Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + 3566264 x^{5} + 15496192 x^{4} - 53008480 x^{3} - 16576192 x^{2} + \cdots - 50564480 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(1.62334\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.62334 | −0.286969 | −0.143484 | − | 0.989653i | \(-0.545831\pi\) | ||||
−0.143484 | + | 0.989653i | \(0.545831\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | −29.3648 | −0.917649 | ||||||||
\(5\) | 103.513 | 1.85169 | 0.925847 | − | 0.377899i | \(-0.123353\pi\) | ||||
0.925847 | + | 0.377899i | \(0.123353\pi\) | |||||||
\(6\) | 14.6101 | 0.165682 | ||||||||
\(7\) | −137.577 | −1.06121 | −0.530604 | − | 0.847620i | \(-0.678035\pi\) | ||||
−0.530604 | + | 0.847620i | \(0.678035\pi\) | |||||||
\(8\) | 99.6159 | 0.550305 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −168.037 | −0.531378 | ||||||||
\(11\) | −636.961 | −1.58720 | −0.793599 | − | 0.608441i | \(-0.791795\pi\) | ||||
−0.793599 | + | 0.608441i | \(0.791795\pi\) | |||||||
\(12\) | 264.283 | 0.529805 | ||||||||
\(13\) | 834.694 | 1.36984 | 0.684919 | − | 0.728619i | \(-0.259838\pi\) | ||||
0.684919 | + | 0.728619i | \(0.259838\pi\) | |||||||
\(14\) | 223.334 | 0.304534 | ||||||||
\(15\) | −931.615 | −1.06908 | ||||||||
\(16\) | 777.962 | 0.759728 | ||||||||
\(17\) | 444.945 | 0.373408 | 0.186704 | − | 0.982416i | \(-0.440219\pi\) | ||||
0.186704 | + | 0.982416i | \(0.440219\pi\) | |||||||
\(18\) | −131.491 | −0.0956563 | ||||||||
\(19\) | −513.762 | −0.326496 | −0.163248 | − | 0.986585i | \(-0.552197\pi\) | ||||
−0.163248 | + | 0.986585i | \(0.552197\pi\) | |||||||
\(20\) | −3039.63 | −1.69920 | ||||||||
\(21\) | 1238.19 | 0.612689 | ||||||||
\(22\) | 1034.01 | 0.455477 | ||||||||
\(23\) | 3568.14 | 1.40644 | 0.703221 | − | 0.710971i | \(-0.251745\pi\) | ||||
0.703221 | + | 0.710971i | \(0.251745\pi\) | |||||||
\(24\) | −896.543 | −0.317719 | ||||||||
\(25\) | 7589.90 | 2.42877 | ||||||||
\(26\) | −1354.99 | −0.393101 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 4039.91 | 0.973816 | ||||||||
\(29\) | −6879.19 | −1.51895 | −0.759473 | − | 0.650538i | \(-0.774543\pi\) | ||||
−0.759473 | + | 0.650538i | \(0.774543\pi\) | |||||||
\(30\) | 1512.33 | 0.306791 | ||||||||
\(31\) | −3639.93 | −0.680281 | −0.340140 | − | 0.940375i | \(-0.610475\pi\) | ||||
−0.340140 | + | 0.940375i | \(0.610475\pi\) | |||||||
\(32\) | −4450.61 | −0.768324 | ||||||||
\(33\) | 5732.65 | 0.916370 | ||||||||
\(34\) | −722.298 | −0.107157 | ||||||||
\(35\) | −14241.0 | −1.96503 | ||||||||
\(36\) | −2378.55 | −0.305883 | ||||||||
\(37\) | −7911.65 | −0.950086 | −0.475043 | − | 0.879963i | \(-0.657568\pi\) | ||||
−0.475043 | + | 0.879963i | \(0.657568\pi\) | |||||||
\(38\) | 834.010 | 0.0936941 | ||||||||
\(39\) | −7512.25 | −0.790876 | ||||||||
\(40\) | 10311.5 | 1.01900 | ||||||||
\(41\) | −19911.3 | −1.84986 | −0.924931 | − | 0.380135i | \(-0.875878\pi\) | ||||
−0.924931 | + | 0.380135i | \(0.875878\pi\) | |||||||
\(42\) | −2010.01 | −0.175823 | ||||||||
\(43\) | −2563.64 | −0.211440 | −0.105720 | − | 0.994396i | \(-0.533715\pi\) | ||||
−0.105720 | + | 0.994396i | \(0.533715\pi\) | |||||||
\(44\) | 18704.2 | 1.45649 | ||||||||
\(45\) | 8384.54 | 0.617231 | ||||||||
\(46\) | −5792.30 | −0.403605 | ||||||||
\(47\) | −22255.9 | −1.46961 | −0.734803 | − | 0.678281i | \(-0.762725\pi\) | ||||
−0.734803 | + | 0.678281i | \(0.762725\pi\) | |||||||
\(48\) | −7001.66 | −0.438629 | ||||||||
\(49\) | 2120.41 | 0.126162 | ||||||||
\(50\) | −12321.0 | −0.696981 | ||||||||
\(51\) | −4004.51 | −0.215587 | ||||||||
\(52\) | −24510.6 | −1.25703 | ||||||||
\(53\) | 29943.8 | 1.46426 | 0.732129 | − | 0.681166i | \(-0.238527\pi\) | ||||
0.732129 | + | 0.681166i | \(0.238527\pi\) | |||||||
\(54\) | 1183.42 | 0.0552272 | ||||||||
\(55\) | −65933.7 | −2.93901 | ||||||||
\(56\) | −13704.9 | −0.583989 | ||||||||
\(57\) | 4623.85 | 0.188502 | ||||||||
\(58\) | 11167.3 | 0.435890 | ||||||||
\(59\) | −3481.00 | −0.130189 | ||||||||
\(60\) | 27356.7 | 0.981036 | ||||||||
\(61\) | −34505.5 | −1.18731 | −0.593655 | − | 0.804720i | \(-0.702316\pi\) | ||||
−0.593655 | + | 0.804720i | \(0.702316\pi\) | |||||||
\(62\) | 5908.84 | 0.195219 | ||||||||
\(63\) | −11143.7 | −0.353736 | ||||||||
\(64\) | −17669.9 | −0.539243 | ||||||||
\(65\) | 86401.6 | 2.53652 | ||||||||
\(66\) | −9306.05 | −0.262970 | ||||||||
\(67\) | 49378.2 | 1.34384 | 0.671921 | − | 0.740623i | \(-0.265470\pi\) | ||||
0.671921 | + | 0.740623i | \(0.265470\pi\) | |||||||
\(68\) | −13065.7 | −0.342658 | ||||||||
\(69\) | −32113.2 | −0.812010 | ||||||||
\(70\) | 23118.0 | 0.563903 | ||||||||
\(71\) | −32409.2 | −0.762996 | −0.381498 | − | 0.924370i | \(-0.624592\pi\) | ||||
−0.381498 | + | 0.924370i | \(0.624592\pi\) | |||||||
\(72\) | 8068.89 | 0.183435 | ||||||||
\(73\) | −7831.86 | −0.172012 | −0.0860058 | − | 0.996295i | \(-0.527410\pi\) | ||||
−0.0860058 | + | 0.996295i | \(0.527410\pi\) | |||||||
\(74\) | 12843.3 | 0.272645 | ||||||||
\(75\) | −68309.1 | −1.40225 | ||||||||
\(76\) | 15086.5 | 0.299609 | ||||||||
\(77\) | 87631.2 | 1.68435 | ||||||||
\(78\) | 12194.9 | 0.226957 | ||||||||
\(79\) | −69257.0 | −1.24852 | −0.624261 | − | 0.781216i | \(-0.714600\pi\) | ||||
−0.624261 | + | 0.781216i | \(0.714600\pi\) | |||||||
\(80\) | 80529.0 | 1.40678 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 32322.8 | 0.530853 | ||||||||
\(83\) | −30470.2 | −0.485489 | −0.242745 | − | 0.970090i | \(-0.578048\pi\) | ||||
−0.242745 | + | 0.970090i | \(0.578048\pi\) | |||||||
\(84\) | −36359.2 | −0.562233 | ||||||||
\(85\) | 46057.5 | 0.691438 | ||||||||
\(86\) | 4161.67 | 0.0606766 | ||||||||
\(87\) | 61912.7 | 0.876964 | ||||||||
\(88\) | −63451.5 | −0.873444 | ||||||||
\(89\) | 20158.9 | 0.269769 | 0.134884 | − | 0.990861i | \(-0.456934\pi\) | ||||
0.134884 | + | 0.990861i | \(0.456934\pi\) | |||||||
\(90\) | −13611.0 | −0.177126 | ||||||||
\(91\) | −114835. | −1.45368 | ||||||||
\(92\) | −104777. | −1.29062 | ||||||||
\(93\) | 32759.3 | 0.392760 | ||||||||
\(94\) | 36128.9 | 0.421731 | ||||||||
\(95\) | −53180.9 | −0.604570 | ||||||||
\(96\) | 40055.5 | 0.443592 | ||||||||
\(97\) | −91622.0 | −0.988713 | −0.494357 | − | 0.869259i | \(-0.664596\pi\) | ||||
−0.494357 | + | 0.869259i | \(0.664596\pi\) | |||||||
\(98\) | −3442.14 | −0.0362046 | ||||||||
\(99\) | −51593.9 | −0.529066 | ||||||||
\(100\) | −222876. | −2.22876 | ||||||||
\(101\) | −95282.8 | −0.929418 | −0.464709 | − | 0.885464i | \(-0.653841\pi\) | ||||
−0.464709 | + | 0.885464i | \(0.653841\pi\) | |||||||
\(102\) | 6500.68 | 0.0618669 | ||||||||
\(103\) | −9335.09 | −0.0867013 | −0.0433506 | − | 0.999060i | \(-0.513803\pi\) | ||||
−0.0433506 | + | 0.999060i | \(0.513803\pi\) | |||||||
\(104\) | 83148.9 | 0.753829 | ||||||||
\(105\) | 128169. | 1.13451 | ||||||||
\(106\) | −48609.0 | −0.420196 | ||||||||
\(107\) | −191457. | −1.61663 | −0.808315 | − | 0.588750i | \(-0.799620\pi\) | ||||
−0.808315 | + | 0.588750i | \(0.799620\pi\) | |||||||
\(108\) | 21406.9 | 0.176602 | ||||||||
\(109\) | −49018.5 | −0.395179 | −0.197589 | − | 0.980285i | \(-0.563311\pi\) | ||||
−0.197589 | + | 0.980285i | \(0.563311\pi\) | |||||||
\(110\) | 107033. | 0.843403 | ||||||||
\(111\) | 71204.9 | 0.548533 | ||||||||
\(112\) | −107030. | −0.806230 | ||||||||
\(113\) | 194538. | 1.43321 | 0.716603 | − | 0.697481i | \(-0.245696\pi\) | ||||
0.716603 | + | 0.697481i | \(0.245696\pi\) | |||||||
\(114\) | −7506.09 | −0.0540943 | ||||||||
\(115\) | 369348. | 2.60430 | ||||||||
\(116\) | 202006. | 1.39386 | ||||||||
\(117\) | 67610.2 | 0.456613 | ||||||||
\(118\) | 5650.85 | 0.0373602 | ||||||||
\(119\) | −61214.2 | −0.396264 | ||||||||
\(120\) | −92803.7 | −0.588318 | ||||||||
\(121\) | 244669. | 1.51920 | ||||||||
\(122\) | 56014.2 | 0.340721 | ||||||||
\(123\) | 179201. | 1.06802 | ||||||||
\(124\) | 106886. | 0.624259 | ||||||||
\(125\) | 462175. | 2.64564 | ||||||||
\(126\) | 18090.1 | 0.101511 | ||||||||
\(127\) | −14170.2 | −0.0779593 | −0.0389796 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389796 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(128\) | 171104. | 0.923070 | ||||||||
\(129\) | 23072.8 | 0.122075 | ||||||||
\(130\) | −140259. | −0.727902 | ||||||||
\(131\) | 194270. | 0.989069 | 0.494534 | − | 0.869158i | \(-0.335339\pi\) | ||||
0.494534 | + | 0.869158i | \(0.335339\pi\) | |||||||
\(132\) | −168338. | −0.840906 | ||||||||
\(133\) | 70681.7 | 0.346480 | ||||||||
\(134\) | −80157.6 | −0.385641 | ||||||||
\(135\) | −75460.8 | −0.356359 | ||||||||
\(136\) | 44323.6 | 0.205489 | ||||||||
\(137\) | −224935. | −1.02389 | −0.511947 | − | 0.859017i | \(-0.671076\pi\) | ||||
−0.511947 | + | 0.859017i | \(0.671076\pi\) | |||||||
\(138\) | 52130.7 | 0.233021 | ||||||||
\(139\) | −94653.9 | −0.415529 | −0.207765 | − | 0.978179i | \(-0.566619\pi\) | ||||
−0.207765 | + | 0.978179i | \(0.566619\pi\) | |||||||
\(140\) | 418183. | 1.80321 | ||||||||
\(141\) | 200303. | 0.848477 | ||||||||
\(142\) | 52611.2 | 0.218956 | ||||||||
\(143\) | −531668. | −2.17420 | ||||||||
\(144\) | 63014.9 | 0.253243 | ||||||||
\(145\) | −712085. | −2.81262 | ||||||||
\(146\) | 12713.8 | 0.0493620 | ||||||||
\(147\) | −19083.7 | −0.0728397 | ||||||||
\(148\) | 232324. | 0.871846 | ||||||||
\(149\) | 31008.8 | 0.114425 | 0.0572123 | − | 0.998362i | \(-0.481779\pi\) | ||||
0.0572123 | + | 0.998362i | \(0.481779\pi\) | |||||||
\(150\) | 110889. | 0.402402 | ||||||||
\(151\) | −74478.6 | −0.265821 | −0.132910 | − | 0.991128i | \(-0.542432\pi\) | ||||
−0.132910 | + | 0.991128i | \(0.542432\pi\) | |||||||
\(152\) | −51178.8 | −0.179672 | ||||||||
\(153\) | 36040.6 | 0.124469 | ||||||||
\(154\) | −142255. | −0.483355 | ||||||||
\(155\) | −376779. | −1.25967 | ||||||||
\(156\) | 220595. | 0.725747 | ||||||||
\(157\) | 438750. | 1.42059 | 0.710293 | − | 0.703906i | \(-0.248562\pi\) | ||||
0.710293 | + | 0.703906i | \(0.248562\pi\) | |||||||
\(158\) | 112428. | 0.358287 | ||||||||
\(159\) | −269494. | −0.845390 | ||||||||
\(160\) | −460695. | −1.42270 | ||||||||
\(161\) | −490893. | −1.49253 | ||||||||
\(162\) | −10650.7 | −0.0318854 | ||||||||
\(163\) | 489187. | 1.44214 | 0.721068 | − | 0.692864i | \(-0.243651\pi\) | ||||
0.721068 | + | 0.692864i | \(0.243651\pi\) | |||||||
\(164\) | 584690. | 1.69752 | ||||||||
\(165\) | 593403. | 1.69684 | ||||||||
\(166\) | 49463.5 | 0.139320 | ||||||||
\(167\) | 277073. | 0.768781 | 0.384391 | − | 0.923171i | \(-0.374412\pi\) | ||||
0.384391 | + | 0.923171i | \(0.374412\pi\) | |||||||
\(168\) | 123344. | 0.337166 | ||||||||
\(169\) | 325422. | 0.876455 | ||||||||
\(170\) | −74767.1 | −0.198421 | ||||||||
\(171\) | −41614.7 | −0.108832 | ||||||||
\(172\) | 75280.8 | 0.194027 | ||||||||
\(173\) | −402349. | −1.02209 | −0.511043 | − | 0.859555i | \(-0.670741\pi\) | ||||
−0.511043 | + | 0.859555i | \(0.670741\pi\) | |||||||
\(174\) | −100506. | −0.251661 | ||||||||
\(175\) | −1.04420e6 | −2.57743 | ||||||||
\(176\) | −495532. | −1.20584 | ||||||||
\(177\) | 31329.0 | 0.0751646 | ||||||||
\(178\) | −32724.7 | −0.0774152 | ||||||||
\(179\) | −492255. | −1.14831 | −0.574153 | − | 0.818748i | \(-0.694668\pi\) | ||||
−0.574153 | + | 0.818748i | \(0.694668\pi\) | |||||||
\(180\) | −246210. | −0.566401 | ||||||||
\(181\) | 83424.0 | 0.189276 | 0.0946378 | − | 0.995512i | \(-0.469831\pi\) | ||||
0.0946378 | + | 0.995512i | \(0.469831\pi\) | |||||||
\(182\) | 186416. | 0.417162 | ||||||||
\(183\) | 310550. | 0.685494 | ||||||||
\(184\) | 355443. | 0.773973 | ||||||||
\(185\) | −818958. | −1.75927 | ||||||||
\(186\) | −53179.6 | −0.112710 | ||||||||
\(187\) | −283413. | −0.592673 | ||||||||
\(188\) | 653540. | 1.34858 | ||||||||
\(189\) | 100294. | 0.204230 | ||||||||
\(190\) | 86330.8 | 0.173493 | ||||||||
\(191\) | 761817. | 1.51101 | 0.755505 | − | 0.655143i | \(-0.227392\pi\) | ||||
0.755505 | + | 0.655143i | \(0.227392\pi\) | |||||||
\(192\) | 159029. | 0.311332 | ||||||||
\(193\) | −245032. | −0.473510 | −0.236755 | − | 0.971569i | \(-0.576084\pi\) | ||||
−0.236755 | + | 0.971569i | \(0.576084\pi\) | |||||||
\(194\) | 148734. | 0.283730 | ||||||||
\(195\) | −777614. | −1.46446 | ||||||||
\(196\) | −62265.3 | −0.115773 | ||||||||
\(197\) | 40850.3 | 0.0749945 | 0.0374973 | − | 0.999297i | \(-0.488061\pi\) | ||||
0.0374973 | + | 0.999297i | \(0.488061\pi\) | |||||||
\(198\) | 83754.4 | 0.151826 | ||||||||
\(199\) | −167233. | −0.299357 | −0.149679 | − | 0.988735i | \(-0.547824\pi\) | ||||
−0.149679 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(200\) | 756075. | 1.33656 | ||||||||
\(201\) | −444404. | −0.775867 | ||||||||
\(202\) | 154676. | 0.266714 | ||||||||
\(203\) | 946418. | 1.61192 | ||||||||
\(204\) | 117591. | 0.197834 | ||||||||
\(205\) | −2.06107e6 | −3.42538 | ||||||||
\(206\) | 15154.0 | 0.0248806 | ||||||||
\(207\) | 289019. | 0.468814 | ||||||||
\(208\) | 649360. | 1.04070 | ||||||||
\(209\) | 327246. | 0.518214 | ||||||||
\(210\) | −208062. | −0.325569 | ||||||||
\(211\) | −489590. | −0.757054 | −0.378527 | − | 0.925590i | \(-0.623569\pi\) | ||||
−0.378527 | + | 0.925590i | \(0.623569\pi\) | |||||||
\(212\) | −879293. | −1.34367 | ||||||||
\(213\) | 291683. | 0.440516 | ||||||||
\(214\) | 310799. | 0.463923 | ||||||||
\(215\) | −265370. | −0.391521 | ||||||||
\(216\) | −72620.0 | −0.105906 | ||||||||
\(217\) | 500770. | 0.721919 | ||||||||
\(218\) | 79573.7 | 0.113404 | ||||||||
\(219\) | 70486.8 | 0.0993110 | ||||||||
\(220\) | 1.93613e6 | 2.69698 | ||||||||
\(221\) | 371393. | 0.511509 | ||||||||
\(222\) | −115590. | −0.157412 | ||||||||
\(223\) | −856174. | −1.15292 | −0.576461 | − | 0.817125i | \(-0.695567\pi\) | ||||
−0.576461 | + | 0.817125i | \(0.695567\pi\) | |||||||
\(224\) | 612301. | 0.815351 | ||||||||
\(225\) | 614782. | 0.809590 | ||||||||
\(226\) | −315802. | −0.411286 | ||||||||
\(227\) | −1.00899e6 | −1.29964 | −0.649821 | − | 0.760087i | \(-0.725156\pi\) | ||||
−0.649821 | + | 0.760087i | \(0.725156\pi\) | |||||||
\(228\) | −135778. | −0.172979 | ||||||||
\(229\) | −507970. | −0.640102 | −0.320051 | − | 0.947400i | \(-0.603700\pi\) | ||||
−0.320051 | + | 0.947400i | \(0.603700\pi\) | |||||||
\(230\) | −599577. | −0.747353 | ||||||||
\(231\) | −788681. | −0.972459 | ||||||||
\(232\) | −685277. | −0.835885 | ||||||||
\(233\) | −156420. | −0.188756 | −0.0943782 | − | 0.995536i | \(-0.530086\pi\) | ||||
−0.0943782 | + | 0.995536i | \(0.530086\pi\) | |||||||
\(234\) | −109754. | −0.131034 | ||||||||
\(235\) | −2.30377e6 | −2.72126 | ||||||||
\(236\) | 102219. | 0.119468 | ||||||||
\(237\) | 623313. | 0.720834 | ||||||||
\(238\) | 99371.5 | 0.113715 | ||||||||
\(239\) | 518961. | 0.587678 | 0.293839 | − | 0.955855i | \(-0.405067\pi\) | ||||
0.293839 | + | 0.955855i | \(0.405067\pi\) | |||||||
\(240\) | −724761. | −0.812207 | ||||||||
\(241\) | 151673. | 0.168216 | 0.0841079 | − | 0.996457i | \(-0.473196\pi\) | ||||
0.0841079 | + | 0.996457i | \(0.473196\pi\) | |||||||
\(242\) | −397181. | −0.435963 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | 1.01325e6 | 1.08953 | ||||||||
\(245\) | 219489. | 0.233614 | ||||||||
\(246\) | −290905. | −0.306488 | ||||||||
\(247\) | −428834. | −0.447246 | ||||||||
\(248\) | −362595. | −0.374362 | ||||||||
\(249\) | 274232. | 0.280297 | ||||||||
\(250\) | −750267. | −0.759217 | ||||||||
\(251\) | 698841. | 0.700155 | 0.350077 | − | 0.936721i | \(-0.386155\pi\) | ||||
0.350077 | + | 0.936721i | \(0.386155\pi\) | |||||||
\(252\) | 327233. | 0.324605 | ||||||||
\(253\) | −2.27276e6 | −2.23230 | ||||||||
\(254\) | 23003.1 | 0.0223719 | ||||||||
\(255\) | −414518. | −0.399202 | ||||||||
\(256\) | 287678. | 0.274351 | ||||||||
\(257\) | 460742. | 0.435136 | 0.217568 | − | 0.976045i | \(-0.430188\pi\) | ||||
0.217568 | + | 0.976045i | \(0.430188\pi\) | |||||||
\(258\) | −37455.0 | −0.0350316 | ||||||||
\(259\) | 1.08846e6 | 1.00824 | ||||||||
\(260\) | −2.53716e6 | −2.32763 | ||||||||
\(261\) | −557215. | −0.506316 | ||||||||
\(262\) | −315366. | −0.283832 | ||||||||
\(263\) | 1.07274e6 | 0.956325 | 0.478163 | − | 0.878271i | \(-0.341303\pi\) | ||||
0.478163 | + | 0.878271i | \(0.341303\pi\) | |||||||
\(264\) | 571063. | 0.504283 | ||||||||
\(265\) | 3.09957e6 | 2.71136 | ||||||||
\(266\) | −114741. | −0.0994290 | ||||||||
\(267\) | −181430. | −0.155751 | ||||||||
\(268\) | −1.44998e6 | −1.23317 | ||||||||
\(269\) | 581921. | 0.490324 | 0.245162 | − | 0.969482i | \(-0.421159\pi\) | ||||
0.245162 | + | 0.969482i | \(0.421159\pi\) | |||||||
\(270\) | 122499. | 0.102264 | ||||||||
\(271\) | −1.54968e6 | −1.28179 | −0.640897 | − | 0.767627i | \(-0.721438\pi\) | ||||
−0.640897 | + | 0.767627i | \(0.721438\pi\) | |||||||
\(272\) | 346150. | 0.283689 | ||||||||
\(273\) | 1.03351e6 | 0.839284 | ||||||||
\(274\) | 365146. | 0.293826 | ||||||||
\(275\) | −4.83447e6 | −3.85494 | ||||||||
\(276\) | 942997. | 0.745140 | ||||||||
\(277\) | 1.52988e6 | 1.19800 | 0.599000 | − | 0.800749i | \(-0.295565\pi\) | ||||
0.599000 | + | 0.800749i | \(0.295565\pi\) | |||||||
\(278\) | 153655. | 0.119244 | ||||||||
\(279\) | −294834. | −0.226760 | ||||||||
\(280\) | −1.41863e6 | −1.08137 | ||||||||
\(281\) | 942600. | 0.712134 | 0.356067 | − | 0.934460i | \(-0.384118\pi\) | ||||
0.356067 | + | 0.934460i | \(0.384118\pi\) | |||||||
\(282\) | −325161. | −0.243487 | ||||||||
\(283\) | −675204. | −0.501151 | −0.250576 | − | 0.968097i | \(-0.580620\pi\) | ||||
−0.250576 | + | 0.968097i | \(0.580620\pi\) | |||||||
\(284\) | 951688. | 0.700162 | ||||||||
\(285\) | 478628. | 0.349049 | ||||||||
\(286\) | 863079. | 0.623929 | ||||||||
\(287\) | 2.73933e6 | 1.96309 | ||||||||
\(288\) | −360499. | −0.256108 | ||||||||
\(289\) | −1.22188e6 | −0.860566 | ||||||||
\(290\) | 1.15596e6 | 0.807136 | ||||||||
\(291\) | 824598. | 0.570834 | ||||||||
\(292\) | 229981. | 0.157846 | ||||||||
\(293\) | −475173. | −0.323357 | −0.161679 | − | 0.986843i | \(-0.551691\pi\) | ||||
−0.161679 | + | 0.986843i | \(0.551691\pi\) | |||||||
\(294\) | 30979.3 | 0.0209027 | ||||||||
\(295\) | −360328. | −0.241070 | ||||||||
\(296\) | −788127. | −0.522838 | ||||||||
\(297\) | 464345. | 0.305457 | ||||||||
\(298\) | −50337.9 | −0.0328363 | ||||||||
\(299\) | 2.97830e6 | 1.92660 | ||||||||
\(300\) | 2.00588e6 | 1.28677 | ||||||||
\(301\) | 352698. | 0.224381 | ||||||||
\(302\) | 120904. | 0.0762823 | ||||||||
\(303\) | 857545. | 0.536600 | ||||||||
\(304\) | −399687. | −0.248048 | ||||||||
\(305\) | −3.57177e6 | −2.19853 | ||||||||
\(306\) | −58506.1 | −0.0357189 | ||||||||
\(307\) | 1.72181e6 | 1.04265 | 0.521325 | − | 0.853358i | \(-0.325438\pi\) | ||||
0.521325 | + | 0.853358i | \(0.325438\pi\) | |||||||
\(308\) | −2.57327e6 | −1.54564 | ||||||||
\(309\) | 84015.8 | 0.0500570 | ||||||||
\(310\) | 611641. | 0.361487 | ||||||||
\(311\) | 234169. | 0.137287 | 0.0686435 | − | 0.997641i | \(-0.478133\pi\) | ||||
0.0686435 | + | 0.997641i | \(0.478133\pi\) | |||||||
\(312\) | −748340. | −0.435224 | ||||||||
\(313\) | −425464. | −0.245472 | −0.122736 | − | 0.992439i | \(-0.539167\pi\) | ||||
−0.122736 | + | 0.992439i | \(0.539167\pi\) | |||||||
\(314\) | −712240. | −0.407664 | ||||||||
\(315\) | −1.15352e6 | −0.655011 | ||||||||
\(316\) | 2.03372e6 | 1.14570 | ||||||||
\(317\) | −3.34935e6 | −1.87203 | −0.936014 | − | 0.351963i | \(-0.885514\pi\) | ||||
−0.936014 | + | 0.351963i | \(0.885514\pi\) | |||||||
\(318\) | 437481. | 0.242601 | ||||||||
\(319\) | 4.38178e6 | 2.41087 | ||||||||
\(320\) | −1.82906e6 | −0.998513 | ||||||||
\(321\) | 1.72311e6 | 0.933362 | ||||||||
\(322\) | 796887. | 0.428309 | ||||||||
\(323\) | −228596. | −0.121916 | ||||||||
\(324\) | −192662. | −0.101961 | ||||||||
\(325\) | 6.33525e6 | 3.32702 | ||||||||
\(326\) | −794118. | −0.413848 | ||||||||
\(327\) | 441166. | 0.228157 | ||||||||
\(328\) | −1.98348e6 | −1.01799 | ||||||||
\(329\) | 3.06190e6 | 1.55956 | ||||||||
\(330\) | −963295. | −0.486939 | ||||||||
\(331\) | −3.15018e6 | −1.58039 | −0.790197 | − | 0.612853i | \(-0.790022\pi\) | ||||
−0.790197 | + | 0.612853i | \(0.790022\pi\) | |||||||
\(332\) | 894750. | 0.445509 | ||||||||
\(333\) | −640844. | −0.316695 | ||||||||
\(334\) | −449784. | −0.220616 | ||||||||
\(335\) | 5.11127e6 | 2.48838 | ||||||||
\(336\) | 963266. | 0.465477 | ||||||||
\(337\) | 1.88668e6 | 0.904950 | 0.452475 | − | 0.891777i | \(-0.350541\pi\) | ||||
0.452475 | + | 0.891777i | \(0.350541\pi\) | |||||||
\(338\) | −528270. | −0.251515 | ||||||||
\(339\) | −1.75084e6 | −0.827462 | ||||||||
\(340\) | −1.35247e6 | −0.634497 | ||||||||
\(341\) | 2.31849e6 | 1.07974 | ||||||||
\(342\) | 67554.8 | 0.0312314 | ||||||||
\(343\) | 2.02054e6 | 0.927324 | ||||||||
\(344\) | −255380. | −0.116356 | ||||||||
\(345\) | −3.32413e6 | −1.50359 | ||||||||
\(346\) | 653149. | 0.293307 | ||||||||
\(347\) | −161465. | −0.0719872 | −0.0359936 | − | 0.999352i | \(-0.511460\pi\) | ||||
−0.0359936 | + | 0.999352i | \(0.511460\pi\) | |||||||
\(348\) | −1.81805e6 | −0.804745 | ||||||||
\(349\) | −2.48443e6 | −1.09185 | −0.545925 | − | 0.837834i | \(-0.683821\pi\) | ||||
−0.545925 | + | 0.837834i | \(0.683821\pi\) | |||||||
\(350\) | 1.69509e6 | 0.739642 | ||||||||
\(351\) | −608492. | −0.263625 | ||||||||
\(352\) | 2.83486e6 | 1.21948 | ||||||||
\(353\) | 503098. | 0.214890 | 0.107445 | − | 0.994211i | \(-0.465733\pi\) | ||||
0.107445 | + | 0.994211i | \(0.465733\pi\) | |||||||
\(354\) | −50857.6 | −0.0215699 | ||||||||
\(355\) | −3.35477e6 | −1.41283 | ||||||||
\(356\) | −591961. | −0.247553 | ||||||||
\(357\) | 550928. | 0.228783 | ||||||||
\(358\) | 799097. | 0.329528 | ||||||||
\(359\) | 1.49405e6 | 0.611826 | 0.305913 | − | 0.952059i | \(-0.401038\pi\) | ||||
0.305913 | + | 0.952059i | \(0.401038\pi\) | |||||||
\(360\) | 835234. | 0.339666 | ||||||||
\(361\) | −2.21215e6 | −0.893400 | ||||||||
\(362\) | −135426. | −0.0543162 | ||||||||
\(363\) | −2.20202e6 | −0.877111 | ||||||||
\(364\) | 3.37209e6 | 1.33397 | ||||||||
\(365\) | −810698. | −0.318513 | ||||||||
\(366\) | −504128. | −0.196715 | ||||||||
\(367\) | 2.46095e6 | 0.953758 | 0.476879 | − | 0.878969i | \(-0.341768\pi\) | ||||
0.476879 | + | 0.878969i | \(0.341768\pi\) | |||||||
\(368\) | 2.77587e6 | 1.06851 | ||||||||
\(369\) | −1.61281e6 | −0.616621 | ||||||||
\(370\) | 1.32945e6 | 0.504855 | ||||||||
\(371\) | −4.11958e6 | −1.55388 | ||||||||
\(372\) | −961970. | −0.360416 | ||||||||
\(373\) | −4.12944e6 | −1.53681 | −0.768404 | − | 0.639965i | \(-0.778949\pi\) | ||||
−0.768404 | + | 0.639965i | \(0.778949\pi\) | |||||||
\(374\) | 460076. | 0.170079 | ||||||||
\(375\) | −4.15957e6 | −1.52746 | ||||||||
\(376\) | −2.21704e6 | −0.808732 | ||||||||
\(377\) | −5.74203e6 | −2.08071 | ||||||||
\(378\) | −162811. | −0.0586075 | ||||||||
\(379\) | 24757.7 | 0.00885345 | 0.00442672 | − | 0.999990i | \(-0.498591\pi\) | ||||
0.00442672 | + | 0.999990i | \(0.498591\pi\) | |||||||
\(380\) | 1.56165e6 | 0.554783 | ||||||||
\(381\) | 127532. | 0.0450098 | ||||||||
\(382\) | −1.23669e6 | −0.433613 | ||||||||
\(383\) | 721550. | 0.251344 | 0.125672 | − | 0.992072i | \(-0.459891\pi\) | ||||
0.125672 | + | 0.992072i | \(0.459891\pi\) | |||||||
\(384\) | −1.53993e6 | −0.532935 | ||||||||
\(385\) | 9.07095e6 | 3.11890 | ||||||||
\(386\) | 397770. | 0.135883 | ||||||||
\(387\) | −207655. | −0.0704799 | ||||||||
\(388\) | 2.69046e6 | 0.907292 | ||||||||
\(389\) | 2.77630e6 | 0.930234 | 0.465117 | − | 0.885249i | \(-0.346012\pi\) | ||||
0.465117 | + | 0.885249i | \(0.346012\pi\) | |||||||
\(390\) | 1.26233e6 | 0.420254 | ||||||||
\(391\) | 1.58762e6 | 0.525177 | ||||||||
\(392\) | 211226. | 0.0694277 | ||||||||
\(393\) | −1.74843e6 | −0.571039 | ||||||||
\(394\) | −66313.9 | −0.0215211 | ||||||||
\(395\) | −7.16899e6 | −2.31188 | ||||||||
\(396\) | 1.51504e6 | 0.485497 | ||||||||
\(397\) | 2.50395e6 | 0.797350 | 0.398675 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398675 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(398\) | 271477. | 0.0859063 | ||||||||
\(399\) | −636136. | −0.200040 | ||||||||
\(400\) | 5.90465e6 | 1.84520 | ||||||||
\(401\) | −3.85075e6 | −1.19587 | −0.597935 | − | 0.801544i | \(-0.704012\pi\) | ||||
−0.597935 | + | 0.801544i | \(0.704012\pi\) | |||||||
\(402\) | 721419. | 0.222650 | ||||||||
\(403\) | −3.03823e6 | −0.931874 | ||||||||
\(404\) | 2.79796e6 | 0.852879 | ||||||||
\(405\) | 679148. | 0.205744 | ||||||||
\(406\) | −1.53636e6 | −0.462570 | ||||||||
\(407\) | 5.03942e6 | 1.50798 | ||||||||
\(408\) | −398913. | −0.118639 | ||||||||
\(409\) | 420063. | 0.124167 | 0.0620835 | − | 0.998071i | \(-0.480225\pi\) | ||||
0.0620835 | + | 0.998071i | \(0.480225\pi\) | |||||||
\(410\) | 3.34582e6 | 0.982977 | ||||||||
\(411\) | 2.02441e6 | 0.591145 | ||||||||
\(412\) | 274123. | 0.0795613 | ||||||||
\(413\) | 478905. | 0.138157 | ||||||||
\(414\) | −469176. | −0.134535 | ||||||||
\(415\) | −3.15405e6 | −0.898978 | ||||||||
\(416\) | −3.71490e6 | −1.05248 | ||||||||
\(417\) | 851885. | 0.239906 | ||||||||
\(418\) | −531232. | −0.148711 | ||||||||
\(419\) | −3.16478e6 | −0.880661 | −0.440330 | − | 0.897836i | \(-0.645139\pi\) | ||||
−0.440330 | + | 0.897836i | \(0.645139\pi\) | |||||||
\(420\) | −3.76365e6 | −1.04108 | ||||||||
\(421\) | −6.88209e6 | −1.89241 | −0.946205 | − | 0.323567i | \(-0.895118\pi\) | ||||
−0.946205 | + | 0.323567i | \(0.895118\pi\) | |||||||
\(422\) | 794772. | 0.217251 | ||||||||
\(423\) | −1.80273e6 | −0.489869 | ||||||||
\(424\) | 2.98288e6 | 0.805789 | ||||||||
\(425\) | 3.37709e6 | 0.906923 | ||||||||
\(426\) | −473500. | −0.126414 | ||||||||
\(427\) | 4.74717e6 | 1.25998 | ||||||||
\(428\) | 5.62208e6 | 1.48350 | ||||||||
\(429\) | 4.78501e6 | 1.25528 | ||||||||
\(430\) | 430786. | 0.112354 | ||||||||
\(431\) | 6.64605e6 | 1.72334 | 0.861668 | − | 0.507472i | \(-0.169420\pi\) | ||||
0.861668 | + | 0.507472i | \(0.169420\pi\) | |||||||
\(432\) | −567134. | −0.146210 | ||||||||
\(433\) | −5.40532e6 | −1.38548 | −0.692742 | − | 0.721186i | \(-0.743597\pi\) | ||||
−0.692742 | + | 0.721186i | \(0.743597\pi\) | |||||||
\(434\) | −812920. | −0.207168 | ||||||||
\(435\) | 6.40876e6 | 1.62387 | ||||||||
\(436\) | 1.43942e6 | 0.362635 | ||||||||
\(437\) | −1.83317e6 | −0.459197 | ||||||||
\(438\) | −114424. | −0.0284992 | ||||||||
\(439\) | 3.49764e6 | 0.866190 | 0.433095 | − | 0.901348i | \(-0.357421\pi\) | ||||
0.433095 | + | 0.901348i | \(0.357421\pi\) | |||||||
\(440\) | −6.56804e6 | −1.61735 | ||||||||
\(441\) | 171753. | 0.0420540 | ||||||||
\(442\) | −602898. | −0.146787 | ||||||||
\(443\) | 7.83503e6 | 1.89684 | 0.948421 | − | 0.317013i | \(-0.102680\pi\) | ||||
0.948421 | + | 0.317013i | \(0.102680\pi\) | |||||||
\(444\) | −2.09091e6 | −0.503360 | ||||||||
\(445\) | 2.08670e6 | 0.499529 | ||||||||
\(446\) | 1.38986e6 | 0.330853 | ||||||||
\(447\) | −279079. | −0.0660631 | ||||||||
\(448\) | 2.43097e6 | 0.572249 | ||||||||
\(449\) | 3.72658e6 | 0.872357 | 0.436178 | − | 0.899860i | \(-0.356332\pi\) | ||||
0.436178 | + | 0.899860i | \(0.356332\pi\) | |||||||
\(450\) | −998001. | −0.232327 | ||||||||
\(451\) | 1.26827e7 | 2.93610 | ||||||||
\(452\) | −5.71257e6 | −1.31518 | ||||||||
\(453\) | 670307. | 0.153472 | ||||||||
\(454\) | 1.63794e6 | 0.372957 | ||||||||
\(455\) | −1.18869e7 | −2.69177 | ||||||||
\(456\) | 460610. | 0.103734 | ||||||||
\(457\) | −1.25040e6 | −0.280065 | −0.140033 | − | 0.990147i | \(-0.544721\pi\) | ||||
−0.140033 | + | 0.990147i | \(0.544721\pi\) | |||||||
\(458\) | 824608. | 0.183689 | ||||||||
\(459\) | −324365. | −0.0718625 | ||||||||
\(460\) | −1.08458e7 | −2.38983 | ||||||||
\(461\) | 3.23924e6 | 0.709890 | 0.354945 | − | 0.934887i | \(-0.384500\pi\) | ||||
0.354945 | + | 0.934887i | \(0.384500\pi\) | |||||||
\(462\) | 1.28030e6 | 0.279065 | ||||||||
\(463\) | 481992. | 0.104493 | 0.0522465 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522465 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(464\) | −5.35175e6 | −1.15399 | ||||||||
\(465\) | 3.39101e6 | 0.727272 | ||||||||
\(466\) | 253923. | 0.0541672 | ||||||||
\(467\) | 4.61594e6 | 0.979418 | 0.489709 | − | 0.871886i | \(-0.337103\pi\) | ||||
0.489709 | + | 0.871886i | \(0.337103\pi\) | |||||||
\(468\) | −1.98536e6 | −0.419010 | ||||||||
\(469\) | −6.79330e6 | −1.42610 | ||||||||
\(470\) | 3.73981e6 | 0.780917 | ||||||||
\(471\) | −3.94875e6 | −0.820176 | ||||||||
\(472\) | −346763. | −0.0716437 | ||||||||
\(473\) | 1.63294e6 | 0.335597 | ||||||||
\(474\) | −1.01185e6 | −0.206857 | ||||||||
\(475\) | −3.89940e6 | −0.792983 | ||||||||
\(476\) | 1.79754e6 | 0.363631 | ||||||||
\(477\) | 2.42545e6 | 0.488086 | ||||||||
\(478\) | −842450. | −0.168645 | ||||||||
\(479\) | −6.61817e6 | −1.31795 | −0.658975 | − | 0.752165i | \(-0.729010\pi\) | ||||
−0.658975 | + | 0.752165i | \(0.729010\pi\) | |||||||
\(480\) | 4.14625e6 | 0.821396 | ||||||||
\(481\) | −6.60381e6 | −1.30146 | ||||||||
\(482\) | −246218. | −0.0482727 | ||||||||
\(483\) | 4.41804e6 | 0.861711 | ||||||||
\(484\) | −7.18464e6 | −1.39409 | ||||||||
\(485\) | −9.48405e6 | −1.83079 | ||||||||
\(486\) | 95856.7 | 0.0184091 | ||||||||
\(487\) | 5.72990e6 | 1.09477 | 0.547387 | − | 0.836879i | \(-0.315623\pi\) | ||||
0.547387 | + | 0.836879i | \(0.315623\pi\) | |||||||
\(488\) | −3.43730e6 | −0.653383 | ||||||||
\(489\) | −4.40269e6 | −0.832618 | ||||||||
\(490\) | −356306. | −0.0670398 | ||||||||
\(491\) | −3.96105e6 | −0.741492 | −0.370746 | − | 0.928734i | \(-0.620898\pi\) | ||||
−0.370746 | + | 0.928734i | \(0.620898\pi\) | |||||||
\(492\) | −5.26221e6 | −0.980066 | ||||||||
\(493\) | −3.06086e6 | −0.567188 | ||||||||
\(494\) | 696144. | 0.128346 | ||||||||
\(495\) | −5.34063e6 | −0.979669 | ||||||||
\(496\) | −2.83172e6 | −0.516829 | ||||||||
\(497\) | 4.45876e6 | 0.809697 | ||||||||
\(498\) | −445171. | −0.0804366 | ||||||||
\(499\) | −2.33209e6 | −0.419269 | −0.209635 | − | 0.977780i | \(-0.567227\pi\) | ||||
−0.209635 | + | 0.977780i | \(0.567227\pi\) | |||||||
\(500\) | −1.35717e7 | −2.42777 | ||||||||
\(501\) | −2.49366e6 | −0.443856 | ||||||||
\(502\) | −1.13446e6 | −0.200923 | ||||||||
\(503\) | −6.88900e6 | −1.21405 | −0.607024 | − | 0.794683i | \(-0.707637\pi\) | ||||
−0.607024 | + | 0.794683i | \(0.707637\pi\) | |||||||
\(504\) | −1.11009e6 | −0.194663 | ||||||||
\(505\) | −9.86299e6 | −1.72100 | ||||||||
\(506\) | 3.68947e6 | 0.640601 | ||||||||
\(507\) | −2.92880e6 | −0.506022 | ||||||||
\(508\) | 416106. | 0.0715392 | ||||||||
\(509\) | 1.16204e6 | 0.198804 | 0.0994019 | − | 0.995047i | \(-0.468307\pi\) | ||||
0.0994019 | + | 0.995047i | \(0.468307\pi\) | |||||||
\(510\) | 672904. | 0.114559 | ||||||||
\(511\) | 1.07748e6 | 0.182540 | ||||||||
\(512\) | −5.94232e6 | −1.00180 | ||||||||
\(513\) | 374532. | 0.0628342 | ||||||||
\(514\) | −747941. | −0.124870 | ||||||||
\(515\) | −966301. | −0.160544 | ||||||||
\(516\) | −677527. | −0.112022 | ||||||||
\(517\) | 1.41762e7 | 2.33256 | ||||||||
\(518\) | −1.76694e6 | −0.289333 | ||||||||
\(519\) | 3.62114e6 | 0.590101 | ||||||||
\(520\) | 8.60697e6 | 1.39586 | ||||||||
\(521\) | 2.98863e6 | 0.482367 | 0.241184 | − | 0.970480i | \(-0.422464\pi\) | ||||
0.241184 | + | 0.970480i | \(0.422464\pi\) | |||||||
\(522\) | 904550. | 0.145297 | ||||||||
\(523\) | 9.74843e6 | 1.55840 | 0.779202 | − | 0.626772i | \(-0.215624\pi\) | ||||
0.779202 | + | 0.626772i | \(0.215624\pi\) | |||||||
\(524\) | −5.70468e6 | −0.907618 | ||||||||
\(525\) | 9.39776e6 | 1.48808 | ||||||||
\(526\) | −1.74143e6 | −0.274436 | ||||||||
\(527\) | −1.61957e6 | −0.254023 | ||||||||
\(528\) | 4.45978e6 | 0.696192 | ||||||||
\(529\) | 6.29525e6 | 0.978078 | ||||||||
\(530\) | −5.03166e6 | −0.778075 | ||||||||
\(531\) | −281961. | −0.0433963 | ||||||||
\(532\) | −2.07555e6 | −0.317947 | ||||||||
\(533\) | −1.66198e7 | −2.53401 | ||||||||
\(534\) | 294523. | 0.0446957 | ||||||||
\(535\) | −1.98182e7 | −2.99350 | ||||||||
\(536\) | 4.91885e6 | 0.739523 | ||||||||
\(537\) | 4.43029e6 | 0.662974 | ||||||||
\(538\) | −944656. | −0.140708 | ||||||||
\(539\) | −1.35062e6 | −0.200244 | ||||||||
\(540\) | 2.21589e6 | 0.327012 | ||||||||
\(541\) | −977703. | −0.143620 | −0.0718098 | − | 0.997418i | \(-0.522877\pi\) | ||||
−0.0718098 | + | 0.997418i | \(0.522877\pi\) | |||||||
\(542\) | 2.51566e6 | 0.367835 | ||||||||
\(543\) | −750816. | −0.109278 | ||||||||
\(544\) | −1.98028e6 | −0.286899 | ||||||||
\(545\) | −5.07404e6 | −0.731750 | ||||||||
\(546\) | −1.67774e6 | −0.240848 | ||||||||
\(547\) | 3.99104e6 | 0.570319 | 0.285159 | − | 0.958480i | \(-0.407953\pi\) | ||||
0.285159 | + | 0.958480i | \(0.407953\pi\) | |||||||
\(548\) | 6.60515e6 | 0.939575 | ||||||||
\(549\) | −2.79495e6 | −0.395770 | ||||||||
\(550\) | 7.84800e6 | 1.10625 | ||||||||
\(551\) | 3.53427e6 | 0.495930 | ||||||||
\(552\) | −3.19899e6 | −0.446853 | ||||||||
\(553\) | 9.52817e6 | 1.32494 | ||||||||
\(554\) | −2.48351e6 | −0.343789 | ||||||||
\(555\) | 7.37062e6 | 1.01571 | ||||||||
\(556\) | 2.77949e6 | 0.381310 | ||||||||
\(557\) | −2.64820e6 | −0.361670 | −0.180835 | − | 0.983513i | \(-0.557880\pi\) | ||||
−0.180835 | + | 0.983513i | \(0.557880\pi\) | |||||||
\(558\) | 478616. | 0.0650731 | ||||||||
\(559\) | −2.13986e6 | −0.289638 | ||||||||
\(560\) | −1.10789e7 | −1.49289 | ||||||||
\(561\) | 2.55072e6 | 0.342180 | ||||||||
\(562\) | −1.53016e6 | −0.204360 | ||||||||
\(563\) | 719804. | 0.0957069 | 0.0478534 | − | 0.998854i | \(-0.484762\pi\) | ||||
0.0478534 | + | 0.998854i | \(0.484762\pi\) | |||||||
\(564\) | −5.88186e6 | −0.778604 | ||||||||
\(565\) | 2.01372e7 | 2.65386 | ||||||||
\(566\) | 1.09609e6 | 0.143815 | ||||||||
\(567\) | −902642. | −0.117912 | ||||||||
\(568\) | −3.22847e6 | −0.419881 | ||||||||
\(569\) | 5.99643e6 | 0.776448 | 0.388224 | − | 0.921565i | \(-0.373089\pi\) | ||||
0.388224 | + | 0.921565i | \(0.373089\pi\) | |||||||
\(570\) | −776977. | −0.100166 | ||||||||
\(571\) | −1.31757e7 | −1.69115 | −0.845577 | − | 0.533854i | \(-0.820743\pi\) | ||||
−0.845577 | + | 0.533854i | \(0.820743\pi\) | |||||||
\(572\) | 1.56123e7 | 1.99516 | ||||||||
\(573\) | −6.85635e6 | −0.872382 | ||||||||
\(574\) | −4.44687e6 | −0.563345 | ||||||||
\(575\) | 2.70818e7 | 3.41592 | ||||||||
\(576\) | −1.43126e6 | −0.179748 | ||||||||
\(577\) | −9.18759e6 | −1.14885 | −0.574424 | − | 0.818558i | \(-0.694774\pi\) | ||||
−0.574424 | + | 0.818558i | \(0.694774\pi\) | |||||||
\(578\) | 1.98353e6 | 0.246956 | ||||||||
\(579\) | 2.20529e6 | 0.273381 | ||||||||
\(580\) | 2.09102e7 | 2.58100 | ||||||||
\(581\) | 4.19199e6 | 0.515205 | ||||||||
\(582\) | −1.33860e6 | −0.163812 | ||||||||
\(583\) | −1.90731e7 | −2.32407 | ||||||||
\(584\) | −780178. | −0.0946590 | ||||||||
\(585\) | 6.99853e6 | 0.845507 | ||||||||
\(586\) | 771368. | 0.0927935 | ||||||||
\(587\) | −4.96246e6 | −0.594431 | −0.297215 | − | 0.954810i | \(-0.596058\pi\) | ||||
−0.297215 | + | 0.954810i | \(0.596058\pi\) | |||||||
\(588\) | 560387. | 0.0668413 | ||||||||
\(589\) | 1.87005e6 | 0.222109 | ||||||||
\(590\) | 584935. | 0.0691796 | ||||||||
\(591\) | −367652. | −0.0432981 | ||||||||
\(592\) | −6.15497e6 | −0.721807 | ||||||||
\(593\) | 1.07757e7 | 1.25837 | 0.629186 | − | 0.777255i | \(-0.283389\pi\) | ||||
0.629186 | + | 0.777255i | \(0.283389\pi\) | |||||||
\(594\) | −753790. | −0.0876565 | ||||||||
\(595\) | −6.33645e6 | −0.733759 | ||||||||
\(596\) | −910567. | −0.105002 | ||||||||
\(597\) | 1.50510e6 | 0.172834 | ||||||||
\(598\) | −4.83480e6 | −0.552873 | ||||||||
\(599\) | 9.20870e6 | 1.04865 | 0.524326 | − | 0.851518i | \(-0.324317\pi\) | ||||
0.524326 | + | 0.851518i | \(0.324317\pi\) | |||||||
\(600\) | −6.80468e6 | −0.771666 | ||||||||
\(601\) | −6.22345e6 | −0.702822 | −0.351411 | − | 0.936221i | \(-0.614298\pi\) | ||||
−0.351411 | + | 0.936221i | \(0.614298\pi\) | |||||||
\(602\) | −572549. | −0.0643905 | ||||||||
\(603\) | 3.99963e6 | 0.447947 | ||||||||
\(604\) | 2.18705e6 | 0.243930 | ||||||||
\(605\) | 2.53263e7 | 2.81309 | ||||||||
\(606\) | −1.39209e6 | −0.153987 | ||||||||
\(607\) | −1.27596e7 | −1.40561 | −0.702805 | − | 0.711382i | \(-0.748069\pi\) | ||||
−0.702805 | + | 0.711382i | \(0.748069\pi\) | |||||||
\(608\) | 2.28655e6 | 0.250855 | ||||||||
\(609\) | −8.51776e6 | −0.930642 | ||||||||
\(610\) | 5.79819e6 | 0.630911 | ||||||||
\(611\) | −1.85769e7 | −2.01312 | ||||||||
\(612\) | −1.05832e6 | −0.114219 | ||||||||
\(613\) | 8.11365e6 | 0.872097 | 0.436049 | − | 0.899923i | \(-0.356378\pi\) | ||||
0.436049 | + | 0.899923i | \(0.356378\pi\) | |||||||
\(614\) | −2.79508e6 | −0.299208 | ||||||||
\(615\) | 1.85496e7 | 1.97764 | ||||||||
\(616\) | 8.72946e6 | 0.926906 | ||||||||
\(617\) | −1.42296e7 | −1.50480 | −0.752399 | − | 0.658707i | \(-0.771104\pi\) | ||||
−0.752399 | + | 0.658707i | \(0.771104\pi\) | |||||||
\(618\) | −136386. | −0.0143648 | ||||||||
\(619\) | −1.08278e6 | −0.113583 | −0.0567916 | − | 0.998386i | \(-0.518087\pi\) | ||||
−0.0567916 | + | 0.998386i | \(0.518087\pi\) | |||||||
\(620\) | 1.10640e7 | 1.15594 | ||||||||
\(621\) | −2.60117e6 | −0.270670 | ||||||||
\(622\) | −380137. | −0.0393971 | ||||||||
\(623\) | −2.77340e6 | −0.286281 | ||||||||
\(624\) | −5.84424e6 | −0.600851 | ||||||||
\(625\) | 2.41226e7 | 2.47015 | ||||||||
\(626\) | 690673. | 0.0704428 | ||||||||
\(627\) | −2.94522e6 | −0.299191 | ||||||||
\(628\) | −1.28838e7 | −1.30360 | ||||||||
\(629\) | −3.52025e6 | −0.354770 | ||||||||
\(630\) | 1.87255e6 | 0.187968 | ||||||||
\(631\) | −5.94918e6 | −0.594817 | −0.297409 | − | 0.954750i | \(-0.596122\pi\) | ||||
−0.297409 | + | 0.954750i | \(0.596122\pi\) | |||||||
\(632\) | −6.89910e6 | −0.687068 | ||||||||
\(633\) | 4.40631e6 | 0.437085 | ||||||||
\(634\) | 5.43714e6 | 0.537214 | ||||||||
\(635\) | −1.46680e6 | −0.144357 | ||||||||
\(636\) | 7.91364e6 | 0.775771 | ||||||||
\(637\) | 1.76989e6 | 0.172822 | ||||||||
\(638\) | −7.11312e6 | −0.691845 | ||||||||
\(639\) | −2.62514e6 | −0.254332 | ||||||||
\(640\) | 1.77114e7 | 1.70924 | ||||||||
\(641\) | 1.50581e7 | 1.44752 | 0.723760 | − | 0.690052i | \(-0.242412\pi\) | ||||
0.723760 | + | 0.690052i | \(0.242412\pi\) | |||||||
\(642\) | −2.79719e6 | −0.267846 | ||||||||
\(643\) | −7.34341e6 | −0.700439 | −0.350219 | − | 0.936668i | \(-0.613893\pi\) | ||||
−0.350219 | + | 0.936668i | \(0.613893\pi\) | |||||||
\(644\) | 1.44150e7 | 1.36962 | ||||||||
\(645\) | 2.38833e6 | 0.226045 | ||||||||
\(646\) | 371089. | 0.0349862 | ||||||||
\(647\) | 1.71639e7 | 1.61196 | 0.805980 | − | 0.591943i | \(-0.201639\pi\) | ||||
0.805980 | + | 0.591943i | \(0.201639\pi\) | |||||||
\(648\) | 653580. | 0.0611451 | ||||||||
\(649\) | 2.21726e6 | 0.206636 | ||||||||
\(650\) | −1.02843e7 | −0.954751 | ||||||||
\(651\) | −4.50693e6 | −0.416800 | ||||||||
\(652\) | −1.43649e7 | −1.32337 | ||||||||
\(653\) | −1.67889e7 | −1.54078 | −0.770390 | − | 0.637573i | \(-0.779938\pi\) | ||||
−0.770390 | + | 0.637573i | \(0.779938\pi\) | |||||||
\(654\) | −716163. | −0.0654738 | ||||||||
\(655\) | 2.01094e7 | 1.83145 | ||||||||
\(656\) | −1.54902e7 | −1.40539 | ||||||||
\(657\) | −634381. | −0.0573372 | ||||||||
\(658\) | −4.97051e6 | −0.447544 | ||||||||
\(659\) | 1.22668e7 | 1.10031 | 0.550157 | − | 0.835061i | \(-0.314568\pi\) | ||||
0.550157 | + | 0.835061i | \(0.314568\pi\) | |||||||
\(660\) | −1.74251e7 | −1.55710 | ||||||||
\(661\) | −2.16263e6 | −0.192522 | −0.0962608 | − | 0.995356i | \(-0.530688\pi\) | ||||
−0.0962608 | + | 0.995356i | \(0.530688\pi\) | |||||||
\(662\) | 5.11382e6 | 0.453524 | ||||||||
\(663\) | −3.34254e6 | −0.295320 | ||||||||
\(664\) | −3.03532e6 | −0.267167 | ||||||||
\(665\) | 7.31647e6 | 0.641575 | ||||||||
\(666\) | 1.04031e6 | 0.0908817 | ||||||||
\(667\) | −2.45459e7 | −2.13631 | ||||||||
\(668\) | −8.13618e6 | −0.705471 | ||||||||
\(669\) | 7.70557e6 | 0.665640 | ||||||||
\(670\) | −8.29734e6 | −0.714088 | ||||||||
\(671\) | 2.19787e7 | 1.88450 | ||||||||
\(672\) | −5.51071e6 | −0.470743 | ||||||||
\(673\) | −3.23411e6 | −0.275243 | −0.137622 | − | 0.990485i | \(-0.543946\pi\) | ||||
−0.137622 | + | 0.990485i | \(0.543946\pi\) | |||||||
\(674\) | −3.06273e6 | −0.259692 | ||||||||
\(675\) | −5.53304e6 | −0.467417 | ||||||||
\(676\) | −9.55593e6 | −0.804278 | ||||||||
\(677\) | 2.05131e7 | 1.72012 | 0.860060 | − | 0.510193i | \(-0.170426\pi\) | ||||
0.860060 | + | 0.510193i | \(0.170426\pi\) | |||||||
\(678\) | 2.84222e6 | 0.237456 | ||||||||
\(679\) | 1.26051e7 | 1.04923 | ||||||||
\(680\) | 4.58806e6 | 0.380502 | ||||||||
\(681\) | 9.08094e6 | 0.750349 | ||||||||
\(682\) | −3.76370e6 | −0.309852 | ||||||||
\(683\) | −1.31062e6 | −0.107504 | −0.0537519 | − | 0.998554i | \(-0.517118\pi\) | ||||
−0.0537519 | + | 0.998554i | \(0.517118\pi\) | |||||||
\(684\) | 1.22201e6 | 0.0998695 | ||||||||
\(685\) | −2.32836e7 | −1.89594 | ||||||||
\(686\) | −3.28002e6 | −0.266113 | ||||||||
\(687\) | 4.57173e6 | 0.369563 | ||||||||
\(688\) | −1.99442e6 | −0.160637 | ||||||||
\(689\) | 2.49939e7 | 2.00580 | ||||||||
\(690\) | 5.39620e6 | 0.431484 | ||||||||
\(691\) | 2.35958e7 | 1.87992 | 0.939959 | − | 0.341287i | \(-0.110863\pi\) | ||||
0.939959 | + | 0.341287i | \(0.110863\pi\) | |||||||
\(692\) | 1.18149e7 | 0.937916 | ||||||||
\(693\) | 7.09812e6 | 0.561449 | ||||||||
\(694\) | 262113. | 0.0206581 | ||||||||
\(695\) | −9.79789e6 | −0.769432 | ||||||||
\(696\) | 6.16750e6 | 0.482598 | ||||||||
\(697\) | −8.85942e6 | −0.690754 | ||||||||
\(698\) | 4.03307e6 | 0.313327 | ||||||||
\(699\) | 1.40778e6 | 0.108979 | ||||||||
\(700\) | 3.06626e7 | 2.36517 | ||||||||
\(701\) | 1.46503e7 | 1.12604 | 0.563018 | − | 0.826445i | \(-0.309640\pi\) | ||||
0.563018 | + | 0.826445i | \(0.309640\pi\) | |||||||
\(702\) | 987790. | 0.0756523 | ||||||||
\(703\) | 4.06470e6 | 0.310199 | ||||||||
\(704\) | 1.12551e7 | 0.855886 | ||||||||
\(705\) | 2.07340e7 | 1.57112 | ||||||||
\(706\) | −816699. | −0.0616667 | ||||||||
\(707\) | 1.31087e7 | 0.986306 | ||||||||
\(708\) | −919969. | −0.0689747 | ||||||||
\(709\) | −4.71244e6 | −0.352071 | −0.176035 | − | 0.984384i | \(-0.556327\pi\) | ||||
−0.176035 | + | 0.984384i | \(0.556327\pi\) | |||||||
\(710\) | 5.44593e6 | 0.405440 | ||||||||
\(711\) | −5.60982e6 | −0.416174 | ||||||||
\(712\) | 2.00815e6 | 0.148455 | ||||||||
\(713\) | −1.29877e7 | −0.956775 | ||||||||
\(714\) | −894343. | −0.0656536 | ||||||||
\(715\) | −5.50345e7 | −4.02596 | ||||||||
\(716\) | 1.44549e7 | 1.05374 | ||||||||
\(717\) | −4.67065e6 | −0.339296 | ||||||||
\(718\) | −2.42535e6 | −0.175575 | ||||||||
\(719\) | −7.34095e6 | −0.529578 | −0.264789 | − | 0.964306i | \(-0.585302\pi\) | ||||
−0.264789 | + | 0.964306i | \(0.585302\pi\) | |||||||
\(720\) | 6.52285e6 | 0.468928 | ||||||||
\(721\) | 1.28429e6 | 0.0920081 | ||||||||
\(722\) | 3.59107e6 | 0.256378 | ||||||||
\(723\) | −1.36506e6 | −0.0971195 | ||||||||
\(724\) | −2.44973e6 | −0.173689 | ||||||||
\(725\) | −5.22124e7 | −3.68917 | ||||||||
\(726\) | 3.57463e6 | 0.251703 | ||||||||
\(727\) | 3.78991e6 | 0.265946 | 0.132973 | − | 0.991120i | \(-0.457548\pi\) | ||||
0.132973 | + | 0.991120i | \(0.457548\pi\) | |||||||
\(728\) | −1.14394e7 | −0.799970 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 1.31604e6 | 0.0914033 | ||||||||
\(731\) | −1.14068e6 | −0.0789533 | ||||||||
\(732\) | −9.11922e6 | −0.629043 | ||||||||
\(733\) | 1.24229e7 | 0.854008 | 0.427004 | − | 0.904250i | \(-0.359569\pi\) | ||||
0.427004 | + | 0.904250i | \(0.359569\pi\) | |||||||
\(734\) | −3.99496e6 | −0.273699 | ||||||||
\(735\) | −1.97540e6 | −0.134877 | ||||||||
\(736\) | −1.58804e7 | −1.08060 | ||||||||
\(737\) | −3.14520e7 | −2.13294 | ||||||||
\(738\) | 2.61815e6 | 0.176951 | ||||||||
\(739\) | −5.27123e6 | −0.355059 | −0.177530 | − | 0.984115i | \(-0.556811\pi\) | ||||
−0.177530 | + | 0.984115i | \(0.556811\pi\) | |||||||
\(740\) | 2.40485e7 | 1.61439 | ||||||||
\(741\) | 3.85951e6 | 0.258218 | ||||||||
\(742\) | 6.68748e6 | 0.445916 | ||||||||
\(743\) | −1.42533e7 | −0.947202 | −0.473601 | − | 0.880740i | \(-0.657046\pi\) | ||||
−0.473601 | + | 0.880740i | \(0.657046\pi\) | |||||||
\(744\) | 3.26335e6 | 0.216138 | ||||||||
\(745\) | 3.20981e6 | 0.211879 | ||||||||
\(746\) | 6.70350e6 | 0.441016 | ||||||||
\(747\) | −2.46808e6 | −0.161830 | ||||||||
\(748\) | 8.32235e6 | 0.543866 | ||||||||
\(749\) | 2.63400e7 | 1.71558 | ||||||||
\(750\) | 6.75240e6 | 0.438334 | ||||||||
\(751\) | −5.30422e6 | −0.343180 | −0.171590 | − | 0.985168i | \(-0.554890\pi\) | ||||
−0.171590 | + | 0.985168i | \(0.554890\pi\) | |||||||
\(752\) | −1.73143e7 | −1.11650 | ||||||||
\(753\) | −6.28957e6 | −0.404235 | ||||||||
\(754\) | 9.32126e6 | 0.597099 | ||||||||
\(755\) | −7.70949e6 | −0.492219 | ||||||||
\(756\) | −2.94510e6 | −0.187411 | ||||||||
\(757\) | 1.55013e7 | 0.983169 | 0.491585 | − | 0.870830i | \(-0.336418\pi\) | ||||
0.491585 | + | 0.870830i | \(0.336418\pi\) | |||||||
\(758\) | −40190.2 | −0.00254066 | ||||||||
\(759\) | 2.04549e7 | 1.28882 | ||||||||
\(760\) | −5.29767e6 | −0.332698 | ||||||||
\(761\) | −1.61620e7 | −1.01165 | −0.505827 | − | 0.862635i | \(-0.668813\pi\) | ||||
−0.505827 | + | 0.862635i | \(0.668813\pi\) | |||||||
\(762\) | −207028. | −0.0129164 | ||||||||
\(763\) | 6.74381e6 | 0.419367 | ||||||||
\(764\) | −2.23706e7 | −1.38658 | ||||||||
\(765\) | 3.73066e6 | 0.230479 | ||||||||
\(766\) | −1.17132e6 | −0.0721280 | ||||||||
\(767\) | −2.90557e6 | −0.178338 | ||||||||
\(768\) | −2.58910e6 | −0.158397 | ||||||||
\(769\) | −5.54537e6 | −0.338154 | −0.169077 | − | 0.985603i | \(-0.554079\pi\) | ||||
−0.169077 | + | 0.985603i | \(0.554079\pi\) | |||||||
\(770\) | −1.47252e7 | −0.895026 | ||||||||
\(771\) | −4.14668e6 | −0.251226 | ||||||||
\(772\) | 7.19531e6 | 0.434516 | ||||||||
\(773\) | 124974. | 0.00752266 | 0.00376133 | − | 0.999993i | \(-0.498803\pi\) | ||||
0.00376133 | + | 0.999993i | \(0.498803\pi\) | |||||||
\(774\) | 337095. | 0.0202255 | ||||||||
\(775\) | −2.76267e7 | −1.65225 | ||||||||
\(776\) | −9.12701e6 | −0.544094 | ||||||||
\(777\) | −9.79615e6 | −0.582107 | ||||||||
\(778\) | −4.50688e6 | −0.266948 | ||||||||
\(779\) | 1.02296e7 | 0.603972 | ||||||||
\(780\) | 2.28345e7 | 1.34386 | ||||||||
\(781\) | 2.06434e7 | 1.21103 | ||||||||
\(782\) | −2.57726e6 | −0.150709 | ||||||||
\(783\) | 5.01493e6 | 0.292321 | ||||||||
\(784\) | 1.64960e6 | 0.0958490 | ||||||||
\(785\) | 4.54162e7 | 2.63049 | ||||||||
\(786\) | 2.83829e6 | 0.163870 | ||||||||
\(787\) | −2.36036e6 | −0.135845 | −0.0679223 | − | 0.997691i | \(-0.521637\pi\) | ||||
−0.0679223 | + | 0.997691i | \(0.521637\pi\) | |||||||
\(788\) | −1.19956e6 | −0.0688186 | ||||||||
\(789\) | −9.65467e6 | −0.552135 | ||||||||
\(790\) | 1.16377e7 | 0.663437 | ||||||||
\(791\) | −2.67640e7 | −1.52093 | ||||||||
\(792\) | −5.13957e6 | −0.291148 | ||||||||
\(793\) | −2.88016e7 | −1.62642 | ||||||||
\(794\) | −4.06476e6 | −0.228814 | ||||||||
\(795\) | −2.78961e7 | −1.56540 | ||||||||
\(796\) | 4.91077e6 | 0.274705 | ||||||||
\(797\) | 3.55059e6 | 0.197995 | 0.0989976 | − | 0.995088i | \(-0.468436\pi\) | ||||
0.0989976 | + | 0.995088i | \(0.468436\pi\) | |||||||
\(798\) | 1.03267e6 | 0.0574053 | ||||||||
\(799\) | −9.90266e6 | −0.548763 | ||||||||
\(800\) | −3.37797e7 | −1.86608 | ||||||||
\(801\) | 1.63287e6 | 0.0899229 | ||||||||
\(802\) | 6.25108e6 | 0.343178 | ||||||||
\(803\) | 4.98859e6 | 0.273017 | ||||||||
\(804\) | 1.30498e7 | 0.711974 | ||||||||
\(805\) | −5.08137e7 | −2.76370 | ||||||||
\(806\) | 4.93208e6 | 0.267419 | ||||||||
\(807\) | −5.23729e6 | −0.283089 | ||||||||
\(808\) | −9.49168e6 | −0.511464 | ||||||||
\(809\) | 1.25623e7 | 0.674837 | 0.337418 | − | 0.941355i | \(-0.390446\pi\) | ||||
0.337418 | + | 0.941355i | \(0.390446\pi\) | |||||||
\(810\) | −1.10249e6 | −0.0590420 | ||||||||
\(811\) | −1.43135e7 | −0.764176 | −0.382088 | − | 0.924126i | \(-0.624795\pi\) | ||||
−0.382088 | + | 0.924126i | \(0.624795\pi\) | |||||||
\(812\) | −2.77914e7 | −1.47918 | ||||||||
\(813\) | 1.39471e7 | 0.740045 | ||||||||
\(814\) | −8.18069e6 | −0.432742 | ||||||||
\(815\) | 5.06372e7 | 2.67039 | ||||||||
\(816\) | −3.11535e6 | −0.163788 | ||||||||
\(817\) | 1.31710e6 | 0.0690342 | ||||||||
\(818\) | −681906. | −0.0356321 | ||||||||
\(819\) | −9.30161e6 | −0.484561 | ||||||||
\(820\) | 6.05229e7 | 3.14329 | ||||||||
\(821\) | −4.11110e6 | −0.212863 | −0.106431 | − | 0.994320i | \(-0.533942\pi\) | ||||
−0.106431 | + | 0.994320i | \(0.533942\pi\) | |||||||
\(822\) | −3.28631e6 | −0.169640 | ||||||||
\(823\) | −1.57208e7 | −0.809050 | −0.404525 | − | 0.914527i | \(-0.632563\pi\) | ||||
−0.404525 | + | 0.914527i | \(0.632563\pi\) | |||||||
\(824\) | −929924. | −0.0477122 | ||||||||
\(825\) | 4.35103e7 | 2.22565 | ||||||||
\(826\) | −777426. | −0.0396469 | ||||||||
\(827\) | −2.20932e7 | −1.12330 | −0.561649 | − | 0.827376i | \(-0.689833\pi\) | ||||
−0.561649 | + | 0.827376i | \(0.689833\pi\) | |||||||
\(828\) | −8.48697e6 | −0.430207 | ||||||||
\(829\) | 5.93151e6 | 0.299763 | 0.149882 | − | 0.988704i | \(-0.452111\pi\) | ||||
0.149882 | + | 0.988704i | \(0.452111\pi\) | |||||||
\(830\) | 5.12010e6 | 0.257979 | ||||||||
\(831\) | −1.37689e7 | −0.691666 | ||||||||
\(832\) | −1.47490e7 | −0.738676 | ||||||||
\(833\) | 943465. | 0.0471100 | ||||||||
\(834\) | −1.38290e6 | −0.0688455 | ||||||||
\(835\) | 2.86806e7 | 1.42355 | ||||||||
\(836\) | −9.60951e6 | −0.475538 | ||||||||
\(837\) | 2.65351e6 | 0.130920 | ||||||||
\(838\) | 5.13752e6 | 0.252722 | ||||||||
\(839\) | 3.16728e7 | 1.55340 | 0.776698 | − | 0.629874i | \(-0.216893\pi\) | ||||
0.776698 | + | 0.629874i | \(0.216893\pi\) | |||||||
\(840\) | 1.27677e7 | 0.624328 | ||||||||
\(841\) | 2.68122e7 | 1.30720 | ||||||||
\(842\) | 1.11720e7 | 0.543063 | ||||||||
\(843\) | −8.48340e6 | −0.411151 | ||||||||
\(844\) | 1.43767e7 | 0.694710 | ||||||||
\(845\) | 3.36853e7 | 1.62293 | ||||||||
\(846\) | 2.92644e6 | 0.140577 | ||||||||
\(847\) | −3.36608e7 | −1.61219 | ||||||||
\(848\) | 2.32952e7 | 1.11244 | ||||||||
\(849\) | 6.07683e6 | 0.289340 | ||||||||
\(850\) | −5.48217e6 | −0.260259 | ||||||||
\(851\) | −2.82299e7 | −1.33624 | ||||||||
\(852\) | −8.56519e6 | −0.404239 | ||||||||
\(853\) | 1.13914e7 | 0.536049 | 0.268024 | − | 0.963412i | \(-0.413629\pi\) | ||||
0.268024 | + | 0.963412i | \(0.413629\pi\) | |||||||
\(854\) | −7.70627e6 | −0.361576 | ||||||||
\(855\) | −4.30765e6 | −0.201523 | ||||||||
\(856\) | −1.90721e7 | −0.889641 | ||||||||
\(857\) | −1.71933e7 | −0.799664 | −0.399832 | − | 0.916588i | \(-0.630932\pi\) | ||||
−0.399832 | + | 0.916588i | \(0.630932\pi\) | |||||||
\(858\) | −7.76771e6 | −0.360226 | ||||||||
\(859\) | −1.03966e7 | −0.480738 | −0.240369 | − | 0.970682i | \(-0.577268\pi\) | ||||
−0.240369 | + | 0.970682i | \(0.577268\pi\) | |||||||
\(860\) | 7.79253e6 | 0.359279 | ||||||||
\(861\) | −2.46540e7 | −1.13339 | ||||||||
\(862\) | −1.07888e7 | −0.494544 | ||||||||
\(863\) | 1.64704e7 | 0.752797 | 0.376399 | − | 0.926458i | \(-0.377162\pi\) | ||||
0.376399 | + | 0.926458i | \(0.377162\pi\) | |||||||
\(864\) | 3.24449e6 | 0.147864 | ||||||||
\(865\) | −4.16482e7 | −1.89259 | ||||||||
\(866\) | 8.77467e6 | 0.397591 | ||||||||
\(867\) | 1.09969e7 | 0.496848 | ||||||||
\(868\) | −1.47050e7 | −0.662469 | ||||||||
\(869\) | 4.41140e7 | 1.98165 | ||||||||
\(870\) | −1.04036e7 | −0.466000 | ||||||||
\(871\) | 4.12157e7 | 1.84084 | ||||||||
\(872\) | −4.88302e6 | −0.217469 | ||||||||
\(873\) | −7.42138e6 | −0.329571 | ||||||||
\(874\) | 2.97586e6 | 0.131775 | ||||||||
\(875\) | −6.35846e7 | −2.80758 | ||||||||
\(876\) | −2.06983e6 | −0.0911326 | ||||||||
\(877\) | −7.65036e6 | −0.335879 | −0.167940 | − | 0.985797i | \(-0.553711\pi\) | ||||
−0.167940 | + | 0.985797i | \(0.553711\pi\) | |||||||
\(878\) | −5.67785e6 | −0.248570 | ||||||||
\(879\) | 4.27656e6 | 0.186690 | ||||||||
\(880\) | −5.12939e7 | −2.23285 | ||||||||
\(881\) | 1.06801e7 | 0.463591 | 0.231795 | − | 0.972765i | \(-0.425540\pi\) | ||||
0.231795 | + | 0.972765i | \(0.425540\pi\) | |||||||
\(882\) | −278814. | −0.0120682 | ||||||||
\(883\) | −1.47279e7 | −0.635679 | −0.317840 | − | 0.948144i | \(-0.602957\pi\) | ||||
−0.317840 | + | 0.948144i | \(0.602957\pi\) | |||||||
\(884\) | −1.09059e7 | −0.469386 | ||||||||
\(885\) | 3.24295e6 | 0.139182 | ||||||||
\(886\) | −1.27189e7 | −0.544335 | ||||||||
\(887\) | −9.04933e6 | −0.386196 | −0.193098 | − | 0.981180i | \(-0.561853\pi\) | ||||
−0.193098 | + | 0.981180i | \(0.561853\pi\) | |||||||
\(888\) | 7.09314e6 | 0.301860 | ||||||||
\(889\) | 1.94950e6 | 0.0827310 | ||||||||
\(890\) | −3.38743e6 | −0.143349 | ||||||||
\(891\) | −4.17910e6 | −0.176355 | ||||||||
\(892\) | 2.51414e7 | 1.05798 | ||||||||
\(893\) | 1.14342e7 | 0.479820 | ||||||||
\(894\) | 453041. | 0.0189581 | ||||||||
\(895\) | −5.09547e7 | −2.12631 | ||||||||
\(896\) | −2.35399e7 | −0.979569 | ||||||||
\(897\) | −2.68047e7 | −1.11232 | ||||||||
\(898\) | −6.04951e6 | −0.250339 | ||||||||
\(899\) | 2.50398e7 | 1.03331 | ||||||||
\(900\) | −1.80529e7 | −0.742919 | ||||||||
\(901\) | 1.33234e7 | 0.546766 | ||||||||
\(902\) | −2.05884e7 | −0.842569 | ||||||||
\(903\) | −3.17428e6 | −0.129547 | ||||||||
\(904\) | 1.93791e7 | 0.788702 | ||||||||
\(905\) | 8.63545e6 | 0.350480 | ||||||||
\(906\) | −1.08814e6 | −0.0440416 | ||||||||
\(907\) | 6.23712e6 | 0.251748 | 0.125874 | − | 0.992046i | \(-0.459827\pi\) | ||||
0.125874 | + | 0.992046i | \(0.459827\pi\) | |||||||
\(908\) | 2.96289e7 | 1.19261 | ||||||||
\(909\) | −7.71791e6 | −0.309806 | ||||||||
\(910\) | 1.92964e7 | 0.772455 | ||||||||
\(911\) | 304116. | 0.0121407 | 0.00607035 | − | 0.999982i | \(-0.498068\pi\) | ||||
0.00607035 | + | 0.999982i | \(0.498068\pi\) | |||||||
\(912\) | 3.59718e6 | 0.143211 | ||||||||
\(913\) | 1.94083e7 | 0.770568 | ||||||||
\(914\) | 2.02983e6 | 0.0803699 | ||||||||
\(915\) | 3.21459e7 | 1.26932 | ||||||||
\(916\) | 1.49164e7 | 0.587389 | ||||||||
\(917\) | −2.67270e7 | −1.04961 | ||||||||
\(918\) | 526555. | 0.0206223 | ||||||||
\(919\) | 4.04845e7 | 1.58125 | 0.790623 | − | 0.612303i | \(-0.209757\pi\) | ||||
0.790623 | + | 0.612303i | \(0.209757\pi\) | |||||||
\(920\) | 3.67929e7 | 1.43316 | ||||||||
\(921\) | −1.54963e7 | −0.601974 | ||||||||
\(922\) | −5.25839e6 | −0.203716 | ||||||||
\(923\) | −2.70518e7 | −1.04518 | ||||||||
\(924\) | 2.31594e7 | 0.892376 | ||||||||
\(925\) | −6.00487e7 | −2.30754 | ||||||||
\(926\) | −782438. | −0.0299863 | ||||||||
\(927\) | −756142. | −0.0289004 | ||||||||
\(928\) | 3.06166e7 | 1.16704 | ||||||||
\(929\) | −3.99001e7 | −1.51682 | −0.758411 | − | 0.651776i | \(-0.774024\pi\) | ||||
−0.758411 | + | 0.651776i | \(0.774024\pi\) | |||||||
\(930\) | −5.50477e6 | −0.208704 | ||||||||
\(931\) | −1.08938e6 | −0.0411914 | ||||||||
\(932\) | 4.59323e6 | 0.173212 | ||||||||
\(933\) | −2.10752e6 | −0.0792626 | ||||||||
\(934\) | −7.49325e6 | −0.281062 | ||||||||
\(935\) | −2.93369e7 | −1.09745 | ||||||||
\(936\) | 6.73506e6 | 0.251276 | ||||||||
\(937\) | −8.96793e6 | −0.333690 | −0.166845 | − | 0.985983i | \(-0.553358\pi\) | ||||
−0.166845 | + | 0.985983i | \(0.553358\pi\) | |||||||
\(938\) | 1.10278e7 | 0.409245 | ||||||||
\(939\) | 3.82917e6 | 0.141723 | ||||||||
\(940\) | 6.76498e7 | 2.49716 | ||||||||
\(941\) | −1.34693e7 | −0.495873 | −0.247937 | − | 0.968776i | \(-0.579752\pi\) | ||||
−0.247937 | + | 0.968776i | \(0.579752\pi\) | |||||||
\(942\) | 6.41016e6 | 0.235365 | ||||||||
\(943\) | −7.10461e7 | −2.60172 | ||||||||
\(944\) | −2.70809e6 | −0.0989082 | ||||||||
\(945\) | 1.03817e7 | 0.378171 | ||||||||
\(946\) | −2.65082e6 | −0.0963058 | ||||||||
\(947\) | 7.49930e6 | 0.271735 | 0.135868 | − | 0.990727i | \(-0.456618\pi\) | ||||
0.135868 | + | 0.990727i | \(0.456618\pi\) | |||||||
\(948\) | −1.83034e7 | −0.661473 | ||||||||
\(949\) | −6.53721e6 | −0.235628 | ||||||||
\(950\) | 6.33006e6 | 0.227561 | ||||||||
\(951\) | 3.01441e7 | 1.08082 | ||||||||
\(952\) | −6.09791e6 | −0.218066 | ||||||||
\(953\) | −2.02266e6 | −0.0721423 | −0.0360711 | − | 0.999349i | \(-0.511484\pi\) | ||||
−0.0360711 | + | 0.999349i | \(0.511484\pi\) | |||||||
\(954\) | −3.93733e6 | −0.140065 | ||||||||
\(955\) | 7.88578e7 | 2.79793 | ||||||||
\(956\) | −1.52392e7 | −0.539283 | ||||||||
\(957\) | −3.94360e7 | −1.39192 | ||||||||
\(958\) | 1.07435e7 | 0.378211 | ||||||||
\(959\) | 3.09458e7 | 1.08656 | ||||||||
\(960\) | 1.64616e7 | 0.576492 | ||||||||
\(961\) | −1.53801e7 | −0.537218 | ||||||||
\(962\) | 1.07202e7 | 0.373480 | ||||||||
\(963\) | −1.55080e7 | −0.538877 | ||||||||
\(964\) | −4.45385e6 | −0.154363 | ||||||||
\(965\) | −2.53639e7 | −0.876796 | ||||||||
\(966\) | −7.17198e6 | −0.247284 | ||||||||
\(967\) | 3.81493e6 | 0.131196 | 0.0655979 | − | 0.997846i | \(-0.479105\pi\) | ||||
0.0655979 | + | 0.997846i | \(0.479105\pi\) | |||||||
\(968\) | 2.43729e7 | 0.836024 | ||||||||
\(969\) | 2.05736e6 | 0.0703884 | ||||||||
\(970\) | 1.53958e7 | 0.525381 | ||||||||
\(971\) | −3.88611e7 | −1.32272 | −0.661359 | − | 0.750070i | \(-0.730020\pi\) | ||||
−0.661359 | + | 0.750070i | \(0.730020\pi\) | |||||||
\(972\) | 1.73396e6 | 0.0588672 | ||||||||
\(973\) | 1.30222e7 | 0.440963 | ||||||||
\(974\) | −9.30158e6 | −0.314166 | ||||||||
\(975\) | −5.70172e7 | −1.92086 | ||||||||
\(976\) | −2.68440e7 | −0.902033 | ||||||||
\(977\) | 3.83275e7 | 1.28462 | 0.642310 | − | 0.766445i | \(-0.277976\pi\) | ||||
0.642310 | + | 0.766445i | \(0.277976\pi\) | |||||||
\(978\) | 7.14706e6 | 0.238935 | ||||||||
\(979\) | −1.28404e7 | −0.428176 | ||||||||
\(980\) | −6.44525e6 | −0.214375 | ||||||||
\(981\) | −3.97050e6 | −0.131726 | ||||||||
\(982\) | 6.43013e6 | 0.212785 | ||||||||
\(983\) | 3.97346e6 | 0.131155 | 0.0655776 | − | 0.997847i | \(-0.479111\pi\) | ||||
0.0655776 | + | 0.997847i | \(0.479111\pi\) | |||||||
\(984\) | 1.78513e7 | 0.587736 | ||||||||
\(985\) | 4.22853e6 | 0.138867 | ||||||||
\(986\) | 4.96883e6 | 0.162765 | ||||||||
\(987\) | −2.75571e7 | −0.900411 | ||||||||
\(988\) | 1.25926e7 | 0.410415 | ||||||||
\(989\) | −9.14743e6 | −0.297378 | ||||||||
\(990\) | 8.66966e6 | 0.281134 | ||||||||
\(991\) | 4.07143e7 | 1.31693 | 0.658465 | − | 0.752612i | \(-0.271206\pi\) | ||||
0.658465 | + | 0.752612i | \(0.271206\pi\) | |||||||
\(992\) | 1.61999e7 | 0.522676 | ||||||||
\(993\) | 2.83516e7 | 0.912441 | ||||||||
\(994\) | −7.23808e6 | −0.232358 | ||||||||
\(995\) | −1.73108e7 | −0.554318 | ||||||||
\(996\) | −8.05275e6 | −0.257215 | ||||||||
\(997\) | 1.23365e7 | 0.393055 | 0.196527 | − | 0.980498i | \(-0.437034\pi\) | ||||
0.196527 | + | 0.980498i | \(0.437034\pi\) | |||||||
\(998\) | 3.78577e6 | 0.120317 | ||||||||
\(999\) | 5.76760e6 | 0.182844 |
(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 | 177.6.a.b.1.6 | ✓ | 12 | |
3.2 | odd | 2 | 531.6.a.d.1.7 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.b.1.6 | ✓ | 12 | 1.1 | even | 1 | trivial | |
531.6.a.d.1.7 | 12 | 3.2 | odd | 2 |