Newspace parameters
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.p (of order \(6\), degree \(2\), minimal) |
Newform invariants
Self dual: | no |
Analytic conductor: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
|
|
Defining polynomial: |
\( x^{4} - 5x^{2} + 25 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 180) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.1 | ||
Root | \(1.93649 - 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.101 |
Dual form | 900.3.p.b.401.1 |
$q$-expansion
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.87298 | + | 10.1723i | −0.838998 | + | 1.45319i | 0.0517360 | + | 0.998661i | \(0.483525\pi\) |
−0.890734 | + | 0.454526i | \(0.849809\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.1190 | + | 7.57423i | 1.19263 | + | 0.688566i | 0.958903 | − | 0.283735i | \(-0.0915737\pi\) |
0.233729 | + | 0.972302i | \(0.424907\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.87298 | − | 15.3685i | −0.682537 | − | 1.18219i | −0.974204 | − | 0.225669i | \(-0.927543\pi\) |
0.291667 | − | 0.956520i | \(-0.405790\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 15.1485i | − | 0.891086i | −0.895261 | − | 0.445543i | \(-0.853011\pi\) | ||
0.895261 | − | 0.445543i | \(-0.146989\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −11.2540 | −0.592318 | −0.296159 | − | 0.955139i | \(-0.595706\pi\) | ||||
−0.296159 | + | 0.955139i | \(0.595706\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 17.6190 | + | 30.5169i | 0.838998 | + | 1.45319i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −29.2379 | + | 16.8805i | −1.27121 | + | 0.733935i | −0.975216 | − | 0.221254i | \(-0.928985\pi\) |
−0.295997 | + | 0.955189i | \(0.595652\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.23790 | + | 4.75615i | 0.284066 | + | 0.164005i | 0.635262 | − | 0.772296i | \(-0.280892\pi\) |
−0.351197 | + | 0.936302i | \(0.614225\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −28.1109 | − | 48.6895i | −0.906803 | − | 1.57063i | −0.818479 | − | 0.574537i | \(-0.805182\pi\) |
−0.0883237 | − | 0.996092i | \(-0.528151\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 39.3569 | − | 22.7227i | 1.19263 | − | 0.688566i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −14.0000 | −0.378378 | −0.189189 | − | 0.981941i | \(-0.560586\pi\) | ||||
−0.189189 | + | 0.981941i | \(0.560586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −53.2379 | −1.36507 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −22.5000 | + | 12.9904i | −0.548780 | + | 0.316839i | −0.748630 | − | 0.662988i | \(-0.769288\pi\) |
0.199849 | + | 0.979827i | \(0.435955\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.99193 | + | 17.3065i | −0.232371 | + | 0.402478i | −0.958505 | − | 0.285075i | \(-0.907982\pi\) |
0.726135 | + | 0.687552i | \(0.241315\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −62.6190 | − | 36.1531i | −1.33232 | − | 0.769214i | −0.346664 | − | 0.937990i | \(-0.612685\pi\) |
−0.985655 | + | 0.168775i | \(0.946019\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −44.4839 | − | 77.0483i | −0.907834 | − | 1.57241i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −39.3569 | − | 22.7227i | −0.771703 | − | 0.445543i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 37.6651i | − | 0.710663i | −0.934740 | − | 0.355331i | \(-0.884368\pi\) | ||
0.934740 | − | 0.355331i | \(-0.115632\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −16.8810 | + | 29.2388i | −0.296159 | + | 0.512962i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −55.1190 | + | 31.8229i | −0.934219 | + | 0.539372i | −0.888144 | − | 0.459566i | \(-0.848005\pi\) |
−0.0460759 | + | 0.998938i | \(0.514672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.618950 | + | 1.07205i | −0.0101467 | + | 0.0175746i | −0.871054 | − | 0.491187i | \(-0.836563\pi\) |
0.860907 | + | 0.508762i | \(0.169897\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 105.714 | 1.67800 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 42.9758 | + | 74.4363i | 0.641430 | + | 1.11099i | 0.985114 | + | 0.171904i | \(0.0549918\pi\) |
−0.343684 | + | 0.939085i | \(0.611675\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 101.283i | 1.46787i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 22.1046i | − | 0.311332i | −0.987810 | − | 0.155666i | \(-0.950248\pi\) | ||
0.987810 | − | 0.155666i | \(-0.0497524\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 60.2379 | 0.825177 | 0.412588 | − | 0.910918i | \(-0.364625\pi\) | ||||
0.412588 | + | 0.910918i | \(0.364625\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −154.095 | + | 88.9666i | −2.00123 | + | 1.15541i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −51.6190 | + | 89.4066i | −0.653404 | + | 1.13173i | 0.328887 | + | 0.944369i | \(0.393327\pi\) |
−0.982291 | + | 0.187360i | \(0.940007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 78.0000 | + | 45.0333i | 0.939759 | + | 0.542570i | 0.889885 | − | 0.456185i | \(-0.150785\pi\) |
0.0498743 | + | 0.998756i | \(0.484118\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.7137 | − | 14.2685i | 0.284066 | − | 0.164005i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 12.0964i | − | 0.135915i | −0.997688 | − | 0.0679574i | \(-0.978352\pi\) | ||
0.997688 | − | 0.0679574i | \(-0.0216482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 208.444 | 2.29059 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −168.665 | −1.81361 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 49.8488 | − | 86.3406i | 0.513905 | − | 0.890110i | −0.485965 | − | 0.873978i | \(-0.661532\pi\) |
0.999870 | − | 0.0161312i | \(-0.00513495\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 136.336i | − | 1.37713i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −134.238 | − | 77.5023i | −1.32909 | − | 0.767349i | −0.343929 | − | 0.938995i | \(-0.611758\pi\) |
−0.985159 | + | 0.171646i | \(0.945091\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 77.8569 | + | 134.852i | 0.755892 | + | 1.30924i | 0.944930 | + | 0.327273i | \(0.106130\pi\) |
−0.189038 | + | 0.981970i | \(0.560537\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 84.8705i | − | 0.793182i | −0.917995 | − | 0.396591i | \(-0.870193\pi\) | ||
0.917995 | − | 0.396591i | \(-0.129807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −38.0323 | −0.348920 | −0.174460 | − | 0.984664i | \(-0.555818\pi\) | ||||
−0.174460 | + | 0.984664i | \(0.555818\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −21.0000 | + | 36.3731i | −0.189189 | + | 0.327685i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.00000 | + | 3.46410i | −0.0530973 | + | 0.0306558i | −0.526314 | − | 0.850290i | \(-0.676426\pi\) |
0.473216 | + | 0.880946i | \(0.343093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −79.8569 | + | 138.316i | −0.682537 | + | 1.18219i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 154.095 | + | 88.9666i | 1.29491 | + | 0.747619i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 54.2379 | + | 93.9428i | 0.448247 | + | 0.776387i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 77.9423i | 0.633677i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −145.903 | −1.14884 | −0.574422 | − | 0.818559i | \(-0.694773\pi\) | ||||
−0.574422 | + | 0.818559i | \(0.694773\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 29.9758 | + | 51.9196i | 0.232371 | + | 0.402478i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 57.7137 | − | 33.3210i | 0.440563 | − | 0.254359i | −0.263274 | − | 0.964721i | \(-0.584802\pi\) |
0.703836 | + | 0.710362i | \(0.251469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 66.0948 | − | 114.479i | 0.496953 | − | 0.860748i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −63.4052 | − | 36.6070i | −0.462812 | − | 0.267205i | 0.250414 | − | 0.968139i | \(-0.419433\pi\) |
−0.713226 | + | 0.700934i | \(0.752767\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 53.3569 | + | 92.4168i | 0.383862 | + | 0.664869i | 0.991611 | − | 0.129261i | \(-0.0412604\pi\) |
−0.607748 | + | 0.794130i | \(0.707927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −187.857 | + | 108.459i | −1.33232 | + | 0.769214i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 268.824i | − | 1.87989i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −266.903 | −1.81567 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −144.333 | + | 83.3305i | −0.968676 | + | 0.559265i | −0.898832 | − | 0.438293i | \(-0.855583\pi\) |
−0.0698433 | + | 0.997558i | \(0.522250\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.71370 | + | 2.96822i | −0.0113490 | + | 0.0196571i | −0.871644 | − | 0.490139i | \(-0.836946\pi\) |
0.860295 | + | 0.509796i | \(0.170279\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −118.071 | + | 68.1681i | −0.771703 | + | 0.445543i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −33.9677 | − | 58.8338i | −0.216355 | − | 0.374738i | 0.737336 | − | 0.675526i | \(-0.236084\pi\) |
−0.953691 | + | 0.300788i | \(0.902750\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −97.8569 | − | 56.4977i | −0.615452 | − | 0.355331i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 396.556i | − | 2.46308i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −76.4113 | −0.468781 | −0.234390 | − | 0.972143i | \(-0.575309\pi\) | ||||
−0.234390 | + | 0.972143i | \(0.575309\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 245.522 | − | 141.752i | 1.47019 | − | 0.848816i | 0.470752 | − | 0.882266i | \(-0.343983\pi\) |
0.999440 | + | 0.0334495i | \(0.0106493\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −72.9597 | + | 126.370i | −0.431714 | + | 0.747751i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 50.6431 | + | 87.7165i | 0.296159 | + | 0.512962i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 116.903 | + | 67.4941i | 0.675741 | + | 0.390139i | 0.798248 | − | 0.602328i | \(-0.205760\pi\) |
−0.122507 | + | 0.992468i | \(0.539094\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 190.938i | 1.07874i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 171.445i | − | 0.957794i | −0.877871 | − | 0.478897i | \(-0.841037\pi\) | ||
0.877871 | − | 0.478897i | \(-0.158963\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 120.794 | 0.667372 | 0.333686 | − | 0.942684i | \(-0.391707\pi\) | ||||
0.333686 | + | 0.942684i | \(0.391707\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.85685 | + | 3.21616i | 0.0101467 | + | 0.0175746i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 114.738 | − | 198.732i | 0.613572 | − | 1.06274i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 158.571 | − | 274.652i | 0.838998 | − | 1.45319i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −241.808 | − | 139.608i | −1.26601 | − | 0.730933i | −0.291782 | − | 0.956485i | \(-0.594248\pi\) |
−0.974231 | + | 0.225552i | \(0.927581\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −52.6431 | − | 91.1806i | −0.272762 | − | 0.472438i | 0.696806 | − | 0.717260i | \(-0.254604\pi\) |
−0.969568 | + | 0.244822i | \(0.921271\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 57.9538i | 0.294182i | 0.989123 | + | 0.147091i | \(0.0469910\pi\) | ||||
−0.989123 | + | 0.147091i | \(0.953009\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.2702 | −0.126986 | −0.0634929 | − | 0.997982i | \(-0.520224\pi\) | ||||
−0.0634929 | + | 0.997982i | \(0.520224\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 257.855 | 1.28286 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −96.7621 | + | 55.8656i | −0.476661 | + | 0.275200i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 263.141 | + | 151.925i | 1.27121 | + | 0.733935i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −147.641 | − | 85.2406i | −0.706417 | − | 0.407850i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 52.0161 | + | 90.0946i | 0.246522 | + | 0.426989i | 0.962558 | − | 0.271074i | \(-0.0873789\pi\) |
−0.716036 | + | 0.698063i | \(0.754046\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −57.4294 | − | 33.1569i | −0.269622 | − | 0.155666i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 660.379 | 3.04322 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 90.3569 | − | 156.503i | 0.412588 | − | 0.714624i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −232.808 | + | 134.412i | −1.05343 | + | 0.608199i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 123.681 | − | 214.223i | 0.554625 | − | 0.960639i | −0.443307 | − | 0.896370i | \(-0.646195\pi\) |
0.997933 | − | 0.0642694i | \(-0.0204717\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −261.738 | − | 151.114i | −1.15303 | − | 0.665702i | −0.203407 | − | 0.979094i | \(-0.565201\pi\) |
−0.949624 | + | 0.313392i | \(0.898535\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −133.111 | − | 230.555i | −0.581270 | − | 1.00679i | −0.995329 | − | 0.0965395i | \(-0.969223\pi\) |
0.414059 | − | 0.910250i | \(-0.364111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 533.800i | 2.31082i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 176.969i | 0.759526i | 0.925084 | + | 0.379763i | \(0.123994\pi\) | ||||
−0.925084 | + | 0.379763i | \(0.876006\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 154.857 | + | 268.220i | 0.653404 | + | 1.13173i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 68.2863 | − | 39.4251i | 0.285717 | − | 0.164959i | −0.350292 | − | 0.936641i | \(-0.613918\pi\) |
0.636009 | + | 0.771682i | \(0.280584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 110.246 | − | 190.952i | 0.457452 | − | 0.792330i | −0.541373 | − | 0.840782i | \(-0.682095\pi\) |
0.998826 | + | 0.0484519i | \(0.0154288\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.500000 | + | 0.866025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 99.8569 | + | 172.957i | 0.404279 | + | 0.700231i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 234.000 | − | 135.100i | 0.939759 | − | 0.542570i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 277.373i | 1.10507i | 0.833490 | + | 0.552535i | \(0.186339\pi\) | ||||
−0.833490 | + | 0.552535i | \(0.813661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −511.427 | −2.02145 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 131.692 | − | 76.0322i | 0.512418 | − | 0.295845i | −0.221409 | − | 0.975181i | \(-0.571065\pi\) |
0.733827 | + | 0.679336i | \(0.237732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 82.2218 | − | 142.412i | 0.317459 | − | 0.549854i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 85.6108i | − | 0.328011i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.95365 | + | 2.85999i | 0.0188352 | + | 0.0108745i | 0.509388 | − | 0.860537i | \(-0.329872\pi\) |
−0.490553 | + | 0.871411i | \(0.663205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −31.4274 | − | 18.1446i | −0.117706 | − | 0.0679574i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 361.531i | 1.34398i | 0.740560 | + | 0.671990i | \(0.234560\pi\) | ||||
−0.740560 | + | 0.671990i | \(0.765440\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 507.427 | 1.87243 | 0.936213 | − | 0.351433i | \(-0.114306\pi\) | ||||
0.936213 | + | 0.351433i | \(0.114306\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 312.665 | − | 541.552i | 1.14529 | − | 1.98371i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 111.778 | − | 193.606i | 0.403532 | − | 0.698937i | −0.590618 | − | 0.806951i | \(-0.701116\pi\) |
0.994149 | + | 0.108014i | \(0.0344492\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −252.998 | + | 438.205i | −0.906803 | + | 1.57063i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −39.8105 | − | 22.9846i | −0.141674 | − | 0.0817957i | 0.427487 | − | 0.904021i | \(-0.359399\pi\) |
−0.569162 | + | 0.822226i | \(0.692732\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 72.0161 | + | 124.736i | 0.254474 | + | 0.440762i | 0.964753 | − | 0.263159i | \(-0.0847643\pi\) |
−0.710279 | + | 0.703921i | \(0.751431\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 305.169i | − | 1.06331i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 59.5242 | 0.205966 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −149.546 | − | 259.022i | −0.513905 | − | 0.890110i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −361.476 | + | 208.698i | −1.23371 | + | 0.712280i | −0.967800 | − | 0.251719i | \(-0.919004\pi\) |
−0.265905 | + | 0.963999i | \(0.585671\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −354.212 | − | 204.504i | −1.19263 | − | 0.688566i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 518.855 | + | 299.561i | 1.73530 | + | 1.00188i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −117.365 | − | 203.282i | −0.389917 | − | 0.675355i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −402.714 | + | 232.507i | −1.32909 | + | 0.767349i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 310.048 | 1.00993 | 0.504965 | − | 0.863140i | \(-0.331505\pi\) | ||||
0.504965 | + | 0.863140i | \(0.331505\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 467.141 | 1.51178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −242.238 | + | 139.856i | −0.778900 | + | 0.449698i | −0.836040 | − | 0.548668i | \(-0.815135\pi\) |
0.0571403 | + | 0.998366i | \(0.481802\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.5786 | + | 25.2509i | −0.0465771 | + | 0.0806738i | −0.888374 | − | 0.459120i | \(-0.848165\pi\) |
0.841797 | + | 0.539794i | \(0.181498\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −109.095 | − | 62.9859i | −0.344147 | − | 0.198694i | 0.317957 | − | 0.948105i | \(-0.397003\pi\) |
−0.662105 | + | 0.749411i | \(0.730337\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 72.0484 | + | 124.791i | 0.225857 | + | 0.391196i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −220.500 | − | 127.306i | −0.686916 | − | 0.396591i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 170.481i | 0.527806i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −57.0484 | + | 98.8107i | −0.174460 | + | 0.302173i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 735.520 | − | 424.653i | 2.23562 | − | 1.29074i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 232.903 | − | 403.400i | 0.703635 | − | 1.21873i | −0.263547 | − | 0.964647i | \(-0.584892\pi\) |
0.967182 | − | 0.254085i | \(-0.0817743\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 63.0000 | + | 109.119i | 0.189189 | + | 0.327685i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 175.087 | + | 303.259i | 0.519545 | + | 0.899878i | 0.999742 | + | 0.0227177i | \(0.00723189\pi\) |
−0.480197 | + | 0.877161i | \(0.659435\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.7846i | 0.0613115i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 851.673i | − | 2.49758i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 469.460 | 1.36869 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −71.1169 | + | 41.0594i | −0.204948 | + | 0.118327i | −0.598961 | − | 0.800778i | \(-0.704420\pi\) |
0.394013 | + | 0.919105i | \(0.371086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.7621 | + | 39.4251i | −0.0652209 | + | 0.112966i | −0.896792 | − | 0.442452i | \(-0.854109\pi\) |
0.831571 | + | 0.555418i | \(0.187442\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 239.571 | + | 414.948i | 0.682537 | + | 1.18219i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −453.877 | − | 262.046i | −1.28577 | − | 0.742340i | −0.307873 | − | 0.951427i | \(-0.599617\pi\) |
−0.977897 | + | 0.209087i | \(0.932951\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 462.284 | − | 266.900i | 1.29491 | − | 0.747619i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 295.601i | 0.823401i | 0.911319 | + | 0.411701i | \(0.135065\pi\) | ||||
−0.911319 | + | 0.411701i | \(0.864935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −234.347 | −0.649160 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 325.427 | 0.896494 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.2379 | + | 28.1249i | −0.0442450 | + | 0.0766345i | −0.887300 | − | 0.461193i | \(-0.847422\pi\) |
0.843055 | + | 0.537828i | \(0.180755\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 202.500 | + | 116.913i | 0.548780 | + | 0.316839i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 383.141 | + | 221.207i | 1.03273 | + | 0.596244i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −123.746 | − | 214.334i | −0.331759 | − | 0.574623i | 0.651098 | − | 0.758994i | \(-0.274309\pi\) |
−0.982857 | + | 0.184371i | \(0.940975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 168.805i | − | 0.447759i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 300.746 | 0.793525 | 0.396762 | − | 0.917921i | \(-0.370134\pi\) | ||||
0.396762 | + | 0.917921i | \(0.370134\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −218.855 | + | 379.068i | −0.574422 | + | 0.994928i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 183.665 | − | 106.039i | 0.479544 | − | 0.276865i | −0.240683 | − | 0.970604i | \(-0.577371\pi\) |
0.720226 | + | 0.693739i | \(0.244038\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 179.855 | 0.464741 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −190.760 | − | 110.135i | −0.490386 | − | 0.283124i | 0.234349 | − | 0.972153i | \(-0.424704\pi\) |
−0.724734 | + | 0.689028i | \(0.758038\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 255.714 | + | 442.909i | 0.653999 | + | 1.13276i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 199.926i | − | 0.508718i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 97.4919 | 0.245572 | 0.122786 | − | 0.992433i | \(-0.460817\pi\) | ||||
0.122786 | + | 0.992433i | \(0.460817\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −198.284 | − | 343.438i | −0.496953 | − | 0.860748i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −66.8347 | + | 38.5870i | −0.166670 | + | 0.0962270i | −0.581015 | − | 0.813893i | \(-0.697344\pi\) |
0.414345 | + | 0.910120i | \(0.364011\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −498.855 | + | 864.042i | −1.23785 | + | 2.14402i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −183.665 | − | 106.039i | −0.451266 | − | 0.260539i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 97.4355 | + | 168.763i | 0.238229 | + | 0.412624i | 0.960206 | − | 0.279293i | \(-0.0900999\pi\) |
−0.721978 | + | 0.691917i | \(0.756767\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −190.216 | + | 109.821i | −0.462812 | + | 0.267205i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 747.582i | − | 1.81013i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 320.141 | 0.767724 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 196.476 | − | 113.435i | 0.468916 | − | 0.270729i | −0.246870 | − | 0.969049i | \(-0.579402\pi\) |
0.715786 | + | 0.698320i | \(0.246069\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 150.857 | − | 261.292i | 0.358330 | − | 0.620645i | −0.629352 | − | 0.777120i | \(-0.716680\pi\) |
0.987682 | + | 0.156475i | \(0.0500130\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 650.755i | 1.53843i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.27017 | − | 12.5923i | −0.0170262 | − | 0.0294902i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −698.425 | − | 403.236i | −1.62803 | − | 0.939944i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 707.661i | − | 1.64191i | −0.570996 | − | 0.820953i | \(-0.693443\pi\) | ||
0.570996 | − | 0.820953i | \(-0.306557\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 669.883 | 1.54707 | 0.773537 | − | 0.633751i | \(-0.218486\pi\) | ||||
0.773537 | + | 0.633751i | \(0.218486\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 329.044 | − | 189.974i | 0.752962 | − | 0.434723i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.3327 | − | 66.3941i | 0.0873181 | − | 0.151239i | −0.819059 | − | 0.573710i | \(-0.805504\pi\) |
0.906377 | + | 0.422471i | \(0.138837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −400.355 | + | 693.435i | −0.907834 | + | 1.57241i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 590.117 | + | 340.704i | 1.33209 | + | 0.769084i | 0.985620 | − | 0.168976i | \(-0.0540462\pi\) |
0.346472 | + | 0.938060i | \(0.387379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 499.983i | 1.11853i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 630.327i | 1.40385i | 0.712253 | + | 0.701923i | \(0.247675\pi\) | ||||
−0.712253 | + | 0.701923i | \(0.752325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −393.569 | −0.872657 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.14110 | + | 8.90465i | 0.0113490 | + | 0.0196571i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −286.498 | + | 496.229i | −0.626910 | + | 1.08584i | 0.361258 | + | 0.932466i | \(0.382347\pi\) |
−0.988168 | + | 0.153374i | \(0.950986\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 409.008i | 0.891086i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 615.950 | + | 355.619i | 1.33612 | + | 0.771407i | 0.986229 | − | 0.165385i | \(-0.0528866\pi\) |
0.349887 | + | 0.936792i | \(0.386220\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 321.190 | + | 556.317i | 0.693714 | + | 1.20155i | 0.970612 | + | 0.240648i | \(0.0773601\pi\) |
−0.276899 | + | 0.960899i | \(0.589307\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 506.331i | 1.08422i | 0.840307 | + | 0.542111i | \(0.182375\pi\) | ||||
−0.840307 | + | 0.542111i | \(0.817625\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1009.58 | −2.15263 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −203.806 | −0.432710 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −262.167 | + | 151.362i | −0.554265 | + | 0.320005i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −293.571 | + | 169.493i | −0.615452 | + | 0.355331i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −644.044 | − | 371.839i | −1.34456 | − | 0.776282i | −0.357087 | − | 0.934071i | \(-0.616230\pi\) |
−0.987473 | + | 0.157789i | \(0.949563\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 124.222 | + | 215.158i | 0.258257 | + | 0.447315i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1030.28 | − | 594.834i | −2.13309 | − | 1.23154i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −154.065 | −0.316354 | −0.158177 | − | 0.987411i | \(-0.550562\pi\) | ||||
−0.158177 | + | 0.987411i | \(0.550562\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −114.617 | + | 198.522i | −0.234390 | + | 0.405976i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −145.167 | + | 83.8124i | −0.295657 | + | 0.170697i | −0.640490 | − | 0.767967i | \(-0.721269\pi\) |
0.344833 | + | 0.938664i | \(0.387935\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 72.0484 | − | 124.791i | 0.146143 | − | 0.253127i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 224.855 | + | 129.820i | 0.452424 | + | 0.261207i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −247.308 | − | 428.351i | −0.495608 | − | 0.858418i | 0.504379 | − | 0.863482i | \(-0.331721\pi\) |
−0.999987 | + | 0.00506391i | \(0.998388\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 850.514i | − | 1.69763i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 711.349i | − | 1.41421i | −0.707107 | − | 0.707106i | \(-0.750000\pi\) | ||
0.707107 | − | 0.707106i | \(-0.250000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 218.879 | + | 379.110i | 0.431714 | + | 0.747751i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −717.714 | + | 414.372i | −1.41005 | + | 0.814091i | −0.995392 | − | 0.0958882i | \(-0.969431\pi\) |
−0.414654 | + | 0.909979i | \(0.636098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −353.776 | + | 612.758i | −0.692321 | + | 1.19914i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 303.859 | 0.592318 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −547.663 | − | 948.581i | −1.05931 | − | 1.83478i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 350.710 | − | 202.482i | 0.675741 | − | 0.390139i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 622.686i | − | 1.19518i | −0.801804 | − | 0.597588i | \(-0.796126\pi\) | ||
0.801804 | − | 0.597588i | \(-0.203874\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 89.4274 | 0.170989 | 0.0854946 | − | 0.996339i | \(-0.472753\pi\) | ||||
0.0854946 | + | 0.996339i | \(0.472753\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −737.571 | + | 425.837i | −1.39956 | + | 0.808039i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 305.403 | − | 528.974i | 0.577322 | − | 0.999951i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 496.071 | + | 286.406i | 0.934219 | + | 0.539372i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 399.284 | + | 230.527i | 0.749126 | + | 0.432508i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −445.427 | − | 257.168i | −0.829474 | − | 0.478897i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1347.72i | − | 2.50042i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 834.629 | 1.54275 | 0.771376 | − | 0.636380i | \(-0.219569\pi\) | ||||
0.771376 | + | 0.636380i | \(0.219569\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 181.192 | − | 313.833i | 0.333686 | − | 0.577961i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 441.782 | − | 765.189i | 0.807646 | − | 1.39888i | −0.106845 | − | 0.994276i | \(-0.534075\pi\) |
0.914490 | − | 0.404608i | \(-0.132592\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.1411 | 0.0202934 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −92.7096 | − | 53.5259i | −0.168257 | − | 0.0971432i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −606.314 | − | 1050.17i | −1.09641 | − | 1.89904i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 256.448i | − | 0.460410i | −0.973142 | − | 0.230205i | \(-0.926060\pi\) | ||
0.973142 | − | 0.230205i | \(-0.0739396\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 354.633 | 0.634406 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −344.214 | − | 596.196i | −0.613572 | − | 1.06274i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 180.024 | − | 103.937i | 0.319759 | − | 0.184613i | −0.331526 | − | 0.943446i | \(-0.607564\pi\) |
0.651285 | + | 0.758833i | \(0.274230\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −475.712 | − | 823.957i | −0.838998 | − | 1.45319i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 430.923 | + | 248.794i | 0.757334 | + | 0.437247i | 0.828338 | − | 0.560229i | \(-0.189287\pi\) |
−0.0710034 | + | 0.997476i | \(0.522620\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −453.817 | − | 786.033i | −0.794775 | − | 1.37659i | −0.922982 | − | 0.384843i | \(-0.874256\pi\) |
0.128207 | − | 0.991747i | \(-0.459078\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −725.425 | + | 418.825i | −1.26601 | + | 0.730933i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −758.810 | −1.31510 | −0.657548 | − | 0.753413i | \(-0.728406\pi\) | ||||
−0.657548 | + | 0.753413i | \(0.728406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −315.859 | −0.545525 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −916.185 | + | 528.960i | −1.57691 | + | 0.910430i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 285.284 | − | 494.127i | 0.489338 | − | 0.847559i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −656.117 | − | 378.809i | −1.11775 | − | 0.645331i | −0.176921 | − | 0.984225i | \(-0.556614\pi\) |
−0.940825 | + | 0.338894i | \(0.889947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 316.361 | + | 547.953i | 0.537115 | + | 0.930311i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 150.569 | + | 86.9308i | 0.254769 | + | 0.147091i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 258.648i | 0.436169i | 0.975930 | + | 0.218084i | \(0.0699808\pi\) | ||||
−0.975930 | + | 0.218084i | \(0.930019\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −37.9052 | + | 65.6538i | −0.0634929 | + | 0.109973i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −495.665 | + | 286.172i | −0.827488 | + | 0.477750i | −0.852992 | − | 0.521924i | \(-0.825214\pi\) |
0.0255038 | + | 0.999675i | \(0.491881\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −68.8186 | + | 119.197i | −0.114507 | + | 0.198332i | −0.917582 | − | 0.397545i | \(-0.869862\pi\) |
0.803076 | + | 0.595877i | \(0.203195\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 386.782 | − | 669.926i | 0.641430 | − | 1.11099i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.23790 | + | 16.0005i | 0.0152189 | + | 0.0263600i | 0.873535 | − | 0.486762i | \(-0.161822\pi\) |
−0.858316 | + | 0.513122i | \(0.828489\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 335.194i | 0.550400i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1283.14i | 2.10007i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −392.569 | −0.640405 | −0.320203 | − | 0.947349i | \(-0.603751\pi\) | ||||
−0.320203 | + | 0.947349i | \(0.603751\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −230.353 | + | 132.994i | −0.373343 | + | 0.215550i | −0.674918 | − | 0.737893i | \(-0.735821\pi\) |
0.301575 | + | 0.953443i | \(0.402488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −416.736 | + | 721.808i | −0.673240 | + | 1.16609i | 0.303739 | + | 0.952755i | \(0.401765\pi\) |
−0.976980 | + | 0.213332i | \(0.931569\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 789.423 | − | 455.774i | 1.27121 | − | 0.733935i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 123.048 | + | 71.0420i | 0.197509 | + | 0.114032i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −442.923 | + | 255.722i | −0.706417 | + | 0.407850i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 212.078i | 0.337168i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −351.875 | −0.557647 | −0.278823 | − | 0.960342i | \(-0.589944\pi\) | ||||
−0.278823 | + | 0.960342i | \(0.589944\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 312.097 | 0.493044 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −789.409 | + | 1367.30i | −1.23926 | + | 2.14646i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −172.288 | + | 99.4707i | −0.269622 | + | 0.155666i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 355.645 | + | 205.332i | 0.554829 | + | 0.320331i | 0.751067 | − | 0.660226i | \(-0.229539\pi\) |
−0.196239 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −110.593 | − | 191.552i | −0.171995 | − | 0.297904i | 0.767122 | − | 0.641501i | \(-0.221688\pi\) |
−0.939117 | + | 0.343597i | \(0.888355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1095.26i | 1.69282i | 0.532529 | + | 0.846412i | \(0.321242\pi\) | ||||
−0.532529 | + | 0.846412i | \(0.678758\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −964.137 | −1.48557 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 990.569 | − | 1715.71i | 1.52161 | − | 2.63551i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −894.048 | + | 516.179i | −1.36914 | + | 0.790473i | −0.990818 | − | 0.135201i | \(-0.956832\pi\) |
−0.378322 | + | 0.925674i | \(0.623499\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −271.071 | − | 469.508i | −0.412588 | − | 0.714624i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −988.851 | − | 570.913i | −1.50053 | − | 0.866333i | −1.00000 | 0.000614829i | \(-0.999804\pi\) | |
−0.500532 | − | 0.865718i | \(-0.666862\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 513.282 | + | 889.031i | 0.776524 | + | 1.34498i | 0.933934 | + | 0.357445i | \(0.116352\pi\) |
−0.157410 | + | 0.987533i | \(0.550315\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 806.472i | 1.21640i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −321.145 | −0.481477 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −371.044 | − | 642.668i | −0.554625 | − | 0.960639i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.2399 | + | 9.37614i | −0.0242026 | + | 0.0139734i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −139.952 | + | 242.403i | −0.207952 | + | 0.360183i | −0.951069 | − | 0.308978i | \(-0.900013\pi\) |
0.743117 | + | 0.669161i | \(0.233346\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 249.520 | + | 144.060i | 0.368567 | + | 0.212792i | 0.672832 | − | 0.739795i | \(-0.265078\pi\) |
−0.304265 | + | 0.952587i | \(0.598411\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 585.522 | + | 1014.15i | 0.862330 | + | 1.49360i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −785.214 | + | 453.343i | −1.15303 | + | 0.665702i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 283.805i | 0.415527i | 0.978179 | + | 0.207763i | \(0.0666184\pi\) | ||||
−0.978179 | + | 0.207763i | \(0.933382\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −798.665 | −1.16254 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −578.855 | + | 334.202i | −0.840138 | + | 0.485054i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −440.331 | + | 762.675i | −0.637237 | + | 1.10373i | 0.348800 | + | 0.937197i | \(0.386589\pi\) |
−0.986037 | + | 0.166529i | \(0.946744\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1386.85 | + | 800.700i | 2.00123 | + | 1.15541i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 196.784 | + | 340.840i | 0.282330 | + | 0.489011i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 459.780 | + | 265.454i | 0.657768 | + | 0.379763i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 680.500i | 0.970757i | 0.874304 | + | 0.485378i | \(0.161318\pi\) | ||||
−0.874304 | + | 0.485378i | \(0.838682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 157.556 | 0.224120 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1576.75 | − | 910.339i | 2.23020 | − | 1.28761i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 289.696 | − | 501.767i | 0.408597 | − | 0.707711i | −0.586135 | − | 0.810213i | \(-0.699351\pi\) |
0.994733 | + | 0.102502i | \(0.0326847\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 929.141 | 1.30681 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1643.81 | + | 949.052i | 2.30548 | + | 1.33107i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 236.551i | − | 0.329917i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 597.306i | − | 0.830746i | −0.909651 | − | 0.415373i | \(-0.863651\pi\) | ||
0.909651 | − | 0.415373i | \(-0.136349\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1829.01 | −2.53677 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −330.738 | − | 572.855i | −0.457452 | − | 0.792330i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −336.905 | + | 583.537i | −0.463419 | + | 0.802664i | −0.999129 | − | 0.0417376i | \(-0.986711\pi\) |
0.535710 | + | 0.844402i | \(0.320044\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 262.167 | + | 151.362i | 0.358642 | + | 0.207062i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −390.760 | − | 676.816i | −0.533097 | − | 0.923351i | −0.999253 | − | 0.0386484i | \(-0.987695\pi\) |
0.466156 | − | 0.884703i | \(-0.345639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1302.03i | 1.76667i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 232.335 | 0.314391 | 0.157195 | − | 0.987568i | \(-0.449755\pi\) | ||||
0.157195 | + | 0.987568i | \(0.449755\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 599.141 | 0.808557 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −434.806 | + | 251.036i | −0.585204 | + | 0.337868i | −0.763199 | − | 0.646164i | \(-0.776372\pi\) |
0.177995 | + | 0.984031i | \(0.443039\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 810.600i | − | 1.08514i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 863.329 | + | 498.443i | 1.15264 | + | 0.665478i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −477.190 | − | 826.516i | −0.635405 | − | 1.10055i | −0.986429 | − | 0.164188i | \(-0.947500\pi\) |
0.351024 | − | 0.936367i | \(-0.385834\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 720.635 | + | 416.059i | 0.957019 | + | 0.552535i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 266.379 | 0.351888 | 0.175944 | − | 0.984400i | \(-0.443702\pi\) | ||||
0.175944 | + | 0.984400i | \(0.443702\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −767.141 | + | 1328.73i | −1.01073 | + | 1.75063i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 294.665 | − | 170.125i | 0.387208 | − | 0.223555i | −0.293742 | − | 0.955885i | \(-0.594901\pi\) |
0.680950 | + | 0.732330i | \(0.261567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 223.363 | − | 386.876i | 0.292743 | − | 0.507046i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 978.139 | + | 564.729i | 1.27528 | + | 0.736283i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −644.552 | − | 1116.40i | −0.838170 | − | 1.45175i | −0.891423 | − | 0.453171i | \(-0.850293\pi\) |
0.0532540 | − | 0.998581i | \(-0.483041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 456.193i | − | 0.591690i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 919.244i | − | 1.18919i | −0.804025 | − | 0.594595i | \(-0.797312\pi\) | ||
0.804025 | − | 0.594595i | \(-0.202688\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −246.665 | − | 427.237i | −0.317459 | − | 0.549854i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 253.216 | − | 146.194i | 0.325052 | − | 0.187669i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 167.425 | − | 289.989i | 0.214373 | − | 0.371305i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −222.423 | − | 128.416i | −0.284066 | − | 0.164005i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −631.855 | − | 1094.40i | −0.802865 | − | 1.39060i | −0.917723 | − | 0.397221i | \(-0.869975\pi\) |
0.114858 | − | 0.993382i | \(-0.463359\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.8609 | − | 8.57997i | 0.0188352 | − | 0.0108745i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 81.3784i | − | 0.102880i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.9677 | 0.0277021 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 530.806 | − | 306.461i | 0.666006 | − | 0.384518i | −0.128556 | − | 0.991702i | \(-0.541034\pi\) |
0.794561 | + | 0.607184i | \(0.207701\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −547.663 | + | 948.581i | −0.685436 | + | 1.18721i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −94.2822 | + | 54.4339i | −0.117706 | + | 0.0679574i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 790.258 | + | 456.256i | 0.984132 | + | 0.568189i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 939.284 | + | 542.296i | 1.16392 | + | 0.671990i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 273.189i | − | 0.337687i | −0.985643 | − | 0.168844i | \(-0.945997\pi\) | ||
0.985643 | − | 0.168844i | \(-0.0540033\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1446.49 | −1.78359 | −0.891793 | − | 0.452444i | \(-0.850552\pi\) | ||||
−0.891793 | + | 0.452444i | \(0.850552\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 761.141 | − | 1318.34i | 0.936213 | − | 1.62157i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 112.450 | − | 194.768i | 0.137637 | − | 0.238395i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −937.996 | − | 1624.66i | −1.14529 | − | 1.98371i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 221.813 | + | 128.064i | 0.270174 | + | 0.155985i | 0.628967 | − | 0.777432i | \(-0.283478\pi\) |
−0.358793 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 615.218 | + | 1065.59i | 0.747531 | + | 1.29476i | 0.949003 | + | 0.315267i | \(0.102094\pi\) |
−0.201473 | + | 0.979494i | \(0.564573\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 726.246i | − | 0.878169i | −0.898446 | − | 0.439085i | \(-0.855303\pi\) | ||
0.898446 | − | 0.439085i | \(-0.144697\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1439.23 | 1.73610 | 0.868052 | − | 0.496474i | \(-0.165372\pi\) | ||||
0.868052 | + | 0.496474i | \(0.165372\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −335.335 | − | 580.817i | −0.403532 | − | 0.698937i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1167.16 | + | 673.862i | −1.40116 | + | 0.808958i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 758.994 | + | 1314.62i | 0.906803 | + | 1.57063i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 968.135 | + | 558.953i | 1.15392 | + | 0.666213i | 0.949838 | − | 0.312742i | \(-0.101247\pi\) |
0.204077 | + | 0.978955i | \(0.434581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −375.258 | − | 649.966i | −0.446205 | − | 0.772849i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −119.431 | + | 68.9538i | −0.141674 | + | 0.0817957i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1274.15 | −1.50431 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 432.097 | 0.508948 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 409.331 | − | 236.327i | 0.481000 | − | 0.277705i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −348.046 | + | 602.834i | −0.408026 | + | 0.706722i | −0.994669 | − | 0.103124i | \(-0.967116\pi\) |
0.586642 | + | 0.809846i | \(0.300449\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −745.040 | − | 430.149i | −0.869358 | − | 0.501924i | −0.00222347 | − | 0.999998i | \(-0.500708\pi\) |
−0.867135 | + | 0.498073i | \(0.834041\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 321.216 | + | 556.362i | 0.373942 | + | 0.647686i | 0.990168 | − | 0.139883i | \(-0.0446727\pi\) |
−0.616226 | + | 0.787569i | \(0.711339\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −792.853 | − | 457.754i | −0.920851 | − | 0.531654i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1466.58i | − | 1.69940i | −0.527269 | − | 0.849698i | \(-0.676784\pi\) | ||
0.527269 | − | 0.849698i | \(-0.323216\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 89.2863 | − | 154.648i | 0.102983 | − | 0.178372i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1354.37 | + | 781.948i | −1.55854 | + | 0.899825i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 762.647 | − | 1320.94i | 0.875599 | − | 1.51658i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −897.278 | −1.02781 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −96.6835 | − | 167.461i | −0.110243 | − | 0.190947i | 0.805625 | − | 0.592426i | \(-0.201830\pi\) |
−0.915868 | + | 0.401479i | \(0.868496\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1252.19i | 1.42456i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 554.368i | 0.629249i | 0.949216 | + | 0.314624i | \(0.101879\pi\) | ||||
−0.949216 | + | 0.314624i | \(0.898121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −352.460 | −0.399162 | −0.199581 | − | 0.979881i | \(-0.563958\pi\) | ||||
−0.199581 | + | 0.979881i | \(0.563958\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −932.087 | + | 538.140i | −1.05083 | + | 0.606697i | −0.922882 | − | 0.385084i | \(-0.874173\pi\) |
−0.127949 | + | 0.991781i | \(0.540839\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 856.887 | − | 1484.17i | 0.963877 | − | 1.66948i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1062.63 | + | 613.513i | −1.19263 | + | 0.688566i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 704.716 | + | 406.868i | 0.789155 | + | 0.455619i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1556.56 | − | 898.683i | 1.73530 | − | 1.00188i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 534.799i | − | 0.594882i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −570.569 | −0.633261 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −704.190 | −0.779833 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −110.496 | + | 191.385i | −0.121826 | + | 0.211008i | −0.920488 | − | 0.390772i | \(-0.872208\pi\) |
0.798662 | + | 0.601780i | \(0.205542\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1395.04i | 1.53470i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1535.28 | + | 886.394i | 1.68527 | + | 0.972991i | 0.958057 | + | 0.286578i | \(0.0925177\pi\) |
0.727212 | + | 0.686413i | \(0.240816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 682.185 | + | 1181.58i | 0.747191 | + | 1.29417i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 782.775i | 0.853626i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1006.85 | 1.09560 | 0.547799 | − | 0.836610i | \(-0.315466\pi\) | ||||
0.547799 | + | 0.836610i | \(0.315466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 465.073 | − | 805.529i | 0.504965 | − | 0.874625i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −339.714 | + | 196.134i | −0.368054 | + | 0.212496i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 700.712 | − | 1213.67i | 0.755892 | − | 1.30924i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −974.758 | − | 562.777i | −1.04926 | − | 0.605788i | −0.126814 | − | 0.991926i | \(-0.540475\pi\) |
−0.922441 | + | 0.386139i | \(0.873809\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 500.623 | + | 867.104i | 0.537726 | + | 0.931369i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 839.137i | 0.899396i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1343.20 | −1.43351 | −0.716756 | − | 0.697324i | \(-0.754374\pi\) | ||||
−0.716756 | + | 0.697324i | \(0.754374\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 43.7359 | + | 75.7527i | 0.0465771 | + | 0.0806738i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 618.375 | − | 357.019i | 0.657147 | − | 0.379404i | −0.134042 | − | 0.990976i | \(-0.542796\pi\) |
0.791189 | + | 0.611572i | \(0.209462\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 438.569 | − | 759.623i | 0.465078 | − | 0.805539i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 620.456 | + | 358.220i | 0.655180 | + | 0.378268i | 0.790438 | − | 0.612542i | \(-0.209853\pi\) |
−0.135258 | + | 0.990810i | \(0.543186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −534.490 | − | 925.764i | −0.563214 | − | 0.975515i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −327.284 | + | 188.958i | −0.344147 | + | 0.198694i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 793.300i | − | 0.832424i | −0.909268 | − | 0.416212i | \(-0.863357\pi\) | ||
0.909268 | − | 0.416212i | \(-0.136643\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 432.290 | 0.451714 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 744.756 | − | 429.985i | 0.776596 | − | 0.448368i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1099.94 | + | 1905.16i | −1.14458 | + | 1.98247i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −661.500 | + | 381.917i | −0.686916 | + | 0.396591i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 914.331 | + | 1583.67i | 0.945533 | + | 1.63771i | 0.754680 | + | 0.656093i | \(0.227792\pi\) |
0.190853 | + | 0.981619i | \(0.438875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 442.923 | + | 255.722i | 0.457093 | + | 0.263903i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1843.33i | − | 1.89839i | −0.314691 | − | 0.949194i | \(-0.601901\pi\) | ||
0.314691 | − | 0.949194i | \(-0.398099\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1253.46 | −1.28824 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −289.591 | + | 167.195i | −0.296408 | + | 0.171131i | −0.640828 | − | 0.767684i | \(-0.721409\pi\) |
0.344420 | + | 0.938816i | \(0.388076\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 91.6210 | − | 158.692i | 0.0935863 | − | 0.162096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 171.145 | + | 296.432i | 0.174460 | + | 0.302173i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1604.71 | − | 926.480i | −1.63246 | − | 0.942502i | −0.983331 | − | 0.181825i | \(-0.941800\pi\) |
−0.649131 | − | 0.760677i | \(-0.724867\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2547.92i | − | 2.58148i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 674.676i | − | 0.682180i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 415.419 | 0.419192 | 0.209596 | − | 0.977788i | \(-0.432785\pi\) | ||||
0.209596 | + | 0.977788i | \(0.432785\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −698.710 | − | 1210.20i | −0.703635 | − | 1.21873i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 596.808 | − | 1033.70i | 0.598604 | − | 1.03681i | −0.394423 | − | 0.918929i | \(-0.629056\pi\) |
0.993027 | − | 0.117884i | \(-0.0376111\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 378.000 | 0.378378 |
(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 | 900.3.p.b.101.1 | 4 | ||
3.2 | odd | 2 | 2700.3.p.a.1601.1 | 4 | |||
5.2 | odd | 4 | 900.3.u.b.749.1 | 8 | |||
5.3 | odd | 4 | 900.3.u.b.749.4 | 8 | |||
5.4 | even | 2 | 180.3.o.a.101.2 | yes | 4 | ||
9.4 | even | 3 | 2700.3.p.a.2501.1 | 4 | |||
9.5 | odd | 6 | inner | 900.3.p.b.401.1 | 4 | ||
15.2 | even | 4 | 2700.3.u.a.2249.1 | 8 | |||
15.8 | even | 4 | 2700.3.u.a.2249.4 | 8 | |||
15.14 | odd | 2 | 540.3.o.a.521.1 | 4 | |||
20.19 | odd | 2 | 720.3.bs.a.641.2 | 4 | |||
45.4 | even | 6 | 540.3.o.a.341.1 | 4 | |||
45.13 | odd | 12 | 2700.3.u.a.449.1 | 8 | |||
45.14 | odd | 6 | 180.3.o.a.41.2 | ✓ | 4 | ||
45.22 | odd | 12 | 2700.3.u.a.449.4 | 8 | |||
45.23 | even | 12 | 900.3.u.b.149.1 | 8 | |||
45.29 | odd | 6 | 1620.3.g.a.161.1 | 4 | |||
45.32 | even | 12 | 900.3.u.b.149.4 | 8 | |||
45.34 | even | 6 | 1620.3.g.a.161.3 | 4 | |||
60.59 | even | 2 | 2160.3.bs.a.1601.1 | 4 | |||
180.59 | even | 6 | 720.3.bs.a.401.2 | 4 | |||
180.139 | odd | 6 | 2160.3.bs.a.881.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
180.3.o.a.41.2 | ✓ | 4 | 45.14 | odd | 6 | ||
180.3.o.a.101.2 | yes | 4 | 5.4 | even | 2 | ||
540.3.o.a.341.1 | 4 | 45.4 | even | 6 | |||
540.3.o.a.521.1 | 4 | 15.14 | odd | 2 | |||
720.3.bs.a.401.2 | 4 | 180.59 | even | 6 | |||
720.3.bs.a.641.2 | 4 | 20.19 | odd | 2 | |||
900.3.p.b.101.1 | 4 | 1.1 | even | 1 | trivial | ||
900.3.p.b.401.1 | 4 | 9.5 | odd | 6 | inner | ||
900.3.u.b.149.1 | 8 | 45.23 | even | 12 | |||
900.3.u.b.149.4 | 8 | 45.32 | even | 12 | |||
900.3.u.b.749.1 | 8 | 5.2 | odd | 4 | |||
900.3.u.b.749.4 | 8 | 5.3 | odd | 4 | |||
1620.3.g.a.161.1 | 4 | 45.29 | odd | 6 | |||
1620.3.g.a.161.3 | 4 | 45.34 | even | 6 | |||
2160.3.bs.a.881.1 | 4 | 180.139 | odd | 6 | |||
2160.3.bs.a.1601.1 | 4 | 60.59 | even | 2 | |||
2700.3.p.a.1601.1 | 4 | 3.2 | odd | 2 | |||
2700.3.p.a.2501.1 | 4 | 9.4 | even | 3 | |||
2700.3.u.a.449.1 | 8 | 45.13 | odd | 12 | |||
2700.3.u.a.449.4 | 8 | 45.22 | odd | 12 | |||
2700.3.u.a.2249.1 | 8 | 15.2 | even | 4 | |||
2700.3.u.a.2249.4 | 8 | 15.8 | even | 4 |