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: | \( x^{16} + 1375 x^{14} + 743087 x^{12} + 198706725 x^{10} + 26872635188 x^{8} + 1612811892960 x^{6} + \cdots + 177426662425600 \) |
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 | 63.6 | ||
Root | \(13.0932i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 160.63 |
Dual form | 160.6.n.c.127.6 |
$q$-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 | ||||||||
\(3\) | 12.0932 | − | 12.0932i | 0.775776 | − | 0.775776i | −0.203334 | − | 0.979110i | \(-0.565178\pi\) |
0.979110 | + | 0.203334i | \(0.0651776\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −34.4070 | + | 44.0586i | −0.615492 | + | 0.788143i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −74.8536 | − | 74.8536i | −0.577388 | − | 0.577388i | 0.356795 | − | 0.934183i | \(-0.383869\pi\) |
−0.934183 | + | 0.356795i | \(0.883869\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 49.4886i | − | 0.203657i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 432.151i | − | 1.07685i | −0.842675 | − | 0.538423i | \(-0.819020\pi\) | ||
0.842675 | − | 0.538423i | \(-0.180980\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 639.311 | + | 639.311i | 1.04919 | + | 1.04919i | 0.998726 | + | 0.0504631i | \(0.0160697\pi\) |
0.0504631 | + | 0.998726i | \(0.483930\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 116.717 | + | 948.896i | 0.133939 | + | 1.08891i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1424.91 | + | 1424.91i | −1.19582 | + | 1.19582i | −0.220416 | + | 0.975406i | \(0.570741\pi\) |
−0.975406 | + | 0.220416i | \(0.929259\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2374.16 | −1.50878 | −0.754391 | − | 0.656426i | \(-0.772068\pi\) | ||||
−0.754391 | + | 0.656426i | \(0.772068\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1810.43 | −0.895847 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 170.300 | − | 170.300i | 0.0671265 | − | 0.0671265i | −0.672747 | − | 0.739873i | \(-0.734886\pi\) |
0.739873 | + | 0.672747i | \(0.234886\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −757.313 | − | 3031.85i | −0.242340 | − | 0.970191i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2340.16 | + | 2340.16i | 0.617784 | + | 0.617784i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5000.18i | 1.10406i | 0.833826 | + | 0.552028i | \(0.186146\pi\) | ||||
−0.833826 | + | 0.552028i | \(0.813854\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7161.45i | 1.33843i | 0.743067 | + | 0.669217i | \(0.233370\pi\) | ||||
−0.743067 | + | 0.669217i | \(0.766630\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5226.06 | − | 5226.06i | −0.835391 | − | 0.835391i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5873.43 | − | 722.451i | 0.810441 | − | 0.0996870i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4647.57 | + | 4647.57i | −0.558113 | + | 0.558113i | −0.928770 | − | 0.370657i | \(-0.879133\pi\) |
0.370657 | + | 0.928770i | \(0.379133\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15462.6 | 1.62787 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1578.52 | 0.146653 | 0.0733264 | − | 0.997308i | \(-0.476639\pi\) | ||||
0.0733264 | + | 0.997308i | \(0.476639\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4528.62 | + | 4528.62i | −0.373504 | + | 0.373504i | −0.868752 | − | 0.495248i | \(-0.835077\pi\) |
0.495248 | + | 0.868752i | \(0.335077\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2180.40 | + | 1702.76i | 0.160511 | + | 0.125349i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 489.826 | + | 489.826i | 0.0323443 | + | 0.0323443i | 0.723094 | − | 0.690750i | \(-0.242719\pi\) |
−0.690750 | + | 0.723094i | \(0.742719\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5600.89i | − | 0.333247i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 34463.4i | 1.85538i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1533.89 | − | 1533.89i | −0.0750073 | − | 0.0750073i | 0.668608 | − | 0.743615i | \(-0.266891\pi\) |
−0.743615 | + | 0.668608i | \(0.766891\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19039.9 | + | 14869.0i | 0.848709 | + | 0.662789i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −28711.1 | + | 28711.1i | −1.17048 | + | 1.17048i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2548.73 | 0.0953222 | 0.0476611 | − | 0.998864i | \(-0.484823\pi\) | ||||
0.0476611 | + | 0.998864i | \(0.484823\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −31490.8 | −1.08358 | −0.541788 | − | 0.840515i | \(-0.682252\pi\) | ||||
−0.541788 | + | 0.840515i | \(0.682252\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3704.40 | + | 3704.40i | −0.117589 | + | 0.117589i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −50163.9 | + | 6170.32i | −1.47268 | + | 0.181144i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −37974.7 | − | 37974.7i | −1.03349 | − | 1.03349i | −0.999419 | − | 0.0340720i | \(-0.989152\pi\) |
−0.0340720 | − | 0.999419i | \(-0.510848\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 4118.92i | − | 0.104150i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 41449.8i | 0.975835i | 0.872890 | + | 0.487917i | \(0.162243\pi\) | ||||
−0.872890 | + | 0.487917i | \(0.837757\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37660.5 | + | 37660.5i | 0.827140 | + | 0.827140i | 0.987120 | − | 0.159980i | \(-0.0511430\pi\) |
−0.159980 | + | 0.987120i | \(0.551143\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −45822.9 | − | 27506.3i | −0.940653 | − | 0.564650i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −32348.0 | + | 32348.0i | −0.621757 | + | 0.621757i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39767.6 | 0.716905 | 0.358453 | − | 0.933548i | \(-0.383304\pi\) | ||||
0.358453 | + | 0.933548i | \(0.383304\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 68625.6 | 1.16218 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −40365.6 | + | 40365.6i | −0.643156 | + | 0.643156i | −0.951330 | − | 0.308174i | \(-0.900282\pi\) |
0.308174 | + | 0.951330i | \(0.400282\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13752.6 | − | 111807.i | −0.206461 | − | 1.67850i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 60468.0 | + | 60468.0i | 0.856500 | + | 0.856500i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 48313.3i | 0.646535i | 0.946308 | + | 0.323267i | \(0.104781\pi\) | ||||
−0.946308 | + | 0.323267i | \(0.895219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 95709.4i | − | 1.21158i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 86604.6 | + | 86604.6i | 1.03833 | + | 1.03833i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 81687.9 | − | 104602.i | 0.928642 | − | 1.18914i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 60161.4 | − | 60161.4i | 0.649216 | − | 0.649216i | −0.303588 | − | 0.952803i | \(-0.598185\pi\) |
0.952803 | + | 0.303588i | \(0.0981846\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21386.5 | −0.219307 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 802.130 | 0.00782422 | 0.00391211 | − | 0.999992i | \(-0.498755\pi\) | ||||
0.00391211 | + | 0.999992i | \(0.498755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12372.7 | − | 12372.7i | 0.114914 | − | 0.114914i | −0.647312 | − | 0.762226i | \(-0.724107\pi\) |
0.762226 | + | 0.647312i | \(0.224107\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 62291.6 | − | 79765.0i | 0.551386 | − | 0.706056i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −143629. | − | 143629.i | −1.21278 | − | 1.21278i | −0.970108 | − | 0.242675i | \(-0.921975\pi\) |
−0.242675 | − | 0.970108i | \(-0.578025\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 226385.i | − | 1.82508i | −0.408992 | − | 0.912538i | \(-0.634120\pi\) | ||
0.408992 | − | 0.912538i | \(-0.365880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 112408.i | 0.865941i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −70878.0 | − | 70878.0i | −0.522174 | − | 0.522174i | 0.396053 | − | 0.918228i | \(-0.370380\pi\) |
−0.918228 | + | 0.396053i | \(0.870380\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1643.65 | + | 13362.7i | 0.0115895 | + | 0.0942211i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 31638.6 | − | 31638.6i | 0.213674 | − | 0.213674i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 213320. | 1.38091 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −25703.1 | −0.159596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 19089.3 | − | 19089.3i | 0.113770 | − | 0.113770i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 159636. | + | 70950.8i | 0.913808 | + | 0.406146i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −234054. | − | 234054.i | −1.28768 | − | 1.28768i | −0.936194 | − | 0.351484i | \(-0.885677\pi\) |
−0.351484 | − | 0.936194i | \(-0.614323\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 109531.i | 0.579510i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 108910.i | 0.554483i | 0.960800 | + | 0.277241i | \(0.0894202\pi\) | ||||
−0.960800 | + | 0.277241i | \(0.910580\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 177714. | + | 177714.i | 0.871152 | + | 0.871152i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −183622. | + | 22586.1i | −0.867143 | + | 0.106661i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 229642. | − | 229642.i | 1.04532 | − | 1.04532i | 0.0463976 | − | 0.998923i | \(-0.485226\pi\) |
0.998923 | − | 0.0463976i | \(-0.0147741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −304587. | −1.33713 | −0.668565 | − | 0.743653i | \(-0.733091\pi\) | ||||
−0.668565 | + | 0.743653i | \(0.733091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11847.1 | 0.0501838 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 276279. | − | 276279.i | 1.12981 | − | 1.12981i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −220301. | − | 172042.i | −0.870154 | − | 0.679537i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −67732.4 | − | 67732.4i | −0.258525 | − | 0.258525i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 306960.i | 1.13270i | 0.824164 | + | 0.566351i | \(0.191645\pi\) | ||||
−0.824164 | + | 0.566351i | \(0.808355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 37640.8i | 0.134343i | 0.997741 | + | 0.0671717i | \(0.0213975\pi\) | ||||
−0.997741 | + | 0.0671717i | \(0.978602\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 70517.0 | + | 70517.0i | 0.243537 | + | 0.243537i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −315523. | − | 246404.i | −1.05488 | − | 0.823795i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −221182. | + | 221182.i | −0.716144 | + | 0.716144i | −0.967813 | − | 0.251669i | \(-0.919020\pi\) |
0.251669 | + | 0.967813i | \(0.419020\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −37099.0 | −0.116378 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −25495.1 | −0.0775160 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 338684. | − | 338684.i | 0.998447 | − | 0.998447i | −0.00155132 | − | 0.999999i | \(-0.500494\pi\) |
0.999999 | + | 0.00155132i | \(0.000493802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 410066. | − | 50439.5i | 1.17258 | − | 0.144232i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 192088. | + | 192088.i | 0.532979 | + | 0.532979i | 0.921458 | − | 0.388479i | \(-0.126999\pi\) |
−0.388479 | + | 0.921458i | \(0.626999\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 446144.i | 1.20160i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 117494.i | 0.307274i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −358281. | − | 358281.i | −0.910142 | − | 0.910142i | 0.0861412 | − | 0.996283i | \(-0.472546\pi\) |
−0.996283 | + | 0.0861412i | \(0.972546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −170257. | + | 283632.i | −0.420252 | + | 0.700101i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30822.2 | − | 30822.2i | 0.0739486 | − | 0.0739486i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 425231. | 0.991956 | 0.495978 | − | 0.868335i | \(-0.334810\pi\) | ||||
0.495978 | + | 0.868335i | \(0.334810\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −698872. | −1.58563 | −0.792813 | − | 0.609465i | \(-0.791384\pi\) | ||||
−0.792813 | + | 0.609465i | \(0.791384\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −380823. | + | 380823.i | −0.840612 | + | 0.840612i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −44856.2 | − | 364675.i | −0.0963591 | − | 0.783387i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 615778. | + | 615778.i | 1.28772 | + | 1.28772i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 350339.i | − | 0.713402i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 191378.i | 0.379584i | 0.981824 | + | 0.189792i | \(0.0607813\pi\) | ||||
−0.981824 | + | 0.189792i | \(0.939219\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 72951.2 | + | 72951.2i | 0.140974 | + | 0.140974i | 0.774072 | − | 0.633098i | \(-0.218217\pi\) |
−0.633098 | + | 0.774072i | \(0.718217\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −532021. | + | 681258.i | −1.00194 | + | 1.28300i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 328053. | − | 328053.i | 0.602252 | − | 0.602252i | −0.338657 | − | 0.940910i | \(-0.609973\pi\) |
0.940910 | + | 0.338657i | \(0.109973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 355637. | 0.636611 | 0.318306 | − | 0.947988i | \(-0.396886\pi\) | ||||
0.318306 | + | 0.947988i | \(0.396886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −918467. | −1.60352 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 374282. | − | 374282.i | 0.637468 | − | 0.637468i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54312.2 | + | 69547.3i | −0.0902636 | + | 0.115583i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8427.89 | − | 8427.89i | −0.0136708 | − | 0.0136708i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.02600e6i | 1.62472i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 636070.i | 0.983555i | 0.870721 | + | 0.491778i | \(0.163653\pi\) | ||||
−0.870721 | + | 0.491778i | \(0.836347\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 501258. | + | 501258.i | 0.757029 | + | 0.757029i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −43708.1 | − | 355341.i | −0.0644861 | − | 0.524263i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 536060. | − | 536060.i | 0.772795 | − | 0.772795i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 910869. | 1.28335 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.82193e6 | −2.50929 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 254820. | − | 254820.i | 0.343140 | − | 0.343140i | −0.514407 | − | 0.857546i | \(-0.671988\pi\) |
0.857546 | + | 0.514407i | \(0.171988\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −150042. | + | 37478.3i | −0.197586 | + | 0.0493542i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 623645. | + | 623645.i | 0.803291 | + | 0.803291i | 0.983608 | − | 0.180318i | \(-0.0577126\pi\) |
−0.180318 | + | 0.983608i | \(0.557713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 156295.i | − | 0.196950i | −0.995140 | − | 0.0984749i | \(-0.968604\pi\) | ||
0.995140 | − | 0.0984749i | \(-0.0313964\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 782379.i | 0.964689i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 580116. | + | 580116.i | 0.700044 | + | 0.700044i | 0.964420 | − | 0.264376i | \(-0.0851660\pi\) |
−0.264376 | + | 0.964420i | \(0.585166\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −38434.5 | + | 4727.57i | −0.0453996 | + | 0.00558429i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 480916. | − | 480916.i | 0.556158 | − | 0.556158i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −909455. | −1.02988 | −0.514940 | − | 0.857226i | \(-0.672186\pi\) | ||||
−0.514940 | + | 0.857226i | \(0.672186\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −955010. | −1.05917 | −0.529585 | − | 0.848257i | \(-0.677652\pi\) | ||||
−0.529585 | + | 0.848257i | \(0.677652\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 261240. | − | 261240.i | 0.283808 | − | 0.283808i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 246767. | + | 192710.i | 0.262647 | + | 0.205111i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.51783e6 | − | 1.51783e6i | −1.58300 | − | 1.58300i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 976296.i | 0.997891i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 211230.i | 0.211627i | 0.994386 | + | 0.105814i | \(0.0337447\pi\) | ||||
−0.994386 | + | 0.105814i | \(0.966255\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −73595.1 | − | 73595.1i | −0.0722849 | − | 0.0722849i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.51841e6 | − | 1.18578e6i | −1.46231 | − | 1.14197i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −398055. | + | 398055.i | −0.375933 | + | 0.375933i | −0.869632 | − | 0.493700i | \(-0.835644\pi\) |
0.493700 | + | 0.869632i | \(0.335644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 695775. | 0.644495 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 247452. | 0.224848 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 359761. | − | 359761.i | 0.320719 | − | 0.320719i | −0.528324 | − | 0.849043i | \(-0.677179\pi\) |
0.849043 | + | 0.528324i | \(0.177179\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 120357. | − | 14804.3i | 0.105283 | − | 0.0129501i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 584260. | + | 584260.i | 0.501566 | + | 0.501566i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.65759e6i | 1.39668i | 0.715768 | + | 0.698338i | \(0.246077\pi\) | ||||
−0.715768 | + | 0.698338i | \(0.753923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14221e6i | 1.77189i | 0.463786 | + | 0.885947i | \(0.346491\pi\) | ||||
−0.463786 | + | 0.885947i | \(0.653509\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.15743e6 | − | 1.15743e6i | −0.939913 | − | 0.939913i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.31021e6 | + | 327273.i | −1.04475 | + | 0.260963i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −889567. | + | 889567.i | −0.696593 | + | 0.696593i | −0.963674 | − | 0.267081i | \(-0.913941\pi\) |
0.267081 | + | 0.963674i | \(0.413941\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 354410. | 0.272581 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.06917e6 | 1.56326 | 0.781628 | − | 0.623744i | \(-0.214389\pi\) | ||||
0.781628 | + | 0.623744i | \(0.214389\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22257.7 | − | 22257.7i | 0.0165201 | − | 0.0165201i | −0.698798 | − | 0.715319i | \(-0.746282\pi\) |
0.715319 | + | 0.698798i | \(0.246282\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −277106. | − | 2.25283e6i | −0.202085 | − | 1.64292i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −118158. | − | 118158.i | −0.0846755 | − | 0.0846755i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 2.64090e6i | − | 1.85998i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.45508e6i | − | 1.00729i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.96878e6 | + | 1.96878e6i | 1.33976 | + | 1.33976i | 0.896285 | + | 0.443478i | \(0.146256\pi\) |
0.443478 | + | 0.896285i | \(0.353744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87694.2 | + | 112293.i | −0.0586700 | + | 0.0751275i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.01130e6 | − | 1.01130e6i | 0.665258 | − | 0.665258i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 217749. | 0.140857 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 677967. | 0.431313 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9700.28 | − | 9700.28i | 0.00606984 | − | 0.00606984i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.08351e6 | − | 1.38744e6i | 0.666932 | − | 0.854013i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.43983e6 | − | 1.43983e6i | −0.871897 | − | 0.871897i | 0.120782 | − | 0.992679i | \(-0.461460\pi\) |
−0.992679 | + | 0.120782i | \(0.961460\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 299251.i | − | 0.178295i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 1.55159e6i | − | 0.909652i | −0.890580 | − | 0.454826i | \(-0.849701\pi\) | ||
0.890580 | − | 0.454826i | \(-0.150299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.08899e6 | + | 1.08899e6i | 0.628293 | + | 0.628293i | 0.947638 | − | 0.319346i | \(-0.103463\pi\) |
−0.319346 | + | 0.947638i | \(0.603463\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −35753.1 | − | 290668.i | −0.0203019 | − | 0.165052i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 408691. | − | 408691.i | 0.228427 | − | 0.228427i | −0.583609 | − | 0.812035i | \(-0.698360\pi\) |
0.812035 | + | 0.583609i | \(0.198360\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.16083e6 | 1.18890 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.47386e6 | −1.88170 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.38298e6 | − | 3.38298e6i | 1.80423 | − | 1.80423i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.45414e6 | − | 2.42245e6i | 0.763654 | − | 1.27217i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.73771e6 | − | 2.73771e6i | −1.41585 | − | 1.41585i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 73330.5i | − | 0.0373504i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.36055e6i | 1.18425i | 0.805846 | + | 0.592125i | \(0.201711\pi\) | ||||
−0.805846 | + | 0.592125i | \(0.798289\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 230002. | + | 230002.i | 0.113663 | + | 0.113663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.97970e6 | − | 366513.i | 1.45064 | − | 0.178434i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 288933. | − | 288933.i | 0.138587 | − | 0.138587i | −0.634410 | − | 0.772997i | \(-0.718757\pi\) |
0.772997 | + | 0.634410i | \(0.218757\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.71428e6 | −0.810181 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.09483e6 | 1.44129 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.67731e6 | + | 1.67731e6i | −0.769800 | + | 0.769800i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 181474. | + | 141720.i | 0.0820853 | + | 0.0641036i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 253490. | + | 253490.i | 0.113015 | + | 0.113015i | 0.761353 | − | 0.648338i | \(-0.224535\pi\) |
−0.648338 | + | 0.761353i | \(0.724535\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.91470e6i | 0.841467i | 0.907184 | + | 0.420734i | \(0.138227\pi\) | ||||
−0.907184 | + | 0.420734i | \(0.861773\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.99218e6i | 1.29634i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.91118e6 | + | 1.91118e6i | 0.816327 | + | 0.816327i | 0.985574 | − | 0.169247i | \(-0.0541335\pi\) |
−0.169247 | + | 0.985574i | \(0.554133\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.82622e6 | − | 1.42616e6i | −0.769098 | − | 0.600618i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.57971e6 | − | 2.57971e6i | 1.07127 | − | 1.07127i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.08922e6 | 0.446046 | 0.223023 | − | 0.974813i | \(-0.428408\pi\) | ||||
0.223023 | + | 0.974813i | \(0.428408\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.16055e6 | 1.27642 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −310832. | + | 310832.i | −0.123811 | + | 0.123811i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.95505e6 | + | 363481.i | −1.16100 | + | 0.142807i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.58206e6 | − | 2.58206e6i | −1.00069 | − | 1.00069i | −1.00000 | 0.000695182i | \(-0.999779\pi\) | |
−0.000695182 | − | 1.00000i | \(-0.500221\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 78118.7i | − | 0.0298668i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 229634.i | 0.0866166i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.18094e6 | − | 2.18094e6i | −0.811656 | − | 0.811656i | 0.173226 | − | 0.984882i | \(-0.444581\pi\) |
−0.984882 | + | 0.173226i | \(0.944581\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.78852e6 | − | 1.07248e6i | 1.02399 | − | 0.393832i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.19667e6 | + | 3.19667e6i | −1.15836 | + | 1.15836i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.02445e6 | −1.79676 | −0.898381 | − | 0.439218i | \(-0.855256\pi\) | ||||
−0.898381 | + | 0.439218i | \(0.855256\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.66091e6 | −1.99790 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.02036e6 | + | 1.02036e6i | −0.355433 | + | 0.355433i | −0.862126 | − | 0.506694i | \(-0.830868\pi\) |
0.506694 | + | 0.862126i | \(0.330868\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −312208. | − | 2.53821e6i | −0.107347 | − | 0.872720i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 224115. | + | 224115.i | 0.0760666 | + | 0.0760666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.41206e6i | 0.808190i | 0.914717 | + | 0.404095i | \(0.132414\pi\) | ||||
−0.914717 | + | 0.404095i | \(0.867586\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 485325.i | 0.160543i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.31706e6 | + | 1.31706e6i | 0.430154 | + | 0.430154i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.36829e6 | + | 1.75210e6i | −0.441249 | + | 0.565024i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.12093e6 | + | 1.12093e6i | −0.356947 | + | 0.356947i | −0.862686 | − | 0.505739i | \(-0.831220\pi\) |
0.505739 | + | 0.862686i | \(0.331220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.29826e6 | 1.35164 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.29941e6 | −0.714095 | −0.357047 | − | 0.934086i | \(-0.616217\pi\) | ||||
−0.357047 | + | 0.934086i | \(0.616217\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.57840e6 | + | 4.57840e6i | −1.40427 | + | 1.40427i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.36120e6 | + | 3.02355e6i | −0.715313 | + | 0.915965i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.00845e6 | + | 2.00845e6i | 0.601001 | + | 0.601001i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 533417.i | − | 0.157673i | −0.996888 | − | 0.0788367i | \(-0.974879\pi\) | ||
0.996888 | − | 0.0788367i | \(-0.0251206\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 5.55419e6i | − | 1.62187i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −190782. | − | 190782.i | −0.0550378 | − | 0.0550378i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −389590. | − | 3.16731e6i | −0.111042 | − | 0.902757i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.68341e6 | + | 3.68341e6i | −1.03731 | + | 1.03731i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.05004e6 | 1.68354 | 0.841769 | − | 0.539838i | \(-0.181514\pi\) | ||||
0.841769 | + | 0.539838i | \(0.181514\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.83846e6 | 1.05548 | 0.527742 | − | 0.849405i | \(-0.323039\pi\) | ||||
0.527742 | + | 0.849405i | \(0.323039\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24240.8 | − | 24240.8i | 0.00658713 | − | 0.00658713i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.39923e6 | + | 3.24102e6i | 1.44997 | + | 0.870381i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.35720e6 | + | 2.35720e6i | 0.625643 | + | 0.625643i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 6.68216e6i | − | 1.75297i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.93974e6i | 1.79949i | 0.436415 | + | 0.899746i | \(0.356248\pi\) | ||||
−0.436415 | + | 0.899746i | \(0.643752\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.39202e6 | − | 1.39202e6i | −0.356800 | − | 0.356800i | 0.505832 | − | 0.862632i | \(-0.331186\pi\) |
−0.862632 | + | 0.505832i | \(0.831186\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.74466e6 | + | 583608.i | −1.20221 | + | 0.147876i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −404319. | + | 404319.i | −0.101279 | + | 0.101279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.54253e6 | 0.382008 | 0.191004 | − | 0.981589i | \(-0.438826\pi\) | ||||
0.191004 | + | 0.981589i | \(0.438826\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −277180. | −0.0678681 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.00791e6 | − | 4.00791e6i | 0.970306 | − | 0.970306i | −0.0292655 | − | 0.999572i | \(-0.509317\pi\) |
0.999572 | + | 0.0292655i | \(0.00931684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.12861e6 | − | 1.66232e6i | −0.509562 | − | 0.397937i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.71211e6 | + | 3.71211e6i | 0.878723 | + | 0.878723i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 736658.i | − | 0.172445i | −0.996276 | − | 0.0862224i | \(-0.972520\pi\) | ||
0.996276 | − | 0.0862224i | \(-0.0274795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 682158.i | − | 0.157922i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 455196. | + | 455196.i | 0.104220 | + | 0.104220i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.21682e6 | + | 3.29308e6i | 0.954897 | + | 0.745716i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 821326. | − | 821326.i | 0.183961 | − | 0.183961i | −0.609119 | − | 0.793079i | \(-0.708477\pi\) |
0.793079 | + | 0.609119i | \(0.208477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.66906e6 | −1.47752 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.76885e6 | 0.387649 | 0.193825 | − | 0.981036i | \(-0.437911\pi\) | ||||
0.193825 | + | 0.981036i | \(0.437911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.41538e6 | − | 1.41538e6i | 0.306847 | − | 0.306847i | −0.536839 | − | 0.843685i | \(-0.680382\pi\) |
0.843685 | + | 0.536839i | \(0.180382\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.79548e6 | + | 835866.i | −1.45743 | + | 0.179269i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.37109e6 | + | 1.37109e6i | 0.290921 | + | 0.290921i | 0.837444 | − | 0.546523i | \(-0.184049\pi\) |
−0.546523 | + | 0.837444i | \(0.684049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.68508e6i | 1.19345i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.34957e6i | 1.11113i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.95705e6 | + | 1.95705e6i | 0.402206 | + | 0.402206i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.79798e6 | + | 7.19810e6i | 0.365638 | + | 1.46381i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −75909.9 | + | 75909.9i | −0.0152757 | + | 0.0152757i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00023e6 | 0.796610 | 0.398305 | − | 0.917253i | \(-0.369599\pi\) | ||||
0.398305 | + | 0.917253i | \(0.369599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.94249e6 | −1.17113 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −308316. | + | 308316.i | −0.0601351 | + | 0.0601351i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 580650. | + | 4.72060e6i | 0.112088 | + | 0.911262i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.10730e6 | + | 3.10730e6i | 0.593691 | + | 0.593691i | 0.938626 | − | 0.344935i | \(-0.112099\pi\) |
−0.344935 | + | 0.938626i | \(0.612099\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8.19151e6i | − | 1.54914i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 1.03641e7i | − | 1.94012i | −0.242871 | − | 0.970059i | \(-0.578089\pi\) | ||
0.242871 | − | 0.970059i | \(-0.421911\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.12483e6 | − | 7.12483e6i | −1.32025 | − | 1.32025i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 735847. | − | 942259.i | 0.134982 | − | 0.172845i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.10266e6 | − | 3.10266e6i | 0.563435 | − | 0.563435i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.57165e6 | −1.18147 | −0.590735 | − | 0.806865i | \(-0.701162\pi\) | ||||
−0.590735 | + | 0.806865i | \(0.701162\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.64591e6 | 0.826944 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.25431e6 | + | 2.25431e6i | −0.397278 | + | 0.397278i | −0.877272 | − | 0.479994i | \(-0.840639\pi\) |
0.479994 | + | 0.877272i | \(0.340639\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27598.9 | + | 35340.7i | −0.00481574 | + | 0.00616661i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.39529e6 | + | 5.39529e6i | 0.932169 | + | 0.932169i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 5.08256e6i | 0.869538i | 0.900542 | + | 0.434769i | \(0.143170\pi\) | ||||
−0.900542 | + | 0.434769i | \(0.856830\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.63805e6i | − | 0.955161i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.55592e6 | − | 5.55592e6i | −0.932101 | − | 0.932101i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 119416. | + | 970835.i | 0.0198401 | + | 0.161297i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 211679. | − | 211679.i | 0.0348298 | − | 0.0348298i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.66550e6 | −1.41213 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.06706e6 | −0.817827 | −0.408914 | − | 0.912573i | \(-0.634092\pi\) | ||||
−0.408914 | + | 0.912573i | \(0.634092\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.85174e6 | + | 1.85174e6i | −0.296023 | + | 0.296023i | −0.839454 | − | 0.543431i | \(-0.817125\pi\) |
0.543431 | + | 0.839454i | \(0.317125\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.37106e6 | + | 5.48895e6i | 0.217100 | + | 0.869143i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.02045e7 | − | 1.02045e7i | −1.60053 | − | 1.60053i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.37834e6i | 0.990988i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 126133.i | − | 0.0194130i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.00916e6 | + | 1.00916e6i | 0.153867 | + | 0.153867i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.12699e7 | − | 1.38624e6i | 1.70230 | − | 0.209389i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.14238e6 | − | 5.14238e6i | 0.769536 | − | 0.769536i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.42043e6 | −0.358856 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.24844e6 | −0.183389 | −0.0916946 | − | 0.995787i | \(-0.529228\pi\) | ||||
−0.0916946 | + | 0.995787i | \(0.529228\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.45156e6 | + | 8.45156e6i | −1.23009 | + | 1.23009i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.97419e6 | + | 7.78923e6i | 1.43842 | + | 1.12332i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.66763e6 | + | 6.66763e6i | 0.952803 | + | 0.952803i | 0.998935 | − | 0.0461324i | \(-0.0146896\pi\) |
−0.0461324 | + | 0.998935i | \(0.514690\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.55844e6i | 0.220678i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.18712e7i | − | 1.66578i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.97675e6 | − | 2.97675e6i | −0.413932 | − | 0.413932i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.95252e6 | − | 3.86761e6i | −0.682486 | − | 0.532979i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.39131e6 | + | 3.39131e6i | −0.463158 | + | 0.463158i | −0.899689 | − | 0.436531i | \(-0.856207\pi\) |
0.436531 | + | 0.899689i | \(0.356207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.79039e6 | −0.783752 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.48934e7 | 1.99796 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.26687e6 | − | 9.26687e6i | 1.23215 | − | 1.23215i | 0.269008 | − | 0.963138i | \(-0.413304\pi\) |
0.963138 | − | 0.269008i | \(-0.0866959\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.56149e6 | − | 684081.i | 0.732942 | − | 0.0901543i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −5.13687e6 | − | 5.13687e6i | −0.671029 | − | 0.671029i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.78965e6i | 0.749673i | 0.927091 | + | 0.374836i | \(0.122301\pi\) | ||||
−0.927091 | + | 0.374836i | \(0.877699\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.05138e7i | − | 1.34948i | −0.738054 | − | 0.674742i | \(-0.764255\pi\) | ||
0.738054 | − | 0.674742i | \(-0.235745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.31436e6 | + | 2.31436e6i | 0.294472 | + | 0.294472i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −645293. | − | 387353.i | −0.0813930 | − | 0.0488581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.25024e6 | + | 2.25024e6i | −0.281378 | + | 0.281378i | −0.833658 | − | 0.552281i | \(-0.813758\pi\) |
0.552281 | + | 0.833658i | \(0.313758\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.76442e6 | 0.218729 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.04303e6 | 0.742701 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −662870. | + | 662870.i | −0.0807713 | + | 0.0807713i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 305361. | + | 2.48254e6i | 0.0368913 | + | 0.299921i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.05778e6 | + | 1.05778e6i | 0.126707 | + | 0.126707i | 0.767617 | − | 0.640909i | \(-0.221443\pi\) |
−0.640909 | + | 0.767617i | \(0.721443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 1.70025e7i | − | 2.01940i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 7.93439e6i | − | 0.934426i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.40420e6 | − | 9.40420e6i | −1.09821 | − | 1.09821i | −0.994620 | − | 0.103590i | \(-0.966967\pi\) |
−0.103590 | − | 0.994620i | \(-0.533033\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.33970e6 | + | 9.39856e6i | −0.849936 | + | 1.08835i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.30077e6 | − | 4.30077e6i | 0.493868 | − | 0.493868i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.44361e6 | −0.164393 | −0.0821963 | − | 0.996616i | \(-0.526193\pi\) | ||||
−0.0821963 | + | 0.996616i | \(0.526193\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18811e7 | 1.34174 | 0.670871 | − | 0.741574i | \(-0.265920\pi\) | ||||
0.670871 | + | 0.741574i | \(0.265920\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.87931e6 | + | 1.87931e6i | −0.210478 | + | 0.210478i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 884368. | − | 1.13244e6i | 0.0982301 | − | 0.125785i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.53042e6 | − | 7.53042e6i | −0.829559 | − | 0.829559i | 0.157897 | − | 0.987456i | \(-0.449529\pi\) |
−0.987456 | + | 0.157897i | \(0.949529\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 9.05249e6i | − | 0.989065i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 626303.i | 0.0678705i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 558618. | + | 558618.i | 0.0600432 | + | 0.0600432i | 0.736491 | − | 0.676448i | \(-0.236481\pi\) |
−0.676448 | + | 0.736491i | \(0.736481\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 184241. | + | 1.49785e6i | 0.0196425 | + | 0.159691i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.59743e6 | + | 1.59743e6i | −0.168930 | + | 0.168930i | −0.786509 | − | 0.617579i | \(-0.788114\pi\) |
0.617579 | + | 0.786509i | \(0.288114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.29227e6 | −0.240458 | −0.120229 | − | 0.992746i | \(-0.538363\pi\) | ||||
−0.120229 | + | 0.992746i | \(0.538363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 797058. | 0.0829394 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.61642e6 | − | 3.61642e6i | 0.373301 | − | 0.373301i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.61858e6 | + | 4.59211e6i | −0.882543 | + | 0.470232i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.24075e7 | + | 1.24075e7i | 1.26042 | + | 1.26042i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.32448e7i | − | 1.33481i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 565332.i | − | 0.0565237i | −0.999601 | − | 0.0282618i | \(-0.991003\pi\) | ||
0.999601 | − | 0.0282618i | \(-0.00899722\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 7.69209e6 | + | 7.69209e6i | 0.763018 | + | 0.763018i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.83652e7 | − | 2.25898e6i | 1.80743 | − | 0.222320i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.58071e6 | − | 3.58071e6i | 0.349639 | − | 0.349639i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.05129e6 | 0.198735 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.12714e7 | 1.08351 | 0.541757 | − | 0.840535i | \(-0.317759\pi\) | ||||
0.541757 | + | 0.840535i | \(0.317759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.13714e7 | − | 1.13714e7i | 1.08464 | − | 1.08464i | 0.0885717 | − | 0.996070i | \(-0.471770\pi\) |
0.996070 | − | 0.0885717i | \(-0.0282303\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.82576e6 | − | 3.76862e6i | −0.456737 | − | 0.356684i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 4.10311e6 | + | 4.10311e6i | 0.385347 | + | 0.385347i | 0.873024 | − | 0.487677i | \(-0.162156\pi\) |
−0.487677 | + | 0.873024i | \(0.662156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.10144e6i | − | 0.102647i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.29653e7i | − | 1.19903i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.43638e6 | − | 3.43638e6i | −0.315369 | − | 0.315369i | 0.531617 | − | 0.846985i | \(-0.321585\pi\) |
−0.846985 | + | 0.531617i | \(0.821585\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.79840e6 | − | 3.74726e6i | −0.437012 | − | 0.341280i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.86377e6 | − | 1.86377e6i | 0.168453 | − | 0.168453i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.20483e7 | −1.08072 | −0.540358 | − | 0.841435i | \(-0.681711\pi\) | ||||
−0.540358 | + | 0.841435i | \(0.681711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.84415e6 | −0.520257 | −0.260128 | − | 0.965574i | \(-0.583765\pi\) | ||||
−0.260128 | + | 0.965574i | \(0.583765\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.20328e7 | + | 2.20328e7i | −1.94664 | + | 1.94664i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.39445e7 | + | 1.71522e6i | −1.22278 | + | 0.150406i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 851529. | + | 851529.i | 0.0741114 | + | 0.0741114i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 6.16315e6i | − | 0.532399i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.36088e7i | 1.16684i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.62607e6 | − | 1.62607e6i | −0.138389 | − | 0.138389i | 0.634519 | − | 0.772907i | \(-0.281198\pi\) |
−0.772907 | + | 0.634519i | \(0.781198\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.32278e6 | − | 8.86725e6i | 0.449655 | − | 0.749082i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.06713e6 | + | 6.06713e6i | −0.508759 | + | 0.508759i | −0.914145 | − | 0.405387i | \(-0.867137\pi\) |
0.405387 | + | 0.914145i | \(0.367137\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.00660e6 | −0.749698 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.50837e7 | 1.24635 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.08238e7 | + | 1.08238e7i | −0.887824 | + | 0.887824i | −0.994314 | − | 0.106490i | \(-0.966039\pi\) |
0.106490 | + | 0.994314i | \(0.466039\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.21639e6 | + | 1.80190e7i | 0.180476 | + | 1.46725i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.89010e6 | − | 1.89010e6i | −0.152789 | − | 0.152789i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.96126e6i | − | 0.157394i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.66507e6i | 0.371675i | 0.982581 | + | 0.185837i | \(0.0594997\pi\) | ||||
−0.982581 | + | 0.185837i | \(0.940500\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.60086e6 | + | 1.60086e6i | 0.126625 | + | 0.126625i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.04799e7 | − | 1.34196e7i | 0.822993 | − | 1.05385i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.24926e6 | + | 2.24926e6i | −0.175371 | + | 0.175371i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.40309e7 | 1.08615 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.20262e7 | 0.924346 | 0.462173 | − | 0.886790i | \(-0.347070\pi\) | ||||
0.462173 | + | 0.886790i | \(0.347070\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.10341e7 | − | 1.10341e7i | 0.842070 | − | 0.842070i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −407623. | + | 521965.i | −0.0308877 | + | 0.0395521i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −60042.3 | − | 60042.3i | −0.00451761 | − | 0.00451761i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 597301.i | − | 0.0446249i | −0.999751 | − | 0.0223125i | \(-0.992897\pi\) | ||
0.999751 | − | 0.0223125i | \(-0.00710287\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1.96804e6i | − | 0.146003i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.21959e6 | + | 1.21959e6i | 0.0898444 | + | 0.0898444i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.66651e6 | + | 2.16784e7i | 0.195064 | + | 1.58585i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.09982e7 | + | 1.09982e7i | −0.798956 | + | 0.798956i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.82261e6 | 0.420044 | 0.210022 | − | 0.977697i | \(-0.432646\pi\) | ||||
0.210022 | + | 0.977697i | \(0.432646\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.85229e6 | −0.132700 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.15491e7 | + | 1.15491e7i | −0.821678 | + | 0.821678i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.51598e7 | − | 3.78670e6i | 1.07115 | − | 0.267557i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.33403e7 | − | 1.33403e7i | −0.936115 | − | 0.936115i | 0.0619631 | − | 0.998078i | \(-0.480264\pi\) |
−0.998078 | + | 0.0619631i | \(0.980264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.03576e7i | 0.721838i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1.29058e7i | − | 0.893288i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.57748e6 | + | 2.57748e6i | 0.177188 | + | 0.177188i | 0.790129 | − | 0.612941i | \(-0.210014\pi\) |
−0.612941 | + | 0.790129i | \(0.710014\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.31466e6 | − | 653720.i | 0.362875 | − | 0.0446348i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64108e7 | + | 1.64108e7i | −1.11291 | + | 1.11291i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.82125e7 | 1.22676 | 0.613378 | − | 0.789790i | \(-0.289810\pi\) | ||||
0.613378 | + | 0.789790i | \(0.289810\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.67106e7 | −2.45610 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.20611e7 | + | 1.20611e7i | −0.801524 | + | 0.801524i | −0.983334 | − | 0.181810i | \(-0.941804\pi\) |
0.181810 | + | 0.983334i | \(0.441804\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.35242e7 | − | 1.05616e7i | −0.892731 | − | 0.697169i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.99764e6 | + | 1.99764e6i | 0.130983 | + | 0.130983i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.15023e7i | 1.40049i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.92692e6i | 0.318769i | 0.987217 | + | 0.159384i | \(0.0509509\pi\) | ||||
−0.987217 | + | 0.159384i | \(0.949049\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.55444e6 | + | 2.55444e6i | 0.164175 | + | 0.164175i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.65840e6 | − | 1.29511e6i | −0.105882 | − | 0.0826872i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.41039e7 | + | 1.41039e7i | −0.894542 | + | 0.894542i | −0.994947 | − | 0.100405i | \(-0.967986\pi\) |
0.100405 | + | 0.994947i | \(0.467986\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.77999e6 | −0.112154 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.16920e7 | −1.35781 | −0.678904 | − | 0.734227i | \(-0.737545\pi\) | ||||
−0.678904 | + | 0.734227i | \(0.737545\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.69457e7 | + | 1.69457e7i | −1.05378 | + | 1.05378i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.53316e6 | + | 680597.i | −0.341837 | + | 0.0420471i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.62943e6 | + | 1.62943e6i | 0.100011 | + | 0.100011i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.75723e6i | 0.290094i | 0.989425 | + | 0.145047i | \(0.0463333\pi\) | ||||
−0.989425 | + | 0.145047i | \(0.953667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.62748e6i | 0.583279i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9.08726e6 | − | 9.08726e6i | −0.546996 | − | 0.546996i | 0.378575 | − | 0.925571i | \(-0.376414\pi\) |
−0.925571 | + | 0.378575i | \(0.876414\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.17124e7 | − | 5.42346e6i | 1.29854 | − | 0.324356i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.41411e6 | − | 8.41411e6i | 0.499984 | − | 0.499984i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.74766e6 | −0.221267 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.79125e7 | 1.05082 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.17012e7 | + | 1.17012e7i | −0.682068 | + | 0.682068i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.13474e6 | − | 1.73552e7i | −0.123643 | − | 1.00520i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.01144e7 | − | 1.01144e7i | −0.582107 | − | 0.582107i | 0.353374 | − | 0.935482i | \(-0.385034\pi\) |
−0.935482 | + | 0.353374i | \(0.885034\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 8.70130e6i | − | 0.497613i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.06109e7i | 0.602994i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.01324e7 | − | 2.01324e7i | −1.13688 | − | 1.13688i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.27647e6 | − | 1.63453e6i | 0.0716295 | − | 0.0917223i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.51655e6 | + | 1.51655e6i | −0.0845687 | + | 0.0845687i | −0.748126 | − | 0.663557i | \(-0.769046\pi\) |
0.663557 | + | 0.748126i | \(0.269046\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.39592e6 | −0.0773560 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.39096e6 | 0.131671 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.62750e7 | − | 1.62750e7i | 0.890702 | − | 0.890702i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 877210. | − | 1.12328e6i | 0.0477105 | − | 0.0610937i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.00454e7 | + | 2.00454e7i | 1.08351 | + | 1.08351i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.03499e6i | − | 0.485351i | −0.970107 | − | 0.242676i | \(-0.921975\pi\) | ||
0.970107 | − | 0.242676i | \(-0.0780251\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.47086e7i | 1.85304i | 0.376242 | + | 0.926521i | \(0.377216\pi\) | ||||
−0.376242 | + | 0.926521i | \(0.622784\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.59060e7 | + | 2.59060e7i | 1.37459 | + | 1.37459i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.26881e6 | + | 2.65750e7i | 0.172384 | + | 1.40146i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.07517e7 | − | 1.07517e7i | 0.563535 | − | 0.563535i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.73652e6 | −0.246746 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.73477e7 | 1.41600 | 0.707999 | − | 0.706213i | \(-0.249598\pi\) | ||||
0.707999 | + | 0.706213i | \(0.249598\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.05348e7 | − | 2.05348e7i | 1.05680 | − | 1.05680i | 0.0585087 | − | 0.998287i | \(-0.481365\pi\) |
0.998287 | − | 0.0585087i | \(-0.0186345\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.18869e7 | + | 1.98024e7i | −0.608040 | + | 1.01294i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.36628e7 | + | 1.36628e7i | 0.694667 | + | 0.694667i | 0.963255 | − | 0.268588i | \(-0.0865572\pi\) |
−0.268588 | + | 0.963255i | \(0.586557\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1.58116e7i | − | 0.799079i | −0.916716 | − | 0.399539i | \(-0.869170\pi\) | ||
0.916716 | − | 0.399539i | \(-0.130830\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.15153e7i | 1.08080i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.98078e6 | + | 7.98078e6i | 0.398504 | + | 0.398504i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.50723e7 | + | 1.85394e6i | −0.748107 | + | 0.0920197i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.67590e7 | + | 1.67590e7i | −0.826863 | + | 0.826863i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.86674e6 | 0.189644 | 0.0948222 | − | 0.995494i | \(-0.469772\pi\) | ||||
0.0948222 | + | 0.995494i | \(0.469772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.49070e6 | −0.218939 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.50228e7 | − | 2.50228e7i | 1.21274 | − | 1.21274i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.96565e7 | − | 1.53505e7i | −0.947029 | − | 0.739572i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.92397e6 | + | 1.92397e6i | 0.0921488 | + | 0.0921488i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 538330.i | − | 0.0256318i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.58296e6i | 0.0749283i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.08725e7 | − | 1.08725e7i | −0.511631 | − | 0.511631i | 0.403395 | − | 0.915026i | \(-0.367830\pi\) |
−0.915026 | + | 0.403395i | \(0.867830\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.17661e6 | − | 4.04262e6i | −0.242176 | − | 0.189124i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.24573e6 | + | 8.24573e6i | −0.383510 | + | 0.383510i | −0.872365 | − | 0.488855i | \(-0.837415\pi\) |
0.488855 | + | 0.872365i | \(0.337415\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.36231e7 | −1.09233 | −0.546164 | − | 0.837678i | \(-0.683913\pi\) | ||||
−0.546164 | + | 0.837678i | \(0.683913\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.85780e6 | −0.131378 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.50486e7 | − | 1.50486e7i | 0.687811 | − | 0.687811i | −0.273937 | − | 0.961748i | \(-0.588326\pi\) |
0.961748 | + | 0.273937i | \(0.0883260\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.81128e7 | − | 3.45796e6i | 1.27751 | − | 0.157138i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.19369e7 | − | 3.19369e7i | −1.44293 | − | 1.44293i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.71856e7i | − | 0.771996i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.85552e7i | − | 2.16866i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.97731e6 | − | 2.97731e6i | −0.132217 | − | 0.132217i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.63838e6 | − | 1.72602e7i | −0.293118 | − | 0.762125i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.37339e7 | − | 2.37339e7i | 1.04201 | − | 1.04201i | 0.0429276 | − | 0.999078i | \(-0.486332\pi\) |
0.999078 | − | 0.0429276i | \(-0.0136685\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.76175e7 | 2.07871 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.33399e7 | 1.01311 | 0.506557 | − | 0.862206i | \(-0.330918\pi\) | ||||
0.506557 | + | 0.862206i | \(0.330918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.05710e6 | + | 1.05710e6i | −0.0456264 | + | 0.0456264i | −0.729552 | − | 0.683925i | \(-0.760271\pi\) |
0.683925 | + | 0.729552i | \(0.260271\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 297481. | + | 2.41848e6i | 0.0127674 | + | 0.103797i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.50661e6 | + | 6.50661e6i | 0.277681 | + | 0.277681i | 0.832182 | − | 0.554502i | \(-0.187091\pi\) |
−0.554502 | + | 0.832182i | \(0.687091\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.50396e7i | 1.48698i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 2.96566e7i | − | 1.25149i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.16293e6 | − | 1.16293e6i | −0.0488004 | − | 0.0488004i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.46309e7 | + | 1.87351e7i | −0.610541 | + | 0.781804i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.63327e6 | − | 2.63327e6i | 0.109273 | − | 0.109273i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.58086e7 | −1.47771 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.37131e6 | 0.179391 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.19876e6 | − | 8.19876e6i | 0.334602 | − | 0.334602i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.40461e7 | − | 3.07913e7i | 0.975940 | − | 1.24970i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.42036e6 | − | 7.42036e6i | −0.299507 | − | 0.299507i | 0.541314 | − | 0.840821i | \(-0.317927\pi\) |
−0.840821 | + | 0.541314i | \(0.817927\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 39696.3i | − | 0.00159346i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.87110e7i | 1.54539i | 0.634776 | + | 0.772696i | \(0.281092\pi\) | ||||
−0.634776 | + | 0.772696i | \(0.718908\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.74440e7 | + | 1.74440e7i | 0.692580 | + | 0.692580i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.67552e6 | − | 2.98815e7i | −0.145133 | − | 1.17991i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.15228e6 | − | 8.15228e6i | 0.320151 | − | 0.320151i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.58482e7 | 0.618999 | 0.309500 | − | 0.950900i | \(-0.399838\pi\) | ||||
0.309500 | + | 0.950900i | \(0.399838\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.48241e7 | −1.35279 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.64993e7 | + | 2.64993e7i | −1.02383 | + | 1.02383i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.76104e7 | + | 1.05711e7i | 0.676729 | + | 0.406223i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −612310. | − | 612310.i | −0.0234030 | − | 0.0234030i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.37736e7i | 1.28392i | 0.766738 | + | 0.641960i | \(0.221878\pi\) | ||||
−0.766738 | + | 0.641960i | \(0.778122\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32974e7i | 0.502797i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.87636e7 | − | 1.87636e7i | −0.705686 | − | 0.705686i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.83173e7 | + | 5.94319e6i | −1.80748 | + | 0.222326i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.44062e7 | − | 1.44062e7i | 0.536045 | − | 0.536045i | −0.386320 | − | 0.922365i | \(-0.626254\pi\) |
0.922365 | + | 0.386320i | \(0.126254\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.63386e7 | 0.974829 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.43127e7 | −1.63138 | −0.815688 | − | 0.578493i | \(-0.803641\pi\) | ||||
−0.815688 | + | 0.578493i | \(0.803641\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 268821. | − | 268821.i | 0.00984429 | − | 0.00984429i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.54354e7 | + | 1.20541e7i | 0.562263 | + | 0.439093i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.80551e7 | − | 2.80551e7i | −1.01657 | − | 1.01657i | −0.999860 | − | 0.0167087i | \(-0.994681\pi\) |
−0.0167087 | − | 0.999860i | \(-0.505319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.81536e7i | 1.73565i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 9.88472e6i | − | 0.354416i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.45210e7 | + | 1.45210e7i | 0.517921 | + | 0.517921i | 0.916942 | − | 0.399021i | \(-0.130650\pi\) |
−0.399021 | + | 0.916942i | \(0.630650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.43182e6 | − | 6.58474e6i | −0.299167 | − | 0.233631i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.61313e7 | − | 2.61313e7i | 0.922318 | − | 0.922318i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.43790e7 | −1.20711 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.26573e7 | −0.791406 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.10800e6 | + | 7.10800e6i | −0.246991 | + | 0.246991i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.72416e6 | + | 704090.i | −0.197876 | + | 0.0243394i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.66187e6 | + | 1.66187e6i | 0.0571519 | + | 0.0571519i | 0.735105 | − | 0.677953i | \(-0.237133\pi\) |
−0.677953 | + | 0.735105i | \(0.737133\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.18217e7i | − | 2.79936i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.51619e6i | − | 0.153718i | −0.997042 | − | 0.0768589i | \(-0.975511\pi\) | ||
0.997042 | − | 0.0768589i | \(-0.0244891\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.27994e7 | + | 2.27994e7i | 0.772043 | + | 0.772043i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.17100e7 | − | 4.68802e7i | −0.394498 | − | 1.57935i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.43956e7 | − | 2.43956e7i | 0.817663 | − | 0.817663i | −0.168106 | − | 0.985769i | \(-0.553765\pi\) |
0.985769 | + | 0.168106i | \(0.0537651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.08786e7 | 0.696218 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.12035e7 | −0.371689 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.60097e7 | − | 1.60097e7i | 0.528445 | − | 0.528445i | −0.391664 | − | 0.920108i | \(-0.628100\pi\) |
0.920108 | + | 0.391664i | \(0.128100\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.16621e6 | + | 2.57409e7i | 0.103980 | + | 0.845343i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −886797. | − | 886797.i | −0.0289755 | − | 0.0289755i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.54244e6i | 0.0501440i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.21742e7i | − | 1.36415i | −0.731281 | − | 0.682076i | \(-0.761077\pi\) | ||
0.731281 | − | 0.682076i | \(-0.238923\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.85465e7 | + | 2.85465e7i | 0.918713 | + | 0.918713i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.22364e7 | + | 1.56689e7i | −0.391829 | + | 0.501741i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.45114e7 | − | 1.45114e7i | 0.462350 | − | 0.462350i | −0.437075 | − | 0.899425i | \(-0.643986\pi\) |
0.899425 | + | 0.437075i | \(0.143986\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.17522e7 | −0.689586 |
(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.c.63.6 | ✓ | 16 | |
4.3 | odd | 2 | 160.6.n.d.63.3 | yes | 16 | ||
5.2 | odd | 4 | 160.6.n.d.127.3 | yes | 16 | ||
20.7 | even | 4 | inner | 160.6.n.c.127.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.6.n.c.63.6 | ✓ | 16 | 1.1 | even | 1 | trivial | |
160.6.n.c.127.6 | yes | 16 | 20.7 | even | 4 | inner | |
160.6.n.d.63.3 | yes | 16 | 4.3 | odd | 2 | ||
160.6.n.d.127.3 | yes | 16 | 5.2 | odd | 4 |