Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [13,3,Mod(5,13)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(13, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("13.5");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 13.d (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(0.354224343668\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.1 | ||
Root | \(-1.58114 - 1.58114i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 13.8 |
Dual form | 13.3.d.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.58114 | − | 2.58114i | −1.29057 | − | 1.29057i | −0.934435 | − | 0.356135i | \(-0.884094\pi\) |
−0.356135 | − | 0.934435i | \(-0.615906\pi\) | |||||||
\(3\) | 2.16228 | 0.720759 | 0.360380 | − | 0.932806i | \(-0.382647\pi\) | ||||
0.360380 | + | 0.932806i | \(0.382647\pi\) | |||||||
\(4\) | 9.32456i | 2.33114i | ||||||||
\(5\) | 0.418861 | + | 0.418861i | 0.0837722 | + | 0.0837722i | 0.747751 | − | 0.663979i | \(-0.231134\pi\) |
−0.663979 | + | 0.747751i | \(0.731134\pi\) | |||||||
\(6\) | −5.58114 | − | 5.58114i | −0.930190 | − | 0.930190i | ||||
\(7\) | −1.41886 | + | 1.41886i | −0.202694 | + | 0.202694i | −0.801153 | − | 0.598459i | \(-0.795780\pi\) |
0.598459 | + | 0.801153i | \(0.295780\pi\) | |||||||
\(8\) | 13.7434 | − | 13.7434i | 1.71793 | − | 1.71793i | ||||
\(9\) | −4.32456 | −0.480506 | ||||||||
\(10\) | − | 2.16228i | − | 0.216228i | ||||||
\(11\) | −7.32456 | + | 7.32456i | −0.665869 | + | 0.665869i | −0.956757 | − | 0.290888i | \(-0.906049\pi\) |
0.290888 | + | 0.956757i | \(0.406049\pi\) | |||||||
\(12\) | 20.1623i | 1.68019i | ||||||||
\(13\) | 9.90569 | − | 8.41886i | 0.761976 | − | 0.647605i | ||||
\(14\) | 7.32456 | 0.523183 | ||||||||
\(15\) | 0.905694 | + | 0.905694i | 0.0603796 | + | 0.0603796i | ||||
\(16\) | −33.6491 | −2.10307 | ||||||||
\(17\) | − | 15.9737i | − | 0.939627i | −0.882766 | − | 0.469814i | \(-0.844321\pi\) | ||
0.882766 | − | 0.469814i | \(-0.155679\pi\) | |||||||
\(18\) | 11.1623 | + | 11.1623i | 0.620127 | + | 0.620127i | ||||
\(19\) | −3.16228 | − | 3.16228i | −0.166436 | − | 0.166436i | 0.618975 | − | 0.785411i | \(-0.287548\pi\) |
−0.785411 | + | 0.618975i | \(0.787548\pi\) | |||||||
\(20\) | −3.90569 | + | 3.90569i | −0.195285 | + | 0.195285i | ||||
\(21\) | −3.06797 | + | 3.06797i | −0.146094 | + | 0.146094i | ||||
\(22\) | 37.8114 | 1.71870 | ||||||||
\(23\) | 27.4868i | 1.19508i | 0.801839 | + | 0.597540i | \(0.203855\pi\) | ||||
−0.801839 | + | 0.597540i | \(0.796145\pi\) | |||||||
\(24\) | 29.7171 | − | 29.7171i | 1.23821 | − | 1.23821i | ||||
\(25\) | − | 24.6491i | − | 0.985964i | ||||||
\(26\) | −47.2982 | − | 3.83772i | −1.81916 | − | 0.147605i | ||||
\(27\) | −28.8114 | −1.06709 | ||||||||
\(28\) | −13.2302 | − | 13.2302i | −0.472509 | − | 0.472509i | ||||
\(29\) | 25.8114 | 0.890048 | 0.445024 | − | 0.895519i | \(-0.353195\pi\) | ||||
0.445024 | + | 0.895519i | \(0.353195\pi\) | |||||||
\(30\) | − | 4.67544i | − | 0.155848i | ||||||
\(31\) | 19.4868 | + | 19.4868i | 0.628608 | + | 0.628608i | 0.947718 | − | 0.319110i | \(-0.103384\pi\) |
−0.319110 | + | 0.947718i | \(0.603384\pi\) | |||||||
\(32\) | 31.8794 | + | 31.8794i | 0.996230 | + | 0.996230i | ||||
\(33\) | −15.8377 | + | 15.8377i | −0.479931 | + | 0.479931i | ||||
\(34\) | −41.2302 | + | 41.2302i | −1.21265 | + | 1.21265i | ||||
\(35\) | −1.18861 | −0.0339603 | ||||||||
\(36\) | − | 40.3246i | − | 1.12013i | ||||||
\(37\) | −4.23025 | + | 4.23025i | −0.114331 | + | 0.114331i | −0.761958 | − | 0.647627i | \(-0.775762\pi\) |
0.647627 | + | 0.761958i | \(0.275762\pi\) | |||||||
\(38\) | 16.3246i | 0.429594i | ||||||||
\(39\) | 21.4189 | − | 18.2039i | 0.549202 | − | 0.466767i | ||||
\(40\) | 11.5132 | 0.287829 | ||||||||
\(41\) | 11.1623 | + | 11.1623i | 0.272251 | + | 0.272251i | 0.830006 | − | 0.557755i | \(-0.188337\pi\) |
−0.557755 | + | 0.830006i | \(0.688337\pi\) | |||||||
\(42\) | 15.8377 | 0.377089 | ||||||||
\(43\) | − | 11.5132i | − | 0.267748i | −0.990998 | − | 0.133874i | \(-0.957258\pi\) | ||
0.990998 | − | 0.133874i | \(-0.0427418\pi\) | |||||||
\(44\) | −68.2982 | − | 68.2982i | −1.55223 | − | 1.55223i | ||||
\(45\) | −1.81139 | − | 1.81139i | −0.0402531 | − | 0.0402531i | ||||
\(46\) | 70.9473 | − | 70.9473i | 1.54233 | − | 1.54233i | ||||
\(47\) | 35.3662 | − | 35.3662i | 0.752472 | − | 0.752472i | −0.222468 | − | 0.974940i | \(-0.571411\pi\) |
0.974940 | + | 0.222468i | \(0.0714112\pi\) | |||||||
\(48\) | −72.7587 | −1.51581 | ||||||||
\(49\) | 44.9737i | 0.917830i | ||||||||
\(50\) | −63.6228 | + | 63.6228i | −1.27246 | + | 1.27246i | ||||
\(51\) | − | 34.5395i | − | 0.677245i | ||||||
\(52\) | 78.5021 | + | 92.3662i | 1.50966 | + | 1.77627i | ||||
\(53\) | −4.18861 | −0.0790304 | −0.0395152 | − | 0.999219i | \(-0.512581\pi\) | ||||
−0.0395152 | + | 0.999219i | \(0.512581\pi\) | |||||||
\(54\) | 74.3662 | + | 74.3662i | 1.37715 | + | 1.37715i | ||||
\(55\) | −6.13594 | −0.111563 | ||||||||
\(56\) | 39.0000i | 0.696429i | ||||||||
\(57\) | −6.83772 | − | 6.83772i | −0.119960 | − | 0.119960i | ||||
\(58\) | −66.6228 | − | 66.6228i | −1.14867 | − | 1.14867i | ||||
\(59\) | −30.2719 | + | 30.2719i | −0.513083 | + | 0.513083i | −0.915470 | − | 0.402387i | \(-0.868181\pi\) |
0.402387 | + | 0.915470i | \(0.368181\pi\) | |||||||
\(60\) | −8.44520 | + | 8.44520i | −0.140753 | + | 0.140753i | ||||
\(61\) | −67.6754 | −1.10943 | −0.554717 | − | 0.832039i | \(-0.687173\pi\) | ||||
−0.554717 | + | 0.832039i | \(0.687173\pi\) | |||||||
\(62\) | − | 100.596i | − | 1.62252i | ||||||
\(63\) | 6.13594 | − | 6.13594i | 0.0973959 | − | 0.0973959i | ||||
\(64\) | − | 29.9737i | − | 0.468339i | ||||||
\(65\) | 7.67544 | + | 0.622777i | 0.118084 | + | 0.00958118i | ||||
\(66\) | 81.7587 | 1.23877 | ||||||||
\(67\) | −81.0833 | − | 81.0833i | −1.21020 | − | 1.21020i | −0.970961 | − | 0.239237i | \(-0.923103\pi\) |
−0.239237 | − | 0.970961i | \(-0.576897\pi\) | |||||||
\(68\) | 148.947 | 2.19040 | ||||||||
\(69\) | 59.4342i | 0.861365i | ||||||||
\(70\) | 3.06797 | + | 3.06797i | 0.0438282 | + | 0.0438282i | ||||
\(71\) | 50.4452 | + | 50.4452i | 0.710496 | + | 0.710496i | 0.966639 | − | 0.256143i | \(-0.0824518\pi\) |
−0.256143 | + | 0.966639i | \(0.582452\pi\) | |||||||
\(72\) | −59.4342 | + | 59.4342i | −0.825475 | + | 0.825475i | ||||
\(73\) | −31.6228 | + | 31.6228i | −0.433189 | + | 0.433189i | −0.889712 | − | 0.456523i | \(-0.849095\pi\) |
0.456523 | + | 0.889712i | \(0.349095\pi\) | |||||||
\(74\) | 21.8377 | 0.295104 | ||||||||
\(75\) | − | 53.2982i | − | 0.710643i | ||||||
\(76\) | 29.4868 | − | 29.4868i | 0.387985 | − | 0.387985i | ||||
\(77\) | − | 20.7851i | − | 0.269936i | ||||||
\(78\) | −102.272 | − | 8.29822i | −1.31118 | − | 0.106387i | ||||
\(79\) | 50.7851 | 0.642849 | 0.321424 | − | 0.946935i | \(-0.395838\pi\) | ||||
0.321424 | + | 0.946935i | \(0.395838\pi\) | |||||||
\(80\) | −14.0943 | − | 14.0943i | −0.176179 | − | 0.176179i | ||||
\(81\) | −23.3772 | −0.288608 | ||||||||
\(82\) | − | 57.6228i | − | 0.702717i | ||||||
\(83\) | 18.6228 | + | 18.6228i | 0.224371 | + | 0.224371i | 0.810336 | − | 0.585965i | \(-0.199285\pi\) |
−0.585965 | + | 0.810336i | \(0.699285\pi\) | |||||||
\(84\) | −28.6075 | − | 28.6075i | −0.340565 | − | 0.340565i | ||||
\(85\) | 6.69075 | − | 6.69075i | 0.0787147 | − | 0.0787147i | ||||
\(86\) | −29.7171 | + | 29.7171i | −0.345547 | + | 0.345547i | ||||
\(87\) | 55.8114 | 0.641510 | ||||||||
\(88\) | 201.329i | 2.28783i | ||||||||
\(89\) | 91.1096 | − | 91.1096i | 1.02370 | − | 1.02370i | 0.0239913 | − | 0.999712i | \(-0.492363\pi\) |
0.999712 | − | 0.0239913i | \(-0.00763740\pi\) | |||||||
\(90\) | 9.35089i | 0.103899i | ||||||||
\(91\) | −2.10961 | + | 26.0000i | −0.0231825 | + | 0.285714i | ||||
\(92\) | −256.302 | −2.78590 | ||||||||
\(93\) | 42.1359 | + | 42.1359i | 0.453075 | + | 0.453075i | ||||
\(94\) | −182.570 | −1.94224 | ||||||||
\(95\) | − | 2.64911i | − | 0.0278854i | ||||||
\(96\) | 68.9320 | + | 68.9320i | 0.718042 | + | 0.718042i | ||||
\(97\) | 87.3552 | + | 87.3552i | 0.900569 | + | 0.900569i | 0.995485 | − | 0.0949165i | \(-0.0302584\pi\) |
−0.0949165 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(98\) | 116.083 | − | 116.083i | 1.18452 | − | 1.18452i | ||||
\(99\) | 31.6754 | − | 31.6754i | 0.319954 | − | 0.319954i | ||||
\(100\) | 229.842 | 2.29842 | ||||||||
\(101\) | − | 8.92100i | − | 0.0883267i | −0.999024 | − | 0.0441634i | \(-0.985938\pi\) | ||
0.999024 | − | 0.0441634i | \(-0.0140622\pi\) | |||||||
\(102\) | −89.1512 | + | 89.1512i | −0.874032 | + | 0.874032i | ||||
\(103\) | 59.4342i | 0.577031i | 0.957475 | + | 0.288515i | \(0.0931616\pi\) | ||||
−0.957475 | + | 0.288515i | \(0.906838\pi\) | |||||||
\(104\) | 20.4342 | − | 251.842i | 0.196482 | − | 2.42156i | ||||
\(105\) | −2.57011 | −0.0244772 | ||||||||
\(106\) | 10.8114 | + | 10.8114i | 0.101994 | + | 0.101994i | ||||
\(107\) | −143.570 | −1.34178 | −0.670888 | − | 0.741558i | \(-0.734087\pi\) | ||||
−0.670888 | + | 0.741558i | \(0.734087\pi\) | |||||||
\(108\) | − | 268.653i | − | 2.48753i | ||||||
\(109\) | −84.7740 | − | 84.7740i | −0.777743 | − | 0.777743i | 0.201703 | − | 0.979447i | \(-0.435352\pi\) |
−0.979447 | + | 0.201703i | \(0.935352\pi\) | |||||||
\(110\) | 15.8377 | + | 15.8377i | 0.143979 | + | 0.143979i | ||||
\(111\) | −9.14697 | + | 9.14697i | −0.0824052 | + | 0.0824052i | ||||
\(112\) | 47.7434 | − | 47.7434i | 0.426281 | − | 0.426281i | ||||
\(113\) | −108.544 | −0.960564 | −0.480282 | − | 0.877114i | \(-0.659466\pi\) | ||||
−0.480282 | + | 0.877114i | \(0.659466\pi\) | |||||||
\(114\) | 35.2982i | 0.309634i | ||||||||
\(115\) | −11.5132 | + | 11.5132i | −0.100114 | + | 0.100114i | ||||
\(116\) | 240.680i | 2.07483i | ||||||||
\(117\) | −42.8377 | + | 36.4078i | −0.366134 | + | 0.311178i | ||||
\(118\) | 156.272 | 1.32434 | ||||||||
\(119\) | 22.6644 | + | 22.6644i | 0.190457 | + | 0.190457i | ||||
\(120\) | 24.8947 | 0.207456 | ||||||||
\(121\) | 13.7018i | 0.113238i | ||||||||
\(122\) | 174.680 | + | 174.680i | 1.43180 | + | 1.43180i | ||||
\(123\) | 24.1359 | + | 24.1359i | 0.196227 | + | 0.196227i | ||||
\(124\) | −181.706 | + | 181.706i | −1.46537 | + | 1.46537i | ||||
\(125\) | 20.7961 | − | 20.7961i | 0.166369 | − | 0.166369i | ||||
\(126\) | −31.6754 | −0.251392 | ||||||||
\(127\) | − | 94.8377i | − | 0.746754i | −0.927680 | − | 0.373377i | \(-0.878200\pi\) | ||
0.927680 | − | 0.373377i | \(-0.121800\pi\) | |||||||
\(128\) | 50.1512 | − | 50.1512i | 0.391807 | − | 0.391807i | ||||
\(129\) | − | 24.8947i | − | 0.192982i | ||||||
\(130\) | −18.2039 | − | 21.4189i | −0.140030 | − | 0.164760i | ||||
\(131\) | −112.268 | −0.857005 | −0.428502 | − | 0.903541i | \(-0.640959\pi\) | ||||
−0.428502 | + | 0.903541i | \(0.640959\pi\) | |||||||
\(132\) | −147.680 | − | 147.680i | −1.11879 | − | 1.11879i | ||||
\(133\) | 8.97367 | 0.0674712 | ||||||||
\(134\) | 418.574i | 3.12369i | ||||||||
\(135\) | −12.0680 | − | 12.0680i | −0.0893924 | − | 0.0893924i | ||||
\(136\) | −219.533 | − | 219.533i | −1.61421 | − | 1.61421i | ||||
\(137\) | 86.7281 | − | 86.7281i | 0.633052 | − | 0.633052i | −0.315780 | − | 0.948832i | \(-0.602266\pi\) |
0.948832 | + | 0.315780i | \(0.102266\pi\) | |||||||
\(138\) | 153.408 | − | 153.408i | 1.11165 | − | 1.11165i | ||||
\(139\) | 78.5395 | 0.565032 | 0.282516 | − | 0.959263i | \(-0.408831\pi\) | ||||
0.282516 | + | 0.959263i | \(0.408831\pi\) | |||||||
\(140\) | − | 11.0833i | − | 0.0791663i | ||||||
\(141\) | 76.4715 | − | 76.4715i | 0.542351 | − | 0.542351i | ||||
\(142\) | − | 260.412i | − | 1.83389i | ||||||
\(143\) | −10.8904 | + | 134.219i | −0.0761566 | + | 0.938596i | ||||
\(144\) | 145.517 | 1.01054 | ||||||||
\(145\) | 10.8114 | + | 10.8114i | 0.0745613 | + | 0.0745613i | ||||
\(146\) | 163.246 | 1.11812 | ||||||||
\(147\) | 97.2456i | 0.661534i | ||||||||
\(148\) | −39.4452 | − | 39.4452i | −0.266522 | − | 0.266522i | ||||
\(149\) | −128.219 | − | 128.219i | −0.860532 | − | 0.860532i | 0.130868 | − | 0.991400i | \(-0.458224\pi\) |
−0.991400 | + | 0.130868i | \(0.958224\pi\) | |||||||
\(150\) | −137.570 | + | 137.570i | −0.917134 | + | 0.917134i | ||||
\(151\) | 29.1776 | − | 29.1776i | 0.193229 | − | 0.193229i | −0.603861 | − | 0.797090i | \(-0.706372\pi\) |
0.797090 | + | 0.603861i | \(0.206372\pi\) | |||||||
\(152\) | −86.9210 | −0.571849 | ||||||||
\(153\) | 69.0790i | 0.451497i | ||||||||
\(154\) | −53.6491 | + | 53.6491i | −0.348371 | + | 0.348371i | ||||
\(155\) | 16.3246i | 0.105320i | ||||||||
\(156\) | 169.743 | + | 199.721i | 1.08810 | + | 1.28027i | ||||
\(157\) | 232.544 | 1.48117 | 0.740585 | − | 0.671962i | \(-0.234548\pi\) | ||||
0.740585 | + | 0.671962i | \(0.234548\pi\) | |||||||
\(158\) | −131.083 | − | 131.083i | −0.829641 | − | 0.829641i | ||||
\(159\) | −9.05694 | −0.0569619 | ||||||||
\(160\) | 26.7061i | 0.166913i | ||||||||
\(161\) | −39.0000 | − | 39.0000i | −0.242236 | − | 0.242236i | ||||
\(162\) | 60.3399 | + | 60.3399i | 0.372468 | + | 0.372468i | ||||
\(163\) | 11.4605 | − | 11.4605i | 0.0703098 | − | 0.0703098i | −0.671077 | − | 0.741387i | \(-0.734168\pi\) |
0.741387 | + | 0.671077i | \(0.234168\pi\) | |||||||
\(164\) | −104.083 | + | 104.083i | −0.634654 | + | 0.634654i | ||||
\(165\) | −13.2676 | −0.0804098 | ||||||||
\(166\) | − | 96.1359i | − | 0.579132i | ||||||
\(167\) | −206.785 | + | 206.785i | −1.23823 | + | 1.23823i | −0.277512 | + | 0.960722i | \(0.589510\pi\) |
−0.960722 | + | 0.277512i | \(0.910490\pi\) | |||||||
\(168\) | 84.3288i | 0.501957i | ||||||||
\(169\) | 27.2456 | − | 166.789i | 0.161216 | − | 0.986919i | ||||
\(170\) | −34.5395 | −0.203174 | ||||||||
\(171\) | 13.6754 | + | 13.6754i | 0.0799734 | + | 0.0799734i | ||||
\(172\) | 107.355 | 0.624158 | ||||||||
\(173\) | − | 91.3815i | − | 0.528217i | −0.964493 | − | 0.264108i | \(-0.914922\pi\) | ||
0.964493 | − | 0.264108i | \(-0.0850777\pi\) | |||||||
\(174\) | −144.057 | − | 144.057i | −0.827913 | − | 0.827913i | ||||
\(175\) | 34.9737 | + | 34.9737i | 0.199850 | + | 0.199850i | ||||
\(176\) | 246.465 | − | 246.465i | 1.40037 | − | 1.40037i | ||||
\(177\) | −65.4562 | + | 65.4562i | −0.369809 | + | 0.369809i | ||||
\(178\) | −470.333 | −2.64232 | ||||||||
\(179\) | − | 71.6712i | − | 0.400398i | −0.979755 | − | 0.200199i | \(-0.935841\pi\) | ||
0.979755 | − | 0.200199i | \(-0.0641588\pi\) | |||||||
\(180\) | 16.8904 | − | 16.8904i | 0.0938355 | − | 0.0938355i | ||||
\(181\) | 274.144i | 1.51461i | 0.653061 | + | 0.757305i | \(0.273484\pi\) | ||||
−0.653061 | + | 0.757305i | \(0.726516\pi\) | |||||||
\(182\) | 72.5548 | − | 61.6644i | 0.398653 | − | 0.338815i | ||||
\(183\) | −146.333 | −0.799634 | ||||||||
\(184\) | 377.763 | + | 377.763i | 2.05306 | + | 2.05306i | ||||
\(185\) | −3.54377 | −0.0191555 | ||||||||
\(186\) | − | 217.517i | − | 1.16945i | ||||||
\(187\) | 117.000 | + | 117.000i | 0.625668 | + | 0.625668i | ||||
\(188\) | 329.774 | + | 329.774i | 1.75412 | + | 1.75412i | ||||
\(189\) | 40.8794 | − | 40.8794i | 0.216293 | − | 0.216293i | ||||
\(190\) | −6.83772 | + | 6.83772i | −0.0359880 | + | 0.0359880i | ||||
\(191\) | 179.706 | 0.940869 | 0.470435 | − | 0.882435i | \(-0.344097\pi\) | ||||
0.470435 | + | 0.882435i | \(0.344097\pi\) | |||||||
\(192\) | − | 64.8114i | − | 0.337559i | ||||||
\(193\) | −1.13594 | + | 1.13594i | −0.00588572 | + | 0.00588572i | −0.710044 | − | 0.704158i | \(-0.751325\pi\) |
0.704158 | + | 0.710044i | \(0.251325\pi\) | |||||||
\(194\) | − | 450.952i | − | 2.32449i | ||||||
\(195\) | 16.5964 | + | 1.34662i | 0.0851100 | + | 0.00690572i | ||||
\(196\) | −419.359 | −2.13959 | ||||||||
\(197\) | 141.906 | + | 141.906i | 0.720333 | + | 0.720333i | 0.968673 | − | 0.248340i | \(-0.0798849\pi\) |
−0.248340 | + | 0.968673i | \(0.579885\pi\) | |||||||
\(198\) | −163.517 | −0.825846 | ||||||||
\(199\) | − | 259.759i | − | 1.30532i | −0.757651 | − | 0.652660i | \(-0.773653\pi\) | ||
0.757651 | − | 0.652660i | \(-0.226347\pi\) | |||||||
\(200\) | −338.763 | − | 338.763i | −1.69381 | − | 1.69381i | ||||
\(201\) | −175.325 | − | 175.325i | −0.872261 | − | 0.872261i | ||||
\(202\) | −23.0263 | + | 23.0263i | −0.113992 | + | 0.113992i | ||||
\(203\) | −36.6228 | + | 36.6228i | −0.180408 | + | 0.180408i | ||||
\(204\) | 322.065 | 1.57875 | ||||||||
\(205\) | 9.35089i | 0.0456141i | ||||||||
\(206\) | 153.408 | − | 153.408i | 0.744698 | − | 0.744698i | ||||
\(207\) | − | 118.868i | − | 0.574243i | ||||||
\(208\) | −333.318 | + | 283.287i | −1.60249 | + | 1.36196i | ||||
\(209\) | 46.3246 | 0.221649 | ||||||||
\(210\) | 6.63381 | + | 6.63381i | 0.0315896 | + | 0.0315896i | ||||
\(211\) | 325.574 | 1.54301 | 0.771503 | − | 0.636225i | \(-0.219505\pi\) | ||||
0.771503 | + | 0.636225i | \(0.219505\pi\) | |||||||
\(212\) | − | 39.0569i | − | 0.184231i | ||||||
\(213\) | 109.077 | + | 109.077i | 0.512096 | + | 0.512096i | ||||
\(214\) | 370.574 | + | 370.574i | 1.73166 | + | 1.73166i | ||||
\(215\) | 4.82242 | − | 4.82242i | 0.0224299 | − | 0.0224299i | ||||
\(216\) | −395.967 | + | 395.967i | −1.83318 | + | 1.83318i | ||||
\(217\) | −55.2982 | −0.254831 | ||||||||
\(218\) | 437.627i | 2.00746i | ||||||||
\(219\) | −68.3772 | + | 68.3772i | −0.312225 | + | 0.312225i | ||||
\(220\) | − | 57.2149i | − | 0.260068i | ||||||
\(221\) | −134.480 | − | 158.230i | −0.608507 | − | 0.715974i | ||||
\(222\) | 47.2192 | 0.212699 | ||||||||
\(223\) | −243.774 | − | 243.774i | −1.09316 | − | 1.09316i | −0.995190 | − | 0.0979674i | \(-0.968766\pi\) |
−0.0979674 | − | 0.995190i | \(-0.531234\pi\) | |||||||
\(224\) | −90.4648 | −0.403861 | ||||||||
\(225\) | 106.596i | 0.473762i | ||||||||
\(226\) | 280.167 | + | 280.167i | 1.23968 | + | 1.23968i | ||||
\(227\) | −100.732 | − | 100.732i | −0.443755 | − | 0.443755i | 0.449517 | − | 0.893272i | \(-0.351596\pi\) |
−0.893272 | + | 0.449517i | \(0.851596\pi\) | |||||||
\(228\) | 63.7587 | − | 63.7587i | 0.279644 | − | 0.279644i | ||||
\(229\) | −240.366 | + | 240.366i | −1.04963 | + | 1.04963i | −0.0509319 | + | 0.998702i | \(0.516219\pi\) |
−0.998702 | + | 0.0509319i | \(0.983781\pi\) | |||||||
\(230\) | 59.4342 | 0.258409 | ||||||||
\(231\) | − | 44.9431i | − | 0.194559i | ||||||
\(232\) | 354.737 | − | 354.737i | 1.52904 | − | 1.52904i | ||||
\(233\) | − | 10.7893i | − | 0.0463061i | −0.999732 | − | 0.0231531i | \(-0.992629\pi\) | ||
0.999732 | − | 0.0231531i | \(-0.00737051\pi\) | |||||||
\(234\) | 204.544 | + | 16.5964i | 0.874119 | + | 0.0709250i | ||||
\(235\) | 29.6271 | 0.126073 | ||||||||
\(236\) | −282.272 | − | 282.272i | −1.19607 | − | 1.19607i | ||||
\(237\) | 109.811 | 0.463339 | ||||||||
\(238\) | − | 117.000i | − | 0.491597i | ||||||
\(239\) | −98.0153 | − | 98.0153i | −0.410106 | − | 0.410106i | 0.471670 | − | 0.881775i | \(-0.343652\pi\) |
−0.881775 | + | 0.471670i | \(0.843652\pi\) | |||||||
\(240\) | −30.4758 | − | 30.4758i | −0.126983 | − | 0.126983i | ||||
\(241\) | −196.197 | + | 196.197i | −0.814096 | + | 0.814096i | −0.985245 | − | 0.171149i | \(-0.945252\pi\) |
0.171149 | + | 0.985245i | \(0.445252\pi\) | |||||||
\(242\) | 35.3662 | − | 35.3662i | 0.146141 | − | 0.146141i | ||||
\(243\) | 208.754 | 0.859072 | ||||||||
\(244\) | − | 631.043i | − | 2.58624i | ||||||
\(245\) | −18.8377 | + | 18.8377i | −0.0768887 | + | 0.0768887i | ||||
\(246\) | − | 124.596i | − | 0.506490i | ||||||
\(247\) | −57.9473 | − | 4.70178i | −0.234605 | − | 0.0190355i | ||||
\(248\) | 535.631 | 2.15980 | ||||||||
\(249\) | 40.2676 | + | 40.2676i | 0.161717 | + | 0.161717i | ||||
\(250\) | −107.355 | −0.429421 | ||||||||
\(251\) | − | 95.8420i | − | 0.381841i | −0.981606 | − | 0.190920i | \(-0.938853\pi\) | ||
0.981606 | − | 0.190920i | \(-0.0611472\pi\) | |||||||
\(252\) | 57.2149 | + | 57.2149i | 0.227043 | + | 0.227043i | ||||
\(253\) | −201.329 | − | 201.329i | −0.795766 | − | 0.795766i | ||||
\(254\) | −244.789 | + | 244.789i | −0.963738 | + | 0.963738i | ||||
\(255\) | 14.4673 | − | 14.4673i | 0.0567343 | − | 0.0567343i | ||||
\(256\) | −378.789 | −1.47965 | ||||||||
\(257\) | 450.579i | 1.75322i | 0.481198 | + | 0.876612i | \(0.340202\pi\) | ||||
−0.481198 | + | 0.876612i | \(0.659798\pi\) | |||||||
\(258\) | −64.2566 | + | 64.2566i | −0.249057 | + | 0.249057i | ||||
\(259\) | − | 12.0043i | − | 0.0463485i | ||||||
\(260\) | −5.80711 | + | 71.5701i | −0.0223351 | + | 0.275270i | ||||
\(261\) | −111.623 | −0.427673 | ||||||||
\(262\) | 289.778 | + | 289.778i | 1.10602 | + | 1.10602i | ||||
\(263\) | 166.982 | 0.634913 | 0.317457 | − | 0.948273i | \(-0.397171\pi\) | ||||
0.317457 | + | 0.948273i | \(0.397171\pi\) | |||||||
\(264\) | 435.329i | 1.64897i | ||||||||
\(265\) | −1.75445 | − | 1.75445i | −0.00662055 | − | 0.00662055i | ||||
\(266\) | −23.1623 | − | 23.1623i | −0.0870762 | − | 0.0870762i | ||||
\(267\) | 197.004 | − | 197.004i | 0.737844 | − | 0.737844i | ||||
\(268\) | 756.065 | − | 756.065i | 2.82114 | − | 2.82114i | ||||
\(269\) | 170.061 | 0.632198 | 0.316099 | − | 0.948726i | \(-0.397627\pi\) | ||||
0.316099 | + | 0.948726i | \(0.397627\pi\) | |||||||
\(270\) | 62.2982i | 0.230734i | ||||||||
\(271\) | −217.072 | + | 217.072i | −0.801005 | + | 0.801005i | −0.983253 | − | 0.182248i | \(-0.941663\pi\) |
0.182248 | + | 0.983253i | \(0.441663\pi\) | |||||||
\(272\) | 537.500i | 1.97610i | ||||||||
\(273\) | −4.56156 | + | 56.2192i | −0.0167090 | + | 0.205931i | ||||
\(274\) | −447.715 | −1.63399 | ||||||||
\(275\) | 180.544 | + | 180.544i | 0.656523 | + | 0.656523i | ||||
\(276\) | −554.197 | −2.00796 | ||||||||
\(277\) | 187.947i | 0.678510i | 0.940694 | + | 0.339255i | \(0.110175\pi\) | ||||
−0.940694 | + | 0.339255i | \(0.889825\pi\) | |||||||
\(278\) | −202.721 | − | 202.721i | −0.729214 | − | 0.729214i | ||||
\(279\) | −84.2719 | − | 84.2719i | −0.302050 | − | 0.302050i | ||||
\(280\) | −16.3356 | + | 16.3356i | −0.0583414 | + | 0.0583414i | ||||
\(281\) | 286.846 | − | 286.846i | 1.02081 | − | 1.02081i | 0.0210263 | − | 0.999779i | \(-0.493307\pi\) |
0.999779 | − | 0.0210263i | \(-0.00669337\pi\) | |||||||
\(282\) | −394.767 | −1.39988 | ||||||||
\(283\) | − | 399.201i | − | 1.41061i | −0.708906 | − | 0.705303i | \(-0.750811\pi\) | ||
0.708906 | − | 0.705303i | \(-0.249189\pi\) | |||||||
\(284\) | −470.379 | + | 470.379i | −1.65626 | + | 1.65626i | ||||
\(285\) | − | 5.72811i | − | 0.0200986i | ||||||
\(286\) | 374.548 | − | 318.329i | 1.30961 | − | 1.11304i | ||||
\(287\) | −31.6754 | −0.110367 | ||||||||
\(288\) | −137.864 | − | 137.864i | −0.478695 | − | 0.478695i | ||||
\(289\) | 33.8420 | 0.117100 | ||||||||
\(290\) | − | 55.8114i | − | 0.192453i | ||||||
\(291\) | 188.886 | + | 188.886i | 0.649093 | + | 0.649093i | ||||
\(292\) | −294.868 | − | 294.868i | −1.00982 | − | 1.00982i | ||||
\(293\) | 136.156 | − | 136.156i | 0.464695 | − | 0.464695i | −0.435496 | − | 0.900191i | \(-0.643427\pi\) |
0.900191 | + | 0.435496i | \(0.143427\pi\) | |||||||
\(294\) | 251.004 | − | 251.004i | 0.853756 | − | 0.853756i | ||||
\(295\) | −25.3594 | −0.0859642 | ||||||||
\(296\) | 116.276i | 0.392825i | ||||||||
\(297\) | 211.031 | − | 211.031i | 0.710541 | − | 0.710541i | ||||
\(298\) | 661.903i | 2.22115i | ||||||||
\(299\) | 231.408 | + | 272.276i | 0.773939 | + | 0.910623i | ||||
\(300\) | 496.982 | 1.65661 | ||||||||
\(301\) | 16.3356 | + | 16.3356i | 0.0542710 | + | 0.0542710i | ||||
\(302\) | −150.623 | −0.498751 | ||||||||
\(303\) | − | 19.2897i | − | 0.0636623i | ||||||
\(304\) | 106.408 | + | 106.408i | 0.350026 | + | 0.350026i | ||||
\(305\) | −28.3466 | − | 28.3466i | −0.0929397 | − | 0.0929397i | ||||
\(306\) | 178.302 | − | 178.302i | 0.582688 | − | 0.582688i | ||||
\(307\) | −235.684 | + | 235.684i | −0.767700 | + | 0.767700i | −0.977701 | − | 0.210001i | \(-0.932653\pi\) |
0.210001 | + | 0.977701i | \(0.432653\pi\) | |||||||
\(308\) | 193.811 | 0.629258 | ||||||||
\(309\) | 128.513i | 0.415900i | ||||||||
\(310\) | 42.1359 | − | 42.1359i | 0.135922 | − | 0.135922i | ||||
\(311\) | − | 113.684i | − | 0.365543i | −0.983155 | − | 0.182772i | \(-0.941493\pi\) | ||
0.983155 | − | 0.182772i | \(-0.0585069\pi\) | |||||||
\(312\) | 44.1843 | − | 544.552i | 0.141616 | − | 1.74536i | ||||
\(313\) | 223.483 | 0.714002 | 0.357001 | − | 0.934104i | \(-0.383799\pi\) | ||||
0.357001 | + | 0.934104i | \(0.383799\pi\) | |||||||
\(314\) | −600.228 | − | 600.228i | −1.91155 | − | 1.91155i | ||||
\(315\) | 5.14022 | 0.0163181 | ||||||||
\(316\) | 473.548i | 1.49857i | ||||||||
\(317\) | −125.140 | − | 125.140i | −0.394764 | − | 0.394764i | 0.481617 | − | 0.876382i | \(-0.340049\pi\) |
−0.876382 | + | 0.481617i | \(0.840049\pi\) | |||||||
\(318\) | 23.3772 | + | 23.3772i | 0.0735133 | + | 0.0735133i | ||||
\(319\) | −189.057 | + | 189.057i | −0.592655 | + | 0.592655i | ||||
\(320\) | 12.5548 | − | 12.5548i | 0.0392338 | − | 0.0392338i | ||||
\(321\) | −310.438 | −0.967098 | ||||||||
\(322\) | 201.329i | 0.625245i | ||||||||
\(323\) | −50.5132 | + | 50.5132i | −0.156388 | + | 0.156388i | ||||
\(324\) | − | 217.982i | − | 0.672785i | ||||||
\(325\) | −207.517 | − | 244.167i | −0.638515 | − | 0.751282i | ||||
\(326\) | −59.1623 | −0.181479 | ||||||||
\(327\) | −183.305 | − | 183.305i | −0.560566 | − | 0.560566i | ||||
\(328\) | 306.816 | 0.935414 | ||||||||
\(329\) | 100.359i | 0.305044i | ||||||||
\(330\) | 34.2456 | + | 34.2456i | 0.103774 | + | 0.103774i | ||||
\(331\) | 309.982 | + | 309.982i | 0.936502 | + | 0.936502i | 0.998101 | − | 0.0615988i | \(-0.0196199\pi\) |
−0.0615988 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(332\) | −173.649 | + | 173.649i | −0.523039 | + | 0.523039i | ||||
\(333\) | 18.2939 | − | 18.2939i | 0.0549368 | − | 0.0549368i | ||||
\(334\) | 1067.48 | 3.19605 | ||||||||
\(335\) | − | 67.9253i | − | 0.202762i | ||||||
\(336\) | 103.235 | − | 103.235i | 0.307246 | − | 0.307246i | ||||
\(337\) | 5.32456i | 0.0157999i | 0.999969 | + | 0.00789993i | \(0.00251465\pi\) | ||||
−0.999969 | + | 0.00789993i | \(0.997485\pi\) | |||||||
\(338\) | −500.831 | + | 360.182i | −1.48175 | + | 1.06563i | ||||
\(339\) | −234.702 | −0.692336 | ||||||||
\(340\) | 62.3883 | + | 62.3883i | 0.183495 | + | 0.183495i | ||||
\(341\) | −285.465 | −0.837140 | ||||||||
\(342\) | − | 70.5964i | − | 0.206422i | ||||||
\(343\) | −133.336 | − | 133.336i | −0.388733 | − | 0.388733i | ||||
\(344\) | −158.230 | − | 158.230i | −0.459972 | − | 0.459972i | ||||
\(345\) | −24.8947 | + | 24.8947i | −0.0721584 | + | 0.0721584i | ||||
\(346\) | −235.868 | + | 235.868i | −0.681700 | + | 0.681700i | ||||
\(347\) | −47.2413 | −0.136142 | −0.0680710 | − | 0.997680i | \(-0.521684\pi\) | ||||
−0.0680710 | + | 0.997680i | \(0.521684\pi\) | |||||||
\(348\) | 520.416i | 1.49545i | ||||||||
\(349\) | 223.581 | − | 223.581i | 0.640634 | − | 0.640634i | −0.310078 | − | 0.950711i | \(-0.600355\pi\) |
0.950711 | + | 0.310078i | \(0.100355\pi\) | |||||||
\(350\) | − | 180.544i | − | 0.515839i | ||||||
\(351\) | −285.397 | + | 242.559i | −0.813096 | + | 0.691052i | ||||
\(352\) | −467.004 | −1.32672 | ||||||||
\(353\) | 110.320 | + | 110.320i | 0.312522 | + | 0.312522i | 0.845886 | − | 0.533364i | \(-0.179072\pi\) |
−0.533364 | + | 0.845886i | \(0.679072\pi\) | |||||||
\(354\) | 337.903 | 0.954529 | ||||||||
\(355\) | 42.2591i | 0.119040i | ||||||||
\(356\) | 849.557 | + | 849.557i | 2.38639 | + | 2.38639i | ||||
\(357\) | 49.0068 | + | 49.0068i | 0.137274 | + | 0.137274i | ||||
\(358\) | −184.993 | + | 184.993i | −0.516741 | + | 0.516741i | ||||
\(359\) | 63.2149 | − | 63.2149i | 0.176086 | − | 0.176086i | −0.613561 | − | 0.789647i | \(-0.710264\pi\) |
0.789647 | + | 0.613561i | \(0.210264\pi\) | |||||||
\(360\) | −49.7893 | −0.138304 | ||||||||
\(361\) | − | 341.000i | − | 0.944598i | ||||||
\(362\) | 707.605 | − | 707.605i | 1.95471 | − | 1.95471i | ||||
\(363\) | 29.6271i | 0.0816172i | ||||||||
\(364\) | −242.438 | − | 19.6712i | −0.666040 | − | 0.0540417i | ||||
\(365\) | −26.4911 | −0.0725784 | ||||||||
\(366\) | 377.706 | + | 377.706i | 1.03198 | + | 1.03198i | ||||
\(367\) | −318.416 | −0.867620 | −0.433810 | − | 0.901004i | \(-0.642831\pi\) | ||||
−0.433810 | + | 0.901004i | \(0.642831\pi\) | |||||||
\(368\) | − | 924.907i | − | 2.51334i | ||||||
\(369\) | −48.2719 | − | 48.2719i | −0.130818 | − | 0.130818i | ||||
\(370\) | 9.14697 | + | 9.14697i | 0.0247216 | + | 0.0247216i | ||||
\(371\) | 5.94306 | − | 5.94306i | 0.0160190 | − | 0.0160190i | ||||
\(372\) | −392.899 | + | 392.899i | −1.05618 | + | 1.05618i | ||||
\(373\) | 8.87688 | 0.0237986 | 0.0118993 | − | 0.999929i | \(-0.496212\pi\) | ||||
0.0118993 | + | 0.999929i | \(0.496212\pi\) | |||||||
\(374\) | − | 603.986i | − | 1.61494i | ||||||
\(375\) | 44.9669 | − | 44.9669i | 0.119912 | − | 0.119912i | ||||
\(376\) | − | 972.105i | − | 2.58538i | ||||||
\(377\) | 255.680 | − | 217.302i | 0.678196 | − | 0.576399i | ||||
\(378\) | −211.031 | −0.558282 | ||||||||
\(379\) | −144.698 | − | 144.698i | −0.381788 | − | 0.381788i | 0.489958 | − | 0.871746i | \(-0.337012\pi\) |
−0.871746 | + | 0.489958i | \(0.837012\pi\) | |||||||
\(380\) | 24.7018 | 0.0650047 | ||||||||
\(381\) | − | 205.065i | − | 0.538230i | ||||||
\(382\) | −463.846 | − | 463.846i | −1.21426 | − | 1.21426i | ||||
\(383\) | 357.261 | + | 357.261i | 0.932796 | + | 0.932796i | 0.997880 | − | 0.0650838i | \(-0.0207315\pi\) |
−0.0650838 | + | 0.997880i | \(0.520731\pi\) | |||||||
\(384\) | 108.441 | − | 108.441i | 0.282398 | − | 0.282398i | ||||
\(385\) | 8.70605 | − | 8.70605i | 0.0226131 | − | 0.0226131i | ||||
\(386\) | 5.86406 | 0.0151919 | ||||||||
\(387\) | 49.7893i | 0.128655i | ||||||||
\(388\) | −814.548 | + | 814.548i | −2.09935 | + | 2.09935i | ||||
\(389\) | 438.342i | 1.12684i | 0.826170 | + | 0.563421i | \(0.190515\pi\) | ||||
−0.826170 | + | 0.563421i | \(0.809485\pi\) | |||||||
\(390\) | −39.3619 | − | 46.3135i | −0.100928 | − | 0.118753i | ||||
\(391\) | 439.065 | 1.12293 | ||||||||
\(392\) | 618.092 | + | 618.092i | 1.57676 | + | 1.57676i | ||||
\(393\) | −242.754 | −0.617694 | ||||||||
\(394\) | − | 732.557i | − | 1.85928i | ||||||
\(395\) | 21.2719 | + | 21.2719i | 0.0538529 | + | 0.0538529i | ||||
\(396\) | 295.359 | + | 295.359i | 0.745857 | + | 0.745857i | ||||
\(397\) | 250.061 | − | 250.061i | 0.629877 | − | 0.629877i | −0.318160 | − | 0.948037i | \(-0.603065\pi\) |
0.948037 | + | 0.318160i | \(0.103065\pi\) | |||||||
\(398\) | −670.473 | + | 670.473i | −1.68461 | + | 1.68461i | ||||
\(399\) | 19.4036 | 0.0486305 | ||||||||
\(400\) | 829.421i | 2.07355i | ||||||||
\(401\) | 93.7018 | − | 93.7018i | 0.233670 | − | 0.233670i | −0.580553 | − | 0.814223i | \(-0.697163\pi\) |
0.814223 | + | 0.580553i | \(0.197163\pi\) | |||||||
\(402\) | 905.074i | 2.25143i | ||||||||
\(403\) | 357.088 | + | 28.9737i | 0.886073 | + | 0.0718950i | ||||
\(404\) | 83.1843 | 0.205902 | ||||||||
\(405\) | −9.79181 | − | 9.79181i | −0.0241773 | − | 0.0241773i | ||||
\(406\) | 189.057 | 0.465657 | ||||||||
\(407\) | − | 61.9694i | − | 0.152259i | ||||||
\(408\) | −474.691 | − | 474.691i | −1.16346 | − | 1.16346i | ||||
\(409\) | 370.140 | + | 370.140i | 0.904988 | + | 0.904988i | 0.995862 | − | 0.0908741i | \(-0.0289661\pi\) |
−0.0908741 | + | 0.995862i | \(0.528966\pi\) | |||||||
\(410\) | 24.1359 | − | 24.1359i | 0.0588682 | − | 0.0588682i | ||||
\(411\) | 187.530 | − | 187.530i | 0.456278 | − | 0.456278i | ||||
\(412\) | −554.197 | −1.34514 | ||||||||
\(413\) | − | 85.9032i | − | 0.207998i | ||||||
\(414\) | −306.816 | + | 306.816i | −0.741101 | + | 0.741101i | ||||
\(415\) | 15.6007i | 0.0375921i | ||||||||
\(416\) | 584.175 | + | 47.3993i | 1.40427 | + | 0.113941i | ||||
\(417\) | 169.824 | 0.407252 | ||||||||
\(418\) | −119.570 | − | 119.570i | −0.286053 | − | 0.286053i | ||||
\(419\) | −658.767 | −1.57224 | −0.786118 | − | 0.618076i | \(-0.787912\pi\) | ||||
−0.786118 | + | 0.618076i | \(0.787912\pi\) | |||||||
\(420\) | − | 23.9651i | − | 0.0570598i | ||||||
\(421\) | −80.3135 | − | 80.3135i | −0.190768 | − | 0.190768i | 0.605260 | − | 0.796028i | \(-0.293069\pi\) |
−0.796028 | + | 0.605260i | \(0.793069\pi\) | |||||||
\(422\) | −840.353 | − | 840.353i | −1.99136 | − | 1.99136i | ||||
\(423\) | −152.943 | + | 152.943i | −0.361568 | + | 0.361568i | ||||
\(424\) | −57.5658 | + | 57.5658i | −0.135768 | + | 0.135768i | ||||
\(425\) | −393.737 | −0.926439 | ||||||||
\(426\) | − | 563.083i | − | 1.32179i | ||||||
\(427\) | 96.0221 | − | 96.0221i | 0.224876 | − | 0.224876i | ||||
\(428\) | − | 1338.73i | − | 3.12787i | ||||||
\(429\) | −23.5480 | + | 290.219i | −0.0548906 | + | 0.676502i | ||||
\(430\) | −24.8947 | −0.0578946 | ||||||||
\(431\) | 296.037 | + | 296.037i | 0.686862 | + | 0.686862i | 0.961537 | − | 0.274675i | \(-0.0885704\pi\) |
−0.274675 | + | 0.961537i | \(0.588570\pi\) | |||||||
\(432\) | 969.478 | 2.24416 | ||||||||
\(433\) | 156.140i | 0.360601i | 0.983612 | + | 0.180300i | \(0.0577070\pi\) | ||||
−0.983612 | + | 0.180300i | \(0.942293\pi\) | |||||||
\(434\) | 142.732 | + | 142.732i | 0.328876 | + | 0.328876i | ||||
\(435\) | 23.3772 | + | 23.3772i | 0.0537407 | + | 0.0537407i | ||||
\(436\) | 790.480 | − | 790.480i | 1.81303 | − | 1.81303i | ||||
\(437\) | 86.9210 | − | 86.9210i | 0.198904 | − | 0.198904i | ||||
\(438\) | 352.982 | 0.805895 | ||||||||
\(439\) | 448.710i | 1.02212i | 0.859545 | + | 0.511060i | \(0.170747\pi\) | ||||
−0.859545 | + | 0.511060i | \(0.829253\pi\) | |||||||
\(440\) | −84.3288 | + | 84.3288i | −0.191656 | + | 0.191656i | ||||
\(441\) | − | 194.491i | − | 0.441023i | ||||||
\(442\) | −61.3025 | + | 755.526i | −0.138693 | + | 1.70933i | ||||
\(443\) | −577.372 | −1.30332 | −0.651662 | − | 0.758510i | \(-0.725928\pi\) | ||||
−0.651662 | + | 0.758510i | \(0.725928\pi\) | |||||||
\(444\) | −85.2915 | − | 85.2915i | −0.192098 | − | 0.192098i | ||||
\(445\) | 76.3246 | 0.171516 | ||||||||
\(446\) | 1258.43i | 2.82159i | ||||||||
\(447\) | −277.246 | − | 277.246i | −0.620236 | − | 0.620236i | ||||
\(448\) | 42.5285 | + | 42.5285i | 0.0949296 | + | 0.0949296i | ||||
\(449\) | −107.127 | + | 107.127i | −0.238591 | + | 0.238591i | −0.816267 | − | 0.577675i | \(-0.803960\pi\) |
0.577675 | + | 0.816267i | \(0.303960\pi\) | |||||||
\(450\) | 275.140 | − | 275.140i | 0.611423 | − | 0.611423i | ||||
\(451\) | −163.517 | −0.362566 | ||||||||
\(452\) | − | 1012.12i | − | 2.23921i | ||||||
\(453\) | 63.0900 | − | 63.0900i | 0.139272 | − | 0.139272i | ||||
\(454\) | 520.009i | 1.14539i | ||||||||
\(455\) | −11.7740 | + | 10.0068i | −0.0258770 | + | 0.0219929i | ||||
\(456\) | −187.947 | −0.412165 | ||||||||
\(457\) | −356.092 | − | 356.092i | −0.779194 | − | 0.779194i | 0.200499 | − | 0.979694i | \(-0.435744\pi\) |
−0.979694 | + | 0.200499i | \(0.935744\pi\) | |||||||
\(458\) | 1240.84 | 2.70925 | ||||||||
\(459\) | 460.223i | 1.00267i | ||||||||
\(460\) | −107.355 | − | 107.355i | −0.233381 | − | 0.233381i | ||||
\(461\) | 33.7477 | + | 33.7477i | 0.0732054 | + | 0.0732054i | 0.742761 | − | 0.669556i | \(-0.233516\pi\) |
−0.669556 | + | 0.742761i | \(0.733516\pi\) | |||||||
\(462\) | −116.004 | + | 116.004i | −0.251092 | + | 0.251092i | ||||
\(463\) | 336.355 | − | 336.355i | 0.726469 | − | 0.726469i | −0.243446 | − | 0.969915i | \(-0.578278\pi\) |
0.969915 | + | 0.243446i | \(0.0782777\pi\) | |||||||
\(464\) | −868.530 | −1.87183 | ||||||||
\(465\) | 35.2982i | 0.0759102i | ||||||||
\(466\) | −27.8488 | + | 27.8488i | −0.0597613 | + | 0.0597613i | ||||
\(467\) | − | 308.263i | − | 0.660093i | −0.943965 | − | 0.330046i | \(-0.892936\pi\) | ||
0.943965 | − | 0.330046i | \(-0.107064\pi\) | |||||||
\(468\) | −339.487 | − | 399.443i | −0.725399 | − | 0.853510i | ||||
\(469\) | 230.092 | 0.490601 | ||||||||
\(470\) | −76.4715 | − | 76.4715i | −0.162705 | − | 0.162705i | ||||
\(471\) | 502.824 | 1.06757 | ||||||||
\(472\) | 832.078i | 1.76288i | ||||||||
\(473\) | 84.3288 | + | 84.3288i | 0.178285 | + | 0.178285i | ||||
\(474\) | −283.438 | − | 283.438i | −0.597971 | − | 0.597971i | ||||
\(475\) | −77.9473 | + | 77.9473i | −0.164100 | + | 0.164100i | ||||
\(476\) | −211.336 | + | 211.336i | −0.443982 | + | 0.443982i | ||||
\(477\) | 18.1139 | 0.0379746 | ||||||||
\(478\) | 505.982i | 1.05854i | ||||||||
\(479\) | 76.6424 | − | 76.6424i | 0.160005 | − | 0.160005i | −0.622564 | − | 0.782569i | \(-0.713909\pi\) |
0.782569 | + | 0.622564i | \(0.213909\pi\) | |||||||
\(480\) | 57.7459i | 0.120304i | ||||||||
\(481\) | −6.28967 | + | 77.5174i | −0.0130762 | + | 0.161159i | ||||
\(482\) | 1012.82 | 2.10130 | ||||||||
\(483\) | −84.3288 | − | 84.3288i | −0.174594 | − | 0.174594i | ||||
\(484\) | −127.763 | −0.263973 | ||||||||
\(485\) | 73.1794i | 0.150885i | ||||||||
\(486\) | −538.824 | − | 538.824i | −1.10869 | − | 1.10869i | ||||
\(487\) | −69.0655 | − | 69.0655i | −0.141818 | − | 0.141818i | 0.632633 | − | 0.774452i | \(-0.281974\pi\) |
−0.774452 | + | 0.632633i | \(0.781974\pi\) | |||||||
\(488\) | −930.092 | + | 930.092i | −1.90593 | + | 1.90593i | ||||
\(489\) | 24.7808 | − | 24.7808i | 0.0506764 | − | 0.0506764i | ||||
\(490\) | 97.2456 | 0.198460 | ||||||||
\(491\) | − | 685.302i | − | 1.39573i | −0.716230 | − | 0.697864i | \(-0.754134\pi\) | ||
0.716230 | − | 0.697864i | \(-0.245866\pi\) | |||||||
\(492\) | −225.057 | + | 225.057i | −0.457433 | + | 0.457433i | ||||
\(493\) | − | 412.302i | − | 0.836313i | ||||||
\(494\) | 137.434 | + | 161.706i | 0.278207 | + | 0.327340i | ||||
\(495\) | 26.5352 | 0.0536065 | ||||||||
\(496\) | −655.715 | − | 655.715i | −1.32201 | − | 1.32201i | ||||
\(497\) | −143.149 | −0.288027 | ||||||||
\(498\) | − | 207.873i | − | 0.417415i | ||||||
\(499\) | 349.329 | + | 349.329i | 0.700058 | + | 0.700058i | 0.964423 | − | 0.264365i | \(-0.0851623\pi\) |
−0.264365 | + | 0.964423i | \(0.585162\pi\) | |||||||
\(500\) | 193.914 | + | 193.914i | 0.387828 | + | 0.387828i | ||||
\(501\) | −447.127 | + | 447.127i | −0.892468 | + | 0.892468i | ||||
\(502\) | −247.381 | + | 247.381i | −0.492792 | + | 0.492792i | ||||
\(503\) | 42.2719 | 0.0840395 | 0.0420198 | − | 0.999117i | \(-0.486621\pi\) | ||||
0.0420198 | + | 0.999117i | \(0.486621\pi\) | |||||||
\(504\) | − | 168.658i | − | 0.334638i | ||||||
\(505\) | 3.73666 | − | 3.73666i | 0.00739933 | − | 0.00739933i | ||||
\(506\) | 1039.32i | 2.05398i | ||||||||
\(507\) | 58.9125 | − | 360.645i | 0.116198 | − | 0.711331i | ||||
\(508\) | 884.320 | 1.74079 | ||||||||
\(509\) | 184.280 | + | 184.280i | 0.362044 | + | 0.362044i | 0.864565 | − | 0.502521i | \(-0.167594\pi\) |
−0.502521 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(510\) | −74.6840 | −0.146439 | ||||||||
\(511\) | − | 89.7367i | − | 0.175610i | ||||||
\(512\) | 777.103 | + | 777.103i | 1.51778 | + | 1.51778i | ||||
\(513\) | 91.1096 | + | 91.1096i | 0.177602 | + | 0.177602i | ||||
\(514\) | 1163.01 | − | 1163.01i | 2.26266 | − | 2.26266i | ||||
\(515\) | −24.8947 | + | 24.8947i | −0.0483392 | + | 0.0483392i | ||||
\(516\) | 232.132 | 0.449868 | ||||||||
\(517\) | 518.083i | 1.00210i | ||||||||
\(518\) | −30.9847 | + | 30.9847i | −0.0598160 | + | 0.0598160i | ||||
\(519\) | − | 197.592i | − | 0.380717i | ||||||
\(520\) | 114.046 | − | 96.9278i | 0.219319 | − | 0.186400i | ||||
\(521\) | −757.122 | −1.45321 | −0.726605 | − | 0.687055i | \(-0.758903\pi\) | ||||
−0.726605 | + | 0.687055i | \(0.758903\pi\) | |||||||
\(522\) | 288.114 | + | 288.114i | 0.551942 | + | 0.551942i | ||||
\(523\) | −221.851 | −0.424188 | −0.212094 | − | 0.977249i | \(-0.568028\pi\) | ||||
−0.212094 | + | 0.977249i | \(0.568028\pi\) | |||||||
\(524\) | − | 1046.85i | − | 1.99780i | ||||||
\(525\) | 75.6228 | + | 75.6228i | 0.144043 | + | 0.144043i | ||||
\(526\) | −431.004 | − | 431.004i | −0.819400 | − | 0.819400i | ||||
\(527\) | 311.276 | − | 311.276i | 0.590657 | − | 0.590657i | ||||
\(528\) | 532.925 | − | 532.925i | 1.00933 | − | 1.00933i | ||||
\(529\) | −226.526 | −0.428215 | ||||||||
\(530\) | 9.05694i | 0.0170886i | ||||||||
\(531\) | 130.912 | − | 130.912i | 0.246539 | − | 0.246539i | ||||
\(532\) | 83.6754i | 0.157285i | ||||||||
\(533\) | 204.544 | + | 16.5964i | 0.383759 | + | 0.0311378i | ||||
\(534\) | −1016.99 | −1.90448 | ||||||||
\(535\) | −60.1359 | − | 60.1359i | −0.112404 | − | 0.112404i | ||||
\(536\) | −2228.72 | −4.15806 | ||||||||
\(537\) | − | 154.973i | − | 0.288590i | ||||||
\(538\) | −438.952 | − | 438.952i | −0.815895 | − | 0.815895i | ||||
\(539\) | −329.412 | − | 329.412i | −0.611154 | − | 0.611154i | ||||
\(540\) | 112.528 | − | 112.528i | 0.208386 | − | 0.208386i | ||||
\(541\) | −243.379 | + | 243.379i | −0.449869 | + | 0.449869i | −0.895311 | − | 0.445442i | \(-0.853047\pi\) |
0.445442 | + | 0.895311i | \(0.353047\pi\) | |||||||
\(542\) | 1120.59 | 2.06750 | ||||||||
\(543\) | 592.777i | 1.09167i | ||||||||
\(544\) | 509.230 | − | 509.230i | 0.936085 | − | 0.936085i | ||||
\(545\) | − | 71.0171i | − | 0.130307i | ||||||
\(546\) | 156.884 | − | 133.336i | 0.287333 | − | 0.244204i | ||||
\(547\) | −317.777 | −0.580944 | −0.290472 | − | 0.956883i | \(-0.593812\pi\) | ||||
−0.290472 | + | 0.956883i | \(0.593812\pi\) | |||||||
\(548\) | 808.701 | + | 808.701i | 1.47573 | + | 1.47573i | ||||
\(549\) | 292.666 | 0.533090 | ||||||||
\(550\) | − | 932.017i | − | 1.69458i | ||||||
\(551\) | −81.6228 | − | 81.6228i | −0.148136 | − | 0.148136i | ||||
\(552\) | 816.828 | + | 816.828i | 1.47976 | + | 1.47976i | ||||
\(553\) | −72.0569 | + | 72.0569i | −0.130302 | + | 0.130302i | ||||
\(554\) | 485.118 | − | 485.118i | 0.875665 | − | 0.875665i | ||||
\(555\) | −7.66262 | −0.0138065 | ||||||||
\(556\) | 732.346i | 1.31717i | ||||||||
\(557\) | −479.423 | + | 479.423i | −0.860724 | + | 0.860724i | −0.991422 | − | 0.130698i | \(-0.958278\pi\) |
0.130698 | + | 0.991422i | \(0.458278\pi\) | |||||||
\(558\) | 435.035i | 0.779632i | ||||||||
\(559\) | −96.9278 | − | 114.046i | −0.173395 | − | 0.204018i | ||||
\(560\) | 39.9957 | 0.0714209 | ||||||||
\(561\) | 252.986 | + | 252.986i | 0.450956 | + | 0.450956i | ||||
\(562\) | −1480.78 | −2.63484 | ||||||||
\(563\) | − | 461.671i | − | 0.820020i | −0.912081 | − | 0.410010i | \(-0.865525\pi\) | ||
0.912081 | − | 0.410010i | \(-0.134475\pi\) | |||||||
\(564\) | 713.063 | + | 713.063i | 1.26430 | + | 1.26430i | ||||
\(565\) | −45.4648 | − | 45.4648i | −0.0804686 | − | 0.0804686i | ||||
\(566\) | −1030.39 | + | 1030.39i | −1.82048 | + | 1.82048i | ||||
\(567\) | 33.1690 | − | 33.1690i | 0.0584992 | − | 0.0584992i | ||||
\(568\) | 1386.58 | 2.44116 | ||||||||
\(569\) | 523.394i | 0.919849i | 0.887958 | + | 0.459925i | \(0.152124\pi\) | ||||
−0.887958 | + | 0.459925i | \(0.847876\pi\) | |||||||
\(570\) | −14.7851 | + | 14.7851i | −0.0259387 | + | 0.0259387i | ||||
\(571\) | 115.715i | 0.202654i | 0.994853 | + | 0.101327i | \(0.0323088\pi\) | ||||
−0.994853 | + | 0.101327i | \(0.967691\pi\) | |||||||
\(572\) | −1251.53 | − | 101.548i | −2.18800 | − | 0.177532i | ||||
\(573\) | 388.574 | 0.678140 | ||||||||
\(574\) | 81.7587 | + | 81.7587i | 0.142437 | + | 0.142437i | ||||
\(575\) | 677.526 | 1.17831 | ||||||||
\(576\) | 129.623i | 0.225040i | ||||||||
\(577\) | 130.158 | + | 130.158i | 0.225577 | + | 0.225577i | 0.810842 | − | 0.585265i | \(-0.199010\pi\) |
−0.585265 | + | 0.810842i | \(0.699010\pi\) | |||||||
\(578\) | −87.3509 | − | 87.3509i | −0.151126 | − | 0.151126i | ||||
\(579\) | −2.45623 | + | 2.45623i | −0.00424219 | + | 0.00424219i | ||||
\(580\) | −100.811 | + | 100.811i | −0.173813 | + | 0.173813i | ||||
\(581\) | −52.8463 | −0.0909574 | ||||||||
\(582\) | − | 975.083i | − | 1.67540i | ||||||
\(583\) | 30.6797 | − | 30.6797i | 0.0526239 | − | 0.0526239i | ||||
\(584\) | 869.210i | 1.48837i | ||||||||
\(585\) | −33.1929 | − | 2.69323i | −0.0567400 | − | 0.00460382i | ||||
\(586\) | −702.873 | −1.19944 | ||||||||
\(587\) | −347.311 | − | 347.311i | −0.591671 | − | 0.591671i | 0.346411 | − | 0.938083i | \(-0.387400\pi\) |
−0.938083 | + | 0.346411i | \(0.887400\pi\) | |||||||
\(588\) | −906.772 | −1.54213 | ||||||||
\(589\) | − | 123.246i | − | 0.209245i | ||||||
\(590\) | 65.4562 | + | 65.4562i | 0.110943 | + | 0.110943i | ||||
\(591\) | 306.840 | + | 306.840i | 0.519187 | + | 0.519187i | ||||
\(592\) | 142.344 | − | 142.344i | 0.240446 | − | 0.240446i | ||||
\(593\) | −240.285 | + | 240.285i | −0.405202 | + | 0.405202i | −0.880062 | − | 0.474860i | \(-0.842499\pi\) |
0.474860 | + | 0.880062i | \(0.342499\pi\) | |||||||
\(594\) | −1089.40 | −1.83400 | ||||||||
\(595\) | 18.9865i | 0.0319101i | ||||||||
\(596\) | 1195.59 | − | 1195.59i | 2.00602 | − | 2.00602i | ||||
\(597\) | − | 561.670i | − | 0.940822i | ||||||
\(598\) | 105.487 | − | 1300.08i | 0.176399 | − | 2.17404i | ||||
\(599\) | 1044.77 | 1.74419 | 0.872096 | − | 0.489334i | \(-0.162760\pi\) | ||||
0.872096 | + | 0.489334i | \(0.162760\pi\) | |||||||
\(600\) | −732.500 | − | 732.500i | −1.22083 | − | 1.22083i | ||||
\(601\) | 933.298 | 1.55291 | 0.776454 | − | 0.630174i | \(-0.217016\pi\) | ||||
0.776454 | + | 0.630174i | \(0.217016\pi\) | |||||||
\(602\) | − | 84.3288i | − | 0.140081i | ||||||
\(603\) | 350.649 | + | 350.649i | 0.581508 | + | 0.581508i | ||||
\(604\) | 272.068 | + | 272.068i | 0.450444 | + | 0.450444i | ||||
\(605\) | −5.73914 | + | 5.73914i | −0.00948619 | + | 0.00948619i | ||||
\(606\) | −49.7893 | + | 49.7893i | −0.0821606 | + | 0.0821606i | ||||
\(607\) | 579.912 | 0.955374 | 0.477687 | − | 0.878530i | \(-0.341475\pi\) | ||||
0.477687 | + | 0.878530i | \(0.341475\pi\) | |||||||
\(608\) | − | 201.623i | − | 0.331616i | ||||||
\(609\) | −79.1886 | + | 79.1886i | −0.130031 | + | 0.130031i | ||||
\(610\) | 146.333i | 0.239890i | ||||||||
\(611\) | 52.5836 | − | 648.070i | 0.0860616 | − | 1.06067i | ||||
\(612\) | −644.131 | −1.05250 | ||||||||
\(613\) | −288.460 | − | 288.460i | −0.470572 | − | 0.470572i | 0.431528 | − | 0.902100i | \(-0.357975\pi\) |
−0.902100 | + | 0.431528i | \(0.857975\pi\) | |||||||
\(614\) | 1216.67 | 1.98154 | ||||||||
\(615\) | 20.2192i | 0.0328768i | ||||||||
\(616\) | −285.658 | − | 285.658i | −0.463730 | − | 0.463730i | ||||
\(617\) | 95.4121 | + | 95.4121i | 0.154639 | + | 0.154639i | 0.780186 | − | 0.625547i | \(-0.215124\pi\) |
−0.625547 | + | 0.780186i | \(0.715124\pi\) | |||||||
\(618\) | 331.710 | − | 331.710i | 0.536748 | − | 0.536748i | ||||
\(619\) | −544.952 | + | 544.952i | −0.880374 | + | 0.880374i | −0.993572 | − | 0.113198i | \(-0.963890\pi\) |
0.113198 | + | 0.993572i | \(0.463890\pi\) | |||||||
\(620\) | −152.219 | −0.245515 | ||||||||
\(621\) | − | 791.934i | − | 1.27526i | ||||||
\(622\) | −293.434 | + | 293.434i | −0.471759 | + | 0.471759i | ||||
\(623\) | 258.544i | 0.414998i | ||||||||
\(624\) | −720.726 | + | 612.546i | −1.15501 | + | 0.981644i | ||||
\(625\) | −598.806 | −0.958090 | ||||||||
\(626\) | −576.840 | − | 576.840i | −0.921469 | − | 0.921469i | ||||
\(627\) | 100.167 | 0.159755 | ||||||||
\(628\) | 2168.37i | 3.45281i | ||||||||
\(629\) | 67.5726 | + | 67.5726i | 0.107429 | + | 0.107429i | ||||
\(630\) | −13.2676 | − | 13.2676i | −0.0210597 | − | 0.0210597i | ||||
\(631\) | −642.537 | + | 642.537i | −1.01828 | + | 1.01828i | −0.0184540 | + | 0.999830i | \(0.505874\pi\) |
−0.999830 | + | 0.0184540i | \(0.994126\pi\) | |||||||
\(632\) | 697.960 | − | 697.960i | 1.10437 | − | 1.10437i | ||||
\(633\) | 703.982 | 1.11214 | ||||||||
\(634\) | 646.009i | 1.01894i | ||||||||
\(635\) | 39.7238 | − | 39.7238i | 0.0625572 | − | 0.0625572i | ||||
\(636\) | − | 84.4520i | − | 0.132786i | ||||||
\(637\) | 378.627 | + | 445.495i | 0.594391 | + | 0.699365i | ||||
\(638\) | 975.964 | 1.52972 | ||||||||
\(639\) | −218.153 | − | 218.153i | −0.341398 | − | 0.341398i | ||||
\(640\) | 42.0128 | 0.0656450 | ||||||||
\(641\) | − | 487.290i | − | 0.760202i | −0.924945 | − | 0.380101i | \(-0.875889\pi\) | ||
0.924945 | − | 0.380101i | \(-0.124111\pi\) | |||||||
\(642\) | 801.285 | + | 801.285i | 1.24811 | + | 1.24811i | ||||
\(643\) | −797.688 | − | 797.688i | −1.24057 | − | 1.24057i | −0.959764 | − | 0.280809i | \(-0.909397\pi\) |
−0.280809 | − | 0.959764i | \(-0.590603\pi\) | |||||||
\(644\) | 363.658 | − | 363.658i | 0.564686 | − | 0.564686i | ||||
\(645\) | 10.4274 | − | 10.4274i | 0.0161665 | − | 0.0161665i | ||||
\(646\) | 260.763 | 0.403658 | ||||||||
\(647\) | 989.526i | 1.52941i | 0.644383 | + | 0.764703i | \(0.277114\pi\) | ||||
−0.644383 | + | 0.764703i | \(0.722886\pi\) | |||||||
\(648\) | −321.283 | + | 321.283i | −0.495807 | + | 0.495807i | ||||
\(649\) | − | 443.456i | − | 0.683292i | ||||||
\(650\) | −94.5964 | + | 1165.86i | −0.145533 | + | 1.79363i | ||||
\(651\) | −119.570 | −0.183671 | ||||||||
\(652\) | 106.864 | + | 106.864i | 0.163902 | + | 0.163902i | ||||
\(653\) | −86.3075 | −0.132171 | −0.0660853 | − | 0.997814i | \(-0.521051\pi\) | ||||
−0.0660853 | + | 0.997814i | \(0.521051\pi\) | |||||||
\(654\) | 946.271i | 1.44690i | ||||||||
\(655\) | −47.0245 | − | 47.0245i | −0.0717932 | − | 0.0717932i | ||||
\(656\) | −375.601 | − | 375.601i | −0.572562 | − | 0.572562i | ||||
\(657\) | 136.754 | − | 136.754i | 0.208150 | − | 0.208150i | ||||
\(658\) | 259.042 | − | 259.042i | 0.393680 | − | 0.393680i | ||||
\(659\) | −1184.99 | −1.79817 | −0.899083 | − | 0.437779i | \(-0.855765\pi\) | ||||
−0.899083 | + | 0.437779i | \(0.855765\pi\) | |||||||
\(660\) | − | 123.715i | − | 0.187446i | ||||||
\(661\) | −194.408 | + | 194.408i | −0.294112 | + | 0.294112i | −0.838702 | − | 0.544590i | \(-0.816685\pi\) |
0.544590 | + | 0.838702i | \(0.316685\pi\) | |||||||
\(662\) | − | 1600.21i | − | 2.41724i | ||||||
\(663\) | −290.783 | − | 342.138i | −0.438587 | − | 0.516045i | ||||
\(664\) | 511.881 | 0.770905 | ||||||||
\(665\) | 3.75872 | + | 3.75872i | 0.00565221 | + | 0.00565221i | ||||
\(666\) | −94.4384 | −0.141799 | ||||||||
\(667\) | 709.473i | 1.06368i | ||||||||
\(668\) | −1928.18 | − | 1928.18i | −2.88650 | − | 2.88650i | ||||
\(669\) | −527.107 | − | 527.107i | −0.787903 | − | 0.787903i | ||||
\(670\) | −175.325 | + | 175.325i | −0.261678 | + | 0.261678i | ||||
\(671\) | 495.693 | − | 495.693i | 0.738737 | − | 0.738737i | ||||
\(672\) | −195.610 | −0.291086 | ||||||||
\(673\) | − | 615.500i | − | 0.914561i | −0.889322 | − | 0.457281i | \(-0.848824\pi\) | ||
0.889322 | − | 0.457281i | \(-0.151176\pi\) | |||||||
\(674\) | 13.7434 | − | 13.7434i | 0.0203908 | − | 0.0203908i | ||||
\(675\) | 710.175i | 1.05211i | ||||||||
\(676\) | 1555.24 | + | 254.053i | 2.30065 | + | 0.375818i | ||||
\(677\) | −412.031 | −0.608612 | −0.304306 | − | 0.952574i | \(-0.598425\pi\) | ||||
−0.304306 | + | 0.952574i | \(0.598425\pi\) | |||||||
\(678\) | 605.798 | + | 605.798i | 0.893507 | + | 0.893507i | ||||
\(679\) | −247.890 | −0.365081 | ||||||||
\(680\) | − | 183.907i | − | 0.270452i | ||||||
\(681\) | −217.811 | − | 217.811i | −0.319841 | − | 0.319841i | ||||
\(682\) | 736.824 | + | 736.824i | 1.08039 | + | 1.08039i | ||||
\(683\) | 129.044 | − | 129.044i | 0.188937 | − | 0.188937i | −0.606299 | − | 0.795237i | \(-0.707347\pi\) |
0.795237 | + | 0.606299i | \(0.207347\pi\) | |||||||
\(684\) | −127.517 | + | 127.517i | −0.186429 | + | 0.186429i | ||||
\(685\) | 72.6541 | 0.106064 | ||||||||
\(686\) | 688.315i | 1.00338i | ||||||||
\(687\) | −519.738 | + | 519.738i | −0.756533 | + | 0.756533i | ||||
\(688\) | 387.408i | 0.563093i | ||||||||
\(689\) | −41.4911 | + | 35.2633i | −0.0602193 | + | 0.0511805i | ||||
\(690\) | 128.513 | 0.186251 | ||||||||
\(691\) | 727.105 | + | 727.105i | 1.05225 | + | 1.05225i | 0.998558 | + | 0.0536923i | \(0.0170990\pi\) |
0.0536923 | + | 0.998558i | \(0.482901\pi\) | |||||||
\(692\) | 852.092 | 1.23135 | ||||||||
\(693\) | 89.8861i | 0.129706i | ||||||||
\(694\) | 121.936 | + | 121.936i | 0.175701 | + | 0.175701i | ||||
\(695\) | 32.8971 | + | 32.8971i | 0.0473340 | + | 0.0473340i | ||||
\(696\) | 767.039 | − | 767.039i | 1.10207 | − | 1.10207i | ||||
\(697\) | 178.302 | − | 178.302i | 0.255814 | − | 0.255814i | ||||
\(698\) | −1154.19 | −1.65356 | ||||||||
\(699\) | − | 23.3295i | − | 0.0333756i | ||||||
\(700\) | −326.114 | + | 326.114i | −0.465877 | + | 0.465877i | ||||
\(701\) | 635.934i | 0.907181i | 0.891210 | + | 0.453590i | \(0.149857\pi\) | ||||
−0.891210 | + | 0.453590i | \(0.850143\pi\) | |||||||
\(702\) | 1362.73 | + | 110.570i | 1.94121 | + | 0.157507i | ||||
\(703\) | 26.7544 | 0.0380575 | ||||||||
\(704\) | 219.544 | + | 219.544i | 0.311852 | + | 0.311852i | ||||
\(705\) | 64.0619 | 0.0908680 | ||||||||
\(706\) | − | 569.504i | − | 0.806663i | ||||||
\(707\) | 12.6577 | + | 12.6577i | 0.0179033 | + | 0.0179033i | ||||
\(708\) | −610.350 | − | 610.350i | −0.862077 | − | 0.862077i | ||||
\(709\) | 695.315 | − | 695.315i | 0.980699 | − | 0.980699i | −0.0191186 | − | 0.999817i | \(-0.506086\pi\) |
0.999817 | + | 0.0191186i | \(0.00608601\pi\) | |||||||
\(710\) | 109.077 | − | 109.077i | 0.153629 | − | 0.153629i | ||||
\(711\) | −219.623 | −0.308893 | ||||||||
\(712\) | − | 2504.31i | − | 3.51730i | ||||||
\(713\) | −535.631 | + | 535.631i | −0.751236 | + | 0.751236i | ||||
\(714\) | − | 252.986i | − | 0.354323i | ||||||
\(715\) | −60.7808 | + | 51.6577i | −0.0850081 | + | 0.0722485i | ||||
\(716\) | 668.302 | 0.933382 | ||||||||
\(717\) | −211.936 | − | 211.936i | −0.295588 | − | 0.295588i | ||||
\(718\) | −326.333 | −0.454503 | ||||||||
\(719\) | − | 859.565i | − | 1.19550i | −0.801682 | − | 0.597750i | \(-0.796061\pi\) | ||
0.801682 | − | 0.597750i | \(-0.203939\pi\) | |||||||
\(720\) | 60.9516 | + | 60.9516i | 0.0846550 | + | 0.0846550i | ||||
\(721\) | −84.3288 | − | 84.3288i | −0.116961 | − | 0.116961i | ||||
\(722\) | −880.168 | + | 880.168i | −1.21907 | + | 1.21907i | ||||
\(723\) | −424.233 | + | 424.233i | −0.586767 | + | 0.586767i | ||||
\(724\) | −2556.28 | −3.53077 | ||||||||
\(725\) | − | 636.228i | − | 0.877556i | ||||||
\(726\) | 76.4715 | − | 76.4715i | 0.105333 | − | 0.105333i | ||||
\(727\) | 437.337i | 0.601564i | 0.953693 | + | 0.300782i | \(0.0972477\pi\) | ||||
−0.953693 | + | 0.300782i | \(0.902752\pi\) | |||||||
\(728\) | 328.336 | + | 386.322i | 0.451010 | + | 0.530662i | ||||
\(729\) | 661.780 | 0.907792 | ||||||||
\(730\) | 68.3772 | + | 68.3772i | 0.0936674 | + | 0.0936674i | ||||
\(731\) | −183.907 | −0.251583 | ||||||||
\(732\) | − | 1364.49i | − | 1.86406i | ||||||
\(733\) | 39.5591 | + | 39.5591i | 0.0539687 | + | 0.0539687i | 0.733576 | − | 0.679607i | \(-0.237850\pi\) |
−0.679607 | + | 0.733576i | \(0.737850\pi\) | |||||||
\(734\) | 821.877 | + | 821.877i | 1.11972 | + | 1.11972i | ||||
\(735\) | −40.7324 | + | 40.7324i | −0.0554182 | + | 0.0554182i | ||||
\(736\) | −876.263 | + | 876.263i | −1.19057 | + | 1.19057i | ||||
\(737\) | 1187.80 | 1.61167 | ||||||||
\(738\) | 249.193i | 0.337660i | ||||||||
\(739\) | 919.732 | − | 919.732i | 1.24456 | − | 1.24456i | 0.286475 | − | 0.958088i | \(-0.407517\pi\) |
0.958088 | − | 0.286475i | \(-0.0924834\pi\) | |||||||
\(740\) | − | 33.0441i | − | 0.0446542i | ||||||
\(741\) | −125.298 | − | 10.1666i | −0.169093 | − | 0.0137200i | ||||
\(742\) | −30.6797 | −0.0413473 | ||||||||
\(743\) | 730.642 | + | 730.642i | 0.983368 | + | 0.983368i | 0.999864 | − | 0.0164960i | \(-0.00525109\pi\) |
−0.0164960 | + | 0.999864i | \(0.505251\pi\) | |||||||
\(744\) | 1158.18 | 1.55670 | ||||||||
\(745\) | − | 107.412i | − | 0.144177i | ||||||
\(746\) | −22.9125 | − | 22.9125i | −0.0307137 | − | 0.0307137i | ||||
\(747\) | −80.5352 | − | 80.5352i | −0.107812 | − | 0.107812i | ||||
\(748\) | −1090.97 | + | 1090.97i | −1.45852 | + | 1.45852i | ||||
\(749\) | 203.706 | − | 203.706i | 0.271971 | − | 0.271971i | ||||
\(750\) | −232.132 | −0.309509 | ||||||||
\(751\) | 199.764i | 0.265997i | 0.991116 | + | 0.132998i | \(0.0424605\pi\) | ||||
−0.991116 | + | 0.132998i | \(0.957539\pi\) | |||||||
\(752\) | −1190.04 | + | 1190.04i | −1.58250 | + | 1.58250i | ||||
\(753\) | − | 207.237i | − | 0.275215i | ||||||
\(754\) | −1220.83 | − | 99.0569i | −1.61914 | − | 0.131375i | ||||
\(755\) | 24.4427 | 0.0323745 | ||||||||
\(756\) | 381.182 | + | 381.182i | 0.504209 | + | 0.504209i | ||||
\(757\) | 124.549 | 0.164529 | 0.0822647 | − | 0.996611i | \(-0.473785\pi\) | ||||
0.0822647 | + | 0.996611i | \(0.473785\pi\) | |||||||
\(758\) | 746.969i | 0.985447i | ||||||||
\(759\) | −435.329 | − | 435.329i | −0.573556 | − | 0.573556i | ||||
\(760\) | −36.4078 | − | 36.4078i | −0.0479050 | − | 0.0479050i | ||||
\(761\) | 161.412 | − | 161.412i | 0.212105 | − | 0.212105i | −0.593056 | − | 0.805161i | \(-0.702079\pi\) |
0.805161 | + | 0.593056i | \(0.202079\pi\) | |||||||
\(762\) | −529.302 | + | 529.302i | −0.694623 | + | 0.694623i | ||||
\(763\) | 240.565 | 0.315289 | ||||||||
\(764\) | 1675.68i | 2.19330i | ||||||||
\(765\) | −28.9345 | + | 28.9345i | −0.0378229 | + | 0.0378229i | ||||
\(766\) | − | 1844.28i | − | 2.40768i | ||||||
\(767\) | −45.0092 | + | 554.719i | −0.0586822 | + | 0.723232i | ||||
\(768\) | −819.048 | −1.06647 | ||||||||
\(769\) | 137.947 | + | 137.947i | 0.179385 | + | 0.179385i | 0.791088 | − | 0.611703i | \(-0.209515\pi\) |
−0.611703 | + | 0.791088i | \(0.709515\pi\) | |||||||
\(770\) | −44.9431 | −0.0583676 | ||||||||
\(771\) | 974.276i | 1.26365i | ||||||||
\(772\) | −10.5922 | − | 10.5922i | −0.0137204 | − | 0.0137204i | ||||
\(773\) | 550.813 | + | 550.813i | 0.712566 | + | 0.712566i | 0.967071 | − | 0.254506i | \(-0.0819128\pi\) |
−0.254506 | + | 0.967071i | \(0.581913\pi\) | |||||||
\(774\) | 128.513 | − | 128.513i | 0.166038 | − | 0.166038i | ||||
\(775\) | 480.333 | − | 480.333i | 0.619785 | − | 0.619785i | ||||
\(776\) | 2401.12 | 3.09422 | ||||||||
\(777\) | − | 25.9566i | − | 0.0334061i | ||||||
\(778\) | 1131.42 | − | 1131.42i | 1.45427 | − | 1.45427i | ||||
\(779\) | − | 70.5964i | − | 0.0906244i | ||||||
\(780\) | −12.5566 | + | 154.754i | −0.0160982 | + | 0.198403i | ||||
\(781\) | −738.977 | −0.946194 | ||||||||
\(782\) | −1133.29 | − | 1133.29i | −1.44922 | − | 1.44922i | ||||
\(783\) | −743.662 | −0.949760 | ||||||||
\(784\) | − | 1513.32i | − | 1.93026i | ||||||
\(785\) | 97.4036 | + | 97.4036i | 0.124081 | + | 0.124081i | ||||
\(786\) | 626.581 | + | 626.581i | 0.797177 | + | 0.797177i | ||||
\(787\) | 729.434 | − | 729.434i | 0.926854 | − | 0.926854i | −0.0706473 | − | 0.997501i | \(-0.522506\pi\) |
0.997501 | + | 0.0706473i | \(0.0225065\pi\) | |||||||
\(788\) | −1323.21 | + | 1323.21i | −1.67920 | + | 1.67920i | ||||
\(789\) | 361.062 | 0.457620 | ||||||||
\(790\) | − | 109.811i | − | 0.139002i | ||||||
\(791\) | 154.009 | − | 154.009i | 0.194701 | − | 0.194701i | ||||
\(792\) | − | 870.658i | − | 1.09932i | ||||||
\(793\) | −670.372 | + | 569.750i | −0.845362 | + | 0.718474i | ||||
\(794\) | −1290.89 | −1.62580 | ||||||||
\(795\) | −3.79360 | − | 3.79360i | −0.00477183 | − | 0.00477183i | ||||
\(796\) | 2422.13 | 3.04288 | ||||||||
\(797\) | 444.974i | 0.558311i | 0.960246 | + | 0.279155i | \(0.0900545\pi\) | ||||
−0.960246 | + | 0.279155i | \(0.909946\pi\) | |||||||
\(798\) | −50.0833 | − | 50.0833i | −0.0627610 | − | 0.0627610i | ||||
\(799\) | −564.928 | − | 564.928i | −0.707043 | − | 0.707043i | ||||
\(800\) | 785.798 | − | 785.798i | 0.982247 | − | 0.982247i | ||||
\(801\) | −394.009 | + | 394.009i | −0.491896 | + | 0.491896i | ||||
\(802\) | −483.715 | −0.603135 | ||||||||
\(803\) | − | 463.246i | − | 0.576894i | ||||||
\(804\) | 1634.82 | − | 1634.82i | 2.03336 | − | 2.03336i | ||||
\(805\) | − | 32.6712i | − | 0.0405853i | ||||||
\(806\) | −846.907 | − | 996.478i | −1.05075 | − | 1.23632i | ||||
\(807\) | 367.720 | 0.455662 | ||||||||
\(808\) | −122.605 | − | 122.605i | −0.151739 | − | 0.151739i | ||||
\(809\) | −1090.36 | −1.34779 | −0.673893 | − | 0.738829i | \(-0.735379\pi\) | ||||
−0.673893 | + | 0.738829i | \(0.735379\pi\) | |||||||
\(810\) | 50.5480i | 0.0624050i | ||||||||
\(811\) | 445.614 | + | 445.614i | 0.549463 | + | 0.549463i | 0.926285 | − | 0.376823i | \(-0.122983\pi\) |
−0.376823 | + | 0.926285i | \(0.622983\pi\) | |||||||
\(812\) | −341.491 | − | 341.491i | −0.420556 | − | 0.420556i | ||||
\(813\) | −469.370 | + | 469.370i | −0.577331 | + | 0.577331i | ||||
\(814\) | −159.952 | + | 159.952i | −0.196501 | + | 0.196501i | ||||
\(815\) | 9.60072 | 0.0117800 | ||||||||
\(816\) | 1162.22i | 1.42429i | ||||||||
\(817\) | −36.4078 | + | 36.4078i | −0.0445628 | + | 0.0445628i | ||||
\(818\) | − | 1910.77i | − | 2.33590i | ||||||
\(819\) | 9.12312 | − | 112.438i | 0.0111393 | − | 0.137287i | ||||
\(820\) | −87.1929 | −0.106333 | ||||||||
\(821\) | −242.186 | − | 242.186i | −0.294989 | − | 0.294989i | 0.544058 | − | 0.839047i | \(-0.316887\pi\) |
−0.839047 | + | 0.544058i | \(0.816887\pi\) | |||||||
\(822\) | −968.083 | −1.17772 | ||||||||
\(823\) | 99.5787i | 0.120995i | 0.998168 | + | 0.0604974i | \(0.0192687\pi\) | ||||
−0.998168 | + | 0.0604974i | \(0.980731\pi\) | |||||||
\(824\) | 816.828 | + | 816.828i | 0.991297 | + | 0.991297i | ||||
\(825\) | 390.386 | + | 390.386i | 0.473195 | + | 0.473195i | ||||
\(826\) | −221.728 | + | 221.728i | −0.268436 | + | 0.268436i | ||||
\(827\) | −899.548 | + | 899.548i | −1.08772 | + | 1.08772i | −0.0919618 | + | 0.995763i | \(0.529314\pi\) |
−0.995763 | + | 0.0919618i | \(0.970686\pi\) | |||||||
\(828\) | 1108.39 | 1.33864 | ||||||||
\(829\) | − | 32.1103i | − | 0.0387338i | −0.999812 | − | 0.0193669i | \(-0.993835\pi\) | ||
0.999812 | − | 0.0193669i | \(-0.00616506\pi\) | |||||||
\(830\) | 40.2676 | − | 40.2676i | 0.0485152 | − | 0.0485152i | ||||
\(831\) | 406.394i | 0.489042i | ||||||||
\(832\) | −252.344 | − | 296.910i | −0.303298 | − | 0.356863i | ||||
\(833\) | 718.394 | 0.862418 | ||||||||
\(834\) | −438.340 | − | 438.340i | −0.525587 | − | 0.525587i | ||||
\(835\) | −173.228 | −0.207459 | ||||||||
\(836\) | 431.956i | 0.516694i | ||||||||
\(837\) | −561.443 | − | 561.443i | −0.670780 | − | 0.670780i | ||||
\(838\) | 1700.37 | + | 1700.37i | 2.02908 | + | 2.02908i | ||||
\(839\) | 408.794 | − | 408.794i | 0.487239 | − | 0.487239i | −0.420195 | − | 0.907434i | \(-0.638038\pi\) |
0.907434 | + | 0.420195i | \(0.138038\pi\) | |||||||
\(840\) | −35.3221 | + | 35.3221i | −0.0420501 | + | 0.0420501i | ||||
\(841\) | −174.772 | −0.207815 | ||||||||
\(842\) | 414.601i | 0.492400i | ||||||||
\(843\) | 620.241 | − | 620.241i | 0.735755 | − | 0.735755i | ||||
\(844\) | 3035.84i | 3.59696i | ||||||||
\(845\) | 81.2737 | − | 58.4495i | 0.0961819 | − | 0.0691710i | ||||
\(846\) | 789.535 | 0.933256 | ||||||||
\(847\) | −19.4409 | − | 19.4409i | −0.0229527 | − | 0.0229527i | ||||
\(848\) | 140.943 | 0.166206 | ||||||||
\(849\) | − | 863.184i | − | 1.01671i | ||||||
\(850\) | 1016.29 | + | 1016.29i | 1.19563 | + | 1.19563i | ||||
\(851\) | −116.276 | − | 116.276i | −0.136635 | − | 0.136635i | ||||
\(852\) | −1017.09 | + | 1017.09i | −1.19377 | + | 1.19377i | ||||
\(853\) | 529.546 | − | 529.546i | 0.620804 | − | 0.620804i | −0.324933 | − | 0.945737i | \(-0.605342\pi\) |
0.945737 | + | 0.324933i | \(0.105342\pi\) | |||||||
\(854\) | −495.693 | −0.580436 | ||||||||
\(855\) | 11.4562i | 0.0133991i | ||||||||
\(856\) | −1973.14 | + | 1973.14i | −2.30507 | + | 2.30507i | ||||
\(857\) | 1586.76i | 1.85153i | 0.378097 | + | 0.925766i | \(0.376579\pi\) | ||||
−0.378097 | + | 0.925766i | \(0.623421\pi\) | |||||||
\(858\) | 809.877 | − | 688.315i | 0.943912 | − | 0.802232i | ||||
\(859\) | 145.062 | 0.168873 | 0.0844365 | − | 0.996429i | \(-0.473091\pi\) | ||||
0.0844365 | + | 0.996429i | \(0.473091\pi\) | |||||||
\(860\) | 44.9669 | + | 44.9669i | 0.0522871 | + | 0.0522871i | ||||
\(861\) | −68.4911 | −0.0795483 | ||||||||
\(862\) | − | 1528.23i | − | 1.77289i | ||||||
\(863\) | −1005.80 | − | 1005.80i | −1.16547 | − | 1.16547i | −0.983258 | − | 0.182216i | \(-0.941673\pi\) |
−0.182216 | − | 0.983258i | \(-0.558327\pi\) | |||||||
\(864\) | −918.489 | − | 918.489i | −1.06307 | − | 1.06307i | ||||
\(865\) | 38.2762 | − | 38.2762i | 0.0442499 | − | 0.0442499i | ||||
\(866\) | 403.020 | − | 403.020i | 0.465381 | − | 0.465381i | ||||
\(867\) | 73.1758 | 0.0844011 | ||||||||
\(868\) | − | 515.631i | − | 0.594045i | ||||||
\(869\) | −371.978 | + | 371.978i | −0.428053 | + | 0.428053i | ||||
\(870\) | − | 120.680i | − | 0.138712i | ||||||
\(871\) | −1485.81 | − | 120.557i | −1.70587 | − | 0.138413i | ||||
\(872\) | −2330.17 | −2.67221 | ||||||||
\(873\) | −377.772 | − | 377.772i | −0.432729 | − | 0.432729i | ||||
\(874\) | −448.710 | −0.513399 | ||||||||
\(875\) | 59.0135i | 0.0674440i | ||||||||
\(876\) | −637.587 | − | 637.587i | −0.727839 | − | 0.727839i | ||||
\(877\) | 689.532 | + | 689.532i | 0.786240 | + | 0.786240i | 0.980876 | − | 0.194636i | \(-0.0623526\pi\) |
−0.194636 | + | 0.980876i | \(0.562353\pi\) | |||||||
\(878\) | 1158.18 | − | 1158.18i | 1.31912 | − | 1.31912i | ||||
\(879\) | 294.406 | − | 294.406i | 0.334933 | − | 0.334933i | ||||
\(880\) | 206.469 | 0.234624 | ||||||||
\(881\) | − | 1607.31i | − | 1.82442i | −0.409722 | − | 0.912210i | \(-0.634374\pi\) | ||
0.409722 | − | 0.912210i | \(-0.365626\pi\) | |||||||
\(882\) | −502.009 | + | 502.009i | −0.569171 | + | 0.569171i | ||||
\(883\) | − | 153.969i | − | 0.174370i | −0.996192 | − | 0.0871850i | \(-0.972213\pi\) | ||
0.996192 | − | 0.0871850i | \(-0.0277871\pi\) | |||||||
\(884\) | 1475.43 | − | 1253.97i | 1.66903 | − | 1.41851i | ||||
\(885\) | −54.8341 | −0.0619595 | ||||||||
\(886\) | 1490.28 | + | 1490.28i | 1.68203 | + | 1.68203i | ||||
\(887\) | 125.273 | 0.141232 | 0.0706159 | − | 0.997504i | \(-0.477504\pi\) | ||||
0.0706159 | + | 0.997504i | \(0.477504\pi\) | |||||||
\(888\) | 251.421i | 0.283132i | ||||||||
\(889\) | 134.562 | + | 134.562i | 0.151363 | + | 0.151363i | ||||
\(890\) | −197.004 | − | 197.004i | −0.221353 | − | 0.221353i | ||||
\(891\) | 171.228 | − | 171.228i | 0.192175 | − | 0.192175i | ||||
\(892\) | 2273.08 | − | 2273.08i | 2.54830 | − | 2.54830i | ||||
\(893\) | −223.675 | −0.250476 | ||||||||
\(894\) | 1431.22i | 1.60092i | ||||||||
\(895\) | 30.0203 | − | 30.0203i | 0.0335422 | − | 0.0335422i | ||||
\(896\) | 142.315i | 0.158834i | ||||||||
\(897\) | 500.368 | + | 588.737i | 0.557824 | + | 0.656340i | ||||
\(898\) | 553.021 | 0.615837 | ||||||||
\(899\) | 502.982 | + | 502.982i | 0.559491 | + | 0.559491i | ||||
\(900\) | −993.964 | −1.10440 | ||||||||
\(901\) | 66.9075i | 0.0742591i | ||||||||
\(902\) | 422.061 | + | 422.061i | 0.467917 | + | 0.467917i | ||||
\(903\) | 35.3221 | + | 35.3221i | 0.0391164 | + | 0.0391164i | ||||
\(904\) | −1491.76 | + | 1491.76i | −1.65018 | + | 1.65018i | ||||
\(905\) | −114.828 | + | 114.828i | −0.126882 | + | 0.126882i | ||||
\(906\) | −325.688 | −0.359479 | ||||||||
\(907\) | − | 354.574i | − | 0.390930i | −0.980711 | − | 0.195465i | \(-0.937378\pi\) | ||
0.980711 | − | 0.195465i | \(-0.0626216\pi\) | |||||||
\(908\) | 939.285 | − | 939.285i | 1.03445 | − | 1.03445i | ||||
\(909\) | 38.5793i | 0.0424415i | ||||||||
\(910\) | 56.2192 | + | 4.56156i | 0.0617794 | + | 0.00501271i | ||||
\(911\) | 1040.31 | 1.14194 | 0.570972 | − | 0.820970i | \(-0.306566\pi\) | ||||
0.570972 | + | 0.820970i | \(0.306566\pi\) | |||||||
\(912\) | 230.083 | + | 230.083i | 0.252284 | + | 0.252284i | ||||
\(913\) | −272.807 | −0.298803 | ||||||||
\(914\) | 1838.24i | 2.01121i | ||||||||
\(915\) | −61.2933 | − | 61.2933i | −0.0669872 | − | 0.0669872i | ||||
\(916\) | −2241.31 | − | 2241.31i | −2.44684 | − | 2.44684i | ||||
\(917\) | 159.292 | − | 159.292i | 0.173710 | − | 0.173710i | ||||
\(918\) | 1187.90 | − | 1187.90i | 1.29401 | − | 1.29401i | ||||
\(919\) | −416.201 | −0.452884 | −0.226442 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226442 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(920\) | 316.460i | 0.343979i | ||||||||
\(921\) | −509.614 | + | 509.614i | −0.553327 | + | 0.553327i | ||||
\(922\) | − | 174.215i | − | 0.188953i | ||||||
\(923\) | 924.386 | + | 75.0036i | 1.00150 | + | 0.0812606i | ||||
\(924\) | 419.074 | 0.453543 | ||||||||
\(925\) | 104.272 | + | 104.272i | 0.112726 | + | 0.112726i | ||||
\(926\) | −1736.36 | −1.87512 | ||||||||
\(927\) | − | 257.026i | − | 0.277267i | ||||||
\(928\) | 822.851 | + | 822.851i | 0.886692 | + | 0.886692i | ||||
\(929\) | −428.403 | − | 428.403i | −0.461144 | − | 0.461144i | 0.437886 | − | 0.899030i | \(-0.355727\pi\) |
−0.899030 | + | 0.437886i | \(0.855727\pi\) | |||||||
\(930\) | 91.1096 | − | 91.1096i | 0.0979673 | − | 0.0979673i | ||||
\(931\) | 142.219 | − | 142.219i | 0.152760 | − | 0.152760i | ||||
\(932\) | 100.606 | 0.107946 | ||||||||
\(933\) | − | 245.816i | − | 0.263469i | ||||||
\(934\) | −795.670 | + | 795.670i | −0.851896 | + | 0.851896i | ||||
\(935\) | 98.0135i | 0.104827i | ||||||||
\(936\) | −88.3687 | + | 1089.10i | −0.0944110 | + | 1.16357i | ||||
\(937\) | −990.702 | −1.05731 | −0.528656 | − | 0.848836i | \(-0.677304\pi\) | ||||
−0.528656 | + | 0.848836i | \(0.677304\pi\) | |||||||
\(938\) | −593.899 | − | 593.899i | −0.633155 | − | 0.633155i | ||||
\(939\) | 483.231 | 0.514623 | ||||||||
\(940\) | 276.259i | 0.293893i | ||||||||
\(941\) | 974.392 | + | 974.392i | 1.03549 | + | 1.03549i | 0.999347 | + | 0.0361387i | \(0.0115058\pi\) |
0.0361387 | + | 0.999347i | \(0.488494\pi\) | |||||||
\(942\) | −1297.86 | − | 1297.86i | −1.37777 | − | 1.37777i | ||||
\(943\) | −306.816 | + | 306.816i | −0.325361 | + | 0.325361i | ||||
\(944\) | 1018.62 | − | 1018.62i | 1.07905 | − | 1.07905i | ||||
\(945\) | 34.2456 | 0.0362387 | ||||||||
\(946\) | − | 435.329i | − | 0.460178i | ||||||
\(947\) | 897.569 | − | 897.569i | 0.947803 | − | 0.947803i | −0.0509007 | − | 0.998704i | \(-0.516209\pi\) |
0.998704 | + | 0.0509007i | \(0.0162092\pi\) | |||||||
\(948\) | 1023.94i | 1.08011i | ||||||||
\(949\) | −47.0178 | + | 579.473i | −0.0495446 | + | 0.610615i | ||||
\(950\) | 402.386 | 0.423564 | ||||||||
\(951\) | −270.588 | − | 270.588i | −0.284530 | − | 0.284530i | ||||
\(952\) | 622.973 | 0.654383 | ||||||||
\(953\) | 1111.71i | 1.16654i | 0.812279 | + | 0.583269i | \(0.198227\pi\) | ||||
−0.812279 | + | 0.583269i | \(0.801773\pi\) | |||||||
\(954\) | −46.7544 | − | 46.7544i | −0.0490089 | − | 0.0490089i | ||||
\(955\) | 75.2719 | + | 75.2719i | 0.0788187 | + | 0.0788187i | ||||
\(956\) | 913.949 | − | 913.949i | 0.956014 | − | 0.956014i | ||||
\(957\) | −408.794 | + | 408.794i | −0.427162 | + | 0.427162i | ||||
\(958\) | −395.649 | −0.412995 | ||||||||
\(959\) | 246.110i | 0.256632i | ||||||||
\(960\) | 27.1470 | − | 27.1470i | 0.0282781 | − | 0.0282781i | ||||
\(961\) | − | 201.527i | − | 0.209705i | ||||||
\(962\) | 216.318 | − | 183.849i | 0.224863 | − | 0.191111i | ||||
\(963\) | 620.877 | 0.644732 | ||||||||
\(964\) | −1829.45 | − | 1829.45i | −1.89777 | − | 1.89777i | ||||
\(965\) | −0.951605 | −0.000986120 | ||||||||
\(966\) | 435.329i | 0.450651i | ||||||||
\(967\) | −1333.92 | − | 1333.92i | −1.37944 | − | 1.37944i | −0.845561 | − | 0.533879i | \(-0.820734\pi\) |
−0.533879 | − | 0.845561i | \(-0.679266\pi\) | |||||||
\(968\) | 188.309 | + | 188.309i | 0.194534 | + | 0.194534i | ||||
\(969\) | −109.223 | + | 109.223i | −0.112718 | + | 0.112718i | ||||
\(970\) | 188.886 | − | 188.886i | 0.194728 | − | 0.194728i | ||||
\(971\) | −556.110 | −0.572718 | −0.286359 | − | 0.958122i | \(-0.592445\pi\) | ||||
−0.286359 | + | 0.958122i | \(0.592445\pi\) | |||||||
\(972\) | 1946.54i | 2.00262i | ||||||||
\(973\) | −111.437 | + | 111.437i | −0.114529 | + | 0.114529i | ||||
\(974\) | 356.535i | 0.366053i | ||||||||
\(975\) | −448.710 | − | 527.956i | −0.460216 | − | 0.541493i | ||||
\(976\) | 2277.22 | 2.33322 | ||||||||
\(977\) | −1103.56 | − | 1103.56i | −1.12954 | − | 1.12954i | −0.990252 | − | 0.139288i | \(-0.955518\pi\) |
−0.139288 | − | 0.990252i | \(-0.544482\pi\) | |||||||
\(978\) | −127.925 | −0.130803 | ||||||||
\(979\) | 1334.67i | 1.36330i | ||||||||
\(980\) | −175.653 | − | 175.653i | −0.179238 | − | 0.179238i | ||||
\(981\) | 366.610 | + | 366.610i | 0.373710 | + | 0.373710i | ||||
\(982\) | −1768.86 | + | 1768.86i | −1.80128 | + | 1.80128i | ||||
\(983\) | −901.475 | + | 901.475i | −0.917065 | + | 0.917065i | −0.996815 | − | 0.0797497i | \(-0.974588\pi\) |
0.0797497 | + | 0.996815i | \(0.474588\pi\) | |||||||
\(984\) | 663.421 | 0.674208 | ||||||||
\(985\) | 118.878i | 0.120688i | ||||||||
\(986\) | −1064.21 | + | 1064.21i | −1.07932 | + | 1.07932i | ||||
\(987\) | 217.005i | 0.219863i | ||||||||
\(988\) | 43.8420 | − | 540.333i | 0.0443745 | − | 0.546896i | ||||
\(989\) | 316.460 | 0.319980 | ||||||||
\(990\) | −68.4911 | − | 68.4911i | −0.0691829 | − | 0.0691829i | ||||
\(991\) | 765.341 | 0.772292 | 0.386146 | − | 0.922438i | \(-0.373806\pi\) | ||||
0.386146 | + | 0.922438i | \(0.373806\pi\) | |||||||
\(992\) | 1242.46i | 1.25248i | ||||||||
\(993\) | 670.268 | + | 670.268i | 0.674993 | + | 0.674993i | ||||
\(994\) | 369.489 | + | 369.489i | 0.371719 | + | 0.371719i | ||||
\(995\) | 108.803 | − | 108.803i | 0.109350 | − | 0.109350i | ||||
\(996\) | −375.478 | + | 375.478i | −0.376986 | + | 0.376986i | ||||
\(997\) | 1075.40 | 1.07863 | 0.539317 | − | 0.842103i | \(-0.318682\pi\) | ||||
0.539317 | + | 0.842103i | \(0.318682\pi\) | |||||||
\(998\) | − | 1803.33i | − | 1.80695i | ||||||
\(999\) | 121.879 | − | 121.879i | 0.122001 | − | 0.122001i |
(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 | 13.3.d.a.8.1 | yes | 4 | |
3.2 | odd | 2 | 117.3.j.a.73.2 | 4 | |||
4.3 | odd | 2 | 208.3.t.c.177.1 | 4 | |||
5.2 | odd | 4 | 325.3.g.b.99.2 | 4 | |||
5.3 | odd | 4 | 325.3.g.a.99.1 | 4 | |||
5.4 | even | 2 | 325.3.j.a.151.2 | 4 | |||
13.2 | odd | 12 | 169.3.f.f.19.1 | 8 | |||
13.3 | even | 3 | 169.3.f.f.150.2 | 8 | |||
13.4 | even | 6 | 169.3.f.d.89.2 | 8 | |||
13.5 | odd | 4 | inner | 13.3.d.a.5.1 | ✓ | 4 | |
13.6 | odd | 12 | 169.3.f.f.80.2 | 8 | |||
13.7 | odd | 12 | 169.3.f.d.80.1 | 8 | |||
13.8 | odd | 4 | 169.3.d.d.70.2 | 4 | |||
13.9 | even | 3 | 169.3.f.f.89.1 | 8 | |||
13.10 | even | 6 | 169.3.f.d.150.1 | 8 | |||
13.11 | odd | 12 | 169.3.f.d.19.2 | 8 | |||
13.12 | even | 2 | 169.3.d.d.99.2 | 4 | |||
39.5 | even | 4 | 117.3.j.a.109.2 | 4 | |||
52.31 | even | 4 | 208.3.t.c.161.1 | 4 | |||
65.18 | even | 4 | 325.3.g.b.174.2 | 4 | |||
65.44 | odd | 4 | 325.3.j.a.226.2 | 4 | |||
65.57 | even | 4 | 325.3.g.a.174.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
13.3.d.a.5.1 | ✓ | 4 | 13.5 | odd | 4 | inner | |
13.3.d.a.8.1 | yes | 4 | 1.1 | even | 1 | trivial | |
117.3.j.a.73.2 | 4 | 3.2 | odd | 2 | |||
117.3.j.a.109.2 | 4 | 39.5 | even | 4 | |||
169.3.d.d.70.2 | 4 | 13.8 | odd | 4 | |||
169.3.d.d.99.2 | 4 | 13.12 | even | 2 | |||
169.3.f.d.19.2 | 8 | 13.11 | odd | 12 | |||
169.3.f.d.80.1 | 8 | 13.7 | odd | 12 | |||
169.3.f.d.89.2 | 8 | 13.4 | even | 6 | |||
169.3.f.d.150.1 | 8 | 13.10 | even | 6 | |||
169.3.f.f.19.1 | 8 | 13.2 | odd | 12 | |||
169.3.f.f.80.2 | 8 | 13.6 | odd | 12 | |||
169.3.f.f.89.1 | 8 | 13.9 | even | 3 | |||
169.3.f.f.150.2 | 8 | 13.3 | even | 3 | |||
208.3.t.c.161.1 | 4 | 52.31 | even | 4 | |||
208.3.t.c.177.1 | 4 | 4.3 | odd | 2 | |||
325.3.g.a.99.1 | 4 | 5.3 | odd | 4 | |||
325.3.g.a.174.1 | 4 | 65.57 | even | 4 | |||
325.3.g.b.99.2 | 4 | 5.2 | odd | 4 | |||
325.3.g.b.174.2 | 4 | 65.18 | even | 4 | |||
325.3.j.a.151.2 | 4 | 5.4 | even | 2 | |||
325.3.j.a.226.2 | 4 | 65.44 | odd | 4 |