Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,6,Mod(107,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, 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("108.107");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.b (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: | \(17.3214525398\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 94 x^{18} + 5872 x^{16} - 207192 x^{14} + 5271952 x^{12} - 76648960 x^{10} + 792478720 x^{8} - 4371873792 x^{6} + 17152147456 x^{4} + \cdots + 41943040000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{50}\cdot 3^{40} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.9 | ||
Root | \(5.25764 - 3.03550i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.107 |
Dual form | 108.6.b.c.107.10 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.821088 | − | 5.59695i | −0.145149 | − | 0.989410i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −30.6516 | + | 9.19117i | −0.957863 | + | 0.287224i | ||||
\(5\) | − | 8.15731i | − | 0.145922i | −0.997335 | − | 0.0729612i | \(-0.976755\pi\) | ||
0.997335 | − | 0.0729612i | \(-0.0232449\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 63.0026i | 0.485974i | 0.970030 | + | 0.242987i | \(0.0781273\pi\) | ||||
−0.970030 | + | 0.242987i | \(0.921873\pi\) | |||||||
\(8\) | 76.6102 | + | 164.009i | 0.423215 | + | 0.906029i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −45.6560 | + | 6.69787i | −0.144377 | + | 0.0211805i | ||||
\(11\) | 442.855 | 1.10352 | 0.551760 | − | 0.834003i | \(-0.313957\pi\) | ||||
0.551760 | + | 0.834003i | \(0.313957\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −76.3186 | −0.125248 | −0.0626242 | − | 0.998037i | \(-0.519947\pi\) | ||||
−0.0626242 | + | 0.998037i | \(0.519947\pi\) | |||||||
\(14\) | 352.622 | − | 51.7307i | 0.480828 | − | 0.0705388i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 855.045 | − | 563.449i | 0.835005 | − | 0.550243i | ||||
\(17\) | 643.601i | 0.540125i | 0.962843 | + | 0.270063i | \(0.0870444\pi\) | ||||
−0.962843 | + | 0.270063i | \(0.912956\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2189.93i | − | 1.39170i | −0.718188 | − | 0.695850i | \(-0.755028\pi\) | ||
0.718188 | − | 0.695850i | \(-0.244972\pi\) | |||||||
\(20\) | 74.9752 | + | 250.035i | 0.0419124 | + | 0.139774i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −363.623 | − | 2478.64i | −0.160175 | − | 1.09183i | ||||
\(23\) | 2735.75 | 1.07834 | 0.539171 | − | 0.842196i | \(-0.318738\pi\) | ||||
0.539171 | + | 0.842196i | \(0.318738\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3058.46 | 0.978707 | ||||||||
\(26\) | 62.6643 | + | 427.151i | 0.0181797 | + | 0.123922i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −579.068 | − | 1931.13i | −0.139584 | − | 0.465497i | ||||
\(29\) | 1503.56i | 0.331990i | 0.986127 | + | 0.165995i | \(0.0530836\pi\) | ||||
−0.986127 | + | 0.165995i | \(0.946916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5500.91i | − | 1.02809i | −0.857764 | − | 0.514044i | \(-0.828147\pi\) | ||
0.857764 | − | 0.514044i | \(-0.171853\pi\) | |||||||
\(32\) | −3855.66 | − | 4323.00i | −0.665616 | − | 0.746294i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3602.20 | − | 528.453i | 0.534405 | − | 0.0783988i | ||||
\(35\) | 513.932 | 0.0709145 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4828.88 | −0.579885 | −0.289943 | − | 0.957044i | \(-0.593636\pi\) | ||||
−0.289943 | + | 0.957044i | \(0.593636\pi\) | |||||||
\(38\) | −12256.9 | + | 1798.12i | −1.37696 | + | 0.202004i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1337.87 | − | 624.933i | 0.132210 | − | 0.0617566i | ||||
\(41\) | − | 10911.9i | − | 1.01377i | −0.862013 | − | 0.506886i | \(-0.830796\pi\) | ||
0.862013 | − | 0.506886i | \(-0.169204\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8358.97i | − | 0.689416i | −0.938710 | − | 0.344708i | \(-0.887978\pi\) | ||
0.938710 | − | 0.344708i | \(-0.112022\pi\) | |||||||
\(44\) | −13574.2 | + | 4070.36i | −1.05702 | + | 0.316957i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2246.29 | − | 15311.8i | −0.156521 | − | 1.06692i | ||||
\(47\) | 13956.1 | 0.921551 | 0.460775 | − | 0.887517i | \(-0.347571\pi\) | ||||
0.460775 | + | 0.887517i | \(0.347571\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12837.7 | 0.763829 | ||||||||
\(50\) | −2511.26 | − | 17118.0i | −0.142058 | − | 0.968342i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2339.29 | − | 701.458i | 0.119971 | − | 0.0359744i | ||||
\(53\) | 22806.4i | 1.11524i | 0.830098 | + | 0.557618i | \(0.188285\pi\) | ||||
−0.830098 | + | 0.557618i | \(0.811715\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3612.50i | − | 0.161028i | ||||||
\(56\) | −10333.0 | + | 4826.64i | −0.440307 | + | 0.205672i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8415.33 | − | 1234.55i | 0.328474 | − | 0.0481881i | ||||
\(59\) | 48313.0 | 1.80690 | 0.903450 | − | 0.428694i | \(-0.141026\pi\) | ||||
0.903450 | + | 0.428694i | \(0.141026\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5102.35 | 0.175568 | 0.0877840 | − | 0.996140i | \(-0.472021\pi\) | ||||
0.0877840 | + | 0.996140i | \(0.472021\pi\) | |||||||
\(62\) | −30788.3 | + | 4516.73i | −1.01720 | + | 0.149226i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −21029.8 | + | 25129.5i | −0.641777 | + | 0.766891i | ||||
\(65\) | 622.555i | 0.0182765i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 37352.3i | 1.01655i | 0.861193 | + | 0.508277i | \(0.169717\pi\) | ||||
−0.861193 | + | 0.508277i | \(0.830283\pi\) | |||||||
\(68\) | −5915.45 | − | 19727.4i | −0.155137 | − | 0.517366i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −421.983 | − | 2876.45i | −0.0102932 | − | 0.0701635i | ||||
\(71\) | 75093.0 | 1.76788 | 0.883942 | − | 0.467597i | \(-0.154880\pi\) | ||||
0.883942 | + | 0.467597i | \(0.154880\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −65283.5 | −1.43382 | −0.716912 | − | 0.697163i | \(-0.754445\pi\) | ||||
−0.716912 | + | 0.697163i | \(0.754445\pi\) | |||||||
\(74\) | 3964.93 | + | 27027.0i | 0.0841698 | + | 0.573744i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 20128.0 | + | 67124.8i | 0.399730 | + | 1.33306i | ||||
\(77\) | 27901.0i | 0.536282i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 73222.7i | 1.32001i | 0.751260 | + | 0.660006i | \(0.229446\pi\) | ||||
−0.751260 | + | 0.660006i | \(0.770554\pi\) | |||||||
\(80\) | −4596.22 | − | 6974.86i | −0.0802927 | − | 0.121846i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −61073.3 | + | 8959.62i | −1.00304 | + | 0.147148i | ||||
\(83\) | 65245.0 | 1.03957 | 0.519783 | − | 0.854299i | \(-0.326013\pi\) | ||||
0.519783 | + | 0.854299i | \(0.326013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5250.05 | 0.0788164 | ||||||||
\(86\) | −46784.7 | + | 6863.45i | −0.682115 | + | 0.100068i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 33927.2 | + | 72632.1i | 0.467026 | + | 0.999820i | ||||
\(89\) | 9200.06i | 0.123116i | 0.998103 | + | 0.0615581i | \(0.0196070\pi\) | ||||
−0.998103 | + | 0.0615581i | \(0.980393\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 4808.27i | − | 0.0608675i | ||||||
\(92\) | −83855.2 | + | 25144.7i | −1.03290 | + | 0.309726i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −11459.2 | − | 78111.5i | −0.133762 | − | 0.911791i | ||||
\(95\) | −17863.9 | −0.203080 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 125288. | 1.35201 | 0.676005 | − | 0.736897i | \(-0.263710\pi\) | ||||
0.676005 | + | 0.736897i | \(0.263710\pi\) | |||||||
\(98\) | −10540.9 | − | 71851.8i | −0.110869 | − | 0.755740i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −93746.7 | + | 28110.8i | −0.937467 | + | 0.281108i | ||||
\(101\) | − | 153747.i | − | 1.49970i | −0.661611 | − | 0.749848i | \(-0.730127\pi\) | ||
0.661611 | − | 0.749848i | \(-0.269873\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 10978.1i | − | 0.101961i | −0.998700 | − | 0.0509807i | \(-0.983765\pi\) | ||
0.998700 | − | 0.0509807i | \(-0.0162347\pi\) | |||||||
\(104\) | −5846.78 | − | 12516.9i | −0.0530071 | − | 0.113479i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 127646. | − | 18726.1i | 1.10343 | − | 0.161876i | ||||
\(107\) | −92087.1 | −0.777570 | −0.388785 | − | 0.921329i | \(-0.627105\pi\) | ||||
−0.388785 | + | 0.921329i | \(0.627105\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −179611. | −1.44800 | −0.723998 | − | 0.689802i | \(-0.757698\pi\) | ||||
−0.723998 | + | 0.689802i | \(0.757698\pi\) | |||||||
\(110\) | −20219.0 | + | 2966.18i | −0.159323 | + | 0.0233731i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 35498.7 | + | 53870.0i | 0.267404 | + | 0.405791i | ||||
\(113\) | 214627.i | 1.58120i | 0.612332 | + | 0.790601i | \(0.290232\pi\) | ||||
−0.612332 | + | 0.790601i | \(0.709768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 22316.3i | − | 0.157354i | ||||||
\(116\) | −13819.5 | − | 46086.5i | −0.0953556 | − | 0.318001i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −39669.2 | − | 270405.i | −0.262270 | − | 1.78776i | ||||
\(119\) | −40548.5 | −0.262487 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 35069.6 | 0.217754 | ||||||||
\(122\) | −4189.47 | − | 28557.6i | −0.0254835 | − | 0.173709i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 50559.8 | + | 168612.i | 0.295292 | + | 0.984768i | ||||
\(125\) | − | 50440.4i | − | 0.288738i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 77928.5i | − | 0.428733i | −0.976753 | − | 0.214367i | \(-0.931231\pi\) | ||
0.976753 | − | 0.214367i | \(-0.0687687\pi\) | |||||||
\(128\) | 157916. | + | 97068.9i | 0.851923 | + | 0.523667i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3484.41 | − | 511.172i | 0.0180830 | − | 0.00265283i | ||||
\(131\) | −191085. | −0.972855 | −0.486428 | − | 0.873721i | \(-0.661700\pi\) | ||||
−0.486428 | + | 0.873721i | \(0.661700\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 137971. | 0.676330 | ||||||||
\(134\) | 209059. | − | 30669.5i | 1.00579 | − | 0.147552i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −105556. | + | 49306.4i | −0.489369 | + | 0.228589i | ||||
\(137\) | − | 334957.i | − | 1.52471i | −0.647159 | − | 0.762355i | \(-0.724043\pi\) | ||
0.647159 | − | 0.762355i | \(-0.275957\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 122670.i | − | 0.538518i | −0.963068 | − | 0.269259i | \(-0.913221\pi\) | ||
0.963068 | − | 0.269259i | \(-0.0867787\pi\) | |||||||
\(140\) | −15752.8 | + | 4723.63i | −0.0679264 | + | 0.0203684i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −61658.0 | − | 420292.i | −0.256607 | − | 1.74916i | ||||
\(143\) | −33798.1 | −0.138214 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 12265.0 | 0.0484448 | ||||||||
\(146\) | 53603.5 | + | 365388.i | 0.208119 | + | 1.41864i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 148013. | − | 44383.0i | 0.555451 | − | 0.166557i | ||||
\(149\) | 344978.i | 1.27299i | 0.771280 | + | 0.636496i | \(0.219617\pi\) | ||||
−0.771280 | + | 0.636496i | \(0.780383\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 208482.i | − | 0.744093i | −0.928214 | − | 0.372046i | \(-0.878656\pi\) | ||
0.928214 | − | 0.372046i | \(-0.121344\pi\) | |||||||
\(152\) | 359167. | − | 167771.i | 1.26092 | − | 0.588989i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 156160. | − | 22909.2i | 0.530603 | − | 0.0778409i | ||||
\(155\) | −44872.6 | −0.150021 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 229386. | 0.742706 | 0.371353 | − | 0.928492i | \(-0.378894\pi\) | ||||
0.371353 | + | 0.928492i | \(0.378894\pi\) | |||||||
\(158\) | 409824. | − | 60122.3i | 1.30603 | − | 0.191599i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −35264.0 | + | 31451.8i | −0.108901 | + | 0.0971282i | ||||
\(161\) | 172359.i | 0.524047i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 358203.i | − | 1.05599i | −0.849247 | − | 0.527996i | \(-0.822944\pi\) | ||
0.849247 | − | 0.527996i | \(-0.177056\pi\) | |||||||
\(164\) | 100293. | + | 334467.i | 0.291180 | + | 0.971055i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −53571.8 | − | 365173.i | −0.150892 | − | 1.02856i | ||||
\(167\) | −323824. | −0.898500 | −0.449250 | − | 0.893406i | \(-0.648309\pi\) | ||||
−0.449250 | + | 0.893406i | \(0.648309\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365468. | −0.984313 | ||||||||
\(170\) | −4310.76 | − | 29384.3i | −0.0114401 | − | 0.0779817i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 76828.7 | + | 256216.i | 0.198017 | + | 0.660367i | ||||
\(173\) | − | 587779.i | − | 1.49313i | −0.665310 | − | 0.746567i | \(-0.731701\pi\) | ||
0.665310 | − | 0.746567i | \(-0.268299\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 192691.i | 0.475626i | ||||||||
\(176\) | 378661. | − | 249526.i | 0.921444 | − | 0.607204i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 51492.2 | − | 7554.06i | 0.121812 | − | 0.0178702i | ||||
\(179\) | −496110. | −1.15730 | −0.578649 | − | 0.815577i | \(-0.696420\pi\) | ||||
−0.578649 | + | 0.815577i | \(0.696420\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 206785. | 0.469163 | 0.234581 | − | 0.972096i | \(-0.424628\pi\) | ||||
0.234581 | + | 0.972096i | \(0.424628\pi\) | |||||||
\(182\) | −26911.6 | + | 3948.01i | −0.0602229 | + | 0.00883487i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 209586. | + | 448687.i | 0.456371 | + | 0.977010i | ||||
\(185\) | 39390.6i | 0.0846182i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 285022.i | 0.596039i | ||||||||
\(188\) | −427777. | + | 128273.i | −0.882720 | + | 0.264692i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14667.8 | + | 99983.3i | 0.0294769 | + | 0.200929i | ||||
\(191\) | −601888. | −1.19380 | −0.596901 | − | 0.802315i | \(-0.703602\pi\) | ||||
−0.596901 | + | 0.802315i | \(0.703602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −267729. | −0.517372 | −0.258686 | − | 0.965961i | \(-0.583289\pi\) | ||||
−0.258686 | + | 0.965961i | \(0.583289\pi\) | |||||||
\(194\) | −102872. | − | 701230.i | −0.196243 | − | 1.33769i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −393496. | + | 117993.i | −0.731644 | + | 0.219390i | ||||
\(197\) | 652488.i | 1.19786i | 0.800800 | + | 0.598931i | \(0.204408\pi\) | ||||
−0.800800 | + | 0.598931i | \(0.795592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.08073e6i | 1.93458i | 0.253675 | + | 0.967289i | \(0.418361\pi\) | ||||
−0.253675 | + | 0.967289i | \(0.581639\pi\) | |||||||
\(200\) | 234309. | + | 501614.i | 0.414204 | + | 0.886737i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −860513. | + | 126240.i | −1.48381 | + | 0.217680i | ||||
\(203\) | −94728.1 | −0.161339 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −89011.7 | −0.147932 | ||||||||
\(206\) | −61444.0 | + | 9014.02i | −0.100882 | + | 0.0147996i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −65255.9 | + | 43001.6i | −0.104583 | + | 0.0689171i | ||||
\(209\) | − | 969820.i | − | 1.53577i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3191.14i | − | 0.00493447i | −0.999997 | − | 0.00246723i | \(-0.999215\pi\) | ||
0.999997 | − | 0.00246723i | \(-0.000785346\pi\) | |||||||
\(212\) | −209617. | − | 699053.i | −0.320323 | − | 1.06824i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 75611.6 | + | 515407.i | 0.112864 | + | 0.769335i | ||||
\(215\) | −68186.7 | −0.100601 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 346572. | 0.499624 | ||||||||
\(218\) | 147477. | + | 1.00527e6i | 0.210175 | + | 1.43266i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 33203.1 | + | 110729.i | 0.0462511 | + | 0.154243i | ||||
\(221\) | − | 49118.8i | − | 0.0676498i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 105595.i | 0.142194i | 0.997469 | + | 0.0710971i | \(0.0226500\pi\) | ||||
−0.997469 | + | 0.0710971i | \(0.977350\pi\) | |||||||
\(224\) | 272360. | − | 242917.i | 0.362680 | − | 0.323472i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.20125e6 | − | 176227.i | 1.56446 | − | 0.229510i | ||||
\(227\) | 620193. | 0.798845 | 0.399423 | − | 0.916767i | \(-0.369211\pi\) | ||||
0.399423 | + | 0.916767i | \(0.369211\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −867924. | −1.09369 | −0.546844 | − | 0.837235i | \(-0.684171\pi\) | ||||
−0.546844 | + | 0.837235i | \(0.684171\pi\) | |||||||
\(230\) | −124903. | + | 18323.7i | −0.155688 | + | 0.0228398i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −246597. | + | 115188.i | −0.300793 | + | 0.140503i | ||||
\(233\) | 296205.i | 0.357440i | 0.983900 | + | 0.178720i | \(0.0571956\pi\) | ||||
−0.983900 | + | 0.178720i | \(0.942804\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 113844.i | − | 0.134475i | ||||||
\(236\) | −1.48087e6 | + | 444053.i | −1.73076 | + | 0.518985i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 33293.9 | + | 226948.i | 0.0380998 | + | 0.259707i | ||||
\(239\) | 696767. | 0.789028 | 0.394514 | − | 0.918890i | \(-0.370913\pi\) | ||||
0.394514 | + | 0.918890i | \(0.370913\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −138720. | −0.153849 | −0.0769247 | − | 0.997037i | \(-0.524510\pi\) | ||||
−0.0769247 | + | 0.997037i | \(0.524510\pi\) | |||||||
\(242\) | −28795.2 | − | 196282.i | −0.0316069 | − | 0.215448i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −156395. | + | 46896.5i | −0.168170 | + | 0.0504273i | ||||
\(245\) | − | 104721.i | − | 0.111460i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 167132.i | 0.174308i | ||||||||
\(248\) | 902197. | − | 421426.i | 0.931477 | − | 0.435103i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −282312. | + | 41416.0i | −0.285680 | + | 0.0419100i | ||||
\(251\) | 730682. | 0.732056 | 0.366028 | − | 0.930604i | \(-0.380717\pi\) | ||||
0.366028 | + | 0.930604i | \(0.380717\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.21154e6 | 1.18997 | ||||||||
\(254\) | −436162. | + | 63986.1i | −0.424193 | + | 0.0622303i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 413627. | − | 963548.i | 0.394466 | − | 0.918911i | ||||
\(257\) | 1.47952e6i | 1.39730i | 0.715465 | + | 0.698649i | \(0.246215\pi\) | ||||
−0.715465 | + | 0.698649i | \(0.753785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 304232.i | − | 0.281809i | ||||||
\(260\) | −5722.01 | − | 19082.3i | −0.00524946 | − | 0.0175064i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 156898. | + | 1.06949e6i | 0.141209 | + | 0.962552i | ||||
\(263\) | 1.91797e6 | 1.70983 | 0.854914 | − | 0.518770i | \(-0.173610\pi\) | ||||
0.854914 | + | 0.518770i | \(0.173610\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 186039. | 0.162738 | ||||||||
\(266\) | −113286. | − | 772216.i | −0.0981688 | − | 0.669168i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −343312. | − | 1.14491e6i | −0.291979 | − | 0.973720i | ||||
\(269\) | 416360.i | 0.350823i | 0.984495 | + | 0.175411i | \(0.0561256\pi\) | ||||
−0.984495 | + | 0.175411i | \(0.943874\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 140033.i | 0.115826i | 0.998322 | + | 0.0579130i | \(0.0184446\pi\) | ||||
−0.998322 | + | 0.0579130i | \(0.981555\pi\) | |||||||
\(272\) | 362636. | + | 550308.i | 0.297200 | + | 0.451007i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.87473e6 | + | 275029.i | −1.50856 | + | 0.221310i | ||||
\(275\) | 1.35445e6 | 1.08002 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.45860e6 | −1.14219 | −0.571095 | − | 0.820884i | \(-0.693481\pi\) | ||||
−0.571095 | + | 0.820884i | \(0.693481\pi\) | |||||||
\(278\) | −686575. | + | 100723.i | −0.532815 | + | 0.0781654i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 39372.4 | + | 84289.3i | 0.0300121 | + | 0.0642506i | ||||
\(281\) | − | 1.04557e6i | − | 0.789927i | −0.918697 | − | 0.394963i | \(-0.870757\pi\) | ||
0.918697 | − | 0.394963i | \(-0.129243\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.18731e6i | − | 0.881244i | −0.897693 | − | 0.440622i | \(-0.854758\pi\) | ||
0.897693 | − | 0.440622i | \(-0.145242\pi\) | |||||||
\(284\) | −2.30172e6 | + | 690193.i | −1.69339 | + | 0.507779i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 27751.2 | + | 189166.i | 0.0200617 | + | 0.136750i | ||||
\(287\) | 687477. | 0.492667 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00563e6 | 0.708265 | ||||||||
\(290\) | −10070.6 | − | 68646.5i | −0.00703172 | − | 0.0479317i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.00104e6 | − | 600032.i | 1.37341 | − | 0.411829i | ||||
\(293\) | 638803.i | 0.434708i | 0.976093 | + | 0.217354i | \(0.0697426\pi\) | ||||
−0.976093 | + | 0.217354i | \(0.930257\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 394104.i | − | 0.263667i | ||||||
\(296\) | −369941. | − | 791978.i | −0.245416 | − | 0.525393i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.93082e6 | − | 283257.i | 1.25951 | − | 0.184774i | ||||
\(299\) | −208789. | −0.135061 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 526637. | 0.335039 | ||||||||
\(302\) | −1.16687e6 | + | 171182.i | −0.736213 | + | 0.108004i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.23391e6 | − | 1.87248e6i | −0.765773 | − | 1.16208i | ||||
\(305\) | − | 41621.4i | − | 0.0256193i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.84508e6i | − | 1.11730i | −0.829404 | − | 0.558650i | \(-0.811320\pi\) | ||
0.829404 | − | 0.558650i | \(-0.188680\pi\) | |||||||
\(308\) | −256443. | − | 855212.i | −0.154033 | − | 0.513685i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 36844.4 | + | 251150.i | 0.0217754 | + | 0.148432i | ||||
\(311\) | −987920. | −0.579189 | −0.289595 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289595 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 76622.6 | 0.0442075 | 0.0221037 | − | 0.999756i | \(-0.492964\pi\) | ||||
0.0221037 | + | 0.999756i | \(0.492964\pi\) | |||||||
\(314\) | −188346. | − | 1.28386e6i | −0.107803 | − | 0.734841i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −673002. | − | 2.24440e6i | −0.379139 | − | 1.26439i | ||||
\(317\) | − | 1.50331e6i | − | 0.840232i | −0.907470 | − | 0.420116i | \(-0.861989\pi\) | ||
0.907470 | − | 0.420116i | \(-0.138011\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 665858.i | 0.366357i | ||||||||
\(320\) | 204989. | + | 171546.i | 0.111907 | + | 0.0936497i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 964686. | − | 141522.i | 0.518497 | − | 0.0760650i | ||||
\(323\) | 1.40944e6 | 0.751692 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −233417. | −0.122581 | ||||||||
\(326\) | −2.00484e6 | + | 294116.i | −1.04481 | + | 0.153276i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.78965e6 | − | 835962.i | 0.918507 | − | 0.429044i | ||||
\(329\) | 879270.i | 0.447850i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 2.95260e6i | − | 1.48127i | −0.671906 | − | 0.740636i | \(-0.734524\pi\) | ||
0.671906 | − | 0.740636i | \(-0.265476\pi\) | |||||||
\(332\) | −1.99986e6 | + | 599678.i | −0.995761 | + | 0.298588i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 265888. | + | 1.81243e6i | 0.130417 | + | 0.888985i | ||||
\(335\) | 304694. | 0.148338 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 376009. | 0.180353 | 0.0901766 | − | 0.995926i | \(-0.471257\pi\) | ||||
0.0901766 | + | 0.995926i | \(0.471257\pi\) | |||||||
\(338\) | 300082. | + | 2.04551e6i | 0.142872 | + | 0.973889i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −160923. | + | 48254.1i | −0.0754953 | + | 0.0226380i | ||||
\(341\) | − | 2.43611e6i | − | 1.13451i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.86769e6i | 0.857176i | ||||||||
\(344\) | 1.37094e6 | − | 640382.i | 0.624631 | − | 0.291772i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.28977e6 | + | 482618.i | −1.47732 | + | 0.216727i | ||||
\(347\) | −1.46748e6 | −0.654255 | −0.327128 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327128 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.03644e6 | 0.894970 | 0.447485 | − | 0.894291i | \(-0.352320\pi\) | ||||
0.447485 | + | 0.894291i | \(0.352320\pi\) | |||||||
\(350\) | 1.07848e6 | − | 158216.i | 0.470589 | − | 0.0690368i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.70750e6 | − | 1.91446e6i | −0.734520 | − | 0.823550i | ||||
\(353\) | 2.68754e6i | 1.14794i | 0.818877 | + | 0.573969i | \(0.194597\pi\) | ||||
−0.818877 | + | 0.573969i | \(0.805403\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 612557.i | − | 0.257974i | ||||||
\(356\) | −84559.3 | − | 281997.i | −0.0353620 | − | 0.117929i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 407350. | + | 2.77670e6i | 0.167981 | + | 1.14504i | ||||
\(359\) | −929088. | −0.380470 | −0.190235 | − | 0.981739i | \(-0.560925\pi\) | ||||
−0.190235 | + | 0.981739i | \(0.560925\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.31968e6 | −0.936827 | ||||||||
\(362\) | −169789. | − | 1.15737e6i | −0.0680986 | − | 0.464194i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 44193.7 | + | 147381.i | 0.0174826 | + | 0.0583028i | ||||
\(365\) | 532537.i | 0.209227i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.08684e6i | 1.97144i | 0.168398 | + | 0.985719i | \(0.446141\pi\) | ||||
−0.168398 | + | 0.985719i | \(0.553859\pi\) | |||||||
\(368\) | 2.33919e6 | − | 1.54145e6i | 0.900421 | − | 0.593350i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 220467. | − | 32343.2i | 0.0837221 | − | 0.0122823i | ||||
\(371\) | −1.43686e6 | −0.541976 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −770228. | −0.286647 | −0.143323 | − | 0.989676i | \(-0.545779\pi\) | ||||
−0.143323 | + | 0.989676i | \(0.545779\pi\) | |||||||
\(374\) | 1.59525e6 | − | 234028.i | 0.589726 | − | 0.0865145i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.06918e6 | + | 2.28892e6i | 0.390014 | + | 0.834952i | ||||
\(377\) | − | 114750.i | − | 0.0415812i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 174443.i | 0.0623815i | 0.999513 | + | 0.0311907i | \(0.00992993\pi\) | ||||
−0.999513 | + | 0.0311907i | \(0.990070\pi\) | |||||||
\(380\) | 547558. | − | 164190.i | 0.194523 | − | 0.0583295i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 494203. | + | 3.36874e6i | 0.173279 | + | 1.18116i | ||||
\(383\) | 1.32370e6 | 0.461096 | 0.230548 | − | 0.973061i | \(-0.425948\pi\) | ||||
0.230548 | + | 0.973061i | \(0.425948\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 227597. | 0.0782555 | ||||||||
\(386\) | 219829. | + | 1.49847e6i | 0.0750961 | + | 0.511893i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.84028e6 | + | 1.15154e6i | −1.29504 | + | 0.388330i | ||||
\(389\) | 2.29230e6i | 0.768064i | 0.923320 | + | 0.384032i | \(0.125465\pi\) | ||||
−0.923320 | + | 0.384032i | \(0.874535\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.76073e6i | 0.582440i | ||||||||
\(392\) | 983496. | + | 2.10549e6i | 0.323264 | + | 0.692051i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.65194e6 | − | 535750.i | 1.18518 | − | 0.173869i | ||||
\(395\) | 597300. | 0.192619 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.02339e6 | −1.59963 | −0.799816 | − | 0.600245i | \(-0.795070\pi\) | ||||
−0.799816 | + | 0.600245i | \(0.795070\pi\) | |||||||
\(398\) | 6.04882e6 | − | 887378.i | 1.91409 | − | 0.280803i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.61512e6 | − | 1.72328e6i | 0.817225 | − | 0.538526i | ||||
\(401\) | − | 5.23840e6i | − | 1.62681i | −0.581696 | − | 0.813406i | \(-0.697611\pi\) | ||
0.581696 | − | 0.813406i | \(-0.302389\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 419822.i | 0.128766i | ||||||||
\(404\) | 1.41311e6 | + | 4.71259e6i | 0.430749 | + | 1.43650i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 77780.1 | + | 530188.i | 0.0234182 | + | 0.159630i | ||||
\(407\) | −2.13849e6 | −0.639914 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.62846e6 | 0.481360 | 0.240680 | − | 0.970605i | \(-0.422630\pi\) | ||||
0.240680 | + | 0.970605i | \(0.422630\pi\) | |||||||
\(410\) | 73086.4 | + | 498193.i | 0.0214722 | + | 0.146365i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 100902. | + | 336498.i | 0.0292858 | + | 0.0976650i | ||||
\(413\) | 3.04385e6i | 0.878107i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 532223.i | − | 0.151696i | ||||||
\(416\) | 294259. | + | 329925.i | 0.0833673 | + | 0.0934722i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.42803e6 | + | 796307.i | −1.51950 | + | 0.222915i | ||||
\(419\) | −1.94936e6 | −0.542446 | −0.271223 | − | 0.962517i | \(-0.587428\pi\) | ||||
−0.271223 | + | 0.962517i | \(0.587428\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.98298e6 | 1.09522 | 0.547611 | − | 0.836733i | \(-0.315537\pi\) | ||||
0.547611 | + | 0.836733i | \(0.315537\pi\) | |||||||
\(422\) | −17860.7 | + | 2620.21i | −0.00488221 | + | 0.000716234i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.74045e6 | + | 1.74720e6i | −1.01044 | + | 0.471985i | ||||
\(425\) | 1.96843e6i | 0.528624i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 321461.i | 0.0853215i | ||||||||
\(428\) | 2.82262e6 | − | 846388.i | 0.744806 | − | 0.223337i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 55987.3 | + | 381637.i | 0.0146022 | + | 0.0995359i | ||||
\(431\) | −7.18163e6 | −1.86222 | −0.931108 | − | 0.364745i | \(-0.881156\pi\) | ||||
−0.931108 | + | 0.364745i | \(0.881156\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 150971. | 0.0386966 | 0.0193483 | − | 0.999813i | \(-0.493841\pi\) | ||||
0.0193483 | + | 0.999813i | \(0.493841\pi\) | |||||||
\(434\) | −284566. | − | 1.93974e6i | −0.0725201 | − | 0.494333i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.50538e6 | − | 1.65084e6i | 1.38698 | − | 0.415899i | ||||
\(437\) | − | 5.99109e6i | − | 1.50073i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.22773e6i | 1.04700i | 0.852026 | + | 0.523499i | \(0.175374\pi\) | ||||
−0.852026 | + | 0.523499i | \(0.824626\pi\) | |||||||
\(440\) | 592482. | − | 276755.i | 0.145896 | − | 0.0681496i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −274915. | + | 40330.8i | −0.0669334 | + | 0.00981932i | ||||
\(443\) | −3.31077e6 | −0.801529 | −0.400764 | − | 0.916181i | \(-0.631255\pi\) | ||||
−0.400764 | + | 0.916181i | \(0.631255\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 75047.7 | 0.0179654 | ||||||||
\(446\) | 591010. | − | 86702.9i | 0.140688 | − | 0.0206394i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.58322e6 | − | 1.32493e6i | −0.372689 | − | 0.311887i | ||||
\(449\) | − | 5.19683e6i | − | 1.21653i | −0.793734 | − | 0.608265i | \(-0.791866\pi\) | ||
0.793734 | − | 0.608265i | \(-0.208134\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.83239e6i | − | 1.11872i | ||||||
\(452\) | −1.97267e6 | − | 6.57865e6i | −0.454159 | − | 1.51458i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −509233. | − | 3.47119e6i | −0.115952 | − | 0.790385i | ||||
\(455\) | −39222.6 | −0.00888193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −851714. | −0.190767 | −0.0953835 | − | 0.995441i | \(-0.530408\pi\) | ||||
−0.0953835 | + | 0.995441i | \(0.530408\pi\) | |||||||
\(458\) | 712642. | + | 4.85773e6i | 0.158748 | + | 1.08210i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 205113. | + | 684032.i | 0.0451959 | + | 0.150724i | ||||
\(461\) | 8.48893e6i | 1.86038i | 0.367084 | + | 0.930188i | \(0.380356\pi\) | ||||
−0.367084 | + | 0.930188i | \(0.619644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.13046e6i | 1.11225i | 0.831098 | + | 0.556127i | \(0.187713\pi\) | ||||
−0.831098 | + | 0.556127i | \(0.812287\pi\) | |||||||
\(464\) | 847178. | + | 1.28561e6i | 0.182675 | + | 0.277213i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.65784e6 | − | 243211.i | 0.353654 | − | 0.0518821i | ||||
\(467\) | −5.02410e6 | −1.06602 | −0.533011 | − | 0.846108i | \(-0.678940\pi\) | ||||
−0.533011 | + | 0.846108i | \(0.678940\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.35329e6 | −0.494019 | ||||||||
\(470\) | −637180. | + | 93476.1i | −0.133051 | + | 0.0195189i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.70127e6 | + | 7.92376e6i | 0.764708 | + | 1.63710i | ||||
\(473\) | − | 3.70181e6i | − | 0.760784i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.69780e6i | − | 1.36207i | ||||||
\(476\) | 1.24288e6 | − | 372689.i | 0.251427 | − | 0.0753926i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −572107. | − | 3.89977e6i | −0.114527 | − | 0.780672i | ||||
\(479\) | −2.68540e6 | −0.534773 | −0.267387 | − | 0.963589i | \(-0.586160\pi\) | ||||
−0.267387 | + | 0.963589i | \(0.586160\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 368533. | 0.0726297 | ||||||||
\(482\) | 113901. | + | 776408.i | 0.0223311 | + | 0.152220i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.07494e6 | + | 322330.i | −0.208579 | + | 0.0625443i | ||||
\(485\) | − | 1.02201e6i | − | 0.197288i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.34008e6i | 1.02029i | 0.860087 | + | 0.510147i | \(0.170409\pi\) | ||||
−0.860087 | + | 0.510147i | \(0.829591\pi\) | |||||||
\(488\) | 390892. | + | 836829.i | 0.0743031 | + | 0.159070i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −586117. | + | 85985.0i | −0.110279 | + | 0.0161783i | ||||
\(491\) | −2.63306e6 | −0.492898 | −0.246449 | − | 0.969156i | \(-0.579264\pi\) | ||||
−0.246449 | + | 0.969156i | \(0.579264\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −967692. | −0.179316 | ||||||||
\(494\) | 935430. | − | 137230.i | 0.172462 | − | 0.0253007i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.09948e6 | − | 4.70352e6i | −0.565698 | − | 0.858458i | ||||
\(497\) | 4.73106e6i | 0.859146i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 9.98944e6i | − | 1.79593i | −0.440066 | − | 0.897966i | \(-0.645045\pi\) | ||
0.440066 | − | 0.897966i | \(-0.354955\pi\) | |||||||
\(500\) | 463606. | + | 1.54608e6i | 0.0829324 | + | 0.276571i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −599954. | − | 4.08959e6i | −0.106257 | − | 0.724303i | ||||
\(503\) | 6.68072e6 | 1.17734 | 0.588672 | − | 0.808372i | \(-0.299651\pi\) | ||||
0.588672 | + | 0.808372i | \(0.299651\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.25416e6 | −0.218839 | ||||||||
\(506\) | −994781. | − | 6.78093e6i | −0.172723 | − | 1.17737i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 716254. | + | 2.38864e6i | 0.123142 | + | 0.410668i | ||||
\(509\) | − | 5.03549e6i | − | 0.861483i | −0.902475 | − | 0.430742i | \(-0.858252\pi\) | ||
0.902475 | − | 0.430742i | \(-0.141748\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 4.11303e6i | − | 0.696802i | ||||||
\(512\) | −5.73255e6 | − | 1.52389e6i | −0.966436 | − | 0.256909i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.28081e6 | − | 1.21482e6i | 1.38250 | − | 0.202817i | ||||
\(515\) | −89552.0 | −0.0148784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.18053e6 | 1.01695 | ||||||||
\(518\) | −1.70277e6 | + | 249801.i | −0.278825 | + | 0.0409044i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −102104. | + | 47694.0i | −0.0165591 | + | 0.00773492i | ||||
\(521\) | 3.01932e6i | 0.487321i | 0.969861 | + | 0.243661i | \(0.0783483\pi\) | ||||
−0.969861 | + | 0.243661i | \(0.921652\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.99932e6i | − | 0.799202i | −0.916689 | − | 0.399601i | \(-0.869149\pi\) | ||
0.916689 | − | 0.399601i | \(-0.130851\pi\) | |||||||
\(524\) | 5.85706e6 | − | 1.75629e6i | 0.931862 | − | 0.279427i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.57482e6 | − | 1.07348e7i | −0.248180 | − | 1.69172i | ||||
\(527\) | 3.54039e6 | 0.555296 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.04798e6 | 0.162823 | ||||||||
\(530\) | −152754. | − | 1.04125e6i | −0.0236213 | − | 0.161014i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.22904e6 | + | 1.26812e6i | −0.647832 | + | 0.194258i | ||||
\(533\) | 832781.i | 0.126973i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 751183.i | 0.113465i | ||||||||
\(536\) | −6.12611e6 | + | 2.86157e6i | −0.921028 | + | 0.430222i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.33034e6 | − | 341868.i | 0.347108 | − | 0.0509217i | ||||
\(539\) | 5.68523e6 | 0.842900 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.44567e6 | 1.38752 | 0.693761 | − | 0.720206i | \(-0.255953\pi\) | ||||
0.693761 | + | 0.720206i | \(0.255953\pi\) | |||||||
\(542\) | 783755. | − | 114979.i | 0.114599 | − | 0.0168121i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.78229e6 | − | 2.48151e6i | 0.403093 | − | 0.359516i | ||||
\(545\) | 1.46514e6i | 0.211295i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 2.41771e6i | − | 0.345491i | −0.984967 | − | 0.172745i | \(-0.944736\pi\) | ||
0.984967 | − | 0.172745i | \(-0.0552638\pi\) | |||||||
\(548\) | 3.07864e6 | + | 1.02670e7i | 0.437933 | + | 1.46046i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.11213e6 | − | 7.58080e6i | −0.156764 | − | 1.06858i | ||||
\(551\) | 3.29268e6 | 0.462030 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.61322e6 | −0.641492 | ||||||||
\(554\) | 1.19764e6 | + | 8.16373e6i | 0.165788 | + | 1.13009i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.12748e6 | + | 3.76002e6i | 0.154675 | + | 0.515826i | ||||
\(557\) | − | 6.84325e6i | − | 0.934597i | −0.884100 | − | 0.467298i | \(-0.845227\pi\) | ||
0.884100 | − | 0.467298i | \(-0.154773\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 637945.i | 0.0863483i | ||||||||
\(560\) | 439434. | − | 289574.i | 0.0592140 | − | 0.0390202i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.85199e6 | + | 858504.i | −0.781561 | + | 0.114657i | ||||
\(563\) | 1.21299e7 | 1.61282 | 0.806411 | − | 0.591355i | \(-0.201407\pi\) | ||||
0.806411 | + | 0.591355i | \(0.201407\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.75077e6 | 0.230733 | ||||||||
\(566\) | −6.64529e6 | + | 974882.i | −0.871912 | + | 0.127912i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 5.75289e6 | + | 1.23159e7i | 0.748196 | + | 1.60175i | ||||
\(569\) | 9.32124e6i | 1.20696i | 0.797378 | + | 0.603480i | \(0.206220\pi\) | ||||
−0.797378 | + | 0.603480i | \(0.793780\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 4.70232e6i | − | 0.603562i | −0.953377 | − | 0.301781i | \(-0.902419\pi\) | ||
0.953377 | − | 0.301781i | \(-0.0975811\pi\) | |||||||
\(572\) | 1.03597e6 | − | 310644.i | 0.132390 | − | 0.0396984i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −564479. | − | 3.84777e6i | −0.0715103 | − | 0.487450i | ||||
\(575\) | 8.36718e6 | 1.05538 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.02368e6 | −0.253048 | −0.126524 | − | 0.991964i | \(-0.540382\pi\) | ||||
−0.126524 | + | 0.991964i | \(0.540382\pi\) | |||||||
\(578\) | −825714. | − | 5.62848e6i | −0.102804 | − | 0.700764i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −375942. | + | 112730.i | −0.0464035 | + | 0.0139145i | ||||
\(581\) | 4.11060e6i | 0.505202i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.00999e7i | 1.23068i | ||||||||
\(584\) | −5.00138e6 | − | 1.07071e7i | −0.606817 | − | 1.29909i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.57534e6 | − | 524513.i | 0.430104 | − | 0.0630975i | ||||
\(587\) | 1.16472e7 | 1.39517 | 0.697586 | − | 0.716501i | \(-0.254258\pi\) | ||||
0.697586 | + | 0.716501i | \(0.254258\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.20466e7 | −1.43079 | ||||||||
\(590\) | −2.20578e6 | + | 323594.i | −0.260875 | + | 0.0382711i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.12891e6 | + | 2.72082e6i | −0.484207 | + | 0.319078i | ||||
\(593\) | − | 1.67099e6i | − | 0.195136i | −0.995229 | − | 0.0975681i | \(-0.968894\pi\) | ||
0.995229 | − | 0.0975681i | \(-0.0311064\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 330767.i | 0.0383027i | ||||||||
\(596\) | −3.17075e6 | − | 1.05741e7i | −0.365634 | − | 1.21935i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 171434. | + | 1.16858e6i | 0.0196040 | + | 0.133630i | ||||
\(599\) | −7.06244e6 | −0.804244 | −0.402122 | − | 0.915586i | \(-0.631727\pi\) | ||||
−0.402122 | + | 0.915586i | \(0.631727\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.79092e6 | −0.879838 | −0.439919 | − | 0.898038i | \(-0.644993\pi\) | ||||
−0.439919 | + | 0.898038i | \(0.644993\pi\) | |||||||
\(602\) | −432415. | − | 2.94756e6i | −0.0486306 | − | 0.331491i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.91620e6 | + | 6.39033e6i | 0.213721 | + | 0.712739i | ||||
\(605\) | − | 286073.i | − | 0.0317752i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.43345e7i | 1.57911i | 0.613682 | + | 0.789553i | \(0.289688\pi\) | ||||
−0.613682 | + | 0.789553i | \(0.710312\pi\) | |||||||
\(608\) | −9.46705e6 | + | 8.44361e6i | −1.03862 | + | 0.926337i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −232953. | + | 34174.8i | −0.0253480 | + | 0.00371862i | ||||
\(611\) | −1.06511e6 | −0.115423 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13027.0 | 0.00140021 | 0.000700105 | − | 1.00000i | \(-0.499777\pi\) | ||||
0.000700105 | 1.00000i | \(0.499777\pi\) | ||||||||
\(614\) | −1.03268e7 | + | 1.51497e6i | −1.10547 | + | 0.162175i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.57601e6 | + | 2.13750e6i | −0.485887 | + | 0.226963i | ||||
\(617\) | 4.07010e6i | 0.430420i | 0.976568 | + | 0.215210i | \(0.0690436\pi\) | ||||
−0.976568 | + | 0.215210i | \(0.930956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.13635e6i | 0.433902i | 0.976183 | + | 0.216951i | \(0.0696111\pi\) | ||||
−0.976183 | + | 0.216951i | \(0.930389\pi\) | |||||||
\(620\) | 1.37542e6 | − | 412432.i | 0.143700 | − | 0.0430896i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 811169. | + | 5.52933e6i | 0.0840689 | + | 0.573056i | ||||
\(623\) | −579628. | −0.0598314 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.14622e6 | 0.936573 | ||||||||
\(626\) | −62913.9 | − | 428853.i | −0.00641668 | − | 0.0437393i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.03104e6 | + | 2.10832e6i | −0.711411 | + | 0.213323i | ||||
\(629\) | − | 3.10787e6i | − | 0.313211i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.49325e6i | 0.749198i | 0.927187 | + | 0.374599i | \(0.122220\pi\) | ||||
−0.927187 | + | 0.374599i | \(0.877780\pi\) | |||||||
\(632\) | −1.20092e7 | + | 5.60960e6i | −1.19597 | + | 0.558650i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.41392e6 | + | 1.23435e6i | −0.831334 | + | 0.121959i | ||||
\(635\) | −635687. | −0.0625617 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −979754. | −0.0956684 | ||||||||
\(638\) | 3.72677e6 | − | 546728.i | 0.362478 | − | 0.0531765i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 791821. | − | 1.28817e6i | 0.0764148 | − | 0.124315i | ||||
\(641\) | − | 8.26174e6i | − | 0.794194i | −0.917777 | − | 0.397097i | \(-0.870018\pi\) | ||
0.917777 | − | 0.397097i | \(-0.129982\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 7.49878e6i | − | 0.715259i | −0.933864 | − | 0.357630i | \(-0.883585\pi\) | ||
0.933864 | − | 0.357630i | \(-0.116415\pi\) | |||||||
\(644\) | −1.58418e6 | − | 5.28309e6i | −0.150519 | − | 0.501965i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.15727e6 | − | 7.88855e6i | −0.109107 | − | 0.743731i | ||||
\(647\) | 9.71856e6 | 0.912728 | 0.456364 | − | 0.889793i | \(-0.349152\pi\) | ||||
0.456364 | + | 0.889793i | \(0.349152\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.13957e7 | 1.99395 | ||||||||
\(650\) | 191656. | + | 1.30642e6i | 0.0177926 | + | 0.121283i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.29231e6 | + | 1.09795e7i | 0.303306 | + | 1.01150i | ||||
\(653\) | 3.11570e6i | 0.285939i | 0.989727 | + | 0.142969i | \(0.0456651\pi\) | ||||
−0.989727 | + | 0.142969i | \(0.954335\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.55874e6i | 0.141961i | ||||||||
\(656\) | −6.14829e6 | − | 9.33016e6i | −0.557821 | − | 0.846505i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.92123e6 | − | 721958.i | 0.443107 | − | 0.0650051i | ||||
\(659\) | −259955. | −0.0233176 | −0.0116588 | − | 0.999932i | \(-0.503711\pi\) | ||||
−0.0116588 | + | 0.999932i | \(0.503711\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.17173e7 | −1.04310 | −0.521548 | − | 0.853222i | \(-0.674645\pi\) | ||||
−0.521548 | + | 0.853222i | \(0.674645\pi\) | |||||||
\(662\) | −1.65256e7 | + | 2.42435e6i | −1.46558 | + | 0.215005i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.99843e6 | + | 1.07007e7i | 0.439960 | + | 0.941876i | ||||
\(665\) | − | 1.12547e6i | − | 0.0986917i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.11336e6i | 0.357999i | ||||||||
\(668\) | 9.92574e6 | − | 2.97632e6i | 0.860640 | − | 0.258071i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −250181. | − | 1.70536e6i | −0.0215311 | − | 0.146767i | ||||
\(671\) | 2.25960e6 | 0.193743 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.35278e7 | −1.15130 | −0.575652 | − | 0.817695i | \(-0.695252\pi\) | ||||
−0.575652 | + | 0.817695i | \(0.695252\pi\) | |||||||
\(674\) | −308737. | − | 2.10450e6i | −0.0261781 | − | 0.178443i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.12022e7 | − | 3.35908e6i | 0.942837 | − | 0.282718i | ||||
\(677\) | 2.52827e6i | 0.212008i | 0.994366 | + | 0.106004i | \(0.0338056\pi\) | ||||
−0.994366 | + | 0.106004i | \(0.966194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.89347e6i | 0.657042i | ||||||||
\(680\) | 402207. | + | 861055.i | 0.0333563 | + | 0.0714099i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.36348e7 | + | 2.00026e6i | −1.12250 | + | 0.164674i | ||||
\(683\) | −1.20227e7 | −0.986170 | −0.493085 | − | 0.869981i | \(-0.664131\pi\) | ||||
−0.493085 | + | 0.869981i | \(0.664131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.73234e6 | −0.222489 | ||||||||
\(686\) | 1.04534e7 | − | 1.53354e6i | 0.848098 | − | 0.124418i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.70985e6 | − | 7.14729e6i | −0.379346 | − | 0.575666i | ||||
\(689\) | − | 1.74055e6i | − | 0.139682i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 2.30168e7i | − | 1.83379i | −0.399129 | − | 0.916895i | \(-0.630688\pi\) | ||
0.399129 | − | 0.916895i | \(-0.369312\pi\) | |||||||
\(692\) | 5.40238e6 | + | 1.80164e7i | 0.428864 | + | 1.43022i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.20493e6 | + | 8.21338e6i | 0.0949646 | + | 0.647327i | ||||
\(695\) | −1.00065e6 | −0.0785818 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.02291e6 | 0.547564 | ||||||||
\(698\) | −1.67210e6 | − | 1.13979e7i | −0.129904 | − | 0.885492i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.77105e6 | − | 5.90629e6i | −0.136611 | − | 0.455585i | ||||
\(701\) | 3.57908e6i | 0.275091i | 0.990495 | + | 0.137545i | \(0.0439213\pi\) | ||||
−0.990495 | + | 0.137545i | \(0.956079\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.05749e7i | 0.807025i | ||||||||
\(704\) | −9.31314e6 | + | 1.11287e7i | −0.708214 | + | 0.846279i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1.50420e7 | − | 2.20671e6i | 1.13578 | − | 0.166622i | ||||
\(707\) | 9.68646e6 | 0.728813 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.92822e6 | −0.741747 | −0.370874 | − | 0.928683i | \(-0.620942\pi\) | ||||
−0.370874 | + | 0.928683i | \(0.620942\pi\) | |||||||
\(710\) | −3.42845e6 | + | 502963.i | −0.255242 | + | 0.0374447i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.50889e6 | + | 704818.i | −0.111547 | + | 0.0521047i | ||||
\(713\) | − | 1.50491e7i | − | 1.10863i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 275701.i | 0.0201685i | ||||||||
\(716\) | 1.52066e7 | − | 4.55983e6i | 1.10853 | − | 0.332404i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 762863. | + | 5.20006e6i | 0.0552250 | + | 0.376441i | ||||
\(719\) | −7.53578e6 | −0.543633 | −0.271817 | − | 0.962349i | \(-0.587624\pi\) | ||||
−0.271817 | + | 0.962349i | \(0.587624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 691651. | 0.0495506 | ||||||||
\(722\) | 1.90466e6 | + | 1.29831e7i | 0.135980 | + | 0.926905i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.33831e6 | + | 1.90060e6i | −0.449394 | + | 0.134755i | ||||
\(725\) | 4.59857e6i | 0.324921i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.14512e7i | 0.803553i | 0.915738 | + | 0.401776i | \(0.131607\pi\) | ||||
−0.915738 | + | 0.401776i | \(0.868393\pi\) | |||||||
\(728\) | 788599. | − | 368363.i | 0.0551477 | − | 0.0257601i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.98058e6 | − | 437260.i | 0.207011 | − | 0.0303691i | ||||
\(731\) | 5.37984e6 | 0.372371 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.93007e6 | 0.476407 | 0.238203 | − | 0.971215i | \(-0.423442\pi\) | ||||
0.238203 | + | 0.971215i | \(0.423442\pi\) | |||||||
\(734\) | 2.84708e7 | − | 4.17675e6i | 1.95056 | − | 0.286153i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.05481e7 | − | 1.18266e7i | −0.717762 | − | 0.804761i | ||||
\(737\) | 1.65417e7i | 1.12179i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 796923.i | 0.0536791i | 0.999640 | + | 0.0268396i | \(0.00854432\pi\) | ||||
−0.999640 | + | 0.0268396i | \(0.991456\pi\) | |||||||
\(740\) | −362046. | − | 1.20739e6i | −0.0243044 | − | 0.0810527i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.17979e6 | + | 8.04204e6i | 0.0786674 | + | 0.536237i | ||||
\(743\) | −4.25494e6 | −0.282762 | −0.141381 | − | 0.989955i | \(-0.545154\pi\) | ||||
−0.141381 | + | 0.989955i | \(0.545154\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.81409e6 | 0.185758 | ||||||||
\(746\) | 632425. | + | 4.31093e6i | 0.0416066 | + | 0.283611i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.61969e6 | − | 8.73639e6i | −0.171197 | − | 0.570924i | ||||
\(749\) | − | 5.80173e6i | − | 0.377879i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1.84503e7i | − | 1.19372i | −0.802344 | − | 0.596862i | \(-0.796414\pi\) | ||
0.802344 | − | 0.596862i | \(-0.203586\pi\) | |||||||
\(752\) | 1.19331e7 | − | 7.86354e6i | 0.769499 | − | 0.507077i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −642247. | + | 94219.4i | −0.0411409 | + | 0.00603548i | ||||
\(755\) | −1.70066e6 | −0.108580 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.70750e6 | 0.425423 | 0.212712 | − | 0.977115i | \(-0.431771\pi\) | ||||
0.212712 | + | 0.977115i | \(0.431771\pi\) | |||||||
\(758\) | 976348. | − | 143233.i | 0.0617208 | − | 0.00905462i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.36856e6 | − | 2.92984e6i | −0.0859466 | − | 0.183996i | ||||
\(761\) | − | 1.01808e6i | − | 0.0637268i | −0.999492 | − | 0.0318634i | \(-0.989856\pi\) | ||
0.999492 | − | 0.0318634i | \(-0.0101442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1.13160e7i | − | 0.703689i | ||||||
\(764\) | 1.84489e7 | − | 5.53206e6i | 1.14350 | − | 0.342889i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.08687e6 | − | 7.40865e6i | −0.0669277 | − | 0.456213i | ||||
\(767\) | −3.68718e6 | −0.226311 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.26712e7 | −0.772683 | −0.386342 | − | 0.922356i | \(-0.626261\pi\) | ||||
−0.386342 | + | 0.922356i | \(0.626261\pi\) | |||||||
\(770\) | −186877. | − | 1.27385e6i | −0.0113587 | − | 0.0774268i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.20634e6 | − | 2.46075e6i | 0.495572 | − | 0.148602i | ||||
\(773\) | 2.04393e7i | 1.23031i | 0.788404 | + | 0.615157i | \(0.210908\pi\) | ||||
−0.788404 | + | 0.615157i | \(0.789092\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.68243e7i | − | 1.00620i | ||||||
\(776\) | 9.59833e6 | + | 2.05483e7i | 0.572192 | + | 1.22496i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.28299e7 | − | 1.88218e6i | 0.759930 | − | 0.111484i | ||||
\(779\) | −2.38962e7 | −1.41087 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32553e7 | 1.95089 | ||||||||
\(782\) | 9.85472e6 | − | 1.44572e6i | 0.576272 | − | 0.0845407i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.09768e7 | − | 7.23337e6i | 0.637801 | − | 0.420291i | ||||
\(785\) | − | 1.87117e6i | − | 0.108377i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.11248e6i | 0.0640258i | 0.999487 | + | 0.0320129i | \(0.0101918\pi\) | ||||
−0.999487 | + | 0.0320129i | \(0.989808\pi\) | |||||||
\(788\) | −5.99713e6 | − | 1.99998e7i | −0.344055 | − | 1.14739i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −490436. | − | 3.34306e6i | −0.0279585 | − | 0.190579i | ||||
\(791\) | −1.35220e7 | −0.768424 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −389404. | −0.0219896 | ||||||||
\(794\) | 4.12464e6 | + | 2.81156e7i | 0.232185 | + | 1.58269i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.93322e6 | − | 3.31263e7i | −0.555658 | − | 1.85306i | ||||
\(797\) | − | 7.04761e6i | − | 0.393003i | −0.980504 | − | 0.196502i | \(-0.937042\pi\) | ||
0.980504 | − | 0.196502i | \(-0.0629581\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.98216e6i | 0.497753i | ||||||||
\(800\) | −1.17924e7 | − | 1.32217e7i | −0.651443 | − | 0.730403i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.93190e7 | + | 4.30118e6i | −1.60958 | + | 0.236131i | ||||
\(803\) | −2.89111e7 | −1.58225 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.40599e6 | 0.0764701 | ||||||||
\(806\) | 2.34972e6 | − | 344711.i | 0.127403 | − | 0.0186903i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.52158e7 | − | 1.17786e7i | 1.35877 | − | 0.634694i | ||||
\(809\) | − | 1.75707e7i | − | 0.943884i | −0.881630 | − | 0.471942i | \(-0.843553\pi\) | ||
0.881630 | − | 0.471942i | \(-0.156447\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.33297e7i | − | 1.77942i | −0.456523 | − | 0.889712i | \(-0.650905\pi\) | ||
0.456523 | − | 0.889712i | \(-0.349095\pi\) | |||||||
\(812\) | 2.90357e6 | − | 870662.i | 0.154540 | − | 0.0463404i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.75589e6 | + | 1.19690e7i | 0.0928830 | + | 0.633137i | ||||
\(815\) | −2.92197e6 | −0.154093 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.83055e7 | −0.959460 | ||||||||
\(818\) | −1.33711e6 | − | 9.11442e6i | −0.0698690 | − | 0.476262i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.72835e6 | − | 818121.i | 0.141699 | − | 0.0424896i | ||||
\(821\) | − | 3.35199e7i | − | 1.73558i | −0.496930 | − | 0.867791i | \(-0.665539\pi\) | ||
0.496930 | − | 0.867791i | \(-0.334461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 7.72304e6i | − | 0.397456i | −0.980055 | − | 0.198728i | \(-0.936319\pi\) | ||
0.980055 | − | 0.198728i | \(-0.0636810\pi\) | |||||||
\(824\) | 1.80051e6 | − | 841037.i | 0.0923799 | − | 0.0431516i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.70362e7 | − | 2.49926e6i | 0.868808 | − | 0.127457i | ||||
\(827\) | 5.63059e6 | 0.286280 | 0.143140 | − | 0.989702i | \(-0.454280\pi\) | ||||
0.143140 | + | 0.989702i | \(0.454280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.05869e7 | −1.54578 | −0.772891 | − | 0.634538i | \(-0.781190\pi\) | ||||
−0.772891 | + | 0.634538i | \(0.781190\pi\) | |||||||
\(830\) | −2.97882e6 | + | 437002.i | −0.150089 | + | 0.0220185i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.60496e6 | − | 1.91785e6i | 0.0803816 | − | 0.0960519i | ||||
\(833\) | 8.26234e6i | 0.412563i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.64153e6i | 0.131111i | ||||||||
\(836\) | 8.91378e6 | + | 2.97265e7i | 0.441109 | + | 1.47105i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.60059e6 | + | 1.09104e7i | 0.0787356 | + | 0.536701i | ||||
\(839\) | −1.63956e7 | −0.804122 | −0.402061 | − | 0.915613i | \(-0.631706\pi\) | ||||
−0.402061 | + | 0.915613i | \(0.631706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.82505e7 | 0.889783 | ||||||||
\(842\) | −3.27037e6 | − | 2.22925e7i | −0.158971 | − | 1.08362i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 29330.4 | + | 97813.8i | 0.00141730 | + | 0.00472655i | ||||
\(845\) | 2.98124e6i | 0.143633i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.20947e6i | 0.105823i | ||||||||
\(848\) | 1.28502e7 | + | 1.95005e7i | 0.613651 | + | 0.931228i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.10172e7 | − | 1.61625e6i | 0.523026 | − | 0.0767294i | ||||
\(851\) | −1.32106e7 | −0.625315 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.34791e7 | 1.57544 | 0.787718 | − | 0.616036i | \(-0.211262\pi\) | ||||
0.787718 | + | 0.616036i | \(0.211262\pi\) | |||||||
\(854\) | 1.79920e6 | − | 263948.i | 0.0844179 | − | 0.0123844i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.05481e6 | − | 1.51031e7i | −0.329080 | − | 0.704501i | ||||
\(857\) | − | 1.62495e7i | − | 0.755766i | −0.925853 | − | 0.377883i | \(-0.876652\pi\) | ||
0.925853 | − | 0.377883i | \(-0.123348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.27770e7i | 1.05321i | 0.850111 | + | 0.526603i | \(0.176535\pi\) | ||||
−0.850111 | + | 0.526603i | \(0.823465\pi\) | |||||||
\(860\) | 2.09003e6 | − | 626715.i | 0.0963623 | − | 0.0288951i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.89675e6 | + | 4.01952e7i | 0.270299 | + | 1.84249i | ||||
\(863\) | −3.13327e7 | −1.43209 | −0.716045 | − | 0.698054i | \(-0.754050\pi\) | ||||
−0.716045 | + | 0.698054i | \(0.754050\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.79469e6 | −0.217882 | ||||||||
\(866\) | −123960. | − | 844975.i | −0.00561679 | − | 0.0382868i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.06230e7 | + | 3.18540e6i | −0.478572 | + | 0.143504i | ||||
\(869\) | 3.24270e7i | 1.45666i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 2.85068e6i | − | 0.127322i | ||||||
\(872\) | −1.37601e7 | − | 2.94578e7i | −0.612814 | − | 1.31193i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.35318e7 | + | 4.91921e6i | −1.48484 | + | 0.217830i | ||||
\(875\) | 3.17787e6 | 0.140319 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.17754e7 | −0.956023 | −0.478011 | − | 0.878354i | \(-0.658642\pi\) | ||||
−0.478011 | + | 0.878354i | \(0.658642\pi\) | |||||||
\(878\) | 2.36624e7 | − | 3.47134e6i | 1.03591 | − | 0.151971i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.03546e6 | − | 3.08885e6i | −0.0886046 | − | 0.134459i | ||||
\(881\) | 2.09030e7i | 0.907335i | 0.891171 | + | 0.453668i | \(0.149885\pi\) | ||||
−0.891171 | + | 0.453668i | \(0.850115\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.36544e7i | 0.589348i | 0.955598 | + | 0.294674i | \(0.0952111\pi\) | ||||
−0.955598 | + | 0.294674i | \(0.904789\pi\) | |||||||
\(884\) | 451459. | + | 1.50557e6i | 0.0194307 | + | 0.0647993i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.71843e6 | + | 1.85302e7i | 0.116341 | + | 0.793041i | ||||
\(887\) | 2.32285e6 | 0.0991318 | 0.0495659 | − | 0.998771i | \(-0.484216\pi\) | ||||
0.0495659 | + | 0.998771i | \(0.484216\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.90970e6 | 0.208353 | ||||||||
\(890\) | −61620.8 | − | 420038.i | −0.00260767 | − | 0.0177752i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −970543. | − | 3.23666e6i | −0.0408416 | − | 0.136203i | ||||
\(893\) | − | 3.05628e7i | − | 1.28252i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04692e6i | 0.168876i | ||||||||
\(896\) | −6.11560e6 | + | 9.94910e6i | −0.254489 | + | 0.414013i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.90864e7 | + | 4.26705e6i | −1.20365 | + | 0.176578i | ||||
\(899\) | 8.27094e6 | 0.341315 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.46782e7 | −0.602367 | ||||||||
\(902\) | −2.70466e7 | + | 3.96781e6i | −1.10687 | + | 0.162381i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.52006e7 | + | 1.64426e7i | −1.43261 | + | 0.669189i | ||||
\(905\) | − | 1.68681e6i | − | 0.0684613i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.91551e7i | 1.58041i | 0.612843 | + | 0.790205i | \(0.290026\pi\) | ||||
−0.612843 | + | 0.790205i | \(0.709974\pi\) | |||||||
\(908\) | −1.90099e7 | + | 5.70030e6i | −0.765184 | + | 0.229448i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32205.2 | + | 219527.i | 0.00128921 | + | 0.00878787i | ||||
\(911\) | 3.29541e7 | 1.31557 | 0.657784 | − | 0.753207i | \(-0.271494\pi\) | ||||
0.657784 | + | 0.753207i | \(0.271494\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.88941e7 | 1.14718 | ||||||||
\(914\) | 699332. | + | 4.76700e6i | 0.0276897 | + | 0.188747i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.66033e7 | − | 7.97724e6i | 1.04760 | − | 0.314133i | ||||
\(917\) | − | 1.20388e7i | − | 0.472783i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.81600e7i | 1.49046i | 0.666809 | + | 0.745229i | \(0.267660\pi\) | ||||
−0.666809 | + | 0.745229i | \(0.732340\pi\) | |||||||
\(920\) | 3.66008e6 | − | 1.70966e6i | 0.142568 | − | 0.0665948i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4.75121e7 | − | 6.97016e6i | 1.84067 | − | 0.270032i | ||||
\(923\) | −5.73100e6 | −0.221425 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.47689e7 | −0.567537 | ||||||||
\(926\) | 2.87149e7 | − | 4.21256e6i | 1.10047 | − | 0.161443i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.49988e6 | − | 5.79721e6i | 0.247762 | − | 0.220978i | ||||
\(929\) | − | 7.13927e6i | − | 0.271403i | −0.990750 | − | 0.135702i | \(-0.956671\pi\) | ||
0.990750 | − | 0.135702i | \(-0.0433288\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.81135e7i | − | 1.06302i | ||||||
\(932\) | −2.72247e6 | − | 9.07917e6i | −0.102665 | − | 0.342379i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.12523e6 | + | 2.81196e7i | 0.154732 | + | 1.05473i | ||||
\(935\) | 2.32501e6 | 0.0869754 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.21923e7 | −1.56995 | −0.784973 | − | 0.619530i | \(-0.787323\pi\) | ||||
−0.784973 | + | 0.619530i | \(0.787323\pi\) | |||||||
\(938\) | 1.93226e6 | + | 1.31713e7i | 0.0717065 | + | 0.488788i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.04636e6 | + | 3.48951e6i | 0.0386244 | + | 0.128809i | ||||
\(941\) | 4.05204e7i | 1.49176i | 0.666080 | + | 0.745881i | \(0.267971\pi\) | ||||
−0.666080 | + | 0.745881i | \(0.732029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.98522e7i | − | 1.09319i | ||||||
\(944\) | 4.13098e7 | − | 2.72219e7i | 1.50877 | − | 0.994234i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.07188e7 | + | 3.03951e6i | −0.752727 | + | 0.110427i | ||||
\(947\) | 3.51812e7 | 1.27478 | 0.637390 | − | 0.770541i | \(-0.280014\pi\) | ||||
0.637390 | + | 0.770541i | \(0.280014\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.98235e6 | 0.179584 | ||||||||
\(950\) | −3.74872e7 | + | 5.49948e6i | −1.34764 | + | 0.197703i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.10643e6 | − | 6.65032e6i | −0.111089 | − | 0.237821i | ||||
\(953\) | 1.63094e7i | 0.581709i | 0.956767 | + | 0.290854i | \(0.0939396\pi\) | ||||
−0.956767 | + | 0.290854i | \(0.906060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.90979e6i | 0.174202i | ||||||||
\(956\) | −2.13570e7 | + | 6.40410e6i | −0.755781 | + | 0.226628i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.20495e6 | + | 1.50300e7i | 0.0776219 | + | 0.529110i | ||||
\(959\) | 2.11031e7 | 0.740970 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63085e6 | −0.0569646 | ||||||||
\(962\) | −302598. | − | 2.06266e6i | −0.0105421 | − | 0.0718605i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.25199e6 | − | 1.27500e6i | 0.147367 | − | 0.0441893i | ||||
\(965\) | 2.18395e6i | 0.0754961i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.44095e7i | 1.52725i | 0.645660 | + | 0.763625i | \(0.276582\pi\) | ||||
−0.645660 | + | 0.763625i | \(0.723418\pi\) | |||||||
\(968\) | 2.68668e6 | + | 5.75171e6i | 0.0921570 | + | 0.197292i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.72015e6 | + | 839162.i | −0.195199 | + | 0.0286363i | ||||
\(971\) | 3.61389e7 | 1.23006 | 0.615031 | − | 0.788503i | \(-0.289143\pi\) | ||||
0.615031 | + | 0.788503i | \(0.289143\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.72850e6 | 0.261706 | ||||||||
\(974\) | 2.98882e7 | − | 4.38468e6i | 1.00949 | − | 0.148095i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.36273e6 | − | 2.87491e6i | 0.146600 | − | 0.0966050i | ||||
\(977\) | 4.44192e7i | 1.48879i | 0.667738 | + | 0.744396i | \(0.267262\pi\) | ||||
−0.667738 | + | 0.744396i | \(0.732738\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.07429e6i | 0.135861i | ||||||||
\(980\) | 962507. | + | 3.20986e6i | 0.0320139 | + | 0.106763i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.16197e6 | + | 1.47371e7i | 0.0715437 | + | 0.487678i | ||||
\(983\) | 2.30500e7 | 0.760830 | 0.380415 | − | 0.924816i | \(-0.375781\pi\) | ||||
0.380415 | + | 0.924816i | \(0.375781\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.32255e6 | 0.174795 | ||||||||
\(986\) | 794560. | + | 5.41612e6i | 0.0260276 | + | 0.177417i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.53614e6 | − | 5.12287e6i | −0.0500655 | − | 0.166963i | ||||
\(989\) | − | 2.28680e7i | − | 0.743427i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 3.51200e7i | − | 1.13598i | −0.823035 | − | 0.567990i | \(-0.807721\pi\) | ||
0.823035 | − | 0.567990i | \(-0.192279\pi\) | |||||||
\(992\) | −2.37804e7 | + | 2.12096e7i | −0.767256 | + | 0.684312i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.64795e7 | − | 3.88461e6i | 0.850048 | − | 0.124704i | ||||
\(995\) | 8.81589e6 | 0.282298 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.12252e7 | 0.994873 | 0.497436 | − | 0.867501i | \(-0.334275\pi\) | ||||
0.497436 | + | 0.867501i | \(0.334275\pi\) | |||||||
\(998\) | −5.59104e7 | + | 8.20221e6i | −1.77691 | + | 0.260678i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.6.b.c.107.9 | ✓ | 20 | |
3.2 | odd | 2 | inner | 108.6.b.c.107.12 | yes | 20 | |
4.3 | odd | 2 | inner | 108.6.b.c.107.11 | yes | 20 | |
12.11 | even | 2 | inner | 108.6.b.c.107.10 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.6.b.c.107.9 | ✓ | 20 | 1.1 | even | 1 | trivial | |
108.6.b.c.107.10 | yes | 20 | 12.11 | even | 2 | inner | |
108.6.b.c.107.11 | yes | 20 | 4.3 | odd | 2 | inner | |
108.6.b.c.107.12 | yes | 20 | 3.2 | odd | 2 | inner |