Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,6,Mod(37,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.37");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.g (of order \(3\), 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: | \(20.2083612964\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{130})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 130x^{2} + 16900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 14) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.2 | ||
Root | \(5.70088 + 9.87421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.37 |
Dual form | 126.6.g.e.109.2 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 3.46410i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −8.00000 | − | 13.8564i | −0.250000 | − | 0.433013i | ||||
\(5\) | −10.5000 | + | 18.1865i | −0.187830 | + | 0.325331i | −0.944526 | − | 0.328436i | \(-0.893479\pi\) |
0.756697 | + | 0.653766i | \(0.226812\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 126.411 | + | 28.7642i | 0.975075 | + | 0.221874i | ||||
\(8\) | 64.0000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −42.0000 | − | 72.7461i | −0.132816 | − | 0.230043i | ||||
\(11\) | −312.937 | − | 542.023i | −0.779785 | − | 1.35063i | −0.932065 | − | 0.362290i | \(-0.881995\pi\) |
0.152280 | − | 0.988337i | \(-0.451338\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.821 | −0.339419 | −0.169710 | − | 0.985494i | \(-0.554283\pi\) | ||||
−0.169710 | + | 0.985494i | \(0.554283\pi\) | |||||||
\(14\) | −352.463 | + | 380.371i | −0.480611 | + | 0.518665i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −128.000 | + | 221.703i | −0.125000 | + | 0.216506i | ||||
\(17\) | 530.732 | + | 919.254i | 0.445402 | + | 0.771460i | 0.998080 | − | 0.0619354i | \(-0.0197273\pi\) |
−0.552678 | + | 0.833395i | \(0.686394\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 941.989 | − | 1631.57i | 0.598635 | − | 1.03687i | −0.394388 | − | 0.918944i | \(-0.629043\pi\) |
0.993023 | − | 0.117922i | \(-0.0376233\pi\) | |||||||
\(20\) | 336.000 | 0.187830 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2503.49 | 1.10278 | ||||||||
\(23\) | 1858.68 | − | 3219.34i | 0.732632 | − | 1.26896i | −0.223122 | − | 0.974790i | \(-0.571625\pi\) |
0.955754 | − | 0.294166i | \(-0.0950418\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1342.00 | + | 2324.41i | 0.429440 | + | 0.743812i | ||||
\(26\) | 413.642 | − | 716.449i | 0.120003 | − | 0.207851i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −612.716 | − | 1981.71i | −0.147694 | − | 0.477689i | ||||
\(29\) | 123.747 | 0.0273238 | 0.0136619 | − | 0.999907i | \(-0.495651\pi\) | ||||
0.0136619 | + | 0.999907i | \(0.495651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4554.63 | + | 7888.85i | 0.851234 | + | 1.47438i | 0.880095 | + | 0.474797i | \(0.157479\pi\) |
−0.0288611 | + | 0.999583i | \(0.509188\pi\) | |||||||
\(32\) | −512.000 | − | 886.810i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4245.85 | −0.629894 | ||||||||
\(35\) | −1850.43 | + | 1996.95i | −0.255331 | + | 0.275547i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3014.36 | − | 5221.03i | 0.361986 | − | 0.626977i | −0.626302 | − | 0.779581i | \(-0.715432\pi\) |
0.988288 | + | 0.152603i | \(0.0487656\pi\) | |||||||
\(38\) | 3767.96 | + | 6526.29i | 0.423299 | + | 0.733175i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −672.000 | + | 1163.94i | −0.0664078 | + | 0.115022i | ||||
\(41\) | 17201.9 | 1.59814 | 0.799071 | − | 0.601236i | \(-0.205325\pi\) | ||||
0.799071 | + | 0.601236i | \(0.205325\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5401.98 | 0.445535 | 0.222767 | − | 0.974872i | \(-0.428491\pi\) | ||||
0.222767 | + | 0.974872i | \(0.428491\pi\) | |||||||
\(44\) | −5006.99 | + | 8672.36i | −0.389893 | + | 0.675314i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7434.74 | + | 12877.3i | 0.518049 | + | 0.897288i | ||||
\(47\) | 937.621 | − | 1624.01i | 0.0619131 | − | 0.107237i | −0.833407 | − | 0.552659i | \(-0.813613\pi\) |
0.895321 | + | 0.445422i | \(0.146946\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15152.2 | + | 7272.19i | 0.901544 | + | 0.432688i | ||||
\(50\) | −10736.0 | −0.607320 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1654.57 | + | 2865.80i | 0.0848548 | + | 0.146973i | ||||
\(53\) | 9353.62 | + | 16200.9i | 0.457393 | + | 0.792229i | 0.998822 | − | 0.0485180i | \(-0.0154498\pi\) |
−0.541429 | + | 0.840747i | \(0.682116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 13143.3 | 0.585867 | ||||||||
\(56\) | 8090.27 | + | 1840.91i | 0.344741 | + | 0.0784444i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −247.495 | + | 428.673i | −0.00966042 | + | 0.0167323i | ||||
\(59\) | −1267.39 | − | 2195.18i | −0.0474002 | − | 0.0820995i | 0.841352 | − | 0.540488i | \(-0.181760\pi\) |
−0.888752 | + | 0.458388i | \(0.848427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1047.35 | − | 1814.07i | 0.0360386 | − | 0.0624208i | −0.847444 | − | 0.530886i | \(-0.821859\pi\) |
0.883482 | + | 0.468465i | \(0.155193\pi\) | |||||||
\(62\) | −36437.1 | −1.20383 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4096.00 | 0.125000 | ||||||||
\(65\) | 2171.62 | − | 3761.36i | 0.0637530 | − | 0.110423i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29310.4 | − | 50767.1i | −0.797691 | − | 1.38164i | −0.921117 | − | 0.389287i | \(-0.872722\pi\) |
0.123426 | − | 0.992354i | \(-0.460612\pi\) | |||||||
\(68\) | 8491.71 | − | 14708.1i | 0.222701 | − | 0.385730i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3216.76 | − | 10404.0i | −0.0784645 | − | 0.253778i | ||||
\(71\) | 31279.5 | 0.736401 | 0.368201 | − | 0.929746i | \(-0.379974\pi\) | ||||
0.368201 | + | 0.929746i | \(0.379974\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3575.24 | + | 6192.49i | 0.0785231 | + | 0.136006i | 0.902613 | − | 0.430453i | \(-0.141646\pi\) |
−0.824090 | + | 0.566459i | \(0.808313\pi\) | |||||||
\(74\) | 12057.5 | + | 20884.1i | 0.255962 | + | 0.443340i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −30143.7 | −0.598635 | ||||||||
\(77\) | −23967.7 | − | 77518.7i | −0.460680 | − | 1.48998i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1489.91 | + | 2580.59i | −0.0268591 | + | 0.0465213i | −0.879143 | − | 0.476559i | \(-0.841884\pi\) |
0.852283 | + | 0.523080i | \(0.175217\pi\) | |||||||
\(80\) | −2688.00 | − | 4655.75i | −0.0469574 | − | 0.0813327i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −34403.7 | + | 59589.0i | −0.565029 | + | 0.978659i | ||||
\(83\) | −45954.6 | −0.732207 | −0.366103 | − | 0.930574i | \(-0.619308\pi\) | ||||
−0.366103 | + | 0.930574i | \(0.619308\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −22290.7 | −0.334639 | ||||||||
\(86\) | −10804.0 | + | 18713.0i | −0.157520 | + | 0.272833i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −20028.0 | − | 34689.4i | −0.275696 | − | 0.477519i | ||||
\(89\) | 49520.0 | − | 85771.1i | 0.662682 | − | 1.14780i | −0.317226 | − | 0.948350i | \(-0.602751\pi\) |
0.979908 | − | 0.199450i | \(-0.0639154\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −26144.4 | − | 5949.04i | −0.330959 | − | 0.0753084i | ||||
\(92\) | −59477.9 | −0.732632 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3750.48 | + | 6496.03i | 0.0437792 | + | 0.0758278i | ||||
\(95\) | 19781.8 | + | 34263.0i | 0.224883 | + | 0.389509i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115548. | −1.24691 | −0.623454 | − | 0.781860i | \(-0.714271\pi\) | ||||
−0.623454 | + | 0.781860i | \(0.714271\pi\) | |||||||
\(98\) | −55496.1 | + | 37944.5i | −0.583710 | + | 0.399102i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 21472.0 | − | 37190.6i | 0.214720 | − | 0.371906i | ||||
\(101\) | 5475.73 | + | 9484.25i | 0.0534120 | + | 0.0925123i | 0.891495 | − | 0.453030i | \(-0.149657\pi\) |
−0.838083 | + | 0.545542i | \(0.816324\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68862.2 | − | 119273.i | 0.639570 | − | 1.10777i | −0.345957 | − | 0.938250i | \(-0.612446\pi\) |
0.985527 | − | 0.169517i | \(-0.0542208\pi\) | |||||||
\(104\) | −13236.5 | −0.120003 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −74828.9 | −0.646852 | ||||||||
\(107\) | 37786.5 | − | 65448.1i | 0.319064 | − | 0.552634i | −0.661229 | − | 0.750184i | \(-0.729965\pi\) |
0.980293 | + | 0.197550i | \(0.0632983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −22263.1 | − | 38560.9i | −0.179482 | − | 0.310871i | 0.762221 | − | 0.647316i | \(-0.224109\pi\) |
−0.941703 | + | 0.336445i | \(0.890775\pi\) | |||||||
\(110\) | −26286.7 | + | 45529.9i | −0.207135 | + | 0.358769i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −22557.6 | + | 24343.7i | −0.169922 | + | 0.183376i | ||||
\(113\) | −90456.5 | −0.666413 | −0.333207 | − | 0.942854i | \(-0.608131\pi\) | ||||
−0.333207 | + | 0.942854i | \(0.608131\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 39032.4 | + | 67606.0i | 0.275220 | + | 0.476695i | ||||
\(116\) | −989.979 | − | 1714.69i | −0.00683095 | − | 0.0118315i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10139.1 | 0.0670340 | ||||||||
\(119\) | 40648.5 | + | 131469.i | 0.263134 | + | 0.851055i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115333. | + | 199763.i | −0.716130 | + | 1.24037i | ||||
\(122\) | 4189.41 | + | 7256.27i | 0.0254832 | + | 0.0441381i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 72874.1 | − | 126222.i | 0.425617 | − | 0.737190i | ||||
\(125\) | −121989. | −0.698306 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 187707. | 1.03269 | 0.516346 | − | 0.856380i | \(-0.327292\pi\) | ||||
0.516346 | + | 0.856380i | \(0.327292\pi\) | |||||||
\(128\) | −8192.00 | + | 14189.0i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8686.48 | + | 15045.4i | 0.0450802 | + | 0.0780812i | ||||
\(131\) | 77206.1 | − | 133725.i | 0.393073 | − | 0.680823i | −0.599780 | − | 0.800165i | \(-0.704745\pi\) |
0.992853 | + | 0.119342i | \(0.0380785\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 166008. | − | 179153.i | 0.813768 | − | 0.878201i | ||||
\(134\) | 234483. | 1.12810 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 33966.8 | + | 58832.3i | 0.157474 | + | 0.272752i | ||||
\(137\) | 54618.9 | + | 94602.7i | 0.248623 | + | 0.430628i | 0.963144 | − | 0.268986i | \(-0.0866886\pi\) |
−0.714521 | + | 0.699614i | \(0.753355\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −204695. | −0.898609 | −0.449305 | − | 0.893379i | \(-0.648328\pi\) | ||||
−0.449305 | + | 0.893379i | \(0.648328\pi\) | |||||||
\(140\) | 42473.9 | + | 9664.77i | 0.183148 | + | 0.0416746i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −62559.1 | + | 108355.i | −0.260357 | + | 0.450952i | ||||
\(143\) | 64721.9 | + | 112102.i | 0.264674 | + | 0.458429i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1299.35 | + | 2250.54i | −0.00513222 | + | 0.00888926i | ||||
\(146\) | −28601.9 | −0.111048 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −96459.6 | −0.361986 | ||||||||
\(149\) | −203154. | + | 351873.i | −0.749651 | + | 1.29843i | 0.198339 | + | 0.980134i | \(0.436445\pi\) |
−0.947990 | + | 0.318300i | \(0.896888\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 208419. | + | 360992.i | 0.743866 | + | 1.28841i | 0.950723 | + | 0.310043i | \(0.100343\pi\) |
−0.206856 | + | 0.978371i | \(0.566323\pi\) | |||||||
\(152\) | 60287.3 | − | 104421.i | 0.211649 | − | 0.366588i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 316468. | + | 72011.0i | 1.07530 | + | 0.244679i | ||||
\(155\) | −191295. | −0.639548 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −59645.3 | − | 103309.i | −0.193120 | − | 0.334493i | 0.753163 | − | 0.657834i | \(-0.228527\pi\) |
−0.946283 | + | 0.323341i | \(0.895194\pi\) | |||||||
\(158\) | −5959.62 | − | 10322.4i | −0.0189922 | − | 0.0328955i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 21504.0 | 0.0664078 | ||||||||
\(161\) | 327559. | − | 353494.i | 0.995920 | − | 1.07478i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23686.2 | + | 41025.7i | −0.0698275 | + | 0.120945i | −0.898825 | − | 0.438307i | \(-0.855578\pi\) |
0.828998 | + | 0.559252i | \(0.188912\pi\) | |||||||
\(164\) | −137615. | − | 238356.i | −0.399536 | − | 0.692016i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 91909.2 | − | 159191.i | 0.258874 | − | 0.448383i | ||||
\(167\) | 231669. | 0.642802 | 0.321401 | − | 0.946943i | \(-0.395846\pi\) | ||||
0.321401 | + | 0.946943i | \(0.395846\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328518. | −0.884795 | ||||||||
\(170\) | 44581.5 | − | 77217.3i | 0.118313 | − | 0.204924i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −43215.8 | − | 74852.0i | −0.111384 | − | 0.192922i | ||||
\(173\) | 67169.6 | − | 116341.i | 0.170631 | − | 0.295541i | −0.768010 | − | 0.640438i | \(-0.778753\pi\) |
0.938641 | + | 0.344897i | \(0.112086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 102783. | + | 332432.i | 0.253704 | + | 0.820554i | ||||
\(176\) | 160224. | 0.389893 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 198080. | + | 343085.i | 0.468587 | + | 0.811617i | ||||
\(179\) | 23292.2 | + | 40343.2i | 0.0543347 | + | 0.0941105i | 0.891913 | − | 0.452206i | \(-0.149363\pi\) |
−0.837579 | + | 0.546317i | \(0.816030\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 829210. | 1.88134 | 0.940672 | − | 0.339317i | \(-0.110196\pi\) | ||||
0.940672 | + | 0.339317i | \(0.110196\pi\) | |||||||
\(182\) | 72896.8 | − | 78668.6i | 0.163129 | − | 0.176045i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 118956. | − | 206037.i | 0.259025 | − | 0.448644i | ||||
\(185\) | 63301.6 | + | 109642.i | 0.135983 | + | 0.235530i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 332171. | − | 575337.i | 0.694636 | − | 1.20315i | ||||
\(188\) | −30003.9 | −0.0619131 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −158254. | −0.318032 | ||||||||
\(191\) | −235958. | + | 408692.i | −0.468006 | + | 0.810611i | −0.999332 | − | 0.0365572i | \(-0.988361\pi\) |
0.531325 | + | 0.847168i | \(0.321694\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −344177. | − | 596132.i | −0.665103 | − | 1.15199i | −0.979257 | − | 0.202620i | \(-0.935054\pi\) |
0.314155 | − | 0.949372i | \(-0.398279\pi\) | |||||||
\(194\) | 231097. | − | 400271.i | 0.440849 | − | 0.763573i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −20451.5 | − | 268133.i | −0.0380263 | − | 0.498552i | ||||
\(197\) | −311915. | −0.572625 | −0.286313 | − | 0.958136i | \(-0.592430\pi\) | ||||
−0.286313 | + | 0.958136i | \(0.592430\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 143606. | + | 248733.i | 0.257063 | + | 0.445246i | 0.965454 | − | 0.260574i | \(-0.0839119\pi\) |
−0.708391 | + | 0.705820i | \(0.750579\pi\) | |||||||
\(200\) | 85888.0 | + | 148762.i | 0.151830 | + | 0.262977i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −43805.9 | −0.0755360 | ||||||||
\(203\) | 15643.0 | + | 3559.49i | 0.0266428 | + | 0.00606245i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −180619. | + | 312842.i | −0.300179 | + | 0.519925i | ||||
\(206\) | 275449. | + | 477091.i | 0.452244 | + | 0.783310i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 26473.1 | − | 45852.7i | 0.0424274 | − | 0.0734864i | ||||
\(209\) | −1.17913e6 | −1.86723 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −460493. | −0.712061 | −0.356031 | − | 0.934474i | \(-0.615870\pi\) | ||||
−0.356031 | + | 0.934474i | \(0.615870\pi\) | |||||||
\(212\) | 149658. | − | 259215.i | 0.228697 | − | 0.396114i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 151146. | + | 261793.i | 0.225612 | + | 0.390771i | ||||
\(215\) | −56720.8 | + | 98243.3i | −0.0836847 | + | 0.144946i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 348837. | + | 1.12824e6i | 0.502890 | + | 1.62650i | ||||
\(218\) | 178105. | 0.253825 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −105147. | − | 182120.i | −0.146467 | − | 0.253688i | ||||
\(221\) | −109766. | − | 190121.i | −0.151178 | − | 0.261848i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.19776e6 | −1.61290 | −0.806449 | − | 0.591304i | \(-0.798613\pi\) | ||||
−0.806449 | + | 0.591304i | \(0.798613\pi\) | |||||||
\(224\) | −39213.8 | − | 126829.i | −0.0522179 | − | 0.168888i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 180913. | − | 313350.i | 0.235613 | − | 0.408093i | ||||
\(227\) | 447281. | + | 774713.i | 0.576123 | + | 0.997875i | 0.995919 | + | 0.0902559i | \(0.0287685\pi\) |
−0.419795 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 129628. | − | 224522.i | 0.163347 | − | 0.282925i | −0.772720 | − | 0.634747i | \(-0.781104\pi\) |
0.936067 | + | 0.351822i | \(0.114438\pi\) | |||||||
\(230\) | −312259. | −0.389220 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7919.83 | 0.00966042 | ||||||||
\(233\) | 105657. | − | 183004.i | 0.127500 | − | 0.220836i | −0.795207 | − | 0.606337i | \(-0.792638\pi\) |
0.922707 | + | 0.385501i | \(0.125971\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19690.0 | + | 34104.2i | 0.0232582 | + | 0.0402845i | ||||
\(236\) | −20278.2 | + | 35122.9i | −0.0237001 | + | 0.0410498i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −536720. | − | 122129.i | −0.614194 | − | 0.139757i | ||||
\(239\) | −463.018 | −0.000524328 | −0.000262164 | − | 1.00000i | \(-0.500083\pi\) | ||||
−0.000262164 | 1.00000i | \(0.500083\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −143197. | − | 248025.i | −0.158815 | − | 0.275076i | 0.775626 | − | 0.631192i | \(-0.217434\pi\) |
−0.934442 | + | 0.356116i | \(0.884101\pi\) | |||||||
\(242\) | −461334. | − | 799053.i | −0.506380 | − | 0.877076i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −33515.3 | −0.0360386 | ||||||||
\(245\) | −291355. | + | 199209.i | −0.310103 | + | 0.212028i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −194823. | + | 337444.i | −0.203188 | + | 0.351932i | ||||
\(248\) | 291496. | + | 504887.i | 0.300957 | + | 0.521272i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 243978. | − | 422582.i | 0.246888 | − | 0.427623i | ||||
\(251\) | 1.37168e6 | 1.37426 | 0.687129 | − | 0.726535i | \(-0.258870\pi\) | ||||
0.687129 | + | 0.726535i | \(0.258870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.32660e6 | −2.28518 | ||||||||
\(254\) | −375414. | + | 650236.i | −0.365112 | + | 0.632392i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32768.0 | − | 56755.8i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −379612. | + | 657507.i | −0.358515 | + | 0.620965i | −0.987713 | − | 0.156279i | \(-0.950050\pi\) |
0.629198 | + | 0.777245i | \(0.283383\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 531226. | − | 573287.i | 0.492073 | − | 0.531035i | ||||
\(260\) | −69491.9 | −0.0637530 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 308825. | + | 534900.i | 0.277945 | + | 0.481415i | ||||
\(263\) | −536222. | − | 928764.i | −0.478030 | − | 0.827973i | 0.521652 | − | 0.853158i | \(-0.325316\pi\) |
−0.999683 | + | 0.0251852i | \(0.991982\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −392852. | −0.343648 | ||||||||
\(266\) | 288586. | + | 933375.i | 0.250075 | + | 0.808820i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −468966. | + | 812273.i | −0.398845 | + | 0.690820i | ||||
\(269\) | −883056. | − | 1.52950e6i | −0.744059 | − | 1.28875i | −0.950633 | − | 0.310317i | \(-0.899565\pi\) |
0.206574 | − | 0.978431i | \(-0.433769\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.02586e6 | − | 1.77684e6i | 0.848522 | − | 1.46968i | −0.0340046 | − | 0.999422i | \(-0.510826\pi\) |
0.882527 | − | 0.470262i | \(-0.155841\pi\) | |||||||
\(272\) | −271735. | −0.222701 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −436951. | −0.351606 | ||||||||
\(275\) | 839922. | − | 1.45479e6i | 0.669742 | − | 1.16003i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −435341. | − | 754033.i | −0.340903 | − | 0.590461i | 0.643698 | − | 0.765280i | \(-0.277399\pi\) |
−0.984601 | + | 0.174819i | \(0.944066\pi\) | |||||||
\(278\) | 409391. | − | 709085.i | 0.317706 | − | 0.550284i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −118428. | + | 127804.i | −0.0902730 | + | 0.0974207i | ||||
\(281\) | −2.35412e6 | −1.77854 | −0.889270 | − | 0.457383i | \(-0.848787\pi\) | ||||
−0.889270 | + | 0.457383i | \(0.848787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.09518e6 | + | 1.89690e6i | 0.812863 | + | 1.40792i | 0.910852 | + | 0.412733i | \(0.135426\pi\) |
−0.0979887 | + | 0.995188i | \(0.531241\pi\) | |||||||
\(284\) | −250236. | − | 433422.i | −0.184100 | − | 0.318871i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −517775. | −0.374306 | ||||||||
\(287\) | 2.17450e6 | + | 494797.i | 1.55831 | + | 0.354587i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 146576. | − | 253878.i | 0.103233 | − | 0.178805i | ||||
\(290\) | −5197.39 | − | 9002.14i | −0.00362903 | − | 0.00628566i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 57203.8 | − | 99079.9i | 0.0392616 | − | 0.0680030i | ||||
\(293\) | 807700. | 0.549644 | 0.274822 | − | 0.961495i | \(-0.411381\pi\) | ||||
0.274822 | + | 0.961495i | \(0.411381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53230.4 | 0.0356127 | ||||||||
\(296\) | 192919. | − | 334146.i | 0.127981 | − | 0.221670i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −812615. | − | 1.40749e6i | −0.530083 | − | 0.918131i | ||||
\(299\) | −384415. | + | 665826.i | −0.248669 | + | 0.430708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 682867. | + | 155384.i | 0.434430 | + | 0.0988528i | ||||
\(302\) | −1.66735e6 | −1.05199 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 241149. | + | 417683.i | 0.149659 | + | 0.259217i | ||||
\(305\) | 21994.4 | + | 38095.4i | 0.0135383 | + | 0.0234489i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 211516. | 0.128085 | 0.0640424 | − | 0.997947i | \(-0.479601\pi\) | ||||
0.0640424 | + | 0.997947i | \(0.479601\pi\) | |||||||
\(308\) | −882390. | + | 952256.i | −0.530009 | + | 0.571975i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 382589. | − | 662664.i | 0.226114 | − | 0.391642i | ||||
\(311\) | −145855. | − | 252627.i | −0.0855104 | − | 0.148108i | 0.820098 | − | 0.572223i | \(-0.193919\pi\) |
−0.905609 | + | 0.424114i | \(0.860585\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 997988. | − | 1.72857e6i | 0.575791 | − | 0.997299i | −0.420165 | − | 0.907448i | \(-0.638028\pi\) |
0.995955 | − | 0.0898507i | \(-0.0286390\pi\) | |||||||
\(314\) | 477162. | 0.273113 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 47677.0 | 0.0268591 | ||||||||
\(317\) | −1.40479e6 | + | 2.43316e6i | −0.785167 | + | 1.35995i | 0.143733 | + | 0.989617i | \(0.454089\pi\) |
−0.928899 | + | 0.370332i | \(0.879244\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −38725.1 | − | 67073.9i | −0.0213067 | − | 0.0369043i | ||||
\(320\) | −43008.0 | + | 74492.0i | −0.0234787 | + | 0.0406663i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 569423. | + | 1.84169e6i | 0.306052 | + | 0.989865i | ||||
\(323\) | 1.99977e6 | 1.06653 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −277554. | − | 480737.i | −0.145760 | − | 0.252464i | ||||
\(326\) | −94744.8 | − | 164103.i | −0.0493755 | − | 0.0855209i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.10092e6 | 0.565029 | ||||||||
\(329\) | 165238. | − | 178322.i | 0.0841630 | − | 0.0908269i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −690248. | + | 1.19554e6i | −0.346286 | + | 0.599785i | −0.985587 | − | 0.169172i | \(-0.945891\pi\) |
0.639301 | + | 0.768957i | \(0.279224\pi\) | |||||||
\(332\) | 367637. | + | 636766.i | 0.183052 | + | 0.317055i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −463338. | + | 802526.i | −0.227265 | + | 0.393634i | ||||
\(335\) | 1.23104e6 | 0.599320 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 566429. | 0.271688 | 0.135844 | − | 0.990730i | \(-0.456625\pi\) | ||||
0.135844 | + | 0.990730i | \(0.456625\pi\) | |||||||
\(338\) | 657036. | − | 1.13802e6i | 0.312822 | − | 0.541824i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 178326. | + | 308869.i | 0.0836598 | + | 0.144903i | ||||
\(341\) | 2.85062e6 | − | 4.93743e6i | 1.32756 | − | 2.29940i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.70622e6 | + | 1.35512e6i | 0.783070 | + | 0.621933i | ||||
\(344\) | 345727. | 0.157520 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 268678. | + | 465365.i | 0.120654 | + | 0.208979i | ||||
\(347\) | 270104. | + | 467833.i | 0.120422 | + | 0.208577i | 0.919934 | − | 0.392073i | \(-0.128242\pi\) |
−0.799512 | + | 0.600650i | \(0.794908\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.73807e6 | 0.763841 | 0.381921 | − | 0.924195i | \(-0.375263\pi\) | ||||
0.381921 | + | 0.924195i | \(0.375263\pi\) | |||||||
\(350\) | −1.35714e6 | − | 308812.i | −0.592183 | − | 0.134749i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −320447. | + | 555031.i | −0.137848 | + | 0.238759i | ||||
\(353\) | 537109. | + | 930300.i | 0.229417 | + | 0.397362i | 0.957635 | − | 0.287983i | \(-0.0929847\pi\) |
−0.728219 | + | 0.685345i | \(0.759651\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −328435. | + | 568866.i | −0.138318 | + | 0.239574i | ||||
\(356\) | −1.58464e6 | −0.662682 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −186337. | −0.0768409 | ||||||||
\(359\) | 60601.9 | − | 104966.i | 0.0248170 | − | 0.0429844i | −0.853350 | − | 0.521338i | \(-0.825433\pi\) |
0.878167 | + | 0.478354i | \(0.158766\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −536639. | − | 929486.i | −0.216728 | − | 0.375383i | ||||
\(362\) | −1.65842e6 | + | 2.87247e6i | −0.665156 | + | 1.15208i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 126723. | + | 409859.i | 0.0501303 | + | 0.162137i | ||||
\(365\) | −150160. | −0.0589959 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 276914. | + | 479630.i | 0.107320 | + | 0.185884i | 0.914684 | − | 0.404171i | \(-0.132440\pi\) |
−0.807364 | + | 0.590054i | \(0.799106\pi\) | |||||||
\(368\) | 475823. | + | 824150.i | 0.183158 | + | 0.317239i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −506413. | −0.192309 | ||||||||
\(371\) | 716389. | + | 2.31702e6i | 0.270218 | + | 0.873966i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 250739. | − | 434293.i | 0.0933146 | − | 0.161626i | −0.815589 | − | 0.578631i | \(-0.803587\pi\) |
0.908904 | + | 0.417006i | \(0.136920\pi\) | |||||||
\(374\) | 1.32868e6 | + | 2.30135e6i | 0.491182 | + | 0.850752i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 60007.7 | − | 103936.i | 0.0218896 | − | 0.0379139i | ||||
\(377\) | −25593.6 | −0.00927422 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 999004. | 0.357248 | 0.178624 | − | 0.983917i | \(-0.442835\pi\) | ||||
0.178624 | + | 0.983917i | \(0.442835\pi\) | |||||||
\(380\) | 316508. | − | 548209.i | 0.112441 | − | 0.194754i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −943833. | − | 1.63477e6i | −0.330930 | − | 0.573188i | ||||
\(383\) | 326232. | − | 565050.i | 0.113640 | − | 0.196829i | −0.803596 | − | 0.595176i | \(-0.797082\pi\) |
0.917235 | + | 0.398346i | \(0.130416\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.66146e6 | + | 378058.i | 0.571265 | + | 0.129989i | ||||
\(386\) | 2.75342e6 | 0.940597 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 924387. | + | 1.60109e6i | 0.311727 | + | 0.539927i | ||||
\(389\) | −39626.5 | − | 68635.1i | −0.0132774 | − | 0.0229971i | 0.859310 | − | 0.511454i | \(-0.170893\pi\) |
−0.872588 | + | 0.488457i | \(0.837560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.94585e6 | 1.30526 | ||||||||
\(392\) | 969743. | + | 465420.i | 0.318744 | + | 0.152978i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 623830. | − | 1.08050e6i | 0.202454 | − | 0.350660i | ||||
\(395\) | −31288.0 | − | 54192.4i | −0.0100899 | − | 0.0174762i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.00443e6 | + | 3.47177e6i | −0.638284 | + | 1.10554i | 0.347525 | + | 0.937671i | \(0.387022\pi\) |
−0.985809 | + | 0.167870i | \(0.946311\pi\) | |||||||
\(398\) | −1.14885e6 | −0.363542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −687104. | −0.214720 | ||||||||
\(401\) | 337209. | − | 584063.i | 0.104722 | − | 0.181384i | −0.808903 | − | 0.587943i | \(-0.799938\pi\) |
0.913625 | + | 0.406559i | \(0.133271\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −941994. | − | 1.63158e6i | −0.288925 | − | 0.500433i | ||||
\(404\) | 87611.7 | − | 151748.i | 0.0267060 | − | 0.0462561i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −43616.4 | + | 47069.8i | −0.0131321 | + | 0.0141719i | ||||
\(407\) | −3.77322e6 | −1.12908 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.42706e6 | + | 2.47175e6i | 0.421828 | + | 0.730627i | 0.996118 | − | 0.0880244i | \(-0.0280553\pi\) |
−0.574291 | + | 0.818652i | \(0.694722\pi\) | |||||||
\(410\) | −722478. | − | 1.25137e6i | −0.212258 | − | 0.367642i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.20359e6 | −0.639570 | ||||||||
\(413\) | −97068.7 | − | 313950.i | −0.0280030 | − | 0.0905701i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 482523. | − | 835755.i | 0.137530 | − | 0.238209i | ||||
\(416\) | 105892. | + | 183411.i | 0.0300007 | + | 0.0519627i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2.35827e6 | − | 4.08464e6i | 0.660164 | − | 1.14344i | ||||
\(419\) | 4.66553e6 | 1.29827 | 0.649136 | − | 0.760672i | \(-0.275130\pi\) | ||||
0.649136 | + | 0.760672i | \(0.275130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.73317e6 | −1.02653 | −0.513266 | − | 0.858229i | \(-0.671565\pi\) | ||||
−0.513266 | + | 0.858229i | \(0.671565\pi\) | |||||||
\(422\) | 920987. | − | 1.59520e6i | 0.251752 | − | 0.436047i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 598631. | + | 1.03686e6i | 0.161713 | + | 0.280095i | ||||
\(425\) | −1.42448e6 | + | 2.46728e6i | −0.382547 | + | 0.662591i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 184577. | − | 199191.i | 0.0489899 | − | 0.0528689i | ||||
\(428\) | −1.20917e6 | −0.319064 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −226883. | − | 392973.i | −0.0591740 | − | 0.102492i | ||||
\(431\) | 482335. | + | 835429.i | 0.125071 | + | 0.216629i | 0.921761 | − | 0.387760i | \(-0.126751\pi\) |
−0.796690 | + | 0.604388i | \(0.793418\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.18096e6 | −1.58429 | −0.792147 | − | 0.610330i | \(-0.791037\pi\) | ||||
−0.792147 | + | 0.610330i | \(0.791037\pi\) | |||||||
\(434\) | −4.60603e6 | − | 1.04808e6i | −1.17382 | − | 0.267098i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −356210. | + | 616974.i | −0.0897409 | + | 0.155436i | ||||
\(437\) | −3.50172e6 | − | 6.06516e6i | −0.877158 | − | 1.51928i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 107567. | − | 186312.i | 0.0266391 | − | 0.0461402i | −0.852399 | − | 0.522893i | \(-0.824853\pi\) |
0.879038 | + | 0.476752i | \(0.158186\pi\) | |||||||
\(440\) | 841174. | 0.207135 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 878132. | 0.213798 | ||||||||
\(443\) | −3.59934e6 | + | 6.23423e6i | −0.871391 | + | 1.50929i | −0.0108335 | + | 0.999941i | \(0.503448\pi\) |
−0.860558 | + | 0.509353i | \(0.829885\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.03992e6 | + | 1.80119e6i | 0.248943 | + | 0.431182i | ||||
\(446\) | 2.39551e6 | − | 4.14915e6i | 0.570245 | − | 0.987694i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 517778. | + | 117818.i | 0.121884 | + | 0.0277343i | ||||
\(449\) | −3.92153e6 | −0.917994 | −0.458997 | − | 0.888438i | \(-0.651791\pi\) | ||||
−0.458997 | + | 0.888438i | \(0.651791\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.38309e6 | − | 9.32379e6i | −1.24621 | − | 2.15850i | ||||
\(452\) | 723652. | + | 1.25340e6i | 0.166603 | + | 0.288565i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.57824e6 | −0.814761 | ||||||||
\(455\) | 382708. | − | 413010.i | 0.0866641 | − | 0.0935260i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −660839. | + | 1.14461e6i | −0.148015 | + | 0.256369i | −0.930494 | − | 0.366308i | \(-0.880622\pi\) |
0.782479 | + | 0.622677i | \(0.213955\pi\) | |||||||
\(458\) | 518512. | + | 898090.i | 0.115504 | + | 0.200058i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 624518. | − | 1.08170e6i | 0.137610 | − | 0.238348i | ||||
\(461\) | 75459.1 | 0.0165371 | 0.00826855 | − | 0.999966i | \(-0.497368\pi\) | ||||
0.00826855 | + | 0.999966i | \(0.497368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.28757e6 | −0.712727 | −0.356363 | − | 0.934347i | \(-0.615984\pi\) | ||||
−0.356363 | + | 0.934347i | \(0.615984\pi\) | |||||||
\(464\) | −15839.7 | + | 27435.1i | −0.00341547 | + | 0.00591577i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 422630. | + | 732016.i | 0.0901561 | + | 0.156155i | ||||
\(467\) | −321691. | + | 557185.i | −0.0682569 | + | 0.118224i | −0.898134 | − | 0.439722i | \(-0.855077\pi\) |
0.829877 | + | 0.557946i | \(0.188410\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.24487e6 | − | 7.26058e6i | −0.471258 | − | 1.52419i | ||||
\(470\) | −157520. | −0.0328921 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −81112.9 | − | 140492.i | −0.0167585 | − | 0.0290266i | ||||
\(473\) | −1.69048e6 | − | 2.92799e6i | −0.347422 | − | 0.601752i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.05660e6 | 1.02831 | ||||||||
\(476\) | 1.49651e6 | − | 1.61500e6i | 0.302734 | − | 0.326704i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 926.036 | − | 1603.94i | 0.000185378 | − | 0.000321084i | ||||
\(479\) | −3.71324e6 | − | 6.43152e6i | −0.739459 | − | 1.28078i | −0.952739 | − | 0.303790i | \(-0.901748\pi\) |
0.213280 | − | 0.976991i | \(-0.431585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −623434. | + | 1.07982e6i | −0.122865 | + | 0.212808i | ||||
\(482\) | 1.14558e6 | 0.224599 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.69067e6 | 0.716130 | ||||||||
\(485\) | 1.21326e6 | − | 2.10143e6i | 0.234207 | − | 0.405658i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.08542e6 | + | 3.61206e6i | 0.398448 | + | 0.690132i | 0.993535 | − | 0.113529i | \(-0.0362156\pi\) |
−0.595087 | + | 0.803662i | \(0.702882\pi\) | |||||||
\(488\) | 67030.6 | − | 116100.i | 0.0127416 | − | 0.0220691i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −107370. | − | 1.40770e6i | −0.0202019 | − | 0.264862i | ||||
\(491\) | 3.73674e6 | 0.699502 | 0.349751 | − | 0.936843i | \(-0.386266\pi\) | ||||
0.349751 | + | 0.936843i | \(0.386266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 65676.6 | + | 113755.i | 0.0121701 | + | 0.0210792i | ||||
\(494\) | −779293. | − | 1.34978e6i | −0.143676 | − | 0.248854i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.33197e6 | −0.425617 | ||||||||
\(497\) | 3.95406e6 | + | 899731.i | 0.718047 | + | 0.163389i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.35431e6 | + | 7.54188e6i | −0.782831 | + | 1.35590i | 0.147456 | + | 0.989069i | \(0.452892\pi\) |
−0.930286 | + | 0.366834i | \(0.880442\pi\) | |||||||
\(500\) | 975912. | + | 1.69033e6i | 0.174576 | + | 0.302375i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.74336e6 | + | 4.75164e6i | −0.485874 | + | 0.841558i | ||||
\(503\) | −3.28384e6 | −0.578711 | −0.289355 | − | 0.957222i | \(-0.593441\pi\) | ||||
−0.289355 | + | 0.957222i | \(0.593441\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −229981. | −0.0401294 | ||||||||
\(506\) | 4.65321e6 | − | 8.05959e6i | 0.807934 | − | 1.39938i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.50166e6 | − | 2.60094e6i | −0.258173 | − | 0.447169i | ||||
\(509\) | −4.71851e6 | + | 8.17271e6i | −0.807255 | + | 1.39821i | 0.107503 | + | 0.994205i | \(0.465714\pi\) |
−0.914758 | + | 0.404002i | \(0.867619\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 273826. | + | 885635.i | 0.0463897 | + | 0.150038i | ||||
\(512\) | 262144. | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.51845e6 | − | 2.63003e6i | −0.253508 | − | 0.439089i | ||||
\(515\) | 1.44611e6 | + | 2.50473e6i | 0.240260 | + | 0.416143i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.17366e6 | −0.193116 | ||||||||
\(518\) | 923474. | + | 2.98680e6i | 0.151217 | + | 0.489081i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 138984. | − | 240727.i | 0.0225401 | − | 0.0390406i | ||||
\(521\) | 2.95363e6 | + | 5.11584e6i | 0.476719 | + | 0.825701i | 0.999644 | − | 0.0266776i | \(-0.00849276\pi\) |
−0.522926 | + | 0.852378i | \(0.675159\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −327168. | + | 566672.i | −0.0523019 | + | 0.0905895i | −0.890991 | − | 0.454021i | \(-0.849989\pi\) |
0.838689 | + | 0.544610i | \(0.183322\pi\) | |||||||
\(524\) | −2.47060e6 | −0.393073 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.28978e6 | 0.676037 | ||||||||
\(527\) | −4.83457e6 | + | 8.37373e6i | −0.758284 | + | 1.31339i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.69124e6 | − | 6.39342e6i | −0.573500 | − | 0.993331i | ||||
\(530\) | 785704. | − | 1.36088e6i | 0.121498 | − | 0.210441i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.81048e6 | − | 867058.i | −0.583714 | − | 0.132822i | ||||
\(533\) | −3.55771e6 | −0.542440 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 793516. | + | 1.37441e6i | 0.119859 | + | 0.207602i | ||||
\(536\) | −1.87586e6 | − | 3.24909e6i | −0.282026 | − | 0.488484i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.06445e6 | 1.05226 | ||||||||
\(539\) | −800002. | − | 1.04886e7i | −0.118609 | − | 1.55505i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 431558. | − | 747480.i | 0.0633936 | − | 0.109801i | −0.832587 | − | 0.553895i | \(-0.813141\pi\) |
0.895980 | + | 0.444094i | \(0.146474\pi\) | |||||||
\(542\) | 4.10342e6 | + | 7.10734e6i | 0.599996 | + | 1.03922i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 543469. | − | 941316.i | 0.0787368 | − | 0.136376i | ||||
\(545\) | 935052. | 0.134848 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.45692e6 | −0.779794 | −0.389897 | − | 0.920859i | \(-0.627489\pi\) | ||||
−0.389897 | + | 0.920859i | \(0.627489\pi\) | |||||||
\(548\) | 873903. | − | 1.51364e6i | 0.124312 | − | 0.215314i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.35969e6 | + | 5.81915e6i | 0.473579 | + | 0.820263i | ||||
\(551\) | 116569. | − | 201903.i | 0.0163570 | − | 0.0283311i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −262568. | + | 283358.i | −0.0365115 | + | 0.0394024i | ||||
\(554\) | 3.48273e6 | 0.482109 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.63756e6 | + | 2.83634e6i | 0.224652 | + | 0.389109i | ||||
\(557\) | 5.58881e6 | + | 9.68010e6i | 0.763275 | + | 1.32203i | 0.941154 | + | 0.337979i | \(0.109743\pi\) |
−0.177879 | + | 0.984052i | \(0.556923\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.11724e6 | −0.151223 | ||||||||
\(560\) | −205873. | − | 665854.i | −0.0277414 | − | 0.0897241i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.70825e6 | − | 8.15493e6i | 0.628809 | − | 1.08913i | ||||
\(563\) | 440132. | + | 762332.i | 0.0585211 | + | 0.101361i | 0.893802 | − | 0.448462i | \(-0.148028\pi\) |
−0.835281 | + | 0.549824i | \(0.814695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 949793. | − | 1.64509e6i | 0.125172 | − | 0.216805i | ||||
\(566\) | −8.76140e6 | −1.14956 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.00189e6 | 0.260357 | ||||||||
\(569\) | −774858. | + | 1.34209e6i | −0.100332 | + | 0.173781i | −0.911822 | − | 0.410587i | \(-0.865324\pi\) |
0.811489 | + | 0.584367i | \(0.198657\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.48507e6 | + | 9.50043e6i | 0.704032 | + | 1.21942i | 0.967040 | + | 0.254625i | \(0.0819521\pi\) |
−0.263008 | + | 0.964794i | \(0.584715\pi\) | |||||||
\(572\) | 1.03555e6 | − | 1.79363e6i | 0.132337 | − | 0.229214i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.06302e6 | + | 6.54308e6i | −0.768085 | + | 0.828900i | ||||
\(575\) | 9.97742e6 | 1.25849 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.29341e6 | + | 1.09005e7i | 0.786948 | + | 1.36303i | 0.927828 | + | 0.373008i | \(0.121674\pi\) |
−0.140880 | + | 0.990027i | \(0.544993\pi\) | |||||||
\(578\) | 586306. | + | 1.01551e6i | 0.0729969 | + | 0.126434i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 41579.1 | 0.00513222 | ||||||||
\(581\) | −5.80915e6 | − | 1.32185e6i | −0.713957 | − | 0.162458i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.85418e6 | − | 1.01397e7i | 0.713337 | − | 1.23554i | ||||
\(584\) | 228815. | + | 396319.i | 0.0277621 | + | 0.0480854i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.61540e6 | + | 2.79796e6i | −0.194328 | + | 0.336587i | ||||
\(587\) | −1.19962e7 | −1.43697 | −0.718484 | − | 0.695544i | \(-0.755164\pi\) | ||||
−0.718484 | + | 0.695544i | \(0.755164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.71617e7 | 2.03831 | ||||||||
\(590\) | −106461. | + | 184395.i | −0.0125910 | + | 0.0218082i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 771677. | + | 1.33658e6i | 0.0904964 | + | 0.156744i | ||||
\(593\) | 2.66154e6 | − | 4.60993e6i | 0.310811 | − | 0.538341i | −0.667727 | − | 0.744406i | \(-0.732733\pi\) |
0.978538 | + | 0.206065i | \(0.0660659\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.81778e6 | − | 641175.i | −0.326298 | − | 0.0742479i | ||||
\(596\) | 6.50092e6 | 0.749651 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.53766e6 | − | 2.66331e6i | −0.175836 | − | 0.304557i | ||||
\(599\) | 3.77757e6 | + | 6.54293e6i | 0.430175 | + | 0.745085i | 0.996888 | − | 0.0788305i | \(-0.0251186\pi\) |
−0.566713 | + | 0.823915i | \(0.691785\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.44758e6 | 0.502270 | 0.251135 | − | 0.967952i | \(-0.419196\pi\) | ||||
0.251135 | + | 0.967952i | \(0.419196\pi\) | |||||||
\(602\) | −1.90400e6 | + | 2.05475e6i | −0.214129 | + | 0.231083i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 3.33470e6 | − | 5.77588e6i | 0.371933 | − | 0.644207i | ||||
\(605\) | −2.42200e6 | − | 4.19503e6i | −0.269021 | − | 0.465958i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.78660e6 | + | 4.82653e6i | −0.306975 | + | 0.531696i | −0.977699 | − | 0.210011i | \(-0.932650\pi\) |
0.670724 | + | 0.741707i | \(0.265983\pi\) | |||||||
\(608\) | −1.92919e6 | −0.211649 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −175955. | −0.0191460 | ||||||||
\(611\) | −193920. | + | 335879.i | −0.0210145 | + | 0.0363982i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.56323e6 | + | 9.63580e6i | 0.597965 | + | 1.03571i | 0.993121 | + | 0.117092i | \(0.0373573\pi\) |
−0.395156 | + | 0.918614i | \(0.629309\pi\) | |||||||
\(614\) | −423032. | + | 732713.i | −0.0452848 | + | 0.0784356i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.53393e6 | − | 4.96120e6i | −0.162875 | − | 0.526787i | ||||
\(617\) | 1.07454e7 | 1.13634 | 0.568170 | − | 0.822911i | \(-0.307651\pi\) | ||||
0.568170 | + | 0.822911i | \(0.307651\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.78781e6 | − | 1.17568e7i | −0.712038 | − | 1.23329i | −0.964091 | − | 0.265572i | \(-0.914439\pi\) |
0.252053 | − | 0.967713i | \(-0.418894\pi\) | |||||||
\(620\) | 1.53036e6 | + | 2.65065e6i | 0.159887 | + | 0.276933i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.16684e6 | 0.120930 | ||||||||
\(623\) | 8.72698e6 | − | 9.41797e6i | 0.900833 | − | 0.972159i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.91287e6 | + | 5.04523e6i | −0.298277 | + | 0.516632i | ||||
\(626\) | 3.99195e6 | + | 6.91427e6i | 0.407145 | + | 0.705197i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −954324. | + | 1.65294e6i | −0.0965599 | + | 0.167247i | ||||
\(629\) | 6.39927e6 | 0.644917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.27986e7 | 1.27964 | 0.639820 | − | 0.768525i | \(-0.279009\pi\) | ||||
0.639820 | + | 0.768525i | \(0.279009\pi\) | |||||||
\(632\) | −95353.9 | + | 165158.i | −0.00949611 | + | 0.0164478i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.61914e6 | − | 9.73264e6i | −0.555197 | − | 0.961629i | ||||
\(635\) | −1.97092e6 | + | 3.41374e6i | −0.193970 | + | 0.335966i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.13380e6 | − | 1.50404e6i | −0.306001 | − | 0.146863i | ||||
\(638\) | 309801. | 0.0301322 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −172032. | − | 297968.i | −0.0166020 | − | 0.0287554i | ||||
\(641\) | −442417. | − | 766288.i | −0.0425291 | − | 0.0736626i | 0.843977 | − | 0.536379i | \(-0.180208\pi\) |
−0.886506 | + | 0.462716i | \(0.846875\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.66271e6 | 0.635511 | 0.317756 | − | 0.948173i | \(-0.397071\pi\) | ||||
0.317756 | + | 0.948173i | \(0.397071\pi\) | |||||||
\(644\) | −7.51863e6 | − | 1.71083e6i | −0.714372 | − | 0.162552i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.99955e6 | + | 6.92742e6i | −0.377077 | + | 0.653116i | ||||
\(647\) | −8.45887e6 | − | 1.46512e7i | −0.794423 | − | 1.37598i | −0.923205 | − | 0.384308i | \(-0.874440\pi\) |
0.128782 | − | 0.991673i | \(-0.458893\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −793226. | + | 1.37391e6i | −0.0739239 | + | 0.128040i | ||||
\(650\) | 2.22043e6 | 0.206136 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 757959. | 0.0698275 | ||||||||
\(653\) | 4.74654e6 | − | 8.22124e6i | 0.435606 | − | 0.754492i | −0.561739 | − | 0.827315i | \(-0.689867\pi\) |
0.997345 | + | 0.0728230i | \(0.0232008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.62133e6 | + | 2.80822e6i | 0.147662 | + | 0.255758i | ||||
\(656\) | −2.20184e6 | + | 3.81369e6i | −0.199768 | + | 0.346008i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 287248. | + | 929046.i | 0.0258638 | + | 0.0836513i | ||||
\(659\) | 4.97563e6 | 0.446308 | 0.223154 | − | 0.974783i | \(-0.428365\pi\) | ||||
0.223154 | + | 0.974783i | \(0.428365\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.05765e7 | − | 1.83191e7i | −0.941543 | − | 1.63080i | −0.762530 | − | 0.646953i | \(-0.776043\pi\) |
−0.179013 | − | 0.983847i | \(-0.557290\pi\) | |||||||
\(662\) | −2.76099e6 | − | 4.78218e6i | −0.244861 | − | 0.424112i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.94110e6 | −0.258874 | ||||||||
\(665\) | 1.51508e6 | + | 4.90022e6i | 0.132856 | + | 0.429696i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 230007. | − | 398384.i | 0.0200183 | − | 0.0346727i | ||||
\(668\) | −1.85335e6 | − | 3.21010e6i | −0.160700 | − | 0.278341i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.46207e6 | + | 4.26443e6i | −0.211892 | + | 0.367007i | ||||
\(671\) | −1.31102e6 | −0.112410 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 417573. | 0.0355382 | 0.0177691 | − | 0.999842i | \(-0.494344\pi\) | ||||
0.0177691 | + | 0.999842i | \(0.494344\pi\) | |||||||
\(674\) | −1.13286e6 | + | 1.96217e6i | −0.0960562 | + | 0.166374i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.62814e6 | + | 4.55208e6i | 0.221199 | + | 0.383127i | ||||
\(677\) | 1.31234e6 | − | 2.27304e6i | 0.110046 | − | 0.190605i | −0.805743 | − | 0.592266i | \(-0.798233\pi\) |
0.915789 | + | 0.401661i | \(0.131567\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.46065e7 | − | 3.32366e6i | −1.21583 | − | 0.276657i | ||||
\(680\) | −1.42661e6 | −0.118313 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.14025e7 | + | 1.97497e7i | 0.938726 | + | 1.62592i | ||||
\(683\) | −4.37227e6 | − | 7.57300e6i | −0.358637 | − | 0.621178i | 0.629096 | − | 0.777328i | \(-0.283425\pi\) |
−0.987733 | + | 0.156149i | \(0.950092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.29399e6 | −0.186795 | ||||||||
\(686\) | −8.10674e6 | + | 3.20029e6i | −0.657712 | + | 0.259644i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −691453. | + | 1.19763e6i | −0.0556919 | + | 0.0964611i | ||||
\(689\) | −1.93452e6 | − | 3.35069e6i | −0.155248 | − | 0.268898i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.19834e6 | + | 3.80763e6i | −0.175146 | + | 0.303361i | −0.940212 | − | 0.340591i | \(-0.889373\pi\) |
0.765066 | + | 0.643952i | \(0.222706\pi\) | |||||||
\(692\) | −2.14943e6 | −0.170631 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.16083e6 | −0.170303 | ||||||||
\(695\) | 2.14930e6 | − | 3.72270e6i | 0.168786 | − | 0.292345i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.12957e6 | + | 1.58129e7i | 0.711817 | + | 1.23290i | ||||
\(698\) | −3.47614e6 | + | 6.02084e6i | −0.270059 | + | 0.467755i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.78404e6 | − | 4.08366e6i | 0.291885 | − | 0.314995i | ||||
\(701\) | −6.51339e6 | −0.500624 | −0.250312 | − | 0.968165i | \(-0.580533\pi\) | ||||
−0.250312 | + | 0.968165i | \(0.580533\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.67900e6 | − | 9.83631e6i | −0.433394 | − | 0.750661i | ||||
\(704\) | −1.28179e6 | − | 2.22012e6i | −0.0974731 | − | 0.168828i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.29687e6 | −0.324445 | ||||||||
\(707\) | 419383. | + | 1.35641e6i | 0.0315546 | + | 0.102057i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.23256e6 | − | 9.06305e6i | 0.390929 | − | 0.677110i | −0.601643 | − | 0.798765i | \(-0.705487\pi\) |
0.992572 | + | 0.121655i | \(0.0388203\pi\) | |||||||
\(710\) | −1.31374e6 | − | 2.27547e6i | −0.0978056 | − | 0.169404i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.16928e6 | − | 5.48935e6i | 0.234294 | − | 0.405808i | ||||
\(713\) | 3.38625e7 | 2.49457 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.71832e6 | −0.198855 | ||||||||
\(716\) | 372675. | − | 645492.i | 0.0271674 | − | 0.0470553i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 242408. | + | 419862.i | 0.0175483 | + | 0.0303946i | ||||
\(719\) | −8.40746e6 | + | 1.45621e7i | −0.606516 | + | 1.05052i | 0.385294 | + | 0.922794i | \(0.374100\pi\) |
−0.991810 | + | 0.127723i | \(0.959233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.21357e7 | − | 1.30966e7i | 0.869414 | − | 0.938252i | ||||
\(722\) | 4.29311e6 | 0.306499 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.63368e6 | − | 1.14899e7i | −0.470336 | − | 0.814646i | ||||
\(725\) | 166069. | + | 287640.i | 0.0117339 | + | 0.0203238i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.71928e7 | −1.20646 | −0.603228 | − | 0.797569i | \(-0.706119\pi\) | ||||
−0.603228 | + | 0.797569i | \(0.706119\pi\) | |||||||
\(728\) | −1.67324e6 | − | 380739.i | −0.117012 | − | 0.0266255i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 300320. | − | 520169.i | 0.0208582 | − | 0.0361275i | ||||
\(731\) | 2.86700e6 | + | 4.96579e6i | 0.198442 | + | 0.343712i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.86827e6 | + | 1.70923e7i | −0.678393 | + | 1.17501i | 0.297072 | + | 0.954855i | \(0.403990\pi\) |
−0.975465 | + | 0.220155i | \(0.929344\pi\) | |||||||
\(734\) | −2.21531e6 | −0.151773 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.80659e6 | −0.259025 | ||||||||
\(737\) | −1.83446e7 | + | 3.17738e7i | −1.24405 | + | 2.15477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.43593e6 | − | 1.11474e7i | −0.433511 | − | 0.750863i | 0.563662 | − | 0.826006i | \(-0.309392\pi\) |
−0.997173 | + | 0.0751426i | \(0.976059\pi\) | |||||||
\(740\) | 1.01283e6 | − | 1.75427e6i | 0.0679916 | − | 0.117765i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.45916e6 | − | 2.15239e6i | −0.630729 | − | 0.143520i | ||||
\(743\) | −2.45606e7 | −1.63218 | −0.816089 | − | 0.577927i | \(-0.803862\pi\) | ||||
−0.816089 | + | 0.577927i | \(0.803862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.26623e6 | − | 7.38933e6i | −0.281614 | − | 0.487769i | ||||
\(746\) | 1.00296e6 | + | 1.73717e6i | 0.0659834 | + | 0.114287i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.06295e7 | −0.694636 | ||||||||
\(749\) | 6.65917e6 | − | 7.18643e6i | 0.433726 | − | 0.468068i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 162983. | − | 282294.i | 0.0105449 | − | 0.0182643i | −0.860705 | − | 0.509104i | \(-0.829977\pi\) |
0.871250 | + | 0.490840i | \(0.163310\pi\) | |||||||
\(752\) | 240031. | + | 415746.i | 0.0154783 | + | 0.0268092i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 51187.1 | − | 88658.7i | 0.00327893 | − | 0.00567928i | ||||
\(755\) | −8.75360e6 | −0.558881 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.84659e7 | 1.17120 | 0.585599 | − | 0.810601i | \(-0.300859\pi\) | ||||
0.585599 | + | 0.810601i | \(0.300859\pi\) | |||||||
\(758\) | −1.99801e6 | + | 3.46065e6i | −0.126306 | + | 0.218769i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.26603e6 | + | 2.19283e6i | 0.0795081 | + | 0.137712i | ||||
\(761\) | 2.56313e6 | − | 4.43947e6i | 0.160439 | − | 0.277888i | −0.774587 | − | 0.632467i | \(-0.782042\pi\) |
0.935026 | + | 0.354579i | \(0.115376\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.70512e6 | − | 5.51488e6i | −0.106034 | − | 0.342945i | ||||
\(764\) | 7.55066e6 | 0.468006 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.30493e6 | + | 2.26020e6i | 0.0803553 | + | 0.139179i | ||||
\(767\) | 262123. | + | 454010.i | 0.0160885 | + | 0.0278662i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.63432e6 | 0.0996602 | 0.0498301 | − | 0.998758i | \(-0.484132\pi\) | ||||
0.0498301 | + | 0.998758i | \(0.484132\pi\) | |||||||
\(770\) | −4.63255e6 | + | 4.99934e6i | −0.281574 | + | 0.303869i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.50683e6 | + | 9.53811e6i | −0.332551 | + | 0.575996i | ||||
\(773\) | −2.14128e6 | − | 3.70881e6i | −0.128892 | − | 0.223247i | 0.794356 | − | 0.607453i | \(-0.207809\pi\) |
−0.923248 | + | 0.384206i | \(0.874475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.22246e7 | + | 2.11737e7i | −0.731108 | + | 1.26632i | ||||
\(776\) | −7.39510e6 | −0.440849 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 317012. | 0.0187770 | ||||||||
\(779\) | 1.62040e7 | − | 2.80661e7i | 0.956704 | − | 1.65706i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.78852e6 | − | 1.69542e7i | −0.574235 | − | 0.994604i | ||||
\(782\) | −7.89170e6 | + | 1.36688e7i | −0.461481 | + | 0.799308i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.55175e6 | + | 2.42845e6i | −0.206373 | + | 0.141104i | ||||
\(785\) | 2.50510e6 | 0.145095 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.91482e6 | + | 6.78066e6i | 0.225307 | + | 0.390243i | 0.956411 | − | 0.292022i | \(-0.0943282\pi\) |
−0.731105 | + | 0.682265i | \(0.760995\pi\) | |||||||
\(788\) | 2.49532e6 | + | 4.32202e6i | 0.143156 | + | 0.247954i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 250304. | 0.0142692 | ||||||||
\(791\) | −1.14346e7 | − | 2.60191e6i | −0.649803 | − | 0.147860i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −216615. | + | 375187.i | −0.0122322 | + | 0.0211868i | ||||
\(794\) | −8.01771e6 | − | 1.38871e7i | −0.451335 | − | 0.781736i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.29769e6 | − | 3.97972e6i | 0.128531 | − | 0.222623i | ||||
\(797\) | 3.68238e6 | 0.205344 | 0.102672 | − | 0.994715i | \(-0.467261\pi\) | ||||
0.102672 | + | 0.994715i | \(0.467261\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.99050e6 | 0.110305 | ||||||||
\(800\) | 1.37421e6 | − | 2.38020e6i | 0.0759150 | − | 0.131489i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.34884e6 | + | 2.33625e6i | 0.0740497 | + | 0.128258i | ||||
\(803\) | 2.23765e6 | − | 3.87572e6i | 0.122462 | − | 0.212111i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.98947e6 | + | 9.66885e6i | 0.162594 | + | 0.525878i | ||||
\(806\) | 7.53595e6 | 0.408602 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 350447. | + | 606992.i | 0.0188840 | + | 0.0327080i | ||||
\(809\) | 1.04091e7 | + | 1.80290e7i | 0.559165 | + | 0.968502i | 0.997566 | + | 0.0697227i | \(0.0222114\pi\) |
−0.438402 | + | 0.898779i | \(0.644455\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.03542e7 | 1.62057 | 0.810283 | − | 0.586039i | \(-0.199313\pi\) | ||||
0.810283 | + | 0.586039i | \(0.199313\pi\) | |||||||
\(812\) | −75822.0 | − | 245231.i | −0.00403557 | − | 0.0130523i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.54644e6 | − | 1.30708e7i | 0.399191 | − | 0.691420i | ||||
\(815\) | −497410. | − | 861540.i | −0.0262314 | − | 0.0454341i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.08861e6 | − | 8.81373e6i | 0.266713 | − | 0.461960i | ||||
\(818\) | −1.14165e7 | −0.596555 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.77982e6 | 0.300179 | ||||||||
\(821\) | 1.37193e7 | − | 2.37626e7i | 0.710355 | − | 1.23037i | −0.254369 | − | 0.967107i | \(-0.581868\pi\) |
0.964724 | − | 0.263264i | \(-0.0847990\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.95629e6 | − | 1.37807e7i | −0.409459 | − | 0.709204i | 0.585370 | − | 0.810766i | \(-0.300949\pi\) |
−0.994829 | + | 0.101562i | \(0.967616\pi\) | |||||||
\(824\) | 4.40718e6 | − | 7.63346e6i | 0.226122 | − | 0.391655i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.28169e6 | + | 291643.i | 0.0653632 | + | 0.0148731i | ||||
\(827\) | −1.40824e7 | −0.716001 | −0.358001 | − | 0.933721i | \(-0.616541\pi\) | ||||
−0.358001 | + | 0.933721i | \(0.616541\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.09441e7 | − | 1.89558e7i | −0.553089 | − | 0.957978i | −0.998049 | − | 0.0624281i | \(-0.980116\pi\) |
0.444960 | − | 0.895550i | \(-0.353218\pi\) | |||||||
\(830\) | 1.93009e6 | + | 3.34302e6i | 0.0972486 | + | 0.168439i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −847139. | −0.0424274 | ||||||||
\(833\) | 1.35678e6 | + | 1.77883e7i | 0.0677480 | + | 0.888225i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.43253e6 | + | 4.21326e6i | −0.120737 | + | 0.209123i | ||||
\(836\) | 9.43306e6 | + | 1.63385e7i | 0.466807 | + | 0.808533i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −9.33106e6 | + | 1.61619e7i | −0.459009 | + | 0.795026i | ||||
\(839\) | 1.98669e7 | 0.974372 | 0.487186 | − | 0.873298i | \(-0.338023\pi\) | ||||
0.487186 | + | 0.873298i | \(0.338023\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.04958e7 | −0.999253 | ||||||||
\(842\) | 7.46635e6 | − | 1.29321e7i | 0.362934 | − | 0.628620i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.68395e6 | + | 6.38078e6i | 0.178015 | + | 0.308332i | ||||
\(845\) | 3.44944e6 | − | 5.97460e6i | 0.166191 | − | 0.287851i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.03254e7 | + | 2.19347e7i | −0.973488 | + | 1.05057i | ||||
\(848\) | −4.78905e6 | −0.228697 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.69793e6 | − | 9.86911e6i | −0.270502 | − | 0.468523i | ||||
\(851\) | −1.12055e7 | − | 1.94085e7i | −0.530405 | − | 0.918688i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.75258e6 | 0.411873 | 0.205937 | − | 0.978565i | \(-0.433976\pi\) | ||||
0.205937 | + | 0.978565i | \(0.433976\pi\) | |||||||
\(854\) | 320865. | + | 1.03777e6i | 0.0150549 | + | 0.0486921i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.41834e6 | − | 4.18868e6i | 0.112806 | − | 0.195386i | ||||
\(857\) | −977384. | − | 1.69288e6i | −0.0454583 | − | 0.0787361i | 0.842401 | − | 0.538851i | \(-0.181141\pi\) |
−0.887859 | + | 0.460115i | \(0.847808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.49225e6 | + | 4.31670e6i | −0.115241 | + | 0.199604i | −0.917876 | − | 0.396867i | \(-0.870098\pi\) |
0.802635 | + | 0.596471i | \(0.203431\pi\) | |||||||
\(860\) | 1.81506e6 | 0.0836847 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.85868e6 | −0.176877 | ||||||||
\(863\) | −8.49654e6 | + | 1.47164e7i | −0.388343 | + | 0.672629i | −0.992227 | − | 0.124443i | \(-0.960286\pi\) |
0.603884 | + | 0.797072i | \(0.293619\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.41056e6 | + | 2.44316e6i | 0.0640991 | + | 0.111023i | ||||
\(866\) | 1.23619e7 | − | 2.14115e7i | 0.560133 | − | 0.970179i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.28427e7 | − | 1.38596e7i | 0.578572 | − | 0.624383i | ||||
\(869\) | 1.86498e6 | 0.0837772 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.06200e6 | + | 1.04997e7i | 0.270751 | + | 0.468955i | ||||
\(872\) | −1.42484e6 | − | 2.46790e6i | −0.0634564 | − | 0.109910i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.80138e7 | 1.24049 | ||||||||
\(875\) | −1.54207e7 | − | 3.50892e6i | −0.680901 | − | 0.154936i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.09797e6 | + | 1.57581e7i | −0.399434 | + | 0.691840i | −0.993656 | − | 0.112461i | \(-0.964127\pi\) |
0.594222 | + | 0.804301i | \(0.297460\pi\) | |||||||
\(878\) | 430269. | + | 745249.i | 0.0188367 | + | 0.0326261i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.68235e6 | + | 2.91391e6i | −0.0732334 | + | 0.126844i | ||||
\(881\) | −1.77637e7 | −0.771068 | −0.385534 | − | 0.922694i | \(-0.625983\pi\) | ||||
−0.385534 | + | 0.922694i | \(0.625983\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.71479e6 | 0.0740131 | 0.0370065 | − | 0.999315i | \(-0.488218\pi\) | ||||
0.0370065 | + | 0.999315i | \(0.488218\pi\) | |||||||
\(884\) | −1.75626e6 | + | 3.04194e6i | −0.0755891 | + | 0.130924i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.43973e7 | − | 2.49369e7i | −0.616167 | − | 1.06723i | ||||
\(887\) | −1.21218e7 | + | 2.09955e7i | −0.517318 | + | 0.896021i | 0.482480 | + | 0.875907i | \(0.339736\pi\) |
−0.999798 | + | 0.0201139i | \(0.993597\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.37281e7 | + | 5.39924e6i | 1.00695 | + | 0.229128i | ||||
\(890\) | −8.31936e6 | −0.352058 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 9.58206e6 | + | 1.65966e7i | 0.403224 | + | 0.698405i | ||||
\(893\) | −1.76646e6 | − | 3.05960e6i | −0.0741267 | − | 0.128391i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −978272. | −0.0408227 | ||||||||
\(896\) | −1.44369e6 | + | 1.55800e6i | −0.0600764 | + | 0.0648331i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 7.84306e6 | − | 1.35846e7i | 0.324560 | − | 0.562154i | ||||
\(899\) | 563624. | + | 976225.i | 0.0232589 | + | 0.0402857i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.92852e6 | + | 1.71967e7i | −0.407448 | + | 0.705721i | ||||
\(902\) | 4.30647e7 | 1.76240 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.78921e6 | −0.235613 | ||||||||
\(905\) | −8.70671e6 | + | 1.50805e7i | −0.353372 | + | 0.612059i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.52161e6 | + | 1.64919e7i | 0.384319 | + | 0.665661i | 0.991675 | − | 0.128770i | \(-0.0411028\pi\) |
−0.607355 | + | 0.794430i | \(0.707769\pi\) | |||||||
\(908\) | 7.15649e6 | − | 1.23954e7i | 0.288062 | − | 0.498937i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 665293. | + | 2.15176e6i | 0.0266324 | + | 0.0861371i | ||||
\(911\) | 3.18731e7 | 1.27242 | 0.636208 | − | 0.771518i | \(-0.280502\pi\) | ||||
0.636208 | + | 0.771518i | \(0.280502\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.43809e7 | + | 2.49084e7i | 0.570964 | + | 0.988939i | ||||
\(914\) | −2.64336e6 | − | 4.57843e6i | −0.104662 | − | 0.181280i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.14810e6 | −0.163347 | ||||||||
\(917\) | 1.36062e7 | − | 1.46835e7i | 0.534333 | − | 0.576641i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.47429e7 | − | 2.55355e7i | 0.575830 | − | 0.997367i | −0.420121 | − | 0.907468i | \(-0.638012\pi\) |
0.995951 | − | 0.0898988i | \(-0.0286544\pi\) | |||||||
\(920\) | 2.49807e6 | + | 4.32679e6i | 0.0973050 | + | 0.168537i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −150918. | + | 261398.i | −0.00584675 | + | 0.0101269i | ||||
\(923\) | −6.46927e6 | −0.249949 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.61811e7 | 0.621804 | ||||||||
\(926\) | 6.57515e6 | − | 1.13885e7i | 0.251987 | − | 0.436454i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −63358.6 | − | 109740.i | −0.00241510 | − | 0.00418308i | ||||
\(929\) | −4.86935e6 | + | 8.43397e6i | −0.185111 | + | 0.320621i | −0.943614 | − | 0.331048i | \(-0.892598\pi\) |
0.758503 | + | 0.651670i | \(0.225931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.61384e7 | − | 1.78717e7i | 0.988335 | − | 0.675757i | ||||
\(932\) | −3.38104e6 | −0.127500 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.28676e6 | − | 2.22874e6i | −0.0482649 | − | 0.0835973i | ||||
\(935\) | 6.97559e6 | + | 1.20821e7i | 0.260947 | + | 0.451973i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.66734e7 | 0.992498 | 0.496249 | − | 0.868180i | \(-0.334710\pi\) | ||||
0.496249 | + | 0.868180i | \(0.334710\pi\) | |||||||
\(938\) | 2.96411e7 | + | 6.74472e6i | 1.09999 | + | 0.250298i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 315041. | − | 545666.i | 0.0116291 | − | 0.0201422i | ||||
\(941\) | 1.61432e6 | + | 2.79609e6i | 0.0594315 | + | 0.102938i | 0.894210 | − | 0.447647i | \(-0.147738\pi\) |
−0.834779 | + | 0.550585i | \(0.814405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.19728e7 | − | 5.53785e7i | 1.17085 | − | 2.02797i | ||||
\(944\) | 648903. | 0.0237001 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.35238e7 | 0.491328 | ||||||||
\(947\) | −2.29622e6 | + | 3.97717e6i | −0.0832029 | + | 0.144112i | −0.904624 | − | 0.426210i | \(-0.859848\pi\) |
0.821421 | + | 0.570322i | \(0.193182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −739434. | − | 1.28074e6i | −0.0266523 | − | 0.0461631i | ||||
\(950\) | −1.01132e7 | + | 1.75166e7i | −0.363563 | + | 0.629709i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.60150e6 | + | 8.41405e6i | 0.0930318 | + | 0.300893i | ||||
\(953\) | −2.97125e7 | −1.05976 | −0.529880 | − | 0.848073i | \(-0.677763\pi\) | ||||
−0.529880 | + | 0.848073i | \(0.677763\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.95512e6 | − | 8.58253e6i | −0.175811 | − | 0.304514i | ||||
\(956\) | 3704.14 | + | 6415.77i | 0.000131082 | + | 0.000227041i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.97059e7 | 1.04575 | ||||||||
\(959\) | 4.18323e6 | + | 1.35299e7i | 0.146881 | + | 0.475058i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.71748e7 | + | 4.70681e7i | −0.949199 | + | 1.64406i | ||||
\(962\) | −2.49373e6 | − | 4.31928e6i | −0.0868786 | − | 0.150478i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.29116e6 | + | 3.96840e6i | −0.0794077 | + | 0.137538i | ||||
\(965\) | 1.44554e7 | 0.499704 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.64435e6 | 0.262890 | 0.131445 | − | 0.991323i | \(-0.458038\pi\) | ||||
0.131445 | + | 0.991323i | \(0.458038\pi\) | |||||||
\(968\) | −7.38134e6 | + | 1.27849e7i | −0.253190 | + | 0.438538i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 4.85303e6 | + | 8.40570e6i | 0.165609 | + | 0.286843i | ||||
\(971\) | −2.49810e7 | + | 4.32684e7i | −0.850281 | + | 1.47273i | 0.0306743 | + | 0.999529i | \(0.490235\pi\) |
−0.880955 | + | 0.473200i | \(0.843099\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.58756e7 | − | 5.88790e6i | −0.876212 | − | 0.199378i | ||||
\(974\) | −1.66834e7 | −0.563491 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 268122. | + | 464401.i | 0.00900966 | + | 0.0156052i | ||||
\(977\) | 2.02697e7 | + | 3.51082e7i | 0.679378 | + | 1.17672i | 0.975169 | + | 0.221464i | \(0.0710836\pi\) |
−0.295791 | + | 0.955253i | \(0.595583\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.19865e7 | −2.06700 | ||||||||
\(980\) | 5.09115e6 | + | 2.44346e6i | 0.169337 | + | 0.0812717i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.47348e6 | + | 1.29445e7i | −0.247311 | + | 0.428356i | ||||
\(983\) | −2.06528e7 | − | 3.57717e7i | −0.681703 | − | 1.18074i | −0.974461 | − | 0.224558i | \(-0.927906\pi\) |
0.292757 | − | 0.956187i | \(-0.405427\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.27511e6 | − | 5.67265e6i | 0.107556 | − | 0.186292i | ||||
\(986\) | −525413. | −0.0172111 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.23434e6 | 0.203188 | ||||||||
\(989\) | 1.00406e7 | − | 1.73908e7i | 0.326413 | − | 0.565364i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.20419e6 | + | 1.59421e7i | 0.297715 | + | 0.515658i | 0.975613 | − | 0.219498i | \(-0.0704420\pi\) |
−0.677897 | + | 0.735156i | \(0.737109\pi\) | |||||||
\(992\) | 4.66394e6 | − | 8.07819e6i | 0.150478 | − | 0.260636i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.10249e7 | + | 1.18978e7i | −0.353922 | + | 0.381945i | ||||
\(995\) | −6.03144e6 | −0.193136 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.69854e7 | + | 2.94196e7i | 0.541175 | + | 0.937343i | 0.998837 | + | 0.0482164i | \(0.0153537\pi\) |
−0.457662 | + | 0.889126i | \(0.651313\pi\) | |||||||
\(998\) | −1.74172e7 | − | 3.01675e7i | −0.553545 | − | 0.958768i | ||||
\(999\) | 0 | 0 |
(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 | 126.6.g.e.37.2 | 4 | ||
3.2 | odd | 2 | 14.6.c.b.9.1 | ✓ | 4 | ||
7.2 | even | 3 | 882.6.a.bt.1.2 | 2 | |||
7.4 | even | 3 | inner | 126.6.g.e.109.2 | 4 | ||
7.5 | odd | 6 | 882.6.a.bl.1.2 | 2 | |||
12.11 | even | 2 | 112.6.i.b.65.2 | 4 | |||
21.2 | odd | 6 | 98.6.a.c.1.2 | 2 | |||
21.5 | even | 6 | 98.6.a.f.1.1 | 2 | |||
21.11 | odd | 6 | 14.6.c.b.11.1 | yes | 4 | ||
21.17 | even | 6 | 98.6.c.f.67.2 | 4 | |||
21.20 | even | 2 | 98.6.c.f.79.2 | 4 | |||
84.11 | even | 6 | 112.6.i.b.81.2 | 4 | |||
84.23 | even | 6 | 784.6.a.bc.1.1 | 2 | |||
84.47 | odd | 6 | 784.6.a.r.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.6.c.b.9.1 | ✓ | 4 | 3.2 | odd | 2 | ||
14.6.c.b.11.1 | yes | 4 | 21.11 | odd | 6 | ||
98.6.a.c.1.2 | 2 | 21.2 | odd | 6 | |||
98.6.a.f.1.1 | 2 | 21.5 | even | 6 | |||
98.6.c.f.67.2 | 4 | 21.17 | even | 6 | |||
98.6.c.f.79.2 | 4 | 21.20 | even | 2 | |||
112.6.i.b.65.2 | 4 | 12.11 | even | 2 | |||
112.6.i.b.81.2 | 4 | 84.11 | even | 6 | |||
126.6.g.e.37.2 | 4 | 1.1 | even | 1 | trivial | ||
126.6.g.e.109.2 | 4 | 7.4 | even | 3 | inner | ||
784.6.a.r.1.2 | 2 | 84.47 | odd | 6 | |||
784.6.a.bc.1.1 | 2 | 84.23 | even | 6 | |||
882.6.a.bl.1.2 | 2 | 7.5 | odd | 6 | |||
882.6.a.bt.1.2 | 2 | 7.2 | even | 3 |