Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1170,2,Mod(451,1170)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1170, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1170.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1170.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: | \(9.34249703649\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1170.991 |
Dual form | 1170.2.i.a.451.1 |
$q$-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 \(\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times\).
\(n\) | \(911\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | − | 1.73205i | 0.377964 | − | 0.654654i | −0.612801 | − | 0.790237i | \(-0.709957\pi\) |
0.990766 | + | 0.135583i | \(0.0432908\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.500000 | + | 0.866025i | 0.158114 | + | 0.273861i | ||||
\(11\) | −2.50000 | − | 4.33013i | −0.753778 | − | 1.30558i | −0.945979 | − | 0.324227i | \(-0.894896\pi\) |
0.192201 | − | 0.981356i | \(-0.438437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | + | 3.46410i | −0.277350 | + | 0.960769i | ||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 0.500000 | − | 0.866025i | 0.111803 | − | 0.193649i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.50000 | + | 4.33013i | −0.533002 | + | 0.923186i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 3.50000 | − | 0.866025i | 0.686406 | − | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | + | 1.73205i | 0.188982 | + | 0.327327i | ||||
\(29\) | 2.50000 | + | 4.33013i | 0.464238 | + | 0.804084i | 0.999167 | − | 0.0408130i | \(-0.0129948\pi\) |
−0.534928 | + | 0.844897i | \(0.679661\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.0000 | −1.97566 | −0.987829 | − | 0.155543i | \(-0.950287\pi\) | ||||
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | −1.00000 | + | 1.73205i | −0.169031 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | − | 2.59808i | −0.246598 | − | 0.427121i | 0.715981 | − | 0.698119i | \(-0.245980\pi\) |
−0.962580 | + | 0.270998i | \(0.912646\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.00000 | − | 1.73205i | −0.156174 | − | 0.270501i | 0.777312 | − | 0.629115i | \(-0.216583\pi\) |
−0.933486 | + | 0.358614i | \(0.883249\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | − | 9.52628i | 0.838742 | − | 1.45274i | −0.0522047 | − | 0.998636i | \(-0.516625\pi\) |
0.890947 | − | 0.454108i | \(-0.150042\pi\) | |||||||
\(44\) | 5.00000 | 0.753778 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | −9.00000 | −1.31278 | −0.656392 | − | 0.754420i | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −0.500000 | − | 0.866025i | −0.0707107 | − | 0.122474i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.50000 | − | 2.59808i | −0.346688 | − | 0.360288i | ||||
\(53\) | −6.00000 | −0.824163 | −0.412082 | − | 0.911147i | \(-0.635198\pi\) | ||||
−0.412082 | + | 0.911147i | \(0.635198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.50000 | + | 4.33013i | 0.337100 | + | 0.583874i | ||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | − | 4.33013i | 0.328266 | − | 0.568574i | ||||
\(59\) | −7.50000 | + | 12.9904i | −0.976417 | + | 1.69120i | −0.301239 | + | 0.953549i | \(0.597400\pi\) |
−0.675178 | + | 0.737655i | \(0.735933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.00000 | + | 8.66025i | −0.640184 | + | 1.10883i | 0.345207 | + | 0.938527i | \(0.387809\pi\) |
−0.985391 | + | 0.170305i | \(0.945525\pi\) | |||||||
\(62\) | 5.50000 | + | 9.52628i | 0.698501 | + | 1.20984i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.00000 | − | 3.46410i | 0.124035 | − | 0.429669i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.00000 | − | 13.8564i | −0.977356 | − | 1.69283i | −0.671932 | − | 0.740613i | \(-0.734535\pi\) |
−0.305424 | − | 0.952217i | \(-0.598798\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | 0.239046 | ||||||||
\(71\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | −10.0000 | −1.13961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.0000 | −1.23760 | −0.618798 | − | 0.785550i | \(-0.712380\pi\) | ||||
−0.618798 | + | 0.785550i | \(0.712380\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.00000 | + | 1.73205i | −0.110432 | + | 0.191273i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.00000 | − | 1.73205i | 0.108465 | − | 0.187867i | ||||
\(86\) | −11.0000 | −1.18616 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 1.00000 | + | 1.73205i | 0.106000 | + | 0.183597i | 0.914146 | − | 0.405385i | \(-0.132862\pi\) |
−0.808146 | + | 0.588982i | \(0.799529\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.00000 | + | 5.19615i | 0.524142 | + | 0.544705i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.50000 | + | 7.79423i | 0.464140 | + | 0.803913i | ||||
\(95\) | −1.00000 | + | 1.73205i | −0.102598 | + | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.00000 | − | 1.73205i | 0.101535 | − | 0.175863i | −0.810782 | − | 0.585348i | \(-0.800958\pi\) |
0.912317 | + | 0.409484i | \(0.134291\pi\) | |||||||
\(98\) | 1.50000 | − | 2.59808i | 0.151523 | − | 0.262445i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | −1.00000 | + | 3.46410i | −0.0980581 | + | 0.339683i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | + | 5.19615i | 0.291386 | + | 0.504695i | ||||
\(107\) | 5.00000 | + | 8.66025i | 0.483368 | + | 0.837218i | 0.999818 | − | 0.0190994i | \(-0.00607989\pi\) |
−0.516449 | + | 0.856318i | \(0.672747\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 2.50000 | − | 4.33013i | 0.238366 | − | 0.412861i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 5.50000 | − | 9.52628i | 0.517396 | − | 0.896157i | −0.482399 | − | 0.875951i | \(-0.660235\pi\) |
0.999796 | − | 0.0202056i | \(-0.00643208\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | −5.00000 | −0.464238 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 15.0000 | 1.38086 | ||||||||
\(119\) | 2.00000 | + | 3.46410i | 0.183340 | + | 0.317554i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | 10.0000 | 0.905357 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.50000 | − | 9.52628i | 0.493915 | − | 0.855485i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | − | 1.73205i | −0.0887357 | − | 0.153695i | 0.818241 | − | 0.574875i | \(-0.194949\pi\) |
−0.906977 | + | 0.421180i | \(0.861616\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.50000 | + | 0.866025i | −0.306970 | + | 0.0759555i | ||||
\(131\) | 1.00000 | 0.0873704 | 0.0436852 | − | 0.999045i | \(-0.486090\pi\) | ||||
0.0436852 | + | 0.999045i | \(0.486090\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | −8.00000 | + | 13.8564i | −0.691095 | + | 1.19701i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | −5.50000 | + | 9.52628i | −0.469897 | + | 0.813885i | −0.999408 | − | 0.0344182i | \(-0.989042\pi\) |
0.529511 | + | 0.848303i | \(0.322376\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.00000 | + | 1.73205i | −0.0848189 | + | 0.146911i | −0.905314 | − | 0.424743i | \(-0.860365\pi\) |
0.820495 | + | 0.571654i | \(0.193698\pi\) | |||||||
\(140\) | −1.00000 | − | 1.73205i | −0.0845154 | − | 0.146385i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.5000 | − | 4.33013i | 1.46342 | − | 0.362103i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.50000 | − | 4.33013i | −0.207614 | − | 0.359597i | ||||
\(146\) | 3.00000 | + | 5.19615i | 0.248282 | + | 0.430037i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.00000 | 0.246598 | ||||||||
\(149\) | 8.50000 | − | 14.7224i | 0.696347 | − | 1.20611i | −0.273377 | − | 0.961907i | \(-0.588141\pi\) |
0.969724 | − | 0.244202i | \(-0.0785259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | 1.00000 | − | 1.73205i | 0.0811107 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.00000 | + | 8.66025i | 0.402911 | + | 0.697863i | ||||
\(155\) | 11.0000 | 0.883541 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.00000 | −0.558661 | −0.279330 | − | 0.960195i | \(-0.590112\pi\) | ||||
−0.279330 | + | 0.960195i | \(0.590112\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.50000 | − | 12.9904i | 0.587445 | − | 1.01749i | −0.407120 | − | 0.913375i | \(-0.633467\pi\) |
0.994566 | − | 0.104111i | \(-0.0331996\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | 1.50000 | + | 2.59808i | 0.116073 | + | 0.201045i | 0.918208 | − | 0.396098i | \(-0.129636\pi\) |
−0.802135 | + | 0.597143i | \(0.796303\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.0000 | − | 6.92820i | −0.846154 | − | 0.532939i | ||||
\(170\) | −2.00000 | −0.153393 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.50000 | + | 9.52628i | 0.419371 | + | 0.726372i | ||||
\(173\) | 10.0000 | − | 17.3205i | 0.760286 | − | 1.31685i | −0.182417 | − | 0.983221i | \(-0.558392\pi\) |
0.942703 | − | 0.333633i | \(-0.108275\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 1.73205i | 0.0755929 | − | 0.130931i | ||||
\(176\) | −2.50000 | + | 4.33013i | −0.188445 | + | 0.326396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.00000 | − | 1.73205i | 0.0749532 | − | 0.129823i | ||||
\(179\) | −6.50000 | − | 11.2583i | −0.485833 | − | 0.841487i | 0.514035 | − | 0.857769i | \(-0.328150\pi\) |
−0.999867 | + | 0.0162823i | \(0.994817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.0000 | −1.18927 | −0.594635 | − | 0.803996i | \(-0.702704\pi\) | ||||
−0.594635 | + | 0.803996i | \(0.702704\pi\) | |||||||
\(182\) | 2.00000 | − | 6.92820i | 0.148250 | − | 0.513553i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.0000 | 0.731272 | ||||||||
\(188\) | 4.50000 | − | 7.79423i | 0.328196 | − | 0.568453i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | 0.145095 | ||||||||
\(191\) | 2.00000 | − | 3.46410i | 0.144715 | − | 0.250654i | −0.784552 | − | 0.620063i | \(-0.787107\pi\) |
0.929267 | + | 0.369410i | \(0.120440\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.0000 | + | 20.7846i | 0.863779 | + | 1.49611i | 0.868255 | + | 0.496119i | \(0.165242\pi\) |
−0.00447566 | + | 0.999990i | \(0.501425\pi\) | |||||||
\(194\) | −2.00000 | −0.143592 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | −4.00000 | − | 6.92820i | −0.284988 | − | 0.493614i | 0.687618 | − | 0.726073i | \(-0.258656\pi\) |
−0.972606 | + | 0.232458i | \(0.925323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0000 | + | 20.7846i | −0.850657 | + | 1.47338i | 0.0299585 | + | 0.999551i | \(0.490462\pi\) |
−0.880616 | + | 0.473831i | \(0.842871\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.00000 | − | 1.73205i | 0.0703598 | − | 0.121867i | ||||
\(203\) | 10.0000 | 0.701862 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00000 | + | 1.73205i | 0.0698430 | + | 0.120972i | ||||
\(206\) | −5.00000 | − | 8.66025i | −0.348367 | − | 0.603388i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.50000 | − | 0.866025i | 0.242681 | − | 0.0600481i | ||||
\(209\) | −10.0000 | −0.691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | + | 3.46410i | 0.137686 | + | 0.238479i | 0.926620 | − | 0.375999i | \(-0.122700\pi\) |
−0.788935 | + | 0.614477i | \(0.789367\pi\) | |||||||
\(212\) | 3.00000 | − | 5.19615i | 0.206041 | − | 0.356873i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.00000 | − | 8.66025i | 0.341793 | − | 0.592003i | ||||
\(215\) | −5.50000 | + | 9.52628i | −0.375097 | + | 0.649687i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.0000 | + | 19.0526i | −0.746729 | + | 1.29337i | ||||
\(218\) | 1.00000 | + | 1.73205i | 0.0677285 | + | 0.117309i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.00000 | −0.337100 | ||||||||
\(221\) | −5.00000 | − | 5.19615i | −0.336336 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.0000 | − | 22.5167i | −0.870544 | − | 1.50783i | −0.861435 | − | 0.507869i | \(-0.830434\pi\) |
−0.00910984 | − | 0.999959i | \(-0.502900\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.0000 | −0.731709 | ||||||||
\(227\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0.500000 | − | 0.866025i | 0.0329690 | − | 0.0571040i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.50000 | + | 4.33013i | 0.164133 | + | 0.284287i | ||||
\(233\) | −1.00000 | −0.0655122 | −0.0327561 | − | 0.999463i | \(-0.510428\pi\) | ||||
−0.0327561 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | −7.50000 | − | 12.9904i | −0.488208 | − | 0.845602i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | − | 3.46410i | 0.129641 | − | 0.224544i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.50000 | − | 6.06218i | 0.225455 | − | 0.390499i | −0.731001 | − | 0.682376i | \(-0.760947\pi\) |
0.956456 | + | 0.291877i | \(0.0942799\pi\) | |||||||
\(242\) | 14.0000 | 0.899954 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.00000 | − | 8.66025i | −0.320092 | − | 0.554416i | ||||
\(245\) | −1.50000 | − | 2.59808i | −0.0958315 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.00000 | + | 5.19615i | 0.318142 | + | 0.330623i | ||||
\(248\) | −11.0000 | −0.698501 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.500000 | + | 0.866025i | 0.0316228 | + | 0.0547723i | ||||
\(251\) | 12.5000 | − | 21.6506i | 0.788993 | − | 1.36658i | −0.137591 | − | 0.990489i | \(-0.543936\pi\) |
0.926584 | − | 0.376087i | \(-0.122731\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.50000 | + | 4.33013i | −0.157174 | + | 0.272233i | ||||
\(254\) | −1.00000 | + | 1.73205i | −0.0627456 | + | 0.108679i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −8.50000 | − | 14.7224i | −0.530215 | − | 0.918360i | −0.999379 | − | 0.0352486i | \(-0.988778\pi\) |
0.469163 | − | 0.883112i | \(-0.344556\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.00000 | −0.372822 | ||||||||
\(260\) | 2.50000 | + | 2.59808i | 0.155043 | + | 0.161126i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.500000 | − | 0.866025i | −0.0308901 | − | 0.0535032i | ||||
\(263\) | 10.5000 | + | 18.1865i | 0.647458 | + | 1.12143i | 0.983728 | + | 0.179664i | \(0.0575011\pi\) |
−0.336270 | + | 0.941766i | \(0.609166\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | 0.368577 | ||||||||
\(266\) | −2.00000 | + | 3.46410i | −0.122628 | + | 0.212398i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.0000 | 0.977356 | ||||||||
\(269\) | 7.00000 | − | 12.1244i | 0.426798 | − | 0.739235i | −0.569789 | − | 0.821791i | \(-0.692975\pi\) |
0.996586 | + | 0.0825561i | \(0.0263084\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.50000 | + | 11.2583i | 0.394847 | + | 0.683895i | 0.993082 | − | 0.117426i | \(-0.0374643\pi\) |
−0.598235 | + | 0.801321i | \(0.704131\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.0000 | 0.664534 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.50000 | − | 9.52628i | 0.330463 | − | 0.572379i | −0.652140 | − | 0.758099i | \(-0.726128\pi\) |
0.982603 | + | 0.185720i | \(0.0594618\pi\) | |||||||
\(278\) | 2.00000 | 0.119952 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.00000 | + | 1.73205i | −0.0597614 | + | 0.103510i | ||||
\(281\) | 10.0000 | 0.596550 | 0.298275 | − | 0.954480i | \(-0.403589\pi\) | ||||
0.298275 | + | 0.954480i | \(0.403589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.50000 | − | 16.4545i | −0.564716 | − | 0.978117i | −0.997076 | − | 0.0764162i | \(-0.975652\pi\) |
0.432360 | − | 0.901701i | \(-0.357681\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.5000 | − | 12.9904i | −0.739140 | − | 0.768137i | ||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −2.50000 | + | 4.33013i | −0.146805 | + | 0.254274i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.00000 | − | 5.19615i | 0.175562 | − | 0.304082i | ||||
\(293\) | 3.00000 | − | 5.19615i | 0.175262 | − | 0.303562i | −0.764990 | − | 0.644042i | \(-0.777256\pi\) |
0.940252 | + | 0.340480i | \(0.110589\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.50000 | − | 12.9904i | 0.436667 | − | 0.756329i | ||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −17.0000 | −0.984784 | ||||||||
\(299\) | 3.50000 | − | 0.866025i | 0.202410 | − | 0.0500835i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.0000 | − | 19.0526i | −0.634029 | − | 1.09817i | ||||
\(302\) | −4.00000 | − | 6.92820i | −0.230174 | − | 0.398673i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | 5.00000 | − | 8.66025i | 0.286299 | − | 0.495885i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(308\) | 5.00000 | − | 8.66025i | 0.284901 | − | 0.493464i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.50000 | − | 9.52628i | −0.312379 | − | 0.541056i | ||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 20.0000 | 1.13047 | 0.565233 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565233 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(314\) | 3.50000 | + | 6.06218i | 0.197516 | + | 0.342108i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.50000 | − | 9.52628i | 0.309399 | − | 0.535895i | ||||
\(317\) | −16.0000 | −0.898650 | −0.449325 | − | 0.893368i | \(-0.648335\pi\) | ||||
−0.449325 | + | 0.893368i | \(0.648335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.5000 | − | 21.6506i | 0.699866 | − | 1.21220i | ||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.00000 | + | 1.73205i | 0.0557278 | + | 0.0965234i | ||||
\(323\) | 2.00000 | + | 3.46410i | 0.111283 | + | 0.192748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.00000 | + | 3.46410i | −0.0554700 | + | 0.192154i | ||||
\(326\) | −15.0000 | −0.830773 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.00000 | − | 1.73205i | −0.0552158 | − | 0.0956365i | ||||
\(329\) | −9.00000 | + | 15.5885i | −0.496186 | + | 0.859419i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | − | 24.2487i | 0.769510 | − | 1.33283i | −0.168320 | − | 0.985732i | \(-0.553834\pi\) |
0.937829 | − | 0.347097i | \(-0.112833\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.50000 | − | 2.59808i | 0.0820763 | − | 0.142160i | ||||
\(335\) | 8.00000 | + | 13.8564i | 0.437087 | + | 0.757056i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | −0.500000 | + | 12.9904i | −0.0271964 | + | 0.706584i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.00000 | + | 1.73205i | 0.0542326 | + | 0.0939336i | ||||
\(341\) | 27.5000 | + | 47.6314i | 1.48921 | + | 2.57938i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 5.50000 | − | 9.52628i | 0.296540 | − | 0.513623i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −20.0000 | −1.07521 | ||||||||
\(347\) | 17.0000 | − | 29.4449i | 0.912608 | − | 1.58068i | 0.102241 | − | 0.994760i | \(-0.467399\pi\) |
0.810366 | − | 0.585923i | \(-0.199268\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.0000 | − | 17.3205i | −0.535288 | − | 0.927146i | −0.999149 | − | 0.0412379i | \(-0.986870\pi\) |
0.463862 | − | 0.885908i | \(-0.346463\pi\) | |||||||
\(350\) | −2.00000 | −0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.00000 | 0.266501 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.50000 | + | 11.2583i | −0.343536 | + | 0.595021i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 8.00000 | + | 13.8564i | 0.420471 | + | 0.728277i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.00000 | + | 1.73205i | −0.366900 | + | 0.0907841i | ||||
\(365\) | 6.00000 | 0.314054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.00000 | + | 13.8564i | 0.417597 | + | 0.723299i | 0.995697 | − | 0.0926670i | \(-0.0295392\pi\) |
−0.578101 | + | 0.815966i | \(0.696206\pi\) | |||||||
\(368\) | −0.500000 | + | 0.866025i | −0.0260643 | + | 0.0451447i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.50000 | − | 2.59808i | 0.0779813 | − | 0.135068i | ||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.50000 | − | 16.4545i | 0.491891 | − | 0.851981i | −0.508065 | − | 0.861319i | \(-0.669639\pi\) |
0.999956 | + | 0.00933789i | \(0.00297238\pi\) | |||||||
\(374\) | −5.00000 | − | 8.66025i | −0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.00000 | −0.464140 | ||||||||
\(377\) | −17.5000 | + | 4.33013i | −0.901296 | + | 0.223013i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | + | 1.73205i | 0.0513665 | + | 0.0889695i | 0.890565 | − | 0.454855i | \(-0.150309\pi\) |
−0.839199 | + | 0.543825i | \(0.816976\pi\) | |||||||
\(380\) | −1.00000 | − | 1.73205i | −0.0512989 | − | 0.0888523i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.00000 | −0.204658 | ||||||||
\(383\) | 15.5000 | − | 26.8468i | 0.792013 | − | 1.37181i | −0.132706 | − | 0.991155i | \(-0.542367\pi\) |
0.924719 | − | 0.380651i | \(-0.124300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 10.0000 | 0.509647 | ||||||||
\(386\) | 12.0000 | − | 20.7846i | 0.610784 | − | 1.05791i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.00000 | + | 1.73205i | 0.0507673 | + | 0.0879316i | ||||
\(389\) | −5.00000 | −0.253510 | −0.126755 | − | 0.991934i | \(-0.540456\pi\) | ||||
−0.126755 | + | 0.991934i | \(0.540456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.00000 | 0.101144 | ||||||||
\(392\) | 1.50000 | + | 2.59808i | 0.0757614 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.00000 | + | 6.92820i | −0.201517 | + | 0.349038i | ||||
\(395\) | 11.0000 | 0.553470 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.50000 | + | 2.59808i | −0.0752828 | + | 0.130394i | −0.901209 | − | 0.433384i | \(-0.857319\pi\) |
0.825926 | + | 0.563778i | \(0.190653\pi\) | |||||||
\(398\) | 24.0000 | 1.20301 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 18.0000 | + | 31.1769i | 0.898877 | + | 1.55690i | 0.828932 | + | 0.559350i | \(0.188949\pi\) |
0.0699455 | + | 0.997551i | \(0.477717\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.0000 | − | 38.1051i | 0.547949 | − | 1.89815i | ||||
\(404\) | −2.00000 | −0.0995037 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.00000 | − | 8.66025i | −0.248146 | − | 0.429801i | ||||
\(407\) | −7.50000 | + | 12.9904i | −0.371761 | + | 0.643909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0000 | + | 25.9808i | −0.741702 | + | 1.28467i | 0.210017 | + | 0.977698i | \(0.432648\pi\) |
−0.951720 | + | 0.306968i | \(0.900685\pi\) | |||||||
\(410\) | 1.00000 | − | 1.73205i | 0.0493865 | − | 0.0855399i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.00000 | + | 8.66025i | −0.246332 | + | 0.426660i | ||||
\(413\) | 15.0000 | + | 25.9808i | 0.738102 | + | 1.27843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | −2.50000 | − | 2.59808i | −0.122573 | − | 0.127381i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.00000 | + | 8.66025i | 0.244558 | + | 0.423587i | ||||
\(419\) | −2.00000 | − | 3.46410i | −0.0977064 | − | 0.169232i | 0.813029 | − | 0.582224i | \(-0.197817\pi\) |
−0.910735 | + | 0.412991i | \(0.864484\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.0000 | −0.779792 | −0.389896 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389896 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(422\) | 2.00000 | − | 3.46410i | 0.0973585 | − | 0.168630i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −1.00000 | + | 1.73205i | −0.0485071 | + | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.0000 | + | 17.3205i | 0.483934 | + | 0.838198i | ||||
\(428\) | −10.0000 | −0.483368 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 11.0000 | 0.530467 | ||||||||
\(431\) | 20.0000 | + | 34.6410i | 0.963366 | + | 1.66860i | 0.713942 | + | 0.700205i | \(0.246908\pi\) |
0.249424 | + | 0.968394i | \(0.419759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | + | 24.2487i | −0.672797 | + | 1.16532i | 0.304311 | + | 0.952573i | \(0.401574\pi\) |
−0.977108 | + | 0.212746i | \(0.931759\pi\) | |||||||
\(434\) | 22.0000 | 1.05603 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.00000 | − | 1.73205i | 0.0478913 | − | 0.0829502i | ||||
\(437\) | −2.00000 | −0.0956730 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.00000 | + | 3.46410i | 0.0954548 | + | 0.165333i | 0.909798 | − | 0.415051i | \(-0.136236\pi\) |
−0.814344 | + | 0.580383i | \(0.802903\pi\) | |||||||
\(440\) | 2.50000 | + | 4.33013i | 0.119183 | + | 0.206431i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.00000 | + | 6.92820i | −0.0951303 | + | 0.329541i | ||||
\(443\) | −20.0000 | −0.950229 | −0.475114 | − | 0.879924i | \(-0.657593\pi\) | ||||
−0.475114 | + | 0.879924i | \(0.657593\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.00000 | − | 1.73205i | −0.0474045 | − | 0.0821071i | ||||
\(446\) | −13.0000 | + | 22.5167i | −0.615568 | + | 1.06619i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | − | 1.73205i | 0.0472456 | − | 0.0818317i | ||||
\(449\) | 6.00000 | − | 10.3923i | 0.283158 | − | 0.490443i | −0.689003 | − | 0.724758i | \(-0.741951\pi\) |
0.972161 | + | 0.234315i | \(0.0752847\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.00000 | + | 8.66025i | −0.235441 | + | 0.407795i | ||||
\(452\) | 5.50000 | + | 9.52628i | 0.258698 | + | 0.448078i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.00000 | − | 5.19615i | −0.234404 | − | 0.243599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.0000 | − | 32.9090i | −0.888783 | − | 1.53942i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
−0.0474665 | − | 0.998873i | \(-0.515115\pi\) | |||||||
\(458\) | −5.00000 | − | 8.66025i | −0.233635 | − | 0.404667i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.00000 | −0.0466252 | ||||||||
\(461\) | −19.5000 | + | 33.7750i | −0.908206 | + | 1.57306i | −0.0916500 | + | 0.995791i | \(0.529214\pi\) |
−0.816556 | + | 0.577267i | \(0.804119\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 2.50000 | − | 4.33013i | 0.116060 | − | 0.201021i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.500000 | + | 0.866025i | 0.0231621 | + | 0.0401179i | ||||
\(467\) | −6.00000 | −0.277647 | −0.138823 | − | 0.990317i | \(-0.544332\pi\) | ||||
−0.138823 | + | 0.990317i | \(0.544332\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −32.0000 | −1.47762 | ||||||||
\(470\) | −4.50000 | − | 7.79423i | −0.207570 | − | 0.359521i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.50000 | + | 12.9904i | −0.345215 | + | 0.597931i | ||||
\(473\) | −55.0000 | −2.52890 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00000 | − | 1.73205i | 0.0458831 | − | 0.0794719i | ||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −10.0000 | − | 17.3205i | −0.457389 | − | 0.792222i | ||||
\(479\) | −12.0000 | − | 20.7846i | −0.548294 | − | 0.949673i | −0.998392 | − | 0.0566937i | \(-0.981944\pi\) |
0.450098 | − | 0.892979i | \(-0.351389\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 2.59808i | 0.478759 | − | 0.118462i | ||||
\(482\) | −7.00000 | −0.318841 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.00000 | − | 12.1244i | −0.318182 | − | 0.551107i | ||||
\(485\) | −1.00000 | + | 1.73205i | −0.0454077 | + | 0.0786484i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.00000 | + | 1.73205i | −0.0453143 | + | 0.0784867i | −0.887793 | − | 0.460243i | \(-0.847762\pi\) |
0.842479 | + | 0.538730i | \(0.181096\pi\) | |||||||
\(488\) | −5.00000 | + | 8.66025i | −0.226339 | + | 0.392031i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.50000 | + | 2.59808i | −0.0677631 | + | 0.117369i | ||||
\(491\) | −8.00000 | − | 13.8564i | −0.361035 | − | 0.625331i | 0.627096 | − | 0.778942i | \(-0.284243\pi\) |
−0.988131 | + | 0.153611i | \(0.950910\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.0000 | −0.450377 | ||||||||
\(494\) | 2.00000 | − | 6.92820i | 0.0899843 | − | 0.311715i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.50000 | + | 9.52628i | 0.246957 | + | 0.427743i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 28.0000 | 1.25345 | 0.626726 | − | 0.779240i | \(-0.284395\pi\) | ||||
0.626726 | + | 0.779240i | \(0.284395\pi\) | |||||||
\(500\) | 0.500000 | − | 0.866025i | 0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −25.0000 | −1.11580 | ||||||||
\(503\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.00000 | − | 1.73205i | −0.0444994 | − | 0.0770752i | ||||
\(506\) | 5.00000 | 0.222277 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | 14.5000 | + | 25.1147i | 0.642701 | + | 1.11319i | 0.984827 | + | 0.173537i | \(0.0555197\pi\) |
−0.342126 | + | 0.939654i | \(0.611147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | + | 10.3923i | −0.265424 | + | 0.459728i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.50000 | + | 14.7224i | −0.374919 | + | 0.649379i | ||||
\(515\) | −10.0000 | −0.440653 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.5000 | + | 38.9711i | 0.989549 | + | 1.71395i | ||||
\(518\) | 3.00000 | + | 5.19615i | 0.131812 | + | 0.228306i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.00000 | − | 3.46410i | 0.0438529 | − | 0.151911i | ||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5000 | + | 26.8468i | 0.677768 | + | 1.17393i | 0.975652 | + | 0.219326i | \(0.0703858\pi\) |
−0.297884 | + | 0.954602i | \(0.596281\pi\) | |||||||
\(524\) | −0.500000 | + | 0.866025i | −0.0218426 | + | 0.0378325i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.5000 | − | 18.1865i | 0.457822 | − | 0.792971i | ||||
\(527\) | 11.0000 | − | 19.0526i | 0.479168 | − | 0.829943i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | −3.00000 | − | 5.19615i | −0.130312 | − | 0.225706i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | 0.173422 | ||||||||
\(533\) | 7.00000 | − | 1.73205i | 0.303204 | − | 0.0750234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.00000 | − | 8.66025i | −0.216169 | − | 0.374415i | ||||
\(536\) | −8.00000 | − | 13.8564i | −0.345547 | − | 0.598506i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.0000 | −0.603583 | ||||||||
\(539\) | 7.50000 | − | 12.9904i | 0.323048 | − | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(542\) | 6.50000 | − | 11.2583i | 0.279199 | − | 0.483587i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.00000 | − | 1.73205i | −0.0428746 | − | 0.0742611i | ||||
\(545\) | 2.00000 | 0.0856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | −5.50000 | − | 9.52628i | −0.234948 | − | 0.406942i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.50000 | + | 4.33013i | −0.106600 | + | 0.184637i | ||||
\(551\) | 10.0000 | 0.426014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −11.0000 | + | 19.0526i | −0.467768 | + | 0.810197i | ||||
\(554\) | −11.0000 | −0.467345 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.00000 | − | 1.73205i | −0.0424094 | − | 0.0734553i | ||||
\(557\) | 13.0000 | + | 22.5167i | 0.550828 | + | 0.954062i | 0.998215 | + | 0.0597213i | \(0.0190212\pi\) |
−0.447387 | + | 0.894340i | \(0.647645\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 27.5000 | + | 28.5788i | 1.16313 | + | 1.20876i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.00000 | − | 8.66025i | −0.210912 | − | 0.365311i | ||||
\(563\) | 6.00000 | − | 10.3923i | 0.252870 | − | 0.437983i | −0.711445 | − | 0.702742i | \(-0.751959\pi\) |
0.964315 | + | 0.264758i | \(0.0852922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.50000 | + | 9.52628i | −0.231387 | + | 0.400774i | ||||
\(566\) | −9.50000 | + | 16.4545i | −0.399315 | + | 0.691633i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.0000 | − | 19.0526i | −0.461144 | − | 0.798725i | 0.537874 | − | 0.843025i | \(-0.319228\pi\) |
−0.999018 | + | 0.0443003i | \(0.985894\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0000 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | −5.00000 | + | 17.3205i | −0.209061 | + | 0.724207i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.00000 | + | 3.46410i | 0.0834784 | + | 0.144589i | ||||
\(575\) | −0.500000 | − | 0.866025i | −0.0208514 | − | 0.0361158i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.0000 | −0.915872 | −0.457936 | − | 0.888985i | \(-0.651411\pi\) | ||||
−0.457936 | + | 0.888985i | \(0.651411\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.00000 | 0.207614 | ||||||||
\(581\) | −6.00000 | + | 10.3923i | −0.248922 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | + | 25.9808i | 0.621237 | + | 1.07601i | ||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | −9.00000 | − | 15.5885i | −0.371470 | − | 0.643404i | 0.618322 | − | 0.785925i | \(-0.287813\pi\) |
−0.989792 | + | 0.142520i | \(0.954479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −11.0000 | + | 19.0526i | −0.453247 | + | 0.785047i | ||||
\(590\) | −15.0000 | −0.617540 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.50000 | + | 2.59808i | −0.0616496 | + | 0.106780i | ||||
\(593\) | −31.0000 | −1.27302 | −0.636509 | − | 0.771270i | \(-0.719622\pi\) | ||||
−0.636509 | + | 0.771270i | \(0.719622\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.00000 | − | 3.46410i | −0.0819920 | − | 0.142014i | ||||
\(596\) | 8.50000 | + | 14.7224i | 0.348174 | + | 0.603054i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.50000 | − | 2.59808i | −0.102233 | − | 0.106243i | ||||
\(599\) | −42.0000 | −1.71607 | −0.858037 | − | 0.513588i | \(-0.828316\pi\) | ||||
−0.858037 | + | 0.513588i | \(0.828316\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50000 | + | 2.59808i | 0.0611863 | + | 0.105978i | 0.894996 | − | 0.446074i | \(-0.147178\pi\) |
−0.833810 | + | 0.552052i | \(0.813845\pi\) | |||||||
\(602\) | −11.0000 | + | 19.0526i | −0.448327 | + | 0.776524i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.00000 | + | 6.92820i | −0.162758 | + | 0.281905i | ||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.00000 | + | 15.5885i | −0.365299 | + | 0.632716i | −0.988824 | − | 0.149087i | \(-0.952366\pi\) |
0.623525 | + | 0.781803i | \(0.285700\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −10.0000 | −0.404888 | ||||||||
\(611\) | 9.00000 | − | 31.1769i | 0.364101 | − | 1.26128i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.5000 | + | 25.1147i | 0.585649 | + | 1.01437i | 0.994794 | + | 0.101905i | \(0.0324938\pi\) |
−0.409145 | + | 0.912470i | \(0.634173\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | −0.402911 | ||||||||
\(617\) | 20.5000 | − | 35.5070i | 0.825299 | − | 1.42946i | −0.0763917 | − | 0.997078i | \(-0.524340\pi\) |
0.901691 | − | 0.432382i | \(-0.142327\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.0000 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(620\) | −5.50000 | + | 9.52628i | −0.220885 | + | 0.382585i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 10.0000 | + | 17.3205i | 0.400963 | + | 0.694489i | ||||
\(623\) | 4.00000 | 0.160257 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −10.0000 | − | 17.3205i | −0.399680 | − | 0.692267i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.50000 | − | 6.06218i | 0.139665 | − | 0.241907i | ||||
\(629\) | 6.00000 | 0.239236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | + | 34.6410i | −0.796187 | + | 1.37904i | 0.125895 | + | 0.992044i | \(0.459820\pi\) |
−0.922082 | + | 0.386994i | \(0.873514\pi\) | |||||||
\(632\) | −11.0000 | −0.437557 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.00000 | + | 13.8564i | 0.317721 | + | 0.550308i | ||||
\(635\) | 1.00000 | + | 1.73205i | 0.0396838 | + | 0.0687343i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.5000 | + | 2.59808i | −0.416025 | + | 0.102940i | ||||
\(638\) | −25.0000 | −0.989759 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.500000 | + | 0.866025i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −15.0000 | + | 25.9808i | −0.592464 | + | 1.02618i | 0.401435 | + | 0.915888i | \(0.368512\pi\) |
−0.993899 | + | 0.110291i | \(0.964822\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | + | 6.92820i | −0.157745 | + | 0.273222i | −0.934055 | − | 0.357129i | \(-0.883756\pi\) |
0.776310 | + | 0.630351i | \(0.217089\pi\) | |||||||
\(644\) | 1.00000 | − | 1.73205i | 0.0394055 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 3.46410i | 0.0786889 | − | 0.136293i | ||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.0000 | 2.94401 | ||||||||
\(650\) | 3.50000 | − | 0.866025i | 0.137281 | − | 0.0339683i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.50000 | + | 12.9904i | 0.293723 | + | 0.508743i | ||||
\(653\) | 17.0000 | + | 29.4449i | 0.665261 | + | 1.15227i | 0.979214 | + | 0.202828i | \(0.0650132\pi\) |
−0.313953 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00000 | −0.0390732 | ||||||||
\(656\) | −1.00000 | + | 1.73205i | −0.0390434 | + | 0.0676252i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 18.0000 | 0.701713 | ||||||||
\(659\) | −19.5000 | + | 33.7750i | −0.759612 | + | 1.31569i | 0.183436 | + | 0.983032i | \(0.441278\pi\) |
−0.943049 | + | 0.332655i | \(0.892055\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.0000 | − | 27.7128i | −0.622328 | − | 1.07790i | −0.989051 | − | 0.147573i | \(-0.952854\pi\) |
0.366723 | − | 0.930330i | \(-0.380480\pi\) | |||||||
\(662\) | −28.0000 | −1.08825 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 2.00000 | + | 3.46410i | 0.0775567 | + | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.50000 | − | 4.33013i | 0.0968004 | − | 0.167663i | ||||
\(668\) | −3.00000 | −0.116073 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.00000 | − | 13.8564i | 0.309067 | − | 0.535320i | ||||
\(671\) | 50.0000 | 1.93023 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.00000 | − | 6.92820i | −0.154189 | − | 0.267063i | 0.778575 | − | 0.627552i | \(-0.215943\pi\) |
−0.932763 | + | 0.360489i | \(0.882610\pi\) | |||||||
\(674\) | 1.00000 | + | 1.73205i | 0.0385186 | + | 0.0667161i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5000 | − | 6.06218i | 0.442308 | − | 0.233161i | ||||
\(677\) | 4.00000 | 0.153732 | 0.0768662 | − | 0.997041i | \(-0.475509\pi\) | ||||
0.0768662 | + | 0.997041i | \(0.475509\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.00000 | − | 3.46410i | −0.0767530 | − | 0.132940i | ||||
\(680\) | 1.00000 | − | 1.73205i | 0.0383482 | − | 0.0664211i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.5000 | − | 47.6314i | 1.05303 | − | 1.82390i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.50000 | − | 9.52628i | 0.210144 | − | 0.363980i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11.0000 | −0.419371 | ||||||||
\(689\) | 6.00000 | − | 20.7846i | 0.228582 | − | 0.791831i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.0000 | + | 25.9808i | 0.570627 | + | 0.988355i | 0.996502 | + | 0.0835727i | \(0.0266331\pi\) |
−0.425875 | + | 0.904782i | \(0.640034\pi\) | |||||||
\(692\) | 10.0000 | + | 17.3205i | 0.380143 | + | 0.658427i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.0000 | −1.29062 | ||||||||
\(695\) | 1.00000 | − | 1.73205i | 0.0379322 | − | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.00000 | 0.151511 | ||||||||
\(698\) | −10.0000 | + | 17.3205i | −0.378506 | + | 0.655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | + | 1.73205i | 0.0377964 | + | 0.0654654i | ||||
\(701\) | −13.0000 | −0.491003 | −0.245502 | − | 0.969396i | \(-0.578953\pi\) | ||||
−0.245502 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.00000 | −0.226294 | ||||||||
\(704\) | −2.50000 | − | 4.33013i | −0.0942223 | − | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.00000 | + | 15.5885i | −0.338719 | + | 0.586679i | ||||
\(707\) | 4.00000 | 0.150435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.00000 | − | 6.92820i | 0.150223 | − | 0.260194i | −0.781086 | − | 0.624423i | \(-0.785334\pi\) |
0.931309 | + | 0.364229i | \(0.118667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.00000 | + | 1.73205i | 0.0374766 | + | 0.0649113i | ||||
\(713\) | 5.50000 | + | 9.52628i | 0.205977 | + | 0.356762i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −17.5000 | + | 4.33013i | −0.654463 | + | 0.161938i | ||||
\(716\) | 13.0000 | 0.485833 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.00000 | + | 10.3923i | 0.223918 | + | 0.387837i | ||||
\(719\) | 12.0000 | − | 20.7846i | 0.447524 | − | 0.775135i | −0.550700 | − | 0.834703i | \(-0.685639\pi\) |
0.998224 | + | 0.0595683i | \(0.0189724\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.0000 | − | 17.3205i | 0.372419 | − | 0.645049i | ||||
\(722\) | 7.50000 | − | 12.9904i | 0.279121 | − | 0.483452i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.00000 | − | 13.8564i | 0.297318 | − | 0.514969i | ||||
\(725\) | 2.50000 | + | 4.33013i | 0.0928477 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.0000 | −1.48352 | −0.741759 | − | 0.670667i | \(-0.766008\pi\) | ||||
−0.741759 | + | 0.670667i | \(0.766008\pi\) | |||||||
\(728\) | 5.00000 | + | 5.19615i | 0.185312 | + | 0.192582i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.00000 | − | 5.19615i | −0.111035 | − | 0.192318i | ||||
\(731\) | 11.0000 | + | 19.0526i | 0.406850 | + | 0.704684i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.00000 | 0.221615 | 0.110808 | − | 0.993842i | \(-0.464656\pi\) | ||||
0.110808 | + | 0.993842i | \(0.464656\pi\) | |||||||
\(734\) | 8.00000 | − | 13.8564i | 0.295285 | − | 0.511449i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −40.0000 | + | 69.2820i | −1.47342 | + | 2.55204i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.0000 | − | 38.1051i | −0.809283 | − | 1.40172i | −0.913361 | − | 0.407150i | \(-0.866523\pi\) |
0.104078 | − | 0.994569i | \(-0.466811\pi\) | |||||||
\(740\) | −3.00000 | −0.110282 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | 25.5000 | + | 44.1673i | 0.935504 | + | 1.62034i | 0.773732 | + | 0.633513i | \(0.218388\pi\) |
0.161772 | + | 0.986828i | \(0.448279\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.50000 | + | 14.7224i | −0.311416 | + | 0.539388i | ||||
\(746\) | −19.0000 | −0.695639 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5.00000 | + | 8.66025i | −0.182818 | + | 0.316650i | ||||
\(749\) | 20.0000 | 0.730784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5000 | + | 19.9186i | 0.419641 | + | 0.726839i | 0.995903 | − | 0.0904254i | \(-0.0288227\pi\) |
−0.576262 | + | 0.817265i | \(0.695489\pi\) | |||||||
\(752\) | 4.50000 | + | 7.79423i | 0.164098 | + | 0.284226i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.5000 | + | 12.9904i | 0.455223 | + | 0.473082i | ||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.00000 | − | 8.66025i | −0.181728 | − | 0.314762i | 0.760741 | − | 0.649056i | \(-0.224836\pi\) |
−0.942469 | + | 0.334293i | \(0.891502\pi\) | |||||||
\(758\) | 1.00000 | − | 1.73205i | 0.0363216 | − | 0.0629109i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.00000 | + | 1.73205i | −0.0362738 | + | 0.0628281i | ||||
\(761\) | 10.0000 | − | 17.3205i | 0.362500 | − | 0.627868i | −0.625872 | − | 0.779926i | \(-0.715257\pi\) |
0.988372 | + | 0.152058i | \(0.0485900\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.00000 | + | 3.46410i | −0.0724049 | + | 0.125409i | ||||
\(764\) | 2.00000 | + | 3.46410i | 0.0723575 | + | 0.125327i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −31.0000 | −1.12008 | ||||||||
\(767\) | −37.5000 | − | 38.9711i | −1.35405 | − | 1.40717i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.5000 | − | 37.2391i | −0.775310 | − | 1.34288i | −0.934620 | − | 0.355647i | \(-0.884260\pi\) |
0.159310 | − | 0.987229i | \(-0.449073\pi\) | |||||||
\(770\) | −5.00000 | − | 8.66025i | −0.180187 | − | 0.312094i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −24.0000 | −0.863779 | ||||||||
\(773\) | 16.0000 | − | 27.7128i | 0.575480 | − | 0.996761i | −0.420509 | − | 0.907288i | \(-0.638149\pi\) |
0.995989 | − | 0.0894724i | \(-0.0285181\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −11.0000 | −0.395132 | ||||||||
\(776\) | 1.00000 | − | 1.73205i | 0.0358979 | − | 0.0621770i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.50000 | + | 4.33013i | 0.0896293 | + | 0.155243i | ||||
\(779\) | −4.00000 | −0.143315 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.00000 | − | 1.73205i | −0.0357599 | − | 0.0619380i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | 7.00000 | 0.249841 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5000 | − | 26.8468i | 0.552515 | − | 0.956985i | −0.445577 | − | 0.895244i | \(-0.647001\pi\) |
0.998092 | − | 0.0617409i | \(-0.0196653\pi\) | |||||||
\(788\) | 8.00000 | 0.284988 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −5.50000 | − | 9.52628i | −0.195681 | − | 0.338930i | ||||
\(791\) | −11.0000 | − | 19.0526i | −0.391115 | − | 0.677431i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −25.0000 | − | 25.9808i | −0.887776 | − | 0.922604i | ||||
\(794\) | 3.00000 | 0.106466 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.0000 | − | 20.7846i | −0.425329 | − | 0.736691i | ||||
\(797\) | 6.00000 | − | 10.3923i | 0.212531 | − | 0.368114i | −0.739975 | − | 0.672634i | \(-0.765163\pi\) |
0.952506 | + | 0.304520i | \(0.0984960\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.00000 | − | 15.5885i | 0.318397 | − | 0.551480i | ||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000 | − | 31.1769i | 0.635602 | − | 1.10090i | ||||
\(803\) | 15.0000 | + | 25.9808i | 0.529339 | + | 0.916841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.00000 | 0.0704907 | ||||||||
\(806\) | −38.5000 | + | 9.52628i | −1.35610 | + | 0.335549i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.00000 | + | 1.73205i | 0.0351799 | + | 0.0609333i | ||||
\(809\) | −15.0000 | − | 25.9808i | −0.527372 | − | 0.913435i | −0.999491 | − | 0.0319002i | \(-0.989844\pi\) |
0.472119 | − | 0.881535i | \(-0.343489\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −5.00000 | + | 8.66025i | −0.175466 | + | 0.303915i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.0000 | 0.525750 | ||||||||
\(815\) | −7.50000 | + | 12.9904i | −0.262714 | + | 0.455033i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −11.0000 | − | 19.0526i | −0.384841 | − | 0.666565i | ||||
\(818\) | 30.0000 | 1.04893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | −25.5000 | − | 44.1673i | −0.889956 | − | 1.54145i | −0.839926 | − | 0.542702i | \(-0.817401\pi\) |
−0.0500305 | − | 0.998748i | \(-0.515932\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.00000 | − | 1.73205i | 0.0348578 | − | 0.0603755i | −0.848070 | − | 0.529884i | \(-0.822235\pi\) |
0.882928 | + | 0.469508i | \(0.155569\pi\) | |||||||
\(824\) | 10.0000 | 0.348367 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | − | 25.9808i | 0.521917 | − | 0.903986i | ||||
\(827\) | 50.0000 | 1.73867 | 0.869335 | − | 0.494223i | \(-0.164547\pi\) | ||||
0.869335 | + | 0.494223i | \(0.164547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.00000 | − | 12.1244i | −0.243120 | − | 0.421096i | 0.718481 | − | 0.695546i | \(-0.244838\pi\) |
−0.961601 | + | 0.274450i | \(0.911504\pi\) | |||||||
\(830\) | −3.00000 | − | 5.19615i | −0.104132 | − | 0.180361i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.00000 | + | 3.46410i | −0.0346688 | + | 0.120096i | ||||
\(833\) | −6.00000 | −0.207888 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50000 | − | 2.59808i | −0.0519096 | − | 0.0899101i | ||||
\(836\) | 5.00000 | − | 8.66025i | 0.172929 | − | 0.299521i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.00000 | + | 3.46410i | −0.0690889 | + | 0.119665i | ||||
\(839\) | −27.0000 | + | 46.7654i | −0.932144 | + | 1.61452i | −0.152493 | + | 0.988304i | \(0.548730\pi\) |
−0.779650 | + | 0.626215i | \(0.784603\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.00000 | − | 3.46410i | 0.0689655 | − | 0.119452i | ||||
\(842\) | 8.00000 | + | 13.8564i | 0.275698 | + | 0.477523i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 11.0000 | + | 6.92820i | 0.378412 | + | 0.238337i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 14.0000 | + | 24.2487i | 0.481046 | + | 0.833196i | ||||
\(848\) | 3.00000 | + | 5.19615i | 0.103020 | + | 0.178437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2.00000 | 0.0685994 | ||||||||
\(851\) | −1.50000 | + | 2.59808i | −0.0514193 | + | 0.0890609i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.0000 | −1.67773 | −0.838864 | − | 0.544341i | \(-0.816780\pi\) | ||||
−0.838864 | + | 0.544341i | \(0.816780\pi\) | |||||||
\(854\) | 10.0000 | − | 17.3205i | 0.342193 | − | 0.592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.00000 | + | 8.66025i | 0.170896 | + | 0.296001i | ||||
\(857\) | 25.0000 | 0.853984 | 0.426992 | − | 0.904255i | \(-0.359573\pi\) | ||||
0.426992 | + | 0.904255i | \(0.359573\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −50.0000 | −1.70598 | −0.852989 | − | 0.521929i | \(-0.825213\pi\) | ||||
−0.852989 | + | 0.521929i | \(0.825213\pi\) | |||||||
\(860\) | −5.50000 | − | 9.52628i | −0.187548 | − | 0.324843i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.0000 | − | 34.6410i | 0.681203 | − | 1.17988i | ||||
\(863\) | −39.0000 | −1.32758 | −0.663788 | − | 0.747921i | \(-0.731052\pi\) | ||||
−0.663788 | + | 0.747921i | \(0.731052\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0000 | + | 17.3205i | −0.340010 | + | 0.588915i | ||||
\(866\) | 28.0000 | 0.951479 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.0000 | − | 19.0526i | −0.373364 | − | 0.646686i | ||||
\(869\) | 27.5000 | + | 47.6314i | 0.932874 | + | 1.61578i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 56.0000 | − | 13.8564i | 1.89749 | − | 0.469506i | ||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.00000 | + | 1.73205i | 0.0338255 | + | 0.0585875i | ||||
\(875\) | −1.00000 | + | 1.73205i | −0.0338062 | + | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.50000 | − | 16.4545i | 0.320792 | − | 0.555628i | −0.659860 | − | 0.751389i | \(-0.729384\pi\) |
0.980652 | + | 0.195761i | \(0.0627176\pi\) | |||||||
\(878\) | 2.00000 | − | 3.46410i | 0.0674967 | − | 0.116908i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.50000 | − | 4.33013i | 0.0842750 | − | 0.145969i | ||||
\(881\) | −9.00000 | − | 15.5885i | −0.303218 | − | 0.525188i | 0.673645 | − | 0.739055i | \(-0.264728\pi\) |
−0.976863 | + | 0.213866i | \(0.931394\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.00000 | −0.0336527 | −0.0168263 | − | 0.999858i | \(-0.505356\pi\) | ||||
−0.0168263 | + | 0.999858i | \(0.505356\pi\) | |||||||
\(884\) | 7.00000 | − | 1.73205i | 0.235435 | − | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.0000 | + | 17.3205i | 0.335957 | + | 0.581894i | ||||
\(887\) | 1.50000 | + | 2.59808i | 0.0503651 | + | 0.0872349i | 0.890109 | − | 0.455748i | \(-0.150628\pi\) |
−0.839744 | + | 0.542983i | \(0.817295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.00000 | −0.134156 | ||||||||
\(890\) | −1.00000 | + | 1.73205i | −0.0335201 | + | 0.0580585i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.0000 | 0.870544 | ||||||||
\(893\) | −9.00000 | + | 15.5885i | −0.301174 | + | 0.521648i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.50000 | + | 11.2583i | 0.217271 | + | 0.376324i | ||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −12.0000 | −0.400445 | ||||||||
\(899\) | −27.5000 | − | 47.6314i | −0.917176 | − | 1.58860i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.00000 | − | 10.3923i | 0.199889 | − | 0.346218i | ||||
\(902\) | 10.0000 | 0.332964 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.50000 | − | 9.52628i | 0.182927 | − | 0.316839i | ||||
\(905\) | 16.0000 | 0.531858 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.50000 | − | 16.4545i | −0.315442 | − | 0.546362i | 0.664089 | − | 0.747653i | \(-0.268820\pi\) |
−0.979531 | + | 0.201291i | \(0.935486\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.00000 | + | 6.92820i | −0.0662994 | + | 0.229668i | ||||
\(911\) | 18.0000 | 0.596367 | 0.298183 | − | 0.954509i | \(-0.403619\pi\) | ||||
0.298183 | + | 0.954509i | \(0.403619\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.0000 | + | 25.9808i | 0.496428 | + | 0.859838i | ||||
\(914\) | −19.0000 | + | 32.9090i | −0.628464 | + | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.00000 | + | 8.66025i | −0.165205 | + | 0.286143i | ||||
\(917\) | 1.00000 | − | 1.73205i | 0.0330229 | − | 0.0571974i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | 0.500000 | + | 0.866025i | 0.0164845 | + | 0.0285520i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 39.0000 | 1.28440 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.50000 | − | 2.59808i | −0.0493197 | − | 0.0854242i | ||||
\(926\) | −7.00000 | − | 12.1244i | −0.230034 | − | 0.398431i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.00000 | −0.164133 | ||||||||
\(929\) | −8.00000 | + | 13.8564i | −0.262471 | + | 0.454614i | −0.966898 | − | 0.255163i | \(-0.917871\pi\) |
0.704427 | + | 0.709777i | \(0.251204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 0.500000 | − | 0.866025i | 0.0163780 | − | 0.0283676i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.00000 | + | 5.19615i | 0.0981630 | + | 0.170023i | ||||
\(935\) | −10.0000 | −0.327035 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.0000 | −1.63343 | −0.816714 | − | 0.577042i | \(-0.804207\pi\) | ||||
−0.816714 | + | 0.577042i | \(0.804207\pi\) | |||||||
\(938\) | 16.0000 | + | 27.7128i | 0.522419 | + | 0.904855i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.50000 | + | 7.79423i | −0.146774 | + | 0.254220i | ||||
\(941\) | 50.0000 | 1.62995 | 0.814977 | − | 0.579494i | \(-0.196750\pi\) | ||||
0.814977 | + | 0.579494i | \(0.196750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.00000 | + | 1.73205i | −0.0325645 | + | 0.0564033i | ||||
\(944\) | 15.0000 | 0.488208 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.5000 | + | 47.6314i | 0.894102 | + | 1.54863i | ||||
\(947\) | 4.00000 | + | 6.92820i | 0.129983 | + | 0.225136i | 0.923670 | − | 0.383190i | \(-0.125175\pi\) |
−0.793687 | + | 0.608326i | \(0.791841\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.00000 | − | 20.7846i | 0.194768 | − | 0.674697i | ||||
\(950\) | −2.00000 | −0.0648886 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.00000 | + | 3.46410i | 0.0648204 | + | 0.112272i | ||||
\(953\) | −25.5000 | + | 44.1673i | −0.826026 | + | 1.43072i | 0.0751066 | + | 0.997176i | \(0.476070\pi\) |
−0.901133 | + | 0.433544i | \(0.857263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.00000 | + | 3.46410i | −0.0647185 | + | 0.112096i | ||||
\(956\) | −10.0000 | + | 17.3205i | −0.323423 | + | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.0000 | + | 20.7846i | −0.387702 | + | 0.671520i | ||||
\(959\) | 11.0000 | + | 19.0526i | 0.355209 | + | 0.615239i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 90.0000 | 2.90323 | ||||||||
\(962\) | −7.50000 | − | 7.79423i | −0.241810 | − | 0.251296i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.50000 | + | 6.06218i | 0.112727 | + | 0.195250i | ||||
\(965\) | −12.0000 | − | 20.7846i | −0.386294 | − | 0.669080i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0000 | 0.643157 | 0.321578 | − | 0.946883i | \(-0.395787\pi\) | ||||
0.321578 | + | 0.946883i | \(0.395787\pi\) | |||||||
\(968\) | −7.00000 | + | 12.1244i | −0.224989 | + | 0.389692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.00000 | 0.0642161 | ||||||||
\(971\) | 24.0000 | − | 41.5692i | 0.770197 | − | 1.33402i | −0.167258 | − | 0.985913i | \(-0.553491\pi\) |
0.937455 | − | 0.348107i | \(-0.113175\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.00000 | + | 3.46410i | 0.0641171 | + | 0.111054i | ||||
\(974\) | 2.00000 | 0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.0000 | 0.320092 | ||||||||
\(977\) | −10.5000 | − | 18.1865i | −0.335925 | − | 0.581839i | 0.647737 | − | 0.761864i | \(-0.275715\pi\) |
−0.983662 | + | 0.180025i | \(0.942382\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.00000 | − | 8.66025i | 0.159801 | − | 0.276783i | ||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.00000 | + | 13.8564i | −0.255290 | + | 0.442176i | ||||
\(983\) | 3.00000 | 0.0956851 | 0.0478426 | − | 0.998855i | \(-0.484765\pi\) | ||||
0.0478426 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.00000 | + | 6.92820i | 0.127451 | + | 0.220751i | ||||
\(986\) | 5.00000 | + | 8.66025i | 0.159232 | + | 0.275799i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.00000 | + | 1.73205i | −0.222700 | + | 0.0551039i | ||||
\(989\) | −11.0000 | −0.349780 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.50000 | + | 14.7224i | 0.270011 | + | 0.467673i | 0.968864 | − | 0.247592i | \(-0.0796392\pi\) |
−0.698853 | + | 0.715265i | \(0.746306\pi\) | |||||||
\(992\) | 5.50000 | − | 9.52628i | 0.174625 | − | 0.302460i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 12.0000 | − | 20.7846i | 0.380426 | − | 0.658916i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.00000 | − | 1.73205i | 0.0316703 | − | 0.0548546i | −0.849756 | − | 0.527176i | \(-0.823251\pi\) |
0.881426 | + | 0.472322i | \(0.156584\pi\) | |||||||
\(998\) | −14.0000 | − | 24.2487i | −0.443162 | − | 0.767580i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1170.2.i.a.991.1 | 2 | ||
3.2 | odd | 2 | 390.2.i.f.211.1 | yes | 2 | ||
13.9 | even | 3 | inner | 1170.2.i.a.451.1 | 2 | ||
15.2 | even | 4 | 1950.2.z.e.1849.1 | 4 | |||
15.8 | even | 4 | 1950.2.z.e.1849.2 | 4 | |||
15.14 | odd | 2 | 1950.2.i.d.601.1 | 2 | |||
39.2 | even | 12 | 5070.2.b.h.1351.2 | 2 | |||
39.11 | even | 12 | 5070.2.b.h.1351.1 | 2 | |||
39.23 | odd | 6 | 5070.2.a.p.1.1 | 1 | |||
39.29 | odd | 6 | 5070.2.a.d.1.1 | 1 | |||
39.35 | odd | 6 | 390.2.i.f.61.1 | ✓ | 2 | ||
195.74 | odd | 6 | 1950.2.i.d.451.1 | 2 | |||
195.113 | even | 12 | 1950.2.z.e.1699.1 | 4 | |||
195.152 | even | 12 | 1950.2.z.e.1699.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.i.f.61.1 | ✓ | 2 | 39.35 | odd | 6 | ||
390.2.i.f.211.1 | yes | 2 | 3.2 | odd | 2 | ||
1170.2.i.a.451.1 | 2 | 13.9 | even | 3 | inner | ||
1170.2.i.a.991.1 | 2 | 1.1 | even | 1 | trivial | ||
1950.2.i.d.451.1 | 2 | 195.74 | odd | 6 | |||
1950.2.i.d.601.1 | 2 | 15.14 | odd | 2 | |||
1950.2.z.e.1699.1 | 4 | 195.113 | even | 12 | |||
1950.2.z.e.1699.2 | 4 | 195.152 | even | 12 | |||
1950.2.z.e.1849.1 | 4 | 15.2 | even | 4 | |||
1950.2.z.e.1849.2 | 4 | 15.8 | even | 4 | |||
5070.2.a.d.1.1 | 1 | 39.29 | odd | 6 | |||
5070.2.a.p.1.1 | 1 | 39.23 | odd | 6 | |||
5070.2.b.h.1351.1 | 2 | 39.11 | even | 12 | |||
5070.2.b.h.1351.2 | 2 | 39.2 | even | 12 |