Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [165,6,Mod(1,165)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(165, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("165.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 165 = 3 \cdot 5 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 165.a (trivial) |
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: | yes |
Analytic conductor: | \(26.4633302691\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.307532.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{3} - x^{2} - 76x + 168 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.30119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 165.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.30119 | 0.760350 | 0.380175 | − | 0.924915i | \(-0.375864\pi\) | ||||
0.380175 | + | 0.924915i | \(0.375864\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −13.4998 | −0.421868 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | −38.7107 | −0.438988 | ||||||||
\(7\) | −148.216 | −1.14327 | −0.571635 | − | 0.820508i | \(-0.693691\pi\) | ||||
−0.571635 | + | 0.820508i | \(0.693691\pi\) | |||||||
\(8\) | −195.703 | −1.08112 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −107.530 | −0.340039 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 121.498 | 0.243565 | ||||||||
\(13\) | 234.137 | 0.384247 | 0.192124 | − | 0.981371i | \(-0.438463\pi\) | ||||
0.192124 | + | 0.981371i | \(0.438463\pi\) | |||||||
\(14\) | −637.504 | −0.869286 | ||||||||
\(15\) | 225.000 | 0.258199 | ||||||||
\(16\) | −409.764 | −0.400160 | ||||||||
\(17\) | 1031.76 | 0.865875 | 0.432937 | − | 0.901424i | \(-0.357477\pi\) | ||||
0.432937 | + | 0.901424i | \(0.357477\pi\) | |||||||
\(18\) | 348.396 | 0.253450 | ||||||||
\(19\) | 1266.29 | 0.804729 | 0.402365 | − | 0.915480i | \(-0.368188\pi\) | ||||
0.402365 | + | 0.915480i | \(0.368188\pi\) | |||||||
\(20\) | 337.494 | 0.188665 | ||||||||
\(21\) | 1333.94 | 0.660068 | ||||||||
\(22\) | 520.444 | 0.229254 | ||||||||
\(23\) | 384.710 | 0.151640 | 0.0758201 | − | 0.997122i | \(-0.475843\pi\) | ||||
0.0758201 | + | 0.997122i | \(0.475843\pi\) | |||||||
\(24\) | 1761.33 | 0.624183 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | 1007.07 | 0.292163 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 2000.88 | 0.482309 | ||||||||
\(29\) | −4484.85 | −0.990268 | −0.495134 | − | 0.868817i | \(-0.664881\pi\) | ||||
−0.495134 | + | 0.868817i | \(0.664881\pi\) | |||||||
\(30\) | 967.768 | 0.196322 | ||||||||
\(31\) | −997.235 | −0.186377 | −0.0931887 | − | 0.995648i | \(-0.529706\pi\) | ||||
−0.0931887 | + | 0.995648i | \(0.529706\pi\) | |||||||
\(32\) | 4500.03 | 0.776856 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 4437.78 | 0.658368 | ||||||||
\(35\) | 3705.39 | 0.511286 | ||||||||
\(36\) | −1093.48 | −0.140623 | ||||||||
\(37\) | 5168.11 | 0.620622 | 0.310311 | − | 0.950635i | \(-0.399567\pi\) | ||||
0.310311 | + | 0.950635i | \(0.399567\pi\) | |||||||
\(38\) | 5446.56 | 0.611876 | ||||||||
\(39\) | −2107.23 | −0.221845 | ||||||||
\(40\) | 4892.58 | 0.483490 | ||||||||
\(41\) | 2259.17 | 0.209889 | 0.104944 | − | 0.994478i | \(-0.466534\pi\) | ||||
0.104944 | + | 0.994478i | \(0.466534\pi\) | |||||||
\(42\) | 5737.54 | 0.501883 | ||||||||
\(43\) | 15818.9 | 1.30469 | 0.652343 | − | 0.757924i | \(-0.273786\pi\) | ||||
0.652343 | + | 0.757924i | \(0.273786\pi\) | |||||||
\(44\) | −1633.47 | −0.127198 | ||||||||
\(45\) | −2025.00 | −0.149071 | ||||||||
\(46\) | 1654.71 | 0.115300 | ||||||||
\(47\) | 12033.2 | 0.794577 | 0.397289 | − | 0.917694i | \(-0.369951\pi\) | ||||
0.397289 | + | 0.917694i | \(0.369951\pi\) | |||||||
\(48\) | 3687.87 | 0.231032 | ||||||||
\(49\) | 5160.90 | 0.307069 | ||||||||
\(50\) | 2688.24 | 0.152070 | ||||||||
\(51\) | −9285.81 | −0.499913 | ||||||||
\(52\) | −3160.79 | −0.162102 | ||||||||
\(53\) | −3851.67 | −0.188347 | −0.0941737 | − | 0.995556i | \(-0.530021\pi\) | ||||
−0.0941737 | + | 0.995556i | \(0.530021\pi\) | |||||||
\(54\) | −3135.57 | −0.146329 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 29006.3 | 1.23601 | ||||||||
\(57\) | −11396.6 | −0.464611 | ||||||||
\(58\) | −19290.2 | −0.752950 | ||||||||
\(59\) | −20261.0 | −0.757760 | −0.378880 | − | 0.925446i | \(-0.623691\pi\) | ||||
−0.378880 | + | 0.925446i | \(0.623691\pi\) | |||||||
\(60\) | −3037.45 | −0.108926 | ||||||||
\(61\) | 2006.88 | 0.0690553 | 0.0345276 | − | 0.999404i | \(-0.489007\pi\) | ||||
0.0345276 | + | 0.999404i | \(0.489007\pi\) | |||||||
\(62\) | −4289.30 | −0.141712 | ||||||||
\(63\) | −12005.5 | −0.381090 | ||||||||
\(64\) | 32467.9 | 0.990842 | ||||||||
\(65\) | −5853.41 | −0.171841 | ||||||||
\(66\) | −4684.00 | −0.132360 | ||||||||
\(67\) | 40945.6 | 1.11435 | 0.557173 | − | 0.830397i | \(-0.311886\pi\) | ||||
0.557173 | + | 0.830397i | \(0.311886\pi\) | |||||||
\(68\) | −13928.5 | −0.365285 | ||||||||
\(69\) | −3462.39 | −0.0875495 | ||||||||
\(70\) | 15937.6 | 0.388757 | ||||||||
\(71\) | 16970.8 | 0.399537 | 0.199769 | − | 0.979843i | \(-0.435981\pi\) | ||||
0.199769 | + | 0.979843i | \(0.435981\pi\) | |||||||
\(72\) | −15852.0 | −0.360372 | ||||||||
\(73\) | −56640.5 | −1.24400 | −0.621999 | − | 0.783018i | \(-0.713679\pi\) | ||||
−0.621999 | + | 0.783018i | \(0.713679\pi\) | |||||||
\(74\) | 22229.0 | 0.471890 | ||||||||
\(75\) | −5625.00 | −0.115470 | ||||||||
\(76\) | −17094.6 | −0.339489 | ||||||||
\(77\) | −17934.1 | −0.344709 | ||||||||
\(78\) | −9063.59 | −0.168680 | ||||||||
\(79\) | 58507.9 | 1.05474 | 0.527372 | − | 0.849635i | \(-0.323178\pi\) | ||||
0.527372 | + | 0.849635i | \(0.323178\pi\) | |||||||
\(80\) | 10244.1 | 0.178957 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 9717.12 | 0.159589 | ||||||||
\(83\) | −52243.8 | −0.832415 | −0.416207 | − | 0.909270i | \(-0.636641\pi\) | ||||
−0.416207 | + | 0.909270i | \(0.636641\pi\) | |||||||
\(84\) | −18007.9 | −0.278461 | ||||||||
\(85\) | −25793.9 | −0.387231 | ||||||||
\(86\) | 68040.2 | 0.992018 | ||||||||
\(87\) | 40363.6 | 0.571732 | ||||||||
\(88\) | −23680.1 | −0.325969 | ||||||||
\(89\) | 55114.4 | 0.737548 | 0.368774 | − | 0.929519i | \(-0.379778\pi\) | ||||
0.368774 | + | 0.929519i | \(0.379778\pi\) | |||||||
\(90\) | −8709.91 | −0.113346 | ||||||||
\(91\) | −34702.7 | −0.439299 | ||||||||
\(92\) | −5193.50 | −0.0639721 | ||||||||
\(93\) | 8975.11 | 0.107605 | ||||||||
\(94\) | 51757.0 | 0.604157 | ||||||||
\(95\) | −31657.3 | −0.359886 | ||||||||
\(96\) | −40500.3 | −0.448518 | ||||||||
\(97\) | 99383.8 | 1.07247 | 0.536237 | − | 0.844068i | \(-0.319846\pi\) | ||||
0.536237 | + | 0.844068i | \(0.319846\pi\) | |||||||
\(98\) | 22198.0 | 0.233480 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | −8437.35 | −0.0843735 | ||||||||
\(101\) | −25334.3 | −0.247118 | −0.123559 | − | 0.992337i | \(-0.539431\pi\) | ||||
−0.123559 | + | 0.992337i | \(0.539431\pi\) | |||||||
\(102\) | −39940.0 | −0.380109 | ||||||||
\(103\) | −93216.6 | −0.865766 | −0.432883 | − | 0.901450i | \(-0.642504\pi\) | ||||
−0.432883 | + | 0.901450i | \(0.642504\pi\) | |||||||
\(104\) | −45821.3 | −0.415416 | ||||||||
\(105\) | −33348.5 | −0.295191 | ||||||||
\(106\) | −16566.8 | −0.143210 | ||||||||
\(107\) | 205830. | 1.73799 | 0.868997 | − | 0.494817i | \(-0.164765\pi\) | ||||
0.868997 | + | 0.494817i | \(0.164765\pi\) | |||||||
\(108\) | 9841.33 | 0.0811885 | ||||||||
\(109\) | −155901. | −1.25684 | −0.628422 | − | 0.777872i | \(-0.716299\pi\) | ||||
−0.628422 | + | 0.777872i | \(0.716299\pi\) | |||||||
\(110\) | −13011.1 | −0.102526 | ||||||||
\(111\) | −46513.0 | −0.358316 | ||||||||
\(112\) | 60733.4 | 0.457491 | ||||||||
\(113\) | 40304.5 | 0.296932 | 0.148466 | − | 0.988917i | \(-0.452566\pi\) | ||||
0.148466 | + | 0.988917i | \(0.452566\pi\) | |||||||
\(114\) | −49019.0 | −0.353267 | ||||||||
\(115\) | −9617.75 | −0.0678155 | ||||||||
\(116\) | 60544.4 | 0.417762 | ||||||||
\(117\) | 18965.1 | 0.128082 | ||||||||
\(118\) | −87146.6 | −0.576163 | ||||||||
\(119\) | −152923. | −0.989929 | ||||||||
\(120\) | −44033.2 | −0.279143 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 8631.97 | 0.0525062 | ||||||||
\(123\) | −20332.5 | −0.121179 | ||||||||
\(124\) | 13462.4 | 0.0786266 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | −51637.8 | −0.289762 | ||||||||
\(127\) | 120825. | 0.664733 | 0.332367 | − | 0.943150i | \(-0.392153\pi\) | ||||
0.332367 | + | 0.943150i | \(0.392153\pi\) | |||||||
\(128\) | −4350.25 | −0.0234687 | ||||||||
\(129\) | −142370. | −0.753260 | ||||||||
\(130\) | −25176.6 | −0.130659 | ||||||||
\(131\) | 266474. | 1.35668 | 0.678338 | − | 0.734750i | \(-0.262701\pi\) | ||||
0.678338 | + | 0.734750i | \(0.262701\pi\) | |||||||
\(132\) | 14701.2 | 0.0734377 | ||||||||
\(133\) | −187684. | −0.920023 | ||||||||
\(134\) | 176115. | 0.847292 | ||||||||
\(135\) | 18225.0 | 0.0860663 | ||||||||
\(136\) | −201918. | −0.936112 | ||||||||
\(137\) | 17176.5 | 0.0781866 | 0.0390933 | − | 0.999236i | \(-0.487553\pi\) | ||||
0.0390933 | + | 0.999236i | \(0.487553\pi\) | |||||||
\(138\) | −14892.4 | −0.0665682 | ||||||||
\(139\) | −5031.99 | −0.0220903 | −0.0110452 | − | 0.999939i | \(-0.503516\pi\) | ||||
−0.0110452 | + | 0.999939i | \(0.503516\pi\) | |||||||
\(140\) | −50021.9 | −0.215695 | ||||||||
\(141\) | −108299. | −0.458749 | ||||||||
\(142\) | 72994.7 | 0.303788 | ||||||||
\(143\) | 28330.5 | 0.115855 | ||||||||
\(144\) | −33190.9 | −0.133387 | ||||||||
\(145\) | 112121. | 0.442861 | ||||||||
\(146\) | −243621. | −0.945874 | ||||||||
\(147\) | −46448.1 | −0.177286 | ||||||||
\(148\) | −69768.3 | −0.261820 | ||||||||
\(149\) | −37407.9 | −0.138038 | −0.0690188 | − | 0.997615i | \(-0.521987\pi\) | ||||
−0.0690188 | + | 0.997615i | \(0.521987\pi\) | |||||||
\(150\) | −24194.2 | −0.0877977 | ||||||||
\(151\) | −225853. | −0.806091 | −0.403046 | − | 0.915180i | \(-0.632048\pi\) | ||||
−0.403046 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(152\) | −247817. | −0.870006 | ||||||||
\(153\) | 83572.3 | 0.288625 | ||||||||
\(154\) | −77138.0 | −0.262100 | ||||||||
\(155\) | 24930.9 | 0.0833505 | ||||||||
\(156\) | 28447.1 | 0.0935894 | ||||||||
\(157\) | −205537. | −0.665489 | −0.332744 | − | 0.943017i | \(-0.607975\pi\) | ||||
−0.332744 | + | 0.943017i | \(0.607975\pi\) | |||||||
\(158\) | 251654. | 0.801974 | ||||||||
\(159\) | 34665.1 | 0.108742 | ||||||||
\(160\) | −112501. | −0.347420 | ||||||||
\(161\) | −57020.1 | −0.173366 | ||||||||
\(162\) | 28220.1 | 0.0844833 | ||||||||
\(163\) | −639398. | −1.88496 | −0.942481 | − | 0.334261i | \(-0.891513\pi\) | ||||
−0.942481 | + | 0.334261i | \(0.891513\pi\) | |||||||
\(164\) | −30498.3 | −0.0885453 | ||||||||
\(165\) | 27225.0 | 0.0778499 | ||||||||
\(166\) | −224711. | −0.632927 | ||||||||
\(167\) | 416990. | 1.15700 | 0.578502 | − | 0.815681i | \(-0.303637\pi\) | ||||
0.578502 | + | 0.815681i | \(0.303637\pi\) | |||||||
\(168\) | −261057. | −0.713611 | ||||||||
\(169\) | −316473. | −0.852354 | ||||||||
\(170\) | −110945. | −0.294431 | ||||||||
\(171\) | 102570. | 0.268243 | ||||||||
\(172\) | −213552. | −0.550405 | ||||||||
\(173\) | 608651. | 1.54615 | 0.773077 | − | 0.634312i | \(-0.218716\pi\) | ||||
0.773077 | + | 0.634312i | \(0.218716\pi\) | |||||||
\(174\) | 173612. | 0.434716 | ||||||||
\(175\) | −92634.8 | −0.228654 | ||||||||
\(176\) | −49581.4 | −0.120653 | ||||||||
\(177\) | 182349. | 0.437493 | ||||||||
\(178\) | 237058. | 0.560795 | ||||||||
\(179\) | 511566. | 1.19335 | 0.596676 | − | 0.802482i | \(-0.296488\pi\) | ||||
0.596676 | + | 0.802482i | \(0.296488\pi\) | |||||||
\(180\) | 27337.0 | 0.0628883 | ||||||||
\(181\) | 56369.0 | 0.127892 | 0.0639460 | − | 0.997953i | \(-0.479631\pi\) | ||||
0.0639460 | + | 0.997953i | \(0.479631\pi\) | |||||||
\(182\) | −149263. | −0.334021 | ||||||||
\(183\) | −18061.9 | −0.0398691 | ||||||||
\(184\) | −75289.0 | −0.163941 | ||||||||
\(185\) | −129203. | −0.277551 | ||||||||
\(186\) | 38603.7 | 0.0818175 | ||||||||
\(187\) | 124843. | 0.261071 | ||||||||
\(188\) | −162445. | −0.335206 | ||||||||
\(189\) | 108049. | 0.220023 | ||||||||
\(190\) | −136164. | −0.273639 | ||||||||
\(191\) | 45986.9 | 0.0912117 | 0.0456059 | − | 0.998960i | \(-0.485478\pi\) | ||||
0.0456059 | + | 0.998960i | \(0.485478\pi\) | |||||||
\(192\) | −292211. | −0.572063 | ||||||||
\(193\) | 360889. | 0.697398 | 0.348699 | − | 0.937235i | \(-0.386624\pi\) | ||||
0.348699 | + | 0.937235i | \(0.386624\pi\) | |||||||
\(194\) | 427469. | 0.815455 | ||||||||
\(195\) | 52680.7 | 0.0992122 | ||||||||
\(196\) | −69671.0 | −0.129542 | ||||||||
\(197\) | 978922. | 1.79714 | 0.898571 | − | 0.438828i | \(-0.144606\pi\) | ||||
0.898571 | + | 0.438828i | \(0.144606\pi\) | |||||||
\(198\) | 42156.0 | 0.0764181 | ||||||||
\(199\) | 902328. | 1.61522 | 0.807610 | − | 0.589717i | \(-0.200761\pi\) | ||||
0.807610 | + | 0.589717i | \(0.200761\pi\) | |||||||
\(200\) | −122314. | −0.216223 | ||||||||
\(201\) | −368510. | −0.643367 | ||||||||
\(202\) | −108968. | −0.187897 | ||||||||
\(203\) | 664725. | 1.13214 | ||||||||
\(204\) | 125356. | 0.210897 | ||||||||
\(205\) | −56479.3 | −0.0938652 | ||||||||
\(206\) | −400942. | −0.658285 | ||||||||
\(207\) | 31161.5 | 0.0505467 | ||||||||
\(208\) | −95940.7 | −0.153760 | ||||||||
\(209\) | 153221. | 0.242635 | ||||||||
\(210\) | −143438. | −0.224449 | ||||||||
\(211\) | 318392. | 0.492330 | 0.246165 | − | 0.969228i | \(-0.420830\pi\) | ||||
0.246165 | + | 0.969228i | \(0.420830\pi\) | |||||||
\(212\) | 51996.7 | 0.0794577 | ||||||||
\(213\) | −152737. | −0.230673 | ||||||||
\(214\) | 885312. | 1.32148 | ||||||||
\(215\) | −395473. | −0.583473 | ||||||||
\(216\) | 142668. | 0.208061 | ||||||||
\(217\) | 147806. | 0.213080 | ||||||||
\(218\) | −670558. | −0.955642 | ||||||||
\(219\) | 509764. | 0.718223 | ||||||||
\(220\) | 40836.8 | 0.0568846 | ||||||||
\(221\) | 241572. | 0.332710 | ||||||||
\(222\) | −200061. | −0.272446 | ||||||||
\(223\) | 661352. | 0.890575 | 0.445287 | − | 0.895388i | \(-0.353101\pi\) | ||||
0.445287 | + | 0.895388i | \(0.353101\pi\) | |||||||
\(224\) | −666975. | −0.888157 | ||||||||
\(225\) | 50625.0 | 0.0666667 | ||||||||
\(226\) | 173357. | 0.225773 | ||||||||
\(227\) | 606704. | 0.781470 | 0.390735 | − | 0.920503i | \(-0.372221\pi\) | ||||
0.390735 | + | 0.920503i | \(0.372221\pi\) | |||||||
\(228\) | 153852. | 0.196004 | ||||||||
\(229\) | −352377. | −0.444036 | −0.222018 | − | 0.975043i | \(-0.571264\pi\) | ||||
−0.222018 | + | 0.975043i | \(0.571264\pi\) | |||||||
\(230\) | −41367.8 | −0.0515635 | ||||||||
\(231\) | 161407. | 0.199018 | ||||||||
\(232\) | 877699. | 1.07060 | ||||||||
\(233\) | 1.49288e6 | 1.80151 | 0.900755 | − | 0.434328i | \(-0.143014\pi\) | ||||
0.900755 | + | 0.434328i | \(0.143014\pi\) | |||||||
\(234\) | 81572.3 | 0.0973875 | ||||||||
\(235\) | −300830. | −0.355346 | ||||||||
\(236\) | 273519. | 0.319675 | ||||||||
\(237\) | −526571. | −0.608956 | ||||||||
\(238\) | −657749. | −0.752693 | ||||||||
\(239\) | 388141. | 0.439536 | 0.219768 | − | 0.975552i | \(-0.429470\pi\) | ||||
0.219768 | + | 0.975552i | \(0.429470\pi\) | |||||||
\(240\) | −92196.8 | −0.103321 | ||||||||
\(241\) | −75337.2 | −0.0835540 | −0.0417770 | − | 0.999127i | \(-0.513302\pi\) | ||||
−0.0417770 | + | 0.999127i | \(0.513302\pi\) | |||||||
\(242\) | 62973.7 | 0.0691227 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −27092.4 | −0.0291322 | ||||||||
\(245\) | −129023. | −0.137325 | ||||||||
\(246\) | −87454.1 | −0.0921388 | ||||||||
\(247\) | 296485. | 0.309215 | ||||||||
\(248\) | 195162. | 0.201496 | ||||||||
\(249\) | 470194. | 0.480595 | ||||||||
\(250\) | −67206.1 | −0.0680078 | ||||||||
\(251\) | −346975. | −0.347627 | −0.173814 | − | 0.984779i | \(-0.555609\pi\) | ||||
−0.173814 | + | 0.984779i | \(0.555609\pi\) | |||||||
\(252\) | 162071. | 0.160770 | ||||||||
\(253\) | 46549.9 | 0.0457212 | ||||||||
\(254\) | 519691. | 0.505430 | ||||||||
\(255\) | 232145. | 0.223568 | ||||||||
\(256\) | −1.05768e6 | −1.00869 | ||||||||
\(257\) | 1.97267e6 | 1.86304 | 0.931518 | − | 0.363696i | \(-0.118485\pi\) | ||||
0.931518 | + | 0.363696i | \(0.118485\pi\) | |||||||
\(258\) | −612362. | −0.572742 | ||||||||
\(259\) | −765995. | −0.709539 | ||||||||
\(260\) | 79019.7 | 0.0724940 | ||||||||
\(261\) | −363273. | −0.330089 | ||||||||
\(262\) | 1.14615e6 | 1.03155 | ||||||||
\(263\) | −190986. | −0.170260 | −0.0851300 | − | 0.996370i | \(-0.527131\pi\) | ||||
−0.0851300 | + | 0.996370i | \(0.527131\pi\) | |||||||
\(264\) | 213121. | 0.188198 | ||||||||
\(265\) | 96291.8 | 0.0842316 | ||||||||
\(266\) | −807266. | −0.699540 | ||||||||
\(267\) | −496030. | −0.425823 | ||||||||
\(268\) | −552755. | −0.470106 | ||||||||
\(269\) | 933912. | 0.786911 | 0.393455 | − | 0.919344i | \(-0.371280\pi\) | ||||
0.393455 | + | 0.919344i | \(0.371280\pi\) | |||||||
\(270\) | 78389.2 | 0.0654405 | ||||||||
\(271\) | −1.17171e6 | −0.969163 | −0.484582 | − | 0.874746i | \(-0.661028\pi\) | ||||
−0.484582 | + | 0.874746i | \(0.661028\pi\) | |||||||
\(272\) | −422776. | −0.346488 | ||||||||
\(273\) | 312325. | 0.253629 | ||||||||
\(274\) | 73879.3 | 0.0594492 | ||||||||
\(275\) | 75625.0 | 0.0603023 | ||||||||
\(276\) | 46741.5 | 0.0369343 | ||||||||
\(277\) | −472512. | −0.370010 | −0.185005 | − | 0.982738i | \(-0.559230\pi\) | ||||
−0.185005 | + | 0.982738i | \(0.559230\pi\) | |||||||
\(278\) | −21643.5 | −0.0167964 | ||||||||
\(279\) | −80776.0 | −0.0621258 | ||||||||
\(280\) | −725157. | −0.552760 | ||||||||
\(281\) | −2.05374e6 | −1.55160 | −0.775798 | − | 0.630981i | \(-0.782652\pi\) | ||||
−0.775798 | + | 0.630981i | \(0.782652\pi\) | |||||||
\(282\) | −465813. | −0.348810 | ||||||||
\(283\) | 465578. | 0.345562 | 0.172781 | − | 0.984960i | \(-0.444725\pi\) | ||||
0.172781 | + | 0.984960i | \(0.444725\pi\) | |||||||
\(284\) | −229102. | −0.168552 | ||||||||
\(285\) | 284916. | 0.207780 | ||||||||
\(286\) | 121855. | 0.0880903 | ||||||||
\(287\) | −334845. | −0.239960 | ||||||||
\(288\) | 364502. | 0.258952 | ||||||||
\(289\) | −355335. | −0.250261 | ||||||||
\(290\) | 482255. | 0.336730 | ||||||||
\(291\) | −894454. | −0.619193 | ||||||||
\(292\) | 764633. | 0.524803 | ||||||||
\(293\) | −1.19434e6 | −0.812751 | −0.406376 | − | 0.913706i | \(-0.633208\pi\) | ||||
−0.406376 | + | 0.913706i | \(0.633208\pi\) | |||||||
\(294\) | −199782. | −0.134800 | ||||||||
\(295\) | 506526. | 0.338881 | ||||||||
\(296\) | −1.01141e6 | −0.670965 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −160898. | −0.104957 | ||||||||
\(299\) | 90074.7 | 0.0582673 | ||||||||
\(300\) | 75936.2 | 0.0487131 | ||||||||
\(301\) | −2.34461e6 | −1.49161 | ||||||||
\(302\) | −971438. | −0.612912 | ||||||||
\(303\) | 228009. | 0.142674 | ||||||||
\(304\) | −518880. | −0.322020 | ||||||||
\(305\) | −50172.0 | −0.0308825 | ||||||||
\(306\) | 359460. | 0.219456 | ||||||||
\(307\) | 1.72251e6 | 1.04308 | 0.521538 | − | 0.853228i | \(-0.325359\pi\) | ||||
0.521538 | + | 0.853228i | \(0.325359\pi\) | |||||||
\(308\) | 242106. | 0.145422 | ||||||||
\(309\) | 838950. | 0.499850 | ||||||||
\(310\) | 107232. | 0.0633755 | ||||||||
\(311\) | −2.60616e6 | −1.52792 | −0.763960 | − | 0.645263i | \(-0.776748\pi\) | ||||
−0.763960 | + | 0.645263i | \(0.776748\pi\) | |||||||
\(312\) | 412391. | 0.239841 | ||||||||
\(313\) | 1.22311e6 | 0.705677 | 0.352839 | − | 0.935684i | \(-0.385216\pi\) | ||||
0.352839 | + | 0.935684i | \(0.385216\pi\) | |||||||
\(314\) | −884053. | −0.506005 | ||||||||
\(315\) | 300137. | 0.170429 | ||||||||
\(316\) | −789843. | −0.444962 | ||||||||
\(317\) | −700043. | −0.391270 | −0.195635 | − | 0.980677i | \(-0.562677\pi\) | ||||
−0.195635 | + | 0.980677i | \(0.562677\pi\) | |||||||
\(318\) | 149101. | 0.0826824 | ||||||||
\(319\) | −542667. | −0.298577 | ||||||||
\(320\) | −811698. | −0.443118 | ||||||||
\(321\) | −1.85247e6 | −1.00343 | ||||||||
\(322\) | −245254. | −0.131819 | ||||||||
\(323\) | 1.30650e6 | 0.696794 | ||||||||
\(324\) | −88572.0 | −0.0468742 | ||||||||
\(325\) | 146335. | 0.0768495 | ||||||||
\(326\) | −2.75017e6 | −1.43323 | ||||||||
\(327\) | 1.40311e6 | 0.725640 | ||||||||
\(328\) | −442127. | −0.226914 | ||||||||
\(329\) | −1.78351e6 | −0.908417 | ||||||||
\(330\) | 117100. | 0.0591932 | ||||||||
\(331\) | 2.78738e6 | 1.39839 | 0.699193 | − | 0.714933i | \(-0.253543\pi\) | ||||
0.699193 | + | 0.714933i | \(0.253543\pi\) | |||||||
\(332\) | 705279. | 0.351169 | ||||||||
\(333\) | 418617. | 0.206874 | ||||||||
\(334\) | 1.79355e6 | 0.879728 | ||||||||
\(335\) | −1.02364e6 | −0.498350 | ||||||||
\(336\) | −546601. | −0.264133 | ||||||||
\(337\) | −795333. | −0.381482 | −0.190741 | − | 0.981640i | \(-0.561089\pi\) | ||||
−0.190741 | + | 0.981640i | \(0.561089\pi\) | |||||||
\(338\) | −1.36121e6 | −0.648087 | ||||||||
\(339\) | −362741. | −0.171434 | ||||||||
\(340\) | 348212. | 0.163360 | ||||||||
\(341\) | −120665. | −0.0561949 | ||||||||
\(342\) | 441171. | 0.203959 | ||||||||
\(343\) | 1.72613e6 | 0.792208 | ||||||||
\(344\) | −3.09581e6 | −1.41052 | ||||||||
\(345\) | 86559.8 | 0.0391533 | ||||||||
\(346\) | 2.61792e6 | 1.17562 | ||||||||
\(347\) | −3.80533e6 | −1.69656 | −0.848278 | − | 0.529551i | \(-0.822361\pi\) | ||||
−0.848278 | + | 0.529551i | \(0.822361\pi\) | |||||||
\(348\) | −544900. | −0.241195 | ||||||||
\(349\) | −798008. | −0.350706 | −0.175353 | − | 0.984506i | \(-0.556107\pi\) | ||||
−0.175353 | + | 0.984506i | \(0.556107\pi\) | |||||||
\(350\) | −398440. | −0.173857 | ||||||||
\(351\) | −170686. | −0.0739484 | ||||||||
\(352\) | 544503. | 0.234231 | ||||||||
\(353\) | 2.48978e6 | 1.06347 | 0.531733 | − | 0.846912i | \(-0.321541\pi\) | ||||
0.531733 | + | 0.846912i | \(0.321541\pi\) | |||||||
\(354\) | 784319. | 0.332648 | ||||||||
\(355\) | −424271. | −0.178678 | ||||||||
\(356\) | −744032. | −0.311148 | ||||||||
\(357\) | 1.37630e6 | 0.571536 | ||||||||
\(358\) | 2.20034e6 | 0.907366 | ||||||||
\(359\) | −2.15148e6 | −0.881050 | −0.440525 | − | 0.897740i | \(-0.645208\pi\) | ||||
−0.440525 | + | 0.897740i | \(0.645208\pi\) | |||||||
\(360\) | 396299. | 0.161163 | ||||||||
\(361\) | −872605. | −0.352411 | ||||||||
\(362\) | 242454. | 0.0972427 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | 468479. | 0.185326 | ||||||||
\(365\) | 1.41601e6 | 0.556333 | ||||||||
\(366\) | −77687.8 | −0.0303145 | ||||||||
\(367\) | 1.47515e6 | 0.571705 | 0.285853 | − | 0.958274i | \(-0.407723\pi\) | ||||
0.285853 | + | 0.958274i | \(0.407723\pi\) | |||||||
\(368\) | −157640. | −0.0606803 | ||||||||
\(369\) | 182993. | 0.0699630 | ||||||||
\(370\) | −555725. | −0.211036 | ||||||||
\(371\) | 570879. | 0.215332 | ||||||||
\(372\) | −121162. | −0.0453951 | ||||||||
\(373\) | −4.71290e6 | −1.75394 | −0.876972 | − | 0.480541i | \(-0.840440\pi\) | ||||
−0.876972 | + | 0.480541i | \(0.840440\pi\) | |||||||
\(374\) | 536972. | 0.198505 | ||||||||
\(375\) | 140625. | 0.0516398 | ||||||||
\(376\) | −2.35493e6 | −0.859031 | ||||||||
\(377\) | −1.05007e6 | −0.380508 | ||||||||
\(378\) | 464740. | 0.167294 | ||||||||
\(379\) | 4.47900e6 | 1.60171 | 0.800853 | − | 0.598861i | \(-0.204380\pi\) | ||||
0.800853 | + | 0.598861i | \(0.204380\pi\) | |||||||
\(380\) | 427366. | 0.151824 | ||||||||
\(381\) | −1.08742e6 | −0.383784 | ||||||||
\(382\) | 197798. | 0.0693528 | ||||||||
\(383\) | −57968.7 | −0.0201928 | −0.0100964 | − | 0.999949i | \(-0.503214\pi\) | ||||
−0.0100964 | + | 0.999949i | \(0.503214\pi\) | |||||||
\(384\) | 39152.3 | 0.0135497 | ||||||||
\(385\) | 448353. | 0.154159 | ||||||||
\(386\) | 1.55225e6 | 0.530267 | ||||||||
\(387\) | 1.28133e6 | 0.434895 | ||||||||
\(388\) | −1.34166e6 | −0.452442 | ||||||||
\(389\) | −4.53325e6 | −1.51892 | −0.759461 | − | 0.650553i | \(-0.774537\pi\) | ||||
−0.759461 | + | 0.650553i | \(0.774537\pi\) | |||||||
\(390\) | 226590. | 0.0754360 | ||||||||
\(391\) | 396927. | 0.131301 | ||||||||
\(392\) | −1.01000e6 | −0.331977 | ||||||||
\(393\) | −2.39826e6 | −0.783277 | ||||||||
\(394\) | 4.21053e6 | 1.36646 | ||||||||
\(395\) | −1.46270e6 | −0.471695 | ||||||||
\(396\) | −132311. | −0.0423993 | ||||||||
\(397\) | 621573. | 0.197932 | 0.0989660 | − | 0.995091i | \(-0.468446\pi\) | ||||
0.0989660 | + | 0.995091i | \(0.468446\pi\) | |||||||
\(398\) | 3.88108e6 | 1.22813 | ||||||||
\(399\) | 1.68916e6 | 0.531176 | ||||||||
\(400\) | −256102. | −0.0800320 | ||||||||
\(401\) | 954326. | 0.296371 | 0.148186 | − | 0.988960i | \(-0.452657\pi\) | ||||
0.148186 | + | 0.988960i | \(0.452657\pi\) | |||||||
\(402\) | −1.58503e6 | −0.489185 | ||||||||
\(403\) | −233489. | −0.0716150 | ||||||||
\(404\) | 342007. | 0.104251 | ||||||||
\(405\) | −164025. | −0.0496904 | ||||||||
\(406\) | 2.85911e6 | 0.860826 | ||||||||
\(407\) | 625341. | 0.187125 | ||||||||
\(408\) | 1.81726e6 | 0.540465 | ||||||||
\(409\) | 3.19864e6 | 0.945491 | 0.472746 | − | 0.881199i | \(-0.343263\pi\) | ||||
0.472746 | + | 0.881199i | \(0.343263\pi\) | |||||||
\(410\) | −242928. | −0.0713704 | ||||||||
\(411\) | −154588. | −0.0451411 | ||||||||
\(412\) | 1.25840e6 | 0.365239 | ||||||||
\(413\) | 3.00301e6 | 0.866325 | ||||||||
\(414\) | 134032. | 0.0384332 | ||||||||
\(415\) | 1.30610e6 | 0.372267 | ||||||||
\(416\) | 1.05362e6 | 0.298505 | ||||||||
\(417\) | 45287.9 | 0.0127539 | ||||||||
\(418\) | 659034. | 0.184487 | ||||||||
\(419\) | −6.60122e6 | −1.83691 | −0.918457 | − | 0.395520i | \(-0.870564\pi\) | ||||
−0.918457 | + | 0.395520i | \(0.870564\pi\) | |||||||
\(420\) | 450198. | 0.124532 | ||||||||
\(421\) | −4.22510e6 | −1.16180 | −0.580901 | − | 0.813974i | \(-0.697300\pi\) | ||||
−0.580901 | + | 0.813974i | \(0.697300\pi\) | |||||||
\(422\) | 1.36946e6 | 0.374343 | ||||||||
\(423\) | 974688. | 0.264859 | ||||||||
\(424\) | 753785. | 0.203626 | ||||||||
\(425\) | 644848. | 0.173175 | ||||||||
\(426\) | −656953. | −0.175392 | ||||||||
\(427\) | −297451. | −0.0789489 | ||||||||
\(428\) | −2.77865e6 | −0.733204 | ||||||||
\(429\) | −254975. | −0.0668889 | ||||||||
\(430\) | −1.70100e6 | −0.443644 | ||||||||
\(431\) | 4.72300e6 | 1.22469 | 0.612344 | − | 0.790592i | \(-0.290227\pi\) | ||||
0.612344 | + | 0.790592i | \(0.290227\pi\) | |||||||
\(432\) | 298718. | 0.0770108 | ||||||||
\(433\) | −882129. | −0.226106 | −0.113053 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113053 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(434\) | 635741. | 0.162015 | ||||||||
\(435\) | −1.00909e6 | −0.255686 | ||||||||
\(436\) | 2.10462e6 | 0.530222 | ||||||||
\(437\) | 487155. | 0.122029 | ||||||||
\(438\) | 2.19259e6 | 0.546101 | ||||||||
\(439\) | −3.07514e6 | −0.761560 | −0.380780 | − | 0.924666i | \(-0.624344\pi\) | ||||
−0.380780 | + | 0.924666i | \(0.624344\pi\) | |||||||
\(440\) | 592002. | 0.145778 | ||||||||
\(441\) | 418033. | 0.102356 | ||||||||
\(442\) | 1.03905e6 | 0.252976 | ||||||||
\(443\) | 3.40381e6 | 0.824055 | 0.412028 | − | 0.911171i | \(-0.364821\pi\) | ||||
0.412028 | + | 0.911171i | \(0.364821\pi\) | |||||||
\(444\) | 627914. | 0.151162 | ||||||||
\(445\) | −1.37786e6 | −0.329841 | ||||||||
\(446\) | 2.84460e6 | 0.677149 | ||||||||
\(447\) | 336671. | 0.0796961 | ||||||||
\(448\) | −4.81226e6 | −1.13280 | ||||||||
\(449\) | −605757. | −0.141802 | −0.0709010 | − | 0.997483i | \(-0.522587\pi\) | ||||
−0.0709010 | + | 0.997483i | \(0.522587\pi\) | |||||||
\(450\) | 217748. | 0.0506900 | ||||||||
\(451\) | 273360. | 0.0632839 | ||||||||
\(452\) | −544102. | −0.125266 | ||||||||
\(453\) | 2.03268e6 | 0.465397 | ||||||||
\(454\) | 2.60955e6 | 0.594191 | ||||||||
\(455\) | 867568. | 0.196460 | ||||||||
\(456\) | 2.23035e6 | 0.502298 | ||||||||
\(457\) | −5.46329e6 | −1.22367 | −0.611834 | − | 0.790986i | \(-0.709568\pi\) | ||||
−0.611834 | + | 0.790986i | \(0.709568\pi\) | |||||||
\(458\) | −1.51564e6 | −0.337623 | ||||||||
\(459\) | −752151. | −0.166638 | ||||||||
\(460\) | 129837. | 0.0286092 | ||||||||
\(461\) | −2.84223e6 | −0.622883 | −0.311441 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311441 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(462\) | 694242. | 0.151323 | ||||||||
\(463\) | −8.51652e6 | −1.84633 | −0.923166 | − | 0.384401i | \(-0.874408\pi\) | ||||
−0.923166 | + | 0.384401i | \(0.874408\pi\) | |||||||
\(464\) | 1.83773e6 | 0.396266 | ||||||||
\(465\) | −224378. | −0.0481224 | ||||||||
\(466\) | 6.42118e6 | 1.36978 | ||||||||
\(467\) | 7.00140e6 | 1.48557 | 0.742784 | − | 0.669531i | \(-0.233505\pi\) | ||||
0.742784 | + | 0.669531i | \(0.233505\pi\) | |||||||
\(468\) | −256024. | −0.0540339 | ||||||||
\(469\) | −6.06877e6 | −1.27400 | ||||||||
\(470\) | −1.29393e6 | −0.270187 | ||||||||
\(471\) | 1.84983e6 | 0.384220 | ||||||||
\(472\) | 3.96515e6 | 0.819228 | ||||||||
\(473\) | 1.91409e6 | 0.393377 | ||||||||
\(474\) | −2.26488e6 | −0.463020 | ||||||||
\(475\) | 791432. | 0.160946 | ||||||||
\(476\) | 2.06442e6 | 0.417619 | ||||||||
\(477\) | −311986. | −0.0627825 | ||||||||
\(478\) | 1.66947e6 | 0.334201 | ||||||||
\(479\) | 1.06826e6 | 0.212734 | 0.106367 | − | 0.994327i | \(-0.466078\pi\) | ||||
0.106367 | + | 0.994327i | \(0.466078\pi\) | |||||||
\(480\) | 1.01251e6 | 0.200583 | ||||||||
\(481\) | 1.21004e6 | 0.238472 | ||||||||
\(482\) | −324040. | −0.0635303 | ||||||||
\(483\) | 513181. | 0.100093 | ||||||||
\(484\) | −197650. | −0.0383516 | ||||||||
\(485\) | −2.48460e6 | −0.479625 | ||||||||
\(486\) | −253981. | −0.0487765 | ||||||||
\(487\) | 1.00308e6 | 0.191652 | 0.0958260 | − | 0.995398i | \(-0.469451\pi\) | ||||
0.0958260 | + | 0.995398i | \(0.469451\pi\) | |||||||
\(488\) | −392753. | −0.0746569 | ||||||||
\(489\) | 5.75458e6 | 1.08828 | ||||||||
\(490\) | −554950. | −0.104415 | ||||||||
\(491\) | 9.23719e6 | 1.72916 | 0.864582 | − | 0.502491i | \(-0.167583\pi\) | ||||
0.864582 | + | 0.502491i | \(0.167583\pi\) | |||||||
\(492\) | 274484. | 0.0511217 | ||||||||
\(493\) | −4.62727e6 | −0.857448 | ||||||||
\(494\) | 1.27524e6 | 0.235112 | ||||||||
\(495\) | −245025. | −0.0449467 | ||||||||
\(496\) | 408631. | 0.0745807 | ||||||||
\(497\) | −2.51534e6 | −0.456779 | ||||||||
\(498\) | 2.02240e6 | 0.365420 | ||||||||
\(499\) | 4.31532e6 | 0.775822 | 0.387911 | − | 0.921697i | \(-0.373197\pi\) | ||||
0.387911 | + | 0.921697i | \(0.373197\pi\) | |||||||
\(500\) | 210934. | 0.0377330 | ||||||||
\(501\) | −3.75291e6 | −0.667997 | ||||||||
\(502\) | −1.49240e6 | −0.264318 | ||||||||
\(503\) | 3.28052e6 | 0.578127 | 0.289064 | − | 0.957310i | \(-0.406656\pi\) | ||||
0.289064 | + | 0.957310i | \(0.406656\pi\) | |||||||
\(504\) | 2.34951e6 | 0.412003 | ||||||||
\(505\) | 633357. | 0.110515 | ||||||||
\(506\) | 200220. | 0.0347641 | ||||||||
\(507\) | 2.84826e6 | 0.492107 | ||||||||
\(508\) | −1.63111e6 | −0.280430 | ||||||||
\(509\) | −2.50882e6 | −0.429215 | −0.214608 | − | 0.976700i | \(-0.568847\pi\) | ||||
−0.214608 | + | 0.976700i | \(0.568847\pi\) | |||||||
\(510\) | 998501. | 0.169990 | ||||||||
\(511\) | 8.39501e6 | 1.42223 | ||||||||
\(512\) | −4.41009e6 | −0.743486 | ||||||||
\(513\) | −923126. | −0.154870 | ||||||||
\(514\) | 8.48482e6 | 1.41656 | ||||||||
\(515\) | 2.33042e6 | 0.387182 | ||||||||
\(516\) | 1.92197e6 | 0.317776 | ||||||||
\(517\) | 1.45602e6 | 0.239574 | ||||||||
\(518\) | −3.29469e6 | −0.539498 | ||||||||
\(519\) | −5.47786e6 | −0.892673 | ||||||||
\(520\) | 1.14553e6 | 0.185780 | ||||||||
\(521\) | −3.63347e6 | −0.586444 | −0.293222 | − | 0.956044i | \(-0.594728\pi\) | ||||
−0.293222 | + | 0.956044i | \(0.594728\pi\) | |||||||
\(522\) | −1.56250e6 | −0.250983 | ||||||||
\(523\) | −7.95990e6 | −1.27249 | −0.636243 | − | 0.771488i | \(-0.719513\pi\) | ||||
−0.636243 | + | 0.771488i | \(0.719513\pi\) | |||||||
\(524\) | −3.59733e6 | −0.572338 | ||||||||
\(525\) | 833713. | 0.132014 | ||||||||
\(526\) | −821468. | −0.129457 | ||||||||
\(527\) | −1.02890e6 | −0.161379 | ||||||||
\(528\) | 446233. | 0.0696589 | ||||||||
\(529\) | −6.28834e6 | −0.977005 | ||||||||
\(530\) | 414170. | 0.0640455 | ||||||||
\(531\) | −1.64114e6 | −0.252587 | ||||||||
\(532\) | 2.53369e6 | 0.388128 | ||||||||
\(533\) | 528954. | 0.0806492 | ||||||||
\(534\) | −2.13352e6 | −0.323775 | ||||||||
\(535\) | −5.14574e6 | −0.777255 | ||||||||
\(536\) | −8.01317e6 | −1.20474 | ||||||||
\(537\) | −4.60409e6 | −0.688983 | ||||||||
\(538\) | 4.01693e6 | 0.598328 | ||||||||
\(539\) | 624469. | 0.0925847 | ||||||||
\(540\) | −246033. | −0.0363086 | ||||||||
\(541\) | 1.20412e6 | 0.176879 | 0.0884395 | − | 0.996082i | \(-0.471812\pi\) | ||||
0.0884395 | + | 0.996082i | \(0.471812\pi\) | |||||||
\(542\) | −5.03975e6 | −0.736903 | ||||||||
\(543\) | −507321. | −0.0738385 | ||||||||
\(544\) | 4.64293e6 | 0.672660 | ||||||||
\(545\) | 3.89752e6 | 0.562078 | ||||||||
\(546\) | 1.34337e6 | 0.192847 | ||||||||
\(547\) | −1.04446e7 | −1.49254 | −0.746268 | − | 0.665646i | \(-0.768156\pi\) | ||||
−0.746268 | + | 0.665646i | \(0.768156\pi\) | |||||||
\(548\) | −231878. | −0.0329844 | ||||||||
\(549\) | 162557. | 0.0230184 | ||||||||
\(550\) | 325277. | 0.0458508 | ||||||||
\(551\) | −5.67912e6 | −0.796897 | ||||||||
\(552\) | 677601. | 0.0946512 | ||||||||
\(553\) | −8.67179e6 | −1.20586 | ||||||||
\(554\) | −2.03236e6 | −0.281337 | ||||||||
\(555\) | 1.16282e6 | 0.160244 | ||||||||
\(556\) | 67930.6 | 0.00931920 | ||||||||
\(557\) | 8.45756e6 | 1.15507 | 0.577534 | − | 0.816367i | \(-0.304015\pi\) | ||||
0.577534 | + | 0.816367i | \(0.304015\pi\) | |||||||
\(558\) | −347433. | −0.0472373 | ||||||||
\(559\) | 3.70379e6 | 0.501322 | ||||||||
\(560\) | −1.51834e6 | −0.204596 | ||||||||
\(561\) | −1.12358e6 | −0.150729 | ||||||||
\(562\) | −8.83350e6 | −1.17976 | ||||||||
\(563\) | 9.96372e6 | 1.32480 | 0.662401 | − | 0.749150i | \(-0.269538\pi\) | ||||
0.662401 | + | 0.749150i | \(0.269538\pi\) | |||||||
\(564\) | 1.46201e6 | 0.193532 | ||||||||
\(565\) | −1.00761e6 | −0.132792 | ||||||||
\(566\) | 2.00254e6 | 0.262748 | ||||||||
\(567\) | −972443. | −0.127030 | ||||||||
\(568\) | −3.32124e6 | −0.431946 | ||||||||
\(569\) | −1.05157e7 | −1.36163 | −0.680813 | − | 0.732458i | \(-0.738373\pi\) | ||||
−0.680813 | + | 0.732458i | \(0.738373\pi\) | |||||||
\(570\) | 1.22548e6 | 0.157986 | ||||||||
\(571\) | 9.02900e6 | 1.15891 | 0.579454 | − | 0.815005i | \(-0.303266\pi\) | ||||
0.579454 | + | 0.815005i | \(0.303266\pi\) | |||||||
\(572\) | −382456. | −0.0488755 | ||||||||
\(573\) | −413882. | −0.0526611 | ||||||||
\(574\) | −1.44023e6 | −0.182453 | ||||||||
\(575\) | 240444. | 0.0303280 | ||||||||
\(576\) | 2.62990e6 | 0.330281 | ||||||||
\(577\) | 6.65688e6 | 0.832398 | 0.416199 | − | 0.909273i | \(-0.363362\pi\) | ||||
0.416199 | + | 0.909273i | \(0.363362\pi\) | |||||||
\(578\) | −1.52836e6 | −0.190286 | ||||||||
\(579\) | −3.24800e6 | −0.402643 | ||||||||
\(580\) | −1.51361e6 | −0.186829 | ||||||||
\(581\) | 7.74336e6 | 0.951676 | ||||||||
\(582\) | −3.84722e6 | −0.470803 | ||||||||
\(583\) | −466053. | −0.0567889 | ||||||||
\(584\) | 1.10847e7 | 1.34491 | ||||||||
\(585\) | −474127. | −0.0572802 | ||||||||
\(586\) | −5.13707e6 | −0.617975 | ||||||||
\(587\) | 2.20946e6 | 0.264661 | 0.132331 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132331 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(588\) | 627039. | 0.0747913 | ||||||||
\(589\) | −1.26279e6 | −0.149983 | ||||||||
\(590\) | 2.17866e6 | 0.257668 | ||||||||
\(591\) | −8.81030e6 | −1.03758 | ||||||||
\(592\) | −2.11770e6 | −0.248348 | ||||||||
\(593\) | −261524. | −0.0305404 | −0.0152702 | − | 0.999883i | \(-0.504861\pi\) | ||||
−0.0152702 | + | 0.999883i | \(0.504861\pi\) | |||||||
\(594\) | −379404. | −0.0441200 | ||||||||
\(595\) | 3.82306e6 | 0.442710 | ||||||||
\(596\) | 504998. | 0.0582336 | ||||||||
\(597\) | −8.12095e6 | −0.932548 | ||||||||
\(598\) | 387429. | 0.0443036 | ||||||||
\(599\) | 7.09631e6 | 0.808101 | 0.404050 | − | 0.914737i | \(-0.367602\pi\) | ||||
0.404050 | + | 0.914737i | \(0.367602\pi\) | |||||||
\(600\) | 1.10083e6 | 0.124837 | ||||||||
\(601\) | 6.04793e6 | 0.683000 | 0.341500 | − | 0.939882i | \(-0.389065\pi\) | ||||
0.341500 | + | 0.939882i | \(0.389065\pi\) | |||||||
\(602\) | −1.00846e7 | −1.13414 | ||||||||
\(603\) | 3.31659e6 | 0.371448 | ||||||||
\(604\) | 3.04897e6 | 0.340064 | ||||||||
\(605\) | −366025. | −0.0406558 | ||||||||
\(606\) | 980708. | 0.108482 | ||||||||
\(607\) | −1.05203e7 | −1.15892 | −0.579461 | − | 0.815000i | \(-0.696737\pi\) | ||||
−0.579461 | + | 0.815000i | \(0.696737\pi\) | |||||||
\(608\) | 5.69835e6 | 0.625158 | ||||||||
\(609\) | −5.98253e6 | −0.653644 | ||||||||
\(610\) | −215799. | −0.0234815 | ||||||||
\(611\) | 2.81741e6 | 0.305314 | ||||||||
\(612\) | −1.12821e6 | −0.121762 | ||||||||
\(613\) | −8.55961e6 | −0.920032 | −0.460016 | − | 0.887911i | \(-0.652156\pi\) | ||||
−0.460016 | + | 0.887911i | \(0.652156\pi\) | |||||||
\(614\) | 7.40884e6 | 0.793103 | ||||||||
\(615\) | 508313. | 0.0541931 | ||||||||
\(616\) | 3.50976e6 | 0.372671 | ||||||||
\(617\) | −6.18055e6 | −0.653604 | −0.326802 | − | 0.945093i | \(-0.605971\pi\) | ||||
−0.326802 | + | 0.945093i | \(0.605971\pi\) | |||||||
\(618\) | 3.60848e6 | 0.380061 | ||||||||
\(619\) | −1.12540e7 | −1.18053 | −0.590267 | − | 0.807208i | \(-0.700978\pi\) | ||||
−0.590267 | + | 0.807208i | \(0.700978\pi\) | |||||||
\(620\) | −336561. | −0.0351629 | ||||||||
\(621\) | −280454. | −0.0291832 | ||||||||
\(622\) | −1.12096e7 | −1.16175 | ||||||||
\(623\) | −8.16882e6 | −0.843217 | ||||||||
\(624\) | 863466. | 0.0887736 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 5.26085e6 | 0.536562 | ||||||||
\(627\) | −1.37899e6 | −0.140085 | ||||||||
\(628\) | 2.77470e6 | 0.280748 | ||||||||
\(629\) | 5.33223e6 | 0.537381 | ||||||||
\(630\) | 1.29095e6 | 0.129586 | ||||||||
\(631\) | 1.17369e7 | 1.17349 | 0.586746 | − | 0.809771i | \(-0.300409\pi\) | ||||
0.586746 | + | 0.809771i | \(0.300409\pi\) | |||||||
\(632\) | −1.14502e7 | −1.14030 | ||||||||
\(633\) | −2.86553e6 | −0.284247 | ||||||||
\(634\) | −3.01102e6 | −0.297502 | ||||||||
\(635\) | −3.02062e6 | −0.297278 | ||||||||
\(636\) | −467970. | −0.0458749 | ||||||||
\(637\) | 1.20836e6 | 0.117990 | ||||||||
\(638\) | −2.33411e6 | −0.227023 | ||||||||
\(639\) | 1.37464e6 | 0.133179 | ||||||||
\(640\) | 108756. | 0.0104955 | ||||||||
\(641\) | 6.80878e6 | 0.654522 | 0.327261 | − | 0.944934i | \(-0.393874\pi\) | ||||
0.327261 | + | 0.944934i | \(0.393874\pi\) | |||||||
\(642\) | −7.96781e6 | −0.762959 | ||||||||
\(643\) | −1.16456e7 | −1.11080 | −0.555400 | − | 0.831583i | \(-0.687435\pi\) | ||||
−0.555400 | + | 0.831583i | \(0.687435\pi\) | |||||||
\(644\) | 769758. | 0.0731374 | ||||||||
\(645\) | 3.55926e6 | 0.336868 | ||||||||
\(646\) | 5.61952e6 | 0.529808 | ||||||||
\(647\) | 2.61990e6 | 0.246050 | 0.123025 | − | 0.992404i | \(-0.460740\pi\) | ||||
0.123025 | + | 0.992404i | \(0.460740\pi\) | |||||||
\(648\) | −1.28401e6 | −0.120124 | ||||||||
\(649\) | −2.45159e6 | −0.228473 | ||||||||
\(650\) | 629416. | 0.0584325 | ||||||||
\(651\) | −1.33025e6 | −0.123022 | ||||||||
\(652\) | 8.63173e6 | 0.795204 | ||||||||
\(653\) | 1.48492e7 | 1.36276 | 0.681379 | − | 0.731931i | \(-0.261381\pi\) | ||||
0.681379 | + | 0.731931i | \(0.261381\pi\) | |||||||
\(654\) | 6.03502e6 | 0.551740 | ||||||||
\(655\) | −6.66184e6 | −0.606724 | ||||||||
\(656\) | −925726. | −0.0839891 | ||||||||
\(657\) | −4.58788e6 | −0.414666 | ||||||||
\(658\) | −7.67120e6 | −0.690715 | ||||||||
\(659\) | −2.47470e6 | −0.221977 | −0.110989 | − | 0.993822i | \(-0.535402\pi\) | ||||
−0.110989 | + | 0.993822i | \(0.535402\pi\) | |||||||
\(660\) | −367531. | −0.0328424 | ||||||||
\(661\) | 7.61212e6 | 0.677645 | 0.338822 | − | 0.940850i | \(-0.389971\pi\) | ||||
0.338822 | + | 0.940850i | \(0.389971\pi\) | |||||||
\(662\) | 1.19891e7 | 1.06326 | ||||||||
\(663\) | −2.17415e6 | −0.192090 | ||||||||
\(664\) | 1.02243e7 | 0.899938 | ||||||||
\(665\) | 4.69211e6 | 0.411447 | ||||||||
\(666\) | 1.80055e6 | 0.157297 | ||||||||
\(667\) | −1.72537e6 | −0.150164 | ||||||||
\(668\) | −5.62927e6 | −0.488103 | ||||||||
\(669\) | −5.95217e6 | −0.514174 | ||||||||
\(670\) | −4.40286e6 | −0.378921 | ||||||||
\(671\) | 242833. | 0.0208210 | ||||||||
\(672\) | 6.00278e6 | 0.512777 | ||||||||
\(673\) | 6.62472e6 | 0.563807 | 0.281903 | − | 0.959443i | \(-0.409034\pi\) | ||||
0.281903 | + | 0.959443i | \(0.409034\pi\) | |||||||
\(674\) | −3.42088e6 | −0.290060 | ||||||||
\(675\) | −455625. | −0.0384900 | ||||||||
\(676\) | 4.27231e6 | 0.359581 | ||||||||
\(677\) | 228067. | 0.0191245 | 0.00956227 | − | 0.999954i | \(-0.496956\pi\) | ||||
0.00956227 | + | 0.999954i | \(0.496956\pi\) | |||||||
\(678\) | −1.56022e6 | −0.130350 | ||||||||
\(679\) | −1.47302e7 | −1.22613 | ||||||||
\(680\) | 5.04795e6 | 0.418642 | ||||||||
\(681\) | −5.46034e6 | −0.451182 | ||||||||
\(682\) | −519005. | −0.0427278 | ||||||||
\(683\) | −1.58370e6 | −0.129903 | −0.0649517 | − | 0.997888i | \(-0.520689\pi\) | ||||
−0.0649517 | + | 0.997888i | \(0.520689\pi\) | |||||||
\(684\) | −1.38467e6 | −0.113163 | ||||||||
\(685\) | −429412. | −0.0349661 | ||||||||
\(686\) | 7.42443e6 | 0.602356 | ||||||||
\(687\) | 3.17139e6 | 0.256364 | ||||||||
\(688\) | −6.48202e6 | −0.522083 | ||||||||
\(689\) | −901818. | −0.0723720 | ||||||||
\(690\) | 372310. | 0.0297702 | ||||||||
\(691\) | 2.07411e7 | 1.65248 | 0.826241 | − | 0.563317i | \(-0.190475\pi\) | ||||
0.826241 | + | 0.563317i | \(0.190475\pi\) | |||||||
\(692\) | −8.21665e6 | −0.652273 | ||||||||
\(693\) | −1.45266e6 | −0.114903 | ||||||||
\(694\) | −1.63674e7 | −1.28998 | ||||||||
\(695\) | 125800. | 0.00987910 | ||||||||
\(696\) | −7.89929e6 | −0.618109 | ||||||||
\(697\) | 2.33091e6 | 0.181737 | ||||||||
\(698\) | −3.43238e6 | −0.266660 | ||||||||
\(699\) | −1.34360e7 | −1.04010 | ||||||||
\(700\) | 1.25055e6 | 0.0964618 | ||||||||
\(701\) | −1.54594e7 | −1.18822 | −0.594109 | − | 0.804384i | \(-0.702495\pi\) | ||||
−0.594109 | + | 0.804384i | \(0.702495\pi\) | |||||||
\(702\) | −734151. | −0.0562267 | ||||||||
\(703\) | 6.54433e6 | 0.499433 | ||||||||
\(704\) | 3.92862e6 | 0.298750 | ||||||||
\(705\) | 2.70747e6 | 0.205159 | ||||||||
\(706\) | 1.07090e7 | 0.808606 | ||||||||
\(707\) | 3.75494e6 | 0.282523 | ||||||||
\(708\) | −2.46167e6 | −0.184564 | ||||||||
\(709\) | −4.71237e6 | −0.352066 | −0.176033 | − | 0.984384i | \(-0.556327\pi\) | ||||
−0.176033 | + | 0.984384i | \(0.556327\pi\) | |||||||
\(710\) | −1.82487e6 | −0.135858 | ||||||||
\(711\) | 4.73914e6 | 0.351581 | ||||||||
\(712\) | −1.07861e7 | −0.797376 | ||||||||
\(713\) | −383646. | −0.0282623 | ||||||||
\(714\) | 5.91974e6 | 0.434567 | ||||||||
\(715\) | −708263. | −0.0518119 | ||||||||
\(716\) | −6.90602e6 | −0.503437 | ||||||||
\(717\) | −3.49327e6 | −0.253766 | ||||||||
\(718\) | −9.25391e6 | −0.669906 | ||||||||
\(719\) | 2.29858e6 | 0.165820 | 0.0829099 | − | 0.996557i | \(-0.473579\pi\) | ||||
0.0829099 | + | 0.996557i | \(0.473579\pi\) | |||||||
\(720\) | 829772. | 0.0596523 | ||||||||
\(721\) | 1.38162e7 | 0.989805 | ||||||||
\(722\) | −3.75324e6 | −0.267956 | ||||||||
\(723\) | 678035. | 0.0482399 | ||||||||
\(724\) | −760968. | −0.0539535 | ||||||||
\(725\) | −2.80303e6 | −0.198054 | ||||||||
\(726\) | −566763. | −0.0399080 | ||||||||
\(727\) | 2.81705e7 | 1.97678 | 0.988391 | − | 0.151933i | \(-0.0485496\pi\) | ||||
0.988391 | + | 0.151933i | \(0.0485496\pi\) | |||||||
\(728\) | 6.79143e6 | 0.474934 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 6.09054e6 | 0.423008 | ||||||||
\(731\) | 1.63213e7 | 1.12969 | ||||||||
\(732\) | 243832. | 0.0168195 | ||||||||
\(733\) | −1.32094e7 | −0.908078 | −0.454039 | − | 0.890982i | \(-0.650017\pi\) | ||||
−0.454039 | + | 0.890982i | \(0.650017\pi\) | |||||||
\(734\) | 6.34492e6 | 0.434696 | ||||||||
\(735\) | 1.16120e6 | 0.0792848 | ||||||||
\(736\) | 1.73121e6 | 0.117802 | ||||||||
\(737\) | 4.95441e6 | 0.335988 | ||||||||
\(738\) | 787087. | 0.0531963 | ||||||||
\(739\) | −6.63649e6 | −0.447021 | −0.223510 | − | 0.974702i | \(-0.571752\pi\) | ||||
−0.223510 | + | 0.974702i | \(0.571752\pi\) | |||||||
\(740\) | 1.74421e6 | 0.117090 | ||||||||
\(741\) | −2.66837e6 | −0.178525 | ||||||||
\(742\) | 2.45546e6 | 0.163728 | ||||||||
\(743\) | −7.93013e6 | −0.526997 | −0.263499 | − | 0.964660i | \(-0.584876\pi\) | ||||
−0.263499 | + | 0.964660i | \(0.584876\pi\) | |||||||
\(744\) | −1.75646e6 | −0.116334 | ||||||||
\(745\) | 935197. | 0.0617323 | ||||||||
\(746\) | −2.02711e7 | −1.33361 | ||||||||
\(747\) | −4.23175e6 | −0.277472 | ||||||||
\(748\) | −1.68535e6 | −0.110137 | ||||||||
\(749\) | −3.05072e7 | −1.98700 | ||||||||
\(750\) | 604855. | 0.0392643 | ||||||||
\(751\) | −1.43446e7 | −0.928086 | −0.464043 | − | 0.885813i | \(-0.653602\pi\) | ||||
−0.464043 | + | 0.885813i | \(0.653602\pi\) | |||||||
\(752\) | −4.93076e6 | −0.317958 | ||||||||
\(753\) | 3.12277e6 | 0.200703 | ||||||||
\(754\) | −4.51654e6 | −0.289319 | ||||||||
\(755\) | 5.64633e6 | 0.360495 | ||||||||
\(756\) | −1.45864e6 | −0.0928204 | ||||||||
\(757\) | 8.38496e6 | 0.531816 | 0.265908 | − | 0.963998i | \(-0.414328\pi\) | ||||
0.265908 | + | 0.963998i | \(0.414328\pi\) | |||||||
\(758\) | 1.92650e7 | 1.21786 | ||||||||
\(759\) | −418949. | −0.0263972 | ||||||||
\(760\) | 6.19543e6 | 0.389079 | ||||||||
\(761\) | 2.68159e7 | 1.67853 | 0.839267 | − | 0.543719i | \(-0.182984\pi\) | ||||
0.839267 | + | 0.543719i | \(0.182984\pi\) | |||||||
\(762\) | −4.67722e6 | −0.291810 | ||||||||
\(763\) | 2.31069e7 | 1.43691 | ||||||||
\(764\) | −620812. | −0.0384793 | ||||||||
\(765\) | −2.08931e6 | −0.129077 | ||||||||
\(766\) | −249334. | −0.0153536 | ||||||||
\(767\) | −4.74385e6 | −0.291167 | ||||||||
\(768\) | 9.51916e6 | 0.582365 | ||||||||
\(769\) | −2.82141e7 | −1.72049 | −0.860243 | − | 0.509884i | \(-0.829688\pi\) | ||||
−0.860243 | + | 0.509884i | \(0.829688\pi\) | |||||||
\(770\) | 1.92845e6 | 0.117215 | ||||||||
\(771\) | −1.77540e7 | −1.07562 | ||||||||
\(772\) | −4.87192e6 | −0.294210 | ||||||||
\(773\) | 2.41553e7 | 1.45400 | 0.727000 | − | 0.686637i | \(-0.240914\pi\) | ||||
0.727000 | + | 0.686637i | \(0.240914\pi\) | |||||||
\(774\) | 5.51125e6 | 0.330673 | ||||||||
\(775\) | −623272. | −0.0372755 | ||||||||
\(776\) | −1.94497e7 | −1.15947 | ||||||||
\(777\) | 6.89395e6 | 0.409653 | ||||||||
\(778\) | −1.94983e7 | −1.15491 | ||||||||
\(779\) | 2.86077e6 | 0.168904 | ||||||||
\(780\) | −711178. | −0.0418544 | ||||||||
\(781\) | 2.05347e6 | 0.120465 | ||||||||
\(782\) | 1.70726e6 | 0.0998350 | ||||||||
\(783\) | 3.26945e6 | 0.190577 | ||||||||
\(784\) | −2.11475e6 | −0.122877 | ||||||||
\(785\) | 5.13842e6 | 0.297616 | ||||||||
\(786\) | −1.03154e7 | −0.595565 | ||||||||
\(787\) | 1.96829e7 | 1.13280 | 0.566400 | − | 0.824131i | \(-0.308336\pi\) | ||||
0.566400 | + | 0.824131i | \(0.308336\pi\) | |||||||
\(788\) | −1.32152e7 | −0.758156 | ||||||||
\(789\) | 1.71888e6 | 0.0982997 | ||||||||
\(790\) | −6.29134e6 | −0.358654 | ||||||||
\(791\) | −5.97376e6 | −0.339474 | ||||||||
\(792\) | −1.91809e6 | −0.108656 | ||||||||
\(793\) | 469884. | 0.0265343 | ||||||||
\(794\) | 2.67351e6 | 0.150498 | ||||||||
\(795\) | −866627. | −0.0486311 | ||||||||
\(796\) | −1.21812e7 | −0.681409 | ||||||||
\(797\) | 2.41989e6 | 0.134943 | 0.0674714 | − | 0.997721i | \(-0.478507\pi\) | ||||
0.0674714 | + | 0.997721i | \(0.478507\pi\) | |||||||
\(798\) | 7.26539e6 | 0.403880 | ||||||||
\(799\) | 1.24153e7 | 0.688004 | ||||||||
\(800\) | 2.81252e6 | 0.155371 | ||||||||
\(801\) | 4.46427e6 | 0.245849 | ||||||||
\(802\) | 4.10474e6 | 0.225346 | ||||||||
\(803\) | −6.85350e6 | −0.375080 | ||||||||
\(804\) | 4.97480e6 | 0.271416 | ||||||||
\(805\) | 1.42550e6 | 0.0775315 | ||||||||
\(806\) | −1.00428e6 | −0.0544525 | ||||||||
\(807\) | −8.40521e6 | −0.454323 | ||||||||
\(808\) | 4.95800e6 | 0.267164 | ||||||||
\(809\) | 2.06594e7 | 1.10981 | 0.554903 | − | 0.831915i | \(-0.312755\pi\) | ||||
0.554903 | + | 0.831915i | \(0.312755\pi\) | |||||||
\(810\) | −705503. | −0.0377821 | ||||||||
\(811\) | 1.38880e7 | 0.741461 | 0.370730 | − | 0.928741i | \(-0.379107\pi\) | ||||
0.370730 | + | 0.928741i | \(0.379107\pi\) | |||||||
\(812\) | −8.97363e6 | −0.477615 | ||||||||
\(813\) | 1.05454e7 | 0.559547 | ||||||||
\(814\) | 2.68971e6 | 0.142280 | ||||||||
\(815\) | 1.59850e7 | 0.842980 | ||||||||
\(816\) | 3.80499e6 | 0.200045 | ||||||||
\(817\) | 2.00314e7 | 1.04992 | ||||||||
\(818\) | 1.37580e7 | 0.718904 | ||||||||
\(819\) | −2.81092e6 | −0.146433 | ||||||||
\(820\) | 762457. | 0.0395987 | ||||||||
\(821\) | 5.26859e6 | 0.272795 | 0.136398 | − | 0.990654i | \(-0.456448\pi\) | ||||
0.136398 | + | 0.990654i | \(0.456448\pi\) | |||||||
\(822\) | −664913. | −0.0343230 | ||||||||
\(823\) | 3.61766e7 | 1.86178 | 0.930890 | − | 0.365299i | \(-0.119033\pi\) | ||||
0.930890 | + | 0.365299i | \(0.119033\pi\) | |||||||
\(824\) | 1.82428e7 | 0.935994 | ||||||||
\(825\) | −680625. | −0.0348155 | ||||||||
\(826\) | 1.29165e7 | 0.658710 | ||||||||
\(827\) | 3.01917e7 | 1.53505 | 0.767527 | − | 0.641017i | \(-0.221487\pi\) | ||||
0.767527 | + | 0.641017i | \(0.221487\pi\) | |||||||
\(828\) | −420673. | −0.0213240 | ||||||||
\(829\) | 2.93884e7 | 1.48522 | 0.742608 | − | 0.669727i | \(-0.233589\pi\) | ||||
0.742608 | + | 0.669727i | \(0.233589\pi\) | |||||||
\(830\) | 5.61777e6 | 0.283053 | ||||||||
\(831\) | 4.25261e6 | 0.213625 | ||||||||
\(832\) | 7.60193e6 | 0.380728 | ||||||||
\(833\) | 5.32479e6 | 0.265883 | ||||||||
\(834\) | 194792. | 0.00969740 | ||||||||
\(835\) | −1.04248e7 | −0.517428 | ||||||||
\(836\) | −2.06845e6 | −0.102360 | ||||||||
\(837\) | 726984. | 0.0358683 | ||||||||
\(838\) | −2.83931e7 | −1.39670 | ||||||||
\(839\) | 1.57845e7 | 0.774150 | 0.387075 | − | 0.922048i | \(-0.373485\pi\) | ||||
0.387075 | + | 0.922048i | \(0.373485\pi\) | |||||||
\(840\) | 6.52641e6 | 0.319136 | ||||||||
\(841\) | −397286. | −0.0193692 | ||||||||
\(842\) | −1.81730e7 | −0.883376 | ||||||||
\(843\) | 1.84836e7 | 0.895814 | ||||||||
\(844\) | −4.29822e6 | −0.207698 | ||||||||
\(845\) | 7.91183e6 | 0.381184 | ||||||||
\(846\) | 4.19232e6 | 0.201386 | ||||||||
\(847\) | −2.17003e6 | −0.103934 | ||||||||
\(848\) | 1.57828e6 | 0.0753691 | ||||||||
\(849\) | −4.19020e6 | −0.199510 | ||||||||
\(850\) | 2.77361e6 | 0.131674 | ||||||||
\(851\) | 1.98822e6 | 0.0941112 | ||||||||
\(852\) | 2.06192e6 | 0.0973134 | ||||||||
\(853\) | 2.68137e7 | 1.26178 | 0.630891 | − | 0.775871i | \(-0.282689\pi\) | ||||
0.630891 | + | 0.775871i | \(0.282689\pi\) | |||||||
\(854\) | −1.27939e6 | −0.0600288 | ||||||||
\(855\) | −2.56424e6 | −0.119962 | ||||||||
\(856\) | −4.02815e7 | −1.87898 | ||||||||
\(857\) | −2.59115e7 | −1.20515 | −0.602574 | − | 0.798063i | \(-0.705858\pi\) | ||||
−0.602574 | + | 0.798063i | \(0.705858\pi\) | |||||||
\(858\) | −1.09669e6 | −0.0508590 | ||||||||
\(859\) | 1.20430e7 | 0.556870 | 0.278435 | − | 0.960455i | \(-0.410184\pi\) | ||||
0.278435 | + | 0.960455i | \(0.410184\pi\) | |||||||
\(860\) | 5.33879e6 | 0.246148 | ||||||||
\(861\) | 3.01360e6 | 0.138541 | ||||||||
\(862\) | 2.03145e7 | 0.931191 | ||||||||
\(863\) | 2.28033e7 | 1.04225 | 0.521125 | − | 0.853481i | \(-0.325513\pi\) | ||||
0.521125 | + | 0.853481i | \(0.325513\pi\) | |||||||
\(864\) | −3.28052e6 | −0.149506 | ||||||||
\(865\) | −1.52163e7 | −0.691461 | ||||||||
\(866\) | −3.79420e6 | −0.171920 | ||||||||
\(867\) | 3.19801e6 | 0.144488 | ||||||||
\(868\) | −1.99534e6 | −0.0898915 | ||||||||
\(869\) | 7.07945e6 | 0.318017 | ||||||||
\(870\) | −4.34029e6 | −0.194411 | ||||||||
\(871\) | 9.58685e6 | 0.428184 | ||||||||
\(872\) | 3.05102e7 | 1.35880 | ||||||||
\(873\) | 8.05009e6 | 0.357491 | ||||||||
\(874\) | 2.09535e6 | 0.0927849 | ||||||||
\(875\) | 2.31587e6 | 0.102257 | ||||||||
\(876\) | −6.88170e6 | −0.302995 | ||||||||
\(877\) | −3.10668e7 | −1.36395 | −0.681974 | − | 0.731376i | \(-0.738878\pi\) | ||||
−0.681974 | + | 0.731376i | \(0.738878\pi\) | |||||||
\(878\) | −1.32268e7 | −0.579052 | ||||||||
\(879\) | 1.07490e7 | 0.469242 | ||||||||
\(880\) | 1.23954e6 | 0.0539575 | ||||||||
\(881\) | −3.45208e7 | −1.49844 | −0.749222 | − | 0.662319i | \(-0.769573\pi\) | ||||
−0.749222 | + | 0.662319i | \(0.769573\pi\) | |||||||
\(882\) | 1.79804e6 | 0.0778265 | ||||||||
\(883\) | −3.29428e7 | −1.42186 | −0.710932 | − | 0.703260i | \(-0.751727\pi\) | ||||
−0.710932 | + | 0.703260i | \(0.751727\pi\) | |||||||
\(884\) | −3.26117e6 | −0.140360 | ||||||||
\(885\) | −4.55873e6 | −0.195653 | ||||||||
\(886\) | 1.46404e7 | 0.626571 | ||||||||
\(887\) | −2.11009e7 | −0.900519 | −0.450260 | − | 0.892898i | \(-0.648669\pi\) | ||||
−0.450260 | + | 0.892898i | \(0.648669\pi\) | |||||||
\(888\) | 9.10273e6 | 0.387382 | ||||||||
\(889\) | −1.79082e7 | −0.759970 | ||||||||
\(890\) | −5.92644e6 | −0.250795 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | −8.92810e6 | −0.375705 | ||||||||
\(893\) | 1.52375e7 | 0.639419 | ||||||||
\(894\) | 1.44809e6 | 0.0605969 | ||||||||
\(895\) | −1.27891e7 | −0.533684 | ||||||||
\(896\) | 644775. | 0.0268311 | ||||||||
\(897\) | −810673. | −0.0336406 | ||||||||
\(898\) | −2.60547e6 | −0.107819 | ||||||||
\(899\) | 4.47245e6 | 0.184564 | ||||||||
\(900\) | −683426. | −0.0281245 | ||||||||
\(901\) | −3.97399e6 | −0.163085 | ||||||||
\(902\) | 1.17577e6 | 0.0481179 | ||||||||
\(903\) | 2.11015e7 | 0.861181 | ||||||||
\(904\) | −7.88772e6 | −0.321019 | ||||||||
\(905\) | −1.40922e6 | −0.0571951 | ||||||||
\(906\) | 8.74294e6 | 0.353865 | ||||||||
\(907\) | 1.30426e7 | 0.526438 | 0.263219 | − | 0.964736i | \(-0.415216\pi\) | ||||
0.263219 | + | 0.964736i | \(0.415216\pi\) | |||||||
\(908\) | −8.19036e6 | −0.329677 | ||||||||
\(909\) | −2.05208e6 | −0.0823728 | ||||||||
\(910\) | 3.73157e6 | 0.149379 | ||||||||
\(911\) | −4.09652e7 | −1.63538 | −0.817690 | − | 0.575658i | \(-0.804746\pi\) | ||||
−0.817690 | + | 0.575658i | \(0.804746\pi\) | |||||||
\(912\) | 4.66992e6 | 0.185918 | ||||||||
\(913\) | −6.32150e6 | −0.250982 | ||||||||
\(914\) | −2.34987e7 | −0.930417 | ||||||||
\(915\) | 451548. | 0.0178300 | ||||||||
\(916\) | 4.75700e6 | 0.187325 | ||||||||
\(917\) | −3.94956e7 | −1.55105 | ||||||||
\(918\) | −3.23514e6 | −0.126703 | ||||||||
\(919\) | 5.59367e6 | 0.218478 | 0.109239 | − | 0.994016i | \(-0.465159\pi\) | ||||
0.109239 | + | 0.994016i | \(0.465159\pi\) | |||||||
\(920\) | 1.88222e6 | 0.0733165 | ||||||||
\(921\) | −1.55026e7 | −0.602220 | ||||||||
\(922\) | −1.22250e7 | −0.473609 | ||||||||
\(923\) | 3.97349e6 | 0.153521 | ||||||||
\(924\) | −2.17896e6 | −0.0839592 | ||||||||
\(925\) | 3.23007e6 | 0.124124 | ||||||||
\(926\) | −3.66312e7 | −1.40386 | ||||||||
\(927\) | −7.55055e6 | −0.288589 | ||||||||
\(928\) | −2.01819e7 | −0.769295 | ||||||||
\(929\) | −4.15645e7 | −1.58010 | −0.790048 | − | 0.613045i | \(-0.789944\pi\) | ||||
−0.790048 | + | 0.613045i | \(0.789944\pi\) | |||||||
\(930\) | −965091. | −0.0365899 | ||||||||
\(931\) | 6.53520e6 | 0.247107 | ||||||||
\(932\) | −2.01536e7 | −0.759999 | ||||||||
\(933\) | 2.34555e7 | 0.882145 | ||||||||
\(934\) | 3.01144e7 | 1.12955 | ||||||||
\(935\) | −3.12106e6 | −0.116755 | ||||||||
\(936\) | −3.71152e6 | −0.138472 | ||||||||
\(937\) | −1.62578e7 | −0.604941 | −0.302470 | − | 0.953159i | \(-0.597811\pi\) | ||||
−0.302470 | + | 0.953159i | \(0.597811\pi\) | |||||||
\(938\) | −2.61030e7 | −0.968685 | ||||||||
\(939\) | −1.10080e7 | −0.407423 | ||||||||
\(940\) | 4.06113e6 | 0.149909 | ||||||||
\(941\) | 1.33538e7 | 0.491622 | 0.245811 | − | 0.969318i | \(-0.420946\pi\) | ||||
0.245811 | + | 0.969318i | \(0.420946\pi\) | |||||||
\(942\) | 7.95648e6 | 0.292142 | ||||||||
\(943\) | 869126. | 0.0318276 | ||||||||
\(944\) | 8.30224e6 | 0.303225 | ||||||||
\(945\) | −2.70123e6 | −0.0983971 | ||||||||
\(946\) | 8.23286e6 | 0.299105 | ||||||||
\(947\) | 1.36642e7 | 0.495117 | 0.247559 | − | 0.968873i | \(-0.420372\pi\) | ||||
0.247559 | + | 0.968873i | \(0.420372\pi\) | |||||||
\(948\) | 7.10859e6 | 0.256899 | ||||||||
\(949\) | −1.32616e7 | −0.478003 | ||||||||
\(950\) | 3.40410e6 | 0.122375 | ||||||||
\(951\) | 6.30038e6 | 0.225900 | ||||||||
\(952\) | 2.99274e7 | 1.07023 | ||||||||
\(953\) | −2.92858e7 | −1.04454 | −0.522270 | − | 0.852780i | \(-0.674915\pi\) | ||||
−0.522270 | + | 0.852780i | \(0.674915\pi\) | |||||||
\(954\) | −1.34191e6 | −0.0477367 | ||||||||
\(955\) | −1.14967e6 | −0.0407911 | ||||||||
\(956\) | −5.23981e6 | −0.185426 | ||||||||
\(957\) | 4.88400e6 | 0.172384 | ||||||||
\(958\) | 4.59478e6 | 0.161752 | ||||||||
\(959\) | −2.54582e6 | −0.0893885 | ||||||||
\(960\) | 7.30528e6 | 0.255834 | ||||||||
\(961\) | −2.76347e7 | −0.965263 | ||||||||
\(962\) | 5.20462e6 | 0.181323 | ||||||||
\(963\) | 1.66722e7 | 0.579332 | ||||||||
\(964\) | 1.01704e6 | 0.0352487 | ||||||||
\(965\) | −9.02223e6 | −0.311886 | ||||||||
\(966\) | 2.20729e6 | 0.0761055 | ||||||||
\(967\) | −4.41255e7 | −1.51748 | −0.758741 | − | 0.651393i | \(-0.774185\pi\) | ||||
−0.758741 | + | 0.651393i | \(0.774185\pi\) | |||||||
\(968\) | −2.86529e6 | −0.0982834 | ||||||||
\(969\) | −1.17585e7 | −0.402294 | ||||||||
\(970\) | −1.06867e7 | −0.364683 | ||||||||
\(971\) | 2.28334e7 | 0.777183 | 0.388592 | − | 0.921410i | \(-0.372962\pi\) | ||||
0.388592 | + | 0.921410i | \(0.372962\pi\) | |||||||
\(972\) | 797148. | 0.0270628 | ||||||||
\(973\) | 745819. | 0.0252552 | ||||||||
\(974\) | 4.31444e6 | 0.145723 | ||||||||
\(975\) | −1.31702e6 | −0.0443691 | ||||||||
\(976\) | −822347. | −0.0276332 | ||||||||
\(977\) | −5.35594e7 | −1.79515 | −0.897573 | − | 0.440866i | \(-0.854671\pi\) | ||||
−0.897573 | + | 0.440866i | \(0.854671\pi\) | |||||||
\(978\) | 2.47516e7 | 0.827476 | ||||||||
\(979\) | 6.66884e6 | 0.222379 | ||||||||
\(980\) | 1.74177e6 | 0.0579331 | ||||||||
\(981\) | −1.26279e7 | −0.418948 | ||||||||
\(982\) | 3.97309e7 | 1.31477 | ||||||||
\(983\) | −2.25516e7 | −0.744378 | −0.372189 | − | 0.928157i | \(-0.621393\pi\) | ||||
−0.372189 | + | 0.928157i | \(0.621393\pi\) | |||||||
\(984\) | 3.97914e6 | 0.131009 | ||||||||
\(985\) | −2.44730e7 | −0.803706 | ||||||||
\(986\) | −1.99028e7 | −0.651961 | ||||||||
\(987\) | 1.60516e7 | 0.524475 | ||||||||
\(988\) | −4.00248e6 | −0.130448 | ||||||||
\(989\) | 6.08570e6 | 0.197843 | ||||||||
\(990\) | −1.05390e6 | −0.0341752 | ||||||||
\(991\) | 7.10889e6 | 0.229942 | 0.114971 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114971 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(992\) | −4.48758e6 | −0.144788 | ||||||||
\(993\) | −2.50865e7 | −0.807358 | ||||||||
\(994\) | −1.08190e7 | −0.347312 | ||||||||
\(995\) | −2.25582e7 | −0.722348 | ||||||||
\(996\) | −6.34752e6 | −0.202747 | ||||||||
\(997\) | 3.59868e7 | 1.14658 | 0.573291 | − | 0.819352i | \(-0.305666\pi\) | ||||
0.573291 | + | 0.819352i | \(0.305666\pi\) | |||||||
\(998\) | 1.85610e7 | 0.589896 | ||||||||
\(999\) | −3.76755e6 | −0.119439 |
(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 | 165.6.a.e.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 495.6.a.a.1.2 | 3 | |||
5.4 | even | 2 | 825.6.a.f.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
495.6.a.a.1.2 | 3 | 3.2 | odd | 2 | |||
825.6.a.f.1.2 | 3 | 5.4 | even | 2 |