Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(1,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, 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("33.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.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: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{313}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 78 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.34590\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.34590 | −1.47536 | −0.737681 | − | 0.675150i | \(-0.764079\pi\) | ||||
−0.737681 | + | 0.675150i | \(0.764079\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 37.6541 | 1.17669 | ||||||||
\(5\) | −107.459 | −1.92229 | −0.961143 | − | 0.276052i | \(-0.910974\pi\) | ||||
−0.961143 | + | 0.276052i | \(0.910974\pi\) | |||||||
\(6\) | 75.1131 | 0.851800 | ||||||||
\(7\) | −26.6918 | −0.205889 | −0.102944 | − | 0.994687i | \(-0.532826\pi\) | ||||
−0.102944 | + | 0.994687i | \(0.532826\pi\) | |||||||
\(8\) | −47.1885 | −0.260682 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 896.843 | 2.83607 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −338.887 | −0.679363 | ||||||||
\(13\) | 904.666 | 1.48467 | 0.742335 | − | 0.670029i | \(-0.233718\pi\) | ||||
0.742335 | + | 0.670029i | \(0.233718\pi\) | |||||||
\(14\) | 222.767 | 0.303760 | ||||||||
\(15\) | 967.131 | 1.10983 | ||||||||
\(16\) | −811.100 | −0.792090 | ||||||||
\(17\) | −495.384 | −0.415738 | −0.207869 | − | 0.978157i | \(-0.566653\pi\) | ||||
−0.207869 | + | 0.978157i | \(0.566653\pi\) | |||||||
\(18\) | −676.018 | −0.491787 | ||||||||
\(19\) | −1501.38 | −0.954130 | −0.477065 | − | 0.878868i | \(-0.658299\pi\) | ||||
−0.477065 | + | 0.878868i | \(0.658299\pi\) | |||||||
\(20\) | −4046.27 | −2.26194 | ||||||||
\(21\) | 240.226 | 0.118870 | ||||||||
\(22\) | −1009.85 | −0.444838 | ||||||||
\(23\) | 2393.01 | 0.943245 | 0.471622 | − | 0.881801i | \(-0.343669\pi\) | ||||
0.471622 | + | 0.881801i | \(0.343669\pi\) | |||||||
\(24\) | 424.697 | 0.150505 | ||||||||
\(25\) | 8422.44 | 2.69518 | ||||||||
\(26\) | −7550.25 | −2.19042 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −1005.06 | −0.242267 | ||||||||
\(29\) | −5132.34 | −1.13324 | −0.566618 | − | 0.823980i | \(-0.691749\pi\) | ||||
−0.566618 | + | 0.823980i | \(0.691749\pi\) | |||||||
\(30\) | −8071.58 | −1.63740 | ||||||||
\(31\) | −410.309 | −0.0766844 | −0.0383422 | − | 0.999265i | \(-0.512208\pi\) | ||||
−0.0383422 | + | 0.999265i | \(0.512208\pi\) | |||||||
\(32\) | 8279.40 | 1.42930 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 4134.42 | 0.613363 | ||||||||
\(35\) | 2868.28 | 0.395777 | ||||||||
\(36\) | 3049.98 | 0.392230 | ||||||||
\(37\) | 5828.69 | 0.699949 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(38\) | 12530.4 | 1.40769 | ||||||||
\(39\) | −8141.99 | −0.857174 | ||||||||
\(40\) | 5070.84 | 0.501106 | ||||||||
\(41\) | 18561.8 | 1.72449 | 0.862245 | − | 0.506491i | \(-0.169058\pi\) | ||||
0.862245 | + | 0.506491i | \(0.169058\pi\) | |||||||
\(42\) | −2004.91 | −0.175376 | ||||||||
\(43\) | −788.920 | −0.0650671 | −0.0325336 | − | 0.999471i | \(-0.510358\pi\) | ||||
−0.0325336 | + | 0.999471i | \(0.510358\pi\) | |||||||
\(44\) | 4556.15 | 0.354786 | ||||||||
\(45\) | −8704.18 | −0.640762 | ||||||||
\(46\) | −19971.8 | −1.39163 | ||||||||
\(47\) | 3979.11 | 0.262749 | 0.131375 | − | 0.991333i | \(-0.458061\pi\) | ||||
0.131375 | + | 0.991333i | \(0.458061\pi\) | |||||||
\(48\) | 7299.90 | 0.457313 | ||||||||
\(49\) | −16094.5 | −0.957610 | ||||||||
\(50\) | −70292.9 | −3.97637 | ||||||||
\(51\) | 4458.45 | 0.240026 | ||||||||
\(52\) | 34064.4 | 1.74700 | ||||||||
\(53\) | 15130.5 | 0.739886 | 0.369943 | − | 0.929055i | \(-0.379377\pi\) | ||||
0.369943 | + | 0.929055i | \(0.379377\pi\) | |||||||
\(54\) | 6084.16 | 0.283933 | ||||||||
\(55\) | −13002.5 | −0.579591 | ||||||||
\(56\) | 1259.55 | 0.0536716 | ||||||||
\(57\) | 13512.5 | 0.550867 | ||||||||
\(58\) | 42834.0 | 1.67193 | ||||||||
\(59\) | 41623.5 | 1.55671 | 0.778357 | − | 0.627822i | \(-0.216053\pi\) | ||||
0.778357 | + | 0.627822i | \(0.216053\pi\) | |||||||
\(60\) | 36416.5 | 1.30593 | ||||||||
\(61\) | −29989.8 | −1.03193 | −0.515964 | − | 0.856610i | \(-0.672566\pi\) | ||||
−0.515964 | + | 0.856610i | \(0.672566\pi\) | |||||||
\(62\) | 3424.40 | 0.113137 | ||||||||
\(63\) | −2162.04 | −0.0686296 | ||||||||
\(64\) | −43143.8 | −1.31665 | ||||||||
\(65\) | −97214.5 | −2.85396 | ||||||||
\(66\) | 9088.69 | 0.256827 | ||||||||
\(67\) | 25890.3 | 0.704613 | 0.352307 | − | 0.935885i | \(-0.385397\pi\) | ||||
0.352307 | + | 0.935885i | \(0.385397\pi\) | |||||||
\(68\) | −18653.2 | −0.489195 | ||||||||
\(69\) | −21537.1 | −0.544582 | ||||||||
\(70\) | −23938.3 | −0.583914 | ||||||||
\(71\) | 58163.0 | 1.36931 | 0.684654 | − | 0.728869i | \(-0.259954\pi\) | ||||
0.684654 | + | 0.728869i | \(0.259954\pi\) | |||||||
\(72\) | −3822.27 | −0.0868941 | ||||||||
\(73\) | 23875.3 | 0.524375 | 0.262187 | − | 0.965017i | \(-0.415556\pi\) | ||||
0.262187 | + | 0.965017i | \(0.415556\pi\) | |||||||
\(74\) | −48645.7 | −1.03268 | ||||||||
\(75\) | −75802.0 | −1.55606 | ||||||||
\(76\) | −56533.2 | −1.12272 | ||||||||
\(77\) | −3229.71 | −0.0620778 | ||||||||
\(78\) | 67952.3 | 1.26464 | ||||||||
\(79\) | 27402.8 | 0.494000 | 0.247000 | − | 0.969016i | \(-0.420555\pi\) | ||||
0.247000 | + | 0.969016i | \(0.420555\pi\) | |||||||
\(80\) | 87160.0 | 1.52262 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −154915. | −2.54425 | ||||||||
\(83\) | 24056.3 | 0.383296 | 0.191648 | − | 0.981464i | \(-0.438617\pi\) | ||||
0.191648 | + | 0.981464i | \(0.438617\pi\) | |||||||
\(84\) | 9045.50 | 0.139873 | ||||||||
\(85\) | 53233.4 | 0.799166 | ||||||||
\(86\) | 6584.25 | 0.0959975 | ||||||||
\(87\) | 46191.1 | 0.654274 | ||||||||
\(88\) | −5709.81 | −0.0785987 | ||||||||
\(89\) | −55820.0 | −0.746990 | −0.373495 | − | 0.927632i | \(-0.621841\pi\) | ||||
−0.373495 | + | 0.927632i | \(0.621841\pi\) | |||||||
\(90\) | 72644.3 | 0.945355 | ||||||||
\(91\) | −24147.2 | −0.305677 | ||||||||
\(92\) | 90106.5 | 1.10991 | ||||||||
\(93\) | 3692.78 | 0.0442737 | ||||||||
\(94\) | −33209.3 | −0.387650 | ||||||||
\(95\) | 161337. | 1.83411 | ||||||||
\(96\) | −74514.6 | −0.825207 | ||||||||
\(97\) | −101188. | −1.09194 | −0.545970 | − | 0.837805i | \(-0.683839\pi\) | ||||
−0.545970 | + | 0.837805i | \(0.683839\pi\) | |||||||
\(98\) | 134324. | 1.41282 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 317139. | 3.17139 | ||||||||
\(101\) | −75190.1 | −0.733428 | −0.366714 | − | 0.930334i | \(-0.619517\pi\) | ||||
−0.366714 | + | 0.930334i | \(0.619517\pi\) | |||||||
\(102\) | −37209.8 | −0.354125 | ||||||||
\(103\) | 176059. | 1.63518 | 0.817590 | − | 0.575801i | \(-0.195310\pi\) | ||||
0.817590 | + | 0.575801i | \(0.195310\pi\) | |||||||
\(104\) | −42689.9 | −0.387027 | ||||||||
\(105\) | −25814.5 | −0.228502 | ||||||||
\(106\) | −126278. | −1.09160 | ||||||||
\(107\) | −124963. | −1.05517 | −0.527586 | − | 0.849501i | \(-0.676903\pi\) | ||||
−0.527586 | + | 0.849501i | \(0.676903\pi\) | |||||||
\(108\) | −27449.8 | −0.226454 | ||||||||
\(109\) | 48001.5 | 0.386980 | 0.193490 | − | 0.981102i | \(-0.438019\pi\) | ||||
0.193490 | + | 0.981102i | \(0.438019\pi\) | |||||||
\(110\) | 108518. | 0.855106 | ||||||||
\(111\) | −52458.2 | −0.404116 | ||||||||
\(112\) | 21649.7 | 0.163082 | ||||||||
\(113\) | 38955.6 | 0.286995 | 0.143497 | − | 0.989651i | \(-0.454165\pi\) | ||||
0.143497 | + | 0.989651i | \(0.454165\pi\) | |||||||
\(114\) | −112774. | −0.812728 | ||||||||
\(115\) | −257150. | −1.81319 | ||||||||
\(116\) | −193254. | −1.33347 | ||||||||
\(117\) | 73277.9 | 0.494890 | ||||||||
\(118\) | −347386. | −2.29672 | ||||||||
\(119\) | 13222.7 | 0.0855957 | ||||||||
\(120\) | −45637.5 | −0.289314 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 250292. | 1.52247 | ||||||||
\(123\) | −167056. | −0.995635 | ||||||||
\(124\) | −15449.8 | −0.0902338 | ||||||||
\(125\) | −569258. | −3.25862 | ||||||||
\(126\) | 18044.1 | 0.101253 | ||||||||
\(127\) | 186757. | 1.02746 | 0.513732 | − | 0.857951i | \(-0.328262\pi\) | ||||
0.513732 | + | 0.857951i | \(0.328262\pi\) | |||||||
\(128\) | 95133.6 | 0.513226 | ||||||||
\(129\) | 7100.28 | 0.0375665 | ||||||||
\(130\) | 811343. | 4.21062 | ||||||||
\(131\) | −363603. | −1.85118 | −0.925592 | − | 0.378523i | \(-0.876432\pi\) | ||||
−0.925592 | + | 0.378523i | \(0.876432\pi\) | |||||||
\(132\) | −41005.3 | −0.204836 | ||||||||
\(133\) | 40074.6 | 0.196445 | ||||||||
\(134\) | −216078. | −1.03956 | ||||||||
\(135\) | 78337.6 | 0.369944 | ||||||||
\(136\) | 23376.4 | 0.108375 | ||||||||
\(137\) | −74002.6 | −0.336857 | −0.168429 | − | 0.985714i | \(-0.553869\pi\) | ||||
−0.168429 | + | 0.985714i | \(0.553869\pi\) | |||||||
\(138\) | 179746. | 0.803456 | ||||||||
\(139\) | 70042.3 | 0.307485 | 0.153742 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153742 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(140\) | 108002. | 0.465707 | ||||||||
\(141\) | −35812.0 | −0.151698 | ||||||||
\(142\) | −485423. | −2.02022 | ||||||||
\(143\) | 109465. | 0.447645 | ||||||||
\(144\) | −65699.1 | −0.264030 | ||||||||
\(145\) | 551516. | 2.17840 | ||||||||
\(146\) | −199261. | −0.773642 | ||||||||
\(147\) | 144851. | 0.552876 | ||||||||
\(148\) | 219474. | 0.823624 | ||||||||
\(149\) | 327767. | 1.20948 | 0.604741 | − | 0.796422i | \(-0.293276\pi\) | ||||
0.604741 | + | 0.796422i | \(0.293276\pi\) | |||||||
\(150\) | 632636. | 2.29576 | ||||||||
\(151\) | 519.828 | 0.00185531 | 0.000927656 | − | 1.00000i | \(-0.499705\pi\) | ||||
0.000927656 | 1.00000i | \(0.499705\pi\) | ||||||||
\(152\) | 70848.1 | 0.248725 | ||||||||
\(153\) | −40126.1 | −0.138579 | ||||||||
\(154\) | 26954.8 | 0.0915872 | ||||||||
\(155\) | 44091.4 | 0.147409 | ||||||||
\(156\) | −306579. | −1.00863 | ||||||||
\(157\) | −119470. | −0.386821 | −0.193411 | − | 0.981118i | \(-0.561955\pi\) | ||||
−0.193411 | + | 0.981118i | \(0.561955\pi\) | |||||||
\(158\) | −228701. | −0.728828 | ||||||||
\(159\) | −136175. | −0.427173 | ||||||||
\(160\) | −889696. | −2.74752 | ||||||||
\(161\) | −63873.7 | −0.194204 | ||||||||
\(162\) | −54757.5 | −0.163929 | ||||||||
\(163\) | 314012. | 0.925716 | 0.462858 | − | 0.886432i | \(-0.346824\pi\) | ||||
0.462858 | + | 0.886432i | \(0.346824\pi\) | |||||||
\(164\) | 698928. | 2.02919 | ||||||||
\(165\) | 117023. | 0.334627 | ||||||||
\(166\) | −200772. | −0.565500 | ||||||||
\(167\) | 281877. | 0.782111 | 0.391056 | − | 0.920367i | \(-0.372110\pi\) | ||||
0.391056 | + | 0.920367i | \(0.372110\pi\) | |||||||
\(168\) | −11335.9 | −0.0309873 | ||||||||
\(169\) | 447127. | 1.20424 | ||||||||
\(170\) | −444281. | −1.17906 | ||||||||
\(171\) | −121612. | −0.318043 | ||||||||
\(172\) | −29706.1 | −0.0765639 | ||||||||
\(173\) | 154131. | 0.391538 | 0.195769 | − | 0.980650i | \(-0.437280\pi\) | ||||
0.195769 | + | 0.980650i | \(0.437280\pi\) | |||||||
\(174\) | −385506. | −0.965291 | ||||||||
\(175\) | −224810. | −0.554908 | ||||||||
\(176\) | −98143.1 | −0.238824 | ||||||||
\(177\) | −374612. | −0.898770 | ||||||||
\(178\) | 465868. | 1.10208 | ||||||||
\(179\) | 603292. | 1.40733 | 0.703664 | − | 0.710533i | \(-0.251546\pi\) | ||||
0.703664 | + | 0.710533i | \(0.251546\pi\) | |||||||
\(180\) | −327748. | −0.753978 | ||||||||
\(181\) | −560418. | −1.27150 | −0.635749 | − | 0.771896i | \(-0.719309\pi\) | ||||
−0.635749 | + | 0.771896i | \(0.719309\pi\) | |||||||
\(182\) | 201530. | 0.450984 | ||||||||
\(183\) | 269909. | 0.595784 | ||||||||
\(184\) | −112922. | −0.245887 | ||||||||
\(185\) | −626345. | −1.34550 | ||||||||
\(186\) | −30819.6 | −0.0653198 | ||||||||
\(187\) | −59941.4 | −0.125350 | ||||||||
\(188\) | 149830. | 0.309175 | ||||||||
\(189\) | 19458.3 | 0.0396233 | ||||||||
\(190\) | −1.34650e6 | −2.70598 | ||||||||
\(191\) | 337255. | 0.668921 | 0.334461 | − | 0.942410i | \(-0.391446\pi\) | ||||
0.334461 | + | 0.942410i | \(0.391446\pi\) | |||||||
\(192\) | 388295. | 0.760166 | ||||||||
\(193\) | 427002. | 0.825158 | 0.412579 | − | 0.910922i | \(-0.364628\pi\) | ||||
0.412579 | + | 0.910922i | \(0.364628\pi\) | |||||||
\(194\) | 844503. | 1.61100 | ||||||||
\(195\) | 874931. | 1.64773 | ||||||||
\(196\) | −606026. | −1.12681 | ||||||||
\(197\) | 387552. | 0.711483 | 0.355741 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355741 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(198\) | −81798.2 | −0.148279 | ||||||||
\(199\) | 564409. | 1.01033 | 0.505163 | − | 0.863024i | \(-0.331432\pi\) | ||||
0.505163 | + | 0.863024i | \(0.331432\pi\) | |||||||
\(200\) | −397443. | −0.702586 | ||||||||
\(201\) | −233013. | −0.406809 | ||||||||
\(202\) | 627529. | 1.08207 | ||||||||
\(203\) | 136991. | 0.233321 | ||||||||
\(204\) | 167879. | 0.282437 | ||||||||
\(205\) | −1.99463e6 | −3.31496 | ||||||||
\(206\) | −1.46937e6 | −2.41248 | ||||||||
\(207\) | 193834. | 0.314415 | ||||||||
\(208\) | −733774. | −1.17599 | ||||||||
\(209\) | −181667. | −0.287681 | ||||||||
\(210\) | 215445. | 0.337123 | ||||||||
\(211\) | 495448. | 0.766112 | 0.383056 | − | 0.923725i | \(-0.374872\pi\) | ||||
0.383056 | + | 0.923725i | \(0.374872\pi\) | |||||||
\(212\) | 569727. | 0.870616 | ||||||||
\(213\) | −523467. | −0.790570 | ||||||||
\(214\) | 1.04293e6 | 1.55676 | ||||||||
\(215\) | 84776.5 | 0.125078 | ||||||||
\(216\) | 34400.4 | 0.0501683 | ||||||||
\(217\) | 10951.9 | 0.0157885 | ||||||||
\(218\) | −400616. | −0.570935 | ||||||||
\(219\) | −214878. | −0.302748 | ||||||||
\(220\) | −489599. | −0.681999 | ||||||||
\(221\) | −448157. | −0.617233 | ||||||||
\(222\) | 437811. | 0.596217 | ||||||||
\(223\) | 1.23517e6 | 1.66327 | 0.831637 | − | 0.555320i | \(-0.187404\pi\) | ||||
0.831637 | + | 0.555320i | \(0.187404\pi\) | |||||||
\(224\) | −220992. | −0.294277 | ||||||||
\(225\) | 682218. | 0.898394 | ||||||||
\(226\) | −325120. | −0.423421 | ||||||||
\(227\) | −802179. | −1.03325 | −0.516627 | − | 0.856211i | \(-0.672812\pi\) | ||||
−0.516627 | + | 0.856211i | \(0.672812\pi\) | |||||||
\(228\) | 508799. | 0.648200 | ||||||||
\(229\) | −162526. | −0.204802 | −0.102401 | − | 0.994743i | \(-0.532652\pi\) | ||||
−0.102401 | + | 0.994743i | \(0.532652\pi\) | |||||||
\(230\) | 2.14615e6 | 2.67510 | ||||||||
\(231\) | 29067.4 | 0.0358407 | ||||||||
\(232\) | 242188. | 0.295415 | ||||||||
\(233\) | −1.45802e6 | −1.75944 | −0.879718 | − | 0.475496i | \(-0.842269\pi\) | ||||
−0.879718 | + | 0.475496i | \(0.842269\pi\) | |||||||
\(234\) | −611570. | −0.730141 | ||||||||
\(235\) | −427592. | −0.505079 | ||||||||
\(236\) | 1.56730e6 | 1.83177 | ||||||||
\(237\) | −246625. | −0.285211 | ||||||||
\(238\) | −110355. | −0.126285 | ||||||||
\(239\) | −582475. | −0.659603 | −0.329802 | − | 0.944050i | \(-0.606982\pi\) | ||||
−0.329802 | + | 0.944050i | \(0.606982\pi\) | |||||||
\(240\) | −784440. | −0.879087 | ||||||||
\(241\) | 434564. | 0.481961 | 0.240980 | − | 0.970530i | \(-0.422531\pi\) | ||||
0.240980 | + | 0.970530i | \(0.422531\pi\) | |||||||
\(242\) | −122192. | −0.134124 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −1.12924e6 | −1.21426 | ||||||||
\(245\) | 1.72950e6 | 1.84080 | ||||||||
\(246\) | 1.39424e6 | 1.46892 | ||||||||
\(247\) | −1.35825e6 | −1.41657 | ||||||||
\(248\) | 19361.9 | 0.0199903 | ||||||||
\(249\) | −216507. | −0.221296 | ||||||||
\(250\) | 4.75097e6 | 4.80765 | ||||||||
\(251\) | −948184. | −0.949967 | −0.474983 | − | 0.879995i | \(-0.657546\pi\) | ||||
−0.474983 | + | 0.879995i | \(0.657546\pi\) | |||||||
\(252\) | −81409.5 | −0.0807558 | ||||||||
\(253\) | 289554. | 0.284399 | ||||||||
\(254\) | −1.55865e6 | −1.51588 | ||||||||
\(255\) | −479101. | −0.461399 | ||||||||
\(256\) | 586627. | 0.559451 | ||||||||
\(257\) | 1.14089e6 | 1.07749 | 0.538744 | − | 0.842470i | \(-0.318899\pi\) | ||||
0.538744 | + | 0.842470i | \(0.318899\pi\) | |||||||
\(258\) | −59258.2 | −0.0554242 | ||||||||
\(259\) | −155578. | −0.144112 | ||||||||
\(260\) | −3.66052e6 | −3.35823 | ||||||||
\(261\) | −415720. | −0.377745 | ||||||||
\(262\) | 3.03460e6 | 2.73116 | ||||||||
\(263\) | 280915. | 0.250430 | 0.125215 | − | 0.992130i | \(-0.460038\pi\) | ||||
0.125215 | + | 0.992130i | \(0.460038\pi\) | |||||||
\(264\) | 51388.3 | 0.0453790 | ||||||||
\(265\) | −1.62591e6 | −1.42227 | ||||||||
\(266\) | −334459. | −0.289827 | ||||||||
\(267\) | 502380. | 0.431275 | ||||||||
\(268\) | 974878. | 0.829112 | ||||||||
\(269\) | 1.08759e6 | 0.916397 | 0.458198 | − | 0.888850i | \(-0.348495\pi\) | ||||
0.458198 | + | 0.888850i | \(0.348495\pi\) | |||||||
\(270\) | −653798. | −0.545801 | ||||||||
\(271\) | 1.17929e6 | 0.975431 | 0.487716 | − | 0.873003i | \(-0.337830\pi\) | ||||
0.487716 | + | 0.873003i | \(0.337830\pi\) | |||||||
\(272\) | 401806. | 0.329302 | ||||||||
\(273\) | 217324. | 0.176483 | ||||||||
\(274\) | 617619. | 0.496986 | ||||||||
\(275\) | 1.01912e6 | 0.812628 | ||||||||
\(276\) | −810958. | −0.640805 | ||||||||
\(277\) | −621357. | −0.486566 | −0.243283 | − | 0.969955i | \(-0.578224\pi\) | ||||
−0.243283 | + | 0.969955i | \(0.578224\pi\) | |||||||
\(278\) | −584566. | −0.453651 | ||||||||
\(279\) | −33235.0 | −0.0255615 | ||||||||
\(280\) | −135350. | −0.103172 | ||||||||
\(281\) | −243988. | −0.184333 | −0.0921666 | − | 0.995744i | \(-0.529379\pi\) | ||||
−0.0921666 | + | 0.995744i | \(0.529379\pi\) | |||||||
\(282\) | 298884. | 0.223810 | ||||||||
\(283\) | −1.84579e6 | −1.36999 | −0.684993 | − | 0.728549i | \(-0.740195\pi\) | ||||
−0.684993 | + | 0.728549i | \(0.740195\pi\) | |||||||
\(284\) | 2.19007e6 | 1.61125 | ||||||||
\(285\) | −1.45204e6 | −1.05892 | ||||||||
\(286\) | −913581. | −0.660438 | ||||||||
\(287\) | −495448. | −0.355053 | ||||||||
\(288\) | 670631. | 0.476434 | ||||||||
\(289\) | −1.17445e6 | −0.827162 | ||||||||
\(290\) | −4.60290e6 | −3.21393 | ||||||||
\(291\) | 910690. | 0.630431 | ||||||||
\(292\) | 899003. | 0.617027 | ||||||||
\(293\) | −1.34899e6 | −0.917995 | −0.458998 | − | 0.888437i | \(-0.651791\pi\) | ||||
−0.458998 | + | 0.888437i | \(0.651791\pi\) | |||||||
\(294\) | −1.20891e6 | −0.815692 | ||||||||
\(295\) | −4.47283e6 | −2.99245 | ||||||||
\(296\) | −275047. | −0.182464 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | −2.73551e6 | −1.78442 | ||||||||
\(299\) | 2.16487e6 | 1.40041 | ||||||||
\(300\) | −2.85426e6 | −1.83101 | ||||||||
\(301\) | 21057.7 | 0.0133966 | ||||||||
\(302\) | −4338.43 | −0.00273726 | ||||||||
\(303\) | 676711. | 0.423445 | ||||||||
\(304\) | 1.21777e6 | 0.755757 | ||||||||
\(305\) | 3.22268e6 | 1.98366 | ||||||||
\(306\) | 334888. | 0.204454 | ||||||||
\(307\) | −1.20545e6 | −0.729970 | −0.364985 | − | 0.931013i | \(-0.618926\pi\) | ||||
−0.364985 | + | 0.931013i | \(0.618926\pi\) | |||||||
\(308\) | −121612. | −0.0730464 | ||||||||
\(309\) | −1.58453e6 | −0.944072 | ||||||||
\(310\) | −367983. | −0.217482 | ||||||||
\(311\) | 636875. | 0.373382 | 0.186691 | − | 0.982419i | \(-0.440224\pi\) | ||||
0.186691 | + | 0.982419i | \(0.440224\pi\) | |||||||
\(312\) | 384209. | 0.223450 | ||||||||
\(313\) | 1.86526e6 | 1.07616 | 0.538081 | − | 0.842893i | \(-0.319150\pi\) | ||||
0.538081 | + | 0.842893i | \(0.319150\pi\) | |||||||
\(314\) | 997086. | 0.570701 | ||||||||
\(315\) | 232330. | 0.131926 | ||||||||
\(316\) | 1.03183e6 | 0.581285 | ||||||||
\(317\) | 2.35417e6 | 1.31580 | 0.657900 | − | 0.753105i | \(-0.271445\pi\) | ||||
0.657900 | + | 0.753105i | \(0.271445\pi\) | |||||||
\(318\) | 1.13650e6 | 0.630235 | ||||||||
\(319\) | −621013. | −0.341684 | ||||||||
\(320\) | 4.63619e6 | 2.53097 | ||||||||
\(321\) | 1.12467e6 | 0.609204 | ||||||||
\(322\) | 533083. | 0.286520 | ||||||||
\(323\) | 743761. | 0.396668 | ||||||||
\(324\) | 247049. | 0.130743 | ||||||||
\(325\) | 7.61950e6 | 4.00145 | ||||||||
\(326\) | −2.62072e6 | −1.36577 | ||||||||
\(327\) | −432013. | −0.223423 | ||||||||
\(328\) | −875905. | −0.449544 | ||||||||
\(329\) | −106210. | −0.0540972 | ||||||||
\(330\) | −976662. | −0.493696 | ||||||||
\(331\) | 1.97887e6 | 0.992768 | 0.496384 | − | 0.868103i | \(-0.334661\pi\) | ||||
0.496384 | + | 0.868103i | \(0.334661\pi\) | |||||||
\(332\) | 905820. | 0.451021 | ||||||||
\(333\) | 472124. | 0.233316 | ||||||||
\(334\) | −2.35252e6 | −1.15390 | ||||||||
\(335\) | −2.78215e6 | −1.35447 | ||||||||
\(336\) | −194848. | −0.0941557 | ||||||||
\(337\) | 2.86225e6 | 1.37288 | 0.686439 | − | 0.727187i | \(-0.259173\pi\) | ||||
0.686439 | + | 0.727187i | \(0.259173\pi\) | |||||||
\(338\) | −3.73168e6 | −1.77669 | ||||||||
\(339\) | −350601. | −0.165697 | ||||||||
\(340\) | 2.00446e6 | 0.940372 | ||||||||
\(341\) | −49647.4 | −0.0231212 | ||||||||
\(342\) | 1.01496e6 | 0.469229 | ||||||||
\(343\) | 878202. | 0.403050 | ||||||||
\(344\) | 37228.0 | 0.0169619 | ||||||||
\(345\) | 2.31435e6 | 1.04684 | ||||||||
\(346\) | −1.28636e6 | −0.577660 | ||||||||
\(347\) | −1.81514e6 | −0.809257 | −0.404629 | − | 0.914481i | \(-0.632599\pi\) | ||||
−0.404629 | + | 0.914481i | \(0.632599\pi\) | |||||||
\(348\) | 1.73928e6 | 0.769878 | ||||||||
\(349\) | −1.77907e6 | −0.781861 | −0.390930 | − | 0.920420i | \(-0.627847\pi\) | ||||
−0.390930 | + | 0.920420i | \(0.627847\pi\) | |||||||
\(350\) | 1.87624e6 | 0.818690 | ||||||||
\(351\) | −659501. | −0.285725 | ||||||||
\(352\) | 1.00181e6 | 0.430950 | ||||||||
\(353\) | −4.18817e6 | −1.78890 | −0.894452 | − | 0.447164i | \(-0.852434\pi\) | ||||
−0.894452 | + | 0.447164i | \(0.852434\pi\) | |||||||
\(354\) | 3.12647e6 | 1.32601 | ||||||||
\(355\) | −6.25014e6 | −2.63220 | ||||||||
\(356\) | −2.10185e6 | −0.878976 | ||||||||
\(357\) | −119004. | −0.0494187 | ||||||||
\(358\) | −5.03502e6 | −2.07632 | ||||||||
\(359\) | 1.13143e6 | 0.463329 | 0.231665 | − | 0.972796i | \(-0.425583\pi\) | ||||
0.231665 | + | 0.972796i | \(0.425583\pi\) | |||||||
\(360\) | 410738. | 0.167035 | ||||||||
\(361\) | −221946. | −0.0896355 | ||||||||
\(362\) | 4.67720e6 | 1.87592 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −909240. | −0.359687 | ||||||||
\(365\) | −2.56562e6 | −1.00800 | ||||||||
\(366\) | −2.25263e6 | −0.878997 | ||||||||
\(367\) | 1.31924e6 | 0.511279 | 0.255639 | − | 0.966772i | \(-0.417714\pi\) | ||||
0.255639 | + | 0.966772i | \(0.417714\pi\) | |||||||
\(368\) | −1.94097e6 | −0.747134 | ||||||||
\(369\) | 1.50351e6 | 0.574830 | ||||||||
\(370\) | 5.22742e6 | 1.98510 | ||||||||
\(371\) | −403861. | −0.152334 | ||||||||
\(372\) | 139048. | 0.0520965 | ||||||||
\(373\) | 741.945 | 0.000276121 0 | 0.000138061 | − | 1.00000i | \(-0.499956\pi\) | ||||
0.000138061 | 1.00000i | \(0.499956\pi\) | ||||||||
\(374\) | 500265. | 0.184936 | ||||||||
\(375\) | 5.12332e6 | 1.88137 | ||||||||
\(376\) | −187769. | −0.0684941 | ||||||||
\(377\) | −4.64305e6 | −1.68248 | ||||||||
\(378\) | −162397. | −0.0584587 | ||||||||
\(379\) | −567437. | −0.202917 | −0.101459 | − | 0.994840i | \(-0.532351\pi\) | ||||
−0.101459 | + | 0.994840i | \(0.532351\pi\) | |||||||
\(380\) | 6.07501e6 | 2.15818 | ||||||||
\(381\) | −1.68081e6 | −0.593207 | ||||||||
\(382\) | −2.81470e6 | −0.986900 | ||||||||
\(383\) | 3.54829e6 | 1.23601 | 0.618006 | − | 0.786174i | \(-0.287941\pi\) | ||||
0.618006 | + | 0.786174i | \(0.287941\pi\) | |||||||
\(384\) | −856202. | −0.296311 | ||||||||
\(385\) | 347061. | 0.119331 | ||||||||
\(386\) | −3.56372e6 | −1.21741 | ||||||||
\(387\) | −63902.5 | −0.0216890 | ||||||||
\(388\) | −3.81013e6 | −1.28487 | ||||||||
\(389\) | 4.09335e6 | 1.37153 | 0.685764 | − | 0.727824i | \(-0.259468\pi\) | ||||
0.685764 | + | 0.727824i | \(0.259468\pi\) | |||||||
\(390\) | −7.30209e6 | −2.43100 | ||||||||
\(391\) | −1.18546e6 | −0.392142 | ||||||||
\(392\) | 759478. | 0.249632 | ||||||||
\(393\) | 3.27243e6 | 1.06878 | ||||||||
\(394\) | −3.23447e6 | −1.04969 | ||||||||
\(395\) | −2.94468e6 | −0.949609 | ||||||||
\(396\) | 369048. | 0.118262 | ||||||||
\(397\) | 153511. | 0.0488835 | 0.0244417 | − | 0.999701i | \(-0.492219\pi\) | ||||
0.0244417 | + | 0.999701i | \(0.492219\pi\) | |||||||
\(398\) | −4.71050e6 | −1.49059 | ||||||||
\(399\) | −360672. | −0.113417 | ||||||||
\(400\) | −6.83144e6 | −2.13483 | ||||||||
\(401\) | 474424. | 0.147335 | 0.0736674 | − | 0.997283i | \(-0.476530\pi\) | ||||
0.0736674 | + | 0.997283i | \(0.476530\pi\) | |||||||
\(402\) | 1.94470e6 | 0.600190 | ||||||||
\(403\) | −371193. | −0.113851 | ||||||||
\(404\) | −2.83122e6 | −0.863017 | ||||||||
\(405\) | −705039. | −0.213587 | ||||||||
\(406\) | −1.14332e6 | −0.344232 | ||||||||
\(407\) | 705271. | 0.211043 | ||||||||
\(408\) | −210388. | −0.0625706 | ||||||||
\(409\) | 2.85246e6 | 0.843164 | 0.421582 | − | 0.906790i | \(-0.361475\pi\) | ||||
0.421582 | + | 0.906790i | \(0.361475\pi\) | |||||||
\(410\) | 1.66470e7 | 4.89077 | ||||||||
\(411\) | 666023. | 0.194484 | ||||||||
\(412\) | 6.62935e6 | 1.92410 | ||||||||
\(413\) | −1.11101e6 | −0.320510 | ||||||||
\(414\) | −1.61772e6 | −0.463875 | ||||||||
\(415\) | −2.58507e6 | −0.736805 | ||||||||
\(416\) | 7.49009e6 | 2.12204 | ||||||||
\(417\) | −630381. | −0.177526 | ||||||||
\(418\) | 1.51618e6 | 0.424434 | ||||||||
\(419\) | 6.61913e6 | 1.84190 | 0.920950 | − | 0.389681i | \(-0.127415\pi\) | ||||
0.920950 | + | 0.389681i | \(0.127415\pi\) | |||||||
\(420\) | −972021. | −0.268876 | ||||||||
\(421\) | 1.67579e6 | 0.460802 | 0.230401 | − | 0.973096i | \(-0.425996\pi\) | ||||
0.230401 | + | 0.973096i | \(0.425996\pi\) | |||||||
\(422\) | −4.13496e6 | −1.13029 | ||||||||
\(423\) | 322308. | 0.0875831 | ||||||||
\(424\) | −713988. | −0.192875 | ||||||||
\(425\) | −4.17234e6 | −1.12049 | ||||||||
\(426\) | 4.36880e6 | 1.16638 | ||||||||
\(427\) | 800483. | 0.212463 | ||||||||
\(428\) | −4.70539e6 | −1.24161 | ||||||||
\(429\) | −985181. | −0.258448 | ||||||||
\(430\) | −707537. | −0.184535 | ||||||||
\(431\) | −4.53856e6 | −1.17686 | −0.588430 | − | 0.808548i | \(-0.700254\pi\) | ||||
−0.588430 | + | 0.808548i | \(0.700254\pi\) | |||||||
\(432\) | 591292. | 0.152438 | ||||||||
\(433\) | 379605. | 0.0972999 | 0.0486500 | − | 0.998816i | \(-0.484508\pi\) | ||||
0.0486500 | + | 0.998816i | \(0.484508\pi\) | |||||||
\(434\) | −91403.4 | −0.0232937 | ||||||||
\(435\) | −4.96365e6 | −1.25770 | ||||||||
\(436\) | 1.80745e6 | 0.455355 | ||||||||
\(437\) | −3.59282e6 | −0.899978 | ||||||||
\(438\) | 1.79335e6 | 0.446663 | ||||||||
\(439\) | −1.97778e6 | −0.489797 | −0.244899 | − | 0.969549i | \(-0.578755\pi\) | ||||
−0.244899 | + | 0.969549i | \(0.578755\pi\) | |||||||
\(440\) | 613571. | 0.151089 | ||||||||
\(441\) | −1.30366e6 | −0.319203 | ||||||||
\(442\) | 3.74027e6 | 0.910641 | ||||||||
\(443\) | 3.58373e6 | 0.867613 | 0.433807 | − | 0.901006i | \(-0.357170\pi\) | ||||
0.433807 | + | 0.901006i | \(0.357170\pi\) | |||||||
\(444\) | −1.97527e6 | −0.475519 | ||||||||
\(445\) | 5.99836e6 | 1.43593 | ||||||||
\(446\) | −1.03086e7 | −2.45393 | ||||||||
\(447\) | −2.94990e6 | −0.698295 | ||||||||
\(448\) | 1.15159e6 | 0.271083 | ||||||||
\(449\) | −1.05735e6 | −0.247515 | −0.123758 | − | 0.992312i | \(-0.539495\pi\) | ||||
−0.123758 | + | 0.992312i | \(0.539495\pi\) | |||||||
\(450\) | −5.69372e6 | −1.32546 | ||||||||
\(451\) | 2.24598e6 | 0.519954 | ||||||||
\(452\) | 1.46684e6 | 0.337704 | ||||||||
\(453\) | −4678.45 | −0.00107117 | ||||||||
\(454\) | 6.69491e6 | 1.52442 | ||||||||
\(455\) | 2.59483e6 | 0.587598 | ||||||||
\(456\) | −637633. | −0.143601 | ||||||||
\(457\) | 1.39016e6 | 0.311368 | 0.155684 | − | 0.987807i | \(-0.450242\pi\) | ||||
0.155684 | + | 0.987807i | \(0.450242\pi\) | |||||||
\(458\) | 1.35643e6 | 0.302157 | ||||||||
\(459\) | 361135. | 0.0800087 | ||||||||
\(460\) | −9.68276e6 | −2.13356 | ||||||||
\(461\) | −1.09360e6 | −0.239666 | −0.119833 | − | 0.992794i | \(-0.538236\pi\) | ||||
−0.119833 | + | 0.992794i | \(0.538236\pi\) | |||||||
\(462\) | −242594. | −0.0528779 | ||||||||
\(463\) | 1.94891e6 | 0.422513 | 0.211256 | − | 0.977431i | \(-0.432244\pi\) | ||||
0.211256 | + | 0.977431i | \(0.432244\pi\) | |||||||
\(464\) | 4.16284e6 | 0.897625 | ||||||||
\(465\) | −396823. | −0.0851068 | ||||||||
\(466\) | 1.21685e7 | 2.59580 | ||||||||
\(467\) | −4.69017e6 | −0.995169 | −0.497584 | − | 0.867416i | \(-0.665780\pi\) | ||||
−0.497584 | + | 0.867416i | \(0.665780\pi\) | |||||||
\(468\) | 2.75921e6 | 0.582332 | ||||||||
\(469\) | −691060. | −0.145072 | ||||||||
\(470\) | 3.56864e6 | 0.745174 | ||||||||
\(471\) | 1.07523e6 | 0.223331 | ||||||||
\(472\) | −1.96415e6 | −0.405808 | ||||||||
\(473\) | −95459.3 | −0.0196185 | ||||||||
\(474\) | 2.05831e6 | 0.420789 | ||||||||
\(475\) | −1.26453e7 | −2.57155 | ||||||||
\(476\) | 497888. | 0.100720 | ||||||||
\(477\) | 1.22557e6 | 0.246629 | ||||||||
\(478\) | 4.86128e6 | 0.973153 | ||||||||
\(479\) | 4.15576e6 | 0.827584 | 0.413792 | − | 0.910372i | \(-0.364204\pi\) | ||||
0.413792 | + | 0.910372i | \(0.364204\pi\) | |||||||
\(480\) | 8.00726e6 | 1.58628 | ||||||||
\(481\) | 5.27302e6 | 1.03919 | ||||||||
\(482\) | −3.62683e6 | −0.711066 | ||||||||
\(483\) | 574863. | 0.112123 | ||||||||
\(484\) | 551294. | 0.106972 | ||||||||
\(485\) | 1.08735e7 | 2.09902 | ||||||||
\(486\) | 492817. | 0.0946445 | ||||||||
\(487\) | −2.37242e6 | −0.453282 | −0.226641 | − | 0.973978i | \(-0.572774\pi\) | ||||
−0.226641 | + | 0.973978i | \(0.572774\pi\) | |||||||
\(488\) | 1.41518e6 | 0.269006 | ||||||||
\(489\) | −2.82611e6 | −0.534463 | ||||||||
\(490\) | −1.44343e7 | −2.71584 | ||||||||
\(491\) | −1.18797e6 | −0.222384 | −0.111192 | − | 0.993799i | \(-0.535467\pi\) | ||||
−0.111192 | + | 0.993799i | \(0.535467\pi\) | |||||||
\(492\) | −6.29036e6 | −1.17155 | ||||||||
\(493\) | 2.54248e6 | 0.471129 | ||||||||
\(494\) | 1.13358e7 | 2.08995 | ||||||||
\(495\) | −1.05321e6 | −0.193197 | ||||||||
\(496\) | 332802. | 0.0607409 | ||||||||
\(497\) | −1.55248e6 | −0.281925 | ||||||||
\(498\) | 1.80695e6 | 0.326492 | ||||||||
\(499\) | 710493. | 0.127735 | 0.0638673 | − | 0.997958i | \(-0.479657\pi\) | ||||
0.0638673 | + | 0.997958i | \(0.479657\pi\) | |||||||
\(500\) | −2.14349e7 | −3.83439 | ||||||||
\(501\) | −2.53689e6 | −0.451552 | ||||||||
\(502\) | 7.91345e6 | 1.40154 | ||||||||
\(503\) | 4.75381e6 | 0.837765 | 0.418882 | − | 0.908041i | \(-0.362422\pi\) | ||||
0.418882 | + | 0.908041i | \(0.362422\pi\) | |||||||
\(504\) | 102023. | 0.0178905 | ||||||||
\(505\) | 8.07986e6 | 1.40986 | ||||||||
\(506\) | −2.41659e6 | −0.419591 | ||||||||
\(507\) | −4.02414e6 | −0.695270 | ||||||||
\(508\) | 7.03215e6 | 1.20901 | ||||||||
\(509\) | −5.05479e6 | −0.864787 | −0.432393 | − | 0.901685i | \(-0.642331\pi\) | ||||
−0.432393 | + | 0.901685i | \(0.642331\pi\) | |||||||
\(510\) | 3.99853e6 | 0.680730 | ||||||||
\(511\) | −637275. | −0.107963 | ||||||||
\(512\) | −7.94021e6 | −1.33862 | ||||||||
\(513\) | 1.09451e6 | 0.183622 | ||||||||
\(514\) | −9.52179e6 | −1.58968 | ||||||||
\(515\) | −1.89191e7 | −3.14328 | ||||||||
\(516\) | 267355. | 0.0442042 | ||||||||
\(517\) | 481473. | 0.0792219 | ||||||||
\(518\) | 1.29844e6 | 0.212617 | ||||||||
\(519\) | −1.38718e6 | −0.226055 | ||||||||
\(520\) | 4.58741e6 | 0.743977 | ||||||||
\(521\) | −4.69775e6 | −0.758220 | −0.379110 | − | 0.925352i | \(-0.623770\pi\) | ||||
−0.379110 | + | 0.925352i | \(0.623770\pi\) | |||||||
\(522\) | 3.46956e6 | 0.557311 | ||||||||
\(523\) | −1.97083e6 | −0.315062 | −0.157531 | − | 0.987514i | \(-0.550353\pi\) | ||||
−0.157531 | + | 0.987514i | \(0.550353\pi\) | |||||||
\(524\) | −1.36912e7 | −2.17827 | ||||||||
\(525\) | 2.02329e6 | 0.320376 | ||||||||
\(526\) | −2.34449e6 | −0.369474 | ||||||||
\(527\) | 203260. | 0.0318806 | ||||||||
\(528\) | 883288. | 0.137885 | ||||||||
\(529\) | −709863. | −0.110290 | ||||||||
\(530\) | 1.35697e7 | 2.09836 | ||||||||
\(531\) | 3.37151e6 | 0.518905 | ||||||||
\(532\) | 1.50897e6 | 0.231155 | ||||||||
\(533\) | 1.67922e7 | 2.56030 | ||||||||
\(534\) | −4.19282e6 | −0.636286 | ||||||||
\(535\) | 1.34285e7 | 2.02834 | ||||||||
\(536\) | −1.22173e6 | −0.183680 | ||||||||
\(537\) | −5.42963e6 | −0.812521 | ||||||||
\(538\) | −9.07690e6 | −1.35202 | ||||||||
\(539\) | −1.94744e6 | −0.288730 | ||||||||
\(540\) | 2.94973e6 | 0.435310 | ||||||||
\(541\) | −5.76437e6 | −0.846757 | −0.423378 | − | 0.905953i | \(-0.639156\pi\) | ||||
−0.423378 | + | 0.905953i | \(0.639156\pi\) | |||||||
\(542\) | −9.84222e6 | −1.43911 | ||||||||
\(543\) | 5.04377e6 | 0.734100 | ||||||||
\(544\) | −4.10148e6 | −0.594214 | ||||||||
\(545\) | −5.15819e6 | −0.743886 | ||||||||
\(546\) | −1.81377e6 | −0.260376 | ||||||||
\(547\) | −4.65202e6 | −0.664772 | −0.332386 | − | 0.943143i | \(-0.607854\pi\) | ||||
−0.332386 | + | 0.943143i | \(0.607854\pi\) | |||||||
\(548\) | −2.78650e6 | −0.396376 | ||||||||
\(549\) | −2.42918e6 | −0.343976 | ||||||||
\(550\) | −8.50544e6 | −1.19892 | ||||||||
\(551\) | 7.70561e6 | 1.08126 | ||||||||
\(552\) | 1.01630e6 | 0.141963 | ||||||||
\(553\) | −731430. | −0.101709 | ||||||||
\(554\) | 5.18578e6 | 0.717860 | ||||||||
\(555\) | 5.63711e6 | 0.776826 | ||||||||
\(556\) | 2.63738e6 | 0.361814 | ||||||||
\(557\) | −4.24834e6 | −0.580204 | −0.290102 | − | 0.956996i | \(-0.593689\pi\) | ||||
−0.290102 | + | 0.956996i | \(0.593689\pi\) | |||||||
\(558\) | 277376. | 0.0377124 | ||||||||
\(559\) | −713709. | −0.0966032 | ||||||||
\(560\) | −2.32646e6 | −0.313491 | ||||||||
\(561\) | 539473. | 0.0723706 | ||||||||
\(562\) | 2.03630e6 | 0.271958 | ||||||||
\(563\) | −3.09512e6 | −0.411534 | −0.205767 | − | 0.978601i | \(-0.565969\pi\) | ||||
−0.205767 | + | 0.978601i | \(0.565969\pi\) | |||||||
\(564\) | −1.34847e6 | −0.178502 | ||||||||
\(565\) | −4.18613e6 | −0.551686 | ||||||||
\(566\) | 1.54048e7 | 2.02122 | ||||||||
\(567\) | −175125. | −0.0228765 | ||||||||
\(568\) | −2.74463e6 | −0.356954 | ||||||||
\(569\) | −7.60568e6 | −0.984821 | −0.492411 | − | 0.870363i | \(-0.663884\pi\) | ||||
−0.492411 | + | 0.870363i | \(0.663884\pi\) | |||||||
\(570\) | 1.21185e7 | 1.56230 | ||||||||
\(571\) | −2.28582e6 | −0.293395 | −0.146697 | − | 0.989181i | \(-0.546864\pi\) | ||||
−0.146697 | + | 0.989181i | \(0.546864\pi\) | |||||||
\(572\) | 4.12179e6 | 0.526739 | ||||||||
\(573\) | −3.03529e6 | −0.386202 | ||||||||
\(574\) | 4.13496e6 | 0.523832 | ||||||||
\(575\) | 2.01550e7 | 2.54222 | ||||||||
\(576\) | −3.49465e6 | −0.438882 | ||||||||
\(577\) | −6.27770e6 | −0.784984 | −0.392492 | − | 0.919755i | \(-0.628387\pi\) | ||||
−0.392492 | + | 0.919755i | \(0.628387\pi\) | |||||||
\(578\) | 9.80186e6 | 1.22036 | ||||||||
\(579\) | −3.84302e6 | −0.476405 | ||||||||
\(580\) | 2.07669e7 | 2.56331 | ||||||||
\(581\) | −642107. | −0.0789164 | ||||||||
\(582\) | −7.60053e6 | −0.930114 | ||||||||
\(583\) | 1.83079e6 | 0.223084 | ||||||||
\(584\) | −1.12664e6 | −0.136695 | ||||||||
\(585\) | −7.87437e6 | −0.951320 | ||||||||
\(586\) | 1.12586e7 | 1.35437 | ||||||||
\(587\) | −1.48651e6 | −0.178063 | −0.0890314 | − | 0.996029i | \(-0.528377\pi\) | ||||
−0.0890314 | + | 0.996029i | \(0.528377\pi\) | |||||||
\(588\) | 5.45423e6 | 0.650564 | ||||||||
\(589\) | 616031. | 0.0731669 | ||||||||
\(590\) | 3.73298e7 | 4.41494 | ||||||||
\(591\) | −3.48797e6 | −0.410775 | ||||||||
\(592\) | −4.72765e6 | −0.554423 | ||||||||
\(593\) | 4.72874e6 | 0.552216 | 0.276108 | − | 0.961127i | \(-0.410955\pi\) | ||||
0.276108 | + | 0.961127i | \(0.410955\pi\) | |||||||
\(594\) | 736184. | 0.0856091 | ||||||||
\(595\) | −1.42090e6 | −0.164539 | ||||||||
\(596\) | 1.23418e7 | 1.42319 | ||||||||
\(597\) | −5.07968e6 | −0.583312 | ||||||||
\(598\) | −1.80678e7 | −2.06611 | ||||||||
\(599\) | −325927. | −0.0371153 | −0.0185577 | − | 0.999828i | \(-0.505907\pi\) | ||||
−0.0185577 | + | 0.999828i | \(0.505907\pi\) | |||||||
\(600\) | 3.57699e6 | 0.405638 | ||||||||
\(601\) | −1.30291e7 | −1.47140 | −0.735698 | − | 0.677310i | \(-0.763146\pi\) | ||||
−0.735698 | + | 0.677310i | \(0.763146\pi\) | |||||||
\(602\) | −175745. | −0.0197648 | ||||||||
\(603\) | 2.09712e6 | 0.234871 | ||||||||
\(604\) | 19573.6 | 0.00218313 | ||||||||
\(605\) | −1.57331e6 | −0.174753 | ||||||||
\(606\) | −5.64776e6 | −0.624734 | ||||||||
\(607\) | −1.45956e6 | −0.160787 | −0.0803933 | − | 0.996763i | \(-0.525618\pi\) | ||||
−0.0803933 | + | 0.996763i | \(0.525618\pi\) | |||||||
\(608\) | −1.24305e7 | −1.36374 | ||||||||
\(609\) | −1.23292e6 | −0.134708 | ||||||||
\(610\) | −2.68962e7 | −2.92662 | ||||||||
\(611\) | 3.59977e6 | 0.390096 | ||||||||
\(612\) | −1.51091e6 | −0.163065 | ||||||||
\(613\) | 1.26574e7 | 1.36048 | 0.680241 | − | 0.732989i | \(-0.261875\pi\) | ||||
0.680241 | + | 0.732989i | \(0.261875\pi\) | |||||||
\(614\) | 1.00606e7 | 1.07697 | ||||||||
\(615\) | 1.79517e7 | 1.91390 | ||||||||
\(616\) | 152405. | 0.0161826 | ||||||||
\(617\) | 2.57472e6 | 0.272281 | 0.136140 | − | 0.990690i | \(-0.456530\pi\) | ||||
0.136140 | + | 0.990690i | \(0.456530\pi\) | |||||||
\(618\) | 1.32244e7 | 1.39285 | ||||||||
\(619\) | −1.82556e7 | −1.91500 | −0.957500 | − | 0.288434i | \(-0.906866\pi\) | ||||
−0.957500 | + | 0.288434i | \(0.906866\pi\) | |||||||
\(620\) | 1.66022e6 | 0.173455 | ||||||||
\(621\) | −1.74450e6 | −0.181527 | ||||||||
\(622\) | −5.31530e6 | −0.550873 | ||||||||
\(623\) | 1.48994e6 | 0.153797 | ||||||||
\(624\) | 6.60397e6 | 0.678959 | ||||||||
\(625\) | 3.48518e7 | 3.56882 | ||||||||
\(626\) | −1.55672e7 | −1.58773 | ||||||||
\(627\) | 1.63501e6 | 0.166093 | ||||||||
\(628\) | −4.49854e6 | −0.455169 | ||||||||
\(629\) | −2.88744e6 | −0.290995 | ||||||||
\(630\) | −1.93901e6 | −0.194638 | ||||||||
\(631\) | 7.91613e6 | 0.791480 | 0.395740 | − | 0.918363i | \(-0.370488\pi\) | ||||
0.395740 | + | 0.918363i | \(0.370488\pi\) | |||||||
\(632\) | −1.29310e6 | −0.128777 | ||||||||
\(633\) | −4.45903e6 | −0.442315 | ||||||||
\(634\) | −1.96477e7 | −1.94128 | ||||||||
\(635\) | −2.00687e7 | −1.97508 | ||||||||
\(636\) | −5.12754e6 | −0.502651 | ||||||||
\(637\) | −1.45602e7 | −1.42173 | ||||||||
\(638\) | 5.18292e6 | 0.504107 | ||||||||
\(639\) | 4.71120e6 | 0.456436 | ||||||||
\(640\) | −1.02230e7 | −0.986568 | ||||||||
\(641\) | −3.40205e6 | −0.327036 | −0.163518 | − | 0.986540i | \(-0.552284\pi\) | ||||
−0.163518 | + | 0.986540i | \(0.552284\pi\) | |||||||
\(642\) | −9.38640e6 | −0.898796 | ||||||||
\(643\) | −6.92901e6 | −0.660912 | −0.330456 | − | 0.943821i | \(-0.607203\pi\) | ||||
−0.330456 | + | 0.943821i | \(0.607203\pi\) | |||||||
\(644\) | −2.40511e6 | −0.228517 | ||||||||
\(645\) | −762989. | −0.0722136 | ||||||||
\(646\) | −6.20736e6 | −0.585228 | ||||||||
\(647\) | 1.11125e7 | 1.04364 | 0.521819 | − | 0.853056i | \(-0.325254\pi\) | ||||
0.521819 | + | 0.853056i | \(0.325254\pi\) | |||||||
\(648\) | −309604. | −0.0289647 | ||||||||
\(649\) | 5.03645e6 | 0.469367 | ||||||||
\(650\) | −6.35916e7 | −5.90359 | ||||||||
\(651\) | −98567.0 | −0.00911547 | ||||||||
\(652\) | 1.18239e7 | 1.08928 | ||||||||
\(653\) | 6.61748e6 | 0.607309 | 0.303654 | − | 0.952782i | \(-0.401793\pi\) | ||||
0.303654 | + | 0.952782i | \(0.401793\pi\) | |||||||
\(654\) | 3.60554e6 | 0.329629 | ||||||||
\(655\) | 3.90725e7 | 3.55850 | ||||||||
\(656\) | −1.50555e7 | −1.36595 | ||||||||
\(657\) | 1.93390e6 | 0.174792 | ||||||||
\(658\) | 886416. | 0.0798128 | ||||||||
\(659\) | 1.88838e7 | 1.69385 | 0.846926 | − | 0.531711i | \(-0.178451\pi\) | ||||
0.846926 | + | 0.531711i | \(0.178451\pi\) | |||||||
\(660\) | 4.40639e6 | 0.393752 | ||||||||
\(661\) | 7.10304e6 | 0.632326 | 0.316163 | − | 0.948705i | \(-0.397605\pi\) | ||||
0.316163 | + | 0.948705i | \(0.397605\pi\) | |||||||
\(662\) | −1.65155e7 | −1.46469 | ||||||||
\(663\) | 4.03341e6 | 0.356360 | ||||||||
\(664\) | −1.13518e6 | −0.0999185 | ||||||||
\(665\) | −4.30638e6 | −0.377623 | ||||||||
\(666\) | −3.94030e6 | −0.344226 | ||||||||
\(667\) | −1.22817e7 | −1.06892 | ||||||||
\(668\) | 1.06138e7 | 0.920303 | ||||||||
\(669\) | −1.11165e7 | −0.960291 | ||||||||
\(670\) | 2.32196e7 | 1.99833 | ||||||||
\(671\) | −3.62877e6 | −0.311138 | ||||||||
\(672\) | 1.98893e6 | 0.169901 | ||||||||
\(673\) | −1.79739e7 | −1.52970 | −0.764849 | − | 0.644209i | \(-0.777187\pi\) | ||||
−0.764849 | + | 0.644209i | \(0.777187\pi\) | |||||||
\(674\) | −2.38880e7 | −2.02549 | ||||||||
\(675\) | −6.13996e6 | −0.518688 | ||||||||
\(676\) | 1.68362e7 | 1.41702 | ||||||||
\(677\) | −617034. | −0.0517413 | −0.0258706 | − | 0.999665i | \(-0.508236\pi\) | ||||
−0.0258706 | + | 0.999665i | \(0.508236\pi\) | |||||||
\(678\) | 2.92608e6 | 0.244462 | ||||||||
\(679\) | 2.70088e6 | 0.224818 | ||||||||
\(680\) | −2.51201e6 | −0.208329 | ||||||||
\(681\) | 7.21961e6 | 0.596549 | ||||||||
\(682\) | 414352. | 0.0341121 | ||||||||
\(683\) | 924287. | 0.0758150 | 0.0379075 | − | 0.999281i | \(-0.487931\pi\) | ||||
0.0379075 | + | 0.999281i | \(0.487931\pi\) | |||||||
\(684\) | −4.57919e6 | −0.374239 | ||||||||
\(685\) | 7.95225e6 | 0.647535 | ||||||||
\(686\) | −7.32939e6 | −0.594644 | ||||||||
\(687\) | 1.46273e6 | 0.118242 | ||||||||
\(688\) | 639893. | 0.0515390 | ||||||||
\(689\) | 1.36881e7 | 1.09849 | ||||||||
\(690\) | −1.93154e7 | −1.54447 | ||||||||
\(691\) | 2.33550e7 | 1.86074 | 0.930368 | − | 0.366627i | \(-0.119487\pi\) | ||||
0.930368 | + | 0.366627i | \(0.119487\pi\) | |||||||
\(692\) | 5.80365e6 | 0.460719 | ||||||||
\(693\) | −261606. | −0.0206926 | ||||||||
\(694\) | 1.51490e7 | 1.19395 | ||||||||
\(695\) | −7.52668e6 | −0.591073 | ||||||||
\(696\) | −2.17969e6 | −0.170558 | ||||||||
\(697\) | −9.19522e6 | −0.716936 | ||||||||
\(698\) | 1.48479e7 | 1.15353 | ||||||||
\(699\) | 1.31222e7 | 1.01581 | ||||||||
\(700\) | −8.46503e6 | −0.652955 | ||||||||
\(701\) | 1.15300e7 | 0.886206 | 0.443103 | − | 0.896471i | \(-0.353878\pi\) | ||||
0.443103 | + | 0.896471i | \(0.353878\pi\) | |||||||
\(702\) | 5.50413e6 | 0.421547 | ||||||||
\(703\) | −8.75110e6 | −0.667843 | ||||||||
\(704\) | −5.22040e6 | −0.396984 | ||||||||
\(705\) | 3.84832e6 | 0.291608 | ||||||||
\(706\) | 3.49540e7 | 2.63928 | ||||||||
\(707\) | 2.00696e6 | 0.151005 | ||||||||
\(708\) | −1.41057e7 | −1.05757 | ||||||||
\(709\) | −1.13035e7 | −0.844497 | −0.422248 | − | 0.906480i | \(-0.638759\pi\) | ||||
−0.422248 | + | 0.906480i | \(0.638759\pi\) | |||||||
\(710\) | 5.21631e7 | 3.88344 | ||||||||
\(711\) | 2.21962e6 | 0.164667 | ||||||||
\(712\) | 2.63407e6 | 0.194727 | ||||||||
\(713\) | −981872. | −0.0723321 | ||||||||
\(714\) | 993197. | 0.0729105 | ||||||||
\(715\) | −1.17630e7 | −0.860501 | ||||||||
\(716\) | 2.27164e7 | 1.65599 | ||||||||
\(717\) | 5.24228e6 | 0.380822 | ||||||||
\(718\) | −9.44276e6 | −0.683578 | ||||||||
\(719\) | 406909. | 0.0293545 | 0.0146773 | − | 0.999892i | \(-0.495328\pi\) | ||||
0.0146773 | + | 0.999892i | \(0.495328\pi\) | |||||||
\(720\) | 7.05996e6 | 0.507541 | ||||||||
\(721\) | −4.69934e6 | −0.336665 | ||||||||
\(722\) | 1.85234e6 | 0.132245 | ||||||||
\(723\) | −3.91108e6 | −0.278260 | ||||||||
\(724\) | −2.11020e7 | −1.49616 | ||||||||
\(725\) | −4.32268e7 | −3.05428 | ||||||||
\(726\) | 1.09973e6 | 0.0774364 | ||||||||
\(727\) | 1.93239e6 | 0.135600 | 0.0678000 | − | 0.997699i | \(-0.478402\pi\) | ||||
0.0678000 | + | 0.997699i | \(0.478402\pi\) | |||||||
\(728\) | 1.13947e6 | 0.0796846 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.14124e7 | 1.48716 | ||||||||
\(731\) | 390818. | 0.0270509 | ||||||||
\(732\) | 1.01632e7 | 0.701054 | ||||||||
\(733\) | 357394. | 0.0245690 | 0.0122845 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122845 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(734\) | −1.10102e7 | −0.754320 | ||||||||
\(735\) | −1.55655e7 | −1.06279 | ||||||||
\(736\) | 1.98126e7 | 1.34818 | ||||||||
\(737\) | 3.13273e6 | 0.212449 | ||||||||
\(738\) | −1.25481e7 | −0.848082 | ||||||||
\(739\) | 2.22117e7 | 1.49613 | 0.748066 | − | 0.663624i | \(-0.230983\pi\) | ||||
0.748066 | + | 0.663624i | \(0.230983\pi\) | |||||||
\(740\) | −2.35845e7 | −1.58324 | ||||||||
\(741\) | 1.22243e7 | 0.817856 | ||||||||
\(742\) | 3.37059e6 | 0.224748 | ||||||||
\(743\) | −2.10894e7 | −1.40149 | −0.700747 | − | 0.713410i | \(-0.747150\pi\) | ||||
−0.700747 | + | 0.713410i | \(0.747150\pi\) | |||||||
\(744\) | −174257. | −0.0115414 | ||||||||
\(745\) | −3.52215e7 | −2.32497 | ||||||||
\(746\) | −6192.20 | −0.000407378 0 | ||||||||
\(747\) | 1.94856e6 | 0.127765 | ||||||||
\(748\) | −2.25704e6 | −0.147498 | ||||||||
\(749\) | 3.33550e6 | 0.217248 | ||||||||
\(750\) | −4.27588e7 | −2.77570 | ||||||||
\(751\) | −3.08277e7 | −1.99453 | −0.997267 | − | 0.0738774i | \(-0.976463\pi\) | ||||
−0.997267 | + | 0.0738774i | \(0.976463\pi\) | |||||||
\(752\) | −3.22746e6 | −0.208121 | ||||||||
\(753\) | 8.53366e6 | 0.548464 | ||||||||
\(754\) | 3.87505e7 | 2.48227 | ||||||||
\(755\) | −55860.2 | −0.00356644 | ||||||||
\(756\) | 732686. | 0.0466244 | ||||||||
\(757\) | 3.26795e6 | 0.207270 | 0.103635 | − | 0.994615i | \(-0.466953\pi\) | ||||
0.103635 | + | 0.994615i | \(0.466953\pi\) | |||||||
\(758\) | 4.73577e6 | 0.299376 | ||||||||
\(759\) | −2.60598e6 | −0.164198 | ||||||||
\(760\) | −7.61327e6 | −0.478120 | ||||||||
\(761\) | 1.01120e7 | 0.632961 | 0.316480 | − | 0.948599i | \(-0.397499\pi\) | ||||
0.316480 | + | 0.948599i | \(0.397499\pi\) | |||||||
\(762\) | 1.40279e7 | 0.875194 | ||||||||
\(763\) | −1.28125e6 | −0.0796748 | ||||||||
\(764\) | 1.26990e7 | 0.787113 | ||||||||
\(765\) | 4.31191e6 | 0.266389 | ||||||||
\(766\) | −2.96137e7 | −1.82356 | ||||||||
\(767\) | 3.76554e7 | 2.31121 | ||||||||
\(768\) | −5.27964e6 | −0.322999 | ||||||||
\(769\) | 2.14392e7 | 1.30735 | 0.653676 | − | 0.756775i | \(-0.273226\pi\) | ||||
0.653676 | + | 0.756775i | \(0.273226\pi\) | |||||||
\(770\) | −2.89654e6 | −0.176057 | ||||||||
\(771\) | −1.02680e7 | −0.622088 | ||||||||
\(772\) | 1.60784e7 | 0.970955 | ||||||||
\(773\) | −1.89394e7 | −1.14003 | −0.570017 | − | 0.821633i | \(-0.693063\pi\) | ||||
−0.570017 | + | 0.821633i | \(0.693063\pi\) | |||||||
\(774\) | 533324. | 0.0319992 | ||||||||
\(775\) | −3.45580e6 | −0.206678 | ||||||||
\(776\) | 4.77490e6 | 0.284649 | ||||||||
\(777\) | 1.40020e6 | 0.0832030 | ||||||||
\(778\) | −3.41627e7 | −2.02350 | ||||||||
\(779\) | −2.78684e7 | −1.64539 | ||||||||
\(780\) | 3.29447e7 | 1.93887 | ||||||||
\(781\) | 7.03772e6 | 0.412862 | ||||||||
\(782\) | 9.89370e6 | 0.578551 | ||||||||
\(783\) | 3.74148e6 | 0.218091 | ||||||||
\(784\) | 1.30543e7 | 0.758513 | ||||||||
\(785\) | 1.28381e7 | 0.743580 | ||||||||
\(786\) | −2.73114e7 | −1.57684 | ||||||||
\(787\) | −1.10351e7 | −0.635096 | −0.317548 | − | 0.948242i | \(-0.602859\pi\) | ||||
−0.317548 | + | 0.948242i | \(0.602859\pi\) | |||||||
\(788\) | 1.45929e7 | 0.837195 | ||||||||
\(789\) | −2.52824e6 | −0.144586 | ||||||||
\(790\) | 2.45760e7 | 1.40102 | ||||||||
\(791\) | −1.03980e6 | −0.0590890 | ||||||||
\(792\) | −462495. | −0.0261996 | ||||||||
\(793\) | −2.71308e7 | −1.53207 | ||||||||
\(794\) | −1.28118e6 | −0.0721208 | ||||||||
\(795\) | 1.46332e7 | 0.821149 | ||||||||
\(796\) | 2.12523e7 | 1.18884 | ||||||||
\(797\) | −1.22483e7 | −0.683015 | −0.341507 | − | 0.939879i | \(-0.610937\pi\) | ||||
−0.341507 | + | 0.939879i | \(0.610937\pi\) | |||||||
\(798\) | 3.01013e6 | 0.167332 | ||||||||
\(799\) | −1.97119e6 | −0.109235 | ||||||||
\(800\) | 6.97327e7 | 3.85223 | ||||||||
\(801\) | −4.52142e6 | −0.248997 | ||||||||
\(802\) | −3.95949e6 | −0.217372 | ||||||||
\(803\) | 2.88891e6 | 0.158105 | ||||||||
\(804\) | −8.77390e6 | −0.478688 | ||||||||
\(805\) | 6.86380e6 | 0.373315 | ||||||||
\(806\) | 3.09794e6 | 0.167971 | ||||||||
\(807\) | −9.78829e6 | −0.529082 | ||||||||
\(808\) | 3.54811e6 | 0.191192 | ||||||||
\(809\) | −2.42528e7 | −1.30284 | −0.651421 | − | 0.758717i | \(-0.725827\pi\) | ||||
−0.651421 | + | 0.758717i | \(0.725827\pi\) | |||||||
\(810\) | 5.88418e6 | 0.315118 | ||||||||
\(811\) | 3.64893e7 | 1.94811 | 0.974055 | − | 0.226311i | \(-0.0726664\pi\) | ||||
0.974055 | + | 0.226311i | \(0.0726664\pi\) | |||||||
\(812\) | 5.15829e6 | 0.274546 | ||||||||
\(813\) | −1.06136e7 | −0.563166 | ||||||||
\(814\) | −5.88613e6 | −0.311364 | ||||||||
\(815\) | −3.37435e7 | −1.77949 | ||||||||
\(816\) | −3.61625e6 | −0.190122 | ||||||||
\(817\) | 1.18447e6 | 0.0620825 | ||||||||
\(818\) | −2.38064e7 | −1.24397 | ||||||||
\(819\) | −1.95592e6 | −0.101892 | ||||||||
\(820\) | −7.51062e7 | −3.90069 | ||||||||
\(821\) | 2.40297e7 | 1.24420 | 0.622100 | − | 0.782938i | \(-0.286280\pi\) | ||||
0.622100 | + | 0.782938i | \(0.286280\pi\) | |||||||
\(822\) | −5.55857e6 | −0.286935 | ||||||||
\(823\) | −1.16283e7 | −0.598432 | −0.299216 | − | 0.954185i | \(-0.596725\pi\) | ||||
−0.299216 | + | 0.954185i | \(0.596725\pi\) | |||||||
\(824\) | −8.30798e6 | −0.426263 | ||||||||
\(825\) | −9.17204e6 | −0.469171 | ||||||||
\(826\) | 9.27236e6 | 0.472868 | ||||||||
\(827\) | 1.01425e7 | 0.515680 | 0.257840 | − | 0.966188i | \(-0.416989\pi\) | ||||
0.257840 | + | 0.966188i | \(0.416989\pi\) | |||||||
\(828\) | 7.29863e6 | 0.369969 | ||||||||
\(829\) | 1.51928e7 | 0.767804 | 0.383902 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383902 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(830\) | 2.15748e7 | 1.08705 | ||||||||
\(831\) | 5.59221e6 | 0.280919 | ||||||||
\(832\) | −3.90307e7 | −1.95478 | ||||||||
\(833\) | 7.97298e6 | 0.398114 | ||||||||
\(834\) | 5.26110e6 | 0.261916 | ||||||||
\(835\) | −3.02902e7 | −1.50344 | ||||||||
\(836\) | −6.84052e6 | −0.338512 | ||||||||
\(837\) | 299115. | 0.0147579 | ||||||||
\(838\) | −5.52426e7 | −2.71747 | ||||||||
\(839\) | −9.62729e6 | −0.472171 | −0.236085 | − | 0.971732i | \(-0.575864\pi\) | ||||
−0.236085 | + | 0.971732i | \(0.575864\pi\) | |||||||
\(840\) | 1.21815e6 | 0.0595665 | ||||||||
\(841\) | 5.82977e6 | 0.284225 | ||||||||
\(842\) | −1.39860e7 | −0.679849 | ||||||||
\(843\) | 2.19590e6 | 0.106425 | ||||||||
\(844\) | 1.86557e7 | 0.901477 | ||||||||
\(845\) | −4.80478e7 | −2.31490 | ||||||||
\(846\) | −2.68995e6 | −0.129217 | ||||||||
\(847\) | −390795. | −0.0187172 | ||||||||
\(848\) | −1.22724e7 | −0.586056 | ||||||||
\(849\) | 1.66121e7 | 0.790962 | ||||||||
\(850\) | 3.48219e7 | 1.65313 | ||||||||
\(851\) | 1.39481e7 | 0.660223 | ||||||||
\(852\) | −1.97107e7 | −0.930256 | ||||||||
\(853\) | 7.49543e6 | 0.352715 | 0.176358 | − | 0.984326i | \(-0.443568\pi\) | ||||
0.176358 | + | 0.984326i | \(0.443568\pi\) | |||||||
\(854\) | −6.68076e6 | −0.313459 | ||||||||
\(855\) | 1.30683e7 | 0.611370 | ||||||||
\(856\) | 5.89684e6 | 0.275065 | ||||||||
\(857\) | −2.69493e6 | −0.125342 | −0.0626708 | − | 0.998034i | \(-0.519962\pi\) | ||||
−0.0626708 | + | 0.998034i | \(0.519962\pi\) | |||||||
\(858\) | 8.22222e6 | 0.381304 | ||||||||
\(859\) | −3.28791e7 | −1.52033 | −0.760164 | − | 0.649731i | \(-0.774882\pi\) | ||||
−0.760164 | + | 0.649731i | \(0.774882\pi\) | |||||||
\(860\) | 3.19218e6 | 0.147178 | ||||||||
\(861\) | 4.45904e6 | 0.204990 | ||||||||
\(862\) | 3.78784e7 | 1.73629 | ||||||||
\(863\) | 3.03331e7 | 1.38640 | 0.693202 | − | 0.720744i | \(-0.256199\pi\) | ||||
0.693202 | + | 0.720744i | \(0.256199\pi\) | |||||||
\(864\) | −6.03568e6 | −0.275069 | ||||||||
\(865\) | −1.65627e7 | −0.752648 | ||||||||
\(866\) | −3.16815e6 | −0.143553 | ||||||||
\(867\) | 1.05701e7 | 0.477562 | ||||||||
\(868\) | 412383. | 0.0185781 | ||||||||
\(869\) | 3.31574e6 | 0.148947 | ||||||||
\(870\) | 4.14261e7 | 1.85556 | ||||||||
\(871\) | 2.34221e7 | 1.04612 | ||||||||
\(872\) | −2.26512e6 | −0.100879 | ||||||||
\(873\) | −8.19621e6 | −0.363980 | ||||||||
\(874\) | 2.99853e7 | 1.32779 | ||||||||
\(875\) | 1.51945e7 | 0.670914 | ||||||||
\(876\) | −8.09103e6 | −0.356241 | ||||||||
\(877\) | −3.81826e7 | −1.67636 | −0.838178 | − | 0.545396i | \(-0.816379\pi\) | ||||
−0.838178 | + | 0.545396i | \(0.816379\pi\) | |||||||
\(878\) | 1.65064e7 | 0.722628 | ||||||||
\(879\) | 1.21409e7 | 0.530005 | ||||||||
\(880\) | 1.05464e7 | 0.459088 | ||||||||
\(881\) | −8.09402e6 | −0.351338 | −0.175669 | − | 0.984449i | \(-0.556209\pi\) | ||||
−0.175669 | + | 0.984449i | \(0.556209\pi\) | |||||||
\(882\) | 1.08802e7 | 0.470940 | ||||||||
\(883\) | 1.90914e7 | 0.824018 | 0.412009 | − | 0.911180i | \(-0.364827\pi\) | ||||
0.412009 | + | 0.911180i | \(0.364827\pi\) | |||||||
\(884\) | −1.68749e7 | −0.726292 | ||||||||
\(885\) | 4.02554e7 | 1.72769 | ||||||||
\(886\) | −2.99095e7 | −1.28004 | ||||||||
\(887\) | 1.40640e7 | 0.600205 | 0.300102 | − | 0.953907i | \(-0.402979\pi\) | ||||
0.300102 | + | 0.953907i | \(0.402979\pi\) | |||||||
\(888\) | 2.47543e6 | 0.105346 | ||||||||
\(889\) | −4.98487e6 | −0.211543 | ||||||||
\(890\) | −5.00618e7 | −2.11851 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 4.65091e7 | 1.95716 | ||||||||
\(893\) | −5.97417e6 | −0.250697 | ||||||||
\(894\) | 2.46196e7 | 1.03024 | ||||||||
\(895\) | −6.48292e7 | −2.70529 | ||||||||
\(896\) | −2.53929e6 | −0.105668 | ||||||||
\(897\) | −1.94838e7 | −0.808525 | ||||||||
\(898\) | 8.82452e6 | 0.365174 | ||||||||
\(899\) | 2.10585e6 | 0.0869015 | ||||||||
\(900\) | 2.56883e7 | 1.05713 | ||||||||
\(901\) | −7.49542e6 | −0.307598 | ||||||||
\(902\) | −1.87447e7 | −0.767119 | ||||||||
\(903\) | −189519. | −0.00773453 | ||||||||
\(904\) | −1.83826e6 | −0.0748145 | ||||||||
\(905\) | 6.02220e7 | 2.44418 | ||||||||
\(906\) | 39045.9 | 0.00158036 | ||||||||
\(907\) | 1.37464e7 | 0.554845 | 0.277423 | − | 0.960748i | \(-0.410520\pi\) | ||||
0.277423 | + | 0.960748i | \(0.410520\pi\) | |||||||
\(908\) | −3.02053e7 | −1.21582 | ||||||||
\(909\) | −6.09040e6 | −0.244476 | ||||||||
\(910\) | −2.16562e7 | −0.866920 | ||||||||
\(911\) | 3.83931e7 | 1.53270 | 0.766350 | − | 0.642423i | \(-0.222071\pi\) | ||||
0.766350 | + | 0.642423i | \(0.222071\pi\) | |||||||
\(912\) | −1.09600e7 | −0.436336 | ||||||||
\(913\) | 2.91082e6 | 0.115568 | ||||||||
\(914\) | −1.16021e7 | −0.459381 | ||||||||
\(915\) | −2.90041e7 | −1.14527 | ||||||||
\(916\) | −6.11977e6 | −0.240988 | ||||||||
\(917\) | 9.70523e6 | 0.381138 | ||||||||
\(918\) | −3.01399e6 | −0.118042 | ||||||||
\(919\) | 1.85935e7 | 0.726227 | 0.363114 | − | 0.931745i | \(-0.381714\pi\) | ||||
0.363114 | + | 0.931745i | \(0.381714\pi\) | |||||||
\(920\) | 1.21345e7 | 0.472665 | ||||||||
\(921\) | 1.08491e7 | 0.421448 | ||||||||
\(922\) | 9.12710e6 | 0.353595 | ||||||||
\(923\) | 5.26181e7 | 2.03297 | ||||||||
\(924\) | 1.09451e6 | 0.0421734 | ||||||||
\(925\) | 4.90918e7 | 1.88649 | ||||||||
\(926\) | −1.62654e7 | −0.623359 | ||||||||
\(927\) | 1.42608e7 | 0.545060 | ||||||||
\(928\) | −4.24927e7 | −1.61974 | ||||||||
\(929\) | −2.77987e7 | −1.05678 | −0.528391 | − | 0.849001i | \(-0.677204\pi\) | ||||
−0.528391 | + | 0.849001i | \(0.677204\pi\) | |||||||
\(930\) | 3.31184e6 | 0.125563 | ||||||||
\(931\) | 2.41641e7 | 0.913684 | ||||||||
\(932\) | −5.49004e7 | −2.07031 | ||||||||
\(933\) | −5.73187e6 | −0.215572 | ||||||||
\(934\) | 3.91437e7 | 1.46823 | ||||||||
\(935\) | 6.44125e6 | 0.240958 | ||||||||
\(936\) | −3.45788e6 | −0.129009 | ||||||||
\(937\) | 4.55794e7 | 1.69598 | 0.847988 | − | 0.530015i | \(-0.177814\pi\) | ||||
0.847988 | + | 0.530015i | \(0.177814\pi\) | |||||||
\(938\) | 5.76752e6 | 0.214034 | ||||||||
\(939\) | −1.67873e7 | −0.621322 | ||||||||
\(940\) | −1.61006e7 | −0.594322 | ||||||||
\(941\) | −2.38944e7 | −0.879676 | −0.439838 | − | 0.898077i | \(-0.644964\pi\) | ||||
−0.439838 | + | 0.898077i | \(0.644964\pi\) | |||||||
\(942\) | −8.97377e6 | −0.329494 | ||||||||
\(943\) | 4.44186e7 | 1.62662 | ||||||||
\(944\) | −3.37609e7 | −1.23306 | ||||||||
\(945\) | −2.09097e6 | −0.0761674 | ||||||||
\(946\) | 796694. | 0.0289443 | ||||||||
\(947\) | 3.52637e7 | 1.27777 | 0.638885 | − | 0.769302i | \(-0.279396\pi\) | ||||
0.638885 | + | 0.769302i | \(0.279396\pi\) | |||||||
\(948\) | −9.28644e6 | −0.335605 | ||||||||
\(949\) | 2.15992e7 | 0.778523 | ||||||||
\(950\) | 1.05537e8 | 3.79397 | ||||||||
\(951\) | −2.11875e7 | −0.759678 | ||||||||
\(952\) | −623959. | −0.0223133 | ||||||||
\(953\) | 5.08550e7 | 1.81385 | 0.906924 | − | 0.421293i | \(-0.138424\pi\) | ||||
0.906924 | + | 0.421293i | \(0.138424\pi\) | |||||||
\(954\) | −1.02285e7 | −0.363866 | ||||||||
\(955\) | −3.62411e7 | −1.28586 | ||||||||
\(956\) | −2.19326e7 | −0.776149 | ||||||||
\(957\) | 5.58912e6 | 0.197271 | ||||||||
\(958\) | −3.46836e7 | −1.22098 | ||||||||
\(959\) | 1.97526e6 | 0.0693551 | ||||||||
\(960\) | −4.17258e7 | −1.46126 | ||||||||
\(961\) | −2.84608e7 | −0.994120 | ||||||||
\(962\) | −4.40081e7 | −1.53319 | ||||||||
\(963\) | −1.01220e7 | −0.351724 | ||||||||
\(964\) | 1.63631e7 | 0.567119 | ||||||||
\(965\) | −4.58853e7 | −1.58619 | ||||||||
\(966\) | −4.79775e6 | −0.165423 | ||||||||
\(967\) | 2.33318e7 | 0.802384 | 0.401192 | − | 0.915994i | \(-0.368596\pi\) | ||||
0.401192 | + | 0.915994i | \(0.368596\pi\) | |||||||
\(968\) | −690887. | −0.0236984 | ||||||||
\(969\) | −6.69385e6 | −0.229016 | ||||||||
\(970\) | −9.07495e7 | −3.09681 | ||||||||
\(971\) | −2.99725e7 | −1.02017 | −0.510087 | − | 0.860123i | \(-0.670387\pi\) | ||||
−0.510087 | + | 0.860123i | \(0.670387\pi\) | |||||||
\(972\) | −2.22344e6 | −0.0754847 | ||||||||
\(973\) | −1.86956e6 | −0.0633077 | ||||||||
\(974\) | 1.97999e7 | 0.668754 | ||||||||
\(975\) | −6.85755e7 | −2.31024 | ||||||||
\(976\) | 2.43248e7 | 0.817380 | ||||||||
\(977\) | 3.06238e7 | 1.02642 | 0.513208 | − | 0.858264i | \(-0.328457\pi\) | ||||
0.513208 | + | 0.858264i | \(0.328457\pi\) | |||||||
\(978\) | 2.35865e7 | 0.788525 | ||||||||
\(979\) | −6.75422e6 | −0.225226 | ||||||||
\(980\) | 6.51229e7 | 2.16605 | ||||||||
\(981\) | 3.88812e6 | 0.128993 | ||||||||
\(982\) | 9.91471e6 | 0.328096 | ||||||||
\(983\) | 2.10228e7 | 0.693915 | 0.346958 | − | 0.937881i | \(-0.387215\pi\) | ||||
0.346958 | + | 0.937881i | \(0.387215\pi\) | |||||||
\(984\) | 7.88315e6 | 0.259545 | ||||||||
\(985\) | −4.16460e7 | −1.36767 | ||||||||
\(986\) | −2.12193e7 | −0.695085 | ||||||||
\(987\) | 955887. | 0.0312330 | ||||||||
\(988\) | −5.11437e7 | −1.66686 | ||||||||
\(989\) | −1.88789e6 | −0.0613742 | ||||||||
\(990\) | 8.78995e6 | 0.285035 | ||||||||
\(991\) | −2.43651e7 | −0.788103 | −0.394052 | − | 0.919088i | \(-0.628927\pi\) | ||||
−0.394052 | + | 0.919088i | \(0.628927\pi\) | |||||||
\(992\) | −3.39711e6 | −0.109605 | ||||||||
\(993\) | −1.78098e7 | −0.573175 | ||||||||
\(994\) | 1.29568e7 | 0.415941 | ||||||||
\(995\) | −6.06508e7 | −1.94213 | ||||||||
\(996\) | −8.15238e6 | −0.260397 | ||||||||
\(997\) | −1.04094e7 | −0.331655 | −0.165827 | − | 0.986155i | \(-0.553029\pi\) | ||||
−0.165827 | + | 0.986155i | \(0.553029\pi\) | |||||||
\(998\) | −5.92971e6 | −0.188455 | ||||||||
\(999\) | −4.24911e6 | −0.134705 |
(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 | 33.6.a.d.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 99.6.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 528.6.a.q.1.1 | 2 | |||
5.4 | even | 2 | 825.6.a.d.1.2 | 2 | |||
11.10 | odd | 2 | 363.6.a.g.1.2 | 2 | |||
33.32 | even | 2 | 1089.6.a.o.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
99.6.a.e.1.2 | 2 | 3.2 | odd | 2 | |||
363.6.a.g.1.2 | 2 | 11.10 | odd | 2 | |||
528.6.a.q.1.1 | 2 | 4.3 | odd | 2 | |||
825.6.a.d.1.2 | 2 | 5.4 | even | 2 | |||
1089.6.a.o.1.1 | 2 | 33.32 | even | 2 |