Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.54095201243136.19 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 102x^{6} + 320x^{5} + 4283x^{4} - 9104x^{3} - 85298x^{2} + 89904x + 714364 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.3 | ||
Root | \(5.10797 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.6.c.h.30.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.90754 | + | 6.76805i | 0.690761 | + | 1.19643i | 0.971589 | + | 0.236676i | \(0.0760578\pi\) |
−0.280827 | + | 0.959758i | \(0.590609\pi\) | |||||||
\(3\) | −11.7593 | + | 20.3677i | −0.754359 | + | 1.30659i | 0.191334 | + | 0.981525i | \(0.438719\pi\) |
−0.945692 | + | 0.325063i | \(0.894615\pi\) | |||||||
\(4\) | −14.5377 | + | 25.1800i | −0.454303 | + | 0.786875i | ||||
\(5\) | 37.1377 | + | 64.3243i | 0.664339 | + | 1.15067i | 0.979464 | + | 0.201618i | \(0.0646201\pi\) |
−0.315125 | + | 0.949050i | \(0.602047\pi\) | |||||||
\(6\) | −183.799 | −2.08433 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 22.8562 | 0.126264 | ||||||||
\(9\) | −155.062 | − | 268.575i | −0.638114 | − | 1.10525i | ||||
\(10\) | −290.234 | + | 502.699i | −0.917799 | + | 1.58967i | ||||
\(11\) | 212.110 | − | 367.385i | 0.528541 | − | 0.915460i | −0.470905 | − | 0.882184i | \(-0.656073\pi\) |
0.999446 | − | 0.0332758i | \(-0.0105940\pi\) | |||||||
\(12\) | −341.906 | − | 592.198i | −0.685414 | − | 1.18717i | ||||
\(13\) | −252.233 | −0.413946 | −0.206973 | − | 0.978347i | \(-0.566361\pi\) | ||||
−0.206973 | + | 0.978347i | \(0.566361\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1746.85 | −2.00460 | ||||||||
\(16\) | 554.517 | + | 960.452i | 0.541521 | + | 0.937942i | ||||
\(17\) | 552.173 | − | 956.392i | 0.463397 | − | 0.802627i | −0.535731 | − | 0.844389i | \(-0.679964\pi\) |
0.999128 | + | 0.0417619i | \(0.0132971\pi\) | |||||||
\(18\) | 1211.82 | − | 2098.93i | 0.881569 | − | 1.52692i | ||||
\(19\) | 3.23550 | + | 5.60405i | 0.00205616 | + | 0.00356138i | 0.867052 | − | 0.498218i | \(-0.166012\pi\) |
−0.864995 | + | 0.501780i | \(0.832679\pi\) | |||||||
\(20\) | −2159.58 | −1.20724 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3315.30 | 1.46038 | ||||||||
\(23\) | 1806.19 | + | 3128.42i | 0.711942 | + | 1.23312i | 0.964127 | + | 0.265440i | \(0.0855173\pi\) |
−0.252186 | + | 0.967679i | \(0.581149\pi\) | |||||||
\(24\) | −268.773 | + | 465.529i | −0.0952484 | + | 0.164975i | ||||
\(25\) | −1195.91 | + | 2071.38i | −0.382692 | + | 0.662842i | ||||
\(26\) | −985.611 | − | 1707.13i | −0.285938 | − | 0.495260i | ||||
\(27\) | 1578.65 | 0.416751 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5005.02 | −1.10512 | −0.552561 | − | 0.833472i | \(-0.686350\pi\) | ||||
−0.552561 | + | 0.833472i | \(0.686350\pi\) | |||||||
\(30\) | −6825.88 | − | 11822.8i | −1.38470 | − | 2.39837i | ||||
\(31\) | −1410.85 | + | 2443.66i | −0.263679 | + | 0.456705i | −0.967217 | − | 0.253953i | \(-0.918269\pi\) |
0.703538 | + | 0.710658i | \(0.251603\pi\) | |||||||
\(32\) | −3967.89 | + | 6872.59i | −0.684991 | + | 1.18644i | ||||
\(33\) | 4988.52 | + | 8640.36i | 0.797419 | + | 1.38117i | ||||
\(34\) | 8630.55 | 1.28039 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9016.95 | 1.15959 | ||||||||
\(37\) | 1023.44 | + | 1772.65i | 0.122902 | + | 0.212872i | 0.920911 | − | 0.389774i | \(-0.127447\pi\) |
−0.798009 | + | 0.602645i | \(0.794113\pi\) | |||||||
\(38\) | −25.2857 | + | 43.7961i | −0.00284063 | + | 0.00492012i | ||||
\(39\) | 2966.08 | − | 5137.41i | 0.312264 | − | 0.540857i | ||||
\(40\) | 848.827 | + | 1470.21i | 0.0838821 | + | 0.145288i | ||||
\(41\) | 9393.81 | 0.872734 | 0.436367 | − | 0.899769i | \(-0.356265\pi\) | ||||
0.436367 | + | 0.899769i | \(0.356265\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10320.8 | 0.851218 | 0.425609 | − | 0.904907i | \(-0.360060\pi\) | ||||
0.425609 | + | 0.904907i | \(0.360060\pi\) | |||||||
\(44\) | 6167.16 | + | 10681.8i | 0.480235 | + | 0.831791i | ||||
\(45\) | 11517.3 | − | 19948.5i | 0.847848 | − | 1.46852i | ||||
\(46\) | −14115.5 | + | 24448.8i | −0.983564 | + | 1.70358i | ||||
\(47\) | −8517.79 | − | 14753.3i | −0.562448 | − | 0.974189i | −0.997282 | − | 0.0736781i | \(-0.976526\pi\) |
0.434834 | − | 0.900511i | \(-0.356807\pi\) | |||||||
\(48\) | −26082.9 | −1.63400 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −18692.3 | −1.05739 | ||||||||
\(51\) | 12986.3 | + | 22493.0i | 0.699135 | + | 1.21094i | ||||
\(52\) | 3666.89 | − | 6351.24i | 0.188057 | − | 0.325724i | ||||
\(53\) | 19753.3 | − | 34213.8i | 0.965941 | − | 1.67306i | 0.258877 | − | 0.965910i | \(-0.416648\pi\) |
0.707064 | − | 0.707149i | \(-0.250019\pi\) | |||||||
\(54\) | 6168.63 | + | 10684.4i | 0.287875 | + | 0.498615i | ||||
\(55\) | 31509.0 | 1.40452 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −152.189 | −0.00620433 | ||||||||
\(58\) | −19557.3 | − | 33874.2i | −0.763376 | − | 1.32221i | ||||
\(59\) | −16974.9 | + | 29401.4i | −0.634859 | + | 1.09961i | 0.351687 | + | 0.936118i | \(0.385608\pi\) |
−0.986545 | + | 0.163489i | \(0.947725\pi\) | |||||||
\(60\) | 25395.1 | − | 43985.7i | 0.910694 | − | 1.57737i | ||||
\(61\) | −14147.6 | − | 24504.4i | −0.486809 | − | 0.843178i | 0.513076 | − | 0.858343i | \(-0.328506\pi\) |
−0.999885 | + | 0.0151652i | \(0.995173\pi\) | |||||||
\(62\) | −22051.7 | −0.728556 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −26529.7 | −0.809621 | ||||||||
\(65\) | −9367.36 | − | 16224.7i | −0.275001 | − | 0.476315i | ||||
\(66\) | −38985.6 | + | 67525.1i | −1.10165 | + | 1.90812i | ||||
\(67\) | −28050.5 | + | 48584.8i | −0.763402 | + | 1.32225i | 0.177686 | + | 0.984087i | \(0.443139\pi\) |
−0.941088 | + | 0.338163i | \(0.890194\pi\) | |||||||
\(68\) | 16054.6 | + | 27807.5i | 0.421045 | + | 0.729271i | ||||
\(69\) | −84958.2 | −2.14824 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15537.4 | −0.365791 | −0.182895 | − | 0.983132i | \(-0.558547\pi\) | ||||
−0.182895 | + | 0.983132i | \(0.558547\pi\) | |||||||
\(72\) | −3544.13 | − | 6138.61i | −0.0805709 | − | 0.139553i | ||||
\(73\) | 39109.8 | − | 67740.1i | 0.858970 | − | 1.48778i | −0.0139419 | − | 0.999903i | \(-0.504438\pi\) |
0.872912 | − | 0.487877i | \(-0.162229\pi\) | |||||||
\(74\) | −7998.24 | + | 13853.4i | −0.169791 | + | 0.294087i | ||||
\(75\) | −28126.1 | − | 48715.9i | −0.577374 | − | 1.00004i | ||||
\(76\) | −188.147 | −0.00373648 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 46360.3 | 0.862800 | ||||||||
\(79\) | 22667.7 | + | 39261.7i | 0.408640 | + | 0.707784i | 0.994738 | − | 0.102456i | \(-0.0326700\pi\) |
−0.586098 | + | 0.810240i | \(0.699337\pi\) | |||||||
\(80\) | −41187.0 | + | 71337.9i | −0.719507 | + | 1.24622i | ||||
\(81\) | 19116.2 | − | 33110.3i | 0.323735 | − | 0.560725i | ||||
\(82\) | 36706.6 | + | 63577.8i | 0.602851 | + | 1.04417i | ||||
\(83\) | 1381.82 | 0.0220169 | 0.0110085 | − | 0.999939i | \(-0.496496\pi\) | ||||
0.0110085 | + | 0.999939i | \(0.496496\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 82025.7 | 1.23141 | ||||||||
\(86\) | 40328.8 | + | 69851.5i | 0.587989 | + | 1.01843i | ||||
\(87\) | 58855.4 | − | 101941.i | 0.833659 | − | 1.44394i | ||||
\(88\) | 4848.03 | − | 8397.03i | 0.0667357 | − | 0.115590i | ||||
\(89\) | 34439.7 | + | 59651.3i | 0.460876 | + | 0.798261i | 0.999005 | − | 0.0446014i | \(-0.0142018\pi\) |
−0.538128 | + | 0.842863i | \(0.680868\pi\) | |||||||
\(90\) | 180016. | 2.34264 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −105031. | −1.29375 | ||||||||
\(93\) | −33181.1 | − | 57471.3i | −0.397817 | − | 0.689039i | ||||
\(94\) | 66567.2 | − | 115298.i | 0.777035 | − | 1.34586i | ||||
\(95\) | −240.318 | + | 416.243i | −0.00273198 | + | 0.00473192i | ||||
\(96\) | −93319.2 | − | 161634.i | −1.03346 | − | 1.79000i | ||||
\(97\) | 108857. | 1.17470 | 0.587351 | − | 0.809332i | \(-0.300171\pi\) | ||||
0.587351 | + | 0.809332i | \(0.300171\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −131560. | −1.34908 | ||||||||
\(100\) | −34771.6 | − | 60226.1i | −0.347716 | − | 0.602261i | ||||
\(101\) | −8986.13 | + | 15564.4i | −0.0876535 | + | 0.151820i | −0.906519 | − | 0.422165i | \(-0.861270\pi\) |
0.818865 | + | 0.573986i | \(0.194604\pi\) | |||||||
\(102\) | −101489. | + | 175784.i | −0.965871 | + | 1.67294i | ||||
\(103\) | −15886.8 | − | 27516.8i | −0.147552 | − | 0.255567i | 0.782770 | − | 0.622311i | \(-0.213806\pi\) |
−0.930322 | + | 0.366744i | \(0.880473\pi\) | |||||||
\(104\) | −5765.11 | −0.0522666 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 308747. | 2.66894 | ||||||||
\(107\) | −4114.68 | − | 7126.84i | −0.0347438 | − | 0.0601780i | 0.848131 | − | 0.529787i | \(-0.177728\pi\) |
−0.882874 | + | 0.469609i | \(0.844395\pi\) | |||||||
\(108\) | −22949.9 | + | 39750.4i | −0.189331 | + | 0.327931i | ||||
\(109\) | 5534.34 | − | 9585.75i | 0.0446169 | − | 0.0772787i | −0.842855 | − | 0.538141i | \(-0.819127\pi\) |
0.887471 | + | 0.460863i | \(0.152460\pi\) | |||||||
\(110\) | 123123. | + | 213255.i | 0.970188 | + | 1.68042i | ||||
\(111\) | −48139.6 | −0.370847 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 65184.3 | 0.480228 | 0.240114 | − | 0.970745i | \(-0.422815\pi\) | ||||
0.240114 | + | 0.970745i | \(0.422815\pi\) | |||||||
\(114\) | −594.683 | − | 1030.02i | −0.00428571 | − | 0.00742308i | ||||
\(115\) | −134156. | + | 232364.i | −0.945941 | + | 1.63842i | ||||
\(116\) | 72761.3 | − | 126026.i | 0.502060 | − | 0.869594i | ||||
\(117\) | 39111.7 | + | 67743.5i | 0.264145 | + | 0.457513i | ||||
\(118\) | −265320. | −1.75414 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −39926.4 | −0.253109 | ||||||||
\(121\) | −9455.43 | − | 16377.3i | −0.0587108 | − | 0.101690i | ||||
\(122\) | 110565. | − | 191504.i | 0.672538 | − | 1.16487i | ||||
\(123\) | −110464. | + | 191330.i | −0.658355 | + | 1.14030i | ||||
\(124\) | −41020.8 | − | 71050.2i | −0.239580 | − | 0.414964i | ||||
\(125\) | 54456.9 | 0.311730 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −194777. | −1.07159 | −0.535796 | − | 0.844348i | \(-0.679988\pi\) | ||||
−0.535796 | + | 0.844348i | \(0.679988\pi\) | |||||||
\(128\) | 23307.0 | + | 40369.0i | 0.125737 | + | 0.217782i | ||||
\(129\) | −121365. | + | 210210.i | −0.642124 | + | 1.11219i | ||||
\(130\) | 73206.6 | − | 126798.i | 0.379920 | − | 0.658040i | ||||
\(131\) | 118252. | + | 204818.i | 0.602046 | + | 1.04277i | 0.992511 | + | 0.122156i | \(0.0389808\pi\) |
−0.390465 | + | 0.920618i | \(0.627686\pi\) | |||||||
\(132\) | −290086. | −1.44908 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −438433. | −2.10931 | ||||||||
\(135\) | 58627.3 | + | 101546.i | 0.276864 | + | 0.479542i | ||||
\(136\) | 12620.6 | − | 21859.5i | 0.0585104 | − | 0.101343i | ||||
\(137\) | 100452. | − | 173987.i | 0.457252 | − | 0.791983i | −0.541563 | − | 0.840660i | \(-0.682167\pi\) |
0.998815 | + | 0.0486772i | \(0.0155005\pi\) | |||||||
\(138\) | −331977. | − | 575001.i | −1.48392 | − | 2.57022i | ||||
\(139\) | 52985.2 | 0.232604 | 0.116302 | − | 0.993214i | \(-0.462896\pi\) | ||||
0.116302 | + | 0.993214i | \(0.462896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 400653. | 1.69715 | ||||||||
\(142\) | −60713.0 | − | 105158.i | −0.252674 | − | 0.437644i | ||||
\(143\) | −53501.1 | + | 92666.6i | −0.218788 | + | 0.378951i | ||||
\(144\) | 171969. | − | 297859.i | 0.691104 | − | 1.19703i | ||||
\(145\) | −185875. | − | 321944.i | −0.734176 | − | 1.27163i | ||||
\(146\) | 611291. | 2.37337 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −59513.7 | −0.223338 | ||||||||
\(149\) | 50385.2 | + | 87269.7i | 0.185925 | + | 0.322031i | 0.943888 | − | 0.330266i | \(-0.107139\pi\) |
−0.757963 | + | 0.652298i | \(0.773805\pi\) | |||||||
\(150\) | 219808. | − | 380718.i | 0.797655 | − | 1.38158i | ||||
\(151\) | 228952. | − | 396556.i | 0.817150 | − | 1.41535i | −0.0906234 | − | 0.995885i | \(-0.528886\pi\) |
0.907774 | − | 0.419460i | \(-0.137781\pi\) | |||||||
\(152\) | 73.9513 | + | 128.087i | 0.000259619 | + | 0.000449674i | ||||
\(153\) | −342484. | −1.18280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −209582. | −0.700688 | ||||||||
\(156\) | 86240.0 | + | 149372.i | 0.283725 | + | 0.491426i | ||||
\(157\) | 89518.6 | − | 155051.i | 0.289844 | − | 0.502024i | −0.683928 | − | 0.729549i | \(-0.739730\pi\) |
0.973772 | + | 0.227525i | \(0.0730633\pi\) | |||||||
\(158\) | −177150. | + | 306833.i | −0.564545 | + | 0.977820i | ||||
\(159\) | 464570. | + | 804659.i | 1.45733 | + | 2.52417i | ||||
\(160\) | −589433. | −1.82027 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 298789. | 0.894494 | ||||||||
\(163\) | −121805. | − | 210972.i | −0.359084 | − | 0.621952i | 0.628724 | − | 0.777629i | \(-0.283578\pi\) |
−0.987808 | + | 0.155677i | \(0.950244\pi\) | |||||||
\(164\) | −136564. | + | 236536.i | −0.396485 | + | 0.686733i | ||||
\(165\) | −370524. | + | 641766.i | −1.05951 | + | 1.83513i | ||||
\(166\) | 5399.52 | + | 9352.24i | 0.0152085 | + | 0.0263418i | ||||
\(167\) | 117033. | 0.324725 | 0.162362 | − | 0.986731i | \(-0.448089\pi\) | ||||
0.162362 | + | 0.986731i | \(0.448089\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −307671. | −0.828648 | ||||||||
\(170\) | 320518. | + | 555154.i | 0.850610 | + | 1.47330i | ||||
\(171\) | 1003.40 | − | 1737.95i | 0.00262413 | − | 0.00454513i | ||||
\(172\) | −150040. | + | 259877.i | −0.386711 | + | 0.669803i | ||||
\(173\) | −134867. | − | 233596.i | −0.342602 | − | 0.593403i | 0.642313 | − | 0.766442i | \(-0.277975\pi\) |
−0.984915 | + | 0.173039i | \(0.944641\pi\) | |||||||
\(174\) | 919919. | 2.30344 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 470474. | 1.14486 | ||||||||
\(177\) | −399225. | − | 691479.i | −0.957822 | − | 1.65900i | ||||
\(178\) | −269149. | + | 466180.i | −0.636711 | + | 1.10282i | ||||
\(179\) | −188262. | + | 326080.i | −0.439168 | + | 0.760661i | −0.997626 | − | 0.0688718i | \(-0.978060\pi\) |
0.558457 | + | 0.829533i | \(0.311393\pi\) | |||||||
\(180\) | 334869. | + | 580009.i | 0.770359 | + | 1.33430i | ||||
\(181\) | −434641. | −0.986131 | −0.493065 | − | 0.869992i | \(-0.664124\pi\) | ||||
−0.493065 | + | 0.869992i | \(0.664124\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 665464. | 1.46891 | ||||||||
\(184\) | 41282.8 | + | 71503.9i | 0.0898927 | + | 0.155699i | ||||
\(185\) | −76016.2 | + | 131664.i | −0.163296 | + | 0.282838i | ||||
\(186\) | 259312. | − | 449142.i | 0.549593 | − | 0.951923i | ||||
\(187\) | −234243. | − | 405720.i | −0.489848 | − | 0.848442i | ||||
\(188\) | 495316. | 1.02209 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3756.20 | −0.00754857 | ||||||||
\(191\) | −282970. | − | 490118.i | −0.561250 | − | 0.972114i | −0.997388 | − | 0.0722342i | \(-0.976987\pi\) |
0.436137 | − | 0.899880i | \(-0.356346\pi\) | |||||||
\(192\) | 311970. | − | 540348.i | 0.610744 | − | 1.05784i | ||||
\(193\) | −257231. | + | 445537.i | −0.497084 | + | 0.860974i | −0.999994 | − | 0.00336433i | \(-0.998929\pi\) |
0.502911 | + | 0.864338i | \(0.332262\pi\) | |||||||
\(194\) | 425363. | + | 736751.i | 0.811439 | + | 1.40545i | ||||
\(195\) | 440614. | 0.829796 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −298541. | −0.548073 | −0.274037 | − | 0.961719i | \(-0.588359\pi\) | ||||
−0.274037 | + | 0.961719i | \(0.588359\pi\) | |||||||
\(198\) | −514077. | − | 890407.i | −0.931891 | − | 1.61408i | ||||
\(199\) | 295959. | − | 512617.i | 0.529785 | − | 0.917614i | −0.469612 | − | 0.882873i | \(-0.655606\pi\) |
0.999396 | − | 0.0347408i | \(-0.0110606\pi\) | |||||||
\(200\) | −27334.0 | + | 47344.0i | −0.0483202 | + | 0.0836931i | ||||
\(201\) | −659707. | − | 1.14265e6i | −1.15176 | − | 1.99490i | ||||
\(202\) | −140455. | −0.242191 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −755165. | −1.27048 | ||||||||
\(205\) | 348864. | + | 604250.i | 0.579791 | + | 1.00423i | ||||
\(206\) | 124157. | − | 215046.i | 0.203846 | − | 0.353072i | ||||
\(207\) | 560143. | − | 970196.i | 0.908600 | − | 1.57374i | ||||
\(208\) | −139868. | − | 242258.i | −0.224161 | − | 0.388258i | ||||
\(209\) | 2745.12 | 0.00434706 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −140535. | −0.217309 | −0.108655 | − | 0.994080i | \(-0.534654\pi\) | ||||
−0.108655 | + | 0.994080i | \(0.534654\pi\) | |||||||
\(212\) | 574335. | + | 994778.i | 0.877659 | + | 1.52015i | ||||
\(213\) | 182709. | − | 316461.i | 0.275937 | − | 0.477938i | ||||
\(214\) | 32156.5 | − | 55696.8i | 0.0479993 | − | 0.0831372i | ||||
\(215\) | 383289. | + | 663877.i | 0.565497 | + | 0.979470i | ||||
\(216\) | 36082.0 | 0.0526206 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 86502.5 | 0.123278 | ||||||||
\(219\) | 919806. | + | 1.59315e6i | 1.29594 | + | 2.24464i | ||||
\(220\) | −458068. | + | 793397.i | −0.638077 | + | 1.10518i | ||||
\(221\) | −139277. | + | 241234.i | −0.191822 | + | 0.332245i | ||||
\(222\) | −188107. | − | 325811.i | −0.256167 | − | 0.443694i | ||||
\(223\) | 490.526 | 0.000660541 | 0.000330271 | − | 1.00000i | \(-0.499895\pi\) | ||||
0.000330271 | 1.00000i | \(0.499895\pi\) | ||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 741761. | 0.976804 | ||||||||
\(226\) | 254710. | + | 441171.i | 0.331723 | + | 0.574561i | ||||
\(227\) | −296949. | + | 514331.i | −0.382488 | + | 0.662488i | −0.991417 | − | 0.130736i | \(-0.958266\pi\) |
0.608930 | + | 0.793224i | \(0.291599\pi\) | |||||||
\(228\) | 2212.47 | − | 3832.11i | 0.00281865 | − | 0.00488204i | ||||
\(229\) | 17940.2 | + | 31073.3i | 0.0226067 | + | 0.0391560i | 0.877107 | − | 0.480294i | \(-0.159470\pi\) |
−0.854501 | + | 0.519450i | \(0.826137\pi\) | |||||||
\(230\) | −2.09687e6 | −2.61368 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −114396. | −0.139537 | ||||||||
\(233\) | −624109. | − | 1.08099e6i | −0.753131 | − | 1.30446i | −0.946298 | − | 0.323295i | \(-0.895209\pi\) |
0.193167 | − | 0.981166i | \(-0.438124\pi\) | |||||||
\(234\) | −305661. | + | 529421.i | −0.364922 | + | 0.632064i | ||||
\(235\) | 632662. | − | 1.09580e6i | 0.747312 | − | 1.29438i | ||||
\(236\) | −493551. | − | 854856.i | −0.576836 | − | 0.999109i | ||||
\(237\) | −1.06623e6 | −1.23304 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −576943. | −0.653339 | −0.326669 | − | 0.945139i | \(-0.605926\pi\) | ||||
−0.326669 | + | 0.945139i | \(0.605926\pi\) | |||||||
\(240\) | −968659. | − | 1.67777e6i | −1.08553 | − | 1.88020i | ||||
\(241\) | 691205. | − | 1.19720e6i | 0.766592 | − | 1.32778i | −0.172809 | − | 0.984955i | \(-0.555284\pi\) |
0.939401 | − | 0.342820i | \(-0.111382\pi\) | |||||||
\(242\) | 73894.9 | − | 127990.i | 0.0811103 | − | 0.140487i | ||||
\(243\) | 641392. | + | 1.11092e6i | 0.696800 | + | 1.20689i | ||||
\(244\) | 822694. | 0.884634 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.72658e6 | −1.81906 | ||||||||
\(247\) | −816.101 | − | 1413.53i | −0.000851141 | − | 0.00147422i | ||||
\(248\) | −32246.6 | + | 55852.8i | −0.0332932 | + | 0.0576654i | ||||
\(249\) | −16249.2 | + | 28144.5i | −0.0166087 | + | 0.0287671i | ||||
\(250\) | 212792. | + | 368567.i | 0.215331 | + | 0.372964i | ||||
\(251\) | 323217. | 0.323824 | 0.161912 | − | 0.986805i | \(-0.448234\pi\) | ||||
0.161912 | + | 0.986805i | \(0.448234\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.53244e6 | 1.50516 | ||||||||
\(254\) | −761100. | − | 1.31826e6i | −0.740214 | − | 1.28209i | ||||
\(255\) | −964564. | + | 1.67067e6i | −0.928925 | + | 1.60895i | ||||
\(256\) | −606621. | + | 1.05070e6i | −0.578519 | + | 1.00202i | ||||
\(257\) | −923007. | − | 1.59870e6i | −0.871711 | − | 1.50985i | −0.860226 | − | 0.509913i | \(-0.829678\pi\) |
−0.0114847 | − | 0.999934i | \(-0.503656\pi\) | |||||||
\(258\) | −1.89695e6 | −1.77422 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 544719. | 0.499734 | ||||||||
\(261\) | 776087. | + | 1.34422e6i | 0.705195 | + | 1.22143i | ||||
\(262\) | −924146. | + | 1.60067e6i | −0.831740 | + | 1.44062i | ||||
\(263\) | 229111. | − | 396832.i | 0.204248 | − | 0.353767i | −0.745645 | − | 0.666343i | \(-0.767859\pi\) |
0.949893 | + | 0.312576i | \(0.101192\pi\) | |||||||
\(264\) | 114019. | + | 197486.i | 0.100685 | + | 0.174392i | ||||
\(265\) | 2.93437e6 | 2.56685 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.61995e6 | −1.39066 | ||||||||
\(268\) | −815577. | − | 1.41262e6i | −0.693631 | − | 1.20140i | ||||
\(269\) | −208479. | + | 361096.i | −0.175663 | + | 0.304258i | −0.940391 | − | 0.340096i | \(-0.889540\pi\) |
0.764727 | + | 0.644354i | \(0.222874\pi\) | |||||||
\(270\) | −458177. | + | 793586.i | −0.382493 | + | 0.662498i | ||||
\(271\) | 450189. | + | 779751.i | 0.372368 | + | 0.644960i | 0.989929 | − | 0.141563i | \(-0.0452127\pi\) |
−0.617562 | + | 0.786523i | \(0.711879\pi\) | |||||||
\(272\) | 1.22476e6 | 1.00376 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.57007e6 | 1.26341 | ||||||||
\(275\) | 507329. | + | 878719.i | 0.404536 | + | 0.700678i | ||||
\(276\) | 1.23509e6 | − | 2.13925e6i | 0.975950 | − | 1.69039i | ||||
\(277\) | 223821. | − | 387669.i | 0.175267 | − | 0.303572i | −0.764986 | − | 0.644046i | \(-0.777254\pi\) |
0.940254 | + | 0.340475i | \(0.110588\pi\) | |||||||
\(278\) | 207042. | + | 358607.i | 0.160674 | + | 0.278295i | ||||
\(279\) | 875072. | 0.673029 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −768521. | −0.580617 | −0.290309 | − | 0.956933i | \(-0.593758\pi\) | ||||
−0.290309 | + | 0.956933i | \(0.593758\pi\) | |||||||
\(282\) | 1.56557e6 | + | 2.71164e6i | 1.17233 | + | 2.03053i | ||||
\(283\) | 1.06610e6 | − | 1.84654e6i | 0.791282 | − | 1.37054i | −0.133892 | − | 0.990996i | \(-0.542747\pi\) |
0.925173 | − | 0.379544i | \(-0.123919\pi\) | |||||||
\(284\) | 225878. | − | 391232.i | 0.166180 | − | 0.287832i | ||||
\(285\) | −5651.93 | − | 9789.43i | −0.00412178 | − | 0.00713913i | ||||
\(286\) | −836230. | −0.604520 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.46107e6 | 1.74841 | ||||||||
\(289\) | 100138. | + | 173443.i | 0.0705266 | + | 0.122156i | ||||
\(290\) | 1.45262e6 | − | 2.51602e6i | 1.01428 | − | 1.75679i | ||||
\(291\) | −1.28008e6 | + | 2.21717e6i | −0.886147 | + | 1.53485i | ||||
\(292\) | 1.13713e6 | + | 1.96957e6i | 0.780465 | + | 1.35180i | ||||
\(293\) | −2.42669e6 | −1.65138 | −0.825688 | − | 0.564128i | \(-0.809213\pi\) | ||||
−0.825688 | + | 0.564128i | \(0.809213\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.52163e6 | −1.68704 | ||||||||
\(296\) | 23391.9 | + | 40516.0i | 0.0155180 | + | 0.0268781i | ||||
\(297\) | 334847. | − | 579971.i | 0.220270 | − | 0.381518i | ||||
\(298\) | −393764. | + | 682019.i | −0.256859 | + | 0.444893i | ||||
\(299\) | −455582. | − | 789091.i | −0.294706 | − | 0.510445i | ||||
\(300\) | 1.63556e6 | 1.04921 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.57855e6 | 2.25782 | ||||||||
\(303\) | −211341. | − | 366054.i | −0.132244 | − | 0.229054i | ||||
\(304\) | −3588.28 | + | 6215.09i | −0.00222691 | + | 0.00385712i | ||||
\(305\) | 1.05082e6 | − | 1.82007e6i | 0.646812 | − | 1.12031i | ||||
\(306\) | −1.33827e6 | − | 2.31795e6i | −0.817033 | − | 1.41514i | ||||
\(307\) | 2.44328e6 | 1.47954 | 0.739772 | − | 0.672857i | \(-0.234933\pi\) | ||||
0.739772 | + | 0.672857i | \(0.234933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 747271. | 0.445228 | ||||||||
\(310\) | −818949. | − | 1.41846e6i | −0.484008 | − | 0.838327i | ||||
\(311\) | 577324. | − | 999955.i | 0.338469 | − | 0.586245i | −0.645676 | − | 0.763611i | \(-0.723424\pi\) |
0.984145 | + | 0.177366i | \(0.0567577\pi\) | |||||||
\(312\) | 67793.5 | − | 117422.i | 0.0394277 | − | 0.0682908i | ||||
\(313\) | 828531. | + | 1.43506e6i | 0.478022 | + | 0.827959i | 0.999683 | − | 0.0251945i | \(-0.00802050\pi\) |
−0.521660 | + | 0.853153i | \(0.674687\pi\) | |||||||
\(314\) | 1.39919e6 | 0.800852 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.31815e6 | −0.742584 | ||||||||
\(317\) | −410680. | − | 711319.i | −0.229539 | − | 0.397573i | 0.728133 | − | 0.685436i | \(-0.240388\pi\) |
−0.957671 | + | 0.287863i | \(0.907055\pi\) | |||||||
\(318\) | −3.63065e6 | + | 6.28847e6i | −2.01334 | + | 3.48720i | ||||
\(319\) | −1.06161e6 | + | 1.83877e6i | −0.584103 | + | 1.01170i | ||||
\(320\) | −985249. | − | 1.70650e6i | −0.537862 | − | 0.931605i | ||||
\(321\) | 193543. | 0.104837 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7146.23 | 0.00381128 | ||||||||
\(324\) | 555811. | + | 962693.i | 0.294147 | + | 0.509478i | ||||
\(325\) | 301649. | − | 522471.i | 0.158414 | − | 0.274381i | ||||
\(326\) | 951915. | − | 1.64877e6i | 0.496083 | − | 0.859241i | ||||
\(327\) | 130160. | + | 225443.i | 0.0673143 | + | 0.116592i | ||||
\(328\) | 214707. | 0.110195 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −5.79134e6 | −2.92748 | ||||||||
\(331\) | 47835.3 | + | 82853.2i | 0.0239982 | + | 0.0415661i | 0.877775 | − | 0.479073i | \(-0.159027\pi\) |
−0.853777 | + | 0.520639i | \(0.825694\pi\) | |||||||
\(332\) | −20088.5 | + | 34794.3i | −0.0100024 | + | 0.0173246i | ||||
\(333\) | 317392. | − | 549740.i | 0.156850 | − | 0.271673i | ||||
\(334\) | 457309. | + | 792082.i | 0.224307 | + | 0.388512i | ||||
\(335\) | −4.16691e6 | −2.02863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.37020e6 | 1.13687 | 0.568435 | − | 0.822728i | \(-0.307549\pi\) | ||||
0.568435 | + | 0.822728i | \(0.307549\pi\) | |||||||
\(338\) | −1.20224e6 | − | 2.08234e6i | −0.572398 | − | 0.991423i | ||||
\(339\) | −766522. | + | 1.32765e6i | −0.362264 | + | 0.627460i | ||||
\(340\) | −1.19246e6 | + | 2.06541e6i | −0.559433 | + | 0.968966i | ||||
\(341\) | 598507. | + | 1.03665e6i | 0.278730 | + | 0.482774i | ||||
\(342\) | 15683.4 | 0.00725060 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 235894. | 0.107478 | ||||||||
\(345\) | −3.15515e6 | − | 5.46488e6i | −1.42716 | − | 2.47191i | ||||
\(346\) | 1.05399e6 | − | 1.82557e6i | 0.473312 | − | 0.819800i | ||||
\(347\) | −245286. | + | 424847.i | −0.109358 | + | 0.189413i | −0.915510 | − | 0.402295i | \(-0.868213\pi\) |
0.806153 | + | 0.591708i | \(0.201546\pi\) | |||||||
\(348\) | 1.71124e6 | + | 2.96396e6i | 0.757467 | + | 1.31197i | ||||
\(349\) | −4.21208e6 | −1.85111 | −0.925557 | − | 0.378607i | \(-0.876403\pi\) | ||||
−0.925557 | + | 0.378607i | \(0.876403\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −398188. | −0.172512 | ||||||||
\(352\) | 1.68326e6 | + | 2.91549e6i | 0.724092 | + | 1.25416i | ||||
\(353\) | −1.58689e6 | + | 2.74858e6i | −0.677814 | + | 1.17401i | 0.297824 | + | 0.954621i | \(0.403739\pi\) |
−0.975638 | + | 0.219387i | \(0.929594\pi\) | |||||||
\(354\) | 3.11997e6 | − | 5.40396e6i | 1.32325 | − | 2.29194i | ||||
\(355\) | −577023. | − | 999433.i | −0.243009 | − | 0.420904i | ||||
\(356\) | −2.00269e6 | −0.837509 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.94257e6 | −1.21344 | ||||||||
\(359\) | 1.70049e6 | + | 2.94533e6i | 0.696366 | + | 1.20614i | 0.969718 | + | 0.244227i | \(0.0785343\pi\) |
−0.273352 | + | 0.961914i | \(0.588132\pi\) | |||||||
\(360\) | 263241. | − | 455947.i | 0.107053 | − | 0.185421i | ||||
\(361\) | 1.23803e6 | − | 2.14433e6i | 0.499992 | − | 0.866011i | ||||
\(362\) | −1.69838e6 | − | 2.94167e6i | −0.681181 | − | 1.17984i | ||||
\(363\) | 444757. | 0.177156 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.80978e6 | 2.28259 | ||||||||
\(366\) | 2.60032e6 | + | 4.50389e6i | 1.01467 | + | 1.75746i | ||||
\(367\) | −984358. | + | 1.70496e6i | −0.381494 | + | 0.660767i | −0.991276 | − | 0.131802i | \(-0.957924\pi\) |
0.609782 | + | 0.792569i | \(0.291257\pi\) | |||||||
\(368\) | −2.00313e6 | + | 3.46952e6i | −0.771063 | + | 1.33552i | ||||
\(369\) | −1.45662e6 | − | 2.52294e6i | −0.556904 | − | 0.964586i | ||||
\(370\) | −1.18814e6 | −0.451196 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1.92950e6 | 0.722917 | ||||||||
\(373\) | 1.73944e6 | + | 3.01280e6i | 0.647349 | + | 1.12124i | 0.983754 | + | 0.179523i | \(0.0574556\pi\) |
−0.336405 | + | 0.941717i | \(0.609211\pi\) | |||||||
\(374\) | 1.83062e6 | − | 3.17073e6i | 0.676737 | − | 1.17214i | ||||
\(375\) | −640375. | + | 1.10916e6i | −0.235156 | + | 0.407302i | ||||
\(376\) | −194685. | − | 337204.i | −0.0710170 | − | 0.123005i | ||||
\(377\) | 1.26243e6 | 0.457462 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −421294. | −0.150656 | −0.0753281 | − | 0.997159i | \(-0.524000\pi\) | ||||
−0.0753281 | + | 0.997159i | \(0.524000\pi\) | |||||||
\(380\) | −6987.33 | − | 12102.4i | −0.00248229 | − | 0.00429945i | ||||
\(381\) | 2.29044e6 | − | 3.96716e6i | 0.808364 | − | 1.40013i | ||||
\(382\) | 2.21143e6 | − | 3.83031e6i | 0.775380 | − | 1.34300i | ||||
\(383\) | −1.33455e6 | − | 2.31151e6i | −0.464877 | − | 0.805190i | 0.534319 | − | 0.845283i | \(-0.320568\pi\) |
−0.999196 | + | 0.0400925i | \(0.987235\pi\) | |||||||
\(384\) | −1.09630e6 | −0.379402 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.02055e6 | −1.37346 | ||||||||
\(387\) | −1.60036e6 | − | 2.77190e6i | −0.543175 | − | 0.940806i | ||||
\(388\) | −1.58253e6 | + | 2.74102e6i | −0.533670 | + | 0.924344i | ||||
\(389\) | −1.55089e6 | + | 2.68622e6i | −0.519645 | + | 0.900051i | 0.480095 | + | 0.877217i | \(0.340602\pi\) |
−0.999739 | + | 0.0228343i | \(0.992731\pi\) | |||||||
\(390\) | 1.72171e6 | + | 2.98210e6i | 0.573191 | + | 0.992797i | ||||
\(391\) | 3.98933e6 | 1.31965 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.56223e6 | −1.81663 | ||||||||
\(394\) | −1.16656e6 | − | 2.02054e6i | −0.378588 | − | 0.655733i | ||||
\(395\) | −1.68365e6 | + | 2.91617e6i | −0.542950 | + | 0.940417i | ||||
\(396\) | 1.91258e6 | − | 3.31269e6i | 0.612889 | − | 1.06156i | ||||
\(397\) | −306629. | − | 531096.i | −0.0976419 | − | 0.169121i | 0.813066 | − | 0.582171i | \(-0.197797\pi\) |
−0.910708 | + | 0.413050i | \(0.864463\pi\) | |||||||
\(398\) | 4.62589e6 | 1.46382 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.65262e6 | −0.828942 | ||||||||
\(401\) | −1.41111e6 | − | 2.44412e6i | −0.438229 | − | 0.759035i | 0.559324 | − | 0.828949i | \(-0.311061\pi\) |
−0.997553 | + | 0.0699139i | \(0.977728\pi\) | |||||||
\(402\) | 5.15566e6 | − | 8.92986e6i | 1.59118 | − | 2.75600i | ||||
\(403\) | 355862. | − | 616371.i | 0.109149 | − | 0.189051i | ||||
\(404\) | −261275. | − | 452542.i | −0.0796425 | − | 0.137945i | ||||
\(405\) | 2.83973e6 | 0.860278 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 868324. | 0.259834 | ||||||||
\(408\) | 296819. | + | 514105.i | 0.0882756 | + | 0.152898i | ||||
\(409\) | −1.14175e6 | + | 1.97757e6i | −0.337492 | + | 0.584553i | −0.983960 | − | 0.178388i | \(-0.942912\pi\) |
0.646469 | + | 0.762941i | \(0.276245\pi\) | |||||||
\(410\) | −2.72640e6 | + | 4.72226e6i | −0.800994 | + | 1.38736i | ||||
\(411\) | 2.36248e6 | + | 4.09193e6i | 0.689864 | + | 1.19488i | ||||
\(412\) | 923831. | 0.268132 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.75511e6 | 2.51050 | ||||||||
\(415\) | 51317.6 | + | 88884.8i | 0.0146267 | + | 0.0253342i | ||||
\(416\) | 1.00084e6 | − | 1.73350e6i | 0.283550 | − | 0.491123i | ||||
\(417\) | −623068. | + | 1.07919e6i | −0.175467 | + | 0.303918i | ||||
\(418\) | 10726.7 | + | 18579.1i | 0.00300278 | + | 0.00520097i | ||||
\(419\) | −2.65270e6 | −0.738163 | −0.369082 | − | 0.929397i | \(-0.620328\pi\) | ||||
−0.369082 | + | 0.929397i | \(0.620328\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.93674e6 | 0.807532 | 0.403766 | − | 0.914862i | \(-0.367701\pi\) | ||||
0.403766 | + | 0.914862i | \(0.367701\pi\) | |||||||
\(422\) | −549146. | − | 951148.i | −0.150109 | − | 0.259996i | ||||
\(423\) | −2.64157e6 | + | 4.57533e6i | −0.717812 | + | 1.24329i | ||||
\(424\) | 451487. | − | 781998.i | 0.121964 | − | 0.211247i | ||||
\(425\) | 1.32070e6 | + | 2.28752e6i | 0.354676 | + | 0.614317i | ||||
\(426\) | 2.85577e6 | 0.762428 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 239272. | 0.0631367 | ||||||||
\(429\) | −1.25827e6 | − | 2.17939e6i | −0.330089 | − | 0.571730i | ||||
\(430\) | −2.99543e6 | + | 5.18824e6i | −0.781247 | + | 1.35316i | ||||
\(431\) | 1.22283e6 | − | 2.11800e6i | 0.317082 | − | 0.549202i | −0.662796 | − | 0.748800i | \(-0.730630\pi\) |
0.979878 | + | 0.199598i | \(0.0639636\pi\) | |||||||
\(432\) | 875389. | + | 1.51622e6i | 0.225679 | + | 0.390888i | ||||
\(433\) | −2.11718e6 | −0.542673 | −0.271336 | − | 0.962485i | \(-0.587466\pi\) | ||||
−0.271336 | + | 0.962485i | \(0.587466\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.74301e6 | 2.21533 | ||||||||
\(436\) | 160913. | + | 278709.i | 0.0405391 | + | 0.0702158i | ||||
\(437\) | −11687.9 | + | 20244.0i | −0.00292773 | + | 0.00507099i | ||||
\(438\) | −7.18835e6 | + | 1.24506e7i | −1.79038 | + | 3.10102i | ||||
\(439\) | −2.32382e6 | − | 4.02498e6i | −0.575495 | − | 0.996786i | −0.995988 | − | 0.0894902i | \(-0.971476\pi\) |
0.420493 | − | 0.907296i | \(-0.361857\pi\) | |||||||
\(440\) | 720178. | 0.177340 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.17691e6 | −0.530012 | ||||||||
\(443\) | −2.21462e6 | − | 3.83584e6i | −0.536155 | − | 0.928648i | −0.999106 | − | 0.0422645i | \(-0.986543\pi\) |
0.462951 | − | 0.886384i | \(-0.346791\pi\) | |||||||
\(444\) | 699839. | − | 1.21216e6i | 0.168477 | − | 0.291811i | ||||
\(445\) | −2.55802e6 | + | 4.43062e6i | −0.612356 | + | 1.06063i | ||||
\(446\) | 1916.75 | + | 3319.91i | 0.000456276 | + | 0.000790294i | ||||
\(447\) | −2.36998e6 | −0.561016 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.70171e6 | −1.56881 | −0.784404 | − | 0.620250i | \(-0.787031\pi\) | ||||
−0.784404 | + | 0.620250i | \(0.787031\pi\) | |||||||
\(450\) | 2.89846e6 | + | 5.02027e6i | 0.674739 | + | 1.16868i | ||||
\(451\) | 1.99252e6 | − | 3.45114e6i | 0.461276 | − | 0.798953i | ||||
\(452\) | −947629. | + | 1.64134e6i | −0.218169 | + | 0.377879i | ||||
\(453\) | 5.38462e6 | + | 9.32644e6i | 1.23285 | + | 2.13536i | ||||
\(454\) | −4.64136e6 | −1.05683 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3478.46 | −0.000783385 | ||||||||
\(457\) | 2.94172e6 | + | 5.09521e6i | 0.658887 | + | 1.14123i | 0.980904 | + | 0.194491i | \(0.0623057\pi\) |
−0.322018 | + | 0.946734i | \(0.604361\pi\) | |||||||
\(458\) | −140204. | + | 242840.i | −0.0312317 | + | 0.0540949i | ||||
\(459\) | 871688. | − | 1.50981e6i | 0.193121 | − | 0.334495i | ||||
\(460\) | −3.90062e6 | − | 6.75607e6i | −0.859487 | − | 1.48867i | ||||
\(461\) | 1.54764e6 | 0.339171 | 0.169585 | − | 0.985515i | \(-0.445757\pi\) | ||||
0.169585 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.93764e6 | −0.853656 | −0.426828 | − | 0.904333i | \(-0.640369\pi\) | ||||
−0.426828 | + | 0.904333i | \(0.640369\pi\) | |||||||
\(464\) | −2.77537e6 | − | 4.80708e6i | −0.598447 | − | 1.03654i | ||||
\(465\) | 2.46453e6 | − | 4.26870e6i | 0.528570 | − | 0.915510i | ||||
\(466\) | 4.87746e6 | − | 8.44800e6i | 1.04047 | − | 1.80214i | ||||
\(467\) | 3.40793e6 | + | 5.90271e6i | 0.723100 | + | 1.25245i | 0.959751 | + | 0.280852i | \(0.0906170\pi\) |
−0.236651 | + | 0.971595i | \(0.576050\pi\) | |||||||
\(468\) | −2.27438e6 | −0.480007 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 9.88860e6 | 2.06486 | ||||||||
\(471\) | 2.10535e6 | + | 3.64657e6i | 0.437293 | + | 0.757413i | ||||
\(472\) | −387982. | + | 672005.i | −0.0801598 | + | 0.138841i | ||||
\(473\) | 2.18913e6 | − | 3.79169e6i | 0.449904 | − | 0.779256i | ||||
\(474\) | −4.16632e6 | − | 7.21627e6i | −0.851739 | − | 1.47525i | ||||
\(475\) | −15477.5 | −0.00314750 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.22519e7 | −2.46552 | ||||||||
\(478\) | −2.25443e6 | − | 3.90478e6i | −0.451301 | − | 0.781677i | ||||
\(479\) | 2.60203e6 | − | 4.50685e6i | 0.518171 | − | 0.897499i | −0.481606 | − | 0.876388i | \(-0.659946\pi\) |
0.999777 | − | 0.0211112i | \(-0.00672039\pi\) | |||||||
\(480\) | 6.93132e6 | − | 1.20054e7i | 1.37313 | − | 2.37834i | ||||
\(481\) | −258145. | − | 447121.i | −0.0508747 | − | 0.0881175i | ||||
\(482\) | 1.08036e7 | 2.11813 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 549840. | 0.106690 | ||||||||
\(485\) | 4.04270e6 | + | 7.00216e6i | 0.780400 | + | 1.35169i | ||||
\(486\) | −5.01253e6 | + | 8.68195e6i | −0.962644 | + | 1.66735i | ||||
\(487\) | 77499.2 | − | 134233.i | 0.0148073 | − | 0.0256469i | −0.858527 | − | 0.512769i | \(-0.828620\pi\) |
0.873334 | + | 0.487122i | \(0.161953\pi\) | |||||||
\(488\) | −323361. | − | 560078.i | −0.0614665 | − | 0.106463i | ||||
\(489\) | 5.72936e6 | 1.08351 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.61951e6 | −0.303165 | −0.151583 | − | 0.988445i | \(-0.548437\pi\) | ||||
−0.151583 | + | 0.988445i | \(0.548437\pi\) | |||||||
\(492\) | −3.21179e6 | − | 5.56299e6i | −0.598184 | − | 1.03609i | ||||
\(493\) | −2.76364e6 | + | 4.78676e6i | −0.512111 | + | 0.887002i | ||||
\(494\) | 6377.89 | − | 11046.8i | 0.00117587 | − | 0.00203667i | ||||
\(495\) | −4.88584e6 | − | 8.46253e6i | −0.896244 | − | 1.55234i | ||||
\(496\) | −3.12935e6 | −0.571150 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −253978. | −0.0458905 | ||||||||
\(499\) | −2.05337e6 | − | 3.55654e6i | −0.369161 | − | 0.639405i | 0.620274 | − | 0.784385i | \(-0.287022\pi\) |
−0.989435 | + | 0.144980i | \(0.953688\pi\) | |||||||
\(500\) | −791678. | + | 1.37123e6i | −0.141620 | + | 0.245292i | ||||
\(501\) | −1.37622e6 | + | 2.38368e6i | −0.244959 | + | 0.424281i | ||||
\(502\) | 1.26298e6 | + | 2.18755e6i | 0.223685 | + | 0.387435i | ||||
\(503\) | −3.40748e6 | −0.600501 | −0.300250 | − | 0.953860i | \(-0.597070\pi\) | ||||
−0.300250 | + | 0.953860i | \(0.597070\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.33490e6 | −0.232927 | ||||||||
\(506\) | 5.98808e6 | + | 1.03717e7i | 1.03971 | + | 1.80083i | ||||
\(507\) | 3.61800e6 | − | 6.26655e6i | 0.625098 | − | 1.08270i | ||||
\(508\) | 2.83161e6 | − | 4.90450e6i | 0.486827 | − | 0.843209i | ||||
\(509\) | −5.35453e6 | − | 9.27432e6i | −0.916067 | − | 1.58667i | −0.805332 | − | 0.592825i | \(-0.798013\pi\) |
−0.110735 | − | 0.993850i | \(-0.535321\pi\) | |||||||
\(510\) | −1.50763e7 | −2.56666 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −7.98992e6 | −1.34700 | ||||||||
\(513\) | 5107.72 | + | 8846.83i | 0.000856907 | + | 0.00148421i | ||||
\(514\) | 7.21337e6 | − | 1.24939e7i | 1.20429 | − | 2.08589i | ||||
\(515\) | 1.18000e6 | − | 2.04382e6i | 0.196049 | − | 0.339566i | ||||
\(516\) | −3.52873e6 | − | 6.11194e6i | −0.583437 | − | 1.01054i | ||||
\(517\) | −7.22682e6 | −1.18911 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.34374e6 | 1.03378 | ||||||||
\(520\) | −214103. | − | 370836.i | −0.0347227 | − | 0.0601415i | ||||
\(521\) | −3.96000e6 | + | 6.85893e6i | −0.639148 | + | 1.10704i | 0.346472 | + | 0.938060i | \(0.387379\pi\) |
−0.985620 | + | 0.168976i | \(0.945954\pi\) | |||||||
\(522\) | −6.06517e6 | + | 1.05052e7i | −0.974242 | + | 1.68744i | ||||
\(523\) | 4.16373e6 | + | 7.21179e6i | 0.665623 | + | 1.15289i | 0.979116 | + | 0.203303i | \(0.0651675\pi\) |
−0.313493 | + | 0.949591i | \(0.601499\pi\) | |||||||
\(524\) | −6.87643e6 | −1.09404 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.58104e6 | 0.564345 | ||||||||
\(527\) | 1.55806e6 | + | 2.69864e6i | 0.244376 | + | 0.423271i | ||||
\(528\) | −5.53244e6 | + | 9.58246e6i | −0.863638 | + | 1.49586i | ||||
\(529\) | −3.30649e6 | + | 5.72701e6i | −0.513722 | + | 0.889793i | ||||
\(530\) | 1.14662e7 | + | 1.98600e7i | 1.77308 | + | 3.07106i | ||||
\(531\) | 1.05286e7 | 1.62045 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.36943e6 | −0.361265 | ||||||||
\(534\) | −6.33000e6 | − | 1.09639e7i | −0.960618 | − | 1.66384i | ||||
\(535\) | 305619. | − | 529348.i | 0.0461632 | − | 0.0799571i | ||||
\(536\) | −641128. | + | 1.11047e6i | −0.0963902 | + | 0.166953i | ||||
\(537\) | −4.42766e6 | − | 7.66893e6i | −0.662581 | − | 1.14762i | ||||
\(538\) | −3.25856e6 | −0.485366 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −3.40922e6 | −0.503119 | ||||||||
\(541\) | −311631. | − | 539760.i | −0.0457770 | − | 0.0792880i | 0.842229 | − | 0.539120i | \(-0.181243\pi\) |
−0.888006 | + | 0.459832i | \(0.847910\pi\) | |||||||
\(542\) | −3.51826e6 | + | 6.09381e6i | −0.514434 | + | 0.891027i | ||||
\(543\) | 5.11107e6 | − | 8.85264e6i | 0.743896 | − | 1.28847i | ||||
\(544\) | 4.38193e6 | + | 7.58973e6i | 0.634846 | + | 1.09959i | ||||
\(545\) | 822129. | 0.118563 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.05691e7 | 1.51032 | 0.755159 | − | 0.655541i | \(-0.227559\pi\) | ||||
0.755159 | + | 0.655541i | \(0.227559\pi\) | |||||||
\(548\) | 2.92067e6 | + | 5.05874e6i | 0.415461 | + | 0.719600i | ||||
\(549\) | −4.38751e6 | + | 7.59939e6i | −0.621280 | + | 1.07609i | ||||
\(550\) | −3.96481e6 | + | 6.86725e6i | −0.558876 | + | 0.968002i | ||||
\(551\) | −16193.7 | − | 28048.4i | −0.00227231 | − | 0.00393576i | ||||
\(552\) | −1.94182e6 | −0.271245 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.49835e6 | 0.484272 | ||||||||
\(555\) | −1.78779e6 | − | 3.09655e6i | −0.246368 | − | 0.426722i | ||||
\(556\) | −770282. | + | 1.33417e6i | −0.105673 | + | 0.183030i | ||||
\(557\) | 6.76989e6 | − | 1.17258e7i | 0.924579 | − | 1.60142i | 0.132341 | − | 0.991204i | \(-0.457751\pi\) |
0.792237 | − | 0.610213i | \(-0.208916\pi\) | |||||||
\(558\) | 3.41938e6 | + | 5.92254e6i | 0.464902 | + | 0.805234i | ||||
\(559\) | −2.60324e6 | −0.352359 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.10181e7 | 1.47809 | ||||||||
\(562\) | −3.00302e6 | − | 5.20139e6i | −0.401068 | − | 0.694670i | ||||
\(563\) | 6.98785e6 | − | 1.21033e7i | 0.929122 | − | 1.60929i | 0.144327 | − | 0.989530i | \(-0.453898\pi\) |
0.784795 | − | 0.619756i | \(-0.212768\pi\) | |||||||
\(564\) | −5.82456e6 | + | 1.00884e7i | −0.771020 | + | 1.33545i | ||||
\(565\) | 2.42079e6 | + | 4.19294e6i | 0.319034 | + | 0.552583i | ||||
\(566\) | 1.66633e7 | 2.18635 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −355127. | −0.0461862 | ||||||||
\(569\) | 2.80997e6 | + | 4.86701e6i | 0.363848 | + | 0.630204i | 0.988591 | − | 0.150627i | \(-0.0481293\pi\) |
−0.624742 | + | 0.780831i | \(0.714796\pi\) | |||||||
\(570\) | 44170.3 | − | 76505.1i | 0.00569433 | − | 0.00986287i | ||||
\(571\) | −4.35395e6 | + | 7.54126e6i | −0.558847 | + | 0.967951i | 0.438746 | + | 0.898611i | \(0.355423\pi\) |
−0.997593 | + | 0.0693403i | \(0.977911\pi\) | |||||||
\(572\) | −1.55556e6 | − | 2.69432e6i | −0.198792 | − | 0.344317i | ||||
\(573\) | 1.33101e7 | 1.69354 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.64019e6 | −1.08982 | ||||||||
\(576\) | 4.11373e6 | + | 7.12520e6i | 0.516630 | + | 0.894830i | ||||
\(577\) | 3.31996e6 | − | 5.75034e6i | 0.415139 | − | 0.719042i | −0.580304 | − | 0.814400i | \(-0.697066\pi\) |
0.995443 | + | 0.0953580i | \(0.0303996\pi\) | |||||||
\(578\) | −782583. | + | 1.35547e6i | −0.0974340 | + | 0.168761i | ||||
\(579\) | −6.04970e6 | − | 1.04784e7i | −0.749959 | − | 1.29897i | ||||
\(580\) | 1.08087e7 | 1.33415 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −2.00079e7 | −2.44846 | ||||||||
\(583\) | −8.37974e6 | − | 1.45141e7i | −1.02108 | − | 1.76856i | ||||
\(584\) | 893902. | − | 1.54828e6i | 0.108457 | − | 0.187853i | ||||
\(585\) | −2.90504e6 | + | 5.03167e6i | −0.350964 | + | 0.607887i | ||||
\(586\) | −9.48239e6 | − | 1.64240e7i | −1.14071 | − | 1.97576i | ||||
\(587\) | −1.36652e7 | −1.63689 | −0.818446 | − | 0.574583i | \(-0.805164\pi\) | ||||
−0.818446 | + | 0.574583i | \(0.805164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18259.2 | −0.00216866 | ||||||||
\(590\) | −9.85337e6 | − | 1.70665e7i | −1.16535 | − | 2.01844i | ||||
\(591\) | 3.51063e6 | − | 6.08059e6i | 0.413444 | − | 0.716106i | ||||
\(592\) | −1.13503e6 | + | 1.96593e6i | −0.133108 | + | 0.230549i | ||||
\(593\) | 3.51295e6 | + | 6.08460e6i | 0.410237 | + | 0.710551i | 0.994915 | − | 0.100714i | \(-0.0321126\pi\) |
−0.584678 | + | 0.811265i | \(0.698779\pi\) | |||||||
\(594\) | 5.23370e6 | 0.608615 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.92994e6 | −0.337864 | ||||||||
\(597\) | 6.96054e6 | + | 1.20560e7i | 0.799295 | + | 1.38442i | ||||
\(598\) | 3.56041e6 | − | 6.16681e6i | 0.407143 | − | 0.705192i | ||||
\(599\) | 1.79331e6 | − | 3.10611e6i | 0.204216 | − | 0.353712i | −0.745667 | − | 0.666319i | \(-0.767869\pi\) |
0.949883 | + | 0.312607i | \(0.101202\pi\) | |||||||
\(600\) | −642858. | − | 1.11346e6i | −0.0729016 | − | 0.126269i | ||||
\(601\) | 1.58600e7 | 1.79108 | 0.895542 | − | 0.444977i | \(-0.146788\pi\) | ||||
0.895542 | + | 0.444977i | \(0.146788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.73982e7 | 1.94855 | ||||||||
\(604\) | 6.65686e6 | + | 1.15300e7i | 0.742467 | + | 1.28599i | ||||
\(605\) | 702305. | − | 1.21643e6i | 0.0780077 | − | 0.135113i | ||||
\(606\) | 1.65165e6 | − | 2.86073e6i | 0.182699 | − | 0.316443i | ||||
\(607\) | −3.22085e6 | − | 5.57867e6i | −0.354812 | − | 0.614553i | 0.632274 | − | 0.774745i | \(-0.282122\pi\) |
−0.987086 | + | 0.160192i | \(0.948789\pi\) | |||||||
\(608\) | −51352.5 | −0.00563381 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.64244e7 | 1.78717 | ||||||||
\(611\) | 2.14847e6 | + | 3.72126e6i | 0.232823 | + | 0.403262i | ||||
\(612\) | 4.97892e6 | − | 8.62375e6i | 0.537349 | − | 0.930716i | ||||
\(613\) | 2.29433e6 | − | 3.97389e6i | 0.246606 | − | 0.427134i | −0.715976 | − | 0.698125i | \(-0.754018\pi\) |
0.962582 | + | 0.270991i | \(0.0873513\pi\) | |||||||
\(614\) | 9.54722e6 | + | 1.65363e7i | 1.02201 | + | 1.77018i | ||||
\(615\) | −1.64096e7 | −1.74948 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.47104e6 | 0.155565 | 0.0777825 | − | 0.996970i | \(-0.475216\pi\) | ||||
0.0777825 | + | 0.996970i | \(0.475216\pi\) | |||||||
\(618\) | 2.91999e6 | + | 5.05757e6i | 0.307546 | + | 0.532685i | ||||
\(619\) | 1.56784e6 | − | 2.71558e6i | 0.164466 | − | 0.284863i | −0.772000 | − | 0.635623i | \(-0.780743\pi\) |
0.936465 | + | 0.350760i | \(0.114077\pi\) | |||||||
\(620\) | 3.04684e6 | − | 5.27727e6i | 0.318324 | − | 0.551354i | ||||
\(621\) | 2.85134e6 | + | 4.93867e6i | 0.296702 | + | 0.513903i | ||||
\(622\) | 9.02366e6 | 0.935205 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.57898e6 | 0.676390 | ||||||||
\(625\) | 5.75963e6 | + | 9.97597e6i | 0.589786 | + | 1.02154i | ||||
\(626\) | −6.47503e6 | + | 1.12151e7i | −0.660399 | + | 1.14384i | ||||
\(627\) | −32280.7 | + | 55911.8i | −0.00327924 | + | 0.00567982i | ||||
\(628\) | 2.60279e6 | + | 4.50816e6i | 0.263354 | + | 0.456142i | ||||
\(629\) | 2.26046e6 | 0.227809 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 484547. | 0.0484465 | 0.0242233 | − | 0.999707i | \(-0.492289\pi\) | ||||
0.0242233 | + | 0.999707i | \(0.492289\pi\) | |||||||
\(632\) | 518099. | + | 897374.i | 0.0515965 | + | 0.0893678i | ||||
\(633\) | 1.65259e6 | − | 2.86237e6i | 0.163929 | − | 0.283934i | ||||
\(634\) | 3.20950e6 | − | 5.55901e6i | 0.317113 | − | 0.549256i | ||||
\(635\) | −7.23358e6 | − | 1.25289e7i | −0.711900 | − | 1.23305i | ||||
\(636\) | −2.70151e7 | −2.64828 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.65932e7 | −1.61390 | ||||||||
\(639\) | 2.40926e6 | + | 4.17296e6i | 0.233416 | + | 0.404289i | ||||
\(640\) | −1.73114e6 | + | 2.99842e6i | −0.167064 | + | 0.289363i | ||||
\(641\) | −1.52042e6 | + | 2.63345e6i | −0.146157 | + | 0.253151i | −0.929804 | − | 0.368055i | \(-0.880024\pi\) |
0.783647 | + | 0.621206i | \(0.213357\pi\) | |||||||
\(642\) | 756276. | + | 1.30991e6i | 0.0724174 | + | 0.125431i | ||||
\(643\) | 5.25888e6 | 0.501609 | 0.250805 | − | 0.968038i | \(-0.419305\pi\) | ||||
0.250805 | + | 0.968038i | \(0.419305\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.80288e7 | −1.70635 | ||||||||
\(646\) | 27924.1 | + | 48366.0i | 0.00263268 | + | 0.00455994i | ||||
\(647\) | −1.05985e7 | + | 1.83571e7i | −0.995368 | + | 1.72403i | −0.414425 | + | 0.910083i | \(0.636017\pi\) |
−0.580942 | + | 0.813945i | \(0.697316\pi\) | |||||||
\(648\) | 436925. | − | 756776.i | 0.0408761 | − | 0.0707994i | ||||
\(649\) | 7.20107e6 | + | 1.24726e7i | 0.671097 | + | 1.16237i | ||||
\(650\) | 4.71481e6 | 0.437705 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.08305e6 | 0.652531 | ||||||||
\(653\) | −6.50529e6 | − | 1.12675e7i | −0.597013 | − | 1.03406i | −0.993259 | − | 0.115912i | \(-0.963021\pi\) |
0.396247 | − | 0.918144i | \(-0.370313\pi\) | |||||||
\(654\) | −1.01721e6 | + | 1.76186e6i | −0.0929962 | + | 0.161074i | ||||
\(655\) | −8.78319e6 | + | 1.52129e7i | −0.799924 | + | 1.38551i | ||||
\(656\) | 5.20903e6 | + | 9.02230e6i | 0.472604 | + | 0.818574i | ||||
\(657\) | −2.42577e7 | −2.19248 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.59874e7 | −1.43405 | −0.717024 | − | 0.697049i | \(-0.754496\pi\) | ||||
−0.717024 | + | 0.697049i | \(0.754496\pi\) | |||||||
\(660\) | −1.07731e7 | − | 1.86596e7i | −0.962678 | − | 1.66741i | ||||
\(661\) | −2.01571e6 | + | 3.49131e6i | −0.179442 | + | 0.310803i | −0.941690 | − | 0.336483i | \(-0.890763\pi\) |
0.762248 | + | 0.647286i | \(0.224096\pi\) | |||||||
\(662\) | −373837. | + | 647504.i | −0.0331541 | + | 0.0574245i | ||||
\(663\) | −3.27559e6 | − | 5.67348e6i | −0.289404 | − | 0.501263i | ||||
\(664\) | 31583.3 | 0.00277995 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.96089e6 | 0.433385 | ||||||||
\(667\) | −9.04002e6 | − | 1.56578e7i | −0.786783 | − | 1.36275i | ||||
\(668\) | −1.70138e6 | + | 2.94688e6i | −0.147523 | + | 0.255518i | ||||
\(669\) | −5768.24 | + | 9990.88i | −0.000498285 | + | 0.000863055i | ||||
\(670\) | −1.62824e7 | − | 2.82019e7i | −1.40130 | − | 2.42712i | ||||
\(671\) | −1.20034e7 | −1.02919 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.98234e6 | 0.253816 | 0.126908 | − | 0.991914i | \(-0.459495\pi\) | ||||
0.126908 | + | 0.991914i | \(0.459495\pi\) | |||||||
\(674\) | 9.26165e6 | + | 1.60416e7i | 0.785305 | + | 1.36019i | ||||
\(675\) | −1.88793e6 | + | 3.26998e6i | −0.159487 | + | 0.276240i | ||||
\(676\) | 4.47283e6 | − | 7.74717e6i | 0.376457 | − | 0.652043i | ||||
\(677\) | −973478. | − | 1.68611e6i | −0.0816309 | − | 0.141389i | 0.822320 | − | 0.569026i | \(-0.192680\pi\) |
−0.903951 | + | 0.427637i | \(0.859346\pi\) | |||||||
\(678\) | −1.19808e7 | −1.00095 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.87480e6 | 0.155483 | ||||||||
\(681\) | −6.98382e6 | − | 1.20963e7i | −0.577066 | − | 0.999507i | ||||
\(682\) | −4.67738e6 | + | 8.10146e6i | −0.385072 | + | 0.666964i | ||||
\(683\) | −5.99700e6 | + | 1.03871e7i | −0.491906 | + | 0.852006i | −0.999957 | − | 0.00932092i | \(-0.997033\pi\) |
0.508050 | + | 0.861327i | \(0.330366\pi\) | |||||||
\(684\) | 29174.3 | + | 50531.4i | 0.00238430 | + | 0.00412973i | ||||
\(685\) | 1.49221e7 | 1.21508 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −843854. | −0.0682143 | ||||||||
\(688\) | 5.72305e6 | + | 9.91261e6i | 0.460953 | + | 0.798393i | ||||
\(689\) | −4.98245e6 | + | 8.62986e6i | −0.399848 | + | 0.692557i | ||||
\(690\) | 2.46577e7 | − | 4.27084e7i | 1.97165 | − | 3.41500i | ||||
\(691\) | 4.33152e6 | + | 7.50242e6i | 0.345100 | + | 0.597731i | 0.985372 | − | 0.170417i | \(-0.0545115\pi\) |
−0.640272 | + | 0.768149i | \(0.721178\pi\) | |||||||
\(692\) | 7.84260e6 | 0.622579 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.83385e6 | −0.302160 | ||||||||
\(695\) | 1.96775e6 | + | 3.40824e6i | 0.154528 | + | 0.267650i | ||||
\(696\) | 1.34521e6 | − | 2.32998e6i | 0.105261 | − | 0.182318i | ||||
\(697\) | 5.18701e6 | − | 8.98416e6i | 0.404422 | − | 0.700480i | ||||
\(698\) | −1.64589e7 | − | 2.85076e7i | −1.27868 | − | 2.21474i | ||||
\(699\) | 2.93563e7 | 2.27252 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.13382e6 | −0.625172 | −0.312586 | − | 0.949889i | \(-0.601195\pi\) | ||||
−0.312586 | + | 0.949889i | \(0.601195\pi\) | |||||||
\(702\) | −1.55593e6 | − | 2.69496e6i | −0.119165 | − | 0.206400i | ||||
\(703\) | −6622.67 | + | 11470.8i | −0.000505411 | + | 0.000875397i | ||||
\(704\) | −5.62719e6 | + | 9.74658e6i | −0.427918 | + | 0.741175i | ||||
\(705\) | 1.48793e7 | + | 2.57717e7i | 1.12748 | + | 1.95286i | ||||
\(706\) | −2.48033e7 | −1.87283 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.32152e7 | 1.74056 | ||||||||
\(709\) | −1.10663e7 | − | 1.91674e7i | −0.826773 | − | 1.43201i | −0.900556 | − | 0.434739i | \(-0.856841\pi\) |
0.0737829 | − | 0.997274i | \(-0.476493\pi\) | |||||||
\(710\) | 4.50948e6 | − | 7.81064e6i | 0.335722 | − | 0.581488i | ||||
\(711\) | 7.02980e6 | − | 1.21760e7i | 0.521517 | − | 0.903295i | ||||
\(712\) | 787162. | + | 1.36341e6i | 0.0581921 | + | 0.100792i | ||||
\(713\) | −1.01930e7 | −0.750896 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.94762e6 | −0.581396 | ||||||||
\(716\) | −5.47379e6 | − | 9.48089e6i | −0.399030 | − | 0.691141i | ||||
\(717\) | 6.78444e6 | − | 1.17510e7i | 0.492852 | − | 0.853644i | ||||
\(718\) | −1.32894e7 | + | 2.30180e7i | −0.962046 | + | 1.66631i | ||||
\(719\) | 3.61598e6 | + | 6.26306e6i | 0.260858 | + | 0.451819i | 0.966470 | − | 0.256779i | \(-0.0826613\pi\) |
−0.705612 | + | 0.708598i | \(0.749328\pi\) | |||||||
\(720\) | 2.55461e7 | 1.83651 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.93506e7 | 1.38150 | ||||||||
\(723\) | 1.62562e7 | + | 2.81565e7i | 1.15657 | + | 2.00324i | ||||
\(724\) | 6.31868e6 | − | 1.09443e7i | 0.448002 | − | 0.775962i | ||||
\(725\) | 5.98556e6 | − | 1.03673e7i | 0.422921 | − | 0.732521i | ||||
\(726\) | 1.73790e6 | + | 3.01014e6i | 0.122373 | + | 0.211955i | ||||
\(727\) | −1.70200e7 | −1.19433 | −0.597163 | − | 0.802120i | \(-0.703705\pi\) | ||||
−0.597163 | + | 0.802120i | \(0.703705\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.08788e7 | −1.45508 | ||||||||
\(730\) | 2.27019e7 | + | 3.93209e7i | 1.57672 | + | 2.73097i | ||||
\(731\) | 5.69886e6 | − | 9.87071e6i | 0.394452 | − | 0.683211i | ||||
\(732\) | −9.67430e6 | + | 1.67564e7i | −0.667332 | + | 1.15585i | ||||
\(733\) | −500056. | − | 866123.i | −0.0343763 | − | 0.0595415i | 0.848325 | − | 0.529475i | \(-0.177611\pi\) |
−0.882702 | + | 0.469934i | \(0.844278\pi\) | |||||||
\(734\) | −1.53857e7 | −1.05409 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.86671e7 | −1.95070 | ||||||||
\(737\) | 1.18995e7 | + | 2.06106e7i | 0.806978 | + | 1.39773i | ||||
\(738\) | 1.13836e7 | − | 1.97170e7i | 0.769376 | − | 1.33260i | ||||
\(739\) | −1.62989e6 | + | 2.82306e6i | −0.109786 | + | 0.190155i | −0.915684 | − | 0.401900i | \(-0.868350\pi\) |
0.805897 | + | 0.592055i | \(0.201683\pi\) | |||||||
\(740\) | −2.21020e6 | − | 3.82818e6i | −0.148372 | − | 0.256988i | ||||
\(741\) | 38387.1 | 0.00256826 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.36125e7 | 0.904617 | 0.452309 | − | 0.891861i | \(-0.350601\pi\) | ||||
0.452309 | + | 0.891861i | \(0.350601\pi\) | |||||||
\(744\) | −758394. | − | 1.31358e6i | −0.0502300 | − | 0.0870008i | ||||
\(745\) | −3.74238e6 | + | 6.48199e6i | −0.247034 | + | 0.427875i | ||||
\(746\) | −1.35939e7 | + | 2.35453e7i | −0.894327 | + | 1.54902i | ||||
\(747\) | −214268. | − | 371123.i | −0.0140493 | − | 0.0243341i | ||||
\(748\) | 1.36214e7 | 0.890158 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.00092e7 | −0.649747 | ||||||||
\(751\) | −3.28272e6 | − | 5.68584e6i | −0.212390 | − | 0.367870i | 0.740072 | − | 0.672528i | \(-0.234791\pi\) |
−0.952462 | + | 0.304657i | \(0.901458\pi\) | |||||||
\(752\) | 9.44653e6 | − | 1.63619e7i | 0.609155 | − | 1.05509i | ||||
\(753\) | −3.80080e6 | + | 6.58318e6i | −0.244280 | + | 0.423105i | ||||
\(754\) | 4.93300e6 | + | 8.54421e6i | 0.315997 | + | 0.547323i | ||||
\(755\) | 3.40110e7 | 2.17146 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.62531e7 | 1.66510 | 0.832551 | − | 0.553948i | \(-0.186879\pi\) | ||||
0.832551 | + | 0.553948i | \(0.186879\pi\) | |||||||
\(758\) | −1.64622e6 | − | 2.85134e6i | −0.104068 | − | 0.180250i | ||||
\(759\) | −1.80204e7 | + | 3.12123e7i | −1.13543 | + | 1.96662i | ||||
\(760\) | −5492.76 | + | 9513.74i | −0.000344950 | + | 0.000597472i | ||||
\(761\) | 2.62555e6 | + | 4.54759e6i | 0.164346 | + | 0.284656i | 0.936423 | − | 0.350874i | \(-0.114115\pi\) |
−0.772077 | + | 0.635529i | \(0.780782\pi\) | |||||||
\(762\) | 3.58000e7 | 2.23355 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 1.64549e7 | 1.01991 | ||||||||
\(765\) | −1.27191e7 | − | 2.20300e7i | −0.785780 | − | 1.36101i | ||||
\(766\) | 1.04296e7 | − | 1.80646e7i | 0.642238 | − | 1.11239i | ||||
\(767\) | 4.28163e6 | − | 7.41601e6i | 0.262797 | − | 0.455179i | ||||
\(768\) | −1.42669e7 | − | 2.47109e7i | −0.872821 | − | 1.51177i | ||||
\(769\) | −1.77307e7 | −1.08121 | −0.540605 | − | 0.841277i | \(-0.681805\pi\) | ||||
−0.540605 | + | 0.841277i | \(0.681805\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.34156e7 | 2.63033 | ||||||||
\(772\) | −7.47907e6 | − | 1.29541e7i | −0.451653 | − | 0.782285i | ||||
\(773\) | −1.91296e6 | + | 3.31334e6i | −0.115148 | + | 0.199442i | −0.917839 | − | 0.396953i | \(-0.870068\pi\) |
0.802691 | + | 0.596395i | \(0.203401\pi\) | |||||||
\(774\) | 1.25069e7 | − | 2.16626e7i | 0.750408 | − | 1.29974i | ||||
\(775\) | −3.37449e6 | − | 5.84479e6i | −0.201815 | − | 0.349554i | ||||
\(776\) | 2.48807e6 | 0.148323 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.42406e7 | −1.43580 | ||||||||
\(779\) | 30393.6 | + | 52643.3i | 0.00179448 | + | 0.00310813i | ||||
\(780\) | −6.40550e6 | + | 1.10947e7i | −0.376979 | + | 0.652946i | ||||
\(781\) | −3.29563e6 | + | 5.70820e6i | −0.193335 | + | 0.334867i | ||||
\(782\) | 1.55884e7 | + | 2.70000e7i | 0.911561 | + | 1.57887i | ||||
\(783\) | −7.90117e6 | −0.460561 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.32980e7 | 0.770218 | ||||||||
\(786\) | −2.17346e7 | − | 3.76454e7i | −1.25486 | − | 2.17348i | ||||
\(787\) | −1.47132e7 | + | 2.54839e7i | −0.846777 | + | 1.46666i | 0.0372915 | + | 0.999304i | \(0.488127\pi\) |
−0.884069 | + | 0.467357i | \(0.845206\pi\) | |||||||
\(788\) | 4.34010e6 | − | 7.51727e6i | 0.248991 | − | 0.431265i | ||||
\(789\) | 5.38837e6 | + | 9.33293e6i | 0.308152 | + | 0.533735i | ||||
\(790\) | −2.63157e7 | −1.50020 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.00697e6 | −0.170340 | ||||||||
\(793\) | 3.56850e6 | + | 6.18082e6i | 0.201513 | + | 0.349031i | ||||
\(794\) | 2.39632e6 | − | 4.15056e6i | 0.134895 | − | 0.233644i | ||||
\(795\) | −3.45061e7 | + | 5.97663e7i | −1.93632 | + | 3.35381i | ||||
\(796\) | 8.60512e6 | + | 1.49045e7i | 0.481365 | + | 0.833749i | ||||
\(797\) | 1.35805e7 | 0.757305 | 0.378653 | − | 0.925539i | \(-0.376387\pi\) | ||||
0.378653 | + | 0.925539i | \(0.376387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.88132e7 | −1.04255 | ||||||||
\(800\) | −9.49050e6 | − | 1.64380e7i | −0.524281 | − | 0.908082i | ||||
\(801\) | 1.06806e7 | − | 1.84993e7i | 0.588184 | − | 1.01876i | ||||
\(802\) | 1.10280e7 | − | 1.91010e7i | 0.605424 | − | 1.04862i | ||||
\(803\) | −1.65911e7 | − | 2.87367e7i | −0.908002 | − | 1.57271i | ||||
\(804\) | 3.83624e7 | 2.09299 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.56218e6 | 0.301583 | ||||||||
\(807\) | −4.90313e6 | − | 8.49247e6i | −0.265027 | − | 0.459039i | ||||
\(808\) | −205389. | + | 355745.i | −0.0110675 | + | 0.0191695i | ||||
\(809\) | 5.78569e6 | − | 1.00211e7i | 0.310802 | − | 0.538325i | −0.667734 | − | 0.744400i | \(-0.732736\pi\) |
0.978536 | + | 0.206075i | \(0.0660691\pi\) | |||||||
\(810\) | 1.10963e7 | + | 1.92194e7i | 0.594247 | + | 1.02927i | ||||
\(811\) | −3.52530e6 | −0.188210 | −0.0941052 | − | 0.995562i | \(-0.529999\pi\) | ||||
−0.0941052 | + | 0.995562i | \(0.529999\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.11756e7 | −1.12360 | ||||||||
\(814\) | 3.39301e6 | + | 5.87686e6i | 0.179483 | + | 0.310874i | ||||
\(815\) | 9.04711e6 | − | 1.56700e7i | 0.477107 | − | 0.826373i | ||||
\(816\) | −1.44023e7 | + | 2.49455e7i | −0.757193 | + | 1.31150i | ||||
\(817\) | 33392.8 | + | 57838.1i | 0.00175024 | + | 0.00303151i | ||||
\(818\) | −1.78457e7 | −0.932505 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.02867e7 | −1.05360 | ||||||||
\(821\) | −8.94756e6 | − | 1.54976e7i | −0.463283 | − | 0.802430i | 0.535839 | − | 0.844320i | \(-0.319995\pi\) |
−0.999122 | + | 0.0418900i | \(0.986662\pi\) | |||||||
\(822\) | −1.84629e7 | + | 3.19787e7i | −0.953062 | + | 1.65075i | ||||
\(823\) | 1.80710e7 | − | 3.12999e7i | 0.930001 | − | 1.61081i | 0.146686 | − | 0.989183i | \(-0.453139\pi\) |
0.783315 | − | 0.621626i | \(-0.213527\pi\) | |||||||
\(824\) | −363113. | − | 628931.i | −0.0186305 | − | 0.0322689i | ||||
\(825\) | −2.38633e7 | −1.22066 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.00605e7 | −0.511512 | −0.255756 | − | 0.966741i | \(-0.582324\pi\) | ||||
−0.255756 | + | 0.966741i | \(0.582324\pi\) | |||||||
\(828\) | 1.62864e7 | + | 2.82088e7i | 0.825559 | + | 1.42991i | ||||
\(829\) | −1.01827e7 | + | 1.76369e7i | −0.514607 | + | 0.891326i | 0.485249 | + | 0.874376i | \(0.338729\pi\) |
−0.999856 | + | 0.0169502i | \(0.994604\pi\) | |||||||
\(830\) | −401051. | + | 694641.i | −0.0202071 | + | 0.0349998i | ||||
\(831\) | 5.26395e6 | + | 9.11742e6i | 0.264429 | + | 0.458004i | ||||
\(832\) | 6.69166e6 | 0.335140 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −9.73865e6 | −0.484823 | ||||||||
\(835\) | 4.34631e6 | + | 7.52804e6i | 0.215727 | + | 0.373650i | ||||
\(836\) | −39907.7 | + | 69122.2i | −0.00197488 | + | 0.00342059i | ||||
\(837\) | −2.22723e6 | + | 3.85767e6i | −0.109888 | + | 0.190332i | ||||
\(838\) | −1.03655e7 | − | 1.79536e7i | −0.509895 | − | 0.883163i | ||||
\(839\) | −5.95014e6 | −0.291825 | −0.145912 | − | 0.989298i | \(-0.546612\pi\) | ||||
−0.145912 | + | 0.989298i | \(0.546612\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.53905e6 | 0.221297 | ||||||||
\(842\) | 1.14754e7 | + | 1.98760e7i | 0.557812 | + | 0.966159i | ||||
\(843\) | 9.03726e6 | − | 1.56530e7i | 0.437994 | − | 0.758627i | ||||
\(844\) | 2.04305e6 | − | 3.53867e6i | 0.0987242 | − | 0.170995i | ||||
\(845\) | −1.14262e7 | − | 1.97907e7i | −0.550503 | − | 0.953499i | ||||
\(846\) | −4.12881e7 | −1.98335 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.38143e7 | 2.09231 | ||||||||
\(849\) | 2.50731e7 | + | 4.34279e7i | 1.19382 | + | 2.06776i | ||||
\(850\) | −1.03214e7 | + | 1.78771e7i | −0.489993 | + | 0.848694i | ||||
\(851\) | −3.69705e6 | + | 6.40348e6i | −0.174997 | + | 0.303105i | ||||
\(852\) | 5.31233e6 | + | 9.20122e6i | 0.250718 | + | 0.434257i | ||||
\(853\) | 1.59836e7 | 0.752146 | 0.376073 | − | 0.926590i | \(-0.377274\pi\) | ||||
0.376073 | + | 0.926590i | \(0.377274\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 149056. | 0.00697325 | ||||||||
\(856\) | −94046.2 | − | 162893.i | −0.00438689 | − | 0.00759831i | ||||
\(857\) | 1.17296e6 | − | 2.03162e6i | 0.0545544 | − | 0.0944910i | −0.837459 | − | 0.546501i | \(-0.815959\pi\) |
0.892013 | + | 0.452010i | \(0.149293\pi\) | |||||||
\(858\) | 9.83347e6 | − | 1.70321e7i | 0.456025 | − | 0.789858i | ||||
\(859\) | 6.51117e6 | + | 1.12777e7i | 0.301076 | + | 0.521479i | 0.976380 | − | 0.216061i | \(-0.0693209\pi\) |
−0.675304 | + | 0.737540i | \(0.735988\pi\) | |||||||
\(860\) | −2.22886e7 | −1.02763 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.91130e7 | 0.876112 | ||||||||
\(863\) | −9.83442e6 | − | 1.70337e7i | −0.449492 | − | 0.778542i | 0.548861 | − | 0.835913i | \(-0.315061\pi\) |
−0.998353 | + | 0.0573712i | \(0.981728\pi\) | |||||||
\(864\) | −6.26391e6 | + | 1.08494e7i | −0.285471 | + | 0.494450i | ||||
\(865\) | 1.00173e7 | − | 1.73504e7i | 0.455207 | − | 0.788442i | ||||
\(866\) | −8.27296e6 | − | 1.43292e7i | −0.374857 | − | 0.649272i | ||||
\(867\) | −4.71019e6 | −0.212809 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.92322e7 | 0.863931 | ||||||||
\(870\) | 3.41636e7 | + | 5.91732e7i | 1.53026 | + | 2.65049i | ||||
\(871\) | 7.07526e6 | − | 1.22547e7i | 0.316007 | − | 0.547341i | ||||
\(872\) | 126494. | − | 219094.i | 0.00563351 | − | 0.00975752i | ||||
\(873\) | −1.68796e7 | − | 2.92363e7i | −0.749594 | − | 1.29834i | ||||
\(874\) | −182683. | −0.00808946 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −5.34874e7 | −2.35500 | ||||||||
\(877\) | −1.17291e7 | − | 2.03153e7i | −0.514950 | − | 0.891919i | −0.999849 | − | 0.0173491i | \(-0.994477\pi\) |
0.484900 | − | 0.874570i | \(-0.338856\pi\) | |||||||
\(878\) | 1.81608e7 | − | 3.14555e7i | 0.795059 | − | 1.37708i | ||||
\(879\) | 2.85362e7 | − | 4.94261e7i | 1.24573 | − | 2.15767i | ||||
\(880\) | 1.74723e7 | + | 3.02629e7i | 0.760577 | + | 1.31736i | ||||
\(881\) | 4.59257e6 | 0.199350 | 0.0996750 | − | 0.995020i | \(-0.468220\pi\) | ||||
0.0996750 | + | 0.995020i | \(0.468220\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.23402e7 | −0.532622 | −0.266311 | − | 0.963887i | \(-0.585805\pi\) | ||||
−0.266311 | + | 0.963887i | \(0.585805\pi\) | |||||||
\(884\) | −4.04952e6 | − | 7.01397e6i | −0.174290 | − | 0.301879i | ||||
\(885\) | 2.96526e7 | − | 5.13598e7i | 1.27264 | − | 2.20427i | ||||
\(886\) | 1.73074e7 | − | 2.99774e7i | 0.740711 | − | 1.28295i | ||||
\(887\) | −6.82772e6 | − | 1.18259e7i | −0.291384 | − | 0.504693i | 0.682753 | − | 0.730649i | \(-0.260783\pi\) |
−0.974137 | + | 0.225957i | \(0.927449\pi\) | |||||||
\(888\) | −1.10029e6 | −0.0468247 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −3.99822e7 | −1.69197 | ||||||||
\(891\) | −8.10946e6 | − | 1.40460e7i | −0.342214 | − | 0.592732i | ||||
\(892\) | −7131.11 | + | 12351.5i | −0.000300086 | + | 0.000519764i | ||||
\(893\) | 55118.6 | − | 95468.3i | 0.00231297 | − | 0.00400618i | ||||
\(894\) | −9.26077e6 | − | 1.60401e7i | −0.387528 | − | 0.671218i | ||||
\(895\) | −2.79665e7 | −1.16703 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.14293e7 | 0.889255 | ||||||||
\(898\) | −2.61872e7 | − | 4.53575e7i | −1.08367 | − | 1.87698i | ||||
\(899\) | 7.06130e6 | − | 1.22305e7i | 0.291397 | − | 0.504715i | ||||
\(900\) | −1.07835e7 | + | 1.86775e7i | −0.443765 | + | 0.768623i | ||||
\(901\) | −2.18145e7 | − | 3.77839e7i | −0.895229 | − | 1.55058i | ||||
\(902\) | 3.11433e7 | 1.27453 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.48987e6 | 0.0606355 | ||||||||
\(905\) | −1.61416e7 | − | 2.79580e7i | −0.655125 | − | 1.13471i | ||||
\(906\) | −4.20812e7 | + | 7.28868e7i | −1.70321 | + | 2.95004i | ||||
\(907\) | −3.69800e6 | + | 6.40512e6i | −0.149262 | + | 0.258529i | −0.930955 | − | 0.365134i | \(-0.881023\pi\) |
0.781693 | + | 0.623663i | \(0.214356\pi\) | |||||||
\(908\) | −8.63390e6 | − | 1.49544e7i | −0.347530 | − | 0.601940i | ||||
\(909\) | 5.57362e6 | 0.223732 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.51041e7 | −1.40140 | −0.700699 | − | 0.713457i | \(-0.747129\pi\) | ||||
−0.700699 | + | 0.713457i | \(0.747129\pi\) | |||||||
\(912\) | −84391.3 | − | 146170.i | −0.00335978 | − | 0.00581930i | ||||
\(913\) | 293098. | − | 507660.i | 0.0116369 | − | 0.0201556i | ||||
\(914\) | −2.29898e7 | + | 3.98194e7i | −0.910267 | + | 1.57663i | ||||
\(915\) | 2.47138e7 | + | 4.28055e7i | 0.975857 | + | 1.69023i | ||||
\(916\) | −1.04323e6 | −0.0410812 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.36246e7 | 0.533602 | ||||||||
\(919\) | 2.40668e7 | + | 4.16850e7i | 0.940005 | + | 1.62814i | 0.765455 | + | 0.643489i | \(0.222514\pi\) |
0.174550 | + | 0.984648i | \(0.444153\pi\) | |||||||
\(920\) | −3.06629e6 | + | 5.31097e6i | −0.119438 | + | 0.206873i | ||||
\(921\) | −2.87313e7 | + | 4.97640e7i | −1.11611 | + | 1.93315i | ||||
\(922\) | 6.04747e6 | + | 1.04745e7i | 0.234286 | + | 0.405795i | ||||
\(923\) | 3.91905e6 | 0.151418 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.89577e6 | −0.188134 | ||||||||
\(926\) | −1.53865e7 | − | 2.66501e7i | −0.589673 | − | 1.02134i | ||||
\(927\) | −4.92688e6 | + | 8.53361e6i | −0.188310 | + | 0.326162i | ||||
\(928\) | 1.98594e7 | − | 3.43975e7i | 0.757000 | − | 1.31116i | ||||
\(929\) | 9.18009e6 | + | 1.59004e7i | 0.348986 | + | 0.604461i | 0.986070 | − | 0.166334i | \(-0.0531929\pi\) |
−0.637084 | + | 0.770794i | \(0.719860\pi\) | |||||||
\(930\) | 3.85210e7 | 1.46046 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.62924e7 | 1.36860 | ||||||||
\(933\) | 1.35778e7 | + | 2.35175e7i | 0.510654 | + | 0.884479i | ||||
\(934\) | −2.66332e7 | + | 4.61301e7i | −0.998980 | + | 1.73028i | ||||
\(935\) | 1.73984e7 | − | 3.01350e7i | 0.650850 | − | 1.12731i | ||||
\(936\) | 893947. | + | 1.54836e6i | 0.0333520 | + | 0.0577674i | ||||
\(937\) | 2.27081e7 | 0.844951 | 0.422475 | − | 0.906374i | \(-0.361161\pi\) | ||||
0.422475 | + | 0.906374i | \(0.361161\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.89718e7 | −1.44240 | ||||||||
\(940\) | 1.83949e7 | + | 3.18609e7i | 0.679012 | + | 1.17608i | ||||
\(941\) | −2.07901e7 | + | 3.60095e7i | −0.765389 | + | 1.32569i | 0.174652 | + | 0.984630i | \(0.444120\pi\) |
−0.940041 | + | 0.341062i | \(0.889213\pi\) | |||||||
\(942\) | −1.64535e7 | + | 2.84982e7i | −0.604130 | + | 1.04638i | ||||
\(943\) | 1.69670e7 | + | 2.93877e7i | 0.621336 | + | 1.07619i | ||||
\(944\) | −3.76515e7 | −1.37516 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.42165e7 | 1.24310 | ||||||||
\(947\) | −7.76705e6 | − | 1.34529e7i | −0.281437 | − | 0.487463i | 0.690302 | − | 0.723521i | \(-0.257478\pi\) |
−0.971739 | + | 0.236058i | \(0.924144\pi\) | |||||||
\(948\) | 1.55005e7 | − | 2.68476e7i | 0.560175 | − | 0.970251i | ||||
\(949\) | −9.86479e6 | + | 1.70863e7i | −0.355568 | + | 0.615861i | ||||
\(950\) | −60478.8 | − | 104752.i | −0.00217417 | − | 0.00376578i | ||||
\(951\) | 1.93172e7 | 0.692618 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.94908e7 | 1.40852 | 0.704262 | − | 0.709940i | \(-0.251278\pi\) | ||||
0.704262 | + | 0.709940i | \(0.251278\pi\) | |||||||
\(954\) | −4.78749e7 | − | 8.29218e7i | −1.70309 | − | 2.94984i | ||||
\(955\) | 2.10177e7 | − | 3.64037e7i | 0.745721 | − | 1.29163i | ||||
\(956\) | 8.38742e6 | − | 1.45274e7i | 0.296813 | − | 0.514096i | ||||
\(957\) | −2.49676e7 | − | 4.32452e7i | −0.881246 | − | 1.52636i | ||||
\(958\) | 4.06701e7 | 1.43173 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 4.63433e7 | 1.62296 | ||||||||
\(961\) | 1.03336e7 | + | 1.78983e7i | 0.360947 | + | 0.625179i | ||||
\(962\) | 2.01742e6 | − | 3.49428e6i | 0.0702845 | − | 0.121736i | ||||
\(963\) | −1.27606e6 | + | 2.21020e6i | −0.0443410 | + | 0.0768008i | ||||
\(964\) | 2.00970e7 | + | 3.48091e7i | 0.696529 | + | 1.20642i | ||||
\(965\) | −3.82118e7 | −1.32093 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.87472e7 | −0.644718 | −0.322359 | − | 0.946617i | \(-0.604476\pi\) | ||||
−0.322359 | + | 0.946617i | \(0.604476\pi\) | |||||||
\(968\) | −216116. | − | 374323.i | −0.00741306 | − | 0.0128398i | ||||
\(969\) | −84034.5 | + | 145552.i | −0.00287507 | + | 0.00497977i | ||||
\(970\) | −3.15940e7 | + | 5.47224e7i | −1.07814 | + | 1.86739i | ||||
\(971\) | 2.67712e7 | + | 4.63690e7i | 0.911211 | + | 1.57826i | 0.812356 | + | 0.583162i | \(0.198185\pi\) |
0.0988552 | + | 0.995102i | \(0.468482\pi\) | |||||||
\(972\) | −3.72974e7 | −1.26623 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.21132e6 | 0.0409131 | ||||||||
\(975\) | 7.09435e6 | + | 1.22878e7i | 0.239002 | + | 0.413963i | ||||
\(976\) | 1.56902e7 | − | 2.71762e7i | 0.527235 | − | 0.913197i | ||||
\(977\) | −2.23052e7 | + | 3.86337e7i | −0.747600 | + | 1.29488i | 0.201370 | + | 0.979515i | \(0.435461\pi\) |
−0.948970 | + | 0.315366i | \(0.897873\pi\) | |||||||
\(978\) | 2.23877e7 | + | 3.87766e7i | 0.748449 | + | 1.29635i | ||||
\(979\) | 2.92200e7 | 0.974368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.43265e6 | −0.113883 | ||||||||
\(982\) | −6.32828e6 | − | 1.09609e7i | −0.209415 | − | 0.362717i | ||||
\(983\) | 1.00034e7 | − | 1.73264e7i | 0.330190 | − | 0.571906i | −0.652359 | − | 0.757910i | \(-0.726221\pi\) |
0.982549 | + | 0.186004i | \(0.0595538\pi\) | |||||||
\(984\) | −2.52480e6 | + | 4.37309e6i | −0.0831265 | + | 0.143979i | ||||
\(985\) | −1.10871e7 | − | 1.92035e7i | −0.364106 | − | 0.630651i | ||||
\(986\) | −4.31961e7 | −1.41498 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 47456.9 | 0.00154670 | ||||||||
\(989\) | 1.86413e7 | + | 3.22877e7i | 0.606018 | + | 1.04965i | ||||
\(990\) | 3.81832e7 | − | 6.61353e7i | 1.23818 | − | 2.14459i | ||||
\(991\) | −1.62317e7 | + | 2.81142e7i | −0.525026 | + | 0.909371i | 0.474550 | + | 0.880229i | \(0.342611\pi\) |
−0.999575 | + | 0.0291424i | \(0.990722\pi\) | |||||||
\(992\) | −1.11962e7 | − | 1.93923e7i | −0.361235 | − | 0.625678i | ||||
\(993\) | −2.25004e6 | −0.0724130 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.39649e7 | 1.40783 | ||||||||
\(996\) | −472453. | − | 818312.i | −0.0150907 | − | 0.0261379i | ||||
\(997\) | −1.39470e7 | + | 2.41569e7i | −0.444368 | + | 0.769668i | −0.998008 | − | 0.0630881i | \(-0.979905\pi\) |
0.553640 | + | 0.832756i | \(0.313238\pi\) | |||||||
\(998\) | 1.60472e7 | − | 2.77946e7i | 0.510004 | − | 0.883353i | ||||
\(999\) | 1.61565e6 | + | 2.79839e6i | 0.0512193 | + | 0.0887144i |
(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 | 49.6.c.h.18.3 | 8 | ||
7.2 | even | 3 | inner | 49.6.c.h.30.3 | 8 | ||
7.3 | odd | 6 | 49.6.a.g.1.1 | ✓ | 4 | ||
7.4 | even | 3 | 49.6.a.g.1.2 | yes | 4 | ||
7.5 | odd | 6 | inner | 49.6.c.h.30.4 | 8 | ||
7.6 | odd | 2 | inner | 49.6.c.h.18.4 | 8 | ||
21.11 | odd | 6 | 441.6.a.z.1.4 | 4 | |||
21.17 | even | 6 | 441.6.a.z.1.3 | 4 | |||
28.3 | even | 6 | 784.6.a.bf.1.4 | 4 | |||
28.11 | odd | 6 | 784.6.a.bf.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
49.6.a.g.1.1 | ✓ | 4 | 7.3 | odd | 6 | ||
49.6.a.g.1.2 | yes | 4 | 7.4 | even | 3 | ||
49.6.c.h.18.3 | 8 | 1.1 | even | 1 | trivial | ||
49.6.c.h.18.4 | 8 | 7.6 | odd | 2 | inner | ||
49.6.c.h.30.3 | 8 | 7.2 | even | 3 | inner | ||
49.6.c.h.30.4 | 8 | 7.5 | odd | 6 | inner | ||
441.6.a.z.1.3 | 4 | 21.17 | even | 6 | |||
441.6.a.z.1.4 | 4 | 21.11 | odd | 6 | |||
784.6.a.bf.1.1 | 4 | 28.11 | odd | 6 | |||
784.6.a.bf.1.4 | 4 | 28.3 | even | 6 |