939\pi\) |
0.455686 | − | 0.890141i | \(-0.349394\pi\) | |||||||
\(8\) | 22.4912 | 0.993981 | ||||||||
\(9\) | −4.37646 | − | 26.6429i | −0.162091 | − | 0.986776i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.1708 | − | 57.4535i | −0.909215 | − | 1.57481i | −0.815157 | − | 0.579240i | \(-0.803349\pi\) |
−0.0940582 | − | 0.995567i | \(-0.529984\pi\) | |||||||
\(12\) | −22.5870 | − | 63.2076i | −0.543358 | − | 1.52054i | ||||
\(13\) | −23.4003 | + | 40.5305i | −0.499237 | + | 0.864703i | −1.00000 | 0.000881222i | \(-0.999719\pi\) | |
0.500763 | + | 0.865584i | \(0.333053\pi\) | |||||||
\(14\) | −45.9977 | + | 79.6704i | −0.878101 | + | 1.52092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.237854 | + | 0.411975i | 0.00371647 | + | 0.00643711i | ||||
\(17\) | 47.6233 | 0.679432 | 0.339716 | − | 0.940528i | \(-0.389669\pi\) | ||||
0.339716 | + | 0.940528i | \(0.389669\pi\) | |||||||
\(18\) | −95.5203 | + | 78.2613i | −1.25080 | + | 1.02480i | ||||
\(19\) | −9.95276 | −0.120175 | −0.0600874 | − | 0.998193i | \(-0.519138\pi\) | ||||
−0.0600874 | + | 0.998193i | \(0.519138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 102.822 | + | 18.7524i | 1.06846 | + | 0.194863i | ||||
\(22\) | −151.709 | + | 262.768i | −1.47021 | + | 2.54647i | ||||
\(23\) | 4.79602 | − | 8.30695i | 0.0434800 | − | 0.0753095i | −0.843466 | − | 0.537182i | \(-0.819489\pi\) |
0.886946 | + | 0.461872i | \(0.152822\pi\) | |||||||
\(24\) | −75.6447 | + | 89.0841i | −0.643371 | + | 0.757675i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 214.046 | 1.61454 | ||||||||
\(27\) | 120.248 | + | 72.2737i | 0.857099 | + | 0.515151i | ||||
\(28\) | 259.832 | 1.75370 | ||||||||
\(29\) | 89.3675 | + | 154.789i | 0.572246 | + | 0.991158i | 0.996335 | + | 0.0855380i | \(0.0272609\pi\) |
−0.424089 | + | 0.905620i | \(0.639406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.0186 | + | 133.400i | −0.446224 | + | 0.772883i | −0.998137 | − | 0.0610190i | \(-0.980565\pi\) |
0.551912 | + | 0.833902i | \(0.313898\pi\) | |||||||
\(32\) | 91.0527 | − | 157.708i | 0.503000 | − | 0.871222i | ||||
\(33\) | 339.127 | + | 61.8491i | 1.78892 | + | 0.326259i | ||||
\(34\) | −108.905 | − | 188.628i | −0.549323 | − | 0.951455i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 326.322 | + | 123.123i | 1.51075 | + | 0.570012i | ||||
\(37\) | −248.864 | −1.10576 | −0.552878 | − | 0.833262i | \(-0.686471\pi\) | ||||
−0.552878 | + | 0.833262i | \(0.686471\pi\) | |||||||
\(38\) | 22.7599 | + | 39.4213i | 0.0971616 | + | 0.168289i | ||||
\(39\) | −81.8326 | − | 229.001i | −0.335992 | − | 0.940244i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.832 | + | 216.216i | −0.475500 | + | 0.823590i | −0.999606 | − | 0.0280628i | \(-0.991066\pi\) |
0.524106 | + | 0.851653i | \(0.324400\pi\) | |||||||
\(42\) | −160.857 | − | 450.145i | −0.590972 | − | 1.65378i | ||||
\(43\) | −106.122 | − | 183.809i | −0.376361 | − | 0.651876i | 0.614169 | − | 0.789175i | \(-0.289491\pi\) |
−0.990530 | + | 0.137299i | \(0.956158\pi\) | |||||||
\(44\) | 856.976 | 2.93623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −43.8700 | −0.140615 | ||||||||
\(47\) | 237.847 | + | 411.963i | 0.738160 | + | 1.27853i | 0.953323 | + | 0.301953i | \(0.0976384\pi\) |
−0.215163 | + | 0.976578i | \(0.569028\pi\) | |||||||
\(48\) | −2.43174 | − | 0.443494i | −0.00731232 | − | 0.00133360i | ||||
\(49\) | −30.7973 | + | 53.3425i | −0.0897880 | + | 0.155517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −160.171 | + | 188.628i | −0.439774 | + | 0.517906i | ||||
\(52\) | −302.277 | − | 523.559i | −0.806120 | − | 1.39624i | ||||
\(53\) | 546.314 | 1.41589 | 0.707944 | − | 0.706269i | \(-0.249623\pi\) | ||||
0.707944 | + | 0.706269i | \(0.249623\pi\) | |||||||
\(54\) | 11.2831 | − | 641.556i | 0.0284341 | − | 1.61675i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −226.200 | − | 391.790i | −0.539773 | − | 0.934914i | ||||
\(57\) | 33.4741 | − | 39.4213i | 0.0777851 | − | 0.0916048i | ||||
\(58\) | 408.729 | − | 707.940i | 0.925324 | − | 1.60271i | ||||
\(59\) | 209.648 | − | 363.121i | 0.462608 | − | 0.801261i | −0.536482 | − | 0.843912i | \(-0.680247\pi\) |
0.999090 | + | 0.0426512i | \(0.0135804\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 272.605 | + | 472.165i | 0.572188 | + | 0.991059i | 0.996341 | + | 0.0854682i | \(0.0272386\pi\) |
−0.424153 | + | 0.905591i | \(0.639428\pi\) | |||||||
\(62\) | 704.502 | 1.44309 | ||||||||
\(63\) | −420.097 | + | 344.192i | −0.840115 | + | 0.688319i | ||||
\(64\) | −829.068 | −1.61927 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −530.538 | − | 1484.66i | −0.989466 | − | 2.76893i | ||||
\(67\) | −223.938 | + | 387.872i | −0.408335 | + | 0.707256i | −0.994703 | − | 0.102788i | \(-0.967224\pi\) |
0.586369 | + | 0.810044i | \(0.300557\pi\) | |||||||
\(68\) | −307.590 | + | 532.762i | −0.548541 | + | 0.950102i | ||||
\(69\) | 16.7720 | + | 46.9350i | 0.0292625 | + | 0.0818885i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 409.542 | 0.684559 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(72\) | −98.4319 | − | 599.232i | −0.161115 | − | 0.980836i | ||||
\(73\) | 358.548 | 0.574861 | 0.287431 | − | 0.957801i | \(-0.407199\pi\) | ||||
0.287431 | + | 0.957801i | \(0.407199\pi\) | |||||||
\(74\) | 569.100 | + | 985.710i | 0.894007 | + | 1.54847i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 64.2831 | − | 111.342i | 0.0970234 | − | 0.168049i | ||||
\(77\) | −667.215 | + | 1155.65i | −0.987483 | + | 1.71037i | ||||
\(78\) | −719.902 | + | 847.803i | −1.04504 | + | 1.23070i | ||||
\(79\) | 325.776 | + | 564.260i | 0.463958 | + | 0.803598i | 0.999154 | − | 0.0411297i | \(-0.0130957\pi\) |
−0.535196 | + | 0.844728i | \(0.679762\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −690.693 | + | 233.204i | −0.947453 | + | 0.319895i | ||||
\(82\) | 1141.86 | 1.53777 | ||||||||
\(83\) | −406.571 | − | 704.202i | −0.537675 | − | 0.931280i | −0.999029 | − | 0.0440636i | \(-0.985970\pi\) |
0.461354 | − | 0.887216i | \(-0.347364\pi\) | |||||||
\(84\) | −873.893 | + | 1029.15i | −1.13511 | + | 1.33678i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −485.359 | + | 840.667i | −0.608577 | + | 1.05409i | ||||
\(87\) | −913.663 | − | 166.631i | −1.12592 | − | 0.205342i | ||||
\(88\) | −746.051 | − | 1292.20i | −0.903743 | − | 1.56533i | ||||
\(89\) | −201.000 | −0.239393 | −0.119696 | − | 0.992811i | \(-0.538192\pi\) | ||||
−0.119696 | + | 0.992811i | \(0.538192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 941.373 | 1.08442 | ||||||||
\(92\) | 61.9532 | + | 107.306i | 0.0702073 | + | 0.121603i | ||||
\(93\) | −269.340 | − | 753.723i | −0.300314 | − | 0.840402i | ||||
\(94\) | 1087.81 | − | 1884.14i | 1.19361 | − | 2.06739i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 318.418 | + | 891.064i | 0.338525 | + | 0.947331i | ||||
\(97\) | 126.074 | + | 218.367i | 0.131968 | + | 0.228576i | 0.924435 | − | 0.381339i | \(-0.124537\pi\) |
−0.792467 | + | 0.609915i | \(0.791204\pi\) | |||||||
\(98\) | 281.708 | 0.290375 | ||||||||
\(99\) | −1385.56 | + | 1135.21i | −1.40661 | + | 1.15245i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −21.8013 | − | 37.7610i | −0.0214783 | − | 0.0372016i | 0.855086 | − | 0.518485i | \(-0.173504\pi\) |
−0.876565 | + | 0.481284i | \(0.840171\pi\) | |||||||
\(102\) | 1113.40 | + | 203.060i | 1.08082 | + | 0.197117i | ||||
\(103\) | −720.176 | + | 1247.38i | −0.688942 | + | 1.19328i | 0.283238 | + | 0.959050i | \(0.408591\pi\) |
−0.972180 | + | 0.234233i | \(0.924742\pi\) | |||||||
\(104\) | −526.301 | + | 911.581i | −0.496232 | + | 0.859498i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1249.31 | − | 2163.86i | −1.14475 | − | 1.98276i | ||||
\(107\) | −355.755 | −0.321422 | −0.160711 | − | 0.987002i | \(-0.551379\pi\) | ||||
−0.160711 | + | 0.987002i | \(0.551379\pi\) | |||||||
\(108\) | −1585.18 | + | 878.409i | −1.41236 | + | 0.782638i | ||||
\(109\) | −1522.51 | −1.33789 | −0.668946 | − | 0.743311i | \(-0.733254\pi\) | ||||
−0.668946 | + | 0.743311i | \(0.733254\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 837.004 | − | 985.710i | 0.715720 | − | 0.842878i | ||||
\(112\) | 4.78432 | − | 8.28669i | 0.00403639 | − | 0.00699124i | ||||
\(113\) | −406.499 | + | 704.077i | −0.338409 | + | 0.586142i | −0.984134 | − | 0.177429i | \(-0.943222\pi\) |
0.645725 | + | 0.763570i | \(0.276555\pi\) | |||||||
\(114\) | −232.689 | − | 42.4373i | −0.191170 | − | 0.0348650i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2308.83 | −1.84802 | ||||||||
\(117\) | 1182.26 | + | 446.073i | 0.934190 | + | 0.352474i | ||||
\(118\) | −1917.69 | −1.49608 | ||||||||
\(119\) | −478.960 | − | 829.584i | −0.368960 | − | 0.639057i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1535.10 | + | 2658.87i | −1.15334 | + | 1.99765i | ||||
\(122\) | 1246.78 | − | 2159.49i | 0.925231 | − | 1.60255i | ||||
\(123\) | −436.547 | − | 1221.64i | −0.320017 | − | 0.895539i | ||||
\(124\) | −994.899 | − | 1723.22i | −0.720521 | − | 1.24798i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2323.96 | + | 876.841i | 1.64313 | + | 0.619962i | ||||
\(127\) | 864.662 | 0.604144 | 0.302072 | − | 0.953285i | \(-0.402322\pi\) | ||||
0.302072 | + | 0.953285i | \(0.402322\pi\) | |||||||
\(128\) | 1167.48 | + | 2022.14i | 0.806187 | + | 1.39636i | ||||
\(129\) | 1084.96 | + | 197.872i | 0.740507 | + | 0.135052i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1089.26 | − | 1886.65i | 0.726482 | − | 1.25830i | −0.231879 | − | 0.972745i | \(-0.574487\pi\) |
0.958361 | − | 0.285559i | \(-0.0921792\pi\) | |||||||
\(132\) | −2882.27 | + | 3394.34i | −1.90052 | + | 2.23818i | ||||
\(133\) | 100.098 | + | 173.374i | 0.0652599 | + | 0.113033i | ||||
\(134\) | 2048.40 | 1.32056 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1071.11 | 0.675343 | ||||||||
\(137\) | −1149.58 | − | 1991.13i | −0.716900 | − | 1.24171i | −0.962222 | − | 0.272266i | \(-0.912227\pi\) |
0.245322 | − | 0.969442i | \(-0.421106\pi\) | |||||||
\(138\) | 147.548 | − | 173.762i | 0.0910152 | − | 0.107185i | ||||
\(139\) | 1066.98 | − | 1848.06i | 0.651077 | − | 1.12770i | −0.331785 | − | 0.943355i | \(-0.607651\pi\) |
0.982862 | − | 0.184343i | \(-0.0590157\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2431.67 | − | 443.481i | −1.45236 | − | 0.264878i | ||||
\(142\) | −936.536 | − | 1622.13i | −0.553467 | − | 0.958634i | ||||
\(143\) | 3104.83 | 1.81565 | ||||||||
\(144\) | 9.93528 | − | 8.14012i | 0.00574958 | − | 0.00471072i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −819.924 | − | 1420.15i | −0.464777 | − | 0.805017i | ||||
\(147\) | −107.700 | − | 301.390i | −0.0604284 | − | 0.169103i | ||||
\(148\) | 1607.37 | − | 2784.04i | 0.892735 | − | 1.54626i | ||||
\(149\) | −875.309 | + | 1516.08i | −0.481263 | + | 0.833572i | −0.999769 | − | 0.0215024i | \(-0.993155\pi\) |
0.518506 | + | 0.855074i | \(0.326488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −437.977 | − | 758.598i | −0.236040 | − | 0.408833i | 0.723534 | − | 0.690288i | \(-0.242516\pi\) |
−0.959574 | + | 0.281455i | \(0.909183\pi\) | |||||||
\(152\) | −223.850 | −0.119451 | ||||||||
\(153\) | −208.421 | − | 1268.83i | −0.110130 | − | 0.670447i | ||||
\(154\) | 6103.12 | 3.19353 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3090.38 | + | 563.615i | 1.58608 | + | 0.289265i | ||||
\(157\) | −129.697 | + | 224.642i | −0.0659298 | + | 0.114194i | −0.897106 | − | 0.441815i | \(-0.854335\pi\) |
0.831176 | + | 0.556009i | \(0.187668\pi\) | |||||||
\(158\) | 1489.96 | − | 2580.69i | 0.750222 | − | 1.29942i | ||||
\(159\) | −1837.42 | + | 2163.86i | −0.916457 | + | 1.07928i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.939 | −0.0944457 | ||||||||
\(162\) | 2503.15 | + | 2202.44i | 1.21399 | + | 1.06815i | ||||
\(163\) | 1201.80 | 0.577498 | 0.288749 | − | 0.957405i | \(-0.406761\pi\) | ||||
0.288749 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(164\) | −1612.54 | − | 2792.99i | −0.767792 | − | 1.32986i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1859.49 | + | 3220.72i | −0.869422 | + | 1.50588i | ||||
\(167\) | −839.452 | + | 1453.97i | −0.388975 | + | 0.673724i | −0.992312 | − | 0.123762i | \(-0.960504\pi\) |
0.603337 | + | 0.797486i | \(0.293837\pi\) | |||||||
\(168\) | 2312.60 | + | 421.765i | 1.06203 | + | 0.193690i | ||||
\(169\) | 3.35162 | + | 5.80518i | 0.00152554 | + | 0.00264232i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.5578 | + | 265.171i | 0.0194792 | + | 0.118586i | ||||
\(172\) | 2741.70 | 1.21542 | ||||||||
\(173\) | 465.899 | + | 806.961i | 0.204749 | + | 0.354636i | 0.950053 | − | 0.312089i | \(-0.101029\pi\) |
−0.745303 | + | 0.666725i | \(0.767695\pi\) | |||||||
\(174\) | 1429.36 | + | 3999.92i | 0.622754 | + | 1.74272i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.7796 | − | 27.3311i | 0.00675814 | − | 0.0117054i | ||||
\(177\) | 733.155 | + | 2051.67i | 0.311341 | + | 0.871259i | ||||
\(178\) | 459.644 | + | 796.127i | 0.193549 | + | 0.335237i | ||||
\(179\) | 1023.40 | 0.427333 | 0.213667 | − | 0.976907i | \(-0.431459\pi\) | ||||
0.213667 | + | 0.976907i | \(0.431459\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2639.93 | 1.08411 | 0.542056 | − | 0.840342i | \(-0.317646\pi\) | ||||
0.542056 | + | 0.840342i | \(0.317646\pi\) | |||||||
\(182\) | −2152.72 | − | 3728.62i | −0.876760 | − | 1.51859i | ||||
\(183\) | −2787.02 | − | 508.289i | −1.12581 | − | 0.205322i | ||||
\(184\) | 107.868 | − | 186.833i | 0.0432182 | − | 0.0748562i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2369.45 | + | 2790.42i | −0.934067 | + | 1.10002i | ||||
\(187\) | −1579.70 | − | 2736.13i | −0.617750 | − | 1.06997i | ||||
\(188\) | −6144.84 | −2.38382 | ||||||||
\(189\) | 49.6230 | − | 2821.56i | 0.0190981 | − | 1.08591i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 406.640 | + | 704.322i | 0.154050 | + | 0.266822i | 0.932713 | − | 0.360621i | \(-0.117435\pi\) |
−0.778663 | + | 0.627442i | \(0.784102\pi\) | |||||||
\(192\) | 2788.40 | − | 3283.80i | 1.04810 | − | 1.23431i | ||||
\(193\) | −407.121 | + | 705.154i | −0.151840 | + | 0.262995i | −0.931904 | − | 0.362705i | \(-0.881853\pi\) |
0.780064 | + | 0.625700i | \(0.215187\pi\) | |||||||
\(194\) | 576.612 | − | 998.720i | 0.213393 | − | 0.369608i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −397.828 | − | 689.059i | −0.144981 | − | 0.251115i | ||||
\(197\) | −4078.41 | −1.47500 | −0.737499 | − | 0.675348i | \(-0.763994\pi\) | ||||
−0.737499 | + | 0.675348i | \(0.763994\pi\) | |||||||
\(198\) | 7664.87 | + | 2891.99i | 2.75110 | + | 1.03800i | ||||
\(199\) | −1342.49 | −0.478224 | −0.239112 | − | 0.970992i | \(-0.576856\pi\) | ||||
−0.239112 | + | 0.970992i | \(0.576856\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −783.129 | − | 2191.51i | −0.274814 | − | 0.769042i | ||||
\(202\) | −99.7101 | + | 172.703i | −0.0347306 | + | 0.0601551i | ||||
\(203\) | 1797.58 | − | 3113.51i | 0.621506 | − | 1.07648i | ||||
\(204\) | −1075.67 | − | 3010.15i | −0.369175 | − | 1.03310i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6587.56 | 2.22805 | ||||||||
\(207\) | −242.311 | − | 91.4250i | −0.0813613 | − | 0.0306980i | ||||
\(208\) | −22.2634 | −0.00742159 | ||||||||
\(209\) | 330.141 | + | 571.821i | 0.109265 | + | 0.189252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1477.49 | − | 2559.08i | 0.482059 | − | 0.834950i | −0.517729 | − | 0.855545i | \(-0.673222\pi\) |
0.999788 | + | 0.0205943i | \(0.00655583\pi\) | |||||||
\(212\) | −3528.55 | + | 6111.62i | −1.14312 | + | 1.97994i | ||||
\(213\) | −1377.41 | + | 1622.13i | −0.443092 | + | 0.521814i | ||||
\(214\) | 813.536 | + | 1409.09i | 0.259870 | + | 0.450108i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2704.52 | + | 1625.52i | 0.851940 | + | 0.512050i | ||||
\(217\) | 3098.39 | 0.969273 | ||||||||
\(218\) | 3481.66 | + | 6030.42i | 1.08169 | + | 1.87354i | ||||
\(219\) | −1205.90 | + | 1420.15i | −0.372089 | + | 0.438196i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1114.40 | + | 1930.20i | −0.339198 | + | 0.587507i | ||||
\(222\) | −5818.29 | − | 1061.12i | −1.75900 | − | 0.320802i | ||||
\(223\) | 1753.43 | + | 3037.03i | 0.526539 | + | 0.911993i | 0.999522 | + | 0.0309212i | \(0.00984409\pi\) |
−0.472982 | + | 0.881072i | \(0.656823\pi\) | |||||||
\(224\) | −3662.97 | −1.09260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3718.31 | 1.09442 | ||||||||
\(227\) | 326.413 | + | 565.364i | 0.0954396 | + | 0.165306i | 0.909792 | − | 0.415064i | \(-0.136241\pi\) |
−0.814352 | + | 0.580371i | \(0.802908\pi\) | |||||||
\(228\) | 224.803 | + | 629.090i | 0.0652979 | + | 0.182730i | ||||
\(229\) | −2291.78 | + | 3969.47i | −0.661331 | + | 1.14546i | 0.318935 | + | 0.947776i | \(0.396675\pi\) |
−0.980266 | + | 0.197682i | \(0.936659\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2333.30 | − | 6529.52i | −0.664588 | − | 1.85979i | ||||
\(232\) | 2009.98 | + | 3481.39i | 0.568801 | + | 0.985192i | ||||
\(233\) | −317.527 | −0.0892785 | −0.0446392 | − | 0.999003i | \(-0.514214\pi\) | ||||
−0.0446392 | + | 0.999003i | \(0.514214\pi\) | |||||||
\(234\) | −936.765 | − | 5702.83i | −0.261702 | − | 1.59319i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2708.16 | + | 4690.67i | 0.746975 | + | 1.29380i | ||||
\(237\) | −3330.62 | − | 607.430i | −0.912858 | − | 0.166485i | ||||
\(238\) | −2190.56 | + | 3794.17i | −0.596610 | + | 1.03336i | ||||
\(239\) | −928.835 | + | 1608.79i | −0.251386 | + | 0.435414i | −0.963908 | − | 0.266236i | \(-0.914220\pi\) |
0.712521 | + | 0.701650i | \(0.247553\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1633.47 | + | 2829.25i | 0.436602 | + | 0.756217i | 0.997425 | − | 0.0717190i | \(-0.0228485\pi\) |
−0.560823 | + | 0.827936i | \(0.689515\pi\) | |||||||
\(242\) | 14041.8 | 3.72993 | ||||||||
\(243\) | 1399.33 | − | 3520.06i | 0.369411 | − | 0.929266i | ||||
\(244\) | −7042.82 | −1.84783 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3840.41 | + | 4522.72i | −0.995349 | + | 1.17219i | ||||
\(247\) | 232.898 | − | 403.390i | 0.0599956 | − | 0.103915i | ||||
\(248\) | −1732.24 | + | 3000.33i | −0.443538 | + | 0.768231i | ||||
\(249\) | 4156.65 | + | 758.079i | 1.05790 | + | 0.192937i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5641.37 | −1.41865 | −0.709323 | − | 0.704884i | \(-0.750999\pi\) | ||||
−0.709323 | + | 0.704884i | \(0.750999\pi\) | |||||||
\(252\) | −1137.15 | − | 6922.70i | −0.284260 | − | 1.73051i | ||||
\(253\) | −636.351 | −0.158131 | ||||||||
\(254\) | −1977.30 | − | 3424.78i | −0.488452 | − | 0.846024i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2023.31 | − | 3504.47i | 0.493971 | − | 0.855584i | ||||
\(257\) | −586.731 | + | 1016.25i | −0.142410 | + | 0.246661i | −0.928404 | − | 0.371574i | \(-0.878818\pi\) |
0.785994 | + | 0.618234i | \(0.212152\pi\) | |||||||
\(258\) | −1697.34 | − | 4749.84i | −0.409580 | − | 1.14617i | ||||
\(259\) | 2502.89 | + | 4335.14i | 0.600472 | + | 1.04005i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3732.92 | − | 3058.44i | 0.885295 | − | 0.725336i | ||||
\(262\) | −9963.64 | −2.34945 | ||||||||
\(263\) | −1448.98 | − | 2509.71i | −0.339726 | − | 0.588423i | 0.644655 | − | 0.764474i | \(-0.277001\pi\) |
−0.984381 | + | 0.176051i | \(0.943668\pi\) | |||||||
\(264\) | 7627.38 | + | 1391.06i | 1.77815 | + | 0.324295i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 457.804 | − | 792.940i | 0.105526 | − | 0.182776i | ||||
\(267\) | 676.022 | − | 796.127i | 0.154951 | − | 0.182480i | ||||
\(268\) | −2892.75 | − | 5010.40i | −0.659340 | − | 1.14201i | ||||
\(269\) | 2930.13 | 0.664138 | 0.332069 | − | 0.943255i | \(-0.392253\pi\) | ||||
0.332069 | + | 0.943255i | \(0.392253\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −668.881 | −0.149932 | −0.0749661 | − | 0.997186i | \(-0.523885\pi\) | ||||
−0.0749661 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(272\) | 11.3274 | + | 19.6196i | 0.00252509 | + | 0.00437358i | ||||
\(273\) | −3166.12 | + | 3728.62i | −0.701912 | + | 0.826617i | ||||
\(274\) | −5257.70 | + | 9106.60i | −1.15923 | + | 2.00785i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −633.389 | − | 115.516i | −0.138136 | − | 0.0251929i | ||||
\(277\) | −316.315 | − | 547.874i | −0.0686121 | − | 0.118840i | 0.829679 | − | 0.558241i | \(-0.188524\pi\) |
−0.898291 | + | 0.439402i | \(0.855190\pi\) | |||||||
\(278\) | −9759.80 | −2.10559 | ||||||||
\(279\) | 3891.24 | + | 1468.18i | 0.834991 | + | 0.315046i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1797.65 | + | 3113.62i | 0.381633 | + | 0.661007i | 0.991296 | − | 0.131653i | \(-0.0420286\pi\) |
−0.609663 | + | 0.792661i | \(0.708695\pi\) | |||||||
\(282\) | 3804.16 | + | 10645.6i | 0.803313 | + | 2.24800i | ||||
\(283\) | 252.184 | − | 436.796i | 0.0529710 | − | 0.0917485i | −0.838324 | − | 0.545172i | \(-0.816464\pi\) |
0.891295 | + | 0.453424i | \(0.149798\pi\) | |||||||
\(284\) | −2645.16 | + | 4581.55i | −0.552680 | + | 0.957270i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7100.08 | − | 12297.7i | −1.46796 | − | 2.54258i | ||||
\(287\) | 5021.88 | 1.03286 | ||||||||
\(288\) | −4600.29 | − | 1735.71i | −0.941232 | − | 0.355131i | ||||
\(289\) | −2645.02 | −0.538372 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1288.94 | − | 235.074i | −0.259654 | − | 0.0473549i | ||||
\(292\) | −2315.80 | + | 4011.08i | −0.464116 | + | 0.803872i | ||||
\(293\) | 3099.25 | − | 5368.06i | 0.617953 | − | 1.07033i | −0.371906 | − | 0.928270i | \(-0.621296\pi\) |
0.989859 | − | 0.142055i | \(-0.0453710\pi\) | |||||||
\(294\) | −947.467 | + | 1115.80i | −0.187950 | + | 0.221343i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5597.26 | −1.09910 | ||||||||
\(297\) | 163.666 | − | 9306.02i | 0.0319760 | − | 1.81815i | ||||
\(298\) | 8006.60 | 1.55641 | ||||||||
\(299\) | 224.457 | + | 388.770i | 0.0434136 | + | 0.0751945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2134.60 | + | 3697.24i | −0.408759 | + | 0.707991i | ||||
\(302\) | −2003.12 | + | 3469.51i | −0.381678 | + | 0.661086i | ||||
\(303\) | 222.889 | + | 40.6500i | 0.0422596 | + | 0.00770719i | ||||
\(304\) | −2.36730 | − | 4.10029i | −0.000446626 | − | 0.000773578i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4548.99 | + | 3727.06i | −0.849832 | + | 0.696281i | ||||
\(307\) | 1966.79 | 0.365636 | 0.182818 | − | 0.983147i | \(-0.441478\pi\) | ||||
0.182818 | + | 0.983147i | \(0.441478\pi\) | |||||||
\(308\) | −8618.84 | − | 14928.3i | −1.59449 | − | 2.76174i | ||||
\(309\) | −2518.51 | − | 7047.81i | −0.463666 | − | 1.29753i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1153.05 | − | 1997.15i | 0.210237 | − | 0.364141i | −0.741552 | − | 0.670896i | \(-0.765910\pi\) |
0.951789 | + | 0.306755i | \(0.0992431\pi\) | |||||||
\(312\) | −1840.51 | − | 5150.51i | −0.333970 | − | 0.934584i | ||||
\(313\) | 5151.20 | + | 8922.14i | 0.930234 | + | 1.61121i | 0.782920 | + | 0.622122i | \(0.213729\pi\) |
0.147314 | + | 0.989090i | \(0.452937\pi\) | |||||||
\(314\) | 1186.36 | 0.213218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8416.51 | −1.49831 | ||||||||
\(317\) | −850.916 | − | 1473.83i | −0.150764 | − | 0.261131i | 0.780745 | − | 0.624850i | \(-0.214840\pi\) |
−0.931509 | + | 0.363719i | \(0.881507\pi\) | |||||||
\(318\) | 12772.5 | + | 2329.41i | 2.25235 | + | 0.410777i | ||||
\(319\) | 5928.78 | − | 10268.9i | 1.04059 | − | 1.80235i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1196.51 | − | 1409.09i | 0.208046 | − | 0.245008i | ||||
\(322\) | 441.212 | + | 764.201i | 0.0763596 | + | 0.132259i | ||||
\(323\) | −473.983 | −0.0816506 | ||||||||
\(324\) | 1852.21 | − | 9233.01i | 0.317595 | − | 1.58316i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2748.26 | − | 4760.13i | −0.466908 | − | 0.808709i | ||||
\(327\) | 5120.66 | − | 6030.42i | 0.865973 | − | 1.01983i | ||||
\(328\) | −2807.63 | + | 4862.95i | −0.472638 | + | 0.818633i | ||||
\(329\) | 4784.18 | − | 8286.44i | 0.801703 | − | 1.38859i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4175.74 | + | 7232.60i | 0.693413 | + | 1.20103i | 0.970713 | + | 0.240243i | \(0.0772271\pi\) |
−0.277300 | + | 0.960783i | \(0.589440\pi\) | |||||||
\(332\) | 10503.9 | 1.73637 | ||||||||
\(333\) | 1089.14 | + | 6630.47i | 0.179233 | + | 1.09113i | ||||
\(334\) | 7678.61 | 1.25795 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.7311 | + | 46.8205i | 0.00271654 | + | 0.00760199i | ||||
\(337\) | −3928.71 | + | 6804.73i | −0.635046 | + | 1.09993i | 0.351459 | + | 0.936203i | \(0.385686\pi\) |
−0.986505 | + | 0.163729i | \(0.947648\pi\) | |||||||
\(338\) | 15.3289 | − | 26.5504i | 0.00246681 | − | 0.00427264i | ||||
\(339\) | −1421.56 | − | 3978.10i | −0.227753 | − | 0.637347i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10219.1 | 1.62286 | ||||||||
\(342\) | 950.691 | − | 778.916i | 0.150314 | − | 0.123155i | ||||
\(343\) | −5660.34 | −0.891048 | ||||||||
\(344\) | −2386.82 | − | 4134.10i | −0.374095 | − | 0.647952i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2130.83 | − | 3690.70i | 0.331081 | − | 0.573449i | ||||
\(347\) | 606.088 | − | 1049.78i | 0.0937652 | − | 0.162406i | −0.815327 | − | 0.579000i | \(-0.803443\pi\) |
0.909093 | + | 0.416594i | \(0.136776\pi\) | |||||||
\(348\) | 7765.29 | − | 9144.91i | 1.19616 | − | 1.40867i | ||||
\(349\) | −699.332 | − | 1211.28i | −0.107262 | − | 0.185783i | 0.807398 | − | 0.590007i | \(-0.200875\pi\) |
−0.914660 | + | 0.404224i | \(0.867542\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5743.12 | + | 3182.47i | −0.873348 | + | 0.483954i | ||||
\(352\) | −12081.2 | −1.82934 | ||||||||
\(353\) | 1314.21 | + | 2276.28i | 0.198154 | + | 0.343214i | 0.947930 | − | 0.318479i | \(-0.103172\pi\) |
−0.749776 | + | 0.661692i | \(0.769839\pi\) | |||||||
\(354\) | 6449.75 | − | 7595.64i | 0.968362 | − | 1.14041i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1298.22 | − | 2248.59i | 0.193274 | − | 0.334761i | ||||
\(357\) | 4896.73 | + | 893.053i | 0.725946 | + | 0.132396i | ||||
\(358\) | −2340.31 | − | 4053.53i | −0.345500 | − | 0.598424i | ||||
\(359\) | 3677.48 | 0.540640 | 0.270320 | − | 0.962770i | \(-0.412870\pi\) | ||||
0.270320 | + | 0.962770i | \(0.412870\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6759.94 | −0.985558 | ||||||||
\(362\) | −6036.96 | − | 10456.3i | −0.876507 | − | 1.51815i | ||||
\(363\) | −5368.36 | − | 15022.9i | −0.776215 | − | 2.17217i | ||||
\(364\) | −6080.16 | + | 10531.1i | −0.875513 | + | 1.51643i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4360.08 | + | 12201.3i | 0.622692 | + | 1.74255i | ||||
\(367\) | 5714.88 | + | 9898.47i | 0.812846 | + | 1.40789i | 0.910864 | + | 0.412706i | \(0.135416\pi\) |
−0.0980185 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(368\) | 4.56301 | 0.000646368 | ||||||||
\(369\) | 6306.94 | + | 2379.64i | 0.889773 | + | 0.335715i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5494.43 | − | 9516.63i | −0.768886 | − | 1.33175i | ||||
\(372\) | 10171.5 | + | 1855.05i | 1.41766 | + | 0.258549i | ||||
\(373\) | 1129.95 | − | 1957.13i | 0.156854 | − | 0.271679i | −0.776879 | − | 0.629650i | \(-0.783198\pi\) |
0.933733 | + | 0.357971i | \(0.116531\pi\) | |||||||
\(374\) | −7224.90 | + | 12513.9i | −0.998905 | + | 1.73015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5349.47 | + | 9265.55i | 0.733717 | + | 1.27084i | ||||
\(377\) | −8364.90 | −1.14274 | ||||||||
\(378\) | −11289.2 | + | 6255.76i | −1.53612 | + | 0.851221i | ||||
\(379\) | −11815.8 | −1.60142 | −0.800709 | − | 0.599053i | \(-0.795544\pi\) | ||||
−0.800709 | + | 0.599053i | \(0.795544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2908.12 | + | 3424.78i | −0.391043 | + | 0.460517i | ||||
\(382\) | 1859.80 | − | 3221.27i | 0.249099 | − | 0.431452i | ||||
\(383\) | −4040.11 | + | 6997.68i | −0.539008 | + | 0.933589i | 0.459950 | + | 0.887945i | \(0.347867\pi\) |
−0.998958 | + | 0.0456440i | \(0.985466\pi\) | |||||||
\(384\) | −11936.0 | − | 2176.85i | −1.58621 | − | 0.289289i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3724.00 | 0.491054 | ||||||||
\(387\) | −4432.78 | + | 3631.85i | −0.582251 | + | 0.477047i | ||||
\(388\) | −3257.17 | −0.426180 | ||||||||
\(389\) | −1550.22 | − | 2685.05i | −0.202054 | − | 0.349968i | 0.747136 | − | 0.664671i | \(-0.231428\pi\) |
−0.949190 | + | 0.314703i | \(0.898095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 228.402 | − | 395.604i | 0.0295417 | − | 0.0511677i | ||||
\(392\) | −692.669 | + | 1199.74i | −0.0892476 | + | 0.154581i | ||||
\(393\) | 3809.22 | + | 10659.8i | 0.488931 | + | 1.36823i | ||||
\(394\) | 9326.47 | + | 16153.9i | 1.19254 | + | 2.06554i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3750.52 | − | 22832.4i | −0.475936 | − | 2.89740i | ||||
\(397\) | 11990.1 | 1.51578 | 0.757890 | − | 0.652382i | \(-0.226230\pi\) | ||||
0.757890 | + | 0.652382i | \(0.226230\pi\) | |||||||
\(398\) | 3069.99 | + | 5317.38i | 0.386645 | + | 0.669689i | ||||
\(399\) | −1023.36 | − | 186.638i | −0.128402 | − | 0.0234176i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6426.63 | + | 11131.3i | −0.800326 | + | 1.38620i | 0.119076 | + | 0.992885i | \(0.462007\pi\) |
−0.919402 | + | 0.393320i | \(0.871327\pi\) | |||||||
\(402\) | −6889.38 | + | 8113.38i | −0.854753 | + | 1.00661i | ||||
\(403\) | −3604.52 | − | 6243.21i | −0.445543 | − | 0.771703i | ||||
\(404\) | 563.243 | 0.0693623 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16442.8 | −2.00996 | ||||||||
\(407\) | 8255.02 | + | 14298.1i | 1.00537 | + | 1.74135i | ||||
\(408\) | −3602.45 | + | 4242.48i | −0.437127 | + | 0.514789i | ||||
\(409\) | −1112.54 | + | 1926.98i | −0.134503 | + | 0.232966i | −0.925408 | − | 0.378974i | \(-0.876277\pi\) |
0.790904 | + | 0.611940i | \(0.209610\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11752.9 | + | 2143.47i | 1.41053 | + | 0.257249i | ||||
\(412\) | −9302.97 | − | 16113.2i | −1.11244 | − | 1.92680i | ||||
\(413\) | −8433.95 | −1.00486 | ||||||||
\(414\) | 191.995 | + | 1168.82i | 0.0227924 | + | 0.138755i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4261.32 | + | 7380.83i | 0.502232 | + | 0.869891i | ||||
\(417\) | 3731.29 | + | 10441.7i | 0.438183 | + | 1.22621i | ||||
\(418\) | 1509.93 | − | 2615.27i | 0.176682 | − | 0.306021i | ||||
\(419\) | −4838.33 | + | 8380.23i | −0.564123 | + | 0.977090i | 0.433007 | + | 0.901390i | \(0.357452\pi\) |
−0.997131 | + | 0.0756998i | \(0.975881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4981.30 | + | 8627.87i | 0.576660 | + | 0.998804i | 0.995859 | + | 0.0909098i | \(0.0289775\pi\) |
−0.419199 | + | 0.907894i | \(0.637689\pi\) | |||||||
\(422\) | −13514.8 | −1.55898 | ||||||||
\(423\) | 9934.98 | − | 8139.88i | 1.14197 | − | 0.935637i | ||||
\(424\) | 12287.3 | 1.40737 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9574.84 | + | 1746.23i | 1.08897 | + | 0.198604i | ||||
\(427\) | 5483.32 | − | 9497.39i | 0.621444 | − | 1.07637i | ||||
\(428\) | 2297.76 | − | 3979.83i | 0.259500 | − | 0.449468i | ||||
\(429\) | −10442.5 | + | 12297.7i | −1.17521 | + | 1.38401i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2461.47 | −0.275092 | −0.137546 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137546 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(432\) | −1.17358 | + | 66.7297i | −0.000130704 | + | 0.00743179i | ||||
\(433\) | −7818.49 | −0.867743 | −0.433871 | − | 0.900975i | \(-0.642853\pi\) | ||||
−0.433871 | + | 0.900975i | \(0.642853\pi\) | |||||||
\(434\) | −7085.36 | − | 12272.2i | −0.783660 | − | 1.35734i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9833.63 | − | 17032.3i | 1.08015 | − | 1.87087i | ||||
\(437\) | −47.7336 | + | 82.6770i | −0.00522519 | + | 0.00905030i | ||||
\(438\) | 8382.64 | + | 1528.80i | 0.914470 | + | 0.166779i | ||||
\(439\) | −3105.91 | − | 5379.60i | −0.337670 | − | 0.584862i | 0.646324 | − | 0.763063i | \(-0.276306\pi\) |
−0.983994 | + | 0.178201i | \(0.942972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1555.98 | + | 587.080i | 0.168015 | + | 0.0633927i | ||||
\(442\) | 10193.6 | 1.09697 | ||||||||
\(443\) | 1492.17 | + | 2584.52i | 0.160034 | + | 0.277188i | 0.934881 | − | 0.354962i | \(-0.115506\pi\) |
−0.774846 | + | 0.632150i | \(0.782173\pi\) | |||||||
\(444\) | 5621.08 | + | 15730.1i | 0.600822 | + | 1.68134i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8019.45 | − | 13890.1i | 0.851417 | − | 1.47470i | ||||
\(447\) | −3061.02 | − | 8565.99i | −0.323896 | − | 0.906392i | ||||
\(448\) | 8338.16 | + | 14442.1i | 0.879333 | + | 1.52305i | ||||
\(449\) | −810.476 | −0.0851865 | −0.0425932 | − | 0.999092i | \(-0.513562\pi\) | ||||
−0.0425932 | + | 0.999092i | \(0.513562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16563.1 | 1.72933 | ||||||||
\(452\) | −5251.01 | − | 9095.01i | −0.546431 | − | 0.946446i | ||||
\(453\) | 4477.73 | + | 816.637i | 0.464420 | + | 0.0846996i | ||||
\(454\) | 1492.88 | − | 2585.74i | 0.154326 | − | 0.267301i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 752.873 | − | 886.632i | 0.0773169 | − | 0.0910534i | ||||
\(457\) | 785.887 | + | 1361.20i | 0.0804425 | + | 0.139331i | 0.903440 | − | 0.428714i | \(-0.141033\pi\) |
−0.822998 | + | 0.568045i | \(0.807700\pi\) | |||||||
\(458\) | 20963.2 | 2.13875 | ||||||||
\(459\) | 5726.59 | + | 3441.91i | 0.582341 | + | 0.350010i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1031.35 | − | 1786.34i | −0.104196 | − | 0.180474i | 0.809213 | − | 0.587515i | \(-0.199894\pi\) |
−0.913410 | + | 0.407042i | \(0.866560\pi\) | |||||||
\(462\) | −20526.6 | + | 24173.5i | −2.06707 | + | 2.43431i | ||||
\(463\) | 1391.62 | − | 2410.35i | 0.139684 | − | 0.241940i | −0.787693 | − | 0.616068i | \(-0.788725\pi\) |
0.927377 | + | 0.374128i | \(0.122058\pi\) | |||||||
\(464\) | −42.5128 | + | 73.6344i | −0.00425347 | + | 0.00736722i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 726.118 | + | 1257.67i | 0.0721819 | + | 0.125023i | ||||
\(467\) | −10939.7 | −1.08400 | −0.541999 | − | 0.840379i | \(-0.682332\pi\) | ||||
−0.541999 | + | 0.840379i | \(0.682332\pi\) | |||||||
\(468\) | −12626.2 | + | 10344.9i | −1.24711 | + | 1.02178i | ||||
\(469\) | 9008.83 | 0.886970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −453.561 | − | 1269.25i | −0.0443716 | − | 0.124170i | ||||
\(472\) | 4715.24 | − | 8167.04i | 0.459823 | − | 0.796438i | ||||
\(473\) | −7040.33 | + | 12194.2i | −0.684386 | + | 1.18539i | ||||
\(474\) | 5210.51 | + | 14581.1i | 0.504908 | + | 1.41294i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12374.1 | 1.19152 | ||||||||
\(477\) | −2390.92 | − | 14555.4i | −0.229503 | − | 1.39716i | ||||
\(478\) | 8496.21 | 0.812986 | ||||||||
\(479\) | −7311.85 | − | 12664.5i | −0.697467 | − | 1.20805i | −0.969342 | − | 0.245716i | \(-0.920977\pi\) |
0.271875 | − | 0.962333i | \(-0.412356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5823.49 | − | 10086.6i | 0.552034 | − | 0.956151i | ||||
\(482\) | 7470.81 | − | 12939.8i | 0.705987 | − | 1.22281i | ||||
\(483\) | 648.913 | − | 764.201i | 0.0611316 | − | 0.0719925i | ||||
\(484\) | −19829.9 | − | 34346.4i | −1.86231 | − | 3.22562i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17142.3 | + | 2507.13i | −1.59998 | + | 0.234003i | ||||
\(487\) | −16473.6 | −1.53284 | −0.766419 | − | 0.642341i | \(-0.777963\pi\) | ||||
−0.766419 | + | 0.642341i | \(0.777963\pi\) | |||||||
\(488\) | 6131.22 | + | 10619.6i | 0.568744 | + | 0.985093i | ||||
\(489\) | −4042.01 | + | 4760.13i | −0.373795 | + | 0.440206i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10264.6 | + | 17778.8i | −0.943450 | + | 1.63410i | −0.184626 | + | 0.982809i | \(0.559107\pi\) |
−0.758825 | + | 0.651295i | \(0.774226\pi\) | |||||||
\(492\) | 16486.0 | + | 3006.68i | 1.51067 | + | 0.275511i | ||||
\(493\) | 4255.97 | + | 7371.56i | 0.388802 | + | 0.673425i | ||||
\(494\) | −2130.35 | −0.194026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −73.2768 | −0.00663352 | ||||||||
\(497\) | −4118.87 | − | 7134.10i | −0.371744 | − | 0.643879i | ||||
\(498\) | −6502.76 | − | 18197.4i | −0.585132 | − | 1.63744i | ||||
\(499\) | 7202.31 | − | 12474.8i | 0.646131 | − | 1.11913i | −0.337908 | − | 0.941179i | \(-0.609719\pi\) |
0.984039 | − | 0.177953i | \(-0.0569475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2935.63 | − | 8215.08i | −0.261785 | − | 0.732580i | ||||
\(502\) | 12900.6 | + | 22344.5i | 1.14698 | + | 1.98663i | ||||
\(503\) | 2953.63 | 0.261821 | 0.130910 | − | 0.991394i | \(-0.458210\pi\) | ||||
0.130910 | + | 0.991394i | \(0.458210\pi\) | |||||||
\(504\) | −9448.49 | + | 7741.30i | −0.835058 | + | 0.684176i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1455.20 | + | 2520.48i | 0.127849 | + | 0.221441i | ||||
\(507\) | −34.2659 | − | 6.24932i | −0.00300158 | − | 0.000547420i | ||||
\(508\) | −5584.69 | + | 9672.98i | −0.487757 | + | 0.844821i | ||||
\(509\) | 8684.44 | − | 15041.9i | 0.756250 | − | 1.30986i | −0.188500 | − | 0.982073i | \(-0.560363\pi\) |
0.944750 | − | 0.327790i | \(-0.106304\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3606.02 | − | 6245.80i | −0.312174 | − | 0.540701i | ||||
\(512\) | 172.223 | 0.0148657 | ||||||||
\(513\) | −1196.80 | − | 719.323i | −0.103002 | − | 0.0619082i | ||||
\(514\) | 5366.92 | 0.460554 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9221.16 | + | 10859.4i | −0.786703 | + | 0.926473i | ||||
\(517\) | 15779.1 | − | 27330.3i | 1.34229 | − | 2.32492i | ||||
\(518\) | 11447.2 | − | 19827.1i | 0.970966 | − | 1.68176i | ||||
\(519\) | −4763.20 | − | 868.699i | −0.402854 | − | 0.0734714i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6146.30 | −0.516841 | −0.258421 | − | 0.966033i | \(-0.583202\pi\) | ||||
−0.258421 | + | 0.966033i | \(0.583202\pi\) | |||||||
\(522\) | −20650.4 | − | 7791.48i | −1.73150 | − | 0.653303i | ||||
\(523\) | 4554.68 | 0.380807 | 0.190404 | − | 0.981706i | \(-0.439020\pi\) | ||||
0.190404 | + | 0.981706i | \(0.439020\pi\) | |||||||
\(524\) | 14070.7 | + | 24371.1i | 1.17305 | + | 2.03179i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6627.03 | + | 11478.4i | −0.549339 | + | 0.951483i | ||||
\(527\) | −3667.88 | + | 6352.96i | −0.303179 | + | 0.525122i | ||||
\(528\) | 55.1824 | + | 154.423i | 0.00454831 | + | 0.0127280i | ||||
\(529\) | 6037.50 | + | 10457.3i | 0.496219 | + | 0.859476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10592.1 | − | 3996.46i | −0.865649 | − | 0.326613i | ||||
\(532\) | −2586.05 | −0.210751 | ||||||||
\(533\) | −5842.22 | − | 10119.0i | −0.474774 | − | 0.822333i | ||||
\(534\) | −4699.25 | − | 857.037i | −0.380817 | − | 0.0694525i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5036.64 | + | 8723.72i | −0.405877 | + | 0.702999i | ||||
\(537\) | −3442.01 | + | 4053.53i | −0.276599 | + | 0.325741i | ||||
\(538\) | −6700.59 | − | 11605.8i | −0.536957 | − | 0.930037i | ||||
\(539\) | 4086.28 | 0.326547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18091.8 | 1.43776 | 0.718879 | − | 0.695135i | \(-0.244655\pi\) | ||||
0.718879 | + | 0.695135i | \(0.244655\pi\) | |||||||
\(542\) | 1529.59 | + | 2649.33i | 0.121221 | + | 0.209960i | ||||
\(543\) | −8878.86 | + | 10456.3i | −0.701710 | + | 0.826379i | ||||
\(544\) | 4336.23 | − | 7510.58i | 0.341754 | − | 0.591936i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22008.7 | + | 4013.89i | 1.72507 | + | 0.314613i | ||||
\(547\) | 7890.69 | + | 13667.1i | 0.616786 | + | 1.06830i | 0.990068 | + | 0.140586i | \(0.0448987\pi\) |
−0.373283 | + | 0.927718i | \(0.621768\pi\) | |||||||
\(548\) | 29699.7 | 2.31516 | ||||||||
\(549\) | 11386.8 | − | 9329.41i | 0.885206 | − | 0.725263i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −889.453 | − | 1540.58i | −0.0687694 | − | 0.119112i | ||||
\(552\) | 377.223 | + | 1055.62i | 0.0290864 | + | 0.0813956i | ||||
\(553\) | 6552.83 | − | 11349.8i | 0.503896 | − | 0.872774i | ||||
\(554\) | −1446.69 | + | 2505.75i | −0.110946 | + | 0.192164i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13782.8 | + | 23872.5i | 1.05130 | + | 1.82090i | ||||
\(557\) | 13954.5 | 1.06153 | 0.530766 | − | 0.847519i | \(-0.321904\pi\) | ||||
0.530766 | + | 0.847519i | \(0.321904\pi\) | |||||||
\(558\) | −3083.22 | − | 18770.0i | −0.233913 | − | 1.42401i | ||||
\(559\) | 9933.18 | 0.751572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16150.4 | + | 2945.46i | 1.21545 | + | 0.221671i | ||||
\(562\) | 8221.69 | − | 14240.4i | 0.617102 | − | 1.06885i | ||||
\(563\) | −6801.97 | + | 11781.4i | −0.509181 | + | 0.881927i | 0.490762 | + | 0.871293i | \(0.336718\pi\) |
−0.999943 | + | 0.0106339i | \(0.996615\pi\) | |||||||
\(564\) | 20666.9 | − | 24338.7i | 1.54297 | − | 1.81710i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2306.77 | −0.171309 | ||||||||
\(567\) | 11008.8 | + | 9686.28i | 0.815392 | + | 0.717435i | ||||
\(568\) | 9211.10 | 0.680438 | ||||||||
\(569\) | 6229.30 | + | 10789.5i | 0.458956 | + | 0.794935i | 0.998906 | − | 0.0467619i | \(-0.0148902\pi\) |
−0.539950 | + | 0.841697i | \(0.681557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6728.56 | − | 11654.2i | 0.493137 | − | 0.854139i | −0.506831 | − | 0.862045i | \(-0.669183\pi\) |
0.999969 | + | 0.00790629i | \(0.00251668\pi\) | |||||||
\(572\) | −20053.5 | + | 34733.7i | −1.46587 | + | 2.53897i | ||||
\(573\) | −4157.36 | − | 758.207i | −0.303100 | − | 0.0552785i | ||||
\(574\) | −11484.0 | − | 19890.8i | −0.835074 | − | 1.44639i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3628.38 | + | 22088.8i | 0.262470 | + | 1.59786i | ||||
\(577\) | −3722.70 | −0.268592 | −0.134296 | − | 0.990941i | \(-0.542877\pi\) | ||||
−0.134296 | + | 0.990941i | \(0.542877\pi\) | |||||||
\(578\) | 6048.61 | + | 10476.5i | 0.435275 | + | 0.753918i | ||||
\(579\) | −1423.73 | − | 3984.18i | −0.102190 | − | 0.285971i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8177.99 | + | 14164.7i | −0.583959 | + | 1.01145i | ||||
\(582\) | 2016.45 | + | 5642.86i | 0.143616 | + | 0.401897i | ||||
\(583\) | −18121.7 | − | 31387.7i | −1.28735 | − | 2.22975i | ||||
\(584\) | 8064.19 | 0.571401 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28349.3 | −1.99847 | ||||||||
\(587\) | −8770.16 | − | 15190.4i | −0.616667 | − | 1.06810i | −0.990090 | − | 0.140437i | \(-0.955149\pi\) |
0.373423 | − | 0.927661i | \(-0.378184\pi\) | |||||||
\(588\) | 4067.27 | + | 741.777i | 0.285257 | + | 0.0520244i | ||||
\(589\) | 766.548 | − | 1327.70i | 0.0536249 | − | 0.0928810i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13716.9 | − | 16153.9i | 0.954718 | − | 1.12434i | ||||
\(592\) | −59.1933 | − | 102.526i | −0.00410951 | − | 0.00711788i | ||||
\(593\) | 22350.6 | 1.54777 | 0.773886 | − | 0.633325i | \(-0.218310\pi\) | ||||
0.773886 | + | 0.633325i | \(0.218310\pi\) | |||||||
\(594\) | −37233.9 | + | 20632.7i | −2.57193 | + | 1.42520i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11306.9 | − | 19584.2i | −0.777097 | − | 1.34597i | ||||
\(597\) | 4515.19 | − | 5317.38i | 0.309539 | − | 0.364533i | ||||
\(598\) | 1026.57 | − | 1778.07i | 0.0702000 | − | 0.121590i | ||||
\(599\) | 1280.81 | − | 2218.43i | 0.0873665 | − | 0.151323i | −0.819031 | − | 0.573750i | \(-0.805488\pi\) |
0.906397 | + | 0.422427i | \(0.138822\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6692.51 | − | 11591.8i | −0.454232 | − | 0.786752i | 0.544412 | − | 0.838818i | \(-0.316753\pi\) |
−0.998644 | + | 0.0520656i | \(0.983420\pi\) | |||||||
\(602\) | 19525.6 | 1.32193 | ||||||||
\(603\) | 11314.1 | + | 4268.87i | 0.764091 | + | 0.288295i | ||||
\(604\) | 11315.3 | 0.762270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −348.693 | − | 975.786i | −0.0233741 | − | 0.0654103i | ||||
\(607\) | −14314.3 | + | 24793.1i | −0.957166 | + | 1.65786i | −0.227835 | + | 0.973700i | \(0.573165\pi\) |
−0.729331 | + | 0.684161i | \(0.760169\pi\) | |||||||
\(608\) | −906.226 | + | 1569.63i | −0.0604479 | + | 0.104699i | ||||
\(609\) | 6286.29 | + | 17591.6i | 0.418281 | + | 1.17052i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22262.8 | −1.47407 | ||||||||
\(612\) | 15540.5 | + | 5863.50i | 1.02645 | + | 0.387284i | ||||
\(613\) | −7188.12 | −0.473614 | −0.236807 | − | 0.971557i | \(-0.576101\pi\) | ||||
−0.236807 | + | 0.971557i | \(0.576101\pi\) | |||||||
\(614\) | −4497.63 | − | 7790.12i | −0.295618 | − | 0.512025i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15006.5 | + | 25992.0i | −0.981539 | + | 1.70008i | ||||
\(617\) | 7766.88 | − | 13452.6i | 0.506779 | − | 0.877767i | −0.493190 | − | 0.869922i | \(-0.664169\pi\) |
0.999969 | − | 0.00784559i | \(-0.00249736\pi\) | |||||||
\(618\) | −22155.9 | + | 26092.3i | −1.44214 | + | 1.69836i | ||||
\(619\) | 11079.9 | + | 19191.0i | 0.719450 | + | 1.24612i | 0.961218 | + | 0.275789i | \(0.0889392\pi\) |
−0.241769 | + | 0.970334i | \(0.577728\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1177.08 | − | 652.265i | 0.0760624 | − | 0.0421490i | ||||
\(622\) | −10547.2 | −0.679908 | ||||||||
\(623\) | 2021.51 | + | 3501.36i | 0.130000 | + | 0.225167i | ||||
\(624\) | 74.8785 | − | 88.1818i | 0.00480375 | − | 0.00565721i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23559.4 | − | 40806.1i | 1.50419 | − | 2.60534i | ||||
\(627\) | −3375.25 | − | 615.569i | −0.214983 | − | 0.0392081i | ||||
\(628\) | −1675.38 | − | 2901.85i | −0.106457 | − | 0.184389i | ||||
\(629\) | −11851.7 | −0.751287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25582.8 | −1.61400 | −0.807002 | − | 0.590549i | \(-0.798911\pi\) | ||||
−0.807002 | + | 0.590549i | \(0.798911\pi\) | |||||||
\(632\) | 7327.10 | + | 12690.9i | 0.461165 | + | 0.798761i | ||||
\(633\) | 5166.88 | + | 14459.0i | 0.324431 | + | 0.907891i | ||||
\(634\) | −3891.73 | + | 6740.68i | −0.243786 | + | 0.422250i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12339.6 | − | 34531.2i | −0.769334 | − | 2.15291i | ||||
\(637\) | −1441.33 | − | 2496.46i | −0.0896510 | − | 0.155280i | ||||
\(638\) | −54231.5 | −3.36527 | ||||||||
\(639\) | −1792.34 | − | 10911.4i | −0.110961 | − | 0.675506i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1905.34 | − | 3300.14i | −0.117405 | − | 0.203351i | 0.801334 | − | 0.598217i | \(-0.204124\pi\) |
−0.918738 | + | 0.394867i | \(0.870791\pi\) | |||||||
\(642\) | −8317.33 | − | 1516.89i | −0.511306 | − | 0.0932507i | ||||
\(643\) | 13360.0 | − | 23140.3i | 0.819391 | − | 1.41923i | −0.0867402 | − | 0.996231i | \(-0.527645\pi\) |
0.906131 | − | 0.422996i | \(-0.139022\pi\) | |||||||
\(644\) | 1246.16 | − | 2158.41i | 0.0762509 | − | 0.132071i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1083.90 | + | 1877.37i | 0.0660147 | + | 0.114341i | ||||
\(647\) | −5114.23 | −0.310759 | −0.155380 | − | 0.987855i | \(-0.549660\pi\) | ||||
−0.155380 | + | 0.987855i | \(0.549660\pi\) | |||||||
\(648\) | −15534.5 | + | 5245.03i | −0.941750 | + | 0.317970i | ||||
\(649\) | −27816.8 | −1.68244 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10420.8 | + | 12272.2i | −0.627378 | + | 0.738842i | ||||
\(652\) | −7762.20 | + | 13444.5i | −0.466244 | + | 0.807559i | ||||
\(653\) | −4435.53 | + | 7682.56i | −0.265813 | + | 0.460401i | −0.967776 | − | 0.251812i | \(-0.918974\pi\) |
0.701964 | + | 0.712213i | \(0.252307\pi\) | |||||||
\(654\) | −35595.4 | − | 6491.79i | −2.12827 | − | 0.388148i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −118.767 | −0.00706872 | ||||||||
\(657\) | −1569.17 | − | 9552.78i | −0.0931799 | − | 0.567259i | ||||
\(658\) | −43761.7 | −2.59272 | ||||||||
\(659\) | 12102.2 | + | 20961.7i | 0.715382 | + | 1.23908i | 0.962812 | + | 0.270172i | \(0.0870805\pi\) |
−0.247430 | + | 0.968906i | \(0.579586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10689.8 | + | 18515.2i | −0.629023 | + | 1.08950i | 0.358726 | + | 0.933443i | \(0.383211\pi\) |
−0.987748 | + | 0.156056i | \(0.950122\pi\) | |||||||
\(662\) | 19098.1 | − | 33078.9i | 1.12125 | − | 1.94207i | ||||
\(663\) | −3897.14 | − | 10905.8i | −0.228284 | − | 0.638832i | ||||
\(664\) | −9144.28 | − | 15838.4i | −0.534438 | − | 0.925674i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23771.6 | − | 19476.4i | 1.38308 | − | 1.13318i | ||||
\(667\) | 1714.43 | 0.0995248 | ||||||||
\(668\) | −10843.7 | − | 18781.9i | −0.628079 | − | 1.08787i | ||||
\(669\) | −17926.5 | − | 3269.38i | −1.03599 | − | 0.188941i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18085.0 | − | 31324.2i | 1.04048 | − | 1.80217i | ||||
\(672\) | 12319.6 | − | 14508.4i | 0.707203 | − | 0.832849i | ||||
\(673\) | 14850.7 | + | 25722.1i | 0.850597 | + | 1.47328i | 0.880670 | + | 0.473730i | \(0.157093\pi\) |
−0.0300732 | + | 0.999548i | \(0.509574\pi\) | |||||||
\(674\) | 35936.6 | 2.05375 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −86.5900 | −0.00492661 | ||||||||
\(677\) | 1330.74 | + | 2304.91i | 0.0755459 | + | 0.130849i | 0.901324 | − | 0.433147i | \(-0.142597\pi\) |
−0.825778 | + | 0.563996i | \(0.809263\pi\) | |||||||
\(678\) | −12505.8 | + | 14727.6i | −0.708381 | + | 0.834235i | ||||
\(679\) | 2535.93 | − | 4392.36i | 0.143328 | − | 0.248252i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3337.14 | − | 608.618i | −0.187782 | − | 0.0342471i | ||||
\(682\) | −23368.9 | − | 40476.1i | −1.31208 | − | 2.27259i | ||||
\(683\) | −28698.1 | −1.60776 | −0.803882 | − | 0.594789i | \(-0.797235\pi\) | ||||
−0.803882 | + | 0.594789i | \(0.797235\pi\) | |||||||
\(684\) | −3247.80 | − | 1225.41i | −0.181554 | − | 0.0685010i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12944.0 | + | 22419.7i | 0.720415 | + | 1.24780i | ||||
\(687\) | −8014.51 | − | 22427.9i | −0.445084 | − | 1.24553i | ||||
\(688\) | 50.4833 | − | 87.4396i | 0.00279747 | − | 0.00484535i | ||||
\(689\) | −12783.9 | + | 22142.4i | −0.706863 | + | 1.22432i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8412.62 | − | 14571.1i | −0.463142 | − | 0.802186i | 0.535973 | − | 0.844235i | \(-0.319945\pi\) |
−0.999116 | + | 0.0420492i | \(0.986611\pi\) | |||||||
\(692\) | −12036.6 | −0.661220 | ||||||||
\(693\) | 33710.0 | + | 12718.9i | 1.84781 | + | 0.697189i | ||||
\(694\) | −5543.99 | −0.303238 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20549.4 | − | 3747.74i | −1.11914 | − | 0.204106i | ||||
\(697\) | −5944.92 | + | 10296.9i | −0.323070 | + | 0.559574i | ||||
\(698\) | −3198.45 | + | 5539.88i | −0.173443 | + | 0.300412i | ||||
\(699\) | 1067.94 | − | 1257.67i | 0.0577870 | − | 0.0680537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −998.795 | −0.0538145 | −0.0269073 | − | 0.999638i | \(-0.508566\pi\) | ||||
−0.0269073 | + | 0.999638i | \(0.508566\pi\) | |||||||
\(702\) | 25738.6 | + | 15469.9i | 1.38382 | + | 0.831730i | ||||
\(703\) | 2476.88 | 0.132884 | ||||||||
\(704\) | 27500.8 | + | 47632.9i | 1.47227 | + | 2.55004i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6010.66 | − | 10410.8i | 0.320417 | − | 0.554978i | ||||
\(707\) | −438.523 | + | 759.545i | −0.0233272 | + | 0.0404040i | ||||
\(708\) | −27687.3 | − | 5049.54i | −1.46971 | − | 0.268041i | ||||
\(709\) | −16626.9 | − | 28798.6i | −0.880727 | − | 1.52546i | −0.850534 | − | 0.525921i | \(-0.823721\pi\) |
−0.0301937 | − | 0.999544i | \(-0.509612\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13607.8 | − | 11149.1i | 0.717768 | − | 0.588078i | ||||
\(712\) | −4520.73 | −0.237952 | ||||||||
\(713\) | 738.765 | + | 1279.58i | 0.0388036 | + | 0.0672099i | ||||
\(714\) | −7660.56 | − | 21437.4i | −0.401526 | − | 1.12363i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6609.97 | + | 11448.8i | −0.345009 | + | 0.597573i | ||||
\(717\) | −3248.21 | − | 9089.81i | −0.169186 | − | 0.473452i | ||||
\(718\) | −8409.62 | − | 14565.9i | −0.437109 | − | 0.757095i | ||||
\(719\) | 1178.94 | 0.0611503 | 0.0305752 | − | 0.999532i | \(-0.490266\pi\) | ||||
0.0305752 | + | 0.999532i | \(0.490266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28972.0 | 1.49650 | ||||||||
\(722\) | 15458.6 | + | 26775.0i | 0.796826 | + | 1.38014i | ||||
\(723\) | −16700.1 | − | 3045.71i | −0.859034 | − | 0.156668i | ||||
\(724\) | −17050.8 | + | 29532.9i | −0.875260 | + | 1.51600i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −47226.8 | + | 55617.4i | −2.41426 | + | 2.84319i | ||||
\(727\) | 6338.35 | + | 10978.3i | 0.323351 | + | 0.560061i | 0.981177 | − | 0.193109i | \(-0.0618571\pi\) |
−0.657826 | + | 0.753170i | \(0.728524\pi\) | |||||||
\(728\) | 21172.6 | 1.07790 | ||||||||
\(729\) | 9236.02 | + | 17381.5i | 0.469238 | + | 0.883072i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5053.90 | − | 8753.61i | −0.255712 | − | 0.442906i | ||||
\(732\) | 23687.1 | − | 27895.5i | 1.19604 | − | 1.40853i | ||||
\(733\) | 4903.42 | − | 8492.98i | 0.247083 | − | 0.427961i | −0.715632 | − | 0.698478i | \(-0.753861\pi\) |
0.962715 | + | 0.270517i | \(0.0871945\pi\) | |||||||
\(734\) | 26137.5 | − | 45271.4i | 1.31438 | − | 2.27657i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −873.381 | − | 1512.74i | −0.0437408 | − | 0.0757613i | ||||
\(737\) | 29712.8 | 1.48506 | ||||||||
\(738\) | −4997.30 | − | 30422.5i | −0.249259 | − | 1.51744i | ||||
\(739\) | −29970.4 | −1.49185 | −0.745927 | − | 0.666028i | \(-0.767993\pi\) | ||||
−0.745927 | + | 0.666028i | \(0.767993\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 814.460 | + | 2279.19i | 0.0403778 | + | 0.112994i | ||||
\(742\) | −25129.2 | + | 43525.1i | −1.24329 | + | 2.15345i | ||||
\(743\) | 10848.8 | − | 18790.6i | 0.535670 | − | 0.927808i | −0.463460 | − | 0.886118i | \(-0.653392\pi\) |
0.999131 | − | 0.0416904i | \(-0.0132743\pi\) | |||||||
\(744\) | −6057.78 | − | 16952.1i | −0.298507 | − | 0.835344i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10335.8 | −0.507267 | ||||||||
\(747\) | −16982.7 | + | 13914.2i | −0.831812 | + | 0.681516i | ||||
\(748\) | 40812.1 | 1.99497 | ||||||||
\(749\) | 3577.92 | + | 6197.14i | 0.174545 | + | 0.302321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8512.10 | + | 14743.4i | −0.413596 | + | 0.716370i | −0.995280 | − | 0.0970452i | \(-0.969061\pi\) |
0.581684 | + | 0.813415i | \(0.302394\pi\) | |||||||
\(752\) | −113.146 | + | 195.974i | −0.00548670 | + | 0.00950324i | ||||
\(753\) | 18973.6 | − | 22344.5i | 0.918243 | − | 1.08138i | ||||
\(754\) | 19128.8 | + | 33132.0i | 0.923911 | + | 1.60026i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 31244.2 | + | 18779.0i | 1.50310 | + | 0.903422i | ||||
\(757\) | −30745.2 | −1.47616 | −0.738080 | − | 0.674714i | \(-0.764267\pi\) | ||||
−0.738080 | + | 0.674714i | \(0.764267\pi\) | |||||||
\(758\) | 27020.3 | + | 46800.5i | 1.29475 | + | 2.24257i | ||||
\(759\) | 2140.24 | − | 2520.48i | 0.102353 | − | 0.120537i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10748.3 | + | 18616.6i | −0.511992 | + | 0.886797i | 0.487911 | + | 0.872893i | \(0.337759\pi\) |
−0.999903 | + | 0.0139035i | \(0.995574\pi\) | |||||||
\(762\) | 20215.3 | + | 3686.81i | 0.961052 | + | 0.175274i | ||||
\(763\) | 15312.3 | + | 26521.7i | 0.726530 | + | 1.25839i | ||||
\(764\) | −10505.7 | −0.497489 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36955.5 | 1.74316 | ||||||||
\(767\) | 9811.66 | + | 16994.3i | 0.461902 | + | 0.800037i | ||||
\(768\) | 7075.65 | + | 19800.6i | 0.332449 | + | 0.930327i | ||||
\(769\) | −11028.7 | + | 19102.4i | −0.517174 | + | 0.895772i | 0.482627 | + | 0.875826i | \(0.339683\pi\) |
−0.999801 | + | 0.0199457i | \(0.993651\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2051.84 | − | 5741.89i | −0.0958434 | − | 0.268209i | ||||
\(772\) | −5259.04 | − | 9108.93i | −0.245178 | − | 0.424660i | ||||
\(773\) | −30155.8 | −1.40314 | −0.701570 | − | 0.712601i | \(-0.747517\pi\) | ||||
−0.701570 | + | 0.712601i | \(0.747517\pi\) | |||||||
\(774\) | 24522.0 | + | 9252.26i | 1.13879 | + | 0.429671i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2835.57 | + | 4911.35i | 0.131174 | + | 0.227200i | ||||
\(777\) | −25588.7 | − | 4666.81i | −1.18146 | − | 0.215471i | ||||
\(778\) | −7090.04 | + | 12280.3i | −0.326723 | + | 0.565900i | ||||
\(779\) | 1242.42 | − | 2151.94i | 0.0571431 | − | 0.0989747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13584.8 | − | 23529.6i | −0.622411 | − | 1.07805i | ||||
\(782\) | −2089.23 | −0.0955381 | ||||||||
\(783\) | −440.943 | + | 25071.9i | −0.0201252 | + | 1.14431i | ||||
\(784\) | −29.3010 | −0.00133478 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 33510.7 | − | 39464.4i | 1.52072 | − | 1.79090i | ||||
\(787\) | −1624.36 | + | 2813.47i | −0.0735733 | + | 0.127433i | −0.900465 | − | 0.434929i | \(-0.856774\pi\) |
0.826892 | + | 0.562361i | \(0.190107\pi\) | |||||||
\(788\) | 26341.7 | − | 45625.2i | 1.19084 | − | 2.06260i | ||||
\(789\) | 14813.9 | + | 2701.72i | 0.668427 | + | 0.121906i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16353.1 | 0.735081 | ||||||||
\(792\) | −31162.9 | + | 25532.3i | −1.39814 | + | 1.14552i | ||||
\(793\) | −25516.1 | −1.14263 | ||||||||
\(794\) | −27418.8 | − | 47490.8i | −1.22551 | − | 2.12265i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8670.90 | − | 15018.4i | 0.386095 | − | 0.668737i | ||||
\(797\) | −13855.1 | + | 23997.7i | −0.615775 | + | 1.06655i | 0.374473 | + | 0.927238i | \(0.377824\pi\) |
−0.990248 | + | 0.139316i | \(0.955510\pi\) | |||||||
\(798\) | 1600.98 | + | 4480.18i | 0.0710199 | + | 0.198743i | ||||
\(799\) | 11327.1 | + | 19619.0i | 0.501530 | + | 0.868675i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 879.667 | + | 5355.23i | 0.0388034 | + | 0.236227i | ||||
\(802\) | 58785.4 | 2.58826 | ||||||||
\(803\) | −11893.3 | − | 20599.8i | −0.522673 | − | 0.905296i | ||||
\(804\) | 29574.6 | + | 5393.73i | 1.29728 | + | 0.236595i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16485.6 | + | 28553.8i | −0.720445 | + | 1.24785i | ||||
\(807\) | −9854.90 | + | 11605.8i | −0.429875 | + | 0.506248i | ||||
\(808\) | −490.338 | − | 849.290i | −0.0213491 | − | 0.0369776i | ||||
\(809\) | −2244.10 | −0.0975259 | −0.0487630 | − | 0.998810i | \(-0.515528\pi\) | ||||
−0.0487630 | + | 0.998810i | \(0.515528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2739.73 | −0.118625 | −0.0593126 | − | 0.998239i | \(-0.518891\pi\) | ||||
−0.0593126 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(812\) | 23220.6 | + | 40219.2i | 1.00355 | + | 1.73820i | ||||
\(813\) | 2249.65 | − | 2649.33i | 0.0970462 | − | 0.114288i | ||||
\(814\) | 37755.0 | − | 65393.5i | 1.62569 | − | 2.81578i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −115.808 | − | 21.1207i | −0.00496823 | − | 0.000906092i | ||||
\(817\) | 1056.21 | + | 1829.41i | 0.0452290 | + | 0.0783390i | ||||
\(818\) | 10176.6 | 0.434984 | ||||||||
\(819\) | −4119.88 | − | 25080.9i | −0.175776 | − | 1.07008i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8616.06 | + | 14923.5i | 0.366264 | + | 0.634388i | 0.988978 | − | 0.148062i | \(-0.0473034\pi\) |
−0.622714 | + | 0.782449i | \(0.713970\pi\) | |||||||
\(822\) | −18386.6 | − | 51453.1i | −0.780177 | − | 2.18325i | ||||
\(823\) | 9642.94 | − | 16702.1i | 0.408422 | − | 0.707409i | −0.586291 | − | 0.810101i | \(-0.699412\pi\) |
0.994713 | + | 0.102692i | \(0.0327457\pi\) | |||||||
\(824\) | −16197.6 | + | 28055.1i | −0.684795 | + | 1.18610i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19286.7 | + | 33405.5i | 0.812433 | + | 1.40717i | ||||
\(827\) | −26379.4 | −1.10919 | −0.554595 | − | 0.832120i | \(-0.687127\pi\) | ||||
−0.554595 | + | 0.832120i | \(0.687127\pi\) | |||||||
\(828\) | 2587.82 | − | 2120.24i | 0.108615 | − | 0.0889896i | ||||
\(829\) | −8718.15 | −0.365252 | −0.182626 | − | 0.983182i | \(-0.558460\pi\) | ||||
−0.182626 | + | 0.983182i | \(0.558460\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3233.90 | + | 589.790i | 0.134997 | + | 0.0246205i | ||||
\(832\) | 19400.4 | − | 33602.6i | 0.808401 | − | 1.40019i | ||||
\(833\) | −1466.67 | + | 2540.35i | −0.0610049 | + | 0.105664i | ||||
\(834\) | 32825.1 | − | 38657.0i | 1.36288 | − | 1.60501i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8529.28 | −0.352860 | ||||||||
\(837\) | −18902.6 | + | 10474.6i | −0.780610 | + | 0.432565i | ||||
\(838\) | 44256.9 | 1.82438 | ||||||||
\(839\) | 6738.10 | + | 11670.7i | 0.277265 | + | 0.480236i | 0.970704 | − | 0.240279i | \(-0.0772388\pi\) |
−0.693439 | + | 0.720515i | \(0.743905\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3778.58 | + | 6544.70i | −0.154930 | + | 0.268346i | ||||
\(842\) | 22782.4 | − | 39460.2i | 0.932462 | − | 1.61507i | ||||
\(843\) | −18378.6 | − | 3351.83i | −0.750880 | − | 0.136943i | ||||
\(844\) | 19085.6 | + | 33057.3i | 0.778383 | + | 1.34820i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −54959.9 | − | 20736.6i | −2.23352 | − | 0.842718i | ||||
\(847\) | 61755.7 | 2.50526 | ||||||||
\(848\) | 129.943 | + | 225.068i | 0.00526210 | + | 0.00911423i | ||||
\(849\) | 881.907 | + | 2467.93i | 0.0356501 | + | 0.0997636i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1193.56 | + | 2067.30i | −0.0480783 | + | 0.0832740i | ||||
\(852\) | −9250.31 | − | 25886.1i | −0.371960 | − | 1.04090i | ||||
\(853\) | −14118.3 | − | 24453.6i | −0.566708 | − | 0.981567i | −0.996889 | − | 0.0788242i | \(-0.974883\pi\) |
0.430181 | − | 0.902743i | \(-0.358450\pi\) | |||||||
\(854\) | −50156.8 | −2.00975 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8001.36 | −0.319487 | ||||||||
\(857\) | 4229.08 | + | 7324.98i | 0.168568 | + | 0.291968i | 0.937917 | − | 0.346861i | \(-0.112752\pi\) |
−0.769349 | + | 0.638829i | \(0.779419\pi\) | |||||||
\(858\) | 72588.9 | + | 13238.6i | 2.88828 | + | 0.526757i | ||||
\(859\) | 11527.2 | − | 19965.6i | 0.457860 | − | 0.793036i | −0.540988 | − | 0.841030i | \(-0.681950\pi\) |
0.998848 | + | 0.0479940i | \(0.0152828\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16890.1 | + | 19890.8i | −0.668539 | + | 0.787315i | ||||
\(862\) | 5628.86 | + | 9749.48i | 0.222413 | + | 0.385230i | ||||
\(863\) | 42314.4 | 1.66906 | 0.834529 | − | 0.550963i | \(-0.185740\pi\) | ||||
0.834529 | + | 0.550963i | \(0.185740\pi\) | |||||||
\(864\) | 22347.0 | − | 12383.3i | 0.879932 | − | 0.487602i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17879.2 | + | 30967.8i | 0.701572 | + | 1.21516i | ||||
\(867\) | 8895.99 | − | 10476.5i | 0.348470 | − | 0.410381i | ||||
\(868\) | −20011.9 | + | 34661.7i | −0.782545 | + | 1.35541i | ||||
\(869\) | 21612.5 | − | 37433.9i | 0.843674 | − | 1.46129i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10480.4 | − | 18152.7i | −0.407711 | − | 0.706176i | ||||
\(872\) | −34243.1 | −1.32984 | ||||||||
\(873\) | 5266.19 | − | 4314.67i | 0.204162 | − | 0.167273i | ||||
\(874\) | 436.627 | 0.0168983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8098.51 | − | 22663.0i | −0.312356 | − | 0.874098i | ||||
\(877\) | −5090.00 | + | 8816.15i | −0.195983 | + | 0.339453i | −0.947222 | − | 0.320577i | \(-0.896123\pi\) |
0.751239 | + | 0.660030i | \(0.229456\pi\) | |||||||
\(878\) | −14205.2 | + | 24604.0i | −0.546014 | + | 0.945725i | ||||
\(879\) | 10838.3 | + | 30330.0i | 0.415890 | + | 1.16383i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6030.64 | 0.230621 | 0.115311 | − | 0.993329i | \(-0.463214\pi\) | ||||
0.115311 | + | 0.993329i | \(0.463214\pi\) | |||||||
\(882\) | −1232.88 | − | 7505.53i | −0.0470673 | − | 0.286535i | ||||
\(883\) | 30238.0 | 1.15242 | 0.576211 | − | 0.817301i | \(-0.304531\pi\) | ||||
0.576211 | + | 0.817301i | \(0.304531\pi\) | |||||||
\(884\) | −14395.4 | − | 24933.6i | −0.547704 | − | 0.948651i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6824.57 | − | 11820.5i | 0.258776 | − | 0.448214i | ||||
\(887\) | 9388.09 | − | 16260.7i | 0.355379 | − | 0.615535i | −0.631804 | − | 0.775129i | \(-0.717685\pi\) |
0.987183 | + | 0.159594i | \(0.0510184\pi\) | |||||||
\(888\) | 18825.2 | − | 22169.8i | 0.711412 | − | 0.837805i | ||||
\(889\) | −8696.14 | − | 15062.1i | −0.328075 | − | 0.568243i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36309.2 | + | 31947.2i | 1.36521 | + | 1.20120i | ||||
\(892\) | −45300.3 | −1.70041 | ||||||||
\(893\) | −2367.23 | − | 4100.17i | −0.0887082 | − | 0.153647i | ||||
\(894\) | −26928.6 | + | 31712.8i | −1.00741 | + | 1.18639i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23483.4 | − | 40674.4i | 0.875586 | − | 1.51656i | ||||
\(897\) | −2294.77 | − | 418.514i | −0.0854182 | − | 0.0155783i | ||||
\(898\) | 1853.39 | + | 3210.16i | 0.0688735 | + | 0.119292i | ||||
\(899\) | −27531.8 | −1.02140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26017.3 | 0.962000 | ||||||||
\(902\) | −37876.4 | − | 65603.8i | −1.39817 | − | 2.42169i | ||||
\(903\) | −7464.86 | − | 20889.7i | −0.275100 | − | 0.769841i | ||||
\(904\) | −9142.66 | + | 15835.6i | −0.336372 | + | 0.582614i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7005.07 | − | 19603.0i | −0.256874 | − | 0.718838i | ||||
\(907\) | −18826.3 | − | 32608.1i | −0.689213 | − | 1.19375i | −0.972093 | − | 0.234597i | \(-0.924623\pi\) |
0.282880 | − | 0.959155i | \(-0.408710\pi\) | |||||||
\(908\) | −8432.97 | −0.308214 | ||||||||
\(909\) | −910.651 | + | 746.111i | −0.0332282 | + | 0.0272243i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23793.1 | + | 41210.8i | 0.865312 | + | 1.49877i | 0.866737 | + | 0.498766i | \(0.166213\pi\) |
−0.00142411 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(912\) | 24.2025 | + | 4.41399i | 0.000878756 | + | 0.000160265i | ||||
\(913\) | −26972.6 | + | 46717.9i | −0.977724 | + | 1.69347i | ||||
\(914\) | 3594.32 | − | 6225.54i | 0.130076 | − | 0.225298i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29604.3 | − | 51276.2i | −1.06785 | − | 1.84958i | ||||
\(917\) | −43819.9 | −1.57804 | ||||||||
\(918\) | 537.340 | − | 30553.0i | 0.0193190 | − | 1.09848i | ||||
\(919\) | 32177.3 | 1.15499 | 0.577493 | − | 0.816396i | \(-0.304031\pi\) | ||||
0.577493 | + | 0.816396i | \(0.304031\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6614.88 | + | 7790.12i | −0.236664 | + | 0.278711i | ||||
\(922\) | −4716.94 | + | 8169.99i | −0.168486 | + | 0.291827i | ||||
\(923\) | −9583.40 | + | 16598.9i | −0.341757 | + | 0.591940i | ||||
\(924\) | 88116.2 | + | 16070.4i | 3.13724 | + | 0.572161i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12729.3 | −0.451741 | ||||||||
\(927\) | 36385.7 | + | 13728.5i | 1.28917 | + | 0.486411i | ||||
\(928\) | 32548.6 | 1.15136 | ||||||||
\(929\) | −20321.8 | − | 35198.4i | −0.717694 | − | 1.24308i | −0.961911 | − | 0.273362i | \(-0.911864\pi\) |
0.244218 | − | 0.969720i | \(-0.421469\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 306.518 | − | 530.905i | 0.0107903 | − | 0.0186893i | ||||
\(932\) | 2050.85 | − | 3552.18i | 0.0720792 | − | 0.124845i | ||||
\(933\) | 4032.31 | + | 11284.1i | 0.141492 | + | 0.395952i | ||||
\(934\) | 25016.7 | + | 43330.2i | 0.876415 | + | 1.51799i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 26590.5 | + | 10032.7i | 0.928567 | + | 0.350352i | ||||
\(937\) | −6077.87 | −0.211905 | −0.105953 | − | 0.994371i | \(-0.533789\pi\) | ||||
−0.105953 | + | 0.994371i | \(0.533789\pi\) | |||||||
\(938\) | −20601.3 | − | 35682.5i | −0.717118 | − | 1.24208i | ||||
\(939\) | −52664.2 | − | 9604.75i | −1.83028 | − | 0.333801i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −732.293 | + | 1268.37i | −0.0253688 | + | 0.0439401i | −0.878431 | − | 0.477869i | \(-0.841409\pi\) |
0.853062 | + | 0.521809i | \(0.174743\pi\) | |||||||
\(942\) | −3990.09 | + | 4698.99i | −0.138009 | + | 0.162528i | ||||
\(943\) | 1197.39 | + | 2073.95i | 0.0413494 | + | 0.0716193i | ||||
\(944\) | 199.463 | 0.00687707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64399.0 | 2.21331 | ||||||||
\(947\) | −5304.36 | − | 9187.43i | −0.182015 | − | 0.315260i | 0.760551 | − | 0.649278i | \(-0.224929\pi\) |
−0.942567 | + | 0.334018i | \(0.891595\pi\) | |||||||
\(948\) | 28307.2 | − | 33336.4i | 0.969806 | − | 1.14211i | ||||
\(949\) | −8390.14 | + | 14532.1i | −0.286992 | + | 0.497085i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8699.48 | + | 1586.59i | 0.296635 | + | 0.0540995i | ||||
\(952\) | −10772.4 | − | 18658.4i | −0.366739 | − | 0.635211i | ||||
\(953\) | 43623.4 | 1.48279 | 0.741396 | − | 0.671068i | \(-0.234164\pi\) | ||||
0.741396 | + | 0.671068i | \(0.234164\pi\) | |||||||
\(954\) | −52184.1 | + | 42755.3i | −1.77099 | + | 1.45100i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11998.4 | − | 20781.8i | −0.405915 | − | 0.703065i | ||||
\(957\) | 20733.4 | + | 58020.4i | 0.700329 | + | 1.95981i | ||||
\(958\) | −33441.3 | + | 57922.1i | −1.12781 | + | 1.95342i | ||||
\(959\) | −23123.3 | + | 40050.7i | −0.778613 | + | 1.34860i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3031.76 | + | 5251.17i | 0.101768 | + | 0.176267i | ||||
\(962\) | −53268.4 | −1.78528 | ||||||||
\(963\) | 1556.95 | + | 9478.35i | 0.0520996 | + | 0.317171i | ||||
\(964\) | −42201.2 | −1.40997 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4510.80 | − | 822.668i | −0.150241 | − | 0.0274005i | ||||
\(967\) | 2540.19 | − | 4399.73i | 0.0844745 | − | 0.146314i | −0.820693 | − | 0.571370i | \(-0.806412\pi\) |
0.905167 | + | 0.425056i | \(0.139746\pi\) | |||||||
\(968\) | −34526.3 | + | 59801.3i | −1.14640 | + | 1.98563i | ||||
\(969\) | 1594.15 | − | 1877.37i | 0.0528497 | − | 0.0622393i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9875.60 | 0.326388 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(972\) | 30340.9 | + | 38389.7i | 1.00122 | + | 1.26682i | ||||
\(973\) | −42923.4 | −1.41425 | ||||||||
\(974\) | 37671.8 | + | 65249.4i | 1.23930 | + | 2.14654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −129.680 | + | 224.613i | −0.00425304 | + | 0.00736648i | ||||
\(977\) | 12290.4 | − | 21287.6i | 0.402461 | − | 0.697084i | −0.591561 | − | 0.806260i | \(-0.701488\pi\) |
0.994022 | + | 0.109177i | \(0.0348214\pi\) | |||||||
\(978\) | 28097.3 | + | 5124.31i | 0.918664 | + | 0.167543i | ||||
\(979\) | 6667.32 | + | 11548.1i | 0.217659 | + | 0.376997i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6663.21 | + | 40564.2i | 0.216860 | + | 1.32020i | ||||
\(982\) | 93891.8 | 3.05113 | ||||||||
\(983\) | −15930.3 | − | 27592.1i | −0.516885 | − | 0.895270i | −0.999808 | − | 0.0196076i | \(-0.993758\pi\) |
0.482923 | − | 0.875663i | \(-0.339575\pi\) | |||||||
\(984\) | −9818.48 | − | 27476.1i | −0.318091 | − | 0.890149i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19465.0 | − | 33714.4i | 0.628695 | − | 1.08893i | ||||
\(987\) | 16730.6 | + | 46819.1i | 0.539556 | + | 1.50990i | ||||
\(988\) | 3008.49 | + | 5210.85i | 0.0968752 | + | 0.167793i | ||||
\(989\) | −2035.86 | −0.0654566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36921.3 | −1.18350 | −0.591748 | − | 0.806123i | \(-0.701562\pi\) | ||||
−0.591748 | + | 0.806123i | \(0.701562\pi\) | |||||||
\(992\) | 14025.5 | + | 24292.9i | 0.448902 | + | 0.777520i | ||||
\(993\) | −42691.4 | − | 7785.95i | −1.36432 | − | 0.248821i | ||||
\(994\) | −18838.0 | + | 32628.4i | −0.601112 | + | 1.04116i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −35327.7 | + | 41604.2i | −1.12390 | + | 1.32357i | ||||
\(997\) | −1867.06 | − | 3233.84i | −0.0593083 | − | 0.102725i | 0.834847 | − | 0.550482i | \(-0.185556\pi\) |
−0.894155 | + | 0.447757i | \(0.852223\pi\) | |||||||
\(998\) | −65880.7 | −2.08959 | ||||||||
\(999\) | −29925.3 | − | 17986.3i | −0.947743 | − | 0.569632i |
(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 | 225.4.e.c.76.1 | 6 | ||
5.2 | odd | 4 | 225.4.k.c.49.6 | 12 | |||
5.3 | odd | 4 | 225.4.k.c.49.1 | 12 | |||
5.4 | even | 2 | 45.4.e.b.31.3 | yes | 6 | ||
9.4 | even | 3 | 2025.4.a.s.1.3 | 3 | |||
9.5 | odd | 6 | 2025.4.a.q.1.1 | 3 | |||
9.7 | even | 3 | inner | 225.4.e.c.151.1 | 6 | ||
15.14 | odd | 2 | 135.4.e.b.91.1 | 6 | |||
45.4 | even | 6 | 405.4.a.h.1.1 | 3 | |||
45.7 | odd | 12 | 225.4.k.c.124.1 | 12 | |||
45.14 | odd | 6 | 405.4.a.j.1.3 | 3 | |||
45.29 | odd | 6 | 135.4.e.b.46.1 | 6 | |||
45.34 | even | 6 | 45.4.e.b.16.3 | ✓ | 6 | ||
45.43 | odd | 12 | 225.4.k.c.124.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.3 | ✓ | 6 | 45.34 | even | 6 | ||
45.4.e.b.31.3 | yes | 6 | 5.4 | even | 2 | ||
135.4.e.b.46.1 | 6 | 45.29 | odd | 6 | |||
135.4.e.b.91.1 | 6 | 15.14 | odd | 2 | |||
225.4.e.c.76.1 | 6 | 1.1 | even | 1 | trivial | ||
225.4.e.c.151.1 | 6 | 9.7 | even | 3 | inner | ||
225.4.k.c.49.1 | 12 | 5.3 | odd | 4 | |||
225.4.k.c.49.6 | 12 | 5.2 | odd | 4 | |||
225.4.k.c.124.1 | 12 | 45.7 | odd | 12 | |||
225.4.k.c.124.6 | 12 | 45.43 | odd | 12 | |||
405.4.a.h.1.1 | 3 | 45.4 | even | 6 | |||
405.4.a.j.1.3 | 3 | 45.14 | odd | 6 | |||
2025.4.a.q.1.1 | 3 | 9.5 | odd | 6 | |||
2025.4.a.s.1.3 | 3 | 9.4 | even | 3 |