Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [471,4,Mod(313,471)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(471, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("471.313");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 471 = 3 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 471.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(27.7898996127\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 313.15 | ||
Character | \(\chi\) | \(=\) | 471.313 |
Dual form | 471.4.b.a.313.26 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/471\mathbb{Z}\right)^\times\).
\(n\) | \(158\) | \(319\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.46936i | − | 0.519498i | −0.965676 | − | 0.259749i | \(-0.916360\pi\) | ||
0.965676 | − | 0.259749i | \(-0.0836398\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 5.84098 | 0.730122 | ||||||||
\(5\) | − | 4.94652i | − | 0.442431i | −0.975225 | − | 0.221215i | \(-0.928998\pi\) | ||
0.975225 | − | 0.221215i | \(-0.0710024\pi\) | |||||||
\(6\) | 4.40809i | 0.299932i | ||||||||
\(7\) | 12.8754i | 0.695209i | 0.937641 | + | 0.347604i | \(0.113005\pi\) | ||||
−0.937641 | + | 0.347604i | \(0.886995\pi\) | |||||||
\(8\) | − | 20.3374i | − | 0.898795i | ||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −7.26823 | −0.229842 | ||||||||
\(11\) | −22.3563 | −0.612790 | −0.306395 | − | 0.951904i | \(-0.599123\pi\) | ||||
−0.306395 | + | 0.951904i | \(0.599123\pi\) | |||||||
\(12\) | −17.5229 | −0.421536 | ||||||||
\(13\) | 72.1239 | 1.53874 | 0.769368 | − | 0.638806i | \(-0.220571\pi\) | ||||
0.769368 | + | 0.638806i | \(0.220571\pi\) | |||||||
\(14\) | 18.9187 | 0.361159 | ||||||||
\(15\) | 14.8396i | 0.255437i | ||||||||
\(16\) | 16.8448 | 0.263200 | ||||||||
\(17\) | 19.7682 | 0.282029 | 0.141014 | − | 0.990008i | \(-0.454964\pi\) | ||||
0.141014 | + | 0.990008i | \(0.454964\pi\) | |||||||
\(18\) | − | 13.2243i | − | 0.173166i | ||||||
\(19\) | −82.0165 | −0.990309 | −0.495155 | − | 0.868805i | \(-0.664889\pi\) | ||||
−0.495155 | + | 0.868805i | \(0.664889\pi\) | |||||||
\(20\) | − | 28.8925i | − | 0.323028i | ||||||
\(21\) | − | 38.6263i | − | 0.401379i | ||||||
\(22\) | 32.8496i | 0.318343i | ||||||||
\(23\) | 50.1678i | 0.454813i | 0.973800 | + | 0.227407i | \(0.0730247\pi\) | ||||
−0.973800 | + | 0.227407i | \(0.926975\pi\) | |||||||
\(24\) | 61.0122i | 0.518919i | ||||||||
\(25\) | 100.532 | 0.804255 | ||||||||
\(26\) | − | 105.976i | − | 0.799370i | ||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 75.2052i | 0.507587i | ||||||||
\(29\) | − | 147.572i | − | 0.944943i | −0.881346 | − | 0.472471i | \(-0.843362\pi\) | ||
0.881346 | − | 0.472471i | \(-0.156638\pi\) | |||||||
\(30\) | 21.8047 | 0.132699 | ||||||||
\(31\) | 144.553 | 0.837500 | 0.418750 | − | 0.908102i | \(-0.362468\pi\) | ||||
0.418750 | + | 0.908102i | \(0.362468\pi\) | |||||||
\(32\) | − | 187.450i | − | 1.03553i | ||||||
\(33\) | 67.0690 | 0.353795 | ||||||||
\(34\) | − | 29.0466i | − | 0.146513i | ||||||
\(35\) | 63.6887 | 0.307582 | ||||||||
\(36\) | 52.5688 | 0.243374 | ||||||||
\(37\) | 221.972 | 0.986269 | 0.493135 | − | 0.869953i | \(-0.335851\pi\) | ||||
0.493135 | + | 0.869953i | \(0.335851\pi\) | |||||||
\(38\) | 120.512i | 0.514464i | ||||||||
\(39\) | −216.372 | −0.888390 | ||||||||
\(40\) | −100.599 | −0.397654 | ||||||||
\(41\) | 22.4304i | 0.0854402i | 0.999087 | + | 0.0427201i | \(0.0136024\pi\) | ||||
−0.999087 | + | 0.0427201i | \(0.986398\pi\) | |||||||
\(42\) | −56.7561 | −0.208515 | ||||||||
\(43\) | 204.958i | 0.726879i | 0.931618 | + | 0.363440i | \(0.118398\pi\) | ||||
−0.931618 | + | 0.363440i | \(0.881602\pi\) | |||||||
\(44\) | −130.583 | −0.447412 | ||||||||
\(45\) | − | 44.5187i | − | 0.147477i | ||||||
\(46\) | 73.7146 | 0.236275 | ||||||||
\(47\) | −84.4528 | −0.262100 | −0.131050 | − | 0.991376i | \(-0.541835\pi\) | ||||
−0.131050 | + | 0.991376i | \(0.541835\pi\) | |||||||
\(48\) | −50.5344 | −0.151959 | ||||||||
\(49\) | 177.223 | 0.516685 | ||||||||
\(50\) | − | 147.718i | − | 0.417809i | ||||||
\(51\) | −59.3045 | −0.162829 | ||||||||
\(52\) | 421.274 | 1.12346 | ||||||||
\(53\) | − | 213.343i | − | 0.552924i | −0.961025 | − | 0.276462i | \(-0.910838\pi\) | ||
0.961025 | − | 0.276462i | \(-0.0891620\pi\) | |||||||
\(54\) | 39.6728i | 0.0999774i | ||||||||
\(55\) | 110.586i | 0.271117i | ||||||||
\(56\) | 261.853 | 0.624850 | ||||||||
\(57\) | 246.050 | 0.571755 | ||||||||
\(58\) | −216.836 | −0.490896 | ||||||||
\(59\) | − | 14.1094i | − | 0.0311336i | −0.999879 | − | 0.0155668i | \(-0.995045\pi\) | ||
0.999879 | − | 0.0155668i | \(-0.00495527\pi\) | |||||||
\(60\) | 86.6776i | 0.186500i | ||||||||
\(61\) | − | 811.300i | − | 1.70289i | −0.524444 | − | 0.851445i | \(-0.675727\pi\) | ||
0.524444 | − | 0.851445i | \(-0.324273\pi\) | |||||||
\(62\) | − | 212.401i | − | 0.435079i | ||||||
\(63\) | 115.879i | 0.231736i | ||||||||
\(64\) | −140.674 | −0.274754 | ||||||||
\(65\) | − | 356.763i | − | 0.680784i | ||||||
\(66\) | − | 98.5487i | − | 0.183795i | ||||||
\(67\) | 19.0720 | 0.0347764 | 0.0173882 | − | 0.999849i | \(-0.494465\pi\) | ||||
0.0173882 | + | 0.999849i | \(0.494465\pi\) | |||||||
\(68\) | 115.465 | 0.205915 | ||||||||
\(69\) | − | 150.503i | − | 0.262587i | ||||||
\(70\) | − | 93.5817i | − | 0.159788i | ||||||
\(71\) | 217.768 | 0.364005 | 0.182003 | − | 0.983298i | \(-0.441742\pi\) | ||||
0.182003 | + | 0.983298i | \(0.441742\pi\) | |||||||
\(72\) | − | 183.037i | − | 0.299598i | ||||||
\(73\) | − | 235.896i | − | 0.378213i | −0.981957 | − | 0.189106i | \(-0.939441\pi\) | ||
0.981957 | − | 0.189106i | \(-0.0605591\pi\) | |||||||
\(74\) | − | 326.157i | − | 0.512365i | ||||||
\(75\) | −301.596 | −0.464337 | ||||||||
\(76\) | −479.056 | −0.723047 | ||||||||
\(77\) | − | 287.848i | − | 0.426017i | ||||||
\(78\) | 317.928i | 0.461516i | ||||||||
\(79\) | − | 1094.10i | − | 1.55818i | −0.626911 | − | 0.779091i | \(-0.715681\pi\) | ||
0.626911 | − | 0.779091i | \(-0.284319\pi\) | |||||||
\(80\) | − | 83.3233i | − | 0.116448i | ||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 32.9584 | 0.0443860 | ||||||||
\(83\) | − | 1229.87i | − | 1.62645i | −0.581947 | − | 0.813226i | \(-0.697709\pi\) | ||
0.581947 | − | 0.813226i | \(-0.302291\pi\) | |||||||
\(84\) | − | 225.615i | − | 0.293056i | ||||||
\(85\) | − | 97.7838i | − | 0.124778i | ||||||
\(86\) | 301.158 | 0.377612 | ||||||||
\(87\) | 442.715i | 0.545563i | ||||||||
\(88\) | 454.670i | 0.550772i | ||||||||
\(89\) | 1399.40 | 1.66670 | 0.833349 | − | 0.552747i | \(-0.186421\pi\) | ||||
0.833349 | + | 0.552747i | \(0.186421\pi\) | |||||||
\(90\) | −65.4141 | −0.0766139 | ||||||||
\(91\) | 928.627i | 1.06974i | ||||||||
\(92\) | 293.029i | 0.332069i | ||||||||
\(93\) | −433.659 | −0.483531 | ||||||||
\(94\) | 124.092i | 0.136160i | ||||||||
\(95\) | 405.697i | 0.438143i | ||||||||
\(96\) | 562.351i | 0.597862i | ||||||||
\(97\) | − | 698.636i | − | 0.731296i | −0.930753 | − | 0.365648i | \(-0.880847\pi\) | ||
0.930753 | − | 0.365648i | \(-0.119153\pi\) | |||||||
\(98\) | − | 260.405i | − | 0.268417i | ||||||
\(99\) | −201.207 | −0.204263 | ||||||||
\(100\) | 587.204 | 0.587204 | ||||||||
\(101\) | −768.315 | −0.756933 | −0.378467 | − | 0.925615i | \(-0.623548\pi\) | ||||
−0.378467 | + | 0.925615i | \(0.623548\pi\) | |||||||
\(102\) | 87.1398i | 0.0845895i | ||||||||
\(103\) | 1193.25i | 1.14150i | 0.821123 | + | 0.570751i | \(0.193348\pi\) | ||||
−0.821123 | + | 0.570751i | \(0.806652\pi\) | |||||||
\(104\) | − | 1466.81i | − | 1.38301i | ||||||
\(105\) | −191.066 | −0.177582 | ||||||||
\(106\) | −313.479 | −0.287243 | ||||||||
\(107\) | − | 1391.57i | − | 1.25727i | −0.777701 | − | 0.628635i | \(-0.783614\pi\) | ||
0.777701 | − | 0.628635i | \(-0.216386\pi\) | |||||||
\(108\) | −157.706 | −0.140512 | ||||||||
\(109\) | 580.300 | 0.509932 | 0.254966 | − | 0.966950i | \(-0.417936\pi\) | ||||
0.254966 | + | 0.966950i | \(0.417936\pi\) | |||||||
\(110\) | 162.491 | 0.140845 | ||||||||
\(111\) | −665.916 | −0.569423 | ||||||||
\(112\) | 216.884i | 0.182979i | ||||||||
\(113\) | 1325.78 | 1.10371 | 0.551855 | − | 0.833940i | \(-0.313920\pi\) | ||||
0.551855 | + | 0.833940i | \(0.313920\pi\) | |||||||
\(114\) | − | 361.536i | − | 0.297026i | ||||||
\(115\) | 248.156 | 0.201223 | ||||||||
\(116\) | − | 861.962i | − | 0.689924i | ||||||
\(117\) | 649.115 | 0.512912 | ||||||||
\(118\) | −20.7318 | −0.0161739 | ||||||||
\(119\) | 254.524i | 0.196069i | ||||||||
\(120\) | 301.798 | 0.229586 | ||||||||
\(121\) | −831.194 | −0.624488 | ||||||||
\(122\) | −1192.09 | −0.884647 | ||||||||
\(123\) | − | 67.2913i | − | 0.0493289i | ||||||
\(124\) | 844.331 | 0.611477 | ||||||||
\(125\) | − | 1115.60i | − | 0.798258i | ||||||
\(126\) | 170.268 | 0.120386 | ||||||||
\(127\) | −1303.18 | −0.910540 | −0.455270 | − | 0.890353i | \(-0.650457\pi\) | ||||
−0.455270 | + | 0.890353i | \(0.650457\pi\) | |||||||
\(128\) | − | 1292.90i | − | 0.892793i | ||||||
\(129\) | − | 614.874i | − | 0.419664i | ||||||
\(130\) | −524.213 | −0.353666 | ||||||||
\(131\) | 1368.57i | 0.912768i | 0.889783 | + | 0.456384i | \(0.150856\pi\) | ||||
−0.889783 | + | 0.456384i | \(0.849144\pi\) | |||||||
\(132\) | 391.749 | 0.258313 | ||||||||
\(133\) | − | 1056.00i | − | 0.688472i | ||||||
\(134\) | − | 28.0237i | − | 0.0180663i | ||||||
\(135\) | 133.556i | 0.0851458i | ||||||||
\(136\) | − | 402.033i | − | 0.253486i | ||||||
\(137\) | 2346.90i | 1.46357i | 0.681534 | + | 0.731786i | \(0.261313\pi\) | ||||
−0.681534 | + | 0.731786i | \(0.738687\pi\) | |||||||
\(138\) | −221.144 | −0.136413 | ||||||||
\(139\) | 1267.34i | 0.773344i | 0.922217 | + | 0.386672i | \(0.126375\pi\) | ||||
−0.922217 | + | 0.386672i | \(0.873625\pi\) | |||||||
\(140\) | 372.004 | 0.224572 | ||||||||
\(141\) | 253.358 | 0.151324 | ||||||||
\(142\) | − | 319.981i | − | 0.189100i | ||||||
\(143\) | −1612.43 | −0.942922 | ||||||||
\(144\) | 151.603 | 0.0877334 | ||||||||
\(145\) | −729.966 | −0.418072 | ||||||||
\(146\) | −346.616 | −0.196481 | ||||||||
\(147\) | −531.669 | −0.298308 | ||||||||
\(148\) | 1296.53 | 0.720097 | ||||||||
\(149\) | 2228.71i | 1.22539i | 0.790320 | + | 0.612694i | \(0.209914\pi\) | ||||
−0.790320 | + | 0.612694i | \(0.790086\pi\) | |||||||
\(150\) | 443.153i | 0.241222i | ||||||||
\(151\) | 595.191i | 0.320768i | 0.987055 | + | 0.160384i | \(0.0512732\pi\) | ||||
−0.987055 | + | 0.160384i | \(0.948727\pi\) | |||||||
\(152\) | 1668.00i | 0.890085i | ||||||||
\(153\) | 177.914 | 0.0940096 | ||||||||
\(154\) | −422.953 | −0.221315 | ||||||||
\(155\) | − | 715.035i | − | 0.370535i | ||||||
\(156\) | −1263.82 | −0.648633 | ||||||||
\(157\) | 729.836 | + | 1826.81i | 0.371002 | + | 0.928632i | ||||
\(158\) | −1607.64 | −0.809472 | ||||||||
\(159\) | 640.030i | 0.319231i | ||||||||
\(160\) | −927.228 | −0.458149 | ||||||||
\(161\) | −645.933 | −0.316190 | ||||||||
\(162\) | − | 119.018i | − | 0.0577220i | ||||||
\(163\) | 865.206i | 0.415756i | 0.978155 | + | 0.207878i | \(0.0666556\pi\) | ||||
−0.978155 | + | 0.207878i | \(0.933344\pi\) | |||||||
\(164\) | 131.016i | 0.0623817i | ||||||||
\(165\) | − | 331.759i | − | 0.156530i | ||||||
\(166\) | −1807.12 | −0.844939 | ||||||||
\(167\) | 1171.86 | 0.543001 | 0.271501 | − | 0.962438i | \(-0.412480\pi\) | ||||
0.271501 | + | 0.962438i | \(0.412480\pi\) | |||||||
\(168\) | −785.559 | −0.360757 | ||||||||
\(169\) | 3004.85 | 1.36771 | ||||||||
\(170\) | −143.680 | −0.0648220 | ||||||||
\(171\) | −738.149 | −0.330103 | ||||||||
\(172\) | 1197.16i | 0.530711i | ||||||||
\(173\) | −3542.12 | −1.55666 | −0.778330 | − | 0.627855i | \(-0.783933\pi\) | ||||
−0.778330 | + | 0.627855i | \(0.783933\pi\) | |||||||
\(174\) | 650.508 | 0.283419 | ||||||||
\(175\) | 1294.39i | 0.559125i | ||||||||
\(176\) | −376.588 | −0.161286 | ||||||||
\(177\) | 42.3281i | 0.0179750i | ||||||||
\(178\) | − | 2056.22i | − | 0.865846i | ||||||
\(179\) | 571.501i | 0.238637i | 0.992856 | + | 0.119318i | \(0.0380709\pi\) | ||||
−0.992856 | + | 0.119318i | \(0.961929\pi\) | |||||||
\(180\) | − | 260.033i | − | 0.107676i | ||||||
\(181\) | 3873.10i | 1.59053i | 0.606264 | + | 0.795263i | \(0.292667\pi\) | ||||
−0.606264 | + | 0.795263i | \(0.707333\pi\) | |||||||
\(182\) | 1364.49 | 0.555729 | ||||||||
\(183\) | 2433.90i | 0.983164i | ||||||||
\(184\) | 1020.28 | 0.408784 | ||||||||
\(185\) | − | 1097.99i | − | 0.436356i | ||||||
\(186\) | 637.202i | 0.251193i | ||||||||
\(187\) | −441.944 | −0.172824 | ||||||||
\(188\) | −493.287 | −0.191365 | ||||||||
\(189\) | − | 347.637i | − | 0.133793i | ||||||
\(190\) | 596.115 | 0.227614 | ||||||||
\(191\) | 283.289i | 0.107320i | 0.998559 | + | 0.0536599i | \(0.0170887\pi\) | ||||
−0.998559 | + | 0.0536599i | \(0.982911\pi\) | |||||||
\(192\) | 422.022 | 0.158629 | ||||||||
\(193\) | −1789.06 | −0.667250 | −0.333625 | − | 0.942706i | \(-0.608272\pi\) | ||||
−0.333625 | + | 0.942706i | \(0.608272\pi\) | |||||||
\(194\) | −1026.55 | −0.379907 | ||||||||
\(195\) | 1070.29i | 0.393051i | ||||||||
\(196\) | 1035.15 | 0.377243 | ||||||||
\(197\) | 967.408 | 0.349873 | 0.174936 | − | 0.984580i | \(-0.444028\pi\) | ||||
0.174936 | + | 0.984580i | \(0.444028\pi\) | |||||||
\(198\) | 295.646i | 0.106114i | ||||||||
\(199\) | 3613.64 | 1.28726 | 0.643628 | − | 0.765339i | \(-0.277429\pi\) | ||||
0.643628 | + | 0.765339i | \(0.277429\pi\) | |||||||
\(200\) | − | 2044.56i | − | 0.722860i | ||||||
\(201\) | −57.2161 | −0.0200782 | ||||||||
\(202\) | 1128.93i | 0.393225i | ||||||||
\(203\) | 1900.05 | 0.656932 | ||||||||
\(204\) | −346.396 | −0.118885 | ||||||||
\(205\) | 110.953 | 0.0378013 | ||||||||
\(206\) | 1753.32 | 0.593008 | ||||||||
\(207\) | 451.510i | 0.151604i | ||||||||
\(208\) | 1214.91 | 0.404996 | ||||||||
\(209\) | 1833.59 | 0.606852 | ||||||||
\(210\) | 280.745i | 0.0922536i | ||||||||
\(211\) | 306.600i | 0.100034i | 0.998748 | + | 0.0500171i | \(0.0159276\pi\) | ||||
−0.998748 | + | 0.0500171i | \(0.984072\pi\) | |||||||
\(212\) | − | 1246.13i | − | 0.403702i | ||||||
\(213\) | −653.305 | −0.210158 | ||||||||
\(214\) | −2044.71 | −0.653149 | ||||||||
\(215\) | 1013.83 | 0.321594 | ||||||||
\(216\) | 549.110i | 0.172973i | ||||||||
\(217\) | 1861.18i | 0.582237i | ||||||||
\(218\) | − | 852.670i | − | 0.264909i | ||||||
\(219\) | 707.688i | 0.218361i | ||||||||
\(220\) | 645.931i | 0.197949i | ||||||||
\(221\) | 1425.76 | 0.433968 | ||||||||
\(222\) | 978.471i | 0.295814i | ||||||||
\(223\) | − | 131.482i | − | 0.0394830i | −0.999805 | − | 0.0197415i | \(-0.993716\pi\) | ||
0.999805 | − | 0.0197415i | \(-0.00628433\pi\) | |||||||
\(224\) | 2413.51 | 0.719907 | ||||||||
\(225\) | 904.787 | 0.268085 | ||||||||
\(226\) | − | 1948.05i | − | 0.573374i | ||||||
\(227\) | − | 4436.26i | − | 1.29711i | −0.761166 | − | 0.648557i | \(-0.775373\pi\) | ||
0.761166 | − | 0.648557i | \(-0.224627\pi\) | |||||||
\(228\) | 1437.17 | 0.417451 | ||||||||
\(229\) | 2543.10i | 0.733854i | 0.930250 | + | 0.366927i | \(0.119590\pi\) | ||||
−0.930250 | + | 0.366927i | \(0.880410\pi\) | |||||||
\(230\) | − | 364.631i | − | 0.104535i | ||||||
\(231\) | 863.544i | 0.245961i | ||||||||
\(232\) | −3001.22 | −0.849310 | ||||||||
\(233\) | 6042.00 | 1.69882 | 0.849409 | − | 0.527736i | \(-0.176959\pi\) | ||||
0.849409 | + | 0.527736i | \(0.176959\pi\) | |||||||
\(234\) | − | 953.785i | − | 0.266457i | ||||||
\(235\) | 417.748i | 0.115961i | ||||||||
\(236\) | − | 82.4125i | − | 0.0227314i | ||||||
\(237\) | 3282.31i | 0.899617i | ||||||||
\(238\) | 373.988 | 0.101857 | ||||||||
\(239\) | −1992.67 | −0.539311 | −0.269655 | − | 0.962957i | \(-0.586910\pi\) | ||||
−0.269655 | + | 0.962957i | \(0.586910\pi\) | |||||||
\(240\) | 249.970i | 0.0672312i | ||||||||
\(241\) | 4488.35i | 1.19967i | 0.800125 | + | 0.599834i | \(0.204767\pi\) | ||||
−0.800125 | + | 0.599834i | \(0.795233\pi\) | |||||||
\(242\) | 1221.32i | 0.324420i | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | − | 4738.78i | − | 1.24332i | ||||||
\(245\) | − | 876.638i | − | 0.228597i | ||||||
\(246\) | −98.8753 | −0.0256263 | ||||||||
\(247\) | −5915.35 | −1.52382 | ||||||||
\(248\) | − | 2939.83i | − | 0.752740i | ||||||
\(249\) | 3689.60i | 0.939033i | ||||||||
\(250\) | −1639.22 | −0.414693 | ||||||||
\(251\) | − | 4885.89i | − | 1.22866i | −0.789048 | − | 0.614332i | \(-0.789426\pi\) | ||
0.789048 | − | 0.614332i | \(-0.210574\pi\) | |||||||
\(252\) | 676.846i | 0.169196i | ||||||||
\(253\) | − | 1121.57i | − | 0.278705i | ||||||
\(254\) | 1914.84i | 0.473023i | ||||||||
\(255\) | 293.351i | 0.0720407i | ||||||||
\(256\) | −3025.13 | −0.738557 | ||||||||
\(257\) | −3532.16 | −0.857314 | −0.428657 | − | 0.903467i | \(-0.641013\pi\) | ||||
−0.428657 | + | 0.903467i | \(0.641013\pi\) | |||||||
\(258\) | −903.473 | −0.218015 | ||||||||
\(259\) | 2857.99i | 0.685663i | ||||||||
\(260\) | − | 2083.84i | − | 0.497055i | ||||||
\(261\) | − | 1328.14i | − | 0.314981i | ||||||
\(262\) | 2010.93 | 0.474181 | ||||||||
\(263\) | 1901.34 | 0.445786 | 0.222893 | − | 0.974843i | \(-0.428450\pi\) | ||||
0.222893 | + | 0.974843i | \(0.428450\pi\) | |||||||
\(264\) | − | 1364.01i | − | 0.317989i | ||||||
\(265\) | −1055.31 | −0.244630 | ||||||||
\(266\) | −1551.64 | −0.357659 | ||||||||
\(267\) | −4198.20 | −0.962268 | ||||||||
\(268\) | 111.399 | 0.0253910 | ||||||||
\(269\) | 6193.20i | 1.40374i | 0.712305 | + | 0.701870i | \(0.247651\pi\) | ||||
−0.712305 | + | 0.701870i | \(0.752349\pi\) | |||||||
\(270\) | 196.242 | 0.0442331 | ||||||||
\(271\) | 7632.45i | 1.71084i | 0.517933 | + | 0.855421i | \(0.326702\pi\) | ||||
−0.517933 | + | 0.855421i | \(0.673298\pi\) | |||||||
\(272\) | 332.991 | 0.0742300 | ||||||||
\(273\) | − | 2785.88i | − | 0.617616i | ||||||
\(274\) | 3448.45 | 0.760323 | ||||||||
\(275\) | −2247.53 | −0.492840 | ||||||||
\(276\) | − | 879.087i | − | 0.191720i | ||||||
\(277\) | −325.575 | −0.0706205 | −0.0353103 | − | 0.999376i | \(-0.511242\pi\) | ||||
−0.0353103 | + | 0.999376i | \(0.511242\pi\) | |||||||
\(278\) | 1862.19 | 0.401750 | ||||||||
\(279\) | 1300.98 | 0.279167 | ||||||||
\(280\) | − | 1295.26i | − | 0.276453i | ||||||
\(281\) | 521.494 | 0.110711 | 0.0553554 | − | 0.998467i | \(-0.482371\pi\) | ||||
0.0553554 | + | 0.998467i | \(0.482371\pi\) | |||||||
\(282\) | − | 372.275i | − | 0.0786123i | ||||||
\(283\) | −6983.45 | −1.46687 | −0.733433 | − | 0.679762i | \(-0.762083\pi\) | ||||
−0.733433 | + | 0.679762i | \(0.762083\pi\) | |||||||
\(284\) | 1271.98 | 0.265768 | ||||||||
\(285\) | − | 1217.09i | − | 0.252962i | ||||||
\(286\) | 2369.24i | 0.489846i | ||||||||
\(287\) | −288.802 | −0.0593987 | ||||||||
\(288\) | − | 1687.05i | − | 0.345176i | ||||||
\(289\) | −4522.22 | −0.920460 | ||||||||
\(290\) | 1072.58i | 0.217187i | ||||||||
\(291\) | 2095.91i | 0.422214i | ||||||||
\(292\) | − | 1377.86i | − | 0.276141i | ||||||
\(293\) | 637.031i | 0.127016i | 0.997981 | + | 0.0635081i | \(0.0202289\pi\) | ||||
−0.997981 | + | 0.0635081i | \(0.979771\pi\) | |||||||
\(294\) | 781.214i | 0.154970i | ||||||||
\(295\) | −69.7924 | −0.0137745 | ||||||||
\(296\) | − | 4514.33i | − | 0.886454i | ||||||
\(297\) | 603.621 | 0.117932 | ||||||||
\(298\) | 3274.78 | 0.636587 | ||||||||
\(299\) | 3618.30i | 0.699838i | ||||||||
\(300\) | −1761.61 | −0.339023 | ||||||||
\(301\) | −2638.93 | −0.505333 | ||||||||
\(302\) | 874.550 | 0.166638 | ||||||||
\(303\) | 2304.95 | 0.437015 | ||||||||
\(304\) | −1381.55 | −0.260650 | ||||||||
\(305\) | −4013.11 | −0.753411 | ||||||||
\(306\) | − | 261.419i | − | 0.0488378i | ||||||
\(307\) | − | 9552.77i | − | 1.77591i | −0.459927 | − | 0.887957i | \(-0.652125\pi\) | ||
0.459927 | − | 0.887957i | \(-0.347875\pi\) | |||||||
\(308\) | − | 1681.31i | − | 0.311044i | ||||||
\(309\) | − | 3579.76i | − | 0.659047i | ||||||
\(310\) | −1050.65 | −0.192492 | ||||||||
\(311\) | −2679.95 | −0.488636 | −0.244318 | − | 0.969695i | \(-0.578564\pi\) | ||||
−0.244318 | + | 0.969695i | \(0.578564\pi\) | |||||||
\(312\) | 4400.44i | 0.798480i | ||||||||
\(313\) | 1862.35 | 0.336314 | 0.168157 | − | 0.985760i | \(-0.446218\pi\) | ||||
0.168157 | + | 0.985760i | \(0.446218\pi\) | |||||||
\(314\) | 2684.24 | − | 1072.39i | 0.482422 | − | 0.192735i | ||||
\(315\) | 573.198 | 0.102527 | ||||||||
\(316\) | − | 6390.64i | − | 1.13766i | ||||||
\(317\) | 616.031 | 0.109147 | 0.0545737 | − | 0.998510i | \(-0.482620\pi\) | ||||
0.0545737 | + | 0.998510i | \(0.482620\pi\) | |||||||
\(318\) | 940.436 | 0.165840 | ||||||||
\(319\) | 3299.16i | 0.579052i | ||||||||
\(320\) | 695.847i | 0.121559i | ||||||||
\(321\) | 4174.70i | 0.725885i | ||||||||
\(322\) | 949.109i | 0.164260i | ||||||||
\(323\) | −1621.32 | −0.279296 | ||||||||
\(324\) | 473.119 | 0.0811247 | ||||||||
\(325\) | 7250.75 | 1.23754 | ||||||||
\(326\) | 1271.30 | 0.215984 | ||||||||
\(327\) | −1740.90 | −0.294410 | ||||||||
\(328\) | 456.177 | 0.0767932 | ||||||||
\(329\) | − | 1087.37i | − | 0.182214i | ||||||
\(330\) | −487.473 | −0.0813168 | ||||||||
\(331\) | −4652.55 | −0.772590 | −0.386295 | − | 0.922375i | \(-0.626245\pi\) | ||||
−0.386295 | + | 0.922375i | \(0.626245\pi\) | |||||||
\(332\) | − | 7183.63i | − | 1.18751i | ||||||
\(333\) | 1997.75 | 0.328756 | ||||||||
\(334\) | − | 1721.89i | − | 0.282088i | ||||||
\(335\) | − | 94.3403i | − | 0.0153862i | ||||||
\(336\) | − | 650.653i | − | 0.105643i | ||||||
\(337\) | 477.677i | 0.0772128i | 0.999254 | + | 0.0386064i | \(0.0122919\pi\) | ||||
−0.999254 | + | 0.0386064i | \(0.987708\pi\) | |||||||
\(338\) | − | 4415.22i | − | 0.710521i | ||||||
\(339\) | −3977.35 | −0.637227 | ||||||||
\(340\) | − | 571.153i | − | 0.0911032i | ||||||
\(341\) | −3231.68 | −0.513211 | ||||||||
\(342\) | 1084.61i | 0.171488i | ||||||||
\(343\) | 6698.10i | 1.05441i | ||||||||
\(344\) | 4168.31 | 0.653315 | ||||||||
\(345\) | −744.469 | −0.116176 | ||||||||
\(346\) | 5204.65i | 0.808682i | ||||||||
\(347\) | 7159.31 | 1.10758 | 0.553792 | − | 0.832655i | \(-0.313180\pi\) | ||||
0.553792 | + | 0.832655i | \(0.313180\pi\) | |||||||
\(348\) | 2585.89i | 0.398328i | ||||||||
\(349\) | −4040.57 | −0.619733 | −0.309867 | − | 0.950780i | \(-0.600284\pi\) | ||||
−0.309867 | + | 0.950780i | \(0.600284\pi\) | |||||||
\(350\) | 1901.93 | 0.290464 | ||||||||
\(351\) | −1947.34 | −0.296130 | ||||||||
\(352\) | 4190.70i | 0.634560i | ||||||||
\(353\) | −3064.42 | −0.462047 | −0.231023 | − | 0.972948i | \(-0.574207\pi\) | ||||
−0.231023 | + | 0.972948i | \(0.574207\pi\) | |||||||
\(354\) | 62.1953 | 0.00933798 | ||||||||
\(355\) | − | 1077.20i | − | 0.161047i | ||||||
\(356\) | 8173.86 | 1.21689 | ||||||||
\(357\) | − | 763.572i | − | 0.113200i | ||||||
\(358\) | 839.741 | 0.123971 | ||||||||
\(359\) | 11621.5i | 1.70852i | 0.519843 | + | 0.854262i | \(0.325990\pi\) | ||||
−0.519843 | + | 0.854262i | \(0.674010\pi\) | |||||||
\(360\) | −905.395 | −0.132551 | ||||||||
\(361\) | −132.293 | −0.0192875 | ||||||||
\(362\) | 5690.99 | 0.826275 | ||||||||
\(363\) | 2493.58 | 0.360548 | ||||||||
\(364\) | 5424.09i | 0.781043i | ||||||||
\(365\) | −1166.87 | −0.167333 | ||||||||
\(366\) | 3576.28 | 0.510751 | ||||||||
\(367\) | − | 1691.85i | − | 0.240637i | −0.992735 | − | 0.120319i | \(-0.961608\pi\) | ||
0.992735 | − | 0.120319i | \(-0.0383916\pi\) | |||||||
\(368\) | 845.067i | 0.119707i | ||||||||
\(369\) | 201.874i | 0.0284801i | ||||||||
\(370\) | −1613.34 | −0.226686 | ||||||||
\(371\) | 2746.89 | 0.384397 | ||||||||
\(372\) | −2532.99 | −0.353036 | ||||||||
\(373\) | − | 12113.6i | − | 1.68155i | −0.541387 | − | 0.840773i | \(-0.682101\pi\) | ||
0.541387 | − | 0.840773i | \(-0.317899\pi\) | |||||||
\(374\) | 649.376i | 0.0897819i | ||||||||
\(375\) | 3346.80i | 0.460874i | ||||||||
\(376\) | 1717.55i | 0.235574i | ||||||||
\(377\) | − | 10643.4i | − | 1.45402i | ||||||
\(378\) | −510.804 | −0.0695052 | ||||||||
\(379\) | − | 4764.05i | − | 0.645681i | −0.946453 | − | 0.322840i | \(-0.895362\pi\) | ||
0.946453 | − | 0.322840i | \(-0.104638\pi\) | |||||||
\(380\) | 2369.66i | 0.319898i | ||||||||
\(381\) | 3909.54 | 0.525700 | ||||||||
\(382\) | 416.255 | 0.0557524 | ||||||||
\(383\) | 307.764i | 0.0410601i | 0.999789 | + | 0.0205301i | \(0.00653538\pi\) | ||||
−0.999789 | + | 0.0205301i | \(0.993465\pi\) | |||||||
\(384\) | 3878.71i | 0.515454i | ||||||||
\(385\) | −1423.85 | −0.188483 | ||||||||
\(386\) | 2628.77i | 0.346635i | ||||||||
\(387\) | 1844.62i | 0.242293i | ||||||||
\(388\) | − | 4080.72i | − | 0.533936i | ||||||
\(389\) | −10499.8 | −1.36854 | −0.684268 | − | 0.729230i | \(-0.739878\pi\) | ||||
−0.684268 | + | 0.729230i | \(0.739878\pi\) | |||||||
\(390\) | 1572.64 | 0.204189 | ||||||||
\(391\) | 991.726i | 0.128270i | ||||||||
\(392\) | − | 3604.25i | − | 0.464394i | ||||||
\(393\) | − | 4105.71i | − | 0.526987i | ||||||
\(394\) | − | 1421.47i | − | 0.181758i | ||||||
\(395\) | −5412.01 | −0.689387 | ||||||||
\(396\) | −1175.25 | −0.149137 | ||||||||
\(397\) | 4285.68i | 0.541794i | 0.962608 | + | 0.270897i | \(0.0873203\pi\) | ||||
−0.962608 | + | 0.270897i | \(0.912680\pi\) | |||||||
\(398\) | − | 5309.74i | − | 0.668726i | ||||||
\(399\) | 3168.00i | 0.397489i | ||||||||
\(400\) | 1693.44 | 0.211680 | ||||||||
\(401\) | − | 1402.14i | − | 0.174612i | −0.996182 | − | 0.0873062i | \(-0.972174\pi\) | ||
0.996182 | − | 0.0873062i | \(-0.0278259\pi\) | |||||||
\(402\) | 84.0712i | 0.0104306i | ||||||||
\(403\) | 10425.7 | 1.28869 | ||||||||
\(404\) | −4487.71 | −0.552653 | ||||||||
\(405\) | − | 400.668i | − | 0.0491590i | ||||||
\(406\) | − | 2791.86i | − | 0.341275i | ||||||
\(407\) | −4962.48 | −0.604376 | ||||||||
\(408\) | 1206.10i | 0.146350i | ||||||||
\(409\) | − | 8387.78i | − | 1.01406i | −0.861929 | − | 0.507028i | \(-0.830744\pi\) | ||
0.861929 | − | 0.507028i | \(-0.169256\pi\) | |||||||
\(410\) | − | 163.030i | − | 0.0196377i | ||||||
\(411\) | − | 7040.71i | − | 0.844994i | ||||||
\(412\) | 6969.77i | 0.833436i | ||||||||
\(413\) | 181.665 | 0.0216444 | ||||||||
\(414\) | 663.432 | 0.0787582 | ||||||||
\(415\) | −6083.57 | −0.719592 | ||||||||
\(416\) | − | 13519.6i | − | 1.59340i | ||||||
\(417\) | − | 3802.03i | − | 0.446490i | ||||||
\(418\) | − | 2694.21i | − | 0.315258i | ||||||
\(419\) | −6080.91 | −0.709002 | −0.354501 | − | 0.935056i | \(-0.615349\pi\) | ||||
−0.354501 | + | 0.935056i | \(0.615349\pi\) | |||||||
\(420\) | −1116.01 | −0.129657 | ||||||||
\(421\) | 1098.58i | 0.127177i | 0.997976 | + | 0.0635883i | \(0.0202545\pi\) | ||||
−0.997976 | + | 0.0635883i | \(0.979746\pi\) | |||||||
\(422\) | 450.506 | 0.0519675 | ||||||||
\(423\) | −760.075 | −0.0873667 | ||||||||
\(424\) | −4338.85 | −0.496965 | ||||||||
\(425\) | 1987.33 | 0.226823 | ||||||||
\(426\) | 959.942i | 0.109177i | ||||||||
\(427\) | 10445.8 | 1.18386 | ||||||||
\(428\) | − | 8128.11i | − | 0.917960i | ||||||
\(429\) | 4837.28 | 0.544396 | ||||||||
\(430\) | − | 1489.68i | − | 0.167067i | ||||||
\(431\) | 7160.80 | 0.800287 | 0.400143 | − | 0.916453i | \(-0.368960\pi\) | ||||
0.400143 | + | 0.916453i | \(0.368960\pi\) | |||||||
\(432\) | −454.810 | −0.0506529 | ||||||||
\(433\) | − | 9273.03i | − | 1.02918i | −0.857437 | − | 0.514588i | \(-0.827945\pi\) | ||
0.857437 | − | 0.514588i | \(-0.172055\pi\) | |||||||
\(434\) | 2734.75 | 0.302471 | ||||||||
\(435\) | 2189.90 | 0.241374 | ||||||||
\(436\) | 3389.52 | 0.372313 | ||||||||
\(437\) | − | 4114.59i | − | 0.450406i | ||||||
\(438\) | 1039.85 | 0.113438 | ||||||||
\(439\) | − | 8210.41i | − | 0.892623i | −0.894878 | − | 0.446312i | \(-0.852737\pi\) | ||
0.894878 | − | 0.446312i | \(-0.147263\pi\) | |||||||
\(440\) | 2249.04 | 0.243679 | ||||||||
\(441\) | 1595.01 | 0.172228 | ||||||||
\(442\) | − | 2094.95i | − | 0.225445i | ||||||
\(443\) | 116.027i | 0.0124438i | 0.999981 | + | 0.00622188i | \(0.00198050\pi\) | ||||
−0.999981 | + | 0.00622188i | \(0.998020\pi\) | |||||||
\(444\) | −3889.60 | −0.415748 | ||||||||
\(445\) | − | 6922.17i | − | 0.737398i | ||||||
\(446\) | −193.195 | −0.0205114 | ||||||||
\(447\) | − | 6686.12i | − | 0.707478i | ||||||
\(448\) | − | 1811.24i | − | 0.191011i | ||||||
\(449\) | − | 432.121i | − | 0.0454188i | −0.999742 | − | 0.0227094i | \(-0.992771\pi\) | ||
0.999742 | − | 0.0227094i | \(-0.00722925\pi\) | |||||||
\(450\) | − | 1329.46i | − | 0.139270i | ||||||
\(451\) | − | 501.463i | − | 0.0523569i | ||||||
\(452\) | 7743.86 | 0.805842 | ||||||||
\(453\) | − | 1785.57i | − | 0.185195i | ||||||
\(454\) | −6518.47 | −0.673848 | ||||||||
\(455\) | 4593.48 | 0.473287 | ||||||||
\(456\) | − | 5004.01i | − | 0.513891i | ||||||
\(457\) | 9018.04 | 0.923076 | 0.461538 | − | 0.887120i | \(-0.347298\pi\) | ||||
0.461538 | + | 0.887120i | \(0.347298\pi\) | |||||||
\(458\) | 3736.73 | 0.381236 | ||||||||
\(459\) | −533.741 | −0.0542764 | ||||||||
\(460\) | 1449.47 | 0.146918 | ||||||||
\(461\) | 625.625 | 0.0632066 | 0.0316033 | − | 0.999500i | \(-0.489939\pi\) | ||||
0.0316033 | + | 0.999500i | \(0.489939\pi\) | |||||||
\(462\) | 1268.86 | 0.127776 | ||||||||
\(463\) | − | 7755.27i | − | 0.778441i | −0.921145 | − | 0.389220i | \(-0.872744\pi\) | ||
0.921145 | − | 0.389220i | \(-0.127256\pi\) | |||||||
\(464\) | − | 2485.81i | − | 0.248709i | ||||||
\(465\) | 2145.10i | 0.213929i | ||||||||
\(466\) | − | 8877.88i | − | 0.882532i | ||||||
\(467\) | −8505.55 | −0.842805 | −0.421402 | − | 0.906874i | \(-0.638462\pi\) | ||||
−0.421402 | + | 0.906874i | \(0.638462\pi\) | |||||||
\(468\) | 3791.46 | 0.374488 | ||||||||
\(469\) | 245.561i | 0.0241769i | ||||||||
\(470\) | 613.823 | 0.0602415 | ||||||||
\(471\) | −2189.51 | − | 5480.43i | −0.214198 | − | 0.536146i | ||||
\(472\) | −286.948 | −0.0279827 | ||||||||
\(473\) | − | 4582.11i | − | 0.445424i | ||||||
\(474\) | 4822.91 | 0.467349 | ||||||||
\(475\) | −8245.27 | −0.796461 | ||||||||
\(476\) | 1486.67i | 0.143154i | ||||||||
\(477\) | − | 1920.09i | − | 0.184308i | ||||||
\(478\) | 2927.96i | 0.280171i | ||||||||
\(479\) | 10755.4i | 1.02594i | 0.858407 | + | 0.512970i | \(0.171455\pi\) | ||||
−0.858407 | + | 0.512970i | \(0.828545\pi\) | |||||||
\(480\) | 2781.68 | 0.264512 | ||||||||
\(481\) | 16009.5 | 1.51761 | ||||||||
\(482\) | 6595.01 | 0.623225 | ||||||||
\(483\) | 1937.80 | 0.182552 | ||||||||
\(484\) | −4854.98 | −0.455953 | ||||||||
\(485\) | −3455.82 | −0.323548 | ||||||||
\(486\) | 357.055i | 0.0333258i | ||||||||
\(487\) | 7624.10 | 0.709406 | 0.354703 | − | 0.934979i | \(-0.384582\pi\) | ||||
0.354703 | + | 0.934979i | \(0.384582\pi\) | |||||||
\(488\) | −16499.7 | −1.53055 | ||||||||
\(489\) | − | 2595.62i | − | 0.240037i | ||||||
\(490\) | −1288.10 | −0.118756 | ||||||||
\(491\) | 18175.8i | 1.67060i | 0.549797 | + | 0.835298i | \(0.314705\pi\) | ||||
−0.549797 | + | 0.835298i | \(0.685295\pi\) | |||||||
\(492\) | − | 393.047i | − | 0.0360161i | ||||||
\(493\) | − | 2917.22i | − | 0.266501i | ||||||
\(494\) | 8691.79i | 0.791623i | ||||||||
\(495\) | 995.276i | 0.0903724i | ||||||||
\(496\) | 2434.97 | 0.220430 | ||||||||
\(497\) | 2803.87i | 0.253060i | ||||||||
\(498\) | 5421.36 | 0.487826 | ||||||||
\(499\) | 14506.9i | 1.30144i | 0.759320 | + | 0.650718i | \(0.225532\pi\) | ||||
−0.759320 | + | 0.650718i | \(0.774468\pi\) | |||||||
\(500\) | − | 6516.19i | − | 0.582826i | ||||||
\(501\) | −3515.58 | −0.313502 | ||||||||
\(502\) | −7179.14 | −0.638288 | ||||||||
\(503\) | 5062.63i | 0.448771i | 0.974500 | + | 0.224385i | \(0.0720374\pi\) | ||||
−0.974500 | + | 0.224385i | \(0.927963\pi\) | |||||||
\(504\) | 2356.68 | 0.208283 | ||||||||
\(505\) | 3800.49i | 0.334890i | ||||||||
\(506\) | −1647.99 | −0.144787 | ||||||||
\(507\) | −9014.56 | −0.789647 | ||||||||
\(508\) | −7611.85 | −0.664805 | ||||||||
\(509\) | 21986.8i | 1.91463i | 0.289050 | + | 0.957314i | \(0.406661\pi\) | ||||
−0.289050 | + | 0.957314i | \(0.593339\pi\) | |||||||
\(510\) | 431.039 | 0.0374250 | ||||||||
\(511\) | 3037.27 | 0.262937 | ||||||||
\(512\) | − | 5898.20i | − | 0.509114i | ||||||
\(513\) | 2214.45 | 0.190585 | ||||||||
\(514\) | 5190.01i | 0.445373i | ||||||||
\(515\) | 5902.46 | 0.505036 | ||||||||
\(516\) | − | 3591.47i | − | 0.306406i | ||||||
\(517\) | 1888.06 | 0.160612 | ||||||||
\(518\) | 4199.42 | 0.356200 | ||||||||
\(519\) | 10626.4 | 0.898738 | ||||||||
\(520\) | −7255.62 | −0.611885 | ||||||||
\(521\) | − | 1498.57i | − | 0.126014i | −0.998013 | − | 0.0630071i | \(-0.979931\pi\) | ||
0.998013 | − | 0.0630071i | \(-0.0200691\pi\) | |||||||
\(522\) | −1951.52 | −0.163632 | ||||||||
\(523\) | −1153.31 | −0.0964255 | −0.0482128 | − | 0.998837i | \(-0.515353\pi\) | ||||
−0.0482128 | + | 0.998837i | \(0.515353\pi\) | |||||||
\(524\) | 7993.79i | 0.666432i | ||||||||
\(525\) | − | 3883.18i | − | 0.322811i | ||||||
\(526\) | − | 2793.76i | − | 0.231585i | ||||||
\(527\) | 2857.55 | 0.236199 | ||||||||
\(528\) | 1129.77 | 0.0931188 | ||||||||
\(529\) | 9650.19 | 0.793145 | ||||||||
\(530\) | 1550.63i | 0.127085i | ||||||||
\(531\) | − | 126.984i | − | 0.0103779i | ||||||
\(532\) | − | 6168.06i | − | 0.502668i | ||||||
\(533\) | 1617.77i | 0.131470i | ||||||||
\(534\) | 6168.67i | 0.499896i | ||||||||
\(535\) | −6883.42 | −0.556254 | ||||||||
\(536\) | − | 387.876i | − | 0.0312569i | ||||||
\(537\) | − | 1714.50i | − | 0.137777i | ||||||
\(538\) | 9100.05 | 0.729240 | ||||||||
\(539\) | −3962.06 | −0.316619 | ||||||||
\(540\) | 780.098i | 0.0621668i | ||||||||
\(541\) | − | 12206.4i | − | 0.970045i | −0.874502 | − | 0.485023i | \(-0.838811\pi\) | ||
0.874502 | − | 0.485023i | \(-0.161189\pi\) | |||||||
\(542\) | 11214.8 | 0.888779 | ||||||||
\(543\) | − | 11619.3i | − | 0.918291i | ||||||
\(544\) | − | 3705.55i | − | 0.292048i | ||||||
\(545\) | − | 2870.47i | − | 0.225610i | ||||||
\(546\) | −4093.47 | −0.320850 | ||||||||
\(547\) | 15505.1 | 1.21197 | 0.605987 | − | 0.795475i | \(-0.292778\pi\) | ||||
0.605987 | + | 0.795475i | \(0.292778\pi\) | |||||||
\(548\) | 13708.2i | 1.06859i | ||||||||
\(549\) | − | 7301.70i | − | 0.567630i | ||||||
\(550\) | 3302.43i | 0.256029i | ||||||||
\(551\) | 12103.3i | 0.935786i | ||||||||
\(552\) | −3060.85 | −0.236011 | ||||||||
\(553\) | 14087.1 | 1.08326 | ||||||||
\(554\) | 478.387i | 0.0366872i | ||||||||
\(555\) | 3293.97i | 0.251930i | ||||||||
\(556\) | 7402.53i | 0.564635i | ||||||||
\(557\) | −12453.1 | −0.947317 | −0.473658 | − | 0.880709i | \(-0.657067\pi\) | ||||
−0.473658 | + | 0.880709i | \(0.657067\pi\) | |||||||
\(558\) | − | 1911.61i | − | 0.145026i | ||||||
\(559\) | 14782.4i | 1.11848i | ||||||||
\(560\) | 1072.82 | 0.0809555 | ||||||||
\(561\) | 1325.83 | 0.0997802 | ||||||||
\(562\) | − | 766.264i | − | 0.0575140i | ||||||
\(563\) | 1763.65i | 0.132023i | 0.997819 | + | 0.0660116i | \(0.0210274\pi\) | ||||
−0.997819 | + | 0.0660116i | \(0.978973\pi\) | |||||||
\(564\) | 1479.86 | 0.110485 | ||||||||
\(565\) | − | 6558.02i | − | 0.488315i | ||||||
\(566\) | 10261.2i | 0.762034i | ||||||||
\(567\) | 1042.91i | 0.0772454i | ||||||||
\(568\) | − | 4428.84i | − | 0.327166i | ||||||
\(569\) | − | 14445.7i | − | 1.06431i | −0.846646 | − | 0.532156i | \(-0.821382\pi\) | ||
0.846646 | − | 0.532156i | \(-0.178618\pi\) | |||||||
\(570\) | −1788.35 | −0.131413 | ||||||||
\(571\) | 837.220 | 0.0613600 | 0.0306800 | − | 0.999529i | \(-0.490233\pi\) | ||||
0.0306800 | + | 0.999529i | \(0.490233\pi\) | |||||||
\(572\) | −9418.14 | −0.688448 | ||||||||
\(573\) | − | 849.868i | − | 0.0619612i | ||||||
\(574\) | 424.354i | 0.0308575i | ||||||||
\(575\) | 5043.46i | 0.365786i | ||||||||
\(576\) | −1266.06 | −0.0915845 | ||||||||
\(577\) | −3624.16 | −0.261483 | −0.130741 | − | 0.991416i | \(-0.541736\pi\) | ||||
−0.130741 | + | 0.991416i | \(0.541736\pi\) | |||||||
\(578\) | 6644.78i | 0.478177i | ||||||||
\(579\) | 5367.17 | 0.385237 | ||||||||
\(580\) | −4263.71 | −0.305243 | ||||||||
\(581\) | 15835.1 | 1.13072 | ||||||||
\(582\) | 3079.65 | 0.219339 | ||||||||
\(583\) | 4769.58i | 0.338826i | ||||||||
\(584\) | −4797.51 | −0.339936 | ||||||||
\(585\) | − | 3210.86i | − | 0.226928i | ||||||
\(586\) | 936.029 | 0.0659846 | ||||||||
\(587\) | 7431.17i | 0.522516i | 0.965269 | + | 0.261258i | \(0.0841374\pi\) | ||||
−0.965269 | + | 0.261258i | \(0.915863\pi\) | |||||||
\(588\) | −3105.46 | −0.217801 | ||||||||
\(589\) | −11855.7 | −0.829384 | ||||||||
\(590\) | 102.550i | 0.00715581i | ||||||||
\(591\) | −2902.22 | −0.201999 | ||||||||
\(592\) | 3739.08 | 0.259586 | ||||||||
\(593\) | −20235.7 | −1.40132 | −0.700659 | − | 0.713496i | \(-0.747111\pi\) | ||||
−0.700659 | + | 0.713496i | \(0.747111\pi\) | |||||||
\(594\) | − | 886.938i | − | 0.0612652i | ||||||
\(595\) | 1259.01 | 0.0867468 | ||||||||
\(596\) | 13017.8i | 0.894683i | ||||||||
\(597\) | −10840.9 | −0.743197 | ||||||||
\(598\) | 5316.59 | 0.363564 | ||||||||
\(599\) | 2676.96i | 0.182601i | 0.995823 | + | 0.0913003i | \(0.0291023\pi\) | ||||
−0.995823 | + | 0.0913003i | \(0.970898\pi\) | |||||||
\(600\) | 6133.67i | 0.417344i | ||||||||
\(601\) | −26488.6 | −1.79783 | −0.898914 | − | 0.438125i | \(-0.855643\pi\) | ||||
−0.898914 | + | 0.438125i | \(0.855643\pi\) | |||||||
\(602\) | 3877.54i | 0.262519i | ||||||||
\(603\) | 171.648 | 0.0115921 | ||||||||
\(604\) | 3476.49i | 0.234200i | ||||||||
\(605\) | 4111.52i | 0.276293i | ||||||||
\(606\) | − | 3386.80i | − | 0.227029i | ||||||
\(607\) | − | 12988.5i | − | 0.868514i | −0.900789 | − | 0.434257i | \(-0.857011\pi\) | ||
0.900789 | − | 0.434257i | \(-0.142989\pi\) | |||||||
\(608\) | 15374.0i | 1.02549i | ||||||||
\(609\) | −5700.15 | −0.379280 | ||||||||
\(610\) | 5896.72i | 0.391395i | ||||||||
\(611\) | −6091.06 | −0.403303 | ||||||||
\(612\) | 1039.19 | 0.0686384 | ||||||||
\(613\) | 3157.14i | 0.208019i | 0.994576 | + | 0.104010i | \(0.0331673\pi\) | ||||
−0.994576 | + | 0.104010i | \(0.966833\pi\) | |||||||
\(614\) | −14036.5 | −0.922583 | ||||||||
\(615\) | −332.858 | −0.0218246 | ||||||||
\(616\) | −5854.08 | −0.382902 | ||||||||
\(617\) | −17269.9 | −1.12684 | −0.563421 | − | 0.826170i | \(-0.690515\pi\) | ||||
−0.563421 | + | 0.826170i | \(0.690515\pi\) | |||||||
\(618\) | −5259.96 | −0.342373 | ||||||||
\(619\) | −4562.08 | −0.296228 | −0.148114 | − | 0.988970i | \(-0.547320\pi\) | ||||
−0.148114 | + | 0.988970i | \(0.547320\pi\) | |||||||
\(620\) | − | 4176.50i | − | 0.270536i | ||||||
\(621\) | − | 1354.53i | − | 0.0875289i | ||||||
\(622\) | 3937.81i | 0.253846i | ||||||||
\(623\) | 18017.9i | 1.15870i | ||||||||
\(624\) | −3644.74 | −0.233824 | ||||||||
\(625\) | 7048.15 | 0.451082 | ||||||||
\(626\) | − | 2736.47i | − | 0.174715i | ||||||
\(627\) | −5500.77 | −0.350366 | ||||||||
\(628\) | 4262.96 | + | 10670.3i | 0.270876 | + | 0.678015i | ||||
\(629\) | 4387.98 | 0.278156 | ||||||||
\(630\) | − | 842.236i | − | 0.0532627i | ||||||
\(631\) | 21537.0 | 1.35876 | 0.679378 | − | 0.733788i | \(-0.262250\pi\) | ||||
0.679378 | + | 0.733788i | \(0.262250\pi\) | |||||||
\(632\) | −22251.2 | −1.40049 | ||||||||
\(633\) | − | 919.799i | − | 0.0577547i | ||||||
\(634\) | − | 905.173i | − | 0.0567019i | ||||||
\(635\) | 6446.21i | 0.402851i | ||||||||
\(636\) | 3738.40i | 0.233077i | ||||||||
\(637\) | 12782.0 | 0.795042 | ||||||||
\(638\) | 4847.66 | 0.300816 | ||||||||
\(639\) | 1959.92 | 0.121335 | ||||||||
\(640\) | −6395.37 | −0.394999 | ||||||||
\(641\) | 23835.8 | 1.46873 | 0.734365 | − | 0.678755i | \(-0.237480\pi\) | ||||
0.734365 | + | 0.678755i | \(0.237480\pi\) | |||||||
\(642\) | 6134.14 | 0.377096 | ||||||||
\(643\) | 16629.0i | 1.01988i | 0.860210 | + | 0.509939i | \(0.170332\pi\) | ||||
−0.860210 | + | 0.509939i | \(0.829668\pi\) | |||||||
\(644\) | −3772.88 | −0.230857 | ||||||||
\(645\) | −3041.49 | −0.185672 | ||||||||
\(646\) | 2382.30i | 0.145093i | ||||||||
\(647\) | −20555.7 | −1.24904 | −0.624519 | − | 0.781010i | \(-0.714705\pi\) | ||||
−0.624519 | + | 0.781010i | \(0.714705\pi\) | |||||||
\(648\) | − | 1647.33i | − | 0.0998661i | ||||||
\(649\) | 315.434i | 0.0190784i | ||||||||
\(650\) | − | 10654.0i | − | 0.642897i | ||||||
\(651\) | − | 5583.55i | − | 0.336155i | ||||||
\(652\) | 5053.65i | 0.303552i | ||||||||
\(653\) | −7123.93 | −0.426923 | −0.213462 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213462 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(654\) | 2558.01i | 0.152945i | ||||||||
\(655\) | 6769.67 | 0.403836 | ||||||||
\(656\) | 377.837i | 0.0224879i | ||||||||
\(657\) | − | 2123.06i | − | 0.126071i | ||||||
\(658\) | −1597.74 | −0.0946599 | ||||||||
\(659\) | −27980.6 | −1.65398 | −0.826988 | − | 0.562220i | \(-0.809948\pi\) | ||||
−0.826988 | + | 0.562220i | \(0.809948\pi\) | |||||||
\(660\) | − | 1937.79i | − | 0.114286i | ||||||
\(661\) | 5269.16 | 0.310055 | 0.155028 | − | 0.987910i | \(-0.450453\pi\) | ||||
0.155028 | + | 0.987910i | \(0.450453\pi\) | |||||||
\(662\) | 6836.28i | 0.401359i | ||||||||
\(663\) | −4277.27 | −0.250551 | ||||||||
\(664\) | −25012.3 | −1.46185 | ||||||||
\(665\) | −5223.52 | −0.304601 | ||||||||
\(666\) | − | 2935.41i | − | 0.170788i | ||||||
\(667\) | 7403.34 | 0.429773 | ||||||||
\(668\) | 6844.80 | 0.396457 | ||||||||
\(669\) | 394.447i | 0.0227955i | ||||||||
\(670\) | −138.620 | −0.00799307 | ||||||||
\(671\) | 18137.7i | 1.04351i | ||||||||
\(672\) | −7240.52 | −0.415638 | ||||||||
\(673\) | − | 3444.16i | − | 0.197270i | −0.995124 | − | 0.0986350i | \(-0.968552\pi\) | ||
0.995124 | − | 0.0986350i | \(-0.0314476\pi\) | |||||||
\(674\) | 701.880 | 0.0401119 | ||||||||
\(675\) | −2714.36 | −0.154779 | ||||||||
\(676\) | 17551.3 | 0.998594 | ||||||||
\(677\) | 31855.2 | 1.80841 | 0.904206 | − | 0.427097i | \(-0.140464\pi\) | ||||
0.904206 | + | 0.427097i | \(0.140464\pi\) | |||||||
\(678\) | 5844.16i | 0.331038i | ||||||||
\(679\) | 8995.25 | 0.508404 | ||||||||
\(680\) | −1988.67 | −0.112150 | ||||||||
\(681\) | 13308.8i | 0.748889i | ||||||||
\(682\) | 4748.50i | 0.266612i | ||||||||
\(683\) | − | 5410.31i | − | 0.303103i | −0.988449 | − | 0.151552i | \(-0.951573\pi\) | ||
0.988449 | − | 0.151552i | \(-0.0484270\pi\) | |||||||
\(684\) | −4311.51 | −0.241016 | ||||||||
\(685\) | 11609.0 | 0.647529 | ||||||||
\(686\) | 9841.93 | 0.547765 | ||||||||
\(687\) | − | 7629.29i | − | 0.423691i | ||||||
\(688\) | 3452.48i | 0.191315i | ||||||||
\(689\) | − | 15387.2i | − | 0.850804i | ||||||
\(690\) | 1093.89i | 0.0603534i | ||||||||
\(691\) | − | 3626.50i | − | 0.199651i | −0.995005 | − | 0.0998253i | \(-0.968172\pi\) | ||
0.995005 | − | 0.0998253i | \(-0.0318284\pi\) | |||||||
\(692\) | −20689.4 | −1.13655 | ||||||||
\(693\) | − | 2590.63i | − | 0.142006i | ||||||
\(694\) | − | 10519.6i | − | 0.575388i | ||||||
\(695\) | 6268.95 | 0.342151 | ||||||||
\(696\) | 9003.66 | 0.490349 | ||||||||
\(697\) | 443.409i | 0.0240966i | ||||||||
\(698\) | 5937.06i | 0.321950i | ||||||||
\(699\) | −18126.0 | −0.980812 | ||||||||
\(700\) | 7560.52i | 0.408230i | ||||||||
\(701\) | − | 9984.62i | − | 0.537966i | −0.963145 | − | 0.268983i | \(-0.913312\pi\) | ||
0.963145 | − | 0.268983i | \(-0.0866875\pi\) | |||||||
\(702\) | 2861.35i | 0.153839i | ||||||||
\(703\) | −18205.4 | −0.976712 | ||||||||
\(704\) | 3144.95 | 0.168366 | ||||||||
\(705\) | − | 1253.24i | − | 0.0669502i | ||||||
\(706\) | 4502.74i | 0.240032i | ||||||||
\(707\) | − | 9892.40i | − | 0.526226i | ||||||
\(708\) | 247.238i | 0.0131240i | ||||||||
\(709\) | −2339.91 | −0.123945 | −0.0619725 | − | 0.998078i | \(-0.519739\pi\) | ||||
−0.0619725 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(710\) | −1582.79 | −0.0836636 | ||||||||
\(711\) | − | 9846.94i | − | 0.519394i | ||||||
\(712\) | − | 28460.2i | − | 1.49802i | ||||||
\(713\) | 7251.90i | 0.380906i | ||||||||
\(714\) | −1121.96 | −0.0588073 | ||||||||
\(715\) | 7975.91i | 0.417178i | ||||||||
\(716\) | 3338.12i | 0.174234i | ||||||||
\(717\) | 5978.02 | 0.311371 | ||||||||
\(718\) | 17076.2 | 0.887574 | ||||||||
\(719\) | − | 5156.13i | − | 0.267442i | −0.991019 | − | 0.133721i | \(-0.957307\pi\) | ||
0.991019 | − | 0.133721i | \(-0.0426927\pi\) | |||||||
\(720\) | − | 749.909i | − | 0.0388159i | ||||||
\(721\) | −15363.7 | −0.793583 | ||||||||
\(722\) | 194.386i | 0.0100198i | ||||||||
\(723\) | − | 13465.0i | − | 0.692628i | ||||||
\(724\) | 22622.7i | 1.16128i | ||||||||
\(725\) | − | 14835.6i | − | 0.759975i | ||||||
\(726\) | − | 3663.97i | − | 0.187304i | ||||||
\(727\) | −16606.9 | −0.847202 | −0.423601 | − | 0.905849i | \(-0.639234\pi\) | ||||
−0.423601 | + | 0.905849i | \(0.639234\pi\) | |||||||
\(728\) | 18885.9 | 0.961479 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 1714.55i | 0.0869291i | ||||||||
\(731\) | 4051.65i | 0.205001i | ||||||||
\(732\) | 14216.3i | 0.717830i | ||||||||
\(733\) | −8724.09 | −0.439607 | −0.219803 | − | 0.975544i | \(-0.570542\pi\) | ||||
−0.219803 | + | 0.975544i | \(0.570542\pi\) | |||||||
\(734\) | −2485.94 | −0.125011 | ||||||||
\(735\) | 2629.91i | 0.131981i | ||||||||
\(736\) | 9403.97 | 0.470971 | ||||||||
\(737\) | −426.381 | −0.0213106 | ||||||||
\(738\) | 296.626 | 0.0147953 | ||||||||
\(739\) | 515.320 | 0.0256514 | 0.0128257 | − | 0.999918i | \(-0.495917\pi\) | ||||
0.0128257 | + | 0.999918i | \(0.495917\pi\) | |||||||
\(740\) | − | 6413.33i | − | 0.318593i | ||||||
\(741\) | 17746.0 | 0.879780 | ||||||||
\(742\) | − | 4036.18i | − | 0.199694i | ||||||
\(743\) | −13435.0 | −0.663369 | −0.331684 | − | 0.943390i | \(-0.607617\pi\) | ||||
−0.331684 | + | 0.943390i | \(0.607617\pi\) | |||||||
\(744\) | 8819.50i | 0.434595i | ||||||||
\(745\) | 11024.4 | 0.542149 | ||||||||
\(746\) | −17799.2 | −0.873560 | ||||||||
\(747\) | − | 11068.8i | − | 0.542151i | ||||||
\(748\) | −2581.39 | −0.126183 | ||||||||
\(749\) | 17917.0 | 0.874064 | ||||||||
\(750\) | 4917.66 | 0.239423 | ||||||||
\(751\) | 9825.29i | 0.477403i | 0.971093 | + | 0.238702i | \(0.0767218\pi\) | ||||
−0.971093 | + | 0.238702i | \(0.923278\pi\) | |||||||
\(752\) | −1422.59 | −0.0689848 | ||||||||
\(753\) | 14657.7i | 0.709369i | ||||||||
\(754\) | −15639.0 | −0.755359 | ||||||||
\(755\) | 2944.13 | 0.141917 | ||||||||
\(756\) | − | 2030.54i | − | 0.0976852i | ||||||
\(757\) | − | 34881.0i | − | 1.67473i | −0.546643 | − | 0.837366i | \(-0.684095\pi\) | ||
0.546643 | − | 0.837366i | \(-0.315905\pi\) | |||||||
\(758\) | −7000.12 | −0.335430 | ||||||||
\(759\) | 3364.71i | 0.160910i | ||||||||
\(760\) | 8250.82 | 0.393801 | ||||||||
\(761\) | 20122.5i | 0.958529i | 0.877670 | + | 0.479265i | \(0.159097\pi\) | ||||
−0.877670 | + | 0.479265i | \(0.840903\pi\) | |||||||
\(762\) | − | 5744.53i | − | 0.273100i | ||||||
\(763\) | 7471.62i | 0.354509i | ||||||||
\(764\) | 1654.69i | 0.0783566i | ||||||||
\(765\) | − | 880.054i | − | 0.0415927i | ||||||
\(766\) | 452.217 | 0.0213306 | ||||||||
\(767\) | − | 1017.62i | − | 0.0479064i | ||||||
\(768\) | 9075.39 | 0.426406 | ||||||||
\(769\) | −17295.1 | −0.811024 | −0.405512 | − | 0.914090i | \(-0.632907\pi\) | ||||
−0.405512 | + | 0.914090i | \(0.632907\pi\) | |||||||
\(770\) | 2092.15i | 0.0979165i | ||||||||
\(771\) | 10596.5 | 0.494971 | ||||||||
\(772\) | −10449.8 | −0.487174 | ||||||||
\(773\) | −21185.8 | −0.985772 | −0.492886 | − | 0.870094i | \(-0.664058\pi\) | ||||
−0.492886 | + | 0.870094i | \(0.664058\pi\) | |||||||
\(774\) | 2710.42 | 0.125871 | ||||||||
\(775\) | 14532.2 | 0.673563 | ||||||||
\(776\) | −14208.4 | −0.657285 | ||||||||
\(777\) | − | 8573.96i | − | 0.395868i | ||||||
\(778\) | 15428.0i | 0.710952i | ||||||||
\(779\) | − | 1839.67i | − | 0.0846122i | ||||||
\(780\) | 6251.52i | 0.286975i | ||||||||
\(781\) | −4868.51 | −0.223059 | ||||||||
\(782\) | 1457.20 | 0.0666362 | ||||||||
\(783\) | 3984.43i | 0.181854i | ||||||||
\(784\) | 2985.29 | 0.135992 | ||||||||
\(785\) | 9036.36 | − | 3610.15i | 0.410855 | − | 0.164142i | ||||
\(786\) | −6032.78 | −0.273768 | ||||||||
\(787\) | 27453.2i | 1.24346i | 0.783232 | + | 0.621729i | \(0.213570\pi\) | ||||
−0.783232 | + | 0.621729i | \(0.786430\pi\) | |||||||
\(788\) | 5650.61 | 0.255450 | ||||||||
\(789\) | −5704.03 | −0.257375 | ||||||||
\(790\) | 7952.21i | 0.358135i | ||||||||
\(791\) | 17070.0i | 0.767308i | ||||||||
\(792\) | 4092.03i | 0.183591i | ||||||||
\(793\) | − | 58514.1i | − | 2.62030i | ||||||
\(794\) | 6297.22 | 0.281461 | ||||||||
\(795\) | 3165.93 | 0.141237 | ||||||||
\(796\) | 21107.2 | 0.939854 | ||||||||
\(797\) | −33862.1 | −1.50497 | −0.752483 | − | 0.658612i | \(-0.771144\pi\) | ||||
−0.752483 | + | 0.658612i | \(0.771144\pi\) | |||||||
\(798\) | 4654.93 | 0.206495 | ||||||||
\(799\) | −1669.48 | −0.0739197 | ||||||||
\(800\) | − | 18844.7i | − | 0.832828i | ||||||
\(801\) | 12594.6 | 0.555566 | ||||||||
\(802\) | −2060.25 | −0.0907108 | ||||||||
\(803\) | 5273.77i | 0.231765i | ||||||||
\(804\) | −334.198 | −0.0146595 | ||||||||
\(805\) | 3195.12i | 0.139892i | ||||||||
\(806\) | − | 15319.2i | − | 0.669472i | ||||||
\(807\) | − | 18579.6i | − | 0.810449i | ||||||
\(808\) | 15625.5i | 0.680327i | ||||||||
\(809\) | 13456.2i | 0.584790i | 0.956298 | + | 0.292395i | \(0.0944522\pi\) | ||||
−0.956298 | + | 0.292395i | \(0.905548\pi\) | |||||||
\(810\) | −588.727 | −0.0255380 | ||||||||
\(811\) | 26653.7i | 1.15405i | 0.816725 | + | 0.577027i | \(0.195787\pi\) | ||||
−0.816725 | + | 0.577027i | \(0.804213\pi\) | |||||||
\(812\) | 11098.1 | 0.479641 | ||||||||
\(813\) | − | 22897.3i | − | 0.987755i | ||||||
\(814\) | 7291.68i | 0.313972i | ||||||||
\(815\) | 4279.76 | 0.183943 | ||||||||
\(816\) | −998.974 | −0.0428567 | ||||||||
\(817\) | − | 16809.9i | − | 0.719835i | ||||||
\(818\) | −12324.7 | −0.526800 | ||||||||
\(819\) | 8357.64i | 0.356581i | ||||||||
\(820\) | 648.072 | 0.0275996 | ||||||||
\(821\) | −19565.6 | −0.831721 | −0.415860 | − | 0.909428i | \(-0.636520\pi\) | ||||
−0.415860 | + | 0.909428i | \(0.636520\pi\) | |||||||
\(822\) | −10345.3 | −0.438973 | ||||||||
\(823\) | − | 34235.1i | − | 1.45001i | −0.688742 | − | 0.725007i | \(-0.741837\pi\) | ||
0.688742 | − | 0.725007i | \(-0.258163\pi\) | |||||||
\(824\) | 24267.7 | 1.02598 | ||||||||
\(825\) | 6742.58 | 0.284541 | ||||||||
\(826\) | − | 266.931i | − | 0.0112442i | ||||||
\(827\) | 17627.0 | 0.741176 | 0.370588 | − | 0.928797i | \(-0.379156\pi\) | ||||
0.370588 | + | 0.928797i | \(0.379156\pi\) | |||||||
\(828\) | 2637.26i | 0.110690i | ||||||||
\(829\) | −25243.5 | −1.05759 | −0.528796 | − | 0.848749i | \(-0.677356\pi\) | ||||
−0.528796 | + | 0.848749i | \(0.677356\pi\) | |||||||
\(830\) | 8938.97i | 0.373827i | ||||||||
\(831\) | 976.724 | 0.0407728 | ||||||||
\(832\) | −10145.9 | −0.422773 | ||||||||
\(833\) | 3503.37 | 0.145720 | ||||||||
\(834\) | −5586.56 | −0.231951 | ||||||||
\(835\) | − | 5796.63i | − | 0.240240i | ||||||
\(836\) | 10710.0 | 0.443076 | ||||||||
\(837\) | −3902.93 | −0.161177 | ||||||||
\(838\) | 8935.06i | 0.368325i | ||||||||
\(839\) | 22414.6i | 0.922335i | 0.887313 | + | 0.461167i | \(0.152569\pi\) | ||||
−0.887313 | + | 0.461167i | \(0.847431\pi\) | |||||||
\(840\) | 3885.79i | 0.159610i | ||||||||
\(841\) | 2611.65 | 0.107083 | ||||||||
\(842\) | 1614.21 | 0.0660680 | ||||||||
\(843\) | −1564.48 | −0.0639189 | ||||||||
\(844\) | 1790.84i | 0.0730371i | ||||||||
\(845\) | − | 14863.6i | − | 0.605116i | ||||||
\(846\) | 1116.83i | 0.0453868i | ||||||||
\(847\) | − | 10702.0i | − | 0.434150i | ||||||
\(848\) | − | 3593.73i | − | 0.145530i | ||||||
\(849\) | 20950.3 | 0.846895 | ||||||||
\(850\) | − | 2920.11i | − | 0.117834i | ||||||
\(851\) | 11135.8i | 0.448568i | ||||||||
\(852\) | −3815.94 | −0.153441 | ||||||||
\(853\) | 39464.0 | 1.58408 | 0.792040 | − | 0.610469i | \(-0.209019\pi\) | ||||
0.792040 | + | 0.610469i | \(0.209019\pi\) | |||||||
\(854\) | − | 15348.7i | − | 0.615015i | ||||||
\(855\) | 3651.27i | 0.146048i | ||||||||
\(856\) | −28300.8 | −1.13003 | ||||||||
\(857\) | 22210.2i | 0.885282i | 0.896699 | + | 0.442641i | \(0.145958\pi\) | ||||
−0.896699 | + | 0.442641i | \(0.854042\pi\) | |||||||
\(858\) | − | 7107.71i | − | 0.282813i | ||||||
\(859\) | − | 15948.7i | − | 0.633485i | −0.948512 | − | 0.316743i | \(-0.897411\pi\) | ||
0.948512 | − | 0.316743i | \(-0.102589\pi\) | |||||||
\(860\) | 5921.76 | 0.234803 | ||||||||
\(861\) | 866.406 | 0.0342939 | ||||||||
\(862\) | − | 10521.8i | − | 0.415747i | ||||||
\(863\) | 15243.5i | 0.601268i | 0.953740 | + | 0.300634i | \(0.0971982\pi\) | ||||
−0.953740 | + | 0.300634i | \(0.902802\pi\) | |||||||
\(864\) | 5061.16i | 0.199287i | ||||||||
\(865\) | 17521.2i | 0.688714i | ||||||||
\(866\) | −13625.4 | −0.534655 | ||||||||
\(867\) | 13566.7 | 0.531428 | ||||||||
\(868\) | 10871.1i | 0.425104i | ||||||||
\(869\) | 24460.2i | 0.954839i | ||||||||
\(870\) | − | 3217.75i | − | 0.125393i | ||||||
\(871\) | 1375.55 | 0.0535117 | ||||||||
\(872\) | − | 11801.8i | − | 0.458325i | ||||||
\(873\) | − | 6287.73i | − | 0.243765i | ||||||
\(874\) | −6045.82 | −0.233985 | ||||||||
\(875\) | 14363.8 | 0.554956 | ||||||||
\(876\) | 4133.59i | 0.159430i | ||||||||
\(877\) | 21667.7i | 0.834282i | 0.908842 | + | 0.417141i | \(0.136968\pi\) | ||||
−0.908842 | + | 0.417141i | \(0.863032\pi\) | |||||||
\(878\) | −12064.1 | −0.463716 | ||||||||
\(879\) | − | 1911.09i | − | 0.0733328i | ||||||
\(880\) | 1862.80i | 0.0713581i | ||||||||
\(881\) | 21646.9i | 0.827814i | 0.910319 | + | 0.413907i | \(0.135836\pi\) | ||||
−0.910319 | + | 0.413907i | \(0.864164\pi\) | |||||||
\(882\) | − | 2343.64i | − | 0.0894722i | ||||||
\(883\) | − | 25828.8i | − | 0.984379i | −0.870488 | − | 0.492190i | \(-0.836197\pi\) | ||
0.870488 | − | 0.492190i | \(-0.163803\pi\) | |||||||
\(884\) | 8327.82 | 0.316849 | ||||||||
\(885\) | 209.377 | 0.00795270 | ||||||||
\(886\) | 170.485 | 0.00646451 | ||||||||
\(887\) | 11755.9i | 0.445012i | 0.974931 | + | 0.222506i | \(0.0714236\pi\) | ||||
−0.974931 | + | 0.222506i | \(0.928576\pi\) | |||||||
\(888\) | 13543.0i | 0.511794i | ||||||||
\(889\) | − | 16779.0i | − | 0.633015i | ||||||
\(890\) | −10171.2 | −0.383077 | ||||||||
\(891\) | −1810.86 | −0.0680878 | ||||||||
\(892\) | − | 767.986i | − | 0.0288274i | ||||||
\(893\) | 6926.52 | 0.259560 | ||||||||
\(894\) | −9824.33 | −0.367533 | ||||||||
\(895\) | 2826.94 | 0.105580 | ||||||||
\(896\) | 16646.7 | 0.620677 | ||||||||
\(897\) | − | 10854.9i | − | 0.404051i | ||||||
\(898\) | −634.942 | −0.0235950 | ||||||||
\(899\) | − | 21331.9i | − | 0.791389i | ||||||
\(900\) | 5284.84 | 0.195735 | ||||||||
\(901\) | − | 4217.41i | − | 0.155940i | ||||||
\(902\) | −736.830 | −0.0271993 | ||||||||
\(903\) | 7916.78 | 0.291754 | ||||||||
\(904\) | − | 26963.0i | − | 0.992008i | ||||||
\(905\) | 19158.4 | 0.703698 | ||||||||
\(906\) | −2623.65 | −0.0962086 | ||||||||
\(907\) | 24991.9 | 0.914932 | 0.457466 | − | 0.889227i | \(-0.348757\pi\) | ||||
0.457466 | + | 0.889227i | \(0.348757\pi\) | |||||||
\(908\) | − | 25912.1i | − | 0.947051i | ||||||
\(909\) | −6914.84 | −0.252311 | ||||||||
\(910\) | − | 6749.48i | − | 0.245871i | ||||||
\(911\) | 21982.0 | 0.799448 | 0.399724 | − | 0.916636i | \(-0.369106\pi\) | ||||
0.399724 | + | 0.916636i | \(0.369106\pi\) | |||||||
\(912\) | 4144.66 | 0.150486 | ||||||||
\(913\) | 27495.4i | 0.996674i | ||||||||
\(914\) | − | 13250.8i | − | 0.479536i | ||||||
\(915\) | 12039.3 | 0.434982 | ||||||||
\(916\) | 14854.2i | 0.535803i | ||||||||
\(917\) | −17621.0 | −0.634564 | ||||||||
\(918\) | 784.258i | 0.0281965i | ||||||||
\(919\) | − | 30542.3i | − | 1.09630i | −0.836381 | − | 0.548149i | \(-0.815333\pi\) | ||
0.836381 | − | 0.548149i | \(-0.184667\pi\) | |||||||
\(920\) | − | 5046.85i | − | 0.180858i | ||||||
\(921\) | 28658.3i | 1.02532i | ||||||||
\(922\) | − | 919.269i | − | 0.0328357i | ||||||
\(923\) | 15706.3 | 0.560108 | ||||||||
\(924\) | 5043.94i | 0.179582i | ||||||||
\(925\) | 22315.3 | 0.793212 | ||||||||
\(926\) | −11395.3 | −0.404398 | ||||||||
\(927\) | 10739.3i | 0.380501i | ||||||||
\(928\) | −27662.3 | −0.978513 | ||||||||
\(929\) | 23792.9 | 0.840280 | 0.420140 | − | 0.907459i | \(-0.361981\pi\) | ||||
0.420140 | + | 0.907459i | \(0.361981\pi\) | |||||||
\(930\) | 3151.94 | 0.111136 | ||||||||
\(931\) | −14535.2 | −0.511678 | ||||||||
\(932\) | 35291.2 | 1.24034 | ||||||||
\(933\) | 8039.85 | 0.282114 | ||||||||
\(934\) | 12497.7i | 0.437835i | ||||||||
\(935\) | 2186.09i | 0.0764628i | ||||||||
\(936\) | − | 13201.3i | − | 0.461003i | ||||||
\(937\) | − | 1866.82i | − | 0.0650869i | −0.999470 | − | 0.0325435i | \(-0.989639\pi\) | ||
0.999470 | − | 0.0325435i | \(-0.0103607\pi\) | |||||||
\(938\) | 360.818 | 0.0125598 | ||||||||
\(939\) | −5587.06 | −0.194171 | ||||||||
\(940\) | 2440.05i | 0.0846657i | ||||||||
\(941\) | 48540.7 | 1.68159 | 0.840797 | − | 0.541350i | \(-0.182087\pi\) | ||||
0.840797 | + | 0.541350i | \(0.182087\pi\) | |||||||
\(942\) | −8052.73 | + | 3217.18i | −0.278527 | + | 0.111275i | ||||
\(943\) | −1125.29 | −0.0388593 | ||||||||
\(944\) | − | 237.670i | − | 0.00819438i | ||||||
\(945\) | −1719.59 | −0.0591941 | ||||||||
\(946\) | −6732.78 | −0.231397 | ||||||||
\(947\) | − | 20709.2i | − | 0.710620i | −0.934748 | − | 0.355310i | \(-0.884375\pi\) | ||
0.934748 | − | 0.355310i | \(-0.115625\pi\) | |||||||
\(948\) | 19171.9i | 0.656830i | ||||||||
\(949\) | − | 17013.7i | − | 0.581970i | ||||||
\(950\) | 12115.3i | 0.413760i | ||||||||
\(951\) | −1848.09 | −0.0630163 | ||||||||
\(952\) | 5176.36 | 0.176226 | ||||||||
\(953\) | 13499.4 | 0.458856 | 0.229428 | − | 0.973326i | \(-0.426315\pi\) | ||||
0.229428 | + | 0.973326i | \(0.426315\pi\) | |||||||
\(954\) | −2821.31 | −0.0957476 | ||||||||
\(955\) | 1401.30 | 0.0474816 | ||||||||
\(956\) | −11639.2 | −0.393763 | ||||||||
\(957\) | − | 9897.48i | − | 0.334316i | ||||||
\(958\) | 15803.5 | 0.532973 | ||||||||
\(959\) | −30217.4 | −1.01749 | ||||||||
\(960\) | − | 2087.54i | − | 0.0701824i | ||||||
\(961\) | −8895.43 | −0.298595 | ||||||||
\(962\) | − | 23523.7i | − | 0.788394i | ||||||
\(963\) | − | 12524.1i | − | 0.419090i | ||||||
\(964\) | 26216.3i | 0.875904i | ||||||||
\(965\) | 8849.62i | 0.295212i | ||||||||
\(966\) | − | 2847.33i | − | 0.0948356i | ||||||
\(967\) | −31713.1 | −1.05463 | −0.527313 | − | 0.849671i | \(-0.676801\pi\) | ||||
−0.527313 | + | 0.849671i | \(0.676801\pi\) | |||||||
\(968\) | 16904.3i | 0.561287i | ||||||||
\(969\) | 4863.95 | 0.161251 | ||||||||
\(970\) | 5077.85i | 0.168082i | ||||||||
\(971\) | − | 816.592i | − | 0.0269883i | −0.999909 | − | 0.0134942i | \(-0.995705\pi\) | ||
0.999909 | − | 0.0134942i | \(-0.00429546\pi\) | |||||||
\(972\) | −1419.36 | −0.0468373 | ||||||||
\(973\) | −16317.6 | −0.537635 | ||||||||
\(974\) | − | 11202.6i | − | 0.368535i | ||||||
\(975\) | −21752.3 | −0.714492 | ||||||||
\(976\) | − | 13666.2i | − | 0.448201i | ||||||
\(977\) | −12860.8 | −0.421138 | −0.210569 | − | 0.977579i | \(-0.567532\pi\) | ||||
−0.210569 | + | 0.977579i | \(0.567532\pi\) | |||||||
\(978\) | −3813.90 | −0.124698 | ||||||||
\(979\) | −31285.5 | −1.02134 | ||||||||
\(980\) | − | 5120.42i | − | 0.166904i | ||||||
\(981\) | 5222.70 | 0.169977 | ||||||||
\(982\) | 26706.8 | 0.867871 | ||||||||
\(983\) | 6932.91i | 0.224949i | 0.993655 | + | 0.112475i | \(0.0358777\pi\) | ||||
−0.993655 | + | 0.112475i | \(0.964122\pi\) | |||||||
\(984\) | −1368.53 | −0.0443365 | ||||||||
\(985\) | − | 4785.31i | − | 0.154795i | ||||||
\(986\) | −4286.45 | −0.138447 | ||||||||
\(987\) | 3262.10i | 0.105201i | ||||||||
\(988\) | −34551.4 | −1.11258 | ||||||||
\(989\) | −10282.3 | −0.330594 | ||||||||
\(990\) | 1462.42 | 0.0469482 | ||||||||
\(991\) | 28801.9 | 0.923233 | 0.461617 | − | 0.887080i | \(-0.347270\pi\) | ||||
0.461617 | + | 0.887080i | \(0.347270\pi\) | |||||||
\(992\) | − | 27096.5i | − | 0.867253i | ||||||
\(993\) | 13957.7 | 0.446055 | ||||||||
\(994\) | 4119.89 | 0.131464 | ||||||||
\(995\) | − | 17874.9i | − | 0.569521i | ||||||
\(996\) | 21550.9i | 0.685609i | ||||||||
\(997\) | 5050.70i | 0.160438i | 0.996777 | + | 0.0802192i | \(0.0255620\pi\) | ||||
−0.996777 | + | 0.0802192i | \(0.974438\pi\) | |||||||
\(998\) | 21315.8 | 0.676093 | ||||||||
\(999\) | −5993.24 | −0.189808 |
(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 | 471.4.b.a.313.15 | ✓ | 40 | |
157.156 | even | 2 | inner | 471.4.b.a.313.26 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
471.4.b.a.313.15 | ✓ | 40 | 1.1 | even | 1 | trivial | |
471.4.b.a.313.26 | yes | 40 | 157.156 | even | 2 | inner |