Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(509,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.509");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.k (of order \(6\), 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 2x^{14} - 94x^{12} - 128x^{10} + 2719x^{8} - 10368x^{6} - 616734x^{4} + 1062882x^{2} + 43046721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{12} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.7 | ||
Root | \(1.34095 + 2.68363i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.521 |
Dual form | 588.4.k.d.509.7 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 4.64818 | − | 2.32260i | 0.894542 | − | 0.446984i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.31912 | + | 5.74888i | 0.296871 | + | 0.514195i | 0.975418 | − | 0.220361i | \(-0.0707236\pi\) |
−0.678548 | + | 0.734556i | \(0.737390\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 16.2111 | − | 21.5917i | 0.600411 | − | 0.799692i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.9734 | − | 21.9239i | −1.04086 | − | 0.600938i | −0.120780 | − | 0.992679i | \(-0.538540\pi\) |
−0.920075 | + | 0.391741i | \(0.871873\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4990i | 0.309331i | 0.987967 | + | 0.154666i | \(0.0494300\pi\) | ||||
−0.987967 | + | 0.154666i | \(0.950570\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 28.7802 | + | 19.0128i | 0.495400 | + | 0.327273i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 16.3257 | − | 28.2769i | 0.232915 | − | 0.403421i | −0.725750 | − | 0.687959i | \(-0.758507\pi\) |
0.958665 | + | 0.284538i | \(0.0918403\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 39.9956 | − | 23.0914i | 0.482927 | − | 0.278818i | −0.238709 | − | 0.971091i | \(-0.576724\pi\) |
0.721635 | + | 0.692273i | \(0.243391\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 91.0734 | − | 52.5812i | 0.825657 | − | 0.476693i | −0.0267064 | − | 0.999643i | \(-0.508502\pi\) |
0.852363 | + | 0.522950i | \(0.175169\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 40.4669 | − | 70.0908i | 0.323735 | − | 0.560726i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.2033 | − | 138.014i | 0.179644 | − | 0.983732i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 236.706i | − | 1.51570i | −0.652430 | − | 0.757849i | \(-0.726250\pi\) | ||
0.652430 | − | 0.757849i | \(-0.273750\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −171.612 | − | 99.0804i | −0.994273 | − | 0.574044i | −0.0877242 | − | 0.996145i | \(-0.527959\pi\) |
−0.906549 | + | 0.422101i | \(0.861293\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −227.428 | − | 13.7096i | −1.19970 | − | 0.0723190i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 140.121 | + | 242.696i | 0.622586 | + | 1.07835i | 0.989002 | + | 0.147900i | \(0.0472514\pi\) |
−0.366416 | + | 0.930451i | \(0.619415\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 33.6754 | + | 67.3940i | 0.138266 | + | 0.276710i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 516.323 | 1.96673 | 0.983367 | − | 0.181631i | \(-0.0581376\pi\) | ||||
0.983367 | + | 0.181631i | \(0.0581376\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.7471 | −0.201252 | −0.100626 | − | 0.994924i | \(-0.532085\pi\) | ||||
−0.100626 | + | 0.994924i | \(0.532085\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 177.934 | + | 21.5304i | 0.589442 | + | 0.0713235i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14.8960 | + | 25.8006i | 0.0462298 | + | 0.0800724i | 0.888214 | − | 0.459429i | \(-0.151946\pi\) |
−0.841985 | + | 0.539502i | \(0.818613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.2088 | − | 169.354i | 0.0280298 | − | 0.464986i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 98.7936 | + | 57.0385i | 0.256044 | + | 0.147827i | 0.622529 | − | 0.782597i | \(-0.286105\pi\) |
−0.366484 | + | 0.930424i | \(0.619439\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 291.073i | − | 0.713604i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 132.274 | − | 200.227i | 0.307371 | − | 0.465275i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 351.717 | − | 609.191i | 0.776095 | − | 1.34424i | −0.158082 | − | 0.987426i | \(-0.550531\pi\) |
0.934177 | − | 0.356810i | \(-0.116136\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 62.7826 | − | 36.2476i | 0.131779 | − | 0.0760824i | −0.432662 | − | 0.901556i | \(-0.642425\pi\) |
0.564440 | + | 0.825474i | \(0.309092\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −83.3531 | + | 48.1239i | −0.159057 | + | 0.0918314i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −284.307 | + | 492.435i | −0.518413 | + | 0.897918i | 0.481358 | + | 0.876524i | \(0.340144\pi\) |
−0.999771 | + | 0.0213938i | \(0.993190\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 301.200 | − | 455.933i | 0.525511 | − | 0.795477i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1078.37i | 1.80252i | 0.433281 | + | 0.901259i | \(0.357356\pi\) | ||||
−0.433281 | + | 0.901259i | \(0.642644\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −517.163 | − | 298.584i | −0.829169 | − | 0.478721i | 0.0243993 | − | 0.999702i | \(-0.492233\pi\) |
−0.853568 | + | 0.520982i | \(0.825566\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 25.3049 | − | 419.783i | 0.0389595 | − | 0.646298i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −200.582 | − | 347.418i | −0.285661 | − | 0.494779i | 0.687108 | − | 0.726555i | \(-0.258880\pi\) |
−0.972769 | + | 0.231776i | \(0.925546\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −203.401 | − | 700.049i | −0.279013 | − | 0.960287i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1117.48 | 1.47783 | 0.738914 | − | 0.673800i | \(-0.235339\pi\) | ||||
0.738914 | + | 0.673800i | \(0.235339\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 216.747 | 0.276583 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −549.773 | − | 1100.25i | −0.677492 | − | 1.35586i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −35.1607 | − | 60.9001i | −0.0418767 | − | 0.0725325i | 0.844327 | − | 0.535828i | \(-0.180000\pi\) |
−0.886204 | + | 0.463295i | \(0.846667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1027.81 | − | 61.9573i | −1.14601 | − | 0.0690825i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 265.500 | + | 153.286i | 0.286734 | + | 0.165546i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1371.56i | − | 1.43567i | −0.696211 | − | 0.717837i | \(-0.745132\pi\) | ||
0.696211 | − | 0.717837i | \(-0.254868\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1088.97 | + | 464.498i | −1.10551 | + | 0.471553i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 290.003 | − | 502.300i | 0.285707 | − | 0.494858i | −0.687074 | − | 0.726588i | \(-0.741105\pi\) |
0.972780 | + | 0.231729i | \(0.0744384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1342.66 | + | 775.185i | −1.28443 | + | 0.741565i | −0.977655 | − | 0.210217i | \(-0.932583\pi\) |
−0.306774 | + | 0.951782i | \(0.599250\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1131.48 | + | 653.261i | −1.02228 | + | 0.590216i | −0.914765 | − | 0.403987i | \(-0.867624\pi\) |
−0.107520 | + | 0.994203i | \(0.534291\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −239.945 | + | 415.598i | −0.210850 | + | 0.365202i | −0.951981 | − | 0.306158i | \(-0.900956\pi\) |
0.741131 | + | 0.671360i | \(0.234290\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1214.99 | + | 802.651i | 1.03893 | + | 0.686344i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 973.206i | − | 0.810190i | −0.914275 | − | 0.405095i | \(-0.867238\pi\) | ||
0.914275 | − | 0.405095i | \(-0.132762\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 604.566 | + | 349.046i | 0.490227 | + | 0.283033i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 313.058 | + | 235.045i | 0.247370 | + | 0.185726i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 295.819 | + | 512.374i | 0.222253 | + | 0.384954i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2399.96 | − | 1199.21i | 1.75933 | − | 0.879098i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1367.04 | 0.978172 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 236.747 | 0.165417 | 0.0827083 | − | 0.996574i | \(-0.473643\pi\) | ||||
0.0827083 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −263.771 | + | 131.801i | −0.180029 | + | 0.0899565i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −813.694 | − | 1409.36i | −0.542693 | − | 0.939971i | −0.998748 | − | 0.0500200i | \(-0.984071\pi\) |
0.456055 | − | 0.889951i | \(-0.349262\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 877.077 | − | 313.193i | 0.559161 | − | 0.199669i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −926.174 | − | 534.727i | −0.577580 | − | 0.333466i | 0.182591 | − | 0.983189i | \(-0.441551\pi\) |
−0.760171 | + | 0.649723i | \(0.774885\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1854.85i | − | 1.13184i | −0.824459 | − | 0.565922i | \(-0.808520\pi\) | ||
0.824459 | − | 0.565922i | \(-0.191480\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 129.164 | + | 85.3284i | 0.0771456 | + | 0.0509642i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 317.876 | − | 550.577i | 0.185889 | − | 0.321969i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1360.79 | − | 785.655i | 0.779365 | − | 0.449966i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1586.85 | − | 916.167i | 0.872481 | − | 0.503727i | 0.00430915 | − | 0.999991i | \(-0.498628\pi\) |
0.868172 | + | 0.496264i | \(0.165295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1622.72 | + | 2810.64i | −0.874539 | + | 1.51475i | −0.0172860 | + | 0.999851i | \(0.505503\pi\) |
−0.857253 | + | 0.514895i | \(0.827831\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −345.888 | − | 810.898i | −0.182767 | − | 0.428478i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1315.44i | − | 0.681667i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 46.0662 | + | 26.5963i | 0.0234171 | + | 0.0135199i | 0.511663 | − | 0.859186i | \(-0.329030\pi\) |
−0.488246 | + | 0.872706i | \(0.662363\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 591.688 | + | 35.6675i | 0.295119 | + | 0.0177900i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1398.28 | + | 2421.90i | 0.671915 | + | 1.16379i | 0.977361 | + | 0.211581i | \(0.0678611\pi\) |
−0.305446 | + | 0.952209i | \(0.598806\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −676.044 | − | 1352.96i | −0.318969 | − | 0.638349i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2577.35 | −1.19426 | −0.597131 | − | 0.802144i | \(-0.703693\pi\) | ||||
−0.597131 | + | 0.802144i | \(0.703693\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1986.78 | 0.904314 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 149.789 | − | 1237.91i | 0.0669863 | − | 0.553598i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 555.853 | + | 962.765i | 0.244281 | + | 0.423108i | 0.961929 | − | 0.273298i | \(-0.0881146\pi\) |
−0.717648 | + | 0.696406i | \(0.754781\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 219.937 | − | 3648.52i | 0.0933980 | − | 1.54938i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 205.307 | + | 118.534i | 0.0857285 | + | 0.0494954i | 0.542251 | − | 0.840216i | \(-0.317572\pi\) |
−0.456523 | + | 0.889712i | \(0.650905\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4627.46i | 1.90031i | 0.311775 | + | 0.950156i | \(0.399077\pi\) | ||||
−0.311775 | + | 0.950156i | \(0.600923\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 207.636 | − | 314.304i | 0.0838738 | − | 0.126962i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −930.153 | + | 1611.07i | −0.369655 | + | 0.640262i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1239.88 | + | 715.846i | −0.484862 | + | 0.279935i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3333.31 | − | 1924.49i | 1.26277 | − | 0.729063i | 0.289164 | − | 0.957280i | \(-0.406623\pi\) |
0.973610 | + | 0.228217i | \(0.0732894\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1013.30 | + | 1755.08i | −0.377921 | + | 0.654578i | −0.990760 | − | 0.135630i | \(-0.956694\pi\) |
0.612839 | + | 0.790208i | \(0.290028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −275.668 | + | 417.284i | −0.101236 | + | 0.153243i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 606.043i | 0.219182i | 0.993977 | + | 0.109591i | \(0.0349541\pi\) | ||||
−0.993977 | + | 0.109591i | \(0.965046\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2526.72 | − | 1458.80i | −0.900072 | − | 0.519657i | −0.0228482 | − | 0.999739i | \(-0.507273\pi\) |
−0.877223 | + | 0.480082i | \(0.840607\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −177.784 | + | 2949.26i | −0.0623877 | + | 1.03495i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1713.74 | + | 2968.28i | 0.583866 | + | 1.01129i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 341.083 | − | 2818.83i | 0.114526 | − | 0.946483i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2025.02 | −0.670209 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 117.626 | 0.0383779 | 0.0191890 | − | 0.999816i | \(-0.493892\pi\) | ||||
0.0191890 | + | 0.999816i | \(0.493892\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2504.61 | + | 5012.45i | 0.805696 | + | 1.61243i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −188.350 | − | 326.232i | −0.0597459 | − | 0.103483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3097.35 | − | 186.712i | −0.955707 | − | 0.0576109i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 409.987 | + | 236.706i | 0.124791 | + | 0.0720479i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2306.55i | 0.692636i | 0.938117 | + | 0.346318i | \(0.112568\pi\) | ||||
−0.938117 | + | 0.346318i | \(0.887432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −857.364 | − | 2010.00i | −0.254034 | − | 0.595555i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −833.988 | + | 1444.51i | −0.243849 | + | 0.422359i | −0.961807 | − | 0.273727i | \(-0.911743\pi\) |
0.717958 | + | 0.696086i | \(0.245077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3061.60 | − | 1767.62i | 0.883477 | − | 0.510076i | 0.0116737 | − | 0.999932i | \(-0.496284\pi\) |
0.871803 | + | 0.489856i | \(0.162951\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4921.10 | + | 2841.20i | −1.38366 | + | 0.798855i | −0.992590 | − | 0.121508i | \(-0.961227\pi\) |
−0.391066 | + | 0.920363i | \(0.627894\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −98.8830 | + | 171.270i | −0.0274486 | + | 0.0475423i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1739.25 | − | 1148.99i | −0.476694 | − | 0.314915i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1525.40i | 0.412845i | 0.978463 | + | 0.206422i | \(0.0661821\pi\) | ||||
−0.978463 | + | 0.206422i | \(0.933818\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4566.11 | + | 2636.25i | 1.22045 | + | 0.704629i | 0.965015 | − | 0.262196i | \(-0.0844467\pi\) |
0.255439 | + | 0.966825i | \(0.417780\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2571.37 | − | 2781.54i | −0.678822 | − | 0.734303i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 334.803 | + | 579.897i | 0.0862471 | + | 0.149384i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5194.26 | − | 2595.46i | 1.32198 | − | 0.660565i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5300.73 | −1.33299 | −0.666493 | − | 0.745512i | \(-0.732205\pi\) | ||||
−0.666493 | + | 0.745512i | \(0.732205\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4611.15 | −1.14585 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1007.48 | − | 503.416i | 0.247415 | − | 0.123628i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1167.16 | + | 2021.58i | 0.283290 | + | 0.490672i | 0.972193 | − | 0.234181i | \(-0.0752409\pi\) |
−0.688903 | + | 0.724853i | \(0.741908\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5110.88 | − | 3837.27i | −1.21209 | − | 0.910042i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1647.04 | + | 950.919i | 0.386163 | + | 0.222951i | 0.680496 | − | 0.732752i | \(-0.261764\pi\) |
−0.294333 | + | 0.955703i | \(0.595098\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 757.270i | 0.175542i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −304.879 | − | 201.410i | −0.0698813 | − | 0.0461652i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3943.87 | + | 6830.99i | −0.893911 | + | 1.54830i | −0.0587651 | + | 0.998272i | \(0.518716\pi\) |
−0.835146 | + | 0.550028i | \(0.814617\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3450.30 | − | 1992.03i | 0.773398 | − | 0.446522i | −0.0606872 | − | 0.998157i | \(-0.519329\pi\) |
0.834086 | + | 0.551635i | \(0.185996\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3073.33 | + | 1774.39i | −0.673924 | + | 0.389090i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2556.78 | + | 4428.47i | −0.554592 | + | 0.960581i | 0.443343 | + | 0.896352i | \(0.353792\pi\) |
−0.997935 | + | 0.0642293i | \(0.979541\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4921.33 | + | 2099.19i | −1.05603 | + | 0.450449i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3540.59i | 0.751651i | 0.926690 | + | 0.375825i | \(0.122641\pi\) | ||||
−0.926690 | + | 0.375825i | \(0.877359\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 992.438 | + | 572.984i | 0.208461 | + | 0.120355i | 0.600596 | − | 0.799553i | \(-0.294930\pi\) |
−0.392135 | + | 0.919908i | \(0.628263\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1590.11 | + | 95.8536i | 0.330492 | + | 0.0199224i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1923.45 | + | 3331.51i | 0.391501 | + | 0.678100i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3185.57 | − | 6375.24i | −0.641723 | − | 1.28427i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −573.089 | −0.114267 | −0.0571335 | − | 0.998367i | \(-0.518196\pi\) | ||||
−0.0571335 | + | 0.998367i | \(0.518196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4669.55 | 0.921600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3982.86 | + | 4688.29i | −0.778145 | + | 0.915968i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 762.376 | + | 1320.47i | 0.147456 | + | 0.255401i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 181.346 | − | 3008.34i | 0.0343829 | − | 0.570378i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 416.766 | + | 240.620i | 0.0782424 | + | 0.0451733i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7901.69i | 1.46897i | 0.678626 | + | 0.734484i | \(0.262576\pi\) | ||||
−0.678626 | + | 0.734484i | \(0.737424\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4440.48 | + | 6721.65i | −0.817508 | + | 1.23748i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4064.64 | − | 7040.16i | 0.741108 | − | 1.28364i | −0.210883 | − | 0.977511i | \(-0.567634\pi\) |
0.951991 | − | 0.306125i | \(-0.0990326\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4554.84 | + | 2629.74i | −0.822540 | + | 0.474893i | −0.851291 | − | 0.524693i | \(-0.824180\pi\) |
0.0287519 | + | 0.999587i | \(0.490847\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1284.32 | − | 741.501i | 0.227553 | − | 0.131378i | −0.381889 | − | 0.924208i | \(-0.624727\pi\) |
0.609443 | + | 0.792830i | \(0.291393\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5189.53 | + | 8988.54i | −0.910840 | + | 1.57762i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3742.06 | + | 5664.45i | −0.650659 | + | 0.984918i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1507.93i | − | 0.259764i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1016.25 | + | 586.731i | 0.173450 | + | 0.100141i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −150.044 | + | 2489.07i | −0.0253744 | + | 0.420935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1968.61 | − | 3409.73i | −0.326902 | − | 0.566211i | 0.654993 | − | 0.755635i | \(-0.272671\pi\) |
−0.981896 | + | 0.189423i | \(0.939338\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7511.72 | + | 908.931i | 1.23616 | + | 0.149577i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3774.60 | −0.615607 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6678.23 | 1.07948 | 0.539742 | − | 0.841830i | \(-0.318522\pi\) | ||||
0.539742 | + | 0.841830i | \(0.318522\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2260.36 | − | 4523.63i | −0.362142 | − | 0.724749i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4344.47 | + | 7524.83i | 0.689930 | + | 1.19499i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3620.82 | + | 218.267i | 0.565039 | + | 0.0340611i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6216.15 | − | 3588.90i | −0.961673 | − | 0.555222i | −0.0649851 | − | 0.997886i | \(-0.520700\pi\) |
−0.896687 | + | 0.442664i | \(0.854033\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 9025.65i | − | 1.38433i | −0.721738 | − | 0.692166i | \(-0.756657\pi\) | ||
0.721738 | − | 0.692166i | \(-0.243343\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2001.06 | + | 365.424i | 0.304299 | + | 0.0555694i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3884.78 | + | 6728.63i | −0.585739 | + | 1.01453i | 0.409044 | + | 0.912515i | \(0.365862\pi\) |
−0.994783 | + | 0.102015i | \(0.967471\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6199.41 | + | 3579.23i | −0.926846 | + | 0.535115i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3172.13 | − | 1831.43i | 0.466347 | − | 0.269245i | −0.248362 | − | 0.968667i | \(-0.579892\pi\) |
0.714709 | + | 0.699422i | \(0.246559\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2363.07 | + | 4092.96i | −0.344521 | + | 0.596728i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2565.06 | + | 1694.54i | 0.370883 | + | 0.245014i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3964.14i | − | 0.568473i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 554.775 | + | 320.299i | 0.0789073 | + | 0.0455572i | 0.538935 | − | 0.842348i | \(-0.318827\pi\) |
−0.460027 | + | 0.887905i | \(0.652160\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 8370.16 | − | 11148.3i | 1.18085 | − | 1.57278i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3630.84 | + | 6288.81i | 0.504016 | + | 0.872981i | 0.999989 | + | 0.00464360i | \(0.00147811\pi\) |
−0.495973 | + | 0.868338i | \(0.665189\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 6354.23 | − | 3175.07i | 0.875016 | − | 0.437227i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3432.01 | 0.468853 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3738.41 | −0.506674 | −0.253337 | − | 0.967378i | \(-0.581528\pi\) | ||||
−0.253337 | + | 0.967378i | \(0.581528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1100.44 | − | 549.868i | 0.147972 | − | 0.0739385i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4953.94 | − | 8580.48i | −0.660926 | − | 1.14476i | −0.980373 | − | 0.197153i | \(-0.936830\pi\) |
0.319447 | − | 0.947604i | \(-0.396503\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −919.933 | + | 1225.26i | −0.120834 | + | 0.160940i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1814.06 | + | 1047.35i | 0.236444 | + | 0.136511i | 0.613541 | − | 0.789663i | \(-0.289745\pi\) |
−0.377098 | + | 0.926174i | \(0.623078\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3433.69i | − | 0.444116i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7055.56 | − | 4661.07i | −0.905613 | − | 0.598269i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1331.51 | − | 2306.24i | 0.169609 | − | 0.293771i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7406.31 | − | 4276.04i | 0.936302 | − | 0.540574i | 0.0475031 | − | 0.998871i | \(-0.484874\pi\) |
0.888799 | + | 0.458297i | \(0.151540\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5260.04 | − | 3036.88i | 0.655047 | − | 0.378191i | −0.135340 | − | 0.990799i | \(-0.543213\pi\) |
0.790387 | + | 0.612608i | \(0.209879\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1436.57 | − | 2488.21i | 0.177570 | − | 0.307560i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3349.39 | − | 3492.87i | 0.410944 | − | 0.428548i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 12288.0i | − | 1.49654i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10829.6 | + | 6252.49i | 1.30927 | + | 0.755906i | 0.981974 | − | 0.189016i | \(-0.0605299\pi\) |
0.327294 | + | 0.944923i | \(0.393863\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5546.98 | − | 334.377i | −0.665723 | − | 0.0401304i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3709.06 | + | 6424.28i | 0.438724 | + | 0.759892i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4308.07 | − | 8621.67i | −0.505916 | − | 1.01248i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4950.15 | 0.577161 | 0.288581 | − | 0.957456i | \(-0.406817\pi\) | ||||
0.288581 | + | 0.957456i | \(0.406817\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7766.30 | 0.899065 | 0.449533 | − | 0.893264i | \(-0.351591\pi\) | ||||
0.449533 | + | 0.893264i | \(0.351591\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 798.558 | + | 96.6269i | 0.0917901 | + | 0.0111068i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1321.30 | − | 2288.56i | −0.150806 | − | 0.261203i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 198.775 | − | 3297.48i | 0.0223705 | − | 0.371104i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4585.49 | + | 2647.43i | 0.512472 | + | 0.295876i | 0.733849 | − | 0.679313i | \(-0.237722\pi\) |
−0.221377 | + | 0.975188i | \(0.571055\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2694.81i | − | 0.299086i | −0.988755 | − | 0.149543i | \(-0.952220\pi\) | ||
0.988755 | − | 0.149543i | \(-0.0477803\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4500.46 | − | 6812.44i | 0.496047 | − | 0.750877i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2428.35 | − | 4206.03i | 0.265821 | − | 0.460416i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5878.97 | + | 3394.23i | −0.639153 | + | 0.369015i | −0.784288 | − | 0.620397i | \(-0.786972\pi\) |
0.145135 | + | 0.989412i | \(0.453638\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4231.11 | + | 2442.84i | −0.453784 | + | 0.261992i | −0.709427 | − | 0.704779i | \(-0.751046\pi\) |
0.255643 | + | 0.966771i | \(0.417713\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 233.405 | − | 404.269i | 0.0248639 | − | 0.0430656i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5248.07 | − | 7944.11i | 0.555313 | − | 0.840590i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9626.53i | 1.01181i | 0.862588 | + | 0.505907i | \(0.168842\pi\) | ||||
−0.862588 | + | 0.505907i | \(0.831158\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19606.5 | − | 11319.8i | −2.04709 | − | 1.18189i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1014.73 | + | 16833.3i | −0.105245 | + | 1.74591i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1526.92 | − | 2644.70i | −0.156294 | − | 0.270708i | 0.777236 | − | 0.629210i | \(-0.216621\pi\) |
−0.933529 | + | 0.358501i | \(0.883288\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3491.14 | − | 2965.84i | −0.355016 | − | 0.301598i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8767.63 | 0.885791 | 0.442895 | − | 0.896573i | \(-0.353951\pi\) | ||||
0.442895 | + | 0.896573i | \(0.353951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10481.9 | −1.05213 | −0.526064 | − | 0.850445i | \(-0.676333\pi\) | ||||
−0.526064 | + | 0.850445i | \(0.676333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3055.23 | − | 6114.38i | −0.304694 | − | 0.609780i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1616.10 | − | 2799.17i | −0.160138 | − | 0.277366i | 0.774780 | − | 0.632231i | \(-0.217860\pi\) |
−0.934918 | + | 0.354864i | \(0.884527\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 275.896 | + | 16.6313i | 0.0269907 | + | 0.00162703i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2154.88 | + | 1244.12i | 0.209475 | + | 0.120940i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 3737.76i | − | 0.361053i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2833.11 | − | 1208.46i | 0.271948 | − | 0.115999i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5717.70 | − | 9903.35i | 0.545404 | − | 0.944667i | −0.453178 | − | 0.891420i | \(-0.649710\pi\) |
0.998581 | − | 0.0532469i | \(-0.0169570\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3518.86 | + | 2031.61i | −0.333568 | + | 0.192585i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7884.91 | − | 4552.35i | 0.738217 | − | 0.426210i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3556.21 | − | 6159.54i | 0.330898 | − | 0.573132i | −0.651790 | − | 0.758399i | \(-0.725982\pi\) |
0.982688 | + | 0.185267i | \(0.0593151\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 12124.6 | + | 8009.77i | 1.12125 | + | 0.740724i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11337.3i | 1.04205i | 0.853542 | + | 0.521025i | \(0.174450\pi\) | ||||
−0.853542 | + | 0.521025i | \(0.825550\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6693.31 | − | 3864.38i | −0.611464 | − | 0.353029i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6284.74 | − | 4718.61i | −0.570663 | − | 0.428456i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5319.80 | − | 9214.16i | −0.477248 | − | 0.826618i | 0.522412 | − | 0.852693i | \(-0.325032\pi\) |
−0.999660 | + | 0.0260752i | \(0.991699\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11980.0 | + | 5986.15i | −1.06832 | + | 0.533816i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11859.2 | 1.05124 | 0.525621 | − | 0.850719i | \(-0.323833\pi\) | ||||
0.525621 | + | 0.850719i | \(0.323833\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3850.21 | 0.339272 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9234.90 | − | 4614.48i | 0.808947 | − | 0.404214i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 753.362 | + | 1304.86i | 0.0656035 | + | 0.113629i | 0.896962 | − | 0.442109i | \(-0.145769\pi\) |
−0.831358 | + | 0.555737i | \(0.812436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2178.92 | − | 6101.92i | −0.187527 | − | 0.525158i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8912.89 | − | 5145.86i | −0.762619 | − | 0.440298i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1306.31i | − | 0.111125i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4819.82 | + | 3184.08i | 0.407642 | + | 0.269298i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1036.22 | − | 1794.78i | 0.0871353 | − | 0.150923i | −0.819164 | − | 0.573560i | \(-0.805562\pi\) |
0.906299 | + | 0.422637i | \(0.138895\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12290.8 | − | 7096.08i | 1.02761 | − | 0.593289i | 0.111308 | − | 0.993786i | \(-0.464496\pi\) |
0.916298 | + | 0.400497i | \(0.131163\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5603.37 | + | 3235.10i | −0.463162 | + | 0.267407i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −553.929 | + | 959.433i | −0.0455271 | + | 0.0788553i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7451.74 | − | 17469.8i | −0.608998 | − | 1.42773i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7486.18i | 0.608372i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7511.04 | − | 4336.50i | −0.606973 | − | 0.350436i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1229.61 | + | 74.1223i | 0.0988114 | + | 0.00595645i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3368.09 | + | 5833.71i | 0.267663 | + | 0.463606i | 0.968258 | − | 0.249953i | \(-0.0804153\pi\) |
−0.700595 | + | 0.713559i | \(0.747082\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10747.7 | + | 21509.3i | 0.849409 | + | 1.69991i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3185.63 | −0.250380 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2429.70 | −0.189921 | −0.0949604 | − | 0.995481i | \(-0.530272\pi\) | ||||
−0.0949604 | + | 0.995481i | \(0.530272\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 235.130 | − | 1943.19i | 0.0182789 | − | 0.151063i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5465.89 | − | 9467.19i | −0.422604 | − | 0.731971i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −581.647 | + | 9648.92i | −0.0444856 | + | 0.737971i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3223.03 | − | 1860.82i | −0.245178 | − | 0.141554i | 0.372376 | − | 0.928082i | \(-0.378543\pi\) |
−0.617554 | + | 0.786528i | \(0.711876\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 822.777i | − | 0.0622536i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4100.57 | + | 6207.12i | −0.308603 | + | 0.467139i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6433.94 | − | 11143.9i | 0.481631 | − | 0.834209i | −0.518147 | − | 0.855292i | \(-0.673378\pi\) |
0.999778 | + | 0.0210824i | \(0.00671125\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5594.84 | − | 3230.18i | 0.416596 | − | 0.240522i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14068.6 | + | 8122.51i | −1.03653 | + | 0.598442i | −0.918849 | − | 0.394609i | \(-0.870880\pi\) |
−0.117683 | + | 0.993051i | \(0.537547\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1046.20 | − | 1812.07i | 0.0766761 | − | 0.132807i | −0.825138 | − | 0.564931i | \(-0.808903\pi\) |
0.901814 | + | 0.432125i | \(0.142236\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 11024.0 | − | 16687.3i | 0.803725 | − | 1.21662i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 8511.20i | − | 0.617290i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4200.54 | + | 2425.18i | 0.303069 | + | 0.174977i | 0.643821 | − | 0.765176i | \(-0.277348\pi\) |
−0.340752 | + | 0.940153i | \(0.610682\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −633.639 | + | 10511.4i | −0.0454803 | + | 0.754472i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2501.02 | − | 4331.89i | −0.177670 | − | 0.307733i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −312.169 | + | 2579.88i | −0.0220626 | + | 0.182333i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11785.0 | 0.828656 | 0.414328 | − | 0.910128i | \(-0.364017\pi\) | ||||
0.414328 | + | 0.910128i | \(0.364017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9151.64 | −0.640215 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1407.59 | + | 2817.00i | 0.0979707 | + | 0.196067i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3574.98 | − | 6192.05i | −0.247566 | − | 0.428798i | 0.715284 | − | 0.698834i | \(-0.246298\pi\) |
−0.962850 | + | 0.270037i | \(0.912964\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −15132.8 | − | 912.222i | −1.03743 | − | 0.0625373i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18893.6 | + | 10908.2i | 1.28877 | + | 0.744071i | 0.978435 | − | 0.206557i | \(-0.0662259\pi\) |
0.310334 | + | 0.950628i | \(0.399559\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5591.30i | − | 0.379490i | −0.981833 | − | 0.189745i | \(-0.939234\pi\) | ||
0.981833 | − | 0.189745i | \(-0.0607662\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6023.56 | + | 14121.6i | 0.406796 | + | 0.953690i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1963.72 | + | 3401.26i | −0.131961 | + | 0.228563i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2180.62 | + | 1258.98i | −0.145813 | + | 0.0841852i | −0.571132 | − | 0.820859i | \(-0.693495\pi\) |
0.425319 | + | 0.905044i | \(0.360162\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −374.083 | + | 215.977i | −0.0247689 | + | 0.0143003i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7826.27 | − | 13555.5i | 0.515661 | − | 0.893151i | −0.484174 | − | 0.874972i | \(-0.660880\pi\) |
0.999835 | − | 0.0181789i | \(-0.00578683\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 14859.9 | + | 9816.76i | 0.974320 | + | 0.643659i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 23431.7i | − | 1.52889i | −0.644688 | − | 0.764446i | \(-0.723013\pi\) | ||
0.644688 | − | 0.764446i | \(-0.276987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6719.35 | + | 3879.42i | 0.436306 | + | 0.251901i | 0.702030 | − | 0.712148i | \(-0.252277\pi\) |
−0.265723 | + | 0.964049i | \(0.585611\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4961.58 | − | 13894.6i | −0.320614 | − | 0.897860i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −521.012 | − | 902.419i | −0.0333448 | − | 0.0577548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9412.66 | + | 4703.31i | −0.599530 | + | 0.299573i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9150.25 | 0.580039 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18052.1 | −1.13889 | −0.569446 | − | 0.822029i | \(-0.692842\pi\) | ||||
−0.569446 | + | 0.822029i | \(0.692842\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 546.749 | − | 273.199i | 0.0343307 | − | 0.0171543i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 785.791 | + | 1361.03i | 0.0491074 | + | 0.0850564i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23283.8 | + | 17481.5i | 1.44146 | + | 1.08225i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4961.27 | + | 2864.39i | 0.305707 | + | 0.176500i | 0.645004 | − | 0.764179i | \(-0.276856\pi\) |
−0.339297 | + | 0.940679i | \(0.610189\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 707.722i | 0.0434056i | 0.999764 | + | 0.0217028i | \(0.00690876\pi\) | ||||
−0.999764 | + | 0.0217028i | \(0.993091\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1633.19 | − | 1078.92i | −0.0997005 | − | 0.0658644i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4440.24 | + | 7690.72i | −0.269805 | + | 0.467316i | −0.968811 | − | 0.247799i | \(-0.920293\pi\) |
0.699006 | + | 0.715116i | \(0.253626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −26711.7 | + | 15422.0i | −1.61561 | + | 0.932770i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8576.46 | + | 4951.62i | −0.513971 | + | 0.296741i | −0.734464 | − | 0.678647i | \(-0.762567\pi\) |
0.220494 | + | 0.975388i | \(0.429233\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5401.49 | − | 9355.65i | 0.322219 | − | 0.558100i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14830.7 | + | 6326.03i | −0.880671 | + | 0.375650i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25271.5i | 1.49384i | 0.664915 | + | 0.746919i | \(0.268468\pi\) | ||||
−0.664915 | + | 0.746919i | \(0.731532\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14626.1 | − | 8444.38i | −0.860649 | − | 0.496896i | 0.00358068 | − | 0.999994i | \(-0.498860\pi\) |
−0.864230 | + | 0.503098i | \(0.832194\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2455.47 | + | 148.018i | 0.143835 | + | 0.00867049i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12446.3 | − | 21557.6i | −0.722523 | − | 1.25145i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5357.18 | + | 10721.2i | 0.309597 | + | 0.619592i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3178.76 | −0.182883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17738.4 | 1.01600 | 0.507999 | − | 0.861358i | \(-0.330385\pi\) | ||||
0.507999 | + | 0.861358i | \(0.330385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8653.59 | − | 7351.51i | −0.493447 | − | 0.419200i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10421.1 | + | 18049.9i | 0.591603 | + | 1.02469i | 0.994017 | + | 0.109228i | \(0.0348379\pi\) |
−0.402414 | + | 0.915458i | \(0.631829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −521.512 | + | 8651.35i | −0.0293457 | + | 0.486814i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21819.3 | − | 12597.4i | −1.22239 | − | 0.705746i | −0.256961 | − | 0.966422i | \(-0.582721\pi\) |
−0.965426 | + | 0.260676i | \(0.916055\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 7099.28i | − | 0.395985i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10125.4 | − | 15327.0i | 0.562312 | − | 0.851184i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −827.003 | + | 1432.41i | −0.0457276 | + | 0.0792025i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1405.33 | − | 811.366i | 0.0773678 | − | 0.0446683i | −0.460817 | − | 0.887495i | \(-0.652444\pi\) |
0.538185 | + | 0.842827i | \(0.319110\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10663.3 | − | 6156.46i | 0.581989 | − | 0.336011i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8429.31 | − | 14600.0i | 0.458082 | − | 0.793421i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16275.2 | + | 24636.1i | −0.880664 | + | 1.33308i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24658.8i | − | 1.32860i | −0.747466 | − | 0.664300i | \(-0.768730\pi\) | ||
0.747466 | − | 0.664300i | \(-0.231270\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11208.4 | + | 6471.18i | 0.601327 | + | 0.347176i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −61.8338 | + | 1025.76i | −0.00330326 | + | 0.0547977i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3438.97 | − | 5956.48i | −0.182163 | − | 0.315515i | 0.760454 | − | 0.649392i | \(-0.224976\pi\) |
−0.942617 | + | 0.333877i | \(0.891643\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10753.0 | − | 1301.13i | −0.567185 | − | 0.0686303i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20839.1 | −1.09457 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4220.27 | 0.220740 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3542.89 | + | 7090.33i | 0.184535 | + | 0.369307i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8473.37 | + | 14676.3i | 0.439504 | + | 0.761243i | 0.997651 | − | 0.0684988i | \(-0.0218209\pi\) |
−0.558147 | + | 0.829742i | \(0.688488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27347.0 | + | 1648.51i | 1.40670 | + | 0.0847976i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −16590.9 | − | 9578.77i | −0.849891 | − | 0.490685i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4172.21i | 0.212845i | 0.994321 | + | 0.106423i | \(0.0339397\pi\) | ||||
−0.994321 | + | 0.106423i | \(0.966060\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −18412.6 | − | 6956.81i | −0.935456 | − | 0.353443i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −926.434 | + | 1604.63i | −0.0468747 | + | 0.0811893i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 26982.1 | − | 15578.1i | 1.35963 | − | 0.784981i | 0.370053 | − | 0.929011i | \(-0.379339\pi\) |
0.989573 | + | 0.144030i | \(0.0460061\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 21592.2 | − | 12466.3i | 1.07919 | − | 0.623068i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4705.41 | + | 8150.01i | −0.234224 | + | 0.405687i | −0.959047 | − | 0.283248i | \(-0.908588\pi\) |
0.724823 | + | 0.688935i | \(0.241921\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2903.09 | + | 1917.85i | 0.143924 | + | 0.0950795i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 26271.3i | 1.29717i | 0.761141 | + | 0.648586i | \(0.224639\pi\) | ||||
−0.761141 | + | 0.648586i | \(0.775361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10533.9 | + | 6081.73i | 0.518028 | + | 0.299084i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18115.6 | − | 24128.3i | 0.887304 | − | 1.18181i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9009.89 | − | 15605.6i | −0.437784 | − | 0.758264i | 0.559735 | − | 0.828672i | \(-0.310903\pi\) |
−0.997518 | + | 0.0704083i | \(0.977570\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −24638.7 | + | 12311.5i | −1.19241 | + | 0.595823i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21544.0 | −1.03850 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15356.6 | 0.737314 | 0.368657 | − | 0.929565i | \(-0.379818\pi\) | ||||
0.368657 | + | 0.929565i | \(0.379818\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −21433.5 | + | 10709.8i | −1.02501 | + | 0.512177i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13195.0 | − | 22854.4i | −0.628538 | − | 1.08866i | −0.987845 | − | 0.155440i | \(-0.950320\pi\) |
0.359308 | − | 0.933219i | \(-0.383013\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3513.71 | − | 4679.93i | 0.166063 | − | 0.221181i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8832.67 | + | 5099.55i | 0.415814 | + | 0.240070i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12445.2i | 0.583594i | 0.956480 | + | 0.291797i | \(0.0942531\pi\) | ||||
−0.956480 | + | 0.291797i | \(0.905747\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10120.5 | + | 6685.82i | 0.472737 | + | 0.312301i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 691.097 | − | 1197.02i | 0.0321566 | − | 0.0556968i | −0.849499 | − | 0.527590i | \(-0.823096\pi\) |
0.881656 | + | 0.471893i | \(0.156429\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13889.2 | + | 8018.96i | −0.643763 | + | 0.371677i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20650.6 | − | 11922.6i | 0.949788 | − | 0.548361i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23642.1 | − | 40949.3i | 1.08320 | − | 1.87616i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −32668.7 | − | 5965.78i | −1.49104 | − | 0.272286i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 353.105i | 0.0160546i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28319.4 | + | 16350.2i | 1.28269 | + | 0.740561i | 0.977339 | − | 0.211679i | \(-0.0678930\pi\) |
0.305351 | + | 0.952240i | \(0.401226\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9864.34 | + | 594.632i | 0.445095 | + | 0.0268308i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 525.554 | + | 910.286i | 0.0235346 | + | 0.0407632i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1758.83 | + | 3519.92i | 0.0784646 | + | 0.157030i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −681.223 | −0.0302762 | −0.0151381 | − | 0.999885i | \(-0.504819\pi\) | ||||
−0.0151381 | + | 0.999885i | \(0.504819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 972.747 | 0.0430705 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1884.93 | − | 228.079i | −0.0831469 | − | 0.0100609i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13092.3 | + | 22676.5i | 0.575363 | + | 0.996558i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2466.20 | + | 40911.7i | −0.107576 | + | 1.78458i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 11581.6 | + | 6686.62i | 0.503321 | + | 0.290592i | 0.730084 | − | 0.683358i | \(-0.239481\pi\) |
−0.226763 | + | 0.973950i | \(0.572814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1304.58i | − | 0.0564858i | −0.999601 | − | 0.0282429i | \(-0.991009\pi\) | ||
0.999601 | − | 0.0282429i | \(-0.00899119\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 11410.9 | − | 17273.0i | 0.492249 | − | 0.745129i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9282.14 | + | 16077.1i | −0.398944 | + | 0.690991i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2269.63 | + | 1310.37i | −0.0971902 | + | 0.0561128i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7252.60 | + | 4187.29i | −0.308304 | + | 0.177999i | −0.646167 | − | 0.763196i | \(-0.723629\pi\) |
0.337863 | + | 0.941195i | \(0.390296\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4020.92 | + | 6964.45i | −0.170305 | + | 0.294976i | −0.938526 | − | 0.345208i | \(-0.887808\pi\) |
0.768222 | + | 0.640184i | \(0.221142\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10164.2 | + | 15385.8i | −0.428936 | + | 0.649290i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 31465.2i | − | 1.32304i | −0.749929 | − | 0.661518i | \(-0.769912\pi\) | ||
0.749929 | − | 0.661518i | \(-0.230088\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18956.6 | + | 10944.6i | 0.794197 | + | 0.458530i | 0.841438 | − | 0.540354i | \(-0.181710\pi\) |
−0.0472413 | + | 0.998884i | \(0.515043\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1598.81 | + | 26522.7i | −0.0667415 | + | 1.10717i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8554.54 | − | 14816.9i | −0.354541 | − | 0.614084i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17999.7 | + | 21187.7i | −0.743320 | + | 0.874974i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2711.16 | −0.111561 | −0.0557805 | − | 0.998443i | \(-0.517765\pi\) | ||||
−0.0557805 | + | 0.998443i | \(0.517765\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31640.8 | −1.29734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8223.36 | + | 16457.3i | 0.335976 | + | 0.672383i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6594.35 | + | 11421.7i | 0.268464 | + | 0.464994i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5943.84 | + | 358.301i | 0.240273 | + | 0.0144839i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25522.5 | + | 14735.4i | 1.02809 | + | 0.593565i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44949.9i | 1.80428i | 0.431439 | + | 0.902142i | \(0.358006\pi\) | ||||
−0.431439 | + | 0.902142i | \(0.641994\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7613.75 | − | 3247.64i | 0.304544 | − | 0.129903i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11539.2 | + | 19986.5i | −0.459944 | + | 0.796646i | −0.998957 | − | 0.0456511i | \(-0.985464\pi\) |
0.539014 | + | 0.842297i | \(0.318797\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8348.67 | + | 4820.11i | −0.331610 | + | 0.191455i | −0.656556 | − | 0.754278i | \(-0.727987\pi\) |
0.324946 | + | 0.945733i | \(0.394654\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5925.92 | + | 3421.33i | −0.233743 | + | 0.134952i | −0.612298 | − | 0.790627i | \(-0.709755\pi\) |
0.378554 | + | 0.925579i | \(0.376421\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3689.88 | + | 6391.06i | −0.145040 | + | 0.251217i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16678.3 | + | 11018.0i | 0.653314 | + | 0.431594i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17590.2i | 0.686658i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7139.82 | − | 4122.18i | −0.277754 | − | 0.160361i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29614.2 | − | 22234.4i | −1.14810 | − | 0.861995i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16666.3 | + | 28866.9i | 0.641712 | + | 1.11148i | 0.985050 | + | 0.172266i | \(0.0551089\pi\) |
−0.343338 | + | 0.939212i | \(0.611558\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2663.82 | + | 1331.05i | −0.102217 | + | 0.0510755i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38528.6 | −1.47339 | −0.736697 | − | 0.676223i | \(-0.763616\pi\) | ||||
−0.736697 | + | 0.676223i | \(0.763616\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22794.5 | −0.868740 | −0.434370 | − | 0.900735i | \(-0.643029\pi\) | ||||
−0.434370 | + | 0.900735i | \(0.643029\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 21704.9 | − | 10845.5i | 0.824410 | − | 0.411940i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3079.33 | + | 5333.55i | 0.116566 | + | 0.201898i | 0.918405 | − | 0.395643i | \(-0.129478\pi\) |
−0.801839 | + | 0.597540i | \(0.796145\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −7624.04 | + | 31042.6i | −0.286661 | + | 1.16719i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1191.55 | + | 687.940i | 0.0446513 | + | 0.0257794i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1573.72i | 0.0587749i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6610.59 | + | 4367.11i | 0.246066 | + | 0.162557i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −23452.9 | + | 40621.7i | −0.870077 | + | 1.50702i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3225.74 | − | 1862.38i | 0.119273 | − | 0.0688623i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26602.7 | + | 15359.1i | −0.977132 | + | 0.564147i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25570.4 | − | 44289.2i | 0.936108 | − | 1.62139i | 0.163463 | − | 0.986549i | \(-0.447734\pi\) |
0.772645 | − | 0.634838i | \(-0.218933\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6144.23 | − | 14404.5i | −0.224193 | − | 0.525596i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15259.4i | − | 0.554959i | −0.960732 | − | 0.277479i | \(-0.910501\pi\) | ||
0.960732 | − | 0.277479i | \(-0.0894990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42434.6 | − | 24499.6i | −1.53821 | − | 0.888083i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2496.06 | + | 150.465i | 0.0901828 | + | 0.00543631i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23084.5 | − | 39983.5i | −0.828604 | − | 1.43518i | −0.899134 | − | 0.437674i | \(-0.855802\pi\) |
0.0705297 | − | 0.997510i | \(-0.477531\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 18352.4 | + | 36728.4i | 0.656605 | + | 1.31405i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −15635.3 | −0.557575 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 22681.0 | 0.806213 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5028.45 | + | 41556.9i | −0.178162 | + | 1.47239i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16030.0 | − | 27764.8i | −0.566122 | − | 0.980552i | −0.996944 | − | 0.0781156i | \(-0.975110\pi\) |
0.430822 | − | 0.902437i | \(-0.358224\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2541.71 | − | 42164.4i | 0.0891875 | − | 1.47953i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8230.62 | − | 4751.95i | −0.287883 | − | 0.166209i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 638.223i | 0.0222517i | 0.999938 | + | 0.0111259i | \(0.00354154\pi\) | ||||
−0.999938 | + | 0.0111259i | \(0.996458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15063.9 | + | 22802.5i | −0.523527 | + | 0.792474i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16765.1 | − | 29038.1i | 0.580794 | − | 1.00597i | −0.414591 | − | 0.910008i | \(-0.636075\pi\) |
0.995385 | − | 0.0959576i | \(-0.0305913\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47023.3 | − | 27148.9i | 1.62385 | − | 0.937529i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30071.3 | + | 17361.7i | −1.03188 | + | 0.595754i | −0.917522 | − | 0.397686i | \(-0.869814\pi\) |
−0.114355 | + | 0.993440i | \(0.536480\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4329.18 | − | 7498.35i | 0.148083 | − | 0.256488i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4247.53 | − | 6429.58i | 0.144832 | − | 0.219236i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49736.7i | 1.69059i | 0.534302 | + | 0.845294i | \(0.320575\pi\) | ||||
−0.534302 | + | 0.845294i | \(0.679425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22127.3 | + | 12775.2i | 0.749762 | + | 0.432875i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3245.14 | + | 53833.5i | −0.109614 | + | 1.81838i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4738.33 | + | 8207.03i | 0.159053 | + | 0.275487i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4237.56 | + | 35020.7i | −0.141800 | + | 1.17188i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13453.0 | −0.448775 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −36764.6 | −1.22262 | −0.611308 | − | 0.791393i | \(-0.709356\pi\) | ||||
−0.611308 | + | 0.791393i | \(0.709356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3502.32 | − | 7009.14i | −0.116110 | − | 0.232369i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9497.23 | − | 16449.7i | −0.313883 | − | 0.543661i | 0.665316 | − | 0.746562i | \(-0.268297\pi\) |
−0.979199 | + | 0.202900i | \(0.934963\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 6086.44 | + | 366.897i | 0.199920 | + | 0.0120514i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −45364.2 | − | 26191.0i | −1.48550 | − | 0.857651i | −0.485632 | − | 0.874163i | \(-0.661411\pi\) |
−0.999864 | + | 0.0165117i | \(0.994744\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3083.44i | 0.100661i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5083.67 | + | 11918.1i | 0.165453 | + | 0.387886i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −634.096 | + | 1098.29i | −0.0205743 | + | 0.0356357i | −0.876129 | − | 0.482076i | \(-0.839883\pi\) |
0.855555 | + | 0.517712i | \(0.173216\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3484.07 | + | 2011.53i | −0.112702 | + | 0.0650687i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5168.15 | + | 2983.83i | −0.166165 | + | 0.0959356i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3885.49 | + | 6729.86i | −0.124548 | + | 0.215723i | −0.921556 | − | 0.388246i | \(-0.873081\pi\) |
0.797008 | + | 0.603968i | \(0.206415\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −17069.9 | − | 11276.8i | −0.545515 | − | 0.360380i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 19367.7i | − | 0.617083i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34262.8 | − | 19781.7i | −1.08838 | − | 0.628376i | −0.155235 | − | 0.987878i | \(-0.549614\pi\) |
−0.933145 | + | 0.359501i | \(0.882947\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 37026.9 | − | 13221.8i | 1.17265 | − | 0.418739i |
(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 | 588.4.k.d.521.7 | 16 | ||
3.2 | odd | 2 | inner | 588.4.k.d.521.5 | 16 | ||
7.2 | even | 3 | inner | 588.4.k.d.509.4 | 16 | ||
7.3 | odd | 6 | 84.4.f.a.41.8 | yes | 8 | ||
7.4 | even | 3 | 84.4.f.a.41.1 | ✓ | 8 | ||
7.5 | odd | 6 | inner | 588.4.k.d.509.5 | 16 | ||
7.6 | odd | 2 | inner | 588.4.k.d.521.2 | 16 | ||
21.2 | odd | 6 | inner | 588.4.k.d.509.2 | 16 | ||
21.5 | even | 6 | inner | 588.4.k.d.509.7 | 16 | ||
21.11 | odd | 6 | 84.4.f.a.41.7 | yes | 8 | ||
21.17 | even | 6 | 84.4.f.a.41.2 | yes | 8 | ||
21.20 | even | 2 | inner | 588.4.k.d.521.4 | 16 | ||
28.3 | even | 6 | 336.4.k.d.209.1 | 8 | |||
28.11 | odd | 6 | 336.4.k.d.209.8 | 8 | |||
84.11 | even | 6 | 336.4.k.d.209.2 | 8 | |||
84.59 | odd | 6 | 336.4.k.d.209.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.f.a.41.1 | ✓ | 8 | 7.4 | even | 3 | ||
84.4.f.a.41.2 | yes | 8 | 21.17 | even | 6 | ||
84.4.f.a.41.7 | yes | 8 | 21.11 | odd | 6 | ||
84.4.f.a.41.8 | yes | 8 | 7.3 | odd | 6 | ||
336.4.k.d.209.1 | 8 | 28.3 | even | 6 | |||
336.4.k.d.209.2 | 8 | 84.11 | even | 6 | |||
336.4.k.d.209.7 | 8 | 84.59 | odd | 6 | |||
336.4.k.d.209.8 | 8 | 28.11 | odd | 6 | |||
588.4.k.d.509.2 | 16 | 21.2 | odd | 6 | inner | ||
588.4.k.d.509.4 | 16 | 7.2 | even | 3 | inner | ||
588.4.k.d.509.5 | 16 | 7.5 | odd | 6 | inner | ||
588.4.k.d.509.7 | 16 | 21.5 | even | 6 | inner | ||
588.4.k.d.521.2 | 16 | 7.6 | odd | 2 | inner | ||
588.4.k.d.521.4 | 16 | 21.20 | even | 2 | inner | ||
588.4.k.d.521.5 | 16 | 3.2 | odd | 2 | inner | ||
588.4.k.d.521.7 | 16 | 1.1 | even | 1 | trivial |