Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(109,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.05503558921\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.109 |
Dual form | 1134.2.h.o.541.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | −5.00000 | −1.50756 | −0.753778 | − | 0.657129i | \(-0.771771\pi\) | ||||
−0.753778 | + | 0.657129i | \(0.771771\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.00000 | + | 5.19615i | −0.832050 | + | 1.44115i | 0.0643593 | + | 0.997927i | \(0.479500\pi\) |
−0.896410 | + | 0.443227i | \(0.853834\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.00000 | + | 3.46410i | −0.485071 | + | 0.840168i | −0.999853 | − | 0.0171533i | \(-0.994540\pi\) |
0.514782 | + | 0.857321i | \(0.327873\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000 | + | 3.46410i | 0.458831 | + | 0.794719i | 0.998899 | − | 0.0469020i | \(-0.0149348\pi\) |
−0.540068 | + | 0.841621i | \(0.681602\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.50000 | + | 4.33013i | −0.533002 | + | 0.923186i | ||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | 3.50000 | + | 6.06218i | 0.649934 | + | 1.12572i | 0.983138 | + | 0.182864i | \(0.0585367\pi\) |
−0.333205 | + | 0.942855i | \(0.608130\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 2.59808i | −0.269408 | − | 0.466628i | 0.699301 | − | 0.714827i | \(-0.253495\pi\) |
−0.968709 | + | 0.248199i | \(0.920161\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 3.46410i | 0.342997 | + | 0.594089i | ||||
\(35\) | −5.00000 | + | 1.73205i | −0.845154 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.00000 | −0.316228 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | − | 6.92820i | −0.609994 | − | 1.05654i | −0.991241 | − | 0.132068i | \(-0.957838\pi\) |
0.381246 | − | 0.924473i | \(-0.375495\pi\) | |||||||
\(44\) | 2.50000 | + | 4.33013i | 0.376889 | + | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | 3.00000 | − | 5.19615i | 0.437595 | − | 0.757937i | −0.559908 | − | 0.828554i | \(-0.689164\pi\) |
0.997503 | + | 0.0706177i | \(0.0224970\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.00000 | 0.832050 | ||||||||
\(53\) | −3.00000 | + | 5.19615i | −0.412082 | + | 0.713746i | −0.995117 | − | 0.0987002i | \(-0.968532\pi\) |
0.583036 | + | 0.812447i | \(0.301865\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0000 | −1.34840 | ||||||||
\(56\) | 2.50000 | − | 0.866025i | 0.334077 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.00000 | 0.919145 | ||||||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.00000 | + | 10.3923i | −0.744208 | + | 1.28901i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | + | 5.19615i | −0.119523 | + | 0.621059i | ||||
\(71\) | 4.00000 | 0.474713 | 0.237356 | − | 0.971423i | \(-0.423719\pi\) | ||||
0.237356 | + | 0.971423i | \(0.423719\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.50000 | + | 11.2583i | −0.760767 | + | 1.31769i | 0.181688 | + | 0.983356i | \(0.441844\pi\) |
−0.942455 | + | 0.334332i | \(0.891489\pi\) | |||||||
\(74\) | −8.00000 | −0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | − | 3.46410i | 0.229416 | − | 0.397360i | ||||
\(77\) | 12.5000 | − | 4.33013i | 1.42451 | − | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | − | 2.59808i | 0.168763 | − | 0.292306i | −0.769222 | − | 0.638982i | \(-0.779356\pi\) |
0.937985 | + | 0.346675i | \(0.112689\pi\) | |||||||
\(80\) | −1.00000 | + | 1.73205i | −0.111803 | + | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | + | 5.19615i | 0.331295 | + | 0.573819i | ||||
\(83\) | −3.50000 | − | 6.06218i | −0.384175 | − | 0.665410i | 0.607479 | − | 0.794335i | \(-0.292181\pi\) |
−0.991654 | + | 0.128925i | \(0.958847\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | + | 6.92820i | −0.433861 | + | 0.751469i | ||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.00000 | 0.533002 | ||||||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | − | 15.5885i | 0.314485 | − | 1.63411i | ||||
\(92\) | −2.00000 | − | 3.46410i | −0.208514 | − | 0.361158i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.00000 | − | 5.19615i | −0.309426 | − | 0.535942i | ||||
\(95\) | 4.00000 | + | 6.92820i | 0.410391 | + | 0.710819i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | + | 4.33013i | 0.253837 | + | 0.439658i | 0.964579 | − | 0.263795i | \(-0.0849741\pi\) |
−0.710742 | + | 0.703452i | \(0.751641\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 5.00000 | 0.497519 | 0.248759 | − | 0.968565i | \(-0.419977\pi\) | ||||
0.248759 | + | 0.968565i | \(0.419977\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 3.00000 | − | 5.19615i | 0.294174 | − | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.00000 | + | 13.8564i | −0.766261 | + | 1.32720i | 0.173316 | + | 0.984866i | \(0.444552\pi\) |
−0.939577 | + | 0.342337i | \(0.888782\pi\) | |||||||
\(110\) | −5.00000 | + | 8.66025i | −0.476731 | + | 0.825723i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 2.00000 | − | 3.46410i | 0.188144 | − | 0.325875i | −0.756487 | − | 0.654008i | \(-0.773086\pi\) |
0.944632 | + | 0.328133i | \(0.106419\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000 | 0.746004 | ||||||||
\(116\) | 3.50000 | − | 6.06218i | 0.324967 | − | 0.562859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 2.00000 | − | 10.3923i | 0.183340 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14.0000 | 1.27273 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.50000 | + | 2.59808i | −0.134704 | + | 0.233314i | ||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.00000 | + | 10.3923i | 0.526235 | + | 0.911465i | ||||
\(131\) | −13.0000 | −1.13582 | −0.567908 | − | 0.823092i | \(-0.692247\pi\) | ||||
−0.567908 | + | 0.823092i | \(0.692247\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | − | 6.92820i | −0.693688 | − | 0.600751i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | − | 3.46410i | 0.171499 | − | 0.297044i | ||||
\(137\) | 8.00000 | 0.683486 | 0.341743 | − | 0.939793i | \(-0.388983\pi\) | ||||
0.341743 | + | 0.939793i | \(0.388983\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | − | 6.92820i | 0.339276 | − | 0.587643i | −0.645021 | − | 0.764165i | \(-0.723151\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(140\) | 4.00000 | + | 3.46410i | 0.338062 | + | 0.292770i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.00000 | − | 3.46410i | 0.167836 | − | 0.290701i | ||||
\(143\) | 15.0000 | − | 25.9808i | 1.25436 | − | 2.17262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.00000 | + | 12.1244i | 0.581318 | + | 1.00687i | ||||
\(146\) | 6.50000 | + | 11.2583i | 0.537944 | + | 0.931746i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | + | 6.92820i | −0.328798 | + | 0.569495i | ||||
\(149\) | −9.00000 | −0.737309 | −0.368654 | − | 0.929567i | \(-0.620181\pi\) | ||||
−0.368654 | + | 0.929567i | \(0.620181\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.0000 | −1.38344 | −0.691720 | − | 0.722166i | \(-0.743147\pi\) | ||||
−0.691720 | + | 0.722166i | \(0.743147\pi\) | |||||||
\(152\) | −2.00000 | − | 3.46410i | −0.162221 | − | 0.280976i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.50000 | − | 12.9904i | 0.201456 | − | 1.04679i | ||||
\(155\) | −3.00000 | − | 5.19615i | −0.240966 | − | 0.417365i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | − | 12.1244i | −0.558661 | − | 0.967629i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.438948 | − | 0.898513i | \(-0.355351\pi\) | |||||||
\(158\) | −1.50000 | − | 2.59808i | −0.119334 | − | 0.206692i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | + | 1.73205i | 0.0790569 | + | 0.136931i | ||||
\(161\) | −10.0000 | + | 3.46410i | −0.788110 | + | 0.273009i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00000 | − | 1.73205i | −0.0783260 | − | 0.135665i | 0.824202 | − | 0.566296i | \(-0.191624\pi\) |
−0.902528 | + | 0.430632i | \(0.858291\pi\) | |||||||
\(164\) | 6.00000 | 0.468521 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.00000 | −0.543305 | ||||||||
\(167\) | −7.00000 | + | 12.1244i | −0.541676 | + | 0.938211i | 0.457132 | + | 0.889399i | \(0.348877\pi\) |
−0.998808 | + | 0.0488118i | \(0.984457\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | − | 19.9186i | −0.884615 | − | 1.53220i | ||||
\(170\) | 4.00000 | + | 6.92820i | 0.306786 | + | 0.531369i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.00000 | + | 6.92820i | −0.304997 | + | 0.528271i | ||||
\(173\) | 0.500000 | − | 0.866025i | 0.0380143 | − | 0.0658427i | −0.846392 | − | 0.532560i | \(-0.821230\pi\) |
0.884407 | + | 0.466717i | \(0.154563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 0.866025i | 0.188982 | − | 0.0654654i | ||||
\(176\) | 2.50000 | − | 4.33013i | 0.188445 | − | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | −7.50000 | + | 12.9904i | −0.560576 | + | 0.970947i | 0.436870 | + | 0.899525i | \(0.356087\pi\) |
−0.997446 | + | 0.0714220i | \(0.977246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | −12.0000 | − | 10.3923i | −0.889499 | − | 0.770329i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | −8.00000 | − | 13.8564i | −0.588172 | − | 1.01874i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | − | 17.3205i | 0.731272 | − | 1.26660i | ||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.50000 | + | 16.4545i | 0.683825 | + | 1.18442i | 0.973805 | + | 0.227387i | \(0.0730182\pi\) |
−0.289980 | + | 0.957033i | \(0.593649\pi\) | |||||||
\(194\) | 5.00000 | 0.358979 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 25.0000 | 1.78118 | 0.890588 | − | 0.454811i | \(-0.150293\pi\) | ||||
0.890588 | + | 0.454811i | \(0.150293\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.50000 | − | 16.4545i | 0.673437 | − | 1.16643i | −0.303486 | − | 0.952836i | \(-0.598151\pi\) |
0.976923 | − | 0.213591i | \(-0.0685161\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.50000 | − | 4.33013i | 0.175899 | − | 0.304667i | ||||
\(203\) | −14.0000 | − | 12.1244i | −0.982607 | − | 0.850963i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | + | 10.3923i | −0.419058 | + | 0.725830i | ||||
\(206\) | 4.00000 | − | 6.92820i | 0.278693 | − | 0.482711i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.00000 | − | 5.19615i | −0.208013 | − | 0.360288i | ||||
\(209\) | −10.0000 | − | 17.3205i | −0.691714 | − | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.0000 | + | 22.5167i | −0.894957 | + | 1.55011i | −0.0610990 | + | 0.998132i | \(0.519461\pi\) |
−0.833858 | + | 0.551979i | \(0.813873\pi\) | |||||||
\(212\) | 6.00000 | 0.412082 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 12.0000 | 0.820303 | ||||||||
\(215\) | −8.00000 | − | 13.8564i | −0.545595 | − | 0.944999i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.00000 | + | 5.19615i | 0.407307 | + | 0.352738i | ||||
\(218\) | 8.00000 | + | 13.8564i | 0.541828 | + | 0.938474i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.00000 | + | 8.66025i | 0.337100 | + | 0.583874i | ||||
\(221\) | −12.0000 | − | 20.7846i | −0.807207 | − | 1.39812i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.500000 | + | 0.866025i | 0.0334825 | + | 0.0579934i | 0.882281 | − | 0.470723i | \(-0.156007\pi\) |
−0.848799 | + | 0.528716i | \(0.822674\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.00000 | − | 3.46410i | −0.133038 | − | 0.230429i | ||||
\(227\) | 27.0000 | 1.79205 | 0.896026 | − | 0.444001i | \(-0.146441\pi\) | ||||
0.896026 | + | 0.444001i | \(0.146441\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.00000 | 0.264327 | 0.132164 | − | 0.991228i | \(-0.457808\pi\) | ||||
0.132164 | + | 0.991228i | \(0.457808\pi\) | |||||||
\(230\) | 4.00000 | − | 6.92820i | 0.263752 | − | 0.456832i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.50000 | − | 6.06218i | −0.229786 | − | 0.398001i | ||||
\(233\) | −11.0000 | − | 19.0526i | −0.720634 | − | 1.24817i | −0.960746 | − | 0.277429i | \(-0.910518\pi\) |
0.240112 | − | 0.970745i | \(-0.422816\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.00000 | − | 10.3923i | 0.391397 | − | 0.677919i | ||||
\(236\) | 3.50000 | − | 6.06218i | 0.227831 | − | 0.394614i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.00000 | − | 6.92820i | −0.518563 | − | 0.449089i | ||||
\(239\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.00000 | −0.0644157 | −0.0322078 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322078 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(242\) | 7.00000 | − | 12.1244i | 0.449977 | − | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.0000 | − | 8.66025i | 0.702764 | − | 0.553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.0000 | −1.52708 | ||||||||
\(248\) | 1.50000 | + | 2.59808i | 0.0952501 | + | 0.164978i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | + | 10.3923i | −0.379473 | + | 0.657267i | ||||
\(251\) | 21.0000 | 1.32551 | 0.662754 | − | 0.748837i | \(-0.269387\pi\) | ||||
0.662754 | + | 0.748837i | \(0.269387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0000 | −1.25739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.0000 | + | 13.8564i | 0.994192 | + | 0.860995i | ||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50000 | + | 11.2583i | −0.401571 | + | 0.695542i | ||||
\(263\) | −12.0000 | −0.739952 | −0.369976 | − | 0.929041i | \(-0.620634\pi\) | ||||
−0.369976 | + | 0.929041i | \(0.620634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | + | 10.3923i | −0.368577 | + | 0.638394i | ||||
\(266\) | −10.0000 | + | 3.46410i | −0.613139 | + | 0.212398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.00000 | + | 8.66025i | −0.305424 | + | 0.529009i | ||||
\(269\) | 15.5000 | − | 26.8468i | 0.945052 | − | 1.63688i | 0.189404 | − | 0.981899i | \(-0.439344\pi\) |
0.755648 | − | 0.654978i | \(-0.227322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −2.00000 | − | 3.46410i | −0.121268 | − | 0.210042i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.00000 | − | 6.92820i | 0.241649 | − | 0.418548i | ||||
\(275\) | 5.00000 | 0.301511 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | 0.120168 | 0.0600842 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600842 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(278\) | −4.00000 | − | 6.92820i | −0.239904 | − | 0.415526i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | − | 1.73205i | 0.298807 | − | 0.103510i | ||||
\(281\) | 1.00000 | + | 1.73205i | 0.0596550 | + | 0.103325i | 0.894311 | − | 0.447447i | \(-0.147667\pi\) |
−0.834656 | + | 0.550772i | \(0.814333\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.00000 | − | 13.8564i | −0.475551 | − | 0.823678i | 0.524057 | − | 0.851683i | \(-0.324418\pi\) |
−0.999608 | + | 0.0280052i | \(0.991084\pi\) | |||||||
\(284\) | −2.00000 | − | 3.46410i | −0.118678 | − | 0.205557i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −15.0000 | − | 25.9808i | −0.886969 | − | 1.53627i | ||||
\(287\) | 3.00000 | − | 15.5885i | 0.177084 | − | 0.920158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 14.0000 | 0.822108 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0000 | 0.760767 | ||||||||
\(293\) | 13.5000 | − | 23.3827i | 0.788678 | − | 1.36603i | −0.138098 | − | 0.990419i | \(-0.544099\pi\) |
0.926777 | − | 0.375613i | \(-0.122568\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00000 | + | 12.1244i | 0.407556 | + | 0.705907i | ||||
\(296\) | 4.00000 | + | 6.92820i | 0.232495 | + | 0.402694i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.50000 | + | 7.79423i | −0.260678 | + | 0.451508i | ||||
\(299\) | −12.0000 | + | 20.7846i | −0.693978 | + | 1.20201i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | + | 13.8564i | 0.922225 | + | 0.798670i | ||||
\(302\) | −8.50000 | + | 14.7224i | −0.489120 | + | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.00000 | −0.229416 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | −10.0000 | − | 8.66025i | −0.569803 | − | 0.493464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.00000 | −0.340777 | ||||||||
\(311\) | 11.0000 | + | 19.0526i | 0.623753 | + | 1.08037i | 0.988781 | + | 0.149375i | \(0.0477261\pi\) |
−0.365028 | + | 0.930997i | \(0.618941\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −5.00000 | + | 8.66025i | −0.282617 | + | 0.489506i | −0.972028 | − | 0.234863i | \(-0.924536\pi\) |
0.689412 | + | 0.724370i | \(0.257869\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | −0.168763 | ||||||||
\(317\) | −16.5000 | + | 28.5788i | −0.926732 | + | 1.60515i | −0.137981 | + | 0.990435i | \(0.544061\pi\) |
−0.788751 | + | 0.614713i | \(0.789272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17.5000 | − | 30.3109i | −0.979812 | − | 1.69708i | ||||
\(320\) | 2.00000 | 0.111803 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.00000 | + | 10.3923i | −0.111456 | + | 0.579141i | ||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | −2.00000 | −0.110770 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | − | 5.19615i | 0.165647 | − | 0.286910i | ||||
\(329\) | −3.00000 | + | 15.5885i | −0.165395 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0000 | + | 27.7128i | −0.879440 | + | 1.52323i | −0.0274825 | + | 0.999622i | \(0.508749\pi\) |
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | −3.50000 | + | 6.06218i | −0.192087 | + | 0.332705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.00000 | + | 12.1244i | 0.383023 | + | 0.663415i | ||||
\(335\) | −10.0000 | − | 17.3205i | −0.546358 | − | 0.946320i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.5000 | − | 23.3827i | 0.735392 | − | 1.27374i | −0.219159 | − | 0.975689i | \(-0.570331\pi\) |
0.954551 | − | 0.298047i | \(-0.0963352\pi\) | |||||||
\(338\) | −23.0000 | −1.25104 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.00000 | 0.433861 | ||||||||
\(341\) | 7.50000 | + | 12.9904i | 0.406148 | + | 0.703469i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 4.00000 | + | 6.92820i | 0.215666 | + | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.500000 | − | 0.866025i | −0.0268802 | − | 0.0465578i | ||||
\(347\) | −13.5000 | − | 23.3827i | −0.724718 | − | 1.25525i | −0.959090 | − | 0.283101i | \(-0.908637\pi\) |
0.234372 | − | 0.972147i | \(-0.424697\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | + | 17.3205i | 0.535288 | + | 0.927146i | 0.999149 | + | 0.0412379i | \(0.0131301\pi\) |
−0.463862 | + | 0.885908i | \(0.653537\pi\) | |||||||
\(350\) | 0.500000 | − | 2.59808i | 0.0267261 | − | 0.138873i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.50000 | − | 4.33013i | −0.133250 | − | 0.230797i | ||||
\(353\) | 30.0000 | 1.59674 | 0.798369 | − | 0.602168i | \(-0.205696\pi\) | ||||
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.00000 | 0.424596 | ||||||||
\(356\) | 3.00000 | − | 5.19615i | 0.159000 | − | 0.275396i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 7.50000 | + | 12.9904i | 0.396387 | + | 0.686563i | ||||
\(359\) | 8.00000 | + | 13.8564i | 0.422224 | + | 0.731313i | 0.996157 | − | 0.0875892i | \(-0.0279163\pi\) |
−0.573933 | + | 0.818902i | \(0.694583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.50000 | − | 2.59808i | 0.0789474 | − | 0.136741i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −15.0000 | + | 5.19615i | −0.786214 | + | 0.272352i | ||||
\(365\) | −13.0000 | + | 22.5167i | −0.680451 | + | 1.17858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | −0.208798 | −0.104399 | − | 0.994535i | \(-0.533292\pi\) | ||||
−0.104399 | + | 0.994535i | \(0.533292\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.0000 | −0.831800 | ||||||||
\(371\) | 3.00000 | − | 15.5885i | 0.155752 | − | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.0000 | −1.03556 | −0.517780 | − | 0.855514i | \(-0.673242\pi\) | ||||
−0.517780 | + | 0.855514i | \(0.673242\pi\) | |||||||
\(374\) | −10.0000 | − | 17.3205i | −0.517088 | − | 0.895622i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | + | 5.19615i | −0.154713 | + | 0.267971i | ||||
\(377\) | −42.0000 | −2.16311 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | 4.00000 | − | 6.92820i | 0.205196 | − | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9.00000 | + | 15.5885i | 0.460480 | + | 0.797575i | ||||
\(383\) | 4.00000 | 0.204390 | 0.102195 | − | 0.994764i | \(-0.467413\pi\) | ||||
0.102195 | + | 0.994764i | \(0.467413\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.0000 | − | 8.66025i | 1.27412 | − | 0.441367i | ||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | −1.00000 | −0.0507020 | −0.0253510 | − | 0.999679i | \(-0.508070\pi\) | ||||
−0.0253510 | + | 0.999679i | \(0.508070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | + | 13.8564i | −0.404577 | + | 0.700749i | ||||
\(392\) | −5.50000 | + | 4.33013i | −0.277792 | + | 0.218704i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5000 | − | 21.6506i | 0.629741 | − | 1.09074i | ||||
\(395\) | 3.00000 | − | 5.19615i | 0.150946 | − | 0.261447i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.00000 | + | 15.5885i | 0.451697 | + | 0.782362i | 0.998492 | − | 0.0549046i | \(-0.0174855\pi\) |
−0.546795 | + | 0.837267i | \(0.684152\pi\) | |||||||
\(398\) | −9.50000 | − | 16.4545i | −0.476192 | − | 0.824789i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0.500000 | − | 0.866025i | 0.0250000 | − | 0.0433013i | ||||
\(401\) | 18.0000 | 0.898877 | 0.449439 | − | 0.893311i | \(-0.351624\pi\) | ||||
0.449439 | + | 0.893311i | \(0.351624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | 0.896644 | ||||||||
\(404\) | −2.50000 | − | 4.33013i | −0.124380 | − | 0.215432i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.5000 | + | 6.06218i | −0.868510 | + | 0.300861i | ||||
\(407\) | 20.0000 | + | 34.6410i | 0.991363 | + | 1.71709i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 6.00000 | + | 10.3923i | 0.296319 | + | 0.513239i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.00000 | − | 6.92820i | −0.197066 | − | 0.341328i | ||||
\(413\) | −14.0000 | − | 12.1244i | −0.688895 | − | 0.596601i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.00000 | − | 12.1244i | −0.343616 | − | 0.595161i | ||||
\(416\) | −6.00000 | −0.294174 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −20.0000 | −0.978232 | ||||||||
\(419\) | 6.00000 | − | 10.3923i | 0.293119 | − | 0.507697i | −0.681426 | − | 0.731887i | \(-0.738640\pi\) |
0.974546 | + | 0.224189i | \(0.0719734\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.00000 | + | 15.5885i | 0.438633 | + | 0.759735i | 0.997584 | − | 0.0694656i | \(-0.0221294\pi\) |
−0.558951 | + | 0.829201i | \(0.688796\pi\) | |||||||
\(422\) | 13.0000 | + | 22.5167i | 0.632830 | + | 1.09609i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | − | 10.3923i | 0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −16.0000 | −0.771589 | ||||||||
\(431\) | −9.00000 | + | 15.5885i | −0.433515 | + | 0.750870i | −0.997173 | − | 0.0751385i | \(-0.976060\pi\) |
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.00000 | −0.336399 | −0.168199 | − | 0.985753i | \(-0.553795\pi\) | ||||
−0.168199 | + | 0.985753i | \(0.553795\pi\) | |||||||
\(434\) | 7.50000 | − | 2.59808i | 0.360012 | − | 0.124712i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.0000 | 0.766261 | ||||||||
\(437\) | 8.00000 | + | 13.8564i | 0.382692 | + | 0.662842i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.50000 | + | 2.59808i | −0.0715911 | + | 0.123999i | −0.899599 | − | 0.436717i | \(-0.856141\pi\) |
0.828008 | + | 0.560717i | \(0.189474\pi\) | |||||||
\(440\) | 10.0000 | 0.476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | 5.50000 | − | 9.52628i | 0.261313 | − | 0.452607i | −0.705278 | − | 0.708931i | \(-0.749178\pi\) |
0.966591 | + | 0.256323i | \(0.0825112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.00000 | + | 10.3923i | 0.284427 | + | 0.492642i | ||||
\(446\) | 1.00000 | 0.0473514 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | 14.0000 | 0.660701 | 0.330350 | − | 0.943858i | \(-0.392833\pi\) | ||||
0.330350 | + | 0.943858i | \(0.392833\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.0000 | − | 25.9808i | 0.706322 | − | 1.22339i | ||||
\(452\) | −4.00000 | −0.188144 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.5000 | − | 23.3827i | 0.633586 | − | 1.09740i | ||||
\(455\) | 6.00000 | − | 31.1769i | 0.281284 | − | 1.46160i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.0000 | − | 22.5167i | 0.608114 | − | 1.05328i | −0.383437 | − | 0.923567i | \(-0.625260\pi\) |
0.991551 | − | 0.129718i | \(-0.0414071\pi\) | |||||||
\(458\) | 2.00000 | − | 3.46410i | 0.0934539 | − | 0.161867i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4.00000 | − | 6.92820i | −0.186501 | − | 0.323029i | ||||
\(461\) | −11.5000 | − | 19.9186i | −0.535608 | − | 0.927701i | −0.999134 | − | 0.0416172i | \(-0.986749\pi\) |
0.463525 | − | 0.886084i | \(-0.346584\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5000 | − | 25.1147i | 0.673872 | − | 1.16718i | −0.302925 | − | 0.953014i | \(-0.597963\pi\) |
0.976797 | − | 0.214166i | \(-0.0687035\pi\) | |||||||
\(464\) | −7.00000 | −0.324967 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −22.0000 | −1.01913 | ||||||||
\(467\) | 3.50000 | + | 6.06218i | 0.161961 | + | 0.280524i | 0.935572 | − | 0.353137i | \(-0.114885\pi\) |
−0.773611 | + | 0.633661i | \(0.781552\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | + | 17.3205i | 0.923514 | + | 0.799787i | ||||
\(470\) | −6.00000 | − | 10.3923i | −0.276759 | − | 0.479361i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.50000 | − | 6.06218i | −0.161101 | − | 0.279034i | ||||
\(473\) | 20.0000 | + | 34.6410i | 0.919601 | + | 1.59280i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | −10.0000 | + | 3.46410i | −0.458349 | + | 0.158777i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.0000 | −1.18797 | −0.593985 | − | 0.804476i | \(-0.702446\pi\) | ||||
−0.593985 | + | 0.804476i | \(0.702446\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 48.0000 | 2.18861 | ||||||||
\(482\) | −0.500000 | + | 0.866025i | −0.0227744 | + | 0.0394464i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | − | 12.1244i | −0.318182 | − | 0.551107i | ||||
\(485\) | 5.00000 | + | 8.66025i | 0.227038 | + | 0.393242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.50000 | − | 11.2583i | 0.294543 | − | 0.510164i | −0.680335 | − | 0.732901i | \(-0.738166\pi\) |
0.974879 | + | 0.222737i | \(0.0714992\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | − | 13.8564i | −0.0903508 | − | 0.625969i | ||||
\(491\) | 6.00000 | − | 10.3923i | 0.270776 | − | 0.468998i | −0.698285 | − | 0.715820i | \(-0.746053\pi\) |
0.969061 | + | 0.246822i | \(0.0793863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.0000 | −1.26106 | ||||||||
\(494\) | −12.0000 | + | 20.7846i | −0.539906 | + | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | −10.0000 | + | 3.46410i | −0.448561 | + | 0.155386i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.00000 | −0.358129 | −0.179065 | − | 0.983837i | \(-0.557307\pi\) | ||||
−0.179065 | + | 0.983837i | \(0.557307\pi\) | |||||||
\(500\) | 6.00000 | + | 10.3923i | 0.268328 | + | 0.464758i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.5000 | − | 18.1865i | 0.468638 | − | 0.811705i | ||||
\(503\) | −6.00000 | −0.267527 | −0.133763 | − | 0.991013i | \(-0.542706\pi\) | ||||
−0.133763 | + | 0.991013i | \(0.542706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | −10.0000 | + | 17.3205i | −0.444554 | + | 0.769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.00000 | −0.132973 | −0.0664863 | − | 0.997787i | \(-0.521179\pi\) | ||||
−0.0664863 | + | 0.997787i | \(0.521179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.50000 | − | 33.7750i | 0.287543 | − | 1.49412i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 16.0000 | 0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | + | 25.9808i | −0.659699 | + | 1.14263i | ||||
\(518\) | 20.0000 | − | 6.92820i | 0.878750 | − | 0.304408i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.00000 | − | 10.3923i | 0.263117 | − | 0.455733i | ||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.0000 | − | 22.5167i | −0.568450 | − | 0.984585i | −0.996719 | − | 0.0809336i | \(-0.974210\pi\) |
0.428269 | − | 0.903651i | \(-0.359124\pi\) | |||||||
\(524\) | 6.50000 | + | 11.2583i | 0.283954 | + | 0.491822i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.00000 | + | 10.3923i | −0.261612 | + | 0.453126i | ||||
\(527\) | 12.0000 | 0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 6.00000 | + | 10.3923i | 0.260623 | + | 0.451413i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.00000 | + | 10.3923i | −0.0867110 | + | 0.450564i | ||||
\(533\) | −18.0000 | − | 31.1769i | −0.779667 | − | 1.35042i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.0000 | + | 20.7846i | 0.518805 | + | 0.898597i | ||||
\(536\) | 5.00000 | + | 8.66025i | 0.215967 | + | 0.374066i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −15.5000 | − | 26.8468i | −0.668252 | − | 1.15745i | ||||
\(539\) | −27.5000 | + | 21.6506i | −1.18451 | + | 0.932559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.0000 | + | 25.9808i | 0.644900 | + | 1.11700i | 0.984325 | + | 0.176367i | \(0.0564345\pi\) |
−0.339424 | + | 0.940633i | \(0.610232\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | −16.0000 | + | 27.7128i | −0.685365 | + | 1.18709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.00000 | + | 15.5885i | 0.384812 | + | 0.666514i | 0.991743 | − | 0.128240i | \(-0.0409329\pi\) |
−0.606931 | + | 0.794755i | \(0.707600\pi\) | |||||||
\(548\) | −4.00000 | − | 6.92820i | −0.170872 | − | 0.295958i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.50000 | − | 4.33013i | 0.106600 | − | 0.184637i | ||||
\(551\) | −14.0000 | + | 24.2487i | −0.596420 | + | 1.03303i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.50000 | + | 7.79423i | −0.0637865 | + | 0.331444i | ||||
\(554\) | 1.00000 | − | 1.73205i | 0.0424859 | − | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | −0.339276 | ||||||||
\(557\) | −5.50000 | + | 9.52628i | −0.233042 | + | 0.403641i | −0.958702 | − | 0.284413i | \(-0.908201\pi\) |
0.725660 | + | 0.688054i | \(0.241535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 48.0000 | 2.03018 | ||||||||
\(560\) | 1.00000 | − | 5.19615i | 0.0422577 | − | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.00000 | 0.0843649 | ||||||||
\(563\) | 10.0000 | + | 17.3205i | 0.421450 | + | 0.729972i | 0.996082 | − | 0.0884397i | \(-0.0281881\pi\) |
−0.574632 | + | 0.818412i | \(0.694855\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | −6.00000 | + | 10.3923i | −0.251533 | + | 0.435668i | −0.963948 | − | 0.266090i | \(-0.914268\pi\) |
0.712415 | + | 0.701758i | \(0.247601\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(572\) | −30.0000 | −1.25436 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12.0000 | − | 10.3923i | −0.500870 | − | 0.433766i | ||||
\(575\) | −4.00000 | −0.166812 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5000 | + | 37.2391i | −0.895057 | + | 1.55028i | −0.0613223 | + | 0.998118i | \(0.519532\pi\) |
−0.833734 | + | 0.552166i | \(0.813802\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.00000 | − | 12.1244i | 0.290659 | − | 0.503436i | ||||
\(581\) | 14.0000 | + | 12.1244i | 0.580818 | + | 0.503003i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | − | 25.9808i | 0.621237 | − | 1.07601i | ||||
\(584\) | 6.50000 | − | 11.2583i | 0.268972 | − | 0.465873i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.5000 | − | 23.3827i | −0.557680 | − | 0.965930i | ||||
\(587\) | 10.0000 | + | 17.3205i | 0.412744 | + | 0.714894i | 0.995189 | − | 0.0979766i | \(-0.0312370\pi\) |
−0.582445 | + | 0.812870i | \(0.697904\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | − | 10.3923i | 0.247226 | − | 0.428207i | ||||
\(590\) | 14.0000 | 0.576371 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.00000 | 0.328798 | ||||||||
\(593\) | 18.0000 | + | 31.1769i | 0.739171 | + | 1.28028i | 0.952869 | + | 0.303383i | \(0.0981160\pi\) |
−0.213697 | + | 0.976900i | \(0.568551\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.00000 | − | 20.7846i | 0.163984 | − | 0.852086i | ||||
\(596\) | 4.50000 | + | 7.79423i | 0.184327 | + | 0.319264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.0000 | + | 20.7846i | 0.490716 | + | 0.849946i | ||||
\(599\) | 15.0000 | + | 25.9808i | 0.612883 | + | 1.06155i | 0.990752 | + | 0.135686i | \(0.0433238\pi\) |
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | + | 8.66025i | 0.203954 | + | 0.353259i | 0.949799 | − | 0.312861i | \(-0.101287\pi\) |
−0.745845 | + | 0.666120i | \(0.767954\pi\) | |||||||
\(602\) | 20.0000 | − | 6.92820i | 0.815139 | − | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.50000 | + | 14.7224i | 0.345860 | + | 0.599047i | ||||
\(605\) | 28.0000 | 1.13836 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.00000 | −0.365299 | −0.182649 | − | 0.983178i | \(-0.558467\pi\) | ||||
−0.182649 | + | 0.983178i | \(0.558467\pi\) | |||||||
\(608\) | −2.00000 | + | 3.46410i | −0.0811107 | + | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0000 | + | 31.1769i | 0.728202 | + | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.00000 | − | 5.19615i | 0.121169 | − | 0.209871i | −0.799060 | − | 0.601251i | \(-0.794669\pi\) |
0.920229 | + | 0.391381i | \(0.128002\pi\) | |||||||
\(614\) | −1.00000 | + | 1.73205i | −0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −12.5000 | + | 4.33013i | −0.503639 | + | 0.174466i | ||||
\(617\) | 1.00000 | − | 1.73205i | 0.0402585 | − | 0.0697297i | −0.845194 | − | 0.534460i | \(-0.820515\pi\) |
0.885453 | + | 0.464730i | \(0.153849\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000 | 0.160774 | 0.0803868 | − | 0.996764i | \(-0.474384\pi\) | ||||
0.0803868 | + | 0.996764i | \(0.474384\pi\) | |||||||
\(620\) | −3.00000 | + | 5.19615i | −0.120483 | + | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.0000 | 0.882120 | ||||||||
\(623\) | −12.0000 | − | 10.3923i | −0.480770 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 5.00000 | + | 8.66025i | 0.199840 | + | 0.346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.00000 | + | 12.1244i | −0.279330 | + | 0.483814i | ||||
\(629\) | 32.0000 | 1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | −1.50000 | + | 2.59808i | −0.0596668 | + | 0.103346i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.5000 | + | 28.5788i | 0.655299 | + | 1.13501i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | + | 41.5692i | 0.237729 | + | 1.64703i | ||||
\(638\) | −35.0000 | −1.38566 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | −14.0000 | −0.552967 | −0.276483 | − | 0.961019i | \(-0.589169\pi\) | ||||
−0.276483 | + | 0.961019i | \(0.589169\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | + | 12.1244i | −0.276053 | + | 0.478138i | −0.970400 | − | 0.241502i | \(-0.922360\pi\) |
0.694347 | + | 0.719640i | \(0.255693\pi\) | |||||||
\(644\) | 8.00000 | + | 6.92820i | 0.315244 | + | 0.273009i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.00000 | + | 13.8564i | −0.314756 | + | 0.545173i | ||||
\(647\) | −9.00000 | + | 15.5885i | −0.353827 | + | 0.612845i | −0.986916 | − | 0.161233i | \(-0.948453\pi\) |
0.633090 | + | 0.774078i | \(0.281786\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −17.5000 | − | 30.3109i | −0.686935 | − | 1.18981i | ||||
\(650\) | −3.00000 | − | 5.19615i | −0.117670 | − | 0.203810i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.00000 | + | 1.73205i | −0.0391630 | + | 0.0678323i | ||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.0000 | −1.01590 | ||||||||
\(656\) | −3.00000 | − | 5.19615i | −0.117130 | − | 0.202876i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000 | + | 10.3923i | 0.467809 | + | 0.405134i | ||||
\(659\) | 20.5000 | + | 35.5070i | 0.798567 | + | 1.38316i | 0.920550 | + | 0.390626i | \(0.127741\pi\) |
−0.121983 | + | 0.992532i | \(0.538925\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.0000 | + | 32.9090i | 0.739014 | + | 1.28001i | 0.952940 | + | 0.303160i | \(0.0980418\pi\) |
−0.213925 | + | 0.976850i | \(0.568625\pi\) | |||||||
\(662\) | 16.0000 | + | 27.7128i | 0.621858 | + | 1.07709i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.50000 | + | 6.06218i | 0.135826 | + | 0.235258i | ||||
\(665\) | −16.0000 | − | 13.8564i | −0.620453 | − | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.0000 | + | 24.2487i | 0.542082 | + | 0.938914i | ||||
\(668\) | 14.0000 | 0.541676 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −20.0000 | −0.772667 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.73205i | −0.0385472 | − | 0.0667657i | 0.846108 | − | 0.533011i | \(-0.178940\pi\) |
−0.884655 | + | 0.466246i | \(0.845606\pi\) | |||||||
\(674\) | −13.5000 | − | 23.3827i | −0.520001 | − | 0.900667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | 4.50000 | − | 7.79423i | 0.172949 | − | 0.299557i | −0.766501 | − | 0.642244i | \(-0.778004\pi\) |
0.939450 | + | 0.342687i | \(0.111337\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.0000 | − | 8.66025i | −0.383765 | − | 0.332350i | ||||
\(680\) | 4.00000 | − | 6.92820i | 0.153393 | − | 0.265684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 15.0000 | 0.574380 | ||||||||
\(683\) | 10.5000 | − | 18.1865i | 0.401771 | − | 0.695888i | −0.592168 | − | 0.805814i | \(-0.701728\pi\) |
0.993940 | + | 0.109926i | \(0.0350613\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | 0.611329 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −18.0000 | − | 31.1769i | −0.685745 | − | 1.18775i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | −1.00000 | −0.0380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | 8.00000 | − | 13.8564i | 0.303457 | − | 0.525603i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0000 | − | 20.7846i | −0.454532 | − | 0.787273i | ||||
\(698\) | 20.0000 | 0.757011 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.00000 | − | 1.73205i | −0.0755929 | − | 0.0654654i | ||||
\(701\) | 14.0000 | 0.528773 | 0.264386 | − | 0.964417i | \(-0.414831\pi\) | ||||
0.264386 | + | 0.964417i | \(0.414831\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.0000 | − | 27.7128i | 0.603451 | − | 1.04521i | ||||
\(704\) | −5.00000 | −0.188445 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | − | 25.9808i | 0.564532 | − | 0.977799i | ||||
\(707\) | −12.5000 | + | 4.33013i | −0.470111 | + | 0.162851i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.00000 | + | 6.92820i | −0.150223 | + | 0.260194i | −0.931309 | − | 0.364229i | \(-0.881333\pi\) |
0.781086 | + | 0.624423i | \(0.214666\pi\) | |||||||
\(710\) | 4.00000 | − | 6.92820i | 0.150117 | − | 0.260011i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.00000 | − | 5.19615i | −0.112430 | − | 0.194734i | ||||
\(713\) | −6.00000 | − | 10.3923i | −0.224702 | − | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 30.0000 | − | 51.9615i | 1.12194 | − | 1.94325i | ||||
\(716\) | 15.0000 | 0.560576 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.0000 | 0.597115 | ||||||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0000 | + | 6.92820i | −0.744839 | + | 0.258020i | ||||
\(722\) | −1.50000 | − | 2.59808i | −0.0558242 | − | 0.0966904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.50000 | − | 6.06218i | −0.129987 | − | 0.225144i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | + | 27.7128i | 0.593407 | + | 1.02781i | 0.993770 | + | 0.111454i | \(0.0355509\pi\) |
−0.400362 | + | 0.916357i | \(0.631116\pi\) | |||||||
\(728\) | −3.00000 | + | 15.5885i | −0.111187 | + | 0.577747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0000 | + | 22.5167i | 0.481152 | + | 0.833379i | ||||
\(731\) | 32.0000 | 1.18356 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −36.0000 | −1.32969 | −0.664845 | − | 0.746981i | \(-0.731502\pi\) | ||||
−0.664845 | + | 0.746981i | \(0.731502\pi\) | |||||||
\(734\) | −2.00000 | + | 3.46410i | −0.0738213 | + | 0.127862i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | + | 3.46410i | 0.0737210 | + | 0.127688i | ||||
\(737\) | 25.0000 | + | 43.3013i | 0.920887 | + | 1.59502i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.00000 | − | 5.19615i | 0.110357 | − | 0.191144i | −0.805557 | − | 0.592518i | \(-0.798134\pi\) |
0.915914 | + | 0.401374i | \(0.131467\pi\) | |||||||
\(740\) | −8.00000 | + | 13.8564i | −0.294086 | + | 0.509372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −12.0000 | − | 10.3923i | −0.440534 | − | 0.381514i | ||||
\(743\) | −3.00000 | + | 5.19615i | −0.110059 | + | 0.190628i | −0.915794 | − | 0.401648i | \(-0.868437\pi\) |
0.805735 | + | 0.592277i | \(0.201771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −18.0000 | −0.659469 | ||||||||
\(746\) | −10.0000 | + | 17.3205i | −0.366126 | + | 0.634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.0000 | −0.731272 | ||||||||
\(749\) | −24.0000 | − | 20.7846i | −0.876941 | − | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.0000 | 0.437886 | 0.218943 | − | 0.975738i | \(-0.429739\pi\) | ||||
0.218943 | + | 0.975738i | \(0.429739\pi\) | |||||||
\(752\) | 3.00000 | + | 5.19615i | 0.109399 | + | 0.189484i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −21.0000 | + | 36.3731i | −0.764775 | + | 1.32463i | ||||
\(755\) | −34.0000 | −1.23739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | 5.00000 | − | 8.66025i | 0.181608 | − | 0.314555i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | − | 6.92820i | −0.145095 | − | 0.251312i | ||||
\(761\) | −8.00000 | −0.290000 | −0.145000 | − | 0.989432i | \(-0.546318\pi\) | ||||
−0.145000 | + | 0.989432i | \(0.546318\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.00000 | − | 41.5692i | 0.289619 | − | 1.50491i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | − | 3.46410i | 0.0722629 | − | 0.125163i | ||||
\(767\) | −42.0000 | −1.51653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.500000 | + | 0.866025i | −0.0180305 | + | 0.0312297i | −0.874900 | − | 0.484304i | \(-0.839073\pi\) |
0.856869 | + | 0.515534i | \(0.172406\pi\) | |||||||
\(770\) | 5.00000 | − | 25.9808i | 0.180187 | − | 0.936282i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 9.50000 | − | 16.4545i | 0.341912 | − | 0.592210i | ||||
\(773\) | −19.0000 | + | 32.9090i | −0.683383 | + | 1.18365i | 0.290560 | + | 0.956857i | \(0.406159\pi\) |
−0.973942 | + | 0.226796i | \(0.927175\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.50000 | + | 2.59808i | 0.0538816 | + | 0.0933257i | ||||
\(776\) | −2.50000 | − | 4.33013i | −0.0897448 | − | 0.155443i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.500000 | + | 0.866025i | −0.0179259 | + | 0.0310485i | ||||
\(779\) | −24.0000 | −0.859889 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.0000 | −0.715656 | ||||||||
\(782\) | 8.00000 | + | 13.8564i | 0.286079 | + | 0.495504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −14.0000 | − | 24.2487i | −0.499681 | − | 0.865474i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.00000 | − | 15.5885i | −0.320815 | − | 0.555668i | 0.659841 | − | 0.751405i | \(-0.270624\pi\) |
−0.980656 | + | 0.195737i | \(0.937290\pi\) | |||||||
\(788\) | −12.5000 | − | 21.6506i | −0.445294 | − | 0.771272i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.00000 | − | 5.19615i | −0.106735 | − | 0.184871i | ||||
\(791\) | −2.00000 | + | 10.3923i | −0.0711118 | + | 0.369508i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 18.0000 | 0.638796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −19.0000 | −0.673437 | ||||||||
\(797\) | 16.5000 | − | 28.5788i | 0.584460 | − | 1.01231i | −0.410483 | − | 0.911868i | \(-0.634640\pi\) |
0.994943 | − | 0.100446i | \(-0.0320269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 12.0000 | + | 20.7846i | 0.424529 | + | 0.735307i | ||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.00000 | − | 15.5885i | 0.317801 | − | 0.550448i | ||||
\(803\) | 32.5000 | − | 56.2917i | 1.14690 | − | 1.98649i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | + | 6.92820i | −0.704907 | + | 0.244187i | ||||
\(806\) | 9.00000 | − | 15.5885i | 0.317011 | − | 0.549080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.00000 | −0.175899 | ||||||||
\(809\) | 17.0000 | − | 29.4449i | 0.597688 | − | 1.03523i | −0.395473 | − | 0.918477i | \(-0.629419\pi\) |
0.993161 | − | 0.116749i | \(-0.0372472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −50.0000 | −1.75574 | −0.877869 | − | 0.478901i | \(-0.841035\pi\) | ||||
−0.877869 | + | 0.478901i | \(0.841035\pi\) | |||||||
\(812\) | −3.50000 | + | 18.1865i | −0.122826 | + | 0.638222i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 40.0000 | 1.40200 | ||||||||
\(815\) | −2.00000 | − | 3.46410i | −0.0700569 | − | 0.121342i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000 | − | 27.7128i | 0.559769 | − | 0.969549i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | −24.5000 | + | 42.4352i | −0.855056 | + | 1.48100i | 0.0215373 | + | 0.999768i | \(0.493144\pi\) |
−0.876593 | + | 0.481232i | \(0.840189\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.50000 | − | 11.2583i | −0.226576 | − | 0.392441i | 0.730215 | − | 0.683217i | \(-0.239420\pi\) |
−0.956791 | + | 0.290776i | \(0.906086\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −17.5000 | + | 6.06218i | −0.608903 | + | 0.210930i | ||||
\(827\) | −51.0000 | −1.77344 | −0.886722 | − | 0.462303i | \(-0.847023\pi\) | ||||
−0.886722 | + | 0.462303i | \(0.847023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0000 | + | 19.0526i | −0.382046 | + | 0.661723i | −0.991355 | − | 0.131210i | \(-0.958114\pi\) |
0.609309 | + | 0.792933i | \(0.291447\pi\) | |||||||
\(830\) | −14.0000 | −0.485947 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | + | 5.19615i | −0.104006 | + | 0.180144i | ||||
\(833\) | 4.00000 | + | 27.7128i | 0.138592 | + | 0.960192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −14.0000 | + | 24.2487i | −0.484490 | + | 0.839161i | ||||
\(836\) | −10.0000 | + | 17.3205i | −0.345857 | + | 0.599042i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.00000 | − | 10.3923i | −0.207267 | − | 0.358996i | ||||
\(839\) | −2.00000 | − | 3.46410i | −0.0690477 | − | 0.119594i | 0.829435 | − | 0.558604i | \(-0.188663\pi\) |
−0.898482 | + | 0.439010i | \(0.855329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | + | 17.3205i | −0.344828 | + | 0.597259i | ||||
\(842\) | 18.0000 | 0.620321 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 26.0000 | 0.894957 | ||||||||
\(845\) | −23.0000 | − | 39.8372i | −0.791224 | − | 1.37044i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.0000 | + | 12.1244i | −1.20261 | + | 0.416598i | ||||
\(848\) | −3.00000 | − | 5.19615i | −0.103020 | − | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.00000 | − | 3.46410i | −0.0685994 | − | 0.118818i | ||||
\(851\) | −16.0000 | − | 27.7128i | −0.548473 | − | 0.949983i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | + | 39.8372i | 0.787505 | + | 1.36400i | 0.927491 | + | 0.373845i | \(0.121961\pi\) |
−0.139986 | + | 0.990153i | \(0.544706\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | −30.0000 | −1.02478 | −0.512390 | − | 0.858753i | \(-0.671240\pi\) | ||||
−0.512390 | + | 0.858753i | \(0.671240\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.0000 | −0.545913 | −0.272956 | − | 0.962026i | \(-0.588002\pi\) | ||||
−0.272956 | + | 0.962026i | \(0.588002\pi\) | |||||||
\(860\) | −8.00000 | + | 13.8564i | −0.272798 | + | 0.472500i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.00000 | + | 15.5885i | 0.306541 | + | 0.530945i | ||||
\(863\) | −19.0000 | − | 32.9090i | −0.646768 | − | 1.12023i | −0.983890 | − | 0.178774i | \(-0.942787\pi\) |
0.337123 | − | 0.941461i | \(-0.390546\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.00000 | − | 1.73205i | 0.0340010 | − | 0.0588915i | ||||
\(866\) | −3.50000 | + | 6.06218i | −0.118935 | + | 0.206001i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.50000 | − | 7.79423i | 0.0509133 | − | 0.264553i | ||||
\(869\) | −7.50000 | + | 12.9904i | −0.254420 | + | 0.440668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 60.0000 | 2.03302 | ||||||||
\(872\) | 8.00000 | − | 13.8564i | 0.270914 | − | 0.469237i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | 30.0000 | − | 10.3923i | 1.01419 | − | 0.351324i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 34.0000 | 1.14810 | 0.574049 | − | 0.818821i | \(-0.305372\pi\) | ||||
0.574049 | + | 0.818821i | \(0.305372\pi\) | |||||||
\(878\) | 1.50000 | + | 2.59808i | 0.0506225 | + | 0.0876808i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.00000 | − | 8.66025i | 0.168550 | − | 0.291937i | ||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | −12.0000 | + | 20.7846i | −0.403604 | + | 0.699062i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.50000 | − | 9.52628i | −0.184776 | − | 0.320042i | ||||
\(887\) | 42.0000 | 1.41022 | 0.705111 | − | 0.709097i | \(-0.250897\pi\) | ||||
0.705111 | + | 0.709097i | \(0.250897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.500000 | − | 0.866025i | 0.0167412 | − | 0.0289967i | ||||
\(893\) | 24.0000 | 0.803129 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0000 | + | 25.9808i | −0.501395 | + | 0.868441i | ||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.00000 | − | 12.1244i | 0.233593 | − | 0.404595i | ||||
\(899\) | 10.5000 | − | 18.1865i | 0.350195 | − | 0.606555i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.0000 | − | 20.7846i | −0.399778 | − | 0.692436i | ||||
\(902\) | −15.0000 | − | 25.9808i | −0.499445 | − | 0.865065i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | + | 3.46410i | −0.0665190 | + | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −42.0000 | −1.39459 | −0.697294 | − | 0.716786i | \(-0.745613\pi\) | ||||
−0.697294 | + | 0.716786i | \(0.745613\pi\) | |||||||
\(908\) | −13.5000 | − | 23.3827i | −0.448013 | − | 0.775982i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −24.0000 | − | 20.7846i | −0.795592 | − | 0.689003i | ||||
\(911\) | 18.0000 | + | 31.1769i | 0.596367 | + | 1.03294i | 0.993352 | + | 0.115113i | \(0.0367229\pi\) |
−0.396986 | + | 0.917825i | \(0.629944\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.5000 | + | 30.3109i | 0.579165 | + | 1.00314i | ||||
\(914\) | −13.0000 | − | 22.5167i | −0.430002 | − | 0.744785i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.00000 | − | 3.46410i | −0.0660819 | − | 0.114457i | ||||
\(917\) | 32.5000 | − | 11.2583i | 1.07324 | − | 0.371783i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.50000 | − | 11.2583i | −0.214415 | − | 0.371378i | 0.738676 | − | 0.674060i | \(-0.235451\pi\) |
−0.953092 | + | 0.302682i | \(0.902118\pi\) | |||||||
\(920\) | −8.00000 | −0.263752 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.0000 | −0.757465 | ||||||||
\(923\) | −12.0000 | + | 20.7846i | −0.394985 | + | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | + | 6.92820i | 0.131519 | + | 0.227798i | ||||
\(926\) | −14.5000 | − | 25.1147i | −0.476500 | − | 0.825321i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.50000 | + | 6.06218i | −0.114893 | + | 0.199001i | ||||
\(929\) | 18.0000 | − | 31.1769i | 0.590561 | − | 1.02288i | −0.403596 | − | 0.914937i | \(-0.632240\pi\) |
0.994157 | − | 0.107944i | \(-0.0344268\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.0000 | + | 10.3923i | 0.852116 | + | 0.340594i | ||||
\(932\) | −11.0000 | + | 19.0526i | −0.360317 | + | 0.624087i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 7.00000 | 0.229047 | ||||||||
\(935\) | 20.0000 | − | 34.6410i | 0.654070 | − | 1.13288i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14.0000 | 0.457360 | 0.228680 | − | 0.973502i | \(-0.426559\pi\) | ||||
0.228680 | + | 0.973502i | \(0.426559\pi\) | |||||||
\(938\) | 25.0000 | − | 8.66025i | 0.816279 | − | 0.282767i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | −0.391397 | ||||||||
\(941\) | 6.50000 | + | 11.2583i | 0.211894 | + | 0.367011i | 0.952307 | − | 0.305141i | \(-0.0987035\pi\) |
−0.740413 | + | 0.672152i | \(0.765370\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.0000 | + | 20.7846i | −0.390774 | + | 0.676840i | ||||
\(944\) | −7.00000 | −0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0000 | 1.30051 | ||||||||
\(947\) | 12.5000 | − | 21.6506i | 0.406195 | − | 0.703551i | −0.588264 | − | 0.808669i | \(-0.700189\pi\) |
0.994460 | + | 0.105118i | \(0.0335219\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.0000 | − | 67.5500i | −1.26599 | − | 2.19277i | ||||
\(950\) | −4.00000 | −0.129777 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.00000 | + | 10.3923i | −0.0648204 | + | 0.336817i | ||||
\(953\) | −2.00000 | −0.0647864 | −0.0323932 | − | 0.999475i | \(-0.510313\pi\) | ||||
−0.0323932 | + | 0.999475i | \(0.510313\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | + | 31.1769i | −0.582466 | + | 1.00886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.0000 | + | 22.5167i | −0.420011 | + | 0.727480i | ||||
\(959\) | −20.0000 | + | 6.92820i | −0.645834 | + | 0.223723i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.0000 | − | 19.0526i | 0.354839 | − | 0.614599i | ||||
\(962\) | 24.0000 | − | 41.5692i | 0.773791 | − | 1.34025i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.500000 | + | 0.866025i | 0.0161039 | + | 0.0278928i | ||||
\(965\) | 19.0000 | + | 32.9090i | 0.611632 | + | 1.05938i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.00000 | + | 6.92820i | −0.128631 | + | 0.222796i | −0.923147 | − | 0.384448i | \(-0.874392\pi\) |
0.794515 | + | 0.607244i | \(0.207725\pi\) | |||||||
\(968\) | −14.0000 | −0.449977 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10.0000 | 0.321081 | ||||||||
\(971\) | 6.00000 | + | 10.3923i | 0.192549 | + | 0.333505i | 0.946094 | − | 0.323891i | \(-0.104991\pi\) |
−0.753545 | + | 0.657396i | \(0.771658\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00000 | + | 20.7846i | −0.128234 | + | 0.666324i | ||||
\(974\) | −6.50000 | − | 11.2583i | −0.208273 | − | 0.360740i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −15.0000 | − | 25.9808i | −0.479402 | − | 0.830349i | ||||
\(980\) | −13.0000 | − | 5.19615i | −0.415270 | − | 0.165985i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −6.00000 | − | 10.3923i | −0.191468 | − | 0.331632i | ||||
\(983\) | −36.0000 | −1.14822 | −0.574111 | − | 0.818778i | \(-0.694652\pi\) | ||||
−0.574111 | + | 0.818778i | \(0.694652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 50.0000 | 1.59313 | ||||||||
\(986\) | −14.0000 | + | 24.2487i | −0.445851 | + | 0.772236i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 12.0000 | + | 20.7846i | 0.381771 | + | 0.661247i | ||||
\(989\) | −16.0000 | − | 27.7128i | −0.508770 | − | 0.881216i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.00000 | + | 6.92820i | −0.127064 | + | 0.220082i | −0.922538 | − | 0.385906i | \(-0.873889\pi\) |
0.795474 | + | 0.605988i | \(0.207222\pi\) | |||||||
\(992\) | 1.50000 | − | 2.59808i | 0.0476250 | − | 0.0824890i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00000 | + | 10.3923i | −0.0634361 | + | 0.329624i | ||||
\(995\) | 19.0000 | − | 32.9090i | 0.602340 | − | 1.04328i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −58.0000 | −1.83688 | −0.918439 | − | 0.395562i | \(-0.870550\pi\) | ||||
−0.918439 | + | 0.395562i | \(0.870550\pi\) | |||||||
\(998\) | −4.00000 | + | 6.92820i | −0.126618 | + | 0.219308i | ||||
\(999\) | 0 | 0 |
(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 | 1134.2.h.o.109.1 | 2 | ||
3.2 | odd | 2 | 1134.2.h.b.109.1 | 2 | |||
7.2 | even | 3 | 1134.2.e.b.919.1 | 2 | |||
9.2 | odd | 6 | 1134.2.e.o.865.1 | 2 | |||
9.4 | even | 3 | 378.2.g.d.109.1 | yes | 2 | ||
9.5 | odd | 6 | 378.2.g.c.109.1 | ✓ | 2 | ||
9.7 | even | 3 | 1134.2.e.b.865.1 | 2 | |||
21.2 | odd | 6 | 1134.2.e.o.919.1 | 2 | |||
63.2 | odd | 6 | 1134.2.h.b.541.1 | 2 | |||
63.4 | even | 3 | 2646.2.a.k.1.1 | 1 | |||
63.16 | even | 3 | inner | 1134.2.h.o.541.1 | 2 | ||
63.23 | odd | 6 | 378.2.g.c.163.1 | yes | 2 | ||
63.31 | odd | 6 | 2646.2.a.c.1.1 | 1 | |||
63.32 | odd | 6 | 2646.2.a.t.1.1 | 1 | |||
63.58 | even | 3 | 378.2.g.d.163.1 | yes | 2 | ||
63.59 | even | 6 | 2646.2.a.bb.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.c.109.1 | ✓ | 2 | 9.5 | odd | 6 | ||
378.2.g.c.163.1 | yes | 2 | 63.23 | odd | 6 | ||
378.2.g.d.109.1 | yes | 2 | 9.4 | even | 3 | ||
378.2.g.d.163.1 | yes | 2 | 63.58 | even | 3 | ||
1134.2.e.b.865.1 | 2 | 9.7 | even | 3 | |||
1134.2.e.b.919.1 | 2 | 7.2 | even | 3 | |||
1134.2.e.o.865.1 | 2 | 9.2 | odd | 6 | |||
1134.2.e.o.919.1 | 2 | 21.2 | odd | 6 | |||
1134.2.h.b.109.1 | 2 | 3.2 | odd | 2 | |||
1134.2.h.b.541.1 | 2 | 63.2 | odd | 6 | |||
1134.2.h.o.109.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.h.o.541.1 | 2 | 63.16 | even | 3 | inner | ||
2646.2.a.c.1.1 | 1 | 63.31 | odd | 6 | |||
2646.2.a.k.1.1 | 1 | 63.4 | even | 3 | |||
2646.2.a.t.1.1 | 1 | 63.32 | odd | 6 | |||
2646.2.a.bb.1.1 | 1 | 63.59 | even | 6 |