Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [175,6,Mod(99,175)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(175, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("175.99");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 175 = 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 175.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.0671684673\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{57})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 29x^{2} + 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 99.2 | ||
Root | \(4.27492i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 175.99 |
Dual form | 175.6.b.c.99.3 |
$q$-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 \(\left(\mathbb{Z}/175\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.725083i | − 0.128178i | −0.997944 | − | 0.0640889i | \(-0.979586\pi\) | ||||
0.997944 | − | 0.0640889i | \(-0.0204141\pi\) | |||||||
\(3\) | 19.6495i | 1.26052i | 0.776386 | + | 0.630258i | \(0.217051\pi\) | ||||
−0.776386 | + | 0.630258i | \(0.782949\pi\) | |||||||
\(4\) | 31.4743 | 0.983570 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 14.2475 | 0.161570 | ||||||||
\(7\) | − 49.0000i | − 0.377964i | ||||||||
\(8\) | − 46.0241i | − 0.254250i | ||||||||
\(9\) | −143.103 | −0.588901 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 666.090 | 1.65978 | 0.829891 | − | 0.557926i | \(-0.188403\pi\) | ||||
0.829891 | + | 0.557926i | \(0.188403\pi\) | |||||||
\(12\) | 618.453i | 1.23981i | ||||||||
\(13\) | − 650.640i | − 1.06778i | −0.845554 | − | 0.533890i | \(-0.820729\pi\) | ||||
0.845554 | − | 0.533890i | \(-0.179271\pi\) | |||||||
\(14\) | −35.5291 | −0.0484466 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 973.805 | 0.950981 | ||||||||
\(17\) | − 1186.89i | − 0.996069i | −0.867157 | − | 0.498035i | \(-0.834055\pi\) | ||||
0.867157 | − | 0.498035i | \(-0.165945\pi\) | |||||||
\(18\) | 103.762i | 0.0754840i | ||||||||
\(19\) | 1565.05 | 0.994591 | 0.497296 | − | 0.867581i | \(-0.334326\pi\) | ||||
0.497296 | + | 0.867581i | \(0.334326\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 962.826 | 0.476430 | ||||||||
\(22\) | − 482.970i | − 0.212747i | ||||||||
\(23\) | − 1100.15i | − 0.433644i | −0.976211 | − | 0.216822i | \(-0.930431\pi\) | ||||
0.976211 | − | 0.216822i | \(-0.0695691\pi\) | |||||||
\(24\) | 904.350 | 0.320486 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −471.768 | −0.136866 | ||||||||
\(27\) | 1962.93i | 0.518197i | ||||||||
\(28\) | − 1542.24i | − 0.371755i | ||||||||
\(29\) | −2396.72 | −0.529203 | −0.264602 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264602 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2048.46 | −0.382844 | −0.191422 | − | 0.981508i | \(-0.561310\pi\) | ||||
−0.191422 | + | 0.981508i | \(0.561310\pi\) | |||||||
\(32\) | − 2178.86i | − 0.376144i | ||||||||
\(33\) | 13088.3i | 2.09218i | ||||||||
\(34\) | −860.596 | −0.127674 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4504.06 | −0.579226 | ||||||||
\(37\) | − 1077.54i | − 0.129399i | −0.997905 | − | 0.0646995i | \(-0.979391\pi\) | ||||
0.997905 | − | 0.0646995i | \(-0.0206089\pi\) | |||||||
\(38\) | − 1134.79i | − 0.127484i | ||||||||
\(39\) | 12784.7 | 1.34595 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1098.21 | 0.102029 | 0.0510147 | − | 0.998698i | \(-0.483754\pi\) | ||||
0.0510147 | + | 0.998698i | \(0.483754\pi\) | |||||||
\(42\) | − 698.128i | − 0.0610678i | ||||||||
\(43\) | 16564.3i | 1.36616i | 0.730343 | + | 0.683081i | \(0.239360\pi\) | ||||
−0.730343 | + | 0.683081i | \(0.760640\pi\) | |||||||
\(44\) | 20964.7 | 1.63251 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −797.702 | −0.0555835 | ||||||||
\(47\) | 8298.39i | 0.547960i | 0.961735 | + | 0.273980i | \(0.0883403\pi\) | ||||
−0.961735 | + | 0.273980i | \(0.911660\pi\) | |||||||
\(48\) | 19134.8i | 1.19873i | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23321.9 | 1.25556 | ||||||||
\(52\) | − 20478.4i | − 1.05024i | ||||||||
\(53\) | 5519.18i | 0.269889i | 0.990853 | + | 0.134944i | \(0.0430856\pi\) | ||||
−0.990853 | + | 0.134944i | \(0.956914\pi\) | |||||||
\(54\) | 1423.28 | 0.0664213 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2255.18 | −0.0960973 | ||||||||
\(57\) | 30752.5i | 1.25370i | ||||||||
\(58\) | 1737.82i | 0.0678321i | ||||||||
\(59\) | 14230.4 | 0.532216 | 0.266108 | − | 0.963943i | \(-0.414262\pi\) | ||||
0.266108 | + | 0.963943i | \(0.414262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14234.7 | −0.489807 | −0.244904 | − | 0.969547i | \(-0.578756\pi\) | ||||
−0.244904 | + | 0.969547i | \(0.578756\pi\) | |||||||
\(62\) | 1485.30i | 0.0490721i | ||||||||
\(63\) | 7012.05i | 0.222584i | ||||||||
\(64\) | 29581.9 | 0.902768 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 9490.12 | 0.268171 | ||||||||
\(67\) | − 19730.4i | − 0.536970i | −0.963284 | − | 0.268485i | \(-0.913477\pi\) | ||||
0.963284 | − | 0.268485i | \(-0.0865229\pi\) | |||||||
\(68\) | − 37356.6i | − 0.979704i | ||||||||
\(69\) | 21617.5 | 0.546615 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 64562.7 | 1.51997 | 0.759986 | − | 0.649940i | \(-0.225206\pi\) | ||||
0.759986 | + | 0.649940i | \(0.225206\pi\) | |||||||
\(72\) | 6586.18i | 0.149728i | ||||||||
\(73\) | 28567.0i | 0.627418i | 0.949519 | + | 0.313709i | \(0.101572\pi\) | ||||
−0.949519 | + | 0.313709i | \(0.898428\pi\) | |||||||
\(74\) | −781.309 | −0.0165861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 49258.8 | 0.978251 | ||||||||
\(77\) | − 32638.4i | − 0.627339i | ||||||||
\(78\) | − 9270.00i | − 0.172521i | ||||||||
\(79\) | 30633.4 | 0.552239 | 0.276119 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276119 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −73344.6 | −1.24210 | ||||||||
\(82\) | − 796.293i | − 0.0130779i | ||||||||
\(83\) | − 675.946i | − 0.0107700i | −0.999986 | − | 0.00538501i | \(-0.998286\pi\) | ||||
0.999986 | − | 0.00538501i | \(-0.00171411\pi\) | |||||||
\(84\) | 30304.2 | 0.468603 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12010.5 | 0.175111 | ||||||||
\(87\) | − 47094.4i | − 0.667069i | ||||||||
\(88\) | − 30656.2i | − 0.421999i | ||||||||
\(89\) | −125971. | −1.68576 | −0.842882 | − | 0.538098i | \(-0.819143\pi\) | ||||
−0.842882 | + | 0.538098i | \(0.819143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −31881.3 | −0.403583 | ||||||||
\(92\) | − 34626.5i | − 0.426520i | ||||||||
\(93\) | − 40251.1i | − 0.482582i | ||||||||
\(94\) | 6017.02 | 0.0702363 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 42813.5 | 0.474136 | ||||||||
\(97\) | 22906.8i | 0.247192i | 0.992333 | + | 0.123596i | \(0.0394427\pi\) | ||||
−0.992333 | + | 0.123596i | \(0.960557\pi\) | |||||||
\(98\) | 1740.92i | 0.0183111i | ||||||||
\(99\) | −95319.4 | −0.977447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −181474. | −1.77015 | −0.885077 | − | 0.465444i | \(-0.845895\pi\) | ||||
−0.885077 | + | 0.465444i | \(0.845895\pi\) | |||||||
\(102\) | − 16910.3i | − 0.160935i | ||||||||
\(103\) | 64772.0i | 0.601581i | 0.953690 | + | 0.300791i | \(0.0972506\pi\) | ||||
−0.953690 | + | 0.300791i | \(0.902749\pi\) | |||||||
\(104\) | −29945.1 | −0.271483 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4001.86 | 0.0345938 | ||||||||
\(107\) | 148170.i | 1.25112i | 0.780175 | + | 0.625562i | \(0.215130\pi\) | ||||
−0.780175 | + | 0.625562i | \(0.784870\pi\) | |||||||
\(108\) | 61781.7i | 0.509683i | ||||||||
\(109\) | 111294. | 0.897237 | 0.448618 | − | 0.893723i | \(-0.351916\pi\) | ||||
0.448618 | + | 0.893723i | \(0.351916\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21173.2 | 0.163110 | ||||||||
\(112\) | − 47716.4i | − 0.359437i | ||||||||
\(113\) | − 43175.5i | − 0.318084i | −0.987272 | − | 0.159042i | \(-0.949160\pi\) | ||||
0.987272 | − | 0.159042i | \(-0.0508405\pi\) | |||||||
\(114\) | 22298.1 | 0.160696 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −75435.0 | −0.520509 | ||||||||
\(117\) | 93108.5i | 0.628817i | ||||||||
\(118\) | − 10318.2i | − 0.0682182i | ||||||||
\(119\) | −58157.8 | −0.376479 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 282625. | 1.75488 | ||||||||
\(122\) | 10321.4i | 0.0627824i | ||||||||
\(123\) | 21579.3i | 0.128610i | ||||||||
\(124\) | −64473.6 | −0.376554 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5084.31 | 0.0285303 | ||||||||
\(127\) | 131449.i | 0.723182i | 0.932337 | + | 0.361591i | \(0.117766\pi\) | ||||
−0.932337 | + | 0.361591i | \(0.882234\pi\) | |||||||
\(128\) | − 91172.8i | − 0.491859i | ||||||||
\(129\) | −325480. | −1.72207 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −349458. | −1.77916 | −0.889582 | − | 0.456775i | \(-0.849005\pi\) | ||||
−0.889582 | + | 0.456775i | \(0.849005\pi\) | |||||||
\(132\) | 411946.i | 2.05781i | ||||||||
\(133\) | − 76687.5i | − 0.375920i | ||||||||
\(134\) | −14306.2 | −0.0688276 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −54625.7 | −0.253250 | ||||||||
\(137\) | − 386434.i | − 1.75903i | −0.475869 | − | 0.879516i | \(-0.657866\pi\) | ||||
0.475869 | − | 0.879516i | \(-0.342134\pi\) | |||||||
\(138\) | − 15674.4i | − 0.0700639i | ||||||||
\(139\) | −17289.3 | −0.0758997 | −0.0379498 | − | 0.999280i | \(-0.512083\pi\) | ||||
−0.0379498 | + | 0.999280i | \(0.512083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −163059. | −0.690713 | ||||||||
\(142\) | − 46813.3i | − 0.194827i | ||||||||
\(143\) | − 433384.i | − 1.77228i | ||||||||
\(144\) | −139354. | −0.560034 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20713.4 | 0.0804210 | ||||||||
\(147\) | − 47178.5i | − 0.180074i | ||||||||
\(148\) | − 33914.9i | − 0.127273i | ||||||||
\(149\) | 112171. | 0.413917 | 0.206959 | − | 0.978350i | \(-0.433643\pi\) | ||||
0.206959 | + | 0.978350i | \(0.433643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30495.4 | 0.108841 | 0.0544205 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544205 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(152\) | − 72030.1i | − 0.252874i | ||||||||
\(153\) | 169848.i | 0.586586i | ||||||||
\(154\) | −23665.5 | −0.0804108 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 402390. | 1.32384 | ||||||||
\(157\) | − 523509.i | − 1.69502i | −0.530780 | − | 0.847510i | \(-0.678101\pi\) | ||||
0.530780 | − | 0.847510i | \(-0.321899\pi\) | |||||||
\(158\) | − 22211.7i | − 0.0707847i | ||||||||
\(159\) | −108449. | −0.340199 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −53907.5 | −0.163902 | ||||||||
\(162\) | 53180.9i | 0.159209i | ||||||||
\(163\) | − 439646.i | − 1.29609i | −0.761604 | − | 0.648043i | \(-0.775588\pi\) | ||||
0.761604 | − | 0.648043i | \(-0.224412\pi\) | |||||||
\(164\) | 34565.3 | 0.100353 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −490.117 | −0.00138048 | ||||||||
\(167\) | − 279353.i | − 0.775107i | −0.921847 | − | 0.387554i | \(-0.873320\pi\) | ||||
0.921847 | − | 0.387554i | \(-0.126680\pi\) | |||||||
\(168\) | − 44313.2i | − 0.121132i | ||||||||
\(169\) | −52038.8 | −0.140156 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −223964. | −0.585716 | ||||||||
\(172\) | 521349.i | 1.34372i | ||||||||
\(173\) | 99699.4i | 0.253266i | 0.991950 | + | 0.126633i | \(0.0404171\pi\) | ||||
−0.991950 | + | 0.126633i | \(0.959583\pi\) | |||||||
\(174\) | −34147.3 | −0.0855034 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 648641. | 1.57842 | ||||||||
\(177\) | 279621.i | 0.670867i | ||||||||
\(178\) | 91339.7i | 0.216077i | ||||||||
\(179\) | −329980. | −0.769760 | −0.384880 | − | 0.922967i | \(-0.625757\pi\) | ||||
−0.384880 | + | 0.922967i | \(0.625757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −505810. | −1.14760 | −0.573800 | − | 0.818995i | \(-0.694531\pi\) | ||||
−0.573800 | + | 0.818995i | \(0.694531\pi\) | |||||||
\(182\) | 23116.6i | 0.0517304i | ||||||||
\(183\) | − 279706.i | − 0.617410i | ||||||||
\(184\) | −50633.5 | −0.110254 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −29185.4 | −0.0618562 | ||||||||
\(187\) | − 790578.i | − 1.65326i | ||||||||
\(188\) | 261186.i | 0.538958i | ||||||||
\(189\) | 96183.4 | 0.195860 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −63835.6 | −0.126613 | −0.0633067 | − | 0.997994i | \(-0.520165\pi\) | ||||
−0.0633067 | + | 0.997994i | \(0.520165\pi\) | |||||||
\(192\) | 581270.i | 1.13795i | ||||||||
\(193\) | 469355.i | 0.907001i | 0.891256 | + | 0.453501i | \(0.149825\pi\) | ||||
−0.891256 | + | 0.453501i | \(0.850175\pi\) | |||||||
\(194\) | 16609.3 | 0.0316845 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −75569.7 | −0.140510 | ||||||||
\(197\) | − 268021.i | − 0.492043i | −0.969264 | − | 0.246021i | \(-0.920877\pi\) | ||||
0.969264 | − | 0.246021i | \(-0.0791234\pi\) | |||||||
\(198\) | 69114.5i | 0.125287i | ||||||||
\(199\) | 605167. | 1.08328 | 0.541642 | − | 0.840609i | \(-0.317803\pi\) | ||||
0.541642 | + | 0.840609i | \(0.317803\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 387693. | 0.676859 | ||||||||
\(202\) | 131584.i | 0.226894i | ||||||||
\(203\) | 117439.i | 0.200020i | ||||||||
\(204\) | 734039. | 1.23493 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 46965.1 | 0.0771094 | ||||||||
\(207\) | 157435.i | 0.255374i | ||||||||
\(208\) | − 633596.i | − 1.01544i | ||||||||
\(209\) | 1.04246e6 | 1.65080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 335389. | 0.518612 | 0.259306 | − | 0.965795i | \(-0.416506\pi\) | ||||
0.259306 | + | 0.965795i | \(0.416506\pi\) | |||||||
\(212\) | 173712.i | 0.265455i | ||||||||
\(213\) | 1.26862e6i | 1.91595i | ||||||||
\(214\) | 107435. | 0.160366 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 90341.9 | 0.131751 | ||||||||
\(217\) | 100374.i | 0.144702i | ||||||||
\(218\) | − 80697.7i | − 0.115006i | ||||||||
\(219\) | −561327. | −0.790871 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −772240. | −1.06358 | ||||||||
\(222\) | − 15352.3i | − 0.0209070i | ||||||||
\(223\) | 1.02526e6i | 1.38061i | 0.723518 | + | 0.690305i | \(0.242524\pi\) | ||||
−0.723518 | + | 0.690305i | \(0.757476\pi\) | |||||||
\(224\) | −106764. | −0.142169 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31305.8 | −0.0407713 | ||||||||
\(227\) | 504226.i | 0.649473i | 0.945805 | + | 0.324736i | \(0.105276\pi\) | ||||
−0.945805 | + | 0.324736i | \(0.894724\pi\) | |||||||
\(228\) | 967912.i | 1.23310i | ||||||||
\(229\) | 1.11939e6 | 1.41057 | 0.705283 | − | 0.708925i | \(-0.250820\pi\) | ||||
0.705283 | + | 0.708925i | \(0.250820\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 641328. | 0.790770 | ||||||||
\(232\) | 110307.i | 0.134550i | ||||||||
\(233\) | 770703.i | 0.930031i | 0.885303 | + | 0.465015i | \(0.153951\pi\) | ||||
−0.885303 | + | 0.465015i | \(0.846049\pi\) | |||||||
\(234\) | 67511.3 | 0.0806004 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 447892. | 0.523472 | ||||||||
\(237\) | 601930.i | 0.696106i | ||||||||
\(238\) | 42169.2i | 0.0482562i | ||||||||
\(239\) | 171646. | 0.194374 | 0.0971871 | − | 0.995266i | \(-0.469015\pi\) | ||||
0.0971871 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −383779. | −0.425637 | −0.212818 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212818 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(242\) | − 204926.i | − 0.224936i | ||||||||
\(243\) | − 964193.i | − 1.04749i | ||||||||
\(244\) | −448028. | −0.481760 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15646.8 | 0.0164849 | ||||||||
\(247\) | − 1.01828e6i | − 1.06201i | ||||||||
\(248\) | 94278.3i | 0.0973380i | ||||||||
\(249\) | 13282.0 | 0.0135758 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.57046e6 | −1.57342 | −0.786708 | − | 0.617325i | \(-0.788216\pi\) | ||||
−0.786708 | + | 0.617325i | \(0.788216\pi\) | |||||||
\(252\) | 220699.i | 0.218927i | ||||||||
\(253\) | − 732801.i | − 0.719755i | ||||||||
\(254\) | 95311.4 | 0.0926959 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 880513. | 0.839723 | ||||||||
\(257\) | − 790656.i | − 0.746715i | −0.927688 | − | 0.373357i | \(-0.878207\pi\) | ||||
0.927688 | − | 0.373357i | \(-0.121793\pi\) | |||||||
\(258\) | 236000.i | 0.220731i | ||||||||
\(259\) | −52799.7 | −0.0489082 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 342978. | 0.311648 | ||||||||
\(262\) | 253386.i | 0.228049i | ||||||||
\(263\) | 464416.i | 0.414017i | 0.978339 | + | 0.207008i | \(0.0663728\pi\) | ||||
−0.978339 | + | 0.207008i | \(0.933627\pi\) | |||||||
\(264\) | 602379. | 0.531936 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −55604.8 | −0.0481846 | ||||||||
\(267\) | − 2.47527e6i | − 2.12493i | ||||||||
\(268\) | − 621001.i | − 0.528147i | ||||||||
\(269\) | −1.99959e6 | −1.68484 | −0.842422 | − | 0.538818i | \(-0.818871\pi\) | ||||
−0.842422 | + | 0.538818i | \(0.818871\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.61296e6 | 1.33414 | 0.667070 | − | 0.744995i | \(-0.267548\pi\) | ||||
0.667070 | + | 0.744995i | \(0.267548\pi\) | |||||||
\(272\) | − 1.15580e6i | − 0.947243i | ||||||||
\(273\) | − 626452.i | − 0.508723i | ||||||||
\(274\) | −280197. | −0.225469 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 680393. | 0.537635 | ||||||||
\(277\) | 2.08119e6i | 1.62972i | 0.579658 | + | 0.814860i | \(0.303186\pi\) | ||||
−0.579658 | + | 0.814860i | \(0.696814\pi\) | |||||||
\(278\) | 12536.2i | 0.00972865i | ||||||||
\(279\) | 293140. | 0.225457 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −982035. | −0.741927 | −0.370964 | − | 0.928647i | \(-0.620973\pi\) | ||||
−0.370964 | + | 0.928647i | \(0.620973\pi\) | |||||||
\(282\) | 118231.i | 0.0885340i | ||||||||
\(283\) | − 1.39622e6i | − 1.03630i | −0.855289 | − | 0.518152i | \(-0.826620\pi\) | ||||
0.855289 | − | 0.518152i | \(-0.173380\pi\) | |||||||
\(284\) | 2.03206e6 | 1.49500 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −314240. | −0.227167 | ||||||||
\(287\) | − 53812.3i | − 0.0385635i | ||||||||
\(288\) | 311801.i | 0.221512i | ||||||||
\(289\) | 11140.3 | 0.00784609 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −450107. | −0.311590 | ||||||||
\(292\) | 899124.i | 0.617110i | ||||||||
\(293\) | 2.56205e6i | 1.74348i | 0.489965 | + | 0.871742i | \(0.337010\pi\) | ||||
−0.489965 | + | 0.871742i | \(0.662990\pi\) | |||||||
\(294\) | −34208.3 | −0.0230814 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −49593.0 | −0.0328996 | ||||||||
\(297\) | 1.30749e6i | 0.860094i | ||||||||
\(298\) | − 81333.0i | − 0.0530550i | ||||||||
\(299\) | −715803. | −0.463037 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 811651. | 0.516361 | ||||||||
\(302\) | − 22111.7i | − 0.0139510i | ||||||||
\(303\) | − 3.56588e6i | − 2.23131i | ||||||||
\(304\) | 1.52405e6 | 0.945838 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 123154. | 0.0751873 | ||||||||
\(307\) | 884855.i | 0.535829i | 0.963443 | + | 0.267915i | \(0.0863345\pi\) | ||||
−0.963443 | + | 0.267915i | \(0.913666\pi\) | |||||||
\(308\) | − 1.02727e6i | − 0.617032i | ||||||||
\(309\) | −1.27274e6 | −0.758303 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.80120e6 | 1.05599 | 0.527997 | − | 0.849246i | \(-0.322943\pi\) | ||||
0.527997 | + | 0.849246i | \(0.322943\pi\) | |||||||
\(312\) | − 588406.i | − 0.342208i | ||||||||
\(313\) | 950366.i | 0.548315i | 0.961685 | + | 0.274158i | \(0.0883990\pi\) | ||||
−0.961685 | + | 0.274158i | \(0.911601\pi\) | |||||||
\(314\) | −379587. | −0.217264 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 964162. | 0.543166 | ||||||||
\(317\) | − 3.04277e6i | − 1.70068i | −0.526237 | − | 0.850338i | \(-0.676398\pi\) | ||||
0.526237 | − | 0.850338i | \(-0.323602\pi\) | |||||||
\(318\) | 78634.6i | 0.0436060i | ||||||||
\(319\) | −1.59643e6 | −0.878362 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.91146e6 | −1.57706 | ||||||||
\(322\) | 39087.4i | 0.0210086i | ||||||||
\(323\) | − 1.85755e6i | − 0.990682i | ||||||||
\(324\) | −2.30847e6 | −1.22169 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −318780. | −0.166129 | ||||||||
\(327\) | 2.18688e6i | 1.13098i | ||||||||
\(328\) | − 50544.1i | − 0.0259409i | ||||||||
\(329\) | 406621. | 0.207110 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.19616e6 | −1.10178 | −0.550889 | − | 0.834579i | \(-0.685711\pi\) | ||||
−0.550889 | + | 0.834579i | \(0.685711\pi\) | |||||||
\(332\) | − 21274.9i | − 0.0105931i | ||||||||
\(333\) | 154200.i | 0.0762032i | ||||||||
\(334\) | −202554. | −0.0993515 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 937604. | 0.453076 | ||||||||
\(337\) | 2.41491e6i | 1.15832i | 0.815216 | + | 0.579158i | \(0.196618\pi\) | ||||
−0.815216 | + | 0.579158i | \(0.803382\pi\) | |||||||
\(338\) | 37732.5i | 0.0179648i | ||||||||
\(339\) | 848377. | 0.400950 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.36446e6 | −0.635438 | ||||||||
\(342\) | 162392.i | 0.0750757i | ||||||||
\(343\) | 117649.i | 0.0539949i | ||||||||
\(344\) | 762357. | 0.347346 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 72290.3 | 0.0324631 | ||||||||
\(347\) | 1.08833e6i | 0.485219i | 0.970124 | + | 0.242609i | \(0.0780033\pi\) | ||||
−0.970124 | + | 0.242609i | \(0.921997\pi\) | |||||||
\(348\) | − 1.48226e6i | − 0.656110i | ||||||||
\(349\) | −2.79267e6 | −1.22731 | −0.613657 | − | 0.789573i | \(-0.710302\pi\) | ||||
−0.613657 | + | 0.789573i | \(0.710302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.27716e6 | 0.553321 | ||||||||
\(352\) | − 1.45132e6i | − 0.624317i | ||||||||
\(353\) | 2.53134e6i | 1.08122i | 0.841273 | + | 0.540610i | \(0.181807\pi\) | ||||
−0.841273 | + | 0.540610i | \(0.818193\pi\) | |||||||
\(354\) | 202748. | 0.0859902 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.96485e6 | −1.65807 | ||||||||
\(357\) | − 1.14277e6i | − 0.474558i | ||||||||
\(358\) | 239263.i | 0.0986661i | ||||||||
\(359\) | −1.09028e6 | −0.446480 | −0.223240 | − | 0.974763i | \(-0.571663\pi\) | ||||
−0.223240 | + | 0.974763i | \(0.571663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26712.8 | −0.0107883 | ||||||||
\(362\) | 366754.i | 0.147097i | ||||||||
\(363\) | 5.55343e6i | 2.21205i | ||||||||
\(364\) | −1.00344e6 | −0.396953 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −202810. | −0.0791382 | ||||||||
\(367\) | − 188070.i | − 0.0728879i | −0.999336 | − | 0.0364439i | \(-0.988397\pi\) | ||||
0.999336 | − | 0.0364439i | \(-0.0116030\pi\) | |||||||
\(368\) | − 1.07133e6i | − 0.412387i | ||||||||
\(369\) | −157157. | −0.0600853 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 270440. | 0.102008 | ||||||||
\(372\) | − 1.26687e6i | − 0.474653i | ||||||||
\(373\) | − 1.79371e6i | − 0.667545i | −0.942654 | − | 0.333772i | \(-0.891678\pi\) | ||||
0.942654 | − | 0.333772i | \(-0.108322\pi\) | |||||||
\(374\) | −573234. | −0.211911 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 381926. | 0.139319 | ||||||||
\(377\) | 1.55940e6i | 0.565073i | ||||||||
\(378\) | − 69740.9i | − 0.0251049i | ||||||||
\(379\) | −3.58806e6 | −1.28310 | −0.641551 | − | 0.767080i | \(-0.721709\pi\) | ||||
−0.641551 | + | 0.767080i | \(0.721709\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.58291e6 | −0.911583 | ||||||||
\(382\) | 46286.1i | 0.0162290i | ||||||||
\(383\) | − 3.42457e6i | − 1.19291i | −0.802645 | − | 0.596457i | \(-0.796575\pi\) | ||||
0.802645 | − | 0.596457i | \(-0.203425\pi\) | |||||||
\(384\) | 1.79150e6 | 0.619996 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 340321. | 0.116257 | ||||||||
\(387\) | − 2.37040e6i | − 0.804534i | ||||||||
\(388\) | 720974.i | 0.243131i | ||||||||
\(389\) | −8625.27 | −0.00289001 | −0.00144500 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144500 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.30576e6 | −0.431940 | ||||||||
\(392\) | 110504.i | 0.0363214i | ||||||||
\(393\) | − 6.86667e6i | − 2.24267i | ||||||||
\(394\) | −194337. | −0.0630690 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.00011e6 | −0.961388 | ||||||||
\(397\) | − 1.25709e6i | − 0.400306i | −0.979765 | − | 0.200153i | \(-0.935856\pi\) | ||||
0.979765 | − | 0.200153i | \(-0.0641439\pi\) | |||||||
\(398\) | − 438796.i | − 0.138853i | ||||||||
\(399\) | 1.50687e6 | 0.473853 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42670e6 | 0.443070 | 0.221535 | − | 0.975152i | \(-0.428893\pi\) | ||||
0.221535 | + | 0.975152i | \(0.428893\pi\) | |||||||
\(402\) | − 281110.i | − 0.0867583i | ||||||||
\(403\) | 1.33281e6i | 0.408794i | ||||||||
\(404\) | −5.71176e6 | −1.74107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 85153.2 | 0.0256381 | ||||||||
\(407\) | − 717741.i | − 0.214774i | ||||||||
\(408\) | − 1.07337e6i | − 0.319226i | ||||||||
\(409\) | 3.06529e6 | 0.906073 | 0.453036 | − | 0.891492i | \(-0.350341\pi\) | ||||
0.453036 | + | 0.891492i | \(0.350341\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.59324e6 | 2.21729 | ||||||||
\(412\) | 2.03865e6i | 0.591698i | ||||||||
\(413\) | − 697291.i | − 0.201159i | ||||||||
\(414\) | 114154. | 0.0327332 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.41765e6 | −0.401640 | ||||||||
\(417\) | − 339726.i | − 0.0956728i | ||||||||
\(418\) | − 755873.i | − 0.211596i | ||||||||
\(419\) | 248240. | 0.0690776 | 0.0345388 | − | 0.999403i | \(-0.489004\pi\) | ||||
0.0345388 | + | 0.999403i | \(0.489004\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.96280e6 | 1.63963 | 0.819814 | − | 0.572630i | \(-0.194077\pi\) | ||||
0.819814 | + | 0.572630i | \(0.194077\pi\) | |||||||
\(422\) | − 243185.i | − 0.0664746i | ||||||||
\(423\) | − 1.18752e6i | − 0.322695i | ||||||||
\(424\) | 254015. | 0.0686192 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 919857. | 0.245582 | ||||||||
\(427\) | 697503.i | 0.185130i | ||||||||
\(428\) | 4.66353e6i | 1.23057i | ||||||||
\(429\) | 8.51579e6 | 2.23399 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.93538e6 | −1.27976 | −0.639879 | − | 0.768476i | \(-0.721015\pi\) | ||||
−0.639879 | + | 0.768476i | \(0.721015\pi\) | |||||||
\(432\) | 1.91151e6i | 0.492795i | ||||||||
\(433\) | 4.15513e6i | 1.06504i | 0.846418 | + | 0.532519i | \(0.178755\pi\) | ||||
−0.846418 | + | 0.532519i | \(0.821245\pi\) | |||||||
\(434\) | 72779.7 | 0.0185475 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50291e6 | 0.882496 | ||||||||
\(437\) | − 1.72180e6i | − 0.431299i | ||||||||
\(438\) | 407008.i | 0.101372i | ||||||||
\(439\) | 227955. | 0.0564531 | 0.0282265 | − | 0.999602i | \(-0.491014\pi\) | ||||
0.0282265 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 343590. | 0.0841287 | ||||||||
\(442\) | 559938.i | 0.136328i | ||||||||
\(443\) | − 1.98462e6i | − 0.480472i | −0.970715 | − | 0.240236i | \(-0.922775\pi\) | ||||
0.970715 | − | 0.240236i | \(-0.0772248\pi\) | |||||||
\(444\) | 666411. | 0.160430 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 743397. | 0.176963 | ||||||||
\(447\) | 2.20410e6i | 0.521749i | ||||||||
\(448\) | − 1.44951e6i | − 0.341214i | ||||||||
\(449\) | −2.61077e6 | −0.611157 | −0.305579 | − | 0.952167i | \(-0.598850\pi\) | ||||
−0.305579 | + | 0.952167i | \(0.598850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 731506. | 0.169347 | ||||||||
\(452\) | − 1.35892e6i | − 0.312858i | ||||||||
\(453\) | 599220.i | 0.137196i | ||||||||
\(454\) | 365606. | 0.0832480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.41536e6 | 0.318752 | ||||||||
\(457\) | 4.09917e6i | 0.918132i | 0.888402 | + | 0.459066i | \(0.151816\pi\) | ||||
−0.888402 | + | 0.459066i | \(0.848184\pi\) | |||||||
\(458\) | − 811652.i | − 0.180803i | ||||||||
\(459\) | 2.32979e6 | 0.516160 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.62378e6 | −0.575009 | −0.287505 | − | 0.957779i | \(-0.592826\pi\) | ||||
−0.287505 | + | 0.957779i | \(0.592826\pi\) | |||||||
\(462\) | − 465016.i | − 0.101359i | ||||||||
\(463\) | − 4.28563e6i | − 0.929100i | −0.885547 | − | 0.464550i | \(-0.846216\pi\) | ||||
0.885547 | − | 0.464550i | \(-0.153784\pi\) | |||||||
\(464\) | −2.33394e6 | −0.503262 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 558824. | 0.119209 | ||||||||
\(467\) | − 990118.i | − 0.210085i | −0.994468 | − | 0.105042i | \(-0.966502\pi\) | ||||
0.994468 | − | 0.105042i | \(-0.0334978\pi\) | |||||||
\(468\) | 2.93052e6i | 0.618486i | ||||||||
\(469\) | −966792. | −0.202955 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.02867e7 | 2.13660 | ||||||||
\(472\) | − 654942.i | − 0.135316i | ||||||||
\(473\) | 1.10333e7i | 2.26753i | ||||||||
\(474\) | 436449. | 0.0892253 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.83047e6 | −0.370293 | ||||||||
\(477\) | − 789812.i | − 0.158938i | ||||||||
\(478\) | − 124457.i | − 0.0249144i | ||||||||
\(479\) | −2.57976e6 | −0.513737 | −0.256868 | − | 0.966446i | \(-0.582691\pi\) | ||||
−0.256868 | + | 0.966446i | \(0.582691\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −701093. | −0.138170 | ||||||||
\(482\) | 278272.i | 0.0545571i | ||||||||
\(483\) | − 1.05926e6i | − 0.206601i | ||||||||
\(484\) | 8.89540e6 | 1.72604 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −699120. | −0.134264 | ||||||||
\(487\) | − 3.21474e6i | − 0.614219i | −0.951674 | − | 0.307109i | \(-0.900638\pi\) | ||||
0.951674 | − | 0.307109i | \(-0.0993618\pi\) | |||||||
\(488\) | 655141.i | 0.124533i | ||||||||
\(489\) | 8.63882e6 | 1.63374 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.86108e6 | −1.47156 | −0.735781 | − | 0.677220i | \(-0.763185\pi\) | ||||
−0.735781 | + | 0.677220i | \(0.763185\pi\) | |||||||
\(492\) | 679192.i | 0.126497i | ||||||||
\(493\) | 2.84465e6i | 0.527123i | ||||||||
\(494\) | −738341. | −0.136125 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.99480e6 | −0.364078 | ||||||||
\(497\) | − 3.16357e6i | − 0.574495i | ||||||||
\(498\) | − 9630.55i | − 0.00174011i | ||||||||
\(499\) | 1.35382e6 | 0.243395 | 0.121697 | − | 0.992567i | \(-0.461166\pi\) | ||||
0.121697 | + | 0.992567i | \(0.461166\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.48914e6 | 0.977035 | ||||||||
\(502\) | 1.13872e6i | 0.201677i | ||||||||
\(503\) | 3.85775e6i | 0.679851i | 0.940452 | + | 0.339926i | \(0.110402\pi\) | ||||
−0.940452 | + | 0.339926i | \(0.889598\pi\) | |||||||
\(504\) | 322723. | 0.0565918 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −531341. | −0.0922565 | ||||||||
\(507\) | − 1.02254e6i | − 0.176669i | ||||||||
\(508\) | 4.13726e6i | 0.711301i | ||||||||
\(509\) | 1.06060e7 | 1.81451 | 0.907253 | − | 0.420585i | \(-0.138175\pi\) | ||||
0.907253 | + | 0.420585i | \(0.138175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.39978e6 | 0.237142 | ||||||||
\(512\) | − 3.55598e6i | − 0.599493i | ||||||||
\(513\) | 3.07208e6i | 0.515394i | ||||||||
\(514\) | −573291. | −0.0957122 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.02443e7 | −1.69378 | ||||||||
\(517\) | 5.52747e6i | 0.909495i | ||||||||
\(518\) | 38284.1i | 0.00626895i | ||||||||
\(519\) | −1.95904e6 | −0.319246 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.17989e6 | −1.48164 | −0.740821 | − | 0.671703i | \(-0.765563\pi\) | ||||
−0.740821 | + | 0.671703i | \(0.765563\pi\) | |||||||
\(522\) | − 248687.i | − 0.0399464i | ||||||||
\(523\) | 9.05585e6i | 1.44769i | 0.689964 | + | 0.723844i | \(0.257627\pi\) | ||||
−0.689964 | + | 0.723844i | \(0.742373\pi\) | |||||||
\(524\) | −1.09989e7 | −1.74993 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 336740. | 0.0530677 | ||||||||
\(527\) | 2.43130e6i | 0.381339i | ||||||||
\(528\) | 1.27455e7i | 1.98963i | ||||||||
\(529\) | 5.22601e6 | 0.811953 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.03642e6 | −0.313422 | ||||||||
\(532\) | − 2.41368e6i | − 0.369744i | ||||||||
\(533\) | − 714539.i | − 0.108945i | ||||||||
\(534\) | −1.79478e6 | −0.272369 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −908075. | −0.136524 | ||||||||
\(537\) | − 6.48394e6i | − 0.970295i | ||||||||
\(538\) | 1.44987e6i | 0.215960i | ||||||||
\(539\) | −1.59928e6 | −0.237112 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21783e7 | 1.78894 | 0.894468 | − | 0.447132i | \(-0.147555\pi\) | ||||
0.894468 | + | 0.447132i | \(0.147555\pi\) | |||||||
\(542\) | − 1.16953e6i | − 0.171007i | ||||||||
\(543\) | − 9.93891e6i | − 1.44657i | ||||||||
\(544\) | −2.58608e6 | −0.374666 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −454230. | −0.0652070 | ||||||||
\(547\) | 9.00451e6i | 1.28674i | 0.765554 | + | 0.643372i | \(0.222465\pi\) | ||||
−0.765554 | + | 0.643372i | \(0.777535\pi\) | |||||||
\(548\) | − 1.21627e7i | − 1.73013i | ||||||||
\(549\) | 2.03703e6 | 0.288448 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.75099e6 | −0.526341 | ||||||||
\(552\) | − 994924.i | − 0.138977i | ||||||||
\(553\) | − 1.50103e6i | − 0.208727i | ||||||||
\(554\) | 1.50904e6 | 0.208894 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −544167. | −0.0746527 | ||||||||
\(557\) | − 1.54461e6i | − 0.210950i | −0.994422 | − | 0.105475i | \(-0.966364\pi\) | ||||
0.994422 | − | 0.105475i | \(-0.0336363\pi\) | |||||||
\(558\) | − 212551.i | − 0.0288986i | ||||||||
\(559\) | 1.07774e7 | 1.45876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.55345e7 | 2.08396 | ||||||||
\(562\) | 712057.i | 0.0950986i | ||||||||
\(563\) | − 1.18748e7i | − 1.57890i | −0.613816 | − | 0.789449i | \(-0.710366\pi\) | ||||
0.613816 | − | 0.789449i | \(-0.289634\pi\) | |||||||
\(564\) | −5.13217e6 | −0.679365 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.01237e6 | −0.132831 | ||||||||
\(567\) | 3.59388e6i | 0.469468i | ||||||||
\(568\) | − 2.97144e6i | − 0.386452i | ||||||||
\(569\) | 1.54308e6 | 0.199806 | 0.0999031 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999031 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.01812e6 | −0.900804 | −0.450402 | − | 0.892826i | \(-0.648719\pi\) | ||||
−0.450402 | + | 0.892826i | \(0.648719\pi\) | |||||||
\(572\) | − 1.36404e7i | − 1.74317i | ||||||||
\(573\) | − 1.25434e6i | − 0.159598i | ||||||||
\(574\) | −39018.4 | −0.00494298 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.23326e6 | −0.531641 | ||||||||
\(577\) | 5.37543e6i | 0.672162i | 0.941833 | + | 0.336081i | \(0.109102\pi\) | ||||
−0.941833 | + | 0.336081i | \(0.890898\pi\) | |||||||
\(578\) | − 8077.66i | − 0.00100569i | ||||||||
\(579\) | −9.22259e6 | −1.14329 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33121.4 | −0.00407069 | ||||||||
\(582\) | 326365.i | 0.0399389i | ||||||||
\(583\) | 3.67627e6i | 0.447957i | ||||||||
\(584\) | 1.31477e6 | 0.159521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.85770e6 | 0.223476 | ||||||||
\(587\) | 2.06682e6i | 0.247575i | 0.992309 | + | 0.123788i | \(0.0395041\pi\) | ||||
−0.992309 | + | 0.123788i | \(0.960496\pi\) | |||||||
\(588\) | − 1.48491e6i | − 0.177115i | ||||||||
\(589\) | −3.20594e6 | −0.380774 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.26648e6 | 0.620228 | ||||||||
\(592\) | − 1.04932e6i | − 0.123056i | ||||||||
\(593\) | − 5.46947e6i | − 0.638717i | −0.947634 | − | 0.319358i | \(-0.896533\pi\) | ||||
0.947634 | − | 0.319358i | \(-0.103467\pi\) | |||||||
\(594\) | 948035. | 0.110245 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.53049e6 | 0.407117 | ||||||||
\(597\) | 1.18912e7i | 1.36550i | ||||||||
\(598\) | 519016.i | 0.0593510i | ||||||||
\(599\) | −1.09943e7 | −1.25199 | −0.625996 | − | 0.779826i | \(-0.715307\pi\) | ||||
−0.625996 | + | 0.779826i | \(0.715307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.58788e7 | 1.79322 | 0.896608 | − | 0.442826i | \(-0.146024\pi\) | ||||
0.896608 | + | 0.442826i | \(0.146024\pi\) | |||||||
\(602\) | − 588514.i | − 0.0661859i | ||||||||
\(603\) | 2.82348e6i | 0.316222i | ||||||||
\(604\) | 959820. | 0.107053 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.58555e6 | −0.286004 | ||||||||
\(607\) | − 5.33262e6i | − 0.587447i | −0.955890 | − | 0.293724i | \(-0.905105\pi\) | ||||
0.955890 | − | 0.293724i | \(-0.0948945\pi\) | |||||||
\(608\) | − 3.41003e6i | − 0.374110i | ||||||||
\(609\) | −2.30762e6 | −0.252128 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.39926e6 | 0.585102 | ||||||||
\(612\) | 5.34584e6i | 0.576949i | ||||||||
\(613\) | − 8.91838e6i | − 0.958594i | −0.877653 | − | 0.479297i | \(-0.840892\pi\) | ||||
0.877653 | − | 0.479297i | \(-0.159108\pi\) | |||||||
\(614\) | 641593. | 0.0686814 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.50215e6 | −0.159501 | ||||||||
\(617\) | − 9.63586e6i | − 1.01901i | −0.860468 | − | 0.509504i | \(-0.829829\pi\) | ||||
0.860468 | − | 0.509504i | \(-0.170171\pi\) | |||||||
\(618\) | 922841.i | 0.0971976i | ||||||||
\(619\) | −1.21747e7 | −1.27712 | −0.638560 | − | 0.769572i | \(-0.720470\pi\) | ||||
−0.638560 | + | 0.769572i | \(0.720470\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.15952e6 | 0.224713 | ||||||||
\(622\) | − 1.30602e6i | − 0.135355i | ||||||||
\(623\) | 6.17260e6i | 0.637159i | ||||||||
\(624\) | 1.24498e7 | 1.27998 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 689094. | 0.0702818 | ||||||||
\(627\) | 2.04839e7i | 2.08087i | ||||||||
\(628\) | − 1.64770e7i | − 1.66717i | ||||||||
\(629\) | −1.27893e6 | −0.128890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.30854e7 | −1.30832 | −0.654161 | − | 0.756356i | \(-0.726978\pi\) | ||||
−0.654161 | + | 0.756356i | \(0.726978\pi\) | |||||||
\(632\) | − 1.40987e6i | − 0.140407i | ||||||||
\(633\) | 6.59023e6i | 0.653719i | ||||||||
\(634\) | −2.20626e6 | −0.217989 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.41336e6 | −0.334610 | ||||||||
\(637\) | 1.56219e6i | 0.152540i | ||||||||
\(638\) | 1.15754e6i | 0.112586i | ||||||||
\(639\) | −9.23911e6 | −0.895113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −441107. | −0.0424032 | −0.0212016 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0212016 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(642\) | 2.11105e6i | 0.202144i | ||||||||
\(643\) | − 4.18888e6i | − 0.399550i | −0.979842 | − | 0.199775i | \(-0.935979\pi\) | ||||
0.979842 | − | 0.199775i | \(-0.0640211\pi\) | |||||||
\(644\) | −1.69670e6 | −0.161209 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.34688e6 | −0.126983 | ||||||||
\(647\) | − 1.87822e7i | − 1.76395i | −0.471300 | − | 0.881973i | \(-0.656215\pi\) | ||||
0.471300 | − | 0.881973i | \(-0.343785\pi\) | |||||||
\(648\) | 3.37562e6i | 0.315803i | ||||||||
\(649\) | 9.47874e6 | 0.883362 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.97231e6 | −0.182399 | ||||||||
\(652\) | − 1.38375e7i | − 1.27479i | ||||||||
\(653\) | − 1.51733e6i | − 0.139251i | −0.997573 | − | 0.0696254i | \(-0.977820\pi\) | ||||
0.997573 | − | 0.0696254i | \(-0.0221804\pi\) | |||||||
\(654\) | 1.58567e6 | 0.144967 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.06944e6 | 0.0970281 | ||||||||
\(657\) | − 4.08802e6i | − 0.369487i | ||||||||
\(658\) | − 294834.i | − 0.0265468i | ||||||||
\(659\) | −1.84809e7 | −1.65772 | −0.828859 | − | 0.559458i | \(-0.811009\pi\) | ||||
−0.828859 | + | 0.559458i | \(0.811009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.03952e7 | −0.925403 | −0.462702 | − | 0.886514i | \(-0.653120\pi\) | ||||
−0.462702 | + | 0.886514i | \(0.653120\pi\) | |||||||
\(662\) | 1.59240e6i | 0.141223i | ||||||||
\(663\) | − 1.51741e7i | − 1.34066i | ||||||||
\(664\) | −31109.8 | −0.00273828 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 111808. | 0.00976756 | ||||||||
\(667\) | 2.63676e6i | 0.229486i | ||||||||
\(668\) | − 8.79242e6i | − 0.762372i | ||||||||
\(669\) | −2.01458e7 | −1.74028 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.48162e6 | −0.812973 | ||||||||
\(672\) | − 2.09786e6i | − 0.179207i | ||||||||
\(673\) | − 1.10398e7i | − 0.939556i | −0.882785 | − | 0.469778i | \(-0.844334\pi\) | ||||
0.882785 | − | 0.469778i | \(-0.155666\pi\) | |||||||
\(674\) | 1.75101e6 | 0.148470 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.63788e6 | −0.137853 | ||||||||
\(677\) | 8.23485e6i | 0.690532i | 0.938505 | + | 0.345266i | \(0.112211\pi\) | ||||
−0.938505 | + | 0.345266i | \(0.887789\pi\) | |||||||
\(678\) | − 615144.i | − 0.0513928i | ||||||||
\(679\) | 1.12243e6 | 0.0934298 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.90780e6 | −0.818671 | ||||||||
\(682\) | 989343.i | 0.0814490i | ||||||||
\(683\) | 1.98437e7i | 1.62768i | 0.581086 | + | 0.813842i | \(0.302628\pi\) | ||||
−0.581086 | + | 0.813842i | \(0.697372\pi\) | |||||||
\(684\) | −7.04909e6 | −0.576093 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 85305.3 | 0.00692095 | ||||||||
\(687\) | 2.19955e7i | 1.77804i | ||||||||
\(688\) | 1.61304e7i | 1.29919i | ||||||||
\(689\) | 3.59100e6 | 0.288182 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.37019e6 | −0.188837 | −0.0944185 | − | 0.995533i | \(-0.530099\pi\) | ||||
−0.0944185 | + | 0.995533i | \(0.530099\pi\) | |||||||
\(692\) | 3.13796e6i | 0.249105i | ||||||||
\(693\) | 4.67065e6i | 0.369440i | ||||||||
\(694\) | 789131. | 0.0621943 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.16748e6 | −0.169602 | ||||||||
\(697\) | − 1.30346e6i | − 0.101628i | ||||||||
\(698\) | 2.02491e6i | 0.157314i | ||||||||
\(699\) | −1.51439e7 | −1.17232 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.56833e7 | −1.20543 | −0.602714 | − | 0.797957i | \(-0.705914\pi\) | ||||
−0.602714 | + | 0.797957i | \(0.705914\pi\) | |||||||
\(702\) | − 926045.i | − 0.0709234i | ||||||||
\(703\) | − 1.68641e6i | − 0.128699i | ||||||||
\(704\) | 1.97042e7 | 1.49840 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.83543e6 | 0.138588 | ||||||||
\(707\) | 8.89223e6i | 0.669056i | ||||||||
\(708\) | 8.80085e6i | 0.659844i | ||||||||
\(709\) | −3.68544e6 | −0.275343 | −0.137671 | − | 0.990478i | \(-0.543962\pi\) | ||||
−0.137671 | + | 0.990478i | \(0.543962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.38373e6 | −0.325214 | ||||||||
\(712\) | 5.79772e6i | 0.428605i | ||||||||
\(713\) | 2.25361e6i | 0.166018i | ||||||||
\(714\) | −828604. | −0.0608277 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.03859e7 | −0.757113 | ||||||||
\(717\) | 3.37276e6i | 0.245012i | ||||||||
\(718\) | 790544.i | 0.0572289i | ||||||||
\(719\) | 1.56427e7 | 1.12847 | 0.564233 | − | 0.825615i | \(-0.309172\pi\) | ||||
0.564233 | + | 0.825615i | \(0.309172\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.17383e6 | 0.227376 | ||||||||
\(722\) | 19369.0i | 0.00138282i | ||||||||
\(723\) | − 7.54107e6i | − 0.536522i | ||||||||
\(724\) | −1.59200e7 | −1.12875 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.02670e6 | 0.283536 | ||||||||
\(727\) | − 1.85908e7i | − 1.30456i | −0.757979 | − | 0.652279i | \(-0.773813\pi\) | ||||
0.757979 | − | 0.652279i | \(-0.226187\pi\) | |||||||
\(728\) | 1.46731e6i | 0.102611i | ||||||||
\(729\) | 1.12318e6 | 0.0782767 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.96601e7 | 1.36079 | ||||||||
\(732\) | − 8.80353e6i | − 0.607266i | ||||||||
\(733\) | 2.49466e7i | 1.71495i | 0.514524 | + | 0.857476i | \(0.327969\pi\) | ||||
−0.514524 | + | 0.857476i | \(0.672031\pi\) | |||||||
\(734\) | −136367. | −0.00934260 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39708e6 | −0.163113 | ||||||||
\(737\) | − 1.31422e7i | − 0.891253i | ||||||||
\(738\) | 113952.i | 0.00770159i | ||||||||
\(739\) | 2.42944e7 | 1.63642 | 0.818211 | − | 0.574918i | \(-0.194966\pi\) | ||||
0.818211 | + | 0.574918i | \(0.194966\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00088e7 | 1.33868 | ||||||||
\(742\) | − 196091.i | − 0.0130752i | ||||||||
\(743\) | 4.16541e6i | 0.276812i | 0.990376 | + | 0.138406i | \(0.0441980\pi\) | ||||
−0.990376 | + | 0.138406i | \(0.955802\pi\) | |||||||
\(744\) | −1.85252e6 | −0.122696 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.30059e6 | −0.0855644 | ||||||||
\(747\) | 96729.9i | 0.00634248i | ||||||||
\(748\) | − 2.48828e7i | − 1.62610i | ||||||||
\(749\) | 7.26032e6 | 0.472880 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.36434e7 | −1.52972 | −0.764858 | − | 0.644199i | \(-0.777191\pi\) | ||||
−0.764858 | + | 0.644199i | \(0.777191\pi\) | |||||||
\(752\) | 8.08101e6i | 0.521100i | ||||||||
\(753\) | − 3.08588e7i | − 1.98332i | ||||||||
\(754\) | 1.13070e6 | 0.0724298 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 3.02730e6 | 0.192642 | ||||||||
\(757\) | − 1.50108e7i | − 0.952062i | −0.879429 | − | 0.476031i | \(-0.842075\pi\) | ||||
0.879429 | − | 0.476031i | \(-0.157925\pi\) | |||||||
\(758\) | 2.60164e6i | 0.164465i | ||||||||
\(759\) | 1.43992e7 | 0.907262 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.92191e6 | 0.182897 | 0.0914483 | − | 0.995810i | \(-0.470850\pi\) | ||||
0.0914483 | + | 0.995810i | \(0.470850\pi\) | |||||||
\(762\) | 1.87282e6i | 0.116845i | ||||||||
\(763\) | − 5.45343e6i | − 0.339124i | ||||||||
\(764\) | −2.00918e6 | −0.124533 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.48310e6 | −0.152905 | ||||||||
\(767\) | − 9.25887e6i | − 0.568290i | ||||||||
\(768\) | 1.73016e7i | 1.05848i | ||||||||
\(769\) | −1.42847e7 | −0.871073 | −0.435536 | − | 0.900171i | \(-0.643441\pi\) | ||||
−0.435536 | + | 0.900171i | \(0.643441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.55360e7 | 0.941246 | ||||||||
\(772\) | 1.47726e7i | 0.892100i | ||||||||
\(773\) | − 1.09012e7i | − 0.656186i | −0.944645 | − | 0.328093i | \(-0.893594\pi\) | ||||
0.944645 | − | 0.328093i | \(-0.106406\pi\) | |||||||
\(774\) | −1.71874e6 | −0.103123 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.05426e6 | 0.0628485 | ||||||||
\(777\) | − 1.03749e6i | − 0.0616496i | ||||||||
\(778\) | 6254.04i | 0 0.000370434i | ||||||||
\(779\) | 1.71875e6 | 0.101478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.30045e7 | 2.52282 | ||||||||
\(782\) | 946787.i | 0.0553650i | ||||||||
\(783\) | − 4.70459e6i | − 0.274231i | ||||||||
\(784\) | −2.33811e6 | −0.135854 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.97890e6 | −0.287460 | ||||||||
\(787\) | 2.56449e7i | 1.47593i | 0.674841 | + | 0.737963i | \(0.264212\pi\) | ||||
−0.674841 | + | 0.737963i | \(0.735788\pi\) | |||||||
\(788\) | − 8.43576e6i | − 0.483959i | ||||||||
\(789\) | −9.12555e6 | −0.521875 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.11560e6 | −0.120224 | ||||||||
\(792\) | 4.38699e6i | 0.248516i | ||||||||
\(793\) | 9.26169e6i | 0.523007i | ||||||||
\(794\) | −911498. | −0.0513103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.90472e7 | 1.06549 | ||||||||
\(797\) | − 7.73086e6i | − 0.431104i | −0.976492 | − | 0.215552i | \(-0.930845\pi\) | ||||
0.976492 | − | 0.215552i | \(-0.0691551\pi\) | |||||||
\(798\) | − 1.09261e6i | − 0.0607375i | ||||||||
\(799\) | 9.84931e6 | 0.545807 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.80269e7 | 0.992748 | ||||||||
\(802\) | − 1.03448e6i | − 0.0567917i | ||||||||
\(803\) | 1.90282e7i | 1.04138i | ||||||||
\(804\) | 1.22024e7 | 0.665738 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 966395. | 0.0523983 | ||||||||
\(807\) | − 3.92909e7i | − 2.12377i | ||||||||
\(808\) | 8.35218e6i | 0.450061i | ||||||||
\(809\) | 1.87811e7 | 1.00890 | 0.504452 | − | 0.863440i | \(-0.331695\pi\) | ||||
0.504452 | + | 0.863440i | \(0.331695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.00729e6 | −0.480886 | −0.240443 | − | 0.970663i | \(-0.577293\pi\) | ||||
−0.240443 | + | 0.970663i | \(0.577293\pi\) | |||||||
\(812\) | 3.69632e6i | 0.196734i | ||||||||
\(813\) | 3.16939e7i | 1.68170i | ||||||||
\(814\) | −520422. | −0.0275293 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.27110e7 | 1.19402 | ||||||||
\(817\) | 2.59240e7i | 1.35877i | ||||||||
\(818\) | − 2.22259e6i | − 0.116138i | ||||||||
\(819\) | 4.56231e6 | 0.237671 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.27965e6 | −0.480478 | −0.240239 | − | 0.970714i | \(-0.577226\pi\) | ||||
−0.240239 | + | 0.970714i | \(0.577226\pi\) | |||||||
\(822\) | − 5.50572e6i | − 0.284207i | ||||||||
\(823\) | − 1.08308e7i | − 0.557393i | −0.960379 | − | 0.278697i | \(-0.910098\pi\) | ||||
0.960379 | − | 0.278697i | \(-0.0899024\pi\) | |||||||
\(824\) | 2.98107e6 | 0.152952 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −505593. | −0.0257841 | ||||||||
\(827\) | 2.05230e7i | 1.04346i | 0.853110 | + | 0.521731i | \(0.174714\pi\) | ||||
−0.853110 | + | 0.521731i | \(0.825286\pi\) | |||||||
\(828\) | 4.95515e6i | 0.251178i | ||||||||
\(829\) | 1.42216e7 | 0.718724 | 0.359362 | − | 0.933198i | \(-0.382994\pi\) | ||||
0.359362 | + | 0.933198i | \(0.382994\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.08944e7 | −2.05429 | ||||||||
\(832\) | − 1.92472e7i | − 0.963958i | ||||||||
\(833\) | 2.84973e6i | 0.142296i | ||||||||
\(834\) | −246329. | −0.0122631 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.28108e7 | 1.62368 | ||||||||
\(837\) | − 4.02097e6i | − 0.198389i | ||||||||
\(838\) | − 179995.i | − 0.00885421i | ||||||||
\(839\) | 9.29934e6 | 0.456087 | 0.228043 | − | 0.973651i | \(-0.426767\pi\) | ||||
0.228043 | + | 0.973651i | \(0.426767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47669e7 | −0.719944 | ||||||||
\(842\) | − 4.32353e6i | − 0.210164i | ||||||||
\(843\) | − 1.92965e7i | − 0.935211i | ||||||||
\(844\) | 1.05561e7 | 0.510092 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −861053. | −0.0413623 | ||||||||
\(847\) | − 1.38486e7i | − 0.663281i | ||||||||
\(848\) | 5.37461e6i | 0.256659i | ||||||||
\(849\) | 2.74350e7 | 1.30628 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.18546e6 | −0.0561131 | ||||||||
\(852\) | 3.99290e7i | 1.88447i | ||||||||
\(853\) | − 3.07436e6i | − 0.144671i | −0.997380 | − | 0.0723357i | \(-0.976955\pi\) | ||||
0.997380 | − | 0.0723357i | \(-0.0230453\pi\) | |||||||
\(854\) | 505747. | 0.0237295 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.81938e6 | 0.318098 | ||||||||
\(857\) | − 3.45835e7i | − 1.60848i | −0.594302 | − | 0.804242i | \(-0.702572\pi\) | ||||
0.594302 | − | 0.804242i | \(-0.297428\pi\) | |||||||
\(858\) | − 6.17465e6i | − 0.286348i | ||||||||
\(859\) | −1.63022e7 | −0.753814 | −0.376907 | − | 0.926251i | \(-0.623012\pi\) | ||||
−0.376907 | + | 0.926251i | \(0.623012\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.05738e6 | 0.0486099 | ||||||||
\(862\) | 3.57856e6i | 0.164036i | ||||||||
\(863\) | 2.56962e7i | 1.17447i | 0.809416 | + | 0.587235i | \(0.199784\pi\) | ||||
−0.809416 | + | 0.587235i | \(0.800216\pi\) | |||||||
\(864\) | 4.27694e6 | 0.194917 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 3.01281e6 | 0.136514 | ||||||||
\(867\) | 218902.i | 0.00989012i | ||||||||
\(868\) | 3.15921e6i | 0.142324i | ||||||||
\(869\) | 2.04046e7 | 0.916596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.28374e7 | −0.573366 | ||||||||
\(872\) | − 5.12222e6i | − 0.228122i | ||||||||
\(873\) | − 3.27803e6i | − 0.145572i | ||||||||
\(874\) | −1.24844e6 | −0.0552829 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.76673e7 | −0.777877 | ||||||||
\(877\) | − 3.30060e7i | − 1.44908i | −0.689230 | − | 0.724542i | \(-0.742051\pi\) | ||||
0.689230 | − | 0.724542i | \(-0.257949\pi\) | |||||||
\(878\) | − 165286.i | − 0.00723603i | ||||||||
\(879\) | −5.03429e7 | −2.19769 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.26705e6 | 0.0984060 | 0.0492030 | − | 0.998789i | \(-0.484332\pi\) | ||||
0.0492030 | + | 0.998789i | \(0.484332\pi\) | |||||||
\(882\) | − 249131.i | − 0.0107834i | ||||||||
\(883\) | 1.97779e7i | 0.853649i | 0.904334 | + | 0.426825i | \(0.140368\pi\) | ||||
−0.904334 | + | 0.426825i | \(0.859632\pi\) | |||||||
\(884\) | −2.43057e7 | −1.04611 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.43901e6 | −0.0615858 | ||||||||
\(887\) | 36468.3i | 0.00155635i | 1.00000 | 0.000778173i | \(0.000247700\pi\) | |||||
−1.00000 | 0.000778173i | \(0.999752\pi\) | ||||||||
\(888\) | − 974478.i | − 0.0414705i | ||||||||
\(889\) | 6.44100e6 | 0.273337 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.88541e7 | −2.06161 | ||||||||
\(892\) | 3.22692e7i | 1.35793i | ||||||||
\(893\) | 1.29874e7i | 0.544997i | ||||||||
\(894\) | 1.59815e6 | 0.0668767 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.46747e6 | −0.185905 | ||||||||
\(897\) | − 1.40652e7i | − 0.583665i | ||||||||
\(898\) | 1.89303e6i | 0.0783367i | ||||||||
\(899\) | 4.90958e6 | 0.202602 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.55068e6 | 0.268828 | ||||||||
\(902\) | − 530403.i | − 0.0217065i | ||||||||
\(903\) | 1.59485e7i | 0.650881i | ||||||||
\(904\) | −1.98711e6 | −0.0808727 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 434484. | 0.0175854 | ||||||||
\(907\) | − 1.62298e7i | − 0.655079i | −0.944837 | − | 0.327540i | \(-0.893781\pi\) | ||||
0.944837 | − | 0.327540i | \(-0.106219\pi\) | |||||||
\(908\) | 1.58702e7i | 0.638802i | ||||||||
\(909\) | 2.59695e7 | 1.04245 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.61699e7 | −1.04474 | −0.522368 | − | 0.852720i | \(-0.674951\pi\) | ||||
−0.522368 | + | 0.852720i | \(0.674951\pi\) | |||||||
\(912\) | 2.99469e7i | 1.19224i | ||||||||
\(913\) | − 450241.i | − 0.0178759i | ||||||||
\(914\) | 2.97224e6 | 0.117684 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.52320e7 | 1.38739 | ||||||||
\(917\) | 1.71234e7i | 0.672461i | ||||||||
\(918\) | − 1.68929e6i | − 0.0661602i | ||||||||
\(919\) | −4.05973e6 | −0.158565 | −0.0792826 | − | 0.996852i | \(-0.525263\pi\) | ||||
−0.0792826 | + | 0.996852i | \(0.525263\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.73870e7 | −0.675421 | ||||||||
\(922\) | 1.90246e6i | 0.0737034i | ||||||||
\(923\) | − 4.20070e7i | − 1.62300i | ||||||||
\(924\) | 2.01853e7 | 0.777778 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.10744e6 | −0.119090 | ||||||||
\(927\) | − 9.26907e6i | − 0.354272i | ||||||||
\(928\) | 5.22212e6i | 0.199057i | ||||||||
\(929\) | −3.69518e6 | −0.140474 | −0.0702370 | − | 0.997530i | \(-0.522376\pi\) | ||||
−0.0702370 | + | 0.997530i | \(0.522376\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.75769e6 | −0.142084 | ||||||||
\(932\) | 2.42573e7i | 0.914751i | ||||||||
\(933\) | 3.53927e7i | 1.33110i | ||||||||
\(934\) | −717918. | −0.0269282 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.28523e6 | 0.159877 | ||||||||
\(937\) | 1.91384e7i | 0.712126i | 0.934462 | + | 0.356063i | \(0.115881\pi\) | ||||
−0.934462 | + | 0.356063i | \(0.884119\pi\) | |||||||
\(938\) | 701004.i | 0.0260144i | ||||||||
\(939\) | −1.86742e7 | −0.691160 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.20954e7 | 0.445294 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(942\) | − 7.45870e6i | − 0.273865i | ||||||||
\(943\) | − 1.20820e6i | − 0.0442445i | ||||||||
\(944\) | 1.38577e7 | 0.506127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00007e6 | 0.290647 | ||||||||
\(947\) | 1.95969e7i | 0.710087i | 0.934850 | + | 0.355044i | \(0.115534\pi\) | ||||
−0.934850 | + | 0.355044i | \(0.884466\pi\) | |||||||
\(948\) | 1.89453e7i | 0.684669i | ||||||||
\(949\) | 1.85868e7 | 0.669945 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.97890e7 | 2.14373 | ||||||||
\(952\) | 2.67666e6i | 0.0957196i | ||||||||
\(953\) | 4.23265e7i | 1.50966i | 0.655918 | + | 0.754832i | \(0.272282\pi\) | ||||
−0.655918 | + | 0.754832i | \(0.727718\pi\) | |||||||
\(954\) | −572679. | −0.0203723 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.40243e6 | 0.191181 | ||||||||
\(957\) | − 3.13691e7i | − 1.10719i | ||||||||
\(958\) | 1.87054e6i | 0.0658496i | ||||||||
\(959\) | −1.89353e7 | −0.664852 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.44330e7 | −0.853430 | ||||||||
\(962\) | 508351.i | 0.0177103i | ||||||||
\(963\) | − 2.12035e7i | − 0.736788i | ||||||||
\(964\) | −1.20792e7 | −0.418644 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −768048. | −0.0264817 | ||||||||
\(967\) | − 1.39211e6i | − 0.0478749i | −0.999713 | − | 0.0239375i | \(-0.992380\pi\) | ||||
0.999713 | − | 0.0239375i | \(-0.00762026\pi\) | |||||||
\(968\) | − 1.30075e7i | − 0.446176i | ||||||||
\(969\) | 3.64999e7 | 1.24877 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.41877e7 | 1.50402 | 0.752009 | − | 0.659153i | \(-0.229085\pi\) | ||||
0.752009 | + | 0.659153i | \(0.229085\pi\) | |||||||
\(972\) | − 3.03473e7i | − 1.03028i | ||||||||
\(973\) | 847175.i | 0.0286874i | ||||||||
\(974\) | −2.33095e6 | −0.0787292 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.38619e7 | −0.465798 | ||||||||
\(977\) | 5.60457e7i | 1.87848i | 0.343264 | + | 0.939239i | \(0.388467\pi\) | ||||
−0.343264 | + | 0.939239i | \(0.611533\pi\) | |||||||
\(978\) | − 6.26386e6i | − 0.209409i | ||||||||
\(979\) | −8.39082e7 | −2.79800 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.59266e7 | −0.528384 | ||||||||
\(982\) | 5.69993e6i | 0.188621i | ||||||||
\(983\) | − 5.00560e7i | − 1.65224i | −0.563497 | − | 0.826118i | \(-0.690544\pi\) | ||||
0.563497 | − | 0.826118i | \(-0.309456\pi\) | |||||||
\(984\) | 993166. | 0.0326990 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.06261e6 | 0.0675654 | ||||||||
\(987\) | 7.98990e6i | 0.261065i | ||||||||
\(988\) | − 3.20497e7i | − 1.04456i | ||||||||
\(989\) | 1.82233e7 | 0.592428 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.59116e7 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(992\) | 4.46330e6i | 0.144005i | ||||||||
\(993\) | − 4.31534e7i | − 1.38881i | ||||||||
\(994\) | −2.29385e6 | −0.0736375 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 418041. | 0.0133528 | ||||||||
\(997\) | − 4.25995e7i | − 1.35727i | −0.734476 | − | 0.678635i | \(-0.762572\pi\) | ||||
0.734476 | − | 0.678635i | \(-0.237428\pi\) | |||||||
\(998\) | − 981634.i | − 0.0311978i | ||||||||
\(999\) | 2.11514e6 | 0.0670542 |
(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 | 175.6.b.c.99.2 | 4 | ||
5.2 | odd | 4 | 7.6.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 175.6.a.c.1.2 | 2 | |||
5.4 | even | 2 | inner | 175.6.b.c.99.3 | 4 | ||
15.2 | even | 4 | 63.6.a.f.1.2 | 2 | |||
20.7 | even | 4 | 112.6.a.h.1.1 | 2 | |||
35.2 | odd | 12 | 49.6.c.e.18.2 | 4 | |||
35.12 | even | 12 | 49.6.c.d.18.2 | 4 | |||
35.17 | even | 12 | 49.6.c.d.30.2 | 4 | |||
35.27 | even | 4 | 49.6.a.f.1.1 | 2 | |||
35.32 | odd | 12 | 49.6.c.e.30.2 | 4 | |||
40.27 | even | 4 | 448.6.a.u.1.2 | 2 | |||
40.37 | odd | 4 | 448.6.a.w.1.1 | 2 | |||
55.32 | even | 4 | 847.6.a.c.1.2 | 2 | |||
60.47 | odd | 4 | 1008.6.a.bq.1.2 | 2 | |||
105.62 | odd | 4 | 441.6.a.l.1.2 | 2 | |||
140.27 | odd | 4 | 784.6.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
49.6.a.f.1.1 | 2 | 35.27 | even | 4 | |||
49.6.c.d.18.2 | 4 | 35.12 | even | 12 | |||
49.6.c.d.30.2 | 4 | 35.17 | even | 12 | |||
49.6.c.e.18.2 | 4 | 35.2 | odd | 12 | |||
49.6.c.e.30.2 | 4 | 35.32 | odd | 12 | |||
63.6.a.f.1.2 | 2 | 15.2 | even | 4 | |||
112.6.a.h.1.1 | 2 | 20.7 | even | 4 | |||
175.6.a.c.1.2 | 2 | 5.3 | odd | 4 | |||
175.6.b.c.99.2 | 4 | 1.1 | even | 1 | trivial | ||
175.6.b.c.99.3 | 4 | 5.4 | even | 2 | inner | ||
441.6.a.l.1.2 | 2 | 105.62 | odd | 4 | |||
448.6.a.u.1.2 | 2 | 40.27 | even | 4 | |||
448.6.a.w.1.1 | 2 | 40.37 | odd | 4 | |||
784.6.a.v.1.2 | 2 | 140.27 | odd | 4 | |||
847.6.a.c.1.2 | 2 | 55.32 | even | 4 | |||
1008.6.a.bq.1.2 | 2 | 60.47 | odd | 4 |