Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [69,7,Mod(22,69)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(69, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("69.22");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 69 = 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 69.d (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: | \(15.8737317698\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.14 | ||
Character | \(\chi\) | \(=\) | 69.22 |
Dual form | 69.7.d.a.22.13 |
$q$-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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.368531 | −0.0460664 | −0.0230332 | − | 0.999735i | \(-0.507332\pi\) | ||||
−0.0230332 | + | 0.999735i | \(0.507332\pi\) | |||||||
\(3\) | 15.5885 | 0.577350 | ||||||||
\(4\) | −63.8642 | −0.997878 | ||||||||
\(5\) | 113.928i | 0.911421i | 0.890128 | + | 0.455711i | \(0.150615\pi\) | ||||
−0.890128 | + | 0.455711i | \(0.849385\pi\) | |||||||
\(6\) | −5.74483 | −0.0265964 | ||||||||
\(7\) | − | 569.901i | − | 1.66152i | −0.556631 | − | 0.830760i | \(-0.687906\pi\) | ||
0.556631 | − | 0.830760i | \(-0.312094\pi\) | |||||||
\(8\) | 47.1219 | 0.0920350 | ||||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 41.9859i | − | 0.0419859i | ||||||
\(11\) | 814.298i | 0.611794i | 0.952065 | + | 0.305897i | \(0.0989563\pi\) | ||||
−0.952065 | + | 0.305897i | \(0.901044\pi\) | |||||||
\(12\) | −995.544 | −0.576125 | ||||||||
\(13\) | 3513.83 | 1.59938 | 0.799689 | − | 0.600415i | \(-0.204998\pi\) | ||||
0.799689 | + | 0.600415i | \(0.204998\pi\) | |||||||
\(14\) | 210.026i | 0.0765402i | ||||||||
\(15\) | 1775.96i | 0.526209i | ||||||||
\(16\) | 4069.94 | 0.993638 | ||||||||
\(17\) | 7484.26i | 1.52336i | 0.647954 | + | 0.761679i | \(0.275625\pi\) | ||||
−0.647954 | + | 0.761679i | \(0.724375\pi\) | |||||||
\(18\) | −89.5530 | −0.0153555 | ||||||||
\(19\) | − | 4283.93i | − | 0.624571i | −0.949988 | − | 0.312285i | \(-0.898905\pi\) | ||
0.949988 | − | 0.312285i | \(-0.101095\pi\) | |||||||
\(20\) | − | 7275.90i | − | 0.909487i | ||||||
\(21\) | − | 8883.88i | − | 0.959279i | ||||||
\(22\) | − | 300.094i | − | 0.0281831i | ||||||
\(23\) | 12048.1 | − | 1696.83i | 0.990227 | − | 0.139462i | ||||
\(24\) | 734.558 | 0.0531364 | ||||||||
\(25\) | 2645.50 | 0.169312 | ||||||||
\(26\) | −1294.96 | −0.0736775 | ||||||||
\(27\) | 3788.00 | 0.192450 | ||||||||
\(28\) | 36396.3i | 1.65799i | ||||||||
\(29\) | −3314.46 | −0.135900 | −0.0679500 | − | 0.997689i | \(-0.521646\pi\) | ||||
−0.0679500 | + | 0.997689i | \(0.521646\pi\) | |||||||
\(30\) | − | 654.495i | − | 0.0242405i | ||||||
\(31\) | 34401.9 | 1.15478 | 0.577388 | − | 0.816470i | \(-0.304072\pi\) | ||||
0.577388 | + | 0.816470i | \(0.304072\pi\) | |||||||
\(32\) | −4515.70 | −0.137808 | ||||||||
\(33\) | 12693.6i | 0.353219i | ||||||||
\(34\) | − | 2758.18i | − | 0.0701756i | ||||||
\(35\) | 64927.5 | 1.51434 | ||||||||
\(36\) | −15519.0 | −0.332626 | ||||||||
\(37\) | 7160.07i | 0.141355i | 0.997499 | + | 0.0706776i | \(0.0225162\pi\) | ||||
−0.997499 | + | 0.0706776i | \(0.977484\pi\) | |||||||
\(38\) | 1578.76i | 0.0287717i | ||||||||
\(39\) | 54775.2 | 0.923401 | ||||||||
\(40\) | 5368.49i | 0.0838826i | ||||||||
\(41\) | 77969.3 | 1.13129 | 0.565643 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565643 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(42\) | 3273.99i | 0.0441905i | ||||||||
\(43\) | − | 113275.i | − | 1.42472i | −0.701815 | − | 0.712359i | \(-0.747627\pi\) | ||
0.701815 | − | 0.712359i | \(-0.252373\pi\) | |||||||
\(44\) | − | 52004.5i | − | 0.610496i | ||||||
\(45\) | 27684.4i | 0.303807i | ||||||||
\(46\) | −4440.10 | + | 625.334i | −0.0456162 | + | 0.00642449i | ||||
\(47\) | −62809.9 | −0.604971 | −0.302485 | − | 0.953154i | \(-0.597816\pi\) | ||||
−0.302485 | + | 0.953154i | \(0.597816\pi\) | |||||||
\(48\) | 63444.1 | 0.573677 | ||||||||
\(49\) | −207138. | −1.76065 | ||||||||
\(50\) | −974.947 | −0.00779958 | ||||||||
\(51\) | 116668.i | 0.879511i | ||||||||
\(52\) | −224408. | −1.59598 | ||||||||
\(53\) | 135215.i | 0.908235i | 0.890942 | + | 0.454118i | \(0.150045\pi\) | ||||
−0.890942 | + | 0.454118i | \(0.849955\pi\) | |||||||
\(54\) | −1395.99 | −0.00886548 | ||||||||
\(55\) | −92771.0 | −0.557602 | ||||||||
\(56\) | − | 26854.8i | − | 0.152918i | ||||||
\(57\) | − | 66779.9i | − | 0.360596i | ||||||
\(58\) | 1221.48 | 0.00626042 | ||||||||
\(59\) | −101668. | −0.495025 | −0.247513 | − | 0.968885i | \(-0.579613\pi\) | ||||
−0.247513 | + | 0.968885i | \(0.579613\pi\) | |||||||
\(60\) | − | 113420.i | − | 0.525093i | ||||||
\(61\) | 38234.1i | 0.168446i | 0.996447 | + | 0.0842231i | \(0.0268409\pi\) | ||||
−0.996447 | + | 0.0842231i | \(0.973159\pi\) | |||||||
\(62\) | −12678.2 | −0.0531963 | ||||||||
\(63\) | − | 138486.i | − | 0.553840i | ||||||
\(64\) | −258812. | −0.987290 | ||||||||
\(65\) | 400322.i | 1.45771i | ||||||||
\(66\) | − | 4678.00i | − | 0.0162715i | ||||||
\(67\) | − | 229273.i | − | 0.762306i | −0.924512 | − | 0.381153i | \(-0.875527\pi\) | ||
0.924512 | − | 0.381153i | \(-0.124473\pi\) | |||||||
\(68\) | − | 477976.i | − | 1.52013i | ||||||
\(69\) | 187811. | − | 26451.0i | 0.571708 | − | 0.0805182i | ||||
\(70\) | −23927.8 | −0.0697603 | ||||||||
\(71\) | −64522.4 | −0.180275 | −0.0901375 | − | 0.995929i | \(-0.528731\pi\) | ||||
−0.0901375 | + | 0.995929i | \(0.528731\pi\) | |||||||
\(72\) | 11450.6 | 0.0306783 | ||||||||
\(73\) | −53631.6 | −0.137864 | −0.0689322 | − | 0.997621i | \(-0.521959\pi\) | ||||
−0.0689322 | + | 0.997621i | \(0.521959\pi\) | |||||||
\(74\) | − | 2638.71i | − | 0.00651172i | ||||||
\(75\) | 41239.2 | 0.0977522 | ||||||||
\(76\) | 273590.i | 0.623245i | ||||||||
\(77\) | 464069. | 1.01651 | ||||||||
\(78\) | −20186.4 | −0.0425377 | ||||||||
\(79\) | 458737.i | 0.930427i | 0.885199 | + | 0.465213i | \(0.154022\pi\) | ||||
−0.885199 | + | 0.465213i | \(0.845978\pi\) | |||||||
\(80\) | 463679.i | 0.905623i | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | −28734.1 | −0.0521142 | ||||||||
\(83\) | − | 1.13063e6i | − | 1.97736i | −0.150055 | − | 0.988678i | \(-0.547945\pi\) | ||
0.150055 | − | 0.988678i | \(-0.452055\pi\) | |||||||
\(84\) | 567362.i | 0.957243i | ||||||||
\(85\) | −852664. | −1.38842 | ||||||||
\(86\) | 41745.4i | 0.0656316i | ||||||||
\(87\) | −51667.4 | −0.0784619 | ||||||||
\(88\) | 38371.3i | 0.0563065i | ||||||||
\(89\) | 829443.i | 1.17657i | 0.808655 | + | 0.588284i | \(0.200196\pi\) | ||||
−0.808655 | + | 0.588284i | \(0.799804\pi\) | |||||||
\(90\) | − | 10202.6i | − | 0.0139953i | ||||||
\(91\) | − | 2.00254e6i | − | 2.65740i | ||||||
\(92\) | −769442. | + | 108367.i | −0.988126 | + | 0.139166i | ||||
\(93\) | 536273. | 0.666710 | ||||||||
\(94\) | 23147.4 | 0.0278688 | ||||||||
\(95\) | 488058. | 0.569247 | ||||||||
\(96\) | −70392.8 | −0.0795637 | ||||||||
\(97\) | 525418.i | 0.575691i | 0.957677 | + | 0.287846i | \(0.0929390\pi\) | ||||
−0.957677 | + | 0.287846i | \(0.907061\pi\) | |||||||
\(98\) | 76337.0 | 0.0811067 | ||||||||
\(99\) | 197874.i | 0.203931i | ||||||||
\(100\) | −168952. | −0.168952 | ||||||||
\(101\) | 1.66810e6 | 1.61904 | 0.809521 | − | 0.587090i | \(-0.199727\pi\) | ||||
0.809521 | + | 0.587090i | \(0.199727\pi\) | |||||||
\(102\) | − | 42995.8i | − | 0.0405159i | ||||||
\(103\) | 226535.i | 0.207311i | 0.994613 | + | 0.103656i | \(0.0330540\pi\) | ||||
−0.994613 | + | 0.103656i | \(0.966946\pi\) | |||||||
\(104\) | 165578. | 0.147199 | ||||||||
\(105\) | 1.01212e6 | 0.874307 | ||||||||
\(106\) | − | 49831.0i | − | 0.0418391i | ||||||
\(107\) | 742387.i | 0.606009i | 0.952989 | + | 0.303004i | \(0.0979897\pi\) | ||||
−0.952989 | + | 0.303004i | \(0.902010\pi\) | |||||||
\(108\) | −241917. | −0.192042 | ||||||||
\(109\) | 2.09107e6i | 1.61469i | 0.590080 | + | 0.807344i | \(0.299096\pi\) | ||||
−0.590080 | + | 0.807344i | \(0.700904\pi\) | |||||||
\(110\) | 34189.0 | 0.0256867 | ||||||||
\(111\) | 111614.i | 0.0816115i | ||||||||
\(112\) | − | 2.31947e6i | − | 1.65095i | ||||||
\(113\) | − | 2.20924e6i | − | 1.53111i | −0.643368 | − | 0.765557i | \(-0.722464\pi\) | ||
0.643368 | − | 0.765557i | \(-0.277536\pi\) | |||||||
\(114\) | 24610.5i | 0.0166114i | ||||||||
\(115\) | 193316. | + | 1.37261e6i | 0.127108 | + | 0.902514i | ||||
\(116\) | 211676. | 0.135612 | ||||||||
\(117\) | 853861. | 0.533126 | ||||||||
\(118\) | 37467.7 | 0.0228040 | ||||||||
\(119\) | 4.26529e6 | 2.53109 | ||||||||
\(120\) | 83686.4i | 0.0484297i | ||||||||
\(121\) | 1.10848e6 | 0.625708 | ||||||||
\(122\) | − | 14090.5i | − | 0.00775971i | ||||||
\(123\) | 1.21542e6 | 0.653148 | ||||||||
\(124\) | −2.19705e6 | −1.15232 | ||||||||
\(125\) | 2.08151e6i | 1.06574i | ||||||||
\(126\) | 51036.4i | 0.0255134i | ||||||||
\(127\) | −723004. | −0.352963 | −0.176482 | − | 0.984304i | \(-0.556472\pi\) | ||||
−0.176482 | + | 0.984304i | \(0.556472\pi\) | |||||||
\(128\) | 384385. | 0.183289 | ||||||||
\(129\) | − | 1.76578e6i | − | 0.822561i | ||||||
\(130\) | − | 147531.i | − | 0.0671512i | ||||||
\(131\) | −3.35181e6 | −1.49096 | −0.745479 | − | 0.666529i | \(-0.767779\pi\) | ||||
−0.745479 | + | 0.666529i | \(0.767779\pi\) | |||||||
\(132\) | − | 810669.i | − | 0.352470i | ||||||
\(133\) | −2.44142e6 | −1.03774 | ||||||||
\(134\) | 84494.3i | 0.0351167i | ||||||||
\(135\) | 431557.i | 0.175403i | ||||||||
\(136\) | 352673.i | 0.140202i | ||||||||
\(137\) | 546016.i | 0.212346i | 0.994348 | + | 0.106173i | \(0.0338597\pi\) | ||||
−0.994348 | + | 0.106173i | \(0.966140\pi\) | |||||||
\(138\) | −69214.3 | + | 9748.00i | −0.0263365 | + | 0.00370918i | ||||
\(139\) | 1.07985e6 | 0.402086 | 0.201043 | − | 0.979582i | \(-0.435567\pi\) | ||||
0.201043 | + | 0.979582i | \(0.435567\pi\) | |||||||
\(140\) | −4.14654e6 | −1.51113 | ||||||||
\(141\) | −979109. | −0.349280 | ||||||||
\(142\) | 23778.5 | 0.00830461 | ||||||||
\(143\) | 2.86131e6i | 0.978489i | ||||||||
\(144\) | 988996. | 0.331213 | ||||||||
\(145\) | − | 377609.i | − | 0.123862i | ||||||
\(146\) | 19764.9 | 0.00635091 | ||||||||
\(147\) | −3.22897e6 | −1.01651 | ||||||||
\(148\) | − | 457272.i | − | 0.141055i | ||||||
\(149\) | − | 4.51099e6i | − | 1.36368i | −0.731501 | − | 0.681840i | \(-0.761180\pi\) | ||
0.731501 | − | 0.681840i | \(-0.238820\pi\) | |||||||
\(150\) | −15197.9 | −0.00450309 | ||||||||
\(151\) | 3.08008e6 | 0.894605 | 0.447302 | − | 0.894383i | \(-0.352385\pi\) | ||||
0.447302 | + | 0.894383i | \(0.352385\pi\) | |||||||
\(152\) | − | 201867.i | − | 0.0574824i | ||||||
\(153\) | 1.81868e6i | 0.507786i | ||||||||
\(154\) | −171024. | −0.0468268 | ||||||||
\(155\) | 3.91933e6i | 1.05249i | ||||||||
\(156\) | −3.49817e6 | −0.921441 | ||||||||
\(157\) | − | 5.92399e6i | − | 1.53079i | −0.643562 | − | 0.765394i | \(-0.722544\pi\) | ||
0.643562 | − | 0.765394i | \(-0.277456\pi\) | |||||||
\(158\) | − | 169059.i | − | 0.0428614i | ||||||
\(159\) | 2.10780e6i | 0.524370i | ||||||||
\(160\) | − | 514463.i | − | 0.125601i | ||||||
\(161\) | −967025. | − | 6.86623e6i | −0.231718 | − | 1.64528i | ||||
\(162\) | −21761.4 | −0.00511849 | ||||||||
\(163\) | 917099. | 0.211765 | 0.105882 | − | 0.994379i | \(-0.466233\pi\) | ||||
0.105882 | + | 0.994379i | \(0.466233\pi\) | |||||||
\(164\) | −4.97945e6 | −1.12888 | ||||||||
\(165\) | −1.44616e6 | −0.321932 | ||||||||
\(166\) | 416671.i | 0.0910896i | ||||||||
\(167\) | −7.58083e6 | −1.62767 | −0.813837 | − | 0.581094i | \(-0.802625\pi\) | ||||
−0.813837 | + | 0.581094i | \(0.802625\pi\) | |||||||
\(168\) | − | 418626.i | − | 0.0882872i | ||||||
\(169\) | 7.52020e6 | 1.55801 | ||||||||
\(170\) | 314233. | 0.0639595 | ||||||||
\(171\) | − | 1.04100e6i | − | 0.208190i | ||||||
\(172\) | 7.23422e6i | 1.42169i | ||||||||
\(173\) | 5.62249e6 | 1.08590 | 0.542951 | − | 0.839765i | \(-0.317307\pi\) | ||||
0.542951 | + | 0.839765i | \(0.317307\pi\) | |||||||
\(174\) | 19041.0 | 0.00361445 | ||||||||
\(175\) | − | 1.50767e6i | − | 0.281315i | ||||||
\(176\) | 3.31414e6i | 0.607902i | ||||||||
\(177\) | −1.58484e6 | −0.285803 | ||||||||
\(178\) | − | 305676.i | − | 0.0542002i | ||||||
\(179\) | 656490. | 0.114464 | 0.0572320 | − | 0.998361i | \(-0.481773\pi\) | ||||
0.0572320 | + | 0.998361i | \(0.481773\pi\) | |||||||
\(180\) | − | 1.76804e6i | − | 0.303162i | ||||||
\(181\) | 9.20126e6i | 1.55171i | 0.630909 | + | 0.775857i | \(0.282682\pi\) | ||||
−0.630909 | + | 0.775857i | \(0.717318\pi\) | |||||||
\(182\) | 737997.i | 0.122417i | ||||||||
\(183\) | 596011.i | 0.0972525i | ||||||||
\(184\) | 567729. | − | 79957.9i | 0.0911356 | − | 0.0128353i | ||||
\(185\) | −815730. | −0.128834 | ||||||||
\(186\) | −197633. | −0.0307129 | ||||||||
\(187\) | −6.09442e6 | −0.931982 | ||||||||
\(188\) | 4.01130e6 | 0.603687 | ||||||||
\(189\) | − | 2.15878e6i | − | 0.319760i | ||||||
\(190\) | −179865. | −0.0262231 | ||||||||
\(191\) | − | 9.24960e6i | − | 1.32746i | −0.747971 | − | 0.663732i | \(-0.768972\pi\) | ||
0.747971 | − | 0.663732i | \(-0.231028\pi\) | |||||||
\(192\) | −4.03448e6 | −0.570012 | ||||||||
\(193\) | −1.56196e6 | −0.217269 | −0.108634 | − | 0.994082i | \(-0.534648\pi\) | ||||
−0.108634 | + | 0.994082i | \(0.534648\pi\) | |||||||
\(194\) | − | 193633.i | − | 0.0265200i | ||||||
\(195\) | 6.24041e6i | 0.841607i | ||||||||
\(196\) | 1.32287e7 | 1.75691 | ||||||||
\(197\) | −1.12002e7 | −1.46496 | −0.732482 | − | 0.680786i | \(-0.761638\pi\) | ||||
−0.732482 | + | 0.680786i | \(0.761638\pi\) | |||||||
\(198\) | − | 72922.8i | − | 0.00939438i | ||||||
\(199\) | − | 4.87456e6i | − | 0.618552i | −0.950972 | − | 0.309276i | \(-0.899913\pi\) | ||
0.950972 | − | 0.309276i | \(-0.100087\pi\) | |||||||
\(200\) | 124661. | 0.0155826 | ||||||||
\(201\) | − | 3.57402e6i | − | 0.440117i | ||||||
\(202\) | −614747. | −0.0745834 | ||||||||
\(203\) | 1.88892e6i | 0.225800i | ||||||||
\(204\) | − | 7.45091e6i | − | 0.877645i | ||||||
\(205\) | 8.88286e6i | 1.03108i | ||||||||
\(206\) | − | 83485.1i | − | 0.00955008i | ||||||
\(207\) | 2.92769e6 | − | 412330.i | 0.330076 | − | 0.0464872i | ||||
\(208\) | 1.43011e7 | 1.58920 | ||||||||
\(209\) | 3.48840e6 | 0.382109 | ||||||||
\(210\) | −372997. | −0.0402762 | ||||||||
\(211\) | 1.01176e7 | 1.07704 | 0.538518 | − | 0.842614i | \(-0.318984\pi\) | ||||
0.538518 | + | 0.842614i | \(0.318984\pi\) | |||||||
\(212\) | − | 8.63542e6i | − | 0.906308i | ||||||
\(213\) | −1.00580e6 | −0.104082 | ||||||||
\(214\) | − | 273593.i | − | 0.0279166i | ||||||
\(215\) | 1.29052e7 | 1.29852 | ||||||||
\(216\) | 178498. | 0.0177121 | ||||||||
\(217\) | − | 1.96057e7i | − | 1.91868i | ||||||
\(218\) | − | 770624.i | − | 0.0743829i | ||||||
\(219\) | −836034. | −0.0795960 | ||||||||
\(220\) | 5.92475e6 | 0.556419 | ||||||||
\(221\) | 2.62984e7i | 2.43642i | ||||||||
\(222\) | − | 41133.4i | − | 0.00375955i | ||||||
\(223\) | −1.27139e7 | −1.14647 | −0.573236 | − | 0.819390i | \(-0.694312\pi\) | ||||
−0.573236 | + | 0.819390i | \(0.694312\pi\) | |||||||
\(224\) | 2.57350e6i | 0.228971i | ||||||||
\(225\) | 642855. | 0.0564372 | ||||||||
\(226\) | 814173.i | 0.0705328i | ||||||||
\(227\) | 1.69641e7i | 1.45028i | 0.688599 | + | 0.725142i | \(0.258226\pi\) | ||||
−0.688599 | + | 0.725142i | \(0.741774\pi\) | |||||||
\(228\) | 4.26484e6i | 0.359831i | ||||||||
\(229\) | 1.22935e7i | 1.02369i | 0.859077 | + | 0.511847i | \(0.171038\pi\) | ||||
−0.859077 | + | 0.511847i | \(0.828962\pi\) | |||||||
\(230\) | −71242.8 | − | 505850.i | −0.00585542 | − | 0.0415756i | ||||
\(231\) | 7.23413e6 | 0.586881 | ||||||||
\(232\) | −156184. | −0.0125075 | ||||||||
\(233\) | −171237. | −0.0135372 | −0.00676861 | − | 0.999977i | \(-0.502155\pi\) | ||||
−0.00676861 | + | 0.999977i | \(0.502155\pi\) | |||||||
\(234\) | −314674. | −0.0245592 | ||||||||
\(235\) | − | 7.15578e6i | − | 0.551383i | ||||||
\(236\) | 6.49293e6 | 0.493975 | ||||||||
\(237\) | 7.15100e6i | 0.537182i | ||||||||
\(238\) | −1.57189e6 | −0.116598 | ||||||||
\(239\) | −543012. | −0.0397755 | −0.0198877 | − | 0.999802i | \(-0.506331\pi\) | ||||
−0.0198877 | + | 0.999802i | \(0.506331\pi\) | |||||||
\(240\) | 7.22804e6i | 0.522862i | ||||||||
\(241\) | 3.84804e6i | 0.274909i | 0.990508 | + | 0.137455i | \(0.0438921\pi\) | ||||
−0.990508 | + | 0.137455i | \(0.956108\pi\) | |||||||
\(242\) | −408509. | −0.0288241 | ||||||||
\(243\) | 920483. | 0.0641500 | ||||||||
\(244\) | − | 2.44179e6i | − | 0.168089i | ||||||
\(245\) | − | 2.35988e7i | − | 1.60469i | ||||||
\(246\) | −447920. | −0.0300882 | ||||||||
\(247\) | − | 1.50530e7i | − | 0.998924i | ||||||
\(248\) | 1.62108e6 | 0.106280 | ||||||||
\(249\) | − | 1.76247e7i | − | 1.14163i | ||||||
\(250\) | − | 767103.i | − | 0.0490946i | ||||||
\(251\) | − | 1.18733e7i | − | 0.750845i | −0.926854 | − | 0.375422i | \(-0.877498\pi\) | ||
0.926854 | − | 0.375422i | \(-0.122502\pi\) | |||||||
\(252\) | 8.84430e6i | 0.552665i | ||||||||
\(253\) | 1.38172e6 | + | 9.81074e6i | 0.0853218 | + | 0.605815i | ||||
\(254\) | 266449. | 0.0162597 | ||||||||
\(255\) | −1.32917e7 | −0.801605 | ||||||||
\(256\) | 1.64223e7 | 0.978846 | ||||||||
\(257\) | −1.02407e7 | −0.603296 | −0.301648 | − | 0.953419i | \(-0.597537\pi\) | ||||
−0.301648 | + | 0.953419i | \(0.597537\pi\) | |||||||
\(258\) | 650746.i | 0.0378924i | ||||||||
\(259\) | 4.08053e6 | 0.234865 | ||||||||
\(260\) | − | 2.55663e7i | − | 1.45461i | ||||||
\(261\) | −805415. | −0.0453000 | ||||||||
\(262\) | 1.23525e6 | 0.0686831 | ||||||||
\(263\) | − | 2.04038e6i | − | 0.112162i | −0.998426 | − | 0.0560809i | \(-0.982140\pi\) | ||
0.998426 | − | 0.0560809i | \(-0.0178605\pi\) | |||||||
\(264\) | 598149.i | 0.0325085i | ||||||||
\(265\) | −1.54048e7 | −0.827785 | ||||||||
\(266\) | 899738. | 0.0478048 | ||||||||
\(267\) | 1.29297e7i | 0.679291i | ||||||||
\(268\) | 1.46424e7i | 0.760688i | ||||||||
\(269\) | −3.09947e7 | −1.59232 | −0.796161 | − | 0.605085i | \(-0.793139\pi\) | ||||
−0.796161 | + | 0.605085i | \(0.793139\pi\) | |||||||
\(270\) | − | 159042.i | − | 0.00808018i | ||||||
\(271\) | −4.55560e6 | −0.228896 | −0.114448 | − | 0.993429i | \(-0.536510\pi\) | ||||
−0.114448 | + | 0.993429i | \(0.536510\pi\) | |||||||
\(272\) | 3.04605e7i | 1.51367i | ||||||||
\(273\) | − | 3.12165e7i | − | 1.53425i | ||||||
\(274\) | − | 201224.i | − | 0.00978200i | ||||||
\(275\) | 2.15422e6i | 0.103584i | ||||||||
\(276\) | −1.19944e7 | + | 1.68927e6i | −0.570495 | + | 0.0803473i | ||||
\(277\) | −1.18273e7 | −0.556475 | −0.278237 | − | 0.960512i | \(-0.589750\pi\) | ||||
−0.278237 | + | 0.960512i | \(0.589750\pi\) | |||||||
\(278\) | −397958. | −0.0185226 | ||||||||
\(279\) | 8.35966e6 | 0.384925 | ||||||||
\(280\) | 3.05951e6 | 0.139373 | ||||||||
\(281\) | 1.70316e7i | 0.767601i | 0.923416 | + | 0.383801i | \(0.125385\pi\) | ||||
−0.923416 | + | 0.383801i | \(0.874615\pi\) | |||||||
\(282\) | 360832. | 0.0160901 | ||||||||
\(283\) | 3.65196e7i | 1.61126i | 0.592418 | + | 0.805631i | \(0.298174\pi\) | ||||
−0.592418 | + | 0.805631i | \(0.701826\pi\) | |||||||
\(284\) | 4.12067e6 | 0.179892 | ||||||||
\(285\) | 7.60807e6 | 0.328655 | ||||||||
\(286\) | − | 1.05448e6i | − | 0.0450755i | ||||||
\(287\) | − | 4.44348e7i | − | 1.87965i | ||||||
\(288\) | −1.09732e6 | −0.0459361 | ||||||||
\(289\) | −3.18766e7 | −1.32062 | ||||||||
\(290\) | 139161.i | 0.00570588i | ||||||||
\(291\) | 8.19045e6i | 0.332375i | ||||||||
\(292\) | 3.42514e6 | 0.137572 | ||||||||
\(293\) | 1.85690e7i | 0.738220i | 0.929386 | + | 0.369110i | \(0.120337\pi\) | ||||
−0.929386 | + | 0.369110i | \(0.879663\pi\) | |||||||
\(294\) | 1.18998e6 | 0.0468270 | ||||||||
\(295\) | − | 1.15828e7i | − | 0.451177i | ||||||
\(296\) | 337396.i | 0.0130096i | ||||||||
\(297\) | 3.08456e6i | 0.117740i | ||||||||
\(298\) | 1.66244e6i | 0.0628198i | ||||||||
\(299\) | 4.23350e7 | − | 5.96237e6i | 1.58375 | − | 0.223052i | ||||
\(300\) | −2.63371e6 | −0.0975447 | ||||||||
\(301\) | −6.45556e7 | −2.36720 | ||||||||
\(302\) | −1.13511e6 | −0.0412112 | ||||||||
\(303\) | 2.60031e7 | 0.934755 | ||||||||
\(304\) | − | 1.74354e7i | − | 0.620597i | ||||||
\(305\) | −4.35592e6 | −0.153525 | ||||||||
\(306\) | − | 670238.i | − | 0.0233919i | ||||||
\(307\) | −3.39160e7 | −1.17217 | −0.586084 | − | 0.810250i | \(-0.699331\pi\) | ||||
−0.586084 | + | 0.810250i | \(0.699331\pi\) | |||||||
\(308\) | −2.96374e7 | −1.01435 | ||||||||
\(309\) | 3.53133e6i | 0.119691i | ||||||||
\(310\) | − | 1.44439e6i | − | 0.0484842i | ||||||
\(311\) | −3.91451e7 | −1.30136 | −0.650679 | − | 0.759353i | \(-0.725516\pi\) | ||||
−0.650679 | + | 0.759353i | \(0.725516\pi\) | |||||||
\(312\) | 2.58111e6 | 0.0849852 | ||||||||
\(313\) | − | 4.03448e7i | − | 1.31569i | −0.753152 | − | 0.657847i | \(-0.771467\pi\) | ||
0.753152 | − | 0.657847i | \(-0.228533\pi\) | |||||||
\(314\) | 2.18317e6i | 0.0705179i | ||||||||
\(315\) | 1.57774e7 | 0.504781 | ||||||||
\(316\) | − | 2.92968e7i | − | 0.928452i | ||||||
\(317\) | 3.59652e7 | 1.12903 | 0.564514 | − | 0.825423i | \(-0.309063\pi\) | ||||
0.564514 | + | 0.825423i | \(0.309063\pi\) | |||||||
\(318\) | − | 776789.i | − | 0.0241558i | ||||||
\(319\) | − | 2.69896e6i | − | 0.0831428i | ||||||
\(320\) | − | 2.94858e7i | − | 0.899837i | ||||||
\(321\) | 1.15727e7i | 0.349879i | ||||||||
\(322\) | 356379. | + | 2.53042e6i | 0.0106744 | + | 0.0757922i | ||||
\(323\) | 3.20621e7 | 0.951445 | ||||||||
\(324\) | −3.77112e6 | −0.110875 | ||||||||
\(325\) | 9.29583e6 | 0.270793 | ||||||||
\(326\) | −337979. | −0.00975523 | ||||||||
\(327\) | 3.25965e7i | 0.932241i | ||||||||
\(328\) | 3.67406e6 | 0.104118 | ||||||||
\(329\) | 3.57954e7i | 1.00517i | ||||||||
\(330\) | 532954. | 0.0148302 | ||||||||
\(331\) | −2.80276e7 | −0.772863 | −0.386431 | − | 0.922318i | \(-0.626292\pi\) | ||||
−0.386431 | + | 0.922318i | \(0.626292\pi\) | |||||||
\(332\) | 7.22065e7i | 1.97316i | ||||||||
\(333\) | 1.73990e6i | 0.0471184i | ||||||||
\(334\) | 2.79377e6 | 0.0749810 | ||||||||
\(335\) | 2.61206e7 | 0.694781 | ||||||||
\(336\) | − | 3.61569e7i | − | 0.953176i | ||||||
\(337\) | − | 3.06197e7i | − | 0.800038i | −0.916507 | − | 0.400019i | \(-0.869003\pi\) | ||
0.916507 | − | 0.400019i | \(-0.130997\pi\) | |||||||
\(338\) | −2.77143e6 | −0.0717717 | ||||||||
\(339\) | − | 3.44386e7i | − | 0.883989i | ||||||
\(340\) | 5.44547e7 | 1.38547 | ||||||||
\(341\) | 2.80134e7i | 0.706485i | ||||||||
\(342\) | 383639.i | 0.00959057i | ||||||||
\(343\) | 5.10002e7i | 1.26383i | ||||||||
\(344\) | − | 5.33774e6i | − | 0.131124i | ||||||
\(345\) | 3.01349e6 | + | 2.13969e7i | 0.0733860 | + | 0.521067i | ||||
\(346\) | −2.07206e6 | −0.0500235 | ||||||||
\(347\) | 7.04261e7 | 1.68556 | 0.842782 | − | 0.538255i | \(-0.180916\pi\) | ||||
0.842782 | + | 0.538255i | \(0.180916\pi\) | |||||||
\(348\) | 3.29969e6 | 0.0782954 | ||||||||
\(349\) | −6.68006e7 | −1.57146 | −0.785731 | − | 0.618568i | \(-0.787713\pi\) | ||||
−0.785731 | + | 0.618568i | \(0.787713\pi\) | |||||||
\(350\) | 555624.i | 0.0129592i | ||||||||
\(351\) | 1.33104e7 | 0.307800 | ||||||||
\(352\) | − | 3.67713e6i | − | 0.0843103i | ||||||
\(353\) | −7.85575e6 | −0.178593 | −0.0892963 | − | 0.996005i | \(-0.528462\pi\) | ||||
−0.0892963 | + | 0.996005i | \(0.528462\pi\) | |||||||
\(354\) | 584064. | 0.0131659 | ||||||||
\(355\) | − | 7.35088e6i | − | 0.164306i | ||||||
\(356\) | − | 5.29717e7i | − | 1.17407i | ||||||
\(357\) | 6.64893e7 | 1.46133 | ||||||||
\(358\) | −241937. | −0.00527294 | ||||||||
\(359\) | 8.88485e6i | 0.192029i | 0.995380 | + | 0.0960145i | \(0.0306095\pi\) | ||||
−0.995380 | + | 0.0960145i | \(0.969390\pi\) | |||||||
\(360\) | 1.30454e6i | 0.0279609i | ||||||||
\(361\) | 2.86938e7 | 0.609911 | ||||||||
\(362\) | − | 3.39095e6i | − | 0.0714818i | ||||||
\(363\) | 1.72795e7 | 0.361253 | ||||||||
\(364\) | 1.27890e8i | 2.65176i | ||||||||
\(365\) | − | 6.11012e6i | − | 0.125652i | ||||||
\(366\) | − | 219648.i | − | 0.00448007i | ||||||
\(367\) | − | 8.43071e7i | − | 1.70556i | −0.522274 | − | 0.852778i | \(-0.674916\pi\) | ||
0.522274 | − | 0.852778i | \(-0.325084\pi\) | |||||||
\(368\) | 4.90351e7 | − | 6.90600e6i | 0.983928 | − | 0.138574i | ||||
\(369\) | 1.89465e7 | 0.377095 | ||||||||
\(370\) | 300622. | 0.00593492 | ||||||||
\(371\) | 7.70594e7 | 1.50905 | ||||||||
\(372\) | −3.42486e7 | −0.665295 | ||||||||
\(373\) | − | 6.67702e7i | − | 1.28664i | −0.765599 | − | 0.643318i | \(-0.777557\pi\) | ||
0.765599 | − | 0.643318i | \(-0.222443\pi\) | |||||||
\(374\) | 2.24598e6 | 0.0429330 | ||||||||
\(375\) | 3.24476e7i | 0.615303i | ||||||||
\(376\) | −2.95972e6 | −0.0556785 | ||||||||
\(377\) | −1.16465e7 | −0.217355 | ||||||||
\(378\) | 795579.i | 0.0147302i | ||||||||
\(379\) | 5.19954e7i | 0.955097i | 0.878605 | + | 0.477549i | \(0.158475\pi\) | ||||
−0.878605 | + | 0.477549i | \(0.841525\pi\) | |||||||
\(380\) | −3.11694e7 | −0.568039 | ||||||||
\(381\) | −1.12705e7 | −0.203783 | ||||||||
\(382\) | 3.40876e6i | 0.0611514i | ||||||||
\(383\) | − | 3.43487e7i | − | 0.611384i | −0.952130 | − | 0.305692i | \(-0.901112\pi\) | ||
0.952130 | − | 0.305692i | \(-0.0988878\pi\) | |||||||
\(384\) | 5.99197e6 | 0.105822 | ||||||||
\(385\) | 5.28703e7i | 0.926467i | ||||||||
\(386\) | 575629. | 0.0100088 | ||||||||
\(387\) | − | 2.75258e7i | − | 0.474906i | ||||||
\(388\) | − | 3.35554e7i | − | 0.574470i | ||||||
\(389\) | − | 7.76864e7i | − | 1.31976i | −0.751369 | − | 0.659882i | \(-0.770606\pi\) | ||
0.751369 | − | 0.659882i | \(-0.229394\pi\) | |||||||
\(390\) | − | 2.29978e6i | − | 0.0387698i | ||||||
\(391\) | 1.26995e7 | + | 9.01711e7i | 0.212450 | + | 1.50847i | ||||
\(392\) | −9.76076e6 | −0.162041 | ||||||||
\(393\) | −5.22496e7 | −0.860805 | ||||||||
\(394\) | 4.12762e6 | 0.0674856 | ||||||||
\(395\) | −5.22628e7 | −0.848011 | ||||||||
\(396\) | − | 1.26371e7i | − | 0.203499i | ||||||
\(397\) | −9.93649e7 | −1.58804 | −0.794020 | − | 0.607892i | \(-0.792015\pi\) | ||||
−0.794020 | + | 0.607892i | \(0.792015\pi\) | |||||||
\(398\) | 1.79643e6i | 0.0284945i | ||||||||
\(399\) | −3.80579e7 | −0.599138 | ||||||||
\(400\) | 1.07670e7 | 0.168235 | ||||||||
\(401\) | − | 3.38580e7i | − | 0.525083i | −0.964921 | − | 0.262542i | \(-0.915439\pi\) | ||
0.964921 | − | 0.262542i | \(-0.0845607\pi\) | |||||||
\(402\) | 1.31714e6i | 0.0202746i | ||||||||
\(403\) | 1.20883e8 | 1.84692 | ||||||||
\(404\) | −1.06532e8 | −1.61561 | ||||||||
\(405\) | 6.72731e6i | 0.101269i | ||||||||
\(406\) | − | 696124.i | − | 0.0104018i | ||||||
\(407\) | −5.83043e6 | −0.0864803 | ||||||||
\(408\) | 5.49762e6i | 0.0809458i | ||||||||
\(409\) | 4.05687e7 | 0.592955 | 0.296477 | − | 0.955040i | \(-0.404188\pi\) | ||||
0.296477 | + | 0.955040i | \(0.404188\pi\) | |||||||
\(410\) | − | 3.27361e6i | − | 0.0474980i | ||||||
\(411\) | 8.51155e6i | 0.122598i | ||||||||
\(412\) | − | 1.44675e7i | − | 0.206871i | ||||||
\(413\) | 5.79406e7i | 0.822494i | ||||||||
\(414\) | −1.07894e6 | + | 151956.i | −0.0152054 | + | 0.00214150i | ||||
\(415\) | 1.28810e8 | 1.80220 | ||||||||
\(416\) | −1.58674e7 | −0.220407 | ||||||||
\(417\) | 1.68332e7 | 0.232144 | ||||||||
\(418\) | −1.28558e6 | −0.0176024 | ||||||||
\(419\) | 8.70221e7i | 1.18301i | 0.806302 | + | 0.591504i | \(0.201466\pi\) | ||||
−0.806302 | + | 0.591504i | \(0.798534\pi\) | |||||||
\(420\) | −6.46382e7 | −0.872452 | ||||||||
\(421\) | − | 6.05889e7i | − | 0.811983i | −0.913877 | − | 0.405991i | \(-0.866926\pi\) | ||
0.913877 | − | 0.405991i | \(-0.133074\pi\) | |||||||
\(422\) | −3.72865e6 | −0.0496152 | ||||||||
\(423\) | −1.52628e7 | −0.201657 | ||||||||
\(424\) | 6.37161e6i | 0.0835894i | ||||||||
\(425\) | 1.97996e7i | 0.257922i | ||||||||
\(426\) | 370670. | 0.00479467 | ||||||||
\(427\) | 2.17897e7 | 0.279877 | ||||||||
\(428\) | − | 4.74119e7i | − | 0.604723i | ||||||
\(429\) | 4.46033e7i | 0.564931i | ||||||||
\(430\) | −4.75595e6 | −0.0598180 | ||||||||
\(431\) | 5.02127e7i | 0.627165i | 0.949561 | + | 0.313583i | \(0.101529\pi\) | ||||
−0.949561 | + | 0.313583i | \(0.898471\pi\) | |||||||
\(432\) | 1.54169e7 | 0.191226 | ||||||||
\(433\) | − | 1.09950e8i | − | 1.35435i | −0.735820 | − | 0.677177i | \(-0.763203\pi\) | ||
0.735820 | − | 0.677177i | \(-0.236797\pi\) | |||||||
\(434\) | 7.22531e6i | 0.0883867i | ||||||||
\(435\) | − | 5.88634e6i | − | 0.0715118i | ||||||
\(436\) | − | 1.33544e8i | − | 1.61126i | ||||||
\(437\) | −7.26910e6 | − | 5.16132e7i | −0.0871037 | − | 0.618467i | ||||
\(438\) | 308104. | 0.00366670 | ||||||||
\(439\) | −3.55005e7 | −0.419606 | −0.209803 | − | 0.977744i | \(-0.567282\pi\) | ||||
−0.209803 | + | 0.977744i | \(0.567282\pi\) | |||||||
\(440\) | −4.37155e6 | −0.0513189 | ||||||||
\(441\) | −5.03347e7 | −0.586883 | ||||||||
\(442\) | − | 9.69179e6i | − | 0.112237i | ||||||
\(443\) | −9.78683e7 | −1.12572 | −0.562861 | − | 0.826552i | \(-0.690299\pi\) | ||||
−0.562861 | + | 0.826552i | \(0.690299\pi\) | |||||||
\(444\) | − | 7.12816e6i | − | 0.0814383i | ||||||
\(445\) | −9.44965e7 | −1.07235 | ||||||||
\(446\) | 4.68546e6 | 0.0528138 | ||||||||
\(447\) | − | 7.03193e7i | − | 0.787322i | ||||||
\(448\) | 1.47497e8i | 1.64040i | ||||||||
\(449\) | −8.49424e7 | −0.938394 | −0.469197 | − | 0.883093i | \(-0.655457\pi\) | ||||
−0.469197 | + | 0.883093i | \(0.655457\pi\) | |||||||
\(450\) | −236912. | −0.00259986 | ||||||||
\(451\) | 6.34903e7i | 0.692114i | ||||||||
\(452\) | 1.41091e8i | 1.52786i | ||||||||
\(453\) | 4.80137e7 | 0.516500 | ||||||||
\(454\) | − | 6.25180e6i | − | 0.0668093i | ||||||
\(455\) | 2.28144e8 | 2.42201 | ||||||||
\(456\) | − | 3.14680e6i | − | 0.0331875i | ||||||
\(457\) | 8.16735e7i | 0.855722i | 0.903844 | + | 0.427861i | \(0.140733\pi\) | ||||
−0.903844 | + | 0.427861i | \(0.859267\pi\) | |||||||
\(458\) | − | 4.53055e6i | − | 0.0471579i | ||||||
\(459\) | 2.83503e7i | 0.293170i | ||||||||
\(460\) | −1.23460e7 | − | 8.76607e7i | −0.126839 | − | 0.900599i | ||||
\(461\) | −1.10947e8 | −1.13243 | −0.566215 | − | 0.824258i | \(-0.691593\pi\) | ||||
−0.566215 | + | 0.824258i | \(0.691593\pi\) | |||||||
\(462\) | −2.66600e6 | −0.0270355 | ||||||||
\(463\) | 1.53700e8 | 1.54857 | 0.774287 | − | 0.632835i | \(-0.218109\pi\) | ||||
0.774287 | + | 0.632835i | \(0.218109\pi\) | |||||||
\(464\) | −1.34897e7 | −0.135035 | ||||||||
\(465\) | 6.10963e7i | 0.607653i | ||||||||
\(466\) | 63106.1 | 0.000623611 | ||||||||
\(467\) | − | 2.80988e7i | − | 0.275890i | −0.990440 | − | 0.137945i | \(-0.955950\pi\) | ||
0.990440 | − | 0.137945i | \(-0.0440498\pi\) | |||||||
\(468\) | −5.45311e7 | −0.531994 | ||||||||
\(469\) | −1.30663e8 | −1.26659 | ||||||||
\(470\) | 2.63713e6i | 0.0254002i | ||||||||
\(471\) | − | 9.23458e7i | − | 0.883801i | ||||||
\(472\) | −4.79078e6 | −0.0455597 | ||||||||
\(473\) | 9.22396e7 | 0.871634 | ||||||||
\(474\) | − | 2.63536e6i | − | 0.0247460i | ||||||
\(475\) | − | 1.13331e7i | − | 0.105747i | ||||||
\(476\) | −2.72399e8 | −2.52572 | ||||||||
\(477\) | 3.28573e7i | 0.302745i | ||||||||
\(478\) | 200117. | 0.00183231 | ||||||||
\(479\) | − | 2.05854e8i | − | 1.87307i | −0.350578 | − | 0.936534i | \(-0.614015\pi\) | ||
0.350578 | − | 0.936534i | \(-0.385985\pi\) | |||||||
\(480\) | − | 8.01969e6i | − | 0.0725160i | ||||||
\(481\) | 2.51593e7i | 0.226080i | ||||||||
\(482\) | − | 1.41812e6i | − | 0.0126641i | ||||||
\(483\) | −1.50744e7 | − | 1.07034e8i | −0.133783 | − | 0.949904i | ||||
\(484\) | −7.07922e7 | −0.624380 | ||||||||
\(485\) | −5.98596e7 | −0.524697 | ||||||||
\(486\) | −339226. | −0.00295516 | ||||||||
\(487\) | 7.83541e7 | 0.678383 | 0.339191 | − | 0.940717i | \(-0.389847\pi\) | ||||
0.339191 | + | 0.940717i | \(0.389847\pi\) | |||||||
\(488\) | 1.80166e6i | 0.0155029i | ||||||||
\(489\) | 1.42962e7 | 0.122262 | ||||||||
\(490\) | 8.69689e6i | 0.0739223i | ||||||||
\(491\) | −9.63485e7 | −0.813955 | −0.406978 | − | 0.913438i | \(-0.633417\pi\) | ||||
−0.406978 | + | 0.913438i | \(0.633417\pi\) | |||||||
\(492\) | −7.76219e7 | −0.651762 | ||||||||
\(493\) | − | 2.48063e7i | − | 0.207024i | ||||||
\(494\) | 5.54750e6i | 0.0460168i | ||||||||
\(495\) | −2.25434e7 | −0.185867 | ||||||||
\(496\) | 1.40014e8 | 1.14743 | ||||||||
\(497\) | 3.67714e7i | 0.299530i | ||||||||
\(498\) | 6.49525e6i | 0.0525906i | ||||||||
\(499\) | −3.11543e7 | −0.250736 | −0.125368 | − | 0.992110i | \(-0.540011\pi\) | ||||
−0.125368 | + | 0.992110i | \(0.540011\pi\) | |||||||
\(500\) | − | 1.32934e8i | − | 1.06347i | ||||||
\(501\) | −1.18173e8 | −0.939738 | ||||||||
\(502\) | 4.37568e6i | 0.0345887i | ||||||||
\(503\) | 5.43218e7i | 0.426845i | 0.976960 | + | 0.213423i | \(0.0684611\pi\) | ||||
−0.976960 | + | 0.213423i | \(0.931539\pi\) | |||||||
\(504\) | − | 6.52573e6i | − | 0.0509727i | ||||||
\(505\) | 1.90043e8i | 1.47563i | ||||||||
\(506\) | −509208. | − | 3.61556e6i | −0.00393047 | − | 0.0279077i | ||||
\(507\) | 1.17228e8 | 0.899516 | ||||||||
\(508\) | 4.61740e7 | 0.352214 | ||||||||
\(509\) | 2.23459e8 | 1.69451 | 0.847255 | − | 0.531187i | \(-0.178254\pi\) | ||||
0.847255 | + | 0.531187i | \(0.178254\pi\) | |||||||
\(510\) | 4.89841e6 | 0.0369270 | ||||||||
\(511\) | 3.05647e7i | 0.229064i | ||||||||
\(512\) | −3.06528e7 | −0.228381 | ||||||||
\(513\) | − | 1.62275e7i | − | 0.120199i | ||||||
\(514\) | 3.77402e6 | 0.0277917 | ||||||||
\(515\) | −2.58086e7 | −0.188948 | ||||||||
\(516\) | 1.12770e8i | 0.820816i | ||||||||
\(517\) | − | 5.11459e7i | − | 0.370117i | ||||||
\(518\) | −1.50380e6 | −0.0108194 | ||||||||
\(519\) | 8.76459e7 | 0.626945 | ||||||||
\(520\) | 1.88640e7i | 0.134160i | ||||||||
\(521\) | − | 1.32853e7i | − | 0.0939415i | −0.998896 | − | 0.0469707i | \(-0.985043\pi\) | ||
0.998896 | − | 0.0469707i | \(-0.0149568\pi\) | |||||||
\(522\) | 296820. | 0.00208681 | ||||||||
\(523\) | 9.24267e7i | 0.646089i | 0.946384 | + | 0.323044i | \(0.104706\pi\) | ||||
−0.946384 | + | 0.323044i | \(0.895294\pi\) | |||||||
\(524\) | 2.14061e8 | 1.48779 | ||||||||
\(525\) | − | 2.35023e7i | − | 0.162417i | ||||||
\(526\) | 751945.i | 0.00516689i | ||||||||
\(527\) | 2.57473e8i | 1.75914i | ||||||||
\(528\) | 5.16624e7i | 0.350972i | ||||||||
\(529\) | 1.42277e8 | − | 4.08871e7i | 0.961101 | − | 0.276197i | ||||
\(530\) | 5.67713e6 | 0.0381330 | ||||||||
\(531\) | −2.47053e7 | −0.165008 | ||||||||
\(532\) | 1.55919e8 | 1.03553 | ||||||||
\(533\) | 2.73971e8 | 1.80935 | ||||||||
\(534\) | − | 4.76501e6i | − | 0.0312925i | ||||||
\(535\) | −8.45784e7 | −0.552329 | ||||||||
\(536\) | − | 1.08038e7i | − | 0.0701588i | ||||||
\(537\) | 1.02337e7 | 0.0660859 | ||||||||
\(538\) | 1.14225e7 | 0.0733525 | ||||||||
\(539\) | − | 1.68672e8i | − | 1.07715i | ||||||
\(540\) | − | 2.75611e7i | − | 0.175031i | ||||||
\(541\) | 5.01668e7 | 0.316829 | 0.158414 | − | 0.987373i | \(-0.449362\pi\) | ||||
0.158414 | + | 0.987373i | \(0.449362\pi\) | |||||||
\(542\) | 1.67888e6 | 0.0105444 | ||||||||
\(543\) | 1.43433e8i | 0.895883i | ||||||||
\(544\) | − | 3.37967e7i | − | 0.209931i | ||||||
\(545\) | −2.38231e8 | −1.47166 | ||||||||
\(546\) | 1.15042e7i | 0.0706773i | ||||||||
\(547\) | 8.48201e7 | 0.518247 | 0.259124 | − | 0.965844i | \(-0.416566\pi\) | ||||
0.259124 | + | 0.965844i | \(0.416566\pi\) | |||||||
\(548\) | − | 3.48709e7i | − | 0.211895i | ||||||
\(549\) | 9.29089e6i | 0.0561488i | ||||||||
\(550\) | − | 793897.i | − | 0.00477173i | ||||||
\(551\) | 1.41989e7i | 0.0848791i | ||||||||
\(552\) | 8.85003e6 | − | 1.24642e6i | 0.0526171 | − | 0.00741049i | ||||
\(553\) | 2.61435e8 | 1.54592 | ||||||||
\(554\) | 4.35872e6 | 0.0256348 | ||||||||
\(555\) | −1.27160e7 | −0.0743824 | ||||||||
\(556\) | −6.89637e7 | −0.401233 | ||||||||
\(557\) | − | 1.80275e8i | − | 1.04321i | −0.853189 | − | 0.521603i | \(-0.825334\pi\) | ||
0.853189 | − | 0.521603i | \(-0.174666\pi\) | |||||||
\(558\) | −3.08080e6 | −0.0177321 | ||||||||
\(559\) | − | 3.98029e8i | − | 2.27866i | ||||||
\(560\) | 2.64251e8 | 1.50471 | ||||||||
\(561\) | −9.50026e7 | −0.538080 | ||||||||
\(562\) | − | 6.27666e6i | − | 0.0353606i | ||||||
\(563\) | 3.03781e8i | 1.70230i | 0.524925 | + | 0.851149i | \(0.324093\pi\) | ||||
−0.524925 | + | 0.851149i | \(0.675907\pi\) | |||||||
\(564\) | 6.25300e7 | 0.348539 | ||||||||
\(565\) | 2.51693e8 | 1.39549 | ||||||||
\(566\) | − | 1.34586e7i | − | 0.0742250i | ||||||
\(567\) | − | 3.36521e7i | − | 0.184613i | ||||||
\(568\) | −3.04042e6 | −0.0165916 | ||||||||
\(569\) | 1.02127e8i | 0.554376i | 0.960816 | + | 0.277188i | \(0.0894025\pi\) | ||||
−0.960816 | + | 0.277188i | \(0.910598\pi\) | |||||||
\(570\) | −2.80381e6 | −0.0151399 | ||||||||
\(571\) | 2.29011e7i | 0.123012i | 0.998107 | + | 0.0615059i | \(0.0195903\pi\) | ||||
−0.998107 | + | 0.0615059i | \(0.980410\pi\) | |||||||
\(572\) | − | 1.82735e8i | − | 0.976413i | ||||||
\(573\) | − | 1.44187e8i | − | 0.766411i | ||||||
\(574\) | 1.63756e7i | 0.0865888i | ||||||||
\(575\) | 3.18732e7 | − | 4.48895e6i | 0.167657 | − | 0.0236125i | ||||
\(576\) | −6.28913e7 | −0.329097 | ||||||||
\(577\) | −2.38699e8 | −1.24257 | −0.621287 | − | 0.783583i | \(-0.713390\pi\) | ||||
−0.621287 | + | 0.783583i | \(0.713390\pi\) | |||||||
\(578\) | 1.17475e7 | 0.0608362 | ||||||||
\(579\) | −2.43485e7 | −0.125440 | ||||||||
\(580\) | 2.41157e7i | 0.123599i | ||||||||
\(581\) | −6.44345e8 | −3.28541 | ||||||||
\(582\) | − | 3.01844e6i | − | 0.0153113i | ||||||
\(583\) | −1.10106e8 | −0.555653 | ||||||||
\(584\) | −2.52722e6 | −0.0126883 | ||||||||
\(585\) | 9.72784e7i | 0.485902i | ||||||||
\(586\) | − | 6.84325e6i | − | 0.0340071i | ||||||
\(587\) | 1.94478e8 | 0.961514 | 0.480757 | − | 0.876854i | \(-0.340362\pi\) | ||||
0.480757 | + | 0.876854i | \(0.340362\pi\) | |||||||
\(588\) | 2.06215e8 | 1.01435 | ||||||||
\(589\) | − | 1.47375e8i | − | 0.721239i | ||||||
\(590\) | 4.26861e6i | 0.0207841i | ||||||||
\(591\) | −1.74594e8 | −0.845798 | ||||||||
\(592\) | 2.91411e7i | 0.140456i | ||||||||
\(593\) | 1.04386e8 | 0.500586 | 0.250293 | − | 0.968170i | \(-0.419473\pi\) | ||||
0.250293 | + | 0.968170i | \(0.419473\pi\) | |||||||
\(594\) | − | 1.13675e6i | − | 0.00542385i | ||||||
\(595\) | 4.85934e8i | 2.30689i | ||||||||
\(596\) | 2.88091e8i | 1.36079i | ||||||||
\(597\) | − | 7.59869e7i | − | 0.357121i | ||||||
\(598\) | −1.56018e7 | + | 2.19732e6i | −0.0729575 | + | 0.0102752i | ||||
\(599\) | −8.10305e7 | −0.377023 | −0.188512 | − | 0.982071i | \(-0.560366\pi\) | ||||
−0.188512 | + | 0.982071i | \(0.560366\pi\) | |||||||
\(600\) | 1.94327e6 | 0.00899662 | ||||||||
\(601\) | −2.22644e7 | −0.102562 | −0.0512812 | − | 0.998684i | \(-0.516330\pi\) | ||||
−0.0512812 | + | 0.998684i | \(0.516330\pi\) | |||||||
\(602\) | 2.37907e7 | 0.109048 | ||||||||
\(603\) | − | 5.57134e7i | − | 0.254102i | ||||||
\(604\) | −1.96707e8 | −0.892707 | ||||||||
\(605\) | 1.26286e8i | 0.570283i | ||||||||
\(606\) | −9.58296e6 | −0.0430608 | ||||||||
\(607\) | −3.25433e8 | −1.45511 | −0.727554 | − | 0.686050i | \(-0.759343\pi\) | ||||
−0.727554 | + | 0.686050i | \(0.759343\pi\) | |||||||
\(608\) | 1.93450e7i | 0.0860710i | ||||||||
\(609\) | 2.94453e7i | 0.130366i | ||||||||
\(610\) | 1.60529e6 | 0.00707236 | ||||||||
\(611\) | −2.20703e8 | −0.967576 | ||||||||
\(612\) | − | 1.16148e8i | − | 0.506709i | ||||||
\(613\) | − | 5.64281e7i | − | 0.244971i | −0.992470 | − | 0.122485i | \(-0.960914\pi\) | ||
0.992470 | − | 0.122485i | \(-0.0390864\pi\) | |||||||
\(614\) | 1.24991e7 | 0.0539975 | ||||||||
\(615\) | 1.38470e8i | 0.595293i | ||||||||
\(616\) | 2.18678e7 | 0.0935543 | ||||||||
\(617\) | − | 1.30168e8i | − | 0.554176i | −0.960845 | − | 0.277088i | \(-0.910631\pi\) | ||
0.960845 | − | 0.277088i | \(-0.0893694\pi\) | |||||||
\(618\) | − | 1.30140e6i | − | 0.00551374i | ||||||
\(619\) | − | 9.93172e7i | − | 0.418748i | −0.977836 | − | 0.209374i | \(-0.932857\pi\) | ||
0.977836 | − | 0.209374i | \(-0.0671426\pi\) | |||||||
\(620\) | − | 2.50305e8i | − | 1.05025i | ||||||
\(621\) | 4.56381e7 | − | 6.42758e6i | 0.190569 | − | 0.0268394i | ||||
\(622\) | 1.44262e7 | 0.0599488 | ||||||||
\(623\) | 4.72701e8 | 1.95489 | ||||||||
\(624\) | 2.22932e8 | 0.917526 | ||||||||
\(625\) | −1.95806e8 | −0.802022 | ||||||||
\(626\) | 1.48683e7i | 0.0606092i | ||||||||
\(627\) | 5.43787e7 | 0.220611 | ||||||||
\(628\) | 3.78331e8i | 1.52754i | ||||||||
\(629\) | −5.35878e7 | −0.215335 | ||||||||
\(630\) | −5.81445e6 | −0.0232534 | ||||||||
\(631\) | − | 2.00601e8i | − | 0.798444i | −0.916854 | − | 0.399222i | \(-0.869280\pi\) | ||
0.916854 | − | 0.399222i | \(-0.130720\pi\) | |||||||
\(632\) | 2.16166e7i | 0.0856318i | ||||||||
\(633\) | 1.57718e8 | 0.621828 | ||||||||
\(634\) | −1.32543e7 | −0.0520103 | ||||||||
\(635\) | − | 8.23701e7i | − | 0.321698i | ||||||
\(636\) | − | 1.34613e8i | − | 0.523257i | ||||||
\(637\) | −7.27850e8 | −2.81594 | ||||||||
\(638\) | 994651.i | 0.00383009i | ||||||||
\(639\) | −1.56789e7 | −0.0600916 | ||||||||
\(640\) | 4.37921e7i | 0.167054i | ||||||||
\(641\) | − | 4.64796e8i | − | 1.76477i | −0.470528 | − | 0.882385i | \(-0.655937\pi\) | ||
0.470528 | − | 0.882385i | \(-0.344063\pi\) | |||||||
\(642\) | − | 4.26489e6i | − | 0.0161177i | ||||||
\(643\) | − | 8.47536e7i | − | 0.318805i | −0.987214 | − | 0.159402i | \(-0.949043\pi\) | ||
0.987214 | − | 0.159402i | \(-0.0509568\pi\) | |||||||
\(644\) | 6.17583e7 | + | 4.38506e8i | 0.231227 | + | 1.64179i | ||||
\(645\) | 2.01172e8 | 0.749700 | ||||||||
\(646\) | −1.18159e7 | −0.0438296 | ||||||||
\(647\) | −1.91959e8 | −0.708752 | −0.354376 | − | 0.935103i | \(-0.615307\pi\) | ||||
−0.354376 | + | 0.935103i | \(0.615307\pi\) | |||||||
\(648\) | 2.78250e6 | 0.0102261 | ||||||||
\(649\) | − | 8.27879e7i | − | 0.302854i | ||||||
\(650\) | −3.42580e6 | −0.0124745 | ||||||||
\(651\) | − | 3.05623e8i | − | 1.10775i | ||||||
\(652\) | −5.85698e7 | −0.211315 | ||||||||
\(653\) | −1.15990e8 | −0.416564 | −0.208282 | − | 0.978069i | \(-0.566787\pi\) | ||||
−0.208282 | + | 0.978069i | \(0.566787\pi\) | |||||||
\(654\) | − | 1.20128e7i | − | 0.0429450i | ||||||
\(655\) | − | 3.81864e8i | − | 1.35889i | ||||||
\(656\) | 3.17331e8 | 1.12409 | ||||||||
\(657\) | −1.30325e7 | −0.0459548 | ||||||||
\(658\) | − | 1.31917e7i | − | 0.0463046i | ||||||
\(659\) | 1.84207e8i | 0.643649i | 0.946799 | + | 0.321824i | \(0.104296\pi\) | ||||
−0.946799 | + | 0.321824i | \(0.895704\pi\) | |||||||
\(660\) | 9.23576e7 | 0.321248 | ||||||||
\(661\) | − | 8.44401e6i | − | 0.0292378i | −0.999893 | − | 0.0146189i | \(-0.995346\pi\) | ||
0.999893 | − | 0.0146189i | \(-0.00465350\pi\) | |||||||
\(662\) | 1.03291e7 | 0.0356030 | ||||||||
\(663\) | 4.09952e8i | 1.40667i | ||||||||
\(664\) | − | 5.32773e7i | − | 0.181986i | ||||||
\(665\) | − | 2.78145e8i | − | 0.945815i | ||||||
\(666\) | − | 641206.i | − | 0.00217057i | ||||||
\(667\) | −3.99330e7 | + | 5.62408e6i | −0.134572 | + | 0.0189528i | ||||
\(668\) | 4.84143e8 | 1.62422 | ||||||||
\(669\) | −1.98190e8 | −0.661916 | ||||||||
\(670\) | −9.62624e6 | −0.0320061 | ||||||||
\(671\) | −3.11339e7 | −0.103054 | ||||||||
\(672\) | 4.01170e7i | 0.132197i | ||||||||
\(673\) | −4.84325e8 | −1.58888 | −0.794441 | − | 0.607341i | \(-0.792236\pi\) | ||||
−0.794441 | + | 0.607341i | \(0.792236\pi\) | |||||||
\(674\) | 1.12843e7i | 0.0368549i | ||||||||
\(675\) | 1.00211e7 | 0.0325841 | ||||||||
\(676\) | −4.80272e8 | −1.55470 | ||||||||
\(677\) | 2.68560e8i | 0.865517i | 0.901510 | + | 0.432759i | \(0.142460\pi\) | ||||
−0.901510 | + | 0.432759i | \(0.857540\pi\) | |||||||
\(678\) | 1.26917e7i | 0.0407222i | ||||||||
\(679\) | 2.99436e8 | 0.956522 | ||||||||
\(680\) | −4.01792e7 | −0.127783 | ||||||||
\(681\) | 2.64444e8i | 0.837322i | ||||||||
\(682\) | − | 1.03238e7i | − | 0.0325452i | ||||||
\(683\) | −4.25685e8 | −1.33606 | −0.668030 | − | 0.744134i | \(-0.732862\pi\) | ||||
−0.668030 | + | 0.744134i | \(0.732862\pi\) | |||||||
\(684\) | 6.64823e7i | 0.207748i | ||||||||
\(685\) | −6.22063e7 | −0.193536 | ||||||||
\(686\) | − | 1.87951e7i | − | 0.0582201i | ||||||
\(687\) | 1.91637e8i | 0.591030i | ||||||||
\(688\) | − | 4.61023e8i | − | 1.41565i | ||||||
\(689\) | 4.75124e8i | 1.45261i | ||||||||
\(690\) | −1.11057e6 | − | 7.88542e6i | −0.00338063 | − | 0.0240037i | ||||
\(691\) | 1.62850e8 | 0.493577 | 0.246788 | − | 0.969069i | \(-0.420625\pi\) | ||||
0.246788 | + | 0.969069i | \(0.420625\pi\) | |||||||
\(692\) | −3.59076e8 | −1.08360 | ||||||||
\(693\) | 1.12769e8 | 0.338836 | ||||||||
\(694\) | −2.59542e7 | −0.0776478 | ||||||||
\(695\) | 1.23025e8i | 0.366470i | ||||||||
\(696\) | −2.43467e6 | −0.00722124 | ||||||||
\(697\) | 5.83543e8i | 1.72335i | ||||||||
\(698\) | 2.46181e7 | 0.0723916 | ||||||||
\(699\) | −2.66932e6 | −0.00781572 | ||||||||
\(700\) | 9.62862e7i | 0.280718i | ||||||||
\(701\) | − | 2.15840e7i | − | 0.0626581i | −0.999509 | − | 0.0313291i | \(-0.990026\pi\) | ||
0.999509 | − | 0.0313291i | \(-0.00997398\pi\) | |||||||
\(702\) | −4.90529e6 | −0.0141792 | ||||||||
\(703\) | 3.06732e7 | 0.0882864 | ||||||||
\(704\) | − | 2.10750e8i | − | 0.604018i | ||||||
\(705\) | − | 1.11548e8i | − | 0.318341i | ||||||
\(706\) | 2.89509e6 | 0.00822711 | ||||||||
\(707\) | − | 9.50653e8i | − | 2.69007i | ||||||
\(708\) | 1.01215e8 | 0.285197 | ||||||||
\(709\) | 4.64513e8i | 1.30334i | 0.758501 | + | 0.651672i | \(0.225932\pi\) | ||||
−0.758501 | + | 0.651672i | \(0.774068\pi\) | |||||||
\(710\) | 2.70903e6i | 0.00756900i | ||||||||
\(711\) | 1.11473e8i | 0.310142i | ||||||||
\(712\) | 3.90850e7i | 0.108285i | ||||||||
\(713\) | 4.14478e8 | − | 5.83742e7i | 1.14349 | − | 0.161047i | ||||
\(714\) | −2.45034e7 | −0.0673180 | ||||||||
\(715\) | −3.25982e8 | −0.891816 | ||||||||
\(716\) | −4.19262e7 | −0.114221 | ||||||||
\(717\) | −8.46471e6 | −0.0229644 | ||||||||
\(718\) | − | 3.27434e6i | − | 0.00884608i | ||||||
\(719\) | −3.55461e8 | −0.956324 | −0.478162 | − | 0.878272i | \(-0.658697\pi\) | ||||
−0.478162 | + | 0.878272i | \(0.658697\pi\) | |||||||
\(720\) | 1.12674e8i | 0.301874i | ||||||||
\(721\) | 1.29102e8 | 0.344452 | ||||||||
\(722\) | −1.05746e7 | −0.0280964 | ||||||||
\(723\) | 5.99851e7i | 0.158719i | ||||||||
\(724\) | − | 5.87631e8i | − | 1.54842i | ||||||
\(725\) | −8.76840e6 | −0.0230094 | ||||||||
\(726\) | −6.36803e6 | −0.0166416 | ||||||||
\(727\) | 9.14852e7i | 0.238094i | 0.992889 | + | 0.119047i | \(0.0379839\pi\) | ||||
−0.992889 | + | 0.119047i | \(0.962016\pi\) | |||||||
\(728\) | − | 9.43634e7i | − | 0.244573i | ||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 2.25177e6i | 0.00578835i | ||||||||
\(731\) | 8.47780e8 | 2.17036 | ||||||||
\(732\) | − | 3.80637e7i | − | 0.0970461i | ||||||
\(733\) | − | 5.88821e8i | − | 1.49510i | −0.664203 | − | 0.747552i | \(-0.731229\pi\) | ||
0.664203 | − | 0.747552i | \(-0.268771\pi\) | |||||||
\(734\) | 3.10698e7i | 0.0785688i | ||||||||
\(735\) | − | 3.67869e8i | − | 0.926469i | ||||||
\(736\) | −5.44056e7 | + | 7.66238e6i | −0.136462 | + | 0.0192190i | ||||
\(737\) | 1.86697e8 | 0.466374 | ||||||||
\(738\) | −6.98239e6 | −0.0173714 | ||||||||
\(739\) | 5.03241e8 | 1.24693 | 0.623466 | − | 0.781850i | \(-0.285724\pi\) | ||||
0.623466 | + | 0.781850i | \(0.285724\pi\) | |||||||
\(740\) | 5.20959e7 | 0.128561 | ||||||||
\(741\) | − | 2.34653e8i | − | 0.576729i | ||||||
\(742\) | −2.83988e7 | −0.0695165 | ||||||||
\(743\) | 5.26147e8i | 1.28275i | 0.767230 | + | 0.641373i | \(0.221635\pi\) | ||||
−0.767230 | + | 0.641373i | \(0.778365\pi\) | |||||||
\(744\) | 2.52702e7 | 0.0613606 | ||||||||
\(745\) | 5.13926e8 | 1.24289 | ||||||||
\(746\) | 2.46069e7i | 0.0592707i | ||||||||
\(747\) | − | 2.74742e8i | − | 0.659118i | ||||||
\(748\) | 3.89215e8 | 0.930004 | ||||||||
\(749\) | 4.23087e8 | 1.00690 | ||||||||
\(750\) | − | 1.19579e7i | − | 0.0283448i | ||||||
\(751\) | 2.74856e8i | 0.648911i | 0.945901 | + | 0.324456i | \(0.105181\pi\) | ||||
−0.945901 | + | 0.324456i | \(0.894819\pi\) | |||||||
\(752\) | −2.55632e8 | −0.601122 | ||||||||
\(753\) | − | 1.85086e8i | − | 0.433500i | ||||||
\(754\) | 4.29208e6 | 0.0100128 | ||||||||
\(755\) | 3.50906e8i | 0.815362i | ||||||||
\(756\) | 1.37869e8i | 0.319081i | ||||||||
\(757\) | 2.98024e8i | 0.687010i | 0.939151 | + | 0.343505i | \(0.111614\pi\) | ||||
−0.939151 | + | 0.343505i | \(0.888386\pi\) | |||||||
\(758\) | − | 1.91619e7i | − | 0.0439979i | ||||||
\(759\) | 2.15390e7 | + | 1.52934e8i | 0.0492606 | + | 0.349768i | ||||
\(760\) | 2.29982e7 | 0.0523906 | ||||||||
\(761\) | −1.44743e8 | −0.328431 | −0.164216 | − | 0.986424i | \(-0.552509\pi\) | ||||
−0.164216 | + | 0.986424i | \(0.552509\pi\) | |||||||
\(762\) | 4.15353e6 | 0.00938756 | ||||||||
\(763\) | 1.19170e9 | 2.68284 | ||||||||
\(764\) | 5.90718e8i | 1.32465i | ||||||||
\(765\) | −2.07197e8 | −0.462807 | ||||||||
\(766\) | 1.26586e7i | 0.0281642i | ||||||||
\(767\) | −3.57244e8 | −0.791732 | ||||||||
\(768\) | 2.55999e8 | 0.565137 | ||||||||
\(769\) | 4.15230e8i | 0.913082i | 0.889702 | + | 0.456541i | \(0.150912\pi\) | ||||
−0.889702 | + | 0.456541i | \(0.849088\pi\) | |||||||
\(770\) | − | 1.94844e7i | − | 0.0426790i | ||||||
\(771\) | −1.59637e8 | −0.348313 | ||||||||
\(772\) | 9.97530e7 | 0.216807 | ||||||||
\(773\) | − | 3.40961e7i | − | 0.0738187i | −0.999319 | − | 0.0369094i | \(-0.988249\pi\) | ||
0.999319 | − | 0.0369094i | \(-0.0117513\pi\) | |||||||
\(774\) | 1.01441e7i | 0.0218772i | ||||||||
\(775\) | 9.10101e7 | 0.195517 | ||||||||
\(776\) | 2.47587e7i | 0.0529837i | ||||||||
\(777\) | 6.36092e7 | 0.135599 | ||||||||
\(778\) | 2.86299e7i | 0.0607968i | ||||||||
\(779\) | − | 3.34015e8i | − | 0.706568i | ||||||
\(780\) | − | 3.98539e8i | − | 0.839821i | ||||||
\(781\) | − | 5.25404e7i | − | 0.110291i | ||||||
\(782\) | −4.68016e6 | − | 3.32308e7i | −0.00978680 | − | 0.0694898i | ||||
\(783\) | −1.25552e7 | −0.0261540 | ||||||||
\(784\) | −8.43042e8 | −1.74945 | ||||||||
\(785\) | 6.74906e8 | 1.39519 | ||||||||
\(786\) | 1.92556e7 | 0.0396542 | ||||||||
\(787\) | 6.07623e8i | 1.24655i | 0.782003 | + | 0.623275i | \(0.214198\pi\) | ||||
−0.782003 | + | 0.623275i | \(0.785802\pi\) | |||||||
\(788\) | 7.15292e8 | 1.46186 | ||||||||
\(789\) | − | 3.18065e7i | − | 0.0647566i | ||||||
\(790\) | 1.92605e7 | 0.0390648 | ||||||||
\(791\) | −1.25905e9 | −2.54398 | ||||||||
\(792\) | 9.32422e6i | 0.0187688i | ||||||||
\(793\) | 1.34348e8i | 0.269409i | ||||||||
\(794\) | 3.66190e7 | 0.0731552 | ||||||||
\(795\) | −2.40136e8 | −0.477922 | ||||||||
\(796\) | 3.11310e8i | 0.617240i | ||||||||
\(797\) | − | 2.55908e8i | − | 0.505485i | −0.967534 | − | 0.252743i | \(-0.918667\pi\) | ||
0.967534 | − | 0.252743i | \(-0.0813326\pi\) | |||||||
\(798\) | 1.40255e7 | 0.0276001 | ||||||||
\(799\) | − | 4.70085e8i | − | 0.921587i | ||||||
\(800\) | −1.19463e7 | −0.0233326 | ||||||||
\(801\) | 2.01555e8i | 0.392189i | ||||||||
\(802\) | 1.24777e7i | 0.0241887i | ||||||||
\(803\) | − | 4.36721e7i | − | 0.0843446i | ||||||
\(804\) | 2.28252e8i | 0.439183i | ||||||||
\(805\) | 7.82253e8 | − | 1.10171e8i | 1.49955 | − | 0.211193i | ||||
\(806\) | −4.45490e7 | −0.0850810 | ||||||||
\(807\) | −4.83160e8 | −0.919327 | ||||||||
\(808\) | 7.86041e7 | 0.149009 | ||||||||
\(809\) | −1.94709e8 | −0.367740 | −0.183870 | − | 0.982951i | \(-0.558862\pi\) | ||||
−0.183870 | + | 0.982951i | \(0.558862\pi\) | |||||||
\(810\) | − | 2.47922e6i | − | 0.00466510i | ||||||
\(811\) | 4.20154e8 | 0.787674 | 0.393837 | − | 0.919180i | \(-0.371148\pi\) | ||||
0.393837 | + | 0.919180i | \(0.371148\pi\) | |||||||
\(812\) | − | 1.20634e8i | − | 0.225321i | ||||||
\(813\) | −7.10148e7 | −0.132153 | ||||||||
\(814\) | 2.14869e6 | 0.00398383 | ||||||||
\(815\) | 1.04483e8i | 0.193007i | ||||||||
\(816\) | 4.74832e8i | 0.873916i | ||||||||
\(817\) | −4.85263e8 | −0.889837 | ||||||||
\(818\) | −1.49508e7 | −0.0273153 | ||||||||
\(819\) | − | 4.86617e8i | − | 0.885799i | ||||||
\(820\) | − | 5.67297e8i | − | 1.02889i | ||||||
\(821\) | −5.01126e8 | −0.905560 | −0.452780 | − | 0.891622i | \(-0.649568\pi\) | ||||
−0.452780 | + | 0.891622i | \(0.649568\pi\) | |||||||
\(822\) | − | 3.13677e6i | − | 0.00564764i | ||||||
\(823\) | 8.26839e8 | 1.48327 | 0.741637 | − | 0.670801i | \(-0.234050\pi\) | ||||
0.741637 | + | 0.670801i | \(0.234050\pi\) | |||||||
\(824\) | 1.06748e7i | 0.0190799i | ||||||||
\(825\) | 3.35810e7i | 0.0598042i | ||||||||
\(826\) | − | 2.13529e7i | − | 0.0378893i | ||||||
\(827\) | − | 3.01216e8i | − | 0.532551i | −0.963897 | − | 0.266276i | \(-0.914207\pi\) | ||
0.963897 | − | 0.266276i | \(-0.0857931\pi\) | |||||||
\(828\) | −1.86974e8 | + | 2.63331e7i | −0.329375 | + | 0.0463886i | ||||
\(829\) | 4.68607e8 | 0.822517 | 0.411259 | − | 0.911519i | \(-0.365089\pi\) | ||||
0.411259 | + | 0.911519i | \(0.365089\pi\) | |||||||
\(830\) | −4.74703e7 | −0.0830210 | ||||||||
\(831\) | −1.84369e8 | −0.321281 | ||||||||
\(832\) | −9.09422e8 | −1.57905 | ||||||||
\(833\) | − | 1.55028e9i | − | 2.68210i | ||||||
\(834\) | −6.20355e6 | −0.0106941 | ||||||||
\(835\) | − | 8.63666e8i | − | 1.48350i | ||||||
\(836\) | −2.22784e8 | −0.381298 | ||||||||
\(837\) | 1.30314e8 | 0.222237 | ||||||||
\(838\) | − | 3.20704e7i | − | 0.0544969i | ||||||
\(839\) | 1.01082e9i | 1.71154i | 0.517353 | + | 0.855772i | \(0.326918\pi\) | ||||
−0.517353 | + | 0.855772i | \(0.673082\pi\) | |||||||
\(840\) | 4.76930e7 | 0.0804668 | ||||||||
\(841\) | −5.83838e8 | −0.981531 | ||||||||
\(842\) | 2.23289e7i | 0.0374051i | ||||||||
\(843\) | 2.65496e8i | 0.443175i | ||||||||
\(844\) | −6.46153e8 | −1.07475 | ||||||||
\(845\) | 8.56759e8i | 1.42000i | ||||||||
\(846\) | 5.62481e6 | 0.00928960 | ||||||||
\(847\) | − | 6.31724e8i | − | 1.03963i | ||||||
\(848\) | 5.50319e8i | 0.902457i | ||||||||
\(849\) | 5.69284e8i | 0.930263i | ||||||||
\(850\) | − | 7.29676e6i | − | 0.0118816i | ||||||
\(851\) | 1.21494e7 | + | 8.62652e7i | 0.0197136 | + | 0.139974i | ||||
\(852\) | 6.42349e7 | 0.103861 | ||||||||
\(853\) | 1.99330e8 | 0.321163 | 0.160581 | − | 0.987023i | \(-0.448663\pi\) | ||||
0.160581 | + | 0.987023i | \(0.448663\pi\) | |||||||
\(854\) | −8.03017e6 | −0.0128929 | ||||||||
\(855\) | 1.18598e8 | 0.189749 | ||||||||
\(856\) | 3.49827e7i | 0.0557740i | ||||||||
\(857\) | 6.74308e8 | 1.07131 | 0.535656 | − | 0.844437i | \(-0.320065\pi\) | ||||
0.535656 | + | 0.844437i | \(0.320065\pi\) | |||||||
\(858\) | − | 1.64377e7i | − | 0.0260243i | ||||||
\(859\) | −2.08702e8 | −0.329266 | −0.164633 | − | 0.986355i | \(-0.552644\pi\) | ||||
−0.164633 | + | 0.986355i | \(0.552644\pi\) | |||||||
\(860\) | −8.24177e8 | −1.29576 | ||||||||
\(861\) | − | 6.92670e8i | − | 1.08522i | ||||||
\(862\) | − | 1.85049e7i | − | 0.0288912i | ||||||
\(863\) | −8.99089e8 | −1.39885 | −0.699424 | − | 0.714707i | \(-0.746560\pi\) | ||||
−0.699424 | + | 0.714707i | \(0.746560\pi\) | |||||||
\(864\) | −1.71055e7 | −0.0265212 | ||||||||
\(865\) | 6.40557e8i | 0.989713i | ||||||||
\(866\) | 4.05200e7i | 0.0623902i | ||||||||
\(867\) | −4.96907e8 | −0.762461 | ||||||||
\(868\) | 1.25210e9i | 1.91461i | ||||||||
\(869\) | −3.73548e8 | −0.569230 | ||||||||
\(870\) | 2.16930e6i | 0.00329429i | ||||||||
\(871\) | − | 8.05628e8i | − | 1.21921i | ||||||
\(872\) | 9.85352e7i | 0.148608i | ||||||||
\(873\) | 1.27677e8i | 0.191897i | ||||||||
\(874\) | 2.67889e6 | + | 1.90211e7i | 0.00401255 | + | 0.0284905i | ||||
\(875\) | 1.18626e9 | 1.77074 | ||||||||
\(876\) | 5.33926e7 | 0.0794271 | ||||||||
\(877\) | 3.34022e8 | 0.495195 | 0.247598 | − | 0.968863i | \(-0.420359\pi\) | ||||
0.247598 | + | 0.968863i | \(0.420359\pi\) | |||||||
\(878\) | 1.30831e7 | 0.0193297 | ||||||||
\(879\) | 2.89462e8i | 0.426211i | ||||||||
\(880\) | −3.77573e8 | −0.554055 | ||||||||
\(881\) | − | 3.45526e8i | − | 0.505304i | −0.967557 | − | 0.252652i | \(-0.918697\pi\) | ||
0.967557 | − | 0.252652i | \(-0.0813028\pi\) | |||||||
\(882\) | 1.85499e7 | 0.0270356 | ||||||||
\(883\) | 7.01907e7 | 0.101952 | 0.0509762 | − | 0.998700i | \(-0.483767\pi\) | ||||
0.0509762 | + | 0.998700i | \(0.483767\pi\) | |||||||
\(884\) | − | 1.67953e9i | − | 2.43125i | ||||||
\(885\) | − | 1.80558e8i | − | 0.260487i | ||||||
\(886\) | 3.60675e7 | 0.0518579 | ||||||||
\(887\) | −5.64947e8 | −0.809537 | −0.404769 | − | 0.914419i | \(-0.632648\pi\) | ||||
−0.404769 | + | 0.914419i | \(0.632648\pi\) | |||||||
\(888\) | 5.25949e6i | 0.00751111i | ||||||||
\(889\) | 4.12041e8i | 0.586455i | ||||||||
\(890\) | 3.48249e7 | 0.0493992 | ||||||||
\(891\) | 4.80835e7i | 0.0679771i | ||||||||
\(892\) | 8.11962e8 | 1.14404 | ||||||||
\(893\) | 2.69073e8i | 0.377847i | ||||||||
\(894\) | 2.59149e7i | 0.0362691i | ||||||||
\(895\) | 7.47924e7i | 0.104325i | ||||||||
\(896\) | − | 2.19062e8i | − | 0.304539i | ||||||
\(897\) | 6.59937e8 | − | 9.29442e7i | 0.914377 | − | 0.128779i | ||||
\(898\) | 3.13039e7 | 0.0432284 | ||||||||
\(899\) | −1.14024e8 | −0.156934 | ||||||||
\(900\) | −4.10554e7 | −0.0563175 | ||||||||
\(901\) | −1.01199e9 | −1.38357 | ||||||||
\(902\) | − | 2.33981e7i | − | 0.0318832i | ||||||
\(903\) | −1.00632e9 | −1.36670 | ||||||||
\(904\) | − | 1.04104e8i | − | 0.140916i | ||||||
\(905\) | −1.04828e9 | −1.41426 | ||||||||
\(906\) | −1.76945e7 | −0.0237933 | ||||||||
\(907\) | 6.29881e8i | 0.844184i | 0.906553 | + | 0.422092i | \(0.138704\pi\) | ||||
−0.906553 | + | 0.422092i | \(0.861296\pi\) | |||||||
\(908\) | − | 1.08340e9i | − | 1.44721i | ||||||
\(909\) | 4.05349e8 | 0.539681 | ||||||||
\(910\) | −8.40782e7 | −0.111573 | ||||||||
\(911\) | − | 4.77257e8i | − | 0.631244i | −0.948885 | − | 0.315622i | \(-0.897787\pi\) | ||
0.948885 | − | 0.315622i | \(-0.102213\pi\) | |||||||
\(912\) | − | 2.71790e8i | − | 0.358302i | ||||||
\(913\) | 9.20666e8 | 1.20973 | ||||||||
\(914\) | − | 3.00992e7i | − | 0.0394200i | ||||||
\(915\) | −6.79021e7 | −0.0886380 | ||||||||
\(916\) | − | 7.85116e8i | − | 1.02152i | ||||||
\(917\) | 1.91020e9i | 2.47726i | ||||||||
\(918\) | − | 1.04480e7i | − | 0.0135053i | ||||||
\(919\) | 1.23534e9i | 1.59163i | 0.605541 | + | 0.795814i | \(0.292957\pi\) | ||||
−0.605541 | + | 0.795814i | \(0.707043\pi\) | |||||||
\(920\) | 9.10941e6 | + | 6.46801e7i | 0.0116984 | + | 0.0830629i | ||||
\(921\) | −5.28698e8 | −0.676751 | ||||||||
\(922\) | 4.08872e7 | 0.0521669 | ||||||||
\(923\) | −2.26721e8 | −0.288328 | ||||||||
\(924\) | −4.62002e8 | −0.585636 | ||||||||
\(925\) | 1.89419e7i | 0.0239331i | ||||||||
\(926\) | −5.66434e7 | −0.0713372 | ||||||||
\(927\) | 5.50479e7i | 0.0691038i | ||||||||
\(928\) | 1.49671e7 | 0.0187281 | ||||||||
\(929\) | 5.67410e8 | 0.707701 | 0.353850 | − | 0.935302i | \(-0.384872\pi\) | ||||
0.353850 | + | 0.935302i | \(0.384872\pi\) | |||||||
\(930\) | − | 2.25159e7i | − | 0.0279924i | ||||||
\(931\) | 8.87367e8i | 1.09965i | ||||||||
\(932\) | 1.09359e7 | 0.0135085 | ||||||||
\(933\) | −6.10212e8 | −0.751339 | ||||||||
\(934\) | 1.03553e7i | 0.0127093i | ||||||||
\(935\) | − | 6.94322e8i | − | 0.849428i | ||||||
\(936\) | 4.02356e7 | 0.0490662 | ||||||||
\(937\) | − | 1.36840e9i | − | 1.66339i | −0.555237 | − | 0.831693i | \(-0.687372\pi\) | ||
0.555237 | − | 0.831693i | \(-0.312628\pi\) | |||||||
\(938\) | 4.81534e7 | 0.0583470 | ||||||||
\(939\) | − | 6.28913e8i | − | 0.759616i | ||||||
\(940\) | 4.56998e8i | 0.550213i | ||||||||
\(941\) | 6.47091e8i | 0.776599i | 0.921533 | + | 0.388299i | \(0.126937\pi\) | ||||
−0.921533 | + | 0.388299i | \(0.873063\pi\) | |||||||
\(942\) | 3.40323e7i | 0.0407135i | ||||||||
\(943\) | 9.39382e8 | − | 1.32301e8i | 1.12023 | − | 0.157771i | ||||
\(944\) | −4.13782e8 | −0.491876 | ||||||||
\(945\) | 2.45945e8 | 0.291436 | ||||||||
\(946\) | −3.39932e7 | −0.0401530 | ||||||||
\(947\) | −1.95225e8 | −0.229871 | −0.114936 | − | 0.993373i | \(-0.536666\pi\) | ||||
−0.114936 | + | 0.993373i | \(0.536666\pi\) | |||||||
\(948\) | − | 4.56693e8i | − | 0.536042i | ||||||
\(949\) | −1.88452e8 | −0.220497 | ||||||||
\(950\) | 4.17661e6i | 0.00487139i | ||||||||
\(951\) | 5.60642e8 | 0.651845 | ||||||||
\(952\) | 2.00989e8 | 0.232949 | ||||||||
\(953\) | 5.88380e8i | 0.679797i | 0.940462 | + | 0.339898i | \(0.110393\pi\) | ||||
−0.940462 | + | 0.339898i | \(0.889607\pi\) | |||||||
\(954\) | − | 1.21089e7i | − | 0.0139464i | ||||||
\(955\) | 1.05378e9 | 1.20988 | ||||||||
\(956\) | 3.46790e7 | 0.0396911 | ||||||||
\(957\) | − | 4.20726e7i | − | 0.0480025i | ||||||
\(958\) | 7.58637e7i | 0.0862854i | ||||||||
\(959\) | 3.11175e8 | 0.352817 | ||||||||
\(960\) | − | 4.59639e8i | − | 0.519521i | ||||||
\(961\) | 2.95988e8 | 0.333506 | ||||||||
\(962\) | − | 9.27197e6i | − | 0.0104147i | ||||||
\(963\) | 1.80400e8i | 0.202003i | ||||||||
\(964\) | − | 2.45752e8i | − | 0.274326i | ||||||
\(965\) | − | 1.77950e8i | − | 0.198023i | ||||||
\(966\) | 5.55540e6 | + | 3.94453e7i | 0.00616288 | + | 0.0437586i | ||||
\(967\) | −1.85929e8 | −0.205621 | −0.102811 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102811 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(968\) | 5.22337e7 | 0.0575870 | ||||||||
\(969\) | 4.99798e8 | 0.549317 | ||||||||
\(970\) | 2.20601e7 | 0.0241709 | ||||||||
\(971\) | − | 2.12025e8i | − | 0.231595i | −0.993273 | − | 0.115798i | \(-0.963058\pi\) | ||
0.993273 | − | 0.115798i | \(-0.0369424\pi\) | |||||||
\(972\) | −5.87859e7 | −0.0640139 | ||||||||
\(973\) | − | 6.15408e8i | − | 0.668074i | ||||||
\(974\) | −2.88759e7 | −0.0312506 | ||||||||
\(975\) | 1.44908e8 | 0.156343 | ||||||||
\(976\) | 1.55611e8i | 0.167375i | ||||||||
\(977\) | − | 4.00645e8i | − | 0.429612i | −0.976657 | − | 0.214806i | \(-0.931088\pi\) | ||
0.976657 | − | 0.214806i | \(-0.0689119\pi\) | |||||||
\(978\) | −5.26858e6 | −0.00563218 | ||||||||
\(979\) | −6.75414e8 | −0.719817 | ||||||||
\(980\) | 1.50712e9i | 1.60129i | ||||||||
\(981\) | 5.08130e8i | 0.538230i | ||||||||
\(982\) | 3.55074e7 | 0.0374960 | ||||||||
\(983\) | 1.40422e9i | 1.47834i | 0.673517 | + | 0.739172i | \(0.264783\pi\) | ||||
−0.673517 | + | 0.739172i | \(0.735217\pi\) | |||||||
\(984\) | 5.72730e7 | 0.0601125 | ||||||||
\(985\) | − | 1.27601e9i | − | 1.33520i | ||||||
\(986\) | 9.14189e6i | 0.00953686i | ||||||||
\(987\) | 5.57995e8i | 0.580335i | ||||||||
\(988\) | 9.61348e8i | 0.996804i | ||||||||
\(989\) | −1.92208e8 | − | 1.36475e9i | −0.198693 | − | 1.41079i | ||||
\(990\) | 8.30793e6 | 0.00856223 | ||||||||
\(991\) | −1.62423e8 | −0.166888 | −0.0834441 | − | 0.996512i | \(-0.526592\pi\) | ||||
−0.0834441 | + | 0.996512i | \(0.526592\pi\) | |||||||
\(992\) | −1.55349e8 | −0.159138 | ||||||||
\(993\) | −4.36908e8 | −0.446213 | ||||||||
\(994\) | − | 1.35514e7i | − | 0.0137983i | ||||||
\(995\) | 5.55347e8 | 0.563761 | ||||||||
\(996\) | 1.12559e9i | 1.13920i | ||||||||
\(997\) | 1.73006e9 | 1.74572 | 0.872861 | − | 0.487970i | \(-0.162262\pi\) | ||||
0.872861 | + | 0.487970i | \(0.162262\pi\) | |||||||
\(998\) | 1.14813e7 | 0.0115505 | ||||||||
\(999\) | 2.71223e7i | 0.0272038i |
(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 | 69.7.d.a.22.14 | yes | 24 | |
3.2 | odd | 2 | 207.7.d.e.91.12 | 24 | |||
23.22 | odd | 2 | inner | 69.7.d.a.22.13 | ✓ | 24 | |
69.68 | even | 2 | 207.7.d.e.91.11 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.7.d.a.22.13 | ✓ | 24 | 23.22 | odd | 2 | inner | |
69.7.d.a.22.14 | yes | 24 | 1.1 | even | 1 | trivial | |
207.7.d.e.91.11 | 24 | 69.68 | even | 2 | |||
207.7.d.e.91.12 | 24 | 3.2 | odd | 2 |