Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(121,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 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("630.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.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: | \(5.03057532734\) |
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 | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.121 |
Dual form | 630.2.i.d.151.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.50000 | + | 0.866025i | 0.866025 | + | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.50000 | + | 2.59808i | 0.500000 | + | 0.866025i | ||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | 1.50000 | + | 0.866025i | 0.433013 | + | 0.250000i | ||||
\(13\) | 2.00000 | − | 3.46410i | 0.554700 | − | 0.960769i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) |
0.997927 | − | 0.0643593i | \(-0.0205004\pi\) | |||||||
\(14\) | −2.00000 | + | 1.73205i | −0.534522 | + | 0.462910i | ||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.50000 | + | 2.59808i | 0.353553 | + | 0.612372i | ||||
\(19\) | −1.00000 | + | 1.73205i | −0.229416 | + | 0.397360i | −0.957635 | − | 0.287984i | \(-0.907015\pi\) |
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0.500000 | + | 0.866025i | 0.111803 | + | 0.193649i | ||||
\(21\) | −4.50000 | + | 0.866025i | −0.981981 | + | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 1.50000 | + | 0.866025i | 0.306186 | + | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.00000 | − | 3.46410i | 0.392232 | − | 0.679366i | ||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | −2.00000 | + | 1.73205i | −0.377964 | + | 0.327327i | ||||
\(29\) | −3.00000 | − | 5.19615i | −0.557086 | − | 0.964901i | −0.997738 | − | 0.0672232i | \(-0.978586\pi\) |
0.440652 | − | 0.897678i | \(-0.354747\pi\) | |||||||
\(30\) | 1.73205i | 0.316228i | ||||||||
\(31\) | 2.00000 | 0.359211 | 0.179605 | − | 0.983739i | \(-0.442518\pi\) | ||||
0.179605 | + | 0.983739i | \(0.442518\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.50000 | − | 0.866025i | −0.422577 | − | 0.146385i | ||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | −1.00000 | + | 1.73205i | −0.164399 | + | 0.284747i | −0.936442 | − | 0.350823i | \(-0.885902\pi\) |
0.772043 | + | 0.635571i | \(0.219235\pi\) | |||||||
\(38\) | −1.00000 | + | 1.73205i | −0.162221 | + | 0.280976i | ||||
\(39\) | 6.00000 | − | 3.46410i | 0.960769 | − | 0.554700i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 3.00000 | − | 5.19615i | 0.468521 | − | 0.811503i | −0.530831 | − | 0.847477i | \(-0.678120\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | −4.50000 | + | 0.866025i | −0.694365 | + | 0.133631i | ||||
\(43\) | −5.50000 | − | 9.52628i | −0.838742 | − | 1.45274i | −0.890947 | − | 0.454108i | \(-0.849958\pi\) |
0.0522047 | − | 0.998636i | \(-0.483375\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | + | 2.59808i | −0.223607 | + | 0.387298i | ||||
\(46\) | 1.50000 | + | 2.59808i | 0.221163 | + | 0.383065i | ||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | 1.50000 | + | 0.866025i | 0.216506 | + | 0.125000i | ||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | −0.500000 | + | 0.866025i | −0.0707107 | + | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | − | 3.46410i | 0.277350 | − | 0.480384i | ||||
\(53\) | −3.00000 | − | 5.19615i | −0.412082 | − | 0.713746i | 0.583036 | − | 0.812447i | \(-0.301865\pi\) |
−0.995117 | + | 0.0987002i | \(0.968532\pi\) | |||||||
\(54\) | 5.19615i | 0.707107i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | −3.00000 | + | 1.73205i | −0.397360 | + | 0.229416i | ||||
\(58\) | −3.00000 | − | 5.19615i | −0.393919 | − | 0.682288i | ||||
\(59\) | 12.0000 | 1.56227 | 0.781133 | − | 0.624364i | \(-0.214642\pi\) | ||||
0.781133 | + | 0.624364i | \(0.214642\pi\) | |||||||
\(60\) | 1.73205i | 0.223607i | ||||||||
\(61\) | −7.00000 | −0.896258 | −0.448129 | − | 0.893969i | \(-0.647910\pi\) | ||||
−0.448129 | + | 0.893969i | \(0.647910\pi\) | |||||||
\(62\) | 2.00000 | 0.254000 | ||||||||
\(63\) | −7.50000 | − | 2.59808i | −0.944911 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.19615i | 0.625543i | ||||||||
\(70\) | −2.50000 | − | 0.866025i | −0.298807 | − | 0.103510i | ||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 1.50000 | + | 2.59808i | 0.176777 | + | 0.306186i | ||||
\(73\) | −1.00000 | − | 1.73205i | −0.117041 | − | 0.202721i | 0.801553 | − | 0.597924i | \(-0.204008\pi\) |
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | −1.00000 | + | 1.73205i | −0.116248 | + | 0.201347i | ||||
\(75\) | −1.50000 | + | 0.866025i | −0.173205 | + | 0.100000i | ||||
\(76\) | −1.00000 | + | 1.73205i | −0.114708 | + | 0.198680i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.00000 | − | 3.46410i | 0.679366 | − | 0.392232i | ||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 3.00000 | − | 5.19615i | 0.331295 | − | 0.573819i | ||||
\(83\) | 6.00000 | + | 10.3923i | 0.658586 | + | 1.14070i | 0.980982 | + | 0.194099i | \(0.0621783\pi\) |
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(84\) | −4.50000 | + | 0.866025i | −0.490990 | + | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.50000 | − | 9.52628i | −0.593080 | − | 1.02725i | ||||
\(87\) | − | 10.3923i | − | 1.11417i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | − | 12.9904i | 0.794998 | − | 1.37698i | −0.127842 | − | 0.991795i | \(-0.540805\pi\) |
0.922840 | − | 0.385183i | \(-0.125862\pi\) | |||||||
\(90\) | −1.50000 | + | 2.59808i | −0.158114 | + | 0.273861i | ||||
\(91\) | 2.00000 | + | 10.3923i | 0.209657 | + | 1.08941i | ||||
\(92\) | 1.50000 | + | 2.59808i | 0.156386 | + | 0.270868i | ||||
\(93\) | 3.00000 | + | 1.73205i | 0.311086 | + | 0.179605i | ||||
\(94\) | 3.00000 | 0.309426 | ||||||||
\(95\) | −2.00000 | −0.205196 | ||||||||
\(96\) | 1.50000 | + | 0.866025i | 0.153093 | + | 0.0883883i | ||||
\(97\) | 5.00000 | + | 8.66025i | 0.507673 | + | 0.879316i | 0.999961 | + | 0.00888289i | \(0.00282755\pi\) |
−0.492287 | + | 0.870433i | \(0.663839\pi\) | |||||||
\(98\) | 1.00000 | − | 6.92820i | 0.101015 | − | 0.699854i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | −1.50000 | + | 2.59808i | −0.149256 | + | 0.258518i | −0.930953 | − | 0.365140i | \(-0.881021\pi\) |
0.781697 | + | 0.623658i | \(0.214354\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.50000 | − | 14.7224i | −0.837530 | − | 1.45064i | −0.891954 | − | 0.452126i | \(-0.850666\pi\) |
0.0544240 | − | 0.998518i | \(-0.482668\pi\) | |||||||
\(104\) | 2.00000 | − | 3.46410i | 0.196116 | − | 0.339683i | ||||
\(105\) | −3.00000 | − | 3.46410i | −0.292770 | − | 0.338062i | ||||
\(106\) | −3.00000 | − | 5.19615i | −0.291386 | − | 0.504695i | ||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 5.19615i | 0.500000i | ||||||||
\(109\) | −1.00000 | − | 1.73205i | −0.0957826 | − | 0.165900i | 0.814152 | − | 0.580651i | \(-0.197202\pi\) |
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | + | 1.73205i | −0.284747 | + | 0.164399i | ||||
\(112\) | −2.00000 | + | 1.73205i | −0.188982 | + | 0.163663i | ||||
\(113\) | 3.00000 | − | 5.19615i | 0.282216 | − | 0.488813i | −0.689714 | − | 0.724082i | \(-0.742264\pi\) |
0.971930 | + | 0.235269i | \(0.0755971\pi\) | |||||||
\(114\) | −3.00000 | + | 1.73205i | −0.280976 | + | 0.162221i | ||||
\(115\) | −1.50000 | + | 2.59808i | −0.139876 | + | 0.242272i | ||||
\(116\) | −3.00000 | − | 5.19615i | −0.278543 | − | 0.482451i | ||||
\(117\) | 12.0000 | 1.10940 | ||||||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.73205i | 0.158114i | ||||||||
\(121\) | 5.50000 | + | 9.52628i | 0.500000 | + | 0.866025i | ||||
\(122\) | −7.00000 | −0.633750 | ||||||||
\(123\) | 9.00000 | − | 5.19615i | 0.811503 | − | 0.468521i | ||||
\(124\) | 2.00000 | 0.179605 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −7.50000 | − | 2.59808i | −0.668153 | − | 0.231455i | ||||
\(127\) | −13.0000 | −1.15356 | −0.576782 | − | 0.816898i | \(-0.695692\pi\) | ||||
−0.576782 | + | 0.816898i | \(0.695692\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | − | 19.0526i | − | 1.67748i | ||||||
\(130\) | 4.00000 | 0.350823 | ||||||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | − | 5.19615i | −0.0867110 | − | 0.450564i | ||||
\(134\) | −7.00000 | −0.604708 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | + | 10.3923i | −0.512615 | + | 0.887875i | 0.487278 | + | 0.873247i | \(0.337990\pi\) |
−0.999893 | + | 0.0146279i | \(0.995344\pi\) | |||||||
\(138\) | 5.19615i | 0.442326i | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | −2.50000 | − | 0.866025i | −0.211289 | − | 0.0731925i | ||||
\(141\) | 4.50000 | + | 2.59808i | 0.378968 | + | 0.218797i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.50000 | + | 2.59808i | 0.125000 | + | 0.216506i | ||||
\(145\) | 3.00000 | − | 5.19615i | 0.249136 | − | 0.431517i | ||||
\(146\) | −1.00000 | − | 1.73205i | −0.0827606 | − | 0.143346i | ||||
\(147\) | 7.50000 | − | 9.52628i | 0.618590 | − | 0.785714i | ||||
\(148\) | −1.00000 | + | 1.73205i | −0.0821995 | + | 0.142374i | ||||
\(149\) | −7.50000 | − | 12.9904i | −0.614424 | − | 1.06421i | −0.990485 | − | 0.137619i | \(-0.956055\pi\) |
0.376061 | − | 0.926595i | \(-0.377278\pi\) | |||||||
\(150\) | −1.50000 | + | 0.866025i | −0.122474 | + | 0.0707107i | ||||
\(151\) | −1.00000 | + | 1.73205i | −0.0813788 | + | 0.140952i | −0.903842 | − | 0.427865i | \(-0.859266\pi\) |
0.822464 | + | 0.568818i | \(0.192599\pi\) | |||||||
\(152\) | −1.00000 | + | 1.73205i | −0.0811107 | + | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | + | 1.73205i | 0.0803219 | + | 0.139122i | ||||
\(156\) | 6.00000 | − | 3.46410i | 0.480384 | − | 0.277350i | ||||
\(157\) | −22.0000 | −1.75579 | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||||
−0.877896 | + | 0.478852i | \(0.841053\pi\) | |||||||
\(158\) | −4.00000 | −0.318223 | ||||||||
\(159\) | − | 10.3923i | − | 0.824163i | ||||||
\(160\) | 0.500000 | + | 0.866025i | 0.0395285 | + | 0.0684653i | ||||
\(161\) | −7.50000 | − | 2.59808i | −0.591083 | − | 0.204757i | ||||
\(162\) | −4.50000 | + | 7.79423i | −0.353553 | + | 0.612372i | ||||
\(163\) | −10.0000 | + | 17.3205i | −0.783260 | + | 1.35665i | 0.146772 | + | 0.989170i | \(0.453112\pi\) |
−0.930033 | + | 0.367477i | \(0.880222\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 1.50000 | − | 2.59808i | 0.116073 | − | 0.201045i | −0.802135 | − | 0.597143i | \(-0.796303\pi\) |
0.918208 | + | 0.396098i | \(0.129636\pi\) | |||||||
\(168\) | −4.50000 | + | 0.866025i | −0.347183 | + | 0.0668153i | ||||
\(169\) | −1.50000 | − | 2.59808i | −0.115385 | − | 0.199852i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | −5.50000 | − | 9.52628i | −0.419371 | − | 0.726372i | ||||
\(173\) | 24.0000 | 1.82469 | 0.912343 | − | 0.409426i | \(-0.134271\pi\) | ||||
0.912343 | + | 0.409426i | \(0.134271\pi\) | |||||||
\(174\) | − | 10.3923i | − | 0.787839i | ||||||
\(175\) | −0.500000 | − | 2.59808i | −0.0377964 | − | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 18.0000 | + | 10.3923i | 1.35296 | + | 0.781133i | ||||
\(178\) | 7.50000 | − | 12.9904i | 0.562149 | − | 0.973670i | ||||
\(179\) | 9.00000 | + | 15.5885i | 0.672692 | + | 1.16514i | 0.977138 | + | 0.212607i | \(0.0681952\pi\) |
−0.304446 | + | 0.952529i | \(0.598471\pi\) | |||||||
\(180\) | −1.50000 | + | 2.59808i | −0.111803 | + | 0.193649i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 2.00000 | + | 10.3923i | 0.148250 | + | 0.770329i | ||||
\(183\) | −10.5000 | − | 6.06218i | −0.776182 | − | 0.448129i | ||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | 3.00000 | + | 1.73205i | 0.219971 | + | 0.127000i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 3.00000 | 0.218797 | ||||||||
\(189\) | −9.00000 | − | 10.3923i | −0.654654 | − | 0.755929i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 18.0000 | 1.30243 | 0.651217 | − | 0.758891i | \(-0.274259\pi\) | ||||
0.651217 | + | 0.758891i | \(0.274259\pi\) | |||||||
\(192\) | 1.50000 | + | 0.866025i | 0.108253 | + | 0.0625000i | ||||
\(193\) | −22.0000 | −1.58359 | −0.791797 | − | 0.610784i | \(-0.790854\pi\) | ||||
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | 5.00000 | + | 8.66025i | 0.358979 | + | 0.621770i | ||||
\(195\) | 6.00000 | + | 3.46410i | 0.429669 | + | 0.248069i | ||||
\(196\) | 1.00000 | − | 6.92820i | 0.0714286 | − | 0.494872i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −10.5000 | − | 6.06218i | −0.740613 | − | 0.427593i | ||||
\(202\) | −1.50000 | + | 2.59808i | −0.105540 | + | 0.182800i | ||||
\(203\) | 15.0000 | + | 5.19615i | 1.05279 | + | 0.364698i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.00000 | 0.419058 | ||||||||
\(206\) | −8.50000 | − | 14.7224i | −0.592223 | − | 1.02576i | ||||
\(207\) | −4.50000 | + | 7.79423i | −0.312772 | + | 0.541736i | ||||
\(208\) | 2.00000 | − | 3.46410i | 0.138675 | − | 0.240192i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.00000 | − | 3.46410i | −0.207020 | − | 0.239046i | ||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | −3.00000 | − | 5.19615i | −0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.50000 | − | 9.52628i | 0.375097 | − | 0.649687i | ||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | −4.00000 | + | 3.46410i | −0.271538 | + | 0.235159i | ||||
\(218\) | −1.00000 | − | 1.73205i | −0.0677285 | − | 0.117309i | ||||
\(219\) | − | 3.46410i | − | 0.234082i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.00000 | + | 1.73205i | −0.201347 | + | 0.116248i | ||||
\(223\) | 9.50000 | + | 16.4545i | 0.636167 | + | 1.10187i | 0.986267 | + | 0.165161i | \(0.0528144\pi\) |
−0.350100 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(224\) | −2.00000 | + | 1.73205i | −0.133631 | + | 0.115728i | ||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | −12.0000 | + | 20.7846i | −0.796468 | + | 1.37952i | 0.125435 | + | 0.992102i | \(0.459967\pi\) |
−0.921903 | + | 0.387421i | \(0.873366\pi\) | |||||||
\(228\) | −3.00000 | + | 1.73205i | −0.198680 | + | 0.114708i | ||||
\(229\) | −14.5000 | − | 25.1147i | −0.958187 | − | 1.65963i | −0.726900 | − | 0.686743i | \(-0.759040\pi\) |
−0.231287 | − | 0.972886i | \(-0.574293\pi\) | |||||||
\(230\) | −1.50000 | + | 2.59808i | −0.0989071 | + | 0.171312i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.00000 | − | 5.19615i | −0.196960 | − | 0.341144i | ||||
\(233\) | −9.00000 | + | 15.5885i | −0.589610 | + | 1.02123i | 0.404674 | + | 0.914461i | \(0.367385\pi\) |
−0.994283 | + | 0.106773i | \(0.965948\pi\) | |||||||
\(234\) | 12.0000 | 0.784465 | ||||||||
\(235\) | 1.50000 | + | 2.59808i | 0.0978492 | + | 0.169480i | ||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | −6.00000 | − | 3.46410i | −0.389742 | − | 0.225018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.0000 | − | 20.7846i | 0.776215 | − | 1.34444i | −0.157893 | − | 0.987456i | \(-0.550470\pi\) |
0.934109 | − | 0.356988i | \(-0.116196\pi\) | |||||||
\(240\) | 1.73205i | 0.111803i | ||||||||
\(241\) | 9.50000 | − | 16.4545i | 0.611949 | − | 1.05993i | −0.378963 | − | 0.925412i | \(-0.623719\pi\) |
0.990912 | − | 0.134515i | \(-0.0429475\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | −13.5000 | + | 7.79423i | −0.866025 | + | 0.500000i | ||||
\(244\) | −7.00000 | −0.448129 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | 9.00000 | − | 5.19615i | 0.573819 | − | 0.331295i | ||||
\(247\) | 4.00000 | + | 6.92820i | 0.254514 | + | 0.440831i | ||||
\(248\) | 2.00000 | 0.127000 | ||||||||
\(249\) | 20.7846i | 1.31717i | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | −7.50000 | − | 2.59808i | −0.472456 | − | 0.163663i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −13.0000 | −0.815693 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 9.00000 | + | 15.5885i | 0.561405 | + | 0.972381i | 0.997374 | + | 0.0724199i | \(0.0230722\pi\) |
−0.435970 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(258\) | − | 19.0526i | − | 1.18616i | ||||||
\(259\) | −1.00000 | − | 5.19615i | −0.0621370 | − | 0.322873i | ||||
\(260\) | 4.00000 | 0.248069 | ||||||||
\(261\) | 9.00000 | − | 15.5885i | 0.557086 | − | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.50000 | + | 7.79423i | −0.277482 | + | 0.480613i | −0.970758 | − | 0.240059i | \(-0.922833\pi\) |
0.693276 | + | 0.720672i | \(0.256167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.00000 | − | 5.19615i | 0.184289 | − | 0.319197i | ||||
\(266\) | −1.00000 | − | 5.19615i | −0.0613139 | − | 0.318597i | ||||
\(267\) | 22.5000 | − | 12.9904i | 1.37698 | − | 0.794998i | ||||
\(268\) | −7.00000 | −0.427593 | ||||||||
\(269\) | 10.5000 | + | 18.1865i | 0.640196 | + | 1.10885i | 0.985389 | + | 0.170321i | \(0.0544803\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(270\) | −4.50000 | + | 2.59808i | −0.273861 | + | 0.158114i | ||||
\(271\) | −10.0000 | + | 17.3205i | −0.607457 | + | 1.05215i | 0.384201 | + | 0.923249i | \(0.374477\pi\) |
−0.991658 | + | 0.128897i | \(0.958856\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.00000 | + | 17.3205i | −0.363137 | + | 1.04828i | ||||
\(274\) | −6.00000 | + | 10.3923i | −0.362473 | + | 0.627822i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 5.19615i | 0.312772i | ||||||||
\(277\) | −16.0000 | + | 27.7128i | −0.961347 | + | 1.66510i | −0.242222 | + | 0.970221i | \(0.577876\pi\) |
−0.719125 | + | 0.694881i | \(0.755457\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | 3.00000 | + | 5.19615i | 0.179605 | + | 0.311086i | ||||
\(280\) | −2.50000 | − | 0.866025i | −0.149404 | − | 0.0517549i | ||||
\(281\) | −10.5000 | − | 18.1865i | −0.626377 | − | 1.08492i | −0.988273 | − | 0.152699i | \(-0.951204\pi\) |
0.361895 | − | 0.932219i | \(-0.382130\pi\) | |||||||
\(282\) | 4.50000 | + | 2.59808i | 0.267971 | + | 0.154713i | ||||
\(283\) | 11.0000 | 0.653882 | 0.326941 | − | 0.945045i | \(-0.393982\pi\) | ||||
0.326941 | + | 0.945045i | \(0.393982\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −3.00000 | − | 1.73205i | −0.177705 | − | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.00000 | + | 15.5885i | 0.177084 | + | 0.920158i | ||||
\(288\) | 1.50000 | + | 2.59808i | 0.0883883 | + | 0.153093i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 3.00000 | − | 5.19615i | 0.176166 | − | 0.305129i | ||||
\(291\) | 17.3205i | 1.01535i | ||||||||
\(292\) | −1.00000 | − | 1.73205i | −0.0585206 | − | 0.101361i | ||||
\(293\) | 15.0000 | − | 25.9808i | 0.876309 | − | 1.51781i | 0.0209480 | − | 0.999781i | \(-0.493332\pi\) |
0.855361 | − | 0.518032i | \(-0.173335\pi\) | |||||||
\(294\) | 7.50000 | − | 9.52628i | 0.437409 | − | 0.555584i | ||||
\(295\) | 6.00000 | + | 10.3923i | 0.349334 | + | 0.605063i | ||||
\(296\) | −1.00000 | + | 1.73205i | −0.0581238 | + | 0.100673i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.50000 | − | 12.9904i | −0.434463 | − | 0.752513i | ||||
\(299\) | 12.0000 | 0.693978 | ||||||||
\(300\) | −1.50000 | + | 0.866025i | −0.0866025 | + | 0.0500000i | ||||
\(301\) | 27.5000 | + | 9.52628i | 1.58507 | + | 0.549086i | ||||
\(302\) | −1.00000 | + | 1.73205i | −0.0575435 | + | 0.0996683i | ||||
\(303\) | −4.50000 | + | 2.59808i | −0.258518 | + | 0.149256i | ||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | −3.50000 | − | 6.06218i | −0.200409 | − | 0.347119i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 20.0000 | 1.14146 | 0.570730 | − | 0.821138i | \(-0.306660\pi\) | ||||
0.570730 | + | 0.821138i | \(0.306660\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 29.4449i | − | 1.67506i | ||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 6.00000 | − | 3.46410i | 0.339683 | − | 0.196116i | ||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | −22.0000 | −1.24153 | ||||||||
\(315\) | −1.50000 | − | 7.79423i | −0.0845154 | − | 0.439155i | ||||
\(316\) | −4.00000 | −0.225018 | ||||||||
\(317\) | −18.0000 | −1.01098 | −0.505490 | − | 0.862832i | \(-0.668688\pi\) | ||||
−0.505490 | + | 0.862832i | \(0.668688\pi\) | |||||||
\(318\) | − | 10.3923i | − | 0.582772i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0.500000 | + | 0.866025i | 0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.50000 | − | 2.59808i | −0.417959 | − | 0.144785i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.50000 | + | 7.79423i | −0.250000 | + | 0.433013i | ||||
\(325\) | 2.00000 | + | 3.46410i | 0.110940 | + | 0.192154i | ||||
\(326\) | −10.0000 | + | 17.3205i | −0.553849 | + | 0.959294i | ||||
\(327\) | − | 3.46410i | − | 0.191565i | ||||||
\(328\) | 3.00000 | − | 5.19615i | 0.165647 | − | 0.286910i | ||||
\(329\) | −6.00000 | + | 5.19615i | −0.330791 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.0000 | 1.42909 | 0.714545 | − | 0.699590i | \(-0.246634\pi\) | ||||
0.714545 | + | 0.699590i | \(0.246634\pi\) | |||||||
\(332\) | 6.00000 | + | 10.3923i | 0.329293 | + | 0.570352i | ||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | −3.50000 | − | 6.06218i | −0.191225 | − | 0.331212i | ||||
\(336\) | −4.50000 | + | 0.866025i | −0.245495 | + | 0.0472456i | ||||
\(337\) | −16.0000 | + | 27.7128i | −0.871576 | + | 1.50961i | −0.0112091 | + | 0.999937i | \(0.503568\pi\) |
−0.860366 | + | 0.509676i | \(0.829765\pi\) | |||||||
\(338\) | −1.50000 | − | 2.59808i | −0.0815892 | − | 0.141317i | ||||
\(339\) | 9.00000 | − | 5.19615i | 0.488813 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −6.00000 | −0.324443 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −5.50000 | − | 9.52628i | −0.296540 | − | 0.513623i | ||||
\(345\) | −4.50000 | + | 2.59808i | −0.242272 | + | 0.139876i | ||||
\(346\) | 24.0000 | 1.29025 | ||||||||
\(347\) | 27.0000 | 1.44944 | 0.724718 | − | 0.689046i | \(-0.241970\pi\) | ||||
0.724718 | + | 0.689046i | \(0.241970\pi\) | |||||||
\(348\) | − | 10.3923i | − | 0.557086i | ||||||
\(349\) | 3.50000 | + | 6.06218i | 0.187351 | + | 0.324501i | 0.944366 | − | 0.328896i | \(-0.106677\pi\) |
−0.757015 | + | 0.653397i | \(0.773343\pi\) | |||||||
\(350\) | −0.500000 | − | 2.59808i | −0.0267261 | − | 0.138873i | ||||
\(351\) | 18.0000 | + | 10.3923i | 0.960769 | + | 0.554700i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 18.0000 | + | 10.3923i | 0.956689 | + | 0.552345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.50000 | − | 12.9904i | 0.397499 | − | 0.688489i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.00000 | + | 15.5885i | 0.475665 | + | 0.823876i | ||||
\(359\) | −3.00000 | + | 5.19615i | −0.158334 | + | 0.274242i | −0.934268 | − | 0.356572i | \(-0.883946\pi\) |
0.775934 | + | 0.630814i | \(0.217279\pi\) | |||||||
\(360\) | −1.50000 | + | 2.59808i | −0.0790569 | + | 0.136931i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 2.00000 | 0.105118 | ||||||||
\(363\) | 19.0526i | 1.00000i | ||||||||
\(364\) | 2.00000 | + | 10.3923i | 0.104828 | + | 0.544705i | ||||
\(365\) | 1.00000 | − | 1.73205i | 0.0523424 | − | 0.0906597i | ||||
\(366\) | −10.5000 | − | 6.06218i | −0.548844 | − | 0.316875i | ||||
\(367\) | −8.50000 | + | 14.7224i | −0.443696 | + | 0.768505i | −0.997960 | − | 0.0638362i | \(-0.979666\pi\) |
0.554264 | + | 0.832341i | \(0.313000\pi\) | |||||||
\(368\) | 1.50000 | + | 2.59808i | 0.0781929 | + | 0.135434i | ||||
\(369\) | 18.0000 | 0.937043 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | 15.0000 | + | 5.19615i | 0.778761 | + | 0.269771i | ||||
\(372\) | 3.00000 | + | 1.73205i | 0.155543 | + | 0.0898027i | ||||
\(373\) | −7.00000 | − | 12.1244i | −0.362446 | − | 0.627775i | 0.625917 | − | 0.779890i | \(-0.284725\pi\) |
−0.988363 | + | 0.152115i | \(0.951392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | − | 0.866025i | −0.0774597 | − | 0.0447214i | ||||
\(376\) | 3.00000 | 0.154713 | ||||||||
\(377\) | −24.0000 | −1.23606 | ||||||||
\(378\) | −9.00000 | − | 10.3923i | −0.462910 | − | 0.534522i | ||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | −2.00000 | −0.102598 | ||||||||
\(381\) | −19.5000 | − | 11.2583i | −0.999015 | − | 0.576782i | ||||
\(382\) | 18.0000 | 0.920960 | ||||||||
\(383\) | 10.5000 | + | 18.1865i | 0.536525 | + | 0.929288i | 0.999088 | + | 0.0427020i | \(0.0135966\pi\) |
−0.462563 | + | 0.886586i | \(0.653070\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0000 | −1.11977 | ||||||||
\(387\) | 16.5000 | − | 28.5788i | 0.838742 | − | 1.45274i | ||||
\(388\) | 5.00000 | + | 8.66025i | 0.253837 | + | 0.439658i | ||||
\(389\) | −13.5000 | + | 23.3827i | −0.684477 | + | 1.18555i | 0.289124 | + | 0.957292i | \(0.406636\pi\) |
−0.973601 | + | 0.228257i | \(0.926697\pi\) | |||||||
\(390\) | 6.00000 | + | 3.46410i | 0.303822 | + | 0.175412i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.0000 | −0.604551 | ||||||||
\(395\) | −2.00000 | − | 3.46410i | −0.100631 | − | 0.174298i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0000 | − | 24.2487i | 0.702640 | − | 1.21701i | −0.264897 | − | 0.964277i | \(-0.585338\pi\) |
0.967537 | − | 0.252731i | \(-0.0813288\pi\) | |||||||
\(398\) | 2.00000 | + | 3.46410i | 0.100251 | + | 0.173640i | ||||
\(399\) | 3.00000 | − | 8.66025i | 0.150188 | − | 0.433555i | ||||
\(400\) | −0.500000 | + | 0.866025i | −0.0250000 | + | 0.0433013i | ||||
\(401\) | −7.50000 | − | 12.9904i | −0.374532 | − | 0.648709i | 0.615725 | − | 0.787961i | \(-0.288863\pi\) |
−0.990257 | + | 0.139253i | \(0.955530\pi\) | |||||||
\(402\) | −10.5000 | − | 6.06218i | −0.523692 | − | 0.302354i | ||||
\(403\) | 4.00000 | − | 6.92820i | 0.199254 | − | 0.345118i | ||||
\(404\) | −1.50000 | + | 2.59808i | −0.0746278 | + | 0.129259i | ||||
\(405\) | −9.00000 | −0.447214 | ||||||||
\(406\) | 15.0000 | + | 5.19615i | 0.744438 | + | 0.257881i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.00000 | −0.0494468 | −0.0247234 | − | 0.999694i | \(-0.507871\pi\) | ||||
−0.0247234 | + | 0.999694i | \(0.507871\pi\) | |||||||
\(410\) | 6.00000 | 0.296319 | ||||||||
\(411\) | −18.0000 | + | 10.3923i | −0.887875 | + | 0.512615i | ||||
\(412\) | −8.50000 | − | 14.7224i | −0.418765 | − | 0.725322i | ||||
\(413\) | −24.0000 | + | 20.7846i | −1.18096 | + | 1.02274i | ||||
\(414\) | −4.50000 | + | 7.79423i | −0.221163 | + | 0.383065i | ||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | 6.00000 | − | 3.46410i | 0.293821 | − | 0.169638i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.0000 | + | 31.1769i | −0.879358 | + | 1.52309i | −0.0273103 | + | 0.999627i | \(0.508694\pi\) |
−0.852047 | + | 0.523465i | \(0.824639\pi\) | |||||||
\(420\) | −3.00000 | − | 3.46410i | −0.146385 | − | 0.169031i | ||||
\(421\) | −8.50000 | − | 14.7224i | −0.414265 | − | 0.717527i | 0.581086 | − | 0.813842i | \(-0.302628\pi\) |
−0.995351 | + | 0.0963145i | \(0.969295\pi\) | |||||||
\(422\) | −4.00000 | + | 6.92820i | −0.194717 | + | 0.337260i | ||||
\(423\) | 4.50000 | + | 7.79423i | 0.218797 | + | 0.378968i | ||||
\(424\) | −3.00000 | − | 5.19615i | −0.145693 | − | 0.252347i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.0000 | − | 12.1244i | 0.677507 | − | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.50000 | − | 9.52628i | 0.265234 | − | 0.459398i | ||||
\(431\) | −15.0000 | − | 25.9808i | −0.722525 | − | 1.25145i | −0.959985 | − | 0.280052i | \(-0.909648\pi\) |
0.237460 | − | 0.971397i | \(-0.423685\pi\) | |||||||
\(432\) | 5.19615i | 0.250000i | ||||||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | −4.00000 | + | 3.46410i | −0.192006 | + | 0.166282i | ||||
\(435\) | 9.00000 | − | 5.19615i | 0.431517 | − | 0.249136i | ||||
\(436\) | −1.00000 | − | 1.73205i | −0.0478913 | − | 0.0829502i | ||||
\(437\) | −6.00000 | −0.287019 | ||||||||
\(438\) | − | 3.46410i | − | 0.165521i | ||||||
\(439\) | 8.00000 | 0.381819 | 0.190910 | − | 0.981608i | \(-0.438856\pi\) | ||||
0.190910 | + | 0.981608i | \(0.438856\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | − | 7.79423i | 0.928571 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | −3.00000 | + | 1.73205i | −0.142374 | + | 0.0821995i | ||||
\(445\) | 15.0000 | 0.711068 | ||||||||
\(446\) | 9.50000 | + | 16.4545i | 0.449838 | + | 0.779142i | ||||
\(447\) | − | 25.9808i | − | 1.22885i | ||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 15.0000 | 0.707894 | 0.353947 | − | 0.935266i | \(-0.384839\pi\) | ||||
0.353947 | + | 0.935266i | \(0.384839\pi\) | |||||||
\(450\) | −3.00000 | −0.141421 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | −3.00000 | + | 1.73205i | −0.140952 | + | 0.0813788i | ||||
\(454\) | −12.0000 | + | 20.7846i | −0.563188 | + | 0.975470i | ||||
\(455\) | −8.00000 | + | 6.92820i | −0.375046 | + | 0.324799i | ||||
\(456\) | −3.00000 | + | 1.73205i | −0.140488 | + | 0.0811107i | ||||
\(457\) | 26.0000 | 1.21623 | 0.608114 | − | 0.793849i | \(-0.291926\pi\) | ||||
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | −14.5000 | − | 25.1147i | −0.677541 | − | 1.17353i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.50000 | + | 2.59808i | −0.0699379 | + | 0.121136i | ||||
\(461\) | −13.5000 | − | 23.3827i | −0.628758 | − | 1.08904i | −0.987801 | − | 0.155719i | \(-0.950230\pi\) |
0.359044 | − | 0.933321i | \(-0.383103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.50000 | + | 4.33013i | −0.116185 | + | 0.201238i | −0.918253 | − | 0.395995i | \(-0.870400\pi\) |
0.802068 | + | 0.597233i | \(0.203733\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | 3.46410i | 0.160644i | ||||||||
\(466\) | −9.00000 | + | 15.5885i | −0.416917 | + | 0.722121i | ||||
\(467\) | −7.50000 | + | 12.9904i | −0.347059 | + | 0.601123i | −0.985726 | − | 0.168360i | \(-0.946153\pi\) |
0.638667 | + | 0.769483i | \(0.279486\pi\) | |||||||
\(468\) | 12.0000 | 0.554700 | ||||||||
\(469\) | 14.0000 | − | 12.1244i | 0.646460 | − | 0.559851i | ||||
\(470\) | 1.50000 | + | 2.59808i | 0.0691898 | + | 0.119840i | ||||
\(471\) | −33.0000 | − | 19.0526i | −1.52056 | − | 0.877896i | ||||
\(472\) | 12.0000 | 0.552345 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −6.00000 | − | 3.46410i | −0.275589 | − | 0.159111i | ||||
\(475\) | −1.00000 | − | 1.73205i | −0.0458831 | − | 0.0794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.00000 | − | 15.5885i | 0.412082 | − | 0.713746i | ||||
\(478\) | 12.0000 | − | 20.7846i | 0.548867 | − | 0.950666i | ||||
\(479\) | −9.00000 | + | 15.5885i | −0.411220 | + | 0.712255i | −0.995023 | − | 0.0996406i | \(-0.968231\pi\) |
0.583803 | + | 0.811895i | \(0.301564\pi\) | |||||||
\(480\) | 1.73205i | 0.0790569i | ||||||||
\(481\) | 4.00000 | + | 6.92820i | 0.182384 | + | 0.315899i | ||||
\(482\) | 9.50000 | − | 16.4545i | 0.432713 | − | 0.749481i | ||||
\(483\) | −9.00000 | − | 10.3923i | −0.409514 | − | 0.472866i | ||||
\(484\) | 5.50000 | + | 9.52628i | 0.250000 | + | 0.433013i | ||||
\(485\) | −5.00000 | + | 8.66025i | −0.227038 | + | 0.393242i | ||||
\(486\) | −13.5000 | + | 7.79423i | −0.612372 | + | 0.353553i | ||||
\(487\) | −10.0000 | − | 17.3205i | −0.453143 | − | 0.784867i | 0.545436 | − | 0.838152i | \(-0.316364\pi\) |
−0.998579 | + | 0.0532853i | \(0.983031\pi\) | |||||||
\(488\) | −7.00000 | −0.316875 | ||||||||
\(489\) | −30.0000 | + | 17.3205i | −1.35665 | + | 0.783260i | ||||
\(490\) | 6.50000 | − | 2.59808i | 0.293640 | − | 0.117369i | ||||
\(491\) | −6.00000 | + | 10.3923i | −0.270776 | + | 0.468998i | −0.969061 | − | 0.246822i | \(-0.920614\pi\) |
0.698285 | + | 0.715820i | \(0.253947\pi\) | |||||||
\(492\) | 9.00000 | − | 5.19615i | 0.405751 | − | 0.234261i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 4.00000 | + | 6.92820i | 0.179969 | + | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 20.7846i | 0.931381i | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 4.50000 | − | 2.59808i | 0.201045 | − | 0.116073i | ||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −7.50000 | − | 2.59808i | −0.334077 | − | 0.115728i | ||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5.19615i | − | 0.230769i | ||||||
\(508\) | −13.0000 | −0.576782 | ||||||||
\(509\) | 9.00000 | + | 15.5885i | 0.398918 | + | 0.690946i | 0.993593 | − | 0.113020i | \(-0.0360525\pi\) |
−0.594675 | + | 0.803966i | \(0.702719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.00000 | + | 1.73205i | 0.221187 | + | 0.0766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −9.00000 | − | 5.19615i | −0.397360 | − | 0.229416i | ||||
\(514\) | 9.00000 | + | 15.5885i | 0.396973 | + | 0.687577i | ||||
\(515\) | 8.50000 | − | 14.7224i | 0.374555 | − | 0.648748i | ||||
\(516\) | − | 19.0526i | − | 0.838742i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.00000 | − | 5.19615i | −0.0439375 | − | 0.228306i | ||||
\(519\) | 36.0000 | + | 20.7846i | 1.58022 | + | 0.912343i | ||||
\(520\) | 4.00000 | 0.175412 | ||||||||
\(521\) | −13.5000 | − | 23.3827i | −0.591446 | − | 1.02441i | −0.994038 | − | 0.109035i | \(-0.965224\pi\) |
0.402592 | − | 0.915379i | \(-0.368109\pi\) | |||||||
\(522\) | 9.00000 | − | 15.5885i | 0.393919 | − | 0.682288i | ||||
\(523\) | −14.5000 | + | 25.1147i | −0.634041 | + | 1.09819i | 0.352677 | + | 0.935745i | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.50000 | − | 4.33013i | 0.0654654 | − | 0.188982i | ||||
\(526\) | −4.50000 | + | 7.79423i | −0.196209 | + | 0.339845i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 3.00000 | − | 5.19615i | 0.130312 | − | 0.225706i | ||||
\(531\) | 18.0000 | + | 31.1769i | 0.781133 | + | 1.35296i | ||||
\(532\) | −1.00000 | − | 5.19615i | −0.0433555 | − | 0.225282i | ||||
\(533\) | −12.0000 | − | 20.7846i | −0.519778 | − | 0.900281i | ||||
\(534\) | 22.5000 | − | 12.9904i | 0.973670 | − | 0.562149i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −7.00000 | −0.302354 | ||||||||
\(537\) | 31.1769i | 1.34538i | ||||||||
\(538\) | 10.5000 | + | 18.1865i | 0.452687 | + | 0.784077i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.50000 | + | 2.59808i | −0.193649 | + | 0.111803i | ||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | −10.0000 | + | 17.3205i | −0.429537 | + | 0.743980i | ||||
\(543\) | 3.00000 | + | 1.73205i | 0.128742 | + | 0.0743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.00000 | − | 1.73205i | 0.0428353 | − | 0.0741929i | ||||
\(546\) | −6.00000 | + | 17.3205i | −0.256776 | + | 0.741249i | ||||
\(547\) | −4.00000 | − | 6.92820i | −0.171028 | − | 0.296229i | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | −6.00000 | + | 10.3923i | −0.256307 | + | 0.443937i | ||||
\(549\) | −10.5000 | − | 18.1865i | −0.448129 | − | 0.776182i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000 | 0.511217 | ||||||||
\(552\) | 5.19615i | 0.221163i | ||||||||
\(553\) | 8.00000 | − | 6.92820i | 0.340195 | − | 0.294617i | ||||
\(554\) | −16.0000 | + | 27.7128i | −0.679775 | + | 1.17740i | ||||
\(555\) | −3.00000 | − | 1.73205i | −0.127343 | − | 0.0735215i | ||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | −3.00000 | − | 5.19615i | −0.127114 | − | 0.220168i | 0.795443 | − | 0.606028i | \(-0.207238\pi\) |
−0.922557 | + | 0.385860i | \(0.873905\pi\) | |||||||
\(558\) | 3.00000 | + | 5.19615i | 0.127000 | + | 0.219971i | ||||
\(559\) | −44.0000 | −1.86100 | ||||||||
\(560\) | −2.50000 | − | 0.866025i | −0.105644 | − | 0.0365963i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.5000 | − | 18.1865i | −0.442916 | − | 0.767153i | ||||
\(563\) | −9.00000 | −0.379305 | −0.189652 | − | 0.981851i | \(-0.560736\pi\) | ||||
−0.189652 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(564\) | 4.50000 | + | 2.59808i | 0.189484 | + | 0.109399i | ||||
\(565\) | 6.00000 | 0.252422 | ||||||||
\(566\) | 11.0000 | 0.462364 | ||||||||
\(567\) | −4.50000 | − | 23.3827i | −0.188982 | − | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.00000 | 0.251533 | 0.125767 | − | 0.992060i | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | −3.00000 | − | 1.73205i | −0.125656 | − | 0.0725476i | ||||
\(571\) | 32.0000 | 1.33916 | 0.669579 | − | 0.742741i | \(-0.266474\pi\) | ||||
0.669579 | + | 0.742741i | \(0.266474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0000 | + | 15.5885i | 1.12794 | + | 0.651217i | ||||
\(574\) | 3.00000 | + | 15.5885i | 0.125218 | + | 0.650650i | ||||
\(575\) | −3.00000 | −0.125109 | ||||||||
\(576\) | 1.50000 | + | 2.59808i | 0.0625000 | + | 0.108253i | ||||
\(577\) | −10.0000 | − | 17.3205i | −0.416305 | − | 0.721062i | 0.579259 | − | 0.815144i | \(-0.303342\pi\) |
−0.995565 | + | 0.0940813i | \(0.970009\pi\) | |||||||
\(578\) | 8.50000 | − | 14.7224i | 0.353553 | − | 0.612372i | ||||
\(579\) | −33.0000 | − | 19.0526i | −1.37143 | − | 0.791797i | ||||
\(580\) | 3.00000 | − | 5.19615i | 0.124568 | − | 0.215758i | ||||
\(581\) | −30.0000 | − | 10.3923i | −1.24461 | − | 0.431145i | ||||
\(582\) | 17.3205i | 0.717958i | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.00000 | − | 1.73205i | −0.0413803 | − | 0.0716728i | ||||
\(585\) | 6.00000 | + | 10.3923i | 0.248069 | + | 0.429669i | ||||
\(586\) | 15.0000 | − | 25.9808i | 0.619644 | − | 1.07326i | ||||
\(587\) | −22.5000 | − | 38.9711i | −0.928674 | − | 1.60851i | −0.785543 | − | 0.618808i | \(-0.787616\pi\) |
−0.143132 | − | 0.989704i | \(-0.545717\pi\) | |||||||
\(588\) | 7.50000 | − | 9.52628i | 0.309295 | − | 0.392857i | ||||
\(589\) | −2.00000 | + | 3.46410i | −0.0824086 | + | 0.142736i | ||||
\(590\) | 6.00000 | + | 10.3923i | 0.247016 | + | 0.427844i | ||||
\(591\) | −18.0000 | − | 10.3923i | −0.740421 | − | 0.427482i | ||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −7.50000 | − | 12.9904i | −0.307212 | − | 0.532107i | ||||
\(597\) | 6.92820i | 0.283552i | ||||||||
\(598\) | 12.0000 | 0.490716 | ||||||||
\(599\) | 6.00000 | 0.245153 | 0.122577 | − | 0.992459i | \(-0.460884\pi\) | ||||
0.122577 | + | 0.992459i | \(0.460884\pi\) | |||||||
\(600\) | −1.50000 | + | 0.866025i | −0.0612372 | + | 0.0353553i | ||||
\(601\) | 5.00000 | + | 8.66025i | 0.203954 | + | 0.353259i | 0.949799 | − | 0.312861i | \(-0.101287\pi\) |
−0.745845 | + | 0.666120i | \(0.767954\pi\) | |||||||
\(602\) | 27.5000 | + | 9.52628i | 1.12082 | + | 0.388262i | ||||
\(603\) | −10.5000 | − | 18.1865i | −0.427593 | − | 0.740613i | ||||
\(604\) | −1.00000 | + | 1.73205i | −0.0406894 | + | 0.0704761i | ||||
\(605\) | −5.50000 | + | 9.52628i | −0.223607 | + | 0.387298i | ||||
\(606\) | −4.50000 | + | 2.59808i | −0.182800 | + | 0.105540i | ||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | −1.00000 | + | 1.73205i | −0.0405554 | + | 0.0702439i | ||||
\(609\) | 18.0000 | + | 20.7846i | 0.729397 | + | 0.842235i | ||||
\(610\) | −3.50000 | − | 6.06218i | −0.141711 | − | 0.245450i | ||||
\(611\) | 6.00000 | − | 10.3923i | 0.242734 | − | 0.420428i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.0000 | − | 32.9090i | −0.767403 | − | 1.32918i | −0.938967 | − | 0.344008i | \(-0.888215\pi\) |
0.171564 | − | 0.985173i | \(-0.445118\pi\) | |||||||
\(614\) | 20.0000 | 0.807134 | ||||||||
\(615\) | 9.00000 | + | 5.19615i | 0.362915 | + | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.00000 | − | 5.19615i | 0.120775 | − | 0.209189i | −0.799298 | − | 0.600935i | \(-0.794795\pi\) |
0.920074 | + | 0.391745i | \(0.128129\pi\) | |||||||
\(618\) | − | 29.4449i | − | 1.18445i | ||||||
\(619\) | 5.00000 | − | 8.66025i | 0.200967 | − | 0.348085i | −0.747873 | − | 0.663842i | \(-0.768925\pi\) |
0.948840 | + | 0.315757i | \(0.102258\pi\) | |||||||
\(620\) | 1.00000 | + | 1.73205i | 0.0401610 | + | 0.0695608i | ||||
\(621\) | −13.5000 | + | 7.79423i | −0.541736 | + | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.50000 | + | 38.9711i | 0.300481 | + | 1.56135i | ||||
\(624\) | 6.00000 | − | 3.46410i | 0.240192 | − | 0.138675i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 26.0000 | 1.03917 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.0000 | −0.877896 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.50000 | − | 7.79423i | −0.0597614 | − | 0.310530i | ||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | −12.0000 | + | 6.92820i | −0.476957 | + | 0.275371i | ||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −6.50000 | − | 11.2583i | −0.257945 | − | 0.446773i | ||||
\(636\) | − | 10.3923i | − | 0.412082i | ||||||
\(637\) | −22.0000 | − | 17.3205i | −0.871672 | − | 0.686264i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | 7.50000 | − | 12.9904i | 0.296232 | − | 0.513089i | −0.679039 | − | 0.734103i | \(-0.737603\pi\) |
0.975271 | + | 0.221013i | \(0.0709364\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.5000 | − | 37.2391i | 0.847877 | − | 1.46857i | −0.0352216 | − | 0.999380i | \(-0.511214\pi\) |
0.883099 | − | 0.469187i | \(-0.155453\pi\) | |||||||
\(644\) | −7.50000 | − | 2.59808i | −0.295541 | − | 0.102379i | ||||
\(645\) | 16.5000 | − | 9.52628i | 0.649687 | − | 0.375097i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | −4.50000 | + | 7.79423i | −0.176777 | + | 0.306186i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 2.00000 | + | 3.46410i | 0.0784465 | + | 0.135873i | ||||
\(651\) | −9.00000 | + | 1.73205i | −0.352738 | + | 0.0678844i | ||||
\(652\) | −10.0000 | + | 17.3205i | −0.391630 | + | 0.678323i | ||||
\(653\) | −15.0000 | − | 25.9808i | −0.586995 | − | 1.01671i | −0.994623 | − | 0.103558i | \(-0.966977\pi\) |
0.407628 | − | 0.913148i | \(-0.366356\pi\) | |||||||
\(654\) | − | 3.46410i | − | 0.135457i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | − | 5.19615i | 0.117130 | − | 0.202876i | ||||
\(657\) | 3.00000 | − | 5.19615i | 0.117041 | − | 0.202721i | ||||
\(658\) | −6.00000 | + | 5.19615i | −0.233904 | + | 0.202567i | ||||
\(659\) | −12.0000 | − | 20.7846i | −0.467454 | − | 0.809653i | 0.531855 | − | 0.846836i | \(-0.321495\pi\) |
−0.999309 | + | 0.0371821i | \(0.988162\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.00000 | 0.194477 | 0.0972387 | − | 0.995261i | \(-0.468999\pi\) | ||||
0.0972387 | + | 0.995261i | \(0.468999\pi\) | |||||||
\(662\) | 26.0000 | 1.01052 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | + | 10.3923i | 0.232845 | + | 0.403300i | ||||
\(665\) | 4.00000 | − | 3.46410i | 0.155113 | − | 0.134332i | ||||
\(666\) | −6.00000 | −0.232495 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 1.50000 | − | 2.59808i | 0.0580367 | − | 0.100523i | ||||
\(669\) | 32.9090i | 1.27233i | ||||||||
\(670\) | −3.50000 | − | 6.06218i | −0.135217 | − | 0.234202i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.50000 | + | 0.866025i | −0.173591 | + | 0.0334077i | ||||
\(673\) | 14.0000 | + | 24.2487i | 0.539660 | + | 0.934719i | 0.998922 | + | 0.0464181i | \(0.0147807\pi\) |
−0.459262 | + | 0.888301i | \(0.651886\pi\) | |||||||
\(674\) | −16.0000 | + | 27.7128i | −0.616297 | + | 1.06746i | ||||
\(675\) | −4.50000 | − | 2.59808i | −0.173205 | − | 0.100000i | ||||
\(676\) | −1.50000 | − | 2.59808i | −0.0576923 | − | 0.0999260i | ||||
\(677\) | −12.0000 | −0.461197 | −0.230599 | − | 0.973049i | \(-0.574068\pi\) | ||||
−0.230599 | + | 0.973049i | \(0.574068\pi\) | |||||||
\(678\) | 9.00000 | − | 5.19615i | 0.345643 | − | 0.199557i | ||||
\(679\) | −25.0000 | − | 8.66025i | −0.959412 | − | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −36.0000 | + | 20.7846i | −1.37952 | + | 0.796468i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −25.5000 | − | 44.1673i | −0.975730 | − | 1.69001i | −0.677503 | − | 0.735520i | \(-0.736938\pi\) |
−0.298227 | − | 0.954495i | \(-0.596395\pi\) | |||||||
\(684\) | −6.00000 | −0.229416 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 10.0000 | + | 15.5885i | 0.381802 | + | 0.595170i | ||||
\(687\) | − | 50.2295i | − | 1.91637i | ||||||
\(688\) | −5.50000 | − | 9.52628i | −0.209686 | − | 0.363186i | ||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | −4.50000 | + | 2.59808i | −0.171312 | + | 0.0989071i | ||||
\(691\) | −46.0000 | −1.74992 | −0.874961 | − | 0.484193i | \(-0.839113\pi\) | ||||
−0.874961 | + | 0.484193i | \(0.839113\pi\) | |||||||
\(692\) | 24.0000 | 0.912343 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 27.0000 | 1.02491 | ||||||||
\(695\) | 4.00000 | 0.151729 | ||||||||
\(696\) | − | 10.3923i | − | 0.393919i | ||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 3.50000 | + | 6.06218i | 0.132477 | + | 0.229457i | ||||
\(699\) | −27.0000 | + | 15.5885i | −1.02123 | + | 0.589610i | ||||
\(700\) | −0.500000 | − | 2.59808i | −0.0188982 | − | 0.0981981i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 18.0000 | + | 10.3923i | 0.679366 | + | 0.392232i | ||||
\(703\) | −2.00000 | − | 3.46410i | −0.0754314 | − | 0.130651i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.19615i | 0.195698i | ||||||||
\(706\) | −12.0000 | + | 20.7846i | −0.451626 | + | 0.782239i | ||||
\(707\) | −1.50000 | − | 7.79423i | −0.0564133 | − | 0.293132i | ||||
\(708\) | 18.0000 | + | 10.3923i | 0.676481 | + | 0.390567i | ||||
\(709\) | −19.0000 | −0.713560 | −0.356780 | − | 0.934188i | \(-0.616125\pi\) | ||||
−0.356780 | + | 0.934188i | \(0.616125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6.00000 | − | 10.3923i | −0.225018 | − | 0.389742i | ||||
\(712\) | 7.50000 | − | 12.9904i | 0.281074 | − | 0.486835i | ||||
\(713\) | 3.00000 | + | 5.19615i | 0.112351 | + | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.00000 | + | 15.5885i | 0.336346 | + | 0.582568i | ||||
\(717\) | 36.0000 | − | 20.7846i | 1.34444 | − | 0.776215i | ||||
\(718\) | −3.00000 | + | 5.19615i | −0.111959 | + | 0.193919i | ||||
\(719\) | 15.0000 | − | 25.9808i | 0.559406 | − | 0.968919i | −0.438141 | − | 0.898906i | \(-0.644363\pi\) |
0.997546 | − | 0.0700124i | \(-0.0223039\pi\) | |||||||
\(720\) | −1.50000 | + | 2.59808i | −0.0559017 | + | 0.0968246i | ||||
\(721\) | 42.5000 | + | 14.7224i | 1.58278 | + | 0.548292i | ||||
\(722\) | 7.50000 | + | 12.9904i | 0.279121 | + | 0.483452i | ||||
\(723\) | 28.5000 | − | 16.4545i | 1.05993 | − | 0.611949i | ||||
\(724\) | 2.00000 | 0.0743294 | ||||||||
\(725\) | 6.00000 | 0.222834 | ||||||||
\(726\) | 19.0526i | 0.707107i | ||||||||
\(727\) | 3.50000 | + | 6.06218i | 0.129808 | + | 0.224834i | 0.923602 | − | 0.383353i | \(-0.125231\pi\) |
−0.793794 | + | 0.608186i | \(0.791897\pi\) | |||||||
\(728\) | 2.00000 | + | 10.3923i | 0.0741249 | + | 0.385164i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 1.00000 | − | 1.73205i | 0.0370117 | − | 0.0641061i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −10.5000 | − | 6.06218i | −0.388091 | − | 0.224065i | ||||
\(733\) | −4.00000 | − | 6.92820i | −0.147743 | − | 0.255899i | 0.782650 | − | 0.622462i | \(-0.213868\pi\) |
−0.930393 | + | 0.366563i | \(0.880534\pi\) | |||||||
\(734\) | −8.50000 | + | 14.7224i | −0.313741 | + | 0.543415i | ||||
\(735\) | 12.0000 | + | 1.73205i | 0.442627 | + | 0.0638877i | ||||
\(736\) | 1.50000 | + | 2.59808i | 0.0552907 | + | 0.0957664i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 18.0000 | 0.662589 | ||||||||
\(739\) | −16.0000 | − | 27.7128i | −0.588570 | − | 1.01943i | −0.994420 | − | 0.105493i | \(-0.966358\pi\) |
0.405851 | − | 0.913939i | \(-0.366975\pi\) | |||||||
\(740\) | −2.00000 | −0.0735215 | ||||||||
\(741\) | 13.8564i | 0.509028i | ||||||||
\(742\) | 15.0000 | + | 5.19615i | 0.550667 | + | 0.190757i | ||||
\(743\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(744\) | 3.00000 | + | 1.73205i | 0.109985 | + | 0.0635001i | ||||
\(745\) | 7.50000 | − | 12.9904i | 0.274779 | − | 0.475931i | ||||
\(746\) | −7.00000 | − | 12.1244i | −0.256288 | − | 0.443904i | ||||
\(747\) | −18.0000 | + | 31.1769i | −0.658586 | + | 1.14070i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50000 | − | 0.866025i | −0.0547723 | − | 0.0316228i | ||||
\(751\) | 11.0000 | + | 19.0526i | 0.401396 | + | 0.695238i | 0.993895 | − | 0.110333i | \(-0.0351919\pi\) |
−0.592499 | + | 0.805571i | \(0.701859\pi\) | |||||||
\(752\) | 3.00000 | 0.109399 | ||||||||
\(753\) | −18.0000 | − | 10.3923i | −0.655956 | − | 0.378717i | ||||
\(754\) | −24.0000 | −0.874028 | ||||||||
\(755\) | −2.00000 | −0.0727875 | ||||||||
\(756\) | −9.00000 | − | 10.3923i | −0.327327 | − | 0.377964i | ||||
\(757\) | 14.0000 | 0.508839 | 0.254419 | − | 0.967094i | \(-0.418116\pi\) | ||||
0.254419 | + | 0.967094i | \(0.418116\pi\) | |||||||
\(758\) | −4.00000 | −0.145287 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.00000 | −0.0725476 | ||||||||
\(761\) | −7.50000 | − | 12.9904i | −0.271875 | − | 0.470901i | 0.697467 | − | 0.716617i | \(-0.254310\pi\) |
−0.969342 | + | 0.245716i | \(0.920977\pi\) | |||||||
\(762\) | −19.5000 | − | 11.2583i | −0.706410 | − | 0.407846i | ||||
\(763\) | 5.00000 | + | 1.73205i | 0.181012 | + | 0.0627044i | ||||
\(764\) | 18.0000 | 0.651217 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 10.5000 | + | 18.1865i | 0.379380 | + | 0.657106i | ||||
\(767\) | 24.0000 | − | 41.5692i | 0.866590 | − | 1.50098i | ||||
\(768\) | 1.50000 | + | 0.866025i | 0.0541266 | + | 0.0312500i | ||||
\(769\) | −2.50000 | + | 4.33013i | −0.0901523 | + | 0.156148i | −0.907575 | − | 0.419890i | \(-0.862069\pi\) |
0.817423 | + | 0.576038i | \(0.195402\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.1769i | 1.12281i | ||||||||
\(772\) | −22.0000 | −0.791797 | ||||||||
\(773\) | 9.00000 | + | 15.5885i | 0.323708 | + | 0.560678i | 0.981250 | − | 0.192740i | \(-0.0617373\pi\) |
−0.657542 | + | 0.753418i | \(0.728404\pi\) | |||||||
\(774\) | 16.5000 | − | 28.5788i | 0.593080 | − | 1.02725i | ||||
\(775\) | −1.00000 | + | 1.73205i | −0.0359211 | + | 0.0622171i | ||||
\(776\) | 5.00000 | + | 8.66025i | 0.179490 | + | 0.310885i | ||||
\(777\) | 3.00000 | − | 8.66025i | 0.107624 | − | 0.310685i | ||||
\(778\) | −13.5000 | + | 23.3827i | −0.483998 | + | 0.838310i | ||||
\(779\) | 6.00000 | + | 10.3923i | 0.214972 | + | 0.372343i | ||||
\(780\) | 6.00000 | + | 3.46410i | 0.214834 | + | 0.124035i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.0000 | − | 15.5885i | 0.964901 | − | 0.557086i | ||||
\(784\) | 1.00000 | − | 6.92820i | 0.0357143 | − | 0.247436i | ||||
\(785\) | −11.0000 | − | 19.0526i | −0.392607 | − | 0.680015i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.00000 | −0.0356462 | −0.0178231 | − | 0.999841i | \(-0.505674\pi\) | ||||
−0.0178231 | + | 0.999841i | \(0.505674\pi\) | |||||||
\(788\) | −12.0000 | −0.427482 | ||||||||
\(789\) | −13.5000 | + | 7.79423i | −0.480613 | + | 0.277482i | ||||
\(790\) | −2.00000 | − | 3.46410i | −0.0711568 | − | 0.123247i | ||||
\(791\) | 3.00000 | + | 15.5885i | 0.106668 | + | 0.554262i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.0000 | + | 24.2487i | −0.497155 | + | 0.861097i | ||||
\(794\) | 14.0000 | − | 24.2487i | 0.496841 | − | 0.860555i | ||||
\(795\) | 9.00000 | − | 5.19615i | 0.319197 | − | 0.184289i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −9.00000 | + | 15.5885i | −0.318796 | + | 0.552171i | −0.980237 | − | 0.197826i | \(-0.936612\pi\) |
0.661441 | + | 0.749997i | \(0.269945\pi\) | |||||||
\(798\) | 3.00000 | − | 8.66025i | 0.106199 | − | 0.306570i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 45.0000 | 1.59000 | ||||||||
\(802\) | −7.50000 | − | 12.9904i | −0.264834 | − | 0.458706i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −10.5000 | − | 6.06218i | −0.370306 | − | 0.213797i | ||||
\(805\) | −1.50000 | − | 7.79423i | −0.0528681 | − | 0.274710i | ||||
\(806\) | 4.00000 | − | 6.92820i | 0.140894 | − | 0.244036i | ||||
\(807\) | 36.3731i | 1.28039i | ||||||||
\(808\) | −1.50000 | + | 2.59808i | −0.0527698 | + | 0.0914000i | ||||
\(809\) | 19.5000 | + | 33.7750i | 0.685583 | + | 1.18747i | 0.973253 | + | 0.229736i | \(0.0737862\pi\) |
−0.287670 | + | 0.957730i | \(0.592880\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | −16.0000 | −0.561836 | −0.280918 | − | 0.959732i | \(-0.590639\pi\) | ||||
−0.280918 | + | 0.959732i | \(0.590639\pi\) | |||||||
\(812\) | 15.0000 | + | 5.19615i | 0.526397 | + | 0.182349i | ||||
\(813\) | −30.0000 | + | 17.3205i | −1.05215 | + | 0.607457i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.0000 | −0.700569 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.0000 | 0.769683 | ||||||||
\(818\) | −1.00000 | −0.0349642 | ||||||||
\(819\) | −24.0000 | + | 20.7846i | −0.838628 | + | 0.726273i | ||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | −3.00000 | −0.104701 | −0.0523504 | − | 0.998629i | \(-0.516671\pi\) | ||||
−0.0523504 | + | 0.998629i | \(0.516671\pi\) | |||||||
\(822\) | −18.0000 | + | 10.3923i | −0.627822 | + | 0.362473i | ||||
\(823\) | 8.00000 | 0.278862 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(824\) | −8.50000 | − | 14.7224i | −0.296112 | − | 0.512880i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −24.0000 | + | 20.7846i | −0.835067 | + | 0.723189i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | −4.50000 | + | 7.79423i | −0.156386 | + | 0.270868i | ||||
\(829\) | 12.5000 | + | 21.6506i | 0.434143 | + | 0.751958i | 0.997225 | − | 0.0744432i | \(-0.0237179\pi\) |
−0.563082 | + | 0.826401i | \(0.690385\pi\) | |||||||
\(830\) | −6.00000 | + | 10.3923i | −0.208263 | + | 0.360722i | ||||
\(831\) | −48.0000 | + | 27.7128i | −1.66510 | + | 0.961347i | ||||
\(832\) | 2.00000 | − | 3.46410i | 0.0693375 | − | 0.120096i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6.00000 | − | 3.46410i | 0.207763 | − | 0.119952i | ||||
\(835\) | 3.00000 | 0.103819 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.3923i | 0.359211i | ||||||||
\(838\) | −18.0000 | + | 31.1769i | −0.621800 | + | 1.07699i | ||||
\(839\) | 9.00000 | + | 15.5885i | 0.310715 | + | 0.538173i | 0.978517 | − | 0.206165i | \(-0.0660984\pi\) |
−0.667803 | + | 0.744338i | \(0.732765\pi\) | |||||||
\(840\) | −3.00000 | − | 3.46410i | −0.103510 | − | 0.119523i | ||||
\(841\) | −3.50000 | + | 6.06218i | −0.120690 | + | 0.209041i | ||||
\(842\) | −8.50000 | − | 14.7224i | −0.292929 | − | 0.507369i | ||||
\(843\) | − | 36.3731i | − | 1.25275i | ||||||
\(844\) | −4.00000 | + | 6.92820i | −0.137686 | + | 0.238479i | ||||
\(845\) | 1.50000 | − | 2.59808i | 0.0516016 | − | 0.0893765i | ||||
\(846\) | 4.50000 | + | 7.79423i | 0.154713 | + | 0.267971i | ||||
\(847\) | −27.5000 | − | 9.52628i | −0.944911 | − | 0.327327i | ||||
\(848\) | −3.00000 | − | 5.19615i | −0.103020 | − | 0.178437i | ||||
\(849\) | 16.5000 | + | 9.52628i | 0.566279 | + | 0.326941i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.00000 | −0.205677 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.00000 | − | 6.92820i | −0.136957 | − | 0.237217i | 0.789386 | − | 0.613897i | \(-0.210399\pi\) |
−0.926343 | + | 0.376680i | \(0.877066\pi\) | |||||||
\(854\) | 14.0000 | − | 12.1244i | 0.479070 | − | 0.414887i | ||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | + | 25.9808i | −0.512390 | + | 0.887486i | 0.487507 | + | 0.873119i | \(0.337907\pi\) |
−0.999897 | + | 0.0143666i | \(0.995427\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.0000 | − | 22.5167i | −0.443554 | − | 0.768259i | 0.554396 | − | 0.832253i | \(-0.312949\pi\) |
−0.997950 | + | 0.0639945i | \(0.979616\pi\) | |||||||
\(860\) | 5.50000 | − | 9.52628i | 0.187548 | − | 0.324843i | ||||
\(861\) | −9.00000 | + | 25.9808i | −0.306719 | + | 0.885422i | ||||
\(862\) | −15.0000 | − | 25.9808i | −0.510902 | − | 0.884908i | ||||
\(863\) | 10.5000 | − | 18.1865i | 0.357424 | − | 0.619077i | −0.630106 | − | 0.776509i | \(-0.716988\pi\) |
0.987530 | + | 0.157433i | \(0.0503217\pi\) | |||||||
\(864\) | 5.19615i | 0.176777i | ||||||||
\(865\) | 12.0000 | + | 20.7846i | 0.408012 | + | 0.706698i | ||||
\(866\) | −4.00000 | −0.135926 | ||||||||
\(867\) | 25.5000 | − | 14.7224i | 0.866025 | − | 0.500000i | ||||
\(868\) | −4.00000 | + | 3.46410i | −0.135769 | + | 0.117579i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 9.00000 | − | 5.19615i | 0.305129 | − | 0.176166i | ||||
\(871\) | −14.0000 | + | 24.2487i | −0.474372 | + | 0.821636i | ||||
\(872\) | −1.00000 | − | 1.73205i | −0.0338643 | − | 0.0586546i | ||||
\(873\) | −15.0000 | + | 25.9808i | −0.507673 | + | 0.879316i | ||||
\(874\) | −6.00000 | −0.202953 | ||||||||
\(875\) | 2.00000 | − | 1.73205i | 0.0676123 | − | 0.0585540i | ||||
\(876\) | − | 3.46410i | − | 0.117041i | ||||||
\(877\) | 17.0000 | + | 29.4449i | 0.574049 | + | 0.994282i | 0.996144 | + | 0.0877308i | \(0.0279615\pi\) |
−0.422095 | + | 0.906552i | \(0.638705\pi\) | |||||||
\(878\) | 8.00000 | 0.269987 | ||||||||
\(879\) | 45.0000 | − | 25.9808i | 1.51781 | − | 0.876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.0000 | 1.11180 | 0.555899 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555899 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(882\) | 19.5000 | − | 7.79423i | 0.656599 | − | 0.262445i | ||||
\(883\) | −43.0000 | −1.44707 | −0.723533 | − | 0.690290i | \(-0.757483\pi\) | ||||
−0.723533 | + | 0.690290i | \(0.757483\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 20.7846i | 0.698667i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.50000 | − | 7.79423i | −0.151095 | − | 0.261705i | 0.780535 | − | 0.625112i | \(-0.214947\pi\) |
−0.931630 | + | 0.363407i | \(0.881613\pi\) | |||||||
\(888\) | −3.00000 | + | 1.73205i | −0.100673 | + | 0.0581238i | ||||
\(889\) | 26.0000 | − | 22.5167i | 0.872012 | − | 0.755185i | ||||
\(890\) | 15.0000 | 0.502801 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.50000 | + | 16.4545i | 0.318084 | + | 0.550937i | ||||
\(893\) | −3.00000 | + | 5.19615i | −0.100391 | + | 0.173883i | ||||
\(894\) | − | 25.9808i | − | 0.868927i | ||||||
\(895\) | −9.00000 | + | 15.5885i | −0.300837 | + | 0.521065i | ||||
\(896\) | −2.00000 | + | 1.73205i | −0.0668153 | + | 0.0578638i | ||||
\(897\) | 18.0000 | + | 10.3923i | 0.601003 | + | 0.346989i | ||||
\(898\) | 15.0000 | 0.500556 | ||||||||
\(899\) | −6.00000 | − | 10.3923i | −0.200111 | − | 0.346603i | ||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 33.0000 | + | 38.1051i | 1.09817 | + | 1.26806i | ||||
\(904\) | 3.00000 | − | 5.19615i | 0.0997785 | − | 0.172821i | ||||
\(905\) | 1.00000 | + | 1.73205i | 0.0332411 | + | 0.0575753i | ||||
\(906\) | −3.00000 | + | 1.73205i | −0.0996683 | + | 0.0575435i | ||||
\(907\) | 2.00000 | − | 3.46410i | 0.0664089 | − | 0.115024i | −0.830909 | − | 0.556408i | \(-0.812179\pi\) |
0.897318 | + | 0.441384i | \(0.145512\pi\) | |||||||
\(908\) | −12.0000 | + | 20.7846i | −0.398234 | + | 0.689761i | ||||
\(909\) | −9.00000 | −0.298511 | ||||||||
\(910\) | −8.00000 | + | 6.92820i | −0.265197 | + | 0.229668i | ||||
\(911\) | 21.0000 | + | 36.3731i | 0.695761 | + | 1.20509i | 0.969923 | + | 0.243410i | \(0.0782661\pi\) |
−0.274162 | + | 0.961683i | \(0.588401\pi\) | |||||||
\(912\) | −3.00000 | + | 1.73205i | −0.0993399 | + | 0.0573539i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 26.0000 | 0.860004 | ||||||||
\(915\) | − | 12.1244i | − | 0.400819i | ||||||
\(916\) | −14.5000 | − | 25.1147i | −0.479093 | − | 0.829814i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0000 | + | 48.4974i | −0.923635 | + | 1.59978i | −0.129893 | + | 0.991528i | \(0.541463\pi\) |
−0.793742 | + | 0.608254i | \(0.791870\pi\) | |||||||
\(920\) | −1.50000 | + | 2.59808i | −0.0494535 | + | 0.0856560i | ||||
\(921\) | 30.0000 | + | 17.3205i | 0.988534 | + | 0.570730i | ||||
\(922\) | −13.5000 | − | 23.3827i | −0.444599 | − | 0.770068i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.00000 | − | 1.73205i | −0.0328798 | − | 0.0569495i | ||||
\(926\) | −2.50000 | + | 4.33013i | −0.0821551 | + | 0.142297i | ||||
\(927\) | 25.5000 | − | 44.1673i | 0.837530 | − | 1.45064i | ||||
\(928\) | −3.00000 | − | 5.19615i | −0.0984798 | − | 0.170572i | ||||
\(929\) | 15.0000 | 0.492134 | 0.246067 | − | 0.969253i | \(-0.420862\pi\) | ||||
0.246067 | + | 0.969253i | \(0.420862\pi\) | |||||||
\(930\) | 3.46410i | 0.113592i | ||||||||
\(931\) | 11.0000 | + | 8.66025i | 0.360510 | + | 0.283828i | ||||
\(932\) | −9.00000 | + | 15.5885i | −0.294805 | + | 0.510617i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.50000 | + | 12.9904i | −0.245407 | + | 0.425058i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 12.0000 | 0.392232 | ||||||||
\(937\) | 44.0000 | 1.43742 | 0.718709 | − | 0.695311i | \(-0.244734\pi\) | ||||
0.718709 | + | 0.695311i | \(0.244734\pi\) | |||||||
\(938\) | 14.0000 | − | 12.1244i | 0.457116 | − | 0.395874i | ||||
\(939\) | 39.0000 | + | 22.5167i | 1.27272 | + | 0.734803i | ||||
\(940\) | 1.50000 | + | 2.59808i | 0.0489246 | + | 0.0847399i | ||||
\(941\) | 15.0000 | 0.488986 | 0.244493 | − | 0.969651i | \(-0.421378\pi\) | ||||
0.244493 | + | 0.969651i | \(0.421378\pi\) | |||||||
\(942\) | −33.0000 | − | 19.0526i | −1.07520 | − | 0.620766i | ||||
\(943\) | 18.0000 | 0.586161 | ||||||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | 4.50000 | − | 12.9904i | 0.146385 | − | 0.422577i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 45.0000 | 1.46230 | 0.731152 | − | 0.682215i | \(-0.238983\pi\) | ||||
0.731152 | + | 0.682215i | \(0.238983\pi\) | |||||||
\(948\) | −6.00000 | − | 3.46410i | −0.194871 | − | 0.112509i | ||||
\(949\) | −8.00000 | −0.259691 | ||||||||
\(950\) | −1.00000 | − | 1.73205i | −0.0324443 | − | 0.0561951i | ||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 18.0000 | 0.583077 | 0.291539 | − | 0.956559i | \(-0.405833\pi\) | ||||
0.291539 | + | 0.956559i | \(0.405833\pi\) | |||||||
\(954\) | 9.00000 | − | 15.5885i | 0.291386 | − | 0.504695i | ||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −9.00000 | + | 15.5885i | −0.290777 | + | 0.503640i | ||||
\(959\) | −6.00000 | − | 31.1769i | −0.193750 | − | 1.00676i | ||||
\(960\) | 1.73205i | 0.0559017i | ||||||||
\(961\) | −27.0000 | −0.870968 | ||||||||
\(962\) | 4.00000 | + | 6.92820i | 0.128965 | + | 0.223374i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 9.50000 | − | 16.4545i | 0.305974 | − | 0.529963i | ||||
\(965\) | −11.0000 | − | 19.0526i | −0.354103 | − | 0.613324i | ||||
\(966\) | −9.00000 | − | 10.3923i | −0.289570 | − | 0.334367i | ||||
\(967\) | 0.500000 | − | 0.866025i | 0.0160789 | − | 0.0278495i | −0.857874 | − | 0.513860i | \(-0.828215\pi\) |
0.873953 | + | 0.486011i | \(0.161548\pi\) | |||||||
\(968\) | 5.50000 | + | 9.52628i | 0.176777 | + | 0.306186i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.00000 | + | 8.66025i | −0.160540 | + | 0.278064i | ||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | −13.5000 | + | 7.79423i | −0.433013 | + | 0.250000i | ||||
\(973\) | 2.00000 | + | 10.3923i | 0.0641171 | + | 0.333162i | ||||
\(974\) | −10.0000 | − | 17.3205i | −0.320421 | − | 0.554985i | ||||
\(975\) | 6.92820i | 0.221880i | ||||||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | 36.0000 | 1.15174 | 0.575871 | − | 0.817541i | \(-0.304663\pi\) | ||||
0.575871 | + | 0.817541i | \(0.304663\pi\) | |||||||
\(978\) | −30.0000 | + | 17.3205i | −0.959294 | + | 0.553849i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 6.50000 | − | 2.59808i | 0.207635 | − | 0.0829925i | ||||
\(981\) | 3.00000 | − | 5.19615i | 0.0957826 | − | 0.165900i | ||||
\(982\) | −6.00000 | + | 10.3923i | −0.191468 | + | 0.331632i | ||||
\(983\) | −12.0000 | + | 20.7846i | −0.382741 | + | 0.662926i | −0.991453 | − | 0.130465i | \(-0.958353\pi\) |
0.608712 | + | 0.793391i | \(0.291686\pi\) | |||||||
\(984\) | 9.00000 | − | 5.19615i | 0.286910 | − | 0.165647i | ||||
\(985\) | −6.00000 | − | 10.3923i | −0.191176 | − | 0.331126i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −13.5000 | + | 2.59808i | −0.429710 | + | 0.0826977i | ||||
\(988\) | 4.00000 | + | 6.92820i | 0.127257 | + | 0.220416i | ||||
\(989\) | 16.5000 | − | 28.5788i | 0.524669 | − | 0.908754i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.0000 | − | 48.4974i | −0.889449 | − | 1.54057i | −0.840528 | − | 0.541769i | \(-0.817755\pi\) |
−0.0489218 | − | 0.998803i | \(-0.515578\pi\) | |||||||
\(992\) | 2.00000 | 0.0635001 | ||||||||
\(993\) | 39.0000 | + | 22.5167i | 1.23763 | + | 0.714545i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.00000 | + | 3.46410i | −0.0634043 | + | 0.109819i | ||||
\(996\) | 20.7846i | 0.658586i | ||||||||
\(997\) | −7.00000 | + | 12.1244i | −0.221692 | + | 0.383982i | −0.955322 | − | 0.295567i | \(-0.904491\pi\) |
0.733630 | + | 0.679549i | \(0.237825\pi\) | |||||||
\(998\) | 14.0000 | + | 24.2487i | 0.443162 | + | 0.767580i | ||||
\(999\) | −9.00000 | − | 5.19615i | −0.284747 | − | 0.164399i |
(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 | 630.2.i.d.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 1890.2.i.a.1171.1 | 2 | |||
7.4 | even | 3 | 630.2.l.b.571.1 | yes | 2 | ||
9.2 | odd | 6 | 1890.2.l.d.1801.1 | 2 | |||
9.7 | even | 3 | 630.2.l.b.331.1 | yes | 2 | ||
21.11 | odd | 6 | 1890.2.l.d.361.1 | 2 | |||
63.11 | odd | 6 | 1890.2.i.a.991.1 | 2 | |||
63.25 | even | 3 | inner | 630.2.i.d.151.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.i.d.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
630.2.i.d.151.1 | yes | 2 | 63.25 | even | 3 | inner | |
630.2.l.b.331.1 | yes | 2 | 9.7 | even | 3 | ||
630.2.l.b.571.1 | yes | 2 | 7.4 | even | 3 | ||
1890.2.i.a.991.1 | 2 | 63.11 | odd | 6 | |||
1890.2.i.a.1171.1 | 2 | 3.2 | odd | 2 | |||
1890.2.l.d.361.1 | 2 | 21.11 | odd | 6 | |||
1890.2.l.d.1801.1 | 2 | 9.2 | odd | 6 |