Properties

Label 128.5.f.b.31.4
Level $128$
Weight $5$
Character 128.31
Analytic conductor $13.231$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 128 = 2^{7} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 128.f (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.2313552747\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
Defining polynomial: \(x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} - 1048576 x + 2097152\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{42} \)
Twist minimal: no (minimal twist has level 16)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 31.4
Root \(-2.40693 - 1.48549i\) of defining polynomial
Character \(\chi\) \(=\) 128.31
Dual form 128.5.f.b.95.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.0461995 + 0.0461995i) q^{3} +(8.04297 + 8.04297i) q^{5} -49.8797 q^{7} -80.9957i q^{9} +O(q^{10})\) \(q+(0.0461995 + 0.0461995i) q^{3} +(8.04297 + 8.04297i) q^{5} -49.8797 q^{7} -80.9957i q^{9} +(84.2573 - 84.2573i) q^{11} +(-19.4838 + 19.4838i) q^{13} +0.743162i q^{15} +437.855 q^{17} +(-349.021 - 349.021i) q^{19} +(-2.30442 - 2.30442i) q^{21} -404.840 q^{23} -495.621i q^{25} +(7.48412 - 7.48412i) q^{27} +(1031.65 - 1031.65i) q^{29} -1506.15i q^{31} +7.78529 q^{33} +(-401.181 - 401.181i) q^{35} +(434.262 + 434.262i) q^{37} -1.80028 q^{39} +696.847i q^{41} +(-917.612 + 917.612i) q^{43} +(651.446 - 651.446i) q^{45} +111.917i q^{47} +86.9810 q^{49} +(20.2287 + 20.2287i) q^{51} +(-1041.19 - 1041.19i) q^{53} +1355.36 q^{55} -32.2492i q^{57} +(1711.60 - 1711.60i) q^{59} +(-3711.24 + 3711.24i) q^{61} +4040.04i q^{63} -313.415 q^{65} +(1854.18 + 1854.18i) q^{67} +(-18.7034 - 18.7034i) q^{69} -1161.89 q^{71} -905.295i q^{73} +(22.8975 - 22.8975i) q^{75} +(-4202.72 + 4202.72i) q^{77} +5869.63i q^{79} -6559.96 q^{81} +(7560.06 + 7560.06i) q^{83} +(3521.65 + 3521.65i) q^{85} +95.3236 q^{87} +6439.80i q^{89} +(971.844 - 971.844i) q^{91} +(69.5835 - 69.5835i) q^{93} -5614.33i q^{95} -413.032 q^{97} +(-6824.48 - 6824.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} + O(q^{10}) \) \( 14q + 2q^{3} + 2q^{5} - 4q^{7} - 94q^{11} + 2q^{13} - 4q^{17} + 706q^{19} + 164q^{21} + 1148q^{23} + 1664q^{27} - 862q^{29} - 4q^{33} - 1340q^{35} + 1826q^{37} + 2684q^{39} - 1694q^{43} - 1410q^{45} + 682q^{49} + 3012q^{51} + 482q^{53} - 11780q^{55} + 2786q^{59} + 3778q^{61} - 2020q^{65} - 7998q^{67} - 9628q^{69} + 19964q^{71} - 17570q^{75} + 9508q^{77} + 1454q^{81} + 17282q^{83} - 9948q^{85} - 49284q^{87} + 28036q^{91} - 8896q^{93} - 4q^{97} - 49214q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(127\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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
\(3\) 0.0461995 + 0.0461995i 0.00513328 + 0.00513328i 0.709669 0.704535i \(-0.248845\pi\)
−0.704535 + 0.709669i \(0.748845\pi\)
\(4\) 0 0
\(5\) 8.04297 + 8.04297i 0.321719 + 0.321719i 0.849426 0.527707i \(-0.176948\pi\)
−0.527707 + 0.849426i \(0.676948\pi\)
\(6\) 0 0
\(7\) −49.8797 −1.01795 −0.508976 0.860781i \(-0.669976\pi\)
−0.508976 + 0.860781i \(0.669976\pi\)
\(8\) 0 0
\(9\) 80.9957i 0.999947i
\(10\) 0 0
\(11\) 84.2573 84.2573i 0.696341 0.696341i −0.267278 0.963619i \(-0.586124\pi\)
0.963619 + 0.267278i \(0.0861243\pi\)
\(12\) 0 0
\(13\) −19.4838 + 19.4838i −0.115289 + 0.115289i −0.762398 0.647109i \(-0.775978\pi\)
0.647109 + 0.762398i \(0.275978\pi\)
\(14\) 0 0
\(15\) 0.743162i 0.00330294i
\(16\) 0 0
\(17\) 437.855 1.51507 0.757535 0.652795i \(-0.226404\pi\)
0.757535 + 0.652795i \(0.226404\pi\)
\(18\) 0 0
\(19\) −349.021 349.021i −0.966817 0.966817i 0.0326494 0.999467i \(-0.489606\pi\)
−0.999467 + 0.0326494i \(0.989606\pi\)
\(20\) 0 0
\(21\) −2.30442 2.30442i −0.00522543 0.00522543i
\(22\) 0 0
\(23\) −404.840 −0.765293 −0.382647 0.923895i \(-0.624987\pi\)
−0.382647 + 0.923895i \(0.624987\pi\)
\(24\) 0 0
\(25\) 495.621i 0.792994i
\(26\) 0 0
\(27\) 7.48412 7.48412i 0.0102663 0.0102663i
\(28\) 0 0
\(29\) 1031.65 1031.65i 1.22670 1.22670i 0.261490 0.965206i \(-0.415786\pi\)
0.965206 0.261490i \(-0.0842139\pi\)
\(30\) 0 0
\(31\) 1506.15i 1.56728i −0.621217 0.783638i \(-0.713362\pi\)
0.621217 0.783638i \(-0.286638\pi\)
\(32\) 0 0
\(33\) 7.78529 0.00714903
\(34\) 0 0
\(35\) −401.181 401.181i −0.327494 0.327494i
\(36\) 0 0
\(37\) 434.262 + 434.262i 0.317211 + 0.317211i 0.847695 0.530484i \(-0.177990\pi\)
−0.530484 + 0.847695i \(0.677990\pi\)
\(38\) 0 0
\(39\) −1.80028 −0.00118362
\(40\) 0 0
\(41\) 696.847i 0.414543i 0.978283 + 0.207272i \(0.0664584\pi\)
−0.978283 + 0.207272i \(0.933542\pi\)
\(42\) 0 0
\(43\) −917.612 + 917.612i −0.496275 + 0.496275i −0.910276 0.414002i \(-0.864131\pi\)
0.414002 + 0.910276i \(0.364131\pi\)
\(44\) 0 0
\(45\) 651.446 651.446i 0.321702 0.321702i
\(46\) 0 0
\(47\) 111.917i 0.0506641i 0.999679 + 0.0253321i \(0.00806431\pi\)
−0.999679 + 0.0253321i \(0.991936\pi\)
\(48\) 0 0
\(49\) 86.9810 0.0362270
\(50\) 0 0
\(51\) 20.2287 + 20.2287i 0.00777728 + 0.00777728i
\(52\) 0 0
\(53\) −1041.19 1041.19i −0.370663 0.370663i 0.497056 0.867719i \(-0.334414\pi\)
−0.867719 + 0.497056i \(0.834414\pi\)
\(54\) 0 0
\(55\) 1355.36 0.448052
\(56\) 0 0
\(57\) 32.2492i 0.00992589i
\(58\) 0 0
\(59\) 1711.60 1711.60i 0.491697 0.491697i −0.417144 0.908841i \(-0.636969\pi\)
0.908841 + 0.417144i \(0.136969\pi\)
\(60\) 0 0
\(61\) −3711.24 + 3711.24i −0.997376 + 0.997376i −0.999997 0.00262076i \(-0.999166\pi\)
0.00262076 + 0.999997i \(0.499166\pi\)
\(62\) 0 0
\(63\) 4040.04i 1.01790i
\(64\) 0 0
\(65\) −313.415 −0.0741810
\(66\) 0 0
\(67\) 1854.18 + 1854.18i 0.413049 + 0.413049i 0.882799 0.469750i \(-0.155656\pi\)
−0.469750 + 0.882799i \(0.655656\pi\)
\(68\) 0 0
\(69\) −18.7034 18.7034i −0.00392846 0.00392846i
\(70\) 0 0
\(71\) −1161.89 −0.230489 −0.115244 0.993337i \(-0.536765\pi\)
−0.115244 + 0.993337i \(0.536765\pi\)
\(72\) 0 0
\(73\) 905.295i 0.169881i −0.996386 0.0849404i \(-0.972930\pi\)
0.996386 0.0849404i \(-0.0270700\pi\)
\(74\) 0 0
\(75\) 22.8975 22.8975i 0.00407066 0.00407066i
\(76\) 0 0
\(77\) −4202.72 + 4202.72i −0.708842 + 0.708842i
\(78\) 0 0
\(79\) 5869.63i 0.940495i 0.882535 + 0.470247i \(0.155835\pi\)
−0.882535 + 0.470247i \(0.844165\pi\)
\(80\) 0 0
\(81\) −6559.96 −0.999842
\(82\) 0 0
\(83\) 7560.06 + 7560.06i 1.09741 + 1.09741i 0.994713 + 0.102698i \(0.0327476\pi\)
0.102698 + 0.994713i \(0.467252\pi\)
\(84\) 0 0
\(85\) 3521.65 + 3521.65i 0.487426 + 0.487426i
\(86\) 0 0
\(87\) 95.3236 0.0125939
\(88\) 0 0
\(89\) 6439.80i 0.813004i 0.913650 + 0.406502i \(0.133252\pi\)
−0.913650 + 0.406502i \(0.866748\pi\)
\(90\) 0 0
\(91\) 971.844 971.844i 0.117358 0.117358i
\(92\) 0 0
\(93\) 69.5835 69.5835i 0.00804527 0.00804527i
\(94\) 0 0
\(95\) 5614.33i 0.622087i
\(96\) 0 0
\(97\) −413.032 −0.0438976 −0.0219488 0.999759i \(-0.506987\pi\)
−0.0219488 + 0.999759i \(0.506987\pi\)
\(98\) 0 0
\(99\) −6824.48 6824.48i −0.696304 0.696304i
\(100\) 0 0
\(101\) −8460.63 8460.63i −0.829392 0.829392i 0.158041 0.987433i \(-0.449482\pi\)
−0.987433 + 0.158041i \(0.949482\pi\)
\(102\) 0 0
\(103\) 17007.9 1.60316 0.801578 0.597891i \(-0.203994\pi\)
0.801578 + 0.597891i \(0.203994\pi\)
\(104\) 0 0
\(105\) 37.0687i 0.00336224i
\(106\) 0 0
\(107\) −9368.65 + 9368.65i −0.818294 + 0.818294i −0.985861 0.167567i \(-0.946409\pi\)
0.167567 + 0.985861i \(0.446409\pi\)
\(108\) 0 0
\(109\) 8308.73 8308.73i 0.699329 0.699329i −0.264937 0.964266i \(-0.585351\pi\)
0.964266 + 0.264937i \(0.0853510\pi\)
\(110\) 0 0
\(111\) 40.1254i 0.00325667i
\(112\) 0 0
\(113\) 5814.63 0.455371 0.227685 0.973735i \(-0.426884\pi\)
0.227685 + 0.973735i \(0.426884\pi\)
\(114\) 0 0
\(115\) −3256.12 3256.12i −0.246209 0.246209i
\(116\) 0 0
\(117\) 1578.10 + 1578.10i 0.115283 + 0.115283i
\(118\) 0 0
\(119\) −21840.1 −1.54227
\(120\) 0 0
\(121\) 442.428i 0.0302185i
\(122\) 0 0
\(123\) −32.1940 + 32.1940i −0.00212797 + 0.00212797i
\(124\) 0 0
\(125\) 9013.12 9013.12i 0.576840 0.576840i
\(126\) 0 0
\(127\) 20367.1i 1.26276i −0.775472 0.631382i \(-0.782488\pi\)
0.775472 0.631382i \(-0.217512\pi\)
\(128\) 0 0
\(129\) −84.7864 −0.00509503
\(130\) 0 0
\(131\) −4414.52 4414.52i −0.257242 0.257242i 0.566690 0.823931i \(-0.308224\pi\)
−0.823931 + 0.566690i \(0.808224\pi\)
\(132\) 0 0
\(133\) 17409.1 + 17409.1i 0.984174 + 0.984174i
\(134\) 0 0
\(135\) 120.389 0.00660571
\(136\) 0 0
\(137\) 11018.7i 0.587067i −0.955949 0.293533i \(-0.905169\pi\)
0.955949 0.293533i \(-0.0948312\pi\)
\(138\) 0 0
\(139\) 14957.2 14957.2i 0.774140 0.774140i −0.204688 0.978827i \(-0.565618\pi\)
0.978827 + 0.204688i \(0.0656178\pi\)
\(140\) 0 0
\(141\) −5.17051 + 5.17051i −0.000260073 + 0.000260073i
\(142\) 0 0
\(143\) 3283.30i 0.160560i
\(144\) 0 0
\(145\) 16595.1 0.789302
\(146\) 0 0
\(147\) 4.01848 + 4.01848i 0.000185963 + 0.000185963i
\(148\) 0 0
\(149\) −15393.9 15393.9i −0.693388 0.693388i 0.269588 0.962976i \(-0.413112\pi\)
−0.962976 + 0.269588i \(0.913112\pi\)
\(150\) 0 0
\(151\) −16971.9 −0.744347 −0.372174 0.928163i \(-0.621387\pi\)
−0.372174 + 0.928163i \(0.621387\pi\)
\(152\) 0 0
\(153\) 35464.4i 1.51499i
\(154\) 0 0
\(155\) 12113.9 12113.9i 0.504222 0.504222i
\(156\) 0 0
\(157\) −1167.73 + 1167.73i −0.0473744 + 0.0473744i −0.730397 0.683023i \(-0.760665\pi\)
0.683023 + 0.730397i \(0.260665\pi\)
\(158\) 0 0
\(159\) 96.2051i 0.00380543i
\(160\) 0 0
\(161\) 20193.3 0.779032
\(162\) 0 0
\(163\) −28076.2 28076.2i −1.05673 1.05673i −0.998291 0.0584383i \(-0.981388\pi\)
−0.0584383 0.998291i \(-0.518612\pi\)
\(164\) 0 0
\(165\) 62.6168 + 62.6168i 0.00229998 + 0.00229998i
\(166\) 0 0
\(167\) −2929.82 −0.105053 −0.0525264 0.998620i \(-0.516727\pi\)
−0.0525264 + 0.998620i \(0.516727\pi\)
\(168\) 0 0
\(169\) 27801.8i 0.973417i
\(170\) 0 0
\(171\) −28269.2 + 28269.2i −0.966767 + 0.966767i
\(172\) 0 0
\(173\) −8560.97 + 8560.97i −0.286043 + 0.286043i −0.835513 0.549470i \(-0.814829\pi\)
0.549470 + 0.835513i \(0.314829\pi\)
\(174\) 0 0
\(175\) 24721.4i 0.807230i
\(176\) 0 0
\(177\) 158.150 0.00504804
\(178\) 0 0
\(179\) 24420.1 + 24420.1i 0.762153 + 0.762153i 0.976711 0.214558i \(-0.0688311\pi\)
−0.214558 + 0.976711i \(0.568831\pi\)
\(180\) 0 0
\(181\) 10946.5 + 10946.5i 0.334133 + 0.334133i 0.854154 0.520021i \(-0.174076\pi\)
−0.520021 + 0.854154i \(0.674076\pi\)
\(182\) 0 0
\(183\) −342.915 −0.0102396
\(184\) 0 0
\(185\) 6985.52i 0.204106i
\(186\) 0 0
\(187\) 36892.5 36892.5i 1.05501 1.05501i
\(188\) 0 0
\(189\) −373.306 + 373.306i −0.0104506 + 0.0104506i
\(190\) 0 0
\(191\) 22384.9i 0.613604i −0.951773 0.306802i \(-0.900741\pi\)
0.951773 0.306802i \(-0.0992590\pi\)
\(192\) 0 0
\(193\) −30429.5 −0.816920 −0.408460 0.912776i \(-0.633934\pi\)
−0.408460 + 0.912776i \(0.633934\pi\)
\(194\) 0 0
\(195\) −14.4796 14.4796i −0.000380792 0.000380792i
\(196\) 0 0
\(197\) −19093.9 19093.9i −0.491997 0.491997i 0.416938 0.908935i \(-0.363103\pi\)
−0.908935 + 0.416938i \(0.863103\pi\)
\(198\) 0 0
\(199\) 67963.8 1.71621 0.858107 0.513470i \(-0.171640\pi\)
0.858107 + 0.513470i \(0.171640\pi\)
\(200\) 0 0
\(201\) 171.324i 0.00424060i
\(202\) 0 0
\(203\) −51458.4 + 51458.4i −1.24872 + 1.24872i
\(204\) 0 0
\(205\) −5604.72 + 5604.72i −0.133366 + 0.133366i
\(206\) 0 0
\(207\) 32790.3i 0.765253i
\(208\) 0 0
\(209\) −58815.1 −1.34647
\(210\) 0 0
\(211\) 55219.8 + 55219.8i 1.24031 + 1.24031i 0.959872 + 0.280438i \(0.0904797\pi\)
0.280438 + 0.959872i \(0.409520\pi\)
\(212\) 0 0
\(213\) −53.6790 53.6790i −0.00118316 0.00118316i
\(214\) 0 0
\(215\) −14760.6 −0.319322
\(216\) 0 0
\(217\) 75126.4i 1.59541i
\(218\) 0 0
\(219\) 41.8242 41.8242i 0.000872046 0.000872046i
\(220\) 0 0
\(221\) −8531.07 + 8531.07i −0.174670 + 0.174670i
\(222\) 0 0
\(223\) 40417.5i 0.812754i −0.913705 0.406377i \(-0.866792\pi\)
0.913705 0.406377i \(-0.133208\pi\)
\(224\) 0 0
\(225\) −40143.2 −0.792952
\(226\) 0 0
\(227\) 1672.85 + 1672.85i 0.0324643 + 0.0324643i 0.723153 0.690688i \(-0.242692\pi\)
−0.690688 + 0.723153i \(0.742692\pi\)
\(228\) 0 0
\(229\) 26519.0 + 26519.0i 0.505691 + 0.505691i 0.913201 0.407510i \(-0.133603\pi\)
−0.407510 + 0.913201i \(0.633603\pi\)
\(230\) 0 0
\(231\) −388.328 −0.00727737
\(232\) 0 0
\(233\) 24163.3i 0.445087i −0.974923 0.222543i \(-0.928564\pi\)
0.974923 0.222543i \(-0.0714359\pi\)
\(234\) 0 0
\(235\) −900.145 + 900.145i −0.0162996 + 0.0162996i
\(236\) 0 0
\(237\) −271.174 + 271.174i −0.00482782 + 0.00482782i
\(238\) 0 0
\(239\) 76356.4i 1.33675i 0.743825 + 0.668374i \(0.233010\pi\)
−0.743825 + 0.668374i \(0.766990\pi\)
\(240\) 0 0
\(241\) 40548.1 0.698130 0.349065 0.937099i \(-0.386499\pi\)
0.349065 + 0.937099i \(0.386499\pi\)
\(242\) 0 0
\(243\) −909.281 909.281i −0.0153988 0.0153988i
\(244\) 0 0
\(245\) 699.586 + 699.586i 0.0116549 + 0.0116549i
\(246\) 0 0
\(247\) 13600.5 0.222926
\(248\) 0 0
\(249\) 698.542i 0.0112666i
\(250\) 0 0
\(251\) 10536.0 10536.0i 0.167235 0.167235i −0.618528 0.785763i \(-0.712271\pi\)
0.785763 + 0.618528i \(0.212271\pi\)
\(252\) 0 0
\(253\) −34110.7 + 34110.7i −0.532905 + 0.532905i
\(254\) 0 0
\(255\) 325.397i 0.00500419i
\(256\) 0 0
\(257\) 37983.9 0.575086 0.287543 0.957768i \(-0.407162\pi\)
0.287543 + 0.957768i \(0.407162\pi\)
\(258\) 0 0
\(259\) −21660.9 21660.9i −0.322906 0.322906i
\(260\) 0 0
\(261\) −83559.4 83559.4i −1.22663 1.22663i
\(262\) 0 0
\(263\) 37545.0 0.542801 0.271400 0.962467i \(-0.412513\pi\)
0.271400 + 0.962467i \(0.412513\pi\)
\(264\) 0 0
\(265\) 16748.6i 0.238498i
\(266\) 0 0
\(267\) −297.516 + 297.516i −0.00417338 + 0.00417338i
\(268\) 0 0
\(269\) −4676.63 + 4676.63i −0.0646291 + 0.0646291i −0.738683 0.674053i \(-0.764552\pi\)
0.674053 + 0.738683i \(0.264552\pi\)
\(270\) 0 0
\(271\) 2746.12i 0.0373922i 0.999825 + 0.0186961i \(0.00595149\pi\)
−0.999825 + 0.0186961i \(0.994049\pi\)
\(272\) 0 0
\(273\) 89.7975 0.00120487
\(274\) 0 0
\(275\) −41759.7 41759.7i −0.552194 0.552194i
\(276\) 0 0
\(277\) 33056.5 + 33056.5i 0.430822 + 0.430822i 0.888908 0.458086i \(-0.151465\pi\)
−0.458086 + 0.888908i \(0.651465\pi\)
\(278\) 0 0
\(279\) −121992. −1.56719
\(280\) 0 0
\(281\) 80033.0i 1.01358i −0.862071 0.506788i \(-0.830833\pi\)
0.862071 0.506788i \(-0.169167\pi\)
\(282\) 0 0
\(283\) 72284.3 72284.3i 0.902549 0.902549i −0.0931068 0.995656i \(-0.529680\pi\)
0.995656 + 0.0931068i \(0.0296798\pi\)
\(284\) 0 0
\(285\) 259.379 259.379i 0.00319334 0.00319334i
\(286\) 0 0
\(287\) 34758.5i 0.421985i
\(288\) 0 0
\(289\) 108196. 1.29544
\(290\) 0 0
\(291\) −19.0819 19.0819i −0.000225339 0.000225339i
\(292\) 0 0
\(293\) 84911.3 + 84911.3i 0.989077 + 0.989077i 0.999941 0.0108641i \(-0.00345823\pi\)
−0.0108641 + 0.999941i \(0.503458\pi\)
\(294\) 0 0
\(295\) 27532.6 0.316376
\(296\) 0 0
\(297\) 1261.18i 0.0142977i
\(298\) 0 0
\(299\) 7887.81 7887.81i 0.0882296 0.0882296i
\(300\) 0 0
\(301\) 45770.2 45770.2i 0.505184 0.505184i
\(302\) 0 0
\(303\) 781.754i 0.00851500i
\(304\) 0 0
\(305\) −59698.7 −0.641749
\(306\) 0 0
\(307\) 55472.5 + 55472.5i 0.588574 + 0.588574i 0.937245 0.348671i \(-0.113367\pi\)
−0.348671 + 0.937245i \(0.613367\pi\)
\(308\) 0 0
\(309\) 785.756 + 785.756i 0.00822944 + 0.00822944i
\(310\) 0 0
\(311\) −127048. −1.31355 −0.656777 0.754084i \(-0.728081\pi\)
−0.656777 + 0.754084i \(0.728081\pi\)
\(312\) 0 0
\(313\) 25469.3i 0.259974i −0.991516 0.129987i \(-0.958507\pi\)
0.991516 0.129987i \(-0.0414935\pi\)
\(314\) 0 0
\(315\) −32493.9 + 32493.9i −0.327477 + 0.327477i
\(316\) 0 0
\(317\) 94218.4 94218.4i 0.937599 0.937599i −0.0605656 0.998164i \(-0.519290\pi\)
0.998164 + 0.0605656i \(0.0192904\pi\)
\(318\) 0 0
\(319\) 173848.i 1.70840i
\(320\) 0 0
\(321\) −865.654 −0.00840107
\(322\) 0 0
\(323\) −152821. 152821.i −1.46480 1.46480i
\(324\) 0 0
\(325\) 9656.57 + 9656.57i 0.0914232 + 0.0914232i
\(326\) 0 0
\(327\) 767.719 0.00717971
\(328\) 0 0
\(329\) 5582.38i 0.0515737i
\(330\) 0 0
\(331\) −65141.3 + 65141.3i −0.594567 + 0.594567i −0.938862 0.344295i \(-0.888118\pi\)
0.344295 + 0.938862i \(0.388118\pi\)
\(332\) 0 0
\(333\) 35173.4 35173.4i 0.317195 0.317195i
\(334\) 0 0
\(335\) 29826.2i 0.265771i
\(336\) 0 0
\(337\) 135004. 1.18874 0.594369 0.804193i \(-0.297402\pi\)
0.594369 + 0.804193i \(0.297402\pi\)
\(338\) 0 0
\(339\) 268.633 + 268.633i 0.00233754 + 0.00233754i
\(340\) 0 0
\(341\) −126904. 126904.i −1.09136 1.09136i
\(342\) 0 0
\(343\) 115422. 0.981075
\(344\) 0 0
\(345\) 300.862i 0.00252772i
\(346\) 0 0
\(347\) −10849.2 + 10849.2i −0.0901025 + 0.0901025i −0.750721 0.660619i \(-0.770294\pi\)
0.660619 + 0.750721i \(0.270294\pi\)
\(348\) 0 0
\(349\) 6073.15 6073.15i 0.0498612 0.0498612i −0.681737 0.731598i \(-0.738775\pi\)
0.731598 + 0.681737i \(0.238775\pi\)
\(350\) 0 0
\(351\) 291.638i 0.00236717i
\(352\) 0 0
\(353\) −143445. −1.15116 −0.575579 0.817746i \(-0.695223\pi\)
−0.575579 + 0.817746i \(0.695223\pi\)
\(354\) 0 0
\(355\) −9345.08 9345.08i −0.0741526 0.0741526i
\(356\) 0 0
\(357\) −1009.00 1009.00i −0.00791690 0.00791690i
\(358\) 0 0
\(359\) 124076. 0.962718 0.481359 0.876523i \(-0.340143\pi\)
0.481359 + 0.876523i \(0.340143\pi\)
\(360\) 0 0
\(361\) 113310.i 0.869472i
\(362\) 0 0
\(363\) −20.4400 + 20.4400i −0.000155120 + 0.000155120i
\(364\) 0 0
\(365\) 7281.26 7281.26i 0.0546538 0.0546538i
\(366\) 0 0
\(367\) 126240.i 0.937268i −0.883392 0.468634i \(-0.844746\pi\)
0.883392 0.468634i \(-0.155254\pi\)
\(368\) 0 0
\(369\) 56441.7 0.414521
\(370\) 0 0
\(371\) 51934.3 + 51934.3i 0.377317 + 0.377317i
\(372\) 0 0
\(373\) 95513.7 + 95513.7i 0.686512 + 0.686512i 0.961459 0.274948i \(-0.0886605\pi\)
−0.274948 + 0.961459i \(0.588661\pi\)
\(374\) 0 0
\(375\) 832.804 0.00592216
\(376\) 0 0
\(377\) 40200.9i 0.282848i
\(378\) 0 0
\(379\) 31220.0 31220.0i 0.217347 0.217347i −0.590032 0.807380i \(-0.700885\pi\)
0.807380 + 0.590032i \(0.200885\pi\)
\(380\) 0 0
\(381\) 940.951 940.951i 0.00648212 0.00648212i
\(382\) 0 0
\(383\) 253102.i 1.72543i 0.505689 + 0.862716i \(0.331238\pi\)
−0.505689 + 0.862716i \(0.668762\pi\)
\(384\) 0 0
\(385\) −67604.7 −0.456095
\(386\) 0 0
\(387\) 74322.6 + 74322.6i 0.496248 + 0.496248i
\(388\) 0 0
\(389\) 43279.4 + 43279.4i 0.286011 + 0.286011i 0.835500 0.549490i \(-0.185178\pi\)
−0.549490 + 0.835500i \(0.685178\pi\)
\(390\) 0 0
\(391\) −177261. −1.15947
\(392\) 0 0
\(393\) 407.898i 0.00264099i
\(394\) 0 0
\(395\) −47209.2 + 47209.2i −0.302575 + 0.302575i
\(396\) 0 0
\(397\) −198533. + 198533.i −1.25965 + 1.25965i −0.308395 + 0.951258i \(0.599792\pi\)
−0.951258 + 0.308395i \(0.900208\pi\)
\(398\) 0 0
\(399\) 1608.58i 0.0101041i
\(400\) 0 0
\(401\) −89330.8 −0.555536 −0.277768 0.960648i \(-0.589595\pi\)
−0.277768 + 0.960648i \(0.589595\pi\)
\(402\) 0 0
\(403\) 29345.5 + 29345.5i 0.180689 + 0.180689i
\(404\) 0 0
\(405\) −52761.6 52761.6i −0.321668 0.321668i
\(406\) 0 0
\(407\) 73179.5 0.441775
\(408\) 0 0
\(409\) 26716.3i 0.159709i 0.996807 + 0.0798545i \(0.0254456\pi\)
−0.996807 + 0.0798545i \(0.974554\pi\)
\(410\) 0 0
\(411\) 509.057 509.057i 0.00301358 0.00301358i
\(412\) 0 0
\(413\) −85373.9 + 85373.9i −0.500524 + 0.500524i
\(414\) 0 0
\(415\) 121611.i 0.706115i
\(416\) 0 0
\(417\) 1382.03 0.00794775
\(418\) 0 0
\(419\) 119011. + 119011.i 0.677889 + 0.677889i 0.959522 0.281633i \(-0.0908761\pi\)
−0.281633 + 0.959522i \(0.590876\pi\)
\(420\) 0 0
\(421\) −126967. 126967.i −0.716355 0.716355i 0.251502 0.967857i \(-0.419075\pi\)
−0.967857 + 0.251502i \(0.919075\pi\)
\(422\) 0 0
\(423\) 9064.80 0.0506614
\(424\) 0 0
\(425\) 217010.i 1.20144i
\(426\) 0 0
\(427\) 185115. 185115.i 1.01528 1.01528i
\(428\) 0 0
\(429\) −151.687 + 151.687i −0.000824201 + 0.000824201i
\(430\) 0 0
\(431\) 82986.1i 0.446736i 0.974734 + 0.223368i \(0.0717051\pi\)
−0.974734 + 0.223368i \(0.928295\pi\)
\(432\) 0 0
\(433\) −153228. −0.817265 −0.408633 0.912699i \(-0.633994\pi\)
−0.408633 + 0.912699i \(0.633994\pi\)
\(434\) 0 0
\(435\) 766.685 + 766.685i 0.00405171 + 0.00405171i
\(436\) 0 0
\(437\) 141298. + 141298.i 0.739899 + 0.739899i
\(438\) 0 0
\(439\) 48984.2 0.254172 0.127086 0.991892i \(-0.459438\pi\)
0.127086 + 0.991892i \(0.459438\pi\)
\(440\) 0 0
\(441\) 7045.09i 0.0362251i
\(442\) 0 0
\(443\) −5464.01 + 5464.01i −0.0278422 + 0.0278422i −0.720891 0.693049i \(-0.756267\pi\)
0.693049 + 0.720891i \(0.256267\pi\)
\(444\) 0 0
\(445\) −51795.1 + 51795.1i −0.261559 + 0.261559i
\(446\) 0 0
\(447\) 1422.38i 0.00711870i
\(448\) 0 0
\(449\) 140068. 0.694776 0.347388 0.937721i \(-0.387069\pi\)
0.347388 + 0.937721i \(0.387069\pi\)
\(450\) 0 0
\(451\) 58714.4 + 58714.4i 0.288664 + 0.288664i
\(452\) 0 0
\(453\) −784.092 784.092i −0.00382094 0.00382094i
\(454\) 0 0
\(455\) 15633.0 0.0755127
\(456\) 0 0
\(457\) 219788.i 1.05238i 0.850368 + 0.526188i \(0.176379\pi\)
−0.850368 + 0.526188i \(0.823621\pi\)
\(458\) 0 0
\(459\) 3276.96 3276.96i 0.0155541 0.0155541i
\(460\) 0 0
\(461\) −124163. + 124163.i −0.584239 + 0.584239i −0.936065 0.351826i \(-0.885561\pi\)
0.351826 + 0.936065i \(0.385561\pi\)
\(462\) 0 0
\(463\) 236566.i 1.10354i 0.833995 + 0.551772i \(0.186048\pi\)
−0.833995 + 0.551772i \(0.813952\pi\)
\(464\) 0 0
\(465\) 1119.32 0.00517663
\(466\) 0 0
\(467\) −73415.5 73415.5i −0.336631 0.336631i 0.518467 0.855098i \(-0.326503\pi\)
−0.855098 + 0.518467i \(0.826503\pi\)
\(468\) 0 0
\(469\) −92485.8 92485.8i −0.420465 0.420465i
\(470\) 0 0
\(471\) −107.897 −0.000486372
\(472\) 0 0
\(473\) 154631.i 0.691153i
\(474\) 0 0
\(475\) −172982. + 172982.i −0.766681 + 0.766681i
\(476\) 0 0
\(477\) −84332.1 + 84332.1i −0.370643 + 0.370643i
\(478\) 0 0
\(479\) 212004.i 0.924003i −0.886879 0.462002i \(-0.847131\pi\)
0.886879 0.462002i \(-0.152869\pi\)
\(480\) 0 0
\(481\) −16922.1 −0.0731417
\(482\) 0 0
\(483\) 932.920 + 932.920i 0.00399899 + 0.00399899i
\(484\) 0 0
\(485\) −3322.01 3322.01i −0.0141227 0.0141227i
\(486\) 0 0
\(487\) 26716.3 0.112647 0.0563234 0.998413i \(-0.482062\pi\)
0.0563234 + 0.998413i \(0.482062\pi\)
\(488\) 0 0
\(489\) 2594.22i 0.0108490i
\(490\) 0 0
\(491\) −99544.8 + 99544.8i −0.412910 + 0.412910i −0.882751 0.469841i \(-0.844311\pi\)
0.469841 + 0.882751i \(0.344311\pi\)
\(492\) 0 0
\(493\) 451714. 451714.i 1.85853 1.85853i
\(494\) 0 0
\(495\) 109778.i 0.448028i
\(496\) 0 0
\(497\) 57954.9 0.234627
\(498\) 0 0
\(499\) −189887. 189887.i −0.762597 0.762597i 0.214194 0.976791i \(-0.431287\pi\)
−0.976791 + 0.214194i \(0.931287\pi\)
\(500\) 0 0
\(501\) −135.356 135.356i −0.000539265 0.000539265i
\(502\) 0 0
\(503\) 188872. 0.746502 0.373251 0.927730i \(-0.378243\pi\)
0.373251 + 0.927730i \(0.378243\pi\)
\(504\) 0 0
\(505\) 136097.i 0.533662i
\(506\) 0 0
\(507\) −1284.43 + 1284.43i −0.00499682 + 0.00499682i
\(508\) 0 0
\(509\) 14343.5 14343.5i 0.0553629 0.0553629i −0.678883 0.734246i \(-0.737536\pi\)
0.734246 + 0.678883i \(0.237536\pi\)
\(510\) 0 0
\(511\) 45155.8i 0.172931i
\(512\) 0 0
\(513\) −5224.23 −0.0198513
\(514\) 0 0
\(515\) 136794. + 136794.i 0.515765 + 0.515765i
\(516\) 0 0
\(517\) 9429.82 + 9429.82i 0.0352795 + 0.0352795i
\(518\) 0 0
\(519\) −791.025 −0.00293667
\(520\) 0 0
\(521\) 65377.4i 0.240853i −0.992722 0.120427i \(-0.961574\pi\)
0.992722 0.120427i \(-0.0384262\pi\)
\(522\) 0 0
\(523\) 143634. 143634.i 0.525113 0.525113i −0.393998 0.919111i \(-0.628908\pi\)
0.919111 + 0.393998i \(0.128908\pi\)
\(524\) 0 0
\(525\) −1142.12 + 1142.12i −0.00414374 + 0.00414374i
\(526\) 0 0
\(527\) 659477.i 2.37453i
\(528\) 0 0
\(529\) −115946. −0.414327
\(530\) 0 0
\(531\) −138632. 138632.i −0.491671 0.491671i
\(532\) 0 0
\(533\) −13577.2 13577.2i −0.0477921 0.0477921i
\(534\) 0 0
\(535\) −150704. −0.526521
\(536\) 0 0
\(537\) 2256.40i 0.00782469i
\(538\) 0 0
\(539\) 7328.78 7328.78i 0.0252263 0.0252263i
\(540\) 0 0
\(541\) 275122. 275122.i 0.940007 0.940007i −0.0582928 0.998300i \(-0.518566\pi\)
0.998300 + 0.0582928i \(0.0185657\pi\)
\(542\) 0 0
\(543\) 1011.45i 0.00343039i
\(544\) 0 0
\(545\) 133654. 0.449975
\(546\) 0 0
\(547\) 1032.53 + 1032.53i 0.00345087 + 0.00345087i 0.708830 0.705379i \(-0.249223\pi\)
−0.705379 + 0.708830i \(0.749223\pi\)
\(548\) 0 0
\(549\) 300594. + 300594.i 0.997323 + 0.997323i
\(550\) 0 0
\(551\) −720136. −2.37198
\(552\) 0 0
\(553\) 292775.i 0.957379i
\(554\) 0 0
\(555\) −322.727 + 322.727i −0.00104773 + 0.00104773i
\(556\) 0 0
\(557\) 223266. 223266.i 0.719635 0.719635i −0.248895 0.968530i \(-0.580067\pi\)
0.968530 + 0.248895i \(0.0800674\pi\)
\(558\) 0 0
\(559\) 35757.1i 0.114430i
\(560\) 0 0
\(561\) 3408.83 0.0108313
\(562\) 0 0
\(563\) −191551. 191551.i −0.604322 0.604322i 0.337134 0.941457i \(-0.390542\pi\)
−0.941457 + 0.337134i \(0.890542\pi\)
\(564\) 0 0
\(565\) 46766.9 + 46766.9i 0.146501 + 0.146501i
\(566\) 0 0
\(567\) 327209. 1.01779
\(568\) 0 0
\(569\) 119746.i 0.369858i 0.982752 + 0.184929i \(0.0592055\pi\)
−0.982752 + 0.184929i \(0.940795\pi\)
\(570\) 0 0
\(571\) −375516. + 375516.i −1.15175 + 1.15175i −0.165544 + 0.986202i \(0.552938\pi\)
−0.986202 + 0.165544i \(0.947062\pi\)
\(572\) 0 0
\(573\) 1034.17 1034.17i 0.00314980 0.00314980i
\(574\) 0 0
\(575\) 200647.i 0.606873i
\(576\) 0 0
\(577\) 185281. 0.556518 0.278259 0.960506i \(-0.410243\pi\)
0.278259 + 0.960506i \(0.410243\pi\)
\(578\) 0 0
\(579\) −1405.83 1405.83i −0.00419348 0.00419348i
\(580\) 0 0
\(581\) −377093. 377093.i −1.11711 1.11711i
\(582\) 0 0
\(583\) −175456. −0.516216
\(584\) 0 0
\(585\) 25385.3i 0.0741771i
\(586\) 0 0
\(587\) 483071. 483071.i 1.40196 1.40196i 0.608081 0.793875i \(-0.291940\pi\)
0.793875 0.608081i \(-0.208060\pi\)
\(588\) 0 0
\(589\) −525679. + 525679.i −1.51527 + 1.51527i
\(590\) 0 0
\(591\) 1764.26i 0.00505112i
\(592\) 0 0
\(593\) 636299. 1.80947 0.904736 0.425973i \(-0.140068\pi\)
0.904736 + 0.425973i \(0.140068\pi\)
\(594\) 0 0
\(595\) −175659. 175659.i −0.496177 0.496177i
\(596\) 0 0
\(597\) 3139.90 + 3139.90i 0.00880981 + 0.00880981i
\(598\) 0 0
\(599\) 410280. 1.14347 0.571737 0.820437i \(-0.306270\pi\)
0.571737 + 0.820437i \(0.306270\pi\)
\(600\) 0 0
\(601\) 531872.i 1.47251i −0.676704 0.736255i \(-0.736592\pi\)
0.676704 0.736255i \(-0.263408\pi\)
\(602\) 0 0
\(603\) 150181. 150181.i 0.413028 0.413028i
\(604\) 0 0
\(605\) −3558.44 + 3558.44i −0.00972184 + 0.00972184i
\(606\) 0 0
\(607\) 505448.i 1.37182i 0.727684 + 0.685912i \(0.240597\pi\)
−0.727684 + 0.685912i \(0.759403\pi\)
\(608\) 0 0
\(609\) −4754.71 −0.0128200
\(610\) 0 0
\(611\) −2180.57 2180.57i −0.00584099 0.00584099i
\(612\) 0 0
\(613\) 31334.4 + 31334.4i 0.0833873 + 0.0833873i 0.747570 0.664183i \(-0.231220\pi\)
−0.664183 + 0.747570i \(0.731220\pi\)
\(614\) 0 0
\(615\) −517.871 −0.00136921
\(616\) 0 0
\(617\) 481833.i 1.26569i 0.774280 + 0.632844i \(0.218112\pi\)
−0.774280 + 0.632844i \(0.781888\pi\)
\(618\) 0 0
\(619\) −55035.5 + 55035.5i −0.143635 + 0.143635i −0.775268 0.631632i \(-0.782385\pi\)
0.631632 + 0.775268i \(0.282385\pi\)
\(620\) 0 0
\(621\) −3029.87 + 3029.87i −0.00785672 + 0.00785672i
\(622\) 0 0
\(623\) 321215.i 0.827599i
\(624\) 0 0
\(625\) −164779. −0.421834
\(626\) 0 0
\(627\) −2717.23 2717.23i −0.00691180 0.00691180i
\(628\) 0 0
\(629\) 190144. + 190144.i 0.480597 + 0.480597i
\(630\) 0 0
\(631\) −188802. −0.474184 −0.237092 0.971487i \(-0.576194\pi\)
−0.237092 + 0.971487i \(0.576194\pi\)
\(632\) 0 0
\(633\) 5102.26i 0.0127337i
\(634\) 0 0
\(635\) 163812. 163812.i 0.406255 0.406255i
\(636\) 0 0
\(637\) −1694.72 + 1694.72i −0.00417656 + 0.00417656i
\(638\) 0 0
\(639\) 94108.5i 0.230477i
\(640\) 0 0
\(641\) −442081. −1.07593 −0.537967 0.842966i \(-0.680807\pi\)
−0.537967 + 0.842966i \(0.680807\pi\)
\(642\) 0 0
\(643\) 246339. + 246339.i 0.595814 + 0.595814i 0.939196 0.343382i \(-0.111573\pi\)
−0.343382 + 0.939196i \(0.611573\pi\)
\(644\) 0 0
\(645\) −681.935 681.935i −0.00163917 0.00163917i
\(646\) 0 0
\(647\) −54549.4 −0.130311 −0.0651555 0.997875i \(-0.520754\pi\)
−0.0651555 + 0.997875i \(0.520754\pi\)
\(648\) 0 0
\(649\) 288429.i 0.684778i
\(650\) 0 0
\(651\) −3470.80 + 3470.80i −0.00818970 + 0.00818970i
\(652\) 0 0
\(653\) −231745. + 231745.i −0.543481 + 0.543481i −0.924548 0.381066i \(-0.875557\pi\)
0.381066 + 0.924548i \(0.375557\pi\)
\(654\) 0 0
\(655\) 71011.8i 0.165519i
\(656\) 0 0
\(657\) −73325.0 −0.169872
\(658\) 0 0
\(659\) 479757. + 479757.i 1.10472 + 1.10472i 0.993833 + 0.110883i \(0.0353678\pi\)
0.110883 + 0.993833i \(0.464632\pi\)
\(660\) 0 0
\(661\) −515798. 515798.i −1.18053 1.18053i −0.979607 0.200922i \(-0.935606\pi\)
−0.200922 0.979607i \(-0.564394\pi\)
\(662\) 0 0
\(663\) −788.263 −0.00179326
\(664\) 0 0
\(665\) 280041.i 0.633254i
\(666\) 0 0
\(667\) −417654. + 417654.i −0.938782 + 0.938782i
\(668\) 0 0
\(669\) 1867.27 1867.27i 0.00417210 0.00417210i
\(670\) 0 0
\(671\) 625397.i 1.38903i
\(672\) 0 0
\(673\) −505551. −1.11618 −0.558090 0.829780i \(-0.688466\pi\)
−0.558090 + 0.829780i \(0.688466\pi\)
\(674\) 0 0
\(675\) −3709.29 3709.29i −0.00814111 0.00814111i
\(676\) 0 0
\(677\) 460825. + 460825.i 1.00545 + 1.00545i 0.999985 + 0.00546007i \(0.00173800\pi\)
0.00546007 + 0.999985i \(0.498262\pi\)
\(678\) 0 0
\(679\) 20601.9 0.0446857
\(680\) 0 0
\(681\) 154.570i 0.000333297i
\(682\) 0 0
\(683\) −120242. + 120242.i −0.257761 + 0.257761i −0.824143 0.566382i \(-0.808343\pi\)
0.566382 + 0.824143i \(0.308343\pi\)
\(684\) 0 0
\(685\) 88622.7 88622.7i 0.188870 0.188870i
\(686\) 0 0
\(687\) 2450.33i 0.00519171i
\(688\) 0 0
\(689\) 40572.7 0.0854664
\(690\) 0 0
\(691\) −166965. 166965.i −0.349678 0.349678i 0.510311 0.859990i \(-0.329530\pi\)
−0.859990 + 0.510311i \(0.829530\pi\)
\(692\) 0 0
\(693\) 340403. + 340403.i 0.708805 + 0.708805i
\(694\) 0 0
\(695\) 240600. 0.498111
\(696\) 0 0
\(697\) 305118.i 0.628062i
\(698\) 0 0
\(699\) 1116.33 1116.33i 0.00228475 0.00228475i
\(700\) 0 0
\(701\) −39689.8 + 39689.8i −0.0807687 + 0.0807687i −0.746337 0.665568i \(-0.768189\pi\)
0.665568 + 0.746337i \(0.268189\pi\)
\(702\) 0 0
\(703\) 303133.i 0.613371i
\(704\) 0 0
\(705\) −83.1725 −0.000167341
\(706\) 0 0
\(707\) 422013. + 422013.i 0.844281 + 0.844281i
\(708\) 0 0
\(709\) −250742. 250742.i −0.498809 0.498809i 0.412258 0.911067i \(-0.364740\pi\)
−0.911067 + 0.412258i \(0.864740\pi\)
\(710\) 0 0
\(711\) 475415. 0.940445
\(712\) 0 0
\(713\) 609751.i 1.19943i
\(714\) 0 0
\(715\) −26407.5 + 26407.5i −0.0516553 + 0.0516553i
\(716\) 0 0
\(717\) −3527.63 + 3527.63i −0.00686190 + 0.00686190i
\(718\) 0 0
\(719\) 133454.i 0.258152i −0.991635 0.129076i \(-0.958799\pi\)
0.991635 0.129076i \(-0.0412011\pi\)
\(720\) 0 0
\(721\) −848347. −1.63194
\(722\) 0 0
\(723\) 1873.30 + 1873.30i 0.00358370 + 0.00358370i
\(724\) 0 0
\(725\) −511309. 511309.i −0.972763 0.972763i
\(726\) 0 0
\(727\) 583370. 1.10376 0.551881 0.833923i \(-0.313910\pi\)
0.551881 + 0.833923i \(0.313910\pi\)
\(728\) 0 0
\(729\) 531273.i 0.999684i
\(730\) 0 0
\(731\) −401781. + 401781.i −0.751891 + 0.751891i
\(732\) 0 0
\(733\) −534516. + 534516.i −0.994838 + 0.994838i −0.999987 0.00514857i \(-0.998361\pi\)
0.00514857 + 0.999987i \(0.498361\pi\)
\(734\) 0 0
\(735\) 64.6410i 0.000119656i
\(736\) 0 0
\(737\) 312456. 0.575247
\(738\) 0 0
\(739\) 91929.4 + 91929.4i 0.168332 + 0.168332i 0.786246 0.617914i \(-0.212022\pi\)
−0.617914 + 0.786246i \(0.712022\pi\)
\(740\) 0 0
\(741\) 628.336 + 628.336i 0.00114434 + 0.00114434i
\(742\) 0 0
\(743\) 83329.2 0.150945 0.0754727 0.997148i \(-0.475953\pi\)
0.0754727 + 0.997148i \(0.475953\pi\)
\(744\) 0 0
\(745\) 247625.i 0.446151i
\(746\) 0 0
\(747\) 612333. 612333.i 1.09735 1.09735i
\(748\) 0 0
\(749\) 467305. 467305.i 0.832985 0.832985i
\(750\) 0 0
\(751\) 318689.i 0.565051i 0.959260 + 0.282525i \(0.0911722\pi\)
−0.959260 + 0.282525i \(0.908828\pi\)
\(752\) 0 0
\(753\) 973.515 0.00171693
\(754\) 0 0
\(755\) −136504. 136504.i −0.239470 0.239470i
\(756\) 0 0
\(757\) 428881. + 428881.i 0.748419 + 0.748419i 0.974182 0.225763i \(-0.0724875\pi\)
−0.225763 + 0.974182i \(0.572488\pi\)
\(758\) 0 0
\(759\) −3151.80 −0.00547110
\(760\) 0 0
\(761\) 718933.i 1.24142i −0.784040 0.620711i \(-0.786844\pi\)
0.784040 0.620711i \(-0.213156\pi\)
\(762\) 0 0
\(763\) −414437. + 414437.i −0.711884 + 0.711884i
\(764\) 0 0
\(765\) 285239. 285239.i 0.487401 0.487401i
\(766\) 0 0
\(767\) 66696.8i 0.113374i
\(768\) 0 0
\(769\) 421326. 0.712468 0.356234 0.934397i \(-0.384061\pi\)
0.356234 + 0.934397i \(0.384061\pi\)
\(770\) 0 0
\(771\) 1754.84 + 1754.84i 0.00295208 + 0.00295208i
\(772\) 0 0
\(773\) −455325. 455325.i −0.762013 0.762013i 0.214673 0.976686i \(-0.431132\pi\)
−0.976686 + 0.214673i \(0.931132\pi\)
\(774\) 0 0
\(775\) −746482. −1.24284
\(776\) 0 0
\(777\) 2001.44i 0.00331513i
\(778\) 0 0
\(779\) 243214. 243214.i 0.400788 0.400788i
\(780\) 0 0
\(781\) −97898.1 + 97898.1i −0.160499 + 0.160499i
\(782\) 0 0
\(783\) 15442.0i 0.0251872i
\(784\) 0 0
\(785\) −18784.0 −0.0304825
\(786\) 0 0
\(787\) −541211. 541211.i −0.873811 0.873811i 0.119074 0.992885i \(-0.462007\pi\)
−0.992885 + 0.119074i \(0.962007\pi\)
\(788\) 0 0
\(789\) 1734.56 + 1734.56i 0.00278635 + 0.00278635i
\(790\) 0 0
\(791\) −290032. −0.463546
\(792\) 0 0
\(793\) 144618.i 0.229972i
\(794\) 0 0
\(795\) 773.775 773.775i 0.00122428 0.00122428i
\(796\) 0