Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [33,6,Mod(32,33)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(33, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("33.32");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 33 = 3 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 33.d (of order \(2\), degree \(1\), 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: | \(5.29266605383\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} - 2121785838 x^{9} + 37710373995 x^{8} - 835758339660 x^{7} + \cdots + 92\!\cdots\!40 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 32.4 | ||
Root | \(-23.0756 - 10.4175i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 33.32 |
Dual form | 33.6.d.b.32.3 |
$q$-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 \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).
\(n\) | \(13\) | \(23\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.47928 | −1.49894 | −0.749469 | − | 0.662039i | \(-0.769691\pi\) | ||||
−0.749469 | + | 0.662039i | \(0.769691\pi\) | |||||||
\(3\) | 11.5964 | + | 10.4175i | 0.743906 | + | 0.668284i | ||||
\(4\) | 39.8981 | 1.24682 | ||||||||
\(5\) | − | 35.7023i | − | 0.638662i | −0.947643 | − | 0.319331i | \(-0.896542\pi\) | ||
0.947643 | − | 0.319331i | \(-0.103458\pi\) | |||||||
\(6\) | −98.3287 | − | 88.3330i | −1.11507 | − | 1.00172i | ||||
\(7\) | 11.5666i | 0.0892193i | 0.999004 | + | 0.0446096i | \(0.0142044\pi\) | ||||
−0.999004 | + | 0.0446096i | \(0.985796\pi\) | |||||||
\(8\) | −66.9703 | −0.369962 | ||||||||
\(9\) | 25.9508 | + | 241.610i | 0.106793 | + | 0.994281i | ||||
\(10\) | 302.729i | 0.957315i | ||||||||
\(11\) | 202.832 | + | 346.281i | 0.505422 | + | 0.862873i | ||||
\(12\) | 462.673 | + | 415.639i | 0.927514 | + | 0.833227i | ||||
\(13\) | 933.326i | 1.53170i | 0.643017 | + | 0.765852i | \(0.277683\pi\) | ||||
−0.643017 | + | 0.765852i | \(0.722317\pi\) | |||||||
\(14\) | − | 98.0760i | − | 0.133734i | ||||||
\(15\) | 371.929 | − | 414.016i | 0.426807 | − | 0.475105i | ||||
\(16\) | −708.880 | −0.692266 | ||||||||
\(17\) | 25.0813 | 0.0210488 | 0.0105244 | − | 0.999945i | \(-0.496650\pi\) | ||||
0.0105244 | + | 0.999945i | \(0.496650\pi\) | |||||||
\(18\) | −220.044 | − | 2048.68i | −0.160077 | − | 1.49037i | ||||
\(19\) | 743.695i | 0.472619i | 0.971678 | + | 0.236309i | \(0.0759379\pi\) | ||||
−0.971678 | + | 0.236309i | \(0.924062\pi\) | |||||||
\(20\) | − | 1424.45i | − | 0.796294i | ||||||
\(21\) | −120.495 | + | 134.130i | −0.0596238 | + | 0.0663708i | ||||
\(22\) | −1719.86 | − | 2936.21i | −0.757596 | − | 1.29339i | ||||
\(23\) | 594.979i | 0.234521i | 0.993101 | + | 0.117261i | \(0.0374113\pi\) | ||||
−0.993101 | + | 0.117261i | \(0.962589\pi\) | |||||||
\(24\) | −776.611 | − | 697.664i | −0.275217 | − | 0.247240i | ||||
\(25\) | 1850.35 | 0.592111 | ||||||||
\(26\) | − | 7913.93i | − | 2.29593i | ||||||
\(27\) | −2216.04 | + | 3072.14i | −0.585018 | + | 0.811020i | ||||
\(28\) | 461.484i | 0.111240i | ||||||||
\(29\) | 3975.05 | 0.877702 | 0.438851 | − | 0.898560i | \(-0.355386\pi\) | ||||
0.438851 | + | 0.898560i | \(0.355386\pi\) | |||||||
\(30\) | −3153.69 | + | 3510.56i | −0.639758 | + | 0.712152i | ||||
\(31\) | −3071.33 | −0.574014 | −0.287007 | − | 0.957928i | \(-0.592660\pi\) | ||||
−0.287007 | + | 0.957928i | \(0.592660\pi\) | |||||||
\(32\) | 8153.84 | 1.40763 | ||||||||
\(33\) | −1255.28 | + | 6128.59i | −0.200657 | + | 0.979661i | ||||
\(34\) | −212.671 | −0.0315509 | ||||||||
\(35\) | 412.952 | 0.0569810 | ||||||||
\(36\) | 1035.39 | + | 9639.80i | 0.133152 | + | 1.23969i | ||||
\(37\) | 10317.8 | 1.23904 | 0.619519 | − | 0.784982i | \(-0.287328\pi\) | ||||
0.619519 | + | 0.784982i | \(0.287328\pi\) | |||||||
\(38\) | − | 6306.00i | − | 0.708426i | ||||||
\(39\) | −9722.94 | + | 10823.2i | −1.02361 | + | 1.13944i | ||||
\(40\) | 2390.99i | 0.236281i | ||||||||
\(41\) | −17759.6 | −1.64996 | −0.824982 | − | 0.565160i | \(-0.808815\pi\) | ||||
−0.824982 | + | 0.565160i | \(0.808815\pi\) | |||||||
\(42\) | 1021.71 | − | 1137.32i | 0.0893724 | − | 0.0994857i | ||||
\(43\) | − | 22910.3i | − | 1.88956i | −0.327711 | − | 0.944778i | \(-0.606277\pi\) | ||
0.327711 | − | 0.944778i | \(-0.393723\pi\) | |||||||
\(44\) | 8092.60 | + | 13815.9i | 0.630168 | + | 1.07584i | ||||
\(45\) | 8626.04 | − | 926.502i | 0.635009 | − | 0.0682048i | ||||
\(46\) | − | 5044.99i | − | 0.351533i | ||||||
\(47\) | 3402.05i | 0.224644i | 0.993672 | + | 0.112322i | \(0.0358289\pi\) | ||||
−0.993672 | + | 0.112322i | \(0.964171\pi\) | |||||||
\(48\) | −8220.42 | − | 7384.77i | −0.514981 | − | 0.462630i | ||||
\(49\) | 16673.2 | 0.992040 | ||||||||
\(50\) | −15689.6 | −0.887538 | ||||||||
\(51\) | 290.852 | + | 261.285i | 0.0156584 | + | 0.0140666i | ||||
\(52\) | 37238.0i | 1.90975i | ||||||||
\(53\) | − | 12325.8i | − | 0.602734i | −0.953508 | − | 0.301367i | \(-0.902557\pi\) | ||
0.953508 | − | 0.301367i | \(-0.0974430\pi\) | |||||||
\(54\) | 18790.5 | − | 26049.5i | 0.876906 | − | 1.21567i | ||||
\(55\) | 12363.0 | − | 7241.55i | 0.551084 | − | 0.322794i | ||||
\(56\) | − | 774.615i | − | 0.0330078i | ||||||
\(57\) | −7747.46 | + | 8624.15i | −0.315844 | + | 0.351584i | ||||
\(58\) | −33705.5 | −1.31562 | ||||||||
\(59\) | 30346.5i | 1.13496i | 0.823389 | + | 0.567478i | \(0.192081\pi\) | ||||
−0.823389 | + | 0.567478i | \(0.807919\pi\) | |||||||
\(60\) | 14839.3 | − | 16518.5i | 0.532150 | − | 0.592368i | ||||
\(61\) | 36444.5i | 1.25403i | 0.779008 | + | 0.627014i | \(0.215723\pi\) | ||||
−0.779008 | + | 0.627014i | \(0.784277\pi\) | |||||||
\(62\) | 26042.7 | 0.860412 | ||||||||
\(63\) | −2794.60 | + | 300.161i | −0.0887091 | + | 0.00952803i | ||||
\(64\) | −46454.5 | −1.41768 | ||||||||
\(65\) | 33321.9 | 0.978241 | ||||||||
\(66\) | 10643.9 | − | 51966.0i | 0.300773 | − | 1.46845i | ||||
\(67\) | −28572.0 | −0.777595 | −0.388798 | − | 0.921323i | \(-0.627109\pi\) | ||||
−0.388798 | + | 0.921323i | \(0.627109\pi\) | |||||||
\(68\) | 1000.70 | 0.0262440 | ||||||||
\(69\) | −6198.20 | + | 6899.59i | −0.156727 | + | 0.174462i | ||||
\(70\) | −3501.54 | −0.0854109 | ||||||||
\(71\) | − | 59302.3i | − | 1.39613i | −0.716035 | − | 0.698065i | \(-0.754045\pi\) | ||
0.716035 | − | 0.698065i | \(-0.245955\pi\) | |||||||
\(72\) | −1737.93 | − | 16180.7i | −0.0395095 | − | 0.367846i | ||||
\(73\) | − | 72406.9i | − | 1.59028i | −0.606428 | − | 0.795139i | \(-0.707398\pi\) | ||
0.606428 | − | 0.795139i | \(-0.292602\pi\) | |||||||
\(74\) | −87487.9 | −1.85724 | ||||||||
\(75\) | 21457.3 | + | 19276.0i | 0.440475 | + | 0.395698i | ||||
\(76\) | 29672.0i | 0.589269i | ||||||||
\(77\) | −4005.27 | + | 2346.06i | −0.0769849 | + | 0.0450934i | ||||
\(78\) | 82443.5 | − | 91772.7i | 1.53433 | − | 1.70796i | ||||
\(79\) | 26947.6i | 0.485794i | 0.970052 | + | 0.242897i | \(0.0780978\pi\) | ||||
−0.970052 | + | 0.242897i | \(0.921902\pi\) | |||||||
\(80\) | 25308.6i | 0.442124i | ||||||||
\(81\) | −57702.1 | + | 12540.0i | −0.977190 | + | 0.212365i | ||||
\(82\) | 150589. | 2.47319 | ||||||||
\(83\) | −32457.1 | −0.517148 | −0.258574 | − | 0.965991i | \(-0.583253\pi\) | ||||
−0.258574 | + | 0.965991i | \(0.583253\pi\) | |||||||
\(84\) | −4807.51 | + | 5351.53i | −0.0743399 | + | 0.0827522i | ||||
\(85\) | − | 895.460i | − | 0.0134431i | ||||||
\(86\) | 194263.i | 2.83233i | ||||||||
\(87\) | 46096.0 | + | 41410.1i | 0.652928 | + | 0.586554i | ||||
\(88\) | −13583.7 | − | 23190.5i | −0.186987 | − | 0.319230i | ||||
\(89\) | − | 10808.1i | − | 0.144635i | −0.997382 | − | 0.0723176i | \(-0.976960\pi\) | ||
0.997382 | − | 0.0723176i | \(-0.0230395\pi\) | |||||||
\(90\) | −73142.6 | + | 7856.07i | −0.951840 | + | 0.102235i | ||||
\(91\) | −10795.4 | −0.136658 | ||||||||
\(92\) | 23738.5i | 0.292405i | ||||||||
\(93\) | −35616.3 | − | 31995.7i | −0.427013 | − | 0.383605i | ||||
\(94\) | − | 28846.9i | − | 0.336728i | ||||||
\(95\) | 26551.6 | 0.301844 | ||||||||
\(96\) | 94554.8 | + | 84942.7i | 1.04714 | + | 0.940694i | ||||
\(97\) | −105449. | −1.13792 | −0.568962 | − | 0.822364i | \(-0.692655\pi\) | ||||
−0.568962 | + | 0.822364i | \(0.692655\pi\) | |||||||
\(98\) | −141377. | −1.48701 | ||||||||
\(99\) | −78401.4 | + | 57992.5i | −0.803962 | + | 0.594680i | ||||
\(100\) | 73825.4 | 0.738254 | ||||||||
\(101\) | 158525. | 1.54630 | 0.773150 | − | 0.634223i | \(-0.218680\pi\) | ||||
0.773150 | + | 0.634223i | \(0.218680\pi\) | |||||||
\(102\) | −2466.21 | − | 2215.51i | −0.0234709 | − | 0.0210849i | ||||
\(103\) | 116352. | 1.08064 | 0.540321 | − | 0.841459i | \(-0.318303\pi\) | ||||
0.540321 | + | 0.841459i | \(0.318303\pi\) | |||||||
\(104\) | − | 62505.1i | − | 0.566673i | ||||||
\(105\) | 4788.74 | + | 4301.94i | 0.0423885 | + | 0.0380795i | ||||
\(106\) | 104514.i | 0.903462i | ||||||||
\(107\) | 46004.0 | 0.388451 | 0.194225 | − | 0.980957i | \(-0.437781\pi\) | ||||
0.194225 | + | 0.980957i | \(0.437781\pi\) | |||||||
\(108\) | −88416.0 | + | 122573.i | −0.729410 | + | 1.01119i | ||||
\(109\) | − | 121732.i | − | 0.981385i | −0.871333 | − | 0.490693i | \(-0.836744\pi\) | ||
0.871333 | − | 0.490693i | \(-0.163256\pi\) | |||||||
\(110\) | −104829. | + | 61403.1i | −0.826041 | + | 0.483848i | ||||
\(111\) | 119649. | + | 107486.i | 0.921728 | + | 0.828029i | ||||
\(112\) | − | 8199.30i | − | 0.0617635i | ||||||
\(113\) | − | 191518.i | − | 1.41096i | −0.708731 | − | 0.705479i | \(-0.750732\pi\) | ||
0.708731 | − | 0.705479i | \(-0.249268\pi\) | |||||||
\(114\) | 65692.8 | − | 73126.6i | 0.473430 | − | 0.527003i | ||||
\(115\) | 21242.1 | 0.149780 | ||||||||
\(116\) | 158597. | 1.09433 | ||||||||
\(117\) | −225501. | + | 24220.5i | −1.52295 | + | 0.163576i | ||||
\(118\) | − | 257316.i | − | 1.70123i | ||||||
\(119\) | 290.104i | 0.00187796i | ||||||||
\(120\) | −24908.2 | + | 27726.8i | −0.157903 | + | 0.175771i | ||||
\(121\) | −78769.7 | + | 140473.i | −0.489098 | + | 0.872229i | ||||
\(122\) | − | 309023.i | − | 1.87971i | ||||||
\(123\) | −205947. | − | 185011.i | −1.22742 | − | 1.10264i | ||||
\(124\) | −122540. | −0.715690 | ||||||||
\(125\) | − | 177631.i | − | 1.01682i | ||||||
\(126\) | 23696.2 | − | 2545.15i | 0.132969 | − | 0.0142819i | ||||
\(127\) | − | 74201.3i | − | 0.408227i | −0.978947 | − | 0.204114i | \(-0.934569\pi\) | ||
0.978947 | − | 0.204114i | \(-0.0654312\pi\) | |||||||
\(128\) | 132978. | 0.717387 | ||||||||
\(129\) | 238668. | − | 265676.i | 1.26276 | − | 1.40565i | ||||
\(130\) | −282545. | −1.46632 | ||||||||
\(131\) | −88605.0 | −0.451107 | −0.225554 | − | 0.974231i | \(-0.572419\pi\) | ||||
−0.225554 | + | 0.974231i | \(0.572419\pi\) | |||||||
\(132\) | −50083.2 | + | 244519.i | −0.250183 | + | 1.22146i | ||||
\(133\) | −8601.99 | −0.0421667 | ||||||||
\(134\) | 242270. | 1.16557 | ||||||||
\(135\) | 109682. | + | 79117.9i | 0.517968 | + | 0.373629i | ||||
\(136\) | −1679.70 | −0.00778727 | ||||||||
\(137\) | − | 176386.i | − | 0.802904i | −0.915880 | − | 0.401452i | \(-0.868506\pi\) | ||
0.915880 | − | 0.401452i | \(-0.131494\pi\) | |||||||
\(138\) | 52556.3 | − | 58503.5i | 0.234924 | − | 0.261507i | ||||
\(139\) | 385558.i | 1.69259i | 0.532712 | + | 0.846297i | \(0.321173\pi\) | ||||
−0.532712 | + | 0.846297i | \(0.678827\pi\) | |||||||
\(140\) | 16476.0 | 0.0710448 | ||||||||
\(141\) | −35440.9 | + | 39451.3i | −0.150126 | + | 0.167114i | ||||
\(142\) | 502841.i | 2.09271i | ||||||||
\(143\) | −323193. | + | 189308.i | −1.32167 | + | 0.774157i | ||||
\(144\) | −18396.0 | − | 171273.i | −0.0739294 | − | 0.688307i | ||||
\(145\) | − | 141918.i | − | 0.560555i | ||||||
\(146\) | 613958.i | 2.38373i | ||||||||
\(147\) | 193348. | + | 173693.i | 0.737985 | + | 0.662964i | ||||
\(148\) | 411663. | 1.54485 | ||||||||
\(149\) | 228625. | 0.843642 | 0.421821 | − | 0.906679i | \(-0.361391\pi\) | ||||
0.421821 | + | 0.906679i | \(0.361391\pi\) | |||||||
\(150\) | −181942. | − | 163447.i | −0.660245 | − | 0.593127i | ||||
\(151\) | 152707.i | 0.545026i | 0.962152 | + | 0.272513i | \(0.0878548\pi\) | ||||
−0.962152 | + | 0.272513i | \(0.912145\pi\) | |||||||
\(152\) | − | 49805.5i | − | 0.174851i | ||||||
\(153\) | 650.879 | + | 6059.90i | 0.00224787 | + | 0.0209284i | ||||
\(154\) | 33961.8 | − | 19892.9i | 0.115396 | − | 0.0675922i | ||||
\(155\) | 109654.i | 0.366601i | ||||||||
\(156\) | −387927. | + | 431824.i | −1.27626 | + | 1.42068i | ||||
\(157\) | −206031. | −0.667089 | −0.333545 | − | 0.942734i | \(-0.608245\pi\) | ||||
−0.333545 | + | 0.942734i | \(0.608245\pi\) | |||||||
\(158\) | − | 228496.i | − | 0.728176i | ||||||
\(159\) | 128404. | − | 142935.i | 0.402798 | − | 0.448378i | ||||
\(160\) | − | 291111.i | − | 0.898997i | ||||||
\(161\) | −6881.85 | −0.0209238 | ||||||||
\(162\) | 489272. | − | 106330.i | 1.46475 | − | 0.318322i | ||||
\(163\) | 363134. | 1.07053 | 0.535264 | − | 0.844685i | \(-0.320212\pi\) | ||||
0.535264 | + | 0.844685i | \(0.320212\pi\) | |||||||
\(164\) | −708576. | −2.05720 | ||||||||
\(165\) | 218805. | + | 44816.3i | 0.625672 | + | 0.128152i | ||||
\(166\) | 275213. | 0.775173 | ||||||||
\(167\) | 514079. | 1.42639 | 0.713196 | − | 0.700965i | \(-0.247247\pi\) | ||||
0.713196 | + | 0.700965i | \(0.247247\pi\) | |||||||
\(168\) | 8069.57 | − | 8982.71i | 0.0220586 | − | 0.0245547i | ||||
\(169\) | −499804. | −1.34612 | ||||||||
\(170\) | 7592.85i | 0.0201503i | ||||||||
\(171\) | −179684. | + | 19299.5i | −0.469916 | + | 0.0504725i | ||||
\(172\) | − | 914078.i | − | 2.35593i | ||||||
\(173\) | −437300. | −1.11087 | −0.555436 | − | 0.831559i | \(-0.687449\pi\) | ||||
−0.555436 | + | 0.831559i | \(0.687449\pi\) | |||||||
\(174\) | −390861. | − | 351128.i | −0.978699 | − | 0.879209i | ||||
\(175\) | 21402.1i | 0.0528277i | ||||||||
\(176\) | −143783. | − | 245472.i | −0.349886 | − | 0.597337i | ||||
\(177\) | −316135. | + | 351909.i | −0.758472 | + | 0.844301i | ||||
\(178\) | 91644.8i | 0.216799i | ||||||||
\(179\) | 205264.i | 0.478828i | 0.970918 | + | 0.239414i | \(0.0769553\pi\) | ||||
−0.970918 | + | 0.239414i | \(0.923045\pi\) | |||||||
\(180\) | 344163. | − | 36965.7i | 0.791740 | − | 0.0850389i | ||||
\(181\) | 274310. | 0.622366 | 0.311183 | − | 0.950350i | \(-0.399275\pi\) | ||||
0.311183 | + | 0.950350i | \(0.399275\pi\) | |||||||
\(182\) | 91536.9 | 0.204841 | ||||||||
\(183\) | −379661. | + | 422623.i | −0.838046 | + | 0.932879i | ||||
\(184\) | − | 39845.9i | − | 0.0867640i | ||||||
\(185\) | − | 368371.i | − | 0.791326i | ||||||
\(186\) | 302000. | + | 271300.i | 0.640066 | + | 0.575000i | ||||
\(187\) | 5087.28 | + | 8685.17i | 0.0106385 | + | 0.0181625i | ||||
\(188\) | 135735.i | 0.280090i | ||||||||
\(189\) | −35534.1 | − | 25632.0i | −0.0723587 | − | 0.0521949i | ||||
\(190\) | −225138. | −0.452445 | ||||||||
\(191\) | 631297.i | 1.25213i | 0.779770 | + | 0.626066i | \(0.215336\pi\) | ||||
−0.779770 | + | 0.626066i | \(0.784664\pi\) | |||||||
\(192\) | −538703. | − | 483940.i | −1.05462 | − | 0.947412i | ||||
\(193\) | 5646.93i | 0.0109124i | 0.999985 | + | 0.00545619i | \(0.00173677\pi\) | ||||
−0.999985 | + | 0.00545619i | \(0.998263\pi\) | |||||||
\(194\) | 894131. | 1.70568 | ||||||||
\(195\) | 386412. | + | 347131.i | 0.727720 | + | 0.653743i | ||||
\(196\) | 665230. | 1.23689 | ||||||||
\(197\) | 739771. | 1.35810 | 0.679050 | − | 0.734092i | \(-0.262392\pi\) | ||||
0.679050 | + | 0.734092i | \(0.262392\pi\) | |||||||
\(198\) | 664787. | − | 491734.i | 1.20509 | − | 0.891389i | ||||
\(199\) | 215092. | 0.385027 | 0.192513 | − | 0.981294i | \(-0.438336\pi\) | ||||
0.192513 | + | 0.981294i | \(0.438336\pi\) | |||||||
\(200\) | −123918. | −0.219059 | ||||||||
\(201\) | −331331. | − | 297649.i | −0.578458 | − | 0.519654i | ||||
\(202\) | −1.34418e6 | −2.31781 | ||||||||
\(203\) | 45977.6i | 0.0783080i | ||||||||
\(204\) | 11604.4 | + | 10424.8i | 0.0195231 | + | 0.0175384i | ||||
\(205\) | 634059.i | 1.05377i | ||||||||
\(206\) | −986584. | −1.61982 | ||||||||
\(207\) | −143753. | + | 15440.2i | −0.233180 | + | 0.0250453i | ||||
\(208\) | − | 661616.i | − | 1.06035i | ||||||
\(209\) | −257527. | + | 150845.i | −0.407810 | + | 0.238872i | ||||
\(210\) | −40605.0 | − | 36477.3i | −0.0635377 | − | 0.0570788i | ||||
\(211\) | − | 197876.i | − | 0.305975i | −0.988228 | − | 0.152988i | \(-0.951111\pi\) | ||
0.988228 | − | 0.152988i | \(-0.0488895\pi\) | |||||||
\(212\) | − | 491777.i | − | 0.751499i | ||||||
\(213\) | 617783. | − | 687690.i | 0.933011 | − | 1.03859i | ||||
\(214\) | −390081. | −0.582264 | ||||||||
\(215\) | −817950. | −1.20679 | ||||||||
\(216\) | 148409. | − | 205742.i | 0.216434 | − | 0.300047i | ||||
\(217\) | − | 35524.7i | − | 0.0512132i | ||||||
\(218\) | 1.03220e6i | 1.47104i | ||||||||
\(219\) | 754300. | − | 839656.i | 1.06276 | − | 1.18302i | ||||
\(220\) | 493261. | − | 288924.i | 0.687100 | − | 0.402464i | ||||
\(221\) | 23409.0i | 0.0322406i | ||||||||
\(222\) | −1.01454e6 | − | 911406.i | −1.38161 | − | 1.24116i | ||||
\(223\) | 122438. | 0.164875 | 0.0824374 | − | 0.996596i | \(-0.473730\pi\) | ||||
0.0824374 | + | 0.996596i | \(0.473730\pi\) | |||||||
\(224\) | 94311.8i | 0.125587i | ||||||||
\(225\) | 48017.9 | + | 447063.i | 0.0632335 | + | 0.588725i | ||||
\(226\) | 1.62394e6i | 2.11494i | ||||||||
\(227\) | −385235. | −0.496205 | −0.248102 | − | 0.968734i | \(-0.579807\pi\) | ||||
−0.248102 | + | 0.968734i | \(0.579807\pi\) | |||||||
\(228\) | −309109. | + | 344087.i | −0.393799 | + | 0.438361i | ||||
\(229\) | 651870. | 0.821434 | 0.410717 | − | 0.911763i | \(-0.365278\pi\) | ||||
0.410717 | + | 0.911763i | \(0.365278\pi\) | |||||||
\(230\) | −180118. | −0.224511 | ||||||||
\(231\) | −70886.7 | − | 14519.2i | −0.0874047 | − | 0.0179025i | ||||
\(232\) | −266210. | −0.324717 | ||||||||
\(233\) | 830485. | 1.00217 | 0.501085 | − | 0.865398i | \(-0.332934\pi\) | ||||
0.501085 | + | 0.865398i | \(0.332934\pi\) | |||||||
\(234\) | 1.91209e6 | − | 205373.i | 2.28280 | − | 0.245190i | ||||
\(235\) | 121461. | 0.143472 | ||||||||
\(236\) | 1.21077e6i | 1.41508i | ||||||||
\(237\) | −280727. | + | 312494.i | −0.324648 | + | 0.361385i | ||||
\(238\) | − | 2459.87i | − | 0.00281495i | ||||||
\(239\) | −1.00232e6 | −1.13504 | −0.567518 | − | 0.823361i | \(-0.692096\pi\) | ||||
−0.567518 | + | 0.823361i | \(0.692096\pi\) | |||||||
\(240\) | −263653. | + | 293488.i | −0.295464 | + | 0.328899i | ||||
\(241\) | − | 1.51157e6i | − | 1.67643i | −0.545341 | − | 0.838214i | \(-0.683600\pi\) | ||
0.545341 | − | 0.838214i | \(-0.316400\pi\) | |||||||
\(242\) | 667910. | − | 1.19111e6i | 0.733128 | − | 1.30742i | ||||
\(243\) | −799769. | − | 455695.i | −0.868858 | − | 0.495061i | ||||
\(244\) | 1.45407e6i | 1.56354i | ||||||||
\(245\) | − | 595272.i | − | 0.633578i | ||||||
\(246\) | 1.74628e6 | + | 1.56876e6i | 1.83982 | + | 1.65279i | ||||
\(247\) | −694110. | −0.723912 | ||||||||
\(248\) | 205688. | 0.212364 | ||||||||
\(249\) | −376384. | − | 338122.i | −0.384710 | − | 0.345602i | ||||
\(250\) | 1.50618e6i | 1.52415i | ||||||||
\(251\) | − | 605116.i | − | 0.606254i | −0.952950 | − | 0.303127i | \(-0.901969\pi\) | ||
0.952950 | − | 0.303127i | \(-0.0980306\pi\) | |||||||
\(252\) | −111499. | + | 11975.9i | −0.110604 | + | 0.0118797i | ||||
\(253\) | −206030. | + | 120681.i | −0.202362 | + | 0.118532i | ||||
\(254\) | 629173.i | 0.611908i | ||||||||
\(255\) | 9328.47 | − | 10384.1i | 0.00898379 | − | 0.0100004i | ||||
\(256\) | 358990. | 0.342360 | ||||||||
\(257\) | − | 825395.i | − | 0.779523i | −0.920916 | − | 0.389762i | \(-0.872557\pi\) | ||
0.920916 | − | 0.389762i | \(-0.127443\pi\) | |||||||
\(258\) | −2.02374e6 | + | 2.25274e6i | −1.89280 | + | 2.10699i | ||||
\(259\) | 119342.i | 0.110546i | ||||||||
\(260\) | 1.32948e6 | 1.21969 | ||||||||
\(261\) | 103156. | + | 960412.i | 0.0937328 | + | 0.872683i | ||||
\(262\) | 751306. | 0.676182 | ||||||||
\(263\) | 1.11413e6 | 0.993218 | 0.496609 | − | 0.867974i | \(-0.334578\pi\) | ||||
0.496609 | + | 0.867974i | \(0.334578\pi\) | |||||||
\(264\) | 84066.4 | − | 410434.i | 0.0742356 | − | 0.362438i | ||||
\(265\) | −440060. | −0.384944 | ||||||||
\(266\) | 72938.6 | 0.0632053 | ||||||||
\(267\) | 112593. | − | 125334.i | 0.0966574 | − | 0.107595i | ||||
\(268\) | −1.13997e6 | −0.969518 | ||||||||
\(269\) | 895983.i | 0.754952i | 0.926019 | + | 0.377476i | \(0.123208\pi\) | ||||
−0.926019 | + | 0.377476i | \(0.876792\pi\) | |||||||
\(270\) | −930028. | − | 670862.i | −0.776402 | − | 0.560046i | ||||
\(271\) | − | 983707.i | − | 0.813659i | −0.913504 | − | 0.406830i | \(-0.866634\pi\) | ||
0.913504 | − | 0.406830i | \(-0.133366\pi\) | |||||||
\(272\) | −17779.6 | −0.0145714 | ||||||||
\(273\) | −125187. | − | 112461.i | −0.101660 | − | 0.0913261i | ||||
\(274\) | 1.49563e6i | 1.20350i | ||||||||
\(275\) | 375309. | + | 640740.i | 0.299266 | + | 0.510916i | ||||
\(276\) | −247297. | + | 275280.i | −0.195409 | + | 0.217522i | ||||
\(277\) | − | 1.30268e6i | − | 1.02009i | −0.860149 | − | 0.510043i | \(-0.829629\pi\) | ||
0.860149 | − | 0.510043i | \(-0.170371\pi\) | |||||||
\(278\) | − | 3.26925e6i | − | 2.53709i | ||||||
\(279\) | −79703.5 | − | 742066.i | −0.0613009 | − | 0.570732i | ||||
\(280\) | −27655.5 | −0.0210808 | ||||||||
\(281\) | −1.05493e6 | −0.796997 | −0.398499 | − | 0.917169i | \(-0.630469\pi\) | ||||
−0.398499 | + | 0.917169i | \(0.630469\pi\) | |||||||
\(282\) | 300513. | − | 334519.i | 0.225030 | − | 0.250494i | ||||
\(283\) | − | 964342.i | − | 0.715756i | −0.933768 | − | 0.357878i | \(-0.883500\pi\) | ||
0.933768 | − | 0.357878i | \(-0.116500\pi\) | |||||||
\(284\) | − | 2.36605e6i | − | 1.74072i | ||||||
\(285\) | 307902. | + | 276602.i | 0.224543 | + | 0.201717i | ||||
\(286\) | 2.74044e6 | − | 1.60519e6i | 1.98110 | − | 1.16041i | ||||
\(287\) | − | 205418.i | − | 0.147209i | ||||||
\(288\) | 211598. | + | 1.97005e6i | 0.150325 | + | 1.39958i | ||||
\(289\) | −1.41923e6 | −0.999557 | ||||||||
\(290\) | 1.20336e6i | 0.840237i | ||||||||
\(291\) | −1.22282e6 | − | 1.09852e6i | −0.846509 | − | 0.760456i | ||||
\(292\) | − | 2.88890e6i | − | 1.98278i | ||||||
\(293\) | 113600. | 0.0773056 | 0.0386528 | − | 0.999253i | \(-0.487693\pi\) | ||||
0.0386528 | + | 0.999253i | \(0.487693\pi\) | |||||||
\(294\) | −1.63946e6 | − | 1.47279e6i | −1.10619 | − | 0.993743i | ||||
\(295\) | 1.08344e6 | 0.724853 | ||||||||
\(296\) | −690989. | −0.458397 | ||||||||
\(297\) | −1.51331e6 | − | 144246.i | −0.995488 | − | 0.0948886i | ||||
\(298\) | −1.93857e6 | −1.26457 | ||||||||
\(299\) | −555309. | −0.359217 | ||||||||
\(300\) | 856105. | + | 769077.i | 0.549192 | + | 0.493363i | ||||
\(301\) | 264993. | 0.168585 | ||||||||
\(302\) | − | 1.29485e6i | − | 0.816960i | ||||||
\(303\) | 1.83831e6 | + | 1.65144e6i | 1.15030 | + | 1.03337i | ||||
\(304\) | − | 527191.i | − | 0.327178i | ||||||
\(305\) | 1.30115e6 | 0.800900 | ||||||||
\(306\) | −5518.99 | − | 51383.6i | −0.00336942 | − | 0.0313705i | ||||
\(307\) | 873188.i | 0.528764i | 0.964418 | + | 0.264382i | \(0.0851679\pi\) | ||||
−0.964418 | + | 0.264382i | \(0.914832\pi\) | |||||||
\(308\) | −159803. | + | 93603.4i | −0.0959860 | + | 0.0562231i | ||||
\(309\) | 1.34926e6 | + | 1.21210e6i | 0.803897 | + | 0.722176i | ||||
\(310\) | − | 929783.i | − | 0.549512i | ||||||
\(311\) | 2.69881e6i | 1.58223i | 0.611665 | + | 0.791117i | \(0.290500\pi\) | ||||
−0.611665 | + | 0.791117i | \(0.709500\pi\) | |||||||
\(312\) | 651148. | − | 724831.i | 0.378698 | − | 0.421551i | ||||
\(313\) | 1.55310e6 | 0.896060 | 0.448030 | − | 0.894018i | \(-0.352126\pi\) | ||||
0.448030 | + | 0.894018i | \(0.352126\pi\) | |||||||
\(314\) | 1.74700e6 | 0.999925 | ||||||||
\(315\) | 10716.4 | + | 99773.5i | 0.00608519 | + | 0.0566551i | ||||
\(316\) | 1.07516e6i | 0.605696i | ||||||||
\(317\) | − | 710129.i | − | 0.396907i | −0.980110 | − | 0.198454i | \(-0.936408\pi\) | ||
0.980110 | − | 0.198454i | \(-0.0635920\pi\) | |||||||
\(318\) | −1.08878e6 | + | 1.21198e6i | −0.603769 | + | 0.672091i | ||||
\(319\) | 806265. | + | 1.37648e6i | 0.443610 | + | 0.757345i | ||||
\(320\) | 1.65853e6i | 0.905417i | ||||||||
\(321\) | 533479. | + | 479247.i | 0.288971 | + | 0.259596i | ||||
\(322\) | 58353.1 | 0.0313635 | ||||||||
\(323\) | 18652.8i | 0.00994807i | ||||||||
\(324\) | −2.30221e6 | + | 500321.i | −1.21838 | + | 0.264780i | ||||
\(325\) | 1.72698e6i | 0.906939i | ||||||||
\(326\) | −3.07911e6 | −1.60465 | ||||||||
\(327\) | 1.26815e6 | − | 1.41165e6i | 0.655844 | − | 0.730059i | ||||
\(328\) | 1.18937e6 | 0.610424 | ||||||||
\(329\) | −39349.9 | −0.0200426 | ||||||||
\(330\) | −1.85531e6 | − | 380010.i | −0.937844 | − | 0.192092i | ||||
\(331\) | −1.75491e6 | −0.880408 | −0.440204 | − | 0.897898i | \(-0.645094\pi\) | ||||
−0.440204 | + | 0.897898i | \(0.645094\pi\) | |||||||
\(332\) | −1.29498e6 | −0.644788 | ||||||||
\(333\) | 267756. | + | 2.49290e6i | 0.132321 | + | 1.23195i | ||||
\(334\) | −4.35902e6 | −2.13807 | ||||||||
\(335\) | 1.02009e6i | 0.496620i | ||||||||
\(336\) | 85416.3 | − | 95081.9i | 0.0412755 | − | 0.0459462i | ||||
\(337\) | 2.45919e6i | 1.17955i | 0.807566 | + | 0.589777i | \(0.200785\pi\) | ||||
−0.807566 | + | 0.589777i | \(0.799215\pi\) | |||||||
\(338\) | 4.23798e6 | 2.01775 | ||||||||
\(339\) | 1.99514e6 | − | 2.22091e6i | 0.942920 | − | 1.04962i | ||||
\(340\) | − | 35727.2i | − | 0.0167610i | ||||||
\(341\) | −622964. | − | 1.06354e6i | −0.290119 | − | 0.495301i | ||||
\(342\) | 1.52359e6 | − | 163646.i | 0.704375 | − | 0.0756552i | ||||
\(343\) | 387251.i | 0.177728i | ||||||||
\(344\) | 1.53431e6i | 0.699064i | ||||||||
\(345\) | 246331. | + | 221290.i | 0.111422 | + | 0.100095i | ||||
\(346\) | 3.70799e6 | 1.66513 | ||||||||
\(347\) | 267251. | 0.119150 | 0.0595752 | − | 0.998224i | \(-0.481025\pi\) | ||||
0.0595752 | + | 0.998224i | \(0.481025\pi\) | |||||||
\(348\) | 1.83915e6 | + | 1.65219e6i | 0.814082 | + | 0.731325i | ||||
\(349\) | − | 1.61566e6i | − | 0.710044i | −0.934858 | − | 0.355022i | \(-0.884473\pi\) | ||
0.934858 | − | 0.355022i | \(-0.115527\pi\) | |||||||
\(350\) | − | 181475.i | − | 0.0791855i | ||||||
\(351\) | −2.86731e6 | − | 2.06829e6i | −1.24224 | − | 0.896075i | ||||
\(352\) | 1.65386e6 | + | 2.82352e6i | 0.711445 | + | 1.21460i | ||||
\(353\) | 2.34705e6i | 1.00250i | 0.865302 | + | 0.501252i | \(0.167127\pi\) | ||||
−0.865302 | + | 0.501252i | \(0.832873\pi\) | |||||||
\(354\) | 2.68060e6 | − | 2.98393e6i | 1.13690 | − | 1.26555i | ||||
\(355\) | −2.11723e6 | −0.891655 | ||||||||
\(356\) | − | 431223.i | − | 0.180334i | ||||||
\(357\) | −3022.16 | + | 3364.15i | −0.00125501 | + | 0.00139703i | ||||
\(358\) | − | 1.74049e6i | − | 0.717734i | ||||||
\(359\) | −2.46802e6 | −1.01068 | −0.505338 | − | 0.862922i | \(-0.668632\pi\) | ||||
−0.505338 | + | 0.862922i | \(0.668632\pi\) | |||||||
\(360\) | −577689. | + | 62048.1i | −0.234929 | + | 0.0252332i | ||||
\(361\) | 1.92302e6 | 0.776631 | ||||||||
\(362\) | −2.32595e6 | −0.932888 | ||||||||
\(363\) | −2.37682e6 | + | 808394.i | −0.946740 | + | 0.322000i | ||||
\(364\) | −430715. | −0.170387 | ||||||||
\(365\) | −2.58509e6 | −1.01565 | ||||||||
\(366\) | 3.21925e6 | − | 3.58354e6i | 1.25618 | − | 1.39833i | ||||
\(367\) | 775093. | 0.300392 | 0.150196 | − | 0.988656i | \(-0.452009\pi\) | ||||
0.150196 | + | 0.988656i | \(0.452009\pi\) | |||||||
\(368\) | − | 421769.i | − | 0.162351i | ||||||
\(369\) | −460876. | − | 4.29091e6i | −0.176205 | − | 1.64053i | ||||
\(370\) | 3.12352e6i | 1.18615i | ||||||||
\(371\) | 142567. | 0.0537755 | ||||||||
\(372\) | −1.42102e6 | − | 1.27657e6i | −0.532407 | − | 0.478284i | ||||
\(373\) | 1.09178e6i | 0.406315i | 0.979146 | + | 0.203158i | \(0.0651204\pi\) | ||||
−0.979146 | + | 0.203158i | \(0.934880\pi\) | |||||||
\(374\) | −43136.5 | − | 73644.0i | −0.0159465 | − | 0.0272244i | ||||
\(375\) | 1.85048e6 | − | 2.05987e6i | 0.679525 | − | 0.756419i | ||||
\(376\) | − | 227836.i | − | 0.0831099i | ||||||
\(377\) | 3.71001e6i | 1.34438i | ||||||||
\(378\) | 301303. | + | 217341.i | 0.108461 | + | 0.0782369i | ||||
\(379\) | 171895. | 0.0614701 | 0.0307351 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307351 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(380\) | 1.05936e6 | 0.376343 | ||||||||
\(381\) | 772993. | − | 860464.i | 0.272812 | − | 0.303683i | ||||
\(382\) | − | 5.35294e6i | − | 1.87687i | ||||||
\(383\) | − | 364164.i | − | 0.126853i | −0.997987 | − | 0.0634263i | \(-0.979797\pi\) | ||
0.997987 | − | 0.0634263i | \(-0.0202028\pi\) | |||||||
\(384\) | 1.54205e6 | + | 1.38530e6i | 0.533669 | + | 0.479418i | ||||
\(385\) | 83759.8 | + | 142997.i | 0.0287994 | + | 0.0491673i | ||||
\(386\) | − | 47881.9i | − | 0.0163570i | ||||||
\(387\) | 5.53537e6 | − | 594540.i | 1.87875 | − | 0.201792i | ||||
\(388\) | −4.20722e6 | −1.41878 | ||||||||
\(389\) | − | 1.57588e6i | − | 0.528020i | −0.964520 | − | 0.264010i | \(-0.914955\pi\) | ||
0.964520 | − | 0.264010i | \(-0.0850451\pi\) | |||||||
\(390\) | −3.27650e6 | − | 2.94342e6i | −1.09081 | − | 0.979920i | ||||
\(391\) | 14922.8i | 0.00493639i | ||||||||
\(392\) | −1.11661e6 | −0.367017 | ||||||||
\(393\) | −1.02749e6 | − | 923044.i | −0.335582 | − | 0.301468i | ||||
\(394\) | −6.27272e6 | −2.03571 | ||||||||
\(395\) | 962091. | 0.310258 | ||||||||
\(396\) | −3.12807e6 | + | 2.31379e6i | −1.00239 | + | 0.741457i | ||||
\(397\) | −2.37799e6 | −0.757241 | −0.378620 | − | 0.925552i | \(-0.623601\pi\) | ||||
−0.378620 | + | 0.925552i | \(0.623601\pi\) | |||||||
\(398\) | −1.82382e6 | −0.577132 | ||||||||
\(399\) | −99751.7 | − | 89611.3i | −0.0313681 | − | 0.0281793i | ||||
\(400\) | −1.31167e6 | −0.409898 | ||||||||
\(401\) | − | 794365.i | − | 0.246694i | −0.992364 | − | 0.123347i | \(-0.960637\pi\) | ||
0.992364 | − | 0.123347i | \(-0.0393629\pi\) | |||||||
\(402\) | 2.80945e6 | + | 2.52385e6i | 0.867073 | + | 0.778930i | ||||
\(403\) | − | 2.86656e6i | − | 0.879221i | ||||||
\(404\) | 6.32484e6 | 1.92795 | ||||||||
\(405\) | 447705. | + | 2.06010e6i | 0.135630 | + | 0.624094i | ||||
\(406\) | − | 389857.i | − | 0.117379i | ||||||
\(407\) | 2.09278e6 | + | 3.57287e6i | 0.626237 | + | 1.06913i | ||||
\(408\) | −19478.4 | − | 17498.3i | −0.00579300 | − | 0.00520411i | ||||
\(409\) | 2.20976e6i | 0.653185i | 0.945165 | + | 0.326593i | \(0.105901\pi\) | ||||
−0.945165 | + | 0.326593i | \(0.894099\pi\) | |||||||
\(410\) | − | 5.37636e6i | − | 1.57953i | ||||||
\(411\) | 1.83751e6 | − | 2.04544e6i | 0.536567 | − | 0.597285i | ||||
\(412\) | 4.64224e6 | 1.34736 | ||||||||
\(413\) | −351005. | −0.101260 | ||||||||
\(414\) | 1.21892e6 | − | 130921.i | 0.349522 | − | 0.0375414i | ||||
\(415\) | 1.15879e6i | 0.330283i | ||||||||
\(416\) | 7.61019e6i | 2.15607i | ||||||||
\(417\) | −4.01656e6 | + | 4.47107e6i | −1.13113 | + | 1.25913i | ||||
\(418\) | 2.18365e6 | − | 1.27906e6i | 0.611282 | − | 0.358054i | ||||
\(419\) | − | 7.13523e6i | − | 1.98551i | −0.120136 | − | 0.992757i | \(-0.538333\pi\) | ||
0.120136 | − | 0.992757i | \(-0.461667\pi\) | |||||||
\(420\) | 191062. | + | 171639.i | 0.0528507 | + | 0.0474781i | ||||
\(421\) | 608256. | 0.167256 | 0.0836279 | − | 0.996497i | \(-0.473349\pi\) | ||||
0.0836279 | + | 0.996497i | \(0.473349\pi\) | |||||||
\(422\) | 1.67784e6i | 0.458638i | ||||||||
\(423\) | −821969. | + | 88285.7i | −0.223360 | + | 0.0239905i | ||||
\(424\) | 825464.i | 0.222989i | ||||||||
\(425\) | 46409.1 | 0.0124632 | ||||||||
\(426\) | −5.23835e6 | + | 5.83112e6i | −1.39853 | + | 1.55678i | ||||
\(427\) | −421537. | −0.111883 | ||||||||
\(428\) | 1.83547e6 | 0.484327 | ||||||||
\(429\) | −5.71998e6 | − | 1.17158e6i | −1.50055 | − | 0.307348i | ||||
\(430\) | 6.93563e6 | 1.80890 | ||||||||
\(431\) | −3.42629e6 | −0.888445 | −0.444222 | − | 0.895917i | \(-0.646520\pi\) | ||||
−0.444222 | + | 0.895917i | \(0.646520\pi\) | |||||||
\(432\) | 1.57091e6 | − | 2.17778e6i | 0.404988 | − | 0.561442i | ||||
\(433\) | 6.94631e6 | 1.78047 | 0.890234 | − | 0.455503i | \(-0.150541\pi\) | ||||
0.890234 | + | 0.455503i | \(0.150541\pi\) | |||||||
\(434\) | 301224.i | 0.0767654i | ||||||||
\(435\) | 1.47844e6 | − | 1.64573e6i | 0.374610 | − | 0.417000i | ||||
\(436\) | − | 4.85689e6i | − | 1.22361i | ||||||
\(437\) | −442483. | −0.110839 | ||||||||
\(438\) | −6.39592e6 | + | 7.11968e6i | −1.59301 | + | 1.77327i | ||||
\(439\) | 2.33491e6i | 0.578240i | 0.957293 | + | 0.289120i | \(0.0933627\pi\) | ||||
−0.957293 | + | 0.289120i | \(0.906637\pi\) | |||||||
\(440\) | −827955. | + | 484969.i | −0.203880 | + | 0.119421i | ||||
\(441\) | 432683. | + | 4.02842e6i | 0.105943 | + | 0.986367i | ||||
\(442\) | − | 198492.i | − | 0.0483266i | ||||||
\(443\) | − | 101850.i | − | 0.0246576i | −0.999924 | − | 0.0123288i | \(-0.996076\pi\) | ||
0.999924 | − | 0.0123288i | \(-0.00392448\pi\) | |||||||
\(444\) | 4.77378e6 | + | 4.28850e6i | 1.14923 | + | 1.03240i | ||||
\(445\) | −385874. | −0.0923730 | ||||||||
\(446\) | −1.03819e6 | −0.247137 | ||||||||
\(447\) | 2.65122e6 | + | 2.38170e6i | 0.627590 | + | 0.563792i | ||||
\(448\) | − | 537318.i | − | 0.126484i | ||||||
\(449\) | − | 3.38226e6i | − | 0.791756i | −0.918303 | − | 0.395878i | \(-0.870440\pi\) | ||
0.918303 | − | 0.395878i | \(-0.129560\pi\) | |||||||
\(450\) | −407157. | − | 3.79077e6i | −0.0947831 | − | 0.882462i | ||||
\(451\) | −3.60221e6 | − | 6.14982e6i | −0.833927 | − | 1.42371i | ||||
\(452\) | − | 7.64121e6i | − | 1.75920i | ||||||
\(453\) | −1.59083e6 | + | 1.77085e6i | −0.364232 | + | 0.405448i | ||||
\(454\) | 3.26651e6 | 0.743781 | ||||||||
\(455\) | 385419.i | 0.0872780i | ||||||||
\(456\) | 518849. | − | 577562.i | 0.116850 | − | 0.130073i | ||||
\(457\) | − | 409738.i | − | 0.0917731i | −0.998947 | − | 0.0458865i | \(-0.985389\pi\) | ||
0.998947 | − | 0.0458865i | \(-0.0146113\pi\) | |||||||
\(458\) | −5.52739e6 | −1.23128 | ||||||||
\(459\) | −55581.3 | + | 77053.3i | −0.0123139 | + | 0.0170710i | ||||
\(460\) | 847520. | 0.186748 | ||||||||
\(461\) | 4.36832e6 | 0.957331 | 0.478666 | − | 0.877997i | \(-0.341121\pi\) | ||||
0.478666 | + | 0.877997i | \(0.341121\pi\) | |||||||
\(462\) | 601068. | + | 123113.i | 0.131014 | + | 0.0268348i | ||||
\(463\) | −597751. | −0.129589 | −0.0647945 | − | 0.997899i | \(-0.520639\pi\) | ||||
−0.0647945 | + | 0.997899i | \(0.520639\pi\) | |||||||
\(464\) | −2.81783e6 | −0.607603 | ||||||||
\(465\) | −1.14232e6 | + | 1.27158e6i | −0.244994 | + | 0.272717i | ||||
\(466\) | −7.04191e6 | −1.50219 | ||||||||
\(467\) | 1.49460e6i | 0.317126i | 0.987349 | + | 0.158563i | \(0.0506860\pi\) | ||||
−0.987349 | + | 0.158563i | \(0.949314\pi\) | |||||||
\(468\) | −8.99707e6 | + | 966354.i | −1.89883 | + | 0.203949i | ||||
\(469\) | − | 330479.i | − | 0.0693765i | ||||||
\(470\) | −1.02990e6 | −0.215055 | ||||||||
\(471\) | −2.38921e6 | − | 2.14633e6i | −0.496252 | − | 0.445805i | ||||
\(472\) | − | 2.03232e6i | − | 0.419891i | ||||||
\(473\) | 7.93340e6 | − | 4.64693e6i | 1.63045 | − | 0.955023i | ||||
\(474\) | 2.38036e6 | − | 2.64972e6i | 0.486628 | − | 0.541695i | ||||
\(475\) | 1.37609e6i | 0.279843i | ||||||||
\(476\) | 11574.6i | 0.00234147i | ||||||||
\(477\) | 2.97804e6 | − | 319865.i | 0.599288 | − | 0.0643680i | ||||
\(478\) | 8.49891e6 | 1.70135 | ||||||||
\(479\) | −1.50621e6 | −0.299948 | −0.149974 | − | 0.988690i | \(-0.547919\pi\) | ||||
−0.149974 | + | 0.988690i | \(0.547919\pi\) | |||||||
\(480\) | 3.03265e6 | − | 3.37582e6i | 0.600785 | − | 0.668769i | ||||
\(481\) | 9.62991e6i | 1.89784i | ||||||||
\(482\) | 1.28170e7i | 2.51286i | ||||||||
\(483\) | −79804.4 | − | 71691.8i | −0.0155654 | − | 0.0139830i | ||||
\(484\) | −3.14276e6 | + | 5.60462e6i | −0.609815 | + | 1.08751i | ||||
\(485\) | 3.76477e6i | 0.726749i | ||||||||
\(486\) | 6.78146e6 | + | 3.86396e6i | 1.30237 | + | 0.742066i | ||||
\(487\) | −7.28245e6 | −1.39141 | −0.695705 | − | 0.718328i | \(-0.744908\pi\) | ||||
−0.695705 | + | 0.718328i | \(0.744908\pi\) | |||||||
\(488\) | − | 2.44070e6i | − | 0.463943i | ||||||
\(489\) | 4.21103e6 | + | 3.78295e6i | 0.796372 | + | 0.715416i | ||||
\(490\) | 5.04747e6i | 0.949694i | ||||||||
\(491\) | 8.22691e6 | 1.54004 | 0.770022 | − | 0.638017i | \(-0.220245\pi\) | ||||
0.770022 | + | 0.638017i | \(0.220245\pi\) | |||||||
\(492\) | −8.21689e6 | − | 7.38160e6i | −1.53036 | − | 1.37479i | ||||
\(493\) | 99699.4 | 0.0184746 | ||||||||
\(494\) | 5.88555e6 | 1.08510 | ||||||||
\(495\) | 2.07046e6 | + | 2.79911e6i | 0.379800 | + | 0.513460i | ||||
\(496\) | 2.17721e6 | 0.397371 | ||||||||
\(497\) | 685923. | 0.124562 | ||||||||
\(498\) | 3.19146e6 | + | 2.86703e6i | 0.576656 | + | 0.518035i | ||||
\(499\) | −8.77367e6 | −1.57736 | −0.788678 | − | 0.614806i | \(-0.789234\pi\) | ||||
−0.788678 | + | 0.614806i | \(0.789234\pi\) | |||||||
\(500\) | − | 7.08715e6i | − | 1.26779i | ||||||
\(501\) | 5.96144e6 | + | 5.35543e6i | 1.06110 | + | 0.953234i | ||||
\(502\) | 5.13095e6i | 0.908737i | ||||||||
\(503\) | −4.73850e6 | −0.835066 | −0.417533 | − | 0.908662i | \(-0.637105\pi\) | ||||
−0.417533 | + | 0.908662i | \(0.637105\pi\) | |||||||
\(504\) | 187155. | − | 20101.9i | 0.0328190 | − | 0.00352501i | ||||
\(505\) | − | 5.65970e6i | − | 0.987563i | ||||||
\(506\) | 1.74698e6 | − | 1.02328e6i | 0.303328 | − | 0.177672i | ||||
\(507\) | −5.79591e6 | − | 5.20672e6i | −1.00139 | − | 0.899589i | ||||
\(508\) | − | 2.96049e6i | − | 0.508985i | ||||||
\(509\) | 1.42203e6i | 0.243285i | 0.992574 | + | 0.121642i | \(0.0388161\pi\) | ||||
−0.992574 | + | 0.121642i | \(0.961184\pi\) | |||||||
\(510\) | −79098.6 | + | 88049.4i | −0.0134662 | + | 0.0149900i | ||||
\(511\) | 837498. | 0.141883 | ||||||||
\(512\) | −7.29926e6 | −1.23056 | ||||||||
\(513\) | −2.28474e6 | − | 1.64806e6i | −0.383303 | − | 0.276490i | ||||
\(514\) | 6.99875e6i | 1.16846i | ||||||||
\(515\) | − | 4.15405e6i | − | 0.690165i | ||||||
\(516\) | 9.52242e6 | − | 1.06000e7i | 1.57443 | − | 1.75259i | ||||
\(517\) | −1.17806e6 | + | 690042.i | −0.193839 | + | 0.113540i | ||||
\(518\) | − | 1.01193e6i | − | 0.165702i | ||||||
\(519\) | −5.07108e6 | − | 4.55558e6i | −0.826385 | − | 0.742378i | ||||
\(520\) | −2.23158e6 | −0.361912 | ||||||||
\(521\) | − | 5.82338e6i | − | 0.939898i | −0.882694 | − | 0.469949i | \(-0.844272\pi\) | ||
0.882694 | − | 0.469949i | \(-0.155728\pi\) | |||||||
\(522\) | −874684. | − | 8.14360e6i | −0.140500 | − | 1.30810i | ||||
\(523\) | − | 7.18394e6i | − | 1.14844i | −0.818701 | − | 0.574220i | \(-0.805305\pi\) | ||
0.818701 | − | 0.574220i | \(-0.194695\pi\) | |||||||
\(524\) | −3.53517e6 | −0.562448 | ||||||||
\(525\) | −222957. | + | 248187.i | −0.0353039 | + | 0.0392989i | ||||
\(526\) | −9.44698e6 | −1.48877 | ||||||||
\(527\) | −77033.1 | −0.0120823 | ||||||||
\(528\) | 889842. | − | 4.34444e6i | 0.138908 | − | 0.678186i | ||||
\(529\) | 6.08234e6 | 0.945000 | ||||||||
\(530\) | 3.73139e6 | 0.577007 | ||||||||
\(531\) | −7.33203e6 | + | 787516.i | −1.12846 | + | 0.121206i | ||||
\(532\) | −343203. | −0.0525741 | ||||||||
\(533\) | − | 1.65755e7i | − | 2.52726i | ||||||
\(534\) | −954711. | + | 1.06275e6i | −0.144883 | + | 0.161278i | ||||
\(535\) | − | 1.64245e6i | − | 0.248089i | ||||||
\(536\) | 1.91348e6 | 0.287681 | ||||||||
\(537\) | −2.13834e6 | + | 2.38031e6i | −0.319993 | + | 0.356203i | ||||
\(538\) | − | 7.59729e6i | − | 1.13163i | ||||||
\(539\) | 3.38185e6 | + | 5.77361e6i | 0.501398 | + | 0.856004i | ||||
\(540\) | 4.37612e6 | + | 3.15665e6i | 0.645811 | + | 0.465846i | ||||
\(541\) | − | 6.78324e6i | − | 0.996424i | −0.867055 | − | 0.498212i | \(-0.833990\pi\) | ||
0.867055 | − | 0.498212i | \(-0.166010\pi\) | |||||||
\(542\) | 8.34112e6i | 1.21962i | ||||||||
\(543\) | 3.18100e6 | + | 2.85763e6i | 0.462982 | + | 0.415917i | ||||
\(544\) | 204509. | 0.0296289 | ||||||||
\(545\) | −4.34612e6 | −0.626773 | ||||||||
\(546\) | 1.06149e6 | + | 953587.i | 0.152383 | + | 0.136892i | ||||
\(547\) | 1.36297e6i | 0.194768i | 0.995247 | + | 0.0973842i | \(0.0310476\pi\) | ||||
−0.995247 | + | 0.0973842i | \(0.968952\pi\) | |||||||
\(548\) | − | 7.03748e6i | − | 1.00107i | ||||||
\(549\) | −8.80536e6 | + | 945762.i | −1.24686 | + | 0.133922i | ||||
\(550\) | −3.18235e6 | − | 5.43301e6i | −0.448581 | − | 0.765832i | ||||
\(551\) | 2.95622e6i | 0.414819i | ||||||||
\(552\) | 415095. | − | 462067.i | 0.0579830 | − | 0.0645443i | ||||
\(553\) | −311691. | −0.0433422 | ||||||||
\(554\) | 1.10458e7i | 1.52905i | ||||||||
\(555\) | 3.83751e6 | − | 4.27176e6i | 0.528831 | − | 0.588673i | ||||
\(556\) | 1.53830e7i | 2.11035i | ||||||||
\(557\) | 7.72310e6 | 1.05476 | 0.527380 | − | 0.849629i | \(-0.323174\pi\) | ||||
0.527380 | + | 0.849629i | \(0.323174\pi\) | |||||||
\(558\) | 675828. | + | 6.29218e6i | 0.0918863 | + | 0.855492i | ||||
\(559\) | 2.13828e7 | 2.89424 | ||||||||
\(560\) | −292734. | −0.0394460 | ||||||||
\(561\) | −31484.0 | + | 153713.i | −0.00422360 | + | 0.0206207i | ||||
\(562\) | 8.94502e6 | 1.19465 | ||||||||
\(563\) | −7.28192e6 | −0.968222 | −0.484111 | − | 0.875007i | \(-0.660857\pi\) | ||||
−0.484111 | + | 0.875007i | \(0.660857\pi\) | |||||||
\(564\) | −1.41402e6 | + | 1.57403e6i | −0.187180 | + | 0.208361i | ||||
\(565\) | −6.83764e6 | −0.901125 | ||||||||
\(566\) | 8.17692e6i | 1.07287i | ||||||||
\(567\) | −145044. | − | 667414.i | −0.0189471 | − | 0.0871842i | ||||
\(568\) | 3.97149e6i | 0.516515i | ||||||||
\(569\) | −8.25749e6 | −1.06922 | −0.534610 | − | 0.845099i | \(-0.679542\pi\) | ||||
−0.534610 | + | 0.845099i | \(0.679542\pi\) | |||||||
\(570\) | −2.61079e6 | − | 2.34538e6i | −0.336577 | − | 0.302362i | ||||
\(571\) | 2.50822e6i | 0.321940i | 0.986959 | + | 0.160970i | \(0.0514623\pi\) | ||||
−0.986959 | + | 0.160970i | \(0.948538\pi\) | |||||||
\(572\) | −1.28948e7 | + | 7.55303e6i | −1.64787 | + | 0.965231i | ||||
\(573\) | −6.57654e6 | + | 7.32074e6i | −0.836780 | + | 0.931469i | ||||
\(574\) | 1.74179e6i | 0.220657i | ||||||||
\(575\) | 1.10092e6i | 0.138863i | ||||||||
\(576\) | −1.20553e6 | − | 1.12239e7i | −0.151399 | − | 1.40957i | ||||
\(577\) | 1.64671e6 | 0.205910 | 0.102955 | − | 0.994686i | \(-0.467170\pi\) | ||||
0.102955 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(578\) | 1.20340e7 | 1.49827 | ||||||||
\(579\) | −58827.0 | + | 65483.8i | −0.00729257 | + | 0.00811779i | ||||
\(580\) | − | 5.66227e6i | − | 0.698909i | ||||||
\(581\) | − | 375417.i | − | 0.0461396i | ||||||
\(582\) | 1.03687e7 | + | 9.31463e6i | 1.26886 | + | 1.13988i | ||||
\(583\) | 4.26819e6 | − | 2.50006e6i | 0.520083 | − | 0.304635i | ||||
\(584\) | 4.84911e6i | 0.588342i | ||||||||
\(585\) | 864728. | + | 8.05091e6i | 0.104470 | + | 0.972647i | ||||
\(586\) | −963249. | −0.115876 | ||||||||
\(587\) | − | 2.51572e6i | − | 0.301348i | −0.988584 | − | 0.150674i | \(-0.951856\pi\) | ||
0.988584 | − | 0.150674i | \(-0.0481443\pi\) | |||||||
\(588\) | 7.71424e6 | + | 6.93004e6i | 0.920131 | + | 0.826595i | ||||
\(589\) | − | 2.28414e6i | − | 0.271290i | ||||||
\(590\) | −9.18679e6 | −1.08651 | ||||||||
\(591\) | 8.57865e6 | + | 7.70658e6i | 1.01030 | + | 0.907597i | ||||
\(592\) | −7.31412e6 | −0.857744 | ||||||||
\(593\) | −1.66834e6 | −0.194827 | −0.0974133 | − | 0.995244i | \(-0.531057\pi\) | ||||
−0.0974133 | + | 0.995244i | \(0.531057\pi\) | |||||||
\(594\) | 1.28317e7 | + | 1.22311e6i | 1.49217 | + | 0.142232i | ||||
\(595\) | 10357.4 | 0.00119938 | ||||||||
\(596\) | 9.12171e6 | 1.05187 | ||||||||
\(597\) | 2.49428e6 | + | 2.24072e6i | 0.286424 | + | 0.257307i | ||||
\(598\) | 4.70862e6 | 0.538444 | ||||||||
\(599\) | 1.36017e7i | 1.54891i | 0.632628 | + | 0.774456i | \(0.281976\pi\) | ||||
−0.632628 | + | 0.774456i | \(0.718024\pi\) | |||||||
\(600\) | −1.43700e6 | − | 1.29092e6i | −0.162959 | − | 0.146393i | ||||
\(601\) | − | 1.08809e7i | − | 1.22880i | −0.788996 | − | 0.614399i | \(-0.789399\pi\) | ||
0.788996 | − | 0.614399i | \(-0.210601\pi\) | |||||||
\(602\) | −2.24695e6 | −0.252698 | ||||||||
\(603\) | −741465. | − | 6.90329e6i | −0.0830420 | − | 0.773148i | ||||
\(604\) | 6.09273e6i | 0.679547i | ||||||||
\(605\) | 5.01522e6 | + | 2.81226e6i | 0.557059 | + | 0.312368i | ||||
\(606\) | −1.55875e7 | − | 1.40030e7i | −1.72423 | − | 1.54895i | ||||
\(607\) | 1.54469e7i | 1.70164i | 0.525453 | + | 0.850822i | \(0.323896\pi\) | ||||
−0.525453 | + | 0.850822i | \(0.676104\pi\) | |||||||
\(608\) | 6.06397e6i | 0.665270i | ||||||||
\(609\) | −478972. | + | 533172.i | −0.0523320 | + | 0.0582538i | ||||
\(610\) | −1.10328e7 | −1.20050 | ||||||||
\(611\) | −3.17522e6 | −0.344089 | ||||||||
\(612\) | 25968.9 | + | 241779.i | 0.00280269 | + | 0.0260939i | ||||
\(613\) | − | 1.71306e7i | − | 1.84128i | −0.390409 | − | 0.920641i | \(-0.627666\pi\) | ||
0.390409 | − | 0.920641i | \(-0.372334\pi\) | |||||||
\(614\) | − | 7.40400e6i | − | 0.792584i | ||||||
\(615\) | −6.60532e6 | + | 7.35277e6i | −0.704216 | + | 0.783905i | ||||
\(616\) | 268234. | − | 157116.i | 0.0284815 | − | 0.0166828i | ||||
\(617\) | 1.25814e7i | 1.33050i | 0.746620 | + | 0.665251i | \(0.231675\pi\) | ||||
−0.746620 | + | 0.665251i | \(0.768325\pi\) | |||||||
\(618\) | −1.14408e7 | − | 1.02778e7i | −1.20499 | − | 1.08250i | ||||
\(619\) | 8.53512e6 | 0.895330 | 0.447665 | − | 0.894201i | \(-0.352256\pi\) | ||||
0.447665 | + | 0.894201i | \(0.352256\pi\) | |||||||
\(620\) | 4.37497e6i | 0.457084i | ||||||||
\(621\) | −1.82786e6 | − | 1.31850e6i | −0.190201 | − | 0.137199i | ||||
\(622\) | − | 2.28839e7i | − | 2.37167i | ||||||
\(623\) | 125012. | 0.0129043 | ||||||||
\(624\) | 6.89240e6 | − | 7.67233e6i | 0.708612 | − | 0.788798i | ||||
\(625\) | −559506. | −0.0572934 | ||||||||
\(626\) | −1.31691e7 | −1.34314 | ||||||||
\(627\) | −4.55781e6 | − | 933545.i | −0.463006 | − | 0.0948345i | ||||
\(628\) | −8.22026e6 | −0.831737 | ||||||||
\(629\) | 258785. | 0.0260803 | ||||||||
\(630\) | −90867.6 | − | 846007.i | −0.00912132 | − | 0.0849225i | ||||
\(631\) | 1.89108e7 | 1.89076 | 0.945382 | − | 0.325964i | \(-0.105689\pi\) | ||||
0.945382 | + | 0.325964i | \(0.105689\pi\) | |||||||
\(632\) | − | 1.80469e6i | − | 0.179725i | ||||||
\(633\) | 2.06137e6 | − | 2.29464e6i | 0.204478 | − | 0.227617i | ||||
\(634\) | 6.02138e6i | 0.594940i | ||||||||
\(635\) | −2.64916e6 | −0.260719 | ||||||||
\(636\) | 5.12309e6 | − | 5.70282e6i | 0.502215 | − | 0.559045i | ||||
\(637\) | 1.55615e7i | 1.51951i | ||||||||
\(638\) | −6.83654e6 | − | 1.16716e7i | −0.664944 | − | 1.13521i | ||||
\(639\) | 1.43281e7 | − | 1.53894e6i | 1.38815 | − | 0.149097i | ||||
\(640\) | − | 4.74760e6i | − | 0.458168i | ||||||
\(641\) | − | 1.39715e7i | − | 1.34307i | −0.740975 | − | 0.671533i | \(-0.765636\pi\) | ||
0.740975 | − | 0.671533i | \(-0.234364\pi\) | |||||||
\(642\) | −4.52351e6 | − | 4.06367e6i | −0.433150 | − | 0.389118i | ||||
\(643\) | −8.35019e6 | −0.796469 | −0.398234 | − | 0.917284i | \(-0.630377\pi\) | ||||
−0.398234 | + | 0.917284i | \(0.630377\pi\) | |||||||
\(644\) | −274573. | −0.0260881 | ||||||||
\(645\) | −9.48524e6 | − | 8.52101e6i | −0.897737 | − | 0.806477i | ||||
\(646\) | − | 158163.i | − | 0.0149115i | ||||||
\(647\) | 5.28911e6i | 0.496732i | 0.968666 | + | 0.248366i | \(0.0798935\pi\) | ||||
−0.968666 | + | 0.248366i | \(0.920106\pi\) | |||||||
\(648\) | 3.86433e6 | − | 839804.i | 0.361523 | − | 0.0785671i | ||||
\(649\) | −1.05084e7 | + | 6.15523e6i | −0.979322 | + | 0.573631i | ||||
\(650\) | − | 1.46435e7i | − | 1.35945i | ||||||
\(651\) | 370080. | − | 411957.i | 0.0342249 | − | 0.0380978i | ||||
\(652\) | 1.44884e7 | 1.33475 | ||||||||
\(653\) | − | 1.31576e7i | − | 1.20752i | −0.797167 | − | 0.603759i | \(-0.793669\pi\) | ||
0.797167 | − | 0.603759i | \(-0.206331\pi\) | |||||||
\(654\) | −1.07530e7 | + | 1.19698e7i | −0.983070 | + | 1.09431i | ||||
\(655\) | 3.16340e6i | 0.288105i | ||||||||
\(656\) | 1.25894e7 | 1.14221 | ||||||||
\(657\) | 1.74943e7 | − | 1.87902e6i | 1.58118 | − | 0.169831i | ||||
\(658\) | 333659. | 0.0300426 | ||||||||
\(659\) | −5.31432e6 | −0.476688 | −0.238344 | − | 0.971181i | \(-0.576605\pi\) | ||||
−0.238344 | + | 0.971181i | \(0.576605\pi\) | |||||||
\(660\) | 8.72990e6 | + | 1.78809e6i | 0.780098 | + | 0.159782i | ||||
\(661\) | −1.46817e7 | −1.30699 | −0.653496 | − | 0.756930i | \(-0.726698\pi\) | ||||
−0.653496 | + | 0.756930i | \(0.726698\pi\) | |||||||
\(662\) | 1.48803e7 | 1.31968 | ||||||||
\(663\) | −243864. | + | 271459.i | −0.0215459 | + | 0.0239840i | ||||
\(664\) | 2.17366e6 | 0.191325 | ||||||||
\(665\) | 307111.i | 0.0269303i | ||||||||
\(666\) | −2.27038e6 | − | 2.11380e7i | −0.198341 | − | 1.84662i | ||||
\(667\) | 2.36507e6i | 0.205840i | ||||||||
\(668\) | 2.05108e7 | 1.77845 | ||||||||
\(669\) | 1.41984e6 | + | 1.27550e6i | 0.122651 | + | 0.110183i | ||||
\(670\) | − | 8.64959e6i | − | 0.744403i | ||||||
\(671\) | −1.26200e7 | + | 7.39209e6i | −1.08207 | + | 0.633813i | ||||
\(672\) | −982495. | + | 1.09367e6i | −0.0839280 | + | 0.0934252i | ||||
\(673\) | 9.05171e6i | 0.770359i | 0.922842 | + | 0.385179i | \(0.125860\pi\) | ||||
−0.922842 | + | 0.385179i | \(0.874140\pi\) | |||||||
\(674\) | − | 2.08522e7i | − | 1.76808i | ||||||
\(675\) | −4.10045e6 | + | 5.68453e6i | −0.346396 | + | 0.480214i | ||||
\(676\) | −1.99413e7 | −1.67836 | ||||||||
\(677\) | 1.80121e7 | 1.51040 | 0.755199 | − | 0.655495i | \(-0.227540\pi\) | ||||
0.755199 | + | 0.655495i | \(0.227540\pi\) | |||||||
\(678\) | −1.69174e7 | + | 1.88317e7i | −1.41338 | + | 1.57332i | ||||
\(679\) | − | 1.21968e6i | − | 0.101525i | ||||||
\(680\) | 59969.2i | 0.00497343i | ||||||||
\(681\) | −4.46732e6 | − | 4.01319e6i | −0.369130 | − | 0.331606i | ||||
\(682\) | 5.28228e6 | + | 9.01808e6i | 0.434871 | + | 0.742426i | ||||
\(683\) | 4.17593e6i | 0.342532i | 0.985225 | + | 0.171266i | \(0.0547857\pi\) | ||||
−0.985225 | + | 0.171266i | \(0.945214\pi\) | |||||||
\(684\) | −7.16907e6 | + | 770013.i | −0.585899 | + | 0.0629300i | ||||
\(685\) | −6.29739e6 | −0.512784 | ||||||||
\(686\) | − | 3.28360e6i | − | 0.266404i | ||||||
\(687\) | 7.55932e6 | + | 6.79087e6i | 0.611070 | + | 0.548951i | ||||
\(688\) | 1.62407e7i | 1.30807i | ||||||||
\(689\) | 1.15040e7 | 0.923211 | ||||||||
\(690\) | −2.08871e6 | − | 1.87638e6i | −0.167015 | − | 0.150037i | ||||
\(691\) | −1.40556e7 | −1.11983 | −0.559917 | − | 0.828549i | \(-0.689167\pi\) | ||||
−0.559917 | + | 0.828549i | \(0.689167\pi\) | |||||||
\(692\) | −1.74474e7 | −1.38505 | ||||||||
\(693\) | −670773. | − | 906833.i | −0.0530570 | − | 0.0717289i | ||||
\(694\) | −2.26609e6 | −0.178599 | ||||||||
\(695\) | 1.37653e7 | 1.08099 | ||||||||
\(696\) | −3.08707e6 | − | 2.77325e6i | −0.241559 | − | 0.217003i | ||||
\(697\) | −445435. | −0.0347298 | ||||||||
\(698\) | 1.36996e7i | 1.06431i | ||||||||
\(699\) | 9.63059e6 | + | 8.65159e6i | 0.745521 | + | 0.669735i | ||||
\(700\) | 853905.i | 0.0658665i | ||||||||
\(701\) | −1.12544e7 | −0.865021 | −0.432510 | − | 0.901629i | \(-0.642372\pi\) | ||||
−0.432510 | + | 0.901629i | \(0.642372\pi\) | |||||||
\(702\) | 2.43127e7 | + | 1.75376e7i | 1.86205 | + | 1.34316i | ||||
\(703\) | 7.67333e6i | 0.585593i | ||||||||
\(704\) | −9.42244e6 | − | 1.60863e7i | −0.716525 | − | 1.22328i | ||||
\(705\) | 1.40850e6 | + | 1.26532e6i | 0.106730 | + | 0.0958799i | ||||
\(706\) | − | 1.99013e7i | − | 1.50269i | ||||||
\(707\) | 1.83359e6i | 0.137960i | ||||||||
\(708\) | −1.26132e7 | + | 1.40405e7i | −0.945676 | + | 1.05269i | ||||
\(709\) | −1.03584e7 | −0.773886 | −0.386943 | − | 0.922104i | \(-0.626469\pi\) | ||||
−0.386943 | + | 0.922104i | \(0.626469\pi\) | |||||||
\(710\) | 1.79526e7 | 1.33654 | ||||||||
\(711\) | −6.51082e6 | + | 699311.i | −0.483016 | + | 0.0518796i | ||||
\(712\) | 723821.i | 0.0535096i | ||||||||
\(713\) | − | 1.82738e6i | − | 0.134619i | ||||||
\(714\) | 25625.8 | − | 28525.6i | 0.00188118 | − | 0.00209406i | ||||
\(715\) | 6.75873e6 | + | 1.15387e7i | 0.494424 | + | 0.844097i | ||||
\(716\) | 8.18964e6i | 0.597011i | ||||||||
\(717\) | −1.16232e7 | − | 1.04416e7i | −0.844360 | − | 0.758526i | ||||
\(718\) | 2.09270e7 | 1.51494 | ||||||||
\(719\) | 2.24287e7i | 1.61802i | 0.587798 | + | 0.809008i | \(0.299995\pi\) | ||||
−0.587798 | + | 0.809008i | \(0.700005\pi\) | |||||||
\(720\) | −6.11483e6 | + | 656779.i | −0.439595 | + | 0.0472159i | ||||
\(721\) | 1.34580e6i | 0.0964142i | ||||||||
\(722\) | −1.63058e7 | −1.16412 | ||||||||
\(723\) | 1.57468e7 | − | 1.75287e7i | 1.12033 | − | 1.24711i | ||||
\(724\) | 1.09445e7 | 0.775976 | ||||||||
\(725\) | 7.35522e6 | 0.519697 | ||||||||
\(726\) | 2.01537e7 | − | 6.85459e6i | 1.41910 | − | 0.482659i | ||||
\(727\) | −997757. | −0.0700146 | −0.0350073 | − | 0.999387i | \(-0.511145\pi\) | ||||
−0.0350073 | + | 0.999387i | \(0.511145\pi\) | |||||||
\(728\) | 722969. | 0.0505581 | ||||||||
\(729\) | −4.52720e6 | − | 1.36160e7i | −0.315508 | − | 0.948923i | ||||
\(730\) | 2.19197e7 | 1.52240 | ||||||||
\(731\) | − | 574620.i | − | 0.0397729i | ||||||
\(732\) | −1.51478e7 | + | 1.68619e7i | −1.04489 | + | 1.16313i | ||||
\(733\) | 7.84829e6i | 0.539529i | 0.962926 | + | 0.269765i | \(0.0869459\pi\) | ||||
−0.962926 | + | 0.269765i | \(0.913054\pi\) | |||||||
\(734\) | −6.57223e6 | −0.450270 | ||||||||
\(735\) | 6.20125e6 | − | 6.90298e6i | 0.423410 | − | 0.471323i | ||||
\(736\) | 4.85136e6i | 0.330118i | ||||||||
\(737\) | −5.79530e6 | − | 9.89393e6i | −0.393013 | − | 0.670965i | ||||
\(738\) | 3.90790e6 | + | 3.63838e7i | 0.264120 | + | 2.45905i | ||||
\(739\) | − | 1.45015e7i | − | 0.976793i | −0.872622 | − | 0.488396i | \(-0.837582\pi\) | ||
0.872622 | − | 0.488396i | \(-0.162418\pi\) | |||||||
\(740\) | − | 1.46973e7i | − | 0.986639i | ||||||
\(741\) | −8.04915e6 | − | 7.23090e6i | −0.538523 | − | 0.483779i | ||||
\(742\) | −1.20887e6 | −0.0806062 | ||||||||
\(743\) | −1.82193e7 | −1.21076 | −0.605382 | − | 0.795935i | \(-0.706979\pi\) | ||||
−0.605382 | + | 0.795935i | \(0.706979\pi\) | |||||||
\(744\) | 2.38523e6 | + | 2.14276e6i | 0.157979 | + | 0.141919i | ||||
\(745\) | − | 8.16243e6i | − | 0.538802i | ||||||
\(746\) | − | 9.25750e6i | − | 0.609041i | ||||||
\(747\) | −842287. | − | 7.84197e6i | −0.0552279 | − | 0.514190i | ||||
\(748\) | 202973. | + | 346522.i | 0.0132643 | + | 0.0226452i | ||||
\(749\) | 532108.i | 0.0346573i | ||||||||
\(750\) | −1.56907e7 | + | 1.74662e7i | −1.01857 | + | 1.13383i | ||||
\(751\) | 7.12675e6 | 0.461097 | 0.230548 | − | 0.973061i | \(-0.425948\pi\) | ||||
0.230548 | + | 0.973061i | \(0.425948\pi\) | |||||||
\(752\) | − | 2.41164e6i | − | 0.155514i | ||||||
\(753\) | 6.30381e6 | − | 7.01714e6i | 0.405150 | − | 0.450996i | ||||
\(754\) | − | 3.14582e7i | − | 2.01514i | ||||||
\(755\) | 5.45200e6 | 0.348087 | ||||||||
\(756\) | −1.41774e6 | − | 1.02267e6i | −0.0902180 | − | 0.0650774i | ||||
\(757\) | 1.78957e7 | 1.13503 | 0.567516 | − | 0.823362i | \(-0.307904\pi\) | ||||
0.567516 | + | 0.823362i | \(0.307904\pi\) | |||||||
\(758\) | −1.45754e6 | −0.0921399 | ||||||||
\(759\) | −3.64638e6 | − | 746864.i | −0.229751 | − | 0.0470584i | ||||
\(760\) | −1.77817e6 | −0.111671 | ||||||||
\(761\) | 1.04149e7 | 0.651916 | 0.325958 | − | 0.945384i | \(-0.394313\pi\) | ||||
0.325958 | + | 0.945384i | \(0.394313\pi\) | |||||||
\(762\) | −6.55442e6 | + | 7.29612e6i | −0.408928 | + | 0.455202i | ||||
\(763\) | 1.40802e6 | 0.0875585 | ||||||||
\(764\) | 2.51876e7i | 1.56118i | ||||||||
\(765\) | 216352. | − | 23237.9i | 0.0133662 | − | 0.00143563i | ||||
\(766\) | 3.08784e6i | 0.190144i | ||||||||
\(767\) | −2.83232e7 | −1.73842 | ||||||||
\(768\) | 4.16298e6 | + | 3.73979e6i | 0.254684 | + | 0.228794i | ||||
\(769\) | − | 1.29678e7i | − | 0.790772i | −0.918515 | − | 0.395386i | \(-0.870611\pi\) | ||
0.918515 | − | 0.395386i | \(-0.129389\pi\) | |||||||
\(770\) | −710222. | − | 1.21251e6i | −0.0431685 | − | 0.0736988i | ||||
\(771\) | 8.59856e6 | − | 9.57157e6i | 0.520943 | − | 0.579892i | ||||
\(772\) | 225302.i | 0.0136057i | ||||||||
\(773\) | 9.88927e6i | 0.595272i | 0.954679 | + | 0.297636i | \(0.0961982\pi\) | ||||
−0.954679 | + | 0.297636i | \(0.903802\pi\) | |||||||
\(774\) | −4.69359e7 | + | 5.04127e6i | −2.81613 | + | 0.302474i | ||||
\(775\) | −5.68303e6 | −0.339880 | ||||||||
\(776\) | 7.06195e6 | 0.420989 | ||||||||
\(777\) | −1.24325e6 | + | 1.38393e6i | −0.0738762 | + | 0.0822360i | ||||
\(778\) | 1.33623e7i | 0.791469i | ||||||||
\(779\) | − | 1.32078e7i | − | 0.779804i | ||||||
\(780\) | 1.54171e7 | + | 1.38499e7i | 0.907333 | + | 0.815097i | ||||
\(781\) | 2.05352e7 | − | 1.20284e7i | 1.20468 | − | 0.705634i | ||||
\(782\) | − | 126535.i | − | 0.00739935i | ||||||
\(783\) | −8.80888e6 | + | 1.22119e7i | −0.513472 | + | 0.711835i | ||||
\(784\) | −1.18193e7 | −0.686755 | ||||||||
\(785\) | 7.35578e6i | 0.426044i | ||||||||
\(786\) | 8.71241e6 | + | 7.82674e6i | 0.503016 | + | 0.451882i | ||||
\(787\) | 27977.4i | 0.00161017i | 1.00000 | 0.000805083i | \(0.000256266\pi\) | |||||
−1.00000 | 0.000805083i | \(0.999744\pi\) | ||||||||
\(788\) | 2.95155e7 | 1.69330 | ||||||||
\(789\) | 1.29198e7 | + | 1.16064e7i | 0.738862 | + | 0.663752i | ||||
\(790\) | −8.15783e6 | −0.465058 | ||||||||
\(791\) | 2.21520e6 | 0.125885 | ||||||||
\(792\) | 5.25056e6 | − | 3.88377e6i | 0.297436 | − | 0.220009i | ||||
\(793\) | −3.40146e7 | −1.92080 | ||||||||
\(794\) | 2.01636e7 | 1.13506 | ||||||||
\(795\) | −5.10309e6 | − | 4.58433e6i | −0.286362 | − | 0.257252i | ||||
\(796\) | 8.58176e6 | 0.480058 | ||||||||
\(797\) | − | 2.58567e7i | − | 1.44187i | −0.693001 | − | 0.720937i | \(-0.743712\pi\) | ||
0.693001 | − | 0.720937i | \(-0.256288\pi\) | |||||||
\(798\) | 845822. | + | 759839.i | 0.0470188 | + | 0.0422391i | ||||
\(799\) | 85327.7i | 0.00472850i | ||||||||
\(800\) | 1.50874e7 | 0.833471 | ||||||||
\(801\) | 2.61135e6 | − | 280478.i | 0.143808 | − | 0.0154461i | ||||
\(802\) | 6.73564e6i | 0.369780i | ||||||||
\(803\) | 2.50731e7 | − | 1.46864e7i | 1.37221 | − | 0.803761i | ||||
\(804\) | −1.32195e7 | − | 1.18756e7i | −0.721231 | − | 0.647913i | ||||
\(805\) | 245698.i | 0.0133632i | ||||||||
\(806\) | 2.43063e7i | 1.31790i | ||||||||
\(807\) | −9.33392e6 | + | 1.03901e7i | −0.504522 | + | 0.561613i | ||||
\(808\) | −1.06165e7 | −0.572073 | ||||||||
\(809\) | −2.57266e7 | −1.38201 | −0.691004 | − | 0.722851i | \(-0.742831\pi\) | ||||
−0.691004 | + | 0.722851i | \(0.742831\pi\) | |||||||
\(810\) | −3.79621e6 | − | 1.74681e7i | −0.203300 | − | 0.935479i | ||||
\(811\) | 1.31342e7i | 0.701214i | 0.936523 | + | 0.350607i | \(0.114025\pi\) | ||||
−0.936523 | + | 0.350607i | \(0.885975\pi\) | |||||||
\(812\) | 1.83442e6i | 0.0976357i | ||||||||
\(813\) | 1.02478e7 | − | 1.14074e7i | 0.543755 | − | 0.605286i | ||||
\(814\) | −1.77453e7 | − | 3.02954e7i | −0.938690 | − | 1.60256i | ||||
\(815\) | − | 1.29647e7i | − | 0.683705i | ||||||
\(816\) | −206179. | − | 185220.i | −0.0108397 | − | 0.00973782i | ||||
\(817\) | 1.70383e7 | 0.893040 | ||||||||
\(818\) | − | 1.87371e7i | − | 0.979085i | ||||||
\(819\) | −280148. | − | 2.60827e6i | −0.0145941 | − | 0.135876i | ||||
\(820\) | 2.52978e7i | 1.31386i | ||||||||
\(821\) | −4.99473e6 | −0.258615 | −0.129308 | − | 0.991605i | \(-0.541276\pi\) | ||||
−0.129308 | + | 0.991605i | \(0.541276\pi\) | |||||||
\(822\) | −1.55807e7 | + | 1.73438e7i | −0.804282 | + | 0.895293i | ||||
\(823\) | −2.45907e7 | −1.26553 | −0.632764 | − | 0.774344i | \(-0.718080\pi\) | ||||
−0.632764 | + | 0.774344i | \(0.718080\pi\) | |||||||
\(824\) | −7.79215e6 | −0.399797 | ||||||||
\(825\) | −2.32270e6 | + | 1.13400e7i | −0.118811 | + | 0.580068i | ||||
\(826\) | 2.97626e6 | 0.151782 | ||||||||
\(827\) | −3.01293e6 | −0.153188 | −0.0765941 | − | 0.997062i | \(-0.524405\pi\) | ||||
−0.0765941 | + | 0.997062i | \(0.524405\pi\) | |||||||
\(828\) | −5.73548e6 | + | 616034.i | −0.290733 | + | 0.0312269i | ||||
\(829\) | 4.32490e6 | 0.218570 | 0.109285 | − | 0.994010i | \(-0.465144\pi\) | ||||
0.109285 | + | 0.994010i | \(0.465144\pi\) | |||||||
\(830\) | − | 9.82573e6i | − | 0.495073i | ||||||
\(831\) | 1.35707e7 | − | 1.51063e7i | 0.681708 | − | 0.758849i | ||||
\(832\) | − | 4.33572e7i | − | 2.17146i | ||||||
\(833\) | 418186. | 0.0208813 | ||||||||
\(834\) | 3.40575e7 | − | 3.79114e7i | 1.69550 | − | 1.88736i | ||||
\(835\) | − | 1.83538e7i | − | 0.910982i | ||||||
\(836\) | −1.02749e7 | + | 6.01843e6i | −0.508464 | + | 0.297829i | ||||
\(837\) | 6.80621e6 | − | 9.43557e6i | 0.335809 | − | 0.465537i | ||||
\(838\) | 6.05016e7i | 2.97616i | ||||||||
\(839\) | 1.46208e7i | 0.717078i | 0.933515 | + | 0.358539i | \(0.116725\pi\) | ||||
−0.933515 | + | 0.358539i | \(0.883275\pi\) | |||||||
\(840\) | −320703. | − | 288102.i | −0.0156821 | − | 0.0140880i | ||||
\(841\) | −4.71015e6 | −0.229639 | ||||||||
\(842\) | −5.15757e6 | −0.250706 | ||||||||
\(843\) | −1.22333e7 | − | 1.09897e7i | −0.592891 | − | 0.532620i | ||||
\(844\) | − | 7.89487e6i | − | 0.381495i | ||||||
\(845\) | 1.78442e7i | 0.859715i | ||||||||
\(846\) | 6.96970e6 | − | 748599.i | 0.334802 | − | 0.0359603i | ||||
\(847\) | −1.62479e6 | − | 911094.i | −0.0778196 | − | 0.0436370i | ||||
\(848\) | 8.73753e6i | 0.417252i | ||||||||
\(849\) | 1.00460e7 | − | 1.11829e7i | 0.478328 | − | 0.532456i | ||||
\(850\) | −393516. | −0.0186816 | ||||||||
\(851\) | 6.13890e6i | 0.290581i | ||||||||
\(852\) | 2.46484e7 | − | 2.74376e7i | 1.16329 | − | 1.29493i | ||||
\(853\) | 3.27986e6i | 0.154341i | 0.997018 | + | 0.0771707i | \(0.0245886\pi\) | ||||
−0.997018 | + | 0.0771707i | \(0.975411\pi\) | |||||||
\(854\) | 3.57433e6 | 0.167706 | ||||||||
\(855\) | 689035. | + | 6.41515e6i | 0.0322349 | + | 0.300117i | ||||
\(856\) | −3.08090e6 | −0.143712 | ||||||||
\(857\) | 1.80385e7 | 0.838973 | 0.419486 | − | 0.907762i | \(-0.362210\pi\) | ||||
0.419486 | + | 0.907762i | \(0.362210\pi\) | |||||||
\(858\) | 4.85013e7 | + | 9.93418e6i | 2.24923 | + | 0.460695i | ||||
\(859\) | 1.84006e7 | 0.850842 | 0.425421 | − | 0.904996i | \(-0.360126\pi\) | ||||
0.425421 | + | 0.904996i | \(0.360126\pi\) | |||||||
\(860\) | −3.26347e7 | −1.50464 | ||||||||
\(861\) | 2.13994e6 | − | 2.38210e6i | 0.0983771 | − | 0.109509i | ||||
\(862\) | 2.90524e7 | 1.33172 | ||||||||
\(863\) | 3.20809e7i | 1.46629i | 0.680073 | + | 0.733144i | \(0.261948\pi\) | ||||
−0.680073 | + | 0.733144i | \(0.738052\pi\) | |||||||
\(864\) | −1.80693e7 | + | 2.50497e7i | −0.823486 | + | 1.14161i | ||||
\(865\) | 1.56126e7i | 0.709472i | ||||||||
\(866\) | −5.88997e7 | −2.66881 | ||||||||
\(867\) | −1.64579e7 | − | 1.47848e7i | −0.743577 | − | 0.667988i | ||||
\(868\) | − | 1.41737e6i | − | 0.0638534i | ||||||
\(869\) | −9.33144e6 | + | 5.46582e6i | −0.419179 | + | 0.245531i | ||||
\(870\) | −1.25361e7 | + | 1.39546e7i | −0.561517 | + | 0.625058i | ||||
\(871\) | − | 2.66670e7i | − | 1.19105i | ||||||
\(872\) | 8.15245e6i | 0.363075i | ||||||||
\(873\) | −2.73648e6 | − | 2.54776e7i | −0.121523 | − | 1.13142i | ||||
\(874\) | 3.75194e6 | 0.166141 | ||||||||
\(875\) | 2.05458e6 | 0.0907200 | ||||||||
\(876\) | 3.00952e7 | − | 3.35007e7i | 1.32506 | − | 1.47501i | ||||
\(877\) | 3.75459e7i | 1.64841i | 0.566295 | + | 0.824203i | \(0.308376\pi\) | ||||
−0.566295 | + | 0.824203i | \(0.691624\pi\) | |||||||
\(878\) | − | 1.97983e7i | − | 0.866746i | ||||||
\(879\) | 1.31735e6 | + | 1.18343e6i | 0.0575081 | + | 0.0516621i | ||||
\(880\) | −8.76389e6 | + | 5.13339e6i | −0.381496 | + | 0.223459i | ||||
\(881\) | 2.20195e7i | 0.955802i | 0.878414 | + | 0.477901i | \(0.158602\pi\) | ||||
−0.878414 | + | 0.477901i | \(0.841398\pi\) | |||||||
\(882\) | −3.66884e6 | − | 3.41581e7i | −0.158802 | − | 1.47850i | ||||
\(883\) | −1.76671e7 | −0.762542 | −0.381271 | − | 0.924463i | \(-0.624514\pi\) | ||||
−0.381271 | + | 0.924463i | \(0.624514\pi\) | |||||||
\(884\) | 933976.i | 0.0401981i | ||||||||
\(885\) | 1.25640e7 | + | 1.12868e7i | 0.539223 | + | 0.484407i | ||||
\(886\) | 863614.i | 0.0369603i | ||||||||
\(887\) | −170484. | −0.00727569 | −0.00363785 | − | 0.999993i | \(-0.501158\pi\) | ||||
−0.00363785 | + | 0.999993i | \(0.501158\pi\) | |||||||
\(888\) | −8.01296e6 | − | 7.19839e6i | −0.341005 | − | 0.306340i | ||||
\(889\) | 858253. | 0.0364218 | ||||||||
\(890\) | 3.27193e6 | 0.138461 | ||||||||
\(891\) | −1.60462e7 | − | 1.74376e7i | −0.677137 | − | 0.735857i | ||||
\(892\) | 4.88505e6 | 0.205569 | ||||||||
\(893\) | −2.53008e6 | −0.106171 | ||||||||
\(894\) | −2.24804e7 | − | 2.01951e7i | −0.940719 | − | 0.845090i | ||||
\(895\) | 7.32838e6 | 0.305809 | ||||||||
\(896\) | 1.53809e6i | 0.0640047i | ||||||||
\(897\) | −6.43956e6 | − | 5.78494e6i | −0.267224 | − | 0.240059i | ||||
\(898\) | 2.86791e7i | 1.18679i | ||||||||
\(899\) | −1.22087e7 | −0.503814 | ||||||||
\(900\) | 1.91583e6 | + | 1.78370e7i | 0.0788406 | + | 0.734032i | ||||
\(901\) | − | 309148.i | − | 0.0126869i | ||||||
\(902\) | 3.05442e7 | + | 5.21460e7i | 1.25001 | + | 2.13405i | ||||
\(903\) | 3.07296e6 | + | 2.76057e6i | 0.125411 | + | 0.112663i | ||||
\(904\) | 1.28260e7i | 0.522001i | ||||||||
\(905\) | − | 9.79351e6i | − | 0.397481i | ||||||
\(906\) | 1.34891e7 | − | 1.50155e7i | 0.545961 | − | 0.607742i | ||||
\(907\) | −3.09220e7 | −1.24810 | −0.624050 | − | 0.781385i | \(-0.714514\pi\) | ||||
−0.624050 | + | 0.781385i | \(0.714514\pi\) | |||||||
\(908\) | −1.53701e7 | −0.618676 | ||||||||
\(909\) | 4.11384e6 | + | 3.83013e7i | 0.165135 | + | 1.53746i | ||||
\(910\) | − | 3.26807e6i | − | 0.130824i | ||||||
\(911\) | 5.31649e6i | 0.212241i | 0.994353 | + | 0.106120i | \(0.0338429\pi\) | ||||
−0.994353 | + | 0.106120i | \(0.966157\pi\) | |||||||
\(912\) | 5.49202e6 | − | 6.11349e6i | 0.218648 | − | 0.243390i | ||||
\(913\) | −6.58333e6 | − | 1.12393e7i | −0.261378 | − | 0.446233i | ||||
\(914\) | 3.47428e6i | 0.137562i | ||||||||
\(915\) | 1.50886e7 | + | 1.35548e7i | 0.595794 | + | 0.535228i | ||||
\(916\) | 2.60084e7 | 1.02418 | ||||||||
\(917\) | − | 1.02485e6i | − | 0.0402475i | ||||||
\(918\) | 471289. | − | 653356.i | 0.0184578 | − | 0.0255884i | ||||
\(919\) | 3.87474e7i | 1.51340i | 0.653761 | + | 0.756701i | \(0.273190\pi\) | ||||
−0.653761 | + | 0.756701i | \(0.726810\pi\) | |||||||
\(920\) | −1.42259e6 | −0.0554128 | ||||||||
\(921\) | −9.09645e6 | + | 1.01258e7i | −0.353364 | + | 0.393351i | ||||
\(922\) | −3.70402e7 | −1.43498 | ||||||||
\(923\) | 5.53484e7 | 2.13846 | ||||||||
\(924\) | −2.82825e6 | − | 579290.i | −0.108978 | − | 0.0223211i | ||||
\(925\) | 1.90916e7 | 0.733648 | ||||||||
\(926\) | 5.06850e6 | 0.194246 | ||||||||
\(927\) | 3.01943e6 | + | 2.81119e7i | 0.115405 | + | 1.07446i | ||||
\(928\) | 3.24119e7 | 1.23548 | ||||||||
\(929\) | 2.35919e7i | 0.896856i | 0.893819 | + | 0.448428i | \(0.148016\pi\) | ||||
−0.893819 | + | 0.448428i | \(0.851984\pi\) | |||||||
\(930\) | 9.68603e6 | − | 1.07821e7i | 0.367230 | − | 0.408786i | ||||
\(931\) | 1.23998e7i | 0.468857i | ||||||||
\(932\) | 3.31348e7 | 1.24952 | ||||||||
\(933\) | −2.81148e7 | + | 3.12963e7i | −1.05738 | + | 1.17703i | ||||
\(934\) | − | 1.26731e7i | − | 0.475352i | ||||||
\(935\) | 310080. | − | 181628.i | 0.0115997 | − | 0.00679442i | ||||
\(936\) | 1.51019e7 | − | 1.62206e6i | 0.563432 | − | 0.0605169i | ||||
\(937\) | − | 2.06130e7i | − | 0.766994i | −0.923542 | − | 0.383497i | \(-0.874720\pi\) | ||
0.923542 | − | 0.383497i | \(-0.125280\pi\) | |||||||
\(938\) | 2.80223e6i | 0.103991i | ||||||||
\(939\) | 1.80102e7 | + | 1.61794e7i | 0.666585 | + | 0.598823i | ||||
\(940\) | 4.84606e6 | 0.178883 | ||||||||
\(941\) | −3.12272e7 | −1.14963 | −0.574817 | − | 0.818282i | \(-0.694927\pi\) | ||||
−0.574817 | + | 0.818282i | \(0.694927\pi\) | |||||||
\(942\) | 2.02588e7 | + | 1.81993e7i | 0.743851 | + | 0.668234i | ||||
\(943\) | − | 1.05666e7i | − | 0.386951i | ||||||
\(944\) | − | 2.15120e7i | − | 0.785691i | ||||||
\(945\) | −915121. | + | 1.26865e6i | −0.0333349 | + | 0.0462127i | ||||
\(946\) | −6.72695e7 | + | 3.94026e7i | −2.44394 | + | 1.43152i | ||||
\(947\) | − | 4.37995e7i | − | 1.58706i | −0.608528 | − | 0.793532i | \(-0.708240\pi\) | ||
0.608528 | − | 0.793532i | \(-0.291760\pi\) | |||||||
\(948\) | −1.12005e7 | + | 1.24679e7i | −0.404777 | + | 0.450581i | ||||
\(949\) | 6.75793e7 | 2.43584 | ||||||||
\(950\) | − | 1.16683e7i | − | 0.419467i | ||||||
\(951\) | 7.39778e6 | − | 8.23491e6i | 0.265247 | − | 0.295262i | ||||
\(952\) | − | 19428.4i | − | 0.000694775i | ||||||
\(953\) | −1.91878e7 | −0.684371 | −0.342186 | − | 0.939632i | \(-0.611167\pi\) | ||||
−0.342186 | + | 0.939632i | \(0.611167\pi\) | |||||||
\(954\) | −2.52517e7 | + | 2.71222e6i | −0.898295 | + | 0.0964837i | ||||
\(955\) | 2.25387e7 | 0.799689 | ||||||||
\(956\) | −3.99905e7 | −1.41518 | ||||||||
\(957\) | −4.98979e6 | + | 2.43615e7i | −0.176117 | + | 0.859851i | ||||
\(958\) | 1.27716e7 | 0.449604 | ||||||||
\(959\) | 2.04018e6 | 0.0716345 | ||||||||
\(960\) | −1.72778e7 | + | 1.92329e7i | −0.605076 | + | 0.673546i | ||||
\(961\) | −1.91961e7 | −0.670507 | ||||||||
\(962\) | − | 8.16547e7i | − | 2.84475i | ||||||
\(963\) | 1.19384e6 | + | 1.11150e7i | 0.0414840 | + | 0.386229i | ||||
\(964\) | − | 6.03087e7i | − | 2.09020i | ||||||
\(965\) | 201608. | 0.00696932 | ||||||||
\(966\) | 676684. | + | 607895.i | 0.0233315 | + | 0.0209597i | ||||
\(967\) | − | 4.71112e7i | − | 1.62016i | −0.586320 | − | 0.810080i | \(-0.699424\pi\) | ||
0.586320 | − | 0.810080i | \(-0.300576\pi\) | |||||||
\(968\) | 5.27523e6 | − | 9.40754e6i | 0.180948 | − | 0.322692i | ||||
\(969\) | −194316. | + | 216305.i | −0.00664813 | + | 0.00740043i | ||||
\(970\) | − | 3.19225e7i | − | 1.08935i | ||||||
\(971\) | − | 3.02870e6i | − | 0.103088i | −0.998671 | − | 0.0515440i | \(-0.983586\pi\) | ||
0.998671 | − | 0.0515440i | \(-0.0164142\pi\) | |||||||
\(972\) | −3.19093e7 | − | 1.81814e7i | −1.08331 | − | 0.617250i | ||||
\(973\) | −4.45958e6 | −0.151012 | ||||||||
\(974\) | 6.17499e7 | 2.08564 | ||||||||
\(975\) | −1.79908e7 | + | 2.00266e7i | −0.606093 | + | 0.674678i | ||||
\(976\) | − | 2.58348e7i | − | 0.868120i | ||||||
\(977\) | 4.75206e7i | 1.59274i | 0.604808 | + | 0.796372i | \(0.293250\pi\) | ||||
−0.604808 | + | 0.796372i | \(0.706750\pi\) | |||||||
\(978\) | −3.57065e7 | − | 3.20767e7i | −1.19371 | − | 1.07236i | ||||
\(979\) | 3.74263e6 | − | 2.19222e6i | 0.124802 | − | 0.0731018i | ||||
\(980\) | − | 2.37502e7i | − | 0.789955i | ||||||
\(981\) | 2.94118e7 | − | 3.15905e6i | 0.975773 | − | 0.104805i | ||||
\(982\) | −6.97583e7 | −2.30843 | ||||||||
\(983\) | − | 5.56618e7i | − | 1.83727i | −0.395104 | − | 0.918636i | \(-0.629292\pi\) | ||
0.395104 | − | 0.918636i | \(-0.370708\pi\) | |||||||
\(984\) | 1.37923e7 | + | 1.23903e7i | 0.454098 | + | 0.407936i | ||||
\(985\) | − | 2.64115e7i | − | 0.867367i | ||||||
\(986\) | −845378. | −0.0276923 | ||||||||
\(987\) | −456316. | − | 409928.i | −0.0149098 | − | 0.0133942i | ||||
\(988\) | −2.76937e7 | −0.902586 | ||||||||
\(989\) | 1.36312e7 | 0.443141 | ||||||||
\(990\) | −1.75560e7 | − | 2.37344e7i | −0.569296 | − | 0.769645i | ||||
\(991\) | 3.21887e7 | 1.04117 | 0.520583 | − | 0.853811i | \(-0.325715\pi\) | ||||
0.520583 | + | 0.853811i | \(0.325715\pi\) | |||||||
\(992\) | −2.50432e7 | −0.807998 | ||||||||
\(993\) | −2.03505e7 | − | 1.82818e7i | −0.654941 | − | 0.588363i | ||||
\(994\) | −5.81613e6 | −0.186710 | ||||||||
\(995\) | − | 7.67927e6i | − | 0.245902i | ||||||
\(996\) | −1.50170e7 | − | 1.34904e7i | −0.479662 | − | 0.430902i | ||||
\(997\) | − | 1.27214e7i | − | 0.405321i | −0.979249 | − | 0.202660i | \(-0.935041\pi\) | ||
0.979249 | − | 0.202660i | \(-0.0649587\pi\) | |||||||
\(998\) | 7.43944e7 | 2.36436 | ||||||||
\(999\) | −2.28648e7 | + | 3.16979e7i | −0.724860 | + | 1.00489i |
(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 | 33.6.d.b.32.4 | yes | 16 | |
3.2 | odd | 2 | inner | 33.6.d.b.32.13 | yes | 16 | |
11.10 | odd | 2 | inner | 33.6.d.b.32.14 | yes | 16 | |
33.32 | even | 2 | inner | 33.6.d.b.32.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.6.d.b.32.3 | ✓ | 16 | 33.32 | even | 2 | inner | |
33.6.d.b.32.4 | yes | 16 | 1.1 | even | 1 | trivial | |
33.6.d.b.32.13 | yes | 16 | 3.2 | odd | 2 | inner | |
33.6.d.b.32.14 | yes | 16 | 11.10 | odd | 2 | inner |