Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [30,6,Mod(17,30)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(30, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("30.17");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 30 = 2 \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 30.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.81151459439\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 1126 x^{18} + 420245 x^{16} + 66878446 x^{14} + 5652274660 x^{12} + 280235806770 x^{10} + \cdots + 87\!\cdots\!24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{25}\cdot 3^{14}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.7 | ||
Root | \(-1.34618i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 30.17 |
Dual form | 30.6.e.a.23.7 |
$q$-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 \(\left(\mathbb{Z}/30\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.82843 | − | 2.82843i | 0.500000 | − | 0.500000i | ||||
\(3\) | −6.50878 | − | 14.1646i | −0.417539 | − | 0.908659i | ||||
\(4\) | − | 16.0000i | − | 0.500000i | ||||||
\(5\) | −55.5060 | + | 6.63996i | −0.992921 | + | 0.118779i | ||||
\(6\) | −58.4731 | − | 21.6539i | −0.663099 | − | 0.245560i | ||||
\(7\) | 1.93288 | + | 1.93288i | 0.0149094 | + | 0.0149094i | 0.714522 | − | 0.699613i | \(-0.246644\pi\) |
−0.699613 | + | 0.714522i | \(0.746644\pi\) | |||||||
\(8\) | −45.2548 | − | 45.2548i | −0.250000 | − | 0.250000i | ||||
\(9\) | −158.272 | + | 184.389i | −0.651323 | + | 0.758800i | ||||
\(10\) | −138.214 | + | 175.775i | −0.437071 | + | 0.555850i | ||||
\(11\) | − | 615.555i | − | 1.53386i | −0.641731 | − | 0.766929i | \(-0.721784\pi\) | ||
0.641731 | − | 0.766929i | \(-0.278216\pi\) | |||||||
\(12\) | −226.634 | + | 104.141i | −0.454330 | + | 0.208769i | ||||
\(13\) | 211.952 | − | 211.952i | 0.347839 | − | 0.347839i | −0.511465 | − | 0.859304i | \(-0.670897\pi\) |
0.859304 | + | 0.511465i | \(0.170897\pi\) | |||||||
\(14\) | 10.9340 | 0.0149094 | ||||||||
\(15\) | 455.328 | + | 743.001i | 0.522512 | + | 0.852632i | ||||
\(16\) | −256.000 | −0.250000 | ||||||||
\(17\) | 272.840 | − | 272.840i | 0.228974 | − | 0.228974i | −0.583290 | − | 0.812264i | \(-0.698235\pi\) |
0.812264 | + | 0.583290i | \(0.198235\pi\) | |||||||
\(18\) | 73.8700 | + | 969.189i | 0.0537387 | + | 0.705062i | ||||
\(19\) | − | 2042.57i | − | 1.29805i | −0.760766 | − | 0.649026i | \(-0.775177\pi\) | ||
0.760766 | − | 0.649026i | \(-0.224823\pi\) | |||||||
\(20\) | 106.239 | + | 888.095i | 0.0593896 | + | 0.496460i | ||||
\(21\) | 14.7978 | − | 39.9593i | 0.00732233 | − | 0.0197728i | ||||
\(22\) | −1741.05 | − | 1741.05i | −0.766929 | − | 0.766929i | ||||
\(23\) | 2977.03 | + | 2977.03i | 1.17345 | + | 1.17345i | 0.981382 | + | 0.192065i | \(0.0615184\pi\) |
0.192065 | + | 0.981382i | \(0.438482\pi\) | |||||||
\(24\) | −346.463 | + | 935.570i | −0.122780 | + | 0.331549i | ||||
\(25\) | 3036.82 | − | 737.114i | 0.971783 | − | 0.235877i | ||||
\(26\) | − | 1198.98i | − | 0.347839i | ||||||
\(27\) | 3641.94 | + | 1041.71i | 0.961444 | + | 0.275002i | ||||
\(28\) | 30.9262 | − | 30.9262i | 0.00745471 | − | 0.00745471i | ||||
\(29\) | −3178.83 | −0.701896 | −0.350948 | − | 0.936395i | \(-0.614141\pi\) | ||||
−0.350948 | + | 0.936395i | \(0.614141\pi\) | |||||||
\(30\) | 3389.39 | + | 813.662i | 0.687572 | + | 0.165060i | ||||
\(31\) | 1657.55 | 0.309787 | 0.154893 | − | 0.987931i | \(-0.450497\pi\) | ||||
0.154893 | + | 0.987931i | \(0.450497\pi\) | |||||||
\(32\) | −724.077 | + | 724.077i | −0.125000 | + | 0.125000i | ||||
\(33\) | −8719.09 | + | 4006.52i | −1.39376 | + | 0.640445i | ||||
\(34\) | − | 1543.42i | − | 0.228974i | ||||||
\(35\) | −120.121 | − | 94.4523i | −0.0165748 | − | 0.0130329i | ||||
\(36\) | 2950.22 | + | 2532.34i | 0.379400 | + | 0.325662i | ||||
\(37\) | −9486.85 | − | 9486.85i | −1.13925 | − | 1.13925i | −0.988585 | − | 0.150661i | \(-0.951860\pi\) |
−0.150661 | − | 0.988585i | \(-0.548140\pi\) | |||||||
\(38\) | −5777.25 | − | 5777.25i | −0.649026 | − | 0.649026i | ||||
\(39\) | −4381.76 | − | 1622.66i | −0.461303 | − | 0.170831i | ||||
\(40\) | 2812.40 | + | 2211.42i | 0.277925 | + | 0.218535i | ||||
\(41\) | − | 1391.07i | − | 0.129237i | −0.997910 | − | 0.0646187i | \(-0.979417\pi\) | ||
0.997910 | − | 0.0646187i | \(-0.0205831\pi\) | |||||||
\(42\) | −71.1673 | − | 154.876i | −0.00622526 | − | 0.0135476i | ||||
\(43\) | −11513.8 | + | 11513.8i | −0.949617 | + | 0.949617i | −0.998790 | − | 0.0491729i | \(-0.984341\pi\) |
0.0491729 | + | 0.998790i | \(0.484341\pi\) | |||||||
\(44\) | −9848.89 | −0.766929 | ||||||||
\(45\) | 7560.68 | − | 11285.6i | 0.556583 | − | 0.830792i | ||||
\(46\) | 16840.6 | 1.17345 | ||||||||
\(47\) | −4029.48 | + | 4029.48i | −0.266075 | + | 0.266075i | −0.827517 | − | 0.561441i | \(-0.810247\pi\) |
0.561441 | + | 0.827517i | \(0.310247\pi\) | |||||||
\(48\) | 1666.25 | + | 3626.14i | 0.104385 | + | 0.227165i | ||||
\(49\) | − | 16799.5i | − | 0.999555i | ||||||
\(50\) | 6504.56 | − | 10674.3i | 0.367953 | − | 0.603830i | ||||
\(51\) | −5640.53 | − | 2088.81i | −0.303665 | − | 0.112454i | ||||
\(52\) | −3391.23 | − | 3391.23i | −0.173920 | − | 0.173920i | ||||
\(53\) | 20105.3 | + | 20105.3i | 0.983151 | + | 0.983151i | 0.999860 | − | 0.0167091i | \(-0.00531893\pi\) |
−0.0167091 | + | 0.999860i | \(0.505319\pi\) | |||||||
\(54\) | 13247.4 | − | 7354.58i | 0.618223 | − | 0.343221i | ||||
\(55\) | 4087.26 | + | 34167.0i | 0.182190 | + | 1.52300i | ||||
\(56\) | − | 174.945i | − | 0.00745471i | ||||||
\(57\) | −28932.1 | + | 13294.6i | −1.17949 | + | 0.541987i | ||||
\(58\) | −8991.10 | + | 8991.10i | −0.350948 | + | 0.350948i | ||||
\(59\) | 36465.5 | 1.36381 | 0.681903 | − | 0.731443i | \(-0.261153\pi\) | ||||
0.681903 | + | 0.731443i | \(0.261153\pi\) | |||||||
\(60\) | 11888.0 | − | 7285.25i | 0.426316 | − | 0.261256i | ||||
\(61\) | 16657.4 | 0.573170 | 0.286585 | − | 0.958055i | \(-0.407480\pi\) | ||||
0.286585 | + | 0.958055i | \(0.407480\pi\) | |||||||
\(62\) | 4688.26 | − | 4688.26i | 0.154893 | − | 0.154893i | ||||
\(63\) | −662.322 | + | 50.4811i | −0.0210241 | + | 0.00160243i | ||||
\(64\) | 4096.00i | 0.125000i | ||||||||
\(65\) | −10357.2 | + | 13171.9i | −0.304061 | + | 0.386693i | ||||
\(66\) | −13329.2 | + | 35993.5i | −0.376655 | + | 1.01710i | ||||
\(67\) | 8472.23 | + | 8472.23i | 0.230574 | + | 0.230574i | 0.812932 | − | 0.582358i | \(-0.197870\pi\) |
−0.582358 | + | 0.812932i | \(0.697870\pi\) | |||||||
\(68\) | −4365.44 | − | 4365.44i | −0.114487 | − | 0.114487i | ||||
\(69\) | 22791.6 | − | 61545.2i | 0.576304 | − | 1.55622i | ||||
\(70\) | −606.905 | + | 72.6016i | −0.0148039 | + | 0.00177093i | ||||
\(71\) | − | 42867.4i | − | 1.00921i | −0.863350 | − | 0.504605i | \(-0.831638\pi\) | ||
0.863350 | − | 0.504605i | \(-0.168362\pi\) | |||||||
\(72\) | 15507.0 | − | 1181.92i | 0.352531 | − | 0.0268693i | ||||
\(73\) | 22731.5 | − | 22731.5i | 0.499254 | − | 0.499254i | −0.411952 | − | 0.911206i | \(-0.635153\pi\) |
0.911206 | + | 0.411952i | \(0.135153\pi\) | |||||||
\(74\) | −53665.7 | −1.13925 | ||||||||
\(75\) | −30206.9 | − | 38217.6i | −0.620088 | − | 0.784532i | ||||
\(76\) | −32681.1 | −0.649026 | ||||||||
\(77\) | 1189.80 | − | 1189.80i | 0.0228690 | − | 0.0228690i | ||||
\(78\) | −16983.1 | + | 7803.89i | −0.316067 | + | 0.145236i | ||||
\(79\) | 77720.3i | 1.40109i | 0.713607 | + | 0.700547i | \(0.247060\pi\) | ||||
−0.713607 | + | 0.700547i | \(0.752940\pi\) | |||||||
\(80\) | 14209.5 | − | 1699.83i | 0.248230 | − | 0.0296948i | ||||
\(81\) | −8949.25 | − | 58366.9i | −0.151556 | − | 0.988449i | ||||
\(82\) | −3934.53 | − | 3934.53i | −0.0646187 | − | 0.0646187i | ||||
\(83\) | 247.467 | + | 247.467i | 0.00394296 | + | 0.00394296i | 0.709076 | − | 0.705133i | \(-0.249113\pi\) |
−0.705133 | + | 0.709076i | \(0.749113\pi\) | |||||||
\(84\) | −639.348 | − | 236.765i | −0.00988642 | − | 0.00366116i | ||||
\(85\) | −13332.6 | + | 16955.9i | −0.200156 | + | 0.254550i | ||||
\(86\) | 65132.1i | 0.949617i | ||||||||
\(87\) | 20690.3 | + | 45026.9i | 0.293069 | + | 0.637785i | ||||
\(88\) | −27856.9 | + | 27856.9i | −0.383465 | + | 0.383465i | ||||
\(89\) | −109920. | −1.47096 | −0.735482 | − | 0.677544i | \(-0.763044\pi\) | ||||
−0.735482 | + | 0.677544i | \(0.763044\pi\) | |||||||
\(90\) | −10535.6 | − | 53305.3i | −0.137105 | − | 0.693687i | ||||
\(91\) | 819.356 | 0.0103722 | ||||||||
\(92\) | 47632.5 | − | 47632.5i | 0.586724 | − | 0.586724i | ||||
\(93\) | −10788.6 | − | 23478.6i | −0.129348 | − | 0.281491i | ||||
\(94\) | 22794.2i | 0.266075i | ||||||||
\(95\) | 13562.6 | + | 113375.i | 0.154182 | + | 1.28886i | ||||
\(96\) | 14969.1 | + | 5543.40i | 0.165775 | + | 0.0613901i | ||||
\(97\) | −39430.4 | − | 39430.4i | −0.425502 | − | 0.425502i | 0.461591 | − | 0.887093i | \(-0.347279\pi\) |
−0.887093 | + | 0.461591i | \(0.847279\pi\) | |||||||
\(98\) | −47516.2 | − | 47516.2i | −0.499778 | − | 0.499778i | ||||
\(99\) | 113501. | + | 97424.9i | 1.16389 | + | 0.999038i | ||||
\(100\) | −11793.8 | − | 48589.2i | −0.117938 | − | 0.485892i | ||||
\(101\) | − | 78317.6i | − | 0.763934i | −0.924176 | − | 0.381967i | \(-0.875247\pi\) | ||
0.924176 | − | 0.381967i | \(-0.124753\pi\) | |||||||
\(102\) | −21861.9 | + | 10045.8i | −0.208059 | + | 0.0956054i | ||||
\(103\) | 119058. | − | 119058.i | 1.10578 | − | 1.10578i | 0.112075 | − | 0.993700i | \(-0.464250\pi\) |
0.993700 | − | 0.112075i | \(-0.0357498\pi\) | |||||||
\(104\) | −19183.7 | −0.173920 | ||||||||
\(105\) | −556.039 | + | 2316.23i | −0.00492189 | + | 0.0205026i | ||||
\(106\) | 113733. | 0.983151 | ||||||||
\(107\) | 79786.7 | − | 79786.7i | 0.673707 | − | 0.673707i | −0.284862 | − | 0.958569i | \(-0.591948\pi\) |
0.958569 | + | 0.284862i | \(0.0919477\pi\) | |||||||
\(108\) | 16667.3 | − | 58271.1i | 0.137501 | − | 0.480722i | ||||
\(109\) | − | 34102.3i | − | 0.274927i | −0.990507 | − | 0.137464i | \(-0.956105\pi\) | ||
0.990507 | − | 0.137464i | \(-0.0438950\pi\) | |||||||
\(110\) | 108199. | + | 85078.3i | 0.852595 | + | 0.670405i | ||||
\(111\) | −72629.6 | + | 196125.i | −0.559508 | + | 1.51087i | ||||
\(112\) | −494.819 | − | 494.819i | −0.00372736 | − | 0.00372736i | ||||
\(113\) | 103180. | + | 103180.i | 0.760150 | + | 0.760150i | 0.976349 | − | 0.216199i | \(-0.0693660\pi\) |
−0.216199 | + | 0.976349i | \(0.569366\pi\) | |||||||
\(114\) | −44229.6 | + | 119435.i | −0.318750 | + | 0.860737i | ||||
\(115\) | −185010. | − | 145475.i | −1.30452 | − | 1.02576i | ||||
\(116\) | 50861.4i | 0.350948i | ||||||||
\(117\) | 5535.54 | + | 72627.3i | 0.0373848 | + | 0.490496i | ||||
\(118\) | 103140. | − | 103140.i | 0.681903 | − | 0.681903i | ||||
\(119\) | 1054.74 | 0.00682774 | ||||||||
\(120\) | 13018.6 | − | 54230.2i | 0.0825298 | − | 0.343786i | ||||
\(121\) | −217857. | −1.35272 | ||||||||
\(122\) | 47114.3 | − | 47114.3i | 0.286585 | − | 0.286585i | ||||
\(123\) | −19703.9 | + | 9054.15i | −0.117433 | + | 0.0539616i | ||||
\(124\) | − | 26520.8i | − | 0.154893i | ||||||
\(125\) | −163667. | + | 61078.6i | −0.936886 | + | 0.349634i | ||||
\(126\) | −1730.55 | + | 2016.11i | −0.00971085 | + | 0.0113133i | ||||
\(127\) | 167198. | + | 167198.i | 0.919861 | + | 0.919861i | 0.997019 | − | 0.0771578i | \(-0.0245845\pi\) |
−0.0771578 | + | 0.997019i | \(0.524585\pi\) | |||||||
\(128\) | 11585.2 | + | 11585.2i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 238030. | + | 88147.7i | 1.25938 | + | 0.466377i | ||||
\(130\) | 7961.17 | + | 66550.5i | 0.0413160 | + | 0.345377i | ||||
\(131\) | − | 238726.i | − | 1.21541i | −0.794164 | − | 0.607704i | \(-0.792091\pi\) | ||
0.794164 | − | 0.607704i | \(-0.207909\pi\) | |||||||
\(132\) | 64104.2 | + | 139505.i | 0.320223 | + | 0.696878i | ||||
\(133\) | 3948.05 | − | 3948.05i | 0.0193532 | − | 0.0193532i | ||||
\(134\) | 47926.2 | 0.230574 | ||||||||
\(135\) | −209066. | − | 33638.6i | −0.987302 | − | 0.158856i | ||||
\(136\) | −24694.7 | −0.114487 | ||||||||
\(137\) | 15989.0 | − | 15989.0i | 0.0727812 | − | 0.0727812i | −0.669779 | − | 0.742560i | \(-0.733611\pi\) |
0.742560 | + | 0.669779i | \(0.233611\pi\) | |||||||
\(138\) | −109612. | − | 238541.i | −0.489959 | − | 1.06626i | ||||
\(139\) | − | 61223.8i | − | 0.268772i | −0.990929 | − | 0.134386i | \(-0.957094\pi\) | ||
0.990929 | − | 0.134386i | \(-0.0429062\pi\) | |||||||
\(140\) | −1511.24 | + | 1921.93i | −0.00651647 | + | 0.00828740i | ||||
\(141\) | 83303.0 | + | 30849.0i | 0.352868 | + | 0.130675i | ||||
\(142\) | −121247. | − | 121247.i | −0.504605 | − | 0.504605i | ||||
\(143\) | −130468. | − | 130468.i | −0.533536 | − | 0.533536i | ||||
\(144\) | 40517.5 | − | 47203.5i | 0.162831 | − | 0.189700i | ||||
\(145\) | 176444. | − | 21107.3i | 0.696927 | − | 0.0833707i | ||||
\(146\) | − | 128589.i | − | 0.499254i | ||||||
\(147\) | −237959. | + | 109344.i | −0.908255 | + | 0.417353i | ||||
\(148\) | −151790. | + | 151790.i | −0.569623 | + | 0.569623i | ||||
\(149\) | −259868. | −0.958930 | −0.479465 | − | 0.877561i | \(-0.659169\pi\) | ||||
−0.479465 | + | 0.877561i | \(0.659169\pi\) | |||||||
\(150\) | −193534. | − | 22657.7i | −0.702310 | − | 0.0822219i | ||||
\(151\) | −186012. | −0.663894 | −0.331947 | − | 0.943298i | \(-0.607705\pi\) | ||||
−0.331947 | + | 0.943298i | \(0.607705\pi\) | |||||||
\(152\) | −92436.0 | + | 92436.0i | −0.324513 | + | 0.324513i | ||||
\(153\) | 7125.76 | + | 93491.4i | 0.0246095 | + | 0.322881i | ||||
\(154\) | − | 6730.51i | − | 0.0228690i | ||||||
\(155\) | −92004.0 | + | 11006.1i | −0.307594 | + | 0.0367962i | ||||
\(156\) | −25962.6 | + | 70108.1i | −0.0854155 | + | 0.230652i | ||||
\(157\) | 157614. | + | 157614.i | 0.510324 | + | 0.510324i | 0.914626 | − | 0.404302i | \(-0.132485\pi\) |
−0.404302 | + | 0.914626i | \(0.632485\pi\) | |||||||
\(158\) | 219826. | + | 219826.i | 0.700547 | + | 0.700547i | ||||
\(159\) | 153922. | − | 415644.i | 0.482846 | − | 1.30385i | ||||
\(160\) | 35382.8 | − | 44998.4i | 0.109268 | − | 0.138962i | ||||
\(161\) | 11508.5i | 0.0349908i | ||||||||
\(162\) | −190399. | − | 139774.i | −0.570002 | − | 0.418446i | ||||
\(163\) | 64473.4 | − | 64473.4i | 0.190069 | − | 0.190069i | −0.605657 | − | 0.795726i | \(-0.707090\pi\) |
0.795726 | + | 0.605657i | \(0.207090\pi\) | |||||||
\(164\) | −22257.1 | −0.0646187 | ||||||||
\(165\) | 457358. | − | 280280.i | 1.30782 | − | 0.801460i | ||||
\(166\) | 1399.89 | 0.00394296 | ||||||||
\(167\) | 100742. | − | 100742.i | 0.279523 | − | 0.279523i | −0.553396 | − | 0.832919i | \(-0.686668\pi\) |
0.832919 | + | 0.553396i | \(0.186668\pi\) | |||||||
\(168\) | −2478.02 | + | 1138.68i | −0.00677379 | + | 0.00311263i | ||||
\(169\) | 281446.i | 0.758016i | ||||||||
\(170\) | 10248.2 | + | 85668.8i | 0.0271973 | + | 0.227353i | ||||
\(171\) | 376626. | + | 323280.i | 0.984963 | + | 0.845451i | ||||
\(172\) | 184221. | + | 184221.i | 0.474809 | + | 0.474809i | ||||
\(173\) | 114178. | + | 114178.i | 0.290047 | + | 0.290047i | 0.837099 | − | 0.547052i | \(-0.184250\pi\) |
−0.547052 | + | 0.837099i | \(0.684250\pi\) | |||||||
\(174\) | 185876. | + | 68834.2i | 0.465427 | + | 0.172358i | ||||
\(175\) | 7294.58 | + | 4445.07i | 0.0180055 | + | 0.0109719i | ||||
\(176\) | 157582.i | 0.383465i | ||||||||
\(177\) | −237346. | − | 516520.i | −0.569442 | − | 1.23923i | ||||
\(178\) | −310901. | + | 310901.i | −0.735482 | + | 0.735482i | ||||
\(179\) | −15895.1 | −0.0370792 | −0.0185396 | − | 0.999828i | \(-0.505902\pi\) | ||||
−0.0185396 | + | 0.999828i | \(0.505902\pi\) | |||||||
\(180\) | −180569. | − | 120971.i | −0.415396 | − | 0.278291i | ||||
\(181\) | 751524. | 1.70509 | 0.852543 | − | 0.522657i | \(-0.175059\pi\) | ||||
0.852543 | + | 0.522657i | \(0.175059\pi\) | |||||||
\(182\) | 2317.49 | − | 2317.49i | 0.00518608 | − | 0.00518608i | ||||
\(183\) | −108420. | − | 235946.i | −0.239320 | − | 0.520816i | ||||
\(184\) | − | 269450.i | − | 0.586724i | ||||||
\(185\) | 589569. | + | 463585.i | 1.26650 | + | 0.995863i | ||||
\(186\) | −96922.3 | − | 35892.5i | −0.205419 | − | 0.0760714i | ||||
\(187\) | −167948. | − | 167948.i | −0.351214 | − | 0.351214i | ||||
\(188\) | 64471.7 | + | 64471.7i | 0.133038 | + | 0.133038i | ||||
\(189\) | 5025.96 | + | 9052.96i | 0.0102344 | + | 0.0184347i | ||||
\(190\) | 359032. | + | 282311.i | 0.721522 | + | 0.567341i | ||||
\(191\) | 109522.i | 0.217229i | 0.994084 | + | 0.108615i | \(0.0346415\pi\) | ||||
−0.994084 | + | 0.108615i | \(0.965359\pi\) | |||||||
\(192\) | 58018.2 | − | 26660.0i | 0.113582 | − | 0.0521923i | ||||
\(193\) | −613686. | + | 613686.i | −1.18591 | + | 1.18591i | −0.207727 | + | 0.978187i | \(0.566607\pi\) |
−0.978187 | + | 0.207727i | \(0.933393\pi\) | |||||||
\(194\) | −223052. | −0.425502 | ||||||||
\(195\) | 253988. | + | 60972.7i | 0.478329 | + | 0.114828i | ||||
\(196\) | −268792. | −0.499778 | ||||||||
\(197\) | 78711.3 | − | 78711.3i | 0.144501 | − | 0.144501i | −0.631155 | − | 0.775657i | \(-0.717419\pi\) |
0.775657 | + | 0.631155i | \(0.217419\pi\) | |||||||
\(198\) | 596589. | − | 45471.1i | 1.08147 | − | 0.0824275i | ||||
\(199\) | − | 175358.i | − | 0.313901i | −0.987606 | − | 0.156951i | \(-0.949834\pi\) | ||
0.987606 | − | 0.156951i | \(-0.0501663\pi\) | |||||||
\(200\) | −170789. | − | 104073.i | −0.301915 | − | 0.183977i | ||||
\(201\) | 64861.8 | − | 175150.i | 0.113240 | − | 0.305787i | ||||
\(202\) | −221516. | − | 221516.i | −0.381967 | − | 0.381967i | ||||
\(203\) | −6144.32 | − | 6144.32i | −0.0104649 | − | 0.0104649i | ||||
\(204\) | −33421.0 | + | 90248.4i | −0.0562269 | + | 0.151832i | ||||
\(205\) | 9236.63 | + | 77212.5i | 0.0153507 | + | 0.128323i | ||||
\(206\) | − | 673496.i | − | 1.10578i | ||||||
\(207\) | −1.02011e6 | + | 77751.0i | −1.65471 | + | 0.126119i | ||||
\(208\) | −54259.6 | + | 54259.6i | −0.0869598 | + | 0.0869598i | ||||
\(209\) | −1.25731e6 | −1.99103 | ||||||||
\(210\) | 4978.58 | + | 8124.01i | 0.00779036 | + | 0.0127122i | ||||
\(211\) | −137396. | −0.212456 | −0.106228 | − | 0.994342i | \(-0.533877\pi\) | ||||
−0.106228 | + | 0.994342i | \(0.533877\pi\) | |||||||
\(212\) | 321684. | − | 321684.i | 0.491576 | − | 0.491576i | ||||
\(213\) | −607200. | + | 279015.i | −0.917028 | + | 0.421384i | ||||
\(214\) | − | 451342.i | − | 0.673707i | ||||||
\(215\) | 562635. | − | 715537.i | 0.830100 | − | 1.05569i | ||||
\(216\) | −117673. | − | 211958.i | −0.171610 | − | 0.309111i | ||||
\(217\) | 3203.86 | + | 3203.86i | 0.00461874 | + | 0.00461874i | ||||
\(218\) | −96455.9 | − | 96455.9i | −0.137464 | − | 0.137464i | ||||
\(219\) | −469938. | − | 174028.i | −0.662110 | − | 0.245194i | ||||
\(220\) | 546672. | − | 65396.2i | 0.761500 | − | 0.0910952i | ||||
\(221\) | − | 115658.i | − | 0.159292i | ||||||
\(222\) | 349299. | + | 760154.i | 0.475679 | + | 1.03519i | ||||
\(223\) | −74950.4 | + | 74950.4i | −0.100928 | + | 0.100928i | −0.755768 | − | 0.654840i | \(-0.772736\pi\) |
0.654840 | + | 0.755768i | \(0.272736\pi\) | |||||||
\(224\) | −2799.12 | −0.00372736 | ||||||||
\(225\) | −344727. | + | 676619.i | −0.453962 | + | 0.891021i | ||||
\(226\) | 583674. | 0.760150 | ||||||||
\(227\) | 240353. | − | 240353.i | 0.309588 | − | 0.309588i | −0.535162 | − | 0.844750i | \(-0.679749\pi\) |
0.844750 | + | 0.535162i | \(0.179749\pi\) | |||||||
\(228\) | 212714. | + | 462914.i | 0.270993 | + | 0.589744i | ||||
\(229\) | 151951.i | 0.191476i | 0.995407 | + | 0.0957378i | \(0.0305210\pi\) | ||||
−0.995407 | + | 0.0957378i | \(0.969479\pi\) | |||||||
\(230\) | −934755. | + | 111821.i | −1.16514 | + | 0.139381i | ||||
\(231\) | −24597.1 | − | 9108.87i | −0.0303288 | − | 0.0112314i | ||||
\(232\) | 143858. | + | 143858.i | 0.175474 | + | 0.175474i | ||||
\(233\) | 269671. | + | 269671.i | 0.325420 | + | 0.325420i | 0.850842 | − | 0.525422i | \(-0.176093\pi\) |
−0.525422 | + | 0.850842i | \(0.676093\pi\) | |||||||
\(234\) | 221078. | + | 189764.i | 0.263940 | + | 0.226556i | ||||
\(235\) | 196905. | − | 250416.i | 0.232587 | − | 0.295796i | ||||
\(236\) | − | 583449.i | − | 0.681903i | ||||||
\(237\) | 1.10088e6 | − | 505865.i | 1.27312 | − | 0.585010i | ||||
\(238\) | 2983.25 | − | 2983.25i | 0.00341387 | − | 0.00341387i | ||||
\(239\) | 995618. | 1.12745 | 0.563726 | − | 0.825962i | \(-0.309367\pi\) | ||||
0.563726 | + | 0.825962i | \(0.309367\pi\) | |||||||
\(240\) | −116564. | − | 190208.i | −0.130628 | − | 0.213158i | ||||
\(241\) | −1.63448e6 | −1.81275 | −0.906373 | − | 0.422478i | \(-0.861160\pi\) | ||||
−0.906373 | + | 0.422478i | \(0.861160\pi\) | |||||||
\(242\) | −616194. | + | 616194.i | −0.676362 | + | 0.676362i | ||||
\(243\) | −768495. | + | 506660.i | −0.834882 | + | 0.550428i | ||||
\(244\) | − | 266519.i | − | 0.286585i | ||||||
\(245\) | 111548. | + | 932474.i | 0.118726 | + | 0.992479i | ||||
\(246\) | −30122.0 | + | 81340.1i | −0.0317356 | + | 0.0856972i | ||||
\(247\) | −432925. | − | 432925.i | −0.451513 | − | 0.451513i | ||||
\(248\) | −75012.2 | − | 75012.2i | −0.0774467 | − | 0.0774467i | ||||
\(249\) | 1894.56 | − | 5115.99i | 0.00193647 | − | 0.00522915i | ||||
\(250\) | −290165. | + | 635677.i | −0.293626 | + | 0.643260i | ||||
\(251\) | 1.42939e6i | 1.43207i | 0.698062 | + | 0.716037i | \(0.254046\pi\) | ||||
−0.698062 | + | 0.716037i | \(0.745954\pi\) | |||||||
\(252\) | 807.698 | + | 10597.2i | 0.000801213 | + | 0.0105121i | ||||
\(253\) | 1.83253e6 | − | 1.83253e6i | 1.79990 | − | 1.79990i | ||||
\(254\) | 945816. | 0.919861 | ||||||||
\(255\) | 326952. | + | 78488.7i | 0.314872 | + | 0.0755887i | ||||
\(256\) | 65536.0 | 0.0625000 | ||||||||
\(257\) | −399795. | + | 399795.i | −0.377576 | + | 0.377576i | −0.870227 | − | 0.492651i | \(-0.836028\pi\) |
0.492651 | + | 0.870227i | \(0.336028\pi\) | |||||||
\(258\) | 922569. | − | 423930.i | 0.862879 | − | 0.396502i | ||||
\(259\) | − | 36674.0i | − | 0.0339710i | ||||||
\(260\) | 210751. | + | 165716.i | 0.193346 | + | 0.152030i | ||||
\(261\) | 503119. | − | 586141.i | 0.457161 | − | 0.532599i | ||||
\(262\) | −675220. | − | 675220.i | −0.607704 | − | 0.607704i | ||||
\(263\) | −33111.1 | − | 33111.1i | −0.0295178 | − | 0.0295178i | 0.692194 | − | 0.721712i | \(-0.256644\pi\) |
−0.721712 | + | 0.692194i | \(0.756644\pi\) | |||||||
\(264\) | 575895. | + | 213267.i | 0.508550 | + | 0.188327i | ||||
\(265\) | −1.24946e6 | − | 982464.i | −1.09297 | − | 0.859413i | ||||
\(266\) | − | 22333.5i | − | 0.0193532i | ||||||
\(267\) | 715446. | + | 1.55697e6i | 0.614184 | + | 1.33661i | ||||
\(268\) | 135556. | − | 135556.i | 0.115287 | − | 0.115287i | ||||
\(269\) | 764920. | 0.644518 | 0.322259 | − | 0.946652i | \(-0.395558\pi\) | ||||
0.322259 | + | 0.946652i | \(0.395558\pi\) | |||||||
\(270\) | −686474. | + | 496185.i | −0.573079 | + | 0.414223i | ||||
\(271\) | 2.00900e6 | 1.66172 | 0.830859 | − | 0.556483i | \(-0.187850\pi\) | ||||
0.830859 | + | 0.556483i | \(0.187850\pi\) | |||||||
\(272\) | −69847.1 | + | 69847.1i | −0.0572435 | + | 0.0572435i | ||||
\(273\) | −5333.01 | − | 11605.8i | −0.00433078 | − | 0.00942476i | ||||
\(274\) | − | 90447.3i | − | 0.0727812i | ||||||
\(275\) | −453735. | − | 1.86933e6i | −0.361801 | − | 1.49058i | ||||
\(276\) | −984724. | − | 364665.i | −0.778111 | − | 0.288152i | ||||
\(277\) | 484721. | + | 484721.i | 0.379571 | + | 0.379571i | 0.870947 | − | 0.491377i | \(-0.163506\pi\) |
−0.491377 | + | 0.870947i | \(0.663506\pi\) | |||||||
\(278\) | −173167. | − | 173167.i | −0.134386 | − | 0.134386i | ||||
\(279\) | −262343. | + | 305634.i | −0.201771 | + | 0.235066i | ||||
\(280\) | 1161.63 | + | 9710.48i | 0.000885464 | + | 0.00740194i | ||||
\(281\) | 1.45938e6i | 1.10256i | 0.834320 | + | 0.551281i | \(0.185861\pi\) | ||||
−0.834320 | + | 0.551281i | \(0.814139\pi\) | |||||||
\(282\) | 322870. | − | 148362.i | 0.241772 | − | 0.111097i | ||||
\(283\) | 57871.0 | − | 57871.0i | 0.0429531 | − | 0.0429531i | −0.685304 | − | 0.728257i | \(-0.740331\pi\) |
0.728257 | + | 0.685304i | \(0.240331\pi\) | |||||||
\(284\) | −685879. | −0.504605 | ||||||||
\(285\) | 1.51763e6 | − | 930039.i | 1.10676 | − | 0.678248i | ||||
\(286\) | −738038. | −0.533536 | ||||||||
\(287\) | 2688.77 | − | 2688.77i | 0.00192686 | − | 0.00192686i | ||||
\(288\) | −18910.7 | − | 248112.i | −0.0134347 | − | 0.176265i | ||||
\(289\) | 1.27097e6i | 0.895142i | ||||||||
\(290\) | 439359. | − | 558760.i | 0.306778 | − | 0.390149i | ||||
\(291\) | −301872. | + | 815159.i | −0.208973 | + | 0.564300i | ||||
\(292\) | −363705. | − | 363705.i | −0.249627 | − | 0.249627i | ||||
\(293\) | −1.67259e6 | − | 1.67259e6i | −1.13821 | − | 1.13821i | −0.988772 | − | 0.149433i | \(-0.952255\pi\) |
−0.149433 | − | 0.988772i | \(-0.547745\pi\) | |||||||
\(294\) | −363775. | + | 982321.i | −0.245451 | + | 0.662804i | ||||
\(295\) | −2.02405e6 | + | 242130.i | −1.35415 | + | 0.161992i | ||||
\(296\) | 858652.i | 0.569623i | ||||||||
\(297\) | 641229. | − | 2.24182e6i | 0.421815 | − | 1.47472i | ||||
\(298\) | −735017. | + | 735017.i | −0.479465 | + | 0.479465i | ||||
\(299\) | 1.26197e6 | 0.816341 | ||||||||
\(300\) | −611482. | + | 483311.i | −0.392266 | + | 0.310044i | ||||
\(301\) | −44509.8 | −0.0283165 | ||||||||
\(302\) | −526121. | + | 526121.i | −0.331947 | + | 0.331947i | ||||
\(303\) | −1.10934e6 | + | 509752.i | −0.694156 | + | 0.318972i | ||||
\(304\) | 522897.i | 0.324513i | ||||||||
\(305\) | −924586. | + | 110605.i | −0.569112 | + | 0.0680806i | ||||
\(306\) | 284588. | + | 244279.i | 0.173745 | + | 0.149136i | ||||
\(307\) | 2.10290e6 | + | 2.10290e6i | 1.27342 | + | 1.27342i | 0.944280 | + | 0.329143i | \(0.106760\pi\) |
0.329143 | + | 0.944280i | \(0.393240\pi\) | |||||||
\(308\) | −19036.8 | − | 19036.8i | −0.0114345 | − | 0.0114345i | ||||
\(309\) | −2.46134e6 | − | 911489.i | −1.46648 | − | 0.543069i | ||||
\(310\) | −229097. | + | 291356.i | −0.135399 | + | 0.172195i | ||||
\(311\) | − | 1.10864e6i | − | 0.649964i | −0.945720 | − | 0.324982i | \(-0.894642\pi\) | ||
0.945720 | − | 0.324982i | \(-0.105358\pi\) | |||||||
\(312\) | 124862. | + | 271729.i | 0.0726181 | + | 0.158034i | ||||
\(313\) | 1.15125e6 | − | 1.15125e6i | 0.664214 | − | 0.664214i | −0.292157 | − | 0.956370i | \(-0.594373\pi\) |
0.956370 | + | 0.292157i | \(0.0943728\pi\) | |||||||
\(314\) | 891600. | 0.510324 | ||||||||
\(315\) | 36427.6 | − | 7199.80i | 0.0206850 | − | 0.00408831i | ||||
\(316\) | 1.24353e6 | 0.700547 | ||||||||
\(317\) | 177254. | − | 177254.i | 0.0990715 | − | 0.0990715i | −0.655834 | − | 0.754905i | \(-0.727683\pi\) |
0.754905 | + | 0.655834i | \(0.227683\pi\) | |||||||
\(318\) | −740261. | − | 1.61098e6i | −0.410504 | − | 0.893349i | ||||
\(319\) | 1.95675e6i | 1.07661i | ||||||||
\(320\) | −27197.3 | − | 227352.i | −0.0148474 | − | 0.124115i | ||||
\(321\) | −1.64946e6 | − | 610832.i | −0.893468 | − | 0.330871i | ||||
\(322\) | 32551.0 | + | 32551.0i | 0.0174954 | + | 0.0174954i | ||||
\(323\) | −557294. | − | 557294.i | −0.297220 | − | 0.297220i | ||||
\(324\) | −933870. | + | 143188.i | −0.494224 | + | 0.0757782i | ||||
\(325\) | 487427. | − | 799892.i | 0.255977 | − | 0.420071i | ||||
\(326\) | − | 364717.i | − | 0.190069i | ||||||
\(327\) | −483045. | + | 221964.i | −0.249815 | + | 0.114793i | ||||
\(328\) | −62952.5 | + | 62952.5i | −0.0323094 | + | 0.0323094i | ||||
\(329\) | −15577.0 | −0.00793406 | ||||||||
\(330\) | 500854. | − | 2.08636e6i | 0.253178 | − | 1.05464i | ||||
\(331\) | −2.03500e6 | −1.02093 | −0.510464 | − | 0.859899i | \(-0.670526\pi\) | ||||
−0.510464 | + | 0.859899i | \(0.670526\pi\) | |||||||
\(332\) | 3959.48 | − | 3959.48i | 0.00197148 | − | 0.00197148i | ||||
\(333\) | 3.25077e6 | − | 247768.i | 1.60648 | − | 0.122443i | ||||
\(334\) | − | 569880.i | − | 0.279523i | ||||||
\(335\) | −526514. | − | 414004.i | −0.256329 | − | 0.201555i | ||||
\(336\) | −3788.24 | + | 10229.6i | −0.00183058 | + | 0.00494321i | ||||
\(337\) | −1.02552e6 | − | 1.02552e6i | −0.491889 | − | 0.491889i | 0.417012 | − | 0.908901i | \(-0.363077\pi\) |
−0.908901 | + | 0.417012i | \(0.863077\pi\) | |||||||
\(338\) | 796050. | + | 796050.i | 0.379008 | + | 0.379008i | ||||
\(339\) | 789927. | − | 2.13308e6i | 0.373325 | − | 1.00811i | ||||
\(340\) | 271294. | + | 213322.i | 0.127275 | + | 0.100078i | ||||
\(341\) | − | 1.02032e6i | − | 0.475169i | ||||||
\(342\) | 1.97963e6 | − | 150884.i | 0.915207 | − | 0.0697556i | ||||
\(343\) | 64957.5 | − | 64957.5i | 0.0298122 | − | 0.0298122i | ||||
\(344\) | 1.04211e6 | 0.474809 | ||||||||
\(345\) | −856411. | + | 3.56746e6i | −0.387377 | + | 1.61366i | ||||
\(346\) | 645890. | 0.290047 | ||||||||
\(347\) | −1.31759e6 | + | 1.31759e6i | −0.587431 | + | 0.587431i | −0.936935 | − | 0.349504i | \(-0.886350\pi\) |
0.349504 | + | 0.936935i | \(0.386350\pi\) | |||||||
\(348\) | 720431. | − | 331045.i | 0.318892 | − | 0.146534i | ||||
\(349\) | 2.12112e6i | 0.932182i | 0.884737 | + | 0.466091i | \(0.154338\pi\) | ||||
−0.884737 | + | 0.466091i | \(0.845662\pi\) | |||||||
\(350\) | 33204.8 | − | 8059.64i | 0.0144887 | − | 0.00351678i | ||||
\(351\) | 992707. | − | 551124.i | 0.430084 | − | 0.238771i | ||||
\(352\) | 445710. | + | 445710.i | 0.191732 | + | 0.191732i | ||||
\(353\) | 1.43096e6 | + | 1.43096e6i | 0.611211 | + | 0.611211i | 0.943262 | − | 0.332050i | \(-0.107740\pi\) |
−0.332050 | + | 0.943262i | \(0.607740\pi\) | |||||||
\(354\) | −2.13225e6 | − | 789621.i | −0.904338 | − | 0.334897i | ||||
\(355\) | 284638. | + | 2.37940e6i | 0.119873 | + | 1.00207i | ||||
\(356\) | 1.75872e6i | 0.735482i | ||||||||
\(357\) | −6865.05 | − | 14939.9i | −0.00285084 | − | 0.00620409i | ||||
\(358\) | −44958.1 | + | 44958.1i | −0.0185396 | + | 0.0185396i | ||||
\(359\) | 3.53537e6 | 1.44777 | 0.723884 | − | 0.689921i | \(-0.242355\pi\) | ||||
0.723884 | + | 0.689921i | \(0.242355\pi\) | |||||||
\(360\) | −852884. | + | 168570.i | −0.346844 | + | 0.0685524i | ||||
\(361\) | −1.69598e6 | −0.684940 | ||||||||
\(362\) | 2.12563e6 | − | 2.12563e6i | 0.852543 | − | 0.852543i | ||||
\(363\) | 1.41799e6 | + | 3.08586e6i | 0.564814 | + | 1.22916i | ||||
\(364\) | − | 13109.7i | − | 0.00518608i | ||||||
\(365\) | −1.11080e6 | + | 1.41267e6i | −0.436419 | + | 0.555021i | ||||
\(366\) | −974012. | − | 360698.i | −0.380068 | − | 0.140748i | ||||
\(367\) | −810434. | − | 810434.i | −0.314089 | − | 0.314089i | 0.532402 | − | 0.846491i | \(-0.321289\pi\) |
−0.846491 | + | 0.532402i | \(0.821289\pi\) | |||||||
\(368\) | −762119. | − | 762119.i | −0.293362 | − | 0.293362i | ||||
\(369\) | 256497. | + | 220166.i | 0.0980655 | + | 0.0841754i | ||||
\(370\) | 2.97877e6 | − | 356338.i | 1.13118 | − | 0.135319i | ||||
\(371\) | 77722.4i | 0.0293164i | ||||||||
\(372\) | −375657. | + | 172618.i | −0.140745 | + | 0.0646740i | ||||
\(373\) | −202954. | + | 202954.i | −0.0755310 | + | 0.0755310i | −0.743863 | − | 0.668332i | \(-0.767009\pi\) |
0.668332 | + | 0.743863i | \(0.267009\pi\) | |||||||
\(374\) | −950058. | −0.351214 | ||||||||
\(375\) | 1.93043e6 | + | 1.92073e6i | 0.708885 | + | 0.705325i | ||||
\(376\) | 364707. | 0.133038 | ||||||||
\(377\) | −673759. | + | 673759.i | −0.244147 | + | 0.244147i | ||||
\(378\) | 39821.2 | + | 11390.1i | 0.0143346 | + | 0.00410013i | ||||
\(379\) | − | 2.26580e6i | − | 0.810257i | −0.914260 | − | 0.405128i | \(-0.867227\pi\) | ||
0.914260 | − | 0.405128i | \(-0.132773\pi\) | |||||||
\(380\) | 1.81399e6 | − | 217001.i | 0.644431 | − | 0.0770908i | ||||
\(381\) | 1.28004e6 | − | 3.45655e6i | 0.451763 | − | 1.21992i | ||||
\(382\) | 309775. | + | 309775.i | 0.108615 | + | 0.108615i | ||||
\(383\) | 348083. | + | 348083.i | 0.121251 | + | 0.121251i | 0.765129 | − | 0.643878i | \(-0.222675\pi\) |
−0.643878 | + | 0.765129i | \(0.722675\pi\) | |||||||
\(384\) | 88694.4 | − | 239506.i | 0.0306950 | − | 0.0828874i | ||||
\(385\) | −58140.7 | + | 73941.1i | −0.0199907 | + | 0.0254234i | ||||
\(386\) | 3.47153e6i | 1.18591i | ||||||||
\(387\) | −300707. | − | 3.94533e6i | −0.102062 | − | 1.33908i | ||||
\(388\) | −630886. | + | 630886.i | −0.212751 | + | 0.212751i | ||||
\(389\) | −3.80422e6 | −1.27465 | −0.637326 | − | 0.770594i | \(-0.719960\pi\) | ||||
−0.637326 | + | 0.770594i | \(0.719960\pi\) | |||||||
\(390\) | 890843. | − | 545929.i | 0.296579 | − | 0.181750i | ||||
\(391\) | 1.62451e6 | 0.537377 | ||||||||
\(392\) | −760260. | + | 760260.i | −0.249889 | + | 0.249889i | ||||
\(393\) | −3.38146e6 | + | 1.55382e6i | −1.10439 | + | 0.507479i | ||||
\(394\) | − | 445258.i | − | 0.144501i | ||||||
\(395\) | −516060. | − | 4.31394e6i | −0.166421 | − | 1.39117i | ||||
\(396\) | 1.55880e6 | − | 1.81602e6i | 0.499519 | − | 0.581946i | ||||
\(397\) | −357043. | − | 357043.i | −0.113696 | − | 0.113696i | 0.647970 | − | 0.761666i | \(-0.275618\pi\) |
−0.761666 | + | 0.647970i | \(0.775618\pi\) | |||||||
\(398\) | −495987. | − | 495987.i | −0.156951 | − | 0.156951i | ||||
\(399\) | −81619.4 | − | 30225.5i | −0.0256662 | − | 0.00950476i | ||||
\(400\) | −777426. | + | 188701.i | −0.242946 | + | 0.0589691i | ||||
\(401\) | − | 4.80511e6i | − | 1.49225i | −0.665804 | − | 0.746126i | \(-0.731911\pi\) | ||
0.665804 | − | 0.746126i | \(-0.268089\pi\) | |||||||
\(402\) | −311941. | − | 678855.i | −0.0962736 | − | 0.209513i | ||||
\(403\) | 351321. | − | 351321.i | 0.107756 | − | 0.107756i | ||||
\(404\) | −1.25308e6 | −0.381967 | ||||||||
\(405\) | 884290. | + | 3.18029e6i | 0.267890 | + | 0.963449i | ||||
\(406\) | −34757.5 | −0.0104649 | ||||||||
\(407\) | −5.83968e6 | + | 5.83968e6i | −1.74744 | + | 1.74744i | ||||
\(408\) | 160732. | + | 349790.i | 0.0478027 | + | 0.104030i | ||||
\(409\) | − | 4.72643e6i | − | 1.39709i | −0.715565 | − | 0.698546i | \(-0.753831\pi\) | ||
0.715565 | − | 0.698546i | \(-0.246169\pi\) | |||||||
\(410\) | 244515. | + | 192265.i | 0.0718366 | + | 0.0564859i | ||||
\(411\) | −330546. | − | 122409.i | −0.0965222 | − | 0.0357443i | ||||
\(412\) | −1.90493e6 | − | 1.90493e6i | −0.552888 | − | 0.552888i | ||||
\(413\) | 70483.7 | + | 70483.7i | 0.0203336 | + | 0.0203336i | ||||
\(414\) | −2.66539e6 | + | 3.10522e6i | −0.764293 | + | 0.890412i | ||||
\(415\) | −15379.1 | − | 12092.7i | −0.00438339 | − | 0.00344671i | ||||
\(416\) | 306939.i | 0.0869598i | ||||||||
\(417\) | −867211. | + | 398493.i | −0.244222 | + | 0.112223i | ||||
\(418\) | −3.55622e6 | + | 3.55622e6i | −0.995515 | + | 0.995515i | ||||
\(419\) | 2.40614e6 | 0.669556 | 0.334778 | − | 0.942297i | \(-0.391339\pi\) | ||||
0.334778 | + | 0.942297i | \(0.391339\pi\) | |||||||
\(420\) | 37059.7 | + | 8896.62i | 0.0102513 | + | 0.00246094i | ||||
\(421\) | 2.26063e6 | 0.621618 | 0.310809 | − | 0.950472i | \(-0.399400\pi\) | ||||
0.310809 | + | 0.950472i | \(0.399400\pi\) | |||||||
\(422\) | −388616. | + | 388616.i | −0.106228 | + | 0.106228i | ||||
\(423\) | −105238. | − | 1.38074e6i | −0.0285971 | − | 0.375199i | ||||
\(424\) | − | 1.81972e6i | − | 0.491576i | ||||||
\(425\) | 627452. | − | 1.02968e6i | 0.168503 | − | 0.276522i | ||||
\(426\) | −928247. | + | 2.50659e6i | −0.247822 | + | 0.669206i | ||||
\(427\) | 32196.9 | + | 32196.9i | 0.00854563 | + | 0.00854563i | ||||
\(428\) | −1.27659e6 | − | 1.27659e6i | −0.336853 | − | 0.336853i | ||||
\(429\) | −998838. | + | 2.69721e6i | −0.262031 | + | 0.707574i | ||||
\(430\) | −432474. | − | 3.61522e6i | −0.112795 | − | 0.942895i | ||||
\(431\) | 3.91972e6i | 1.01639i | 0.861241 | + | 0.508196i | \(0.169688\pi\) | ||||
−0.861241 | + | 0.508196i | \(0.830312\pi\) | |||||||
\(432\) | −932338. | − | 266677.i | −0.240361 | − | 0.0687506i | ||||
\(433\) | −3.06422e6 | + | 3.06422e6i | −0.785416 | + | 0.785416i | −0.980739 | − | 0.195323i | \(-0.937424\pi\) |
0.195323 | + | 0.980739i | \(0.437424\pi\) | |||||||
\(434\) | 18123.8 | 0.00461874 | ||||||||
\(435\) | −1.44741e6 | − | 2.36188e6i | −0.366750 | − | 0.598459i | ||||
\(436\) | −545637. | −0.137464 | ||||||||
\(437\) | 6.08078e6 | − | 6.08078e6i | 1.52320 | − | 1.52320i | ||||
\(438\) | −1.82141e6 | + | 836958.i | −0.453652 | + | 0.208458i | ||||
\(439\) | − | 3.10595e6i | − | 0.769188i | −0.923086 | − | 0.384594i | \(-0.874341\pi\) | ||
0.923086 | − | 0.384594i | \(-0.125659\pi\) | |||||||
\(440\) | 1.36125e6 | − | 1.73119e6i | 0.335202 | − | 0.426298i | ||||
\(441\) | 3.09764e6 | + | 2.65889e6i | 0.758463 | + | 0.651034i | ||||
\(442\) | −327130. | − | 327130.i | −0.0796460 | − | 0.0796460i | ||||
\(443\) | −2.85228e6 | − | 2.85228e6i | −0.690532 | − | 0.690532i | 0.271817 | − | 0.962349i | \(-0.412375\pi\) |
−0.962349 | + | 0.271817i | \(0.912375\pi\) | |||||||
\(444\) | 3.13800e6 | + | 1.16207e6i | 0.755433 | + | 0.279754i | ||||
\(445\) | 6.10122e6 | − | 729865.i | 1.46055 | − | 0.174720i | ||||
\(446\) | 423983.i | 0.100928i | ||||||||
\(447\) | 1.69142e6 | + | 3.68092e6i | 0.400390 | + | 0.871340i | ||||
\(448\) | −7917.10 | + | 7917.10i | −0.00186368 | + | 0.00186368i | ||||
\(449\) | 522216. | 0.122246 | 0.0611229 | − | 0.998130i | \(-0.480532\pi\) | ||||
0.0611229 | + | 0.998130i | \(0.480532\pi\) | |||||||
\(450\) | 938733. | + | 2.88880e6i | 0.218530 | + | 0.672491i | ||||
\(451\) | −856279. | −0.198232 | ||||||||
\(452\) | 1.65088e6 | − | 1.65088e6i | 0.380075 | − | 0.380075i | ||||
\(453\) | 1.21071e6 | + | 2.63479e6i | 0.277201 | + | 0.603253i | ||||
\(454\) | − | 1.35964e6i | − | 0.309588i | ||||||
\(455\) | −45479.1 | + | 5440.49i | −0.0102987 | + | 0.00123200i | ||||
\(456\) | 1.91096e6 | + | 707673.i | 0.430368 | + | 0.159375i | ||||
\(457\) | 3.29898e6 | + | 3.29898e6i | 0.738905 | + | 0.738905i | 0.972366 | − | 0.233461i | \(-0.0750052\pi\) |
−0.233461 | + | 0.972366i | \(0.575005\pi\) | |||||||
\(458\) | 429781. | + | 429781.i | 0.0957378 | + | 0.0957378i | ||||
\(459\) | 1.27789e6 | − | 709449.i | 0.283114 | − | 0.157177i | ||||
\(460\) | −2.32761e6 | + | 2.96016e6i | −0.512879 | + | 0.652260i | ||||
\(461\) | 2.80680e6i | 0.615118i | 0.951529 | + | 0.307559i | \(0.0995122\pi\) | ||||
−0.951529 | + | 0.307559i | \(0.900488\pi\) | |||||||
\(462\) | −95335.0 | + | 43807.4i | −0.0207801 | + | 0.00954867i | ||||
\(463\) | 535649. | − | 535649.i | 0.116126 | − | 0.116126i | −0.646656 | − | 0.762782i | \(-0.723833\pi\) |
0.762782 | + | 0.646656i | \(0.223833\pi\) | |||||||
\(464\) | 813782. | 0.175474 | ||||||||
\(465\) | 754731. | + | 1.23156e6i | 0.161867 | + | 0.264134i | ||||
\(466\) | 1.52549e6 | 0.325420 | ||||||||
\(467\) | 406464. | − | 406464.i | 0.0862441 | − | 0.0862441i | −0.662669 | − | 0.748913i | \(-0.730576\pi\) |
0.748913 | + | 0.662669i | \(0.230576\pi\) | |||||||
\(468\) | 1.16204e6 | − | 88568.6i | 0.245248 | − | 0.0186924i | ||||
\(469\) | 32751.7i | 0.00687546i | ||||||||
\(470\) | −151352. | − | 1.26521e6i | −0.0316042 | − | 0.264192i | ||||
\(471\) | 1.20666e6 | − | 3.25842e6i | 0.250631 | − | 0.676791i | ||||
\(472\) | −1.65024e6 | − | 1.65024e6i | −0.340951 | − | 0.340951i | ||||
\(473\) | 7.08740e6 | + | 7.08740e6i | 1.45658 | + | 1.45658i | ||||
\(474\) | 1.68295e6 | − | 4.54455e6i | 0.344053 | − | 0.929063i | ||||
\(475\) | −1.50560e6 | − | 6.20291e6i | −0.306180 | − | 1.26143i | ||||
\(476\) | − | 16875.8i | − | 0.00341387i | ||||||
\(477\) | −6.88927e6 | + | 525089.i | −1.38636 | + | 0.105666i | ||||
\(478\) | 2.81603e6 | − | 2.81603e6i | 0.563726 | − | 0.563726i | ||||
\(479\) | 2.36702e6 | 0.471371 | 0.235686 | − | 0.971829i | \(-0.424266\pi\) | ||||
0.235686 | + | 0.971829i | \(0.424266\pi\) | |||||||
\(480\) | −867683. | − | 208297.i | −0.171893 | − | 0.0412649i | ||||
\(481\) | −4.02151e6 | −0.792549 | ||||||||
\(482\) | −4.62301e6 | + | 4.62301e6i | −0.906373 | + | 0.906373i | ||||
\(483\) | 163013. | − | 74906.4i | 0.0317947 | − | 0.0146100i | ||||
\(484\) | 3.48572e6i | 0.676362i | ||||||||
\(485\) | 2.45044e6 | + | 1.92680e6i | 0.473030 | + | 0.371949i | ||||
\(486\) | −740581. | + | 3.60668e6i | −0.142227 | + | 0.692655i | ||||
\(487\) | −3.33072e6 | − | 3.33072e6i | −0.636378 | − | 0.636378i | 0.313282 | − | 0.949660i | \(-0.398571\pi\) |
−0.949660 | + | 0.313282i | \(0.898571\pi\) | |||||||
\(488\) | −753829. | − | 753829.i | −0.143292 | − | 0.143292i | ||||
\(489\) | −1.33288e6 | − | 493596.i | −0.252069 | − | 0.0933469i | ||||
\(490\) | 2.95294e6 | + | 2.32193e6i | 0.555603 | + | 0.436876i | ||||
\(491\) | 785451.i | 0.147033i | 0.997294 | + | 0.0735166i | \(0.0234222\pi\) | ||||
−0.997294 | + | 0.0735166i | \(0.976578\pi\) | |||||||
\(492\) | 144866. | + | 315262.i | 0.0269808 | + | 0.0587164i | ||||
\(493\) | −867314. | + | 867314.i | −0.160716 | + | 0.160716i | ||||
\(494\) | −2.44899e6 | −0.451513 | ||||||||
\(495\) | −6.94690e6 | − | 4.65402e6i | −1.27432 | − | 0.853719i | ||||
\(496\) | −424333. | −0.0774467 | ||||||||
\(497\) | 82857.8 | − | 82857.8i | 0.0150467 | − | 0.0150467i | ||||
\(498\) | −9111.56 | − | 19828.8i | −0.00164634 | − | 0.00358281i | ||||
\(499\) | − | 968793.i | − | 0.174173i | −0.996201 | − | 0.0870863i | \(-0.972244\pi\) | ||
0.996201 | − | 0.0870863i | \(-0.0277556\pi\) | |||||||
\(500\) | 977258. | + | 2.61868e6i | 0.174817 | + | 0.468443i | ||||
\(501\) | −2.08267e6 | − | 771258.i | −0.370703 | − | 0.137279i | ||||
\(502\) | 4.04292e6 | + | 4.04292e6i | 0.716037 | + | 0.716037i | ||||
\(503\) | −1.69640e6 | − | 1.69640e6i | −0.298958 | − | 0.298958i | 0.541648 | − | 0.840605i | \(-0.317801\pi\) |
−0.840605 | + | 0.541648i | \(0.817801\pi\) | |||||||
\(504\) | 32257.8 | + | 27688.8i | 0.00565664 | + | 0.00485543i | ||||
\(505\) | 520026. | + | 4.34709e6i | 0.0907395 | + | 0.758526i | ||||
\(506\) | − | 1.03663e7i | − | 1.79990i | ||||||
\(507\) | 3.98657e6 | − | 1.83187e6i | 0.688778 | − | 0.316501i | ||||
\(508\) | 2.67517e6 | − | 2.67517e6i | 0.459931 | − | 0.459931i | ||||
\(509\) | 1.32955e6 | 0.227463 | 0.113731 | − | 0.993512i | \(-0.463720\pi\) | ||||
0.113731 | + | 0.993512i | \(0.463720\pi\) | |||||||
\(510\) | 1.14676e6 | − | 702761.i | 0.195230 | − | 0.119642i | ||||
\(511\) | 87874.9 | 0.0148872 | ||||||||
\(512\) | 185364. | − | 185364.i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 2.12776e6 | − | 7.43891e6i | 0.356967 | − | 1.24800i | ||||
\(514\) | 2.26158e6i | 0.377576i | ||||||||
\(515\) | −5.81791e6 | + | 7.39899e6i | −0.966604 | + | 1.22929i | ||||
\(516\) | 1.41036e6 | − | 3.80848e6i | 0.233188 | − | 0.629690i | ||||
\(517\) | 2.48037e6 | + | 2.48037e6i | 0.408122 | + | 0.408122i | ||||
\(518\) | −103730. | − | 103730.i | −0.0169855 | − | 0.0169855i | ||||
\(519\) | 874128. | − | 2.36045e6i | 0.142448 | − | 0.384660i | ||||
\(520\) | 1.06481e6 | − | 127379.i | 0.172688 | − | 0.0206580i | ||||
\(521\) | − | 9.14428e6i | − | 1.47589i | −0.674858 | − | 0.737947i | \(-0.735795\pi\) | ||
0.674858 | − | 0.737947i | \(-0.264205\pi\) | |||||||
\(522\) | −234821. | − | 3.08089e6i | −0.0377190 | − | 0.494880i | ||||
\(523\) | −1.87262e6 | + | 1.87262e6i | −0.299361 | + | 0.299361i | −0.840763 | − | 0.541403i | \(-0.817893\pi\) |
0.541403 | + | 0.840763i | \(0.317893\pi\) | |||||||
\(524\) | −3.81962e6 | −0.607704 | ||||||||
\(525\) | 15483.8 | − | 132257.i | 0.00245176 | − | 0.0209421i | ||||
\(526\) | −187305. | −0.0295178 | ||||||||
\(527\) | 452247. | − | 452247.i | 0.0709331 | − | 0.0709331i | ||||
\(528\) | 2.23209e6 | − | 1.02567e6i | 0.348439 | − | 0.160111i | ||||
\(529\) | 1.12891e7i | 1.75396i | ||||||||
\(530\) | −6.31284e6 | + | 755180.i | −0.976191 | + | 0.116778i | ||||
\(531\) | −5.77146e6 | + | 6.72383e6i | −0.888278 | + | 1.03486i | ||||
\(532\) | −63168.7 | − | 63168.7i | −0.00967661 | − | 0.00967661i | ||||
\(533\) | −294839. | − | 294839.i | −0.0449538 | − | 0.0449538i | ||||
\(534\) | 6.42737e6 | + | 2.38020e6i | 0.975395 | + | 0.361210i | ||||
\(535\) | −3.89886e6 | + | 4.95842e6i | −0.588915 | + | 0.748960i | ||||
\(536\) | − | 766819.i | − | 0.115287i | ||||||
\(537\) | 103458. | + | 225148.i | 0.0154820 | + | 0.0336924i | ||||
\(538\) | 2.16352e6 | − | 2.16352e6i | 0.322259 | − | 0.322259i | ||||
\(539\) | −1.03410e7 | −1.53318 | ||||||||
\(540\) | −538218. | + | 3.34506e6i | −0.0794280 | + | 0.493651i | ||||
\(541\) | −7.21750e6 | −1.06021 | −0.530107 | − | 0.847931i | \(-0.677848\pi\) | ||||
−0.530107 | + | 0.847931i | \(0.677848\pi\) | |||||||
\(542\) | 5.68232e6 | − | 5.68232e6i | 0.830859 | − | 0.830859i | ||||
\(543\) | −4.89151e6 | − | 1.06450e7i | −0.711939 | − | 1.54934i | ||||
\(544\) | 395115.i | 0.0572435i | ||||||||
\(545\) | 226438. | + | 1.89288e6i | 0.0326556 | + | 0.272981i | ||||
\(546\) | −47910.3 | − | 17742.3i | −0.00687777 | − | 0.00254699i | ||||
\(547\) | 5.27000e6 | + | 5.27000e6i | 0.753082 | + | 0.753082i | 0.975053 | − | 0.221971i | \(-0.0712490\pi\) |
−0.221971 | + | 0.975053i | \(0.571249\pi\) | |||||||
\(548\) | −255824. | − | 255824.i | −0.0363906 | − | 0.0363906i | ||||
\(549\) | −2.63640e6 | + | 3.07144e6i | −0.373319 | + | 0.434921i | ||||
\(550\) | −6.57063e6 | − | 4.00391e6i | −0.926190 | − | 0.564388i | ||||
\(551\) | 6.49298e6i | 0.911098i | ||||||||
\(552\) | −3.81665e6 | + | 1.75379e6i | −0.533132 | + | 0.244980i | ||||
\(553\) | −150224. | + | 150224.i | −0.0208895 | + | 0.0208895i | ||||
\(554\) | 2.74200e6 | 0.379571 | ||||||||
\(555\) | 2.72911e6 | − | 1.13684e7i | 0.376087 | − | 1.56663i | ||||
\(556\) | −979581. | −0.134386 | ||||||||
\(557\) | 4.43782e6 | − | 4.43782e6i | 0.606083 | − | 0.606083i | −0.335837 | − | 0.941920i | \(-0.609019\pi\) |
0.941920 | + | 0.335837i | \(0.109019\pi\) | |||||||
\(558\) | 122443. | + | 1.60648e6i | 0.0166475 | + | 0.218419i | ||||
\(559\) | 4.88075e6i | 0.660628i | ||||||||
\(560\) | 30750.9 | + | 24179.8i | 0.00414370 | + | 0.00325824i | ||||
\(561\) | −1.28578e6 | + | 3.47206e6i | −0.172488 | + | 0.465779i | ||||
\(562\) | 4.12775e6 | + | 4.12775e6i | 0.551281 | + | 0.551281i | ||||
\(563\) | 3.22886e6 | + | 3.22886e6i | 0.429318 | + | 0.429318i | 0.888396 | − | 0.459078i | \(-0.151820\pi\) |
−0.459078 | + | 0.888396i | \(0.651820\pi\) | |||||||
\(564\) | 493583. | − | 1.33285e6i | 0.0653375 | − | 0.176434i | ||||
\(565\) | −6.41221e6 | − | 5.04199e6i | −0.845059 | − | 0.664479i | ||||
\(566\) | − | 327368.i | − | 0.0429531i | ||||||
\(567\) | 95518.6 | − | 130114.i | 0.0124776 | − | 0.0169968i | ||||
\(568\) | −1.93996e6 | + | 1.93996e6i | −0.252302 | + | 0.252302i | ||||
\(569\) | −7.44498e6 | −0.964013 | −0.482007 | − | 0.876168i | \(-0.660092\pi\) | ||||
−0.482007 | + | 0.876168i | \(0.660092\pi\) | |||||||
\(570\) | 1.66196e6 | − | 6.92305e6i | 0.214256 | − | 0.892504i | ||||
\(571\) | 9.56951e6 | 1.22829 | 0.614143 | − | 0.789195i | \(-0.289502\pi\) | ||||
0.614143 | + | 0.789195i | \(0.289502\pi\) | |||||||
\(572\) | −2.08749e6 | + | 2.08749e6i | −0.266768 | + | 0.266768i | ||||
\(573\) | 1.55134e6 | − | 712856.i | 0.197388 | − | 0.0907017i | ||||
\(574\) | − | 15210.0i | − | 0.00192686i | ||||||
\(575\) | 1.12351e7 | + | 6.84630e6i | 1.41712 | + | 0.863547i | ||||
\(576\) | −755255. | − | 648280.i | −0.0948501 | − | 0.0814154i | ||||
\(577\) | −4.11905e6 | − | 4.11905e6i | −0.515060 | − | 0.515060i | 0.401013 | − | 0.916073i | \(-0.368658\pi\) |
−0.916073 | + | 0.401013i | \(0.868658\pi\) | |||||||
\(578\) | 3.59486e6 | + | 3.59486e6i | 0.447571 | + | 0.447571i | ||||
\(579\) | 1.26870e7 | + | 4.69827e6i | 1.57276 | + | 0.582427i | ||||
\(580\) | −337717. | − | 2.82311e6i | −0.0416853 | − | 0.348464i | ||||
\(581\) | 956.652i | 0.000117575i | ||||||||
\(582\) | 1.45180e6 | + | 3.15944e6i | 0.177663 | + | 0.386636i | ||||
\(583\) | 1.23759e7 | − | 1.23759e7i | 1.50802 | − | 1.50802i | ||||
\(584\) | −2.05742e6 | −0.249627 | ||||||||
\(585\) | −789498. | − | 3.99449e6i | −0.0953809 | − | 0.482583i | ||||
\(586\) | −9.46160e6 | −1.13821 | ||||||||
\(587\) | 3.62213e6 | − | 3.62213e6i | 0.433879 | − | 0.433879i | −0.456066 | − | 0.889946i | \(-0.650742\pi\) |
0.889946 | + | 0.456066i | \(0.150742\pi\) | |||||||
\(588\) | 1.74951e6 | + | 3.80734e6i | 0.208676 | + | 0.454128i | ||||
\(589\) | − | 3.38566e6i | − | 0.402119i | ||||||
\(590\) | −5.04004e6 | + | 6.40974e6i | −0.596080 | + | 0.758071i | ||||
\(591\) | −1.62723e6 | − | 602599.i | −0.191637 | − | 0.0709676i | ||||
\(592\) | 2.42863e6 | + | 2.42863e6i | 0.284812 | + | 0.284812i | ||||
\(593\) | −6.47872e6 | − | 6.47872e6i | −0.756575 | − | 0.756575i | 0.219122 | − | 0.975697i | \(-0.429681\pi\) |
−0.975697 | + | 0.219122i | \(0.929681\pi\) | |||||||
\(594\) | −4.52715e6 | − | 8.15449e6i | −0.526452 | − | 0.948267i | ||||
\(595\) | −58544.2 | + | 7003.41i | −0.00677940 | + | 0.000810993i | ||||
\(596\) | 4.15788e6i | 0.479465i | ||||||||
\(597\) | −2.48388e6 | + | 1.14137e6i | −0.285229 | + | 0.131066i | ||||
\(598\) | 3.56940e6 | − | 3.56940e6i | 0.408171 | − | 0.408171i | ||||
\(599\) | 2.21327e6 | 0.252039 | 0.126019 | − | 0.992028i | \(-0.459780\pi\) | ||||
0.126019 | + | 0.992028i | \(0.459780\pi\) | |||||||
\(600\) | −362523. | + | 3.09654e6i | −0.0411109 | + | 0.351155i | ||||
\(601\) | 1.51975e7 | 1.71627 | 0.858135 | − | 0.513424i | \(-0.171623\pi\) | ||||
0.858135 | + | 0.513424i | \(0.171623\pi\) | |||||||
\(602\) | −125893. | + | 125893.i | −0.0141582 | + | 0.0141582i | ||||
\(603\) | −2.90309e6 | + | 221269.i | −0.325138 | + | 0.0247815i | ||||
\(604\) | 2.97619e6i | 0.331947i | ||||||||
\(605\) | 1.20924e7 | − | 1.44656e6i | 1.34315 | − | 0.160675i | ||||
\(606\) | −1.69588e6 | + | 4.57948e6i | −0.187592 | + | 0.506564i | ||||
\(607\) | −6.37228e6 | − | 6.37228e6i | −0.701978 | − | 0.701978i | 0.262857 | − | 0.964835i | \(-0.415335\pi\) |
−0.964835 | + | 0.262857i | \(0.915335\pi\) | |||||||
\(608\) | 1.47898e6 | + | 1.47898e6i | 0.162257 | + | 0.162257i | ||||
\(609\) | −47039.8 | + | 127024.i | −0.00513951 | + | 0.0138785i | ||||
\(610\) | −2.30229e6 | + | 2.92796e6i | −0.250516 | + | 0.318596i | ||||
\(611\) | 1.70811e6i | 0.185103i | ||||||||
\(612\) | 1.49586e6 | − | 114012.i | 0.161441 | − | 0.0123047i | ||||
\(613\) | −7.00623e6 | + | 7.00623e6i | −0.753066 | + | 0.753066i | −0.975050 | − | 0.221984i | \(-0.928747\pi\) |
0.221984 | + | 0.975050i | \(0.428747\pi\) | |||||||
\(614\) | 1.18958e7 | 1.27342 | ||||||||
\(615\) | 1.03356e6 | − | 633392.i | 0.110192 | − | 0.0675282i | ||||
\(616\) | −107688. | −0.0114345 | ||||||||
\(617\) | 2.77828e6 | − | 2.77828e6i | 0.293808 | − | 0.293808i | −0.544775 | − | 0.838582i | \(-0.683385\pi\) |
0.838582 | + | 0.544775i | \(0.183385\pi\) | |||||||
\(618\) | −9.53980e6 | + | 4.38364e6i | −1.00477 | + | 0.461704i | ||||
\(619\) | 6.32328e6i | 0.663309i | 0.943401 | + | 0.331654i | \(0.107607\pi\) | ||||
−0.943401 | + | 0.331654i | \(0.892393\pi\) | |||||||
\(620\) | 176097. | + | 1.47206e6i | 0.0183981 | + | 0.153797i | ||||
\(621\) | 7.74098e6 | + | 1.39434e7i | 0.805502 | + | 1.45090i | ||||
\(622\) | −3.13571e6 | − | 3.13571e6i | −0.324982 | − | 0.324982i | ||||
\(623\) | −212463. | − | 212463.i | −0.0219312 | − | 0.0219312i | ||||
\(624\) | 1.12173e6 | + | 415401.i | 0.115326 | + | 0.0427077i | ||||
\(625\) | 8.67895e6 | − | 4.47697e6i | 0.888724 | − | 0.458442i | ||||
\(626\) | − | 6.51244e6i | − | 0.664214i | ||||||
\(627\) | 8.18357e6 | + | 1.78093e7i | 0.831331 | + | 1.80917i | ||||
\(628\) | 2.52183e6 | − | 2.52183e6i | 0.255162 | − | 0.255162i | ||||
\(629\) | −5.17679e6 | −0.521715 | ||||||||
\(630\) | 82668.8 | − | 123397.i | 0.00829833 | − | 0.0123866i | ||||
\(631\) | −2.83767e6 | −0.283719 | −0.141859 | − | 0.989887i | \(-0.545308\pi\) | ||||
−0.141859 | + | 0.989887i | \(0.545308\pi\) | |||||||
\(632\) | 3.51722e6 | − | 3.51722e6i | 0.350273 | − | 0.350273i | ||||
\(633\) | 894283. | + | 1.94616e6i | 0.0887086 | + | 0.193050i | ||||
\(634\) | − | 1.00270e6i | − | 0.0990715i | ||||||
\(635\) | −1.03907e7 | − | 8.17031e6i | −1.02261 | − | 0.804089i | ||||
\(636\) | −6.65030e6 | − | 2.46276e6i | −0.651927 | − | 0.241423i | ||||
\(637\) | −3.56069e6 | − | 3.56069e6i | −0.347684 | − | 0.347684i | ||||
\(638\) | 5.53452e6 | + | 5.53452e6i | 0.538305 | + | 0.538305i | ||||
\(639\) | 7.90426e6 | + | 6.78469e6i | 0.765789 | + | 0.657322i | ||||
\(640\) | −719975. | − | 566124.i | −0.0694812 | − | 0.0546338i | ||||
\(641\) | − | 1.78673e6i | − | 0.171757i | −0.996306 | − | 0.0858783i | \(-0.972630\pi\) | ||
0.996306 | − | 0.0858783i | \(-0.0273696\pi\) | |||||||
\(642\) | −6.39307e6 | + | 2.93768e6i | −0.612170 | + | 0.281299i | ||||
\(643\) | −5.31029e6 | + | 5.31029e6i | −0.506513 | + | 0.506513i | −0.913454 | − | 0.406941i | \(-0.866595\pi\) |
0.406941 | + | 0.913454i | \(0.366595\pi\) | |||||||
\(644\) | 184136. | 0.0174954 | ||||||||
\(645\) | −1.37974e7 | − | 3.31222e6i | −1.30586 | − | 0.313487i | ||||
\(646\) | −3.15253e6 | −0.297220 | ||||||||
\(647\) | 1.93842e6 | − | 1.93842e6i | 0.182048 | − | 0.182048i | −0.610199 | − | 0.792248i | \(-0.708911\pi\) |
0.792248 | + | 0.610199i | \(0.208911\pi\) | |||||||
\(648\) | −2.23639e6 | + | 3.04638e6i | −0.209223 | + | 0.285001i | ||||
\(649\) | − | 2.24466e7i | − | 2.09189i | ||||||
\(650\) | −883785. | − | 3.64109e6i | −0.0820471 | − | 0.338024i | ||||
\(651\) | 24528.1 | − | 66234.5i | 0.00226836 | − | 0.00612537i | ||||
\(652\) | −1.03157e6 | − | 1.03157e6i | −0.0950346 | − | 0.0950346i | ||||
\(653\) | −6.54118e6 | − | 6.54118e6i | −0.600306 | − | 0.600306i | 0.340087 | − | 0.940394i | \(-0.389543\pi\) |
−0.940394 | + | 0.340087i | \(0.889543\pi\) | |||||||
\(654\) | −738448. | + | 1.99407e6i | −0.0675112 | + | 0.182304i | ||||
\(655\) | 1.58513e6 | + | 1.32507e7i | 0.144365 | + | 1.20680i | ||||
\(656\) | 356113.i | 0.0323094i | ||||||||
\(657\) | 593679. | + | 7.78919e6i | 0.0536585 | + | 0.704010i | ||||
\(658\) | −44058.5 | + | 44058.5i | −0.00396703 | + | 0.00396703i | ||||
\(659\) | −1.55193e7 | −1.39206 | −0.696030 | − | 0.718013i | \(-0.745052\pi\) | ||||
−0.696030 | + | 0.718013i | \(0.745052\pi\) | |||||||
\(660\) | −4.48448e6 | − | 7.31774e6i | −0.400730 | − | 0.653908i | ||||
\(661\) | 260063. | 0.0231513 | 0.0115757 | − | 0.999933i | \(-0.496315\pi\) | ||||
0.0115757 | + | 0.999933i | \(0.496315\pi\) | |||||||
\(662\) | −5.75586e6 | + | 5.75586e6i | −0.510464 | + | 0.510464i | ||||
\(663\) | −1.63825e6 | + | 752791.i | −0.144742 | + | 0.0665106i | ||||
\(664\) | − | 22398.2i | − | 0.00197148i | ||||||
\(665\) | −192925. | + | 245355.i | −0.0169174 | + | 0.0215150i | ||||
\(666\) | 8.49376e6 | − | 9.89535e6i | 0.742018 | − | 0.864461i | ||||
\(667\) | −9.46348e6 | − | 9.46348e6i | −0.823638 | − | 0.823638i | ||||
\(668\) | −1.61186e6 | − | 1.61186e6i | −0.139761 | − | 0.139761i | ||||
\(669\) | 1.54948e6 | + | 573806.i | 0.133850 | + | 0.0495678i | ||||
\(670\) | −2.66019e6 | + | 318228.i | −0.228942 | + | 0.0273874i | ||||
\(671\) | − | 1.02536e7i | − | 0.879161i | ||||||
\(672\) | 18218.8 | + | 39648.3i | 0.00155631 | + | 0.00338690i | ||||
\(673\) | 9.33490e6 | − | 9.33490e6i | 0.794460 | − | 0.794460i | −0.187756 | − | 0.982216i | \(-0.560121\pi\) |
0.982216 | + | 0.187756i | \(0.0601213\pi\) | |||||||
\(674\) | −5.80119e6 | −0.491889 | ||||||||
\(675\) | 1.18278e7 | + | 478952.i | 0.999181 | + | 0.0404606i | ||||
\(676\) | 4.50314e6 | 0.379008 | ||||||||
\(677\) | −9.53310e6 | + | 9.53310e6i | −0.799397 | + | 0.799397i | −0.983000 | − | 0.183604i | \(-0.941224\pi\) |
0.183604 | + | 0.983000i | \(0.441224\pi\) | |||||||
\(678\) | −3.79901e6 | − | 8.26751e6i | −0.317392 | − | 0.690717i | ||||
\(679\) | − | 152429.i | − | 0.0126880i | ||||||
\(680\) | 1.37070e6 | − | 163971.i | 0.113676 | − | 0.0135987i | ||||
\(681\) | −4.96890e6 | − | 1.84010e6i | −0.410575 | − | 0.152045i | ||||
\(682\) | −2.88589e6 | − | 2.88589e6i | −0.237585 | − | 0.237585i | ||||
\(683\) | −1.57744e6 | − | 1.57744e6i | −0.129390 | − | 0.129390i | 0.639446 | − | 0.768836i | \(-0.279164\pi\) |
−0.768836 | + | 0.639446i | \(0.779164\pi\) | |||||||
\(684\) | 5.17248e6 | − | 6.02601e6i | 0.422726 | − | 0.492481i | ||||
\(685\) | −781317. | + | 993649.i | −0.0636211 | + | 0.0809108i | ||||
\(686\) | − | 367455.i | − | 0.0298122i | ||||||
\(687\) | 2.15232e6 | − | 989013.i | 0.173986 | − | 0.0799485i | ||||
\(688\) | 2.94754e6 | − | 2.94754e6i | 0.237404 | − | 0.237404i | ||||
\(689\) | 8.52269e6 | 0.683957 | ||||||||
\(690\) | 7.66801e6 | + | 1.25126e7i | 0.613141 | + | 1.00052i | ||||
\(691\) | −3.72618e6 | −0.296872 | −0.148436 | − | 0.988922i | \(-0.547424\pi\) | ||||
−0.148436 | + | 0.988922i | \(0.547424\pi\) | |||||||
\(692\) | 1.82685e6 | − | 1.82685e6i | 0.145024 | − | 0.145024i | ||||
\(693\) | 31073.9 | + | 407696.i | 0.00245789 | + | 0.0322481i | ||||
\(694\) | 7.45342e6i | 0.587431i | ||||||||
\(695\) | 406524. | + | 3.39829e6i | 0.0319245 | + | 0.266869i | ||||
\(696\) | 1.10135e6 | − | 2.97402e6i | 0.0861790 | − | 0.232713i | ||||
\(697\) | −379539. | − | 379539.i | −0.0295920 | − | 0.0295920i | ||||
\(698\) | 5.99942e6 | + | 5.99942e6i | 0.466091 | + | 0.466091i | ||||
\(699\) | 2.06455e6 | − | 5.57500e6i | 0.159820 | − | 0.431571i | ||||
\(700\) | 71121.1 | − | 116713.i | 0.00548597 | − | 0.00900275i | ||||
\(701\) | 9.29171e6i | 0.714168i | 0.934072 | + | 0.357084i | \(0.116229\pi\) | ||||
−0.934072 | + | 0.357084i | \(0.883771\pi\) | |||||||
\(702\) | 1.24899e6 | − | 4.36661e6i | 0.0956565 | − | 0.334428i | ||||
\(703\) | −1.93775e7 | + | 1.93775e7i | −1.47880 | + | 1.47880i | ||||
\(704\) | 2.52131e6 | 0.191732 | ||||||||
\(705\) | −4.82865e6 | − | 1.15917e6i | −0.365892 | − | 0.0878366i | ||||
\(706\) | 8.09474e6 | 0.611211 | ||||||||
\(707\) | 151379. | − | 151379.i | 0.0113898 | − | 0.0113898i | ||||
\(708\) | −8.26431e6 | + | 3.79754e6i | −0.619617 | + | 0.284721i | ||||
\(709\) | − | 1.87653e7i | − | 1.40197i | −0.713174 | − | 0.700987i | \(-0.752743\pi\) | ||
0.713174 | − | 0.700987i | \(-0.247257\pi\) | |||||||
\(710\) | 7.53503e6 | + | 5.92487e6i | 0.560969 | + | 0.441096i | ||||
\(711\) | −1.43307e7 | − | 1.23009e7i | −1.06315 | − | 0.912564i | ||||
\(712\) | 4.97442e6 | + | 4.97442e6i | 0.367741 | + | 0.367741i | ||||
\(713\) | 4.93458e6 | + | 4.93458e6i | 0.363518 | + | 0.363518i | ||||
\(714\) | −61673.8 | − | 22839.2i | −0.00452746 | − | 0.00167662i | ||||
\(715\) | 8.10805e6 | + | 6.37545e6i | 0.593132 | + | 0.466386i | ||||
\(716\) | 254321.i | 0.0185396i | ||||||||
\(717\) | −6.48026e6 | − | 1.41025e7i | −0.470755 | − | 1.02447i | ||||
\(718\) | 9.99955e6 | − | 9.99955e6i | 0.723884 | − | 0.723884i | ||||
\(719\) | −3.20828e6 | −0.231446 | −0.115723 | − | 0.993282i | \(-0.536918\pi\) | ||||
−0.115723 | + | 0.993282i | \(0.536918\pi\) | |||||||
\(720\) | −1.93553e6 | + | 2.88911e6i | −0.139146 | + | 0.207698i | ||||
\(721\) | 460252. | 0.0329729 | ||||||||
\(722\) | −4.79695e6 | + | 4.79695e6i | −0.342470 | + | 0.342470i | ||||
\(723\) | 1.06385e7 | + | 2.31518e7i | 0.756892 | + | 1.64717i | ||||
\(724\) | − | 1.20244e7i | − | 0.852543i | ||||||
\(725\) | −9.65356e6 | + | 2.34316e6i | −0.682091 | + | 0.165561i | ||||
\(726\) | 1.27388e7 | + | 4.71747e6i | 0.896989 | + | 0.332175i | ||||
\(727\) | 971909. | + | 971909.i | 0.0682008 | + | 0.0682008i | 0.740384 | − | 0.672184i | \(-0.234643\pi\) |
−0.672184 | + | 0.740384i | \(0.734643\pi\) | |||||||
\(728\) | −37079.8 | − | 37079.8i | −0.00259304 | − | 0.00259304i | ||||
\(729\) | 1.21786e7 | + | 7.58768e6i | 0.848747 | + | 0.528798i | ||||
\(730\) | 853826. | + | 7.13746e6i | 0.0593010 | + | 0.495720i | ||||
\(731\) | 6.28287e6i | 0.434875i | ||||||||
\(732\) | −3.77513e6 | + | 1.73471e6i | −0.260408 | + | 0.119660i | ||||
\(733\) | −1.95035e7 | + | 1.95035e7i | −1.34077 | + | 1.34077i | −0.445471 | + | 0.895296i | \(0.646964\pi\) |
−0.895296 | + | 0.445471i | \(0.853036\pi\) | |||||||
\(734\) | −4.58451e6 | −0.314089 | ||||||||
\(735\) | 1.24821e7 | − | 7.64930e6i | 0.852253 | − | 0.522280i | ||||
\(736\) | −4.31120e6 | −0.293362 | ||||||||
\(737\) | 5.21513e6 | − | 5.21513e6i | 0.353668 | − | 0.353668i | ||||
\(738\) | 1.34821e6 | − | 102758.i | 0.0911204 | − | 0.00694505i | ||||
\(739\) | 3.62268e6i | 0.244016i | 0.992529 | + | 0.122008i | \(0.0389334\pi\) | ||||
−0.992529 | + | 0.122008i | \(0.961067\pi\) | |||||||
\(740\) | 7.41735e6 | − | 9.43311e6i | 0.497931 | − | 0.633250i | ||||
\(741\) | −3.31439e6 | + | 8.95003e6i | −0.221747 | + | 0.598796i | ||||
\(742\) | 219832. | + | 219832.i | 0.0146582 | + | 0.0146582i | ||||
\(743\) | 1.70630e7 | + | 1.70630e7i | 1.13393 | + | 1.13393i | 0.989518 | + | 0.144407i | \(0.0461276\pi\) |
0.144407 | + | 0.989518i | \(0.453872\pi\) | |||||||
\(744\) | −574280. | + | 1.55076e6i | −0.0380357 | + | 0.102710i | ||||
\(745\) | 1.44242e7 | − | 1.72551e6i | 0.952141 | − | 0.113901i | ||||
\(746\) | 1.14808e6i | 0.0755310i | ||||||||
\(747\) | −84797.2 | + | 6463.10i | −0.00556006 | + | 0.000423779i | ||||
\(748\) | −2.68717e6 | + | 2.68717e6i | −0.175607 | + | 0.175607i | ||||
\(749\) | 308437. | 0.0200892 | ||||||||
\(750\) | 1.08927e7 | − | 27420.3i | 0.707105 | − | 0.00178000i | ||||
\(751\) | 2.46605e7 | 1.59552 | 0.797760 | − | 0.602975i | \(-0.206018\pi\) | ||||
0.797760 | + | 0.602975i | \(0.206018\pi\) | |||||||
\(752\) | 1.03155e6 | − | 1.03155e6i | 0.0665188 | − | 0.0665188i | ||||
\(753\) | 2.02467e7 | − | 9.30357e6i | 1.30127 | − | 0.597946i | ||||
\(754\) | 3.81136e6i | 0.244147i | ||||||||
\(755\) | 1.03248e7 | − | 1.23511e6i | 0.659194 | − | 0.0788568i | ||||
\(756\) | 144847. | − | 80415.3i | 0.00921735 | − | 0.00511722i | ||||
\(757\) | 2.31958e6 | + | 2.31958e6i | 0.147119 | + | 0.147119i | 0.776830 | − | 0.629710i | \(-0.216826\pi\) |
−0.629710 | + | 0.776830i | \(0.716826\pi\) | |||||||
\(758\) | −6.40864e6 | − | 6.40864e6i | −0.405128 | − | 0.405128i | ||||
\(759\) | −3.78845e7 | − | 1.40295e7i | −2.38703 | − | 0.883969i | ||||
\(760\) | 4.51698e6 | − | 5.74452e6i | 0.283670 | − | 0.360761i | ||||
\(761\) | − | 1.57529e7i | − | 0.986048i | −0.870016 | − | 0.493024i | \(-0.835891\pi\) | ||
0.870016 | − | 0.493024i | \(-0.164109\pi\) | |||||||
\(762\) | −6.15611e6 | − | 1.33971e7i | −0.384077 | − | 0.835840i | ||||
\(763\) | 65915.8 | − | 65915.8i | 0.00409900 | − | 0.00409900i | ||||
\(764\) | 1.75235e6 | 0.108615 | ||||||||
\(765\) | −1.01630e6 | − | 5.14201e6i | −0.0627869 | − | 0.317673i | ||||
\(766\) | 1.96905e6 | 0.121251 | ||||||||
\(767\) | 7.72893e6 | − | 7.72893e6i | 0.474385 | − | 0.474385i | ||||
\(768\) | −426560. | − | 928291.i | −0.0260962 | − | 0.0567912i | ||||
\(769\) | 8.72370e6i | 0.531967i | 0.963978 | + | 0.265984i | \(0.0856967\pi\) | ||||
−0.963978 | + | 0.265984i | \(0.914303\pi\) | |||||||
\(770\) | 44690.3 | + | 373583.i | 0.00271636 | + | 0.0227071i | ||||
\(771\) | 8.26512e6 | + | 3.06076e6i | 0.500741 | + | 0.185436i | ||||
\(772\) | 9.81898e6 | + | 9.81898e6i | 0.592957 | + | 0.592957i | ||||
\(773\) | −666455. | − | 666455.i | −0.0401164 | − | 0.0401164i | 0.686764 | − | 0.726880i | \(-0.259031\pi\) |
−0.726880 | + | 0.686764i | \(0.759031\pi\) | |||||||
\(774\) | −1.20096e7 | − | 1.03086e7i | −0.720570 | − | 0.618508i | ||||
\(775\) | 5.03369e6 | − | 1.22181e6i | 0.301046 | − | 0.0730714i | ||||
\(776\) | 3.56883e6i | 0.212751i | ||||||||
\(777\) | −519472. | + | 238703.i | −0.0308681 | + | 0.0141842i | ||||
\(778\) | −1.07600e7 | + | 1.07600e7i | −0.637326 | + | 0.637326i | ||||
\(779\) | −2.84135e6 | −0.167757 | ||||||||
\(780\) | 975564. | − | 4.06381e6i | 0.0574142 | − | 0.239164i | ||||
\(781\) | −2.63873e7 | −1.54799 | ||||||||
\(782\) | 4.59480e6 | − | 4.59480e6i | 0.268689 | − | 0.268689i | ||||
\(783\) | −1.15771e7 | − | 3.31142e6i | −0.674834 | − | 0.193023i | ||||
\(784\) | 4.30068e6i | 0.249889i | ||||||||
\(785\) | −9.79507e6 | − | 7.70197e6i | −0.567327 | − | 0.446095i | ||||
\(786\) | −5.16936e6 | + | 1.39591e7i | −0.298456 | + | 0.805935i | ||||
\(787\) | −5.83122e6 | − | 5.83122e6i | −0.335601 | − | 0.335601i | 0.519108 | − | 0.854709i | \(-0.326264\pi\) |
−0.854709 | + | 0.519108i | \(0.826264\pi\) | |||||||
\(788\) | −1.25938e6 | − | 1.25938e6i | −0.0722506 | − | 0.0722506i | ||||
\(789\) | −253492. | + | 684518.i | −0.0144968 | + | 0.0391464i | ||||
\(790\) | −1.36613e7 | − | 1.07420e7i | −0.778798 | − | 0.612377i | ||||
\(791\) | 398870.i | 0.0226668i | ||||||||
\(792\) | −727537. | − | 9.54543e6i | −0.0412138 | − | 0.540733i | ||||
\(793\) | 3.53057e6 | − | 3.53057e6i | 0.199371 | − | 0.199371i | ||||
\(794\) | −2.01974e6 | −0.113696 | ||||||||
\(795\) | −5.78374e6 | + | 2.40928e7i | −0.324557 | + | 1.35197i | ||||
\(796\) | −2.80573e6 | −0.156951 | ||||||||
\(797\) | −1.23360e7 | + | 1.23360e7i | −0.687903 | + | 0.687903i | −0.961768 | − | 0.273865i | \(-0.911698\pi\) |
0.273865 | + | 0.961768i | \(0.411698\pi\) | |||||||
\(798\) | −316345. | + | 145364.i | −0.0175855 | + | 0.00808071i | ||||
\(799\) | 2.19881e6i | 0.121849i | ||||||||
\(800\) | −1.66517e6 | + | 2.73262e6i | −0.0919883 | + | 0.150957i | ||||
\(801\) | 1.73972e7 | − | 2.02680e7i | 0.958073 | − | 1.11617i | ||||
\(802\) | −1.35909e7 | − | 1.35909e7i | −0.746126 | − | 0.746126i | ||||
\(803\) | −1.39925e7 | − | 1.39925e7i | −0.765786 | − | 0.765786i | ||||
\(804\) | −2.80239e6 | − | 1.03779e6i | −0.152894 | − | 0.0566199i | ||||
\(805\) | −76416.0 | − | 638791.i | −0.00415618 | − | 0.0347431i | ||||
\(806\) | − | 1.98737e6i | − | 0.107756i | ||||||
\(807\) | −4.97869e6 | − | 1.08348e7i | −0.269111 | − | 0.585647i | ||||
\(808\) | −3.54425e6 | + | 3.54425e6i | −0.190984 | + | 0.190984i | ||||
\(809\) | 1.48239e7 | 0.796328 | 0.398164 | − | 0.917314i | \(-0.369647\pi\) | ||||
0.398164 | + | 0.917314i | \(0.369647\pi\) | |||||||
\(810\) | 1.14964e7 | + | 6.49406e6i | 0.615670 | + | 0.347779i | ||||
\(811\) | −366386. | −0.0195608 | −0.00978039 | − | 0.999952i | \(-0.503113\pi\) | ||||
−0.00978039 | + | 0.999952i | \(0.503113\pi\) | |||||||
\(812\) | −98309.2 | + | 98309.2i | −0.00523244 | + | 0.00523244i | ||||
\(813\) | −1.30762e7 | − | 2.84567e7i | −0.693831 | − | 1.50994i | ||||
\(814\) | 3.30342e7i | 1.74744i | ||||||||
\(815\) | −3.15056e6 | + | 4.00676e6i | −0.166147 | + | 0.211300i | ||||
\(816\) | 1.44397e6 | + | 534736.i | 0.0759161 | + | 0.0281134i | ||||
\(817\) | 2.35178e7 | + | 2.35178e7i | 1.23265 | + | 1.23265i | ||||
\(818\) | −1.33684e7 | − | 1.33684e7i | −0.698546 | − | 0.698546i | ||||
\(819\) | −129681. | + | 151080.i | −0.00675563 | + | 0.00787040i | ||||
\(820\) | 1.23540e6 | − | 147786.i | 0.0641613 | − | 0.00767536i | ||||
\(821\) | 1.39801e7i | 0.723855i | 0.932206 | + | 0.361928i | \(0.117881\pi\) | ||||
−0.932206 | + | 0.361928i | \(0.882119\pi\) | |||||||
\(822\) | −1.28115e6 | + | 588702.i | −0.0661333 | + | 0.0303889i | ||||
\(823\) | 1.09055e7 | − | 1.09055e7i | 0.561237 | − | 0.561237i | −0.368422 | − | 0.929659i | \(-0.620102\pi\) |
0.929659 | + | 0.368422i | \(0.120102\pi\) | |||||||
\(824\) | −1.07759e7 | −0.552888 | ||||||||
\(825\) | −2.35251e7 | + | 1.85940e7i | −1.20336 | + | 0.951128i | ||||
\(826\) | 398716. | 0.0203336 | ||||||||
\(827\) | −802797. | + | 802797.i | −0.0408171 | + | 0.0408171i | −0.727221 | − | 0.686404i | \(-0.759188\pi\) |
0.686404 | + | 0.727221i | \(0.259188\pi\) | |||||||
\(828\) | 1.24402e6 | + | 1.63217e7i | 0.0630595 | + | 0.827353i | ||||
\(829\) | 2.52860e7i | 1.27789i | 0.769252 | + | 0.638946i | \(0.220629\pi\) | ||||
−0.769252 | + | 0.638946i | \(0.779371\pi\) | |||||||
\(830\) | −77702.0 | + | 9295.19i | −0.00391505 | + | 0.000468342i | ||||
\(831\) | 3.71094e6 | − | 1.00208e7i | 0.186415 | − | 0.503386i | ||||
\(832\) | 868154. | + | 868154.i | 0.0434799 | + | 0.0434799i | ||||
\(833\) | −4.58358e6 | − | 4.58358e6i | −0.228872 | − | 0.228872i | ||||
\(834\) | −1.32574e6 | + | 3.57995e6i | −0.0659997 | + | 0.178222i | ||||
\(835\) | −4.92284e6 | + | 6.26067e6i | −0.244343 | + | 0.310746i | ||||
\(836\) | 2.01170e7i | 0.995515i | ||||||||
\(837\) | 6.03671e6 | + | 1.72668e6i | 0.297843 | + | 0.0851921i | ||||
\(838\) | 6.80560e6 | − | 6.80560e6i | 0.334778 | − | 0.334778i | ||||
\(839\) | 2.22871e7 | 1.09307 | 0.546536 | − | 0.837435i | \(-0.315946\pi\) | ||||
0.546536 | + | 0.837435i | \(0.315946\pi\) | |||||||
\(840\) | 129984. | − | 79657.3i | 0.00635612 | − | 0.00389518i | ||||
\(841\) | −1.04062e7 | −0.507342 | ||||||||
\(842\) | 6.39402e6 | − | 6.39402e6i | 0.310809 | − | 0.310809i | ||||
\(843\) | 2.06716e7 | − | 9.49880e6i | 1.00185 | − | 0.460362i | ||||
\(844\) | 2.19834e6i | 0.106228i | ||||||||
\(845\) | −1.86879e6 | − | 1.56219e7i | −0.0900365 | − | 0.752650i | ||||
\(846\) | −4.20299e6 | − | 3.60767e6i | −0.201898 | − | 0.173301i | ||||
\(847\) | −421093. | − | 421093.i | −0.0201683 | − | 0.0201683i | ||||
\(848\) | −5.14695e6 | − | 5.14695e6i | −0.245788 | − | 0.245788i | ||||
\(849\) | −1.19639e6 | − | 443050.i | −0.0569644 | − | 0.0210952i | ||||
\(850\) | −1.13767e6 | − | 4.68708e6i | −0.0540096 | − | 0.222513i | ||||
\(851\) | − | 5.64853e7i | − | 2.67369i | ||||||
\(852\) | 4.46424e6 | + | 9.71520e6i | 0.210692 | + | 0.458514i | ||||
\(853\) | 808864. | − | 808864.i | 0.0380630 | − | 0.0380630i | −0.687819 | − | 0.725882i | \(-0.741432\pi\) |
0.725882 | + | 0.687819i | \(0.241432\pi\) | |||||||
\(854\) | 182133. | 0.00854563 | ||||||||
\(855\) | −2.30515e7 | − | 1.54432e7i | −1.07841 | − | 0.722473i | ||||
\(856\) | −7.22147e6 | −0.336853 | ||||||||
\(857\) | −1.82494e7 | + | 1.82494e7i | −0.848783 | + | 0.848783i | −0.989981 | − | 0.141198i | \(-0.954904\pi\) |
0.141198 | + | 0.989981i | \(0.454904\pi\) | |||||||
\(858\) | 4.80373e6 | + | 1.04540e7i | 0.222772 | + | 0.484802i | ||||
\(859\) | − | 3.76682e7i | − | 1.74177i | −0.491483 | − | 0.870887i | \(-0.663545\pi\) | ||
0.491483 | − | 0.870887i | \(-0.336455\pi\) | |||||||
\(860\) | −1.14486e7 | − | 9.00216e6i | −0.527845 | − | 0.415050i | ||||
\(861\) | −55586.0 | − | 20584.7i | −0.00255539 | − | 0.000946319i | ||||
\(862\) | 1.10866e7 | + | 1.10866e7i | 0.508196 | + | 0.508196i | ||||
\(863\) | 2.54896e7 | + | 2.54896e7i | 1.16503 | + | 1.16503i | 0.983360 | + | 0.181668i | \(0.0581498\pi\) |
0.181668 | + | 0.983360i | \(0.441850\pi\) | |||||||
\(864\) | −3.39133e6 | + | 1.88277e6i | −0.154556 | + | 0.0858052i | ||||
\(865\) | −7.09572e6 | − | 5.57944e6i | −0.322445 | − | 0.253542i | ||||
\(866\) | 1.73338e7i | 0.785416i | ||||||||
\(867\) | 1.80028e7 | − | 8.27249e6i | 0.813379 | − | 0.373756i | ||||
\(868\) | 51261.7 | − | 51261.7i | 0.00230937 | − | 0.00230937i | ||||
\(869\) | 4.78412e7 | 2.14908 | ||||||||
\(870\) | −1.07743e7 | − | 2.58650e6i | −0.482604 | − | 0.115855i | ||||
\(871\) | 3.59141e6 | 0.160405 | ||||||||
\(872\) | −1.54329e6 | + | 1.54329e6i | −0.0687318 | + | 0.0687318i | ||||
\(873\) | 1.35112e7 | − | 1.02980e6i | 0.600010 | − | 0.0457318i | ||||
\(874\) | − | 3.43981e7i | − | 1.52320i | ||||||
\(875\) | −434408. | − | 198292.i | −0.0191813 | − | 0.00875559i | ||||
\(876\) | −2.78446e6 | + | 7.51900e6i | −0.122597 | + | 0.331055i | ||||
\(877\) | 1.32079e7 | + | 1.32079e7i | 0.579873 | + | 0.579873i | 0.934868 | − | 0.354995i | \(-0.115517\pi\) |
−0.354995 | + | 0.934868i | \(0.615517\pi\) | |||||||
\(878\) | −8.78494e6 | − | 8.78494e6i | −0.384594 | − | 0.384594i | ||||
\(879\) | −1.28050e7 | + | 3.45781e7i | −0.558996 | + | 1.50949i | ||||
\(880\) | −1.04634e6 | − | 8.74675e6i | −0.0455476 | − | 0.380750i | ||||
\(881\) | 4.17368e7i | 1.81167i | 0.423628 | + | 0.905836i | \(0.360756\pi\) | ||||
−0.423628 | + | 0.905836i | \(0.639244\pi\) | |||||||
\(882\) | 1.62819e7 | − | 1.24098e6i | 0.704748 | − | 0.0537148i | ||||
\(883\) | 2.31670e7 | − | 2.31670e7i | 0.999927 | − | 0.999927i | −7.31900e−5 | − | 1.00000i | \(-0.500023\pi\) |
1.00000 | 7.31900e-5i | \(2.32971e-5\pi\) | ||||||||
\(884\) | −1.85052e6 | −0.0796460 | ||||||||
\(885\) | 1.66038e7 | + | 2.70939e7i | 0.712606 | + | 1.16282i | ||||
\(886\) | −1.61350e7 | −0.690532 | ||||||||
\(887\) | −2.36679e7 | + | 2.36679e7i | −1.01007 | + | 1.01007i | −0.0101211 | + | 0.999949i | \(0.503222\pi\) |
−0.999949 | + | 0.0101211i | \(0.996778\pi\) | |||||||
\(888\) | 1.21625e7 | − | 5.58878e6i | 0.517594 | − | 0.237840i | ||||
\(889\) | 646350.i | 0.0274292i | ||||||||
\(890\) | 1.51925e7 | − | 1.93212e7i | 0.642915 | − | 0.817635i | ||||
\(891\) | −3.59281e7 | + | 5.50876e6i | −1.51614 | + | 0.232466i | ||||
\(892\) | 1.19921e6 | + | 1.19921e6i | 0.0504640 | + | 0.0504640i | ||||
\(893\) | 8.23048e6 | + | 8.23048e6i | 0.345380 | + | 0.345380i | ||||
\(894\) | 1.51953e7 | + | 5.62715e6i | 0.635865 | + | 0.235475i | ||||
\(895\) | 882272. | − | 105543.i | 0.0368167 | − | 0.00440424i | ||||
\(896\) | 44785.9i | 0.00186368i | ||||||||
\(897\) | −8.21390e6 | − | 1.78753e7i | −0.340854 | − | 0.741776i | ||||
\(898\) | 1.47705e6 | − | 1.47705e6i | 0.0611229 | − | 0.0611229i | ||||
\(899\) | −5.26908e6 | −0.217438 | ||||||||
\(900\) | 1.08259e7 | + | 5.51563e6i | 0.445511 | + | 0.226981i | ||||
\(901\) | 1.09710e7 | 0.450232 | ||||||||
\(902\) | −2.42192e6 | + | 2.42192e6i | −0.0991160 | + | 0.0991160i | ||||
\(903\) | 289705. | + | 630464.i | 0.0118232 | + | 0.0257300i | ||||
\(904\) | − | 9.33879e6i | − | 0.380075i | ||||||
\(905\) | −4.17141e7 | + | 4.99009e6i | −1.69302 | + | 0.202529i | ||||
\(906\) | 1.08767e7 | + | 4.02789e6i | 0.440227 | + | 0.163026i | ||||
\(907\) | −2.80206e7 | − | 2.80206e7i | −1.13099 | − | 1.13099i | −0.990013 | − | 0.140977i | \(-0.954976\pi\) |
−0.140977 | − | 0.990013i | \(-0.545024\pi\) | |||||||
\(908\) | −3.84564e6 | − | 3.84564e6i | −0.154794 | − | 0.154794i | ||||
\(909\) | 1.44409e7 | + | 1.23954e7i | 0.579674 | + | 0.497568i | ||||
\(910\) | −113246. | + | 144022.i | −0.00453337 | + | 0.00576536i | ||||
\(911\) | 1.80401e7i | 0.720182i | 0.932917 | + | 0.360091i | \(0.117254\pi\) | ||||
−0.932917 | + | 0.360091i | \(0.882746\pi\) | |||||||
\(912\) | 7.40662e6 | − | 3.40342e6i | 0.294872 | − | 0.135497i | ||||
\(913\) | 152330. | − | 152330.i | 0.00604795 | − | 0.00604795i | ||||
\(914\) | 1.86618e7 | 0.738905 | ||||||||
\(915\) | 7.58460e6 | + | 1.23765e7i | 0.299488 | + | 0.488703i | ||||
\(916\) | 2.43121e6 | 0.0957378 | ||||||||
\(917\) | 461430. | − | 461430.i | 0.0181210 | − | 0.0181210i | ||||
\(918\) | 1.60779e6 | − | 5.62104e6i | 0.0629683 | − | 0.220145i | ||||
\(919\) | − | 3.85473e6i | − | 0.150559i | −0.997162 | − | 0.0752793i | \(-0.976015\pi\) | ||
0.997162 | − | 0.0752793i | \(-0.0239848\pi\) | |||||||
\(920\) | 1.78914e6 | + | 1.49561e7i | 0.0696905 | + | 0.582570i | ||||
\(921\) | 1.60994e7 | − | 4.34740e7i | 0.625404 | − | 1.68881i | ||||
\(922\) | 7.93882e6 | + | 7.93882e6i | 0.307559 | + | 0.307559i | ||||
\(923\) | −9.08582e6 | − | 9.08582e6i | −0.351043 | − | 0.351043i | ||||
\(924\) | −145742. | + | 393554.i | −0.00561571 | + | 0.0151644i | ||||
\(925\) | −3.58028e7 | − | 2.18170e7i | −1.37582 | − | 0.838379i | ||||
\(926\) | − | 3.03009e6i | − | 0.116126i | ||||||
\(927\) | 3.10945e6 | + | 4.07965e7i | 0.118846 | + | 1.55928i | ||||
\(928\) | 2.30172e6 | − | 2.30172e6i | 0.0877370 | − | 0.0877370i | ||||
\(929\) | 4.71857e7 | 1.79379 | 0.896895 | − | 0.442244i | \(-0.145817\pi\) | ||||
0.896895 | + | 0.442244i | \(0.145817\pi\) | |||||||
\(930\) | 5.61809e6 | + | 1.34869e6i | 0.213001 | + | 0.0511333i | ||||
\(931\) | −3.43142e7 | −1.29748 | ||||||||
\(932\) | 4.31473e6 | − | 4.31473e6i | 0.162710 | − | 0.162710i | ||||
\(933\) | −1.57034e7 | + | 7.21589e6i | −0.590596 | + | 0.271385i | ||||
\(934\) | − | 2.29931e6i | − | 0.0862441i | ||||||
\(935\) | 1.04373e7 | + | 8.20695e6i | 0.390444 | + | 0.307010i | ||||
\(936\) | 3.03623e6 | − | 3.53725e6i | 0.113278 | − | 0.131970i | ||||
\(937\) | 3.50679e7 | + | 3.50679e7i | 1.30485 | + | 1.30485i | 0.925080 | + | 0.379771i | \(0.123997\pi\) |
0.379771 | + | 0.925080i | \(0.376003\pi\) | |||||||
\(938\) | 92635.8 | + | 92635.8i | 0.00343773 | + | 0.00343773i | ||||
\(939\) | −2.38002e7 | − | 8.81374e6i | −0.880879 | − | 0.326209i | ||||
\(940\) | −4.00665e6 | − | 3.15047e6i | −0.147898 | − | 0.116294i | ||||
\(941\) | 3.28687e7i | 1.21007i | 0.796201 | + | 0.605033i | \(0.206840\pi\) | ||||
−0.796201 | + | 0.605033i | \(0.793160\pi\) | |||||||
\(942\) | −5.80323e6 | − | 1.26292e7i | −0.213080 | − | 0.463711i | ||||
\(943\) | 4.14125e6 | − | 4.14125e6i | 0.151653 | − | 0.151653i | ||||
\(944\) | −9.33518e6 | −0.340951 | ||||||||
\(945\) | −339082. | − | 469121.i | −0.0123516 | − | 0.0170886i | ||||
\(946\) | 4.00924e7 | 1.45658 | ||||||||
\(947\) | 2.17688e7 | − | 2.17688e7i | 0.788787 | − | 0.788787i | −0.192509 | − | 0.981295i | \(-0.561662\pi\) |
0.981295 | + | 0.192509i | \(0.0616623\pi\) | |||||||
\(948\) | −8.09384e6 | − | 1.76140e7i | −0.292505 | − | 0.636558i | ||||
\(949\) | − | 9.63597e6i | − | 0.347320i | ||||||
\(950\) | −2.18030e7 | − | 1.32860e7i | −0.783803 | − | 0.477623i | ||||
\(951\) | −3.66445e6 | − | 1.35703e6i | −0.131388 | − | 0.0486561i | ||||
\(952\) | −47731.9 | − | 47731.9i | −0.00170693 | − | 0.00170693i | ||||
\(953\) | −3.08708e7 | − | 3.08708e7i | −1.10107 | − | 1.10107i | −0.994282 | − | 0.106790i | \(-0.965943\pi\) |
−0.106790 | − | 0.994282i | \(-0.534057\pi\) | |||||||
\(954\) | −1.80006e7 | + | 2.09710e7i | −0.640349 | + | 0.746016i | ||||
\(955\) | −727223. | − | 6.07913e6i | −0.0258023 | − | 0.215692i | ||||
\(956\) | − | 1.59299e7i | − | 0.563726i | ||||||
\(957\) | 2.77166e7 | − | 1.27361e7i | 0.978272 | − | 0.449526i | ||||
\(958\) | 6.69495e6 | − | 6.69495e6i | 0.235686 | − | 0.235686i | ||||
\(959\) | 61809.7 | 0.00217025 | ||||||||
\(960\) | −3.04333e6 | + | 1.86503e6i | −0.106579 | + | 0.0653141i | ||||
\(961\) | −2.58817e7 | −0.904032 | ||||||||
\(962\) | −1.13745e7 | + | 1.13745e7i | −0.396274 | + | 0.396274i | ||||
\(963\) | 2.08379e6 | + | 2.73397e7i | 0.0724082 | + | 0.950010i | ||||
\(964\) | 2.61517e7i | 0.906373i | ||||||||
\(965\) | 2.99884e7 | − | 3.81381e7i | 1.03666 | − | 1.31838i | ||||
\(966\) | 249204. | − | 672939.i | 0.00859236 | − | 0.0232024i | ||||
\(967\) | −2.40260e7 | − | 2.40260e7i | −0.826258 | − | 0.826258i | 0.160739 | − | 0.986997i | \(-0.448612\pi\) |
−0.986997 | + | 0.160739i | \(0.948612\pi\) | |||||||
\(968\) | 9.85910e6 | + | 9.85910e6i | 0.338181 | + | 0.338181i | ||||
\(969\) | −4.26654e6 | + | 1.15211e7i | −0.145971 | + | 0.394172i | ||||
\(970\) | 1.23807e7 | − | 1.48105e6i | 0.422490 | − | 0.0505408i | ||||
\(971\) | − | 7.01170e6i | − | 0.238657i | −0.992855 | − | 0.119329i | \(-0.961926\pi\) | ||
0.992855 | − | 0.119329i | \(-0.0380742\pi\) | |||||||
\(972\) | 8.10656e6 | + | 1.22959e7i | 0.275214 | + | 0.417441i | ||||
\(973\) | 118339. | − | 118339.i | 0.00400723 | − | 0.00400723i | ||||
\(974\) | −1.88414e7 | −0.636378 | ||||||||
\(975\) | −1.45027e7 | − | 1.69788e6i | −0.488582 | − | 0.0572000i | ||||
\(976\) | −4.26430e6 | −0.143292 | ||||||||
\(977\) | −1.55490e7 | + | 1.55490e7i | −0.521154 | + | 0.521154i | −0.917920 | − | 0.396766i | \(-0.870132\pi\) |
0.396766 | + | 0.917920i | \(0.370132\pi\) | |||||||
\(978\) | −5.16606e6 | + | 2.37386e6i | −0.172708 | + | 0.0793612i | ||||
\(979\) | 6.76619e7i | 2.25625i | ||||||||
\(980\) | 1.49196e7 | − | 1.78477e6i | 0.496240 | − | 0.0593632i | ||||
\(981\) | 6.28807e6 | + | 5.39742e6i | 0.208615 | + | 0.179066i | ||||
\(982\) | 2.22159e6 | + | 2.22159e6i | 0.0735166 | + | 0.0735166i | ||||
\(983\) | −2.90905e7 | − | 2.90905e7i | −0.960213 | − | 0.960213i | 0.0390251 | − | 0.999238i | \(-0.487575\pi\) |
−0.999238 | + | 0.0390251i | \(0.987575\pi\) | |||||||
\(984\) | 1.30144e6 | + | 481953.i | 0.0428486 | + | 0.0158678i | ||||
\(985\) | −3.84631e6 | + | 4.89159e6i | −0.126315 | + | 0.160642i | ||||
\(986\) | 4.90627e6i | 0.160716i | ||||||||
\(987\) | 101388. | + | 220643.i | 0.00331278 | + | 0.00720936i | ||||
\(988\) | −6.92680e6 | + | 6.92680e6i | −0.225757 | + | 0.225757i | ||||
\(989\) | −6.85540e7 | −2.22865 | ||||||||
\(990\) | −3.28123e7 | + | 6.48524e6i | −1.06402 | + | 0.210300i | ||||
\(991\) | 3.48056e6 | 0.112581 | 0.0562905 | − | 0.998414i | \(-0.482073\pi\) | ||||
0.0562905 | + | 0.998414i | \(0.482073\pi\) | |||||||
\(992\) | −1.20020e6 | + | 1.20020e6i | −0.0387234 | + | 0.0387234i | ||||
\(993\) | 1.32454e7 | + | 2.88250e7i | 0.426277 | + | 0.927675i | ||||
\(994\) | − | 468714.i | − | 0.0150467i | ||||||
\(995\) | 1.16437e6 | + | 9.73341e6i | 0.0372849 | + | 0.311679i | ||||
\(996\) | −81855.8 | − | 30313.0i | −0.00261457 | − | 0.000968235i | ||||
\(997\) | −2.04407e7 | − | 2.04407e7i | −0.651264 | − | 0.651264i | 0.302033 | − | 0.953297i | \(-0.402335\pi\) |
−0.953297 | + | 0.302033i | \(0.902335\pi\) | |||||||
\(998\) | −2.74016e6 | − | 2.74016e6i | −0.0870863 | − | 0.0870863i | ||||
\(999\) | −2.46681e7 | − | 4.44331e7i | −0.782026 | − | 1.40862i |
(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 | 30.6.e.a.17.7 | yes | 20 | |
3.2 | odd | 2 | inner | 30.6.e.a.17.5 | ✓ | 20 | |
5.2 | odd | 4 | 150.6.e.b.143.6 | 20 | |||
5.3 | odd | 4 | inner | 30.6.e.a.23.5 | yes | 20 | |
5.4 | even | 2 | 150.6.e.b.107.4 | 20 | |||
15.2 | even | 4 | 150.6.e.b.143.4 | 20 | |||
15.8 | even | 4 | inner | 30.6.e.a.23.7 | yes | 20 | |
15.14 | odd | 2 | 150.6.e.b.107.6 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
30.6.e.a.17.5 | ✓ | 20 | 3.2 | odd | 2 | inner | |
30.6.e.a.17.7 | yes | 20 | 1.1 | even | 1 | trivial | |
30.6.e.a.23.5 | yes | 20 | 5.3 | odd | 4 | inner | |
30.6.e.a.23.7 | yes | 20 | 15.8 | even | 4 | inner | |
150.6.e.b.107.4 | 20 | 5.4 | even | 2 | |||
150.6.e.b.107.6 | 20 | 15.14 | odd | 2 | |||
150.6.e.b.143.4 | 20 | 15.2 | even | 4 | |||
150.6.e.b.143.6 | 20 | 5.2 | odd | 4 |