Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,7,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.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: | \(81.4391456014\) |
Analytic rank: | \(0\) |
Dimension: | \(60\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.20 | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.7.d.a.235.19 |
$q$-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 \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685i | 0.707107i | ||||||||
\(3\) | −15.5885 | −0.577350 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | −96.2981 | −0.770385 | −0.385192 | − | 0.922836i | \(-0.625865\pi\) | ||||
−0.385192 | + | 0.922836i | \(0.625865\pi\) | |||||||
\(6\) | − | 88.1816i | − | 0.408248i | ||||||
\(7\) | −484.887 | −1.41366 | −0.706832 | − | 0.707381i | \(-0.749877\pi\) | ||||
−0.706832 | + | 0.707381i | \(0.749877\pi\) | |||||||
\(8\) | − | 181.019i | − | 0.353553i | ||||||
\(9\) | 243.000 | 0.333333 | ||||||||
\(10\) | − | 544.744i | − | 0.544744i | ||||||
\(11\) | − | 1209.66i | − | 0.908833i | −0.890789 | − | 0.454416i | \(-0.849848\pi\) | ||
0.890789 | − | 0.454416i | \(-0.150152\pi\) | |||||||
\(12\) | 498.831 | 0.288675 | ||||||||
\(13\) | 1553.53i | 0.707115i | 0.935413 | + | 0.353558i | \(0.115028\pi\) | ||||
−0.935413 | + | 0.353558i | \(0.884972\pi\) | |||||||
\(14\) | − | 2742.94i | − | 0.999612i | ||||||
\(15\) | 1501.14 | 0.444782 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | 6745.19 | 1.37293 | 0.686463 | − | 0.727164i | \(-0.259162\pi\) | ||||
0.686463 | + | 0.727164i | \(0.259162\pi\) | |||||||
\(18\) | 1374.62i | 0.235702i | ||||||||
\(19\) | 11357.4 | 1.65584 | 0.827920 | − | 0.560847i | \(-0.189524\pi\) | ||||
0.827920 | + | 0.560847i | \(0.189524\pi\) | |||||||
\(20\) | 3081.54 | 0.385192 | ||||||||
\(21\) | 7558.64 | 0.816180 | ||||||||
\(22\) | 6842.85 | 0.642642 | ||||||||
\(23\) | 21259.9i | 1.74735i | 0.486514 | + | 0.873673i | \(0.338268\pi\) | ||||
−0.486514 | + | 0.873673i | \(0.661732\pi\) | |||||||
\(24\) | 2821.81i | 0.204124i | ||||||||
\(25\) | −6351.68 | −0.406507 | ||||||||
\(26\) | −8788.11 | −0.500006 | ||||||||
\(27\) | −3788.00 | −0.192450 | ||||||||
\(28\) | 15516.4 | 0.706832 | ||||||||
\(29\) | −17805.3 | −0.730055 | −0.365027 | − | 0.930997i | \(-0.618940\pi\) | ||||
−0.365027 | + | 0.930997i | \(0.618940\pi\) | |||||||
\(30\) | 8491.72i | 0.314508i | ||||||||
\(31\) | − | 36428.3i | − | 1.22279i | −0.791324 | − | 0.611397i | \(-0.790608\pi\) | ||
0.791324 | − | 0.611397i | \(-0.209392\pi\) | |||||||
\(32\) | 5792.62i | 0.176777i | ||||||||
\(33\) | 18856.7i | 0.524715i | ||||||||
\(34\) | 38156.5i | 0.970806i | ||||||||
\(35\) | 46693.7 | 1.08907 | ||||||||
\(36\) | −7776.00 | −0.166667 | ||||||||
\(37\) | − | 47212.4i | − | 0.932075i | −0.884765 | − | 0.466037i | \(-0.845681\pi\) | ||
0.884765 | − | 0.466037i | \(-0.154319\pi\) | |||||||
\(38\) | 64247.2i | 1.17086i | ||||||||
\(39\) | − | 24217.2i | − | 0.408253i | ||||||
\(40\) | 17431.8i | 0.272372i | ||||||||
\(41\) | 136149. | 1.97544 | 0.987720 | − | 0.156236i | \(-0.0499361\pi\) | ||||
0.987720 | + | 0.156236i | \(0.0499361\pi\) | |||||||
\(42\) | 42758.1i | 0.577126i | ||||||||
\(43\) | − | 41734.3i | − | 0.524913i | −0.964944 | − | 0.262457i | \(-0.915467\pi\) | ||
0.964944 | − | 0.262457i | \(-0.0845327\pi\) | |||||||
\(44\) | 38709.0i | 0.454416i | ||||||||
\(45\) | −23400.4 | −0.256795 | ||||||||
\(46\) | −120264. | −1.23556 | ||||||||
\(47\) | 108720.i | 1.04717i | 0.851975 | + | 0.523583i | \(0.175405\pi\) | ||||
−0.851975 | + | 0.523583i | \(0.824595\pi\) | |||||||
\(48\) | −15962.6 | −0.144338 | ||||||||
\(49\) | 117466. | 0.998449 | ||||||||
\(50\) | − | 35930.5i | − | 0.287444i | ||||||
\(51\) | −105147. | −0.792660 | ||||||||
\(52\) | − | 49713.0i | − | 0.353558i | ||||||
\(53\) | −142756. | −0.958888 | −0.479444 | − | 0.877572i | \(-0.659162\pi\) | ||||
−0.479444 | + | 0.877572i | \(0.659162\pi\) | |||||||
\(54\) | − | 21428.1i | − | 0.136083i | ||||||
\(55\) | 116488.i | 0.700151i | ||||||||
\(56\) | 87773.9i | 0.499806i | ||||||||
\(57\) | −177044. | −0.955999 | ||||||||
\(58\) | − | 100722.i | − | 0.516227i | ||||||
\(59\) | −81810.6 | − | 188381.i | −0.398340 | − | 0.917238i | ||||
\(60\) | −48036.4 | −0.222391 | ||||||||
\(61\) | 70678.1i | 0.311383i | 0.987806 | + | 0.155692i | \(0.0497606\pi\) | ||||
−0.987806 | + | 0.155692i | \(0.950239\pi\) | |||||||
\(62\) | 206069. | 0.864646 | ||||||||
\(63\) | −117828. | −0.471222 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | − | 149602.i | − | 0.544751i | ||||||
\(66\) | −106669. | −0.371029 | ||||||||
\(67\) | 221377.i | 0.736050i | 0.929816 | + | 0.368025i | \(0.119966\pi\) | ||||
−0.929816 | + | 0.368025i | \(0.880034\pi\) | |||||||
\(68\) | −215846. | −0.686463 | ||||||||
\(69\) | − | 331410.i | − | 1.00883i | ||||||
\(70\) | 264139.i | 0.770086i | ||||||||
\(71\) | 72810.0 | 0.203430 | 0.101715 | − | 0.994814i | \(-0.467567\pi\) | ||||
0.101715 | + | 0.994814i | \(0.467567\pi\) | |||||||
\(72\) | − | 43987.7i | − | 0.117851i | ||||||
\(73\) | 206404.i | 0.530580i | 0.964169 | + | 0.265290i | \(0.0854676\pi\) | ||||
−0.964169 | + | 0.265290i | \(0.914532\pi\) | |||||||
\(74\) | 267074. | 0.659076 | ||||||||
\(75\) | 99012.9 | 0.234697 | ||||||||
\(76\) | −363437. | −0.827920 | ||||||||
\(77\) | 586547.i | 1.28479i | ||||||||
\(78\) | 136993. | 0.288679 | ||||||||
\(79\) | −91271.7 | −0.185121 | −0.0925604 | − | 0.995707i | \(-0.529505\pi\) | ||||
−0.0925604 | + | 0.995707i | \(0.529505\pi\) | |||||||
\(80\) | −98609.2 | −0.192596 | ||||||||
\(81\) | 59049.0 | 0.111111 | ||||||||
\(82\) | 770177.i | 1.39685i | ||||||||
\(83\) | − | 588230.i | − | 1.02876i | −0.857563 | − | 0.514379i | \(-0.828023\pi\) | ||
0.857563 | − | 0.514379i | \(-0.171977\pi\) | |||||||
\(84\) | −241877. | −0.408090 | ||||||||
\(85\) | −649549. | −1.05768 | ||||||||
\(86\) | 236085. | 0.371170 | ||||||||
\(87\) | 277557. | 0.421497 | ||||||||
\(88\) | −218971. | −0.321321 | ||||||||
\(89\) | 861372.i | 1.22186i | 0.791686 | + | 0.610929i | \(0.209204\pi\) | ||||
−0.791686 | + | 0.610929i | \(0.790796\pi\) | |||||||
\(90\) | − | 132373.i | − | 0.181581i | ||||||
\(91\) | − | 753288.i | − | 0.999624i | ||||||
\(92\) | − | 680318.i | − | 0.873673i | ||||||
\(93\) | 567860.i | 0.705980i | ||||||||
\(94\) | −615012. | −0.740458 | ||||||||
\(95\) | −1.09370e6 | −1.27563 | ||||||||
\(96\) | − | 90298.0i | − | 0.102062i | ||||||
\(97\) | − | 686994.i | − | 0.752727i | −0.926472 | − | 0.376364i | \(-0.877174\pi\) | ||
0.926472 | − | 0.376364i | \(-0.122826\pi\) | |||||||
\(98\) | 664491.i | 0.706010i | ||||||||
\(99\) | − | 293947.i | − | 0.302944i | ||||||
\(100\) | 203254. | 0.203254 | ||||||||
\(101\) | − | 1.58295e6i | − | 1.53639i | −0.640215 | − | 0.768196i | \(-0.721155\pi\) | ||
0.640215 | − | 0.768196i | \(-0.278845\pi\) | |||||||
\(102\) | − | 594802.i | − | 0.560495i | ||||||
\(103\) | 90265.4i | 0.0826057i | 0.999147 | + | 0.0413028i | \(0.0131508\pi\) | ||||
−0.999147 | + | 0.0413028i | \(0.986849\pi\) | |||||||
\(104\) | 281219. | 0.250003 | ||||||||
\(105\) | −727883. | −0.628772 | ||||||||
\(106\) | − | 807552.i | − | 0.678036i | ||||||
\(107\) | −1.36331e6 | −1.11286 | −0.556432 | − | 0.830893i | \(-0.687830\pi\) | ||||
−0.556432 | + | 0.830893i | \(0.687830\pi\) | |||||||
\(108\) | 121216. | 0.0962250 | ||||||||
\(109\) | 2.05270e6i | 1.58506i | 0.609832 | + | 0.792531i | \(0.291237\pi\) | ||||
−0.609832 | + | 0.792531i | \(0.708763\pi\) | |||||||
\(110\) | −658953. | −0.495081 | ||||||||
\(111\) | 735968.i | 0.538134i | ||||||||
\(112\) | −496524. | −0.353416 | ||||||||
\(113\) | 902711.i | 0.625624i | 0.949815 | + | 0.312812i | \(0.101271\pi\) | ||||
−0.949815 | + | 0.312812i | \(0.898729\pi\) | |||||||
\(114\) | − | 1.00151e6i | − | 0.675993i | ||||||
\(115\) | − | 2.04729e6i | − | 1.34613i | ||||||
\(116\) | 569770. | 0.365027 | ||||||||
\(117\) | 377508.i | 0.235705i | ||||||||
\(118\) | 1.06565e6 | − | 462791.i | 0.648585 | − | 0.281669i | ||||
\(119\) | −3.27065e6 | −1.94086 | ||||||||
\(120\) | − | 271735.i | − | 0.157254i | ||||||
\(121\) | 308292. | 0.174023 | ||||||||
\(122\) | −399816. | −0.220181 | ||||||||
\(123\) | −2.12236e6 | −1.14052 | ||||||||
\(124\) | 1.16570e6i | 0.611397i | ||||||||
\(125\) | 2.11631e6 | 1.08355 | ||||||||
\(126\) | − | 666533.i | − | 0.333204i | ||||||
\(127\) | −889383. | −0.434188 | −0.217094 | − | 0.976151i | \(-0.569658\pi\) | ||||
−0.217094 | + | 0.976151i | \(0.569658\pi\) | |||||||
\(128\) | − | 185364.i | − | 0.0883883i | ||||||
\(129\) | 650573.i | 0.303059i | ||||||||
\(130\) | 846278. | 0.385197 | ||||||||
\(131\) | − | 2.93521e6i | − | 1.30565i | −0.757511 | − | 0.652823i | \(-0.773585\pi\) | ||
0.757511 | − | 0.652823i | \(-0.226415\pi\) | |||||||
\(132\) | − | 603414.i | − | 0.262357i | ||||||
\(133\) | −5.50706e6 | −2.34080 | ||||||||
\(134\) | −1.25230e6 | −0.520466 | ||||||||
\(135\) | 364777. | 0.148261 | ||||||||
\(136\) | − | 1.22101e6i | − | 0.485403i | ||||||
\(137\) | −1.03431e6 | −0.402245 | −0.201122 | − | 0.979566i | \(-0.564459\pi\) | ||||
−0.201122 | + | 0.979566i | \(0.564459\pi\) | |||||||
\(138\) | 1.87474e6 | 0.713351 | ||||||||
\(139\) | 2.44154e6 | 0.909116 | 0.454558 | − | 0.890717i | \(-0.349797\pi\) | ||||
0.454558 | + | 0.890717i | \(0.349797\pi\) | |||||||
\(140\) | −1.49420e6 | −0.544533 | ||||||||
\(141\) | − | 1.69477e6i | − | 0.604581i | ||||||
\(142\) | 411875.i | 0.143847i | ||||||||
\(143\) | 1.87924e6 | 0.642650 | ||||||||
\(144\) | 248832. | 0.0833333 | ||||||||
\(145\) | 1.71462e6 | 0.562423 | ||||||||
\(146\) | −1.16760e6 | −0.375176 | ||||||||
\(147\) | −1.83112e6 | −0.576455 | ||||||||
\(148\) | 1.51080e6i | 0.466037i | ||||||||
\(149\) | 1.37696e6i | 0.416259i | 0.978101 | + | 0.208130i | \(0.0667376\pi\) | ||||
−0.978101 | + | 0.208130i | \(0.933262\pi\) | |||||||
\(150\) | 560101.i | 0.165956i | ||||||||
\(151\) | − | 260207.i | − | 0.0755767i | −0.999286 | − | 0.0377883i | \(-0.987969\pi\) | ||
0.999286 | − | 0.0377883i | \(-0.0120313\pi\) | |||||||
\(152\) | − | 2.05591e6i | − | 0.585428i | ||||||
\(153\) | 1.63908e6 | 0.457642 | ||||||||
\(154\) | −3.31801e6 | −0.908480 | ||||||||
\(155\) | 3.50797e6i | 0.942022i | ||||||||
\(156\) | 774950.i | 0.204127i | ||||||||
\(157\) | 3.25031e6i | 0.839896i | 0.907548 | + | 0.419948i | \(0.137952\pi\) | ||||
−0.907548 | + | 0.419948i | \(0.862048\pi\) | |||||||
\(158\) | − | 516311.i | − | 0.130900i | ||||||
\(159\) | 2.22535e6 | 0.553614 | ||||||||
\(160\) | − | 557818.i | − | 0.136186i | ||||||
\(161\) | − | 1.03087e7i | − | 2.47016i | ||||||
\(162\) | 334032.i | 0.0785674i | ||||||||
\(163\) | −4.35919e6 | −1.00657 | −0.503284 | − | 0.864121i | \(-0.667875\pi\) | ||||
−0.503284 | + | 0.864121i | \(0.667875\pi\) | |||||||
\(164\) | −4.35678e6 | −0.987720 | ||||||||
\(165\) | − | 1.81586e6i | − | 0.404232i | ||||||
\(166\) | 3.32753e6 | 0.727441 | ||||||||
\(167\) | −2.69927e6 | −0.579558 | −0.289779 | − | 0.957094i | \(-0.593582\pi\) | ||||
−0.289779 | + | 0.957094i | \(0.593582\pi\) | |||||||
\(168\) | − | 1.36826e6i | − | 0.288563i | ||||||
\(169\) | 2.41335e6 | 0.499988 | ||||||||
\(170\) | − | 3.67440e6i | − | 0.747894i | ||||||
\(171\) | 2.75985e6 | 0.551946 | ||||||||
\(172\) | 1.33550e6i | 0.262457i | ||||||||
\(173\) | 2.28386e6i | 0.441094i | 0.975376 | + | 0.220547i | \(0.0707843\pi\) | ||||
−0.975376 | + | 0.220547i | \(0.929216\pi\) | |||||||
\(174\) | 1.57010e6i | 0.298044i | ||||||||
\(175\) | 3.07985e6 | 0.574665 | ||||||||
\(176\) | − | 1.23869e6i | − | 0.227208i | ||||||
\(177\) | 1.27530e6 | + | 2.93658e6i | 0.229981 | + | 0.529568i | ||||
\(178\) | −4.87265e6 | −0.863984 | ||||||||
\(179\) | − | 6.94771e6i | − | 1.21139i | −0.795699 | − | 0.605693i | \(-0.792896\pi\) | ||
0.795699 | − | 0.605693i | \(-0.207104\pi\) | |||||||
\(180\) | 748814. | 0.128397 | ||||||||
\(181\) | −2.14818e6 | −0.362273 | −0.181136 | − | 0.983458i | \(-0.557978\pi\) | ||||
−0.181136 | + | 0.983458i | \(0.557978\pi\) | |||||||
\(182\) | 4.26124e6 | 0.706841 | ||||||||
\(183\) | − | 1.10176e6i | − | 0.179777i | ||||||
\(184\) | 3.84846e6 | 0.617780 | ||||||||
\(185\) | 4.54646e6i | 0.718056i | ||||||||
\(186\) | −3.21230e6 | −0.499203 | ||||||||
\(187\) | − | 8.15936e6i | − | 1.24776i | ||||||
\(188\) | − | 3.47903e6i | − | 0.523583i | ||||||
\(189\) | 1.83675e6 | 0.272060 | ||||||||
\(190\) | − | 6.18688e6i | − | 0.902009i | ||||||
\(191\) | − | 5.87137e6i | − | 0.842634i | −0.906913 | − | 0.421317i | \(-0.861568\pi\) | ||
0.906913 | − | 0.421317i | \(-0.138432\pi\) | |||||||
\(192\) | 510803. | 0.0721688 | ||||||||
\(193\) | −1.38306e7 | −1.92384 | −0.961919 | − | 0.273333i | \(-0.911874\pi\) | ||||
−0.961919 | + | 0.273333i | \(0.911874\pi\) | |||||||
\(194\) | 3.88622e6 | 0.532259 | ||||||||
\(195\) | 2.33207e6i | 0.314512i | ||||||||
\(196\) | −3.75893e6 | −0.499224 | ||||||||
\(197\) | −1.48020e7 | −1.93608 | −0.968039 | − | 0.250800i | \(-0.919306\pi\) | ||||
−0.968039 | + | 0.250800i | \(0.919306\pi\) | |||||||
\(198\) | 1.66281e6 | 0.214214 | ||||||||
\(199\) | 173100. | 0.0219653 | 0.0109826 | − | 0.999940i | \(-0.496504\pi\) | ||||
0.0109826 | + | 0.999940i | \(0.496504\pi\) | |||||||
\(200\) | 1.14978e6i | 0.143722i | ||||||||
\(201\) | − | 3.45092e6i | − | 0.424959i | ||||||
\(202\) | 8.95450e6 | 1.08639 | ||||||||
\(203\) | 8.63356e6 | 1.03205 | ||||||||
\(204\) | 3.36471e6 | 0.396330 | ||||||||
\(205\) | −1.31109e7 | −1.52185 | ||||||||
\(206\) | −510618. | −0.0584110 | ||||||||
\(207\) | 5.16617e6i | 0.582448i | ||||||||
\(208\) | 1.59082e6i | 0.176779i | ||||||||
\(209\) | − | 1.37386e7i | − | 1.50488i | ||||||
\(210\) | − | 4.11753e6i | − | 0.444609i | ||||||
\(211\) | 1.43898e7i | 1.53182i | 0.642947 | + | 0.765910i | \(0.277711\pi\) | ||||
−0.642947 | + | 0.765910i | \(0.722289\pi\) | |||||||
\(212\) | 4.56820e6 | 0.479444 | ||||||||
\(213\) | −1.13499e6 | −0.117451 | ||||||||
\(214\) | − | 7.71202e6i | − | 0.786914i | ||||||
\(215\) | 4.01893e6i | 0.404385i | ||||||||
\(216\) | 685700.i | 0.0680414i | ||||||||
\(217\) | 1.76636e7i | 1.72862i | ||||||||
\(218\) | −1.16118e7 | −1.12081 | ||||||||
\(219\) | − | 3.21753e6i | − | 0.306330i | ||||||
\(220\) | − | 3.72760e6i | − | 0.350075i | ||||||
\(221\) | 1.04789e7i | 0.970818i | ||||||||
\(222\) | −4.16326e6 | −0.380518 | ||||||||
\(223\) | 916397. | 0.0826359 | 0.0413180 | − | 0.999146i | \(-0.486844\pi\) | ||||
0.0413180 | + | 0.999146i | \(0.486844\pi\) | |||||||
\(224\) | − | 2.80877e6i | − | 0.249903i | ||||||
\(225\) | −1.54346e6 | −0.135502 | ||||||||
\(226\) | −5.10651e6 | −0.442383 | ||||||||
\(227\) | 2.09769e7i | 1.79334i | 0.442696 | + | 0.896672i | \(0.354022\pi\) | ||||
−0.442696 | + | 0.896672i | \(0.645978\pi\) | |||||||
\(228\) | 5.66542e6 | 0.478000 | ||||||||
\(229\) | 1.10845e7i | 0.923016i | 0.887136 | + | 0.461508i | \(0.152691\pi\) | ||||
−0.887136 | + | 0.461508i | \(0.847309\pi\) | |||||||
\(230\) | 1.15812e7 | 0.951856 | ||||||||
\(231\) | − | 9.14336e6i | − | 0.741771i | ||||||
\(232\) | 3.22311e6i | 0.258113i | ||||||||
\(233\) | − | 4.82794e6i | − | 0.381675i | −0.981622 | − | 0.190838i | \(-0.938880\pi\) | ||
0.981622 | − | 0.190838i | \(-0.0611204\pi\) | |||||||
\(234\) | −2.13551e6 | −0.166669 | ||||||||
\(235\) | − | 1.04695e7i | − | 0.806720i | ||||||
\(236\) | 2.61794e6 | + | 6.02821e6i | 0.199170 | + | 0.458619i | ||||
\(237\) | 1.42279e6 | 0.106880 | ||||||||
\(238\) | − | 1.85016e7i | − | 1.37239i | ||||||
\(239\) | −1.02169e7 | −0.748388 | −0.374194 | − | 0.927350i | \(-0.622081\pi\) | ||||
−0.374194 | + | 0.927350i | \(0.622081\pi\) | |||||||
\(240\) | 1.53717e6 | 0.111195 | ||||||||
\(241\) | −1.83758e7 | −1.31279 | −0.656394 | − | 0.754419i | \(-0.727919\pi\) | ||||
−0.656394 | + | 0.754419i | \(0.727919\pi\) | |||||||
\(242\) | 1.74396e6i | 0.123053i | ||||||||
\(243\) | −920483. | −0.0641500 | ||||||||
\(244\) | − | 2.26170e6i | − | 0.155692i | ||||||
\(245\) | −1.13118e7 | −0.769190 | ||||||||
\(246\) | − | 1.20059e7i | − | 0.806470i | ||||||
\(247\) | 1.76441e7i | 1.17087i | ||||||||
\(248\) | −6.59422e6 | −0.432323 | ||||||||
\(249\) | 9.16960e6i | 0.593953i | ||||||||
\(250\) | 1.19717e7i | 0.766187i | ||||||||
\(251\) | 5.81400e6 | 0.367666 | 0.183833 | − | 0.982957i | \(-0.441149\pi\) | ||||
0.183833 | + | 0.982957i | \(0.441149\pi\) | |||||||
\(252\) | 3.77048e6 | 0.235611 | ||||||||
\(253\) | 2.57172e7 | 1.58804 | ||||||||
\(254\) | − | 5.03111e6i | − | 0.307017i | ||||||
\(255\) | 1.01255e7 | 0.610653 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 2.44206e7 | 1.43866 | 0.719328 | − | 0.694670i | \(-0.244450\pi\) | ||||
0.719328 | + | 0.694670i | \(0.244450\pi\) | |||||||
\(258\) | −3.68020e6 | −0.214295 | ||||||||
\(259\) | 2.28927e7i | 1.31764i | ||||||||
\(260\) | 4.78727e6i | 0.272375i | ||||||||
\(261\) | −4.32669e6 | −0.243352 | ||||||||
\(262\) | 1.66041e7 | 0.923231 | ||||||||
\(263\) | 6.22939e6 | 0.342435 | 0.171217 | − | 0.985233i | \(-0.445230\pi\) | ||||
0.171217 | + | 0.985233i | \(0.445230\pi\) | |||||||
\(264\) | 3.41342e6 | 0.185515 | ||||||||
\(265\) | 1.37472e7 | 0.738713 | ||||||||
\(266\) | − | 3.11526e7i | − | 1.65520i | ||||||
\(267\) | − | 1.34275e7i | − | 0.705440i | ||||||
\(268\) | − | 7.08405e6i | − | 0.368025i | ||||||
\(269\) | 4.34695e6i | 0.223320i | 0.993746 | + | 0.111660i | \(0.0356168\pi\) | ||||
−0.993746 | + | 0.111660i | \(0.964383\pi\) | |||||||
\(270\) | 2.06349e6i | 0.104836i | ||||||||
\(271\) | −5.24553e6 | −0.263561 | −0.131781 | − | 0.991279i | \(-0.542069\pi\) | ||||
−0.131781 | + | 0.991279i | \(0.542069\pi\) | |||||||
\(272\) | 6.90707e6 | 0.343232 | ||||||||
\(273\) | 1.17426e7i | 0.577133i | ||||||||
\(274\) | − | 5.85096e6i | − | 0.284430i | ||||||
\(275\) | 7.68335e6i | 0.369447i | ||||||||
\(276\) | 1.06051e7i | 0.504415i | ||||||||
\(277\) | 1.01301e7 | 0.476623 | 0.238311 | − | 0.971189i | \(-0.423406\pi\) | ||||
0.238311 | + | 0.971189i | \(0.423406\pi\) | |||||||
\(278\) | 1.38114e7i | 0.642842i | ||||||||
\(279\) | − | 8.85206e6i | − | 0.407598i | ||||||
\(280\) | − | 8.45246e6i | − | 0.385043i | ||||||
\(281\) | 2.20004e7 | 0.991543 | 0.495771 | − | 0.868453i | \(-0.334885\pi\) | ||||
0.495771 | + | 0.868453i | \(0.334885\pi\) | |||||||
\(282\) | 9.58709e6 | 0.427503 | ||||||||
\(283\) | 2.54701e7i | 1.12376i | 0.827220 | + | 0.561878i | \(0.189921\pi\) | ||||
−0.827220 | + | 0.561878i | \(0.810079\pi\) | |||||||
\(284\) | −2.32992e6 | −0.101715 | ||||||||
\(285\) | 1.70490e7 | 0.736487 | ||||||||
\(286\) | 1.06306e7i | 0.454422i | ||||||||
\(287\) | −6.60170e7 | −2.79261 | ||||||||
\(288\) | 1.40761e6i | 0.0589256i | ||||||||
\(289\) | 2.13600e7 | 0.884928 | ||||||||
\(290\) | 9.69934e6i | 0.397693i | ||||||||
\(291\) | 1.07092e7i | 0.434587i | ||||||||
\(292\) | − | 6.60494e6i | − | 0.265290i | ||||||
\(293\) | −4.78962e7 | −1.90414 | −0.952069 | − | 0.305884i | \(-0.901048\pi\) | ||||
−0.952069 | + | 0.305884i | \(0.901048\pi\) | |||||||
\(294\) | − | 1.03584e7i | − | 0.407615i | ||||||
\(295\) | 7.87820e6 | + | 1.81408e7i | 0.306875 | + | 0.706626i | ||||
\(296\) | −8.54635e6 | −0.329538 | ||||||||
\(297\) | 4.58217e6i | 0.174905i | ||||||||
\(298\) | −7.78928e6 | −0.294340 | ||||||||
\(299\) | −3.30280e7 | −1.23557 | ||||||||
\(300\) | −3.16841e6 | −0.117349 | ||||||||
\(301\) | 2.02364e7i | 0.742052i | ||||||||
\(302\) | 1.47195e6 | 0.0534408 | ||||||||
\(303\) | 2.46757e7i | 0.887036i | ||||||||
\(304\) | 1.16300e7 | 0.413960 | ||||||||
\(305\) | − | 6.80617e6i | − | 0.239885i | ||||||
\(306\) | 9.27204e6i | 0.323602i | ||||||||
\(307\) | 2.38135e7 | 0.823015 | 0.411507 | − | 0.911406i | \(-0.365002\pi\) | ||||
0.411507 | + | 0.911406i | \(0.365002\pi\) | |||||||
\(308\) | − | 1.87695e7i | − | 0.642393i | ||||||
\(309\) | − | 1.40710e6i | − | 0.0476924i | ||||||
\(310\) | −1.98441e7 | −0.666110 | ||||||||
\(311\) | 2.44963e7 | 0.814366 | 0.407183 | − | 0.913347i | \(-0.366511\pi\) | ||||
0.407183 | + | 0.913347i | \(0.366511\pi\) | |||||||
\(312\) | −4.38378e6 | −0.144339 | ||||||||
\(313\) | 1.58989e7i | 0.518483i | 0.965813 | + | 0.259242i | \(0.0834726\pi\) | ||||
−0.965813 | + | 0.259242i | \(0.916527\pi\) | |||||||
\(314\) | −1.83865e7 | −0.593896 | ||||||||
\(315\) | 1.13466e7 | 0.363022 | ||||||||
\(316\) | 2.92070e6 | 0.0925604 | ||||||||
\(317\) | −3.23668e7 | −1.01607 | −0.508033 | − | 0.861338i | \(-0.669627\pi\) | ||||
−0.508033 | + | 0.861338i | \(0.669627\pi\) | |||||||
\(318\) | 1.25885e7i | 0.391464i | ||||||||
\(319\) | 2.15383e7i | 0.663498i | ||||||||
\(320\) | 3.15550e6 | 0.0962981 | ||||||||
\(321\) | 2.12518e7 | 0.642512 | ||||||||
\(322\) | 5.83147e7 | 1.74667 | ||||||||
\(323\) | 7.66078e7 | 2.27335 | ||||||||
\(324\) | −1.88957e6 | −0.0555556 | ||||||||
\(325\) | − | 9.86754e6i | − | 0.287448i | ||||||
\(326\) | − | 2.46593e7i | − | 0.711752i | ||||||
\(327\) | − | 3.19984e7i | − | 0.915136i | ||||||
\(328\) | − | 2.46456e7i | − | 0.698423i | ||||||
\(329\) | − | 5.27168e7i | − | 1.48034i | ||||||
\(330\) | 1.02721e7 | 0.285835 | ||||||||
\(331\) | −6.21208e7 | −1.71298 | −0.856492 | − | 0.516161i | \(-0.827361\pi\) | ||||
−0.856492 | + | 0.516161i | \(0.827361\pi\) | |||||||
\(332\) | 1.88234e7i | 0.514379i | ||||||||
\(333\) | − | 1.14726e7i | − | 0.310692i | ||||||
\(334\) | − | 1.52694e7i | − | 0.409809i | ||||||
\(335\) | − | 2.13182e7i | − | 0.567042i | ||||||
\(336\) | 7.74005e6 | 0.204045 | ||||||||
\(337\) | 4.23741e7i | 1.10716i | 0.832796 | + | 0.553581i | \(0.186739\pi\) | ||||
−0.832796 | + | 0.553581i | \(0.813261\pi\) | |||||||
\(338\) | 1.36519e7i | 0.353545i | ||||||||
\(339\) | − | 1.40719e7i | − | 0.361204i | ||||||
\(340\) | 2.07856e7 | 0.528841 | ||||||||
\(341\) | −4.40657e7 | −1.11132 | ||||||||
\(342\) | 1.56121e7i | 0.390285i | ||||||||
\(343\) | 88499.0 | 0.00219309 | ||||||||
\(344\) | −7.55471e6 | −0.185585 | ||||||||
\(345\) | 3.19141e7i | 0.777187i | ||||||||
\(346\) | −1.29195e7 | −0.311901 | ||||||||
\(347\) | − | 2.48057e7i | − | 0.593694i | −0.954925 | − | 0.296847i | \(-0.904065\pi\) | ||
0.954925 | − | 0.296847i | \(-0.0959352\pi\) | |||||||
\(348\) | −8.88183e6 | −0.210749 | ||||||||
\(349\) | 9.69535e6i | 0.228080i | 0.993476 | + | 0.114040i | \(0.0363792\pi\) | ||||
−0.993476 | + | 0.114040i | \(0.963621\pi\) | |||||||
\(350\) | 1.74222e7i | 0.406350i | ||||||||
\(351\) | − | 5.88477e6i | − | 0.136084i | ||||||
\(352\) | 7.00708e6 | 0.160660 | ||||||||
\(353\) | 5.91784e7i | 1.34536i | 0.739932 | + | 0.672681i | \(0.234857\pi\) | ||||
−0.739932 | + | 0.672681i | \(0.765143\pi\) | |||||||
\(354\) | −1.66118e7 | + | 7.21419e6i | −0.374461 | + | 0.162621i | ||||
\(355\) | −7.01146e6 | −0.156720 | ||||||||
\(356\) | − | 2.75639e7i | − | 0.610929i | ||||||
\(357\) | 5.09845e7 | 1.12056 | ||||||||
\(358\) | 3.93022e7 | 0.856579 | ||||||||
\(359\) | 5.54850e6 | 0.119920 | 0.0599601 | − | 0.998201i | \(-0.480903\pi\) | ||||
0.0599601 | + | 0.998201i | \(0.480903\pi\) | |||||||
\(360\) | 4.23593e6i | 0.0907907i | ||||||||
\(361\) | 8.19447e7 | 1.74180 | ||||||||
\(362\) | − | 1.21520e7i | − | 0.256166i | ||||||
\(363\) | −4.80580e6 | −0.100472 | ||||||||
\(364\) | 2.41052e7i | 0.499812i | ||||||||
\(365\) | − | 1.98764e7i | − | 0.408750i | ||||||
\(366\) | 6.23251e6 | 0.127122 | ||||||||
\(367\) | 7.93803e6i | 0.160589i | 0.996771 | + | 0.0802943i | \(0.0255860\pi\) | ||||
−0.996771 | + | 0.0802943i | \(0.974414\pi\) | |||||||
\(368\) | 2.17702e7i | 0.436836i | ||||||||
\(369\) | 3.30843e7 | 0.658480 | ||||||||
\(370\) | −2.57187e7 | −0.507742 | ||||||||
\(371\) | 6.92207e7 | 1.35555 | ||||||||
\(372\) | − | 1.81715e7i | − | 0.352990i | ||||||
\(373\) | 6.18624e7 | 1.19207 | 0.596033 | − | 0.802960i | \(-0.296743\pi\) | ||||
0.596033 | + | 0.802960i | \(0.296743\pi\) | |||||||
\(374\) | 4.61563e7 | 0.882300 | ||||||||
\(375\) | −3.29900e7 | −0.625589 | ||||||||
\(376\) | 1.96804e7 | 0.370229 | ||||||||
\(377\) | − | 2.76611e7i | − | 0.516233i | ||||||
\(378\) | 1.03902e7i | 0.192375i | ||||||||
\(379\) | 7.05181e7 | 1.29534 | 0.647668 | − | 0.761922i | \(-0.275744\pi\) | ||||
0.647668 | + | 0.761922i | \(0.275744\pi\) | |||||||
\(380\) | 3.49983e7 | 0.637817 | ||||||||
\(381\) | 1.38641e7 | 0.250679 | ||||||||
\(382\) | 3.32135e7 | 0.595832 | ||||||||
\(383\) | −6.13632e7 | −1.09222 | −0.546112 | − | 0.837712i | \(-0.683893\pi\) | ||||
−0.546112 | + | 0.837712i | \(0.683893\pi\) | |||||||
\(384\) | 2.88954e6i | 0.0510310i | ||||||||
\(385\) | − | 5.64833e7i | − | 0.989779i | ||||||
\(386\) | − | 7.82376e7i | − | 1.36036i | ||||||
\(387\) | − | 1.01414e7i | − | 0.174971i | ||||||
\(388\) | 2.19838e7i | 0.376364i | ||||||||
\(389\) | −7.29573e7 | −1.23942 | −0.619712 | − | 0.784829i | \(-0.712751\pi\) | ||||
−0.619712 | + | 0.784829i | \(0.712751\pi\) | |||||||
\(390\) | −1.31922e7 | −0.222394 | ||||||||
\(391\) | 1.43402e8i | 2.39898i | ||||||||
\(392\) | − | 2.12637e7i | − | 0.353005i | ||||||
\(393\) | 4.57554e7i | 0.753815i | ||||||||
\(394\) | − | 8.37330e7i | − | 1.36901i | ||||||
\(395\) | 8.78929e6 | 0.142614 | ||||||||
\(396\) | 9.40629e6i | 0.151472i | ||||||||
\(397\) | − | 4.18309e7i | − | 0.668537i | −0.942478 | − | 0.334268i | \(-0.891511\pi\) | ||
0.942478 | − | 0.334268i | \(-0.108489\pi\) | |||||||
\(398\) | 979200.i | 0.0155318i | ||||||||
\(399\) | 8.58465e7 | 1.35146 | ||||||||
\(400\) | −6.50412e6 | −0.101627 | ||||||||
\(401\) | 3.32904e7i | 0.516280i | 0.966107 | + | 0.258140i | \(0.0831096\pi\) | ||||
−0.966107 | + | 0.258140i | \(0.916890\pi\) | |||||||
\(402\) | 1.95214e7 | 0.300491 | ||||||||
\(403\) | 5.65925e7 | 0.864656 | ||||||||
\(404\) | 5.06543e7i | 0.768196i | ||||||||
\(405\) | −5.68631e6 | −0.0855983 | ||||||||
\(406\) | 4.88388e7i | 0.729772i | ||||||||
\(407\) | −5.71108e7 | −0.847100 | ||||||||
\(408\) | 1.90337e7i | 0.280247i | ||||||||
\(409\) | − | 3.59064e7i | − | 0.524809i | −0.964958 | − | 0.262405i | \(-0.915484\pi\) | ||
0.964958 | − | 0.262405i | \(-0.0845155\pi\) | |||||||
\(410\) | − | 7.41665e7i | − | 1.07611i | ||||||
\(411\) | 1.61233e7 | 0.232236 | ||||||||
\(412\) | − | 2.88849e6i | − | 0.0413028i | ||||||
\(413\) | 3.96689e7 | + | 9.13437e7i | 0.563119 | + | 1.29667i | ||||
\(414\) | −2.92243e7 | −0.411853 | ||||||||
\(415\) | 5.66454e7i | 0.792539i | ||||||||
\(416\) | −8.99902e6 | −0.125002 | ||||||||
\(417\) | −3.80598e7 | −0.524879 | ||||||||
\(418\) | 7.77170e7 | 1.06411 | ||||||||
\(419\) | 3.52266e6i | 0.0478882i | 0.999713 | + | 0.0239441i | \(0.00762237\pi\) | ||||
−0.999713 | + | 0.0239441i | \(0.992378\pi\) | |||||||
\(420\) | 2.32922e7 | 0.314386 | ||||||||
\(421\) | − | 3.59243e7i | − | 0.481439i | −0.970595 | − | 0.240720i | \(-0.922617\pi\) | ||
0.970595 | − | 0.240720i | \(-0.0773835\pi\) | |||||||
\(422\) | −8.14011e7 | −1.08316 | ||||||||
\(423\) | 2.64189e7i | 0.349055i | ||||||||
\(424\) | 2.58417e7i | 0.339018i | ||||||||
\(425\) | −4.28433e7 | −0.558105 | ||||||||
\(426\) | − | 6.42050e6i | − | 0.0830501i | ||||||
\(427\) | − | 3.42709e7i | − | 0.440192i | ||||||
\(428\) | 4.36258e7 | 0.556432 | ||||||||
\(429\) | −2.92945e7 | −0.371034 | ||||||||
\(430\) | −2.27345e7 | −0.285944 | ||||||||
\(431\) | − | 2.35726e6i | − | 0.0294425i | −0.999892 | − | 0.0147213i | \(-0.995314\pi\) | ||
0.999892 | − | 0.0147213i | \(-0.00468609\pi\) | |||||||
\(432\) | −3.87891e6 | −0.0481125 | ||||||||
\(433\) | 3.16666e7 | 0.390066 | 0.195033 | − | 0.980797i | \(-0.437519\pi\) | ||||
0.195033 | + | 0.980797i | \(0.437519\pi\) | |||||||
\(434\) | −9.99203e7 | −1.22232 | ||||||||
\(435\) | −2.67282e7 | −0.324715 | ||||||||
\(436\) | − | 6.56864e7i | − | 0.792531i | ||||||
\(437\) | 2.41458e8i | 2.89332i | ||||||||
\(438\) | 1.82011e7 | 0.216608 | ||||||||
\(439\) | 1.11257e7 | 0.131502 | 0.0657511 | − | 0.997836i | \(-0.479056\pi\) | ||||
0.0657511 | + | 0.997836i | \(0.479056\pi\) | |||||||
\(440\) | 2.10865e7 | 0.247541 | ||||||||
\(441\) | 2.85444e7 | 0.332816 | ||||||||
\(442\) | −5.92774e7 | −0.686472 | ||||||||
\(443\) | − | 1.42196e8i | − | 1.63560i | −0.575503 | − | 0.817800i | \(-0.695194\pi\) | ||
0.575503 | − | 0.817800i | \(-0.304806\pi\) | |||||||
\(444\) | − | 2.35510e7i | − | 0.269067i | ||||||
\(445\) | − | 8.29484e7i | − | 0.941300i | ||||||
\(446\) | 5.18392e6i | 0.0584324i | ||||||||
\(447\) | − | 2.14647e7i | − | 0.240327i | ||||||
\(448\) | 1.58888e7 | 0.176708 | ||||||||
\(449\) | −7.96695e7 | −0.880142 | −0.440071 | − | 0.897963i | \(-0.645047\pi\) | ||||
−0.440071 | + | 0.897963i | \(0.645047\pi\) | |||||||
\(450\) | − | 8.73112e6i | − | 0.0958147i | ||||||
\(451\) | − | 1.64694e8i | − | 1.79534i | ||||||
\(452\) | − | 2.88868e7i | − | 0.312812i | ||||||
\(453\) | 4.05622e6i | 0.0436342i | ||||||||
\(454\) | −1.18663e8 | −1.26809 | ||||||||
\(455\) | 7.25402e7i | 0.770095i | ||||||||
\(456\) | 3.20484e7i | 0.337997i | ||||||||
\(457\) | − | 1.52943e8i | − | 1.60244i | −0.598373 | − | 0.801218i | \(-0.704186\pi\) | ||
0.598373 | − | 0.801218i | \(-0.295814\pi\) | |||||||
\(458\) | −6.27033e7 | −0.652671 | ||||||||
\(459\) | −2.55507e7 | −0.264220 | ||||||||
\(460\) | 6.55134e7i | 0.673064i | ||||||||
\(461\) | −2.69808e7 | −0.275392 | −0.137696 | − | 0.990475i | \(-0.543970\pi\) | ||||
−0.137696 | + | 0.990475i | \(0.543970\pi\) | |||||||
\(462\) | 5.17227e7 | 0.524511 | ||||||||
\(463\) | 1.28669e7i | 0.129638i | 0.997897 | + | 0.0648188i | \(0.0206469\pi\) | ||||
−0.997897 | + | 0.0648188i | \(0.979353\pi\) | |||||||
\(464\) | −1.82326e7 | −0.182514 | ||||||||
\(465\) | − | 5.46839e7i | − | 0.543876i | ||||||
\(466\) | 2.73110e7 | 0.269885 | ||||||||
\(467\) | − | 1.81660e8i | − | 1.78365i | −0.452385 | − | 0.891823i | \(-0.649427\pi\) | ||
0.452385 | − | 0.891823i | \(-0.350573\pi\) | |||||||
\(468\) | − | 1.20803e7i | − | 0.117853i | ||||||
\(469\) | − | 1.07343e8i | − | 1.04053i | ||||||
\(470\) | 5.92245e7 | 0.570437 | ||||||||
\(471\) | − | 5.06673e7i | − | 0.484914i | ||||||
\(472\) | −3.41007e7 | + | 1.48093e7i | −0.324293 | + | 0.140834i | ||||
\(473\) | −5.04842e7 | −0.477059 | ||||||||
\(474\) | 8.04849e6i | 0.0755752i | ||||||||
\(475\) | −7.21385e7 | −0.673111 | ||||||||
\(476\) | 1.04661e8 | 0.970429 | ||||||||
\(477\) | −3.46898e7 | −0.319629 | ||||||||
\(478\) | − | 5.77957e7i | − | 0.529190i | ||||||
\(479\) | 7.95713e7 | 0.724019 | 0.362009 | − | 0.932174i | \(-0.382091\pi\) | ||||
0.362009 | + | 0.932174i | \(0.382091\pi\) | |||||||
\(480\) | 8.69552e6i | 0.0786271i | ||||||||
\(481\) | 7.33460e7 | 0.659084 | ||||||||
\(482\) | − | 1.03949e8i | − | 0.928281i | ||||||
\(483\) | 1.60696e8i | 1.42615i | ||||||||
\(484\) | −9.86535e6 | −0.0870115 | ||||||||
\(485\) | 6.61562e7i | 0.579890i | ||||||||
\(486\) | − | 5.20704e6i | − | 0.0453609i | ||||||
\(487\) | −1.77168e8 | −1.53391 | −0.766953 | − | 0.641704i | \(-0.778228\pi\) | ||||
−0.766953 | + | 0.641704i | \(0.778228\pi\) | |||||||
\(488\) | 1.27941e7 | 0.110091 | ||||||||
\(489\) | 6.79531e7 | 0.581143 | ||||||||
\(490\) | − | 6.39892e7i | − | 0.543899i | ||||||
\(491\) | 6.28678e7 | 0.531109 | 0.265555 | − | 0.964096i | \(-0.414445\pi\) | ||||
0.265555 | + | 0.964096i | \(0.414445\pi\) | |||||||
\(492\) | 6.79154e7 | 0.570260 | ||||||||
\(493\) | −1.20100e8 | −1.00231 | ||||||||
\(494\) | −9.98101e7 | −0.827930 | ||||||||
\(495\) | 2.83065e7i | 0.233384i | ||||||||
\(496\) | − | 3.73025e7i | − | 0.305698i | ||||||
\(497\) | −3.53046e7 | −0.287582 | ||||||||
\(498\) | −5.18711e7 | −0.419988 | ||||||||
\(499\) | −2.45486e8 | −1.97572 | −0.987860 | − | 0.155344i | \(-0.950351\pi\) | ||||
−0.987860 | + | 0.155344i | \(0.950351\pi\) | |||||||
\(500\) | −6.77220e7 | −0.541776 | ||||||||
\(501\) | 4.20775e7 | 0.334608 | ||||||||
\(502\) | 3.28889e7i | 0.259979i | ||||||||
\(503\) | − | 1.55411e8i | − | 1.22118i | −0.791949 | − | 0.610588i | \(-0.790933\pi\) | ||
0.791949 | − | 0.610588i | \(-0.209067\pi\) | |||||||
\(504\) | 2.13291e7i | 0.166602i | ||||||||
\(505\) | 1.52435e8i | 1.18361i | ||||||||
\(506\) | 1.45479e8i | 1.12292i | ||||||||
\(507\) | −3.76203e7 | −0.288668 | ||||||||
\(508\) | 2.84603e7 | 0.217094 | ||||||||
\(509\) | 2.69695e7i | 0.204512i | 0.994758 | + | 0.102256i | \(0.0326061\pi\) | ||||
−0.994758 | + | 0.102256i | \(0.967394\pi\) | |||||||
\(510\) | 5.72783e7i | 0.431797i | ||||||||
\(511\) | − | 1.00083e8i | − | 0.750062i | ||||||
\(512\) | 5.93164e6i | 0.0441942i | ||||||||
\(513\) | −4.30218e7 | −0.318666 | ||||||||
\(514\) | 1.38144e8i | 1.01728i | ||||||||
\(515\) | − | 8.69239e6i | − | 0.0636381i | ||||||
\(516\) | − | 2.08183e7i | − | 0.151529i | ||||||
\(517\) | 1.31514e8 | 0.951698 | ||||||||
\(518\) | −1.29501e8 | −0.931713 | ||||||||
\(519\) | − | 3.56019e7i | − | 0.254666i | ||||||
\(520\) | −2.70809e7 | −0.192599 | ||||||||
\(521\) | −1.73264e8 | −1.22517 | −0.612583 | − | 0.790406i | \(-0.709869\pi\) | ||||
−0.612583 | + | 0.790406i | \(0.709869\pi\) | |||||||
\(522\) | − | 2.44755e7i | − | 0.172076i | ||||||
\(523\) | 5.70724e7 | 0.398952 | 0.199476 | − | 0.979903i | \(-0.436076\pi\) | ||||
0.199476 | + | 0.979903i | \(0.436076\pi\) | |||||||
\(524\) | 9.39267e7i | 0.652823i | ||||||||
\(525\) | −4.80101e7 | −0.331783 | ||||||||
\(526\) | 3.52387e7i | 0.242138i | ||||||||
\(527\) | − | 2.45715e8i | − | 1.67881i | ||||||
\(528\) | 1.93092e7i | 0.131179i | ||||||||
\(529\) | −3.03950e8 | −2.05322 | ||||||||
\(530\) | 7.77657e7i | 0.522349i | ||||||||
\(531\) | −1.98800e7 | − | 4.57767e7i | −0.132780 | − | 0.305746i | ||||
\(532\) | 1.76226e8 | 1.17040 | ||||||||
\(533\) | 2.11512e8i | 1.39686i | ||||||||
\(534\) | 7.59572e7 | 0.498821 | ||||||||
\(535\) | 1.31284e8 | 0.857333 | ||||||||
\(536\) | 4.00735e7 | 0.260233 | ||||||||
\(537\) | 1.08304e8i | 0.699394i | ||||||||
\(538\) | −2.45901e7 | −0.157911 | ||||||||
\(539\) | − | 1.42094e8i | − | 0.907423i | ||||||
\(540\) | −1.16729e7 | −0.0741303 | ||||||||
\(541\) | 3.08310e8i | 1.94713i | 0.228406 | + | 0.973566i | \(0.426649\pi\) | ||||
−0.228406 | + | 0.973566i | \(0.573351\pi\) | |||||||
\(542\) | − | 2.96732e7i | − | 0.186366i | ||||||
\(543\) | 3.34869e7 | 0.209158 | ||||||||
\(544\) | 3.90723e7i | 0.242701i | ||||||||
\(545\) | − | 1.97671e8i | − | 1.22111i | ||||||
\(546\) | −6.64262e7 | −0.408095 | ||||||||
\(547\) | 1.01408e8 | 0.619597 | 0.309799 | − | 0.950802i | \(-0.399738\pi\) | ||||
0.309799 | + | 0.950802i | \(0.399738\pi\) | |||||||
\(548\) | 3.30980e7 | 0.201122 | ||||||||
\(549\) | 1.71748e7i | 0.103794i | ||||||||
\(550\) | −4.34636e7 | −0.261239 | ||||||||
\(551\) | −2.02222e8 | −1.20885 | ||||||||
\(552\) | −5.99916e7 | −0.356675 | ||||||||
\(553\) | 4.42565e7 | 0.261699 | ||||||||
\(554\) | 5.73046e7i | 0.337023i | ||||||||
\(555\) | − | 7.08723e7i | − | 0.414570i | ||||||
\(556\) | −7.81293e7 | −0.454558 | ||||||||
\(557\) | −8.87719e7 | −0.513701 | −0.256850 | − | 0.966451i | \(-0.582685\pi\) | ||||
−0.256850 | + | 0.966451i | \(0.582685\pi\) | |||||||
\(558\) | 5.00748e7 | 0.288215 | ||||||||
\(559\) | 6.48356e7 | 0.371174 | ||||||||
\(560\) | 4.78143e7 | 0.272266 | ||||||||
\(561\) | 1.27192e8i | 0.720395i | ||||||||
\(562\) | 1.24453e8i | 0.701127i | ||||||||
\(563\) | 1.40331e8i | 0.786370i | 0.919459 | + | 0.393185i | \(0.128627\pi\) | ||||
−0.919459 | + | 0.393185i | \(0.871373\pi\) | |||||||
\(564\) | 5.42328e7i | 0.302291i | ||||||||
\(565\) | − | 8.69294e7i | − | 0.481971i | ||||||
\(566\) | −1.44081e8 | −0.794616 | ||||||||
\(567\) | −2.86321e7 | −0.157074 | ||||||||
\(568\) | − | 1.31800e7i | − | 0.0719235i | ||||||
\(569\) | − | 1.25934e7i | − | 0.0683606i | −0.999416 | − | 0.0341803i | \(-0.989118\pi\) | ||
0.999416 | − | 0.0341803i | \(-0.0108820\pi\) | |||||||
\(570\) | 9.64439e7i | 0.520775i | ||||||||
\(571\) | 1.67521e8i | 0.899830i | 0.893071 | + | 0.449915i | \(0.148546\pi\) | ||||
−0.893071 | + | 0.449915i | \(0.851454\pi\) | |||||||
\(572\) | −6.01357e7 | −0.321325 | ||||||||
\(573\) | 9.15256e7i | 0.486495i | ||||||||
\(574\) | − | 3.73449e8i | − | 1.97467i | ||||||
\(575\) | − | 1.35036e8i | − | 0.710309i | ||||||
\(576\) | −7.96262e6 | −0.0416667 | ||||||||
\(577\) | 6.14313e7 | 0.319788 | 0.159894 | − | 0.987134i | \(-0.448885\pi\) | ||||
0.159894 | + | 0.987134i | \(0.448885\pi\) | |||||||
\(578\) | 1.20830e8i | 0.625738i | ||||||||
\(579\) | 2.15598e8 | 1.11073 | ||||||||
\(580\) | −5.48677e7 | −0.281212 | ||||||||
\(581\) | 2.85225e8i | 1.45432i | ||||||||
\(582\) | −6.05802e7 | −0.307300 | ||||||||
\(583\) | 1.72686e8i | 0.871469i | ||||||||
\(584\) | 3.73632e7 | 0.187588 | ||||||||
\(585\) | − | 3.63533e7i | − | 0.181584i | ||||||
\(586\) | − | 2.70942e8i | − | 1.34643i | ||||||
\(587\) | − | 2.18923e8i | − | 1.08237i | −0.840902 | − | 0.541187i | \(-0.817975\pi\) | ||
0.840902 | − | 0.541187i | \(-0.182025\pi\) | |||||||
\(588\) | 5.85959e7 | 0.288227 | ||||||||
\(589\) | − | 4.13730e8i | − | 2.02475i | ||||||
\(590\) | −1.02620e8 | + | 4.45658e7i | −0.499660 | + | 0.216993i | ||||
\(591\) | 2.30741e8 | 1.11780 | ||||||||
\(592\) | − | 4.83455e7i | − | 0.233019i | ||||||
\(593\) | −1.32061e8 | −0.633301 | −0.316651 | − | 0.948542i | \(-0.602558\pi\) | ||||
−0.316651 | + | 0.948542i | \(0.602558\pi\) | |||||||
\(594\) | −2.59207e7 | −0.123676 | ||||||||
\(595\) | 3.14958e8 | 1.49521 | ||||||||
\(596\) | − | 4.40628e7i | − | 0.208130i | ||||||
\(597\) | −2.69836e6 | −0.0126817 | ||||||||
\(598\) | − | 1.86835e8i | − | 0.873683i | ||||||
\(599\) | −3.65742e8 | −1.70174 | −0.850872 | − | 0.525373i | \(-0.823926\pi\) | ||||
−0.850872 | + | 0.525373i | \(0.823926\pi\) | |||||||
\(600\) | − | 1.79232e7i | − | 0.0829780i | ||||||
\(601\) | 1.30989e8i | 0.603408i | 0.953402 | + | 0.301704i | \(0.0975554\pi\) | ||||
−0.953402 | + | 0.301704i | \(0.902445\pi\) | |||||||
\(602\) | −1.14474e8 | −0.524710 | ||||||||
\(603\) | 5.37945e7i | 0.245350i | ||||||||
\(604\) | 8.32662e6i | 0.0377883i | ||||||||
\(605\) | −2.96880e7 | −0.134065 | ||||||||
\(606\) | −1.39587e8 | −0.627230 | ||||||||
\(607\) | 2.79266e8 | 1.24868 | 0.624342 | − | 0.781151i | \(-0.285367\pi\) | ||||
0.624342 | + | 0.781151i | \(0.285367\pi\) | |||||||
\(608\) | 6.57891e7i | 0.292714i | ||||||||
\(609\) | −1.34584e8 | −0.595856 | ||||||||
\(610\) | 3.85015e7 | 0.169624 | ||||||||
\(611\) | −1.68900e8 | −0.740467 | ||||||||
\(612\) | −5.24506e7 | −0.228821 | ||||||||
\(613\) | 3.16953e8i | 1.37599i | 0.725717 | + | 0.687993i | \(0.241508\pi\) | ||||
−0.725717 | + | 0.687993i | \(0.758492\pi\) | |||||||
\(614\) | 1.34709e8i | 0.581959i | ||||||||
\(615\) | 2.04379e8 | 0.878640 | ||||||||
\(616\) | 1.06176e8 | 0.454240 | ||||||||
\(617\) | −4.07741e8 | −1.73592 | −0.867959 | − | 0.496636i | \(-0.834568\pi\) | ||||
−0.867959 | + | 0.496636i | \(0.834568\pi\) | |||||||
\(618\) | 7.95975e6 | 0.0337236 | ||||||||
\(619\) | −2.85584e8 | −1.20410 | −0.602049 | − | 0.798459i | \(-0.705649\pi\) | ||||
−0.602049 | + | 0.798459i | \(0.705649\pi\) | |||||||
\(620\) | − | 1.12255e8i | − | 0.471011i | ||||||
\(621\) | − | 8.05326e7i | − | 0.336277i | ||||||
\(622\) | 1.38572e8i | 0.575844i | ||||||||
\(623\) | − | 4.17668e8i | − | 1.72730i | ||||||
\(624\) | − | 2.47984e7i | − | 0.102063i | ||||||
\(625\) | −1.04552e8 | −0.428244 | ||||||||
\(626\) | −8.99379e7 | −0.366623 | ||||||||
\(627\) | 2.14163e8i | 0.868843i | ||||||||
\(628\) | − | 1.04010e8i | − | 0.419948i | ||||||
\(629\) | − | 3.18456e8i | − | 1.27967i | ||||||
\(630\) | 6.41859e7i | 0.256695i | ||||||||
\(631\) | 1.30499e8 | 0.519421 | 0.259710 | − | 0.965687i | \(-0.416373\pi\) | ||||
0.259710 | + | 0.965687i | \(0.416373\pi\) | |||||||
\(632\) | 1.65220e7i | 0.0654501i | ||||||||
\(633\) | − | 2.24315e8i | − | 0.884397i | ||||||
\(634\) | − | 1.83094e8i | − | 0.718467i | ||||||
\(635\) | 8.56459e7 | 0.334492 | ||||||||
\(636\) | −7.12113e7 | −0.276807 | ||||||||
\(637\) | 1.82488e8i | 0.706018i | ||||||||
\(638\) | −1.21839e8 | −0.469164 | ||||||||
\(639\) | 1.76928e7 | 0.0678101 | ||||||||
\(640\) | 1.78502e7i | 0.0680930i | ||||||||
\(641\) | 1.85260e8 | 0.703409 | 0.351704 | − | 0.936111i | \(-0.385602\pi\) | ||||
0.351704 | + | 0.936111i | \(0.385602\pi\) | |||||||
\(642\) | 1.20219e8i | 0.454325i | ||||||||
\(643\) | 9.95522e6 | 0.0374471 | 0.0187235 | − | 0.999825i | \(-0.494040\pi\) | ||||
0.0187235 | + | 0.999825i | \(0.494040\pi\) | |||||||
\(644\) | 3.29878e8i | 1.23508i | ||||||||
\(645\) | − | 6.26490e7i | − | 0.233472i | ||||||
\(646\) | 4.33359e8i | 1.60750i | ||||||||
\(647\) | 1.38325e8 | 0.510724 | 0.255362 | − | 0.966845i | \(-0.417805\pi\) | ||||
0.255362 | + | 0.966845i | \(0.417805\pi\) | |||||||
\(648\) | − | 1.06890e7i | − | 0.0392837i | ||||||
\(649\) | −2.27877e8 | + | 9.89627e7i | −0.833616 | + | 0.362024i | ||||
\(650\) | 5.58192e7 | 0.203256 | ||||||||
\(651\) | − | 2.75348e8i | − | 0.998020i | ||||||
\(652\) | 1.39494e8 | 0.503284 | ||||||||
\(653\) | −3.95730e8 | −1.42121 | −0.710606 | − | 0.703590i | \(-0.751579\pi\) | ||||
−0.710606 | + | 0.703590i | \(0.751579\pi\) | |||||||
\(654\) | 1.81011e8 | 0.647099 | ||||||||
\(655\) | 2.82655e8i | 1.00585i | ||||||||
\(656\) | 1.39417e8 | 0.493860 | ||||||||
\(657\) | 5.01563e7i | 0.176860i | ||||||||
\(658\) | 2.98211e8 | 1.04676 | ||||||||
\(659\) | − | 2.30747e8i | − | 0.806269i | −0.915141 | − | 0.403134i | \(-0.867921\pi\) | ||
0.915141 | − | 0.403134i | \(-0.132079\pi\) | |||||||
\(660\) | 5.81076e7i | 0.202116i | ||||||||
\(661\) | −5.18516e8 | −1.79539 | −0.897693 | − | 0.440622i | \(-0.854758\pi\) | ||||
−0.897693 | + | 0.440622i | \(0.854758\pi\) | |||||||
\(662\) | − | 3.51408e8i | − | 1.21126i | ||||||
\(663\) | − | 1.63349e8i | − | 0.560502i | ||||||
\(664\) | −1.06481e8 | −0.363721 | ||||||||
\(665\) | 5.30319e8 | 1.80332 | ||||||||
\(666\) | 6.48989e7 | 0.219692 | ||||||||
\(667\) | − | 3.78540e8i | − | 1.27566i | ||||||
\(668\) | 8.63766e7 | 0.289779 | ||||||||
\(669\) | −1.42852e7 | −0.0477099 | ||||||||
\(670\) | 1.20594e8 | 0.400959 | ||||||||
\(671\) | 8.54962e7 | 0.282995 | ||||||||
\(672\) | 4.37843e7i | 0.144282i | ||||||||
\(673\) | 5.69561e8i | 1.86851i | 0.356609 | + | 0.934254i | \(0.383933\pi\) | ||||
−0.356609 | + | 0.934254i | \(0.616067\pi\) | |||||||
\(674\) | −2.39704e8 | −0.782881 | ||||||||
\(675\) | 2.40601e7 | 0.0782324 | ||||||||
\(676\) | −7.72271e7 | −0.249994 | ||||||||
\(677\) | −2.95557e8 | −0.952523 | −0.476261 | − | 0.879304i | \(-0.658008\pi\) | ||||
−0.476261 | + | 0.879304i | \(0.658008\pi\) | |||||||
\(678\) | 7.96025e7 | 0.255410 | ||||||||
\(679\) | 3.33114e8i | 1.06410i | ||||||||
\(680\) | 1.17581e8i | 0.373947i | ||||||||
\(681\) | − | 3.26997e8i | − | 1.03539i | ||||||
\(682\) | − | 2.49273e8i | − | 0.785818i | ||||||
\(683\) | − | 6.28756e7i | − | 0.197342i | −0.995120 | − | 0.0986711i | \(-0.968541\pi\) | ||
0.995120 | − | 0.0986711i | \(-0.0314592\pi\) | |||||||
\(684\) | −8.83151e7 | −0.275973 | ||||||||
\(685\) | 9.96023e7 | 0.309883 | ||||||||
\(686\) | 500626.i | 0.00155075i | ||||||||
\(687\) | − | 1.72790e8i | − | 0.532903i | ||||||
\(688\) | − | 4.27359e7i | − | 0.131228i | ||||||
\(689\) | − | 2.21777e8i | − | 0.678045i | ||||||
\(690\) | −1.80534e8 | −0.549554 | ||||||||
\(691\) | − | 5.64077e8i | − | 1.70964i | −0.518927 | − | 0.854818i | \(-0.673668\pi\) | ||
0.518927 | − | 0.854818i | \(-0.326332\pi\) | |||||||
\(692\) | − | 7.30836e7i | − | 0.220547i | ||||||
\(693\) | 1.42531e8i | 0.428262i | ||||||||
\(694\) | 1.40322e8 | 0.419805 | ||||||||
\(695\) | −2.35116e8 | −0.700369 | ||||||||
\(696\) | − | 5.02432e7i | − | 0.149022i | ||||||
\(697\) | 9.18352e8 | 2.71213 | ||||||||
\(698\) | −5.48452e7 | −0.161277 | ||||||||
\(699\) | 7.52602e7i | 0.220360i | ||||||||
\(700\) | −9.85551e7 | −0.287333 | ||||||||
\(701\) | − | 2.43173e8i | − | 0.705930i | −0.935636 | − | 0.352965i | \(-0.885173\pi\) | ||
0.935636 | − | 0.352965i | \(-0.114827\pi\) | |||||||
\(702\) | 3.32893e7 | 0.0962262 | ||||||||
\(703\) | − | 5.36210e8i | − | 1.54337i | ||||||
\(704\) | 3.96380e7i | 0.113604i | ||||||||
\(705\) | 1.63204e8i | 0.465760i | ||||||||
\(706\) | −3.34764e8 | −0.951315 | ||||||||
\(707\) | 7.67550e8i | 2.17194i | ||||||||
\(708\) | −4.08096e7 | − | 9.39704e7i | −0.114991 | − | 0.264784i | ||||
\(709\) | 2.32305e6 | 0.00651808 | 0.00325904 | − | 0.999995i | \(-0.498963\pi\) | ||||
0.00325904 | + | 0.999995i | \(0.498963\pi\) | |||||||
\(710\) | − | 3.96628e7i | − | 0.110818i | ||||||
\(711\) | −2.21790e7 | −0.0617069 | ||||||||
\(712\) | 1.55925e8 | 0.431992 | ||||||||
\(713\) | 7.74463e8 | 2.13664 | ||||||||
\(714\) | 2.88412e8i | 0.792352i | ||||||||
\(715\) | −1.80967e8 | −0.495087 | ||||||||
\(716\) | 2.22327e8i | 0.605693i | ||||||||
\(717\) | 1.59266e8 | 0.432082 | ||||||||
\(718\) | 3.13870e7i | 0.0847963i | ||||||||
\(719\) | − | 2.75575e8i | − | 0.741401i | −0.928752 | − | 0.370701i | \(-0.879118\pi\) | ||
0.928752 | − | 0.370701i | \(-0.120882\pi\) | |||||||
\(720\) | −2.39620e7 | −0.0641987 | ||||||||
\(721\) | − | 4.37685e7i | − | 0.116777i | ||||||
\(722\) | 4.63549e8i | 1.23164i | ||||||||
\(723\) | 2.86450e8 | 0.757938 | ||||||||
\(724\) | 6.87419e7 | 0.181136 | ||||||||
\(725\) | 1.13094e8 | 0.296773 | ||||||||
\(726\) | − | 2.71857e7i | − | 0.0710446i | ||||||
\(727\) | −4.51085e8 | −1.17396 | −0.586982 | − | 0.809600i | \(-0.699684\pi\) | ||||
−0.586982 | + | 0.809600i | \(0.699684\pi\) | |||||||
\(728\) | −1.36360e8 | −0.353421 | ||||||||
\(729\) | 1.43489e7 | 0.0370370 | ||||||||
\(730\) | 1.12438e8 | 0.289030 | ||||||||
\(731\) | − | 2.81506e8i | − | 0.720668i | ||||||
\(732\) | 3.52564e7i | 0.0898886i | ||||||||
\(733\) | 5.04739e8 | 1.28161 | 0.640803 | − | 0.767705i | \(-0.278601\pi\) | ||||
0.640803 | + | 0.767705i | \(0.278601\pi\) | |||||||
\(734\) | −4.49043e7 | −0.113553 | ||||||||
\(735\) | 1.76333e8 | 0.444092 | ||||||||
\(736\) | −1.23151e8 | −0.308890 | ||||||||
\(737\) | 2.67790e8 | 0.668947 | ||||||||
\(738\) | 1.87153e8i | 0.465616i | ||||||||
\(739\) | 3.61892e8i | 0.896697i | 0.893859 | + | 0.448349i | \(0.147988\pi\) | ||||
−0.893859 | + | 0.448349i | \(0.852012\pi\) | |||||||
\(740\) | − | 1.45487e8i | − | 0.359028i | ||||||
\(741\) | − | 2.75044e8i | − | 0.676002i | ||||||
\(742\) | 3.91572e8i | 0.958516i | ||||||||
\(743\) | 1.82011e8 | 0.443742 | 0.221871 | − | 0.975076i | \(-0.428784\pi\) | ||||
0.221871 | + | 0.975076i | \(0.428784\pi\) | |||||||
\(744\) | 1.02794e8 | 0.249602 | ||||||||
\(745\) | − | 1.32599e8i | − | 0.320680i | ||||||
\(746\) | 3.49947e8i | 0.842918i | ||||||||
\(747\) | − | 1.42940e8i | − | 0.342919i | ||||||
\(748\) | 2.61100e8i | 0.623880i | ||||||||
\(749\) | 6.61050e8 | 1.57322 | ||||||||
\(750\) | − | 1.86620e8i | − | 0.442358i | ||||||
\(751\) | 2.25377e8i | 0.532096i | 0.963960 | + | 0.266048i | \(0.0857179\pi\) | ||||
−0.963960 | + | 0.266048i | \(0.914282\pi\) | |||||||
\(752\) | 1.11329e8i | 0.261791i | ||||||||
\(753\) | −9.06312e7 | −0.212272 | ||||||||
\(754\) | 1.56475e8 | 0.365032 | ||||||||
\(755\) | 2.50574e7i | 0.0582231i | ||||||||
\(756\) | −5.87760e7 | −0.136030 | ||||||||
\(757\) | −1.78181e8 | −0.410746 | −0.205373 | − | 0.978684i | \(-0.565841\pi\) | ||||
−0.205373 | + | 0.978684i | \(0.565841\pi\) | |||||||
\(758\) | 3.98910e8i | 0.915941i | ||||||||
\(759\) | −4.00892e8 | −0.916858 | ||||||||
\(760\) | 1.97980e8i | 0.451004i | ||||||||
\(761\) | 1.51836e7 | 0.0344525 | 0.0172262 | − | 0.999852i | \(-0.494516\pi\) | ||||
0.0172262 | + | 0.999852i | \(0.494516\pi\) | |||||||
\(762\) | 7.84273e7i | 0.177257i | ||||||||
\(763\) | − | 9.95328e8i | − | 2.24075i | ||||||
\(764\) | 1.87884e8i | 0.421317i | ||||||||
\(765\) | −1.57840e8 | −0.352561 | ||||||||
\(766\) | − | 3.47123e8i | − | 0.772319i | ||||||
\(767\) | 2.92657e8 | − | 1.27095e8i | 0.648593 | − | 0.281672i | ||||
\(768\) | −1.63457e7 | −0.0360844 | ||||||||
\(769\) | − | 1.40680e7i | − | 0.0309353i | −0.999880 | − | 0.0154676i | \(-0.995076\pi\) | ||
0.999880 | − | 0.0154676i | \(-0.00492370\pi\) | |||||||
\(770\) | 3.19518e8 | 0.699879 | ||||||||
\(771\) | −3.80680e8 | −0.830609 | ||||||||
\(772\) | 4.42579e8 | 0.961919 | ||||||||
\(773\) | 2.32040e8i | 0.502370i | 0.967939 | + | 0.251185i | \(0.0808203\pi\) | ||||
−0.967939 | + | 0.251185i | \(0.919180\pi\) | |||||||
\(774\) | 5.73686e7 | 0.123723 | ||||||||
\(775\) | 2.31381e8i | 0.497075i | ||||||||
\(776\) | −1.24359e8 | −0.266129 | ||||||||
\(777\) | − | 3.56861e8i | − | 0.760741i | ||||||
\(778\) | − | 4.12709e8i | − | 0.876405i | ||||||
\(779\) | 1.54630e9 | 3.27101 | ||||||||
\(780\) | − | 7.46262e7i | − | 0.157256i | ||||||
\(781\) | − | 8.80750e7i | − | 0.184884i | ||||||
\(782\) | −8.11206e8 | −1.69633 | ||||||||
\(783\) | 6.74464e7 | 0.140499 | ||||||||
\(784\) | 1.20286e8 | 0.249612 | ||||||||
\(785\) | − | 3.12998e8i | − | 0.647043i | ||||||
\(786\) | −2.58832e8 | −0.533027 | ||||||||
\(787\) | −4.47870e7 | −0.0918814 | −0.0459407 | − | 0.998944i | \(-0.514629\pi\) | ||||
−0.0459407 | + | 0.998944i | \(0.514629\pi\) | |||||||
\(788\) | 4.73665e8 | 0.968039 | ||||||||
\(789\) | −9.71065e7 | −0.197705 | ||||||||
\(790\) | 4.97198e7i | 0.100843i | ||||||||
\(791\) | − | 4.37713e8i | − | 0.884423i | ||||||
\(792\) | −5.32100e7 | −0.107107 | ||||||||
\(793\) | −1.09801e8 | −0.220184 | ||||||||
\(794\) | 2.36631e8 | 0.472727 | ||||||||
\(795\) | −2.14297e8 | −0.426496 | ||||||||
\(796\) | −5.53919e6 | −0.0109826 | ||||||||
\(797\) | − | 5.69778e8i | − | 1.12546i | −0.826640 | − | 0.562731i | \(-0.809751\pi\) | ||
0.826640 | − | 0.562731i | \(-0.190249\pi\) | |||||||
\(798\) | 4.85621e8i | 0.955628i | ||||||||
\(799\) | 7.33336e8i | 1.43768i | ||||||||
\(800\) | − | 3.67928e7i | − | 0.0718610i | ||||||
\(801\) | 2.09313e8i | 0.407286i | ||||||||
\(802\) | −1.88319e8 | −0.365065 | ||||||||
\(803\) | 2.49678e8 | 0.482208 | ||||||||
\(804\) | 1.10429e8i | 0.212479i | ||||||||
\(805\) | 9.92706e8i | 1.90297i | ||||||||
\(806\) | 3.20135e8i | 0.611404i | ||||||||
\(807\) | − | 6.77623e7i | − | 0.128934i | ||||||
\(808\) | −2.86544e8 | −0.543197 | ||||||||
\(809\) | 7.98785e8i | 1.50864i | 0.656509 | + | 0.754318i | \(0.272032\pi\) | ||||
−0.656509 | + | 0.754318i | \(0.727968\pi\) | |||||||
\(810\) | − | 3.21666e7i | − | 0.0605271i | ||||||
\(811\) | 2.80075e8i | 0.525064i | 0.964923 | + | 0.262532i | \(0.0845575\pi\) | ||||
−0.964923 | + | 0.262532i | \(0.915442\pi\) | |||||||
\(812\) | −2.76274e8 | −0.516026 | ||||||||
\(813\) | 8.17697e7 | 0.152167 | ||||||||
\(814\) | − | 3.23067e8i | − | 0.598990i | ||||||
\(815\) | 4.19782e8 | 0.775445 | ||||||||
\(816\) | −1.07671e8 | −0.198165 | ||||||||
\(817\) | − | 4.73993e8i | − | 0.869172i | ||||||
\(818\) | 2.03117e8 | 0.371096 | ||||||||
\(819\) | − | 1.83049e8i | − | 0.333208i | ||||||
\(820\) | 4.19549e8 | 0.760924 | ||||||||
\(821\) | − | 4.15041e8i | − | 0.750001i | −0.927025 | − | 0.375001i | \(-0.877642\pi\) | ||
0.927025 | − | 0.375001i | \(-0.122358\pi\) | |||||||
\(822\) | 9.12074e7i | 0.164216i | ||||||||
\(823\) | 5.73292e8i | 1.02843i | 0.857660 | + | 0.514217i | \(0.171917\pi\) | ||||
−0.857660 | + | 0.514217i | \(0.828083\pi\) | |||||||
\(824\) | 1.63398e7 | 0.0292055 | ||||||||
\(825\) | − | 1.19772e8i | − | 0.213300i | ||||||
\(826\) | −5.16718e8 | + | 2.24401e8i | −0.916882 | + | 0.398185i | ||||
\(827\) | −2.00658e8 | −0.354765 | −0.177382 | − | 0.984142i | \(-0.556763\pi\) | ||||
−0.177382 | + | 0.984142i | \(0.556763\pi\) | |||||||
\(828\) | − | 1.65317e8i | − | 0.291224i | ||||||
\(829\) | −4.37927e8 | −0.768667 | −0.384334 | − | 0.923194i | \(-0.625569\pi\) | ||||
−0.384334 | + | 0.923194i | \(0.625569\pi\) | |||||||
\(830\) | −3.20435e8 | −0.560410 | ||||||||
\(831\) | −1.57913e8 | −0.275178 | ||||||||
\(832\) | − | 5.09062e7i | − | 0.0883894i | ||||||
\(833\) | 7.92334e8 | 1.37080 | ||||||||
\(834\) | − | 2.15299e8i | − | 0.371145i | ||||||
\(835\) | 2.59935e8 | 0.446483 | ||||||||
\(836\) | 4.39634e8i | 0.752440i | ||||||||
\(837\) | 1.37990e8i | 0.235327i | ||||||||
\(838\) | −1.99272e7 | −0.0338621 | ||||||||
\(839\) | − | 5.51306e8i | − | 0.933485i | −0.884393 | − | 0.466742i | \(-0.845428\pi\) | ||
0.884393 | − | 0.466742i | \(-0.154572\pi\) | |||||||
\(840\) | 1.31761e8i | 0.222305i | ||||||||
\(841\) | −2.77794e8 | −0.467020 | ||||||||
\(842\) | 2.03218e8 | 0.340429 | ||||||||
\(843\) | −3.42952e8 | −0.572467 | ||||||||
\(844\) | − | 4.60474e8i | − | 0.765910i | ||||||
\(845\) | −2.32401e8 | −0.385183 | ||||||||
\(846\) | −1.49448e8 | −0.246819 | ||||||||
\(847\) | −1.49487e8 | −0.246010 | ||||||||
\(848\) | −1.46183e8 | −0.239722 | ||||||||
\(849\) | − | 3.97040e8i | − | 0.648801i | ||||||
\(850\) | − | 2.42358e8i | − | 0.394640i | ||||||
\(851\) | 1.00373e9 | 1.62866 | ||||||||
\(852\) | 3.63198e7 | 0.0587253 | ||||||||
\(853\) | −3.16637e8 | −0.510169 | −0.255085 | − | 0.966919i | \(-0.582103\pi\) | ||||
−0.255085 | + | 0.966919i | \(0.582103\pi\) | |||||||
\(854\) | 1.93865e8 | 0.311263 | ||||||||
\(855\) | −2.65768e8 | −0.425211 | ||||||||
\(856\) | 2.46785e8i | 0.393457i | ||||||||
\(857\) | − | 8.21327e8i | − | 1.30489i | −0.757837 | − | 0.652444i | \(-0.773744\pi\) | ||
0.757837 | − | 0.652444i | \(-0.226256\pi\) | |||||||
\(858\) | − | 1.65715e8i | − | 0.262361i | ||||||
\(859\) | − | 8.41438e7i | − | 0.132752i | −0.997795 | − | 0.0663762i | \(-0.978856\pi\) | ||
0.997795 | − | 0.0663762i | \(-0.0211437\pi\) | |||||||
\(860\) | − | 1.28606e8i | − | 0.202193i | ||||||
\(861\) | 1.02910e9 | 1.61231 | ||||||||
\(862\) | 1.33347e7 | 0.0208190 | ||||||||
\(863\) | − | 4.15889e8i | − | 0.647061i | −0.946218 | − | 0.323531i | \(-0.895130\pi\) | ||
0.946218 | − | 0.323531i | \(-0.104870\pi\) | |||||||
\(864\) | − | 2.19424e7i | − | 0.0340207i | ||||||
\(865\) | − | 2.19932e8i | − | 0.339812i | ||||||
\(866\) | 1.79134e8i | 0.275818i | ||||||||
\(867\) | −3.32969e8 | −0.510913 | ||||||||
\(868\) | − | 5.65235e8i | − | 0.864310i | ||||||
\(869\) | 1.10407e8i | 0.168244i | ||||||||
\(870\) | − | 1.51198e8i | − | 0.229608i | ||||||
\(871\) | −3.43916e8 | −0.520473 | ||||||||
\(872\) | 3.71579e8 | 0.560404 | ||||||||
\(873\) | − | 1.66939e8i | − | 0.250909i | ||||||
\(874\) | −1.36589e9 | −2.04589 | ||||||||
\(875\) | −1.02617e9 | −1.53178 | ||||||||
\(876\) | 1.02961e8i | 0.153165i | ||||||||
\(877\) | 6.99610e8 | 1.03719 | 0.518593 | − | 0.855021i | \(-0.326456\pi\) | ||||
0.518593 | + | 0.855021i | \(0.326456\pi\) | |||||||
\(878\) | 6.29363e7i | 0.0929861i | ||||||||
\(879\) | 7.46628e8 | 1.09935 | ||||||||
\(880\) | 1.19283e8i | 0.175038i | ||||||||
\(881\) | 8.40662e8i | 1.22940i | 0.788760 | + | 0.614701i | \(0.210723\pi\) | ||||
−0.788760 | + | 0.614701i | \(0.789277\pi\) | |||||||
\(882\) | 1.61471e8i | 0.235337i | ||||||||
\(883\) | −8.39866e8 | −1.21991 | −0.609955 | − | 0.792436i | \(-0.708812\pi\) | ||||
−0.609955 | + | 0.792436i | \(0.708812\pi\) | |||||||
\(884\) | − | 3.35324e8i | − | 0.485409i | ||||||
\(885\) | −1.22809e8 | − | 2.82787e8i | −0.177174 | − | 0.407971i | ||||
\(886\) | 8.04384e8 | 1.15654 | ||||||||
\(887\) | 6.76545e8i | 0.969451i | 0.874666 | + | 0.484725i | \(0.161080\pi\) | ||||
−0.874666 | + | 0.484725i | \(0.838920\pi\) | |||||||
\(888\) | 1.33224e8 | 0.190259 | ||||||||
\(889\) | 4.31250e8 | 0.613796 | ||||||||
\(890\) | 4.69227e8 | 0.665600 | ||||||||
\(891\) | − | 7.14290e7i | − | 0.100981i | ||||||
\(892\) | −2.93247e7 | −0.0413180 | ||||||||
\(893\) | 1.23477e9i | 1.73394i | ||||||||
\(894\) | 1.21423e8 | 0.169937 | ||||||||
\(895\) | 6.69051e8i | 0.933233i | ||||||||
\(896\) | 8.98805e7i | 0.124952i | ||||||||
\(897\) | 5.14856e8 | 0.713359 | ||||||||
\(898\) | − | 4.50678e8i | − | 0.622354i | ||||||
\(899\) | 6.48616e8i | 0.892707i | ||||||||
\(900\) | 4.93906e7 | 0.0677512 | ||||||||
\(901\) | −9.62919e8 | −1.31648 | ||||||||
\(902\) | 9.31649e8 | 1.26950 | ||||||||
\(903\) | − | 3.15455e8i | − | 0.428424i | ||||||
\(904\) | 1.63408e8 | 0.221192 | ||||||||
\(905\) | 2.06866e8 | 0.279090 | ||||||||
\(906\) | −2.29455e7 | −0.0308540 | ||||||||
\(907\) | −1.01769e9 | −1.36393 | −0.681967 | − | 0.731383i | \(-0.738875\pi\) | ||||
−0.681967 | + | 0.731383i | \(0.738875\pi\) | |||||||
\(908\) | − | 6.71261e8i | − | 0.896672i | ||||||
\(909\) | − | 3.84656e8i | − | 0.512131i | ||||||
\(910\) | −4.10349e8 | −0.544540 | ||||||||
\(911\) | 8.60976e8 | 1.13877 | 0.569385 | − | 0.822071i | \(-0.307181\pi\) | ||||
0.569385 | + | 0.822071i | \(0.307181\pi\) | |||||||
\(912\) | −1.81293e8 | −0.239000 | ||||||||
\(913\) | −7.11556e8 | −0.934968 | ||||||||
\(914\) | 8.65175e8 | 1.13309 | ||||||||
\(915\) | 1.06098e8i | 0.138498i | ||||||||
\(916\) | − | 3.54704e8i | − | 0.461508i | ||||||
\(917\) | 1.42324e9i | 1.84574i | ||||||||
\(918\) | − | 1.44537e8i | − | 0.186832i | ||||||
\(919\) | 8.40861e8i | 1.08337i | 0.840581 | + | 0.541686i | \(0.182214\pi\) | ||||
−0.840581 | + | 0.541686i | \(0.817786\pi\) | |||||||
\(920\) | −3.70600e8 | −0.475928 | ||||||||
\(921\) | −3.71215e8 | −0.475168 | ||||||||
\(922\) | − | 1.52626e8i | − | 0.194732i | ||||||
\(923\) | 1.13113e8i | 0.143849i | ||||||||
\(924\) | 2.92588e8i | 0.370886i | ||||||||
\(925\) | 2.99878e8i | 0.378895i | ||||||||
\(926\) | −7.27861e7 | −0.0916676 | ||||||||
\(927\) | 2.19345e7i | 0.0275352i | ||||||||
\(928\) | − | 1.03139e8i | − | 0.129057i | ||||||
\(929\) | − | 6.55950e8i | − | 0.818132i | −0.912505 | − | 0.409066i | \(-0.865855\pi\) | ||
0.912505 | − | 0.409066i | \(-0.134145\pi\) | |||||||
\(930\) | 3.09339e8 | 0.384579 | ||||||||
\(931\) | 1.33411e9 | 1.65327 | ||||||||
\(932\) | 1.54494e8i | 0.190838i | ||||||||
\(933\) | −3.81860e8 | −0.470175 | ||||||||
\(934\) | 1.02762e9 | 1.26123 | ||||||||
\(935\) | 7.85731e8i | 0.961256i | ||||||||
\(936\) | 6.83363e7 | 0.0833344 | ||||||||
\(937\) | 5.07264e8i | 0.616616i | 0.951287 | + | 0.308308i | \(0.0997628\pi\) | ||||
−0.951287 | + | 0.308308i | \(0.900237\pi\) | |||||||
\(938\) | 6.07222e8 | 0.735765 | ||||||||
\(939\) | − | 2.47840e8i | − | 0.299346i | ||||||
\(940\) | 3.35024e8i | 0.403360i | ||||||||
\(941\) | 1.31730e9i | 1.58094i | 0.612499 | + | 0.790471i | \(0.290164\pi\) | ||||
−0.612499 | + | 0.790471i | \(0.709836\pi\) | |||||||
\(942\) | 2.86617e8 | 0.342886 | ||||||||
\(943\) | 2.89453e9i | 3.45177i | ||||||||
\(944\) | −8.37740e7 | − | 1.92903e8i | −0.0995849 | − | 0.229310i | ||||
\(945\) | −1.76876e8 | −0.209591 | ||||||||
\(946\) | − | 2.85582e8i | − | 0.337331i | ||||||
\(947\) | 2.50024e8 | 0.294396 | 0.147198 | − | 0.989107i | \(-0.452974\pi\) | ||||
0.147198 | + | 0.989107i | \(0.452974\pi\) | |||||||
\(948\) | −4.55291e7 | −0.0534398 | ||||||||
\(949\) | −3.20656e8 | −0.375181 | ||||||||
\(950\) | − | 4.08077e8i | − | 0.475961i | ||||||
\(951\) | 5.04548e8 | 0.586626 | ||||||||
\(952\) | 5.92052e8i | 0.686197i | ||||||||
\(953\) | −9.44099e8 | −1.09078 | −0.545392 | − | 0.838181i | \(-0.683619\pi\) | ||||
−0.545392 | + | 0.838181i | \(0.683619\pi\) | |||||||
\(954\) | − | 1.96235e8i | − | 0.226012i | ||||||
\(955\) | 5.65401e8i | 0.649153i | ||||||||
\(956\) | 3.26942e8 | 0.374194 | ||||||||
\(957\) | − | 3.35749e8i | − | 0.383071i | ||||||
\(958\) | 4.50123e8i | 0.511958i | ||||||||
\(959\) | 5.01525e8 | 0.568639 | ||||||||
\(960\) | −4.91893e7 | −0.0555977 | ||||||||
\(961\) | −4.39514e8 | −0.495225 | ||||||||
\(962\) | 4.14907e8i | 0.466043i | ||||||||
\(963\) | −3.31283e8 | −0.370955 | ||||||||
\(964\) | 5.88024e8 | 0.656394 | ||||||||
\(965\) | 1.33186e9 | 1.48210 | ||||||||
\(966\) | −9.09036e8 | −1.00844 | ||||||||
\(967\) | − | 1.02380e9i | − | 1.13223i | −0.824325 | − | 0.566117i | \(-0.808445\pi\) | ||
0.824325 | − | 0.566117i | \(-0.191555\pi\) | |||||||
\(968\) | − | 5.58069e7i | − | 0.0615264i | ||||||
\(969\) | −1.19420e9 | −1.31252 | ||||||||
\(970\) | −3.74236e8 | −0.410044 | ||||||||
\(971\) | −7.02238e8 | −0.767055 | −0.383528 | − | 0.923529i | \(-0.625291\pi\) | ||||
−0.383528 | + | 0.923529i | \(0.625291\pi\) | |||||||
\(972\) | 2.94555e7 | 0.0320750 | ||||||||
\(973\) | −1.18387e9 | −1.28519 | ||||||||
\(974\) | − | 1.00221e9i | − | 1.08463i | ||||||
\(975\) | 1.53820e8i | 0.165958i | ||||||||
\(976\) | 7.23744e7i | 0.0778458i | ||||||||
\(977\) | − | 1.30511e9i | − | 1.39946i | −0.714405 | − | 0.699732i | \(-0.753303\pi\) | ||
0.714405 | − | 0.699732i | \(-0.246697\pi\) | |||||||
\(978\) | 3.84401e8i | 0.410930i | ||||||||
\(979\) | 1.04196e9 | 1.11046 | ||||||||
\(980\) | 3.61978e8 | 0.384595 | ||||||||
\(981\) | 4.98806e8i | 0.528354i | ||||||||
\(982\) | 3.55634e8i | 0.375551i | ||||||||
\(983\) | 7.66861e8i | 0.807339i | 0.914905 | + | 0.403670i | \(0.132265\pi\) | ||||
−0.914905 | + | 0.403670i | \(0.867735\pi\) | |||||||
\(984\) | 3.84188e8i | 0.403235i | ||||||||
\(985\) | 1.42541e9 | 1.49152 | ||||||||
\(986\) | − | 6.79389e8i | − | 0.708741i | ||||||
\(987\) | 8.21774e8i | 0.854675i | ||||||||
\(988\) | − | 5.64611e8i | − | 0.585435i | ||||||
\(989\) | 8.87269e8 | 0.917205 | ||||||||
\(990\) | −1.60126e8 | −0.165027 | ||||||||
\(991\) | − | 1.81812e9i | − | 1.86811i | −0.357133 | − | 0.934054i | \(-0.616246\pi\) | ||
0.357133 | − | 0.934054i | \(-0.383754\pi\) | |||||||
\(992\) | 2.11015e8 | 0.216161 | ||||||||
\(993\) | 9.68368e8 | 0.988991 | ||||||||
\(994\) | − | 1.99713e8i | − | 0.203351i | ||||||
\(995\) | −1.66692e7 | −0.0169217 | ||||||||
\(996\) | − | 2.93427e8i | − | 0.296977i | ||||||
\(997\) | −7.87647e8 | −0.794778 | −0.397389 | − | 0.917650i | \(-0.630084\pi\) | ||||
−0.397389 | + | 0.917650i | \(0.630084\pi\) | |||||||
\(998\) | − | 1.38868e9i | − | 1.39705i | ||||||
\(999\) | 1.78840e8i | 0.179378i |
(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 | 354.7.d.a.235.20 | yes | 60 | |
59.58 | odd | 2 | inner | 354.7.d.a.235.19 | ✓ | 60 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.7.d.a.235.19 | ✓ | 60 | 59.58 | odd | 2 | inner | |
354.7.d.a.235.20 | yes | 60 | 1.1 | even | 1 | trivial |