Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [245,6,Mod(1,245)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(245, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("245.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 245 = 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 245.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: | \(39.2940358542\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 109x^{4} + 41x^{3} + 2208x^{2} - 3204x + 560 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 35) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(4.12050\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 245.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.12050 | 0.551631 | 0.275816 | − | 0.961211i | \(-0.411052\pi\) | ||||
0.275816 | + | 0.961211i | \(0.411052\pi\) | |||||||
\(3\) | 27.8717 | 1.78797 | 0.893986 | − | 0.448096i | \(-0.147898\pi\) | ||||
0.893986 | + | 0.448096i | \(0.147898\pi\) | |||||||
\(4\) | −22.2625 | −0.695703 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 86.9736 | 0.986301 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −169.326 | −0.935403 | ||||||||
\(9\) | 533.832 | 2.19684 | ||||||||
\(10\) | −78.0125 | −0.246697 | ||||||||
\(11\) | −405.258 | −1.00983 | −0.504916 | − | 0.863168i | \(-0.668477\pi\) | ||||
−0.504916 | + | 0.863168i | \(0.668477\pi\) | |||||||
\(12\) | −620.494 | −1.24390 | ||||||||
\(13\) | −931.313 | −1.52840 | −0.764200 | − | 0.644979i | \(-0.776866\pi\) | ||||
−0.764200 | + | 0.644979i | \(0.776866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −696.793 | −0.799605 | ||||||||
\(16\) | 184.018 | 0.179705 | ||||||||
\(17\) | −736.293 | −0.617914 | −0.308957 | − | 0.951076i | \(-0.599980\pi\) | ||||
−0.308957 | + | 0.951076i | \(0.599980\pi\) | |||||||
\(18\) | 1665.82 | 1.21185 | ||||||||
\(19\) | −994.229 | −0.631833 | −0.315917 | − | 0.948787i | \(-0.602312\pi\) | ||||
−0.315917 | + | 0.948787i | \(0.602312\pi\) | |||||||
\(20\) | 556.562 | 0.311128 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1264.61 | −0.557055 | ||||||||
\(23\) | 1224.83 | 0.482789 | 0.241394 | − | 0.970427i | \(-0.422395\pi\) | ||||
0.241394 | + | 0.970427i | \(0.422395\pi\) | |||||||
\(24\) | −4719.41 | −1.67247 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −2906.16 | −0.843114 | ||||||||
\(27\) | 8106.00 | 2.13992 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5585.88 | −1.23338 | −0.616689 | − | 0.787207i | \(-0.711527\pi\) | ||||
−0.616689 | + | 0.787207i | \(0.711527\pi\) | |||||||
\(30\) | −2174.34 | −0.441087 | ||||||||
\(31\) | 3149.58 | 0.588638 | 0.294319 | − | 0.955707i | \(-0.404907\pi\) | ||||
0.294319 | + | 0.955707i | \(0.404907\pi\) | |||||||
\(32\) | 5992.66 | 1.03453 | ||||||||
\(33\) | −11295.2 | −1.80555 | ||||||||
\(34\) | −2297.60 | −0.340861 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11884.4 | −1.52835 | ||||||||
\(37\) | −9613.78 | −1.15449 | −0.577245 | − | 0.816571i | \(-0.695872\pi\) | ||||
−0.577245 | + | 0.816571i | \(0.695872\pi\) | |||||||
\(38\) | −3102.49 | −0.348539 | ||||||||
\(39\) | −25957.3 | −2.73274 | ||||||||
\(40\) | 4233.15 | 0.418325 | ||||||||
\(41\) | −14680.2 | −1.36387 | −0.681933 | − | 0.731414i | \(-0.738861\pi\) | ||||
−0.681933 | + | 0.731414i | \(0.738861\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3526.05 | 0.290815 | 0.145408 | − | 0.989372i | \(-0.453551\pi\) | ||||
0.145408 | + | 0.989372i | \(0.453551\pi\) | |||||||
\(44\) | 9022.04 | 0.702544 | ||||||||
\(45\) | −13345.8 | −0.982457 | ||||||||
\(46\) | 3822.09 | 0.266321 | ||||||||
\(47\) | 18567.6 | 1.22606 | 0.613031 | − | 0.790059i | \(-0.289950\pi\) | ||||
0.613031 | + | 0.790059i | \(0.289950\pi\) | |||||||
\(48\) | 5128.90 | 0.321308 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1950.31 | 0.110326 | ||||||||
\(51\) | −20521.7 | −1.10481 | ||||||||
\(52\) | 20733.3 | 1.06331 | ||||||||
\(53\) | −5457.99 | −0.266896 | −0.133448 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133448 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(54\) | 25294.8 | 1.18045 | ||||||||
\(55\) | 10131.4 | 0.451611 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27710.9 | −1.12970 | ||||||||
\(58\) | −17430.7 | −0.680371 | ||||||||
\(59\) | −7767.95 | −0.290520 | −0.145260 | − | 0.989393i | \(-0.546402\pi\) | ||||
−0.145260 | + | 0.989393i | \(0.546402\pi\) | |||||||
\(60\) | 15512.3 | 0.556287 | ||||||||
\(61\) | 18874.7 | 0.649465 | 0.324733 | − | 0.945806i | \(-0.394726\pi\) | ||||
0.324733 | + | 0.945806i | \(0.394726\pi\) | |||||||
\(62\) | 9828.25 | 0.324711 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12811.5 | 0.390976 | ||||||||
\(65\) | 23282.8 | 0.683522 | ||||||||
\(66\) | −35246.7 | −0.995999 | ||||||||
\(67\) | −66704.4 | −1.81538 | −0.907691 | − | 0.419640i | \(-0.862156\pi\) | ||||
−0.907691 | + | 0.419640i | \(0.862156\pi\) | |||||||
\(68\) | 16391.7 | 0.429885 | ||||||||
\(69\) | 34138.2 | 0.863212 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 30994.2 | 0.729683 | 0.364842 | − | 0.931070i | \(-0.381123\pi\) | ||||
0.364842 | + | 0.931070i | \(0.381123\pi\) | |||||||
\(72\) | −90391.7 | −2.05493 | ||||||||
\(73\) | 37314.5 | 0.819541 | 0.409771 | − | 0.912189i | \(-0.365609\pi\) | ||||
0.409771 | + | 0.912189i | \(0.365609\pi\) | |||||||
\(74\) | −29999.8 | −0.636852 | ||||||||
\(75\) | 17419.8 | 0.357594 | ||||||||
\(76\) | 22134.0 | 0.439568 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −80999.7 | −1.50746 | ||||||||
\(79\) | −15661.5 | −0.282335 | −0.141167 | − | 0.989986i | \(-0.545086\pi\) | ||||
−0.141167 | + | 0.989986i | \(0.545086\pi\) | |||||||
\(80\) | −4600.45 | −0.0803666 | ||||||||
\(81\) | 96206.8 | 1.62927 | ||||||||
\(82\) | −45809.5 | −0.752352 | ||||||||
\(83\) | 70001.9 | 1.11536 | 0.557679 | − | 0.830057i | \(-0.311692\pi\) | ||||
0.557679 | + | 0.830057i | \(0.311692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18407.3 | 0.276340 | ||||||||
\(86\) | 11003.0 | 0.160423 | ||||||||
\(87\) | −155688. | −2.20525 | ||||||||
\(88\) | 68620.7 | 0.944601 | ||||||||
\(89\) | −7904.17 | −0.105775 | −0.0528873 | − | 0.998600i | \(-0.516842\pi\) | ||||
−0.0528873 | + | 0.998600i | \(0.516842\pi\) | |||||||
\(90\) | −41645.6 | −0.541954 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −27267.8 | −0.335877 | ||||||||
\(93\) | 87784.1 | 1.05247 | ||||||||
\(94\) | 57940.3 | 0.676334 | ||||||||
\(95\) | 24855.7 | 0.282564 | ||||||||
\(96\) | 167026. | 1.84972 | ||||||||
\(97\) | −149459. | −1.61284 | −0.806420 | − | 0.591343i | \(-0.798598\pi\) | ||||
−0.806420 | + | 0.591343i | \(0.798598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −216340. | −2.21844 | ||||||||
\(100\) | −13914.1 | −0.139141 | ||||||||
\(101\) | −126933. | −1.23814 | −0.619070 | − | 0.785336i | \(-0.712490\pi\) | ||||
−0.619070 | + | 0.785336i | \(0.712490\pi\) | |||||||
\(102\) | −64038.1 | −0.609450 | ||||||||
\(103\) | 13500.5 | 0.125388 | 0.0626941 | − | 0.998033i | \(-0.480031\pi\) | ||||
0.0626941 | + | 0.998033i | \(0.480031\pi\) | |||||||
\(104\) | 157696. | 1.42967 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17031.6 | −0.147228 | ||||||||
\(107\) | 74431.6 | 0.628489 | 0.314245 | − | 0.949342i | \(-0.398249\pi\) | ||||
0.314245 | + | 0.949342i | \(0.398249\pi\) | |||||||
\(108\) | −180460. | −1.48875 | ||||||||
\(109\) | 137681. | 1.10996 | 0.554982 | − | 0.831862i | \(-0.312725\pi\) | ||||
0.554982 | + | 0.831862i | \(0.312725\pi\) | |||||||
\(110\) | 31615.1 | 0.249123 | ||||||||
\(111\) | −267953. | −2.06419 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 62258.8 | 0.458674 | 0.229337 | − | 0.973347i | \(-0.426344\pi\) | ||||
0.229337 | + | 0.973347i | \(0.426344\pi\) | |||||||
\(114\) | −86471.7 | −0.623178 | ||||||||
\(115\) | −30620.8 | −0.215910 | ||||||||
\(116\) | 124356. | 0.858065 | ||||||||
\(117\) | −497165. | −3.35765 | ||||||||
\(118\) | −24239.9 | −0.160260 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 117985. | 0.747953 | ||||||||
\(121\) | 3182.74 | 0.0197623 | ||||||||
\(122\) | 58898.5 | 0.358265 | ||||||||
\(123\) | −409162. | −2.43855 | ||||||||
\(124\) | −70117.4 | −0.409517 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −264361. | −1.45442 | −0.727208 | − | 0.686417i | \(-0.759183\pi\) | ||||
−0.727208 | + | 0.686417i | \(0.759183\pi\) | |||||||
\(128\) | −151787. | −0.818859 | ||||||||
\(129\) | 98277.0 | 0.519969 | ||||||||
\(130\) | 72654.0 | 0.377052 | ||||||||
\(131\) | 109994. | 0.560006 | 0.280003 | − | 0.959999i | \(-0.409665\pi\) | ||||
0.280003 | + | 0.959999i | \(0.409665\pi\) | |||||||
\(132\) | 251460. | 1.25613 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −208151. | −1.00142 | ||||||||
\(135\) | −202650. | −0.957000 | ||||||||
\(136\) | 124674. | 0.577999 | ||||||||
\(137\) | −281879. | −1.28310 | −0.641552 | − | 0.767080i | \(-0.721709\pi\) | ||||
−0.641552 | + | 0.767080i | \(0.721709\pi\) | |||||||
\(138\) | 106528. | 0.476175 | ||||||||
\(139\) | 236209. | 1.03696 | 0.518478 | − | 0.855091i | \(-0.326499\pi\) | ||||
0.518478 | + | 0.855091i | \(0.326499\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 517512. | 2.19216 | ||||||||
\(142\) | 96717.3 | 0.402516 | ||||||||
\(143\) | 377422. | 1.54343 | ||||||||
\(144\) | 98234.8 | 0.394784 | ||||||||
\(145\) | 139647. | 0.551584 | ||||||||
\(146\) | 116440. | 0.452085 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 214027. | 0.803181 | ||||||||
\(149\) | −25639.9 | −0.0946128 | −0.0473064 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473064 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(150\) | 54358.5 | 0.197260 | ||||||||
\(151\) | 262577. | 0.937162 | 0.468581 | − | 0.883420i | \(-0.344765\pi\) | ||||
0.468581 | + | 0.883420i | \(0.344765\pi\) | |||||||
\(152\) | 168349. | 0.591019 | ||||||||
\(153\) | −393057. | −1.35746 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −78739.4 | −0.263247 | ||||||||
\(156\) | 577874. | 1.90117 | ||||||||
\(157\) | 262263. | 0.849157 | 0.424578 | − | 0.905391i | \(-0.360422\pi\) | ||||
0.424578 | + | 0.905391i | \(0.360422\pi\) | |||||||
\(158\) | −48871.6 | −0.155745 | ||||||||
\(159\) | −152123. | −0.477203 | ||||||||
\(160\) | −149817. | −0.462658 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 300213. | 0.898757 | ||||||||
\(163\) | 285382. | 0.841312 | 0.420656 | − | 0.907220i | \(-0.361800\pi\) | ||||
0.420656 | + | 0.907220i | \(0.361800\pi\) | |||||||
\(164\) | 326817. | 0.948846 | ||||||||
\(165\) | 282381. | 0.807467 | ||||||||
\(166\) | 218441. | 0.615267 | ||||||||
\(167\) | 467133. | 1.29613 | 0.648067 | − | 0.761583i | \(-0.275578\pi\) | ||||
0.648067 | + | 0.761583i | \(0.275578\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 496051. | 1.33601 | ||||||||
\(170\) | 57440.0 | 0.152438 | ||||||||
\(171\) | −530752. | −1.38804 | ||||||||
\(172\) | −78498.6 | −0.202321 | ||||||||
\(173\) | −30164.3 | −0.0766263 | −0.0383132 | − | 0.999266i | \(-0.512198\pi\) | ||||
−0.0383132 | + | 0.999266i | \(0.512198\pi\) | |||||||
\(174\) | −485824. | −1.21648 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −74574.8 | −0.181472 | ||||||||
\(177\) | −216506. | −0.519442 | ||||||||
\(178\) | −24664.9 | −0.0583486 | ||||||||
\(179\) | −594377. | −1.38653 | −0.693265 | − | 0.720683i | \(-0.743828\pi\) | ||||
−0.693265 | + | 0.720683i | \(0.743828\pi\) | |||||||
\(180\) | 297111. | 0.683498 | ||||||||
\(181\) | 155232. | 0.352197 | 0.176099 | − | 0.984373i | \(-0.443652\pi\) | ||||
0.176099 | + | 0.984373i | \(0.443652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 526071. | 1.16123 | ||||||||
\(184\) | −207396. | −0.451602 | ||||||||
\(185\) | 240344. | 0.516303 | ||||||||
\(186\) | 273930. | 0.580574 | ||||||||
\(187\) | 298388. | 0.623990 | ||||||||
\(188\) | −413362. | −0.852974 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 77562.2 | 0.155871 | ||||||||
\(191\) | 320961. | 0.636603 | 0.318302 | − | 0.947990i | \(-0.396888\pi\) | ||||
0.318302 | + | 0.947990i | \(0.396888\pi\) | |||||||
\(192\) | 357079. | 0.699054 | ||||||||
\(193\) | −727235. | −1.40534 | −0.702670 | − | 0.711516i | \(-0.748009\pi\) | ||||
−0.702670 | + | 0.711516i | \(0.748009\pi\) | |||||||
\(194\) | −466385. | −0.889693 | ||||||||
\(195\) | 648932. | 1.22212 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −752919. | −1.38224 | −0.691119 | − | 0.722741i | \(-0.742882\pi\) | ||||
−0.691119 | + | 0.722741i | \(0.742882\pi\) | |||||||
\(198\) | −675088. | −1.22376 | ||||||||
\(199\) | 96635.3 | 0.172983 | 0.0864915 | − | 0.996253i | \(-0.472434\pi\) | ||||
0.0864915 | + | 0.996253i | \(0.472434\pi\) | |||||||
\(200\) | −105829. | −0.187081 | ||||||||
\(201\) | −1.85917e6 | −3.24585 | ||||||||
\(202\) | −396093. | −0.682996 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 456865. | 0.768622 | ||||||||
\(205\) | 367005. | 0.609940 | ||||||||
\(206\) | 42128.3 | 0.0691681 | ||||||||
\(207\) | 653855. | 1.06061 | ||||||||
\(208\) | −171378. | −0.274662 | ||||||||
\(209\) | 402919. | 0.638046 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −373868. | −0.578112 | −0.289056 | − | 0.957312i | \(-0.593341\pi\) | ||||
−0.289056 | + | 0.957312i | \(0.593341\pi\) | |||||||
\(212\) | 121508. | 0.185681 | ||||||||
\(213\) | 863861. | 1.30465 | ||||||||
\(214\) | 232264. | 0.346694 | ||||||||
\(215\) | −88151.2 | −0.130057 | ||||||||
\(216\) | −1.37256e6 | −2.00169 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 429634. | 0.612291 | ||||||||
\(219\) | 1.04002e6 | 1.46532 | ||||||||
\(220\) | −225551. | −0.314187 | ||||||||
\(221\) | 685719. | 0.944421 | ||||||||
\(222\) | −836145. | −1.13867 | ||||||||
\(223\) | 545786. | 0.734954 | 0.367477 | − | 0.930033i | \(-0.380222\pi\) | ||||
0.367477 | + | 0.930033i | \(0.380222\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 333645. | 0.439368 | ||||||||
\(226\) | 194278. | 0.253019 | ||||||||
\(227\) | −123277. | −0.158787 | −0.0793937 | − | 0.996843i | \(-0.525298\pi\) | ||||
−0.0793937 | + | 0.996843i | \(0.525298\pi\) | |||||||
\(228\) | 616913. | 0.785935 | ||||||||
\(229\) | 1.07833e6 | 1.35882 | 0.679412 | − | 0.733757i | \(-0.262235\pi\) | ||||
0.679412 | + | 0.733757i | \(0.262235\pi\) | |||||||
\(230\) | −95552.2 | −0.119103 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 945835. | 1.15371 | ||||||||
\(233\) | 141208. | 0.170400 | 0.0852002 | − | 0.996364i | \(-0.472847\pi\) | ||||
0.0852002 | + | 0.996364i | \(0.472847\pi\) | |||||||
\(234\) | −1.55140e6 | −1.85219 | ||||||||
\(235\) | −464191. | −0.548311 | ||||||||
\(236\) | 172934. | 0.202116 | ||||||||
\(237\) | −436512. | −0.504807 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −508655. | −0.576008 | −0.288004 | − | 0.957629i | \(-0.592992\pi\) | ||||
−0.288004 | + | 0.957629i | \(0.592992\pi\) | |||||||
\(240\) | −128223. | −0.143693 | ||||||||
\(241\) | −25696.1 | −0.0284987 | −0.0142493 | − | 0.999898i | \(-0.504536\pi\) | ||||
−0.0142493 | + | 0.999898i | \(0.504536\pi\) | |||||||
\(242\) | 9931.75 | 0.0109015 | ||||||||
\(243\) | 711691. | 0.773171 | ||||||||
\(244\) | −420198. | −0.451835 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.27679e6 | −1.34518 | ||||||||
\(247\) | 925938. | 0.965694 | ||||||||
\(248\) | −533305. | −0.550613 | ||||||||
\(249\) | 1.95107e6 | 1.99423 | ||||||||
\(250\) | −48757.8 | −0.0493394 | ||||||||
\(251\) | −30939.4 | −0.0309975 | −0.0154988 | − | 0.999880i | \(-0.504934\pi\) | ||||
−0.0154988 | + | 0.999880i | \(0.504934\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −496373. | −0.487536 | ||||||||
\(254\) | −824939. | −0.802302 | ||||||||
\(255\) | 513044. | 0.494087 | ||||||||
\(256\) | −883619. | −0.842685 | ||||||||
\(257\) | 256109. | 0.241876 | 0.120938 | − | 0.992660i | \(-0.461410\pi\) | ||||
0.120938 | + | 0.992660i | \(0.461410\pi\) | |||||||
\(258\) | 306673. | 0.286831 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −518334. | −0.475528 | ||||||||
\(261\) | −2.98192e6 | −2.70954 | ||||||||
\(262\) | 343238. | 0.308917 | ||||||||
\(263\) | 1.02074e6 | 0.909969 | 0.454985 | − | 0.890499i | \(-0.349645\pi\) | ||||
0.454985 | + | 0.890499i | \(0.349645\pi\) | |||||||
\(264\) | 1.91258e6 | 1.68892 | ||||||||
\(265\) | 136450. | 0.119360 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −220303. | −0.189122 | ||||||||
\(268\) | 1.48501e6 | 1.26297 | ||||||||
\(269\) | −493765. | −0.416045 | −0.208022 | − | 0.978124i | \(-0.566703\pi\) | ||||
−0.208022 | + | 0.978124i | \(0.566703\pi\) | |||||||
\(270\) | −632369. | −0.527911 | ||||||||
\(271\) | −1.47579e6 | −1.22068 | −0.610340 | − | 0.792140i | \(-0.708967\pi\) | ||||
−0.610340 | + | 0.792140i | \(0.708967\pi\) | |||||||
\(272\) | −135491. | −0.111042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −879604. | −0.707800 | ||||||||
\(275\) | −253286. | −0.201967 | ||||||||
\(276\) | −760001. | −0.600539 | ||||||||
\(277\) | −877911. | −0.687466 | −0.343733 | − | 0.939067i | \(-0.611692\pi\) | ||||
−0.343733 | + | 0.939067i | \(0.611692\pi\) | |||||||
\(278\) | 737091. | 0.572017 | ||||||||
\(279\) | 1.68135e6 | 1.29314 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.46598e6 | −1.10755 | −0.553774 | − | 0.832667i | \(-0.686813\pi\) | ||||
−0.553774 | + | 0.832667i | \(0.686813\pi\) | |||||||
\(282\) | 1.61490e6 | 1.20927 | ||||||||
\(283\) | 1.73108e6 | 1.28484 | 0.642422 | − | 0.766351i | \(-0.277929\pi\) | ||||
0.642422 | + | 0.766351i | \(0.277929\pi\) | |||||||
\(284\) | −690008. | −0.507643 | ||||||||
\(285\) | 692772. | 0.505217 | ||||||||
\(286\) | 1.17774e6 | 0.851404 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.19908e6 | 2.27271 | ||||||||
\(289\) | −877730. | −0.618182 | ||||||||
\(290\) | 435768. | 0.304271 | ||||||||
\(291\) | −4.16566e6 | −2.88371 | ||||||||
\(292\) | −830714. | −0.570157 | ||||||||
\(293\) | −623726. | −0.424449 | −0.212224 | − | 0.977221i | \(-0.568071\pi\) | ||||
−0.212224 | + | 0.977221i | \(0.568071\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 194199. | 0.129925 | ||||||||
\(296\) | 1.62786e6 | 1.07991 | ||||||||
\(297\) | −3.28502e6 | −2.16096 | ||||||||
\(298\) | −80009.1 | −0.0521914 | ||||||||
\(299\) | −1.14070e6 | −0.737895 | ||||||||
\(300\) | −387809. | −0.248779 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 819372. | 0.516968 | ||||||||
\(303\) | −3.53783e6 | −2.21376 | ||||||||
\(304\) | −182956. | −0.113544 | ||||||||
\(305\) | −471868. | −0.290450 | ||||||||
\(306\) | −1.22653e6 | −0.748817 | ||||||||
\(307\) | −1.92297e6 | −1.16446 | −0.582232 | − | 0.813022i | \(-0.697821\pi\) | ||||
−0.582232 | + | 0.813022i | \(0.697821\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 376282. | 0.224191 | ||||||||
\(310\) | −245706. | −0.145215 | ||||||||
\(311\) | 2.10305e6 | 1.23296 | 0.616478 | − | 0.787372i | \(-0.288559\pi\) | ||||
0.616478 | + | 0.787372i | \(0.288559\pi\) | |||||||
\(312\) | 4.39524e6 | 2.55621 | ||||||||
\(313\) | 2.74351e6 | 1.58287 | 0.791437 | − | 0.611250i | \(-0.209333\pi\) | ||||
0.791437 | + | 0.611250i | \(0.209333\pi\) | |||||||
\(314\) | 818391. | 0.468422 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 348663. | 0.196421 | ||||||||
\(317\) | −1.51211e6 | −0.845150 | −0.422575 | − | 0.906328i | \(-0.638874\pi\) | ||||
−0.422575 | + | 0.906328i | \(0.638874\pi\) | |||||||
\(318\) | −474701. | −0.263240 | ||||||||
\(319\) | 2.26372e6 | 1.24551 | ||||||||
\(320\) | −320288. | −0.174850 | ||||||||
\(321\) | 2.07454e6 | 1.12372 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 732044. | 0.390419 | ||||||||
\(324\) | −2.14180e6 | −1.13349 | ||||||||
\(325\) | −582071. | −0.305680 | ||||||||
\(326\) | 890533. | 0.464094 | ||||||||
\(327\) | 3.83742e6 | 1.98458 | ||||||||
\(328\) | 2.48574e6 | 1.27576 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 881168. | 0.445424 | ||||||||
\(331\) | 782778. | 0.392707 | 0.196353 | − | 0.980533i | \(-0.437090\pi\) | ||||
0.196353 | + | 0.980533i | \(0.437090\pi\) | |||||||
\(332\) | −1.55842e6 | −0.775958 | ||||||||
\(333\) | −5.13215e6 | −2.53623 | ||||||||
\(334\) | 1.45769e6 | 0.714988 | ||||||||
\(335\) | 1.66761e6 | 0.811863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.98847e6 | −1.43342 | −0.716711 | − | 0.697370i | \(-0.754354\pi\) | ||||
−0.716711 | + | 0.697370i | \(0.754354\pi\) | |||||||
\(338\) | 1.54793e6 | 0.736985 | ||||||||
\(339\) | 1.73526e6 | 0.820097 | ||||||||
\(340\) | −409793. | −0.192250 | ||||||||
\(341\) | −1.27639e6 | −0.594425 | ||||||||
\(342\) | −1.65621e6 | −0.765685 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −597052. | −0.272029 | ||||||||
\(345\) | −853455. | −0.386040 | ||||||||
\(346\) | −94127.6 | −0.0422695 | ||||||||
\(347\) | −614063. | −0.273772 | −0.136886 | − | 0.990587i | \(-0.543709\pi\) | ||||
−0.136886 | + | 0.990587i | \(0.543709\pi\) | |||||||
\(348\) | 3.46600e6 | 1.53420 | ||||||||
\(349\) | −3.34125e6 | −1.46841 | −0.734203 | − | 0.678930i | \(-0.762444\pi\) | ||||
−0.734203 | + | 0.678930i | \(0.762444\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.54922e6 | −3.27065 | ||||||||
\(352\) | −2.42857e6 | −1.04471 | ||||||||
\(353\) | −3.62123e6 | −1.54675 | −0.773374 | − | 0.633950i | \(-0.781433\pi\) | ||||
−0.773374 | + | 0.633950i | \(0.781433\pi\) | |||||||
\(354\) | −675607. | −0.286541 | ||||||||
\(355\) | −774855. | −0.326324 | ||||||||
\(356\) | 175966. | 0.0735876 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.85475e6 | −0.764854 | ||||||||
\(359\) | 3.58244e6 | 1.46704 | 0.733522 | − | 0.679666i | \(-0.237875\pi\) | ||||
0.733522 | + | 0.679666i | \(0.237875\pi\) | |||||||
\(360\) | 2.25979e6 | 0.918993 | ||||||||
\(361\) | −1.48761e6 | −0.600787 | ||||||||
\(362\) | 484402. | 0.194283 | ||||||||
\(363\) | 88708.6 | 0.0353345 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −932863. | −0.366510 | ||||||||
\(366\) | 1.64160e6 | 0.640568 | ||||||||
\(367\) | 2.88029e6 | 1.11628 | 0.558138 | − | 0.829748i | \(-0.311516\pi\) | ||||
0.558138 | + | 0.829748i | \(0.311516\pi\) | |||||||
\(368\) | 225391. | 0.0867597 | ||||||||
\(369\) | −7.83676e6 | −2.99620 | ||||||||
\(370\) | 749995. | 0.284809 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.95429e6 | −0.732204 | ||||||||
\(373\) | −3.91807e6 | −1.45814 | −0.729071 | − | 0.684438i | \(-0.760048\pi\) | ||||
−0.729071 | + | 0.684438i | \(0.760048\pi\) | |||||||
\(374\) | 931120. | 0.344213 | ||||||||
\(375\) | −435496. | −0.159921 | ||||||||
\(376\) | −3.14398e6 | −1.14686 | ||||||||
\(377\) | 5.20220e6 | 1.88510 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −795965. | −0.284640 | −0.142320 | − | 0.989821i | \(-0.545456\pi\) | ||||
−0.142320 | + | 0.989821i | \(0.545456\pi\) | |||||||
\(380\) | −553350. | −0.196581 | ||||||||
\(381\) | −7.36821e6 | −2.60046 | ||||||||
\(382\) | 1.00156e6 | 0.351170 | ||||||||
\(383\) | 2.02575e6 | 0.705651 | 0.352825 | − | 0.935689i | \(-0.385221\pi\) | ||||
0.352825 | + | 0.935689i | \(0.385221\pi\) | |||||||
\(384\) | −4.23056e6 | −1.46410 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.26934e6 | −0.775230 | ||||||||
\(387\) | 1.88232e6 | 0.638875 | ||||||||
\(388\) | 3.32732e6 | 1.12206 | ||||||||
\(389\) | −2.60319e6 | −0.872233 | −0.436117 | − | 0.899890i | \(-0.643646\pi\) | ||||
−0.436117 | + | 0.899890i | \(0.643646\pi\) | |||||||
\(390\) | 2.02499e6 | 0.674158 | ||||||||
\(391\) | −901836. | −0.298322 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.06573e6 | 1.00127 | ||||||||
\(394\) | −2.34948e6 | −0.762486 | ||||||||
\(395\) | 391537. | 0.126264 | ||||||||
\(396\) | 4.81626e6 | 1.54338 | ||||||||
\(397\) | −5.16774e6 | −1.64560 | −0.822800 | − | 0.568331i | \(-0.807589\pi\) | ||||
−0.822800 | + | 0.568331i | \(0.807589\pi\) | |||||||
\(398\) | 301550. | 0.0954228 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 115011. | 0.0359410 | ||||||||
\(401\) | 1.35062e6 | 0.419441 | 0.209720 | − | 0.977761i | \(-0.432745\pi\) | ||||
0.209720 | + | 0.977761i | \(0.432745\pi\) | |||||||
\(402\) | −5.80153e6 | −1.79051 | ||||||||
\(403\) | −2.93324e6 | −0.899674 | ||||||||
\(404\) | 2.82583e6 | 0.861377 | ||||||||
\(405\) | −2.40517e6 | −0.728632 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.89606e6 | 1.16584 | ||||||||
\(408\) | 3.47487e6 | 1.03345 | ||||||||
\(409\) | −2.77803e6 | −0.821163 | −0.410581 | − | 0.911824i | \(-0.634674\pi\) | ||||
−0.410581 | + | 0.911824i | \(0.634674\pi\) | |||||||
\(410\) | 1.14524e6 | 0.336462 | ||||||||
\(411\) | −7.85646e6 | −2.29415 | ||||||||
\(412\) | −300555. | −0.0872330 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 2.04035e6 | 0.585066 | ||||||||
\(415\) | −1.75005e6 | −0.498803 | ||||||||
\(416\) | −5.58104e6 | −1.58118 | ||||||||
\(417\) | 6.58356e6 | 1.85405 | ||||||||
\(418\) | 1.25731e6 | 0.351966 | ||||||||
\(419\) | 1.67370e6 | 0.465739 | 0.232869 | − | 0.972508i | \(-0.425189\pi\) | ||||
0.232869 | + | 0.972508i | \(0.425189\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.23947e6 | 0.890776 | 0.445388 | − | 0.895338i | \(-0.353066\pi\) | ||||
0.445388 | + | 0.895338i | \(0.353066\pi\) | |||||||
\(422\) | −1.16665e6 | −0.318905 | ||||||||
\(423\) | 9.91201e6 | 2.69346 | ||||||||
\(424\) | 924179. | 0.249656 | ||||||||
\(425\) | −460183. | −0.123583 | ||||||||
\(426\) | 2.69568e6 | 0.719687 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −1.65703e6 | −0.437242 | ||||||||
\(429\) | 1.05194e7 | 2.75961 | ||||||||
\(430\) | −275076. | −0.0717433 | ||||||||
\(431\) | 3.16320e6 | 0.820225 | 0.410112 | − | 0.912035i | \(-0.365489\pi\) | ||||
0.410112 | + | 0.912035i | \(0.365489\pi\) | |||||||
\(432\) | 1.49165e6 | 0.384554 | ||||||||
\(433\) | −5.42491e6 | −1.39050 | −0.695252 | − | 0.718766i | \(-0.744707\pi\) | ||||
−0.695252 | + | 0.718766i | \(0.744707\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.89220e6 | 0.986216 | ||||||||
\(436\) | −3.06513e6 | −0.772205 | ||||||||
\(437\) | −1.21776e6 | −0.305042 | ||||||||
\(438\) | 3.24538e6 | 0.808314 | ||||||||
\(439\) | 507432. | 0.125666 | 0.0628328 | − | 0.998024i | \(-0.479987\pi\) | ||||
0.0628328 | + | 0.998024i | \(0.479987\pi\) | |||||||
\(440\) | −1.71552e6 | −0.422438 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.13979e6 | 0.520972 | ||||||||
\(443\) | −3.38396e6 | −0.819248 | −0.409624 | − | 0.912254i | \(-0.634340\pi\) | ||||
−0.409624 | + | 0.912254i | \(0.634340\pi\) | |||||||
\(444\) | 5.96529e6 | 1.43607 | ||||||||
\(445\) | 197604. | 0.0473038 | ||||||||
\(446\) | 1.70312e6 | 0.405424 | ||||||||
\(447\) | −714627. | −0.169165 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00014e6 | 0.468215 | 0.234108 | − | 0.972211i | \(-0.424783\pi\) | ||||
0.234108 | + | 0.972211i | \(0.424783\pi\) | |||||||
\(450\) | 1.04114e6 | 0.242369 | ||||||||
\(451\) | 5.94926e6 | 1.37728 | ||||||||
\(452\) | −1.38604e6 | −0.319101 | ||||||||
\(453\) | 7.31848e6 | 1.67562 | ||||||||
\(454\) | −384685. | −0.0875922 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.69217e6 | 1.05672 | ||||||||
\(457\) | −1.18467e6 | −0.265342 | −0.132671 | − | 0.991160i | \(-0.542355\pi\) | ||||
−0.132671 | + | 0.991160i | \(0.542355\pi\) | |||||||
\(458\) | 3.36493e6 | 0.749570 | ||||||||
\(459\) | −5.96839e6 | −1.32229 | ||||||||
\(460\) | 681696. | 0.150209 | ||||||||
\(461\) | −8.48869e6 | −1.86032 | −0.930161 | − | 0.367152i | \(-0.880333\pi\) | ||||
−0.930161 | + | 0.367152i | \(0.880333\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.81635e6 | 1.04416 | 0.522079 | − | 0.852897i | \(-0.325157\pi\) | ||||
0.522079 | + | 0.852897i | \(0.325157\pi\) | |||||||
\(464\) | −1.02790e6 | −0.221645 | ||||||||
\(465\) | −2.19460e6 | −0.470678 | ||||||||
\(466\) | 440640. | 0.0939982 | ||||||||
\(467\) | −4.54734e6 | −0.964863 | −0.482431 | − | 0.875934i | \(-0.660246\pi\) | ||||
−0.482431 | + | 0.875934i | \(0.660246\pi\) | |||||||
\(468\) | 1.10681e7 | 2.33593 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.44851e6 | −0.302466 | ||||||||
\(471\) | 7.30972e6 | 1.51827 | ||||||||
\(472\) | 1.31532e6 | 0.271754 | ||||||||
\(473\) | −1.42896e6 | −0.293675 | ||||||||
\(474\) | −1.36213e6 | −0.278467 | ||||||||
\(475\) | −621393. | −0.126367 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.91365e6 | −0.586329 | ||||||||
\(478\) | −1.58726e6 | −0.317744 | ||||||||
\(479\) | −8.74449e6 | −1.74139 | −0.870694 | − | 0.491825i | \(-0.836330\pi\) | ||||
−0.870694 | + | 0.491825i | \(0.836330\pi\) | |||||||
\(480\) | −4.17564e6 | −0.827219 | ||||||||
\(481\) | 8.95344e6 | 1.76452 | ||||||||
\(482\) | −80184.6 | −0.0157208 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −70855.8 | −0.0137487 | ||||||||
\(485\) | 3.73646e6 | 0.721284 | ||||||||
\(486\) | 2.22083e6 | 0.426505 | ||||||||
\(487\) | −9.05551e6 | −1.73018 | −0.865088 | − | 0.501620i | \(-0.832738\pi\) | ||||
−0.865088 | + | 0.501620i | \(0.832738\pi\) | |||||||
\(488\) | −3.19598e6 | −0.607512 | ||||||||
\(489\) | 7.95408e6 | 1.50424 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.29340e6 | −0.803706 | −0.401853 | − | 0.915704i | \(-0.631634\pi\) | ||||
−0.401853 | + | 0.915704i | \(0.631634\pi\) | |||||||
\(492\) | 9.10896e6 | 1.69651 | ||||||||
\(493\) | 4.11284e6 | 0.762123 | ||||||||
\(494\) | 2.88939e6 | 0.532707 | ||||||||
\(495\) | 5.40849e6 | 0.992118 | ||||||||
\(496\) | 579579. | 0.105781 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 6.08832e6 | 1.10008 | ||||||||
\(499\) | −3.65835e6 | −0.657709 | −0.328855 | − | 0.944381i | \(-0.606663\pi\) | ||||
−0.328855 | + | 0.944381i | \(0.606663\pi\) | |||||||
\(500\) | 347851. | 0.0622256 | ||||||||
\(501\) | 1.30198e7 | 2.31745 | ||||||||
\(502\) | −96546.2 | −0.0170992 | ||||||||
\(503\) | −248395. | −0.0437746 | −0.0218873 | − | 0.999760i | \(-0.506968\pi\) | ||||
−0.0218873 | + | 0.999760i | \(0.506968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.17331e6 | 0.553713 | ||||||||
\(506\) | −1.54893e6 | −0.268940 | ||||||||
\(507\) | 1.38258e7 | 2.38875 | ||||||||
\(508\) | 5.88534e6 | 1.01184 | ||||||||
\(509\) | 8.12053e6 | 1.38928 | 0.694640 | − | 0.719357i | \(-0.255564\pi\) | ||||
0.694640 | + | 0.719357i | \(0.255564\pi\) | |||||||
\(510\) | 1.60095e6 | 0.272554 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 2.09985e6 | 0.354008 | ||||||||
\(513\) | −8.05922e6 | −1.35207 | ||||||||
\(514\) | 799188. | 0.133426 | ||||||||
\(515\) | −337513. | −0.0560753 | ||||||||
\(516\) | −2.18789e6 | −0.361744 | ||||||||
\(517\) | −7.52468e6 | −1.23812 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −840731. | −0.137006 | ||||||||
\(520\) | −3.94239e6 | −0.639368 | ||||||||
\(521\) | 7.02461e6 | 1.13378 | 0.566889 | − | 0.823794i | \(-0.308147\pi\) | ||||
0.566889 | + | 0.823794i | \(0.308147\pi\) | |||||||
\(522\) | −9.30509e6 | −1.49467 | ||||||||
\(523\) | −403325. | −0.0644764 | −0.0322382 | − | 0.999480i | \(-0.510264\pi\) | ||||
−0.0322382 | + | 0.999480i | \(0.510264\pi\) | |||||||
\(524\) | −2.44875e6 | −0.389598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.18522e6 | 0.501968 | ||||||||
\(527\) | −2.31901e6 | −0.363728 | ||||||||
\(528\) | −2.07853e6 | −0.324467 | ||||||||
\(529\) | −4.93613e6 | −0.766915 | ||||||||
\(530\) | 425791. | 0.0658426 | ||||||||
\(531\) | −4.14679e6 | −0.638227 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.36718e7 | 2.08453 | ||||||||
\(534\) | −687454. | −0.104326 | ||||||||
\(535\) | −1.86079e6 | −0.281069 | ||||||||
\(536\) | 1.12948e7 | 1.69811 | ||||||||
\(537\) | −1.65663e7 | −2.47908 | ||||||||
\(538\) | −1.54079e6 | −0.229503 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 4.51149e6 | 0.665788 | ||||||||
\(541\) | 1.28608e6 | 0.188919 | 0.0944593 | − | 0.995529i | \(-0.469888\pi\) | ||||
0.0944593 | + | 0.995529i | \(0.469888\pi\) | |||||||
\(542\) | −4.60520e6 | −0.673365 | ||||||||
\(543\) | 4.32659e6 | 0.629718 | ||||||||
\(544\) | −4.41235e6 | −0.639253 | ||||||||
\(545\) | −3.44203e6 | −0.496391 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.76839e6 | −1.11010 | −0.555051 | − | 0.831816i | \(-0.687301\pi\) | ||||
−0.555051 | + | 0.831816i | \(0.687301\pi\) | |||||||
\(548\) | 6.27534e6 | 0.892659 | ||||||||
\(549\) | 1.00759e7 | 1.42677 | ||||||||
\(550\) | −790379. | −0.111411 | ||||||||
\(551\) | 5.55364e6 | 0.779290 | ||||||||
\(552\) | −5.78048e6 | −0.807451 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.73952e6 | −0.379228 | ||||||||
\(555\) | 6.69881e6 | 0.923135 | ||||||||
\(556\) | −5.25861e6 | −0.721413 | ||||||||
\(557\) | −6.66949e6 | −0.910867 | −0.455433 | − | 0.890270i | \(-0.650516\pi\) | ||||
−0.455433 | + | 0.890270i | \(0.650516\pi\) | |||||||
\(558\) | 5.24664e6 | 0.713338 | ||||||||
\(559\) | −3.28386e6 | −0.444482 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.31659e6 | 1.11568 | ||||||||
\(562\) | −4.57459e6 | −0.610958 | ||||||||
\(563\) | −1.70653e6 | −0.226905 | −0.113452 | − | 0.993543i | \(-0.536191\pi\) | ||||
−0.113452 | + | 0.993543i | \(0.536191\pi\) | |||||||
\(564\) | −1.15211e7 | −1.52509 | ||||||||
\(565\) | −1.55647e6 | −0.205125 | ||||||||
\(566\) | 5.40183e6 | 0.708761 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.24812e6 | −0.682548 | ||||||||
\(569\) | −2.21728e6 | −0.287104 | −0.143552 | − | 0.989643i | \(-0.545852\pi\) | ||||
−0.143552 | + | 0.989643i | \(0.545852\pi\) | |||||||
\(570\) | 2.16179e6 | 0.278694 | ||||||||
\(571\) | −6.37563e6 | −0.818338 | −0.409169 | − | 0.912459i | \(-0.634181\pi\) | ||||
−0.409169 | + | 0.912459i | \(0.634181\pi\) | |||||||
\(572\) | −8.40235e6 | −1.07377 | ||||||||
\(573\) | 8.94573e6 | 1.13823 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 765520. | 0.0965578 | ||||||||
\(576\) | 6.83920e6 | 0.858913 | ||||||||
\(577\) | −2.91197e6 | −0.364122 | −0.182061 | − | 0.983287i | \(-0.558277\pi\) | ||||
−0.182061 | + | 0.983287i | \(0.558277\pi\) | |||||||
\(578\) | −2.73895e6 | −0.341008 | ||||||||
\(579\) | −2.02693e7 | −2.51271 | ||||||||
\(580\) | −3.10889e6 | −0.383738 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.29989e7 | −1.59075 | ||||||||
\(583\) | 2.21189e6 | 0.269521 | ||||||||
\(584\) | −6.31832e6 | −0.766601 | ||||||||
\(585\) | 1.24291e7 | 1.50159 | ||||||||
\(586\) | −1.94634e6 | −0.234139 | ||||||||
\(587\) | 1.61871e7 | 1.93899 | 0.969494 | − | 0.245116i | \(-0.0788259\pi\) | ||||
0.969494 | + | 0.245116i | \(0.0788259\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.13140e6 | −0.371921 | ||||||||
\(590\) | 605997. | 0.0716705 | ||||||||
\(591\) | −2.09852e7 | −2.47140 | ||||||||
\(592\) | −1.76911e6 | −0.207468 | ||||||||
\(593\) | −8.34065e6 | −0.974010 | −0.487005 | − | 0.873399i | \(-0.661911\pi\) | ||||
−0.487005 | + | 0.873399i | \(0.661911\pi\) | |||||||
\(594\) | −1.02509e7 | −1.19205 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 570807. | 0.0658224 | ||||||||
\(597\) | 2.69339e6 | 0.309289 | ||||||||
\(598\) | −3.55956e6 | −0.407046 | ||||||||
\(599\) | 1.40996e7 | 1.60561 | 0.802805 | − | 0.596242i | \(-0.203340\pi\) | ||||
0.802805 | + | 0.596242i | \(0.203340\pi\) | |||||||
\(600\) | −2.94963e6 | −0.334495 | ||||||||
\(601\) | −6.75584e6 | −0.762945 | −0.381472 | − | 0.924380i | \(-0.624583\pi\) | ||||
−0.381472 | + | 0.924380i | \(0.624583\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.56090e7 | −3.98810 | ||||||||
\(604\) | −5.84562e6 | −0.651986 | ||||||||
\(605\) | −79568.6 | −0.00883799 | ||||||||
\(606\) | −1.10398e7 | −1.22118 | ||||||||
\(607\) | 1.20208e7 | 1.32422 | 0.662110 | − | 0.749406i | \(-0.269661\pi\) | ||||
0.662110 | + | 0.749406i | \(0.269661\pi\) | |||||||
\(608\) | −5.95808e6 | −0.653653 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.47246e6 | −0.160221 | ||||||||
\(611\) | −1.72923e7 | −1.87391 | ||||||||
\(612\) | 8.75043e6 | 0.944389 | ||||||||
\(613\) | −1.45941e6 | −0.156865 | −0.0784323 | − | 0.996919i | \(-0.524991\pi\) | ||||
−0.0784323 | + | 0.996919i | \(0.524991\pi\) | |||||||
\(614\) | −6.00062e6 | −0.642355 | ||||||||
\(615\) | 1.02290e7 | 1.09055 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.88916e6 | −0.728540 | −0.364270 | − | 0.931293i | \(-0.618681\pi\) | ||||
−0.364270 | + | 0.931293i | \(0.618681\pi\) | |||||||
\(618\) | 1.17419e6 | 0.123671 | ||||||||
\(619\) | −1.17088e7 | −1.22824 | −0.614121 | − | 0.789212i | \(-0.710489\pi\) | ||||
−0.614121 | + | 0.789212i | \(0.710489\pi\) | |||||||
\(620\) | 1.75294e6 | 0.183141 | ||||||||
\(621\) | 9.92849e6 | 1.03313 | ||||||||
\(622\) | 6.56255e6 | 0.680137 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −4.77661e6 | −0.491087 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 8.56113e6 | 0.873163 | ||||||||
\(627\) | 1.12300e7 | 1.14081 | ||||||||
\(628\) | −5.83863e6 | −0.590761 | ||||||||
\(629\) | 7.07856e6 | 0.713375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.08769e6 | 0.208734 | 0.104367 | − | 0.994539i | \(-0.466718\pi\) | ||||
0.104367 | + | 0.994539i | \(0.466718\pi\) | |||||||
\(632\) | 2.65189e6 | 0.264097 | ||||||||
\(633\) | −1.04203e7 | −1.03365 | ||||||||
\(634\) | −4.71852e6 | −0.466211 | ||||||||
\(635\) | 6.60904e6 | 0.650435 | ||||||||
\(636\) | 3.38665e6 | 0.331992 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 7.06394e6 | 0.687061 | ||||||||
\(639\) | 1.65457e7 | 1.60300 | ||||||||
\(640\) | 3.79467e6 | 0.366205 | ||||||||
\(641\) | 1.25720e7 | 1.20853 | 0.604266 | − | 0.796783i | \(-0.293466\pi\) | ||||
0.604266 | + | 0.796783i | \(0.293466\pi\) | |||||||
\(642\) | 6.47358e6 | 0.619879 | ||||||||
\(643\) | −5.47387e6 | −0.522116 | −0.261058 | − | 0.965323i | \(-0.584071\pi\) | ||||
−0.261058 | + | 0.965323i | \(0.584071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.45693e6 | −0.232537 | ||||||||
\(646\) | 2.28434e6 | 0.215367 | ||||||||
\(647\) | 33033.0 | 0.00310233 | 0.00155116 | − | 0.999999i | \(-0.499506\pi\) | ||||
0.00155116 | + | 0.999999i | \(0.499506\pi\) | |||||||
\(648\) | −1.62903e7 | −1.52402 | ||||||||
\(649\) | 3.14802e6 | 0.293377 | ||||||||
\(650\) | −1.81635e6 | −0.168623 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.35331e6 | −0.585303 | ||||||||
\(653\) | 6.78770e6 | 0.622930 | 0.311465 | − | 0.950258i | \(-0.399180\pi\) | ||||
0.311465 | + | 0.950258i | \(0.399180\pi\) | |||||||
\(654\) | 1.19746e7 | 1.09476 | ||||||||
\(655\) | −2.74986e6 | −0.250442 | ||||||||
\(656\) | −2.70142e6 | −0.245094 | ||||||||
\(657\) | 1.99197e7 | 1.80040 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.30322e7 | 1.16898 | 0.584488 | − | 0.811403i | \(-0.301296\pi\) | ||||
0.584488 | + | 0.811403i | \(0.301296\pi\) | |||||||
\(660\) | −6.28650e6 | −0.561757 | ||||||||
\(661\) | −1.58081e7 | −1.40726 | −0.703632 | − | 0.710564i | \(-0.748440\pi\) | ||||
−0.703632 | + | 0.710564i | \(0.748440\pi\) | |||||||
\(662\) | 2.44266e6 | 0.216629 | ||||||||
\(663\) | 1.91122e7 | 1.68860 | ||||||||
\(664\) | −1.18531e7 | −1.04331 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.60149e7 | −1.39906 | ||||||||
\(667\) | −6.84177e6 | −0.595462 | ||||||||
\(668\) | −1.03996e7 | −0.901724 | ||||||||
\(669\) | 1.52120e7 | 1.31408 | ||||||||
\(670\) | 5.20378e6 | 0.447849 | ||||||||
\(671\) | −7.64912e6 | −0.655851 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.94847e7 | 1.65827 | 0.829137 | − | 0.559045i | \(-0.188832\pi\) | ||||
0.829137 | + | 0.559045i | \(0.188832\pi\) | |||||||
\(674\) | −9.32552e6 | −0.790721 | ||||||||
\(675\) | 5.06625e6 | 0.427984 | ||||||||
\(676\) | −1.10433e7 | −0.929465 | ||||||||
\(677\) | 7.97082e6 | 0.668392 | 0.334196 | − | 0.942504i | \(-0.391535\pi\) | ||||
0.334196 | + | 0.942504i | \(0.391535\pi\) | |||||||
\(678\) | 5.41487e6 | 0.452391 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.11684e6 | −0.258489 | ||||||||
\(681\) | −3.43593e6 | −0.283907 | ||||||||
\(682\) | −3.98297e6 | −0.327904 | ||||||||
\(683\) | −9.93020e6 | −0.814528 | −0.407264 | − | 0.913310i | \(-0.633517\pi\) | ||||
−0.407264 | + | 0.913310i | \(0.633517\pi\) | |||||||
\(684\) | 1.18159e7 | 0.965661 | ||||||||
\(685\) | 7.04698e6 | 0.573821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.00549e7 | 2.42954 | ||||||||
\(688\) | 648857. | 0.0522610 | ||||||||
\(689\) | 5.08309e6 | 0.407925 | ||||||||
\(690\) | −2.66320e6 | −0.212952 | ||||||||
\(691\) | 6.39227e6 | 0.509284 | 0.254642 | − | 0.967035i | \(-0.418042\pi\) | ||||
0.254642 | + | 0.967035i | \(0.418042\pi\) | |||||||
\(692\) | 671532. | 0.0533091 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.91618e6 | −0.151021 | ||||||||
\(695\) | −5.90524e6 | −0.463741 | ||||||||
\(696\) | 2.63620e7 | 2.06279 | ||||||||
\(697\) | 1.08089e7 | 0.842753 | ||||||||
\(698\) | −1.04264e7 | −0.810018 | ||||||||
\(699\) | 3.93572e6 | 0.304671 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.78581e6 | −0.444702 | −0.222351 | − | 0.974967i | \(-0.571373\pi\) | ||||
−0.222351 | + | 0.974967i | \(0.571373\pi\) | |||||||
\(702\) | −2.35573e7 | −1.80419 | ||||||||
\(703\) | 9.55830e6 | 0.729444 | ||||||||
\(704\) | −5.19196e6 | −0.394821 | ||||||||
\(705\) | −1.29378e7 | −0.980365 | ||||||||
\(706\) | −1.13001e7 | −0.853235 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.81997e6 | 0.361377 | ||||||||
\(709\) | −2.42588e7 | −1.81240 | −0.906198 | − | 0.422854i | \(-0.861028\pi\) | ||||
−0.906198 | + | 0.422854i | \(0.861028\pi\) | |||||||
\(710\) | −2.41793e6 | −0.180011 | ||||||||
\(711\) | −8.36060e6 | −0.620245 | ||||||||
\(712\) | 1.33838e6 | 0.0989418 | ||||||||
\(713\) | 3.85770e6 | 0.284188 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.43554e6 | −0.690243 | ||||||||
\(716\) | 1.32323e7 | 0.964613 | ||||||||
\(717\) | −1.41771e7 | −1.02989 | ||||||||
\(718\) | 1.11790e7 | 0.809267 | ||||||||
\(719\) | 6.70633e6 | 0.483797 | 0.241898 | − | 0.970302i | \(-0.422230\pi\) | ||||
0.241898 | + | 0.970302i | \(0.422230\pi\) | |||||||
\(720\) | −2.45587e6 | −0.176553 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −4.64208e6 | −0.331413 | ||||||||
\(723\) | −716194. | −0.0509548 | ||||||||
\(724\) | −3.45586e6 | −0.245025 | ||||||||
\(725\) | −3.49117e6 | −0.246676 | ||||||||
\(726\) | 276815. | 0.0194916 | ||||||||
\(727\) | −1.44972e7 | −1.01730 | −0.508649 | − | 0.860974i | \(-0.669855\pi\) | ||||
−0.508649 | + | 0.860974i | \(0.669855\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −3.54221e6 | −0.246863 | ||||||||
\(730\) | −2.91100e6 | −0.202178 | ||||||||
\(731\) | −2.59621e6 | −0.179699 | ||||||||
\(732\) | −1.17116e7 | −0.807868 | ||||||||
\(733\) | 1.07253e7 | 0.737308 | 0.368654 | − | 0.929567i | \(-0.379819\pi\) | ||||
0.368654 | + | 0.929567i | \(0.379819\pi\) | |||||||
\(734\) | 8.98795e6 | 0.615773 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.34001e6 | 0.499461 | ||||||||
\(737\) | 2.70325e7 | 1.83323 | ||||||||
\(738\) | −2.44546e7 | −1.65280 | ||||||||
\(739\) | −3.54704e6 | −0.238921 | −0.119461 | − | 0.992839i | \(-0.538116\pi\) | ||||
−0.119461 | + | 0.992839i | \(0.538116\pi\) | |||||||
\(740\) | −5.35067e6 | −0.359194 | ||||||||
\(741\) | 2.58075e7 | 1.72663 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.10764e6 | −0.538794 | −0.269397 | − | 0.963029i | \(-0.586824\pi\) | ||||
−0.269397 | + | 0.963029i | \(0.586824\pi\) | |||||||
\(744\) | −1.48641e7 | −0.984481 | ||||||||
\(745\) | 640996. | 0.0423121 | ||||||||
\(746\) | −1.22263e7 | −0.804357 | ||||||||
\(747\) | 3.73693e7 | 2.45027 | ||||||||
\(748\) | −6.64287e6 | −0.434112 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.35896e6 | −0.0882175 | ||||||||
\(751\) | −2.43974e7 | −1.57850 | −0.789250 | − | 0.614072i | \(-0.789530\pi\) | ||||
−0.789250 | + | 0.614072i | \(0.789530\pi\) | |||||||
\(752\) | 3.41678e6 | 0.220330 | ||||||||
\(753\) | −862333. | −0.0554227 | ||||||||
\(754\) | 1.62335e7 | 1.03988 | ||||||||
\(755\) | −6.56443e6 | −0.419112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.35579e6 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(758\) | −2.48381e6 | −0.157016 | ||||||||
\(759\) | −1.38348e7 | −0.871700 | ||||||||
\(760\) | −4.20872e6 | −0.264312 | ||||||||
\(761\) | −1.73774e7 | −1.08773 | −0.543867 | − | 0.839171i | \(-0.683040\pi\) | ||||
−0.543867 | + | 0.839171i | \(0.683040\pi\) | |||||||
\(762\) | −2.29925e7 | −1.43449 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −7.14539e6 | −0.442886 | ||||||||
\(765\) | 9.82643e6 | 0.607075 | ||||||||
\(766\) | 6.32136e6 | 0.389259 | ||||||||
\(767\) | 7.23440e6 | 0.444032 | ||||||||
\(768\) | −2.46280e7 | −1.50670 | ||||||||
\(769\) | 4.58080e6 | 0.279335 | 0.139667 | − | 0.990198i | \(-0.455397\pi\) | ||||
0.139667 | + | 0.990198i | \(0.455397\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.13820e6 | 0.432467 | ||||||||
\(772\) | 1.61901e7 | 0.977699 | ||||||||
\(773\) | 2.37429e7 | 1.42917 | 0.714585 | − | 0.699548i | \(-0.246615\pi\) | ||||
0.714585 | + | 0.699548i | \(0.246615\pi\) | |||||||
\(774\) | 5.87378e6 | 0.352424 | ||||||||
\(775\) | 1.96849e6 | 0.117728 | ||||||||
\(776\) | 2.53072e7 | 1.50866 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −8.12326e6 | −0.481151 | ||||||||
\(779\) | 1.45955e7 | 0.861736 | ||||||||
\(780\) | −1.44468e7 | −0.850230 | ||||||||
\(781\) | −1.25606e7 | −0.736858 | ||||||||
\(782\) | −2.81418e6 | −0.164564 | ||||||||
\(783\) | −4.52791e7 | −2.63933 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.55657e6 | −0.379754 | ||||||||
\(786\) | 9.56662e6 | 0.552335 | ||||||||
\(787\) | 1.48241e7 | 0.853162 | 0.426581 | − | 0.904449i | \(-0.359718\pi\) | ||||
0.426581 | + | 0.904449i | \(0.359718\pi\) | |||||||
\(788\) | 1.67619e7 | 0.961627 | ||||||||
\(789\) | 2.84498e7 | 1.62700 | ||||||||
\(790\) | 1.22179e6 | 0.0696512 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.66319e7 | 2.07514 | ||||||||
\(793\) | −1.75783e7 | −0.992643 | ||||||||
\(794\) | −1.61259e7 | −0.907764 | ||||||||
\(795\) | 3.80309e6 | 0.213412 | ||||||||
\(796\) | −2.15134e6 | −0.120345 | ||||||||
\(797\) | −1.29629e7 | −0.722866 | −0.361433 | − | 0.932398i | \(-0.617712\pi\) | ||||
−0.361433 | + | 0.932398i | \(0.617712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.36712e7 | −0.757601 | ||||||||
\(800\) | 3.74541e6 | 0.206907 | ||||||||
\(801\) | −4.21950e6 | −0.232370 | ||||||||
\(802\) | 4.21459e6 | 0.231377 | ||||||||
\(803\) | −1.51220e7 | −0.827600 | ||||||||
\(804\) | 4.13897e7 | 2.25815 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.15318e6 | −0.496288 | ||||||||
\(807\) | −1.37621e7 | −0.743876 | ||||||||
\(808\) | 2.14930e7 | 1.15816 | ||||||||
\(809\) | 3.00021e7 | 1.61169 | 0.805843 | − | 0.592130i | \(-0.201713\pi\) | ||||
0.805843 | + | 0.592130i | \(0.201713\pi\) | |||||||
\(810\) | −7.50533e6 | −0.401936 | ||||||||
\(811\) | −9.00717e6 | −0.480880 | −0.240440 | − | 0.970664i | \(-0.577292\pi\) | ||||
−0.240440 | + | 0.970664i | \(0.577292\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.11328e7 | −2.18254 | ||||||||
\(814\) | 1.21576e7 | 0.643115 | ||||||||
\(815\) | −7.13454e6 | −0.376246 | ||||||||
\(816\) | −3.77637e6 | −0.198541 | ||||||||
\(817\) | −3.50570e6 | −0.183747 | ||||||||
\(818\) | −8.66885e6 | −0.452979 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.17044e6 | −0.424337 | ||||||||
\(821\) | 3.10235e7 | 1.60633 | 0.803163 | − | 0.595760i | \(-0.203149\pi\) | ||||
0.803163 | + | 0.595760i | \(0.203149\pi\) | |||||||
\(822\) | −2.45161e7 | −1.26553 | ||||||||
\(823\) | 1.18388e7 | 0.609270 | 0.304635 | − | 0.952469i | \(-0.401466\pi\) | ||||
0.304635 | + | 0.952469i | \(0.401466\pi\) | |||||||
\(824\) | −2.28599e6 | −0.117289 | ||||||||
\(825\) | −7.05952e6 | −0.361110 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.17753e7 | 1.61557 | 0.807785 | − | 0.589478i | \(-0.200666\pi\) | ||||
0.807785 | + | 0.589478i | \(0.200666\pi\) | |||||||
\(828\) | −1.45564e7 | −0.737870 | ||||||||
\(829\) | 1.31310e7 | 0.663608 | 0.331804 | − | 0.943348i | \(-0.392343\pi\) | ||||
0.331804 | + | 0.943348i | \(0.392343\pi\) | |||||||
\(830\) | −5.46102e6 | −0.275156 | ||||||||
\(831\) | −2.44689e7 | −1.22917 | ||||||||
\(832\) | −1.19315e7 | −0.597568 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.05440e7 | 1.02275 | ||||||||
\(835\) | −1.16783e7 | −0.579649 | ||||||||
\(836\) | −8.96998e6 | −0.443890 | ||||||||
\(837\) | 2.55305e7 | 1.25964 | ||||||||
\(838\) | 5.22278e6 | 0.256916 | ||||||||
\(839\) | 1.51638e7 | 0.743707 | 0.371853 | − | 0.928291i | \(-0.378722\pi\) | ||||
0.371853 | + | 0.928291i | \(0.378722\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.06909e7 | 0.521224 | ||||||||
\(842\) | 1.01088e7 | 0.491380 | ||||||||
\(843\) | −4.08594e7 | −1.98026 | ||||||||
\(844\) | 8.32323e6 | 0.402194 | ||||||||
\(845\) | −1.24013e7 | −0.597481 | ||||||||
\(846\) | 3.09304e7 | 1.48580 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.00437e6 | −0.0479627 | ||||||||
\(849\) | 4.82481e7 | 2.29727 | ||||||||
\(850\) | −1.43600e6 | −0.0681722 | ||||||||
\(851\) | −1.17753e7 | −0.557374 | ||||||||
\(852\) | −1.92317e7 | −0.907650 | ||||||||
\(853\) | 1.27022e7 | 0.597733 | 0.298866 | − | 0.954295i | \(-0.403392\pi\) | ||||
0.298866 | + | 0.954295i | \(0.403392\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.32688e7 | 0.620749 | ||||||||
\(856\) | −1.26032e7 | −0.587890 | ||||||||
\(857\) | 2.53820e6 | 0.118052 | 0.0590260 | − | 0.998256i | \(-0.481201\pi\) | ||||
0.0590260 | + | 0.998256i | \(0.481201\pi\) | |||||||
\(858\) | 3.28257e7 | 1.52229 | ||||||||
\(859\) | −1.82606e6 | −0.0844367 | −0.0422184 | − | 0.999108i | \(-0.513443\pi\) | ||||
−0.0422184 | + | 0.999108i | \(0.513443\pi\) | |||||||
\(860\) | 1.96247e6 | 0.0904807 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.87075e6 | 0.452462 | ||||||||
\(863\) | 3.79256e7 | 1.73343 | 0.866714 | − | 0.498805i | \(-0.166227\pi\) | ||||
0.866714 | + | 0.498805i | \(0.166227\pi\) | |||||||
\(864\) | 4.85765e7 | 2.21382 | ||||||||
\(865\) | 754107. | 0.0342683 | ||||||||
\(866\) | −1.69284e7 | −0.767046 | ||||||||
\(867\) | −2.44638e7 | −1.10529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.34693e6 | 0.285111 | ||||||||
\(870\) | 1.21456e7 | 0.544028 | ||||||||
\(871\) | 6.21227e7 | 2.77463 | ||||||||
\(872\) | −2.33130e7 | −1.03826 | ||||||||
\(873\) | −7.97858e7 | −3.54315 | ||||||||
\(874\) | −3.80003e6 | −0.168271 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −2.31534e7 | −1.01942 | ||||||||
\(877\) | −1.60537e7 | −0.704816 | −0.352408 | − | 0.935847i | \(-0.614637\pi\) | ||||
−0.352408 | + | 0.935847i | \(0.614637\pi\) | |||||||
\(878\) | 1.58344e6 | 0.0693211 | ||||||||
\(879\) | −1.73843e7 | −0.758902 | ||||||||
\(880\) | 1.86437e6 | 0.0811568 | ||||||||
\(881\) | −2.93698e6 | −0.127486 | −0.0637428 | − | 0.997966i | \(-0.520304\pi\) | ||||
−0.0637428 | + | 0.997966i | \(0.520304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.42066e6 | 0.233965 | 0.116982 | − | 0.993134i | \(-0.462678\pi\) | ||||
0.116982 | + | 0.993134i | \(0.462678\pi\) | |||||||
\(884\) | −1.52658e7 | −0.657036 | ||||||||
\(885\) | 5.41265e6 | 0.232302 | ||||||||
\(886\) | −1.05596e7 | −0.451923 | ||||||||
\(887\) | 3.93701e6 | 0.168018 | 0.0840092 | − | 0.996465i | \(-0.473227\pi\) | ||||
0.0840092 | + | 0.996465i | \(0.473227\pi\) | |||||||
\(888\) | 4.53713e7 | 1.93085 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 616624. | 0.0260943 | ||||||||
\(891\) | −3.89885e7 | −1.64529 | ||||||||
\(892\) | −1.21506e7 | −0.511310 | ||||||||
\(893\) | −1.84605e7 | −0.774666 | ||||||||
\(894\) | −2.22999e6 | −0.0933167 | ||||||||
\(895\) | 1.48594e7 | 0.620075 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.17933e7 | −1.31933 | ||||||||
\(898\) | 6.24145e6 | 0.258282 | ||||||||
\(899\) | −1.75932e7 | −0.726013 | ||||||||
\(900\) | −7.42777e6 | −0.305670 | ||||||||
\(901\) | 4.01868e6 | 0.164919 | ||||||||
\(902\) | 1.85646e7 | 0.759749 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.05420e7 | −0.429045 | ||||||||
\(905\) | −3.88081e6 | −0.157507 | ||||||||
\(906\) | 2.28373e7 | 0.924324 | ||||||||
\(907\) | 1.95342e6 | 0.0788455 | 0.0394228 | − | 0.999223i | \(-0.487448\pi\) | ||||
0.0394228 | + | 0.999223i | \(0.487448\pi\) | |||||||
\(908\) | 2.74445e6 | 0.110469 | ||||||||
\(909\) | −6.77607e7 | −2.72000 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.17289e7 | 1.26666 | 0.633329 | − | 0.773882i | \(-0.281688\pi\) | ||||
0.633329 | + | 0.773882i | \(0.281688\pi\) | |||||||
\(912\) | −5.09930e6 | −0.203013 | ||||||||
\(913\) | −2.83688e7 | −1.12633 | ||||||||
\(914\) | −3.69675e6 | −0.146371 | ||||||||
\(915\) | −1.31518e7 | −0.519316 | ||||||||
\(916\) | −2.40063e7 | −0.945338 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.86243e7 | −0.729415 | ||||||||
\(919\) | −491150. | −0.0191834 | −0.00959169 | − | 0.999954i | \(-0.503053\pi\) | ||||
−0.00959169 | + | 0.999954i | \(0.503053\pi\) | |||||||
\(920\) | 5.18490e6 | 0.201963 | ||||||||
\(921\) | −5.35964e7 | −2.08203 | ||||||||
\(922\) | −2.64889e7 | −1.02621 | ||||||||
\(923\) | −2.88653e7 | −1.11525 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00861e6 | −0.230898 | ||||||||
\(926\) | 1.50294e7 | 0.575990 | ||||||||
\(927\) | 7.20701e6 | 0.275458 | ||||||||
\(928\) | −3.34743e7 | −1.27597 | ||||||||
\(929\) | 2.77950e7 | 1.05664 | 0.528320 | − | 0.849045i | \(-0.322822\pi\) | ||||
0.528320 | + | 0.849045i | \(0.322822\pi\) | |||||||
\(930\) | −6.84825e6 | −0.259641 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.14365e6 | −0.118548 | ||||||||
\(933\) | 5.86155e7 | 2.20449 | ||||||||
\(934\) | −1.41900e7 | −0.532249 | ||||||||
\(935\) | −7.45971e6 | −0.279057 | ||||||||
\(936\) | 8.41830e7 | 3.14076 | ||||||||
\(937\) | 2.96127e7 | 1.10187 | 0.550934 | − | 0.834549i | \(-0.314272\pi\) | ||||
0.550934 | + | 0.834549i | \(0.314272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.64665e7 | 2.83013 | ||||||||
\(940\) | 1.03340e7 | 0.381462 | ||||||||
\(941\) | 4.93546e7 | 1.81699 | 0.908497 | − | 0.417890i | \(-0.137230\pi\) | ||||
0.908497 | + | 0.417890i | \(0.137230\pi\) | |||||||
\(942\) | 2.28100e7 | 0.837524 | ||||||||
\(943\) | −1.79808e7 | −0.658460 | ||||||||
\(944\) | −1.42944e6 | −0.0522080 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.45906e6 | −0.162000 | ||||||||
\(947\) | −1.16917e7 | −0.423647 | −0.211823 | − | 0.977308i | \(-0.567940\pi\) | ||||
−0.211823 | + | 0.977308i | \(0.567940\pi\) | |||||||
\(948\) | 9.71784e6 | 0.351195 | ||||||||
\(949\) | −3.47515e7 | −1.25259 | ||||||||
\(950\) | −1.93906e6 | −0.0697078 | ||||||||
\(951\) | −4.21450e7 | −1.51110 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.11241e7 | 1.82345 | 0.911725 | − | 0.410802i | \(-0.134751\pi\) | ||||
0.911725 | + | 0.410802i | \(0.134751\pi\) | |||||||
\(954\) | −9.09204e6 | −0.323438 | ||||||||
\(955\) | −8.02402e6 | −0.284698 | ||||||||
\(956\) | 1.13239e7 | 0.400730 | ||||||||
\(957\) | 6.30938e7 | 2.22693 | ||||||||
\(958\) | −2.72872e7 | −0.960604 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −8.92697e6 | −0.312627 | ||||||||
\(961\) | −1.87093e7 | −0.653506 | ||||||||
\(962\) | 2.79392e7 | 0.973366 | ||||||||
\(963\) | 3.97340e7 | 1.38069 | ||||||||
\(964\) | 572059. | 0.0198266 | ||||||||
\(965\) | 1.81809e7 | 0.628487 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.09492e7 | 1.06435 | 0.532173 | − | 0.846636i | \(-0.321376\pi\) | ||||
0.532173 | + | 0.846636i | \(0.321376\pi\) | |||||||
\(968\) | −538921. | −0.0184858 | ||||||||
\(969\) | 2.04033e7 | 0.698058 | ||||||||
\(970\) | 1.16596e7 | 0.397883 | ||||||||
\(971\) | 4.69439e7 | 1.59783 | 0.798917 | − | 0.601442i | \(-0.205407\pi\) | ||||
0.798917 | + | 0.601442i | \(0.205407\pi\) | |||||||
\(972\) | −1.58440e7 | −0.537897 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.82577e7 | −0.954420 | ||||||||
\(975\) | −1.62233e7 | −0.546547 | ||||||||
\(976\) | 3.47329e6 | 0.116712 | ||||||||
\(977\) | 3.39213e7 | 1.13693 | 0.568467 | − | 0.822706i | \(-0.307537\pi\) | ||||
0.568467 | + | 0.822706i | \(0.307537\pi\) | |||||||
\(978\) | 2.48207e7 | 0.829787 | ||||||||
\(979\) | 3.20322e6 | 0.106815 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.34988e7 | 2.43841 | ||||||||
\(982\) | −1.33975e7 | −0.443349 | ||||||||
\(983\) | 1.47261e7 | 0.486077 | 0.243038 | − | 0.970017i | \(-0.421856\pi\) | ||||
0.243038 | + | 0.970017i | \(0.421856\pi\) | |||||||
\(984\) | 6.92818e7 | 2.28103 | ||||||||
\(985\) | 1.88230e7 | 0.618156 | ||||||||
\(986\) | 1.28341e7 | 0.420411 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.06137e7 | −0.671836 | ||||||||
\(989\) | 4.31882e6 | 0.140402 | ||||||||
\(990\) | 1.68772e7 | 0.547283 | ||||||||
\(991\) | 822773. | 0.0266131 | 0.0133066 | − | 0.999911i | \(-0.495764\pi\) | ||||
0.0133066 | + | 0.999911i | \(0.495764\pi\) | |||||||
\(992\) | 1.88743e7 | 0.608965 | ||||||||
\(993\) | 2.18174e7 | 0.702148 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.41588e6 | −0.0773603 | ||||||||
\(996\) | −4.34357e7 | −1.38739 | ||||||||
\(997\) | 1.10066e7 | 0.350685 | 0.175342 | − | 0.984508i | \(-0.443897\pi\) | ||||
0.175342 | + | 0.984508i | \(0.443897\pi\) | |||||||
\(998\) | −1.14159e7 | −0.362813 | ||||||||
\(999\) | −7.79293e7 | −2.47051 |
(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 | 245.6.a.i.1.5 | 6 | ||
7.2 | even | 3 | 35.6.e.a.11.2 | ✓ | 12 | ||
7.4 | even | 3 | 35.6.e.a.16.2 | yes | 12 | ||
7.6 | odd | 2 | 245.6.a.h.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
35.6.e.a.11.2 | ✓ | 12 | 7.2 | even | 3 | ||
35.6.e.a.16.2 | yes | 12 | 7.4 | even | 3 | ||
245.6.a.h.1.5 | 6 | 7.6 | odd | 2 | |||
245.6.a.i.1.5 | 6 | 1.1 | even | 1 | trivial |