Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,8,Mod(36,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.36");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.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: | \(11.5582459429\) |
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: | \( x^{20} + 1702 x^{18} + 1194509 x^{16} + 450999516 x^{14} + 100204783492 x^{12} + 13461378480848 x^{10} + \cdots + 13\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{19}\cdot 3^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 36.20 | ||
Root | \(21.7545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 37.36 |
Dual form | 37.8.b.a.36.1 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21.7545i | 1.92285i | 0.275075 | + | 0.961423i | \(0.411297\pi\) | ||||
−0.275075 | + | 0.961423i | \(0.588703\pi\) | |||||||
\(3\) | 44.4956 | 0.951466 | 0.475733 | − | 0.879590i | \(-0.342183\pi\) | ||||
0.475733 | + | 0.879590i | \(0.342183\pi\) | |||||||
\(4\) | −345.259 | −2.69734 | ||||||||
\(5\) | 104.884i | 0.375244i | 0.982241 | + | 0.187622i | \(0.0600781\pi\) | ||||
−0.982241 | + | 0.187622i | \(0.939922\pi\) | |||||||
\(6\) | 967.981i | 1.82952i | ||||||||
\(7\) | −454.964 | −0.501342 | −0.250671 | − | 0.968072i | \(-0.580651\pi\) | ||||
−0.250671 | + | 0.968072i | \(0.580651\pi\) | |||||||
\(8\) | − | 4726.36i | − | 3.26371i | ||||||
\(9\) | −207.137 | −0.0947129 | ||||||||
\(10\) | −2281.70 | −0.721537 | ||||||||
\(11\) | −4886.81 | −1.10701 | −0.553504 | − | 0.832846i | \(-0.686710\pi\) | ||||
−0.553504 | + | 0.832846i | \(0.686710\pi\) | |||||||
\(12\) | −15362.5 | −2.56642 | ||||||||
\(13\) | − | 2167.39i | − | 0.273612i | −0.990598 | − | 0.136806i | \(-0.956316\pi\) | ||
0.990598 | − | 0.136806i | \(-0.0436836\pi\) | |||||||
\(14\) | − | 9897.53i | − | 0.964004i | ||||||
\(15\) | 4666.88i | 0.357032i | ||||||||
\(16\) | 58626.6 | 3.57828 | ||||||||
\(17\) | 33286.0i | 1.64320i | 0.570066 | + | 0.821599i | \(0.306918\pi\) | ||||
−0.570066 | + | 0.821599i | \(0.693082\pi\) | |||||||
\(18\) | − | 4506.17i | − | 0.182118i | ||||||
\(19\) | − | 24585.0i | − | 0.822304i | −0.911567 | − | 0.411152i | \(-0.865127\pi\) | ||
0.911567 | − | 0.411152i | \(-0.134873\pi\) | |||||||
\(20\) | − | 36212.1i | − | 1.01216i | ||||||
\(21\) | −20243.9 | −0.477010 | ||||||||
\(22\) | − | 106310.i | − | 2.12861i | ||||||
\(23\) | 62365.5i | 1.06880i | 0.845231 | + | 0.534401i | \(0.179463\pi\) | ||||
−0.845231 | + | 0.534401i | \(0.820537\pi\) | |||||||
\(24\) | − | 210303.i | − | 3.10531i | ||||||
\(25\) | 67124.3 | 0.859192 | ||||||||
\(26\) | 47150.4 | 0.526113 | ||||||||
\(27\) | −106529. | −1.04158 | ||||||||
\(28\) | 157081. | 1.35229 | ||||||||
\(29\) | 61128.3i | 0.465424i | 0.972546 | + | 0.232712i | \(0.0747600\pi\) | ||||
−0.972546 | + | 0.232712i | \(0.925240\pi\) | |||||||
\(30\) | −101526. | −0.686518 | ||||||||
\(31\) | 34740.4i | 0.209445i | 0.994502 | + | 0.104722i | \(0.0333954\pi\) | ||||
−0.994502 | + | 0.104722i | \(0.966605\pi\) | |||||||
\(32\) | 670419.i | 3.61677i | ||||||||
\(33\) | −217442. | −1.05328 | ||||||||
\(34\) | −724120. | −3.15962 | ||||||||
\(35\) | − | 47718.5i | − | 0.188126i | ||||||
\(36\) | 71516.0 | 0.255473 | ||||||||
\(37\) | −29898.6 | + | 306656.i | −0.0970385 | + | 0.995281i | ||||
\(38\) | 534835. | 1.58116 | ||||||||
\(39\) | − | 96439.3i | − | 0.260332i | ||||||
\(40\) | 495720. | 1.22469 | ||||||||
\(41\) | −645608. | −1.46294 | −0.731468 | − | 0.681876i | \(-0.761165\pi\) | ||||
−0.731468 | + | 0.681876i | \(0.761165\pi\) | |||||||
\(42\) | − | 440397.i | − | 0.917216i | ||||||
\(43\) | − | 524254.i | − | 1.00555i | −0.864419 | − | 0.502773i | \(-0.832313\pi\) | ||
0.864419 | − | 0.502773i | \(-0.167687\pi\) | |||||||
\(44\) | 1.68721e6 | 2.98597 | ||||||||
\(45\) | − | 21725.4i | − | 0.0355405i | ||||||
\(46\) | −1.35673e6 | −2.05514 | ||||||||
\(47\) | −1.03728e6 | −1.45731 | −0.728656 | − | 0.684880i | \(-0.759855\pi\) | ||||
−0.728656 | + | 0.684880i | \(0.759855\pi\) | |||||||
\(48\) | 2.60863e6 | 3.40461 | ||||||||
\(49\) | −616550. | −0.748656 | ||||||||
\(50\) | 1.46026e6i | 1.65209i | ||||||||
\(51\) | 1.48108e6i | 1.56345i | ||||||||
\(52\) | 748310.i | 0.738022i | ||||||||
\(53\) | 2.01545e6 | 1.85955 | 0.929773 | − | 0.368133i | \(-0.120003\pi\) | ||||
0.929773 | + | 0.368133i | \(0.120003\pi\) | |||||||
\(54\) | − | 2.31748e6i | − | 2.00280i | ||||||
\(55\) | − | 512548.i | − | 0.415399i | ||||||
\(56\) | 2.15033e6i | 1.63624i | ||||||||
\(57\) | − | 1.09393e6i | − | 0.782394i | ||||||
\(58\) | −1.32982e6 | −0.894939 | ||||||||
\(59\) | 2.51705e6i | 1.59555i | 0.602957 | + | 0.797774i | \(0.293989\pi\) | ||||
−0.602957 | + | 0.797774i | \(0.706011\pi\) | |||||||
\(60\) | − | 1.61128e6i | − | 0.963035i | ||||||
\(61\) | − | 981203.i | − | 0.553483i | −0.960944 | − | 0.276742i | \(-0.910745\pi\) | ||
0.960944 | − | 0.276742i | \(-0.0892546\pi\) | |||||||
\(62\) | −755761. | −0.402730 | ||||||||
\(63\) | 94240.0 | 0.0474836 | ||||||||
\(64\) | −7.08043e6 | −3.37621 | ||||||||
\(65\) | 227324. | 0.102671 | ||||||||
\(66\) | − | 4.73034e6i | − | 2.02530i | ||||||
\(67\) | 941977. | 0.382630 | 0.191315 | − | 0.981529i | \(-0.438725\pi\) | ||||
0.191315 | + | 0.981529i | \(0.438725\pi\) | |||||||
\(68\) | − | 1.14923e7i | − | 4.43226i | ||||||
\(69\) | 2.77499e6i | 1.01693i | ||||||||
\(70\) | 1.03809e6 | 0.361737 | ||||||||
\(71\) | −2.67347e6 | −0.886485 | −0.443242 | − | 0.896402i | \(-0.646172\pi\) | ||||
−0.443242 | + | 0.896402i | \(0.646172\pi\) | |||||||
\(72\) | 979006.i | 0.309116i | ||||||||
\(73\) | 4.46976e6 | 1.34479 | 0.672394 | − | 0.740193i | \(-0.265266\pi\) | ||||
0.672394 | + | 0.740193i | \(0.265266\pi\) | |||||||
\(74\) | −6.67115e6 | − | 650429.i | −1.91377 | − | 0.186590i | ||||
\(75\) | 2.98674e6 | 0.817491 | ||||||||
\(76\) | 8.48819e6i | 2.21803i | ||||||||
\(77\) | 2.22332e6 | 0.554990 | ||||||||
\(78\) | 2.09799e6 | 0.500578 | ||||||||
\(79\) | 4.48534e6i | 1.02353i | 0.859126 | + | 0.511765i | \(0.171008\pi\) | ||||
−0.859126 | + | 0.511765i | \(0.828992\pi\) | |||||||
\(80\) | 6.14899e6i | 1.34273i | ||||||||
\(81\) | −4.28705e6 | −0.896317 | ||||||||
\(82\) | − | 1.40449e7i | − | 2.81300i | ||||||
\(83\) | 6.80298e6 | 1.30595 | 0.652974 | − | 0.757380i | \(-0.273521\pi\) | ||||
0.652974 | + | 0.757380i | \(0.273521\pi\) | |||||||
\(84\) | 6.98940e6 | 1.28666 | ||||||||
\(85\) | −3.49116e6 | −0.616601 | ||||||||
\(86\) | 1.14049e7 | 1.93351 | ||||||||
\(87\) | 2.71994e6i | 0.442835i | ||||||||
\(88\) | 2.30968e7i | 3.61296i | ||||||||
\(89\) | 746269.i | 0.112210i | 0.998425 | + | 0.0561049i | \(0.0178681\pi\) | ||||
−0.998425 | + | 0.0561049i | \(0.982132\pi\) | |||||||
\(90\) | 472625. | 0.0683389 | ||||||||
\(91\) | 986084.i | 0.137173i | ||||||||
\(92\) | − | 2.15322e7i | − | 2.88292i | ||||||
\(93\) | 1.54580e6i | 0.199279i | ||||||||
\(94\) | − | 2.25655e7i | − | 2.80219i | ||||||
\(95\) | 2.57857e6 | 0.308565 | ||||||||
\(96\) | 2.98307e7i | 3.44123i | ||||||||
\(97\) | 3.11369e6i | 0.346398i | 0.984887 | + | 0.173199i | \(0.0554103\pi\) | ||||
−0.984887 | + | 0.173199i | \(0.944590\pi\) | |||||||
\(98\) | − | 1.34128e7i | − | 1.43955i | ||||||
\(99\) | 1.01224e6 | 0.104848 | ||||||||
\(100\) | −2.31753e7 | −2.31753 | ||||||||
\(101\) | 6.76405e6 | 0.653254 | 0.326627 | − | 0.945153i | \(-0.394088\pi\) | ||||
0.326627 | + | 0.945153i | \(0.394088\pi\) | |||||||
\(102\) | −3.22202e7 | −3.00627 | ||||||||
\(103\) | 8.86414e6i | 0.799293i | 0.916669 | + | 0.399647i | \(0.130867\pi\) | ||||
−0.916669 | + | 0.399647i | \(0.869133\pi\) | |||||||
\(104\) | −1.02439e7 | −0.892990 | ||||||||
\(105\) | − | 2.12326e6i | − | 0.178995i | ||||||
\(106\) | 4.38452e7i | 3.57562i | ||||||||
\(107\) | 3.59428e6 | 0.283641 | 0.141820 | − | 0.989892i | \(-0.454704\pi\) | ||||
0.141820 | + | 0.989892i | \(0.454704\pi\) | |||||||
\(108\) | 3.67800e7 | 2.80950 | ||||||||
\(109\) | − | 1.73029e7i | − | 1.27975i | −0.768477 | − | 0.639877i | \(-0.778985\pi\) | ||
0.768477 | − | 0.639877i | \(-0.221015\pi\) | |||||||
\(110\) | 1.11502e7 | 0.798748 | ||||||||
\(111\) | −1.33036e6 | + | 1.36449e7i | −0.0923288 | + | 0.946975i | ||||
\(112\) | −2.66730e7 | −1.79394 | ||||||||
\(113\) | − | 3.00271e6i | − | 0.195767i | −0.995198 | − | 0.0978834i | \(-0.968793\pi\) | ||
0.995198 | − | 0.0978834i | \(-0.0312072\pi\) | |||||||
\(114\) | 2.37978e7 | 1.50442 | ||||||||
\(115\) | −6.54114e6 | −0.401062 | ||||||||
\(116\) | − | 2.11051e7i | − | 1.25541i | ||||||
\(117\) | 448946.i | 0.0259146i | ||||||||
\(118\) | −5.47572e7 | −3.06799 | ||||||||
\(119\) | − | 1.51439e7i | − | 0.823804i | ||||||
\(120\) | 2.20574e7 | 1.16525 | ||||||||
\(121\) | 4.39374e6 | 0.225469 | ||||||||
\(122\) | 2.13456e7 | 1.06426 | ||||||||
\(123\) | −2.87268e7 | −1.39193 | ||||||||
\(124\) | − | 1.19944e7i | − | 0.564942i | ||||||
\(125\) | 1.52343e7i | 0.697651i | ||||||||
\(126\) | 2.05015e6i | 0.0913036i | ||||||||
\(127\) | −1.72118e6 | −0.0745612 | −0.0372806 | − | 0.999305i | \(-0.511870\pi\) | ||||
−0.0372806 | + | 0.999305i | \(0.511870\pi\) | |||||||
\(128\) | − | 6.82177e7i | − | 2.87516i | ||||||
\(129\) | − | 2.33270e7i | − | 0.956742i | ||||||
\(130\) | 4.94533e6i | 0.197421i | ||||||||
\(131\) | − | 2.53833e6i | − | 0.0986503i | −0.998783 | − | 0.0493252i | \(-0.984293\pi\) | ||
0.998783 | − | 0.0493252i | \(-0.0157071\pi\) | |||||||
\(132\) | 7.50737e7 | 2.84105 | ||||||||
\(133\) | 1.11853e7i | 0.412256i | ||||||||
\(134\) | 2.04923e7i | 0.735738i | ||||||||
\(135\) | − | 1.11732e7i | − | 0.390848i | ||||||
\(136\) | 1.57322e8 | 5.36293 | ||||||||
\(137\) | −8.62321e6 | −0.286515 | −0.143257 | − | 0.989685i | \(-0.545758\pi\) | ||||
−0.143257 | + | 0.989685i | \(0.545758\pi\) | |||||||
\(138\) | −6.03686e7 | −1.95539 | ||||||||
\(139\) | 6.63374e6 | 0.209511 | 0.104755 | − | 0.994498i | \(-0.466594\pi\) | ||||
0.104755 | + | 0.994498i | \(0.466594\pi\) | |||||||
\(140\) | 1.64752e7i | 0.507438i | ||||||||
\(141\) | −4.61543e7 | −1.38658 | ||||||||
\(142\) | − | 5.81601e7i | − | 1.70457i | ||||||
\(143\) | 1.05916e7i | 0.302891i | ||||||||
\(144\) | −1.21437e7 | −0.338910 | ||||||||
\(145\) | −6.41138e6 | −0.174648 | ||||||||
\(146\) | 9.72374e7i | 2.58582i | ||||||||
\(147\) | −2.74338e7 | −0.712321 | ||||||||
\(148\) | 1.03227e7 | − | 1.05876e8i | 0.261745 | − | 2.68461i | ||||
\(149\) | −6.28548e7 | −1.55663 | −0.778317 | − | 0.627872i | \(-0.783926\pi\) | ||||
−0.778317 | + | 0.627872i | \(0.783926\pi\) | |||||||
\(150\) | 6.49751e7i | 1.57191i | ||||||||
\(151\) | 2.77490e6 | 0.0655886 | 0.0327943 | − | 0.999462i | \(-0.489559\pi\) | ||||
0.0327943 | + | 0.999462i | \(0.489559\pi\) | |||||||
\(152\) | −1.16198e8 | −2.68377 | ||||||||
\(153\) | − | 6.89476e6i | − | 0.155632i | ||||||
\(154\) | 4.83673e7i | 1.06716i | ||||||||
\(155\) | −3.64371e6 | −0.0785929 | ||||||||
\(156\) | 3.32965e7i | 0.702203i | ||||||||
\(157\) | −3.15080e6 | −0.0649789 | −0.0324894 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324894 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(158\) | −9.75764e7 | −1.96809 | ||||||||
\(159\) | 8.96788e7 | 1.76929 | ||||||||
\(160\) | −7.03162e7 | −1.35717 | ||||||||
\(161\) | − | 2.83741e7i | − | 0.535835i | ||||||
\(162\) | − | 9.32628e7i | − | 1.72348i | ||||||
\(163\) | − | 7.61252e7i | − | 1.37680i | −0.725330 | − | 0.688401i | \(-0.758313\pi\) | ||
0.725330 | − | 0.688401i | \(-0.241687\pi\) | |||||||
\(164\) | 2.22902e8 | 3.94603 | ||||||||
\(165\) | − | 2.28062e7i | − | 0.395238i | ||||||
\(166\) | 1.47996e8i | 2.51114i | ||||||||
\(167\) | − | 5.09259e7i | − | 0.846118i | −0.906102 | − | 0.423059i | \(-0.860956\pi\) | ||
0.906102 | − | 0.423059i | \(-0.139044\pi\) | |||||||
\(168\) | 9.56802e7i | 1.55682i | ||||||||
\(169\) | 5.80510e7 | 0.925137 | ||||||||
\(170\) | − | 7.59486e7i | − | 1.18563i | ||||||
\(171\) | 5.09247e6i | 0.0778828i | ||||||||
\(172\) | 1.81003e8i | 2.71229i | ||||||||
\(173\) | 9.72088e7 | 1.42739 | 0.713697 | − | 0.700454i | \(-0.247019\pi\) | ||||
0.713697 | + | 0.700454i | \(0.247019\pi\) | |||||||
\(174\) | −5.91710e7 | −0.851504 | ||||||||
\(175\) | −3.05392e7 | −0.430749 | ||||||||
\(176\) | −2.86497e8 | −3.96119 | ||||||||
\(177\) | 1.11998e8i | 1.51811i | ||||||||
\(178\) | −1.62347e7 | −0.215762 | ||||||||
\(179\) | 1.19521e8i | 1.55761i | 0.627265 | + | 0.778806i | \(0.284174\pi\) | ||||
−0.627265 | + | 0.778806i | \(0.715826\pi\) | |||||||
\(180\) | 7.50088e6i | 0.0958646i | ||||||||
\(181\) | 3.00909e7 | 0.377191 | 0.188595 | − | 0.982055i | \(-0.439607\pi\) | ||||
0.188595 | + | 0.982055i | \(0.439607\pi\) | |||||||
\(182\) | −2.14518e7 | −0.263763 | ||||||||
\(183\) | − | 4.36593e7i | − | 0.526621i | ||||||
\(184\) | 2.94762e8 | 3.48826 | ||||||||
\(185\) | −3.21633e7 | − | 3.13588e6i | −0.373473 | − | 0.0364132i | ||||
\(186\) | −3.36281e7 | −0.383183 | ||||||||
\(187\) | − | 1.62662e8i | − | 1.81903i | ||||||
\(188\) | 3.58129e8 | 3.93086 | ||||||||
\(189\) | 4.84668e7 | 0.522189 | ||||||||
\(190\) | 5.60956e7i | 0.593323i | ||||||||
\(191\) | − | 1.24539e8i | − | 1.29327i | −0.762800 | − | 0.646634i | \(-0.776176\pi\) | ||
0.762800 | − | 0.646634i | \(-0.223824\pi\) | |||||||
\(192\) | −3.15048e8 | −3.21235 | ||||||||
\(193\) | 1.77832e8i | 1.78057i | 0.455401 | + | 0.890286i | \(0.349496\pi\) | ||||
−0.455401 | + | 0.890286i | \(0.650504\pi\) | |||||||
\(194\) | −6.77369e7 | −0.666069 | ||||||||
\(195\) | 1.01149e7 | 0.0976882 | ||||||||
\(196\) | 2.12870e8 | 2.01938 | ||||||||
\(197\) | 1.29509e8 | 1.20689 | 0.603445 | − | 0.797405i | \(-0.293794\pi\) | ||||
0.603445 | + | 0.797405i | \(0.293794\pi\) | |||||||
\(198\) | 2.20208e7i | 0.201607i | ||||||||
\(199\) | − | 6.68192e7i | − | 0.601056i | −0.953773 | − | 0.300528i | \(-0.902837\pi\) | ||
0.953773 | − | 0.300528i | \(-0.0971630\pi\) | |||||||
\(200\) | − | 3.17254e8i | − | 2.80416i | ||||||
\(201\) | 4.19139e7 | 0.364059 | ||||||||
\(202\) | 1.47149e8i | 1.25611i | ||||||||
\(203\) | − | 2.78112e7i | − | 0.233337i | ||||||
\(204\) | − | 5.11356e8i | − | 4.21714i | ||||||
\(205\) | − | 6.77139e7i | − | 0.548959i | ||||||
\(206\) | −1.92835e8 | −1.53692 | ||||||||
\(207\) | − | 1.29182e7i | − | 0.101229i | ||||||
\(208\) | − | 1.27066e8i | − | 0.979060i | ||||||
\(209\) | 1.20142e8i | 0.910298i | ||||||||
\(210\) | 4.61906e7 | 0.344180 | ||||||||
\(211\) | −2.32513e8 | −1.70396 | −0.851978 | − | 0.523578i | \(-0.824597\pi\) | ||||
−0.851978 | + | 0.523578i | \(0.824597\pi\) | |||||||
\(212\) | −6.95853e8 | −5.01582 | ||||||||
\(213\) | −1.18958e8 | −0.843460 | ||||||||
\(214\) | 7.81917e7i | 0.545397i | ||||||||
\(215\) | 5.49858e7 | 0.377325 | ||||||||
\(216\) | 5.03493e8i | 3.39943i | ||||||||
\(217\) | − | 1.58056e7i | − | 0.105003i | ||||||
\(218\) | 3.76417e8 | 2.46077 | ||||||||
\(219\) | 1.98885e8 | 1.27952 | ||||||||
\(220\) | 1.76962e8i | 1.12047i | ||||||||
\(221\) | 7.21435e7 | 0.449598 | ||||||||
\(222\) | −2.96837e8 | − | 2.89412e7i | −1.82089 | − | 0.177534i | ||||
\(223\) | −8.13089e7 | −0.490988 | −0.245494 | − | 0.969398i | \(-0.578950\pi\) | ||||
−0.245494 | + | 0.969398i | \(0.578950\pi\) | |||||||
\(224\) | − | 3.05017e8i | − | 1.81324i | ||||||
\(225\) | −1.39039e7 | −0.0813766 | ||||||||
\(226\) | 6.53226e7 | 0.376429 | ||||||||
\(227\) | 8.95466e7i | 0.508111i | 0.967190 | + | 0.254056i | \(0.0817646\pi\) | ||||
−0.967190 | + | 0.254056i | \(0.918235\pi\) | |||||||
\(228\) | 3.77687e8i | 2.11038i | ||||||||
\(229\) | −1.46451e8 | −0.805877 | −0.402938 | − | 0.915227i | \(-0.632011\pi\) | ||||
−0.402938 | + | 0.915227i | \(0.632011\pi\) | |||||||
\(230\) | − | 1.42299e8i | − | 0.771180i | ||||||
\(231\) | 9.89283e7 | 0.528054 | ||||||||
\(232\) | 2.88914e8 | 1.51901 | ||||||||
\(233\) | −1.67528e8 | −0.867645 | −0.433822 | − | 0.900998i | \(-0.642835\pi\) | ||||
−0.433822 | + | 0.900998i | \(0.642835\pi\) | |||||||
\(234\) | −9.76661e6 | −0.0498297 | ||||||||
\(235\) | − | 1.08794e8i | − | 0.546848i | ||||||
\(236\) | − | 8.69034e8i | − | 4.30373i | ||||||
\(237\) | 1.99578e8i | 0.973854i | ||||||||
\(238\) | 3.29449e8 | 1.58405 | ||||||||
\(239\) | 4.76626e7i | 0.225832i | 0.993605 | + | 0.112916i | \(0.0360191\pi\) | ||||
−0.993605 | + | 0.112916i | \(0.963981\pi\) | |||||||
\(240\) | 2.73603e8i | 1.27756i | ||||||||
\(241\) | 2.47131e8i | 1.13728i | 0.822587 | + | 0.568639i | \(0.192530\pi\) | ||||
−0.822587 | + | 0.568639i | \(0.807470\pi\) | |||||||
\(242\) | 9.55838e7i | 0.433541i | ||||||||
\(243\) | 4.22230e7 | 0.188767 | ||||||||
\(244\) | 3.38769e8i | 1.49293i | ||||||||
\(245\) | − | 6.46663e7i | − | 0.280929i | ||||||
\(246\) | − | 6.24937e8i | − | 2.67647i | ||||||
\(247\) | −5.32852e7 | −0.224992 | ||||||||
\(248\) | 1.64196e8 | 0.683567 | ||||||||
\(249\) | 3.02703e8 | 1.24257 | ||||||||
\(250\) | −3.31415e8 | −1.34148 | ||||||||
\(251\) | − | 3.41733e8i | − | 1.36405i | −0.731331 | − | 0.682023i | \(-0.761101\pi\) | ||
0.731331 | − | 0.682023i | \(-0.238899\pi\) | |||||||
\(252\) | −3.25372e7 | −0.128079 | ||||||||
\(253\) | − | 3.04768e8i | − | 1.18317i | ||||||
\(254\) | − | 3.74434e7i | − | 0.143370i | ||||||
\(255\) | −1.55342e8 | −0.586674 | ||||||||
\(256\) | 5.77748e8 | 2.15228 | ||||||||
\(257\) | 3.73033e8i | 1.37082i | 0.728156 | + | 0.685411i | \(0.240377\pi\) | ||||
−0.728156 | + | 0.685411i | \(0.759623\pi\) | |||||||
\(258\) | 5.07468e8 | 1.83967 | ||||||||
\(259\) | 1.36028e7 | − | 1.39518e8i | 0.0486495 | − | 0.498976i | ||||
\(260\) | −7.84857e7 | −0.276939 | ||||||||
\(261\) | − | 1.26619e7i | − | 0.0440817i | ||||||
\(262\) | 5.52201e7 | 0.189689 | ||||||||
\(263\) | 1.08376e8 | 0.367358 | 0.183679 | − | 0.982986i | \(-0.441199\pi\) | ||||
0.183679 | + | 0.982986i | \(0.441199\pi\) | |||||||
\(264\) | 1.02771e9i | 3.43761i | ||||||||
\(265\) | 2.11389e8i | 0.697784i | ||||||||
\(266\) | −2.43331e8 | −0.792704 | ||||||||
\(267\) | 3.32057e7i | 0.106764i | ||||||||
\(268\) | −3.25226e8 | −1.03208 | ||||||||
\(269\) | −1.95365e8 | −0.611948 | −0.305974 | − | 0.952040i | \(-0.598982\pi\) | ||||
−0.305974 | + | 0.952040i | \(0.598982\pi\) | |||||||
\(270\) | 2.43067e8 | 0.751540 | ||||||||
\(271\) | −4.54585e8 | −1.38747 | −0.693733 | − | 0.720232i | \(-0.744035\pi\) | ||||
−0.693733 | + | 0.720232i | \(0.744035\pi\) | |||||||
\(272\) | 1.95144e9i | 5.87983i | ||||||||
\(273\) | 4.38764e7i | 0.130515i | ||||||||
\(274\) | − | 1.87594e8i | − | 0.550924i | ||||||
\(275\) | −3.28024e8 | −0.951133 | ||||||||
\(276\) | − | 9.58091e8i | − | 2.74300i | ||||||
\(277\) | 3.64988e8i | 1.03181i | 0.856646 | + | 0.515905i | \(0.172544\pi\) | ||||
−0.856646 | + | 0.515905i | \(0.827456\pi\) | |||||||
\(278\) | 1.44314e8i | 0.402857i | ||||||||
\(279\) | − | 7.19603e6i | − | 0.0198371i | ||||||
\(280\) | −2.25535e8 | −0.613989 | ||||||||
\(281\) | 5.72410e8i | 1.53899i | 0.638655 | + | 0.769493i | \(0.279491\pi\) | ||||
−0.638655 | + | 0.769493i | \(0.720509\pi\) | |||||||
\(282\) | − | 1.00407e9i | − | 2.66618i | ||||||
\(283\) | 1.27520e7i | 0.0334446i | 0.999860 | + | 0.0167223i | \(0.00532312\pi\) | ||||
−0.999860 | + | 0.0167223i | \(0.994677\pi\) | |||||||
\(284\) | 9.23040e8 | 2.39115 | ||||||||
\(285\) | 1.14735e8 | 0.293589 | ||||||||
\(286\) | −2.30415e8 | −0.582412 | ||||||||
\(287\) | 2.93729e8 | 0.733432 | ||||||||
\(288\) | − | 1.38869e8i | − | 0.342555i | ||||||
\(289\) | −6.97616e8 | −1.70010 | ||||||||
\(290\) | − | 1.39476e8i | − | 0.335821i | ||||||
\(291\) | 1.38546e8i | 0.329585i | ||||||||
\(292\) | −1.54322e9 | −3.62734 | ||||||||
\(293\) | −3.96104e8 | −0.919968 | −0.459984 | − | 0.887927i | \(-0.652145\pi\) | ||||
−0.459984 | + | 0.887927i | \(0.652145\pi\) | |||||||
\(294\) | − | 5.96809e8i | − | 1.36968i | ||||||
\(295\) | −2.63998e8 | −0.598720 | ||||||||
\(296\) | 1.44937e9 | + | 1.41311e8i | 3.24831 | + | 0.316706i | ||||
\(297\) | 5.20585e8 | 1.15304 | ||||||||
\(298\) | − | 1.36738e9i | − | 2.99317i | ||||||
\(299\) | 1.35170e8 | 0.292436 | ||||||||
\(300\) | −1.03120e9 | −2.20505 | ||||||||
\(301\) | 2.38517e8i | 0.504123i | ||||||||
\(302\) | 6.03666e7i | 0.126117i | ||||||||
\(303\) | 3.00971e8 | 0.621549 | ||||||||
\(304\) | − | 1.44133e9i | − | 2.94244i | ||||||
\(305\) | 1.02913e8 | 0.207692 | ||||||||
\(306\) | 1.49992e8 | 0.299257 | ||||||||
\(307\) | −2.49480e8 | −0.492097 | −0.246049 | − | 0.969257i | \(-0.579132\pi\) | ||||
−0.246049 | + | 0.969257i | \(0.579132\pi\) | |||||||
\(308\) | −7.67623e8 | −1.49699 | ||||||||
\(309\) | 3.94416e8i | 0.760500i | ||||||||
\(310\) | − | 7.92672e7i | − | 0.151122i | ||||||
\(311\) | − | 4.75503e8i | − | 0.896380i | −0.893938 | − | 0.448190i | \(-0.852069\pi\) | ||
0.893938 | − | 0.448190i | \(-0.147931\pi\) | |||||||
\(312\) | −4.55807e8 | −0.849650 | ||||||||
\(313\) | 4.15781e8i | 0.766406i | 0.923664 | + | 0.383203i | \(0.125179\pi\) | ||||
−0.923664 | + | 0.383203i | \(0.874821\pi\) | |||||||
\(314\) | − | 6.85442e7i | − | 0.124944i | ||||||
\(315\) | 9.88427e6i | 0.0178179i | ||||||||
\(316\) | − | 1.54860e9i | − | 2.76080i | ||||||
\(317\) | 8.03197e8 | 1.41617 | 0.708084 | − | 0.706128i | \(-0.249560\pi\) | ||||
0.708084 | + | 0.706128i | \(0.249560\pi\) | |||||||
\(318\) | 1.95092e9i | 3.40208i | ||||||||
\(319\) | − | 2.98722e8i | − | 0.515229i | ||||||
\(320\) | − | 7.42624e8i | − | 1.26690i | ||||||
\(321\) | 1.59930e8 | 0.269874 | ||||||||
\(322\) | 6.17264e8 | 1.03033 | ||||||||
\(323\) | 8.18335e8 | 1.35121 | ||||||||
\(324\) | 1.48014e9 | 2.41767 | ||||||||
\(325\) | − | 1.45484e8i | − | 0.235085i | ||||||
\(326\) | 1.65607e9 | 2.64738 | ||||||||
\(327\) | − | 7.69905e8i | − | 1.21764i | ||||||
\(328\) | 3.05138e9i | 4.77461i | ||||||||
\(329\) | 4.71924e8 | 0.730612 | ||||||||
\(330\) | 4.96137e8 | 0.759981 | ||||||||
\(331\) | − | 2.23396e8i | − | 0.338593i | −0.985565 | − | 0.169296i | \(-0.945850\pi\) | ||
0.985565 | − | 0.169296i | \(-0.0541495\pi\) | |||||||
\(332\) | −2.34879e9 | −3.52258 | ||||||||
\(333\) | 6.19310e6 | − | 6.35199e7i | 0.00919080 | − | 0.0942660i | ||||
\(334\) | 1.10787e9 | 1.62696 | ||||||||
\(335\) | 9.87984e7i | 0.143580i | ||||||||
\(336\) | −1.18683e9 | −1.70688 | ||||||||
\(337\) | −4.04797e8 | −0.576146 | −0.288073 | − | 0.957608i | \(-0.593015\pi\) | ||||
−0.288073 | + | 0.957608i | \(0.593015\pi\) | |||||||
\(338\) | 1.26287e9i | 1.77890i | ||||||||
\(339\) | − | 1.33608e8i | − | 0.186265i | ||||||
\(340\) | 1.20536e9 | 1.66318 | ||||||||
\(341\) | − | 1.69770e8i | − | 0.231857i | ||||||
\(342\) | −1.10784e8 | −0.149757 | ||||||||
\(343\) | 6.55191e8 | 0.876675 | ||||||||
\(344\) | −2.47781e9 | −3.28181 | ||||||||
\(345\) | −2.91052e8 | −0.381596 | ||||||||
\(346\) | 2.11473e9i | 2.74466i | ||||||||
\(347\) | 8.74771e7i | 0.112394i | 0.998420 | + | 0.0561968i | \(0.0178974\pi\) | ||||
−0.998420 | + | 0.0561968i | \(0.982103\pi\) | |||||||
\(348\) | − | 9.39084e8i | − | 1.19448i | ||||||
\(349\) | 1.35954e8 | 0.171200 | 0.0856000 | − | 0.996330i | \(-0.472719\pi\) | ||||
0.0856000 | + | 0.996330i | \(0.472719\pi\) | |||||||
\(350\) | − | 6.64365e8i | − | 0.828264i | ||||||
\(351\) | 2.30889e8i | 0.284989i | ||||||||
\(352\) | − | 3.27621e9i | − | 4.00380i | ||||||
\(353\) | − | 1.11183e9i | − | 1.34533i | −0.739948 | − | 0.672664i | \(-0.765150\pi\) | ||
0.739948 | − | 0.672664i | \(-0.234850\pi\) | |||||||
\(354\) | −2.43646e9 | −2.91909 | ||||||||
\(355\) | − | 2.80404e8i | − | 0.332648i | ||||||
\(356\) | − | 2.57656e8i | − | 0.302667i | ||||||
\(357\) | − | 6.73839e8i | − | 0.783822i | ||||||
\(358\) | −2.60012e9 | −2.99505 | ||||||||
\(359\) | 7.81492e8 | 0.891444 | 0.445722 | − | 0.895172i | \(-0.352947\pi\) | ||||
0.445722 | + | 0.895172i | \(0.352947\pi\) | |||||||
\(360\) | −1.02682e8 | −0.115994 | ||||||||
\(361\) | 2.89450e8 | 0.323816 | ||||||||
\(362\) | 6.54614e8i | 0.725279i | ||||||||
\(363\) | 1.95502e8 | 0.214526 | ||||||||
\(364\) | − | 3.40454e8i | − | 0.370002i | ||||||
\(365\) | 4.68806e8i | 0.504624i | ||||||||
\(366\) | 9.49787e8 | 1.01261 | ||||||||
\(367\) | 8.22805e8 | 0.868892 | 0.434446 | − | 0.900698i | \(-0.356944\pi\) | ||||
0.434446 | + | 0.900698i | \(0.356944\pi\) | |||||||
\(368\) | 3.65628e9i | 3.82447i | ||||||||
\(369\) | 1.33729e8 | 0.138559 | ||||||||
\(370\) | 6.82195e7 | − | 6.99697e8i | 0.0700169 | − | 0.718132i | ||||
\(371\) | −9.16959e8 | −0.932269 | ||||||||
\(372\) | − | 5.33700e8i | − | 0.537523i | ||||||
\(373\) | −4.90669e8 | −0.489562 | −0.244781 | − | 0.969578i | \(-0.578716\pi\) | ||||
−0.244781 | + | 0.969578i | \(0.578716\pi\) | |||||||
\(374\) | 3.53864e9 | 3.49772 | ||||||||
\(375\) | 6.77861e8i | 0.663791i | ||||||||
\(376\) | 4.90255e9i | 4.75625i | ||||||||
\(377\) | 1.32489e8 | 0.127346 | ||||||||
\(378\) | 1.05437e9i | 1.00409i | ||||||||
\(379\) | −1.17562e9 | −1.10926 | −0.554628 | − | 0.832099i | \(-0.687139\pi\) | ||||
−0.554628 | + | 0.832099i | \(0.687139\pi\) | |||||||
\(380\) | −8.90275e8 | −0.832303 | ||||||||
\(381\) | −7.65849e7 | −0.0709424 | ||||||||
\(382\) | 2.70929e9 | 2.48676 | ||||||||
\(383\) | − | 1.66864e9i | − | 1.51764i | −0.651303 | − | 0.758818i | \(-0.725777\pi\) | ||
0.651303 | − | 0.758818i | \(-0.274223\pi\) | |||||||
\(384\) | − | 3.03539e9i | − | 2.73562i | ||||||
\(385\) | 2.33191e8i | 0.208257i | ||||||||
\(386\) | −3.86865e9 | −3.42377 | ||||||||
\(387\) | 1.08592e8i | 0.0952382i | ||||||||
\(388\) | − | 1.07503e9i | − | 0.934351i | ||||||
\(389\) | − | 2.49220e8i | − | 0.214664i | −0.994223 | − | 0.107332i | \(-0.965769\pi\) | ||
0.994223 | − | 0.107332i | \(-0.0342308\pi\) | |||||||
\(390\) | 2.20045e8i | 0.187839i | ||||||||
\(391\) | −2.07590e9 | −1.75625 | ||||||||
\(392\) | 2.91404e9i | 2.44340i | ||||||||
\(393\) | − | 1.12945e8i | − | 0.0938624i | ||||||
\(394\) | 2.81740e9i | 2.32066i | ||||||||
\(395\) | −4.70440e8 | −0.384074 | ||||||||
\(396\) | −3.49485e8 | −0.282810 | ||||||||
\(397\) | −5.57512e8 | −0.447185 | −0.223592 | − | 0.974683i | \(-0.571778\pi\) | ||||
−0.223592 | + | 0.974683i | \(0.571778\pi\) | |||||||
\(398\) | 1.45362e9 | 1.15574 | ||||||||
\(399\) | 4.97697e8i | 0.392247i | ||||||||
\(400\) | 3.93527e9 | 3.07443 | ||||||||
\(401\) | − | 3.66785e8i | − | 0.284057i | −0.989863 | − | 0.142029i | \(-0.954637\pi\) | ||
0.989863 | − | 0.142029i | \(-0.0453625\pi\) | |||||||
\(402\) | 9.11817e8i | 0.700029i | ||||||||
\(403\) | 7.52959e7 | 0.0573065 | ||||||||
\(404\) | −2.33535e9 | −1.76205 | ||||||||
\(405\) | − | 4.49643e8i | − | 0.336338i | ||||||
\(406\) | 6.05019e8 | 0.448671 | ||||||||
\(407\) | 1.46109e8 | − | 1.49857e9i | 0.107422 | − | 1.10178i | ||||
\(408\) | 7.00012e9 | 5.10264 | ||||||||
\(409\) | 6.12382e7i | 0.0442579i | 0.999755 | + | 0.0221289i | \(0.00704444\pi\) | ||||
−0.999755 | + | 0.0221289i | \(0.992956\pi\) | |||||||
\(410\) | 1.47308e9 | 1.05556 | ||||||||
\(411\) | −3.83695e8 | −0.272609 | ||||||||
\(412\) | − | 3.06042e9i | − | 2.15596i | ||||||
\(413\) | − | 1.14517e9i | − | 0.799915i | ||||||
\(414\) | 2.81029e8 | 0.194648 | ||||||||
\(415\) | 7.13524e8i | 0.490050i | ||||||||
\(416\) | 1.45306e9 | 0.989591 | ||||||||
\(417\) | 2.95173e8 | 0.199342 | ||||||||
\(418\) | −2.61364e9 | −1.75036 | ||||||||
\(419\) | 1.50934e9 | 1.00239 | 0.501196 | − | 0.865334i | \(-0.332894\pi\) | ||||
0.501196 | + | 0.865334i | \(0.332894\pi\) | |||||||
\(420\) | 7.33076e8i | 0.482810i | ||||||||
\(421\) | − | 5.95797e8i | − | 0.389144i | −0.980888 | − | 0.194572i | \(-0.937668\pi\) | ||
0.980888 | − | 0.194572i | \(-0.0623319\pi\) | |||||||
\(422\) | − | 5.05820e9i | − | 3.27644i | ||||||
\(423\) | 2.14859e8 | 0.138026 | ||||||||
\(424\) | − | 9.52576e9i | − | 6.06903i | ||||||
\(425\) | 2.23430e9i | 1.41182i | ||||||||
\(426\) | − | 2.58787e9i | − | 1.62184i | ||||||
\(427\) | 4.46413e8i | 0.277485i | ||||||||
\(428\) | −1.24096e9 | −0.765074 | ||||||||
\(429\) | 4.71280e8i | 0.288190i | ||||||||
\(430\) | 1.19619e9i | 0.725539i | ||||||||
\(431\) | 2.58548e9i | 1.55550i | 0.628574 | + | 0.777750i | \(0.283639\pi\) | ||||
−0.628574 | + | 0.777750i | \(0.716361\pi\) | |||||||
\(432\) | −6.24541e9 | −3.72707 | ||||||||
\(433\) | −2.04513e9 | −1.21063 | −0.605316 | − | 0.795985i | \(-0.706953\pi\) | ||||
−0.605316 | + | 0.795985i | \(0.706953\pi\) | |||||||
\(434\) | 3.43844e8 | 0.201905 | ||||||||
\(435\) | −2.85278e8 | −0.166171 | ||||||||
\(436\) | 5.97399e9i | 3.45193i | ||||||||
\(437\) | 1.53325e9 | 0.878880 | ||||||||
\(438\) | 4.32664e9i | 2.46032i | ||||||||
\(439\) | − | 1.41260e9i | − | 0.796879i | −0.917195 | − | 0.398440i | \(-0.869552\pi\) | ||
0.917195 | − | 0.398440i | \(-0.130448\pi\) | |||||||
\(440\) | −2.42249e9 | −1.35574 | ||||||||
\(441\) | 1.27711e8 | 0.0709074 | ||||||||
\(442\) | 1.56945e9i | 0.864508i | ||||||||
\(443\) | −2.39107e9 | −1.30671 | −0.653356 | − | 0.757050i | \(-0.726640\pi\) | ||||
−0.653356 | + | 0.757050i | \(0.726640\pi\) | |||||||
\(444\) | 4.59317e8 | − | 4.71101e9i | 0.249042 | − | 2.55431i | ||||
\(445\) | −7.82717e7 | −0.0421061 | ||||||||
\(446\) | − | 1.76884e9i | − | 0.944094i | ||||||
\(447\) | −2.79676e9 | −1.48108 | ||||||||
\(448\) | 3.22134e9 | 1.69264 | ||||||||
\(449\) | 3.25453e9i | 1.69678i | 0.529371 | + | 0.848390i | \(0.322428\pi\) | ||||
−0.529371 | + | 0.848390i | \(0.677572\pi\) | |||||||
\(450\) | − | 3.02474e8i | − | 0.156475i | ||||||
\(451\) | 3.15496e9 | 1.61948 | ||||||||
\(452\) | 1.03671e9i | 0.528049i | ||||||||
\(453\) | 1.23471e8 | 0.0624053 | ||||||||
\(454\) | −1.94804e9 | −0.977019 | ||||||||
\(455\) | −1.03424e8 | −0.0514734 | ||||||||
\(456\) | −5.17029e9 | −2.55351 | ||||||||
\(457\) | − | 1.33143e9i | − | 0.652546i | −0.945276 | − | 0.326273i | \(-0.894207\pi\) | ||
0.945276 | − | 0.326273i | \(-0.105793\pi\) | |||||||
\(458\) | − | 3.18597e9i | − | 1.54958i | ||||||
\(459\) | − | 3.54591e9i | − | 1.71153i | ||||||
\(460\) | 2.25839e9 | 1.08180 | ||||||||
\(461\) | 2.82943e9i | 1.34507i | 0.740063 | + | 0.672537i | \(0.234795\pi\) | ||||
−0.740063 | + | 0.672537i | \(0.765205\pi\) | |||||||
\(462\) | 2.15214e9i | 1.01537i | ||||||||
\(463\) | − | 1.56953e9i | − | 0.734914i | −0.930040 | − | 0.367457i | \(-0.880228\pi\) | ||
0.930040 | − | 0.367457i | \(-0.119772\pi\) | |||||||
\(464\) | 3.58374e9i | 1.66542i | ||||||||
\(465\) | −1.62129e8 | −0.0747784 | ||||||||
\(466\) | − | 3.64449e9i | − | 1.66835i | ||||||
\(467\) | 1.74773e9i | 0.794084i | 0.917800 | + | 0.397042i | \(0.129963\pi\) | ||||
−0.917800 | + | 0.397042i | \(0.870037\pi\) | |||||||
\(468\) | − | 1.55003e8i | − | 0.0699003i | ||||||
\(469\) | −4.28566e8 | −0.191828 | ||||||||
\(470\) | 2.36676e9 | 1.05150 | ||||||||
\(471\) | −1.40197e8 | −0.0618252 | ||||||||
\(472\) | 1.18965e10 | 5.20741 | ||||||||
\(473\) | 2.56193e9i | 1.11315i | ||||||||
\(474\) | −4.34172e9 | −1.87257 | ||||||||
\(475\) | − | 1.65025e9i | − | 0.706517i | ||||||
\(476\) | 5.22858e9i | 2.22208i | ||||||||
\(477\) | −4.17475e8 | −0.176123 | ||||||||
\(478\) | −1.03688e9 | −0.434240 | ||||||||
\(479\) | − | 3.15497e9i | − | 1.31166i | −0.754910 | − | 0.655829i | \(-0.772319\pi\) | ||
0.754910 | − | 0.655829i | \(-0.227681\pi\) | |||||||
\(480\) | −3.12876e9 | −1.29130 | ||||||||
\(481\) | 6.64642e8 | + | 6.48017e7i | 0.272320 | + | 0.0265509i | ||||
\(482\) | −5.37621e9 | −2.18681 | ||||||||
\(483\) | − | 1.26252e9i | − | 0.509829i | ||||||
\(484\) | −1.51698e9 | −0.608164 | ||||||||
\(485\) | −3.26577e8 | −0.129984 | ||||||||
\(486\) | 9.18541e8i | 0.362971i | ||||||||
\(487\) | 1.60592e9i | 0.630045i | 0.949084 | + | 0.315022i | \(0.102012\pi\) | ||||
−0.949084 | + | 0.315022i | \(0.897988\pi\) | |||||||
\(488\) | −4.63752e9 | −1.80641 | ||||||||
\(489\) | − | 3.38724e9i | − | 1.30998i | ||||||
\(490\) | 1.40678e9 | 0.540183 | ||||||||
\(491\) | 1.43396e9 | 0.546703 | 0.273352 | − | 0.961914i | \(-0.411868\pi\) | ||||
0.273352 | + | 0.961914i | \(0.411868\pi\) | |||||||
\(492\) | 9.91817e9 | 3.75451 | ||||||||
\(493\) | −2.03471e9 | −0.764784 | ||||||||
\(494\) | − | 1.15919e9i | − | 0.432625i | ||||||
\(495\) | 1.06168e8i | 0.0393436i | ||||||||
\(496\) | 2.03671e9i | 0.749452i | ||||||||
\(497\) | 1.21633e9 | 0.444432 | ||||||||
\(498\) | 6.58516e9i | 2.38926i | ||||||||
\(499\) | 3.31967e9i | 1.19603i | 0.801484 | + | 0.598016i | \(0.204044\pi\) | ||||
−0.801484 | + | 0.598016i | \(0.795956\pi\) | |||||||
\(500\) | − | 5.25979e9i | − | 1.88180i | ||||||
\(501\) | − | 2.26598e9i | − | 0.805053i | ||||||
\(502\) | 7.43423e9 | 2.62285 | ||||||||
\(503\) | 3.12094e8i | 0.109345i | 0.998504 | + | 0.0546723i | \(0.0174114\pi\) | ||||
−0.998504 | + | 0.0546723i | \(0.982589\pi\) | |||||||
\(504\) | − | 4.45413e8i | − | 0.154973i | ||||||
\(505\) | 7.09441e8i | 0.245130i | ||||||||
\(506\) | 6.63009e9 | 2.27506 | ||||||||
\(507\) | 2.58301e9 | 0.880236 | ||||||||
\(508\) | 5.94252e8 | 0.201116 | ||||||||
\(509\) | −9.19098e8 | −0.308922 | −0.154461 | − | 0.987999i | \(-0.549364\pi\) | ||||
−0.154461 | + | 0.987999i | \(0.549364\pi\) | |||||||
\(510\) | − | 3.37938e9i | − | 1.12808i | ||||||
\(511\) | −2.03358e9 | −0.674199 | ||||||||
\(512\) | 3.83677e9i | 1.26334i | ||||||||
\(513\) | 2.61901e9i | 0.856497i | ||||||||
\(514\) | −8.11515e9 | −2.63588 | ||||||||
\(515\) | −9.29706e8 | −0.299930 | ||||||||
\(516\) | 8.05386e9i | 2.58066i | ||||||||
\(517\) | 5.06898e9 | 1.61326 | ||||||||
\(518\) | 3.03514e9 | + | 2.95922e8i | 0.959454 | + | 0.0935455i | ||||
\(519\) | 4.32537e9 | 1.35812 | ||||||||
\(520\) | − | 1.07442e9i | − | 0.335090i | ||||||
\(521\) | 3.12185e9 | 0.967118 | 0.483559 | − | 0.875312i | \(-0.339344\pi\) | ||||
0.483559 | + | 0.875312i | \(0.339344\pi\) | |||||||
\(522\) | 2.75454e8 | 0.0847623 | ||||||||
\(523\) | 2.00814e9i | 0.613816i | 0.951739 | + | 0.306908i | \(0.0992944\pi\) | ||||
−0.951739 | + | 0.306908i | \(0.900706\pi\) | |||||||
\(524\) | 8.76381e8i | 0.266093i | ||||||||
\(525\) | −1.35886e9 | −0.409843 | ||||||||
\(526\) | 2.35768e9i | 0.706374i | ||||||||
\(527\) | −1.15637e9 | −0.344159 | ||||||||
\(528\) | −1.27479e10 | −3.76894 | ||||||||
\(529\) | −4.84629e8 | −0.142336 | ||||||||
\(530\) | −4.59866e9 | −1.34173 | ||||||||
\(531\) | − | 5.21375e8i | − | 0.151119i | ||||||
\(532\) | − | 3.86182e9i | − | 1.11199i | ||||||
\(533\) | 1.39928e9i | 0.400276i | ||||||||
\(534\) | −7.22375e8 | −0.205290 | ||||||||
\(535\) | 3.76982e8i | 0.106435i | ||||||||
\(536\) | − | 4.45213e9i | − | 1.24879i | ||||||
\(537\) | 5.31817e9i | 1.48201i | ||||||||
\(538\) | − | 4.25008e9i | − | 1.17668i | ||||||
\(539\) | 3.01296e9 | 0.828769 | ||||||||
\(540\) | 3.85763e9i | 1.05425i | ||||||||
\(541\) | − | 2.86739e9i | − | 0.778569i | −0.921118 | − | 0.389284i | \(-0.872722\pi\) | ||
0.921118 | − | 0.389284i | \(-0.127278\pi\) | |||||||
\(542\) | − | 9.88928e9i | − | 2.66788i | ||||||
\(543\) | 1.33892e9 | 0.358884 | ||||||||
\(544\) | −2.23155e10 | −5.94307 | ||||||||
\(545\) | 1.81480e9 | 0.480221 | ||||||||
\(546\) | −9.54510e8 | −0.250961 | ||||||||
\(547\) | − | 5.00927e8i | − | 0.130864i | −0.997857 | − | 0.0654318i | \(-0.979158\pi\) | ||
0.997857 | − | 0.0654318i | \(-0.0208425\pi\) | |||||||
\(548\) | 2.97724e9 | 0.772827 | ||||||||
\(549\) | 2.03244e8i | 0.0524220i | ||||||||
\(550\) | − | 7.13600e9i | − | 1.82888i | ||||||
\(551\) | 1.50284e9 | 0.382720 | ||||||||
\(552\) | 1.31156e10 | 3.31896 | ||||||||
\(553\) | − | 2.04067e9i | − | 0.513139i | ||||||
\(554\) | −7.94015e9 | −1.98401 | ||||||||
\(555\) | −1.43113e9 | − | 1.39533e8i | −0.355347 | − | 0.0346459i | ||||
\(556\) | −2.29036e9 | −0.565121 | ||||||||
\(557\) | − | 2.30833e9i | − | 0.565985i | −0.959122 | − | 0.282993i | \(-0.908673\pi\) | ||
0.959122 | − | 0.282993i | \(-0.0913272\pi\) | |||||||
\(558\) | 1.56546e8 | 0.0381437 | ||||||||
\(559\) | −1.13626e9 | −0.275129 | ||||||||
\(560\) | − | 2.79757e9i | − | 0.673167i | ||||||
\(561\) | − | 7.23776e9i | − | 1.73075i | ||||||
\(562\) | −1.24525e10 | −2.95923 | ||||||||
\(563\) | 4.87705e9i | 1.15180i | 0.817520 | + | 0.575900i | \(0.195348\pi\) | ||||
−0.817520 | + | 0.575900i | \(0.804652\pi\) | |||||||
\(564\) | 1.59352e10 | 3.74008 | ||||||||
\(565\) | 3.14936e8 | 0.0734604 | ||||||||
\(566\) | −2.77414e8 | −0.0643088 | ||||||||
\(567\) | 1.95046e9 | 0.449361 | ||||||||
\(568\) | 1.26358e10i | 2.89323i | ||||||||
\(569\) | 6.83355e9i | 1.55508i | 0.628831 | + | 0.777542i | \(0.283534\pi\) | ||||
−0.628831 | + | 0.777542i | \(0.716466\pi\) | |||||||
\(570\) | 2.49601e9i | 0.564526i | ||||||||
\(571\) | 1.74276e9 | 0.391753 | 0.195876 | − | 0.980629i | \(-0.437245\pi\) | ||||
0.195876 | + | 0.980629i | \(0.437245\pi\) | |||||||
\(572\) | − | 3.65685e9i | − | 0.816997i | ||||||
\(573\) | − | 5.54145e9i | − | 1.23050i | ||||||
\(574\) | 6.38992e9i | 1.41028i | ||||||||
\(575\) | 4.18624e9i | 0.918305i | ||||||||
\(576\) | 1.46662e9 | 0.319771 | ||||||||
\(577\) | 7.52277e9i | 1.63028i | 0.579263 | + | 0.815141i | \(0.303340\pi\) | ||||
−0.579263 | + | 0.815141i | \(0.696660\pi\) | |||||||
\(578\) | − | 1.51763e10i | − | 3.26903i | ||||||
\(579\) | 7.91276e9i | 1.69415i | ||||||||
\(580\) | 2.21359e9 | 0.471084 | ||||||||
\(581\) | −3.09511e9 | −0.654727 | ||||||||
\(582\) | −3.01400e9 | −0.633742 | ||||||||
\(583\) | −9.84913e9 | −2.05853 | ||||||||
\(584\) | − | 2.11257e10i | − | 4.38900i | ||||||
\(585\) | −4.70873e7 | −0.00972429 | ||||||||
\(586\) | − | 8.61706e9i | − | 1.76896i | ||||||
\(587\) | − | 2.16464e9i | − | 0.441726i | −0.975305 | − | 0.220863i | \(-0.929113\pi\) | ||
0.975305 | − | 0.220863i | \(-0.0708873\pi\) | |||||||
\(588\) | 9.47177e9 | 1.92137 | ||||||||
\(589\) | 8.54093e8 | 0.172227 | ||||||||
\(590\) | − | 5.74315e9i | − | 1.15125i | ||||||
\(591\) | 5.76258e9 | 1.14831 | ||||||||
\(592\) | −1.75285e9 | + | 1.79782e10i | −0.347231 | + | 3.56140i | ||||
\(593\) | −4.03004e9 | −0.793630 | −0.396815 | − | 0.917899i | \(-0.629885\pi\) | ||||
−0.396815 | + | 0.917899i | \(0.629885\pi\) | |||||||
\(594\) | 1.13251e10i | 2.21712i | ||||||||
\(595\) | 1.58836e9 | 0.309128 | ||||||||
\(596\) | 2.17012e10 | 4.19876 | ||||||||
\(597\) | − | 2.97316e9i | − | 0.571885i | ||||||
\(598\) | 2.94056e9i | 0.562310i | ||||||||
\(599\) | −3.02810e9 | −0.575674 | −0.287837 | − | 0.957679i | \(-0.592936\pi\) | ||||
−0.287837 | + | 0.957679i | \(0.592936\pi\) | |||||||
\(600\) | − | 1.41164e10i | − | 2.66806i | ||||||
\(601\) | 2.35007e9 | 0.441590 | 0.220795 | − | 0.975320i | \(-0.429135\pi\) | ||||
0.220795 | + | 0.975320i | \(0.429135\pi\) | |||||||
\(602\) | −5.18882e9 | −0.969350 | ||||||||
\(603\) | −1.95119e8 | −0.0362400 | ||||||||
\(604\) | −9.58059e8 | −0.176914 | ||||||||
\(605\) | 4.60833e8i | 0.0846058i | ||||||||
\(606\) | 6.54748e9i | 1.19514i | ||||||||
\(607\) | 3.02142e9i | 0.548341i | 0.961681 | + | 0.274171i | \(0.0884033\pi\) | ||||
−0.961681 | + | 0.274171i | \(0.911597\pi\) | |||||||
\(608\) | 1.64822e10 | 2.97409 | ||||||||
\(609\) | − | 1.23748e9i | − | 0.222012i | ||||||
\(610\) | 2.23881e9i | 0.399359i | ||||||||
\(611\) | 2.24818e9i | 0.398737i | ||||||||
\(612\) | 2.38048e9i | 0.419792i | ||||||||
\(613\) | 3.24180e9 | 0.568428 | 0.284214 | − | 0.958761i | \(-0.408267\pi\) | ||||
0.284214 | + | 0.958761i | \(0.408267\pi\) | |||||||
\(614\) | − | 5.42731e9i | − | 0.946228i | ||||||
\(615\) | − | 3.01298e9i | − | 0.522315i | ||||||
\(616\) | − | 1.05082e10i | − | 1.81133i | ||||||
\(617\) | −1.02520e10 | −1.75716 | −0.878582 | − | 0.477592i | \(-0.841510\pi\) | ||||
−0.878582 | + | 0.477592i | \(0.841510\pi\) | |||||||
\(618\) | −8.58032e9 | −1.46232 | ||||||||
\(619\) | −5.38103e9 | −0.911901 | −0.455951 | − | 0.890005i | \(-0.650701\pi\) | ||||
−0.455951 | + | 0.890005i | \(0.650701\pi\) | |||||||
\(620\) | 1.25802e9 | 0.211991 | ||||||||
\(621\) | − | 6.64371e9i | − | 1.11324i | ||||||
\(622\) | 1.03443e10 | 1.72360 | ||||||||
\(623\) | − | 3.39526e8i | − | 0.0562555i | ||||||
\(624\) | − | 5.65391e9i | − | 0.931542i | ||||||
\(625\) | 3.64625e9 | 0.597402 | ||||||||
\(626\) | −9.04511e9 | −1.47368 | ||||||||
\(627\) | 5.34580e9i | 0.866117i | ||||||||
\(628\) | 1.08784e9 | 0.175270 | ||||||||
\(629\) | −1.02073e10 | − | 9.95202e8i | −1.63544 | − | 0.159453i | ||||
\(630\) | −2.15028e8 | −0.0342612 | ||||||||
\(631\) | − | 8.47871e9i | − | 1.34347i | −0.740793 | − | 0.671733i | \(-0.765550\pi\) | ||
0.740793 | − | 0.671733i | \(-0.234450\pi\) | |||||||
\(632\) | 2.11993e10 | 3.34051 | ||||||||
\(633\) | −1.03458e10 | −1.62126 | ||||||||
\(634\) | 1.74732e10i | 2.72307i | ||||||||
\(635\) | − | 1.80524e8i | − | 0.0279787i | ||||||
\(636\) | −3.09624e10 | −4.77238 | ||||||||
\(637\) | 1.33630e9i | 0.204841i | ||||||||
\(638\) | 6.49856e9 | 0.990706 | ||||||||
\(639\) | 5.53775e8 | 0.0839616 | ||||||||
\(640\) | 7.15495e9 | 1.07889 | ||||||||
\(641\) | 4.21164e9 | 0.631609 | 0.315804 | − | 0.948824i | \(-0.397726\pi\) | ||||
0.315804 | + | 0.948824i | \(0.397726\pi\) | |||||||
\(642\) | 3.47919e9i | 0.518927i | ||||||||
\(643\) | − | 9.74205e8i | − | 0.144515i | −0.997386 | − | 0.0722573i | \(-0.976980\pi\) | ||
0.997386 | − | 0.0722573i | \(-0.0230203\pi\) | |||||||
\(644\) | 9.79640e9i | 1.44533i | ||||||||
\(645\) | 2.44663e9 | 0.359012 | ||||||||
\(646\) | 1.78025e10i | 2.59816i | ||||||||
\(647\) | 2.45205e9i | 0.355930i | 0.984037 | + | 0.177965i | \(0.0569514\pi\) | ||||
−0.984037 | + | 0.177965i | \(0.943049\pi\) | |||||||
\(648\) | 2.02622e10i | 2.92532i | ||||||||
\(649\) | − | 1.23003e10i | − | 1.76628i | ||||||
\(650\) | 3.16494e9 | 0.452032 | ||||||||
\(651\) | − | 7.03283e8i | − | 0.0999071i | ||||||
\(652\) | 2.62829e10i | 3.71370i | ||||||||
\(653\) | − | 1.17683e10i | − | 1.65393i | −0.562256 | − | 0.826963i | \(-0.690066\pi\) | ||
0.562256 | − | 0.826963i | \(-0.309934\pi\) | |||||||
\(654\) | 1.67489e10 | 2.34134 | ||||||||
\(655\) | 2.66230e8 | 0.0370180 | ||||||||
\(656\) | −3.78498e10 | −5.23480 | ||||||||
\(657\) | −9.25853e8 | −0.127369 | ||||||||
\(658\) | 1.02665e10i | 1.40485i | ||||||||
\(659\) | −3.61797e8 | −0.0492454 | −0.0246227 | − | 0.999697i | \(-0.507838\pi\) | ||||
−0.0246227 | + | 0.999697i | \(0.507838\pi\) | |||||||
\(660\) | 7.87403e9i | 1.06609i | ||||||||
\(661\) | − | 3.26094e9i | − | 0.439175i | −0.975593 | − | 0.219588i | \(-0.929529\pi\) | ||
0.975593 | − | 0.219588i | \(-0.0704712\pi\) | |||||||
\(662\) | 4.85988e9 | 0.651062 | ||||||||
\(663\) | 3.21007e9 | 0.427777 | ||||||||
\(664\) | − | 3.21534e10i | − | 4.26224i | ||||||
\(665\) | −1.17316e9 | −0.154697 | ||||||||
\(666\) | 1.38184e9 | + | 1.34728e8i | 0.181259 | + | 0.0176725i | ||||
\(667\) | −3.81230e9 | −0.497446 | ||||||||
\(668\) | 1.75826e10i | 2.28227i | ||||||||
\(669\) | −3.61789e9 | −0.467158 | ||||||||
\(670\) | −2.14931e9 | −0.276082 | ||||||||
\(671\) | 4.79496e9i | 0.612711i | ||||||||
\(672\) | − | 1.35719e10i | − | 1.72524i | ||||||
\(673\) | 1.13675e10 | 1.43751 | 0.718756 | − | 0.695263i | \(-0.244712\pi\) | ||||
0.718756 | + | 0.695263i | \(0.244712\pi\) | |||||||
\(674\) | − | 8.80617e9i | − | 1.10784i | ||||||
\(675\) | −7.15067e9 | −0.894918 | ||||||||
\(676\) | −2.00426e10 | −2.49540 | ||||||||
\(677\) | 1.33905e10 | 1.65858 | 0.829291 | − | 0.558817i | \(-0.188745\pi\) | ||||
0.829291 | + | 0.558817i | \(0.188745\pi\) | |||||||
\(678\) | 2.90657e9 | 0.358160 | ||||||||
\(679\) | − | 1.41662e9i | − | 0.173664i | ||||||
\(680\) | 1.65005e10i | 2.01241i | ||||||||
\(681\) | 3.98443e9i | 0.483450i | ||||||||
\(682\) | 3.69326e9 | 0.445825 | ||||||||
\(683\) | 6.45078e9i | 0.774712i | 0.921930 | + | 0.387356i | \(0.126611\pi\) | ||||
−0.921930 | + | 0.387356i | \(0.873389\pi\) | |||||||
\(684\) | − | 1.75822e9i | − | 0.210076i | ||||||
\(685\) | − | 9.04437e8i | − | 0.107513i | ||||||
\(686\) | 1.42534e10i | 1.68571i | ||||||||
\(687\) | −6.51644e9 | −0.766764 | ||||||||
\(688\) | − | 3.07352e10i | − | 3.59813i | ||||||
\(689\) | − | 4.36826e9i | − | 0.508793i | ||||||
\(690\) | − | 6.33170e9i | − | 0.733751i | ||||||
\(691\) | 7.44952e9 | 0.858924 | 0.429462 | − | 0.903085i | \(-0.358703\pi\) | ||||
0.429462 | + | 0.903085i | \(0.358703\pi\) | |||||||
\(692\) | −3.35622e10 | −3.85016 | ||||||||
\(693\) | −4.60533e8 | −0.0525648 | ||||||||
\(694\) | −1.90302e9 | −0.216115 | ||||||||
\(695\) | 6.95773e8i | 0.0786178i | ||||||||
\(696\) | 1.28554e10 | 1.44529 | ||||||||
\(697\) | − | 2.14897e10i | − | 2.40389i | ||||||
\(698\) | 2.95762e9i | 0.329191i | ||||||||
\(699\) | −7.45427e9 | −0.825534 | ||||||||
\(700\) | 1.05439e10 | 1.16187 | ||||||||
\(701\) | 5.42774e9i | 0.595121i | 0.954703 | + | 0.297561i | \(0.0961731\pi\) | ||||
−0.954703 | + | 0.297561i | \(0.903827\pi\) | |||||||
\(702\) | −5.02287e9 | −0.547990 | ||||||||
\(703\) | 7.53914e9 | + | 7.35056e8i | 0.818423 | + | 0.0797952i | ||||
\(704\) | 3.46007e10 | 3.73750 | ||||||||
\(705\) | − | 4.84085e9i | − | 0.520307i | ||||||
\(706\) | 2.41874e10 | 2.58686 | ||||||||
\(707\) | −3.07740e9 | −0.327504 | ||||||||
\(708\) | − | 3.86682e10i | − | 4.09485i | ||||||
\(709\) | − | 1.51095e9i | − | 0.159216i | −0.996826 | − | 0.0796082i | \(-0.974633\pi\) | ||
0.996826 | − | 0.0796082i | \(-0.0253669\pi\) | |||||||
\(710\) | 6.10006e9 | 0.639632 | ||||||||
\(711\) | − | 9.29081e8i | − | 0.0969415i | ||||||
\(712\) | 3.52714e9 | 0.366220 | ||||||||
\(713\) | −2.16660e9 | −0.223855 | ||||||||
\(714\) | 1.46590e10 | 1.50717 | ||||||||
\(715\) | −1.11089e9 | −0.113658 | ||||||||
\(716\) | − | 4.12657e10i | − | 4.20140i | ||||||
\(717\) | 2.12078e9i | 0.214871i | ||||||||
\(718\) | 1.70010e10i | 1.71411i | ||||||||
\(719\) | 1.00886e10 | 1.01223 | 0.506114 | − | 0.862467i | \(-0.331082\pi\) | ||||
0.506114 | + | 0.862467i | \(0.331082\pi\) | |||||||
\(720\) | − | 1.27368e9i | − | 0.127174i | ||||||
\(721\) | − | 4.03287e9i | − | 0.400719i | ||||||
\(722\) | 6.29684e9i | 0.622648i | ||||||||
\(723\) | 1.09962e10i | 1.08208i | ||||||||
\(724\) | −1.03892e10 | −1.01741 | ||||||||
\(725\) | 4.10320e9i | 0.399889i | ||||||||
\(726\) | 4.25306e9i | 0.412500i | ||||||||
\(727\) | 1.71908e10i | 1.65930i | 0.558285 | + | 0.829649i | \(0.311460\pi\) | ||||
−0.558285 | + | 0.829649i | \(0.688540\pi\) | |||||||
\(728\) | 4.66059e9 | 0.447694 | ||||||||
\(729\) | 1.12545e10 | 1.07592 | ||||||||
\(730\) | −1.01986e10 | −0.970314 | ||||||||
\(731\) | 1.74503e10 | 1.65231 | ||||||||
\(732\) | 1.50738e10i | 1.42047i | ||||||||
\(733\) | −8.12481e9 | −0.761990 | −0.380995 | − | 0.924577i | \(-0.624419\pi\) | ||||
−0.380995 | + | 0.924577i | \(0.624419\pi\) | |||||||
\(734\) | 1.78997e10i | 1.67074i | ||||||||
\(735\) | − | 2.87737e9i | − | 0.267294i | ||||||
\(736\) | −4.18110e10 | −3.86561 | ||||||||
\(737\) | −4.60327e9 | −0.423574 | ||||||||
\(738\) | 2.90922e9i | 0.266428i | ||||||||
\(739\) | 5.94655e9 | 0.542013 | 0.271006 | − | 0.962578i | \(-0.412644\pi\) | ||||
0.271006 | + | 0.962578i | \(0.412644\pi\) | |||||||
\(740\) | 1.11047e10 | + | 1.08269e9i | 1.00738 | + | 0.0982185i | ||||
\(741\) | −2.37096e9 | −0.214072 | ||||||||
\(742\) | − | 1.99480e10i | − | 1.79261i | ||||||
\(743\) | −1.45771e10 | −1.30380 | −0.651899 | − | 0.758306i | \(-0.726027\pi\) | ||||
−0.651899 | + | 0.758306i | \(0.726027\pi\) | |||||||
\(744\) | 7.30600e9 | 0.650391 | ||||||||
\(745\) | − | 6.59246e9i | − | 0.584118i | ||||||
\(746\) | − | 1.06743e10i | − | 0.941352i | ||||||
\(747\) | −1.40915e9 | −0.123690 | ||||||||
\(748\) | 5.61606e10i | 4.90655i | ||||||||
\(749\) | −1.63527e9 | −0.142201 | ||||||||
\(750\) | −1.47465e10 | −1.27637 | ||||||||
\(751\) | 4.58555e9 | 0.395050 | 0.197525 | − | 0.980298i | \(-0.436710\pi\) | ||||
0.197525 | + | 0.980298i | \(0.436710\pi\) | |||||||
\(752\) | −6.08120e10 | −5.21467 | ||||||||
\(753\) | − | 1.52056e10i | − | 1.29784i | ||||||
\(754\) | 2.88223e9i | 0.244866i | ||||||||
\(755\) | 2.91043e8i | 0.0246117i | ||||||||
\(756\) | −1.67336e10 | −1.40852 | ||||||||
\(757\) | 2.34942e9i | 0.196845i | 0.995145 | + | 0.0984227i | \(0.0313797\pi\) | ||||
−0.995145 | + | 0.0984227i | \(0.968620\pi\) | |||||||
\(758\) | − | 2.55751e10i | − | 2.13293i | ||||||
\(759\) | − | 1.35609e10i | − | 1.12575i | ||||||
\(760\) | − | 1.21873e10i | − | 1.00707i | ||||||
\(761\) | 7.10749e9 | 0.584615 | 0.292307 | − | 0.956324i | \(-0.405577\pi\) | ||||
0.292307 | + | 0.956324i | \(0.405577\pi\) | |||||||
\(762\) | − | 1.66607e9i | − | 0.136411i | ||||||
\(763\) | 7.87221e9i | 0.641595i | ||||||||
\(764\) | 4.29982e10i | 3.48838i | ||||||||
\(765\) | 7.23150e8 | 0.0584001 | ||||||||
\(766\) | 3.63005e10 | 2.91818 | ||||||||
\(767\) | 5.45542e9 | 0.436560 | ||||||||
\(768\) | 2.57073e10 | 2.04782 | ||||||||
\(769\) | 3.75931e9i | 0.298103i | 0.988829 | + | 0.149051i | \(0.0476220\pi\) | ||||
−0.988829 | + | 0.149051i | \(0.952378\pi\) | |||||||
\(770\) | −5.07296e9 | −0.400446 | ||||||||
\(771\) | 1.65983e10i | 1.30429i | ||||||||
\(772\) | − | 6.13981e10i | − | 4.80280i | ||||||
\(773\) | −4.84455e9 | −0.377247 | −0.188623 | − | 0.982049i | \(-0.560403\pi\) | ||||
−0.188623 | + | 0.982049i | \(0.560403\pi\) | |||||||
\(774\) | −2.36238e9 | −0.183128 | ||||||||
\(775\) | 2.33193e9i | 0.179953i | ||||||||
\(776\) | 1.47164e10 | 1.13054 | ||||||||
\(777\) | 6.05264e8 | − | 6.20793e9i | 0.0462883 | − | 0.474759i | ||||
\(778\) | 5.42166e9 | 0.412766 | ||||||||
\(779\) | 1.58723e10i | 1.20298i | ||||||||
\(780\) | −3.49227e9 | −0.263498 | ||||||||
\(781\) | 1.30647e10 | 0.981347 | ||||||||
\(782\) | − | 4.51601e10i | − | 3.37700i | ||||||
\(783\) | − | 6.51192e9i | − | 0.484778i | ||||||
\(784\) | −3.61463e10 | −2.67890 | ||||||||
\(785\) | − | 3.30469e8i | − | 0.0243830i | ||||||
\(786\) | 2.45706e9 | 0.180483 | ||||||||
\(787\) | 2.27702e10 | 1.66516 | 0.832579 | − | 0.553906i | \(-0.186863\pi\) | ||||
0.832579 | + | 0.553906i | \(0.186863\pi\) | |||||||
\(788\) | −4.47141e10 | −3.25539 | ||||||||
\(789\) | 4.82228e9 | 0.349529 | ||||||||
\(790\) | − | 1.02342e10i | − | 0.738515i | ||||||
\(791\) | 1.36613e9i | 0.0981462i | ||||||||
\(792\) | − | 4.78421e9i | − | 0.342194i | ||||||
\(793\) | −2.12665e9 | −0.151440 | ||||||||
\(794\) | − | 1.21284e10i | − | 0.859867i | ||||||
\(795\) | 9.40588e9i | 0.663918i | ||||||||
\(796\) | 2.30699e10i | 1.62125i | ||||||||
\(797\) | 2.27331e10i | 1.59058i | 0.606230 | + | 0.795290i | \(0.292681\pi\) | ||||
−0.606230 | + | 0.795290i | \(0.707319\pi\) | |||||||
\(798\) | −1.08272e10 | −0.754231 | ||||||||
\(799\) | − | 3.45268e10i | − | 2.39465i | ||||||
\(800\) | 4.50014e10i | 3.10750i | ||||||||
\(801\) | − | 1.54580e8i | − | 0.0106277i | ||||||
\(802\) | 7.97922e9 | 0.546198 | ||||||||
\(803\) | −2.18428e10 | −1.48869 | ||||||||
\(804\) | −1.44711e10 | −0.981989 | ||||||||
\(805\) | 2.97599e9 | 0.201069 | ||||||||
\(806\) | 1.63803e9i | 0.110191i | ||||||||
\(807\) | −8.69291e9 | −0.582248 | ||||||||
\(808\) | − | 3.19694e10i | − | 2.13204i | ||||||
\(809\) | 1.13452e10i | 0.753345i | 0.926347 | + | 0.376672i | \(0.122932\pi\) | ||||
−0.926347 | + | 0.376672i | \(0.877068\pi\) | |||||||
\(810\) | 9.78177e9 | 0.646726 | ||||||||
\(811\) | 1.40064e10 | 0.922045 | 0.461023 | − | 0.887388i | \(-0.347483\pi\) | ||||
0.461023 | + | 0.887388i | \(0.347483\pi\) | |||||||
\(812\) | 9.60206e9i | 0.629388i | ||||||||
\(813\) | −2.02271e10 | −1.32013 | ||||||||
\(814\) | 3.26007e10 | + | 3.17852e9i | 2.11856 | + | 0.206557i | ||||
\(815\) | 7.98431e9 | 0.516637 | ||||||||
\(816\) | 8.68307e10i | 5.59445i | ||||||||
\(817\) | −1.28888e10 | −0.826864 | ||||||||
\(818\) | −1.33221e9 | −0.0851011 | ||||||||
\(819\) | − | 2.04255e8i | − | 0.0129921i | ||||||
\(820\) | 2.33788e10i | 1.48073i | ||||||||
\(821\) | 1.18355e10 | 0.746421 | 0.373211 | − | 0.927747i | \(-0.378257\pi\) | ||||
0.373211 | + | 0.927747i | \(0.378257\pi\) | |||||||
\(822\) | − | 8.34711e9i | − | 0.524185i | ||||||
\(823\) | 6.47971e9 | 0.405188 | 0.202594 | − | 0.979263i | \(-0.435063\pi\) | ||||
0.202594 | + | 0.979263i | \(0.435063\pi\) | |||||||
\(824\) | 4.18951e10 | 2.60866 | ||||||||
\(825\) | −1.45956e10 | −0.904970 | ||||||||
\(826\) | 2.49126e10 | 1.53811 | ||||||||
\(827\) | − | 1.43752e10i | − | 0.883782i | −0.897069 | − | 0.441891i | \(-0.854308\pi\) | ||
0.897069 | − | 0.441891i | \(-0.145692\pi\) | |||||||
\(828\) | 4.46013e9i | 0.273049i | ||||||||
\(829\) | 2.63001e10i | 1.60331i | 0.597789 | + | 0.801654i | \(0.296046\pi\) | ||||
−0.597789 | + | 0.801654i | \(0.703954\pi\) | |||||||
\(830\) | −1.55224e10 | −0.942290 | ||||||||
\(831\) | 1.62404e10i | 0.981732i | ||||||||
\(832\) | 1.53460e10i | 0.923771i | ||||||||
\(833\) | − | 2.05225e10i | − | 1.23019i | ||||||
\(834\) | 6.42134e9i | 0.383305i | ||||||||
\(835\) | 5.34131e9 | 0.317501 | ||||||||
\(836\) | − | 4.14802e10i | − | 2.45538i | ||||||
\(837\) | − | 3.70085e9i | − | 0.218154i | ||||||
\(838\) | 3.28349e10i | 1.92744i | ||||||||
\(839\) | −1.52010e10 | −0.888601 | −0.444300 | − | 0.895878i | \(-0.646548\pi\) | ||||
−0.444300 | + | 0.895878i | \(0.646548\pi\) | |||||||
\(840\) | −1.00353e10 | −0.584189 | ||||||||
\(841\) | 1.35132e10 | 0.783380 | ||||||||
\(842\) | 1.29613e10 | 0.748265 | ||||||||
\(843\) | 2.54697e10i | 1.46429i | ||||||||
\(844\) | 8.02771e10 | 4.59614 | ||||||||
\(845\) | 6.08862e9i | 0.347152i | ||||||||
\(846\) | 4.67415e9i | 0.265403i | ||||||||
\(847\) | −1.99900e9 | −0.113037 | ||||||||
\(848\) | 1.18159e11 | 6.65398 | ||||||||
\(849\) | 5.67409e8i | 0.0318214i | ||||||||
\(850\) | −4.86061e10 | −2.71472 | ||||||||
\(851\) | −1.91248e10 | − | 1.86464e9i | −1.06376 | − | 0.103715i | ||||
\(852\) | 4.10713e10 | 2.27509 | ||||||||
\(853\) | − | 8.22207e9i | − | 0.453586i | −0.973943 | − | 0.226793i | \(-0.927176\pi\) | ||
0.973943 | − | 0.226793i | \(-0.0728241\pi\) | |||||||
\(854\) | −9.71149e9 | −0.533560 | ||||||||
\(855\) | −5.34118e8 | −0.0292251 | ||||||||
\(856\) | − | 1.69879e10i | − | 0.925722i | ||||||
\(857\) | 1.78926e8i | 0.00971048i | 0.999988 | + | 0.00485524i | \(0.00154548\pi\) | ||||
−0.999988 | + | 0.00485524i | \(0.998455\pi\) | |||||||
\(858\) | −1.02525e10 | −0.554145 | ||||||||
\(859\) | − | 2.16162e10i | − | 1.16360i | −0.813333 | − | 0.581799i | \(-0.802349\pi\) | ||
0.813333 | − | 0.581799i | \(-0.197651\pi\) | |||||||
\(860\) | −1.89843e10 | −1.01777 | ||||||||
\(861\) | 1.30696e10 | 0.697835 | ||||||||
\(862\) | −5.62458e10 | −2.99099 | ||||||||
\(863\) | −2.23399e10 | −1.18316 | −0.591580 | − | 0.806246i | \(-0.701496\pi\) | ||||
−0.591580 | + | 0.806246i | \(0.701496\pi\) | |||||||
\(864\) | − | 7.14188e10i | − | 3.76716i | ||||||
\(865\) | 1.01956e10i | 0.535622i | ||||||||
\(866\) | − | 4.44907e10i | − | 2.32786i | ||||||
\(867\) | −3.10409e10 | −1.61759 | ||||||||
\(868\) | 5.45704e9i | 0.283229i | ||||||||
\(869\) | − | 2.19190e10i | − | 1.13306i | ||||||
\(870\) | − | 6.20609e9i | − | 0.319522i | ||||||
\(871\) | − | 2.04163e9i | − | 0.104692i | ||||||
\(872\) | −8.17799e10 | −4.17675 | ||||||||
\(873\) | − | 6.44962e8i | − | 0.0328083i | ||||||
\(874\) | 3.33552e10i | 1.68995i | ||||||||
\(875\) | − | 6.93108e9i | − | 0.349762i | ||||||
\(876\) | −6.86667e10 | −3.45129 | ||||||||
\(877\) | 2.04101e9 | 0.102175 | 0.0510876 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510876 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(878\) | 3.07304e10 | 1.53228 | ||||||||
\(879\) | −1.76249e10 | −0.875318 | ||||||||
\(880\) | − | 3.00490e10i | − | 1.48641i | ||||||
\(881\) | −2.83294e10 | −1.39580 | −0.697898 | − | 0.716197i | \(-0.745881\pi\) | ||||
−0.697898 | + | 0.716197i | \(0.745881\pi\) | |||||||
\(882\) | 2.77828e9i | 0.136344i | ||||||||
\(883\) | 1.99398e9i | 0.0974672i | 0.998812 | + | 0.0487336i | \(0.0155185\pi\) | ||||
−0.998812 | + | 0.0487336i | \(0.984481\pi\) | |||||||
\(884\) | −2.49082e10 | −1.21272 | ||||||||
\(885\) | −1.17468e10 | −0.569662 | ||||||||
\(886\) | − | 5.20167e10i | − | 2.51261i | ||||||
\(887\) | 3.53659e10 | 1.70158 | 0.850789 | − | 0.525508i | \(-0.176125\pi\) | ||||
0.850789 | + | 0.525508i | \(0.176125\pi\) | |||||||
\(888\) | 6.44906e10 | + | 6.28774e9i | 3.09066 | + | 0.301335i | ||||
\(889\) | 7.83074e8 | 0.0373807 | ||||||||
\(890\) | − | 1.70276e9i | − | 0.0809635i | ||||||
\(891\) | 2.09500e10 | 0.992230 | ||||||||
\(892\) | 2.80726e10 | 1.32436 | ||||||||
\(893\) | 2.55015e10i | 1.19835i | ||||||||
\(894\) | − | 6.08423e10i | − | 2.84790i | ||||||
\(895\) | −1.25359e10 | −0.584485 | ||||||||
\(896\) | 3.10366e10i | 1.44144i | ||||||||
\(897\) | 6.01448e9 | 0.278243 | ||||||||
\(898\) | −7.08007e10 | −3.26265 | ||||||||
\(899\) | −2.12362e9 | −0.0974806 | ||||||||
\(900\) | 4.80046e9 | 0.219500 | ||||||||
\(901\) | 6.70863e10i | 3.05560i | ||||||||
\(902\) | 6.86347e10i | 3.11402i | ||||||||
\(903\) | 1.06130e10i | 0.479655i | ||||||||
\(904\) | −1.41919e10 | −0.638927 | ||||||||
\(905\) | 3.15606e9i | 0.141539i | ||||||||
\(906\) | 2.68605e9i | 0.119996i | ||||||||
\(907\) | − | 2.43851e10i | − | 1.08517i | −0.840000 | − | 0.542586i | \(-0.817445\pi\) | ||
0.840000 | − | 0.542586i | \(-0.182555\pi\) | |||||||
\(908\) | − | 3.09168e10i | − | 1.37055i | ||||||
\(909\) | −1.40109e9 | −0.0618716 | ||||||||
\(910\) | − | 2.24995e9i | − | 0.0989754i | ||||||
\(911\) | − | 1.61283e10i | − | 0.706766i | −0.935479 | − | 0.353383i | \(-0.885031\pi\) | ||
0.935479 | − | 0.353383i | \(-0.114969\pi\) | |||||||
\(912\) | − | 6.41331e10i | − | 2.79963i | ||||||
\(913\) | −3.32449e10 | −1.44570 | ||||||||
\(914\) | 2.89646e10 | 1.25474 | ||||||||
\(915\) | 4.57916e9 | 0.197611 | ||||||||
\(916\) | 5.05636e10 | 2.17372 | ||||||||
\(917\) | 1.15485e9i | 0.0494576i | ||||||||
\(918\) | 7.71395e10 | 3.29100 | ||||||||
\(919\) | − | 5.84343e9i | − | 0.248350i | −0.992260 | − | 0.124175i | \(-0.960372\pi\) | ||
0.992260 | − | 0.124175i | \(-0.0396284\pi\) | |||||||
\(920\) | 3.09158e10i | 1.30895i | ||||||||
\(921\) | −1.11008e10 | −0.468214 | ||||||||
\(922\) | −6.15530e10 | −2.58637 | ||||||||
\(923\) | 5.79445e9i | 0.242553i | ||||||||
\(924\) | −3.41559e10 | −1.42434 | ||||||||
\(925\) | −2.00692e9 | + | 2.05841e10i | −0.0833747 | + | 0.855137i | ||||
\(926\) | 3.41444e10 | 1.41313 | ||||||||
\(927\) | − | 1.83609e9i | − | 0.0757034i | ||||||
\(928\) | −4.09815e10 | −1.68333 | ||||||||
\(929\) | 1.63783e10 | 0.670213 | 0.335106 | − | 0.942180i | \(-0.391228\pi\) | ||||
0.335106 | + | 0.942180i | \(0.391228\pi\) | |||||||
\(930\) | − | 3.52705e9i | − | 0.143787i | ||||||
\(931\) | 1.51579e10i | 0.615623i | ||||||||
\(932\) | 5.78406e10 | 2.34033 | ||||||||
\(933\) | − | 2.11578e10i | − | 0.852875i | ||||||
\(934\) | −3.80211e10 | −1.52690 | ||||||||
\(935\) | 1.70607e10 | 0.682582 | ||||||||
\(936\) | 2.12188e9 | 0.0845777 | ||||||||
\(937\) | 8.69763e9 | 0.345392 | 0.172696 | − | 0.984975i | \(-0.444752\pi\) | ||||
0.172696 | + | 0.984975i | \(0.444752\pi\) | |||||||
\(938\) | − | 9.32325e9i | − | 0.368856i | ||||||
\(939\) | 1.85004e10i | 0.729209i | ||||||||
\(940\) | 3.75620e10i | 1.47503i | ||||||||
\(941\) | −3.36939e9 | −0.131822 | −0.0659110 | − | 0.997826i | \(-0.520995\pi\) | ||||
−0.0659110 | + | 0.997826i | \(0.520995\pi\) | |||||||
\(942\) | − | 3.04992e9i | − | 0.118880i | ||||||
\(943\) | − | 4.02637e10i | − | 1.56359i | ||||||
\(944\) | 1.47566e11i | 5.70932i | ||||||||
\(945\) | 5.08339e9i | 0.195948i | ||||||||
\(946\) | −5.57335e10 | −2.14041 | ||||||||
\(947\) | 2.64380e10i | 1.01159i | 0.862655 | + | 0.505794i | \(0.168800\pi\) | ||||
−0.862655 | + | 0.505794i | \(0.831200\pi\) | |||||||
\(948\) | − | 6.89061e10i | − | 2.62681i | ||||||
\(949\) | − | 9.68769e9i | − | 0.367950i | ||||||
\(950\) | 3.59004e10 | 1.35852 | ||||||||
\(951\) | 3.57388e10 | 1.34744 | ||||||||
\(952\) | −7.15757e10 | −2.68866 | ||||||||
\(953\) | 2.70801e10 | 1.01350 | 0.506752 | − | 0.862092i | \(-0.330846\pi\) | ||||
0.506752 | + | 0.862092i | \(0.330846\pi\) | |||||||
\(954\) | − | 9.08197e9i | − | 0.338657i | ||||||
\(955\) | 1.30622e10 | 0.485292 | ||||||||
\(956\) | − | 1.64559e10i | − | 0.609144i | ||||||
\(957\) | − | 1.32918e10i | − | 0.490223i | ||||||
\(958\) | 6.86348e10 | 2.52211 | ||||||||
\(959\) | 3.92325e9 | 0.143642 | ||||||||
\(960\) | − | 3.30435e10i | − | 1.20542i | ||||||
\(961\) | 2.63057e10 | 0.956133 | ||||||||
\(962\) | −1.40973e9 | + | 1.44590e10i | −0.0510532 | + | 0.523630i | ||||
\(963\) | −7.44508e8 | −0.0268644 | ||||||||
\(964\) | − | 8.53241e10i | − | 3.06762i | ||||||
\(965\) | −1.86517e10 | −0.668150 | ||||||||
\(966\) | 2.74656e10 | 0.980322 | ||||||||
\(967\) | − | 4.09717e10i | − | 1.45711i | −0.684990 | − | 0.728553i | \(-0.740193\pi\) | ||
0.684990 | − | 0.728553i | \(-0.259807\pi\) | |||||||
\(968\) | − | 2.07664e10i | − | 0.735865i | ||||||
\(969\) | 3.64123e10 | 1.28563 | ||||||||
\(970\) | − | 7.10452e9i | − | 0.249939i | ||||||
\(971\) | −2.06611e10 | −0.724247 | −0.362123 | − | 0.932130i | \(-0.617948\pi\) | ||||
−0.362123 | + | 0.932130i | \(0.617948\pi\) | |||||||
\(972\) | −1.45779e10 | −0.509169 | ||||||||
\(973\) | −3.01811e9 | −0.105037 | ||||||||
\(974\) | −3.49359e10 | −1.21148 | ||||||||
\(975\) | − | 6.47342e9i | − | 0.223675i | ||||||
\(976\) | − | 5.75246e10i | − | 1.98052i | ||||||
\(977\) | 2.77000e10i | 0.950272i | 0.879912 | + | 0.475136i | \(0.157601\pi\) | ||||
−0.879912 | + | 0.475136i | \(0.842399\pi\) | |||||||
\(978\) | 7.36878e10 | 2.51889 | ||||||||
\(979\) | − | 3.64688e9i | − | 0.124217i | ||||||
\(980\) | 2.23266e10i | 0.757760i | ||||||||
\(981\) | 3.58408e9i | 0.121209i | ||||||||
\(982\) | 3.11951e10i | 1.05123i | ||||||||
\(983\) | −1.35597e8 | −0.00455317 | −0.00227658 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227658 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(984\) | 1.35773e11i | 4.54287i | ||||||||
\(985\) | 1.35834e10i | 0.452879i | ||||||||
\(986\) | − | 4.42642e10i | − | 1.47056i | ||||||
\(987\) | 2.09986e10 | 0.695152 | ||||||||
\(988\) | 1.83972e10 | 0.606879 | ||||||||
\(989\) | 3.26953e10 | 1.07473 | ||||||||
\(990\) | −2.30963e9 | −0.0756518 | ||||||||
\(991\) | − | 6.02898e9i | − | 0.196782i | −0.995148 | − | 0.0983911i | \(-0.968630\pi\) | ||
0.995148 | − | 0.0983911i | \(-0.0313696\pi\) | |||||||
\(992\) | −2.32906e10 | −0.757513 | ||||||||
\(993\) | − | 9.94016e9i | − | 0.322160i | ||||||
\(994\) | 2.64608e10i | 0.854575i | ||||||||
\(995\) | 7.00826e9 | 0.225543 | ||||||||
\(996\) | −1.04511e11 | −3.35161 | ||||||||
\(997\) | 2.38603e10i | 0.762505i | 0.924471 | + | 0.381253i | \(0.124507\pi\) | ||||
−0.924471 | + | 0.381253i | \(0.875493\pi\) | |||||||
\(998\) | −7.22178e10 | −2.29979 | ||||||||
\(999\) | 3.18505e9 | − | 3.26677e10i | 0.101074 | − | 1.03667i |
(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 | 37.8.b.a.36.20 | yes | 20 | |
37.36 | even | 2 | inner | 37.8.b.a.36.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.8.b.a.36.1 | ✓ | 20 | 37.36 | even | 2 | inner | |
37.8.b.a.36.20 | yes | 20 | 1.1 | even | 1 | trivial |