Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,6,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(4.65113077458\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.3257317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 34x^{2} - 27x + 10 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-5.34807\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −9.21534 | −1.62906 | −0.814529 | − | 0.580123i | \(-0.803004\pi\) | ||||
−0.814529 | + | 0.580123i | \(0.803004\pi\) | |||||||
\(3\) | 0.734546 | 0.0471211 | 0.0235606 | − | 0.999722i | \(-0.492500\pi\) | ||||
0.0235606 | + | 0.999722i | \(0.492500\pi\) | |||||||
\(4\) | 52.9225 | 1.65383 | ||||||||
\(5\) | 41.6400 | 0.744879 | 0.372440 | − | 0.928056i | \(-0.378521\pi\) | ||||
0.372440 | + | 0.928056i | \(0.378521\pi\) | |||||||
\(6\) | −6.76909 | −0.0767630 | ||||||||
\(7\) | −90.0205 | −0.694379 | −0.347189 | − | 0.937795i | \(-0.612864\pi\) | ||||
−0.347189 | + | 0.937795i | \(0.612864\pi\) | |||||||
\(8\) | −192.808 | −1.06512 | ||||||||
\(9\) | −242.460 | −0.997780 | ||||||||
\(10\) | −383.727 | −1.21345 | ||||||||
\(11\) | −269.080 | −0.670502 | −0.335251 | − | 0.942129i | \(-0.608821\pi\) | ||||
−0.335251 | + | 0.942129i | \(0.608821\pi\) | |||||||
\(12\) | 38.8740 | 0.0779302 | ||||||||
\(13\) | −444.579 | −0.729610 | −0.364805 | − | 0.931084i | \(-0.618864\pi\) | ||||
−0.364805 | + | 0.931084i | \(0.618864\pi\) | |||||||
\(14\) | 829.569 | 1.13118 | ||||||||
\(15\) | 30.5865 | 0.0350995 | ||||||||
\(16\) | 83.2700 | 0.0813183 | ||||||||
\(17\) | 485.649 | 0.407569 | 0.203784 | − | 0.979016i | \(-0.434676\pi\) | ||||
0.203784 | + | 0.979016i | \(0.434676\pi\) | |||||||
\(18\) | 2234.36 | 1.62544 | ||||||||
\(19\) | −1572.80 | −0.999513 | −0.499756 | − | 0.866166i | \(-0.666577\pi\) | ||||
−0.499756 | + | 0.866166i | \(0.666577\pi\) | |||||||
\(20\) | 2203.69 | 1.23190 | ||||||||
\(21\) | −66.1242 | −0.0327199 | ||||||||
\(22\) | 2479.66 | 1.09229 | ||||||||
\(23\) | −398.704 | −0.157156 | −0.0785781 | − | 0.996908i | \(-0.525038\pi\) | ||||
−0.0785781 | + | 0.996908i | \(0.525038\pi\) | |||||||
\(24\) | −141.626 | −0.0501898 | ||||||||
\(25\) | −1391.11 | −0.445155 | ||||||||
\(26\) | 4096.95 | 1.18858 | ||||||||
\(27\) | −356.593 | −0.0941376 | ||||||||
\(28\) | −4764.11 | −1.14838 | ||||||||
\(29\) | −841.000 | −0.185695 | ||||||||
\(30\) | −281.865 | −0.0571792 | ||||||||
\(31\) | −8469.77 | −1.58295 | −0.791475 | − | 0.611202i | \(-0.790686\pi\) | ||||
−0.791475 | + | 0.611202i | \(0.790686\pi\) | |||||||
\(32\) | 5402.49 | 0.932651 | ||||||||
\(33\) | −197.652 | −0.0315948 | ||||||||
\(34\) | −4475.43 | −0.663952 | ||||||||
\(35\) | −3748.45 | −0.517228 | ||||||||
\(36\) | −12831.6 | −1.65016 | ||||||||
\(37\) | 3339.33 | 0.401010 | 0.200505 | − | 0.979693i | \(-0.435742\pi\) | ||||
0.200505 | + | 0.979693i | \(0.435742\pi\) | |||||||
\(38\) | 14493.8 | 1.62826 | ||||||||
\(39\) | −326.564 | −0.0343801 | ||||||||
\(40\) | −8028.52 | −0.793388 | ||||||||
\(41\) | 18154.2 | 1.68662 | 0.843311 | − | 0.537425i | \(-0.180603\pi\) | ||||
0.843311 | + | 0.537425i | \(0.180603\pi\) | |||||||
\(42\) | 609.357 | 0.0533026 | ||||||||
\(43\) | 9996.71 | 0.824491 | 0.412246 | − | 0.911073i | \(-0.364745\pi\) | ||||
0.412246 | + | 0.911073i | \(0.364745\pi\) | |||||||
\(44\) | −14240.4 | −1.10889 | ||||||||
\(45\) | −10096.1 | −0.743225 | ||||||||
\(46\) | 3674.20 | 0.256016 | ||||||||
\(47\) | 12568.0 | 0.829890 | 0.414945 | − | 0.909846i | \(-0.363801\pi\) | ||||
0.414945 | + | 0.909846i | \(0.363801\pi\) | |||||||
\(48\) | 61.1656 | 0.00383181 | ||||||||
\(49\) | −8703.31 | −0.517838 | ||||||||
\(50\) | 12819.6 | 0.725183 | ||||||||
\(51\) | 356.732 | 0.0192051 | ||||||||
\(52\) | −23528.2 | −1.20665 | ||||||||
\(53\) | −21343.1 | −1.04368 | −0.521841 | − | 0.853043i | \(-0.674755\pi\) | ||||
−0.521841 | + | 0.853043i | \(0.674755\pi\) | |||||||
\(54\) | 3286.12 | 0.153356 | ||||||||
\(55\) | −11204.5 | −0.499443 | ||||||||
\(56\) | 17356.7 | 0.739598 | ||||||||
\(57\) | −1155.29 | −0.0470982 | ||||||||
\(58\) | 7750.10 | 0.302508 | ||||||||
\(59\) | −30036.1 | −1.12334 | −0.561672 | − | 0.827360i | \(-0.689842\pi\) | ||||
−0.561672 | + | 0.827360i | \(0.689842\pi\) | |||||||
\(60\) | 1618.71 | 0.0580486 | ||||||||
\(61\) | 49792.6 | 1.71333 | 0.856663 | − | 0.515877i | \(-0.172534\pi\) | ||||
0.856663 | + | 0.515877i | \(0.172534\pi\) | |||||||
\(62\) | 78051.8 | 2.57872 | ||||||||
\(63\) | 21826.4 | 0.692837 | ||||||||
\(64\) | −52450.4 | −1.60066 | ||||||||
\(65\) | −18512.3 | −0.543471 | ||||||||
\(66\) | 1821.43 | 0.0514697 | ||||||||
\(67\) | 47588.2 | 1.29513 | 0.647563 | − | 0.762012i | \(-0.275788\pi\) | ||||
0.647563 | + | 0.762012i | \(0.275788\pi\) | |||||||
\(68\) | 25701.8 | 0.674048 | ||||||||
\(69\) | −292.867 | −0.00740538 | ||||||||
\(70\) | 34543.3 | 0.842594 | ||||||||
\(71\) | −50164.6 | −1.18101 | −0.590503 | − | 0.807036i | \(-0.701070\pi\) | ||||
−0.590503 | + | 0.807036i | \(0.701070\pi\) | |||||||
\(72\) | 46748.3 | 1.06276 | ||||||||
\(73\) | −44770.3 | −0.983294 | −0.491647 | − | 0.870795i | \(-0.663605\pi\) | ||||
−0.491647 | + | 0.870795i | \(0.663605\pi\) | |||||||
\(74\) | −30773.1 | −0.653269 | ||||||||
\(75\) | −1021.83 | −0.0209762 | ||||||||
\(76\) | −83236.3 | −1.65302 | ||||||||
\(77\) | 24222.7 | 0.465582 | ||||||||
\(78\) | 3009.40 | 0.0560071 | ||||||||
\(79\) | −78464.6 | −1.41451 | −0.707255 | − | 0.706959i | \(-0.750067\pi\) | ||||
−0.707255 | + | 0.706959i | \(0.750067\pi\) | |||||||
\(80\) | 3467.36 | 0.0605723 | ||||||||
\(81\) | 58656.0 | 0.993344 | ||||||||
\(82\) | −167297. | −2.74761 | ||||||||
\(83\) | 46721.8 | 0.744430 | 0.372215 | − | 0.928146i | \(-0.378598\pi\) | ||||
0.372215 | + | 0.928146i | \(0.378598\pi\) | |||||||
\(84\) | −3499.46 | −0.0541131 | ||||||||
\(85\) | 20222.4 | 0.303589 | ||||||||
\(86\) | −92123.1 | −1.34314 | ||||||||
\(87\) | −617.753 | −0.00875017 | ||||||||
\(88\) | 51880.7 | 0.714167 | ||||||||
\(89\) | −39465.7 | −0.528135 | −0.264068 | − | 0.964504i | \(-0.585064\pi\) | ||||
−0.264068 | + | 0.964504i | \(0.585064\pi\) | |||||||
\(90\) | 93038.6 | 1.21076 | ||||||||
\(91\) | 40021.2 | 0.506626 | ||||||||
\(92\) | −21100.4 | −0.259909 | ||||||||
\(93\) | −6221.43 | −0.0745904 | ||||||||
\(94\) | −115818. | −1.35194 | ||||||||
\(95\) | −65491.2 | −0.744516 | ||||||||
\(96\) | 3968.38 | 0.0439476 | ||||||||
\(97\) | 48336.3 | 0.521608 | 0.260804 | − | 0.965392i | \(-0.416012\pi\) | ||||
0.260804 | + | 0.965392i | \(0.416012\pi\) | |||||||
\(98\) | 80204.0 | 0.843589 | ||||||||
\(99\) | 65241.3 | 0.669013 | ||||||||
\(100\) | −73621.0 | −0.736210 | ||||||||
\(101\) | 111417. | 1.08680 | 0.543399 | − | 0.839475i | \(-0.317137\pi\) | ||||
0.543399 | + | 0.839475i | \(0.317137\pi\) | |||||||
\(102\) | −3287.40 | −0.0312862 | ||||||||
\(103\) | −1416.34 | −0.0131545 | −0.00657726 | − | 0.999978i | \(-0.502094\pi\) | ||||
−0.00657726 | + | 0.999978i | \(0.502094\pi\) | |||||||
\(104\) | 85718.4 | 0.777124 | ||||||||
\(105\) | −2753.41 | −0.0243724 | ||||||||
\(106\) | 196684. | 1.70022 | ||||||||
\(107\) | −162530. | −1.37238 | −0.686188 | − | 0.727424i | \(-0.740717\pi\) | ||||
−0.686188 | + | 0.727424i | \(0.740717\pi\) | |||||||
\(108\) | −18871.8 | −0.155687 | ||||||||
\(109\) | 152425. | 1.22882 | 0.614411 | − | 0.788986i | \(-0.289394\pi\) | ||||
0.614411 | + | 0.788986i | \(0.289394\pi\) | |||||||
\(110\) | 103253. | 0.813621 | ||||||||
\(111\) | 2452.89 | 0.0188961 | ||||||||
\(112\) | −7496.00 | −0.0564657 | ||||||||
\(113\) | 256365. | 1.88870 | 0.944350 | − | 0.328942i | \(-0.106692\pi\) | ||||
0.944350 | + | 0.328942i | \(0.106692\pi\) | |||||||
\(114\) | 10646.4 | 0.0767256 | ||||||||
\(115\) | −16602.1 | −0.117062 | ||||||||
\(116\) | −44507.8 | −0.307108 | ||||||||
\(117\) | 107793. | 0.727990 | ||||||||
\(118\) | 276792. | 1.82999 | ||||||||
\(119\) | −43718.4 | −0.283007 | ||||||||
\(120\) | −5897.31 | −0.0373853 | ||||||||
\(121\) | −88646.9 | −0.550428 | ||||||||
\(122\) | −458855. | −2.79111 | ||||||||
\(123\) | 13335.1 | 0.0794756 | ||||||||
\(124\) | −448241. | −2.61793 | ||||||||
\(125\) | −188051. | −1.07647 | ||||||||
\(126\) | −201138. | −1.12867 | ||||||||
\(127\) | −145336. | −0.799585 | −0.399792 | − | 0.916606i | \(-0.630918\pi\) | ||||
−0.399792 | + | 0.916606i | \(0.630918\pi\) | |||||||
\(128\) | 310469. | 1.67492 | ||||||||
\(129\) | 7343.04 | 0.0388510 | ||||||||
\(130\) | 170597. | 0.885346 | ||||||||
\(131\) | −259373. | −1.32052 | −0.660262 | − | 0.751035i | \(-0.729555\pi\) | ||||
−0.660262 | + | 0.751035i | \(0.729555\pi\) | |||||||
\(132\) | −10460.2 | −0.0522523 | ||||||||
\(133\) | 141584. | 0.694040 | ||||||||
\(134\) | −438541. | −2.10984 | ||||||||
\(135\) | −14848.5 | −0.0701212 | ||||||||
\(136\) | −93637.0 | −0.434111 | ||||||||
\(137\) | 94701.8 | 0.431079 | 0.215539 | − | 0.976495i | \(-0.430849\pi\) | ||||
0.215539 | + | 0.976495i | \(0.430849\pi\) | |||||||
\(138\) | 2698.87 | 0.0120638 | ||||||||
\(139\) | 237100. | 1.04086 | 0.520432 | − | 0.853903i | \(-0.325771\pi\) | ||||
0.520432 | + | 0.853903i | \(0.325771\pi\) | |||||||
\(140\) | −198377. | −0.855406 | ||||||||
\(141\) | 9231.75 | 0.0391054 | ||||||||
\(142\) | 462284. | 1.92393 | ||||||||
\(143\) | 119627. | 0.489205 | ||||||||
\(144\) | −20189.7 | −0.0811378 | ||||||||
\(145\) | −35019.2 | −0.138321 | ||||||||
\(146\) | 412574. | 1.60184 | ||||||||
\(147\) | −6392.98 | −0.0244011 | ||||||||
\(148\) | 176726. | 0.663202 | ||||||||
\(149\) | −81590.7 | −0.301075 | −0.150538 | − | 0.988604i | \(-0.548100\pi\) | ||||
−0.150538 | + | 0.988604i | \(0.548100\pi\) | |||||||
\(150\) | 9416.55 | 0.0341715 | ||||||||
\(151\) | −199008. | −0.710276 | −0.355138 | − | 0.934814i | \(-0.615566\pi\) | ||||
−0.355138 | + | 0.934814i | \(0.615566\pi\) | |||||||
\(152\) | 303247. | 1.06460 | ||||||||
\(153\) | −117751. | −0.406664 | ||||||||
\(154\) | −223221. | −0.758460 | ||||||||
\(155\) | −352681. | −1.17911 | ||||||||
\(156\) | −17282.6 | −0.0568587 | ||||||||
\(157\) | −321167. | −1.03988 | −0.519938 | − | 0.854204i | \(-0.674045\pi\) | ||||
−0.519938 | + | 0.854204i | \(0.674045\pi\) | |||||||
\(158\) | 723078. | 2.30432 | ||||||||
\(159\) | −15677.5 | −0.0491795 | ||||||||
\(160\) | 224960. | 0.694712 | ||||||||
\(161\) | 35891.6 | 0.109126 | ||||||||
\(162\) | −540535. | −1.61821 | ||||||||
\(163\) | −621023. | −1.83079 | −0.915395 | − | 0.402557i | \(-0.868121\pi\) | ||||
−0.915395 | + | 0.402557i | \(0.868121\pi\) | |||||||
\(164\) | 960767. | 2.78938 | ||||||||
\(165\) | −8230.21 | −0.0235343 | ||||||||
\(166\) | −430557. | −1.21272 | ||||||||
\(167\) | −59437.0 | −0.164917 | −0.0824585 | − | 0.996594i | \(-0.526277\pi\) | ||||
−0.0824585 | + | 0.996594i | \(0.526277\pi\) | |||||||
\(168\) | 12749.3 | 0.0348507 | ||||||||
\(169\) | −173642. | −0.467669 | ||||||||
\(170\) | −186357. | −0.494564 | ||||||||
\(171\) | 381341. | 0.997293 | ||||||||
\(172\) | 529051. | 1.36357 | ||||||||
\(173\) | 175144. | 0.444918 | 0.222459 | − | 0.974942i | \(-0.428592\pi\) | ||||
0.222459 | + | 0.974942i | \(0.428592\pi\) | |||||||
\(174\) | 5692.80 | 0.0142545 | ||||||||
\(175\) | 125228. | 0.309106 | ||||||||
\(176\) | −22406.3 | −0.0545241 | ||||||||
\(177\) | −22062.9 | −0.0529332 | ||||||||
\(178\) | 363690. | 0.860362 | ||||||||
\(179\) | −421857. | −0.984086 | −0.492043 | − | 0.870571i | \(-0.663750\pi\) | ||||
−0.492043 | + | 0.870571i | \(0.663750\pi\) | |||||||
\(180\) | −534308. | −1.22917 | ||||||||
\(181\) | 313961. | 0.712326 | 0.356163 | − | 0.934424i | \(-0.384085\pi\) | ||||
0.356163 | + | 0.934424i | \(0.384085\pi\) | |||||||
\(182\) | −368809. | −0.825322 | ||||||||
\(183\) | 36574.9 | 0.0807338 | ||||||||
\(184\) | 76873.3 | 0.167391 | ||||||||
\(185\) | 139050. | 0.298704 | ||||||||
\(186\) | 57332.6 | 0.121512 | ||||||||
\(187\) | −130679. | −0.273275 | ||||||||
\(188\) | 665128. | 1.37250 | ||||||||
\(189\) | 32100.7 | 0.0653672 | ||||||||
\(190\) | 603524. | 1.21286 | ||||||||
\(191\) | 85652.5 | 0.169886 | 0.0849428 | − | 0.996386i | \(-0.472929\pi\) | ||||
0.0849428 | + | 0.996386i | \(0.472929\pi\) | |||||||
\(192\) | −38527.2 | −0.0754249 | ||||||||
\(193\) | 356203. | 0.688343 | 0.344171 | − | 0.938907i | \(-0.388160\pi\) | ||||
0.344171 | + | 0.938907i | \(0.388160\pi\) | |||||||
\(194\) | −445436. | −0.849729 | ||||||||
\(195\) | −13598.1 | −0.0256090 | ||||||||
\(196\) | −460601. | −0.856416 | ||||||||
\(197\) | 2000.17 | 0.00367199 | 0.00183599 | − | 0.999998i | \(-0.499416\pi\) | ||||
0.00183599 | + | 0.999998i | \(0.499416\pi\) | |||||||
\(198\) | −601220. | −1.08986 | ||||||||
\(199\) | −241348. | −0.432027 | −0.216014 | − | 0.976390i | \(-0.569306\pi\) | ||||
−0.216014 | + | 0.976390i | \(0.569306\pi\) | |||||||
\(200\) | 268217. | 0.474145 | ||||||||
\(201\) | 34955.7 | 0.0610278 | ||||||||
\(202\) | −1.02675e6 | −1.77045 | ||||||||
\(203\) | 75707.2 | 0.128943 | ||||||||
\(204\) | 18879.1 | 0.0317619 | ||||||||
\(205\) | 755942. | 1.25633 | ||||||||
\(206\) | 13052.1 | 0.0214295 | ||||||||
\(207\) | 96670.0 | 0.156807 | ||||||||
\(208\) | −37020.1 | −0.0593307 | ||||||||
\(209\) | 423208. | 0.670175 | ||||||||
\(210\) | 25373.6 | 0.0397040 | ||||||||
\(211\) | −611130. | −0.944991 | −0.472495 | − | 0.881333i | \(-0.656647\pi\) | ||||
−0.472495 | + | 0.881333i | \(0.656647\pi\) | |||||||
\(212\) | −1.12953e6 | −1.72607 | ||||||||
\(213\) | −36848.2 | −0.0556503 | ||||||||
\(214\) | 1.49777e6 | 2.23568 | ||||||||
\(215\) | 416263. | 0.614146 | ||||||||
\(216\) | 68753.9 | 0.100268 | ||||||||
\(217\) | 762452. | 1.09917 | ||||||||
\(218\) | −1.40465e6 | −2.00182 | ||||||||
\(219\) | −32885.9 | −0.0463339 | ||||||||
\(220\) | −592970. | −0.825992 | ||||||||
\(221\) | −215910. | −0.297366 | ||||||||
\(222\) | −22604.2 | −0.0307828 | ||||||||
\(223\) | 702678. | 0.946225 | 0.473112 | − | 0.881002i | \(-0.343130\pi\) | ||||
0.473112 | + | 0.881002i | \(0.343130\pi\) | |||||||
\(224\) | −486335. | −0.647613 | ||||||||
\(225\) | 337289. | 0.444167 | ||||||||
\(226\) | −2.36249e6 | −3.07680 | ||||||||
\(227\) | 933943. | 1.20297 | 0.601487 | − | 0.798883i | \(-0.294575\pi\) | ||||
0.601487 | + | 0.798883i | \(0.294575\pi\) | |||||||
\(228\) | −61140.8 | −0.0778923 | ||||||||
\(229\) | −1.02337e6 | −1.28956 | −0.644782 | − | 0.764367i | \(-0.723052\pi\) | ||||
−0.644782 | + | 0.764367i | \(0.723052\pi\) | |||||||
\(230\) | 152994. | 0.190701 | ||||||||
\(231\) | 17792.7 | 0.0219387 | ||||||||
\(232\) | 162151. | 0.197788 | ||||||||
\(233\) | −994807. | −1.20046 | −0.600232 | − | 0.799826i | \(-0.704925\pi\) | ||||
−0.600232 | + | 0.799826i | \(0.704925\pi\) | |||||||
\(234\) | −993348. | −1.18594 | ||||||||
\(235\) | 523330. | 0.618168 | ||||||||
\(236\) | −1.58958e6 | −1.85782 | ||||||||
\(237\) | −57635.8 | −0.0666533 | ||||||||
\(238\) | 402880. | 0.461034 | ||||||||
\(239\) | −111950. | −0.126773 | −0.0633867 | − | 0.997989i | \(-0.520190\pi\) | ||||
−0.0633867 | + | 0.997989i | \(0.520190\pi\) | |||||||
\(240\) | 2546.94 | 0.00285424 | ||||||||
\(241\) | 1.31520e6 | 1.45865 | 0.729323 | − | 0.684169i | \(-0.239835\pi\) | ||||
0.729323 | + | 0.684169i | \(0.239835\pi\) | |||||||
\(242\) | 816911. | 0.896678 | ||||||||
\(243\) | 129738. | 0.140945 | ||||||||
\(244\) | 2.63515e6 | 2.83355 | ||||||||
\(245\) | −362406. | −0.385727 | ||||||||
\(246\) | −122888. | −0.129470 | ||||||||
\(247\) | 699232. | 0.729255 | ||||||||
\(248\) | 1.63304e6 | 1.68604 | ||||||||
\(249\) | 34319.3 | 0.0350784 | ||||||||
\(250\) | 1.73295e6 | 1.75362 | ||||||||
\(251\) | −440669. | −0.441498 | −0.220749 | − | 0.975331i | \(-0.570850\pi\) | ||||
−0.220749 | + | 0.975331i | \(0.570850\pi\) | |||||||
\(252\) | 1.15511e6 | 1.14583 | ||||||||
\(253\) | 107283. | 0.105373 | ||||||||
\(254\) | 1.33932e6 | 1.30257 | ||||||||
\(255\) | 14854.3 | 0.0143055 | ||||||||
\(256\) | −1.18266e6 | −1.12787 | ||||||||
\(257\) | −554939. | −0.524098 | −0.262049 | − | 0.965055i | \(-0.584398\pi\) | ||||
−0.262049 | + | 0.965055i | \(0.584398\pi\) | |||||||
\(258\) | −67668.6 | −0.0632904 | ||||||||
\(259\) | −300608. | −0.278453 | ||||||||
\(260\) | −979716. | −0.898808 | ||||||||
\(261\) | 203909. | 0.185283 | ||||||||
\(262\) | 2.39021e6 | 2.15121 | ||||||||
\(263\) | −1.24351e6 | −1.10856 | −0.554279 | − | 0.832331i | \(-0.687006\pi\) | ||||
−0.554279 | + | 0.832331i | \(0.687006\pi\) | |||||||
\(264\) | 38108.8 | 0.0336523 | ||||||||
\(265\) | −888728. | −0.777417 | ||||||||
\(266\) | −1.30474e6 | −1.13063 | ||||||||
\(267\) | −28989.4 | −0.0248863 | ||||||||
\(268\) | 2.51849e6 | 2.14192 | ||||||||
\(269\) | 598804. | 0.504549 | 0.252275 | − | 0.967656i | \(-0.418821\pi\) | ||||
0.252275 | + | 0.967656i | \(0.418821\pi\) | |||||||
\(270\) | 136834. | 0.114231 | ||||||||
\(271\) | 654368. | 0.541251 | 0.270626 | − | 0.962685i | \(-0.412769\pi\) | ||||
0.270626 | + | 0.962685i | \(0.412769\pi\) | |||||||
\(272\) | 40440.0 | 0.0331428 | ||||||||
\(273\) | 29397.4 | 0.0238728 | ||||||||
\(274\) | −872709. | −0.702252 | ||||||||
\(275\) | 374320. | 0.298477 | ||||||||
\(276\) | −15499.2 | −0.0122472 | ||||||||
\(277\) | −1.76929e6 | −1.38548 | −0.692739 | − | 0.721188i | \(-0.743596\pi\) | ||||
−0.692739 | + | 0.721188i | \(0.743596\pi\) | |||||||
\(278\) | −2.18495e6 | −1.69563 | ||||||||
\(279\) | 2.05358e6 | 1.57943 | ||||||||
\(280\) | 722731. | 0.550911 | ||||||||
\(281\) | −495309. | −0.374206 | −0.187103 | − | 0.982340i | \(-0.559910\pi\) | ||||
−0.187103 | + | 0.982340i | \(0.559910\pi\) | |||||||
\(282\) | −85073.7 | −0.0637049 | ||||||||
\(283\) | −785235. | −0.582819 | −0.291409 | − | 0.956598i | \(-0.594124\pi\) | ||||
−0.291409 | + | 0.956598i | \(0.594124\pi\) | |||||||
\(284\) | −2.65484e6 | −1.95318 | ||||||||
\(285\) | −48106.3 | −0.0350824 | ||||||||
\(286\) | −1.10241e6 | −0.796943 | ||||||||
\(287\) | −1.63425e6 | −1.17115 | ||||||||
\(288\) | −1.30989e6 | −0.930580 | ||||||||
\(289\) | −1.18400e6 | −0.833888 | ||||||||
\(290\) | 322714. | 0.225332 | ||||||||
\(291\) | 35505.2 | 0.0245788 | ||||||||
\(292\) | −2.36936e6 | −1.62620 | ||||||||
\(293\) | 1.72437e6 | 1.17344 | 0.586719 | − | 0.809790i | \(-0.300419\pi\) | ||||
0.586719 | + | 0.809790i | \(0.300419\pi\) | |||||||
\(294\) | 58913.5 | 0.0397508 | ||||||||
\(295\) | −1.25070e6 | −0.836755 | ||||||||
\(296\) | −643850. | −0.427125 | ||||||||
\(297\) | 95952.0 | 0.0631194 | ||||||||
\(298\) | 751886. | 0.490469 | ||||||||
\(299\) | 177256. | 0.114663 | ||||||||
\(300\) | −54078.0 | −0.0346911 | ||||||||
\(301\) | −899909. | −0.572509 | ||||||||
\(302\) | 1.83392e6 | 1.15708 | ||||||||
\(303\) | 81841.0 | 0.0512111 | ||||||||
\(304\) | −130967. | −0.0812787 | ||||||||
\(305\) | 2.07336e6 | 1.27622 | ||||||||
\(306\) | 1.08511e6 | 0.662478 | ||||||||
\(307\) | −3.12637e6 | −1.89319 | −0.946597 | − | 0.322419i | \(-0.895504\pi\) | ||||
−0.946597 | + | 0.322419i | \(0.895504\pi\) | |||||||
\(308\) | 1.28193e6 | 0.769992 | ||||||||
\(309\) | −1040.37 | −0.000619856 0 | ||||||||
\(310\) | 3.25008e6 | 1.92083 | ||||||||
\(311\) | 2.08430e6 | 1.22196 | 0.610982 | − | 0.791644i | \(-0.290775\pi\) | ||||
0.610982 | + | 0.791644i | \(0.290775\pi\) | |||||||
\(312\) | 62964.1 | 0.0366190 | ||||||||
\(313\) | −2.27357e6 | −1.31174 | −0.655871 | − | 0.754873i | \(-0.727698\pi\) | ||||
−0.655871 | + | 0.754873i | \(0.727698\pi\) | |||||||
\(314\) | 2.95966e6 | 1.69402 | ||||||||
\(315\) | 908852. | 0.516080 | ||||||||
\(316\) | −4.15254e6 | −2.33935 | ||||||||
\(317\) | −891538. | −0.498301 | −0.249151 | − | 0.968465i | \(-0.580151\pi\) | ||||
−0.249151 | + | 0.968465i | \(0.580151\pi\) | |||||||
\(318\) | 144473. | 0.0801162 | ||||||||
\(319\) | 226296. | 0.124509 | ||||||||
\(320\) | −2.18404e6 | −1.19230 | ||||||||
\(321\) | −119385. | −0.0646679 | ||||||||
\(322\) | −330753. | −0.177772 | ||||||||
\(323\) | −763827. | −0.407370 | ||||||||
\(324\) | 3.10422e6 | 1.64282 | ||||||||
\(325\) | 618459. | 0.324790 | ||||||||
\(326\) | 5.72293e6 | 2.98246 | ||||||||
\(327\) | 111963. | 0.0579035 | ||||||||
\(328\) | −3.50028e6 | −1.79646 | ||||||||
\(329\) | −1.13138e6 | −0.576258 | ||||||||
\(330\) | 75844.2 | 0.0383387 | ||||||||
\(331\) | −768207. | −0.385397 | −0.192698 | − | 0.981258i | \(-0.561724\pi\) | ||||
−0.192698 | + | 0.981258i | \(0.561724\pi\) | |||||||
\(332\) | 2.47263e6 | 1.23116 | ||||||||
\(333\) | −809656. | −0.400120 | ||||||||
\(334\) | 547732. | 0.268659 | ||||||||
\(335\) | 1.98157e6 | 0.964713 | ||||||||
\(336\) | −5506.16 | −0.00266073 | ||||||||
\(337\) | −740054. | −0.354968 | −0.177484 | − | 0.984124i | \(-0.556796\pi\) | ||||
−0.177484 | + | 0.984124i | \(0.556796\pi\) | |||||||
\(338\) | 1.60017e6 | 0.761860 | ||||||||
\(339\) | 188312. | 0.0889977 | ||||||||
\(340\) | 1.07022e6 | 0.502084 | ||||||||
\(341\) | 2.27904e6 | 1.06137 | ||||||||
\(342\) | −3.51418e6 | −1.62465 | ||||||||
\(343\) | 2.29645e6 | 1.05395 | ||||||||
\(344\) | −1.92744e6 | −0.878184 | ||||||||
\(345\) | −12195.0 | −0.00551611 | ||||||||
\(346\) | −1.61401e6 | −0.724796 | ||||||||
\(347\) | 2.65308e6 | 1.18284 | 0.591420 | − | 0.806363i | \(-0.298567\pi\) | ||||
0.591420 | + | 0.806363i | \(0.298567\pi\) | |||||||
\(348\) | −32693.0 | −0.0144713 | ||||||||
\(349\) | 1.02314e6 | 0.449646 | 0.224823 | − | 0.974400i | \(-0.427820\pi\) | ||||
0.224823 | + | 0.974400i | \(0.427820\pi\) | |||||||
\(350\) | −1.15402e6 | −0.503552 | ||||||||
\(351\) | 158534. | 0.0686838 | ||||||||
\(352\) | −1.45370e6 | −0.625344 | ||||||||
\(353\) | −2.17906e6 | −0.930747 | −0.465374 | − | 0.885114i | \(-0.654080\pi\) | ||||
−0.465374 | + | 0.885114i | \(0.654080\pi\) | |||||||
\(354\) | 203317. | 0.0862313 | ||||||||
\(355\) | −2.08886e6 | −0.879706 | ||||||||
\(356\) | −2.08862e6 | −0.873445 | ||||||||
\(357\) | −32113.2 | −0.0133356 | ||||||||
\(358\) | 3.88756e6 | 1.60313 | ||||||||
\(359\) | 4.09152e6 | 1.67552 | 0.837759 | − | 0.546041i | \(-0.183866\pi\) | ||||
0.837759 | + | 0.546041i | \(0.183866\pi\) | |||||||
\(360\) | 1.94660e6 | 0.791626 | ||||||||
\(361\) | −2413.03 | −0.000974529 0 | ||||||||
\(362\) | −2.89325e6 | −1.16042 | ||||||||
\(363\) | −65115.2 | −0.0259368 | ||||||||
\(364\) | 2.11802e6 | 0.837871 | ||||||||
\(365\) | −1.86424e6 | −0.732435 | ||||||||
\(366\) | −337050. | −0.131520 | ||||||||
\(367\) | −113276. | −0.0439009 | −0.0219504 | − | 0.999759i | \(-0.506988\pi\) | ||||
−0.0219504 | + | 0.999759i | \(0.506988\pi\) | |||||||
\(368\) | −33200.1 | −0.0127797 | ||||||||
\(369\) | −4.40168e6 | −1.68288 | ||||||||
\(370\) | −1.28139e6 | −0.486606 | ||||||||
\(371\) | 1.92132e6 | 0.724711 | ||||||||
\(372\) | −329254. | −0.123360 | ||||||||
\(373\) | −1.74960e6 | −0.651130 | −0.325565 | − | 0.945520i | \(-0.605554\pi\) | ||||
−0.325565 | + | 0.945520i | \(0.605554\pi\) | |||||||
\(374\) | 1.20425e6 | 0.445181 | ||||||||
\(375\) | −138132. | −0.0507243 | ||||||||
\(376\) | −2.42320e6 | −0.883935 | ||||||||
\(377\) | 373891. | 0.135485 | ||||||||
\(378\) | −295819. | −0.106487 | ||||||||
\(379\) | 2.62142e6 | 0.937429 | 0.468714 | − | 0.883350i | \(-0.344717\pi\) | ||||
0.468714 | + | 0.883350i | \(0.344717\pi\) | |||||||
\(380\) | −3.46596e6 | −1.23130 | ||||||||
\(381\) | −106756. | −0.0376773 | ||||||||
\(382\) | −789317. | −0.276753 | ||||||||
\(383\) | 4.63046e6 | 1.61297 | 0.806486 | − | 0.591253i | \(-0.201367\pi\) | ||||
0.806486 | + | 0.591253i | \(0.201367\pi\) | |||||||
\(384\) | 228053. | 0.0789239 | ||||||||
\(385\) | 1.00863e6 | 0.346802 | ||||||||
\(386\) | −3.28254e6 | −1.12135 | ||||||||
\(387\) | −2.42381e6 | −0.822660 | ||||||||
\(388\) | 2.55808e6 | 0.862650 | ||||||||
\(389\) | −3.41385e6 | −1.14385 | −0.571927 | − | 0.820305i | \(-0.693804\pi\) | ||||
−0.571927 | + | 0.820305i | \(0.693804\pi\) | |||||||
\(390\) | 125311. | 0.0417185 | ||||||||
\(391\) | −193631. | −0.0640519 | ||||||||
\(392\) | 1.67807e6 | 0.551562 | ||||||||
\(393\) | −190521. | −0.0622246 | ||||||||
\(394\) | −18432.2 | −0.00598188 | ||||||||
\(395\) | −3.26726e6 | −1.05364 | ||||||||
\(396\) | 3.45273e6 | 1.10643 | ||||||||
\(397\) | −2.05992e6 | −0.655954 | −0.327977 | − | 0.944686i | \(-0.606367\pi\) | ||||
−0.327977 | + | 0.944686i | \(0.606367\pi\) | |||||||
\(398\) | 2.22410e6 | 0.703797 | ||||||||
\(399\) | 104000. | 0.0327040 | ||||||||
\(400\) | −115838. | −0.0361993 | ||||||||
\(401\) | 4.48615e6 | 1.39320 | 0.696599 | − | 0.717461i | \(-0.254696\pi\) | ||||
0.696599 | + | 0.717461i | \(0.254696\pi\) | |||||||
\(402\) | −322129. | −0.0994178 | ||||||||
\(403\) | 3.76548e6 | 1.15494 | ||||||||
\(404\) | 5.89647e6 | 1.79738 | ||||||||
\(405\) | 2.44243e6 | 0.739921 | ||||||||
\(406\) | −697668. | −0.210055 | ||||||||
\(407\) | −898548. | −0.268878 | ||||||||
\(408\) | −68780.7 | −0.0204558 | ||||||||
\(409\) | −5.12907e6 | −1.51611 | −0.758055 | − | 0.652191i | \(-0.773850\pi\) | ||||
−0.758055 | + | 0.652191i | \(0.773850\pi\) | |||||||
\(410\) | −6.96626e6 | −2.04663 | ||||||||
\(411\) | 69562.8 | 0.0203129 | ||||||||
\(412\) | −74956.3 | −0.0217553 | ||||||||
\(413\) | 2.70386e6 | 0.780026 | ||||||||
\(414\) | −890847. | −0.255448 | ||||||||
\(415\) | 1.94549e6 | 0.554511 | ||||||||
\(416\) | −2.40183e6 | −0.680471 | ||||||||
\(417\) | 174161. | 0.0490467 | ||||||||
\(418\) | −3.90000e6 | −1.09175 | ||||||||
\(419\) | −2.21170e6 | −0.615446 | −0.307723 | − | 0.951476i | \(-0.599567\pi\) | ||||
−0.307723 | + | 0.951476i | \(0.599567\pi\) | |||||||
\(420\) | −145717. | −0.0403077 | ||||||||
\(421\) | 751122. | 0.206540 | 0.103270 | − | 0.994653i | \(-0.467069\pi\) | ||||
0.103270 | + | 0.994653i | \(0.467069\pi\) | |||||||
\(422\) | 5.63177e6 | 1.53944 | ||||||||
\(423\) | −3.04724e6 | −0.828047 | ||||||||
\(424\) | 4.11512e6 | 1.11165 | ||||||||
\(425\) | −675592. | −0.181431 | ||||||||
\(426\) | 339569. | 0.0906575 | ||||||||
\(427\) | −4.48235e6 | −1.18970 | ||||||||
\(428\) | −8.60147e6 | −2.26967 | ||||||||
\(429\) | 87871.8 | 0.0230519 | ||||||||
\(430\) | −3.83601e6 | −1.00048 | ||||||||
\(431\) | 2.98345e6 | 0.773615 | 0.386808 | − | 0.922160i | \(-0.373578\pi\) | ||||
0.386808 | + | 0.922160i | \(0.373578\pi\) | |||||||
\(432\) | −29693.5 | −0.00765511 | ||||||||
\(433\) | −2.17337e6 | −0.557075 | −0.278537 | − | 0.960425i | \(-0.589850\pi\) | ||||
−0.278537 | + | 0.960425i | \(0.589850\pi\) | |||||||
\(434\) | −7.02626e6 | −1.79060 | ||||||||
\(435\) | −25723.2 | −0.00651782 | ||||||||
\(436\) | 8.06670e6 | 2.03226 | ||||||||
\(437\) | 627081. | 0.157080 | ||||||||
\(438\) | 303054. | 0.0754806 | ||||||||
\(439\) | 24436.8 | 0.00605178 | 0.00302589 | − | 0.999995i | \(-0.499037\pi\) | ||||
0.00302589 | + | 0.999995i | \(0.499037\pi\) | |||||||
\(440\) | 2.16031e6 | 0.531968 | ||||||||
\(441\) | 2.11021e6 | 0.516689 | ||||||||
\(442\) | 1.98968e6 | 0.484426 | ||||||||
\(443\) | −6.19315e6 | −1.49935 | −0.749674 | − | 0.661808i | \(-0.769789\pi\) | ||||
−0.749674 | + | 0.661808i | \(0.769789\pi\) | |||||||
\(444\) | 129813. | 0.0312508 | ||||||||
\(445\) | −1.64335e6 | −0.393397 | ||||||||
\(446\) | −6.47542e6 | −1.54145 | ||||||||
\(447\) | −59932.1 | −0.0141870 | ||||||||
\(448\) | 4.72161e6 | 1.11146 | ||||||||
\(449\) | 7.56136e6 | 1.77004 | 0.885022 | − | 0.465548i | \(-0.154143\pi\) | ||||
0.885022 | + | 0.465548i | \(0.154143\pi\) | |||||||
\(450\) | −3.10823e6 | −0.723573 | ||||||||
\(451\) | −4.88494e6 | −1.13088 | ||||||||
\(452\) | 1.35675e7 | 3.12359 | ||||||||
\(453\) | −146180. | −0.0334690 | ||||||||
\(454\) | −8.60661e6 | −1.95971 | ||||||||
\(455\) | 1.66648e6 | 0.377375 | ||||||||
\(456\) | 222749. | 0.0501653 | ||||||||
\(457\) | 5.02930e6 | 1.12646 | 0.563232 | − | 0.826299i | \(-0.309558\pi\) | ||||
0.563232 | + | 0.826299i | \(0.309558\pi\) | |||||||
\(458\) | 9.43067e6 | 2.10077 | ||||||||
\(459\) | −173179. | −0.0383675 | ||||||||
\(460\) | −878622. | −0.193601 | ||||||||
\(461\) | 3.58934e6 | 0.786615 | 0.393308 | − | 0.919407i | \(-0.371331\pi\) | ||||
0.393308 | + | 0.919407i | \(0.371331\pi\) | |||||||
\(462\) | −163966. | −0.0357395 | ||||||||
\(463\) | 8.86551e6 | 1.92199 | 0.960996 | − | 0.276563i | \(-0.0891955\pi\) | ||||
0.960996 | + | 0.276563i | \(0.0891955\pi\) | |||||||
\(464\) | −70030.0 | −0.0151004 | ||||||||
\(465\) | −259060. | −0.0555608 | ||||||||
\(466\) | 9.16748e6 | 1.95562 | ||||||||
\(467\) | 3.24975e6 | 0.689537 | 0.344769 | − | 0.938688i | \(-0.387957\pi\) | ||||
0.344769 | + | 0.938688i | \(0.387957\pi\) | |||||||
\(468\) | 5.70467e6 | 1.20397 | ||||||||
\(469\) | −4.28391e6 | −0.899308 | ||||||||
\(470\) | −4.82267e6 | −1.00703 | ||||||||
\(471\) | −235912. | −0.0490001 | ||||||||
\(472\) | 5.79119e6 | 1.19650 | ||||||||
\(473\) | −2.68992e6 | −0.552823 | ||||||||
\(474\) | 531134. | 0.108582 | ||||||||
\(475\) | 2.18793e6 | 0.444938 | ||||||||
\(476\) | −2.31369e6 | −0.468045 | ||||||||
\(477\) | 5.17486e6 | 1.04136 | ||||||||
\(478\) | 1.03166e6 | 0.206521 | ||||||||
\(479\) | −2.33334e6 | −0.464664 | −0.232332 | − | 0.972637i | \(-0.574636\pi\) | ||||
−0.232332 | + | 0.972637i | \(0.574636\pi\) | |||||||
\(480\) | 165243. | 0.0327356 | ||||||||
\(481\) | −1.48460e6 | −0.292581 | ||||||||
\(482\) | −1.21200e7 | −2.37622 | ||||||||
\(483\) | 26364.0 | 0.00514213 | ||||||||
\(484\) | −4.69142e6 | −0.910312 | ||||||||
\(485\) | 2.01272e6 | 0.388535 | ||||||||
\(486\) | −1.19558e6 | −0.229608 | ||||||||
\(487\) | 1.35787e6 | 0.259440 | 0.129720 | − | 0.991551i | \(-0.458592\pi\) | ||||
0.129720 | + | 0.991551i | \(0.458592\pi\) | |||||||
\(488\) | −9.60039e6 | −1.82490 | ||||||||
\(489\) | −456170. | −0.0862689 | ||||||||
\(490\) | 3.33969e6 | 0.628371 | ||||||||
\(491\) | 4.42097e6 | 0.827587 | 0.413794 | − | 0.910371i | \(-0.364203\pi\) | ||||
0.413794 | + | 0.910371i | \(0.364203\pi\) | |||||||
\(492\) | 705727. | 0.131439 | ||||||||
\(493\) | −408431. | −0.0756836 | ||||||||
\(494\) | −6.44366e6 | −1.18800 | ||||||||
\(495\) | 2.71665e6 | 0.498334 | ||||||||
\(496\) | −705277. | −0.128723 | ||||||||
\(497\) | 4.51585e6 | 0.820065 | ||||||||
\(498\) | −316264. | −0.0571447 | ||||||||
\(499\) | −9.61078e6 | −1.72785 | −0.863927 | − | 0.503617i | \(-0.832002\pi\) | ||||
−0.863927 | + | 0.503617i | \(0.832002\pi\) | |||||||
\(500\) | −9.95212e6 | −1.78029 | ||||||||
\(501\) | −43659.2 | −0.00777108 | ||||||||
\(502\) | 4.06092e6 | 0.719225 | ||||||||
\(503\) | −6.10366e6 | −1.07565 | −0.537824 | − | 0.843057i | \(-0.680754\pi\) | ||||
−0.537824 | + | 0.843057i | \(0.680754\pi\) | |||||||
\(504\) | −4.20830e6 | −0.737956 | ||||||||
\(505\) | 4.63941e6 | 0.809532 | ||||||||
\(506\) | −988653. | −0.171659 | ||||||||
\(507\) | −127548. | −0.0220371 | ||||||||
\(508\) | −7.69155e6 | −1.32238 | ||||||||
\(509\) | −1.01562e7 | −1.73755 | −0.868775 | − | 0.495208i | \(-0.835092\pi\) | ||||
−0.868775 | + | 0.495208i | \(0.835092\pi\) | |||||||
\(510\) | −136888. | −0.0233044 | ||||||||
\(511\) | 4.03025e6 | 0.682778 | ||||||||
\(512\) | 963628. | 0.162456 | ||||||||
\(513\) | 560848. | 0.0940918 | ||||||||
\(514\) | 5.11395e6 | 0.853785 | ||||||||
\(515\) | −58976.4 | −0.00979852 | ||||||||
\(516\) | 388612. | 0.0642528 | ||||||||
\(517\) | −3.38179e6 | −0.556443 | ||||||||
\(518\) | 2.77021e6 | 0.453616 | ||||||||
\(519\) | 128651. | 0.0209650 | ||||||||
\(520\) | 3.56931e6 | 0.578864 | ||||||||
\(521\) | 2.42580e6 | 0.391526 | 0.195763 | − | 0.980651i | \(-0.437282\pi\) | ||||
0.195763 | + | 0.980651i | \(0.437282\pi\) | |||||||
\(522\) | −1.87909e6 | −0.301837 | ||||||||
\(523\) | −328610. | −0.0525322 | −0.0262661 | − | 0.999655i | \(-0.508362\pi\) | ||||
−0.0262661 | + | 0.999655i | \(0.508362\pi\) | |||||||
\(524\) | −1.37267e7 | −2.18392 | ||||||||
\(525\) | 91986.0 | 0.0145654 | ||||||||
\(526\) | 1.14593e7 | 1.80591 | ||||||||
\(527\) | −4.11334e6 | −0.645160 | ||||||||
\(528\) | −16458.4 | −0.00256924 | ||||||||
\(529\) | −6.27738e6 | −0.975302 | ||||||||
\(530\) | 8.18993e6 | 1.26646 | ||||||||
\(531\) | 7.28255e6 | 1.12085 | ||||||||
\(532\) | 7.49297e6 | 1.14782 | ||||||||
\(533\) | −8.07099e6 | −1.23058 | ||||||||
\(534\) | 267147. | 0.0405413 | ||||||||
\(535\) | −6.76773e6 | −1.02225 | ||||||||
\(536\) | −9.17538e6 | −1.37947 | ||||||||
\(537\) | −309874. | −0.0463713 | ||||||||
\(538\) | −5.51818e6 | −0.821940 | ||||||||
\(539\) | 2.34189e6 | 0.347212 | ||||||||
\(540\) | −785821. | −0.115968 | ||||||||
\(541\) | 5.52172e6 | 0.811113 | 0.405557 | − | 0.914070i | \(-0.367078\pi\) | ||||
0.405557 | + | 0.914070i | \(0.367078\pi\) | |||||||
\(542\) | −6.03022e6 | −0.881729 | ||||||||
\(543\) | 230618. | 0.0335656 | ||||||||
\(544\) | 2.62372e6 | 0.380119 | ||||||||
\(545\) | 6.34697e6 | 0.915324 | ||||||||
\(546\) | −270907. | −0.0388901 | ||||||||
\(547\) | 2.61929e6 | 0.374296 | 0.187148 | − | 0.982332i | \(-0.440076\pi\) | ||||
0.187148 | + | 0.982332i | \(0.440076\pi\) | |||||||
\(548\) | 5.01185e6 | 0.712930 | ||||||||
\(549\) | −1.20727e7 | −1.70952 | ||||||||
\(550\) | −3.44949e6 | −0.486237 | ||||||||
\(551\) | 1.32272e6 | 0.185605 | ||||||||
\(552\) | 56467.0 | 0.00788764 | ||||||||
\(553\) | 7.06342e6 | 0.982205 | ||||||||
\(554\) | 1.63046e7 | 2.25702 | ||||||||
\(555\) | 102138. | 0.0140753 | ||||||||
\(556\) | 1.25479e7 | 1.72141 | ||||||||
\(557\) | 4.95349e6 | 0.676509 | 0.338254 | − | 0.941055i | \(-0.390164\pi\) | ||||
0.338254 | + | 0.941055i | \(0.390164\pi\) | |||||||
\(558\) | −1.89245e7 | −2.57299 | ||||||||
\(559\) | −4.44433e6 | −0.601557 | ||||||||
\(560\) | −312134. | −0.0420601 | ||||||||
\(561\) | −95989.4 | −0.0128770 | ||||||||
\(562\) | 4.56444e6 | 0.609602 | ||||||||
\(563\) | −2.28738e6 | −0.304135 | −0.152068 | − | 0.988370i | \(-0.548593\pi\) | ||||
−0.152068 | + | 0.988370i | \(0.548593\pi\) | |||||||
\(564\) | 488567. | 0.0646735 | ||||||||
\(565\) | 1.06751e7 | 1.40685 | ||||||||
\(566\) | 7.23620e6 | 0.949445 | ||||||||
\(567\) | −5.28024e6 | −0.689757 | ||||||||
\(568\) | 9.67214e6 | 1.25792 | ||||||||
\(569\) | −3.25672e6 | −0.421696 | −0.210848 | − | 0.977519i | \(-0.567622\pi\) | ||||
−0.210848 | + | 0.977519i | \(0.567622\pi\) | |||||||
\(570\) | 443316. | 0.0571513 | ||||||||
\(571\) | −9.92284e6 | −1.27364 | −0.636819 | − | 0.771013i | \(-0.719750\pi\) | ||||
−0.636819 | + | 0.771013i | \(0.719750\pi\) | |||||||
\(572\) | 6.33098e6 | 0.809060 | ||||||||
\(573\) | 62915.7 | 0.00800520 | ||||||||
\(574\) | 1.50602e7 | 1.90788 | ||||||||
\(575\) | 554642. | 0.0699589 | ||||||||
\(576\) | 1.27171e7 | 1.59711 | ||||||||
\(577\) | 1.23237e6 | 0.154100 | 0.0770498 | − | 0.997027i | \(-0.475450\pi\) | ||||
0.0770498 | + | 0.997027i | \(0.475450\pi\) | |||||||
\(578\) | 1.09110e7 | 1.35845 | ||||||||
\(579\) | 261648. | 0.0324355 | ||||||||
\(580\) | −1.85331e6 | −0.228758 | ||||||||
\(581\) | −4.20592e6 | −0.516916 | ||||||||
\(582\) | −327193. | −0.0400402 | ||||||||
\(583\) | 5.74301e6 | 0.699791 | ||||||||
\(584\) | 8.63207e6 | 1.04733 | ||||||||
\(585\) | 4.48850e6 | 0.542265 | ||||||||
\(586\) | −1.58906e7 | −1.91160 | ||||||||
\(587\) | −1.02407e7 | −1.22669 | −0.613345 | − | 0.789815i | \(-0.710177\pi\) | ||||
−0.613345 | + | 0.789815i | \(0.710177\pi\) | |||||||
\(588\) | −338332. | −0.0403553 | ||||||||
\(589\) | 1.33212e7 | 1.58218 | ||||||||
\(590\) | 1.15256e7 | 1.36312 | ||||||||
\(591\) | 1469.22 | 0.000173028 0 | ||||||||
\(592\) | 278066. | 0.0326095 | ||||||||
\(593\) | −1.53106e7 | −1.78795 | −0.893977 | − | 0.448114i | \(-0.852096\pi\) | ||||
−0.893977 | + | 0.448114i | \(0.852096\pi\) | |||||||
\(594\) | −884231. | −0.102825 | ||||||||
\(595\) | −1.82043e6 | −0.210806 | ||||||||
\(596\) | −4.31798e6 | −0.497926 | ||||||||
\(597\) | −177281. | −0.0203576 | ||||||||
\(598\) | −1.63347e6 | −0.186792 | ||||||||
\(599\) | −1.37662e6 | −0.156764 | −0.0783819 | − | 0.996923i | \(-0.524975\pi\) | ||||
−0.0783819 | + | 0.996923i | \(0.524975\pi\) | |||||||
\(600\) | 197018. | 0.0223422 | ||||||||
\(601\) | −1.39459e7 | −1.57492 | −0.787462 | − | 0.616363i | \(-0.788606\pi\) | ||||
−0.787462 | + | 0.616363i | \(0.788606\pi\) | |||||||
\(602\) | 8.29297e6 | 0.932650 | ||||||||
\(603\) | −1.15383e7 | −1.29225 | ||||||||
\(604\) | −1.05320e7 | −1.17467 | ||||||||
\(605\) | −3.69126e6 | −0.410002 | ||||||||
\(606\) | −754192. | −0.0834258 | ||||||||
\(607\) | −2.10503e6 | −0.231892 | −0.115946 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115946 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(608\) | −8.49701e6 | −0.932196 | ||||||||
\(609\) | 55610.4 | 0.00607593 | ||||||||
\(610\) | −1.91067e7 | −2.07904 | ||||||||
\(611\) | −5.58746e6 | −0.605496 | ||||||||
\(612\) | −6.23166e6 | −0.672551 | ||||||||
\(613\) | 1.75643e7 | 1.88790 | 0.943950 | − | 0.330088i | \(-0.107078\pi\) | ||||
0.943950 | + | 0.330088i | \(0.107078\pi\) | |||||||
\(614\) | 2.88106e7 | 3.08412 | ||||||||
\(615\) | 555274. | 0.0591997 | ||||||||
\(616\) | −4.67033e6 | −0.495902 | ||||||||
\(617\) | −6.68190e6 | −0.706622 | −0.353311 | − | 0.935506i | \(-0.614944\pi\) | ||||
−0.353311 | + | 0.935506i | \(0.614944\pi\) | |||||||
\(618\) | 9587.34 | 0.00100978 | ||||||||
\(619\) | −6.69302e6 | −0.702095 | −0.351047 | − | 0.936358i | \(-0.614174\pi\) | ||||
−0.351047 | + | 0.936358i | \(0.614174\pi\) | |||||||
\(620\) | −1.86648e7 | −1.95004 | ||||||||
\(621\) | 142175. | 0.0147943 | ||||||||
\(622\) | −1.92075e7 | −1.99065 | ||||||||
\(623\) | 3.55272e6 | 0.366726 | ||||||||
\(624\) | −27193.0 | −0.00279573 | ||||||||
\(625\) | −3.48322e6 | −0.356682 | ||||||||
\(626\) | 2.09518e7 | 2.13690 | ||||||||
\(627\) | 310866. | 0.0315794 | ||||||||
\(628\) | −1.69969e7 | −1.71977 | ||||||||
\(629\) | 1.62175e6 | 0.163439 | ||||||||
\(630\) | −8.37538e6 | −0.840723 | ||||||||
\(631\) | 7.79549e6 | 0.779417 | 0.389709 | − | 0.920938i | \(-0.372576\pi\) | ||||
0.389709 | + | 0.920938i | \(0.372576\pi\) | |||||||
\(632\) | 1.51286e7 | 1.50663 | ||||||||
\(633\) | −448903. | −0.0445290 | ||||||||
\(634\) | 8.21583e6 | 0.811761 | ||||||||
\(635\) | −6.05180e6 | −0.595594 | ||||||||
\(636\) | −829692. | −0.0813344 | ||||||||
\(637\) | 3.86931e6 | 0.377820 | ||||||||
\(638\) | −2.08540e6 | −0.202832 | ||||||||
\(639\) | 1.21629e7 | 1.17838 | ||||||||
\(640\) | 1.29279e7 | 1.24761 | ||||||||
\(641\) | 6.27067e6 | 0.602794 | 0.301397 | − | 0.953499i | \(-0.402547\pi\) | ||||
0.301397 | + | 0.953499i | \(0.402547\pi\) | |||||||
\(642\) | 1.10018e6 | 0.105348 | ||||||||
\(643\) | −1.59445e7 | −1.52084 | −0.760420 | − | 0.649432i | \(-0.775007\pi\) | ||||
−0.760420 | + | 0.649432i | \(0.775007\pi\) | |||||||
\(644\) | 1.89947e6 | 0.180475 | ||||||||
\(645\) | 305764. | 0.0289393 | ||||||||
\(646\) | 7.03893e6 | 0.663629 | ||||||||
\(647\) | 1.59290e7 | 1.49598 | 0.747992 | − | 0.663707i | \(-0.231018\pi\) | ||||
0.747992 | + | 0.663707i | \(0.231018\pi\) | |||||||
\(648\) | −1.13093e7 | −1.05803 | ||||||||
\(649\) | 8.08210e6 | 0.753204 | ||||||||
\(650\) | −5.69931e6 | −0.529101 | ||||||||
\(651\) | 560056. | 0.0517940 | ||||||||
\(652\) | −3.28661e7 | −3.02781 | ||||||||
\(653\) | 2.65262e6 | 0.243440 | 0.121720 | − | 0.992564i | \(-0.461159\pi\) | ||||
0.121720 | + | 0.992564i | \(0.461159\pi\) | |||||||
\(654\) | −1.03178e6 | −0.0943282 | ||||||||
\(655\) | −1.08003e7 | −0.983631 | ||||||||
\(656\) | 1.51170e6 | 0.137153 | ||||||||
\(657\) | 1.08550e7 | 0.981111 | ||||||||
\(658\) | 1.04260e7 | 0.938757 | ||||||||
\(659\) | 1.35066e7 | 1.21152 | 0.605761 | − | 0.795647i | \(-0.292869\pi\) | ||||
0.605761 | + | 0.795647i | \(0.292869\pi\) | |||||||
\(660\) | −435563. | −0.0389217 | ||||||||
\(661\) | 1.17111e7 | 1.04254 | 0.521272 | − | 0.853391i | \(-0.325458\pi\) | ||||
0.521272 | + | 0.853391i | \(0.325458\pi\) | |||||||
\(662\) | 7.07928e6 | 0.627833 | ||||||||
\(663\) | −158596. | −0.0140122 | ||||||||
\(664\) | −9.00832e6 | −0.792910 | ||||||||
\(665\) | 5.89555e6 | 0.516976 | ||||||||
\(666\) | 7.46126e6 | 0.651818 | ||||||||
\(667\) | 335310. | 0.0291832 | ||||||||
\(668\) | −3.14555e6 | −0.272744 | ||||||||
\(669\) | 516149. | 0.0445872 | ||||||||
\(670\) | −1.82609e7 | −1.57157 | ||||||||
\(671\) | −1.33982e7 | −1.14879 | ||||||||
\(672\) | −357235. | −0.0305162 | ||||||||
\(673\) | 1.81529e7 | 1.54492 | 0.772462 | − | 0.635061i | \(-0.219025\pi\) | ||||
0.772462 | + | 0.635061i | \(0.219025\pi\) | |||||||
\(674\) | 6.81985e6 | 0.578263 | ||||||||
\(675\) | 496060. | 0.0419059 | ||||||||
\(676\) | −9.18958e6 | −0.773444 | ||||||||
\(677\) | −3.81675e6 | −0.320053 | −0.160027 | − | 0.987113i | \(-0.551158\pi\) | ||||
−0.160027 | + | 0.987113i | \(0.551158\pi\) | |||||||
\(678\) | −1.73536e6 | −0.144982 | ||||||||
\(679\) | −4.35126e6 | −0.362193 | ||||||||
\(680\) | −3.89905e6 | −0.323360 | ||||||||
\(681\) | 686024. | 0.0566855 | ||||||||
\(682\) | −2.10022e7 | −1.72903 | ||||||||
\(683\) | −2.60743e6 | −0.213876 | −0.106938 | − | 0.994266i | \(-0.534105\pi\) | ||||
−0.106938 | + | 0.994266i | \(0.534105\pi\) | |||||||
\(684\) | 2.01815e7 | 1.64935 | ||||||||
\(685\) | 3.94338e6 | 0.321102 | ||||||||
\(686\) | −2.11626e7 | −1.71695 | ||||||||
\(687\) | −751710. | −0.0607657 | ||||||||
\(688\) | 832426. | 0.0670462 | ||||||||
\(689\) | 9.48871e6 | 0.761481 | ||||||||
\(690\) | 112381. | 0.00898606 | ||||||||
\(691\) | 81457.6 | 0.00648988 | 0.00324494 | − | 0.999995i | \(-0.498967\pi\) | ||||
0.00324494 | + | 0.999995i | \(0.498967\pi\) | |||||||
\(692\) | 9.26905e6 | 0.735817 | ||||||||
\(693\) | −5.87305e6 | −0.464548 | ||||||||
\(694\) | −2.44490e7 | −1.92692 | ||||||||
\(695\) | 9.87283e6 | 0.775318 | ||||||||
\(696\) | 119108. | 0.00932001 | ||||||||
\(697\) | 8.81659e6 | 0.687414 | ||||||||
\(698\) | −9.42856e6 | −0.732499 | ||||||||
\(699\) | −730731. | −0.0565672 | ||||||||
\(700\) | 6.62740e6 | 0.511208 | ||||||||
\(701\) | −2.32967e7 | −1.79060 | −0.895300 | − | 0.445464i | \(-0.853039\pi\) | ||||
−0.895300 | + | 0.445464i | \(0.853039\pi\) | |||||||
\(702\) | −1.46094e6 | −0.111890 | ||||||||
\(703\) | −5.25209e6 | −0.400815 | ||||||||
\(704\) | 1.41134e7 | 1.07324 | ||||||||
\(705\) | 384410. | 0.0291288 | ||||||||
\(706\) | 2.00807e7 | 1.51624 | ||||||||
\(707\) | −1.00298e7 | −0.754649 | ||||||||
\(708\) | −1.16762e6 | −0.0875425 | ||||||||
\(709\) | 7.52252e6 | 0.562015 | 0.281008 | − | 0.959706i | \(-0.409331\pi\) | ||||
0.281008 | + | 0.959706i | \(0.409331\pi\) | |||||||
\(710\) | 1.92495e7 | 1.43309 | ||||||||
\(711\) | 1.90246e7 | 1.41137 | ||||||||
\(712\) | 7.60930e6 | 0.562529 | ||||||||
\(713\) | 3.37693e6 | 0.248770 | ||||||||
\(714\) | 295934. | 0.0217245 | ||||||||
\(715\) | 4.98129e6 | 0.364398 | ||||||||
\(716\) | −2.23257e7 | −1.62751 | ||||||||
\(717\) | −82232.2 | −0.00597371 | ||||||||
\(718\) | −3.77048e7 | −2.72951 | ||||||||
\(719\) | 1.30064e7 | 0.938289 | 0.469144 | − | 0.883121i | \(-0.344562\pi\) | ||||
0.469144 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(720\) | −840698. | −0.0604378 | ||||||||
\(721\) | 127500. | 0.00913421 | ||||||||
\(722\) | 22236.9 | 0.00158756 | ||||||||
\(723\) | 966076. | 0.0687331 | ||||||||
\(724\) | 1.66156e7 | 1.17806 | ||||||||
\(725\) | 1.16992e6 | 0.0826632 | ||||||||
\(726\) | 600059. | 0.0422525 | ||||||||
\(727\) | 1.98038e7 | 1.38967 | 0.694835 | − | 0.719169i | \(-0.255477\pi\) | ||||
0.694835 | + | 0.719169i | \(0.255477\pi\) | |||||||
\(728\) | −7.71641e6 | −0.539618 | ||||||||
\(729\) | −1.41581e7 | −0.986702 | ||||||||
\(730\) | 1.71796e7 | 1.19318 | ||||||||
\(731\) | 4.85490e6 | 0.336037 | ||||||||
\(732\) | 1.93564e6 | 0.133520 | ||||||||
\(733\) | 1.81414e7 | 1.24713 | 0.623565 | − | 0.781772i | \(-0.285684\pi\) | ||||
0.623565 | + | 0.781772i | \(0.285684\pi\) | |||||||
\(734\) | 1.04388e6 | 0.0715170 | ||||||||
\(735\) | −266204. | −0.0181759 | ||||||||
\(736\) | −2.15400e6 | −0.146572 | ||||||||
\(737\) | −1.28050e7 | −0.868385 | ||||||||
\(738\) | 4.05630e7 | 2.74150 | ||||||||
\(739\) | −2.22326e7 | −1.49754 | −0.748771 | − | 0.662829i | \(-0.769355\pi\) | ||||
−0.748771 | + | 0.662829i | \(0.769355\pi\) | |||||||
\(740\) | 7.35887e6 | 0.494005 | ||||||||
\(741\) | 513618. | 0.0343633 | ||||||||
\(742\) | −1.77056e7 | −1.18059 | ||||||||
\(743\) | −1.40248e6 | −0.0932021 | −0.0466011 | − | 0.998914i | \(-0.514839\pi\) | ||||
−0.0466011 | + | 0.998914i | \(0.514839\pi\) | |||||||
\(744\) | 1.19954e6 | 0.0794479 | ||||||||
\(745\) | −3.39744e6 | −0.224264 | ||||||||
\(746\) | 1.61232e7 | 1.06073 | ||||||||
\(747\) | −1.13282e7 | −0.742777 | ||||||||
\(748\) | −6.91584e6 | −0.451950 | ||||||||
\(749\) | 1.46310e7 | 0.952948 | ||||||||
\(750\) | 1.27293e6 | 0.0826328 | ||||||||
\(751\) | 1.92135e7 | 1.24310 | 0.621552 | − | 0.783373i | \(-0.286503\pi\) | ||||
0.621552 | + | 0.783373i | \(0.286503\pi\) | |||||||
\(752\) | 1.04653e6 | 0.0674853 | ||||||||
\(753\) | −323692. | −0.0208039 | ||||||||
\(754\) | −3.44553e6 | −0.220713 | ||||||||
\(755\) | −8.28668e6 | −0.529070 | ||||||||
\(756\) | 1.69885e6 | 0.108106 | ||||||||
\(757\) | −1.23078e7 | −0.780621 | −0.390310 | − | 0.920683i | \(-0.627632\pi\) | ||||
−0.390310 | + | 0.920683i | \(0.627632\pi\) | |||||||
\(758\) | −2.41573e7 | −1.52713 | ||||||||
\(759\) | 78804.6 | 0.00496532 | ||||||||
\(760\) | 1.26272e7 | 0.793001 | ||||||||
\(761\) | 4.65071e6 | 0.291110 | 0.145555 | − | 0.989350i | \(-0.453503\pi\) | ||||
0.145555 | + | 0.989350i | \(0.453503\pi\) | |||||||
\(762\) | 983794. | 0.0613786 | ||||||||
\(763\) | −1.37214e7 | −0.853268 | ||||||||
\(764\) | 4.53294e6 | 0.280961 | ||||||||
\(765\) | −4.90314e6 | −0.302915 | ||||||||
\(766\) | −4.26712e7 | −2.62762 | ||||||||
\(767\) | 1.33534e7 | 0.819603 | ||||||||
\(768\) | −868719. | −0.0531467 | ||||||||
\(769\) | 1.54937e6 | 0.0944800 | 0.0472400 | − | 0.998884i | \(-0.484957\pi\) | ||||
0.0472400 | + | 0.998884i | \(0.484957\pi\) | |||||||
\(770\) | −9.29491e6 | −0.564961 | ||||||||
\(771\) | −407628. | −0.0246961 | ||||||||
\(772\) | 1.88512e7 | 1.13840 | ||||||||
\(773\) | −1.71208e7 | −1.03056 | −0.515282 | − | 0.857021i | \(-0.672313\pi\) | ||||
−0.515282 | + | 0.857021i | \(0.672313\pi\) | |||||||
\(774\) | 2.23362e7 | 1.34016 | ||||||||
\(775\) | 1.17824e7 | 0.704658 | ||||||||
\(776\) | −9.31962e6 | −0.555577 | ||||||||
\(777\) | −220811. | −0.0131210 | ||||||||
\(778\) | 3.14598e7 | 1.86340 | ||||||||
\(779\) | −2.85529e7 | −1.68580 | ||||||||
\(780\) | −719646. | −0.0423528 | ||||||||
\(781\) | 1.34983e7 | 0.791866 | ||||||||
\(782\) | 1.78437e6 | 0.104344 | ||||||||
\(783\) | 299895. | 0.0174809 | ||||||||
\(784\) | −724724. | −0.0421097 | ||||||||
\(785\) | −1.33734e7 | −0.774581 | ||||||||
\(786\) | 1.75572e6 | 0.101367 | ||||||||
\(787\) | −681275. | −0.0392090 | −0.0196045 | − | 0.999808i | \(-0.506241\pi\) | ||||
−0.0196045 | + | 0.999808i | \(0.506241\pi\) | |||||||
\(788\) | 105854. | 0.00607284 | ||||||||
\(789\) | −913412. | −0.0522365 | ||||||||
\(790\) | 3.01090e7 | 1.71644 | ||||||||
\(791\) | −2.30781e7 | −1.31147 | ||||||||
\(792\) | −1.25790e7 | −0.712581 | ||||||||
\(793\) | −2.21367e7 | −1.25006 | ||||||||
\(794\) | 1.89828e7 | 1.06859 | ||||||||
\(795\) | −652811. | −0.0366328 | ||||||||
\(796\) | −1.27727e7 | −0.714498 | ||||||||
\(797\) | 530445. | 0.0295798 | 0.0147899 | − | 0.999891i | \(-0.495292\pi\) | ||||
0.0147899 | + | 0.999891i | \(0.495292\pi\) | |||||||
\(798\) | −958394. | −0.0532766 | ||||||||
\(799\) | 6.10363e6 | 0.338237 | ||||||||
\(800\) | −7.51546e6 | −0.415174 | ||||||||
\(801\) | 9.56888e6 | 0.526962 | ||||||||
\(802\) | −4.13414e7 | −2.26960 | ||||||||
\(803\) | 1.20468e7 | 0.659300 | ||||||||
\(804\) | 1.84994e6 | 0.100930 | ||||||||
\(805\) | 1.49452e6 | 0.0812856 | ||||||||
\(806\) | −3.47002e7 | −1.88146 | ||||||||
\(807\) | 439849. | 0.0237749 | ||||||||
\(808\) | −2.14821e7 | −1.15757 | ||||||||
\(809\) | −2.65631e7 | −1.42694 | −0.713472 | − | 0.700684i | \(-0.752878\pi\) | ||||
−0.713472 | + | 0.700684i | \(0.752878\pi\) | |||||||
\(810\) | −2.25079e7 | −1.20537 | ||||||||
\(811\) | 1.11660e7 | 0.596137 | 0.298069 | − | 0.954544i | \(-0.403658\pi\) | ||||
0.298069 | + | 0.954544i | \(0.403658\pi\) | |||||||
\(812\) | 4.00662e6 | 0.213249 | ||||||||
\(813\) | 480663. | 0.0255044 | ||||||||
\(814\) | 8.28043e6 | 0.438018 | ||||||||
\(815\) | −2.58594e7 | −1.36372 | ||||||||
\(816\) | 29705.0 | 0.00156173 | ||||||||
\(817\) | −1.57228e7 | −0.824089 | ||||||||
\(818\) | 4.72661e7 | 2.46983 | ||||||||
\(819\) | −9.70357e6 | −0.505501 | ||||||||
\(820\) | 4.00063e7 | 2.07775 | ||||||||
\(821\) | −3.42932e7 | −1.77562 | −0.887811 | − | 0.460209i | \(-0.847774\pi\) | ||||
−0.887811 | + | 0.460209i | \(0.847774\pi\) | |||||||
\(822\) | −641045. | −0.0330909 | ||||||||
\(823\) | 1.93467e7 | 0.995651 | 0.497825 | − | 0.867277i | \(-0.334132\pi\) | ||||
0.497825 | + | 0.867277i | \(0.334132\pi\) | |||||||
\(824\) | 273082. | 0.0140112 | ||||||||
\(825\) | 274955. | 0.0140646 | ||||||||
\(826\) | −2.49170e7 | −1.27071 | ||||||||
\(827\) | 2.67747e7 | 1.36132 | 0.680662 | − | 0.732598i | \(-0.261692\pi\) | ||||
0.680662 | + | 0.732598i | \(0.261692\pi\) | |||||||
\(828\) | 5.11602e6 | 0.259332 | ||||||||
\(829\) | −2.44308e7 | −1.23467 | −0.617335 | − | 0.786700i | \(-0.711788\pi\) | ||||
−0.617335 | + | 0.786700i | \(0.711788\pi\) | |||||||
\(830\) | −1.79284e7 | −0.903330 | ||||||||
\(831\) | −1.29962e6 | −0.0652853 | ||||||||
\(832\) | 2.33184e7 | 1.16786 | ||||||||
\(833\) | −4.22676e6 | −0.211055 | ||||||||
\(834\) | −1.60495e6 | −0.0798999 | ||||||||
\(835\) | −2.47496e6 | −0.122843 | ||||||||
\(836\) | 2.23972e7 | 1.10835 | ||||||||
\(837\) | 3.02026e6 | 0.149015 | ||||||||
\(838\) | 2.03815e7 | 1.00260 | ||||||||
\(839\) | 9.17559e6 | 0.450017 | 0.225009 | − | 0.974357i | \(-0.427759\pi\) | ||||
0.225009 | + | 0.974357i | \(0.427759\pi\) | |||||||
\(840\) | 530879. | 0.0259596 | ||||||||
\(841\) | 707281. | 0.0344828 | ||||||||
\(842\) | −6.92184e6 | −0.336466 | ||||||||
\(843\) | −363827. | −0.0176330 | ||||||||
\(844\) | −3.23425e7 | −1.56285 | ||||||||
\(845\) | −7.23046e6 | −0.348357 | ||||||||
\(846\) | 2.80813e7 | 1.34894 | ||||||||
\(847\) | 7.98004e6 | 0.382205 | ||||||||
\(848\) | −1.77724e6 | −0.0848705 | ||||||||
\(849\) | −576791. | −0.0274631 | ||||||||
\(850\) | 6.22581e6 | 0.295562 | ||||||||
\(851\) | −1.33141e6 | −0.0630212 | ||||||||
\(852\) | −1.95010e6 | −0.0920360 | ||||||||
\(853\) | 1.34195e7 | 0.631487 | 0.315744 | − | 0.948845i | \(-0.397746\pi\) | ||||
0.315744 | + | 0.948845i | \(0.397746\pi\) | |||||||
\(854\) | 4.13064e7 | 1.93808 | ||||||||
\(855\) | 1.58790e7 | 0.742863 | ||||||||
\(856\) | 3.13370e7 | 1.46175 | ||||||||
\(857\) | 4.82712e6 | 0.224510 | 0.112255 | − | 0.993679i | \(-0.464193\pi\) | ||||
0.112255 | + | 0.993679i | \(0.464193\pi\) | |||||||
\(858\) | −809769. | −0.0375528 | ||||||||
\(859\) | 2.23698e7 | 1.03438 | 0.517188 | − | 0.855872i | \(-0.326979\pi\) | ||||
0.517188 | + | 0.855872i | \(0.326979\pi\) | |||||||
\(860\) | 2.20297e7 | 1.01569 | ||||||||
\(861\) | −1.20043e6 | −0.0551861 | ||||||||
\(862\) | −2.74935e7 | −1.26026 | ||||||||
\(863\) | −2.28440e6 | −0.104411 | −0.0522054 | − | 0.998636i | \(-0.516625\pi\) | ||||
−0.0522054 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(864\) | −1.92649e6 | −0.0877975 | ||||||||
\(865\) | 7.29299e6 | 0.331410 | ||||||||
\(866\) | 2.00283e7 | 0.907507 | ||||||||
\(867\) | −869703. | −0.0392937 | ||||||||
\(868\) | 4.03509e7 | 1.81783 | ||||||||
\(869\) | 2.11132e7 | 0.948431 | ||||||||
\(870\) | 237048. | 0.0106179 | ||||||||
\(871\) | −2.11567e7 | −0.944938 | ||||||||
\(872\) | −2.93887e7 | −1.30885 | ||||||||
\(873\) | −1.17196e7 | −0.520450 | ||||||||
\(874\) | −5.77876e6 | −0.255892 | ||||||||
\(875\) | 1.69284e7 | 0.747475 | ||||||||
\(876\) | −1.74040e6 | −0.0766283 | ||||||||
\(877\) | 2.19674e7 | 0.964452 | 0.482226 | − | 0.876047i | \(-0.339828\pi\) | ||||
0.482226 | + | 0.876047i | \(0.339828\pi\) | |||||||
\(878\) | −225194. | −0.00985870 | ||||||||
\(879\) | 1.26663e6 | 0.0552938 | ||||||||
\(880\) | −932998. | −0.0406138 | ||||||||
\(881\) | 2.81070e6 | 0.122004 | 0.0610021 | − | 0.998138i | \(-0.480570\pi\) | ||||
0.0610021 | + | 0.998138i | \(0.480570\pi\) | |||||||
\(882\) | −1.94463e7 | −0.841715 | ||||||||
\(883\) | −3.24911e7 | −1.40237 | −0.701186 | − | 0.712978i | \(-0.747346\pi\) | ||||
−0.701186 | + | 0.712978i | \(0.747346\pi\) | |||||||
\(884\) | −1.14265e7 | −0.491792 | ||||||||
\(885\) | −918697. | −0.0394289 | ||||||||
\(886\) | 5.70720e7 | 2.44252 | ||||||||
\(887\) | 3.68463e7 | 1.57248 | 0.786239 | − | 0.617923i | \(-0.212026\pi\) | ||||
0.786239 | + | 0.617923i | \(0.212026\pi\) | |||||||
\(888\) | −472937. | −0.0201266 | ||||||||
\(889\) | 1.30832e7 | 0.555215 | ||||||||
\(890\) | 1.51441e7 | 0.640866 | ||||||||
\(891\) | −1.57831e7 | −0.666039 | ||||||||
\(892\) | 3.71875e7 | 1.56489 | ||||||||
\(893\) | −1.97669e7 | −0.829486 | ||||||||
\(894\) | 552294. | 0.0231114 | ||||||||
\(895\) | −1.75661e7 | −0.733025 | ||||||||
\(896\) | −2.79485e7 | −1.16303 | ||||||||
\(897\) | 130202. | 0.00540304 | ||||||||
\(898\) | −6.96805e7 | −2.88350 | ||||||||
\(899\) | 7.12307e6 | 0.293946 | ||||||||
\(900\) | 1.78502e7 | 0.734575 | ||||||||
\(901\) | −1.03653e7 | −0.425372 | ||||||||
\(902\) | 4.50164e7 | 1.84227 | ||||||||
\(903\) | −661024. | −0.0269773 | ||||||||
\(904\) | −4.94292e7 | −2.01170 | ||||||||
\(905\) | 1.30733e7 | 0.530597 | ||||||||
\(906\) | 1.34710e6 | 0.0545230 | ||||||||
\(907\) | 6.77134e6 | 0.273311 | 0.136655 | − | 0.990619i | \(-0.456365\pi\) | ||||
0.136655 | + | 0.990619i | \(0.456365\pi\) | |||||||
\(908\) | 4.94266e7 | 1.98951 | ||||||||
\(909\) | −2.70142e7 | −1.08438 | ||||||||
\(910\) | −1.53572e7 | −0.614765 | ||||||||
\(911\) | 1.38061e7 | 0.551156 | 0.275578 | − | 0.961279i | \(-0.411131\pi\) | ||||
0.275578 | + | 0.961279i | \(0.411131\pi\) | |||||||
\(912\) | −96201.0 | −0.00382994 | ||||||||
\(913\) | −1.25719e7 | −0.499142 | ||||||||
\(914\) | −4.63467e7 | −1.83507 | ||||||||
\(915\) | 1.52298e6 | 0.0601369 | ||||||||
\(916\) | −5.41591e7 | −2.13272 | ||||||||
\(917\) | 2.33489e7 | 0.916943 | ||||||||
\(918\) | 1.59590e6 | 0.0625029 | ||||||||
\(919\) | −3.45509e7 | −1.34949 | −0.674746 | − | 0.738050i | \(-0.735747\pi\) | ||||
−0.674746 | + | 0.738050i | \(0.735747\pi\) | |||||||
\(920\) | 3.20101e6 | 0.124686 | ||||||||
\(921\) | −2.29647e6 | −0.0892094 | ||||||||
\(922\) | −3.30770e7 | −1.28144 | ||||||||
\(923\) | 2.23022e7 | 0.861673 | ||||||||
\(924\) | 941634. | 0.0362829 | ||||||||
\(925\) | −4.64538e6 | −0.178512 | ||||||||
\(926\) | −8.16987e7 | −3.13103 | ||||||||
\(927\) | 343407. | 0.0131253 | ||||||||
\(928\) | −4.54349e6 | −0.173189 | ||||||||
\(929\) | −2.47472e7 | −0.940776 | −0.470388 | − | 0.882460i | \(-0.655886\pi\) | ||||
−0.470388 | + | 0.882460i | \(0.655886\pi\) | |||||||
\(930\) | 2.38733e6 | 0.0905118 | ||||||||
\(931\) | 1.36885e7 | 0.517586 | ||||||||
\(932\) | −5.26477e7 | −1.98536 | ||||||||
\(933\) | 1.53101e6 | 0.0575803 | ||||||||
\(934\) | −2.99476e7 | −1.12330 | ||||||||
\(935\) | −5.44146e6 | −0.203557 | ||||||||
\(936\) | −2.07833e7 | −0.775399 | ||||||||
\(937\) | 1.40114e6 | 0.0521352 | 0.0260676 | − | 0.999660i | \(-0.491701\pi\) | ||||
0.0260676 | + | 0.999660i | \(0.491701\pi\) | |||||||
\(938\) | 3.94777e7 | 1.46502 | ||||||||
\(939\) | −1.67004e6 | −0.0618107 | ||||||||
\(940\) | 2.76959e7 | 1.02234 | ||||||||
\(941\) | −2.79452e7 | −1.02881 | −0.514403 | − | 0.857548i | \(-0.671987\pi\) | ||||
−0.514403 | + | 0.857548i | \(0.671987\pi\) | |||||||
\(942\) | 2.17400e6 | 0.0798240 | ||||||||
\(943\) | −7.23817e6 | −0.265063 | ||||||||
\(944\) | −2.50110e6 | −0.0913484 | ||||||||
\(945\) | 1.33667e6 | 0.0486906 | ||||||||
\(946\) | 2.47885e7 | 0.900580 | ||||||||
\(947\) | 3.03936e7 | 1.10131 | 0.550653 | − | 0.834734i | \(-0.314379\pi\) | ||||
0.550653 | + | 0.834734i | \(0.314379\pi\) | |||||||
\(948\) | −3.05023e6 | −0.110233 | ||||||||
\(949\) | 1.99040e7 | 0.717421 | ||||||||
\(950\) | −2.01625e7 | −0.724830 | ||||||||
\(951\) | −654876. | −0.0234805 | ||||||||
\(952\) | 8.42925e6 | 0.301437 | ||||||||
\(953\) | 3.75892e7 | 1.34070 | 0.670349 | − | 0.742046i | \(-0.266144\pi\) | ||||
0.670349 | + | 0.742046i | \(0.266144\pi\) | |||||||
\(954\) | −4.76881e7 | −1.69644 | ||||||||
\(955\) | 3.56657e6 | 0.126544 | ||||||||
\(956\) | −5.92466e6 | −0.209661 | ||||||||
\(957\) | 166225. | 0.00586701 | ||||||||
\(958\) | 2.15025e7 | 0.756964 | ||||||||
\(959\) | −8.52510e6 | −0.299332 | ||||||||
\(960\) | −1.60427e6 | −0.0561824 | ||||||||
\(961\) | 4.31078e7 | 1.50573 | ||||||||
\(962\) | 1.36811e7 | 0.476632 | ||||||||
\(963\) | 3.94070e7 | 1.36933 | ||||||||
\(964\) | 6.96038e7 | 2.41235 | ||||||||
\(965\) | 1.48323e7 | 0.512732 | ||||||||
\(966\) | −242953. | −0.00837683 | ||||||||
\(967\) | 4.14600e7 | 1.42582 | 0.712908 | − | 0.701258i | \(-0.247378\pi\) | ||||
0.712908 | + | 0.701258i | \(0.247378\pi\) | |||||||
\(968\) | 1.70918e7 | 0.586273 | ||||||||
\(969\) | −561066. | −0.0191957 | ||||||||
\(970\) | −1.85479e7 | −0.632946 | ||||||||
\(971\) | −5.71685e6 | −0.194585 | −0.0972924 | − | 0.995256i | \(-0.531018\pi\) | ||||
−0.0972924 | + | 0.995256i | \(0.531018\pi\) | |||||||
\(972\) | 6.86603e6 | 0.233099 | ||||||||
\(973\) | −2.13438e7 | −0.722754 | ||||||||
\(974\) | −1.25133e7 | −0.422642 | ||||||||
\(975\) | 454286. | 0.0153045 | ||||||||
\(976\) | 4.14622e6 | 0.139325 | ||||||||
\(977\) | 2.35225e6 | 0.0788400 | 0.0394200 | − | 0.999223i | \(-0.487449\pi\) | ||||
0.0394200 | + | 0.999223i | \(0.487449\pi\) | |||||||
\(978\) | 4.20376e6 | 0.140537 | ||||||||
\(979\) | 1.06194e7 | 0.354115 | ||||||||
\(980\) | −1.91794e7 | −0.637926 | ||||||||
\(981\) | −3.69570e7 | −1.22609 | ||||||||
\(982\) | −4.07407e7 | −1.34819 | ||||||||
\(983\) | −2.67280e7 | −0.882232 | −0.441116 | − | 0.897450i | \(-0.645417\pi\) | ||||
−0.441116 | + | 0.897450i | \(0.645417\pi\) | |||||||
\(984\) | −2.57111e6 | −0.0846512 | ||||||||
\(985\) | 83287.1 | 0.00273519 | ||||||||
\(986\) | 3.76383e6 | 0.123293 | ||||||||
\(987\) | −831047. | −0.0271539 | ||||||||
\(988\) | 3.70051e7 | 1.20606 | ||||||||
\(989\) | −3.98573e6 | −0.129574 | ||||||||
\(990\) | −2.50348e7 | −0.811814 | ||||||||
\(991\) | −1.24011e7 | −0.401122 | −0.200561 | − | 0.979681i | \(-0.564276\pi\) | ||||
−0.200561 | + | 0.979681i | \(0.564276\pi\) | |||||||
\(992\) | −4.57578e7 | −1.47634 | ||||||||
\(993\) | −564283. | −0.0181603 | ||||||||
\(994\) | −4.16151e7 | −1.33593 | ||||||||
\(995\) | −1.00497e7 | −0.321808 | ||||||||
\(996\) | 1.81626e6 | 0.0580136 | ||||||||
\(997\) | 1.41176e7 | 0.449803 | 0.224902 | − | 0.974381i | \(-0.427794\pi\) | ||||
0.224902 | + | 0.974381i | \(0.427794\pi\) | |||||||
\(998\) | 8.85666e7 | 2.81477 | ||||||||
\(999\) | −1.19078e6 | −0.0377502 |
(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 | 29.6.a.a.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 261.6.a.a.1.4 | 4 | |||
4.3 | odd | 2 | 464.6.a.i.1.2 | 4 | |||
5.4 | even | 2 | 725.6.a.a.1.4 | 4 | |||
29.28 | even | 2 | 841.6.a.a.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.6.a.a.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
261.6.a.a.1.4 | 4 | 3.2 | odd | 2 | |||
464.6.a.i.1.2 | 4 | 4.3 | odd | 2 | |||
725.6.a.a.1.4 | 4 | 5.4 | even | 2 | |||
841.6.a.a.1.4 | 4 | 29.28 | even | 2 |