Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8033,2,Mod(1,8033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8033, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8033 = 29 \cdot 277 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8033.a (trivial) |
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: | yes |
Analytic conductor: | \(64.1438279437\) |
Analytic rank: | \(1\) |
Dimension: | \(154\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8033.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.66581 | −1.88501 | −0.942505 | − | 0.334192i | \(-0.891537\pi\) | ||||
−0.942505 | + | 0.334192i | \(0.891537\pi\) | |||||||
\(3\) | −3.36665 | −1.94374 | −0.971868 | − | 0.235526i | \(-0.924319\pi\) | ||||
−0.971868 | + | 0.235526i | \(0.924319\pi\) | |||||||
\(4\) | 5.10653 | 2.55326 | ||||||||
\(5\) | −1.10799 | −0.495509 | −0.247754 | − | 0.968823i | \(-0.579693\pi\) | ||||
−0.247754 | + | 0.968823i | \(0.579693\pi\) | |||||||
\(6\) | 8.97484 | 3.66396 | ||||||||
\(7\) | −4.45627 | −1.68431 | −0.842156 | − | 0.539234i | \(-0.818714\pi\) | ||||
−0.842156 | + | 0.539234i | \(0.818714\pi\) | |||||||
\(8\) | −8.28140 | −2.92792 | ||||||||
\(9\) | 8.33433 | 2.77811 | ||||||||
\(10\) | 2.95369 | 0.934039 | ||||||||
\(11\) | −4.32851 | −1.30509 | −0.652547 | − | 0.757748i | \(-0.726300\pi\) | ||||
−0.652547 | + | 0.757748i | \(0.726300\pi\) | |||||||
\(12\) | −17.1919 | −4.96287 | ||||||||
\(13\) | −5.75777 | −1.59692 | −0.798459 | − | 0.602049i | \(-0.794351\pi\) | ||||
−0.798459 | + | 0.602049i | \(0.794351\pi\) | |||||||
\(14\) | 11.8796 | 3.17495 | ||||||||
\(15\) | 3.73022 | 0.963138 | ||||||||
\(16\) | 11.8636 | 2.96589 | ||||||||
\(17\) | −6.70001 | −1.62499 | −0.812495 | − | 0.582968i | \(-0.801891\pi\) | ||||
−0.812495 | + | 0.582968i | \(0.801891\pi\) | |||||||
\(18\) | −22.2177 | −5.23677 | ||||||||
\(19\) | −7.99128 | −1.83333 | −0.916663 | − | 0.399661i | \(-0.869128\pi\) | ||||
−0.916663 | + | 0.399661i | \(0.869128\pi\) | |||||||
\(20\) | −5.65799 | −1.26516 | ||||||||
\(21\) | 15.0027 | 3.27386 | ||||||||
\(22\) | 11.5390 | 2.46012 | ||||||||
\(23\) | −2.90229 | −0.605170 | −0.302585 | − | 0.953122i | \(-0.597850\pi\) | ||||
−0.302585 | + | 0.953122i | \(0.597850\pi\) | |||||||
\(24\) | 27.8806 | 5.69110 | ||||||||
\(25\) | −3.77236 | −0.754471 | ||||||||
\(26\) | 15.3491 | 3.01021 | ||||||||
\(27\) | −17.9588 | −3.45618 | ||||||||
\(28\) | −22.7561 | −4.30049 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −9.94404 | −1.81553 | ||||||||
\(31\) | −7.11406 | −1.27772 | −0.638862 | − | 0.769322i | \(-0.720594\pi\) | ||||
−0.638862 | + | 0.769322i | \(0.720594\pi\) | |||||||
\(32\) | −15.0632 | −2.66282 | ||||||||
\(33\) | 14.5726 | 2.53676 | ||||||||
\(34\) | 17.8609 | 3.06312 | ||||||||
\(35\) | 4.93751 | 0.834591 | ||||||||
\(36\) | 42.5595 | 7.09325 | ||||||||
\(37\) | 5.50479 | 0.904983 | 0.452491 | − | 0.891769i | \(-0.350535\pi\) | ||||
0.452491 | + | 0.891769i | \(0.350535\pi\) | |||||||
\(38\) | 21.3032 | 3.45584 | ||||||||
\(39\) | 19.3844 | 3.10399 | ||||||||
\(40\) | 9.17572 | 1.45081 | ||||||||
\(41\) | −2.93502 | −0.458374 | −0.229187 | − | 0.973382i | \(-0.573607\pi\) | ||||
−0.229187 | + | 0.973382i | \(0.573607\pi\) | |||||||
\(42\) | −39.9943 | −6.17126 | ||||||||
\(43\) | −1.55429 | −0.237027 | −0.118513 | − | 0.992952i | \(-0.537813\pi\) | ||||
−0.118513 | + | 0.992952i | \(0.537813\pi\) | |||||||
\(44\) | −22.1036 | −3.33225 | ||||||||
\(45\) | −9.23437 | −1.37658 | ||||||||
\(46\) | 7.73696 | 1.14075 | ||||||||
\(47\) | −5.22730 | −0.762480 | −0.381240 | − | 0.924476i | \(-0.624503\pi\) | ||||
−0.381240 | + | 0.924476i | \(0.624503\pi\) | |||||||
\(48\) | −39.9404 | −5.76491 | ||||||||
\(49\) | 12.8584 | 1.83691 | ||||||||
\(50\) | 10.0564 | 1.42219 | ||||||||
\(51\) | 22.5566 | 3.15855 | ||||||||
\(52\) | −29.4022 | −4.07735 | ||||||||
\(53\) | −2.60392 | −0.357676 | −0.178838 | − | 0.983879i | \(-0.557234\pi\) | ||||
−0.178838 | + | 0.983879i | \(0.557234\pi\) | |||||||
\(54\) | 47.8748 | 6.51493 | ||||||||
\(55\) | 4.79595 | 0.646686 | ||||||||
\(56\) | 36.9042 | 4.93153 | ||||||||
\(57\) | 26.9039 | 3.56350 | ||||||||
\(58\) | −2.66581 | −0.350038 | ||||||||
\(59\) | 6.36172 | 0.828226 | 0.414113 | − | 0.910226i | \(-0.364092\pi\) | ||||
0.414113 | + | 0.910226i | \(0.364092\pi\) | |||||||
\(60\) | 19.0485 | 2.45915 | ||||||||
\(61\) | −13.9229 | −1.78265 | −0.891324 | − | 0.453367i | \(-0.850223\pi\) | ||||
−0.891324 | + | 0.453367i | \(0.850223\pi\) | |||||||
\(62\) | 18.9647 | 2.40852 | ||||||||
\(63\) | −37.1400 | −4.67921 | ||||||||
\(64\) | 16.4284 | 2.05354 | ||||||||
\(65\) | 6.37956 | 0.791287 | ||||||||
\(66\) | −38.8477 | −4.78182 | ||||||||
\(67\) | −0.349472 | −0.0426948 | −0.0213474 | − | 0.999772i | \(-0.506796\pi\) | ||||
−0.0213474 | + | 0.999772i | \(0.506796\pi\) | |||||||
\(68\) | −34.2138 | −4.14903 | ||||||||
\(69\) | 9.77101 | 1.17629 | ||||||||
\(70\) | −13.1624 | −1.57321 | ||||||||
\(71\) | −6.97042 | −0.827237 | −0.413618 | − | 0.910450i | \(-0.635735\pi\) | ||||
−0.413618 | + | 0.910450i | \(0.635735\pi\) | |||||||
\(72\) | −69.0199 | −8.13408 | ||||||||
\(73\) | 11.1466 | 1.30461 | 0.652307 | − | 0.757955i | \(-0.273801\pi\) | ||||
0.652307 | + | 0.757955i | \(0.273801\pi\) | |||||||
\(74\) | −14.6747 | −1.70590 | ||||||||
\(75\) | 12.7002 | 1.46649 | ||||||||
\(76\) | −40.8077 | −4.68096 | ||||||||
\(77\) | 19.2890 | 2.19819 | ||||||||
\(78\) | −51.6751 | −5.85105 | ||||||||
\(79\) | 0.734753 | 0.0826661 | 0.0413331 | − | 0.999145i | \(-0.486840\pi\) | ||||
0.0413331 | + | 0.999145i | \(0.486840\pi\) | |||||||
\(80\) | −13.1447 | −1.46962 | ||||||||
\(81\) | 35.4581 | 3.93979 | ||||||||
\(82\) | 7.82421 | 0.864039 | ||||||||
\(83\) | 4.15474 | 0.456042 | 0.228021 | − | 0.973656i | \(-0.426775\pi\) | ||||
0.228021 | + | 0.973656i | \(0.426775\pi\) | |||||||
\(84\) | 76.6117 | 8.35902 | ||||||||
\(85\) | 7.42355 | 0.805197 | ||||||||
\(86\) | 4.14343 | 0.446798 | ||||||||
\(87\) | −3.36665 | −0.360943 | ||||||||
\(88\) | 35.8461 | 3.82121 | ||||||||
\(89\) | 2.52229 | 0.267362 | 0.133681 | − | 0.991024i | \(-0.457320\pi\) | ||||
0.133681 | + | 0.991024i | \(0.457320\pi\) | |||||||
\(90\) | 24.6170 | 2.59486 | ||||||||
\(91\) | 25.6582 | 2.68971 | ||||||||
\(92\) | −14.8206 | −1.54516 | ||||||||
\(93\) | 23.9506 | 2.48356 | ||||||||
\(94\) | 13.9350 | 1.43728 | ||||||||
\(95\) | 8.85427 | 0.908429 | ||||||||
\(96\) | 50.7124 | 5.17581 | ||||||||
\(97\) | 5.34178 | 0.542376 | 0.271188 | − | 0.962526i | \(-0.412584\pi\) | ||||
0.271188 | + | 0.962526i | \(0.412584\pi\) | |||||||
\(98\) | −34.2779 | −3.46259 | ||||||||
\(99\) | −36.0752 | −3.62570 | ||||||||
\(100\) | −19.2636 | −1.92636 | ||||||||
\(101\) | −5.05772 | −0.503262 | −0.251631 | − | 0.967823i | \(-0.580967\pi\) | ||||
−0.251631 | + | 0.967823i | \(0.580967\pi\) | |||||||
\(102\) | −60.1315 | −5.95391 | ||||||||
\(103\) | −12.9852 | −1.27947 | −0.639733 | − | 0.768598i | \(-0.720955\pi\) | ||||
−0.639733 | + | 0.768598i | \(0.720955\pi\) | |||||||
\(104\) | 47.6824 | 4.67564 | ||||||||
\(105\) | −16.6229 | −1.62223 | ||||||||
\(106\) | 6.94156 | 0.674223 | ||||||||
\(107\) | 1.43422 | 0.138651 | 0.0693257 | − | 0.997594i | \(-0.477915\pi\) | ||||
0.0693257 | + | 0.997594i | \(0.477915\pi\) | |||||||
\(108\) | −91.7072 | −8.82453 | ||||||||
\(109\) | −5.33818 | −0.511304 | −0.255652 | − | 0.966769i | \(-0.582290\pi\) | ||||
−0.255652 | + | 0.966769i | \(0.582290\pi\) | |||||||
\(110\) | −12.7851 | −1.21901 | ||||||||
\(111\) | −18.5327 | −1.75905 | ||||||||
\(112\) | −52.8672 | −4.99548 | ||||||||
\(113\) | −9.94896 | −0.935920 | −0.467960 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467960 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(114\) | −71.7205 | −6.71724 | ||||||||
\(115\) | 3.21572 | 0.299867 | ||||||||
\(116\) | 5.10653 | 0.474129 | ||||||||
\(117\) | −47.9872 | −4.43642 | ||||||||
\(118\) | −16.9591 | −1.56121 | ||||||||
\(119\) | 29.8571 | 2.73699 | ||||||||
\(120\) | −30.8914 | −2.81999 | ||||||||
\(121\) | 7.73598 | 0.703271 | ||||||||
\(122\) | 37.1158 | 3.36031 | ||||||||
\(123\) | 9.88120 | 0.890958 | ||||||||
\(124\) | −36.3281 | −3.26236 | ||||||||
\(125\) | 9.71969 | 0.869356 | ||||||||
\(126\) | 99.0082 | 8.82035 | ||||||||
\(127\) | −18.7585 | −1.66455 | −0.832273 | − | 0.554367i | \(-0.812961\pi\) | ||||
−0.832273 | + | 0.554367i | \(0.812961\pi\) | |||||||
\(128\) | −13.6685 | −1.20814 | ||||||||
\(129\) | 5.23274 | 0.460717 | ||||||||
\(130\) | −17.0067 | −1.49158 | ||||||||
\(131\) | 5.88061 | 0.513791 | 0.256896 | − | 0.966439i | \(-0.417300\pi\) | ||||
0.256896 | + | 0.966439i | \(0.417300\pi\) | |||||||
\(132\) | 74.4152 | 6.47701 | ||||||||
\(133\) | 35.6113 | 3.08789 | ||||||||
\(134\) | 0.931624 | 0.0804801 | ||||||||
\(135\) | 19.8982 | 1.71257 | ||||||||
\(136\) | 55.4854 | 4.75784 | ||||||||
\(137\) | −13.0288 | −1.11312 | −0.556561 | − | 0.830807i | \(-0.687880\pi\) | ||||
−0.556561 | + | 0.830807i | \(0.687880\pi\) | |||||||
\(138\) | −26.0476 | −2.21732 | ||||||||
\(139\) | −14.9439 | −1.26752 | −0.633762 | − | 0.773528i | \(-0.718490\pi\) | ||||
−0.633762 | + | 0.773528i | \(0.718490\pi\) | |||||||
\(140\) | 25.2135 | 2.13093 | ||||||||
\(141\) | 17.5985 | 1.48206 | ||||||||
\(142\) | 18.5818 | 1.55935 | ||||||||
\(143\) | 24.9226 | 2.08413 | ||||||||
\(144\) | 98.8748 | 8.23957 | ||||||||
\(145\) | −1.10799 | −0.0920137 | ||||||||
\(146\) | −29.7147 | −2.45921 | ||||||||
\(147\) | −43.2896 | −3.57046 | ||||||||
\(148\) | 28.1104 | 2.31066 | ||||||||
\(149\) | 5.10797 | 0.418461 | 0.209231 | − | 0.977866i | \(-0.432904\pi\) | ||||
0.209231 | + | 0.977866i | \(0.432904\pi\) | |||||||
\(150\) | −33.8563 | −2.76435 | ||||||||
\(151\) | −16.1551 | −1.31469 | −0.657343 | − | 0.753592i | \(-0.728320\pi\) | ||||
−0.657343 | + | 0.753592i | \(0.728320\pi\) | |||||||
\(152\) | 66.1790 | 5.36783 | ||||||||
\(153\) | −55.8401 | −4.51440 | ||||||||
\(154\) | −51.4208 | −4.14360 | ||||||||
\(155\) | 7.88232 | 0.633123 | ||||||||
\(156\) | 98.9869 | 7.92530 | ||||||||
\(157\) | −3.26552 | −0.260617 | −0.130308 | − | 0.991474i | \(-0.541597\pi\) | ||||
−0.130308 | + | 0.991474i | \(0.541597\pi\) | |||||||
\(158\) | −1.95871 | −0.155826 | ||||||||
\(159\) | 8.76650 | 0.695228 | ||||||||
\(160\) | 16.6898 | 1.31945 | ||||||||
\(161\) | 12.9334 | 1.01930 | ||||||||
\(162\) | −94.5244 | −7.42654 | ||||||||
\(163\) | 24.4925 | 1.91840 | 0.959199 | − | 0.282730i | \(-0.0912402\pi\) | ||||
0.959199 | + | 0.282730i | \(0.0912402\pi\) | |||||||
\(164\) | −14.9878 | −1.17035 | ||||||||
\(165\) | −16.1463 | −1.25699 | ||||||||
\(166\) | −11.0757 | −0.859644 | ||||||||
\(167\) | 9.92242 | 0.767820 | 0.383910 | − | 0.923371i | \(-0.374577\pi\) | ||||
0.383910 | + | 0.923371i | \(0.374577\pi\) | |||||||
\(168\) | −124.243 | −9.58559 | ||||||||
\(169\) | 20.1519 | 1.55015 | ||||||||
\(170\) | −19.7898 | −1.51780 | ||||||||
\(171\) | −66.6020 | −5.09318 | ||||||||
\(172\) | −7.93701 | −0.605191 | ||||||||
\(173\) | 5.40800 | 0.411163 | 0.205581 | − | 0.978640i | \(-0.434091\pi\) | ||||
0.205581 | + | 0.978640i | \(0.434091\pi\) | |||||||
\(174\) | 8.97484 | 0.680381 | ||||||||
\(175\) | 16.8106 | 1.27076 | ||||||||
\(176\) | −51.3515 | −3.87077 | ||||||||
\(177\) | −21.4177 | −1.60985 | ||||||||
\(178\) | −6.72394 | −0.503980 | ||||||||
\(179\) | −0.384232 | −0.0287188 | −0.0143594 | − | 0.999897i | \(-0.504571\pi\) | ||||
−0.0143594 | + | 0.999897i | \(0.504571\pi\) | |||||||
\(180\) | −47.1555 | −3.51477 | ||||||||
\(181\) | −14.1508 | −1.05182 | −0.525909 | − | 0.850541i | \(-0.676275\pi\) | ||||
−0.525909 | + | 0.850541i | \(0.676275\pi\) | |||||||
\(182\) | −68.3998 | −5.07013 | ||||||||
\(183\) | 46.8736 | 3.46500 | ||||||||
\(184\) | 24.0351 | 1.77189 | ||||||||
\(185\) | −6.09926 | −0.448427 | ||||||||
\(186\) | −63.8476 | −4.68153 | ||||||||
\(187\) | 29.0010 | 2.12077 | ||||||||
\(188\) | −26.6933 | −1.94681 | ||||||||
\(189\) | 80.0294 | 5.82128 | ||||||||
\(190\) | −23.6038 | −1.71240 | ||||||||
\(191\) | −9.88678 | −0.715382 | −0.357691 | − | 0.933840i | \(-0.616436\pi\) | ||||
−0.357691 | + | 0.933840i | \(0.616436\pi\) | |||||||
\(192\) | −55.3085 | −3.99155 | ||||||||
\(193\) | −14.0061 | −1.00818 | −0.504091 | − | 0.863651i | \(-0.668172\pi\) | ||||
−0.504091 | + | 0.863651i | \(0.668172\pi\) | |||||||
\(194\) | −14.2402 | −1.02238 | ||||||||
\(195\) | −21.4777 | −1.53805 | ||||||||
\(196\) | 65.6615 | 4.69011 | ||||||||
\(197\) | −5.76858 | −0.410994 | −0.205497 | − | 0.978658i | \(-0.565881\pi\) | ||||
−0.205497 | + | 0.978658i | \(0.565881\pi\) | |||||||
\(198\) | 96.1696 | 6.83447 | ||||||||
\(199\) | −11.8468 | −0.839800 | −0.419900 | − | 0.907570i | \(-0.637935\pi\) | ||||
−0.419900 | + | 0.907570i | \(0.637935\pi\) | |||||||
\(200\) | 31.2404 | 2.20903 | ||||||||
\(201\) | 1.17655 | 0.0829874 | ||||||||
\(202\) | 13.4829 | 0.948653 | ||||||||
\(203\) | −4.45627 | −0.312769 | ||||||||
\(204\) | 115.186 | 8.06462 | ||||||||
\(205\) | 3.25198 | 0.227128 | ||||||||
\(206\) | 34.6159 | 2.41181 | ||||||||
\(207\) | −24.1887 | −1.68123 | ||||||||
\(208\) | −68.3077 | −4.73628 | ||||||||
\(209\) | 34.5903 | 2.39266 | ||||||||
\(210\) | 44.3133 | 3.05791 | ||||||||
\(211\) | −4.38911 | −0.302159 | −0.151079 | − | 0.988522i | \(-0.548275\pi\) | ||||
−0.151079 | + | 0.988522i | \(0.548275\pi\) | |||||||
\(212\) | −13.2970 | −0.913242 | ||||||||
\(213\) | 23.4670 | 1.60793 | ||||||||
\(214\) | −3.82336 | −0.261359 | ||||||||
\(215\) | 1.72214 | 0.117449 | ||||||||
\(216\) | 148.724 | 10.1194 | ||||||||
\(217\) | 31.7022 | 2.15209 | ||||||||
\(218\) | 14.2305 | 0.963814 | ||||||||
\(219\) | −37.5268 | −2.53583 | ||||||||
\(220\) | 24.4906 | 1.65116 | ||||||||
\(221\) | 38.5771 | 2.59498 | ||||||||
\(222\) | 49.4046 | 3.31582 | ||||||||
\(223\) | 8.11508 | 0.543426 | 0.271713 | − | 0.962378i | \(-0.412410\pi\) | ||||
0.271713 | + | 0.962378i | \(0.412410\pi\) | |||||||
\(224\) | 67.1255 | 4.48501 | ||||||||
\(225\) | −31.4401 | −2.09600 | ||||||||
\(226\) | 26.5220 | 1.76422 | ||||||||
\(227\) | 1.17650 | 0.0780868 | 0.0390434 | − | 0.999238i | \(-0.487569\pi\) | ||||
0.0390434 | + | 0.999238i | \(0.487569\pi\) | |||||||
\(228\) | 137.385 | 9.09856 | ||||||||
\(229\) | −0.0269009 | −0.00177766 | −0.000888832 | − | 1.00000i | \(-0.500283\pi\) | ||||
−0.000888832 | 1.00000i | \(0.500283\pi\) | ||||||||
\(230\) | −8.57248 | −0.565252 | ||||||||
\(231\) | −64.9393 | −4.27269 | ||||||||
\(232\) | −8.28140 | −0.543700 | ||||||||
\(233\) | 19.7364 | 1.29298 | 0.646488 | − | 0.762924i | \(-0.276237\pi\) | ||||
0.646488 | + | 0.762924i | \(0.276237\pi\) | |||||||
\(234\) | 127.925 | 8.36269 | ||||||||
\(235\) | 5.79180 | 0.377815 | ||||||||
\(236\) | 32.4863 | 2.11468 | ||||||||
\(237\) | −2.47365 | −0.160681 | ||||||||
\(238\) | −79.5931 | −5.15926 | ||||||||
\(239\) | 12.5020 | 0.808687 | 0.404344 | − | 0.914607i | \(-0.367500\pi\) | ||||
0.404344 | + | 0.914607i | \(0.367500\pi\) | |||||||
\(240\) | 44.2537 | 2.85656 | ||||||||
\(241\) | −8.73806 | −0.562868 | −0.281434 | − | 0.959581i | \(-0.590810\pi\) | ||||
−0.281434 | + | 0.959581i | \(0.590810\pi\) | |||||||
\(242\) | −20.6226 | −1.32567 | ||||||||
\(243\) | −65.4985 | −4.20173 | ||||||||
\(244\) | −71.0978 | −4.55157 | ||||||||
\(245\) | −14.2469 | −0.910204 | ||||||||
\(246\) | −26.3414 | −1.67946 | ||||||||
\(247\) | 46.0120 | 2.92767 | ||||||||
\(248\) | 58.9144 | 3.74107 | ||||||||
\(249\) | −13.9876 | −0.886425 | ||||||||
\(250\) | −25.9108 | −1.63874 | ||||||||
\(251\) | 24.2161 | 1.52851 | 0.764254 | − | 0.644916i | \(-0.223108\pi\) | ||||
0.764254 | + | 0.644916i | \(0.223108\pi\) | |||||||
\(252\) | −189.657 | −11.9472 | ||||||||
\(253\) | 12.5626 | 0.789804 | ||||||||
\(254\) | 50.0065 | 3.13768 | ||||||||
\(255\) | −24.9925 | −1.56509 | ||||||||
\(256\) | 3.58087 | 0.223805 | ||||||||
\(257\) | −3.54015 | −0.220828 | −0.110414 | − | 0.993886i | \(-0.535218\pi\) | ||||
−0.110414 | + | 0.993886i | \(0.535218\pi\) | |||||||
\(258\) | −13.9495 | −0.868457 | ||||||||
\(259\) | −24.5309 | −1.52427 | ||||||||
\(260\) | 32.5774 | 2.02036 | ||||||||
\(261\) | 8.33433 | 0.515882 | ||||||||
\(262\) | −15.6766 | −0.968502 | ||||||||
\(263\) | −26.2570 | −1.61907 | −0.809537 | − | 0.587068i | \(-0.800282\pi\) | ||||
−0.809537 | + | 0.587068i | \(0.800282\pi\) | |||||||
\(264\) | −120.681 | −7.42742 | ||||||||
\(265\) | 2.88512 | 0.177232 | ||||||||
\(266\) | −94.9329 | −5.82071 | ||||||||
\(267\) | −8.49167 | −0.519682 | ||||||||
\(268\) | −1.78459 | −0.109011 | ||||||||
\(269\) | 24.5324 | 1.49577 | 0.747884 | − | 0.663830i | \(-0.231070\pi\) | ||||
0.747884 | + | 0.663830i | \(0.231070\pi\) | |||||||
\(270\) | −53.0448 | −3.22821 | ||||||||
\(271\) | −24.8018 | −1.50660 | −0.753301 | − | 0.657676i | \(-0.771540\pi\) | ||||
−0.753301 | + | 0.657676i | \(0.771540\pi\) | |||||||
\(272\) | −79.4859 | −4.81954 | ||||||||
\(273\) | −86.3821 | −5.22809 | ||||||||
\(274\) | 34.7322 | 2.09825 | ||||||||
\(275\) | 16.3287 | 0.984656 | ||||||||
\(276\) | 49.8959 | 3.00338 | ||||||||
\(277\) | 1.00000 | 0.0600842 | ||||||||
\(278\) | 39.8375 | 2.38930 | ||||||||
\(279\) | −59.2910 | −3.54966 | ||||||||
\(280\) | −40.8895 | −2.44361 | ||||||||
\(281\) | −1.75991 | −0.104987 | −0.0524936 | − | 0.998621i | \(-0.516717\pi\) | ||||
−0.0524936 | + | 0.998621i | \(0.516717\pi\) | |||||||
\(282\) | −46.9141 | −2.79370 | ||||||||
\(283\) | 4.98113 | 0.296097 | 0.148049 | − | 0.988980i | \(-0.452701\pi\) | ||||
0.148049 | + | 0.988980i | \(0.452701\pi\) | |||||||
\(284\) | −35.5946 | −2.11215 | ||||||||
\(285\) | −29.8092 | −1.76575 | ||||||||
\(286\) | −66.4387 | −3.92860 | ||||||||
\(287\) | 13.0793 | 0.772045 | ||||||||
\(288\) | −125.541 | −7.39760 | ||||||||
\(289\) | 27.8901 | 1.64060 | ||||||||
\(290\) | 2.95369 | 0.173447 | ||||||||
\(291\) | −17.9839 | −1.05423 | ||||||||
\(292\) | 56.9205 | 3.33102 | ||||||||
\(293\) | 0.564979 | 0.0330064 | 0.0165032 | − | 0.999864i | \(-0.494747\pi\) | ||||
0.0165032 | + | 0.999864i | \(0.494747\pi\) | |||||||
\(294\) | 115.402 | 6.73036 | ||||||||
\(295\) | −7.04873 | −0.410393 | ||||||||
\(296\) | −45.5874 | −2.64971 | ||||||||
\(297\) | 77.7349 | 4.51064 | ||||||||
\(298\) | −13.6169 | −0.788804 | ||||||||
\(299\) | 16.7107 | 0.966407 | ||||||||
\(300\) | 64.8539 | 3.74434 | ||||||||
\(301\) | 6.92633 | 0.399227 | ||||||||
\(302\) | 43.0665 | 2.47820 | ||||||||
\(303\) | 17.0276 | 0.978208 | ||||||||
\(304\) | −94.8051 | −5.43744 | ||||||||
\(305\) | 15.4265 | 0.883318 | ||||||||
\(306\) | 148.859 | 8.50970 | ||||||||
\(307\) | −26.1812 | −1.49424 | −0.747119 | − | 0.664690i | \(-0.768563\pi\) | ||||
−0.747119 | + | 0.664690i | \(0.768563\pi\) | |||||||
\(308\) | 98.4998 | 5.61255 | ||||||||
\(309\) | 43.7165 | 2.48694 | ||||||||
\(310\) | −21.0127 | −1.19344 | ||||||||
\(311\) | −5.93303 | −0.336431 | −0.168216 | − | 0.985750i | \(-0.553800\pi\) | ||||
−0.168216 | + | 0.985750i | \(0.553800\pi\) | |||||||
\(312\) | −160.530 | −9.08822 | ||||||||
\(313\) | −18.0557 | −1.02057 | −0.510286 | − | 0.860005i | \(-0.670460\pi\) | ||||
−0.510286 | + | 0.860005i | \(0.670460\pi\) | |||||||
\(314\) | 8.70524 | 0.491265 | ||||||||
\(315\) | 41.1508 | 2.31859 | ||||||||
\(316\) | 3.75203 | 0.211068 | ||||||||
\(317\) | 22.5229 | 1.26501 | 0.632507 | − | 0.774555i | \(-0.282026\pi\) | ||||
0.632507 | + | 0.774555i | \(0.282026\pi\) | |||||||
\(318\) | −23.3698 | −1.31051 | ||||||||
\(319\) | −4.32851 | −0.242350 | ||||||||
\(320\) | −18.2025 | −1.01755 | ||||||||
\(321\) | −4.82852 | −0.269502 | ||||||||
\(322\) | −34.4780 | −1.92138 | ||||||||
\(323\) | 53.5417 | 2.97914 | ||||||||
\(324\) | 181.068 | 10.0593 | ||||||||
\(325\) | 21.7204 | 1.20483 | ||||||||
\(326\) | −65.2922 | −3.61620 | ||||||||
\(327\) | 17.9718 | 0.993841 | ||||||||
\(328\) | 24.3061 | 1.34208 | ||||||||
\(329\) | 23.2943 | 1.28425 | ||||||||
\(330\) | 43.0429 | 2.36943 | ||||||||
\(331\) | 13.9915 | 0.769042 | 0.384521 | − | 0.923116i | \(-0.374367\pi\) | ||||
0.384521 | + | 0.923116i | \(0.374367\pi\) | |||||||
\(332\) | 21.2163 | 1.16440 | ||||||||
\(333\) | 45.8788 | 2.51414 | ||||||||
\(334\) | −26.4512 | −1.44735 | ||||||||
\(335\) | 0.387212 | 0.0211556 | ||||||||
\(336\) | 177.985 | 9.70990 | ||||||||
\(337\) | −6.15743 | −0.335417 | −0.167708 | − | 0.985837i | \(-0.553637\pi\) | ||||
−0.167708 | + | 0.985837i | \(0.553637\pi\) | |||||||
\(338\) | −53.7211 | −2.92205 | ||||||||
\(339\) | 33.4947 | 1.81918 | ||||||||
\(340\) | 37.9086 | 2.05588 | ||||||||
\(341\) | 30.7933 | 1.66755 | ||||||||
\(342\) | 177.548 | 9.60070 | ||||||||
\(343\) | −26.1064 | −1.40961 | ||||||||
\(344\) | 12.8717 | 0.693994 | ||||||||
\(345\) | −10.8262 | −0.582863 | ||||||||
\(346\) | −14.4167 | −0.775046 | ||||||||
\(347\) | −18.8041 | −1.00946 | −0.504728 | − | 0.863278i | \(-0.668407\pi\) | ||||
−0.504728 | + | 0.863278i | \(0.668407\pi\) | |||||||
\(348\) | −17.1919 | −0.921582 | ||||||||
\(349\) | −14.9830 | −0.802021 | −0.401010 | − | 0.916074i | \(-0.631341\pi\) | ||||
−0.401010 | + | 0.916074i | \(0.631341\pi\) | |||||||
\(350\) | −44.8139 | −2.39540 | ||||||||
\(351\) | 103.403 | 5.51923 | ||||||||
\(352\) | 65.2010 | 3.47522 | ||||||||
\(353\) | 12.3216 | 0.655811 | 0.327905 | − | 0.944711i | \(-0.393657\pi\) | ||||
0.327905 | + | 0.944711i | \(0.393657\pi\) | |||||||
\(354\) | 57.0954 | 3.03459 | ||||||||
\(355\) | 7.72316 | 0.409903 | ||||||||
\(356\) | 12.8801 | 0.682646 | ||||||||
\(357\) | −100.518 | −5.31999 | ||||||||
\(358\) | 1.02429 | 0.0541353 | ||||||||
\(359\) | 8.37134 | 0.441823 | 0.220911 | − | 0.975294i | \(-0.429097\pi\) | ||||
0.220911 | + | 0.975294i | \(0.429097\pi\) | |||||||
\(360\) | 76.4735 | 4.03051 | ||||||||
\(361\) | 44.8606 | 2.36108 | ||||||||
\(362\) | 37.7232 | 1.98269 | ||||||||
\(363\) | −26.0443 | −1.36697 | ||||||||
\(364\) | 131.024 | 6.86754 | ||||||||
\(365\) | −12.3504 | −0.646447 | ||||||||
\(366\) | −124.956 | −6.53156 | ||||||||
\(367\) | −17.3782 | −0.907137 | −0.453569 | − | 0.891221i | \(-0.649849\pi\) | ||||
−0.453569 | + | 0.891221i | \(0.649849\pi\) | |||||||
\(368\) | −34.4315 | −1.79487 | ||||||||
\(369\) | −24.4615 | −1.27341 | ||||||||
\(370\) | 16.2595 | 0.845289 | ||||||||
\(371\) | 11.6038 | 0.602439 | ||||||||
\(372\) | 122.304 | 6.34118 | ||||||||
\(373\) | −21.0646 | −1.09068 | −0.545342 | − | 0.838213i | \(-0.683600\pi\) | ||||
−0.545342 | + | 0.838213i | \(0.683600\pi\) | |||||||
\(374\) | −77.3112 | −3.99767 | ||||||||
\(375\) | −32.7228 | −1.68980 | ||||||||
\(376\) | 43.2893 | 2.23248 | ||||||||
\(377\) | −5.75777 | −0.296540 | ||||||||
\(378\) | −213.343 | −10.9732 | ||||||||
\(379\) | 24.6186 | 1.26457 | 0.632286 | − | 0.774735i | \(-0.282117\pi\) | ||||
0.632286 | + | 0.774735i | \(0.282117\pi\) | |||||||
\(380\) | 45.2146 | 2.31946 | ||||||||
\(381\) | 63.1532 | 3.23544 | ||||||||
\(382\) | 26.3562 | 1.34850 | ||||||||
\(383\) | −14.6477 | −0.748462 | −0.374231 | − | 0.927336i | \(-0.622093\pi\) | ||||
−0.374231 | + | 0.927336i | \(0.622093\pi\) | |||||||
\(384\) | 46.0170 | 2.34830 | ||||||||
\(385\) | −21.3720 | −1.08922 | ||||||||
\(386\) | 37.3376 | 1.90043 | ||||||||
\(387\) | −12.9539 | −0.658486 | ||||||||
\(388\) | 27.2779 | 1.38483 | ||||||||
\(389\) | 0.770700 | 0.0390760 | 0.0195380 | − | 0.999809i | \(-0.493780\pi\) | ||||
0.0195380 | + | 0.999809i | \(0.493780\pi\) | |||||||
\(390\) | 57.2555 | 2.89925 | ||||||||
\(391\) | 19.4454 | 0.983396 | ||||||||
\(392\) | −106.485 | −5.37831 | ||||||||
\(393\) | −19.7980 | −0.998675 | ||||||||
\(394\) | 15.3779 | 0.774728 | ||||||||
\(395\) | −0.814099 | −0.0409618 | ||||||||
\(396\) | −184.219 | −9.25736 | ||||||||
\(397\) | 29.1697 | 1.46398 | 0.731992 | − | 0.681313i | \(-0.238591\pi\) | ||||
0.731992 | + | 0.681313i | \(0.238591\pi\) | |||||||
\(398\) | 31.5814 | 1.58303 | ||||||||
\(399\) | −119.891 | −6.00205 | ||||||||
\(400\) | −44.7536 | −2.23768 | ||||||||
\(401\) | 14.7192 | 0.735043 | 0.367522 | − | 0.930015i | \(-0.380206\pi\) | ||||
0.367522 | + | 0.930015i | \(0.380206\pi\) | |||||||
\(402\) | −3.13645 | −0.156432 | ||||||||
\(403\) | 40.9611 | 2.04042 | ||||||||
\(404\) | −25.8274 | −1.28496 | ||||||||
\(405\) | −39.2873 | −1.95220 | ||||||||
\(406\) | 11.8796 | 0.589573 | ||||||||
\(407\) | −23.8275 | −1.18109 | ||||||||
\(408\) | −186.800 | −9.24798 | ||||||||
\(409\) | 17.4378 | 0.862244 | 0.431122 | − | 0.902294i | \(-0.358118\pi\) | ||||
0.431122 | + | 0.902294i | \(0.358118\pi\) | |||||||
\(410\) | −8.66915 | −0.428139 | ||||||||
\(411\) | 43.8633 | 2.16362 | ||||||||
\(412\) | −66.3090 | −3.26681 | ||||||||
\(413\) | −28.3496 | −1.39499 | ||||||||
\(414\) | 64.4824 | 3.16914 | ||||||||
\(415\) | −4.60342 | −0.225973 | ||||||||
\(416\) | 86.7302 | 4.25230 | ||||||||
\(417\) | 50.3108 | 2.46373 | ||||||||
\(418\) | −92.2111 | −4.51019 | ||||||||
\(419\) | 3.17712 | 0.155213 | 0.0776063 | − | 0.996984i | \(-0.475272\pi\) | ||||
0.0776063 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(420\) | −84.8851 | −4.14197 | ||||||||
\(421\) | 0.705545 | 0.0343862 | 0.0171931 | − | 0.999852i | \(-0.494527\pi\) | ||||
0.0171931 | + | 0.999852i | \(0.494527\pi\) | |||||||
\(422\) | 11.7005 | 0.569572 | ||||||||
\(423\) | −43.5660 | −2.11825 | ||||||||
\(424\) | 21.5641 | 1.04725 | ||||||||
\(425\) | 25.2748 | 1.22601 | ||||||||
\(426\) | −62.5584 | −3.03096 | ||||||||
\(427\) | 62.0443 | 3.00254 | ||||||||
\(428\) | 7.32389 | 0.354013 | ||||||||
\(429\) | −83.9055 | −4.05100 | ||||||||
\(430\) | −4.59088 | −0.221392 | ||||||||
\(431\) | 26.2543 | 1.26463 | 0.632313 | − | 0.774713i | \(-0.282106\pi\) | ||||
0.632313 | + | 0.774713i | \(0.282106\pi\) | |||||||
\(432\) | −213.056 | −10.2506 | ||||||||
\(433\) | 3.45592 | 0.166081 | 0.0830405 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830405 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(434\) | −84.5119 | −4.05670 | ||||||||
\(435\) | 3.73022 | 0.178850 | ||||||||
\(436\) | −27.2595 | −1.30549 | ||||||||
\(437\) | 23.1931 | 1.10947 | ||||||||
\(438\) | 100.039 | 4.78006 | ||||||||
\(439\) | 13.2029 | 0.630141 | 0.315071 | − | 0.949068i | \(-0.397972\pi\) | ||||
0.315071 | + | 0.949068i | \(0.397972\pi\) | |||||||
\(440\) | −39.7172 | −1.89344 | ||||||||
\(441\) | 107.166 | 5.10313 | ||||||||
\(442\) | −102.839 | −4.89156 | ||||||||
\(443\) | 21.8804 | 1.03957 | 0.519784 | − | 0.854298i | \(-0.326012\pi\) | ||||
0.519784 | + | 0.854298i | \(0.326012\pi\) | |||||||
\(444\) | −94.6378 | −4.49131 | ||||||||
\(445\) | −2.79468 | −0.132480 | ||||||||
\(446\) | −21.6332 | −1.02436 | ||||||||
\(447\) | −17.1968 | −0.813379 | ||||||||
\(448\) | −73.2092 | −3.45881 | ||||||||
\(449\) | 2.53849 | 0.119799 | 0.0598993 | − | 0.998204i | \(-0.480922\pi\) | ||||
0.0598993 | + | 0.998204i | \(0.480922\pi\) | |||||||
\(450\) | 83.8131 | 3.95099 | ||||||||
\(451\) | 12.7043 | 0.598221 | ||||||||
\(452\) | −50.8046 | −2.38965 | ||||||||
\(453\) | 54.3887 | 2.55540 | ||||||||
\(454\) | −3.13631 | −0.147194 | ||||||||
\(455\) | −28.4290 | −1.33277 | ||||||||
\(456\) | −222.802 | −10.4336 | ||||||||
\(457\) | 7.27784 | 0.340443 | 0.170222 | − | 0.985406i | \(-0.445552\pi\) | ||||
0.170222 | + | 0.985406i | \(0.445552\pi\) | |||||||
\(458\) | 0.0717127 | 0.00335091 | ||||||||
\(459\) | 120.324 | 5.61626 | ||||||||
\(460\) | 16.4211 | 0.765640 | ||||||||
\(461\) | 10.1036 | 0.470573 | 0.235287 | − | 0.971926i | \(-0.424397\pi\) | ||||
0.235287 | + | 0.971926i | \(0.424397\pi\) | |||||||
\(462\) | 173.116 | 8.05407 | ||||||||
\(463\) | −3.87135 | −0.179917 | −0.0899585 | − | 0.995946i | \(-0.528673\pi\) | ||||
−0.0899585 | + | 0.995946i | \(0.528673\pi\) | |||||||
\(464\) | 11.8636 | 0.550752 | ||||||||
\(465\) | −26.5370 | −1.23062 | ||||||||
\(466\) | −52.6135 | −2.43727 | ||||||||
\(467\) | 23.2730 | 1.07694 | 0.538472 | − | 0.842643i | \(-0.319002\pi\) | ||||
0.538472 | + | 0.842643i | \(0.319002\pi\) | |||||||
\(468\) | −245.048 | −11.3273 | ||||||||
\(469\) | 1.55734 | 0.0719113 | ||||||||
\(470\) | −15.4398 | −0.712186 | ||||||||
\(471\) | 10.9939 | 0.506570 | ||||||||
\(472\) | −52.6840 | −2.42498 | ||||||||
\(473\) | 6.72775 | 0.309342 | ||||||||
\(474\) | 6.59429 | 0.302886 | ||||||||
\(475\) | 30.1460 | 1.38319 | ||||||||
\(476\) | 152.466 | 6.98826 | ||||||||
\(477\) | −21.7020 | −0.993664 | ||||||||
\(478\) | −33.3279 | −1.52438 | ||||||||
\(479\) | 18.3285 | 0.837450 | 0.418725 | − | 0.908113i | \(-0.362477\pi\) | ||||
0.418725 | + | 0.908113i | \(0.362477\pi\) | |||||||
\(480\) | −56.1889 | −2.56466 | ||||||||
\(481\) | −31.6953 | −1.44518 | ||||||||
\(482\) | 23.2940 | 1.06101 | ||||||||
\(483\) | −43.5423 | −1.98124 | ||||||||
\(484\) | 39.5040 | 1.79564 | ||||||||
\(485\) | −5.91864 | −0.268752 | ||||||||
\(486\) | 174.606 | 7.92031 | ||||||||
\(487\) | −24.6474 | −1.11688 | −0.558441 | − | 0.829544i | \(-0.688600\pi\) | ||||
−0.558441 | + | 0.829544i | \(0.688600\pi\) | |||||||
\(488\) | 115.301 | 5.21945 | ||||||||
\(489\) | −82.4576 | −3.72886 | ||||||||
\(490\) | 37.9796 | 1.71574 | ||||||||
\(491\) | −23.1001 | −1.04249 | −0.521245 | − | 0.853407i | \(-0.674532\pi\) | ||||
−0.521245 | + | 0.853407i | \(0.674532\pi\) | |||||||
\(492\) | 50.4586 | 2.27485 | ||||||||
\(493\) | −6.70001 | −0.301753 | ||||||||
\(494\) | −122.659 | −5.51869 | ||||||||
\(495\) | 39.9710 | 1.79656 | ||||||||
\(496\) | −84.3981 | −3.78959 | ||||||||
\(497\) | 31.0621 | 1.39332 | ||||||||
\(498\) | 37.2881 | 1.67092 | ||||||||
\(499\) | −1.66936 | −0.0747307 | −0.0373654 | − | 0.999302i | \(-0.511897\pi\) | ||||
−0.0373654 | + | 0.999302i | \(0.511897\pi\) | |||||||
\(500\) | 49.6339 | 2.21969 | ||||||||
\(501\) | −33.4053 | −1.49244 | ||||||||
\(502\) | −64.5555 | −2.88125 | ||||||||
\(503\) | −30.7057 | −1.36910 | −0.684549 | − | 0.728966i | \(-0.740001\pi\) | ||||
−0.684549 | + | 0.728966i | \(0.740001\pi\) | |||||||
\(504\) | 307.572 | 13.7003 | ||||||||
\(505\) | 5.60390 | 0.249370 | ||||||||
\(506\) | −33.4895 | −1.48879 | ||||||||
\(507\) | −67.8445 | −3.01308 | ||||||||
\(508\) | −95.7906 | −4.25002 | ||||||||
\(509\) | −43.5643 | −1.93095 | −0.965477 | − | 0.260487i | \(-0.916117\pi\) | ||||
−0.965477 | + | 0.260487i | \(0.916117\pi\) | |||||||
\(510\) | 66.6252 | 2.95021 | ||||||||
\(511\) | −49.6724 | −2.19738 | ||||||||
\(512\) | 17.7911 | 0.786262 | ||||||||
\(513\) | 143.514 | 6.33630 | ||||||||
\(514\) | 9.43735 | 0.416264 | ||||||||
\(515\) | 14.3874 | 0.633986 | ||||||||
\(516\) | 26.7211 | 1.17633 | ||||||||
\(517\) | 22.6264 | 0.995108 | ||||||||
\(518\) | 65.3945 | 2.87327 | ||||||||
\(519\) | −18.2069 | −0.799192 | ||||||||
\(520\) | −52.8317 | −2.31682 | ||||||||
\(521\) | −35.8719 | −1.57157 | −0.785787 | − | 0.618497i | \(-0.787742\pi\) | ||||
−0.785787 | + | 0.618497i | \(0.787742\pi\) | |||||||
\(522\) | −22.2177 | −0.972443 | ||||||||
\(523\) | −9.26124 | −0.404966 | −0.202483 | − | 0.979286i | \(-0.564901\pi\) | ||||
−0.202483 | + | 0.979286i | \(0.564901\pi\) | |||||||
\(524\) | 30.0295 | 1.31184 | ||||||||
\(525\) | −56.5955 | −2.47003 | ||||||||
\(526\) | 69.9960 | 3.05197 | ||||||||
\(527\) | 47.6643 | 2.07629 | ||||||||
\(528\) | 172.883 | 7.52375 | ||||||||
\(529\) | −14.5767 | −0.633769 | ||||||||
\(530\) | −7.69118 | −0.334084 | ||||||||
\(531\) | 53.0207 | 2.30090 | ||||||||
\(532\) | 181.850 | 7.88420 | ||||||||
\(533\) | 16.8992 | 0.731986 | ||||||||
\(534\) | 22.6371 | 0.979605 | ||||||||
\(535\) | −1.58910 | −0.0687030 | ||||||||
\(536\) | 2.89411 | 0.125007 | ||||||||
\(537\) | 1.29357 | 0.0558218 | ||||||||
\(538\) | −65.3987 | −2.81954 | ||||||||
\(539\) | −55.6575 | −2.39734 | ||||||||
\(540\) | 101.611 | 4.37263 | ||||||||
\(541\) | −31.4531 | −1.35227 | −0.676137 | − | 0.736776i | \(-0.736347\pi\) | ||||
−0.676137 | + | 0.736776i | \(0.736347\pi\) | |||||||
\(542\) | 66.1168 | 2.83996 | ||||||||
\(543\) | 47.6407 | 2.04446 | ||||||||
\(544\) | 100.923 | 4.32705 | ||||||||
\(545\) | 5.91465 | 0.253356 | ||||||||
\(546\) | 230.278 | 9.85499 | ||||||||
\(547\) | 40.2618 | 1.72147 | 0.860736 | − | 0.509052i | \(-0.170004\pi\) | ||||
0.860736 | + | 0.509052i | \(0.170004\pi\) | |||||||
\(548\) | −66.5317 | −2.84209 | ||||||||
\(549\) | −116.038 | −4.95239 | ||||||||
\(550\) | −43.5291 | −1.85609 | ||||||||
\(551\) | −7.99128 | −0.340440 | ||||||||
\(552\) | −80.9176 | −3.44408 | ||||||||
\(553\) | −3.27426 | −0.139236 | ||||||||
\(554\) | −2.66581 | −0.113259 | ||||||||
\(555\) | 20.5341 | 0.871623 | ||||||||
\(556\) | −76.3113 | −3.23632 | ||||||||
\(557\) | 18.4929 | 0.783568 | 0.391784 | − | 0.920057i | \(-0.371858\pi\) | ||||
0.391784 | + | 0.920057i | \(0.371858\pi\) | |||||||
\(558\) | 158.058 | 6.69114 | ||||||||
\(559\) | 8.94923 | 0.378512 | ||||||||
\(560\) | 58.5764 | 2.47531 | ||||||||
\(561\) | −97.6364 | −4.12221 | ||||||||
\(562\) | 4.69157 | 0.197902 | ||||||||
\(563\) | −5.12018 | −0.215790 | −0.107895 | − | 0.994162i | \(-0.534411\pi\) | ||||
−0.107895 | + | 0.994162i | \(0.534411\pi\) | |||||||
\(564\) | 89.8671 | 3.78409 | ||||||||
\(565\) | 11.0234 | 0.463756 | ||||||||
\(566\) | −13.2787 | −0.558146 | ||||||||
\(567\) | −158.011 | −6.63583 | ||||||||
\(568\) | 57.7248 | 2.42208 | ||||||||
\(569\) | −17.3938 | −0.729188 | −0.364594 | − | 0.931167i | \(-0.618792\pi\) | ||||
−0.364594 | + | 0.931167i | \(0.618792\pi\) | |||||||
\(570\) | 79.4657 | 3.32845 | ||||||||
\(571\) | −36.0678 | −1.50939 | −0.754696 | − | 0.656075i | \(-0.772216\pi\) | ||||
−0.754696 | + | 0.656075i | \(0.772216\pi\) | |||||||
\(572\) | 127.268 | 5.32133 | ||||||||
\(573\) | 33.2853 | 1.39051 | ||||||||
\(574\) | −34.8668 | −1.45531 | ||||||||
\(575\) | 10.9485 | 0.456583 | ||||||||
\(576\) | 136.919 | 5.70497 | ||||||||
\(577\) | −24.0492 | −1.00118 | −0.500590 | − | 0.865684i | \(-0.666884\pi\) | ||||
−0.500590 | + | 0.865684i | \(0.666884\pi\) | |||||||
\(578\) | −74.3497 | −3.09254 | ||||||||
\(579\) | 47.1537 | 1.95964 | ||||||||
\(580\) | −5.65799 | −0.234935 | ||||||||
\(581\) | −18.5146 | −0.768117 | ||||||||
\(582\) | 47.9416 | 1.98724 | ||||||||
\(583\) | 11.2711 | 0.466801 | ||||||||
\(584\) | −92.3097 | −3.81980 | ||||||||
\(585\) | 53.1694 | 2.19828 | ||||||||
\(586\) | −1.50613 | −0.0622175 | ||||||||
\(587\) | 5.47614 | 0.226024 | 0.113012 | − | 0.993594i | \(-0.463950\pi\) | ||||
0.113012 | + | 0.993594i | \(0.463950\pi\) | |||||||
\(588\) | −221.059 | −9.11633 | ||||||||
\(589\) | 56.8505 | 2.34248 | ||||||||
\(590\) | 18.7906 | 0.773595 | ||||||||
\(591\) | 19.4208 | 0.798864 | ||||||||
\(592\) | 65.3064 | 2.68408 | ||||||||
\(593\) | 29.5768 | 1.21457 | 0.607286 | − | 0.794483i | \(-0.292258\pi\) | ||||
0.607286 | + | 0.794483i | \(0.292258\pi\) | |||||||
\(594\) | −207.226 | −8.50260 | ||||||||
\(595\) | −33.0814 | −1.35620 | ||||||||
\(596\) | 26.0840 | 1.06844 | ||||||||
\(597\) | 39.8841 | 1.63235 | ||||||||
\(598\) | −44.5476 | −1.82169 | ||||||||
\(599\) | −1.71453 | −0.0700540 | −0.0350270 | − | 0.999386i | \(-0.511152\pi\) | ||||
−0.0350270 | + | 0.999386i | \(0.511152\pi\) | |||||||
\(600\) | −105.175 | −4.29377 | ||||||||
\(601\) | −9.09289 | −0.370907 | −0.185453 | − | 0.982653i | \(-0.559375\pi\) | ||||
−0.185453 | + | 0.982653i | \(0.559375\pi\) | |||||||
\(602\) | −18.4642 | −0.752547 | ||||||||
\(603\) | −2.91261 | −0.118611 | ||||||||
\(604\) | −82.4966 | −3.35674 | ||||||||
\(605\) | −8.57140 | −0.348477 | ||||||||
\(606\) | −45.3922 | −1.84393 | ||||||||
\(607\) | 17.6703 | 0.717214 | 0.358607 | − | 0.933489i | \(-0.383252\pi\) | ||||
0.358607 | + | 0.933489i | \(0.383252\pi\) | |||||||
\(608\) | 120.374 | 4.88181 | ||||||||
\(609\) | 15.0027 | 0.607940 | ||||||||
\(610\) | −41.1240 | −1.66506 | ||||||||
\(611\) | 30.0976 | 1.21762 | ||||||||
\(612\) | −285.149 | −11.5265 | ||||||||
\(613\) | −5.00671 | −0.202219 | −0.101110 | − | 0.994875i | \(-0.532239\pi\) | ||||
−0.101110 | + | 0.994875i | \(0.532239\pi\) | |||||||
\(614\) | 69.7939 | 2.81665 | ||||||||
\(615\) | −10.9483 | −0.441477 | ||||||||
\(616\) | −159.740 | −6.43611 | ||||||||
\(617\) | −38.6754 | −1.55701 | −0.778506 | − | 0.627637i | \(-0.784022\pi\) | ||||
−0.778506 | + | 0.627637i | \(0.784022\pi\) | |||||||
\(618\) | −116.540 | −4.68791 | ||||||||
\(619\) | −22.4207 | −0.901164 | −0.450582 | − | 0.892735i | \(-0.648783\pi\) | ||||
−0.450582 | + | 0.892735i | \(0.648783\pi\) | |||||||
\(620\) | 40.2513 | 1.61653 | ||||||||
\(621\) | 52.1218 | 2.09158 | ||||||||
\(622\) | 15.8163 | 0.634176 | ||||||||
\(623\) | −11.2400 | −0.450321 | ||||||||
\(624\) | 229.968 | 9.20609 | ||||||||
\(625\) | 8.09245 | 0.323698 | ||||||||
\(626\) | 48.1331 | 1.92379 | ||||||||
\(627\) | −116.454 | −4.65071 | ||||||||
\(628\) | −16.6755 | −0.665423 | ||||||||
\(629\) | −36.8822 | −1.47059 | ||||||||
\(630\) | −109.700 | −4.37056 | ||||||||
\(631\) | −28.2285 | −1.12376 | −0.561880 | − | 0.827219i | \(-0.689922\pi\) | ||||
−0.561880 | + | 0.827219i | \(0.689922\pi\) | |||||||
\(632\) | −6.08478 | −0.242040 | ||||||||
\(633\) | 14.7766 | 0.587317 | ||||||||
\(634\) | −60.0417 | −2.38456 | ||||||||
\(635\) | 20.7842 | 0.824797 | ||||||||
\(636\) | 44.7663 | 1.77510 | ||||||||
\(637\) | −74.0355 | −2.93339 | ||||||||
\(638\) | 11.5390 | 0.456832 | ||||||||
\(639\) | −58.0938 | −2.29815 | ||||||||
\(640\) | 15.1446 | 0.598642 | ||||||||
\(641\) | −34.9886 | −1.38197 | −0.690984 | − | 0.722870i | \(-0.742822\pi\) | ||||
−0.690984 | + | 0.722870i | \(0.742822\pi\) | |||||||
\(642\) | 12.8719 | 0.508014 | ||||||||
\(643\) | 4.53293 | 0.178761 | 0.0893807 | − | 0.995998i | \(-0.471511\pi\) | ||||
0.0893807 | + | 0.995998i | \(0.471511\pi\) | |||||||
\(644\) | 66.0448 | 2.60253 | ||||||||
\(645\) | −5.79783 | −0.228289 | ||||||||
\(646\) | −142.732 | −5.61571 | ||||||||
\(647\) | 1.60769 | 0.0632046 | 0.0316023 | − | 0.999501i | \(-0.489939\pi\) | ||||
0.0316023 | + | 0.999501i | \(0.489939\pi\) | |||||||
\(648\) | −293.643 | −11.5354 | ||||||||
\(649\) | −27.5368 | −1.08091 | ||||||||
\(650\) | −57.9023 | −2.27111 | ||||||||
\(651\) | −106.730 | −4.18309 | ||||||||
\(652\) | 125.071 | 4.89818 | ||||||||
\(653\) | −22.2198 | −0.869527 | −0.434763 | − | 0.900545i | \(-0.643168\pi\) | ||||
−0.434763 | + | 0.900545i | \(0.643168\pi\) | |||||||
\(654\) | −47.9093 | −1.87340 | ||||||||
\(655\) | −6.51566 | −0.254588 | ||||||||
\(656\) | −34.8198 | −1.35949 | ||||||||
\(657\) | 92.8997 | 3.62436 | ||||||||
\(658\) | −62.0980 | −2.42083 | ||||||||
\(659\) | 17.4171 | 0.678476 | 0.339238 | − | 0.940701i | \(-0.389831\pi\) | ||||
0.339238 | + | 0.940701i | \(0.389831\pi\) | |||||||
\(660\) | −82.4514 | −3.20942 | ||||||||
\(661\) | 12.2302 | 0.475699 | 0.237849 | − | 0.971302i | \(-0.423558\pi\) | ||||
0.237849 | + | 0.971302i | \(0.423558\pi\) | |||||||
\(662\) | −37.2986 | −1.44965 | ||||||||
\(663\) | −129.876 | −5.04395 | ||||||||
\(664\) | −34.4071 | −1.33525 | ||||||||
\(665\) | −39.4570 | −1.53008 | ||||||||
\(666\) | −122.304 | −4.73918 | ||||||||
\(667\) | −2.90229 | −0.112377 | ||||||||
\(668\) | 50.6691 | 1.96045 | ||||||||
\(669\) | −27.3206 | −1.05628 | ||||||||
\(670\) | −1.03223 | −0.0398786 | ||||||||
\(671\) | 60.2655 | 2.32652 | ||||||||
\(672\) | −225.988 | −8.71768 | ||||||||
\(673\) | 3.63996 | 0.140310 | 0.0701552 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701552 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(674\) | 16.4145 | 0.632264 | ||||||||
\(675\) | 67.7471 | 2.60759 | ||||||||
\(676\) | 102.906 | 3.95794 | ||||||||
\(677\) | 28.9773 | 1.11369 | 0.556844 | − | 0.830617i | \(-0.312012\pi\) | ||||
0.556844 | + | 0.830617i | \(0.312012\pi\) | |||||||
\(678\) | −89.2903 | −3.42917 | ||||||||
\(679\) | −23.8044 | −0.913530 | ||||||||
\(680\) | −61.4774 | −2.35755 | ||||||||
\(681\) | −3.96085 | −0.151780 | ||||||||
\(682\) | −82.0889 | −3.14335 | ||||||||
\(683\) | 43.9545 | 1.68187 | 0.840937 | − | 0.541134i | \(-0.182005\pi\) | ||||
0.840937 | + | 0.541134i | \(0.182005\pi\) | |||||||
\(684\) | −340.105 | −13.0042 | ||||||||
\(685\) | 14.4358 | 0.551562 | ||||||||
\(686\) | 69.5946 | 2.65714 | ||||||||
\(687\) | 0.0905660 | 0.00345531 | ||||||||
\(688\) | −18.4394 | −0.702995 | ||||||||
\(689\) | 14.9928 | 0.571180 | ||||||||
\(690\) | 28.8605 | 1.09870 | ||||||||
\(691\) | −32.4109 | −1.23297 | −0.616485 | − | 0.787366i | \(-0.711444\pi\) | ||||
−0.616485 | + | 0.787366i | \(0.711444\pi\) | |||||||
\(692\) | 27.6161 | 1.04981 | ||||||||
\(693\) | 160.761 | 6.10680 | ||||||||
\(694\) | 50.1280 | 1.90283 | ||||||||
\(695\) | 16.5577 | 0.628069 | ||||||||
\(696\) | 27.8806 | 1.05681 | ||||||||
\(697\) | 19.6647 | 0.744853 | ||||||||
\(698\) | 39.9417 | 1.51182 | ||||||||
\(699\) | −66.4456 | −2.51320 | ||||||||
\(700\) | 85.8440 | 3.24460 | ||||||||
\(701\) | −34.7606 | −1.31289 | −0.656444 | − | 0.754375i | \(-0.727940\pi\) | ||||
−0.656444 | + | 0.754375i | \(0.727940\pi\) | |||||||
\(702\) | −275.652 | −10.4038 | ||||||||
\(703\) | −43.9904 | −1.65913 | ||||||||
\(704\) | −71.1103 | −2.68007 | ||||||||
\(705\) | −19.4990 | −0.734373 | ||||||||
\(706\) | −32.8469 | −1.23621 | ||||||||
\(707\) | 22.5386 | 0.847650 | ||||||||
\(708\) | −109.370 | −4.11038 | ||||||||
\(709\) | −10.7733 | −0.404601 | −0.202300 | − | 0.979324i | \(-0.564842\pi\) | ||||
−0.202300 | + | 0.979324i | \(0.564842\pi\) | |||||||
\(710\) | −20.5885 | −0.772671 | ||||||||
\(711\) | 6.12367 | 0.229656 | ||||||||
\(712\) | −20.8881 | −0.782814 | ||||||||
\(713\) | 20.6471 | 0.773240 | ||||||||
\(714\) | 267.962 | 10.0282 | ||||||||
\(715\) | −27.6140 | −1.03270 | ||||||||
\(716\) | −1.96209 | −0.0733267 | ||||||||
\(717\) | −42.0899 | −1.57187 | ||||||||
\(718\) | −22.3164 | −0.832840 | ||||||||
\(719\) | 26.7574 | 0.997882 | 0.498941 | − | 0.866636i | \(-0.333722\pi\) | ||||
0.498941 | + | 0.866636i | \(0.333722\pi\) | |||||||
\(720\) | −109.552 | −4.08278 | ||||||||
\(721\) | 57.8654 | 2.15502 | ||||||||
\(722\) | −119.590 | −4.45067 | ||||||||
\(723\) | 29.4180 | 1.09407 | ||||||||
\(724\) | −72.2612 | −2.68557 | ||||||||
\(725\) | −3.77236 | −0.140102 | ||||||||
\(726\) | 69.4292 | 2.57676 | ||||||||
\(727\) | −39.9725 | −1.48250 | −0.741248 | − | 0.671231i | \(-0.765766\pi\) | ||||
−0.741248 | + | 0.671231i | \(0.765766\pi\) | |||||||
\(728\) | −212.486 | −7.87524 | ||||||||
\(729\) | 114.136 | 4.22727 | ||||||||
\(730\) | 32.9237 | 1.21856 | ||||||||
\(731\) | 10.4137 | 0.385166 | ||||||||
\(732\) | 239.361 | 8.84705 | ||||||||
\(733\) | 18.2900 | 0.675557 | 0.337778 | − | 0.941226i | \(-0.390325\pi\) | ||||
0.337778 | + | 0.941226i | \(0.390325\pi\) | |||||||
\(734\) | 46.3271 | 1.70996 | ||||||||
\(735\) | 47.9645 | 1.76920 | ||||||||
\(736\) | 43.7177 | 1.61146 | ||||||||
\(737\) | 1.51269 | 0.0557207 | ||||||||
\(738\) | 65.2096 | 2.40040 | ||||||||
\(739\) | −8.35613 | −0.307385 | −0.153693 | − | 0.988119i | \(-0.549117\pi\) | ||||
−0.153693 | + | 0.988119i | \(0.549117\pi\) | |||||||
\(740\) | −31.1460 | −1.14495 | ||||||||
\(741\) | −154.906 | −5.69062 | ||||||||
\(742\) | −30.9335 | −1.13560 | ||||||||
\(743\) | 0.443321 | 0.0162639 | 0.00813193 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813193 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(744\) | −198.344 | −7.27165 | ||||||||
\(745\) | −5.65959 | −0.207351 | ||||||||
\(746\) | 56.1542 | 2.05595 | ||||||||
\(747\) | 34.6270 | 1.26694 | ||||||||
\(748\) | 148.095 | 5.41487 | ||||||||
\(749\) | −6.39128 | −0.233532 | ||||||||
\(750\) | 87.2327 | 3.18529 | ||||||||
\(751\) | −49.0327 | −1.78923 | −0.894614 | − | 0.446840i | \(-0.852549\pi\) | ||||
−0.894614 | + | 0.446840i | \(0.852549\pi\) | |||||||
\(752\) | −62.0143 | −2.26143 | ||||||||
\(753\) | −81.5272 | −2.97101 | ||||||||
\(754\) | 15.3491 | 0.558981 | ||||||||
\(755\) | 17.8997 | 0.651438 | ||||||||
\(756\) | 408.672 | 14.8633 | ||||||||
\(757\) | −19.0583 | −0.692687 | −0.346343 | − | 0.938108i | \(-0.612577\pi\) | ||||
−0.346343 | + | 0.938108i | \(0.612577\pi\) | |||||||
\(758\) | −65.6284 | −2.38373 | ||||||||
\(759\) | −42.2939 | −1.53517 | ||||||||
\(760\) | −73.3258 | −2.65980 | ||||||||
\(761\) | −39.9263 | −1.44733 | −0.723664 | − | 0.690153i | \(-0.757543\pi\) | ||||
−0.723664 | + | 0.690153i | \(0.757543\pi\) | |||||||
\(762\) | −168.354 | −6.09883 | ||||||||
\(763\) | 23.7884 | 0.861196 | ||||||||
\(764\) | −50.4871 | −1.82656 | ||||||||
\(765\) | 61.8703 | 2.23693 | ||||||||
\(766\) | 39.0479 | 1.41086 | ||||||||
\(767\) | −36.6293 | −1.32261 | ||||||||
\(768\) | −12.0555 | −0.435017 | ||||||||
\(769\) | −1.91460 | −0.0690422 | −0.0345211 | − | 0.999404i | \(-0.510991\pi\) | ||||
−0.0345211 | + | 0.999404i | \(0.510991\pi\) | |||||||
\(770\) | 56.9738 | 2.05319 | ||||||||
\(771\) | 11.9184 | 0.429232 | ||||||||
\(772\) | −71.5226 | −2.57415 | ||||||||
\(773\) | −15.7324 | −0.565854 | −0.282927 | − | 0.959141i | \(-0.591305\pi\) | ||||
−0.282927 | + | 0.959141i | \(0.591305\pi\) | |||||||
\(774\) | 34.5327 | 1.24125 | ||||||||
\(775\) | 26.8368 | 0.964005 | ||||||||
\(776\) | −44.2374 | −1.58803 | ||||||||
\(777\) | 82.5868 | 2.96279 | ||||||||
\(778\) | −2.05454 | −0.0736587 | ||||||||
\(779\) | 23.4546 | 0.840349 | ||||||||
\(780\) | −109.677 | −3.92705 | ||||||||
\(781\) | 30.1715 | 1.07962 | ||||||||
\(782\) | −51.8377 | −1.85371 | ||||||||
\(783\) | −17.9588 | −0.641796 | ||||||||
\(784\) | 152.546 | 5.44807 | ||||||||
\(785\) | 3.61817 | 0.129138 | ||||||||
\(786\) | 52.7775 | 1.88251 | ||||||||
\(787\) | −17.4189 | −0.620917 | −0.310459 | − | 0.950587i | \(-0.600483\pi\) | ||||
−0.310459 | + | 0.950587i | \(0.600483\pi\) | |||||||
\(788\) | −29.4574 | −1.04938 | ||||||||
\(789\) | 88.3981 | 3.14705 | ||||||||
\(790\) | 2.17023 | 0.0772134 | ||||||||
\(791\) | 44.3353 | 1.57638 | ||||||||
\(792\) | 298.753 | 10.6157 | ||||||||
\(793\) | 80.1650 | 2.84674 | ||||||||
\(794\) | −77.7607 | −2.75962 | ||||||||
\(795\) | −9.71320 | −0.344492 | ||||||||
\(796\) | −60.4962 | −2.14423 | ||||||||
\(797\) | −48.8965 | −1.73200 | −0.866001 | − | 0.500043i | \(-0.833318\pi\) | ||||
−0.866001 | + | 0.500043i | \(0.833318\pi\) | |||||||
\(798\) | 319.606 | 11.3139 | ||||||||
\(799\) | 35.0229 | 1.23902 | ||||||||
\(800\) | 56.8236 | 2.00902 | ||||||||
\(801\) | 21.0216 | 0.742762 | ||||||||
\(802\) | −39.2386 | −1.38556 | ||||||||
\(803\) | −48.2483 | −1.70264 | ||||||||
\(804\) | 6.00808 | 0.211889 | ||||||||
\(805\) | −14.3301 | −0.505070 | ||||||||
\(806\) | −109.195 | −3.84621 | ||||||||
\(807\) | −82.5920 | −2.90738 | ||||||||
\(808\) | 41.8850 | 1.47351 | ||||||||
\(809\) | 51.7985 | 1.82114 | 0.910570 | − | 0.413355i | \(-0.135643\pi\) | ||||
0.910570 | + | 0.413355i | \(0.135643\pi\) | |||||||
\(810\) | 104.732 | 3.67992 | ||||||||
\(811\) | −14.4334 | −0.506826 | −0.253413 | − | 0.967358i | \(-0.581553\pi\) | ||||
−0.253413 | + | 0.967358i | \(0.581553\pi\) | |||||||
\(812\) | −22.7561 | −0.798581 | ||||||||
\(813\) | 83.4990 | 2.92844 | ||||||||
\(814\) | 63.5196 | 2.22636 | ||||||||
\(815\) | −27.1374 | −0.950583 | ||||||||
\(816\) | 267.601 | 9.36792 | ||||||||
\(817\) | 12.4208 | 0.434547 | ||||||||
\(818\) | −46.4858 | −1.62534 | ||||||||
\(819\) | 213.844 | 7.47231 | ||||||||
\(820\) | 16.6063 | 0.579918 | ||||||||
\(821\) | 4.70525 | 0.164214 | 0.0821071 | − | 0.996624i | \(-0.473835\pi\) | ||||
0.0821071 | + | 0.996624i | \(0.473835\pi\) | |||||||
\(822\) | −116.931 | −4.07844 | ||||||||
\(823\) | 54.5921 | 1.90296 | 0.951480 | − | 0.307711i | \(-0.0995629\pi\) | ||||
0.951480 | + | 0.307711i | \(0.0995629\pi\) | |||||||
\(824\) | 107.535 | 3.74617 | ||||||||
\(825\) | −54.9729 | −1.91391 | ||||||||
\(826\) | 75.5745 | 2.62957 | ||||||||
\(827\) | 8.81000 | 0.306354 | 0.153177 | − | 0.988199i | \(-0.451050\pi\) | ||||
0.153177 | + | 0.988199i | \(0.451050\pi\) | |||||||
\(828\) | −123.520 | −4.29262 | ||||||||
\(829\) | 2.67669 | 0.0929654 | 0.0464827 | − | 0.998919i | \(-0.485199\pi\) | ||||
0.0464827 | + | 0.998919i | \(0.485199\pi\) | |||||||
\(830\) | 12.2718 | 0.425961 | ||||||||
\(831\) | −3.36665 | −0.116788 | ||||||||
\(832\) | −94.5907 | −3.27934 | ||||||||
\(833\) | −86.1511 | −2.98496 | ||||||||
\(834\) | −134.119 | −4.64416 | ||||||||
\(835\) | −10.9940 | −0.380461 | ||||||||
\(836\) | 176.636 | 6.10910 | ||||||||
\(837\) | 127.760 | 4.41604 | ||||||||
\(838\) | −8.46960 | −0.292577 | ||||||||
\(839\) | −40.3416 | −1.39275 | −0.696373 | − | 0.717680i | \(-0.745204\pi\) | ||||
−0.696373 | + | 0.717680i | \(0.745204\pi\) | |||||||
\(840\) | 137.661 | 4.74974 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.88085 | −0.0648183 | ||||||||
\(843\) | 5.92499 | 0.204068 | ||||||||
\(844\) | −22.4131 | −0.771491 | ||||||||
\(845\) | −22.3282 | −0.768112 | ||||||||
\(846\) | 116.139 | 3.99293 | ||||||||
\(847\) | −34.4736 | −1.18453 | ||||||||
\(848\) | −30.8918 | −1.06083 | ||||||||
\(849\) | −16.7697 | −0.575535 | ||||||||
\(850\) | −67.3778 | −2.31104 | ||||||||
\(851\) | −15.9765 | −0.547668 | ||||||||
\(852\) | 119.835 | 4.10547 | ||||||||
\(853\) | 8.28156 | 0.283555 | 0.141778 | − | 0.989899i | \(-0.454718\pi\) | ||||
0.141778 | + | 0.989899i | \(0.454718\pi\) | |||||||
\(854\) | −165.398 | −5.65981 | ||||||||
\(855\) | 73.7944 | 2.52372 | ||||||||
\(856\) | −11.8774 | −0.405960 | ||||||||
\(857\) | −45.7888 | −1.56412 | −0.782058 | − | 0.623206i | \(-0.785830\pi\) | ||||
−0.782058 | + | 0.623206i | \(0.785830\pi\) | |||||||
\(858\) | 223.676 | 7.63617 | ||||||||
\(859\) | −50.9471 | −1.73829 | −0.869146 | − | 0.494556i | \(-0.835331\pi\) | ||||
−0.869146 | + | 0.494556i | \(0.835331\pi\) | |||||||
\(860\) | 8.79414 | 0.299878 | ||||||||
\(861\) | −44.0333 | −1.50065 | ||||||||
\(862\) | −69.9889 | −2.38383 | ||||||||
\(863\) | 0.804565 | 0.0273877 | 0.0136939 | − | 0.999906i | \(-0.495641\pi\) | ||||
0.0136939 | + | 0.999906i | \(0.495641\pi\) | |||||||
\(864\) | 270.517 | 9.20316 | ||||||||
\(865\) | −5.99202 | −0.203735 | ||||||||
\(866\) | −9.21282 | −0.313064 | ||||||||
\(867\) | −93.8963 | −3.18888 | ||||||||
\(868\) | 161.888 | 5.49484 | ||||||||
\(869\) | −3.18038 | −0.107887 | ||||||||
\(870\) | −9.94404 | −0.337135 | ||||||||
\(871\) | 2.01218 | 0.0681801 | ||||||||
\(872\) | 44.2076 | 1.49706 | ||||||||
\(873\) | 44.5202 | 1.50678 | ||||||||
\(874\) | −61.8282 | −2.09137 | ||||||||
\(875\) | −43.3136 | −1.46427 | ||||||||
\(876\) | −191.632 | −6.47463 | ||||||||
\(877\) | 26.8808 | 0.907699 | 0.453850 | − | 0.891078i | \(-0.350050\pi\) | ||||
0.453850 | + | 0.891078i | \(0.350050\pi\) | |||||||
\(878\) | −35.1965 | −1.18782 | ||||||||
\(879\) | −1.90209 | −0.0641558 | ||||||||
\(880\) | 56.8970 | 1.91800 | ||||||||
\(881\) | 13.8169 | 0.465505 | 0.232752 | − | 0.972536i | \(-0.425227\pi\) | ||||
0.232752 | + | 0.972536i | \(0.425227\pi\) | |||||||
\(882\) | −285.683 | −9.61946 | ||||||||
\(883\) | 43.6135 | 1.46771 | 0.733856 | − | 0.679306i | \(-0.237719\pi\) | ||||
0.733856 | + | 0.679306i | \(0.237719\pi\) | |||||||
\(884\) | 196.995 | 6.62566 | ||||||||
\(885\) | 23.7306 | 0.797696 | ||||||||
\(886\) | −58.3288 | −1.95960 | ||||||||
\(887\) | −18.8824 | −0.634008 | −0.317004 | − | 0.948424i | \(-0.602677\pi\) | ||||
−0.317004 | + | 0.948424i | \(0.602677\pi\) | |||||||
\(888\) | 153.477 | 5.15034 | ||||||||
\(889\) | 83.5928 | 2.80361 | ||||||||
\(890\) | 7.45006 | 0.249727 | ||||||||
\(891\) | −153.481 | −5.14180 | ||||||||
\(892\) | 41.4399 | 1.38751 | ||||||||
\(893\) | 41.7728 | 1.39787 | ||||||||
\(894\) | 45.8432 | 1.53323 | ||||||||
\(895\) | 0.425725 | 0.0142304 | ||||||||
\(896\) | 60.9105 | 2.03488 | ||||||||
\(897\) | −56.2592 | −1.87844 | ||||||||
\(898\) | −6.76711 | −0.225821 | ||||||||
\(899\) | −7.11406 | −0.237267 | ||||||||
\(900\) | −160.550 | −5.35165 | ||||||||
\(901\) | 17.4463 | 0.581221 | ||||||||
\(902\) | −33.8672 | −1.12765 | ||||||||
\(903\) | −23.3185 | −0.775992 | ||||||||
\(904\) | 82.3913 | 2.74030 | ||||||||
\(905\) | 15.6789 | 0.521185 | ||||||||
\(906\) | −144.990 | −4.81696 | ||||||||
\(907\) | −8.07972 | −0.268283 | −0.134141 | − | 0.990962i | \(-0.542828\pi\) | ||||
−0.134141 | + | 0.990962i | \(0.542828\pi\) | |||||||
\(908\) | 6.00781 | 0.199376 | ||||||||
\(909\) | −42.1527 | −1.39812 | ||||||||
\(910\) | 75.7863 | 2.51229 | ||||||||
\(911\) | −25.6534 | −0.849935 | −0.424967 | − | 0.905209i | \(-0.639714\pi\) | ||||
−0.424967 | + | 0.905209i | \(0.639714\pi\) | |||||||
\(912\) | 319.175 | 10.5690 | ||||||||
\(913\) | −17.9838 | −0.595178 | ||||||||
\(914\) | −19.4013 | −0.641739 | ||||||||
\(915\) | −51.9356 | −1.71694 | ||||||||
\(916\) | −0.137370 | −0.00453884 | ||||||||
\(917\) | −26.2056 | −0.865385 | ||||||||
\(918\) | −320.761 | −10.5867 | ||||||||
\(919\) | −0.259809 | −0.00857031 | −0.00428516 | − | 0.999991i | \(-0.501364\pi\) | ||||
−0.00428516 | + | 0.999991i | \(0.501364\pi\) | |||||||
\(920\) | −26.6306 | −0.877986 | ||||||||
\(921\) | 88.1428 | 2.90440 | ||||||||
\(922\) | −26.9343 | −0.887035 | ||||||||
\(923\) | 40.1341 | 1.32103 | ||||||||
\(924\) | −331.614 | −10.9093 | ||||||||
\(925\) | −20.7660 | −0.682783 | ||||||||
\(926\) | 10.3203 | 0.339145 | ||||||||
\(927\) | −108.223 | −3.55450 | ||||||||
\(928\) | −15.0632 | −0.494472 | ||||||||
\(929\) | 38.1853 | 1.25282 | 0.626409 | − | 0.779495i | \(-0.284524\pi\) | ||||
0.626409 | + | 0.779495i | \(0.284524\pi\) | |||||||
\(930\) | 70.7425 | 2.31974 | ||||||||
\(931\) | −102.755 | −3.36765 | ||||||||
\(932\) | 100.785 | 3.30131 | ||||||||
\(933\) | 19.9744 | 0.653933 | ||||||||
\(934\) | −62.0413 | −2.03005 | ||||||||
\(935\) | −32.1329 | −1.05086 | ||||||||
\(936\) | 397.401 | 12.9895 | ||||||||
\(937\) | −11.2206 | −0.366562 | −0.183281 | − | 0.983061i | \(-0.558672\pi\) | ||||
−0.183281 | + | 0.983061i | \(0.558672\pi\) | |||||||
\(938\) | −4.15157 | −0.135554 | ||||||||
\(939\) | 60.7874 | 1.98372 | ||||||||
\(940\) | 29.5760 | 0.964662 | ||||||||
\(941\) | −5.85844 | −0.190980 | −0.0954898 | − | 0.995430i | \(-0.530442\pi\) | ||||
−0.0954898 | + | 0.995430i | \(0.530442\pi\) | |||||||
\(942\) | −29.3075 | −0.954890 | ||||||||
\(943\) | 8.51831 | 0.277394 | ||||||||
\(944\) | 75.4727 | 2.45643 | ||||||||
\(945\) | −88.6719 | −2.88450 | ||||||||
\(946\) | −17.9349 | −0.583113 | ||||||||
\(947\) | 8.63521 | 0.280607 | 0.140303 | − | 0.990109i | \(-0.455192\pi\) | ||||
0.140303 | + | 0.990109i | \(0.455192\pi\) | |||||||
\(948\) | −12.6318 | −0.410261 | ||||||||
\(949\) | −64.1797 | −2.08336 | ||||||||
\(950\) | −80.3633 | −2.60733 | ||||||||
\(951\) | −75.8268 | −2.45885 | ||||||||
\(952\) | −247.258 | −8.01368 | ||||||||
\(953\) | 23.4163 | 0.758528 | 0.379264 | − | 0.925288i | \(-0.376177\pi\) | ||||
0.379264 | + | 0.925288i | \(0.376177\pi\) | |||||||
\(954\) | 57.8532 | 1.87307 | ||||||||
\(955\) | 10.9545 | 0.354478 | ||||||||
\(956\) | 63.8418 | 2.06479 | ||||||||
\(957\) | 14.5726 | 0.471064 | ||||||||
\(958\) | −48.8602 | −1.57860 | ||||||||
\(959\) | 58.0597 | 1.87485 | ||||||||
\(960\) | 61.2813 | 1.97785 | ||||||||
\(961\) | 19.6099 | 0.632577 | ||||||||
\(962\) | 84.4937 | 2.72419 | ||||||||
\(963\) | 11.9533 | 0.385189 | ||||||||
\(964\) | −44.6211 | −1.43715 | ||||||||
\(965\) | 15.5186 | 0.499563 | ||||||||
\(966\) | 116.075 | 3.73466 | ||||||||
\(967\) | −15.3480 | −0.493560 | −0.246780 | − | 0.969072i | \(-0.579372\pi\) | ||||
−0.246780 | + | 0.969072i | \(0.579372\pi\) | |||||||
\(968\) | −64.0648 | −2.05912 | ||||||||
\(969\) | −180.256 | −5.79066 | ||||||||
\(970\) | 15.7780 | 0.506600 | ||||||||
\(971\) | −41.9796 | −1.34719 | −0.673594 | − | 0.739101i | \(-0.735250\pi\) | ||||
−0.673594 | + | 0.739101i | \(0.735250\pi\) | |||||||
\(972\) | −334.470 | −10.7281 | ||||||||
\(973\) | 66.5940 | 2.13491 | ||||||||
\(974\) | 65.7053 | 2.10533 | ||||||||
\(975\) | −73.1248 | −2.34187 | ||||||||
\(976\) | −165.175 | −5.28714 | ||||||||
\(977\) | −4.93207 | −0.157791 | −0.0788955 | − | 0.996883i | \(-0.525139\pi\) | ||||
−0.0788955 | + | 0.996883i | \(0.525139\pi\) | |||||||
\(978\) | 219.816 | 7.02894 | ||||||||
\(979\) | −10.9178 | −0.348933 | ||||||||
\(980\) | −72.7524 | −2.32399 | ||||||||
\(981\) | −44.4901 | −1.42046 | ||||||||
\(982\) | 61.5803 | 1.96511 | ||||||||
\(983\) | −35.9897 | −1.14789 | −0.573947 | − | 0.818893i | \(-0.694588\pi\) | ||||
−0.573947 | + | 0.818893i | \(0.694588\pi\) | |||||||
\(984\) | −81.8302 | −2.60865 | ||||||||
\(985\) | 6.39153 | 0.203651 | ||||||||
\(986\) | 17.8609 | 0.568808 | ||||||||
\(987\) | −78.4236 | −2.49625 | ||||||||
\(988\) | 234.961 | 7.47512 | ||||||||
\(989\) | 4.51100 | 0.143441 | ||||||||
\(990\) | −106.555 | −3.38654 | ||||||||
\(991\) | 13.1905 | 0.419010 | 0.209505 | − | 0.977808i | \(-0.432815\pi\) | ||||
0.209505 | + | 0.977808i | \(0.432815\pi\) | |||||||
\(992\) | 107.160 | 3.40234 | ||||||||
\(993\) | −47.1044 | −1.49481 | ||||||||
\(994\) | −82.8055 | −2.62643 | ||||||||
\(995\) | 13.1262 | 0.416128 | ||||||||
\(996\) | −71.4278 | −2.26328 | ||||||||
\(997\) | 5.61341 | 0.177778 | 0.0888892 | − | 0.996042i | \(-0.471668\pi\) | ||||
0.0888892 | + | 0.996042i | \(0.471668\pi\) | |||||||
\(998\) | 4.45019 | 0.140868 | ||||||||
\(999\) | −98.8597 | −3.12778 |
(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 | 8033.2.a.c.1.7 | ✓ | 154 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8033.2.a.c.1.7 | ✓ | 154 | 1.1 | even | 1 | trivial |