Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,6,Mod(129,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.129");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3228223402\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 41x^{6} + 460x^{4} + 969x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{31}\cdot 5^{3} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 129.8 | ||
Root | \(-1.64654i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 320.129 |
Dual form | 320.6.c.i.129.1 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 28.9338i | 1.85610i | 0.372451 | + | 0.928052i | \(0.378518\pi\) | ||||
−0.372451 | + | 0.928052i | \(0.621482\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 13.1588 | − | 54.3309i | 0.235392 | − | 0.971901i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 146.828i | 1.13257i | 0.824211 | + | 0.566283i | \(0.191619\pi\) | ||||
−0.824211 | + | 0.566283i | \(0.808381\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −594.165 | −2.44512 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 191.129 | 0.476260 | 0.238130 | − | 0.971233i | \(-0.423466\pi\) | ||||
0.238130 | + | 0.971233i | \(0.423466\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 83.9971i | − | 0.137850i | −0.997622 | − | 0.0689249i | \(-0.978043\pi\) | ||
0.997622 | − | 0.0689249i | \(-0.0219569\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1572.00 | + | 380.734i | 1.80395 | + | 0.436912i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2000.23i | 1.67864i | 0.543635 | + | 0.839322i | \(0.317048\pi\) | ||||
−0.543635 | + | 0.839322i | \(0.682952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −677.481 | −0.430540 | −0.215270 | − | 0.976555i | \(-0.569063\pi\) | ||||
−0.215270 | + | 0.976555i | \(0.569063\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4248.29 | −2.10216 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1296.23i | − | 0.510931i | −0.966818 | − | 0.255466i | \(-0.917771\pi\) | ||
0.966818 | − | 0.255466i | \(-0.0822288\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2778.69 | − | 1429.86i | −0.889181 | − | 0.457555i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 10160.5i | − | 2.68230i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3266.00 | −0.721143 | −0.360571 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360571 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6157.98 | −1.15089 | −0.575445 | − | 0.817841i | \(-0.695171\pi\) | ||||
−0.575445 | + | 0.817841i | \(0.695171\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5530.08i | 0.883989i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7977.29 | + | 1932.08i | 1.10074 | + | 0.266597i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 11369.5i | − | 1.36533i | −0.730730 | − | 0.682667i | \(-0.760820\pi\) | ||
0.730730 | − | 0.682667i | \(-0.239180\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2430.36 | 0.255863 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10599.8 | −0.984774 | −0.492387 | − | 0.870376i | \(-0.663876\pi\) | ||||
−0.492387 | + | 0.870376i | \(0.663876\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12926.2i | 1.06610i | 0.846082 | + | 0.533052i | \(0.178955\pi\) | ||||
−0.846082 | + | 0.533052i | \(0.821045\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7818.50 | + | 32281.5i | −0.575562 | + | 2.37642i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9521.88i | 0.628750i | 0.949299 | + | 0.314375i | \(0.101795\pi\) | ||||
−0.949299 | + | 0.314375i | \(0.898205\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4751.45 | −0.282706 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −57874.4 | −3.11574 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 14786.8i | − | 0.723078i | −0.932357 | − | 0.361539i | \(-0.882251\pi\) | ||
0.932357 | − | 0.361539i | \(-0.117749\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2515.03 | − | 10384.2i | 0.112108 | − | 0.462878i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 19602.1i | − | 0.799126i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 38226.9 | 1.42968 | 0.714841 | − | 0.699287i | \(-0.246499\pi\) | ||||
0.714841 | + | 0.699287i | \(0.246499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3581.69 | 0.123243 | 0.0616217 | − | 0.998100i | \(-0.480373\pi\) | ||||
0.0616217 | + | 0.998100i | \(0.480373\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 87240.0i | − | 2.76926i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4563.64 | − | 1105.30i | −0.133976 | − | 0.0324487i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 21780.0i | − | 0.592748i | −0.955072 | − | 0.296374i | \(-0.904223\pi\) | ||
0.955072 | − | 0.296374i | \(-0.0957774\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 37504.9 | 0.948341 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51390.1 | −1.20986 | −0.604928 | − | 0.796280i | \(-0.706798\pi\) | ||||
−0.604928 | + | 0.796280i | \(0.706798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 13305.9i | − | 0.292238i | −0.989267 | − | 0.146119i | \(-0.953322\pi\) | ||
0.989267 | − | 0.146119i | \(-0.0466782\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41371.3 | − | 80398.1i | 0.849270 | − | 1.65041i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28063.1i | 0.539396i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15944.3 | 0.287434 | 0.143717 | − | 0.989619i | \(-0.454094\pi\) | ||||
0.143717 | + | 0.989619i | \(0.454094\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 149601. | 2.53350 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 53305.0i | − | 0.849323i | −0.905352 | − | 0.424662i | \(-0.860393\pi\) | ||
0.905352 | − | 0.424662i | \(-0.139607\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 108675. | + | 26320.7i | 1.63148 | + | 0.395139i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 94497.8i | − | 1.33852i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 51330.4 | 0.686910 | 0.343455 | − | 0.939169i | \(-0.388403\pi\) | ||||
0.343455 | + | 0.939169i | \(0.388403\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12333.1 | 0.156124 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 178174.i | − | 2.13617i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8914.84 | + | 36808.1i | −0.101346 | + | 0.418442i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 80849.9i | − | 0.872469i | −0.899833 | − | 0.436234i | \(-0.856312\pi\) | ||
0.899833 | − | 0.436234i | \(-0.143688\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −113562. | −1.16451 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −89471.2 | −0.872729 | −0.436365 | − | 0.899770i | \(-0.643734\pi\) | ||||
−0.436365 | + | 0.899770i | \(0.643734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 44184.6i | 0.410372i | 0.978723 | + | 0.205186i | \(0.0657799\pi\) | ||||
−0.978723 | + | 0.205186i | \(0.934220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −55902.4 | + | 230813.i | −0.494832 | + | 2.04309i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 56446.0i | − | 0.476622i | −0.971189 | − | 0.238311i | \(-0.923406\pi\) | ||
0.971189 | − | 0.238311i | \(-0.0765937\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 52651.1 | 0.424465 | 0.212232 | − | 0.977219i | \(-0.431927\pi\) | ||||
0.212232 | + | 0.977219i | \(0.431927\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 328964. | 2.53420 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 78399.6i | − | 0.577587i | −0.957391 | − | 0.288794i | \(-0.906746\pi\) | ||
0.957391 | − | 0.288794i | \(-0.0932542\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −70425.3 | − | 17056.8i | −0.496574 | − | 0.120269i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 49908.1i | 0.337059i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −293690. | −1.90118 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124521. | −0.773176 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 306691.i | − | 1.82784i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −114250. | + | 132154.i | −0.654004 | + | 0.756491i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 296102.i | − | 1.62904i | −0.580133 | − | 0.814522i | \(-0.696999\pi\) | ||
0.580133 | − | 0.814522i | \(-0.303001\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −374004. | −1.97880 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −199030. | −1.01331 | −0.506653 | − | 0.862150i | \(-0.669117\pi\) | ||||
−0.506653 | + | 0.862150i | \(0.669117\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 99473.2i | − | 0.487615i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −552031. | − | 133700.i | −2.60693 | − | 0.631391i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 361224.i | 1.64428i | 0.569288 | + | 0.822138i | \(0.307219\pi\) | ||||
−0.569288 | + | 0.822138i | \(0.692781\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 257315. | 1.12961 | 0.564805 | − | 0.825224i | \(-0.308951\pi\) | ||||
0.564805 | + | 0.825224i | \(0.308951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −275504. | −1.16702 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 16054.3i | − | 0.0656524i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −42976.7 | + | 177445.i | −0.169751 | + | 0.700879i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 137477.i | − | 0.524733i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −478333. | −1.76508 | −0.882540 | − | 0.470238i | \(-0.844168\pi\) | ||||
−0.882540 | + | 0.470238i | \(0.844168\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 193483. | 0.690558 | 0.345279 | − | 0.938500i | \(-0.387784\pi\) | ||||
0.345279 | + | 0.938500i | \(0.387784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.18847e6i | − | 4.10449i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −81031.6 | + | 334568.i | −0.270910 | + | 1.11855i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 460294.i | 1.49034i | 0.666873 | + | 0.745172i | \(0.267633\pi\) | ||||
−0.666873 | + | 0.745172i | \(0.732367\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 427839. | 1.34211 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 190323. | 0.578663 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 372211.i | 1.09729i | 0.836057 | + | 0.548643i | \(0.184855\pi\) | ||||
−0.836057 | + | 0.548643i | \(0.815145\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 300454. | + | 72769.3i | 0.859149 | + | 0.208084i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 423266.i | 1.17442i | 0.809436 | + | 0.587208i | \(0.199773\pi\) | ||||
−0.809436 | + | 0.587208i | \(0.800227\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 364237. | 0.980997 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 402535. | 1.05272 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 223915.i | − | 0.568810i | −0.958704 | − | 0.284405i | \(-0.908204\pi\) | ||
0.958704 | − | 0.284405i | \(-0.0917961\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 209943. | − | 407990.i | 0.518211 | − | 1.00706i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.10605e6i | 2.65364i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 29324.8 | 0.0684072 | 0.0342036 | − | 0.999415i | \(-0.489111\pi\) | ||||
0.0342036 | + | 0.999415i | \(0.489111\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 46594.3 | 0.105715 | 0.0528574 | − | 0.998602i | \(-0.483167\pi\) | ||||
0.0528574 | + | 0.998602i | \(0.483167\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 103632.i | 0.228752i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −617718. | − | 149610.i | −1.32697 | − | 0.321388i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 382302.i | 0.799472i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.49185e6 | 3.03788 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −327452. | −0.649477 | −0.324739 | − | 0.945804i | \(-0.605276\pi\) | ||||
−0.324739 | + | 0.945804i | \(0.605276\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 406622.i | − | 0.785773i | −0.919587 | − | 0.392887i | \(-0.871476\pi\) | ||
0.919587 | − | 0.392887i | \(-0.128524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 31980.6 | − | 132043.i | 0.0602282 | − | 0.248674i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 364071.i | − | 0.668376i | −0.942506 | − | 0.334188i | \(-0.891538\pi\) | ||
0.942506 | − | 0.334188i | \(-0.108462\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 55181.3 | 0.0987777 | 0.0493889 | − | 0.998780i | \(-0.484273\pi\) | ||||
0.0493889 | + | 0.998780i | \(0.484273\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 630177. | 1.10020 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 479540.i | − | 0.816742i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −139480. | + | 575895.i | −0.231808 | + | 0.957102i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 770174.i | 1.24929i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −129486. | −0.205049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −831145. | −1.28520 | −0.642600 | − | 0.766202i | \(-0.722144\pi\) | ||||
−0.642600 | + | 0.766202i | \(0.722144\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 1.48691e6i | − | 2.24562i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 702292. | + | 170093.i | 1.03615 | + | 0.250952i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 904163.i | − | 1.30346i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 384989. | 0.542423 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 168014. | 0.231401 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 458628.i | 0.617587i | 0.951129 | + | 0.308793i | \(0.0999252\pi\) | ||||
−0.951129 | + | 0.308793i | \(0.900075\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.65100e6 | + | 849572.i | 2.17416 | + | 1.11878i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 22779.7i | 0.0293416i | 0.999892 | + | 0.0146708i | \(0.00467003\pi\) | ||||
−0.999892 | + | 0.0146708i | \(0.995330\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.36560e6 | −1.72082 | −0.860408 | − | 0.509606i | \(-0.829791\pi\) | ||||
−0.860408 | + | 0.509606i | \(0.829791\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −811971. | −1.00118 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 673470.i | 0.812696i | 0.913718 | + | 0.406348i | \(0.133198\pi\) | ||||
−0.913718 | + | 0.406348i | \(0.866802\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 517332. | + | 125297.i | 0.611082 | + | 0.148003i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 461330.i | 0.533508i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 461339. | 0.522426 | 0.261213 | − | 0.965281i | \(-0.415877\pi\) | ||||
0.261213 | + | 0.965281i | \(0.415877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −842868. | −0.934796 | −0.467398 | − | 0.884047i | \(-0.654809\pi\) | ||||
−0.467398 | + | 0.884047i | \(0.654809\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.85951e6i | 2.02014i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −62523.4 | + | 258150.i | −0.0665468 | + | 0.274763i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 56906.4i | 0.0593498i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.54232e6 | 1.57643 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.34039e6 | −1.34291 | −0.671457 | − | 0.741044i | \(-0.734331\pi\) | ||||
−0.671457 | + | 0.741044i | \(0.734331\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 247747.i | − | 0.243336i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −761558. | + | 3.14437e6i | −0.733419 | + | 3.02819i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 337841.i | − | 0.319066i | −0.987193 | − | 0.159533i | \(-0.949001\pi\) | ||
0.987193 | − | 0.159533i | \(-0.0509988\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.66937e6 | 1.54633 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.94054e6 | 1.76328 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 836410.i | 0.745641i | 0.927903 | + | 0.372821i | \(0.121609\pi\) | ||||
−0.927903 | + | 0.372821i | \(0.878391\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −803381. | − | 194577.i | −0.702760 | − | 0.170207i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.48518e6i | 1.27498i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −36624.0 | −0.0308592 | −0.0154296 | − | 0.999881i | \(-0.504912\pi\) | ||||
−0.0154296 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.92834e6 | −1.59500 | −0.797500 | − | 0.603319i | \(-0.793845\pi\) | ||||
−0.797500 | + | 0.603319i | \(0.793845\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 356844.i | 0.289782i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −531088. | − | 273287.i | −0.423482 | − | 0.217915i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.42694e6i | 1.11739i | 0.829373 | + | 0.558696i | \(0.188698\pi\) | ||||
−0.829373 | + | 0.558696i | \(0.811302\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.65885e6 | 2.81407 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.36724e6 | −1.78845 | −0.894223 | − | 0.447621i | \(-0.852271\pi\) | ||||
−0.894223 | + | 0.447621i | \(0.852271\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.35021e6i | 1.00215i | 0.865403 | + | 0.501077i | \(0.167063\pi\) | ||||
−0.865403 | + | 0.501077i | \(0.832937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.06500e6 | − | 257940.i | −0.776671 | − | 0.188108i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.55634e6i | − | 1.11532i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.58108e6 | −1.81785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.33929e6 | 1.61939 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 506336.i | − | 0.344564i | −0.985048 | − | 0.172282i | \(-0.944886\pi\) | ||
0.985048 | − | 0.172282i | \(-0.0551140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 503021. | − | 2.07690e6i | 0.336536 | − | 1.38951i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.94197e6i | − | 1.27747i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −108880. | −0.0704317 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89793e6 | −1.20743 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 2.58874e6i | − | 1.61988i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 47130.8 | − | 194596.i | 0.0290105 | − | 0.119780i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.15053e6i | − | 0.696712i | −0.937362 | − | 0.348356i | \(-0.886740\pi\) | ||
0.937362 | − | 0.348356i | \(-0.113260\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.27843e6 | −0.761693 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 742231. | 0.435149 | 0.217574 | − | 0.976044i | \(-0.430185\pi\) | ||||
0.217574 | + | 0.976044i | \(0.430185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.67101e6i | 0.964090i | 0.876146 | + | 0.482045i | \(0.160106\pi\) | ||||
−0.876146 | + | 0.482045i | \(0.839894\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −4.73983e6 | − | 1.14797e6i | −2.69145 | − | 0.651862i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 646531.i | − | 0.361361i | −0.983542 | − | 0.180681i | \(-0.942170\pi\) | ||
0.983542 | − | 0.180681i | \(-0.0578300\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −624227. | −0.343452 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.63320e6 | 0.884660 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.35512e6i | − | 0.722723i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −120104. | + | 233402.i | −0.0630738 | + | 0.122573i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.52340e6i | 0.787851i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.39808e6 | −0.712101 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.73052e6 | 1.36986 | 0.684928 | − | 0.728610i | \(-0.259834\pi\) | ||||
0.684928 | + | 0.728610i | \(0.259834\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.75538e6i | 3.33841i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.18332e6 | − | 286598.i | −0.576092 | − | 0.139528i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 390252.i | − | 0.187185i | −0.995611 | − | 0.0935923i | \(-0.970165\pi\) | ||
0.995611 | − | 0.0935923i | \(-0.0298350\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.26840e6 | 1.07206 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.17697e6 | −0.548123 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.77009e6i | 0.812382i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 493519. | − | 2.03767e6i | 0.223232 | − | 0.921694i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.23128e6i | 0.994788i | 0.867525 | + | 0.497394i | \(0.165710\pi\) | ||||
−0.867525 | + | 0.497394i | \(0.834290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −502679. | −0.220916 | −0.110458 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110458 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −853455. | −0.369754 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.57148e6i | 1.95263i | 0.216350 | + | 0.976316i | \(0.430585\pi\) | ||||
−0.216350 | + | 0.976316i | \(0.569415\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −676232. | + | 2.79207e6i | −0.284790 | + | 1.17586i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 8.49758e6i | − | 3.52878i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −448308. | −0.183586 | −0.0917931 | − | 0.995778i | \(-0.529260\pi\) | ||||
−0.0917931 | + | 0.995778i | \(0.529260\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.01712e6 | −0.814636 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 3.60286e6i | − | 1.43510i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −722920. | − | 175089.i | −0.284026 | − | 0.0687903i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.56484e6i | 0.994018i | 0.867745 | + | 0.497009i | \(0.165568\pi\) | ||||
−0.867745 | + | 0.497009i | \(0.834432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.29801e6 | 2.40789 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.17112e6 | 0.818934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 484728.i | − | 0.180396i | −0.995924 | − | 0.0901978i | \(-0.971250\pi\) | ||
0.995924 | − | 0.0901978i | \(-0.0287499\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.82370e6 | − | 3.30568e6i | −1.40413 | − | 1.21390i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 274335.i | 0.0994094i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.26934e6 | −1.52673 | −0.763366 | − | 0.645966i | \(-0.776455\pi\) | ||||
−0.763366 | + | 0.645966i | \(0.776455\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.56737e6 | 3.02367 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.27791e6i | 0.445147i | 0.974916 | + | 0.222573i | \(0.0714457\pi\) | ||||
−0.974916 | + | 0.222573i | \(0.928554\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.52469e6 | + | 369276.i | 0.524240 | + | 0.126970i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 7.68029e6i | − | 2.60676i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.37341e6 | 1.13030 | 0.565151 | − | 0.824987i | \(-0.308818\pi\) | ||||
0.565151 | + | 0.824987i | \(0.308818\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.59276e6 | 0.857672 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 5.75870e6i | − | 1.88080i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 209808. | − | 866270.i | 0.0676597 | − | 0.279357i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.82804e6i | 0.582117i | 0.956705 | + | 0.291058i | \(0.0940074\pi\) | ||||
−0.956705 | + | 0.291058i | \(0.905993\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.87814e6 | 0.905064 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.34118e6 | 0.416511 | 0.208256 | − | 0.978074i | \(-0.433221\pi\) | ||||
0.208256 | + | 0.978074i | \(0.433221\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 517252.i | 0.158650i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.96857e6 | − | 8.12794e6i | 0.596365 | − | 2.46231i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.17305e6i | − | 0.650254i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 803937. | 0.237637 | 0.118818 | − | 0.992916i | \(-0.462089\pi\) | ||||
0.118818 | + | 0.992916i | \(0.462089\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.04516e7 | −3.05195 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.61278e6i | 1.61921i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.89611e6 | − | 701430.i | −0.825458 | − | 0.199924i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.44511e6i | 2.09667i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.90295e6 | 1.08607 | 0.543035 | − | 0.839710i | \(-0.317275\pi\) | ||||
0.543035 | + | 0.839710i | \(0.317275\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.04306e6 | −0.836769 | −0.418384 | − | 0.908270i | \(-0.637403\pi\) | ||||
−0.418384 | + | 0.908270i | \(0.637403\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.65756e6i | − | 1.53737i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.86005e6 | − | 5.55804e6i | 0.768072 | − | 1.49262i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 525892.i | 0.139581i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 464511. | 0.121858 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −772580. | −0.200332 | −0.100166 | − | 0.994971i | \(-0.531937\pi\) | ||||
−0.100166 | + | 0.994971i | \(0.531937\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.83430e6i | 1.23912i | 0.784948 | + | 0.619561i | \(0.212689\pi\) | ||||
−0.784948 | + | 0.619561i | \(0.787311\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.13415e6 | − | 1.24348e6i | −1.30090 | − | 0.315076i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 878171.i | 0.219976i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.98655e6 | 1.23492 | 0.617460 | − | 0.786602i | \(-0.288162\pi\) | ||||
0.617460 | + | 0.786602i | \(0.288162\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82314e6 | 0.691252 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 7.63238e6i | − | 1.84778i | −0.382655 | − | 0.923891i | \(-0.624990\pi\) | ||
0.382655 | − | 0.923891i | \(-0.375010\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 675447. | − | 2.78883e6i | 0.161693 | − | 0.667608i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.38400e7i | − | 3.27617i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.92156e6 | −0.449819 | −0.224910 | − | 0.974380i | \(-0.572209\pi\) | ||||
−0.224910 | + | 0.974380i | \(0.572209\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.02592e6 | −0.469009 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.59820e6i | 1.28175i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 162289. | − | 670070.i | 0.0367503 | − | 0.151737i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.64057e6i | − | 1.48735i | −0.668539 | − | 0.743677i | \(-0.733080\pi\) | ||
0.668539 | − | 0.743677i | \(-0.266920\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.03234e7 | 4.50262 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.78658e6 | −1.26815 | −0.634074 | − | 0.773272i | \(-0.718619\pi\) | ||||
−0.634074 | + | 0.773272i | \(0.718619\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.55738e6i | 0.988013i | 0.869458 | + | 0.494007i | \(0.164468\pi\) | ||||
−0.869458 | + | 0.494007i | \(0.835532\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.68033e6 | − | 2.34455e6i | −2.07615 | − | 0.502837i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 1.02351e6i | − | 0.217171i | −0.994087 | − | 0.108585i | \(-0.965368\pi\) | ||
0.994087 | − | 0.108585i | \(-0.0346321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.19791e6 | 0.671326 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.33181e7 | −2.76623 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.47057e6i | 0.507743i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.88251e6 | + | 968703.i | 0.382828 | + | 0.196996i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 8.78581e6i | 1.76801i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.42421e6 | 1.08018 | 0.540092 | − | 0.841606i | \(-0.318390\pi\) | ||||
0.540092 | + | 0.841606i | \(0.318390\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −955009. | −0.188211 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.50676e6i | 1.07406i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.39265e6 | − | 1.06389e6i | −0.847953 | − | 0.205372i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.76364e6i | 1.67441i | 0.546888 | + | 0.837206i | \(0.315812\pi\) | ||||
−0.546888 | + | 0.837206i | \(0.684188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.07695e7 | −2.03668 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.44420e6 | 0.457545 | 0.228772 | − | 0.973480i | \(-0.426529\pi\) | ||||
0.228772 | + | 0.973480i | \(0.426529\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.53277e6i | − | 1.21054i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.49434e6 | + | 6.16992e6i | −0.274117 | + | 1.13179i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7.54550e6i | − | 1.37024i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.77888e6 | −1.03894 | −0.519472 | − | 0.854487i | \(-0.673871\pi\) | ||||
−0.519472 | + | 0.854487i | \(0.673871\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.22467e7 | −2.17984 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.58777e6i | − | 0.984733i | −0.870388 | − | 0.492367i | \(-0.836132\pi\) | ||
0.870388 | − | 0.492367i | \(-0.163868\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.17733e6 | + | 4.86105e6i | −0.205433 | + | 0.848206i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.05388e7i | 1.82083i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −9.32211e6 | −1.59485 | −0.797425 | − | 0.603418i | \(-0.793805\pi\) | ||||
−0.797425 | + | 0.603418i | \(0.793805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.95367e6 | 0.330978 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.88357e6i | 1.15484i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.40059e6 | + | 581416.i | 0.398841 | + | 0.0965983i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.81990e6i | 0.299449i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.47871e6 | 1.05577 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.51696e6 | 1.21324 | 0.606622 | − | 0.794991i | \(-0.292524\pi\) | ||||
0.606622 | + | 0.794991i | \(0.292524\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 618460.i | − | 0.0988683i | −0.998777 | − | 0.0494342i | \(-0.984258\pi\) | ||
0.998777 | − | 0.0494342i | \(-0.0157418\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.18047e7 | + | 6.07446e6i | 1.86920 | + | 0.961854i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.23174e7i | − | 1.93193i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.75613e6 | 0.738949 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.27131e7 | −3.49575 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 890350.i | 0.135751i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.06676e6 | − | 742762.i | −0.463229 | − | 0.112193i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 848477.i | 0.126971i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −908138. | −0.134642 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.78044e6 | 1.14291 | 0.571454 | − | 0.820634i | \(-0.306380\pi\) | ||||
0.571454 | + | 0.820634i | \(0.306380\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.34815e6i | 0.196218i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 692826. | − | 2.86058e6i | 0.0999155 | − | 0.412537i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 6.38809e6i | − | 0.912857i | −0.889760 | − | 0.456428i | \(-0.849128\pi\) | ||
0.889760 | − | 0.456428i | \(-0.150872\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.12811e6 | −0.301345 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.21265e6 | 0.310481 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.34107e6i | 0.325538i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.32878e6 | − | 1.78729e7i | 0.596530 | − | 2.46299i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.07422e6i | − | 1.10271i | −0.834270 | − | 0.551356i | \(-0.814110\pi\) | ||
0.834270 | − | 0.551356i | \(-0.185890\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.08576e6 | 0.146962 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.10615e7 | −1.48390 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.02445e6i | 0.668064i | 0.942562 | + | 0.334032i | \(0.108409\pi\) | ||||
−0.942562 | + | 0.334032i | \(0.891591\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.25952e6 | − | 1.03165e6i | −0.561357 | − | 0.135959i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.19656e7i | 2.86936i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.36647e6 | −1.08333 | −0.541666 | − | 0.840594i | \(-0.682206\pi\) | ||||
−0.541666 | + | 0.840594i | \(0.682206\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −831558. | −0.106734 | −0.0533670 | − | 0.998575i | \(-0.516995\pi\) | ||||
−0.0533670 | + | 0.998575i | \(0.516995\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9.47443e6i | − | 1.20550i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.85343e6 | + | 3.60182e6i | −0.233779 | + | 0.454310i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.63868e6i | 0.705080i | 0.935797 | + | 0.352540i | \(0.114682\pi\) | ||||
−0.935797 | + | 0.352540i | \(0.885318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.17651e7 | 1.45848 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.82667e6 | 0.961915 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.82619e6i | − | 0.344373i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.71155e6 | + | 656731.i | 0.327588 | + | 0.0793411i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.13074e6i | 0.494803i | 0.968913 | + | 0.247402i | \(0.0795767\pi\) | ||||
−0.968913 | + | 0.247402i | \(0.920423\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.17191e6 | 0.495504 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.05340e7 | 1.24057 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 2.07710e6i | − | 0.242561i | −0.992618 | − | 0.121280i | \(-0.961300\pi\) | ||
0.992618 | − | 0.121280i | \(-0.0387000\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.86461e6 | + | 1.59565e7i | −0.447521 | + | 1.84775i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.59660e6i | 0.183342i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.44039e7 | −1.64026 | −0.820128 | − | 0.572180i | \(-0.806098\pi\) | ||||
−0.820128 | + | 0.572180i | \(0.806098\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.16092e7 | 1.31104 | 0.655522 | − | 0.755176i | \(-0.272449\pi\) | ||||
0.655522 | + | 0.755176i | \(0.272449\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.29409e7i | 1.44934i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.63854e6 | + | 6.76533e6i | −0.181999 | + | 0.751450i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.75662e7i | 1.93511i | 0.252654 | + | 0.967557i | \(0.418696\pi\) | ||||
−0.252654 | + | 0.967557i | \(0.581304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.38749e7 | 1.51596 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 799810. | 0.0866730 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.76294e7i | − | 1.89490i | −0.319906 | − | 0.947449i | \(-0.603651\pi\) | ||
0.319906 | − | 0.947449i | \(-0.396349\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.66628e7 | − | 4.03569e6i | −1.77648 | − | 0.430259i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.44774e6i | 0.681859i | 0.940089 | + | 0.340930i | \(0.110742\pi\) | ||||
−0.940089 | + | 0.340930i | \(0.889258\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.48717e7 | 1.56003 | 0.780017 | − | 0.625758i | \(-0.215210\pi\) | ||||
0.780017 | + | 0.625758i | \(0.215210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.31704e7 | −1.37047 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.53674e6i | 0.777971i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.67663e6 | + | 7.94628e6i | 0.581287 | + | 0.813699i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 3.74653e6i | − | 0.380592i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.27418e7 | 2.29191 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.05549e6 | 0.505464 | 0.252732 | − | 0.967536i | \(-0.418671\pi\) | ||||
0.252732 | + | 0.967536i | \(0.418671\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 2.40482e7i | − | 2.38547i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.60875e7 | − | 3.89635e6i | −1.58327 | − | 0.383464i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 399108.i | 0.0389710i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.05342e7 | 2.95824 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.66243e6 | 0.640453 | 0.320226 | − | 0.947341i | \(-0.396241\pi\) | ||||
0.320226 | + | 0.947341i | \(0.396241\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.29414e6i | 0.314206i | 0.987582 | + | 0.157103i | \(0.0502155\pi\) | ||||
−0.987582 | + | 0.157103i | \(0.949784\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.92145e6 | + | 2.03200e7i | −0.465794 | + | 1.92320i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.79219e6i | 0.450063i | 0.974351 | + | 0.225032i | \(0.0722486\pi\) | ||||
−0.974351 | + | 0.225032i | \(0.927751\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.30627e6 | 0.680901 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.61609e7 | 2.41936 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.27962e7i | 1.17435i | 0.809459 | + | 0.587177i | \(0.199761\pi\) | ||||
−0.809459 | + | 0.587177i | \(0.800239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.61900e6 | + | 1.08135e7i | −0.238524 | + | 0.984832i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.90588e6i | 0.714556i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.06887e6 | 0.275274 | 0.137637 | − | 0.990483i | \(-0.456049\pi\) | ||||
0.137637 | + | 0.990483i | \(0.456049\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.79240e6 | 0.159563 | 0.0797814 | − | 0.996812i | \(-0.474578\pi\) | ||||
0.0797814 | + | 0.996812i | \(0.474578\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.86128e6i | 0.429504i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.40447e6 | − | 1.30895e6i | −0.473913 | − | 0.114781i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.23349e6i | 0.368454i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.32698e7 | −1.14631 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 684564. | 0.0586959 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.37614e7i | − | 1.17119i | −0.810605 | − | 0.585593i | \(-0.800862\pi\) | ||
0.810605 | − | 0.585593i | \(-0.199138\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.45281e7 | + | 2.82330e7i | −1.22730 | + | 2.38505i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.01097e7i | − | 1.68629i | −0.537684 | − | 0.843147i | \(-0.680700\pi\) | ||
0.537684 | − | 0.843147i | \(-0.319300\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.18710e7 | 0.988129 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −659104. | −0.0544611 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.08331e6i | 0.498986i | 0.968377 | + | 0.249493i | \(0.0802639\pi\) | ||||
−0.968377 | + | 0.249493i | \(0.919736\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.96256e7 | + | 4.75327e6i | 1.59807 | + | 0.387049i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.95120e7i | − | 3.19401i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.24205e6 | −0.0996761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.23063e7 | 1.77719 | 0.888593 | − | 0.458697i | \(-0.151684\pi\) | ||||
0.888593 | + | 0.458697i | \(0.151684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.66741e7i | − | 1.31889i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.38596e6 | − | 1.39802e7i | 0.265901 | − | 1.09787i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.12020e7i | − | 1.65308i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.94860e7 | −1.50845 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.01349e7 | 1.54758 | 0.773792 | − | 0.633439i | \(-0.218357\pi\) | ||||
0.773792 | + | 0.633439i | \(0.218357\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.70265e6i | 0.587830i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −3.62530e6 | + | 1.49684e7i | −0.274708 | + | 1.13423i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 1.31369e7i | − | 0.988424i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.09436e6 | −0.530027 | −0.265013 | − | 0.964245i | \(-0.585376\pi\) | ||||
−0.265013 | + | 0.964245i | \(0.585376\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.47356e6 | −0.702812 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.98215e6i | 0.588026i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −872243. | − | 211255.i | −0.0638076 | − | 0.0154540i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.33483e7i | 0.969677i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.57591e7 | −1.13686 | −0.568432 | − | 0.822730i | \(-0.692450\pi\) | ||||
−0.568432 | + | 0.822730i | \(0.692450\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.48753e6 | −0.464774 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 2.43874e7i | − | 1.73508i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.07521e6 | + | 4.66992e6i | 0.641227 | + | 0.329963i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.93222e7i | 1.35588i | 0.735118 | + | 0.677939i | \(0.237127\pi\) | ||||
−0.735118 | + | 0.677939i | \(0.762873\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.74496e7 | −1.21610 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.58554e7 | −1.78961 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.53614e6i | 0.518071i | 0.965868 | + | 0.259035i | \(0.0834046\pi\) | ||||
−0.965868 | + | 0.259035i | \(0.916595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.46927e6 | − | 1.80904e6i | −0.509988 | − | 0.123518i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.16278e6i | − | 0.282302i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08996e6 | 0.410207 | 0.205104 | − | 0.978740i | \(-0.434247\pi\) | ||||
0.205104 | + | 0.978740i | \(0.434247\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.64652e6 | −0.110159 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.29284e6i | − | 0.351736i | −0.984414 | − | 0.175868i | \(-0.943727\pi\) | ||
0.984414 | − | 0.175868i | \(-0.0562731\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.29429e6 | + | 2.59882e7i | −0.415485 | + | 1.71548i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.16720e7i | 2.07670i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.28785e6 | 0.539806 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.58109e7 | −1.02296 | −0.511478 | − | 0.859296i | \(-0.670902\pi\) | ||||
−0.511478 | + | 0.859296i | \(0.670902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 3.87827e7i | − | 2.49259i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.54600e6 | − | 1.05121e7i | 0.162552 | − | 0.671154i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.01450e7i | 1.27770i | 0.769332 | + | 0.638849i | \(0.220589\pi\) | ||||
−0.769332 | + | 0.638849i | \(0.779411\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.16826e6 | 0.451657 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.10320e7 | −1.31650 | −0.658248 | − | 0.752801i | \(-0.728702\pi\) | ||||
−0.658248 | + | 0.752801i | \(0.728702\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.73066e6i | 0.480734i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.45706e7 | − | 1.56388e7i | −3.98916 | − | 0.966164i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 3.21095e6i | − | 0.197081i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.09332e6 | 0.249609 | 0.124804 | − | 0.992181i | \(-0.460170\pi\) | ||||
0.124804 | + | 0.992181i | \(0.460170\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.77503e6 | 0.592219 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.09247e7i | 0.657599i | 0.944400 | + | 0.328799i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328799i | \(0.893356\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.71111e7 | + | 8.80504e6i | 1.02335 | + | 0.526595i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.83011e7i | 2.87015i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.18114e6 | 0.423984 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.82213e6 | −0.576206 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.31843e7i | 1.93432i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.50082e7 | + | 6.05692e6i | 1.44847 | + | 0.350815i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.38257e7i | 0.795700i | 0.917450 | + | 0.397850i | \(0.130244\pi\) | ||||
−0.917450 | + | 0.397850i | \(0.869756\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.42005e7 | −1.38399 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.15113e7 | 0.654156 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 300852.i | − | 0.0169891i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.62985e6 | − | 2.32449e7i | 0.315921 | − | 1.30440i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1.38429e6i | − | 0.0771937i | −0.999255 | − | 0.0385969i | \(-0.987711\pi\) | ||
0.999255 | − | 0.0385969i | \(-0.0122888\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.90460e7 | −1.05545 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.04987e7 | −1.67958 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 2.54313e6i | − | 0.139181i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.50442e6 | − | 1.03404e7i | 0.136213 | − | 0.562403i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 1.05967e6i | − | 0.0572780i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.08074e7 | 1.11776 | 0.558878 | − | 0.829250i | \(-0.311232\pi\) | ||||
0.558878 | + | 0.829250i | \(0.311232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.24363e7 | −1.19784 | −0.598919 | − | 0.800810i | \(-0.704403\pi\) | ||||
−0.598919 | + | 0.800810i | \(0.704403\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.57942e7i | − | 2.96049i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.02225e7 | + | 4.89785e6i | 1.06645 | + | 0.258292i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.75726e6i | − | 0.459000i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.32791e6 | −0.381742 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.30693e7 | −0.676698 | −0.338349 | − | 0.941021i | \(-0.609869\pi\) | ||||
−0.338349 | + | 0.941021i | \(0.609869\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.09593e7i | − | 1.07864i | −0.842100 | − | 0.539321i | \(-0.818681\pi\) | ||
0.842100 | − | 0.539321i | \(-0.181319\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.90724e6 | − | 1.53664e7i | 0.404473 | − | 0.786026i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.54670e6i | 0.231171i | 0.993298 | + | 0.115585i | \(0.0368744\pi\) | ||||
−0.993298 | + | 0.115585i | \(0.963126\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.05898e7 | −1.04055 | −0.520277 | − | 0.853997i | \(-0.674171\pi\) | ||||
−0.520277 | + | 0.853997i | \(0.674171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.12867e7 | −2.07399 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 9.50401e6i | − | 0.474564i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29964e7 | + | 5.56967e6i | 1.14142 | + | 0.276448i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.25683e7i | 3.08703i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.09532e7 | 0.537200 | 0.268600 | − | 0.963252i | \(-0.413439\pi\) | ||||
0.268600 | + | 0.963252i | \(0.413439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.84438e6 | −0.479953 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 6.84932e7i | − | 3.31954i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.79293e6 | − | 1.97893e7i | 0.230919 | − | 0.953432i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.82831e7i | − | 0.875673i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.90666e7 | −1.86010 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.47375e7 | −0.697592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.27066e7i | 0.597939i | 0.954263 | + | 0.298970i | \(0.0966429\pi\) | ||||
−0.954263 | + | 0.298970i | \(0.903357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.29688e6 | − | 2.18701e7i | 0.247802 | − | 1.02314i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.46258e6i | 0.347086i | 0.984826 | + | 0.173543i | \(0.0555216\pi\) | ||||
−0.984826 | + | 0.173543i | \(0.944478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.13390e7 | −0.524315 | −0.262158 | − | 0.965025i | \(-0.584434\pi\) | ||||
−0.262158 | + | 0.965025i | \(0.584434\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.50309e7 | 2.07015 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1.61275e7i | − | 0.737121i | −0.929604 | − | 0.368561i | \(-0.879851\pi\) | ||
0.929604 | − | 0.368561i | \(-0.120149\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.21655e7 | − | 2.94645e6i | −0.552827 | − | 0.133893i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 7.46805e7i | − | 3.37411i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.04742e6 | 0.136894 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.82945e6 | −0.0817101 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.80381e7i | 2.13329i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.94038e7 | − | 1.67751e7i | −0.856776 | − | 0.740703i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.89336e7i | − | 1.70933i | −0.519182 | − | 0.854663i | \(-0.673763\pi\) | ||
0.519182 | − | 0.854663i | \(-0.326237\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.46502e7 | 0.639546 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.57060e7 | 1.54989 | 0.774946 | − | 0.632027i | \(-0.217777\pi\) | ||||
0.774946 | + | 0.632027i | \(0.217777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.48264e7i | 1.50317i | 0.659638 | + | 0.751583i | \(0.270709\pi\) | ||||
−0.659638 | + | 0.751583i | \(0.729291\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00927e7 | + | 1.45543e7i | 2.57907 | + | 0.624645i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 9.97196e6i | − | 0.425571i | −0.977099 | − | 0.212785i | \(-0.931747\pi\) | ||
0.977099 | − | 0.212785i | \(-0.0682535\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.34761e7 | 1.84500 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.85930e7 | 1.20661 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 6.45089e6i | − | 0.270702i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 385879. | − | 1.59324e6i | 0.0161025 | − | 0.0664850i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 3.15030e6i | − | 0.130729i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.01120e7 | 0.829956 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.95771e7 | 1.21379 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.49143e7i | − | 2.24112i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 613125. | − | 2.53151e6i | 0.0248844 | − | 0.102744i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.17790e7i | 0.879064i | 0.898227 | + | 0.439532i | \(0.144856\pi\) | ||||
−0.898227 | + | 0.439532i | \(0.855144\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.31606e7 | 2.13393 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.45704e7 | −1.77931 | −0.889653 | − | 0.456637i | \(-0.849054\pi\) | ||||
−0.889653 | + | 0.456637i | \(0.849054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.01881e7i | − | 0.404499i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.63041e6 | + | 1.36367e6i | 0.222325 | + | 0.0538465i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.92232e7i | − | 1.14764i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.05848e7 | 1.97575 | 0.987873 | − | 0.155264i | \(-0.0496227\pi\) | ||||
0.987873 | + | 0.155264i | \(0.0496227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.32893e7 | 1.29317 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.31662e6i | 0.166778i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.62569e7 | + | 3.15925e7i | −0.624715 | + | 1.21403i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.62529e7i | − | 1.00341i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.61614e6 | −0.365563 | −0.182781 | − | 0.983154i | \(-0.558510\pi\) | ||||
−0.182781 | + | 0.983154i | \(0.558510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.21902e6 | 0.121716 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.14756e7i | 0.807682i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.07708e7 | + | 5.03064e6i | 0.777007 | + | 0.188189i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.07884e7i | − | 1.14562i | −0.819690 | − | 0.572808i | \(-0.805854\pi\) | ||
0.819690 | − | 0.572808i | \(-0.194146\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.83486e7 | −1.78945 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.94367e7 | −1.45186 | −0.725932 | − | 0.687766i | \(-0.758591\pi\) | ||||
−0.725932 | + | 0.687766i | \(0.758591\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.37397e7i | 0.503152i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.96310e7 | − | 8.10535e7i | 0.715092 | − | 2.95252i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 2.02857e7i | − | 0.735045i | −0.930015 | − | 0.367523i | \(-0.880206\pi\) | ||
0.930015 | − | 0.367523i | \(-0.119794\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.11765e6 | −0.0402849 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.87066e7 | 0.670724 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.23933e6i | 0.258206i | 0.991631 | + | 0.129103i | \(0.0412098\pi\) | ||||
−0.991631 | + | 0.129103i | \(0.958790\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.30888e6 | + | 1.77908e7i | −0.152882 | + | 0.631227i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.80613e7i | − | 0.637482i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5.30377e7 | −1.86225 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.29152e6 | 0.324548 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.35382e7i | 1.16540i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.20921e7 | − | 5.35066e6i | −0.763693 | − | 0.184965i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.74626e7i | 1.63224i | 0.577880 | + | 0.816122i | \(0.303880\pi\) | ||||
−0.577880 | + | 0.816122i | \(0.696120\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.92088e7 | 1.34145 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.13308e7 | −0.385668 | −0.192834 | − | 0.981231i | \(-0.561768\pi\) | ||||
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.77811e7i | 1.27936i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.75321e6 | − | 3.47507e6i | −0.227509 | − | 0.117072i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 4.09471e7i | − | 1.37242i | −0.727404 | − | 0.686210i | \(-0.759273\pi\) | ||
0.727404 | − | 0.686210i | \(-0.240727\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.81072e6 | 0.327148 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.12835e7 | −1.03787 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.17862e7i | − | 0.389036i | −0.980899 | − | 0.194518i | \(-0.937686\pi\) | ||
0.980899 | − | 0.194518i | \(-0.0623143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.97803e7 | − | 4.79074e6i | −0.649595 | − | 0.157330i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 4.04517e7i | − | 1.32173i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.67553e7 | 0.544706 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.78243e7 | 1.54691 | 0.773454 | − | 0.633853i | \(-0.218527\pi\) | ||||
0.773454 | + | 0.633853i | \(0.218527\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 7.90043e7i | 2.54260i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 726120. | − | 2.99805e6i | 0.0232515 | − | 0.0960021i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.93264e6i | − | 0.189021i | −0.995524 | − | 0.0945105i | \(-0.969871\pi\) | ||
0.995524 | − | 0.0945105i | \(-0.0301286\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.15521e8 | −3.66223 |
(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 | 320.6.c.i.129.8 | 8 | ||
4.3 | odd | 2 | 320.6.c.j.129.1 | 8 | |||
5.4 | even | 2 | inner | 320.6.c.i.129.1 | 8 | ||
8.3 | odd | 2 | 40.6.c.a.9.8 | yes | 8 | ||
8.5 | even | 2 | 80.6.c.d.49.1 | 8 | |||
20.19 | odd | 2 | 320.6.c.j.129.8 | 8 | |||
24.5 | odd | 2 | 720.6.f.n.289.5 | 8 | |||
24.11 | even | 2 | 360.6.f.b.289.5 | 8 | |||
40.3 | even | 4 | 200.6.a.j.1.1 | 4 | |||
40.13 | odd | 4 | 400.6.a.ba.1.4 | 4 | |||
40.19 | odd | 2 | 40.6.c.a.9.1 | ✓ | 8 | ||
40.27 | even | 4 | 200.6.a.k.1.4 | 4 | |||
40.29 | even | 2 | 80.6.c.d.49.8 | 8 | |||
40.37 | odd | 4 | 400.6.a.z.1.1 | 4 | |||
120.29 | odd | 2 | 720.6.f.n.289.6 | 8 | |||
120.59 | even | 2 | 360.6.f.b.289.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.c.a.9.1 | ✓ | 8 | 40.19 | odd | 2 | ||
40.6.c.a.9.8 | yes | 8 | 8.3 | odd | 2 | ||
80.6.c.d.49.1 | 8 | 8.5 | even | 2 | |||
80.6.c.d.49.8 | 8 | 40.29 | even | 2 | |||
200.6.a.j.1.1 | 4 | 40.3 | even | 4 | |||
200.6.a.k.1.4 | 4 | 40.27 | even | 4 | |||
320.6.c.i.129.1 | 8 | 5.4 | even | 2 | inner | ||
320.6.c.i.129.8 | 8 | 1.1 | even | 1 | trivial | ||
320.6.c.j.129.1 | 8 | 4.3 | odd | 2 | |||
320.6.c.j.129.8 | 8 | 20.19 | odd | 2 | |||
360.6.f.b.289.5 | 8 | 24.11 | even | 2 | |||
360.6.f.b.289.6 | 8 | 120.59 | even | 2 | |||
400.6.a.z.1.1 | 4 | 40.37 | odd | 4 | |||
400.6.a.ba.1.4 | 4 | 40.13 | odd | 4 | |||
720.6.f.n.289.5 | 8 | 24.5 | odd | 2 | |||
720.6.f.n.289.6 | 8 | 120.29 | odd | 2 |