Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [380,2,Mod(121,380)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(380, 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("380.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 380 = 2^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 380.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: | \(3.03431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.2 | ||
Root | \(1.09935 - 1.90412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 380.121 |
Dual form | 380.2.i.b.201.2 |
$q$-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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(77\) | \(191\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 0.182224 | + | 0.315621i | 0.105207 | + | 0.182224i | 0.913823 | − | 0.406113i | \(-0.133116\pi\) |
−0.808616 | + | 0.588337i | \(0.799783\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.635552 | 0.240216 | 0.120108 | − | 0.992761i | \(-0.461676\pi\) | ||||
0.120108 | + | 0.992761i | \(0.461676\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.43359 | − | 2.48305i | 0.477863 | − | 0.827683i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.63555 | 0.493137 | 0.246569 | − | 0.969125i | \(-0.420697\pi\) | ||||
0.246569 | + | 0.969125i | \(0.420697\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.182224 | + | 0.315621i | −0.0470500 | + | 0.0814931i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.29804 | + | 5.71237i | 0.799891 | + | 1.38545i | 0.919686 | + | 0.392654i | \(0.128443\pi\) |
−0.119795 | + | 0.992799i | \(0.538224\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0466721 | + | 4.35865i | 0.0107073 | + | 0.999943i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.115813 | + | 0.200594i | 0.0252724 | + | 0.0437731i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.433589 | + | 0.750998i | −0.0904095 | + | 0.156594i | −0.907684 | − | 0.419655i | \(-0.862151\pi\) |
0.817274 | + | 0.576249i | \(0.195484\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.13828 | 0.411512 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54940 | − | 7.87979i | 0.844803 | − | 1.46324i | −0.0409898 | − | 0.999160i | \(-0.513051\pi\) |
0.885792 | − | 0.464082i | \(-0.153616\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.86718 | −0.335355 | −0.167677 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167677 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.298037 | + | 0.516215i | 0.0518816 | + | 0.0898615i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.317776 | + | 0.550404i | 0.0537139 | + | 0.0930353i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.635552 | 0.104484 | 0.0522420 | − | 0.998634i | \(-0.483363\pi\) | ||||
0.0522420 | + | 0.998634i | \(0.483363\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.364448 | 0.0583584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.953328 | − | 1.65121i | −0.148885 | − | 0.257876i | 0.781931 | − | 0.623365i | \(-0.214235\pi\) |
−0.930816 | + | 0.365489i | \(0.880902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.98026 | − | 3.42991i | −0.301987 | − | 0.523057i | 0.674599 | − | 0.738184i | \(-0.264317\pi\) |
−0.976586 | + | 0.215128i | \(0.930983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.86718 | 0.427414 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.54940 | + | 7.87979i | −0.663598 | + | 1.14939i | 0.316065 | + | 0.948738i | \(0.397638\pi\) |
−0.979663 | + | 0.200649i | \(0.935695\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.59607 | −0.942296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20196 | + | 2.08186i | −0.168309 | + | 0.291519i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.93359 | − | 8.54523i | 0.677681 | − | 1.17378i | −0.297997 | − | 0.954567i | \(-0.596319\pi\) |
0.975678 | − | 0.219210i | \(-0.0703481\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.817776 | + | 1.41643i | 0.110269 | + | 0.190991i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.36718 | + | 0.808981i | −0.181087 | + | 0.107152i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.54940 | − | 7.87979i | −0.592282 | − | 1.02586i | −0.993924 | − | 0.110065i | \(-0.964894\pi\) |
0.401643 | − | 0.915796i | \(-0.368439\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13555 | + | 1.96683i | −0.145393 | + | 0.251827i | −0.929519 | − | 0.368773i | \(-0.879778\pi\) |
0.784127 | + | 0.620601i | \(0.213111\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.911120 | − | 1.57811i | 0.114790 | − | 0.198823i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.23163 | + | 10.7935i | −0.761314 | + | 1.31863i | 0.180859 | + | 0.983509i | \(0.442112\pi\) |
−0.942173 | + | 0.335126i | \(0.891221\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.316041 | −0.0380469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.25136 | − | 2.16743i | −0.148510 | − | 0.257226i | 0.782167 | − | 0.623069i | \(-0.214114\pi\) |
−0.930677 | + | 0.365842i | \(0.880781\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.201963 | + | 0.349810i | 0.0236380 | + | 0.0409422i | 0.877602 | − | 0.479389i | \(-0.159142\pi\) |
−0.853964 | + | 0.520331i | \(0.825808\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.364448 | −0.0420828 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.03948 | 0.118460 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.36445 | − | 9.29150i | −0.603548 | − | 1.04538i | −0.992279 | − | 0.124024i | \(-0.960420\pi\) |
0.388732 | − | 0.921351i | \(-0.372913\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.91112 | − | 6.77426i | −0.434569 | − | 0.752695i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8672 | −1.74165 | −0.870825 | − | 0.491594i | \(-0.836414\pi\) | ||||
−0.870825 | + | 0.491594i | \(0.836414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.29804 | + | 5.71237i | −0.357722 | + | 0.619593i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.31604 | 0.355517 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.271104 | + | 0.469566i | −0.0287370 | + | 0.0497739i | −0.880036 | − | 0.474907i | \(-0.842482\pi\) |
0.851299 | + | 0.524680i | \(0.175815\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.317776 | − | 0.550404i | 0.0333120 | − | 0.0576980i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.340245 | − | 0.589321i | −0.0352817 | − | 0.0611097i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.75136 | + | 2.21974i | −0.384882 | + | 0.227741i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.68495 | + | 6.38253i | 0.374150 | + | 0.648047i | 0.990199 | − | 0.139660i | \(-0.0446011\pi\) |
−0.616049 | + | 0.787708i | \(0.711268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.34471 | − | 4.06116i | 0.235652 | − | 0.408161i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.66248 | − | 8.07566i | 0.463935 | − | 0.803558i | −0.535218 | − | 0.844714i | \(-0.679771\pi\) |
0.999153 | + | 0.0411556i | \(0.0131039\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.8672 | −1.07077 | −0.535387 | − | 0.844607i | \(-0.679834\pi\) | ||||
−0.535387 | + | 0.844607i | \(0.679834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.115813 | + | 0.200594i | −0.0113022 | + | 0.0195759i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3304 | 1.09535 | 0.547677 | − | 0.836690i | \(-0.315512\pi\) | ||||
0.547677 | + | 0.836690i | \(0.315512\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.61581 | − | 11.4589i | −0.633680 | − | 1.09757i | −0.986793 | − | 0.161985i | \(-0.948210\pi\) |
0.353113 | − | 0.935581i | \(-0.385123\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.115813 | + | 0.200594i | 0.0109925 | + | 0.0190395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.09334 | 0.667286 | 0.333643 | − | 0.942700i | \(-0.391722\pi\) | ||||
0.333643 | + | 0.942700i | \(0.391722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.867178 | −0.0808647 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.43359 | − | 2.48305i | −0.132535 | − | 0.229558i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.09607 | + | 3.63051i | 0.192147 | + | 0.332808i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.32497 | −0.756815 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.347439 | − | 0.601781i | 0.0313275 | − | 0.0542608i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.13828 | + | 14.0959i | −0.722156 | + | 1.25081i | 0.237978 | + | 0.971270i | \(0.423515\pi\) |
−0.960134 | + | 0.279540i | \(0.909818\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.721702 | − | 1.25002i | 0.0635423 | − | 0.110059i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31778 | + | 9.21066i | 0.464616 | + | 0.804739i | 0.999184 | − | 0.0403866i | \(-0.0128590\pi\) |
−0.534568 | + | 0.845126i | \(0.679526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0296625 | + | 2.77015i | 0.00257207 | + | 0.240202i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.06914 | + | 1.85181i | 0.0920170 | + | 0.159378i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.74864 | + | 3.02873i | −0.149396 | + | 0.258761i | −0.931004 | − | 0.365008i | \(-0.881066\pi\) |
0.781608 | + | 0.623769i | \(0.214400\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.367178 | + | 0.635970i | −0.0311436 | + | 0.0539423i | −0.881177 | − | 0.472786i | \(-0.843248\pi\) |
0.850034 | + | 0.526729i | \(0.176582\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31604 | −0.279261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.817776 | − | 1.41643i | 0.0683859 | − | 0.118448i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.09880 | 0.755614 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.20196 | − | 2.08186i | −0.0991362 | − | 0.171709i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.06914 | − | 8.78001i | −0.415280 | − | 0.719286i | 0.580178 | − | 0.814490i | \(-0.302983\pi\) |
−0.995458 | + | 0.0952036i | \(0.969650\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.81331 | 0.228944 | 0.114472 | − | 0.993426i | \(-0.463482\pi\) | ||||
0.114472 | + | 0.993426i | \(0.463482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.9121 | 1.52895 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.933589 | − | 1.61702i | −0.0749877 | − | 0.129882i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.480261 | − | 0.831836i | −0.0383290 | − | 0.0663878i | 0.846225 | − | 0.532826i | \(-0.178870\pi\) |
−0.884554 | + | 0.466439i | \(0.845537\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.59607 | 0.285187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.275568 | + | 0.477298i | −0.0217178 | + | 0.0376164i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.13828 | 0.245809 | 0.122905 | − | 0.992418i | \(-0.460779\pi\) | ||||
0.122905 | + | 0.992418i | \(0.460779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.298037 | + | 0.516215i | −0.0232021 | + | 0.0401873i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.31778 | − | 9.21066i | 0.411502 | − | 0.712742i | −0.583552 | − | 0.812076i | \(-0.698338\pi\) |
0.995054 | + | 0.0993334i | \(0.0316710\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.8896 | + | 6.13262i | 0.832752 | + | 0.468973i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.18495 | − | 10.7127i | −0.470233 | − | 0.814468i | 0.529187 | − | 0.848505i | \(-0.322497\pi\) |
−0.999421 | + | 0.0340371i | \(0.989164\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.317776 | + | 0.550404i | −0.0240216 | + | 0.0416066i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.65802 | − | 2.87178i | 0.124624 | − | 0.215856i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.324970 | −0.0242894 | −0.0121447 | − | 0.999926i | \(-0.503866\pi\) | ||||
−0.0121447 | + | 0.999926i | \(0.503866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.40666 | + | 7.63255i | −0.327544 | + | 0.567323i | −0.982024 | − | 0.188756i | \(-0.939554\pi\) |
0.654480 | + | 0.756079i | \(0.272888\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.827699 | −0.0611853 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.317776 | + | 0.550404i | 0.0233634 | + | 0.0404665i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.39411 | + | 9.34287i | 0.394456 | + | 0.683219i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.35899 | 0.0988519 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 25.1921 | 1.82284 | 0.911420 | − | 0.411478i | \(-0.134987\pi\) | ||||
0.911420 | + | 0.411478i | \(0.134987\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 9.43632 | + | 16.3442i | 0.679241 | + | 1.17648i | 0.975210 | + | 0.221282i | \(0.0710243\pi\) |
−0.295969 | + | 0.955198i | \(0.595642\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.182224 | + | 0.315621i | 0.0130493 | + | 0.0226021i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.36445 | −0.524695 | −0.262348 | − | 0.964973i | \(-0.584497\pi\) | ||||
−0.262348 | + | 0.964973i | \(0.584497\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.38419 | + | 2.39748i | −0.0981224 | + | 0.169953i | −0.910907 | − | 0.412611i | \(-0.864617\pi\) |
0.812785 | + | 0.582564i | \(0.197950\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.54221 | −0.320383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.89138 | − | 5.00802i | 0.202935 | − | 0.351494i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.953328 | − | 1.65121i | 0.0665833 | − | 0.115326i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.24318 | + | 2.15324i | 0.0864067 | + | 0.149661i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0763346 | + | 7.12880i | 0.00528018 | + | 0.493109i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.46325 | − | 14.6588i | −0.582634 | − | 1.00915i | −0.995166 | − | 0.0982088i | \(-0.968689\pi\) |
0.412532 | − | 0.910943i | \(-0.364645\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.456057 | − | 0.789915i | 0.0312485 | − | 0.0541241i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.98026 | − | 3.42991i | 0.135053 | − | 0.233918i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.18669 | −0.0805577 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.0736051 | + | 0.127488i | −0.00497377 | + | 0.00861482i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.59607 | 0.443700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.32051 | − | 7.48334i | −0.289322 | − | 0.501121i | 0.684326 | − | 0.729176i | \(-0.260097\pi\) |
−0.973648 | + | 0.228055i | \(0.926763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.43359 | + | 2.48305i | 0.0955726 | + | 0.165537i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.9265 | 1.38894 | 0.694470 | − | 0.719521i | \(-0.255639\pi\) | ||||
0.694470 | + | 0.719521i | \(0.255639\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.3754 | 1.47861 | 0.739303 | − | 0.673373i | \(-0.235155\pi\) | ||||
0.739303 | + | 0.673373i | \(0.235155\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.189418 | + | 0.328081i | 0.0124628 | + | 0.0215862i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.61854 | + | 16.6598i | 0.630132 | + | 1.09142i | 0.987524 | + | 0.157466i | \(0.0503324\pi\) |
−0.357393 | + | 0.933954i | \(0.616334\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.09880 | −0.593540 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.95506 | − | 3.38627i | 0.126995 | − | 0.219962i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.13282 | −0.137961 | −0.0689804 | − | 0.997618i | \(-0.521975\pi\) | ||||
−0.0689804 | + | 0.997618i | \(0.521975\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2316 | + | 21.1858i | −0.787908 | + | 1.36470i | 0.139338 | + | 0.990245i | \(0.455503\pi\) |
−0.927246 | + | 0.374452i | \(0.877831\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.63282 | − | 8.02428i | 0.297196 | − | 0.514758i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.29804 | − | 5.71237i | −0.210704 | − | 0.364950i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.79804 | + | 2.13891i | 0.241663 | + | 0.136095i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.89138 | − | 5.00802i | −0.183234 | − | 0.317370i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64002 | + | 2.84059i | −0.103517 | + | 0.179297i | −0.913131 | − | 0.407666i | \(-0.866343\pi\) |
0.809614 | + | 0.586962i | \(0.199676\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.709157 | + | 1.22830i | −0.0445843 | + | 0.0772223i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.40393 | −0.150540 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.81778 | − | 6.61258i | 0.238146 | − | 0.412482i | −0.722036 | − | 0.691855i | \(-0.756794\pi\) |
0.960182 | + | 0.279374i | \(0.0901269\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.403926 | 0.0250988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0439 | − | 22.5928i | −0.807400 | − | 1.39846i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.36445 | − | 12.7556i | −0.454111 | − | 0.786544i | 0.544525 | − | 0.838744i | \(-0.316710\pi\) |
−0.998637 | + | 0.0522005i | \(0.983376\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.86718 | 0.606136 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.197607 | −0.0120933 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.73163 | + | 11.6595i | 0.410434 | + | 0.710893i | 0.994937 | − | 0.100498i | \(-0.0320437\pi\) |
−0.584503 | + | 0.811392i | \(0.698710\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.93086 | − | 3.34435i | −0.117291 | − | 0.203155i | 0.801402 | − | 0.598126i | \(-0.204088\pi\) |
−0.918693 | + | 0.394971i | \(0.870754\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.231626 | 0.0140186 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.817776 | + | 1.41643i | −0.0493137 | + | 0.0854139i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −24.2766 | −1.45864 | −0.729319 | − | 0.684174i | \(-0.760163\pi\) | ||||
−0.729319 | + | 0.684174i | \(0.760163\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.67676 | + | 4.63629i | −0.160254 | + | 0.277568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.248635 | + | 0.430649i | −0.0148323 | + | 0.0256904i | −0.873346 | − | 0.487100i | \(-0.838055\pi\) |
0.858514 | + | 0.512790i | \(0.171388\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.57906 | + | 13.1273i | 0.450529 | + | 0.780338i | 0.998419 | − | 0.0562118i | \(-0.0179022\pi\) |
−0.547890 | + | 0.836550i | \(0.684569\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.38419 | − | 0.779520i | −0.0819922 | − | 0.0461748i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.605889 | − | 1.04943i | −0.0357645 | − | 0.0619460i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.2541 | + | 22.9568i | −0.779653 | + | 1.35040i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.34297 | + | 2.32610i | −0.0787265 | + | 0.136358i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.4094 | −0.783385 | −0.391692 | − | 0.920096i | \(-0.628110\pi\) | ||||
−0.391692 | + | 0.920096i | \(0.628110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.54940 | − | 7.87979i | 0.264876 | − | 0.458779i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.49727 | 0.202932 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.433589 | + | 0.750998i | 0.0250751 | + | 0.0434313i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.25856 | − | 2.17989i | −0.0725421 | − | 0.125647i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.39847 | 0.195237 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.27110 | −0.130043 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.1033 | − | 27.8917i | −0.919062 | − | 1.59186i | −0.800843 | − | 0.598875i | \(-0.795615\pi\) |
−0.118219 | − | 0.992988i | \(-0.537719\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.98026 | − | 3.42991i | −0.112653 | − | 0.195121i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.3699 | 0.701433 | 0.350717 | − | 0.936482i | \(-0.385938\pi\) | ||||
0.350717 | + | 0.936482i | \(0.385938\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.3941 | + | 21.4672i | −0.700557 | + | 1.21340i | 0.267715 | + | 0.963498i | \(0.413732\pi\) |
−0.968271 | + | 0.249901i | \(0.919602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.82224 | 0.102672 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.65529 | + | 6.33115i | −0.205302 | + | 0.355593i | −0.950229 | − | 0.311553i | \(-0.899151\pi\) |
0.744927 | + | 0.667146i | \(0.232484\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.44078 | − | 12.8878i | 0.416604 | − | 0.721579i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.06468 | + | 3.57612i | 0.115239 | + | 0.199600i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.7443 | + | 14.6416i | −1.37681 | + | 0.814680i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.500000 | + | 0.866025i | 0.0277350 | + | 0.0480384i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.41112 | − | 4.17618i | 0.133335 | − | 0.230943i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.89138 | + | 5.00802i | −0.159407 | + | 0.276101i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4722 | 1.01532 | 0.507661 | − | 0.861557i | \(-0.330510\pi\) | ||||
0.507661 | + | 0.861557i | \(0.330510\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.911120 | − | 1.57811i | 0.0499291 | − | 0.0864797i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4633 | −0.680940 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.2316 | − | 26.3819i | −0.829720 | − | 1.43712i | −0.898258 | − | 0.439468i | \(-0.855167\pi\) |
0.0685388 | − | 0.997648i | \(-0.478166\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.29258 | + | 2.23881i | 0.0702032 | + | 0.121595i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.05387 | −0.165376 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.64101 | −0.466571 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.158021 | − | 0.273700i | −0.00850754 | − | 0.0147355i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.6608 | − | 20.1970i | −0.625982 | − | 1.08423i | −0.988350 | − | 0.152197i | \(-0.951365\pi\) |
0.362368 | − | 0.932035i | \(-0.381968\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.6894 | −0.946893 | −0.473446 | − | 0.880823i | \(-0.656990\pi\) | ||||
−0.473446 | + | 0.880823i | \(0.656990\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06914 | − | 1.85181i | 0.0570665 | − | 0.0988421i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.13828 | −0.379932 | −0.189966 | − | 0.981791i | \(-0.560838\pi\) | ||||
−0.189966 | + | 0.981791i | \(0.560838\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.25136 | − | 2.16743i | 0.0664155 | − | 0.115035i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.763910 | + | 1.32313i | −0.0404304 | + | 0.0700275i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.0719 | + | 26.1052i | 0.795463 | + | 1.37778i | 0.922545 | + | 0.385890i | \(0.126106\pi\) |
−0.127082 | + | 0.991892i | \(0.540561\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9956 | + | 0.406855i | −0.999771 | + | 0.0214134i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.51701 | − | 2.62754i | −0.0796224 | − | 0.137910i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.201963 | + | 0.349810i | −0.0105712 | + | 0.0183099i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1015 | − | 26.1566i | 0.788294 | − | 1.36536i | −0.138718 | − | 0.990332i | \(-0.544298\pi\) |
0.927012 | − | 0.375033i | \(-0.122369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.46672 | −0.284586 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13555 | − | 5.43094i | 0.162790 | − | 0.281960i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0449 | 1.50389 | 0.751945 | − | 0.659226i | \(-0.229116\pi\) | ||||
0.751945 | + | 0.659226i | \(0.229116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.182224 | − | 0.315621i | −0.00941001 | − | 0.0162986i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.54940 | − | 7.87979i | −0.234306 | − | 0.405830i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.76837 | 0.142202 | 0.0711009 | − | 0.997469i | \(-0.477349\pi\) | ||||
0.0711009 | + | 0.997469i | \(0.477349\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.93196 | −0.303904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.3052 | − | 23.0453i | −0.679866 | − | 1.17756i | −0.975021 | − | 0.222112i | \(-0.928705\pi\) |
0.295156 | − | 0.955449i | \(-0.404629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.519739 | + | 0.900215i | 0.0264884 | + | 0.0458792i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −11.3555 | −0.577233 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.77830 | − | 4.81215i | 0.140865 | − | 0.243986i | −0.786957 | − | 0.617007i | \(-0.788345\pi\) |
0.927823 | + | 0.373021i | \(0.121678\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.71997 | −0.289271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.93805 | + | 3.35681i | −0.0977618 | + | 0.169328i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.36445 | − | 9.29150i | 0.269915 | − | 0.467506i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.35725 | − | 2.35083i | −0.0681186 | − | 0.117985i | 0.829955 | − | 0.557831i | \(-0.188366\pi\) |
−0.898073 | + | 0.439846i | \(0.855033\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.868912 | + | 0.514150i | −0.0435000 | + | 0.0257397i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.94078 | + | 15.4859i | 0.446481 | + | 0.773328i | 0.998154 | − | 0.0607322i | \(-0.0193436\pi\) |
−0.551673 | + | 0.834061i | \(0.686010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.933589 | + | 1.61702i | −0.0465054 | + | 0.0805497i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.91112 | − | 6.77426i | 0.194345 | − | 0.336616i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.03948 | 0.0515250 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.1625 | + | 22.7981i | −0.650843 | + | 1.12729i | 0.332076 | + | 0.943253i | \(0.392251\pi\) |
−0.982919 | + | 0.184040i | \(0.941082\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27457 | −0.0628701 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.89138 | − | 5.00802i | −0.142276 | − | 0.246428i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.93359 | − | 13.7414i | −0.389445 | − | 0.674538i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.267634 | −0.0131061 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3250 | 0.748674 | 0.374337 | − | 0.927293i | \(-0.377870\pi\) | ||||
0.374337 | + | 0.927293i | \(0.377870\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9166 | − | 18.9081i | −0.532042 | − | 0.921523i | −0.999300 | − | 0.0374023i | \(-0.988092\pi\) |
0.467259 | − | 0.884121i | \(-0.345242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 13.0439 | + | 22.5928i | 0.634218 | + | 1.09850i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −6.59607 | −0.319957 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.721702 | + | 1.25002i | −0.0349256 | + | 0.0604929i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.596074 | 0.0287787 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6427 | + | 20.1658i | −0.560811 | + | 0.971354i | 0.436615 | + | 0.899649i | \(0.356177\pi\) |
−0.997426 | + | 0.0717050i | \(0.977156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.95060 | − | 3.37854i | 0.0937398 | − | 0.162362i | −0.815342 | − | 0.578979i | \(-0.803451\pi\) |
0.909082 | + | 0.416617i | \(0.136784\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.65802 | + | 2.87178i | 0.0794960 | + | 0.137691i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.29357 | − | 1.85481i | −0.157553 | − | 0.0887276i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.73882 | + | 16.8681i | 0.464808 | + | 0.805072i | 0.999193 | − | 0.0401697i | \(-0.0127898\pi\) |
−0.534384 | + | 0.845242i | \(0.679457\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.45606 | + | 16.3784i | −0.450288 | + | 0.779922i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.953328 | + | 1.65121i | −0.0452940 | + | 0.0784515i | −0.887784 | − | 0.460261i | \(-0.847756\pi\) |
0.842490 | + | 0.538713i | \(0.181089\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.542208 | −0.0257031 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.84744 | − | 3.19986i | 0.0873808 | − | 0.151348i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.05933 | −0.380343 | −0.190172 | − | 0.981751i | \(-0.560904\pi\) | ||||
−0.190172 | + | 0.981751i | \(0.560904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55922 | − | 2.70064i | −0.0734207 | − | 0.127168i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.512653 | + | 0.887941i | 0.0240865 | + | 0.0417191i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.635552 | 0.0297951 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3250 | 0.529760 | 0.264880 | − | 0.964281i | \(-0.414668\pi\) | ||||
0.264880 | + | 0.964281i | \(0.414668\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.05213 | + | 12.2146i | 0.329165 | + | 0.570131i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0521 | − | 17.4108i | −0.468174 | − | 0.810902i | 0.531164 | − | 0.847269i | \(-0.321755\pi\) |
−0.999338 | + | 0.0363671i | \(0.988421\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33043 | 0.0618303 | 0.0309151 | − | 0.999522i | \(-0.490158\pi\) | ||||
0.0309151 | + | 0.999522i | \(0.490158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.340245 | − | 0.589321i | 0.0157785 | − | 0.0273291i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 10.0844 | 0.466651 | 0.233326 | − | 0.972399i | \(-0.425039\pi\) | ||||
0.233326 | + | 0.972399i | \(0.425039\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.96052 | + | 6.85982i | −0.182880 | + | 0.316757i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.175030 | − | 0.303161i | 0.00806496 | − | 0.0139689i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.23882 | − | 5.60980i | −0.148921 | − | 0.257939i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.79804 | − | 2.13891i | −0.174266 | − | 0.0981397i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −14.1455 | − | 24.5007i | −0.647677 | − | 1.12181i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.44078 | + | 7.69166i | −0.202905 | + | 0.351441i | −0.949463 | − | 0.313879i | \(-0.898371\pi\) |
0.746559 | + | 0.665320i | \(0.231705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.317776 | − | 0.550404i | 0.0144893 | − | 0.0250963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.200861 | −0.00913947 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.68495 | + | 6.38253i | −0.167325 | + | 0.289816i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.32497 | 0.241297 | 0.120649 | − | 0.992695i | \(-0.461503\pi\) | ||||
0.120649 | + | 0.992695i | \(0.461503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.571870 | + | 0.990508i | 0.0258609 | + | 0.0447923i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.70469 | + | 16.8090i | 0.437967 | + | 0.758580i | 0.997533 | − | 0.0702054i | \(-0.0223655\pi\) |
−0.559566 | + | 0.828786i | \(0.689032\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 60.0164 | 2.70300 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.68942 | 0.210774 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.795307 | − | 1.37751i | −0.0356744 | − | 0.0617899i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.79357 | − | 10.0348i | −0.259356 | − | 0.449218i | 0.706714 | − | 0.707500i | \(-0.250177\pi\) |
−0.966070 | + | 0.258282i | \(0.916844\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.87611 | 0.173172 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.5521 | + | 30.4012i | −0.782611 | + | 1.35552i | 0.147805 | + | 0.989017i | \(0.452779\pi\) |
−0.930416 | + | 0.366505i | \(0.880554\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.32497 | 0.414956 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.18669 | + | 3.78746i | −0.0971142 | + | 0.168207i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.93359 | − | 13.7414i | 0.351650 | − | 0.609076i | −0.634889 | − | 0.772604i | \(-0.718954\pi\) |
0.986539 | + | 0.163528i | \(0.0522873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.128358 | + | 0.222323i | 0.00567823 | + | 0.00983498i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0997981 | + | 9.32002i | 0.00440619 | + | 0.411489i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.43359 | − | 9.41125i | −0.239433 | − | 0.414709i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.44078 | + | 12.8878i | −0.327245 | + | 0.566805i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.25409 | − | 3.90421i | 0.0989438 | − | 0.171376i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.6949 | 1.60763 | 0.803816 | − | 0.594878i | \(-0.202800\pi\) | ||||
0.803816 | + | 0.594878i | \(0.202800\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.5127 | − | 26.8687i | 0.678321 | − | 1.17489i | −0.297165 | − | 0.954826i | \(-0.596041\pi\) |
0.975486 | − | 0.220060i | \(-0.0706254\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.231626 | −0.0101090 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.15802 | − | 10.6660i | −0.268248 | − | 0.464618i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.1240 | + | 19.2673i | 0.483652 | + | 0.837710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0879 | −1.13212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.90666 | −0.0825864 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.66521 | + | 9.81244i | 0.244929 | + | 0.424229i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.0592173 | − | 0.102567i | −0.00255542 | − | 0.00442611i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −10.7882 | −0.464682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.79357 | − | 6.57066i | 0.163098 | − | 0.282495i | −0.772880 | − | 0.634552i | \(-0.781185\pi\) |
0.935978 | + | 0.352058i | \(0.114518\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.21199 | −0.137840 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.61581 | − | 11.4589i | 0.283390 | − | 0.490846i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.3914 | − | 26.6587i | 0.658088 | − | 1.13984i | −0.323022 | − | 0.946391i | \(-0.604699\pi\) |
0.981110 | − | 0.193450i | \(-0.0619678\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.25583 | + | 5.63926i | 0.138955 | + | 0.240678i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 34.5576 | + | 19.4615i | 1.47220 | + | 0.829087i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.40939 | − | 5.90523i | −0.144982 | − | 0.251116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.115813 | + | 0.200594i | −0.00491598 | + | 0.00851473i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.5369 | + | 26.9106i | −0.658318 | + | 1.14024i | 0.322733 | + | 0.946490i | \(0.395398\pi\) |
−0.981051 | + | 0.193750i | \(0.937935\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.96052 | −0.167512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96587 | + | 3.40499i | −0.0829992 | + | 0.143759i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −23.2766 | −0.980990 | −0.490495 | − | 0.871444i | \(-0.663184\pi\) | ||||
−0.490495 | + | 0.871444i | \(0.663184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.54667 | + | 6.14302i | 0.149210 | + | 0.258439i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.48572 | − | 4.30539i | −0.104390 | − | 0.180810i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 24.1976 | 1.01442 | 0.507208 | − | 0.861824i | \(-0.330678\pi\) | ||||
0.507208 | + | 0.861824i | \(0.330678\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8475 | 1.24908 | 0.624540 | − | 0.780992i | \(-0.285286\pi\) | ||||
0.624540 | + | 0.780992i | \(0.285286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.59061 | + | 7.95118i | 0.191776 | + | 0.332165i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.433589 | − | 0.750998i | −0.0180819 | − | 0.0313188i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.7882 | 1.40662 | 0.703311 | − | 0.710882i | \(-0.251704\pi\) | ||||
0.703311 | + | 0.710882i | \(0.251704\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.43905 | + | 5.95661i | −0.142922 | + | 0.247548i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0844 | −0.418372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.06914 | − | 13.9762i | 0.334190 | − | 0.578833i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.43359 | − | 2.48305i | 0.0592716 | − | 0.102661i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.3474 | + | 26.5825i | 0.633457 | + | 1.09718i | 0.986840 | + | 0.161700i | \(0.0516978\pi\) |
−0.353383 | + | 0.935479i | \(0.614969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.0871451 | − | 8.13837i | −0.00359075 | − | 0.335336i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.34198 | − | 2.32438i | −0.0552017 | − | 0.0956121i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.49727 | + | 6.05745i | −0.143616 | + | 0.248750i | −0.928856 | − | 0.370442i | \(-0.879206\pi\) |
0.785240 | + | 0.619192i | \(0.212540\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.09607 | + | 3.63051i | −0.0859306 | + | 0.148836i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.00893 | −0.0412927 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.26837 | − | 3.92894i | 0.0926833 | − | 0.160532i | −0.815956 | − | 0.578114i | \(-0.803789\pi\) |
0.908639 | + | 0.417582i | \(0.137122\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0790 | 0.655874 | 0.327937 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327937 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 17.8672 | + | 30.9469i | 0.727608 | + | 1.26025i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.16248 | − | 7.20964i | −0.169229 | − | 0.293113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.0702 | −1.38287 | −0.691434 | − | 0.722439i | \(-0.743021\pi\) | ||||
−0.691434 | + | 0.722439i | \(0.743021\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.10752 | 0.0854009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.54940 | + | 7.87979i | 0.184049 | + | 0.318782i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.7191 | + | 34.1544i | 0.796446 | + | 1.37949i | 0.921917 | + | 0.387388i | \(0.126623\pi\) |
−0.125471 | + | 0.992097i | \(0.540044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.694877 | 0.0280201 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.6257 | − | 33.9928i | 0.790102 | − | 1.36850i | −0.135801 | − | 0.990736i | \(-0.543361\pi\) |
0.925903 | − | 0.377761i | \(-0.123306\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.3644 | 0.979290 | 0.489645 | − | 0.871922i | \(-0.337126\pi\) | ||||
0.489645 | + | 0.871922i | \(0.337126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.927135 | + | 1.60584i | −0.0372046 | + | 0.0644403i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.172301 | + | 0.298433i | −0.00690308 | + | 0.0119565i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.23609 | + | 1.32313i | −0.0893008 | + | 0.0528408i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.09607 | + | 3.63051i | 0.0835759 | + | 0.144758i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6949 | − | 30.6484i | 0.704422 | − | 1.22009i | −0.262478 | − | 0.964938i | \(-0.584540\pi\) |
0.966900 | − | 0.255157i | \(-0.0821270\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.08442 | − | 5.34236i | 0.122595 | − | 0.212340i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.2766 | −0.645916 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.29804 | + | 5.71237i | −0.130673 | + | 0.226332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.17577 | −0.283869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8546 | − | 30.9251i | −0.705216 | − | 1.22147i | −0.966614 | − | 0.256238i | \(-0.917517\pi\) |
0.261398 | − | 0.965231i | \(-0.415816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.5549 | − | 18.2816i | −0.416243 | − | 0.720954i | 0.579315 | − | 0.815104i | \(-0.303320\pi\) |
−0.995558 | + | 0.0941496i | \(0.969987\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44340 | 0.0568340 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 43.7058 | 1.71825 | 0.859126 | − | 0.511764i | \(-0.171008\pi\) | ||||
0.859126 | + | 0.511764i | \(0.171008\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.44078 | − | 12.8878i | −0.292076 | − | 0.505891i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.216243 | − | 0.374544i | −0.00847524 | − | 0.0146795i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.1887 | −0.946576 | −0.473288 | − | 0.880908i | \(-0.656933\pi\) | ||||
−0.473288 | + | 0.880908i | \(0.656933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.31778 | + | 9.21066i | −0.207783 | + | 0.359890i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.15813 | 0.0451829 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.9956 | + | 29.4373i | −0.662056 | + | 1.14672i | 0.318018 | + | 0.948085i | \(0.396983\pi\) |
−0.980074 | + | 0.198630i | \(0.936351\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.27830 | + | 3.94613i | −0.0886155 | + | 0.153487i | −0.906926 | − | 0.421290i | \(-0.861578\pi\) |
0.818311 | + | 0.574776i | \(0.194911\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.20196 | + | 2.08186i | 0.0466804 | + | 0.0808528i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.38419 | + | 1.41076i | −0.0924548 | + | 0.0547070i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.94514 | + | 6.83318i | 0.152756 | + | 0.264582i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.57460 | − | 2.72729i | 0.0608775 | − | 0.105443i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.85725 | + | 3.21686i | −0.0716985 | + | 0.124185i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22.7487 | −0.876900 | −0.438450 | − | 0.898756i | \(-0.644472\pi\) | ||||
−0.438450 | + | 0.898756i | \(0.644472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.06914 | + | 1.85181i | −0.0411512 | + | 0.0712760i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.6949 | −0.603203 | −0.301602 | − | 0.953434i | \(-0.597521\pi\) | ||||
−0.301602 | + | 0.953434i | \(0.597521\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.34198 | + | 4.05643i | 0.0898769 | + | 0.155671i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.81331 | + | 6.60485i | 0.146126 | + | 0.253098i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.82770 | −0.337783 | −0.168891 | − | 0.985635i | \(-0.554019\pi\) | ||||
−0.168891 | + | 0.985635i | \(0.554019\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.49727 | −0.133624 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.07733 | + | 7.06214i | 0.155560 | + | 0.269438i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.93359 | − | 8.54523i | −0.187955 | − | 0.325547i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.0198 | −0.875716 | −0.437858 | − | 0.899044i | \(-0.644263\pi\) | ||||
−0.437858 | + | 0.899044i | \(0.644263\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.49018 | − | 2.58107i | 0.0566074 | − | 0.0980469i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.734355 | −0.0278557 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.28822 | − | 10.8915i | 0.238183 | − | 0.412546i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.50546 | + | 6.07163i | −0.132589 | + | 0.229650i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.95606 | + | 8.58414i | 0.187188 | + | 0.324219i | 0.944312 | − | 0.329053i | \(-0.106729\pi\) |
−0.757124 | + | 0.653271i | \(0.773396\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.0296625 | + | 2.77015i | 0.00111874 | + | 0.104478i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.65802 | − | 2.87178i | −0.0624447 | − | 0.108157i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.96325 | − | 5.13250i | 0.111445 | − | 0.193028i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.0521 | − | 31.2672i | 0.677962 | − | 1.17426i | −0.297632 | − | 0.954681i | \(-0.596197\pi\) |
0.975594 | − | 0.219584i | \(-0.0704700\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.7617 | −1.15365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.809587 | − | 1.40225i | 0.0303193 | − | 0.0525145i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63555 | 0.0611662 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.388651 | − | 0.673164i | −0.0145145 | − | 0.0251398i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.50546 | + | 16.4639i | 0.354494 | + | 0.614001i | 0.987031 | − | 0.160529i | \(-0.0513199\pi\) |
−0.632537 | + | 0.774530i | \(0.717987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.90666 | −0.257217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.91558 | −0.331574 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.54940 | + | 7.87979i | 0.168961 | + | 0.292648i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.44351 | + | 2.50024i | 0.0535369 | + | 0.0927286i | 0.891552 | − | 0.452919i | \(-0.149617\pi\) |
−0.838015 | + | 0.545647i | \(0.816284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.0899 | −0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0619 | − | 22.6240i | 0.483114 | − | 0.836777i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.9463 | 1.66013 | 0.830066 | − | 0.557666i | \(-0.188303\pi\) | ||||
0.830066 | + | 0.557666i | \(0.188303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.20196 | − | 2.08186i | 0.0443351 | − | 0.0767906i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.1921 | + | 17.6533i | −0.375433 | + | 0.650268i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.4956 | − | 44.1597i | −0.937872 | − | 1.62444i | −0.769430 | − | 0.638731i | \(-0.779460\pi\) |
−0.168442 | − | 0.985711i | \(-0.553874\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0170096 | + | 1.58850i | 0.000624862 | + | 0.0583550i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.43805 | − | 16.3472i | −0.346249 | − | 0.599720i | 0.639331 | − | 0.768931i | \(-0.279211\pi\) |
−0.985580 | + | 0.169211i | \(0.945878\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.06914 | − | 8.78001i | 0.185719 | − | 0.321675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.7470 | + | 39.3990i | −0.832270 | + | 1.44153i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.20108 | 0.263122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0127 | + | 22.5386i | −0.474838 | + | 0.822444i | −0.999585 | − | 0.0288143i | \(-0.990827\pi\) |
0.524746 | + | 0.851259i | \(0.324160\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.19540 | −0.0435629 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.40666 | + | 2.43640i | 0.0511934 | + | 0.0886697i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.95779 | + | 10.3192i | 0.216540 | + | 0.375058i | 0.953748 | − | 0.300608i | \(-0.0971896\pi\) |
−0.737208 | + | 0.675666i | \(0.763856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.516902 | −0.0187623 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.39500 | −0.0868186 | −0.0434093 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434093 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.20469 | − | 7.28274i | −0.152220 | − | 0.263653i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.45606 | + | 16.3784i | 0.341884 | + | 0.592161i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.09880 | −0.328539 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.66248 | + | 4.61156i | −0.0960117 | + | 0.166297i | −0.910030 | − | 0.414542i | \(-0.863942\pi\) |
0.814019 | + | 0.580839i | \(0.197275\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78276 | 0.100219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.2486 | − | 21.2153i | 0.440553 | − | 0.763060i | −0.557178 | − | 0.830393i | \(-0.688116\pi\) |
0.997731 | + | 0.0673334i | \(0.0214491\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.933589 | − | 1.61702i | 0.0335355 | − | 0.0580852i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0736051 | + | 0.127488i | 0.00264057 | + | 0.00457360i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.15256 | − | 4.23229i | 0.256267 | − | 0.151637i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.04667 | − | 3.54494i | −0.0732357 | − | 0.126848i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.72790 | − | 16.8492i | 0.347647 | − | 0.602142i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.480261 | − | 0.831836i | 0.0171412 | − | 0.0296895i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.5171 | −0.731356 | −0.365678 | − | 0.930741i | \(-0.619163\pi\) | ||||
−0.365678 | + | 0.930741i | \(0.619163\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 2.68396 | − | 4.64875i | 0.0955515 | − | 0.165500i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.50819 | 0.160293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.13555 | + | 1.96683i | 0.0403246 | + | 0.0698443i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.79804 | + | 3.11429i | 0.0637698 | + | 0.110453i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.0144 | −0.815211 | −0.407606 | − | 0.913158i | \(-0.633636\pi\) | ||||
−0.407606 | + | 0.913158i | \(0.633636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −60.0164 | −2.12323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.777303 | + | 1.34633i | 0.0274647 | + | 0.0475702i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.330321 | + | 0.572133i | 0.0116568 | + | 0.0201901i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.551136 | −0.0194250 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.45333 | + | 4.24929i | −0.0863612 | + | 0.149582i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −28.3195 | −0.995661 | −0.497830 | − | 0.867274i | \(-0.665870\pi\) | ||||
−0.497830 | + | 0.867274i | \(0.665870\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7766 | + | 34.2540i | −0.694449 | + | 1.20282i | 0.275917 | + | 0.961181i | \(0.411019\pi\) |
−0.970366 | + | 0.241640i | \(0.922315\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.703698 | − | 1.21884i | 0.0246798 | − | 0.0427466i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.56914 | + | 2.71783i | 0.0549646 | + | 0.0952015i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.8574 | − | 8.79134i | 0.519793 | − | 0.307570i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.911120 | − | 1.57811i | −0.0318371 | − | 0.0551435i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4013 | + | 26.6758i | −0.537509 | + | 0.930993i | 0.461528 | + | 0.887126i | \(0.347301\pi\) |
−0.999037 | + | 0.0438677i | \(0.986032\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.00000 | − | 13.8564i | 0.278862 | − | 0.483004i | −0.692240 | − | 0.721668i | \(-0.743376\pi\) |
0.971102 | + | 0.238664i | \(0.0767093\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.596074 | −0.0207526 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10.1427 | + | 17.5678i | −0.352698 | + | 0.610891i | −0.986721 | − | 0.162423i | \(-0.948069\pi\) |
0.634023 | + | 0.773314i | \(0.281402\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.0792 | 1.53093 | 0.765466 | − | 0.643476i | \(-0.222508\pi\) | ||||
0.765466 | + | 0.643476i | \(0.222508\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.42377 | − | 7.66220i | −0.153459 | − | 0.265799i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.7541 | − | 37.6792i | −0.753735 | − | 1.30551i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10.6356 | 0.368058 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.99255 | −0.138003 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.9534 | − | 46.6847i | −0.930536 | − | 1.61174i | −0.782407 | − | 0.622767i | \(-0.786008\pi\) |
−0.148129 | − | 0.988968i | \(-0.547325\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8941 | − | 46.5820i | −0.927383 | − | 1.60627i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.181229 | −0.00624187 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.00000 | + | 10.3923i | −0.206406 | + | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.29095 | −0.181799 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.76218 | + | 4.78423i | −0.0947976 | + | 0.164194i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.275568 | + | 0.477298i | −0.00944636 | + | 0.0163616i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5324 | − | 23.4388i | −0.463340 | − | 0.802529i | 0.535785 | − | 0.844355i | \(-0.320016\pi\) |
−0.999125 | + | 0.0418258i | \(0.986683\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.133817 | + | 12.4970i | 0.00457645 | + | 0.427389i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.67676 | + | 2.90424i | 0.0572772 | + | 0.0992070i | 0.893242 | − | 0.449576i | \(-0.148425\pi\) |
−0.835965 | + | 0.548783i | \(0.815091\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.8529 | − | 46.5106i | 0.916209 | − | 1.58692i | 0.111088 | − | 0.993811i | \(-0.464567\pi\) |
0.805121 | − | 0.593110i | \(-0.202100\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.220815 | − | 0.382463i | 0.00752536 | − | 0.0130343i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.1527 | −1.33277 | −0.666386 | − | 0.745607i | \(-0.732160\pi\) | ||||
−0.666386 | + | 0.745607i | \(0.732160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.18495 | − | 10.7127i | 0.210295 | − | 0.364241i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.66086 | −0.328100 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.77383 | − | 15.1967i | −0.297632 | − | 0.515514i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.23163 | + | 10.7935i | 0.211151 | + | 0.365724i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 21.1308 | 0.715170 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.635552 | −0.0214856 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.8260 | + | 25.6793i | 0.500637 | + | 0.867129i | 1.00000 | 0.000735993i | \(0.000234274\pi\) | |
−0.499362 | + | 0.866393i | \(0.666432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.44351 | − | 4.23229i | −0.0824176 | − | 0.142752i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.2820 | 1.45821 | 0.729104 | − | 0.684403i | \(-0.239937\pi\) | ||||
0.729104 | + | 0.684403i | \(0.239937\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −28.4830 | + | 49.3340i | −0.958529 | + | 1.66022i | −0.232451 | + | 0.972608i | \(0.574675\pi\) |
−0.726078 | + | 0.687613i | \(0.758659\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.31604 | 0.111468 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.1158 | + | 17.5211i | −0.339656 | + | 0.588301i | −0.984368 | − | 0.176124i | \(-0.943644\pi\) |
0.644712 | + | 0.764425i | \(0.276977\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.17230 | + | 8.95869i | −0.173473 | + | 0.300465i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.39684 | − | 11.0797i | −0.214302 | − | 0.371182i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −34.5576 | − | 19.4615i | −1.15643 | − | 0.651254i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.162485 | − | 0.281432i | −0.00543127 | − | 0.00940724i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.158021 | + | 0.273700i | −0.00527615 | + | 0.00913857i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −8.49454 | + | 14.7130i | −0.283309 | + | 0.490705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.0846 | 2.16828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.458679 | − | 0.794456i | 0.0152639 | − | 0.0264378i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.81331 | −0.292964 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.00000 | + | 8.66025i | 0.166022 | + | 0.287559i | 0.937018 | − | 0.349281i | \(-0.113574\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.3682 | − | 23.1544i | −0.443394 | − | 0.767981i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.0109 | −1.82259 | −0.911297 | − | 0.411751i | \(-0.864917\pi\) | ||||
−0.911297 | + | 0.411751i | \(0.864917\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.9516 | −0.858872 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.413850 | − | 0.716809i | −0.0136814 | − | 0.0236970i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.37972 | + | 5.85385i | 0.111608 | + | 0.193311i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 48.6159 | 1.60369 | 0.801846 | − | 0.597531i | \(-0.203852\pi\) | ||||
0.801846 | + | 0.597531i | \(0.203852\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.86880 | − | 10.1651i | 0.193384 | − | 0.334950i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.50273 | −0.0823783 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.317776 | + | 0.550404i | −0.0104484 | + | 0.0180972i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.5791 | + | 26.9837i | −0.511684 | + | 0.886262i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.66075 | − | 9.80471i | −0.185723 | − | 0.321682i | 0.758097 | − | 0.652142i | \(-0.226129\pi\) |
−0.943820 | + | 0.330460i | \(0.892796\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.307853 | − | 28.7500i | −0.0100895 | − | 0.942242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.25409 | + | 3.90421i | 0.0737957 | + | 0.127818i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.39411 | + | 9.34287i | −0.176406 | + | 0.305545i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.24864 | − | 9.09090i | 0.171465 | − | 0.296987i | −0.767467 | − | 0.641088i | \(-0.778483\pi\) |
0.938932 | + | 0.344102i | \(0.111816\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.03402 | −0.294814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.40939 | − | 2.44113i | 0.0459447 | − | 0.0795785i | −0.842139 | − | 0.539261i | \(-0.818704\pi\) |
0.888083 | + | 0.459683i | \(0.152037\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.65341 | 0.0538424 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.679494 | + | 1.17692i | 0.0221040 | + | 0.0382852i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.7568 | + | 39.4160i | 0.739497 | + | 1.28085i | 0.952722 | + | 0.303844i | \(0.0982701\pi\) |
−0.213224 | + | 0.977003i | \(0.568397\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.403926 | 0.0131120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.66433 | −0.0863967 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.3600 | + | 17.9440i | 0.335593 | + | 0.581264i | 0.983599 | − | 0.180372i | \(-0.0577301\pi\) |
−0.648006 | + | 0.761635i | \(0.724397\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.5961 | + | 21.8170i | 0.407599 | + | 0.705983i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.42356 | 0.175319 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.11135 | + | 1.92491i | −0.0358873 | + | 0.0621587i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5136 | −0.887537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 16.2432 | − | 28.1340i | 0.523429 | − | 0.906606i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.43632 | + | 16.3442i | −0.303766 | + | 0.526138i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.73436 | + | 11.6642i | 0.216562 | + | 0.375097i | 0.953755 | − | 0.300586i | \(-0.0971822\pi\) |
−0.737192 | + | 0.675683i | \(0.763849\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.13020 | − | 5.14177i | −0.293304 | − | 0.165177i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5252 | + | 40.7468i | 0.754960 | + | 1.30763i | 0.945394 | + | 0.325928i | \(0.105677\pi\) |
−0.190435 | + | 0.981700i | \(0.560990\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.233360 | + | 0.404192i | −0.00748119 | + | 0.0129578i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.182224 | + | 0.315621i | −0.00583584 | + | 0.0101080i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 43.0648 | 1.37776 | 0.688882 | − | 0.724873i | \(-0.258102\pi\) | ||||
0.688882 | + | 0.724873i | \(0.258102\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.443404 | + | 0.767999i | −0.0141713 | + | 0.0245454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9374 | −1.21125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.0396 | + | 46.8339i | 0.862429 | + | 1.49377i | 0.869578 | + | 0.493796i | \(0.164391\pi\) |
−0.00714884 | + | 0.999974i | \(0.502276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.68222 | − | 6.37780i | −0.117325 | − | 0.203214i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.10752 | −0.0670830 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.43448 | 0.109210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6356 | − | 35.7418i | −0.655510 | − | 1.13538i | −0.981766 | − | 0.190095i | \(-0.939120\pi\) |
0.326256 | − | 0.945282i | \(-0.394213\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.36608 | + | 5.83021i | 0.106819 | + | 0.185016i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.76837 | −0.0877634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.544937 | − | 0.943859i | 0.0172583 | − | 0.0298923i | −0.857267 | − | 0.514872i | \(-0.827840\pi\) |
0.874526 | + | 0.484979i | \(0.161173\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.35899 | 0.0429965 |
(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 | 380.2.i.b.121.2 | ✓ | 6 | |
3.2 | odd | 2 | 3420.2.t.v.1261.2 | 6 | |||
4.3 | odd | 2 | 1520.2.q.i.881.2 | 6 | |||
5.2 | odd | 4 | 1900.2.s.c.349.4 | 12 | |||
5.3 | odd | 4 | 1900.2.s.c.349.3 | 12 | |||
5.4 | even | 2 | 1900.2.i.c.501.2 | 6 | |||
19.7 | even | 3 | 7220.2.a.n.1.2 | 3 | |||
19.11 | even | 3 | inner | 380.2.i.b.201.2 | yes | 6 | |
19.12 | odd | 6 | 7220.2.a.o.1.2 | 3 | |||
57.11 | odd | 6 | 3420.2.t.v.3241.2 | 6 | |||
76.11 | odd | 6 | 1520.2.q.i.961.2 | 6 | |||
95.49 | even | 6 | 1900.2.i.c.201.2 | 6 | |||
95.68 | odd | 12 | 1900.2.s.c.49.4 | 12 | |||
95.87 | odd | 12 | 1900.2.s.c.49.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
380.2.i.b.201.2 | yes | 6 | 19.11 | even | 3 | inner | |
1520.2.q.i.881.2 | 6 | 4.3 | odd | 2 | |||
1520.2.q.i.961.2 | 6 | 76.11 | odd | 6 | |||
1900.2.i.c.201.2 | 6 | 95.49 | even | 6 | |||
1900.2.i.c.501.2 | 6 | 5.4 | even | 2 | |||
1900.2.s.c.49.3 | 12 | 95.87 | odd | 12 | |||
1900.2.s.c.49.4 | 12 | 95.68 | odd | 12 | |||
1900.2.s.c.349.3 | 12 | 5.3 | odd | 4 | |||
1900.2.s.c.349.4 | 12 | 5.2 | odd | 4 | |||
3420.2.t.v.1261.2 | 6 | 3.2 | odd | 2 | |||
3420.2.t.v.3241.2 | 6 | 57.11 | odd | 6 | |||
7220.2.a.n.1.2 | 3 | 19.7 | even | 3 | |||
7220.2.a.o.1.2 | 3 | 19.12 | odd | 6 |