Properties

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

Related objects

Downloads

Learn more about

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.a.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 0.704535 0.709669i \(-0.251155\pi\)
−0.709669 + 0.704535i \(0.751155\pi\)
\(4\) 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 \(-0.330024\pi\)
0.508976 + 0.860781i \(0.330024\pi\)
\(8\) 0 0
\(9\) 80.9957i 0.999947i
\(10\) 0 0
\(11\) −84.2573 + 84.2573i −0.696341 + 0.696341i −0.963619 0.267278i \(-0.913876\pi\)
0.267278 + 0.963619i \(0.413876\pi\)
\(12\) 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 0.999467 0.0326494i \(-0.0103945\pi\)
−0.0326494 + 0.999467i \(0.510394\pi\)
\(20\) 0 0
\(21\) −2.30442 2.30442i −0.00522543 0.00522543i
\(22\) 0 0
\(23\) 404.840 0.765293 0.382647 0.923895i \(-0.375013\pi\)
0.382647 + 0.923895i \(0.375013\pi\)
\(24\) 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 \(0.286638\pi\)
−0.621217 + 0.783638i \(0.713362\pi\)
\(32\) 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 −0.414002 0.910276i \(-0.635869\pi\)
0.910276 + 0.414002i \(0.135869\pi\)
\(44\) 0 0
\(45\) 651.446 651.446i 0.321702 0.321702i
\(46\) 0 0
\(47\) 111.917i 0.0506641i −0.999679 0.0253321i \(-0.991936\pi\)
0.999679 0.0253321i \(-0.00806431\pi\)
\(48\) 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 −0.908841 0.417144i \(-0.863031\pi\)
0.417144 + 0.908841i \(0.363031\pi\)
\(60\) 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 0.469750 0.882799i \(-0.344344\pi\)
−0.882799 + 0.469750i \(0.844344\pi\)
\(68\) 0 0
\(69\) −18.7034 18.7034i −0.00392846 0.00392846i
\(70\) 0 0
\(71\) 1161.89 0.230489 0.115244 0.993337i \(-0.463235\pi\)
0.115244 + 0.993337i \(0.463235\pi\)
\(72\) 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 \(-0.844165\pi\)
0.882535 0.470247i \(-0.155835\pi\)
\(80\) 0 0
\(81\) −6559.96 −0.999842
\(82\) 0 0
\(83\) −7560.06 7560.06i −1.09741 1.09741i −0.994713 0.102698i \(-0.967252\pi\)
−0.102698 0.994713i \(-0.532748\pi\)
\(84\) 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 \(-0.796006\pi\)
−0.801578 + 0.597891i \(0.796006\pi\)
\(104\) 0 0
\(105\) 37.0687i 0.00336224i
\(106\) 0 0
\(107\) 9368.65 9368.65i 0.818294 0.818294i −0.167567 0.985861i \(-0.553591\pi\)
0.985861 + 0.167567i \(0.0535909\pi\)
\(108\) 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 \(0.217512\pi\)
−0.775472 + 0.631382i \(0.782488\pi\)
\(128\) 0 0
\(129\) −84.7864 −0.00509503
\(130\) 0 0
\(131\) 4414.52 + 4414.52i 0.257242 + 0.257242i 0.823931 0.566690i \(-0.191776\pi\)
−0.566690 + 0.823931i \(0.691776\pi\)
\(132\) 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 −0.978827 0.204688i \(-0.934382\pi\)
0.204688 + 0.978827i \(0.434382\pi\)
\(140\) 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 \(-0.378613\pi\)
0.372174 + 0.928163i \(0.378613\pi\)
\(152\) 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 \(0.0186121\pi\)
0.0584383 + 0.998291i \(0.481388\pi\)
\(164\) 0 0
\(165\) 62.6168 + 62.6168i 0.00229998 + 0.00229998i
\(166\) 0 0
\(167\) 2929.82 0.105053 0.0525264 0.998620i \(-0.483273\pi\)
0.0525264 + 0.998620i \(0.483273\pi\)
\(168\) 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 0.214558 0.976711i \(-0.431169\pi\)
−0.976711 + 0.214558i \(0.931169\pi\)
\(180\) 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 \(0.0992590\pi\)
−0.951773 + 0.306802i \(0.900741\pi\)
\(192\) 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 \(-0.828360\pi\)
−0.858107 + 0.513470i \(0.828360\pi\)
\(200\) 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 \(-0.909520\pi\)
−0.280438 0.959872i \(-0.590480\pi\)
\(212\) 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 \(0.133208\pi\)
−0.913705 + 0.406377i \(0.866792\pi\)
\(224\) 0 0
\(225\) −40143.2 −0.792952
\(226\) 0 0
\(227\) −1672.85 1672.85i −0.0324643 0.0324643i 0.690688 0.723153i \(-0.257308\pi\)
−0.723153 + 0.690688i \(0.757308\pi\)
\(228\) 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 \(-0.766990\pi\)
0.743825 0.668374i \(-0.233010\pi\)
\(240\) 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 −0.785763 0.618528i \(-0.787729\pi\)
0.618528 + 0.785763i \(0.287729\pi\)
\(252\) 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 \(-0.587487\pi\)
−0.271400 + 0.962467i \(0.587487\pi\)
\(264\) 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 \(-0.994049\pi\)
0.999825 0.0186961i \(-0.00595149\pi\)
\(272\) 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 −0.995656 0.0931068i \(-0.970320\pi\)
0.0931068 + 0.995656i \(0.470320\pi\)
\(284\) 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 0.348671 0.937245i \(-0.386633\pi\)
−0.937245 + 0.348671i \(0.886633\pi\)
\(308\) 0 0
\(309\) 785.756 + 785.756i 0.00822944 + 0.00822944i
\(310\) 0 0
\(311\) 127048. 1.31355 0.656777 0.754084i \(-0.271919\pi\)
0.656777 + 0.754084i \(0.271919\pi\)
\(312\) 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 −0.344295 0.938862i \(-0.611882\pi\)
0.938862 + 0.344295i \(0.111882\pi\)
\(332\) 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 −0.660619 0.750721i \(-0.729706\pi\)
0.750721 + 0.660619i \(0.229706\pi\)
\(348\) 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 \(-0.659857\pi\)
−0.481359 + 0.876523i \(0.659857\pi\)
\(360\) 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 \(0.155254\pi\)
−0.883392 + 0.468634i \(0.844746\pi\)
\(368\) 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 −0.807380 0.590032i \(-0.799115\pi\)
0.590032 + 0.807380i \(0.299115\pi\)
\(380\) 0 0
\(381\) 940.951 940.951i 0.00648212 0.00648212i
\(382\) 0 0
\(383\) 253102.i 1.72543i −0.505689 0.862716i \(-0.668762\pi\)
0.505689 0.862716i \(-0.331238\pi\)
\(384\) 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 0.281633 0.959522i \(-0.409124\pi\)
−0.959522 + 0.281633i \(0.909124\pi\)
\(420\) 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 \(-0.928295\pi\)
0.974734 0.223368i \(-0.0717051\pi\)
\(432\) 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 \(-0.540562\pi\)
−0.127086 + 0.991892i \(0.540562\pi\)
\(440\) 0 0
\(441\) 7045.09i 0.0362251i
\(442\) 0 0
\(443\) 5464.01 5464.01i 0.0278422 0.0278422i −0.693049 0.720891i \(-0.743733\pi\)
0.720891 + 0.693049i \(0.243733\pi\)
\(444\) 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 \(-0.813952\pi\)
0.833995 0.551772i \(-0.186048\pi\)
\(464\) 0 0
\(465\) 1119.32 0.00517663
\(466\) 0 0
\(467\) 73415.5 + 73415.5i 0.336631 + 0.336631i 0.855098 0.518467i \(-0.173497\pi\)
−0.518467 + 0.855098i \(0.673497\pi\)
\(468\) 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 \(0.152869\pi\)
−0.886879 + 0.462002i \(0.847131\pi\)
\(480\) 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 \(-0.517938\pi\)
−0.0563234 + 0.998413i \(0.517938\pi\)
\(488\) 0 0
\(489\) 2594.22i 0.0108490i
\(490\) 0 0
\(491\) 99544.8 99544.8i 0.412910 0.412910i −0.469841 0.882751i \(-0.655689\pi\)
0.882751 + 0.469841i \(0.155689\pi\)
\(492\) 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 0.976791 0.214194i \(-0.0687125\pi\)
−0.214194 + 0.976791i \(0.568713\pi\)
\(500\) 0 0
\(501\) −135.356 135.356i −0.000539265 0.000539265i
\(502\) 0 0
\(503\) −188872. −0.746502 −0.373251 0.927730i \(-0.621757\pi\)
−0.373251 + 0.927730i \(0.621757\pi\)
\(504\) 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 −0.919111 0.393998i \(-0.871092\pi\)
0.393998 + 0.919111i \(0.371092\pi\)
\(524\) 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 0.705379 0.708830i \(-0.250777\pi\)
−0.708830 + 0.705379i \(0.750777\pi\)
\(548\) 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 0.941457 0.337134i \(-0.109458\pi\)
−0.337134 + 0.941457i \(0.609458\pi\)
\(564\) 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 \(-0.447062\pi\)
0.986202 0.165544i \(-0.0529379\pi\)
\(572\) 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 \(0.708060\pi\)
−0.793875 + 0.608081i \(0.791940\pi\)
\(588\) 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 \(-0.693730\pi\)
−0.571737 + 0.820437i \(0.693730\pi\)
\(600\) 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 \(-0.759403\pi\)
0.727684 0.685912i \(-0.240597\pi\)
\(608\) 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 −0.631632 0.775268i \(-0.717615\pi\)
0.775268 + 0.631632i \(0.217615\pi\)
\(620\) 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 \(-0.423806\pi\)
0.237092 + 0.971487i \(0.423806\pi\)
\(632\) 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 0.343382 0.939196i \(-0.388427\pi\)
−0.939196 + 0.343382i \(0.888427\pi\)
\(644\) 0 0
\(645\) −681.935 681.935i −0.00163917 0.00163917i
\(646\) 0 0
\(647\) 54549.4 0.130311 0.0651555 0.997875i \(-0.479246\pi\)
0.0651555 + 0.997875i \(0.479246\pi\)
\(648\) 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 \(-0.964632\pi\)
−0.110883 0.993833i \(-0.535368\pi\)
\(660\) 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 −0.566382 0.824143i \(-0.691657\pi\)
0.824143 + 0.566382i \(0.191657\pi\)
\(684\) 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 0.859990 0.510311i \(-0.170470\pi\)
−0.510311 + 0.859990i \(0.670470\pi\)
\(692\) 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 \(0.0412011\pi\)
−0.991635 + 0.129076i \(0.958799\pi\)
\(720\) 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 \(-0.686090\pi\)
−0.551881 + 0.833923i \(0.686090\pi\)
\(728\) 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 0.617914 0.786246i \(-0.287978\pi\)
−0.786246 + 0.617914i \(0.787978\pi\)
\(740\) 0 0
\(741\) 628.336 + 628.336i 0.00114434 + 0.00114434i
\(742\) 0 0
\(743\) −83329.2 −0.150945 −0.0754727 0.997148i \(-0.524047\pi\)
−0.0754727 + 0.997148i \(0.524047\pi\)
\(744\) 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 \(-0.908828\pi\)
0.959260 0.282525i \(-0.0911722\pi\)
\(752\) 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 0.992885 0.119074i \(-0.0379927\pi\)
−0.119074 + 0.992885i \(0.537993\pi\)
\(788\) 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