Properties

Label 336.7.bh.b.241.4
Level $336$
Weight $7$
Character 336.241
Analytic conductor $77.298$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 336.bh (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(77.2981720963\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Defining polynomial: \(x^{8} - x^{7} + 212 x^{6} - 787 x^{5} + 38792 x^{4} - 92833 x^{3} + 1563109 x^{2} + 3107772 x + 38787984\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{6}\cdot 3\cdot 7^{2} \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 241.4
Root \(4.15432 + 7.19549i\) of defining polynomial
Character \(\chi\) \(=\) 336.241
Dual form 336.7.bh.b.145.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +O(q^{10})\) \(q+(-13.5000 - 7.79423i) q^{3} +(151.343 - 87.3778i) q^{5} +(271.614 + 209.463i) q^{7} +(121.500 + 210.444i) q^{9} +(-92.6996 + 160.560i) q^{11} -3981.73i q^{13} -2724.17 q^{15} +(6101.23 + 3522.55i) q^{17} +(4064.58 - 2346.69i) q^{19} +(-2034.18 - 4944.78i) q^{21} +(-3322.00 - 5753.87i) q^{23} +(7457.27 - 12916.4i) q^{25} -3788.00i q^{27} +19385.8 q^{29} +(-20743.8 - 11976.4i) q^{31} +(2502.89 - 1445.04i) q^{33} +(59409.3 + 7967.73i) q^{35} +(19784.8 + 34268.3i) q^{37} +(-31034.5 + 53753.4i) q^{39} +46285.6i q^{41} +93128.7 q^{43} +(36776.3 + 21232.8i) q^{45} +(-129449. + 74737.3i) q^{47} +(29899.3 + 113786. i) q^{49} +(-54911.1 - 95108.8i) q^{51} +(50912.7 - 88183.4i) q^{53} +32399.5i q^{55} -73162.4 q^{57} +(-131933. - 76171.6i) q^{59} +(-145966. + 84273.5i) q^{61} +(-11079.2 + 82609.4i) q^{63} +(-347915. - 602606. i) q^{65} +(30552.0 - 52917.6i) q^{67} +103570. i q^{69} +485262. q^{71} +(-7732.72 - 4464.49i) q^{73} +(-201346. + 116247. i) q^{75} +(-58810.0 + 24193.3i) q^{77} +(221938. + 384409. i) q^{79} +(-29524.5 + 51137.9i) q^{81} -559383. i q^{83} +1.23117e6 q^{85} +(-261708. - 151097. i) q^{87} +(-179055. + 103378. i) q^{89} +(834026. - 1.08149e6i) q^{91} +(186694. + 323364. i) q^{93} +(410097. - 710308. i) q^{95} -1.23197e6i q^{97} -45052.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + O(q^{10}) \) \( 8 q - 108 q^{3} - 42 q^{5} - 748 q^{7} + 972 q^{9} + 1070 q^{11} + 756 q^{15} + 7212 q^{17} + 24606 q^{19} + 8154 q^{21} + 15224 q^{23} + 22274 q^{25} + 32524 q^{29} - 40200 q^{31} - 28890 q^{33} + 242436 q^{35} - 45670 q^{37} - 93366 q^{39} + 445660 q^{43} - 10206 q^{45} - 82884 q^{47} + 24116 q^{49} - 64908 q^{51} - 13034 q^{53} - 442908 q^{57} - 1810362 q^{59} - 392856 q^{61} - 38394 q^{63} - 389004 q^{65} - 384094 q^{67} - 225688 q^{71} + 903078 q^{73} - 601398 q^{75} - 327674 q^{77} + 559592 q^{79} - 236196 q^{81} + 1953576 q^{85} - 439074 q^{87} - 1770036 q^{89} + 2960718 q^{91} + 361800 q^{93} - 1160112 q^{95} + 520020 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{6}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −13.5000 7.79423i −0.500000 0.288675i
\(4\) 0 0
\(5\) 151.343 87.3778i 1.21074 0.699023i 0.247821 0.968806i \(-0.420285\pi\)
0.962921 + 0.269783i \(0.0869520\pi\)
\(6\) 0 0
\(7\) 271.614 + 209.463i 0.791877 + 0.610680i
\(8\) 0 0
\(9\) 121.500 + 210.444i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) −92.6996 + 160.560i −0.0696466 + 0.120631i −0.898746 0.438470i \(-0.855520\pi\)
0.829099 + 0.559102i \(0.188854\pi\)
\(12\) 0 0
\(13\) 3981.73i 1.81235i −0.422904 0.906174i \(-0.638989\pi\)
0.422904 0.906174i \(-0.361011\pi\)
\(14\) 0 0
\(15\) −2724.17 −0.807162
\(16\) 0 0
\(17\) 6101.23 + 3522.55i 1.24185 + 0.716985i 0.969471 0.245204i \(-0.0788550\pi\)
0.272383 + 0.962189i \(0.412188\pi\)
\(18\) 0 0
\(19\) 4064.58 2346.69i 0.592591 0.342132i −0.173531 0.984828i \(-0.555518\pi\)
0.766121 + 0.642696i \(0.222184\pi\)
\(20\) 0 0
\(21\) −2034.18 4944.78i −0.219651 0.533935i
\(22\) 0 0
\(23\) −3322.00 5753.87i −0.273033 0.472908i 0.696604 0.717456i \(-0.254694\pi\)
−0.969637 + 0.244549i \(0.921360\pi\)
\(24\) 0 0
\(25\) 7457.27 12916.4i 0.477265 0.826647i
\(26\) 0 0
\(27\) 3788.00i 0.192450i
\(28\) 0 0
\(29\) 19385.8 0.794857 0.397429 0.917633i \(-0.369903\pi\)
0.397429 + 0.917633i \(0.369903\pi\)
\(30\) 0 0
\(31\) −20743.8 11976.4i −0.696311 0.402015i 0.109661 0.993969i \(-0.465023\pi\)
−0.805972 + 0.591954i \(0.798357\pi\)
\(32\) 0 0
\(33\) 2502.89 1445.04i 0.0696466 0.0402105i
\(34\) 0 0
\(35\) 59409.3 + 7967.73i 1.38564 + 0.185836i
\(36\) 0 0
\(37\) 19784.8 + 34268.3i 0.390595 + 0.676531i 0.992528 0.122016i \(-0.0389359\pi\)
−0.601933 + 0.798547i \(0.705603\pi\)
\(38\) 0 0
\(39\) −31034.5 + 53753.4i −0.523180 + 0.906174i
\(40\) 0 0
\(41\) 46285.6i 0.671575i 0.941938 + 0.335787i \(0.109002\pi\)
−0.941938 + 0.335787i \(0.890998\pi\)
\(42\) 0 0
\(43\) 93128.7 1.17133 0.585664 0.810554i \(-0.300834\pi\)
0.585664 + 0.810554i \(0.300834\pi\)
\(44\) 0 0
\(45\) 36776.3 + 21232.8i 0.403581 + 0.233008i
\(46\) 0 0
\(47\) −129449. + 74737.3i −1.24682 + 0.719853i −0.970474 0.241205i \(-0.922457\pi\)
−0.276347 + 0.961058i \(0.589124\pi\)
\(48\) 0 0
\(49\) 29899.3 + 113786.i 0.254140 + 0.967168i
\(50\) 0 0
\(51\) −54911.1 95108.8i −0.413951 0.716985i
\(52\) 0 0
\(53\) 50912.7 88183.4i 0.341978 0.592324i −0.642822 0.766016i \(-0.722236\pi\)
0.984800 + 0.173692i \(0.0555698\pi\)
\(54\) 0 0
\(55\) 32399.5i 0.194738i
\(56\) 0 0
\(57\) −73162.4 −0.395060
\(58\) 0 0
\(59\) −131933. 76171.6i −0.642388 0.370883i 0.143146 0.989702i \(-0.454278\pi\)
−0.785534 + 0.618819i \(0.787612\pi\)
\(60\) 0 0
\(61\) −145966. + 84273.5i −0.643076 + 0.371280i −0.785798 0.618483i \(-0.787748\pi\)
0.142723 + 0.989763i \(0.454414\pi\)
\(62\) 0 0
\(63\) −11079.2 + 82609.4i −0.0443086 + 0.330375i
\(64\) 0 0
\(65\) −347915. 602606.i −1.26687 2.19429i
\(66\) 0 0
\(67\) 30552.0 52917.6i 0.101582 0.175944i −0.810755 0.585386i \(-0.800943\pi\)
0.912336 + 0.409441i \(0.134276\pi\)
\(68\) 0 0
\(69\) 103570.i 0.315272i
\(70\) 0 0
\(71\) 485262. 1.35582 0.677909 0.735146i \(-0.262886\pi\)
0.677909 + 0.735146i \(0.262886\pi\)
\(72\) 0 0
\(73\) −7732.72 4464.49i −0.0198776 0.0114763i 0.490028 0.871707i \(-0.336986\pi\)
−0.509906 + 0.860230i \(0.670320\pi\)
\(74\) 0 0
\(75\) −201346. + 116247.i −0.477265 + 0.275549i
\(76\) 0 0
\(77\) −58810.0 + 24193.3i −0.128819 + 0.0529935i
\(78\) 0 0
\(79\) 221938. + 384409.i 0.450144 + 0.779672i 0.998395 0.0566422i \(-0.0180394\pi\)
−0.548251 + 0.836314i \(0.684706\pi\)
\(80\) 0 0
\(81\) −29524.5 + 51137.9i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 559383.i 0.978306i −0.872198 0.489153i \(-0.837306\pi\)
0.872198 0.489153i \(-0.162694\pi\)
\(84\) 0 0
\(85\) 1.23117e6 2.00475
\(86\) 0 0
\(87\) −261708. 151097.i −0.397429 0.229456i
\(88\) 0 0
\(89\) −179055. + 103378.i −0.253990 + 0.146641i −0.621590 0.783343i \(-0.713513\pi\)
0.367600 + 0.929984i \(0.380180\pi\)
\(90\) 0 0
\(91\) 834026. 1.08149e6i 1.10677 1.43516i
\(92\) 0 0
\(93\) 186694. + 323364.i 0.232104 + 0.402015i
\(94\) 0 0
\(95\) 410097. 710308.i 0.478316 0.828468i
\(96\) 0 0
\(97\) 1.23197e6i 1.34984i −0.737889 0.674922i \(-0.764177\pi\)
0.737889 0.674922i \(-0.235823\pi\)
\(98\) 0 0
\(99\) −45052.0 −0.0464310
\(100\) 0 0
\(101\) −776728. 448444.i −0.753884 0.435255i 0.0732114 0.997316i \(-0.476675\pi\)
−0.827096 + 0.562061i \(0.810009\pi\)
\(102\) 0 0
\(103\) 1.15489e6 666775.i 1.05689 0.610194i 0.132317 0.991207i \(-0.457758\pi\)
0.924569 + 0.381014i \(0.124425\pi\)
\(104\) 0 0
\(105\) −739923. 570614.i −0.639173 0.492918i
\(106\) 0 0
\(107\) −50509.0 87484.1i −0.0412304 0.0714131i 0.844674 0.535281i \(-0.179794\pi\)
−0.885904 + 0.463868i \(0.846461\pi\)
\(108\) 0 0
\(109\) 976298. 1.69100e6i 0.753881 1.30576i −0.192047 0.981386i \(-0.561513\pi\)
0.945928 0.324375i \(-0.105154\pi\)
\(110\) 0 0
\(111\) 616829.i 0.451020i
\(112\) 0 0
\(113\) 1.13981e6 0.789945 0.394972 0.918693i \(-0.370754\pi\)
0.394972 + 0.918693i \(0.370754\pi\)
\(114\) 0 0
\(115\) −1.00552e6 580537.i −0.661146 0.381713i
\(116\) 0 0
\(117\) 837932. 483780.i 0.523180 0.302058i
\(118\) 0 0
\(119\) 919335. + 2.23476e6i 0.545548 + 1.32614i
\(120\) 0 0
\(121\) 868594. + 1.50445e6i 0.490299 + 0.849222i
\(122\) 0 0
\(123\) 360760. 624855.i 0.193867 0.335787i
\(124\) 0 0
\(125\) 124158.i 0.0635691i
\(126\) 0 0
\(127\) −3.37006e6 −1.64523 −0.822614 0.568600i \(-0.807485\pi\)
−0.822614 + 0.568600i \(0.807485\pi\)
\(128\) 0 0
\(129\) −1.25724e6 725867.i −0.585664 0.338133i
\(130\) 0 0
\(131\) 2.59143e6 1.49616e6i 1.15273 0.665527i 0.203176 0.979142i \(-0.434874\pi\)
0.949550 + 0.313616i \(0.101540\pi\)
\(132\) 0 0
\(133\) 1.59554e6 + 213987.i 0.678192 + 0.0909564i
\(134\) 0 0
\(135\) −330987. 573286.i −0.134527 0.233008i
\(136\) 0 0
\(137\) 1.27232e6 2.20372e6i 0.494804 0.857026i −0.505178 0.863015i \(-0.668573\pi\)
0.999982 + 0.00598920i \(0.00190643\pi\)
\(138\) 0 0
\(139\) 1.61651e6i 0.601913i −0.953638 0.300956i \(-0.902694\pi\)
0.953638 0.300956i \(-0.0973059\pi\)
\(140\) 0 0
\(141\) 2.33008e6 0.831214
\(142\) 0 0
\(143\) 639308. + 369105.i 0.218626 + 0.126224i
\(144\) 0 0
\(145\) 2.93390e6 1.69389e6i 0.962368 0.555623i
\(146\) 0 0
\(147\) 483236. 1.76916e6i 0.152127 0.556948i
\(148\) 0 0
\(149\) −570326. 987833.i −0.172411 0.298624i 0.766851 0.641825i \(-0.221822\pi\)
−0.939262 + 0.343201i \(0.888489\pi\)
\(150\) 0 0
\(151\) −218027. + 377635.i −0.0633258 + 0.109683i −0.895950 0.444155i \(-0.853504\pi\)
0.832624 + 0.553838i \(0.186837\pi\)
\(152\) 0 0
\(153\) 1.71196e6i 0.477990i
\(154\) 0 0
\(155\) −4.18590e6 −1.12407
\(156\) 0 0
\(157\) −4.62942e6 2.67280e6i −1.19627 0.690664i −0.236545 0.971621i \(-0.576015\pi\)
−0.959721 + 0.280956i \(0.909348\pi\)
\(158\) 0 0
\(159\) −1.37464e6 + 793650.i −0.341978 + 0.197441i
\(160\) 0 0
\(161\) 302923. 2.25867e6i 0.0725863 0.541221i
\(162\) 0 0
\(163\) 835252. + 1.44670e6i 0.192866 + 0.334053i 0.946199 0.323586i \(-0.104889\pi\)
−0.753333 + 0.657639i \(0.771555\pi\)
\(164\) 0 0
\(165\) 252529. 437394.i 0.0562160 0.0973690i
\(166\) 0 0
\(167\) 144090.i 0.0309375i −0.999880 0.0154687i \(-0.995076\pi\)
0.999880 0.0154687i \(-0.00492405\pi\)
\(168\) 0 0
\(169\) −1.10274e7 −2.28461
\(170\) 0 0
\(171\) 987693. + 570245.i 0.197530 + 0.114044i
\(172\) 0 0
\(173\) −1.52276e6 + 879168.i −0.294100 + 0.169798i −0.639789 0.768550i \(-0.720978\pi\)
0.345690 + 0.938349i \(0.387645\pi\)
\(174\) 0 0
\(175\) 4.73100e6 1.94624e6i 0.882752 0.363147i
\(176\) 0 0
\(177\) 1.18740e6 + 2.05663e6i 0.214129 + 0.370883i
\(178\) 0 0
\(179\) 4.99233e6 8.64696e6i 0.870450 1.50766i 0.00891827 0.999960i \(-0.497161\pi\)
0.861532 0.507704i \(-0.169505\pi\)
\(180\) 0 0
\(181\) 7.80413e6i 1.31610i 0.752974 + 0.658050i \(0.228618\pi\)
−0.752974 + 0.658050i \(0.771382\pi\)
\(182\) 0 0
\(183\) 2.62739e6 0.428717
\(184\) 0 0
\(185\) 5.98858e6 + 3.45751e6i 0.945820 + 0.546070i
\(186\) 0 0
\(187\) −1.13116e6 + 653077.i −0.172982 + 0.0998710i
\(188\) 0 0
\(189\) 793446. 1.02887e6i 0.117525 0.152397i
\(190\) 0 0
\(191\) −255812. 443079.i −0.0367130 0.0635888i 0.847085 0.531457i \(-0.178355\pi\)
−0.883798 + 0.467869i \(0.845022\pi\)
\(192\) 0 0
\(193\) 4.35329e6 7.54012e6i 0.605544 1.04883i −0.386421 0.922322i \(-0.626289\pi\)
0.991965 0.126511i \(-0.0403778\pi\)
\(194\) 0 0
\(195\) 1.08469e7i 1.46286i
\(196\) 0 0
\(197\) 4.44972e6 0.582015 0.291007 0.956721i \(-0.406010\pi\)
0.291007 + 0.956721i \(0.406010\pi\)
\(198\) 0 0
\(199\) −6.16428e6 3.55895e6i −0.782210 0.451609i 0.0550030 0.998486i \(-0.482483\pi\)
−0.837213 + 0.546877i \(0.815816\pi\)
\(200\) 0 0
\(201\) −824903. + 476258.i −0.101582 + 0.0586482i
\(202\) 0 0
\(203\) 5.26545e6 + 4.06061e6i 0.629430 + 0.485404i
\(204\) 0 0
\(205\) 4.04433e6 + 7.00499e6i 0.469446 + 0.813104i
\(206\) 0 0
\(207\) 807245. 1.39819e6i 0.0910111 0.157636i
\(208\) 0 0
\(209\) 870147.i 0.0953134i
\(210\) 0 0
\(211\) 1.12917e7 1.20203 0.601013 0.799239i \(-0.294764\pi\)
0.601013 + 0.799239i \(0.294764\pi\)
\(212\) 0 0
\(213\) −6.55104e6 3.78225e6i −0.677909 0.391391i
\(214\) 0 0
\(215\) 1.40944e7 8.13738e6i 1.41818 0.818784i
\(216\) 0 0
\(217\) −3.12568e6 7.59803e6i −0.305890 0.743570i
\(218\) 0 0
\(219\) 69594.5 + 120541.i 0.00662586 + 0.0114763i
\(220\) 0 0
\(221\) 1.40258e7 2.42935e7i 1.29943 2.25067i
\(222\) 0 0
\(223\) 1.12380e6i 0.101338i −0.998715 0.0506692i \(-0.983865\pi\)
0.998715 0.0506692i \(-0.0161354\pi\)
\(224\) 0 0
\(225\) 3.62423e6 0.318177
\(226\) 0 0
\(227\) −8.63563e6 4.98578e6i −0.738272 0.426241i 0.0831688 0.996535i \(-0.473496\pi\)
−0.821441 + 0.570294i \(0.806829\pi\)
\(228\) 0 0
\(229\) −1.69249e7 + 9.77161e6i −1.40936 + 0.813692i −0.995326 0.0965721i \(-0.969212\pi\)
−0.414029 + 0.910264i \(0.635879\pi\)
\(230\) 0 0
\(231\) 982503. + 131769.i 0.0797073 + 0.0106900i
\(232\) 0 0
\(233\) 1.60120e6 + 2.77335e6i 0.126583 + 0.219249i 0.922351 0.386354i \(-0.126266\pi\)
−0.795767 + 0.605602i \(0.792932\pi\)
\(234\) 0 0
\(235\) −1.30608e7 + 2.26219e7i −1.00639 + 1.74311i
\(236\) 0 0
\(237\) 6.91935e6i 0.519781i
\(238\) 0 0
\(239\) −1.42350e7 −1.04271 −0.521355 0.853340i \(-0.674573\pi\)
−0.521355 + 0.853340i \(0.674573\pi\)
\(240\) 0 0
\(241\) −4.38064e6 2.52916e6i −0.312958 0.180686i 0.335291 0.942115i \(-0.391165\pi\)
−0.648249 + 0.761428i \(0.724499\pi\)
\(242\) 0 0
\(243\) 797162. 460241.i 0.0555556 0.0320750i
\(244\) 0 0
\(245\) 1.44674e7 + 1.46082e7i 0.983770 + 0.993342i
\(246\) 0 0
\(247\) −9.34387e6 1.61841e7i −0.620063 1.07398i
\(248\) 0 0
\(249\) −4.35996e6 + 7.55167e6i −0.282413 + 0.489153i
\(250\) 0 0
\(251\) 1.09278e7i 0.691050i 0.938409 + 0.345525i \(0.112299\pi\)
−0.938409 + 0.345525i \(0.887701\pi\)
\(252\) 0 0
\(253\) 1.23179e6 0.0760633
\(254\) 0 0
\(255\) −1.66208e7 9.59602e6i −1.00238 0.578723i
\(256\) 0 0
\(257\) −8.37770e6 + 4.83687e6i −0.493543 + 0.284947i −0.726043 0.687649i \(-0.758643\pi\)
0.232500 + 0.972596i \(0.425309\pi\)
\(258\) 0 0
\(259\) −1.80412e6 + 1.34519e7i −0.103840 + 0.774258i
\(260\) 0 0
\(261\) 2.35537e6 + 4.07962e6i 0.132476 + 0.229456i
\(262\) 0 0
\(263\) 1.17936e7 2.04272e7i 0.648307 1.12290i −0.335220 0.942140i \(-0.608811\pi\)
0.983527 0.180760i \(-0.0578559\pi\)
\(264\) 0 0
\(265\) 1.77946e7i 0.956202i
\(266\) 0 0
\(267\) 3.22300e6 0.169327
\(268\) 0 0
\(269\) 1.03935e7 + 6.00069e6i 0.533956 + 0.308280i 0.742626 0.669707i \(-0.233580\pi\)
−0.208670 + 0.977986i \(0.566913\pi\)
\(270\) 0 0
\(271\) 3.37870e6 1.95070e6i 0.169763 0.0980125i −0.412711 0.910862i \(-0.635418\pi\)
0.582474 + 0.812849i \(0.302085\pi\)
\(272\) 0 0
\(273\) −1.96888e7 + 8.09957e6i −0.967677 + 0.398083i
\(274\) 0 0
\(275\) 1.38257e6 + 2.39468e6i 0.0664797 + 0.115146i
\(276\) 0 0
\(277\) −1.06268e7 + 1.84062e7i −0.499992 + 0.866012i −1.00000 9.05599e-6i \(-0.999997\pi\)
0.500008 + 0.866021i \(0.333330\pi\)
\(278\) 0 0
\(279\) 5.82055e6i 0.268010i
\(280\) 0 0
\(281\) −1.01968e7 −0.459561 −0.229781 0.973242i \(-0.573801\pi\)
−0.229781 + 0.973242i \(0.573801\pi\)
\(282\) 0 0
\(283\) 3.34021e6 + 1.92847e6i 0.147372 + 0.0850851i 0.571873 0.820342i \(-0.306217\pi\)
−0.424501 + 0.905427i \(0.639550\pi\)
\(284\) 0 0
\(285\) −1.10726e7 + 6.39277e6i −0.478316 + 0.276156i
\(286\) 0 0
\(287\) −9.69513e6 + 1.25718e7i −0.410117 + 0.531805i
\(288\) 0 0
\(289\) 1.27479e7 + 2.20800e7i 0.528134 + 0.914756i
\(290\) 0 0
\(291\) −9.60222e6 + 1.66315e7i −0.389666 + 0.674922i
\(292\) 0 0
\(293\) 2.88091e7i 1.14532i −0.819793 0.572660i \(-0.805911\pi\)
0.819793 0.572660i \(-0.194089\pi\)
\(294\) 0 0
\(295\) −2.66228e7 −1.03702
\(296\) 0 0
\(297\) 608202. + 351145.i 0.0232155 + 0.0134035i
\(298\) 0 0
\(299\) −2.29103e7 + 1.32273e7i −0.857073 + 0.494832i
\(300\) 0 0
\(301\) 2.52951e7 + 1.95070e7i 0.927548 + 0.715306i
\(302\) 0 0
\(303\) 6.99055e6 + 1.21080e7i 0.251295 + 0.435255i
\(304\) 0 0
\(305\) −1.47273e7 + 2.55084e7i −0.519066 + 0.899049i
\(306\) 0 0
\(307\) 2.70175e7i 0.933747i 0.884324 + 0.466874i \(0.154620\pi\)
−0.884324 + 0.466874i \(0.845380\pi\)
\(308\) 0 0
\(309\) −2.07880e7 −0.704591
\(310\) 0 0
\(311\) 4.85470e6 + 2.80286e6i 0.161392 + 0.0931795i 0.578520 0.815668i \(-0.303630\pi\)
−0.417129 + 0.908847i \(0.636964\pi\)
\(312\) 0 0
\(313\) 2.49380e7 1.43979e7i 0.813257 0.469534i −0.0348283 0.999393i \(-0.511088\pi\)
0.848086 + 0.529859i \(0.177755\pi\)
\(314\) 0 0
\(315\) 5.54146e6 + 1.34704e7i 0.177294 + 0.430972i
\(316\) 0 0
\(317\) 1.82746e7 + 3.16525e7i 0.573679 + 0.993641i 0.996184 + 0.0872807i \(0.0278177\pi\)
−0.422505 + 0.906361i \(0.638849\pi\)
\(318\) 0 0
\(319\) −1.79705e6 + 3.11259e6i −0.0553591 + 0.0958847i
\(320\) 0 0
\(321\) 1.57471e6i 0.0476087i
\(322\) 0 0
\(323\) 3.30652e7 0.981215
\(324\) 0 0
\(325\) −5.14295e7 2.96928e7i −1.49817 0.864971i
\(326\) 0 0
\(327\) −2.63601e7 + 1.52190e7i −0.753881 + 0.435254i
\(328\) 0 0
\(329\) −5.08148e7 6.81507e6i −1.42693 0.191374i
\(330\) 0 0
\(331\) 1.16042e7 + 2.00991e7i 0.319987 + 0.554234i 0.980485 0.196594i \(-0.0629881\pi\)
−0.660498 + 0.750828i \(0.729655\pi\)
\(332\) 0 0
\(333\) −4.80771e6 + 8.32720e6i −0.130198 + 0.225510i
\(334\) 0 0
\(335\) 1.06783e7i 0.284031i
\(336\) 0 0
\(337\) 2.11044e7 0.551421 0.275710 0.961241i \(-0.411087\pi\)
0.275710 + 0.961241i \(0.411087\pi\)
\(338\) 0 0
\(339\) −1.53874e7 8.88393e6i −0.394972 0.228037i
\(340\) 0 0
\(341\) 3.84588e6 2.22042e6i 0.0969913 0.0559979i
\(342\) 0 0
\(343\) −1.57130e7 + 3.71687e7i −0.389383 + 0.921076i
\(344\) 0 0
\(345\) 9.04968e6 + 1.56745e7i 0.220382 + 0.381713i
\(346\) 0 0
\(347\) −403396. + 698702.i −0.00965479 + 0.0167226i −0.870812 0.491615i \(-0.836407\pi\)
0.861158 + 0.508338i \(0.169740\pi\)
\(348\) 0 0
\(349\) 6.98266e7i 1.64265i 0.570462 + 0.821324i \(0.306764\pi\)
−0.570462 + 0.821324i \(0.693236\pi\)
\(350\) 0 0
\(351\) −1.50828e7 −0.348787
\(352\) 0 0
\(353\) 2.32047e7 + 1.33972e7i 0.527535 + 0.304572i 0.740012 0.672594i \(-0.234820\pi\)
−0.212477 + 0.977166i \(0.568153\pi\)
\(354\) 0 0
\(355\) 7.34410e7 4.24012e7i 1.64155 0.947748i
\(356\) 0 0
\(357\) 5.00718e6 3.73347e7i 0.110050 0.820556i
\(358\) 0 0
\(359\) 1.28065e7 + 2.21815e7i 0.276787 + 0.479410i 0.970585 0.240761i \(-0.0773969\pi\)
−0.693797 + 0.720171i \(0.744064\pi\)
\(360\) 0 0
\(361\) −1.25091e7 + 2.16664e7i −0.265891 + 0.460537i
\(362\) 0 0
\(363\) 2.70801e7i 0.566148i
\(364\) 0 0
\(365\) −1.56039e6 −0.0320889
\(366\) 0 0
\(367\) 2.41602e7 + 1.39489e7i 0.488767 + 0.282190i 0.724063 0.689734i \(-0.242273\pi\)
−0.235296 + 0.971924i \(0.575606\pi\)
\(368\) 0 0
\(369\) −9.74053e6 + 5.62370e6i −0.193867 + 0.111929i
\(370\) 0 0
\(371\) 3.22998e7 1.32875e7i 0.632525 0.260208i
\(372\) 0 0
\(373\) −1.11791e7 1.93627e7i −0.215416 0.373112i 0.737985 0.674817i \(-0.235778\pi\)
−0.953401 + 0.301705i \(0.902444\pi\)
\(374\) 0 0
\(375\) 967720. 1.67614e6i 0.0183508 0.0317846i
\(376\) 0 0
\(377\) 7.71889e7i 1.44056i
\(378\) 0 0
\(379\) −5.91089e7 −1.08576 −0.542882 0.839809i \(-0.682667\pi\)
−0.542882 + 0.839809i \(0.682667\pi\)
\(380\) 0 0
\(381\) 4.54958e7 + 2.62670e7i 0.822614 + 0.474936i
\(382\) 0 0
\(383\) 3.98770e7 2.30230e7i 0.709785 0.409794i −0.101197 0.994866i \(-0.532267\pi\)
0.810981 + 0.585072i \(0.198934\pi\)
\(384\) 0 0
\(385\) −6.78651e6 + 8.80017e6i −0.118923 + 0.154209i
\(386\) 0 0
\(387\) 1.13151e7 + 1.95984e7i 0.195221 + 0.338133i
\(388\) 0 0
\(389\) 2.16981e7 3.75821e7i 0.368614 0.638458i −0.620735 0.784020i \(-0.713166\pi\)
0.989349 + 0.145562i \(0.0464991\pi\)
\(390\) 0 0
\(391\) 4.68075e7i 0.783043i
\(392\) 0 0
\(393\) −4.66458e7 −0.768484
\(394\) 0 0
\(395\) 6.71776e7 + 3.87850e7i 1.09002 + 0.629321i
\(396\) 0 0
\(397\) −3.39493e7 + 1.96007e7i −0.542575 + 0.313256i −0.746122 0.665809i \(-0.768086\pi\)
0.203547 + 0.979065i \(0.434753\pi\)
\(398\) 0 0
\(399\) −1.98719e7 1.53248e7i −0.312839 0.241256i
\(400\) 0 0
\(401\) 4.77624e7 + 8.27269e7i 0.740718 + 1.28296i 0.952169 + 0.305572i \(0.0988478\pi\)
−0.211451 + 0.977389i \(0.567819\pi\)
\(402\) 0 0
\(403\) −4.76869e7 + 8.25962e7i −0.728592 + 1.26196i
\(404\) 0 0
\(405\) 1.03191e7i 0.155338i
\(406\) 0 0
\(407\) −7.33617e6 −0.108814
\(408\) 0 0
\(409\) 1.64736e7 + 9.51105e6i 0.240779 + 0.139014i 0.615535 0.788110i \(-0.288940\pi\)
−0.374756 + 0.927124i \(0.622273\pi\)
\(410\) 0 0
\(411\) −3.43525e7 + 1.98334e7i −0.494804 + 0.285675i
\(412\) 0 0
\(413\) −1.98797e7 4.83244e7i −0.282202 0.685988i
\(414\) 0 0
\(415\) −4.88777e7 8.46586e7i −0.683858 1.18448i
\(416\) 0 0
\(417\) −1.25994e7 + 2.18229e7i −0.173757 + 0.300956i
\(418\) 0 0
\(419\) 3.79635e7i 0.516089i −0.966133 0.258044i \(-0.916922\pi\)
0.966133 0.258044i \(-0.0830781\pi\)
\(420\) 0 0
\(421\) −1.18733e8 −1.59120 −0.795600 0.605823i \(-0.792844\pi\)
−0.795600 + 0.605823i \(0.792844\pi\)
\(422\) 0 0
\(423\) −3.14560e7 1.81612e7i −0.415607 0.239951i
\(424\) 0 0
\(425\) 9.09970e7 5.25371e7i 1.18539 0.684383i
\(426\) 0 0
\(427\) −5.72986e7 7.68465e6i −0.735970 0.0987053i
\(428\) 0 0
\(429\) −5.75377e6 9.96583e6i −0.0728754 0.126224i
\(430\) 0 0
\(431\) −2.94287e7 + 5.09719e7i −0.367569 + 0.636648i −0.989185 0.146674i \(-0.953143\pi\)
0.621616 + 0.783322i \(0.286476\pi\)
\(432\) 0 0
\(433\) 5.48589e7i 0.675746i 0.941192 + 0.337873i \(0.109707\pi\)
−0.941192 + 0.337873i \(0.890293\pi\)
\(434\) 0 0
\(435\) −5.28102e7 −0.641578
\(436\) 0 0
\(437\) −2.70050e7 1.55914e7i −0.323594 0.186827i
\(438\) 0 0
\(439\) −6.23635e7 + 3.60056e7i −0.737117 + 0.425575i −0.821020 0.570899i \(-0.806595\pi\)
0.0839029 + 0.996474i \(0.473261\pi\)
\(440\) 0 0
\(441\) −2.03129e7 + 2.01172e7i −0.236841 + 0.234558i
\(442\) 0 0
\(443\) 6.73580e7 + 1.16667e8i 0.774779 + 1.34196i 0.934919 + 0.354862i \(0.115472\pi\)
−0.160140 + 0.987094i \(0.551195\pi\)
\(444\) 0 0
\(445\) −1.80658e7 + 3.12909e7i −0.205011 + 0.355090i
\(446\) 0 0
\(447\) 1.77810e7i 0.199083i
\(448\) 0 0
\(449\) 1.73542e8 1.91719 0.958594 0.284777i \(-0.0919196\pi\)
0.958594 + 0.284777i \(0.0919196\pi\)
\(450\) 0 0
\(451\) −7.43163e6 4.29065e6i −0.0810130 0.0467728i
\(452\) 0 0
\(453\) 5.88674e6 3.39871e6i 0.0633258 0.0365611i
\(454\) 0 0
\(455\) 3.17253e7 2.36552e8i 0.336800 2.51126i
\(456\) 0 0
\(457\) −7.31723e7 1.26738e8i −0.766652 1.32788i −0.939369 0.342908i \(-0.888588\pi\)
0.172717 0.984971i \(-0.444745\pi\)
\(458\) 0 0
\(459\) 1.33434e7 2.31114e7i 0.137984 0.238995i
\(460\) 0 0
\(461\) 6.84094e7i 0.698254i −0.937075 0.349127i \(-0.886478\pi\)
0.937075 0.349127i \(-0.113522\pi\)
\(462\) 0 0
\(463\) −2.01813e7 −0.203332 −0.101666 0.994819i \(-0.532417\pi\)
−0.101666 + 0.994819i \(0.532417\pi\)
\(464\) 0 0
\(465\) 5.65096e7 + 3.26258e7i 0.562035 + 0.324491i
\(466\) 0 0
\(467\) 6.85001e7 3.95486e7i 0.672575 0.388311i −0.124477 0.992223i \(-0.539725\pi\)
0.797052 + 0.603911i \(0.206392\pi\)
\(468\) 0 0
\(469\) 1.93826e7 7.97364e6i 0.187886 0.0772926i
\(470\) 0 0
\(471\) 4.16648e7 + 7.21655e7i 0.398755 + 0.690664i
\(472\) 0 0
\(473\) −8.63299e6 + 1.49528e7i −0.0815789 + 0.141299i
\(474\) 0 0
\(475\) 6.99994e7i 0.653151i
\(476\) 0 0
\(477\) 2.47436e7 0.227985
\(478\) 0 0
\(479\) 2.63942e6 + 1.52387e6i 0.0240161 + 0.0138657i 0.511960 0.859009i \(-0.328920\pi\)
−0.487944 + 0.872875i \(0.662253\pi\)
\(480\) 0 0
\(481\) 1.36447e8 7.87778e7i 1.22611 0.707895i
\(482\) 0 0
\(483\) −2.16940e7 + 2.81309e7i −0.192530 + 0.249657i
\(484\) 0 0
\(485\) −1.07646e8 1.86449e8i −0.943571 1.63431i
\(486\) 0 0
\(487\) −3.68761e7 + 6.38713e7i −0.319270 + 0.552992i −0.980336 0.197336i \(-0.936771\pi\)
0.661066 + 0.750328i \(0.270104\pi\)
\(488\) 0 0
\(489\) 2.60406e7i 0.222702i
\(490\) 0 0
\(491\) 8.29108e7 0.700433 0.350216 0.936669i \(-0.386108\pi\)
0.350216 + 0.936669i \(0.386108\pi\)
\(492\) 0 0
\(493\) 1.18277e8 + 6.82873e7i 0.987097 + 0.569901i
\(494\) 0 0
\(495\) −6.81829e6 + 3.93654e6i −0.0562160 + 0.0324563i
\(496\) 0 0
\(497\) 1.31804e8 + 1.01645e8i 1.07364 + 0.827971i
\(498\) 0 0
\(499\) 2.45539e7 + 4.25286e7i 0.197615 + 0.342279i 0.947755 0.319001i \(-0.103347\pi\)
−0.750140 + 0.661279i \(0.770014\pi\)
\(500\) 0 0
\(501\) −1.12307e6 + 1.94522e6i −0.00893088 + 0.0154687i
\(502\) 0 0
\(503\) 1.66557e8i 1.30875i −0.756169 0.654377i \(-0.772931\pi\)
0.756169 0.654377i \(-0.227069\pi\)
\(504\) 0 0
\(505\) −1.56736e8 −1.21701
\(506\) 0 0
\(507\) 1.48869e8 + 8.59498e7i 1.14230 + 0.659510i
\(508\) 0 0
\(509\) 8.07268e7 4.66076e7i 0.612159 0.353430i −0.161651 0.986848i \(-0.551682\pi\)
0.773810 + 0.633418i \(0.218348\pi\)
\(510\) 0 0
\(511\) −1.16517e6 2.83234e6i −0.00873225 0.0212267i
\(512\) 0 0
\(513\) −8.88923e6 1.53966e7i −0.0658434 0.114044i
\(514\) 0 0
\(515\) 1.16523e8 2.01823e8i 0.853078 1.47757i
\(516\) 0 0
\(517\) 2.77124e7i 0.200541i
\(518\) 0 0
\(519\) 2.74098e7 0.196066
\(520\) 0 0
\(521\) −1.07746e8 6.22072e7i −0.761882 0.439873i 0.0680889 0.997679i \(-0.478310\pi\)
−0.829971 + 0.557806i \(0.811643\pi\)
\(522\) 0 0
\(523\) 5.54978e7 3.20417e7i 0.387945 0.223980i −0.293324 0.956013i \(-0.594762\pi\)
0.681269 + 0.732033i \(0.261428\pi\)
\(524\) 0 0
\(525\) −7.90380e7 1.06002e7i −0.546208 0.0732551i
\(526\) 0 0
\(527\) −8.43751e7 1.46142e8i −0.576477 0.998488i
\(528\) 0 0
\(529\) 5.19466e7 8.99742e7i 0.350906 0.607786i
\(530\) 0 0
\(531\) 3.70194e7i 0.247255i
\(532\) 0 0
\(533\) 1.84297e8 1.21713
\(534\) 0 0
\(535\) −1.52883e7 8.82673e6i −0.0998387 0.0576419i
\(536\) 0 0
\(537\) −1.34793e8 + 7.78227e7i −0.870450 + 0.502555i
\(538\) 0 0
\(539\) −2.10412e7 5.74730e6i −0.134371 0.0367027i
\(540\) 0 0
\(541\) −5.86026e7 1.01503e8i −0.370105 0.641041i 0.619476 0.785015i \(-0.287345\pi\)
−0.989581 + 0.143975i \(0.954012\pi\)
\(542\) 0 0
\(543\) 6.08272e7 1.05356e8i 0.379925 0.658050i
\(544\) 0 0
\(545\) 3.41227e8i 2.10792i
\(546\) 0 0
\(547\) 1.64328e8 1.00403 0.502017 0.864858i \(-0.332591\pi\)
0.502017 + 0.864858i \(0.332591\pi\)
\(548\) 0 0
\(549\) −3.54697e7 2.04785e7i −0.214359 0.123760i
\(550\) 0 0
\(551\) 7.87950e7 4.54923e7i 0.471025 0.271946i
\(552\) 0 0
\(553\) −2.02379e7 + 1.50899e8i −0.119671 + 0.892298i
\(554\) 0 0
\(555\) −5.38972e7 9.33527e7i −0.315273 0.546070i
\(556\) 0 0
\(557\) −1.01102e8 + 1.75114e8i −0.585052 + 1.01334i 0.409817 + 0.912168i \(0.365593\pi\)
−0.994869 + 0.101172i \(0.967741\pi\)
\(558\) 0 0
\(559\) 3.70813e8i 2.12285i
\(560\) 0 0
\(561\) 2.03609e7 0.115321
\(562\) 0 0
\(563\) 1.22757e8 + 7.08737e7i 0.687892 + 0.397155i 0.802822 0.596219i \(-0.203331\pi\)
−0.114930 + 0.993374i \(0.536664\pi\)
\(564\) 0 0
\(565\) 1.72502e8 9.95940e7i 0.956419 0.552189i
\(566\) 0 0
\(567\) −1.87308e7 + 7.70548e6i −0.102756 + 0.0422718i
\(568\) 0 0
\(569\) 1.70801e8 + 2.95835e8i 0.927156 + 1.60588i 0.788057 + 0.615603i \(0.211087\pi\)
0.139099 + 0.990278i \(0.455579\pi\)
\(570\) 0 0
\(571\) −1.31414e8 + 2.27616e8i −0.705883 + 1.22263i 0.260488 + 0.965477i \(0.416116\pi\)
−0.966372 + 0.257149i \(0.917217\pi\)
\(572\) 0 0
\(573\) 7.97541e6i 0.0423925i
\(574\) 0 0
\(575\) −9.90920e7 −0.521237
\(576\) 0 0
\(577\) −1.79880e8 1.03854e8i −0.936389 0.540625i −0.0475627 0.998868i \(-0.515145\pi\)
−0.888827 + 0.458244i \(0.848479\pi\)
\(578\) 0 0
\(579\) −1.17539e8 + 6.78611e7i −0.605544 + 0.349611i
\(580\) 0 0
\(581\) 1.17170e8 1.51936e8i 0.597432 0.774699i
\(582\) 0 0
\(583\) 9.43917e6 + 1.63491e7i 0.0476352 + 0.0825066i
\(584\) 0 0
\(585\) 8.45433e7 1.46433e8i 0.422291 0.731429i
\(586\) 0 0
\(587\) 2.00752e8i 0.992537i 0.868169 + 0.496268i \(0.165297\pi\)
−0.868169 + 0.496268i \(0.834703\pi\)
\(588\) 0 0
\(589\) −1.12420e8 −0.550169
\(590\) 0 0
\(591\) −6.00712e7 3.46821e7i −0.291007 0.168013i
\(592\) 0 0
\(593\) −1.38061e8 + 7.97096e7i −0.662075 + 0.382249i −0.793067 0.609134i \(-0.791517\pi\)
0.130992 + 0.991383i \(0.458184\pi\)
\(594\) 0 0
\(595\) 3.34403e8 + 2.57885e8i 1.58752 + 1.22426i
\(596\) 0 0
\(597\) 5.54785e7 + 9.60917e7i 0.260737 + 0.451609i
\(598\) 0 0
\(599\) 4.27029e7 7.39635e7i 0.198690 0.344142i −0.749414 0.662102i \(-0.769665\pi\)
0.948104 + 0.317960i \(0.102998\pi\)
\(600\) 0 0
\(601\) 1.61501e8i 0.743962i −0.928240 0.371981i \(-0.878679\pi\)
0.928240 0.371981i \(-0.121321\pi\)
\(602\) 0 0
\(603\) 1.48483e7 0.0677211
\(604\) 0 0
\(605\) 2.62911e8 + 1.51792e8i 1.18725 + 0.685460i
\(606\) 0 0
\(607\) 2.02413e7 1.16863e7i 0.0905049 0.0522530i −0.454064 0.890969i \(-0.650026\pi\)
0.544569 + 0.838716i \(0.316693\pi\)
\(608\) 0 0
\(609\) −3.94342e7 9.58583e7i −0.174591 0.424402i
\(610\) 0 0
\(611\) 2.97584e8 + 5.15430e8i 1.30462 + 2.25968i
\(612\) 0 0
\(613\) −1.66743e8 + 2.88807e8i −0.723878 + 1.25379i 0.235557 + 0.971861i \(0.424309\pi\)
−0.959434 + 0.281932i \(0.909025\pi\)
\(614\) 0 0
\(615\) 1.26090e8i 0.542069i
\(616\) 0 0
\(617\) −1.74626e8 −0.743451 −0.371726 0.928343i \(-0.621234\pi\)
−0.371726 + 0.928343i \(0.621234\pi\)
\(618\) 0 0
\(619\) 4.50581e7 + 2.60143e7i 0.189977 + 0.109683i 0.591972 0.805959i \(-0.298350\pi\)
−0.401995 + 0.915642i \(0.631683\pi\)
\(620\) 0 0
\(621\) −2.17956e7 + 1.25837e7i −0.0910111 + 0.0525453i
\(622\) 0 0
\(623\) −7.02877e7 9.42670e6i −0.290680 0.0389848i
\(624\) 0 0
\(625\) 1.27368e8 + 2.20609e8i 0.521701 + 0.903613i
\(626\) 0 0
\(627\) 6.78212e6 1.17470e7i 0.0275146 0.0476567i
\(628\) 0 0
\(629\) 2.78772e8i 1.12020i
\(630\) 0 0
\(631\) −3.39999e8 −1.35329 −0.676643 0.736311i \(-0.736566\pi\)
−0.676643 + 0.736311i \(0.736566\pi\)
\(632\) 0 0
\(633\) −1.52439e8 8.80105e7i −0.601013 0.346995i
\(634\) 0 0
\(635\) −5.10034e8 + 2.94468e8i −1.99195 + 1.15005i
\(636\) 0 0
\(637\) 4.53066e8 1.19051e8i 1.75285 0.460590i
\(638\) 0 0
\(639\) 5.89594e7 + 1.02121e8i 0.225970 + 0.391391i
\(640\) 0 0
\(641\) 7.72851e6 1.33862e7i 0.0293441 0.0508256i −0.850980 0.525197i \(-0.823991\pi\)
0.880325 + 0.474372i \(0.157325\pi\)
\(642\) 0 0
\(643\) 1.06911e8i 0.402152i 0.979576 + 0.201076i \(0.0644438\pi\)
−0.979576 + 0.201076i \(0.935556\pi\)
\(644\) 0 0
\(645\) −2.53699e8 −0.945451
\(646\) 0 0
\(647\) −4.33160e8 2.50085e8i −1.59932 0.923369i −0.991618 0.129205i \(-0.958757\pi\)
−0.607704 0.794163i \(-0.707909\pi\)
\(648\) 0 0
\(649\) 2.44603e7 1.41221e7i 0.0894803 0.0516615i
\(650\) 0 0
\(651\) −1.70241e7 + 1.26936e8i −0.0617051 + 0.460088i
\(652\) 0 0
\(653\) −9.83335e7 1.70319e8i −0.353152 0.611677i 0.633648 0.773622i \(-0.281557\pi\)
−0.986800 + 0.161944i \(0.948224\pi\)
\(654\) 0 0
\(655\) 2.61463e8 4.52867e8i 0.930436 1.61156i
\(656\) 0 0
\(657\) 2.16974e6i 0.00765089i
\(658\) 0 0
\(659\) −2.58438e8 −0.903026 −0.451513 0.892264i \(-0.649116\pi\)
−0.451513 + 0.892264i \(0.649116\pi\)
\(660\) 0 0
\(661\) 4.01236e8 + 2.31654e8i 1.38930 + 0.802111i 0.993236 0.116112i \(-0.0370433\pi\)
0.396062 + 0.918224i \(0.370377\pi\)
\(662\) 0 0
\(663\) −3.78697e8 + 2.18641e8i −1.29943 + 0.750224i
\(664\) 0 0
\(665\) 2.60171e8 1.07029e8i 0.884697 0.363947i
\(666\) 0 0
\(667\) −6.43995e7 1.11543e8i −0.217023 0.375894i
\(668\) 0 0
\(669\) −8.75915e6 + 1.51713e7i −0.0292539 + 0.0506692i
\(670\) 0 0
\(671\) 3.12485e7i 0.103433i
\(672\) 0 0
\(673\) −3.81262e8 −1.25077 −0.625385 0.780316i \(-0.715058\pi\)
−0.625385 + 0.780316i \(0.715058\pi\)
\(674\) 0 0
\(675\) −4.89271e7 2.82481e7i −0.159088 0.0918497i
\(676\) 0 0
\(677\) −3.72384e8 + 2.14996e8i −1.20012 + 0.692890i −0.960582 0.277997i \(-0.910329\pi\)
−0.239538 + 0.970887i \(0.576996\pi\)
\(678\) 0 0
\(679\) 2.58052e8 3.34619e8i 0.824323 1.06891i
\(680\) 0 0
\(681\) 7.77206e7 + 1.34616e8i 0.246091 + 0.426241i
\(682\) 0 0
\(683\) 7.64651e7 1.32441e8i 0.239995 0.415683i −0.720718 0.693228i \(-0.756188\pi\)
0.960712 + 0.277546i \(0.0895210\pi\)
\(684\) 0 0
\(685\) 4.44689e8i 1.38352i
\(686\) 0 0
\(687\) 3.04649e8 0.939570
\(688\) 0 0
\(689\) −3.51122e8 2.02721e8i −1.07350 0.619784i
\(690\) 0 0
\(691\) −1.99349e8 + 1.15094e8i −0.604198 + 0.348834i −0.770691 0.637209i \(-0.780089\pi\)
0.166493 + 0.986043i \(0.446756\pi\)
\(692\) 0 0
\(693\) −1.22367e7 9.43674e6i −0.0367677 0.0283545i
\(694\) 0 0
\(695\) −1.41247e8 2.44647e8i −0.420751 0.728761i
\(696\) 0 0
\(697\) −1.63043e8 + 2.82399e8i −0.481509 + 0.833998i
\(698\) 0 0
\(699\) 4.99204e7i 0.146166i
\(700\) 0 0
\(701\) 8.76414e7 0.254422 0.127211 0.991876i \(-0.459397\pi\)
0.127211 + 0.991876i \(0.459397\pi\)
\(702\) 0 0
\(703\) 1.60834e8 + 9.28575e7i 0.462926 + 0.267270i
\(704\) 0 0
\(705\) 3.52640e8 2.03597e8i 1.00639 0.581037i
\(706\) 0 0
\(707\) −1.17038e8 2.84500e8i −0.331182 0.805051i
\(708\) 0 0
\(709\) −1.56656e8 2.71336e8i −0.439550 0.761324i 0.558104 0.829771i \(-0.311529\pi\)
−0.997655 + 0.0684471i \(0.978196\pi\)
\(710\) 0 0
\(711\) −5.39310e7 + 9.34113e7i −0.150048 + 0.259891i
\(712\) 0 0
\(713\) 1.59143e8i 0.439054i
\(714\) 0 0
\(715\) 1.29006e8 0.352933
\(716\) 0 0
\(717\) 1.92172e8 + 1.10951e8i 0.521355 + 0.301004i
\(718\) 0 0
\(719\) 6.19602e8 3.57727e8i 1.66696 0.962421i 0.697701 0.716389i \(-0.254207\pi\)
0.969262 0.246032i \(-0.0791268\pi\)
\(720\) 0 0
\(721\) 4.53349e8 + 6.08013e7i 1.20956 + 0.162221i
\(722\) 0 0
\(723\) 3.94257e7 + 6.82874e7i 0.104319 + 0.180686i
\(724\) 0 0
\(725\) 1.44565e8 2.50394e8i 0.379358 0.657067i
\(726\) 0 0
\(727\) 7.42437e8i 1.93222i 0.258132 + 0.966110i \(0.416893\pi\)
−0.258132 + 0.966110i \(0.583107\pi\)
\(728\) 0 0
\(729\) −1.43489e7 −0.0370370
\(730\) 0 0
\(731\) 5.68200e8 + 3.28050e8i 1.45462 + 0.839824i
\(732\) 0 0
\(733\) −3.85053e8 + 2.22311e8i −0.977707 + 0.564479i −0.901577 0.432619i \(-0.857590\pi\)
−0.0761299 + 0.997098i \(0.524256\pi\)
\(734\) 0 0
\(735\) −8.14507e7 3.09973e8i −0.205132 0.780661i
\(736\) 0 0
\(737\) 5.66431e6 + 9.81087e6i 0.0141496 + 0.0245078i
\(738\) 0 0
\(739\) −2.38987e8 + 4.13937e8i −0.592162 + 1.02566i 0.401778 + 0.915737i \(0.368392\pi\)
−0.993941 + 0.109918i \(0.964941\pi\)
\(740\) 0 0
\(741\) 2.91313e8i 0.715987i
\(742\) 0 0
\(743\) −4.11550e8 −1.00336 −0.501679 0.865054i \(-0.667284\pi\)
−0.501679 + 0.865054i \(0.667284\pi\)
\(744\) 0 0
\(745\) −1.72629e8 9.96676e7i −0.417490 0.241038i
\(746\) 0 0
\(747\) 1.17719e8 6.79650e7i 0.282413 0.163051i
\(748\) 0 0
\(749\) 4.60577e6 3.43417e7i 0.0109612 0.0817290i
\(750\) 0 0
\(751\) 4.02795e6 + 6.97662e6i 0.00950965 + 0.0164712i 0.870741 0.491742i \(-0.163640\pi\)
−0.861231 + 0.508213i \(0.830306\pi\)
\(752\) 0 0
\(753\) 8.51734e7 1.47525e8i 0.199489 0.345525i
\(754\) 0 0
\(755\) 7.62031e7i 0.177065i
\(756\) 0 0
\(757\) −6.97539e7 −0.160798 −0.0803990 0.996763i \(-0.525619\pi\)
−0.0803990 + 0.996763i \(0.525619\pi\)
\(758\) 0 0
\(759\) −1.66292e7 9.60086e6i −0.0380317 0.0219576i
\(760\) 0 0
\(761\) −3.33426e8 + 1.92503e8i −0.756563 + 0.436802i −0.828060 0.560639i \(-0.810556\pi\)
0.0714973 + 0.997441i \(0.477222\pi\)
\(762\) 0 0
\(763\) 6.19378e8 2.54800e8i 1.39438 0.573622i
\(764\) 0 0
\(765\) 1.49587e8 + 2.59092e8i 0.334126 + 0.578723i
\(766\) 0 0
\(767\) −3.03295e8 + 5.25322e8i −0.672170 + 1.16423i
\(768\) 0 0
\(769\) 5.19869e8i 1.14318i 0.820539 + 0.571590i \(0.193673\pi\)
−0.820539 + 0.571590i \(0.806327\pi\)
\(770\) 0 0
\(771\) 1.50799e8 0.329029
\(772\) 0 0
\(773\) 3.28958e8 + 1.89924e8i 0.712199 + 0.411188i 0.811875 0.583832i \(-0.198447\pi\)
−0.0996756 + 0.995020i \(0.531781\pi\)
\(774\) 0 0
\(775\) −3.09384e8 + 1.78623e8i −0.664649 + 0.383735i
\(776\) 0 0
\(777\) 1.29203e8 1.67539e8i 0.275429 0.357153i
\(778\) 0 0
\(779\) 1.08618e8 + 1.88131e8i 0.229767 + 0.397969i
\(780\) 0 0
\(781\) −4.49836e7 + 7.79139e7i −0.0944281 + 0.163554i
\(782\) 0 0
\(783\) 7.34332e7i 0.152970i
\(784\) 0 0
\(785\) −9.34173e8 −1.93116