Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, 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("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} - 176x^{6} + 272x^{5} + 9055x^{4} - 15851x^{3} - 118840x^{2} + 149572x - 33248 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(5.43413\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −6.43413 | −1.13740 | −0.568702 | − | 0.822544i | \(-0.692554\pi\) | ||||
−0.568702 | + | 0.822544i | \(0.692554\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 9.39797 | 0.293687 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −57.9071 | −0.656680 | ||||||||
\(7\) | 9.96708 | 0.0768817 | 0.0384408 | − | 0.999261i | \(-0.487761\pi\) | ||||
0.0384408 | + | 0.999261i | \(0.487761\pi\) | |||||||
\(8\) | 145.424 | 0.803363 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | 84.5818 | 0.169560 | ||||||||
\(13\) | −813.596 | −1.33521 | −0.667606 | − | 0.744515i | \(-0.732681\pi\) | ||||
−0.667606 | + | 0.744515i | \(0.732681\pi\) | |||||||
\(14\) | −64.1295 | −0.0874455 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1236.41 | −1.20743 | ||||||||
\(17\) | 616.038 | 0.516994 | 0.258497 | − | 0.966012i | \(-0.416773\pi\) | ||||
0.258497 | + | 0.966012i | \(0.416773\pi\) | |||||||
\(18\) | −521.164 | −0.379134 | ||||||||
\(19\) | 1989.66 | 1.26443 | 0.632217 | − | 0.774792i | \(-0.282145\pi\) | ||||
0.632217 | + | 0.774792i | \(0.282145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 89.7037 | 0.0443877 | ||||||||
\(22\) | 778.529 | 0.342940 | ||||||||
\(23\) | 545.944 | 0.215193 | 0.107597 | − | 0.994195i | \(-0.465685\pi\) | ||||
0.107597 | + | 0.994195i | \(0.465685\pi\) | |||||||
\(24\) | 1308.82 | 0.463822 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5234.78 | 1.51868 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 93.6704 | 0.0225791 | ||||||||
\(29\) | −670.788 | −0.148112 | −0.0740560 | − | 0.997254i | \(-0.523594\pi\) | ||||
−0.0740560 | + | 0.997254i | \(0.523594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1229.55 | −0.229796 | −0.114898 | − | 0.993377i | \(-0.536654\pi\) | ||||
−0.114898 | + | 0.993377i | \(0.536654\pi\) | |||||||
\(32\) | 3301.66 | 0.569977 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | −3963.67 | −0.588031 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 761.236 | 0.0978956 | ||||||||
\(37\) | −9820.34 | −1.17929 | −0.589647 | − | 0.807661i | \(-0.700733\pi\) | ||||
−0.589647 | + | 0.807661i | \(0.700733\pi\) | |||||||
\(38\) | −12801.8 | −1.43817 | ||||||||
\(39\) | −7322.36 | −0.770885 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5587.84 | 0.519140 | 0.259570 | − | 0.965724i | \(-0.416419\pi\) | ||||
0.259570 | + | 0.965724i | \(0.416419\pi\) | |||||||
\(42\) | −577.165 | −0.0504867 | ||||||||
\(43\) | 6305.91 | 0.520088 | 0.260044 | − | 0.965597i | \(-0.416263\pi\) | ||||
0.260044 | + | 0.965597i | \(0.416263\pi\) | |||||||
\(44\) | −1137.15 | −0.0885499 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3512.67 | −0.244761 | ||||||||
\(47\) | 10680.8 | 0.705276 | 0.352638 | − | 0.935760i | \(-0.385285\pi\) | ||||
0.352638 | + | 0.935760i | \(0.385285\pi\) | |||||||
\(48\) | −11127.7 | −0.697113 | ||||||||
\(49\) | −16707.7 | −0.994089 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5544.35 | 0.298487 | ||||||||
\(52\) | −7646.15 | −0.392134 | ||||||||
\(53\) | −21821.5 | −1.06708 | −0.533538 | − | 0.845776i | \(-0.679138\pi\) | ||||
−0.533538 | + | 0.845776i | \(0.679138\pi\) | |||||||
\(54\) | −4690.48 | −0.218893 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1449.46 | 0.0617639 | ||||||||
\(57\) | 17907.0 | 0.730021 | ||||||||
\(58\) | 4315.93 | 0.168463 | ||||||||
\(59\) | −2157.19 | −0.0806788 | −0.0403394 | − | 0.999186i | \(-0.512844\pi\) | ||||
−0.0403394 | + | 0.999186i | \(0.512844\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6743.79 | −0.232049 | −0.116024 | − | 0.993246i | \(-0.537015\pi\) | ||||
−0.116024 | + | 0.993246i | \(0.537015\pi\) | |||||||
\(62\) | 7911.10 | 0.261371 | ||||||||
\(63\) | 807.334 | 0.0256272 | ||||||||
\(64\) | 18321.9 | 0.559141 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7006.76 | 0.197997 | ||||||||
\(67\) | 38984.7 | 1.06098 | 0.530490 | − | 0.847691i | \(-0.322008\pi\) | ||||
0.530490 | + | 0.847691i | \(0.322008\pi\) | |||||||
\(68\) | 5789.51 | 0.151834 | ||||||||
\(69\) | 4913.49 | 0.124242 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 25270.9 | 0.594941 | 0.297471 | − | 0.954731i | \(-0.403857\pi\) | ||||
0.297471 | + | 0.954731i | \(0.403857\pi\) | |||||||
\(72\) | 11779.4 | 0.267788 | ||||||||
\(73\) | 23958.4 | 0.526201 | 0.263100 | − | 0.964768i | \(-0.415255\pi\) | ||||
0.263100 | + | 0.964768i | \(0.415255\pi\) | |||||||
\(74\) | 63185.3 | 1.34133 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 18698.8 | 0.371347 | ||||||||
\(77\) | −1206.02 | −0.0231807 | ||||||||
\(78\) | 47113.0 | 0.876808 | ||||||||
\(79\) | −101544. | −1.83057 | −0.915284 | − | 0.402810i | \(-0.868034\pi\) | ||||
−0.915284 | + | 0.402810i | \(0.868034\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −35952.9 | −0.590472 | ||||||||
\(83\) | 14547.0 | 0.231781 | 0.115891 | − | 0.993262i | \(-0.463028\pi\) | ||||
0.115891 | + | 0.993262i | \(0.463028\pi\) | |||||||
\(84\) | 843.033 | 0.0130361 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −40573.0 | −0.591550 | ||||||||
\(87\) | −6037.09 | −0.0855125 | ||||||||
\(88\) | −17596.3 | −0.242223 | ||||||||
\(89\) | −80447.7 | −1.07656 | −0.538281 | − | 0.842766i | \(-0.680926\pi\) | ||||
−0.538281 | + | 0.842766i | \(0.680926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8109.18 | −0.102653 | ||||||||
\(92\) | 5130.76 | 0.0631993 | ||||||||
\(93\) | −11066.0 | −0.132673 | ||||||||
\(94\) | −68721.6 | −0.802184 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 29715.0 | 0.329077 | ||||||||
\(97\) | 78631.2 | 0.848527 | 0.424264 | − | 0.905539i | \(-0.360533\pi\) | ||||
0.424264 | + | 0.905539i | \(0.360533\pi\) | |||||||
\(98\) | 107499. | 1.13068 | ||||||||
\(99\) | −9801.00 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 22024.1 | 0.214830 | 0.107415 | − | 0.994214i | \(-0.465743\pi\) | ||||
0.107415 | + | 0.994214i | \(0.465743\pi\) | |||||||
\(102\) | −35673.0 | −0.339500 | ||||||||
\(103\) | 85005.4 | 0.789503 | 0.394751 | − | 0.918788i | \(-0.370831\pi\) | ||||
0.394751 | + | 0.918788i | \(0.370831\pi\) | |||||||
\(104\) | −118317. | −1.07266 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 140403. | 1.21370 | ||||||||
\(107\) | 129131. | 1.09036 | 0.545181 | − | 0.838319i | \(-0.316461\pi\) | ||||
0.545181 | + | 0.838319i | \(0.316461\pi\) | |||||||
\(108\) | 6851.12 | 0.0565200 | ||||||||
\(109\) | −153961. | −1.24121 | −0.620605 | − | 0.784124i | \(-0.713113\pi\) | ||||
−0.620605 | + | 0.784124i | \(0.713113\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −88383.0 | −0.680866 | ||||||||
\(112\) | −12323.4 | −0.0928296 | ||||||||
\(113\) | −139946. | −1.03102 | −0.515508 | − | 0.856885i | \(-0.672397\pi\) | ||||
−0.515508 | + | 0.856885i | \(0.672397\pi\) | |||||||
\(114\) | −115216. | −0.830328 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6304.04 | −0.0434985 | ||||||||
\(117\) | −65901.3 | −0.445071 | ||||||||
\(118\) | 13879.7 | 0.0917643 | ||||||||
\(119\) | 6140.10 | 0.0397474 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 43390.4 | 0.263933 | ||||||||
\(123\) | 50290.6 | 0.299726 | ||||||||
\(124\) | −11555.3 | −0.0674881 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −5194.49 | −0.0291485 | ||||||||
\(127\) | 119781. | 0.658992 | 0.329496 | − | 0.944157i | \(-0.393121\pi\) | ||||
0.329496 | + | 0.944157i | \(0.393121\pi\) | |||||||
\(128\) | −223539. | −1.20595 | ||||||||
\(129\) | 56753.2 | 0.300273 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 167797. | 0.854293 | 0.427147 | − | 0.904182i | \(-0.359519\pi\) | ||||
0.427147 | + | 0.904182i | \(0.359519\pi\) | |||||||
\(132\) | −10234.4 | −0.0511243 | ||||||||
\(133\) | 19831.2 | 0.0972118 | ||||||||
\(134\) | −250832. | −1.20676 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 89586.9 | 0.415334 | ||||||||
\(137\) | −23349.3 | −0.106285 | −0.0531425 | − | 0.998587i | \(-0.516924\pi\) | ||||
−0.0531425 | + | 0.998587i | \(0.516924\pi\) | |||||||
\(138\) | −31614.0 | −0.141313 | ||||||||
\(139\) | −108551. | −0.476537 | −0.238269 | − | 0.971199i | \(-0.576580\pi\) | ||||
−0.238269 | + | 0.971199i | \(0.576580\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 96127.2 | 0.407191 | ||||||||
\(142\) | −162596. | −0.676688 | ||||||||
\(143\) | 98445.1 | 0.402582 | ||||||||
\(144\) | −100149. | −0.402478 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −154152. | −0.598502 | ||||||||
\(147\) | −150369. | −0.573938 | ||||||||
\(148\) | −92291.3 | −0.346343 | ||||||||
\(149\) | −276956. | −1.02199 | −0.510993 | − | 0.859585i | \(-0.670722\pi\) | ||||
−0.510993 | + | 0.859585i | \(0.670722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 326462. | 1.16517 | 0.582587 | − | 0.812769i | \(-0.302041\pi\) | ||||
0.582587 | + | 0.812769i | \(0.302041\pi\) | |||||||
\(152\) | 289346. | 1.01580 | ||||||||
\(153\) | 49899.1 | 0.172331 | ||||||||
\(154\) | 7759.66 | 0.0263658 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −68815.4 | −0.226399 | ||||||||
\(157\) | 366289. | 1.18597 | 0.592986 | − | 0.805213i | \(-0.297949\pi\) | ||||
0.592986 | + | 0.805213i | \(0.297949\pi\) | |||||||
\(158\) | 653346. | 2.08209 | ||||||||
\(159\) | −196394. | −0.616077 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5441.46 | 0.0165444 | ||||||||
\(162\) | −42214.3 | −0.126378 | ||||||||
\(163\) | 642723. | 1.89476 | 0.947381 | − | 0.320107i | \(-0.103719\pi\) | ||||
0.947381 | + | 0.320107i | \(0.103719\pi\) | |||||||
\(164\) | 52514.4 | 0.152464 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −93597.3 | −0.263629 | ||||||||
\(167\) | −259189. | −0.719159 | −0.359579 | − | 0.933115i | \(-0.617080\pi\) | ||||
−0.359579 | + | 0.933115i | \(0.617080\pi\) | |||||||
\(168\) | 13045.1 | 0.0356594 | ||||||||
\(169\) | 290645. | 0.782792 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 161163. | 0.421478 | ||||||||
\(172\) | 59262.8 | 0.152743 | ||||||||
\(173\) | −242721. | −0.616585 | −0.308292 | − | 0.951292i | \(-0.599758\pi\) | ||||
−0.308292 | + | 0.951292i | \(0.599758\pi\) | |||||||
\(174\) | 38843.4 | 0.0972622 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 149606. | 0.364055 | ||||||||
\(177\) | −19414.8 | −0.0465799 | ||||||||
\(178\) | 517611. | 1.22448 | ||||||||
\(179\) | −214184. | −0.499638 | −0.249819 | − | 0.968293i | \(-0.580371\pi\) | ||||
−0.249819 | + | 0.968293i | \(0.580371\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −247705. | −0.562003 | −0.281002 | − | 0.959707i | \(-0.590667\pi\) | ||||
−0.281002 | + | 0.959707i | \(0.590667\pi\) | |||||||
\(182\) | 52175.5 | 0.116758 | ||||||||
\(183\) | −60694.1 | −0.133973 | ||||||||
\(184\) | 79393.4 | 0.172878 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 71199.9 | 0.150903 | ||||||||
\(187\) | −74540.6 | −0.155880 | ||||||||
\(188\) | 100378. | 0.207130 | ||||||||
\(189\) | 7266.00 | 0.0147959 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −410762. | −0.814718 | −0.407359 | − | 0.913268i | \(-0.633550\pi\) | ||||
−0.407359 | + | 0.913268i | \(0.633550\pi\) | |||||||
\(192\) | 164897. | 0.322820 | ||||||||
\(193\) | −150990. | −0.291780 | −0.145890 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145890 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(194\) | −505923. | −0.965118 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −157018. | −0.291951 | ||||||||
\(197\) | −151624. | −0.278357 | −0.139178 | − | 0.990267i | \(-0.544446\pi\) | ||||
−0.139178 | + | 0.990267i | \(0.544446\pi\) | |||||||
\(198\) | 63060.9 | 0.114313 | ||||||||
\(199\) | 464676. | 0.831797 | 0.415898 | − | 0.909411i | \(-0.363467\pi\) | ||||
0.415898 | + | 0.909411i | \(0.363467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 350862. | 0.612557 | ||||||||
\(202\) | −141706. | −0.244349 | ||||||||
\(203\) | −6685.80 | −0.0113871 | ||||||||
\(204\) | 52105.6 | 0.0876615 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −546936. | −0.897983 | ||||||||
\(207\) | 44221.4 | 0.0717310 | ||||||||
\(208\) | 1.00594e6 | 1.61218 | ||||||||
\(209\) | −240749. | −0.381241 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.17253e6 | −1.81308 | −0.906541 | − | 0.422117i | \(-0.861287\pi\) | ||||
−0.906541 | + | 0.422117i | \(0.861287\pi\) | |||||||
\(212\) | −205078. | −0.313386 | ||||||||
\(213\) | 227438. | 0.343490 | ||||||||
\(214\) | −830844. | −1.24018 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 106014. | 0.154607 | ||||||||
\(217\) | −12255.1 | −0.0176671 | ||||||||
\(218\) | 990606. | 1.41176 | ||||||||
\(219\) | 215626. | 0.303802 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −501206. | −0.690297 | ||||||||
\(222\) | 568668. | 0.774419 | ||||||||
\(223\) | −494387. | −0.665740 | −0.332870 | − | 0.942973i | \(-0.608017\pi\) | ||||
−0.332870 | + | 0.942973i | \(0.608017\pi\) | |||||||
\(224\) | 32907.9 | 0.0438208 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 900432. | 1.17268 | ||||||||
\(227\) | −219419. | −0.282624 | −0.141312 | − | 0.989965i | \(-0.545132\pi\) | ||||
−0.141312 | + | 0.989965i | \(0.545132\pi\) | |||||||
\(228\) | 168289. | 0.214397 | ||||||||
\(229\) | −1.23652e6 | −1.55816 | −0.779080 | − | 0.626925i | \(-0.784313\pi\) | ||||
−0.779080 | + | 0.626925i | \(0.784313\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10854.2 | −0.0133834 | ||||||||
\(232\) | −97548.8 | −0.118988 | ||||||||
\(233\) | 84155.4 | 0.101553 | 0.0507764 | − | 0.998710i | \(-0.483830\pi\) | ||||
0.0507764 | + | 0.998710i | \(0.483830\pi\) | |||||||
\(234\) | 424017. | 0.506225 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −20273.3 | −0.0236943 | ||||||||
\(237\) | −913894. | −1.05688 | ||||||||
\(238\) | −39506.2 | −0.0452088 | ||||||||
\(239\) | −113266. | −0.128264 | −0.0641320 | − | 0.997941i | \(-0.520428\pi\) | ||||
−0.0641320 | + | 0.997941i | \(0.520428\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −616377. | −0.683603 | −0.341801 | − | 0.939772i | \(-0.611037\pi\) | ||||
−0.341801 | + | 0.939772i | \(0.611037\pi\) | |||||||
\(242\) | −94202.0 | −0.103400 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | −63378.0 | −0.0681497 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −323576. | −0.340909 | ||||||||
\(247\) | −1.61878e6 | −1.68829 | ||||||||
\(248\) | −178807. | −0.184610 | ||||||||
\(249\) | 130923. | 0.133819 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.34829e6 | −1.35082 | −0.675412 | − | 0.737441i | \(-0.736034\pi\) | ||||
−0.675412 | + | 0.737441i | \(0.736034\pi\) | |||||||
\(252\) | 7587.30 | 0.00752638 | ||||||||
\(253\) | −66059.2 | −0.0648831 | ||||||||
\(254\) | −770689. | −0.749540 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 851975. | 0.812506 | ||||||||
\(257\) | 715746. | 0.675968 | 0.337984 | − | 0.941152i | \(-0.390255\pi\) | ||||
0.337984 | + | 0.941152i | \(0.390255\pi\) | |||||||
\(258\) | −365157. | −0.341531 | ||||||||
\(259\) | −97880.1 | −0.0906661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −54333.8 | −0.0493707 | ||||||||
\(262\) | −1.07963e6 | −0.971676 | ||||||||
\(263\) | −2.10033e6 | −1.87239 | −0.936197 | − | 0.351475i | \(-0.885680\pi\) | ||||
−0.936197 | + | 0.351475i | \(0.885680\pi\) | |||||||
\(264\) | −158367. | −0.139848 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −127596. | −0.110569 | ||||||||
\(267\) | −724029. | −0.621553 | ||||||||
\(268\) | 366377. | 0.311596 | ||||||||
\(269\) | −1.41437e6 | −1.19174 | −0.595871 | − | 0.803080i | \(-0.703193\pi\) | ||||
−0.595871 | + | 0.803080i | \(0.703193\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 190480. | 0.157553 | 0.0787763 | − | 0.996892i | \(-0.474899\pi\) | ||||
0.0787763 | + | 0.996892i | \(0.474899\pi\) | |||||||
\(272\) | −761678. | −0.624236 | ||||||||
\(273\) | −72982.6 | −0.0592670 | ||||||||
\(274\) | 150232. | 0.120889 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 46176.9 | 0.0364881 | ||||||||
\(277\) | −998049. | −0.781542 | −0.390771 | − | 0.920488i | \(-0.627792\pi\) | ||||
−0.390771 | + | 0.920488i | \(0.627792\pi\) | |||||||
\(278\) | 698430. | 0.542015 | ||||||||
\(279\) | −99593.8 | −0.0765988 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.43088e6 | −1.08103 | −0.540515 | − | 0.841334i | \(-0.681771\pi\) | ||||
−0.540515 | + | 0.841334i | \(0.681771\pi\) | |||||||
\(282\) | −618495. | −0.463141 | ||||||||
\(283\) | 2.40496e6 | 1.78501 | 0.892506 | − | 0.451035i | \(-0.148945\pi\) | ||||
0.892506 | + | 0.451035i | \(0.148945\pi\) | |||||||
\(284\) | 237495. | 0.174726 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −633408. | −0.457898 | ||||||||
\(287\) | 55694.5 | 0.0399124 | ||||||||
\(288\) | 267435. | 0.189992 | ||||||||
\(289\) | −1.04035e6 | −0.732717 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 707681. | 0.489897 | ||||||||
\(292\) | 225161. | 0.154538 | ||||||||
\(293\) | −689179. | −0.468990 | −0.234495 | − | 0.972117i | \(-0.575344\pi\) | ||||
−0.234495 | + | 0.972117i | \(0.575344\pi\) | |||||||
\(294\) | 967492. | 0.652799 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.42812e6 | −0.947401 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 1.78197e6 | 1.16241 | ||||||||
\(299\) | −444177. | −0.287328 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 62851.5 | 0.0399852 | ||||||||
\(302\) | −2.10050e6 | −1.32527 | ||||||||
\(303\) | 198217. | 0.124032 | ||||||||
\(304\) | −2.46005e6 | −1.52672 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −321057. | −0.196010 | ||||||||
\(307\) | 986212. | 0.597206 | 0.298603 | − | 0.954377i | \(-0.403479\pi\) | ||||
0.298603 | + | 0.954377i | \(0.403479\pi\) | |||||||
\(308\) | −11334.1 | −0.00680786 | ||||||||
\(309\) | 765049. | 0.455819 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.70281e6 | −0.998308 | −0.499154 | − | 0.866513i | \(-0.666356\pi\) | ||||
−0.499154 | + | 0.866513i | \(0.666356\pi\) | |||||||
\(312\) | −1.06485e6 | −0.619301 | ||||||||
\(313\) | −2.92333e6 | −1.68662 | −0.843309 | − | 0.537428i | \(-0.819396\pi\) | ||||
−0.843309 | + | 0.537428i | \(0.819396\pi\) | |||||||
\(314\) | −2.35675e6 | −1.34893 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −954306. | −0.537613 | ||||||||
\(317\) | −1.69795e6 | −0.949022 | −0.474511 | − | 0.880250i | \(-0.657375\pi\) | ||||
−0.474511 | + | 0.880250i | \(0.657375\pi\) | |||||||
\(318\) | 1.26362e6 | 0.700728 | ||||||||
\(319\) | 81165.3 | 0.0446574 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.16218e6 | 0.629520 | ||||||||
\(322\) | −35011.1 | −0.0188177 | ||||||||
\(323\) | 1.22571e6 | 0.653704 | ||||||||
\(324\) | 61660.1 | 0.0326319 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.13536e6 | −2.15511 | ||||||||
\(327\) | −1.38565e6 | −0.716612 | ||||||||
\(328\) | 812608. | 0.417058 | ||||||||
\(329\) | 106456. | 0.0542228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.44074e6 | 0.722795 | 0.361397 | − | 0.932412i | \(-0.382300\pi\) | ||||
0.361397 | + | 0.932412i | \(0.382300\pi\) | |||||||
\(332\) | 136712. | 0.0680711 | ||||||||
\(333\) | −795447. | −0.393098 | ||||||||
\(334\) | 1.66765e6 | 0.817973 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −110911. | −0.0535952 | ||||||||
\(337\) | −967187. | −0.463912 | −0.231956 | − | 0.972726i | \(-0.574513\pi\) | ||||
−0.231956 | + | 0.972726i | \(0.574513\pi\) | |||||||
\(338\) | −1.87005e6 | −0.890351 | ||||||||
\(339\) | −1.25952e6 | −0.595257 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 148776. | 0.0692862 | ||||||||
\(342\) | −1.03694e6 | −0.479390 | ||||||||
\(343\) | −334043. | −0.153309 | ||||||||
\(344\) | 917032. | 0.417819 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.56170e6 | 0.701306 | ||||||||
\(347\) | −2.81126e6 | −1.25336 | −0.626682 | − | 0.779275i | \(-0.715587\pi\) | ||||
−0.626682 | + | 0.779275i | \(0.715587\pi\) | |||||||
\(348\) | −56736.4 | −0.0251139 | ||||||||
\(349\) | −1.64221e6 | −0.721713 | −0.360856 | − | 0.932621i | \(-0.617516\pi\) | ||||
−0.360856 | + | 0.932621i | \(0.617516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −593111. | −0.256962 | ||||||||
\(352\) | −399501. | −0.171855 | ||||||||
\(353\) | −2.89812e6 | −1.23788 | −0.618941 | − | 0.785438i | \(-0.712438\pi\) | ||||
−0.618941 | + | 0.785438i | \(0.712438\pi\) | |||||||
\(354\) | 124917. | 0.0529802 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −756045. | −0.316172 | ||||||||
\(357\) | 55260.9 | 0.0229482 | ||||||||
\(358\) | 1.37809e6 | 0.568290 | ||||||||
\(359\) | 3.03267e6 | 1.24191 | 0.620954 | − | 0.783847i | \(-0.286745\pi\) | ||||
0.620954 | + | 0.783847i | \(0.286745\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.48267e6 | 0.598792 | ||||||||
\(362\) | 1.59377e6 | 0.639224 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | −76209.8 | −0.0301479 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 390514. | 0.152382 | ||||||||
\(367\) | −1.16998e6 | −0.453431 | −0.226716 | − | 0.973961i | \(-0.572799\pi\) | ||||
−0.226716 | + | 0.973961i | \(0.572799\pi\) | |||||||
\(368\) | −675012. | −0.259832 | ||||||||
\(369\) | 452615. | 0.173047 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −217497. | −0.0820387 | ||||||||
\(372\) | −103998. | −0.0389643 | ||||||||
\(373\) | −1.47636e6 | −0.549438 | −0.274719 | − | 0.961525i | \(-0.588585\pi\) | ||||
−0.274719 | + | 0.961525i | \(0.588585\pi\) | |||||||
\(374\) | 479604. | 0.177298 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.55325e6 | 0.566593 | ||||||||
\(377\) | 545750. | 0.197761 | ||||||||
\(378\) | −46750.4 | −0.0168289 | ||||||||
\(379\) | 4.95103e6 | 1.77051 | 0.885253 | − | 0.465110i | \(-0.153985\pi\) | ||||
0.885253 | + | 0.465110i | \(0.153985\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.07803e6 | 0.380469 | ||||||||
\(382\) | 2.64290e6 | 0.926663 | ||||||||
\(383\) | −1.41125e6 | −0.491594 | −0.245797 | − | 0.969321i | \(-0.579050\pi\) | ||||
−0.245797 | + | 0.969321i | \(0.579050\pi\) | |||||||
\(384\) | −2.01185e6 | −0.696253 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 971492. | 0.331872 | ||||||||
\(387\) | 510779. | 0.173363 | ||||||||
\(388\) | 738974. | 0.249201 | ||||||||
\(389\) | 1.35721e6 | 0.454750 | 0.227375 | − | 0.973807i | \(-0.426986\pi\) | ||||
0.227375 | + | 0.973807i | \(0.426986\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 336322. | 0.111253 | ||||||||
\(392\) | −2.42970e6 | −0.798615 | ||||||||
\(393\) | 1.51018e6 | 0.493226 | ||||||||
\(394\) | 975566. | 0.316604 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −92109.5 | −0.0295166 | ||||||||
\(397\) | −1.77467e6 | −0.565122 | −0.282561 | − | 0.959249i | \(-0.591184\pi\) | ||||
−0.282561 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(398\) | −2.98978e6 | −0.946089 | ||||||||
\(399\) | 178480. | 0.0561252 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.69680e6 | 1.14806 | 0.574030 | − | 0.818834i | \(-0.305379\pi\) | ||||
0.574030 | + | 0.818834i | \(0.305379\pi\) | |||||||
\(402\) | −2.25749e6 | −0.696725 | ||||||||
\(403\) | 1.00036e6 | 0.306827 | ||||||||
\(404\) | 206982. | 0.0630928 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 43017.3 | 0.0129517 | ||||||||
\(407\) | 1.18826e6 | 0.355571 | ||||||||
\(408\) | 806282. | 0.239793 | ||||||||
\(409\) | −824495. | −0.243714 | −0.121857 | − | 0.992548i | \(-0.538885\pi\) | ||||
−0.121857 | + | 0.992548i | \(0.538885\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −210144. | −0.0613637 | ||||||||
\(412\) | 798879. | 0.231866 | ||||||||
\(413\) | −21500.9 | −0.00620272 | ||||||||
\(414\) | −284526. | −0.0815871 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.68622e6 | −0.761041 | ||||||||
\(417\) | −976959. | −0.275129 | ||||||||
\(418\) | 1.54901e6 | 0.433625 | ||||||||
\(419\) | −5.87905e6 | −1.63596 | −0.817979 | − | 0.575249i | \(-0.804905\pi\) | ||||
−0.817979 | + | 0.575249i | \(0.804905\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.48720e6 | 0.958895 | 0.479448 | − | 0.877570i | \(-0.340837\pi\) | ||||
0.479448 | + | 0.877570i | \(0.340837\pi\) | |||||||
\(422\) | 7.54420e6 | 2.06221 | ||||||||
\(423\) | 865145. | 0.235092 | ||||||||
\(424\) | −3.17338e6 | −0.857250 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.46336e6 | −0.390686 | ||||||||
\(427\) | −67215.9 | −0.0178403 | ||||||||
\(428\) | 1.21357e6 | 0.320225 | ||||||||
\(429\) | 886006. | 0.232431 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.41226e6 | −1.14411 | −0.572055 | − | 0.820215i | \(-0.693854\pi\) | ||||
−0.572055 | + | 0.820215i | \(0.693854\pi\) | |||||||
\(432\) | −901345. | −0.232371 | ||||||||
\(433\) | −989722. | −0.253684 | −0.126842 | − | 0.991923i | \(-0.540484\pi\) | ||||
−0.126842 | + | 0.991923i | \(0.540484\pi\) | |||||||
\(434\) | 78850.6 | 0.0200947 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.44692e6 | −0.364527 | ||||||||
\(437\) | 1.08624e6 | 0.272097 | ||||||||
\(438\) | −1.38736e6 | −0.345545 | ||||||||
\(439\) | −2.69582e6 | −0.667621 | −0.333811 | − | 0.942640i | \(-0.608335\pi\) | ||||
−0.333811 | + | 0.942640i | \(0.608335\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.35332e6 | −0.331363 | ||||||||
\(442\) | 3.22482e6 | 0.785146 | ||||||||
\(443\) | −1.84727e6 | −0.447221 | −0.223610 | − | 0.974679i | \(-0.571784\pi\) | ||||
−0.223610 | + | 0.974679i | \(0.571784\pi\) | |||||||
\(444\) | −830621. | −0.199961 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.18095e6 | 0.757215 | ||||||||
\(447\) | −2.49260e6 | −0.590044 | ||||||||
\(448\) | 182616. | 0.0429877 | ||||||||
\(449\) | −806296. | −0.188746 | −0.0943732 | − | 0.995537i | \(-0.530085\pi\) | ||||
−0.0943732 | + | 0.995537i | \(0.530085\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −676129. | −0.156527 | ||||||||
\(452\) | −1.31521e6 | −0.302796 | ||||||||
\(453\) | 2.93816e6 | 0.672713 | ||||||||
\(454\) | 1.41177e6 | 0.321457 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.60411e6 | 0.586472 | ||||||||
\(457\) | −4.78463e6 | −1.07166 | −0.535830 | − | 0.844326i | \(-0.680001\pi\) | ||||
−0.535830 | + | 0.844326i | \(0.680001\pi\) | |||||||
\(458\) | 7.95592e6 | 1.77226 | ||||||||
\(459\) | 449092. | 0.0994955 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.05029e6 | −1.76425 | −0.882123 | − | 0.471019i | \(-0.843886\pi\) | ||||
−0.882123 | + | 0.471019i | \(0.843886\pi\) | |||||||
\(462\) | 69837.0 | 0.0152223 | ||||||||
\(463\) | 646347. | 0.140124 | 0.0700622 | − | 0.997543i | \(-0.477680\pi\) | ||||
0.0700622 | + | 0.997543i | \(0.477680\pi\) | |||||||
\(464\) | 829371. | 0.178836 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −541466. | −0.115507 | ||||||||
\(467\) | 5.97613e6 | 1.26803 | 0.634013 | − | 0.773323i | \(-0.281407\pi\) | ||||
0.634013 | + | 0.773323i | \(0.281407\pi\) | |||||||
\(468\) | −619338. | −0.130711 | ||||||||
\(469\) | 388564. | 0.0815699 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.29660e6 | 0.684721 | ||||||||
\(472\) | −313709. | −0.0648144 | ||||||||
\(473\) | −763015. | −0.156812 | ||||||||
\(474\) | 5.88011e6 | 1.20210 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 57704.5 | 0.0116733 | ||||||||
\(477\) | −1.76754e6 | −0.355692 | ||||||||
\(478\) | 728768. | 0.145888 | ||||||||
\(479\) | −7.53887e6 | −1.50130 | −0.750650 | − | 0.660700i | \(-0.770260\pi\) | ||||
−0.750650 | + | 0.660700i | \(0.770260\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.98979e6 | 1.57461 | ||||||||
\(482\) | 3.96585e6 | 0.777532 | ||||||||
\(483\) | 48973.2 | 0.00955191 | ||||||||
\(484\) | 137596. | 0.0266988 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −379929. | −0.0729645 | ||||||||
\(487\) | 6.72146e6 | 1.28423 | 0.642113 | − | 0.766610i | \(-0.278058\pi\) | ||||
0.642113 | + | 0.766610i | \(0.278058\pi\) | |||||||
\(488\) | −980711. | −0.186420 | ||||||||
\(489\) | 5.78451e6 | 1.09394 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.38900e6 | −0.447212 | −0.223606 | − | 0.974680i | \(-0.571783\pi\) | ||||
−0.223606 | + | 0.974680i | \(0.571783\pi\) | |||||||
\(492\) | 472629. | 0.0880254 | ||||||||
\(493\) | −413231. | −0.0765730 | ||||||||
\(494\) | 1.04155e7 | 1.92026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.52024e6 | 0.277464 | ||||||||
\(497\) | 251877. | 0.0457401 | ||||||||
\(498\) | −842376. | −0.152206 | ||||||||
\(499\) | −4.78068e6 | −0.859485 | −0.429742 | − | 0.902952i | \(-0.641396\pi\) | ||||
−0.429742 | + | 0.902952i | \(0.641396\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.33270e6 | −0.415206 | ||||||||
\(502\) | 8.67506e6 | 1.53643 | ||||||||
\(503\) | −7.98014e6 | −1.40634 | −0.703170 | − | 0.711021i | \(-0.748233\pi\) | ||||
−0.703170 | + | 0.711021i | \(0.748233\pi\) | |||||||
\(504\) | 117406. | 0.0205880 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 425033. | 0.0737983 | ||||||||
\(507\) | 2.61581e6 | 0.451945 | ||||||||
\(508\) | 1.12570e6 | 0.193537 | ||||||||
\(509\) | 888027. | 0.151926 | 0.0759630 | − | 0.997111i | \(-0.475797\pi\) | ||||
0.0759630 | + | 0.997111i | \(0.475797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 238796. | 0.0404552 | ||||||||
\(512\) | 1.67153e6 | 0.281798 | ||||||||
\(513\) | 1.45047e6 | 0.243340 | ||||||||
\(514\) | −4.60520e6 | −0.768848 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 533365. | 0.0881861 | ||||||||
\(517\) | −1.29238e6 | −0.212649 | ||||||||
\(518\) | 629773. | 0.103124 | ||||||||
\(519\) | −2.18449e6 | −0.355985 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.40559e6 | 0.711066 | 0.355533 | − | 0.934664i | \(-0.384299\pi\) | ||||
0.355533 | + | 0.934664i | \(0.384299\pi\) | |||||||
\(522\) | 349591. | 0.0561543 | ||||||||
\(523\) | −3.95891e6 | −0.632879 | −0.316440 | − | 0.948613i | \(-0.602487\pi\) | ||||
−0.316440 | + | 0.948613i | \(0.602487\pi\) | |||||||
\(524\) | 1.57696e6 | 0.250895 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.35138e7 | 2.12967 | ||||||||
\(527\) | −757452. | −0.118803 | ||||||||
\(528\) | 1.34645e6 | 0.210187 | ||||||||
\(529\) | −6.13829e6 | −0.953692 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −174733. | −0.0268929 | ||||||||
\(532\) | 186373. | 0.0285498 | ||||||||
\(533\) | −4.54625e6 | −0.693162 | ||||||||
\(534\) | 4.65850e6 | 0.706956 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.66932e6 | 0.852352 | ||||||||
\(537\) | −1.92766e6 | −0.288466 | ||||||||
\(538\) | 9.10023e6 | 1.35549 | ||||||||
\(539\) | 2.02163e6 | 0.299729 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.12527e6 | 1.19356 | 0.596780 | − | 0.802405i | \(-0.296446\pi\) | ||||
0.596780 | + | 0.802405i | \(0.296446\pi\) | |||||||
\(542\) | −1.22557e6 | −0.179201 | ||||||||
\(543\) | −2.22935e6 | −0.324473 | ||||||||
\(544\) | 2.03395e6 | 0.294675 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 469579. | 0.0674104 | ||||||||
\(547\) | 1.49316e6 | 0.213373 | 0.106686 | − | 0.994293i | \(-0.465976\pi\) | ||||
0.106686 | + | 0.994293i | \(0.465976\pi\) | |||||||
\(548\) | −219436. | −0.0312145 | ||||||||
\(549\) | −546247. | −0.0773496 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.33464e6 | −0.187278 | ||||||||
\(552\) | 714541. | 0.0998112 | ||||||||
\(553\) | −1.01210e6 | −0.140737 | ||||||||
\(554\) | 6.42157e6 | 0.888929 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.02016e6 | −0.139953 | ||||||||
\(557\) | −3.54818e6 | −0.484582 | −0.242291 | − | 0.970204i | \(-0.577899\pi\) | ||||
−0.242291 | + | 0.970204i | \(0.577899\pi\) | |||||||
\(558\) | 640799. | 0.0871237 | ||||||||
\(559\) | −5.13046e6 | −0.694428 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −670866. | −0.0899971 | ||||||||
\(562\) | 9.20647e6 | 1.22957 | ||||||||
\(563\) | −6.70997e6 | −0.892174 | −0.446087 | − | 0.894990i | \(-0.647183\pi\) | ||||
−0.446087 | + | 0.894990i | \(0.647183\pi\) | |||||||
\(564\) | 903401. | 0.119587 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.54738e7 | −2.03028 | ||||||||
\(567\) | 65394.0 | 0.00854241 | ||||||||
\(568\) | 3.67500e6 | 0.477954 | ||||||||
\(569\) | 6.17393e6 | 0.799431 | 0.399716 | − | 0.916639i | \(-0.369109\pi\) | ||||
0.399716 | + | 0.916639i | \(0.369109\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.82693e6 | 0.234494 | 0.117247 | − | 0.993103i | \(-0.462593\pi\) | ||||
0.117247 | + | 0.993103i | \(0.462593\pi\) | |||||||
\(572\) | 925184. | 0.118233 | ||||||||
\(573\) | −3.69686e6 | −0.470377 | ||||||||
\(574\) | −358345. | −0.0453965 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.48408e6 | 0.186380 | ||||||||
\(577\) | 7.62349e6 | 0.953267 | 0.476633 | − | 0.879102i | \(-0.341857\pi\) | ||||
0.476633 | + | 0.879102i | \(0.341857\pi\) | |||||||
\(578\) | 6.69377e6 | 0.833395 | ||||||||
\(579\) | −1.35891e6 | −0.168460 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 144991. | 0.0178197 | ||||||||
\(582\) | −4.55331e6 | −0.557211 | ||||||||
\(583\) | 2.64041e6 | 0.321736 | ||||||||
\(584\) | 3.48414e6 | 0.422730 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.43427e6 | 0.533430 | ||||||||
\(587\) | 1.53545e7 | 1.83925 | 0.919623 | − | 0.392803i | \(-0.128495\pi\) | ||||
0.919623 | + | 0.392803i | \(0.128495\pi\) | |||||||
\(588\) | −1.41316e6 | −0.168558 | ||||||||
\(589\) | −2.44640e6 | −0.290562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.36461e6 | −0.160709 | ||||||||
\(592\) | 1.21420e7 | 1.42392 | ||||||||
\(593\) | −8.62212e6 | −1.00688 | −0.503439 | − | 0.864031i | \(-0.667932\pi\) | ||||
−0.503439 | + | 0.864031i | \(0.667932\pi\) | |||||||
\(594\) | 567548. | 0.0659988 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.60282e6 | −0.300144 | ||||||||
\(597\) | 4.18208e6 | 0.480238 | ||||||||
\(598\) | 2.85789e6 | 0.326808 | ||||||||
\(599\) | −2.18726e6 | −0.249077 | −0.124539 | − | 0.992215i | \(-0.539745\pi\) | ||||
−0.124539 | + | 0.992215i | \(0.539745\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.77734e6 | −0.426579 | −0.213290 | − | 0.976989i | \(-0.568418\pi\) | ||||
−0.213290 | + | 0.976989i | \(0.568418\pi\) | |||||||
\(602\) | −404395. | −0.0454793 | ||||||||
\(603\) | 3.15776e6 | 0.353660 | ||||||||
\(604\) | 3.06808e6 | 0.342196 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.27535e6 | −0.141075 | ||||||||
\(607\) | 1.39714e7 | 1.53910 | 0.769550 | − | 0.638587i | \(-0.220481\pi\) | ||||
0.769550 | + | 0.638587i | \(0.220481\pi\) | |||||||
\(608\) | 6.56920e6 | 0.720698 | ||||||||
\(609\) | −60172.2 | −0.00657434 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.68986e6 | −0.941694 | ||||||||
\(612\) | 468950. | 0.0506114 | ||||||||
\(613\) | 8.72631e6 | 0.937949 | 0.468974 | − | 0.883212i | \(-0.344624\pi\) | ||||
0.468974 | + | 0.883212i | \(0.344624\pi\) | |||||||
\(614\) | −6.34541e6 | −0.679264 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −175384. | −0.0186225 | ||||||||
\(617\) | 8.27444e6 | 0.875035 | 0.437518 | − | 0.899210i | \(-0.355858\pi\) | ||||
0.437518 | + | 0.899210i | \(0.355858\pi\) | |||||||
\(618\) | −4.92242e6 | −0.518451 | ||||||||
\(619\) | 1.25043e7 | 1.31169 | 0.655846 | − | 0.754894i | \(-0.272312\pi\) | ||||
0.655846 | + | 0.754894i | \(0.272312\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 397993. | 0.0414139 | ||||||||
\(622\) | 1.09561e7 | 1.13548 | ||||||||
\(623\) | −801829. | −0.0827678 | ||||||||
\(624\) | 9.05347e6 | 0.930794 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.88091e7 | 1.91837 | ||||||||
\(627\) | −2.16675e6 | −0.220110 | ||||||||
\(628\) | 3.44237e6 | 0.348304 | ||||||||
\(629\) | −6.04970e6 | −0.609688 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.59310e7 | 1.59283 | 0.796416 | − | 0.604750i | \(-0.206727\pi\) | ||||
0.796416 | + | 0.604750i | \(0.206727\pi\) | |||||||
\(632\) | −1.47669e7 | −1.47061 | ||||||||
\(633\) | −1.05528e7 | −1.04678 | ||||||||
\(634\) | 1.09248e7 | 1.07942 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.84570e6 | −0.180934 | ||||||||
\(637\) | 1.35933e7 | 1.32732 | ||||||||
\(638\) | −522228. | −0.0507935 | ||||||||
\(639\) | 2.04694e6 | 0.198314 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.06724e6 | −0.487109 | −0.243555 | − | 0.969887i | \(-0.578313\pi\) | ||||
−0.243555 | + | 0.969887i | \(0.578313\pi\) | |||||||
\(642\) | −7.47759e6 | −0.716019 | ||||||||
\(643\) | −5.24812e6 | −0.500583 | −0.250292 | − | 0.968170i | \(-0.580526\pi\) | ||||
−0.250292 | + | 0.968170i | \(0.580526\pi\) | |||||||
\(644\) | 51138.7 | 0.00485887 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.88637e6 | −0.743526 | ||||||||
\(647\) | −1.34119e7 | −1.25959 | −0.629797 | − | 0.776760i | \(-0.716862\pi\) | ||||
−0.629797 | + | 0.776760i | \(0.716862\pi\) | |||||||
\(648\) | 954129. | 0.0892626 | ||||||||
\(649\) | 261021. | 0.0243256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −110296. | −0.0102001 | ||||||||
\(652\) | 6.04029e6 | 0.556467 | ||||||||
\(653\) | −4.94854e6 | −0.454144 | −0.227072 | − | 0.973878i | \(-0.572915\pi\) | ||||
−0.227072 | + | 0.973878i | \(0.572915\pi\) | |||||||
\(654\) | 8.91545e6 | 0.815077 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.90888e6 | −0.626828 | ||||||||
\(657\) | 1.94063e6 | 0.175400 | ||||||||
\(658\) | −684954. | −0.0616732 | ||||||||
\(659\) | 1.09443e7 | 0.981687 | 0.490844 | − | 0.871248i | \(-0.336689\pi\) | ||||
0.490844 | + | 0.871248i | \(0.336689\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.35940e6 | −0.833191 | −0.416595 | − | 0.909092i | \(-0.636777\pi\) | ||||
−0.416595 | + | 0.909092i | \(0.636777\pi\) | |||||||
\(662\) | −9.26989e6 | −0.822109 | ||||||||
\(663\) | −4.51086e6 | −0.398543 | ||||||||
\(664\) | 2.11549e6 | 0.186205 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.11801e6 | 0.447111 | ||||||||
\(667\) | −366212. | −0.0318727 | ||||||||
\(668\) | −2.43585e6 | −0.211207 | ||||||||
\(669\) | −4.44948e6 | −0.384365 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 815999. | 0.0699654 | ||||||||
\(672\) | 296171. | 0.0253000 | ||||||||
\(673\) | 2.66957e6 | 0.227197 | 0.113599 | − | 0.993527i | \(-0.463762\pi\) | ||||
0.113599 | + | 0.993527i | \(0.463762\pi\) | |||||||
\(674\) | 6.22300e6 | 0.527655 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.73148e6 | 0.229896 | ||||||||
\(677\) | 1.36620e7 | 1.14563 | 0.572814 | − | 0.819685i | \(-0.305852\pi\) | ||||
0.572814 | + | 0.819685i | \(0.305852\pi\) | |||||||
\(678\) | 8.10389e6 | 0.677048 | ||||||||
\(679\) | 783724. | 0.0652362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.97477e6 | −0.163173 | ||||||||
\(682\) | −957243. | −0.0788064 | ||||||||
\(683\) | 5.01005e6 | 0.410951 | 0.205475 | − | 0.978662i | \(-0.434126\pi\) | ||||
0.205475 | + | 0.978662i | \(0.434126\pi\) | |||||||
\(684\) | 1.51460e6 | 0.123782 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.14928e6 | 0.174374 | ||||||||
\(687\) | −1.11287e7 | −0.899604 | ||||||||
\(688\) | −7.79671e6 | −0.627972 | ||||||||
\(689\) | 1.77539e7 | 1.42477 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.37818e6 | 0.109802 | 0.0549009 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549009 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(692\) | −2.28109e6 | −0.181083 | ||||||||
\(693\) | −97687.4 | −0.00772690 | ||||||||
\(694\) | 1.80880e7 | 1.42558 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −877939. | −0.0686976 | ||||||||
\(697\) | 3.44232e6 | 0.268392 | ||||||||
\(698\) | 1.05662e7 | 0.820879 | ||||||||
\(699\) | 757399. | 0.0586316 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.98776e7 | 1.52781 | 0.763906 | − | 0.645328i | \(-0.223279\pi\) | ||||
0.763906 | + | 0.645328i | \(0.223279\pi\) | |||||||
\(702\) | 3.81615e6 | 0.292269 | ||||||||
\(703\) | −1.95392e7 | −1.49114 | ||||||||
\(704\) | −2.21695e6 | −0.168587 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.86468e7 | 1.40797 | ||||||||
\(707\) | 219516. | 0.0165165 | ||||||||
\(708\) | −182459. | −0.0136799 | ||||||||
\(709\) | −5.68213e6 | −0.424518 | −0.212259 | − | 0.977213i | \(-0.568082\pi\) | ||||
−0.212259 | + | 0.977213i | \(0.568082\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.22505e6 | −0.610189 | ||||||||
\(712\) | −1.16991e7 | −0.864870 | ||||||||
\(713\) | −671267. | −0.0494506 | ||||||||
\(714\) | −355556. | −0.0261013 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.01290e6 | −0.146737 | ||||||||
\(717\) | −1.01939e6 | −0.0740533 | ||||||||
\(718\) | −1.95126e7 | −1.41255 | ||||||||
\(719\) | −4.90403e6 | −0.353778 | −0.176889 | − | 0.984231i | \(-0.556603\pi\) | ||||
−0.176889 | + | 0.984231i | \(0.556603\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 847256. | 0.0606983 | ||||||||
\(722\) | −9.53967e6 | −0.681068 | ||||||||
\(723\) | −5.54739e6 | −0.394678 | ||||||||
\(724\) | −2.32793e6 | −0.165053 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −847818. | −0.0596982 | ||||||||
\(727\) | 2.17098e7 | 1.52342 | 0.761711 | − | 0.647917i | \(-0.224359\pi\) | ||||
0.761711 | + | 0.647917i | \(0.224359\pi\) | |||||||
\(728\) | −1.17927e6 | −0.0824680 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.88468e6 | 0.268882 | ||||||||
\(732\) | −570402. | −0.0393462 | ||||||||
\(733\) | −1.22771e7 | −0.843985 | −0.421992 | − | 0.906599i | \(-0.638669\pi\) | ||||
−0.421992 | + | 0.906599i | \(0.638669\pi\) | |||||||
\(734\) | 7.52777e6 | 0.515734 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.80252e6 | 0.122655 | ||||||||
\(737\) | −4.71715e6 | −0.319898 | ||||||||
\(738\) | −2.91218e6 | −0.196824 | ||||||||
\(739\) | −1.86424e7 | −1.25571 | −0.627857 | − | 0.778329i | \(-0.716068\pi\) | ||||
−0.627857 | + | 0.778329i | \(0.716068\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.45690e7 | −0.974733 | ||||||||
\(742\) | 1.39940e6 | 0.0933111 | ||||||||
\(743\) | −9.40769e6 | −0.625188 | −0.312594 | − | 0.949887i | \(-0.601198\pi\) | ||||
−0.312594 | + | 0.949887i | \(0.601198\pi\) | |||||||
\(744\) | −1.60926e6 | −0.106585 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 9.49906e6 | 0.624933 | ||||||||
\(747\) | 1.17831e6 | 0.0772605 | ||||||||
\(748\) | −700531. | −0.0457797 | ||||||||
\(749\) | 1.28706e6 | 0.0838288 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.32683e6 | −0.215244 | −0.107622 | − | 0.994192i | \(-0.534324\pi\) | ||||
−0.107622 | + | 0.994192i | \(0.534324\pi\) | |||||||
\(752\) | −1.32059e7 | −0.851575 | ||||||||
\(753\) | −1.21346e7 | −0.779899 | ||||||||
\(754\) | −3.51142e6 | −0.224934 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 68285.7 | 0.00434535 | ||||||||
\(757\) | 3.52278e6 | 0.223432 | 0.111716 | − | 0.993740i | \(-0.464365\pi\) | ||||
0.111716 | + | 0.993740i | \(0.464365\pi\) | |||||||
\(758\) | −3.18555e7 | −2.01378 | ||||||||
\(759\) | −594533. | −0.0374603 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.43213e6 | 0.214833 | 0.107417 | − | 0.994214i | \(-0.465742\pi\) | ||||
0.107417 | + | 0.994214i | \(0.465742\pi\) | |||||||
\(762\) | −6.93620e6 | −0.432747 | ||||||||
\(763\) | −1.53454e6 | −0.0954263 | ||||||||
\(764\) | −3.86033e6 | −0.239272 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.08014e6 | 0.559140 | ||||||||
\(767\) | 1.75508e6 | 0.107723 | ||||||||
\(768\) | 7.66777e6 | 0.469101 | ||||||||
\(769\) | −1.40196e7 | −0.854908 | −0.427454 | − | 0.904037i | \(-0.640589\pi\) | ||||
−0.427454 | + | 0.904037i | \(0.640589\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.44171e6 | 0.390270 | ||||||||
\(772\) | −1.41900e6 | −0.0856920 | ||||||||
\(773\) | 3.40453e6 | 0.204931 | 0.102466 | − | 0.994737i | \(-0.467327\pi\) | ||||
0.102466 | + | 0.994737i | \(0.467327\pi\) | |||||||
\(774\) | −3.28641e6 | −0.197183 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.14349e7 | 0.681675 | ||||||||
\(777\) | −880921. | −0.0523461 | ||||||||
\(778\) | −8.73246e6 | −0.517235 | ||||||||
\(779\) | 1.11179e7 | 0.656418 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.05777e6 | −0.179382 | ||||||||
\(782\) | −2.16394e6 | −0.126540 | ||||||||
\(783\) | −489004. | −0.0285042 | ||||||||
\(784\) | 2.06576e7 | 1.20030 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.71667e6 | −0.560998 | ||||||||
\(787\) | −5.77229e6 | −0.332209 | −0.166105 | − | 0.986108i | \(-0.553119\pi\) | ||||
−0.166105 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(788\) | −1.42496e6 | −0.0817497 | ||||||||
\(789\) | −1.89029e7 | −1.08103 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.39486e6 | −0.0792662 | ||||||||
\(792\) | −1.42530e6 | −0.0807410 | ||||||||
\(793\) | 5.48672e6 | 0.309835 | ||||||||
\(794\) | 1.14185e7 | 0.642771 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.36701e6 | 0.244288 | ||||||||
\(797\) | −3.55488e7 | −1.98234 | −0.991171 | − | 0.132589i | \(-0.957671\pi\) | ||||
−0.991171 | + | 0.132589i | \(0.957671\pi\) | |||||||
\(798\) | −1.14837e6 | −0.0638370 | ||||||||
\(799\) | 6.57978e6 | 0.364624 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.51626e6 | −0.358854 | ||||||||
\(802\) | −2.37857e7 | −1.30581 | ||||||||
\(803\) | −2.89897e6 | −0.158655 | ||||||||
\(804\) | 3.29739e6 | 0.179900 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.43644e6 | −0.348986 | ||||||||
\(807\) | −1.27293e7 | −0.688052 | ||||||||
\(808\) | 3.20284e6 | 0.172587 | ||||||||
\(809\) | 8.35527e6 | 0.448838 | 0.224419 | − | 0.974493i | \(-0.427952\pi\) | ||||
0.224419 | + | 0.974493i | \(0.427952\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.83660e6 | 0.204831 | 0.102415 | − | 0.994742i | \(-0.467343\pi\) | ||||
0.102415 | + | 0.994742i | \(0.467343\pi\) | |||||||
\(812\) | −62832.9 | −0.00334424 | ||||||||
\(813\) | 1.71432e6 | 0.0909630 | ||||||||
\(814\) | −7.64542e6 | −0.404427 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.85510e6 | −0.360403 | ||||||||
\(817\) | 1.25466e7 | 0.657616 | ||||||||
\(818\) | 5.30491e6 | 0.277201 | ||||||||
\(819\) | −656843. | −0.0342178 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.99705e6 | −0.517624 | −0.258812 | − | 0.965928i | \(-0.583331\pi\) | ||||
−0.258812 | + | 0.965928i | \(0.583331\pi\) | |||||||
\(822\) | 1.35209e6 | 0.0697953 | ||||||||
\(823\) | 2.67331e7 | 1.37578 | 0.687890 | − | 0.725815i | \(-0.258537\pi\) | ||||
0.687890 | + | 0.725815i | \(0.258537\pi\) | |||||||
\(824\) | 1.23619e7 | 0.634257 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 138340. | 0.00705500 | ||||||||
\(827\) | −951161. | −0.0483605 | −0.0241802 | − | 0.999708i | \(-0.507698\pi\) | ||||
−0.0241802 | + | 0.999708i | \(0.507698\pi\) | |||||||
\(828\) | 415592. | 0.0210664 | ||||||||
\(829\) | −1.44000e7 | −0.727741 | −0.363870 | − | 0.931450i | \(-0.618545\pi\) | ||||
−0.363870 | + | 0.931450i | \(0.618545\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.98244e6 | −0.451223 | ||||||||
\(832\) | −1.49066e7 | −0.746572 | ||||||||
\(833\) | −1.02926e7 | −0.513938 | ||||||||
\(834\) | 6.28587e6 | 0.312932 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.26256e6 | −0.111965 | ||||||||
\(837\) | −896344. | −0.0442243 | ||||||||
\(838\) | 3.78265e7 | 1.86074 | ||||||||
\(839\) | 3.42903e6 | 0.168177 | 0.0840884 | − | 0.996458i | \(-0.473202\pi\) | ||||
0.0840884 | + | 0.996458i | \(0.473202\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.00612e7 | −0.978063 | ||||||||
\(842\) | −2.24371e7 | −1.09065 | ||||||||
\(843\) | −1.28779e7 | −0.624133 | ||||||||
\(844\) | −1.10194e7 | −0.532478 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.56645e6 | −0.267395 | ||||||||
\(847\) | 145928. | 0.00698924 | ||||||||
\(848\) | 2.69804e7 | 1.28843 | ||||||||
\(849\) | 2.16446e7 | 1.03058 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.36135e6 | −0.253776 | ||||||||
\(852\) | 2.13745e6 | 0.100878 | ||||||||
\(853\) | −1.57990e7 | −0.743460 | −0.371730 | − | 0.928341i | \(-0.621235\pi\) | ||||
−0.371730 | + | 0.928341i | \(0.621235\pi\) | |||||||
\(854\) | 432476. | 0.0202916 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.87788e7 | 0.875956 | ||||||||
\(857\) | −5.06147e6 | −0.235410 | −0.117705 | − | 0.993049i | \(-0.537554\pi\) | ||||
−0.117705 | + | 0.993049i | \(0.537554\pi\) | |||||||
\(858\) | −5.70067e6 | −0.264367 | ||||||||
\(859\) | −2.48302e7 | −1.14815 | −0.574074 | − | 0.818803i | \(-0.694638\pi\) | ||||
−0.574074 | + | 0.818803i | \(0.694638\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 501250. | 0.0230434 | ||||||||
\(862\) | 2.83890e7 | 1.30131 | ||||||||
\(863\) | −1.03123e7 | −0.471336 | −0.235668 | − | 0.971834i | \(-0.575728\pi\) | ||||
−0.235668 | + | 0.971834i | \(0.575728\pi\) | |||||||
\(864\) | 2.40691e6 | 0.109692 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.36800e6 | 0.288541 | ||||||||
\(867\) | −9.36318e6 | −0.423035 | ||||||||
\(868\) | −115173. | −0.00518860 | ||||||||
\(869\) | 1.22868e7 | 0.551937 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.17178e7 | −1.41663 | ||||||||
\(872\) | −2.23897e7 | −0.997142 | ||||||||
\(873\) | 6.36913e6 | 0.282842 | ||||||||
\(874\) | −6.98904e6 | −0.309484 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.02645e6 | 0.0892226 | ||||||||
\(877\) | −1.04098e7 | −0.457027 | −0.228514 | − | 0.973541i | \(-0.573387\pi\) | ||||
−0.228514 | + | 0.973541i | \(0.573387\pi\) | |||||||
\(878\) | 1.73453e7 | 0.759355 | ||||||||
\(879\) | −6.20261e6 | −0.270771 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.99961e7 | −0.867970 | −0.433985 | − | 0.900920i | \(-0.642893\pi\) | ||||
−0.433985 | + | 0.900920i | \(0.642893\pi\) | |||||||
\(882\) | 8.70743e6 | 0.376894 | ||||||||
\(883\) | 2.42565e7 | 1.04695 | 0.523475 | − | 0.852041i | \(-0.324636\pi\) | ||||
0.523475 | + | 0.852041i | \(0.324636\pi\) | |||||||
\(884\) | −4.71032e6 | −0.202731 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.18856e7 | 0.508671 | ||||||||
\(887\) | −3.28464e7 | −1.40178 | −0.700888 | − | 0.713271i | \(-0.747213\pi\) | ||||
−0.700888 | + | 0.713271i | \(0.747213\pi\) | |||||||
\(888\) | −1.28530e7 | −0.546983 | ||||||||
\(889\) | 1.19387e6 | 0.0506644 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −793881. | −0.0335013 | ||||||||
\(892\) | −4.64624e6 | −0.195519 | ||||||||
\(893\) | 2.12512e7 | 0.891775 | ||||||||
\(894\) | 1.60377e7 | 0.671118 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.22803e6 | −0.0927151 | ||||||||
\(897\) | −3.99760e6 | −0.165889 | ||||||||
\(898\) | 5.18781e6 | 0.214681 | ||||||||
\(899\) | 824769. | 0.0340356 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.34429e7 | −0.551672 | ||||||||
\(902\) | 4.35030e6 | 0.178034 | ||||||||
\(903\) | 565664. | 0.0230855 | ||||||||
\(904\) | −2.03516e7 | −0.828280 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.89045e7 | −0.765146 | ||||||||
\(907\) | 1.54289e7 | 0.622753 | 0.311377 | − | 0.950287i | \(-0.399210\pi\) | ||||
0.311377 | + | 0.950287i | \(0.399210\pi\) | |||||||
\(908\) | −2.06209e6 | −0.0830029 | ||||||||
\(909\) | 1.78395e6 | 0.0716101 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.82548e7 | 1.52718 | 0.763590 | − | 0.645701i | \(-0.223435\pi\) | ||||
0.763590 | + | 0.645701i | \(0.223435\pi\) | |||||||
\(912\) | −2.21404e7 | −0.881453 | ||||||||
\(913\) | −1.76019e6 | −0.0698847 | ||||||||
\(914\) | 3.07849e7 | 1.21891 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.16208e7 | −0.457611 | ||||||||
\(917\) | 1.67245e6 | 0.0656795 | ||||||||
\(918\) | −2.88951e6 | −0.113167 | ||||||||
\(919\) | 3.21575e7 | 1.25601 | 0.628005 | − | 0.778209i | \(-0.283872\pi\) | ||||
0.628005 | + | 0.778209i | \(0.283872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.87591e6 | 0.344797 | ||||||||
\(922\) | 5.17966e7 | 2.00666 | ||||||||
\(923\) | −2.05603e7 | −0.794373 | ||||||||
\(924\) | −102007. | −0.00393052 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.15868e6 | −0.159378 | ||||||||
\(927\) | 6.88544e6 | 0.263168 | ||||||||
\(928\) | −2.21471e6 | −0.0844204 | ||||||||
\(929\) | 2.16438e7 | 0.822802 | 0.411401 | − | 0.911455i | \(-0.365040\pi\) | ||||
0.411401 | + | 0.911455i | \(0.365040\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.32426e7 | −1.25696 | ||||||||
\(932\) | 790890. | 0.0298247 | ||||||||
\(933\) | −1.53253e7 | −0.576374 | ||||||||
\(934\) | −3.84512e7 | −1.44226 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −9.58364e6 | −0.357554 | ||||||||
\(937\) | 2.80993e7 | 1.04555 | 0.522776 | − | 0.852470i | \(-0.324896\pi\) | ||||
0.522776 | + | 0.852470i | \(0.324896\pi\) | |||||||
\(938\) | −2.50007e6 | −0.0927779 | ||||||||
\(939\) | −2.63100e7 | −0.973770 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.13300e7 | −0.417116 | −0.208558 | − | 0.978010i | \(-0.566877\pi\) | ||||
−0.208558 | + | 0.978010i | \(0.566877\pi\) | |||||||
\(942\) | −2.12107e7 | −0.778804 | ||||||||
\(943\) | 3.05065e6 | 0.111715 | ||||||||
\(944\) | 2.66718e6 | 0.0974144 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.90933e6 | 0.178359 | ||||||||
\(947\) | 3.04381e7 | 1.10292 | 0.551458 | − | 0.834203i | \(-0.314072\pi\) | ||||
0.551458 | + | 0.834203i | \(0.314072\pi\) | |||||||
\(948\) | −8.58875e6 | −0.310391 | ||||||||
\(949\) | −1.94925e7 | −0.702589 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.52815e7 | −0.547918 | ||||||||
\(952\) | 892920. | 0.0319316 | ||||||||
\(953\) | −2.97688e7 | −1.06177 | −0.530883 | − | 0.847445i | \(-0.678140\pi\) | ||||
−0.530883 | + | 0.847445i | \(0.678140\pi\) | |||||||
\(954\) | 1.13726e7 | 0.404566 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.06447e6 | −0.0376694 | ||||||||
\(957\) | 730488. | 0.0257830 | ||||||||
\(958\) | 4.85060e7 | 1.70758 | ||||||||
\(959\) | −232724. | −0.00817137 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.71174e7 | −0.947194 | ||||||||
\(962\) | −5.14073e7 | −1.79096 | ||||||||
\(963\) | 1.04596e7 | 0.363454 | ||||||||
\(964\) | −5.79270e6 | −0.200765 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −315100. | −0.0108644 | ||||||||
\(967\) | −1.65127e7 | −0.567875 | −0.283937 | − | 0.958843i | \(-0.591641\pi\) | ||||
−0.283937 | + | 0.958843i | \(0.591641\pi\) | |||||||
\(968\) | 2.12916e6 | 0.0730330 | ||||||||
\(969\) | 1.10314e7 | 0.377416 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.43022e7 | 1.16755 | 0.583773 | − | 0.811917i | \(-0.301576\pi\) | ||||
0.583773 | + | 0.811917i | \(0.301576\pi\) | |||||||
\(972\) | 554941. | 0.0188400 | ||||||||
\(973\) | −1.08194e6 | −0.0366370 | ||||||||
\(974\) | −4.32467e7 | −1.46068 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.33811e6 | 0.280184 | ||||||||
\(977\) | 4.76980e7 | 1.59869 | 0.799344 | − | 0.600873i | \(-0.205180\pi\) | ||||
0.799344 | + | 0.600873i | \(0.205180\pi\) | |||||||
\(978\) | −3.72182e7 | −1.24425 | ||||||||
\(979\) | 9.73417e6 | 0.324595 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.24709e7 | −0.413736 | ||||||||
\(982\) | 1.53711e7 | 0.508660 | ||||||||
\(983\) | 4.43331e6 | 0.146334 | 0.0731669 | − | 0.997320i | \(-0.476689\pi\) | ||||
0.0731669 | + | 0.997320i | \(0.476689\pi\) | |||||||
\(984\) | 7.31347e6 | 0.240789 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.65878e6 | 0.0870944 | ||||||||
\(987\) | 958108. | 0.0313056 | ||||||||
\(988\) | −1.52133e7 | −0.495827 | ||||||||
\(989\) | 3.44267e6 | 0.111919 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.98431e6 | −0.322949 | −0.161474 | − | 0.986877i | \(-0.551625\pi\) | ||||
−0.161474 | + | 0.986877i | \(0.551625\pi\) | |||||||
\(992\) | −4.05957e6 | −0.130979 | ||||||||
\(993\) | 1.29666e7 | 0.417306 | ||||||||
\(994\) | −1.62061e6 | −0.0520249 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.23041e6 | 0.0393009 | ||||||||
\(997\) | −3.98385e7 | −1.26930 | −0.634652 | − | 0.772798i | \(-0.718856\pi\) | ||||
−0.634652 | + | 0.772798i | \(0.718856\pi\) | |||||||
\(998\) | 3.07595e7 | 0.977581 | ||||||||
\(999\) | −7.15903e6 | −0.226955 |
(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 | 825.6.a.p.1.3 | ✓ | 8 | |
5.4 | even | 2 | 825.6.a.q.1.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.p.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
825.6.a.q.1.6 | yes | 8 | 5.4 | even | 2 |