Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,6,Mod(1,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, 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("325.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.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: | \(52.1247414392\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - 5 x^{10} - 257 x^{9} + 1165 x^{8} + 22234 x^{7} - 90282 x^{6} - 751180 x^{5} + 2564400 x^{4} + \cdots + 44115200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-1.96479\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.96479 | 0.347329 | 0.173664 | − | 0.984805i | \(-0.444439\pi\) | ||||
0.173664 | + | 0.984805i | \(0.444439\pi\) | |||||||
\(3\) | 29.7675 | 1.90958 | 0.954792 | − | 0.297274i | \(-0.0960774\pi\) | ||||
0.954792 | + | 0.297274i | \(0.0960774\pi\) | |||||||
\(4\) | −28.1396 | −0.879363 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 58.4868 | 0.663254 | ||||||||
\(7\) | −176.972 | −1.36508 | −0.682540 | − | 0.730848i | \(-0.739125\pi\) | ||||
−0.682540 | + | 0.730848i | \(0.739125\pi\) | |||||||
\(8\) | −118.162 | −0.652757 | ||||||||
\(9\) | 643.103 | 2.64651 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −62.7908 | −0.156464 | −0.0782320 | − | 0.996935i | \(-0.524927\pi\) | ||||
−0.0782320 | + | 0.996935i | \(0.524927\pi\) | |||||||
\(12\) | −837.645 | −1.67922 | ||||||||
\(13\) | −169.000 | −0.277350 | ||||||||
\(14\) | −347.712 | −0.474132 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 668.304 | 0.652641 | ||||||||
\(17\) | 1825.19 | 1.53175 | 0.765873 | − | 0.642992i | \(-0.222307\pi\) | ||||
0.765873 | + | 0.642992i | \(0.222307\pi\) | |||||||
\(18\) | 1263.56 | 0.919211 | ||||||||
\(19\) | 2509.78 | 1.59497 | 0.797483 | − | 0.603342i | \(-0.206165\pi\) | ||||
0.797483 | + | 0.603342i | \(0.206165\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5268.00 | −2.60674 | ||||||||
\(22\) | −123.371 | −0.0543445 | ||||||||
\(23\) | −137.706 | −0.0542791 | −0.0271396 | − | 0.999632i | \(-0.508640\pi\) | ||||
−0.0271396 | + | 0.999632i | \(0.508640\pi\) | |||||||
\(24\) | −3517.37 | −1.24649 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −332.049 | −0.0963317 | ||||||||
\(27\) | 11910.0 | 3.14416 | ||||||||
\(28\) | 4979.91 | 1.20040 | ||||||||
\(29\) | 5978.98 | 1.32018 | 0.660088 | − | 0.751188i | \(-0.270519\pi\) | ||||
0.660088 | + | 0.751188i | \(0.270519\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5203.47 | −0.972499 | −0.486249 | − | 0.873820i | \(-0.661635\pi\) | ||||
−0.486249 | + | 0.873820i | \(0.661635\pi\) | |||||||
\(32\) | 5094.25 | 0.879438 | ||||||||
\(33\) | −1869.12 | −0.298781 | ||||||||
\(34\) | 3586.12 | 0.532020 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −18096.7 | −2.32724 | ||||||||
\(37\) | 4275.33 | 0.513412 | 0.256706 | − | 0.966490i | \(-0.417363\pi\) | ||||
0.256706 | + | 0.966490i | \(0.417363\pi\) | |||||||
\(38\) | 4931.19 | 0.553978 | ||||||||
\(39\) | −5030.70 | −0.529623 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16780.1 | 1.55896 | 0.779481 | − | 0.626426i | \(-0.215483\pi\) | ||||
0.779481 | + | 0.626426i | \(0.215483\pi\) | |||||||
\(42\) | −10350.5 | −0.905395 | ||||||||
\(43\) | 21508.6 | 1.77395 | 0.886974 | − | 0.461819i | \(-0.152803\pi\) | ||||
0.886974 | + | 0.461819i | \(0.152803\pi\) | |||||||
\(44\) | 1766.91 | 0.137589 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −270.563 | −0.0188527 | ||||||||
\(47\) | −16741.5 | −1.10548 | −0.552739 | − | 0.833354i | \(-0.686417\pi\) | ||||
−0.552739 | + | 0.833354i | \(0.686417\pi\) | |||||||
\(48\) | 19893.7 | 1.24627 | ||||||||
\(49\) | 14511.9 | 0.863445 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 54331.4 | 2.92500 | ||||||||
\(52\) | 4755.59 | 0.243891 | ||||||||
\(53\) | −2749.61 | −0.134457 | −0.0672283 | − | 0.997738i | \(-0.521416\pi\) | ||||
−0.0672283 | + | 0.997738i | \(0.521416\pi\) | |||||||
\(54\) | 23400.7 | 1.09206 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 20911.2 | 0.891066 | ||||||||
\(57\) | 74709.8 | 3.04572 | ||||||||
\(58\) | 11747.4 | 0.458536 | ||||||||
\(59\) | 16631.5 | 0.622015 | 0.311007 | − | 0.950407i | \(-0.399334\pi\) | ||||
0.311007 | + | 0.950407i | \(0.399334\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −25005.7 | −0.860429 | −0.430214 | − | 0.902727i | \(-0.641562\pi\) | ||||
−0.430214 | + | 0.902727i | \(0.641562\pi\) | |||||||
\(62\) | −10223.7 | −0.337777 | ||||||||
\(63\) | −113811. | −3.61270 | ||||||||
\(64\) | −11376.6 | −0.347187 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −3672.44 | −0.103775 | ||||||||
\(67\) | −29425.1 | −0.800812 | −0.400406 | − | 0.916338i | \(-0.631131\pi\) | ||||
−0.400406 | + | 0.916338i | \(0.631131\pi\) | |||||||
\(68\) | −51360.2 | −1.34696 | ||||||||
\(69\) | −4099.16 | −0.103651 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −26909.1 | −0.633509 | −0.316754 | − | 0.948508i | \(-0.602593\pi\) | ||||
−0.316754 | + | 0.948508i | \(0.602593\pi\) | |||||||
\(72\) | −75990.1 | −1.72753 | ||||||||
\(73\) | −33664.0 | −0.739365 | −0.369683 | − | 0.929158i | \(-0.620534\pi\) | ||||
−0.369683 | + | 0.929158i | \(0.620534\pi\) | |||||||
\(74\) | 8400.13 | 0.178323 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −70624.2 | −1.40255 | ||||||||
\(77\) | 11112.2 | 0.213586 | ||||||||
\(78\) | −9884.27 | −0.183954 | ||||||||
\(79\) | −13528.9 | −0.243891 | −0.121945 | − | 0.992537i | \(-0.538913\pi\) | ||||
−0.121945 | + | 0.992537i | \(0.538913\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 198258. | 3.35752 | ||||||||
\(82\) | 32969.4 | 0.541473 | ||||||||
\(83\) | −790.985 | −0.0126030 | −0.00630148 | − | 0.999980i | \(-0.502006\pi\) | ||||
−0.00630148 | + | 0.999980i | \(0.502006\pi\) | |||||||
\(84\) | 148239. | 2.29227 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 42259.9 | 0.616144 | ||||||||
\(87\) | 177979. | 2.52099 | ||||||||
\(88\) | 7419.47 | 0.102133 | ||||||||
\(89\) | −72223.8 | −0.966508 | −0.483254 | − | 0.875480i | \(-0.660545\pi\) | ||||
−0.483254 | + | 0.875480i | \(0.660545\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29908.2 | 0.378605 | ||||||||
\(92\) | 3874.99 | 0.0477310 | ||||||||
\(93\) | −154894. | −1.85707 | ||||||||
\(94\) | −32893.6 | −0.383965 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 151643. | 1.67936 | ||||||||
\(97\) | 5458.83 | 0.0589075 | 0.0294538 | − | 0.999566i | \(-0.490623\pi\) | ||||
0.0294538 | + | 0.999566i | \(0.490623\pi\) | |||||||
\(98\) | 28512.9 | 0.299899 | ||||||||
\(99\) | −40380.9 | −0.414084 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −87461.4 | −0.853125 | −0.426563 | − | 0.904458i | \(-0.640276\pi\) | ||||
−0.426563 | + | 0.904458i | \(0.640276\pi\) | |||||||
\(102\) | 106750. | 1.01594 | ||||||||
\(103\) | 75287.7 | 0.699248 | 0.349624 | − | 0.936890i | \(-0.386309\pi\) | ||||
0.349624 | + | 0.936890i | \(0.386309\pi\) | |||||||
\(104\) | 19969.3 | 0.181042 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5402.41 | −0.0467007 | ||||||||
\(107\) | −77781.0 | −0.656771 | −0.328386 | − | 0.944544i | \(-0.606505\pi\) | ||||
−0.328386 | + | 0.944544i | \(0.606505\pi\) | |||||||
\(108\) | −335144. | −2.76485 | ||||||||
\(109\) | 175666. | 1.41619 | 0.708096 | − | 0.706116i | \(-0.249554\pi\) | ||||
0.708096 | + | 0.706116i | \(0.249554\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 127266. | 0.980403 | ||||||||
\(112\) | −118271. | −0.890908 | ||||||||
\(113\) | 2350.11 | 0.0173138 | 0.00865691 | − | 0.999963i | \(-0.497244\pi\) | ||||
0.00865691 | + | 0.999963i | \(0.497244\pi\) | |||||||
\(114\) | 146789. | 1.05787 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −168246. | −1.16091 | ||||||||
\(117\) | −108684. | −0.734011 | ||||||||
\(118\) | 32677.4 | 0.216044 | ||||||||
\(119\) | −323007. | −2.09096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157108. | −0.975519 | ||||||||
\(122\) | −49131.0 | −0.298852 | ||||||||
\(123\) | 499502. | 2.97697 | ||||||||
\(124\) | 146424. | 0.855179 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −223614. | −1.25480 | ||||||||
\(127\) | 266534. | 1.46637 | 0.733183 | − | 0.680031i | \(-0.238034\pi\) | ||||
0.733183 | + | 0.680031i | \(0.238034\pi\) | |||||||
\(128\) | −185369. | −1.00003 | ||||||||
\(129\) | 640257. | 3.38750 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 118703. | 0.604341 | 0.302170 | − | 0.953254i | \(-0.402289\pi\) | ||||
0.302170 | + | 0.953254i | \(0.402289\pi\) | |||||||
\(132\) | 52596.4 | 0.262737 | ||||||||
\(133\) | −444159. | −2.17726 | ||||||||
\(134\) | −57814.1 | −0.278145 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −215668. | −0.999858 | ||||||||
\(137\) | 163850. | 0.745838 | 0.372919 | − | 0.927864i | \(-0.378357\pi\) | ||||
0.372919 | + | 0.927864i | \(0.378357\pi\) | |||||||
\(138\) | −8053.98 | −0.0360008 | ||||||||
\(139\) | 218277. | 0.958231 | 0.479115 | − | 0.877752i | \(-0.340958\pi\) | ||||
0.479115 | + | 0.877752i | \(0.340958\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −498353. | −2.11100 | ||||||||
\(142\) | −52870.6 | −0.220036 | ||||||||
\(143\) | 10611.6 | 0.0433953 | ||||||||
\(144\) | 429788. | 1.72722 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −66142.7 | −0.256803 | ||||||||
\(147\) | 431983. | 1.64882 | ||||||||
\(148\) | −120306. | −0.451475 | ||||||||
\(149\) | −79310.9 | −0.292663 | −0.146331 | − | 0.989236i | \(-0.546747\pi\) | ||||
−0.146331 | + | 0.989236i | \(0.546747\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 368505. | 1.31523 | 0.657615 | − | 0.753355i | \(-0.271566\pi\) | ||||
0.657615 | + | 0.753355i | \(0.271566\pi\) | |||||||
\(152\) | −296560. | −1.04113 | ||||||||
\(153\) | 1.17379e6 | 4.05378 | ||||||||
\(154\) | 21833.1 | 0.0741846 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 141562. | 0.465731 | ||||||||
\(157\) | −30957.2 | −0.100233 | −0.0501166 | − | 0.998743i | \(-0.515959\pi\) | ||||
−0.0501166 | + | 0.998743i | \(0.515959\pi\) | |||||||
\(158\) | −26581.5 | −0.0847103 | ||||||||
\(159\) | −81849.1 | −0.256756 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 24370.0 | 0.0740954 | ||||||||
\(162\) | 389535. | 1.16616 | ||||||||
\(163\) | 204546. | 0.603006 | 0.301503 | − | 0.953465i | \(-0.402512\pi\) | ||||
0.301503 | + | 0.953465i | \(0.402512\pi\) | |||||||
\(164\) | −472186. | −1.37089 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1554.12 | −0.00437738 | ||||||||
\(167\) | −158449. | −0.439641 | −0.219821 | − | 0.975540i | \(-0.570547\pi\) | ||||
−0.219821 | + | 0.975540i | \(0.570547\pi\) | |||||||
\(168\) | 622475. | 1.70157 | ||||||||
\(169\) | 28561.0 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.61404e6 | 4.22110 | ||||||||
\(172\) | −605243. | −1.55994 | ||||||||
\(173\) | −230663. | −0.585952 | −0.292976 | − | 0.956120i | \(-0.594646\pi\) | ||||
−0.292976 | + | 0.956120i | \(0.594646\pi\) | |||||||
\(174\) | 349692. | 0.875613 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −41963.4 | −0.102115 | ||||||||
\(177\) | 495077. | 1.18779 | ||||||||
\(178\) | −141905. | −0.335696 | ||||||||
\(179\) | 791891. | 1.84728 | 0.923640 | − | 0.383260i | \(-0.125199\pi\) | ||||
0.923640 | + | 0.383260i | \(0.125199\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −272694. | −0.618699 | −0.309350 | − | 0.950948i | \(-0.600111\pi\) | ||||
−0.309350 | + | 0.950948i | \(0.600111\pi\) | |||||||
\(182\) | 58763.3 | 0.131501 | ||||||||
\(183\) | −744358. | −1.64306 | ||||||||
\(184\) | 16271.5 | 0.0354311 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −304335. | −0.645014 | ||||||||
\(187\) | −114605. | −0.239663 | ||||||||
\(188\) | 471100. | 0.972116 | ||||||||
\(189\) | −2.10774e6 | −4.29203 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 603069. | 1.19614 | 0.598072 | − | 0.801442i | \(-0.295933\pi\) | ||||
0.598072 | + | 0.801442i | \(0.295933\pi\) | |||||||
\(192\) | −338653. | −0.662982 | ||||||||
\(193\) | 59043.0 | 0.114097 | 0.0570486 | − | 0.998371i | \(-0.481831\pi\) | ||||
0.0570486 | + | 0.998371i | \(0.481831\pi\) | |||||||
\(194\) | 10725.5 | 0.0204603 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −408360. | −0.759281 | ||||||||
\(197\) | −815964. | −1.49798 | −0.748989 | − | 0.662582i | \(-0.769461\pi\) | ||||
−0.748989 | + | 0.662582i | \(0.769461\pi\) | |||||||
\(198\) | −79340.1 | −0.143823 | ||||||||
\(199\) | 490593. | 0.878190 | 0.439095 | − | 0.898441i | \(-0.355299\pi\) | ||||
0.439095 | + | 0.898441i | \(0.355299\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −875911. | −1.52922 | ||||||||
\(202\) | −171843. | −0.296315 | ||||||||
\(203\) | −1.05811e6 | −1.80215 | ||||||||
\(204\) | −1.52886e6 | −2.57213 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 147925. | 0.242869 | ||||||||
\(207\) | −88559.0 | −0.143650 | ||||||||
\(208\) | −112943. | −0.181010 | ||||||||
\(209\) | −157591. | −0.249555 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 593914. | 0.918370 | 0.459185 | − | 0.888341i | \(-0.348142\pi\) | ||||
0.459185 | + | 0.888341i | \(0.348142\pi\) | |||||||
\(212\) | 77373.0 | 0.118236 | ||||||||
\(213\) | −801015. | −1.20974 | ||||||||
\(214\) | −152823. | −0.228116 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.40731e6 | −2.05237 | ||||||||
\(217\) | 920866. | 1.32754 | ||||||||
\(218\) | 345147. | 0.491884 | ||||||||
\(219\) | −1.00209e6 | −1.41188 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −308458. | −0.424830 | ||||||||
\(222\) | 250051. | 0.340522 | ||||||||
\(223\) | 893543. | 1.20324 | 0.601621 | − | 0.798781i | \(-0.294522\pi\) | ||||
0.601621 | + | 0.798781i | \(0.294522\pi\) | |||||||
\(224\) | −901537. | −1.20050 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4617.48 | 0.00601359 | ||||||||
\(227\) | −1.10400e6 | −1.42201 | −0.711006 | − | 0.703186i | \(-0.751760\pi\) | ||||
−0.711006 | + | 0.703186i | \(0.751760\pi\) | |||||||
\(228\) | −2.10230e6 | −2.67829 | ||||||||
\(229\) | −662093. | −0.834315 | −0.417158 | − | 0.908834i | \(-0.636974\pi\) | ||||
−0.417158 | + | 0.908834i | \(0.636974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 330782. | 0.407860 | ||||||||
\(232\) | −706486. | −0.861755 | ||||||||
\(233\) | −828333. | −0.999574 | −0.499787 | − | 0.866148i | \(-0.666588\pi\) | ||||
−0.499787 | + | 0.866148i | \(0.666588\pi\) | |||||||
\(234\) | −213542. | −0.254943 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −468003. | −0.546977 | ||||||||
\(237\) | −402722. | −0.465730 | ||||||||
\(238\) | −634641. | −0.726250 | ||||||||
\(239\) | 359216. | 0.406781 | 0.203391 | − | 0.979098i | \(-0.434804\pi\) | ||||
0.203391 | + | 0.979098i | \(0.434804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −928812. | −1.03011 | −0.515057 | − | 0.857156i | \(-0.672229\pi\) | ||||
−0.515057 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(242\) | −308685. | −0.338826 | ||||||||
\(243\) | 3.00750e6 | 3.26731 | ||||||||
\(244\) | 703651. | 0.756629 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 981416. | 1.03399 | ||||||||
\(247\) | −424152. | −0.442364 | ||||||||
\(248\) | 614851. | 0.634805 | ||||||||
\(249\) | −23545.6 | −0.0240664 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −102334. | −0.102526 | −0.0512631 | − | 0.998685i | \(-0.516325\pi\) | ||||
−0.0512631 | + | 0.998685i | \(0.516325\pi\) | |||||||
\(252\) | 3.20259e6 | 3.17688 | ||||||||
\(253\) | 8646.66 | 0.00849273 | ||||||||
\(254\) | 523682. | 0.509312 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −158.767 | −0.000151412 0 | ||||||||
\(257\) | −1.17461e6 | −1.10933 | −0.554664 | − | 0.832075i | \(-0.687153\pi\) | ||||
−0.554664 | + | 0.832075i | \(0.687153\pi\) | |||||||
\(258\) | 1.25797e6 | 1.17658 | ||||||||
\(259\) | −756612. | −0.700848 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.84510e6 | 3.49387 | ||||||||
\(262\) | 233226. | 0.209905 | ||||||||
\(263\) | −99506.0 | −0.0887074 | −0.0443537 | − | 0.999016i | \(-0.514123\pi\) | ||||
−0.0443537 | + | 0.999016i | \(0.514123\pi\) | |||||||
\(264\) | 220859. | 0.195032 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −872679. | −0.756224 | ||||||||
\(267\) | −2.14992e6 | −1.84563 | ||||||||
\(268\) | 828010. | 0.704204 | ||||||||
\(269\) | −558985. | −0.470999 | −0.235499 | − | 0.971874i | \(-0.575673\pi\) | ||||
−0.235499 | + | 0.971874i | \(0.575673\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −503763. | −0.416680 | −0.208340 | − | 0.978056i | \(-0.566806\pi\) | ||||
−0.208340 | + | 0.978056i | \(0.566806\pi\) | |||||||
\(272\) | 1.21978e6 | 0.999680 | ||||||||
\(273\) | 890291. | 0.722979 | ||||||||
\(274\) | 321930. | 0.259051 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 115349. | 0.0911464 | ||||||||
\(277\) | 1.08351e6 | 0.848466 | 0.424233 | − | 0.905553i | \(-0.360544\pi\) | ||||
0.424233 | + | 0.905553i | \(0.360544\pi\) | |||||||
\(278\) | 428867. | 0.332821 | ||||||||
\(279\) | −3.34637e6 | −2.57373 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.46593e6 | −1.10751 | −0.553756 | − | 0.832679i | \(-0.686806\pi\) | ||||
−0.553756 | + | 0.832679i | \(0.686806\pi\) | |||||||
\(282\) | −979158. | −0.733213 | ||||||||
\(283\) | −2.11337e6 | −1.56859 | −0.784294 | − | 0.620390i | \(-0.786974\pi\) | ||||
−0.784294 | + | 0.620390i | \(0.786974\pi\) | |||||||
\(284\) | 757210. | 0.557084 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20849.7 | 0.0150724 | ||||||||
\(287\) | −2.96960e6 | −2.12811 | ||||||||
\(288\) | 3.27613e6 | 2.32744 | ||||||||
\(289\) | 1.91147e6 | 1.34624 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 162496. | 0.112489 | ||||||||
\(292\) | 947293. | 0.650170 | ||||||||
\(293\) | 2.71115e6 | 1.84495 | 0.922475 | − | 0.386057i | \(-0.126163\pi\) | ||||
0.922475 | + | 0.386057i | \(0.126163\pi\) | |||||||
\(294\) | 848756. | 0.572683 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −505180. | −0.335133 | ||||||||
\(297\) | −747842. | −0.491947 | ||||||||
\(298\) | −155829. | −0.101650 | ||||||||
\(299\) | 23272.3 | 0.0150543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.80641e6 | −2.42158 | ||||||||
\(302\) | 724035. | 0.456817 | ||||||||
\(303\) | −2.60350e6 | −1.62911 | ||||||||
\(304\) | 1.67730e6 | 1.04094 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.30624e6 | 1.40800 | ||||||||
\(307\) | −1.55774e6 | −0.943297 | −0.471648 | − | 0.881787i | \(-0.656341\pi\) | ||||
−0.471648 | + | 0.881787i | \(0.656341\pi\) | |||||||
\(308\) | −312693. | −0.187820 | ||||||||
\(309\) | 2.24113e6 | 1.33527 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.57327e6 | −1.50863 | −0.754316 | − | 0.656511i | \(-0.772032\pi\) | ||||
−0.754316 | + | 0.656511i | \(0.772032\pi\) | |||||||
\(312\) | 594436. | 0.345715 | ||||||||
\(313\) | 563667. | 0.325208 | 0.162604 | − | 0.986691i | \(-0.448011\pi\) | ||||
0.162604 | + | 0.986691i | \(0.448011\pi\) | |||||||
\(314\) | −60824.3 | −0.0348139 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 380698. | 0.214468 | ||||||||
\(317\) | 1.49727e6 | 0.836858 | 0.418429 | − | 0.908250i | \(-0.362581\pi\) | ||||
0.418429 | + | 0.908250i | \(0.362581\pi\) | |||||||
\(318\) | −160816. | −0.0891789 | ||||||||
\(319\) | −375425. | −0.206560 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31534e6 | −1.25416 | ||||||||
\(322\) | 47881.9 | 0.0257355 | ||||||||
\(323\) | 4.58083e6 | 2.44308 | ||||||||
\(324\) | −5.57890e6 | −2.95248 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 401889. | 0.209441 | ||||||||
\(327\) | 5.22914e6 | 2.70434 | ||||||||
\(328\) | −1.98277e6 | −1.01762 | ||||||||
\(329\) | 2.96277e6 | 1.50907 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.48241e6 | 1.24538 | 0.622692 | − | 0.782467i | \(-0.286039\pi\) | ||||
0.622692 | + | 0.782467i | \(0.286039\pi\) | |||||||
\(332\) | 22258.0 | 0.0110826 | ||||||||
\(333\) | 2.74948e6 | 1.35875 | ||||||||
\(334\) | −311319. | −0.152700 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −3.52063e6 | −1.70126 | ||||||||
\(337\) | −2.17057e6 | −1.04112 | −0.520558 | − | 0.853827i | \(-0.674276\pi\) | ||||
−0.520558 | + | 0.853827i | \(0.674276\pi\) | |||||||
\(338\) | 56116.4 | 0.0267176 | ||||||||
\(339\) | 69957.0 | 0.0330622 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 326730. | 0.152161 | ||||||||
\(342\) | 3.17126e6 | 1.46611 | ||||||||
\(343\) | 406164. | 0.186409 | ||||||||
\(344\) | −2.54149e6 | −1.15796 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −453204. | −0.203518 | ||||||||
\(347\) | −3.93089e6 | −1.75254 | −0.876269 | − | 0.481821i | \(-0.839975\pi\) | ||||
−0.876269 | + | 0.481821i | \(0.839975\pi\) | |||||||
\(348\) | −5.00826e6 | −2.21686 | ||||||||
\(349\) | 378915. | 0.166524 | 0.0832622 | − | 0.996528i | \(-0.473466\pi\) | ||||
0.0832622 | + | 0.996528i | \(0.473466\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.01280e6 | −0.872032 | ||||||||
\(352\) | −319872. | −0.137600 | ||||||||
\(353\) | 1.13031e6 | 0.482792 | 0.241396 | − | 0.970427i | \(-0.422395\pi\) | ||||
0.241396 | + | 0.970427i | \(0.422395\pi\) | |||||||
\(354\) | 972722. | 0.412554 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.03235e6 | 0.849911 | ||||||||
\(357\) | −9.61511e6 | −3.99286 | ||||||||
\(358\) | 1.55590e6 | 0.641614 | ||||||||
\(359\) | 3.35579e6 | 1.37423 | 0.687114 | − | 0.726550i | \(-0.258877\pi\) | ||||
0.687114 | + | 0.726550i | \(0.258877\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.82289e6 | 1.54391 | ||||||||
\(362\) | −535787. | −0.214892 | ||||||||
\(363\) | −4.67672e6 | −1.86284 | ||||||||
\(364\) | −841605. | −0.332931 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.46251e6 | −0.570683 | ||||||||
\(367\) | −1.99093e6 | −0.771597 | −0.385799 | − | 0.922583i | \(-0.626074\pi\) | ||||
−0.385799 | + | 0.922583i | \(0.626074\pi\) | |||||||
\(368\) | −92029.4 | −0.0354248 | ||||||||
\(369\) | 1.07913e7 | 4.12581 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 486603. | 0.183544 | ||||||||
\(372\) | 4.35866e6 | 1.63304 | ||||||||
\(373\) | −1.39554e6 | −0.519362 | −0.259681 | − | 0.965694i | \(-0.583617\pi\) | ||||
−0.259681 | + | 0.965694i | \(0.583617\pi\) | |||||||
\(374\) | −225175. | −0.0832419 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.97821e6 | 0.721609 | ||||||||
\(377\) | −1.01045e6 | −0.366151 | ||||||||
\(378\) | −4.14126e6 | −1.49075 | ||||||||
\(379\) | 3.81965e6 | 1.36592 | 0.682960 | − | 0.730455i | \(-0.260692\pi\) | ||||
0.682960 | + | 0.730455i | \(0.260692\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.93403e6 | 2.80015 | ||||||||
\(382\) | 1.18490e6 | 0.415456 | ||||||||
\(383\) | −4.30052e6 | −1.49804 | −0.749020 | − | 0.662547i | \(-0.769475\pi\) | ||||
−0.749020 | + | 0.662547i | \(0.769475\pi\) | |||||||
\(384\) | −5.51796e6 | −1.90963 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 116007. | 0.0396293 | ||||||||
\(387\) | 1.38322e7 | 4.69478 | ||||||||
\(388\) | −153609. | −0.0518011 | ||||||||
\(389\) | 5.63218e6 | 1.88713 | 0.943567 | − | 0.331182i | \(-0.107447\pi\) | ||||
0.943567 | + | 0.331182i | \(0.107447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −251340. | −0.0831418 | ||||||||
\(392\) | −1.71475e6 | −0.563620 | ||||||||
\(393\) | 3.53348e6 | 1.15404 | ||||||||
\(394\) | −1.60320e6 | −0.520291 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.13630e6 | 0.364130 | ||||||||
\(397\) | −1.02692e6 | −0.327011 | −0.163505 | − | 0.986542i | \(-0.552280\pi\) | ||||
−0.163505 | + | 0.986542i | \(0.552280\pi\) | |||||||
\(398\) | 963911. | 0.305021 | ||||||||
\(399\) | −1.32215e7 | −4.15766 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.07636e6 | −0.334269 | −0.167134 | − | 0.985934i | \(-0.553451\pi\) | ||||
−0.167134 | + | 0.985934i | \(0.553451\pi\) | |||||||
\(402\) | −1.72098e6 | −0.531142 | ||||||||
\(403\) | 879387. | 0.269723 | ||||||||
\(404\) | 2.46113e6 | 0.750206 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.07896e6 | −0.625938 | ||||||||
\(407\) | −268452. | −0.0803304 | ||||||||
\(408\) | −6.41989e6 | −1.90931 | ||||||||
\(409\) | −4.48956e6 | −1.32708 | −0.663538 | − | 0.748143i | \(-0.730946\pi\) | ||||
−0.663538 | + | 0.748143i | \(0.730946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.87739e6 | 1.42424 | ||||||||
\(412\) | −2.11857e6 | −0.614892 | ||||||||
\(413\) | −2.94330e6 | −0.849100 | ||||||||
\(414\) | −174000. | −0.0498939 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −860928. | −0.243912 | ||||||||
\(417\) | 6.49754e6 | 1.82982 | ||||||||
\(418\) | −309633. | −0.0866776 | ||||||||
\(419\) | −2.90095e6 | −0.807245 | −0.403622 | − | 0.914926i | \(-0.632249\pi\) | ||||
−0.403622 | + | 0.914926i | \(0.632249\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.69840e6 | −1.56692 | −0.783461 | − | 0.621441i | \(-0.786548\pi\) | ||||
−0.783461 | + | 0.621441i | \(0.786548\pi\) | |||||||
\(422\) | 1.16692e6 | 0.318977 | ||||||||
\(423\) | −1.07665e7 | −2.92566 | ||||||||
\(424\) | 324899. | 0.0877675 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.57383e6 | −0.420177 | ||||||||
\(427\) | 4.42530e6 | 1.17455 | ||||||||
\(428\) | 2.18873e6 | 0.577540 | ||||||||
\(429\) | 315882. | 0.0828670 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.25477e6 | 1.88118 | 0.940590 | − | 0.339545i | \(-0.110273\pi\) | ||||
0.940590 | + | 0.339545i | \(0.110273\pi\) | |||||||
\(432\) | 7.95954e6 | 2.05201 | ||||||||
\(433\) | −2.92650e6 | −0.750115 | −0.375058 | − | 0.927001i | \(-0.622377\pi\) | ||||
−0.375058 | + | 0.927001i | \(0.622377\pi\) | |||||||
\(434\) | 1.80931e6 | 0.461093 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.94318e6 | −1.24535 | ||||||||
\(437\) | −345611. | −0.0865733 | ||||||||
\(438\) | −1.96890e6 | −0.490387 | ||||||||
\(439\) | 2.15422e6 | 0.533492 | 0.266746 | − | 0.963767i | \(-0.414051\pi\) | ||||
0.266746 | + | 0.963767i | \(0.414051\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.33266e6 | 2.28512 | ||||||||
\(442\) | −606054. | −0.147556 | ||||||||
\(443\) | −7.40975e6 | −1.79388 | −0.896942 | − | 0.442148i | \(-0.854217\pi\) | ||||
−0.896942 | + | 0.442148i | \(0.854217\pi\) | |||||||
\(444\) | −3.58121e6 | −0.862130 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.75562e6 | 0.417921 | ||||||||
\(447\) | −2.36088e6 | −0.558864 | ||||||||
\(448\) | 2.01334e6 | 0.473938 | ||||||||
\(449\) | −1.90284e6 | −0.445438 | −0.222719 | − | 0.974883i | \(-0.571493\pi\) | ||||
−0.222719 | + | 0.974883i | \(0.571493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.05364e6 | −0.243921 | ||||||||
\(452\) | −66131.3 | −0.0152251 | ||||||||
\(453\) | 1.09695e7 | 2.51154 | ||||||||
\(454\) | −2.16912e6 | −0.493906 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −8.82783e6 | −1.98812 | ||||||||
\(457\) | −2.79693e6 | −0.626457 | −0.313229 | − | 0.949678i | \(-0.601411\pi\) | ||||
−0.313229 | + | 0.949678i | \(0.601411\pi\) | |||||||
\(458\) | −1.30087e6 | −0.289782 | ||||||||
\(459\) | 2.17381e7 | 4.81605 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.18307e6 | 0.916733 | 0.458366 | − | 0.888763i | \(-0.348435\pi\) | ||||
0.458366 | + | 0.888763i | \(0.348435\pi\) | |||||||
\(462\) | 649917. | 0.141662 | ||||||||
\(463\) | 2.51126e6 | 0.544427 | 0.272213 | − | 0.962237i | \(-0.412244\pi\) | ||||
0.272213 | + | 0.962237i | \(0.412244\pi\) | |||||||
\(464\) | 3.99578e6 | 0.861602 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.62750e6 | −0.347181 | ||||||||
\(467\) | −2.17175e6 | −0.460806 | −0.230403 | − | 0.973095i | \(-0.574004\pi\) | ||||
−0.230403 | + | 0.973095i | \(0.574004\pi\) | |||||||
\(468\) | 3.05833e6 | 0.645462 | ||||||||
\(469\) | 5.20740e6 | 1.09317 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −921517. | −0.191404 | ||||||||
\(472\) | −1.96520e6 | −0.406025 | ||||||||
\(473\) | −1.35054e6 | −0.277559 | ||||||||
\(474\) | −791263. | −0.161761 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.08930e6 | 1.83871 | ||||||||
\(477\) | −1.76828e6 | −0.355841 | ||||||||
\(478\) | 705784. | 0.141287 | ||||||||
\(479\) | −9.46791e6 | −1.88545 | −0.942726 | − | 0.333568i | \(-0.891747\pi\) | ||||
−0.942726 | + | 0.333568i | \(0.891747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −722531. | −0.142395 | ||||||||
\(482\) | −1.82492e6 | −0.357788 | ||||||||
\(483\) | 725434. | 0.141491 | ||||||||
\(484\) | 4.42097e6 | 0.857835 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.90911e6 | 1.13483 | ||||||||
\(487\) | −4.87785e6 | −0.931979 | −0.465989 | − | 0.884790i | \(-0.654302\pi\) | ||||
−0.465989 | + | 0.884790i | \(0.654302\pi\) | |||||||
\(488\) | 2.95472e6 | 0.561651 | ||||||||
\(489\) | 6.08881e6 | 1.15149 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.86456e6 | −0.723429 | −0.361715 | − | 0.932289i | \(-0.617808\pi\) | ||||
−0.361715 | + | 0.932289i | \(0.617808\pi\) | |||||||
\(492\) | −1.40558e7 | −2.61784 | ||||||||
\(493\) | 1.09128e7 | 2.02217 | ||||||||
\(494\) | −833370. | −0.153646 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.47750e6 | −0.634693 | ||||||||
\(497\) | 4.76214e6 | 0.864791 | ||||||||
\(498\) | −46262.2 | −0.00835897 | ||||||||
\(499\) | 5.75229e6 | 1.03416 | 0.517082 | − | 0.855936i | \(-0.327018\pi\) | ||||
0.517082 | + | 0.855936i | \(0.327018\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.71663e6 | −0.839532 | ||||||||
\(502\) | −201064. | −0.0356103 | ||||||||
\(503\) | 5.93696e6 | 1.04627 | 0.523136 | − | 0.852249i | \(-0.324762\pi\) | ||||
0.523136 | + | 0.852249i | \(0.324762\pi\) | |||||||
\(504\) | 1.34481e7 | 2.35822 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 16988.9 | 0.00294977 | ||||||||
\(507\) | 850189. | 0.146891 | ||||||||
\(508\) | −7.50015e6 | −1.28947 | ||||||||
\(509\) | −563930. | −0.0964785 | −0.0482393 | − | 0.998836i | \(-0.515361\pi\) | ||||
−0.0482393 | + | 0.998836i | \(0.515361\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.95758e6 | 1.00929 | ||||||||
\(512\) | 5.93149e6 | 0.999974 | ||||||||
\(513\) | 2.98916e7 | 5.01482 | ||||||||
\(514\) | −2.30786e6 | −0.385302 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.80166e7 | −2.97884 | ||||||||
\(517\) | 1.05121e6 | 0.172968 | ||||||||
\(518\) | −1.48658e6 | −0.243425 | ||||||||
\(519\) | −6.86625e6 | −1.11892 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.09272e6 | 0.176366 | 0.0881828 | − | 0.996104i | \(-0.471894\pi\) | ||||
0.0881828 | + | 0.996104i | \(0.471894\pi\) | |||||||
\(522\) | 7.55481e6 | 1.21352 | ||||||||
\(523\) | −2.47626e6 | −0.395861 | −0.197930 | − | 0.980216i | \(-0.563422\pi\) | ||||
−0.197930 | + | 0.980216i | \(0.563422\pi\) | |||||||
\(524\) | −3.34024e6 | −0.531435 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −195508. | −0.0308107 | ||||||||
\(527\) | −9.49734e6 | −1.48962 | ||||||||
\(528\) | −1.24914e6 | −0.194997 | ||||||||
\(529\) | −6.41738e6 | −0.997054 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.06957e7 | 1.64617 | ||||||||
\(532\) | 1.24985e7 | 1.91460 | ||||||||
\(533\) | −2.83584e6 | −0.432378 | ||||||||
\(534\) | −4.22414e6 | −0.641041 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.47692e6 | 0.522736 | ||||||||
\(537\) | 2.35726e7 | 3.52754 | ||||||||
\(538\) | −1.09829e6 | −0.163592 | ||||||||
\(539\) | −911215. | −0.135098 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.78515e6 | −0.849810 | −0.424905 | − | 0.905238i | \(-0.639692\pi\) | ||||
−0.424905 | + | 0.905238i | \(0.639692\pi\) | |||||||
\(542\) | −989788. | −0.144725 | ||||||||
\(543\) | −8.11742e6 | −1.18146 | ||||||||
\(544\) | 9.29799e6 | 1.34708 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.74923e6 | 0.251111 | ||||||||
\(547\) | 1.26151e7 | 1.80269 | 0.901345 | − | 0.433102i | \(-0.142581\pi\) | ||||
0.901345 | + | 0.433102i | \(0.142581\pi\) | |||||||
\(548\) | −4.61067e6 | −0.655862 | ||||||||
\(549\) | −1.60813e7 | −2.27714 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.50059e7 | 2.10564 | ||||||||
\(552\) | 484363. | 0.0676586 | ||||||||
\(553\) | 2.39423e6 | 0.332930 | ||||||||
\(554\) | 2.12887e6 | 0.294697 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.14222e6 | −0.842632 | ||||||||
\(557\) | 9.93482e6 | 1.35682 | 0.678409 | − | 0.734684i | \(-0.262670\pi\) | ||||
0.678409 | + | 0.734684i | \(0.262670\pi\) | |||||||
\(558\) | −6.57491e6 | −0.893931 | ||||||||
\(559\) | −3.63495e6 | −0.492005 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.41151e6 | −0.457657 | ||||||||
\(562\) | −2.88025e6 | −0.384671 | ||||||||
\(563\) | −8.72418e6 | −1.15999 | −0.579994 | − | 0.814621i | \(-0.696945\pi\) | ||||
−0.579994 | + | 0.814621i | \(0.696945\pi\) | |||||||
\(564\) | 1.40234e7 | 1.85634 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.15232e6 | −0.544816 | ||||||||
\(567\) | −3.50860e7 | −4.58328 | ||||||||
\(568\) | 3.17962e6 | 0.413527 | ||||||||
\(569\) | 5.33272e6 | 0.690508 | 0.345254 | − | 0.938509i | \(-0.387793\pi\) | ||||
0.345254 | + | 0.938509i | \(0.387793\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.46290e7 | −1.87769 | −0.938847 | − | 0.344334i | \(-0.888105\pi\) | ||||
−0.938847 | + | 0.344334i | \(0.888105\pi\) | |||||||
\(572\) | −298608. | −0.0381602 | ||||||||
\(573\) | 1.79519e7 | 2.28414 | ||||||||
\(574\) | −5.83465e6 | −0.739154 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.31633e6 | −0.918834 | ||||||||
\(577\) | −7.62278e6 | −0.953177 | −0.476589 | − | 0.879126i | \(-0.658127\pi\) | ||||
−0.476589 | + | 0.879126i | \(0.658127\pi\) | |||||||
\(578\) | 3.75564e6 | 0.467590 | ||||||||
\(579\) | 1.75756e6 | 0.217878 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 139982. | 0.0172041 | ||||||||
\(582\) | 319270. | 0.0390706 | ||||||||
\(583\) | 172650. | 0.0210376 | ||||||||
\(584\) | 3.97780e6 | 0.482626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.32684e6 | 0.640805 | ||||||||
\(587\) | −7.92637e6 | −0.949465 | −0.474732 | − | 0.880130i | \(-0.657455\pi\) | ||||
−0.474732 | + | 0.880130i | \(0.657455\pi\) | |||||||
\(588\) | −1.21558e7 | −1.44991 | ||||||||
\(589\) | −1.30596e7 | −1.55110 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.42892e7 | −2.86052 | ||||||||
\(592\) | 2.85722e6 | 0.335074 | ||||||||
\(593\) | −1.13806e7 | −1.32901 | −0.664507 | − | 0.747282i | \(-0.731358\pi\) | ||||
−0.664507 | + | 0.747282i | \(0.731358\pi\) | |||||||
\(594\) | −1.46935e6 | −0.170868 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.23178e6 | 0.257356 | ||||||||
\(597\) | 1.46037e7 | 1.67698 | ||||||||
\(598\) | 45725.1 | 0.00522880 | ||||||||
\(599\) | 7.12203e6 | 0.811030 | 0.405515 | − | 0.914088i | \(-0.367092\pi\) | ||||
0.405515 | + | 0.914088i | \(0.367092\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.50084e6 | 0.169492 | 0.0847458 | − | 0.996403i | \(-0.472992\pi\) | ||||
0.0847458 | + | 0.996403i | \(0.472992\pi\) | |||||||
\(602\) | −7.47879e6 | −0.841086 | ||||||||
\(603\) | −1.89234e7 | −2.11936 | ||||||||
\(604\) | −1.03696e7 | −1.15656 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.11534e6 | −0.565839 | ||||||||
\(607\) | 1.39958e7 | 1.54179 | 0.770897 | − | 0.636960i | \(-0.219808\pi\) | ||||
0.770897 | + | 0.636960i | \(0.219808\pi\) | |||||||
\(608\) | 1.27854e7 | 1.40267 | ||||||||
\(609\) | −3.14972e7 | −3.44135 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.82932e6 | 0.306604 | ||||||||
\(612\) | −3.30299e7 | −3.56475 | ||||||||
\(613\) | −4.60575e6 | −0.495050 | −0.247525 | − | 0.968882i | \(-0.579617\pi\) | ||||
−0.247525 | + | 0.968882i | \(0.579617\pi\) | |||||||
\(614\) | −3.06063e6 | −0.327634 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.31303e6 | −0.139420 | ||||||||
\(617\) | −5.55212e6 | −0.587146 | −0.293573 | − | 0.955937i | \(-0.594844\pi\) | ||||
−0.293573 | + | 0.955937i | \(0.594844\pi\) | |||||||
\(618\) | 4.40334e6 | 0.463779 | ||||||||
\(619\) | −2.71815e6 | −0.285133 | −0.142566 | − | 0.989785i | \(-0.545535\pi\) | ||||
−0.142566 | + | 0.989785i | \(0.545535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.64008e6 | −0.170662 | ||||||||
\(622\) | −5.05592e6 | −0.523992 | ||||||||
\(623\) | 1.27816e7 | 1.31936 | ||||||||
\(624\) | −3.36204e6 | −0.345654 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.10749e6 | 0.112954 | ||||||||
\(627\) | −4.69109e6 | −0.476546 | ||||||||
\(628\) | 871122. | 0.0881414 | ||||||||
\(629\) | 7.80331e6 | 0.786416 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.93426e6 | −0.193393 | −0.0966964 | − | 0.995314i | \(-0.530828\pi\) | ||||
−0.0966964 | + | 0.995314i | \(0.530828\pi\) | |||||||
\(632\) | 1.59860e6 | 0.159201 | ||||||||
\(633\) | 1.76793e7 | 1.75371 | ||||||||
\(634\) | 2.94182e6 | 0.290665 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 2.30320e6 | 0.225782 | ||||||||
\(637\) | −2.45251e6 | −0.239477 | ||||||||
\(638\) | −737631. | −0.0717443 | ||||||||
\(639\) | −1.73053e7 | −1.67659 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.58248e6 | 0.921155 | 0.460578 | − | 0.887619i | \(-0.347642\pi\) | ||||
0.460578 | + | 0.887619i | \(0.347642\pi\) | |||||||
\(642\) | −4.54916e6 | −0.435606 | ||||||||
\(643\) | −2.46659e6 | −0.235272 | −0.117636 | − | 0.993057i | \(-0.537532\pi\) | ||||
−0.117636 | + | 0.993057i | \(0.537532\pi\) | |||||||
\(644\) | −685762. | −0.0651567 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00037e6 | 0.848553 | ||||||||
\(647\) | 2.72804e6 | 0.256207 | 0.128103 | − | 0.991761i | \(-0.459111\pi\) | ||||
0.128103 | + | 0.991761i | \(0.459111\pi\) | |||||||
\(648\) | −2.34265e7 | −2.19164 | ||||||||
\(649\) | −1.04430e6 | −0.0973229 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.74119e7 | 2.53505 | ||||||||
\(652\) | −5.75584e6 | −0.530261 | ||||||||
\(653\) | −9.94071e6 | −0.912293 | −0.456147 | − | 0.889905i | \(-0.650771\pi\) | ||||
−0.456147 | + | 0.889905i | \(0.650771\pi\) | |||||||
\(654\) | 1.02742e7 | 0.939295 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.12142e7 | 1.01744 | ||||||||
\(657\) | −2.16494e7 | −1.95674 | ||||||||
\(658\) | 5.82122e6 | 0.524143 | ||||||||
\(659\) | 440385. | 0.0395019 | 0.0197510 | − | 0.999805i | \(-0.493713\pi\) | ||||
0.0197510 | + | 0.999805i | \(0.493713\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.85089e6 | 0.431835 | 0.215918 | − | 0.976412i | \(-0.430726\pi\) | ||||
0.215918 | + | 0.976412i | \(0.430726\pi\) | |||||||
\(662\) | 4.87741e6 | 0.432558 | ||||||||
\(663\) | −9.18201e6 | −0.811248 | ||||||||
\(664\) | 93464.0 | 0.00822668 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.40215e6 | 0.471933 | ||||||||
\(667\) | −823340. | −0.0716580 | ||||||||
\(668\) | 4.45869e6 | 0.386604 | ||||||||
\(669\) | 2.65985e7 | 2.29769 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.57013e6 | 0.134626 | ||||||||
\(672\) | −2.68365e7 | −2.29246 | ||||||||
\(673\) | −2.15372e6 | −0.183296 | −0.0916479 | − | 0.995791i | \(-0.529213\pi\) | ||||
−0.0916479 | + | 0.995791i | \(0.529213\pi\) | |||||||
\(674\) | −4.26471e6 | −0.361609 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −803695. | −0.0676433 | ||||||||
\(677\) | −4.93215e6 | −0.413585 | −0.206792 | − | 0.978385i | \(-0.566302\pi\) | ||||
−0.206792 | + | 0.978385i | \(0.566302\pi\) | |||||||
\(678\) | 137451. | 0.0114835 | ||||||||
\(679\) | −966058. | −0.0804135 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.28632e7 | −2.71545 | ||||||||
\(682\) | 641956. | 0.0528499 | ||||||||
\(683\) | 1.39352e7 | 1.14304 | 0.571521 | − | 0.820588i | \(-0.306354\pi\) | ||||
0.571521 | + | 0.820588i | \(0.306354\pi\) | |||||||
\(684\) | −4.54186e7 | −3.71187 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 798026. | 0.0647451 | ||||||||
\(687\) | −1.97088e7 | −1.59320 | ||||||||
\(688\) | 1.43743e7 | 1.15775 | ||||||||
\(689\) | 464685. | 0.0372915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.71835e7 | 1.36904 | 0.684520 | − | 0.728994i | \(-0.260012\pi\) | ||||
0.684520 | + | 0.728994i | \(0.260012\pi\) | |||||||
\(692\) | 6.49076e6 | 0.515264 | ||||||||
\(693\) | 7.14628e6 | 0.565258 | ||||||||
\(694\) | −7.72338e6 | −0.608708 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.10303e7 | −1.64559 | ||||||||
\(697\) | 3.06270e7 | 2.38793 | ||||||||
\(698\) | 744488. | 0.0578387 | ||||||||
\(699\) | −2.46574e7 | −1.90877 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.18640e6 | 0.321770 | 0.160885 | − | 0.986973i | \(-0.448565\pi\) | ||||
0.160885 | + | 0.986973i | \(0.448565\pi\) | |||||||
\(702\) | −3.95472e6 | −0.302882 | ||||||||
\(703\) | 1.07301e7 | 0.818874 | ||||||||
\(704\) | 714347. | 0.0543222 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.22082e6 | 0.167688 | ||||||||
\(707\) | 1.54782e7 | 1.16458 | ||||||||
\(708\) | −1.39313e7 | −1.04450 | ||||||||
\(709\) | −7.30623e6 | −0.545855 | −0.272928 | − | 0.962035i | \(-0.587992\pi\) | ||||
−0.272928 | + | 0.962035i | \(0.587992\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.70048e6 | −0.645460 | ||||||||
\(712\) | 8.53409e6 | 0.630895 | ||||||||
\(713\) | 716548. | 0.0527864 | ||||||||
\(714\) | −1.88917e7 | −1.38684 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.22835e7 | −1.62443 | ||||||||
\(717\) | 1.06930e7 | 0.776783 | ||||||||
\(718\) | 6.59342e6 | 0.477309 | ||||||||
\(719\) | −1.22435e7 | −0.883249 | −0.441625 | − | 0.897200i | \(-0.645598\pi\) | ||||
−0.441625 | + | 0.897200i | \(0.645598\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.33238e7 | −0.954530 | ||||||||
\(722\) | 7.51117e6 | 0.536246 | ||||||||
\(723\) | −2.76484e7 | −1.96709 | ||||||||
\(724\) | 7.67351e6 | 0.544061 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −9.18877e6 | −0.647017 | ||||||||
\(727\) | −612630. | −0.0429895 | −0.0214947 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214947 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(728\) | −3.53400e6 | −0.247137 | ||||||||
\(729\) | 4.13490e7 | 2.88169 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.92574e7 | 2.71724 | ||||||||
\(732\) | 2.09459e7 | 1.44485 | ||||||||
\(733\) | −1.54190e7 | −1.05998 | −0.529989 | − | 0.848004i | \(-0.677804\pi\) | ||||
−0.529989 | + | 0.848004i | \(0.677804\pi\) | |||||||
\(734\) | −3.91176e6 | −0.267998 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −701508. | −0.0477351 | ||||||||
\(737\) | 1.84763e6 | 0.125298 | ||||||||
\(738\) | 2.12027e7 | 1.43301 | ||||||||
\(739\) | 1.10414e7 | 0.743724 | 0.371862 | − | 0.928288i | \(-0.378720\pi\) | ||||
0.371862 | + | 0.928288i | \(0.378720\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.26259e7 | −0.844731 | ||||||||
\(742\) | 956073. | 0.0637502 | ||||||||
\(743\) | 1.66010e7 | 1.10322 | 0.551611 | − | 0.834102i | \(-0.314013\pi\) | ||||
0.551611 | + | 0.834102i | \(0.314013\pi\) | |||||||
\(744\) | 1.83026e7 | 1.21221 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.74194e6 | −0.180390 | ||||||||
\(747\) | −508684. | −0.0333539 | ||||||||
\(748\) | 3.22495e6 | 0.210751 | ||||||||
\(749\) | 1.37650e7 | 0.896546 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.04497e6 | 0.0676089 | 0.0338045 | − | 0.999428i | \(-0.489238\pi\) | ||||
0.0338045 | + | 0.999428i | \(0.489238\pi\) | |||||||
\(752\) | −1.11884e7 | −0.721481 | ||||||||
\(753\) | −3.04622e6 | −0.195782 | ||||||||
\(754\) | −1.98532e6 | −0.127175 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.93109e7 | 3.77425 | ||||||||
\(757\) | −5.93460e6 | −0.376402 | −0.188201 | − | 0.982131i | \(-0.560266\pi\) | ||||
−0.188201 | + | 0.982131i | \(0.560266\pi\) | |||||||
\(758\) | 7.50481e6 | 0.474424 | ||||||||
\(759\) | 257389. | 0.0162176 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.89549e6 | 0.369027 | 0.184514 | − | 0.982830i | \(-0.440929\pi\) | ||||
0.184514 | + | 0.982830i | \(0.440929\pi\) | |||||||
\(762\) | 1.55887e7 | 0.972574 | ||||||||
\(763\) | −3.10879e7 | −1.93322 | ||||||||
\(764\) | −1.69701e7 | −1.05185 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.44961e6 | −0.520313 | ||||||||
\(767\) | −2.81072e6 | −0.172516 | ||||||||
\(768\) | −4726.10 | −0.000289134 0 | ||||||||
\(769\) | −1.30498e7 | −0.795769 | −0.397884 | − | 0.917436i | \(-0.630256\pi\) | ||||
−0.397884 | + | 0.917436i | \(0.630256\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.49651e7 | −2.11835 | ||||||||
\(772\) | −1.66145e6 | −0.100333 | ||||||||
\(773\) | 2.29371e7 | 1.38067 | 0.690334 | − | 0.723491i | \(-0.257464\pi\) | ||||
0.690334 | + | 0.723491i | \(0.257464\pi\) | |||||||
\(774\) | 2.71774e7 | 1.63063 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −645025. | −0.0384523 | ||||||||
\(777\) | −2.25224e7 | −1.33833 | ||||||||
\(778\) | 1.10661e7 | 0.655456 | ||||||||
\(779\) | 4.21144e7 | 2.48649 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.68964e6 | 0.0991213 | ||||||||
\(782\) | −493830. | −0.0288775 | ||||||||
\(783\) | 7.12099e7 | 4.15084 | ||||||||
\(784\) | 9.69838e6 | 0.563520 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.94254e6 | 0.400831 | ||||||||
\(787\) | 1.68766e7 | 0.971291 | 0.485645 | − | 0.874156i | \(-0.338585\pi\) | ||||
0.485645 | + | 0.874156i | \(0.338585\pi\) | |||||||
\(788\) | 2.29609e7 | 1.31727 | ||||||||
\(789\) | −2.96204e6 | −0.169394 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −415903. | −0.0236348 | ||||||||
\(792\) | 4.77148e6 | 0.270296 | ||||||||
\(793\) | 4.22597e6 | 0.238640 | ||||||||
\(794\) | −2.01769e6 | −0.113580 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.38051e7 | −0.772247 | ||||||||
\(797\) | 4.13009e6 | 0.230311 | 0.115155 | − | 0.993348i | \(-0.463263\pi\) | ||||
0.115155 | + | 0.993348i | \(0.463263\pi\) | |||||||
\(798\) | −2.59775e7 | −1.44407 | ||||||||
\(799\) | −3.05565e7 | −1.69331 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.64474e7 | −2.55788 | ||||||||
\(802\) | −2.11482e6 | −0.116101 | ||||||||
\(803\) | 2.11379e6 | 0.115684 | ||||||||
\(804\) | 2.46478e7 | 1.34474 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.72781e6 | 0.0936825 | ||||||||
\(807\) | −1.66396e7 | −0.899412 | ||||||||
\(808\) | 1.03346e7 | 0.556884 | ||||||||
\(809\) | 1.01709e7 | 0.546369 | 0.273185 | − | 0.961962i | \(-0.411923\pi\) | ||||
0.273185 | + | 0.961962i | \(0.411923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.22723e7 | −1.18909 | −0.594543 | − | 0.804064i | \(-0.702667\pi\) | ||||
−0.594543 | + | 0.804064i | \(0.702667\pi\) | |||||||
\(812\) | 2.97748e7 | 1.58474 | ||||||||
\(813\) | −1.49957e7 | −0.795686 | ||||||||
\(814\) | −527451. | −0.0279011 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.63099e7 | 1.90897 | ||||||||
\(817\) | 5.39818e7 | 2.82939 | ||||||||
\(818\) | −8.82104e6 | −0.460932 | ||||||||
\(819\) | 1.92340e7 | 1.00198 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.65506e6 | 0.189250 | 0.0946251 | − | 0.995513i | \(-0.469835\pi\) | ||||
0.0946251 | + | 0.995513i | \(0.469835\pi\) | |||||||
\(822\) | 9.58305e6 | 0.494680 | ||||||||
\(823\) | 7.29867e6 | 0.375616 | 0.187808 | − | 0.982206i | \(-0.439862\pi\) | ||||
0.187808 | + | 0.982206i | \(0.439862\pi\) | |||||||
\(824\) | −8.89612e6 | −0.456439 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.78296e6 | −0.294917 | ||||||||
\(827\) | −3.19608e7 | −1.62500 | −0.812502 | − | 0.582958i | \(-0.801895\pi\) | ||||
−0.812502 | + | 0.582958i | \(0.801895\pi\) | |||||||
\(828\) | 2.49201e6 | 0.126321 | ||||||||
\(829\) | 9.74730e6 | 0.492604 | 0.246302 | − | 0.969193i | \(-0.420785\pi\) | ||||
0.246302 | + | 0.969193i | \(0.420785\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.22534e7 | 1.62022 | ||||||||
\(832\) | 1.92265e6 | 0.0962923 | ||||||||
\(833\) | 2.64871e7 | 1.32258 | ||||||||
\(834\) | 1.27663e7 | 0.635550 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.43455e6 | 0.219449 | ||||||||
\(837\) | −6.19736e7 | −3.05769 | ||||||||
\(838\) | −5.69976e6 | −0.280380 | ||||||||
\(839\) | −6.75711e6 | −0.331403 | −0.165701 | − | 0.986176i | \(-0.552989\pi\) | ||||
−0.165701 | + | 0.986176i | \(0.552989\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.52371e7 | 0.742867 | ||||||||
\(842\) | −1.11962e7 | −0.544238 | ||||||||
\(843\) | −4.36371e7 | −2.11489 | ||||||||
\(844\) | −1.67125e7 | −0.807580 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.11539e7 | −1.01617 | ||||||||
\(847\) | 2.78037e7 | 1.33166 | ||||||||
\(848\) | −1.83758e6 | −0.0877519 | ||||||||
\(849\) | −6.29096e7 | −2.99535 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −588738. | −0.0278675 | ||||||||
\(852\) | 2.25402e7 | 1.06380 | ||||||||
\(853\) | −2.85698e7 | −1.34442 | −0.672209 | − | 0.740362i | \(-0.734654\pi\) | ||||
−0.672209 | + | 0.740362i | \(0.734654\pi\) | |||||||
\(854\) | 8.69479e6 | 0.407957 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.19073e6 | 0.428712 | ||||||||
\(857\) | −2.35895e6 | −0.109715 | −0.0548577 | − | 0.998494i | \(-0.517471\pi\) | ||||
−0.0548577 | + | 0.998494i | \(0.517471\pi\) | |||||||
\(858\) | 620642. | 0.0287821 | ||||||||
\(859\) | 1.07995e7 | 0.499368 | 0.249684 | − | 0.968327i | \(-0.419673\pi\) | ||||
0.249684 | + | 0.968327i | \(0.419673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.83976e7 | −4.06380 | ||||||||
\(862\) | 1.42541e7 | 0.653388 | ||||||||
\(863\) | 2.27989e7 | 1.04204 | 0.521022 | − | 0.853543i | \(-0.325551\pi\) | ||||
0.521022 | + | 0.853543i | \(0.325551\pi\) | |||||||
\(864\) | 6.06728e7 | 2.76509 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.74995e6 | −0.260537 | ||||||||
\(867\) | 5.68998e7 | 2.57077 | ||||||||
\(868\) | −2.59128e7 | −1.16739 | ||||||||
\(869\) | 849491. | 0.0381601 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.97284e6 | 0.222105 | ||||||||
\(872\) | −2.07570e7 | −0.924429 | ||||||||
\(873\) | 3.51059e6 | 0.155899 | ||||||||
\(874\) | −679053. | −0.0300694 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.81985e7 | 1.24155 | ||||||||
\(877\) | −3.23124e7 | −1.41863 | −0.709317 | − | 0.704890i | \(-0.750997\pi\) | ||||
−0.709317 | + | 0.704890i | \(0.750997\pi\) | |||||||
\(878\) | 4.23258e6 | 0.185297 | ||||||||
\(879\) | 8.07041e7 | 3.52309 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.40863e7 | 0.611447 | 0.305723 | − | 0.952120i | \(-0.401102\pi\) | ||||
0.305723 | + | 0.952120i | \(0.401102\pi\) | |||||||
\(882\) | 1.83367e7 | 0.793688 | ||||||||
\(883\) | −4.14803e7 | −1.79036 | −0.895180 | − | 0.445705i | \(-0.852953\pi\) | ||||
−0.895180 | + | 0.445705i | \(0.852953\pi\) | |||||||
\(884\) | 8.67988e6 | 0.373579 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.45586e7 | −0.623068 | ||||||||
\(887\) | 6.64591e6 | 0.283626 | 0.141813 | − | 0.989893i | \(-0.454707\pi\) | ||||
0.141813 | + | 0.989893i | \(0.454707\pi\) | |||||||
\(888\) | −1.50379e7 | −0.639965 | ||||||||
\(889\) | −4.71689e7 | −2.00171 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.24488e7 | −0.525331 | ||||||||
\(892\) | −2.51439e7 | −1.05809 | ||||||||
\(893\) | −4.20175e7 | −1.76320 | ||||||||
\(894\) | −4.63864e6 | −0.194110 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 3.28050e7 | 1.36512 | ||||||||
\(897\) | 692757. | 0.0287475 | ||||||||
\(898\) | −3.73869e6 | −0.154713 | ||||||||
\(899\) | −3.11115e7 | −1.28387 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.01858e6 | −0.205953 | ||||||||
\(902\) | −2.07018e6 | −0.0847210 | ||||||||
\(903\) | −1.13307e8 | −4.62422 | ||||||||
\(904\) | −277693. | −0.0113017 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.15527e7 | 0.872331 | ||||||||
\(907\) | −1.12437e7 | −0.453827 | −0.226914 | − | 0.973915i | \(-0.572863\pi\) | ||||
−0.226914 | + | 0.973915i | \(0.572863\pi\) | |||||||
\(908\) | 3.10660e7 | 1.25046 | ||||||||
\(909\) | −5.62466e7 | −2.25781 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.28294e7 | 0.911377 | 0.455689 | − | 0.890139i | \(-0.349393\pi\) | ||||
0.455689 | + | 0.890139i | \(0.349393\pi\) | |||||||
\(912\) | 4.99289e7 | 1.98776 | ||||||||
\(913\) | 49666.6 | 0.00197191 | ||||||||
\(914\) | −5.49538e6 | −0.217587 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.86310e7 | 0.733666 | ||||||||
\(917\) | −2.10070e7 | −0.824974 | ||||||||
\(918\) | 4.27109e7 | 1.67275 | ||||||||
\(919\) | 3.58183e7 | 1.39899 | 0.699497 | − | 0.714635i | \(-0.253407\pi\) | ||||
0.699497 | + | 0.714635i | \(0.253407\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.63699e7 | −1.80130 | ||||||||
\(922\) | 8.21885e6 | 0.318408 | ||||||||
\(923\) | 4.54763e6 | 0.175704 | ||||||||
\(924\) | −9.30807e6 | −0.358657 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 4.93410e6 | 0.189095 | ||||||||
\(927\) | 4.84177e7 | 1.85057 | ||||||||
\(928\) | 3.04584e7 | 1.16101 | ||||||||
\(929\) | −1.37009e7 | −0.520847 | −0.260424 | − | 0.965494i | \(-0.583862\pi\) | ||||
−0.260424 | + | 0.965494i | \(0.583862\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.64217e7 | 1.37716 | ||||||||
\(932\) | 2.33090e7 | 0.878988 | ||||||||
\(933\) | −7.65996e7 | −2.88086 | ||||||||
\(934\) | −4.26704e6 | −0.160051 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.28423e7 | 0.479131 | ||||||||
\(937\) | −2.45732e7 | −0.914352 | −0.457176 | − | 0.889376i | \(-0.651139\pi\) | ||||
−0.457176 | + | 0.889376i | \(0.651139\pi\) | |||||||
\(938\) | 1.02315e7 | 0.379691 | ||||||||
\(939\) | 1.67789e7 | 0.621013 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.53611e7 | 1.30182 | 0.650912 | − | 0.759153i | \(-0.274387\pi\) | ||||
0.650912 | + | 0.759153i | \(0.274387\pi\) | |||||||
\(942\) | −1.81059e6 | −0.0664801 | ||||||||
\(943\) | −2.31072e6 | −0.0846191 | ||||||||
\(944\) | 1.11149e7 | 0.405952 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.65353e6 | −0.0964043 | ||||||||
\(947\) | −4.90338e7 | −1.77673 | −0.888364 | − | 0.459140i | \(-0.848158\pi\) | ||||
−0.888364 | + | 0.459140i | \(0.848158\pi\) | |||||||
\(948\) | 1.13324e7 | 0.409545 | ||||||||
\(949\) | 5.68922e6 | 0.205063 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.45699e7 | 1.59805 | ||||||||
\(952\) | 3.81671e7 | 1.36489 | ||||||||
\(953\) | 1.81532e7 | 0.647472 | 0.323736 | − | 0.946147i | \(-0.395061\pi\) | ||||
0.323736 | + | 0.946147i | \(0.395061\pi\) | |||||||
\(954\) | −3.47431e6 | −0.123594 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.01082e7 | −0.357708 | ||||||||
\(957\) | −1.11755e7 | −0.394444 | ||||||||
\(958\) | −1.86025e7 | −0.654872 | ||||||||
\(959\) | −2.89967e7 | −1.01813 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.55304e6 | −0.0542466 | ||||||||
\(962\) | −1.41962e6 | −0.0494578 | ||||||||
\(963\) | −5.00212e7 | −1.73815 | ||||||||
\(964\) | 2.61364e7 | 0.905844 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1.42532e6 | 0.0491441 | ||||||||
\(967\) | −5.23618e7 | −1.80073 | −0.900365 | − | 0.435135i | \(-0.856701\pi\) | ||||
−0.900365 | + | 0.435135i | \(0.856701\pi\) | |||||||
\(968\) | 1.85642e7 | 0.636777 | ||||||||
\(969\) | 1.36360e8 | 4.66527 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.95200e7 | 1.00477 | 0.502387 | − | 0.864643i | \(-0.332455\pi\) | ||||
0.502387 | + | 0.864643i | \(0.332455\pi\) | |||||||
\(972\) | −8.46299e7 | −2.87315 | ||||||||
\(973\) | −3.86287e7 | −1.30806 | ||||||||
\(974\) | −9.58395e6 | −0.323703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.67114e7 | −0.561551 | ||||||||
\(977\) | 1.21759e7 | 0.408098 | 0.204049 | − | 0.978961i | \(-0.434590\pi\) | ||||
0.204049 | + | 0.978961i | \(0.434590\pi\) | |||||||
\(978\) | 1.19632e7 | 0.399946 | ||||||||
\(979\) | 4.53499e6 | 0.151224 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.12971e8 | 3.74797 | ||||||||
\(982\) | −7.59304e6 | −0.251268 | ||||||||
\(983\) | 1.46087e6 | 0.0482200 | 0.0241100 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241100 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(984\) | −5.90220e7 | −1.94324 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.14413e7 | 0.702360 | ||||||||
\(987\) | 8.81942e7 | 2.88169 | ||||||||
\(988\) | 1.19355e7 | 0.388998 | ||||||||
\(989\) | −2.96186e6 | −0.0962883 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.16160e7 | 1.02264 | 0.511320 | − | 0.859390i | \(-0.329157\pi\) | ||||
0.511320 | + | 0.859390i | \(0.329157\pi\) | |||||||
\(992\) | −2.65078e7 | −0.855252 | ||||||||
\(993\) | 7.38951e7 | 2.37817 | ||||||||
\(994\) | 9.35660e6 | 0.300367 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 662564. | 0.0211631 | ||||||||
\(997\) | 3.93744e7 | 1.25452 | 0.627258 | − | 0.778812i | \(-0.284177\pi\) | ||||
0.627258 | + | 0.778812i | \(0.284177\pi\) | |||||||
\(998\) | 1.13020e7 | 0.359195 | ||||||||
\(999\) | 5.09194e7 | 1.61425 |
(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 | 325.6.a.j.1.7 | ✓ | 11 | |
5.2 | odd | 4 | 325.6.b.i.274.13 | 22 | |||
5.3 | odd | 4 | 325.6.b.i.274.10 | 22 | |||
5.4 | even | 2 | 325.6.a.k.1.5 | yes | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.6.a.j.1.7 | ✓ | 11 | 1.1 | even | 1 | trivial | |
325.6.a.k.1.5 | yes | 11 | 5.4 | even | 2 | ||
325.6.b.i.274.10 | 22 | 5.3 | odd | 4 | |||
325.6.b.i.274.13 | 22 | 5.2 | odd | 4 |