Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1300,2,Mod(549,1300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1300, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1300.549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1300 = 2^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1300.bb (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: | \(10.3805522628\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 260) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 549.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1300.549 |
Dual form | 1300.2.bb.c.1049.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1300\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(651\) | \(677\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | −0.228714 | − | 0.973494i | \(-0.573452\pi\) |
0.728714 | + | 0.684819i | \(0.240119\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.33013 | − | 2.50000i | −1.63663 | − | 0.944911i | −0.981981 | − | 0.188982i | \(-0.939481\pi\) |
−0.654654 | − | 0.755929i | \(-0.727186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 1.73205i | −0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410 | + | 1.00000i | 0.960769 | + | 0.277350i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.866025 | + | 0.500000i | 0.210042 | + | 0.121268i | 0.601331 | − | 0.799000i | \(-0.294637\pi\) |
−0.391289 | + | 0.920268i | \(0.627971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.50000 | + | 2.59808i | −0.344124 | + | 0.596040i | −0.985194 | − | 0.171442i | \(-0.945157\pi\) |
0.641071 | + | 0.767482i | \(0.278491\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.00000 | −1.09109 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59808 | + | 1.50000i | −0.541736 | + | 0.312772i | −0.745782 | − | 0.666190i | \(-0.767924\pi\) |
0.204046 | + | 0.978961i | \(0.434591\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.500000 | − | 0.866025i | −0.0928477 | − | 0.160817i | 0.815861 | − | 0.578249i | \(-0.196264\pi\) |
−0.908708 | + | 0.417432i | \(0.862930\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.33013 | + | 2.50000i | 0.753778 | + | 0.435194i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.06218 | − | 3.50000i | 0.996616 | − | 0.575396i | 0.0893706 | − | 0.995998i | \(-0.471514\pi\) |
0.907245 | + | 0.420602i | \(0.138181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.50000 | − | 0.866025i | 0.560449 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | + | 4.33013i | 0.390434 | + | 0.676252i | 0.992507 | − | 0.122189i | \(-0.0389915\pi\) |
−0.602072 | + | 0.798441i | \(0.705658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.33013 | + | 2.50000i | 0.660338 | + | 0.381246i | 0.792406 | − | 0.609994i | \(-0.208828\pi\) |
−0.132068 | + | 0.991241i | \(0.542162\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.0000i | 1.75038i | 0.483779 | + | 0.875190i | \(0.339264\pi\) | ||||
−0.483779 | + | 0.875190i | \(0.660736\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.00000 | + | 15.5885i | 1.28571 | + | 2.22692i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.00000i | 0.397360i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50000 | + | 9.52628i | −0.716039 | + | 1.24022i | 0.246518 | + | 0.969138i | \(0.420713\pi\) |
−0.962557 | + | 0.271078i | \(0.912620\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50000 | − | 11.2583i | 0.832240 | − | 1.44148i | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) |
0.896258 | − | 0.443533i | \(-0.146275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 8.66025 | − | 5.00000i | 1.09109 | − | 0.629941i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.59808 | − | 1.50000i | 0.317406 | − | 0.183254i | −0.332830 | − | 0.942987i | \(-0.608004\pi\) |
0.650236 | + | 0.759733i | \(0.274670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.50000 | + | 2.59808i | −0.180579 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.50000 | + | 11.2583i | −0.771408 | + | 1.33612i | 0.165383 | + | 0.986229i | \(0.447114\pi\) |
−0.936791 | + | 0.349889i | \(0.886219\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000i | 0.234082i | 0.993127 | + | 0.117041i | \(0.0373409\pi\) | ||||
−0.993127 | + | 0.117041i | \(0.962659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 25.0000i | − | 2.84901i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.0000i | − | 1.31717i | −0.752506 | − | 0.658586i | \(-0.771155\pi\) | ||
0.752506 | − | 0.658586i | \(-0.228845\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.866025 | − | 0.500000i | −0.0928477 | − | 0.0536056i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.50000 | + | 6.06218i | 0.370999 | + | 0.642590i | 0.989720 | − | 0.143022i | \(-0.0456819\pi\) |
−0.618720 | + | 0.785611i | \(0.712349\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5000 | − | 12.9904i | −1.31036 | − | 1.36176i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.52628 | − | 5.50000i | −0.967247 | − | 0.558440i | −0.0688512 | − | 0.997627i | \(-0.521933\pi\) |
−0.898396 | + | 0.439187i | \(0.855267\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.0000 | −1.00504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.50000 | + | 11.2583i | 0.646774 | + | 1.12025i | 0.983889 | + | 0.178782i | \(0.0572157\pi\) |
−0.337115 | + | 0.941464i | \(0.609451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.79423 | + | 4.50000i | −0.753497 | + | 0.435031i | −0.826956 | − | 0.562267i | \(-0.809929\pi\) |
0.0734594 | + | 0.997298i | \(0.476596\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.0000 | −1.72409 | −0.862044 | − | 0.506834i | \(-0.830816\pi\) | ||||
−0.862044 | + | 0.506834i | \(0.830816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.50000 | − | 6.06218i | 0.332205 | − | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.866025 | − | 0.500000i | −0.0814688 | − | 0.0470360i | 0.458712 | − | 0.888585i | \(-0.348311\pi\) |
−0.540181 | + | 0.841549i | \(0.681644\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.19615 | + | 5.00000i | −0.480384 | + | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.50000 | − | 4.33013i | −0.229175 | − | 0.396942i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.33013 | + | 2.50000i | 0.390434 | + | 0.225417i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.06218 | − | 3.50000i | 0.537931 | − | 0.310575i | −0.206309 | − | 0.978487i | \(-0.566145\pi\) |
0.744240 | + | 0.667912i | \(0.232812\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.00000 | 0.440225 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | 0.349482 | 0.174741 | − | 0.984614i | \(-0.444091\pi\) | ||||
0.174741 | + | 0.984614i | \(0.444091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.9904 | − | 7.50000i | 1.12641 | − | 0.650332i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.59808 | − | 1.50000i | −0.221969 | − | 0.128154i | 0.384893 | − | 0.922961i | \(-0.374238\pi\) |
−0.606861 | + | 0.794808i | \(0.707572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50000 | − | 11.2583i | 0.551323 | − | 0.954919i | −0.446857 | − | 0.894606i | \(-0.647457\pi\) |
0.998179 | − | 0.0603135i | \(-0.0192101\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | + | 10.3923i | 0.505291 | + | 0.875190i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.33013 | + | 17.5000i | 0.362103 | + | 1.46342i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 15.5885 | + | 9.00000i | 1.28571 | + | 0.742307i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.50000 | − | 9.52628i | 0.450578 | − | 0.780423i | −0.547844 | − | 0.836580i | \(-0.684551\pi\) |
0.998422 | + | 0.0561570i | \(0.0178847\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −24.0000 | −1.95309 | −0.976546 | − | 0.215308i | \(-0.930924\pi\) | ||||
−0.976546 | + | 0.215308i | \(0.930924\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.73205 | + | 1.00000i | −0.140028 | + | 0.0808452i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.0000i | 0.798087i | 0.916932 | + | 0.399043i | \(0.130658\pi\) | ||||
−0.916932 | + | 0.399043i | \(0.869342\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.00000 | − | 1.73205i | −0.0793052 | − | 0.137361i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0000 | 1.18217 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.33013 | + | 2.50000i | 0.339162 | + | 0.195815i | 0.659901 | − | 0.751352i | \(-0.270598\pi\) |
−0.320740 | + | 0.947167i | \(0.603931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.2583 | + | 6.50000i | −0.871196 | + | 0.502985i | −0.867745 | − | 0.497009i | \(-0.834432\pi\) |
−0.00345033 | + | 0.999994i | \(0.501098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.0000 | + | 6.92820i | 0.846154 | + | 0.532939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.7224 | − | 8.50000i | −1.11933 | − | 0.646243i | −0.178097 | − | 0.984013i | \(-0.556994\pi\) |
−0.941229 | + | 0.337770i | \(0.890327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.0000i | 0.826811i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.50000 | + | 9.52628i | 0.411089 | + | 0.712028i | 0.995009 | − | 0.0997838i | \(-0.0318151\pi\) |
−0.583920 | + | 0.811811i | \(0.698482\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 13.0000i | − | 0.960988i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.00000i | 0.365636i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5000 | − | 21.6506i | 0.909241 | − | 1.57485i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.50000 | − | 12.9904i | 0.542681 | − | 0.939951i | −0.456068 | − | 0.889945i | \(-0.650743\pi\) |
0.998749 | − | 0.0500060i | \(-0.0159241\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.9186 | + | 11.5000i | −1.43377 | + | 0.827788i | −0.997406 | − | 0.0719816i | \(-0.977068\pi\) |
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.3827 | − | 13.5000i | 1.66595 | − | 0.961835i | 0.696159 | − | 0.717888i | \(-0.254891\pi\) |
0.969788 | − | 0.243947i | \(-0.0784425\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | − | 18.1865i | 0.744325 | − | 1.28921i | −0.206184 | − | 0.978513i | \(-0.566105\pi\) |
0.950509 | − | 0.310696i | \(-0.100562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.50000 | − | 2.59808i | 0.105802 | − | 0.183254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.00000i | 0.350931i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.50000 | + | 4.33013i | 0.172107 | + | 0.298098i | 0.939156 | − | 0.343490i | \(-0.111609\pi\) |
−0.767049 | + | 0.641588i | \(0.778276\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.0000i | 0.890745i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.00000 | + | 1.73205i | 0.0675737 | + | 0.117041i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | + | 2.59808i | 0.168168 | + | 0.174766i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.4545 | + | 9.50000i | −1.10187 | + | 0.636167i | −0.936713 | − | 0.350100i | \(-0.886148\pi\) |
−0.165161 | + | 0.986267i | \(0.552814\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.7224 | − | 8.50000i | −0.977162 | − | 0.564165i | −0.0757500 | − | 0.997127i | \(-0.524135\pi\) |
−0.901412 | + | 0.432962i | \(0.857468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.0000 | −0.660819 | −0.330409 | − | 0.943838i | \(-0.607187\pi\) | ||||
−0.330409 | + | 0.943838i | \(0.607187\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.5000 | − | 21.6506i | −0.822440 | − | 1.42451i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.46410 | − | 2.00000i | 0.225018 | − | 0.129914i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.8564 | − | 8.00000i | −0.888889 | − | 0.513200i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.79423 | + | 7.50000i | −0.495935 | + | 0.477214i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.50000 | − | 12.9904i | 0.473396 | − | 0.819946i | −0.526140 | − | 0.850398i | \(-0.676361\pi\) |
0.999536 | + | 0.0304521i | \(0.00969471\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.9904 | − | 7.50000i | −0.816698 | − | 0.471521i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.9904 | − | 7.50000i | 0.810318 | − | 0.467837i | −0.0367485 | − | 0.999325i | \(-0.511700\pi\) |
0.847066 | + | 0.531487i | \(0.178367\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.0000 | −2.17479 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.52628 | + | 5.50000i | −0.587416 | + | 0.339145i | −0.764075 | − | 0.645128i | \(-0.776804\pi\) |
0.176659 | + | 0.984272i | \(0.443471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.06218 | + | 3.50000i | 0.370999 | + | 0.214197i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.50000 | + | 7.79423i | −0.274370 | + | 0.475223i | −0.969976 | − | 0.243201i | \(-0.921803\pi\) |
0.695606 | + | 0.718423i | \(0.255136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.50000 | − | 6.06218i | −0.212610 | − | 0.368251i | 0.739921 | − | 0.672694i | \(-0.234863\pi\) |
−0.952531 | + | 0.304443i | \(0.901530\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −17.3205 | − | 5.00000i | −1.04828 | − | 0.302614i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.2583 | + | 6.50000i | 0.676448 | + | 0.390547i | 0.798515 | − | 0.601975i | \(-0.205619\pi\) |
−0.122068 | + | 0.992522i | \(0.538953\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.0000 | 1.78965 | 0.894825 | − | 0.446417i | \(-0.147300\pi\) | ||||
0.894825 | + | 0.446417i | \(0.147300\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −19.9186 | + | 11.5000i | −1.18404 | + | 0.683604i | −0.956945 | − | 0.290269i | \(-0.906255\pi\) |
−0.227092 | + | 0.973873i | \(0.572922\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 25.0000i | − | 1.47570i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | − | 13.8564i | −0.470588 | − | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0000 | −0.644831 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.06218 | + | 3.50000i | 0.354156 | + | 0.204472i | 0.666514 | − | 0.745492i | \(-0.267786\pi\) |
−0.312358 | + | 0.949964i | \(0.601119\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.6506 | + | 12.5000i | −1.25630 | + | 0.725324i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −10.5000 | + | 2.59808i | −0.607231 | + | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.5000 | − | 21.6506i | −0.720488 | − | 1.24792i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.2583 | + | 6.50000i | 0.646774 | + | 0.373415i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.0000i | − | 0.684876i | −0.939540 | − | 0.342438i | \(-0.888747\pi\) | ||
0.939540 | − | 0.342438i | \(-0.111253\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.00000i | − | 0.339140i | −0.985518 | − | 0.169570i | \(-0.945762\pi\) | ||
0.985518 | − | 0.169570i | \(-0.0542379\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50000 | − | 4.33013i | 0.139973 | − | 0.242441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 7.79423i | −0.251166 | + | 0.435031i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.59808 | + | 1.50000i | −0.144561 | + | 0.0834622i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5885 | + | 9.00000i | −0.862044 | + | 0.497701i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.0000 | − | 51.9615i | 1.65395 | − | 2.86473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.500000 | + | 0.866025i | −0.0274825 | + | 0.0476011i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.851957 | + | 0.523612i | \(0.175416\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 14.0000i | 0.767195i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.0000i | 0.762629i | 0.924445 | + | 0.381314i | \(0.124528\pi\) | ||||
−0.924445 | + | 0.381314i | \(0.875472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.00000 | −0.0543125 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 55.0000i | − | 2.96972i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.3827 | + | 13.5000i | 1.25525 | + | 0.724718i | 0.972147 | − | 0.234372i | \(-0.0753034\pi\) |
0.283101 | + | 0.959090i | \(0.408637\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5000 | + | 30.3109i | 0.936754 | + | 1.62250i | 0.771477 | + | 0.636257i | \(0.219518\pi\) |
0.165277 | + | 0.986247i | \(0.447148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | + | 17.3205i | −0.266880 | + | 0.924500i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.33013 | − | 2.50000i | 0.230469 | − | 0.133062i | −0.380319 | − | 0.924855i | \(-0.624186\pi\) |
0.610789 | + | 0.791794i | \(0.290853\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.33013 | − | 2.50000i | −0.229175 | − | 0.132314i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | + | 8.66025i | 0.263158 | + | 0.455803i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.0000i | 0.734809i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.59808 | − | 1.50000i | 0.135618 | − | 0.0782994i | −0.430656 | − | 0.902516i | \(-0.641718\pi\) |
0.566274 | + | 0.824217i | \(0.308384\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.0000 | −0.520579 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00000 | + | 8.66025i | −0.259587 | + | 0.449618i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.4545 | + | 9.50000i | 0.851981 | + | 0.491891i | 0.861319 | − | 0.508065i | \(-0.169639\pi\) |
−0.00933789 | + | 0.999956i | \(0.502972\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.866025 | − | 3.50000i | −0.0446026 | − | 0.180259i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.5000 | − | 18.1865i | −0.539349 | − | 0.934179i | −0.998939 | − | 0.0460485i | \(-0.985337\pi\) |
0.459590 | − | 0.888131i | \(-0.347996\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.50000 | − | 6.06218i | 0.179310 | − | 0.310575i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.59808 | − | 1.50000i | −0.132755 | − | 0.0766464i | 0.432151 | − | 0.901801i | \(-0.357755\pi\) |
−0.564907 | + | 0.825155i | \(0.691088\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.66025 | + | 5.00000i | −0.440225 | + | 0.254164i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 10.0000 | 0.507020 | 0.253510 | − | 0.967333i | \(-0.418415\pi\) | ||||
0.253510 | + | 0.967333i | \(0.418415\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.00000 | −0.151717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.46410 | − | 2.00000i | 0.174741 | − | 0.100887i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.2583 | + | 6.50000i | 0.565039 | + | 0.326226i | 0.755166 | − | 0.655534i | \(-0.227556\pi\) |
−0.190126 | + | 0.981760i | \(0.560890\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.50000 | − | 12.9904i | 0.375470 | − | 0.650332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | − | 23.3827i | −0.674158 | − | 1.16768i | −0.976714 | − | 0.214544i | \(-0.931173\pi\) |
0.302556 | − | 0.953131i | \(-0.402160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.3109 | + | 17.5000i | 1.50245 | + | 0.867443i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.50000 | − | 16.4545i | 0.469745 | − | 0.813622i | −0.529657 | − | 0.848212i | \(-0.677679\pi\) |
0.999402 | + | 0.0345902i | \(0.0110126\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00000 | −0.147979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 47.6314 | − | 27.5000i | 2.34379 | − | 1.35319i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 13.0000i | − | 0.636613i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.50000 | − | 14.7224i | −0.415252 | − | 0.719238i | 0.580203 | − | 0.814472i | \(-0.302973\pi\) |
−0.995455 | + | 0.0952342i | \(0.969640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.7846 | − | 12.0000i | −1.01058 | − | 0.583460i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −56.2917 | + | 32.5000i | −2.72414 | + | 1.57279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.5000 | + | 12.9904i | 0.603506 | + | 0.627182i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.5000 | + | 18.1865i | 0.505767 | + | 0.876014i | 0.999978 | + | 0.00667224i | \(0.00212386\pi\) |
−0.494211 | + | 0.869342i | \(0.664543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.06218 | + | 3.50000i | 0.291330 | + | 0.168199i | 0.638541 | − | 0.769588i | \(-0.279538\pi\) |
−0.347212 | + | 0.937787i | \(0.612871\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 9.00000i | − | 0.430528i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.5000 | − | 25.1147i | −0.692047 | − | 1.19866i | −0.971166 | − | 0.238404i | \(-0.923376\pi\) |
0.279119 | − | 0.960257i | \(-0.409958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.0000 | −1.71429 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000i | 0.950229i | 0.879924 | + | 0.475114i | \(0.157593\pi\) | ||||
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.0000i | − | 0.520282i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.5000 | + | 18.1865i | −0.495526 | + | 0.858276i | −0.999987 | − | 0.00515887i | \(-0.998358\pi\) |
0.504461 | + | 0.863434i | \(0.331691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5000 | + | 21.6506i | −0.588602 | + | 1.01949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.7846 | + | 12.0000i | −0.976546 | + | 0.563809i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.52628 | − | 5.50000i | 0.445621 | − | 0.257279i | −0.260358 | − | 0.965512i | \(-0.583841\pi\) |
0.705979 | + | 0.708233i | \(0.250507\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.50000 | + | 4.33013i | −0.116690 | + | 0.202113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.5000 | − | 28.5788i | 0.768482 | − | 1.33105i | −0.169904 | − | 0.985461i | \(-0.554346\pi\) |
0.938386 | − | 0.345589i | \(-0.112321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.00000i | 0.371792i | 0.982569 | + | 0.185896i | \(0.0595187\pi\) | ||||
−0.982569 | + | 0.185896i | \(0.940481\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 8.00000i | − | 0.370196i | −0.982720 | − | 0.185098i | \(-0.940740\pi\) | ||
0.982720 | − | 0.185098i | \(-0.0592602\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | −0.692636 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.00000 | + | 8.66025i | 0.230388 | + | 0.399043i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.0000i | 1.14950i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.46410 | + | 2.00000i | 0.158610 | + | 0.0915737i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.50000 | + | 9.52628i | 0.251301 | + | 0.435267i | 0.963884 | − | 0.266321i | \(-0.0858081\pi\) |
−0.712583 | + | 0.701588i | \(0.752475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5000 | − | 6.06218i | 1.11710 | − | 0.276412i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.9904 | − | 7.50000i | 0.591083 | − | 0.341262i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.7224 | − | 8.50000i | −0.667137 | − | 0.385172i | 0.127854 | − | 0.991793i | \(-0.459191\pi\) |
−0.794991 | + | 0.606621i | \(0.792524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.00000 | 0.226108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | − | 12.9904i | −0.338470 | − | 0.586248i | 0.645675 | − | 0.763612i | \(-0.276576\pi\) |
−0.984145 | + | 0.177365i | \(0.943243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 1.00000i | − | 0.0450377i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 56.2917 | − | 32.5000i | 2.52503 | − | 1.45782i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | 0.179065 | 0.0895323 | − | 0.995984i | \(-0.471463\pi\) | ||||
0.0895323 | + | 0.995984i | \(0.471463\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.50000 | + | 11.2583i | −0.290399 | + | 0.502985i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.52628 | − | 5.50000i | −0.424756 | − | 0.245233i | 0.272354 | − | 0.962197i | \(-0.412198\pi\) |
−0.697110 | + | 0.716964i | \(0.745531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.9904 | + | 0.500000i | 0.576923 | + | 0.0222058i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.50000 | + | 2.59808i | 0.0664863 | + | 0.115158i | 0.897352 | − | 0.441315i | \(-0.145488\pi\) |
−0.830866 | + | 0.556473i | \(0.812154\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | − | 8.66025i | 0.221187 | − | 0.383107i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9904 | − | 7.50000i | −0.573539 | − | 0.331133i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −51.9615 | + | 30.0000i | −2.28527 | + | 1.31940i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.0000 | −0.746217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.1865 | − | 10.5000i | 0.795242 | − | 0.459133i | −0.0465630 | − | 0.998915i | \(-0.514827\pi\) |
0.841805 | + | 0.539782i | \(0.181493\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −11.0000 | − | 19.0526i | −0.477359 | − | 0.826811i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.33013 | + | 17.5000i | 0.187559 | + | 0.758009i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.52628 | + | 5.50000i | 0.411089 | + | 0.237343i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −45.0000 | + | 77.9423i | −1.93829 | + | 3.35721i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | −0.0859867 | −0.0429934 | − | 0.999075i | \(-0.513689\pi\) | ||||
−0.0429934 | + | 0.999075i | \(0.513689\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.66025 | − | 5.00000i | 0.371647 | − | 0.214571i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 20.0000i | − | 0.855138i | −0.903983 | − | 0.427569i | \(-0.859370\pi\) | ||
0.903983 | − | 0.427569i | \(-0.140630\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.0000 | + | 22.5167i | 0.554826 | + | 0.960988i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.00000 | 0.127804 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −17.3205 | − | 10.0000i | −0.736543 | − | 0.425243i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.2583 | + | 6.50000i | −0.477031 | + | 0.275414i | −0.719178 | − | 0.694826i | \(-0.755482\pi\) |
0.242147 | + | 0.970239i | \(0.422148\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.5000 | + | 12.9904i | 0.528694 | + | 0.549435i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.50000 | + | 4.33013i | 0.105550 | + | 0.182818i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.79423 | + | 4.50000i | 0.328488 | + | 0.189652i | 0.655169 | − | 0.755482i | \(-0.272597\pi\) |
−0.326682 | + | 0.945134i | \(0.605931\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.00000i | 0.209980i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.5000 | + | 33.7750i | 0.817483 | + | 1.41592i | 0.907532 | + | 0.419984i | \(0.137964\pi\) |
−0.0900490 | + | 0.995937i | \(0.528702\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 15.0000i | − | 0.626634i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 42.0000i | − | 1.74848i | −0.485491 | − | 0.874241i | \(-0.661359\pi\) | ||
0.485491 | − | 0.874241i | \(-0.338641\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.5000 | + | 19.9186i | −0.477924 | + | 0.827788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −30.0000 | + | 51.9615i | −1.24461 | + | 2.15573i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.66025 | − | 5.00000i | 0.358671 | − | 0.207079i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.59808 | − | 1.50000i | 0.107234 | − | 0.0619116i | −0.445424 | − | 0.895320i | \(-0.646947\pi\) |
0.552658 | + | 0.833408i | \(0.313614\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5000 | − | 23.3827i | 0.555316 | − | 0.961835i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000i | 0.0821302i | 0.999156 | + | 0.0410651i | \(0.0130751\pi\) | ||||
−0.999156 | + | 0.0410651i | \(0.986925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 21.0000i | − | 0.859473i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 36.0000 | 1.47092 | 0.735460 | − | 0.677568i | \(-0.236966\pi\) | ||||
0.735460 | + | 0.677568i | \(0.236966\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.50000 | + | 4.33013i | 0.101977 | + | 0.176630i | 0.912499 | − | 0.409079i | \(-0.134150\pi\) |
−0.810522 | + | 0.585708i | \(0.800816\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.00000i | 0.244339i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8468 | + | 15.5000i | 1.08968 | + | 0.629126i | 0.933491 | − | 0.358602i | \(-0.116746\pi\) |
0.156187 | + | 0.987728i | \(0.450080\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.50000 | + | 4.33013i | 0.101305 | + | 0.175466i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.0000 | + | 41.5692i | −0.485468 | + | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.6506 | − | 12.5000i | 0.874461 | − | 0.504870i | 0.00563283 | − | 0.999984i | \(-0.498207\pi\) |
0.868828 | + | 0.495114i | \(0.164874\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.3827 | − | 13.5000i | −0.941351 | − | 0.543490i | −0.0509678 | − | 0.998700i | \(-0.516231\pi\) |
−0.890384 | + | 0.455211i | \(0.849564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.50000 | − | 12.9904i | −0.300965 | − | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 35.0000i | − | 1.40225i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.9904 | + | 7.50000i | −0.518786 | + | 0.299521i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.00000 | 0.279108 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.5000 | − | 23.3827i | 0.537427 | − | 0.930850i | −0.461615 | − | 0.887080i | \(-0.652730\pi\) |
0.999042 | − | 0.0437697i | \(-0.0139368\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.33013 | + | 2.50000i | 0.172107 | + | 0.0993661i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5885 | + | 63.0000i | 0.617637 | + | 2.49615i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.0000 | − | 22.5167i | −0.514272 | − | 0.890745i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | + | 23.3827i | −0.533218 | + | 0.923561i | 0.466029 | + | 0.884769i | \(0.345684\pi\) |
−0.999247 | + | 0.0387913i | \(0.987649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.33013 | + | 2.50000i | 0.170764 | + | 0.0985904i | 0.582946 | − | 0.812511i | \(-0.301900\pi\) |
−0.412182 | + | 0.911101i | \(0.635233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.79423 | + | 4.50000i | −0.306423 | + | 0.176913i | −0.645325 | − | 0.763908i | \(-0.723278\pi\) |
0.338902 | + | 0.940822i | \(0.389945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −55.0000 | −2.15894 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −33.7750 | + | 19.5000i | −1.32172 | + | 0.763094i | −0.984003 | − | 0.178154i | \(-0.942987\pi\) |
−0.337715 | + | 0.941248i | \(0.609654\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.46410 | − | 2.00000i | −0.135147 | − | 0.0780274i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.50000 | − | 14.7224i | 0.331113 | − | 0.573505i | −0.651617 | − | 0.758548i | \(-0.725909\pi\) |
0.982730 | + | 0.185043i | \(0.0592425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.50000 | − | 2.59808i | −0.0583432 | − | 0.101053i | 0.835379 | − | 0.549675i | \(-0.185248\pi\) |
−0.893722 | + | 0.448622i | \(0.851915\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.46410 | + | 1.00000i | 0.134535 | + | 0.0388368i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.59808 | + | 1.50000i | 0.100598 | + | 0.0580802i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50000 | + | 16.4545i | −0.367291 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 65.0000 | 2.50930 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.52628 | + | 5.50000i | −0.367211 | + | 0.212009i | −0.672239 | − | 0.740334i | \(-0.734667\pi\) |
0.305028 | + | 0.952343i | \(0.401334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000i | 1.61419i | 0.590421 | + | 0.807096i | \(0.298962\pi\) | ||||
−0.590421 | + | 0.807096i | \(0.701038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 27.5000 | + | 47.6314i | 1.05535 | + | 1.82793i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.0000 | −0.651441 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.4352 | + | 24.5000i | 1.62374 | + | 0.937466i | 0.985908 | + | 0.167291i | \(0.0535019\pi\) |
0.637832 | + | 0.770176i | \(0.279831\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.66025 | + | 5.00000i | −0.330409 | + | 0.190762i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00000 | − | 6.92820i | 0.0761939 | − | 0.263944i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.50000 | + | 4.33013i | 0.0951045 | + | 0.164726i | 0.909652 | − | 0.415371i | \(-0.136348\pi\) |
−0.814548 | + | 0.580097i | \(0.803015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 43.3013 | + | 25.0000i | 1.64488 | + | 0.949671i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.00000i | 0.189389i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 21.0000i | 0.792030i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 65.0000i | − | 2.44458i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.5000 | − | 19.9186i | 0.431892 | − | 0.748058i | −0.565145 | − | 0.824992i | \(-0.691180\pi\) |
0.997036 | + | 0.0769337i | \(0.0245130\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | + | 6.92820i | −0.150012 | + | 0.259828i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.92820 | − | 4.00000i | 0.258738 | − | 0.149383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.5000 | − | 28.5788i | 0.615346 | − | 1.06581i | −0.374978 | − | 0.927034i | \(-0.622350\pi\) |
0.990324 | − | 0.138777i | \(-0.0443171\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.0000i | 0.409094i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.00000i | − | 0.296704i | −0.988935 | − | 0.148352i | \(-0.952603\pi\) | ||
0.988935 | − | 0.148352i | \(-0.0473968\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50000 | + | 4.33013i | 0.0924658 | + | 0.160156i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0000i | 1.25582i | 0.778287 | + | 0.627909i | \(0.216089\pi\) | ||||
−0.778287 | + | 0.627909i | \(0.783911\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9904 | + | 7.50000i | 0.478507 | + | 0.276266i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.50000 | + | 12.9904i | 0.275892 | + | 0.477859i | 0.970360 | − | 0.241665i | \(-0.0776935\pi\) |
−0.694468 | + | 0.719524i | \(0.744360\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.00000 | + | 10.3923i | −0.110208 | + | 0.381771i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.79423 | − | 4.50000i | 0.285943 | − | 0.165089i | −0.350168 | − | 0.936687i | \(-0.613876\pi\) |
0.636111 | + | 0.771598i | \(0.280542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 20.7846 | + | 12.0000i | 0.760469 | + | 0.439057i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45.0000 | 1.64426 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.5000 | + | 21.6506i | 0.456131 | + | 0.790043i | 0.998752 | − | 0.0499348i | \(-0.0159013\pi\) |
−0.542621 | + | 0.839978i | \(0.682568\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 15.0000i | − | 0.546630i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.79423 | + | 4.50000i | −0.283286 | + | 0.163555i | −0.634910 | − | 0.772586i | \(-0.718963\pi\) |
0.351624 | + | 0.936141i | \(0.385630\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15.0000 | −0.544466 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.50000 | + | 16.4545i | −0.344375 | + | 0.596475i | −0.985240 | − | 0.171179i | \(-0.945242\pi\) |
0.640865 | + | 0.767653i | \(0.278576\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 77.9423 | + | 45.0000i | 2.82170 | + | 1.62911i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −28.5788 | + | 27.5000i | −1.03192 | + | 0.992967i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 9.50000 | + | 16.4545i | 0.342579 | + | 0.593364i | 0.984911 | − | 0.173063i | \(-0.0553663\pi\) |
−0.642332 | + | 0.766426i | \(0.722033\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.50000 | − | 12.9904i | 0.270106 | − | 0.467837i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.0429 | − | 18.5000i | −1.15250 | − | 0.665399i | −0.203008 | − | 0.979177i | \(-0.565072\pi\) |
−0.949496 | + | 0.313778i | \(0.898405\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −30.3109 | + | 17.5000i | −1.08740 | + | 0.627809i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.0000 | −0.537431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −65.0000 | −2.32588 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.33013 | − | 2.50000i | 0.154746 | − | 0.0893427i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.52628 | + | 5.50000i | 0.339575 | + | 0.196054i | 0.660084 | − | 0.751192i | \(-0.270521\pi\) |
−0.320509 | + | 0.947245i | \(0.603854\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.50000 | + | 9.52628i | −0.195805 | + | 0.339145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.50000 | + | 4.33013i | 0.0888898 | + | 0.153962i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 33.7750 | − | 32.5000i | 1.19939 | − | 1.15411i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −19.9186 | − | 11.5000i | −0.705552 | − | 0.407351i | 0.103860 | − | 0.994592i | \(-0.466881\pi\) |
−0.809412 | + | 0.587241i | \(0.800214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | + | 10.3923i | −0.212265 | + | 0.367653i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.66025 | + | 5.00000i | −0.305614 | + | 0.176446i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.00000i | 0.316815i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.5000 | − | 32.0429i | −0.650425 | − | 1.12657i | −0.983020 | − | 0.183500i | \(-0.941257\pi\) |
0.332594 | − | 0.943070i | \(-0.392076\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.00000 | −0.280918 | −0.140459 | − | 0.990086i | \(-0.544858\pi\) | ||||
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.06218 | − | 3.50000i | −0.212610 | − | 0.122750i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −12.9904 | + | 7.50000i | −0.454476 | + | 0.262392i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 35.0000 | − | 8.66025i | 1.22300 | − | 0.302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.5000 | + | 21.6506i | 0.436253 | + | 0.755612i | 0.997397 | − | 0.0721058i | \(-0.0229719\pi\) |
−0.561144 | + | 0.827718i | \(0.689639\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.8468 | − | 15.5000i | −0.935820 | − | 0.540296i | −0.0471726 | − | 0.998887i | \(-0.515021\pi\) |
−0.888648 | + | 0.458591i | \(0.848354\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000i | 0.417281i | 0.977992 | + | 0.208640i | \(0.0669038\pi\) | ||||
−0.977992 | + | 0.208640i | \(0.933096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5000 | − | 21.6506i | −0.434143 | − | 0.751958i | 0.563082 | − | 0.826401i | \(-0.309615\pi\) |
−0.997225 | + | 0.0744432i | \(0.976282\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0000 | 0.450965 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0000i | 0.623663i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.5000 | + | 37.2391i | −0.742262 | + | 1.28564i | 0.209200 | + | 0.977873i | \(0.432914\pi\) |
−0.951463 | + | 0.307763i | \(0.900419\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 25.9808 | − | 15.0000i | 0.894825 | − | 0.516627i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 60.6218 | − | 35.0000i | 2.08299 | − | 1.20261i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.5000 | + | 19.9186i | −0.394679 | + | 0.683604i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.5000 | + | 18.1865i | −0.359935 | + | 0.623426i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 34.0000i | − | 1.16414i | −0.813139 | − | 0.582069i | \(-0.802243\pi\) | ||
0.813139 | − | 0.582069i | \(-0.197757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 26.0000i | − | 0.888143i | −0.895991 | − | 0.444072i | \(-0.853534\pi\) | ||
0.895991 | − | 0.444072i | \(-0.146466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.0000 | 1.22830 | 0.614152 | − | 0.789188i | \(-0.289498\pi\) | ||||
0.614152 | + | 0.789188i | \(0.289498\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.5000 | − | 21.6506i | −0.425999 | − | 0.737852i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 24.0000i | − | 0.816970i | −0.912765 | − | 0.408485i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408485i | \(-0.133943\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8564 | − | 8.00000i | −0.470588 | − | 0.271694i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 10.0000 | + | 17.3205i | 0.339227 | + | 0.587558i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5000 | − | 2.59808i | 0.355779 | − | 0.0880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.0526 | − | 11.0000i | 0.644831 | − | 0.372294i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.8468 | − | 15.5000i | −0.906552 | − | 0.523398i | −0.0272316 | − | 0.999629i | \(-0.508669\pi\) |
−0.879320 | + | 0.476231i | \(0.842002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.00000 | 0.236104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.5000 | + | 38.9711i | 0.758044 | + | 1.31297i | 0.943847 | + | 0.330384i | \(0.107178\pi\) |
−0.185802 | + | 0.982587i | \(0.559488\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.0000i | − | 0.673054i | −0.941674 | − | 0.336527i | \(-0.890748\pi\) | ||
0.941674 | − | 0.336527i | \(-0.109252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.8468 | − | 15.5000i | 0.901427 | − | 0.520439i | 0.0237640 | − | 0.999718i | \(-0.492435\pi\) |
0.877663 | + | 0.479279i | \(0.159102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.0000 | −1.17386 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −31.1769 | − | 18.0000i | −1.04330 | − | 0.602347i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.79423 | + | 7.50000i | −0.260242 | + | 0.250418i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.00000 | − | 1.73205i | 0.0333148 | − | 0.0577030i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.6506 | − | 12.5000i | −0.720488 | − | 0.415974i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.7224 | + | 8.50000i | −0.488850 | + | 0.282238i | −0.724097 | − | 0.689698i | \(-0.757743\pi\) |
0.235247 | + | 0.971936i | \(0.424410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.0000 | −0.862366 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.00000 | −0.265052 | −0.132526 | − | 0.991180i | \(-0.542309\pi\) | ||||
−0.132526 | + | 0.991180i | \(0.542309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 51.9615 | − | 30.0000i | 1.71968 | − | 0.992855i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −17.3205 | − | 10.0000i | −0.571974 | − | 0.330229i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.5000 | − | 42.4352i | 0.808180 | − | 1.39981i | −0.105942 | − | 0.994372i | \(-0.533786\pi\) |
0.914123 | − | 0.405437i | \(-0.132881\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6.00000 | − | 10.3923i | −0.197707 | − | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.7750 | + | 32.5000i | −1.11172 | + | 1.06975i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.5000 | + | 38.9711i | −0.738201 | + | 1.27860i | 0.215104 | + | 0.976591i | \(0.430991\pi\) |
−0.953305 | + | 0.302010i | \(0.902342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −54.0000 | −1.76978 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 18.0000i | − | 0.588034i | −0.955800 | − | 0.294017i | \(-0.905008\pi\) | ||
0.955800 | − | 0.294017i | \(-0.0949923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.0000 | 0.456387 | 0.228193 | − | 0.973616i | \(-0.426718\pi\) | ||||
0.228193 | + | 0.973616i | \(0.426718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.9904 | − | 7.50000i | −0.423025 | − | 0.244234i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.8468 | − | 15.5000i | 0.872403 | − | 0.503682i | 0.00425721 | − | 0.999991i | \(-0.498645\pi\) |
0.868146 | + | 0.496309i | \(0.165312\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.00000 | + | 6.92820i | −0.0649227 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.00000 | − | 15.5885i | −0.291845 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.59808 | + | 1.50000i | 0.0841599 | + | 0.0485898i | 0.541489 | − | 0.840708i | \(-0.317861\pi\) |
−0.457329 | + | 0.889297i | \(0.651194\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 5.00000i | − | 0.161627i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.50000 | + | 12.9904i | 0.242188 | + | 0.419481i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 18.0000i | − | 0.580042i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.0000i | 0.514525i | 0.966342 | + | 0.257263i | \(0.0828206\pi\) | ||||
−0.966342 | + | 0.257263i | \(0.917179\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.50000 | + | 2.59808i | −0.0481869 | + | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.50000 | − | 6.06218i | 0.112320 | − | 0.194545i | −0.804385 | − | 0.594108i | \(-0.797505\pi\) |
0.916705 | + | 0.399564i | \(0.130838\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −56.2917 | + | 32.5000i | −1.80463 | + | 1.04190i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −38.9711 | + | 22.5000i | −1.24680 | + | 0.719839i | −0.970469 | − | 0.241225i | \(-0.922451\pi\) |
−0.276328 | + | 0.961063i | \(0.589118\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −17.5000 | + | 30.3109i | −0.559302 | + | 0.968740i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | − | 31.1769i | 0.574696 | − | 0.995402i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.0000i | 0.510321i | 0.966899 | + | 0.255160i | \(0.0821283\pi\) | ||||
−0.966899 | + | 0.255160i | \(0.917872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 60.0000i | − | 1.90982i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −15.0000 | −0.476972 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.50000 | − | 2.59808i | −0.0476491 | − | 0.0825306i | 0.841217 | − | 0.540697i | \(-0.181840\pi\) |
−0.888866 | + | 0.458167i | \(0.848506\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.00000i | 0.0317340i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.06218 | − | 3.50000i | −0.191991 | − | 0.110846i | 0.400923 | − | 0.916112i | \(-0.368689\pi\) |
−0.592914 | + | 0.805266i | \(0.702023\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 17.5000 | + | 30.3109i | 0.553675 | + | 0.958994i |
(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 | 1300.2.bb.c.549.2 | 4 | ||
5.2 | odd | 4 | 1300.2.i.c.601.1 | 2 | |||
5.3 | odd | 4 | 260.2.i.c.81.1 | yes | 2 | ||
5.4 | even | 2 | inner | 1300.2.bb.c.549.1 | 4 | ||
13.9 | even | 3 | inner | 1300.2.bb.c.1049.1 | 4 | ||
15.8 | even | 4 | 2340.2.q.c.2161.1 | 2 | |||
20.3 | even | 4 | 1040.2.q.f.81.1 | 2 | |||
65.3 | odd | 12 | 3380.2.a.d.1.1 | 1 | |||
65.9 | even | 6 | inner | 1300.2.bb.c.1049.2 | 4 | ||
65.22 | odd | 12 | 1300.2.i.c.1101.1 | 2 | |||
65.23 | odd | 12 | 3380.2.a.e.1.1 | 1 | |||
65.28 | even | 12 | 3380.2.f.c.3041.2 | 2 | |||
65.48 | odd | 12 | 260.2.i.c.61.1 | ✓ | 2 | ||
65.63 | even | 12 | 3380.2.f.c.3041.1 | 2 | |||
195.113 | even | 12 | 2340.2.q.c.1621.1 | 2 | |||
260.243 | even | 12 | 1040.2.q.f.321.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
260.2.i.c.61.1 | ✓ | 2 | 65.48 | odd | 12 | ||
260.2.i.c.81.1 | yes | 2 | 5.3 | odd | 4 | ||
1040.2.q.f.81.1 | 2 | 20.3 | even | 4 | |||
1040.2.q.f.321.1 | 2 | 260.243 | even | 12 | |||
1300.2.i.c.601.1 | 2 | 5.2 | odd | 4 | |||
1300.2.i.c.1101.1 | 2 | 65.22 | odd | 12 | |||
1300.2.bb.c.549.1 | 4 | 5.4 | even | 2 | inner | ||
1300.2.bb.c.549.2 | 4 | 1.1 | even | 1 | trivial | ||
1300.2.bb.c.1049.1 | 4 | 13.9 | even | 3 | inner | ||
1300.2.bb.c.1049.2 | 4 | 65.9 | even | 6 | inner | ||
2340.2.q.c.1621.1 | 2 | 195.113 | even | 12 | |||
2340.2.q.c.2161.1 | 2 | 15.8 | even | 4 | |||
3380.2.a.d.1.1 | 1 | 65.3 | odd | 12 | |||
3380.2.a.e.1.1 | 1 | 65.23 | odd | 12 | |||
3380.2.f.c.3041.1 | 2 | 65.63 | even | 12 | |||
3380.2.f.c.3041.2 | 2 | 65.28 | even | 12 |