Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(76,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.76");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.i (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: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 76.8 | ||
Root | \(-0.396143 + 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.76 |
Dual form | 1155.2.i.a.76.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.52434i | 1.78498i | 0.451071 | + | 0.892488i | \(0.351042\pi\) | ||||
−0.451071 | + | 0.892488i | \(0.648958\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −4.37228 | −2.18614 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | −2.52434 | −1.03056 | ||||||||
\(7\) | −2.52434 | − | 0.792287i | −0.954110 | − | 0.299456i | ||||
\(8\) | − | 5.98844i | − | 2.11723i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.52434 | 0.798266 | ||||||||
\(11\) | − | 3.31662i | − | 1.00000i | ||||||
\(12\) | − | 4.37228i | − | 1.26217i | ||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 2.00000 | − | 6.37228i | 0.534522 | − | 1.70306i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 6.37228 | 1.59307 | ||||||||
\(17\) | 5.84096 | 1.41664 | 0.708321 | − | 0.705891i | \(-0.249453\pi\) | ||||
0.708321 | + | 0.705891i | \(0.249453\pi\) | |||||||
\(18\) | − | 2.52434i | − | 0.594992i | ||||||
\(19\) | 7.72049 | 1.77120 | 0.885601 | − | 0.464447i | \(-0.153747\pi\) | ||||
0.885601 | + | 0.464447i | \(0.153747\pi\) | |||||||
\(20\) | 4.37228i | 0.977672i | ||||||||
\(21\) | 0.792287 | − | 2.52434i | 0.172891 | − | 0.550856i | ||||
\(22\) | 8.37228 | 1.78498 | ||||||||
\(23\) | −8.11684 | −1.69248 | −0.846239 | − | 0.532803i | \(-0.821139\pi\) | ||||
−0.846239 | + | 0.532803i | \(0.821139\pi\) | |||||||
\(24\) | 5.98844 | 1.22239 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 11.0371 | + | 3.46410i | 2.08582 | + | 0.654654i | ||||
\(29\) | 2.67181i | 0.496144i | 0.968742 | + | 0.248072i | \(0.0797969\pi\) | ||||
−0.968742 | + | 0.248072i | \(0.920203\pi\) | |||||||
\(30\) | 2.52434i | 0.460879i | ||||||||
\(31\) | − | 4.74456i | − | 0.852149i | −0.904688 | − | 0.426074i | \(-0.859896\pi\) | ||
0.904688 | − | 0.426074i | \(-0.140104\pi\) | |||||||
\(32\) | 4.10891i | 0.726360i | ||||||||
\(33\) | 3.31662 | 0.577350 | ||||||||
\(34\) | 14.7446i | 2.52867i | ||||||||
\(35\) | −0.792287 | + | 2.52434i | −0.133921 | + | 0.426691i | ||||
\(36\) | 4.37228 | 0.728714 | ||||||||
\(37\) | −0.744563 | −0.122405 | −0.0612027 | − | 0.998125i | \(-0.519494\pi\) | ||||
−0.0612027 | + | 0.998125i | \(0.519494\pi\) | |||||||
\(38\) | 19.4891i | 3.16155i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.98844 | −0.946855 | ||||||||
\(41\) | 8.21782 | 1.28341 | 0.641704 | − | 0.766952i | \(-0.278228\pi\) | ||||
0.641704 | + | 0.766952i | \(0.278228\pi\) | |||||||
\(42\) | 6.37228 | + | 2.00000i | 0.983264 | + | 0.308607i | ||||
\(43\) | − | 5.84096i | − | 0.890738i | −0.895347 | − | 0.445369i | \(-0.853072\pi\) | ||
0.895347 | − | 0.445369i | \(-0.146928\pi\) | |||||||
\(44\) | 14.5012i | 2.18614i | ||||||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | − | 20.4897i | − | 3.02103i | ||||||
\(47\) | − | 1.25544i | − | 0.183124i | −0.995799 | − | 0.0915622i | \(-0.970814\pi\) | ||
0.995799 | − | 0.0915622i | \(-0.0291860\pi\) | |||||||
\(48\) | 6.37228i | 0.919760i | ||||||||
\(49\) | 5.74456 | + | 4.00000i | 0.820652 | + | 0.571429i | ||||
\(50\) | − | 2.52434i | − | 0.356995i | ||||||
\(51\) | 5.84096i | 0.817898i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.37228 | −1.01266 | −0.506330 | − | 0.862340i | \(-0.668998\pi\) | ||||
−0.506330 | + | 0.862340i | \(0.668998\pi\) | |||||||
\(54\) | 2.52434 | 0.343519 | ||||||||
\(55\) | −3.31662 | −0.447214 | ||||||||
\(56\) | −4.74456 | + | 15.1168i | −0.634019 | + | 2.02007i | ||||
\(57\) | 7.72049i | 1.02260i | ||||||||
\(58\) | −6.74456 | −0.885604 | ||||||||
\(59\) | − | 7.37228i | − | 0.959789i | −0.877326 | − | 0.479895i | \(-0.840675\pi\) | ||
0.877326 | − | 0.479895i | \(-0.159325\pi\) | |||||||
\(60\) | −4.37228 | −0.564459 | ||||||||
\(61\) | 1.08724 | 0.139207 | 0.0696034 | − | 0.997575i | \(-0.477827\pi\) | ||||
0.0696034 | + | 0.997575i | \(0.477827\pi\) | |||||||
\(62\) | 11.9769 | 1.52107 | ||||||||
\(63\) | 2.52434 | + | 0.792287i | 0.318037 | + | 0.0998188i | ||||
\(64\) | 2.37228 | 0.296535 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.37228i | 1.03056i | ||||||||
\(67\) | 6.74456 | 0.823979 | 0.411990 | − | 0.911188i | \(-0.364834\pi\) | ||||
0.411990 | + | 0.911188i | \(0.364834\pi\) | |||||||
\(68\) | −25.5383 | −3.09698 | ||||||||
\(69\) | − | 8.11684i | − | 0.977153i | ||||||
\(70\) | −6.37228 | − | 2.00000i | −0.761633 | − | 0.239046i | ||||
\(71\) | 14.7446 | 1.74986 | 0.874929 | − | 0.484252i | \(-0.160908\pi\) | ||||
0.874929 | + | 0.484252i | \(0.160908\pi\) | |||||||
\(72\) | 5.98844i | 0.705744i | ||||||||
\(73\) | −6.92820 | −0.810885 | −0.405442 | − | 0.914121i | \(-0.632883\pi\) | ||||
−0.405442 | + | 0.914121i | \(0.632883\pi\) | |||||||
\(74\) | − | 1.87953i | − | 0.218491i | ||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −33.7562 | −3.87210 | ||||||||
\(77\) | −2.62772 | + | 8.37228i | −0.299456 | + | 0.954110i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.5615i | − | 1.52578i | −0.646527 | − | 0.762891i | \(-0.723779\pi\) | ||
0.646527 | − | 0.762891i | \(-0.276221\pi\) | |||||||
\(80\) | − | 6.37228i | − | 0.712443i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 20.7446i | 2.29085i | ||||||||
\(83\) | 6.13592 | 0.673504 | 0.336752 | − | 0.941593i | \(-0.390672\pi\) | ||||
0.336752 | + | 0.941593i | \(0.390672\pi\) | |||||||
\(84\) | −3.46410 | + | 11.0371i | −0.377964 | + | 1.20425i | ||||
\(85\) | − | 5.84096i | − | 0.633541i | ||||||
\(86\) | 14.7446 | 1.58995 | ||||||||
\(87\) | −2.67181 | −0.286449 | ||||||||
\(88\) | −19.8614 | −2.11723 | ||||||||
\(89\) | 2.62772i | 0.278538i | 0.990255 | + | 0.139269i | \(0.0444752\pi\) | ||||
−0.990255 | + | 0.139269i | \(0.955525\pi\) | |||||||
\(90\) | −2.52434 | −0.266089 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 35.4891 | 3.70000 | ||||||||
\(93\) | 4.74456 | 0.491988 | ||||||||
\(94\) | 3.16915 | 0.326873 | ||||||||
\(95\) | − | 7.72049i | − | 0.792106i | ||||||
\(96\) | −4.10891 | −0.419364 | ||||||||
\(97\) | − | 2.62772i | − | 0.266804i | −0.991062 | − | 0.133402i | \(-0.957410\pi\) | ||
0.991062 | − | 0.133402i | \(-0.0425902\pi\) | |||||||
\(98\) | −10.0974 | + | 14.5012i | −1.01999 | + | 1.46484i | ||||
\(99\) | 3.31662i | 0.333333i | ||||||||
\(100\) | 4.37228 | 0.437228 | ||||||||
\(101\) | 10.3923 | 1.03407 | 0.517036 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517036 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(102\) | −14.7446 | −1.45993 | ||||||||
\(103\) | − | 6.11684i | − | 0.602711i | −0.953512 | − | 0.301355i | \(-0.902561\pi\) | ||
0.953512 | − | 0.301355i | \(-0.0974390\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.52434 | − | 0.792287i | −0.246350 | − | 0.0773193i | ||||
\(106\) | − | 18.6101i | − | 1.80758i | ||||||
\(107\) | 15.1460i | 1.46422i | 0.681186 | + | 0.732111i | \(0.261465\pi\) | ||||
−0.681186 | + | 0.732111i | \(0.738535\pi\) | |||||||
\(108\) | 4.37228i | 0.420723i | ||||||||
\(109\) | − | 8.51278i | − | 0.815376i | −0.913121 | − | 0.407688i | \(-0.866335\pi\) | ||
0.913121 | − | 0.407688i | \(-0.133665\pi\) | |||||||
\(110\) | − | 8.37228i | − | 0.798266i | ||||||
\(111\) | − | 0.744563i | − | 0.0706708i | ||||||
\(112\) | −16.0858 | − | 5.04868i | −1.51996 | − | 0.477055i | ||||
\(113\) | −7.37228 | −0.693526 | −0.346763 | − | 0.937953i | \(-0.612719\pi\) | ||||
−0.346763 | + | 0.937953i | \(0.612719\pi\) | |||||||
\(114\) | −19.4891 | −1.82532 | ||||||||
\(115\) | 8.11684i | 0.756900i | ||||||||
\(116\) | − | 11.6819i | − | 1.08464i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.6101 | 1.71320 | ||||||||
\(119\) | −14.7446 | − | 4.62772i | −1.35163 | − | 0.424222i | ||||
\(120\) | − | 5.98844i | − | 0.546667i | ||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 2.74456i | 0.248481i | ||||||||
\(123\) | 8.21782i | 0.740976i | ||||||||
\(124\) | 20.7446i | 1.86292i | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −2.00000 | + | 6.37228i | −0.178174 | + | 0.567688i | ||||
\(127\) | − | 19.6974i | − | 1.74786i | −0.486053 | − | 0.873929i | \(-0.661564\pi\) | ||
0.486053 | − | 0.873929i | \(-0.338436\pi\) | |||||||
\(128\) | 14.2063i | 1.25567i | ||||||||
\(129\) | 5.84096 | 0.514268 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6101 | −1.62597 | −0.812987 | − | 0.582282i | \(-0.802160\pi\) | ||||
−0.812987 | + | 0.582282i | \(0.802160\pi\) | |||||||
\(132\) | −14.5012 | −1.26217 | ||||||||
\(133\) | −19.4891 | − | 6.11684i | −1.68992 | − | 0.530398i | ||||
\(134\) | 17.0256i | 1.47078i | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | − | 34.9783i | − | 2.99936i | ||||||
\(137\) | 1.25544 | 0.107259 | 0.0536296 | − | 0.998561i | \(-0.482921\pi\) | ||||
0.0536296 | + | 0.998561i | \(0.482921\pi\) | |||||||
\(138\) | 20.4897 | 1.74420 | ||||||||
\(139\) | −3.46410 | −0.293821 | −0.146911 | − | 0.989150i | \(-0.546933\pi\) | ||||
−0.146911 | + | 0.989150i | \(0.546933\pi\) | |||||||
\(140\) | 3.46410 | − | 11.0371i | 0.292770 | − | 0.932806i | ||||
\(141\) | 1.25544 | 0.105727 | ||||||||
\(142\) | 37.2203i | 3.12345i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.37228 | −0.531023 | ||||||||
\(145\) | 2.67181 | 0.221882 | ||||||||
\(146\) | − | 17.4891i | − | 1.44741i | ||||||
\(147\) | −4.00000 | + | 5.74456i | −0.329914 | + | 0.473804i | ||||
\(148\) | 3.25544 | 0.267595 | ||||||||
\(149\) | − | 13.8564i | − | 1.13516i | −0.823318 | − | 0.567581i | \(-0.807880\pi\) | ||
0.823318 | − | 0.567581i | \(-0.192120\pi\) | |||||||
\(150\) | 2.52434 | 0.206111 | ||||||||
\(151\) | − | 1.87953i | − | 0.152954i | −0.997071 | − | 0.0764769i | \(-0.975633\pi\) | ||
0.997071 | − | 0.0764769i | \(-0.0243671\pi\) | |||||||
\(152\) | − | 46.2337i | − | 3.75005i | ||||||
\(153\) | −5.84096 | −0.472214 | ||||||||
\(154\) | −21.1345 | − | 6.63325i | −1.70306 | − | 0.534522i | ||||
\(155\) | −4.74456 | −0.381092 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 20.1168i | − | 1.60550i | −0.596316 | − | 0.802749i | \(-0.703370\pi\) | ||
0.596316 | − | 0.802749i | \(-0.296630\pi\) | |||||||
\(158\) | 34.2337 | 2.72349 | ||||||||
\(159\) | − | 7.37228i | − | 0.584660i | ||||||
\(160\) | 4.10891 | 0.324838 | ||||||||
\(161\) | 20.4897 | + | 6.43087i | 1.61481 | + | 0.506824i | ||||
\(162\) | 2.52434i | 0.198331i | ||||||||
\(163\) | 16.2337 | 1.27152 | 0.635760 | − | 0.771887i | \(-0.280687\pi\) | ||||
0.635760 | + | 0.771887i | \(0.280687\pi\) | |||||||
\(164\) | −35.9306 | −2.80571 | ||||||||
\(165\) | − | 3.31662i | − | 0.258199i | ||||||
\(166\) | 15.4891i | 1.20219i | ||||||||
\(167\) | 23.6588 | 1.83077 | 0.915387 | − | 0.402576i | \(-0.131885\pi\) | ||||
0.915387 | + | 0.402576i | \(0.131885\pi\) | |||||||
\(168\) | −15.1168 | − | 4.74456i | −1.16629 | − | 0.366051i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 14.7446 | 1.13086 | ||||||||
\(171\) | −7.72049 | −0.590401 | ||||||||
\(172\) | 25.5383i | 1.94728i | ||||||||
\(173\) | −6.92820 | −0.526742 | −0.263371 | − | 0.964695i | \(-0.584834\pi\) | ||||
−0.263371 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(174\) | − | 6.74456i | − | 0.511304i | ||||||
\(175\) | 2.52434 | + | 0.792287i | 0.190822 | + | 0.0598913i | ||||
\(176\) | − | 21.1345i | − | 1.59307i | ||||||
\(177\) | 7.37228 | 0.554135 | ||||||||
\(178\) | −6.63325 | −0.497183 | ||||||||
\(179\) | 1.48913 | 0.111302 | 0.0556512 | − | 0.998450i | \(-0.482277\pi\) | ||||
0.0556512 | + | 0.998450i | \(0.482277\pi\) | |||||||
\(180\) | − | 4.37228i | − | 0.325891i | ||||||
\(181\) | − | 5.25544i | − | 0.390634i | −0.980740 | − | 0.195317i | \(-0.937426\pi\) | ||
0.980740 | − | 0.195317i | \(-0.0625735\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.08724i | 0.0803711i | ||||||||
\(184\) | 48.6072i | 3.58337i | ||||||||
\(185\) | 0.744563i | 0.0547413i | ||||||||
\(186\) | 11.9769i | 0.878187i | ||||||||
\(187\) | − | 19.3723i | − | 1.41664i | ||||||
\(188\) | 5.48913i | 0.400336i | ||||||||
\(189\) | −0.792287 | + | 2.52434i | −0.0576304 | + | 0.183619i | ||||
\(190\) | 19.4891 | 1.41389 | ||||||||
\(191\) | 2.74456 | 0.198590 | 0.0992948 | − | 0.995058i | \(-0.468341\pi\) | ||||
0.0992948 | + | 0.995058i | \(0.468341\pi\) | |||||||
\(192\) | 2.37228i | 0.171205i | ||||||||
\(193\) | 15.1460i | 1.09023i | 0.838360 | + | 0.545117i | \(0.183515\pi\) | ||||
−0.838360 | + | 0.545117i | \(0.816485\pi\) | |||||||
\(194\) | 6.63325 | 0.476240 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.1168 | − | 17.4891i | −1.79406 | − | 1.24922i | ||||
\(197\) | 10.0974i | 0.719406i | 0.933067 | + | 0.359703i | \(0.117122\pi\) | ||||
−0.933067 | + | 0.359703i | \(0.882878\pi\) | |||||||
\(198\) | −8.37228 | −0.594992 | ||||||||
\(199\) | − | 4.74456i | − | 0.336333i | −0.985759 | − | 0.168167i | \(-0.946215\pi\) | ||
0.985759 | − | 0.168167i | \(-0.0537846\pi\) | |||||||
\(200\) | 5.98844i | 0.423447i | ||||||||
\(201\) | 6.74456i | 0.475725i | ||||||||
\(202\) | 26.2337i | 1.84580i | ||||||||
\(203\) | 2.11684 | − | 6.74456i | 0.148573 | − | 0.473375i | ||||
\(204\) | − | 25.5383i | − | 1.78804i | ||||||
\(205\) | − | 8.21782i | − | 0.573958i | ||||||
\(206\) | 15.4410 | 1.07582 | ||||||||
\(207\) | 8.11684 | 0.564160 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 25.6060i | − | 1.77120i | ||||||
\(210\) | 2.00000 | − | 6.37228i | 0.138013 | − | 0.439729i | ||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | 32.2337 | 2.21382 | ||||||||
\(213\) | 14.7446i | 1.01028i | ||||||||
\(214\) | −38.2337 | −2.61360 | ||||||||
\(215\) | −5.84096 | −0.398350 | ||||||||
\(216\) | −5.98844 | −0.407462 | ||||||||
\(217\) | −3.75906 | + | 11.9769i | −0.255181 | + | 0.813044i | ||||
\(218\) | 21.4891 | 1.45543 | ||||||||
\(219\) | − | 6.92820i | − | 0.468165i | ||||||
\(220\) | 14.5012 | 0.977672 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.87953 | 0.126146 | ||||||||
\(223\) | − | 8.62772i | − | 0.577755i | −0.957366 | − | 0.288877i | \(-0.906718\pi\) | ||
0.957366 | − | 0.288877i | \(-0.0932820\pi\) | |||||||
\(224\) | 3.25544 | − | 10.3723i | 0.217513 | − | 0.693027i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | − | 18.6101i | − | 1.23793i | ||||||
\(227\) | −1.38219 | −0.0917395 | −0.0458697 | − | 0.998947i | \(-0.514606\pi\) | ||||
−0.0458697 | + | 0.998947i | \(0.514606\pi\) | |||||||
\(228\) | − | 33.7562i | − | 2.23556i | ||||||
\(229\) | 22.7446i | 1.50300i | 0.659731 | + | 0.751502i | \(0.270670\pi\) | ||||
−0.659731 | + | 0.751502i | \(0.729330\pi\) | |||||||
\(230\) | −20.4897 | −1.35105 | ||||||||
\(231\) | −8.37228 | − | 2.62772i | −0.550856 | − | 0.172891i | ||||
\(232\) | 16.0000 | 1.05045 | ||||||||
\(233\) | 23.3639i | 1.53062i | 0.643664 | + | 0.765308i | \(0.277414\pi\) | ||||
−0.643664 | + | 0.765308i | \(0.722586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.25544 | −0.0818957 | ||||||||
\(236\) | 32.2337i | 2.09823i | ||||||||
\(237\) | 13.5615 | 0.880911 | ||||||||
\(238\) | 11.6819 | − | 37.2203i | 0.757227 | − | 2.41263i | ||||
\(239\) | − | 15.6434i | − | 1.01188i | −0.862567 | − | 0.505942i | \(-0.831145\pi\) | ||
0.862567 | − | 0.505942i | \(-0.168855\pi\) | |||||||
\(240\) | 6.37228 | 0.411329 | ||||||||
\(241\) | 13.8564 | 0.892570 | 0.446285 | − | 0.894891i | \(-0.352747\pi\) | ||||
0.446285 | + | 0.894891i | \(0.352747\pi\) | |||||||
\(242\) | − | 27.7677i | − | 1.78498i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −4.75372 | −0.304326 | ||||||||
\(245\) | 4.00000 | − | 5.74456i | 0.255551 | − | 0.367007i | ||||
\(246\) | −20.7446 | −1.32263 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −28.4125 | −1.80420 | ||||||||
\(249\) | 6.13592i | 0.388848i | ||||||||
\(250\) | −2.52434 | −0.159653 | ||||||||
\(251\) | 5.48913i | 0.346471i | 0.984880 | + | 0.173235i | \(0.0554221\pi\) | ||||
−0.984880 | + | 0.173235i | \(0.944578\pi\) | |||||||
\(252\) | −11.0371 | − | 3.46410i | −0.695273 | − | 0.218218i | ||||
\(253\) | 26.9205i | 1.69248i | ||||||||
\(254\) | 49.7228 | 3.11989 | ||||||||
\(255\) | 5.84096 | 0.365775 | ||||||||
\(256\) | −31.1168 | −1.94480 | ||||||||
\(257\) | 10.2337i | 0.638360i | 0.947694 | + | 0.319180i | \(0.103407\pi\) | ||||
−0.947694 | + | 0.319180i | \(0.896593\pi\) | |||||||
\(258\) | 14.7446i | 0.917956i | ||||||||
\(259\) | 1.87953 | + | 0.589907i | 0.116788 | + | 0.0366551i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 2.67181i | − | 0.165381i | ||||||
\(262\) | − | 46.9783i | − | 2.90233i | ||||||
\(263\) | 9.80240i | 0.604442i | 0.953238 | + | 0.302221i | \(0.0977280\pi\) | ||||
−0.953238 | + | 0.302221i | \(0.902272\pi\) | |||||||
\(264\) | − | 19.8614i | − | 1.22239i | ||||||
\(265\) | 7.37228i | 0.452876i | ||||||||
\(266\) | 15.4410 | − | 49.1971i | 0.946747 | − | 3.01647i | ||||
\(267\) | −2.62772 | −0.160814 | ||||||||
\(268\) | −29.4891 | −1.80134 | ||||||||
\(269\) | 25.3723i | 1.54698i | 0.633811 | + | 0.773488i | \(0.281490\pi\) | ||||
−0.633811 | + | 0.773488i | \(0.718510\pi\) | |||||||
\(270\) | − | 2.52434i | − | 0.153626i | ||||||
\(271\) | −0.792287 | −0.0481280 | −0.0240640 | − | 0.999710i | \(-0.507661\pi\) | ||||
−0.0240640 | + | 0.999710i | \(0.507661\pi\) | |||||||
\(272\) | 37.2203 | 2.25681 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.16915i | 0.191455i | ||||||||
\(275\) | 3.31662i | 0.200000i | ||||||||
\(276\) | 35.4891i | 2.13619i | ||||||||
\(277\) | − | 15.7359i | − | 0.945481i | −0.881202 | − | 0.472740i | \(-0.843265\pi\) | ||
0.881202 | − | 0.472740i | \(-0.156735\pi\) | |||||||
\(278\) | − | 8.74456i | − | 0.524464i | ||||||
\(279\) | 4.74456i | 0.284050i | ||||||||
\(280\) | 15.1168 | + | 4.74456i | 0.903404 | + | 0.283542i | ||||
\(281\) | − | 27.1229i | − | 1.61802i | −0.587797 | − | 0.809008i | \(-0.700005\pi\) | ||
0.587797 | − | 0.809008i | \(-0.299995\pi\) | |||||||
\(282\) | 3.16915i | 0.188720i | ||||||||
\(283\) | 22.0742 | 1.31218 | 0.656088 | − | 0.754684i | \(-0.272210\pi\) | ||||
0.656088 | + | 0.754684i | \(0.272210\pi\) | |||||||
\(284\) | −64.4674 | −3.82543 | ||||||||
\(285\) | 7.72049 | 0.457322 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.7446 | − | 6.51087i | −1.22451 | − | 0.384325i | ||||
\(288\) | − | 4.10891i | − | 0.242120i | ||||||
\(289\) | 17.1168 | 1.00687 | ||||||||
\(290\) | 6.74456i | 0.396054i | ||||||||
\(291\) | 2.62772 | 0.154040 | ||||||||
\(292\) | 30.2921 | 1.77271 | ||||||||
\(293\) | −25.0410 | −1.46291 | −0.731455 | − | 0.681889i | \(-0.761159\pi\) | ||||
−0.731455 | + | 0.681889i | \(0.761159\pi\) | |||||||
\(294\) | −14.5012 | − | 10.0974i | −0.845728 | − | 0.588889i | ||||
\(295\) | −7.37228 | −0.429231 | ||||||||
\(296\) | 4.45877i | 0.259161i | ||||||||
\(297\) | −3.31662 | −0.192450 | ||||||||
\(298\) | 34.9783 | 2.02624 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.37228i | 0.252434i | ||||||||
\(301\) | −4.62772 | + | 14.7446i | −0.266737 | + | 0.849862i | ||||
\(302\) | 4.74456 | 0.273019 | ||||||||
\(303\) | 10.3923i | 0.597022i | ||||||||
\(304\) | 49.1971 | 2.82165 | ||||||||
\(305\) | − | 1.08724i | − | 0.0622552i | ||||||
\(306\) | − | 14.7446i | − | 0.842891i | ||||||
\(307\) | 8.80773 | 0.502684 | 0.251342 | − | 0.967898i | \(-0.419128\pi\) | ||||
0.251342 | + | 0.967898i | \(0.419128\pi\) | |||||||
\(308\) | 11.4891 | − | 36.6060i | 0.654654 | − | 2.08582i | ||||
\(309\) | 6.11684 | 0.347975 | ||||||||
\(310\) | − | 11.9769i | − | 0.680241i | ||||||
\(311\) | − | 16.0000i | − | 0.907277i | −0.891186 | − | 0.453638i | \(-0.850126\pi\) | ||
0.891186 | − | 0.453638i | \(-0.149874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 6.86141i | − | 0.387830i | −0.981018 | − | 0.193915i | \(-0.937881\pi\) | ||
0.981018 | − | 0.193915i | \(-0.0621185\pi\) | |||||||
\(314\) | 50.7817 | 2.86578 | ||||||||
\(315\) | 0.792287 | − | 2.52434i | 0.0446403 | − | 0.142230i | ||||
\(316\) | 59.2945i | 3.33558i | ||||||||
\(317\) | −13.2554 | −0.744500 | −0.372250 | − | 0.928133i | \(-0.621414\pi\) | ||||
−0.372250 | + | 0.928133i | \(0.621414\pi\) | |||||||
\(318\) | 18.6101 | 1.04360 | ||||||||
\(319\) | 8.86141 | 0.496144 | ||||||||
\(320\) | − | 2.37228i | − | 0.132615i | ||||||
\(321\) | −15.1460 | −0.845369 | ||||||||
\(322\) | −16.2337 | + | 51.7228i | −0.904668 | + | 2.88240i | ||||
\(323\) | 45.0951 | 2.50916 | ||||||||
\(324\) | −4.37228 | −0.242905 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 40.9793i | 2.26963i | ||||||||
\(327\) | 8.51278 | 0.470758 | ||||||||
\(328\) | − | 49.2119i | − | 2.71727i | ||||||
\(329\) | −0.994667 | + | 3.16915i | −0.0548377 | + | 0.174721i | ||||
\(330\) | 8.37228 | 0.460879 | ||||||||
\(331\) | −15.3723 | −0.844937 | −0.422468 | − | 0.906378i | \(-0.638836\pi\) | ||||
−0.422468 | + | 0.906378i | \(0.638836\pi\) | |||||||
\(332\) | −26.8280 | −1.47238 | ||||||||
\(333\) | 0.744563 | 0.0408018 | ||||||||
\(334\) | 59.7228i | 3.26789i | ||||||||
\(335\) | − | 6.74456i | − | 0.368495i | ||||||
\(336\) | 5.04868 | − | 16.0858i | 0.275428 | − | 0.877552i | ||||
\(337\) | − | 22.5716i | − | 1.22955i | −0.788702 | − | 0.614776i | \(-0.789247\pi\) | ||
0.788702 | − | 0.614776i | \(-0.210753\pi\) | |||||||
\(338\) | − | 32.8164i | − | 1.78498i | ||||||
\(339\) | − | 7.37228i | − | 0.400407i | ||||||
\(340\) | 25.5383i | 1.38501i | ||||||||
\(341\) | −15.7359 | −0.852149 | ||||||||
\(342\) | − | 19.4891i | − | 1.05385i | ||||||
\(343\) | −11.3321 | − | 14.6487i | −0.611874 | − | 0.790955i | ||||
\(344\) | −34.9783 | −1.88590 | ||||||||
\(345\) | −8.11684 | −0.436996 | ||||||||
\(346\) | − | 17.4891i | − | 0.940221i | ||||||
\(347\) | 24.2487i | 1.30174i | 0.759190 | + | 0.650870i | \(0.225596\pi\) | ||||
−0.759190 | + | 0.650870i | \(0.774404\pi\) | |||||||
\(348\) | 11.6819 | 0.626217 | ||||||||
\(349\) | 17.5229 | 0.937979 | 0.468989 | − | 0.883204i | \(-0.344618\pi\) | ||||
0.468989 | + | 0.883204i | \(0.344618\pi\) | |||||||
\(350\) | −2.00000 | + | 6.37228i | −0.106904 | + | 0.340613i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 13.6277 | 0.726360 | ||||||||
\(353\) | 28.7446i | 1.52992i | 0.644079 | + | 0.764959i | \(0.277241\pi\) | ||||
−0.644079 | + | 0.764959i | \(0.722759\pi\) | |||||||
\(354\) | 18.6101i | 0.989117i | ||||||||
\(355\) | − | 14.7446i | − | 0.782560i | ||||||
\(356\) | − | 11.4891i | − | 0.608922i | ||||||
\(357\) | 4.62772 | − | 14.7446i | 0.244925 | − | 0.780365i | ||||
\(358\) | 3.75906i | 0.198672i | ||||||||
\(359\) | − | 22.5716i | − | 1.19128i | −0.803251 | − | 0.595641i | \(-0.796898\pi\) | ||
0.803251 | − | 0.595641i | \(-0.203102\pi\) | |||||||
\(360\) | 5.98844 | 0.315618 | ||||||||
\(361\) | 40.6060 | 2.13716 | ||||||||
\(362\) | 13.2665 | 0.697272 | ||||||||
\(363\) | − | 11.0000i | − | 0.577350i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.92820i | 0.362639i | ||||||||
\(366\) | −2.74456 | −0.143461 | ||||||||
\(367\) | 6.11684i | 0.319297i | 0.987174 | + | 0.159648i | \(0.0510360\pi\) | ||||
−0.987174 | + | 0.159648i | \(0.948964\pi\) | |||||||
\(368\) | −51.7228 | −2.69624 | ||||||||
\(369\) | −8.21782 | −0.427803 | ||||||||
\(370\) | −1.87953 | −0.0977120 | ||||||||
\(371\) | 18.6101 | + | 5.84096i | 0.966190 | + | 0.303248i | ||||
\(372\) | −20.7446 | −1.07556 | ||||||||
\(373\) | − | 18.4077i | − | 0.953117i | −0.879143 | − | 0.476559i | \(-0.841884\pi\) | ||
0.879143 | − | 0.476559i | \(-0.158116\pi\) | |||||||
\(374\) | 48.9022 | 2.52867 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −7.51811 | −0.387717 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −6.37228 | − | 2.00000i | −0.327755 | − | 0.102869i | ||||
\(379\) | 24.6277 | 1.26504 | 0.632520 | − | 0.774544i | \(-0.282020\pi\) | ||||
0.632520 | + | 0.774544i | \(0.282020\pi\) | |||||||
\(380\) | 33.7562i | 1.73165i | ||||||||
\(381\) | 19.6974 | 1.00913 | ||||||||
\(382\) | 6.92820i | 0.354478i | ||||||||
\(383\) | − | 4.23369i | − | 0.216331i | −0.994133 | − | 0.108166i | \(-0.965502\pi\) | ||
0.994133 | − | 0.108166i | \(-0.0344977\pi\) | |||||||
\(384\) | −14.2063 | −0.724960 | ||||||||
\(385\) | 8.37228 | + | 2.62772i | 0.426691 | + | 0.133921i | ||||
\(386\) | −38.2337 | −1.94604 | ||||||||
\(387\) | 5.84096i | 0.296913i | ||||||||
\(388\) | 11.4891i | 0.583272i | ||||||||
\(389\) | −2.00000 | −0.101404 | −0.0507020 | − | 0.998714i | \(-0.516146\pi\) | ||||
−0.0507020 | + | 0.998714i | \(0.516146\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −47.4102 | −2.39764 | ||||||||
\(392\) | 23.9538 | − | 34.4010i | 1.20985 | − | 1.73751i | ||||
\(393\) | − | 18.6101i | − | 0.938757i | ||||||
\(394\) | −25.4891 | −1.28412 | ||||||||
\(395\) | −13.5615 | −0.682351 | ||||||||
\(396\) | − | 14.5012i | − | 0.728714i | ||||||
\(397\) | − | 4.51087i | − | 0.226394i | −0.993573 | − | 0.113197i | \(-0.963891\pi\) | ||
0.993573 | − | 0.113197i | \(-0.0361092\pi\) | |||||||
\(398\) | 11.9769 | 0.600347 | ||||||||
\(399\) | 6.11684 | − | 19.4891i | 0.306225 | − | 0.975677i | ||||
\(400\) | −6.37228 | −0.318614 | ||||||||
\(401\) | −27.7228 | −1.38441 | −0.692206 | − | 0.721700i | \(-0.743361\pi\) | ||||
−0.692206 | + | 0.721700i | \(0.743361\pi\) | |||||||
\(402\) | −17.0256 | −0.849157 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −45.4381 | −2.26063 | ||||||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 17.0256 | + | 5.34363i | 0.844964 | + | 0.265200i | ||||
\(407\) | 2.46943i | 0.122405i | ||||||||
\(408\) | 34.9783 | 1.73168 | ||||||||
\(409\) | −34.6410 | −1.71289 | −0.856444 | − | 0.516240i | \(-0.827331\pi\) | ||||
−0.856444 | + | 0.516240i | \(0.827331\pi\) | |||||||
\(410\) | 20.7446 | 1.02450 | ||||||||
\(411\) | 1.25544i | 0.0619262i | ||||||||
\(412\) | 26.7446i | 1.31761i | ||||||||
\(413\) | −5.84096 | + | 18.6101i | −0.287415 | + | 0.915745i | ||||
\(414\) | 20.4897i | 1.00701i | ||||||||
\(415\) | − | 6.13592i | − | 0.301200i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.46410i | − | 0.169638i | ||||||
\(418\) | 64.6381 | 3.16155 | ||||||||
\(419\) | − | 4.62772i | − | 0.226079i | −0.993591 | − | 0.113039i | \(-0.963941\pi\) | ||
0.993591 | − | 0.113039i | \(-0.0360586\pi\) | |||||||
\(420\) | 11.0371 | + | 3.46410i | 0.538556 | + | 0.169031i | ||||
\(421\) | 18.8614 | 0.919249 | 0.459624 | − | 0.888113i | \(-0.347984\pi\) | ||||
0.459624 | + | 0.888113i | \(0.347984\pi\) | |||||||
\(422\) | −8.74456 | −0.425679 | ||||||||
\(423\) | 1.25544i | 0.0610415i | ||||||||
\(424\) | 44.1485i | 2.14404i | ||||||||
\(425\) | −5.84096 | −0.283328 | ||||||||
\(426\) | −37.2203 | −1.80333 | ||||||||
\(427\) | −2.74456 | − | 0.861407i | −0.132819 | − | 0.0416864i | ||||
\(428\) | − | 66.2227i | − | 3.20099i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 14.7446i | − | 0.711046i | ||||||
\(431\) | 26.8280i | 1.29226i | 0.763229 | + | 0.646128i | \(0.223613\pi\) | ||||
−0.763229 | + | 0.646128i | \(0.776387\pi\) | |||||||
\(432\) | − | 6.37228i | − | 0.306587i | ||||||
\(433\) | − | 32.9783i | − | 1.58483i | −0.609980 | − | 0.792417i | \(-0.708823\pi\) | ||
0.609980 | − | 0.792417i | \(-0.291177\pi\) | |||||||
\(434\) | −30.2337 | − | 9.48913i | −1.45126 | − | 0.455493i | ||||
\(435\) | 2.67181i | 0.128104i | ||||||||
\(436\) | 37.2203i | 1.78253i | ||||||||
\(437\) | −62.6660 | −2.99772 | ||||||||
\(438\) | 17.4891 | 0.835663 | ||||||||
\(439\) | −18.8125 | −0.897872 | −0.448936 | − | 0.893564i | \(-0.648197\pi\) | ||||
−0.448936 | + | 0.893564i | \(0.648197\pi\) | |||||||
\(440\) | 19.8614i | 0.946855i | ||||||||
\(441\) | −5.74456 | − | 4.00000i | −0.273551 | − | 0.190476i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −34.2337 | −1.62649 | −0.813246 | − | 0.581920i | \(-0.802302\pi\) | ||||
−0.813246 | + | 0.581920i | \(0.802302\pi\) | |||||||
\(444\) | 3.25544i | 0.154496i | ||||||||
\(445\) | 2.62772 | 0.124566 | ||||||||
\(446\) | 21.7793 | 1.03128 | ||||||||
\(447\) | 13.8564 | 0.655386 | ||||||||
\(448\) | −5.98844 | − | 1.87953i | −0.282927 | − | 0.0887993i | ||||
\(449\) | −31.7228 | −1.49709 | −0.748546 | − | 0.663083i | \(-0.769248\pi\) | ||||
−0.748546 | + | 0.663083i | \(0.769248\pi\) | |||||||
\(450\) | 2.52434i | 0.118998i | ||||||||
\(451\) | − | 27.2554i | − | 1.28341i | ||||||
\(452\) | 32.2337 | 1.51615 | ||||||||
\(453\) | 1.87953 | 0.0883079 | ||||||||
\(454\) | − | 3.48913i | − | 0.163753i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 46.2337 | 2.16509 | ||||||||
\(457\) | − | 8.31040i | − | 0.388744i | −0.980928 | − | 0.194372i | \(-0.937733\pi\) | ||
0.980928 | − | 0.194372i | \(-0.0622669\pi\) | |||||||
\(458\) | −57.4150 | −2.68282 | ||||||||
\(459\) | − | 5.84096i | − | 0.272633i | ||||||
\(460\) | − | 35.4891i | − | 1.65469i | ||||||
\(461\) | 9.80240 | 0.456543 | 0.228272 | − | 0.973597i | \(-0.426693\pi\) | ||||
0.228272 | + | 0.973597i | \(0.426693\pi\) | |||||||
\(462\) | 6.63325 | − | 21.1345i | 0.308607 | − | 0.983264i | ||||
\(463\) | −25.4891 | −1.18458 | −0.592290 | − | 0.805725i | \(-0.701776\pi\) | ||||
−0.592290 | + | 0.805725i | \(0.701776\pi\) | |||||||
\(464\) | 17.0256i | 0.790392i | ||||||||
\(465\) | − | 4.74456i | − | 0.220024i | ||||||
\(466\) | −58.9783 | −2.73211 | ||||||||
\(467\) | − | 38.9783i | − | 1.80370i | −0.432051 | − | 0.901849i | \(-0.642210\pi\) | ||
0.432051 | − | 0.901849i | \(-0.357790\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.0256 | − | 5.34363i | −0.786167 | − | 0.246746i | ||||
\(470\) | − | 3.16915i | − | 0.146182i | ||||||
\(471\) | 20.1168 | 0.926935 | ||||||||
\(472\) | −44.1485 | −2.03210 | ||||||||
\(473\) | −19.3723 | −0.890738 | ||||||||
\(474\) | 34.2337i | 1.57241i | ||||||||
\(475\) | −7.72049 | −0.354240 | ||||||||
\(476\) | 64.4674 | + | 20.2337i | 2.95486 | + | 0.927410i | ||||
\(477\) | 7.37228 | 0.337554 | ||||||||
\(478\) | 39.4891 | 1.80619 | ||||||||
\(479\) | 7.51811 | 0.343511 | 0.171756 | − | 0.985140i | \(-0.445056\pi\) | ||||
0.171756 | + | 0.985140i | \(0.445056\pi\) | |||||||
\(480\) | 4.10891i | 0.187545i | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 34.9783i | 1.59322i | ||||||||
\(483\) | −6.43087 | + | 20.4897i | −0.292615 | + | 0.932312i | ||||
\(484\) | 48.0951 | 2.18614 | ||||||||
\(485\) | −2.62772 | −0.119319 | ||||||||
\(486\) | −2.52434 | −0.114506 | ||||||||
\(487\) | −14.9783 | −0.678729 | −0.339365 | − | 0.940655i | \(-0.610212\pi\) | ||||
−0.339365 | + | 0.940655i | \(0.610212\pi\) | |||||||
\(488\) | − | 6.51087i | − | 0.294733i | ||||||
\(489\) | 16.2337i | 0.734113i | ||||||||
\(490\) | 14.5012 | + | 10.0974i | 0.655098 | + | 0.456152i | ||||
\(491\) | 19.4024i | 0.875619i | 0.899068 | + | 0.437809i | \(0.144246\pi\) | ||||
−0.899068 | + | 0.437809i | \(0.855754\pi\) | |||||||
\(492\) | − | 35.9306i | − | 1.61988i | ||||||
\(493\) | 15.6060i | 0.702858i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.31662 | 0.149071 | ||||||||
\(496\) | − | 30.2337i | − | 1.35753i | ||||||
\(497\) | −37.2203 | − | 11.6819i | −1.66956 | − | 0.524006i | ||||
\(498\) | −15.4891 | −0.694084 | ||||||||
\(499\) | −34.3505 | −1.53774 | −0.768870 | − | 0.639405i | \(-0.779181\pi\) | ||||
−0.768870 | + | 0.639405i | \(0.779181\pi\) | |||||||
\(500\) | − | 4.37228i | − | 0.195534i | ||||||
\(501\) | 23.6588i | 1.05700i | ||||||||
\(502\) | −13.8564 | −0.618442 | ||||||||
\(503\) | 10.8896 | 0.485545 | 0.242772 | − | 0.970083i | \(-0.421943\pi\) | ||||
0.242772 | + | 0.970083i | \(0.421943\pi\) | |||||||
\(504\) | 4.74456 | − | 15.1168i | 0.211340 | − | 0.673358i | ||||
\(505\) | − | 10.3923i | − | 0.462451i | ||||||
\(506\) | −67.9565 | −3.02103 | ||||||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | 86.1224i | 3.82107i | ||||||||
\(509\) | 10.6277i | 0.471065i | 0.971866 | + | 0.235533i | \(0.0756835\pi\) | ||||
−0.971866 | + | 0.235533i | \(0.924317\pi\) | |||||||
\(510\) | 14.7446i | 0.652900i | ||||||||
\(511\) | 17.4891 | + | 5.48913i | 0.773673 | + | 0.242825i | ||||
\(512\) | − | 50.1369i | − | 2.21576i | ||||||
\(513\) | − | 7.72049i | − | 0.340868i | ||||||
\(514\) | −25.8333 | −1.13946 | ||||||||
\(515\) | −6.11684 | −0.269540 | ||||||||
\(516\) | −25.5383 | −1.12426 | ||||||||
\(517\) | −4.16381 | −0.183124 | ||||||||
\(518\) | −1.48913 | + | 4.74456i | −0.0654284 | + | 0.208464i | ||||
\(519\) | − | 6.92820i | − | 0.304114i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 22.6277i | 0.991338i | 0.868511 | + | 0.495669i | \(0.165077\pi\) | ||||
−0.868511 | + | 0.495669i | \(0.834923\pi\) | |||||||
\(522\) | 6.74456 | 0.295201 | ||||||||
\(523\) | −10.3923 | −0.454424 | −0.227212 | − | 0.973845i | \(-0.572961\pi\) | ||||
−0.227212 | + | 0.973845i | \(0.572961\pi\) | |||||||
\(524\) | 81.3687 | 3.55461 | ||||||||
\(525\) | −0.792287 | + | 2.52434i | −0.0345782 | + | 0.110171i | ||||
\(526\) | −24.7446 | −1.07891 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | 21.1345 | 0.919760 | ||||||||
\(529\) | 42.8832 | 1.86449 | ||||||||
\(530\) | −18.6101 | −0.808372 | ||||||||
\(531\) | 7.37228i | 0.319930i | ||||||||
\(532\) | 85.2119 | + | 26.7446i | 3.69441 | + | 1.15952i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 6.63325i | − | 0.287049i | ||||||
\(535\) | 15.1460 | 0.654820 | ||||||||
\(536\) | − | 40.3894i | − | 1.74456i | ||||||
\(537\) | 1.48913i | 0.0642605i | ||||||||
\(538\) | −64.0482 | −2.76131 | ||||||||
\(539\) | 13.2665 | − | 19.0526i | 0.571429 | − | 0.820652i | ||||
\(540\) | 4.37228 | 0.188153 | ||||||||
\(541\) | 9.50744i | 0.408757i | 0.978892 | + | 0.204378i | \(0.0655173\pi\) | ||||
−0.978892 | + | 0.204378i | \(0.934483\pi\) | |||||||
\(542\) | − | 2.00000i | − | 0.0859074i | ||||||
\(543\) | 5.25544 | 0.225532 | ||||||||
\(544\) | 24.0000i | 1.02899i | ||||||||
\(545\) | −8.51278 | −0.364647 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4511i | 1.04545i | 0.852500 | + | 0.522727i | \(0.175085\pi\) | ||||
−0.852500 | + | 0.522727i | \(0.824915\pi\) | |||||||
\(548\) | −5.48913 | −0.234484 | ||||||||
\(549\) | −1.08724 | −0.0464023 | ||||||||
\(550\) | −8.37228 | −0.356995 | ||||||||
\(551\) | 20.6277i | 0.878770i | ||||||||
\(552\) | −48.6072 | −2.06886 | ||||||||
\(553\) | −10.7446 | + | 34.2337i | −0.456905 | + | 1.45576i | ||||
\(554\) | 39.7228 | 1.68766 | ||||||||
\(555\) | −0.744563 | −0.0316049 | ||||||||
\(556\) | 15.1460 | 0.642335 | ||||||||
\(557\) | 33.4612i | 1.41780i | 0.705311 | + | 0.708898i | \(0.250807\pi\) | ||||
−0.705311 | + | 0.708898i | \(0.749193\pi\) | |||||||
\(558\) | −11.9769 | −0.507022 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −5.04868 | + | 16.0858i | −0.213345 | + | 0.679749i | ||||
\(561\) | 19.3723 | 0.817898 | ||||||||
\(562\) | 68.4674 | 2.88812 | ||||||||
\(563\) | 17.9104 | 0.754834 | 0.377417 | − | 0.926043i | \(-0.376812\pi\) | ||||
0.377417 | + | 0.926043i | \(0.376812\pi\) | |||||||
\(564\) | −5.48913 | −0.231134 | ||||||||
\(565\) | 7.37228i | 0.310154i | ||||||||
\(566\) | 55.7228i | 2.34220i | ||||||||
\(567\) | −2.52434 | − | 0.792287i | −0.106012 | − | 0.0332729i | ||||
\(568\) | − | 88.2969i | − | 3.70486i | ||||||
\(569\) | 5.25106i | 0.220136i | 0.993924 | + | 0.110068i | \(0.0351068\pi\) | ||||
−0.993924 | + | 0.110068i | \(0.964893\pi\) | |||||||
\(570\) | 19.4891i | 0.816310i | ||||||||
\(571\) | 10.3923i | 0.434904i | 0.976071 | + | 0.217452i | \(0.0697746\pi\) | ||||
−0.976071 | + | 0.217452i | \(0.930225\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.74456i | 0.114656i | ||||||||
\(574\) | 16.4356 | − | 52.3663i | 0.686011 | − | 2.18573i | ||||
\(575\) | 8.11684 | 0.338496 | ||||||||
\(576\) | −2.37228 | −0.0988451 | ||||||||
\(577\) | 42.4674i | 1.76794i | 0.467544 | + | 0.883970i | \(0.345139\pi\) | ||||
−0.467544 | + | 0.883970i | \(0.654861\pi\) | |||||||
\(578\) | 43.2087i | 1.79724i | ||||||||
\(579\) | −15.1460 | −0.629447 | ||||||||
\(580\) | −11.6819 | −0.485066 | ||||||||
\(581\) | −15.4891 | − | 4.86141i | −0.642597 | − | 0.201685i | ||||
\(582\) | 6.63325i | 0.274957i | ||||||||
\(583\) | 24.4511i | 1.01266i | ||||||||
\(584\) | 41.4891i | 1.71683i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 63.2119i | − | 2.61126i | ||||||
\(587\) | − | 4.00000i | − | 0.165098i | −0.996587 | − | 0.0825488i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825488i | \(-0.0263060\pi\) | |||||||
\(588\) | 17.4891 | − | 25.1168i | 0.721239 | − | 1.03580i | ||||
\(589\) | − | 36.6303i | − | 1.50933i | ||||||
\(590\) | − | 18.6101i | − | 0.766167i | ||||||
\(591\) | −10.0974 | −0.415350 | ||||||||
\(592\) | −4.74456 | −0.195000 | ||||||||
\(593\) | 40.3894 | 1.65859 | 0.829297 | − | 0.558808i | \(-0.188741\pi\) | ||||
0.829297 | + | 0.558808i | \(0.188741\pi\) | |||||||
\(594\) | − | 8.37228i | − | 0.343519i | ||||||
\(595\) | −4.62772 | + | 14.7446i | −0.189718 | + | 0.604468i | ||||
\(596\) | 60.5841i | 2.48162i | ||||||||
\(597\) | 4.74456 | 0.194182 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.7228 | 0.560699 | 0.280349 | − | 0.959898i | \(-0.409550\pi\) | ||||
0.280349 | + | 0.959898i | \(0.409550\pi\) | |||||||
\(600\) | −5.98844 | −0.244477 | ||||||||
\(601\) | 16.5282 | 0.674200 | 0.337100 | − | 0.941469i | \(-0.390554\pi\) | ||||
0.337100 | + | 0.941469i | \(0.390554\pi\) | |||||||
\(602\) | −37.2203 | − | 11.6819i | −1.51698 | − | 0.476120i | ||||
\(603\) | −6.74456 | −0.274660 | ||||||||
\(604\) | 8.21782i | 0.334378i | ||||||||
\(605\) | 11.0000i | 0.447214i | ||||||||
\(606\) | −26.2337 | −1.06567 | ||||||||
\(607\) | −6.04334 | −0.245292 | −0.122646 | − | 0.992451i | \(-0.539138\pi\) | ||||
−0.122646 | + | 0.992451i | \(0.539138\pi\) | |||||||
\(608\) | 31.7228i | 1.28653i | ||||||||
\(609\) | 6.74456 | + | 2.11684i | 0.273303 | + | 0.0857788i | ||||
\(610\) | 2.74456 | 0.111124 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 25.5383 | 1.03233 | ||||||||
\(613\) | 5.63858i | 0.227740i | 0.993496 | + | 0.113870i | \(0.0363248\pi\) | ||||
−0.993496 | + | 0.113870i | \(0.963675\pi\) | |||||||
\(614\) | 22.2337i | 0.897279i | ||||||||
\(615\) | 8.21782 | 0.331375 | ||||||||
\(616\) | 50.1369 | + | 15.7359i | 2.02007 | + | 0.634019i | ||||
\(617\) | 14.7446 | 0.593594 | 0.296797 | − | 0.954941i | \(-0.404082\pi\) | ||||
0.296797 | + | 0.954941i | \(0.404082\pi\) | |||||||
\(618\) | 15.4410i | 0.621127i | ||||||||
\(619\) | − | 19.4891i | − | 0.783334i | −0.920107 | − | 0.391667i | \(-0.871899\pi\) | ||
0.920107 | − | 0.391667i | \(-0.128101\pi\) | |||||||
\(620\) | 20.7446 | 0.833122 | ||||||||
\(621\) | 8.11684i | 0.325718i | ||||||||
\(622\) | 40.3894 | 1.61947 | ||||||||
\(623\) | 2.08191 | − | 6.63325i | 0.0834099 | − | 0.265756i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 17.3205 | 0.692267 | ||||||||
\(627\) | 25.6060 | 1.02260 | ||||||||
\(628\) | 87.9565i | 3.50985i | ||||||||
\(629\) | −4.34896 | −0.173404 | ||||||||
\(630\) | 6.37228 | + | 2.00000i | 0.253878 | + | 0.0796819i | ||||
\(631\) | 23.6060 | 0.939739 | 0.469869 | − | 0.882736i | \(-0.344301\pi\) | ||||
0.469869 | + | 0.882736i | \(0.344301\pi\) | |||||||
\(632\) | −81.2119 | −3.23044 | ||||||||
\(633\) | −3.46410 | −0.137686 | ||||||||
\(634\) | − | 33.4612i | − | 1.32891i | ||||||
\(635\) | −19.6974 | −0.781666 | ||||||||
\(636\) | 32.2337i | 1.27815i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.3692i | 0.885604i | ||||||||
\(639\) | −14.7446 | −0.583286 | ||||||||
\(640\) | 14.2063 | 0.561552 | ||||||||
\(641\) | 44.7446 | 1.76730 | 0.883652 | − | 0.468144i | \(-0.155077\pi\) | ||||
0.883652 | + | 0.468144i | \(0.155077\pi\) | |||||||
\(642\) | − | 38.2337i | − | 1.50896i | ||||||
\(643\) | − | 0.627719i | − | 0.0247548i | −0.999923 | − | 0.0123774i | \(-0.996060\pi\) | ||
0.999923 | − | 0.0123774i | \(-0.00393995\pi\) | |||||||
\(644\) | −89.5865 | − | 28.1176i | −3.53020 | − | 1.10799i | ||||
\(645\) | − | 5.84096i | − | 0.229988i | ||||||
\(646\) | 113.835i | 4.47879i | ||||||||
\(647\) | 3.76631i | 0.148069i | 0.997256 | + | 0.0740345i | \(0.0235875\pi\) | ||||
−0.997256 | + | 0.0740345i | \(0.976413\pi\) | |||||||
\(648\) | − | 5.98844i | − | 0.235248i | ||||||
\(649\) | −24.4511 | −0.959789 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.9769 | − | 3.75906i | −0.469411 | − | 0.147329i | ||||
\(652\) | −70.9783 | −2.77972 | ||||||||
\(653\) | −38.3505 | −1.50077 | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||||
−0.750386 | + | 0.661000i | \(0.770132\pi\) | |||||||
\(654\) | 21.4891i | 0.840291i | ||||||||
\(655\) | 18.6101i | 0.727158i | ||||||||
\(656\) | 52.3663 | 2.04456 | ||||||||
\(657\) | 6.92820 | 0.270295 | ||||||||
\(658\) | −8.00000 | − | 2.51087i | −0.311872 | − | 0.0978841i | ||||
\(659\) | − | 19.9923i | − | 0.778790i | −0.921071 | − | 0.389395i | \(-0.872684\pi\) | ||
0.921071 | − | 0.389395i | \(-0.127316\pi\) | |||||||
\(660\) | 14.5012i | 0.564459i | ||||||||
\(661\) | − | 20.2337i | − | 0.786999i | −0.919325 | − | 0.393500i | \(-0.871264\pi\) | ||
0.919325 | − | 0.393500i | \(-0.128736\pi\) | |||||||
\(662\) | − | 38.8048i | − | 1.50819i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 36.7446i | − | 1.42597i | ||||||
\(665\) | −6.11684 | + | 19.4891i | −0.237201 | + | 0.755756i | ||||
\(666\) | 1.87953i | 0.0728302i | ||||||||
\(667\) | − | 21.6867i | − | 0.839712i | ||||||
\(668\) | −103.443 | −4.00233 | ||||||||
\(669\) | 8.62772 | 0.333567 | ||||||||
\(670\) | 17.0256 | 0.657755 | ||||||||
\(671\) | − | 3.60597i | − | 0.139207i | ||||||
\(672\) | 10.3723 | + | 3.25544i | 0.400119 | + | 0.125581i | ||||
\(673\) | 24.7460i | 0.953890i | 0.878933 | + | 0.476945i | \(0.158256\pi\) | ||||
−0.878933 | + | 0.476945i | \(0.841744\pi\) | |||||||
\(674\) | 56.9783 | 2.19472 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 56.8397 | 2.18614 | ||||||||
\(677\) | −25.6309 | −0.985076 | −0.492538 | − | 0.870291i | \(-0.663931\pi\) | ||||
−0.492538 | + | 0.870291i | \(0.663931\pi\) | |||||||
\(678\) | 18.6101 | 0.714718 | ||||||||
\(679\) | −2.08191 | + | 6.63325i | −0.0798963 | + | 0.254561i | ||||
\(680\) | −34.9783 | −1.34135 | ||||||||
\(681\) | − | 1.38219i | − | 0.0529658i | ||||||
\(682\) | − | 39.7228i | − | 1.52107i | ||||||
\(683\) | −8.74456 | −0.334601 | −0.167301 | − | 0.985906i | \(-0.553505\pi\) | ||||
−0.167301 | + | 0.985906i | \(0.553505\pi\) | |||||||
\(684\) | 33.7562 | 1.29070 | ||||||||
\(685\) | − | 1.25544i | − | 0.0479678i | ||||||
\(686\) | 36.9783 | − | 28.6060i | 1.41184 | − | 1.09218i | ||||
\(687\) | −22.7446 | −0.867759 | ||||||||
\(688\) | − | 37.2203i | − | 1.41901i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | − | 20.4897i | − | 0.780028i | ||||||
\(691\) | 26.4674i | 1.00687i | 0.864034 | + | 0.503433i | \(0.167930\pi\) | ||||
−0.864034 | + | 0.503433i | \(0.832070\pi\) | |||||||
\(692\) | 30.2921 | 1.15153 | ||||||||
\(693\) | 2.62772 | − | 8.37228i | 0.0998188 | − | 0.318037i | ||||
\(694\) | −61.2119 | −2.32357 | ||||||||
\(695\) | 3.46410i | 0.131401i | ||||||||
\(696\) | 16.0000i | 0.606478i | ||||||||
\(697\) | 48.0000 | 1.81813 | ||||||||
\(698\) | 44.2337i | 1.67427i | ||||||||
\(699\) | −23.3639 | −0.883702 | ||||||||
\(700\) | −11.0371 | − | 3.46410i | −0.417164 | − | 0.130931i | ||||
\(701\) | 18.7027i | 0.706391i | 0.935549 | + | 0.353196i | \(0.114905\pi\) | ||||
−0.935549 | + | 0.353196i | \(0.885095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.74839 | −0.216805 | ||||||||
\(704\) | − | 7.86797i | − | 0.296535i | ||||||
\(705\) | − | 1.25544i | − | 0.0472825i | ||||||
\(706\) | −72.5610 | −2.73087 | ||||||||
\(707\) | −26.2337 | − | 8.23369i | −0.986619 | − | 0.309660i | ||||
\(708\) | −32.2337 | −1.21142 | ||||||||
\(709\) | −43.0951 | −1.61847 | −0.809235 | − | 0.587485i | \(-0.800118\pi\) | ||||
−0.809235 | + | 0.587485i | \(0.800118\pi\) | |||||||
\(710\) | 37.2203 | 1.39685 | ||||||||
\(711\) | 13.5615i | 0.508594i | ||||||||
\(712\) | 15.7359 | 0.589729 | ||||||||
\(713\) | 38.5109i | 1.44224i | ||||||||
\(714\) | 37.2203 | + | 11.6819i | 1.39293 | + | 0.437185i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.51087 | −0.243323 | ||||||||
\(717\) | 15.6434 | 0.584212 | ||||||||
\(718\) | 56.9783 | 2.12641 | ||||||||
\(719\) | − | 11.3723i | − | 0.424115i | −0.977257 | − | 0.212057i | \(-0.931984\pi\) | ||
0.977257 | − | 0.212057i | \(-0.0680163\pi\) | |||||||
\(720\) | 6.37228i | 0.237481i | ||||||||
\(721\) | −4.84630 | + | 15.4410i | −0.180485 | + | 0.575052i | ||||
\(722\) | 102.503i | 3.81477i | ||||||||
\(723\) | 13.8564i | 0.515325i | ||||||||
\(724\) | 22.9783i | 0.853980i | ||||||||
\(725\) | − | 2.67181i | − | 0.0992287i | ||||||
\(726\) | 27.7677 | 1.03056 | ||||||||
\(727\) | 42.1168i | 1.56203i | 0.624514 | + | 0.781014i | \(0.285297\pi\) | ||||
−0.624514 | + | 0.781014i | \(0.714703\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −17.4891 | −0.647302 | ||||||||
\(731\) | − | 34.1168i | − | 1.26186i | ||||||
\(732\) | − | 4.75372i | − | 0.175703i | ||||||
\(733\) | 45.7330 | 1.68919 | 0.844594 | − | 0.535407i | \(-0.179842\pi\) | ||||
0.844594 | + | 0.535407i | \(0.179842\pi\) | |||||||
\(734\) | −15.4410 | −0.569937 | ||||||||
\(735\) | 5.74456 | + | 4.00000i | 0.211891 | + | 0.147542i | ||||
\(736\) | − | 33.3514i | − | 1.22935i | ||||||
\(737\) | − | 22.3692i | − | 0.823979i | ||||||
\(738\) | − | 20.7446i | − | 0.763618i | ||||||
\(739\) | − | 16.3258i | − | 0.600556i | −0.953852 | − | 0.300278i | \(-0.902921\pi\) | ||
0.953852 | − | 0.300278i | \(-0.0970794\pi\) | |||||||
\(740\) | − | 3.25544i | − | 0.119672i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −14.7446 | + | 46.9783i | −0.541290 | + | 1.72463i | ||||
\(743\) | 22.0742i | 0.809825i | 0.914355 | + | 0.404912i | \(0.132698\pi\) | ||||
−0.914355 | + | 0.404912i | \(0.867302\pi\) | |||||||
\(744\) | − | 28.4125i | − | 1.04165i | ||||||
\(745\) | −13.8564 | −0.507659 | ||||||||
\(746\) | 46.4674 | 1.70129 | ||||||||
\(747\) | −6.13592 | −0.224501 | ||||||||
\(748\) | 84.7011i | 3.09698i | ||||||||
\(749\) | 12.0000 | − | 38.2337i | 0.438470 | − | 1.39703i | ||||
\(750\) | − | 2.52434i | − | 0.0921758i | ||||||
\(751\) | 0.861407 | 0.0314332 | 0.0157166 | − | 0.999876i | \(-0.494997\pi\) | ||||
0.0157166 | + | 0.999876i | \(0.494997\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | −5.48913 | −0.200035 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.87953 | −0.0684030 | ||||||||
\(756\) | 3.46410 | − | 11.0371i | 0.125988 | − | 0.401416i | ||||
\(757\) | −0.978251 | −0.0355551 | −0.0177776 | − | 0.999842i | \(-0.505659\pi\) | ||||
−0.0177776 | + | 0.999842i | \(0.505659\pi\) | |||||||
\(758\) | 62.1687i | 2.25807i | ||||||||
\(759\) | −26.9205 | −0.977153 | ||||||||
\(760\) | −46.2337 | −1.67707 | ||||||||
\(761\) | −1.87953 | −0.0681328 | −0.0340664 | − | 0.999420i | \(-0.510846\pi\) | ||||
−0.0340664 | + | 0.999420i | \(0.510846\pi\) | |||||||
\(762\) | 49.7228i | 1.80127i | ||||||||
\(763\) | −6.74456 | + | 21.4891i | −0.244170 | + | 0.777959i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 5.84096i | 0.211180i | ||||||||
\(766\) | 10.6873 | 0.386146 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 31.1168i | − | 1.12283i | ||||||
\(769\) | 8.60535 | 0.310317 | 0.155158 | − | 0.987890i | \(-0.450411\pi\) | ||||
0.155158 | + | 0.987890i | \(0.450411\pi\) | |||||||
\(770\) | −6.63325 | + | 21.1345i | −0.239046 | + | 0.761633i | ||||
\(771\) | −10.2337 | −0.368557 | ||||||||
\(772\) | − | 66.2227i | − | 2.38341i | ||||||
\(773\) | − | 34.4674i | − | 1.23971i | −0.784718 | − | 0.619853i | \(-0.787192\pi\) | ||
0.784718 | − | 0.619853i | \(-0.212808\pi\) | |||||||
\(774\) | −14.7446 | −0.529982 | ||||||||
\(775\) | 4.74456i | 0.170430i | ||||||||
\(776\) | −15.7359 | −0.564887 | ||||||||
\(777\) | −0.589907 | + | 1.87953i | −0.0211628 | + | 0.0674277i | ||||
\(778\) | − | 5.04868i | − | 0.181004i | ||||||
\(779\) | 63.4456 | 2.27318 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 48.9022i | − | 1.74986i | ||||||
\(782\) | − | 119.679i | − | 4.27972i | ||||||
\(783\) | 2.67181 | 0.0954829 | ||||||||
\(784\) | 36.6060 | + | 25.4891i | 1.30736 | + | 0.910326i | ||||
\(785\) | −20.1168 | −0.718001 | ||||||||
\(786\) | 46.9783 | 1.67566 | ||||||||
\(787\) | −34.9360 | −1.24533 | −0.622666 | − | 0.782487i | \(-0.713951\pi\) | ||||
−0.622666 | + | 0.782487i | \(0.713951\pi\) | |||||||
\(788\) | − | 44.1485i | − | 1.57272i | ||||||
\(789\) | −9.80240 | −0.348975 | ||||||||
\(790\) | − | 34.2337i | − | 1.21798i | ||||||
\(791\) | 18.6101 | + | 5.84096i | 0.661700 | + | 0.207681i | ||||
\(792\) | 19.8614 | 0.705744 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 11.3870 | 0.404108 | ||||||||
\(795\) | −7.37228 | −0.261468 | ||||||||
\(796\) | 20.7446i | 0.735272i | ||||||||
\(797\) | 46.0000i | 1.62940i | 0.579880 | + | 0.814702i | \(0.303099\pi\) | ||||
−0.579880 | + | 0.814702i | \(0.696901\pi\) | |||||||
\(798\) | 49.1971 | + | 15.4410i | 1.74156 | + | 0.546605i | ||||
\(799\) | − | 7.33296i | − | 0.259422i | ||||||
\(800\) | − | 4.10891i | − | 0.145272i | ||||||
\(801\) | − | 2.62772i | − | 0.0928459i | ||||||
\(802\) | − | 69.9817i | − | 2.47114i | ||||||
\(803\) | 22.9783i | 0.810885i | ||||||||
\(804\) | − | 29.4891i | − | 1.04000i | ||||||
\(805\) | 6.43087 | − | 20.4897i | 0.226658 | − | 0.722165i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −25.3723 | −0.893147 | ||||||||
\(808\) | − | 62.2337i | − | 2.18937i | ||||||
\(809\) | − | 13.2665i | − | 0.466425i | −0.972426 | − | 0.233213i | \(-0.925076\pi\) | ||
0.972426 | − | 0.233213i | \(-0.0749238\pi\) | |||||||
\(810\) | 2.52434 | 0.0886962 | ||||||||
\(811\) | 6.63325 | 0.232925 | 0.116462 | − | 0.993195i | \(-0.462845\pi\) | ||||
0.116462 | + | 0.993195i | \(0.462845\pi\) | |||||||
\(812\) | −9.25544 | + | 29.4891i | −0.324802 | + | 1.03487i | ||||
\(813\) | − | 0.792287i | − | 0.0277867i | ||||||
\(814\) | −6.23369 | −0.218491 | ||||||||
\(815\) | − | 16.2337i | − | 0.568641i | ||||||
\(816\) | 37.2203i | 1.30297i | ||||||||
\(817\) | − | 45.0951i | − | 1.57768i | ||||||
\(818\) | − | 87.4456i | − | 3.05746i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 35.9306i | 1.25475i | ||||||||
\(821\) | 16.5282i | 0.576839i | 0.957504 | + | 0.288419i | \(0.0931297\pi\) | ||||
−0.957504 | + | 0.288419i | \(0.906870\pi\) | |||||||
\(822\) | −3.16915 | −0.110537 | ||||||||
\(823\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(824\) | −36.6303 | −1.27608 | ||||||||
\(825\) | −3.31662 | −0.115470 | ||||||||
\(826\) | −46.9783 | − | 14.7446i | −1.63458 | − | 0.513029i | ||||
\(827\) | − | 11.9769i | − | 0.416477i | −0.978078 | − | 0.208238i | \(-0.933227\pi\) | ||
0.978078 | − | 0.208238i | \(-0.0667730\pi\) | |||||||
\(828\) | −35.4891 | −1.23333 | ||||||||
\(829\) | − | 21.4891i | − | 0.746348i | −0.927761 | − | 0.373174i | \(-0.878269\pi\) | ||
0.927761 | − | 0.373174i | \(-0.121731\pi\) | |||||||
\(830\) | 15.4891 | 0.537635 | ||||||||
\(831\) | 15.7359 | 0.545874 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.5538 | + | 23.3639i | 1.16257 | + | 0.809509i | ||||
\(834\) | 8.74456 | 0.302799 | ||||||||
\(835\) | − | 23.6588i | − | 0.818747i | ||||||
\(836\) | 111.957i | 3.87210i | ||||||||
\(837\) | −4.74456 | −0.163996 | ||||||||
\(838\) | 11.6819 | 0.403545 | ||||||||
\(839\) | 6.11684i | 0.211177i | 0.994410 | + | 0.105588i | \(0.0336726\pi\) | ||||
−0.994410 | + | 0.105588i | \(0.966327\pi\) | |||||||
\(840\) | −4.74456 | + | 15.1168i | −0.163703 | + | 0.521581i | ||||
\(841\) | 21.8614 | 0.753842 | ||||||||
\(842\) | 47.6126i | 1.64084i | ||||||||
\(843\) | 27.1229 | 0.934162 | ||||||||
\(844\) | − | 15.1460i | − | 0.521348i | ||||||
\(845\) | 13.0000i | 0.447214i | ||||||||
\(846\) | −3.16915 | −0.108958 | ||||||||
\(847\) | 27.7677 | + | 8.71516i | 0.954110 | + | 0.299456i | ||||
\(848\) | −46.9783 | −1.61324 | ||||||||
\(849\) | 22.0742i | 0.757586i | ||||||||
\(850\) | − | 14.7446i | − | 0.505734i | ||||||
\(851\) | 6.04350 | 0.207168 | ||||||||
\(852\) | − | 64.4674i | − | 2.20862i | ||||||
\(853\) | 38.4001 | 1.31479 | 0.657397 | − | 0.753545i | \(-0.271658\pi\) | ||||
0.657397 | + | 0.753545i | \(0.271658\pi\) | |||||||
\(854\) | 2.17448 | − | 6.92820i | 0.0744092 | − | 0.237078i | ||||
\(855\) | 7.72049i | 0.264035i | ||||||||
\(856\) | 90.7011 | 3.10010 | ||||||||
\(857\) | 20.7846 | 0.709989 | 0.354994 | − | 0.934868i | \(-0.384483\pi\) | ||||
0.354994 | + | 0.934868i | \(0.384483\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 47.7228i | − | 1.62828i | −0.580668 | − | 0.814141i | \(-0.697208\pi\) | ||
0.580668 | − | 0.814141i | \(-0.302792\pi\) | |||||||
\(860\) | 25.5383 | 0.870850 | ||||||||
\(861\) | 6.51087 | − | 20.7446i | 0.221890 | − | 0.706973i | ||||
\(862\) | −67.7228 | −2.30665 | ||||||||
\(863\) | −44.1168 | −1.50175 | −0.750877 | − | 0.660442i | \(-0.770369\pi\) | ||||
−0.750877 | + | 0.660442i | \(0.770369\pi\) | |||||||
\(864\) | 4.10891 | 0.139788 | ||||||||
\(865\) | 6.92820i | 0.235566i | ||||||||
\(866\) | 83.2482 | 2.82889 | ||||||||
\(867\) | 17.1168i | 0.581318i | ||||||||
\(868\) | 16.4356 | − | 52.3663i | 0.557862 | − | 1.77743i | ||||
\(869\) | −44.9783 | −1.52578 | ||||||||
\(870\) | −6.74456 | −0.228662 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −50.9783 | −1.72634 | ||||||||
\(873\) | 2.62772i | 0.0889348i | ||||||||
\(874\) | − | 158.190i | − | 5.35086i | ||||||
\(875\) | 0.792287 | − | 2.52434i | 0.0267842 | − | 0.0853382i | ||||
\(876\) | 30.2921i | 1.02347i | ||||||||
\(877\) | 13.6540i | 0.461064i | 0.973065 | + | 0.230532i | \(0.0740466\pi\) | ||||
−0.973065 | + | 0.230532i | \(0.925953\pi\) | |||||||
\(878\) | − | 47.4891i | − | 1.60268i | ||||||
\(879\) | − | 25.0410i | − | 0.844612i | ||||||
\(880\) | −21.1345 | −0.712443 | ||||||||
\(881\) | 1.37228i | 0.0462333i | 0.999733 | + | 0.0231167i | \(0.00735892\pi\) | ||||
−0.999733 | + | 0.0231167i | \(0.992641\pi\) | |||||||
\(882\) | 10.0974 | − | 14.5012i | 0.339996 | − | 0.488281i | ||||
\(883\) | −49.7228 | −1.67331 | −0.836653 | − | 0.547733i | \(-0.815491\pi\) | ||||
−0.836653 | + | 0.547733i | \(0.815491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 7.37228i | − | 0.247817i | ||||||
\(886\) | − | 86.4174i | − | 2.90325i | ||||||
\(887\) | 40.7769 | 1.36916 | 0.684578 | − | 0.728940i | \(-0.259987\pi\) | ||||
0.684578 | + | 0.728940i | \(0.259987\pi\) | |||||||
\(888\) | −4.45877 | −0.149626 | ||||||||
\(889\) | −15.6060 | + | 49.7228i | −0.523407 | + | 1.66765i | ||||
\(890\) | 6.63325i | 0.222347i | ||||||||
\(891\) | − | 3.31662i | − | 0.111111i | ||||||
\(892\) | 37.7228i | 1.26305i | ||||||||
\(893\) | − | 9.69259i | − | 0.324350i | ||||||
\(894\) | 34.9783i | 1.16985i | ||||||||
\(895\) | − | 1.48913i | − | 0.0497760i | ||||||
\(896\) | 11.2554 | − | 35.8614i | 0.376018 | − | 1.19805i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 80.0791i | − | 2.67227i | ||||||
\(899\) | 12.6766 | 0.422788 | ||||||||
\(900\) | −4.37228 | −0.145743 | ||||||||
\(901\) | −43.0612 | −1.43458 | ||||||||
\(902\) | 68.8019 | 2.29085 | ||||||||
\(903\) | −14.7446 | − | 4.62772i | −0.490668 | − | 0.154001i | ||||
\(904\) | 44.1485i | 1.46836i | ||||||||
\(905\) | −5.25544 | −0.174697 | ||||||||
\(906\) | 4.74456i | 0.157628i | ||||||||
\(907\) | 24.4674 | 0.812426 | 0.406213 | − | 0.913778i | \(-0.366849\pi\) | ||||
0.406213 | + | 0.913778i | \(0.366849\pi\) | |||||||
\(908\) | 6.04334 | 0.200555 | ||||||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.2554 | −0.439172 | −0.219586 | − | 0.975593i | \(-0.570471\pi\) | ||||
−0.219586 | + | 0.975593i | \(0.570471\pi\) | |||||||
\(912\) | 49.1971i | 1.62908i | ||||||||
\(913\) | − | 20.3505i | − | 0.673504i | ||||||
\(914\) | 20.9783 | 0.693899 | ||||||||
\(915\) | 1.08724 | 0.0359431 | ||||||||
\(916\) | − | 99.4456i | − | 3.28578i | ||||||
\(917\) | 46.9783 | + | 14.7446i | 1.55136 | + | 0.486908i | ||||
\(918\) | 14.7446 | 0.486643 | ||||||||
\(919\) | 29.9971i | 0.989513i | 0.869032 | + | 0.494757i | \(0.164743\pi\) | ||||
−0.869032 | + | 0.494757i | \(0.835257\pi\) | |||||||
\(920\) | 48.6072 | 1.60253 | ||||||||
\(921\) | 8.80773i | 0.290225i | ||||||||
\(922\) | 24.7446i | 0.814919i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 36.6060 | + | 11.4891i | 1.20425 | + | 0.377964i | ||||
\(925\) | 0.744563 | 0.0244811 | ||||||||
\(926\) | − | 64.3432i | − | 2.11445i | ||||||
\(927\) | 6.11684i | 0.200904i | ||||||||
\(928\) | −10.9783 | −0.360379 | ||||||||
\(929\) | 59.4891i | 1.95177i | 0.218274 | + | 0.975887i | \(0.429957\pi\) | ||||
−0.218274 | + | 0.975887i | \(0.570043\pi\) | |||||||
\(930\) | 11.9769 | 0.392737 | ||||||||
\(931\) | 44.3508 | + | 30.8820i | 1.45354 | + | 1.01212i | ||||
\(932\) | − | 102.153i | − | 3.34614i | ||||||
\(933\) | 16.0000 | 0.523816 | ||||||||
\(934\) | 98.3943 | 3.21956 | ||||||||
\(935\) | −19.3723 | −0.633541 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.92287 | 0.258829 | 0.129414 | − | 0.991591i | \(-0.458690\pi\) | ||||
0.129414 | + | 0.991591i | \(0.458690\pi\) | |||||||
\(938\) | 13.4891 | − | 42.9783i | 0.440436 | − | 1.40329i | ||||
\(939\) | 6.86141 | 0.223914 | ||||||||
\(940\) | 5.48913 | 0.179036 | ||||||||
\(941\) | 26.4232 | 0.861371 | 0.430686 | − | 0.902502i | \(-0.358272\pi\) | ||||
0.430686 | + | 0.902502i | \(0.358272\pi\) | |||||||
\(942\) | 50.7817i | 1.65456i | ||||||||
\(943\) | −66.7028 | −2.17214 | ||||||||
\(944\) | − | 46.9783i | − | 1.52901i | ||||||
\(945\) | 2.52434 | + | 0.792287i | 0.0821167 | + | 0.0257731i | ||||
\(946\) | − | 48.9022i | − | 1.58995i | ||||||
\(947\) | 48.3505 | 1.57118 | 0.785591 | − | 0.618747i | \(-0.212359\pi\) | ||||
0.785591 | + | 0.618747i | \(0.212359\pi\) | |||||||
\(948\) | −59.2945 | −1.92580 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | − | 19.4891i | − | 0.632311i | ||||||
\(951\) | − | 13.2554i | − | 0.429837i | ||||||
\(952\) | −27.7128 | + | 88.2969i | −0.898177 | + | 2.86172i | ||||
\(953\) | − | 41.3841i | − | 1.34056i | −0.742108 | − | 0.670281i | \(-0.766174\pi\) | ||
0.742108 | − | 0.670281i | \(-0.233826\pi\) | |||||||
\(954\) | 18.6101i | 0.602525i | ||||||||
\(955\) | − | 2.74456i | − | 0.0888120i | ||||||
\(956\) | 68.3972i | 2.21212i | ||||||||
\(957\) | 8.86141i | 0.286449i | ||||||||
\(958\) | 18.9783i | 0.613159i | ||||||||
\(959\) | −3.16915 | − | 0.994667i | −0.102337 | − | 0.0321195i | ||||
\(960\) | 2.37228 | 0.0765651 | ||||||||
\(961\) | 8.48913 | 0.273843 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 15.1460i | − | 0.488074i | ||||||
\(964\) | −60.5841 | −1.95128 | ||||||||
\(965\) | 15.1460 | 0.487568 | ||||||||
\(966\) | −51.7228 | − | 16.2337i | −1.66415 | − | 0.522310i | ||||
\(967\) | − | 8.01544i | − | 0.257759i | −0.991660 | − | 0.128880i | \(-0.958862\pi\) | ||
0.991660 | − | 0.128880i | \(-0.0411381\pi\) | |||||||
\(968\) | 65.8728i | 2.11723i | ||||||||
\(969\) | 45.0951i | 1.44866i | ||||||||
\(970\) | − | 6.63325i | − | 0.212981i | ||||||
\(971\) | − | 7.37228i | − | 0.236588i | −0.992979 | − | 0.118294i | \(-0.962258\pi\) | ||
0.992979 | − | 0.118294i | \(-0.0377425\pi\) | |||||||
\(972\) | − | 4.37228i | − | 0.140241i | ||||||
\(973\) | 8.74456 | + | 2.74456i | 0.280338 | + | 0.0879866i | ||||
\(974\) | − | 37.8102i | − | 1.21152i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.92820 | 0.221766 | ||||||||
\(977\) | 33.0951 | 1.05881 | 0.529403 | − | 0.848371i | \(-0.322416\pi\) | ||||
0.529403 | + | 0.848371i | \(0.322416\pi\) | |||||||
\(978\) | −40.9793 | −1.31037 | ||||||||
\(979\) | 8.71516 | 0.278538 | ||||||||
\(980\) | −17.4891 | + | 25.1168i | −0.558670 | + | 0.802328i | ||||
\(981\) | 8.51278i | 0.271792i | ||||||||
\(982\) | −48.9783 | −1.56296 | ||||||||
\(983\) | 40.4674i | 1.29071i | 0.763883 | + | 0.645354i | \(0.223290\pi\) | ||||
−0.763883 | + | 0.645354i | \(0.776710\pi\) | |||||||
\(984\) | 49.2119 | 1.56882 | ||||||||
\(985\) | 10.0974 | 0.321728 | ||||||||
\(986\) | −39.3947 | −1.25458 | ||||||||
\(987\) | −3.16915 | − | 0.994667i | −0.100875 | − | 0.0316606i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.4102i | 1.50756i | ||||||||
\(990\) | 8.37228i | 0.266089i | ||||||||
\(991\) | −44.6277 | −1.41765 | −0.708823 | − | 0.705386i | \(-0.750774\pi\) | ||||
−0.708823 | + | 0.705386i | \(0.750774\pi\) | |||||||
\(992\) | 19.4950 | 0.618967 | ||||||||
\(993\) | − | 15.3723i | − | 0.487825i | ||||||
\(994\) | 29.4891 | − | 93.9565i | 0.935338 | − | 2.98012i | ||||
\(995\) | −4.74456 | −0.150413 | ||||||||
\(996\) | − | 26.8280i | − | 0.850076i | ||||||
\(997\) | 39.3947 | 1.24764 | 0.623822 | − | 0.781566i | \(-0.285579\pi\) | ||||
0.623822 | + | 0.781566i | \(0.285579\pi\) | |||||||
\(998\) | − | 86.7123i | − | 2.74483i | ||||||
\(999\) | 0.744563i | 0.0235569i |
(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 | 1155.2.i.a.76.8 | yes | 8 | |
7.6 | odd | 2 | inner | 1155.2.i.a.76.7 | yes | 8 | |
11.10 | odd | 2 | inner | 1155.2.i.a.76.2 | yes | 8 | |
77.76 | even | 2 | inner | 1155.2.i.a.76.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.i.a.76.1 | ✓ | 8 | 77.76 | even | 2 | inner | |
1155.2.i.a.76.2 | yes | 8 | 11.10 | odd | 2 | inner | |
1155.2.i.a.76.7 | yes | 8 | 7.6 | odd | 2 | inner | |
1155.2.i.a.76.8 | yes | 8 | 1.1 | even | 1 | trivial |