Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,6,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(1.60383819813\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 | \(-0.220356\pi\) | ||||
0.769800 | + | 0.638285i | \(0.220356\pi\) | |||||||
\(4\) | 16.0000 | 0.500000 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | −96.0000 | −1.08866 | ||||||||
\(7\) | −172.000 | −1.32673 | −0.663366 | − | 0.748295i | \(-0.730873\pi\) | ||||
−0.663366 | + | 0.748295i | \(0.730873\pi\) | |||||||
\(8\) | −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 | \(-0.782882\pi\) | ||||
−0.776252 | + | 0.630423i | \(0.782882\pi\) | |||||||
\(14\) | 688.000 | 0.938142 | ||||||||
\(15\) | 600.000 | 0.688530 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | −222.000 | −0.186308 | −0.0931538 | − | 0.995652i | \(-0.529695\pi\) | ||||
−0.0931538 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(18\) | −1332.00 | −0.968998 | ||||||||
\(19\) | 500.000 | 0.317750 | 0.158875 | − | 0.987299i | \(-0.449213\pi\) | ||||
0.158875 | + | 0.987299i | \(0.449213\pi\) | |||||||
\(20\) | 400.000 | 0.223607 | ||||||||
\(21\) | −4128.00 | −2.04264 | ||||||||
\(22\) | −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 | ||||||||
\(28\) | −2752.00 | −0.663366 | ||||||||
\(29\) | 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 | \(-0.430683\pi\) | ||||
0.216050 | + | 0.976382i | \(0.430683\pi\) | |||||||
\(32\) | −1024.00 | −0.176777 | ||||||||
\(33\) | 3168.00 | 0.506408 | ||||||||
\(34\) | 888.000 | 0.131739 | ||||||||
\(35\) | −4300.00 | −0.593333 | ||||||||
\(36\) | 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 | \(-0.481625\pi\) | ||||
0.0576942 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(42\) | 16512.0 | 1.44436 | ||||||||
\(43\) | 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 | \(-0.430207\pi\) | ||||
0.217510 | + | 0.976058i | \(0.430207\pi\) | |||||||
\(48\) | 6144.00 | 0.384900 | ||||||||
\(49\) | 12777.0 | 0.760219 | ||||||||
\(50\) | −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 | ||||||||
\(56\) | 11008.0 | 0.469071 | ||||||||
\(57\) | 12000.0 | 0.489209 | ||||||||
\(58\) | −8760.00 | −0.341928 | ||||||||
\(59\) | 7980.00 | 0.298451 | 0.149225 | − | 0.988803i | \(-0.452322\pi\) | ||||
0.149225 | + | 0.988803i | \(0.452322\pi\) | |||||||
\(60\) | 9600.00 | 0.344265 | ||||||||
\(61\) | 16622.0 | 0.571951 | 0.285975 | − | 0.958237i | \(-0.407682\pi\) | ||||
0.285975 | + | 0.958237i | \(0.407682\pi\) | |||||||
\(62\) | −9248.00 | −0.305540 | ||||||||
\(63\) | −57276.0 | −1.81811 | ||||||||
\(64\) | 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 | ||||||||
\(70\) | 17200.0 | 0.419550 | ||||||||
\(71\) | −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 | \(-0.427815\pi\) | ||||
0.224836 | + | 0.974397i | \(0.427815\pi\) | |||||||
\(74\) | 44968.0 | 0.954606 | ||||||||
\(75\) | 15000.0 | 0.307920 | ||||||||
\(76\) | 8000.00 | 0.158875 | ||||||||
\(77\) | −22704.0 | −0.436391 | ||||||||
\(78\) | 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 | \(-0.634781\pi\) | ||||
−0.410887 | + | 0.911686i | \(0.634781\pi\) | |||||||
\(84\) | −66048.0 | −1.02132 | ||||||||
\(85\) | −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 | \(-0.764272\pi\) | ||||
−0.738091 | + | 0.674701i | \(0.764272\pi\) | |||||||
\(90\) | −33300.0 | −0.433349 | ||||||||
\(91\) | 162712. | 2.05976 | ||||||||
\(92\) | 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 | \(-0.638994\pi\) | ||||
−0.422919 | + | 0.906168i | \(0.638994\pi\) | |||||||
\(98\) | −51108.0 | −0.537556 | ||||||||
\(99\) | 43956.0 | 0.450744 | ||||||||
\(100\) | 10000.0 | 0.100000 | ||||||||
\(101\) | 141942. | 1.38455 | 0.692273 | − | 0.721636i | \(-0.256609\pi\) | ||||
0.692273 | + | 0.721636i | \(0.256609\pi\) | |||||||
\(102\) | 21312.0 | 0.202826 | ||||||||
\(103\) | −436.000 | −0.00404943 | −0.00202471 | − | 0.999998i | \(-0.500644\pi\) | ||||
−0.00202471 | + | 0.999998i | \(0.500644\pi\) | |||||||
\(104\) | 60544.0 | 0.548893 | ||||||||
\(105\) | −103200. | −0.913496 | ||||||||
\(106\) | 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 | ||||||||
\(112\) | −44032.0 | −0.331683 | ||||||||
\(113\) | 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 | ||||||||
\(119\) | 38184.0 | 0.247180 | ||||||||
\(120\) | −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 | ||||||||
\(126\) | 229104. | 1.28560 | ||||||||
\(127\) | −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 | \(-0.711168\pi\) | ||||
−0.615803 | + | 0.787900i | \(0.711168\pi\) | |||||||
\(132\) | 50688.0 | 0.253204 | ||||||||
\(133\) | −86000.0 | −0.421570 | ||||||||
\(134\) | −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 | \(-0.639662\pi\) | ||||
−0.424819 | + | 0.905278i | \(0.639662\pi\) | |||||||
\(140\) | −68800.0 | −0.296666 | ||||||||
\(141\) | 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 | ||||||||
\(147\) | 306648. | 1.17043 | ||||||||
\(148\) | −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 | ||||||||
\(154\) | 90816.0 | 0.308575 | ||||||||
\(155\) | 57800.0 | 0.193241 | ||||||||
\(156\) | −363264. | −1.19512 | ||||||||
\(157\) | −555922. | −1.79997 | −0.899984 | − | 0.435923i | \(-0.856422\pi\) | ||||
−0.899984 | + | 0.435923i | \(0.856422\pi\) | |||||||
\(158\) | 184960. | 0.589434 | ||||||||
\(159\) | −505584. | −1.58599 | ||||||||
\(160\) | −25600.0 | −0.0790569 | ||||||||
\(161\) | −613008. | −1.86381 | ||||||||
\(162\) | 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 | \(-0.592114\pi\) | ||||
−0.285362 | + | 0.958420i | \(0.592114\pi\) | |||||||
\(168\) | 264192. | 0.722182 | ||||||||
\(169\) | 523623. | 1.41027 | ||||||||
\(170\) | 22200.0 | 0.0589156 | ||||||||
\(171\) | 166500. | 0.435436 | ||||||||
\(172\) | 329984. | 0.850495 | ||||||||
\(173\) | 433854. | 1.10212 | 0.551059 | − | 0.834466i | \(-0.314224\pi\) | ||||
0.551059 | + | 0.834466i | \(0.314224\pi\) | |||||||
\(174\) | −210240. | −0.526432 | ||||||||
\(175\) | −107500. | −0.265346 | ||||||||
\(176\) | 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 | \(-0.196092\pi\) | ||||
0.816172 | + | 0.577810i | \(0.196092\pi\) | |||||||
\(182\) | −650848. | −1.45647 | ||||||||
\(183\) | 398928. | 0.880576 | ||||||||
\(184\) | −228096. | −0.496676 | ||||||||
\(185\) | −281050. | −0.603746 | ||||||||
\(186\) | −221952. | −0.470410 | ||||||||
\(187\) | −29304.0 | −0.0612806 | ||||||||
\(188\) | 105408. | 0.217510 | ||||||||
\(189\) | −371520. | −0.756533 | ||||||||
\(190\) | −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 | ||||||||
\(196\) | 204432. | 0.380109 | ||||||||
\(197\) | 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 | \(-0.455077\pi\) | ||||
0.140663 | + | 0.990058i | \(0.455077\pi\) | |||||||
\(200\) | −40000.0 | −0.0707107 | ||||||||
\(201\) | 43392.0 | 0.0757564 | ||||||||
\(202\) | −567768. | −0.979022 | ||||||||
\(203\) | −376680. | −0.641553 | ||||||||
\(204\) | −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 | ||||||||
\(210\) | 412800. | 0.645939 | ||||||||
\(211\) | 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 | ||||||||
\(217\) | −397664. | −0.573280 | ||||||||
\(218\) | 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 | \(-0.242878\pi\) | ||||
0.722749 | + | 0.691111i | \(0.242878\pi\) | |||||||
\(224\) | 176128. | 0.234535 | ||||||||
\(225\) | 208125. | 0.274074 | ||||||||
\(226\) | −731976. | −0.953292 | ||||||||
\(227\) | −626832. | −0.807396 | −0.403698 | − | 0.914892i | \(-0.632275\pi\) | ||||
−0.403698 | + | 0.914892i | \(0.632275\pi\) | |||||||
\(228\) | 192000. | 0.244604 | ||||||||
\(229\) | −116650. | −0.146993 | −0.0734964 | − | 0.997295i | \(-0.523416\pi\) | ||||
−0.0734964 | + | 0.997295i | \(0.523416\pi\) | |||||||
\(230\) | −356400. | −0.444240 | ||||||||
\(231\) | −544896. | −0.671868 | ||||||||
\(232\) | −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 | ||||||||
\(238\) | −152736. | −0.174783 | ||||||||
\(239\) | 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 | \(-0.716197\pi\) | ||||
−0.628174 | + | 0.778073i | \(0.716197\pi\) | |||||||
\(242\) | 574508. | 0.630605 | ||||||||
\(243\) | −1.22278e6 | −1.32841 | ||||||||
\(244\) | 265952. | 0.285975 | ||||||||
\(245\) | 319425. | 0.339980 | ||||||||
\(246\) | −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 | \(-0.350112\pi\) | ||||
0.453677 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(252\) | −916416. | −0.909057 | ||||||||
\(253\) | 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 | \(-0.131350\pi\) | ||||
0.916062 | + | 0.401036i | \(0.131350\pi\) | |||||||
\(258\) | −1.97990e6 | −1.85180 | ||||||||
\(259\) | 1.93362e6 | 1.79111 | ||||||||
\(260\) | −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 | ||||||||
\(266\) | 344000. | 0.298095 | ||||||||
\(267\) | −2.64744e6 | −2.27273 | ||||||||
\(268\) | 28928.0 | 0.0246026 | ||||||||
\(269\) | −858690. | −0.723529 | −0.361764 | − | 0.932270i | \(-0.617825\pi\) | ||||
−0.361764 | + | 0.932270i | \(0.617825\pi\) | |||||||
\(270\) | −216000. | −0.180320 | ||||||||
\(271\) | −383608. | −0.317296 | −0.158648 | − | 0.987335i | \(-0.550713\pi\) | ||||
−0.158648 | + | 0.987335i | \(0.550713\pi\) | |||||||
\(272\) | −56832.0 | −0.0465769 | ||||||||
\(273\) | 3.90509e6 | 3.17120 | ||||||||
\(274\) | −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 | ||||||||
\(280\) | 275200. | 0.209775 | ||||||||
\(281\) | 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 | \(-0.526199\pi\) | ||||
−0.0822145 | + | 0.996615i | \(0.526199\pi\) | |||||||
\(284\) | −392448. | −0.288726 | ||||||||
\(285\) | 300000. | 0.218781 | ||||||||
\(286\) | 499488. | 0.361085 | ||||||||
\(287\) | −213624. | −0.153089 | ||||||||
\(288\) | −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 | \(-0.535000\pi\) | ||||
−0.109733 | + | 0.993961i | \(0.535000\pi\) | |||||||
\(294\) | −1.22659e6 | −0.827622 | ||||||||
\(295\) | 199500. | 0.133471 | ||||||||
\(296\) | 719488. | 0.477303 | ||||||||
\(297\) | 285120. | 0.187558 | ||||||||
\(298\) | −562200. | −0.366733 | ||||||||
\(299\) | −3.37154e6 | −2.18098 | ||||||||
\(300\) | 240000. | 0.153960 | ||||||||
\(301\) | −3.54733e6 | −2.25676 | ||||||||
\(302\) | −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 | \(-0.356073\pi\) | ||||
0.436911 | + | 0.899505i | \(0.356073\pi\) | |||||||
\(308\) | −363264. | −0.218195 | ||||||||
\(309\) | −10464.0 | −0.00623450 | ||||||||
\(310\) | −231200. | −0.136642 | ||||||||
\(311\) | 171312. | 0.100435 | 0.0502177 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502177 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(312\) | 1.45306e6 | 0.845076 | ||||||||
\(313\) | −1.02689e6 | −0.592463 | −0.296232 | − | 0.955116i | \(-0.595730\pi\) | ||||
−0.296232 | + | 0.955116i | \(0.595730\pi\) | |||||||
\(314\) | 2.22369e6 | 1.27277 | ||||||||
\(315\) | −1.43190e6 | −0.813086 | ||||||||
\(316\) | −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 | ||||||||
\(322\) | 2.45203e6 | 1.31791 | ||||||||
\(323\) | −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 | ||||||||
\(329\) | −1.13314e6 | −0.577155 | ||||||||
\(330\) | −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 | ||||||||
\(336\) | −1.05677e6 | −0.510660 | ||||||||
\(337\) | −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 | ||||||||
\(343\) | 693160. | 0.318125 | ||||||||
\(344\) | −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 | \(-0.294173\pi\) | ||||
0.602495 | + | 0.798123i | \(0.294173\pi\) | |||||||
\(350\) | 430000. | 0.187628 | ||||||||
\(351\) | −2.04336e6 | −0.885273 | ||||||||
\(352\) | −135168. | −0.0581456 | ||||||||
\(353\) | −2.38957e6 | −1.02066 | −0.510331 | − | 0.859978i | \(-0.670477\pi\) | ||||
−0.510331 | + | 0.859978i | \(0.670477\pi\) | |||||||
\(354\) | −766080. | −0.324912 | ||||||||
\(355\) | −613200. | −0.258245 | ||||||||
\(356\) | −1.76496e6 | −0.738091 | ||||||||
\(357\) | 916416. | 0.380559 | ||||||||
\(358\) | 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 | ||||||||
\(364\) | 2.60339e6 | 1.02988 | ||||||||
\(365\) | 511850. | 0.201099 | ||||||||
\(366\) | −1.59571e6 | −0.622661 | ||||||||
\(367\) | −2.47637e6 | −0.959734 | −0.479867 | − | 0.877341i | \(-0.659315\pi\) | ||||
−0.479867 | + | 0.877341i | \(0.659315\pi\) | |||||||
\(368\) | 912384. | 0.351203 | ||||||||
\(369\) | 413586. | 0.158125 | ||||||||
\(370\) | 1.12420e6 | 0.426913 | ||||||||
\(371\) | 3.62335e6 | 1.36671 | ||||||||
\(372\) | 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 | ||||||||
\(378\) | 1.48608e6 | 0.534949 | ||||||||
\(379\) | −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 | \(-0.307958\pi\) | ||||
0.567377 | + | 0.823458i | \(0.307958\pi\) | |||||||
\(384\) | −393216. | −0.136083 | ||||||||
\(385\) | −567600. | −0.195160 | ||||||||
\(386\) | 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 | ||||||||
\(392\) | −817728. | −0.268778 | ||||||||
\(393\) | −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 | \(-0.209051\pi\) | ||||
0.791978 | + | 0.610549i | \(0.209051\pi\) | |||||||
\(398\) | −628640. | −0.198927 | ||||||||
\(399\) | −2.06400e6 | −0.649049 | ||||||||
\(400\) | 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 | ||||||||
\(406\) | 1.50672e6 | 0.453646 | ||||||||
\(407\) | −1.48394e6 | −0.444050 | ||||||||
\(408\) | 340992. | 0.101413 | ||||||||
\(409\) | −1.09423e6 | −0.323445 | −0.161722 | − | 0.986836i | \(-0.551705\pi\) | ||||
−0.161722 | + | 0.986836i | \(0.551705\pi\) | |||||||
\(410\) | −124200. | −0.0364890 | ||||||||
\(411\) | 6.65035e6 | 1.94196 | ||||||||
\(412\) | −6976.00 | −0.00202471 | ||||||||
\(413\) | −1.37256e6 | −0.395964 | ||||||||
\(414\) | −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 | \(-0.542378\pi\) | ||||
−0.132743 | + | 0.991151i | \(0.542378\pi\) | |||||||
\(420\) | −1.65120e6 | −0.456748 | ||||||||
\(421\) | −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 | ||||||||
\(427\) | −2.85898e6 | −0.758826 | ||||||||
\(428\) | 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 | \(-0.341649\pi\) | ||||
0.477208 | + | 0.878790i | \(0.341649\pi\) | |||||||
\(434\) | 1.59066e6 | 0.405370 | ||||||||
\(435\) | 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 | \(-0.603646\pi\) | ||||
−0.319890 | + | 0.947455i | \(0.603646\pi\) | |||||||
\(440\) | −211200. | −0.0520071 | ||||||||
\(441\) | 4.25474e6 | 1.04178 | ||||||||
\(442\) | −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 | ||||||||
\(448\) | −704512. | −0.165842 | ||||||||
\(449\) | 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 | ||||||||
\(455\) | 4.06780e6 | 0.921152 | ||||||||
\(456\) | −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 | \(-0.441893\pi\) | ||||
0.181536 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(462\) | 2.17958e6 | 0.475082 | ||||||||
\(463\) | −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 | \(-0.743470\pi\) | ||||
−0.692454 | + | 0.721462i | \(0.743470\pi\) | |||||||
\(468\) | −5.04029e6 | −1.06375 | ||||||||
\(469\) | −310976. | −0.0652822 | ||||||||
\(470\) | −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 | ||||||||
\(476\) | 610944. | 0.123590 | ||||||||
\(477\) | −7.01498e6 | −1.41166 | ||||||||
\(478\) | −3.91488e6 | −0.783698 | ||||||||
\(479\) | −5.96232e6 | −1.18734 | −0.593672 | − | 0.804707i | \(-0.702322\pi\) | ||||
−0.593672 | + | 0.804707i | \(0.702322\pi\) | |||||||
\(480\) | −614400. | −0.121716 | ||||||||
\(481\) | 1.06349e7 | 2.09591 | ||||||||
\(482\) | 4.53119e6 | 0.888372 | ||||||||
\(483\) | −1.47122e7 | −2.86952 | ||||||||
\(484\) | −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 | ||||||||
\(490\) | −1.27770e6 | −0.240402 | ||||||||
\(491\) | −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 | ||||||||
\(497\) | 4.21882e6 | 0.766125 | ||||||||
\(498\) | 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 | \(-0.595662\pi\) | ||||
−0.296027 | + | 0.955179i | \(0.595662\pi\) | |||||||
\(504\) | 3.66566e6 | 0.642801 | ||||||||
\(505\) | 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 | \(-0.569633\pi\) | ||||
−0.217019 | + | 0.976167i | \(0.569633\pi\) | |||||||
\(510\) | 532800. | 0.0907066 | ||||||||
\(511\) | −3.52153e6 | −0.596594 | ||||||||
\(512\) | −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 | ||||||||
\(518\) | −7.73450e6 | −1.26651 | ||||||||
\(519\) | 1.04125e7 | 1.69682 | ||||||||
\(520\) | 1.51360e6 | 0.245472 | ||||||||
\(521\) | −9.31580e6 | −1.50358 | −0.751789 | − | 0.659404i | \(-0.770809\pi\) | ||||
−0.751789 | + | 0.659404i | \(0.770809\pi\) | |||||||
\(522\) | −2.91708e6 | −0.468567 | ||||||||
\(523\) | −5.02802e6 | −0.803790 | −0.401895 | − | 0.915686i | \(-0.631648\pi\) | ||||
−0.401895 | + | 0.915686i | \(0.631648\pi\) | |||||||
\(524\) | −3.87053e6 | −0.615803 | ||||||||
\(525\) | −2.58000e6 | −0.408528 | ||||||||
\(526\) | 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 | ||||||||
\(532\) | −1.37600e6 | −0.210785 | ||||||||
\(533\) | −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 | ||||||||
\(539\) | 1.68656e6 | 0.250052 | ||||||||
\(540\) | 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 | ||||||||
\(546\) | −1.56204e7 | −2.24238 | ||||||||
\(547\) | 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 | ||||||||
\(553\) | 7.95328e6 | 1.10594 | ||||||||
\(554\) | −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 | ||||||||
\(560\) | −1.10080e6 | −0.148333 | ||||||||
\(561\) | −703296. | −0.0943476 | ||||||||
\(562\) | −810408. | −0.108234 | ||||||||
\(563\) | −1.03029e7 | −1.36990 | −0.684952 | − | 0.728588i | \(-0.740177\pi\) | ||||
−0.684952 | + | 0.728588i | \(0.740177\pi\) | |||||||
\(564\) | 2.52979e6 | 0.334878 | ||||||||
\(565\) | 4.57485e6 | 0.602915 | ||||||||
\(566\) | 886144. | 0.116269 | ||||||||
\(567\) | 5.00159e6 | 0.653357 | ||||||||
\(568\) | 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 | ||||||||
\(574\) | 854496. | 0.108251 | ||||||||
\(575\) | 2.22750e6 | 0.280962 | ||||||||
\(576\) | 1.36397e6 | 0.171296 | ||||||||
\(577\) | 1.62682e6 | 0.203423 | 0.101711 | − | 0.994814i | \(-0.467568\pi\) | ||||
0.101711 | + | 0.994814i | \(0.467568\pi\) | |||||||
\(578\) | 5.48229e6 | 0.682563 | ||||||||
\(579\) | −1.41937e7 | −1.75955 | ||||||||
\(580\) | 876000. | 0.108127 | ||||||||
\(581\) | 8.87107e6 | 1.09027 | ||||||||
\(582\) | 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 | \(-0.363114\pi\) | ||||
0.416907 | + | 0.908949i | \(0.363114\pi\) | |||||||
\(588\) | 4.90637e6 | 0.585217 | ||||||||
\(589\) | 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 | \(-0.730942\pi\) | ||||
−0.663529 | + | 0.748150i | \(0.730942\pi\) | |||||||
\(594\) | −1.14048e6 | −0.132624 | ||||||||
\(595\) | 954600. | 0.110542 | ||||||||
\(596\) | 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 | \(-0.522236\pi\) | ||||
−0.0697981 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(602\) | 1.41893e7 | 1.59577 | ||||||||
\(603\) | 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 | \(-0.740522\pi\) | ||||
−0.685743 | + | 0.727844i | \(0.740522\pi\) | |||||||
\(608\) | −512000. | −0.0561709 | ||||||||
\(609\) | −9.04032e6 | −0.987735 | ||||||||
\(610\) | −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 | ||||||||
\(616\) | 1.45306e6 | 0.154287 | ||||||||
\(617\) | 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 | \(-0.779353\pi\) | ||||
−0.769216 | + | 0.638988i | \(0.779353\pi\) | |||||||
\(620\) | 924800. | 0.0966203 | ||||||||
\(621\) | 7.69824e6 | 0.801055 | ||||||||
\(622\) | −685248. | −0.0710186 | ||||||||
\(623\) | 1.89733e7 | 1.95850 | ||||||||
\(624\) | −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 | ||||||||
\(630\) | 5.72760e6 | 0.574938 | ||||||||
\(631\) | −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 | ||||||||
\(637\) | −1.20870e7 | −1.18024 | ||||||||
\(638\) | −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 | \(-0.534247\pi\) | ||||
−0.107381 | + | 0.994218i | \(0.534247\pi\) | |||||||
\(644\) | −9.80813e6 | −0.931905 | ||||||||
\(645\) | 1.23744e7 | 1.17118 | ||||||||
\(646\) | 444000. | 0.0418602 | ||||||||
\(647\) | 8.05319e6 | 0.756323 | 0.378161 | − | 0.925740i | \(-0.376556\pi\) | ||||
0.378161 | + | 0.925740i | \(0.376556\pi\) | |||||||
\(648\) | 1.86106e6 | 0.174109 | ||||||||
\(649\) | 1.05336e6 | 0.0981669 | ||||||||
\(650\) | 2.36500e6 | 0.219557 | ||||||||
\(651\) | −9.54394e6 | −0.882623 | ||||||||
\(652\) | −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 | ||||||||
\(658\) | 4.53254e6 | 0.408110 | ||||||||
\(659\) | 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 | \(-0.524037\pi\) | ||||
−0.0754432 | + | 0.997150i | \(0.524037\pi\) | |||||||
\(662\) | −7.97653e6 | −0.707406 | ||||||||
\(663\) | 5.04029e6 | 0.445319 | ||||||||
\(664\) | 3.30086e6 | 0.290541 | ||||||||
\(665\) | −2.15000e6 | −0.188532 | ||||||||
\(666\) | 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 | ||||||||
\(672\) | 4.22707e6 | 0.361091 | ||||||||
\(673\) | −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 | \(-0.704482\pi\) | ||||
−0.599118 | + | 0.800661i | \(0.704482\pi\) | |||||||
\(678\) | −1.75674e7 | −1.46769 | ||||||||
\(679\) | 1.34817e7 | 1.12220 | ||||||||
\(680\) | 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 | ||||||||
\(686\) | −2.77264e6 | −0.224949 | ||||||||
\(687\) | −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 | \(-0.491145\pi\) | ||||
0.0278155 | + | 0.999613i | \(0.491145\pi\) | |||||||
\(692\) | 6.94166e6 | 0.551059 | ||||||||
\(693\) | −7.56043e6 | −0.598017 | ||||||||
\(694\) | −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 | ||||||||
\(700\) | −1.72000e6 | −0.132673 | ||||||||
\(701\) | 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 | ||||||||
\(707\) | −2.44140e7 | −1.83692 | ||||||||
\(708\) | 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 | ||||||||
\(714\) | −3.66566e6 | −0.269096 | ||||||||
\(715\) | −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 | \(-0.427940\pi\) | ||||
0.224454 | + | 0.974485i | \(0.427940\pi\) | |||||||
\(720\) | 2.13120e6 | 0.153212 | ||||||||
\(721\) | 74992.0 | 0.00537250 | ||||||||
\(722\) | 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 | \(-0.587858\pi\) | ||||
−0.272523 | + | 0.962149i | \(0.587858\pi\) | |||||||
\(728\) | −1.04136e7 | −0.728234 | ||||||||
\(729\) | −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 | \(-0.187139\pi\) | ||||
0.832099 | + | 0.554627i | \(0.187139\pi\) | |||||||
\(734\) | 9.90549e6 | 0.678634 | ||||||||
\(735\) | 7.66620e6 | 0.523434 | ||||||||
\(736\) | −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 | ||||||||
\(742\) | −1.44934e7 | −0.966409 | ||||||||
\(743\) | 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 | ||||||||
\(749\) | −4.00705e7 | −2.60988 | ||||||||
\(750\) | −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 | ||||||||
\(756\) | −5.94432e6 | −0.378266 | ||||||||
\(757\) | −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 | \(-0.250260\pi\) | ||||
0.706529 | + | 0.707684i | \(0.250260\pi\) | |||||||
\(762\) | 1.17554e7 | 0.733415 | ||||||||
\(763\) | 3.00742e7 | 1.87018 | ||||||||
\(764\) | −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 | \(-0.506137\pi\) | ||||
−0.0192802 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(770\) | 2.27040e6 | 0.137999 | ||||||||
\(771\) | 4.65585e7 | 2.82074 | ||||||||
\(772\) | −9.46250e6 | −0.571429 | ||||||||
\(773\) | −1.25867e7 | −0.757643 | −0.378822 | − | 0.925470i | \(-0.623671\pi\) | ||||
−0.378822 | + | 0.925470i | \(0.623671\pi\) | |||||||
\(774\) | −2.74712e7 | −1.64826 | ||||||||
\(775\) | 1.44500e6 | 0.0864199 | ||||||||
\(776\) | 5.01645e6 | 0.299049 | ||||||||
\(777\) | 4.64070e7 | 2.75760 | ||||||||
\(778\) | −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 | ||||||||
\(784\) | 3.27091e6 | 0.190055 | ||||||||
\(785\) | −1.38980e7 | −0.804970 | ||||||||
\(786\) | 2.32232e7 | 1.34080 | ||||||||
\(787\) | 2.15792e7 | 1.24194 | 0.620968 | − | 0.783836i | \(-0.286740\pi\) | ||||
0.620968 | + | 0.783836i | \(0.286740\pi\) | |||||||
\(788\) | 7.19165e6 | 0.412584 | ||||||||
\(789\) | −1.93314e7 | −1.10553 | ||||||||
\(790\) | 4.62400e6 | 0.263603 | ||||||||
\(791\) | −3.14750e7 | −1.78864 | ||||||||
\(792\) | −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 | \(-0.831842\pi\) | ||||
−0.863673 | + | 0.504052i | \(0.831842\pi\) | |||||||
\(798\) | 8.25600e6 | 0.458947 | ||||||||
\(799\) | −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 | ||||||||
\(805\) | −1.53252e7 | −0.833521 | ||||||||
\(806\) | 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 | \(-0.470871\pi\) | ||||
0.0913833 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(812\) | −6.02688e6 | −0.320776 | ||||||||
\(813\) | −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 | ||||||||
\(819\) | 5.41831e7 | 2.82263 | ||||||||
\(820\) | 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 | ||||||||
\(826\) | 5.49024e6 | 0.279989 | ||||||||
\(827\) | −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 | \(-0.651829\pi\) | ||||
−0.459104 | + | 0.888383i | \(0.651829\pi\) | |||||||
\(830\) | 5.15760e6 | 0.259868 | ||||||||
\(831\) | 4.82582e7 | 2.42420 | ||||||||
\(832\) | −3.87482e6 | −0.194063 | ||||||||
\(833\) | −2.83649e6 | −0.141635 | ||||||||
\(834\) | 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 | \(-0.581072\pi\) | ||||
−0.251951 | + | 0.967740i | \(0.581072\pi\) | |||||||
\(840\) | 6.60480e6 | 0.322969 | ||||||||
\(841\) | −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 | ||||||||
\(847\) | 2.47038e7 | 1.18319 | ||||||||
\(848\) | −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 | \(-0.452748\pi\) | ||||
0.147901 | + | 0.989002i | \(0.452748\pi\) | |||||||
\(854\) | 1.14359e7 | 0.536571 | ||||||||
\(855\) | 4.16250e6 | 0.194733 | ||||||||
\(856\) | −1.49100e7 | −0.695492 | ||||||||
\(857\) | 1.54050e7 | 0.716490 | 0.358245 | − | 0.933628i | \(-0.383375\pi\) | ||||
0.358245 | + | 0.933628i | \(0.383375\pi\) | |||||||
\(858\) | 1.19877e7 | 0.555927 | ||||||||
\(859\) | 1.43526e7 | 0.663664 | 0.331832 | − | 0.943338i | \(-0.392333\pi\) | ||||
0.331832 | + | 0.943338i | \(0.392333\pi\) | |||||||
\(860\) | 8.24960e6 | 0.380353 | ||||||||
\(861\) | −5.12698e6 | −0.235697 | ||||||||
\(862\) | 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 | ||||||||
\(868\) | −6.36262e6 | −0.286640 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | −2.68750e6 | −0.118667 | ||||||||
\(876\) | 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 | \(-0.391082\pi\) | ||||
0.335537 | + | 0.942027i | \(0.391082\pi\) | |||||||
\(882\) | −1.70190e7 | −0.736651 | ||||||||
\(883\) | −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 | \(-0.519523\pi\) | ||||
−0.0612960 | + | 0.998120i | \(0.519523\pi\) | |||||||
\(888\) | 1.72677e7 | 0.734856 | ||||||||
\(889\) | 2.10617e7 | 0.893799 | ||||||||
\(890\) | 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 | ||||||||
\(896\) | 2.81805e6 | 0.117268 | ||||||||
\(897\) | −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 | ||||||||
\(903\) | −8.51359e7 | −3.47451 | ||||||||
\(904\) | −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 | ||||||||
\(910\) | −1.62712e7 | −0.651353 | ||||||||
\(911\) | 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 | ||||||||
\(917\) | 4.16082e7 | 1.63401 | ||||||||
\(918\) | 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 | ||||||||
\(924\) | −8.71834e6 | −0.335934 | ||||||||
\(925\) | −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 | \(-0.545813\pi\) | ||||
−0.143430 | + | 0.989660i | \(0.545813\pi\) | |||||||
\(930\) | −5.54880e6 | −0.210374 | ||||||||
\(931\) | 6.38850e6 | 0.241560 | ||||||||
\(932\) | −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 | \(-0.611530\pi\) | ||||
−0.343256 | + | 0.939242i | \(0.611530\pi\) | |||||||
\(938\) | 1.24390e6 | 0.0461615 | ||||||||
\(939\) | −2.46453e7 | −0.912157 | ||||||||
\(940\) | 2.63520e6 | 0.0972734 | ||||||||
\(941\) | 6.75046e6 | 0.248519 | 0.124259 | − | 0.992250i | \(-0.460344\pi\) | ||||
0.124259 | + | 0.992250i | \(0.460344\pi\) | |||||||
\(942\) | 5.33685e7 | 1.95956 | ||||||||
\(943\) | 4.42649e6 | 0.162099 | ||||||||
\(944\) | 2.04288e6 | 0.0746127 | ||||||||
\(945\) | −9.28800e6 | −0.338332 | ||||||||
\(946\) | −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 | ||||||||
\(952\) | −2.44378e6 | −0.0873915 | ||||||||
\(953\) | −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 | ||||||||
\(959\) | −4.76609e7 | −1.67346 | ||||||||
\(960\) | 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 | ||||||||
\(966\) | 5.88488e7 | 2.02906 | ||||||||
\(967\) | −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 | \(-0.531314\pi\) | ||||
−0.0982164 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(972\) | −1.95644e7 | −0.664204 | ||||||||
\(973\) | 3.32889e7 | 1.12724 | ||||||||
\(974\) | −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 | ||||||||
\(980\) | 5.11080e6 | 0.169990 | ||||||||
\(981\) | −5.82250e7 | −1.93169 | ||||||||
\(982\) | 4.81675e6 | 0.159395 | ||||||||
\(983\) | 4.59362e7 | 1.51625 | 0.758126 | − | 0.652108i | \(-0.226115\pi\) | ||||
0.758126 | + | 0.652108i | \(0.226115\pi\) | |||||||
\(984\) | −1.90771e6 | −0.0628095 | ||||||||
\(985\) | 1.12370e7 | 0.369027 | ||||||||
\(986\) | 1.94472e6 | 0.0637037 | ||||||||
\(987\) | −2.71953e7 | −0.888588 | ||||||||
\(988\) | −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 | ||||||||
\(994\) | −1.68753e7 | −0.541732 | ||||||||
\(995\) | 3.92900e6 | 0.125813 | ||||||||
\(996\) | −1.98052e7 | −0.632602 | ||||||||
\(997\) | −2.37364e7 | −0.756271 | −0.378136 | − | 0.925750i | \(-0.623435\pi\) | ||||
−0.378136 | + | 0.925750i | \(0.623435\pi\) | |||||||
\(998\) | −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 | 10.6.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 90.6.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 80.6.a.a.1.1 | 1 | |||
5.2 | odd | 4 | 50.6.b.a.49.1 | 2 | |||
5.3 | odd | 4 | 50.6.b.a.49.2 | 2 | |||
5.4 | even | 2 | 50.6.a.d.1.1 | 1 | |||
7.6 | odd | 2 | 490.6.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 320.6.a.o.1.1 | 1 | |||
8.5 | even | 2 | 320.6.a.b.1.1 | 1 | |||
12.11 | even | 2 | 720.6.a.j.1.1 | 1 | |||
15.2 | even | 4 | 450.6.c.h.199.2 | 2 | |||
15.8 | even | 4 | 450.6.c.h.199.1 | 2 | |||
15.14 | odd | 2 | 450.6.a.l.1.1 | 1 | |||
20.3 | even | 4 | 400.6.c.b.49.1 | 2 | |||
20.7 | even | 4 | 400.6.c.b.49.2 | 2 | |||
20.19 | odd | 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 | 1.1 | even | 1 | trivial | |
50.6.a.d.1.1 | 1 | 5.4 | even | 2 | |||
50.6.b.a.49.1 | 2 | 5.2 | odd | 4 | |||
50.6.b.a.49.2 | 2 | 5.3 | odd | 4 | |||
80.6.a.a.1.1 | 1 | 4.3 | odd | 2 | |||
90.6.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
320.6.a.b.1.1 | 1 | 8.5 | even | 2 | |||
320.6.a.o.1.1 | 1 | 8.3 | odd | 2 | |||
400.6.a.n.1.1 | 1 | 20.19 | odd | 2 | |||
400.6.c.b.49.1 | 2 | 20.3 | even | 4 | |||
400.6.c.b.49.2 | 2 | 20.7 | even | 4 | |||
450.6.a.l.1.1 | 1 | 15.14 | odd | 2 | |||
450.6.c.h.199.1 | 2 | 15.8 | even | 4 | |||
450.6.c.h.199.2 | 2 | 15.2 | even | 4 | |||
490.6.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
720.6.a.j.1.1 | 1 | 12.11 | even | 2 |