Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,4,Mod(116,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("245.116");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.e (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: | \(14.4554679514\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 27 x^{10} + 22 x^{9} + 399 x^{8} + 492 x^{7} + 4046 x^{6} + 8784 x^{5} + 22536 x^{4} + \cdots + 784 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 226.2 | ||
Root | \(-0.120924 - 0.209447i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.226 |
Dual form | 245.4.e.p.116.2 |
$q$-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 \(\left(\mathbb{Z}/245\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.828031 | + | 1.43419i | −0.292753 | + | 0.507063i | −0.974460 | − | 0.224562i | \(-0.927905\pi\) |
0.681707 | + | 0.731626i | \(0.261238\pi\) | |||||||
\(3\) | 0.166444 | + | 0.288289i | 0.0320321 | + | 0.0554813i | 0.881597 | − | 0.472003i | \(-0.156469\pi\) |
−0.849565 | + | 0.527484i | \(0.823135\pi\) | |||||||
\(4\) | 2.62873 | + | 4.55309i | 0.328591 | + | 0.569137i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | −0.551283 | −0.0375100 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −21.9552 | −0.970291 | ||||||||
\(9\) | 13.4446 | − | 23.2867i | 0.497948 | − | 0.862471i | ||||
\(10\) | 4.14016 | + | 7.17096i | 0.130923 | + | 0.226766i | ||||
\(11\) | −34.7863 | − | 60.2517i | −0.953497 | − | 1.65151i | −0.737770 | − | 0.675052i | \(-0.764121\pi\) |
−0.215727 | − | 0.976454i | \(-0.569212\pi\) | |||||||
\(12\) | −0.875071 | + | 1.51567i | −0.0210509 | + | 0.0364613i | ||||
\(13\) | 68.4326 | 1.45998 | 0.729991 | − | 0.683456i | \(-0.239524\pi\) | ||||
0.729991 | + | 0.683456i | \(0.239524\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.66444 | 0.0286504 | ||||||||
\(16\) | −2.85026 | + | 4.93680i | −0.0445354 | + | 0.0771375i | ||||
\(17\) | −52.1659 | − | 90.3539i | −0.744240 | − | 1.28906i | −0.950549 | − | 0.310574i | \(-0.899479\pi\) |
0.206309 | − | 0.978487i | \(-0.433855\pi\) | |||||||
\(18\) | 22.2651 | + | 38.5643i | 0.291552 | + | 0.504982i | ||||
\(19\) | −35.9465 | + | 62.2611i | −0.434036 | + | 0.751772i | −0.997216 | − | 0.0745616i | \(-0.976244\pi\) |
0.563180 | + | 0.826334i | \(0.309578\pi\) | |||||||
\(20\) | 26.2873 | 0.293901 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 115.217 | 1.11656 | ||||||||
\(23\) | 50.5154 | − | 87.4952i | 0.457964 | − | 0.793218i | −0.540889 | − | 0.841094i | \(-0.681912\pi\) |
0.998853 | + | 0.0478764i | \(0.0152453\pi\) | |||||||
\(24\) | −3.65430 | − | 6.32944i | −0.0310805 | − | 0.0538330i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −56.6643 | + | 98.1454i | −0.427415 | + | 0.740304i | ||||
\(27\) | 17.9390 | 0.127866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −114.661 | −0.734205 | −0.367102 | − | 0.930181i | \(-0.619650\pi\) | ||||
−0.367102 | + | 0.930181i | \(0.619650\pi\) | |||||||
\(30\) | −1.37821 | + | 2.38712i | −0.00838750 | + | 0.0145276i | ||||
\(31\) | 36.8252 | + | 63.7832i | 0.213355 | + | 0.369542i | 0.952762 | − | 0.303716i | \(-0.0982275\pi\) |
−0.739407 | + | 0.673258i | \(0.764894\pi\) | |||||||
\(32\) | −92.5409 | − | 160.286i | −0.511221 | − | 0.885461i | ||||
\(33\) | 11.5799 | − | 20.0570i | 0.0610851 | − | 0.105802i | ||||
\(34\) | 172.780 | 0.871514 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 141.369 | 0.654485 | ||||||||
\(37\) | 100.467 | − | 174.013i | 0.446395 | − | 0.773178i | −0.551753 | − | 0.834007i | \(-0.686041\pi\) |
0.998148 | + | 0.0608289i | \(0.0193744\pi\) | |||||||
\(38\) | −59.5296 | − | 103.108i | −0.254131 | − | 0.440168i | ||||
\(39\) | 11.3902 | + | 19.7284i | 0.0467663 | + | 0.0810017i | ||||
\(40\) | −54.8879 | + | 95.0687i | −0.216964 | + | 0.375792i | ||||
\(41\) | 417.308 | 1.58957 | 0.794786 | − | 0.606889i | \(-0.207583\pi\) | ||||
0.794786 | + | 0.606889i | \(0.207583\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 311.175 | 1.10357 | 0.551787 | − | 0.833985i | \(-0.313946\pi\) | ||||
0.551787 | + | 0.833985i | \(0.313946\pi\) | |||||||
\(44\) | 182.888 | − | 316.771i | 0.626621 | − | 1.08534i | ||||
\(45\) | −67.2230 | − | 116.434i | −0.222689 | − | 0.385709i | ||||
\(46\) | 83.6566 | + | 144.897i | 0.268141 | + | 0.464434i | ||||
\(47\) | −74.8485 | + | 129.641i | −0.232293 | + | 0.402344i | −0.958483 | − | 0.285151i | \(-0.907956\pi\) |
0.726189 | + | 0.687495i | \(0.241290\pi\) | |||||||
\(48\) | −1.89763 | −0.00570625 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 41.4016 | 0.117101 | ||||||||
\(51\) | 17.3654 | − | 30.0777i | 0.0476792 | − | 0.0825827i | ||||
\(52\) | 179.891 | + | 311.580i | 0.479737 | + | 0.830929i | ||||
\(53\) | −135.737 | − | 235.104i | −0.351791 | − | 0.609320i | 0.634772 | − | 0.772699i | \(-0.281094\pi\) |
−0.986563 | + | 0.163379i | \(0.947761\pi\) | |||||||
\(54\) | −14.8541 | + | 25.7280i | −0.0374331 | + | 0.0648360i | ||||
\(55\) | −347.863 | −0.852834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23.9323 | −0.0556124 | ||||||||
\(58\) | 94.9425 | − | 164.445i | 0.214941 | − | 0.372288i | ||||
\(59\) | 259.014 | + | 448.625i | 0.571538 | + | 0.989933i | 0.996408 | + | 0.0846788i | \(0.0269864\pi\) |
−0.424870 | + | 0.905254i | \(0.639680\pi\) | |||||||
\(60\) | 4.37536 | + | 7.57834i | 0.00941427 | + | 0.0163060i | ||||
\(61\) | 109.963 | − | 190.461i | 0.230808 | − | 0.399771i | −0.727238 | − | 0.686385i | \(-0.759196\pi\) |
0.958046 | + | 0.286614i | \(0.0925297\pi\) | |||||||
\(62\) | −121.970 | −0.249842 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 260.903 | 0.509576 | ||||||||
\(65\) | 171.081 | − | 296.322i | 0.326462 | − | 0.565449i | ||||
\(66\) | 19.1771 | + | 33.2157i | 0.0357657 | + | 0.0619480i | ||||
\(67\) | −40.3475 | − | 69.8839i | −0.0735706 | − | 0.127428i | 0.826893 | − | 0.562359i | \(-0.190106\pi\) |
−0.900464 | + | 0.434931i | \(0.856773\pi\) | |||||||
\(68\) | 274.260 | − | 475.032i | 0.489101 | − | 0.847148i | ||||
\(69\) | 33.6319 | 0.0586783 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −91.0463 | −0.152186 | −0.0760930 | − | 0.997101i | \(-0.524245\pi\) | ||||
−0.0760930 | + | 0.997101i | \(0.524245\pi\) | |||||||
\(72\) | −295.178 | + | 511.264i | −0.483154 | + | 0.836848i | ||||
\(73\) | −441.141 | − | 764.078i | −0.707283 | − | 1.22505i | −0.965861 | − | 0.259059i | \(-0.916588\pi\) |
0.258579 | − | 0.965990i | \(-0.416746\pi\) | |||||||
\(74\) | 166.379 | + | 288.177i | 0.261367 | + | 0.452701i | ||||
\(75\) | 4.16110 | − | 7.20723i | 0.00640643 | − | 0.0110963i | ||||
\(76\) | −377.974 | −0.570481 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −37.7257 | −0.0547640 | ||||||||
\(79\) | −299.939 | + | 519.509i | −0.427161 | + | 0.739865i | −0.996620 | − | 0.0821553i | \(-0.973820\pi\) |
0.569458 | + | 0.822020i | \(0.307153\pi\) | |||||||
\(80\) | 14.2513 | + | 24.6840i | 0.0199168 | + | 0.0344969i | ||||
\(81\) | −360.018 | − | 623.570i | −0.493852 | − | 0.855377i | ||||
\(82\) | −345.544 | + | 598.499i | −0.465353 | + | 0.806014i | ||||
\(83\) | 70.8820 | 0.0937387 | 0.0468694 | − | 0.998901i | \(-0.485076\pi\) | ||||
0.0468694 | + | 0.998901i | \(0.485076\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −521.659 | −0.665668 | ||||||||
\(86\) | −257.662 | + | 446.284i | −0.323075 | + | 0.559582i | ||||
\(87\) | −19.0845 | − | 33.0554i | −0.0235181 | − | 0.0407346i | ||||
\(88\) | 763.740 | + | 1322.84i | 0.925170 | + | 1.60244i | ||||
\(89\) | −401.296 | + | 695.065i | −0.477947 | + | 0.827828i | −0.999680 | − | 0.0252802i | \(-0.991952\pi\) |
0.521733 | + | 0.853109i | \(0.325286\pi\) | |||||||
\(90\) | 222.651 | 0.260772 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 531.165 | 0.601932 | ||||||||
\(93\) | −12.2587 | + | 21.2326i | −0.0136684 | + | 0.0236744i | ||||
\(94\) | −123.954 | − | 214.694i | −0.136009 | − | 0.235575i | ||||
\(95\) | 179.732 | + | 311.305i | 0.194107 | + | 0.336203i | ||||
\(96\) | 30.8057 | − | 53.3571i | 0.0327510 | − | 0.0567264i | ||||
\(97\) | 145.648 | 0.152457 | 0.0762283 | − | 0.997090i | \(-0.475712\pi\) | ||||
0.0762283 | + | 0.997090i | \(0.475712\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1870.75 | −1.89917 | ||||||||
\(100\) | 65.7182 | − | 113.827i | 0.0657182 | − | 0.113827i | ||||
\(101\) | 309.718 | + | 536.447i | 0.305129 | + | 0.528499i | 0.977290 | − | 0.211906i | \(-0.0679670\pi\) |
−0.672161 | + | 0.740405i | \(0.734634\pi\) | |||||||
\(102\) | 28.7581 | + | 49.8105i | 0.0279165 | + | 0.0483527i | ||||
\(103\) | 911.040 | − | 1577.97i | 0.871528 | − | 1.50953i | 0.0111125 | − | 0.999938i | \(-0.496463\pi\) |
0.860416 | − | 0.509593i | \(-0.170204\pi\) | |||||||
\(104\) | −1502.45 | −1.41661 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 449.578 | 0.411952 | ||||||||
\(107\) | −544.851 | + | 943.709i | −0.492268 | + | 0.852634i | −0.999960 | − | 0.00890504i | \(-0.997165\pi\) |
0.507692 | + | 0.861539i | \(0.330499\pi\) | |||||||
\(108\) | 47.1569 | + | 81.6781i | 0.0420155 | + | 0.0727730i | ||||
\(109\) | −294.833 | − | 510.666i | −0.259082 | − | 0.448743i | 0.706914 | − | 0.707299i | \(-0.250087\pi\) |
−0.965996 | + | 0.258556i | \(0.916753\pi\) | |||||||
\(110\) | 288.042 | − | 498.903i | 0.249670 | − | 0.432441i | ||||
\(111\) | 66.8882 | 0.0571959 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −900.358 | −0.749544 | −0.374772 | − | 0.927117i | \(-0.622279\pi\) | ||||
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(114\) | 19.8167 | − | 34.3235i | 0.0162807 | − | 0.0281990i | ||||
\(115\) | −252.577 | − | 437.476i | −0.204808 | − | 0.354738i | ||||
\(116\) | −301.412 | − | 522.060i | −0.241253 | − | 0.417863i | ||||
\(117\) | 920.048 | − | 1593.57i | 0.726995 | − | 1.25919i | ||||
\(118\) | −857.887 | −0.669279 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −36.5430 | −0.0277992 | ||||||||
\(121\) | −1754.68 | + | 3039.19i | −1.31831 | + | 2.28339i | ||||
\(122\) | 182.105 | + | 315.415i | 0.135140 | + | 0.234069i | ||||
\(123\) | 69.4583 | + | 120.305i | 0.0509174 | + | 0.0881915i | ||||
\(124\) | −193.607 | + | 335.337i | −0.140213 | + | 0.242856i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1755.75 | −1.22676 | −0.613378 | − | 0.789790i | \(-0.710190\pi\) | ||||
−0.613378 | + | 0.789790i | \(0.710190\pi\) | |||||||
\(128\) | 524.292 | − | 908.100i | 0.362041 | − | 0.627074i | ||||
\(129\) | 51.7931 | + | 89.7083i | 0.0353498 | + | 0.0612277i | ||||
\(130\) | 283.321 | + | 490.727i | 0.191146 | + | 0.331074i | ||||
\(131\) | −904.549 | + | 1566.72i | −0.603289 | + | 1.04493i | 0.389031 | + | 0.921225i | \(0.372810\pi\) |
−0.992319 | + | 0.123702i | \(0.960523\pi\) | |||||||
\(132\) | 121.762 | 0.0802881 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 133.636 | 0.0861521 | ||||||||
\(135\) | 44.8476 | − | 77.6783i | 0.0285916 | − | 0.0495221i | ||||
\(136\) | 1145.31 | + | 1983.74i | 0.722129 | + | 1.25076i | ||||
\(137\) | 9.25670 | + | 16.0331i | 0.00577265 | + | 0.00999852i | 0.868897 | − | 0.494992i | \(-0.164829\pi\) |
−0.863125 | + | 0.504991i | \(0.831496\pi\) | |||||||
\(138\) | −27.8482 | + | 48.2346i | −0.0171783 | + | 0.0297536i | ||||
\(139\) | −625.608 | −0.381751 | −0.190875 | − | 0.981614i | \(-0.561133\pi\) | ||||
−0.190875 | + | 0.981614i | \(0.561133\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −49.8323 | −0.0297634 | ||||||||
\(142\) | 75.3892 | − | 130.578i | 0.0445530 | − | 0.0771680i | ||||
\(143\) | −2380.52 | − | 4123.18i | −1.39209 | − | 2.41117i | ||||
\(144\) | 76.6413 | + | 132.747i | 0.0443526 | + | 0.0768209i | ||||
\(145\) | −286.651 | + | 496.495i | −0.164173 | + | 0.284356i | ||||
\(146\) | 1461.11 | 0.828237 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1056.40 | 0.586725 | ||||||||
\(149\) | 514.317 | − | 890.823i | 0.282782 | − | 0.489792i | −0.689287 | − | 0.724488i | \(-0.742076\pi\) |
0.972069 | + | 0.234696i | \(0.0754095\pi\) | |||||||
\(150\) | 6.89103 | + | 11.9356i | 0.00375100 | + | 0.00649693i | ||||
\(151\) | −35.5037 | − | 61.4942i | −0.0191341 | − | 0.0331412i | 0.856300 | − | 0.516479i | \(-0.172758\pi\) |
−0.875434 | + | 0.483338i | \(0.839424\pi\) | |||||||
\(152\) | 789.211 | − | 1366.95i | 0.421141 | − | 0.729438i | ||||
\(153\) | −2805.39 | −1.48237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 368.252 | 0.190831 | ||||||||
\(156\) | −59.8834 | + | 103.721i | −0.0307340 | + | 0.0532329i | ||||
\(157\) | 1030.66 | + | 1785.16i | 0.523922 | + | 0.907459i | 0.999612 | + | 0.0278461i | \(0.00886484\pi\) |
−0.475691 | + | 0.879613i | \(0.657802\pi\) | |||||||
\(158\) | −496.717 | − | 860.339i | −0.250106 | − | 0.433196i | ||||
\(159\) | 45.1852 | − | 78.2631i | 0.0225372 | − | 0.0390356i | ||||
\(160\) | −925.409 | −0.457250 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1192.42 | 0.578307 | ||||||||
\(163\) | 981.899 | − | 1700.70i | 0.471830 | − | 0.817234i | −0.527651 | − | 0.849462i | \(-0.676927\pi\) |
0.999481 | + | 0.0322280i | \(0.0102603\pi\) | |||||||
\(164\) | 1096.99 | + | 1900.04i | 0.522320 | + | 0.904684i | ||||
\(165\) | −57.8997 | − | 100.285i | −0.0273181 | − | 0.0473163i | ||||
\(166\) | −58.6925 | + | 101.658i | −0.0274423 | + | 0.0475315i | ||||
\(167\) | 2855.04 | 1.32293 | 0.661467 | − | 0.749974i | \(-0.269934\pi\) | ||||
0.661467 | + | 0.749974i | \(0.269934\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2486.01 | 1.13155 | ||||||||
\(170\) | 431.950 | − | 748.158i | 0.194877 | − | 0.337536i | ||||
\(171\) | 966.571 | + | 1674.15i | 0.432255 | + | 0.748687i | ||||
\(172\) | 817.994 | + | 1416.81i | 0.362625 | + | 0.628084i | ||||
\(173\) | 776.603 | − | 1345.12i | 0.341295 | − | 0.591140i | −0.643378 | − | 0.765548i | \(-0.722468\pi\) |
0.984673 | + | 0.174408i | \(0.0558011\pi\) | |||||||
\(174\) | 63.2104 | 0.0275400 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 396.601 | 0.169857 | ||||||||
\(177\) | −86.2226 | + | 149.342i | −0.0366152 | + | 0.0634193i | ||||
\(178\) | −664.571 | − | 1151.07i | −0.279841 | − | 0.484699i | ||||
\(179\) | −134.920 | − | 233.689i | −0.0563376 | − | 0.0975795i | 0.836481 | − | 0.547996i | \(-0.184609\pi\) |
−0.892819 | + | 0.450416i | \(0.851276\pi\) | |||||||
\(180\) | 353.422 | − | 612.145i | 0.146347 | − | 0.253481i | ||||
\(181\) | 2229.61 | 0.915613 | 0.457806 | − | 0.889052i | \(-0.348635\pi\) | ||||
0.457806 | + | 0.889052i | \(0.348635\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 73.2105 | 0.0295731 | ||||||||
\(184\) | −1109.07 | + | 1920.97i | −0.444359 | + | 0.769652i | ||||
\(185\) | −502.333 | − | 870.066i | −0.199634 | − | 0.345776i | ||||
\(186\) | −20.3011 | − | 35.1626i | −0.00800296 | − | 0.0138615i | ||||
\(187\) | −3629.32 | + | 6286.16i | −1.41926 | + | 2.45823i | ||||
\(188\) | −787.026 | −0.305318 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −595.296 | −0.227302 | ||||||||
\(191\) | 232.960 | − | 403.498i | 0.0882533 | − | 0.152859i | −0.818520 | − | 0.574479i | \(-0.805205\pi\) |
0.906773 | + | 0.421619i | \(0.138538\pi\) | |||||||
\(192\) | 43.4257 | + | 75.2154i | 0.0163228 | + | 0.0282719i | ||||
\(193\) | 2207.23 | + | 3823.04i | 0.823212 | + | 1.42585i | 0.903278 | + | 0.429056i | \(0.141154\pi\) |
−0.0800657 | + | 0.996790i | \(0.525513\pi\) | |||||||
\(194\) | −120.601 | + | 208.887i | −0.0446321 | + | 0.0773051i | ||||
\(195\) | 113.902 | 0.0418291 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −289.812 | −0.104814 | −0.0524068 | − | 0.998626i | \(-0.516689\pi\) | ||||
−0.0524068 | + | 0.998626i | \(0.516689\pi\) | |||||||
\(198\) | 1549.04 | − | 2683.02i | 0.555987 | − | 0.962998i | ||||
\(199\) | −2408.87 | − | 4172.28i | −0.858091 | − | 1.48626i | −0.873748 | − | 0.486380i | \(-0.838317\pi\) |
0.0156567 | − | 0.999877i | \(-0.495016\pi\) | |||||||
\(200\) | 274.440 | + | 475.343i | 0.0970291 | + | 0.168059i | ||||
\(201\) | 13.4312 | − | 23.2635i | 0.00471324 | − | 0.00816358i | ||||
\(202\) | −1025.82 | −0.357310 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 182.595 | 0.0626678 | ||||||||
\(205\) | 1043.27 | − | 1806.99i | 0.355439 | − | 0.615639i | ||||
\(206\) | 1508.74 | + | 2613.21i | 0.510285 | + | 0.883840i | ||||
\(207\) | −1358.32 | − | 2352.67i | −0.456085 | − | 0.789962i | ||||
\(208\) | −195.051 | + | 337.838i | −0.0650209 | + | 0.112619i | ||||
\(209\) | 5001.78 | 1.65541 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2022.01 | 0.659719 | 0.329859 | − | 0.944030i | \(-0.392999\pi\) | ||||
0.329859 | + | 0.944030i | \(0.392999\pi\) | |||||||
\(212\) | 713.632 | − | 1236.05i | 0.231191 | − | 0.400434i | ||||
\(213\) | −15.1541 | − | 26.2477i | −0.00487484 | − | 0.00844347i | ||||
\(214\) | −902.306 | − | 1562.84i | −0.288226 | − | 0.499222i | ||||
\(215\) | 777.937 | − | 1347.43i | 0.246767 | − | 0.427412i | ||||
\(216\) | −393.855 | −0.124067 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 976.525 | 0.303388 | ||||||||
\(219\) | 146.850 | − | 254.352i | 0.0453115 | − | 0.0784819i | ||||
\(220\) | −914.438 | − | 1583.85i | −0.280234 | − | 0.485379i | ||||
\(221\) | −3569.84 | − | 6183.15i | −1.08658 | − | 1.88201i | ||||
\(222\) | −55.3855 | + | 95.9305i | −0.0167443 | + | 0.0290019i | ||||
\(223\) | 4343.86 | 1.30442 | 0.652211 | − | 0.758037i | \(-0.273842\pi\) | ||||
0.652211 | + | 0.758037i | \(0.273842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −672.230 | −0.199179 | ||||||||
\(226\) | 745.524 | − | 1291.29i | 0.219432 | − | 0.380067i | ||||
\(227\) | 1323.80 | + | 2292.88i | 0.387064 | + | 0.670414i | 0.992053 | − | 0.125819i | \(-0.0401560\pi\) |
−0.604989 | + | 0.796234i | \(0.706823\pi\) | |||||||
\(228\) | −62.9114 | − | 108.966i | −0.0182737 | − | 0.0316510i | ||||
\(229\) | 722.545 | − | 1251.49i | 0.208503 | − | 0.361137i | −0.742740 | − | 0.669580i | \(-0.766474\pi\) |
0.951243 | + | 0.308442i | \(0.0998076\pi\) | |||||||
\(230\) | 836.566 | 0.239833 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2517.39 | 0.712392 | ||||||||
\(233\) | 3122.96 | − | 5409.12i | 0.878076 | − | 1.52087i | 0.0246255 | − | 0.999697i | \(-0.492161\pi\) |
0.853450 | − | 0.521175i | \(-0.174506\pi\) | |||||||
\(234\) | 1523.66 | + | 2639.05i | 0.425660 | + | 0.737265i | ||||
\(235\) | 374.243 | + | 648.207i | 0.103885 | + | 0.179934i | ||||
\(236\) | −1361.76 | + | 2358.63i | −0.375605 | + | 0.650566i | ||||
\(237\) | −199.692 | −0.0547315 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1340.24 | 0.362731 | 0.181366 | − | 0.983416i | \(-0.441948\pi\) | ||||
0.181366 | + | 0.983416i | \(0.441948\pi\) | |||||||
\(240\) | −4.74409 | + | 8.21700i | −0.00127596 | + | 0.00221002i | ||||
\(241\) | −1684.96 | − | 2918.44i | −0.450364 | − | 0.780054i | 0.548044 | − | 0.836449i | \(-0.315373\pi\) |
−0.998409 | + | 0.0563953i | \(0.982039\pi\) | |||||||
\(242\) | −2905.85 | − | 5033.08i | −0.771881 | − | 1.33694i | ||||
\(243\) | 362.023 | − | 627.042i | 0.0955710 | − | 0.165534i | ||||
\(244\) | 1156.25 | 0.303366 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −230.054 | −0.0596249 | ||||||||
\(247\) | −2459.91 | + | 4260.69i | −0.633685 | + | 1.09757i | ||||
\(248\) | −808.504 | − | 1400.37i | −0.207016 | − | 0.358563i | ||||
\(249\) | 11.7979 | + | 20.4345i | 0.00300265 | + | 0.00520074i | ||||
\(250\) | 103.504 | − | 179.274i | 0.0261846 | − | 0.0453531i | ||||
\(251\) | −3592.64 | −0.903449 | −0.451724 | − | 0.892158i | \(-0.649191\pi\) | ||||
−0.451724 | + | 0.892158i | \(0.649191\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7028.97 | −1.74667 | ||||||||
\(254\) | 1453.82 | − | 2518.09i | 0.359137 | − | 0.622043i | ||||
\(255\) | −86.8268 | − | 150.388i | −0.0213228 | − | 0.0369321i | ||||
\(256\) | 1911.87 | + | 3311.46i | 0.466765 | + | 0.808461i | ||||
\(257\) | 1.42381 | − | 2.46612i | 0.000345584 | − | 0.000598569i | −0.865853 | − | 0.500299i | \(-0.833223\pi\) |
0.866198 | + | 0.499701i | \(0.166557\pi\) | |||||||
\(258\) | −171.545 | −0.0413951 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1798.91 | 0.429090 | ||||||||
\(261\) | −1541.56 | + | 2670.07i | −0.365596 | + | 0.633230i | ||||
\(262\) | −1497.99 | − | 2594.59i | −0.353229 | − | 0.611811i | ||||
\(263\) | 1408.54 | + | 2439.66i | 0.330244 | + | 0.571999i | 0.982560 | − | 0.185948i | \(-0.0595357\pi\) |
−0.652316 | + | 0.757947i | \(0.726202\pi\) | |||||||
\(264\) | −254.239 | + | 440.356i | −0.0592703 | + | 0.102659i | ||||
\(265\) | −1357.37 | −0.314652 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −267.173 | −0.0612386 | ||||||||
\(268\) | 212.125 | − | 367.412i | 0.0483493 | − | 0.0837434i | ||||
\(269\) | 723.716 | + | 1253.51i | 0.164036 | + | 0.284119i | 0.936313 | − | 0.351168i | \(-0.114215\pi\) |
−0.772276 | + | 0.635287i | \(0.780882\pi\) | |||||||
\(270\) | 74.2704 | + | 128.640i | 0.0167406 | + | 0.0289955i | ||||
\(271\) | −4027.25 | + | 6975.40i | −0.902724 | + | 1.56356i | −0.0787797 | + | 0.996892i | \(0.525102\pi\) |
−0.823944 | + | 0.566671i | \(0.808231\pi\) | |||||||
\(272\) | 594.746 | 0.132580 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −30.6593 | −0.00675985 | ||||||||
\(275\) | −869.658 | + | 1506.29i | −0.190699 | + | 0.330301i | ||||
\(276\) | 88.4091 | + | 153.129i | 0.0192812 | + | 0.0333960i | ||||
\(277\) | 285.650 | + | 494.760i | 0.0619604 | + | 0.107319i | 0.895342 | − | 0.445380i | \(-0.146931\pi\) |
−0.833381 | + | 0.552699i | \(0.813598\pi\) | |||||||
\(278\) | 518.023 | − | 897.242i | 0.111759 | − | 0.193572i | ||||
\(279\) | 1980.40 | 0.424959 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1784.48 | −0.378837 | −0.189418 | − | 0.981896i | \(-0.560660\pi\) | ||||
−0.189418 | + | 0.981896i | \(0.560660\pi\) | |||||||
\(282\) | 41.2627 | − | 71.4691i | 0.00871333 | − | 0.0150919i | ||||
\(283\) | −1660.52 | − | 2876.11i | −0.348791 | − | 0.604124i | 0.637244 | − | 0.770662i | \(-0.280074\pi\) |
−0.986035 | + | 0.166538i | \(0.946741\pi\) | |||||||
\(284\) | −239.336 | − | 414.542i | −0.0500070 | − | 0.0866146i | ||||
\(285\) | −59.8307 | + | 103.630i | −0.0124353 | + | 0.0215386i | ||||
\(286\) | 7884.57 | 1.63015 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −4976.70 | −1.01825 | ||||||||
\(289\) | −2986.05 | + | 5172.00i | −0.607786 | + | 1.05272i | ||||
\(290\) | −474.713 | − | 822.226i | −0.0961244 | − | 0.166492i | ||||
\(291\) | 24.2422 | + | 41.9887i | 0.00488351 | + | 0.00845848i | ||||
\(292\) | 2319.28 | − | 4017.11i | 0.464814 | − | 0.805081i | ||||
\(293\) | −5049.54 | −1.00682 | −0.503408 | − | 0.864049i | \(-0.667921\pi\) | ||||
−0.503408 | + | 0.864049i | \(0.667921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2590.14 | 0.511199 | ||||||||
\(296\) | −2205.76 | + | 3820.49i | −0.433133 | + | 0.750208i | ||||
\(297\) | −624.033 | − | 1080.86i | −0.121919 | − | 0.211171i | ||||
\(298\) | 851.740 | + | 1475.26i | 0.165570 | + | 0.286776i | ||||
\(299\) | 3456.90 | − | 5987.52i | 0.668620 | − | 1.15808i | ||||
\(300\) | 43.7536 | 0.00842038 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 117.593 | 0.0224063 | ||||||||
\(303\) | −103.101 | + | 178.576i | −0.0195479 | + | 0.0338579i | ||||
\(304\) | −204.914 | − | 354.921i | −0.0386599 | − | 0.0669609i | ||||
\(305\) | −549.814 | − | 952.305i | −0.103220 | − | 0.178783i | ||||
\(306\) | 2322.95 | − | 4023.47i | 0.433969 | − | 0.751656i | ||||
\(307\) | −1535.73 | −0.285500 | −0.142750 | − | 0.989759i | \(-0.545595\pi\) | ||||
−0.142750 | + | 0.989759i | \(0.545595\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 606.548 | 0.111668 | ||||||||
\(310\) | −304.924 | + | 528.145i | −0.0558663 | + | 0.0967632i | ||||
\(311\) | 4641.52 | + | 8039.35i | 0.846291 | + | 1.46582i | 0.884495 | + | 0.466550i | \(0.154503\pi\) |
−0.0382037 | + | 0.999270i | \(0.512164\pi\) | |||||||
\(312\) | −250.073 | − | 433.140i | −0.0453770 | − | 0.0785952i | ||||
\(313\) | −3012.72 | + | 5218.18i | −0.544054 | + | 0.942329i | 0.454612 | + | 0.890690i | \(0.349778\pi\) |
−0.998666 | + | 0.0516393i | \(0.983555\pi\) | |||||||
\(314\) | −3413.68 | −0.613519 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3153.83 | −0.561445 | ||||||||
\(317\) | 3488.79 | − | 6042.76i | 0.618139 | − | 1.07065i | −0.371686 | − | 0.928358i | \(-0.621220\pi\) |
0.989825 | − | 0.142289i | \(-0.0454464\pi\) | |||||||
\(318\) | 74.8295 | + | 129.609i | 0.0131957 | + | 0.0228556i | ||||
\(319\) | 3988.62 | + | 6908.49i | 0.700062 | + | 1.21254i | ||||
\(320\) | 652.257 | − | 1129.74i | 0.113945 | − | 0.197358i | ||||
\(321\) | −362.748 | −0.0630736 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7500.71 | 1.29211 | ||||||||
\(324\) | 1892.78 | − | 3278.39i | 0.324551 | − | 0.562139i | ||||
\(325\) | −855.407 | − | 1481.61i | −0.145998 | − | 0.252876i | ||||
\(326\) | 1626.09 | + | 2816.46i | 0.276259 | + | 0.478495i | ||||
\(327\) | 98.1464 | − | 169.995i | 0.0165979 | − | 0.0287484i | ||||
\(328\) | −9162.06 | −1.54235 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 191.771 | 0.0319898 | ||||||||
\(331\) | −492.439 | + | 852.930i | −0.0817731 | + | 0.141635i | −0.904012 | − | 0.427508i | \(-0.859392\pi\) |
0.822239 | + | 0.569143i | \(0.192725\pi\) | |||||||
\(332\) | 186.330 | + | 322.732i | 0.0308017 | + | 0.0533501i | ||||
\(333\) | −2701.46 | − | 4679.07i | −0.444563 | − | 0.770005i | ||||
\(334\) | −2364.07 | + | 4094.68i | −0.387293 | + | 0.670812i | ||||
\(335\) | −403.475 | −0.0658035 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 51.9653 | 0.00839979 | 0.00419990 | − | 0.999991i | \(-0.498663\pi\) | ||||
0.00419990 | + | 0.999991i | \(0.498663\pi\) | |||||||
\(338\) | −2058.50 | + | 3565.42i | −0.331265 | + | 0.573767i | ||||
\(339\) | −149.859 | − | 259.563i | −0.0240095 | − | 0.0415857i | ||||
\(340\) | −1371.30 | − | 2375.16i | −0.218733 | − | 0.378856i | ||||
\(341\) | 2562.03 | − | 4437.56i | 0.406867 | − | 0.704714i | ||||
\(342\) | −3201.40 | −0.506176 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −6831.89 | −1.07079 | ||||||||
\(345\) | 84.0797 | − | 145.630i | 0.0131209 | − | 0.0227260i | ||||
\(346\) | 1286.10 | + | 2227.60i | 0.199830 | + | 0.346116i | ||||
\(347\) | 5650.24 | + | 9786.50i | 0.874123 | + | 1.51403i | 0.857694 | + | 0.514161i | \(0.171897\pi\) |
0.0164299 | + | 0.999865i | \(0.494770\pi\) | |||||||
\(348\) | 100.336 | − | 173.787i | 0.0154557 | − | 0.0267701i | ||||
\(349\) | −2016.91 | −0.309349 | −0.154674 | − | 0.987966i | \(-0.549433\pi\) | ||||
−0.154674 | + | 0.987966i | \(0.549433\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1227.61 | 0.186682 | ||||||||
\(352\) | −6438.31 | + | 11151.5i | −0.974896 | + | 1.68857i | ||||
\(353\) | 3794.71 | + | 6572.62i | 0.572158 | + | 0.991007i | 0.996344 | + | 0.0854319i | \(0.0272270\pi\) |
−0.424186 | + | 0.905575i | \(0.639440\pi\) | |||||||
\(354\) | −142.790 | − | 247.319i | −0.0214384 | − | 0.0371324i | ||||
\(355\) | −227.616 | + | 394.242i | −0.0340298 | + | 0.0589414i | ||||
\(356\) | −4219.59 | −0.628196 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 446.873 | 0.0659720 | ||||||||
\(359\) | −4367.12 | + | 7564.08i | −0.642027 | + | 1.11202i | 0.342952 | + | 0.939353i | \(0.388573\pi\) |
−0.984980 | + | 0.172671i | \(0.944760\pi\) | |||||||
\(360\) | 1475.89 | + | 2556.32i | 0.216073 | + | 0.374250i | ||||
\(361\) | 845.204 | + | 1463.94i | 0.123226 | + | 0.213433i | ||||
\(362\) | −1846.19 | + | 3197.69i | −0.268049 | + | 0.464274i | ||||
\(363\) | −1168.22 | −0.168914 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4411.41 | −0.632613 | ||||||||
\(366\) | −60.6206 | + | 104.998i | −0.00865762 | + | 0.0149954i | ||||
\(367\) | 945.271 | + | 1637.26i | 0.134449 | + | 0.232872i | 0.925387 | − | 0.379024i | \(-0.123740\pi\) |
−0.790938 | + | 0.611896i | \(0.790407\pi\) | |||||||
\(368\) | 287.964 | + | 498.769i | 0.0407912 | + | 0.0706525i | ||||
\(369\) | 5610.53 | − | 9717.72i | 0.791524 | − | 1.37096i | ||||
\(370\) | 1663.79 | 0.233774 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −128.899 | −0.0179653 | ||||||||
\(373\) | −1356.94 | + | 2350.29i | −0.188364 | + | 0.326256i | −0.944705 | − | 0.327922i | \(-0.893652\pi\) |
0.756341 | + | 0.654178i | \(0.226985\pi\) | |||||||
\(374\) | −6010.37 | − | 10410.3i | −0.830987 | − | 1.43931i | ||||
\(375\) | −20.8055 | − | 36.0361i | −0.00286504 | − | 0.00496240i | ||||
\(376\) | 1643.31 | − | 2846.30i | 0.225392 | − | 0.390390i | ||||
\(377\) | −7846.52 | −1.07193 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8941.19 | 1.21182 | 0.605908 | − | 0.795535i | \(-0.292810\pi\) | ||||
0.605908 | + | 0.795535i | \(0.292810\pi\) | |||||||
\(380\) | −944.935 | + | 1636.68i | −0.127564 | + | 0.220947i | ||||
\(381\) | −292.234 | − | 506.165i | −0.0392956 | − | 0.0680620i | ||||
\(382\) | 385.796 | + | 668.218i | 0.0516729 | + | 0.0895001i | ||||
\(383\) | 4646.94 | − | 8048.74i | 0.619968 | − | 1.07382i | −0.369524 | − | 0.929221i | \(-0.620479\pi\) |
0.989491 | − | 0.144594i | \(-0.0461876\pi\) | |||||||
\(384\) | 349.060 | 0.0463878 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7310.62 | −0.963992 | ||||||||
\(387\) | 4183.62 | − | 7246.24i | 0.549522 | − | 0.951801i | ||||
\(388\) | 382.868 | + | 663.147i | 0.0500959 | + | 0.0867686i | ||||
\(389\) | −5227.38 | − | 9054.08i | −0.681333 | − | 1.18010i | −0.974574 | − | 0.224065i | \(-0.928067\pi\) |
0.293242 | − | 0.956038i | \(-0.405266\pi\) | |||||||
\(390\) | −94.3142 | + | 163.357i | −0.0122456 | + | 0.0212100i | ||||
\(391\) | −10540.7 | −1.36334 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −602.226 | −0.0772985 | ||||||||
\(394\) | 239.974 | − | 415.646i | 0.0306845 | − | 0.0531471i | ||||
\(395\) | 1499.69 | + | 2597.54i | 0.191032 | + | 0.330878i | ||||
\(396\) | −4917.70 | − | 8517.70i | −0.624050 | − | 1.08089i | ||||
\(397\) | 1813.01 | − | 3140.23i | 0.229200 | − | 0.396987i | −0.728371 | − | 0.685183i | \(-0.759722\pi\) |
0.957571 | + | 0.288196i | \(0.0930556\pi\) | |||||||
\(398\) | 7978.47 | 1.00484 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 142.513 | 0.0178141 | ||||||||
\(401\) | 4211.26 | − | 7294.12i | 0.524440 | − | 0.908356i | −0.475156 | − | 0.879902i | \(-0.657608\pi\) |
0.999595 | − | 0.0284542i | \(-0.00905846\pi\) | |||||||
\(402\) | 22.2429 | + | 38.5258i | 0.00275963 | + | 0.00477983i | ||||
\(403\) | 2520.04 | + | 4364.85i | 0.311495 | + | 0.539525i | ||||
\(404\) | −1628.33 | + | 2820.35i | −0.200526 | + | 0.347320i | ||||
\(405\) | −3600.18 | −0.441715 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13979.5 | −1.70254 | ||||||||
\(408\) | −381.260 | + | 660.361i | −0.0462627 | + | 0.0801293i | ||||
\(409\) | 7290.34 | + | 12627.2i | 0.881379 | + | 1.52659i | 0.849808 | + | 0.527092i | \(0.176718\pi\) |
0.0315714 | + | 0.999502i | \(0.489949\pi\) | |||||||
\(410\) | 1727.72 | + | 2992.50i | 0.208112 | + | 0.360461i | ||||
\(411\) | −3.08144 | + | 5.33721i | −0.000369820 | + | 0.000640548i | ||||
\(412\) | 9579.51 | 1.14551 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 4498.92 | 0.534081 | ||||||||
\(415\) | 177.205 | − | 306.928i | 0.0209606 | − | 0.0363049i | ||||
\(416\) | −6332.81 | − | 10968.8i | −0.746374 | − | 1.29276i | ||||
\(417\) | −104.129 | − | 180.356i | −0.0122283 | − | 0.0211800i | ||||
\(418\) | −4141.63 | + | 7173.51i | −0.484626 | + | 0.839397i | ||||
\(419\) | −2537.53 | −0.295863 | −0.147931 | − | 0.988998i | \(-0.547261\pi\) | ||||
−0.147931 | + | 0.988998i | \(0.547261\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9649.52 | 1.11708 | 0.558538 | − | 0.829479i | \(-0.311363\pi\) | ||||
0.558538 | + | 0.829479i | \(0.311363\pi\) | |||||||
\(422\) | −1674.28 | + | 2899.94i | −0.193135 | + | 0.334519i | ||||
\(423\) | 2012.62 | + | 3485.95i | 0.231340 | + | 0.400692i | ||||
\(424\) | 2980.13 | + | 5161.74i | 0.341340 | + | 0.591218i | ||||
\(425\) | −1304.15 | + | 2258.85i | −0.148848 | + | 0.257812i | ||||
\(426\) | 50.1922 | 0.00570850 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5729.06 | −0.647020 | ||||||||
\(429\) | 792.444 | − | 1372.55i | 0.0891832 | − | 0.154470i | ||||
\(430\) | 1288.31 | + | 2231.42i | 0.144483 | + | 0.250253i | ||||
\(431\) | 3631.28 | + | 6289.57i | 0.405830 | + | 0.702918i | 0.994418 | − | 0.105515i | \(-0.0336492\pi\) |
−0.588588 | + | 0.808433i | \(0.700316\pi\) | |||||||
\(432\) | −51.1310 | + | 88.5615i | −0.00569454 | + | 0.00986323i | ||||
\(433\) | 11345.0 | 1.25914 | 0.629570 | − | 0.776944i | \(-0.283231\pi\) | ||||
0.629570 | + | 0.776944i | \(0.283231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −190.845 | −0.0210353 | ||||||||
\(436\) | 1550.07 | − | 2684.81i | 0.170264 | − | 0.294906i | ||||
\(437\) | 3631.70 | + | 6290.28i | 0.397546 | + | 0.688570i | ||||
\(438\) | 243.193 | + | 421.223i | 0.0265302 | + | 0.0459516i | ||||
\(439\) | −5852.94 | + | 10137.6i | −0.636323 | + | 1.10214i | 0.349911 | + | 0.936783i | \(0.386212\pi\) |
−0.986233 | + | 0.165360i | \(0.947121\pi\) | |||||||
\(440\) | 7637.40 | 0.827497 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11823.8 | 1.27240 | ||||||||
\(443\) | −7538.99 | + | 13057.9i | −0.808551 | + | 1.40045i | 0.105316 | + | 0.994439i | \(0.466415\pi\) |
−0.913867 | + | 0.406013i | \(0.866919\pi\) | |||||||
\(444\) | 175.831 | + | 304.548i | 0.0187941 | + | 0.0325523i | ||||
\(445\) | 2006.48 | + | 3475.32i | 0.213744 | + | 0.370216i | ||||
\(446\) | −3596.85 | + | 6229.92i | −0.381874 | + | 0.661425i | ||||
\(447\) | 342.419 | 0.0362324 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1075.45 | 0.113037 | 0.0565185 | − | 0.998402i | \(-0.482000\pi\) | ||||
0.0565185 | + | 0.998402i | \(0.482000\pi\) | |||||||
\(450\) | 556.627 | − | 964.106i | 0.0583103 | − | 0.100996i | ||||
\(451\) | −14516.6 | − | 25143.5i | −1.51565 | − | 2.62519i | ||||
\(452\) | −2366.80 | − | 4099.41i | −0.246294 | − | 0.426593i | ||||
\(453\) | 11.8187 | − | 20.4706i | 0.00122581 | − | 0.00212317i | ||||
\(454\) | −4384.58 | −0.453257 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 525.437 | 0.0539602 | ||||||||
\(457\) | 5368.47 | − | 9298.47i | 0.549511 | − | 0.951781i | −0.448797 | − | 0.893634i | \(-0.648147\pi\) |
0.998308 | − | 0.0581472i | \(-0.0185193\pi\) | |||||||
\(458\) | 1196.58 | + | 2072.54i | 0.122080 | + | 0.211448i | ||||
\(459\) | −935.805 | − | 1620.86i | −0.0951627 | − | 0.164827i | ||||
\(460\) | 1327.91 | − | 2300.01i | 0.134596 | − | 0.233127i | ||||
\(461\) | 452.568 | 0.0457228 | 0.0228614 | − | 0.999739i | \(-0.492722\pi\) | ||||
0.0228614 | + | 0.999739i | \(0.492722\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7118.15 | 0.714489 | 0.357244 | − | 0.934011i | \(-0.383716\pi\) | ||||
0.357244 | + | 0.934011i | \(0.383716\pi\) | |||||||
\(464\) | 326.813 | − | 566.057i | 0.0326981 | − | 0.0566347i | ||||
\(465\) | 61.2933 | + | 106.163i | 0.00611271 | + | 0.0105875i | ||||
\(466\) | 5171.81 | + | 8957.83i | 0.514119 | + | 0.890480i | ||||
\(467\) | −486.900 | + | 843.335i | −0.0482463 | + | 0.0835651i | −0.889140 | − | 0.457635i | \(-0.848697\pi\) |
0.840894 | + | 0.541200i | \(0.182030\pi\) | |||||||
\(468\) | 9674.23 | 0.955537 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1239.54 | −0.121650 | ||||||||
\(471\) | −343.094 | + | 594.257i | −0.0335646 | + | 0.0581357i | ||||
\(472\) | −5686.70 | − | 9849.65i | −0.554558 | − | 0.960523i | ||||
\(473\) | −10824.6 | − | 18748.8i | −1.05225 | − | 1.82256i | ||||
\(474\) | 165.351 | − | 286.396i | 0.0160228 | − | 0.0277524i | ||||
\(475\) | 1797.32 | 0.173614 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7299.72 | −0.700695 | ||||||||
\(478\) | −1109.76 | + | 1922.16i | −0.106191 | + | 0.183928i | ||||
\(479\) | −4857.00 | − | 8412.57i | −0.463303 | − | 0.802464i | 0.535820 | − | 0.844332i | \(-0.320002\pi\) |
−0.999123 | + | 0.0418680i | \(0.986669\pi\) | |||||||
\(480\) | −154.029 | − | 266.785i | −0.0146467 | − | 0.0253688i | ||||
\(481\) | 6875.19 | − | 11908.2i | 0.651729 | − | 1.12883i | ||||
\(482\) | 5580.80 | 0.527383 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −18450.3 | −1.73274 | ||||||||
\(485\) | 364.119 | − | 630.673i | 0.0340903 | − | 0.0590462i | ||||
\(486\) | 599.532 | + | 1038.42i | 0.0559575 | + | 0.0969212i | ||||
\(487\) | −461.694 | − | 799.678i | −0.0429597 | − | 0.0744084i | 0.843746 | − | 0.536743i | \(-0.180345\pi\) |
−0.886706 | + | 0.462334i | \(0.847012\pi\) | |||||||
\(488\) | −2414.25 | + | 4181.61i | −0.223951 | + | 0.387894i | ||||
\(489\) | 653.724 | 0.0604549 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1289.11 | 0.118486 | 0.0592430 | − | 0.998244i | \(-0.481131\pi\) | ||||
0.0592430 | + | 0.998244i | \(0.481131\pi\) | |||||||
\(492\) | −365.174 | + | 632.500i | −0.0334620 | + | 0.0579579i | ||||
\(493\) | 5981.37 | + | 10360.0i | 0.546424 | + | 0.946435i | ||||
\(494\) | −4073.76 | − | 7055.96i | −0.371027 | − | 0.642637i | ||||
\(495\) | −4676.88 | + | 8100.59i | −0.424667 | + | 0.735544i | ||||
\(496\) | −419.846 | −0.0380074 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −39.0760 | −0.00351614 | ||||||||
\(499\) | 9669.15 | − | 16747.5i | 0.867436 | − | 1.50244i | 0.00282829 | − | 0.999996i | \(-0.499100\pi\) |
0.864608 | − | 0.502447i | \(-0.167567\pi\) | |||||||
\(500\) | −328.591 | − | 569.137i | −0.0293901 | − | 0.0509051i | ||||
\(501\) | 475.205 | + | 823.078i | 0.0423764 | + | 0.0733981i | ||||
\(502\) | 2974.82 | − | 5152.54i | 0.264488 | − | 0.458106i | ||||
\(503\) | −1772.84 | −0.157151 | −0.0785757 | − | 0.996908i | \(-0.525037\pi\) | ||||
−0.0785757 | + | 0.996908i | \(0.525037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3097.18 | 0.272916 | ||||||||
\(506\) | 5820.21 | − | 10080.9i | 0.511344 | − | 0.885673i | ||||
\(507\) | 413.782 | + | 716.691i | 0.0362459 | + | 0.0627798i | ||||
\(508\) | −4615.40 | − | 7994.11i | −0.403101 | − | 0.698192i | ||||
\(509\) | −1575.88 | + | 2729.50i | −0.137229 | + | 0.237687i | −0.926447 | − | 0.376426i | \(-0.877153\pi\) |
0.789218 | + | 0.614113i | \(0.210486\pi\) | |||||||
\(510\) | 287.581 | 0.0249692 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2056.31 | 0.177494 | ||||||||
\(513\) | −644.845 | + | 1116.90i | −0.0554983 | + | 0.0961258i | ||||
\(514\) | 2.35792 | + | 4.08404i | 0.000202341 | + | 0.000350466i | ||||
\(515\) | −4555.20 | − | 7889.83i | −0.389759 | − | 0.675083i | ||||
\(516\) | −272.300 | + | 471.637i | −0.0232313 | + | 0.0402377i | ||||
\(517\) | 10414.8 | 0.885964 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 517.043 | 0.0437296 | ||||||||
\(520\) | −3756.12 | + | 6505.79i | −0.316763 | + | 0.548650i | ||||
\(521\) | 5514.69 | + | 9551.72i | 0.463729 | + | 0.803202i | 0.999143 | − | 0.0413875i | \(-0.0131778\pi\) |
−0.535414 | + | 0.844590i | \(0.679844\pi\) | |||||||
\(522\) | −2552.93 | − | 4421.80i | −0.214059 | − | 0.370760i | ||||
\(523\) | −7224.21 | + | 12512.7i | −0.604002 | + | 1.04616i | 0.388207 | + | 0.921572i | \(0.373095\pi\) |
−0.992208 | + | 0.124589i | \(0.960239\pi\) | |||||||
\(524\) | −9511.26 | −0.792941 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4665.25 | −0.386720 | ||||||||
\(527\) | 3842.04 | − | 6654.61i | 0.317575 | − | 0.550056i | ||||
\(528\) | 66.0117 | + | 114.336i | 0.00544089 | + | 0.00942390i | ||||
\(529\) | 979.894 | + | 1697.23i | 0.0805371 | + | 0.139494i | ||||
\(530\) | 1123.95 | − | 1946.73i | 0.0921153 | − | 0.159548i | ||||
\(531\) | 13929.4 | 1.13838 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28557.4 | 2.32075 | ||||||||
\(534\) | 221.227 | − | 383.177i | 0.0179278 | − | 0.0310519i | ||||
\(535\) | 2724.25 | + | 4718.54i | 0.220149 | + | 0.381309i | ||||
\(536\) | 885.836 | + | 1534.31i | 0.0713849 | + | 0.123642i | ||||
\(537\) | 44.9133 | − | 77.7922i | 0.00360922 | − | 0.00625136i | ||||
\(538\) | −2397.04 | −0.192089 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 471.569 | 0.0375798 | ||||||||
\(541\) | 11137.4 | − | 19290.5i | 0.885091 | − | 1.53302i | 0.0394817 | − | 0.999220i | \(-0.487429\pi\) |
0.845609 | − | 0.533802i | \(-0.179237\pi\) | |||||||
\(542\) | −6669.38 | − | 11551.7i | −0.528551 | − | 0.915476i | ||||
\(543\) | 371.105 | + | 642.773i | 0.0293290 | + | 0.0507994i | ||||
\(544\) | −9654.95 | + | 16722.9i | −0.760942 | + | 1.31799i | ||||
\(545\) | −2948.33 | −0.231730 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18642.6 | 1.45722 | 0.728609 | − | 0.684930i | \(-0.240167\pi\) | ||||
0.728609 | + | 0.684930i | \(0.240167\pi\) | |||||||
\(548\) | −48.6667 | + | 84.2932i | −0.00379368 | + | 0.00657085i | ||||
\(549\) | −2956.81 | − | 5121.34i | −0.229861 | − | 0.398130i | ||||
\(550\) | −1440.21 | − | 2494.51i | −0.111656 | − | 0.193393i | ||||
\(551\) | 4121.64 | − | 7138.89i | 0.318671 | − | 0.551955i | ||||
\(552\) | −738.394 | −0.0569350 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −946.108 | −0.0725565 | ||||||||
\(555\) | 167.220 | − | 289.634i | 0.0127894 | − | 0.0221519i | ||||
\(556\) | −1644.55 | − | 2848.45i | −0.125440 | − | 0.217268i | ||||
\(557\) | 10715.9 | + | 18560.5i | 0.815165 | + | 1.41191i | 0.909209 | + | 0.416339i | \(0.136687\pi\) |
−0.0940446 | + | 0.995568i | \(0.529980\pi\) | |||||||
\(558\) | −1639.83 | + | 2840.28i | −0.124408 | + | 0.215481i | ||||
\(559\) | 21294.5 | 1.61120 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2416.31 | −0.181848 | ||||||||
\(562\) | 1477.60 | − | 2559.29i | 0.110906 | − | 0.192094i | ||||
\(563\) | 3077.43 | + | 5330.26i | 0.230370 | + | 0.399012i | 0.957917 | − | 0.287046i | \(-0.0926732\pi\) |
−0.727547 | + | 0.686057i | \(0.759340\pi\) | |||||||
\(564\) | −130.996 | − | 226.891i | −0.00977998 | − | 0.0169394i | ||||
\(565\) | −2250.89 | + | 3898.66i | −0.167603 | + | 0.290297i | ||||
\(566\) | 5499.86 | 0.408439 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1998.94 | 0.147665 | ||||||||
\(569\) | 4194.99 | − | 7265.94i | 0.309074 | − | 0.535333i | −0.669086 | − | 0.743185i | \(-0.733314\pi\) |
0.978160 | + | 0.207853i | \(0.0666475\pi\) | |||||||
\(570\) | −99.0833 | − | 171.617i | −0.00728095 | − | 0.0126110i | ||||
\(571\) | 300.251 | + | 520.050i | 0.0220055 | + | 0.0381146i | 0.876818 | − | 0.480822i | \(-0.159662\pi\) |
−0.854813 | + | 0.518936i | \(0.826328\pi\) | |||||||
\(572\) | 12515.5 | − | 21677.4i | 0.914856 | − | 1.58458i | ||||
\(573\) | 155.099 | 0.0113078 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2525.77 | −0.183186 | ||||||||
\(576\) | 3507.73 | − | 6075.57i | 0.253742 | − | 0.439494i | ||||
\(577\) | −2031.17 | − | 3518.10i | −0.146549 | − | 0.253831i | 0.783401 | − | 0.621517i | \(-0.213483\pi\) |
−0.929950 | + | 0.367686i | \(0.880150\pi\) | |||||||
\(578\) | −4945.09 | − | 8565.15i | −0.355863 | − | 0.616372i | ||||
\(579\) | −734.760 | + | 1272.64i | −0.0527385 | + | 0.0913457i | ||||
\(580\) | −3014.12 | −0.215783 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −80.2931 | −0.00571865 | ||||||||
\(583\) | −9443.59 | + | 16356.8i | −0.670864 | + | 1.16197i | ||||
\(584\) | 9685.32 | + | 16775.5i | 0.686270 | + | 1.18865i | ||||
\(585\) | −4600.24 | − | 7967.85i | −0.325122 | − | 0.563128i | ||||
\(586\) | 4181.18 | − | 7242.01i | 0.294749 | − | 0.510520i | ||||
\(587\) | −8387.50 | −0.589760 | −0.294880 | − | 0.955534i | \(-0.595280\pi\) | ||||
−0.294880 | + | 0.955534i | \(0.595280\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5294.95 | −0.370415 | ||||||||
\(590\) | −2144.72 | + | 3714.76i | −0.149655 | + | 0.259210i | ||||
\(591\) | −48.2375 | − | 83.5497i | −0.00335740 | − | 0.00581519i | ||||
\(592\) | 572.713 | + | 991.967i | 0.0397607 | + | 0.0688676i | ||||
\(593\) | 7671.31 | − | 13287.1i | 0.531236 | − | 0.920128i | −0.468099 | − | 0.883676i | \(-0.655061\pi\) |
0.999335 | − | 0.0364520i | \(-0.0116056\pi\) | |||||||
\(594\) | 2066.88 | 0.142769 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5408.00 | 0.371678 | ||||||||
\(597\) | 801.882 | − | 1388.90i | 0.0549730 | − | 0.0952159i | ||||
\(598\) | 5724.83 | + | 9915.70i | 0.391481 | + | 0.678066i | ||||
\(599\) | 9854.23 | + | 17068.0i | 0.672175 | + | 1.16424i | 0.977286 | + | 0.211925i | \(0.0679731\pi\) |
−0.305111 | + | 0.952317i | \(0.598694\pi\) | |||||||
\(600\) | −91.3576 | + | 158.236i | −0.00621610 | + | 0.0107666i | ||||
\(601\) | −19002.5 | −1.28973 | −0.644866 | − | 0.764295i | \(-0.723087\pi\) | ||||
−0.644866 | + | 0.764295i | \(0.723087\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2169.82 | −0.146537 | ||||||||
\(604\) | 186.659 | − | 323.303i | 0.0125746 | − | 0.0217798i | ||||
\(605\) | 8773.38 | + | 15195.9i | 0.589568 | + | 1.02116i | ||||
\(606\) | −170.742 | − | 295.734i | −0.0114454 | − | 0.0198240i | ||||
\(607\) | −14726.6 | + | 25507.1i | −0.984732 | + | 1.70561i | −0.341612 | + | 0.939841i | \(0.610973\pi\) |
−0.643121 | + | 0.765765i | \(0.722361\pi\) | |||||||
\(608\) | 13306.1 | 0.887553 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1821.05 | 0.120873 | ||||||||
\(611\) | −5122.08 | + | 8871.70i | −0.339144 | + | 0.587415i | ||||
\(612\) | −7374.62 | − | 12773.2i | −0.487094 | − | 0.843671i | ||||
\(613\) | −4993.63 | − | 8649.23i | −0.329023 | − | 0.569884i | 0.653295 | − | 0.757103i | \(-0.273386\pi\) |
−0.982318 | + | 0.187219i | \(0.940053\pi\) | |||||||
\(614\) | 1271.63 | − | 2202.53i | 0.0835811 | − | 0.144767i | ||||
\(615\) | 694.583 | 0.0455419 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −21076.1 | −1.37519 | −0.687593 | − | 0.726096i | \(-0.741333\pi\) | ||||
−0.687593 | + | 0.726096i | \(0.741333\pi\) | |||||||
\(618\) | −502.240 | + | 869.906i | −0.0326910 | + | 0.0566226i | ||||
\(619\) | 157.334 | + | 272.511i | 0.0102161 | + | 0.0176949i | 0.871088 | − | 0.491126i | \(-0.163415\pi\) |
−0.860872 | + | 0.508821i | \(0.830081\pi\) | |||||||
\(620\) | 968.036 | + | 1676.69i | 0.0627052 | + | 0.108609i | ||||
\(621\) | 906.197 | − | 1569.58i | 0.0585579 | − | 0.101425i | ||||
\(622\) | −15373.3 | −0.991018 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −129.860 | −0.00833103 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −4989.25 | − | 8641.63i | −0.318547 | − | 0.551740i | ||||
\(627\) | 832.515 | + | 1441.96i | 0.0530262 | + | 0.0918442i | ||||
\(628\) | −5418.66 | + | 9385.39i | −0.344312 | + | 0.596366i | ||||
\(629\) | −20963.7 | −1.32890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3314.96 | 0.209138 | 0.104569 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104569 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(632\) | 6585.21 | − | 11405.9i | 0.414471 | − | 0.717884i | ||||
\(633\) | 336.550 | + | 582.922i | 0.0211322 | + | 0.0366020i | ||||
\(634\) | 5777.65 | + | 10007.2i | 0.361924 | + | 0.626871i | ||||
\(635\) | −4389.39 | + | 7602.64i | −0.274311 | + | 0.475121i | ||||
\(636\) | 475.119 | 0.0296221 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −13210.8 | −0.819782 | ||||||||
\(639\) | −1224.08 | + | 2120.17i | −0.0757807 | + | 0.131256i | ||||
\(640\) | −2621.46 | − | 4540.50i | −0.161910 | − | 0.280436i | ||||
\(641\) | −1502.56 | − | 2602.51i | −0.0925858 | − | 0.160363i | 0.816013 | − | 0.578034i | \(-0.196180\pi\) |
−0.908598 | + | 0.417671i | \(0.862847\pi\) | |||||||
\(642\) | 300.367 | − | 520.250i | 0.0184650 | − | 0.0319823i | ||||
\(643\) | 21225.7 | 1.30180 | 0.650902 | − | 0.759162i | \(-0.274391\pi\) | ||||
0.650902 | + | 0.759162i | \(0.274391\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 517.931 | 0.0316178 | ||||||||
\(646\) | −6210.82 | + | 10757.5i | −0.378269 | + | 0.655180i | ||||
\(647\) | 1370.18 | + | 2373.21i | 0.0832568 | + | 0.144205i | 0.904647 | − | 0.426162i | \(-0.140134\pi\) |
−0.821390 | + | 0.570367i | \(0.806801\pi\) | |||||||
\(648\) | 7904.26 | + | 13690.6i | 0.479180 | + | 0.829964i | ||||
\(649\) | 18020.3 | − | 31212.1i | 1.08992 | − | 1.88780i | ||||
\(650\) | 2833.21 | 0.170966 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10324.6 | 0.620157 | ||||||||
\(653\) | −11395.3 | + | 19737.3i | −0.682900 | + | 1.18282i | 0.291191 | + | 0.956665i | \(0.405948\pi\) |
−0.974092 | + | 0.226153i | \(0.927385\pi\) | |||||||
\(654\) | 162.536 | + | 281.521i | 0.00971817 | + | 0.0168324i | ||||
\(655\) | 4522.74 | + | 7833.62i | 0.269799 | + | 0.467305i | ||||
\(656\) | −1189.44 | + | 2060.16i | −0.0707922 | + | 0.122616i | ||||
\(657\) | −23723.8 | −1.40876 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19405.1 | 1.14706 | 0.573532 | − | 0.819183i | \(-0.305573\pi\) | ||||
0.573532 | + | 0.819183i | \(0.305573\pi\) | |||||||
\(660\) | 304.405 | − | 527.245i | 0.0179530 | − | 0.0310954i | ||||
\(661\) | −7818.63 | − | 13542.3i | −0.460075 | − | 0.796873i | 0.538889 | − | 0.842377i | \(-0.318844\pi\) |
−0.998964 | + | 0.0455035i | \(0.985511\pi\) | |||||||
\(662\) | −815.510 | − | 1412.50i | −0.0478787 | − | 0.0829283i | ||||
\(663\) | 1188.36 | − | 2058.29i | 0.0696108 | − | 0.120569i | ||||
\(664\) | −1556.23 | −0.0909538 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8947.59 | 0.520589 | ||||||||
\(667\) | −5792.12 | + | 10032.3i | −0.336240 | + | 0.582384i | ||||
\(668\) | 7505.14 | + | 12999.3i | 0.434704 | + | 0.752930i | ||||
\(669\) | 723.008 | + | 1252.29i | 0.0417834 | + | 0.0723710i | ||||
\(670\) | 334.090 | − | 578.660i | 0.0192642 | − | 0.0333666i | ||||
\(671\) | −15300.8 | −0.880299 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2579.54 | −0.147747 | −0.0738735 | − | 0.997268i | \(-0.523536\pi\) | ||||
−0.0738735 | + | 0.997268i | \(0.523536\pi\) | |||||||
\(674\) | −43.0289 | + | 74.5282i | −0.00245907 | + | 0.00425923i | ||||
\(675\) | −224.238 | − | 388.392i | −0.0127866 | − | 0.0221470i | ||||
\(676\) | 6535.06 | + | 11319.1i | 0.371817 | + | 0.644006i | ||||
\(677\) | −4079.78 | + | 7066.39i | −0.231608 | + | 0.401157i | −0.958282 | − | 0.285826i | \(-0.907732\pi\) |
0.726673 | + | 0.686983i | \(0.241065\pi\) | |||||||
\(678\) | 496.351 | 0.0281154 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 11453.1 | 0.645892 | ||||||||
\(681\) | −440.676 | + | 763.272i | −0.0247969 | + | 0.0429496i | ||||
\(682\) | 4242.88 | + | 7348.88i | 0.238223 | + | 0.412615i | ||||
\(683\) | 10264.6 | + | 17778.9i | 0.575059 | + | 0.996032i | 0.996035 | + | 0.0889598i | \(0.0283543\pi\) |
−0.420976 | + | 0.907072i | \(0.638312\pi\) | |||||||
\(684\) | −5081.71 | + | 8801.77i | −0.284070 | + | 0.492024i | ||||
\(685\) | 92.5670 | 0.00516321 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 481.053 | 0.0267151 | ||||||||
\(688\) | −886.930 | + | 1536.21i | −0.0491481 | + | 0.0851270i | ||||
\(689\) | −9288.84 | − | 16088.7i | −0.513609 | − | 0.889597i | ||||
\(690\) | 139.241 | + | 241.173i | 0.00768235 | + | 0.0133062i | ||||
\(691\) | 458.647 | − | 794.401i | 0.0252500 | − | 0.0437343i | −0.853124 | − | 0.521708i | \(-0.825295\pi\) |
0.878374 | + | 0.477973i | \(0.158628\pi\) | |||||||
\(692\) | 8165.92 | 0.448586 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18714.3 | −1.02361 | ||||||||
\(695\) | −1564.02 | + | 2708.96i | −0.0853621 | + | 0.147851i | ||||
\(696\) | 419.005 | + | 725.737i | 0.0228194 | + | 0.0395244i | ||||
\(697\) | −21769.2 | − | 37705.4i | −1.18302 | − | 2.04906i | ||||
\(698\) | 1670.06 | − | 2892.63i | 0.0905628 | − | 0.156859i | ||||
\(699\) | 2079.19 | 0.112507 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10491.3 | −0.565266 | −0.282633 | − | 0.959228i | \(-0.591208\pi\) | ||||
−0.282633 | + | 0.959228i | \(0.591208\pi\) | |||||||
\(702\) | −1016.50 | + | 1760.63i | −0.0546516 | + | 0.0946594i | ||||
\(703\) | 7222.84 | + | 12510.3i | 0.387503 | + | 0.671175i | ||||
\(704\) | −9075.85 | − | 15719.8i | −0.485879 | − | 0.841567i | ||||
\(705\) | −124.581 | + | 215.780i | −0.00665530 | + | 0.0115273i | ||||
\(706\) | −12568.5 | −0.670005 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −906.623 | −0.0481257 | ||||||||
\(709\) | −11918.8 | + | 20643.9i | −0.631339 | + | 1.09351i | 0.355939 | + | 0.934509i | \(0.384161\pi\) |
−0.987278 | + | 0.159002i | \(0.949172\pi\) | |||||||
\(710\) | −376.946 | − | 652.889i | −0.0199247 | − | 0.0345106i | ||||
\(711\) | 8065.11 | + | 13969.2i | 0.425408 | + | 0.736828i | ||||
\(712\) | 8810.52 | − | 15260.3i | 0.463748 | − | 0.803234i | ||||
\(713\) | 7440.96 | 0.390836 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −23805.2 | −1.24512 | ||||||||
\(716\) | 709.338 | − | 1228.61i | 0.0370240 | − | 0.0641275i | ||||
\(717\) | 223.074 | + | 386.376i | 0.0116190 | + | 0.0201248i | ||||
\(718\) | −7232.22 | − | 12526.6i | −0.375911 | − | 0.651097i | ||||
\(719\) | 1963.10 | − | 3400.18i | 0.101824 | − | 0.176364i | −0.810612 | − | 0.585583i | \(-0.800866\pi\) |
0.912436 | + | 0.409219i | \(0.134199\pi\) | |||||||
\(720\) | 766.413 | 0.0396702 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −2799.42 | −0.144299 | ||||||||
\(723\) | 560.902 | − | 971.512i | 0.0288523 | − | 0.0499736i | ||||
\(724\) | 5861.05 | + | 10151.6i | 0.300862 | + | 0.521109i | ||||
\(725\) | 1433.26 | + | 2482.47i | 0.0734205 | + | 0.127168i | ||||
\(726\) | 967.322 | − | 1675.45i | 0.0494500 | − | 0.0856499i | ||||
\(727\) | −21071.2 | −1.07495 | −0.537474 | − | 0.843281i | \(-0.680621\pi\) | ||||
−0.537474 | + | 0.843281i | \(0.680621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19200.0 | −0.975459 | ||||||||
\(730\) | 3652.78 | − | 6326.81i | 0.185199 | − | 0.320775i | ||||
\(731\) | −16232.7 | − | 28115.8i | −0.821324 | − | 1.42257i | ||||
\(732\) | 192.451 | + | 333.334i | 0.00971745 | + | 0.0168311i | ||||
\(733\) | 11420.3 | − | 19780.6i | 0.575470 | − | 0.996744i | −0.420520 | − | 0.907283i | \(-0.638152\pi\) |
0.995990 | − | 0.0894605i | \(-0.0285143\pi\) | |||||||
\(734\) | −3130.86 | −0.157441 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18699.0 | −0.936485 | ||||||||
\(737\) | −2807.08 | + | 4862.01i | −0.140299 | + | 0.243004i | ||||
\(738\) | 9291.39 | + | 16093.2i | 0.463443 | + | 0.802706i | ||||
\(739\) | −5418.67 | − | 9385.42i | −0.269728 | − | 0.467183i | 0.699063 | − | 0.715060i | \(-0.253600\pi\) |
−0.968792 | + | 0.247877i | \(0.920267\pi\) | |||||||
\(740\) | 2640.99 | − | 4574.34i | 0.131196 | − | 0.227238i | ||||
\(741\) | −1637.75 | −0.0811931 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21631.9 | −1.06810 | −0.534050 | − | 0.845453i | \(-0.679331\pi\) | ||||
−0.534050 | + | 0.845453i | \(0.679331\pi\) | |||||||
\(744\) | 269.141 | − | 466.166i | 0.0132624 | − | 0.0229711i | ||||
\(745\) | −2571.58 | − | 4454.11i | −0.126464 | − | 0.219042i | ||||
\(746\) | −2247.18 | − | 3892.23i | −0.110288 | − | 0.191025i | ||||
\(747\) | 952.980 | − | 1650.61i | 0.0466770 | − | 0.0808469i | ||||
\(748\) | −38161.9 | −1.86543 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 68.9103 | 0.00335500 | ||||||||
\(751\) | 8089.58 | − | 14011.6i | 0.393067 | − | 0.680812i | −0.599786 | − | 0.800161i | \(-0.704747\pi\) |
0.992852 | + | 0.119349i | \(0.0380808\pi\) | |||||||
\(752\) | −426.676 | − | 739.025i | −0.0206905 | − | 0.0358370i | ||||
\(753\) | −597.973 | − | 1035.72i | −0.0289394 | − | 0.0501245i | ||||
\(754\) | 6497.16 | − | 11253.4i | 0.313810 | − | 0.543535i | ||||
\(755\) | −355.037 | −0.0171140 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −40930.9 | −1.96520 | −0.982601 | − | 0.185727i | \(-0.940536\pi\) | ||||
−0.982601 | + | 0.185727i | \(0.940536\pi\) | |||||||
\(758\) | −7403.59 | + | 12823.4i | −0.354763 | + | 0.614467i | ||||
\(759\) | −1169.93 | − | 2026.38i | −0.0559496 | − | 0.0969075i | ||||
\(760\) | −3946.05 | − | 6834.77i | −0.188340 | − | 0.326215i | ||||
\(761\) | −1591.99 | + | 2757.40i | −0.0758337 | + | 0.131348i | −0.901449 | − | 0.432886i | \(-0.857495\pi\) |
0.825615 | + | 0.564234i | \(0.190828\pi\) | |||||||
\(762\) | 967.917 | 0.0460157 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2449.55 | 0.115997 | ||||||||
\(765\) | −7013.49 | + | 12147.7i | −0.331468 | + | 0.574120i | ||||
\(766\) | 7695.62 | + | 13329.2i | 0.362995 | + | 0.628726i | ||||
\(767\) | 17725.0 | + | 30700.6i | 0.834436 | + | 1.44529i | ||||
\(768\) | −636.438 | + | 1102.34i | −0.0299030 | + | 0.0517935i | ||||
\(769\) | 33595.8 | 1.57542 | 0.787708 | − | 0.616048i | \(-0.211267\pi\) | ||||
0.787708 | + | 0.616048i | \(0.211267\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.947940 | 4.42791e−5 | ||||||||
\(772\) | −11604.4 | + | 20099.5i | −0.541000 | + | 0.937040i | ||||
\(773\) | −17193.0 | − | 29779.1i | −0.799986 | − | 1.38562i | −0.919624 | − | 0.392799i | \(-0.871507\pi\) |
0.119638 | − | 0.992818i | \(-0.461826\pi\) | |||||||
\(774\) | 6928.33 | + | 12000.2i | 0.321749 | + | 0.557285i | ||||
\(775\) | 920.631 | − | 1594.58i | 0.0426710 | − | 0.0739084i | ||||
\(776\) | −3197.72 | −0.147927 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17313.7 | 0.797849 | ||||||||
\(779\) | −15000.7 | + | 25982.0i | −0.689932 | + | 1.19500i | ||||
\(780\) | 299.417 | + | 518.605i | 0.0137447 | + | 0.0238065i | ||||
\(781\) | 3167.17 | + | 5485.69i | 0.145109 | + | 0.251336i | ||||
\(782\) | 8728.04 | − | 15117.4i | 0.399123 | − | 0.691301i | ||||
\(783\) | −2056.90 | −0.0938795 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10306.6 | 0.468610 | ||||||||
\(786\) | 498.662 | − | 863.708i | 0.0226294 | − | 0.0391952i | ||||
\(787\) | 4106.22 | + | 7112.18i | 0.185986 | + | 0.322137i | 0.943908 | − | 0.330208i | \(-0.107119\pi\) |
−0.757922 | + | 0.652345i | \(0.773785\pi\) | |||||||
\(788\) | −761.838 | − | 1319.54i | −0.0344408 | − | 0.0596532i | ||||
\(789\) | −468.885 | + | 812.132i | −0.0211568 | + | 0.0366447i | ||||
\(790\) | −4967.17 | −0.223701 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 41072.7 | 1.84274 | ||||||||
\(793\) | 7525.03 | − | 13033.7i | 0.336976 | − | 0.583659i | ||||
\(794\) | 3002.46 | + | 5200.42i | 0.134198 | + | 0.232438i | ||||
\(795\) | −225.926 | − | 391.316i | −0.0100790 | − | 0.0174573i | ||||
\(796\) | 12664.5 | − | 21935.6i | 0.563922 | − | 0.976742i | ||||
\(797\) | 36798.3 | 1.63546 | 0.817732 | − | 0.575600i | \(-0.195231\pi\) | ||||
0.817732 | + | 0.575600i | \(0.195231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15618.2 | 0.691528 | ||||||||
\(800\) | −2313.52 | + | 4007.14i | −0.102244 | + | 0.177092i | ||||
\(801\) | 10790.5 | + | 18689.7i | 0.475985 | + | 0.824431i | ||||
\(802\) | 6974.11 | + | 12079.5i | 0.307063 | + | 0.531848i | ||||
\(803\) | −30691.3 | + | 53158.9i | −1.34878 | + | 2.33616i | ||||
\(804\) | 141.228 | 0.00619492 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8346.70 | −0.364764 | ||||||||
\(807\) | −240.916 | + | 417.279i | −0.0105089 | + | 0.0182019i | ||||
\(808\) | −6799.91 | − | 11777.8i | −0.296064 | − | 0.512798i | ||||
\(809\) | −5093.08 | − | 8821.48i | −0.221339 | − | 0.383370i | 0.733876 | − | 0.679284i | \(-0.237709\pi\) |
−0.955215 | + | 0.295913i | \(0.904376\pi\) | |||||||
\(810\) | 2981.06 | − | 5163.35i | 0.129313 | − | 0.223977i | ||||
\(811\) | 21196.9 | 0.917786 | 0.458893 | − | 0.888492i | \(-0.348246\pi\) | ||||
0.458893 | + | 0.888492i | \(0.348246\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2681.24 | −0.115665 | ||||||||
\(814\) | 11575.4 | − | 20049.2i | 0.498425 | − | 0.863298i | ||||
\(815\) | −4909.50 | − | 8503.50i | −0.211009 | − | 0.365478i | ||||
\(816\) | 98.9917 | + | 171.459i | 0.00424682 | + | 0.00735571i | ||||
\(817\) | −11185.6 | + | 19374.1i | −0.478991 | + | 0.829636i | ||||
\(818\) | −24146.5 | −1.03211 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10969.9 | 0.467177 | ||||||||
\(821\) | −3781.97 | + | 6550.56i | −0.160769 | + | 0.278461i | −0.935145 | − | 0.354266i | \(-0.884731\pi\) |
0.774376 | + | 0.632726i | \(0.218064\pi\) | |||||||
\(822\) | −5.10306 | − | 8.83875i | −0.000216532 | − | 0.000375045i | ||||
\(823\) | −4199.90 | − | 7274.44i | −0.177885 | − | 0.308106i | 0.763271 | − | 0.646079i | \(-0.223592\pi\) |
−0.941156 | + | 0.337973i | \(0.890259\pi\) | |||||||
\(824\) | −20002.0 | + | 34644.5i | −0.845636 | + | 1.46468i | ||||
\(825\) | −578.997 | −0.0244340 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5479.54 | 0.230402 | 0.115201 | − | 0.993342i | \(-0.463249\pi\) | ||||
0.115201 | + | 0.993342i | \(0.463249\pi\) | |||||||
\(828\) | 7141.30 | − | 12369.1i | 0.299731 | − | 0.519149i | ||||
\(829\) | −4626.28 | − | 8012.95i | −0.193821 | − | 0.335707i | 0.752693 | − | 0.658372i | \(-0.228755\pi\) |
−0.946513 | + | 0.322665i | \(0.895421\pi\) | |||||||
\(830\) | 293.463 | + | 508.292i | 0.0122726 | + | 0.0212567i | ||||
\(831\) | −95.0893 | + | 164.700i | −0.00396945 | + | 0.00687529i | ||||
\(832\) | 17854.2 | 0.743972 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 344.887 | 0.0143195 | ||||||||
\(835\) | 7137.61 | − | 12362.7i | 0.295817 | − | 0.512370i | ||||
\(836\) | 13148.3 | + | 22773.6i | 0.543952 | + | 0.942153i | ||||
\(837\) | 660.609 | + | 1144.21i | 0.0272808 | + | 0.0472517i | ||||
\(838\) | 2101.15 | − | 3639.31i | 0.0866148 | − | 0.150021i | ||||
\(839\) | −34517.6 | −1.42036 | −0.710178 | − | 0.704022i | \(-0.751386\pi\) | ||||
−0.710178 | + | 0.704022i | \(0.751386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11241.9 | −0.460943 | ||||||||
\(842\) | −7990.10 | + | 13839.3i | −0.327027 | + | 0.566428i | ||||
\(843\) | −297.016 | − | 514.446i | −0.0121349 | − | 0.0210183i | ||||
\(844\) | 5315.31 | + | 9206.38i | 0.216778 | + | 0.375470i | ||||
\(845\) | 6215.04 | − | 10764.8i | 0.253022 | − | 0.438247i | ||||
\(846\) | −6666.04 | −0.270902 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1547.55 | 0.0626686 | ||||||||
\(849\) | 552.768 | − | 957.422i | 0.0223450 | − | 0.0387027i | ||||
\(850\) | −2159.75 | − | 3740.79i | −0.0871514 | − | 0.150951i | ||||
\(851\) | −10150.2 | − | 17580.7i | −0.408866 | − | 0.708177i | ||||
\(852\) | 79.6720 | − | 137.996i | 0.00320366 | − | 0.00554890i | ||||
\(853\) | −1498.57 | −0.0601525 | −0.0300763 | − | 0.999548i | \(-0.509575\pi\) | ||||
−0.0300763 | + | 0.999548i | \(0.509575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9665.71 | 0.386620 | ||||||||
\(856\) | 11962.3 | − | 20719.3i | 0.477643 | − | 0.827302i | ||||
\(857\) | 4678.51 | + | 8103.41i | 0.186482 | + | 0.322996i | 0.944075 | − | 0.329731i | \(-0.106958\pi\) |
−0.757593 | + | 0.652727i | \(0.773625\pi\) | |||||||
\(858\) | 1312.34 | + | 2273.03i | 0.0522173 | + | 0.0904430i | ||||
\(859\) | 14980.5 | − | 25946.9i | 0.595025 | − | 1.03061i | −0.398518 | − | 0.917161i | \(-0.630475\pi\) |
0.993543 | − | 0.113454i | \(-0.0361914\pi\) | |||||||
\(860\) | 8179.94 | 0.324341 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12027.3 | −0.475232 | ||||||||
\(863\) | 16970.5 | − | 29393.8i | 0.669389 | − | 1.15942i | −0.308687 | − | 0.951164i | \(-0.599889\pi\) |
0.978075 | − | 0.208252i | \(-0.0667773\pi\) | |||||||
\(864\) | −1660.10 | − | 2875.37i | −0.0653676 | − | 0.113220i | ||||
\(865\) | −3883.02 | − | 6725.58i | −0.152632 | − | 0.264366i | ||||
\(866\) | −9394.05 | + | 16271.0i | −0.368617 | + | 0.638464i | ||||
\(867\) | −1988.04 | −0.0778747 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 41735.0 | 1.62919 | ||||||||
\(870\) | 158.026 | − | 273.709i | 0.00615814 | − | 0.0106662i | ||||
\(871\) | −2761.08 | − | 4782.33i | −0.107412 | − | 0.186043i | ||||
\(872\) | 6473.12 | + | 11211.8i | 0.251385 | + | 0.435411i | ||||
\(873\) | 1958.17 | − | 3391.66i | 0.0759154 | − | 0.131489i | ||||
\(874\) | −12028.6 | −0.465532 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1544.12 | 0.0595559 | ||||||||
\(877\) | 19718.3 | − | 34153.1i | 0.759224 | − | 1.31501i | −0.184023 | − | 0.982922i | \(-0.558912\pi\) |
0.943247 | − | 0.332092i | \(-0.107755\pi\) | |||||||
\(878\) | −9692.84 | − | 16788.5i | −0.372571 | − | 0.645312i | ||||
\(879\) | −840.465 | − | 1455.73i | −0.0322505 | − | 0.0558595i | ||||
\(880\) | 991.502 | − | 1717.33i | 0.0379813 | − | 0.0657855i | ||||
\(881\) | 32411.4 | 1.23946 | 0.619732 | − | 0.784813i | \(-0.287241\pi\) | ||||
0.619732 | + | 0.784813i | \(0.287241\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17121.4 | −0.652526 | −0.326263 | − | 0.945279i | \(-0.605790\pi\) | ||||
−0.326263 | + | 0.945279i | \(0.605790\pi\) | |||||||
\(884\) | 18768.3 | − | 32507.6i | 0.714079 | − | 1.23682i | ||||
\(885\) | 431.113 | + | 746.709i | 0.0163748 | + | 0.0283620i | ||||
\(886\) | −12485.0 | − | 21624.7i | −0.473412 | − | 0.819974i | ||||
\(887\) | 343.899 | − | 595.650i | 0.0130180 | − | 0.0225479i | −0.859443 | − | 0.511232i | \(-0.829189\pi\) |
0.872461 | + | 0.488684i | \(0.162523\pi\) | |||||||
\(888\) | −1468.54 | −0.0554967 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6645.71 | −0.250297 | ||||||||
\(891\) | −25047.4 | + | 43383.4i | −0.941773 | + | 1.63120i | ||||
\(892\) | 11418.8 | + | 19778.0i | 0.428621 | + | 0.742394i | ||||
\(893\) | −5381.08 | − | 9320.30i | −0.201647 | − | 0.349263i | ||||
\(894\) | −283.534 | + | 491.095i | −0.0106071 | + | 0.0183721i | ||||
\(895\) | −1349.20 | −0.0503898 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2301.52 | 0.0856693 | ||||||||
\(898\) | −890.506 | + | 1542.40i | −0.0330919 | + | 0.0573169i | ||||
\(899\) | −4222.40 | − | 7313.42i | −0.156646 | − | 0.271319i | ||||
\(900\) | −1767.11 | − | 3060.72i | −0.0654485 | − | 0.113360i | ||||
\(901\) | −14161.7 | + | 24528.8i | −0.523634 | + | 0.906961i | ||||
\(902\) | 48080.8 | 1.77485 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19767.5 | 0.727276 | ||||||||
\(905\) | 5574.03 | − | 9654.51i | 0.204737 | − | 0.354615i | ||||
\(906\) | 19.5726 | + | 33.9007i | 0.000717720 | + | 0.00124313i | ||||
\(907\) | −9552.10 | − | 16544.7i | −0.349694 | − | 0.605688i | 0.636501 | − | 0.771276i | \(-0.280381\pi\) |
−0.986195 | + | 0.165588i | \(0.947048\pi\) | |||||||
\(908\) | −6959.81 | + | 12054.7i | −0.254371 | + | 0.440584i | ||||
\(909\) | 16656.1 | 0.607754 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23135.3 | 0.841390 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(912\) | 68.2133 | − | 118.149i | 0.00247672 | − | 0.00428980i | ||||
\(913\) | −2465.73 | − | 4270.76i | −0.0893796 | − | 0.154810i | ||||
\(914\) | 8890.52 | + | 15398.8i | 0.321742 | + | 0.557274i | ||||
\(915\) | 183.026 | − | 317.011i | 0.00661274 | − | 0.0114536i | ||||
\(916\) | 7597.50 | 0.274049 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3099.50 | 0.111437 | ||||||||
\(919\) | −23687.0 | + | 41027.0i | −0.850230 | + | 1.47264i | 0.0307713 | + | 0.999526i | \(0.490204\pi\) |
−0.881001 | + | 0.473114i | \(0.843130\pi\) | |||||||
\(920\) | 5545.37 | + | 9604.86i | 0.198723 | + | 0.344199i | ||||
\(921\) | −255.612 | − | 442.733i | −0.00914517 | − | 0.0158399i | ||||
\(922\) | −374.741 | + | 649.070i | −0.0133855 | + | 0.0231844i | ||||
\(923\) | −6230.53 | −0.222189 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5023.33 | −0.178558 | ||||||||
\(926\) | −5894.05 | + | 10208.8i | −0.209169 | + | 0.362291i | ||||
\(927\) | −24497.1 | − | 42430.2i | −0.867951 | − | 1.50334i | ||||
\(928\) | 10610.8 | + | 18378.4i | 0.375341 | + | 0.650110i | ||||
\(929\) | 3808.86 | − | 6597.14i | 0.134515 | − | 0.232987i | −0.790897 | − | 0.611949i | \(-0.790386\pi\) |
0.925412 | + | 0.378962i | \(0.123719\pi\) | |||||||
\(930\) | −203.011 | −0.00715806 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32837.6 | 1.15411 | ||||||||
\(933\) | −1545.11 | + | 2676.20i | −0.0542170 | + | 0.0939066i | ||||
\(934\) | −806.336 | − | 1396.62i | −0.0282485 | − | 0.0489279i | ||||
\(935\) | 18146.6 | + | 31430.8i | 0.634713 | + | 1.09936i | ||||
\(936\) | −20199.8 | + | 34987.1i | −0.705397 | + | 1.22178i | ||||
\(937\) | −52091.2 | −1.81616 | −0.908082 | − | 0.418792i | \(-0.862454\pi\) | ||||
−0.908082 | + | 0.418792i | \(0.862454\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2005.79 | −0.0697088 | ||||||||
\(940\) | −1967.57 | + | 3407.92i | −0.0682712 | + | 0.118249i | ||||
\(941\) | 28382.6 | + | 49160.0i | 0.983257 | + | 1.70305i | 0.649440 | + | 0.760413i | \(0.275003\pi\) |
0.333817 | + | 0.942638i | \(0.391663\pi\) | |||||||
\(942\) | −568.185 | − | 984.126i | −0.0196523 | − | 0.0340388i | ||||
\(943\) | 21080.4 | − | 36512.4i | 0.727968 | − | 1.26088i | ||||
\(944\) | −2953.03 | −0.101815 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 35852.5 | 1.23220 | ||||||||
\(947\) | 23814.6 | − | 41248.1i | 0.817181 | − | 1.41540i | −0.0905695 | − | 0.995890i | \(-0.528869\pi\) |
0.907751 | − | 0.419510i | \(-0.137798\pi\) | |||||||
\(948\) | −524.935 | − | 909.215i | −0.0179843 | − | 0.0311497i | ||||
\(949\) | −30188.4 | − | 52287.8i | −1.03262 | − | 1.78855i | ||||
\(950\) | −1488.24 | + | 2577.71i | −0.0508262 | + | 0.0880335i | ||||
\(951\) | 2322.75 | 0.0792012 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12893.5 | 0.438259 | 0.219129 | − | 0.975696i | \(-0.429678\pi\) | ||||
0.219129 | + | 0.975696i | \(0.429678\pi\) | |||||||
\(954\) | 6044.40 | − | 10469.2i | 0.205131 | − | 0.355297i | ||||
\(955\) | −1164.80 | − | 2017.49i | −0.0394681 | − | 0.0683607i | ||||
\(956\) | 3523.12 | + | 6102.22i | 0.119190 | + | 0.206443i | ||||
\(957\) | −1327.76 | + | 2299.75i | −0.0448490 | + | 0.0776807i | ||||
\(958\) | 16087.0 | 0.542534 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 434.257 | 0.0145996 | ||||||||
\(961\) | 12183.3 | − | 21102.1i | 0.408959 | − | 0.708338i | ||||
\(962\) | 11385.7 | + | 19720.7i | 0.381591 | + | 0.660936i | ||||
\(963\) | 14650.6 | + | 25375.6i | 0.490248 | + | 0.849134i | ||||
\(964\) | 8858.61 | − | 15343.6i | 0.295972 | − | 0.512638i | ||||
\(965\) | 22072.3 | 0.736303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28420.0 | −0.945114 | −0.472557 | − | 0.881300i | \(-0.656669\pi\) | ||||
−0.472557 | + | 0.881300i | \(0.656669\pi\) | |||||||
\(968\) | 38524.2 | − | 66725.9i | 1.27915 | − | 2.21555i | ||||
\(969\) | 1248.45 | + | 2162.37i | 0.0413890 | + | 0.0716878i | ||||
\(970\) | 603.004 | + | 1044.43i | 0.0199601 | + | 0.0345719i | ||||
\(971\) | −14636.9 | + | 25351.8i | −0.483749 | + | 0.837877i | −0.999826 | − | 0.0186650i | \(-0.994058\pi\) |
0.516077 | + | 0.856542i | \(0.327392\pi\) | |||||||
\(972\) | 3806.64 | 0.125615 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1529.19 | 0.0503063 | ||||||||
\(975\) | 284.754 | − | 493.209i | 0.00935327 | − | 0.0162003i | ||||
\(976\) | 626.846 | + | 1085.73i | 0.0205582 | + | 0.0356079i | ||||
\(977\) | −6027.51 | − | 10439.9i | −0.197377 | − | 0.341866i | 0.750300 | − | 0.661097i | \(-0.229909\pi\) |
−0.947677 | + | 0.319231i | \(0.896576\pi\) | |||||||
\(978\) | −541.304 | + | 937.566i | −0.0176984 | + | 0.0306545i | ||||
\(979\) | 55838.4 | 1.82288 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −15855.7 | −0.516037 | ||||||||
\(982\) | −1067.42 | + | 1848.83i | −0.0346872 | + | 0.0600799i | ||||
\(983\) | −5302.53 | − | 9184.25i | −0.172049 | − | 0.297998i | 0.767087 | − | 0.641543i | \(-0.221706\pi\) |
−0.939136 | + | 0.343545i | \(0.888372\pi\) | |||||||
\(984\) | −1524.97 | − | 2641.32i | −0.0494047 | − | 0.0855714i | ||||
\(985\) | −724.531 | + | 1254.92i | −0.0234370 | + | 0.0405941i | ||||
\(986\) | −19811.0 | −0.639870 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −25865.7 | −0.832893 | ||||||||
\(989\) | 15719.1 | − | 27226.3i | 0.505398 | − | 0.875374i | ||||
\(990\) | −7745.20 | − | 13415.1i | −0.248645 | − | 0.430666i | ||||
\(991\) | −22614.5 | − | 39169.5i | −0.724898 | − | 1.25556i | −0.959016 | − | 0.283352i | \(-0.908553\pi\) |
0.234117 | − | 0.972208i | \(-0.424780\pi\) | |||||||
\(992\) | 6815.68 | − | 11805.1i | 0.218143 | − | 0.377835i | ||||
\(993\) | −327.854 | −0.0104775 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −24088.7 | −0.767500 | ||||||||
\(996\) | −62.0268 | + | 107.434i | −0.00197329 | + | 0.00341784i | ||||
\(997\) | 24838.4 | + | 43021.4i | 0.789008 | + | 1.36660i | 0.926575 | + | 0.376109i | \(0.122738\pi\) |
−0.137568 | + | 0.990492i | \(0.543928\pi\) | |||||||
\(998\) | 16012.7 | + | 27734.8i | 0.507889 | + | 0.879690i | ||||
\(999\) | 1802.27 | − | 3121.63i | 0.0570785 | − | 0.0988629i |
(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 | 245.4.e.p.226.2 | 12 | ||
7.2 | even | 3 | 245.4.a.p.1.5 | yes | 6 | ||
7.3 | odd | 6 | 245.4.e.q.116.2 | 12 | |||
7.4 | even | 3 | inner | 245.4.e.p.116.2 | 12 | ||
7.5 | odd | 6 | 245.4.a.o.1.5 | ✓ | 6 | ||
7.6 | odd | 2 | 245.4.e.q.226.2 | 12 | |||
21.2 | odd | 6 | 2205.4.a.ca.1.2 | 6 | |||
21.5 | even | 6 | 2205.4.a.bz.1.2 | 6 | |||
35.9 | even | 6 | 1225.4.a.bi.1.2 | 6 | |||
35.19 | odd | 6 | 1225.4.a.bj.1.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
245.4.a.o.1.5 | ✓ | 6 | 7.5 | odd | 6 | ||
245.4.a.p.1.5 | yes | 6 | 7.2 | even | 3 | ||
245.4.e.p.116.2 | 12 | 7.4 | even | 3 | inner | ||
245.4.e.p.226.2 | 12 | 1.1 | even | 1 | trivial | ||
245.4.e.q.116.2 | 12 | 7.3 | odd | 6 | |||
245.4.e.q.226.2 | 12 | 7.6 | odd | 2 | |||
1225.4.a.bi.1.2 | 6 | 35.9 | even | 6 | |||
1225.4.a.bj.1.2 | 6 | 35.19 | odd | 6 | |||
2205.4.a.bz.1.2 | 6 | 21.5 | even | 6 | |||
2205.4.a.ca.1.2 | 6 | 21.2 | odd | 6 |