Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4100,2,Mod(1149,4100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4100.1149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4100.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.7386648287\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 4x^{5} + 14x^{4} - 14x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 164) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.6 | ||
Root | \(0.626295 + 0.626295i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4100.1149 |
Dual form | 4100.2.d.c.1149.3 |
$q$-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 \(\left(\mathbb{Z}/4100\mathbb{Z}\right)^\times\).
\(n\) | \(1477\) | \(2051\) | \(3901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.21551i | 1.27913i | 0.768739 | + | 0.639563i | \(0.220885\pi\) | ||||
−0.768739 | + | 0.639563i | \(0.779115\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.06479i | 1.91431i | 0.289574 | + | 0.957156i | \(0.406486\pi\) | ||||
−0.289574 | + | 0.957156i | \(0.593514\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.90849 | −0.636162 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.55961 | −0.771753 | −0.385876 | − | 0.922551i | \(-0.626101\pi\) | ||||
−0.385876 | + | 0.922551i | \(0.626101\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.93620i | − 1.36906i | −0.728987 | − | 0.684528i | \(-0.760009\pi\) | ||||
0.728987 | − | 0.684528i | \(-0.239991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 2.68821i | − 0.651986i | −0.945372 | − | 0.325993i | \(-0.894301\pi\) | ||||
0.945372 | − | 0.325993i | \(-0.105699\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.72069 | −1.08300 | −0.541500 | − | 0.840701i | \(-0.682143\pi\) | ||||
−0.541500 | + | 0.840701i | \(0.682143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −11.2211 | −2.44864 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.49482i | − 0.311692i | −0.987781 | − | 0.155846i | \(-0.950190\pi\) | ||||
0.987781 | − | 0.155846i | \(-0.0498103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.41826i | 0.465395i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.43102 | −0.451429 | −0.225715 | − | 0.974193i | \(-0.572472\pi\) | ||||
−0.225715 | + | 0.974193i | \(0.572472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.19339 | 0.573549 | 0.286774 | − | 0.957998i | \(-0.407417\pi\) | ||||
0.286774 | + | 0.957998i | \(0.407417\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.67085i | − 0.987168i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 2.90849i | − 0.478152i | −0.971001 | − | 0.239076i | \(-0.923155\pi\) | ||||
0.971001 | − | 0.239076i | \(-0.0768445\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.9362 | 1.75119 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.62441i | − 1.16271i | −0.813650 | − | 0.581356i | \(-0.802523\pi\) | ||||
0.813650 | − | 0.581356i | \(-0.197477\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.15171i | − 0.751454i | −0.926730 | − | 0.375727i | \(-0.877393\pi\) | ||||
0.926730 | − | 0.375727i | \(-0.122607\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −18.6521 | −2.66459 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.95575 | 0.833972 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 11.1192i | − 1.52734i | −0.645605 | − | 0.763672i | \(-0.723395\pi\) | ||||
0.645605 | − | 0.763672i | \(-0.276605\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 10.4587i | − 1.38529i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.49482 | −0.194609 | −0.0973046 | − | 0.995255i | \(-0.531022\pi\) | ||||
−0.0973046 | + | 0.995255i | \(0.531022\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.06380 | 0.136206 | 0.0681029 | − | 0.997678i | \(-0.478305\pi\) | ||||
0.0681029 | + | 0.997678i | \(0.478305\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 9.66608i | − 1.21781i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 10.5596i | − 1.29006i | −0.764156 | − | 0.645031i | \(-0.776844\pi\) | ||||
0.764156 | − | 0.645031i | \(-0.223156\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.31179 | 0.398693 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6023 | −1.49562 | −0.747808 | − | 0.663915i | \(-0.768894\pi\) | ||||
−0.747808 | + | 0.663915i | \(0.768894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.28490i | 0.969674i | 0.874604 | + | 0.484837i | \(0.161121\pi\) | ||||
−0.874604 | + | 0.484837i | \(0.838879\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 12.9639i | − 1.47737i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.28967 | 0.482625 | 0.241313 | − | 0.970447i | \(-0.422422\pi\) | ||||
0.241313 | + | 0.970447i | \(0.422422\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0831 | −1.23146 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.5606i | 1.15918i | 0.814909 | + | 0.579588i | \(0.196787\pi\) | ||||
−0.814909 | + | 0.579588i | \(0.803213\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 5.38595i | − 0.577435i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.36722 | −0.992923 | −0.496462 | − | 0.868059i | \(-0.665368\pi\) | ||||
−0.496462 | + | 0.868059i | \(0.665368\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 25.0008 | 2.62080 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.07498i | 0.733641i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.37641i | 0.342823i | 0.985200 | + | 0.171411i | \(0.0548328\pi\) | ||||
−0.985200 | + | 0.171411i | \(0.945167\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.88499 | 0.490960 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.24799 | −0.422691 | −0.211345 | − | 0.977411i | \(-0.567785\pi\) | ||||
−0.211345 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.11923i | 0.110281i | 0.998479 | + | 0.0551404i | \(0.0175606\pi\) | ||||
−0.998479 | + | 0.0551404i | \(0.982439\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.322149i | 0.0311434i | 0.999879 | + | 0.0155717i | \(0.00495682\pi\) | ||||
−0.999879 | + | 0.0155717i | \(0.995043\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.23763 | −0.310109 | −0.155055 | − | 0.987906i | \(-0.549555\pi\) | ||||
−0.155055 | + | 0.987906i | \(0.549555\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.44378 | 0.611616 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.10187i | 0.197727i | 0.995101 | + | 0.0988637i | \(0.0315208\pi\) | ||||
−0.995101 | + | 0.0988637i | \(0.968479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.42066i | 0.870941i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 13.6152 | 1.24810 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.44838 | −0.404398 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 2.21551i | − 0.199766i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0658i | 1.15940i | 0.814830 | + | 0.579700i | \(0.196830\pi\) | ||||
−0.814830 | + | 0.579700i | \(0.803170\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 16.8919 | 1.48725 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.43102 | 0.736622 | 0.368311 | − | 0.929703i | \(-0.379936\pi\) | ||||
0.368311 | + | 0.929703i | \(0.379936\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 23.9093i | − 2.07320i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.5606i | 1.41487i | 0.706779 | + | 0.707434i | \(0.250147\pi\) | ||||
−0.706779 | + | 0.707434i | \(0.749853\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.18303 | 0.185162 | 0.0925810 | − | 0.995705i | \(-0.470488\pi\) | ||||
0.0925810 | + | 0.995705i | \(0.470488\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.4137 | 0.961204 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.6348i | 1.05657i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 41.3240i | − 3.40834i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.43102 | −0.199157 | −0.0995785 | − | 0.995030i | \(-0.531749\pi\) | ||||
−0.0995785 | + | 0.995030i | \(0.531749\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.343113 | −0.0279221 | −0.0139611 | − | 0.999903i | \(-0.504444\pi\) | ||||
−0.0139611 | + | 0.999903i | \(0.504444\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.13040i | 0.414769i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6348i | 0.848746i | 0.905487 | + | 0.424373i | \(0.139506\pi\) | ||||
−0.905487 | + | 0.424373i | \(0.860494\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.6348 | 1.95366 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.57096 | 0.596675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 0.173834i | − 0.0136157i | −0.999977 | − | 0.00680785i | \(-0.997833\pi\) | ||||
0.999977 | − | 0.00680785i | \(-0.00216702\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 14.5596i | − 1.12666i | −0.826233 | − | 0.563328i | \(-0.809521\pi\) | ||||
0.826233 | − | 0.563328i | \(-0.190479\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3661 | −0.874312 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.00937 | 0.688963 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 22.2592i | − 1.69233i | −0.532918 | − | 0.846167i | \(-0.678905\pi\) | ||||
0.532918 | − | 0.846167i | \(-0.321095\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 3.31179i | − 0.248930i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 17.9268 | 1.33991 | 0.669957 | − | 0.742400i | \(-0.266312\pi\) | ||||
0.669957 | + | 0.742400i | \(0.266312\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.9916 | 1.56030 | 0.780148 | − | 0.625595i | \(-0.215144\pi\) | ||||
0.780148 | + | 0.625595i | \(0.215144\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.35686i | 0.174224i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.88077i | 0.503172i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −12.2480 | −0.890910 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.45074 | 0.466759 | 0.233380 | − | 0.972386i | \(-0.425022\pi\) | ||||
0.233380 | + | 0.972386i | \(0.425022\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.20374i | 0.446555i | 0.974755 | + | 0.223278i | \(0.0716756\pi\) | ||||
−0.974755 | + | 0.223278i | \(0.928324\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.1850i | − 1.01064i | −0.862932 | − | 0.505320i | \(-0.831374\pi\) | ||||
0.862932 | − | 0.505320i | \(-0.168626\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.7099 | −1.32631 | −0.663155 | − | 0.748482i | \(-0.730783\pi\) | ||||
−0.663155 | + | 0.748482i | \(0.730783\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 23.3949 | 1.65015 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 12.3126i | − 0.864176i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.85285i | 0.198286i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0831 | 0.835808 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.6984 | 1.01188 | 0.505940 | − | 0.862569i | \(-0.331146\pi\) | ||||
0.505940 | + | 0.862569i | \(0.331146\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 27.9205i | − 1.91308i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.1738i | 1.09795i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −18.3553 | −1.24033 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.2695 | −0.892605 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.1109i | 1.34672i | 0.739314 | + | 0.673361i | \(0.235150\pi\) | ||||
−0.739314 | + | 0.673361i | \(0.764850\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.71149i | 0.445457i | 0.974880 | + | 0.222729i | \(0.0714964\pi\) | ||||
−0.974880 | + | 0.222729i | \(0.928504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.7624 | −0.843361 | −0.421680 | − | 0.906745i | \(-0.638560\pi\) | ||||
−0.421680 | + | 0.906745i | \(0.638560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 28.7217 | 1.88975 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 29.0750i | − 1.90477i | −0.304906 | − | 0.952383i | \(-0.598625\pi\) | ||||
0.304906 | − | 0.952383i | \(-0.401375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.50380i | 0.617338i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.0971 | −1.68808 | −0.844041 | − | 0.536279i | \(-0.819829\pi\) | ||||
−0.844041 | + | 0.536279i | \(0.819829\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.06380 | 0.0685255 | 0.0342627 | − | 0.999413i | \(-0.489092\pi\) | ||||
0.0342627 | + | 0.999413i | \(0.489092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 17.3000i | − 1.10980i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.3023i | 1.48269i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −23.3971 | −1.48273 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.82815 | −0.494108 | −0.247054 | − | 0.969002i | \(-0.579463\pi\) | ||||
−0.247054 | + | 0.969002i | \(0.579463\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.82617i | 0.240549i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 7.49482i | − 0.467514i | −0.972295 | − | 0.233757i | \(-0.924898\pi\) | ||||
0.972295 | − | 0.233757i | \(-0.0751020\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.7309 | 0.915332 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.63957 | 0.287182 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5919i | 0.961439i | 0.876874 | + | 0.480720i | \(0.159625\pi\) | ||||
−0.876874 | + | 0.480720i | \(0.840375\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 20.7532i | − 1.27007i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −8.80860 | −0.537070 | −0.268535 | − | 0.963270i | \(-0.586539\pi\) | ||||
−0.268535 | + | 0.963270i | \(0.586539\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.8816 | −1.20772 | −0.603860 | − | 0.797090i | \(-0.706372\pi\) | ||||
−0.603860 | + | 0.797090i | \(0.706372\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 55.3896i | 3.35233i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.08232i | 0.425535i | 0.977103 | + | 0.212768i | \(0.0682477\pi\) | ||||
−0.977103 | + | 0.212768i | \(0.931752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −6.09453 | −0.364870 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.2695 | −1.86538 | −0.932692 | − | 0.360675i | \(-0.882547\pi\) | ||||
−0.932692 | + | 0.360675i | \(0.882547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 2.18303i | − 0.129768i | −0.997893 | − | 0.0648838i | \(-0.979332\pi\) | ||||
0.997893 | − | 0.0648838i | \(-0.0206677\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 5.06479i | − 0.298965i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.77354 | 0.574914 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.48048 | −0.438514 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 33.6798i | − 1.96760i | −0.179278 | − | 0.983798i | \(-0.557376\pi\) | ||||
0.179278 | − | 0.983798i | \(-0.442624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 6.18982i | − 0.359170i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.37874 | −0.426723 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.6160 | 2.22579 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 9.41147i | − 0.540675i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.7532i | 0.727862i | 0.931426 | + | 0.363931i | \(0.118566\pi\) | ||||
−0.931426 | + | 0.363931i | \(0.881434\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.47966 | −0.141063 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.18204 | 0.123732 | 0.0618660 | − | 0.998084i | \(-0.480295\pi\) | ||||
0.0618660 | + | 0.998084i | \(0.480295\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 29.3042i | − 1.65637i | −0.560452 | − | 0.828187i | \(-0.689373\pi\) | ||||
0.560452 | − | 0.828187i | \(-0.310627\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.5511i | 1.60359i | 0.597601 | + | 0.801794i | \(0.296121\pi\) | ||||
−0.597601 | + | 0.801794i | \(0.703879\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.22247 | 0.348392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.713725 | −0.0398363 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.6902i | 0.706101i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 7.17301i | − 0.396669i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 26.0923 | 1.43852 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.80761 | −0.264250 | −0.132125 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132125 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.55080i | 0.304182i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 16.3148i | − 0.888724i | −0.895847 | − | 0.444362i | \(-0.853430\pi\) | ||||
0.895847 | − | 0.444362i | \(-0.146570\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.65672 | −0.252918 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.17383 | −0.442638 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 59.0156i | − 3.18654i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 31.6034i | − 1.69656i | −0.529547 | − | 0.848281i | \(-0.677638\pi\) | ||||
0.529547 | − | 0.848281i | \(-0.322362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.97311 | −0.266204 | −0.133102 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133102 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 11.9370 | 0.637151 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.72430i | 0.0917750i | 0.998947 | + | 0.0458875i | \(0.0146116\pi\) | ||||
−0.998947 | + | 0.0458875i | \(0.985388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.1646i | 1.59648i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.13796 | 0.376727 | 0.188364 | − | 0.982099i | \(-0.439682\pi\) | ||||
0.188364 | + | 0.982099i | \(0.439682\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.28490 | 0.172889 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 9.85542i | − 0.517276i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.38595i | 0.489943i | 0.969530 | + | 0.244971i | \(0.0787785\pi\) | ||||
−0.969530 | + | 0.244971i | \(0.921221\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.90849 | 0.0993518 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 56.3166 | 2.92381 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.1212i | 1.19717i | 0.801059 | + | 0.598585i | \(0.204270\pi\) | ||||
−0.801059 | + | 0.598585i | \(0.795730\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.99080 | −0.307727 | −0.153863 | − | 0.988092i | \(-0.549172\pi\) | ||||
−0.153863 | + | 0.988092i | \(0.549172\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.9474 | −1.48302 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 29.5811i | − 1.51153i | −0.654845 | − | 0.755763i | \(-0.727266\pi\) | ||||
0.654845 | − | 0.755763i | \(-0.272734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.5511i | 0.739672i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.8620 | −1.15915 | −0.579576 | − | 0.814918i | \(-0.696782\pi\) | ||||
−0.579576 | + | 0.814918i | \(0.696782\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.01839 | −0.203219 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 18.6790i | 0.942232i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.588531i | 0.0295375i | 0.999891 | + | 0.0147688i | \(0.00470122\pi\) | ||||
−0.999891 | + | 0.0147688i | \(0.995299\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 52.9713 | 2.65188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.0926758 | −0.00462801 | −0.00231400 | − | 0.999997i | \(-0.500737\pi\) | ||||
−0.00231400 | + | 0.999997i | \(0.500737\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 15.7632i | − 0.785220i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.44460i | 0.369015i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.29526 | 0.0640463 | 0.0320232 | − | 0.999487i | \(-0.489805\pi\) | ||||
0.0320232 | + | 0.999487i | \(0.489805\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −36.6902 | −1.80979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 7.57096i | − 0.372543i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.83652i | 0.236846i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.75201 | −0.0855912 | −0.0427956 | − | 0.999084i | \(-0.513626\pi\) | ||||
−0.0427956 | + | 0.999084i | \(0.513626\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.7364 | 1.79042 | 0.895212 | − | 0.445641i | \(-0.147024\pi\) | ||||
0.895212 | + | 0.445641i | \(0.147024\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.83196i | 0.478046i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.38793i | 0.260740i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −27.9924 | −1.35149 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3126 | 0.593078 | 0.296539 | − | 0.955021i | \(-0.404168\pi\) | ||||
0.296539 | + | 0.955021i | \(0.404168\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 17.7632i | − 0.853644i | −0.904336 | − | 0.426822i | \(-0.859633\pi\) | ||||
0.904336 | − | 0.426822i | \(-0.140367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.05659i | 0.337562i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.22230 | −0.153792 | −0.0768961 | − | 0.997039i | \(-0.524501\pi\) | ||||
−0.0768961 | + | 0.997039i | \(0.524501\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 35.5973 | 1.69511 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 35.8537i | − 1.70346i | −0.523982 | − | 0.851730i | \(-0.675554\pi\) | ||||
0.523982 | − | 0.851730i | \(-0.324446\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 5.38595i | − 0.254747i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.3437 | 0.724113 | 0.362057 | − | 0.932156i | \(-0.382075\pi\) | ||||
0.362057 | + | 0.932156i | \(0.382075\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.55961 | 0.120528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 0.760170i | − 0.0357159i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 27.5917i | − 1.29068i | −0.763894 | − | 0.645342i | \(-0.776715\pi\) | ||||
0.763894 | − | 0.645342i | \(-0.223285\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.50079 | 0.303431 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.08116 | −0.376377 | −0.188189 | − | 0.982133i | \(-0.560262\pi\) | ||||
−0.188189 | + | 0.982133i | \(0.560262\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 8.23622i | − 0.382770i | −0.981515 | − | 0.191385i | \(-0.938702\pi\) | ||||
0.981515 | − | 0.191385i | \(-0.0612979\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.7333i | 1.09825i | 0.835742 | + | 0.549123i | \(0.185038\pi\) | ||||
−0.835742 | + | 0.549123i | \(0.814962\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 53.4822 | 2.46958 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.5614 | −1.08565 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.5155i | 0.897325i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 21.2209i | 0.971638i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.6987 | 0.762985 | 0.381492 | − | 0.924372i | \(-0.375410\pi\) | ||||
0.381492 | + | 0.924372i | \(0.375410\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.3569 | −0.654617 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.7735i | 0.763223i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 0.927003i | − 0.0420065i | −0.999779 | − | 0.0210033i | \(-0.993314\pi\) | ||||
0.999779 | − | 0.0210033i | \(-0.00668604\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.385130 | 0.0174162 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.8752 | −1.21286 | −0.606430 | − | 0.795137i | \(-0.707399\pi\) | ||||
−0.606430 | + | 0.795137i | \(0.707399\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.53509i | 0.294326i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 63.8279i | − 2.86307i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.2155 | −0.815438 | −0.407719 | − | 0.913107i | \(-0.633676\pi\) | ||||
−0.407719 | + | 0.913107i | \(0.633676\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.2570 | 1.44114 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.9591i | 0.845346i | 0.906282 | + | 0.422673i | \(0.138908\pi\) | ||||
−0.906282 | + | 0.422673i | \(0.861092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 25.1816i | − 1.11835i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.4218 | −0.550588 | −0.275294 | − | 0.961360i | \(-0.588775\pi\) | ||||
−0.275294 | + | 0.961360i | \(0.588775\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.9613 | −1.85626 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 11.4159i | − 0.504022i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.1864i | 0.579937i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 49.3154 | 2.16471 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.17267 | −0.314240 | −0.157120 | − | 0.987579i | \(-0.550221\pi\) | ||||
−0.157120 | + | 0.987579i | \(0.550221\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.6563i | 1.55914i | 0.626315 | + | 0.779570i | \(0.284563\pi\) | ||||
−0.626315 | + | 0.779570i | \(0.715437\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.58448i | − 0.373946i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.7655 | 0.902848 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.85285 | 0.123803 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.93620i | 0.213811i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.7171i | 1.71392i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 47.7422 | 2.05640 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.9731 | 1.24565 | 0.622826 | − | 0.782361i | \(-0.285985\pi\) | ||||
0.622826 | + | 0.782361i | \(0.285985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 46.5072i | 1.99581i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 16.1178i | − 0.689148i | −0.938759 | − | 0.344574i | \(-0.888023\pi\) | ||||
0.938759 | − | 0.344574i | \(-0.111977\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.03025 | −0.0866489 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.4761 | 0.488898 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.7263i | 0.923895i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2675i | 1.15536i | 0.816262 | + | 0.577681i | \(0.196042\pi\) | ||||
−0.816262 | + | 0.577681i | \(0.803958\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −37.6356 | −1.59182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.2444 | −0.643620 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.9173i | 1.76660i | 0.468805 | + | 0.883302i | \(0.344685\pi\) | ||||
−0.468805 | + | 0.883302i | \(0.655315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 56.1338i | − 2.35740i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.3762 | −1.56689 | −0.783446 | − | 0.621460i | \(-0.786540\pi\) | ||||
−0.783446 | + | 0.621460i | \(0.786540\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −26.3228 | −1.10157 | −0.550787 | − | 0.834646i | \(-0.685673\pi\) | ||||
−0.550787 | + | 0.834646i | \(0.685673\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.2917i | 0.597044i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.8262i | 0.575591i | 0.957692 | + | 0.287795i | \(0.0929223\pi\) | ||||
−0.957692 | + | 0.287795i | \(0.907078\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.7445 | −0.571200 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −53.4873 | −2.21903 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 28.4609i | 1.17873i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 22.7004i | − 0.936945i | −0.883478 | − | 0.468472i | \(-0.844805\pi\) | ||||
0.883478 | − | 0.468472i | \(-0.155195\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −15.0750 | −0.621154 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.4270 | 1.29274 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4167i | 0.674152i | 0.941477 | + | 0.337076i | \(0.109438\pi\) | ||||
−0.941477 | + | 0.337076i | \(0.890562\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 41.4520i | − 1.69652i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.54909 | 0.267588 | 0.133794 | − | 0.991009i | \(-0.457284\pi\) | ||||
0.133794 | + | 0.991009i | \(0.457284\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −24.7783 | −1.01073 | −0.505365 | − | 0.862906i | \(-0.668642\pi\) | ||||
−0.505365 | + | 0.862906i | \(0.668642\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.1529i | 0.820688i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.7982i | 0.641231i | 0.947209 | + | 0.320615i | \(0.103890\pi\) | ||||
−0.947209 | + | 0.320615i | \(0.896110\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 27.2787 | 1.10539 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −25.4299 | −1.02878 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 39.3415i | 1.58899i | 0.607272 | + | 0.794494i | \(0.292264\pi\) | ||||
−0.607272 | + | 0.794494i | \(0.707736\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.4075i | 1.06313i | 0.847019 | + | 0.531563i | \(0.178395\pi\) | ||||
−0.847019 | + | 0.531563i | \(0.821605\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.9278 | −1.36367 | −0.681837 | − | 0.731504i | \(-0.738819\pi\) | ||||
−0.681837 | + | 0.731504i | \(0.738819\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.61487 | 0.145060 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 47.4430i | − 1.90076i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 26.7703i | 1.06910i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.81861 | −0.311748 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.68017 | −0.226124 | −0.113062 | − | 0.993588i | \(-0.536066\pi\) | ||||
−0.113062 | + | 0.993588i | \(0.536066\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 32.5644i | 1.29432i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 92.0706i | 3.64797i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.0513 | 0.951454 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.5802 | 0.615379 | 0.307690 | − | 0.951487i | \(-0.400444\pi\) | ||||
0.307690 | + | 0.951487i | \(0.400444\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.9372i | 0.904554i | 0.891877 | + | 0.452277i | \(0.149388\pi\) | ||||
−0.891877 | + | 0.452277i | \(0.850612\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 15.0546i | − 0.591858i | −0.955210 | − | 0.295929i | \(-0.904371\pi\) | ||||
0.955210 | − | 0.295929i | \(-0.0956291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.82617 | 0.150190 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −35.8333 | −1.40442 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 45.8652i | − 1.79484i | −0.441174 | − | 0.897422i | \(-0.645438\pi\) | ||||
0.441174 | − | 0.897422i | \(-0.354562\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 15.8116i | − 0.616870i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4.37302 | 0.170349 | 0.0851744 | − | 0.996366i | \(-0.472855\pi\) | ||||
0.0851744 | + | 0.996366i | \(0.472855\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −25.4946 | −0.991625 | −0.495813 | − | 0.868430i | \(-0.665130\pi\) | ||||
−0.495813 | + | 0.868430i | \(0.665130\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 29.3988i | − 1.14175i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.63394i | 0.140707i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −44.5558 | −1.72263 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.72292 | −0.105117 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 31.7540i | 1.22403i | 0.790848 | + | 0.612013i | \(0.209640\pi\) | ||||
−0.790848 | + | 0.612013i | \(0.790360\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.8998i | 1.07228i | 0.844131 | + | 0.536138i | \(0.180117\pi\) | ||||
−0.844131 | + | 0.536138i | \(0.819883\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.1008 | −0.656270 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.8694 | −0.569796 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.11782i | 0.310620i | 0.987866 | + | 0.155310i | \(0.0496376\pi\) | ||||
−0.987866 | + | 0.155310i | \(0.950362\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 28.2752i | − 1.07876i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −54.8867 | −2.09102 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −26.6390 | −1.01339 | −0.506697 | − | 0.862124i | \(-0.669134\pi\) | ||||
−0.506697 | + | 0.862124i | \(0.669134\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 24.7414i | 0.939850i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.68821i | 0.101823i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 64.4159 | 2.43643 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.1302 | 1.62900 | 0.814502 | − | 0.580160i | \(-0.197010\pi\) | ||||
0.814502 | + | 0.580160i | \(0.197010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7301i | 0.517839i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 21.5152i | − 0.809162i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −49.5175 | −1.85967 | −0.929835 | − | 0.367978i | \(-0.880050\pi\) | ||||
−0.929835 | + | 0.367978i | \(0.880050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.18677 | −0.307028 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 4.77354i | − 0.178771i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 57.8184i | − 2.15927i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4839 | 0.614745 | 0.307372 | − | 0.951589i | \(-0.400550\pi\) | ||||
0.307372 | + | 0.951589i | \(0.400550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.66866 | −0.211112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.35686i | 0.0876527i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 48.5947i | − 1.80228i | −0.433530 | − | 0.901139i | \(-0.642732\pi\) | ||||
0.433530 | − | 0.901139i | \(-0.357268\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5.07896 | 0.188110 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.4960 | −0.758071 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.8166i | 0.436457i | 0.975898 | + | 0.218229i | \(0.0700278\pi\) | ||||
−0.975898 | + | 0.218229i | \(0.929972\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 27.0285i | 0.995609i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.68017 | 0.208949 | 0.104474 | − | 0.994528i | \(-0.466684\pi\) | ||||
0.104474 | + | 0.994528i | \(0.466684\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −51.6264 | −1.89654 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 24.4980i | − 0.898743i | −0.893345 | − | 0.449372i | \(-0.851648\pi\) | ||||
0.893345 | − | 0.449372i | \(-0.148352\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 20.1548i | − 0.737424i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.63162 | −0.0596181 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −35.7897 | −1.30598 | −0.652992 | − | 0.757365i | \(-0.726487\pi\) | ||||
−0.652992 | + | 0.757365i | \(0.726487\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 17.3433i | − 0.632027i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 37.7169i | − 1.37084i | −0.728147 | − | 0.685421i | \(-0.759618\pi\) | ||||
0.728147 | − | 0.685421i | \(-0.240382\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.47691 | −0.307692 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22.6533 | −0.821181 | −0.410590 | − | 0.911820i | \(-0.634677\pi\) | ||||
−0.410590 | + | 0.911820i | \(0.634677\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 16.3979i | − 0.593646i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.37874i | 0.266431i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.6292 | 1.53725 | 0.768624 | − | 0.639701i | \(-0.220942\pi\) | ||||
0.768624 | + | 0.639701i | \(0.220942\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6049 | 0.598009 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.7635i | 0.423105i | 0.977367 | + | 0.211552i | \(0.0678519\pi\) | ||||
−0.977367 | + | 0.211552i | \(0.932148\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 32.6364i | 1.17082i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.72069 | 0.169136 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.2570 | 1.15425 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 5.87884i | − 0.210093i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 34.4517i | − 1.22807i | −0.789278 | − | 0.614036i | \(-0.789545\pi\) | ||||
0.789278 | − | 0.614036i | \(-0.210455\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.5441 | −1.22980 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6455 | −0.378512 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 5.25113i | − 0.186473i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 41.2161i | − 1.45995i | −0.683475 | − | 0.729974i | \(-0.739532\pi\) | ||||
0.683475 | − | 0.729974i | \(-0.260468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.8489 | −0.489937 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8772 | 0.631660 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 21.2061i | − 0.748349i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 19.5155i | − 0.686979i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.4123 | −0.436393 | −0.218196 | − | 0.975905i | \(-0.570017\pi\) | ||||
−0.218196 | + | 0.975905i | \(0.570017\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.91665 | 0.137532 | 0.0687660 | − | 0.997633i | \(-0.478094\pi\) | ||||
0.0687660 | + | 0.997633i | \(0.478094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 44.0479i | − 1.54483i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.9924i | 1.25922i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −47.7137 | −1.66725 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6326 | 0.999283 | 0.499642 | − | 0.866232i | \(-0.333465\pi\) | ||||
0.499642 | + | 0.866232i | \(0.333465\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.8212i | 1.52751i | 0.645506 | + | 0.763755i | \(0.276647\pi\) | ||||
−0.645506 | + | 0.763755i | \(0.723353\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 11.1924i | − 0.389198i | −0.980883 | − | 0.194599i | \(-0.937659\pi\) | ||||
0.980883 | − | 0.194599i | \(-0.0623405\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −26.6278 | −0.924820 | −0.462410 | − | 0.886666i | \(-0.653015\pi\) | ||||
−0.462410 | + | 0.886666i | \(0.653015\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.6910 | −0.544313 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 50.1408i | 1.73727i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.72244i | 0.266927i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.43085 | −0.325589 | −0.162795 | − | 0.986660i | \(-0.552051\pi\) | ||||
−0.162795 | + | 0.986660i | \(0.552051\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0901 | −0.796212 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 69.2780i | − 2.38606i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 22.5301i | − 0.774144i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.83652 | 0.165989 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.34767 | −0.149036 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.6045i | 1.11636i | 0.829721 | + | 0.558179i | \(0.188500\pi\) | ||||
−0.829721 | + | 0.558179i | \(0.811500\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.25499i | 0.145348i | 0.997356 | + | 0.0726739i | \(0.0231532\pi\) | ||||
−0.997356 | + | 0.0726739i | \(0.976847\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.5164 | −0.836487 | −0.418244 | − | 0.908335i | \(-0.637354\pi\) | ||||
−0.418244 | + | 0.908335i | \(0.637354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.2211 | 0.382414 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 4.11643i | − 0.140125i | −0.997543 | − | 0.0700624i | \(-0.977680\pi\) | ||||
0.997543 | − | 0.0700624i | \(-0.0223198\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 21.6534i | 0.735387i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.9799 | −0.372467 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −52.1244 | −1.76617 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 6.44384i | − 0.218091i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.17301i | 0.107145i | 0.998564 | + | 0.0535725i | \(0.0170608\pi\) | ||||
−0.998564 | + | 0.0535725i | \(0.982939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 74.6180 | 2.51680 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.0391 | 0.540371 | 0.270186 | − | 0.962808i | \(-0.412915\pi\) | ||||
0.270186 | + | 0.962808i | \(0.412915\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 36.5648i | − 1.23050i | −0.788330 | − | 0.615252i | \(-0.789054\pi\) | ||||
0.788330 | − | 0.615252i | \(-0.210946\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 44.6498i | 1.49919i | 0.661896 | + | 0.749596i | \(0.269752\pi\) | ||||
−0.661896 | + | 0.749596i | \(0.730248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −66.1755 | −2.21945 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.3686 | 0.950382 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.3196i | 0.813825i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 16.3477i | − 0.545833i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.76319 | −0.258917 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.8908 | −0.995807 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 85.5542i | 2.84707i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.2692i | 1.43673i | 0.695667 | + | 0.718365i | \(0.255109\pi\) | ||||
−0.695667 | + | 0.718365i | \(0.744891\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.10723 | 0.268900 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.64116 | −0.0543739 | −0.0271870 | − | 0.999630i | \(-0.508655\pi\) | ||||
−0.0271870 | + | 0.999630i | \(0.508655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 27.0311i | − 0.894598i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.7014i | 1.41012i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.67802 | −0.220288 | −0.110144 | − | 0.993916i | \(-0.535131\pi\) | ||||
−0.110144 | + | 0.993916i | \(0.535131\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −28.2548 | −0.931027 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 62.2074i | 2.04758i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 2.13603i | − 0.0701564i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.3505 | 0.766104 | 0.383052 | − | 0.923727i | \(-0.374873\pi\) | ||||
0.383052 | + | 0.923727i | \(0.374873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 88.0508 | 2.88575 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.83433i | 0.158269i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 45.9295i | − 1.50045i | −0.661182 | − | 0.750225i | \(-0.729945\pi\) | ||||
0.661182 | − | 0.750225i | \(-0.270055\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 64.9238 | 2.11871 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.2488 | −0.431899 | −0.215949 | − | 0.976405i | \(-0.569285\pi\) | ||||
−0.215949 | + | 0.976405i | \(0.569285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.49482i | 0.0486781i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.1017i | 0.718207i | 0.933298 | + | 0.359104i | \(0.116918\pi\) | ||||
−0.933298 | + | 0.359104i | \(0.883082\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 40.8959 | 1.32754 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −63.2552 | −2.05119 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 18.2642i | − 0.591635i | −0.955244 | − | 0.295818i | \(-0.904408\pi\) | ||||
0.955244 | − | 0.295818i | \(-0.0955920\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 13.7860i | 0.445637i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −83.8760 | −2.70850 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.8023 | −0.671042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 0.614817i | − 0.0198122i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.0843i | 0.903132i | 0.892238 | + | 0.451566i | \(0.149134\pi\) | ||||
−0.892238 | + | 0.451566i | \(0.850866\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.1152 | −0.903192 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.1505 | −1.09594 | −0.547972 | − | 0.836497i | \(-0.684600\pi\) | ||||
−0.547972 | + | 0.836497i | \(0.684600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.0566i | 0.354458i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 41.4597i | − 1.32641i | −0.748437 | − | 0.663206i | \(-0.769195\pi\) | ||||
0.748437 | − | 0.663206i | \(-0.230805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 23.9765 | 0.766291 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.17898 | 0.197280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 34.1240i | − 1.08839i | −0.838960 | − | 0.544193i | \(-0.816836\pi\) | ||||
0.838960 | − | 0.544193i | \(-0.183164\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 57.8078i | 1.84004i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.3971 | −0.362408 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.3535 | −0.678315 | −0.339158 | − | 0.940730i | \(-0.610142\pi\) | ||||
−0.339158 | + | 0.940730i | \(0.610142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 10.6513i | − 0.338009i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.3560i | 0.613012i | 0.951869 | + | 0.306506i | \(0.0991600\pi\) | ||||
−0.951869 | + | 0.306506i | \(0.900840\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.03348 | 0.222529 |
(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 | 4100.2.d.c.1149.6 | 8 | ||
5.2 | odd | 4 | 164.2.a.a.1.3 | ✓ | 4 | ||
5.3 | odd | 4 | 4100.2.a.c.1.2 | 4 | |||
5.4 | even | 2 | inner | 4100.2.d.c.1149.3 | 8 | ||
15.2 | even | 4 | 1476.2.a.g.1.1 | 4 | |||
20.7 | even | 4 | 656.2.a.i.1.2 | 4 | |||
35.27 | even | 4 | 8036.2.a.i.1.2 | 4 | |||
40.27 | even | 4 | 2624.2.a.y.1.3 | 4 | |||
40.37 | odd | 4 | 2624.2.a.v.1.2 | 4 | |||
60.47 | odd | 4 | 5904.2.a.bp.1.1 | 4 | |||
205.122 | odd | 4 | 6724.2.a.c.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.3 | ✓ | 4 | 5.2 | odd | 4 | ||
656.2.a.i.1.2 | 4 | 20.7 | even | 4 | |||
1476.2.a.g.1.1 | 4 | 15.2 | even | 4 | |||
2624.2.a.v.1.2 | 4 | 40.37 | odd | 4 | |||
2624.2.a.y.1.3 | 4 | 40.27 | even | 4 | |||
4100.2.a.c.1.2 | 4 | 5.3 | odd | 4 | |||
4100.2.d.c.1149.3 | 8 | 5.4 | even | 2 | inner | ||
4100.2.d.c.1149.6 | 8 | 1.1 | even | 1 | trivial | ||
5904.2.a.bp.1.1 | 4 | 60.47 | odd | 4 | |||
6724.2.a.c.1.2 | 4 | 205.122 | odd | 4 | |||
8036.2.a.i.1.2 | 4 | 35.27 | even | 4 |