Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(197,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.197");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.c (of order \(2\), degree \(1\), 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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 4x^{10} - 8x^{9} + 17x^{8} - 16x^{7} + 88x^{6} - 48x^{5} + 153x^{4} - 216x^{3} + 324x^{2} + 729 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.10 | ||
Root | \(-0.0383715 + 1.73163i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1386.197 |
Dual form | 1386.2.c.a.197.3 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.50315i | 1.11944i | 0.828680 | + | 0.559722i | \(0.189092\pi\) | ||||
−0.828680 | + | 0.559722i | \(0.810908\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 2.50315i | − | 0.791567i | ||||||
\(11\) | −3.23848 | − | 0.715732i | −0.976437 | − | 0.215801i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.06863i | − | 0.296384i | −0.988959 | − | 0.148192i | \(-0.952655\pi\) | ||
0.988959 | − | 0.148192i | \(-0.0473454\pi\) | |||||||
\(14\) | − | 1.00000i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.11665 | −0.270826 | −0.135413 | − | 0.990789i | \(-0.543236\pi\) | ||||
−0.135413 | + | 0.990789i | \(0.543236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 0.185274i | − | 0.0425047i | −0.999774 | − | 0.0212524i | \(-0.993235\pi\) | ||
0.999774 | − | 0.0212524i | \(-0.00676535\pi\) | |||||||
\(20\) | 2.50315i | 0.559722i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.23848 | + | 0.715732i | 0.690445 | + | 0.152595i | ||||
\(23\) | 5.70439i | 1.18945i | 0.803930 | + | 0.594724i | \(0.202739\pi\) | ||||
−0.803930 | + | 0.594724i | \(0.797261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.26578 | −0.253156 | ||||||||
\(26\) | 1.06863i | 0.209575i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | −7.80144 | −1.44869 | −0.724346 | − | 0.689437i | \(-0.757858\pi\) | ||||
−0.724346 | + | 0.689437i | \(0.757858\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.60956 | −1.54632 | −0.773161 | − | 0.634210i | \(-0.781326\pi\) | ||||
−0.773161 | + | 0.634210i | \(0.781326\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.11665 | 0.191503 | ||||||||
\(35\) | −2.50315 | −0.423110 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.67494 | 0.768556 | 0.384278 | − | 0.923218i | \(-0.374450\pi\) | ||||
0.384278 | + | 0.923218i | \(0.374450\pi\) | |||||||
\(38\) | 0.185274i | 0.0300554i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 2.50315i | − | 0.395783i | ||||||
\(41\) | 0.132606 | 0.0207096 | 0.0103548 | − | 0.999946i | \(-0.496704\pi\) | ||||
0.0103548 | + | 0.999946i | \(0.496704\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.83979i | − | 1.34805i | −0.738706 | − | 0.674027i | \(-0.764563\pi\) | ||
0.738706 | − | 0.674027i | \(-0.235437\pi\) | |||||||
\(44\) | −3.23848 | − | 0.715732i | −0.488219 | − | 0.107901i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 5.70439i | − | 0.841066i | ||||||
\(47\) | − | 5.08738i | − | 0.742071i | −0.928619 | − | 0.371035i | \(-0.879003\pi\) | ||
0.928619 | − | 0.371035i | \(-0.120997\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.26578 | 0.179008 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 1.06863i | − | 0.148192i | ||||||
\(53\) | 0.0980758i | 0.0134717i | 0.999977 | + | 0.00673587i | \(0.00214411\pi\) | ||||
−0.999977 | + | 0.00673587i | \(0.997856\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.79159 | − | 8.10640i | 0.241578 | − | 1.09307i | ||||
\(56\) | − | 1.00000i | − | 0.133631i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.80144 | 1.02438 | ||||||||
\(59\) | 6.33137i | 0.824274i | 0.911122 | + | 0.412137i | \(0.135217\pi\) | ||||
−0.911122 | + | 0.412137i | \(0.864783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.93768i | − | 0.504168i | −0.967705 | − | 0.252084i | \(-0.918884\pi\) | ||
0.967705 | − | 0.252084i | \(-0.0811160\pi\) | |||||||
\(62\) | 8.60956 | 1.09342 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.67494 | 0.331786 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.49907 | −0.549649 | −0.274825 | − | 0.961494i | \(-0.588620\pi\) | ||||
−0.274825 | + | 0.961494i | \(0.588620\pi\) | |||||||
\(68\) | −1.11665 | −0.135413 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.50315 | 0.299184 | ||||||||
\(71\) | 0.698081i | 0.0828469i | 0.999142 | + | 0.0414235i | \(0.0131893\pi\) | ||||
−0.999142 | + | 0.0414235i | \(0.986811\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.169232i | 0.0198071i | 0.999951 | + | 0.00990357i | \(0.00315246\pi\) | ||||
−0.999951 | + | 0.00990357i | \(0.996848\pi\) | |||||||
\(74\) | −4.67494 | −0.543451 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 0.185274i | − | 0.0212524i | ||||||
\(77\) | 0.715732 | − | 3.23848i | 0.0815652 | − | 0.369059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.63002i | − | 0.183392i | −0.995787 | − | 0.0916958i | \(-0.970771\pi\) | ||
0.995787 | − | 0.0916958i | \(-0.0292287\pi\) | |||||||
\(80\) | 2.50315i | 0.279861i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.132606 | −0.0146439 | ||||||||
\(83\) | −6.27564 | −0.688841 | −0.344420 | − | 0.938816i | \(-0.611925\pi\) | ||||
−0.344420 | + | 0.938816i | \(0.611925\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.79514i | − | 0.303175i | ||||||
\(86\) | 8.83979i | 0.953219i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.23848 | + | 0.715732i | 0.345223 | + | 0.0762973i | ||||
\(89\) | − | 15.2423i | − | 1.61568i | −0.589405 | − | 0.807838i | \(-0.700638\pi\) | ||
0.589405 | − | 0.807838i | \(-0.299362\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.06863 | 0.112023 | ||||||||
\(92\) | 5.70439i | 0.594724i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.08738i | 0.524723i | ||||||||
\(95\) | 0.463769 | 0.0475817 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.71024 | −0.275184 | −0.137592 | − | 0.990489i | \(-0.543936\pi\) | ||||
−0.137592 | + | 0.990489i | \(0.543936\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.26578 | −0.126578 | ||||||||
\(101\) | −10.3811 | −1.03296 | −0.516478 | − | 0.856300i | \(-0.672757\pi\) | ||||
−0.516478 | + | 0.856300i | \(0.672757\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −17.5234 | −1.72663 | −0.863316 | − | 0.504664i | \(-0.831617\pi\) | ||||
−0.863316 | + | 0.504664i | \(0.831617\pi\) | |||||||
\(104\) | 1.06863i | 0.104788i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.0980758i | − | 0.00952596i | ||||||
\(107\) | −11.8692 | −1.14744 | −0.573721 | − | 0.819051i | \(-0.694501\pi\) | ||||
−0.573721 | + | 0.819051i | \(0.694501\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.39312i | 0.803915i | 0.915658 | + | 0.401958i | \(0.131670\pi\) | ||||
−0.915658 | + | 0.401958i | \(0.868330\pi\) | |||||||
\(110\) | −1.79159 | + | 8.10640i | −0.170821 | + | 0.772915i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | − | 14.8006i | − | 1.39232i | −0.717885 | − | 0.696162i | \(-0.754890\pi\) | ||
0.717885 | − | 0.696162i | \(-0.245110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −14.2790 | −1.33152 | ||||||||
\(116\) | −7.80144 | −0.724346 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 6.33137i | − | 0.582850i | ||||||
\(119\) | − | 1.11665i | − | 0.102363i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.97546 | + | 4.63576i | 0.906860 | + | 0.421433i | ||||
\(122\) | 3.93768i | 0.356501i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.60956 | −0.773161 | ||||||||
\(125\) | 9.34733i | 0.836050i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.09732i | 0.0973718i | 0.998814 | + | 0.0486859i | \(0.0155033\pi\) | ||||
−0.998814 | + | 0.0486859i | \(0.984497\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2.67494 | −0.234608 | ||||||||
\(131\) | 13.8373 | 1.20897 | 0.604483 | − | 0.796618i | \(-0.293380\pi\) | ||||
0.604483 | + | 0.796618i | \(0.293380\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.185274 | 0.0160653 | ||||||||
\(134\) | 4.49907 | 0.388661 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.11665 | 0.0957516 | ||||||||
\(137\) | − | 4.53927i | − | 0.387816i | −0.981020 | − | 0.193908i | \(-0.937884\pi\) | ||
0.981020 | − | 0.193908i | \(-0.0621164\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3511i | 1.30206i | 0.759050 | + | 0.651032i | \(0.225664\pi\) | ||||
−0.759050 | + | 0.651032i | \(0.774336\pi\) | |||||||
\(140\) | −2.50315 | −0.211555 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 0.698081i | − | 0.0585816i | ||||||
\(143\) | −0.764851 | + | 3.46073i | −0.0639601 | + | 0.289401i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 19.5282i | − | 1.62173i | ||||||
\(146\) | − | 0.169232i | − | 0.0140058i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.67494 | 0.384278 | ||||||||
\(149\) | 8.97546 | 0.735298 | 0.367649 | − | 0.929965i | \(-0.380163\pi\) | ||||
0.367649 | + | 0.929965i | \(0.380163\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.4441i | 1.58234i | 0.611598 | + | 0.791168i | \(0.290527\pi\) | ||||
−0.611598 | + | 0.791168i | \(0.709473\pi\) | |||||||
\(152\) | 0.185274i | 0.0150277i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.715732 | + | 3.23848i | −0.0576753 | + | 0.260964i | ||||
\(155\) | − | 21.5511i | − | 1.73102i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.21542 | −0.496044 | −0.248022 | − | 0.968754i | \(-0.579781\pi\) | ||||
−0.248022 | + | 0.968754i | \(0.579781\pi\) | |||||||
\(158\) | 1.63002i | 0.129677i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 2.50315i | − | 0.197892i | ||||||
\(161\) | −5.70439 | −0.449569 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.4877 | −1.52640 | −0.763198 | − | 0.646165i | \(-0.776372\pi\) | ||||
−0.763198 | + | 0.646165i | \(0.776372\pi\) | |||||||
\(164\) | 0.132606 | 0.0103548 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.27564 | 0.487084 | ||||||||
\(167\) | −18.1273 | −1.40274 | −0.701368 | − | 0.712799i | \(-0.747427\pi\) | ||||
−0.701368 | + | 0.712799i | \(0.747427\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.8580 | 0.912156 | ||||||||
\(170\) | 2.79514i | 0.214377i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.83979i | − | 0.674027i | ||||||
\(173\) | −10.0672 | −0.765397 | −0.382698 | − | 0.923873i | \(-0.625005\pi\) | ||||
−0.382698 | + | 0.923873i | \(0.625005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.26578i | − | 0.0956840i | ||||||
\(176\) | −3.23848 | − | 0.715732i | −0.244109 | − | 0.0539503i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.2423i | 1.14246i | ||||||||
\(179\) | − | 20.8254i | − | 1.55656i | −0.627916 | − | 0.778281i | \(-0.716092\pi\) | ||
0.627916 | − | 0.778281i | \(-0.283908\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.54233 | 0.188970 | 0.0944851 | − | 0.995526i | \(-0.469880\pi\) | ||||
0.0944851 | + | 0.995526i | \(0.469880\pi\) | |||||||
\(182\) | −1.06863 | −0.0792120 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 5.70439i | − | 0.420533i | ||||||
\(185\) | 11.7021i | 0.860355i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.61623 | + | 0.799219i | 0.264445 | + | 0.0584447i | ||||
\(188\) | − | 5.08738i | − | 0.371035i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.463769 | −0.0336453 | ||||||||
\(191\) | 10.0668i | 0.728406i | 0.931320 | + | 0.364203i | \(0.118659\pi\) | ||||
−0.931320 | + | 0.364203i | \(0.881341\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.9537i | 0.860448i | 0.902722 | + | 0.430224i | \(0.141565\pi\) | ||||
−0.902722 | + | 0.430224i | \(0.858435\pi\) | |||||||
\(194\) | 2.71024 | 0.194584 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −3.02214 | −0.215318 | −0.107659 | − | 0.994188i | \(-0.534336\pi\) | ||||
−0.107659 | + | 0.994188i | \(0.534336\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.2611 | −1.15272 | −0.576359 | − | 0.817197i | \(-0.695527\pi\) | ||||
−0.576359 | + | 0.817197i | \(0.695527\pi\) | |||||||
\(200\) | 1.26578 | 0.0895042 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 10.3811 | 0.730410 | ||||||||
\(203\) | − | 7.80144i | − | 0.547554i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.331934i | 0.0231833i | ||||||||
\(206\) | 17.5234 | 1.22091 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.06863i | − | 0.0740960i | ||||||
\(209\) | −0.132606 | + | 0.600005i | −0.00917257 | + | 0.0415032i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 4.79412i | − | 0.330040i | −0.986290 | − | 0.165020i | \(-0.947231\pi\) | ||
0.986290 | − | 0.165020i | \(-0.0527689\pi\) | |||||||
\(212\) | 0.0980758i | 0.00673587i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.8692 | 0.811364 | ||||||||
\(215\) | 22.1273 | 1.50907 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.60956i | − | 0.584455i | ||||||
\(218\) | − | 8.39312i | − | 0.568454i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.79159 | − | 8.10640i | 0.120789 | − | 0.546534i | ||||
\(221\) | 1.19328i | 0.0802686i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.562049 | 0.0376376 | 0.0188188 | − | 0.999823i | \(-0.494009\pi\) | ||||
0.0188188 | + | 0.999823i | \(0.494009\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 14.8006i | 0.984522i | ||||||||
\(227\) | 4.42647 | 0.293795 | 0.146897 | − | 0.989152i | \(-0.453071\pi\) | ||||
0.146897 | + | 0.989152i | \(0.453071\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.64297 | −0.438980 | −0.219490 | − | 0.975615i | \(-0.570439\pi\) | ||||
−0.219490 | + | 0.975615i | \(0.570439\pi\) | |||||||
\(230\) | 14.2790 | 0.941527 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.80144 | 0.512190 | ||||||||
\(233\) | 7.25486 | 0.475282 | 0.237641 | − | 0.971353i | \(-0.423626\pi\) | ||||
0.237641 | + | 0.971353i | \(0.423626\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7345 | 0.830707 | ||||||||
\(236\) | 6.33137i | 0.412137i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.11665i | 0.0723814i | ||||||||
\(239\) | 20.6125 | 1.33331 | 0.666657 | − | 0.745365i | \(-0.267725\pi\) | ||||
0.666657 | + | 0.745365i | \(0.267725\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.4491i | 1.31724i | 0.752475 | + | 0.658620i | \(0.228860\pi\) | ||||
−0.752475 | + | 0.658620i | \(0.771140\pi\) | |||||||
\(242\) | −9.97546 | − | 4.63576i | −0.641247 | − | 0.297998i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 3.93768i | − | 0.252084i | ||||||
\(245\) | − | 2.50315i | − | 0.159921i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.197989 | −0.0125977 | ||||||||
\(248\) | 8.60956 | 0.546708 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 9.34733i | − | 0.591177i | ||||||
\(251\) | − | 23.7330i | − | 1.49802i | −0.662561 | − | 0.749008i | \(-0.730530\pi\) | ||
0.662561 | − | 0.749008i | \(-0.269470\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.08281 | − | 18.4735i | 0.256684 | − | 1.16142i | ||||
\(254\) | − | 1.09732i | − | 0.0688523i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 20.6457i | 1.28784i | 0.765092 | + | 0.643921i | \(0.222693\pi\) | ||||
−0.765092 | + | 0.643921i | \(0.777307\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.67494i | 0.290487i | ||||||||
\(260\) | 2.67494 | 0.165893 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.8373 | −0.854869 | ||||||||
\(263\) | −0.605313 | −0.0373252 | −0.0186626 | − | 0.999826i | \(-0.505941\pi\) | ||||
−0.0186626 | + | 0.999826i | \(0.505941\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.245499 | −0.0150809 | ||||||||
\(266\) | −0.185274 | −0.0113599 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −4.49907 | −0.274825 | ||||||||
\(269\) | 21.8291i | 1.33094i | 0.746423 | + | 0.665472i | \(0.231770\pi\) | ||||
−0.746423 | + | 0.665472i | \(0.768230\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 4.52103i | − | 0.274633i | −0.990527 | − | 0.137316i | \(-0.956152\pi\) | ||
0.990527 | − | 0.137316i | \(-0.0438477\pi\) | |||||||
\(272\) | −1.11665 | −0.0677066 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.53927i | 0.274227i | ||||||||
\(275\) | 4.09920 | + | 0.905959i | 0.247191 | + | 0.0546314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 6.25586i | − | 0.375878i | −0.982181 | − | 0.187939i | \(-0.939819\pi\) | ||
0.982181 | − | 0.187939i | \(-0.0601808\pi\) | |||||||
\(278\) | − | 15.3511i | − | 0.920698i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.50315 | 0.149592 | ||||||||
\(281\) | 31.9977 | 1.90882 | 0.954412 | − | 0.298493i | \(-0.0964838\pi\) | ||||
0.954412 | + | 0.298493i | \(0.0964838\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.2203i | 1.38031i | 0.723663 | + | 0.690153i | \(0.242457\pi\) | ||||
−0.723663 | + | 0.690153i | \(0.757543\pi\) | |||||||
\(284\) | 0.698081i | 0.0414235i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.764851 | − | 3.46073i | 0.0452266 | − | 0.204637i | ||||
\(287\) | 0.132606i | 0.00782751i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.7531 | −0.926653 | ||||||||
\(290\) | 19.5282i | 1.14674i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.169232i | 0.00990357i | ||||||||
\(293\) | 3.48219 | 0.203432 | 0.101716 | − | 0.994813i | \(-0.467567\pi\) | ||||
0.101716 | + | 0.994813i | \(0.467567\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.8484 | −0.922729 | ||||||||
\(296\) | −4.67494 | −0.271725 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.97546 | −0.519934 | ||||||||
\(299\) | 6.09587 | 0.352533 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.83979 | 0.509517 | ||||||||
\(302\) | − | 19.4441i | − | 1.11888i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 0.185274i | − | 0.0106262i | ||||||
\(305\) | 9.85662 | 0.564388 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.61453i | 0.548730i | 0.961626 | + | 0.274365i | \(0.0884677\pi\) | ||||
−0.961626 | + | 0.274365i | \(0.911532\pi\) | |||||||
\(308\) | 0.715732 | − | 3.23848i | 0.0407826 | − | 0.184529i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 21.5511i | 1.22402i | ||||||||
\(311\) | 19.7571i | 1.12032i | 0.828383 | + | 0.560162i | \(0.189261\pi\) | ||||
−0.828383 | + | 0.560162i | \(0.810739\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0067 | 0.791703 | 0.395851 | − | 0.918315i | \(-0.370450\pi\) | ||||
0.395851 | + | 0.918315i | \(0.370450\pi\) | |||||||
\(314\) | 6.21542 | 0.350756 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 1.63002i | − | 0.0916958i | ||||||
\(317\) | − | 7.26821i | − | 0.408223i | −0.978948 | − | 0.204112i | \(-0.934569\pi\) | ||
0.978948 | − | 0.204112i | \(-0.0654305\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.2648 | + | 5.58374i | 1.41456 | + | 0.312629i | ||||
\(320\) | 2.50315i | 0.139931i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.70439 | 0.317893 | ||||||||
\(323\) | 0.206885i | 0.0115114i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.35265i | 0.0750314i | ||||||||
\(326\) | 19.4877 | 1.07932 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.132606 | −0.00732196 | ||||||||
\(329\) | 5.08738 | 0.280476 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.6086 | −0.747994 | −0.373997 | − | 0.927430i | \(-0.622013\pi\) | ||||
−0.373997 | + | 0.927430i | \(0.622013\pi\) | |||||||
\(332\) | −6.27564 | −0.344420 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 18.1273 | 0.991884 | ||||||||
\(335\) | − | 11.2619i | − | 0.615302i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 2.85239i | − | 0.155380i | −0.996978 | − | 0.0776899i | \(-0.975246\pi\) | ||
0.996978 | − | 0.0776899i | \(-0.0247544\pi\) | |||||||
\(338\) | −11.8580 | −0.644992 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 2.79514i | − | 0.151588i | ||||||
\(341\) | 27.8819 | + | 6.16213i | 1.50989 | + | 0.333698i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 8.83979i | 0.476609i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.0672 | 0.541217 | ||||||||
\(347\) | 7.05827 | 0.378908 | 0.189454 | − | 0.981890i | \(-0.439328\pi\) | ||||
0.189454 | + | 0.981890i | \(0.439328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.87266i | 0.314356i | 0.987570 | + | 0.157178i | \(0.0502397\pi\) | ||||
−0.987570 | + | 0.157178i | \(0.949760\pi\) | |||||||
\(350\) | 1.26578i | 0.0676588i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.23848 | + | 0.715732i | 0.172611 | + | 0.0381486i | ||||
\(353\) | 20.5326i | 1.09284i | 0.837512 | + | 0.546420i | \(0.184010\pi\) | ||||
−0.837512 | + | 0.546420i | \(0.815990\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.74740 | −0.0927425 | ||||||||
\(356\) | − | 15.2423i | − | 0.807838i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 20.8254i | 1.10066i | ||||||||
\(359\) | 9.66516 | 0.510108 | 0.255054 | − | 0.966927i | \(-0.417907\pi\) | ||||
0.255054 | + | 0.966927i | \(0.417907\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9657 | 0.998193 | ||||||||
\(362\) | −2.54233 | −0.133622 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.06863 | 0.0560113 | ||||||||
\(365\) | −0.423615 | −0.0221730 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5991 | 1.33626 | 0.668132 | − | 0.744043i | \(-0.267094\pi\) | ||||
0.668132 | + | 0.744043i | \(0.267094\pi\) | |||||||
\(368\) | 5.70439i | 0.297362i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 11.7021i | − | 0.608363i | ||||||
\(371\) | −0.0980758 | −0.00509184 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.9547i | 1.55100i | 0.631350 | + | 0.775498i | \(0.282501\pi\) | ||||
−0.631350 | + | 0.775498i | \(0.717499\pi\) | |||||||
\(374\) | −3.61623 | − | 0.799219i | −0.186991 | − | 0.0413266i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.08738i | 0.262362i | ||||||||
\(377\) | 8.33684i | 0.429369i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.34578 | 0.223228 | 0.111614 | − | 0.993752i | \(-0.464398\pi\) | ||||
0.111614 | + | 0.993752i | \(0.464398\pi\) | |||||||
\(380\) | 0.463769 | 0.0237908 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 10.0668i | − | 0.515061i | ||||||
\(383\) | 15.6402i | 0.799179i | 0.916694 | + | 0.399589i | \(0.130847\pi\) | ||||
−0.916694 | + | 0.399589i | \(0.869153\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.10640 | + | 1.79159i | 0.413141 | + | 0.0913077i | ||||
\(386\) | − | 11.9537i | − | 0.608428i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.71024 | −0.137592 | ||||||||
\(389\) | − | 25.6591i | − | 1.30097i | −0.759519 | − | 0.650485i | \(-0.774566\pi\) | ||
0.759519 | − | 0.650485i | \(-0.225434\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.36978i | − | 0.322134i | ||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.02214 | 0.152253 | ||||||||
\(395\) | 4.08019 | 0.205297 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.3197 | −1.32095 | −0.660475 | − | 0.750848i | \(-0.729645\pi\) | ||||
−0.660475 | + | 0.750848i | \(0.729645\pi\) | |||||||
\(398\) | 16.2611 | 0.815095 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.26578 | −0.0632890 | ||||||||
\(401\) | 25.8351i | 1.29014i | 0.764122 | + | 0.645072i | \(0.223173\pi\) | ||||
−0.764122 | + | 0.645072i | \(0.776827\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.20042i | 0.458305i | ||||||||
\(404\) | −10.3811 | −0.516478 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.80144i | 0.387179i | ||||||||
\(407\) | −15.1397 | − | 3.34600i | −0.750446 | − | 0.165855i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 5.55129i | − | 0.274494i | −0.990537 | − | 0.137247i | \(-0.956175\pi\) | ||
0.990537 | − | 0.137247i | \(-0.0438254\pi\) | |||||||
\(410\) | − | 0.331934i | − | 0.0163931i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −17.5234 | −0.863316 | ||||||||
\(413\) | −6.33137 | −0.311546 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.7089i | − | 0.771119i | ||||||
\(416\) | 1.06863i | 0.0523938i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.132606 | − | 0.600005i | 0.00648599 | − | 0.0293472i | ||||
\(419\) | − | 25.8709i | − | 1.26388i | −0.775019 | − | 0.631938i | \(-0.782260\pi\) | ||
0.775019 | − | 0.631938i | \(-0.217740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.6798 | 1.59271 | 0.796357 | − | 0.604827i | \(-0.206758\pi\) | ||||
0.796357 | + | 0.604827i | \(0.206758\pi\) | |||||||
\(422\) | 4.79412i | 0.233374i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 0.0980758i | − | 0.00476298i | ||||||
\(425\) | 1.41343 | 0.0685613 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.93768 | 0.190558 | ||||||||
\(428\) | −11.8692 | −0.573721 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.1273 | −1.06708 | ||||||||
\(431\) | −33.2571 | −1.60194 | −0.800970 | − | 0.598705i | \(-0.795682\pi\) | ||||
−0.800970 | + | 0.598705i | \(0.795682\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.8532 | 1.81911 | 0.909554 | − | 0.415585i | \(-0.136423\pi\) | ||||
0.909554 | + | 0.415585i | \(0.136423\pi\) | |||||||
\(434\) | 8.60956i | 0.413272i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.39312i | 0.401958i | ||||||||
\(437\) | 1.05687 | 0.0505571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.8480i | 1.37684i | 0.725313 | + | 0.688419i | \(0.241695\pi\) | ||||
−0.725313 | + | 0.688419i | \(0.758305\pi\) | |||||||
\(440\) | −1.79159 | + | 8.10640i | −0.0854105 | + | 0.386458i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 1.19328i | − | 0.0567585i | ||||||
\(443\) | − | 8.29505i | − | 0.394110i | −0.980392 | − | 0.197055i | \(-0.936862\pi\) | ||
0.980392 | − | 0.197055i | \(-0.0631377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 38.1537 | 1.80866 | ||||||||
\(446\) | −0.562049 | −0.0266138 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | − | 14.7839i | − | 0.697698i | −0.937179 | − | 0.348849i | \(-0.886573\pi\) | ||
0.937179 | − | 0.348849i | \(-0.113427\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.429443 | − | 0.0949106i | −0.0202217 | − | 0.00446916i | ||||
\(452\) | − | 14.8006i | − | 0.696162i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.42647 | −0.207744 | ||||||||
\(455\) | 2.67494i | 0.125403i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.70169i | 0.173158i | 0.996245 | + | 0.0865789i | \(0.0275935\pi\) | ||||
−0.996245 | + | 0.0865789i | \(0.972407\pi\) | |||||||
\(458\) | 6.64297 | 0.310405 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −14.2790 | −0.665760 | ||||||||
\(461\) | 22.9799 | 1.07028 | 0.535140 | − | 0.844764i | \(-0.320259\pi\) | ||||
0.535140 | + | 0.844764i | \(0.320259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.2666 | −0.616552 | −0.308276 | − | 0.951297i | \(-0.599752\pi\) | ||||
−0.308276 | + | 0.951297i | \(0.599752\pi\) | |||||||
\(464\) | −7.80144 | −0.362173 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.25486 | −0.336075 | ||||||||
\(467\) | − | 3.25013i | − | 0.150398i | −0.997169 | − | 0.0751991i | \(-0.976041\pi\) | ||
0.997169 | − | 0.0751991i | \(-0.0239592\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 4.49907i | − | 0.207748i | ||||||
\(470\) | −12.7345 | −0.587399 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 6.33137i | − | 0.291425i | ||||||
\(473\) | −6.32692 | + | 28.6274i | −0.290912 | + | 1.31629i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.234516i | 0.0107603i | ||||||||
\(476\) | − | 1.11665i | − | 0.0511814i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.6125 | −0.942795 | ||||||||
\(479\) | 30.7002 | 1.40273 | 0.701363 | − | 0.712804i | \(-0.252575\pi\) | ||||
0.701363 | + | 0.712804i | \(0.252575\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.99577i | − | 0.227788i | ||||||
\(482\) | − | 20.4491i | − | 0.931430i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.97546 | + | 4.63576i | 0.453430 | + | 0.210716i | ||||
\(485\) | − | 6.78416i | − | 0.308053i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.4008 | −0.561934 | −0.280967 | − | 0.959717i | \(-0.590655\pi\) | ||||
−0.280967 | + | 0.959717i | \(0.590655\pi\) | |||||||
\(488\) | 3.93768i | 0.178250i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.50315i | 0.113081i | ||||||||
\(491\) | −40.0902 | −1.80925 | −0.904623 | − | 0.426213i | \(-0.859847\pi\) | ||||
−0.904623 | + | 0.426213i | \(0.859847\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.71145 | 0.392344 | ||||||||
\(494\) | 0.197989 | 0.00890794 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.60956 | −0.386581 | ||||||||
\(497\) | −0.698081 | −0.0313132 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.2350 | −1.04014 | −0.520070 | − | 0.854123i | \(-0.674094\pi\) | ||||
−0.520070 | + | 0.854123i | \(0.674094\pi\) | |||||||
\(500\) | 9.34733i | 0.418025i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 23.7330i | 1.05926i | ||||||||
\(503\) | −28.0211 | −1.24940 | −0.624701 | − | 0.780864i | \(-0.714779\pi\) | ||||
−0.624701 | + | 0.780864i | \(0.714779\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 25.9854i | − | 1.15634i | ||||||
\(506\) | −4.08281 | + | 18.4735i | −0.181503 | + | 0.821248i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.09732i | 0.0486859i | ||||||||
\(509\) | 29.5301i | 1.30890i | 0.756107 | + | 0.654448i | \(0.227099\pi\) | ||||
−0.756107 | + | 0.654448i | \(0.772901\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.169232 | −0.00748640 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 20.6457i | − | 0.910642i | ||||||
\(515\) | − | 43.8638i | − | 1.93287i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.64120 | + | 16.4754i | −0.160140 | + | 0.724586i | ||||
\(518\) | − | 4.67494i | − | 0.205405i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.67494 | −0.117304 | ||||||||
\(521\) | 30.2772i | 1.32647i | 0.748412 | + | 0.663234i | \(0.230817\pi\) | ||||
−0.748412 | + | 0.663234i | \(0.769183\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.4615i | − | 1.81299i | −0.422221 | − | 0.906493i | \(-0.638749\pi\) | ||
0.422221 | − | 0.906493i | \(-0.361251\pi\) | |||||||
\(524\) | 13.8373 | 0.604483 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.605313 | 0.0263929 | ||||||||
\(527\) | 9.61383 | 0.418785 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.54005 | −0.414785 | ||||||||
\(530\) | 0.245499 | 0.0106638 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.185274 | 0.00803264 | ||||||||
\(533\) | − | 0.141707i | − | 0.00613801i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 29.7105i | − | 1.28450i | ||||||
\(536\) | 4.49907 | 0.194330 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 21.8291i | − | 0.941119i | ||||||
\(539\) | 3.23848 | + | 0.715732i | 0.139491 | + | 0.0308287i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.2080i | − | 0.567855i | −0.958846 | − | 0.283927i | \(-0.908363\pi\) | ||
0.958846 | − | 0.283927i | \(-0.0916375\pi\) | |||||||
\(542\) | 4.52103i | 0.194195i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.11665 | 0.0478758 | ||||||||
\(545\) | −21.0093 | −0.899938 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4642i | 1.04601i | 0.852328 | + | 0.523007i | \(0.175190\pi\) | ||||
−0.852328 | + | 0.523007i | \(0.824810\pi\) | |||||||
\(548\) | − | 4.53927i | − | 0.193908i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.09920 | − | 0.905959i | −0.174790 | − | 0.0386302i | ||||
\(551\) | 1.44540i | 0.0615763i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.63002 | 0.0693155 | ||||||||
\(554\) | 6.25586i | 0.265786i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.3511i | 0.651032i | ||||||||
\(557\) | −38.1747 | −1.61751 | −0.808757 | − | 0.588143i | \(-0.799859\pi\) | ||||
−0.808757 | + | 0.588143i | \(0.799859\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.44645 | −0.399542 | ||||||||
\(560\) | −2.50315 | −0.105778 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −31.9977 | −1.34974 | ||||||||
\(563\) | −5.14634 | −0.216892 | −0.108446 | − | 0.994102i | \(-0.534587\pi\) | ||||
−0.108446 | + | 0.994102i | \(0.534587\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 37.0482 | 1.55863 | ||||||||
\(566\) | − | 23.2203i | − | 0.976024i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 0.698081i | − | 0.0292908i | ||||||
\(569\) | 12.4086 | 0.520195 | 0.260098 | − | 0.965582i | \(-0.416245\pi\) | ||||
0.260098 | + | 0.965582i | \(0.416245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 31.2262i | − | 1.30678i | −0.757023 | − | 0.653388i | \(-0.773347\pi\) | ||
0.757023 | − | 0.653388i | \(-0.226653\pi\) | |||||||
\(572\) | −0.764851 | + | 3.46073i | −0.0319800 | + | 0.144700i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 0.132606i | − | 0.00553488i | ||||||
\(575\) | − | 7.22050i | − | 0.301116i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −24.6322 | −1.02545 | −0.512727 | − | 0.858552i | \(-0.671365\pi\) | ||||
−0.512727 | + | 0.858552i | \(0.671365\pi\) | |||||||
\(578\) | 15.7531 | 0.655243 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 19.5282i | − | 0.810865i | ||||||
\(581\) | − | 6.27564i | − | 0.260357i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.0701959 | − | 0.317616i | 0.00290722 | − | 0.0131543i | ||||
\(584\) | − | 0.169232i | − | 0.00700288i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3.48219 | −0.143848 | ||||||||
\(587\) | − | 8.06347i | − | 0.332815i | −0.986057 | − | 0.166407i | \(-0.946783\pi\) | ||
0.986057 | − | 0.166407i | \(-0.0532167\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.59513i | 0.0657260i | ||||||||
\(590\) | 15.8484 | 0.652468 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.67494 | 0.192139 | ||||||||
\(593\) | 10.5472 | 0.433120 | 0.216560 | − | 0.976269i | \(-0.430516\pi\) | ||||
0.216560 | + | 0.976269i | \(0.430516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.79514 | 0.114589 | ||||||||
\(596\) | 8.97546 | 0.367649 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.09587 | −0.249279 | ||||||||
\(599\) | 21.5467i | 0.880372i | 0.897907 | + | 0.440186i | \(0.145088\pi\) | ||||
−0.897907 | + | 0.440186i | \(0.854912\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2592i | 1.03035i | 0.857086 | + | 0.515173i | \(0.172272\pi\) | ||||
−0.857086 | + | 0.515173i | \(0.827728\pi\) | |||||||
\(602\) | −8.83979 | −0.360283 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 19.4441i | 0.791168i | ||||||||
\(605\) | −11.6040 | + | 24.9701i | −0.471771 | + | 1.01518i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 9.79879i | − | 0.397721i | −0.980028 | − | 0.198860i | \(-0.936276\pi\) | ||
0.980028 | − | 0.198860i | \(-0.0637240\pi\) | |||||||
\(608\) | 0.185274i | 0.00751385i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.85662 | −0.399083 | ||||||||
\(611\) | −5.43652 | −0.219938 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 43.9777i | − | 1.77624i | −0.459610 | − | 0.888121i | \(-0.652011\pi\) | ||
0.459610 | − | 0.888121i | \(-0.347989\pi\) | |||||||
\(614\) | − | 9.61453i | − | 0.388011i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.715732 | + | 3.23848i | −0.0288377 | + | 0.130482i | ||||
\(617\) | − | 4.41152i | − | 0.177601i | −0.996049 | − | 0.0888005i | \(-0.971697\pi\) | ||
0.996049 | − | 0.0888005i | \(-0.0283034\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.6155 | −1.35112 | −0.675561 | − | 0.737304i | \(-0.736098\pi\) | ||||
−0.675561 | + | 0.737304i | \(0.736098\pi\) | |||||||
\(620\) | − | 21.5511i | − | 0.865511i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 19.7571i | − | 0.792188i | ||||||
\(623\) | 15.2423 | 0.610668 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.7267 | −1.18907 | ||||||||
\(626\) | −14.0067 | −0.559819 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.21542 | −0.248022 | ||||||||
\(629\) | −5.22025 | −0.208145 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.0266 | 1.31477 | 0.657385 | − | 0.753555i | \(-0.271663\pi\) | ||||
0.657385 | + | 0.753555i | \(0.271663\pi\) | |||||||
\(632\) | 1.63002i | 0.0648387i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 7.26821i | 0.288657i | ||||||||
\(635\) | −2.74677 | −0.109002 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.06863i | 0.0423406i | ||||||||
\(638\) | −25.2648 | − | 5.58374i | −1.00024 | − | 0.221062i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 2.50315i | − | 0.0989459i | ||||||
\(641\) | 2.69865i | 0.106590i | 0.998579 | + | 0.0532951i | \(0.0169724\pi\) | ||||
−0.998579 | + | 0.0532951i | \(0.983028\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.6860 | 1.64394 | 0.821968 | − | 0.569534i | \(-0.192876\pi\) | ||||
0.821968 | + | 0.569534i | \(0.192876\pi\) | |||||||
\(644\) | −5.70439 | −0.224784 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 0.206885i | − | 0.00813979i | ||||||
\(647\) | 3.68211i | 0.144759i | 0.997377 | + | 0.0723793i | \(0.0230592\pi\) | ||||
−0.997377 | + | 0.0723793i | \(0.976941\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.53156 | − | 20.5040i | 0.177879 | − | 0.804852i | ||||
\(650\) | − | 1.35265i | − | 0.0530552i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −19.4877 | −0.763198 | ||||||||
\(653\) | 30.4080i | 1.18996i | 0.803742 | + | 0.594978i | \(0.202839\pi\) | ||||
−0.803742 | + | 0.594978i | \(0.797161\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 34.6368i | 1.35337i | ||||||||
\(656\) | 0.132606 | 0.00517741 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.08738 | −0.198327 | ||||||||
\(659\) | −18.6322 | −0.725809 | −0.362905 | − | 0.931826i | \(-0.618215\pi\) | ||||
−0.362905 | + | 0.931826i | \(0.618215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7097 | −0.649934 | −0.324967 | − | 0.945725i | \(-0.605353\pi\) | ||||
−0.324967 | + | 0.945725i | \(0.605353\pi\) | |||||||
\(662\) | 13.6086 | 0.528912 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.27564 | 0.243542 | ||||||||
\(665\) | 0.463769i | 0.0179842i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 44.5025i | − | 1.72314i | ||||||
\(668\) | −18.1273 | −0.701368 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11.2619i | 0.435084i | ||||||||
\(671\) | −2.81832 | + | 12.7521i | −0.108800 | + | 0.492289i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 39.0503i | − | 1.50528i | −0.658433 | − | 0.752639i | \(-0.728780\pi\) | ||
0.658433 | − | 0.752639i | \(-0.271220\pi\) | |||||||
\(674\) | 2.85239i | 0.109870i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.8580 | 0.456078 | ||||||||
\(677\) | −24.9257 | −0.957971 | −0.478986 | − | 0.877823i | \(-0.658995\pi\) | ||||
−0.478986 | + | 0.877823i | \(0.658995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 2.71024i | − | 0.104010i | ||||||
\(680\) | 2.79514i | 0.107189i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.8819 | − | 6.16213i | −1.06765 | − | 0.235960i | ||||
\(683\) | − | 23.5527i | − | 0.901220i | −0.892721 | − | 0.450610i | \(-0.851207\pi\) | ||
0.892721 | − | 0.450610i | \(-0.148793\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.3625 | 0.434139 | ||||||||
\(686\) | 1.00000i | 0.0381802i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 8.83979i | − | 0.337014i | ||||||
\(689\) | 0.104807 | 0.00399281 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.5706 | −0.516248 | −0.258124 | − | 0.966112i | \(-0.583104\pi\) | ||||
−0.258124 | + | 0.966112i | \(0.583104\pi\) | |||||||
\(692\) | −10.0672 | −0.382698 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.05827 | −0.267928 | ||||||||
\(695\) | −38.4262 | −1.45759 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.148074 | −0.00560871 | ||||||||
\(698\) | − | 5.87266i | − | 0.222283i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | − | 1.26578i | − | 0.0478420i | ||||||
\(701\) | 32.7927 | 1.23856 | 0.619281 | − | 0.785170i | \(-0.287424\pi\) | ||||
0.619281 | + | 0.785170i | \(0.287424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.866144i | − | 0.0326673i | ||||||
\(704\) | −3.23848 | − | 0.715732i | −0.122055 | − | 0.0269752i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 20.5326i | − | 0.772754i | ||||||
\(707\) | − | 10.3811i | − | 0.390421i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35.7358 | 1.34209 | 0.671043 | − | 0.741419i | \(-0.265847\pi\) | ||||
0.671043 | + | 0.741419i | \(0.265847\pi\) | |||||||
\(710\) | 1.74740 | 0.0655789 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.2423i | 0.571228i | ||||||||
\(713\) | − | 49.1123i | − | 1.83927i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8.66273 | − | 1.91454i | −0.323968 | − | 0.0715997i | ||||
\(716\) | − | 20.8254i | − | 0.778281i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.66516 | −0.360701 | ||||||||
\(719\) | − | 10.2851i | − | 0.383571i | −0.981437 | − | 0.191785i | \(-0.938572\pi\) | ||
0.981437 | − | 0.191785i | \(-0.0614278\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 17.5234i | − | 0.652606i | ||||||
\(722\) | −18.9657 | −0.705829 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.54233 | 0.0944851 | ||||||||
\(725\) | 9.87491 | 0.366745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −27.1407 | −1.00659 | −0.503296 | − | 0.864114i | \(-0.667879\pi\) | ||||
−0.503296 | + | 0.864114i | \(0.667879\pi\) | |||||||
\(728\) | −1.06863 | −0.0396060 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.423615 | 0.0156787 | ||||||||
\(731\) | 9.87091i | 0.365089i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.5878i | 1.42527i | 0.701533 | + | 0.712637i | \(0.252499\pi\) | ||||
−0.701533 | + | 0.712637i | \(0.747501\pi\) | |||||||
\(734\) | −25.5991 | −0.944881 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.70439i | − | 0.210267i | ||||||
\(737\) | 14.5701 | + | 3.22013i | 0.536698 | + | 0.118615i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.7365i | 0.836377i | 0.908360 | + | 0.418188i | \(0.137335\pi\) | ||||
−0.908360 | + | 0.418188i | \(0.862665\pi\) | |||||||
\(740\) | 11.7021i | 0.430178i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.0980758 | 0.00360047 | ||||||||
\(743\) | 34.6798 | 1.27228 | 0.636138 | − | 0.771575i | \(-0.280531\pi\) | ||||
0.636138 | + | 0.771575i | \(0.280531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.4669i | 0.823125i | ||||||||
\(746\) | − | 29.9547i | − | 1.09672i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.61623 | + | 0.799219i | 0.132222 | + | 0.0292223i | ||||
\(749\) | − | 11.8692i | − | 0.433692i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8291 | −0.395160 | −0.197580 | − | 0.980287i | \(-0.563308\pi\) | ||||
−0.197580 | + | 0.980287i | \(0.563308\pi\) | |||||||
\(752\) | − | 5.08738i | − | 0.185518i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 8.33684i | − | 0.303610i | ||||||
\(755\) | −48.6715 | −1.77134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.4465 | −0.961213 | −0.480607 | − | 0.876936i | \(-0.659583\pi\) | ||||
−0.480607 | + | 0.876936i | \(0.659583\pi\) | |||||||
\(758\) | −4.34578 | −0.157846 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.463769 | −0.0168227 | ||||||||
\(761\) | −34.7276 | −1.25887 | −0.629437 | − | 0.777052i | \(-0.716714\pi\) | ||||
−0.629437 | + | 0.777052i | \(0.716714\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.39312 | −0.303851 | ||||||||
\(764\) | 10.0668i | 0.364203i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 15.6402i | − | 0.565105i | ||||||
\(767\) | 6.76588 | 0.244302 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.7806i | 0.965734i | 0.875694 | + | 0.482867i | \(0.160405\pi\) | ||||
−0.875694 | + | 0.482867i | \(0.839595\pi\) | |||||||
\(770\) | −8.10640 | − | 1.79159i | −0.292135 | − | 0.0645643i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 11.9537i | 0.430224i | ||||||||
\(773\) | 39.2042i | 1.41008i | 0.709169 | + | 0.705039i | \(0.249070\pi\) | ||||
−0.709169 | + | 0.705039i | \(0.750930\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8978 | 0.391461 | ||||||||
\(776\) | 2.71024 | 0.0972921 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.6591i | 0.919925i | ||||||||
\(779\) | − | 0.0245685i | − | 0.000880257i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.499638 | − | 2.26072i | 0.0178785 | − | 0.0808948i | ||||
\(782\) | 6.36978i | 0.227783i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | − | 15.5581i | − | 0.555294i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.2615i | 0.615308i | 0.951498 | + | 0.307654i | \(0.0995439\pi\) | ||||
−0.951498 | + | 0.307654i | \(0.900456\pi\) | |||||||
\(788\) | −3.02214 | −0.107659 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.08019 | −0.145167 | ||||||||
\(791\) | 14.8006 | 0.526249 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.20792 | −0.149427 | ||||||||
\(794\) | 26.3197 | 0.934052 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.2611 | −0.576359 | ||||||||
\(797\) | 2.24242i | 0.0794305i | 0.999211 | + | 0.0397153i | \(0.0126451\pi\) | ||||
−0.999211 | + | 0.0397153i | \(0.987355\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.68080i | 0.200972i | ||||||||
\(800\) | 1.26578 | 0.0447521 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 25.8351i | − | 0.912270i | ||||||
\(803\) | 0.121125 | − | 0.548055i | 0.00427441 | − | 0.0193404i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 14.2790i | − | 0.503267i | ||||||
\(806\) | − | 9.20042i | − | 0.324071i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 10.3811 | 0.365205 | ||||||||
\(809\) | −34.3573 | −1.20794 | −0.603968 | − | 0.797008i | \(-0.706415\pi\) | ||||
−0.603968 | + | 0.797008i | \(0.706415\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8512i | 0.591725i | 0.955231 | + | 0.295862i | \(0.0956069\pi\) | ||||
−0.955231 | + | 0.295862i | \(0.904393\pi\) | |||||||
\(812\) | − | 7.80144i | − | 0.273777i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.1397 | + | 3.34600i | 0.530646 | + | 0.117277i | ||||
\(815\) | − | 48.7807i | − | 1.70871i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.63778 | −0.0572987 | ||||||||
\(818\) | 5.55129i | 0.194096i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.331934i | 0.0115916i | ||||||||
\(821\) | 30.1344 | 1.05170 | 0.525850 | − | 0.850577i | \(-0.323747\pi\) | ||||
0.525850 | + | 0.850577i | \(0.323747\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 30.2285 | 1.05370 | 0.526849 | − | 0.849959i | \(-0.323373\pi\) | ||||
0.526849 | + | 0.849959i | \(0.323373\pi\) | |||||||
\(824\) | 17.5234 | 0.610457 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.33137 | 0.220296 | ||||||||
\(827\) | −20.0319 | −0.696577 | −0.348288 | − | 0.937387i | \(-0.613237\pi\) | ||||
−0.348288 | + | 0.937387i | \(0.613237\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.420503 | 0.0146047 | 0.00730234 | − | 0.999973i | \(-0.497676\pi\) | ||||
0.00730234 | + | 0.999973i | \(0.497676\pi\) | |||||||
\(830\) | 15.7089i | 0.545263i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 1.06863i | − | 0.0370480i | ||||||
\(833\) | 1.11665 | 0.0386895 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 45.3755i | − | 1.57029i | ||||||
\(836\) | −0.132606 | + | 0.600005i | −0.00458629 | + | 0.0207516i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.8709i | 0.893696i | ||||||||
\(839\) | 49.3044i | 1.70218i | 0.525023 | + | 0.851088i | \(0.324057\pi\) | ||||
−0.525023 | + | 0.851088i | \(0.675943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.8625 | 1.09871 | ||||||||
\(842\) | −32.6798 | −1.12622 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 4.79412i | − | 0.165020i | ||||||
\(845\) | 29.6825i | 1.02111i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.63576 | + | 9.97546i | −0.159287 | + | 0.342761i | ||||
\(848\) | 0.0980758i | 0.00336794i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.41343 | −0.0484802 | ||||||||
\(851\) | 26.6677i | 0.914156i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.3388i | 1.17574i | 0.808956 | + | 0.587870i | \(0.200033\pi\) | ||||
−0.808956 | + | 0.587870i | \(0.799967\pi\) | |||||||
\(854\) | −3.93768 | −0.134745 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11.8692 | 0.405682 | ||||||||
\(857\) | −52.2385 | −1.78443 | −0.892216 | − | 0.451609i | \(-0.850850\pi\) | ||||
−0.892216 | + | 0.451609i | \(0.850850\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −51.7082 | −1.76426 | −0.882131 | − | 0.471004i | \(-0.843892\pi\) | ||||
−0.882131 | + | 0.471004i | \(0.843892\pi\) | |||||||
\(860\) | 22.1273 | 0.754536 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.2571 | 1.13274 | ||||||||
\(863\) | 37.3394i | 1.27105i | 0.772082 | + | 0.635523i | \(0.219216\pi\) | ||||
−0.772082 | + | 0.635523i | \(0.780784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 25.1998i | − | 0.856819i | ||||||
\(866\) | −37.8532 | −1.28630 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 8.60956i | − | 0.292227i | ||||||
\(869\) | −1.16666 | + | 5.27878i | −0.0395761 | + | 0.179070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.80783i | 0.162907i | ||||||||
\(872\) | − | 8.39312i | − | 0.284227i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.05687 | −0.0357493 | ||||||||
\(875\) | −9.34733 | −0.315997 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 26.8942i | − | 0.908152i | −0.890963 | − | 0.454076i | \(-0.849969\pi\) | ||
0.890963 | − | 0.454076i | \(-0.150031\pi\) | |||||||
\(878\) | − | 28.8480i | − | 0.973572i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.79159 | − | 8.10640i | 0.0603944 | − | 0.273267i | ||||
\(881\) | 48.7635i | 1.64288i | 0.570292 | + | 0.821442i | \(0.306830\pi\) | ||||
−0.570292 | + | 0.821442i | \(0.693170\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.1578 | 0.341838 | 0.170919 | − | 0.985285i | \(-0.445326\pi\) | ||||
0.170919 | + | 0.985285i | \(0.445326\pi\) | |||||||
\(884\) | 1.19328i | 0.0401343i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.29505i | 0.278678i | ||||||||
\(887\) | −42.3535 | −1.42209 | −0.711046 | − | 0.703145i | \(-0.751778\pi\) | ||||
−0.711046 | + | 0.703145i | \(0.751778\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.09732 | −0.0368031 | ||||||||
\(890\) | −38.1537 | −1.27892 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.562049 | 0.0188188 | ||||||||
\(893\) | −0.942559 | −0.0315415 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 52.1291 | 1.74248 | ||||||||
\(896\) | − | 1.00000i | − | 0.0334077i | ||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 14.7839i | 0.493347i | ||||||||
\(899\) | 67.1670 | 2.24014 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.109516i | − | 0.00364850i | ||||||
\(902\) | 0.429443 | + | 0.0949106i | 0.0142989 | + | 0.00316018i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 14.8006i | 0.492261i | ||||||||
\(905\) | 6.36386i | 0.211542i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.5243 | −0.814316 | −0.407158 | − | 0.913358i | \(-0.633480\pi\) | ||||
−0.407158 | + | 0.913358i | \(0.633480\pi\) | |||||||
\(908\) | 4.42647 | 0.146897 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − | 2.67494i | − | 0.0886734i | ||||||
\(911\) | 9.61511i | 0.318563i | 0.987233 | + | 0.159281i | \(0.0509177\pi\) | ||||
−0.987233 | + | 0.159281i | \(0.949082\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.3235 | + | 4.49167i | 0.672610 | + | 0.148653i | ||||
\(914\) | − | 3.70169i | − | 0.122441i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.64297 | −0.219490 | ||||||||
\(917\) | 13.8373i | 0.456947i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.8699i | − | 0.820381i | −0.912000 | − | 0.410191i | \(-0.865462\pi\) | ||
0.912000 | − | 0.410191i | \(-0.134538\pi\) | |||||||
\(920\) | 14.2790 | 0.470763 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −22.9799 | −0.756802 | ||||||||
\(923\) | 0.745989 | 0.0245545 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.91745 | −0.194564 | ||||||||
\(926\) | 13.2666 | 0.435968 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 7.80144 | 0.256095 | ||||||||
\(929\) | − | 3.89344i | − | 0.127740i | −0.997958 | − | 0.0638698i | \(-0.979656\pi\) | ||
0.997958 | − | 0.0638698i | \(-0.0203443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.185274i | 0.00607210i | ||||||||
\(932\) | 7.25486 | 0.237641 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.25013i | 0.106348i | ||||||||
\(935\) | −2.00057 | + | 9.05198i | −0.0654255 | + | 0.296031i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 39.8350i | − | 1.30135i | −0.759355 | − | 0.650676i | \(-0.774486\pi\) | ||
0.759355 | − | 0.650676i | \(-0.225514\pi\) | |||||||
\(938\) | 4.49907i | 0.146900i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.7345 | 0.415354 | ||||||||
\(941\) | −19.7807 | −0.644833 | −0.322417 | − | 0.946598i | \(-0.604495\pi\) | ||||
−0.322417 | + | 0.946598i | \(0.604495\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.756438i | 0.0246330i | ||||||||
\(944\) | 6.33137i | 0.206068i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.32692 | − | 28.6274i | 0.205706 | − | 0.930758i | ||||
\(947\) | 9.25486i | 0.300743i | 0.988630 | + | 0.150371i | \(0.0480469\pi\) | ||||
−0.988630 | + | 0.150371i | \(0.951953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.180846 | 0.00587053 | ||||||||
\(950\) | − | 0.234516i | − | 0.00760870i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.11665i | 0.0361907i | ||||||||
\(953\) | 33.1689 | 1.07445 | 0.537223 | − | 0.843440i | \(-0.319473\pi\) | ||||
0.537223 | + | 0.843440i | \(0.319473\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.1987 | −0.815410 | ||||||||
\(956\) | 20.6125 | 0.666657 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −30.7002 | −0.991878 | ||||||||
\(959\) | 4.53927 | 0.146581 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43.1245 | 1.39111 | ||||||||
\(962\) | 4.99577i | 0.161070i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.4491i | 0.658620i | ||||||||
\(965\) | −29.9220 | −0.963223 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.3192i | − | 0.717737i | −0.933388 | − | 0.358869i | \(-0.883163\pi\) | ||
0.933388 | − | 0.358869i | \(-0.116837\pi\) | |||||||
\(968\) | −9.97546 | − | 4.63576i | −0.320623 | − | 0.148999i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.78416i | 0.217826i | ||||||||
\(971\) | − | 15.7712i | − | 0.506121i | −0.967451 | − | 0.253060i | \(-0.918563\pi\) | ||
0.967451 | − | 0.253060i | \(-0.0814371\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.3511 | −0.492134 | ||||||||
\(974\) | 12.4008 | 0.397347 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 3.93768i | − | 0.126042i | ||||||
\(977\) | 9.68067i | 0.309712i | 0.987937 | + | 0.154856i | \(0.0494914\pi\) | ||||
−0.987937 | + | 0.154856i | \(0.950509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.9094 | + | 49.3617i | −0.348665 | + | 1.57761i | ||||
\(980\) | − | 2.50315i | − | 0.0799603i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 40.0902 | 1.27933 | ||||||||
\(983\) | 6.18360i | 0.197226i | 0.995126 | + | 0.0986131i | \(0.0314406\pi\) | ||||
−0.995126 | + | 0.0986131i | \(0.968559\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 7.56488i | − | 0.241037i | ||||||
\(986\) | −8.71145 | −0.277429 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.197989 | −0.00629886 | ||||||||
\(989\) | 50.4256 | 1.60344 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33.9326 | −1.07791 | −0.538953 | − | 0.842336i | \(-0.681180\pi\) | ||||
−0.538953 | + | 0.842336i | \(0.681180\pi\) | |||||||
\(992\) | 8.60956 | 0.273354 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0.698081 | 0.0221418 | ||||||||
\(995\) | − | 40.7040i | − | 1.29040i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 33.2430i | − | 1.05282i | −0.850232 | − | 0.526409i | \(-0.823538\pi\) | ||
0.850232 | − | 0.526409i | \(-0.176462\pi\) | |||||||
\(998\) | 23.2350 | 0.735491 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1386.2.c.a.197.10 | yes | 12 | |
3.2 | odd | 2 | 1386.2.c.b.197.3 | yes | 12 | ||
11.10 | odd | 2 | 1386.2.c.b.197.10 | yes | 12 | ||
33.32 | even | 2 | inner | 1386.2.c.a.197.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.c.a.197.3 | ✓ | 12 | 33.32 | even | 2 | inner | |
1386.2.c.a.197.10 | yes | 12 | 1.1 | even | 1 | trivial | |
1386.2.c.b.197.3 | yes | 12 | 3.2 | odd | 2 | ||
1386.2.c.b.197.10 | yes | 12 | 11.10 | odd | 2 |