Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.i (of order \(3\), degree \(2\), 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: | \(7.42608738798\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 811.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.811 |
Dual form | 930.2.i.e.211.1 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 3.00000 | + | 5.19615i | 0.832050 | + | 1.44115i | 0.896410 | + | 0.443227i | \(0.146166\pi\) |
−0.0643593 | + | 0.997927i | \(0.520500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.500000 | − | 0.866025i | 0.121268 | − | 0.210042i | −0.799000 | − | 0.601331i | \(-0.794637\pi\) |
0.920268 | + | 0.391289i | \(0.127971\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −2.00000 | + | 3.46410i | −0.458831 | + | 0.794719i | −0.998899 | − | 0.0469020i | \(-0.985065\pi\) |
0.540068 | + | 0.841621i | \(0.318398\pi\) | |||||||
\(20\) | −0.500000 | − | 0.866025i | −0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.500000 | + | 0.866025i | 0.106600 | + | 0.184637i | ||||
\(23\) | 7.00000 | 1.45960 | 0.729800 | − | 0.683660i | \(-0.239613\pi\) | ||||
0.729800 | + | 0.683660i | \(0.239613\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 3.00000 | + | 5.19615i | 0.588348 | + | 1.01905i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000 | 1.11417 | 0.557086 | − | 0.830455i | \(-0.311919\pi\) | ||||
0.557086 | + | 0.830455i | \(0.311919\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 2.00000 | − | 5.19615i | 0.359211 | − | 0.933257i | ||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 0.500000 | − | 0.866025i | 0.0857493 | − | 0.148522i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −3.50000 | + | 6.06218i | −0.575396 | + | 0.996616i | 0.420602 | + | 0.907245i | \(0.361819\pi\) |
−0.995998 | + | 0.0893706i | \(0.971514\pi\) | |||||||
\(38\) | −2.00000 | + | 3.46410i | −0.324443 | + | 0.561951i | ||||
\(39\) | −6.00000 | −0.960769 | ||||||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | 1.00000 | + | 1.73205i | 0.156174 | + | 0.270501i | 0.933486 | − | 0.358614i | \(-0.116751\pi\) |
−0.777312 | + | 0.629115i | \(0.783417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | − | 6.06218i | 0.533745 | − | 0.924473i | −0.465478 | − | 0.885059i | \(-0.654118\pi\) |
0.999223 | − | 0.0394140i | \(-0.0125491\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 7.00000 | 1.03209 | ||||||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 0.500000 | + | 0.866025i | 0.0700140 | + | 0.121268i | ||||
\(52\) | 3.00000 | + | 5.19615i | 0.416025 | + | 0.720577i | ||||
\(53\) | 2.00000 | + | 3.46410i | 0.274721 | + | 0.475831i | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0.500000 | − | 0.866025i | 0.0674200 | − | 0.116775i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | − | 3.46410i | −0.264906 | − | 0.458831i | ||||
\(58\) | 6.00000 | 0.787839 | ||||||||
\(59\) | −6.00000 | + | 10.3923i | −0.781133 | + | 1.35296i | 0.150148 | + | 0.988663i | \(0.452025\pi\) |
−0.931282 | + | 0.364299i | \(0.881308\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −14.0000 | −1.79252 | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 2.00000 | − | 5.19615i | 0.254000 | − | 0.659912i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.00000 | − | 5.19615i | 0.372104 | − | 0.644503i | ||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0.500000 | − | 0.866025i | 0.0606339 | − | 0.105021i | ||||
\(69\) | −3.50000 | + | 6.06218i | −0.421350 | + | 0.729800i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.00000 | − | 5.19615i | −0.356034 | − | 0.616670i | 0.631260 | − | 0.775571i | \(-0.282538\pi\) |
−0.987294 | + | 0.158901i | \(0.949205\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | −3.50000 | + | 6.06218i | −0.406867 | + | 0.704714i | ||||
\(75\) | −0.500000 | − | 0.866025i | −0.0577350 | − | 0.100000i | ||||
\(76\) | −2.00000 | + | 3.46410i | −0.229416 | + | 0.397360i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −6.00000 | −0.679366 | ||||||||
\(79\) | −1.50000 | + | 2.59808i | −0.168763 | + | 0.292306i | −0.937985 | − | 0.346675i | \(-0.887311\pi\) |
0.769222 | + | 0.638982i | \(0.220644\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.00000 | + | 1.73205i | 0.110432 | + | 0.191273i | ||||
\(83\) | −8.00000 | − | 13.8564i | −0.878114 | − | 1.52094i | −0.853408 | − | 0.521243i | \(-0.825468\pi\) |
−0.0247060 | − | 0.999695i | \(-0.507865\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | −0.108465 | ||||||||
\(86\) | 3.50000 | − | 6.06218i | 0.377415 | − | 0.653701i | ||||
\(87\) | −3.00000 | + | 5.19615i | −0.321634 | + | 0.557086i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 4.00000 | 0.423999 | 0.212000 | − | 0.977270i | \(-0.432002\pi\) | ||||
0.212000 | + | 0.977270i | \(0.432002\pi\) | |||||||
\(90\) | −0.500000 | + | 0.866025i | −0.0527046 | + | 0.0912871i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 7.00000 | 0.729800 | ||||||||
\(93\) | 3.50000 | + | 4.33013i | 0.362933 | + | 0.449013i | ||||
\(94\) | 3.00000 | 0.309426 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 3.50000 | + | 6.06218i | 0.353553 | + | 0.612372i | ||||
\(99\) | 0.500000 | − | 0.866025i | 0.0502519 | − | 0.0870388i | ||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 15.0000 | 1.49256 | 0.746278 | − | 0.665635i | \(-0.231839\pi\) | ||||
0.746278 | + | 0.665635i | \(0.231839\pi\) | |||||||
\(102\) | 0.500000 | + | 0.866025i | 0.0495074 | + | 0.0857493i | ||||
\(103\) | 1.00000 | + | 1.73205i | 0.0985329 | + | 0.170664i | 0.911078 | − | 0.412235i | \(-0.135252\pi\) |
−0.812545 | + | 0.582899i | \(0.801918\pi\) | |||||||
\(104\) | 3.00000 | + | 5.19615i | 0.294174 | + | 0.509525i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00000 | + | 3.46410i | 0.194257 | + | 0.336463i | ||||
\(107\) | 2.00000 | − | 3.46410i | 0.193347 | − | 0.334887i | −0.753010 | − | 0.658009i | \(-0.771399\pi\) |
0.946357 | + | 0.323122i | \(0.104732\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 0.500000 | − | 0.866025i | 0.0476731 | − | 0.0825723i | ||||
\(111\) | −3.50000 | − | 6.06218i | −0.332205 | − | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.50000 | − | 16.4545i | −0.893685 | − | 1.54791i | −0.835424 | − | 0.549606i | \(-0.814778\pi\) |
−0.0582609 | − | 0.998301i | \(-0.518556\pi\) | |||||||
\(114\) | −2.00000 | − | 3.46410i | −0.187317 | − | 0.324443i | ||||
\(115\) | −3.50000 | − | 6.06218i | −0.326377 | − | 0.565301i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | 3.00000 | − | 5.19615i | 0.277350 | − | 0.480384i | ||||
\(118\) | −6.00000 | + | 10.3923i | −0.552345 | + | 0.956689i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | −14.0000 | −1.26750 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 2.00000 | − | 5.19615i | 0.179605 | − | 0.466628i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.00000 | − | 15.5885i | 0.798621 | − | 1.38325i | −0.121894 | − | 0.992543i | \(-0.538897\pi\) |
0.920514 | − | 0.390709i | \(-0.127770\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.50000 | + | 6.06218i | 0.308158 | + | 0.533745i | ||||
\(130\) | 3.00000 | − | 5.19615i | 0.263117 | − | 0.455733i | ||||
\(131\) | 0.500000 | − | 0.866025i | 0.0436852 | − | 0.0756650i | −0.843356 | − | 0.537355i | \(-0.819423\pi\) |
0.887041 | + | 0.461690i | \(0.152757\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −2.50000 | − | 4.33013i | −0.215967 | − | 0.374066i | ||||
\(135\) | −0.500000 | − | 0.866025i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | 0.500000 | − | 0.866025i | 0.0428746 | − | 0.0742611i | ||||
\(137\) | 3.50000 | + | 6.06218i | 0.299025 | + | 0.517927i | 0.975913 | − | 0.218159i | \(-0.0700052\pi\) |
−0.676888 | + | 0.736086i | \(0.736672\pi\) | |||||||
\(138\) | −3.50000 | + | 6.06218i | −0.297940 | + | 0.516047i | ||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.50000 | + | 2.59808i | −0.126323 | + | 0.218797i | ||||
\(142\) | −3.00000 | − | 5.19615i | −0.251754 | − | 0.436051i | ||||
\(143\) | −3.00000 | + | 5.19615i | −0.250873 | + | 0.434524i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −3.00000 | − | 5.19615i | −0.249136 | − | 0.431517i | ||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | −3.50000 | + | 6.06218i | −0.287698 | + | 0.498308i | ||||
\(149\) | −7.00000 | + | 12.1244i | −0.573462 | + | 0.993266i | 0.422744 | + | 0.906249i | \(0.361067\pi\) |
−0.996207 | + | 0.0870170i | \(0.972267\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | −7.00000 | −0.569652 | −0.284826 | − | 0.958579i | \(-0.591936\pi\) | ||||
−0.284826 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(152\) | −2.00000 | + | 3.46410i | −0.162221 | + | 0.280976i | ||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.50000 | + | 0.866025i | −0.441771 | + | 0.0695608i | ||||
\(156\) | −6.00000 | −0.480384 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | −1.50000 | + | 2.59808i | −0.119334 | + | 0.206692i | ||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | −0.500000 | − | 0.866025i | −0.0395285 | − | 0.0684653i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 5.00000 | 0.391630 | 0.195815 | − | 0.980641i | \(-0.437265\pi\) | ||||
0.195815 | + | 0.980641i | \(0.437265\pi\) | |||||||
\(164\) | 1.00000 | + | 1.73205i | 0.0780869 | + | 0.135250i | ||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | −8.00000 | − | 13.8564i | −0.620920 | − | 1.07547i | ||||
\(167\) | 12.0000 | − | 20.7846i | 0.928588 | − | 1.60836i | 0.142901 | − | 0.989737i | \(-0.454357\pi\) |
0.785687 | − | 0.618624i | \(-0.212310\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.5000 | + | 19.9186i | −0.884615 | + | 1.53220i | ||||
\(170\) | −1.00000 | −0.0766965 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 3.50000 | − | 6.06218i | 0.266872 | − | 0.462237i | ||||
\(173\) | −1.00000 | − | 1.73205i | −0.0760286 | − | 0.131685i | 0.825505 | − | 0.564396i | \(-0.190891\pi\) |
−0.901533 | + | 0.432710i | \(0.857557\pi\) | |||||||
\(174\) | −3.00000 | + | 5.19615i | −0.227429 | + | 0.393919i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.500000 | + | 0.866025i | 0.0376889 | + | 0.0652791i | ||||
\(177\) | −6.00000 | − | 10.3923i | −0.450988 | − | 0.781133i | ||||
\(178\) | 4.00000 | 0.299813 | ||||||||
\(179\) | 5.50000 | − | 9.52628i | 0.411089 | − | 0.712028i | −0.583920 | − | 0.811811i | \(-0.698482\pi\) |
0.995009 | + | 0.0997838i | \(0.0318151\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | −10.0000 | − | 17.3205i | −0.743294 | − | 1.28742i | −0.950988 | − | 0.309229i | \(-0.899929\pi\) |
0.207693 | − | 0.978194i | \(-0.433404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.00000 | − | 12.1244i | 0.517455 | − | 0.896258i | ||||
\(184\) | 7.00000 | 0.516047 | ||||||||
\(185\) | 7.00000 | 0.514650 | ||||||||
\(186\) | 3.50000 | + | 4.33013i | 0.256632 | + | 0.317500i | ||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | 3.00000 | + | 5.19615i | 0.217072 | + | 0.375980i | 0.953912 | − | 0.300088i | \(-0.0970159\pi\) |
−0.736839 | + | 0.676068i | \(0.763683\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −5.00000 | + | 8.66025i | −0.359908 | + | 0.623379i | −0.987945 | − | 0.154805i | \(-0.950525\pi\) |
0.628037 | + | 0.778183i | \(0.283859\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 3.00000 | + | 5.19615i | 0.214834 | + | 0.372104i | ||||
\(196\) | 3.50000 | + | 6.06218i | 0.250000 | + | 0.433013i | ||||
\(197\) | −4.00000 | − | 6.92820i | −0.284988 | − | 0.493614i | 0.687618 | − | 0.726073i | \(-0.258656\pi\) |
−0.972606 | + | 0.232458i | \(0.925323\pi\) | |||||||
\(198\) | 0.500000 | − | 0.866025i | 0.0355335 | − | 0.0615457i | ||||
\(199\) | −8.00000 | − | 13.8564i | −0.567105 | − | 0.982255i | −0.996850 | − | 0.0793045i | \(-0.974730\pi\) |
0.429745 | − | 0.902950i | \(-0.358603\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | 5.00000 | 0.352673 | ||||||||
\(202\) | 15.0000 | 1.05540 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.500000 | + | 0.866025i | 0.0350070 | + | 0.0606339i | ||||
\(205\) | 1.00000 | − | 1.73205i | 0.0698430 | − | 0.120972i | ||||
\(206\) | 1.00000 | + | 1.73205i | 0.0696733 | + | 0.120678i | ||||
\(207\) | −3.50000 | − | 6.06218i | −0.243267 | − | 0.421350i | ||||
\(208\) | 3.00000 | + | 5.19615i | 0.208013 | + | 0.360288i | ||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | − | 6.92820i | 0.275371 | − | 0.476957i | −0.694857 | − | 0.719148i | \(-0.744533\pi\) |
0.970229 | + | 0.242190i | \(0.0778659\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 2.00000 | − | 3.46410i | 0.136717 | − | 0.236801i | ||||
\(215\) | −7.00000 | −0.477396 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −12.0000 | −0.812743 | ||||||||
\(219\) | 2.00000 | 0.135147 | ||||||||
\(220\) | 0.500000 | − | 0.866025i | 0.0337100 | − | 0.0583874i | ||||
\(221\) | 6.00000 | 0.403604 | ||||||||
\(222\) | −3.50000 | − | 6.06218i | −0.234905 | − | 0.406867i | ||||
\(223\) | −7.00000 | + | 12.1244i | −0.468755 | + | 0.811907i | −0.999362 | − | 0.0357107i | \(-0.988630\pi\) |
0.530607 | + | 0.847618i | \(0.321964\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −9.50000 | − | 16.4545i | −0.631931 | − | 1.09454i | ||||
\(227\) | 4.00000 | + | 6.92820i | 0.265489 | + | 0.459841i | 0.967692 | − | 0.252136i | \(-0.0811332\pi\) |
−0.702202 | + | 0.711977i | \(0.747800\pi\) | |||||||
\(228\) | −2.00000 | − | 3.46410i | −0.132453 | − | 0.229416i | ||||
\(229\) | −10.0000 | + | 17.3205i | −0.660819 | + | 1.14457i | 0.319582 | + | 0.947559i | \(0.396457\pi\) |
−0.980401 | + | 0.197013i | \(0.936876\pi\) | |||||||
\(230\) | −3.50000 | − | 6.06218i | −0.230783 | − | 0.399728i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.00000 | 0.393919 | ||||||||
\(233\) | 25.0000 | 1.63780 | 0.818902 | − | 0.573933i | \(-0.194583\pi\) | ||||
0.818902 | + | 0.573933i | \(0.194583\pi\) | |||||||
\(234\) | 3.00000 | − | 5.19615i | 0.196116 | − | 0.339683i | ||||
\(235\) | −1.50000 | − | 2.59808i | −0.0978492 | − | 0.169480i | ||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | −1.50000 | − | 2.59808i | −0.0974355 | − | 0.168763i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.00000 | − | 15.5885i | −0.582162 | − | 1.00833i | −0.995223 | − | 0.0976302i | \(-0.968874\pi\) |
0.413061 | − | 0.910703i | \(-0.364460\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −9.00000 | + | 15.5885i | −0.579741 | + | 1.00414i | 0.415768 | + | 0.909471i | \(0.363513\pi\) |
−0.995509 | + | 0.0946700i | \(0.969820\pi\) | |||||||
\(242\) | 5.00000 | − | 8.66025i | 0.321412 | − | 0.556702i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −14.0000 | −0.896258 | ||||||||
\(245\) | 3.50000 | − | 6.06218i | 0.223607 | − | 0.387298i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | −24.0000 | −1.52708 | ||||||||
\(248\) | 2.00000 | − | 5.19615i | 0.127000 | − | 0.329956i | ||||
\(249\) | 16.0000 | 1.01396 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −1.50000 | + | 2.59808i | −0.0946792 | + | 0.163989i | −0.909475 | − | 0.415759i | \(-0.863516\pi\) |
0.814795 | + | 0.579748i | \(0.196849\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.50000 | + | 6.06218i | 0.220043 | + | 0.381126i | ||||
\(254\) | 9.00000 | − | 15.5885i | 0.564710 | − | 0.978107i | ||||
\(255\) | 0.500000 | − | 0.866025i | 0.0313112 | − | 0.0542326i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.5000 | − | 19.9186i | −0.717350 | − | 1.24249i | −0.962046 | − | 0.272887i | \(-0.912021\pi\) |
0.244696 | − | 0.969600i | \(-0.421312\pi\) | |||||||
\(258\) | 3.50000 | + | 6.06218i | 0.217900 | + | 0.377415i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.00000 | − | 5.19615i | 0.186052 | − | 0.322252i | ||||
\(261\) | −3.00000 | − | 5.19615i | −0.185695 | − | 0.321634i | ||||
\(262\) | 0.500000 | − | 0.866025i | 0.0308901 | − | 0.0535032i | ||||
\(263\) | −11.0000 | −0.678289 | −0.339145 | − | 0.940734i | \(-0.610138\pi\) | ||||
−0.339145 | + | 0.940734i | \(0.610138\pi\) | |||||||
\(264\) | −1.00000 | −0.0615457 | ||||||||
\(265\) | 2.00000 | − | 3.46410i | 0.122859 | − | 0.212798i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.00000 | + | 3.46410i | −0.122398 | + | 0.212000i | ||||
\(268\) | −2.50000 | − | 4.33013i | −0.152712 | − | 0.264505i | ||||
\(269\) | 12.5000 | + | 21.6506i | 0.762138 | + | 1.32006i | 0.941746 | + | 0.336324i | \(0.109184\pi\) |
−0.179608 | + | 0.983738i | \(0.557483\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 0.500000 | − | 0.866025i | 0.0303170 | − | 0.0525105i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.50000 | + | 6.06218i | 0.211443 | + | 0.366230i | ||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | −3.50000 | + | 6.06218i | −0.210675 | + | 0.364900i | ||||
\(277\) | 13.0000 | 0.781094 | 0.390547 | − | 0.920583i | \(-0.372286\pi\) | ||||
0.390547 | + | 0.920583i | \(0.372286\pi\) | |||||||
\(278\) | −10.0000 | −0.599760 | ||||||||
\(279\) | −5.50000 | + | 0.866025i | −0.329276 | + | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0000 | 1.31241 | 0.656205 | − | 0.754583i | \(-0.272161\pi\) | ||||
0.656205 | + | 0.754583i | \(0.272161\pi\) | |||||||
\(282\) | −1.50000 | + | 2.59808i | −0.0893237 | + | 0.154713i | ||||
\(283\) | −19.0000 | −1.12943 | −0.564716 | − | 0.825285i | \(-0.691014\pi\) | ||||
−0.564716 | + | 0.825285i | \(0.691014\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | −2.00000 | + | 3.46410i | −0.118470 | + | 0.205196i | ||||
\(286\) | −3.00000 | + | 5.19615i | −0.177394 | + | 0.307255i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | −3.00000 | − | 5.19615i | −0.176166 | − | 0.305129i | ||||
\(291\) | 3.00000 | − | 5.19615i | 0.175863 | − | 0.304604i | ||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | −8.00000 | + | 13.8564i | −0.467365 | + | 0.809500i | −0.999305 | − | 0.0372823i | \(-0.988130\pi\) |
0.531940 | + | 0.846782i | \(0.321463\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | −3.50000 | + | 6.06218i | −0.203433 | + | 0.352357i | ||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | −7.00000 | + | 12.1244i | −0.405499 | + | 0.702345i | ||||
\(299\) | 21.0000 | + | 36.3731i | 1.21446 | + | 2.10351i | ||||
\(300\) | −0.500000 | − | 0.866025i | −0.0288675 | − | 0.0500000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −7.00000 | −0.402805 | ||||||||
\(303\) | −7.50000 | + | 12.9904i | −0.430864 | + | 0.746278i | ||||
\(304\) | −2.00000 | + | 3.46410i | −0.114708 | + | 0.198680i | ||||
\(305\) | 7.00000 | + | 12.1244i | 0.400819 | + | 0.694239i | ||||
\(306\) | −1.00000 | −0.0571662 | ||||||||
\(307\) | −8.00000 | + | 13.8564i | −0.456584 | + | 0.790827i | −0.998778 | − | 0.0494267i | \(-0.984261\pi\) |
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.00000 | −0.113776 | ||||||||
\(310\) | −5.50000 | + | 0.866025i | −0.312379 | + | 0.0491869i | ||||
\(311\) | −6.00000 | −0.340229 | −0.170114 | − | 0.985424i | \(-0.554414\pi\) | ||||
−0.170114 | + | 0.985424i | \(0.554414\pi\) | |||||||
\(312\) | −6.00000 | −0.339683 | ||||||||
\(313\) | −3.00000 | + | 5.19615i | −0.169570 | + | 0.293704i | −0.938269 | − | 0.345907i | \(-0.887571\pi\) |
0.768699 | + | 0.639611i | \(0.220905\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.50000 | + | 2.59808i | −0.0843816 | + | 0.146153i | ||||
\(317\) | 6.00000 | − | 10.3923i | 0.336994 | − | 0.583690i | −0.646872 | − | 0.762598i | \(-0.723923\pi\) |
0.983866 | + | 0.178908i | \(0.0572566\pi\) | |||||||
\(318\) | −4.00000 | −0.224309 | ||||||||
\(319\) | 3.00000 | + | 5.19615i | 0.167968 | + | 0.290929i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 2.00000 | + | 3.46410i | 0.111629 | + | 0.193347i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000 | + | 3.46410i | 0.111283 | + | 0.192748i | ||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −6.00000 | −0.332820 | ||||||||
\(326\) | 5.00000 | 0.276924 | ||||||||
\(327\) | 6.00000 | − | 10.3923i | 0.331801 | − | 0.574696i | ||||
\(328\) | 1.00000 | + | 1.73205i | 0.0552158 | + | 0.0956365i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.500000 | + | 0.866025i | 0.0275241 | + | 0.0476731i | ||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | −8.00000 | − | 13.8564i | −0.439057 | − | 0.760469i | ||||
\(333\) | 7.00000 | 0.383598 | ||||||||
\(334\) | 12.0000 | − | 20.7846i | 0.656611 | − | 1.13728i | ||||
\(335\) | −2.50000 | + | 4.33013i | −0.136590 | + | 0.236580i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | −11.5000 | + | 19.9186i | −0.625518 | + | 1.08343i | ||||
\(339\) | 19.0000 | 1.03194 | ||||||||
\(340\) | −1.00000 | −0.0542326 | ||||||||
\(341\) | 5.50000 | − | 0.866025i | 0.297842 | − | 0.0468979i | ||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.50000 | − | 6.06218i | 0.188707 | − | 0.326851i | ||||
\(345\) | 7.00000 | 0.376867 | ||||||||
\(346\) | −1.00000 | − | 1.73205i | −0.0537603 | − | 0.0931156i | ||||
\(347\) | 7.00000 | − | 12.1244i | 0.375780 | − | 0.650870i | −0.614664 | − | 0.788789i | \(-0.710708\pi\) |
0.990443 | + | 0.137920i | \(0.0440416\pi\) | |||||||
\(348\) | −3.00000 | + | 5.19615i | −0.160817 | + | 0.278543i | ||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.00000 | + | 5.19615i | 0.160128 | + | 0.277350i | ||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | 5.50000 | − | 9.52628i | 0.292735 | − | 0.507033i | −0.681720 | − | 0.731613i | \(-0.738768\pi\) |
0.974456 | + | 0.224580i | \(0.0721011\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | −3.00000 | + | 5.19615i | −0.159223 | + | 0.275783i | ||||
\(356\) | 4.00000 | 0.212000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.50000 | − | 9.52628i | 0.290684 | − | 0.503480i | ||||
\(359\) | −10.0000 | − | 17.3205i | −0.527780 | − | 0.914141i | −0.999476 | − | 0.0323801i | \(-0.989691\pi\) |
0.471696 | − | 0.881761i | \(-0.343642\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | 1.50000 | + | 2.59808i | 0.0789474 | + | 0.136741i | ||||
\(362\) | −10.0000 | − | 17.3205i | −0.525588 | − | 0.910346i | ||||
\(363\) | 5.00000 | + | 8.66025i | 0.262432 | + | 0.454545i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.00000 | + | 1.73205i | −0.0523424 | + | 0.0906597i | ||||
\(366\) | 7.00000 | − | 12.1244i | 0.365896 | − | 0.633750i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | 7.00000 | 0.364900 | ||||||||
\(369\) | 1.00000 | − | 1.73205i | 0.0520579 | − | 0.0901670i | ||||
\(370\) | 7.00000 | 0.363913 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 3.50000 | + | 4.33013i | 0.181467 | + | 0.224507i | ||||
\(373\) | −19.0000 | −0.983783 | −0.491891 | − | 0.870657i | \(-0.663694\pi\) | ||||
−0.491891 | + | 0.870657i | \(0.663694\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | −0.500000 | + | 0.866025i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | 18.0000 | + | 31.1769i | 0.927047 | + | 1.60569i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.00000 | + | 5.19615i | −0.154100 | + | 0.266908i | −0.932731 | − | 0.360573i | \(-0.882581\pi\) |
0.778631 | + | 0.627482i | \(0.215914\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 9.00000 | + | 15.5885i | 0.461084 | + | 0.798621i | ||||
\(382\) | 3.00000 | + | 5.19615i | 0.153493 | + | 0.265858i | ||||
\(383\) | −9.50000 | − | 16.4545i | −0.485427 | − | 0.840785i | 0.514432 | − | 0.857531i | \(-0.328003\pi\) |
−0.999860 | + | 0.0167461i | \(0.994669\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.00000 | + | 8.66025i | −0.254493 | + | 0.440795i | ||||
\(387\) | −7.00000 | −0.355830 | ||||||||
\(388\) | −6.00000 | −0.304604 | ||||||||
\(389\) | −4.50000 | + | 7.79423i | −0.228159 | + | 0.395183i | −0.957263 | − | 0.289220i | \(-0.906604\pi\) |
0.729103 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(390\) | 3.00000 | + | 5.19615i | 0.151911 | + | 0.263117i | ||||
\(391\) | 3.50000 | − | 6.06218i | 0.177003 | − | 0.306578i | ||||
\(392\) | 3.50000 | + | 6.06218i | 0.176777 | + | 0.306186i | ||||
\(393\) | 0.500000 | + | 0.866025i | 0.0252217 | + | 0.0436852i | ||||
\(394\) | −4.00000 | − | 6.92820i | −0.201517 | − | 0.349038i | ||||
\(395\) | 3.00000 | 0.150946 | ||||||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | 10.5000 | − | 18.1865i | 0.526980 | − | 0.912756i | −0.472526 | − | 0.881317i | \(-0.656658\pi\) |
0.999506 | − | 0.0314391i | \(-0.0100090\pi\) | |||||||
\(398\) | −8.00000 | − | 13.8564i | −0.401004 | − | 0.694559i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 5.00000 | 0.249377 | ||||||||
\(403\) | 33.0000 | − | 5.19615i | 1.64385 | − | 0.258839i | ||||
\(404\) | 15.0000 | 0.746278 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.00000 | −0.346977 | ||||||||
\(408\) | 0.500000 | + | 0.866025i | 0.0247537 | + | 0.0428746i | ||||
\(409\) | −9.50000 | + | 16.4545i | −0.469745 | + | 0.813622i | −0.999402 | − | 0.0345902i | \(-0.988987\pi\) |
0.529657 | + | 0.848212i | \(0.322321\pi\) | |||||||
\(410\) | 1.00000 | − | 1.73205i | 0.0493865 | − | 0.0855399i | ||||
\(411\) | −7.00000 | −0.345285 | ||||||||
\(412\) | 1.00000 | + | 1.73205i | 0.0492665 | + | 0.0853320i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.50000 | − | 6.06218i | −0.172016 | − | 0.297940i | ||||
\(415\) | −8.00000 | + | 13.8564i | −0.392705 | + | 0.680184i | ||||
\(416\) | 3.00000 | + | 5.19615i | 0.147087 | + | 0.254762i | ||||
\(417\) | 5.00000 | − | 8.66025i | 0.244851 | − | 0.424094i | ||||
\(418\) | −4.00000 | −0.195646 | ||||||||
\(419\) | 7.00000 | 0.341972 | 0.170986 | − | 0.985273i | \(-0.445305\pi\) | ||||
0.170986 | + | 0.985273i | \(0.445305\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | − | 22.5167i | −0.633581 | − | 1.09739i | −0.986814 | − | 0.161859i | \(-0.948251\pi\) |
0.353233 | − | 0.935536i | \(-0.385082\pi\) | |||||||
\(422\) | 4.00000 | − | 6.92820i | 0.194717 | − | 0.337260i | ||||
\(423\) | −1.50000 | − | 2.59808i | −0.0729325 | − | 0.126323i | ||||
\(424\) | 2.00000 | + | 3.46410i | 0.0971286 | + | 0.168232i | ||||
\(425\) | 0.500000 | + | 0.866025i | 0.0242536 | + | 0.0420084i | ||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.00000 | − | 3.46410i | 0.0966736 | − | 0.167444i | ||||
\(429\) | −3.00000 | − | 5.19615i | −0.144841 | − | 0.250873i | ||||
\(430\) | −7.00000 | −0.337570 | ||||||||
\(431\) | −15.0000 | + | 25.9808i | −0.722525 | + | 1.25145i | 0.237460 | + | 0.971397i | \(0.423685\pi\) |
−0.959985 | + | 0.280052i | \(0.909648\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 8.00000 | 0.384455 | 0.192228 | − | 0.981350i | \(-0.438429\pi\) | ||||
0.192228 | + | 0.981350i | \(0.438429\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.00000 | 0.287678 | ||||||||
\(436\) | −12.0000 | −0.574696 | ||||||||
\(437\) | −14.0000 | + | 24.2487i | −0.669711 | + | 1.15997i | ||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 17.5000 | + | 30.3109i | 0.835229 | + | 1.44666i | 0.893843 | + | 0.448379i | \(0.147999\pi\) |
−0.0586141 | + | 0.998281i | \(0.518668\pi\) | |||||||
\(440\) | 0.500000 | − | 0.866025i | 0.0238366 | − | 0.0412861i | ||||
\(441\) | 3.50000 | − | 6.06218i | 0.166667 | − | 0.288675i | ||||
\(442\) | 6.00000 | 0.285391 | ||||||||
\(443\) | −17.0000 | − | 29.4449i | −0.807694 | − | 1.39897i | −0.914457 | − | 0.404683i | \(-0.867382\pi\) |
0.106763 | − | 0.994285i | \(-0.465952\pi\) | |||||||
\(444\) | −3.50000 | − | 6.06218i | −0.166103 | − | 0.287698i | ||||
\(445\) | −2.00000 | − | 3.46410i | −0.0948091 | − | 0.164214i | ||||
\(446\) | −7.00000 | + | 12.1244i | −0.331460 | + | 0.574105i | ||||
\(447\) | −7.00000 | − | 12.1244i | −0.331089 | − | 0.573462i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −1.00000 | + | 1.73205i | −0.0470882 | + | 0.0815591i | ||||
\(452\) | −9.50000 | − | 16.4545i | −0.446842 | − | 0.773954i | ||||
\(453\) | 3.50000 | − | 6.06218i | 0.164444 | − | 0.284826i | ||||
\(454\) | 4.00000 | + | 6.92820i | 0.187729 | + | 0.325157i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | − | 3.46410i | −0.0936586 | − | 0.162221i | ||||
\(457\) | 32.0000 | 1.49690 | 0.748448 | − | 0.663193i | \(-0.230799\pi\) | ||||
0.748448 | + | 0.663193i | \(0.230799\pi\) | |||||||
\(458\) | −10.0000 | + | 17.3205i | −0.467269 | + | 0.809334i | ||||
\(459\) | 0.500000 | − | 0.866025i | 0.0233380 | − | 0.0404226i | ||||
\(460\) | −3.50000 | − | 6.06218i | −0.163188 | − | 0.282650i | ||||
\(461\) | 33.0000 | 1.53696 | 0.768482 | − | 0.639872i | \(-0.221013\pi\) | ||||
0.768482 | + | 0.639872i | \(0.221013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.0000 | 0.929479 | 0.464739 | − | 0.885448i | \(-0.346148\pi\) | ||||
0.464739 | + | 0.885448i | \(0.346148\pi\) | |||||||
\(464\) | 6.00000 | 0.278543 | ||||||||
\(465\) | 2.00000 | − | 5.19615i | 0.0927478 | − | 0.240966i | ||||
\(466\) | 25.0000 | 1.15810 | ||||||||
\(467\) | 12.0000 | 0.555294 | 0.277647 | − | 0.960683i | \(-0.410445\pi\) | ||||
0.277647 | + | 0.960683i | \(0.410445\pi\) | |||||||
\(468\) | 3.00000 | − | 5.19615i | 0.138675 | − | 0.240192i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.50000 | − | 2.59808i | −0.0691898 | − | 0.119840i | ||||
\(471\) | −7.00000 | + | 12.1244i | −0.322543 | + | 0.558661i | ||||
\(472\) | −6.00000 | + | 10.3923i | −0.276172 | + | 0.478345i | ||||
\(473\) | 7.00000 | 0.321860 | ||||||||
\(474\) | −1.50000 | − | 2.59808i | −0.0688973 | − | 0.119334i | ||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | − | 3.46410i | 0.0915737 | − | 0.158610i | ||||
\(478\) | −9.00000 | − | 15.5885i | −0.411650 | − | 0.712999i | ||||
\(479\) | −9.00000 | + | 15.5885i | −0.411220 | + | 0.712255i | −0.995023 | − | 0.0996406i | \(-0.968231\pi\) |
0.583803 | + | 0.811895i | \(0.301564\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −42.0000 | −1.91504 | ||||||||
\(482\) | −9.00000 | + | 15.5885i | −0.409939 | + | 0.710035i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5.00000 | − | 8.66025i | 0.227273 | − | 0.393648i | ||||
\(485\) | 3.00000 | + | 5.19615i | 0.136223 | + | 0.235945i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | −16.0000 | − | 27.7128i | −0.725029 | − | 1.25579i | −0.958962 | − | 0.283535i | \(-0.908493\pi\) |
0.233933 | − | 0.972253i | \(-0.424840\pi\) | |||||||
\(488\) | −14.0000 | −0.633750 | ||||||||
\(489\) | −2.50000 | + | 4.33013i | −0.113054 | + | 0.195815i | ||||
\(490\) | 3.50000 | − | 6.06218i | 0.158114 | − | 0.273861i | ||||
\(491\) | 14.5000 | + | 25.1147i | 0.654376 | + | 1.13341i | 0.982050 | + | 0.188621i | \(0.0604019\pi\) |
−0.327674 | + | 0.944791i | \(0.606265\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | 3.00000 | − | 5.19615i | 0.135113 | − | 0.234023i | ||||
\(494\) | −24.0000 | −1.07981 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 2.00000 | − | 5.19615i | 0.0898027 | − | 0.233314i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 16.0000 | 0.716977 | ||||||||
\(499\) | 10.0000 | − | 17.3205i | 0.447661 | − | 0.775372i | −0.550572 | − | 0.834788i | \(-0.685590\pi\) |
0.998233 | + | 0.0594153i | \(0.0189236\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 12.0000 | + | 20.7846i | 0.536120 | + | 0.928588i | ||||
\(502\) | −1.50000 | + | 2.59808i | −0.0669483 | + | 0.115958i | ||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.50000 | − | 12.9904i | −0.333746 | − | 0.578064i | ||||
\(506\) | 3.50000 | + | 6.06218i | 0.155594 | + | 0.269497i | ||||
\(507\) | −11.5000 | − | 19.9186i | −0.510733 | − | 0.884615i | ||||
\(508\) | 9.00000 | − | 15.5885i | 0.399310 | − | 0.691626i | ||||
\(509\) | −14.5000 | − | 25.1147i | −0.642701 | − | 1.11319i | −0.984827 | − | 0.173537i | \(-0.944480\pi\) |
0.342126 | − | 0.939654i | \(-0.388853\pi\) | |||||||
\(510\) | 0.500000 | − | 0.866025i | 0.0221404 | − | 0.0383482i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −2.00000 | + | 3.46410i | −0.0883022 | + | 0.152944i | ||||
\(514\) | −11.5000 | − | 19.9186i | −0.507243 | − | 0.878571i | ||||
\(515\) | 1.00000 | − | 1.73205i | 0.0440653 | − | 0.0763233i | ||||
\(516\) | 3.50000 | + | 6.06218i | 0.154079 | + | 0.266872i | ||||
\(517\) | 1.50000 | + | 2.59808i | 0.0659699 | + | 0.114263i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.00000 | 0.0877903 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(522\) | −3.00000 | − | 5.19615i | −0.131306 | − | 0.227429i | ||||
\(523\) | 29.0000 | 1.26808 | 0.634041 | − | 0.773300i | \(-0.281395\pi\) | ||||
0.634041 | + | 0.773300i | \(0.281395\pi\) | |||||||
\(524\) | 0.500000 | − | 0.866025i | 0.0218426 | − | 0.0378325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.0000 | −0.479623 | ||||||||
\(527\) | −3.50000 | − | 4.33013i | −0.152462 | − | 0.188623i | ||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | 26.0000 | 1.13043 | ||||||||
\(530\) | 2.00000 | − | 3.46410i | 0.0868744 | − | 0.150471i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.00000 | + | 10.3923i | −0.259889 | + | 0.450141i | ||||
\(534\) | −2.00000 | + | 3.46410i | −0.0865485 | + | 0.149906i | ||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | −2.50000 | − | 4.33013i | −0.107984 | − | 0.187033i | ||||
\(537\) | 5.50000 | + | 9.52628i | 0.237343 | + | 0.411089i | ||||
\(538\) | 12.5000 | + | 21.6506i | 0.538913 | + | 0.933425i | ||||
\(539\) | −3.50000 | + | 6.06218i | −0.150756 | + | 0.261116i | ||||
\(540\) | −0.500000 | − | 0.866025i | −0.0215166 | − | 0.0372678i | ||||
\(541\) | 5.00000 | − | 8.66025i | 0.214967 | − | 0.372333i | −0.738296 | − | 0.674477i | \(-0.764369\pi\) |
0.953262 | + | 0.302144i | \(0.0977023\pi\) | |||||||
\(542\) | −28.0000 | −1.20270 | ||||||||
\(543\) | 20.0000 | 0.858282 | ||||||||
\(544\) | 0.500000 | − | 0.866025i | 0.0214373 | − | 0.0371305i | ||||
\(545\) | 6.00000 | + | 10.3923i | 0.257012 | + | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.50000 | + | 14.7224i | 0.363434 | + | 0.629486i | 0.988524 | − | 0.151067i | \(-0.0482710\pi\) |
−0.625090 | + | 0.780553i | \(0.714938\pi\) | |||||||
\(548\) | 3.50000 | + | 6.06218i | 0.149513 | + | 0.258963i | ||||
\(549\) | 7.00000 | + | 12.1244i | 0.298753 | + | 0.517455i | ||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | −12.0000 | + | 20.7846i | −0.511217 | + | 0.885454i | ||||
\(552\) | −3.50000 | + | 6.06218i | −0.148970 | + | 0.258023i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 13.0000 | 0.552317 | ||||||||
\(555\) | −3.50000 | + | 6.06218i | −0.148567 | + | 0.257325i | ||||
\(556\) | −10.0000 | −0.424094 | ||||||||
\(557\) | 12.0000 | 0.508456 | 0.254228 | − | 0.967144i | \(-0.418179\pi\) | ||||
0.254228 | + | 0.967144i | \(0.418179\pi\) | |||||||
\(558\) | −5.50000 | + | 0.866025i | −0.232834 | + | 0.0366618i | ||||
\(559\) | 42.0000 | 1.77641 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.500000 | + | 0.866025i | −0.0211100 | + | 0.0365636i | ||||
\(562\) | 22.0000 | 0.928014 | ||||||||
\(563\) | −9.00000 | − | 15.5885i | −0.379305 | − | 0.656975i | 0.611656 | − | 0.791123i | \(-0.290503\pi\) |
−0.990961 | + | 0.134148i | \(0.957170\pi\) | |||||||
\(564\) | −1.50000 | + | 2.59808i | −0.0631614 | + | 0.109399i | ||||
\(565\) | −9.50000 | + | 16.4545i | −0.399668 | + | 0.692245i | ||||
\(566\) | −19.0000 | −0.798630 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | − | 5.19615i | −0.125877 | − | 0.218026i | ||||
\(569\) | −17.0000 | − | 29.4449i | −0.712677 | − | 1.23439i | −0.963849 | − | 0.266450i | \(-0.914149\pi\) |
0.251172 | − | 0.967943i | \(-0.419184\pi\) | |||||||
\(570\) | −2.00000 | + | 3.46410i | −0.0837708 | + | 0.145095i | ||||
\(571\) | 16.0000 | + | 27.7128i | 0.669579 | + | 1.15975i | 0.978022 | + | 0.208502i | \(0.0668588\pi\) |
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(572\) | −3.00000 | + | 5.19615i | −0.125436 | + | 0.217262i | ||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.50000 | + | 6.06218i | −0.145960 | + | 0.252810i | ||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −16.0000 | + | 27.7128i | −0.666089 | + | 1.15370i | 0.312900 | + | 0.949786i | \(0.398699\pi\) |
−0.978989 | + | 0.203913i | \(0.934634\pi\) | |||||||
\(578\) | 8.00000 | + | 13.8564i | 0.332756 | + | 0.576351i | ||||
\(579\) | −5.00000 | − | 8.66025i | −0.207793 | − | 0.359908i | ||||
\(580\) | −3.00000 | − | 5.19615i | −0.124568 | − | 0.215758i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.00000 | − | 5.19615i | 0.124354 | − | 0.215387i | ||||
\(583\) | −2.00000 | + | 3.46410i | −0.0828315 | + | 0.143468i | ||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | −6.00000 | −0.248069 | ||||||||
\(586\) | −8.00000 | + | 13.8564i | −0.330477 | + | 0.572403i | ||||
\(587\) | 18.0000 | 0.742940 | 0.371470 | − | 0.928445i | \(-0.378854\pi\) | ||||
0.371470 | + | 0.928445i | \(0.378854\pi\) | |||||||
\(588\) | −7.00000 | −0.288675 | ||||||||
\(589\) | 14.0000 | + | 17.3205i | 0.576860 | + | 0.713679i | ||||
\(590\) | 12.0000 | 0.494032 | ||||||||
\(591\) | 8.00000 | 0.329076 | ||||||||
\(592\) | −3.50000 | + | 6.06218i | −0.143849 | + | 0.249154i | ||||
\(593\) | 6.00000 | 0.246390 | 0.123195 | − | 0.992382i | \(-0.460686\pi\) | ||||
0.123195 | + | 0.992382i | \(0.460686\pi\) | |||||||
\(594\) | 0.500000 | + | 0.866025i | 0.0205152 | + | 0.0355335i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.00000 | + | 12.1244i | −0.286731 | + | 0.496633i | ||||
\(597\) | 16.0000 | 0.654836 | ||||||||
\(598\) | 21.0000 | + | 36.3731i | 0.858754 | + | 1.48741i | ||||
\(599\) | −17.0000 | − | 29.4449i | −0.694601 | − | 1.20308i | −0.970315 | − | 0.241845i | \(-0.922248\pi\) |
0.275714 | − | 0.961240i | \(-0.411086\pi\) | |||||||
\(600\) | −0.500000 | − | 0.866025i | −0.0204124 | − | 0.0353553i | ||||
\(601\) | 21.5000 | − | 37.2391i | 0.877003 | − | 1.51901i | 0.0223900 | − | 0.999749i | \(-0.492872\pi\) |
0.854613 | − | 0.519265i | \(-0.173794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.50000 | + | 4.33013i | −0.101808 | + | 0.176336i | ||||
\(604\) | −7.00000 | −0.284826 | ||||||||
\(605\) | −10.0000 | −0.406558 | ||||||||
\(606\) | −7.50000 | + | 12.9904i | −0.304667 | + | 0.527698i | ||||
\(607\) | −10.0000 | − | 17.3205i | −0.405887 | − | 0.703018i | 0.588537 | − | 0.808470i | \(-0.299704\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | −2.00000 | + | 3.46410i | −0.0811107 | + | 0.140488i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7.00000 | + | 12.1244i | 0.283422 | + | 0.490901i | ||||
\(611\) | 9.00000 | + | 15.5885i | 0.364101 | + | 0.630641i | ||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | −1.00000 | + | 1.73205i | −0.0403896 | + | 0.0699569i | −0.885514 | − | 0.464614i | \(-0.846193\pi\) |
0.845124 | + | 0.534570i | \(0.179527\pi\) | |||||||
\(614\) | −8.00000 | + | 13.8564i | −0.322854 | + | 0.559199i | ||||
\(615\) | 1.00000 | + | 1.73205i | 0.0403239 | + | 0.0698430i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.50000 | − | 6.06218i | 0.140905 | − | 0.244054i | −0.786933 | − | 0.617039i | \(-0.788332\pi\) |
0.927838 | + | 0.372985i | \(0.121666\pi\) | |||||||
\(618\) | −2.00000 | −0.0804518 | ||||||||
\(619\) | 36.0000 | 1.44696 | 0.723481 | − | 0.690344i | \(-0.242541\pi\) | ||||
0.723481 | + | 0.690344i | \(0.242541\pi\) | |||||||
\(620\) | −5.50000 | + | 0.866025i | −0.220885 | + | 0.0347804i | ||||
\(621\) | 7.00000 | 0.280900 | ||||||||
\(622\) | −6.00000 | −0.240578 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −6.00000 | −0.240192 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −3.00000 | + | 5.19615i | −0.119904 | + | 0.207680i | ||||
\(627\) | 2.00000 | − | 3.46410i | 0.0798723 | − | 0.138343i | ||||
\(628\) | 14.0000 | 0.558661 | ||||||||
\(629\) | 3.50000 | + | 6.06218i | 0.139554 | + | 0.241715i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14.5000 | − | 25.1147i | −0.577236 | − | 0.999802i | −0.995795 | − | 0.0916122i | \(-0.970798\pi\) |
0.418559 | − | 0.908190i | \(-0.362535\pi\) | |||||||
\(632\) | −1.50000 | + | 2.59808i | −0.0596668 | + | 0.103346i | ||||
\(633\) | 4.00000 | + | 6.92820i | 0.158986 | + | 0.275371i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | −18.0000 | −0.714308 | ||||||||
\(636\) | −4.00000 | −0.158610 | ||||||||
\(637\) | −21.0000 | + | 36.3731i | −0.832050 | + | 1.44115i | ||||
\(638\) | 3.00000 | + | 5.19615i | 0.118771 | + | 0.205718i | ||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | −2.00000 | − | 3.46410i | −0.0789953 | − | 0.136824i | 0.823821 | − | 0.566849i | \(-0.191838\pi\) |
−0.902817 | + | 0.430026i | \(0.858505\pi\) | |||||||
\(642\) | 2.00000 | + | 3.46410i | 0.0789337 | + | 0.136717i | ||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.50000 | − | 6.06218i | 0.137812 | − | 0.238698i | ||||
\(646\) | 2.00000 | + | 3.46410i | 0.0786889 | + | 0.136293i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −12.0000 | −0.471041 | ||||||||
\(650\) | −6.00000 | −0.235339 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.00000 | 0.195815 | ||||||||
\(653\) | −12.0000 | −0.469596 | −0.234798 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234798 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(654\) | 6.00000 | − | 10.3923i | 0.234619 | − | 0.406371i | ||||
\(655\) | −1.00000 | −0.0390732 | ||||||||
\(656\) | 1.00000 | + | 1.73205i | 0.0390434 | + | 0.0676252i | ||||
\(657\) | −1.00000 | + | 1.73205i | −0.0390137 | + | 0.0675737i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.0000 | −1.44132 | −0.720658 | − | 0.693291i | \(-0.756160\pi\) | ||||
−0.720658 | + | 0.693291i | \(0.756160\pi\) | |||||||
\(660\) | 0.500000 | + | 0.866025i | 0.0194625 | + | 0.0337100i | ||||
\(661\) | 5.00000 | + | 8.66025i | 0.194477 | + | 0.336845i | 0.946729 | − | 0.322031i | \(-0.104366\pi\) |
−0.752252 | + | 0.658876i | \(0.771032\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | −3.00000 | + | 5.19615i | −0.116510 | + | 0.201802i | ||||
\(664\) | −8.00000 | − | 13.8564i | −0.310460 | − | 0.537733i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | 42.0000 | 1.62625 | ||||||||
\(668\) | 12.0000 | − | 20.7846i | 0.464294 | − | 0.804181i | ||||
\(669\) | −7.00000 | − | 12.1244i | −0.270636 | − | 0.468755i | ||||
\(670\) | −2.50000 | + | 4.33013i | −0.0965834 | + | 0.167287i | ||||
\(671\) | −7.00000 | − | 12.1244i | −0.270232 | − | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.00000 | − | 8.66025i | −0.192736 | − | 0.333828i | 0.753420 | − | 0.657539i | \(-0.228403\pi\) |
−0.946156 | + | 0.323711i | \(0.895069\pi\) | |||||||
\(674\) | 8.00000 | 0.308148 | ||||||||
\(675\) | −0.500000 | + | 0.866025i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −11.5000 | + | 19.9186i | −0.442308 | + | 0.766099i | ||||
\(677\) | 25.0000 | + | 43.3013i | 0.960828 | + | 1.66420i | 0.720429 | + | 0.693529i | \(0.243945\pi\) |
0.240399 | + | 0.970674i | \(0.422722\pi\) | |||||||
\(678\) | 19.0000 | 0.729691 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.00000 | −0.0383482 | ||||||||
\(681\) | −8.00000 | −0.306561 | ||||||||
\(682\) | 5.50000 | − | 0.866025i | 0.210606 | − | 0.0331618i | ||||
\(683\) | −4.00000 | −0.153056 | −0.0765279 | − | 0.997067i | \(-0.524383\pi\) | ||||
−0.0765279 | + | 0.997067i | \(0.524383\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | 3.50000 | − | 6.06218i | 0.133728 | − | 0.231624i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | − | 17.3205i | −0.381524 | − | 0.660819i | ||||
\(688\) | 3.50000 | − | 6.06218i | 0.133436 | − | 0.231118i | ||||
\(689\) | −12.0000 | + | 20.7846i | −0.457164 | + | 0.791831i | ||||
\(690\) | 7.00000 | 0.266485 | ||||||||
\(691\) | 11.0000 | + | 19.0526i | 0.418460 | + | 0.724793i | 0.995785 | − | 0.0917209i | \(-0.0292368\pi\) |
−0.577325 | + | 0.816514i | \(0.695903\pi\) | |||||||
\(692\) | −1.00000 | − | 1.73205i | −0.0380143 | − | 0.0658427i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.00000 | − | 12.1244i | 0.265716 | − | 0.460234i | ||||
\(695\) | 5.00000 | + | 8.66025i | 0.189661 | + | 0.328502i | ||||
\(696\) | −3.00000 | + | 5.19615i | −0.113715 | + | 0.196960i | ||||
\(697\) | 2.00000 | 0.0757554 | ||||||||
\(698\) | 18.0000 | 0.681310 | ||||||||
\(699\) | −12.5000 | + | 21.6506i | −0.472793 | + | 0.818902i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.5000 | + | 21.6506i | −0.472118 | + | 0.817733i | −0.999491 | − | 0.0319010i | \(-0.989844\pi\) |
0.527373 | + | 0.849634i | \(0.323177\pi\) | |||||||
\(702\) | 3.00000 | + | 5.19615i | 0.113228 | + | 0.196116i | ||||
\(703\) | −14.0000 | − | 24.2487i | −0.528020 | − | 0.914557i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 3.00000 | 0.112987 | ||||||||
\(706\) | 5.50000 | − | 9.52628i | 0.206995 | − | 0.358526i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −6.00000 | − | 10.3923i | −0.225494 | − | 0.390567i | ||||
\(709\) | −10.0000 | −0.375558 | −0.187779 | − | 0.982211i | \(-0.560129\pi\) | ||||
−0.187779 | + | 0.982211i | \(0.560129\pi\) | |||||||
\(710\) | −3.00000 | + | 5.19615i | −0.112588 | + | 0.195008i | ||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 4.00000 | 0.149906 | ||||||||
\(713\) | 14.0000 | − | 36.3731i | 0.524304 | − | 1.36218i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000 | 0.224387 | ||||||||
\(716\) | 5.50000 | − | 9.52628i | 0.205545 | − | 0.356014i | ||||
\(717\) | 18.0000 | 0.672222 | ||||||||
\(718\) | −10.0000 | − | 17.3205i | −0.373197 | − | 0.646396i | ||||
\(719\) | −2.00000 | + | 3.46410i | −0.0745874 | + | 0.129189i | −0.900907 | − | 0.434013i | \(-0.857097\pi\) |
0.826319 | + | 0.563202i | \(0.190431\pi\) | |||||||
\(720\) | −0.500000 | + | 0.866025i | −0.0186339 | + | 0.0322749i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.50000 | + | 2.59808i | 0.0558242 | + | 0.0966904i | ||||
\(723\) | −9.00000 | − | 15.5885i | −0.334714 | − | 0.579741i | ||||
\(724\) | −10.0000 | − | 17.3205i | −0.371647 | − | 0.643712i | ||||
\(725\) | −3.00000 | + | 5.19615i | −0.111417 | + | 0.192980i | ||||
\(726\) | 5.00000 | + | 8.66025i | 0.185567 | + | 0.321412i | ||||
\(727\) | −12.0000 | + | 20.7846i | −0.445055 | + | 0.770859i | −0.998056 | − | 0.0623223i | \(-0.980149\pi\) |
0.553001 | + | 0.833181i | \(0.313483\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −1.00000 | + | 1.73205i | −0.0370117 | + | 0.0641061i | ||||
\(731\) | −3.50000 | − | 6.06218i | −0.129452 | − | 0.224218i | ||||
\(732\) | 7.00000 | − | 12.1244i | 0.258727 | − | 0.448129i | ||||
\(733\) | 17.5000 | + | 30.3109i | 0.646377 | + | 1.11956i | 0.983982 | + | 0.178270i | \(0.0570501\pi\) |
−0.337604 | + | 0.941288i | \(0.609617\pi\) | |||||||
\(734\) | 2.00000 | + | 3.46410i | 0.0738213 | + | 0.127862i | ||||
\(735\) | 3.50000 | + | 6.06218i | 0.129099 | + | 0.223607i | ||||
\(736\) | 7.00000 | 0.258023 | ||||||||
\(737\) | 2.50000 | − | 4.33013i | 0.0920887 | − | 0.159502i | ||||
\(738\) | 1.00000 | − | 1.73205i | 0.0368105 | − | 0.0637577i | ||||
\(739\) | 19.0000 | + | 32.9090i | 0.698926 | + | 1.21058i | 0.968839 | + | 0.247691i | \(0.0796718\pi\) |
−0.269913 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(740\) | 7.00000 | 0.257325 | ||||||||
\(741\) | 12.0000 | − | 20.7846i | 0.440831 | − | 0.763542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27.0000 | −0.990534 | −0.495267 | − | 0.868741i | \(-0.664930\pi\) | ||||
−0.495267 | + | 0.868741i | \(0.664930\pi\) | |||||||
\(744\) | 3.50000 | + | 4.33013i | 0.128316 | + | 0.158750i | ||||
\(745\) | 14.0000 | 0.512920 | ||||||||
\(746\) | −19.0000 | −0.695639 | ||||||||
\(747\) | −8.00000 | + | 13.8564i | −0.292705 | + | 0.506979i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −0.500000 | + | 0.866025i | −0.0182574 | + | 0.0316228i | ||||
\(751\) | 12.5000 | − | 21.6506i | 0.456131 | − | 0.790043i | −0.542621 | − | 0.839978i | \(-0.682568\pi\) |
0.998752 | + | 0.0499348i | \(0.0159013\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | −1.50000 | − | 2.59808i | −0.0546630 | − | 0.0946792i | ||||
\(754\) | 18.0000 | + | 31.1769i | 0.655521 | + | 1.13540i | ||||
\(755\) | 3.50000 | + | 6.06218i | 0.127378 | + | 0.220625i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.50000 | + | 16.4545i | 0.345283 | + | 0.598048i | 0.985405 | − | 0.170225i | \(-0.0544495\pi\) |
−0.640122 | + | 0.768273i | \(0.721116\pi\) | |||||||
\(758\) | −3.00000 | + | 5.19615i | −0.108965 | + | 0.188733i | ||||
\(759\) | −7.00000 | −0.254084 | ||||||||
\(760\) | 4.00000 | 0.145095 | ||||||||
\(761\) | 8.00000 | − | 13.8564i | 0.290000 | − | 0.502294i | −0.683810 | − | 0.729661i | \(-0.739678\pi\) |
0.973809 | + | 0.227366i | \(0.0730114\pi\) | |||||||
\(762\) | 9.00000 | + | 15.5885i | 0.326036 | + | 0.564710i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 3.00000 | + | 5.19615i | 0.108536 | + | 0.187990i | ||||
\(765\) | 0.500000 | + | 0.866025i | 0.0180775 | + | 0.0313112i | ||||
\(766\) | −9.50000 | − | 16.4545i | −0.343249 | − | 0.594525i | ||||
\(767\) | −72.0000 | −2.59977 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | 13.0000 | − | 22.5167i | 0.468792 | − | 0.811972i | −0.530572 | − | 0.847640i | \(-0.678023\pi\) |
0.999364 | + | 0.0356685i | \(0.0113561\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.0000 | 0.828325 | ||||||||
\(772\) | −5.00000 | + | 8.66025i | −0.179954 | + | 0.311689i | ||||
\(773\) | −30.0000 | −1.07903 | −0.539513 | − | 0.841978i | \(-0.681391\pi\) | ||||
−0.539513 | + | 0.841978i | \(0.681391\pi\) | |||||||
\(774\) | −7.00000 | −0.251610 | ||||||||
\(775\) | 3.50000 | + | 4.33013i | 0.125724 | + | 0.155543i | ||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.50000 | + | 7.79423i | −0.161333 | + | 0.279437i | ||||
\(779\) | −8.00000 | −0.286630 | ||||||||
\(780\) | 3.00000 | + | 5.19615i | 0.107417 | + | 0.186052i | ||||
\(781\) | 3.00000 | − | 5.19615i | 0.107348 | − | 0.185933i | ||||
\(782\) | 3.50000 | − | 6.06218i | 0.125160 | − | 0.216783i | ||||
\(783\) | 6.00000 | 0.214423 | ||||||||
\(784\) | 3.50000 | + | 6.06218i | 0.125000 | + | 0.216506i | ||||
\(785\) | −7.00000 | − | 12.1244i | −0.249841 | − | 0.432737i | ||||
\(786\) | 0.500000 | + | 0.866025i | 0.0178344 | + | 0.0308901i | ||||
\(787\) | 4.50000 | − | 7.79423i | 0.160408 | − | 0.277834i | −0.774607 | − | 0.632443i | \(-0.782052\pi\) |
0.935015 | + | 0.354608i | \(0.115386\pi\) | |||||||
\(788\) | −4.00000 | − | 6.92820i | −0.142494 | − | 0.246807i | ||||
\(789\) | 5.50000 | − | 9.52628i | 0.195805 | − | 0.339145i | ||||
\(790\) | 3.00000 | 0.106735 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.500000 | − | 0.866025i | 0.0177667 | − | 0.0307729i | ||||
\(793\) | −42.0000 | − | 72.7461i | −1.49146 | − | 2.58329i | ||||
\(794\) | 10.5000 | − | 18.1865i | 0.372631 | − | 0.645416i | ||||
\(795\) | 2.00000 | + | 3.46410i | 0.0709327 | + | 0.122859i | ||||
\(796\) | −8.00000 | − | 13.8564i | −0.283552 | − | 0.491127i | ||||
\(797\) | −6.00000 | − | 10.3923i | −0.212531 | − | 0.368114i | 0.739975 | − | 0.672634i | \(-0.234837\pi\) |
−0.952506 | + | 0.304520i | \(0.901504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.50000 | − | 2.59808i | 0.0530662 | − | 0.0919133i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −2.00000 | − | 3.46410i | −0.0706665 | − | 0.122398i | ||||
\(802\) | 2.00000 | 0.0706225 | ||||||||
\(803\) | 1.00000 | − | 1.73205i | 0.0352892 | − | 0.0611227i | ||||
\(804\) | 5.00000 | 0.176336 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 33.0000 | − | 5.19615i | 1.16238 | − | 0.183027i | ||||
\(807\) | −25.0000 | −0.880042 | ||||||||
\(808\) | 15.0000 | 0.527698 | ||||||||
\(809\) | 6.00000 | − | 10.3923i | 0.210949 | − | 0.365374i | −0.741063 | − | 0.671436i | \(-0.765678\pi\) |
0.952012 | + | 0.306062i | \(0.0990113\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −10.0000 | − | 17.3205i | −0.351147 | − | 0.608205i | 0.635303 | − | 0.772263i | \(-0.280875\pi\) |
−0.986451 | + | 0.164057i | \(0.947542\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.0000 | − | 24.2487i | 0.491001 | − | 0.850439i | ||||
\(814\) | −7.00000 | −0.245350 | ||||||||
\(815\) | −2.50000 | − | 4.33013i | −0.0875712 | − | 0.151678i | ||||
\(816\) | 0.500000 | + | 0.866025i | 0.0175035 | + | 0.0303170i | ||||
\(817\) | 14.0000 | + | 24.2487i | 0.489798 | + | 0.848355i | ||||
\(818\) | −9.50000 | + | 16.4545i | −0.332160 | + | 0.575317i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.00000 | − | 1.73205i | 0.0349215 | − | 0.0604858i | ||||
\(821\) | −15.0000 | −0.523504 | −0.261752 | − | 0.965135i | \(-0.584300\pi\) | ||||
−0.261752 | + | 0.965135i | \(0.584300\pi\) | |||||||
\(822\) | −7.00000 | −0.244153 | ||||||||
\(823\) | 23.0000 | − | 39.8372i | 0.801730 | − | 1.38864i | −0.116747 | − | 0.993162i | \(-0.537247\pi\) |
0.918477 | − | 0.395475i | \(-0.129420\pi\) | |||||||
\(824\) | 1.00000 | + | 1.73205i | 0.0348367 | + | 0.0603388i | ||||
\(825\) | 0.500000 | − | 0.866025i | 0.0174078 | − | 0.0301511i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −18.0000 | − | 31.1769i | −0.625921 | − | 1.08413i | −0.988362 | − | 0.152121i | \(-0.951390\pi\) |
0.362441 | − | 0.932007i | \(-0.381944\pi\) | |||||||
\(828\) | −3.50000 | − | 6.06218i | −0.121633 | − | 0.210675i | ||||
\(829\) | −38.0000 | −1.31979 | −0.659897 | − | 0.751356i | \(-0.729400\pi\) | ||||
−0.659897 | + | 0.751356i | \(0.729400\pi\) | |||||||
\(830\) | −8.00000 | + | 13.8564i | −0.277684 | + | 0.480963i | ||||
\(831\) | −6.50000 | + | 11.2583i | −0.225483 | + | 0.390547i | ||||
\(832\) | 3.00000 | + | 5.19615i | 0.104006 | + | 0.180144i | ||||
\(833\) | 7.00000 | 0.242536 | ||||||||
\(834\) | 5.00000 | − | 8.66025i | 0.173136 | − | 0.299880i | ||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | −4.00000 | −0.138343 | ||||||||
\(837\) | 2.00000 | − | 5.19615i | 0.0691301 | − | 0.179605i | ||||
\(838\) | 7.00000 | 0.241811 | ||||||||
\(839\) | −6.00000 | −0.207143 | −0.103572 | − | 0.994622i | \(-0.533027\pi\) | ||||
−0.103572 | + | 0.994622i | \(0.533027\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | −13.0000 | − | 22.5167i | −0.448010 | − | 0.775975i | ||||
\(843\) | −11.0000 | + | 19.0526i | −0.378860 | + | 0.656205i | ||||
\(844\) | 4.00000 | − | 6.92820i | 0.137686 | − | 0.238479i | ||||
\(845\) | 23.0000 | 0.791224 | ||||||||
\(846\) | −1.50000 | − | 2.59808i | −0.0515711 | − | 0.0893237i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 2.00000 | + | 3.46410i | 0.0686803 | + | 0.118958i | ||||
\(849\) | 9.50000 | − | 16.4545i | 0.326039 | − | 0.564716i | ||||
\(850\) | 0.500000 | + | 0.866025i | 0.0171499 | + | 0.0297044i | ||||
\(851\) | −24.5000 | + | 42.4352i | −0.839849 | + | 1.45466i | ||||
\(852\) | 6.00000 | 0.205557 | ||||||||
\(853\) | −14.0000 | −0.479351 | −0.239675 | − | 0.970853i | \(-0.577041\pi\) | ||||
−0.239675 | + | 0.970853i | \(0.577041\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.00000 | − | 3.46410i | −0.0683986 | − | 0.118470i | ||||
\(856\) | 2.00000 | − | 3.46410i | 0.0683586 | − | 0.118401i | ||||
\(857\) | 4.50000 | + | 7.79423i | 0.153717 | + | 0.266246i | 0.932591 | − | 0.360935i | \(-0.117542\pi\) |
−0.778874 | + | 0.627180i | \(0.784209\pi\) | |||||||
\(858\) | −3.00000 | − | 5.19615i | −0.102418 | − | 0.177394i | ||||
\(859\) | −10.0000 | − | 17.3205i | −0.341196 | − | 0.590968i | 0.643459 | − | 0.765480i | \(-0.277499\pi\) |
−0.984655 | + | 0.174512i | \(0.944165\pi\) | |||||||
\(860\) | −7.00000 | −0.238698 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.0000 | + | 25.9808i | −0.510902 | + | 0.884908i | ||||
\(863\) | 15.5000 | + | 26.8468i | 0.527626 | + | 0.913875i | 0.999481 | + | 0.0321993i | \(0.0102511\pi\) |
−0.471855 | + | 0.881676i | \(0.656416\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −1.00000 | + | 1.73205i | −0.0340010 | + | 0.0588915i | ||||
\(866\) | 8.00000 | 0.271851 | ||||||||
\(867\) | −16.0000 | −0.543388 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.00000 | −0.101768 | ||||||||
\(870\) | 6.00000 | 0.203419 | ||||||||
\(871\) | 15.0000 | − | 25.9808i | 0.508256 | − | 0.880325i | ||||
\(872\) | −12.0000 | −0.406371 | ||||||||
\(873\) | 3.00000 | + | 5.19615i | 0.101535 | + | 0.175863i | ||||
\(874\) | −14.0000 | + | 24.2487i | −0.473557 | + | 0.820225i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.00000 | 0.0675737 | ||||||||
\(877\) | −18.5000 | − | 32.0429i | −0.624701 | − | 1.08201i | −0.988599 | − | 0.150574i | \(-0.951888\pi\) |
0.363898 | − | 0.931439i | \(-0.381446\pi\) | |||||||
\(878\) | 17.5000 | + | 30.3109i | 0.590596 | + | 1.02294i | ||||
\(879\) | −8.00000 | − | 13.8564i | −0.269833 | − | 0.467365i | ||||
\(880\) | 0.500000 | − | 0.866025i | 0.0168550 | − | 0.0291937i | ||||
\(881\) | −10.0000 | − | 17.3205i | −0.336909 | − | 0.583543i | 0.646941 | − | 0.762540i | \(-0.276048\pi\) |
−0.983850 | + | 0.178997i | \(0.942715\pi\) | |||||||
\(882\) | 3.50000 | − | 6.06218i | 0.117851 | − | 0.204124i | ||||
\(883\) | 1.00000 | 0.0336527 | 0.0168263 | − | 0.999858i | \(-0.494644\pi\) | ||||
0.0168263 | + | 0.999858i | \(0.494644\pi\) | |||||||
\(884\) | 6.00000 | 0.201802 | ||||||||
\(885\) | −6.00000 | + | 10.3923i | −0.201688 | + | 0.349334i | ||||
\(886\) | −17.0000 | − | 29.4449i | −0.571126 | − | 0.989220i | ||||
\(887\) | −10.5000 | + | 18.1865i | −0.352555 | + | 0.610644i | −0.986696 | − | 0.162573i | \(-0.948021\pi\) |
0.634141 | + | 0.773217i | \(0.281354\pi\) | |||||||
\(888\) | −3.50000 | − | 6.06218i | −0.117452 | − | 0.203433i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.00000 | − | 3.46410i | −0.0670402 | − | 0.116117i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | −7.00000 | + | 12.1244i | −0.234377 | + | 0.405953i | ||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | −7.00000 | − | 12.1244i | −0.234115 | − | 0.405499i | ||||
\(895\) | −11.0000 | −0.367689 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −42.0000 | −1.40234 | ||||||||
\(898\) | −30.0000 | −1.00111 | ||||||||
\(899\) | 12.0000 | − | 31.1769i | 0.400222 | − | 1.03981i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 4.00000 | 0.133259 | ||||||||
\(902\) | −1.00000 | + | 1.73205i | −0.0332964 | + | 0.0576710i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.50000 | − | 16.4545i | −0.315965 | − | 0.547268i | ||||
\(905\) | −10.0000 | + | 17.3205i | −0.332411 | + | 0.575753i | ||||
\(906\) | 3.50000 | − | 6.06218i | 0.116280 | − | 0.201402i | ||||
\(907\) | 48.0000 | 1.59381 | 0.796907 | − | 0.604102i | \(-0.206468\pi\) | ||||
0.796907 | + | 0.604102i | \(0.206468\pi\) | |||||||
\(908\) | 4.00000 | + | 6.92820i | 0.132745 | + | 0.229920i | ||||
\(909\) | −7.50000 | − | 12.9904i | −0.248759 | − | 0.430864i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.0000 | − | 24.2487i | 0.463841 | − | 0.803396i | −0.535308 | − | 0.844657i | \(-0.679804\pi\) |
0.999148 | + | 0.0412615i | \(0.0131377\pi\) | |||||||
\(912\) | −2.00000 | − | 3.46410i | −0.0662266 | − | 0.114708i | ||||
\(913\) | 8.00000 | − | 13.8564i | 0.264761 | − | 0.458580i | ||||
\(914\) | 32.0000 | 1.05847 | ||||||||
\(915\) | −14.0000 | −0.462826 | ||||||||
\(916\) | −10.0000 | + | 17.3205i | −0.330409 | + | 0.572286i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.500000 | − | 0.866025i | 0.0165025 | − | 0.0285831i | ||||
\(919\) | −12.5000 | − | 21.6506i | −0.412337 | − | 0.714189i | 0.582808 | − | 0.812610i | \(-0.301954\pi\) |
−0.995145 | + | 0.0984214i | \(0.968621\pi\) | |||||||
\(920\) | −3.50000 | − | 6.06218i | −0.115392 | − | 0.199864i | ||||
\(921\) | −8.00000 | − | 13.8564i | −0.263609 | − | 0.456584i | ||||
\(922\) | 33.0000 | 1.08680 | ||||||||
\(923\) | 18.0000 | − | 31.1769i | 0.592477 | − | 1.02620i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.50000 | − | 6.06218i | −0.115079 | − | 0.199323i | ||||
\(926\) | 20.0000 | 0.657241 | ||||||||
\(927\) | 1.00000 | − | 1.73205i | 0.0328443 | − | 0.0568880i | ||||
\(928\) | 6.00000 | 0.196960 | ||||||||
\(929\) | −56.0000 | −1.83730 | −0.918650 | − | 0.395072i | \(-0.870720\pi\) | ||||
−0.918650 | + | 0.395072i | \(0.870720\pi\) | |||||||
\(930\) | 2.00000 | − | 5.19615i | 0.0655826 | − | 0.170389i | ||||
\(931\) | −28.0000 | −0.917663 | ||||||||
\(932\) | 25.0000 | 0.818902 | ||||||||
\(933\) | 3.00000 | − | 5.19615i | 0.0982156 | − | 0.170114i | ||||
\(934\) | 12.0000 | 0.392652 | ||||||||
\(935\) | −0.500000 | − | 0.866025i | −0.0163517 | − | 0.0283221i | ||||
\(936\) | 3.00000 | − | 5.19615i | 0.0980581 | − | 0.169842i | ||||
\(937\) | −23.0000 | + | 39.8372i | −0.751377 | + | 1.30142i | 0.195778 | + | 0.980648i | \(0.437277\pi\) |
−0.947155 | + | 0.320775i | \(0.896057\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.00000 | − | 5.19615i | −0.0979013 | − | 0.169570i | ||||
\(940\) | −1.50000 | − | 2.59808i | −0.0489246 | − | 0.0847399i | ||||
\(941\) | −30.5000 | − | 52.8275i | −0.994272 | − | 1.72213i | −0.589699 | − | 0.807623i | \(-0.700754\pi\) |
−0.404572 | − | 0.914506i | \(-0.632580\pi\) | |||||||
\(942\) | −7.00000 | + | 12.1244i | −0.228072 | + | 0.395033i | ||||
\(943\) | 7.00000 | + | 12.1244i | 0.227951 | + | 0.394823i | ||||
\(944\) | −6.00000 | + | 10.3923i | −0.195283 | + | 0.338241i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.00000 | 0.227590 | ||||||||
\(947\) | −9.00000 | + | 15.5885i | −0.292461 | + | 0.506557i | −0.974391 | − | 0.224860i | \(-0.927807\pi\) |
0.681930 | + | 0.731417i | \(0.261141\pi\) | |||||||
\(948\) | −1.50000 | − | 2.59808i | −0.0487177 | − | 0.0843816i | ||||
\(949\) | 6.00000 | − | 10.3923i | 0.194768 | − | 0.337348i | ||||
\(950\) | −2.00000 | − | 3.46410i | −0.0648886 | − | 0.112390i | ||||
\(951\) | 6.00000 | + | 10.3923i | 0.194563 | + | 0.336994i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 2.00000 | − | 3.46410i | 0.0647524 | − | 0.112154i | ||||
\(955\) | 3.00000 | − | 5.19615i | 0.0970777 | − | 0.168144i | ||||
\(956\) | −9.00000 | − | 15.5885i | −0.291081 | − | 0.504167i | ||||
\(957\) | −6.00000 | −0.193952 | ||||||||
\(958\) | −9.00000 | + | 15.5885i | −0.290777 | + | 0.503640i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −23.0000 | − | 20.7846i | −0.741935 | − | 0.670471i | ||||
\(962\) | −42.0000 | −1.35413 | ||||||||
\(963\) | −4.00000 | −0.128898 | ||||||||
\(964\) | −9.00000 | + | 15.5885i | −0.289870 | + | 0.502070i | ||||
\(965\) | 10.0000 | 0.321911 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0000 | − | 48.4974i | 0.900419 | − | 1.55957i | 0.0734686 | − | 0.997298i | \(-0.476593\pi\) |
0.826951 | − | 0.562274i | \(-0.190074\pi\) | |||||||
\(968\) | 5.00000 | − | 8.66025i | 0.160706 | − | 0.278351i | ||||
\(969\) | −4.00000 | −0.128499 | ||||||||
\(970\) | 3.00000 | + | 5.19615i | 0.0963242 | + | 0.166838i | ||||
\(971\) | 16.5000 | + | 28.5788i | 0.529510 | + | 0.917139i | 0.999408 | + | 0.0344175i | \(0.0109576\pi\) |
−0.469897 | + | 0.882721i | \(0.655709\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −16.0000 | − | 27.7128i | −0.512673 | − | 0.887976i | ||||
\(975\) | 3.00000 | − | 5.19615i | 0.0960769 | − | 0.166410i | ||||
\(976\) | −14.0000 | −0.448129 | ||||||||
\(977\) | −30.0000 | −0.959785 | −0.479893 | − | 0.877327i | \(-0.659324\pi\) | ||||
−0.479893 | + | 0.877327i | \(0.659324\pi\) | |||||||
\(978\) | −2.50000 | + | 4.33013i | −0.0799412 | + | 0.138462i | ||||
\(979\) | 2.00000 | + | 3.46410i | 0.0639203 | + | 0.110713i | ||||
\(980\) | 3.50000 | − | 6.06218i | 0.111803 | − | 0.193649i | ||||
\(981\) | 6.00000 | + | 10.3923i | 0.191565 | + | 0.331801i | ||||
\(982\) | 14.5000 | + | 25.1147i | 0.462714 | + | 0.801443i | ||||
\(983\) | 12.0000 | + | 20.7846i | 0.382741 | + | 0.662926i | 0.991453 | − | 0.130465i | \(-0.0416470\pi\) |
−0.608712 | + | 0.793391i | \(0.708314\pi\) | |||||||
\(984\) | −2.00000 | −0.0637577 | ||||||||
\(985\) | −4.00000 | + | 6.92820i | −0.127451 | + | 0.220751i | ||||
\(986\) | 3.00000 | − | 5.19615i | 0.0955395 | − | 0.165479i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −24.0000 | −0.763542 | ||||||||
\(989\) | 24.5000 | − | 42.4352i | 0.779055 | − | 1.34936i | ||||
\(990\) | −1.00000 | −0.0317821 | ||||||||
\(991\) | −40.0000 | −1.27064 | −0.635321 | − | 0.772248i | \(-0.719132\pi\) | ||||
−0.635321 | + | 0.772248i | \(0.719132\pi\) | |||||||
\(992\) | 2.00000 | − | 5.19615i | 0.0635001 | − | 0.164978i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | + | 13.8564i | −0.253617 | + | 0.439278i | ||||
\(996\) | 16.0000 | 0.506979 | ||||||||
\(997\) | 9.00000 | + | 15.5885i | 0.285033 | + | 0.493691i | 0.972617 | − | 0.232413i | \(-0.0746622\pi\) |
−0.687584 | + | 0.726105i | \(0.741329\pi\) | |||||||
\(998\) | 10.0000 | − | 17.3205i | 0.316544 | − | 0.548271i | ||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(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 | 930.2.i.e.811.1 | yes | 2 | |
31.25 | even | 3 | inner | 930.2.i.e.211.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.e.211.1 | ✓ | 2 | 31.25 | even | 3 | inner | |
930.2.i.e.811.1 | yes | 2 | 1.1 | even | 1 | trivial |