Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(49,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.s (of order \(6\), degree \(2\), not 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: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(1.90412 - 1.09935i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.49 |
Dual form | 1900.2.s.c.349.4 |
$q$-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 \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.315621 | + | 0.182224i | 0.182224 | + | 0.105207i | 0.588337 | − | 0.808616i | \(-0.299783\pi\) |
−0.406113 | + | 0.913823i | \(0.633116\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.635552i | − | 0.240216i | −0.992761 | − | 0.120108i | \(-0.961676\pi\) | ||
0.992761 | − | 0.120108i | \(-0.0383241\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −0.866025 | + | 0.500000i | −0.240192 | + | 0.138675i | −0.615265 | − | 0.788320i | \(-0.710951\pi\) |
0.375073 | + | 0.926995i | \(0.377618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.71237 | − | 3.29804i | −1.38545 | − | 0.799891i | −0.392654 | − | 0.919686i | \(-0.628443\pi\) |
−0.992799 | + | 0.119795i | \(0.961776\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | 0.750998 | − | 0.433589i | 0.156594 | − | 0.0904095i | −0.419655 | − | 0.907684i | \(-0.637849\pi\) |
0.576249 | + | 0.817274i | \(0.304516\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.13828i | − | 0.411512i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.54940 | − | 7.87979i | −0.844803 | − | 1.46324i | −0.885792 | − | 0.464082i | \(-0.846384\pi\) |
0.0409898 | − | 0.999160i | \(-0.486949\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.86718 | −0.335355 | −0.167677 | − | 0.985842i | \(-0.553627\pi\) | ||||
−0.167677 | + | 0.985842i | \(0.553627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.516215 | + | 0.298037i | 0.0898615 | + | 0.0518816i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.635552i | − | 0.104484i | −0.998634 | − | 0.0522420i | \(-0.983363\pi\) | ||
0.998634 | − | 0.0522420i | \(-0.0166367\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.364448 | −0.0583584 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.953328 | + | 1.65121i | −0.148885 | + | 0.257876i | −0.930816 | − | 0.365489i | \(-0.880902\pi\) |
0.781931 | + | 0.623365i | \(0.214235\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.42991 | − | 1.98026i | −0.523057 | − | 0.301987i | 0.215128 | − | 0.976586i | \(-0.430983\pi\) |
−0.738184 | + | 0.674599i | \(0.764317\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.87979 | + | 4.54940i | −1.14939 | + | 0.663598i | −0.948738 | − | 0.316065i | \(-0.897638\pi\) |
−0.200649 | + | 0.979663i | \(0.564305\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.59607 | 0.942296 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.20196 | − | 2.08186i | −0.168309 | − | 0.291519i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.54523 | + | 4.93359i | −1.17378 | + | 0.677681i | −0.954567 | − | 0.297997i | \(-0.903681\pi\) |
−0.219210 | + | 0.975678i | \(0.570348\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.808981 | + | 1.36718i | −0.107152 | + | 0.181087i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.54940 | − | 7.87979i | 0.592282 | − | 1.02586i | −0.401643 | − | 0.915796i | \(-0.631561\pi\) |
0.993924 | − | 0.110065i | \(-0.0351060\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.13555 | − | 1.96683i | −0.145393 | − | 0.251827i | 0.784127 | − | 0.620601i | \(-0.213111\pi\) |
−0.929519 | + | 0.368773i | \(0.879778\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.57811 | + | 0.911120i | −0.198823 | + | 0.114790i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.7935 | + | 6.23163i | −1.31863 | + | 0.761314i | −0.983509 | − | 0.180859i | \(-0.942112\pi\) |
−0.335126 | + | 0.942173i | \(0.608779\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.316041 | 0.0380469 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.25136 | + | 2.16743i | −0.148510 | + | 0.257226i | −0.930677 | − | 0.365842i | \(-0.880781\pi\) |
0.782167 | + | 0.623069i | \(0.214114\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.349810 | + | 0.201963i | 0.0409422 | + | 0.0236380i | 0.520331 | − | 0.853964i | \(-0.325808\pi\) |
−0.479389 | + | 0.877602i | \(0.659142\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1.03948i | − | 0.118460i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.36445 | − | 9.29150i | 0.603548 | − | 1.04538i | −0.388732 | − | 0.921351i | \(-0.627087\pi\) |
0.992279 | − | 0.124024i | \(-0.0395800\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.91112 | + | 6.77426i | −0.434569 | + | 0.752695i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 15.8672i | − | 1.74165i | −0.491594 | − | 0.870825i | \(-0.663586\pi\) | ||
0.491594 | − | 0.870825i | \(-0.336414\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 3.31604i | − | 0.355517i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.271104 | + | 0.469566i | 0.0287370 | + | 0.0497739i | 0.880036 | − | 0.474907i | \(-0.157518\pi\) |
−0.851299 | + | 0.524680i | \(0.824185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.317776 | + | 0.550404i | 0.0333120 | + | 0.0576980i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.589321 | − | 0.340245i | −0.0611097 | − | 0.0352817i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.38253 | − | 3.68495i | −0.648047 | − | 0.374150i | 0.139660 | − | 0.990199i | \(-0.455399\pi\) |
−0.787708 | + | 0.616049i | \(0.788732\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.34471 | − | 4.06116i | −0.235652 | − | 0.408161i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.66248 | + | 8.07566i | 0.463935 | + | 0.803558i | 0.999153 | − | 0.0411556i | \(-0.0131039\pi\) |
−0.535218 | + | 0.844714i | \(0.679771\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10.8672i | − | 1.07077i | −0.844607 | − | 0.535387i | \(-0.820166\pi\) | ||
0.844607 | − | 0.535387i | \(-0.179834\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.3304i | − | 1.09535i | −0.836690 | − | 0.547677i | \(-0.815512\pi\) | ||
0.836690 | − | 0.547677i | \(-0.184488\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.61581 | − | 11.4589i | 0.633680 | − | 1.09757i | −0.353113 | − | 0.935581i | \(-0.614877\pi\) |
0.986793 | − | 0.161985i | \(-0.0517897\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.115813 | − | 0.200594i | 0.0109925 | − | 0.0190395i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.09334i | 0.667286i | 0.942700 | + | 0.333643i | \(0.108278\pi\) | ||||
−0.942700 | + | 0.333643i | \(0.891722\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.48305 | + | 1.43359i | 0.229558 | + | 0.132535i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.09607 | + | 3.63051i | −0.192147 | + | 0.332808i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.32497 | −0.756815 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.601781 | + | 0.347439i | −0.0542608 | + | 0.0313275i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.0959 | + | 8.13828i | −1.25081 | + | 0.722156i | −0.971270 | − | 0.237978i | \(-0.923515\pi\) |
−0.279540 | + | 0.960134i | \(0.590182\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.721702 | − | 1.25002i | −0.0635423 | − | 0.110059i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.31778 | − | 9.21066i | 0.464616 | − | 0.804739i | −0.534568 | − | 0.845126i | \(-0.679526\pi\) |
0.999184 | + | 0.0403866i | \(0.0128590\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.77015 | + | 0.0296625i | 0.240202 | + | 0.00257207i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.02873 | + | 1.74864i | −0.258761 | + | 0.149396i | −0.623769 | − | 0.781608i | \(-0.714400\pi\) |
0.365008 | + | 0.931004i | \(0.381066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.367178 | + | 0.635970i | 0.0311436 | + | 0.0539423i | 0.881177 | − | 0.472786i | \(-0.156752\pi\) |
−0.850034 | + | 0.526729i | \(0.823418\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.31604 | −0.279261 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.41643 | + | 0.817776i | −0.118448 | + | 0.0683859i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.08186 | + | 1.20196i | 0.171709 | + | 0.0991362i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.06914 | − | 8.78001i | 0.415280 | − | 0.719286i | −0.580178 | − | 0.814490i | \(-0.697017\pi\) |
0.995458 | + | 0.0952036i | \(0.0303502\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.81331 | 0.228944 | 0.114472 | − | 0.993426i | \(-0.463482\pi\) | ||||
0.114472 | + | 0.993426i | \(0.463482\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.9121i | 1.52895i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.831836 | + | 0.480261i | 0.0663878 | + | 0.0383290i | 0.532826 | − | 0.846225i | \(-0.321130\pi\) |
−0.466439 | + | 0.884554i | \(0.654463\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.59607 | −0.285187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.275568 | − | 0.477298i | −0.0217178 | − | 0.0376164i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.13828i | 0.245809i | 0.992418 | + | 0.122905i | \(0.0392209\pi\) | ||||
−0.992418 | + | 0.122905i | \(0.960779\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.21066 | − | 5.31778i | 0.712742 | − | 0.411502i | −0.0993334 | − | 0.995054i | \(-0.531671\pi\) |
0.812076 | + | 0.583552i | \(0.198338\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | −10.7127 | − | 6.18495i | −0.814468 | − | 0.470233i | 0.0340371 | − | 0.999421i | \(-0.489164\pi\) |
−0.848505 | + | 0.529187i | \(0.822497\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.87178 | − | 1.65802i | 0.215856 | − | 0.124624i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.324970 | 0.0242894 | 0.0121447 | − | 0.999926i | \(-0.496134\pi\) | ||||
0.0121447 | + | 0.999926i | \(0.496134\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.40666 | − | 7.63255i | −0.327544 | − | 0.567323i | 0.654480 | − | 0.756079i | \(-0.272888\pi\) |
−0.982024 | + | 0.188756i | \(0.939554\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 0.827699i | − | 0.0611853i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.34287 | − | 5.39411i | −0.683219 | − | 0.394456i | ||||
\(188\) | 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 | ||||||||
\(193\) | 16.3442 | + | 9.43632i | 1.17648 | + | 0.679241i | 0.955198 | − | 0.295969i | \(-0.0956424\pi\) |
0.221282 | + | 0.975210i | \(0.428976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.36445i | 0.524695i | 0.964973 | + | 0.262348i | \(0.0844967\pi\) | ||||
−0.964973 | + | 0.262348i | \(0.915503\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.38419 | + | 2.39748i | 0.0981224 | + | 0.169953i | 0.910907 | − | 0.412611i | \(-0.135383\pi\) |
−0.812785 | + | 0.582564i | \(0.802050\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.54221 | −0.320383 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.00802 | + | 2.89138i | −0.351494 | + | 0.202935i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.15324 | − | 1.24318i | −0.149661 | − | 0.0864067i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0763346 | + | 7.12880i | −0.00528018 | + | 0.493109i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.46325 | + | 14.6588i | −0.582634 | + | 1.00915i | 0.412532 | + | 0.910943i | \(0.364645\pi\) |
−0.995166 | + | 0.0982088i | \(0.968689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.789915 | + | 0.456057i | −0.0541241 | + | 0.0312485i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.18669i | 0.0805577i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0736051 | + | 0.127488i | 0.00497377 | + | 0.00861482i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.59607 | 0.443700 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.48334 | − | 4.32051i | −0.501121 | − | 0.289322i | 0.228055 | − | 0.973648i | \(-0.426763\pi\) |
−0.729176 | + | 0.684326i | \(0.760097\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 20.9265i | − | 1.38894i | −0.719521 | − | 0.694470i | \(-0.755639\pi\) | ||
0.719521 | − | 0.694470i | \(-0.244361\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.3754 | −1.47861 | −0.739303 | − | 0.673373i | \(-0.764845\pi\) | ||||
−0.739303 | + | 0.673373i | \(0.764845\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.189418 | − | 0.328081i | 0.0124628 | − | 0.0215862i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6598 | + | 9.61854i | 1.09142 | + | 0.630132i | 0.933954 | − | 0.357393i | \(-0.116334\pi\) |
0.157466 | + | 0.987524i | \(0.449668\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.38627 | − | 1.95506i | 0.219962 | − | 0.126995i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.13282 | 0.137961 | 0.0689804 | − | 0.997618i | \(-0.478025\pi\) | ||||
0.0689804 | + | 0.997618i | \(0.478025\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.2316 | − | 21.1858i | −0.787908 | − | 1.36470i | −0.927246 | − | 0.374452i | \(-0.877831\pi\) |
0.139338 | − | 0.990245i | \(-0.455503\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.02428 | + | 4.63282i | −0.514758 | + | 0.297196i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.13891 | − | 3.79804i | −0.136095 | − | 0.241663i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.89138 | − | 5.00802i | 0.183234 | − | 0.317370i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.64002 | − | 2.84059i | −0.103517 | − | 0.179297i | 0.809614 | − | 0.586962i | \(-0.199676\pi\) |
−0.913131 | + | 0.407666i | \(0.866343\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.22830 | − | 0.709157i | 0.0772223 | − | 0.0445843i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.61258 | − | 3.81778i | 0.412482 | − | 0.238146i | −0.279374 | − | 0.960182i | \(-0.590127\pi\) |
0.691855 | + | 0.722036i | \(0.256794\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.403926 | −0.0250988 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.0439 | + | 22.5928i | −0.807400 | + | 1.39846i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.7556 | − | 7.36445i | −0.786544 | − | 0.454111i | 0.0522005 | − | 0.998637i | \(-0.483376\pi\) |
−0.838744 | + | 0.544525i | \(0.816710\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.197607i | 0.0120933i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −6.73163 | + | 11.6595i | −0.410434 | + | 0.710893i | −0.994937 | − | 0.100498i | \(-0.967956\pi\) |
0.584503 | + | 0.811392i | \(0.301290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.93086 | + | 3.34435i | −0.117291 | + | 0.203155i | −0.918693 | − | 0.394971i | \(-0.870754\pi\) |
0.801402 | + | 0.598126i | \(0.204088\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.231626i | 0.0140186i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.2766i | 1.45864i | 0.684174 | + | 0.729319i | \(0.260163\pi\) | ||||
−0.684174 | + | 0.729319i | \(0.739837\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.67676 | + | 4.63629i | 0.160254 | + | 0.277568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −0.248635 | − | 0.430649i | −0.0148323 | − | 0.0256904i | 0.858514 | − | 0.512790i | \(-0.171388\pi\) |
−0.873346 | + | 0.487100i | \(0.838055\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.1273 | + | 7.57906i | 0.780338 | + | 0.450529i | 0.836550 | − | 0.547890i | \(-0.184569\pi\) |
−0.0562118 | + | 0.998419i | \(0.517902\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.04943 | + | 0.605889i | 0.0619460 | + | 0.0357645i | ||||
\(288\) | 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 | ||||||||
\(293\) | − | 13.4094i | − | 0.783385i | −0.920096 | − | 0.391692i | \(-0.871890\pi\) | ||
0.920096 | − | 0.391692i | \(-0.128110\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 3.49727i | − | 0.202932i | ||||||
\(298\) | 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 | ||||||||
\(303\) | 3.39847i | 0.195237i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.8917 | + | 16.1033i | 1.59186 | + | 0.919062i | 0.992988 | + | 0.118219i | \(0.0377186\pi\) |
0.598875 | + | 0.800843i | \(0.295615\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 21.4672 | − | 12.3941i | 1.21340 | − | 0.700557i | 0.249901 | − | 0.968271i | \(-0.419602\pi\) |
0.963498 | + | 0.267715i | \(0.0862685\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.33115 | + | 3.65529i | −0.355593 | + | 0.205302i | −0.667146 | − | 0.744927i | \(-0.732484\pi\) |
0.311553 | + | 0.950229i | \(0.399151\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 14.6416 | − | 24.7443i | 0.814680 | − | 1.37681i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.17618 | − | 2.41112i | 0.230943 | − | 0.133335i | ||||
\(328\) | 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 | ||||||||
\(333\) | −1.57811 | + | 0.911120i | −0.0864797 | + | 0.0499291i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.3819 | + | 15.2316i | 1.43712 | + | 0.829720i | 0.997648 | − | 0.0685388i | \(-0.0218337\pi\) |
0.439468 | + | 0.898258i | \(0.355167\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.29258 | + | 2.23881i | −0.0702032 | + | 0.121595i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.05387 | −0.165376 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.64101i | − | 0.466571i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.1970 | + | 11.6608i | 1.08423 | + | 0.625982i | 0.932035 | − | 0.362368i | \(-0.118032\pi\) |
0.152197 | + | 0.988350i | \(0.451365\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.6894 | 0.946893 | 0.473446 | − | 0.880823i | \(-0.343010\pi\) | ||||
0.473446 | + | 0.880823i | \(0.343010\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.06914 | + | 1.85181i | 0.0570665 | + | 0.0988421i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7.13828i | − | 0.379932i | −0.981791 | − | 0.189966i | \(-0.939162\pi\) | ||
0.981791 | − | 0.189966i | \(-0.0608378\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.32313 | + | 0.763910i | −0.0700275 | + | 0.0404304i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.0719 | + | 26.1052i | −0.795463 | + | 1.37778i | 0.127082 | + | 0.991892i | \(0.459439\pi\) |
−0.922545 | + | 0.385890i | \(0.873894\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9956 | − | 0.406855i | −0.999771 | − | 0.0214134i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.62754 | − | 1.51701i | −0.137910 | − | 0.0796224i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 26.1566 | − | 15.1015i | 1.36536 | − | 0.788294i | 0.375033 | − | 0.927012i | \(-0.377631\pi\) |
0.990332 | + | 0.138718i | \(0.0442982\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.46672 | 0.284586 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.13555 | + | 5.43094i | 0.162790 | + | 0.281960i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.0449i | 1.50389i | 0.659226 | + | 0.751945i | \(0.270884\pi\) | ||||
−0.659226 | + | 0.751945i | \(0.729116\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.87979 | + | 4.54940i | 0.405830 | + | 0.234306i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.76837 | −0.142202 | −0.0711009 | − | 0.997469i | \(-0.522651\pi\) | ||||
−0.0711009 | + | 0.997469i | \(0.522651\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.93196 | −0.303904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.0453 | − | 13.3052i | −1.17756 | − | 0.679866i | −0.222112 | − | 0.975021i | \(-0.571295\pi\) |
−0.955449 | + | 0.295156i | \(0.904629\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.3555i | 0.577233i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.77830 | − | 4.81215i | −0.140865 | − | 0.243986i | 0.786957 | − | 0.617007i | \(-0.211655\pi\) |
−0.927823 | + | 0.373021i | \(0.878322\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.71997 | −0.289271 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.35681 | − | 1.93805i | 0.169328 | − | 0.0977618i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.35083 | + | 1.35725i | 0.117985 | + | 0.0681186i | 0.557831 | − | 0.829955i | \(-0.311634\pi\) |
−0.439846 | + | 0.898073i | \(0.644967\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.868912 | + | 0.514150i | 0.0435000 | + | 0.0257397i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.94078 | − | 15.4859i | 0.446481 | − | 0.773328i | −0.551673 | − | 0.834061i | \(-0.686010\pi\) |
0.998154 | + | 0.0607322i | \(0.0193436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.61702 | − | 0.933589i | 0.0805497 | − | 0.0465054i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.03948i | − | 0.0515250i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.1625 | + | 22.7981i | 0.650843 | + | 1.12729i | 0.982919 | + | 0.184040i | \(0.0589177\pi\) |
−0.332076 | + | 0.943253i | \(0.607749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.27457 | −0.0628701 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.00802 | − | 2.89138i | −0.246428 | − | 0.142276i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.267634i | 0.0131061i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.3250 | −0.748674 | −0.374337 | − | 0.927293i | \(-0.622130\pi\) | ||||
−0.374337 | + | 0.927293i | \(0.622130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.9166 | + | 18.9081i | −0.532042 | + | 0.921523i | 0.467259 | + | 0.884121i | \(0.345242\pi\) |
−0.999300 | + | 0.0374023i | \(0.988092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.5928 | + | 13.0439i | 1.09850 | + | 0.634218i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.25002 | + | 0.721702i | −0.0604929 | + | 0.0349256i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.596074 | −0.0287787 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6427 | − | 20.1658i | −0.560811 | − | 0.971354i | −0.997426 | − | 0.0717050i | \(-0.977156\pi\) |
0.436615 | − | 0.899649i | \(-0.356177\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.37854 | + | 1.95060i | −0.162362 | + | 0.0937398i | −0.578979 | − | 0.815342i | \(-0.696549\pi\) |
0.416617 | + | 0.909082i | \(0.363216\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.85481 | + | 3.29357i | 0.0887276 | + | 0.157553i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.73882 | + | 16.8681i | −0.464808 | + | 0.805072i | −0.999193 | − | 0.0401697i | \(-0.987210\pi\) |
0.534384 | + | 0.845242i | \(0.320543\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.45606 | − | 16.3784i | −0.450288 | − | 0.779922i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.65121 | − | 0.953328i | 0.0784515 | − | 0.0452940i | −0.460261 | − | 0.887784i | \(-0.652244\pi\) |
0.538713 | + | 0.842490i | \(0.318911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.19986 | − | 1.84744i | 0.151348 | − | 0.0873808i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.05933 | 0.380343 | 0.190172 | − | 0.981751i | \(-0.439096\pi\) | ||||
0.190172 | + | 0.981751i | \(0.439096\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.55922 | + | 2.70064i | −0.0734207 | + | 0.127168i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.887941 | + | 0.512653i | 0.0417191 | + | 0.0240865i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 11.3250i | − | 0.529760i | −0.964281 | − | 0.264880i | \(-0.914668\pi\) | ||
0.964281 | − | 0.264880i | \(-0.0853323\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.05213 | + | 12.2146i | −0.329165 | + | 0.570131i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0521 | + | 17.4108i | −0.468174 | + | 0.810902i | −0.999338 | − | 0.0363671i | \(-0.988421\pi\) |
0.531164 | + | 0.847269i | \(0.321755\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.33043i | 0.0618303i | 0.999522 | + | 0.0309151i | \(0.00984216\pi\) | ||||
−0.999522 | + | 0.0309151i | \(0.990158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 10.0844i | − | 0.466651i | −0.972399 | − | 0.233326i | \(-0.925039\pi\) | ||
0.972399 | − | 0.233326i | \(-0.0749608\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | −5.60980 | − | 3.23882i | −0.257939 | − | 0.148921i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.5007 | + | 14.1455i | 1.12181 | + | 0.647677i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.44078 | + | 7.69166i | 0.202905 | + | 0.351441i | 0.949463 | − | 0.313879i | \(-0.101629\pi\) |
−0.746559 | + | 0.665320i | \(0.768295\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.317776 | + | 0.550404i | 0.0144893 | + | 0.0250963i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 0.200861i | − | 0.00913947i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.32497i | − | 0.241297i | −0.992695 | − | 0.120649i | \(-0.961503\pi\) | ||
0.992695 | − | 0.120649i | \(-0.0384975\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.571870 | + | 0.990508i | −0.0258609 | + | 0.0447923i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.70469 | − | 16.8090i | 0.437967 | − | 0.758580i | −0.559566 | − | 0.828786i | \(-0.689032\pi\) |
0.997533 | + | 0.0702054i | \(0.0223655\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 60.0164i | 2.70300i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.37751 | + | 0.795307i | 0.0617899 | + | 0.0356744i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.79357 | − | 10.0348i | 0.259356 | − | 0.449218i | −0.706714 | − | 0.707500i | \(-0.749823\pi\) |
0.966070 | + | 0.258282i | \(0.0831564\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.87611 | 0.173172 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.4012 | − | 17.5521i | 1.35552 | − | 0.782611i | 0.366505 | − | 0.930416i | \(-0.380554\pi\) |
0.989017 | + | 0.147805i | \(0.0472208\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.78746 | + | 2.18669i | −0.168207 | + | 0.0971142i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −7.93359 | − | 13.7414i | −0.351650 | − | 0.609076i | 0.634889 | − | 0.772604i | \(-0.281046\pi\) |
−0.986539 | + | 0.163528i | \(0.947713\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.128358 | − | 0.222323i | 0.00567823 | − | 0.00983498i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.32002 | + | 0.0997981i | 0.411489 | + | 0.00440619i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.8878 | + | 7.44078i | −0.566805 | + | 0.327245i | ||||
\(518\) | 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 | ||||||||
\(523\) | −26.8687 | + | 15.5127i | −1.17489 | + | 0.678321i | −0.954826 | − | 0.297165i | \(-0.903959\pi\) |
−0.220060 | + | 0.975486i | \(0.570625\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.6660 | + | 6.15802i | 0.464618 | + | 0.268248i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.1240 | + | 19.2673i | −0.483652 | + | 0.837710i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −26.0879 | −1.13212 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 1.90666i | − | 0.0825864i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.102567 | + | 0.0592173i | 0.00442611 | + | 0.00255542i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.7882 | 0.464682 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.79357 | + | 6.57066i | 0.163098 | + | 0.282495i | 0.935978 | − | 0.352058i | \(-0.114518\pi\) |
−0.772880 | + | 0.634552i | \(0.781185\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 3.21199i | − | 0.137840i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.6587 | − | 15.3914i | 1.13984 | − | 0.658088i | 0.193450 | − | 0.981110i | \(-0.438032\pi\) |
0.946391 | + | 0.323022i | \(0.104699\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | −5.90523 | − | 3.40939i | −0.251116 | − | 0.144982i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.9106 | + | 15.5369i | −1.14024 | + | 0.658318i | −0.946490 | − | 0.322733i | \(-0.895398\pi\) |
−0.193750 | + | 0.981051i | \(0.562065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.96052 | 0.167512 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.96587 | − | 3.40499i | −0.0829992 | − | 0.143759i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 23.2766i | − | 0.980990i | −0.871444 | − | 0.490495i | \(-0.836816\pi\) | ||
0.871444 | − | 0.490495i | \(-0.163184\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.30539 | + | 2.48572i | 0.180810 | + | 0.104390i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −24.1976 | −1.01442 | −0.507208 | − | 0.861824i | \(-0.669322\pi\) | ||||
−0.507208 | + | 0.861824i | \(0.669322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.8475 | 1.24908 | 0.624540 | − | 0.780992i | \(-0.285286\pi\) | ||||
0.624540 | + | 0.780992i | \(0.285286\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.95118 | + | 4.59061i | 0.332165 | + | 0.191776i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 33.7882i | − | 1.40662i | −0.710882 | − | 0.703311i | \(-0.751704\pi\) | ||
0.710882 | − | 0.703311i | \(-0.248296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.43905 | + | 5.95661i | 0.142922 | + | 0.247548i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.0844 | −0.418372 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.9762 | + | 8.06914i | −0.578833 | + | 0.334190i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.5825 | − | 15.3474i | −1.09718 | − | 0.633457i | −0.161700 | − | 0.986840i | \(-0.551698\pi\) |
−0.935479 | + | 0.353383i | \(0.885031\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 6.05745 | − | 3.49727i | 0.248750 | − | 0.143616i | −0.370442 | − | 0.928856i | \(-0.620794\pi\) |
0.619192 | + | 0.785240i | \(0.287460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.00893i | 0.0412927i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.26837 | − | 3.92894i | −0.0926833 | − | 0.160532i | 0.815956 | − | 0.578114i | \(-0.196211\pi\) |
−0.908639 | + | 0.417582i | \(0.862878\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0790 | 0.655874 | 0.327937 | − | 0.944700i | \(-0.393647\pi\) | ||||
0.327937 | + | 0.944700i | \(0.393647\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.9469 | + | 17.8672i | 1.26025 | + | 0.727608i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.0702i | 1.38287i | 0.722439 | + | 0.691434i | \(0.243021\pi\) | ||||
−0.722439 | + | 0.691434i | \(0.756979\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.10752 | −0.0854009 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.54940 | − | 7.87979i | 0.184049 | − | 0.318782i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.1544 | + | 19.7191i | 1.37949 | + | 0.796446i | 0.992097 | − | 0.125471i | \(-0.0400441\pi\) |
0.387388 | + | 0.921917i | \(0.373377\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.9928 | − | 19.6257i | 1.36850 | − | 0.790102i | 0.377761 | − | 0.925903i | \(-0.376694\pi\) |
0.990736 | + | 0.135801i | \(0.0433607\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.3644 | −0.979290 | −0.489645 | − | 0.871922i | \(-0.662874\pi\) | ||||
−0.489645 | + | 0.871922i | \(0.662874\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.927135 | − | 1.60584i | −0.0372046 | − | 0.0644403i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.298433 | − | 0.172301i | 0.0119565 | − | 0.00690308i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.32313 | + | 2.23609i | −0.0528408 | + | 0.0893008i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.09607 | + | 3.63051i | −0.0835759 | + | 0.144758i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.6949 | + | 30.6484i | 0.704422 | + | 1.22009i | 0.966900 | + | 0.255157i | \(0.0821270\pi\) |
−0.262478 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.34236 | + | 3.08442i | −0.212340 | + | 0.122595i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.71237 | + | 3.29804i | −0.226332 | + | 0.130673i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.17577 | 0.283869 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8546 | + | 30.9251i | −0.705216 | + | 1.22147i | 0.261398 | + | 0.965231i | \(0.415816\pi\) |
−0.966614 | + | 0.256238i | \(0.917517\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.2816 | − | 10.5549i | −0.720954 | − | 0.416243i | 0.0941496 | − | 0.995558i | \(-0.469987\pi\) |
−0.815104 | + | 0.579315i | \(0.803320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 43.7058i | − | 1.71825i | −0.511764 | − | 0.859126i | \(-0.671008\pi\) | ||
0.511764 | − | 0.859126i | \(-0.328992\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | − | 24.1887i | − | 0.946576i | −0.880908 | − | 0.473288i | \(-0.843067\pi\) | ||
0.880908 | − | 0.473288i | \(-0.156933\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1.15813i | − | 0.0451829i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.9956 | + | 29.4373i | 0.662056 | + | 1.14672i | 0.980074 | + | 0.198630i | \(0.0636494\pi\) |
−0.318018 | + | 0.948085i | \(0.603017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.27830 | − | 3.94613i | −0.0886155 | − | 0.153487i | 0.818311 | − | 0.574776i | \(-0.194911\pi\) |
−0.906926 | + | 0.421290i | \(0.861578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.08186 | + | 1.20196i | 0.0808528 | + | 0.0466804i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.83318 | − | 3.94514i | −0.264582 | − | 0.152756i | ||||
\(668\) | 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 | ||||||||
\(673\) | − | 22.7487i | − | 0.876900i | −0.898756 | − | 0.438450i | \(-0.855528\pi\) | ||
0.898756 | − | 0.438450i | \(-0.144472\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.6949i | 0.603203i | 0.953434 | + | 0.301602i | \(0.0975212\pi\) | ||||
−0.953434 | + | 0.301602i | \(0.902479\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | − | 8.82770i | − | 0.337783i | −0.985635 | − | 0.168891i | \(-0.945981\pi\) | ||
0.985635 | − | 0.168891i | \(-0.0540187\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.06214 | − | 4.07733i | −0.269438 | − | 0.155560i | ||||
\(688\) | 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 | ||||||||
\(693\) | −2.58107 | + | 1.49018i | −0.0980469 | + | 0.0566074i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8915 | − | 6.28822i | 0.412546 | − | 0.238183i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.50546 | + | 6.07163i | 0.132589 | + | 0.229650i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.95606 | − | 8.58414i | 0.187188 | − | 0.324219i | −0.757124 | − | 0.653271i | \(-0.773396\pi\) |
0.944312 | + | 0.329053i | \(0.106729\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.77015 | + | 0.0296625i | 0.104478 | + | 0.00111874i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.13250 | − | 2.96325i | 0.193028 | − | 0.111445i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.0521 | − | 31.2672i | −0.677962 | − | 1.17426i | −0.975594 | − | 0.219584i | \(-0.929530\pi\) |
0.297632 | − | 0.954681i | \(-0.403803\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30.7617 | −1.15365 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.40225 | + | 0.809587i | −0.0525145 | + | 0.0303193i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.673164 | + | 0.388651i | 0.0251398 | + | 0.0145145i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.50546 | + | 16.4639i | −0.354494 | + | 0.614001i | −0.987031 | − | 0.160529i | \(-0.948680\pi\) |
0.632537 | + | 0.774530i | \(0.282013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.90666 | −0.257217 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8.91558i | − | 0.331574i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.50024 | − | 1.44351i | −0.0927286 | − | 0.0535369i | 0.452919 | − | 0.891552i | \(-0.350383\pi\) |
−0.545647 | + | 0.838015i | \(0.683716\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0899 | 0.744069 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.0619 | + | 22.6240i | 0.483114 | + | 0.836777i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.9463i | 1.66013i | 0.557666 | + | 0.830066i | \(0.311697\pi\) | ||||
−0.557666 | + | 0.830066i | \(0.688303\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −17.6533 | + | 10.1921i | −0.650268 | + | 0.375433i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.4956 | − | 44.1597i | 0.937872 | − | 1.62444i | 0.168442 | − | 0.985711i | \(-0.446126\pi\) |
0.769430 | − | 0.638731i | \(-0.220540\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.0170096 | − | 1.58850i | 0.000624862 | − | 0.0583550i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.3472 | − | 9.43805i | −0.599720 | − | 0.346249i | 0.169211 | − | 0.985580i | \(-0.445878\pi\) |
−0.768931 | + | 0.639331i | \(0.779211\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39.3990 | + | 22.7470i | −1.44153 | + | 0.832270i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7.20108 | −0.263122 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0127 | − | 22.5386i | −0.474838 | − | 0.822444i | 0.524746 | − | 0.851259i | \(-0.324160\pi\) |
−0.999585 | + | 0.0288143i | \(0.990827\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 1.19540i | − | 0.0435629i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.3192 | − | 5.95779i | −0.375058 | − | 0.216540i | 0.300608 | − | 0.953748i | \(-0.402810\pi\) |
−0.675666 | + | 0.737208i | \(0.736144\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | −7.28274 | − | 4.20469i | −0.263653 | − | 0.152220i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.09880i | 0.328539i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.66248 | + | 4.61156i | 0.0960117 | + | 0.166297i | 0.910030 | − | 0.414542i | \(-0.136058\pi\) |
−0.814019 | + | 0.580839i | \(0.802725\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.78276 | 0.100219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2153 | + | 12.2486i | −0.763060 | + | 0.440553i | −0.830393 | − | 0.557178i | \(-0.811884\pi\) |
0.0673334 | + | 0.997731i | \(0.478551\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −0.127488 | − | 0.0736051i | −0.00457360 | − | 0.00264057i | ||||
\(778\) | 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 | ||||||||
\(783\) | −16.8492 | + | 9.72790i | −0.602142 | + | 0.347647i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.5171i | 0.731356i | 0.930741 | + | 0.365678i | \(0.119163\pi\) | ||||
−0.930741 | + | 0.365678i | \(0.880837\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.68396 | − | 4.64875i | −0.0955515 | − | 0.165500i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.50819 | 0.160293 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.96683 | + | 1.13555i | 0.0698443 | + | 0.0403246i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 23.0144i | 0.815211i | 0.913158 | + | 0.407606i | \(0.133636\pi\) | ||||
−0.913158 | + | 0.407606i | \(0.866364\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 60.0164 | 2.12323 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.777303 | − | 1.34633i | 0.0274647 | − | 0.0475702i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.572133 | + | 0.330321i | 0.0201901 | + | 0.0116568i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.24929 | + | 2.45333i | −0.149582 | + | 0.0863612i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.3195 | 0.995661 | 0.497830 | − | 0.867274i | \(-0.334130\pi\) | ||||
0.497830 | + | 0.867274i | \(0.334130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −19.7766 | − | 34.2540i | −0.694449 | − | 1.20282i | −0.970366 | − | 0.241640i | \(-0.922315\pi\) |
0.275917 | − | 0.961181i | \(-0.411019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.21884 | + | 0.703698i | −0.0427466 | + | 0.0246798i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.79134 | − | 14.8574i | 0.307570 | − | 0.519793i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.911120 | − | 1.57811i | 0.0318371 | − | 0.0551435i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.4013 | − | 26.6758i | −0.537509 | − | 0.930993i | −0.999037 | − | 0.0438677i | \(-0.986032\pi\) |
0.461528 | − | 0.887126i | \(-0.347301\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.8564 | + | 8.00000i | −0.483004 | + | 0.278862i | −0.721668 | − | 0.692240i | \(-0.756624\pi\) |
0.238664 | + | 0.971102i | \(0.423291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.5678 | + | 10.1427i | −0.610891 | + | 0.352698i | −0.773314 | − | 0.634023i | \(-0.781402\pi\) |
0.162423 | + | 0.986721i | \(0.448069\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.0792 | −1.53093 | −0.765466 | − | 0.643476i | \(-0.777492\pi\) | ||||
−0.765466 | + | 0.643476i | \(0.777492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.42377 | + | 7.66220i | −0.153459 | + | 0.265799i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −37.6792 | − | 21.7541i | −1.30551 | − | 0.753735i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.99255i | 0.138003i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 26.9534 | − | 46.6847i | 0.930536 | − | 1.61174i | 0.148129 | − | 0.988968i | \(-0.452675\pi\) |
0.782407 | − | 0.622767i | \(-0.213992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8941 | + | 46.5820i | −0.927383 | + | 1.60627i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.181229i | − | 0.00624187i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.29095i | 0.181799i | ||||||||
\(848\) | 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 | ||||||||
\(853\) | −23.4388 | − | 13.5324i | −0.802529 | − | 0.463340i | 0.0418258 | − | 0.999125i | \(-0.486683\pi\) |
−0.844355 | + | 0.535785i | \(0.820016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.90424 | − | 1.67676i | −0.0992070 | − | 0.0572772i | 0.449576 | − | 0.893242i | \(-0.351575\pi\) |
−0.548783 | + | 0.835965i | \(0.684909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.8529 | − | 46.5106i | −0.916209 | − | 1.58692i | −0.805121 | − | 0.593110i | \(-0.797900\pi\) |
−0.111088 | − | 0.993811i | \(-0.535433\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.220815 | + | 0.382463i | 0.00752536 | + | 0.0130343i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 39.1527i | − | 1.33277i | −0.745607 | − | 0.666386i | \(-0.767840\pi\) | ||
0.745607 | − | 0.666386i | \(-0.232160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.66086i | 0.328100i | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 21.1308i | 0.715170i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −25.6793 | − | 14.8260i | −0.867129 | − | 0.500637i | −0.000735993 | − | 1.00000i | \(-0.500234\pi\) |
−0.866393 | + | 0.499362i | \(0.833568\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 49.3340 | − | 28.4830i | 1.66022 | − | 0.958529i | 0.687613 | − | 0.726078i | \(-0.258659\pi\) |
0.972608 | − | 0.232451i | \(-0.0746747\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.5211 | + | 10.1158i | −0.588301 | + | 0.339656i | −0.764425 | − | 0.644712i | \(-0.776977\pi\) |
0.176124 | + | 0.984368i | \(0.443644\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −19.4615 | − | 34.5576i | −0.651254 | − | 1.15643i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.273700 | + | 0.158021i | −0.00913857 | + | 0.00527615i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.49454 | + | 14.7130i | 0.283309 | + | 0.490705i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 65.0846 | 2.16828 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.794456 | + | 0.458679i | −0.0264378 | + | 0.0152639i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.66025 | − | 5.00000i | −0.287559 | − | 0.166022i | 0.349281 | − | 0.937018i | \(-0.386426\pi\) |
−0.636841 | + | 0.770996i | \(0.719759\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 25.9516i | − | 0.858872i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5.85385 | − | 3.37972i | −0.193311 | − | 0.111608i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.6159 | −1.60369 | −0.801846 | − | 0.597531i | \(-0.796148\pi\) | ||||
−0.801846 | + | 0.597531i | \(0.796148\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.86880 | + | 10.1651i | 0.193384 | + | 0.334950i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.50273i | − | 0.0823783i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −26.9837 | + | 15.5791i | −0.886262 | + | 0.511684i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.66075 | − | 9.80471i | 0.185723 | − | 0.321682i | −0.758097 | − | 0.652142i | \(-0.773871\pi\) |
0.943820 | + | 0.330460i | \(0.107204\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.307853 | + | 28.7500i | −0.0100895 | + | 0.942242i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.90421 | + | 2.25409i | 0.127818 | + | 0.0737957i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.09090 | − | 5.24864i | 0.296987 | − | 0.171465i | −0.344102 | − | 0.938932i | \(-0.611816\pi\) |
0.641088 | + | 0.767467i | \(0.278483\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.03402 | 0.294814 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.40939 | + | 2.44113i | 0.0459447 | + | 0.0795785i | 0.888083 | − | 0.459683i | \(-0.152037\pi\) |
−0.842139 | + | 0.539261i | \(0.818704\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.65341i | 0.0538424i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.4160 | − | 22.7568i | −1.28085 | − | 0.739497i | −0.303844 | − | 0.952722i | \(-0.598270\pi\) |
−0.977003 | + | 0.213224i | \(0.931603\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.403926 | −0.0131120 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.66433 | −0.0863967 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.9440 | + | 10.3600i | 0.581264 | + | 0.335593i | 0.761635 | − | 0.648006i | \(-0.224397\pi\) |
−0.180372 | + | 0.983599i | \(0.557730\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 5.42356i | − | 0.175319i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.11135 | + | 1.92491i | 0.0358873 | + | 0.0621587i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.5136 | −0.887537 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −28.1340 | + | 16.2432i | −0.906606 | + | 0.523429i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −11.6642 | − | 6.73436i | −0.375097 | − | 0.216562i | 0.300586 | − | 0.953755i | \(-0.402818\pi\) |
−0.675683 | + | 0.737192i | \(0.736151\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.13020 | − | 5.14177i | 0.293304 | − | 0.165177i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.5252 | − | 40.7468i | 0.754960 | − | 1.30763i | −0.190435 | − | 0.981700i | \(-0.560990\pi\) |
0.945394 | − | 0.325928i | \(-0.105677\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.404192 | − | 0.233360i | 0.0129578 | − | 0.00748119i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 43.0648i | − | 1.37776i | −0.724873 | − | 0.688882i | \(-0.758102\pi\) | ||
0.724873 | − | 0.688882i | \(-0.241898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.443404 | + | 0.767999i | 0.0141713 | + | 0.0245454i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −37.9374 | −1.21125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 46.8339 | + | 27.0396i | 1.49377 | + | 0.862429i | 0.999974 | − | 0.00714884i | \(-0.00227557\pi\) |
0.493796 | + | 0.869578i | \(0.335609\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.10752i | 0.0670830i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.43448 | −0.109210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.6356 | + | 35.7418i | −0.655510 | + | 1.13538i | 0.326256 | + | 0.945282i | \(0.394213\pi\) |
−0.981766 | + | 0.190095i | \(0.939120\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.83021 | + | 3.36608i | 0.185016 | + | 0.106819i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.943859 | − | 0.544937i | 0.0298923 | − | 0.0172583i | −0.484979 | − | 0.874526i | \(-0.661173\pi\) |
0.514872 | + | 0.857267i | \(0.327840\pi\) | |||||||
\(998\) | 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 | 1900.2.s.c.49.4 | 12 | ||
5.2 | odd | 4 | 380.2.i.b.201.2 | yes | 6 | ||
5.3 | odd | 4 | 1900.2.i.c.201.2 | 6 | |||
5.4 | even | 2 | inner | 1900.2.s.c.49.3 | 12 | ||
15.2 | even | 4 | 3420.2.t.v.3241.2 | 6 | |||
19.7 | even | 3 | inner | 1900.2.s.c.349.3 | 12 | ||
20.7 | even | 4 | 1520.2.q.i.961.2 | 6 | |||
95.7 | odd | 12 | 380.2.i.b.121.2 | ✓ | 6 | ||
95.27 | even | 12 | 7220.2.a.o.1.2 | 3 | |||
95.64 | even | 6 | inner | 1900.2.s.c.349.4 | 12 | ||
95.83 | odd | 12 | 1900.2.i.c.501.2 | 6 | |||
95.87 | odd | 12 | 7220.2.a.n.1.2 | 3 | |||
285.197 | even | 12 | 3420.2.t.v.1261.2 | 6 | |||
380.7 | even | 12 | 1520.2.q.i.881.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.2 | ✓ | 6 | 95.7 | odd | 12 | ||
380.2.i.b.201.2 | yes | 6 | 5.2 | odd | 4 | ||
1520.2.q.i.881.2 | 6 | 380.7 | even | 12 | |||
1520.2.q.i.961.2 | 6 | 20.7 | even | 4 | |||
1900.2.i.c.201.2 | 6 | 5.3 | odd | 4 | |||
1900.2.i.c.501.2 | 6 | 95.83 | odd | 12 | |||
1900.2.s.c.49.3 | 12 | 5.4 | even | 2 | inner | ||
1900.2.s.c.49.4 | 12 | 1.1 | even | 1 | trivial | ||
1900.2.s.c.349.3 | 12 | 19.7 | even | 3 | inner | ||
1900.2.s.c.349.4 | 12 | 95.64 | even | 6 | inner | ||
3420.2.t.v.1261.2 | 6 | 285.197 | even | 12 | |||
3420.2.t.v.3241.2 | 6 | 15.2 | even | 4 | |||
7220.2.a.n.1.2 | 3 | 95.87 | odd | 12 | |||
7220.2.a.o.1.2 | 3 | 95.27 | even | 12 |