Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [490,6,Mod(1,490)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(490, 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("490.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 490 = 2 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 490.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: | \(78.5880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 10) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 490.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.00000 | −0.707107 | ||||||||
\(3\) | −24.0000 | −1.53960 | −0.769800 | − | 0.638285i | \(-0.779644\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | −25.0000 | −0.447214 | ||||||||
\(6\) | 96.0000 | 1.08866 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −64.0000 | −0.353553 | ||||||||
\(9\) | 333.000 | 1.37037 | ||||||||
\(10\) | 100.000 | 0.316228 | ||||||||
\(11\) | 132.000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | −384.000 | −0.769800 | ||||||||
\(13\) | 946.000 | 1.55250 | 0.776252 | − | 0.630423i | \(-0.217118\pi\) | ||||
0.776252 | + | 0.630423i | \(0.217118\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 600.000 | 0.688530 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | 222.000 | 0.186308 | 0.0931538 | − | 0.995652i | \(-0.470305\pi\) | ||||
0.0931538 | + | 0.995652i | \(0.470305\pi\) | |||||||
\(18\) | −1332.00 | −0.968998 | ||||||||
\(19\) | −500.000 | −0.317750 | −0.158875 | − | 0.987299i | \(-0.550787\pi\) | ||||
−0.158875 | + | 0.987299i | \(0.550787\pi\) | |||||||
\(20\) | −400.000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −528.000 | −0.232583 | ||||||||
\(23\) | 3564.00 | 1.40481 | 0.702406 | − | 0.711777i | \(-0.252109\pi\) | ||||
0.702406 | + | 0.711777i | \(0.252109\pi\) | |||||||
\(24\) | 1536.00 | 0.544331 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −3784.00 | −1.09779 | ||||||||
\(27\) | −2160.00 | −0.570222 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2190.00 | 0.483559 | 0.241779 | − | 0.970331i | \(-0.422269\pi\) | ||||
0.241779 | + | 0.970331i | \(0.422269\pi\) | |||||||
\(30\) | −2400.00 | −0.486864 | ||||||||
\(31\) | −2312.00 | −0.432099 | −0.216050 | − | 0.976382i | \(-0.569317\pi\) | ||||
−0.216050 | + | 0.976382i | \(0.569317\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | −3168.00 | −0.506408 | ||||||||
\(34\) | −888.000 | −0.131739 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5328.00 | 0.685185 | ||||||||
\(37\) | −11242.0 | −1.35002 | −0.675009 | − | 0.737810i | \(-0.735860\pi\) | ||||
−0.675009 | + | 0.737810i | \(0.735860\pi\) | |||||||
\(38\) | 2000.00 | 0.224683 | ||||||||
\(39\) | −22704.0 | −2.39024 | ||||||||
\(40\) | 1600.00 | 0.158114 | ||||||||
\(41\) | −1242.00 | −0.115388 | −0.0576942 | − | 0.998334i | \(-0.518375\pi\) | ||||
−0.0576942 | + | 0.998334i | \(0.518375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20624.0 | 1.70099 | 0.850495 | − | 0.525983i | \(-0.176303\pi\) | ||||
0.850495 | + | 0.525983i | \(0.176303\pi\) | |||||||
\(44\) | 2112.00 | 0.164461 | ||||||||
\(45\) | −8325.00 | −0.612848 | ||||||||
\(46\) | −14256.0 | −0.993352 | ||||||||
\(47\) | −6588.00 | −0.435020 | −0.217510 | − | 0.976058i | \(-0.569793\pi\) | ||||
−0.217510 | + | 0.976058i | \(0.569793\pi\) | |||||||
\(48\) | −6144.00 | −0.384900 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2500.00 | −0.141421 | ||||||||
\(51\) | −5328.00 | −0.286839 | ||||||||
\(52\) | 15136.0 | 0.776252 | ||||||||
\(53\) | −21066.0 | −1.03013 | −0.515065 | − | 0.857151i | \(-0.672232\pi\) | ||||
−0.515065 | + | 0.857151i | \(0.672232\pi\) | |||||||
\(54\) | 8640.00 | 0.403208 | ||||||||
\(55\) | −3300.00 | −0.147098 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 12000.0 | 0.489209 | ||||||||
\(58\) | −8760.00 | −0.341928 | ||||||||
\(59\) | −7980.00 | −0.298451 | −0.149225 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149225 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(60\) | 9600.00 | 0.344265 | ||||||||
\(61\) | −16622.0 | −0.571951 | −0.285975 | − | 0.958237i | \(-0.592318\pi\) | ||||
−0.285975 | + | 0.958237i | \(0.592318\pi\) | |||||||
\(62\) | 9248.00 | 0.305540 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | −23650.0 | −0.694301 | ||||||||
\(66\) | 12672.0 | 0.358084 | ||||||||
\(67\) | 1808.00 | 0.0492052 | 0.0246026 | − | 0.999697i | \(-0.492168\pi\) | ||||
0.0246026 | + | 0.999697i | \(0.492168\pi\) | |||||||
\(68\) | 3552.00 | 0.0931538 | ||||||||
\(69\) | −85536.0 | −2.16285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24528.0 | −0.577452 | −0.288726 | − | 0.957412i | \(-0.593232\pi\) | ||||
−0.288726 | + | 0.957412i | \(0.593232\pi\) | |||||||
\(72\) | −21312.0 | −0.484499 | ||||||||
\(73\) | −20474.0 | −0.449672 | −0.224836 | − | 0.974397i | \(-0.572185\pi\) | ||||
−0.224836 | + | 0.974397i | \(0.572185\pi\) | |||||||
\(74\) | 44968.0 | 0.954606 | ||||||||
\(75\) | −15000.0 | −0.307920 | ||||||||
\(76\) | −8000.00 | −0.158875 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 90816.0 | 1.69015 | ||||||||
\(79\) | −46240.0 | −0.833585 | −0.416793 | − | 0.909002i | \(-0.636846\pi\) | ||||
−0.416793 | + | 0.909002i | \(0.636846\pi\) | |||||||
\(80\) | −6400.00 | −0.111803 | ||||||||
\(81\) | −29079.0 | −0.492455 | ||||||||
\(82\) | 4968.00 | 0.0815919 | ||||||||
\(83\) | 51576.0 | 0.821774 | 0.410887 | − | 0.911686i | \(-0.365219\pi\) | ||||
0.410887 | + | 0.911686i | \(0.365219\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5550.00 | −0.0833193 | ||||||||
\(86\) | −82496.0 | −1.20278 | ||||||||
\(87\) | −52560.0 | −0.744487 | ||||||||
\(88\) | −8448.00 | −0.116291 | ||||||||
\(89\) | 110310. | 1.47618 | 0.738091 | − | 0.674701i | \(-0.235728\pi\) | ||||
0.738091 | + | 0.674701i | \(0.235728\pi\) | |||||||
\(90\) | 33300.0 | 0.433349 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 57024.0 | 0.702406 | ||||||||
\(93\) | 55488.0 | 0.665260 | ||||||||
\(94\) | 26352.0 | 0.307605 | ||||||||
\(95\) | 12500.0 | 0.142102 | ||||||||
\(96\) | 24576.0 | 0.272166 | ||||||||
\(97\) | 78382.0 | 0.845838 | 0.422919 | − | 0.906168i | \(-0.361006\pi\) | ||||
0.422919 | + | 0.906168i | \(0.361006\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43956.0 | 0.450744 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | −141942. | −1.38455 | −0.692273 | − | 0.721636i | \(-0.743391\pi\) | ||||
−0.692273 | + | 0.721636i | \(0.743391\pi\) | |||||||
\(102\) | 21312.0 | 0.202826 | ||||||||
\(103\) | 436.000 | 0.00404943 | 0.00202471 | − | 0.999998i | \(-0.499356\pi\) | ||||
0.00202471 | + | 0.999998i | \(0.499356\pi\) | |||||||
\(104\) | −60544.0 | −0.548893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 84264.0 | 0.728413 | ||||||||
\(107\) | 232968. | 1.96715 | 0.983574 | − | 0.180508i | \(-0.0577742\pi\) | ||||
0.983574 | + | 0.180508i | \(0.0577742\pi\) | |||||||
\(108\) | −34560.0 | −0.285111 | ||||||||
\(109\) | −174850. | −1.40961 | −0.704806 | − | 0.709400i | \(-0.748966\pi\) | ||||
−0.704806 | + | 0.709400i | \(0.748966\pi\) | |||||||
\(110\) | 13200.0 | 0.104014 | ||||||||
\(111\) | 269808. | 2.07849 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 182994. | 1.34816 | 0.674079 | − | 0.738659i | \(-0.264541\pi\) | ||||
0.674079 | + | 0.738659i | \(0.264541\pi\) | |||||||
\(114\) | −48000.0 | −0.345923 | ||||||||
\(115\) | −89100.0 | −0.628251 | ||||||||
\(116\) | 35040.0 | 0.241779 | ||||||||
\(117\) | 315018. | 2.12751 | ||||||||
\(118\) | 31920.0 | 0.211037 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −38400.0 | −0.243432 | ||||||||
\(121\) | −143627. | −0.891811 | ||||||||
\(122\) | 66488.0 | 0.404430 | ||||||||
\(123\) | 29808.0 | 0.177652 | ||||||||
\(124\) | −36992.0 | −0.216050 | ||||||||
\(125\) | −15625.0 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −122452. | −0.673685 | −0.336842 | − | 0.941561i | \(-0.609359\pi\) | ||||
−0.336842 | + | 0.941561i | \(0.609359\pi\) | |||||||
\(128\) | −16384.0 | −0.0883883 | ||||||||
\(129\) | −494976. | −2.61885 | ||||||||
\(130\) | 94600.0 | 0.490945 | ||||||||
\(131\) | 241908. | 1.23161 | 0.615803 | − | 0.787900i | \(-0.288832\pi\) | ||||
0.615803 | + | 0.787900i | \(0.288832\pi\) | |||||||
\(132\) | −50688.0 | −0.253204 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −7232.00 | −0.0347934 | ||||||||
\(135\) | 54000.0 | 0.255011 | ||||||||
\(136\) | −14208.0 | −0.0658697 | ||||||||
\(137\) | 277098. | 1.26134 | 0.630670 | − | 0.776051i | \(-0.282780\pi\) | ||||
0.630670 | + | 0.776051i | \(0.282780\pi\) | |||||||
\(138\) | 342144. | 1.52937 | ||||||||
\(139\) | 193540. | 0.849638 | 0.424819 | − | 0.905278i | \(-0.360338\pi\) | ||||
0.424819 | + | 0.905278i | \(0.360338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 158112. | 0.669757 | ||||||||
\(142\) | 98112.0 | 0.408321 | ||||||||
\(143\) | 124872. | 0.510652 | ||||||||
\(144\) | 85248.0 | 0.342593 | ||||||||
\(145\) | −54750.0 | −0.216254 | ||||||||
\(146\) | 81896.0 | 0.317966 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −179872. | −0.675009 | ||||||||
\(149\) | 140550. | 0.518639 | 0.259320 | − | 0.965792i | \(-0.416502\pi\) | ||||
0.259320 | + | 0.965792i | \(0.416502\pi\) | |||||||
\(150\) | 60000.0 | 0.217732 | ||||||||
\(151\) | 433952. | 1.54881 | 0.774407 | − | 0.632688i | \(-0.218048\pi\) | ||||
0.774407 | + | 0.632688i | \(0.218048\pi\) | |||||||
\(152\) | 32000.0 | 0.112342 | ||||||||
\(153\) | 73926.0 | 0.255310 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 57800.0 | 0.193241 | ||||||||
\(156\) | −363264. | −1.19512 | ||||||||
\(157\) | 555922. | 1.79997 | 0.899984 | − | 0.435923i | \(-0.143578\pi\) | ||||
0.899984 | + | 0.435923i | \(0.143578\pi\) | |||||||
\(158\) | 184960. | 0.589434 | ||||||||
\(159\) | 505584. | 1.58599 | ||||||||
\(160\) | 25600.0 | 0.0790569 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 116316. | 0.348219 | ||||||||
\(163\) | −66616.0 | −0.196386 | −0.0981928 | − | 0.995167i | \(-0.531306\pi\) | ||||
−0.0981928 | + | 0.995167i | \(0.531306\pi\) | |||||||
\(164\) | −19872.0 | −0.0576942 | ||||||||
\(165\) | 79200.0 | 0.226472 | ||||||||
\(166\) | −206304. | −0.581082 | ||||||||
\(167\) | 205692. | 0.570724 | 0.285362 | − | 0.958420i | \(-0.407886\pi\) | ||||
0.285362 | + | 0.958420i | \(0.407886\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 523623. | 1.41027 | ||||||||
\(170\) | 22200.0 | 0.0589156 | ||||||||
\(171\) | −166500. | −0.435436 | ||||||||
\(172\) | 329984. | 0.850495 | ||||||||
\(173\) | −433854. | −1.10212 | −0.551059 | − | 0.834466i | \(-0.685776\pi\) | ||||
−0.551059 | + | 0.834466i | \(0.685776\pi\) | |||||||
\(174\) | 210240. | 0.526432 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 33792.0 | 0.0822304 | ||||||||
\(177\) | 191520. | 0.459495 | ||||||||
\(178\) | −441240. | −1.04382 | ||||||||
\(179\) | −489180. | −1.14113 | −0.570566 | − | 0.821252i | \(-0.693276\pi\) | ||||
−0.570566 | + | 0.821252i | \(0.693276\pi\) | |||||||
\(180\) | −133200. | −0.306424 | ||||||||
\(181\) | −719462. | −1.63234 | −0.816172 | − | 0.577810i | \(-0.803908\pi\) | ||||
−0.816172 | + | 0.577810i | \(0.803908\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 398928. | 0.880576 | ||||||||
\(184\) | −228096. | −0.496676 | ||||||||
\(185\) | 281050. | 0.603746 | ||||||||
\(186\) | −221952. | −0.470410 | ||||||||
\(187\) | 29304.0 | 0.0612806 | ||||||||
\(188\) | −105408. | −0.217510 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −50000.0 | −0.100481 | ||||||||
\(191\) | −185928. | −0.368775 | −0.184387 | − | 0.982854i | \(-0.559030\pi\) | ||||
−0.184387 | + | 0.982854i | \(0.559030\pi\) | |||||||
\(192\) | −98304.0 | −0.192450 | ||||||||
\(193\) | −591406. | −1.14286 | −0.571429 | − | 0.820651i | \(-0.693611\pi\) | ||||
−0.571429 | + | 0.820651i | \(0.693611\pi\) | |||||||
\(194\) | −313528. | −0.598098 | ||||||||
\(195\) | 567600. | 1.06895 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 449478. | 0.825169 | 0.412584 | − | 0.910919i | \(-0.364626\pi\) | ||||
0.412584 | + | 0.910919i | \(0.364626\pi\) | |||||||
\(198\) | −175824. | −0.318724 | ||||||||
\(199\) | −157160. | −0.281326 | −0.140663 | − | 0.990058i | \(-0.544923\pi\) | ||||
−0.140663 | + | 0.990058i | \(0.544923\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | −43392.0 | −0.0757564 | ||||||||
\(202\) | 567768. | 0.979022 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −85248.0 | −0.143420 | ||||||||
\(205\) | 31050.0 | 0.0516032 | ||||||||
\(206\) | −1744.00 | −0.00286338 | ||||||||
\(207\) | 1.18681e6 | 1.92511 | ||||||||
\(208\) | 242176. | 0.388126 | ||||||||
\(209\) | −66000.0 | −0.104515 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 253052. | 0.391294 | 0.195647 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195647 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(212\) | −337056. | −0.515065 | ||||||||
\(213\) | 588672. | 0.889046 | ||||||||
\(214\) | −931872. | −1.39098 | ||||||||
\(215\) | −515600. | −0.760706 | ||||||||
\(216\) | 138240. | 0.201604 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 699400. | 0.996746 | ||||||||
\(219\) | 491376. | 0.692315 | ||||||||
\(220\) | −52800.0 | −0.0735491 | ||||||||
\(221\) | 210012. | 0.289243 | ||||||||
\(222\) | −1.07923e6 | −1.46971 | ||||||||
\(223\) | −1.07344e6 | −1.44550 | −0.722749 | − | 0.691111i | \(-0.757122\pi\) | ||||
−0.722749 | + | 0.691111i | \(0.757122\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 208125. | 0.274074 | ||||||||
\(226\) | −731976. | −0.953292 | ||||||||
\(227\) | 626832. | 0.807396 | 0.403698 | − | 0.914892i | \(-0.367725\pi\) | ||||
0.403698 | + | 0.914892i | \(0.367725\pi\) | |||||||
\(228\) | 192000. | 0.244604 | ||||||||
\(229\) | 116650. | 0.146993 | 0.0734964 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734964 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(230\) | 356400. | 0.444240 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −140160. | −0.170964 | ||||||||
\(233\) | −743046. | −0.896656 | −0.448328 | − | 0.893869i | \(-0.647980\pi\) | ||||
−0.448328 | + | 0.893869i | \(0.647980\pi\) | |||||||
\(234\) | −1.26007e6 | −1.50437 | ||||||||
\(235\) | 164700. | 0.194547 | ||||||||
\(236\) | −127680. | −0.149225 | ||||||||
\(237\) | 1.10976e6 | 1.28339 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 978720. | 1.10832 | 0.554158 | − | 0.832411i | \(-0.313040\pi\) | ||||
0.554158 | + | 0.832411i | \(0.313040\pi\) | |||||||
\(240\) | 153600. | 0.172133 | ||||||||
\(241\) | 1.13280e6 | 1.25635 | 0.628174 | − | 0.778073i | \(-0.283803\pi\) | ||||
0.628174 | + | 0.778073i | \(0.283803\pi\) | |||||||
\(242\) | 574508. | 0.630605 | ||||||||
\(243\) | 1.22278e6 | 1.32841 | ||||||||
\(244\) | −265952. | −0.285975 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −119232. | −0.125619 | ||||||||
\(247\) | −473000. | −0.493309 | ||||||||
\(248\) | 147968. | 0.152770 | ||||||||
\(249\) | −1.23782e6 | −1.26520 | ||||||||
\(250\) | 62500.0 | 0.0632456 | ||||||||
\(251\) | −905652. | −0.907355 | −0.453677 | − | 0.891166i | \(-0.649888\pi\) | ||||
−0.453677 | + | 0.891166i | \(0.649888\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 470448. | 0.462073 | ||||||||
\(254\) | 489808. | 0.476367 | ||||||||
\(255\) | 133200. | 0.128278 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −1.93994e6 | −1.83212 | −0.916062 | − | 0.401036i | \(-0.868650\pi\) | ||||
−0.916062 | + | 0.401036i | \(0.868650\pi\) | |||||||
\(258\) | 1.97990e6 | 1.85180 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −378400. | −0.347150 | ||||||||
\(261\) | 729270. | 0.662654 | ||||||||
\(262\) | −967632. | −0.870877 | ||||||||
\(263\) | −805476. | −0.718064 | −0.359032 | − | 0.933325i | \(-0.616893\pi\) | ||||
−0.359032 | + | 0.933325i | \(0.616893\pi\) | |||||||
\(264\) | 202752. | 0.179042 | ||||||||
\(265\) | 526650. | 0.460689 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.64744e6 | −2.27273 | ||||||||
\(268\) | 28928.0 | 0.0246026 | ||||||||
\(269\) | 858690. | 0.723529 | 0.361764 | − | 0.932270i | \(-0.382175\pi\) | ||||
0.361764 | + | 0.932270i | \(0.382175\pi\) | |||||||
\(270\) | −216000. | −0.180320 | ||||||||
\(271\) | 383608. | 0.317296 | 0.158648 | − | 0.987335i | \(-0.449287\pi\) | ||||
0.158648 | + | 0.987335i | \(0.449287\pi\) | |||||||
\(272\) | 56832.0 | 0.0465769 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.10839e6 | −0.891902 | ||||||||
\(275\) | 82500.0 | 0.0657843 | ||||||||
\(276\) | −1.36858e6 | −1.08142 | ||||||||
\(277\) | 2.01076e6 | 1.57456 | 0.787282 | − | 0.616593i | \(-0.211488\pi\) | ||||
0.787282 | + | 0.616593i | \(0.211488\pi\) | |||||||
\(278\) | −774160. | −0.600785 | ||||||||
\(279\) | −769896. | −0.592136 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202602. | 0.153066 | 0.0765329 | − | 0.997067i | \(-0.475615\pi\) | ||||
0.0765329 | + | 0.997067i | \(0.475615\pi\) | |||||||
\(282\) | −632448. | −0.473589 | ||||||||
\(283\) | 221536. | 0.164429 | 0.0822145 | − | 0.996615i | \(-0.473801\pi\) | ||||
0.0822145 | + | 0.996615i | \(0.473801\pi\) | |||||||
\(284\) | −392448. | −0.288726 | ||||||||
\(285\) | −300000. | −0.218781 | ||||||||
\(286\) | −499488. | −0.361085 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −340992. | −0.242250 | ||||||||
\(289\) | −1.37057e6 | −0.965289 | ||||||||
\(290\) | 219000. | 0.152915 | ||||||||
\(291\) | −1.88117e6 | −1.30225 | ||||||||
\(292\) | −327584. | −0.224836 | ||||||||
\(293\) | 322506. | 0.219467 | 0.109733 | − | 0.993961i | \(-0.465000\pi\) | ||||
0.109733 | + | 0.993961i | \(0.465000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 199500. | 0.133471 | ||||||||
\(296\) | 719488. | 0.477303 | ||||||||
\(297\) | −285120. | −0.187558 | ||||||||
\(298\) | −562200. | −0.366733 | ||||||||
\(299\) | 3.37154e6 | 2.18098 | ||||||||
\(300\) | −240000. | −0.153960 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.73581e6 | −1.09518 | ||||||||
\(303\) | 3.40661e6 | 2.13165 | ||||||||
\(304\) | −128000. | −0.0794376 | ||||||||
\(305\) | 415550. | 0.255784 | ||||||||
\(306\) | −295704. | −0.180532 | ||||||||
\(307\) | −1.44301e6 | −0.873822 | −0.436911 | − | 0.899505i | \(-0.643927\pi\) | ||||
−0.436911 | + | 0.899505i | \(0.643927\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10464.0 | −0.00623450 | ||||||||
\(310\) | −231200. | −0.136642 | ||||||||
\(311\) | −171312. | −0.100435 | −0.0502177 | − | 0.998738i | \(-0.515992\pi\) | ||||
−0.0502177 | + | 0.998738i | \(0.515992\pi\) | |||||||
\(312\) | 1.45306e6 | 0.845076 | ||||||||
\(313\) | 1.02689e6 | 0.592463 | 0.296232 | − | 0.955116i | \(-0.404270\pi\) | ||||
0.296232 | + | 0.955116i | \(0.404270\pi\) | |||||||
\(314\) | −2.22369e6 | −1.27277 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −739840. | −0.416793 | ||||||||
\(317\) | 752958. | 0.420845 | 0.210423 | − | 0.977610i | \(-0.432516\pi\) | ||||
0.210423 | + | 0.977610i | \(0.432516\pi\) | |||||||
\(318\) | −2.02234e6 | −1.12146 | ||||||||
\(319\) | 289080. | 0.159053 | ||||||||
\(320\) | −102400. | −0.0559017 | ||||||||
\(321\) | −5.59123e6 | −3.02862 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −111000. | −0.0591993 | ||||||||
\(324\) | −465264. | −0.246228 | ||||||||
\(325\) | 591250. | 0.310501 | ||||||||
\(326\) | 266464. | 0.138866 | ||||||||
\(327\) | 4.19640e6 | 2.17024 | ||||||||
\(328\) | 79488.0 | 0.0407959 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −316800. | −0.160140 | ||||||||
\(331\) | 1.99413e6 | 1.00042 | 0.500212 | − | 0.865903i | \(-0.333255\pi\) | ||||
0.500212 | + | 0.865903i | \(0.333255\pi\) | |||||||
\(332\) | 825216. | 0.410887 | ||||||||
\(333\) | −3.74359e6 | −1.85002 | ||||||||
\(334\) | −822768. | −0.403563 | ||||||||
\(335\) | −45200.0 | −0.0220053 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −987022. | −0.473426 | −0.236713 | − | 0.971580i | \(-0.576070\pi\) | ||||
−0.236713 | + | 0.971580i | \(0.576070\pi\) | |||||||
\(338\) | −2.09449e6 | −0.997211 | ||||||||
\(339\) | −4.39186e6 | −2.07562 | ||||||||
\(340\) | −88800.0 | −0.0416597 | ||||||||
\(341\) | −305184. | −0.142127 | ||||||||
\(342\) | 666000. | 0.307899 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.31994e6 | −0.601391 | ||||||||
\(345\) | 2.13840e6 | 0.967256 | ||||||||
\(346\) | 1.73542e6 | 0.779316 | ||||||||
\(347\) | 2.20601e6 | 0.983520 | 0.491760 | − | 0.870731i | \(-0.336354\pi\) | ||||
0.491760 | + | 0.870731i | \(0.336354\pi\) | |||||||
\(348\) | −840960. | −0.372244 | ||||||||
\(349\) | −2.74187e6 | −1.20499 | −0.602495 | − | 0.798123i | \(-0.705827\pi\) | ||||
−0.602495 | + | 0.798123i | \(0.705827\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.04336e6 | −0.885273 | ||||||||
\(352\) | −135168. | −0.0581456 | ||||||||
\(353\) | 2.38957e6 | 1.02066 | 0.510331 | − | 0.859978i | \(-0.329523\pi\) | ||||
0.510331 | + | 0.859978i | \(0.329523\pi\) | |||||||
\(354\) | −766080. | −0.324912 | ||||||||
\(355\) | 613200. | 0.258245 | ||||||||
\(356\) | 1.76496e6 | 0.738091 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.95672e6 | 0.806903 | ||||||||
\(359\) | −279480. | −0.114450 | −0.0572248 | − | 0.998361i | \(-0.518225\pi\) | ||||
−0.0572248 | + | 0.998361i | \(0.518225\pi\) | |||||||
\(360\) | 532800. | 0.216675 | ||||||||
\(361\) | −2.22610e6 | −0.899035 | ||||||||
\(362\) | 2.87785e6 | 1.15424 | ||||||||
\(363\) | 3.44705e6 | 1.37303 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 511850. | 0.201099 | ||||||||
\(366\) | −1.59571e6 | −0.622661 | ||||||||
\(367\) | 2.47637e6 | 0.959734 | 0.479867 | − | 0.877341i | \(-0.340685\pi\) | ||||
0.479867 | + | 0.877341i | \(0.340685\pi\) | |||||||
\(368\) | 912384. | 0.351203 | ||||||||
\(369\) | −413586. | −0.158125 | ||||||||
\(370\) | −1.12420e6 | −0.426913 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 887808. | 0.332630 | ||||||||
\(373\) | 2.74525e6 | 1.02167 | 0.510835 | − | 0.859679i | \(-0.329336\pi\) | ||||
0.510835 | + | 0.859679i | \(0.329336\pi\) | |||||||
\(374\) | −117216. | −0.0433319 | ||||||||
\(375\) | 375000. | 0.137706 | ||||||||
\(376\) | 421632. | 0.153803 | ||||||||
\(377\) | 2.07174e6 | 0.750727 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.18906e6 | −0.425212 | −0.212606 | − | 0.977138i | \(-0.568195\pi\) | ||||
−0.212606 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(380\) | 200000. | 0.0710511 | ||||||||
\(381\) | 2.93885e6 | 1.03721 | ||||||||
\(382\) | 743712. | 0.260763 | ||||||||
\(383\) | −3.25760e6 | −1.13475 | −0.567377 | − | 0.823458i | \(-0.692042\pi\) | ||||
−0.567377 | + | 0.823458i | \(0.692042\pi\) | |||||||
\(384\) | 393216. | 0.136083 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.36562e6 | 0.808123 | ||||||||
\(387\) | 6.86779e6 | 2.33099 | ||||||||
\(388\) | 1.25411e6 | 0.422919 | ||||||||
\(389\) | 1.98351e6 | 0.664600 | 0.332300 | − | 0.943174i | \(-0.392175\pi\) | ||||
0.332300 | + | 0.943174i | \(0.392175\pi\) | |||||||
\(390\) | −2.27040e6 | −0.755859 | ||||||||
\(391\) | 791208. | 0.261727 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.80579e6 | −1.89618 | ||||||||
\(394\) | −1.79791e6 | −0.583483 | ||||||||
\(395\) | 1.15600e6 | 0.372791 | ||||||||
\(396\) | 703296. | 0.225372 | ||||||||
\(397\) | −4.97416e6 | −1.58396 | −0.791978 | − | 0.610549i | \(-0.790949\pi\) | ||||
−0.791978 | + | 0.610549i | \(0.790949\pi\) | |||||||
\(398\) | 628640. | 0.198927 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 160000. | 0.0500000 | ||||||||
\(401\) | −1.34264e6 | −0.416963 | −0.208482 | − | 0.978026i | \(-0.566852\pi\) | ||||
−0.208482 | + | 0.978026i | \(0.566852\pi\) | |||||||
\(402\) | 173568. | 0.0535679 | ||||||||
\(403\) | −2.18715e6 | −0.670836 | ||||||||
\(404\) | −2.27107e6 | −0.692273 | ||||||||
\(405\) | 726975. | 0.220233 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.48394e6 | −0.444050 | ||||||||
\(408\) | 340992. | 0.101413 | ||||||||
\(409\) | 1.09423e6 | 0.323445 | 0.161722 | − | 0.986836i | \(-0.448295\pi\) | ||||
0.161722 | + | 0.986836i | \(0.448295\pi\) | |||||||
\(410\) | −124200. | −0.0364890 | ||||||||
\(411\) | −6.65035e6 | −1.94196 | ||||||||
\(412\) | 6976.00 | 0.00202471 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −4.74725e6 | −1.36126 | ||||||||
\(415\) | −1.28940e6 | −0.367509 | ||||||||
\(416\) | −968704. | −0.274447 | ||||||||
\(417\) | −4.64496e6 | −1.30810 | ||||||||
\(418\) | 264000. | 0.0739032 | ||||||||
\(419\) | 954060. | 0.265485 | 0.132743 | − | 0.991151i | \(-0.457622\pi\) | ||||
0.132743 | + | 0.991151i | \(0.457622\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.59390e6 | −0.438284 | −0.219142 | − | 0.975693i | \(-0.570326\pi\) | ||||
−0.219142 | + | 0.975693i | \(0.570326\pi\) | |||||||
\(422\) | −1.01221e6 | −0.276687 | ||||||||
\(423\) | −2.19380e6 | −0.596138 | ||||||||
\(424\) | 1.34822e6 | 0.364206 | ||||||||
\(425\) | 138750. | 0.0372615 | ||||||||
\(426\) | −2.35469e6 | −0.628651 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.72749e6 | 0.983574 | ||||||||
\(429\) | −2.99693e6 | −0.786200 | ||||||||
\(430\) | 2.06240e6 | 0.537900 | ||||||||
\(431\) | −2.64665e6 | −0.686283 | −0.343141 | − | 0.939284i | \(-0.611491\pi\) | ||||
−0.343141 | + | 0.939284i | \(0.611491\pi\) | |||||||
\(432\) | −552960. | −0.142556 | ||||||||
\(433\) | −3.72355e6 | −0.954416 | −0.477208 | − | 0.878790i | \(-0.658351\pi\) | ||||
−0.477208 | + | 0.878790i | \(0.658351\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.31400e6 | 0.332945 | ||||||||
\(436\) | −2.79760e6 | −0.704806 | ||||||||
\(437\) | −1.78200e6 | −0.446379 | ||||||||
\(438\) | −1.96550e6 | −0.489541 | ||||||||
\(439\) | 2.58340e6 | 0.639780 | 0.319890 | − | 0.947455i | \(-0.396354\pi\) | ||||
0.319890 | + | 0.947455i | \(0.396354\pi\) | |||||||
\(440\) | 211200. | 0.0520071 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −840048. | −0.204526 | ||||||||
\(443\) | 7.56206e6 | 1.83076 | 0.915379 | − | 0.402593i | \(-0.131891\pi\) | ||||
0.915379 | + | 0.402593i | \(0.131891\pi\) | |||||||
\(444\) | 4.31693e6 | 1.03924 | ||||||||
\(445\) | −2.75775e6 | −0.660169 | ||||||||
\(446\) | 4.29378e6 | 1.02212 | ||||||||
\(447\) | −3.37320e6 | −0.798497 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.30773e6 | 1.00840 | 0.504200 | − | 0.863587i | \(-0.331788\pi\) | ||||
0.504200 | + | 0.863587i | \(0.331788\pi\) | |||||||
\(450\) | −832500. | −0.193800 | ||||||||
\(451\) | −163944. | −0.0379537 | ||||||||
\(452\) | 2.92790e6 | 0.674079 | ||||||||
\(453\) | −1.04148e7 | −2.38456 | ||||||||
\(454\) | −2.50733e6 | −0.570915 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −768000. | −0.172961 | ||||||||
\(457\) | −2.24354e6 | −0.502509 | −0.251254 | − | 0.967921i | \(-0.580843\pi\) | ||||
−0.251254 | + | 0.967921i | \(0.580843\pi\) | |||||||
\(458\) | −466600. | −0.103940 | ||||||||
\(459\) | −479520. | −0.106237 | ||||||||
\(460\) | −1.42560e6 | −0.314125 | ||||||||
\(461\) | −1.65670e6 | −0.363071 | −0.181536 | − | 0.983384i | \(-0.558107\pi\) | ||||
−0.181536 | + | 0.983384i | \(0.558107\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.89160e6 | −0.626881 | −0.313441 | − | 0.949608i | \(-0.601482\pi\) | ||||
−0.313441 | + | 0.949608i | \(0.601482\pi\) | |||||||
\(464\) | 560640. | 0.120890 | ||||||||
\(465\) | −1.38720e6 | −0.297514 | ||||||||
\(466\) | 2.97218e6 | 0.634032 | ||||||||
\(467\) | 6.52699e6 | 1.38491 | 0.692454 | − | 0.721462i | \(-0.256530\pi\) | ||||
0.692454 | + | 0.721462i | \(0.256530\pi\) | |||||||
\(468\) | 5.04029e6 | 1.06375 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −658800. | −0.137565 | ||||||||
\(471\) | −1.33421e7 | −2.77123 | ||||||||
\(472\) | 510720. | 0.105518 | ||||||||
\(473\) | 2.72237e6 | 0.559492 | ||||||||
\(474\) | −4.43904e6 | −0.907493 | ||||||||
\(475\) | −312500. | −0.0635501 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.01498e6 | −1.41166 | ||||||||
\(478\) | −3.91488e6 | −0.783698 | ||||||||
\(479\) | 5.96232e6 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(480\) | −614400. | −0.121716 | ||||||||
\(481\) | −1.06349e7 | −2.09591 | ||||||||
\(482\) | −4.53119e6 | −0.888372 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.29803e6 | −0.445905 | ||||||||
\(485\) | −1.95955e6 | −0.378270 | ||||||||
\(486\) | −4.89110e6 | −0.939326 | ||||||||
\(487\) | 2.99191e6 | 0.571644 | 0.285822 | − | 0.958283i | \(-0.407733\pi\) | ||||
0.285822 | + | 0.958283i | \(0.407733\pi\) | |||||||
\(488\) | 1.06381e6 | 0.202215 | ||||||||
\(489\) | 1.59878e6 | 0.302355 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.20419e6 | −0.225419 | −0.112710 | − | 0.993628i | \(-0.535953\pi\) | ||||
−0.112710 | + | 0.993628i | \(0.535953\pi\) | |||||||
\(492\) | 476928. | 0.0888260 | ||||||||
\(493\) | 486180. | 0.0900907 | ||||||||
\(494\) | 1.89200e6 | 0.348822 | ||||||||
\(495\) | −1.09890e6 | −0.201579 | ||||||||
\(496\) | −591872. | −0.108025 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.95130e6 | 0.894634 | ||||||||
\(499\) | 9.20546e6 | 1.65499 | 0.827493 | − | 0.561477i | \(-0.189767\pi\) | ||||
0.827493 | + | 0.561477i | \(0.189767\pi\) | |||||||
\(500\) | −250000. | −0.0447214 | ||||||||
\(501\) | −4.93661e6 | −0.878687 | ||||||||
\(502\) | 3.62261e6 | 0.641597 | ||||||||
\(503\) | 3.35956e6 | 0.592055 | 0.296027 | − | 0.955179i | \(-0.404338\pi\) | ||||
0.296027 | + | 0.955179i | \(0.404338\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.54855e6 | 0.619188 | ||||||||
\(506\) | −1.88179e6 | −0.326735 | ||||||||
\(507\) | −1.25670e7 | −2.17125 | ||||||||
\(508\) | −1.95923e6 | −0.336842 | ||||||||
\(509\) | 2.53701e6 | 0.434038 | 0.217019 | − | 0.976167i | \(-0.430367\pi\) | ||||
0.217019 | + | 0.976167i | \(0.430367\pi\) | |||||||
\(510\) | −532800. | −0.0907066 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −262144. | −0.0441942 | ||||||||
\(513\) | 1.08000e6 | 0.181188 | ||||||||
\(514\) | 7.75975e6 | 1.29551 | ||||||||
\(515\) | −10900.0 | −0.00181096 | ||||||||
\(516\) | −7.91962e6 | −1.30942 | ||||||||
\(517\) | −869616. | −0.143087 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.04125e7 | 1.69682 | ||||||||
\(520\) | 1.51360e6 | 0.245472 | ||||||||
\(521\) | 9.31580e6 | 1.50358 | 0.751789 | − | 0.659404i | \(-0.229191\pi\) | ||||
0.751789 | + | 0.659404i | \(0.229191\pi\) | |||||||
\(522\) | −2.91708e6 | −0.468567 | ||||||||
\(523\) | 5.02802e6 | 0.803790 | 0.401895 | − | 0.915686i | \(-0.368352\pi\) | ||||
0.401895 | + | 0.915686i | \(0.368352\pi\) | |||||||
\(524\) | 3.87053e6 | 0.615803 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.22190e6 | 0.507748 | ||||||||
\(527\) | −513264. | −0.0805034 | ||||||||
\(528\) | −811008. | −0.126602 | ||||||||
\(529\) | 6.26575e6 | 0.973496 | ||||||||
\(530\) | −2.10660e6 | −0.325756 | ||||||||
\(531\) | −2.65734e6 | −0.408988 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.17493e6 | −0.179141 | ||||||||
\(534\) | 1.05898e7 | 1.60706 | ||||||||
\(535\) | −5.82420e6 | −0.879735 | ||||||||
\(536\) | −115712. | −0.0173967 | ||||||||
\(537\) | 1.17403e7 | 1.75689 | ||||||||
\(538\) | −3.43476e6 | −0.511612 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 864000. | 0.127506 | ||||||||
\(541\) | 134222. | 0.0197165 | 0.00985827 | − | 0.999951i | \(-0.496862\pi\) | ||||
0.00985827 | + | 0.999951i | \(0.496862\pi\) | |||||||
\(542\) | −1.53443e6 | −0.224362 | ||||||||
\(543\) | 1.72671e7 | 2.51316 | ||||||||
\(544\) | −227328. | −0.0329348 | ||||||||
\(545\) | 4.37125e6 | 0.630397 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 605648. | 0.0865470 | 0.0432735 | − | 0.999063i | \(-0.486221\pi\) | ||||
0.0432735 | + | 0.999063i | \(0.486221\pi\) | |||||||
\(548\) | 4.43357e6 | 0.630670 | ||||||||
\(549\) | −5.53513e6 | −0.783784 | ||||||||
\(550\) | −330000. | −0.0465165 | ||||||||
\(551\) | −1.09500e6 | −0.153651 | ||||||||
\(552\) | 5.47430e6 | 0.764683 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −8.04303e6 | −1.11339 | ||||||||
\(555\) | −6.74520e6 | −0.929528 | ||||||||
\(556\) | 3.09664e6 | 0.424819 | ||||||||
\(557\) | −7.06240e6 | −0.964527 | −0.482264 | − | 0.876026i | \(-0.660185\pi\) | ||||
−0.482264 | + | 0.876026i | \(0.660185\pi\) | |||||||
\(558\) | 3.07958e6 | 0.418703 | ||||||||
\(559\) | 1.95103e7 | 2.64079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −703296. | −0.0943476 | ||||||||
\(562\) | −810408. | −0.108234 | ||||||||
\(563\) | 1.03029e7 | 1.36990 | 0.684952 | − | 0.728588i | \(-0.259823\pi\) | ||||
0.684952 | + | 0.728588i | \(0.259823\pi\) | |||||||
\(564\) | 2.52979e6 | 0.334878 | ||||||||
\(565\) | −4.57485e6 | −0.602915 | ||||||||
\(566\) | −886144. | −0.116269 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.56979e6 | 0.204160 | ||||||||
\(569\) | 1.04769e6 | 0.135660 | 0.0678300 | − | 0.997697i | \(-0.478392\pi\) | ||||
0.0678300 | + | 0.997697i | \(0.478392\pi\) | |||||||
\(570\) | 1.20000e6 | 0.154701 | ||||||||
\(571\) | 1.40765e7 | 1.80677 | 0.903385 | − | 0.428830i | \(-0.141074\pi\) | ||||
0.903385 | + | 0.428830i | \(0.141074\pi\) | |||||||
\(572\) | 1.99795e6 | 0.255326 | ||||||||
\(573\) | 4.46227e6 | 0.567766 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.22750e6 | 0.280962 | ||||||||
\(576\) | 1.36397e6 | 0.171296 | ||||||||
\(577\) | −1.62682e6 | −0.203423 | −0.101711 | − | 0.994814i | \(-0.532432\pi\) | ||||
−0.101711 | + | 0.994814i | \(0.532432\pi\) | |||||||
\(578\) | 5.48229e6 | 0.682563 | ||||||||
\(579\) | 1.41937e7 | 1.75955 | ||||||||
\(580\) | −876000. | −0.108127 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 7.52467e6 | 0.920831 | ||||||||
\(583\) | −2.78071e6 | −0.338832 | ||||||||
\(584\) | 1.31034e6 | 0.158983 | ||||||||
\(585\) | −7.87545e6 | −0.951449 | ||||||||
\(586\) | −1.29002e6 | −0.155186 | ||||||||
\(587\) | −6.96089e6 | −0.833814 | −0.416907 | − | 0.908949i | \(-0.636886\pi\) | ||||
−0.416907 | + | 0.908949i | \(0.636886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15600e6 | 0.137300 | ||||||||
\(590\) | −798000. | −0.0943785 | ||||||||
\(591\) | −1.07875e7 | −1.27043 | ||||||||
\(592\) | −2.87795e6 | −0.337504 | ||||||||
\(593\) | 1.13639e7 | 1.32706 | 0.663529 | − | 0.748150i | \(-0.269058\pi\) | ||||
0.663529 | + | 0.748150i | \(0.269058\pi\) | |||||||
\(594\) | 1.14048e6 | 0.132624 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.24880e6 | 0.259320 | ||||||||
\(597\) | 3.77184e6 | 0.433129 | ||||||||
\(598\) | −1.34862e7 | −1.54218 | ||||||||
\(599\) | 1.48688e7 | 1.69321 | 0.846603 | − | 0.532224i | \(-0.178644\pi\) | ||||
0.846603 | + | 0.532224i | \(0.178644\pi\) | |||||||
\(600\) | 960000. | 0.108866 | ||||||||
\(601\) | 1.23612e6 | 0.139596 | 0.0697981 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0697981 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 602064. | 0.0674294 | ||||||||
\(604\) | 6.94323e6 | 0.774407 | ||||||||
\(605\) | 3.59067e6 | 0.398830 | ||||||||
\(606\) | −1.36264e7 | −1.50730 | ||||||||
\(607\) | 1.24498e7 | 1.37149 | 0.685743 | − | 0.727844i | \(-0.259478\pi\) | ||||
0.685743 | + | 0.727844i | \(0.259478\pi\) | |||||||
\(608\) | 512000. | 0.0561709 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.66220e6 | −0.180867 | ||||||||
\(611\) | −6.23225e6 | −0.675370 | ||||||||
\(612\) | 1.18282e6 | 0.127655 | ||||||||
\(613\) | −8.73491e6 | −0.938873 | −0.469437 | − | 0.882966i | \(-0.655543\pi\) | ||||
−0.469437 | + | 0.882966i | \(0.655543\pi\) | |||||||
\(614\) | 5.77203e6 | 0.617885 | ||||||||
\(615\) | −745200. | −0.0794484 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.25495e7 | 1.32713 | 0.663565 | − | 0.748119i | \(-0.269043\pi\) | ||||
0.663565 | + | 0.748119i | \(0.269043\pi\) | |||||||
\(618\) | 41856.0 | 0.00440846 | ||||||||
\(619\) | 1.46658e7 | 1.53843 | 0.769216 | − | 0.638988i | \(-0.220647\pi\) | ||||
0.769216 | + | 0.638988i | \(0.220647\pi\) | |||||||
\(620\) | 924800. | 0.0966203 | ||||||||
\(621\) | −7.69824e6 | −0.801055 | ||||||||
\(622\) | 685248. | 0.0710186 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −5.81222e6 | −0.597559 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −4.10754e6 | −0.418935 | ||||||||
\(627\) | 1.58400e6 | 0.160911 | ||||||||
\(628\) | 8.89475e6 | 0.899984 | ||||||||
\(629\) | −2.49572e6 | −0.251519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −196288. | −0.0196255 | −0.00981274 | − | 0.999952i | \(-0.503124\pi\) | ||||
−0.00981274 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(632\) | 2.95936e6 | 0.294717 | ||||||||
\(633\) | −6.07325e6 | −0.602437 | ||||||||
\(634\) | −3.01183e6 | −0.297583 | ||||||||
\(635\) | 3.06130e6 | 0.301281 | ||||||||
\(636\) | 8.08934e6 | 0.792995 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.15632e6 | −0.112467 | ||||||||
\(639\) | −8.16782e6 | −0.791324 | ||||||||
\(640\) | 409600. | 0.0395285 | ||||||||
\(641\) | −1.11596e7 | −1.07276 | −0.536381 | − | 0.843976i | \(-0.680209\pi\) | ||||
−0.536381 | + | 0.843976i | \(0.680209\pi\) | |||||||
\(642\) | 2.23649e7 | 2.14156 | ||||||||
\(643\) | 2.25158e6 | 0.214763 | 0.107381 | − | 0.994218i | \(-0.465753\pi\) | ||||
0.107381 | + | 0.994218i | \(0.465753\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.23744e7 | 1.17118 | ||||||||
\(646\) | 444000. | 0.0418602 | ||||||||
\(647\) | −8.05319e6 | −0.756323 | −0.378161 | − | 0.925740i | \(-0.623444\pi\) | ||||
−0.378161 | + | 0.925740i | \(0.623444\pi\) | |||||||
\(648\) | 1.86106e6 | 0.174109 | ||||||||
\(649\) | −1.05336e6 | −0.0981669 | ||||||||
\(650\) | −2.36500e6 | −0.219557 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.06586e6 | −0.0981928 | ||||||||
\(653\) | −416466. | −0.0382205 | −0.0191103 | − | 0.999817i | \(-0.506083\pi\) | ||||
−0.0191103 | + | 0.999817i | \(0.506083\pi\) | |||||||
\(654\) | −1.67856e7 | −1.53459 | ||||||||
\(655\) | −6.04770e6 | −0.550791 | ||||||||
\(656\) | −317952. | −0.0288471 | ||||||||
\(657\) | −6.81784e6 | −0.616217 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.31721e7 | 1.18152 | 0.590761 | − | 0.806847i | \(-0.298828\pi\) | ||||
0.590761 | + | 0.806847i | \(0.298828\pi\) | |||||||
\(660\) | 1.26720e6 | 0.113236 | ||||||||
\(661\) | 1.69494e6 | 0.150886 | 0.0754432 | − | 0.997150i | \(-0.475963\pi\) | ||||
0.0754432 | + | 0.997150i | \(0.475963\pi\) | |||||||
\(662\) | −7.97653e6 | −0.707406 | ||||||||
\(663\) | −5.04029e6 | −0.445319 | ||||||||
\(664\) | −3.30086e6 | −0.290541 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.49743e7 | 1.30816 | ||||||||
\(667\) | 7.80516e6 | 0.679309 | ||||||||
\(668\) | 3.29107e6 | 0.285362 | ||||||||
\(669\) | 2.57627e7 | 2.22549 | ||||||||
\(670\) | 180800. | 0.0155601 | ||||||||
\(671\) | −2.19410e6 | −0.188127 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.91605e6 | −0.758813 | −0.379406 | − | 0.925230i | \(-0.623872\pi\) | ||||
−0.379406 | + | 0.925230i | \(0.623872\pi\) | |||||||
\(674\) | 3.94809e6 | 0.334763 | ||||||||
\(675\) | −1.35000e6 | −0.114044 | ||||||||
\(676\) | 8.37797e6 | 0.705134 | ||||||||
\(677\) | 1.42894e7 | 1.19824 | 0.599118 | − | 0.800661i | \(-0.295518\pi\) | ||||
0.599118 | + | 0.800661i | \(0.295518\pi\) | |||||||
\(678\) | 1.75674e7 | 1.46769 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 355200. | 0.0294578 | ||||||||
\(681\) | −1.50440e7 | −1.24307 | ||||||||
\(682\) | 1.22074e6 | 0.100499 | ||||||||
\(683\) | −5.33314e6 | −0.437452 | −0.218726 | − | 0.975786i | \(-0.570190\pi\) | ||||
−0.218726 | + | 0.975786i | \(0.570190\pi\) | |||||||
\(684\) | −2.66400e6 | −0.217718 | ||||||||
\(685\) | −6.92745e6 | −0.564088 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.79960e6 | −0.226310 | ||||||||
\(688\) | 5.27974e6 | 0.425248 | ||||||||
\(689\) | −1.99284e7 | −1.59928 | ||||||||
\(690\) | −8.55360e6 | −0.683953 | ||||||||
\(691\) | −698252. | −0.0556310 | −0.0278155 | − | 0.999613i | \(-0.508855\pi\) | ||||
−0.0278155 | + | 0.999613i | \(0.508855\pi\) | |||||||
\(692\) | −6.94166e6 | −0.551059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.82403e6 | −0.695454 | ||||||||
\(695\) | −4.83850e6 | −0.379969 | ||||||||
\(696\) | 3.36384e6 | 0.263216 | ||||||||
\(697\) | −275724. | −0.0214977 | ||||||||
\(698\) | 1.09675e7 | 0.852056 | ||||||||
\(699\) | 1.78331e7 | 1.38049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.79880e7 | 1.38257 | 0.691285 | − | 0.722582i | \(-0.257045\pi\) | ||||
0.691285 | + | 0.722582i | \(0.257045\pi\) | |||||||
\(702\) | 8.17344e6 | 0.625982 | ||||||||
\(703\) | 5.62100e6 | 0.428968 | ||||||||
\(704\) | 540672. | 0.0411152 | ||||||||
\(705\) | −3.95280e6 | −0.299524 | ||||||||
\(706\) | −9.55826e6 | −0.721718 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 3.06432e6 | 0.229748 | ||||||||
\(709\) | −1.39464e7 | −1.04195 | −0.520975 | − | 0.853572i | \(-0.674432\pi\) | ||||
−0.520975 | + | 0.853572i | \(0.674432\pi\) | |||||||
\(710\) | −2.45280e6 | −0.182607 | ||||||||
\(711\) | −1.53979e7 | −1.14232 | ||||||||
\(712\) | −7.05984e6 | −0.521909 | ||||||||
\(713\) | −8.23997e6 | −0.607018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.12180e6 | −0.228370 | ||||||||
\(716\) | −7.82688e6 | −0.570566 | ||||||||
\(717\) | −2.34893e7 | −1.70636 | ||||||||
\(718\) | 1.11792e6 | 0.0809282 | ||||||||
\(719\) | −6.22272e6 | −0.448909 | −0.224454 | − | 0.974485i | \(-0.572060\pi\) | ||||
−0.224454 | + | 0.974485i | \(0.572060\pi\) | |||||||
\(720\) | −2.13120e6 | −0.153212 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.90440e6 | 0.635714 | ||||||||
\(723\) | −2.71872e7 | −1.93427 | ||||||||
\(724\) | −1.15114e7 | −0.816172 | ||||||||
\(725\) | 1.36875e6 | 0.0967117 | ||||||||
\(726\) | −1.37882e7 | −0.970880 | ||||||||
\(727\) | 7.76729e6 | 0.545047 | 0.272523 | − | 0.962149i | \(-0.412142\pi\) | ||||
0.272523 | + | 0.962149i | \(0.412142\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.22804e7 | −1.55276 | ||||||||
\(730\) | −2.04740e6 | −0.142199 | ||||||||
\(731\) | 4.57853e6 | 0.316907 | ||||||||
\(732\) | 6.38285e6 | 0.440288 | ||||||||
\(733\) | −2.42083e7 | −1.66420 | −0.832099 | − | 0.554627i | \(-0.812861\pi\) | ||||
−0.832099 | + | 0.554627i | \(0.812861\pi\) | |||||||
\(734\) | −9.90549e6 | −0.678634 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.64954e6 | −0.248338 | ||||||||
\(737\) | 238656. | 0.0161847 | ||||||||
\(738\) | 1.65434e6 | 0.111811 | ||||||||
\(739\) | 1.26850e7 | 0.854434 | 0.427217 | − | 0.904149i | \(-0.359494\pi\) | ||||
0.427217 | + | 0.904149i | \(0.359494\pi\) | |||||||
\(740\) | 4.49680e6 | 0.301873 | ||||||||
\(741\) | 1.13520e7 | 0.759498 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.97632e7 | 1.31337 | 0.656684 | − | 0.754166i | \(-0.271959\pi\) | ||||
0.656684 | + | 0.754166i | \(0.271959\pi\) | |||||||
\(744\) | −3.55123e6 | −0.235205 | ||||||||
\(745\) | −3.51375e6 | −0.231942 | ||||||||
\(746\) | −1.09810e7 | −0.722429 | ||||||||
\(747\) | 1.71748e7 | 1.12613 | ||||||||
\(748\) | 468864. | 0.0306403 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.50000e6 | −0.0973729 | ||||||||
\(751\) | −9.01761e6 | −0.583434 | −0.291717 | − | 0.956505i | \(-0.594226\pi\) | ||||
−0.291717 | + | 0.956505i | \(0.594226\pi\) | |||||||
\(752\) | −1.68653e6 | −0.108755 | ||||||||
\(753\) | 2.17356e7 | 1.39696 | ||||||||
\(754\) | −8.28696e6 | −0.530844 | ||||||||
\(755\) | −1.08488e7 | −0.692651 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.12556e6 | −0.0713887 | −0.0356944 | − | 0.999363i | \(-0.511364\pi\) | ||||
−0.0356944 | + | 0.999363i | \(0.511364\pi\) | |||||||
\(758\) | 4.75624e6 | 0.300670 | ||||||||
\(759\) | −1.12908e7 | −0.711407 | ||||||||
\(760\) | −800000. | −0.0502407 | ||||||||
\(761\) | −2.25747e7 | −1.41306 | −0.706529 | − | 0.707684i | \(-0.749740\pi\) | ||||
−0.706529 | + | 0.707684i | \(0.749740\pi\) | |||||||
\(762\) | −1.17554e7 | −0.733415 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.97485e6 | −0.184387 | ||||||||
\(765\) | −1.84815e6 | −0.114178 | ||||||||
\(766\) | 1.30304e7 | 0.802392 | ||||||||
\(767\) | −7.54908e6 | −0.463346 | ||||||||
\(768\) | −1.57286e6 | −0.0962250 | ||||||||
\(769\) | 632350. | 0.0385604 | 0.0192802 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192802 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.65585e7 | 2.82074 | ||||||||
\(772\) | −9.46250e6 | −0.571429 | ||||||||
\(773\) | 1.25867e7 | 0.757643 | 0.378822 | − | 0.925470i | \(-0.376329\pi\) | ||||
0.378822 | + | 0.925470i | \(0.376329\pi\) | |||||||
\(774\) | −2.74712e7 | −1.64826 | ||||||||
\(775\) | −1.44500e6 | −0.0864199 | ||||||||
\(776\) | −5.01645e6 | −0.299049 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.93404e6 | −0.469943 | ||||||||
\(779\) | 621000. | 0.0366647 | ||||||||
\(780\) | 9.08160e6 | 0.534473 | ||||||||
\(781\) | −3.23770e6 | −0.189937 | ||||||||
\(782\) | −3.16483e6 | −0.185069 | ||||||||
\(783\) | −4.73040e6 | −0.275736 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.38980e7 | −0.804970 | ||||||||
\(786\) | 2.32232e7 | 1.34080 | ||||||||
\(787\) | −2.15792e7 | −1.24194 | −0.620968 | − | 0.783836i | \(-0.713260\pi\) | ||||
−0.620968 | + | 0.783836i | \(0.713260\pi\) | |||||||
\(788\) | 7.19165e6 | 0.412584 | ||||||||
\(789\) | 1.93314e7 | 1.10553 | ||||||||
\(790\) | −4.62400e6 | −0.263603 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −2.81318e6 | −0.159362 | ||||||||
\(793\) | −1.57244e7 | −0.887956 | ||||||||
\(794\) | 1.98966e7 | 1.12003 | ||||||||
\(795\) | −1.26396e7 | −0.709276 | ||||||||
\(796\) | −2.51456e6 | −0.140663 | ||||||||
\(797\) | 3.09760e7 | 1.72735 | 0.863673 | − | 0.504052i | \(-0.168158\pi\) | ||||
0.863673 | + | 0.504052i | \(0.168158\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.46254e6 | −0.0810475 | ||||||||
\(800\) | −640000. | −0.0353553 | ||||||||
\(801\) | 3.67332e7 | 2.02292 | ||||||||
\(802\) | 5.37055e6 | 0.294838 | ||||||||
\(803\) | −2.70257e6 | −0.147907 | ||||||||
\(804\) | −694272. | −0.0378782 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.74861e6 | 0.474353 | ||||||||
\(807\) | −2.06086e7 | −1.11395 | ||||||||
\(808\) | 9.08429e6 | 0.489511 | ||||||||
\(809\) | 4.24929e6 | 0.228268 | 0.114134 | − | 0.993465i | \(-0.463591\pi\) | ||||
0.114134 | + | 0.993465i | \(0.463591\pi\) | |||||||
\(810\) | −2.90790e6 | −0.155728 | ||||||||
\(811\) | −3.42333e6 | −0.182767 | −0.0913833 | − | 0.995816i | \(-0.529129\pi\) | ||||
−0.0913833 | + | 0.995816i | \(0.529129\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.20659e6 | −0.488509 | ||||||||
\(814\) | 5.93578e6 | 0.313990 | ||||||||
\(815\) | 1.66540e6 | 0.0878263 | ||||||||
\(816\) | −1.36397e6 | −0.0717098 | ||||||||
\(817\) | −1.03120e7 | −0.540490 | ||||||||
\(818\) | −4.37692e6 | −0.228710 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 496800. | 0.0258016 | ||||||||
\(821\) | 3.10571e7 | 1.60806 | 0.804030 | − | 0.594588i | \(-0.202685\pi\) | ||||
0.804030 | + | 0.594588i | \(0.202685\pi\) | |||||||
\(822\) | 2.66014e7 | 1.37317 | ||||||||
\(823\) | −3.11904e7 | −1.60517 | −0.802584 | − | 0.596538i | \(-0.796542\pi\) | ||||
−0.802584 | + | 0.596538i | \(0.796542\pi\) | |||||||
\(824\) | −27904.0 | −0.00143169 | ||||||||
\(825\) | −1.98000e6 | −0.101282 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.28487e6 | −0.421233 | −0.210616 | − | 0.977569i | \(-0.567547\pi\) | ||||
−0.210616 | + | 0.977569i | \(0.567547\pi\) | |||||||
\(828\) | 1.89890e7 | 0.962556 | ||||||||
\(829\) | 1.81688e7 | 0.918208 | 0.459104 | − | 0.888383i | \(-0.348171\pi\) | ||||
0.459104 | + | 0.888383i | \(0.348171\pi\) | |||||||
\(830\) | 5.15760e6 | 0.259868 | ||||||||
\(831\) | −4.82582e7 | −2.42420 | ||||||||
\(832\) | 3.87482e6 | 0.194063 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 1.85798e7 | 0.924968 | ||||||||
\(835\) | −5.14230e6 | −0.255236 | ||||||||
\(836\) | −1.05600e6 | −0.0522575 | ||||||||
\(837\) | 4.99392e6 | 0.246393 | ||||||||
\(838\) | −3.81624e6 | −0.187727 | ||||||||
\(839\) | 1.02743e7 | 0.503902 | 0.251951 | − | 0.967740i | \(-0.418928\pi\) | ||||
0.251951 | + | 0.967740i | \(0.418928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.57150e7 | −0.766171 | ||||||||
\(842\) | 6.37559e6 | 0.309913 | ||||||||
\(843\) | −4.86245e6 | −0.235660 | ||||||||
\(844\) | 4.04883e6 | 0.195647 | ||||||||
\(845\) | −1.30906e7 | −0.630691 | ||||||||
\(846\) | 8.77522e6 | 0.421533 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.39290e6 | −0.257533 | ||||||||
\(849\) | −5.31686e6 | −0.253155 | ||||||||
\(850\) | −555000. | −0.0263479 | ||||||||
\(851\) | −4.00665e7 | −1.89652 | ||||||||
\(852\) | 9.41875e6 | 0.444523 | ||||||||
\(853\) | −6.28597e6 | −0.295801 | −0.147901 | − | 0.989002i | \(-0.547252\pi\) | ||||
−0.147901 | + | 0.989002i | \(0.547252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.16250e6 | 0.194733 | ||||||||
\(856\) | −1.49100e7 | −0.695492 | ||||||||
\(857\) | −1.54050e7 | −0.716490 | −0.358245 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358245 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(858\) | 1.19877e7 | 0.555927 | ||||||||
\(859\) | −1.43526e7 | −0.663664 | −0.331832 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331832 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(860\) | −8.24960e6 | −0.380353 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.05866e7 | 0.485275 | ||||||||
\(863\) | 1.33278e7 | 0.609158 | 0.304579 | − | 0.952487i | \(-0.401484\pi\) | ||||
0.304579 | + | 0.952487i | \(0.401484\pi\) | |||||||
\(864\) | 2.21184e6 | 0.100802 | ||||||||
\(865\) | 1.08464e7 | 0.492882 | ||||||||
\(866\) | 1.48942e7 | 0.674874 | ||||||||
\(867\) | 3.28938e7 | 1.48616 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.10368e6 | −0.274184 | ||||||||
\(870\) | −5.25600e6 | −0.235428 | ||||||||
\(871\) | 1.71037e6 | 0.0763913 | ||||||||
\(872\) | 1.11904e7 | 0.498373 | ||||||||
\(873\) | 2.61012e7 | 1.15911 | ||||||||
\(874\) | 7.12800e6 | 0.315638 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.86202e6 | 0.346157 | ||||||||
\(877\) | 3.24846e7 | 1.42620 | 0.713098 | − | 0.701065i | \(-0.247292\pi\) | ||||
0.713098 | + | 0.701065i | \(0.247292\pi\) | |||||||
\(878\) | −1.03336e7 | −0.452392 | ||||||||
\(879\) | −7.74014e6 | −0.337891 | ||||||||
\(880\) | −844800. | −0.0367745 | ||||||||
\(881\) | −1.54600e7 | −0.671073 | −0.335537 | − | 0.942027i | \(-0.608918\pi\) | ||||
−0.335537 | + | 0.942027i | \(0.608918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.69478e6 | −0.0731494 | −0.0365747 | − | 0.999331i | \(-0.511645\pi\) | ||||
−0.0365747 | + | 0.999331i | \(0.511645\pi\) | |||||||
\(884\) | 3.36019e6 | 0.144622 | ||||||||
\(885\) | −4.78800e6 | −0.205492 | ||||||||
\(886\) | −3.02483e7 | −1.29454 | ||||||||
\(887\) | 2.87257e6 | 0.122592 | 0.0612960 | − | 0.998120i | \(-0.480477\pi\) | ||||
0.0612960 | + | 0.998120i | \(0.480477\pi\) | |||||||
\(888\) | −1.72677e7 | −0.734856 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1.10310e7 | 0.466810 | ||||||||
\(891\) | −3.83843e6 | −0.161979 | ||||||||
\(892\) | −1.71751e7 | −0.722749 | ||||||||
\(893\) | 3.29400e6 | 0.138228 | ||||||||
\(894\) | 1.34928e7 | 0.564623 | ||||||||
\(895\) | 1.22295e7 | 0.510330 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.09171e7 | −3.35783 | ||||||||
\(898\) | −1.72309e7 | −0.713046 | ||||||||
\(899\) | −5.06328e6 | −0.208945 | ||||||||
\(900\) | 3.33000e6 | 0.137037 | ||||||||
\(901\) | −4.67665e6 | −0.191921 | ||||||||
\(902\) | 655776. | 0.0268373 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.17116e7 | −0.476646 | ||||||||
\(905\) | 1.79866e7 | 0.730006 | ||||||||
\(906\) | 4.16594e7 | 1.68614 | ||||||||
\(907\) | 3.95422e7 | 1.59603 | 0.798017 | − | 0.602635i | \(-0.205882\pi\) | ||||
0.798017 | + | 0.602635i | \(0.205882\pi\) | |||||||
\(908\) | 1.00293e7 | 0.403698 | ||||||||
\(909\) | −4.72667e7 | −1.89734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.13178e7 | 0.451819 | 0.225909 | − | 0.974148i | \(-0.427465\pi\) | ||||
0.225909 | + | 0.974148i | \(0.427465\pi\) | |||||||
\(912\) | 3.07200e6 | 0.122302 | ||||||||
\(913\) | 6.80803e6 | 0.270299 | ||||||||
\(914\) | 8.97417e6 | 0.355327 | ||||||||
\(915\) | −9.97320e6 | −0.393806 | ||||||||
\(916\) | 1.86640e6 | 0.0734964 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.91808e6 | 0.0751208 | ||||||||
\(919\) | 8.51348e6 | 0.332520 | 0.166260 | − | 0.986082i | \(-0.446831\pi\) | ||||
0.166260 | + | 0.986082i | \(0.446831\pi\) | |||||||
\(920\) | 5.70240e6 | 0.222120 | ||||||||
\(921\) | 3.46322e7 | 1.34534 | ||||||||
\(922\) | 6.62681e6 | 0.256730 | ||||||||
\(923\) | −2.32035e7 | −0.896497 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.02625e6 | −0.270003 | ||||||||
\(926\) | 1.15664e7 | 0.443272 | ||||||||
\(927\) | 145188. | 0.00554921 | ||||||||
\(928\) | −2.24256e6 | −0.0854819 | ||||||||
\(929\) | 7.54587e6 | 0.286860 | 0.143430 | − | 0.989660i | \(-0.454187\pi\) | ||||
0.143430 | + | 0.989660i | \(0.454187\pi\) | |||||||
\(930\) | 5.54880e6 | 0.210374 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.18887e7 | −0.448328 | ||||||||
\(933\) | 4.11149e6 | 0.154630 | ||||||||
\(934\) | −2.61080e7 | −0.979278 | ||||||||
\(935\) | −732600. | −0.0274055 | ||||||||
\(936\) | −2.01612e7 | −0.752187 | ||||||||
\(937\) | 1.84500e7 | 0.686512 | 0.343256 | − | 0.939242i | \(-0.388470\pi\) | ||||
0.343256 | + | 0.939242i | \(0.388470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.46453e7 | −0.912157 | ||||||||
\(940\) | 2.63520e6 | 0.0972734 | ||||||||
\(941\) | −6.75046e6 | −0.248519 | −0.124259 | − | 0.992250i | \(-0.539656\pi\) | ||||
−0.124259 | + | 0.992250i | \(0.539656\pi\) | |||||||
\(942\) | 5.33685e7 | 1.95956 | ||||||||
\(943\) | −4.42649e6 | −0.162099 | ||||||||
\(944\) | −2.04288e6 | −0.0746127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.08895e7 | −0.395621 | ||||||||
\(947\) | 6.45677e6 | 0.233959 | 0.116980 | − | 0.993134i | \(-0.462679\pi\) | ||||
0.116980 | + | 0.993134i | \(0.462679\pi\) | |||||||
\(948\) | 1.77562e7 | 0.641694 | ||||||||
\(949\) | −1.93684e7 | −0.698117 | ||||||||
\(950\) | 1.25000e6 | 0.0449367 | ||||||||
\(951\) | −1.80710e7 | −0.647934 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.96648e7 | −1.41473 | −0.707364 | − | 0.706849i | \(-0.750116\pi\) | ||||
−0.707364 | + | 0.706849i | \(0.750116\pi\) | |||||||
\(954\) | 2.80599e7 | 0.998195 | ||||||||
\(955\) | 4.64820e6 | 0.164921 | ||||||||
\(956\) | 1.56595e7 | 0.554158 | ||||||||
\(957\) | −6.93792e6 | −0.244878 | ||||||||
\(958\) | −2.38493e7 | −0.839579 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.45760e6 | 0.0860663 | ||||||||
\(961\) | −2.32838e7 | −0.813290 | ||||||||
\(962\) | 4.25397e7 | 1.48203 | ||||||||
\(963\) | 7.75783e7 | 2.69572 | ||||||||
\(964\) | 1.81248e7 | 0.628174 | ||||||||
\(965\) | 1.47851e7 | 0.511102 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.43015e7 | −1.17963 | −0.589816 | − | 0.807538i | \(-0.700800\pi\) | ||||
−0.589816 | + | 0.807538i | \(0.700800\pi\) | |||||||
\(968\) | 9.19213e6 | 0.315303 | ||||||||
\(969\) | 2.66400e6 | 0.0911433 | ||||||||
\(970\) | 7.83820e6 | 0.267477 | ||||||||
\(971\) | 5.77115e6 | 0.196433 | 0.0982164 | − | 0.995165i | \(-0.468686\pi\) | ||||
0.0982164 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(972\) | 1.95644e7 | 0.664204 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −1.19676e7 | −0.404214 | ||||||||
\(975\) | −1.41900e7 | −0.478047 | ||||||||
\(976\) | −4.25523e6 | −0.142988 | ||||||||
\(977\) | 7.08746e6 | 0.237549 | 0.118775 | − | 0.992921i | \(-0.462103\pi\) | ||||
0.118775 | + | 0.992921i | \(0.462103\pi\) | |||||||
\(978\) | −6.39514e6 | −0.213798 | ||||||||
\(979\) | 1.45609e7 | 0.485548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.82250e7 | −1.93169 | ||||||||
\(982\) | 4.81675e6 | 0.159395 | ||||||||
\(983\) | −4.59362e7 | −1.51625 | −0.758126 | − | 0.652108i | \(-0.773885\pi\) | ||||
−0.758126 | + | 0.652108i | \(0.773885\pi\) | |||||||
\(984\) | −1.90771e6 | −0.0628095 | ||||||||
\(985\) | −1.12370e7 | −0.369027 | ||||||||
\(986\) | −1.94472e6 | −0.0637037 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.56800e6 | −0.246654 | ||||||||
\(989\) | 7.35039e7 | 2.38957 | ||||||||
\(990\) | 4.39560e6 | 0.142538 | ||||||||
\(991\) | −4.50298e7 | −1.45652 | −0.728260 | − | 0.685301i | \(-0.759671\pi\) | ||||
−0.728260 | + | 0.685301i | \(0.759671\pi\) | |||||||
\(992\) | 2.36749e6 | 0.0763851 | ||||||||
\(993\) | −4.78592e7 | −1.54025 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.92900e6 | 0.125813 | ||||||||
\(996\) | −1.98052e7 | −0.632602 | ||||||||
\(997\) | 2.37364e7 | 0.756271 | 0.378136 | − | 0.925750i | \(-0.376565\pi\) | ||||
0.378136 | + | 0.925750i | \(0.376565\pi\) | |||||||
\(998\) | −3.68218e7 | −1.17025 | ||||||||
\(999\) | 2.42827e7 | 0.769810 |
(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 | 490.6.a.a.1.1 | 1 | ||
7.6 | odd | 2 | 10.6.a.b.1.1 | ✓ | 1 | ||
21.20 | even | 2 | 90.6.a.d.1.1 | 1 | |||
28.27 | even | 2 | 80.6.a.a.1.1 | 1 | |||
35.13 | even | 4 | 50.6.b.a.49.2 | 2 | |||
35.27 | even | 4 | 50.6.b.a.49.1 | 2 | |||
35.34 | odd | 2 | 50.6.a.d.1.1 | 1 | |||
56.13 | odd | 2 | 320.6.a.b.1.1 | 1 | |||
56.27 | even | 2 | 320.6.a.o.1.1 | 1 | |||
84.83 | odd | 2 | 720.6.a.j.1.1 | 1 | |||
105.62 | odd | 4 | 450.6.c.h.199.2 | 2 | |||
105.83 | odd | 4 | 450.6.c.h.199.1 | 2 | |||
105.104 | even | 2 | 450.6.a.l.1.1 | 1 | |||
140.27 | odd | 4 | 400.6.c.b.49.2 | 2 | |||
140.83 | odd | 4 | 400.6.c.b.49.1 | 2 | |||
140.139 | even | 2 | 400.6.a.n.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.b.1.1 | ✓ | 1 | 7.6 | odd | 2 | ||
50.6.a.d.1.1 | 1 | 35.34 | odd | 2 | |||
50.6.b.a.49.1 | 2 | 35.27 | even | 4 | |||
50.6.b.a.49.2 | 2 | 35.13 | even | 4 | |||
80.6.a.a.1.1 | 1 | 28.27 | even | 2 | |||
90.6.a.d.1.1 | 1 | 21.20 | even | 2 | |||
320.6.a.b.1.1 | 1 | 56.13 | odd | 2 | |||
320.6.a.o.1.1 | 1 | 56.27 | even | 2 | |||
400.6.a.n.1.1 | 1 | 140.139 | even | 2 | |||
400.6.c.b.49.1 | 2 | 140.83 | odd | 4 | |||
400.6.c.b.49.2 | 2 | 140.27 | odd | 4 | |||
450.6.a.l.1.1 | 1 | 105.104 | even | 2 | |||
450.6.c.h.199.1 | 2 | 105.83 | odd | 4 | |||
450.6.c.h.199.2 | 2 | 105.62 | odd | 4 | |||
490.6.a.a.1.1 | 1 | 1.1 | even | 1 | trivial | ||
720.6.a.j.1.1 | 1 | 84.83 | odd | 2 |