Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(191,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("960.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.h (of order \(2\), degree \(1\), 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: | \(7.66563859404\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 480) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.1 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.191 |
Dual form | 960.2.h.a.191.4 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.828427i | − | 0.313116i | −0.987669 | − | 0.156558i | \(-0.949960\pi\) | ||
0.987669 | − | 0.156558i | \(-0.0500398\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.828427 | 0.249780 | 0.124890 | − | 0.992171i | \(-0.460142\pi\) | ||||
0.124890 | + | 0.992171i | \(0.460142\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.82843 | −1.89386 | −0.946932 | − | 0.321433i | \(-0.895836\pi\) | ||||
−0.946932 | + | 0.321433i | \(0.895836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.41421 | + | 1.00000i | −0.365148 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.82843i | 1.17107i | 0.810649 | + | 0.585533i | \(0.199115\pi\) | ||||
−0.810649 | + | 0.585533i | \(0.800885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.00000i | − | 1.37649i | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||
0.725476 | − | 0.688247i | \(-0.241620\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.17157 | + | 0.828427i | −0.255658 | + | 0.180778i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.82843 | −1.00680 | −0.503398 | − | 0.864054i | \(-0.667917\pi\) | ||||
−0.503398 | + | 0.864054i | \(0.667917\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.00000i | 1.11417i | 0.830455 | + | 0.557086i | \(0.188081\pi\) | ||||
−0.830455 | + | 0.557086i | \(0.811919\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.00000i | − | 0.359211i | −0.983739 | − | 0.179605i | \(-0.942518\pi\) | ||
0.983739 | − | 0.179605i | \(-0.0574821\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.828427 | − | 1.17157i | −0.144211 | − | 0.203945i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.828427 | −0.140030 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.17157 | −0.192605 | −0.0963027 | − | 0.995352i | \(-0.530702\pi\) | ||||
−0.0963027 | + | 0.995352i | \(0.530702\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.82843 | + | 9.65685i | 1.09342 | + | 1.54633i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.65685i | 0.258757i | 0.991595 | + | 0.129379i | \(0.0412982\pi\) | ||||
−0.991595 | + | 0.129379i | \(0.958702\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.82843i | 1.04133i | 0.853762 | + | 0.520663i | \(0.174315\pi\) | ||||
−0.853762 | + | 0.520663i | \(0.825685\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.82843 | + | 1.00000i | 0.421637 | + | 0.149071i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.82843 | −1.28776 | −0.643879 | − | 0.765127i | \(-0.722676\pi\) | ||||
−0.643879 | + | 0.765127i | \(0.722676\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.82843 | − | 4.82843i | 0.956171 | − | 0.676115i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.65685i | 0.502308i | 0.967947 | + | 0.251154i | \(0.0808100\pi\) | ||||
−0.967947 | + | 0.251154i | \(0.919190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.828427i | − | 0.111705i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.48528 | + | 6.00000i | −1.12390 | + | 0.794719i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.17157 | −0.933659 | −0.466830 | − | 0.884347i | \(-0.654604\pi\) | ||||
−0.466830 | + | 0.884347i | \(0.654604\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.31371 | −1.19250 | −0.596249 | − | 0.802799i | \(-0.703343\pi\) | ||||
−0.596249 | + | 0.802799i | \(0.703343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.34315 | + | 0.828427i | 0.295209 | + | 0.104372i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.82843i | 0.846962i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4853i | 1.52532i | 0.646800 | + | 0.762660i | \(0.276107\pi\) | ||||
−0.646800 | + | 0.762660i | \(0.723893\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.82843 | + | 6.82843i | 0.581274 | + | 0.822046i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3137 | 1.34269 | 0.671345 | − | 0.741145i | \(-0.265717\pi\) | ||||
0.671345 | + | 0.741145i | \(0.265717\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.00000 | −0.234082 | −0.117041 | − | 0.993127i | \(-0.537341\pi\) | ||||
−0.117041 | + | 0.993127i | \(0.537341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000 | + | 1.41421i | 0.115470 | + | 0.163299i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.686292i | − | 0.0782102i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 6.00000i | − | 0.675053i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.3137 | −1.90043 | −0.950213 | − | 0.311601i | \(-0.899135\pi\) | ||||
−0.950213 | + | 0.311601i | \(0.899135\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.82843 | 0.523716 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.48528 | − | 6.00000i | 0.909718 | − | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.65685i | 0.592999i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.82843 | + | 2.00000i | −0.293294 | + | 0.207390i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.00000 | −0.615587 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.828427 | + | 2.34315i | −0.0832601 | + | 0.235495i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 3.65685i | − | 0.363871i | −0.983311 | − | 0.181935i | \(-0.941764\pi\) | ||
0.983311 | − | 0.181935i | \(-0.0582361\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.82843i | 0.475759i | 0.971295 | + | 0.237880i | \(0.0764523\pi\) | ||||
−0.971295 | + | 0.237880i | \(0.923548\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.828427 | + | 1.17157i | 0.0808462 | + | 0.114334i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.3137 | 1.67378 | 0.836890 | − | 0.547372i | \(-0.184372\pi\) | ||||
0.836890 | + | 0.547372i | \(0.184372\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.65685 | 0.350263 | 0.175132 | − | 0.984545i | \(-0.443965\pi\) | ||||
0.175132 | + | 0.984545i | \(0.443965\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.17157 | + | 1.65685i | 0.111201 | + | 0.157262i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.8284i | − | 1.20680i | −0.797440 | − | 0.603398i | \(-0.793813\pi\) | ||
0.797440 | − | 0.603398i | \(-0.206187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.82843i | 0.450253i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.82843 | − | 19.3137i | 0.631288 | − | 1.78555i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.3137 | −0.937610 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.34315 | − | 1.65685i | 0.211274 | − | 0.149394i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.4853i | − | 0.930418i | −0.885201 | − | 0.465209i | \(-0.845979\pi\) | ||
0.885201 | − | 0.465209i | \(-0.154021\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.65685 | − | 6.82843i | 0.850239 | − | 0.601209i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4853 | −1.26558 | −0.632792 | − | 0.774321i | \(-0.718091\pi\) | ||||
−0.632792 | + | 0.774321i | \(0.718091\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.97056 | −0.431002 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.41421 | − | 5.00000i | −0.121716 | − | 0.430331i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 12.1421i | − | 1.03737i | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||
0.854965 | − | 0.518686i | \(-0.173579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.31371i | − | 0.111427i | −0.998447 | − | 0.0557137i | \(-0.982257\pi\) | ||
0.998447 | − | 0.0557137i | \(-0.0177434\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.82843 | + | 12.4853i | 0.743488 | + | 1.05145i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.31371 | − | 8.92893i | −0.520746 | − | 0.736446i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 23.6569i | 1.93805i | 0.246972 | + | 0.969023i | \(0.420564\pi\) | ||||
−0.246972 | + | 0.969023i | \(0.579436\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 3.65685i | − | 0.297591i | −0.988868 | − | 0.148795i | \(-0.952460\pi\) | ||
0.988868 | − | 0.148795i | \(-0.0475395\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −13.6569 | − | 4.82843i | −1.10409 | − | 0.390355i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | −0.160644 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.4853 | 1.31567 | 0.657834 | − | 0.753163i | \(-0.271473\pi\) | ||||
0.657834 | + | 0.753163i | \(0.271473\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.17157 | − | 3.65685i | 0.410132 | − | 0.290007i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.00000i | 0.315244i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 16.4853i | − | 1.29123i | −0.763664 | − | 0.645613i | \(-0.776602\pi\) | ||
0.763664 | − | 0.645613i | \(-0.223398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.17157 | + | 0.828427i | −0.0912068 | + | 0.0644930i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −19.1716 | −1.48354 | −0.741770 | − | 0.670654i | \(-0.766014\pi\) | ||||
−0.741770 | + | 0.670654i | \(0.766014\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.6274 | 2.58672 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | + | 6.00000i | 1.29777 | + | 0.458831i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 22.9706i | − | 1.74642i | −0.487345 | − | 0.873210i | \(-0.662034\pi\) | ||
0.487345 | − | 0.873210i | \(-0.337966\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.828427i | 0.0626232i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.17157 | + | 10.1421i | 0.539048 | + | 0.762330i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.82843 | −0.659868 | −0.329934 | − | 0.944004i | \(-0.607026\pi\) | ||||
−0.329934 | + | 0.944004i | \(0.607026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.31371 | + | 13.1716i | 0.688489 | + | 0.973671i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.17157i | 0.0861358i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.00000i | 0.292509i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.17157 | − | 4.14214i | −0.0852194 | − | 0.301296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.0000 | −0.868290 | −0.434145 | − | 0.900843i | \(-0.642949\pi\) | ||||
−0.434145 | + | 0.900843i | \(0.642949\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9706 | −1.07760 | −0.538802 | − | 0.842432i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.65685 | − | 6.82843i | 0.691542 | − | 0.488994i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.31371i | − | 0.663574i | −0.943354 | − | 0.331787i | \(-0.892348\pi\) | ||
0.943354 | − | 0.331787i | \(-0.107652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.65685i | 0.259228i | 0.991565 | + | 0.129614i | \(0.0413737\pi\) | ||||
−0.991565 | + | 0.129614i | \(0.958626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.6569 | − | 12.4853i | 1.24542 | − | 0.880644i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.97056 | 0.348865 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.65685 | 0.115720 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.82843 | − | 13.6569i | 0.335599 | − | 0.949217i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4.97056i | − | 0.343821i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 26.9706i | − | 1.85673i | −0.371670 | − | 0.928365i | \(-0.621215\pi\) | ||
0.371670 | − | 0.928365i | \(-0.378785\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.3137 | − | 16.0000i | −0.775203 | − | 1.09630i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.82843 | 0.465695 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.65685 | −0.112475 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.00000 | + | 2.82843i | 0.135147 | + | 0.191127i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 32.9706i | − | 2.21784i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.4853i | − | 0.702146i | −0.936348 | − | 0.351073i | \(-0.885817\pi\) | ||
0.936348 | − | 0.351073i | \(-0.114183\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | − | 2.82843i | 0.0666667 | − | 0.188562i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.343146 | −0.0227754 | −0.0113877 | − | 0.999935i | \(-0.503625\pi\) | ||||
−0.0113877 | + | 0.999935i | \(0.503625\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.9706 | 0.989283 | 0.494641 | − | 0.869097i | \(-0.335299\pi\) | ||||
0.494641 | + | 0.869097i | \(0.335299\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.970563 | + | 0.686292i | −0.0638583 | + | 0.0451547i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 15.1716i | − | 0.993923i | −0.867773 | − | 0.496961i | \(-0.834449\pi\) | ||
0.867773 | − | 0.496961i | \(-0.165551\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.82843i | 0.575903i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.48528 | + | 6.00000i | −0.551178 | + | 0.389742i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −16.9706 | −1.09773 | −0.548867 | − | 0.835910i | \(-0.684941\pi\) | ||||
−0.548867 | + | 0.835910i | \(0.684941\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 6.31371i | − | 0.403368i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 40.9706i | 2.60689i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.3137 | + | 24.4853i | 1.09721 | + | 1.55169i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −21.7990 | −1.37594 | −0.687970 | − | 0.725739i | \(-0.741498\pi\) | ||||
−0.687970 | + | 0.725739i | \(0.741498\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.82843 | − | 6.82843i | −0.302368 | − | 0.427613i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.51472i | 0.593512i | 0.954953 | + | 0.296756i | \(0.0959048\pi\) | ||||
−0.954953 | + | 0.296756i | \(0.904095\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.970563i | 0.0603078i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.9706 | − | 6.00000i | −1.05045 | − | 0.371391i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.4853 | 0.893201 | 0.446600 | − | 0.894734i | \(-0.352635\pi\) | ||||
0.446600 | + | 0.894734i | \(0.352635\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.65685 | 0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 7.65685i | − | 0.466847i | −0.972375 | − | 0.233423i | \(-0.925007\pi\) | ||
0.972375 | − | 0.233423i | \(-0.0749928\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.9706i | 1.15238i | 0.817316 | + | 0.576190i | \(0.195461\pi\) | ||||
−0.817316 | + | 0.576190i | \(0.804539\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.00000 | − | 5.65685i | 0.484182 | − | 0.342368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.828427 | −0.0499560 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −20.4853 | −1.23084 | −0.615421 | − | 0.788199i | \(-0.711014\pi\) | ||||
−0.615421 | + | 0.788199i | \(0.711014\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65685 | + | 2.00000i | 0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 0.686292i | − | 0.0409407i | −0.999790 | − | 0.0204704i | \(-0.993484\pi\) | ||
0.999790 | − | 0.0204704i | \(-0.00651637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 22.8284i | − | 1.35701i | −0.734596 | − | 0.678505i | \(-0.762628\pi\) | ||
0.734596 | − | 0.678505i | \(-0.237372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | + | 8.48528i | 0.355409 | + | 0.502625i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.37258 | 0.0810210 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | + | 8.48528i | 0.351726 | + | 0.497416i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.6569i | 0.681001i | 0.940244 | + | 0.340500i | \(0.110596\pi\) | ||||
−0.940244 | + | 0.340500i | \(0.889404\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.17157i | 0.417545i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.14214 | − | 1.17157i | 0.240351 | − | 0.0679816i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 32.9706 | 1.90674 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65685 | 0.326056 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.17157 | + | 3.65685i | −0.297099 | + | 0.210081i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.31371i | 0.533301i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.51472i | 0.200596i | 0.994957 | + | 0.100298i | \(0.0319796\pi\) | ||||
−0.994957 | + | 0.100298i | \(0.968020\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.82843 | − | 4.82843i | 0.388456 | − | 0.274680i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.3137 | 0.641542 | 0.320771 | − | 0.947157i | \(-0.396058\pi\) | ||||
0.320771 | + | 0.947157i | \(0.396058\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.68629 | 0.151838 | 0.0759191 | − | 0.997114i | \(-0.475811\pi\) | ||||
0.0759191 | + | 0.997114i | \(0.475811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.828427 | − | 2.34315i | 0.0466766 | − | 0.132021i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3137i | 0.972435i | 0.873838 | + | 0.486217i | \(0.161624\pi\) | ||||
−0.873838 | + | 0.486217i | \(0.838376\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.97056i | 0.278298i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.3137 | − | 24.4853i | −0.966357 | − | 1.36664i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 28.9706 | 1.61197 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.82843 | 0.378773 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.65685 | − | 5.17157i | −0.202225 | − | 0.285989i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.31371i | 0.403218i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.9706i | 1.26258i | 0.775548 | + | 0.631288i | \(0.217473\pi\) | ||||
−0.775548 | + | 0.631288i | \(0.782527\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.17157 | − | 3.31371i | 0.0642018 | − | 0.181590i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.4853 | 0.682144 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.02944 | 0.0560770 | 0.0280385 | − | 0.999607i | \(-0.491074\pi\) | ||||
0.0280385 | + | 0.999607i | \(0.491074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −18.1421 | + | 12.8284i | −0.985346 | + | 0.696745i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.65685i | − | 0.0897237i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 11.0294i | − | 0.595534i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.82843 | − | 4.82843i | 0.367630 | − | 0.259954i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.31371 | −0.499986 | −0.249993 | − | 0.968248i | \(-0.580428\pi\) | ||||
−0.249993 | + | 0.968248i | \(0.580428\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9706 | 1.22959 | 0.614793 | − | 0.788688i | \(-0.289240\pi\) | ||||
0.614793 | + | 0.788688i | \(0.289240\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −34.1421 | + | 9.65685i | −1.82237 | + | 0.515445i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1716i | 0.594603i | 0.954784 | + | 0.297301i | \(0.0960866\pi\) | ||||
−0.954784 | + | 0.297301i | \(0.903913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 11.3137i | − | 0.600469i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.00000 | − | 5.65685i | −0.211702 | − | 0.299392i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.68629 | −0.458445 | −0.229222 | − | 0.973374i | \(-0.573618\pi\) | ||||
−0.229222 | + | 0.973374i | \(0.573618\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.3137 | + | 14.5858i | 0.541329 | + | 0.765555i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000i | 0.104685i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 0.142136i | − | 0.00741942i | −0.999993 | − | 0.00370971i | \(-0.998819\pi\) | ||
0.999993 | − | 0.00370971i | \(-0.00118084\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.68629 | − | 1.65685i | −0.243959 | − | 0.0862524i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.02944 | 0.157281 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.485281 | 0.0251269 | 0.0125635 | − | 0.999921i | \(-0.496001\pi\) | ||||
0.0125635 | + | 0.999921i | \(0.496001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.41421 | − | 1.00000i | 0.0730297 | − | 0.0516398i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40.9706i | − | 2.11009i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 33.3137i | − | 1.71121i | −0.517629 | − | 0.855605i | \(-0.673185\pi\) | ||
0.517629 | − | 0.855605i | \(-0.326815\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −14.8284 | + | 10.4853i | −0.759683 | + | 0.537177i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.14214 | 0.211653 | 0.105827 | − | 0.994385i | \(-0.466251\pi\) | ||||
0.105827 | + | 0.994385i | \(0.466251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.686292 | −0.0349767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −19.3137 | − | 6.82843i | −0.981771 | − | 0.347108i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.6274i | 0.843044i | 0.906818 | + | 0.421522i | \(0.138504\pi\) | ||||
−0.906818 | + | 0.421522i | \(0.861496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 23.3137i | − | 1.17902i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.4853 | + | 20.4853i | 0.730686 | + | 1.03335i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.00000 | −0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.51472 | 0.377153 | 0.188576 | − | 0.982059i | \(-0.439613\pi\) | ||||
0.188576 | + | 0.982059i | \(0.439613\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.97056 | + | 7.02944i | 0.248839 | + | 0.351912i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.9706i | 0.847469i | 0.905786 | + | 0.423735i | \(0.139281\pi\) | ||||
−0.905786 | + | 0.423735i | \(0.860719\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 13.6569i | 0.680296i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.65685 | + | 7.00000i | −0.281091 | + | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.970563 | −0.0481090 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −33.3137 | −1.64726 | −0.823628 | − | 0.567130i | \(-0.808054\pi\) | ||||
−0.823628 | + | 0.567130i | \(0.808054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.1716 | + | 12.1421i | −0.847011 | + | 0.598927i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.94113i | 0.292344i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.3137i | 0.849897i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.85786 | + | 1.31371i | −0.0909800 | + | 0.0643326i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.1716 | −0.545767 | −0.272884 | − | 0.962047i | \(-0.587977\pi\) | ||||
−0.272884 | + | 0.962047i | \(0.587977\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.82843 | − | 24.9706i | 0.429253 | − | 1.21411i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.82843i | − | 0.234213i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.71573i | 0.373390i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.65685 | + | 8.00000i | 0.273115 | + | 0.386244i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.34315 | 0.305539 | 0.152769 | − | 0.988262i | \(-0.451181\pi\) | ||||
0.152769 | + | 0.988262i | \(0.451181\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −30.0000 | −1.44171 | −0.720854 | − | 0.693087i | \(-0.756250\pi\) | ||||
−0.720854 | + | 0.693087i | \(0.756250\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.00000 | − | 8.48528i | −0.287678 | − | 0.406838i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 28.9706i | 1.38585i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 30.2843i | − | 1.44539i | −0.691167 | − | 0.722695i | \(-0.742903\pi\) | ||
0.691167 | − | 0.722695i | \(-0.257097\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.31371 | + | 17.8579i | −0.300653 | + | 0.850374i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.34315 | 0.396395 | 0.198197 | − | 0.980162i | \(-0.436491\pi\) | ||||
0.198197 | + | 0.980162i | \(0.436491\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 33.4558 | − | 23.6569i | 1.58241 | − | 1.11893i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6569i | 1.58837i | 0.607679 | + | 0.794183i | \(0.292101\pi\) | ||||
−0.607679 | + | 0.794183i | \(0.707899\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37258i | 0.0646324i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.17157 | + | 3.65685i | −0.242982 | + | 0.171814i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.65685 | 0.265197 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.02944 | −0.0481550 | −0.0240775 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240775 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.82843 | + | 24.1421i | 0.318724 | + | 1.12686i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.31371i | 0.433783i | 0.976196 | + | 0.216891i | \(0.0695917\pi\) | ||||
−0.976196 | + | 0.216891i | \(0.930408\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12.8284i | − | 0.596188i | −0.954537 | − | 0.298094i | \(-0.903649\pi\) | ||
0.954537 | − | 0.298094i | \(-0.0963508\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | + | 2.82843i | 0.0927478 | + | 0.131165i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.3431 | −0.571173 | −0.285586 | − | 0.958353i | \(-0.592188\pi\) | ||||
−0.285586 | + | 0.958353i | \(0.592188\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.3431 | 0.477602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.4853 | − | 23.3137i | −0.759602 | − | 1.07424i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.65685i | 0.260102i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.00000i | 0.275299i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.3431 | − | 3.65685i | −0.473580 | − | 0.167436i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 13.6569 | 0.623998 | 0.311999 | − | 0.950082i | \(-0.399002\pi\) | ||||
0.311999 | + | 0.950082i | \(0.399002\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | 0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.65685 | − | 4.00000i | 0.257396 | − | 0.182006i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.00000i | 0.272446i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 27.4558i | 1.24414i | 0.782960 | + | 0.622072i | \(0.213709\pi\) | ||||
−0.782960 | + | 0.622072i | \(0.786291\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.3137 | + | 16.4853i | −1.05428 | + | 0.745490i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8284 | −0.939974 | −0.469987 | − | 0.882673i | \(-0.655741\pi\) | ||||
−0.469987 | + | 0.882673i | \(0.655741\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.9706 | −1.30477 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.34315 | + | 0.828427i | 0.105317 | + | 0.0372350i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 9.37258i | − | 0.420418i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 2.68629i | − | 0.120255i | −0.998191 | − | 0.0601275i | \(-0.980849\pi\) | ||
0.998191 | − | 0.0601275i | \(-0.0191507\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 19.1716 | + | 27.1127i | 0.856523 | + | 1.21131i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.82843 | −0.215289 | −0.107644 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107644 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.65685 | −0.162728 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.6274 | − | 47.5563i | −1.49345 | − | 2.11205i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 23.6569i | − | 1.04857i | −0.851542 | − | 0.524286i | \(-0.824332\pi\) | ||
0.851542 | − | 0.524286i | \(-0.175668\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.65685i | 0.0732949i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.48528 | − | 30.0000i | −0.374634 | − | 1.32453i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.82843 | 0.212766 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.31371 | −0.321657 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.4853 | + | 22.9706i | −1.42595 | + | 1.00830i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0000i | 0.525730i | 0.964833 | + | 0.262865i | \(0.0846673\pi\) | ||||
−0.964833 | + | 0.262865i | \(0.915333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.4853i | 0.545943i | 0.962022 | + | 0.272972i | \(0.0880065\pi\) | ||||
−0.962022 | + | 0.272972i | \(0.911993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.17157 | − | 0.828427i | 0.0511316 | − | 0.0361555i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.65685 | 0.420659 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.17157 | − | 20.2843i | 0.311220 | − | 0.880262i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.3137i | − | 0.490051i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 17.3137i | − | 0.748537i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.82843 | + | 12.4853i | 0.380975 | + | 0.538780i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.23045 | 0.225291 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.62742 | 0.370922 | 0.185461 | − | 0.982652i | \(-0.440622\pi\) | ||||
0.185461 | + | 0.982652i | \(0.440622\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | − | 2.82843i | −0.0858282 | − | 0.121379i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.65685i | − | 0.156642i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.4558i | 1.25944i | 0.776822 | + | 0.629720i | \(0.216831\pi\) | ||||
−0.776822 | + | 0.629720i | \(0.783169\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.31371 | − | 26.3431i | 0.397499 | − | 1.12430i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 36.0000 | 1.53365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.97056 | −0.211370 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.65685 | − | 1.17157i | 0.0703295 | − | 0.0497305i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.9706i | 1.48175i | 0.671643 | + | 0.740875i | \(0.265589\pi\) | ||||
−0.671643 | + | 0.740875i | \(0.734411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 46.6274i | − | 1.97213i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.65685 | − | 4.00000i | 0.238833 | − | 0.168880i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.31371 | −0.223946 | −0.111973 | − | 0.993711i | \(-0.535717\pi\) | ||||
−0.111973 | + | 0.993711i | \(0.535717\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.8284 | −0.539696 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4.68629 | + | 5.79899i | −0.196806 | + | 0.243535i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.02944i | − | 0.0430806i | −0.999768 | − | 0.0215403i | \(-0.993143\pi\) | ||
0.999768 | − | 0.0215403i | \(-0.00685702\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | + | 16.9706i | 0.501307 | + | 0.708955i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82843 | 0.201359 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9706 | 0.789755 | 0.394877 | − | 0.918734i | \(-0.370787\pi\) | ||||
0.394877 | + | 0.918734i | \(0.370787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 14.9706 | + | 21.1716i | 0.622155 | + | 0.879861i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.3431i | 0.595054i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.02944i | 0.125466i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −19.3137 | − | 6.82843i | −0.798524 | − | 0.282321i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.6274 | 1.18158 | 0.590790 | − | 0.806825i | \(-0.298816\pi\) | ||||
0.590790 | + | 0.806825i | \(0.298816\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.1716 | + | 9.31371i | −0.541806 | + | 0.383115i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.85786i | 0.322684i | 0.986899 | + | 0.161342i | \(0.0515822\pi\) | ||||
−0.986899 | + | 0.161342i | \(0.948418\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 4.00000i | − | 0.163984i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.17157 | − | 3.65685i | 0.211658 | − | 0.149665i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.6274 | −1.08797 | −0.543983 | − | 0.839096i | \(-0.683085\pi\) | ||||
−0.543983 | + | 0.839096i | \(0.683085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.62742 | 0.351920 | 0.175960 | − | 0.984397i | \(-0.443697\pi\) | ||||
0.175960 | + | 0.984397i | \(0.443697\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −35.3137 | − | 12.4853i | −1.43809 | − | 0.508440i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.3137i | 0.419312i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 38.4853i | 1.56207i | 0.624488 | + | 0.781035i | \(0.285308\pi\) | ||||
−0.624488 | + | 0.781035i | \(0.714692\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.97056 | − | 7.02944i | −0.201417 | − | 0.284847i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 60.2843 | 2.43884 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.4558 | 1.02815 | 0.514076 | − | 0.857745i | \(-0.328135\pi\) | ||||
0.514076 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.65685 | − | 2.34315i | −0.0668108 | − | 0.0944848i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 8.82843i | − | 0.355419i | −0.984083 | − | 0.177710i | \(-0.943131\pi\) | ||
0.984083 | − | 0.177710i | \(-0.0568688\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.00000i | − | 0.241160i | −0.992704 | − | 0.120580i | \(-0.961525\pi\) | ||
0.992704 | − | 0.120580i | \(-0.0384755\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −24.1421 | + | 6.82843i | −0.968791 | + | 0.274015i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.02944 | + | 4.97056i | −0.280729 | + | 0.198505i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.65685i | − | 0.225554i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.6863i | 0.425415i | 0.977116 | + | 0.212707i | \(0.0682281\pi\) | ||||
−0.977116 | + | 0.212707i | \(0.931772\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −38.1421 | + | 26.9706i | −1.51601 | + | 1.07198i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.4853 | −0.416096 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −43.1127 | −1.70819 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3137 | + | 32.0000i | −0.447563 | + | 1.26590i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 30.6274i | 1.20971i | 0.796336 | + | 0.604855i | \(0.206769\pi\) | ||||
−0.796336 | + | 0.604855i | \(0.793231\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.8284i | 0.427031i | 0.976940 | + | 0.213516i | \(0.0684915\pi\) | ||||
−0.976940 | + | 0.213516i | \(0.931509\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.82843 | − | 9.65685i | −0.268869 | − | 0.380238i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.8284 | 0.818850 | 0.409425 | − | 0.912344i | \(-0.365729\pi\) | ||||
0.409425 | + | 0.912344i | \(0.365729\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.94113 | −0.233210 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.65685 | + | 2.34315i | 0.0649372 | + | 0.0918351i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 26.2843i | − | 1.02858i | −0.857615 | − | 0.514292i | \(-0.828055\pi\) | ||
0.857615 | − | 0.514292i | \(-0.171945\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.4853i | 0.565987i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.00000 | − | 5.65685i | 0.0780274 | − | 0.220695i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 45.7990 | 1.78408 | 0.892038 | − | 0.451961i | \(-0.149275\pi\) | ||||
0.892038 | + | 0.451961i | \(0.149275\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −46.6274 | + | 32.9706i | −1.81086 | + | 1.28047i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.97056i | 0.192750i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 28.9706i | − | 1.12174i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.8284 | + | 10.4853i | −0.573300 | + | 0.405384i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.71573 | −0.297862 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.9411 | 1.38543 | 0.692714 | − | 0.721212i | \(-0.256415\pi\) | ||||
0.692714 | + | 0.721212i | \(0.256415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.00000 | + | 1.41421i | −0.192450 | + | 0.0544331i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.343146i | 0.0131882i | 0.999978 | + | 0.00659408i | \(0.00209898\pi\) | ||||
−0.999978 | + | 0.00659408i | \(0.997901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.97056i | 0.190753i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.343146 | + | 0.485281i | 0.0131494 | + | 0.0185960i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.3431 | 0.778409 | 0.389204 | − | 0.921151i | \(-0.372750\pi\) | ||||
0.389204 | + | 0.921151i | \(0.372750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1421 | −0.463927 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.9706 | − | 21.1716i | −0.571163 | − | 0.807746i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 24.9706i | − | 0.951303i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.02944i | − | 0.343496i | −0.985141 | − | 0.171748i | \(-0.945059\pi\) | ||
0.985141 | − | 0.171748i | \(-0.0549415\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.94113 | + | 0.686292i | 0.0737373 | + | 0.0260701i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.31371 | −0.0498318 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.00000 | −0.303022 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.4558 | + | 15.1716i | −0.811535 | + | 0.573842i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.9411i | − | 1.05532i | −0.849455 | − | 0.527661i | \(-0.823069\pi\) | ||
0.849455 | − | 0.527661i | \(-0.176931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.02944i | 0.265120i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.4853 | − | 8.82843i | 0.470223 | − | 0.332498i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.02944 | −0.113934 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.9706 | −1.61379 | −0.806897 | − | 0.590693i | \(-0.798855\pi\) | ||||
−0.806897 | + | 0.590693i | \(0.798855\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 16.9706 | + | 6.00000i | 0.636446 | + | 0.225018i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 9.65685i | 0.361652i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.65685i | 0.211554i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 16.9706 | + | 24.0000i | 0.633777 | + | 0.896296i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.3137 | 1.61533 | 0.807664 | − | 0.589642i | \(-0.200731\pi\) | ||||
0.807664 | + | 0.589642i | \(0.200731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.00000 | 0.148968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.00000 | − | 8.48528i | −0.223142 | − | 0.315571i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.00000i | − | 0.222834i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19.1716i | − | 0.711034i | −0.934670 | − | 0.355517i | \(-0.884305\pi\) | ||
0.934670 | − | 0.355517i | \(-0.115695\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.9706 | −1.21946 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.8284 | 1.13867 | 0.569337 | − | 0.822104i | \(-0.307200\pi\) | ||||
0.569337 | + | 0.822104i | \(0.307200\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.92893 | + | 6.31371i | −0.329349 | + | 0.232885i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.3431i | 0.380995i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.3137i | 0.784037i | 0.919957 | + | 0.392019i | \(0.128223\pi\) | ||||
−0.919957 | + | 0.392019i | \(0.871777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 57.9411 | − | 40.9706i | 2.12852 | − | 1.50509i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.4558 | −0.713766 | −0.356883 | − | 0.934149i | \(-0.616160\pi\) | ||||
−0.356883 | + | 0.934149i | \(0.616160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.6569 | 0.866720 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 17.3137 | − | 48.9706i | 0.633475 | − | 1.79174i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 14.3431i | − | 0.524087i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.3137i | 0.923710i | 0.886955 | + | 0.461855i | \(0.152816\pi\) | ||||
−0.886955 | + | 0.461855i | \(0.847184\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 21.7990 | + | 30.8284i | 0.794399 | + | 1.12345i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.65685 | −0.133087 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 10.1421 | 0.368622 | 0.184311 | − | 0.982868i | \(-0.440995\pi\) | ||||
0.184311 | + | 0.982868i | \(0.440995\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 4.00000 | + | 5.65685i | 0.145191 | + | 0.205331i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 31.3137i | − | 1.13512i | −0.823332 | − | 0.567561i | \(-0.807887\pi\) | ||
0.823332 | − | 0.567561i | \(-0.192113\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 3.02944i | − | 0.109673i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.82843 | + | 13.6569i | −0.174572 | + | 0.493765i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48.9706 | 1.76822 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.6863 | 0.385358 | 0.192679 | − | 0.981262i | \(-0.438282\pi\) | ||||
0.192679 | + | 0.981262i | \(0.438282\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 13.4558 | − | 9.51472i | 0.484600 | − | 0.342664i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.3137i | 1.05434i | 0.849760 | + | 0.527170i | \(0.176747\pi\) | ||||
−0.849760 | + | 0.527170i | \(0.823253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000i | 0.0718421i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.37258 | − | 0.970563i | 0.0492411 | − | 0.0348187i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.94113 | 0.356178 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.37258 | 0.335377 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.48528 | + | 30.0000i | 0.303239 | + | 1.07211i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 16.4853i | − | 0.588385i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 39.7990i | 1.41868i | 0.704866 | + | 0.709340i | \(0.251007\pi\) | ||||
−0.704866 | + | 0.709340i | \(0.748993\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.4853 | − | 20.4853i | −0.515690 | − | 0.729295i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6274 | −0.377867 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 63.5980 | 2.25843 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.65685 | − | 5.17157i | −0.129695 | − | 0.183417i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 48.6274i | − | 1.72247i | −0.508206 | − | 0.861236i | \(-0.669691\pi\) | ||
0.508206 | − | 0.861236i | \(-0.330309\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 42.6274i | − | 1.50805i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.65685 | −0.0584691 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.8284 | + | 7.65685i | −0.381179 | + | 0.269534i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 5.65685i | − | 0.198884i | −0.995043 | − | 0.0994422i | \(-0.968294\pi\) | ||
0.995043 | − | 0.0994422i | \(-0.0317058\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.2843i | 0.642048i | 0.947071 | + | 0.321024i | \(0.104027\pi\) | ||||
−0.947071 | + | 0.321024i | \(0.895973\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 26.8284 | − | 18.9706i | 0.940914 | − | 0.665327i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.4853 | −0.577454 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 40.9706 | 1.43338 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −16.0000 | − | 5.65685i | −0.559085 | − | 0.197666i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 24.3431i | − | 0.849582i | −0.905292 | − | 0.424791i | \(-0.860348\pi\) | ||
0.905292 | − | 0.424791i | \(-0.139652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4558i | 0.399326i | 0.979865 | + | 0.199663i | \(0.0639847\pi\) | ||||
−0.979865 | + | 0.199663i | \(0.936015\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.828427 | + | 1.17157i | 0.0288421 | + | 0.0407889i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.6863 | 0.510692 | 0.255346 | − | 0.966850i | \(-0.417811\pi\) | ||||
0.255346 | + | 0.966850i | \(0.417811\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −44.9117 | −1.55985 | −0.779924 | − | 0.625875i | \(-0.784742\pi\) | ||||
−0.779924 | + | 0.625875i | \(0.784742\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 20.4853 | + | 28.9706i | 0.710627 | + | 1.00498i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.4853i | 1.05625i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 19.1716i | 0.663460i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.82843 | − | 10.0000i | −0.0977647 | − | 0.345651i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45.9411 | −1.58606 | −0.793032 | − | 0.609180i | \(-0.791499\pi\) | ||||
−0.793032 | + | 0.609180i | \(0.791499\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.970563 | + | 0.686292i | −0.0334280 | + | 0.0236371i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 33.6274i | − | 1.15682i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.54416i | 0.293581i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −32.2843 | + | 22.8284i | −1.10799 | + | 0.783470i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.65685 | 0.193914 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.5147 | 1.07904 | 0.539522 | − | 0.841972i | \(-0.318605\pi\) | ||||
0.539522 | + | 0.841972i | \(0.318605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.00000 | − | 16.9706i | 0.205196 | − | 0.580381i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 29.7990i | 1.01791i | 0.860792 | + | 0.508957i | \(0.169969\pi\) | ||||
−0.860792 | + | 0.508957i | \(0.830031\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 22.0000i | − | 0.750630i | −0.926897 | − | 0.375315i | \(-0.877534\pi\) | ||
0.926897 | − | 0.375315i | \(-0.122466\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.37258 | − | 1.94113i | −0.0467775 | − | 0.0661534i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.2010 | 0.619570 | 0.309785 | − | 0.950807i | \(-0.399743\pi\) | ||||
0.309785 | + | 0.950807i | \(0.399743\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.9706 | −0.781023 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.31371 | + | 8.92893i | 0.214425 | + | 0.303242i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.97056i | − | 0.168615i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 85.2548i | − | 2.88875i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.00000 | − | 16.9706i | 0.203069 | − | 0.574367i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.828427 | 0.0280059 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7990 | 0.398424 | 0.199212 | − | 0.979956i | \(-0.436162\pi\) | ||||
0.199212 | + | 0.979956i | \(0.436162\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.4853 | − | 11.6569i | 0.556035 | − | 0.393176i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 39.5980i | − | 1.33409i | −0.745018 | − | 0.667045i | \(-0.767559\pi\) | ||
0.745018 | − | 0.667045i | \(-0.232441\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 32.4853i | − | 1.09322i | −0.837388 | − | 0.546608i | \(-0.815919\pi\) | ||
0.837388 | − | 0.546608i | \(-0.184081\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10.1421 | − | 7.17157i | 0.340924 | − | 0.241070i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −35.1716 | −1.18095 | −0.590473 | − | 0.807057i | \(-0.701059\pi\) | ||||
−0.590473 | + | 0.807057i | \(0.701059\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.68629 | −0.291329 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.79899 | − | 4.68629i | −0.194273 | − | 0.156997i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.9706i | 1.77259i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.82843i | 0.295102i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −32.9706 | − | 46.6274i | −1.10086 | − | 1.55684i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −17.6569 | −0.588235 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.65685 | − | 8.00000i | −0.188248 | − | 0.266223i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.00000i | − | 0.0664822i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.17157i | 0.171719i | 0.996307 | + | 0.0858596i | \(0.0273637\pi\) | ||||
−0.996307 | + | 0.0858596i | \(0.972636\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.3431 | + | 3.65685i | 0.343060 | + | 0.121290i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27.5980 | 0.914362 | 0.457181 | − | 0.889374i | \(-0.348859\pi\) | ||||
0.457181 | + | 0.889374i | \(0.348859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.3431 | −0.474689 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.1716 | − | 9.31371i | 0.435439 | − | 0.307902i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12.0000i | 0.396275i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.68629i | − | 0.0886126i | −0.999018 | − | 0.0443063i | \(-0.985892\pi\) | ||
0.999018 | − | 0.0443063i | \(-0.0141077\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.97056 | − | 3.51472i | 0.163786 | − | 0.115814i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −77.2548 | −2.54287 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.17157 | 0.0385211 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.6569 | − | 4.82843i | −0.448550 | − | 0.158586i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 41.6569i | − | 1.36672i | −0.730083 | − | 0.683359i | \(-0.760519\pi\) | ||
0.730083 | − | 0.683359i | \(-0.239481\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 37.8823i | − | 1.24154i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −11.3137 | − | 16.0000i | −0.370394 | − | 0.523816i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | 0.130814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −26.9706 | −0.881090 | −0.440545 | − | 0.897731i | \(-0.645215\pi\) | ||||
−0.440545 | + | 0.897731i | \(0.645215\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.68629 | − | 3.79899i | −0.0876638 | − | 0.123975i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.5980i | 1.22566i | 0.790215 | + | 0.612830i | \(0.209969\pi\) | ||||
−0.790215 | + | 0.612830i | \(0.790031\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.00000i | − | 0.260516i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.14214 | + | 1.17157i | −0.134744 | + | 0.0381113i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.2843 | −0.334194 | −0.167097 | − | 0.985940i | \(-0.553439\pi\) | ||||
−0.167097 | + | 0.985940i | \(0.553439\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6569 | 0.443320 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 24.4853 | − | 17.3137i | 0.793990 | − | 0.561435i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 37.7990i | − | 1.22443i | −0.790692 | − | 0.612215i | \(-0.790279\pi\) | ||
0.790692 | − | 0.612215i | \(-0.209721\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.0000i | 0.388311i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.02944 | − | 4.97056i | 0.227229 | − | 0.160675i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0589 | −0.324818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.3137 | + | 48.9706i | −0.557926 | + | 1.57805i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.9706i | 0.481919i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.51472i | 0.0487101i | 0.999703 | + | 0.0243550i | \(0.00775321\pi\) | ||||
−0.999703 | + | 0.0243550i | \(0.992247\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.9706 | − | 40.9706i | −0.930669 | − | 1.31616i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 50.7696 | 1.62927 | 0.814636 | − | 0.579972i | \(-0.196937\pi\) | ||||
0.814636 | + | 0.579972i | \(0.196937\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.08831 | −0.0348897 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.82843 | − | 9.65685i | −0.218685 | − | 0.309267i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 9.79899i | − | 0.313497i | −0.987639 | − | 0.156749i | \(-0.949899\pi\) | ||
0.987639 | − | 0.156749i | \(-0.0501013\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.65685 | + | 10.3431i | −0.116754 | + | 0.330231i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −20.8284 | −0.664324 | −0.332162 | − | 0.943222i | \(-0.607778\pi\) | ||||
−0.332162 | + | 0.943222i | \(0.607778\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.31371 | −0.296759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.3431 | − | 7.31371i | 0.329226 | − | 0.232798i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 32.9706i | − | 1.04840i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2843i | 0.453755i | 0.973923 | + | 0.226877i | \(0.0728517\pi\) | ||||
−0.973923 | + | 0.226877i | \(0.927148\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.4853 | − | 22.9706i | 1.03089 | − | 0.728949i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.65685 | 0.115930 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.4853 | 1.40886 | 0.704431 | − | 0.709772i | \(-0.251202\pi\) | ||||
0.704431 | + | 0.709772i | \(0.251202\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.85786 | + | 1.65685i | −0.185335 | + | 0.0524205i |
(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 | 960.2.h.a.191.1 | 4 | ||
3.2 | odd | 2 | 960.2.h.e.191.2 | 4 | |||
4.3 | odd | 2 | 960.2.h.e.191.3 | 4 | |||
8.3 | odd | 2 | 480.2.h.a.191.2 | ✓ | 4 | ||
8.5 | even | 2 | 480.2.h.c.191.4 | yes | 4 | ||
12.11 | even | 2 | inner | 960.2.h.a.191.4 | 4 | ||
24.5 | odd | 2 | 480.2.h.a.191.3 | yes | 4 | ||
24.11 | even | 2 | 480.2.h.c.191.1 | yes | 4 | ||
40.3 | even | 4 | 2400.2.o.d.2399.3 | 4 | |||
40.13 | odd | 4 | 2400.2.o.g.2399.2 | 4 | |||
40.19 | odd | 2 | 2400.2.h.d.1151.4 | 4 | |||
40.27 | even | 4 | 2400.2.o.f.2399.2 | 4 | |||
40.29 | even | 2 | 2400.2.h.a.1151.1 | 4 | |||
40.37 | odd | 4 | 2400.2.o.e.2399.3 | 4 | |||
120.29 | odd | 2 | 2400.2.h.d.1151.1 | 4 | |||
120.53 | even | 4 | 2400.2.o.f.2399.1 | 4 | |||
120.59 | even | 2 | 2400.2.h.a.1151.4 | 4 | |||
120.77 | even | 4 | 2400.2.o.d.2399.4 | 4 | |||
120.83 | odd | 4 | 2400.2.o.e.2399.4 | 4 | |||
120.107 | odd | 4 | 2400.2.o.g.2399.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.h.a.191.2 | ✓ | 4 | 8.3 | odd | 2 | ||
480.2.h.a.191.3 | yes | 4 | 24.5 | odd | 2 | ||
480.2.h.c.191.1 | yes | 4 | 24.11 | even | 2 | ||
480.2.h.c.191.4 | yes | 4 | 8.5 | even | 2 | ||
960.2.h.a.191.1 | 4 | 1.1 | even | 1 | trivial | ||
960.2.h.a.191.4 | 4 | 12.11 | even | 2 | inner | ||
960.2.h.e.191.2 | 4 | 3.2 | odd | 2 | |||
960.2.h.e.191.3 | 4 | 4.3 | odd | 2 | |||
2400.2.h.a.1151.1 | 4 | 40.29 | even | 2 | |||
2400.2.h.a.1151.4 | 4 | 120.59 | even | 2 | |||
2400.2.h.d.1151.1 | 4 | 120.29 | odd | 2 | |||
2400.2.h.d.1151.4 | 4 | 40.19 | odd | 2 | |||
2400.2.o.d.2399.3 | 4 | 40.3 | even | 4 | |||
2400.2.o.d.2399.4 | 4 | 120.77 | even | 4 | |||
2400.2.o.e.2399.3 | 4 | 40.37 | odd | 4 | |||
2400.2.o.e.2399.4 | 4 | 120.83 | odd | 4 | |||
2400.2.o.f.2399.1 | 4 | 120.53 | even | 4 | |||
2400.2.o.f.2399.2 | 4 | 40.27 | even | 4 | |||
2400.2.o.g.2399.1 | 4 | 120.107 | odd | 4 | |||
2400.2.o.g.2399.2 | 4 | 40.13 | odd | 4 |