Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,7,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(9.89232559565\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1038 x^{18} + 455829 x^{16} + 110435384 x^{14} + 16133606976 x^{12} + 1458210485616 x^{10} + \cdots + 64\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{15} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.1 | ||
Root | \(-15.3591i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.7.b.b.42.20 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 15.3591i | − | 1.91988i | −0.280199 | − | 0.959942i | \(-0.590401\pi\) | ||
0.280199 | − | 0.959942i | \(-0.409599\pi\) | |||||||
\(3\) | − | 12.8491i | − | 0.475891i | −0.971278 | − | 0.237946i | \(-0.923526\pi\) | ||
0.971278 | − | 0.237946i | \(-0.0764740\pi\) | |||||||
\(4\) | −171.901 | −2.68595 | ||||||||
\(5\) | − | 213.900i | − | 1.71120i | −0.517639 | − | 0.855599i | \(-0.673189\pi\) | ||
0.517639 | − | 0.855599i | \(-0.326811\pi\) | |||||||
\(6\) | −197.350 | −0.913656 | ||||||||
\(7\) | − | 274.602i | − | 0.800588i | −0.916387 | − | 0.400294i | \(-0.868908\pi\) | ||
0.916387 | − | 0.400294i | \(-0.131092\pi\) | |||||||
\(8\) | 1657.26i | 3.23683i | ||||||||
\(9\) | 563.902 | 0.773528 | ||||||||
\(10\) | −3285.30 | −3.28530 | ||||||||
\(11\) | 1533.32 | 1.15200 | 0.576001 | − | 0.817449i | \(-0.304612\pi\) | ||||
0.576001 | + | 0.817449i | \(0.304612\pi\) | |||||||
\(12\) | 2208.77i | 1.27822i | ||||||||
\(13\) | −2261.41 | −1.02932 | −0.514658 | − | 0.857395i | \(-0.672081\pi\) | ||||
−0.514658 | + | 0.857395i | \(0.672081\pi\) | |||||||
\(14\) | −4217.62 | −1.53704 | ||||||||
\(15\) | −2748.41 | −0.814344 | ||||||||
\(16\) | 14452.3 | 3.52839 | ||||||||
\(17\) | 8925.29 | 1.81667 | 0.908334 | − | 0.418245i | \(-0.137355\pi\) | ||||
0.908334 | + | 0.418245i | \(0.137355\pi\) | |||||||
\(18\) | − | 8661.00i | − | 1.48508i | ||||||
\(19\) | 851.013i | 0.124073i | 0.998074 | + | 0.0620363i | \(0.0197594\pi\) | ||||
−0.998074 | + | 0.0620363i | \(0.980241\pi\) | |||||||
\(20\) | 36769.6i | 4.59620i | ||||||||
\(21\) | −3528.37 | −0.380993 | ||||||||
\(22\) | − | 23550.3i | − | 2.21171i | ||||||
\(23\) | 1902.42 | 0.156359 | 0.0781794 | − | 0.996939i | \(-0.475089\pi\) | ||||
0.0781794 | + | 0.996939i | \(0.475089\pi\) | |||||||
\(24\) | 21294.2 | 1.54038 | ||||||||
\(25\) | −30128.1 | −1.92820 | ||||||||
\(26\) | 34733.1i | 1.97617i | ||||||||
\(27\) | − | 16612.6i | − | 0.844006i | ||||||
\(28\) | 47204.3i | 2.15034i | ||||||||
\(29\) | − | 8479.42i | − | 0.347674i | −0.984774 | − | 0.173837i | \(-0.944383\pi\) | ||
0.984774 | − | 0.173837i | \(-0.0556166\pi\) | |||||||
\(30\) | 42213.0i | 1.56345i | ||||||||
\(31\) | −14740.7 | −0.494803 | −0.247402 | − | 0.968913i | \(-0.579577\pi\) | ||||
−0.247402 | + | 0.968913i | \(0.579577\pi\) | |||||||
\(32\) | − | 115909.i | − | 3.53727i | ||||||
\(33\) | − | 19701.7i | − | 0.548228i | ||||||
\(34\) | − | 137084.i | − | 3.48779i | ||||||
\(35\) | −58737.2 | −1.36996 | ||||||||
\(36\) | −96935.3 | −2.07766 | ||||||||
\(37\) | 39610.5i | 0.781997i | 0.920391 | + | 0.390998i | \(0.127870\pi\) | ||||
−0.920391 | + | 0.390998i | \(0.872130\pi\) | |||||||
\(38\) | 13070.8 | 0.238205 | ||||||||
\(39\) | 29057.0i | 0.489842i | ||||||||
\(40\) | 354487. | 5.53887 | ||||||||
\(41\) | −72090.6 | −1.04599 | −0.522995 | − | 0.852336i | \(-0.675185\pi\) | ||||
−0.522995 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(42\) | 54192.5i | 0.731461i | ||||||||
\(43\) | 4441.34 | + | 79382.9i | 0.0558610 | + | 0.998439i | ||||
\(44\) | −263579. | −3.09423 | ||||||||
\(45\) | − | 120618.i | − | 1.32366i | ||||||
\(46\) | − | 29219.4i | − | 0.300191i | ||||||
\(47\) | 84141.9 | 0.810436 | 0.405218 | − | 0.914220i | \(-0.367196\pi\) | ||||
0.405218 | + | 0.914220i | \(0.367196\pi\) | |||||||
\(48\) | − | 185698.i | − | 1.67913i | ||||||
\(49\) | 42243.0 | 0.359059 | ||||||||
\(50\) | 462740.i | 3.70192i | ||||||||
\(51\) | − | 114682.i | − | 0.864536i | ||||||
\(52\) | 388738. | 2.76470 | ||||||||
\(53\) | −139864. | −0.939457 | −0.469729 | − | 0.882811i | \(-0.655648\pi\) | ||||
−0.469729 | + | 0.882811i | \(0.655648\pi\) | |||||||
\(54\) | −255154. | −1.62039 | ||||||||
\(55\) | − | 327976.i | − | 1.97131i | ||||||
\(56\) | 455086. | 2.59137 | ||||||||
\(57\) | 10934.7 | 0.0590450 | ||||||||
\(58\) | −130236. | −0.667494 | ||||||||
\(59\) | 106075. | 0.516485 | 0.258243 | − | 0.966080i | \(-0.416857\pi\) | ||||
0.258243 | + | 0.966080i | \(0.416857\pi\) | |||||||
\(60\) | 472455. | 2.18729 | ||||||||
\(61\) | − | 89596.6i | − | 0.394732i | −0.980330 | − | 0.197366i | \(-0.936761\pi\) | ||
0.980330 | − | 0.197366i | \(-0.0632387\pi\) | |||||||
\(62\) | 226403.i | 0.949965i | ||||||||
\(63\) | − | 154848.i | − | 0.619277i | ||||||
\(64\) | −855310. | −3.26275 | ||||||||
\(65\) | 483715.i | 1.76136i | ||||||||
\(66\) | −302599. | −1.05253 | ||||||||
\(67\) | 221025. | 0.734881 | 0.367441 | − | 0.930047i | \(-0.380234\pi\) | ||||
0.367441 | + | 0.930047i | \(0.380234\pi\) | |||||||
\(68\) | −1.53427e6 | −4.87949 | ||||||||
\(69\) | − | 24444.3i | − | 0.0744098i | ||||||
\(70\) | 902149.i | 2.63017i | ||||||||
\(71\) | − | 238817.i | − | 0.667252i | −0.942705 | − | 0.333626i | \(-0.891728\pi\) | ||
0.942705 | − | 0.333626i | \(-0.108272\pi\) | |||||||
\(72\) | 934531.i | 2.50378i | ||||||||
\(73\) | 259632.i | 0.667406i | 0.942678 | + | 0.333703i | \(0.108298\pi\) | ||||
−0.942678 | + | 0.333703i | \(0.891702\pi\) | |||||||
\(74\) | 608380. | 1.50134 | ||||||||
\(75\) | 387118.i | 0.917613i | ||||||||
\(76\) | − | 146290.i | − | 0.333253i | ||||||
\(77\) | − | 421051.i | − | 0.922279i | ||||||
\(78\) | 446288. | 0.940441 | ||||||||
\(79\) | 232291. | 0.471141 | 0.235571 | − | 0.971857i | \(-0.424304\pi\) | ||||
0.235571 | + | 0.971857i | \(0.424304\pi\) | |||||||
\(80\) | − | 3.09134e6i | − | 6.03778i | ||||||
\(81\) | 197628. | 0.371873 | ||||||||
\(82\) | 1.10724e6i | 2.00818i | ||||||||
\(83\) | 373116. | 0.652544 | 0.326272 | − | 0.945276i | \(-0.394207\pi\) | ||||
0.326272 | + | 0.945276i | \(0.394207\pi\) | |||||||
\(84\) | 606531. | 1.02333 | ||||||||
\(85\) | − | 1.90912e6i | − | 3.10868i | ||||||
\(86\) | 1.21925e6 | − | 68214.8i | 1.91689 | − | 0.107247i | ||||
\(87\) | −108953. | −0.165455 | ||||||||
\(88\) | 2.54110e6i | 3.72884i | ||||||||
\(89\) | − | 277468.i | − | 0.393589i | −0.980445 | − | 0.196794i | \(-0.936947\pi\) | ||
0.980445 | − | 0.196794i | \(-0.0630531\pi\) | |||||||
\(90\) | −1.85259e6 | −2.54127 | ||||||||
\(91\) | 620986.i | 0.824058i | ||||||||
\(92\) | −327027. | −0.419972 | ||||||||
\(93\) | 189404.i | 0.235472i | ||||||||
\(94\) | − | 1.29234e6i | − | 1.55594i | ||||||
\(95\) | 182032. | 0.212313 | ||||||||
\(96\) | −1.48932e6 | −1.68335 | ||||||||
\(97\) | 810136. | 0.887652 | 0.443826 | − | 0.896113i | \(-0.353621\pi\) | ||||
0.443826 | + | 0.896113i | \(0.353621\pi\) | |||||||
\(98\) | − | 648813.i | − | 0.689352i | ||||||
\(99\) | 864639. | 0.891106 | ||||||||
\(100\) | 5.17906e6 | 5.17906 | ||||||||
\(101\) | 980348. | 0.951516 | 0.475758 | − | 0.879576i | \(-0.342174\pi\) | ||||
0.475758 | + | 0.879576i | \(0.342174\pi\) | |||||||
\(102\) | −1.76140e6 | −1.65981 | ||||||||
\(103\) | −1.38382e6 | −1.26639 | −0.633197 | − | 0.773991i | \(-0.718258\pi\) | ||||
−0.633197 | + | 0.773991i | \(0.718258\pi\) | |||||||
\(104\) | − | 3.74774e6i | − | 3.33173i | ||||||
\(105\) | 754718.i | 0.651954i | ||||||||
\(106\) | 2.14817e6i | 1.80365i | ||||||||
\(107\) | −1.50507e6 | −1.22859 | −0.614294 | − | 0.789077i | \(-0.710559\pi\) | ||||
−0.614294 | + | 0.789077i | \(0.710559\pi\) | |||||||
\(108\) | 2.85572e6i | 2.26696i | ||||||||
\(109\) | −357123. | −0.275765 | −0.137882 | − | 0.990449i | \(-0.544030\pi\) | ||||
−0.137882 | + | 0.990449i | \(0.544030\pi\) | |||||||
\(110\) | −5.03741e6 | −3.78468 | ||||||||
\(111\) | 508958. | 0.372145 | ||||||||
\(112\) | − | 3.96862e6i | − | 2.82479i | ||||||
\(113\) | 2.14958e6i | 1.48977i | 0.667194 | + | 0.744884i | \(0.267495\pi\) | ||||
−0.667194 | + | 0.744884i | \(0.732505\pi\) | |||||||
\(114\) | − | 167947.i | − | 0.113360i | ||||||
\(115\) | − | 406927.i | − | 0.267561i | ||||||
\(116\) | 1.45762e6i | 0.933836i | ||||||||
\(117\) | −1.27521e6 | −0.796205 | ||||||||
\(118\) | − | 1.62922e6i | − | 0.991592i | ||||||
\(119\) | − | 2.45090e6i | − | 1.45440i | ||||||
\(120\) | − | 4.55483e6i | − | 2.63590i | ||||||
\(121\) | 579496. | 0.327111 | ||||||||
\(122\) | −1.37612e6 | −0.757839 | ||||||||
\(123\) | 926297.i | 0.497777i | ||||||||
\(124\) | 2.53394e6 | 1.32902 | ||||||||
\(125\) | 3.10222e6i | 1.58833i | ||||||||
\(126\) | −2.37833e6 | −1.18894 | ||||||||
\(127\) | −500467. | −0.244323 | −0.122161 | − | 0.992510i | \(-0.538983\pi\) | ||||
−0.122161 | + | 0.992510i | \(0.538983\pi\) | |||||||
\(128\) | 5.71858e6i | 2.72683i | ||||||||
\(129\) | 1.02000e6 | − | 57067.0i | 0.475148 | − | 0.0265837i | ||||
\(130\) | 7.42941e6 | 3.38161 | ||||||||
\(131\) | − | 3.30633e6i | − | 1.47073i | −0.677672 | − | 0.735364i | \(-0.737011\pi\) | ||
0.677672 | − | 0.735364i | \(-0.262989\pi\) | |||||||
\(132\) | 3.38674e6i | 1.47251i | ||||||||
\(133\) | 233690. | 0.0993309 | ||||||||
\(134\) | − | 3.39474e6i | − | 1.41089i | ||||||
\(135\) | −3.55343e6 | −1.44426 | ||||||||
\(136\) | 1.47915e7i | 5.88025i | ||||||||
\(137\) | 59153.5i | 0.0230048i | 0.999934 | + | 0.0115024i | \(0.00366141\pi\) | ||||
−0.999934 | + | 0.0115024i | \(0.996339\pi\) | |||||||
\(138\) | −375441. | −0.142858 | ||||||||
\(139\) | −3.92748e6 | −1.46241 | −0.731206 | − | 0.682156i | \(-0.761042\pi\) | ||||
−0.731206 | + | 0.682156i | \(0.761042\pi\) | |||||||
\(140\) | 1.00970e7 | 3.67966 | ||||||||
\(141\) | − | 1.08114e6i | − | 0.385679i | ||||||
\(142\) | −3.66801e6 | −1.28105 | ||||||||
\(143\) | −3.46745e6 | −1.18578 | ||||||||
\(144\) | 8.14967e6 | 2.72931 | ||||||||
\(145\) | −1.81375e6 | −0.594939 | ||||||||
\(146\) | 3.98771e6 | 1.28134 | ||||||||
\(147\) | − | 542783.i | − | 0.170873i | ||||||
\(148\) | − | 6.80908e6i | − | 2.10041i | ||||||
\(149\) | 2.29558e6i | 0.693958i | 0.937873 | + | 0.346979i | \(0.112793\pi\) | ||||
−0.937873 | + | 0.346979i | \(0.887207\pi\) | |||||||
\(150\) | 5.94577e6 | 1.76171 | ||||||||
\(151\) | − | 3.65749e6i | − | 1.06231i | −0.847274 | − | 0.531157i | \(-0.821758\pi\) | ||
0.847274 | − | 0.531157i | \(-0.178242\pi\) | |||||||
\(152\) | −1.41035e6 | −0.401602 | ||||||||
\(153\) | 5.03299e6 | 1.40524 | ||||||||
\(154\) | −6.46695e6 | −1.77067 | ||||||||
\(155\) | 3.15303e6i | 0.846706i | ||||||||
\(156\) | − | 4.99492e6i | − | 1.31569i | ||||||
\(157\) | 4.30465e6i | 1.11234i | 0.831068 | + | 0.556171i | \(0.187730\pi\) | ||||
−0.831068 | + | 0.556171i | \(0.812270\pi\) | |||||||
\(158\) | − | 3.56777e6i | − | 0.904537i | ||||||
\(159\) | 1.79712e6i | 0.447079i | ||||||||
\(160\) | −2.47929e7 | −6.05297 | ||||||||
\(161\) | − | 522407.i | − | 0.125179i | ||||||
\(162\) | − | 3.03539e6i | − | 0.713952i | ||||||
\(163\) | 4.48968e6i | 1.03670i | 0.855169 | + | 0.518349i | \(0.173453\pi\) | ||||
−0.855169 | + | 0.518349i | \(0.826547\pi\) | |||||||
\(164\) | 1.23925e7 | 2.80948 | ||||||||
\(165\) | −4.21418e6 | −0.938127 | ||||||||
\(166\) | − | 5.73072e6i | − | 1.25281i | ||||||
\(167\) | 7.58942e6 | 1.62952 | 0.814760 | − | 0.579799i | \(-0.196869\pi\) | ||||
0.814760 | + | 0.579799i | \(0.196869\pi\) | |||||||
\(168\) | − | 5.84743e6i | − | 1.23321i | ||||||
\(169\) | 287156. | 0.0594920 | ||||||||
\(170\) | −2.93223e7 | −5.96830 | ||||||||
\(171\) | 479888.i | 0.0959735i | ||||||||
\(172\) | −763471. | − | 1.36460e7i | −0.150040 | − | 2.68176i | ||||
\(173\) | −4.30786e6 | −0.832001 | −0.416000 | − | 0.909364i | \(-0.636569\pi\) | ||||
−0.416000 | + | 0.909364i | \(0.636569\pi\) | |||||||
\(174\) | 1.67341e6i | 0.317654i | ||||||||
\(175\) | 8.27323e6i | 1.54369i | ||||||||
\(176\) | 2.21599e7 | 4.06472 | ||||||||
\(177\) | − | 1.36297e6i | − | 0.245791i | ||||||
\(178\) | −4.26165e6 | −0.755645 | ||||||||
\(179\) | − | 9.22540e6i | − | 1.60852i | −0.594278 | − | 0.804260i | \(-0.702562\pi\) | ||
0.594278 | − | 0.804260i | \(-0.297438\pi\) | |||||||
\(180\) | 2.07344e7i | 3.55529i | ||||||||
\(181\) | 2.31947e6 | 0.391159 | 0.195580 | − | 0.980688i | \(-0.437341\pi\) | ||||
0.195580 | + | 0.980688i | \(0.437341\pi\) | |||||||
\(182\) | 9.53777e6 | 1.58210 | ||||||||
\(183\) | −1.15123e6 | −0.187849 | ||||||||
\(184\) | 3.15280e6i | 0.506107i | ||||||||
\(185\) | 8.47268e6 | 1.33815 | ||||||||
\(186\) | 2.90907e6 | 0.452080 | ||||||||
\(187\) | 1.36853e7 | 2.09281 | ||||||||
\(188\) | −1.44641e7 | −2.17679 | ||||||||
\(189\) | −4.56184e6 | −0.675701 | ||||||||
\(190\) | − | 2.79584e6i | − | 0.407616i | ||||||
\(191\) | 1.07589e7i | 1.54408i | 0.635575 | + | 0.772039i | \(0.280763\pi\) | ||||
−0.635575 | + | 0.772039i | \(0.719237\pi\) | |||||||
\(192\) | 1.09899e7i | 1.55271i | ||||||||
\(193\) | 8.52106e6 | 1.18528 | 0.592641 | − | 0.805467i | \(-0.298085\pi\) | ||||
0.592641 | + | 0.805467i | \(0.298085\pi\) | |||||||
\(194\) | − | 1.24429e7i | − | 1.70419i | ||||||
\(195\) | 6.21528e6 | 0.838218 | ||||||||
\(196\) | −7.26161e6 | −0.964417 | ||||||||
\(197\) | −3.31316e6 | −0.433354 | −0.216677 | − | 0.976243i | \(-0.569522\pi\) | ||||
−0.216677 | + | 0.976243i | \(0.569522\pi\) | |||||||
\(198\) | − | 1.32801e7i | − | 1.71082i | ||||||
\(199\) | − | 9.97517e6i | − | 1.26579i | −0.774238 | − | 0.632894i | \(-0.781867\pi\) | ||
0.774238 | − | 0.632894i | \(-0.218133\pi\) | |||||||
\(200\) | − | 4.99301e7i | − | 6.24126i | ||||||
\(201\) | − | 2.83996e6i | − | 0.349723i | ||||||
\(202\) | − | 1.50572e7i | − | 1.82680i | ||||||
\(203\) | −2.32846e6 | −0.278343 | ||||||||
\(204\) | 1.97139e7i | 2.32210i | ||||||||
\(205\) | 1.54202e7i | 1.78990i | ||||||||
\(206\) | 2.12542e7i | 2.43133i | ||||||||
\(207\) | 1.07278e6 | 0.120948 | ||||||||
\(208\) | −3.26825e7 | −3.63183 | ||||||||
\(209\) | 1.30487e6i | 0.142932i | ||||||||
\(210\) | 1.15918e7 | 1.25168 | ||||||||
\(211\) | − | 6.67494e6i | − | 0.710558i | −0.934760 | − | 0.355279i | \(-0.884386\pi\) | ||
0.934760 | − | 0.355279i | \(-0.115614\pi\) | |||||||
\(212\) | 2.40427e7 | 2.52334 | ||||||||
\(213\) | −3.06857e6 | −0.317539 | ||||||||
\(214\) | 2.31165e7i | 2.35875i | ||||||||
\(215\) | 1.69800e7 | − | 950002.i | 1.70853 | − | 0.0955892i | ||||
\(216\) | 2.75313e7 | 2.73191 | ||||||||
\(217\) | 4.04781e6i | 0.396133i | ||||||||
\(218\) | 5.48508e6i | 0.529436i | ||||||||
\(219\) | 3.33603e6 | 0.317613 | ||||||||
\(220\) | 5.63794e7i | 5.29483i | ||||||||
\(221\) | −2.01837e7 | −1.86993 | ||||||||
\(222\) | − | 7.81711e6i | − | 0.714476i | ||||||
\(223\) | − | 1.44149e7i | − | 1.29986i | −0.759993 | − | 0.649931i | \(-0.774798\pi\) | ||
0.759993 | − | 0.649931i | \(-0.225202\pi\) | |||||||
\(224\) | −3.18288e7 | −2.83189 | ||||||||
\(225\) | −1.69893e7 | −1.49152 | ||||||||
\(226\) | 3.30156e7 | 2.86018 | ||||||||
\(227\) | − | 3.62378e6i | − | 0.309802i | −0.987930 | − | 0.154901i | \(-0.950494\pi\) | ||
0.987930 | − | 0.154901i | \(-0.0495059\pi\) | |||||||
\(228\) | −1.87969e6 | −0.158592 | ||||||||
\(229\) | −6.20931e6 | −0.517055 | −0.258528 | − | 0.966004i | \(-0.583237\pi\) | ||||
−0.258528 | + | 0.966004i | \(0.583237\pi\) | |||||||
\(230\) | −6.25001e6 | −0.513686 | ||||||||
\(231\) | −5.41011e6 | −0.438905 | ||||||||
\(232\) | 1.40526e7 | 1.12536 | ||||||||
\(233\) | 1.98080e7i | 1.56593i | 0.622066 | + | 0.782965i | \(0.286294\pi\) | ||||
−0.622066 | + | 0.782965i | \(0.713706\pi\) | |||||||
\(234\) | 1.95861e7i | 1.52862i | ||||||||
\(235\) | − | 1.79979e7i | − | 1.38682i | ||||||
\(236\) | −1.82344e7 | −1.38726 | ||||||||
\(237\) | − | 2.98472e6i | − | 0.224212i | ||||||
\(238\) | −3.76435e7 | −2.79228 | ||||||||
\(239\) | 3.26633e6 | 0.239258 | 0.119629 | − | 0.992819i | \(-0.461829\pi\) | ||||
0.119629 | + | 0.992819i | \(0.461829\pi\) | |||||||
\(240\) | −3.97208e7 | −2.87332 | ||||||||
\(241\) | − | 1.10191e7i | − | 0.787218i | −0.919278 | − | 0.393609i | \(-0.871226\pi\) | ||
0.919278 | − | 0.393609i | \(-0.128774\pi\) | |||||||
\(242\) | − | 8.90053e6i | − | 0.628014i | ||||||
\(243\) | − | 1.46499e7i | − | 1.02098i | ||||||
\(244\) | 1.54018e7i | 1.06023i | ||||||||
\(245\) | − | 9.03577e6i | − | 0.614422i | ||||||
\(246\) | 1.42271e7 | 0.955674 | ||||||||
\(247\) | − | 1.92449e6i | − | 0.127710i | ||||||
\(248\) | − | 2.44291e7i | − | 1.60160i | ||||||
\(249\) | − | 4.79420e6i | − | 0.310540i | ||||||
\(250\) | 4.76472e7 | 3.04942 | ||||||||
\(251\) | 1.04228e7 | 0.659117 | 0.329558 | − | 0.944135i | \(-0.393100\pi\) | ||||
0.329558 | + | 0.944135i | \(0.393100\pi\) | |||||||
\(252\) | 2.66186e7i | 1.66335i | ||||||||
\(253\) | 2.91701e6 | 0.180126 | ||||||||
\(254\) | 7.68670e6i | 0.469071i | ||||||||
\(255\) | −2.45304e7 | −1.47939 | ||||||||
\(256\) | 3.30922e7 | 1.97245 | ||||||||
\(257\) | 2.59317e7i | 1.52768i | 0.645407 | + | 0.763839i | \(0.276688\pi\) | ||||
−0.645407 | + | 0.763839i | \(0.723312\pi\) | |||||||
\(258\) | −876497. | − | 1.56662e7i | −0.0510377 | − | 0.912229i | ||||
\(259\) | 1.08771e7 | 0.626057 | ||||||||
\(260\) | − | 8.31510e7i | − | 4.73094i | ||||||
\(261\) | − | 4.78156e6i | − | 0.268935i | ||||||
\(262\) | −5.07822e7 | −2.82363 | ||||||||
\(263\) | − | 1.65481e7i | − | 0.909666i | −0.890577 | − | 0.454833i | \(-0.849699\pi\) | ||
0.890577 | − | 0.454833i | \(-0.150301\pi\) | |||||||
\(264\) | 3.26508e7 | 1.77452 | ||||||||
\(265\) | 2.99168e7i | 1.60760i | ||||||||
\(266\) | − | 3.58925e6i | − | 0.190704i | ||||||
\(267\) | −3.56520e6 | −0.187305 | ||||||||
\(268\) | −3.79944e7 | −1.97386 | ||||||||
\(269\) | −1.71681e7 | −0.881996 | −0.440998 | − | 0.897508i | \(-0.645375\pi\) | ||||
−0.440998 | + | 0.897508i | \(0.645375\pi\) | |||||||
\(270\) | 5.45773e7i | 2.77281i | ||||||||
\(271\) | 3.10767e7 | 1.56145 | 0.780723 | − | 0.624878i | \(-0.214851\pi\) | ||||
0.780723 | + | 0.624878i | \(0.214851\pi\) | |||||||
\(272\) | 1.28991e8 | 6.40992 | ||||||||
\(273\) | 7.97909e6 | 0.392162 | ||||||||
\(274\) | 908543. | 0.0441666 | ||||||||
\(275\) | −4.61959e7 | −2.22129 | ||||||||
\(276\) | 4.20200e6i | 0.199861i | ||||||||
\(277\) | − | 1.00741e7i | − | 0.473986i | −0.971511 | − | 0.236993i | \(-0.923838\pi\) | ||
0.971511 | − | 0.236993i | \(-0.0761618\pi\) | |||||||
\(278\) | 6.03225e7i | 2.80766i | ||||||||
\(279\) | −8.31229e6 | −0.382744 | ||||||||
\(280\) | − | 9.73428e7i | − | 4.43435i | ||||||
\(281\) | 1.56495e6 | 0.0705311 | 0.0352655 | − | 0.999378i | \(-0.488772\pi\) | ||||
0.0352655 | + | 0.999378i | \(0.488772\pi\) | |||||||
\(282\) | −1.66054e7 | −0.740459 | ||||||||
\(283\) | −2.45515e6 | −0.108323 | −0.0541613 | − | 0.998532i | \(-0.517249\pi\) | ||||
−0.0541613 | + | 0.998532i | \(0.517249\pi\) | |||||||
\(284\) | 4.10529e7i | 1.79221i | ||||||||
\(285\) | − | 2.33894e6i | − | 0.101038i | ||||||
\(286\) | 5.32568e7i | 2.27655i | ||||||||
\(287\) | 1.97962e7i | 0.837406i | ||||||||
\(288\) | − | 6.53614e7i | − | 2.73617i | ||||||
\(289\) | 5.55232e7 | 2.30028 | ||||||||
\(290\) | 2.78575e7i | 1.14221i | ||||||||
\(291\) | − | 1.04095e7i | − | 0.422426i | ||||||
\(292\) | − | 4.46311e7i | − | 1.79262i | ||||||
\(293\) | −6.96069e6 | −0.276726 | −0.138363 | − | 0.990382i | \(-0.544184\pi\) | ||||
−0.138363 | + | 0.990382i | \(0.544184\pi\) | |||||||
\(294\) | −8.33664e6 | −0.328057 | ||||||||
\(295\) | − | 2.26895e7i | − | 0.883809i | ||||||
\(296\) | −6.56448e7 | −2.53119 | ||||||||
\(297\) | − | 2.54723e7i | − | 0.972297i | ||||||
\(298\) | 3.52580e7 | 1.33232 | ||||||||
\(299\) | −4.30214e6 | −0.160943 | ||||||||
\(300\) | − | 6.65460e7i | − | 2.46467i | ||||||
\(301\) | 2.17987e7 | − | 1.21960e6i | 0.799338 | − | 0.0447216i | ||||
\(302\) | −5.61757e7 | −2.03952 | ||||||||
\(303\) | − | 1.25965e7i | − | 0.452818i | ||||||
\(304\) | 1.22991e7i | 0.437776i | ||||||||
\(305\) | −1.91647e7 | −0.675465 | ||||||||
\(306\) | − | 7.73020e7i | − | 2.69790i | ||||||
\(307\) | −3.61363e7 | −1.24890 | −0.624451 | − | 0.781064i | \(-0.714677\pi\) | ||||
−0.624451 | + | 0.781064i | \(0.714677\pi\) | |||||||
\(308\) | 7.23791e7i | 2.47720i | ||||||||
\(309\) | 1.77808e7i | 0.602665i | ||||||||
\(310\) | 4.84276e7 | 1.62558 | ||||||||
\(311\) | −6.46269e6 | −0.214849 | −0.107424 | − | 0.994213i | \(-0.534260\pi\) | ||||
−0.107424 | + | 0.994213i | \(0.534260\pi\) | |||||||
\(312\) | −4.81549e7 | −1.58554 | ||||||||
\(313\) | 3.01930e6i | 0.0984629i | 0.998787 | + | 0.0492315i | \(0.0156772\pi\) | ||||
−0.998787 | + | 0.0492315i | \(0.984323\pi\) | |||||||
\(314\) | 6.61154e7 | 2.13557 | ||||||||
\(315\) | −3.31220e7 | −1.05971 | ||||||||
\(316\) | −3.99311e7 | −1.26546 | ||||||||
\(317\) | −5.16124e7 | −1.62023 | −0.810115 | − | 0.586271i | \(-0.800595\pi\) | ||||
−0.810115 | + | 0.586271i | \(0.800595\pi\) | |||||||
\(318\) | 2.76020e7 | 0.858340 | ||||||||
\(319\) | − | 1.30016e7i | − | 0.400521i | ||||||
\(320\) | 1.82951e8i | 5.58321i | ||||||||
\(321\) | 1.93388e7i | 0.584675i | ||||||||
\(322\) | −8.02368e6 | −0.240329 | ||||||||
\(323\) | 7.59554e6i | 0.225399i | ||||||||
\(324\) | −3.39725e7 | −0.998832 | ||||||||
\(325\) | 6.81320e7 | 1.98473 | ||||||||
\(326\) | 6.89572e7 | 1.99034 | ||||||||
\(327\) | 4.58870e6i | 0.131234i | ||||||||
\(328\) | − | 1.19473e8i | − | 3.38569i | ||||||
\(329\) | − | 2.31055e7i | − | 0.648825i | ||||||
\(330\) | 6.47259e7i | 1.80109i | ||||||||
\(331\) | 2.44942e7i | 0.675428i | 0.941249 | + | 0.337714i | \(0.109654\pi\) | ||||
−0.941249 | + | 0.337714i | \(0.890346\pi\) | |||||||
\(332\) | −6.41391e7 | −1.75270 | ||||||||
\(333\) | 2.23364e7i | 0.604896i | ||||||||
\(334\) | − | 1.16566e8i | − | 3.12849i | ||||||
\(335\) | − | 4.72772e7i | − | 1.25753i | ||||||
\(336\) | −5.09931e7 | −1.34429 | ||||||||
\(337\) | 6.86964e7 | 1.79492 | 0.897458 | − | 0.441100i | \(-0.145412\pi\) | ||||
0.897458 | + | 0.441100i | \(0.145412\pi\) | |||||||
\(338\) | − | 4.41045e6i | − | 0.114218i | ||||||
\(339\) | 2.76201e7 | 0.708967 | ||||||||
\(340\) | 3.28179e8i | 8.34977i | ||||||||
\(341\) | −2.26021e7 | −0.570015 | ||||||||
\(342\) | 7.37063e6 | 0.184258 | ||||||||
\(343\) | − | 4.39066e7i | − | 1.08805i | ||||||
\(344\) | −1.31558e8 | + | 7.36045e6i | −3.23178 | + | 0.180813i | ||||
\(345\) | −5.22863e6 | −0.127330 | ||||||||
\(346\) | 6.61648e7i | 1.59734i | ||||||||
\(347\) | − | 5.05288e7i | − | 1.20935i | −0.796474 | − | 0.604673i | \(-0.793304\pi\) | ||
0.796474 | − | 0.604673i | \(-0.206696\pi\) | |||||||
\(348\) | 1.87291e7 | 0.444404 | ||||||||
\(349\) | 7.43877e7i | 1.74995i | 0.484172 | + | 0.874973i | \(0.339121\pi\) | ||||
−0.484172 | + | 0.874973i | \(0.660879\pi\) | |||||||
\(350\) | 1.27069e8 | 2.96371 | ||||||||
\(351\) | 3.75678e7i | 0.868749i | ||||||||
\(352\) | − | 1.77725e8i | − | 4.07494i | ||||||
\(353\) | 6.81991e7 | 1.55044 | 0.775219 | − | 0.631692i | \(-0.217639\pi\) | ||||
0.775219 | + | 0.631692i | \(0.217639\pi\) | |||||||
\(354\) | −2.09339e7 | −0.471890 | ||||||||
\(355\) | −5.10829e7 | −1.14180 | ||||||||
\(356\) | 4.76970e7i | 1.05716i | ||||||||
\(357\) | −3.14917e7 | −0.692137 | ||||||||
\(358\) | −1.41694e8 | −3.08817 | ||||||||
\(359\) | 4.74093e7 | 1.02466 | 0.512331 | − | 0.858788i | \(-0.328782\pi\) | ||||
0.512331 | + | 0.858788i | \(0.328782\pi\) | |||||||
\(360\) | 1.99896e8 | 4.28447 | ||||||||
\(361\) | 4.63217e7 | 0.984606 | ||||||||
\(362\) | − | 3.56249e7i | − | 0.750980i | ||||||
\(363\) | − | 7.44598e6i | − | 0.155669i | ||||||
\(364\) | − | 1.06748e8i | − | 2.21338i | ||||||
\(365\) | 5.55353e7 | 1.14206 | ||||||||
\(366\) | 1.76819e7i | 0.360649i | ||||||||
\(367\) | 1.93390e7 | 0.391233 | 0.195617 | − | 0.980680i | \(-0.437329\pi\) | ||||
0.195617 | + | 0.980680i | \(0.437329\pi\) | |||||||
\(368\) | 2.74943e7 | 0.551695 | ||||||||
\(369\) | −4.06520e7 | −0.809102 | ||||||||
\(370\) | − | 1.30132e8i | − | 2.56910i | ||||||
\(371\) | 3.84068e7i | 0.752118i | ||||||||
\(372\) | − | 3.25587e7i | − | 0.632468i | ||||||
\(373\) | 9.21753e7i | 1.77618i | 0.459665 | + | 0.888092i | \(0.347969\pi\) | ||||
−0.459665 | + | 0.888092i | \(0.652031\pi\) | |||||||
\(374\) | − | 2.10193e8i | − | 4.01795i | ||||||
\(375\) | 3.98606e7 | 0.755874 | ||||||||
\(376\) | 1.39445e8i | 2.62325i | ||||||||
\(377\) | 1.91754e7i | 0.357866i | ||||||||
\(378\) | 7.00656e7i | 1.29727i | ||||||||
\(379\) | 2.95380e6 | 0.0542579 | 0.0271290 | − | 0.999632i | \(-0.491364\pi\) | ||||
0.0271290 | + | 0.999632i | \(0.491364\pi\) | |||||||
\(380\) | −3.12914e7 | −0.570262 | ||||||||
\(381\) | 6.43053e6i | 0.116271i | ||||||||
\(382\) | 1.65247e8 | 2.96445 | ||||||||
\(383\) | 3.91227e7i | 0.696358i | 0.937428 | + | 0.348179i | \(0.113200\pi\) | ||||
−0.937428 | + | 0.348179i | \(0.886800\pi\) | |||||||
\(384\) | 7.34784e7 | 1.29768 | ||||||||
\(385\) | −9.00627e7 | −1.57820 | ||||||||
\(386\) | − | 1.30876e8i | − | 2.27560i | ||||||
\(387\) | 2.50448e6 | + | 4.47641e7i | 0.0432100 | + | 0.772320i | ||||
\(388\) | −1.39263e8 | −2.38419 | ||||||||
\(389\) | − | 1.61920e7i | − | 0.275076i | −0.990496 | − | 0.137538i | \(-0.956081\pi\) | ||
0.990496 | − | 0.137538i | \(-0.0439189\pi\) | |||||||
\(390\) | − | 9.54609e7i | − | 1.60928i | ||||||
\(391\) | 1.69796e7 | 0.284052 | ||||||||
\(392\) | 7.00076e7i | 1.16222i | ||||||||
\(393\) | −4.24833e7 | −0.699907 | ||||||||
\(394\) | 5.08870e7i | 0.831990i | ||||||||
\(395\) | − | 4.96870e7i | − | 0.806216i | ||||||
\(396\) | −1.48632e8 | −2.39347 | ||||||||
\(397\) | 8.82551e7 | 1.41048 | 0.705242 | − | 0.708967i | \(-0.250838\pi\) | ||||
0.705242 | + | 0.708967i | \(0.250838\pi\) | |||||||
\(398\) | −1.53209e8 | −2.43017 | ||||||||
\(399\) | − | 3.00269e6i | − | 0.0472707i | ||||||
\(400\) | −4.35420e8 | −6.80344 | ||||||||
\(401\) | −3.91351e7 | −0.606923 | −0.303461 | − | 0.952844i | \(-0.598142\pi\) | ||||
−0.303461 | + | 0.952844i | \(0.598142\pi\) | |||||||
\(402\) | −4.36192e7 | −0.671428 | ||||||||
\(403\) | 3.33347e7 | 0.509309 | ||||||||
\(404\) | −1.68523e8 | −2.55573 | ||||||||
\(405\) | − | 4.22727e7i | − | 0.636348i | ||||||
\(406\) | 3.57630e7i | 0.534387i | ||||||||
\(407\) | 6.07354e7i | 0.900863i | ||||||||
\(408\) | 1.90057e8 | 2.79836 | ||||||||
\(409\) | 1.45715e7i | 0.212978i | 0.994314 | + | 0.106489i | \(0.0339609\pi\) | ||||
−0.994314 | + | 0.106489i | \(0.966039\pi\) | |||||||
\(410\) | 2.36839e8 | 3.43639 | ||||||||
\(411\) | 760067. | 0.0109478 | ||||||||
\(412\) | 2.37880e8 | 3.40147 | ||||||||
\(413\) | − | 2.91284e7i | − | 0.413492i | ||||||
\(414\) | − | 1.64768e7i | − | 0.232206i | ||||||
\(415\) | − | 7.98095e7i | − | 1.11663i | ||||||
\(416\) | 2.62118e8i | 3.64097i | ||||||||
\(417\) | 5.04645e7i | 0.695949i | ||||||||
\(418\) | 2.00416e7 | 0.274413 | ||||||||
\(419\) | − | 1.23103e7i | − | 0.167350i | −0.996493 | − | 0.0836750i | \(-0.973334\pi\) | ||
0.996493 | − | 0.0836750i | \(-0.0266658\pi\) | |||||||
\(420\) | − | 1.29737e8i | − | 1.75112i | ||||||
\(421\) | − | 9.02713e7i | − | 1.20977i | −0.796312 | − | 0.604886i | \(-0.793219\pi\) | ||
0.796312 | − | 0.604886i | \(-0.206781\pi\) | |||||||
\(422\) | −1.02521e8 | −1.36419 | ||||||||
\(423\) | 4.74477e7 | 0.626894 | ||||||||
\(424\) | − | 2.31790e8i | − | 3.04087i | ||||||
\(425\) | −2.68902e8 | −3.50290 | ||||||||
\(426\) | 4.71304e7i | 0.609639i | ||||||||
\(427\) | −2.46034e7 | −0.316017 | ||||||||
\(428\) | 2.58724e8 | 3.29993 | ||||||||
\(429\) | 4.45535e7i | 0.564300i | ||||||||
\(430\) | −1.45911e7 | − | 2.60797e8i | −0.183520 | − | 3.28017i | ||||
\(431\) | −6.09927e7 | −0.761809 | −0.380905 | − | 0.924614i | \(-0.624387\pi\) | ||||
−0.380905 | + | 0.924614i | \(0.624387\pi\) | |||||||
\(432\) | − | 2.40090e8i | − | 2.97798i | ||||||
\(433\) | 9.68502e7i | 1.19299i | 0.802617 | + | 0.596495i | \(0.203440\pi\) | ||||
−0.802617 | + | 0.596495i | \(0.796560\pi\) | |||||||
\(434\) | 6.21707e7 | 0.760530 | ||||||||
\(435\) | 2.33049e7i | 0.283126i | ||||||||
\(436\) | 6.13899e7 | 0.740691 | ||||||||
\(437\) | 1.61898e6i | 0.0193998i | ||||||||
\(438\) | − | 5.12383e7i | − | 0.609779i | ||||||
\(439\) | −4.73443e7 | −0.559596 | −0.279798 | − | 0.960059i | \(-0.590267\pi\) | ||||
−0.279798 | + | 0.960059i | \(0.590267\pi\) | |||||||
\(440\) | 5.43541e8 | 6.38079 | ||||||||
\(441\) | 2.38209e7 | 0.277742 | ||||||||
\(442\) | 3.10003e8i | 3.59004i | ||||||||
\(443\) | 6.31480e7 | 0.726354 | 0.363177 | − | 0.931720i | \(-0.381692\pi\) | ||||
0.363177 | + | 0.931720i | \(0.381692\pi\) | |||||||
\(444\) | −8.74903e7 | −0.999565 | ||||||||
\(445\) | −5.93503e7 | −0.673508 | ||||||||
\(446\) | −2.21400e8 | −2.49558 | ||||||||
\(447\) | 2.94960e7 | 0.330249 | ||||||||
\(448\) | 2.34870e8i | 2.61212i | ||||||||
\(449\) | 1.36056e8i | 1.50307i | 0.659694 | + | 0.751535i | \(0.270686\pi\) | ||||
−0.659694 | + | 0.751535i | \(0.729314\pi\) | |||||||
\(450\) | 2.60940e8i | 2.86354i | ||||||||
\(451\) | −1.10538e8 | −1.20498 | ||||||||
\(452\) | − | 3.69515e8i | − | 4.00145i | ||||||
\(453\) | −4.69954e7 | −0.505546 | ||||||||
\(454\) | −5.56579e7 | −0.594784 | ||||||||
\(455\) | 1.32829e8 | 1.41013 | ||||||||
\(456\) | 1.81217e7i | 0.191119i | ||||||||
\(457\) | − | 7.83614e7i | − | 0.821020i | −0.911856 | − | 0.410510i | \(-0.865351\pi\) | ||
0.911856 | − | 0.410510i | \(-0.134649\pi\) | |||||||
\(458\) | 9.53692e7i | 0.992686i | ||||||||
\(459\) | − | 1.48272e8i | − | 1.53328i | ||||||
\(460\) | 6.99511e7i | 0.718656i | ||||||||
\(461\) | 7.38666e6 | 0.0753955 | 0.0376977 | − | 0.999289i | \(-0.487998\pi\) | ||||
0.0376977 | + | 0.999289i | \(0.487998\pi\) | |||||||
\(462\) | 8.30942e7i | 0.842646i | ||||||||
\(463\) | 1.21692e8i | 1.22608i | 0.790053 | + | 0.613038i | \(0.210053\pi\) | ||||
−0.790053 | + | 0.613038i | \(0.789947\pi\) | |||||||
\(464\) | − | 1.22547e8i | − | 1.22673i | ||||||
\(465\) | 4.05135e7 | 0.402940 | ||||||||
\(466\) | 3.04232e8 | 3.00640 | ||||||||
\(467\) | 4.52041e7i | 0.443840i | 0.975065 | + | 0.221920i | \(0.0712325\pi\) | ||||
−0.975065 | + | 0.221920i | \(0.928768\pi\) | |||||||
\(468\) | 2.19210e8 | 2.13857 | ||||||||
\(469\) | − | 6.06938e7i | − | 0.588337i | ||||||
\(470\) | −2.76431e8 | −2.66253 | ||||||||
\(471\) | 5.53107e7 | 0.529354 | ||||||||
\(472\) | 1.75794e8i | 1.67178i | ||||||||
\(473\) | 6.80998e6 | + | 1.21719e8i | 0.0643520 | + | 1.15020i | ||||
\(474\) | −4.58426e7 | −0.430461 | ||||||||
\(475\) | − | 2.56394e7i | − | 0.239237i | ||||||
\(476\) | 4.21312e8i | 3.90646i | ||||||||
\(477\) | −7.88693e7 | −0.726696 | ||||||||
\(478\) | − | 5.01678e7i | − | 0.459348i | ||||||
\(479\) | 1.31849e7 | 0.119970 | 0.0599848 | − | 0.998199i | \(-0.480895\pi\) | ||||
0.0599848 | + | 0.998199i | \(0.480895\pi\) | |||||||
\(480\) | 3.18566e8i | 2.88055i | ||||||||
\(481\) | − | 8.95755e7i | − | 0.804922i | ||||||
\(482\) | −1.69243e8 | −1.51137 | ||||||||
\(483\) | −6.71244e6 | −0.0595715 | ||||||||
\(484\) | −9.96160e7 | −0.878604 | ||||||||
\(485\) | − | 1.73288e8i | − | 1.51895i | ||||||
\(486\) | −2.25009e8 | −1.96016 | ||||||||
\(487\) | −1.42982e8 | −1.23793 | −0.618964 | − | 0.785420i | \(-0.712447\pi\) | ||||
−0.618964 | + | 0.785420i | \(0.712447\pi\) | |||||||
\(488\) | 1.48485e8 | 1.27768 | ||||||||
\(489\) | 5.76881e7 | 0.493355 | ||||||||
\(490\) | −1.38781e8 | −1.17962 | ||||||||
\(491\) | 1.24890e8i | 1.05507i | 0.849532 | + | 0.527537i | \(0.176885\pi\) | ||||
−0.849532 | + | 0.527537i | \(0.823115\pi\) | |||||||
\(492\) | − | 1.59231e8i | − | 1.33701i | ||||||
\(493\) | − | 7.56813e7i | − | 0.631608i | ||||||
\(494\) | −2.95583e7 | −0.245188 | ||||||||
\(495\) | − | 1.84946e8i | − | 1.52486i | ||||||
\(496\) | −2.13037e8 | −1.74586 | ||||||||
\(497\) | −6.55795e7 | −0.534194 | ||||||||
\(498\) | −7.36344e7 | −0.596201 | ||||||||
\(499\) | 8.63178e7i | 0.694703i | 0.937735 | + | 0.347351i | \(0.112919\pi\) | ||||
−0.937735 | + | 0.347351i | \(0.887081\pi\) | |||||||
\(500\) | − | 5.33274e8i | − | 4.26619i | ||||||
\(501\) | − | 9.75170e7i | − | 0.775474i | ||||||
\(502\) | − | 1.60084e8i | − | 1.26543i | ||||||
\(503\) | − | 2.41745e7i | − | 0.189956i | −0.995479 | − | 0.0949782i | \(-0.969722\pi\) | ||
0.995479 | − | 0.0949782i | \(-0.0302781\pi\) | |||||||
\(504\) | 2.56624e8 | 2.00450 | ||||||||
\(505\) | − | 2.09696e8i | − | 1.62823i | ||||||
\(506\) | − | 4.48025e7i | − | 0.345820i | ||||||
\(507\) | − | 3.68969e6i | − | 0.0283117i | ||||||
\(508\) | 8.60307e7 | 0.656240 | ||||||||
\(509\) | 1.75528e8 | 1.33105 | 0.665524 | − | 0.746376i | \(-0.268208\pi\) | ||||
0.665524 | + | 0.746376i | \(0.268208\pi\) | |||||||
\(510\) | 3.76764e8i | 2.84026i | ||||||||
\(511\) | 7.12954e7 | 0.534317 | ||||||||
\(512\) | − | 1.42277e8i | − | 1.06004i | ||||||
\(513\) | 1.41375e7 | 0.104718 | ||||||||
\(514\) | 3.98287e8 | 2.93296 | ||||||||
\(515\) | 2.95999e8i | 2.16705i | ||||||||
\(516\) | −1.75338e8 | + | 9.80988e6i | −1.27623 | + | 0.0714027i | ||||
\(517\) | 1.29016e8 | 0.933624 | ||||||||
\(518\) | − | 1.67062e8i | − | 1.20196i | ||||||
\(519\) | 5.53520e7i | 0.395942i | ||||||||
\(520\) | −8.01641e8 | −5.70124 | ||||||||
\(521\) | 6.01580e7i | 0.425383i | 0.977119 | + | 0.212691i | \(0.0682229\pi\) | ||||
−0.977119 | + | 0.212691i | \(0.931777\pi\) | |||||||
\(522\) | −7.34403e7 | −0.516325 | ||||||||
\(523\) | − | 2.27924e8i | − | 1.59326i | −0.604470 | − | 0.796628i | \(-0.706615\pi\) | ||
0.604470 | − | 0.796628i | \(-0.293385\pi\) | |||||||
\(524\) | 5.68362e8i | 3.95031i | ||||||||
\(525\) | 1.06303e8 | 0.734630 | ||||||||
\(526\) | −2.54164e8 | −1.74645 | ||||||||
\(527\) | −1.31565e8 | −0.898893 | ||||||||
\(528\) | − | 2.84734e8i | − | 1.93436i | ||||||
\(529\) | −1.44417e8 | −0.975552 | ||||||||
\(530\) | 4.59494e8 | 3.08640 | ||||||||
\(531\) | 5.98160e7 | 0.399516 | ||||||||
\(532\) | −4.01715e7 | −0.266798 | ||||||||
\(533\) | 1.63026e8 | 1.07665 | ||||||||
\(534\) | 5.47582e7i | 0.359605i | ||||||||
\(535\) | 3.21935e8i | 2.10236i | ||||||||
\(536\) | 3.66296e8i | 2.37869i | ||||||||
\(537\) | −1.18538e8 | −0.765480 | ||||||||
\(538\) | 2.63687e8i | 1.69333i | ||||||||
\(539\) | 6.47718e7 | 0.413638 | ||||||||
\(540\) | 6.10837e8 | 3.87922 | ||||||||
\(541\) | −8.34449e7 | −0.526997 | −0.263499 | − | 0.964660i | \(-0.584876\pi\) | ||||
−0.263499 | + | 0.964660i | \(0.584876\pi\) | |||||||
\(542\) | − | 4.77309e8i | − | 2.99779i | ||||||
\(543\) | − | 2.98030e7i | − | 0.186149i | ||||||
\(544\) | − | 1.03452e9i | − | 6.42604i | ||||||
\(545\) | 7.63886e7i | 0.471888i | ||||||||
\(546\) | − | 1.22551e8i | − | 0.752905i | ||||||
\(547\) | −1.02571e8 | −0.626701 | −0.313351 | − | 0.949638i | \(-0.601451\pi\) | ||||
−0.313351 | + | 0.949638i | \(0.601451\pi\) | |||||||
\(548\) | − | 1.01686e7i | − | 0.0617899i | ||||||
\(549\) | − | 5.05237e7i | − | 0.305336i | ||||||
\(550\) | 7.09527e8i | 4.26462i | ||||||||
\(551\) | 7.21610e6 | 0.0431368 | ||||||||
\(552\) | 4.05105e7 | 0.240852 | ||||||||
\(553\) | − | 6.37875e7i | − | 0.377190i | ||||||
\(554\) | −1.54728e8 | −0.909998 | ||||||||
\(555\) | − | 1.08866e8i | − | 0.636815i | ||||||
\(556\) | 6.75138e8 | 3.92797 | ||||||||
\(557\) | −1.75878e8 | −1.01776 | −0.508880 | − | 0.860837i | \(-0.669940\pi\) | ||||
−0.508880 | + | 0.860837i | \(0.669940\pi\) | |||||||
\(558\) | 1.27669e8i | 0.734824i | ||||||||
\(559\) | −1.00437e7 | − | 1.79517e8i | −0.0574986 | − | 1.02771i | ||||
\(560\) | −8.48887e8 | −4.83377 | ||||||||
\(561\) | − | 1.75843e8i | − | 0.995948i | ||||||
\(562\) | − | 2.40361e7i | − | 0.135411i | ||||||
\(563\) | 2.10250e8 | 1.17818 | 0.589088 | − | 0.808069i | \(-0.299487\pi\) | ||||
0.589088 | + | 0.808069i | \(0.299487\pi\) | |||||||
\(564\) | 1.85850e8i | 1.03592i | ||||||||
\(565\) | 4.59795e8 | 2.54929 | ||||||||
\(566\) | 3.77088e7i | 0.207967i | ||||||||
\(567\) | − | 5.42691e7i | − | 0.297717i | ||||||
\(568\) | 3.95782e8 | 2.15978 | ||||||||
\(569\) | 1.85858e8 | 1.00889 | 0.504445 | − | 0.863444i | \(-0.331697\pi\) | ||||
0.504445 | + | 0.863444i | \(0.331697\pi\) | |||||||
\(570\) | −3.59239e7 | −0.193981 | ||||||||
\(571\) | − | 6.24130e7i | − | 0.335248i | −0.985851 | − | 0.167624i | \(-0.946391\pi\) | ||
0.985851 | − | 0.167624i | \(-0.0536095\pi\) | |||||||
\(572\) | 5.96059e8 | 3.18494 | ||||||||
\(573\) | 1.38242e8 | 0.734813 | ||||||||
\(574\) | 3.04051e8 | 1.60772 | ||||||||
\(575\) | −5.73163e7 | −0.301491 | ||||||||
\(576\) | −4.82311e8 | −2.52383 | ||||||||
\(577\) | − | 5.34888e7i | − | 0.278442i | −0.990261 | − | 0.139221i | \(-0.955540\pi\) | ||
0.990261 | − | 0.139221i | \(-0.0444599\pi\) | |||||||
\(578\) | − | 8.52785e8i | − | 4.41628i | ||||||
\(579\) | − | 1.09488e8i | − | 0.564065i | ||||||
\(580\) | 3.11785e8 | 1.59798 | ||||||||
\(581\) | − | 1.02458e8i | − | 0.522419i | ||||||
\(582\) | −1.59880e8 | −0.811008 | ||||||||
\(583\) | −2.14455e8 | −1.08226 | ||||||||
\(584\) | −4.30278e8 | −2.16028 | ||||||||
\(585\) | 2.72768e8i | 1.36246i | ||||||||
\(586\) | 1.06910e8i | 0.531281i | ||||||||
\(587\) | 6.51087e7i | 0.321903i | 0.986962 | + | 0.160951i | \(0.0514563\pi\) | ||||
−0.986962 | + | 0.160951i | \(0.948544\pi\) | |||||||
\(588\) | 9.33049e7i | 0.458957i | ||||||||
\(589\) | − | 1.25445e7i | − | 0.0613915i | ||||||
\(590\) | −3.48489e8 | −1.69681 | ||||||||
\(591\) | 4.25709e7i | 0.206229i | ||||||||
\(592\) | 5.72462e8i | 2.75919i | ||||||||
\(593\) | 1.65528e8i | 0.793796i | 0.917863 | + | 0.396898i | \(0.129913\pi\) | ||||
−0.917863 | + | 0.396898i | \(0.870087\pi\) | |||||||
\(594\) | −3.91231e8 | −1.86670 | ||||||||
\(595\) | −5.24247e8 | −2.48877 | ||||||||
\(596\) | − | 3.94612e8i | − | 1.86394i | ||||||
\(597\) | −1.28172e8 | −0.602378 | ||||||||
\(598\) | 6.60769e7i | 0.308991i | ||||||||
\(599\) | 3.37403e8 | 1.56989 | 0.784944 | − | 0.619566i | \(-0.212691\pi\) | ||||
0.784944 | + | 0.619566i | \(0.212691\pi\) | |||||||
\(600\) | −6.41555e8 | −2.97016 | ||||||||
\(601\) | − | 3.47057e8i | − | 1.59874i | −0.600842 | − | 0.799368i | \(-0.705168\pi\) | ||
0.600842 | − | 0.799368i | \(-0.294832\pi\) | |||||||
\(602\) | −1.87319e7 | − | 3.34807e8i | −0.0858603 | − | 1.53464i | ||||
\(603\) | 1.24636e8 | 0.568451 | ||||||||
\(604\) | 6.28727e8i | 2.85332i | ||||||||
\(605\) | − | 1.23954e8i | − | 0.559751i | ||||||
\(606\) | −1.93471e8 | −0.869358 | ||||||||
\(607\) | 2.68929e8i | 1.20246i | 0.799074 | + | 0.601232i | \(0.205323\pi\) | ||||
−0.799074 | + | 0.601232i | \(0.794677\pi\) | |||||||
\(608\) | 9.86402e7 | 0.438878 | ||||||||
\(609\) | 2.99185e7i | 0.132461i | ||||||||
\(610\) | 2.94352e8i | 1.29681i | ||||||||
\(611\) | −1.90279e8 | −0.834195 | ||||||||
\(612\) | −8.65175e8 | −3.77442 | ||||||||
\(613\) | 1.60012e8 | 0.694658 | 0.347329 | − | 0.937743i | \(-0.387089\pi\) | ||||
0.347329 | + | 0.937743i | \(0.387089\pi\) | |||||||
\(614\) | 5.55019e8i | 2.39775i | ||||||||
\(615\) | 1.98135e8 | 0.851795 | ||||||||
\(616\) | 6.97790e8 | 2.98526 | ||||||||
\(617\) | −3.99697e8 | −1.70167 | −0.850835 | − | 0.525433i | \(-0.823903\pi\) | ||||
−0.850835 | + | 0.525433i | \(0.823903\pi\) | |||||||
\(618\) | 2.73097e8 | 1.15705 | ||||||||
\(619\) | 2.89266e8 | 1.21962 | 0.609812 | − | 0.792546i | \(-0.291245\pi\) | ||||
0.609812 | + | 0.792546i | \(0.291245\pi\) | |||||||
\(620\) | − | 5.42009e8i | − | 2.27421i | ||||||
\(621\) | − | 3.16040e7i | − | 0.131968i | ||||||
\(622\) | 9.92610e7i | 0.412484i | ||||||||
\(623\) | −7.61931e7 | −0.315102 | ||||||||
\(624\) | 4.19940e8i | 1.72836i | ||||||||
\(625\) | 1.92811e8 | 0.789756 | ||||||||
\(626\) | 4.63736e7 | 0.189037 | ||||||||
\(627\) | 1.67664e7 | 0.0680200 | ||||||||
\(628\) | − | 7.39973e8i | − | 2.98770i | ||||||
\(629\) | 3.53535e8i | 1.42063i | ||||||||
\(630\) | 5.08723e8i | 2.03451i | ||||||||
\(631\) | 4.58916e8i | 1.82661i | 0.407280 | + | 0.913303i | \(0.366477\pi\) | ||||
−0.407280 | + | 0.913303i | \(0.633523\pi\) | |||||||
\(632\) | 3.84966e8i | 1.52501i | ||||||||
\(633\) | −8.57667e7 | −0.338148 | ||||||||
\(634\) | 7.92719e8i | 3.11065i | ||||||||
\(635\) | 1.07050e8i | 0.418085i | ||||||||
\(636\) | − | 3.08926e8i | − | 1.20083i | ||||||
\(637\) | −9.55286e7 | −0.369586 | ||||||||
\(638\) | −1.99693e8 | −0.768955 | ||||||||
\(639\) | − | 1.34669e8i | − | 0.516138i | ||||||
\(640\) | 1.22320e9 | 4.66615 | ||||||||
\(641\) | − | 1.71310e8i | − | 0.650444i | −0.945638 | − | 0.325222i | \(-0.894561\pi\) | ||
0.945638 | − | 0.325222i | \(-0.105439\pi\) | |||||||
\(642\) | 2.97026e8 | 1.12251 | ||||||||
\(643\) | 2.81858e8 | 1.06023 | 0.530113 | − | 0.847927i | \(-0.322150\pi\) | ||||
0.530113 | + | 0.847927i | \(0.322150\pi\) | |||||||
\(644\) | 8.98022e7i | 0.336225i | ||||||||
\(645\) | −1.22066e7 | − | 2.18177e8i | −0.0454901 | − | 0.813073i | ||||
\(646\) | 1.16660e8 | 0.432739 | ||||||||
\(647\) | − | 2.11105e8i | − | 0.779447i | −0.920932 | − | 0.389724i | \(-0.872571\pi\) | ||
0.920932 | − | 0.389724i | \(-0.127429\pi\) | |||||||
\(648\) | 3.27521e8i | 1.20369i | ||||||||
\(649\) | 1.62647e8 | 0.594993 | ||||||||
\(650\) | − | 1.04644e9i | − | 3.81045i | ||||||
\(651\) | 5.20106e7 | 0.188516 | ||||||||
\(652\) | − | 7.71780e8i | − | 2.78452i | ||||||
\(653\) | − | 4.34044e8i | − | 1.55881i | −0.626519 | − | 0.779406i | \(-0.715521\pi\) | ||
0.626519 | − | 0.779406i | \(-0.284479\pi\) | |||||||
\(654\) | 7.04781e7 | 0.251954 | ||||||||
\(655\) | −7.07224e8 | −2.51671 | ||||||||
\(656\) | −1.04187e9 | −3.69066 | ||||||||
\(657\) | 1.46407e8i | 0.516257i | ||||||||
\(658\) | −3.54879e8 | −1.24567 | ||||||||
\(659\) | −4.74544e7 | −0.165814 | −0.0829068 | − | 0.996557i | \(-0.526420\pi\) | ||||
−0.0829068 | + | 0.996557i | \(0.526420\pi\) | |||||||
\(660\) | 7.24422e8 | 2.51976 | ||||||||
\(661\) | −7.15485e7 | −0.247740 | −0.123870 | − | 0.992298i | \(-0.539531\pi\) | ||||
−0.123870 | + | 0.992298i | \(0.539531\pi\) | |||||||
\(662\) | 3.76208e8 | 1.29674 | ||||||||
\(663\) | 2.59342e8i | 0.889881i | ||||||||
\(664\) | 6.18351e8i | 2.11218i | ||||||||
\(665\) | − | 4.99862e7i | − | 0.169975i | ||||||
\(666\) | 3.43067e8 | 1.16133 | ||||||||
\(667\) | − | 1.61314e7i | − | 0.0543619i | ||||||
\(668\) | −1.30463e9 | −4.37681 | ||||||||
\(669\) | −1.85218e8 | −0.618593 | ||||||||
\(670\) | −7.26134e8 | −2.41431 | ||||||||
\(671\) | − | 1.37380e8i | − | 0.454732i | ||||||
\(672\) | 4.08971e8i | 1.34767i | ||||||||
\(673\) | 2.15921e7i | 0.0708352i | 0.999373 | + | 0.0354176i | \(0.0112761\pi\) | ||||
−0.999373 | + | 0.0354176i | \(0.988724\pi\) | |||||||
\(674\) | − | 1.05511e9i | − | 3.44603i | ||||||
\(675\) | 5.00506e8i | 1.62741i | ||||||||
\(676\) | −4.93625e7 | −0.159793 | ||||||||
\(677\) | − | 1.59757e8i | − | 0.514864i | −0.966296 | − | 0.257432i | \(-0.917124\pi\) | ||
0.966296 | − | 0.257432i | \(-0.0828764\pi\) | |||||||
\(678\) | − | 4.24219e8i | − | 1.36113i | ||||||
\(679\) | − | 2.22465e8i | − | 0.710643i | ||||||
\(680\) | 3.16390e9 | 10.0623 | ||||||||
\(681\) | −4.65622e7 | −0.147432 | ||||||||
\(682\) | 3.47148e8i | 1.09436i | ||||||||
\(683\) | 2.73296e8 | 0.857771 | 0.428886 | − | 0.903359i | \(-0.358906\pi\) | ||||
0.428886 | + | 0.903359i | \(0.358906\pi\) | |||||||
\(684\) | − | 8.24932e7i | − | 0.257780i | ||||||
\(685\) | 1.26529e7 | 0.0393658 | ||||||||
\(686\) | −6.74364e8 | −2.08892 | ||||||||
\(687\) | 7.97838e7i | 0.246062i | ||||||||
\(688\) | 6.41875e7 | + | 1.14726e9i | 0.197099 | + | 3.52288i | ||||
\(689\) | 3.16289e8 | 0.966999 | ||||||||
\(690\) | 8.03068e7i | 0.244459i | ||||||||
\(691\) | − | 2.18660e8i | − | 0.662729i | −0.943503 | − | 0.331364i | \(-0.892491\pi\) | ||
0.943503 | − | 0.331364i | \(-0.107509\pi\) | |||||||
\(692\) | 7.40526e8 | 2.23472 | ||||||||
\(693\) | − | 2.37431e8i | − | 0.713408i | ||||||
\(694\) | −7.76075e8 | −2.32180 | ||||||||
\(695\) | 8.40088e8i | 2.50248i | ||||||||
\(696\) | − | 1.80563e8i | − | 0.535550i | ||||||
\(697\) | −6.43430e8 | −1.90022 | ||||||||
\(698\) | 1.14253e9 | 3.35969 | ||||||||
\(699\) | 2.54514e8 | 0.745212 | ||||||||
\(700\) | − | 1.42218e9i | − | 4.14629i | ||||||
\(701\) | −4.06383e8 | −1.17973 | −0.589863 | − | 0.807503i | \(-0.700818\pi\) | ||||
−0.589863 | + | 0.807503i | \(0.700818\pi\) | |||||||
\(702\) | 5.77006e8 | 1.66790 | ||||||||
\(703\) | −3.37091e7 | −0.0970243 | ||||||||
\(704\) | −1.31146e9 | −3.75870 | ||||||||
\(705\) | −2.31256e8 | −0.659974 | ||||||||
\(706\) | − | 1.04747e9i | − | 2.97666i | ||||||
\(707\) | − | 2.69205e8i | − | 0.761772i | ||||||
\(708\) | 2.34295e8i | 0.660183i | ||||||||
\(709\) | −2.66283e8 | −0.747145 | −0.373573 | − | 0.927601i | \(-0.621867\pi\) | ||||
−0.373573 | + | 0.927601i | \(0.621867\pi\) | |||||||
\(710\) | 7.84586e8i | 2.19213i | ||||||||
\(711\) | 1.30989e8 | 0.364441 | ||||||||
\(712\) | 4.59836e8 | 1.27398 | ||||||||
\(713\) | −2.80429e7 | −0.0773668 | ||||||||
\(714\) | 4.83684e8i | 1.32882i | ||||||||
\(715\) | 7.41687e8i | 2.02910i | ||||||||
\(716\) | 1.58586e9i | 4.32041i | ||||||||
\(717\) | − | 4.19693e7i | − | 0.113861i | ||||||
\(718\) | − | 7.28163e8i | − | 1.96723i | ||||||
\(719\) | −4.99086e8 | −1.34273 | −0.671366 | − | 0.741126i | \(-0.734292\pi\) | ||||
−0.671366 | + | 0.741126i | \(0.734292\pi\) | |||||||
\(720\) | − | 1.74321e9i | − | 4.67039i | ||||||
\(721\) | 3.80000e8i | 1.01386i | ||||||||
\(722\) | − | 7.11458e8i | − | 1.89033i | ||||||
\(723\) | −1.41585e8 | −0.374630 | ||||||||
\(724\) | −3.98720e8 | −1.05064 | ||||||||
\(725\) | 2.55469e8i | 0.670385i | ||||||||
\(726\) | −1.14363e8 | −0.298866 | ||||||||
\(727\) | − | 2.89743e8i | − | 0.754066i | −0.926200 | − | 0.377033i | \(-0.876944\pi\) | ||
0.926200 | − | 0.377033i | \(-0.123056\pi\) | |||||||
\(728\) | −1.02913e9 | −2.66734 | ||||||||
\(729\) | −4.41664e7 | −0.114001 | ||||||||
\(730\) | − | 8.52971e8i | − | 2.19263i | ||||||
\(731\) | 3.96402e7 | + | 7.08515e8i | 0.101481 | + | 1.81383i | ||||
\(732\) | 1.97898e8 | 0.504555 | ||||||||
\(733\) | − | 1.87282e8i | − | 0.475536i | −0.971322 | − | 0.237768i | \(-0.923584\pi\) | ||
0.971322 | − | 0.237768i | \(-0.0764159\pi\) | |||||||
\(734\) | − | 2.97029e8i | − | 0.751122i | ||||||
\(735\) | −1.16101e8 | −0.292398 | ||||||||
\(736\) | − | 2.20508e8i | − | 0.553083i | ||||||
\(737\) | 3.38901e8 | 0.846585 | ||||||||
\(738\) | 6.24377e8i | 1.55338i | ||||||||
\(739\) | − | 8.30923e6i | − | 0.0205886i | −0.999947 | − | 0.0102943i | \(-0.996723\pi\) | ||
0.999947 | − | 0.0102943i | \(-0.00327684\pi\) | |||||||
\(740\) | −1.45646e9 | −3.59421 | ||||||||
\(741\) | −2.47279e7 | −0.0607760 | ||||||||
\(742\) | 5.89892e8 | 1.44398 | ||||||||
\(743\) | − | 1.16504e8i | − | 0.284037i | −0.989864 | − | 0.142019i | \(-0.954641\pi\) | ||
0.989864 | − | 0.142019i | \(-0.0453593\pi\) | |||||||
\(744\) | −3.13891e8 | −0.762185 | ||||||||
\(745\) | 4.91024e8 | 1.18750 | ||||||||
\(746\) | 1.41573e9 | 3.41007 | ||||||||
\(747\) | 2.10401e8 | 0.504761 | ||||||||
\(748\) | −2.35251e9 | −5.62118 | ||||||||
\(749\) | 4.13296e8i | 0.983593i | ||||||||
\(750\) | − | 6.12221e8i | − | 1.45119i | ||||||
\(751\) | − | 1.60100e8i | − | 0.377982i | −0.981979 | − | 0.188991i | \(-0.939478\pi\) | ||
0.981979 | − | 0.188991i | \(-0.0605216\pi\) | |||||||
\(752\) | 1.21604e9 | 2.85953 | ||||||||
\(753\) | − | 1.33923e8i | − | 0.313668i | ||||||
\(754\) | 2.94517e8 | 0.687062 | ||||||||
\(755\) | −7.82337e8 | −1.81783 | ||||||||
\(756\) | 7.84185e8 | 1.81490 | ||||||||
\(757\) | − | 6.51063e7i | − | 0.150084i | −0.997180 | − | 0.0750422i | \(-0.976091\pi\) | ||
0.997180 | − | 0.0750422i | \(-0.0239092\pi\) | |||||||
\(758\) | − | 4.53676e7i | − | 0.104169i | ||||||
\(759\) | − | 3.74808e7i | − | 0.0857203i | ||||||
\(760\) | 3.01674e8i | 0.687221i | ||||||||
\(761\) | 6.42727e8i | 1.45839i | 0.684308 | + | 0.729193i | \(0.260104\pi\) | ||||
−0.684308 | + | 0.729193i | \(0.739896\pi\) | |||||||
\(762\) | 9.87669e7 | 0.223227 | ||||||||
\(763\) | 9.80666e7i | 0.220774i | ||||||||
\(764\) | − | 1.84947e9i | − | 4.14732i | ||||||
\(765\) | − | 1.07655e9i | − | 2.40465i | ||||||
\(766\) | 6.00888e8 | 1.33693 | ||||||||
\(767\) | −2.39879e8 | −0.531627 | ||||||||
\(768\) | − | 4.25204e8i | − | 0.938672i | ||||||
\(769\) | −7.77041e7 | −0.170870 | −0.0854349 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854349 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(770\) | 1.38328e9i | 3.02997i | ||||||||
\(771\) | 3.33198e8 | 0.727008 | ||||||||
\(772\) | −1.46478e9 | −3.18361 | ||||||||
\(773\) | 2.33836e8i | 0.506260i | 0.967432 | + | 0.253130i | \(0.0814600\pi\) | ||||
−0.967432 | + | 0.253130i | \(0.918540\pi\) | |||||||
\(774\) | 6.87535e8 | − | 3.84665e7i | 1.48276 | − | 0.0829582i | ||||
\(775\) | 4.44109e8 | 0.954080 | ||||||||
\(776\) | 1.34260e9i | 2.87318i | ||||||||
\(777\) | − | 1.39761e8i | − | 0.297935i | ||||||
\(778\) | −2.48695e8 | −0.528114 | ||||||||
\(779\) | − | 6.13501e7i | − | 0.129779i | ||||||
\(780\) | −1.06841e9 | −2.25141 | ||||||||
\(781\) | − | 3.66182e8i | − | 0.768677i | ||||||
\(782\) | − | 2.60791e8i | − | 0.545347i | ||||||
\(783\) | −1.40865e8 | −0.293439 | ||||||||
\(784\) | 6.10508e8 | 1.26690 | ||||||||
\(785\) | 9.20763e8 | 1.90344 | ||||||||
\(786\) | 6.52503e8i | 1.34374i | ||||||||
\(787\) | 8.30477e7 | 0.170374 | 0.0851870 | − | 0.996365i | \(-0.472851\pi\) | ||||
0.0851870 | + | 0.996365i | \(0.472851\pi\) | |||||||
\(788\) | 5.69535e8 | 1.16397 | ||||||||
\(789\) | −2.12628e8 | −0.432902 | ||||||||
\(790\) | −7.63146e8 | −1.54784 | ||||||||
\(791\) | 5.90278e8 | 1.19269 | ||||||||
\(792\) | 1.43293e9i | 2.88436i | ||||||||
\(793\) | 2.02615e8i | 0.406304i | ||||||||
\(794\) | − | 1.35552e9i | − | 2.70797i | ||||||
\(795\) | 3.84403e8 | 0.765042 | ||||||||
\(796\) | 1.71474e9i | 3.39985i | ||||||||
\(797\) | 1.84780e8 | 0.364989 | 0.182495 | − | 0.983207i | \(-0.441583\pi\) | ||||
0.182495 | + | 0.983207i | \(0.441583\pi\) | |||||||
\(798\) | −4.61186e7 | −0.0907543 | ||||||||
\(799\) | 7.50991e8 | 1.47229 | ||||||||
\(800\) | 3.49213e9i | 6.82056i | ||||||||
\(801\) | − | 1.56465e8i | − | 0.304452i | ||||||
\(802\) | 6.01079e8i | 1.16522i | ||||||||
\(803\) | 3.98098e8i | 0.768854i | ||||||||
\(804\) | 4.88193e8i | 0.939341i | ||||||||
\(805\) | −1.11743e8 | −0.214206 | ||||||||
\(806\) | − | 5.11990e8i | − | 0.977814i | ||||||
\(807\) | 2.20595e8i | 0.419734i | ||||||||
\(808\) | 1.62469e9i | 3.07990i | ||||||||
\(809\) | 3.45503e8 | 0.652539 | 0.326269 | − | 0.945277i | \(-0.394208\pi\) | ||||
0.326269 | + | 0.945277i | \(0.394208\pi\) | |||||||
\(810\) | −6.49269e8 | −1.22171 | ||||||||
\(811\) | − | 5.17319e8i | − | 0.969831i | −0.874561 | − | 0.484915i | \(-0.838850\pi\) | ||
0.874561 | − | 0.484915i | \(-0.161150\pi\) | |||||||
\(812\) | 4.00265e8 | 0.747618 | ||||||||
\(813\) | − | 3.99306e8i | − | 0.743078i | ||||||
\(814\) | 9.32839e8 | 1.72955 | ||||||||
\(815\) | 9.60341e8 | 1.77400 | ||||||||
\(816\) | − | 1.65741e9i | − | 3.05042i | ||||||
\(817\) | −6.75559e7 | + | 3.77964e6i | −0.123879 | + | 0.00693081i | ||||
\(818\) | 2.23805e8 | 0.408893 | ||||||||
\(819\) | 3.50175e8i | 0.637432i | ||||||||
\(820\) | − | 2.65074e9i | − | 4.80758i | ||||||
\(821\) | 3.54323e8 | 0.640279 | 0.320140 | − | 0.947370i | \(-0.396270\pi\) | ||||
0.320140 | + | 0.947370i | \(0.396270\pi\) | |||||||
\(822\) | − | 1.16739e7i | − | 0.0210185i | ||||||
\(823\) | −6.44087e8 | −1.15543 | −0.577717 | − | 0.816237i | \(-0.696056\pi\) | ||||
−0.577717 | + | 0.816237i | \(0.696056\pi\) | |||||||
\(824\) | − | 2.29335e9i | − | 4.09910i | ||||||
\(825\) | 5.93574e8i | 1.05709i | ||||||||
\(826\) | −4.47386e8 | −0.793856 | ||||||||
\(827\) | −9.70326e8 | −1.71554 | −0.857771 | − | 0.514033i | \(-0.828151\pi\) | ||||
−0.857771 | + | 0.514033i | \(0.828151\pi\) | |||||||
\(828\) | −1.84411e8 | −0.324860 | ||||||||
\(829\) | − | 1.86684e8i | − | 0.327674i | −0.986487 | − | 0.163837i | \(-0.947613\pi\) | ||
0.986487 | − | 0.163837i | \(-0.0523872\pi\) | |||||||
\(830\) | −1.22580e9 | −2.14381 | ||||||||
\(831\) | −1.29442e8 | −0.225566 | ||||||||
\(832\) | 1.93421e9 | 3.35840 | ||||||||
\(833\) | 3.77031e8 | 0.652292 | ||||||||
\(834\) | 7.75087e8 | 1.33614 | ||||||||
\(835\) | − | 1.62338e9i | − | 2.78843i | ||||||
\(836\) | − | 2.24309e8i | − | 0.383908i | ||||||
\(837\) | 2.44881e8i | 0.417617i | ||||||||
\(838\) | −1.89074e8 | −0.321292 | ||||||||
\(839\) | − | 6.54445e8i | − | 1.10812i | −0.832476 | − | 0.554061i | \(-0.813077\pi\) | ||
0.832476 | − | 0.554061i | \(-0.186923\pi\) | |||||||
\(840\) | −1.25076e9 | −2.11027 | ||||||||
\(841\) | 5.22923e8 | 0.879123 | ||||||||
\(842\) | −1.38648e9 | −2.32262 | ||||||||
\(843\) | − | 2.01081e7i | − | 0.0335651i | ||||||
\(844\) | 1.14743e9i | 1.90853i | ||||||||
\(845\) | − | 6.14227e7i | − | 0.101803i | ||||||
\(846\) | − | 7.28753e8i | − | 1.20356i | ||||||
\(847\) | − | 1.59131e8i | − | 0.261881i | ||||||
\(848\) | −2.02135e9 | −3.31477 | ||||||||
\(849\) | 3.15464e7i | 0.0515497i | ||||||||
\(850\) | 4.13009e9i | 6.72516i | ||||||||
\(851\) | 7.53557e7i | 0.122272i | ||||||||
\(852\) | 5.27491e8 | 0.852896 | ||||||||
\(853\) | −3.26019e8 | −0.525286 | −0.262643 | − | 0.964893i | \(-0.584594\pi\) | ||||
−0.262643 | + | 0.964893i | \(0.584594\pi\) | |||||||
\(854\) | 3.77885e8i | 0.606717i | ||||||||
\(855\) | 1.02648e8 | 0.164230 | ||||||||
\(856\) | − | 2.49430e9i | − | 3.97674i | ||||||
\(857\) | −5.10541e8 | −0.811126 | −0.405563 | − | 0.914067i | \(-0.632925\pi\) | ||||
−0.405563 | + | 0.914067i | \(0.632925\pi\) | |||||||
\(858\) | 6.84300e8 | 1.08339 | ||||||||
\(859\) | 2.39639e8i | 0.378075i | 0.981970 | + | 0.189037i | \(0.0605367\pi\) | ||||
−0.981970 | + | 0.189037i | \(0.939463\pi\) | |||||||
\(860\) | −2.91888e9 | + | 1.63306e8i | −4.58902 | + | 0.256748i | ||||
\(861\) | 2.54363e8 | 0.398514 | ||||||||
\(862\) | 9.36792e8i | 1.46259i | ||||||||
\(863\) | 4.53996e8i | 0.706349i | 0.935557 | + | 0.353175i | \(0.114898\pi\) | ||||
−0.935557 | + | 0.353175i | \(0.885102\pi\) | |||||||
\(864\) | −1.92555e9 | −2.98547 | ||||||||
\(865\) | 9.21451e8i | 1.42372i | ||||||||
\(866\) | 1.48753e9 | 2.29040 | ||||||||
\(867\) | − | 7.13421e8i | − | 1.09468i | ||||||
\(868\) | − | 6.95823e8i | − | 1.06400i | ||||||
\(869\) | 3.56176e8 | 0.542756 | ||||||||
\(870\) | 3.57942e8 | 0.543569 | ||||||||
\(871\) | −4.99828e8 | −0.756425 | ||||||||
\(872\) | − | 5.91846e8i | − | 0.892605i | ||||||
\(873\) | 4.56837e8 | 0.686623 | ||||||||
\(874\) | 2.48661e7 | 0.0372454 | ||||||||
\(875\) | 8.51873e8 | 1.27160 | ||||||||
\(876\) | −5.73467e8 | −0.853093 | ||||||||
\(877\) | −1.77324e8 | −0.262886 | −0.131443 | − | 0.991324i | \(-0.541961\pi\) | ||||
−0.131443 | + | 0.991324i | \(0.541961\pi\) | |||||||
\(878\) | 7.27165e8i | 1.07436i | ||||||||
\(879\) | 8.94384e7i | 0.131691i | ||||||||
\(880\) | − | 4.74000e9i | − | 6.95554i | ||||||
\(881\) | −2.01503e8 | −0.294681 | −0.147341 | − | 0.989086i | \(-0.547071\pi\) | ||||
−0.147341 | + | 0.989086i | \(0.547071\pi\) | |||||||
\(882\) | − | 3.65867e8i | − | 0.533233i | ||||||
\(883\) | −5.21198e8 | −0.757043 | −0.378521 | − | 0.925593i | \(-0.623567\pi\) | ||||
−0.378521 | + | 0.925593i | \(0.623567\pi\) | |||||||
\(884\) | 3.46960e9 | 5.02253 | ||||||||
\(885\) | −2.91538e8 | −0.420597 | ||||||||
\(886\) | − | 9.69894e8i | − | 1.39451i | ||||||
\(887\) | 4.21223e8i | 0.603588i | 0.953373 | + | 0.301794i | \(0.0975856\pi\) | ||||
−0.953373 | + | 0.301794i | \(0.902414\pi\) | |||||||
\(888\) | 8.43475e8i | 1.20457i | ||||||||
\(889\) | 1.37429e8i | 0.195602i | ||||||||
\(890\) | 9.11566e8i | 1.29306i | ||||||||
\(891\) | 3.03027e8 | 0.428398 | ||||||||
\(892\) | 2.47794e9i | 3.49137i | ||||||||
\(893\) | 7.16058e7i | 0.100553i | ||||||||
\(894\) | − | 4.53032e8i | − | 0.634039i | ||||||
\(895\) | −1.97331e9 | −2.75250 | ||||||||
\(896\) | 1.57033e9 | 2.18307 | ||||||||
\(897\) | 5.52785e7i | 0.0765912i | ||||||||
\(898\) | 2.08970e9 | 2.88572 | ||||||||
\(899\) | 1.24992e8i | 0.172030i | ||||||||
\(900\) | 2.92048e9 | 4.00614 | ||||||||
\(901\) | −1.24832e9 | −1.70668 | ||||||||
\(902\) | 1.69776e9i | 2.31343i | ||||||||
\(903\) | −1.56707e7 | − | 2.80092e8i | −0.0212826 | − | 0.380398i | ||||
\(904\) | −3.56241e9 | −4.82213 | ||||||||
\(905\) | − | 4.96135e8i | − | 0.669351i | ||||||
\(906\) | 7.21805e8i | 0.970589i | ||||||||
\(907\) | −8.15320e8 | −1.09271 | −0.546357 | − | 0.837553i | \(-0.683986\pi\) | ||||
−0.546357 | + | 0.837553i | \(0.683986\pi\) | |||||||
\(908\) | 6.22932e8i | 0.832114i | ||||||||
\(909\) | 5.52820e8 | 0.736024 | ||||||||
\(910\) | − | 2.04013e9i | − | 2.70728i | ||||||
\(911\) | − | 2.96417e7i | − | 0.0392056i | −0.999808 | − | 0.0196028i | \(-0.993760\pi\) | ||
0.999808 | − | 0.0196028i | \(-0.00624017\pi\) | |||||||
\(912\) | 1.58032e8 | 0.208334 | ||||||||
\(913\) | 5.72105e8 | 0.751733 | ||||||||
\(914\) | −1.20356e9 | −1.57626 | ||||||||
\(915\) | 2.46248e8i | 0.321448i | ||||||||
\(916\) | 1.06739e9 | 1.38879 | ||||||||
\(917\) | −9.07924e8 | −1.17745 | ||||||||
\(918\) | −2.27732e9 | −2.94372 | ||||||||
\(919\) | 8.04796e8 | 1.03691 | 0.518453 | − | 0.855106i | \(-0.326508\pi\) | ||||
0.518453 | + | 0.855106i | \(0.326508\pi\) | |||||||
\(920\) | 6.74383e8 | 0.866050 | ||||||||
\(921\) | 4.64317e8i | 0.594341i | ||||||||
\(922\) | − | 1.13452e8i | − | 0.144751i | ||||||
\(923\) | 5.40063e8i | 0.686814i | ||||||||
\(924\) | 9.30003e8 | 1.17888 | ||||||||
\(925\) | − | 1.19339e9i | − | 1.50785i | ||||||
\(926\) | 1.86907e9 | 2.35392 | ||||||||
\(927\) | −7.80339e8 | −0.979590 | ||||||||
\(928\) | −9.82843e8 | −1.22982 | ||||||||
\(929\) | − | 1.14654e9i | − | 1.43002i | −0.699116 | − | 0.715009i | \(-0.746423\pi\) | ||
0.699116 | − | 0.715009i | \(-0.253577\pi\) | |||||||
\(930\) | − | 6.22249e8i | − | 0.773598i | ||||||
\(931\) | 3.59493e7i | 0.0445494i | ||||||||
\(932\) | − | 3.40501e9i | − | 4.20601i | ||||||
\(933\) | 8.30395e7i | 0.102245i | ||||||||
\(934\) | 6.94292e8 | 0.852122 | ||||||||
\(935\) | − | 2.92728e9i | − | 3.58121i | ||||||
\(936\) | − | 2.11336e9i | − | 2.57718i | ||||||
\(937\) | 1.12604e9i | 1.36879i | 0.729113 | + | 0.684393i | \(0.239933\pi\) | ||||
−0.729113 | + | 0.684393i | \(0.760067\pi\) | |||||||
\(938\) | −9.32201e8 | −1.12954 | ||||||||
\(939\) | 3.87951e7 | 0.0468576 | ||||||||
\(940\) | 3.09386e9i | 3.72492i | ||||||||
\(941\) | −7.16788e8 | −0.860244 | −0.430122 | − | 0.902771i | \(-0.641529\pi\) | ||||
−0.430122 | + | 0.902771i | \(0.641529\pi\) | |||||||
\(942\) | − | 8.49521e8i | − | 1.01630i | ||||||
\(943\) | −1.37146e8 | −0.163550 | ||||||||
\(944\) | 1.53303e9 | 1.82236 | ||||||||
\(945\) | 9.75776e8i | 1.15626i | ||||||||
\(946\) | 1.86949e9 | − | 1.04595e8i | 2.20826 | − | 0.123548i | ||||
\(947\) | −2.57246e8 | −0.302899 | −0.151450 | − | 0.988465i | \(-0.548394\pi\) | ||||
−0.151450 | + | 0.988465i | \(0.548394\pi\) | |||||||
\(948\) | 5.13077e8i | 0.602223i | ||||||||
\(949\) | − | 5.87135e8i | − | 0.686972i | ||||||
\(950\) | −3.93798e8 | −0.459307 | ||||||||
\(951\) | 6.63171e8i | 0.771053i | ||||||||
\(952\) | 4.06177e9 | 4.70766 | ||||||||
\(953\) | − | 5.52951e8i | − | 0.638864i | −0.947609 | − | 0.319432i | \(-0.896508\pi\) | ||
0.947609 | − | 0.319432i | \(-0.103492\pi\) | |||||||
\(954\) | 1.21136e9i | 1.39517i | ||||||||
\(955\) | 2.30133e9 | 2.64222 | ||||||||
\(956\) | −5.61486e8 | −0.642636 | ||||||||
\(957\) | −1.67059e8 | −0.190605 | ||||||||
\(958\) | − | 2.02508e8i | − | 0.230328i | ||||||
\(959\) | 1.62437e7 | 0.0184174 | ||||||||
\(960\) | 2.35074e9 | 2.65700 | ||||||||
\(961\) | −6.70216e8 | −0.755170 | ||||||||
\(962\) | −1.37580e9 | −1.54536 | ||||||||
\(963\) | −8.48714e8 | −0.950347 | ||||||||
\(964\) | 1.89419e9i | 2.11443i | ||||||||
\(965\) | − | 1.82265e9i | − | 2.02825i | ||||||
\(966\) | 1.03097e8i | 0.114370i | ||||||||
\(967\) | 8.89206e8 | 0.983383 | 0.491692 | − | 0.870769i | \(-0.336379\pi\) | ||||
0.491692 | + | 0.870769i | \(0.336379\pi\) | |||||||
\(968\) | 9.60376e8i | 1.05880i | ||||||||
\(969\) | 9.75956e7 | 0.107265 | ||||||||
\(970\) | −2.66154e9 | −2.91620 | ||||||||
\(971\) | 3.96400e8 | 0.432988 | 0.216494 | − | 0.976284i | \(-0.430538\pi\) | ||||
0.216494 | + | 0.976284i | \(0.430538\pi\) | |||||||
\(972\) | 2.51833e9i | 2.74230i | ||||||||
\(973\) | 1.07849e9i | 1.17079i | ||||||||
\(974\) | 2.19607e9i | 2.37668i | ||||||||
\(975\) | − | 8.75432e8i | − | 0.944514i | ||||||
\(976\) | − | 1.29488e9i | − | 1.39277i | ||||||
\(977\) | −2.87804e8 | −0.308613 | −0.154306 | − | 0.988023i | \(-0.549314\pi\) | ||||
−0.154306 | + | 0.988023i | \(0.549314\pi\) | |||||||
\(978\) | − | 8.86036e8i | − | 0.947185i | ||||||
\(979\) | − | 4.25446e8i | − | 0.453415i | ||||||
\(980\) | 1.55326e9i | 1.65031i | ||||||||
\(981\) | −2.01382e8 | −0.213312 | ||||||||
\(982\) | 1.91819e9 | 2.02562 | ||||||||
\(983\) | 1.48295e9i | 1.56123i | 0.625012 | + | 0.780615i | \(0.285094\pi\) | ||||
−0.625012 | + | 0.780615i | \(0.714906\pi\) | |||||||
\(984\) | −1.53511e9 | −1.61122 | ||||||||
\(985\) | 7.08683e8i | 0.741555i | ||||||||
\(986\) | −1.16239e9 | −1.21261 | ||||||||
\(987\) | −2.96884e8 | −0.308770 | ||||||||
\(988\) | 3.30821e8i | 0.343023i | ||||||||
\(989\) | 8.44928e6 | + | 1.51019e8i | 0.00873435 | + | 0.156115i | ||||
\(990\) | −2.84060e9 | −2.92755 | ||||||||
\(991\) | 9.61662e7i | 0.0988102i | 0.998779 | + | 0.0494051i | \(0.0157325\pi\) | ||||
−0.998779 | + | 0.0494051i | \(0.984267\pi\) | |||||||
\(992\) | 1.70858e9i | 1.75025i | ||||||||
\(993\) | 3.14727e8 | 0.321430 | ||||||||
\(994\) | 1.00724e9i | 1.02559i | ||||||||
\(995\) | −2.13369e9 | −2.16602 | ||||||||
\(996\) | 8.24127e8i | 0.834096i | ||||||||
\(997\) | − | 1.29421e9i | − | 1.30593i | −0.757390 | − | 0.652963i | \(-0.773526\pi\) | ||
0.757390 | − | 0.652963i | \(-0.226474\pi\) | |||||||
\(998\) | 1.32576e9 | 1.33375 | ||||||||
\(999\) | 6.58032e8 | 0.660010 |
(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 | 43.7.b.b.42.1 | ✓ | 20 | |
43.42 | odd | 2 | inner | 43.7.b.b.42.20 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.7.b.b.42.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
43.7.b.b.42.20 | yes | 20 | 43.42 | odd | 2 | inner |