Properties

Label 76.6.e.a.45.3
Level $76$
Weight $6$
Character 76.45
Analytic conductor $12.189$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 76.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.1891703058\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Defining polynomial: \(x^{18} - 2 x^{17} + 1540 x^{16} - 768 x^{15} + 1608492 x^{14} - 1027368 x^{13} + 897054160 x^{12} - 1275481376 x^{11} + 361098181456 x^{10} - 863969476320 x^{9} + 79755165392064 x^{8} - 375077568148992 x^{7} + 12736924096193536 x^{6} - 57314532742553600 x^{5} + 977121800205220864 x^{4} - 4977732006498379776 x^{3} + 53672321824823513088 x^{2} - 185653809995679793152 x + 804303742853852430336\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{16}\cdot 3^{3}\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 45.3
Root \(6.29505 - 10.9033i\) of defining polynomial
Character \(\chi\) \(=\) 76.45
Dual form 76.6.e.a.49.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-6.79505 - 11.7694i) q^{3} +(-47.4871 - 82.2500i) q^{5} +189.860 q^{7} +(29.1546 - 50.4972i) q^{9} +O(q^{10})\) \(q+(-6.79505 - 11.7694i) q^{3} +(-47.4871 - 82.2500i) q^{5} +189.860 q^{7} +(29.1546 - 50.4972i) q^{9} -530.005 q^{11} +(-353.895 + 612.964i) q^{13} +(-645.354 + 1117.79i) q^{15} +(-764.589 - 1324.31i) q^{17} +(654.031 + 1431.20i) q^{19} +(-1290.11 - 2234.53i) q^{21} +(497.425 - 861.565i) q^{23} +(-2947.54 + 5105.29i) q^{25} -4094.82 q^{27} +(-1290.66 + 2235.49i) q^{29} -2790.81 q^{31} +(3601.41 + 6237.82i) q^{33} +(-9015.88 - 15616.0i) q^{35} +7238.14 q^{37} +9618.94 q^{39} +(2181.63 + 3778.69i) q^{41} +(-3121.70 - 5406.94i) q^{43} -5537.86 q^{45} +(12320.9 - 21340.4i) q^{47} +19239.7 q^{49} +(-10390.8 + 17997.5i) q^{51} +(-15497.6 + 26842.6i) q^{53} +(25168.4 + 43592.9i) q^{55} +(12400.2 - 17422.6i) q^{57} +(-18177.7 - 31484.8i) q^{59} +(2886.93 - 5000.30i) q^{61} +(5535.27 - 9587.38i) q^{63} +67221.7 q^{65} +(30388.4 - 52634.2i) q^{67} -13520.1 q^{69} +(14829.0 + 25684.5i) q^{71} +(-39002.3 - 67553.9i) q^{73} +80114.7 q^{75} -100627. q^{77} +(-33427.5 - 57898.2i) q^{79} +(20740.0 + 35922.7i) q^{81} -21919.5 q^{83} +(-72616.2 + 125775. i) q^{85} +35080.4 q^{87} +(-45374.8 + 78591.5i) q^{89} +(-67190.4 + 116377. i) q^{91} +(18963.7 + 32846.0i) q^{93} +(86658.4 - 121758. i) q^{95} +(-30757.3 - 53273.1i) q^{97} +(-15452.1 + 26763.7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} + O(q^{10}) \) \( 18q - 11q^{3} + 11q^{5} + 336q^{7} - 902q^{9} - 320q^{11} + 227q^{13} - 101q^{15} + 179q^{17} - 868q^{19} - 5700q^{21} - 3425q^{23} - 7054q^{25} + 14722q^{27} - 7349q^{29} - 9960q^{31} - 2998q^{33} + 15888q^{35} + 26444q^{37} - 30246q^{39} - 7311q^{41} - 8283q^{43} - 62164q^{45} + 37603q^{47} + 124738q^{49} + 47227q^{51} - 20337q^{53} + 716q^{55} - 57555q^{57} - 74455q^{59} - 7569q^{61} - 52544q^{63} + 188998q^{65} - 26177q^{67} + 116282q^{69} - 53463q^{71} - 14103q^{73} + 120912q^{75} - 31960q^{77} + 31825q^{79} - 21137q^{81} + 82600q^{83} - 50787q^{85} - 339766q^{87} - 155197q^{89} - 2800q^{91} - 46460q^{93} + 49315q^{95} + 111241q^{97} - 193544q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

Coefficient data

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

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
\(3\) −6.79505 11.7694i −0.435903 0.755006i 0.561466 0.827500i \(-0.310238\pi\)
−0.997369 + 0.0724940i \(0.976904\pi\)
\(4\) 0 0
\(5\) −47.4871 82.2500i −0.849474 1.47133i −0.881678 0.471851i \(-0.843586\pi\)
0.0322040 0.999481i \(-0.489747\pi\)
\(6\) 0 0
\(7\) 189.860 1.46449 0.732247 0.681039i \(-0.238472\pi\)
0.732247 + 0.681039i \(0.238472\pi\)
\(8\) 0 0
\(9\) 29.1546 50.4972i 0.119978 0.207807i
\(10\) 0 0
\(11\) −530.005 −1.32068 −0.660341 0.750966i \(-0.729588\pi\)
−0.660341 + 0.750966i \(0.729588\pi\)
\(12\) 0 0
\(13\) −353.895 + 612.964i −0.580786 + 1.00595i 0.414600 + 0.910004i \(0.363921\pi\)
−0.995386 + 0.0959473i \(0.969412\pi\)
\(14\) 0 0
\(15\) −645.354 + 1117.79i −0.740576 + 1.28272i
\(16\) 0 0
\(17\) −764.589 1324.31i −0.641661 1.11139i −0.985062 0.172201i \(-0.944912\pi\)
0.343401 0.939189i \(-0.388421\pi\)
\(18\) 0 0
\(19\) 654.031 + 1431.20i 0.415637 + 0.909530i
\(20\) 0 0
\(21\) −1290.11 2234.53i −0.638377 1.10570i
\(22\) 0 0
\(23\) 497.425 861.565i 0.196068 0.339600i −0.751182 0.660095i \(-0.770516\pi\)
0.947250 + 0.320495i \(0.103849\pi\)
\(24\) 0 0
\(25\) −2947.54 + 5105.29i −0.943213 + 1.63369i
\(26\) 0 0
\(27\) −4094.82 −1.08100
\(28\) 0 0
\(29\) −1290.66 + 2235.49i −0.284982 + 0.493603i −0.972605 0.232465i \(-0.925321\pi\)
0.687623 + 0.726068i \(0.258654\pi\)
\(30\) 0 0
\(31\) −2790.81 −0.521585 −0.260793 0.965395i \(-0.583984\pi\)
−0.260793 + 0.965395i \(0.583984\pi\)
\(32\) 0 0
\(33\) 3601.41 + 6237.82i 0.575689 + 0.997122i
\(34\) 0 0
\(35\) −9015.88 15616.0i −1.24405 2.15476i
\(36\) 0 0
\(37\) 7238.14 0.869206 0.434603 0.900622i \(-0.356889\pi\)
0.434603 + 0.900622i \(0.356889\pi\)
\(38\) 0 0
\(39\) 9618.94 1.01266
\(40\) 0 0
\(41\) 2181.63 + 3778.69i 0.202685 + 0.351060i 0.949393 0.314092i \(-0.101700\pi\)
−0.746708 + 0.665152i \(0.768367\pi\)
\(42\) 0 0
\(43\) −3121.70 5406.94i −0.257466 0.445944i 0.708096 0.706116i \(-0.249554\pi\)
−0.965562 + 0.260172i \(0.916221\pi\)
\(44\) 0 0
\(45\) −5537.86 −0.407671
\(46\) 0 0
\(47\) 12320.9 21340.4i 0.813576 1.40915i −0.0967705 0.995307i \(-0.530851\pi\)
0.910346 0.413848i \(-0.135815\pi\)
\(48\) 0 0
\(49\) 19239.7 1.14474
\(50\) 0 0
\(51\) −10390.8 + 17997.5i −0.559404 + 0.968916i
\(52\) 0 0
\(53\) −15497.6 + 26842.6i −0.757833 + 1.31261i 0.186120 + 0.982527i \(0.440409\pi\)
−0.943953 + 0.330079i \(0.892925\pi\)
\(54\) 0 0
\(55\) 25168.4 + 43592.9i 1.12188 + 1.94316i
\(56\) 0 0
\(57\) 12400.2 17422.6i 0.505523 0.710275i
\(58\) 0 0
\(59\) −18177.7 31484.8i −0.679845 1.17753i −0.975027 0.222085i \(-0.928714\pi\)
0.295182 0.955441i \(-0.404620\pi\)
\(60\) 0 0
\(61\) 2886.93 5000.30i 0.0993370 0.172057i −0.812073 0.583555i \(-0.801661\pi\)
0.911410 + 0.411499i \(0.134994\pi\)
\(62\) 0 0
\(63\) 5535.27 9587.38i 0.175706 0.304333i
\(64\) 0 0
\(65\) 67221.7 1.97345
\(66\) 0 0
\(67\) 30388.4 52634.2i 0.827029 1.43246i −0.0733301 0.997308i \(-0.523363\pi\)
0.900359 0.435148i \(-0.143304\pi\)
\(68\) 0 0
\(69\) −13520.1 −0.341867
\(70\) 0 0
\(71\) 14829.0 + 25684.5i 0.349112 + 0.604680i 0.986092 0.166201i \(-0.0531500\pi\)
−0.636980 + 0.770880i \(0.719817\pi\)
\(72\) 0 0
\(73\) −39002.3 67553.9i −0.856609 1.48369i −0.875144 0.483862i \(-0.839234\pi\)
0.0185353 0.999828i \(-0.494100\pi\)
\(74\) 0 0
\(75\) 80114.7 1.64460
\(76\) 0 0
\(77\) −100627. −1.93413
\(78\) 0 0
\(79\) −33427.5 57898.2i −0.602611 1.04375i −0.992424 0.122858i \(-0.960794\pi\)
0.389814 0.920894i \(-0.372539\pi\)
\(80\) 0 0
\(81\) 20740.0 + 35922.7i 0.351233 + 0.608354i
\(82\) 0 0
\(83\) −21919.5 −0.349250 −0.174625 0.984635i \(-0.555871\pi\)
−0.174625 + 0.984635i \(0.555871\pi\)
\(84\) 0 0
\(85\) −72616.2 + 125775.i −1.09015 + 1.88819i
\(86\) 0 0
\(87\) 35080.4 0.496898
\(88\) 0 0
\(89\) −45374.8 + 78591.5i −0.607211 + 1.05172i 0.384487 + 0.923131i \(0.374378\pi\)
−0.991698 + 0.128590i \(0.958955\pi\)
\(90\) 0 0
\(91\) −67190.4 + 116377.i −0.850558 + 1.47321i
\(92\) 0 0
\(93\) 18963.7 + 32846.0i 0.227360 + 0.393800i
\(94\) 0 0
\(95\) 86658.4 121758.i 0.985149 1.38416i
\(96\) 0 0
\(97\) −30757.3 53273.1i −0.331908 0.574882i 0.650978 0.759097i \(-0.274359\pi\)
−0.982886 + 0.184215i \(0.941026\pi\)
\(98\) 0 0
\(99\) −15452.1 + 26763.7i −0.158452 + 0.274447i
\(100\) 0 0
\(101\) 5882.91 10189.5i 0.0573837 0.0993915i −0.835906 0.548872i \(-0.815057\pi\)
0.893290 + 0.449480i \(0.148391\pi\)
\(102\) 0 0
\(103\) −57682.4 −0.535735 −0.267868 0.963456i \(-0.586319\pi\)
−0.267868 + 0.963456i \(0.586319\pi\)
\(104\) 0 0
\(105\) −122527. + 212222.i −1.08457 + 1.87853i
\(106\) 0 0
\(107\) −79892.9 −0.674604 −0.337302 0.941397i \(-0.609514\pi\)
−0.337302 + 0.941397i \(0.609514\pi\)
\(108\) 0 0
\(109\) −98323.4 170301.i −0.792667 1.37294i −0.924310 0.381642i \(-0.875359\pi\)
0.131643 0.991297i \(-0.457975\pi\)
\(110\) 0 0
\(111\) −49183.5 85188.4i −0.378889 0.656255i
\(112\) 0 0
\(113\) 205714. 1.51554 0.757770 0.652521i \(-0.226289\pi\)
0.757770 + 0.652521i \(0.226289\pi\)
\(114\) 0 0
\(115\) −94484.9 −0.666220
\(116\) 0 0
\(117\) 20635.3 + 35741.4i 0.139363 + 0.241383i
\(118\) 0 0
\(119\) −145165. 251433.i −0.939709 1.62762i
\(120\) 0 0
\(121\) 119854. 0.744199
\(122\) 0 0
\(123\) 29648.6 51352.8i 0.176702 0.306056i
\(124\) 0 0
\(125\) 263086. 1.50599
\(126\) 0 0
\(127\) −143.620 + 248.756i −0.000790141 + 0.00136856i −0.866420 0.499316i \(-0.833585\pi\)
0.865630 + 0.500684i \(0.166918\pi\)
\(128\) 0 0
\(129\) −42424.2 + 73480.9i −0.224460 + 0.388777i
\(130\) 0 0
\(131\) −21086.6 36523.1i −0.107357 0.185947i 0.807342 0.590084i \(-0.200905\pi\)
−0.914699 + 0.404137i \(0.867572\pi\)
\(132\) 0 0
\(133\) 124174. + 271728.i 0.608698 + 1.33200i
\(134\) 0 0
\(135\) 194451. + 336799.i 0.918281 + 1.59051i
\(136\) 0 0
\(137\) −52318.5 + 90618.2i −0.238152 + 0.412491i −0.960184 0.279369i \(-0.909875\pi\)
0.722032 + 0.691859i \(0.243208\pi\)
\(138\) 0 0
\(139\) 64404.7 111552.i 0.282736 0.489713i −0.689322 0.724455i \(-0.742091\pi\)
0.972058 + 0.234743i \(0.0754247\pi\)
\(140\) 0 0
\(141\) −334885. −1.41856
\(142\) 0 0
\(143\) 187566. 324874.i 0.767033 1.32854i
\(144\) 0 0
\(145\) 245159. 0.968339
\(146\) 0 0
\(147\) −130735. 226439.i −0.498997 0.864288i
\(148\) 0 0
\(149\) −136506. 236435.i −0.503716 0.872462i −0.999991 0.00429614i \(-0.998632\pi\)
0.496275 0.868165i \(-0.334701\pi\)
\(150\) 0 0
\(151\) 68761.9 0.245418 0.122709 0.992443i \(-0.460842\pi\)
0.122709 + 0.992443i \(0.460842\pi\)
\(152\) 0 0
\(153\) −89165.0 −0.307940
\(154\) 0 0
\(155\) 132527. + 229544.i 0.443073 + 0.767425i
\(156\) 0 0
\(157\) 275998. + 478042.i 0.893628 + 1.54781i 0.835494 + 0.549500i \(0.185182\pi\)
0.0581337 + 0.998309i \(0.481485\pi\)
\(158\) 0 0
\(159\) 421227. 1.32137
\(160\) 0 0
\(161\) 94440.9 163576.i 0.287141 0.497343i
\(162\) 0 0
\(163\) −153395. −0.452211 −0.226106 0.974103i \(-0.572599\pi\)
−0.226106 + 0.974103i \(0.572599\pi\)
\(164\) 0 0
\(165\) 342041. 592432.i 0.978065 1.69406i
\(166\) 0 0
\(167\) 146626. 253963.i 0.406836 0.704660i −0.587697 0.809081i \(-0.699965\pi\)
0.994533 + 0.104421i \(0.0332988\pi\)
\(168\) 0 0
\(169\) −64836.9 112301.i −0.174625 0.302459i
\(170\) 0 0
\(171\) 91339.7 + 8699.36i 0.238874 + 0.0227508i
\(172\) 0 0
\(173\) −114249. 197885.i −0.290227 0.502688i 0.683636 0.729823i \(-0.260398\pi\)
−0.973863 + 0.227135i \(0.927064\pi\)
\(174\) 0 0
\(175\) −559619. + 969289.i −1.38133 + 2.39253i
\(176\) 0 0
\(177\) −247037. + 427881.i −0.592693 + 1.02657i
\(178\) 0 0
\(179\) 247143. 0.576521 0.288261 0.957552i \(-0.406923\pi\)
0.288261 + 0.957552i \(0.406923\pi\)
\(180\) 0 0
\(181\) 353864. 612910.i 0.802859 1.39059i −0.114867 0.993381i \(-0.536644\pi\)
0.917727 0.397213i \(-0.130022\pi\)
\(182\) 0 0
\(183\) −78467.2 −0.173205
\(184\) 0 0
\(185\) −343718. 595337.i −0.738368 1.27889i
\(186\) 0 0
\(187\) 405236. + 701889.i 0.847430 + 1.46779i
\(188\) 0 0
\(189\) −777442. −1.58312
\(190\) 0 0
\(191\) 10502.1 0.0208301 0.0104151 0.999946i \(-0.496685\pi\)
0.0104151 + 0.999946i \(0.496685\pi\)
\(192\) 0 0
\(193\) 496794. + 860472.i 0.960025 + 1.66281i 0.722424 + 0.691450i \(0.243028\pi\)
0.237601 + 0.971363i \(0.423639\pi\)
\(194\) 0 0
\(195\) −456775. 791158.i −0.860233 1.48997i
\(196\) 0 0
\(197\) −185300. −0.340182 −0.170091 0.985428i \(-0.554406\pi\)
−0.170091 + 0.985428i \(0.554406\pi\)
\(198\) 0 0
\(199\) 43149.9 74737.8i 0.0772408 0.133785i −0.824818 0.565399i \(-0.808722\pi\)
0.902059 + 0.431614i \(0.142056\pi\)
\(200\) 0 0
\(201\) −825963. −1.44202
\(202\) 0 0
\(203\) −245045. + 424430.i −0.417354 + 0.722879i
\(204\) 0 0
\(205\) 207198. 358878.i 0.344351 0.596433i
\(206\) 0 0
\(207\) −29004.4 50237.1i −0.0470476 0.0814889i
\(208\) 0 0
\(209\) −346640. 758544.i −0.548924 1.20120i
\(210\) 0 0
\(211\) 151234. + 261945.i 0.233853 + 0.405045i 0.958939 0.283613i \(-0.0915332\pi\)
−0.725086 + 0.688659i \(0.758200\pi\)
\(212\) 0 0
\(213\) 201527. 349055.i 0.304358 0.527163i
\(214\) 0 0
\(215\) −296481. + 513519.i −0.437422 + 0.757636i
\(216\) 0 0
\(217\) −529861. −0.763858
\(218\) 0 0
\(219\) −530045. + 918064.i −0.746796 + 1.29349i
\(220\) 0 0
\(221\) 1.08234e6 1.49067
\(222\) 0 0
\(223\) −339486. 588007.i −0.457151 0.791809i 0.541658 0.840599i \(-0.317797\pi\)
−0.998809 + 0.0487901i \(0.984463\pi\)
\(224\) 0 0
\(225\) 171868. + 297685.i 0.226329 + 0.392013i
\(226\) 0 0
\(227\) 231581. 0.298289 0.149145 0.988815i \(-0.452348\pi\)
0.149145 + 0.988815i \(0.452348\pi\)
\(228\) 0 0
\(229\) 33377.9 0.0420601 0.0210300 0.999779i \(-0.493305\pi\)
0.0210300 + 0.999779i \(0.493305\pi\)
\(230\) 0 0
\(231\) 683762. + 1.18431e6i 0.843093 + 1.46028i
\(232\) 0 0
\(233\) 542190. + 939100.i 0.654277 + 1.13324i 0.982075 + 0.188493i \(0.0603602\pi\)
−0.327798 + 0.944748i \(0.606306\pi\)
\(234\) 0 0
\(235\) −2.34033e6 −2.76445
\(236\) 0 0
\(237\) −454284. + 786843.i −0.525359 + 0.909949i
\(238\) 0 0
\(239\) −284041. −0.321652 −0.160826 0.986983i \(-0.551416\pi\)
−0.160826 + 0.986983i \(0.551416\pi\)
\(240\) 0 0
\(241\) 306804. 531400.i 0.340266 0.589357i −0.644216 0.764843i \(-0.722816\pi\)
0.984482 + 0.175486i \(0.0561497\pi\)
\(242\) 0 0
\(243\) −215663. + 373539.i −0.234293 + 0.405807i
\(244\) 0 0
\(245\) −913637. 1.58246e6i −0.972430 1.68430i
\(246\) 0 0
\(247\) −1.10873e6 105598.i −1.15634 0.110132i
\(248\) 0 0
\(249\) 148944. + 257979.i 0.152239 + 0.263685i
\(250\) 0 0
\(251\) 369089. 639282.i 0.369783 0.640484i −0.619748 0.784801i \(-0.712765\pi\)
0.989531 + 0.144317i \(0.0460986\pi\)
\(252\) 0 0
\(253\) −263637. + 456633.i −0.258944 + 0.448504i
\(254\) 0 0
\(255\) 1.97372e6 1.90080
\(256\) 0 0
\(257\) 686359. 1.18881e6i 0.648214 1.12274i −0.335335 0.942099i \(-0.608849\pi\)
0.983549 0.180641i \(-0.0578172\pi\)
\(258\) 0 0
\(259\) 1.37423e6 1.27295
\(260\) 0 0
\(261\) 75257.3 + 130349.i 0.0683829 + 0.118443i
\(262\) 0 0
\(263\) −146329. 253449.i −0.130449 0.225944i 0.793401 0.608699i \(-0.208308\pi\)
−0.923850 + 0.382756i \(0.874975\pi\)
\(264\) 0 0
\(265\) 2.94373e6 2.57504
\(266\) 0 0
\(267\) 1.23330e6 1.05874
\(268\) 0 0
\(269\) −977718. 1.69346e6i −0.823821 1.42690i −0.902817 0.430025i \(-0.858505\pi\)
0.0789962 0.996875i \(-0.474828\pi\)
\(270\) 0 0
\(271\) −713502. 1.23582e6i −0.590163 1.02219i −0.994210 0.107454i \(-0.965730\pi\)
0.404047 0.914738i \(-0.367603\pi\)
\(272\) 0 0
\(273\) 1.82625e6 1.48304
\(274\) 0 0
\(275\) 1.56221e6 2.70583e6i 1.24568 2.15759i
\(276\) 0 0
\(277\) −1.20887e6 −0.946629 −0.473315 0.880893i \(-0.656943\pi\)
−0.473315 + 0.880893i \(0.656943\pi\)
\(278\) 0 0
\(279\) −81364.7 + 140928.i −0.0625785 + 0.108389i
\(280\) 0 0
\(281\) −996432. + 1.72587e6i −0.752804 + 1.30389i 0.193655 + 0.981070i \(0.437966\pi\)
−0.946459 + 0.322825i \(0.895367\pi\)
\(282\) 0 0
\(283\) 33435.3 + 57911.6i 0.0248164 + 0.0429832i 0.878167 0.478354i \(-0.158767\pi\)
−0.853350 + 0.521338i \(0.825433\pi\)
\(284\) 0 0
\(285\) −2.02186e6 192566.i −1.47448 0.140432i
\(286\) 0 0
\(287\) 414203. + 717421.i 0.296831 + 0.514126i
\(288\) 0 0
\(289\) −459264. + 795469.i −0.323458 + 0.560246i
\(290\) 0 0
\(291\) −417994. + 723987.i −0.289360 + 0.501185i
\(292\) 0 0
\(293\) 1.98637e6 1.35173 0.675866 0.737025i \(-0.263770\pi\)
0.675866 + 0.737025i \(0.263770\pi\)
\(294\) 0 0
\(295\) −1.72641e6 + 2.99024e6i −1.15502 + 2.00056i
\(296\) 0 0
\(297\) 2.17027e6 1.42766
\(298\) 0 0
\(299\) 352072. + 609807.i 0.227748 + 0.394470i
\(300\) 0 0
\(301\) −592685. 1.02656e6i −0.377058 0.653083i
\(302\) 0 0
\(303\) −159899. −0.100055
\(304\) 0 0
\(305\) −548366. −0.337537
\(306\) 0 0
\(307\) 932152. + 1.61454e6i 0.564470 + 0.977691i 0.997099 + 0.0761187i \(0.0242528\pi\)
−0.432629 + 0.901572i \(0.642414\pi\)
\(308\) 0 0
\(309\) 391955. + 678886.i 0.233528 + 0.404483i
\(310\) 0 0
\(311\) 1.73570e6 1.01759 0.508796 0.860887i \(-0.330091\pi\)
0.508796 + 0.860887i \(0.330091\pi\)
\(312\) 0 0
\(313\) 26566.2 46014.0i 0.0153274 0.0265478i −0.858260 0.513215i \(-0.828454\pi\)
0.873587 + 0.486667i \(0.161788\pi\)
\(314\) 0 0
\(315\) −1.05142e6 −0.597032
\(316\) 0 0
\(317\) −690554. + 1.19607e6i −0.385966 + 0.668514i −0.991903 0.127000i \(-0.959465\pi\)
0.605936 + 0.795513i \(0.292799\pi\)
\(318\) 0 0
\(319\) 684056. 1.18482e6i 0.376370 0.651892i
\(320\) 0 0
\(321\) 542876. + 940289.i 0.294062 + 0.509330i
\(322\) 0 0
\(323\) 1.39529e6 1.96042e6i 0.744144 1.04555i
\(324\) 0 0
\(325\) −2.08624e6 3.61347e6i −1.09561 1.89765i
\(326\) 0 0
\(327\) −1.33623e6 + 2.31441e6i −0.691051 + 1.19694i
\(328\) 0 0
\(329\) 2.33924e6 4.05169e6i 1.19148 2.06370i
\(330\) 0 0
\(331\) −79218.6 −0.0397427 −0.0198713 0.999803i \(-0.506326\pi\)
−0.0198713 + 0.999803i \(0.506326\pi\)
\(332\) 0 0
\(333\) 211025. 365506.i 0.104285 0.180627i
\(334\) 0 0
\(335\) −5.77222e6 −2.81016
\(336\) 0 0
\(337\) 1.06653e6 + 1.84729e6i 0.511563 + 0.886053i 0.999910 + 0.0134034i \(0.00426657\pi\)
−0.488347 + 0.872649i \(0.662400\pi\)
\(338\) 0 0
\(339\) −1.39784e6 2.42112e6i −0.660628 1.14424i
\(340\) 0 0
\(341\) 1.47914e6 0.688848
\(342\) 0 0
\(343\) 461871. 0.211976
\(344\) 0 0
\(345\) 642030. + 1.11203e6i 0.290407 + 0.503000i
\(346\) 0 0
\(347\) 988867. + 1.71277e6i 0.440874 + 0.763616i 0.997755 0.0669767i \(-0.0213353\pi\)
−0.556881 + 0.830592i \(0.688002\pi\)
\(348\) 0 0
\(349\) −2.01158e6 −0.884043 −0.442022 0.897004i \(-0.645739\pi\)
−0.442022 + 0.897004i \(0.645739\pi\)
\(350\) 0 0
\(351\) 1.44914e6 2.50998e6i 0.627829 1.08743i
\(352\) 0 0
\(353\) −2.89132e6 −1.23498 −0.617490 0.786579i \(-0.711850\pi\)
−0.617490 + 0.786579i \(0.711850\pi\)
\(354\) 0 0
\(355\) 1.40837e6 2.43936e6i 0.593123 1.02732i
\(356\) 0 0
\(357\) −1.97280e6 + 3.41699e6i −0.819243 + 1.41897i
\(358\) 0 0
\(359\) −371558. 643557.i −0.152156 0.263543i 0.779864 0.625950i \(-0.215288\pi\)
−0.932020 + 0.362407i \(0.881955\pi\)
\(360\) 0 0
\(361\) −1.62059e6 + 1.87210e6i −0.654491 + 0.756070i
\(362\) 0 0
\(363\) −814414. 1.41061e6i −0.324398 0.561875i
\(364\) 0 0
\(365\) −3.70420e6 + 6.41587e6i −1.45533 + 2.52071i
\(366\) 0 0
\(367\) 2.21010e6 3.82801e6i 0.856540 1.48357i −0.0186695 0.999826i \(-0.505943\pi\)
0.875209 0.483745i \(-0.160724\pi\)
\(368\) 0 0
\(369\) 254418. 0.0972705
\(370\) 0 0
\(371\) −2.94236e6 + 5.09632e6i −1.10984 + 1.92230i
\(372\) 0 0
\(373\) −2.07890e6 −0.773680 −0.386840 0.922147i \(-0.626433\pi\)
−0.386840 + 0.922147i \(0.626433\pi\)
\(374\) 0 0
\(375\) −1.78768e6 3.09636e6i −0.656466 1.13703i
\(376\) 0 0
\(377\) −913517. 1.58226e6i −0.331027 0.573355i
\(378\) 0 0
\(379\) 3.87208e6 1.38467 0.692335 0.721576i \(-0.256582\pi\)
0.692335 + 0.721576i \(0.256582\pi\)
\(380\) 0 0
\(381\) 3903.61 0.00137770
\(382\) 0 0
\(383\) −72504.1 125581.i −0.0252560 0.0437448i 0.853121 0.521713i \(-0.174707\pi\)
−0.878377 + 0.477968i \(0.841373\pi\)
\(384\) 0 0
\(385\) 4.77846e6 + 8.27653e6i 1.64299 + 2.84575i
\(386\) 0 0
\(387\) −364047. −0.123561
\(388\) 0 0
\(389\) 670618. 1.16154e6i 0.224699 0.389190i −0.731530 0.681809i \(-0.761193\pi\)
0.956229 + 0.292619i \(0.0945268\pi\)
\(390\) 0 0
\(391\) −1.52130e6 −0.503238
\(392\) 0 0
\(393\) −286570. + 496353.i −0.0935942 + 0.162110i
\(394\) 0 0
\(395\) −3.17475e6 + 5.49883e6i −1.02380 + 1.77328i
\(396\) 0 0
\(397\) −635788. 1.10122e6i −0.202458 0.350668i 0.746862 0.664980i \(-0.231560\pi\)
−0.949320 + 0.314311i \(0.898226\pi\)
\(398\) 0 0
\(399\) 2.35430e6 3.30786e6i 0.740336 1.04019i
\(400\) 0 0
\(401\) 722427. + 1.25128e6i 0.224354 + 0.388592i 0.956125 0.292958i \(-0.0946396\pi\)
−0.731772 + 0.681550i \(0.761306\pi\)
\(402\) 0 0
\(403\) 987652. 1.71066e6i 0.302929 0.524689i
\(404\) 0 0
\(405\) 1.96976e6 3.41172e6i 0.596727 1.03356i
\(406\) 0 0
\(407\) −3.83625e6 −1.14794
\(408\) 0 0
\(409\) 306511. 530893.i 0.0906020 0.156927i −0.817163 0.576407i \(-0.804454\pi\)
0.907765 + 0.419480i \(0.137788\pi\)
\(410\) 0 0
\(411\) 1.42203e6 0.415244
\(412\) 0 0
\(413\) −3.45122e6 5.97769e6i −0.995629 1.72448i
\(414\) 0 0
\(415\) 1.04089e6 + 1.80288e6i 0.296679 + 0.513862i
\(416\) 0 0
\(417\) −1.75053e6 −0.492981
\(418\) 0 0
\(419\) 6.30914e6 1.75564 0.877820 0.478991i \(-0.158997\pi\)
0.877820 + 0.478991i \(0.158997\pi\)
\(420\) 0 0
\(421\) −1.28732e6 2.22970e6i −0.353981 0.613113i 0.632962 0.774183i \(-0.281839\pi\)
−0.986943 + 0.161070i \(0.948506\pi\)
\(422\) 0 0
\(423\) −718421. 1.24434e6i −0.195222 0.338134i
\(424\) 0 0
\(425\) 9.01463e6 2.42089
\(426\) 0 0
\(427\) 548111. 949356.i 0.145478 0.251976i
\(428\) 0 0
\(429\) −5.09808e6 −1.33741
\(430\) 0 0
\(431\) −921074. + 1.59535e6i −0.238837 + 0.413678i −0.960381 0.278691i \(-0.910099\pi\)
0.721544 + 0.692369i \(0.243433\pi\)
\(432\) 0 0
\(433\) −2.48716e6 + 4.30788e6i −0.637505 + 1.10419i 0.348474 + 0.937318i \(0.386700\pi\)
−0.985979 + 0.166872i \(0.946633\pi\)
\(434\) 0 0
\(435\) −1.66587e6 2.88537e6i −0.422102 0.731101i
\(436\) 0 0
\(437\) 1.55841e6 + 148425.i 0.390370 + 0.0371796i
\(438\) 0 0
\(439\) 1.97430e6 + 3.41959e6i 0.488936 + 0.846863i 0.999919 0.0127283i \(-0.00405165\pi\)
−0.510983 + 0.859591i \(0.670718\pi\)
\(440\) 0 0
\(441\) 560925. 971550.i 0.137344 0.237886i
\(442\) 0 0
\(443\) 3.42436e6 5.93117e6i 0.829031 1.43592i −0.0697689 0.997563i \(-0.522226\pi\)
0.898799 0.438360i \(-0.144440\pi\)
\(444\) 0 0
\(445\) 8.61886e6 2.06324
\(446\) 0 0
\(447\) −1.85513e6 + 3.21318e6i −0.439142 + 0.760617i
\(448\) 0 0
\(449\) −3.05530e6 −0.715216 −0.357608 0.933872i \(-0.616408\pi\)
−0.357608 + 0.933872i \(0.616408\pi\)
\(450\) 0 0
\(451\) −1.15627e6 2.00272e6i −0.267682 0.463639i
\(452\) 0 0
\(453\) −467241. 809285.i −0.106978 0.185292i
\(454\) 0 0
\(455\) 1.27627e7 2.89011
\(456\) 0 0
\(457\) −5.86875e6 −1.31448 −0.657242 0.753680i \(-0.728277\pi\)
−0.657242 + 0.753680i \(0.728277\pi\)
\(458\) 0 0
\(459\) 3.13086e6 + 5.42280e6i 0.693636 + 1.20141i
\(460\) 0 0
\(461\) 970738. + 1.68137e6i 0.212740 + 0.368477i 0.952571 0.304316i \(-0.0984279\pi\)
−0.739831 + 0.672793i \(0.765095\pi\)
\(462\) 0 0
\(463\) 2.37394e6 0.514656 0.257328 0.966324i \(-0.417158\pi\)
0.257328 + 0.966324i \(0.417158\pi\)
\(464\) 0 0
\(465\) 1.80106e6 3.11952e6i 0.386274 0.669046i
\(466\) 0 0
\(467\) −2.72608e6 −0.578425 −0.289212 0.957265i \(-0.593393\pi\)
−0.289212 + 0.957265i \(0.593393\pi\)
\(468\) 0 0
\(469\) 5.76953e6 9.99312e6i 1.21118 2.09782i
\(470\) 0 0
\(471\) 3.75084e6 6.49664e6i 0.779069 1.34939i
\(472\) 0 0
\(473\) 1.65452e6 + 2.86570e6i 0.340031 + 0.588950i
\(474\) 0 0
\(475\) −9.23449e6 879510.i −1.87793 0.178857i
\(476\) 0 0
\(477\) 903649. + 1.56517e6i 0.181846 + 0.314967i
\(478\) 0 0
\(479\) −2.64917e6 + 4.58849e6i −0.527558 + 0.913757i 0.471926 + 0.881638i \(0.343559\pi\)
−0.999484 + 0.0321192i \(0.989774\pi\)
\(480\) 0 0
\(481\) −2.56154e6 + 4.43672e6i −0.504823 + 0.874378i
\(482\) 0 0
\(483\) −2.56692e6 −0.500662
\(484\) 0 0
\(485\) −2.92114e6 + 5.05957e6i −0.563895 + 0.976695i
\(486\) 0 0
\(487\) 5.45937e6 1.04309 0.521543 0.853225i \(-0.325356\pi\)
0.521543 + 0.853225i \(0.325356\pi\)
\(488\) 0 0
\(489\) 1.04233e6 + 1.80536e6i 0.197120 + 0.341422i
\(490\) 0 0
\(491\) −3.95495e6 6.85017e6i −0.740350 1.28232i −0.952336 0.305051i \(-0.901326\pi\)
0.211986 0.977273i \(-0.432007\pi\)
\(492\) 0 0
\(493\) 3.94730e6 0.731447
\(494\) 0 0
\(495\) 2.93509e6 0.538404
\(496\) 0 0
\(497\) 2.81542e6 + 4.87645e6i 0.511272 + 0.885550i
\(498\) 0 0
\(499\) −4.75343e6 8.23318e6i −0.854586 1.48019i −0.877029 0.480438i \(-0.840478\pi\)
0.0224433 0.999748i \(-0.492855\pi\)
\(500\) 0 0
\(501\) −3.98532e6 −0.709363
\(502\) 0 0
\(503\) −3.72038e6 + 6.44389e6i −0.655643 + 1.13561i 0.326090 + 0.945339i \(0.394269\pi\)
−0.981732 + 0.190268i \(0.939064\pi\)
\(504\) 0 0
\(505\) −1.11745e6 −0.194984
\(506\) 0 0
\(507\) −881141. + 1.52618e6i −0.152239 + 0.263685i
\(508\) 0 0
\(509\) 513257. 888987.i 0.0878092 0.152090i −0.818776 0.574114i \(-0.805347\pi\)
0.906585 + 0.422024i \(0.138680\pi\)
\(510\) 0 0
\(511\) −7.40496e6 1.28258e7i −1.25450 2.17286i
\(512\) 0 0
\(513\) −2.67814e6 5.86052e6i −0.449304 0.983202i
\(514\) 0 0
\(515\) 2.73917e6 + 4.74438e6i 0.455093 + 0.788245i
\(516\) 0 0
\(517\) −6.53014e6 + 1.13105e7i −1.07447 + 1.86104i
\(518\) 0 0
\(519\) −1.55266e6 + 2.68928e6i −0.253022 + 0.438246i
\(520\) 0 0
\(521\) 5.83600e6 0.941936 0.470968 0.882150i \(-0.343905\pi\)
0.470968 + 0.882150i \(0.343905\pi\)
\(522\) 0 0
\(523\) 1.68243e6 2.91406e6i 0.268958 0.465848i −0.699635 0.714500i \(-0.746654\pi\)
0.968593 + 0.248652i \(0.0799875\pi\)
\(524\) 0 0
\(525\) 1.52106e7 2.40850
\(526\) 0 0
\(527\) 2.13382e6 + 3.69588e6i 0.334681 + 0.579684i
\(528\) 0 0
\(529\) 2.72331e6 + 4.71691e6i 0.423114 + 0.732856i
\(530\) 0 0
\(531\) −2.11986e6 −0.326265
\(532\) 0 0
\(533\) −3.08827e6 −0.470866
\(534\) 0 0
\(535\) 3.79388e6 + 6.57119e6i 0.573058 + 0.992566i
\(536\) 0 0
\(537\) −1.67935e6 2.90872e6i −0.251307 0.435277i
\(538\) 0 0
\(539\) −1.01971e7 −1.51184
\(540\) 0 0
\(541\) 4.79104e6 8.29833e6i 0.703780 1.21898i −0.263350 0.964700i \(-0.584827\pi\)
0.967130 0.254282i \(-0.0818393\pi\)
\(542\) 0 0
\(543\) −9.61809e6 −1.39987
\(544\) 0 0
\(545\) −9.33818e6 + 1.61742e7i −1.34670 + 2.33255i
\(546\) 0 0
\(547\) −2.53036e6 + 4.38271e6i −0.361588 + 0.626289i −0.988222 0.153024i \(-0.951099\pi\)
0.626634 + 0.779314i \(0.284432\pi\)
\(548\) 0 0
\(549\) −168334. 291563.i −0.0238364 0.0412859i
\(550\) 0 0
\(551\) −4.04357e6 385117.i −0.567396 0.0540398i
\(552\) 0 0
\(553\) −6.34654e6 1.09925e7i −0.882520 1.52857i
\(554\) 0 0
\(555\) −4.67116e6 + 8.09069e6i −0.643713 + 1.11494i
\(556\) 0 0
\(557\) −3.89885e6 + 6.75300e6i −0.532474 + 0.922271i 0.466807 + 0.884359i \(0.345404\pi\)
−0.999281 + 0.0379124i \(0.987929\pi\)
\(558\) 0 0
\(559\) 4.41902e6 0.598131
\(560\) 0 0
\(561\) 5.50720e6 9.53874e6i 0.738794 1.27963i
\(562\) 0 0
\(563\) 4.30439e6 0.572323 0.286161 0.958181i \(-0.407621\pi\)
0.286161 + 0.958181i \(0.407621\pi\)
\(564\) 0 0
\(565\) −9.76875e6 1.69200e7i −1.28741 2.22986i
\(566\) 0 0
\(567\) 3.93768e6 + 6.82027e6i 0.514379 + 0.890930i
\(568\) 0 0
\(569\) −9.79289e6 −1.26803 −0.634016 0.773320i \(-0.718595\pi\)
−0.634016 + 0.773320i \(0.718595\pi\)
\(570\) 0 0
\(571\) −6.14671e6 −0.788955 −0.394477 0.918906i \(-0.629074\pi\)
−0.394477 + 0.918906i \(0.629074\pi\)
\(572\) 0 0
\(573\) −71362.1 123603.i −0.00907990 0.0157269i
\(574\) 0 0
\(575\) 2.93236e6 + 5.07899e6i 0.369869 + 0.640631i
\(576\) 0 0
\(577\) −704051. −0.0880369 −0.0440185 0.999031i \(-0.514016\pi\)
−0.0440185 + 0.999031i \(0.514016\pi\)
\(578\) 0 0
\(579\) 6.75148e6 1.16939e7i 0.836955 1.44965i
\(580\) 0 0
\(581\) −4.16163e6 −0.511474
\(582\) 0 0
\(583\) 8.21378e6 1.42267e7i 1.00086 1.73353i
\(584\) 0 0
\(585\) 1.95982e6 3.39451e6i 0.236770 0.410097i
\(586\) 0 0
\(587\) 4.80763e6 + 8.32707e6i 0.575885 + 0.997463i 0.995945 + 0.0899662i \(0.0286759\pi\)
−0.420059 + 0.907497i \(0.637991\pi\)
\(588\) 0 0
\(589\) −1.82527e6 3.99421e6i −0.216790 0.474398i
\(590\) 0 0
\(591\) 1.25913e6 + 2.18087e6i 0.148286 + 0.256839i
\(592\) 0 0
\(593\) 5.57887e6 9.66289e6i 0.651493 1.12842i −0.331268 0.943537i \(-0.607476\pi\)
0.982761 0.184882i \(-0.0591903\pi\)
\(594\) 0 0
\(595\) −1.37869e7 + 2.38796e7i −1.59652 + 2.76525i
\(596\) 0 0
\(597\) −1.17282e6 −0.134678
\(598\) 0 0
\(599\) 4.00898e6 6.94376e6i 0.456528 0.790729i −0.542247 0.840219i \(-0.682426\pi\)
0.998775 + 0.0494902i \(0.0157597\pi\)
\(600\) 0 0
\(601\) 1.34115e7 1.51458 0.757290 0.653079i \(-0.226523\pi\)
0.757290 + 0.653079i \(0.226523\pi\)
\(602\) 0 0
\(603\) −1.77192e6 3.06905e6i −0.198450 0.343725i
\(604\) 0 0
\(605\) −5.69151e6 9.85799e6i −0.632178 1.09496i
\(606\) 0 0
\(607\) 3.14504e6 0.346461 0.173231 0.984881i \(-0.444579\pi\)
0.173231 + 0.984881i \(0.444579\pi\)
\(608\) 0 0
\(609\) 6.66036e6 0.727704
\(610\) 0 0
\(611\) 8.72061e6 + 1.51045e7i 0.945027 + 1.63683i
\(612\) 0 0
\(613\) 1.86161e6 + 3.22440e6i 0.200095 + 0.346575i 0.948559 0.316601i \(-0.102542\pi\)
−0.748464 + 0.663176i \(0.769208\pi\)
\(614\) 0 0
\(615\) −5.63169e6 −0.600414
\(616\) 0 0
\(617\) −650699. + 1.12704e6i −0.0688125 + 0.119187i −0.898379 0.439221i \(-0.855254\pi\)
0.829566 + 0.558408i \(0.188588\pi\)
\(618\) 0 0
\(619\) 1.44161e7 1.51224 0.756118 0.654435i \(-0.227093\pi\)
0.756118 + 0.654435i \(0.227093\pi\)
\(620\) 0 0
\(621\) −2.03687e6 + 3.52795e6i −0.211950 + 0.367108i
\(622\) 0 0
\(623\) −8.61485e6 + 1.49214e7i −0.889257 + 1.54024i
\(624\) 0 0
\(625\) −3.28211e6 5.68478e6i −0.336088 0.582122i
\(626\) 0 0
\(627\) −6.57216e6 + 9.23408e6i −0.667635 + 0.938047i
\(628\) 0 0
\(629\) −5.53420e6 9.58552e6i −0.557736 0.966026i
\(630\) 0 0
\(631\) 1.56517e6 2.71095e6i 0.156490 0.271049i −0.777110 0.629364i \(-0.783315\pi\)
0.933601 + 0.358315i \(0.116649\pi\)
\(632\) 0 0
\(633\) 2.05528e6 3.55986e6i 0.203874 0.353121i
\(634\) 0 0
\(635\) 27280.3 0.00268482
\(636\) 0 0
\(637\) −6.80883e6 + 1.17932e7i −0.664851 + 1.15156i
\(638\) 0 0
\(639\) 1.72933e6 0.167542
\(640\) 0 0
\(641\) −2.12325e6 3.67757e6i −0.204106 0.353522i 0.745742 0.666235i \(-0.232095\pi\)
−0.949848 + 0.312713i \(0.898762\pi\)
\(642\) 0 0
\(643\) 5.08032e6 + 8.79938e6i 0.484578 + 0.839314i 0.999843 0.0177168i \(-0.00563972\pi\)
−0.515265 + 0.857031i \(0.672306\pi\)
\(644\) 0 0
\(645\) 8.05840e6 0.762693
\(646\) 0 0
\(647\) 3.33300e6 0.313022 0.156511 0.987676i \(-0.449975\pi\)
0.156511 + 0.987676i \(0.449975\pi\)
\(648\) 0 0
\(649\) 9.63429e6 + 1.66871e7i 0.897859 + 1.55514i
\(650\) 0 0
\(651\) 3.60044e6 + 6.23614e6i 0.332968 + 0.576718i
\(652\) 0 0
\(653\) −3.56244e6 −0.326938 −0.163469 0.986549i \(-0.552268\pi\)
−0.163469 + 0.986549i \(0.552268\pi\)
\(654\) 0 0
\(655\) −2.00269e6 + 3.46875e6i −0.182394 + 0.315915i
\(656\) 0 0
\(657\) −4.54837e6 −0.411096
\(658\) 0 0
\(659\) 9.65732e6 1.67270e7i 0.866249 1.50039i 0.000448081 1.00000i \(-0.499857\pi\)
0.865801 0.500388i \(-0.166809\pi\)
\(660\) 0 0
\(661\) 5.55793e6 9.62662e6i 0.494777 0.856979i −0.505205 0.863000i \(-0.668583\pi\)
0.999982 + 0.00602036i \(0.00191635\pi\)
\(662\) 0 0
\(663\) −7.35454e6 1.27384e7i −0.649788 1.12547i
\(664\) 0 0
\(665\) 1.64529e7 2.31169e7i 1.44274 2.02710i
\(666\) 0 0
\(667\) 1.28401e6 + 2.22398e6i 0.111752 + 0.193560i
\(668\) 0 0
\(669\) −4.61365e6 + 7.99108e6i −0.398547 + 0.690303i
\(670\) 0 0
\(671\) −1.53008e6 + 2.65018e6i −0.131193 + 0.227232i
\(672\) 0 0
\(673\) 4.82842e6 0.410929 0.205465 0.978665i \(-0.434129\pi\)
0.205465 + 0.978665i \(0.434129\pi\)
\(674\) 0 0
\(675\) 1.20697e7 2.09052e7i 1.01961 1.76602i
\(676\) 0 0
\(677\) −3.20527e6 −0.268777 −0.134389 0.990929i \(-0.542907\pi\)
−0.134389 + 0.990929i \(0.542907\pi\)
\(678\) 0 0
\(679\) −5.83956e6 1.01144e7i −0.486078 0.841912i
\(680\) 0 0
\(681\) −1.57360e6 2.72556e6i −0.130025 0.225210i
\(682\) 0 0
\(683\) 2.29678e7 1.88395 0.941973 0.335688i \(-0.108969\pi\)
0.941973 + 0.335688i \(0.108969\pi\)
\(684\) 0 0
\(685\) 9.93780e6 0.809215
\(686\) 0 0
\(687\) −226804. 392837.i −0.0183341 0.0317556i
\(688\) 0 0
\(689\) −1.09690e7 1.89989e7i −0.880278 1.52469i
\(690\) 0 0
\(691\) 7.10876e6 0.566368 0.283184 0.959066i \(-0.408609\pi\)
0.283184 + 0.959066i \(0.408609\pi\)
\(692\) 0 0
\(693\) −2.93372e6 + 5.08135e6i −0.232052 + 0.401926i
\(694\) 0 0
\(695\) −1.22336e7 −0.960707
\(696\) 0 0
\(697\) 3.33610e6 5.77829e6i 0.260110 0.450523i
\(698\) 0 0
\(699\) 7.36841e6 1.27625e7i 0.570402 0.987965i
\(700\) 0 0
\(701\) 7.73351e6 + 1.33948e7i 0.594403 + 1.02954i 0.993631 + 0.112685i \(0.0359451\pi\)
−0.399227 + 0.916852i \(0.630722\pi\)
\(702\) 0 0
\(703\) 4.73397e6 + 1.03592e7i 0.361274 + 0.790569i
\(704\) 0 0
\(705\) 1.59027e7 + 2.75443e7i 1.20503 + 2.08717i
\(706\) 0 0
\(707\) 1.11693e6 1.93458e6i 0.0840381 0.145558i
\(708\) 0 0
\(709\) 6.30537e6 1.09212e7i 0.471081 0.815936i −0.528372 0.849013i \(-0.677197\pi\)
0.999453 + 0.0330772i \(0.0105307\pi\)
\(710\) 0 0
\(711\) −3.89826e6 −0.289199
\(712\) 0 0
\(713\) −1.38822e6 + 2.40446e6i −0.102266 + 0.177131i
\(714\) 0 0
\(715\) −3.56278e7 −2.60630
\(716\) 0 0
\(717\) 1.93007e6 + 3.34298e6i 0.140209 + 0.242849i
\(718\) 0 0
\(719\) −1.02749e7 1.77967e7i −0.741234 1.28386i −0.951934 0.306304i \(-0.900907\pi\)
0.210699 0.977551i \(-0.432426\pi\)
\(720\) 0 0
\(721\) −1.09516e7 −0.784581
\(722\) 0 0
\(723\) −8.33899e6 −0.593291
\(724\) 0 0
\(725\) −7.60855e6 1.31784e7i −0.537597 0.931146i
\(726\) 0 0
\(727\) −8.28557e6 1.43510e7i −0.581415 1.00704i −0.995312 0.0967169i \(-0.969166\pi\)
0.413897 0.910324i \(-0.364167\pi\)
\(728\) 0 0
\(729\) 1.59414e7 1.11098
\(730\) 0 0
\(731\) −4.77363e6 + 8.26818e6i −0.330412 + 0.572290i
\(732\) 0 0
\(733\) 2.52568e7 1.73628 0.868139 0.496321i \(-0.165316\pi\)
0.868139 + 0.496321i \(0.165316\pi\)
\(734\) 0 0
\(735\) −1.24164e7 + 2.15059e7i −0.847770 + 1.46838i
\(736\) 0 0
\(737\) −1.61060e7 + 2.78964e7i −1.09224 + 1.89182i
\(738\) 0 0
\(739\) 6.54248e6 + 1.13319e7i 0.440688 + 0.763294i 0.997741 0.0671833i \(-0.0214012\pi\)
−0.557053 + 0.830477i \(0.688068\pi\)
\(740\) 0 0
\(741\) 6.29109e6 + 1.37667e7i 0.420901 + 0.921049i
\(742\) 0 0
\(743\) 1.18603e6 + 2.05426e6i 0.0788177 + 0.136516i 0.902740 0.430186i \(-0.141552\pi\)
−0.823922 + 0.566703i \(0.808219\pi\)
\(744\) 0 0
\(745\) −1.29645e7 + 2.24552e7i −0.855787 + 1.48227i
\(746\) 0 0
\(747\) −639054. + 1.10687e6i −0.0419021 + 0.0725766i
\(748\) 0 0
\(749\) −1.51684e7 −0.987953
\(750\) 0 0
\(751\) −1.34919e7 + 2.33686e7i −0.872916 + 1.51193i −0.0139493 + 0.999903i \(0.504440\pi\)
−0.858966 + 0.512032i \(0.828893\pi\)
\(752\) 0 0
\(753\) −1.00319e7 −0.644758
\(754\) 0 0
\(755\) −3.26530e6 5.65567e6i −0.208476 0.361091i
\(756\) 0 0
\(757\) 1.46311e7 + 2.53419e7i 0.927980 + 1.60731i 0.786697 + 0.617340i \(0.211790\pi\)
0.141284 + 0.989969i \(0.454877\pi\)
\(758\) 0 0
\(759\) 7.16572e6 0.451497
\(760\) 0 0
\(761\) −2.62075e7 −1.64045 −0.820226 0.572040i \(-0.806152\pi\)
−0.820226 + 0.572040i \(0.806152\pi\)
\(762\) 0 0
\(763\) −1.86677e7 3.23333e7i −1.16086 2.01066i
\(764\) 0 0
\(765\) 4.23418e6 + 7.33382e6i 0.261587 + 0.453082i
\(766\) 0 0
\(767\) 2.57321e7 1.57938
\(768\) 0 0
\(769\) 2.54995e6 4.41664e6i 0.155495 0.269325i −0.777744 0.628581i \(-0.783636\pi\)
0.933239 + 0.359256i \(0.116969\pi\)
\(770\) 0 0
\(771\) −1.86554e7 −1.13023
\(772\) 0 0
\(773\) −8.67472e6 + 1.50250e7i −0.522164 + 0.904414i 0.477504 + 0.878630i \(0.341542\pi\)
−0.999668 + 0.0257842i \(0.991792\pi\)
\(774\) 0 0
\(775\) 8.22601e6 1.42479e7i 0.491966 0.852110i
\(776\) 0 0
\(777\) −9.33797e6 1.61738e7i −0.554881 0.961082i
\(778\) 0 0
\(779\) −3.98122e6 + 5.59373e6i −0.235057 + 0.330262i
\(780\) 0 0
\(781\) −7.85942e6 1.36129e7i −0.461066 0.798589i
\(782\) 0 0
\(783\) 5.28503e6 9.15394e6i 0.308065 0.533585i
\(784\) 0 0
\(785\) 2.62126e7 4.54016e7i 1.51823 2.62965i
\(786\) 0 0
\(787\) 3.89085e6 0.223928 0.111964 0.993712i \(-0.464286\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(788\) 0 0
\(789\) −1.98862e6 + 3.44439e6i −0.113726