Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(865,1134)]
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([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.e (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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 865.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.865 |
Dual form | 1134.2.e.b.919.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | + | 1.73205i | −0.447214 | + | 0.774597i | −0.998203 | − | 0.0599153i | \(-0.980917\pi\) |
0.550990 | + | 0.834512i | \(0.314250\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | + | 1.73205i | 0.755929 | + | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 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 | ||||||||
\(13\) | −3.00000 | − | 5.19615i | −0.832050 | − | 1.44115i | −0.896410 | − | 0.443227i | \(-0.853834\pi\) |
0.0643593 | − | 0.997927i | \(-0.479500\pi\) | |||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −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 | ||||
\(23\) | −2.00000 | + | 3.46410i | −0.417029 | + | 0.722315i | −0.995639 | − | 0.0932891i | \(-0.970262\pi\) |
0.578610 | + | 0.815604i | \(0.303595\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | 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 | −0.333205 | − | 0.942855i | \(-0.608130\pi\) |
0.983138 | − | 0.182864i | \(-0.0585367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | 0.538816 | 0.269408 | − | 0.963026i | \(-0.413172\pi\) | ||||
0.269408 | + | 0.963026i | \(0.413172\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 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 | \(-0.395093\pi\) | |||||||
\(38\) | −2.00000 | − | 3.46410i | −0.324443 | − | 0.561951i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | − | 1.73205i | 0.158114 | − | 0.273861i | ||||
\(41\) | −3.00000 | − | 5.19615i | −0.468521 | − | 0.811503i | 0.530831 | − | 0.847477i | \(-0.321880\pi\) |
−0.999353 | + | 0.0359748i | \(0.988546\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | 2.50000 | + | 4.33013i | 0.376889 | + | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.00000 | − | 3.46410i | 0.294884 | − | 0.510754i | ||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.00000 | − | 5.19615i | −0.416025 | − | 0.720577i | ||||
\(53\) | −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 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.50000 | + | 6.06218i | −0.459573 | + | 0.796003i | ||||
\(59\) | −7.00000 | −0.911322 | −0.455661 | − | 0.890153i | \(-0.650597\pi\) | ||||
−0.455661 | + | 0.890153i | \(0.650597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(62\) | −3.00000 | −0.381000 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 12.0000 | 1.48842 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.0000 | 1.22169 | 0.610847 | − | 0.791748i | \(-0.290829\pi\) | ||||
0.610847 | + | 0.791748i | \(0.290829\pi\) | |||||||
\(68\) | −2.00000 | + | 3.46410i | −0.242536 | + | 0.420084i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.00000 | − | 1.73205i | 0.597614 | − | 0.207020i | ||||
\(71\) | 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 | \(0.891489\pi\) | |||||||
\(74\) | 4.00000 | + | 6.92820i | 0.464991 | + | 0.805387i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.00000 | + | 3.46410i | 0.229416 | + | 0.397360i | ||||
\(77\) | −2.50000 | + | 12.9904i | −0.284901 | + | 1.48039i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.00000 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(80\) | −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 | −0.991654 | − | 0.128925i | \(-0.958847\pi\) |
0.607479 | + | 0.794335i | \(0.292181\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | − | 6.92820i | −0.433861 | − | 0.751469i | ||||
\(86\) | 4.00000 | − | 6.92820i | 0.431331 | − | 0.747087i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 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 | ||||||||
\(94\) | 6.00000 | 0.618853 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.50000 | − | 4.33013i | 0.253837 | − | 0.439658i | −0.710742 | − | 0.703452i | \(-0.751641\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | −1.00000 | − | 6.92820i | −0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −2.50000 | − | 4.33013i | −0.248759 | − | 0.430864i | 0.714423 | − | 0.699715i | \(-0.246689\pi\) |
−0.963182 | + | 0.268851i | \(0.913356\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 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 | \(0.888782\pi\) | |||||||
\(110\) | 10.0000 | 0.953463 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 2.00000 | + | 3.46410i | 0.188144 | + | 0.325875i | 0.944632 | − | 0.328133i | \(-0.106419\pi\) |
−0.756487 | + | 0.654008i | \(0.773086\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.00000 | − | 6.92820i | −0.373002 | − | 0.646058i | ||||
\(116\) | 3.50000 | − | 6.06218i | 0.324967 | − | 0.562859i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | −10.0000 | + | 3.46410i | −0.916698 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | 0.269408 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.0000 | −1.05247 | ||||||||
\(131\) | 6.50000 | − | 11.2583i | 0.567908 | − | 0.983645i | −0.428865 | − | 0.903369i | \(-0.641086\pi\) |
0.996773 | − | 0.0802763i | \(-0.0255803\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 10.3923i | −0.173422 | + | 0.901127i | ||||
\(134\) | −10.0000 | −0.863868 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | − | 3.46410i | 0.171499 | − | 0.297044i | ||||
\(137\) | −4.00000 | − | 6.92820i | −0.341743 | − | 0.591916i | 0.643013 | − | 0.765855i | \(-0.277684\pi\) |
−0.984757 | + | 0.173939i | \(0.944351\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.00000 | + | 6.92820i | 0.339276 | + | 0.587643i | 0.984297 | − | 0.176522i | \(-0.0564848\pi\) |
−0.645021 | + | 0.764165i | \(0.723151\pi\) | |||||||
\(140\) | −5.00000 | + | 1.73205i | −0.422577 | + | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.00000 | −0.335673 | ||||||||
\(143\) | 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 | ||||
\(149\) | 4.50000 | − | 7.79423i | 0.368654 | − | 0.638528i | −0.620701 | − | 0.784047i | \(-0.713152\pi\) |
0.989355 | + | 0.145519i | \(0.0464853\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | −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 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 3.00000 | 0.238667 | ||||||||
\(159\) | 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 | \(0.858291\pi\) | |||||||
\(164\) | −3.00000 | − | 5.19615i | −0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.50000 | − | 6.06218i | 0.271653 | − | 0.470516i | ||||
\(167\) | −7.00000 | − | 12.1244i | −0.541676 | − | 0.938211i | −0.998808 | − | 0.0488118i | \(-0.984457\pi\) |
0.457132 | − | 0.889399i | \(-0.348877\pi\) | |||||||
\(168\) | 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 | ||||
\(173\) | −1.00000 | −0.0760286 | −0.0380143 | − | 0.999277i | \(-0.512103\pi\) | ||||
−0.0380143 | + | 0.999277i | \(0.512103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.500000 | + | 2.59808i | −0.0377964 | + | 0.196396i | ||||
\(176\) | 2.50000 | + | 4.33013i | 0.188445 | + | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.00000 | − | 5.19615i | −0.224860 | − | 0.389468i | ||||
\(179\) | −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 | \(0.5\pi\) | |||||||||
\(182\) | −3.00000 | + | 15.5885i | −0.222375 | + | 1.15549i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 16.0000 | 1.17634 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −20.0000 | −1.46254 | ||||||||
\(188\) | −6.00000 | −0.437595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.00000 | 0.580381 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.0000 | −1.36765 | −0.683825 | − | 0.729646i | \(-0.739685\pi\) | ||||
−0.683825 | + | 0.729646i | \(0.739685\pi\) | |||||||
\(194\) | −2.50000 | + | 4.33013i | −0.179490 | + | 0.310885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | 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 | \(-0.0685161\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.50000 | + | 4.33013i | 0.175899 | + | 0.304667i | ||||
\(203\) | 17.5000 | − | 6.06218i | 1.22826 | − | 0.425481i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.0000 | 0.838116 | ||||||||
\(206\) | 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 | −0.833858 | − | 0.551979i | \(-0.813873\pi\) |
−0.0610990 | − | 0.998132i | \(-0.519461\pi\) | |||||||
\(212\) | −3.00000 | + | 5.19615i | −0.206041 | + | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.00000 | − | 10.3923i | −0.410152 | − | 0.710403i | ||||
\(215\) | −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 | ||||||||
\(220\) | −10.0000 | −0.674200 | ||||||||
\(221\) | 24.0000 | 1.61441 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.500000 | − | 0.866025i | 0.0334825 | − | 0.0579934i | −0.848799 | − | 0.528716i | \(-0.822674\pi\) |
0.882281 | + | 0.470723i | \(0.156007\pi\) | |||||||
\(224\) | −2.00000 | − | 1.73205i | −0.133631 | − | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.00000 | − | 3.46410i | −0.133038 | − | 0.230429i | ||||
\(227\) | −13.5000 | − | 23.3827i | −0.896026 | − | 1.55196i | −0.832529 | − | 0.553981i | \(-0.813108\pi\) |
−0.0634974 | − | 0.997982i | \(-0.520225\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.00000 | + | 3.46410i | −0.132164 | + | 0.228914i | −0.924510 | − | 0.381157i | \(-0.875526\pi\) |
0.792347 | + | 0.610071i | \(0.208859\pi\) | |||||||
\(230\) | 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 | ||||
\(236\) | −7.00000 | −0.455661 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 10.0000 | − | 3.46410i | 0.648204 | − | 0.224544i | ||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 7.00000 | − | 12.1244i | 0.449977 | − | 0.779383i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −13.0000 | − | 5.19615i | −0.830540 | − | 0.331970i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000 | − | 20.7846i | 0.763542 | − | 1.32249i | ||||
\(248\) | −3.00000 | −0.190500 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 12.0000 | 0.758947 | ||||||||
\(251\) | 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 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | − | 20.7846i | 0.248548 | − | 1.29149i | ||||
\(260\) | 12.0000 | 0.744208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.50000 | + | 11.2583i | −0.401571 | + | 0.695542i | ||||
\(263\) | 6.00000 | + | 10.3923i | 0.369976 | + | 0.640817i | 0.989561 | − | 0.144112i | \(-0.0460326\pi\) |
−0.619586 | + | 0.784929i | \(0.712699\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | − | 10.3923i | −0.368577 | − | 0.638394i | ||||
\(266\) | 2.00000 | − | 10.3923i | 0.122628 | − | 0.637193i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.0000 | 0.610847 | ||||||||
\(269\) | 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 | ||||
\(275\) | −2.50000 | + | 4.33013i | −0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.00000 | − | 1.73205i | −0.0600842 | − | 0.104069i | 0.834419 | − | 0.551131i | \(-0.185804\pi\) |
−0.894503 | + | 0.447062i | \(0.852470\pi\) | |||||||
\(278\) | −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 | −0.834656 | − | 0.550772i | \(-0.814333\pi\) |
0.894311 | + | 0.447447i | \(0.147667\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 16.0000 | 0.951101 | 0.475551 | − | 0.879688i | \(-0.342249\pi\) | ||||
0.475551 | + | 0.879688i | \(0.342249\pi\) | |||||||
\(284\) | 4.00000 | 0.237356 | ||||||||
\(285\) | 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 | ||||
\(290\) | −7.00000 | − | 12.1244i | −0.411054 | − | 0.711967i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.50000 | + | 11.2583i | −0.380384 | + | 0.658844i | ||||
\(293\) | 13.5000 | + | 23.3827i | 0.788678 | + | 1.36603i | 0.926777 | + | 0.375613i | \(0.122568\pi\) |
−0.138098 | + | 0.990419i | \(0.544099\pi\) | |||||||
\(294\) | 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 | ||||
\(299\) | 24.0000 | 1.38796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −20.0000 | + | 6.92820i | −1.15278 | + | 0.399335i | ||||
\(302\) | −8.50000 | − | 14.7224i | −0.489120 | − | 0.847181i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.00000 | + | 3.46410i | 0.114708 | + | 0.198680i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | −2.50000 | + | 12.9904i | −0.142451 | + | 0.740196i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.00000 | − | 5.19615i | 0.170389 | − | 0.295122i | ||||
\(311\) | −22.0000 | −1.24751 | −0.623753 | − | 0.781622i | \(-0.714393\pi\) | ||||
−0.623753 | + | 0.781622i | \(0.714393\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.0000 | 0.565233 | 0.282617 | − | 0.959233i | \(-0.408798\pi\) | ||||
0.282617 | + | 0.959233i | \(0.408798\pi\) | |||||||
\(314\) | −14.0000 | −0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.00000 | −0.168763 | ||||||||
\(317\) | 33.0000 | 1.85346 | 0.926732 | − | 0.375722i | \(-0.122605\pi\) | ||||
0.926732 | + | 0.375722i | \(0.122605\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 35.0000 | 1.95962 | ||||||||
\(320\) | −1.00000 | + | 1.73205i | −0.0559017 | + | 0.0968246i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.0000 | − | 3.46410i | 0.557278 | − | 0.193047i | ||||
\(323\) | −16.0000 | −0.890264 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.00000 | − | 5.19615i | 0.166410 | − | 0.288231i | ||||
\(326\) | 1.00000 | + | 1.73205i | 0.0553849 | + | 0.0959294i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.00000 | + | 5.19615i | 0.165647 | + | 0.286910i | ||||
\(329\) | −12.0000 | − | 10.3923i | −0.661581 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | −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 | 0.954551 | + | 0.298047i | \(0.0963352\pi\) |
−0.219159 | + | 0.975689i | \(0.570331\pi\) | |||||||
\(338\) | 11.5000 | − | 19.9186i | 0.625518 | − | 1.08343i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.00000 | − | 6.92820i | −0.216930 | − | 0.375735i | ||||
\(341\) | 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 | ||||||||
\(346\) | 1.00000 | 0.0537603 | ||||||||
\(347\) | 27.0000 | 1.44944 | 0.724718 | − | 0.689046i | \(-0.241970\pi\) | ||||
0.724718 | + | 0.689046i | \(0.241970\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.0000 | − | 17.3205i | 0.535288 | − | 0.927146i | −0.463862 | − | 0.885908i | \(-0.653537\pi\) |
0.999149 | − | 0.0412379i | \(-0.0131301\pi\) | |||||||
\(350\) | 0.500000 | − | 2.59808i | 0.0267261 | − | 0.138873i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.50000 | − | 4.33013i | −0.133250 | − | 0.230797i | ||||
\(353\) | −15.0000 | − | 25.9808i | −0.798369 | − | 1.38282i | −0.920677 | − | 0.390324i | \(-0.872363\pi\) |
0.122308 | − | 0.992492i | \(-0.460970\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | + | 6.92820i | −0.212298 | + | 0.367711i | ||||
\(356\) | 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 | ||||||||
\(364\) | 3.00000 | − | 15.5885i | 0.157243 | − | 0.817057i | ||||
\(365\) | −13.0000 | − | 22.5167i | −0.680451 | − | 1.17858i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −2.00000 | + | 3.46410i | −0.104257 | + | 0.180579i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −16.0000 | −0.831800 | ||||||||
\(371\) | −15.0000 | + | 5.19615i | −0.778761 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0000 | − | 17.3205i | 0.517780 | − | 0.896822i | −0.482006 | − | 0.876168i | \(-0.660092\pi\) |
0.999787 | − | 0.0206542i | \(-0.00657489\pi\) | |||||||
\(374\) | 20.0000 | 1.03418 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | −42.0000 | −2.16311 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | 0.513665 | 0.256833 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256833 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(380\) | −8.00000 | −0.410391 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18.0000 | −0.920960 | ||||||||
\(383\) | −2.00000 | + | 3.46410i | −0.102195 | + | 0.177007i | −0.912589 | − | 0.408879i | \(-0.865920\pi\) |
0.810394 | + | 0.585886i | \(0.199253\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.0000 | − | 17.3205i | −1.01929 | − | 0.882735i | ||||
\(386\) | 19.0000 | 0.967075 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.50000 | − | 4.33013i | 0.126918 | − | 0.219829i | ||||
\(389\) | 0.500000 | + | 0.866025i | 0.0253510 | + | 0.0439092i | 0.878423 | − | 0.477885i | \(-0.158596\pi\) |
−0.853072 | + | 0.521794i | \(0.825263\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | − | 13.8564i | −0.404577 | − | 0.700749i | ||||
\(392\) | −1.00000 | − | 6.92820i | −0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −25.0000 | −1.25948 | ||||||||
\(395\) | 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 | ||||
\(401\) | −9.00000 | + | 15.5885i | −0.449439 | + | 0.778450i | −0.998350 | − | 0.0574304i | \(-0.981709\pi\) |
0.548911 | + | 0.835881i | \(0.315043\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.00000 | − | 15.5885i | −0.448322 | − | 0.776516i | ||||
\(404\) | −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 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | −12.0000 | −0.592638 | ||||||||
\(411\) | 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 | ||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 10.0000 | − | 17.3205i | 0.489116 | − | 0.847174i | ||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.00000 | − | 15.5885i | 0.438633 | − | 0.759735i | −0.558951 | − | 0.829201i | \(-0.688796\pi\) |
0.997584 | + | 0.0694656i | \(0.0221294\pi\) | |||||||
\(422\) | 13.0000 | + | 22.5167i | 0.632830 | + | 1.09609i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | −4.00000 | −0.194029 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 6.00000 | + | 10.3923i | 0.290021 | + | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | + | 13.8564i | 0.385794 | + | 0.668215i | ||||
\(431\) | −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 | \(0.553795\pi\) | |||||||
\(434\) | −6.00000 | − | 5.19615i | −0.288009 | − | 0.249423i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.00000 | + | 13.8564i | −0.383131 | + | 0.663602i | ||||
\(437\) | −16.0000 | −0.765384 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00000 | 0.143182 | 0.0715911 | − | 0.997434i | \(-0.477192\pi\) | ||||
0.0715911 | + | 0.997434i | \(0.477192\pi\) | |||||||
\(440\) | 10.0000 | 0.476731 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −24.0000 | −1.14156 | ||||||||
\(443\) | −11.0000 | −0.522626 | −0.261313 | − | 0.965254i | \(-0.584155\pi\) | ||||
−0.261313 | + | 0.965254i | \(0.584155\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.0000 | −0.568855 | ||||||||
\(446\) | −0.500000 | + | 0.866025i | −0.0236757 | + | 0.0410075i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.00000 | + | 1.73205i | 0.0944911 | + | 0.0818317i | ||||
\(449\) | 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 | ||||
\(452\) | 2.00000 | + | 3.46410i | 0.0940721 | + | 0.162938i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.5000 | + | 23.3827i | 0.633586 | + | 1.09740i | ||||
\(455\) | 24.0000 | + | 20.7846i | 1.12514 | + | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −26.0000 | −1.21623 | −0.608114 | − | 0.793849i | \(-0.708074\pi\) | ||||
−0.608114 | + | 0.793849i | \(0.708074\pi\) | |||||||
\(458\) | 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 | 0.463525 | + | 0.886084i | \(0.346584\pi\) |
−0.999134 | + | 0.0416172i | \(0.986749\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.5000 | + | 25.1147i | 0.673872 | + | 1.16718i | 0.976797 | + | 0.214166i | \(0.0687035\pi\) |
−0.302925 | + | 0.953014i | \(0.597963\pi\) | |||||||
\(464\) | 3.50000 | − | 6.06218i | 0.162483 | − | 0.281430i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 11.0000 | + | 19.0526i | 0.509565 | + | 0.882593i | ||||
\(467\) | 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 | ||||||||
\(472\) | 7.00000 | 0.322201 | ||||||||
\(473\) | −40.0000 | −1.83920 | ||||||||
\(474\) | 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 | ||||||||
\(479\) | 13.0000 | + | 22.5167i | 0.593985 | + | 1.02881i | 0.993689 | + | 0.112168i | \(0.0357796\pi\) |
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.0000 | + | 41.5692i | −1.09431 | + | 1.89539i | ||||
\(482\) | −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 | ||||||||
\(490\) | 13.0000 | + | 5.19615i | 0.587280 | + | 0.234738i | ||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.0000 | + | 24.2487i | 0.630528 | + | 1.09211i | ||||
\(494\) | −12.0000 | + | 20.7846i | −0.539906 | + | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.00000 | 0.134704 | ||||||||
\(497\) | 8.00000 | + | 6.92820i | 0.358849 | + | 0.310772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.00000 | − | 6.92820i | 0.179065 | − | 0.310149i | −0.762496 | − | 0.646993i | \(-0.776026\pi\) |
0.941560 | + | 0.336844i | \(0.109360\pi\) | |||||||
\(500\) | −12.0000 | −0.536656 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −21.0000 | −0.937276 | ||||||||
\(503\) | −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 | ||||||||
\(506\) | 20.0000 | 0.889108 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.50000 | − | 2.59808i | 0.0664863 | − | 0.115158i | −0.830866 | − | 0.556473i | \(-0.812154\pi\) |
0.897352 | + | 0.441315i | \(0.145488\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.5000 | + | 11.2583i | −1.43772 | + | 0.498039i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | − | 25.9808i | −0.659699 | − | 1.14263i | ||||
\(518\) | −4.00000 | + | 20.7846i | −0.175750 | + | 0.913223i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −12.0000 | −0.526235 | ||||||||
\(521\) | 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 | ||||
\(527\) | −6.00000 | + | 10.3923i | −0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | 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 | ||||||||
\(535\) | −24.0000 | −1.03761 | ||||||||
\(536\) | −10.0000 | −0.431934 | ||||||||
\(537\) | 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 | ||||||||
\(544\) | 2.00000 | − | 3.46410i | 0.0857493 | − | 0.148522i | ||||
\(545\) | −16.0000 | − | 27.7128i | −0.685365 | − | 1.18709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.00000 | − | 15.5885i | 0.384812 | − | 0.666514i | −0.606931 | − | 0.794755i | \(-0.707600\pi\) |
0.991743 | + | 0.128240i | \(0.0409329\pi\) | |||||||
\(548\) | −4.00000 | − | 6.92820i | −0.170872 | − | 0.295958i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.50000 | − | 4.33013i | 0.106600 | − | 0.184637i | ||||
\(551\) | 28.0000 | 1.19284 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | − | 5.19615i | −0.255146 | − | 0.220963i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | + | 6.92820i | 0.169638 | + | 0.293821i | ||||
\(557\) | −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 | ||||||||
\(560\) | −5.00000 | + | 1.73205i | −0.211289 | + | 0.0731925i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.00000 | + | 1.73205i | −0.0421825 | + | 0.0730622i | ||||
\(563\) | −20.0000 | −0.842900 | −0.421450 | − | 0.906852i | \(-0.638479\pi\) | ||||
−0.421450 | + | 0.906852i | \(0.638479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.00000 | −0.336563 | ||||||||
\(566\) | −16.0000 | −0.672530 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.00000 | −0.167836 | ||||||||
\(569\) | 12.0000 | 0.503066 | 0.251533 | − | 0.967849i | \(-0.419065\pi\) | ||||
0.251533 | + | 0.967849i | \(0.419065\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(572\) | 15.0000 | − | 25.9808i | 0.627182 | − | 1.08631i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.00000 | + | 15.5885i | −0.125218 | + | 0.650650i | ||||
\(575\) | −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 | \(0.813802\pi\) | |||||||
\(578\) | −0.500000 | − | 0.866025i | −0.0207973 | − | 0.0360219i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.00000 | + | 12.1244i | 0.290659 | + | 0.503436i | ||||
\(581\) | −17.5000 | + | 6.06218i | −0.726022 | + | 0.251502i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.0000 | −1.24247 | ||||||||
\(584\) | 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 | −0.582445 | − | 0.812870i | \(-0.697904\pi\) |
0.995189 | + | 0.0979766i | \(0.0312370\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.00000 | + | 10.3923i | 0.247226 | + | 0.428207i | ||||
\(590\) | −7.00000 | + | 12.1244i | −0.288185 | + | 0.499152i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.00000 | − | 6.92820i | −0.164399 | − | 0.284747i | ||||
\(593\) | 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 | ||||||||
\(598\) | −24.0000 | −0.981433 | ||||||||
\(599\) | −30.0000 | −1.22577 | −0.612883 | − | 0.790173i | \(-0.709990\pi\) | ||||
−0.612883 | + | 0.790173i | \(0.709990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.00000 | − | 8.66025i | 0.203954 | − | 0.353259i | −0.745845 | − | 0.666120i | \(-0.767954\pi\) |
0.949799 | + | 0.312861i | \(0.101287\pi\) | |||||||
\(602\) | 20.0000 | − | 6.92820i | 0.815139 | − | 0.282372i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.50000 | + | 14.7224i | 0.345860 | + | 0.599047i | ||||
\(605\) | −14.0000 | − | 24.2487i | −0.569181 | − | 0.985850i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.50000 | − | 7.79423i | 0.182649 | − | 0.316358i | −0.760133 | − | 0.649768i | \(-0.774866\pi\) |
0.942782 | + | 0.333410i | \(0.108199\pi\) | |||||||
\(608\) | −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 | \(0.128002\pi\) | |||||||
\(614\) | 2.00000 | 0.0807134 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.50000 | − | 12.9904i | 0.100728 | − | 0.523397i | ||||
\(617\) | 1.00000 | + | 1.73205i | 0.0402585 | + | 0.0697297i | 0.885453 | − | 0.464730i | \(-0.153849\pi\) |
−0.845194 | + | 0.534460i | \(0.820515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.00000 | − | 3.46410i | −0.0803868 | − | 0.139234i | 0.823029 | − | 0.567999i | \(-0.192282\pi\) |
−0.903416 | + | 0.428765i | \(0.858949\pi\) | |||||||
\(620\) | −3.00000 | + | 5.19615i | −0.120483 | + | 0.208683i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 22.0000 | 0.882120 | ||||||||
\(623\) | −3.00000 | + | 15.5885i | −0.120192 | + | 0.624538i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.50000 | − | 16.4545i | 0.380000 | − | 0.658179i | ||||
\(626\) | −10.0000 | −0.399680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 32.0000 | 1.27592 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | 3.00000 | 0.119334 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −33.0000 | −1.31060 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 33.0000 | − | 25.9808i | 1.30751 | − | 1.02940i | ||||
\(638\) | −35.0000 | −1.38566 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 7.00000 | + | 12.1244i | 0.276483 | + | 0.478883i | 0.970508 | − | 0.241068i | \(-0.0774976\pi\) |
−0.694025 | + | 0.719951i | \(0.744164\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.00000 | − | 12.1244i | −0.276053 | − | 0.478138i | 0.694347 | − | 0.719640i | \(-0.255693\pi\) |
−0.970400 | + | 0.241502i | \(0.922360\pi\) | |||||||
\(644\) | −10.0000 | + | 3.46410i | −0.394055 | + | 0.136505i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 16.0000 | 0.629512 | ||||||||
\(647\) | −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 | ||||
\(653\) | 9.00000 | − | 15.5885i | 0.352197 | − | 0.610023i | −0.634437 | − | 0.772975i | \(-0.718768\pi\) |
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.0000 | + | 22.5167i | 0.507952 | + | 0.879799i | ||||
\(656\) | −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 | −0.121983 | − | 0.992532i | \(-0.538925\pi\) |
0.920550 | − | 0.390626i | \(-0.127741\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.0000 | −1.47803 | −0.739014 | − | 0.673690i | \(-0.764708\pi\) | ||||
−0.739014 | + | 0.673690i | \(0.764708\pi\) | |||||||
\(662\) | −32.0000 | −1.24372 | ||||||||
\(663\) | 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 | ||||
\(668\) | −7.00000 | − | 12.1244i | −0.270838 | − | 0.469105i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.0000 | − | 17.3205i | 0.386334 | − | 0.669150i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | + | 1.73205i | −0.0385472 | + | 0.0667657i | −0.884655 | − | 0.466246i | \(-0.845606\pi\) |
0.846108 | + | 0.533011i | \(0.178940\pi\) | |||||||
\(674\) | −13.5000 | − | 23.3827i | −0.520001 | − | 0.900667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | −9.00000 | −0.345898 | −0.172949 | − | 0.984931i | \(-0.555330\pi\) | ||||
−0.172949 | + | 0.984931i | \(0.555330\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.5000 | − | 4.33013i | 0.479706 | − | 0.166175i | ||||
\(680\) | 4.00000 | + | 6.92820i | 0.153393 | + | 0.265684i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.50000 | − | 12.9904i | −0.287190 | − | 0.497427i | ||||
\(683\) | 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 | ||||||||
\(686\) | 10.0000 | − | 15.5885i | 0.381802 | − | 0.595170i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.00000 | + | 6.92820i | −0.152499 | + | 0.264135i | ||||
\(689\) | 36.0000 | 1.37149 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.00000 | 0.304334 | 0.152167 | − | 0.988355i | \(-0.451375\pi\) | ||||
0.152167 | + | 0.988355i | \(0.451375\pi\) | |||||||
\(692\) | −1.00000 | −0.0380143 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.0000 | −1.02491 | ||||||||
\(695\) | −16.0000 | −0.606915 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 24.0000 | 0.909065 | ||||||||
\(698\) | −10.0000 | + | 17.3205i | −0.378506 | + | 0.655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.500000 | + | 2.59808i | −0.0188982 | + | 0.0981981i | ||||
\(701\) | 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 | ||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 15.0000 | + | 25.9808i | 0.564532 | + | 0.977799i | ||||
\(707\) | 2.50000 | − | 12.9904i | 0.0940222 | − | 0.488554i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.00000 | 0.300446 | 0.150223 | − | 0.988652i | \(-0.452001\pi\) | ||||
0.150223 | + | 0.988652i | \(0.452001\pi\) | |||||||
\(710\) | 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 | ||||
\(716\) | −7.50000 | + | 12.9904i | −0.280288 | + | 0.485473i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.00000 | − | 13.8564i | −0.298557 | − | 0.517116i | ||||
\(719\) | 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 | ||||||||
\(725\) | 7.00000 | 0.259973 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.0000 | − | 27.7128i | 0.593407 | − | 1.02781i | −0.400362 | − | 0.916357i | \(-0.631116\pi\) |
0.993770 | − | 0.111454i | \(-0.0355509\pi\) | |||||||
\(728\) | −3.00000 | + | 15.5885i | −0.111187 | + | 0.577747i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.0000 | + | 22.5167i | 0.481152 | + | 0.833379i | ||||
\(731\) | −16.0000 | − | 27.7128i | −0.591781 | − | 1.02500i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.0000 | − | 31.1769i | 0.664845 | − | 1.15155i | −0.314482 | − | 0.949263i | \(-0.601831\pi\) |
0.979327 | − | 0.202282i | \(-0.0648358\pi\) | |||||||
\(734\) | −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 | \(0.131467\pi\) | |||||||
\(740\) | 16.0000 | 0.588172 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 15.0000 | − | 5.19615i | 0.550667 | − | 0.190757i | ||||
\(743\) | −3.00000 | − | 5.19615i | −0.110059 | − | 0.190628i | 0.805735 | − | 0.592277i | \(-0.201771\pi\) |
−0.915794 | + | 0.401648i | \(0.868437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | + | 15.5885i | 0.329734 | + | 0.571117i | ||||
\(746\) | −10.0000 | + | 17.3205i | −0.366126 | + | 0.634149i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −20.0000 | −0.731272 | ||||||||
\(749\) | −6.00000 | + | 31.1769i | −0.219235 | + | 1.13918i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00000 | + | 10.3923i | −0.218943 | + | 0.379221i | −0.954485 | − | 0.298259i | \(-0.903594\pi\) |
0.735542 | + | 0.677479i | \(0.236928\pi\) | |||||||
\(752\) | −6.00000 | −0.218797 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 42.0000 | 1.52955 | ||||||||
\(755\) | −34.0000 | −1.23739 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | −10.0000 | −0.363216 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.00000 | 0.290191 | ||||||||
\(761\) | 4.00000 | − | 6.92820i | 0.145000 | − | 0.251147i | −0.784373 | − | 0.620289i | \(-0.787015\pi\) |
0.929373 | + | 0.369142i | \(0.120348\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −40.0000 | + | 13.8564i | −1.44810 | + | 0.501636i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.00000 | − | 3.46410i | 0.0722629 | − | 0.125163i | ||||
\(767\) | 21.0000 | + | 36.3731i | 0.758266 | + | 1.31336i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.500000 | − | 0.866025i | −0.0180305 | − | 0.0312297i | 0.856869 | − | 0.515534i | \(-0.172406\pi\) |
−0.874900 | + | 0.484304i | \(0.839073\pi\) | |||||||
\(770\) | 20.0000 | + | 17.3205i | 0.720750 | + | 0.624188i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −19.0000 | −0.683825 | ||||||||
\(773\) | −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 | ||||
\(779\) | 12.0000 | − | 20.7846i | 0.429945 | − | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.0000 | + | 17.3205i | 0.357828 | + | 0.619777i | ||||
\(782\) | 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 | ||||||||
\(787\) | 18.0000 | 0.641631 | 0.320815 | − | 0.947142i | \(-0.396043\pi\) | ||||
0.320815 | + | 0.947142i | \(0.396043\pi\) | |||||||
\(788\) | 25.0000 | 0.890588 | ||||||||
\(789\) | 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 | ||||||||
\(794\) | −9.00000 | − | 15.5885i | −0.319398 | − | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.50000 | − | 16.4545i | 0.336719 | − | 0.583214i | ||||
\(797\) | 16.5000 | + | 28.5788i | 0.584460 | + | 1.01231i | 0.994943 | + | 0.100446i | \(0.0320269\pi\) |
−0.410483 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(798\) | 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 | ||||
\(803\) | −65.0000 | −2.29380 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | − | 20.7846i | 0.140981 | − | 0.732561i | ||||
\(806\) | 9.00000 | + | 15.5885i | 0.317011 | + | 0.549080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.50000 | + | 4.33013i | 0.0879497 | + | 0.152333i | ||||
\(809\) | 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 | \(0.841035\pi\) | |||||||
\(812\) | 17.5000 | − | 6.06218i | 0.614130 | − | 0.212741i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −20.0000 | + | 34.6410i | −0.701000 | + | 1.21417i | ||||
\(815\) | 4.00000 | 0.140114 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −32.0000 | −1.11954 | ||||||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | 49.0000 | 1.71011 | 0.855056 | − | 0.518536i | \(-0.173523\pi\) | ||||
0.855056 | + | 0.518536i | \(0.173523\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.0000 | 0.453152 | 0.226576 | − | 0.973994i | \(-0.427247\pi\) | ||||
0.226576 | + | 0.973994i | \(0.427247\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 14.0000 | + | 12.1244i | 0.487122 | + | 0.421860i | ||||
\(827\) | −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 | \(0.291447\pi\) | |||||||
\(830\) | 7.00000 | + | 12.1244i | 0.242974 | + | 0.420843i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.00000 | − | 5.19615i | −0.104006 | − | 0.180144i | ||||
\(833\) | −26.0000 | − | 10.3923i | −0.900847 | − | 0.360072i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.0000 | 0.968980 | ||||||||
\(836\) | −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 | −0.898482 | − | 0.439010i | \(-0.855329\pi\) |
0.829435 | + | 0.558604i | \(0.188663\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | −9.00000 | + | 15.5885i | −0.310160 | + | 0.537214i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −13.0000 | − | 22.5167i | −0.447478 | − | 0.775055i | ||||
\(845\) | −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 | ||||||||
\(850\) | 4.00000 | 0.137199 | ||||||||
\(851\) | 32.0000 | 1.09695 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.0000 | − | 39.8372i | 0.787505 | − | 1.36400i | −0.139986 | − | 0.990153i | \(-0.544706\pi\) |
0.927491 | − | 0.373845i | \(-0.121961\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.00000 | − | 10.3923i | −0.205076 | − | 0.355202i | ||||
\(857\) | 15.0000 | + | 25.9808i | 0.512390 | + | 0.887486i | 0.999897 | + | 0.0143666i | \(0.00457319\pi\) |
−0.487507 | + | 0.873119i | \(0.662093\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.00000 | − | 13.8564i | 0.272956 | − | 0.472774i | −0.696661 | − | 0.717400i | \(-0.745332\pi\) |
0.969618 | + | 0.244626i | \(0.0786652\pi\) | |||||||
\(860\) | −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 | ||||
\(866\) | 7.00000 | 0.237870 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.00000 | + | 5.19615i | 0.203653 | + | 0.176369i | ||||
\(869\) | −7.50000 | − | 12.9904i | −0.254420 | − | 0.440668i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | − | 51.9615i | −1.01651 | − | 1.76065i | ||||
\(872\) | 8.00000 | − | 13.8564i | 0.270914 | − | 0.469237i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | −24.0000 | − | 20.7846i | −0.811348 | − | 0.702648i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.0000 | + | 29.4449i | −0.574049 | + | 0.994282i | 0.422095 | + | 0.906552i | \(0.361295\pi\) |
−0.996144 | + | 0.0877308i | \(0.972038\pi\) | |||||||
\(878\) | −3.00000 | −0.101245 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.0000 | −0.337100 | ||||||||
\(881\) | 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 | \(0.489286\pi\) | |||||||
\(884\) | 24.0000 | 0.807207 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.0000 | 0.369552 | ||||||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.500000 | − | 0.866025i | 0.0167412 | − | 0.0289967i | ||||
\(893\) | −12.0000 | − | 20.7846i | −0.401565 | − | 0.695530i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0000 | − | 25.9808i | −0.501395 | − | 0.868441i | ||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −14.0000 | −0.467186 | ||||||||
\(899\) | 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 | ||||||||
\(907\) | 21.0000 | + | 36.3731i | 0.697294 | + | 1.20775i | 0.969401 | + | 0.245481i | \(0.0789459\pi\) |
−0.272108 | + | 0.962267i | \(0.587721\pi\) | |||||||
\(908\) | −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 | −0.396986 | − | 0.917825i | \(-0.629944\pi\) |
0.993352 | − | 0.115113i | \(-0.0367229\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.0000 | −1.15833 | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | 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 | \(0.902118\pi\) | |||||||
\(920\) | 4.00000 | + | 6.92820i | 0.131876 | + | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.5000 | − | 19.9186i | 0.378732 | − | 0.655984i | ||||
\(923\) | −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 | ||||
\(929\) | −36.0000 | −1.18112 | −0.590561 | − | 0.806993i | \(-0.701093\pi\) | ||||
−0.590561 | + | 0.806993i | \(0.701093\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0000 | + | 17.3205i | −0.721021 | + | 0.567657i | ||||
\(932\) | −11.0000 | − | 19.0526i | −0.360317 | − | 0.624087i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.50000 | − | 6.06218i | −0.114523 | − | 0.198361i | ||||
\(935\) | 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 | \(0.426559\pi\) | |||||||
\(938\) | −20.0000 | − | 17.3205i | −0.653023 | − | 0.565535i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.00000 | − | 10.3923i | 0.195698 | − | 0.338960i | ||||
\(941\) | −13.0000 | −0.423788 | −0.211894 | − | 0.977293i | \(-0.567963\pi\) | ||||
−0.211894 | + | 0.977293i | \(0.567963\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0000 | 0.781548 | ||||||||
\(944\) | −7.00000 | −0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 40.0000 | 1.30051 | ||||||||
\(947\) | −25.0000 | −0.812391 | −0.406195 | − | 0.913786i | \(-0.633145\pi\) | ||||
−0.406195 | + | 0.913786i | \(0.633145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 78.0000 | 2.53199 | ||||||||
\(950\) | 2.00000 | − | 3.46410i | 0.0648886 | − | 0.112390i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.0000 | − | 3.46410i | 0.324102 | − | 0.112272i | ||||
\(953\) | −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 | ||||
\(959\) | 4.00000 | − | 20.7846i | 0.129167 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.0000 | −0.709677 | ||||||||
\(962\) | 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 | 0.794515 | − | 0.607244i | \(-0.207725\pi\) |
−0.923147 | + | 0.384448i | \(0.874392\pi\) | |||||||
\(968\) | 7.00000 | − | 12.1244i | 0.224989 | − | 0.389692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | − | 8.66025i | −0.160540 | − | 0.278064i | ||||
\(971\) | 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 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 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 | ||||
\(983\) | 18.0000 | + | 31.1769i | 0.574111 | + | 0.994389i | 0.996138 | + | 0.0878058i | \(0.0279855\pi\) |
−0.422027 | + | 0.906583i | \(0.638681\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25.0000 | + | 43.3013i | −0.796566 | + | 1.37969i | ||||
\(986\) | −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 | \(0.207222\pi\) | |||||||
\(992\) | −3.00000 | −0.0952501 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.00000 | − | 6.92820i | −0.253745 | − | 0.219749i | ||||
\(995\) | 19.0000 | + | 32.9090i | 0.602340 | + | 1.04328i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.0000 | + | 50.2295i | 0.918439 | + | 1.59078i | 0.801786 | + | 0.597611i | \(0.203883\pi\) |
0.116653 | + | 0.993173i | \(0.462784\pi\) | |||||||
\(998\) | −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.e.b.865.1 | 2 | ||
3.2 | odd | 2 | 1134.2.e.o.865.1 | 2 | |||
7.2 | even | 3 | 1134.2.h.o.541.1 | 2 | |||
9.2 | odd | 6 | 378.2.g.c.109.1 | ✓ | 2 | ||
9.4 | even | 3 | 1134.2.h.o.109.1 | 2 | |||
9.5 | odd | 6 | 1134.2.h.b.109.1 | 2 | |||
9.7 | even | 3 | 378.2.g.d.109.1 | yes | 2 | ||
21.2 | odd | 6 | 1134.2.h.b.541.1 | 2 | |||
63.2 | odd | 6 | 378.2.g.c.163.1 | yes | 2 | ||
63.11 | odd | 6 | 2646.2.a.t.1.1 | 1 | |||
63.16 | even | 3 | 378.2.g.d.163.1 | yes | 2 | ||
63.23 | odd | 6 | 1134.2.e.o.919.1 | 2 | |||
63.25 | even | 3 | 2646.2.a.k.1.1 | 1 | |||
63.38 | even | 6 | 2646.2.a.bb.1.1 | 1 | |||
63.52 | odd | 6 | 2646.2.a.c.1.1 | 1 | |||
63.58 | even | 3 | inner | 1134.2.e.b.919.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.g.c.109.1 | ✓ | 2 | 9.2 | odd | 6 | ||
378.2.g.c.163.1 | yes | 2 | 63.2 | odd | 6 | ||
378.2.g.d.109.1 | yes | 2 | 9.7 | even | 3 | ||
378.2.g.d.163.1 | yes | 2 | 63.16 | even | 3 | ||
1134.2.e.b.865.1 | 2 | 1.1 | even | 1 | trivial | ||
1134.2.e.b.919.1 | 2 | 63.58 | even | 3 | inner | ||
1134.2.e.o.865.1 | 2 | 3.2 | odd | 2 | |||
1134.2.e.o.919.1 | 2 | 63.23 | odd | 6 | |||
1134.2.h.b.109.1 | 2 | 9.5 | odd | 6 | |||
1134.2.h.b.541.1 | 2 | 21.2 | odd | 6 | |||
1134.2.h.o.109.1 | 2 | 9.4 | even | 3 | |||
1134.2.h.o.541.1 | 2 | 7.2 | even | 3 | |||
2646.2.a.c.1.1 | 1 | 63.52 | odd | 6 | |||
2646.2.a.k.1.1 | 1 | 63.25 | even | 3 | |||
2646.2.a.t.1.1 | 1 | 63.11 | odd | 6 | |||
2646.2.a.bb.1.1 | 1 | 63.38 | even | 6 |