Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(63,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 3]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.63");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.n (of order \(4\), degree \(2\), 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + 24971013117824 x^{4} + \cdots + 177426662425600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{41}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 63.5 | ||
Root | \(2.29308i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.63 |
Dual form | 160.6.n.d.127.5 |
$q$-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 \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 3.29308 | − | 3.29308i | 0.211251 | − | 0.211251i | −0.593548 | − | 0.804799i | \(-0.702273\pi\) |
0.804799 | + | 0.593548i | \(0.202273\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 35.3847 | − | 43.2773i | 0.632980 | − | 0.774168i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.96093 | − | 5.96093i | −0.0459800 | − | 0.0459800i | 0.683743 | − | 0.729723i | \(-0.260351\pi\) |
−0.729723 | + | 0.683743i | \(0.760351\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 221.311i | 0.910746i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 634.109i | 1.58009i | 0.613048 | + | 0.790045i | \(0.289943\pi\) | ||||
−0.613048 | + | 0.790045i | \(0.710057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 226.441 | + | 226.441i | 0.371618 | + | 0.371618i | 0.868066 | − | 0.496448i | \(-0.165363\pi\) |
−0.496448 | + | 0.868066i | \(0.665363\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −25.9911 | − | 259.040i | −0.0298260 | − | 0.297261i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 429.196 | − | 429.196i | 0.360192 | − | 0.360192i | −0.503692 | − | 0.863883i | \(-0.668025\pi\) |
0.863883 | + | 0.503692i | \(0.168025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 540.685 | 0.343606 | 0.171803 | − | 0.985131i | \(-0.445041\pi\) | ||||
0.171803 | + | 0.985131i | \(0.445041\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.2596 | −0.0194266 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1345.21 | − | 1345.21i | 0.530237 | − | 0.530237i | −0.390406 | − | 0.920643i | \(-0.627665\pi\) |
0.920643 | + | 0.390406i | \(0.127665\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −620.850 | − | 3062.71i | −0.198672 | − | 0.980066i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1529.01 | + | 1529.01i | 0.403647 | + | 0.403647i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1942.50i | 0.428910i | 0.976734 | + | 0.214455i | \(0.0687975\pi\) | ||||
−0.976734 | + | 0.214455i | \(0.931202\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8018.95i | 1.49869i | 0.662177 | + | 0.749347i | \(0.269633\pi\) | ||||
−0.662177 | + | 0.749347i | \(0.730367\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2088.17 | + | 2088.17i | 0.333796 | + | 0.333796i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −468.898 | + | 47.0474i | −0.0647006 | + | 0.00649181i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11033.1 | − | 11033.1i | 1.32493 | − | 1.32493i | 0.415205 | − | 0.909728i | \(-0.363710\pi\) |
0.909728 | − | 0.415205i | \(-0.136290\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1491.37 | 0.157009 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13026.2 | 1.21021 | 0.605103 | − | 0.796147i | \(-0.293132\pi\) | ||||
0.605103 | + | 0.796147i | \(0.293132\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10539.1 | + | 10539.1i | −0.869226 | + | 0.869226i | −0.992387 | − | 0.123161i | \(-0.960697\pi\) |
0.123161 | + | 0.992387i | \(0.460697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9577.76 | + | 7831.03i | 0.705070 | + | 0.576484i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 14464.6 | + | 14464.6i | 0.955126 | + | 0.955126i | 0.999035 | − | 0.0439100i | \(-0.0139815\pi\) |
−0.0439100 | + | 0.999035i | \(0.513981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 16735.9i | − | 0.995772i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 2826.75i | − | 0.152182i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6059.07 | − | 6059.07i | −0.296290 | − | 0.296290i | 0.543269 | − | 0.839559i | \(-0.317186\pi\) |
−0.839559 | + | 0.543269i | \(0.817186\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 27442.5 | + | 22437.7i | 1.22326 | + | 1.00017i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1780.52 | − | 1780.52i | 0.0725870 | − | 0.0725870i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −405.643 | −0.0151710 | −0.00758550 | − | 0.999971i | \(-0.502415\pi\) | ||||
−0.00758550 | + | 0.999971i | \(0.502415\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10881.1 | 0.374412 | 0.187206 | − | 0.982321i | \(-0.440057\pi\) | ||||
0.187206 | + | 0.982321i | \(0.440057\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1319.22 | − | 1319.22i | 0.0418761 | − | 0.0418761i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 17812.3 | − | 1787.22i | 0.522921 | − | 0.0524679i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8886.87 | − | 8886.87i | −0.241859 | − | 0.241859i | 0.575760 | − | 0.817619i | \(-0.304706\pi\) |
−0.817619 | + | 0.575760i | \(0.804706\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 8859.76i | − | 0.224026i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12438.9i | 0.292844i | 0.989222 | + | 0.146422i | \(0.0467758\pi\) | ||||
−0.989222 | + | 0.146422i | \(0.953224\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 17069.9 | + | 17069.9i | 0.374907 | + | 0.374907i | 0.869261 | − | 0.494354i | \(-0.164595\pi\) |
−0.494354 | + | 0.869261i | \(0.664595\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12130.2 | − | 8041.22i | −0.249010 | − | 0.165070i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3779.87 | − | 3779.87i | 0.0726525 | − | 0.0726525i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69057.3 | 1.24492 | 0.622460 | − | 0.782651i | \(-0.286133\pi\) | ||||
0.622460 | + | 0.782651i | \(0.286133\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43708.3 | −0.740204 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −40609.1 | + | 40609.1i | −0.647035 | + | 0.647035i | −0.952275 | − | 0.305240i | \(-0.901263\pi\) |
0.305240 | + | 0.952275i | \(0.401263\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3387.49 | − | 33761.4i | −0.0508546 | − | 0.506843i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6396.80 | + | 6396.80i | 0.0906076 | + | 0.0906076i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 64770.8i | 0.866771i | 0.901209 | + | 0.433386i | \(0.142681\pi\) | ||||
−0.901209 | + | 0.433386i | \(0.857319\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2699.59i | − | 0.0341739i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 26407.0 | + | 26407.0i | 0.316601 | + | 0.316601i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19132.0 | − | 23399.4i | 0.217496 | − | 0.266008i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 35342.6 | − | 35342.6i | 0.381390 | − | 0.381390i | −0.490213 | − | 0.871603i | \(-0.663081\pi\) |
0.871603 | + | 0.490213i | \(0.163081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −140335. | −1.43906 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −104115. | −1.01557 | −0.507784 | − | 0.861484i | \(-0.669535\pi\) | ||||
−0.507784 | + | 0.861484i | \(0.669535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43067.5 | − | 43067.5i | 0.399997 | − | 0.399997i | −0.478235 | − | 0.878232i | \(-0.658723\pi\) |
0.878232 | + | 0.478235i | \(0.158723\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1389.19 | + | 1699.05i | −0.0122967 | + | 0.0150395i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −139966. | − | 139966.i | −1.18185 | − | 1.18185i | −0.979265 | − | 0.202585i | \(-0.935066\pi\) |
−0.202585 | − | 0.979265i | \(-0.564934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 96865.6i | 0.780914i | 0.920621 | + | 0.390457i | \(0.127683\pi\) | ||||
−0.920621 | + | 0.390457i | \(0.872317\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 72665.8i | − | 0.559787i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −58802.8 | − | 58802.8i | −0.433213 | − | 0.433213i | 0.456507 | − | 0.889720i | \(-0.349100\pi\) |
−0.889720 | + | 0.456507i | \(0.849100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10617.3 | − | 105817.i | −0.0748630 | − | 0.746123i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −50113.9 | + | 50113.9i | −0.338449 | + | 0.338449i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5116.81 | −0.0331232 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −241043. | −1.49669 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 42896.4 | − | 42896.4i | 0.255657 | − | 0.255657i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −154514. | − | 81504.1i | −0.884491 | − | 0.466557i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 156941. | + | 156941.i | 0.863428 | + | 0.863428i | 0.991735 | − | 0.128306i | \(-0.0409540\pi\) |
−0.128306 | + | 0.991735i | \(0.540954\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 69412.2i | 0.367250i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 328683.i | − | 1.67340i | −0.547663 | − | 0.836699i | \(-0.684482\pi\) | ||
0.547663 | − | 0.836699i | \(-0.315518\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3222.98 | − | 3222.98i | −0.0157990 | − | 0.0157990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 120275. | − | 12067.9i | 0.567991 | − | 0.0569900i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −68941.8 | + | 68941.8i | −0.313820 | + | 0.313820i | −0.846388 | − | 0.532567i | \(-0.821227\pi\) |
0.532567 | + | 0.846388i | \(0.321227\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −357947. | −1.57138 | −0.785692 | − | 0.618618i | \(-0.787693\pi\) | ||||
−0.785692 | + | 0.618618i | \(0.787693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 95265.8 | 0.403542 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −143588. | + | 143588.i | −0.587190 | + | 0.587190i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 84066.2 | + | 68734.7i | 0.332048 | + | 0.271492i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −55112.7 | − | 55112.7i | −0.210358 | − | 0.210358i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 181781.i | 0.670784i | 0.942079 | + | 0.335392i | \(0.108869\pi\) | ||||
−0.942079 | + | 0.335392i | \(0.891131\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 281792.i | − | 1.00574i | −0.864361 | − | 0.502871i | \(-0.832277\pi\) | ||
0.864361 | − | 0.502871i | \(-0.167723\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 94986.0 | + | 94986.0i | 0.328043 | + | 0.328043i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 347039. | + | 283748.i | 1.16024 | + | 0.948644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18154.8 | − | 18154.8i | 0.0587817 | − | 0.0587817i | −0.677105 | − | 0.735887i | \(-0.736766\pi\) |
0.735887 | + | 0.677105i | \(0.236766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −39906.0 | −0.125183 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −16037.4 | −0.0487606 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −288172. | + | 288172.i | −0.849537 | + | 0.849537i | −0.990075 | − | 0.140538i | \(-0.955117\pi\) |
0.140538 | + | 0.990075i | \(0.455117\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 164259. | − | 16481.2i | 0.469700 | − | 0.0471279i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 31141.0 | + | 31141.0i | 0.0864055 | + | 0.0864055i | 0.748989 | − | 0.662583i | \(-0.230540\pi\) |
−0.662583 | + | 0.748989i | \(0.730540\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 268742.i | − | 0.723800i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 119660.i | 0.312937i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 159322. | + | 159322.i | 0.404726 | + | 0.404726i | 0.879895 | − | 0.475169i | \(-0.157613\pi\) |
−0.475169 | + | 0.879895i | \(0.657613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14555.7 | + | 21957.4i | −0.0359285 | + | 0.0541983i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1335.81 | + | 1335.81i | −0.00320489 | + | 0.00320489i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 657790. | 1.53446 | 0.767229 | − | 0.641373i | \(-0.221635\pi\) | ||||
0.767229 | + | 0.641373i | \(0.221635\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −662330. | −1.50272 | −0.751360 | − | 0.659892i | \(-0.770602\pi\) | ||||
−0.751360 | + | 0.659892i | \(0.770602\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35832.4 | − | 35832.4i | 0.0790949 | − | 0.0790949i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −87080.4 | − | 867887.i | −0.187064 | − | 1.86438i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 272157. | + | 272157.i | 0.569135 | + | 0.569135i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 18228.7i | − | 0.0371193i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 414623.i | − | 0.822375i | −0.911551 | − | 0.411187i | \(-0.865114\pi\) | ||
0.911551 | − | 0.411187i | \(-0.134886\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 688506. | + | 688506.i | 1.33050 | + | 1.33050i | 0.904923 | + | 0.425575i | \(0.139928\pi\) |
0.425575 | + | 0.904923i | \(0.360072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 52771.8 | − | 64542.7i | 0.0993837 | − | 0.121552i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 683608. | − | 683608.i | 1.25499 | − | 1.25499i | 0.301540 | − | 0.953453i | \(-0.402499\pi\) |
0.953453 | − | 0.301540i | \(-0.0975007\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −808934. | −1.44804 | −0.724020 | − | 0.689779i | \(-0.757708\pi\) | ||||
−0.724020 | + | 0.689779i | \(0.757708\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −58530.3 | −0.102186 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11579.1 | − | 11579.1i | 0.0197213 | − | 0.0197213i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 460929. | − | 563740.i | 0.766036 | − | 0.936903i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 297710. | + | 297710.i | 0.482912 | + | 0.482912i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 342853.i | 0.542928i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 308765.i | 0.477444i | 0.971088 | + | 0.238722i | \(0.0767284\pi\) | ||||
−0.971088 | + | 0.238722i | \(0.923272\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 40962.3 | + | 40962.3i | 0.0618636 | + | 0.0618636i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 83181.3 | + | 829027.i | 0.122724 | + | 1.22313i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 47800.4 | − | 47800.4i | 0.0689099 | − | 0.0689099i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 112425. | 0.158399 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 194375. | 0.267707 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −410489. | + | 410489.i | −0.552763 | + | 0.552763i | −0.927237 | − | 0.374474i | \(-0.877823\pi\) |
0.374474 | + | 0.927237i | \(0.377823\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 677812. | − | 137401.i | 0.892591 | − | 0.180940i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 811943. | + | 811943.i | 1.04583 | + | 1.04583i | 0.998898 | + | 0.0469317i | \(0.0149443\pi\) |
0.0469317 | + | 0.998898i | \(0.485056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 681576.i | 0.858866i | 0.903099 | + | 0.429433i | \(0.141287\pi\) | ||||
−0.903099 | + | 0.429433i | \(0.858713\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 24894.8i | − | 0.0306958i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −130959. | − | 130959.i | −0.158032 | − | 0.158032i | 0.623662 | − | 0.781694i | \(-0.285644\pi\) |
−0.781694 | + | 0.623662i | \(0.785644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.13781e6 | − | 114163.i | 1.34400 | − | 0.134852i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 227411. | − | 227411.i | 0.262991 | − | 0.262991i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −697425. | −0.789773 | −0.394887 | − | 0.918730i | \(-0.629216\pi\) | ||||
−0.394887 | + | 0.918730i | \(0.629216\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −82389.9 | −0.0913758 | −0.0456879 | − | 0.998956i | \(-0.514548\pi\) | ||||
−0.0456879 | + | 0.998956i | \(0.514548\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −515485. | + | 515485.i | −0.560016 | + | 0.560016i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −724286. | − | 592196.i | −0.770895 | − | 0.630304i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 122433. | + | 122433.i | 0.127690 | + | 0.127690i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 267458.i | 0.273374i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 863770.i | − | 0.865394i | −0.901540 | − | 0.432697i | \(-0.857562\pi\) | ||
0.901540 | − | 0.432697i | \(-0.142438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 853009. | + | 853009.i | 0.837823 | + | 0.837823i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −122334. | − | 100024.i | −0.117814 | − | 0.0963280i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 993849. | − | 993849.i | 0.938615 | − | 0.938615i | −0.0596069 | − | 0.998222i | \(-0.518985\pi\) |
0.998222 | + | 0.0596069i | \(0.0189847\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −131535. | −0.121841 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −429897. | −0.390628 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 180655. | − | 180655.i | 0.161050 | − | 0.161050i | −0.621982 | − | 0.783032i | \(-0.713672\pi\) |
0.783032 | + | 0.621982i | \(0.213672\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −476619. | + | 47822.1i | −0.416924 | + | 0.0418325i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 213295. | + | 213295.i | 0.183106 | + | 0.183106i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 72265.9i | 0.0608909i | 0.999536 | + | 0.0304455i | \(0.00969259\pi\) | ||||
−0.999536 | + | 0.0304455i | \(0.990307\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.05138e6i | − | 1.69677i | −0.529379 | − | 0.848385i | \(-0.677575\pi\) | ||
0.529379 | − | 0.848385i | \(-0.322425\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −8889.97 | − | 8889.97i | −0.00721928 | − | 0.00721928i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.94209e6 | − | 393687.i | 1.54859 | − | 0.313920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −958531. | + | 958531.i | −0.750597 | + | 0.750597i | −0.974591 | − | 0.223994i | \(-0.928090\pi\) |
0.223994 | + | 0.974591i | \(0.428090\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.77468e6 | −1.36493 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.20230e6 | −1.66384 | −0.831920 | − | 0.554896i | \(-0.812758\pi\) | ||||
−0.831920 | + | 0.554896i | \(0.812758\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −872678. | + | 872678.i | −0.647721 | + | 0.647721i | −0.952442 | − | 0.304721i | \(-0.901437\pi\) |
0.304721 | + | 0.952442i | \(0.401437\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14053.0 | − | 140059.i | −0.0102484 | − | 0.102141i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −77648.4 | − | 77648.4i | −0.0556452 | − | 0.0556452i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.05144e6i | 0.740524i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 232772.i | − | 0.161138i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −811890. | − | 811890.i | −0.552495 | − | 0.552495i | 0.374665 | − | 0.927160i | \(-0.377758\pi\) |
−0.927160 | + | 0.374665i | \(0.877758\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14353.6 | + | 17555.2i | −0.00960295 | + | 0.0117449i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −969560. | + | 969560.i | −0.637799 | + | 0.637799i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 609221. | 0.394091 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 125646. | 0.0799339 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −342858. | + | 342858.i | −0.214540 | + | 0.214540i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 385025. | − | 470906.i | 0.236995 | − | 0.289858i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.50108e6 | − | 1.50108e6i | −0.908989 | − | 0.908989i | 0.0872016 | − | 0.996191i | \(-0.472208\pi\) |
−0.996191 | + | 0.0872016i | \(0.972208\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 283649.i | − | 0.168999i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 2.99788e6i | − | 1.75757i | −0.477213 | − | 0.878787i | \(-0.658353\pi\) | ||
0.477213 | − | 0.878787i | \(-0.341647\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 186130. | + | 186130.i | 0.107388 | + | 0.107388i | 0.758759 | − | 0.651371i | \(-0.225806\pi\) |
−0.651371 | + | 0.758759i | \(0.725806\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10412.1 | − | 103772.i | −0.00591239 | − | 0.0589258i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −269555. | + | 269555.i | −0.150661 | + | 0.150661i | −0.778413 | − | 0.627752i | \(-0.783975\pi\) |
0.627752 | + | 0.778413i | \(0.283975\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.23176e6 | −0.677717 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −921835. | −0.499334 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 232060. | − | 232060.i | 0.123764 | − | 0.123764i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 552936. | − | 834108.i | 0.290380 | − | 0.438040i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 318986. | + | 318986.i | 0.164969 | + | 0.164969i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 172444.i | − | 0.0878333i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 656419.i | 0.329315i | 0.986351 | + | 0.164657i | \(0.0526518\pi\) | ||||
−0.986351 | + | 0.164657i | \(0.947348\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.44175e6 | + | 2.44175e6i | 1.20668 | + | 1.20668i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −699059. | + | 70140.8i | −0.340331 | + | 0.0341475i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.29668e6 | − | 1.29668e6i | 0.621954 | − | 0.621954i | −0.324077 | − | 0.946031i | \(-0.605054\pi\) |
0.946031 | + | 0.324077i | \(0.105054\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −387284. | −0.183033 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.08489e6 | −2.36807 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −199947. | + | 199947.i | −0.0917655 | + | 0.0917655i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −383426. | − | 313500.i | −0.173434 | − | 0.141804i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.79696e6 | − | 2.79696e6i | −1.24699 | − | 1.24699i | −0.957042 | − | 0.289948i | \(-0.906362\pi\) |
−0.289948 | − | 0.957042i | \(-0.593638\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.63211e6i | 1.15675i | 0.815770 | + | 0.578376i | \(0.196313\pi\) | ||||
−0.815770 | + | 0.578376i | \(0.803687\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 692462.i | 0.300005i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 324347. | + | 324347.i | 0.138539 | + | 0.138539i | 0.772975 | − | 0.634436i | \(-0.218768\pi\) |
−0.634436 | + | 0.772975i | \(0.718768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 538323. | + | 440147.i | 0.226711 | + | 0.185365i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −16850.1 | + | 16850.1i | −0.00699731 | + | 0.00699731i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.87581e6 | 1.17767 | 0.588835 | − | 0.808253i | \(-0.299587\pi\) | ||||
0.588835 | + | 0.808253i | \(0.299587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.18376e6 | −0.881935 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −793772. | + | 793772.i | −0.316176 | + | 0.316176i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.34275e6 | − | 134727.i | 0.527550 | − | 0.0529323i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.93322e6 | + | 1.93322e6i | 0.749232 | + | 0.749232i | 0.974335 | − | 0.225103i | \(-0.0722719\pi\) |
−0.225103 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.88285e6i | 1.10219i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 72235.4i | 0.0272468i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.22939e6 | − | 2.22939e6i | −0.829685 | − | 0.829685i | 0.157788 | − | 0.987473i | \(-0.449564\pi\) |
−0.987473 | + | 0.157788i | \(0.949564\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −777227. | + | 240428.i | −0.285410 | + | 0.0882890i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −439862. | + | 439862.i | −0.159391 | + | 0.159391i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.42092e6 | −0.508127 | −0.254064 | − | 0.967187i | \(-0.581767\pi\) | ||||
−0.254064 | + | 0.967187i | \(0.581767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.03364e6 | 0.364800 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.39383e6 | − | 3.39383e6i | 1.18220 | − | 1.18220i | 0.203032 | − | 0.979172i | \(-0.434920\pi\) |
0.979172 | − | 0.203032i | \(-0.0650797\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −29833.2 | − | 297332.i | −0.0102576 | − | 0.102233i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.33242e6 | − | 2.33242e6i | −0.791644 | − | 0.791644i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 3.31303e6i | − | 1.11007i | −0.831826 | − | 0.555036i | \(-0.812704\pi\) | ||
0.831826 | − | 0.555036i | \(-0.187296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 1.15472e6i | − | 0.381974i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.08238e6 | − | 1.08238e6i | −0.353507 | − | 0.353507i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.44357e6 | − | 2.98861e6i | 0.788010 | − | 0.963778i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.40606e6 | − | 2.40606e6i | 0.766179 | − | 0.766179i | −0.211253 | − | 0.977431i | \(-0.567754\pi\) |
0.977431 | + | 0.211253i | \(0.0677544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −21227.1 | −0.00667510 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.13661e6 | 1.59520 | 0.797601 | − | 0.603185i | \(-0.206102\pi\) | ||||
0.797601 | + | 0.603185i | \(0.206102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.81582e6 | + | 1.81582e6i | −0.556942 | + | 0.556942i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.54660e6 | + | 1.89158e6i | −0.468535 | + | 0.573043i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.99619e6 | + | 6.99619e6i | 2.09351 | + | 2.09351i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.51107e6i | − | 0.446658i | −0.974743 | − | 0.223329i | \(-0.928308\pi\) | ||
0.974743 | − | 0.223329i | \(-0.0716924\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 454061.i | 0.132590i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2418.01 | + | 2418.01i | 0.000697562 | + | 0.000697562i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 320513. | + | 3.19439e6i | 0.0913534 | + | 0.910474i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.17875e6 | + | 1.17875e6i | −0.331956 | + | 0.331956i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.07646e6 | −0.299544 | −0.149772 | − | 0.988721i | \(-0.547854\pi\) | ||||
−0.149772 | + | 0.988721i | \(0.547854\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.18241e6 | 0.875086 | 0.437543 | − | 0.899197i | \(-0.355849\pi\) | ||||
0.437543 | + | 0.899197i | \(0.355849\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.20117e6 | + | 3.20117e6i | −0.869877 | + | 0.869877i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.58097e6 | − | 1.04804e6i | −0.424572 | − | 0.281452i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −64861.6 | − | 64861.6i | −0.0172154 | − | 0.0172154i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 945694.i | 0.248089i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.46800e6i | 0.380657i | 0.981720 | + | 0.190329i | \(0.0609553\pi\) | ||||
−0.981720 | + | 0.190329i | \(0.939045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.49367e6 | + | 4.49367e6i | 1.15181 | + | 1.15181i | 0.986189 | + | 0.165623i | \(0.0529634\pi\) |
0.165623 | + | 0.986189i | \(0.447037\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 503185. | − | 50487.6i | 0.127498 | − | 0.0127927i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 727335. | − | 727335.i | 0.182193 | − | 0.182193i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25222.7 | −0.00624641 | −0.00312320 | − | 0.999995i | \(-0.500994\pi\) | ||||
−0.00312320 | + | 0.999995i | \(0.500994\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.70385e6 | 0.906895 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.20085e6 | + | 3.20085e6i | −0.774919 | + | 0.774919i | −0.978962 | − | 0.204043i | \(-0.934592\pi\) |
0.204043 | + | 0.978962i | \(0.434592\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.80311e6 | + | 2.29189e6i | 0.671027 | + | 0.548649i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 598618. | + | 598618.i | 0.141704 | + | 0.141704i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 4.85115e6i | − | 1.13561i | −0.823164 | − | 0.567804i | \(-0.807793\pi\) | ||
0.823164 | − | 0.567804i | \(-0.192207\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.26005e6i | 1.91224i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −927963. | − | 927963.i | −0.212464 | − | 0.212464i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −116831. | − | 95524.3i | −0.0264564 | − | 0.0216314i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.87370e6 | − | 1.87370e6i | 0.419671 | − | 0.419671i | −0.465419 | − | 0.885090i | \(-0.654097\pi\) |
0.885090 | + | 0.465419i | \(0.154097\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.31249e6 | 0.290780 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.47636e6 | 0.542702 | 0.271351 | − | 0.962480i | \(-0.412530\pi\) | ||||
0.271351 | + | 0.962480i | \(0.412530\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.78796e6 | − | 5.78796e6i | 1.25480 | − | 1.25480i | 0.301252 | − | 0.953544i | \(-0.402595\pi\) |
0.953544 | − | 0.301252i | \(-0.0974046\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.07723e6 | − | 208421.i | 0.445504 | − | 0.0447001i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.55806e6 | − | 1.55806e6i | −0.330591 | − | 0.330591i | 0.522220 | − | 0.852811i | \(-0.325104\pi\) |
−0.852811 | + | 0.522220i | \(0.825104\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 105948.i | 0.0222413i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 119570.i | − | 0.0248354i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.68294e6 | − | 6.68294e6i | −1.37346 | − | 1.37346i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −335684. | − | 1.65596e6i | −0.0682649 | − | 0.336756i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.34094e6 | − | 1.34094e6i | 0.269845 | − | 0.269845i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.81391e6 | 0.361224 | 0.180612 | − | 0.983554i | \(-0.442192\pi\) | ||||
0.180612 | + | 0.983554i | \(0.442192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.99670e6 | 0.984737 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −52812.3 | + | 52812.3i | −0.0103007 | + | 0.0103007i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −278946. | − | 2.78012e6i | −0.0538476 | − | 0.536673i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −898602. | − | 898602.i | −0.171690 | − | 0.171690i | 0.616031 | − | 0.787722i | \(-0.288739\pi\) |
−0.787722 | + | 0.616031i | \(0.788739\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.89794e6i | 0.358931i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.86137e6i | 0.348441i | 0.984707 | + | 0.174220i | \(0.0557405\pi\) | ||||
−0.984707 | + | 0.174220i | \(0.944260\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 833714. | + | 833714.i | 0.154490 | + | 0.154490i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.96572e6 | + | 6.07334e6i | −0.910897 | + | 1.11408i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 74147.5 | − | 74147.5i | 0.0134650 | − | 0.0134650i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.04071e6 | 0.546668 | 0.273334 | − | 0.961919i | \(-0.411874\pi\) | ||||
0.273334 | + | 0.961919i | \(0.411874\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 205099. | 0.0365065 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.23935e6 | − | 7.23935e6i | 1.27579 | − | 1.27579i | 0.332791 | − | 0.943001i | \(-0.392010\pi\) |
0.943001 | − | 0.332791i | \(-0.107990\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.68407e6 | + | 4.50581e6i | −0.642835 | + | 0.786221i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −884988. | − | 884988.i | −0.152904 | − | 0.152904i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.84454e6i | − | 1.51315i | −0.653910 | − | 0.756573i | \(-0.726872\pi\) | ||
0.653910 | − | 0.756573i | \(-0.273128\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 203505.i | − | 0.0344764i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 826714. | + | 826714.i | 0.138695 | + | 0.138695i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −339916. | − | 3.38777e6i | −0.0564747 | − | 0.562855i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.17210e6 | + | 9.17210e6i | −1.50918 | + | 1.50918i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.04932e6 | 0.170998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.43074e6 | −1.52213 | −0.761065 | − | 0.648676i | \(-0.775323\pi\) | ||||
−0.761065 | + | 0.648676i | \(0.775323\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.70150e6 | + | 3.70150e6i | −0.591729 | + | 0.591729i | −0.938098 | − | 0.346369i | \(-0.887415\pi\) |
0.346369 | + | 0.938098i | \(0.387415\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 24374.3 | + | 120241.i | 0.00385953 | + | 0.0190394i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.44170e6 | + | 3.44170e6i | 0.539817 | + | 0.539817i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.81716e6i | 0.437696i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 89773.5i | − | 0.0138169i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.94967e6 | + | 2.94967e6i | 0.449734 | + | 0.449734i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.10100e7 | + | 1.10470e6i | −1.66304 | + | 0.166863i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.16615e6 | − | 2.16615e6i | 0.324156 | − | 0.324156i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.06124e7 | 1.57341 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.64526e6 | 0.682365 | 0.341183 | − | 0.939997i | \(-0.389173\pi\) | ||||
0.341183 | + | 0.939997i | \(0.389173\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.18110e6 | + | 2.18110e6i | −0.317451 | + | 0.317451i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.19208e6 | + | 3.42756e6i | 0.604559 | + | 0.494303i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.51024e6 | − | 8.51024e6i | −1.21611 | − | 1.21611i | −0.968983 | − | 0.247128i | \(-0.920513\pi\) |
−0.247128 | − | 0.968983i | \(-0.579487\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.40812e6i | 0.340994i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.05028e6i | 0.147376i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −411645. | − | 411645.i | −0.0572414 | − | 0.0572414i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.14478e6 | − | 2.57125e6i | −0.433369 | − | 0.354334i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.60437e6 | + | 1.60437e6i | −0.219113 | + | 0.219113i | −0.808124 | − | 0.589012i | \(-0.799517\pi\) |
0.589012 | + | 0.808124i | \(0.299517\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.77297e6 | −0.646040 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.79247e6 | 0.240461 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.82070e6 | − | 9.82070e6i | 1.30578 | − | 1.30578i | 0.381355 | − | 0.924429i | \(-0.375458\pi\) |
0.924429 | − | 0.381355i | \(-0.124542\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.62554e6 | + | 464109.i | −0.609595 | + | 0.0611644i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 260542. | + | 260542.i | 0.0340346 | + | 0.0340346i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 7.73484e6i | − | 1.00155i | −0.865579 | − | 0.500773i | \(-0.833049\pi\) | ||
0.865579 | − | 0.500773i | \(-0.166951\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.13215e6i | 1.04380i | 0.853008 | + | 0.521898i | \(0.174776\pi\) | ||||
−0.853008 | + | 0.521898i | \(0.825224\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.36538e6 | − | 1.36538e6i | −0.173727 | − | 0.173727i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.95516e6 | − | 3.28481e6i | −0.625011 | − | 0.414324i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.27077e6 | + | 5.27077e6i | −0.659074 | + | 0.659074i | −0.955161 | − | 0.296087i | \(-0.904318\pi\) |
0.296087 | + | 0.955161i | \(0.404318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.53460e6 | 0.562138 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 484135. | 0.0595013 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.84211e6 | − | 3.84211e6i | 0.468165 | − | 0.468165i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 395531. | + | 3.94206e6i | 0.0477849 | + | 0.476249i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.02268e6 | − | 4.02268e6i | −0.481859 | − | 0.481859i | 0.423866 | − | 0.905725i | \(-0.360673\pi\) |
−0.905725 | + | 0.423866i | \(0.860673\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.33573e6i | 0.514960i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 4.50235e6i | − | 0.530237i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.59217e6 | − | 5.59217e6i | −0.653046 | − | 0.653046i | 0.300679 | − | 0.953725i | \(-0.402787\pi\) |
−0.953725 | + | 0.300679i | \(0.902787\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −181057. | + | 221442.i | −0.0209663 | + | 0.0256429i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.66388e6 | + | 2.66388e6i | −0.305900 | + | 0.305900i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.15230e7 | −1.31220 | −0.656099 | − | 0.754675i | \(-0.727795\pi\) | ||||
−0.656099 | + | 0.754675i | \(0.727795\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.44067e6 | 0.275628 | 0.137814 | − | 0.990458i | \(-0.455992\pi\) | ||||
0.137814 | + | 0.990458i | \(0.455992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.96676e6 | − | 1.96676e6i | 0.220272 | − | 0.220272i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.52922e6 | + | 1.04317e7i | −0.947373 | + | 1.15869i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.35790e6 | − | 3.35790e6i | −0.369910 | − | 0.369910i | 0.497535 | − | 0.867444i | \(-0.334239\pi\) |
−0.867444 | + | 0.497535i | \(0.834239\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 76261.7i | − | 0.00833227i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.55073e6i | 0.709883i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.00846e7 | − | 1.00846e7i | −1.08395 | − | 1.08395i | −0.996137 | − | 0.0878091i | \(-0.972013\pi\) |
−0.0878091 | − | 0.996137i | \(-0.527987\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −338566. | − | 3.37431e6i | −0.0360957 | − | 0.359748i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.65775e6 | + | 8.65775e6i | −0.915571 | + | 0.915571i | −0.996703 | − | 0.0811322i | \(-0.974146\pi\) |
0.0811322 | + | 0.996703i | \(0.474146\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −691475. | −0.0725354 | −0.0362677 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362677 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.11369e6 | 0.428057 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 386094. | − | 386094.i | 0.0398541 | − | 0.0398541i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.99471e6 | + | 3.80296e6i | −0.921059 | + | 0.389424i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.12904e6 | + | 1.12904e6i | 0.114694 | + | 0.114694i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.47074e6i | − | 0.954459i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.44466e7i | − | 1.44441i | −0.691677 | − | 0.722207i | \(-0.743128\pi\) | ||
0.691677 | − | 0.722207i | \(-0.256872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.01679e6 | + | 1.01679e6i | 0.100860 | + | 0.100860i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.23453e7 | − | 1.23868e6i | 1.21497 | − | 0.121906i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.78970e6 | − | 3.78970e6i | 0.370047 | − | 0.370047i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.75287e6 | −0.266707 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.13910e7 | 1.09501 | 0.547504 | − | 0.836803i | \(-0.315578\pi\) | ||||
0.547504 | + | 0.836803i | \(0.315578\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.53859e6 | + | 7.53859e6i | −0.719056 | + | 0.719056i | −0.968412 | − | 0.249356i | \(-0.919781\pi\) |
0.249356 | + | 0.968412i | \(0.419781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.00397e6 | + | 2.45613e6i | 0.284313 | + | 0.232462i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.23733e6 | − | 8.23733e6i | −0.773616 | − | 0.773616i | 0.205120 | − | 0.978737i | \(-0.434241\pi\) |
−0.978737 | + | 0.205120i | \(0.934241\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 257222.i | − | 0.0239716i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 314820.i | − | 0.0291146i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.48193e6 | − | 7.48193e6i | −0.686642 | − | 0.686642i | 0.274846 | − | 0.961488i | \(-0.411373\pi\) |
−0.961488 | + | 0.274846i | \(0.911373\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.42245e7 | − | 1.16303e7i | −1.29549 | − | 1.05923i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.77776e6 | + | 3.77776e6i | −0.341445 | + | 0.341445i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.09855e7 | 0.985390 | 0.492695 | − | 0.870202i | \(-0.336012\pi\) | ||||
0.492695 | + | 0.870202i | \(0.336012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.62528e6 | 0.589795 | 0.294897 | − | 0.955529i | \(-0.404715\pi\) | ||||
0.294897 | + | 0.955529i | \(0.404715\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 640092. | − | 640092.i | 0.0565534 | − | 0.0565534i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −253526. | + | 25437.8i | −0.0222315 | + | 0.00223062i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.61307e6 | + | 2.61307e6i | 0.227424 | + | 0.227424i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.70354e6i | 0.233544i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.89982e6i | 0.591605i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.68585e6 | − | 5.68585e6i | −0.483902 | − | 0.483902i | 0.422473 | − | 0.906375i | \(-0.361162\pi\) |
−0.906375 | + | 0.422473i | \(0.861162\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.73363e6 | − | 5.63220e6i | 0.315407 | − | 0.475794i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.53436e6 | − | 2.53436e6i | 0.212519 | − | 0.212519i | −0.592818 | − | 0.805337i | \(-0.701985\pi\) |
0.805337 | + | 0.592818i | \(0.201985\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −421350. | −0.0350726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.34758e6 | 0.441865 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.05560e7 | − | 1.05560e7i | 0.865864 | − | 0.865864i | −0.126148 | − | 0.992011i | \(-0.540261\pi\) |
0.992011 | + | 0.126148i | \(0.0402614\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 544132. | + | 5.42310e6i | 0.0443076 | + | 0.441592i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.24448e6 | + | 2.24448e6i | 0.181436 | + | 0.181436i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.74404e6i | − | 0.220213i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.17073e7i | 1.72946i | 0.502239 | + | 0.864729i | \(0.332510\pi\) | ||||
−0.502239 | + | 0.864729i | \(0.667490\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 836529. | + | 836529.i | 0.0661680 | + | 0.0661680i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.26658e7 | + | 1.54910e7i | −0.994654 | + | 1.21651i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.59081e6 | − | 5.59081e6i | 0.435906 | − | 0.435906i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −862514. | −0.0667687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.03600e6 | −0.156488 | −0.0782441 | − | 0.996934i | \(-0.524931\pi\) | ||||
−0.0782441 | + | 0.996934i | \(0.524931\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.96544e6 | − | 5.96544e6i | 0.455254 | − | 0.455254i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.37095e6 | − | 4.12285e6i | 0.255434 | − | 0.312410i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 620621. | + | 620621.i | 0.0466958 | + | 0.0466958i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.59025e6i | 0.417653i | 0.977953 | + | 0.208827i | \(0.0669644\pi\) | ||||
−0.977953 | + | 0.208827i | \(0.933036\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.52832e7i | 1.13381i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.07872e7 | + | 1.07872e7i | 0.794664 | + | 0.794664i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.13329e6 | + | 1.12949e7i | 0.0829040 | + | 0.826263i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.29667e6 | + | 2.29667e6i | −0.166840 | + | 0.166840i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.30592e7 | 0.942093 | 0.471046 | − | 0.882108i | \(-0.343876\pi\) | ||||
0.471046 | + | 0.882108i | \(0.343876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −513444. | −0.0367837 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −271316. | + | 271316.i | −0.0193032 | + | 0.0193032i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.94931e6 | − | 1.20600e6i | 0.420360 | − | 0.0852125i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.15104e7 | + | 1.15104e7i | 0.807707 | + | 0.807707i | 0.984286 | − | 0.176579i | \(-0.0565032\pi\) |
−0.176579 | + | 0.984286i | \(0.556503\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 7.22606e6i | − | 0.503597i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.04669e6i | 0.626176i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.05032e7 | + | 1.05032e7i | 0.722038 | + | 0.722038i | 0.969020 | − | 0.246982i | \(-0.0794388\pi\) |
−0.246982 | + | 0.969020i | \(0.579439\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.33527e6 | + | 434985.i | −0.296004 | + | 0.0296999i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.63524e6 | − | 5.63524e6i | 0.382159 | − | 0.382159i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.39982e6 | 0.633153 | 0.316576 | − | 0.948567i | \(-0.397467\pi\) | ||||
0.316576 | + | 0.948567i | \(0.397467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 806364. | 0.0539493 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.05839e7 | + | 1.05839e7i | −0.703354 | + | 0.703354i | −0.965129 | − | 0.261775i | \(-0.915692\pi\) |
0.261775 | + | 0.965129i | \(0.415692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.86699e6 | + | 6.43226e6i | 0.519299 | + | 0.424593i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.98724e6 | − | 8.98724e6i | −0.589285 | − | 0.589285i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.66865e6i | 0.108683i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.49520e6i | 0.161438i | 0.996737 | + | 0.0807189i | \(0.0257216\pi\) | ||||
−0.996737 | + | 0.0807189i | \(0.974278\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.84446e6 | − | 2.84446e6i | −0.182815 | − | 0.182815i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.21952e7 | − | 9.97113e6i | −0.778613 | − | 0.636615i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.90732e7 | − | 1.90732e7i | 1.20972 | − | 1.20972i | 0.238597 | − | 0.971119i | \(-0.423312\pi\) |
0.971119 | − | 0.238597i | \(-0.0766876\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.61805e6 | 0.353982 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.61451e6 | 0.163655 | 0.0818274 | − | 0.996647i | \(-0.473924\pi\) | ||||
0.0818274 | + | 0.996647i | \(0.473924\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 577409. | − | 577409.i | 0.0359064 | − | 0.0359064i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.47178e6 | − | 749690.i | 0.461605 | − | 0.0463157i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −91854.3 | − | 91854.3i | −0.00563782 | − | 0.00563782i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.65153e7i | − | 1.00709i | −0.863968 | − | 0.503547i | \(-0.832028\pi\) | ||
0.863968 | − | 0.503547i | \(-0.167972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 6.54564e6i | − | 0.396567i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −5.55165e6 | − | 5.55165e6i | −0.334174 | − | 0.334174i | 0.519995 | − | 0.854169i | \(-0.325934\pi\) |
−0.854169 | + | 0.519995i | \(0.825934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.45597e7 | − | 4.97857e6i | 1.46882 | − | 0.297749i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −433155. | + | 433155.i | −0.0257390 | + | 0.0257390i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.04309e6 | 0.415834 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.88763e6 | −0.462721 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.97011e6 | + | 2.97011e6i | −0.173128 | + | 0.173128i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −143289. | − | 1.42809e6i | −0.00829925 | − | 0.0827145i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.86188e6 | + | 7.86188e6i | 0.452470 | + | 0.452470i | 0.896174 | − | 0.443704i | \(-0.146336\pi\) |
−0.443704 | + | 0.896174i | \(0.646336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.18982e6i | − | 0.0680438i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 701038.i | 0.0398382i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.46393e6 | + | 2.46393e6i | 0.139138 | + | 0.139138i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.41206e6 | + | 1.72702e6i | −0.0792383 | + | 0.0969126i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.64771e6 | + | 1.64771e6i | −0.0918830 | + | 0.0918830i | −0.751554 | − | 0.659671i | \(-0.770696\pi\) |
0.659671 | + | 0.751554i | \(0.270696\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.24163e7 | 0.688056 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.43345e7 | −0.789409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.08242e7 | + | 1.08242e7i | −0.592388 | + | 0.592388i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −567478. | + | 694055.i | −0.0308645 | + | 0.0377489i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 237977. | + | 237977.i | 0.0128633 | + | 0.0128633i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.20143e7i | 0.645396i | 0.946502 | + | 0.322698i | \(0.104590\pi\) | ||||
−0.946502 | + | 0.322698i | \(0.895410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.17390e7i | 0.626727i | 0.949633 | + | 0.313364i | \(0.101456\pi\) | ||||
−0.949633 | + | 0.313364i | \(0.898544\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.75535e6 | − | 6.75535e6i | −0.358444 | − | 0.358444i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.27444e6 | + | 2.26682e7i | 0.119944 | + | 1.19543i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.69834e6 | + | 5.69834e6i | −0.298671 | + | 0.298671i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 597451. | 0.0311238 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.76061e7 | 1.42938 | 0.714690 | − | 0.699441i | \(-0.246568\pi\) | ||||
0.714690 | + | 0.699441i | \(0.246568\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.25518e7 | − | 2.25518e7i | 1.16060 | − | 1.16060i | 0.176250 | − | 0.984345i | \(-0.443603\pi\) |
0.984345 | − | 0.176250i | \(-0.0563966\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.09901e6 | − | 7.69189e6i | 0.260826 | − | 0.393458i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.00811e7 | − | 1.00811e7i | −0.512559 | − | 0.512559i | 0.402750 | − | 0.915310i | \(-0.368054\pi\) |
−0.915310 | + | 0.402750i | \(0.868054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.93364e7i | − | 1.48259i | −0.671180 | − | 0.741294i | \(-0.734212\pi\) | ||
0.671180 | − | 0.741294i | \(-0.265788\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.31303e6i | 0.317128i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.18300e6 | − | 7.18300e6i | −0.358669 | − | 0.358669i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.44961e6 | − | 245785.i | 0.121585 | − | 0.0121994i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.22611e7 | + | 1.22611e7i | −0.604944 | + | 0.604944i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.26054e7 | −0.618230 | −0.309115 | − | 0.951025i | \(-0.600033\pi\) | ||||
−0.309115 | + | 0.951025i | \(0.600033\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.67378e7 | 0.816036 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.25235e6 | + | 7.25235e6i | −0.351488 | + | 0.351488i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.16304e7 | − | 9.50935e6i | −0.560343 | − | 0.458151i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.43684e6 | + | 1.43684e6i | 0.0688176 | + | 0.0688176i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.74759e6i | 0.273663i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.96837e7i | − | 1.40506i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.64758e7 | + | 1.64758e7i | 0.775310 | + | 0.775310i | 0.979029 | − | 0.203720i | \(-0.0653031\pi\) |
−0.203720 | + | 0.979029i | \(0.565303\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 5.17855e6 | + | 4.23412e6i | 0.242266 | + | 0.198083i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.84182e7 | − | 1.84182e7i | 0.856635 | − | 0.856635i | −0.134305 | − | 0.990940i | \(-0.542880\pi\) |
0.990940 | + | 0.134305i | \(0.0428803\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.03573e7 | −1.86612 | −0.933060 | − | 0.359720i | \(-0.882872\pi\) | ||||
−0.933060 | + | 0.359720i | \(0.882872\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −511404. | −0.0235102 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.37186e7 | + | 1.37186e7i | −0.627020 | + | 0.627020i | −0.947317 | − | 0.320297i | \(-0.896217\pi\) |
0.320297 | + | 0.947317i | \(0.396217\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.25326e7 | − | 1.25747e6i | 0.569510 | − | 0.0571424i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.46247e6 | + | 3.46247e6i | 0.156436 | + | 0.156436i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.37898e7i | 1.96709i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.02470e6i | − | 0.179758i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.82172e6 | + | 7.82172e6i | 0.347350 | + | 0.347350i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 435208. | + | 1.40689e6i | 0.0192166 | + | 0.0621211i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7.68375e6 | + | 7.68375e6i | −0.337345 | + | 0.337345i | −0.855367 | − | 0.518022i | \(-0.826668\pi\) |
0.518022 | + | 0.855367i | \(0.326668\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.34723e6 | −0.233430 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.78611e7 | −0.775298 | −0.387649 | − | 0.921807i | \(-0.626713\pi\) | ||||
−0.387649 | + | 0.921807i | \(0.626713\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.62792e7 | + | 1.62792e7i | −0.702637 | + | 0.702637i | −0.964976 | − | 0.262339i | \(-0.915506\pi\) |
0.262339 | + | 0.964976i | \(0.415506\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 10543.1 | + | 105078.i | 0.000452491 | + | 0.00450975i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.07996e6 | + | 5.07996e6i | 0.216796 | + | 0.216796i | 0.807147 | − | 0.590351i | \(-0.201011\pi\) |
−0.590351 | + | 0.807147i | \(0.701011\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.87102e6i | − | 0.0794008i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.77158e7i | − | 1.16959i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.82077e6 | + | 7.82077e6i | 0.328187 | + | 0.328187i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.32757e7 | − | 2.84674e7i | 0.971281 | − | 1.18793i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.00621e6 | − | 2.00621e6i | 0.0832522 | − | 0.0832522i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.55768e7 | −0.642805 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.20106e6 | −0.213442 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 413761. | − | 413761.i | 0.0168861 | − | 0.0168861i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.34363e7 | + | 2.86639e7i | −0.951192 | + | 1.16336i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.23719e7 | + | 1.23719e7i | 0.499367 | + | 0.499367i | 0.911241 | − | 0.411874i | \(-0.135126\pi\) |
−0.411874 | + | 0.911241i | \(0.635126\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 2.30418e7i | − | 0.924925i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.71338e7i | − | 0.684003i | −0.939699 | − | 0.342002i | \(-0.888895\pi\) | ||
0.939699 | − | 0.342002i | \(-0.111105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.57506e7 | − | 2.57506e7i | −1.02237 | − | 1.02237i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −282812. | − | 2.81865e6i | −0.0111672 | − | 0.111298i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.95926e6 | + | 1.95926e6i | −0.0769428 | + | 0.0769428i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.74717e6 | −0.0682411 | −0.0341206 | − | 0.999418i | \(-0.510863\pi\) | ||||
−0.0341206 | + | 0.999418i | \(0.510863\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.88636e6 | −0.384050 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.81668e6 | + | 2.81668e6i | −0.108826 | + | 0.108826i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.06411e7 | − | 2.69413e7i | −1.56175 | − | 1.03529i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 9.53132e6 | + | 9.53132e6i | 0.364296 | + | 0.364296i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.80243e7i | 1.44551i | 0.691102 | + | 0.722757i | \(0.257125\pi\) | ||||
−0.691102 | + | 0.722757i | \(0.742875\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 9.04887e6i | − | 0.342153i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.87226e6 | − | 9.87226e6i | −0.371289 | − | 0.371289i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.14084e7 | − | 2.14804e6i | 0.800858 | − | 0.0803550i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.05384e7 | + | 1.05384e7i | −0.392127 | + | 0.392127i | −0.875445 | − | 0.483318i | \(-0.839432\pi\) |
0.483318 | + | 0.875445i | \(0.339432\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.22588e6 | 0.0453717 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.44456e7 | −1.63627 | −0.818135 | − | 0.575026i | \(-0.804992\pi\) | ||||
−0.818135 | + | 0.575026i | \(0.804992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.75230e7 | − | 1.75230e7i | 0.641697 | − | 0.641697i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −788887. | − | 645015.i | −0.0287366 | − | 0.0234958i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.69931e7 | − | 1.69931e7i | −0.615740 | − | 0.615740i | 0.328696 | − | 0.944436i | \(-0.393391\pi\) |
−0.944436 | + | 0.328696i | \(0.893391\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73065e6i | 0.278644i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.77533e6i | 0.0636544i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.89702e7 | + | 2.89702e7i | 1.03328 | + | 1.03328i | 0.999427 | + | 0.0338563i | \(0.0107788\pi\) |
0.0338563 | + | 0.999427i | \(0.489221\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.79438e7 | − | 1.46713e7i | −0.636656 | − | 0.520547i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.05627e6 | + | 4.05627e6i | −0.143168 | + | 0.143168i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 821914. | 0.0288589 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.56744e7 | −1.24609 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.09760e7 | − | 3.09760e7i | 1.07636 | − | 1.07636i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.41592e7 | − | 5.43413e6i | 1.87221 | − | 0.187850i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.69845e7 | − | 1.69845e7i | −0.584101 | − | 0.584101i | 0.351927 | − | 0.936028i | \(-0.385527\pi\) |
−0.936028 | + | 0.351927i | \(0.885527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1.52838e6i | − | 0.0522905i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.58022e7i | − | 1.55897i | −0.626419 | − | 0.779486i | \(-0.715480\pi\) | ||
0.626419 | − | 0.779486i | \(-0.284520\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.13370e6 | + | 2.13370e6i | 0.0722521 | + | 0.0722521i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −925920. | − | 4.56764e6i | −0.0311934 | − | 0.153879i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.14731e7 | + | 1.14731e7i | −0.384544 | + | 0.384544i | −0.872736 | − | 0.488192i | \(-0.837657\pi\) |
0.488192 | + | 0.872736i | \(0.337657\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.10718e7 | −1.36958 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.14375e7 | −0.711215 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.41644e7 | + | 2.41644e7i | −0.797613 | + | 0.797613i | −0.982719 | − | 0.185106i | \(-0.940737\pi\) |
0.185106 | + | 0.982719i | \(0.440737\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.39547e6 | − | 5.37739e7i | −0.177190 | − | 1.76596i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −567872. | − | 567872.i | −0.0185549 | − | 0.0185549i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.83546e7i | 0.921792i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.55838e7i | − | 0.504067i | −0.967719 | − | 0.252033i | \(-0.918901\pi\) | ||
0.967719 | − | 0.252033i | \(-0.0810993\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.16164e6 | + | 2.16164e6i | 0.0695680 | + | 0.0695680i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.86239e7 | + | 3.50085e7i | −0.916581 | + | 1.12103i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.51999e6 | − | 6.51999e6i | 0.207735 | − | 0.207735i | −0.595569 | − | 0.803304i | \(-0.703073\pi\) |
0.803304 | + | 0.595569i | \(0.203073\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.37395e7 | 1.06961 |
(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 | 160.6.n.d.63.5 | yes | 16 | |
4.3 | odd | 2 | 160.6.n.c.63.4 | ✓ | 16 | ||
5.2 | odd | 4 | 160.6.n.c.127.4 | yes | 16 | ||
20.7 | even | 4 | inner | 160.6.n.d.127.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.n.c.63.4 | ✓ | 16 | 4.3 | odd | 2 | ||
160.6.n.c.127.4 | yes | 16 | 5.2 | odd | 4 | ||
160.6.n.d.63.5 | yes | 16 | 1.1 | even | 1 | trivial | |
160.6.n.d.127.5 | yes | 16 | 20.7 | even | 4 | inner |