Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,5,Mod(26,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.26");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.2582416939\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 38x^{4} - 12x^{3} + 496x^{2} + 336x + 1188 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 26.3 | ||
Root | \(-0.273659 - 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.26 |
Dual form | 225.5.c.c.26.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.80123i | − 0.450306i | −0.974323 | − | 0.225153i | \(-0.927712\pi\) | ||||
0.974323 | − | 0.225153i | \(-0.0722883\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 12.7556 | 0.797224 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.1136 | 0.247217 | 0.123609 | − | 0.992331i | \(-0.460553\pi\) | ||||
0.123609 | + | 0.992331i | \(0.460553\pi\) | |||||||
\(8\) | − 51.7953i | − 0.809302i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 60.4434i | 0.499532i | 0.968306 | + | 0.249766i | \(0.0803537\pi\) | ||||
−0.968306 | + | 0.249766i | \(0.919646\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 168.896 | 0.999387 | 0.499694 | − | 0.866202i | \(-0.333446\pi\) | ||||
0.499694 | + | 0.866202i | \(0.333446\pi\) | |||||||
\(14\) | − 21.8194i | − 0.111323i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 110.794 | 0.432790 | ||||||||
\(17\) | − 377.366i | − 1.30576i | −0.757460 | − | 0.652882i | \(-0.773560\pi\) | ||||
0.757460 | − | 0.652882i | \(-0.226440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45.1263 | −0.125004 | −0.0625018 | − | 0.998045i | \(-0.519908\pi\) | ||||
−0.0625018 | + | 0.998045i | \(0.519908\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 108.872 | 0.224943 | ||||||||
\(23\) | 1.37206i | 0.00259369i | 0.999999 | + | 0.00129685i | \(0.000412799\pi\) | ||||
−0.999999 | + | 0.00129685i | \(0.999587\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − 304.221i | − 0.450030i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 154.516 | 0.197087 | ||||||||
\(29\) | 1401.24i | 1.66615i | 0.553156 | + | 0.833077i | \(0.313423\pi\) | ||||
−0.553156 | + | 0.833077i | \(0.686577\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1605.80 | 1.67097 | 0.835483 | − | 0.549517i | \(-0.185188\pi\) | ||||
0.835483 | + | 0.549517i | \(0.185188\pi\) | |||||||
\(32\) | − 1028.29i | − 1.00419i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −679.721 | −0.587994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1324.72 | 0.967652 | 0.483826 | − | 0.875164i | \(-0.339247\pi\) | ||||
0.483826 | + | 0.875164i | \(0.339247\pi\) | |||||||
\(38\) | 81.2826i | 0.0562899i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2354.07i | − 1.40040i | −0.713948 | − | 0.700199i | \(-0.753095\pi\) | ||||
0.713948 | − | 0.700199i | \(-0.246905\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 468.707 | 0.253492 | 0.126746 | − | 0.991935i | \(-0.459547\pi\) | ||||
0.126746 | + | 0.991935i | \(0.459547\pi\) | |||||||
\(44\) | 770.991i | 0.398239i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.47139 | 0.00116796 | ||||||||
\(47\) | − 3910.98i | − 1.77047i | −0.465141 | − | 0.885237i | \(-0.653996\pi\) | ||||
0.465141 | − | 0.885237i | \(-0.346004\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2254.26 | −0.938884 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2154.37 | 0.796735 | ||||||||
\(53\) | − 3228.98i | − 1.14951i | −0.818325 | − | 0.574756i | \(-0.805097\pi\) | ||||
0.818325 | − | 0.574756i | \(-0.194903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 627.429i | − 0.200073i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2523.94 | 0.750280 | ||||||||
\(59\) | 2543.15i | 0.730582i | 0.930893 | + | 0.365291i | \(0.119030\pi\) | ||||
−0.930893 | + | 0.365291i | \(0.880970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −254.070 | −0.0682800 | −0.0341400 | − | 0.999417i | \(-0.510869\pi\) | ||||
−0.0341400 | + | 0.999417i | \(0.510869\pi\) | |||||||
\(62\) | − 2892.40i | − 0.752446i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −79.4731 | −0.0194026 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7493.35 | 1.66927 | 0.834634 | − | 0.550805i | \(-0.185679\pi\) | ||||
0.834634 | + | 0.550805i | \(0.185679\pi\) | |||||||
\(68\) | − 4813.52i | − 1.04099i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4143.85i | − 0.822029i | −0.911629 | − | 0.411014i | \(-0.865175\pi\) | ||||
0.911629 | − | 0.411014i | \(-0.134825\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3711.28 | −0.696431 | −0.348215 | − | 0.937415i | \(-0.613212\pi\) | ||||
−0.348215 | + | 0.937415i | \(0.613212\pi\) | |||||||
\(74\) | − 2386.11i | − 0.435740i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −575.612 | −0.0996559 | ||||||||
\(77\) | 732.189i | 0.123493i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 80.2118 | 0.0128524 | 0.00642620 | − | 0.999979i | \(-0.497954\pi\) | ||||
0.00642620 | + | 0.999979i | \(0.497954\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4240.21 | −0.630608 | ||||||||
\(83\) | 5159.51i | 0.748949i | 0.927237 | + | 0.374474i | \(0.122177\pi\) | ||||
−0.927237 | + | 0.374474i | \(0.877823\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − 844.248i | − 0.114149i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3130.68 | 0.404272 | ||||||||
\(89\) | 5870.07i | 0.741076i | 0.928817 | + | 0.370538i | \(0.120827\pi\) | ||||
−0.928817 | + | 0.370538i | \(0.879173\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2045.95 | 0.247065 | ||||||||
\(92\) | 17.5015i | 0.00206775i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −7044.55 | −0.797256 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8921.02 | −0.948137 | −0.474068 | − | 0.880488i | \(-0.657215\pi\) | ||||
−0.474068 | + | 0.880488i | \(0.657215\pi\) | |||||||
\(98\) | 4060.43i | 0.422785i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2618.57i | 0.256697i | 0.991729 | + | 0.128349i | \(0.0409676\pi\) | ||||
−0.991729 | + | 0.128349i | \(0.959032\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9021.12 | −0.850327 | −0.425164 | − | 0.905116i | \(-0.639783\pi\) | ||||
−0.425164 | + | 0.905116i | \(0.639783\pi\) | |||||||
\(104\) | − 8748.04i | − 0.808805i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5816.12 | −0.517632 | ||||||||
\(107\) | 17075.5i | 1.49144i | 0.666257 | + | 0.745722i | \(0.267895\pi\) | ||||
−0.666257 | + | 0.745722i | \(0.732105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11156.2 | 0.938997 | 0.469498 | − | 0.882933i | \(-0.344435\pi\) | ||||
0.469498 | + | 0.882933i | \(0.344435\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1342.12 | 0.106993 | ||||||||
\(113\) | 15403.5i | 1.20632i | 0.797621 | + | 0.603160i | \(0.206092\pi\) | ||||
−0.797621 | + | 0.603160i | \(0.793908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 17873.6i | 1.32830i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4580.80 | 0.328986 | ||||||||
\(119\) | − 4571.27i | − 0.322807i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10987.6 | 0.750468 | ||||||||
\(122\) | 457.637i | 0.0307469i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 20482.9 | 1.33213 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −24976.5 | −1.54855 | −0.774273 | − | 0.632852i | \(-0.781884\pi\) | ||||
−0.774273 | + | 0.632852i | \(0.781884\pi\) | |||||||
\(128\) | − 16309.5i | − 0.995453i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17627.3i | 1.02717i | 0.858039 | + | 0.513585i | \(0.171683\pi\) | ||||
−0.858039 | + | 0.513585i | \(0.828317\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −546.643 | −0.0309030 | ||||||||
\(134\) | − 13497.2i | − 0.751682i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −19545.8 | −1.05676 | ||||||||
\(137\) | 24784.3i | 1.32049i | 0.751049 | + | 0.660247i | \(0.229548\pi\) | ||||
−0.751049 | + | 0.660247i | \(0.770452\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −241.690 | −0.0125092 | −0.00625460 | − | 0.999980i | \(-0.501991\pi\) | ||||
−0.00625460 | + | 0.999980i | \(0.501991\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7464.00 | −0.370165 | ||||||||
\(143\) | 10208.7i | 0.499226i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 6684.85i | 0.313607i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16897.5 | 0.771436 | ||||||||
\(149\) | − 12802.4i | − 0.576657i | −0.957532 | − | 0.288328i | \(-0.906901\pi\) | ||||
0.957532 | − | 0.288328i | \(-0.0930995\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14780.0 | −0.648218 | −0.324109 | − | 0.946020i | \(-0.605065\pi\) | ||||
−0.324109 | + | 0.946020i | \(0.605065\pi\) | |||||||
\(152\) | 2337.33i | 0.101166i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1318.84 | 0.0556096 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9720.94 | −0.394375 | −0.197187 | − | 0.980366i | \(-0.563181\pi\) | ||||
−0.197187 | + | 0.980366i | \(0.563181\pi\) | |||||||
\(158\) | − 144.480i | − 0.00578752i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 16.6207i | 0 0.000641204i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −34436.1 | −1.29610 | −0.648051 | − | 0.761597i | \(-0.724416\pi\) | ||||
−0.648051 | + | 0.761597i | \(0.724416\pi\) | |||||||
\(164\) | − 30027.5i | − 1.11643i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9293.44 | 0.337256 | ||||||||
\(167\) | 16921.4i | 0.606740i | 0.952873 | + | 0.303370i | \(0.0981118\pi\) | ||||
−0.952873 | + | 0.303370i | \(0.901888\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −35.0031 | −0.00122555 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5978.64 | 0.202090 | ||||||||
\(173\) | 39172.9i | 1.30886i | 0.756122 | + | 0.654431i | \(0.227092\pi\) | ||||
−0.756122 | + | 0.654431i | \(0.772908\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6696.79i | 0.216193i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 10573.3 | 0.333711 | ||||||||
\(179\) | 51682.6i | 1.61301i | 0.591224 | + | 0.806507i | \(0.298645\pi\) | ||||
−0.591224 | + | 0.806507i | \(0.701355\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 662.351 | 0.0202177 | 0.0101088 | − | 0.999949i | \(-0.496782\pi\) | ||||
0.0101088 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(182\) | − 3685.22i | − 0.111255i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 71.0664 | 0.00209908 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22809.3 | 0.652271 | ||||||||
\(188\) | − 49886.8i | − 1.41146i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 63272.8i | − 1.73440i | −0.497956 | − | 0.867202i | \(-0.665916\pi\) | ||||
0.497956 | − | 0.867202i | \(-0.334084\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −51567.4 | −1.38440 | −0.692198 | − | 0.721707i | \(-0.743358\pi\) | ||||
−0.692198 | + | 0.721707i | \(0.743358\pi\) | |||||||
\(194\) | 16068.8i | 0.426952i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −28754.4 | −0.748501 | ||||||||
\(197\) | 11639.8i | 0.299926i | 0.988692 | + | 0.149963i | \(0.0479154\pi\) | ||||
−0.988692 | + | 0.149963i | \(0.952085\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −44340.2 | −1.11967 | −0.559837 | − | 0.828603i | \(-0.689136\pi\) | ||||
−0.559837 | + | 0.828603i | \(0.689136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4716.63 | 0.115592 | ||||||||
\(203\) | 16974.1i | 0.411902i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 16249.1i | 0.382908i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18712.8 | 0.432525 | ||||||||
\(209\) | − 2727.59i | − 0.0624433i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 34425.8 | 0.773249 | 0.386624 | − | 0.922237i | \(-0.373641\pi\) | ||||
0.386624 | + | 0.922237i | \(0.373641\pi\) | |||||||
\(212\) | − 41187.5i | − 0.916418i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 30756.9 | 0.671607 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19452.0 | 0.413091 | ||||||||
\(218\) | − 20094.9i | − 0.422836i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 63735.7i | − 1.30496i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 80710.8 | 1.62301 | 0.811506 | − | 0.584344i | \(-0.198648\pi\) | ||||
0.811506 | + | 0.584344i | \(0.198648\pi\) | |||||||
\(224\) | − 12456.3i | − 0.248253i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 27745.2 | 0.543213 | ||||||||
\(227\) | − 96827.1i | − 1.87908i | −0.342441 | − | 0.939539i | \(-0.611254\pi\) | ||||
0.342441 | − | 0.939539i | \(-0.388746\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −63732.2 | −1.21531 | −0.607656 | − | 0.794200i | \(-0.707890\pi\) | ||||
−0.607656 | + | 0.794200i | \(0.707890\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 72577.5 | 1.34842 | ||||||||
\(233\) | − 22886.7i | − 0.421571i | −0.977532 | − | 0.210786i | \(-0.932398\pi\) | ||||
0.977532 | − | 0.210786i | \(-0.0676022\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 32439.4i | 0.582437i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8233.89 | −0.145362 | ||||||||
\(239\) | 26181.9i | 0.458358i | 0.973384 | + | 0.229179i | \(0.0736041\pi\) | ||||
−0.973384 | + | 0.229179i | \(0.926396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5080.09 | 0.0874657 | 0.0437328 | − | 0.999043i | \(-0.486075\pi\) | ||||
0.0437328 | + | 0.999043i | \(0.486075\pi\) | |||||||
\(242\) | − 19791.1i | − 0.337940i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3240.81 | −0.0544345 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7621.67 | −0.124927 | ||||||||
\(248\) | − 83172.8i | − 1.35231i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 23074.8i | − 0.366260i | −0.983089 | − | 0.183130i | \(-0.941377\pi\) | ||||
0.983089 | − | 0.183130i | \(-0.0586230\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −82.9321 | −0.00129563 | ||||||||
\(254\) | 44988.3i | 0.697320i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −30648.7 | −0.467661 | ||||||||
\(257\) | − 51974.3i | − 0.786905i | −0.919345 | − | 0.393452i | \(-0.871281\pi\) | ||||
0.919345 | − | 0.393452i | \(-0.128719\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16047.1 | 0.239220 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 31750.7 | 0.462541 | ||||||||
\(263\) | 24353.6i | 0.352089i | 0.984382 | + | 0.176044i | \(0.0563302\pi\) | ||||
−0.984382 | + | 0.176044i | \(0.943670\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 984.628i | 0.0139158i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 95582.0 | 1.33078 | ||||||||
\(269\) | 98409.2i | 1.35998i | 0.733223 | + | 0.679988i | \(0.238015\pi\) | ||||
−0.733223 | + | 0.679988i | \(0.761985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 135833. | 1.84956 | 0.924778 | − | 0.380508i | \(-0.124251\pi\) | ||||
0.924778 | + | 0.380508i | \(0.124251\pi\) | |||||||
\(272\) | − 41810.0i | − 0.565122i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 44642.2 | 0.594627 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19597.6 | 0.255413 | 0.127706 | − | 0.991812i | \(-0.459238\pi\) | ||||
0.127706 | + | 0.991812i | \(0.459238\pi\) | |||||||
\(278\) | 435.339i | 0.00563297i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25457.8i | 0.322409i | 0.986921 | + | 0.161205i | \(0.0515379\pi\) | ||||
−0.986921 | + | 0.161205i | \(0.948462\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −88022.8 | −1.09906 | −0.549531 | − | 0.835473i | \(-0.685194\pi\) | ||||
−0.549531 | + | 0.835473i | \(0.685194\pi\) | |||||||
\(284\) | − 52857.2i | − 0.655341i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18388.1 | 0.224805 | ||||||||
\(287\) | − 28516.3i | − 0.346202i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −58883.9 | −0.705020 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −47339.5 | −0.555211 | ||||||||
\(293\) | 91729.0i | 1.06849i | 0.845329 | + | 0.534246i | \(0.179404\pi\) | ||||
−0.845329 | + | 0.534246i | \(0.820596\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − 68614.1i | − 0.783123i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −23059.9 | −0.259672 | ||||||||
\(299\) | 231.736i | 0.00259210i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5677.75 | 0.0626676 | ||||||||
\(302\) | 26622.2i | 0.291897i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4999.74 | −0.0541004 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1346.81 | 0.0142899 | 0.00714494 | − | 0.999974i | \(-0.497726\pi\) | ||||
0.00714494 | + | 0.999974i | \(0.497726\pi\) | |||||||
\(308\) | 9339.50i | 0.0984515i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 48663.9i | − 0.503137i | −0.967839 | − | 0.251568i | \(-0.919054\pi\) | ||||
0.967839 | − | 0.251568i | \(-0.0809464\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 106387. | 1.08593 | 0.542963 | − | 0.839757i | \(-0.317302\pi\) | ||||
0.542963 | + | 0.839757i | \(0.317302\pi\) | |||||||
\(314\) | 17509.6i | 0.177589i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1023.15 | 0.0102462 | ||||||||
\(317\) | 92241.5i | 0.917926i | 0.888455 | + | 0.458963i | \(0.151779\pi\) | ||||
−0.888455 | + | 0.458963i | \(0.848221\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −84695.5 | −0.832298 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 29.9376 | 0.000288738 0 | ||||||||
\(323\) | 17029.1i | 0.163225i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 62027.2i | 0.583643i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −121930. | −1.13334 | ||||||||
\(329\) | − 47376.1i | − 0.437691i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −160354. | −1.46361 | −0.731803 | − | 0.681516i | \(-0.761321\pi\) | ||||
−0.731803 | + | 0.681516i | \(0.761321\pi\) | |||||||
\(332\) | 65812.5i | 0.597080i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 30479.2 | 0.273219 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −213689. | −1.88158 | −0.940788 | − | 0.338996i | \(-0.889913\pi\) | ||||
−0.940788 | + | 0.338996i | \(0.889913\pi\) | |||||||
\(338\) | 63.0484i | 0 0.000551875i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 97059.9i | 0.834701i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −56392.1 | −0.479325 | ||||||||
\(344\) | − 24276.8i | − 0.205152i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 70559.3 | 0.589389 | ||||||||
\(347\) | 61402.4i | 0.509948i | 0.966948 | + | 0.254974i | \(0.0820670\pi\) | ||||
−0.966948 | + | 0.254974i | \(0.917933\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 215730. | 1.77117 | 0.885585 | − | 0.464477i | \(-0.153758\pi\) | ||||
0.885585 | + | 0.464477i | \(0.153758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 62153.4 | 0.501625 | ||||||||
\(353\) | − 13643.8i | − 0.109493i | −0.998500 | − | 0.0547465i | \(-0.982565\pi\) | ||||
0.998500 | − | 0.0547465i | \(-0.0174351\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 74876.1i | 0.590804i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 93092.0 | 0.726351 | ||||||||
\(359\) | − 130543.i | − 1.01290i | −0.862270 | − | 0.506449i | \(-0.830958\pi\) | ||||
0.862270 | − | 0.506449i | \(-0.169042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −128285. | −0.984374 | ||||||||
\(362\) | − 1193.04i | − 0.00910414i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 26097.3 | 0.196967 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 168011. | 1.24740 | 0.623701 | − | 0.781663i | \(-0.285628\pi\) | ||||
0.623701 | + | 0.781663i | \(0.285628\pi\) | |||||||
\(368\) | 152.017i | 0.00112252i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 39114.6i | − 0.284179i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −158259. | −1.13750 | −0.568750 | − | 0.822510i | \(-0.692573\pi\) | ||||
−0.568750 | + | 0.822510i | \(0.692573\pi\) | |||||||
\(374\) | − 41084.6i | − 0.293722i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −202570. | −1.43285 | ||||||||
\(377\) | 236664.i | 1.66513i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −18061.8 | −0.125743 | −0.0628715 | − | 0.998022i | \(-0.520026\pi\) | ||||
−0.0628715 | + | 0.998022i | \(0.520026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −113969. | −0.781013 | ||||||||
\(383\) | − 110035.i | − 0.750126i | −0.926999 | − | 0.375063i | \(-0.877621\pi\) | ||||
0.926999 | − | 0.375063i | \(-0.122379\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 92884.5i | 0.623403i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −113793. | −0.755877 | ||||||||
\(389\) | − 247517.i | − 1.63571i | −0.575425 | − | 0.817855i | \(-0.695163\pi\) | ||||
0.575425 | − | 0.817855i | \(-0.304837\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 517.769 | 0.00338675 | ||||||||
\(392\) | 116760.i | 0.759840i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 20966.0 | 0.135059 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −170927. | −1.08450 | −0.542249 | − | 0.840218i | \(-0.682427\pi\) | ||||
−0.542249 | + | 0.840218i | \(0.682427\pi\) | |||||||
\(398\) | 79866.7i | 0.504196i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 209413.i | 1.30231i | 0.758944 | + | 0.651156i | \(0.225716\pi\) | ||||
−0.758944 | + | 0.651156i | \(0.774284\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 271213. | 1.66994 | ||||||||
\(404\) | 33401.4i | 0.204645i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 30574.1 | 0.185482 | ||||||||
\(407\) | 80070.3i | 0.483374i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 47045.0 | 0.281233 | 0.140617 | − | 0.990064i | \(-0.455092\pi\) | ||||
0.140617 | + | 0.990064i | \(0.455092\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −115070. | −0.677902 | ||||||||
\(413\) | 30806.8i | 0.180612i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − 173675.i | − 1.00357i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −4913.00 | −0.0281186 | ||||||||
\(419\) | 88341.4i | 0.503195i | 0.967832 | + | 0.251597i | \(0.0809559\pi\) | ||||
−0.967832 | + | 0.251597i | \(0.919044\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −146004. | −0.823759 | −0.411879 | − | 0.911238i | \(-0.635127\pi\) | ||||
−0.411879 | + | 0.911238i | \(0.635127\pi\) | |||||||
\(422\) | − 62008.6i | − 0.348199i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −167246. | −0.930301 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3077.71 | −0.0168800 | ||||||||
\(428\) | 217809.i | 1.18901i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 38335.8i | 0.206372i | 0.994662 | + | 0.103186i | \(0.0329036\pi\) | ||||
−0.994662 | + | 0.103186i | \(0.967096\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −236134. | −1.25946 | −0.629728 | − | 0.776815i | \(-0.716834\pi\) | ||||
−0.629728 | + | 0.776815i | \(0.716834\pi\) | |||||||
\(434\) | − 35037.5i | − 0.186018i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 142304. | 0.748591 | ||||||||
\(437\) | − 61.9161i | 0 0.000324221i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 240933. | 1.25017 | 0.625083 | − | 0.780558i | \(-0.285065\pi\) | ||||
0.625083 | + | 0.780558i | \(0.285065\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −114802. | −0.587633 | ||||||||
\(443\) | − 70261.5i | − 0.358022i | −0.983847 | − | 0.179011i | \(-0.942710\pi\) | ||||
0.983847 | − | 0.179011i | \(-0.0572898\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − 145378.i | − 0.730853i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −962.708 | −0.00479666 | ||||||||
\(449\) | − 93152.3i | − 0.462062i | −0.972946 | − | 0.231031i | \(-0.925790\pi\) | ||||
0.972946 | − | 0.231031i | \(-0.0742100\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 142288. | 0.699544 | ||||||||
\(452\) | 196481.i | 0.961707i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −174407. | −0.846161 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 145652. | 0.697406 | 0.348703 | − | 0.937233i | \(-0.386622\pi\) | ||||
0.348703 | + | 0.937233i | \(0.386622\pi\) | |||||||
\(458\) | 114796.i | 0.547263i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 128000.i | 0.602294i | 0.953578 | + | 0.301147i | \(0.0973695\pi\) | ||||
−0.953578 | + | 0.301147i | \(0.902630\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −112886. | −0.526597 | −0.263298 | − | 0.964714i | \(-0.584810\pi\) | ||||
−0.263298 | + | 0.964714i | \(0.584810\pi\) | |||||||
\(464\) | 155249.i | 0.721096i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −41224.1 | −0.189836 | ||||||||
\(467\) | − 317214.i | − 1.45452i | −0.686364 | − | 0.727258i | \(-0.740794\pi\) | ||||
0.686364 | − | 0.727258i | \(-0.259206\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 90771.7 | 0.412672 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 131723. | 0.591261 | ||||||||
\(473\) | 28330.3i | 0.126628i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − 58309.2i | − 0.257350i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 47159.4 | 0.206402 | ||||||||
\(479\) | 374765.i | 1.63338i | 0.577073 | + | 0.816692i | \(0.304195\pi\) | ||||
−0.577073 | + | 0.816692i | \(0.695805\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 223740. | 0.967059 | ||||||||
\(482\) | − 9150.40i | − 0.0393864i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 140153. | 0.598291 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −47680.4 | −0.201040 | −0.100520 | − | 0.994935i | \(-0.532051\pi\) | ||||
−0.100520 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(488\) | 13159.6i | 0.0552591i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 153766.i | 0.637817i | 0.947786 | + | 0.318908i | \(0.103316\pi\) | ||||
−0.947786 | + | 0.318908i | \(0.896684\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 528779. | 2.17561 | ||||||||
\(494\) | 13728.3i | 0.0562554i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 177913. | 0.723178 | ||||||||
\(497\) | − 50197.0i | − 0.203220i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −348851. | −1.40100 | −0.700501 | − | 0.713651i | \(-0.747040\pi\) | ||||
−0.700501 | + | 0.713651i | \(0.747040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −41562.9 | −0.164929 | ||||||||
\(503\) | − 269552.i | − 1.06539i | −0.846308 | − | 0.532693i | \(-0.821180\pi\) | ||||
0.846308 | − | 0.532693i | \(-0.178820\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 149.379i | 0 0.000583431i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −318590. | −1.23454 | ||||||||
\(509\) | − 177376.i | − 0.684636i | −0.939584 | − | 0.342318i | \(-0.888788\pi\) | ||||
0.939584 | − | 0.342318i | \(-0.111212\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −44957.1 | −0.172170 | ||||||||
\(512\) | − 205747.i | − 0.784862i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −93617.4 | −0.354348 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 236393. | 0.884409 | ||||||||
\(518\) | − 28904.5i | − 0.107722i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 233062.i | − 0.858609i | −0.903160 | − | 0.429305i | \(-0.858759\pi\) | ||||
0.903160 | − | 0.429305i | \(-0.141241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 315841. | 1.15469 | 0.577345 | − | 0.816501i | \(-0.304089\pi\) | ||||
0.577345 | + | 0.816501i | \(0.304089\pi\) | |||||||
\(524\) | 224846.i | 0.818885i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43866.4 | 0.158548 | ||||||||
\(527\) | − 605973.i | − 2.18189i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 279839. | 0.999993 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6972.76 | −0.0246366 | ||||||||
\(533\) | − 397594.i | − 1.39954i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − 388120.i | − 1.35094i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 177257. | 0.612406 | ||||||||
\(539\) | − 136255.i | − 0.469003i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −186404. | −0.636886 | −0.318443 | − | 0.947942i | \(-0.603160\pi\) | ||||
−0.318443 | + | 0.947942i | \(0.603160\pi\) | |||||||
\(542\) | − 244666.i | − 0.832867i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −388042. | −1.31123 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 443355. | 1.48176 | 0.740879 | − | 0.671639i | \(-0.234409\pi\) | ||||
0.740879 | + | 0.671639i | \(0.234409\pi\) | |||||||
\(548\) | 316139.i | 1.05273i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 63232.6i | − 0.208275i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 971.657 | 0.00317733 | ||||||||
\(554\) | − 35299.7i | − 0.115014i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3082.90 | −0.00997263 | ||||||||
\(557\) | 82562.1i | 0.266116i | 0.991108 | + | 0.133058i | \(0.0424796\pi\) | ||||
−0.991108 | + | 0.133058i | \(0.957520\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 79163.0 | 0.253337 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 45855.2 | 0.145183 | ||||||||
\(563\) | − 518910.i | − 1.63710i | −0.574435 | − | 0.818550i | \(-0.694778\pi\) | ||||
0.574435 | − | 0.818550i | \(-0.305222\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 158549.i | 0.494915i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −214632. | −0.665269 | ||||||||
\(569\) | 152195.i | 0.470085i | 0.971985 | + | 0.235042i | \(0.0755229\pi\) | ||||
−0.971985 | + | 0.235042i | \(0.924477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 414409. | 1.27103 | 0.635516 | − | 0.772088i | \(-0.280787\pi\) | ||||
0.635516 | + | 0.772088i | \(0.280787\pi\) | |||||||
\(572\) | 130218.i | 0.397995i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −51364.4 | −0.155897 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31681.0 | −0.0951585 | −0.0475793 | − | 0.998867i | \(-0.515151\pi\) | ||||
−0.0475793 | + | 0.998867i | \(0.515151\pi\) | |||||||
\(578\) | 106063.i | 0.317475i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62500.4i | 0.185153i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 195170. | 0.574218 | ||||||||
\(584\) | 192227.i | 0.563622i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 165225. | 0.481149 | ||||||||
\(587\) | − 347152.i | − 1.00750i | −0.863850 | − | 0.503748i | \(-0.831954\pi\) | ||||
0.863850 | − | 0.503748i | \(-0.168046\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −72463.7 | −0.208877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 146771. | 0.418791 | ||||||||
\(593\) | − 27468.2i | − 0.0781125i | −0.999237 | − | 0.0390563i | \(-0.987565\pi\) | ||||
0.999237 | − | 0.0390563i | \(-0.0124352\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 163302.i | − 0.459725i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 417.409 | 0.00116724 | ||||||||
\(599\) | 600764.i | 1.67436i | 0.546924 | + | 0.837182i | \(0.315799\pi\) | ||||
−0.546924 | + | 0.837182i | \(0.684201\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −494521. | −1.36910 | −0.684551 | − | 0.728965i | \(-0.740002\pi\) | ||||
−0.684551 | + | 0.728965i | \(0.740002\pi\) | |||||||
\(602\) | − 10226.9i | − 0.0282196i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −188528. | −0.516775 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 578761. | 1.57080 | 0.785401 | − | 0.618987i | \(-0.212457\pi\) | ||||
0.785401 | + | 0.618987i | \(0.212457\pi\) | |||||||
\(608\) | 46402.9i | 0.125527i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 660550.i | − 1.76939i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −538455. | −1.43294 | −0.716471 | − | 0.697616i | \(-0.754244\pi\) | ||||
−0.716471 | + | 0.697616i | \(0.754244\pi\) | |||||||
\(614\) | − 2425.90i | − 0.00643483i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37924.0 | 0.0999430 | ||||||||
\(617\) | 486339.i | 1.27752i | 0.769404 | + | 0.638762i | \(0.220553\pi\) | ||||
−0.769404 | + | 0.638762i | \(0.779447\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −163391. | −0.426430 | −0.213215 | − | 0.977005i | \(-0.568394\pi\) | ||||
−0.213215 | + | 0.977005i | \(0.568394\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −87654.7 | −0.226566 | ||||||||
\(623\) | 71107.8i | 0.183207i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − 191627.i | − 0.488999i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −123996. | −0.314405 | ||||||||
\(629\) | − 499903.i | − 1.26353i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −132675. | −0.333220 | −0.166610 | − | 0.986023i | \(-0.553282\pi\) | ||||
−0.166610 | + | 0.986023i | \(0.553282\pi\) | |||||||
\(632\) | − 4154.60i | − 0.0104015i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 166148. | 0.413348 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −380736. | −0.938308 | ||||||||
\(638\) | 152556.i | 0.374789i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 648011.i | 1.57713i | 0.614954 | + | 0.788563i | \(0.289174\pi\) | ||||
−0.614954 | + | 0.788563i | \(0.710826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −62712.3 | −0.151681 | −0.0758405 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758405 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(644\) | 212.006i | 0 0.000511184i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 30673.3 | 0.0735013 | ||||||||
\(647\) | − 472097.i | − 1.12778i | −0.825852 | − | 0.563888i | \(-0.809305\pi\) | ||||
0.825852 | − | 0.563888i | \(-0.190695\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −153717. | −0.364949 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −439253. | −1.03328 | ||||||||
\(653\) | 233253.i | 0.547017i | 0.961870 | + | 0.273509i | \(0.0881842\pi\) | ||||
−0.961870 | + | 0.273509i | \(0.911816\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − 260818.i | − 0.606079i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −85335.1 | −0.197095 | ||||||||
\(659\) | − 399872.i | − 0.920768i | −0.887720 | − | 0.460384i | \(-0.847712\pi\) | ||||
0.887720 | − | 0.460384i | \(-0.152288\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 112993. | 0.258613 | 0.129306 | − | 0.991605i | \(-0.458725\pi\) | ||||
0.129306 | + | 0.991605i | \(0.458725\pi\) | |||||||
\(662\) | 288834.i | 0.659071i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 267238. | 0.606125 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1922.58 | −0.00432149 | ||||||||
\(668\) | 215842.i | 0.483708i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 15356.9i | − 0.0341081i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 544760. | 1.20275 | 0.601374 | − | 0.798967i | \(-0.294620\pi\) | ||||
0.601374 | + | 0.798967i | \(0.294620\pi\) | |||||||
\(674\) | 384901.i | 0.847285i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −446.485 | −0.000977042 0 | ||||||||
\(677\) | 475103.i | 1.03660i | 0.855199 | + | 0.518299i | \(0.173435\pi\) | ||||
−0.855199 | + | 0.518299i | \(0.826565\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −108066. | −0.234396 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 174827. | 0.375871 | ||||||||
\(683\) | − 53819.1i | − 0.115371i | −0.998335 | − | 0.0576853i | \(-0.981628\pi\) | ||||
0.998335 | − | 0.0576853i | \(-0.0183720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 101575.i | 0.215843i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 51930.1 | 0.109709 | ||||||||
\(689\) | − 545363.i | − 1.14881i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −400653. | −0.839097 | −0.419548 | − | 0.907733i | \(-0.637812\pi\) | ||||
−0.419548 | + | 0.907733i | \(0.637812\pi\) | |||||||
\(692\) | 499673.i | 1.04346i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 110600. | 0.229633 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −888345. | −1.82859 | ||||||||
\(698\) | − 388579.i | − 0.797569i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 860604.i | 1.75133i | 0.482921 | + | 0.875664i | \(0.339576\pi\) | ||||
−0.482921 | + | 0.875664i | \(0.660424\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −59779.5 | −0.120960 | ||||||||
\(704\) | − 4803.63i | − 0.00969223i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −24575.6 | −0.0493054 | ||||||||
\(707\) | 31720.4i | 0.0634599i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 489913. | 0.974601 | 0.487300 | − | 0.873234i | \(-0.337982\pi\) | ||||
0.487300 | + | 0.873234i | \(0.337982\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 304042. | 0.599754 | ||||||||
\(713\) | 2203.25i | 0.00433397i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 659242.i | 1.28593i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −235138. | −0.456114 | ||||||||
\(719\) | − 288471.i | − 0.558014i | −0.960289 | − | 0.279007i | \(-0.909995\pi\) | ||||
0.960289 | − | 0.279007i | \(-0.0900053\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −109279. | −0.210215 | ||||||||
\(722\) | 231070.i | 0.443270i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8448.67 | 0.0161180 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 75173.7 | 0.142232 | 0.0711160 | − | 0.997468i | \(-0.477344\pi\) | ||||
0.0711160 | + | 0.997468i | \(0.477344\pi\) | |||||||
\(728\) | − 105971.i | − 0.199950i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 176874.i | − 0.331001i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −108535. | −0.202005 | −0.101003 | − | 0.994886i | \(-0.532205\pi\) | ||||
−0.101003 | + | 0.994886i | \(0.532205\pi\) | |||||||
\(734\) | − 302627.i | − 0.561714i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1410.88 | 0.00260456 | ||||||||
\(737\) | 452923.i | 0.833853i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 654768. | 1.19894 | 0.599472 | − | 0.800396i | \(-0.295377\pi\) | ||||
0.599472 | + | 0.800396i | \(0.295377\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −70454.3 | −0.127967 | ||||||||
\(743\) | 423118.i | 0.766450i | 0.923655 | + | 0.383225i | \(0.125187\pi\) | ||||
−0.923655 | + | 0.383225i | \(0.874813\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 285061.i | 0.512224i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 290946. | 0.520006 | ||||||||
\(749\) | 206847.i | 0.368710i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 93003.6 | 0.164900 | 0.0824498 | − | 0.996595i | \(-0.473726\pi\) | ||||
0.0824498 | + | 0.996595i | \(0.473726\pi\) | |||||||
\(752\) | − 433314.i | − 0.766244i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 426285. | 0.749820 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −849613. | −1.48262 | −0.741309 | − | 0.671164i | \(-0.765795\pi\) | ||||
−0.741309 | + | 0.671164i | \(0.765795\pi\) | |||||||
\(758\) | 32533.4i | 0.0566228i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 407917.i | 0.704373i | 0.935930 | + | 0.352186i | \(0.114562\pi\) | ||||
−0.935930 | + | 0.352186i | \(0.885438\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 135142. | 0.232136 | ||||||||
\(764\) | − 807082.i | − 1.38271i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −198198. | −0.337787 | ||||||||
\(767\) | 429530.i | 0.730134i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 569500. | 0.963033 | 0.481517 | − | 0.876437i | \(-0.340086\pi\) | ||||
0.481517 | + | 0.876437i | \(0.340086\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −657772. | −1.10367 | ||||||||
\(773\) | 711311.i | 1.19042i | 0.803570 | + | 0.595211i | \(0.202931\pi\) | ||||
−0.803570 | + | 0.595211i | \(0.797069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 462067.i | 0.767329i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −445834. | −0.736571 | ||||||||
\(779\) | 106230.i | 0.175055i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 250468. | 0.410630 | ||||||||
\(782\) | − 932.619i | − 0.00152507i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −249759. | −0.406340 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −215275. | −0.347572 | −0.173786 | − | 0.984783i | \(-0.555600\pi\) | ||||
−0.173786 | + | 0.984783i | \(0.555600\pi\) | |||||||
\(788\) | 148473.i | 0.239108i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 186592.i | 0.298223i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42911.5 | −0.0682382 | ||||||||
\(794\) | 307878.i | 0.488357i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −565585. | −0.892630 | ||||||||
\(797\) | 623058.i | 0.980871i | 0.871478 | + | 0.490435i | \(0.163162\pi\) | ||||
−0.871478 | + | 0.490435i | \(0.836838\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.47587e6 | −2.31182 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 377200. | 0.586440 | ||||||||
\(803\) | − 224322.i | − 0.347890i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 488517.i | − 0.751985i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 135630. | 0.207745 | ||||||||
\(809\) | − 385095.i | − 0.588398i | −0.955744 | − | 0.294199i | \(-0.904947\pi\) | ||||
0.955744 | − | 0.294199i | \(-0.0950528\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 586828. | 0.892215 | 0.446107 | − | 0.894979i | \(-0.352810\pi\) | ||||
0.446107 | + | 0.894979i | \(0.352810\pi\) | |||||||
\(812\) | 216514.i | 0.328378i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 144225. | 0.217666 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21151.0 | −0.0316875 | ||||||||
\(818\) | − 84738.6i | − 0.126641i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 879206.i | − 1.30438i | −0.758055 | − | 0.652191i | \(-0.773850\pi\) | ||||
0.758055 | − | 0.652191i | \(-0.226150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 56403.1 | 0.0832728 | 0.0416364 | − | 0.999133i | \(-0.486743\pi\) | ||||
0.0416364 | + | 0.999133i | \(0.486743\pi\) | |||||||
\(824\) | 467252.i | 0.688171i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 55490.1 | 0.0813308 | ||||||||
\(827\) | − 201627.i | − 0.294807i | −0.989076 | − | 0.147403i | \(-0.952908\pi\) | ||||
0.989076 | − | 0.147403i | \(-0.0470916\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −85071.2 | −0.123787 | −0.0618933 | − | 0.998083i | \(-0.519714\pi\) | ||||
−0.0618933 | + | 0.998083i | \(0.519714\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −13422.7 | −0.0193907 | ||||||||
\(833\) | 850681.i | 1.22596i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − 34792.0i | − 0.0497813i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 159123. | 0.226592 | ||||||||
\(839\) | 150877.i | 0.214338i | 0.994241 | + | 0.107169i | \(0.0341785\pi\) | ||||
−0.994241 | + | 0.107169i | \(0.965821\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.25618e6 | −1.77607 | ||||||||
\(842\) | 262986.i | 0.370944i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 439121. | 0.616452 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 133100. | 0.185528 | ||||||||
\(848\) | − 357752.i | − 0.497497i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1817.59i | 0.00250979i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.17719e6 | −1.61788 | −0.808941 | − | 0.587890i | \(-0.799959\pi\) | ||||
−0.808941 | + | 0.587890i | \(0.799959\pi\) | |||||||
\(854\) | 5543.65i | 0.00760117i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 884433. | 1.20703 | ||||||||
\(857\) | 341140.i | 0.464485i | 0.972658 | + | 0.232242i | \(0.0746062\pi\) | ||||
−0.972658 | + | 0.232242i | \(0.925394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44556.7 | 0.0603846 | 0.0301923 | − | 0.999544i | \(-0.490388\pi\) | ||||
0.0301923 | + | 0.999544i | \(0.490388\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 69051.4 | 0.0929304 | ||||||||
\(863\) | − 5280.21i | − 0.00708973i | −0.999994 | − | 0.00354486i | \(-0.998872\pi\) | ||||
0.999994 | − | 0.00354486i | \(-0.00112837\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 425331.i | 0.567141i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 248122. | 0.329326 | ||||||||
\(869\) | 4848.27i | 0.00642019i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.26560e6 | 1.66825 | ||||||||
\(872\) | − 577840.i | − 0.759932i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −111.525 | −0.000145999 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1228.71 | 0.00159754 | 0.000798768 | − | 1.00000i | \(-0.499746\pi\) | ||||
0.000798768 | 1.00000i | \(0.499746\pi\) | ||||||||
\(878\) | − 433975.i | − 0.562958i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 513912.i | − 0.662120i | −0.943610 | − | 0.331060i | \(-0.892594\pi\) | ||||
0.943610 | − | 0.331060i | \(-0.107406\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 116500. | 0.149419 | 0.0747093 | − | 0.997205i | \(-0.476197\pi\) | ||||
0.0747093 | + | 0.997205i | \(0.476197\pi\) | |||||||
\(884\) | − 812987.i | − 1.04035i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −126557. | −0.161220 | ||||||||
\(887\) | − 1.23199e6i | − 1.56588i | −0.622096 | − | 0.782941i | \(-0.713719\pi\) | ||||
0.622096 | − | 0.782941i | \(-0.286281\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −302556. | −0.382827 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.02951e6 | 1.29390 | ||||||||
\(893\) | 176488.i | 0.221316i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − 197567.i | − 0.246093i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −167788. | −0.208070 | ||||||||
\(899\) | 2.25010e6i | 2.78409i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.21851e6 | −1.50099 | ||||||||
\(902\) | − 256293.i | − 0.315009i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 797828. | 0.976276 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.02123e6 | 1.24139 | 0.620694 | − | 0.784053i | \(-0.286851\pi\) | ||||
0.620694 | + | 0.784053i | \(0.286851\pi\) | |||||||
\(908\) | − 1.23509e6i | − 1.49805i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.49023e6i | − 1.79562i | −0.440378 | − | 0.897812i | \(-0.645156\pi\) | ||||
0.440378 | − | 0.897812i | \(-0.354844\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −311858. | −0.374124 | ||||||||
\(914\) | − 262353.i | − 0.314046i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −812942. | −0.968877 | ||||||||
\(917\) | 213530.i | 0.253934i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.16759e6 | −1.38248 | −0.691240 | − | 0.722625i | \(-0.742935\pi\) | ||||
−0.691240 | + | 0.722625i | \(0.742935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 230557. | 0.271217 | ||||||||
\(923\) | − 699881.i | − 0.821525i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 203333.i | 0.237130i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.44088e6 | 1.67314 | ||||||||
\(929\) | − 709717.i | − 0.822345i | −0.911558 | − | 0.411172i | \(-0.865119\pi\) | ||||
0.911558 | − | 0.411172i | \(-0.134881\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 101726. | 0.117364 | ||||||||
\(932\) | − 291933.i | − 0.336087i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −571374. | −0.654978 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 294273. | 0.335175 | 0.167587 | − | 0.985857i | \(-0.446402\pi\) | ||||
0.167587 | + | 0.985857i | \(0.446402\pi\) | |||||||
\(938\) | − 163500.i | − 0.185829i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 783701.i | 0.885057i | 0.896755 | + | 0.442528i | \(0.145918\pi\) | ||||
−0.896755 | + | 0.442528i | \(0.854082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3229.93 | 0.00363220 | ||||||||
\(944\) | 281767.i | 0.316189i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 51029.2 | 0.0570212 | ||||||||
\(947\) | − 1.35618e6i | − 1.51222i | −0.654442 | − | 0.756112i | \(-0.727096\pi\) | ||||
0.654442 | − | 0.756112i | \(-0.272904\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −626822. | −0.696004 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −236770. | −0.261248 | ||||||||
\(953\) | − 226626.i | − 0.249531i | −0.992186 | − | 0.124766i | \(-0.960182\pi\) | ||||
0.992186 | − | 0.124766i | \(-0.0398179\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 333965.i | 0.365414i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 675037. | 0.735524 | ||||||||
\(959\) | 300228.i | 0.326448i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.65507e6 | 1.79212 | ||||||||
\(962\) | − 403006.i | − 0.435473i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 64799.6 | 0.0697298 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 688811. | 0.736626 | 0.368313 | − | 0.929702i | \(-0.379935\pi\) | ||||
0.368313 | + | 0.929702i | \(0.379935\pi\) | |||||||
\(968\) | − 569106.i | − 0.607355i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.30899e6i | − 1.38835i | −0.719807 | − | 0.694174i | \(-0.755770\pi\) | ||||
0.719807 | − | 0.694174i | \(-0.244230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2927.75 | −0.00309249 | ||||||||
\(974\) | 85883.2i | 0.0905295i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28149.5 | −0.0295509 | ||||||||
\(977\) | − 29454.1i | − 0.0308572i | −0.999881 | − | 0.0154286i | \(-0.995089\pi\) | ||||
0.999881 | − | 0.0154286i | \(-0.00491127\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −354807. | −0.370192 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 276966. | 0.287213 | ||||||||
\(983\) | 369377.i | 0.382264i | 0.981564 | + | 0.191132i | \(0.0612158\pi\) | ||||
−0.981564 | + | 0.191132i | \(0.938784\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − 952450.i | − 0.979689i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −97218.9 | −0.0995948 | ||||||||
\(989\) | 643.096i | 0 0.000657481i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 121176. | 0.123387 | 0.0616933 | − | 0.998095i | \(-0.480350\pi\) | ||||
0.0616933 | + | 0.998095i | \(0.480350\pi\) | |||||||
\(992\) | − 1.65123e6i | − 1.67797i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −90416.2 | −0.0915110 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 277965. | 0.279640 | 0.139820 | − | 0.990177i | \(-0.455348\pi\) | ||||
0.139820 | + | 0.990177i | \(0.455348\pi\) | |||||||
\(998\) | 628359.i | 0.630880i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.5.c.c.26.3 | ✓ | 6 | |
3.2 | odd | 2 | inner | 225.5.c.c.26.4 | yes | 6 | |
5.2 | odd | 4 | 225.5.d.c.224.8 | 12 | |||
5.3 | odd | 4 | 225.5.d.c.224.5 | 12 | |||
5.4 | even | 2 | 225.5.c.d.26.4 | yes | 6 | ||
15.2 | even | 4 | 225.5.d.c.224.6 | 12 | |||
15.8 | even | 4 | 225.5.d.c.224.7 | 12 | |||
15.14 | odd | 2 | 225.5.c.d.26.3 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.5.c.c.26.3 | ✓ | 6 | 1.1 | even | 1 | trivial | |
225.5.c.c.26.4 | yes | 6 | 3.2 | odd | 2 | inner | |
225.5.c.d.26.3 | yes | 6 | 15.14 | odd | 2 | ||
225.5.c.d.26.4 | yes | 6 | 5.4 | even | 2 | ||
225.5.d.c.224.5 | 12 | 5.3 | odd | 4 | |||
225.5.d.c.224.6 | 12 | 15.2 | even | 4 | |||
225.5.d.c.224.7 | 12 | 15.8 | even | 4 | |||
225.5.d.c.224.8 | 12 | 5.2 | odd | 4 |