Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, 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("210.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.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: | \(1.67685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.151 |
Dual form | 210.2.i.b.121.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | −0.500000 | + | 0.866025i | −0.158114 | + | 0.273861i | ||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −5.00000 | −1.38675 | −0.693375 | − | 0.720577i | \(-0.743877\pi\) | ||||
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −0.500000 | + | 2.59808i | −0.133631 | + | 0.694365i | ||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.00000 | − | 3.46410i | 0.485071 | − | 0.840168i | −0.514782 | − | 0.857321i | \(-0.672127\pi\) |
0.999853 | + | 0.0171533i | \(0.00546033\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 3.50000 | + | 6.06218i | 0.802955 | + | 1.39076i | 0.917663 | + | 0.397360i | \(0.130073\pi\) |
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −2.50000 | + | 0.866025i | −0.545545 | + | 0.188982i | ||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.50000 | + | 4.33013i | 0.490290 | + | 0.849208i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.50000 | − | 0.866025i | 0.472456 | − | 0.163663i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0.500000 | + | 0.866025i | 0.0912871 | + | 0.158114i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.50000 | − | 4.33013i | −0.435194 | − | 0.753778i | ||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −0.500000 | + | 2.59808i | −0.0845154 | + | 0.439155i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −0.500000 | − | 0.866025i | −0.0821995 | − | 0.142374i | 0.821995 | − | 0.569495i | \(-0.192861\pi\) |
−0.904194 | + | 0.427121i | \(0.859528\pi\) | |||||||
\(38\) | 3.50000 | − | 6.06218i | 0.567775 | − | 0.983415i | ||||
\(39\) | −2.50000 | + | 4.33013i | −0.400320 | + | 0.693375i | ||||
\(40\) | −0.500000 | − | 0.866025i | −0.0790569 | − | 0.136931i | ||||
\(41\) | 5.00000 | 0.780869 | 0.390434 | − | 0.920631i | \(-0.372325\pi\) | ||||
0.390434 | + | 0.920631i | \(0.372325\pi\) | |||||||
\(42\) | 2.00000 | + | 1.73205i | 0.308607 | + | 0.267261i | ||||
\(43\) | 12.0000 | 1.82998 | 0.914991 | − | 0.403473i | \(-0.132197\pi\) | ||||
0.914991 | + | 0.403473i | \(0.132197\pi\) | |||||||
\(44\) | 2.50000 | + | 4.33013i | 0.376889 | + | 0.652791i | ||||
\(45\) | −0.500000 | + | 0.866025i | −0.0745356 | + | 0.129099i | ||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | 5.50000 | + | 9.52628i | 0.802257 | + | 1.38955i | 0.918127 | + | 0.396286i | \(0.129701\pi\) |
−0.115870 | + | 0.993264i | \(0.536965\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −2.00000 | − | 3.46410i | −0.280056 | − | 0.485071i | ||||
\(52\) | 2.50000 | − | 4.33013i | 0.346688 | − | 0.600481i | ||||
\(53\) | 4.50000 | − | 7.79423i | 0.618123 | − | 1.07062i | −0.371706 | − | 0.928351i | \(-0.621227\pi\) |
0.989828 | − | 0.142269i | \(-0.0454398\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | −2.00000 | − | 1.73205i | −0.267261 | − | 0.231455i | ||||
\(57\) | 7.00000 | 0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0.500000 | − | 0.866025i | 0.0645497 | − | 0.111803i | ||||
\(61\) | −2.00000 | − | 3.46410i | −0.256074 | − | 0.443533i | 0.709113 | − | 0.705095i | \(-0.249096\pi\) |
−0.965187 | + | 0.261562i | \(0.915762\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | −0.500000 | + | 2.59808i | −0.0629941 | + | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.50000 | + | 4.33013i | 0.310087 | + | 0.537086i | ||||
\(66\) | −2.50000 | + | 4.33013i | −0.307729 | + | 0.533002i | ||||
\(67\) | 6.00000 | − | 10.3923i | 0.733017 | − | 1.26962i | −0.222571 | − | 0.974916i | \(-0.571445\pi\) |
0.955588 | − | 0.294706i | \(-0.0952216\pi\) | |||||||
\(68\) | 2.00000 | + | 3.46410i | 0.242536 | + | 0.420084i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 2.50000 | − | 0.866025i | 0.298807 | − | 0.103510i | ||||
\(71\) | 2.00000 | 0.237356 | 0.118678 | − | 0.992933i | \(-0.462134\pi\) | ||||
0.118678 | + | 0.992933i | \(0.462134\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −5.00000 | + | 8.66025i | −0.585206 | + | 1.01361i | 0.409644 | + | 0.912245i | \(0.365653\pi\) |
−0.994850 | + | 0.101361i | \(0.967680\pi\) | |||||||
\(74\) | −0.500000 | + | 0.866025i | −0.0581238 | + | 0.100673i | ||||
\(75\) | 0.500000 | + | 0.866025i | 0.0577350 | + | 0.100000i | ||||
\(76\) | −7.00000 | −0.802955 | ||||||||
\(77\) | −12.5000 | + | 4.33013i | −1.42451 | + | 0.493464i | ||||
\(78\) | 5.00000 | 0.566139 | ||||||||
\(79\) | 6.00000 | + | 10.3923i | 0.675053 | + | 1.16923i | 0.976453 | + | 0.215728i | \(0.0692125\pi\) |
−0.301401 | + | 0.953498i | \(0.597454\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −2.50000 | − | 4.33013i | −0.276079 | − | 0.478183i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 0.500000 | − | 2.59808i | 0.0545545 | − | 0.283473i | ||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | −6.00000 | − | 10.3923i | −0.646997 | − | 1.12063i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.50000 | − | 4.33013i | 0.266501 | − | 0.461593i | ||||
\(89\) | −7.00000 | − | 12.1244i | −0.741999 | − | 1.28518i | −0.951584 | − | 0.307389i | \(-0.900545\pi\) |
0.209585 | − | 0.977790i | \(-0.432789\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 10.0000 | + | 8.66025i | 1.04828 | + | 0.907841i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | 5.50000 | − | 9.52628i | 0.567282 | − | 0.982561i | ||||
\(95\) | 3.50000 | − | 6.06218i | 0.359092 | − | 0.621966i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | 5.50000 | − | 4.33013i | 0.555584 | − | 0.437409i | ||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | −2.00000 | + | 3.46410i | −0.198030 | + | 0.342997i | ||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −5.00000 | −0.490290 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | −9.00000 | −0.874157 | ||||||||
\(107\) | 1.00000 | + | 1.73205i | 0.0966736 | + | 0.167444i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | 2.50000 | + | 4.33013i | 0.238366 | + | 0.412861i | ||||
\(111\) | −1.00000 | −0.0949158 | ||||||||
\(112\) | −0.500000 | + | 2.59808i | −0.0472456 | + | 0.245495i | ||||
\(113\) | −14.0000 | −1.31701 | −0.658505 | − | 0.752577i | \(-0.728811\pi\) | ||||
−0.658505 | + | 0.752577i | \(0.728811\pi\) | |||||||
\(114\) | −3.50000 | − | 6.06218i | −0.327805 | − | 0.567775i | ||||
\(115\) | −0.500000 | + | 0.866025i | −0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.50000 | + | 4.33013i | 0.231125 | + | 0.400320i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | −10.0000 | + | 3.46410i | −0.916698 | + | 0.317554i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | −2.00000 | + | 3.46410i | −0.181071 | + | 0.313625i | ||||
\(123\) | 2.50000 | − | 4.33013i | 0.225417 | − | 0.390434i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | 9.00000 | 0.798621 | 0.399310 | − | 0.916816i | \(-0.369250\pi\) | ||||
0.399310 | + | 0.916816i | \(0.369250\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 6.00000 | − | 10.3923i | 0.528271 | − | 0.914991i | ||||
\(130\) | 2.50000 | − | 4.33013i | 0.219265 | − | 0.379777i | ||||
\(131\) | 4.50000 | + | 7.79423i | 0.393167 | + | 0.680985i | 0.992865 | − | 0.119241i | \(-0.0380462\pi\) |
−0.599699 | + | 0.800226i | \(0.704713\pi\) | |||||||
\(132\) | 5.00000 | 0.435194 | ||||||||
\(133\) | 3.50000 | − | 18.1865i | 0.303488 | − | 1.57697i | ||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0.500000 | + | 0.866025i | 0.0430331 | + | 0.0745356i | ||||
\(136\) | 2.00000 | − | 3.46410i | 0.171499 | − | 0.297044i | ||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | 0.500000 | + | 0.866025i | 0.0425628 | + | 0.0737210i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | −2.00000 | − | 1.73205i | −0.169031 | − | 0.146385i | ||||
\(141\) | 11.0000 | 0.926367 | ||||||||
\(142\) | −1.00000 | − | 1.73205i | −0.0839181 | − | 0.145350i | ||||
\(143\) | −12.5000 | + | 21.6506i | −1.04530 | + | 1.81052i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 10.0000 | 0.827606 | ||||||||
\(147\) | 6.50000 | + | 2.59808i | 0.536111 | + | 0.214286i | ||||
\(148\) | 1.00000 | 0.0821995 | ||||||||
\(149\) | −6.00000 | − | 10.3923i | −0.491539 | − | 0.851371i | 0.508413 | − | 0.861113i | \(-0.330232\pi\) |
−0.999953 | + | 0.00974235i | \(0.996899\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | −7.00000 | + | 12.1244i | −0.569652 | + | 0.986666i | 0.426948 | + | 0.904276i | \(0.359589\pi\) |
−0.996600 | + | 0.0823900i | \(0.973745\pi\) | |||||||
\(152\) | 3.50000 | + | 6.06218i | 0.283887 | + | 0.491708i | ||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 10.0000 | + | 8.66025i | 0.805823 | + | 0.697863i | ||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | −2.50000 | − | 4.33013i | −0.200160 | − | 0.346688i | ||||
\(157\) | −5.50000 | + | 9.52628i | −0.438948 | + | 0.760280i | −0.997609 | − | 0.0691164i | \(-0.977982\pi\) |
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 6.00000 | − | 10.3923i | 0.477334 | − | 0.826767i | ||||
\(159\) | −4.50000 | − | 7.79423i | −0.356873 | − | 0.618123i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −0.500000 | + | 2.59808i | −0.0394055 | + | 0.204757i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 12.0000 | + | 20.7846i | 0.939913 | + | 1.62798i | 0.765631 | + | 0.643280i | \(0.222427\pi\) |
0.174282 | + | 0.984696i | \(0.444240\pi\) | |||||||
\(164\) | −2.50000 | + | 4.33013i | −0.195217 | + | 0.338126i | ||||
\(165\) | −2.50000 | + | 4.33013i | −0.194625 | + | 0.337100i | ||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | 11.0000 | 0.851206 | 0.425603 | − | 0.904910i | \(-0.360062\pi\) | ||||
0.425603 | + | 0.904910i | \(0.360062\pi\) | |||||||
\(168\) | −2.50000 | + | 0.866025i | −0.192879 | + | 0.0668153i | ||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 2.00000 | + | 3.46410i | 0.153393 | + | 0.265684i | ||||
\(171\) | 3.50000 | − | 6.06218i | 0.267652 | − | 0.463586i | ||||
\(172\) | −6.00000 | + | 10.3923i | −0.457496 | + | 0.792406i | ||||
\(173\) | 6.50000 | + | 11.2583i | 0.494186 | + | 0.855955i | 0.999978 | − | 0.00670064i | \(-0.00213290\pi\) |
−0.505792 | + | 0.862656i | \(0.668800\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.50000 | − | 0.866025i | 0.188982 | − | 0.0654654i | ||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | −7.00000 | + | 12.1244i | −0.524672 | + | 0.908759i | ||||
\(179\) | 11.5000 | − | 19.9186i | 0.859550 | − | 1.48878i | −0.0128080 | − | 0.999918i | \(-0.504077\pi\) |
0.872358 | − | 0.488867i | \(-0.162590\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 20.0000 | 1.48659 | 0.743294 | − | 0.668965i | \(-0.233262\pi\) | ||||
0.743294 | + | 0.668965i | \(0.233262\pi\) | |||||||
\(182\) | 2.50000 | − | 12.9904i | 0.185312 | − | 0.962911i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | −0.500000 | + | 0.866025i | −0.0367607 | + | 0.0636715i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −10.0000 | − | 17.3205i | −0.731272 | − | 1.26660i | ||||
\(188\) | −11.0000 | −0.802257 | ||||||||
\(189\) | 2.00000 | + | 1.73205i | 0.145479 | + | 0.125988i | ||||
\(190\) | −7.00000 | −0.507833 | ||||||||
\(191\) | −7.00000 | − | 12.1244i | −0.506502 | − | 0.877288i | −0.999972 | − | 0.00752447i | \(-0.997605\pi\) |
0.493469 | − | 0.869763i | \(-0.335728\pi\) | |||||||
\(192\) | 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 | \(0.283859\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | 5.00000 | 0.358057 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 2.50000 | + | 4.33013i | 0.177667 | + | 0.307729i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | −0.500000 | + | 0.866025i | −0.0353553 | + | 0.0612372i | ||||
\(201\) | −6.00000 | − | 10.3923i | −0.423207 | − | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | −2.50000 | − | 4.33013i | −0.174608 | − | 0.302429i | ||||
\(206\) | −4.00000 | + | 6.92820i | −0.278693 | + | 0.482711i | ||||
\(207\) | −0.500000 | + | 0.866025i | −0.0347524 | + | 0.0601929i | ||||
\(208\) | 2.50000 | + | 4.33013i | 0.173344 | + | 0.300240i | ||||
\(209\) | 35.0000 | 2.42100 | ||||||||
\(210\) | 0.500000 | − | 2.59808i | 0.0345033 | − | 0.179284i | ||||
\(211\) | 17.0000 | 1.17033 | 0.585164 | − | 0.810915i | \(-0.301030\pi\) | ||||
0.585164 | + | 0.810915i | \(0.301030\pi\) | |||||||
\(212\) | 4.50000 | + | 7.79423i | 0.309061 | + | 0.535310i | ||||
\(213\) | 1.00000 | − | 1.73205i | 0.0685189 | − | 0.118678i | ||||
\(214\) | 1.00000 | − | 1.73205i | 0.0683586 | − | 0.118401i | ||||
\(215\) | −6.00000 | − | 10.3923i | −0.409197 | − | 0.708749i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −5.00000 | + | 1.73205i | −0.339422 | + | 0.117579i | ||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | 5.00000 | + | 8.66025i | 0.337869 | + | 0.585206i | ||||
\(220\) | 2.50000 | − | 4.33013i | 0.168550 | − | 0.291937i | ||||
\(221\) | −10.0000 | + | 17.3205i | −0.672673 | + | 1.16510i | ||||
\(222\) | 0.500000 | + | 0.866025i | 0.0335578 | + | 0.0581238i | ||||
\(223\) | −12.0000 | −0.803579 | −0.401790 | − | 0.915732i | \(-0.631612\pi\) | ||||
−0.401790 | + | 0.915732i | \(0.631612\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 7.00000 | + | 12.1244i | 0.465633 | + | 0.806500i | ||||
\(227\) | 6.00000 | − | 10.3923i | 0.398234 | − | 0.689761i | −0.595274 | − | 0.803523i | \(-0.702957\pi\) |
0.993508 | + | 0.113761i | \(0.0362899\pi\) | |||||||
\(228\) | −3.50000 | + | 6.06218i | −0.231793 | + | 0.401478i | ||||
\(229\) | −5.00000 | − | 8.66025i | −0.330409 | − | 0.572286i | 0.652183 | − | 0.758062i | \(-0.273853\pi\) |
−0.982592 | + | 0.185776i | \(0.940520\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | −2.50000 | + | 12.9904i | −0.164488 | + | 0.854704i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00000 | + | 12.1244i | 0.458585 | + | 0.794293i | 0.998886 | − | 0.0471787i | \(-0.0150230\pi\) |
−0.540301 | + | 0.841472i | \(0.681690\pi\) | |||||||
\(234\) | 2.50000 | − | 4.33013i | 0.163430 | − | 0.283069i | ||||
\(235\) | 5.50000 | − | 9.52628i | 0.358780 | − | 0.621426i | ||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 12.0000 | 0.779484 | ||||||||
\(238\) | 8.00000 | + | 6.92820i | 0.518563 | + | 0.449089i | ||||
\(239\) | −22.0000 | −1.42306 | −0.711531 | − | 0.702655i | \(-0.751998\pi\) | ||||
−0.711531 | + | 0.702655i | \(0.751998\pi\) | |||||||
\(240\) | 0.500000 | + | 0.866025i | 0.0322749 | + | 0.0559017i | ||||
\(241\) | −7.50000 | + | 12.9904i | −0.483117 | + | 0.836784i | −0.999812 | − | 0.0193858i | \(-0.993829\pi\) |
0.516695 | + | 0.856170i | \(0.327162\pi\) | |||||||
\(242\) | −7.00000 | + | 12.1244i | −0.449977 | + | 0.779383i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 5.50000 | − | 4.33013i | 0.351382 | − | 0.276642i | ||||
\(246\) | −5.00000 | −0.318788 | ||||||||
\(247\) | −17.5000 | − | 30.3109i | −1.11350 | − | 1.92864i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | −6.00000 | + | 10.3923i | −0.380235 | + | 0.658586i | ||||
\(250\) | −0.500000 | − | 0.866025i | −0.0316228 | − | 0.0547723i | ||||
\(251\) | 1.00000 | 0.0631194 | 0.0315597 | − | 0.999502i | \(-0.489953\pi\) | ||||
0.0315597 | + | 0.999502i | \(0.489953\pi\) | |||||||
\(252\) | −2.00000 | − | 1.73205i | −0.125988 | − | 0.109109i | ||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | −4.50000 | − | 7.79423i | −0.282355 | − | 0.489053i | ||||
\(255\) | −2.00000 | + | 3.46410i | −0.125245 | + | 0.216930i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 8.00000 | + | 13.8564i | 0.499026 | + | 0.864339i | 0.999999 | − | 0.00112398i | \(-0.000357774\pi\) |
−0.500973 | + | 0.865463i | \(0.667024\pi\) | |||||||
\(258\) | −12.0000 | −0.747087 | ||||||||
\(259\) | −0.500000 | + | 2.59808i | −0.0310685 | + | 0.161437i | ||||
\(260\) | −5.00000 | −0.310087 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.50000 | − | 7.79423i | 0.278011 | − | 0.481529i | ||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −2.50000 | − | 4.33013i | −0.153864 | − | 0.266501i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | −17.5000 | + | 6.06218i | −1.07299 | + | 0.371696i | ||||
\(267\) | −14.0000 | −0.856786 | ||||||||
\(268\) | 6.00000 | + | 10.3923i | 0.366508 | + | 0.634811i | ||||
\(269\) | 12.0000 | − | 20.7846i | 0.731653 | − | 1.26726i | −0.224523 | − | 0.974469i | \(-0.572083\pi\) |
0.956176 | − | 0.292791i | \(-0.0945841\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 12.5000 | − | 4.33013i | 0.756534 | − | 0.262071i | ||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 2.50000 | + | 4.33013i | 0.150756 | + | 0.261116i | ||||
\(276\) | 0.500000 | − | 0.866025i | 0.0300965 | − | 0.0521286i | ||||
\(277\) | −7.00000 | + | 12.1244i | −0.420589 | + | 0.728482i | −0.995997 | − | 0.0893846i | \(-0.971510\pi\) |
0.575408 | + | 0.817867i | \(0.304843\pi\) | |||||||
\(278\) | 2.00000 | + | 3.46410i | 0.119952 | + | 0.207763i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | −0.500000 | + | 2.59808i | −0.0298807 | + | 0.155265i | ||||
\(281\) | 7.00000 | 0.417585 | 0.208792 | − | 0.977960i | \(-0.433047\pi\) | ||||
0.208792 | + | 0.977960i | \(0.433047\pi\) | |||||||
\(282\) | −5.50000 | − | 9.52628i | −0.327520 | − | 0.567282i | ||||
\(283\) | 5.00000 | − | 8.66025i | 0.297219 | − | 0.514799i | −0.678280 | − | 0.734804i | \(-0.737274\pi\) |
0.975499 | + | 0.220005i | \(0.0706075\pi\) | |||||||
\(284\) | −1.00000 | + | 1.73205i | −0.0593391 | + | 0.102778i | ||||
\(285\) | −3.50000 | − | 6.06218i | −0.207322 | − | 0.359092i | ||||
\(286\) | 25.0000 | 1.47828 | ||||||||
\(287\) | −10.0000 | − | 8.66025i | −0.590281 | − | 0.511199i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.500000 | + | 0.866025i | 0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | −5.00000 | − | 8.66025i | −0.292603 | − | 0.506803i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | 4.00000 | 0.232889 | ||||||||
\(296\) | −0.500000 | − | 0.866025i | −0.0290619 | − | 0.0503367i | ||||
\(297\) | −2.50000 | + | 4.33013i | −0.145065 | + | 0.251259i | ||||
\(298\) | −6.00000 | + | 10.3923i | −0.347571 | + | 0.602010i | ||||
\(299\) | 2.50000 | + | 4.33013i | 0.144579 | + | 0.250418i | ||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | −24.0000 | − | 20.7846i | −1.38334 | − | 1.19800i | ||||
\(302\) | 14.0000 | 0.805609 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.50000 | − | 6.06218i | 0.200739 | − | 0.347690i | ||||
\(305\) | −2.00000 | + | 3.46410i | −0.114520 | + | 0.198354i | ||||
\(306\) | 2.00000 | + | 3.46410i | 0.114332 | + | 0.198030i | ||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 2.50000 | − | 12.9904i | 0.142451 | − | 0.740196i | ||||
\(309\) | −8.00000 | −0.455104 | ||||||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | −4.00000 | + | 6.92820i | −0.226819 | + | 0.392862i | −0.956864 | − | 0.290537i | \(-0.906166\pi\) |
0.730044 | + | 0.683400i | \(0.239499\pi\) | |||||||
\(312\) | −2.50000 | + | 4.33013i | −0.141535 | + | 0.245145i | ||||
\(313\) | −8.00000 | − | 13.8564i | −0.452187 | − | 0.783210i | 0.546335 | − | 0.837567i | \(-0.316023\pi\) |
−0.998522 | + | 0.0543564i | \(0.982689\pi\) | |||||||
\(314\) | 11.0000 | 0.620766 | ||||||||
\(315\) | 2.50000 | − | 0.866025i | 0.140859 | − | 0.0487950i | ||||
\(316\) | −12.0000 | −0.675053 | ||||||||
\(317\) | 11.0000 | + | 19.0526i | 0.617822 | + | 1.07010i | 0.989882 | + | 0.141890i | \(0.0453179\pi\) |
−0.372061 | + | 0.928208i | \(0.621349\pi\) | |||||||
\(318\) | −4.50000 | + | 7.79423i | −0.252347 | + | 0.437079i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 2.00000 | 0.111629 | ||||||||
\(322\) | 2.50000 | − | 0.866025i | 0.139320 | − | 0.0482617i | ||||
\(323\) | 28.0000 | 1.55796 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.50000 | − | 4.33013i | 0.138675 | − | 0.240192i | ||||
\(326\) | 12.0000 | − | 20.7846i | 0.664619 | − | 1.15115i | ||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 5.00000 | 0.276079 | ||||||||
\(329\) | 5.50000 | − | 28.5788i | 0.303225 | − | 1.57560i | ||||
\(330\) | 5.00000 | 0.275241 | ||||||||
\(331\) | −15.5000 | − | 26.8468i | −0.851957 | − | 1.47563i | −0.879440 | − | 0.476011i | \(-0.842082\pi\) |
0.0274825 | − | 0.999622i | \(-0.491251\pi\) | |||||||
\(332\) | 6.00000 | − | 10.3923i | 0.329293 | − | 0.570352i | ||||
\(333\) | −0.500000 | + | 0.866025i | −0.0273998 | + | 0.0474579i | ||||
\(334\) | −5.50000 | − | 9.52628i | −0.300947 | − | 0.521255i | ||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | 2.00000 | + | 1.73205i | 0.109109 | + | 0.0944911i | ||||
\(337\) | −16.0000 | −0.871576 | −0.435788 | − | 0.900049i | \(-0.643530\pi\) | ||||
−0.435788 | + | 0.900049i | \(0.643530\pi\) | |||||||
\(338\) | −6.00000 | − | 10.3923i | −0.326357 | − | 0.565267i | ||||
\(339\) | −7.00000 | + | 12.1244i | −0.380188 | + | 0.658505i | ||||
\(340\) | 2.00000 | − | 3.46410i | 0.108465 | − | 0.187867i | ||||
\(341\) | −5.00000 | − | 8.66025i | −0.270765 | − | 0.468979i | ||||
\(342\) | −7.00000 | −0.378517 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 0.500000 | + | 0.866025i | 0.0269191 | + | 0.0466252i | ||||
\(346\) | 6.50000 | − | 11.2583i | 0.349442 | − | 0.605252i | ||||
\(347\) | 9.00000 | − | 15.5885i | 0.483145 | − | 0.836832i | −0.516667 | − | 0.856186i | \(-0.672828\pi\) |
0.999813 | + | 0.0193540i | \(0.00616095\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.00000 | −0.214115 | −0.107058 | − | 0.994253i | \(-0.534143\pi\) | ||||
−0.107058 | + | 0.994253i | \(0.534143\pi\) | |||||||
\(350\) | −2.00000 | − | 1.73205i | −0.106904 | − | 0.0925820i | ||||
\(351\) | 5.00000 | 0.266880 | ||||||||
\(352\) | 2.50000 | + | 4.33013i | 0.133250 | + | 0.230797i | ||||
\(353\) | −12.0000 | + | 20.7846i | −0.638696 | + | 1.10625i | 0.347024 | + | 0.937856i | \(0.387192\pi\) |
−0.985719 | + | 0.168397i | \(0.946141\pi\) | |||||||
\(354\) | 2.00000 | − | 3.46410i | 0.106299 | − | 0.184115i | ||||
\(355\) | −1.00000 | − | 1.73205i | −0.0530745 | − | 0.0919277i | ||||
\(356\) | 14.0000 | 0.741999 | ||||||||
\(357\) | −2.00000 | + | 10.3923i | −0.105851 | + | 0.550019i | ||||
\(358\) | −23.0000 | −1.21559 | ||||||||
\(359\) | 10.0000 | + | 17.3205i | 0.527780 | + | 0.914141i | 0.999476 | + | 0.0323801i | \(0.0103087\pi\) |
−0.471696 | + | 0.881761i | \(0.656358\pi\) | |||||||
\(360\) | −0.500000 | + | 0.866025i | −0.0263523 | + | 0.0456435i | ||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | −10.0000 | − | 17.3205i | −0.525588 | − | 0.910346i | ||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | −12.5000 | + | 4.33013i | −0.655178 | + | 0.226960i | ||||
\(365\) | 10.0000 | 0.523424 | ||||||||
\(366\) | 2.00000 | + | 3.46410i | 0.104542 | + | 0.181071i | ||||
\(367\) | −3.50000 | + | 6.06218i | −0.182699 | + | 0.316443i | −0.942799 | − | 0.333363i | \(-0.891817\pi\) |
0.760100 | + | 0.649806i | \(0.225150\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | −2.50000 | − | 4.33013i | −0.130145 | − | 0.225417i | ||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | −22.5000 | + | 7.79423i | −1.16814 | + | 0.404656i | ||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | −10.0000 | + | 17.3205i | −0.517088 | + | 0.895622i | ||||
\(375\) | 0.500000 | − | 0.866025i | 0.0258199 | − | 0.0447214i | ||||
\(376\) | 5.50000 | + | 9.52628i | 0.283641 | + | 0.491280i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0.500000 | − | 2.59808i | 0.0257172 | − | 0.133631i | ||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 3.50000 | + | 6.06218i | 0.179546 | + | 0.310983i | ||||
\(381\) | 4.50000 | − | 7.79423i | 0.230542 | − | 0.399310i | ||||
\(382\) | −7.00000 | + | 12.1244i | −0.358151 | + | 0.620336i | ||||
\(383\) | −10.5000 | − | 18.1865i | −0.536525 | − | 0.929288i | −0.999088 | − | 0.0427020i | \(-0.986403\pi\) |
0.462563 | − | 0.886586i | \(-0.346930\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 10.0000 | + | 8.66025i | 0.509647 | + | 0.441367i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | −6.00000 | − | 10.3923i | −0.304997 | − | 0.528271i | ||||
\(388\) | 4.00000 | − | 6.92820i | 0.203069 | − | 0.351726i | ||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | −2.50000 | − | 4.33013i | −0.126592 | − | 0.219265i | ||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | 9.00000 | 0.453990 | ||||||||
\(394\) | 1.50000 | + | 2.59808i | 0.0755689 | + | 0.130889i | ||||
\(395\) | 6.00000 | − | 10.3923i | 0.301893 | − | 0.522894i | ||||
\(396\) | 2.50000 | − | 4.33013i | 0.125630 | − | 0.217597i | ||||
\(397\) | 7.00000 | + | 12.1244i | 0.351320 | + | 0.608504i | 0.986481 | − | 0.163876i | \(-0.0523996\pi\) |
−0.635161 | + | 0.772380i | \(0.719066\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | −14.0000 | − | 12.1244i | −0.700877 | − | 0.606977i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 10.5000 | + | 18.1865i | 0.524345 | + | 0.908192i | 0.999598 | + | 0.0283431i | \(0.00902310\pi\) |
−0.475253 | + | 0.879849i | \(0.657644\pi\) | |||||||
\(402\) | −6.00000 | + | 10.3923i | −0.299253 | + | 0.518321i | ||||
\(403\) | −5.00000 | + | 8.66025i | −0.249068 | + | 0.431398i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5.00000 | −0.247841 | ||||||||
\(408\) | −2.00000 | − | 3.46410i | −0.0990148 | − | 0.171499i | ||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | −2.50000 | + | 4.33013i | −0.123466 | + | 0.213850i | ||||
\(411\) | −1.00000 | − | 1.73205i | −0.0493264 | − | 0.0854358i | ||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 10.0000 | − | 3.46410i | 0.492068 | − | 0.170457i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 6.00000 | + | 10.3923i | 0.294528 | + | 0.510138i | ||||
\(416\) | 2.50000 | − | 4.33013i | 0.122573 | − | 0.212302i | ||||
\(417\) | −2.00000 | + | 3.46410i | −0.0979404 | + | 0.169638i | ||||
\(418\) | −17.5000 | − | 30.3109i | −0.855953 | − | 1.48255i | ||||
\(419\) | 15.0000 | 0.732798 | 0.366399 | − | 0.930458i | \(-0.380591\pi\) | ||||
0.366399 | + | 0.930458i | \(0.380591\pi\) | |||||||
\(420\) | −2.50000 | + | 0.866025i | −0.121988 | + | 0.0422577i | ||||
\(421\) | 10.0000 | 0.487370 | 0.243685 | − | 0.969854i | \(-0.421644\pi\) | ||||
0.243685 | + | 0.969854i | \(0.421644\pi\) | |||||||
\(422\) | −8.50000 | − | 14.7224i | −0.413774 | − | 0.716677i | ||||
\(423\) | 5.50000 | − | 9.52628i | 0.267419 | − | 0.463184i | ||||
\(424\) | 4.50000 | − | 7.79423i | 0.218539 | − | 0.378521i | ||||
\(425\) | 2.00000 | + | 3.46410i | 0.0970143 | + | 0.168034i | ||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | −2.00000 | + | 10.3923i | −0.0967868 | + | 0.502919i | ||||
\(428\) | −2.00000 | −0.0966736 | ||||||||
\(429\) | 12.5000 | + | 21.6506i | 0.603506 | + | 1.04530i | ||||
\(430\) | −6.00000 | + | 10.3923i | −0.289346 | + | 0.501161i | ||||
\(431\) | −6.00000 | + | 10.3923i | −0.289010 | + | 0.500580i | −0.973574 | − | 0.228373i | \(-0.926659\pi\) |
0.684564 | + | 0.728953i | \(0.259993\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 24.0000 | 1.15337 | 0.576683 | − | 0.816968i | \(-0.304347\pi\) | ||||
0.576683 | + | 0.816968i | \(0.304347\pi\) | |||||||
\(434\) | 4.00000 | + | 3.46410i | 0.192006 | + | 0.166282i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | 3.50000 | − | 6.06218i | 0.167428 | − | 0.289993i | ||||
\(438\) | 5.00000 | − | 8.66025i | 0.238909 | − | 0.413803i | ||||
\(439\) | 20.0000 | + | 34.6410i | 0.954548 | + | 1.65333i | 0.735399 | + | 0.677634i | \(0.236995\pi\) |
0.219149 | + | 0.975691i | \(0.429672\pi\) | |||||||
\(440\) | −5.00000 | −0.238366 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 20.0000 | 0.951303 | ||||||||
\(443\) | 14.0000 | + | 24.2487i | 0.665160 | + | 1.15209i | 0.979242 | + | 0.202695i | \(0.0649700\pi\) |
−0.314082 | + | 0.949396i | \(0.601697\pi\) | |||||||
\(444\) | 0.500000 | − | 0.866025i | 0.0237289 | − | 0.0410997i | ||||
\(445\) | −7.00000 | + | 12.1244i | −0.331832 | + | 0.574750i | ||||
\(446\) | 6.00000 | + | 10.3923i | 0.284108 | + | 0.492090i | ||||
\(447\) | −12.0000 | −0.567581 | ||||||||
\(448\) | −2.00000 | − | 1.73205i | −0.0944911 | − | 0.0818317i | ||||
\(449\) | −29.0000 | −1.36859 | −0.684297 | − | 0.729203i | \(-0.739891\pi\) | ||||
−0.684297 | + | 0.729203i | \(0.739891\pi\) | |||||||
\(450\) | −0.500000 | − | 0.866025i | −0.0235702 | − | 0.0408248i | ||||
\(451\) | 12.5000 | − | 21.6506i | 0.588602 | − | 1.01949i | ||||
\(452\) | 7.00000 | − | 12.1244i | 0.329252 | − | 0.570282i | ||||
\(453\) | 7.00000 | + | 12.1244i | 0.328889 | + | 0.569652i | ||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | 2.50000 | − | 12.9904i | 0.117202 | − | 0.608998i | ||||
\(456\) | 7.00000 | 0.327805 | ||||||||
\(457\) | 7.00000 | + | 12.1244i | 0.327446 | + | 0.567153i | 0.982004 | − | 0.188858i | \(-0.0604787\pi\) |
−0.654558 | + | 0.756012i | \(0.727145\pi\) | |||||||
\(458\) | −5.00000 | + | 8.66025i | −0.233635 | + | 0.404667i | ||||
\(459\) | −2.00000 | + | 3.46410i | −0.0933520 | + | 0.161690i | ||||
\(460\) | −0.500000 | − | 0.866025i | −0.0233126 | − | 0.0403786i | ||||
\(461\) | −4.00000 | −0.186299 | −0.0931493 | − | 0.995652i | \(-0.529693\pi\) | ||||
−0.0931493 | + | 0.995652i | \(0.529693\pi\) | |||||||
\(462\) | 12.5000 | − | 4.33013i | 0.581553 | − | 0.201456i | ||||
\(463\) | −19.0000 | −0.883005 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.00000 | + | 1.73205i | −0.0463739 | + | 0.0803219i | ||||
\(466\) | 7.00000 | − | 12.1244i | 0.324269 | − | 0.561650i | ||||
\(467\) | 10.0000 | + | 17.3205i | 0.462745 | + | 0.801498i | 0.999097 | − | 0.0424970i | \(-0.0135313\pi\) |
−0.536352 | + | 0.843995i | \(0.680198\pi\) | |||||||
\(468\) | −5.00000 | −0.231125 | ||||||||
\(469\) | −30.0000 | + | 10.3923i | −1.38527 | + | 0.479872i | ||||
\(470\) | −11.0000 | −0.507392 | ||||||||
\(471\) | 5.50000 | + | 9.52628i | 0.253427 | + | 0.438948i | ||||
\(472\) | −2.00000 | + | 3.46410i | −0.0920575 | + | 0.159448i | ||||
\(473\) | 30.0000 | − | 51.9615i | 1.37940 | − | 2.38919i | ||||
\(474\) | −6.00000 | − | 10.3923i | −0.275589 | − | 0.477334i | ||||
\(475\) | −7.00000 | −0.321182 | ||||||||
\(476\) | 2.00000 | − | 10.3923i | 0.0916698 | − | 0.476331i | ||||
\(477\) | −9.00000 | −0.412082 | ||||||||
\(478\) | 11.0000 | + | 19.0526i | 0.503128 | + | 0.871444i | ||||
\(479\) | −9.00000 | + | 15.5885i | −0.411220 | + | 0.712255i | −0.995023 | − | 0.0996406i | \(-0.968231\pi\) |
0.583803 | + | 0.811895i | \(0.301564\pi\) | |||||||
\(480\) | 0.500000 | − | 0.866025i | 0.0228218 | − | 0.0395285i | ||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | 15.0000 | 0.683231 | ||||||||
\(483\) | 2.00000 | + | 1.73205i | 0.0910032 | + | 0.0788110i | ||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 4.00000 | + | 6.92820i | 0.181631 | + | 0.314594i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(488\) | −2.00000 | − | 3.46410i | −0.0905357 | − | 0.156813i | ||||
\(489\) | 24.0000 | 1.08532 | ||||||||
\(490\) | −6.50000 | − | 2.59808i | −0.293640 | − | 0.117369i | ||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 2.50000 | + | 4.33013i | 0.112709 | + | 0.195217i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −17.5000 | + | 30.3109i | −0.787362 | + | 1.36375i | ||||
\(495\) | 2.50000 | + | 4.33013i | 0.112367 | + | 0.194625i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −4.00000 | − | 3.46410i | −0.179425 | − | 0.155386i | ||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | −20.0000 | − | 34.6410i | −0.895323 | − | 1.55074i | −0.833404 | − | 0.552664i | \(-0.813611\pi\) |
−0.0619186 | − | 0.998081i | \(-0.519722\pi\) | |||||||
\(500\) | −0.500000 | + | 0.866025i | −0.0223607 | + | 0.0387298i | ||||
\(501\) | 5.50000 | − | 9.52628i | 0.245722 | − | 0.425603i | ||||
\(502\) | −0.500000 | − | 0.866025i | −0.0223161 | − | 0.0386526i | ||||
\(503\) | −20.0000 | −0.891756 | −0.445878 | − | 0.895094i | \(-0.647108\pi\) | ||||
−0.445878 | + | 0.895094i | \(0.647108\pi\) | |||||||
\(504\) | −0.500000 | + | 2.59808i | −0.0222718 | + | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 2.50000 | + | 4.33013i | 0.111139 | + | 0.192498i | ||||
\(507\) | 6.00000 | − | 10.3923i | 0.266469 | − | 0.461538i | ||||
\(508\) | −4.50000 | + | 7.79423i | −0.199655 | + | 0.345813i | ||||
\(509\) | 5.00000 | + | 8.66025i | 0.221621 | + | 0.383859i | 0.955300 | − | 0.295637i | \(-0.0955319\pi\) |
−0.733679 | + | 0.679496i | \(0.762199\pi\) | |||||||
\(510\) | 4.00000 | 0.177123 | ||||||||
\(511\) | 25.0000 | − | 8.66025i | 1.10593 | − | 0.383107i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −3.50000 | − | 6.06218i | −0.154529 | − | 0.267652i | ||||
\(514\) | 8.00000 | − | 13.8564i | 0.352865 | − | 0.611180i | ||||
\(515\) | −4.00000 | + | 6.92820i | −0.176261 | + | 0.305293i | ||||
\(516\) | 6.00000 | + | 10.3923i | 0.264135 | + | 0.457496i | ||||
\(517\) | 55.0000 | 2.41890 | ||||||||
\(518\) | 2.50000 | − | 0.866025i | 0.109844 | − | 0.0380510i | ||||
\(519\) | 13.0000 | 0.570637 | ||||||||
\(520\) | 2.50000 | + | 4.33013i | 0.109632 | + | 0.189889i | ||||
\(521\) | 16.5000 | − | 28.5788i | 0.722878 | − | 1.25206i | −0.236963 | − | 0.971519i | \(-0.576152\pi\) |
0.959841 | − | 0.280543i | \(-0.0905145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.0000 | + | 19.0526i | 0.480996 | + | 0.833110i | 0.999762 | − | 0.0218062i | \(-0.00694167\pi\) |
−0.518766 | + | 0.854916i | \(0.673608\pi\) | |||||||
\(524\) | −9.00000 | −0.393167 | ||||||||
\(525\) | 0.500000 | − | 2.59808i | 0.0218218 | − | 0.113389i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | −2.50000 | + | 4.33013i | −0.108799 | + | 0.188445i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | 14.0000 | + | 12.1244i | 0.606977 | + | 0.525657i | ||||
\(533\) | −25.0000 | −1.08287 | ||||||||
\(534\) | 7.00000 | + | 12.1244i | 0.302920 | + | 0.524672i | ||||
\(535\) | 1.00000 | − | 1.73205i | 0.0432338 | − | 0.0748831i | ||||
\(536\) | 6.00000 | − | 10.3923i | 0.259161 | − | 0.448879i | ||||
\(537\) | −11.5000 | − | 19.9186i | −0.496262 | − | 0.859550i | ||||
\(538\) | −24.0000 | −1.03471 | ||||||||
\(539\) | 32.5000 | + | 12.9904i | 1.39987 | + | 0.559535i | ||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −1.00000 | − | 1.73205i | −0.0429934 | − | 0.0744667i | 0.843728 | − | 0.536771i | \(-0.180356\pi\) |
−0.886721 | + | 0.462304i | \(0.847023\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.0000 | − | 17.3205i | 0.429141 | − | 0.743294i | ||||
\(544\) | 2.00000 | + | 3.46410i | 0.0857493 | + | 0.148522i | ||||
\(545\) | −2.00000 | −0.0856706 | ||||||||
\(546\) | −10.0000 | − | 8.66025i | −0.427960 | − | 0.370625i | ||||
\(547\) | 28.0000 | 1.19719 | 0.598597 | − | 0.801050i | \(-0.295725\pi\) | ||||
0.598597 | + | 0.801050i | \(0.295725\pi\) | |||||||
\(548\) | 1.00000 | + | 1.73205i | 0.0427179 | + | 0.0739895i | ||||
\(549\) | −2.00000 | + | 3.46410i | −0.0853579 | + | 0.147844i | ||||
\(550\) | 2.50000 | − | 4.33013i | 0.106600 | − | 0.184637i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 6.00000 | − | 31.1769i | 0.255146 | − | 1.32578i | ||||
\(554\) | 14.0000 | 0.594803 | ||||||||
\(555\) | 0.500000 | + | 0.866025i | 0.0212238 | + | 0.0367607i | ||||
\(556\) | 2.00000 | − | 3.46410i | 0.0848189 | − | 0.146911i | ||||
\(557\) | −18.5000 | + | 32.0429i | −0.783870 | + | 1.35770i | 0.145802 | + | 0.989314i | \(0.453424\pi\) |
−0.929672 | + | 0.368389i | \(0.879909\pi\) | |||||||
\(558\) | 1.00000 | + | 1.73205i | 0.0423334 | + | 0.0733236i | ||||
\(559\) | −60.0000 | −2.53773 | ||||||||
\(560\) | 2.50000 | − | 0.866025i | 0.105644 | − | 0.0365963i | ||||
\(561\) | −20.0000 | −0.844401 | ||||||||
\(562\) | −3.50000 | − | 6.06218i | −0.147639 | − | 0.255718i | ||||
\(563\) | 9.00000 | − | 15.5885i | 0.379305 | − | 0.656975i | −0.611656 | − | 0.791123i | \(-0.709497\pi\) |
0.990961 | + | 0.134148i | \(0.0428299\pi\) | |||||||
\(564\) | −5.50000 | + | 9.52628i | −0.231592 | + | 0.401129i | ||||
\(565\) | 7.00000 | + | 12.1244i | 0.294492 | + | 0.510075i | ||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 2.50000 | − | 0.866025i | 0.104990 | − | 0.0363696i | ||||
\(568\) | 2.00000 | 0.0839181 | ||||||||
\(569\) | −19.5000 | − | 33.7750i | −0.817483 | − | 1.41592i | −0.907532 | − | 0.419984i | \(-0.862036\pi\) |
0.0900490 | − | 0.995937i | \(-0.471298\pi\) | |||||||
\(570\) | −3.50000 | + | 6.06218i | −0.146599 | + | 0.253917i | ||||
\(571\) | −20.0000 | + | 34.6410i | −0.836974 | + | 1.44968i | 0.0554391 | + | 0.998462i | \(0.482344\pi\) |
−0.892413 | + | 0.451219i | \(0.850989\pi\) | |||||||
\(572\) | −12.5000 | − | 21.6506i | −0.522651 | − | 0.905259i | ||||
\(573\) | −14.0000 | −0.584858 | ||||||||
\(574\) | −2.50000 | + | 12.9904i | −0.104348 | + | 0.542208i | ||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −13.0000 | + | 22.5167i | −0.541197 | + | 0.937381i | 0.457639 | + | 0.889138i | \(0.348695\pi\) |
−0.998836 | + | 0.0482425i | \(0.984638\pi\) | |||||||
\(578\) | 0.500000 | − | 0.866025i | 0.0207973 | − | 0.0360219i | ||||
\(579\) | 5.00000 | + | 8.66025i | 0.207793 | + | 0.359908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | −22.5000 | − | 38.9711i | −0.931855 | − | 1.61402i | ||||
\(584\) | −5.00000 | + | 8.66025i | −0.206901 | + | 0.358364i | ||||
\(585\) | 2.50000 | − | 4.33013i | 0.103362 | − | 0.179029i | ||||
\(586\) | −4.50000 | − | 7.79423i | −0.185893 | − | 0.321977i | ||||
\(587\) | −30.0000 | −1.23823 | −0.619116 | − | 0.785299i | \(-0.712509\pi\) | ||||
−0.619116 | + | 0.785299i | \(0.712509\pi\) | |||||||
\(588\) | −5.50000 | + | 4.33013i | −0.226816 | + | 0.178571i | ||||
\(589\) | 14.0000 | 0.576860 | ||||||||
\(590\) | −2.00000 | − | 3.46410i | −0.0823387 | − | 0.142615i | ||||
\(591\) | −1.50000 | + | 2.59808i | −0.0617018 | + | 0.106871i | ||||
\(592\) | −0.500000 | + | 0.866025i | −0.0205499 | + | 0.0355934i | ||||
\(593\) | −18.0000 | − | 31.1769i | −0.739171 | − | 1.28028i | −0.952869 | − | 0.303383i | \(-0.901884\pi\) |
0.213697 | − | 0.976900i | \(-0.431449\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 8.00000 | + | 6.92820i | 0.327968 | + | 0.284029i | ||||
\(596\) | 12.0000 | 0.491539 | ||||||||
\(597\) | −2.00000 | − | 3.46410i | −0.0818546 | − | 0.141776i | ||||
\(598\) | 2.50000 | − | 4.33013i | 0.102233 | − | 0.177072i | ||||
\(599\) | 5.00000 | − | 8.66025i | 0.204294 | − | 0.353848i | −0.745613 | − | 0.666379i | \(-0.767843\pi\) |
0.949908 | + | 0.312531i | \(0.101177\pi\) | |||||||
\(600\) | 0.500000 | + | 0.866025i | 0.0204124 | + | 0.0353553i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | −6.00000 | + | 31.1769i | −0.244542 | + | 1.27068i | ||||
\(603\) | −12.0000 | −0.488678 | ||||||||
\(604\) | −7.00000 | − | 12.1244i | −0.284826 | − | 0.493333i | ||||
\(605\) | −7.00000 | + | 12.1244i | −0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.5000 | + | 23.3827i | 0.547948 | + | 0.949074i | 0.998415 | + | 0.0562808i | \(0.0179242\pi\) |
−0.450467 | + | 0.892793i | \(0.648742\pi\) | |||||||
\(608\) | −7.00000 | −0.283887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.00000 | 0.161955 | ||||||||
\(611\) | −27.5000 | − | 47.6314i | −1.11253 | − | 1.92696i | ||||
\(612\) | 2.00000 | − | 3.46410i | 0.0808452 | − | 0.140028i | ||||
\(613\) | 21.5000 | − | 37.2391i | 0.868377 | − | 1.50407i | 0.00472215 | − | 0.999989i | \(-0.498497\pi\) |
0.863655 | − | 0.504084i | \(-0.168170\pi\) | |||||||
\(614\) | −4.00000 | − | 6.92820i | −0.161427 | − | 0.279600i | ||||
\(615\) | −5.00000 | −0.201619 | ||||||||
\(616\) | −12.5000 | + | 4.33013i | −0.503639 | + | 0.174466i | ||||
\(617\) | −8.00000 | −0.322068 | −0.161034 | − | 0.986949i | \(-0.551483\pi\) | ||||
−0.161034 | + | 0.986949i | \(0.551483\pi\) | |||||||
\(618\) | 4.00000 | + | 6.92820i | 0.160904 | + | 0.278693i | ||||
\(619\) | −12.5000 | + | 21.6506i | −0.502417 | + | 0.870212i | 0.497579 | + | 0.867419i | \(0.334223\pi\) |
−0.999996 | + | 0.00279365i | \(0.999111\pi\) | |||||||
\(620\) | 1.00000 | − | 1.73205i | 0.0401610 | − | 0.0695608i | ||||
\(621\) | 0.500000 | + | 0.866025i | 0.0200643 | + | 0.0347524i | ||||
\(622\) | 8.00000 | 0.320771 | ||||||||
\(623\) | −7.00000 | + | 36.3731i | −0.280449 | + | 1.45726i | ||||
\(624\) | 5.00000 | 0.200160 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −8.00000 | + | 13.8564i | −0.319744 | + | 0.553813i | ||||
\(627\) | 17.5000 | − | 30.3109i | 0.698883 | − | 1.21050i | ||||
\(628\) | −5.50000 | − | 9.52628i | −0.219474 | − | 0.380140i | ||||
\(629\) | −4.00000 | −0.159490 | ||||||||
\(630\) | −2.00000 | − | 1.73205i | −0.0796819 | − | 0.0690066i | ||||
\(631\) | 6.00000 | 0.238856 | 0.119428 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119428 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(632\) | 6.00000 | + | 10.3923i | 0.238667 | + | 0.413384i | ||||
\(633\) | 8.50000 | − | 14.7224i | 0.337845 | − | 0.585164i | ||||
\(634\) | 11.0000 | − | 19.0526i | 0.436866 | − | 0.756674i | ||||
\(635\) | −4.50000 | − | 7.79423i | −0.178577 | − | 0.309305i | ||||
\(636\) | 9.00000 | 0.356873 | ||||||||
\(637\) | −5.00000 | − | 34.6410i | −0.198107 | − | 1.37253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.00000 | − | 1.73205i | −0.0395594 | − | 0.0685189i | ||||
\(640\) | −0.500000 | + | 0.866025i | −0.0197642 | + | 0.0342327i | ||||
\(641\) | −10.5000 | + | 18.1865i | −0.414725 | + | 0.718325i | −0.995400 | − | 0.0958109i | \(-0.969456\pi\) |
0.580674 | + | 0.814136i | \(0.302789\pi\) | |||||||
\(642\) | −1.00000 | − | 1.73205i | −0.0394669 | − | 0.0683586i | ||||
\(643\) | 34.0000 | 1.34083 | 0.670415 | − | 0.741987i | \(-0.266116\pi\) | ||||
0.670415 | + | 0.741987i | \(0.266116\pi\) | |||||||
\(644\) | −2.00000 | − | 1.73205i | −0.0788110 | − | 0.0682524i | ||||
\(645\) | −12.0000 | −0.472500 | ||||||||
\(646\) | −14.0000 | − | 24.2487i | −0.550823 | − | 0.954053i | ||||
\(647\) | 11.5000 | − | 19.9186i | 0.452112 | − | 0.783080i | −0.546405 | − | 0.837521i | \(-0.684004\pi\) |
0.998517 | + | 0.0544405i | \(0.0173375\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 10.0000 | + | 17.3205i | 0.392534 | + | 0.679889i | ||||
\(650\) | −5.00000 | −0.196116 | ||||||||
\(651\) | −1.00000 | + | 5.19615i | −0.0391931 | + | 0.203653i | ||||
\(652\) | −24.0000 | −0.939913 | ||||||||
\(653\) | 9.50000 | + | 16.4545i | 0.371764 | + | 0.643914i | 0.989837 | − | 0.142207i | \(-0.0454198\pi\) |
−0.618073 | + | 0.786121i | \(0.712086\pi\) | |||||||
\(654\) | −1.00000 | + | 1.73205i | −0.0391031 | + | 0.0677285i | ||||
\(655\) | 4.50000 | − | 7.79423i | 0.175830 | − | 0.304546i | ||||
\(656\) | −2.50000 | − | 4.33013i | −0.0976086 | − | 0.169063i | ||||
\(657\) | 10.0000 | 0.390137 | ||||||||
\(658\) | −27.5000 | + | 9.52628i | −1.07206 | + | 0.371373i | ||||
\(659\) | −20.0000 | −0.779089 | −0.389545 | − | 0.921008i | \(-0.627368\pi\) | ||||
−0.389545 | + | 0.921008i | \(0.627368\pi\) | |||||||
\(660\) | −2.50000 | − | 4.33013i | −0.0973124 | − | 0.168550i | ||||
\(661\) | 20.0000 | − | 34.6410i | 0.777910 | − | 1.34738i | −0.155235 | − | 0.987878i | \(-0.549613\pi\) |
0.933144 | − | 0.359502i | \(-0.117053\pi\) | |||||||
\(662\) | −15.5000 | + | 26.8468i | −0.602425 | + | 1.04343i | ||||
\(663\) | 10.0000 | + | 17.3205i | 0.388368 | + | 0.672673i | ||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | −17.5000 | + | 6.06218i | −0.678621 | + | 0.235081i | ||||
\(666\) | 1.00000 | 0.0387492 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −5.50000 | + | 9.52628i | −0.212801 | + | 0.368583i | ||||
\(669\) | −6.00000 | + | 10.3923i | −0.231973 | + | 0.401790i | ||||
\(670\) | 6.00000 | + | 10.3923i | 0.231800 | + | 0.401490i | ||||
\(671\) | −20.0000 | −0.772091 | ||||||||
\(672\) | 0.500000 | − | 2.59808i | 0.0192879 | − | 0.100223i | ||||
\(673\) | −4.00000 | −0.154189 | −0.0770943 | − | 0.997024i | \(-0.524564\pi\) | ||||
−0.0770943 | + | 0.997024i | \(0.524564\pi\) | |||||||
\(674\) | 8.00000 | + | 13.8564i | 0.308148 | + | 0.533729i | ||||
\(675\) | 0.500000 | − | 0.866025i | 0.0192450 | − | 0.0333333i | ||||
\(676\) | −6.00000 | + | 10.3923i | −0.230769 | + | 0.399704i | ||||
\(677\) | −16.5000 | − | 28.5788i | −0.634147 | − | 1.09837i | −0.986695 | − | 0.162581i | \(-0.948018\pi\) |
0.352549 | − | 0.935793i | \(-0.385315\pi\) | |||||||
\(678\) | 14.0000 | 0.537667 | ||||||||
\(679\) | 16.0000 | + | 13.8564i | 0.614024 | + | 0.531760i | ||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | −6.00000 | − | 10.3923i | −0.229920 | − | 0.398234i | ||||
\(682\) | −5.00000 | + | 8.66025i | −0.191460 | + | 0.331618i | ||||
\(683\) | 2.00000 | − | 3.46410i | 0.0765279 | − | 0.132550i | −0.825222 | − | 0.564809i | \(-0.808950\pi\) |
0.901750 | + | 0.432259i | \(0.142283\pi\) | |||||||
\(684\) | 3.50000 | + | 6.06218i | 0.133826 | + | 0.231793i | ||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | −18.5000 | − | 0.866025i | −0.706333 | − | 0.0330650i | ||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | −6.00000 | − | 10.3923i | −0.228748 | − | 0.396203i | ||||
\(689\) | −22.5000 | + | 38.9711i | −0.857182 | + | 1.48468i | ||||
\(690\) | 0.500000 | − | 0.866025i | 0.0190347 | − | 0.0329690i | ||||
\(691\) | −14.0000 | − | 24.2487i | −0.532585 | − | 0.922464i | −0.999276 | − | 0.0380440i | \(-0.987887\pi\) |
0.466691 | − | 0.884420i | \(-0.345446\pi\) | |||||||
\(692\) | −13.0000 | −0.494186 | ||||||||
\(693\) | 10.0000 | + | 8.66025i | 0.379869 | + | 0.328976i | ||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | 2.00000 | + | 3.46410i | 0.0758643 | + | 0.131401i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0000 | − | 17.3205i | 0.378777 | − | 0.656061i | ||||
\(698\) | 2.00000 | + | 3.46410i | 0.0757011 | + | 0.131118i | ||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | −0.500000 | + | 2.59808i | −0.0188982 | + | 0.0981981i | ||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | −2.50000 | − | 4.33013i | −0.0943564 | − | 0.163430i | ||||
\(703\) | 3.50000 | − | 6.06218i | 0.132005 | − | 0.228639i | ||||
\(704\) | 2.50000 | − | 4.33013i | 0.0942223 | − | 0.163198i | ||||
\(705\) | −5.50000 | − | 9.52628i | −0.207142 | − | 0.358780i | ||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −14.0000 | − | 24.2487i | −0.525781 | − | 0.910679i | −0.999549 | − | 0.0300298i | \(-0.990440\pi\) |
0.473768 | − | 0.880650i | \(-0.342894\pi\) | |||||||
\(710\) | −1.00000 | + | 1.73205i | −0.0375293 | + | 0.0650027i | ||||
\(711\) | 6.00000 | − | 10.3923i | 0.225018 | − | 0.389742i | ||||
\(712\) | −7.00000 | − | 12.1244i | −0.262336 | − | 0.454379i | ||||
\(713\) | −2.00000 | −0.0749006 | ||||||||
\(714\) | 10.0000 | − | 3.46410i | 0.374241 | − | 0.129641i | ||||
\(715\) | 25.0000 | 0.934947 | ||||||||
\(716\) | 11.5000 | + | 19.9186i | 0.429775 | + | 0.744392i | ||||
\(717\) | −11.0000 | + | 19.0526i | −0.410803 | + | 0.711531i | ||||
\(718\) | 10.0000 | − | 17.3205i | 0.373197 | − | 0.646396i | ||||
\(719\) | 3.00000 | + | 5.19615i | 0.111881 | + | 0.193784i | 0.916529 | − | 0.399969i | \(-0.130979\pi\) |
−0.804648 | + | 0.593753i | \(0.797646\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −4.00000 | + | 20.7846i | −0.148968 | + | 0.774059i | ||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | 7.50000 | + | 12.9904i | 0.278928 | + | 0.483117i | ||||
\(724\) | −10.0000 | + | 17.3205i | −0.371647 | + | 0.643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | + | 12.1244i | 0.259794 | + | 0.449977i | ||||
\(727\) | −3.00000 | −0.111264 | −0.0556319 | − | 0.998451i | \(-0.517717\pi\) | ||||
−0.0556319 | + | 0.998451i | \(0.517717\pi\) | |||||||
\(728\) | 10.0000 | + | 8.66025i | 0.370625 | + | 0.320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −5.00000 | − | 8.66025i | −0.185058 | − | 0.320530i | ||||
\(731\) | 24.0000 | − | 41.5692i | 0.887672 | − | 1.53749i | ||||
\(732\) | 2.00000 | − | 3.46410i | 0.0739221 | − | 0.128037i | ||||
\(733\) | −4.50000 | − | 7.79423i | −0.166211 | − | 0.287886i | 0.770873 | − | 0.636988i | \(-0.219820\pi\) |
−0.937085 | + | 0.349102i | \(0.886487\pi\) | |||||||
\(734\) | 7.00000 | 0.258375 | ||||||||
\(735\) | −1.00000 | − | 6.92820i | −0.0368856 | − | 0.255551i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −30.0000 | − | 51.9615i | −1.10506 | − | 1.91403i | ||||
\(738\) | −2.50000 | + | 4.33013i | −0.0920263 | + | 0.159394i | ||||
\(739\) | 7.50000 | − | 12.9904i | 0.275892 | − | 0.477859i | −0.694468 | − | 0.719524i | \(-0.744360\pi\) |
0.970360 | + | 0.241665i | \(0.0776935\pi\) | |||||||
\(740\) | −0.500000 | − | 0.866025i | −0.0183804 | − | 0.0318357i | ||||
\(741\) | −35.0000 | −1.28576 | ||||||||
\(742\) | 18.0000 | + | 15.5885i | 0.660801 | + | 0.572270i | ||||
\(743\) | 15.0000 | 0.550297 | 0.275148 | − | 0.961402i | \(-0.411273\pi\) | ||||
0.275148 | + | 0.961402i | \(0.411273\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | −6.00000 | + | 10.3923i | −0.219823 | + | 0.380745i | ||||
\(746\) | 11.0000 | − | 19.0526i | 0.402739 | − | 0.697564i | ||||
\(747\) | 6.00000 | + | 10.3923i | 0.219529 | + | 0.380235i | ||||
\(748\) | 20.0000 | 0.731272 | ||||||||
\(749\) | 1.00000 | − | 5.19615i | 0.0365392 | − | 0.189863i | ||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 25.0000 | + | 43.3013i | 0.912263 | + | 1.58009i | 0.810860 | + | 0.585240i | \(0.199000\pi\) |
0.101403 | + | 0.994845i | \(0.467667\pi\) | |||||||
\(752\) | 5.50000 | − | 9.52628i | 0.200564 | − | 0.347388i | ||||
\(753\) | 0.500000 | − | 0.866025i | 0.0182210 | − | 0.0315597i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0000 | 0.509512 | ||||||||
\(756\) | −2.50000 | + | 0.866025i | −0.0909241 | + | 0.0314970i | ||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | −0.500000 | − | 0.866025i | −0.0181608 | − | 0.0314555i | ||||
\(759\) | −2.50000 | + | 4.33013i | −0.0907443 | + | 0.157174i | ||||
\(760\) | 3.50000 | − | 6.06218i | 0.126958 | − | 0.219898i | ||||
\(761\) | 18.5000 | + | 32.0429i | 0.670624 | + | 1.16156i | 0.977727 | + | 0.209879i | \(0.0673071\pi\) |
−0.307103 | + | 0.951676i | \(0.599360\pi\) | |||||||
\(762\) | −9.00000 | −0.326036 | ||||||||
\(763\) | −5.00000 | + | 1.73205i | −0.181012 | + | 0.0627044i | ||||
\(764\) | 14.0000 | 0.506502 | ||||||||
\(765\) | 2.00000 | + | 3.46410i | 0.0723102 | + | 0.125245i | ||||
\(766\) | −10.5000 | + | 18.1865i | −0.379380 | + | 0.657106i | ||||
\(767\) | 10.0000 | − | 17.3205i | 0.361079 | − | 0.625407i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −5.00000 | −0.180305 | −0.0901523 | − | 0.995928i | \(-0.528735\pi\) | ||||
−0.0901523 | + | 0.995928i | \(0.528735\pi\) | |||||||
\(770\) | 2.50000 | − | 12.9904i | 0.0900937 | − | 0.468141i | ||||
\(771\) | 16.0000 | 0.576226 | ||||||||
\(772\) | −5.00000 | − | 8.66025i | −0.179954 | − | 0.311689i | ||||
\(773\) | 2.50000 | − | 4.33013i | 0.0899188 | − | 0.155744i | −0.817558 | − | 0.575846i | \(-0.804673\pi\) |
0.907477 | + | 0.420103i | \(0.138006\pi\) | |||||||
\(774\) | −6.00000 | + | 10.3923i | −0.215666 | + | 0.373544i | ||||
\(775\) | 1.00000 | + | 1.73205i | 0.0359211 | + | 0.0622171i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 2.00000 | + | 1.73205i | 0.0717496 | + | 0.0621370i | ||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | 17.5000 | + | 30.3109i | 0.627003 | + | 1.08600i | ||||
\(780\) | −2.50000 | + | 4.33013i | −0.0895144 | + | 0.155043i | ||||
\(781\) | 5.00000 | − | 8.66025i | 0.178914 | − | 0.309888i | ||||
\(782\) | 2.00000 | + | 3.46410i | 0.0715199 | + | 0.123876i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | 11.0000 | 0.392607 | ||||||||
\(786\) | −4.50000 | − | 7.79423i | −0.160510 | − | 0.278011i | ||||
\(787\) | −1.00000 | + | 1.73205i | −0.0356462 | + | 0.0617409i | −0.883298 | − | 0.468812i | \(-0.844682\pi\) |
0.847652 | + | 0.530553i | \(0.178016\pi\) | |||||||
\(788\) | 1.50000 | − | 2.59808i | 0.0534353 | − | 0.0925526i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.0000 | −0.426941 | ||||||||
\(791\) | 28.0000 | + | 24.2487i | 0.995565 | + | 0.862185i | ||||
\(792\) | −5.00000 | −0.177667 | ||||||||
\(793\) | 10.0000 | + | 17.3205i | 0.355110 | + | 0.615069i | ||||
\(794\) | 7.00000 | − | 12.1244i | 0.248421 | − | 0.430277i | ||||
\(795\) | −4.50000 | + | 7.79423i | −0.159599 | + | 0.276433i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −54.0000 | −1.91278 | −0.956389 | − | 0.292096i | \(-0.905647\pi\) | ||||
−0.956389 | + | 0.292096i | \(0.905647\pi\) | |||||||
\(798\) | −3.50000 | + | 18.1865i | −0.123899 | + | 0.643796i | ||||
\(799\) | 44.0000 | 1.55661 | ||||||||
\(800\) | −0.500000 | − | 0.866025i | −0.0176777 | − | 0.0306186i | ||||
\(801\) | −7.00000 | + | 12.1244i | −0.247333 | + | 0.428393i | ||||
\(802\) | 10.5000 | − | 18.1865i | 0.370768 | − | 0.642189i | ||||
\(803\) | 25.0000 | + | 43.3013i | 0.882231 | + | 1.52807i | ||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | 2.50000 | − | 0.866025i | 0.0881134 | − | 0.0305234i | ||||
\(806\) | 10.0000 | 0.352235 | ||||||||
\(807\) | −12.0000 | − | 20.7846i | −0.422420 | − | 0.731653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.5000 | + | 21.6506i | −0.439477 | + | 0.761196i | −0.997649 | − | 0.0685291i | \(-0.978169\pi\) |
0.558173 | + | 0.829725i | \(0.311503\pi\) | |||||||
\(810\) | −0.500000 | − | 0.866025i | −0.0175682 | − | 0.0304290i | ||||
\(811\) | 21.0000 | 0.737410 | 0.368705 | − | 0.929547i | \(-0.379801\pi\) | ||||
0.368705 | + | 0.929547i | \(0.379801\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.50000 | + | 4.33013i | 0.0876250 | + | 0.151771i | ||||
\(815\) | 12.0000 | − | 20.7846i | 0.420342 | − | 0.728053i | ||||
\(816\) | −2.00000 | + | 3.46410i | −0.0700140 | + | 0.121268i | ||||
\(817\) | 42.0000 | + | 72.7461i | 1.46939 | + | 2.54507i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | 2.50000 | − | 12.9904i | 0.0873571 | − | 0.453921i | ||||
\(820\) | 5.00000 | 0.174608 | ||||||||
\(821\) | −5.00000 | − | 8.66025i | −0.174501 | − | 0.302245i | 0.765487 | − | 0.643451i | \(-0.222498\pi\) |
−0.939989 | + | 0.341206i | \(0.889165\pi\) | |||||||
\(822\) | −1.00000 | + | 1.73205i | −0.0348790 | + | 0.0604122i | ||||
\(823\) | −20.0000 | + | 34.6410i | −0.697156 | + | 1.20751i | 0.272292 | + | 0.962215i | \(0.412218\pi\) |
−0.969448 | + | 0.245295i | \(0.921115\pi\) | |||||||
\(824\) | −4.00000 | − | 6.92820i | −0.139347 | − | 0.241355i | ||||
\(825\) | 5.00000 | 0.174078 | ||||||||
\(826\) | −8.00000 | − | 6.92820i | −0.278356 | − | 0.241063i | ||||
\(827\) | −6.00000 | −0.208640 | −0.104320 | − | 0.994544i | \(-0.533267\pi\) | ||||
−0.104320 | + | 0.994544i | \(0.533267\pi\) | |||||||
\(828\) | −0.500000 | − | 0.866025i | −0.0173762 | − | 0.0300965i | ||||
\(829\) | 26.0000 | − | 45.0333i | 0.903017 | − | 1.56407i | 0.0794606 | − | 0.996838i | \(-0.474680\pi\) |
0.823557 | − | 0.567234i | \(-0.191986\pi\) | |||||||
\(830\) | 6.00000 | − | 10.3923i | 0.208263 | − | 0.360722i | ||||
\(831\) | 7.00000 | + | 12.1244i | 0.242827 | + | 0.420589i | ||||
\(832\) | −5.00000 | −0.173344 | ||||||||
\(833\) | 26.0000 | + | 10.3923i | 0.900847 | + | 0.360072i | ||||
\(834\) | 4.00000 | 0.138509 | ||||||||
\(835\) | −5.50000 | − | 9.52628i | −0.190335 | − | 0.329670i | ||||
\(836\) | −17.5000 | + | 30.3109i | −0.605250 | + | 1.04832i | ||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | −7.50000 | − | 12.9904i | −0.259083 | − | 0.448745i | ||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 2.00000 | + | 1.73205i | 0.0690066 | + | 0.0597614i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | −5.00000 | − | 8.66025i | −0.172311 | − | 0.298452i | ||||
\(843\) | 3.50000 | − | 6.06218i | 0.120546 | − | 0.208792i | ||||
\(844\) | −8.50000 | + | 14.7224i | −0.292582 | + | 0.506767i | ||||
\(845\) | −6.00000 | − | 10.3923i | −0.206406 | − | 0.357506i | ||||
\(846\) | −11.0000 | −0.378188 | ||||||||
\(847\) | −7.00000 | + | 36.3731i | −0.240523 | + | 1.24979i | ||||
\(848\) | −9.00000 | −0.309061 | ||||||||
\(849\) | −5.00000 | − | 8.66025i | −0.171600 | − | 0.297219i | ||||
\(850\) | 2.00000 | − | 3.46410i | 0.0685994 | − | 0.118818i | ||||
\(851\) | −0.500000 | + | 0.866025i | −0.0171398 | + | 0.0296870i | ||||
\(852\) | 1.00000 | + | 1.73205i | 0.0342594 | + | 0.0593391i | ||||
\(853\) | −11.0000 | −0.376633 | −0.188316 | − | 0.982108i | \(-0.560303\pi\) | ||||
−0.188316 | + | 0.982108i | \(0.560303\pi\) | |||||||
\(854\) | 10.0000 | − | 3.46410i | 0.342193 | − | 0.118539i | ||||
\(855\) | −7.00000 | −0.239395 | ||||||||
\(856\) | 1.00000 | + | 1.73205i | 0.0341793 | + | 0.0592003i | ||||
\(857\) | −1.00000 | + | 1.73205i | −0.0341593 | + | 0.0591657i | −0.882600 | − | 0.470125i | \(-0.844209\pi\) |
0.848440 | + | 0.529291i | \(0.177542\pi\) | |||||||
\(858\) | 12.5000 | − | 21.6506i | 0.426743 | − | 0.739140i | ||||
\(859\) | 2.00000 | + | 3.46410i | 0.0682391 | + | 0.118194i | 0.898126 | − | 0.439738i | \(-0.144929\pi\) |
−0.829887 | + | 0.557931i | \(0.811595\pi\) | |||||||
\(860\) | 12.0000 | 0.409197 | ||||||||
\(861\) | −12.5000 | + | 4.33013i | −0.425999 | + | 0.147570i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | −22.5000 | − | 38.9711i | −0.765909 | − | 1.32659i | −0.939765 | − | 0.341822i | \(-0.888956\pi\) |
0.173856 | − | 0.984771i | \(-0.444377\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 6.50000 | − | 11.2583i | 0.221007 | − | 0.382795i | ||||
\(866\) | −12.0000 | − | 20.7846i | −0.407777 | − | 0.706290i | ||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 1.00000 | − | 5.19615i | 0.0339422 | − | 0.176369i | ||||
\(869\) | 60.0000 | 2.03536 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.0000 | + | 51.9615i | −1.01651 | + | 1.76065i | ||||
\(872\) | 1.00000 | − | 1.73205i | 0.0338643 | − | 0.0586546i | ||||
\(873\) | 4.00000 | + | 6.92820i | 0.135379 | + | 0.234484i | ||||
\(874\) | −7.00000 | −0.236779 | ||||||||
\(875\) | −2.00000 | − | 1.73205i | −0.0676123 | − | 0.0585540i | ||||
\(876\) | −10.0000 | −0.337869 | ||||||||
\(877\) | 18.5000 | + | 32.0429i | 0.624701 | + | 1.08201i | 0.988599 | + | 0.150574i | \(0.0481123\pi\) |
−0.363898 | + | 0.931439i | \(0.618554\pi\) | |||||||
\(878\) | 20.0000 | − | 34.6410i | 0.674967 | − | 1.16908i | ||||
\(879\) | 4.50000 | − | 7.79423i | 0.151781 | − | 0.262893i | ||||
\(880\) | 2.50000 | + | 4.33013i | 0.0842750 | + | 0.145969i | ||||
\(881\) | 3.00000 | 0.101073 | 0.0505363 | − | 0.998722i | \(-0.483907\pi\) | ||||
0.0505363 | + | 0.998722i | \(0.483907\pi\) | |||||||
\(882\) | −6.50000 | − | 2.59808i | −0.218866 | − | 0.0874818i | ||||
\(883\) | −50.0000 | −1.68263 | −0.841317 | − | 0.540542i | \(-0.818219\pi\) | ||||
−0.841317 | + | 0.540542i | \(0.818219\pi\) | |||||||
\(884\) | −10.0000 | − | 17.3205i | −0.336336 | − | 0.582552i | ||||
\(885\) | 2.00000 | − | 3.46410i | 0.0672293 | − | 0.116445i | ||||
\(886\) | 14.0000 | − | 24.2487i | 0.470339 | − | 0.814651i | ||||
\(887\) | 22.0000 | + | 38.1051i | 0.738688 | + | 1.27944i | 0.953086 | + | 0.302698i | \(0.0978875\pi\) |
−0.214399 | + | 0.976746i | \(0.568779\pi\) | |||||||
\(888\) | −1.00000 | −0.0335578 | ||||||||
\(889\) | −18.0000 | − | 15.5885i | −0.603701 | − | 0.522820i | ||||
\(890\) | 14.0000 | 0.469281 | ||||||||
\(891\) | 2.50000 | + | 4.33013i | 0.0837532 | + | 0.145065i | ||||
\(892\) | 6.00000 | − | 10.3923i | 0.200895 | − | 0.347960i | ||||
\(893\) | −38.5000 | + | 66.6840i | −1.28835 | + | 2.23149i | ||||
\(894\) | 6.00000 | + | 10.3923i | 0.200670 | + | 0.347571i | ||||
\(895\) | −23.0000 | −0.768805 | ||||||||
\(896\) | −0.500000 | + | 2.59808i | −0.0167038 | + | 0.0867956i | ||||
\(897\) | 5.00000 | 0.166945 | ||||||||
\(898\) | 14.5000 | + | 25.1147i | 0.483871 | + | 0.838090i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −0.500000 | + | 0.866025i | −0.0166667 | + | 0.0288675i | ||||
\(901\) | −18.0000 | − | 31.1769i | −0.599667 | − | 1.03865i | ||||
\(902\) | −25.0000 | −0.832409 | ||||||||
\(903\) | −30.0000 | + | 10.3923i | −0.998337 | + | 0.345834i | ||||
\(904\) | −14.0000 | −0.465633 | ||||||||
\(905\) | −10.0000 | − | 17.3205i | −0.332411 | − | 0.575753i | ||||
\(906\) | 7.00000 | − | 12.1244i | 0.232559 | − | 0.402805i | ||||
\(907\) | 9.00000 | − | 15.5885i | 0.298840 | − | 0.517606i | −0.677031 | − | 0.735955i | \(-0.736734\pi\) |
0.975871 | + | 0.218348i | \(0.0700669\pi\) | |||||||
\(908\) | 6.00000 | + | 10.3923i | 0.199117 | + | 0.344881i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.5000 | + | 4.33013i | −0.414371 | + | 0.143542i | ||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | −3.50000 | − | 6.06218i | −0.115897 | − | 0.200739i | ||||
\(913\) | −30.0000 | + | 51.9615i | −0.992855 | + | 1.71968i | ||||
\(914\) | 7.00000 | − | 12.1244i | 0.231539 | − | 0.401038i | ||||
\(915\) | 2.00000 | + | 3.46410i | 0.0661180 | + | 0.114520i | ||||
\(916\) | 10.0000 | 0.330409 | ||||||||
\(917\) | 4.50000 | − | 23.3827i | 0.148603 | − | 0.772164i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | −14.0000 | − | 24.2487i | −0.461817 | − | 0.799891i | 0.537234 | − | 0.843433i | \(-0.319469\pi\) |
−0.999052 | + | 0.0435419i | \(0.986136\pi\) | |||||||
\(920\) | −0.500000 | + | 0.866025i | −0.0164845 | + | 0.0285520i | ||||
\(921\) | 4.00000 | − | 6.92820i | 0.131804 | − | 0.228292i | ||||
\(922\) | 2.00000 | + | 3.46410i | 0.0658665 | + | 0.114084i | ||||
\(923\) | −10.0000 | −0.329154 | ||||||||
\(924\) | −10.0000 | − | 8.66025i | −0.328976 | − | 0.284901i | ||||
\(925\) | 1.00000 | 0.0328798 | ||||||||
\(926\) | 9.50000 | + | 16.4545i | 0.312189 | + | 0.540728i | ||||
\(927\) | −4.00000 | + | 6.92820i | −0.131377 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.50000 | − | 16.4545i | −0.311685 | − | 0.539854i | 0.667042 | − | 0.745020i | \(-0.267560\pi\) |
−0.978727 | + | 0.205166i | \(0.934227\pi\) | |||||||
\(930\) | 2.00000 | 0.0655826 | ||||||||
\(931\) | −38.5000 | + | 30.3109i | −1.26179 | + | 0.993399i | ||||
\(932\) | −14.0000 | −0.458585 | ||||||||
\(933\) | 4.00000 | + | 6.92820i | 0.130954 | + | 0.226819i | ||||
\(934\) | 10.0000 | − | 17.3205i | 0.327210 | − | 0.566744i | ||||
\(935\) | −10.0000 | + | 17.3205i | −0.327035 | + | 0.566441i | ||||
\(936\) | 2.50000 | + | 4.33013i | 0.0817151 | + | 0.141535i | ||||
\(937\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(938\) | 24.0000 | + | 20.7846i | 0.783628 | + | 0.678642i | ||||
\(939\) | −16.0000 | −0.522140 | ||||||||
\(940\) | 5.50000 | + | 9.52628i | 0.179390 | + | 0.310713i | ||||
\(941\) | 3.00000 | − | 5.19615i | 0.0977972 | − | 0.169390i | −0.812975 | − | 0.582298i | \(-0.802154\pi\) |
0.910773 | + | 0.412908i | \(0.135487\pi\) | |||||||
\(942\) | 5.50000 | − | 9.52628i | 0.179200 | − | 0.310383i | ||||
\(943\) | −2.50000 | − | 4.33013i | −0.0814112 | − | 0.141008i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0.500000 | − | 2.59808i | 0.0162650 | − | 0.0845154i | ||||
\(946\) | −60.0000 | −1.95077 | ||||||||
\(947\) | 21.0000 | + | 36.3731i | 0.682408 | + | 1.18197i | 0.974244 | + | 0.225497i | \(0.0724007\pi\) |
−0.291835 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(948\) | −6.00000 | + | 10.3923i | −0.194871 | + | 0.337526i | ||||
\(949\) | 25.0000 | − | 43.3013i | 0.811534 | − | 1.40562i | ||||
\(950\) | 3.50000 | + | 6.06218i | 0.113555 | + | 0.196683i | ||||
\(951\) | 22.0000 | 0.713399 | ||||||||
\(952\) | −10.0000 | + | 3.46410i | −0.324102 | + | 0.112272i | ||||
\(953\) | 12.0000 | 0.388718 | 0.194359 | − | 0.980930i | \(-0.437737\pi\) | ||||
0.194359 | + | 0.980930i | \(0.437737\pi\) | |||||||
\(954\) | 4.50000 | + | 7.79423i | 0.145693 | + | 0.252347i | ||||
\(955\) | −7.00000 | + | 12.1244i | −0.226515 | + | 0.392335i | ||||
\(956\) | 11.0000 | − | 19.0526i | 0.355765 | − | 0.616204i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.0000 | 0.581554 | ||||||||
\(959\) | −5.00000 | + | 1.73205i | −0.161458 | + | 0.0559308i | ||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 2.50000 | − | 4.33013i | 0.0806032 | − | 0.139609i | ||||
\(963\) | 1.00000 | − | 1.73205i | 0.0322245 | − | 0.0558146i | ||||
\(964\) | −7.50000 | − | 12.9904i | −0.241559 | − | 0.418392i | ||||
\(965\) | 10.0000 | 0.321911 | ||||||||
\(966\) | 0.500000 | − | 2.59808i | 0.0160872 | − | 0.0835917i | ||||
\(967\) | 4.00000 | 0.128631 | 0.0643157 | − | 0.997930i | \(-0.479514\pi\) | ||||
0.0643157 | + | 0.997930i | \(0.479514\pi\) | |||||||
\(968\) | −7.00000 | − | 12.1244i | −0.224989 | − | 0.389692i | ||||
\(969\) | 14.0000 | − | 24.2487i | 0.449745 | − | 0.778981i | ||||
\(970\) | 4.00000 | − | 6.92820i | 0.128432 | − | 0.222451i | ||||
\(971\) | −7.50000 | − | 12.9904i | −0.240686 | − | 0.416881i | 0.720224 | − | 0.693742i | \(-0.244039\pi\) |
−0.960910 | + | 0.276861i | \(0.910706\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 8.00000 | + | 6.92820i | 0.256468 | + | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.50000 | − | 4.33013i | −0.0800641 | − | 0.138675i | ||||
\(976\) | −2.00000 | + | 3.46410i | −0.0640184 | + | 0.110883i | ||||
\(977\) | 15.0000 | − | 25.9808i | 0.479893 | − | 0.831198i | −0.519841 | − | 0.854263i | \(-0.674009\pi\) |
0.999734 | + | 0.0230645i | \(0.00734232\pi\) | |||||||
\(978\) | −12.0000 | − | 20.7846i | −0.383718 | − | 0.664619i | ||||
\(979\) | −70.0000 | −2.23721 | ||||||||
\(980\) | 1.00000 | + | 6.92820i | 0.0319438 | + | 0.221313i | ||||
\(981\) | −2.00000 | −0.0638551 | ||||||||
\(982\) | 18.0000 | + | 31.1769i | 0.574403 | + | 0.994895i | ||||
\(983\) | 12.5000 | − | 21.6506i | 0.398688 | − | 0.690548i | −0.594876 | − | 0.803817i | \(-0.702799\pi\) |
0.993564 | + | 0.113269i | \(0.0361323\pi\) | |||||||
\(984\) | 2.50000 | − | 4.33013i | 0.0796971 | − | 0.138039i | ||||
\(985\) | 1.50000 | + | 2.59808i | 0.0477940 | + | 0.0827816i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.0000 | − | 19.0526i | −0.700268 | − | 0.606450i | ||||
\(988\) | 35.0000 | 1.11350 | ||||||||
\(989\) | −6.00000 | − | 10.3923i | −0.190789 | − | 0.330456i | ||||
\(990\) | 2.50000 | − | 4.33013i | 0.0794552 | − | 0.137620i | ||||
\(991\) | 19.0000 | − | 32.9090i | 0.603555 | − | 1.04539i | −0.388723 | − | 0.921355i | \(-0.627084\pi\) |
0.992278 | − | 0.124033i | \(-0.0395829\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | −31.0000 | −0.983755 | ||||||||
\(994\) | −1.00000 | + | 5.19615i | −0.0317181 | + | 0.164812i | ||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | −6.00000 | − | 10.3923i | −0.190117 | − | 0.329293i | ||||
\(997\) | 11.0000 | − | 19.0526i | 0.348373 | − | 0.603401i | −0.637587 | − | 0.770378i | \(-0.720067\pi\) |
0.985961 | + | 0.166978i | \(0.0534008\pi\) | |||||||
\(998\) | −20.0000 | + | 34.6410i | −0.633089 | + | 1.09654i | ||||
\(999\) | 0.500000 | + | 0.866025i | 0.0158193 | + | 0.0273998i |
(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 | 210.2.i.b.151.1 | yes | 2 | |
3.2 | odd | 2 | 630.2.k.g.361.1 | 2 | |||
4.3 | odd | 2 | 1680.2.bg.d.1201.1 | 2 | |||
5.2 | odd | 4 | 1050.2.o.g.949.2 | 4 | |||
5.3 | odd | 4 | 1050.2.o.g.949.1 | 4 | |||
5.4 | even | 2 | 1050.2.i.p.151.1 | 2 | |||
7.2 | even | 3 | inner | 210.2.i.b.121.1 | ✓ | 2 | |
7.3 | odd | 6 | 1470.2.a.o.1.1 | 1 | |||
7.4 | even | 3 | 1470.2.a.l.1.1 | 1 | |||
7.5 | odd | 6 | 1470.2.i.e.961.1 | 2 | |||
7.6 | odd | 2 | 1470.2.i.e.361.1 | 2 | |||
21.2 | odd | 6 | 630.2.k.g.541.1 | 2 | |||
21.11 | odd | 6 | 4410.2.a.j.1.1 | 1 | |||
21.17 | even | 6 | 4410.2.a.u.1.1 | 1 | |||
28.23 | odd | 6 | 1680.2.bg.d.961.1 | 2 | |||
35.2 | odd | 12 | 1050.2.o.g.499.1 | 4 | |||
35.4 | even | 6 | 7350.2.a.u.1.1 | 1 | |||
35.9 | even | 6 | 1050.2.i.p.751.1 | 2 | |||
35.23 | odd | 12 | 1050.2.o.g.499.2 | 4 | |||
35.24 | odd | 6 | 7350.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.b.121.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
210.2.i.b.151.1 | yes | 2 | 1.1 | even | 1 | trivial | |
630.2.k.g.361.1 | 2 | 3.2 | odd | 2 | |||
630.2.k.g.541.1 | 2 | 21.2 | odd | 6 | |||
1050.2.i.p.151.1 | 2 | 5.4 | even | 2 | |||
1050.2.i.p.751.1 | 2 | 35.9 | even | 6 | |||
1050.2.o.g.499.1 | 4 | 35.2 | odd | 12 | |||
1050.2.o.g.499.2 | 4 | 35.23 | odd | 12 | |||
1050.2.o.g.949.1 | 4 | 5.3 | odd | 4 | |||
1050.2.o.g.949.2 | 4 | 5.2 | odd | 4 | |||
1470.2.a.l.1.1 | 1 | 7.4 | even | 3 | |||
1470.2.a.o.1.1 | 1 | 7.3 | odd | 6 | |||
1470.2.i.e.361.1 | 2 | 7.6 | odd | 2 | |||
1470.2.i.e.961.1 | 2 | 7.5 | odd | 6 | |||
1680.2.bg.d.961.1 | 2 | 28.23 | odd | 6 | |||
1680.2.bg.d.1201.1 | 2 | 4.3 | odd | 2 | |||
4410.2.a.j.1.1 | 1 | 21.11 | odd | 6 | |||
4410.2.a.u.1.1 | 1 | 21.17 | even | 6 | |||
7350.2.a.a.1.1 | 1 | 35.24 | odd | 6 | |||
7350.2.a.u.1.1 | 1 | 35.4 | even | 6 |