Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,6,Mod(24,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("115.24");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.b (of order \(2\), degree \(1\), 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: | \(18.4441392785\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.36 | ||
Character | \(\chi\) | \(=\) | 115.24 |
Dual form | 115.6.b.a.24.19 |
$q$-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 \(\left(\mathbb{Z}/115\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.13410i | 0.554036i | 0.960865 | + | 0.277018i | \(0.0893462\pi\) | ||||
−0.960865 | + | 0.277018i | \(0.910654\pi\) | |||||||
\(3\) | 27.5349i | 1.76637i | 0.469028 | + | 0.883183i | \(0.344604\pi\) | ||||
−0.469028 | + | 0.883183i | \(0.655396\pi\) | |||||||
\(4\) | 22.1774 | 0.693044 | ||||||||
\(5\) | 23.6107 | + | 50.6709i | 0.422361 | + | 0.906428i | ||||
\(6\) | −86.2973 | −0.978631 | ||||||||
\(7\) | − | 98.9863i | − | 0.763537i | −0.924258 | − | 0.381768i | \(-0.875315\pi\) | ||
0.924258 | − | 0.381768i | \(-0.124685\pi\) | |||||||
\(8\) | 169.798i | 0.938008i | ||||||||
\(9\) | −515.172 | −2.12005 | ||||||||
\(10\) | −158.808 | + | 73.9983i | −0.502194 | + | 0.234003i | ||||
\(11\) | −172.976 | −0.431027 | −0.215514 | − | 0.976501i | \(-0.569143\pi\) | ||||
−0.215514 | + | 0.976501i | \(0.569143\pi\) | |||||||
\(12\) | 610.653i | 1.22417i | ||||||||
\(13\) | 499.623i | 0.819944i | 0.912098 | + | 0.409972i | \(0.134462\pi\) | ||||
−0.912098 | + | 0.409972i | \(0.865538\pi\) | |||||||
\(14\) | 310.233 | 0.423027 | ||||||||
\(15\) | −1395.22 | + | 650.119i | −1.60108 | + | 0.746044i | ||||
\(16\) | 177.514 | 0.173353 | ||||||||
\(17\) | − | 185.294i | − | 0.155503i | −0.996973 | − | 0.0777516i | \(-0.975226\pi\) | ||
0.996973 | − | 0.0777516i | \(-0.0247741\pi\) | |||||||
\(18\) | − | 1614.60i | − | 1.17458i | ||||||
\(19\) | 457.866 | 0.290974 | 0.145487 | − | 0.989360i | \(-0.453525\pi\) | ||||
0.145487 | + | 0.989360i | \(0.453525\pi\) | |||||||
\(20\) | 523.624 | + | 1123.75i | 0.292715 | + | 0.628194i | ||||
\(21\) | 2725.58 | 1.34869 | ||||||||
\(22\) | − | 542.125i | − | 0.238805i | ||||||
\(23\) | − | 529.000i | − | 0.208514i | ||||||
\(24\) | −4675.36 | −1.65687 | ||||||||
\(25\) | −2010.07 | + | 2392.75i | −0.643222 | + | 0.765679i | ||||
\(26\) | −1565.87 | −0.454279 | ||||||||
\(27\) | − | 7494.24i | − | 1.97842i | ||||||
\(28\) | − | 2195.26i | − | 0.529164i | ||||||
\(29\) | −4657.20 | −1.02832 | −0.514161 | − | 0.857693i | \(-0.671897\pi\) | ||||
−0.514161 | + | 0.857693i | \(0.671897\pi\) | |||||||
\(30\) | −2037.54 | − | 4372.76i | −0.413336 | − | 0.887058i | ||||
\(31\) | 9047.26 | 1.69088 | 0.845440 | − | 0.534070i | \(-0.179338\pi\) | ||||
0.845440 | + | 0.534070i | \(0.179338\pi\) | |||||||
\(32\) | 5989.87i | 1.03405i | ||||||||
\(33\) | − | 4762.89i | − | 0.761352i | ||||||
\(34\) | 580.731 | 0.0861545 | ||||||||
\(35\) | 5015.72 | − | 2337.14i | 0.692091 | − | 0.322488i | ||||
\(36\) | −11425.2 | −1.46929 | ||||||||
\(37\) | − | 5379.45i | − | 0.646002i | −0.946399 | − | 0.323001i | \(-0.895308\pi\) | ||
0.946399 | − | 0.323001i | \(-0.104692\pi\) | |||||||
\(38\) | 1435.00i | 0.161210i | ||||||||
\(39\) | −13757.1 | −1.44832 | ||||||||
\(40\) | −8603.79 | + | 4009.04i | −0.850236 | + | 0.396178i | ||||
\(41\) | 957.099 | 0.0889195 | 0.0444598 | − | 0.999011i | \(-0.485843\pi\) | ||||
0.0444598 | + | 0.999011i | \(0.485843\pi\) | |||||||
\(42\) | 8542.25i | 0.747221i | ||||||||
\(43\) | − | 19714.5i | − | 1.62598i | −0.582279 | − | 0.812989i | \(-0.697839\pi\) | ||
0.582279 | − | 0.812989i | \(-0.302161\pi\) | |||||||
\(44\) | −3836.16 | −0.298721 | ||||||||
\(45\) | −12163.6 | − | 26104.2i | −0.895426 | − | 1.92167i | ||||
\(46\) | 1657.94 | 0.115525 | ||||||||
\(47\) | 22583.7i | 1.49125i | 0.666368 | + | 0.745623i | \(0.267848\pi\) | ||||
−0.666368 | + | 0.745623i | \(0.732152\pi\) | |||||||
\(48\) | 4887.83i | 0.306206i | ||||||||
\(49\) | 7008.71 | 0.417012 | ||||||||
\(50\) | −7499.12 | − | 6299.77i | −0.424214 | − | 0.356369i | ||||
\(51\) | 5102.06 | 0.274676 | ||||||||
\(52\) | 11080.3i | 0.568257i | ||||||||
\(53\) | 15608.8i | 0.763271i | 0.924313 | + | 0.381635i | \(0.124639\pi\) | ||||
−0.924313 | + | 0.381635i | \(0.875361\pi\) | |||||||
\(54\) | 23487.7 | 1.09612 | ||||||||
\(55\) | −4084.09 | − | 8764.85i | −0.182049 | − | 0.390695i | ||||
\(56\) | 16807.6 | 0.716203 | ||||||||
\(57\) | 12607.3i | 0.513967i | ||||||||
\(58\) | − | 14596.1i | − | 0.569728i | ||||||
\(59\) | −506.470 | −0.0189419 | −0.00947096 | − | 0.999955i | \(-0.503015\pi\) | ||||
−0.00947096 | + | 0.999955i | \(0.503015\pi\) | |||||||
\(60\) | −30942.3 | + | 14417.9i | −1.10962 | + | 0.517041i | ||||
\(61\) | 31327.9 | 1.07797 | 0.538985 | − | 0.842316i | \(-0.318808\pi\) | ||||
0.538985 | + | 0.842316i | \(0.318808\pi\) | |||||||
\(62\) | 28355.1i | 0.936809i | ||||||||
\(63\) | 50995.0i | 1.61874i | ||||||||
\(64\) | −13092.4 | −0.399549 | ||||||||
\(65\) | −25316.3 | + | 11796.4i | −0.743220 | + | 0.346312i | ||||
\(66\) | 14927.4 | 0.421817 | ||||||||
\(67\) | − | 43689.5i | − | 1.18902i | −0.804087 | − | 0.594511i | \(-0.797346\pi\) | ||
0.804087 | − | 0.594511i | \(-0.202654\pi\) | |||||||
\(68\) | − | 4109.34i | − | 0.107771i | ||||||
\(69\) | 14566.0 | 0.368313 | ||||||||
\(70\) | 7324.82 | + | 15719.8i | 0.178670 | + | 0.383444i | ||||
\(71\) | −18754.4 | −0.441526 | −0.220763 | − | 0.975327i | \(-0.570855\pi\) | ||||
−0.220763 | + | 0.975327i | \(0.570855\pi\) | |||||||
\(72\) | − | 87475.0i | − | 1.98862i | ||||||
\(73\) | 39706.2i | 0.872070i | 0.899930 | + | 0.436035i | \(0.143618\pi\) | ||||
−0.899930 | + | 0.436035i | \(0.856382\pi\) | |||||||
\(74\) | 16859.8 | 0.357909 | ||||||||
\(75\) | −65884.1 | − | 55347.1i | −1.35247 | − | 1.13617i | ||||
\(76\) | 10154.3 | 0.201658 | ||||||||
\(77\) | 17122.3i | 0.329105i | ||||||||
\(78\) | − | 43116.1i | − | 0.802423i | ||||||
\(79\) | 21075.0 | 0.379927 | 0.189964 | − | 0.981791i | \(-0.439163\pi\) | ||||
0.189964 | + | 0.981791i | \(0.439163\pi\) | |||||||
\(80\) | 4191.23 | + | 8994.78i | 0.0732177 | + | 0.157132i | ||||
\(81\) | 81166.6 | 1.37456 | ||||||||
\(82\) | 2999.65i | 0.0492646i | ||||||||
\(83\) | 59205.2i | 0.943333i | 0.881777 | + | 0.471666i | \(0.156347\pi\) | ||||
−0.881777 | + | 0.471666i | \(0.843653\pi\) | |||||||
\(84\) | 60446.3 | 0.934698 | ||||||||
\(85\) | 9389.01 | − | 4374.92i | 0.140952 | − | 0.0656785i | ||||
\(86\) | 61787.3 | 0.900851 | ||||||||
\(87\) | − | 128236.i | − | 1.81639i | ||||||
\(88\) | − | 29370.9i | − | 0.404307i | ||||||
\(89\) | 74791.3 | 1.00087 | 0.500433 | − | 0.865775i | \(-0.333174\pi\) | ||||
0.500433 | + | 0.865775i | \(0.333174\pi\) | |||||||
\(90\) | 81813.3 | − | 38121.9i | 1.06468 | − | 0.496099i | ||||
\(91\) | 49455.8 | 0.626057 | ||||||||
\(92\) | − | 11731.8i | − | 0.144510i | ||||||
\(93\) | 249116.i | 2.98672i | ||||||||
\(94\) | −70779.5 | −0.826205 | ||||||||
\(95\) | 10810.5 | + | 23200.5i | 0.122896 | + | 0.263747i | ||||
\(96\) | −164931. | −1.82651 | ||||||||
\(97\) | 46828.3i | 0.505335i | 0.967553 | + | 0.252668i | \(0.0813079\pi\) | ||||
−0.967553 | + | 0.252668i | \(0.918692\pi\) | |||||||
\(98\) | 21966.0i | 0.231040i | ||||||||
\(99\) | 89112.5 | 0.913799 | ||||||||
\(100\) | −44578.1 | + | 53064.9i | −0.445781 | + | 0.530649i | ||||
\(101\) | 124353. | 1.21297 | 0.606487 | − | 0.795094i | \(-0.292578\pi\) | ||||
0.606487 | + | 0.795094i | \(0.292578\pi\) | |||||||
\(102\) | 15990.4i | 0.152180i | ||||||||
\(103\) | 165230.i | 1.53460i | 0.641290 | + | 0.767299i | \(0.278400\pi\) | ||||
−0.641290 | + | 0.767299i | \(0.721600\pi\) | |||||||
\(104\) | −84834.8 | −0.769114 | ||||||||
\(105\) | 64352.8 | + | 138107.i | 0.569632 | + | 1.22249i | ||||
\(106\) | −48919.5 | −0.422880 | ||||||||
\(107\) | 136352.i | 1.15133i | 0.817684 | + | 0.575667i | \(0.195257\pi\) | ||||
−0.817684 | + | 0.575667i | \(0.804743\pi\) | |||||||
\(108\) | − | 166203.i | − | 1.37113i | ||||||
\(109\) | −223278. | −1.80003 | −0.900016 | − | 0.435858i | \(-0.856445\pi\) | ||||
−0.900016 | + | 0.435858i | \(0.856445\pi\) | |||||||
\(110\) | 27469.9 | − | 12800.0i | 0.216459 | − | 0.100862i | ||||
\(111\) | 148123. | 1.14108 | ||||||||
\(112\) | − | 17571.4i | − | 0.132362i | ||||||
\(113\) | − | 106206.i | − | 0.782443i | −0.920297 | − | 0.391222i | \(-0.872053\pi\) | ||
0.920297 | − | 0.391222i | \(-0.127947\pi\) | |||||||
\(114\) | −39512.6 | −0.284756 | ||||||||
\(115\) | 26804.9 | − | 12490.1i | 0.189003 | − | 0.0880683i | ||||
\(116\) | −103284. | −0.712673 | ||||||||
\(117\) | − | 257392.i | − | 1.73832i | ||||||
\(118\) | − | 1587.33i | − | 0.0104945i | ||||||
\(119\) | −18341.6 | −0.118732 | ||||||||
\(120\) | −110389. | − | 236905.i | −0.699795 | − | 1.50183i | ||||
\(121\) | −131130. | −0.814216 | ||||||||
\(122\) | 98184.8i | 0.597234i | ||||||||
\(123\) | 26353.6i | 0.157064i | ||||||||
\(124\) | 200645. | 1.17185 | ||||||||
\(125\) | −168702. | − | 45357.5i | −0.965705 | − | 0.259642i | ||||
\(126\) | −159824. | −0.896839 | ||||||||
\(127\) | 295410.i | 1.62524i | 0.582797 | + | 0.812618i | \(0.301958\pi\) | ||||
−0.582797 | + | 0.812618i | \(0.698042\pi\) | |||||||
\(128\) | 150643.i | 0.812687i | ||||||||
\(129\) | 542838. | 2.87207 | ||||||||
\(130\) | −36971.3 | − | 79344.0i | −0.191870 | − | 0.411771i | ||||
\(131\) | −75570.6 | −0.384746 | −0.192373 | − | 0.981322i | \(-0.561618\pi\) | ||||
−0.192373 | + | 0.981322i | \(0.561618\pi\) | |||||||
\(132\) | − | 105628.i | − | 0.527650i | ||||||
\(133\) | − | 45322.5i | − | 0.222170i | ||||||
\(134\) | 136927. | 0.658762 | ||||||||
\(135\) | 379740. | − | 176944.i | 1.79329 | − | 0.835607i | ||||
\(136\) | 31462.5 | 0.145863 | ||||||||
\(137\) | − | 400299.i | − | 1.82215i | −0.412245 | − | 0.911073i | \(-0.635255\pi\) | ||
0.412245 | − | 0.911073i | \(-0.364745\pi\) | |||||||
\(138\) | 45651.3i | 0.204059i | ||||||||
\(139\) | −66371.9 | −0.291371 | −0.145686 | − | 0.989331i | \(-0.546539\pi\) | ||||
−0.145686 | + | 0.989331i | \(0.546539\pi\) | |||||||
\(140\) | 111236. | − | 51831.6i | 0.479649 | − | 0.223498i | ||||
\(141\) | −621839. | −2.63409 | ||||||||
\(142\) | − | 58778.1i | − | 0.244622i | ||||||
\(143\) | − | 86422.9i | − | 0.353418i | ||||||
\(144\) | −91450.2 | −0.367518 | ||||||||
\(145\) | −109960. | − | 235984.i | −0.434323 | − | 0.932100i | ||||
\(146\) | −124443. | −0.483158 | ||||||||
\(147\) | 192984.i | 0.736595i | ||||||||
\(148\) | − | 119302.i | − | 0.447708i | ||||||
\(149\) | −181608. | −0.670147 | −0.335073 | − | 0.942192i | \(-0.608761\pi\) | ||||
−0.335073 | + | 0.942192i | \(0.608761\pi\) | |||||||
\(150\) | 173464. | − | 206488.i | 0.629478 | − | 0.749318i | ||||
\(151\) | −179415. | −0.640350 | −0.320175 | − | 0.947358i | \(-0.603742\pi\) | ||||
−0.320175 | + | 0.947358i | \(0.603742\pi\) | |||||||
\(152\) | 77744.5i | 0.272936i | ||||||||
\(153\) | 95458.4i | 0.329675i | ||||||||
\(154\) | −53663.0 | −0.182336 | ||||||||
\(155\) | 213612. | + | 458433.i | 0.714162 | + | 1.53266i | ||||
\(156\) | −305096. | −1.00375 | ||||||||
\(157\) | − | 574225.i | − | 1.85923i | −0.368531 | − | 0.929615i | \(-0.620139\pi\) | ||
0.368531 | − | 0.929615i | \(-0.379861\pi\) | |||||||
\(158\) | 66051.3i | 0.210494i | ||||||||
\(159\) | −429786. | −1.34822 | ||||||||
\(160\) | −303512. | + | 141425.i | −0.937293 | + | 0.436743i | ||||
\(161\) | −52363.8 | −0.159208 | ||||||||
\(162\) | 254384.i | 0.761558i | ||||||||
\(163\) | − | 157294.i | − | 0.463705i | −0.972751 | − | 0.231853i | \(-0.925521\pi\) | ||
0.972751 | − | 0.231853i | \(-0.0744787\pi\) | |||||||
\(164\) | 21226.0 | 0.0616251 | ||||||||
\(165\) | 241340. | − | 112455.i | 0.690111 | − | 0.321565i | ||||
\(166\) | −185555. | −0.522640 | ||||||||
\(167\) | 150221.i | 0.416811i | 0.978042 | + | 0.208406i | \(0.0668274\pi\) | ||||
−0.978042 | + | 0.208406i | \(0.933173\pi\) | |||||||
\(168\) | 462797.i | 1.26508i | ||||||||
\(169\) | 121670. | 0.327692 | ||||||||
\(170\) | 13711.5 | + | 29426.1i | 0.0363883 | + | 0.0780928i | ||||
\(171\) | −235880. | −0.616880 | ||||||||
\(172\) | − | 437217.i | − | 1.12687i | ||||||
\(173\) | 408467.i | 1.03763i | 0.854887 | + | 0.518813i | \(0.173626\pi\) | ||||
−0.854887 | + | 0.518813i | \(0.826374\pi\) | |||||||
\(174\) | 401903. | 1.00635 | ||||||||
\(175\) | 236849. | + | 198969.i | 0.584624 | + | 0.491124i | ||||
\(176\) | −30705.7 | −0.0747200 | ||||||||
\(177\) | − | 13945.6i | − | 0.0334584i | ||||||
\(178\) | 234404.i | 0.554517i | ||||||||
\(179\) | −83182.2 | −0.194043 | −0.0970214 | − | 0.995282i | \(-0.530932\pi\) | ||||
−0.0970214 | + | 0.995282i | \(0.530932\pi\) | |||||||
\(180\) | −269756. | − | 578924.i | −0.620570 | − | 1.33180i | ||||
\(181\) | 383086. | 0.869160 | 0.434580 | − | 0.900633i | \(-0.356897\pi\) | ||||
0.434580 | + | 0.900633i | \(0.356897\pi\) | |||||||
\(182\) | 155000.i | 0.346859i | ||||||||
\(183\) | 862611.i | 1.90409i | ||||||||
\(184\) | 89822.9 | 0.195588 | ||||||||
\(185\) | 272581. | − | 127013.i | 0.585554 | − | 0.272846i | ||||
\(186\) | −780754. | −1.65475 | ||||||||
\(187\) | 32051.5i | 0.0670261i | ||||||||
\(188\) | 500847.i | 1.03350i | ||||||||
\(189\) | −741827. | −1.51060 | ||||||||
\(190\) | −72712.6 | + | 33881.3i | −0.146125 | + | 0.0680889i | ||||
\(191\) | 906396. | 1.79777 | 0.898886 | − | 0.438182i | \(-0.144377\pi\) | ||||
0.898886 | + | 0.438182i | \(0.144377\pi\) | |||||||
\(192\) | − | 360499.i | − | 0.705750i | ||||||
\(193\) | 609358.i | 1.17755i | 0.808297 | + | 0.588775i | \(0.200390\pi\) | ||||
−0.808297 | + | 0.588775i | \(0.799610\pi\) | |||||||
\(194\) | −146765. | −0.279974 | ||||||||
\(195\) | −324814. | − | 697083.i | −0.611714 | − | 1.31280i | ||||
\(196\) | 155435. | 0.289007 | ||||||||
\(197\) | − | 690338.i | − | 1.26735i | −0.773600 | − | 0.633675i | \(-0.781546\pi\) | ||
0.773600 | − | 0.633675i | \(-0.218454\pi\) | |||||||
\(198\) | 279288.i | 0.506278i | ||||||||
\(199\) | 118685. | 0.212452 | 0.106226 | − | 0.994342i | \(-0.466123\pi\) | ||||
0.106226 | + | 0.994342i | \(0.466123\pi\) | |||||||
\(200\) | −406283. | − | 341305.i | −0.718213 | − | 0.603348i | ||||
\(201\) | 1.20299e6 | 2.10025 | ||||||||
\(202\) | 389734.i | 0.672031i | ||||||||
\(203\) | 460999.i | 0.785162i | ||||||||
\(204\) | 113150. | 0.190362 | ||||||||
\(205\) | 22597.8 | + | 48497.0i | 0.0375561 | + | 0.0805991i | ||||
\(206\) | −517846. | −0.850223 | ||||||||
\(207\) | 272526.i | 0.442061i | ||||||||
\(208\) | 88690.0i | 0.142140i | ||||||||
\(209\) | −79199.9 | −0.125418 | ||||||||
\(210\) | −432843. | + | 201688.i | −0.677302 | + | 0.315597i | ||||
\(211\) | 1.18355e6 | 1.83012 | 0.915062 | − | 0.403314i | \(-0.132142\pi\) | ||||
0.915062 | + | 0.403314i | \(0.132142\pi\) | |||||||
\(212\) | 346162.i | 0.528980i | ||||||||
\(213\) | − | 516400.i | − | 0.779897i | ||||||
\(214\) | −427340. | −0.637881 | ||||||||
\(215\) | 998951. | − | 465473.i | 1.47383 | − | 0.686750i | ||||
\(216\) | 1.27250e6 | 1.85577 | ||||||||
\(217\) | − | 895555.i | − | 1.29105i | ||||||
\(218\) | − | 699777.i | − | 0.997283i | ||||||
\(219\) | −1.09331e6 | −1.54039 | ||||||||
\(220\) | −90574.5 | − | 194382.i | −0.126168 | − | 0.270769i | ||||
\(221\) | 92577.3 | 0.127504 | ||||||||
\(222\) | 464232.i | 0.632198i | ||||||||
\(223\) | − | 1.37756e6i | − | 1.85501i | −0.373806 | − | 0.927507i | \(-0.621948\pi\) | ||
0.373806 | − | 0.927507i | \(-0.378052\pi\) | |||||||
\(224\) | 592915. | 0.789537 | ||||||||
\(225\) | 1.03553e6 | − | 1.23268e6i | 1.36366 | − | 1.62328i | ||||
\(226\) | 332860. | 0.433502 | ||||||||
\(227\) | 1.14830e6i | 1.47908i | 0.673114 | + | 0.739539i | \(0.264957\pi\) | ||||
−0.673114 | + | 0.739539i | \(0.735043\pi\) | |||||||
\(228\) | 279597.i | 0.356202i | ||||||||
\(229\) | −171814. | −0.216506 | −0.108253 | − | 0.994123i | \(-0.534526\pi\) | ||||
−0.108253 | + | 0.994123i | \(0.534526\pi\) | |||||||
\(230\) | 39145.1 | + | 84009.2i | 0.0487931 | + | 0.104715i | ||||
\(231\) | −471461. | −0.581320 | ||||||||
\(232\) | − | 790780.i | − | 0.964575i | ||||||
\(233\) | − | 651670.i | − | 0.786390i | −0.919455 | − | 0.393195i | \(-0.871370\pi\) | ||
0.919455 | − | 0.393195i | \(-0.128630\pi\) | |||||||
\(234\) | 806693. | 0.963094 | ||||||||
\(235\) | −1.14433e6 | + | 533216.i | −1.35171 | + | 0.629844i | ||||
\(236\) | −11232.2 | −0.0131276 | ||||||||
\(237\) | 580300.i | 0.671091i | ||||||||
\(238\) | − | 57484.4i | − | 0.0657821i | ||||||
\(239\) | 1.53723e6 | 1.74078 | 0.870389 | − | 0.492365i | \(-0.163867\pi\) | ||||
0.870389 | + | 0.492365i | \(0.163867\pi\) | |||||||
\(240\) | −247671. | + | 115405.i | −0.277553 | + | 0.129329i | ||||
\(241\) | 913293. | 1.01290 | 0.506451 | − | 0.862269i | \(-0.330957\pi\) | ||||
0.506451 | + | 0.862269i | \(0.330957\pi\) | |||||||
\(242\) | − | 410976.i | − | 0.451105i | ||||||
\(243\) | 413814.i | 0.449562i | ||||||||
\(244\) | 694771. | 0.747080 | ||||||||
\(245\) | 165481. | + | 355137.i | 0.176129 | + | 0.377991i | ||||
\(246\) | −82595.0 | −0.0870194 | ||||||||
\(247\) | 228760.i | 0.238583i | ||||||||
\(248\) | 1.53620e6i | 1.58606i | ||||||||
\(249\) | −1.63021e6 | −1.66627 | ||||||||
\(250\) | 142155. | − | 528729.i | 0.143851 | − | 0.535036i | ||||
\(251\) | 432806. | 0.433620 | 0.216810 | − | 0.976214i | \(-0.430435\pi\) | ||||
0.216810 | + | 0.976214i | \(0.430435\pi\) | |||||||
\(252\) | 1.13094e6i | 1.12186i | ||||||||
\(253\) | 91504.4i | 0.0898754i | ||||||||
\(254\) | −925846. | −0.900440 | ||||||||
\(255\) | 120463. | + | 258526.i | 0.116012 | + | 0.248974i | ||||
\(256\) | −891087. | −0.849807 | ||||||||
\(257\) | − | 1.43836e6i | − | 1.35842i | −0.733944 | − | 0.679210i | \(-0.762323\pi\) | ||
0.733944 | − | 0.679210i | \(-0.237677\pi\) | |||||||
\(258\) | 1.70131e6i | 1.59123i | ||||||||
\(259\) | −532492. | −0.493246 | ||||||||
\(260\) | −561450. | + | 261615.i | −0.515084 | + | 0.240010i | ||||
\(261\) | 2.39926e6 | 2.18010 | ||||||||
\(262\) | − | 236846.i | − | 0.213163i | ||||||
\(263\) | 172554.i | 0.153828i | 0.997038 | + | 0.0769142i | \(0.0245068\pi\) | ||||
−0.997038 | + | 0.0769142i | \(0.975493\pi\) | |||||||
\(264\) | 808727. | 0.714154 | ||||||||
\(265\) | −790909. | + | 368534.i | −0.691850 | + | 0.322376i | ||||
\(266\) | 142045. | 0.123090 | ||||||||
\(267\) | 2.05937e6i | 1.76790i | ||||||||
\(268\) | − | 968920.i | − | 0.824045i | ||||||
\(269\) | 243007. | 0.204757 | 0.102378 | − | 0.994746i | \(-0.467355\pi\) | ||||
0.102378 | + | 0.994746i | \(0.467355\pi\) | |||||||
\(270\) | 554561. | + | 1.19014e6i | 0.462957 | + | 0.993550i | ||||
\(271\) | −2.16968e6 | −1.79462 | −0.897310 | − | 0.441400i | \(-0.854482\pi\) | ||||
−0.897310 | + | 0.441400i | \(0.854482\pi\) | |||||||
\(272\) | − | 32892.3i | − | 0.0269570i | ||||||
\(273\) | 1.36176e6i | 1.10585i | ||||||||
\(274\) | 1.25458e6 | 1.00954 | ||||||||
\(275\) | 347694. | − | 413889.i | 0.277246 | − | 0.330029i | ||||
\(276\) | 323035. | 0.255257 | ||||||||
\(277\) | − | 858654.i | − | 0.672386i | −0.941793 | − | 0.336193i | \(-0.890860\pi\) | ||
0.941793 | − | 0.336193i | \(-0.109140\pi\) | |||||||
\(278\) | − | 208016.i | − | 0.161430i | ||||||
\(279\) | −4.66090e6 | −3.58475 | ||||||||
\(280\) | 396840. | + | 851657.i | 0.302496 | + | 0.649187i | ||||
\(281\) | 2.29812e6 | 1.73623 | 0.868115 | − | 0.496363i | \(-0.165331\pi\) | ||||
0.868115 | + | 0.496363i | \(0.165331\pi\) | |||||||
\(282\) | − | 1.94891e6i | − | 1.45938i | ||||||
\(283\) | 382115.i | 0.283614i | 0.989894 | + | 0.141807i | \(0.0452912\pi\) | ||||
−0.989894 | + | 0.141807i | \(0.954709\pi\) | |||||||
\(284\) | −415923. | −0.305997 | ||||||||
\(285\) | −638823. | + | 297667.i | −0.465874 | + | 0.217080i | ||||
\(286\) | 270858. | 0.195807 | ||||||||
\(287\) | − | 94739.6i | − | 0.0678933i | ||||||
\(288\) | − | 3.08581e6i | − | 2.19224i | ||||||
\(289\) | 1.38552e6 | 0.975819 | ||||||||
\(290\) | 739598. | − | 344625.i | 0.516417 | − | 0.240631i | ||||
\(291\) | −1.28942e6 | −0.892607 | ||||||||
\(292\) | 880580.i | 0.604382i | ||||||||
\(293\) | − | 4228.48i | − | 0.00287750i | −0.999999 | − | 0.00143875i | \(-0.999542\pi\) | ||
0.999999 | − | 0.00143875i | \(-0.000457969\pi\) | |||||||
\(294\) | −604833. | −0.408100 | ||||||||
\(295\) | −11958.1 | − | 25663.3i | −0.00800032 | − | 0.0171695i | ||||
\(296\) | 913418. | 0.605955 | ||||||||
\(297\) | 1.29633e6i | 0.852752i | ||||||||
\(298\) | − | 569179.i | − | 0.371286i | ||||||
\(299\) | 264301. | 0.170970 | ||||||||
\(300\) | −1.46114e6 | − | 1.22746e6i | −0.937321 | − | 0.787413i | ||||
\(301\) | −1.95147e6 | −1.24149 | ||||||||
\(302\) | − | 562306.i | − | 0.354777i | ||||||
\(303\) | 3.42404e6i | 2.14255i | ||||||||
\(304\) | 81277.6 | 0.0504414 | ||||||||
\(305\) | 739673. | + | 1.58741e6i | 0.455292 | + | 0.977101i | ||||
\(306\) | −299176. | −0.182652 | ||||||||
\(307\) | 454799.i | 0.275406i | 0.990474 | + | 0.137703i | \(0.0439719\pi\) | ||||
−0.990474 | + | 0.137703i | \(0.956028\pi\) | |||||||
\(308\) | 379728.i | 0.228084i | ||||||||
\(309\) | −4.54958e6 | −2.71066 | ||||||||
\(310\) | −1.43677e6 | + | 669483.i | −0.849150 | + | 0.395672i | ||||
\(311\) | −2.90140e6 | −1.70101 | −0.850506 | − | 0.525966i | \(-0.823704\pi\) | ||||
−0.850506 | + | 0.525966i | \(0.823704\pi\) | |||||||
\(312\) | − | 2.33592e6i | − | 1.35854i | ||||||
\(313\) | − | 2.58180e6i | − | 1.48957i | −0.667304 | − | 0.744785i | \(-0.732552\pi\) | ||
0.667304 | − | 0.744785i | \(-0.267448\pi\) | |||||||
\(314\) | 1.79968e6 | 1.03008 | ||||||||
\(315\) | −2.58396e6 | + | 1.20403e6i | −1.46727 | + | 0.683691i | ||||
\(316\) | 467389. | 0.263306 | ||||||||
\(317\) | − | 2.07352e6i | − | 1.15894i | −0.814995 | − | 0.579468i | \(-0.803260\pi\) | ||
0.814995 | − | 0.579468i | \(-0.196740\pi\) | |||||||
\(318\) | − | 1.34699e6i | − | 0.746961i | ||||||
\(319\) | 805584. | 0.443235 | ||||||||
\(320\) | −309121. | − | 663404.i | −0.168754 | − | 0.362162i | ||||
\(321\) | −3.75443e6 | −2.03368 | ||||||||
\(322\) | − | 164113.i | − | 0.0882073i | ||||||
\(323\) | − | 84839.9i | − | 0.0452474i | ||||||
\(324\) | 1.80006e6 | 0.952632 | ||||||||
\(325\) | −1.19547e6 | − | 1.00428e6i | −0.627814 | − | 0.527406i | ||||
\(326\) | 492974. | 0.256909 | ||||||||
\(327\) | − | 6.14795e6i | − | 3.17951i | ||||||
\(328\) | 162513.i | 0.0834072i | ||||||||
\(329\) | 2.23547e6 | 1.13862 | ||||||||
\(330\) | 352446. | + | 756383.i | 0.178159 | + | 0.382346i | ||||
\(331\) | 3.30721e6 | 1.65917 | 0.829587 | − | 0.558377i | \(-0.188576\pi\) | ||||
0.829587 | + | 0.558377i | \(0.188576\pi\) | |||||||
\(332\) | 1.31302e6i | 0.653771i | ||||||||
\(333\) | 2.77134e6i | 1.36956i | ||||||||
\(334\) | −470808. | −0.230929 | ||||||||
\(335\) | 2.21378e6 | − | 1.03154e6i | 1.07776 | − | 0.502197i | ||||
\(336\) | 483828. | 0.233799 | ||||||||
\(337\) | 1.83038e6i | 0.877945i | 0.898500 | + | 0.438973i | \(0.144658\pi\) | ||||
−0.898500 | + | 0.438973i | \(0.855342\pi\) | |||||||
\(338\) | 381325.i | 0.181553i | ||||||||
\(339\) | 2.92437e6 | 1.38208 | ||||||||
\(340\) | 208224. | − | 97024.5i | 0.0976862 | − | 0.0455181i | ||||
\(341\) | −1.56496e6 | −0.728816 | ||||||||
\(342\) | − | 739272.i | − | 0.341774i | ||||||
\(343\) | − | 2.35743e6i | − | 1.08194i | ||||||
\(344\) | 3.34747e6 | 1.52518 | ||||||||
\(345\) | 343913. | + | 738070.i | 0.155561 | + | 0.333849i | ||||
\(346\) | −1.28018e6 | −0.574883 | ||||||||
\(347\) | 1.81015e6i | 0.807030i | 0.914973 | + | 0.403515i | \(0.132212\pi\) | ||||
−0.914973 | + | 0.403515i | \(0.867788\pi\) | |||||||
\(348\) | − | 2.84393e6i | − | 1.25884i | ||||||
\(349\) | −1.63329e6 | −0.717793 | −0.358896 | − | 0.933377i | \(-0.616847\pi\) | ||||
−0.358896 | + | 0.933377i | \(0.616847\pi\) | |||||||
\(350\) | −623591. | + | 742310.i | −0.272101 | + | 0.323903i | ||||
\(351\) | 3.74430e6 | 1.62219 | ||||||||
\(352\) | − | 1.03610e6i | − | 0.445704i | ||||||
\(353\) | − | 833243.i | − | 0.355906i | −0.984039 | − | 0.177953i | \(-0.943053\pi\) | ||
0.984039 | − | 0.177953i | \(-0.0569475\pi\) | |||||||
\(354\) | 43707.0 | 0.0185371 | ||||||||
\(355\) | −442804. | − | 950299.i | −0.186483 | − | 0.400212i | ||||
\(356\) | 1.65868e6 | 0.693644 | ||||||||
\(357\) | − | 505034.i | − | 0.209725i | ||||||
\(358\) | − | 260701.i | − | 0.107507i | ||||||
\(359\) | 636036. | 0.260463 | 0.130231 | − | 0.991484i | \(-0.458428\pi\) | ||||
0.130231 | + | 0.991484i | \(0.458428\pi\) | |||||||
\(360\) | 4.43243e6 | − | 2.06534e6i | 1.80254 | − | 0.839917i | ||||
\(361\) | −2.26646e6 | −0.915334 | ||||||||
\(362\) | 1.20063e6i | 0.481546i | ||||||||
\(363\) | − | 3.61066e6i | − | 1.43820i | ||||||
\(364\) | 1.09680e6 | 0.433885 | ||||||||
\(365\) | −2.01195e6 | + | 937491.i | −0.790468 | + | 0.368328i | ||||
\(366\) | −2.70351e6 | −1.05493 | ||||||||
\(367\) | − | 372220.i | − | 0.144256i | −0.997395 | − | 0.0721282i | \(-0.977021\pi\) | ||
0.997395 | − | 0.0721282i | \(-0.0229791\pi\) | |||||||
\(368\) | − | 93904.8i | − | 0.0361467i | ||||||
\(369\) | −493071. | −0.188514 | ||||||||
\(370\) | 398071. | + | 854298.i | 0.151167 | + | 0.324418i | ||||
\(371\) | 1.54505e6 | 0.582785 | ||||||||
\(372\) | 5.52474e6i | 2.06992i | ||||||||
\(373\) | − | 18520.2i | − | 0.00689245i | −0.999994 | − | 0.00344622i | \(-0.998903\pi\) | ||
0.999994 | − | 0.00344622i | \(-0.00109697\pi\) | |||||||
\(374\) | −100453. | −0.0371349 | ||||||||
\(375\) | 1.24892e6 | − | 4.64519e6i | 0.458622 | − | 1.70579i | ||||
\(376\) | −3.83465e6 | −1.39880 | ||||||||
\(377\) | − | 2.32684e6i | − | 0.843167i | ||||||
\(378\) | − | 2.32496e6i | − | 0.836925i | ||||||
\(379\) | −4.32941e6 | −1.54821 | −0.774106 | − | 0.633056i | \(-0.781800\pi\) | ||||
−0.774106 | + | 0.633056i | \(0.781800\pi\) | |||||||
\(380\) | 239750. | + | 514526.i | 0.0851724 | + | 0.182788i | ||||
\(381\) | −8.13410e6 | −2.87076 | ||||||||
\(382\) | 2.84074e6i | 0.996031i | ||||||||
\(383\) | 3.16493e6i | 1.10247i | 0.834350 | + | 0.551235i | \(0.185843\pi\) | ||||
−0.834350 | + | 0.551235i | \(0.814157\pi\) | |||||||
\(384\) | −4.14794e6 | −1.43550 | ||||||||
\(385\) | −867600. | + | 404269.i | −0.298310 | + | 0.139001i | ||||
\(386\) | −1.90979e6 | −0.652406 | ||||||||
\(387\) | 1.01564e7i | 3.44716i | ||||||||
\(388\) | 1.03853e6i | 0.350219i | ||||||||
\(389\) | 2.47737e6 | 0.830074 | 0.415037 | − | 0.909804i | \(-0.363769\pi\) | ||||
0.415037 | + | 0.909804i | \(0.363769\pi\) | |||||||
\(390\) | 2.18473e6 | − | 1.01800e6i | 0.727338 | − | 0.338912i | ||||
\(391\) | −98020.6 | −0.0324247 | ||||||||
\(392\) | 1.19006e6i | 0.391160i | ||||||||
\(393\) | − | 2.08083e6i | − | 0.679603i | ||||||
\(394\) | 2.16359e6 | 0.702158 | ||||||||
\(395\) | 497596. | + | 1.06789e6i | 0.160466 | + | 0.344377i | ||||
\(396\) | 1.97628e6 | 0.633303 | ||||||||
\(397\) | − | 1.98642e6i | − | 0.632550i | −0.948667 | − | 0.316275i | \(-0.897568\pi\) | ||
0.948667 | − | 0.316275i | \(-0.102432\pi\) | |||||||
\(398\) | 371970.i | 0.117706i | ||||||||
\(399\) | 1.24795e6 | 0.392433 | ||||||||
\(400\) | −356815. | + | 424746.i | −0.111505 | + | 0.132733i | ||||
\(401\) | −3.05157e6 | −0.947681 | −0.473840 | − | 0.880611i | \(-0.657133\pi\) | ||||
−0.473840 | + | 0.880611i | \(0.657133\pi\) | |||||||
\(402\) | 3.77029e6i | 1.16361i | ||||||||
\(403\) | 4.52022e6i | 1.38643i | ||||||||
\(404\) | 2.75782e6 | 0.840643 | ||||||||
\(405\) | 1.91640e6 | + | 4.11278e6i | 0.580562 | + | 1.24594i | ||||
\(406\) | −1.44482e6 | −0.435008 | ||||||||
\(407\) | 930517.i | 0.278444i | ||||||||
\(408\) | 866318.i | 0.257648i | ||||||||
\(409\) | 1.54349e6 | 0.456243 | 0.228122 | − | 0.973633i | \(-0.426742\pi\) | ||||
0.228122 | + | 0.973633i | \(0.426742\pi\) | |||||||
\(410\) | −151995. | + | 70823.7i | −0.0446548 | + | 0.0208075i | ||||
\(411\) | 1.10222e7 | 3.21858 | ||||||||
\(412\) | 3.66436e6i | 1.06354i | ||||||||
\(413\) | 50133.6i | 0.0144628i | ||||||||
\(414\) | −854125. | −0.244918 | ||||||||
\(415\) | −2.99998e6 | + | 1.39788e6i | −0.855063 | + | 0.398427i | ||||
\(416\) | −2.99268e6 | −0.847865 | ||||||||
\(417\) | − | 1.82754e6i | − | 0.514669i | ||||||
\(418\) | − | 248221.i | − | 0.0694860i | ||||||
\(419\) | −782997. | −0.217884 | −0.108942 | − | 0.994048i | \(-0.534746\pi\) | ||||
−0.108942 | + | 0.994048i | \(0.534746\pi\) | |||||||
\(420\) | 1.42718e6 | + | 3.06286e6i | 0.394780 | + | 0.847236i | ||||
\(421\) | −1.89001e6 | −0.519707 | −0.259854 | − | 0.965648i | \(-0.583674\pi\) | ||||
−0.259854 | + | 0.965648i | \(0.583674\pi\) | |||||||
\(422\) | 3.70937e6i | 1.01395i | ||||||||
\(423\) | − | 1.16345e7i | − | 3.16152i | ||||||
\(424\) | −2.65033e6 | −0.715954 | ||||||||
\(425\) | 443362. | + | 372454.i | 0.119066 | + | 0.100023i | ||||
\(426\) | 1.61845e6 | 0.432091 | ||||||||
\(427\) | − | 3.10103e6i | − | 0.823069i | ||||||
\(428\) | 3.02393e6i | 0.797925i | ||||||||
\(429\) | 2.37965e6 | 0.624266 | ||||||||
\(430\) | 1.45884e6 | + | 3.13081e6i | 0.380484 | + | 0.816556i | ||||
\(431\) | 1.47121e6 | 0.381489 | 0.190745 | − | 0.981640i | \(-0.438910\pi\) | ||||
0.190745 | + | 0.981640i | \(0.438910\pi\) | |||||||
\(432\) | − | 1.33033e6i | − | 0.342966i | ||||||
\(433\) | 1638.32i | 0.000419931i | 1.00000 | 0.000209966i | \(6.68341e-5\pi\) | |||||
−1.00000 | 0.000209966i | \(0.999933\pi\) | ||||||||
\(434\) | 2.80676e6 | 0.715289 | ||||||||
\(435\) | 6.49780e6 | − | 3.02773e6i | 1.64643 | − | 0.767174i | ||||
\(436\) | −4.95173e6 | −1.24750 | ||||||||
\(437\) | − | 242211.i | − | 0.0606723i | ||||||
\(438\) | − | 3.42654e6i | − | 0.853435i | ||||||
\(439\) | 6.97689e6 | 1.72783 | 0.863914 | − | 0.503640i | \(-0.168006\pi\) | ||||
0.863914 | + | 0.503640i | \(0.168006\pi\) | |||||||
\(440\) | 1.48825e6 | − | 693468.i | 0.366475 | − | 0.170763i | ||||
\(441\) | −3.61069e6 | −0.884085 | ||||||||
\(442\) | 290147.i | 0.0706418i | ||||||||
\(443\) | − | 3.49744e6i | − | 0.846723i | −0.905961 | − | 0.423361i | \(-0.860850\pi\) | ||
0.905961 | − | 0.423361i | \(-0.139150\pi\) | |||||||
\(444\) | 3.28498e6 | 0.790816 | ||||||||
\(445\) | 1.76588e6 | + | 3.78974e6i | 0.422727 | + | 0.907213i | ||||
\(446\) | 4.31740e6 | 1.02774 | ||||||||
\(447\) | − | 5.00057e6i | − | 1.18372i | ||||||
\(448\) | 1.29597e6i | 0.305070i | ||||||||
\(449\) | 4.00137e6 | 0.936684 | 0.468342 | − | 0.883547i | \(-0.344851\pi\) | ||||
0.468342 | + | 0.883547i | \(0.344851\pi\) | |||||||
\(450\) | 3.86334e6 | + | 3.24546e6i | 0.899355 | + | 0.755519i | ||||
\(451\) | −165555. | −0.0383267 | ||||||||
\(452\) | − | 2.35537e6i | − | 0.542267i | ||||||
\(453\) | − | 4.94019e6i | − | 1.13109i | ||||||
\(454\) | −3.59889e6 | −0.819463 | ||||||||
\(455\) | 1.16769e6 | + | 2.50597e6i | 0.264422 | + | 0.567476i | ||||
\(456\) | −2.14069e6 | −0.482105 | ||||||||
\(457\) | 4.37124e6i | 0.979072i | 0.871983 | + | 0.489536i | \(0.162834\pi\) | ||||
−0.871983 | + | 0.489536i | \(0.837166\pi\) | |||||||
\(458\) | − | 538482.i | − | 0.119952i | ||||||
\(459\) | −1.38864e6 | −0.307651 | ||||||||
\(460\) | 594463. | − | 276997.i | 0.130988 | − | 0.0610352i | ||||
\(461\) | 1.70022e6 | 0.372610 | 0.186305 | − | 0.982492i | \(-0.440349\pi\) | ||||
0.186305 | + | 0.982492i | \(0.440349\pi\) | |||||||
\(462\) | − | 1.47761e6i | − | 0.322073i | ||||||
\(463\) | − | 5.77097e6i | − | 1.25111i | −0.780179 | − | 0.625557i | \(-0.784872\pi\) | ||
0.780179 | − | 0.625557i | \(-0.215128\pi\) | |||||||
\(464\) | −826717. | −0.178263 | ||||||||
\(465\) | −1.26229e7 | + | 5.88180e6i | −2.70724 | + | 1.26147i | ||||
\(466\) | 2.04240e6 | 0.435689 | ||||||||
\(467\) | − | 3.25780e6i | − | 0.691246i | −0.938373 | − | 0.345623i | \(-0.887668\pi\) | ||
0.938373 | − | 0.345623i | \(-0.112332\pi\) | |||||||
\(468\) | − | 5.70828e6i | − | 1.20473i | ||||||
\(469\) | −4.32466e6 | −0.907863 | ||||||||
\(470\) | −1.67115e6 | − | 3.58646e6i | −0.348957 | − | 0.748895i | ||||
\(471\) | 1.58113e7 | 3.28408 | ||||||||
\(472\) | − | 85997.4i | − | 0.0177677i | ||||||
\(473\) | 3.41014e6i | 0.700841i | ||||||||
\(474\) | −1.81872e6 | −0.371809 | ||||||||
\(475\) | −920343. | + | 1.09556e6i | −0.187161 | + | 0.222793i | ||||
\(476\) | −406769. | −0.0822868 | ||||||||
\(477\) | − | 8.04120e6i | − | 1.61817i | ||||||
\(478\) | 4.81783e6i | 0.964454i | ||||||||
\(479\) | 5.35349e6 | 1.06610 | 0.533051 | − | 0.846083i | \(-0.321045\pi\) | ||||
0.533051 | + | 0.846083i | \(0.321045\pi\) | |||||||
\(480\) | −3.89413e6 | − | 8.35717e6i | −0.771448 | − | 1.65560i | ||||
\(481\) | 2.68770e6 | 0.529685 | ||||||||
\(482\) | 2.86236e6i | 0.561185i | ||||||||
\(483\) | − | 1.44183e6i | − | 0.281220i | ||||||
\(484\) | −2.90813e6 | −0.564287 | ||||||||
\(485\) | −2.37283e6 | + | 1.10565e6i | −0.458050 | + | 0.213434i | ||||
\(486\) | −1.29694e6 | −0.249074 | ||||||||
\(487\) | − | 3.94606e6i | − | 0.753948i | −0.926224 | − | 0.376974i | \(-0.876965\pi\) | ||
0.926224 | − | 0.376974i | \(-0.123035\pi\) | |||||||
\(488\) | 5.31940e6i | 1.01114i | ||||||||
\(489\) | 4.33107e6 | 0.819073 | ||||||||
\(490\) | −1.11304e6 | + | 518633.i | −0.209421 | + | 0.0975821i | ||||
\(491\) | −4.46612e6 | −0.836038 | −0.418019 | − | 0.908438i | \(-0.637276\pi\) | ||||
−0.418019 | + | 0.908438i | \(0.637276\pi\) | |||||||
\(492\) | 584455.i | 0.108853i | ||||||||
\(493\) | 862951.i | 0.159908i | ||||||||
\(494\) | −716959. | −0.132183 | ||||||||
\(495\) | 2.10401e6 | + | 4.51541e6i | 0.385953 | + | 0.828293i | ||||
\(496\) | 1.60601e6 | 0.293120 | ||||||||
\(497\) | 1.85642e6i | 0.337121i | ||||||||
\(498\) | − | 5.10925e6i | − | 0.923175i | ||||||
\(499\) | −421495. | −0.0757777 | −0.0378889 | − | 0.999282i | \(-0.512063\pi\) | ||||
−0.0378889 | + | 0.999282i | \(0.512063\pi\) | |||||||
\(500\) | −3.74137e6 | − | 1.00591e6i | −0.669276 | − | 0.179943i | ||||
\(501\) | −4.13633e6 | −0.736242 | ||||||||
\(502\) | 1.35646e6i | 0.240241i | ||||||||
\(503\) | − | 165744.i | − | 0.0292090i | −0.999893 | − | 0.0146045i | \(-0.995351\pi\) | ||
0.999893 | − | 0.0146045i | \(-0.00464892\pi\) | |||||||
\(504\) | −8.65882e6 | −1.51839 | ||||||||
\(505\) | 2.93605e6 | + | 6.30105e6i | 0.512312 | + | 1.09947i | ||||
\(506\) | −286784. | −0.0497942 | ||||||||
\(507\) | 3.35017e6i | 0.578824i | ||||||||
\(508\) | 6.55143e6i | 1.12636i | ||||||||
\(509\) | 2.54136e6 | 0.434782 | 0.217391 | − | 0.976085i | \(-0.430245\pi\) | ||||
0.217391 | + | 0.976085i | \(0.430245\pi\) | |||||||
\(510\) | −810246. | + | 377544.i | −0.137940 | + | 0.0642750i | ||||
\(511\) | 3.93037e6 | 0.665857 | ||||||||
\(512\) | 2.02781e6i | 0.341863i | ||||||||
\(513\) | − | 3.43136e6i | − | 0.575669i | ||||||
\(514\) | 4.50796e6 | 0.752614 | ||||||||
\(515\) | −8.37232e6 | + | 3.90118e6i | −1.39100 | + | 0.648154i | ||||
\(516\) | 1.20387e7 | 1.99047 | ||||||||
\(517\) | − | 3.90643e6i | − | 0.642768i | ||||||
\(518\) | − | 1.66889e6i | − | 0.273276i | ||||||
\(519\) | −1.12471e7 | −1.83283 | ||||||||
\(520\) | −2.00301e6 | − | 4.29865e6i | −0.324844 | − | 0.697146i | ||||
\(521\) | −1.00488e7 | −1.62189 | −0.810944 | − | 0.585124i | \(-0.801046\pi\) | ||||
−0.810944 | + | 0.585124i | \(0.801046\pi\) | |||||||
\(522\) | 7.51952e6i | 1.20785i | ||||||||
\(523\) | − | 5.25311e6i | − | 0.839774i | −0.907576 | − | 0.419887i | \(-0.862070\pi\) | ||
0.907576 | − | 0.419887i | \(-0.137930\pi\) | |||||||
\(524\) | −1.67596e6 | −0.266646 | ||||||||
\(525\) | −5.47861e6 | + | 6.52163e6i | −0.867505 | + | 1.03266i | ||||
\(526\) | −540803. | −0.0852265 | ||||||||
\(527\) | − | 1.67641e6i | − | 0.262937i | ||||||
\(528\) | − | 845479.i | − | 0.131983i | ||||||
\(529\) | −279841. | −0.0434783 | ||||||||
\(530\) | −1.15502e6 | − | 2.47879e6i | −0.178608 | − | 0.383310i | ||||
\(531\) | 260919. | 0.0401578 | ||||||||
\(532\) | − | 1.00513e6i | − | 0.153973i | ||||||
\(533\) | 478189.i | 0.0729090i | ||||||||
\(534\) | −6.45429e6 | −0.979479 | ||||||||
\(535\) | −6.90906e6 | + | 3.21936e6i | −1.04360 | + | 0.486278i | ||||
\(536\) | 7.41837e6 | 1.11531 | ||||||||
\(537\) | − | 2.29042e6i | − | 0.342751i | ||||||
\(538\) | 761609.i | 0.113443i | ||||||||
\(539\) | −1.21234e6 | −0.179743 | ||||||||
\(540\) | 8.42164e6 | − | 3.92416e6i | 1.24283 | − | 0.579112i | ||||
\(541\) | 4.45549e6 | 0.654489 | 0.327244 | − | 0.944940i | \(-0.393880\pi\) | ||||
0.327244 | + | 0.944940i | \(0.393880\pi\) | |||||||
\(542\) | − | 6.80000e6i | − | 0.994285i | ||||||
\(543\) | 1.05482e7i | 1.53526i | ||||||||
\(544\) | 1.10989e6 | 0.160798 | ||||||||
\(545\) | −5.27175e6 | − | 1.13137e7i | −0.760263 | − | 1.63160i | ||||
\(546\) | −4.26791e6 | −0.612679 | ||||||||
\(547\) | 2.77840e6i | 0.397033i | 0.980098 | + | 0.198516i | \(0.0636123\pi\) | ||||
−0.980098 | + | 0.198516i | \(0.936388\pi\) | |||||||
\(548\) | − | 8.87759e6i | − | 1.26283i | ||||||
\(549\) | −1.61393e7 | −2.28535 | ||||||||
\(550\) | 1.29717e6 | + | 1.08971e6i | 0.182848 | + | 0.153605i | ||||
\(551\) | −2.13237e6 | −0.299215 | ||||||||
\(552\) | 2.47327e6i | 0.345480i | ||||||||
\(553\) | − | 2.08614e6i | − | 0.290089i | ||||||
\(554\) | 2.69111e6 | 0.372527 | ||||||||
\(555\) | 3.49728e6 | + | 7.50551e6i | 0.481946 | + | 1.03430i | ||||
\(556\) | −1.47196e6 | −0.201933 | ||||||||
\(557\) | 1.26464e7i | 1.72715i | 0.504220 | + | 0.863575i | \(0.331780\pi\) | ||||
−0.504220 | + | 0.863575i | \(0.668220\pi\) | |||||||
\(558\) | − | 1.46077e7i | − | 1.98608i | ||||||
\(559\) | 9.84982e6 | 1.33321 | ||||||||
\(560\) | 890360. | − | 414874.i | 0.119976 | − | 0.0559044i | ||||
\(561\) | −882535. | −0.118393 | ||||||||
\(562\) | 7.20255e6i | 0.961935i | ||||||||
\(563\) | − | 3.99645e6i | − | 0.531377i | −0.964059 | − | 0.265689i | \(-0.914401\pi\) | ||
0.964059 | − | 0.265689i | \(-0.0855993\pi\) | |||||||
\(564\) | −1.37908e7 | −1.82554 | ||||||||
\(565\) | 5.38155e6 | − | 2.50760e6i | 0.709228 | − | 0.330473i | ||||
\(566\) | −1.19759e6 | −0.157132 | ||||||||
\(567\) | − | 8.03438e6i | − | 1.04953i | ||||||
\(568\) | − | 3.18444e6i | − | 0.414155i | ||||||
\(569\) | 1.09077e6 | 0.141238 | 0.0706191 | − | 0.997503i | \(-0.477503\pi\) | ||||
0.0706191 | + | 0.997503i | \(0.477503\pi\) | |||||||
\(570\) | −932920. | − | 2.00214e6i | −0.120270 | − | 0.258111i | ||||
\(571\) | 226191. | 0.0290325 | 0.0145162 | − | 0.999895i | \(-0.495379\pi\) | ||||
0.0145162 | + | 0.999895i | \(0.495379\pi\) | |||||||
\(572\) | − | 1.91664e6i | − | 0.244934i | ||||||
\(573\) | 2.49576e7i | 3.17553i | ||||||||
\(574\) | 296924. | 0.0376154 | ||||||||
\(575\) | 1.26576e6 | + | 1.06333e6i | 0.159655 | + | 0.134121i | ||||
\(576\) | 6.74485e6 | 0.847064 | ||||||||
\(577\) | − | 3.28573e6i | − | 0.410858i | −0.978672 | − | 0.205429i | \(-0.934141\pi\) | ||
0.978672 | − | 0.205429i | \(-0.0658590\pi\) | |||||||
\(578\) | 4.34237e6i | 0.540639i | ||||||||
\(579\) | −1.67786e7 | −2.07999 | ||||||||
\(580\) | −2.43862e6 | − | 5.23351e6i | −0.301005 | − | 0.645986i | ||||
\(581\) | 5.86051e6 | 0.720269 | ||||||||
\(582\) | − | 4.04116e6i | − | 0.494537i | ||||||
\(583\) | − | 2.69994e6i | − | 0.328991i | ||||||
\(584\) | −6.74202e6 | −0.818008 | ||||||||
\(585\) | 1.30423e7 | − | 6.07720e6i | 1.57566 | − | 0.734199i | ||||
\(586\) | 13252.5 | 0.00159424 | ||||||||
\(587\) | 7.43016e6i | 0.890027i | 0.895524 | + | 0.445013i | \(0.146801\pi\) | ||||
−0.895524 | + | 0.445013i | \(0.853199\pi\) | |||||||
\(588\) | 4.27989e6i | 0.510493i | ||||||||
\(589\) | 4.14244e6 | 0.492003 | ||||||||
\(590\) | 80431.3 | − | 37478.0i | 0.00951251 | − | 0.00443247i | ||||
\(591\) | 1.90084e7 | 2.23860 | ||||||||
\(592\) | − | 954928.i | − | 0.111987i | ||||||
\(593\) | − | 8.97683e6i | − | 1.04830i | −0.851626 | − | 0.524151i | \(-0.824383\pi\) | ||
0.851626 | − | 0.524151i | \(-0.175617\pi\) | |||||||
\(594\) | −4.06282e6 | −0.472456 | ||||||||
\(595\) | −433058. | − | 929384.i | −0.0501480 | − | 0.107622i | ||||
\(596\) | −4.02760e6 | −0.464441 | ||||||||
\(597\) | 3.26797e6i | 0.375269i | ||||||||
\(598\) | 828345.i | 0.0947237i | ||||||||
\(599\) | 1.40377e7 | 1.59856 | 0.799280 | − | 0.600959i | \(-0.205215\pi\) | ||||
0.799280 | + | 0.600959i | \(0.205215\pi\) | |||||||
\(600\) | 9.39781e6 | − | 1.11870e7i | 1.06573 | − | 1.26863i | ||||
\(601\) | 9.15574e6 | 1.03397 | 0.516984 | − | 0.855995i | \(-0.327055\pi\) | ||||
0.516984 | + | 0.855995i | \(0.327055\pi\) | |||||||
\(602\) | − | 6.11610e6i | − | 0.687833i | ||||||
\(603\) | 2.25076e7i | 2.52079i | ||||||||
\(604\) | −3.97897e6 | −0.443790 | ||||||||
\(605\) | −3.09608e6 | − | 6.64448e6i | −0.343893 | − | 0.738028i | ||||
\(606\) | −1.07313e7 | −1.18705 | ||||||||
\(607\) | − | 7.53570e6i | − | 0.830141i | −0.909789 | − | 0.415070i | \(-0.863757\pi\) | ||
0.909789 | − | 0.415070i | \(-0.136243\pi\) | |||||||
\(608\) | 2.74256e6i | 0.300882i | ||||||||
\(609\) | −1.26936e7 | −1.38688 | ||||||||
\(610\) | −4.97511e6 | + | 2.31821e6i | −0.541350 | + | 0.252248i | ||||
\(611\) | −1.12833e7 | −1.22274 | ||||||||
\(612\) | 2.11702e6i | 0.228479i | ||||||||
\(613\) | − | 9.98554e6i | − | 1.07330i | −0.843805 | − | 0.536649i | \(-0.819690\pi\) | ||
0.843805 | − | 0.536649i | \(-0.180310\pi\) | |||||||
\(614\) | −1.42539e6 | −0.152585 | ||||||||
\(615\) | −1.33536e6 | + | 622228.i | −0.142368 | + | 0.0663379i | ||||
\(616\) | −2.90732e6 | −0.308703 | ||||||||
\(617\) | − | 6.82945e6i | − | 0.722226i | −0.932522 | − | 0.361113i | \(-0.882397\pi\) | ||
0.932522 | − | 0.361113i | \(-0.117603\pi\) | |||||||
\(618\) | − | 1.42589e7i | − | 1.50181i | ||||||
\(619\) | 9.08935e6 | 0.953468 | 0.476734 | − | 0.879047i | \(-0.341820\pi\) | ||||
0.476734 | + | 0.879047i | \(0.341820\pi\) | |||||||
\(620\) | 4.73736e6 | + | 1.01668e7i | 0.494946 | + | 1.06220i | ||||
\(621\) | −3.96445e6 | −0.412529 | ||||||||
\(622\) | − | 9.09330e6i | − | 0.942422i | ||||||
\(623\) | − | 7.40332e6i | − | 0.764199i | ||||||
\(624\) | −2.44207e6 | −0.251071 | ||||||||
\(625\) | −1.68486e6 | − | 9.61918e6i | −0.172530 | − | 0.985004i | ||||
\(626\) | 8.09161e6 | 0.825276 | ||||||||
\(627\) | − | 2.18076e6i | − | 0.221534i | ||||||
\(628\) | − | 1.27348e7i | − | 1.28853i | ||||||
\(629\) | −996781. | −0.100455 | ||||||||
\(630\) | −3.77354e6 | − | 8.09839e6i | −0.378790 | − | 0.812920i | ||||
\(631\) | 5.93201e6 | 0.593100 | 0.296550 | − | 0.955017i | \(-0.404164\pi\) | ||||
0.296550 | + | 0.955017i | \(0.404164\pi\) | |||||||
\(632\) | 3.57849e6i | 0.356375i | ||||||||
\(633\) | 3.25890e7i | 3.23267i | ||||||||
\(634\) | 6.49862e6 | 0.642093 | ||||||||
\(635\) | −1.49687e7 | + | 6.97484e6i | −1.47316 | + | 0.686436i | ||||
\(636\) | −9.53154e6 | −0.934373 | ||||||||
\(637\) | 3.50172e6i | 0.341926i | ||||||||
\(638\) | 2.52478e6i | 0.245568i | ||||||||
\(639\) | 9.66173e6 | 0.936058 | ||||||||
\(640\) | −7.63320e6 | + | 3.55678e6i | −0.736642 | + | 0.343247i | ||||
\(641\) | −1.20892e7 | −1.16212 | −0.581062 | − | 0.813859i | \(-0.697363\pi\) | ||||
−0.581062 | + | 0.813859i | \(0.697363\pi\) | |||||||
\(642\) | − | 1.17668e7i | − | 1.12673i | ||||||
\(643\) | 1.09118e7i | 1.04081i | 0.853920 | + | 0.520404i | \(0.174219\pi\) | ||||
−0.853920 | + | 0.520404i | \(0.825781\pi\) | |||||||
\(644\) | −1.16129e6 | −0.110338 | ||||||||
\(645\) | 1.28168e7 | + | 2.75060e7i | 1.21305 | + | 2.60333i | ||||
\(646\) | 265897. | 0.0250687 | ||||||||
\(647\) | 8.06391e6i | 0.757330i | 0.925534 | + | 0.378665i | \(0.123617\pi\) | ||||
−0.925534 | + | 0.378665i | \(0.876383\pi\) | |||||||
\(648\) | 1.37819e7i | 1.28935i | ||||||||
\(649\) | 87607.3 | 0.00816448 | ||||||||
\(650\) | 3.14751e6 | − | 3.74673e6i | 0.292202 | − | 0.347832i | ||||
\(651\) | 2.46590e7 | 2.28047 | ||||||||
\(652\) | − | 3.48836e6i | − | 0.321368i | ||||||
\(653\) | 897296.i | 0.0823479i | 0.999152 | + | 0.0411740i | \(0.0131098\pi\) | ||||
−0.999152 | + | 0.0411740i | \(0.986890\pi\) | |||||||
\(654\) | 1.92683e7 | 1.76157 | ||||||||
\(655\) | −1.78427e6 | − | 3.82923e6i | −0.162502 | − | 0.348745i | ||||
\(656\) | 169898. | 0.0154145 | ||||||||
\(657\) | − | 2.04555e7i | − | 1.84883i | ||||||
\(658\) | 7.00620e6i | 0.630838i | ||||||||
\(659\) | −1.32258e6 | −0.118634 | −0.0593168 | − | 0.998239i | \(-0.518892\pi\) | ||||
−0.0593168 | + | 0.998239i | \(0.518892\pi\) | |||||||
\(660\) | 5.35228e6 | − | 2.49396e6i | 0.478277 | − | 0.222859i | ||||
\(661\) | −1.38914e7 | −1.23663 | −0.618317 | − | 0.785929i | \(-0.712185\pi\) | ||||
−0.618317 | + | 0.785929i | \(0.712185\pi\) | |||||||
\(662\) | 1.03651e7i | 0.919243i | ||||||||
\(663\) | 2.54911e6i | 0.225219i | ||||||||
\(664\) | −1.00529e7 | −0.884853 | ||||||||
\(665\) | 2.29653e6 | − | 1.07009e6i | 0.201381 | − | 0.0938357i | ||||
\(666\) | −8.68568e6 | −0.758784 | ||||||||
\(667\) | 2.46366e6i | 0.214420i | ||||||||
\(668\) | 3.33151e6i | 0.288869i | ||||||||
\(669\) | 3.79309e7 | 3.27663 | ||||||||
\(670\) | 3.23295e6 | + | 6.93823e6i | 0.278235 | + | 0.597120i | ||||
\(671\) | −5.41898e6 | −0.464634 | ||||||||
\(672\) | 1.63259e7i | 1.39461i | ||||||||
\(673\) | − | 1.38217e7i | − | 1.17632i | −0.808745 | − | 0.588159i | \(-0.799853\pi\) | ||
0.808745 | − | 0.588159i | \(-0.200147\pi\) | |||||||
\(674\) | −5.73661e6 | −0.486414 | ||||||||
\(675\) | 1.79318e7 | + | 1.50640e7i | 1.51483 | + | 1.27256i | ||||
\(676\) | 2.69832e6 | 0.227105 | ||||||||
\(677\) | − | 4.26668e6i | − | 0.357782i | −0.983869 | − | 0.178891i | \(-0.942749\pi\) | ||
0.983869 | − | 0.178891i | \(-0.0572509\pi\) | |||||||
\(678\) | 9.16529e6i | 0.765723i | ||||||||
\(679\) | 4.63536e6 | 0.385842 | ||||||||
\(680\) | 742851. | + | 1.59423e6i | 0.0616069 | + | 0.132215i | ||||
\(681\) | −3.16184e7 | −2.61259 | ||||||||
\(682\) | − | 4.90475e6i | − | 0.403790i | ||||||
\(683\) | − | 1.34750e6i | − | 0.110529i | −0.998472 | − | 0.0552646i | \(-0.982400\pi\) | ||
0.998472 | − | 0.0552646i | \(-0.0176002\pi\) | |||||||
\(684\) | −5.23120e6 | −0.427525 | ||||||||
\(685\) | 2.02835e7 | − | 9.45134e6i | 1.65164 | − | 0.769603i | ||||
\(686\) | 7.38843e6 | 0.599434 | ||||||||
\(687\) | − | 4.73088e6i | − | 0.382429i | ||||||
\(688\) | − | 3.49960e6i | − | 0.281869i | ||||||
\(689\) | −7.79850e6 | −0.625839 | ||||||||
\(690\) | −2.31319e6 | + | 1.07786e6i | −0.184964 | + | 0.0861864i | ||||
\(691\) | −1.29881e7 | −1.03478 | −0.517392 | − | 0.855748i | \(-0.673097\pi\) | ||||
−0.517392 | + | 0.855748i | \(0.673097\pi\) | |||||||
\(692\) | 9.05873e6i | 0.719121i | ||||||||
\(693\) | − | 8.82092e6i | − | 0.697719i | ||||||
\(694\) | −5.67318e6 | −0.447124 | ||||||||
\(695\) | −1.56709e6 | − | 3.36312e6i | −0.123064 | − | 0.264107i | ||||
\(696\) | 2.17741e7 | 1.70379 | ||||||||
\(697\) | − | 177345.i | − | 0.0138273i | ||||||
\(698\) | − | 5.11889e6i | − | 0.397683i | ||||||
\(699\) | 1.79437e7 | 1.38905 | ||||||||
\(700\) | 5.25270e6 | + | 4.41262e6i | 0.405170 | + | 0.340370i | ||||
\(701\) | −1.78237e7 | −1.36994 | −0.684970 | − | 0.728571i | \(-0.740185\pi\) | ||||
−0.684970 | + | 0.728571i | \(0.740185\pi\) | |||||||
\(702\) | 1.17350e7i | 0.898754i | ||||||||
\(703\) | − | 2.46307e6i | − | 0.187970i | ||||||
\(704\) | 2.26468e6 | 0.172216 | ||||||||
\(705\) | −1.46821e7 | − | 3.15091e7i | −1.11254 | − | 2.38761i | ||||
\(706\) | 2.61147e6 | 0.197185 | ||||||||
\(707\) | − | 1.23092e7i | − | 0.926150i | ||||||
\(708\) | − | 309278.i | − | 0.0231881i | ||||||
\(709\) | 1.38491e7 | 1.03468 | 0.517341 | − | 0.855779i | \(-0.326922\pi\) | ||||
0.517341 | + | 0.855779i | \(0.326922\pi\) | |||||||
\(710\) | 2.97834e6 | − | 1.38779e6i | 0.221732 | − | 0.103319i | ||||
\(711\) | −1.08573e7 | −0.805465 | ||||||||
\(712\) | 1.26994e7i | 0.938821i | ||||||||
\(713\) | − | 4.78600e6i | − | 0.352573i | ||||||
\(714\) | 1.58283e6 | 0.116195 | ||||||||
\(715\) | 4.37912e6 | − | 2.04051e6i | 0.320348 | − | 0.149270i | ||||
\(716\) | −1.84476e6 | −0.134480 | ||||||||
\(717\) | 4.23274e7i | 3.07485i | ||||||||
\(718\) | 1.99340e6i | 0.144306i | ||||||||
\(719\) | 6.39208e6 | 0.461126 | 0.230563 | − | 0.973057i | \(-0.425943\pi\) | ||||
0.230563 | + | 0.973057i | \(0.425943\pi\) | |||||||
\(720\) | −2.15920e6 | − | 4.63386e6i | −0.155225 | − | 0.333128i | ||||
\(721\) | 1.63555e7 | 1.17172 | ||||||||
\(722\) | − | 7.10331e6i | − | 0.507128i | ||||||
\(723\) | 2.51475e7i | 1.78916i | ||||||||
\(724\) | 8.49585e6 | 0.602366 | ||||||||
\(725\) | 9.36129e6 | − | 1.11435e7i | 0.661440 | − | 0.787366i | ||||
\(726\) | 1.13162e7 | 0.796817 | ||||||||
\(727\) | − | 9.15468e6i | − | 0.642403i | −0.947011 | − | 0.321201i | \(-0.895913\pi\) | ||
0.947011 | − | 0.321201i | \(-0.104087\pi\) | |||||||
\(728\) | 8.39748e6i | 0.587247i | ||||||||
\(729\) | 8.32912e6 | 0.580471 | ||||||||
\(730\) | −2.93819e6 | − | 6.30565e6i | −0.204067 | − | 0.437948i | ||||
\(731\) | −3.65298e6 | −0.252845 | ||||||||
\(732\) | 1.91305e7i | 1.31962i | ||||||||
\(733\) | − | 1.29905e7i | − | 0.893028i | −0.894777 | − | 0.446514i | \(-0.852665\pi\) | ||
0.894777 | − | 0.446514i | \(-0.147335\pi\) | |||||||
\(734\) | 1.16658e6 | 0.0799232 | ||||||||
\(735\) | −9.77868e6 | + | 4.55650e6i | −0.667670 | + | 0.311109i | ||||
\(736\) | 3.16864e6 | 0.215615 | ||||||||
\(737\) | 7.55725e6i | 0.512501i | ||||||||
\(738\) | − | 1.54533e6i | − | 0.104444i | ||||||
\(739\) | 3.98014e6 | 0.268094 | 0.134047 | − | 0.990975i | \(-0.457203\pi\) | ||||
0.134047 | + | 0.990975i | \(0.457203\pi\) | |||||||
\(740\) | 6.04515e6 | − | 2.81681e6i | 0.405815 | − | 0.189094i | ||||
\(741\) | −6.29890e6 | −0.421424 | ||||||||
\(742\) | 4.84236e6i | 0.322884i | ||||||||
\(743\) | − | 1.96581e6i | − | 0.130638i | −0.997864 | − | 0.0653192i | \(-0.979193\pi\) | ||
0.997864 | − | 0.0653192i | \(-0.0208065\pi\) | |||||||
\(744\) | −4.22992e7 | −2.80156 | ||||||||
\(745\) | −4.28790e6 | − | 9.20224e6i | −0.283044 | − | 0.607439i | ||||
\(746\) | 58044.2 | 0.00381867 | ||||||||
\(747\) | − | 3.05009e7i | − | 1.99991i | ||||||
\(748\) | 710819.i | 0.0464520i | ||||||||
\(749\) | 1.34970e7 | 0.879086 | ||||||||
\(750\) | 1.45585e7 | + | 3.91423e6i | 0.945069 | + | 0.254093i | ||||
\(751\) | 3.00617e6 | 0.194497 | 0.0972487 | − | 0.995260i | \(-0.468996\pi\) | ||||
0.0972487 | + | 0.995260i | \(0.468996\pi\) | |||||||
\(752\) | 4.00891e6i | 0.258513i | ||||||||
\(753\) | 1.19173e7i | 0.765931i | ||||||||
\(754\) | 7.29256e6 | 0.467145 | ||||||||
\(755\) | −4.23612e6 | − | 9.09113e6i | −0.270459 | − | 0.580431i | ||||
\(756\) | −1.64518e7 | −1.04691 | ||||||||
\(757\) | − | 8.54036e6i | − | 0.541672i | −0.962626 | − | 0.270836i | \(-0.912700\pi\) | ||
0.962626 | − | 0.270836i | \(-0.0873001\pi\) | |||||||
\(758\) | − | 1.35688e7i | − | 0.857766i | ||||||
\(759\) | −2.51957e6 | −0.158753 | ||||||||
\(760\) | −3.93938e6 | + | 1.83560e6i | −0.247397 | + | 0.115278i | ||||
\(761\) | −4.00401e6 | −0.250630 | −0.125315 | − | 0.992117i | \(-0.539994\pi\) | ||||
−0.125315 | + | 0.992117i | \(0.539994\pi\) | |||||||
\(762\) | − | 2.54931e7i | − | 1.59051i | ||||||
\(763\) | 2.21015e7i | 1.37439i | ||||||||
\(764\) | 2.01015e7 | 1.24594 | ||||||||
\(765\) | −4.83696e6 | + | 2.25384e6i | −0.298826 | + | 0.139242i | ||||
\(766\) | −9.91921e6 | −0.610809 | ||||||||
\(767\) | − | 253044.i | − | 0.0155313i | ||||||
\(768\) | − | 2.45360e7i | − | 1.50107i | ||||||
\(769\) | 3.19689e6 | 0.194945 | 0.0974725 | − | 0.995238i | \(-0.468924\pi\) | ||||
0.0974725 | + | 0.995238i | \(0.468924\pi\) | |||||||
\(770\) | −1.26702e6 | − | 2.71915e6i | −0.0770117 | − | 0.165275i | ||||
\(771\) | 3.96051e7 | 2.39947 | ||||||||
\(772\) | 1.35140e7i | 0.816094i | ||||||||
\(773\) | 1.56246e7i | 0.940503i | 0.882532 | + | 0.470251i | \(0.155837\pi\) | ||||
−0.882532 | + | 0.470251i | \(0.844163\pi\) | |||||||
\(774\) | −3.18311e7 | −1.90985 | ||||||||
\(775\) | −1.81856e7 | + | 2.16478e7i | −1.08761 | + | 1.29467i | ||||
\(776\) | −7.95134e6 | −0.474008 | ||||||||
\(777\) | − | 1.46621e7i | − | 0.871254i | ||||||
\(778\) | 7.76433e6i | 0.459891i | ||||||||
\(779\) | 438223. | 0.0258733 | ||||||||
\(780\) | −7.20354e6 | − | 1.54595e7i | −0.423945 | − | 0.909827i | ||||
\(781\) | 3.24406e6 | 0.190310 | ||||||||
\(782\) | − | 307207.i | − | 0.0179644i | ||||||
\(783\) | 3.49021e7i | 2.03445i | ||||||||
\(784\) | 1.24414e6 | 0.0722904 | ||||||||
\(785\) | 2.90965e7 | − | 1.35579e7i | 1.68526 | − | 0.785266i | ||||
\(786\) | 6.52154e6 | 0.376525 | ||||||||
\(787\) | − | 2.27061e7i | − | 1.30679i | −0.757018 | − | 0.653395i | \(-0.773344\pi\) | ||
0.757018 | − | 0.653395i | \(-0.226656\pi\) | |||||||
\(788\) | − | 1.53099e7i | − | 0.878329i | ||||||
\(789\) | −4.75127e6 | −0.271717 | ||||||||
\(790\) | −3.34688e6 | + | 1.55952e6i | −0.190797 | + | 0.0889043i | ||||
\(791\) | −1.05129e7 | −0.597424 | ||||||||
\(792\) | 1.51311e7i | 0.857151i | ||||||||
\(793\) | 1.56521e7i | 0.883874i | ||||||||
\(794\) | 6.22565e6 | 0.350456 | ||||||||
\(795\) | −1.01475e7 | − | 2.17776e7i | −0.569434 | − | 1.22206i | ||||
\(796\) | 2.63212e6 | 0.147239 | ||||||||
\(797\) | − | 2.22676e7i | − | 1.24173i | −0.783916 | − | 0.620866i | \(-0.786781\pi\) | ||
0.783916 | − | 0.620866i | \(-0.213219\pi\) | |||||||
\(798\) | 3.91121e6i | 0.217422i | ||||||||
\(799\) | 4.18462e6 | 0.231894 | ||||||||
\(800\) | −1.43322e7 | − | 1.20401e7i | −0.791752 | − | 0.665125i | ||||
\(801\) | −3.85304e7 | −2.12189 | ||||||||
\(802\) | − | 9.56393e6i | − | 0.525050i | ||||||
\(803\) | − | 6.86823e6i | − | 0.375886i | ||||||
\(804\) | 2.66791e7 | 1.45557 | ||||||||
\(805\) | −1.23634e6 | − | 2.65332e6i | −0.0672434 | − | 0.144311i | ||||
\(806\) | −1.41668e7 | −0.768131 | ||||||||
\(807\) | 6.69118e6i | 0.361676i | ||||||||
\(808\) | 2.11148e7i | 1.13778i | ||||||||
\(809\) | −3.12578e7 | −1.67914 | −0.839570 | − | 0.543251i | \(-0.817193\pi\) | ||||
−0.839570 | + | 0.543251i | \(0.817193\pi\) | |||||||
\(810\) | −1.28899e7 | + | 6.00619e6i | −0.690297 | + | 0.321652i | ||||
\(811\) | −5.17398e6 | −0.276231 | −0.138116 | − | 0.990416i | \(-0.544105\pi\) | ||||
−0.138116 | + | 0.990416i | \(0.544105\pi\) | |||||||
\(812\) | 1.02237e7i | 0.544152i | ||||||||
\(813\) | − | 5.97420e7i | − | 3.16996i | ||||||
\(814\) | −2.91634e6 | −0.154268 | ||||||||
\(815\) | 7.97020e6 | − | 3.71381e6i | 0.420315 | − | 0.195851i | ||||
\(816\) | 905687. | 0.0476160 | ||||||||
\(817\) | − | 9.02660e6i | − | 0.473118i | ||||||
\(818\) | 4.83747e6i | 0.252775i | ||||||||
\(819\) | −2.54783e7 | −1.32727 | ||||||||
\(820\) | 501160. | + | 1.07554e6i | 0.0260280 | + | 0.0558587i | ||||
\(821\) | −2.51567e7 | −1.30255 | −0.651277 | − | 0.758840i | \(-0.725766\pi\) | ||||
−0.651277 | + | 0.758840i | \(0.725766\pi\) | |||||||
\(822\) | 3.45447e7i | 1.78321i | ||||||||
\(823\) | 2.17605e7i | 1.11988i | 0.828535 | + | 0.559938i | \(0.189175\pi\) | ||||
−0.828535 | + | 0.559938i | \(0.810825\pi\) | |||||||
\(824\) | −2.80556e7 | −1.43946 | ||||||||
\(825\) | 1.13964e7 | + | 9.57374e6i | 0.582952 | + | 0.489719i | ||||
\(826\) | −157124. | −0.00801294 | ||||||||
\(827\) | 2.25721e7i | 1.14765i | 0.818979 | + | 0.573823i | \(0.194540\pi\) | ||||
−0.818979 | + | 0.573823i | \(0.805460\pi\) | |||||||
\(828\) | 6.04392e6i | 0.306368i | ||||||||
\(829\) | −1.17900e6 | −0.0595836 | −0.0297918 | − | 0.999556i | \(-0.509484\pi\) | ||||
−0.0297918 | + | 0.999556i | \(0.509484\pi\) | |||||||
\(830\) | −4.38109e6 | − | 9.40224e6i | −0.220743 | − | 0.473736i | ||||
\(831\) | 2.36430e7 | 1.18768 | ||||||||
\(832\) | − | 6.54127e6i | − | 0.327608i | ||||||
\(833\) | − | 1.29867e6i | − | 0.0648467i | ||||||
\(834\) | 5.72771e6 | 0.285145 | ||||||||
\(835\) | −7.61183e6 | + | 3.54682e6i | −0.377809 | + | 0.176045i | ||||
\(836\) | −1.75645e6 | −0.0869200 | ||||||||
\(837\) | − | 6.78024e7i | − | 3.34527i | ||||||
\(838\) | − | 2.45399e6i | − | 0.120716i | ||||||
\(839\) | −5.57632e6 | −0.273491 | −0.136746 | − | 0.990606i | \(-0.543664\pi\) | ||||
−0.136746 | + | 0.990606i | \(0.543664\pi\) | |||||||
\(840\) | −2.34503e7 | + | 1.09270e7i | −1.14670 | + | 0.534319i | ||||
\(841\) | 1.17832e6 | 0.0574477 | ||||||||
\(842\) | − | 5.92349e6i | − | 0.287937i | ||||||
\(843\) | 6.32786e7i | 3.06682i | ||||||||
\(844\) | 2.62481e7 | 1.26836 | ||||||||
\(845\) | 2.87271e6 | + | 6.16511e6i | 0.138404 | + | 0.297029i | ||||
\(846\) | 3.64636e7 | 1.75160 | ||||||||
\(847\) | 1.29801e7i | 0.621684i | ||||||||
\(848\) | 2.77077e6i | 0.132316i | ||||||||
\(849\) | −1.05215e7 | −0.500966 | ||||||||
\(850\) | −1.16731e6 | + | 1.38954e6i | −0.0554165 | + | 0.0659667i | ||||
\(851\) | −2.84573e6 | −0.134701 | ||||||||
\(852\) | − | 1.14524e7i | − | 0.540503i | ||||||
\(853\) | 2.78507e7i | 1.31058i | 0.755378 | + | 0.655289i | \(0.227453\pi\) | ||||
−0.755378 | + | 0.655289i | \(0.772547\pi\) | |||||||
\(854\) | 9.71895e6 | 0.456010 | ||||||||
\(855\) | −5.56929e6 | − | 1.19522e7i | −0.260546 | − | 0.559157i | ||||
\(856\) | −2.31522e7 | −1.07996 | ||||||||
\(857\) | − | 7.89202e6i | − | 0.367059i | −0.983014 | − | 0.183530i | \(-0.941248\pi\) | ||
0.983014 | − | 0.183530i | \(-0.0587523\pi\) | |||||||
\(858\) | 7.45806e6i | 0.345866i | ||||||||
\(859\) | −1.81190e7 | −0.837823 | −0.418911 | − | 0.908027i | \(-0.637588\pi\) | ||||
−0.418911 | + | 0.908027i | \(0.637588\pi\) | |||||||
\(860\) | 2.21541e7 | − | 1.03230e7i | 1.02143 | − | 0.475948i | ||||
\(861\) | 2.60865e6 | 0.119924 | ||||||||
\(862\) | 4.61093e6i | 0.211359i | ||||||||
\(863\) | − | 272254.i | − | 0.0124437i | −0.999981 | − | 0.00622183i | \(-0.998020\pi\) | ||
0.999981 | − | 0.00622183i | \(-0.00198048\pi\) | |||||||
\(864\) | 4.48895e7 | 2.04579 | ||||||||
\(865\) | −2.06973e7 | + | 9.64418e6i | −0.940534 | + | 0.438253i | ||||
\(866\) | −5134.65 | −0.000232657 | ||||||||
\(867\) | 3.81503e7i | 1.72365i | ||||||||
\(868\) | − | 1.98611e7i | − | 0.894754i | ||||||
\(869\) | −3.64548e6 | −0.163759 | ||||||||
\(870\) | 9.48922e6 | + | 2.03648e7i | 0.425042 | + | 0.912182i | ||||
\(871\) | 2.18283e7 | 0.974932 | ||||||||
\(872\) | − | 3.79121e7i | − | 1.68844i | ||||||
\(873\) | − | 2.41247e7i | − | 1.07134i | ||||||
\(874\) | 759115. | 0.0336147 | ||||||||
\(875\) | −4.48977e6 | + | 1.66992e7i | −0.198246 | + | 0.737351i | ||||
\(876\) | −2.42467e7 | −1.06756 | ||||||||
\(877\) | − | 8.51694e6i | − | 0.373925i | −0.982367 | − | 0.186962i | \(-0.940136\pi\) | ||
0.982367 | − | 0.186962i | \(-0.0598643\pi\) | |||||||
\(878\) | 2.18663e7i | 0.957279i | ||||||||
\(879\) | 116431. | 0.00508272 | ||||||||
\(880\) | −724982. | − | 1.55588e6i | −0.0315588 | − | 0.0677283i | ||||
\(881\) | −475215. | −0.0206277 | −0.0103138 | − | 0.999947i | \(-0.503283\pi\) | ||||
−0.0103138 | + | 0.999947i | \(0.503283\pi\) | |||||||
\(882\) | − | 1.13163e7i | − | 0.489815i | ||||||
\(883\) | 2.40143e7i | 1.03650i | 0.855230 | + | 0.518249i | \(0.173416\pi\) | ||||
−0.855230 | + | 0.518249i | \(0.826584\pi\) | |||||||
\(884\) | 2.05312e6 | 0.0883658 | ||||||||
\(885\) | 706636. | − | 329266.i | 0.0303276 | − | 0.0141315i | ||||
\(886\) | 1.09613e7 | 0.469115 | ||||||||
\(887\) | − | 840273.i | − | 0.0358601i | −0.999839 | − | 0.0179300i | \(-0.994292\pi\) | ||
0.999839 | − | 0.0179300i | \(-0.00570762\pi\) | |||||||
\(888\) | 2.51509e7i | 1.07034i | ||||||||
\(889\) | 2.92416e7 | 1.24093 | ||||||||
\(890\) | −1.18774e7 | + | 5.53443e6i | −0.502629 | + | 0.234206i | ||||
\(891\) | −1.40399e7 | −0.592474 | ||||||||
\(892\) | − | 3.05506e7i | − | 1.28561i | ||||||
\(893\) | 1.03403e7i | 0.433914i | ||||||||
\(894\) | 1.56723e7 | 0.655826 | ||||||||
\(895\) | −1.96399e6 | − | 4.21491e6i | −0.0819561 | − | 0.175886i | ||||
\(896\) | 1.49116e7 | 0.620517 | ||||||||
\(897\) | 7.27750e6i | 0.301996i | ||||||||
\(898\) | 1.25407e7i | 0.518957i | ||||||||
\(899\) | −4.21349e7 | −1.73877 | ||||||||
\(900\) | 2.29654e7 | − | 2.73376e7i | 0.945079 | − | 1.12500i | ||||
\(901\) | 2.89221e6 | 0.118691 | ||||||||
\(902\) | − | 518867.i | − | 0.0212344i | ||||||
\(903\) | − | 5.37335e7i | − | 2.19293i | ||||||
\(904\) | 1.80335e7 | 0.733938 | ||||||||
\(905\) | 9.04493e6 | + | 1.94113e7i | 0.367099 | + | 0.787831i | ||||
\(906\) | 1.54831e7 | 0.626666 | ||||||||
\(907\) | − | 2.64919e7i | − | 1.06929i | −0.845078 | − | 0.534643i | \(-0.820446\pi\) | ||
0.845078 | − | 0.534643i | \(-0.179554\pi\) | |||||||
\(908\) | 2.54663e7i | 1.02507i | ||||||||
\(909\) | −6.40630e7 | −2.57156 | ||||||||
\(910\) | −7.85397e6 | + | 3.65965e6i | −0.314402 | + | 0.146500i | ||||
\(911\) | −1.82537e7 | −0.728709 | −0.364355 | − | 0.931260i | \(-0.618710\pi\) | ||||
−0.364355 | + | 0.931260i | \(0.618710\pi\) | |||||||
\(912\) | 2.23797e6i | 0.0890979i | ||||||||
\(913\) | − | 1.02411e7i | − | 0.406602i | ||||||
\(914\) | −1.36999e7 | −0.542441 | ||||||||
\(915\) | −4.37092e7 | + | 2.03668e7i | −1.72592 | + | 0.804213i | ||||
\(916\) | −3.81038e6 | −0.150048 | ||||||||
\(917\) | 7.48045e6i | 0.293768i | ||||||||
\(918\) | − | 4.35214e6i | − | 0.170450i | ||||||
\(919\) | −3.48435e7 | −1.36092 | −0.680461 | − | 0.732784i | \(-0.738220\pi\) | ||||
−0.680461 | + | 0.732784i | \(0.738220\pi\) | |||||||
\(920\) | 2.12078e6 | + | 4.55140e6i | 0.0826088 | + | 0.177287i | ||||
\(921\) | −1.25228e7 | −0.486468 | ||||||||
\(922\) | 5.32868e6i | 0.206439i | ||||||||
\(923\) | − | 9.37011e6i | − | 0.362027i | ||||||
\(924\) | −1.04558e7 | −0.402880 | ||||||||
\(925\) | 1.28717e7 | + | 1.08131e7i | 0.494630 | + | 0.415523i | ||||
\(926\) | 1.80868e7 | 0.693162 | ||||||||
\(927\) | − | 8.51217e7i | − | 3.25342i | ||||||
\(928\) | − | 2.78960e7i | − | 1.06334i | ||||||
\(929\) | 4.36870e6 | 0.166078 | 0.0830391 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830391 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(930\) | −1.84342e7 | − | 3.95615e7i | −0.698901 | − | 1.49991i | ||||
\(931\) | 3.20905e6 | 0.121340 | ||||||||
\(932\) | − | 1.44523e7i | − | 0.545003i | ||||||
\(933\) | − | 7.98899e7i | − | 3.00461i | ||||||
\(934\) | 1.02103e7 | 0.382975 | ||||||||
\(935\) | −1.62408e6 | + | 756758.i | −0.0607544 | + | 0.0283092i | ||||
\(936\) | 4.37045e7 | 1.63056 | ||||||||
\(937\) | 1.90567e7i | 0.709087i | 0.935040 | + | 0.354543i | \(0.115364\pi\) | ||||
−0.935040 | + | 0.354543i | \(0.884636\pi\) | |||||||
\(938\) | − | 1.35539e7i | − | 0.502989i | ||||||
\(939\) | 7.10895e7 | 2.63113 | ||||||||
\(940\) | −2.53783e7 | + | 1.18253e7i | −0.936792 | + | 0.436510i | ||||
\(941\) | −6.86363e6 | −0.252685 | −0.126343 | − | 0.991987i | \(-0.540324\pi\) | ||||
−0.126343 | + | 0.991987i | \(0.540324\pi\) | |||||||
\(942\) | 4.95541e7i | 1.81950i | ||||||||
\(943\) | − | 506305.i | − | 0.0185410i | ||||||
\(944\) | −89905.5 | −0.00328364 | ||||||||
\(945\) | −1.75151e7 | − | 3.75890e7i | −0.638017 | − | 1.36925i | ||||
\(946\) | −1.06877e7 | −0.388291 | ||||||||
\(947\) | 2.04942e7i | 0.742602i | 0.928513 | + | 0.371301i | \(0.121088\pi\) | ||||
−0.928513 | + | 0.371301i | \(0.878912\pi\) | |||||||
\(948\) | 1.28695e7i | 0.465095i | ||||||||
\(949\) | −1.98381e7 | −0.715048 | ||||||||
\(950\) | −3.43359e6 | − | 2.88445e6i | −0.123435 | − | 0.103694i | ||||
\(951\) | 5.70942e7 | 2.04711 | ||||||||
\(952\) | − | 3.11436e6i | − | 0.111372i | ||||||
\(953\) | − | 2.36728e6i | − | 0.0844341i | −0.999108 | − | 0.0422170i | \(-0.986558\pi\) | ||
0.999108 | − | 0.0422170i | \(-0.0134421\pi\) | |||||||
\(954\) | 2.52019e7 | 0.896526 | ||||||||
\(955\) | 2.14007e7 | + | 4.59279e7i | 0.759309 | + | 1.62955i | ||||
\(956\) | 3.40917e7 | 1.20644 | ||||||||
\(957\) | 2.21817e7i | 0.782916i | ||||||||
\(958\) | 1.67784e7i | 0.590659i | ||||||||
\(959\) | −3.96241e7 | −1.39128 | ||||||||
\(960\) | 1.82668e7 | − | 8.51163e6i | 0.639711 | − | 0.298081i | ||||
\(961\) | 5.32238e7 | 1.85908 | ||||||||
\(962\) | 8.42353e6i | 0.293465i | ||||||||
\(963\) | − | 7.02446e7i | − | 2.44089i | ||||||
\(964\) | 2.02545e7 | 0.701986 | ||||||||
\(965\) | −3.08767e7 | + | 1.43874e7i | −1.06736 | + | 0.497351i | ||||
\(966\) | 4.51885e6 | 0.155806 | ||||||||
\(967\) | 193505.i | 0.00665465i | 0.999994 | + | 0.00332732i | \(0.00105912\pi\) | ||||
−0.999994 | + | 0.00332732i | \(0.998941\pi\) | |||||||
\(968\) | − | 2.22656e7i | − | 0.763740i | ||||||
\(969\) | 2.33606e6 | 0.0799236 | ||||||||
\(970\) | −3.46522e6 | − | 7.43670e6i | −0.118250 | − | 0.253776i | ||||
\(971\) | 1.18283e7 | 0.402602 | 0.201301 | − | 0.979529i | \(-0.435483\pi\) | ||||
0.201301 | + | 0.979529i | \(0.435483\pi\) | |||||||
\(972\) | 9.17733e6i | 0.311566i | ||||||||
\(973\) | 6.56990e6i | 0.222473i | ||||||||
\(974\) | 1.23674e7 | 0.417715 | ||||||||
\(975\) | 2.76527e7 | − | 3.29172e7i | 0.931593 | − | 1.10895i | ||||
\(976\) | 5.56113e6 | 0.186870 | ||||||||
\(977\) | 1.27220e7i | 0.426400i | 0.977009 | + | 0.213200i | \(0.0683886\pi\) | ||||
−0.977009 | + | 0.213200i | \(0.931611\pi\) | |||||||
\(978\) | 1.35740e7i | 0.453796i | ||||||||
\(979\) | −1.29371e7 | −0.431401 | ||||||||
\(980\) | 3.66993e6 | + | 7.87602e6i | 0.122065 | + | 0.261964i | ||||
\(981\) | 1.15027e8 | 3.81616 | ||||||||
\(982\) | − | 1.39973e7i | − | 0.463196i | ||||||
\(983\) | − | 2.62540e7i | − | 0.866588i | −0.901253 | − | 0.433294i | \(-0.857351\pi\) | ||
0.901253 | − | 0.433294i | \(-0.142649\pi\) | |||||||
\(984\) | −4.47478e6 | −0.147328 | ||||||||
\(985\) | 3.49800e7 | − | 1.62994e7i | 1.14876 | − | 0.535279i | ||||
\(986\) | −2.70458e6 | −0.0885946 | ||||||||
\(987\) | 6.15536e7i | 2.01122i | ||||||||
\(988\) | 5.07331e6i | 0.165348i | ||||||||
\(989\) | −1.04290e7 | −0.339040 | ||||||||
\(990\) | −1.41518e7 | + | 6.59418e6i | −0.458904 | + | 0.213832i | ||||
\(991\) | 5.49258e7 | 1.77661 | 0.888306 | − | 0.459253i | \(-0.151883\pi\) | ||||
0.888306 | + | 0.459253i | \(0.151883\pi\) | |||||||
\(992\) | 5.41919e7i | 1.74846i | ||||||||
\(993\) | 9.10638e7i | 2.93071i | ||||||||
\(994\) | −5.81823e6 | −0.186778 | ||||||||
\(995\) | 2.80223e6 | + | 6.01385e6i | 0.0897316 | + | 0.192573i | ||||
\(996\) | −3.61539e7 | −1.15480 | ||||||||
\(997\) | 3.45837e7i | 1.10188i | 0.834545 | + | 0.550939i | \(0.185730\pi\) | ||||
−0.834545 | + | 0.550939i | \(0.814270\pi\) | |||||||
\(998\) | − | 1.32101e6i | − | 0.0419836i | ||||||
\(999\) | −4.03149e7 | −1.27806 |
(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 | 115.6.b.a.24.36 | yes | 54 | |
5.2 | odd | 4 | 575.6.a.m.1.9 | 27 | |||
5.3 | odd | 4 | 575.6.a.l.1.19 | 27 | |||
5.4 | even | 2 | inner | 115.6.b.a.24.19 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.6.b.a.24.19 | ✓ | 54 | 5.4 | even | 2 | inner | |
115.6.b.a.24.36 | yes | 54 | 1.1 | even | 1 | trivial | |
575.6.a.l.1.19 | 27 | 5.3 | odd | 4 | |||
575.6.a.m.1.9 | 27 | 5.2 | odd | 4 |