Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1657.4 | ||
Character | \(\chi\) | \(=\) | 2100.1657 |
Dual form | 2100.2.ce.c.493.4 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 0.258819 | − | 0.965926i | 0.149429 | − | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.36577 | + | 1.18454i | 0.894176 | + | 0.447716i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25649 | − | 3.90835i | −0.680357 | − | 1.17841i | −0.974872 | − | 0.222766i | \(-0.928492\pi\) |
0.294515 | − | 0.955647i | \(-0.404842\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.37238 | − | 4.37238i | −1.21268 | − | 1.21268i | −0.970142 | − | 0.242537i | \(-0.922020\pi\) |
−0.242537 | − | 0.970142i | \(-0.577980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.35920 | − | 1.16804i | −1.05726 | − | 0.283292i | −0.312012 | − | 0.950078i | \(-0.601003\pi\) |
−0.745249 | + | 0.666786i | \(0.767670\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.51045 | + | 4.34823i | −0.575937 | + | 0.997552i | 0.420003 | + | 0.907523i | \(0.362029\pi\) |
−0.995939 | + | 0.0900286i | \(0.971304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.75649 | − | 1.97857i | 0.383297 | − | 0.431760i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.44721 | + | 5.40108i | 0.301765 | + | 1.12620i | 0.935694 | + | 0.352812i | \(0.114774\pi\) |
−0.633929 | + | 0.773391i | \(0.718559\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.92124 | + | 2.26393i | −0.704275 | + | 0.406613i | −0.808938 | − | 0.587894i | \(-0.799957\pi\) |
0.104663 | + | 0.994508i | \(0.466624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.35920 | + | 1.16804i | −0.758839 | + | 0.203330i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.67303 | − | 0.448288i | 0.275045 | − | 0.0736980i | −0.118660 | − | 0.992935i | \(-0.537860\pi\) |
0.393705 | + | 0.919237i | \(0.371193\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.35505 | + | 3.09174i | −0.857494 | + | 0.495074i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.22509i | 0.347501i | 0.984790 | + | 0.173751i | \(0.0555887\pi\) | ||||
−0.984790 | + | 0.173751i | \(0.944411\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.85281 | + | 7.85281i | −1.19754 | + | 1.19754i | −0.222642 | + | 0.974900i | \(0.571468\pi\) |
−0.974900 | + | 0.222642i | \(0.928532\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.33357 | − | 12.4411i | −0.486251 | − | 1.81471i | −0.574359 | − | 0.818604i | \(-0.694749\pi\) |
0.0881077 | − | 0.996111i | \(-0.471918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.19371 | + | 5.60471i | 0.599101 | + | 0.800673i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.25649 | + | 3.90835i | −0.315972 | + | 0.547279i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.8489 | − | 3.17491i | −1.62757 | − | 0.436107i | −0.674359 | − | 0.738404i | \(-0.735580\pi\) |
−0.953214 | + | 0.302297i | \(0.902247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.55031 | + | 3.55031i | 0.470250 | + | 0.470250i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.11255 | − | 1.92699i | −0.144841 | − | 0.250873i | 0.784472 | − | 0.620164i | \(-0.212934\pi\) |
−0.929314 | + | 0.369291i | \(0.879601\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.34248 | + | 3.66183i | 0.812071 | + | 0.468849i | 0.847674 | − | 0.530517i | \(-0.178002\pi\) |
−0.0356037 | + | 0.999366i | \(0.511335\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.45654 | − | 2.20873i | −0.183507 | − | 0.278274i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.29950 | − | 4.84982i | 0.158760 | − | 0.592499i | −0.839994 | − | 0.542595i | \(-0.817442\pi\) |
0.998754 | − | 0.0499041i | \(-0.0158916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.59161 | 0.673151 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.3670 | 1.70504 | 0.852522 | − | 0.522692i | \(-0.175072\pi\) | ||||
0.852522 | + | 0.522692i | \(0.175072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.12353 | − | 4.19308i | 0.131500 | − | 0.490763i | −0.868488 | − | 0.495710i | \(-0.834908\pi\) |
0.999988 | + | 0.00494658i | \(0.00157455\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.708707 | − | 11.9192i | −0.0807646 | − | 1.35831i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.58312 | − | 0.914012i | −0.178114 | − | 0.102834i | 0.408292 | − | 0.912851i | \(-0.366125\pi\) |
−0.586406 | + | 0.810017i | \(0.699458\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.2105 | − | 11.2105i | −1.23051 | − | 1.23051i | −0.963769 | − | 0.266738i | \(-0.914054\pi\) |
−0.266738 | − | 0.963769i | \(-0.585946\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.90835 | + | 6.76946i | −0.414284 | + | 0.717562i | −0.995353 | − | 0.0962928i | \(-0.969301\pi\) |
0.581069 | + | 0.813855i | \(0.302635\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.16475 | − | 15.5233i | −0.541413 | − | 1.62728i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.17190 | + | 4.37357i | 0.121520 | + | 0.453518i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.53553 | + | 3.53553i | −0.358979 | + | 0.358979i | −0.863437 | − | 0.504457i | \(-0.831693\pi\) |
0.504457 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.51298i | 0.453571i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.08451 | + | 3.51290i | −0.605432 | + | 0.349546i | −0.771175 | − | 0.636623i | \(-0.780331\pi\) |
0.165744 | + | 0.986169i | \(0.446998\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.02982 | − | 1.07979i | 0.397070 | − | 0.106395i | −0.0547581 | − | 0.998500i | \(-0.517439\pi\) |
0.451828 | + | 0.892105i | \(0.350772\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.78639 | − | 1.81841i | 0.656065 | − | 0.175792i | 0.0845956 | − | 0.996415i | \(-0.473040\pi\) |
0.571470 | + | 0.820623i | \(0.306373\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7125 | + | 6.76224i | −1.12186 | + | 0.647705i | −0.941875 | − | 0.335965i | \(-0.890938\pi\) |
−0.179983 | + | 0.983670i | \(0.557604\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 1.73205i | − | 0.164399i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.34847 | − | 7.34847i | 0.691286 | − | 0.691286i | −0.271229 | − | 0.962515i | \(-0.587430\pi\) |
0.962515 | + | 0.271229i | \(0.0874301\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.60040 | + | 5.97278i | 0.147957 | + | 0.552184i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.92925 | − | 7.92699i | −0.818543 | − | 0.726666i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.68348 | + | 8.11202i | −0.425771 | + | 0.737456i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.14928 | + | 0.575897i | 0.193794 | + | 0.0519269i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.7059 | − | 10.7059i | −0.949991 | − | 0.949991i | 0.0488168 | − | 0.998808i | \(-0.484455\pi\) |
−0.998808 | + | 0.0488168i | \(0.984455\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.55278 | + | 9.61769i | 0.488895 | + | 0.846790i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.8540 | + | 7.42125i | 1.12306 | + | 0.648397i | 0.942180 | − | 0.335108i | \(-0.108773\pi\) |
0.180878 | + | 0.983506i | \(0.442106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.0898 | + | 7.31315i | −0.961608 | + | 0.634131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.295421 | + | 1.10253i | −0.0252395 | + | 0.0941953i | −0.977397 | − | 0.211414i | \(-0.932193\pi\) |
0.952157 | + | 0.305609i | \(0.0988600\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.5766 | −1.74529 | −0.872644 | − | 0.488357i | \(-0.837596\pi\) | ||||
−0.872644 | + | 0.488357i | \(0.837596\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.8799 | −1.08469 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.22257 | + | 26.9550i | −0.603982 | + | 2.25409i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.49915 | − | 2.60020i | 0.536041 | − | 0.214461i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9212 | − | 9.76946i | −1.38624 | − | 0.800346i | −0.393350 | − | 0.919389i | \(-0.628684\pi\) |
−0.992889 | + | 0.119043i | \(0.962017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.75649 | + | 9.97053i | 0.468456 | + | 0.811390i | 0.999350 | − | 0.0360482i | \(-0.0114770\pi\) |
−0.530894 | + | 0.847438i | \(0.678144\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.19116 | + | 3.19116i | 0.257990 | + | 0.257990i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.75247 | + | 2.07727i | 0.618715 | + | 0.165784i | 0.554543 | − | 0.832155i | \(-0.312893\pi\) |
0.0641713 | + | 0.997939i | \(0.479560\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.13345 | + | 10.6234i | −0.486414 | + | 0.842494i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.97405 | + | 14.4920i | −0.234388 | + | 1.14213i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.11490 | + | 4.16087i | 0.0873259 | + | 0.325905i | 0.995744 | − | 0.0921571i | \(-0.0293762\pi\) |
−0.908419 | + | 0.418062i | \(0.862710\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.119519 | − | 0.119519i | 0.00924866 | − | 0.00924866i | −0.702467 | − | 0.711716i | \(-0.747918\pi\) |
0.711716 | + | 0.702467i | \(0.247918\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.2354i | 1.94118i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.34823 | − | 2.51045i | 0.332517 | − | 0.191979i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.5140 | + | 3.88900i | −1.10348 | + | 0.295675i | −0.764179 | − | 0.645004i | \(-0.776856\pi\) |
−0.339296 | + | 0.940679i | \(0.610189\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.14928 | + | 0.575897i | −0.161549 | + | 0.0432871i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.0676 | − | 9.85398i | 1.27569 | − | 0.736521i | 0.299638 | − | 0.954053i | \(-0.403134\pi\) |
0.976053 | + | 0.217532i | \(0.0698007\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.32855i | − | 0.693386i | −0.937979 | − | 0.346693i | \(-0.887305\pi\) | ||
0.937979 | − | 0.346693i | \(-0.112695\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.17861 | − | 5.17861i | 0.382814 | − | 0.382814i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.27136 | + | 19.6730i | 0.385480 | + | 1.43863i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.51045 | + | 0.835250i | −0.182608 | + | 0.0607555i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.95294 | − | 13.7749i | 0.575455 | − | 0.996717i | −0.420538 | − | 0.907275i | \(-0.638158\pi\) |
0.995992 | − | 0.0894414i | \(-0.0285082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.37357 | + | 1.17190i | 0.314817 | + | 0.0843549i | 0.412768 | − | 0.910836i | \(-0.364562\pi\) |
−0.0979510 | + | 0.995191i | \(0.531229\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −17.5959 | − | 17.5959i | −1.25365 | − | 1.25365i | −0.954071 | − | 0.299582i | \(-0.903153\pi\) |
−0.299582 | − | 0.954071i | \(-0.596847\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.59912 | + | 7.96592i | 0.326023 | + | 0.564689i | 0.981719 | − | 0.190336i | \(-0.0609579\pi\) |
−0.655696 | + | 0.755025i | \(0.727625\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.34823 | − | 2.51045i | −0.306700 | − | 0.177073i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.44721 | − | 5.40108i | 0.100588 | − | 0.375401i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.6592 | 1.56737 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.14602 | 0.216581 | 0.108291 | − | 0.994119i | \(-0.465462\pi\) | ||||
0.108291 | + | 0.994119i | \(0.465462\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 3.71844 | − | 13.8774i | 0.254783 | − | 0.950865i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.9585 | + | 0.711043i | −0.811793 | + | 0.0482688i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.75942 | − | 2.17050i | −0.254038 | − | 0.146669i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 13.9529 | + | 24.1672i | 0.938576 | + | 1.62566i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.46722 | − | 6.46722i | −0.433077 | − | 0.433077i | 0.456597 | − | 0.889674i | \(-0.349068\pi\) |
−0.889674 | + | 0.456597i | \(0.849068\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −15.1505 | − | 4.05956i | −1.00557 | − | 0.269443i | −0.281795 | − | 0.959475i | \(-0.590930\pi\) |
−0.723779 | + | 0.690032i | \(0.757596\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.21461 | − | 15.9602i | 0.608918 | − | 1.05468i | −0.382501 | − | 0.923955i | \(-0.624937\pi\) |
0.991419 | − | 0.130722i | \(-0.0417296\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.6965 | − | 2.40035i | −0.769570 | − | 0.157931i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.666615 | + | 2.48784i | 0.0436714 | + | 0.162984i | 0.984318 | − | 0.176404i | \(-0.0564466\pi\) |
−0.940646 | + | 0.339388i | \(0.889780\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.29261 | + | 1.29261i | −0.0839640 | + | 0.0839640i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.607095i | 0.0392697i | 0.999807 | + | 0.0196349i | \(0.00625037\pi\) | ||||
−0.999807 | + | 0.0196349i | \(0.993750\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.50000 | + | 4.33013i | −0.483117 | + | 0.278928i | −0.721715 | − | 0.692191i | \(-0.756646\pi\) |
0.238597 | + | 0.971119i | \(0.423312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.965926 | − | 0.258819i | 0.0619642 | − | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 29.9887 | − | 8.03545i | 1.90814 | − | 0.511284i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.7299 | + | 7.92699i | −0.870100 | + | 0.502352i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 28.2508i | − | 1.78318i | −0.452848 | − | 0.891588i | \(-0.649592\pi\) | ||
0.452848 | − | 0.891588i | \(-0.350408\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.8437 | − | 17.8437i | 1.12182 | − | 1.12182i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.33861 | + | 4.99574i | 0.0834999 | + | 0.311626i | 0.995026 | − | 0.0996165i | \(-0.0317616\pi\) |
−0.911526 | + | 0.411243i | \(0.865095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.48902 | + | 0.921238i | 0.278934 | + | 0.0572429i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.4393 | + | 4.13694i | 0.952027 | + | 0.255095i | 0.701222 | − | 0.712943i | \(-0.252638\pi\) |
0.250805 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.52724 | + | 5.52724i | 0.338262 | + | 0.338262i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.75400 | − | 15.1624i | −0.533741 | − | 0.924466i | −0.999223 | − | 0.0394089i | \(-0.987453\pi\) |
0.465483 | − | 0.885057i | \(-0.345881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.38140 | − | 5.41636i | −0.569880 | − | 0.329020i | 0.187222 | − | 0.982318i | \(-0.440052\pi\) |
−0.757101 | + | 0.653298i | \(0.773385\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16.3311 | + | 0.971038i | −0.988403 | + | 0.0587699i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.02719 | + | 11.2976i | −0.181887 | + | 0.678810i | 0.813389 | + | 0.581720i | \(0.197620\pi\) |
−0.995276 | + | 0.0970897i | \(0.969047\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.52786 | 0.271076 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.5389 | 1.52352 | 0.761762 | − | 0.647857i | \(-0.224334\pi\) | ||||
0.761762 | + | 0.647857i | \(0.224334\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.41038 | − | 16.4598i | 0.262170 | − | 0.978431i | −0.701790 | − | 0.712384i | \(-0.747616\pi\) |
0.963960 | − | 0.266048i | \(-0.0857178\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.63572 | + | 5.26406i | −0.155582 | + | 0.310727i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.91587 | + | 1.68348i | 0.171522 | + | 0.0990280i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.50000 | + | 4.33013i | 0.146553 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.429281 | − | 0.429281i | −0.0250789 | − | 0.0250789i | 0.694456 | − | 0.719535i | \(-0.255645\pi\) |
−0.719535 | + | 0.694456i | \(0.755645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.35920 | + | 1.16804i | 0.252946 | + | 0.0677768i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.2878 | − | 29.9433i | 0.999779 | − | 1.73167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.8799 | + | 9.27591i | −1.60697 | + | 0.534655i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.81841 | + | 6.78639i | 0.104465 | + | 0.389868i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.2390 | − | 11.2390i | 0.641445 | − | 0.641445i | −0.309466 | − | 0.950911i | \(-0.600150\pi\) |
0.950911 | + | 0.309466i | \(0.100150\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.17198i | − | 0.237335i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.988499 | + | 0.570710i | −0.0560526 | + | 0.0323620i | −0.527764 | − | 0.849391i | \(-0.676970\pi\) |
0.471712 | + | 0.881753i | \(0.343636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.34809 | + | 1.16507i | −0.245769 | + | 0.0658535i | −0.379600 | − | 0.925151i | \(-0.623939\pi\) |
0.133832 | + | 0.991004i | \(0.457272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −9.36107 | + | 2.50829i | −0.525770 | + | 0.140880i | −0.511934 | − | 0.859025i | \(-0.671071\pi\) |
−0.0138358 | + | 0.999904i | \(0.504404\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 7.02579i | − | 0.392141i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.0225 | − | 16.0225i | 0.891514 | − | 0.891514i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.50039 | + | 13.0636i | 0.193572 | + | 0.722421i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.85054 | − | 33.3814i | 0.377682 | − | 1.84038i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.90251 | + | 3.29525i | −0.104571 | + | 0.181123i | −0.913563 | − | 0.406697i | \(-0.866680\pi\) |
0.808992 | + | 0.587820i | \(0.200014\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.67303 | − | 0.448288i | −0.0916816 | − | 0.0245660i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.8616 | + | 10.8616i | 0.591667 | + | 0.591667i | 0.938082 | − | 0.346415i | \(-0.112601\pi\) |
−0.346415 | + | 0.938082i | \(0.612601\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.19615 | − | 9.00000i | −0.282216 | − | 0.488813i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.6965 | + | 10.2171i | 0.958317 | + | 0.553284i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.28230 | + | 18.2271i | 0.177227 | + | 0.984170i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.47033 | − | 12.9514i | 0.186297 | − | 0.695270i | −0.808052 | − | 0.589111i | \(-0.799478\pi\) |
0.994349 | − | 0.106159i | \(-0.0338552\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 35.2766 | 1.88831 | 0.944156 | − | 0.329497i | \(-0.106879\pi\) | ||||
0.944156 | + | 0.329497i | \(0.106879\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.18348 | 0.330050 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.15461 | + | 4.30906i | −0.0614537 | + | 0.229348i | −0.989821 | − | 0.142314i | \(-0.954546\pi\) |
0.928368 | + | 0.371663i | \(0.121212\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.96794 | + | 6.57334i | −0.527559 | + | 0.347898i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0129 | + | 5.78097i | 0.528462 | + | 0.305108i | 0.740390 | − | 0.672178i | \(-0.234641\pi\) |
−0.211928 | + | 0.977285i | \(0.567974\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.10471 | − | 5.37752i | −0.163406 | − | 0.283028i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.62344 | + | 6.62344i | 0.347640 | + | 0.347640i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.72055 | − | 0.728970i | −0.142012 | − | 0.0380519i | 0.187113 | − | 0.982338i | \(-0.440087\pi\) |
−0.329125 | + | 0.944286i | \(0.606754\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.11255 | − | 1.92699i | 0.0579169 | − | 0.100315i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.2709 | − | 21.5467i | −1.26008 | − | 1.11865i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.10306 | + | 22.7769i | 0.316004 | + | 1.17934i | 0.923051 | + | 0.384678i | \(0.125688\pi\) |
−0.607046 | + | 0.794667i | \(0.707646\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.6445i | 0.649507i | 0.945799 | + | 0.324753i | \(0.105281\pi\) | ||||
−0.945799 | + | 0.324753i | \(0.894719\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.1119 | + | 7.57018i | −0.671745 | + | 0.387832i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.08186 | + | 2.16553i | −0.412964 | + | 0.110653i | −0.459318 | − | 0.888272i | \(-0.651906\pi\) |
0.0463547 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.7271 | − | 2.87433i | 0.545291 | − | 0.146110i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.77182 | − | 2.75501i | 0.241941 | − | 0.139685i | −0.374128 | − | 0.927377i | \(-0.622058\pi\) |
0.616069 | + | 0.787693i | \(0.288724\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 25.2348i | − | 1.27618i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.4952 | − | 10.4952i | 0.529414 | − | 0.529414i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.49612 | + | 20.5118i | 0.275842 | + | 1.02946i | 0.955275 | + | 0.295720i | \(0.0955594\pi\) |
−0.679432 | + | 0.733738i | \(0.737774\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.19371 | + | 12.6047i | 0.209948 | + | 0.631025i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.26799 | + | 12.5885i | −0.362946 | + | 0.628641i | −0.988444 | − | 0.151585i | \(-0.951562\pi\) |
0.625498 | + | 0.780226i | \(0.284896\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 27.0439 | + | 7.24639i | 1.34715 | + | 0.360968i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.52724 | − | 5.52724i | −0.273975 | − | 0.273975i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.21461 | − | 15.9602i | −0.455633 | − | 0.789179i | 0.543091 | − | 0.839674i | \(-0.317254\pi\) |
−0.998724 | + | 0.0504942i | \(0.983920\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.988499 | + | 0.570710i | 0.0487591 | + | 0.0281511i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.349423 | − | 5.87667i | −0.0171940 | − | 0.289172i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.32563 | + | 19.8755i | −0.260797 | + | 0.973308i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.74904 | −0.476272 | −0.238136 | − | 0.971232i | \(-0.576536\pi\) | ||||
−0.238136 | + | 0.971232i | \(0.576536\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.6330 | 0.518223 | 0.259112 | − | 0.965847i | \(-0.416570\pi\) | ||||
0.259112 | + | 0.965847i | \(0.416570\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.33357 | + | 12.4411i | −0.162084 | + | 0.604905i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.6672 | + | 16.1760i | 0.516223 | + | 0.782811i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 24.1672 | + | 13.9529i | 1.16680 | + | 0.673654i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.2354 | − | 28.1205i | −0.782031 | − | 1.35452i | −0.930757 | − | 0.365639i | \(-0.880851\pi\) |
0.148726 | − | 0.988878i | \(-0.452483\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.2782 | − | 23.2782i | −1.11868 | − | 1.11868i | −0.991936 | − | 0.126743i | \(-0.959548\pi\) |
−0.126743 | − | 0.991936i | \(-0.540452\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −27.1183 | − | 7.26632i | −1.29724 | − | 0.347595i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.99947 | + | 12.1234i | −0.334067 | + | 0.578620i | −0.983305 | − | 0.181965i | \(-0.941754\pi\) |
0.649239 | + | 0.760585i | \(0.275088\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.829500 | − | 6.95068i | −0.0395000 | − | 0.330985i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.204704 | − | 0.763964i | −0.00972576 | − | 0.0362970i | 0.960892 | − | 0.276922i | \(-0.0893143\pi\) |
−0.970618 | + | 0.240625i | \(0.922648\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.8161 | + | 13.8161i | −0.653480 | + | 0.653480i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 15.9059i | − | 0.750645i | −0.926894 | − | 0.375322i | \(-0.877532\pi\) | ||
0.926894 | − | 0.375322i | \(-0.122468\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.69645 | − | 5.02090i | 0.409500 | − | 0.236425i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.1207 | − | 2.97978i | 0.522495 | − | 0.140002i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −35.4090 | + | 9.48783i | −1.65637 | + | 0.443822i | −0.961385 | − | 0.275207i | \(-0.911254\pi\) |
−0.694980 | + | 0.719029i | \(0.744587\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.90835 | − | 2.25649i | 0.182426 | − | 0.105324i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1415i | 0.658634i | 0.944219 | + | 0.329317i | \(0.106819\pi\) | ||||
−0.944219 | + | 0.329317i | \(0.893181\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.4119 | − | 16.4119i | 0.762728 | − | 0.762728i | −0.214087 | − | 0.976815i | \(-0.568678\pi\) |
0.976815 | + | 0.214087i | \(0.0686776\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.22509 | − | 23.2324i | −0.288063 | − | 1.07507i | −0.946572 | − | 0.322492i | \(-0.895479\pi\) |
0.658509 | − | 0.752573i | \(-0.271187\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.81915 | − | 9.93421i | 0.407230 | − | 0.458719i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.01298 | − | 6.95068i | 0.184908 | − | 0.320270i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 48.4113 | + | 12.9718i | 2.22596 | + | 0.596443i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.67400 | + | 8.67400i | 0.397155 | + | 0.397155i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.146380 | + | 0.253538i | 0.00668829 | + | 0.0115845i | 0.869350 | − | 0.494197i | \(-0.164538\pi\) |
−0.862662 | + | 0.505781i | \(0.831204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.27521 | − | 5.35505i | −0.422913 | − | 0.244169i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.2284 | + | 6.62351i | 0.601915 | + | 0.301380i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.08118 | + | 4.03501i | −0.0489928 | + | 0.182844i | −0.986086 | − | 0.166235i | \(-0.946839\pi\) |
0.937093 | + | 0.349079i | \(0.113506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.30765 | 0.194799 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.28910 | 0.238694 | 0.119347 | − | 0.992853i | \(-0.461920\pi\) | ||||
0.119347 | + | 0.992853i | \(0.461920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 33.9889 | + | 17.0183i | 1.52461 | + | 0.763375i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4675 | − | 14.7037i | −1.14008 | − | 0.658227i | −0.193632 | − | 0.981074i | \(-0.562027\pi\) |
−0.946451 | + | 0.322847i | \(0.895360\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.0845127 | − | 0.146380i | −0.00377575 | − | 0.00653979i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.4558 | − | 25.4558i | −1.13502 | − | 1.13502i | −0.989330 | − | 0.145690i | \(-0.953460\pi\) |
−0.145690 | − | 0.989330i | \(-0.546540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.3755 | + | 6.53140i | 1.08255 | + | 0.290070i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.76686 | + | 9.98850i | −0.255612 | + | 0.442732i | −0.965061 | − | 0.262024i | \(-0.915610\pi\) |
0.709450 | + | 0.704756i | \(0.248944\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.62492 | − | 8.58899i | 0.337306 | − | 0.379954i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.29950 | − | 4.84982i | −0.0573745 | − | 0.214125i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.1019 | + | 41.1019i | −1.80766 | + | 1.80766i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 15.0260i | 0.659566i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.684951 | − | 0.395457i | 0.0300083 | − | 0.0173253i | −0.484921 | − | 0.874558i | \(-0.661152\pi\) |
0.514929 | + | 0.857233i | \(0.327818\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.9888 | − | 9.64318i | 1.57368 | − | 0.421667i | 0.636719 | − | 0.771096i | \(-0.280291\pi\) |
0.936963 | + | 0.349429i | \(0.113624\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.7378 | − | 5.28874i | 0.859793 | − | 0.230381i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.15865 | + | 4.13305i | −0.311246 | + | 0.179698i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.22509i | 0.0965609i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.72895 | − | 9.72895i | 0.421408 | − | 0.421408i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5.10079 | − | 19.0364i | −0.220115 | − | 0.821482i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.4421 | − | 29.0375i | 0.535921 | − | 1.25073i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.05429 | + | 1.82608i | −0.0453273 | + | 0.0785091i | −0.887799 | − | 0.460232i | \(-0.847766\pi\) |
0.842472 | + | 0.538741i | \(0.181100\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.01069 | − | 2.41441i | −0.386686 | − | 0.103612i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.7426 | + | 20.7426i | 0.886890 | + | 0.886890i | 0.994223 | − | 0.107333i | \(-0.0342311\pi\) |
−0.107333 | + | 0.994223i | \(0.534231\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.66183 | − | 6.34248i | −0.156283 | − | 0.270690i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.66259 | − | 4.03761i | −0.113225 | − | 0.171697i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.98515 | + | 11.1407i | −0.126485 | + | 0.472048i | −0.999888 | − | 0.0149497i | \(-0.995241\pi\) |
0.873403 | + | 0.486997i | \(0.161908\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 68.6709 | 2.90447 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.3670 | 0.859893 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.62353 | − | 6.05909i | 0.0684236 | − | 0.255360i | −0.923238 | − | 0.384228i | \(-0.874468\pi\) |
0.991662 | + | 0.128868i | \(0.0411343\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.157038 | + | 2.64109i | 0.00659496 | + | 0.110915i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −26.1721 | − | 15.1105i | −1.09719 | − | 0.633464i | −0.161709 | − | 0.986838i | \(-0.551701\pi\) |
−0.935482 | + | 0.353375i | \(0.885034\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.7037 | + | 32.3957i | 0.782725 | + | 1.35572i | 0.930349 | + | 0.366675i | \(0.119504\pi\) |
−0.147624 | + | 0.989043i | \(0.547163\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.2472 | − | 11.2472i | −0.469857 | − | 0.469857i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.8711 | + | 4.78853i | 0.743982 | + | 0.199349i | 0.610847 | − | 0.791749i | \(-0.290829\pi\) |
0.133135 | + | 0.991098i | \(0.457496\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.26393 | − | 3.92124i | 0.0940856 | − | 0.162961i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −13.2420 | − | 39.8006i | −0.549372 | − | 1.65121i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 14.3283 | + | 53.4738i | 0.593416 | + | 2.21466i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.17461 | − | 5.17461i | 0.213579 | − | 0.213579i | −0.592207 | − | 0.805786i | \(-0.701743\pi\) |
0.805786 | + | 0.592207i | \(0.201743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 22.7339i | − | 0.936734i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.5504 | + | 12.4421i | −0.886466 | + | 0.511802i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.0827 | − | 10.7401i | 1.64600 | − | 0.441045i | 0.687512 | − | 0.726173i | \(-0.258703\pi\) |
0.958489 | + | 0.285128i | \(0.0920363\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.88483 | − | 2.38068i | 0.363632 | − | 0.0974348i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.2716 | − | 20.9414i | 1.48202 | − | 0.855644i | 0.482227 | − | 0.876046i | \(-0.339828\pi\) |
0.999792 | + | 0.0204023i | \(0.00649469\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 3.49682i | − | 0.142638i | −0.997454 | − | 0.0713191i | \(-0.977279\pi\) | ||
0.997454 | − | 0.0713191i | \(-0.0227209\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.55031 | + | 3.55031i | −0.144580 | + | 0.144580i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.54613 | − | 16.9664i | −0.184522 | − | 0.688644i | −0.994732 | − | 0.102505i | \(-0.967314\pi\) |
0.810211 | − | 0.586138i | \(-0.199353\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −39.8214 | + | 68.9726i | −1.61100 | + | 2.79033i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.6025 | − | 9.53966i | −1.43797 | − | 0.385303i | −0.546149 | − | 0.837688i | \(-0.683907\pi\) |
−0.891823 | + | 0.452385i | \(0.850573\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11.3023 | − | 11.3023i | −0.455015 | − | 0.455015i | 0.442000 | − | 0.897015i | \(-0.354269\pi\) |
−0.897015 | + | 0.442000i | \(0.854269\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.7956 | − | 39.4832i | −0.916233 | − | 1.58696i | −0.805086 | − | 0.593159i | \(-0.797881\pi\) |
−0.111148 | − | 0.993804i | \(-0.535453\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.84248 | − | 2.79580i | −0.194322 | − | 0.112192i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.2650 | + | 11.3854i | −0.691707 | + | 0.456145i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.86463 | − | 21.8871i | 0.234211 | − | 0.874087i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.81670 | −0.311672 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.9029 | 1.34965 | 0.674827 | − | 0.737976i | \(-0.264218\pi\) | ||||
0.674827 | + | 0.737976i | \(0.264218\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.814251 | − | 3.03883i | 0.0323636 | − | 0.120782i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.16946 | − | 42.8424i | 0.244443 | − | 1.69748i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −12.4421 | − | 7.18348i | −0.492204 | − | 0.284174i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0634 | + | 34.7508i | 0.792457 | + | 1.37258i | 0.924442 | + | 0.381324i | \(0.124532\pi\) |
−0.131985 | + | 0.991252i | \(0.542135\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.5960 | + | 18.5960i | 0.733357 | + | 0.733357i | 0.971283 | − | 0.237927i | \(-0.0764678\pi\) |
−0.237927 | + | 0.971283i | \(0.576468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.2049 | + | 2.73439i | 0.401196 | + | 0.107500i | 0.453774 | − | 0.891117i | \(-0.350077\pi\) |
−0.0525785 | + | 0.998617i | \(0.516744\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.02090 | + | 8.69645i | −0.197088 | + | 0.341366i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.40826 | + | 11.7350i | −0.0943872 | + | 0.459932i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.1534 | + | 41.6249i | 0.436465 | + | 1.62891i | 0.737536 | + | 0.675308i | \(0.235989\pi\) |
−0.301071 | + | 0.953602i | \(0.597344\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.06955 | + | 3.06955i | −0.119755 | + | 0.119755i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.4611i | 0.407506i | 0.979022 | + | 0.203753i | \(0.0653139\pi\) | ||||
−0.979022 | + | 0.203753i | \(0.934686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.7584 | + | 21.2225i | −1.42974 | + | 0.825458i | −0.997099 | − | 0.0761106i | \(-0.975750\pi\) |
−0.432636 | + | 0.901569i | \(0.642416\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 26.9550 | − | 7.22257i | 1.04685 | − | 0.280502i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.92069 | + | 4.57301i | −0.306232 | + | 0.176803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 33.0515i | − | 1.27594i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0223 | − | 23.0223i | 0.887445 | − | 0.887445i | −0.106832 | − | 0.994277i | \(-0.534071\pi\) |
0.994277 | + | 0.106832i | \(0.0340708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.39579 | + | 5.20915i | 0.0536444 | + | 0.200204i | 0.987547 | − | 0.157324i | \(-0.0502866\pi\) |
−0.933903 | + | 0.357527i | \(0.883620\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.5522 | + | 4.17625i | −0.481711 | + | 0.160270i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.84248 | + | 13.5836i | −0.300524 | + | 0.520523i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.9010 | + | 9.88759i | 1.41198 | + | 0.378338i | 0.882630 | − | 0.470068i | \(-0.155771\pi\) |
0.529346 | + | 0.848406i | \(0.322437\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.0314 | − | 13.0314i | −0.497180 | − | 0.497180i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.9260 | + | 65.6898i | 1.44487 | + | 2.50258i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.58451 | − | 2.64687i | −0.174403 | − | 0.100692i | 0.410257 | − | 0.911970i | \(-0.365439\pi\) |
−0.584660 | + | 0.811278i | \(0.698772\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.34582 | + | 10.6766i | −0.203071 | + | 0.405572i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.59901 | − | 9.69963i | 0.0984445 | − | 0.367400i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.57560 | 0.0974182 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.8310 | 0.673467 | 0.336733 | − | 0.941600i | \(-0.390678\pi\) | ||||
0.336733 | + | 0.941600i | \(0.390678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.25081 | + | 8.40013i | −0.0848908 | + | 0.316817i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18.5557 | + | 1.10331i | −0.697860 | + | 0.0414944i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.63289 | − | 3.82950i | −0.249103 | − | 0.143820i | 0.370250 | − | 0.928932i | \(-0.379272\pi\) |
−0.619354 | + | 0.785112i | \(0.712605\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.914012 | + | 1.58312i | 0.0342781 | + | 0.0593715i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.9025 | − | 17.9025i | −0.670455 | − | 0.670455i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.586409 | + | 0.157128i | 0.0218998 | + | 0.00586804i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.30870 | + | 10.9270i | −0.235275 | + | 0.407508i | −0.959353 | − | 0.282210i | \(-0.908932\pi\) |
0.724078 | + | 0.689718i | \(0.242266\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.8127 | + | 2.21898i | 0.402685 | + | 0.0826390i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.24144 | + | 8.36516i | 0.0833600 | + | 0.311104i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.4799 | − | 13.4799i | 0.499940 | − | 0.499940i | −0.411479 | − | 0.911419i | \(-0.634988\pi\) |
0.911419 | + | 0.411479i | \(0.134988\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 43.4044 | − | 25.0595i | 1.60537 | − | 0.926861i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.67111 | − | 2.32342i | 0.320275 | − | 0.0858174i | −0.0951000 | − | 0.995468i | \(-0.530317\pi\) |
0.415375 | + | 0.909650i | \(0.363650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −21.8871 | + | 5.86463i | −0.806222 | + | 0.216026i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.5911 | + | 7.26946i | −0.463170 | + | 0.267412i | −0.713376 | − | 0.700781i | \(-0.752835\pi\) |
0.250206 | + | 0.968193i | \(0.419502\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 31.0466i | − | 1.14053i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.4486 | + | 24.4486i | −0.896933 | + | 0.896933i | −0.995164 | − | 0.0982305i | \(-0.968682\pi\) |
0.0982305 | + | 0.995164i | \(0.468682\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.10331 | + | 15.3138i | 0.150132 | + | 0.560301i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.2090 | + | 3.73686i | 0.665343 | + | 0.136542i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.4644 | + | 37.1775i | −0.783249 | + | 1.35663i | 0.146791 | + | 0.989168i | \(0.453105\pi\) |
−0.930040 | + | 0.367459i | \(0.880228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.2882 | − | 7.31185i | −0.994437 | − | 0.266459i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.43514 | + | 6.43514i | 0.233889 | + | 0.233889i | 0.814314 | − | 0.580425i | \(-0.197113\pi\) |
−0.580425 | + | 0.814314i | \(0.697113\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −12.6174 | − | 21.8540i | −0.457983 | − | 0.793249i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 12.2969 | + | 7.09961i | 0.445762 | + | 0.257361i | 0.706039 | − | 0.708173i | \(-0.250480\pi\) |
−0.260277 | + | 0.965534i | \(0.583814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.7193 | + | 2.12385i | −1.29313 | + | 0.0768886i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.56104 | + | 13.2900i | −0.128582 | + | 0.479874i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.7272 | −0.458955 | −0.229478 | − | 0.973314i | \(-0.573702\pi\) | ||||
−0.229478 | + | 0.973314i | \(0.573702\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.17198 | 0.186264 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.21166 | + | 23.1822i | −0.223418 | + | 0.833806i | 0.759614 | + | 0.650374i | \(0.225388\pi\) |
−0.983032 | + | 0.183433i | \(0.941279\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.05169 | − | 4.09763i | 0.0736040 | − | 0.147002i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.67521 | − | 5.58599i | −0.346651 | − | 0.200139i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −32.4189 | − | 56.1511i | −1.16004 | − | 2.00924i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00190 | + | 1.07231i | 0.142652 | + | 0.0382236i | 0.329439 | − | 0.944177i | \(-0.393141\pi\) |
−0.186786 | + | 0.982401i | \(0.559807\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.99196 | − | 13.8425i | 0.284521 | − | 0.492805i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.0894 | − | 8.68017i | 0.927631 | − | 0.308631i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.7208 | − | 43.7426i | −0.416218 | − | 1.55335i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.2306 | + | 13.2306i | −0.468652 | + | 0.468652i | −0.901478 | − | 0.432826i | \(-0.857517\pi\) |
0.432826 | + | 0.901478i | \(0.357517\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 58.1268i | 2.05638i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6.76946 | − | 3.90835i | 0.239187 | − | 0.138095i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.9233 | + | 5.07048i | −0.667788 | + | 0.178933i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.9114 | + | 4.53140i | −0.595310 | + | 0.159513i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −8.68017 | + | 5.01150i | −0.305179 | + | 0.176195i | −0.644767 | − | 0.764379i | \(-0.723046\pi\) |
0.339588 | + | 0.940574i | \(0.389712\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1243i | − | 1.09292i | −0.837485 | − | 0.546461i | \(-0.815975\pi\) | ||
0.837485 | − | 0.546461i | \(-0.184025\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.65988 | + | 7.65988i | −0.268644 | + | 0.268644i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.4317 | − | 53.8599i | −0.504902 | − | 1.88432i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.28885 | + | 16.0260i | −0.114922 | + | 0.559992i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.74351 | + | 11.6801i | −0.235350 | + | 0.407638i | −0.959374 | − | 0.282136i | \(-0.908957\pi\) |
0.724024 | + | 0.689775i | \(0.242290\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −36.7944 | − | 9.85902i | −1.28257 | − | 0.343664i | −0.447737 | − | 0.894165i | \(-0.647770\pi\) |
−0.834834 | + | 0.550502i | \(0.814436\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 28.6503 | + | 28.6503i | 0.996270 | + | 0.996270i | 0.999993 | − | 0.00372312i | \(-0.00118511\pi\) |
−0.00372312 | + | 0.999993i | \(0.501185\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23.8430 | + | 41.2973i | 0.828102 | + | 1.43431i | 0.899525 | + | 0.436869i | \(0.143913\pi\) |
−0.0714231 | + | 0.997446i | \(0.522754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1292 | + | 5.84809i | 0.351378 | + | 0.202868i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −11.7347 | − | 29.3305i | −0.406582 | − | 1.01624i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.17190 | − | 4.37357i | 0.0405066 | − | 0.151173i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.8941 | −0.997534 | −0.498767 | − | 0.866736i | \(-0.666214\pi\) | ||||
−0.498767 | + | 0.866736i | \(0.666214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.60996 | − | 24.6687i | 0.227659 | − | 0.849636i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −20.6891 | + | 13.6434i | −0.710885 | + | 0.468791i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.7574 | − | 8.52020i | −0.506473 | − | 0.292413i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.84248 | + | 8.38741i | 0.165998 | + | 0.287517i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.80855 | + | 9.80855i | 0.335838 | + | 0.335838i | 0.854798 | − | 0.518960i | \(-0.173681\pi\) |
−0.518960 | + | 0.854798i | \(0.673681\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −10.6280 | − | 2.84777i | −0.363047 | − | 0.0972781i | 0.0726843 | − | 0.997355i | \(-0.476843\pi\) |
−0.435731 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.76197 | + | 6.51593i | −0.128357 | + | 0.222321i | −0.923040 | − | 0.384704i | \(-0.874304\pi\) |
0.794683 | + | 0.607024i | \(0.207637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.40251 | + | 3.90835i | 0.150037 | + | 0.133196i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.21271 | − | 15.7221i | −0.143402 | − | 0.535185i | −0.999821 | − | 0.0189036i | \(-0.993982\pi\) |
0.856419 | − | 0.516282i | \(-0.172684\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.38080 | − | 2.38080i | 0.0808560 | − | 0.0808560i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.24983i | 0.279856i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.8872 | + | 15.5233i | −0.911036 | + | 0.525987i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.82963 | − | 1.29410i | 0.163458 | − | 0.0437985i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.3233 | − | 7.05332i | 0.888876 | − | 0.238174i | 0.214643 | − | 0.976693i | \(-0.431141\pi\) |
0.674233 | + | 0.738519i | \(0.264474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.525760 | + | 0.303548i | −0.0177334 | + | 0.0102384i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.9839i | − | 0.538512i | −0.963069 | − | 0.269256i | \(-0.913222\pi\) | ||
0.963069 | − | 0.269256i | \(-0.0867777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.9349 | − | 37.9349i | 1.27661 | − | 1.27661i | 0.334059 | − | 0.942552i | \(-0.391581\pi\) |
0.942552 | − | 0.334059i | \(-0.108419\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.35779 | + | 34.9237i | 0.314204 | + | 1.17262i | 0.924729 | + | 0.380627i | \(0.124292\pi\) |
−0.610525 | + | 0.791997i | \(0.709041\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.6460 | − | 38.0091i | −0.424133 | − | 1.27478i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.25649 | − | 3.90835i | 0.0755952 | − | 0.130935i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.4653 | + | 16.7375i | 2.09032 | + | 0.560100i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −24.4486 | − | 24.4486i | −0.816316 | − | 0.816316i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.9433 | + | 27.6801i | 1.59722 | + | 0.922158i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.74399 | + | 29.3307i | 0.0580363 | + | 0.976065i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.04499 | − | 26.2923i | 0.233925 | − | 0.873021i | −0.744705 | − | 0.667394i | \(-0.767410\pi\) |
0.978630 | − | 0.205627i | \(-0.0659234\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.02579 | 0.233031 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.1009 | −0.434051 | −0.217025 | − | 0.976166i | \(-0.569635\pi\) | ||||
−0.217025 | + | 0.976166i | \(0.569635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.5181 | + | 69.1107i | −0.612861 | + | 2.28723i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.6187 | + | 32.7831i | 0.713913 | + | 1.08259i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.08965 | + | 4.09321i | 0.233866 | + | 0.135023i | 0.612354 | − | 0.790583i | \(-0.290223\pi\) |
−0.378488 | + | 0.925606i | \(0.623556\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.94719 | − | 13.7649i | −0.261869 | − | 0.453570i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −62.8178 | − | 62.8178i | −2.06767 | − | 2.06767i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.02982 | − | 1.07979i | −0.132357 | − | 0.0354648i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.8136 | + | 25.6579i | −0.486019 | + | 0.841810i | −0.999871 | − | 0.0160692i | \(-0.994885\pi\) |
0.513852 | + | 0.857879i | \(0.328218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −34.8987 | + | 4.16483i | −1.14376 | + | 0.136497i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.295421 | + | 1.10253i | 0.00967166 | + | 0.0360951i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.01202 | + | 2.01202i | −0.0657298 | + | 0.0657298i | −0.739208 | − | 0.673478i | \(-0.764800\pi\) |
0.673478 | + | 0.739208i | \(0.264800\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.50147i | 0.146900i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.2239 | + | 18.6045i | −1.05047 | + | 0.606488i | −0.922780 | − | 0.385326i | \(-0.874089\pi\) |
−0.127688 | + | 0.991814i | \(0.540756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0179 | + | 3.22019i | −0.391357 | + | 0.104864i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 24.4618 | − | 6.55451i | 0.794901 | − | 0.212993i | 0.161557 | − | 0.986863i | \(-0.448348\pi\) |
0.633344 | + | 0.773870i | \(0.281682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23.2463 | + | 13.4212i | −0.754606 | + | 0.435672i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.69129i | 0.314262i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.4345 | + | 23.4345i | −0.759118 | + | 0.759118i | −0.976162 | − | 0.217044i | \(-0.930359\pi\) |
0.217044 | + | 0.976162i | \(0.430359\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00489 | + | 2.25838i | −0.0647413 | + | 0.0729270i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.24926 | + | 9.09199i | −0.169331 | + | 0.293290i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.78639 | − | 1.81841i | −0.218688 | − | 0.0585974i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.2925 | − | 35.2925i | −1.13493 | − | 1.13493i | −0.989346 | − | 0.145584i | \(-0.953494\pi\) |
−0.145584 | − | 0.989346i | \(-0.546506\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −11.3296 | − | 19.6234i | −0.363959 | − | 0.630396i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.5438 | − | 29.7588i | −1.65412 | − | 0.955006i | −0.975353 | − | 0.220651i | \(-0.929182\pi\) |
−0.678765 | − | 0.734355i | \(-0.737485\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −48.6795 | − | 24.3740i | −1.56059 | − | 0.781393i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.45522 | + | 20.3592i | −0.174528 | + | 0.651348i | 0.822103 | + | 0.569338i | \(0.192800\pi\) |
−0.996632 | + | 0.0820096i | \(0.973866\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.2766 | 1.12744 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.5245 | 0.431803 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.45773 | + | 35.2967i | −0.301655 | + | 1.12579i | 0.634132 | + | 0.773225i | \(0.281358\pi\) |
−0.935787 | + | 0.352566i | \(0.885309\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30.4709 | − | 15.2569i | −0.969900 | − | 0.485631i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −53.7784 | − | 31.0490i | −1.71005 | − | 0.987299i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0903 | + | 24.4051i | 0.447592 | + | 0.775252i | 0.998229 | − | 0.0594929i | \(-0.0189484\pi\) |
−0.550637 | + | 0.834745i | \(0.685615\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.69056 | + | 2.69056i | 0.0853823 | + | 0.0853823i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.0890 | + | 6.72258i | 0.794577 | + | 0.212906i | 0.633202 | − | 0.773987i | \(-0.281740\pi\) |
0.161375 | + | 0.986893i | \(0.448407\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.866025 | + | 1.50000i | −0.0273998 | + | 0.0474579i |
(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 | 2100.2.ce.c.1657.4 | yes | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.c.1993.3 | yes | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.c.1993.4 | yes | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.c.1657.2 | yes | 24 | |
7.3 | odd | 6 | inner | 2100.2.ce.c.157.4 | yes | 24 | |
35.3 | even | 12 | inner | 2100.2.ce.c.493.4 | yes | 24 | |
35.17 | even | 12 | inner | 2100.2.ce.c.493.2 | yes | 24 | |
35.24 | odd | 6 | inner | 2100.2.ce.c.157.3 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.c.157.3 | ✓ | 24 | 35.24 | odd | 6 | inner | |
2100.2.ce.c.157.4 | yes | 24 | 7.3 | odd | 6 | inner | |
2100.2.ce.c.493.2 | yes | 24 | 35.17 | even | 12 | inner | |
2100.2.ce.c.493.4 | yes | 24 | 35.3 | even | 12 | inner | |
2100.2.ce.c.1657.2 | yes | 24 | 5.4 | even | 2 | inner | |
2100.2.ce.c.1657.4 | yes | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.c.1993.3 | yes | 24 | 5.2 | odd | 4 | inner | |
2100.2.ce.c.1993.4 | yes | 24 | 5.3 | odd | 4 | inner |