Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [50,6,Mod(49,50)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(50, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("50.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 50 = 2 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 50.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(8.01919099065\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 10) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 50.49 |
Dual form | 50.6.b.a.49.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).
\(n\) | \(27\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 4.00000i | − 0.707107i | ||||||||
\(3\) | − 24.0000i | − 1.53960i | −0.638285 | − | 0.769800i | \(-0.720356\pi\) | ||||
0.638285 | − | 0.769800i | \(-0.279644\pi\) | |||||||
\(4\) | −16.0000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −96.0000 | −1.08866 | ||||||||
\(7\) | − 172.000i | − 1.32673i | −0.748295 | − | 0.663366i | \(-0.769127\pi\) | ||||
0.748295 | − | 0.663366i | \(-0.230873\pi\) | |||||||
\(8\) | 64.0000i | 0.353553i | ||||||||
\(9\) | −333.000 | −1.37037 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 132.000 | 0.328921 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(12\) | 384.000i | 0.769800i | ||||||||
\(13\) | 946.000i | 1.55250i | 0.630423 | + | 0.776252i | \(0.282882\pi\) | ||||
−0.630423 | + | 0.776252i | \(0.717118\pi\) | |||||||
\(14\) | −688.000 | −0.938142 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 256.000 | 0.250000 | ||||||||
\(17\) | − 222.000i | − 0.186308i | −0.995652 | − | 0.0931538i | \(-0.970305\pi\) | ||||
0.995652 | − | 0.0931538i | \(-0.0296948\pi\) | |||||||
\(18\) | 1332.00i | 0.968998i | ||||||||
\(19\) | −500.000 | −0.317750 | −0.158875 | − | 0.987299i | \(-0.550787\pi\) | ||||
−0.158875 | + | 0.987299i | \(0.550787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4128.00 | −2.04264 | ||||||||
\(22\) | − 528.000i | − 0.232583i | ||||||||
\(23\) | − 3564.00i | − 1.40481i | −0.711777 | − | 0.702406i | \(-0.752109\pi\) | ||||
0.711777 | − | 0.702406i | \(-0.247891\pi\) | |||||||
\(24\) | 1536.00 | 0.544331 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3784.00 | 1.09779 | ||||||||
\(27\) | 2160.00i | 0.570222i | ||||||||
\(28\) | 2752.00i | 0.663366i | ||||||||
\(29\) | −2190.00 | −0.483559 | −0.241779 | − | 0.970331i | \(-0.577731\pi\) | ||||
−0.241779 | + | 0.970331i | \(0.577731\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2312.00 | 0.432099 | 0.216050 | − | 0.976382i | \(-0.430683\pi\) | ||||
0.216050 | + | 0.976382i | \(0.430683\pi\) | |||||||
\(32\) | − 1024.00i | − 0.176777i | ||||||||
\(33\) | − 3168.00i | − 0.506408i | ||||||||
\(34\) | −888.000 | −0.131739 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5328.00 | 0.685185 | ||||||||
\(37\) | − 11242.0i | − 1.35002i | −0.737810 | − | 0.675009i | \(-0.764140\pi\) | ||||
0.737810 | − | 0.675009i | \(-0.235860\pi\) | |||||||
\(38\) | 2000.00i | 0.224683i | ||||||||
\(39\) | 22704.0 | 2.39024 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1242.00 | 0.115388 | 0.0576942 | − | 0.998334i | \(-0.481625\pi\) | ||||
0.0576942 | + | 0.998334i | \(0.481625\pi\) | |||||||
\(42\) | 16512.0i | 1.44436i | ||||||||
\(43\) | − 20624.0i | − 1.70099i | −0.525983 | − | 0.850495i | \(-0.676303\pi\) | ||||
0.525983 | − | 0.850495i | \(-0.323697\pi\) | |||||||
\(44\) | −2112.00 | −0.164461 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −14256.0 | −0.993352 | ||||||||
\(47\) | 6588.00i | 0.435020i | 0.976058 | + | 0.217510i | \(0.0697934\pi\) | ||||
−0.976058 | + | 0.217510i | \(0.930207\pi\) | |||||||
\(48\) | − 6144.00i | − 0.384900i | ||||||||
\(49\) | −12777.0 | −0.760219 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5328.00 | −0.286839 | ||||||||
\(52\) | − 15136.0i | − 0.776252i | ||||||||
\(53\) | 21066.0i | 1.03013i | 0.857151 | + | 0.515065i | \(0.172232\pi\) | ||||
−0.857151 | + | 0.515065i | \(0.827768\pi\) | |||||||
\(54\) | 8640.00 | 0.403208 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11008.0 | 0.469071 | ||||||||
\(57\) | 12000.0i | 0.489209i | ||||||||
\(58\) | 8760.00i | 0.341928i | ||||||||
\(59\) | −7980.00 | −0.298451 | −0.149225 | − | 0.988803i | \(-0.547678\pi\) | ||||
−0.149225 | + | 0.988803i | \(0.547678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 16622.0 | 0.571951 | 0.285975 | − | 0.958237i | \(-0.407682\pi\) | ||||
0.285975 | + | 0.958237i | \(0.407682\pi\) | |||||||
\(62\) | − 9248.00i | − 0.305540i | ||||||||
\(63\) | 57276.0i | 1.81811i | ||||||||
\(64\) | −4096.00 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −12672.0 | −0.358084 | ||||||||
\(67\) | 1808.00i | 0.0492052i | 0.999697 | + | 0.0246026i | \(0.00783205\pi\) | ||||
−0.999697 | + | 0.0246026i | \(0.992168\pi\) | |||||||
\(68\) | 3552.00i | 0.0931538i | ||||||||
\(69\) | −85536.0 | −2.16285 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −24528.0 | −0.577452 | −0.288726 | − | 0.957412i | \(-0.593232\pi\) | ||||
−0.288726 | + | 0.957412i | \(0.593232\pi\) | |||||||
\(72\) | − 21312.0i | − 0.484499i | ||||||||
\(73\) | − 20474.0i | − 0.449672i | −0.974397 | − | 0.224836i | \(-0.927815\pi\) | ||||
0.974397 | − | 0.224836i | \(-0.0721846\pi\) | |||||||
\(74\) | −44968.0 | −0.954606 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8000.00 | 0.158875 | ||||||||
\(77\) | − 22704.0i | − 0.436391i | ||||||||
\(78\) | − 90816.0i | − 1.69015i | ||||||||
\(79\) | 46240.0 | 0.833585 | 0.416793 | − | 0.909002i | \(-0.363154\pi\) | ||||
0.416793 | + | 0.909002i | \(0.363154\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −29079.0 | −0.492455 | ||||||||
\(82\) | − 4968.00i | − 0.0815919i | ||||||||
\(83\) | 51576.0i | 0.821774i | 0.911686 | + | 0.410887i | \(0.134781\pi\) | ||||
−0.911686 | + | 0.410887i | \(0.865219\pi\) | |||||||
\(84\) | 66048.0 | 1.02132 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −82496.0 | −1.20278 | ||||||||
\(87\) | 52560.0i | 0.744487i | ||||||||
\(88\) | 8448.00i | 0.116291i | ||||||||
\(89\) | 110310. | 1.47618 | 0.738091 | − | 0.674701i | \(-0.235728\pi\) | ||||
0.738091 | + | 0.674701i | \(0.235728\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 162712. | 2.05976 | ||||||||
\(92\) | 57024.0i | 0.702406i | ||||||||
\(93\) | − 55488.0i | − 0.665260i | ||||||||
\(94\) | 26352.0 | 0.307605 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −24576.0 | −0.272166 | ||||||||
\(97\) | − 78382.0i | − 0.845838i | −0.906168 | − | 0.422919i | \(-0.861006\pi\) | ||||
0.906168 | − | 0.422919i | \(-0.138994\pi\) | |||||||
\(98\) | 51108.0i | 0.537556i | ||||||||
\(99\) | −43956.0 | −0.450744 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 141942. | 1.38455 | 0.692273 | − | 0.721636i | \(-0.256609\pi\) | ||||
0.692273 | + | 0.721636i | \(0.256609\pi\) | |||||||
\(102\) | 21312.0i | 0.202826i | ||||||||
\(103\) | 436.000i | 0.00404943i | 0.999998 | + | 0.00202471i | \(0.000644487\pi\) | ||||
−0.999998 | + | 0.00202471i | \(0.999356\pi\) | |||||||
\(104\) | −60544.0 | −0.548893 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 84264.0 | 0.728413 | ||||||||
\(107\) | 232968.i | 1.96715i | 0.180508 | + | 0.983574i | \(0.442226\pi\) | ||||
−0.180508 | + | 0.983574i | \(0.557774\pi\) | |||||||
\(108\) | − 34560.0i | − 0.285111i | ||||||||
\(109\) | 174850. | 1.40961 | 0.704806 | − | 0.709400i | \(-0.251034\pi\) | ||||
0.704806 | + | 0.709400i | \(0.251034\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −269808. | −2.07849 | ||||||||
\(112\) | − 44032.0i | − 0.331683i | ||||||||
\(113\) | − 182994.i | − 1.34816i | −0.738659 | − | 0.674079i | \(-0.764541\pi\) | ||||
0.738659 | − | 0.674079i | \(-0.235459\pi\) | |||||||
\(114\) | 48000.0 | 0.345923 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 35040.0 | 0.241779 | ||||||||
\(117\) | − 315018.i | − 2.12751i | ||||||||
\(118\) | 31920.0i | 0.211037i | ||||||||
\(119\) | −38184.0 | −0.247180 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −143627. | −0.891811 | ||||||||
\(122\) | − 66488.0i | − 0.404430i | ||||||||
\(123\) | − 29808.0i | − 0.177652i | ||||||||
\(124\) | −36992.0 | −0.216050 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 229104. | 1.28560 | ||||||||
\(127\) | − 122452.i | − 0.673685i | −0.941561 | − | 0.336842i | \(-0.890641\pi\) | ||||
0.941561 | − | 0.336842i | \(-0.109359\pi\) | |||||||
\(128\) | 16384.0i | 0.0883883i | ||||||||
\(129\) | −494976. | −2.61885 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −241908. | −1.23161 | −0.615803 | − | 0.787900i | \(-0.711168\pi\) | ||||
−0.615803 | + | 0.787900i | \(0.711168\pi\) | |||||||
\(132\) | 50688.0i | 0.253204i | ||||||||
\(133\) | 86000.0i | 0.421570i | ||||||||
\(134\) | 7232.00 | 0.0347934 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 14208.0 | 0.0658697 | ||||||||
\(137\) | 277098.i | 1.26134i | 0.776051 | + | 0.630670i | \(0.217220\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(138\) | 342144.i | 1.52937i | ||||||||
\(139\) | 193540. | 0.849638 | 0.424819 | − | 0.905278i | \(-0.360338\pi\) | ||||
0.424819 | + | 0.905278i | \(0.360338\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 158112. | 0.669757 | ||||||||
\(142\) | 98112.0i | 0.408321i | ||||||||
\(143\) | 124872.i | 0.510652i | ||||||||
\(144\) | −85248.0 | −0.342593 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −81896.0 | −0.317966 | ||||||||
\(147\) | 306648.i | 1.17043i | ||||||||
\(148\) | 179872.i | 0.675009i | ||||||||
\(149\) | −140550. | −0.518639 | −0.259320 | − | 0.965792i | \(-0.583498\pi\) | ||||
−0.259320 | + | 0.965792i | \(0.583498\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 433952. | 1.54881 | 0.774407 | − | 0.632688i | \(-0.218048\pi\) | ||||
0.774407 | + | 0.632688i | \(0.218048\pi\) | |||||||
\(152\) | − 32000.0i | − 0.112342i | ||||||||
\(153\) | 73926.0i | 0.255310i | ||||||||
\(154\) | −90816.0 | −0.308575 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −363264. | −1.19512 | ||||||||
\(157\) | − 555922.i | − 1.79997i | −0.435923 | − | 0.899984i | \(-0.643578\pi\) | ||||
0.435923 | − | 0.899984i | \(-0.356422\pi\) | |||||||
\(158\) | − 184960.i | − 0.589434i | ||||||||
\(159\) | 505584. | 1.58599 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −613008. | −1.86381 | ||||||||
\(162\) | 116316.i | 0.348219i | ||||||||
\(163\) | 66616.0i | 0.196386i | 0.995167 | + | 0.0981928i | \(0.0313062\pi\) | ||||
−0.995167 | + | 0.0981928i | \(0.968694\pi\) | |||||||
\(164\) | −19872.0 | −0.0576942 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 206304. | 0.581082 | ||||||||
\(167\) | − 205692.i | − 0.570724i | −0.958420 | − | 0.285362i | \(-0.907886\pi\) | ||||
0.958420 | − | 0.285362i | \(-0.0921138\pi\) | |||||||
\(168\) | − 264192.i | − 0.722182i | ||||||||
\(169\) | −523623. | −1.41027 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 166500. | 0.435436 | ||||||||
\(172\) | 329984.i | 0.850495i | ||||||||
\(173\) | − 433854.i | − 1.10212i | −0.834466 | − | 0.551059i | \(-0.814224\pi\) | ||||
0.834466 | − | 0.551059i | \(-0.185776\pi\) | |||||||
\(174\) | 210240. | 0.526432 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 33792.0 | 0.0822304 | ||||||||
\(177\) | 191520.i | 0.459495i | ||||||||
\(178\) | − 441240.i | − 1.04382i | ||||||||
\(179\) | 489180. | 1.14113 | 0.570566 | − | 0.821252i | \(-0.306724\pi\) | ||||
0.570566 | + | 0.821252i | \(0.306724\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 719462. | 1.63234 | 0.816172 | − | 0.577810i | \(-0.196092\pi\) | ||||
0.816172 | + | 0.577810i | \(0.196092\pi\) | |||||||
\(182\) | − 650848.i | − 1.45647i | ||||||||
\(183\) | − 398928.i | − 0.880576i | ||||||||
\(184\) | 228096. | 0.496676 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −221952. | −0.470410 | ||||||||
\(187\) | − 29304.0i | − 0.0612806i | ||||||||
\(188\) | − 105408.i | − 0.217510i | ||||||||
\(189\) | 371520. | 0.756533 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −185928. | −0.368775 | −0.184387 | − | 0.982854i | \(-0.559030\pi\) | ||||
−0.184387 | + | 0.982854i | \(0.559030\pi\) | |||||||
\(192\) | 98304.0i | 0.192450i | ||||||||
\(193\) | 591406.i | 1.14286i | 0.820651 | + | 0.571429i | \(0.193611\pi\) | ||||
−0.820651 | + | 0.571429i | \(0.806389\pi\) | |||||||
\(194\) | −313528. | −0.598098 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 204432. | 0.380109 | ||||||||
\(197\) | 449478.i | 0.825169i | 0.910919 | + | 0.412584i | \(0.135374\pi\) | ||||
−0.910919 | + | 0.412584i | \(0.864626\pi\) | |||||||
\(198\) | 175824.i | 0.318724i | ||||||||
\(199\) | −157160. | −0.281326 | −0.140663 | − | 0.990058i | \(-0.544923\pi\) | ||||
−0.140663 | + | 0.990058i | \(0.544923\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 43392.0 | 0.0757564 | ||||||||
\(202\) | − 567768.i | − 0.979022i | ||||||||
\(203\) | 376680.i | 0.641553i | ||||||||
\(204\) | 85248.0 | 0.143420 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1744.00 | 0.00286338 | ||||||||
\(207\) | 1.18681e6i | 1.92511i | ||||||||
\(208\) | 242176.i | 0.388126i | ||||||||
\(209\) | −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.i | − 0.515065i | ||||||||
\(213\) | 588672.i | 0.889046i | ||||||||
\(214\) | 931872. | 1.39098 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −138240. | −0.201604 | ||||||||
\(217\) | − 397664.i | − 0.573280i | ||||||||
\(218\) | − 699400.i | − 0.996746i | ||||||||
\(219\) | −491376. | −0.692315 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 210012. | 0.289243 | ||||||||
\(222\) | 1.07923e6i | 1.46971i | ||||||||
\(223\) | − 1.07344e6i | − 1.44550i | −0.691111 | − | 0.722749i | \(-0.742878\pi\) | ||||
0.691111 | − | 0.722749i | \(-0.257122\pi\) | |||||||
\(224\) | −176128. | −0.234535 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −731976. | −0.953292 | ||||||||
\(227\) | − 626832.i | − 0.807396i | −0.914892 | − | 0.403698i | \(-0.867725\pi\) | ||||
0.914892 | − | 0.403698i | \(-0.132275\pi\) | |||||||
\(228\) | − 192000.i | − 0.244604i | ||||||||
\(229\) | 116650. | 0.146993 | 0.0734964 | − | 0.997295i | \(-0.476584\pi\) | ||||
0.0734964 | + | 0.997295i | \(0.476584\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −544896. | −0.671868 | ||||||||
\(232\) | − 140160.i | − 0.170964i | ||||||||
\(233\) | 743046.i | 0.896656i | 0.893869 | + | 0.448328i | \(0.147980\pi\) | ||||
−0.893869 | + | 0.448328i | \(0.852020\pi\) | |||||||
\(234\) | −1.26007e6 | −1.50437 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 127680. | 0.149225 | ||||||||
\(237\) | − 1.10976e6i | − 1.28339i | ||||||||
\(238\) | 152736.i | 0.174783i | ||||||||
\(239\) | −978720. | −1.10832 | −0.554158 | − | 0.832411i | \(-0.686960\pi\) | ||||
−0.554158 | + | 0.832411i | \(0.686960\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.13280e6 | −1.25635 | −0.628174 | − | 0.778073i | \(-0.716197\pi\) | ||||
−0.628174 | + | 0.778073i | \(0.716197\pi\) | |||||||
\(242\) | 574508.i | 0.630605i | ||||||||
\(243\) | 1.22278e6i | 1.32841i | ||||||||
\(244\) | −265952. | −0.285975 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −119232. | −0.125619 | ||||||||
\(247\) | − 473000.i | − 0.493309i | ||||||||
\(248\) | 147968.i | 0.152770i | ||||||||
\(249\) | 1.23782e6 | 1.26520 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 905652. | 0.907355 | 0.453677 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453677 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(252\) | − 916416.i | − 0.909057i | ||||||||
\(253\) | − 470448.i | − 0.462073i | ||||||||
\(254\) | −489808. | −0.476367 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | 1.93994e6i | 1.83212i | 0.401036 | + | 0.916062i | \(0.368650\pi\) | ||||
−0.401036 | + | 0.916062i | \(0.631350\pi\) | |||||||
\(258\) | 1.97990e6i | 1.85180i | ||||||||
\(259\) | −1.93362e6 | −1.79111 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 729270. | 0.662654 | ||||||||
\(262\) | 967632.i | 0.870877i | ||||||||
\(263\) | 805476.i | 0.718064i | 0.933325 | + | 0.359032i | \(0.116893\pi\) | ||||
−0.933325 | + | 0.359032i | \(0.883107\pi\) | |||||||
\(264\) | 202752. | 0.179042 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 344000. | 0.298095 | ||||||||
\(267\) | − 2.64744e6i | − 2.27273i | ||||||||
\(268\) | − 28928.0i | − 0.0246026i | ||||||||
\(269\) | 858690. | 0.723529 | 0.361764 | − | 0.932270i | \(-0.382175\pi\) | ||||
0.361764 | + | 0.932270i | \(0.382175\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −383608. | −0.317296 | −0.158648 | − | 0.987335i | \(-0.550713\pi\) | ||||
−0.158648 | + | 0.987335i | \(0.550713\pi\) | |||||||
\(272\) | − 56832.0i | − 0.0465769i | ||||||||
\(273\) | − 3.90509e6i | − 3.17120i | ||||||||
\(274\) | 1.10839e6 | 0.891902 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.36858e6 | 1.08142 | ||||||||
\(277\) | 2.01076e6i | 1.57456i | 0.616593 | + | 0.787282i | \(0.288512\pi\) | ||||
−0.616593 | + | 0.787282i | \(0.711488\pi\) | |||||||
\(278\) | − 774160.i | − 0.600785i | ||||||||
\(279\) | −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.i | − 0.473589i | ||||||||
\(283\) | 221536.i | 0.164429i | 0.996615 | + | 0.0822145i | \(0.0261992\pi\) | ||||
−0.996615 | + | 0.0822145i | \(0.973801\pi\) | |||||||
\(284\) | 392448. | 0.288726 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 499488. | 0.361085 | ||||||||
\(287\) | − 213624.i | − 0.153089i | ||||||||
\(288\) | 340992.i | 0.242250i | ||||||||
\(289\) | 1.37057e6 | 0.965289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.88117e6 | −1.30225 | ||||||||
\(292\) | 327584.i | 0.224836i | ||||||||
\(293\) | 322506.i | 0.219467i | 0.993961 | + | 0.109733i | \(0.0349997\pi\) | ||||
−0.993961 | + | 0.109733i | \(0.965000\pi\) | |||||||
\(294\) | 1.22659e6 | 0.827622 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 719488. | 0.477303 | ||||||||
\(297\) | 285120.i | 0.187558i | ||||||||
\(298\) | 562200.i | 0.366733i | ||||||||
\(299\) | 3.37154e6 | 2.18098 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.54733e6 | −2.25676 | ||||||||
\(302\) | − 1.73581e6i | − 1.09518i | ||||||||
\(303\) | − 3.40661e6i | − 2.13165i | ||||||||
\(304\) | −128000. | −0.0794376 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 295704. | 0.180532 | ||||||||
\(307\) | 1.44301e6i | 0.873822i | 0.899505 | + | 0.436911i | \(0.143927\pi\) | ||||
−0.899505 | + | 0.436911i | \(0.856073\pi\) | |||||||
\(308\) | 363264.i | 0.218195i | ||||||||
\(309\) | 10464.0 | 0.00623450 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 171312. | 0.100435 | 0.0502177 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502177 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(312\) | 1.45306e6i | 0.845076i | ||||||||
\(313\) | 1.02689e6i | 0.592463i | 0.955116 | + | 0.296232i | \(0.0957300\pi\) | ||||
−0.955116 | + | 0.296232i | \(0.904270\pi\) | |||||||
\(314\) | −2.22369e6 | −1.27277 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −739840. | −0.416793 | ||||||||
\(317\) | 752958.i | 0.420845i | 0.977610 | + | 0.210423i | \(0.0674840\pi\) | ||||
−0.977610 | + | 0.210423i | \(0.932516\pi\) | |||||||
\(318\) | − 2.02234e6i | − 1.12146i | ||||||||
\(319\) | −289080. | −0.159053 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.59123e6 | 3.02862 | ||||||||
\(322\) | 2.45203e6i | 1.31791i | ||||||||
\(323\) | 111000.i | 0.0591993i | ||||||||
\(324\) | 465264. | 0.246228 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 266464. | 0.138866 | ||||||||
\(327\) | − 4.19640e6i | − 2.17024i | ||||||||
\(328\) | 79488.0i | 0.0407959i | ||||||||
\(329\) | 1.13314e6 | 0.577155 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.99413e6 | 1.00042 | 0.500212 | − | 0.865903i | \(-0.333255\pi\) | ||||
0.500212 | + | 0.865903i | \(0.333255\pi\) | |||||||
\(332\) | − 825216.i | − 0.410887i | ||||||||
\(333\) | 3.74359e6i | 1.85002i | ||||||||
\(334\) | −822768. | −0.403563 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.05677e6 | −0.510660 | ||||||||
\(337\) | − 987022.i | − 0.473426i | −0.971580 | − | 0.236713i | \(-0.923930\pi\) | ||||
0.971580 | − | 0.236713i | \(-0.0760701\pi\) | |||||||
\(338\) | 2.09449e6i | 0.997211i | ||||||||
\(339\) | −4.39186e6 | −2.07562 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 305184. | 0.142127 | ||||||||
\(342\) | − 666000.i | − 0.307899i | ||||||||
\(343\) | − 693160.i | − 0.318125i | ||||||||
\(344\) | 1.31994e6 | 0.601391 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.73542e6 | −0.779316 | ||||||||
\(347\) | 2.20601e6i | 0.983520i | 0.870731 | + | 0.491760i | \(0.163646\pi\) | ||||
−0.870731 | + | 0.491760i | \(0.836354\pi\) | |||||||
\(348\) | − 840960.i | − 0.372244i | ||||||||
\(349\) | −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.i | − 0.0581456i | ||||||||
\(353\) | 2.38957e6i | 1.02066i | 0.859978 | + | 0.510331i | \(0.170477\pi\) | ||||
−0.859978 | + | 0.510331i | \(0.829523\pi\) | |||||||
\(354\) | 766080. | 0.324912 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.76496e6 | −0.738091 | ||||||||
\(357\) | 916416.i | 0.380559i | ||||||||
\(358\) | − 1.95672e6i | − 0.806903i | ||||||||
\(359\) | 279480. | 0.114450 | 0.0572248 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572248 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.22610e6 | −0.899035 | ||||||||
\(362\) | − 2.87785e6i | − 1.15424i | ||||||||
\(363\) | 3.44705e6i | 1.37303i | ||||||||
\(364\) | −2.60339e6 | −1.02988 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.59571e6 | −0.622661 | ||||||||
\(367\) | − 2.47637e6i | − 0.959734i | −0.877341 | − | 0.479867i | \(-0.840685\pi\) | ||||
0.877341 | − | 0.479867i | \(-0.159315\pi\) | |||||||
\(368\) | − 912384.i | − 0.351203i | ||||||||
\(369\) | −413586. | −0.158125 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.62335e6 | 1.36671 | ||||||||
\(372\) | 887808.i | 0.332630i | ||||||||
\(373\) | − 2.74525e6i | − 1.02167i | −0.859679 | − | 0.510835i | \(-0.829336\pi\) | ||||
0.859679 | − | 0.510835i | \(-0.170664\pi\) | |||||||
\(374\) | −117216. | −0.0433319 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −421632. | −0.153803 | ||||||||
\(377\) | − 2.07174e6i | − 0.750727i | ||||||||
\(378\) | − 1.48608e6i | − 0.534949i | ||||||||
\(379\) | 1.18906e6 | 0.425212 | 0.212606 | − | 0.977138i | \(-0.431805\pi\) | ||||
0.212606 | + | 0.977138i | \(0.431805\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.93885e6 | −1.03721 | ||||||||
\(382\) | 743712.i | 0.260763i | ||||||||
\(383\) | − 3.25760e6i | − 1.13475i | −0.823458 | − | 0.567377i | \(-0.807958\pi\) | ||||
0.823458 | − | 0.567377i | \(-0.192042\pi\) | |||||||
\(384\) | 393216. | 0.136083 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.36562e6 | 0.808123 | ||||||||
\(387\) | 6.86779e6i | 2.33099i | ||||||||
\(388\) | 1.25411e6i | 0.422919i | ||||||||
\(389\) | −1.98351e6 | −0.664600 | −0.332300 | − | 0.943174i | \(-0.607825\pi\) | ||||
−0.332300 | + | 0.943174i | \(0.607825\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −791208. | −0.261727 | ||||||||
\(392\) | − 817728.i | − 0.268778i | ||||||||
\(393\) | 5.80579e6i | 1.89618i | ||||||||
\(394\) | 1.79791e6 | 0.583483 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 703296. | 0.225372 | ||||||||
\(397\) | 4.97416e6i | 1.58396i | 0.610549 | + | 0.791978i | \(0.290949\pi\) | ||||
−0.610549 | + | 0.791978i | \(0.709051\pi\) | |||||||
\(398\) | 628640.i | 0.198927i | ||||||||
\(399\) | 2.06400e6 | 0.649049 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.34264e6 | −0.416963 | −0.208482 | − | 0.978026i | \(-0.566852\pi\) | ||||
−0.208482 | + | 0.978026i | \(0.566852\pi\) | |||||||
\(402\) | − 173568.i | − 0.0535679i | ||||||||
\(403\) | 2.18715e6i | 0.670836i | ||||||||
\(404\) | −2.27107e6 | −0.692273 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.50672e6 | 0.453646 | ||||||||
\(407\) | − 1.48394e6i | − 0.444050i | ||||||||
\(408\) | − 340992.i | − 0.101413i | ||||||||
\(409\) | 1.09423e6 | 0.323445 | 0.161722 | − | 0.986836i | \(-0.448295\pi\) | ||||
0.161722 | + | 0.986836i | \(0.448295\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.65035e6 | 1.94196 | ||||||||
\(412\) | − 6976.00i | − 0.00202471i | ||||||||
\(413\) | 1.37256e6i | 0.395964i | ||||||||
\(414\) | 4.74725e6 | 1.36126 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 968704. | 0.274447 | ||||||||
\(417\) | − 4.64496e6i | − 1.30810i | ||||||||
\(418\) | 264000.i | 0.0739032i | ||||||||
\(419\) | 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 | \(0.570326\pi\) | |||||||
\(422\) | − 1.01221e6i | − 0.276687i | ||||||||
\(423\) | − 2.19380e6i | − 0.596138i | ||||||||
\(424\) | −1.34822e6 | −0.364206 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.35469e6 | 0.628651 | ||||||||
\(427\) | − 2.85898e6i | − 0.758826i | ||||||||
\(428\) | − 3.72749e6i | − 0.983574i | ||||||||
\(429\) | 2.99693e6 | 0.786200 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.64665e6 | −0.686283 | −0.343141 | − | 0.939284i | \(-0.611491\pi\) | ||||
−0.343141 | + | 0.939284i | \(0.611491\pi\) | |||||||
\(432\) | 552960.i | 0.142556i | ||||||||
\(433\) | − 3.72355e6i | − 0.954416i | −0.878790 | − | 0.477208i | \(-0.841649\pi\) | ||||
0.878790 | − | 0.477208i | \(-0.158351\pi\) | |||||||
\(434\) | −1.59066e6 | −0.405370 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.79760e6 | −0.704806 | ||||||||
\(437\) | 1.78200e6i | 0.446379i | ||||||||
\(438\) | 1.96550e6i | 0.489541i | ||||||||
\(439\) | 2.58340e6 | 0.639780 | 0.319890 | − | 0.947455i | \(-0.396354\pi\) | ||||
0.319890 | + | 0.947455i | \(0.396354\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.25474e6 | 1.04178 | ||||||||
\(442\) | − 840048.i | − 0.204526i | ||||||||
\(443\) | − 7.56206e6i | − 1.83076i | −0.402593 | − | 0.915379i | \(-0.631891\pi\) | ||||
0.402593 | − | 0.915379i | \(-0.368109\pi\) | |||||||
\(444\) | 4.31693e6 | 1.03924 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −4.29378e6 | −1.02212 | ||||||||
\(447\) | 3.37320e6i | 0.798497i | ||||||||
\(448\) | 704512.i | 0.165842i | ||||||||
\(449\) | −4.30773e6 | −1.00840 | −0.504200 | − | 0.863587i | \(-0.668212\pi\) | ||||
−0.504200 | + | 0.863587i | \(0.668212\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 163944. | 0.0379537 | ||||||||
\(452\) | 2.92790e6i | 0.674079i | ||||||||
\(453\) | − 1.04148e7i | − 2.38456i | ||||||||
\(454\) | −2.50733e6 | −0.570915 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −768000. | −0.172961 | ||||||||
\(457\) | − 2.24354e6i | − 0.502509i | −0.967921 | − | 0.251254i | \(-0.919157\pi\) | ||||
0.967921 | − | 0.251254i | \(-0.0808431\pi\) | |||||||
\(458\) | − 466600.i | − 0.103940i | ||||||||
\(459\) | 479520. | 0.106237 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.65670e6 | 0.363071 | 0.181536 | − | 0.983384i | \(-0.441893\pi\) | ||||
0.181536 | + | 0.983384i | \(0.441893\pi\) | |||||||
\(462\) | 2.17958e6i | 0.475082i | ||||||||
\(463\) | 2.89160e6i | 0.626881i | 0.949608 | + | 0.313441i | \(0.101482\pi\) | ||||
−0.949608 | + | 0.313441i | \(0.898518\pi\) | |||||||
\(464\) | −560640. | −0.120890 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.97218e6 | 0.634032 | ||||||||
\(467\) | − 6.52699e6i | − 1.38491i | −0.721462 | − | 0.692454i | \(-0.756530\pi\) | ||||
0.721462 | − | 0.692454i | \(-0.243470\pi\) | |||||||
\(468\) | 5.04029e6i | 1.06375i | ||||||||
\(469\) | 310976. | 0.0652822 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.33421e7 | −2.77123 | ||||||||
\(472\) | − 510720.i | − 0.105518i | ||||||||
\(473\) | − 2.72237e6i | − 0.559492i | ||||||||
\(474\) | −4.43904e6 | −0.907493 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 610944. | 0.123590 | ||||||||
\(477\) | − 7.01498e6i | − 1.41166i | ||||||||
\(478\) | 3.91488e6i | 0.783698i | ||||||||
\(479\) | 5.96232e6 | 1.18734 | 0.593672 | − | 0.804707i | \(-0.297678\pi\) | ||||
0.593672 | + | 0.804707i | \(0.297678\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.06349e7 | 2.09591 | ||||||||
\(482\) | 4.53119e6i | 0.888372i | ||||||||
\(483\) | 1.47122e7i | 2.86952i | ||||||||
\(484\) | 2.29803e6 | 0.445905 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.89110e6 | 0.939326 | ||||||||
\(487\) | 2.99191e6i | 0.571644i | 0.958283 | + | 0.285822i | \(0.0922666\pi\) | ||||
−0.958283 | + | 0.285822i | \(0.907733\pi\) | |||||||
\(488\) | 1.06381e6i | 0.202215i | ||||||||
\(489\) | 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.i | 0.0888260i | ||||||||
\(493\) | 486180.i | 0.0900907i | ||||||||
\(494\) | −1.89200e6 | −0.348822 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 591872. | 0.108025 | ||||||||
\(497\) | 4.21882e6i | 0.766125i | ||||||||
\(498\) | − 4.95130e6i | − 0.894634i | ||||||||
\(499\) | −9.20546e6 | −1.65499 | −0.827493 | − | 0.561477i | \(-0.810233\pi\) | ||||
−0.827493 | + | 0.561477i | \(0.810233\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.93661e6 | −0.878687 | ||||||||
\(502\) | − 3.62261e6i | − 0.641597i | ||||||||
\(503\) | 3.35956e6i | 0.592055i | 0.955179 | + | 0.296027i | \(0.0956620\pi\) | ||||
−0.955179 | + | 0.296027i | \(0.904338\pi\) | |||||||
\(504\) | −3.66566e6 | −0.642801 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.88179e6 | −0.326735 | ||||||||
\(507\) | 1.25670e7i | 2.17125i | ||||||||
\(508\) | 1.95923e6i | 0.336842i | ||||||||
\(509\) | 2.53701e6 | 0.434038 | 0.217019 | − | 0.976167i | \(-0.430367\pi\) | ||||
0.217019 | + | 0.976167i | \(0.430367\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.52153e6 | −0.596594 | ||||||||
\(512\) | − 262144.i | − 0.0441942i | ||||||||
\(513\) | − 1.08000e6i | − 0.181188i | ||||||||
\(514\) | 7.75975e6 | 1.29551 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.91962e6 | 1.30942 | ||||||||
\(517\) | 869616.i | 0.143087i | ||||||||
\(518\) | 7.73450e6i | 1.26651i | ||||||||
\(519\) | −1.04125e7 | −1.69682 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.31580e6 | −1.50358 | −0.751789 | − | 0.659404i | \(-0.770809\pi\) | ||||
−0.751789 | + | 0.659404i | \(0.770809\pi\) | |||||||
\(522\) | − 2.91708e6i | − 0.468567i | ||||||||
\(523\) | 5.02802e6i | 0.803790i | 0.915686 | + | 0.401895i | \(0.131648\pi\) | ||||
−0.915686 | + | 0.401895i | \(0.868352\pi\) | |||||||
\(524\) | 3.87053e6 | 0.615803 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.22190e6 | 0.507748 | ||||||||
\(527\) | − 513264.i | − 0.0805034i | ||||||||
\(528\) | − 811008.i | − 0.126602i | ||||||||
\(529\) | −6.26575e6 | −0.973496 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.65734e6 | 0.408988 | ||||||||
\(532\) | − 1.37600e6i | − 0.210785i | ||||||||
\(533\) | 1.17493e6i | 0.179141i | ||||||||
\(534\) | −1.05898e7 | −1.60706 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −115712. | −0.0173967 | ||||||||
\(537\) | − 1.17403e7i | − 1.75689i | ||||||||
\(538\) | − 3.43476e6i | − 0.511612i | ||||||||
\(539\) | −1.68656e6 | −0.250052 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 134222. | 0.0197165 | 0.00985827 | − | 0.999951i | \(-0.496862\pi\) | ||||
0.00985827 | + | 0.999951i | \(0.496862\pi\) | |||||||
\(542\) | 1.53443e6i | 0.224362i | ||||||||
\(543\) | − 1.72671e7i | − 2.51316i | ||||||||
\(544\) | −227328. | −0.0329348 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.56204e7 | −2.24238 | ||||||||
\(547\) | 605648.i | 0.0865470i | 0.999063 | + | 0.0432735i | \(0.0137787\pi\) | ||||
−0.999063 | + | 0.0432735i | \(0.986221\pi\) | |||||||
\(548\) | − 4.43357e6i | − 0.630670i | ||||||||
\(549\) | −5.53513e6 | −0.783784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.09500e6 | 0.153651 | ||||||||
\(552\) | − 5.47430e6i | − 0.764683i | ||||||||
\(553\) | − 7.95328e6i | − 1.10594i | ||||||||
\(554\) | 8.04303e6 | 1.11339 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.09664e6 | −0.424819 | ||||||||
\(557\) | − 7.06240e6i | − 0.964527i | −0.876026 | − | 0.482264i | \(-0.839815\pi\) | ||||
0.876026 | − | 0.482264i | \(-0.160185\pi\) | |||||||
\(558\) | 3.07958e6i | 0.418703i | ||||||||
\(559\) | 1.95103e7 | 2.64079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −703296. | −0.0943476 | ||||||||
\(562\) | − 810408.i | − 0.108234i | ||||||||
\(563\) | 1.03029e7i | 1.36990i | 0.728588 | + | 0.684952i | \(0.240177\pi\) | ||||
−0.728588 | + | 0.684952i | \(0.759823\pi\) | |||||||
\(564\) | −2.52979e6 | −0.334878 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 886144. | 0.116269 | ||||||||
\(567\) | 5.00159e6i | 0.653357i | ||||||||
\(568\) | − 1.56979e6i | − 0.204160i | ||||||||
\(569\) | −1.04769e6 | −0.135660 | −0.0678300 | − | 0.997697i | \(-0.521608\pi\) | ||||
−0.0678300 | + | 0.997697i | \(0.521608\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.40765e7 | 1.80677 | 0.903385 | − | 0.428830i | \(-0.141074\pi\) | ||||
0.903385 | + | 0.428830i | \(0.141074\pi\) | |||||||
\(572\) | − 1.99795e6i | − 0.255326i | ||||||||
\(573\) | 4.46227e6i | 0.567766i | ||||||||
\(574\) | −854496. | −0.108251 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.36397e6 | 0.171296 | ||||||||
\(577\) | 1.62682e6i | 0.203423i | 0.994814 | + | 0.101711i | \(0.0324318\pi\) | ||||
−0.994814 | + | 0.101711i | \(0.967568\pi\) | |||||||
\(578\) | − 5.48229e6i | − 0.682563i | ||||||||
\(579\) | 1.41937e7 | 1.75955 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.87107e6 | 1.09027 | ||||||||
\(582\) | 7.52467e6i | 0.920831i | ||||||||
\(583\) | 2.78071e6i | 0.338832i | ||||||||
\(584\) | 1.31034e6 | 0.158983 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.29002e6 | 0.155186 | ||||||||
\(587\) | 6.96089e6i | 0.833814i | 0.908949 | + | 0.416907i | \(0.136886\pi\) | ||||
−0.908949 | + | 0.416907i | \(0.863114\pi\) | |||||||
\(588\) | − 4.90637e6i | − 0.585217i | ||||||||
\(589\) | −1.15600e6 | −0.137300 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.07875e7 | 1.27043 | ||||||||
\(592\) | − 2.87795e6i | − 0.337504i | ||||||||
\(593\) | 1.13639e7i | 1.32706i | 0.748150 | + | 0.663529i | \(0.230942\pi\) | ||||
−0.748150 | + | 0.663529i | \(0.769058\pi\) | |||||||
\(594\) | 1.14048e6 | 0.132624 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.24880e6 | 0.259320 | ||||||||
\(597\) | 3.77184e6i | 0.433129i | ||||||||
\(598\) | − 1.34862e7i | − 1.54218i | ||||||||
\(599\) | −1.48688e7 | −1.69321 | −0.846603 | − | 0.532224i | \(-0.821356\pi\) | ||||
−0.846603 | + | 0.532224i | \(0.821356\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.23612e6 | −0.139596 | −0.0697981 | − | 0.997561i | \(-0.522236\pi\) | ||||
−0.0697981 | + | 0.997561i | \(0.522236\pi\) | |||||||
\(602\) | 1.41893e7i | 1.59577i | ||||||||
\(603\) | − 602064.i | − 0.0674294i | ||||||||
\(604\) | −6.94323e6 | −0.774407 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.36264e7 | −1.50730 | ||||||||
\(607\) | − 1.24498e7i | − 1.37149i | −0.727844 | − | 0.685743i | \(-0.759478\pi\) | ||||
0.727844 | − | 0.685743i | \(-0.240522\pi\) | |||||||
\(608\) | 512000.i | 0.0561709i | ||||||||
\(609\) | 9.04032e6 | 0.987735 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.23225e6 | −0.675370 | ||||||||
\(612\) | − 1.18282e6i | − 0.127655i | ||||||||
\(613\) | 8.73491e6i | 0.938873i | 0.882966 | + | 0.469437i | \(0.155543\pi\) | ||||
−0.882966 | + | 0.469437i | \(0.844457\pi\) | |||||||
\(614\) | 5.77203e6 | 0.617885 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.45306e6 | 0.154287 | ||||||||
\(617\) | 1.25495e7i | 1.32713i | 0.748119 | + | 0.663565i | \(0.230957\pi\) | ||||
−0.748119 | + | 0.663565i | \(0.769043\pi\) | |||||||
\(618\) | − 41856.0i | − 0.00440846i | ||||||||
\(619\) | 1.46658e7 | 1.53843 | 0.769216 | − | 0.638988i | \(-0.220647\pi\) | ||||
0.769216 | + | 0.638988i | \(0.220647\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.69824e6 | 0.801055 | ||||||||
\(622\) | − 685248.i | − 0.0710186i | ||||||||
\(623\) | − 1.89733e7i | − 1.95850i | ||||||||
\(624\) | 5.81222e6 | 0.597559 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 4.10754e6 | 0.418935 | ||||||||
\(627\) | 1.58400e6i | 0.160911i | ||||||||
\(628\) | 8.89475e6i | 0.899984i | ||||||||
\(629\) | −2.49572e6 | −0.251519 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −196288. | −0.0196255 | −0.00981274 | − | 0.999952i | \(-0.503124\pi\) | ||||
−0.00981274 | + | 0.999952i | \(0.503124\pi\) | |||||||
\(632\) | 2.95936e6i | 0.294717i | ||||||||
\(633\) | − 6.07325e6i | − 0.602437i | ||||||||
\(634\) | 3.01183e6 | 0.297583 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −8.08934e6 | −0.792995 | ||||||||
\(637\) | − 1.20870e7i | − 1.18024i | ||||||||
\(638\) | 1.15632e6i | 0.112467i | ||||||||
\(639\) | 8.16782e6 | 0.791324 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.11596e7 | −1.07276 | −0.536381 | − | 0.843976i | \(-0.680209\pi\) | ||||
−0.536381 | + | 0.843976i | \(0.680209\pi\) | |||||||
\(642\) | − 2.23649e7i | − 2.14156i | ||||||||
\(643\) | 2.25158e6i | 0.214763i | 0.994218 | + | 0.107381i | \(0.0342466\pi\) | ||||
−0.994218 | + | 0.107381i | \(0.965753\pi\) | |||||||
\(644\) | 9.80813e6 | 0.931905 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 444000. | 0.0418602 | ||||||||
\(647\) | 8.05319e6i | 0.756323i | 0.925740 | + | 0.378161i | \(0.123444\pi\) | ||||
−0.925740 | + | 0.378161i | \(0.876556\pi\) | |||||||
\(648\) | − 1.86106e6i | − 0.174109i | ||||||||
\(649\) | −1.05336e6 | −0.0981669 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.54394e6 | −0.882623 | ||||||||
\(652\) | − 1.06586e6i | − 0.0981928i | ||||||||
\(653\) | 416466.i | 0.0382205i | 0.999817 | + | 0.0191103i | \(0.00608336\pi\) | ||||
−0.999817 | + | 0.0191103i | \(0.993917\pi\) | |||||||
\(654\) | −1.67856e7 | −1.53459 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 317952. | 0.0288471 | ||||||||
\(657\) | 6.81784e6i | 0.616217i | ||||||||
\(658\) | − 4.53254e6i | − 0.408110i | ||||||||
\(659\) | −1.31721e7 | −1.18152 | −0.590761 | − | 0.806847i | \(-0.701172\pi\) | ||||
−0.590761 | + | 0.806847i | \(0.701172\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.69494e6 | −0.150886 | −0.0754432 | − | 0.997150i | \(-0.524037\pi\) | ||||
−0.0754432 | + | 0.997150i | \(0.524037\pi\) | |||||||
\(662\) | − 7.97653e6i | − 0.707406i | ||||||||
\(663\) | − 5.04029e6i | − 0.445319i | ||||||||
\(664\) | −3.30086e6 | −0.290541 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.49743e7 | 1.30816 | ||||||||
\(667\) | 7.80516e6i | 0.679309i | ||||||||
\(668\) | 3.29107e6i | 0.285362i | ||||||||
\(669\) | −2.57627e7 | −2.22549 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.19410e6 | 0.188127 | ||||||||
\(672\) | 4.22707e6i | 0.361091i | ||||||||
\(673\) | 8.91605e6i | 0.758813i | 0.925230 | + | 0.379406i | \(0.123872\pi\) | ||||
−0.925230 | + | 0.379406i | \(0.876128\pi\) | |||||||
\(674\) | −3.94809e6 | −0.334763 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8.37797e6 | 0.705134 | ||||||||
\(677\) | − 1.42894e7i | − 1.19824i | −0.800661 | − | 0.599118i | \(-0.795518\pi\) | ||||
0.800661 | − | 0.599118i | \(-0.204482\pi\) | |||||||
\(678\) | 1.75674e7i | 1.46769i | ||||||||
\(679\) | −1.34817e7 | −1.12220 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.50440e7 | −1.24307 | ||||||||
\(682\) | − 1.22074e6i | − 0.100499i | ||||||||
\(683\) | 5.33314e6i | 0.437452i | 0.975786 | + | 0.218726i | \(0.0701902\pi\) | ||||
−0.975786 | + | 0.218726i | \(0.929810\pi\) | |||||||
\(684\) | −2.66400e6 | −0.217718 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.77264e6 | −0.224949 | ||||||||
\(687\) | − 2.79960e6i | − 0.226310i | ||||||||
\(688\) | − 5.27974e6i | − 0.425248i | ||||||||
\(689\) | −1.99284e7 | −1.59928 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 698252. | 0.0556310 | 0.0278155 | − | 0.999613i | \(-0.491145\pi\) | ||||
0.0278155 | + | 0.999613i | \(0.491145\pi\) | |||||||
\(692\) | 6.94166e6i | 0.551059i | ||||||||
\(693\) | 7.56043e6i | 0.598017i | ||||||||
\(694\) | 8.82403e6 | 0.695454 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −3.36384e6 | −0.263216 | ||||||||
\(697\) | − 275724.i | − 0.0214977i | ||||||||
\(698\) | 1.09675e7i | 0.852056i | ||||||||
\(699\) | 1.78331e7 | 1.38049 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.79880e7 | 1.38257 | 0.691285 | − | 0.722582i | \(-0.257045\pi\) | ||||
0.691285 | + | 0.722582i | \(0.257045\pi\) | |||||||
\(702\) | 8.17344e6i | 0.625982i | ||||||||
\(703\) | 5.62100e6i | 0.428968i | ||||||||
\(704\) | −540672. | −0.0411152 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.55826e6 | 0.721718 | ||||||||
\(707\) | − 2.44140e7i | − 1.83692i | ||||||||
\(708\) | − 3.06432e6i | − 0.229748i | ||||||||
\(709\) | 1.39464e7 | 1.04195 | 0.520975 | − | 0.853572i | \(-0.325568\pi\) | ||||
0.520975 | + | 0.853572i | \(0.325568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.53979e7 | −1.14232 | ||||||||
\(712\) | 7.05984e6i | 0.521909i | ||||||||
\(713\) | − 8.23997e6i | − 0.607018i | ||||||||
\(714\) | 3.66566e6 | 0.269096 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −7.82688e6 | −0.570566 | ||||||||
\(717\) | 2.34893e7i | 1.70636i | ||||||||
\(718\) | − 1.11792e6i | − 0.0809282i | ||||||||
\(719\) | −6.22272e6 | −0.448909 | −0.224454 | − | 0.974485i | \(-0.572060\pi\) | ||||
−0.224454 | + | 0.974485i | \(0.572060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 74992.0 | 0.00537250 | ||||||||
\(722\) | 8.90440e6i | 0.635714i | ||||||||
\(723\) | 2.71872e7i | 1.93427i | ||||||||
\(724\) | −1.15114e7 | −0.816172 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.37882e7 | 0.970880 | ||||||||
\(727\) | − 7.76729e6i | − 0.545047i | −0.962149 | − | 0.272523i | \(-0.912142\pi\) | ||||
0.962149 | − | 0.272523i | \(-0.0878582\pi\) | |||||||
\(728\) | 1.04136e7i | 0.728234i | ||||||||
\(729\) | 2.22804e7 | 1.55276 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.57853e6 | −0.316907 | ||||||||
\(732\) | 6.38285e6i | 0.440288i | ||||||||
\(733\) | − 2.42083e7i | − 1.66420i | −0.554627 | − | 0.832099i | \(-0.687139\pi\) | ||||
0.554627 | − | 0.832099i | \(-0.312861\pi\) | |||||||
\(734\) | −9.90549e6 | −0.678634 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.64954e6 | −0.248338 | ||||||||
\(737\) | 238656.i | 0.0161847i | ||||||||
\(738\) | 1.65434e6i | 0.111811i | ||||||||
\(739\) | −1.26850e7 | −0.854434 | −0.427217 | − | 0.904149i | \(-0.640506\pi\) | ||||
−0.427217 | + | 0.904149i | \(0.640506\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.13520e7 | −0.759498 | ||||||||
\(742\) | − 1.44934e7i | − 0.966409i | ||||||||
\(743\) | − 1.97632e7i | − 1.31337i | −0.754166 | − | 0.656684i | \(-0.771959\pi\) | ||||
0.754166 | − | 0.656684i | \(-0.228041\pi\) | |||||||
\(744\) | 3.55123e6 | 0.235205 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.09810e7 | −0.722429 | ||||||||
\(747\) | − 1.71748e7i | − 1.12613i | ||||||||
\(748\) | 468864.i | 0.0306403i | ||||||||
\(749\) | 4.00705e7 | 2.60988 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.01761e6 | −0.583434 | −0.291717 | − | 0.956505i | \(-0.594226\pi\) | ||||
−0.291717 | + | 0.956505i | \(0.594226\pi\) | |||||||
\(752\) | 1.68653e6i | 0.108755i | ||||||||
\(753\) | − 2.17356e7i | − 1.39696i | ||||||||
\(754\) | −8.28696e6 | −0.530844 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.94432e6 | −0.378266 | ||||||||
\(757\) | − 1.12556e6i | − 0.0713887i | −0.999363 | − | 0.0356944i | \(-0.988636\pi\) | ||||
0.999363 | − | 0.0356944i | \(-0.0113643\pi\) | |||||||
\(758\) | − 4.75624e6i | − 0.300670i | ||||||||
\(759\) | −1.12908e7 | −0.711407 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.25747e7 | 1.41306 | 0.706529 | − | 0.707684i | \(-0.250260\pi\) | ||||
0.706529 | + | 0.707684i | \(0.250260\pi\) | |||||||
\(762\) | 1.17554e7i | 0.733415i | ||||||||
\(763\) | − 3.00742e7i | − 1.87018i | ||||||||
\(764\) | 2.97485e6 | 0.184387 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.30304e7 | −0.802392 | ||||||||
\(767\) | − 7.54908e6i | − 0.463346i | ||||||||
\(768\) | − 1.57286e6i | − 0.0962250i | ||||||||
\(769\) | 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 | ||||||||
\(772\) | − 9.46250e6i | − 0.571429i | ||||||||
\(773\) | 1.25867e7i | 0.757643i | 0.925470 | + | 0.378822i | \(0.123671\pi\) | ||||
−0.925470 | + | 0.378822i | \(0.876329\pi\) | |||||||
\(774\) | 2.74712e7 | 1.64826 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.01645e6 | 0.299049 | ||||||||
\(777\) | 4.64070e7i | 2.75760i | ||||||||
\(778\) | 7.93404e6i | 0.469943i | ||||||||
\(779\) | −621000. | −0.0366647 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.23770e6 | −0.189937 | ||||||||
\(782\) | 3.16483e6i | 0.185069i | ||||||||
\(783\) | − 4.73040e6i | − 0.275736i | ||||||||
\(784\) | −3.27091e6 | −0.190055 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.32232e7 | 1.34080 | ||||||||
\(787\) | 2.15792e7i | 1.24194i | 0.783836 | + | 0.620968i | \(0.213260\pi\) | ||||
−0.783836 | + | 0.620968i | \(0.786740\pi\) | |||||||
\(788\) | − 7.19165e6i | − 0.412584i | ||||||||
\(789\) | 1.93314e7 | 1.10553 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.14750e7 | −1.78864 | ||||||||
\(792\) | − 2.81318e6i | − 0.159362i | ||||||||
\(793\) | 1.57244e7i | 0.887956i | ||||||||
\(794\) | 1.98966e7 | 1.12003 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.51456e6 | 0.140663 | ||||||||
\(797\) | − 3.09760e7i | − 1.72735i | −0.504052 | − | 0.863673i | \(-0.668158\pi\) | ||||
0.504052 | − | 0.863673i | \(-0.331842\pi\) | |||||||
\(798\) | − 8.25600e6i | − 0.458947i | ||||||||
\(799\) | 1.46254e6 | 0.0810475 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.67332e7 | −2.02292 | ||||||||
\(802\) | 5.37055e6i | 0.294838i | ||||||||
\(803\) | − 2.70257e6i | − 0.147907i | ||||||||
\(804\) | −694272. | −0.0378782 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 8.74861e6 | 0.474353 | ||||||||
\(807\) | − 2.06086e7i | − 1.11395i | ||||||||
\(808\) | 9.08429e6i | 0.489511i | ||||||||
\(809\) | −4.24929e6 | −0.228268 | −0.114134 | − | 0.993465i | \(-0.536409\pi\) | ||||
−0.114134 | + | 0.993465i | \(0.536409\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.42333e6 | 0.182767 | 0.0913833 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913833 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(812\) | − 6.02688e6i | − 0.320776i | ||||||||
\(813\) | 9.20659e6i | 0.488509i | ||||||||
\(814\) | −5.93578e6 | −0.313990 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.36397e6 | −0.0717098 | ||||||||
\(817\) | 1.03120e7i | 0.540490i | ||||||||
\(818\) | − 4.37692e6i | − 0.228710i | ||||||||
\(819\) | −5.41831e7 | −2.82263 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.10571e7 | 1.60806 | 0.804030 | − | 0.594588i | \(-0.202685\pi\) | ||||
0.804030 | + | 0.594588i | \(0.202685\pi\) | |||||||
\(822\) | − 2.66014e7i | − 1.37317i | ||||||||
\(823\) | 3.11904e7i | 1.60517i | 0.596538 | + | 0.802584i | \(0.296542\pi\) | ||||
−0.596538 | + | 0.802584i | \(0.703458\pi\) | |||||||
\(824\) | −27904.0 | −0.00143169 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.49024e6 | 0.279989 | ||||||||
\(827\) | − 8.28487e6i | − 0.421233i | −0.977569 | − | 0.210616i | \(-0.932453\pi\) | ||||
0.977569 | − | 0.210616i | \(-0.0675471\pi\) | |||||||
\(828\) | − 1.89890e7i | − 0.962556i | ||||||||
\(829\) | 1.81688e7 | 0.918208 | 0.459104 | − | 0.888383i | \(-0.348171\pi\) | ||||
0.459104 | + | 0.888383i | \(0.348171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.82582e7 | 2.42420 | ||||||||
\(832\) | − 3.87482e6i | − 0.194063i | ||||||||
\(833\) | 2.83649e6i | 0.141635i | ||||||||
\(834\) | −1.85798e7 | −0.924968 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.05600e6 | 0.0522575 | ||||||||
\(837\) | 4.99392e6i | 0.246393i | ||||||||
\(838\) | − 3.81624e6i | − 0.187727i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 6.37559e6i | 0.309913i | ||||||||
\(843\) | − 4.86245e6i | − 0.235660i | ||||||||
\(844\) | −4.04883e6 | −0.195647 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −8.77522e6 | −0.421533 | ||||||||
\(847\) | 2.47038e7i | 1.18319i | ||||||||
\(848\) | 5.39290e6i | 0.257533i | ||||||||
\(849\) | 5.31686e6 | 0.253155 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00665e7 | −1.89652 | ||||||||
\(852\) | − 9.41875e6i | − 0.444523i | ||||||||
\(853\) | − 6.28597e6i | − 0.295801i | −0.989002 | − | 0.147901i | \(-0.952748\pi\) | ||||
0.989002 | − | 0.147901i | \(-0.0472516\pi\) | |||||||
\(854\) | −1.14359e7 | −0.536571 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.49100e7 | −0.695492 | ||||||||
\(857\) | 1.54050e7i | 0.716490i | 0.933628 | + | 0.358245i | \(0.116625\pi\) | ||||
−0.933628 | + | 0.358245i | \(0.883375\pi\) | |||||||
\(858\) | − 1.19877e7i | − 0.555927i | ||||||||
\(859\) | −1.43526e7 | −0.663664 | −0.331832 | − | 0.943338i | \(-0.607667\pi\) | ||||
−0.331832 | + | 0.943338i | \(0.607667\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.12698e6 | −0.235697 | ||||||||
\(862\) | 1.05866e7i | 0.485275i | ||||||||
\(863\) | − 1.33278e7i | − 0.609158i | −0.952487 | − | 0.304579i | \(-0.901484\pi\) | ||||
0.952487 | − | 0.304579i | \(-0.0985158\pi\) | |||||||
\(864\) | 2.21184e6 | 0.100802 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.48942e7 | −0.674874 | ||||||||
\(867\) | − 3.28938e7i | − 1.48616i | ||||||||
\(868\) | 6.36262e6i | 0.286640i | ||||||||
\(869\) | 6.10368e6 | 0.274184 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.71037e6 | −0.0763913 | ||||||||
\(872\) | 1.11904e7i | 0.498373i | ||||||||
\(873\) | 2.61012e7i | 1.15911i | ||||||||
\(874\) | 7.12800e6 | 0.315638 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.86202e6 | 0.346157 | ||||||||
\(877\) | 3.24846e7i | 1.42620i | 0.701065 | + | 0.713098i | \(0.252708\pi\) | ||||
−0.701065 | + | 0.713098i | \(0.747292\pi\) | |||||||
\(878\) | − 1.03336e7i | − 0.452392i | ||||||||
\(879\) | 7.74014e6 | 0.337891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.54600e7 | 0.671073 | 0.335537 | − | 0.942027i | \(-0.391082\pi\) | ||||
0.335537 | + | 0.942027i | \(0.391082\pi\) | |||||||
\(882\) | − 1.70190e7i | − 0.736651i | ||||||||
\(883\) | 1.69478e6i | 0.0731494i | 0.999331 | + | 0.0365747i | \(0.0116447\pi\) | ||||
−0.999331 | + | 0.0365747i | \(0.988355\pi\) | |||||||
\(884\) | −3.36019e6 | −0.144622 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.02483e7 | −1.29454 | ||||||||
\(887\) | − 2.87257e6i | − 0.122592i | −0.998120 | − | 0.0612960i | \(-0.980477\pi\) | ||||
0.998120 | − | 0.0612960i | \(-0.0195233\pi\) | |||||||
\(888\) | − 1.72677e7i | − 0.734856i | ||||||||
\(889\) | −2.10617e7 | −0.893799 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.83843e6 | −0.161979 | ||||||||
\(892\) | 1.71751e7i | 0.722749i | ||||||||
\(893\) | − 3.29400e6i | − 0.138228i | ||||||||
\(894\) | 1.34928e7 | 0.564623 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.81805e6 | 0.117268 | ||||||||
\(897\) | − 8.09171e7i | − 3.35783i | ||||||||
\(898\) | 1.72309e7i | 0.713046i | ||||||||
\(899\) | −5.06328e6 | −0.208945 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.67665e6 | 0.191921 | ||||||||
\(902\) | − 655776.i | − 0.0268373i | ||||||||
\(903\) | 8.51359e7i | 3.47451i | ||||||||
\(904\) | 1.17116e7 | 0.476646 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −4.16594e7 | −1.68614 | ||||||||
\(907\) | 3.95422e7i | 1.59603i | 0.602635 | + | 0.798017i | \(0.294118\pi\) | ||||
−0.602635 | + | 0.798017i | \(0.705882\pi\) | |||||||
\(908\) | 1.00293e7i | 0.403698i | ||||||||
\(909\) | −4.72667e7 | −1.89734 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.13178e7 | 0.451819 | 0.225909 | − | 0.974148i | \(-0.427465\pi\) | ||||
0.225909 | + | 0.974148i | \(0.427465\pi\) | |||||||
\(912\) | 3.07200e6i | 0.122302i | ||||||||
\(913\) | 6.80803e6i | 0.270299i | ||||||||
\(914\) | −8.97417e6 | −0.355327 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.86640e6 | −0.0734964 | ||||||||
\(917\) | 4.16082e7i | 1.63401i | ||||||||
\(918\) | − 1.91808e6i | − 0.0751208i | ||||||||
\(919\) | −8.51348e6 | −0.332520 | −0.166260 | − | 0.986082i | \(-0.553169\pi\) | ||||
−0.166260 | + | 0.986082i | \(0.553169\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.46322e7 | 1.34534 | ||||||||
\(922\) | − 6.62681e6i | − 0.256730i | ||||||||
\(923\) | − 2.32035e7i | − 0.896497i | ||||||||
\(924\) | 8.71834e6 | 0.335934 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.15664e7 | 0.443272 | ||||||||
\(927\) | − 145188.i | − 0.00554921i | ||||||||
\(928\) | 2.24256e6i | 0.0854819i | ||||||||
\(929\) | 7.54587e6 | 0.286860 | 0.143430 | − | 0.989660i | \(-0.454187\pi\) | ||||
0.143430 | + | 0.989660i | \(0.454187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.38850e6 | 0.241560 | ||||||||
\(932\) | − 1.18887e7i | − 0.448328i | ||||||||
\(933\) | − 4.11149e6i | − 0.154630i | ||||||||
\(934\) | −2.61080e7 | −0.979278 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.01612e7 | 0.752187 | ||||||||
\(937\) | − 1.84500e7i | − 0.686512i | −0.939242 | − | 0.343256i | \(-0.888470\pi\) | ||||
0.939242 | − | 0.343256i | \(-0.111530\pi\) | |||||||
\(938\) | − 1.24390e6i | − 0.0461615i | ||||||||
\(939\) | 2.46453e7 | 0.912157 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.75046e6 | 0.248519 | 0.124259 | − | 0.992250i | \(-0.460344\pi\) | ||||
0.124259 | + | 0.992250i | \(0.460344\pi\) | |||||||
\(942\) | 5.33685e7i | 1.95956i | ||||||||
\(943\) | − 4.42649e6i | − 0.162099i | ||||||||
\(944\) | −2.04288e6 | −0.0746127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.08895e7 | −0.395621 | ||||||||
\(947\) | 6.45677e6i | 0.233959i | 0.993134 | + | 0.116980i | \(0.0373212\pi\) | ||||
−0.993134 | + | 0.116980i | \(0.962679\pi\) | |||||||
\(948\) | 1.77562e7i | 0.641694i | ||||||||
\(949\) | 1.93684e7 | 0.698117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.80710e7 | 0.647934 | ||||||||
\(952\) | − 2.44378e6i | − 0.0873915i | ||||||||
\(953\) | 3.96648e7i | 1.41473i | 0.706849 | + | 0.707364i | \(0.250116\pi\) | ||||
−0.706849 | + | 0.707364i | \(0.749884\pi\) | |||||||
\(954\) | −2.80599e7 | −0.998195 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 1.56595e7 | 0.554158 | ||||||||
\(957\) | 6.93792e6i | 0.244878i | ||||||||
\(958\) | − 2.38493e7i | − 0.839579i | ||||||||
\(959\) | 4.76609e7 | 1.67346 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.32838e7 | −0.813290 | ||||||||
\(962\) | − 4.25397e7i | − 1.48203i | ||||||||
\(963\) | − 7.75783e7i | − 2.69572i | ||||||||
\(964\) | 1.81248e7 | 0.628174 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.88488e7 | 2.02906 | ||||||||
\(967\) | − 3.43015e7i | − 1.17963i | −0.807538 | − | 0.589816i | \(-0.799200\pi\) | ||||
0.807538 | − | 0.589816i | \(-0.200800\pi\) | |||||||
\(968\) | − 9.19213e6i | − 0.315303i | ||||||||
\(969\) | 2.66400e6 | 0.0911433 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.77115e6 | −0.196433 | −0.0982164 | − | 0.995165i | \(-0.531314\pi\) | ||||
−0.0982164 | + | 0.995165i | \(0.531314\pi\) | |||||||
\(972\) | − 1.95644e7i | − 0.664204i | ||||||||
\(973\) | − 3.32889e7i | − 1.12724i | ||||||||
\(974\) | 1.19676e7 | 0.404214 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.25523e6 | 0.142988 | ||||||||
\(977\) | 7.08746e6i | 0.237549i | 0.992921 | + | 0.118775i | \(0.0378966\pi\) | ||||
−0.992921 | + | 0.118775i | \(0.962103\pi\) | |||||||
\(978\) | − 6.39514e6i | − 0.213798i | ||||||||
\(979\) | 1.45609e7 | 0.485548 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.82250e7 | −1.93169 | ||||||||
\(982\) | 4.81675e6i | 0.159395i | ||||||||
\(983\) | − 4.59362e7i | − 1.51625i | −0.652108 | − | 0.758126i | \(-0.726115\pi\) | ||||
0.652108 | − | 0.758126i | \(-0.273885\pi\) | |||||||
\(984\) | 1.90771e6 | 0.0628095 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.94472e6 | 0.0637037 | ||||||||
\(987\) | − 2.71953e7i | − 0.888588i | ||||||||
\(988\) | 7.56800e6i | 0.246654i | ||||||||
\(989\) | −7.35039e7 | −2.38957 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.50298e7 | −1.45652 | −0.728260 | − | 0.685301i | \(-0.759671\pi\) | ||||
−0.728260 | + | 0.685301i | \(0.759671\pi\) | |||||||
\(992\) | − 2.36749e6i | − 0.0763851i | ||||||||
\(993\) | − 4.78592e7i | − 1.54025i | ||||||||
\(994\) | 1.68753e7 | 0.541732 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.98052e7 | −0.632602 | ||||||||
\(997\) | − 2.37364e7i | − 0.756271i | −0.925750 | − | 0.378136i | \(-0.876565\pi\) | ||||
0.925750 | − | 0.378136i | \(-0.123435\pi\) | |||||||
\(998\) | 3.68218e7i | 1.17025i | ||||||||
\(999\) | 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 | 50.6.b.a.49.1 | 2 | ||
3.2 | odd | 2 | 450.6.c.h.199.2 | 2 | |||
4.3 | odd | 2 | 400.6.c.b.49.2 | 2 | |||
5.2 | odd | 4 | 50.6.a.d.1.1 | 1 | |||
5.3 | odd | 4 | 10.6.a.b.1.1 | ✓ | 1 | ||
5.4 | even | 2 | inner | 50.6.b.a.49.2 | 2 | ||
15.2 | even | 4 | 450.6.a.l.1.1 | 1 | |||
15.8 | even | 4 | 90.6.a.d.1.1 | 1 | |||
15.14 | odd | 2 | 450.6.c.h.199.1 | 2 | |||
20.3 | even | 4 | 80.6.a.a.1.1 | 1 | |||
20.7 | even | 4 | 400.6.a.n.1.1 | 1 | |||
20.19 | odd | 2 | 400.6.c.b.49.1 | 2 | |||
35.13 | even | 4 | 490.6.a.a.1.1 | 1 | |||
40.3 | even | 4 | 320.6.a.o.1.1 | 1 | |||
40.13 | odd | 4 | 320.6.a.b.1.1 | 1 | |||
60.23 | odd | 4 | 720.6.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.6.a.b.1.1 | ✓ | 1 | 5.3 | odd | 4 | ||
50.6.a.d.1.1 | 1 | 5.2 | odd | 4 | |||
50.6.b.a.49.1 | 2 | 1.1 | even | 1 | trivial | ||
50.6.b.a.49.2 | 2 | 5.4 | even | 2 | inner | ||
80.6.a.a.1.1 | 1 | 20.3 | even | 4 | |||
90.6.a.d.1.1 | 1 | 15.8 | even | 4 | |||
320.6.a.b.1.1 | 1 | 40.13 | odd | 4 | |||
320.6.a.o.1.1 | 1 | 40.3 | even | 4 | |||
400.6.a.n.1.1 | 1 | 20.7 | even | 4 | |||
400.6.c.b.49.1 | 2 | 20.19 | odd | 2 | |||
400.6.c.b.49.2 | 2 | 4.3 | odd | 2 | |||
450.6.a.l.1.1 | 1 | 15.2 | even | 4 | |||
450.6.c.h.199.1 | 2 | 15.14 | odd | 2 | |||
450.6.c.h.199.2 | 2 | 3.2 | odd | 2 | |||
490.6.a.a.1.1 | 1 | 35.13 | even | 4 | |||
720.6.a.j.1.1 | 1 | 60.23 | odd | 4 |