Properties

Label 384.4.f.g.191.5
Level $384$
Weight $4$
Character 384.191
Analytic conductor $22.657$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 384.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(22.6567334422\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.12745506816.1
Defining polynomial: \(x^{8} + 23 x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 191.5
Root \(-1.54779 + 1.54779i\) of defining polynomial
Character \(\chi\) \(=\) 384.191
Dual form 384.4.f.g.191.7

$q$-expansion

\(f(q)\) \(=\) \(q+(2.44949 - 4.58258i) q^{3} -17.2813 q^{5} +0.269691i q^{7} +(-15.0000 - 22.4499i) q^{9} +O(q^{10})\) \(q+(2.44949 - 4.58258i) q^{3} -17.2813 q^{5} +0.269691i q^{7} +(-15.0000 - 22.4499i) q^{9} +41.1652i q^{11} +64.6606i q^{13} +(-42.3303 + 79.1927i) q^{15} -63.4170i q^{17} +154.026 q^{19} +(1.23588 + 0.660606i) q^{21} -43.3394 q^{23} +173.642 q^{25} +(-139.621 + 13.7477i) q^{27} +240.702 q^{29} -79.1927i q^{31} +(188.642 + 100.834i) q^{33} -4.66061i q^{35} +132.624i q^{37} +(296.312 + 158.385i) q^{39} +101.216i q^{41} +120.317 q^{43} +(259.219 + 387.964i) q^{45} -293.285 q^{47} +342.927 q^{49} +(-290.613 - 155.339i) q^{51} +6.17940 q^{53} -711.386i q^{55} +(377.285 - 705.835i) q^{57} -45.8258i q^{59} +651.230i q^{61} +(6.05455 - 4.04537i) q^{63} -1117.42i q^{65} -685.273 q^{67} +(-106.159 + 198.606i) q^{69} +836.515 q^{71} +285.927 q^{73} +(425.335 - 795.730i) q^{75} -11.1019 q^{77} +940.874i q^{79} +(-279.000 + 673.498i) q^{81} +1011.11i q^{83} +1095.93i q^{85} +(589.597 - 1103.03i) q^{87} +432.503i q^{89} -17.4384 q^{91} +(-362.907 - 193.982i) q^{93} -2661.76 q^{95} +1007.28 q^{97} +(924.155 - 617.477i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 120 q^{9} + O(q^{10}) \) \( 8 q - 120 q^{9} - 192 q^{15} - 640 q^{23} + 216 q^{25} + 336 q^{33} + 1344 q^{39} - 776 q^{49} + 672 q^{57} + 2688 q^{63} - 640 q^{71} - 1232 q^{73} - 2232 q^{81} + 1344 q^{87} - 9856 q^{95} + 5712 q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

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
\(3\) 2.44949 4.58258i 0.471405 0.881917i
\(4\) 0 0
\(5\) −17.2813 −1.54568 −0.772842 0.634598i \(-0.781166\pi\)
−0.772842 + 0.634598i \(0.781166\pi\)
\(6\) 0 0
\(7\) 0.269691i 0.0145620i 0.999973 + 0.00728098i \(0.00231763\pi\)
−0.999973 + 0.00728098i \(0.997682\pi\)
\(8\) 0 0
\(9\) −15.0000 22.4499i −0.555556 0.831479i
\(10\) 0 0
\(11\) 41.1652i 1.12834i 0.825658 + 0.564171i \(0.190804\pi\)
−0.825658 + 0.564171i \(0.809196\pi\)
\(12\) 0 0
\(13\) 64.6606i 1.37951i 0.724043 + 0.689755i \(0.242282\pi\)
−0.724043 + 0.689755i \(0.757718\pi\)
\(14\) 0 0
\(15\) −42.3303 + 79.1927i −0.728642 + 1.36317i
\(16\) 0 0
\(17\) 63.4170i 0.904758i −0.891826 0.452379i \(-0.850575\pi\)
0.891826 0.452379i \(-0.149425\pi\)
\(18\) 0 0
\(19\) 154.026 1.85979 0.929894 0.367828i \(-0.119899\pi\)
0.929894 + 0.367828i \(0.119899\pi\)
\(20\) 0 0
\(21\) 1.23588 + 0.660606i 0.0128424 + 0.00686457i
\(22\) 0 0
\(23\) −43.3394 −0.392908 −0.196454 0.980513i \(-0.562943\pi\)
−0.196454 + 0.980513i \(0.562943\pi\)
\(24\) 0 0
\(25\) 173.642 1.38914
\(26\) 0 0
\(27\) −139.621 + 13.7477i −0.995187 + 0.0979908i
\(28\) 0 0
\(29\) 240.702 1.54128 0.770642 0.637268i \(-0.219936\pi\)
0.770642 + 0.637268i \(0.219936\pi\)
\(30\) 0 0
\(31\) 79.1927i 0.458821i −0.973330 0.229410i \(-0.926320\pi\)
0.973330 0.229410i \(-0.0736797\pi\)
\(32\) 0 0
\(33\) 188.642 + 100.834i 0.995104 + 0.531905i
\(34\) 0 0
\(35\) 4.66061i 0.0225082i
\(36\) 0 0
\(37\) 132.624i 0.589278i 0.955609 + 0.294639i \(0.0951994\pi\)
−0.955609 + 0.294639i \(0.904801\pi\)
\(38\) 0 0
\(39\) 296.312 + 158.385i 1.21661 + 0.650307i
\(40\) 0 0
\(41\) 101.216i 0.385543i 0.981244 + 0.192772i \(0.0617476\pi\)
−0.981244 + 0.192772i \(0.938252\pi\)
\(42\) 0 0
\(43\) 120.317 0.426701 0.213351 0.976976i \(-0.431562\pi\)
0.213351 + 0.976976i \(0.431562\pi\)
\(44\) 0 0
\(45\) 259.219 + 387.964i 0.858713 + 1.28520i
\(46\) 0 0
\(47\) −293.285 −0.910213 −0.455106 0.890437i \(-0.650399\pi\)
−0.455106 + 0.890437i \(0.650399\pi\)
\(48\) 0 0
\(49\) 342.927 0.999788
\(50\) 0 0
\(51\) −290.613 155.339i −0.797922 0.426507i
\(52\) 0 0
\(53\) 6.17940 0.0160152 0.00800760 0.999968i \(-0.497451\pi\)
0.00800760 + 0.999968i \(0.497451\pi\)
\(54\) 0 0
\(55\) 711.386i 1.74406i
\(56\) 0 0
\(57\) 377.285 705.835i 0.876712 1.64018i
\(58\) 0 0
\(59\) 45.8258i 0.101119i −0.998721 0.0505594i \(-0.983900\pi\)
0.998721 0.0505594i \(-0.0161004\pi\)
\(60\) 0 0
\(61\) 651.230i 1.36691i 0.729993 + 0.683455i \(0.239523\pi\)
−0.729993 + 0.683455i \(0.760477\pi\)
\(62\) 0 0
\(63\) 6.05455 4.04537i 0.0121080 0.00808997i
\(64\) 0 0
\(65\) 1117.42i 2.13229i
\(66\) 0 0
\(67\) −685.273 −1.24954 −0.624772 0.780807i \(-0.714808\pi\)
−0.624772 + 0.780807i \(0.714808\pi\)
\(68\) 0 0
\(69\) −106.159 + 198.606i −0.185219 + 0.346512i
\(70\) 0 0
\(71\) 836.515 1.39825 0.699127 0.714997i \(-0.253572\pi\)
0.699127 + 0.714997i \(0.253572\pi\)
\(72\) 0 0
\(73\) 285.927 0.458428 0.229214 0.973376i \(-0.426384\pi\)
0.229214 + 0.973376i \(0.426384\pi\)
\(74\) 0 0
\(75\) 425.335 795.730i 0.654847 1.22511i
\(76\) 0 0
\(77\) −11.1019 −0.0164309
\(78\) 0 0
\(79\) 940.874i 1.33996i 0.742381 + 0.669978i \(0.233697\pi\)
−0.742381 + 0.669978i \(0.766303\pi\)
\(80\) 0 0
\(81\) −279.000 + 673.498i −0.382716 + 0.923866i
\(82\) 0 0
\(83\) 1011.11i 1.33715i 0.743643 + 0.668577i \(0.233096\pi\)
−0.743643 + 0.668577i \(0.766904\pi\)
\(84\) 0 0
\(85\) 1095.93i 1.39847i
\(86\) 0 0
\(87\) 589.597 1103.03i 0.726568 1.35928i
\(88\) 0 0
\(89\) 432.503i 0.515115i 0.966263 + 0.257558i \(0.0829177\pi\)
−0.966263 + 0.257558i \(0.917082\pi\)
\(90\) 0 0
\(91\) −17.4384 −0.0200884
\(92\) 0 0
\(93\) −362.907 193.982i −0.404642 0.216290i
\(94\) 0 0
\(95\) −2661.76 −2.87464
\(96\) 0 0
\(97\) 1007.28 1.05437 0.527187 0.849749i \(-0.323247\pi\)
0.527187 + 0.849749i \(0.323247\pi\)
\(98\) 0 0
\(99\) 924.155 617.477i 0.938193 0.626857i
\(100\) 0 0
\(101\) 1217.08 1.19905 0.599526 0.800355i \(-0.295356\pi\)
0.599526 + 0.800355i \(0.295356\pi\)
\(102\) 0 0
\(103\) 1357.60i 1.29872i 0.760479 + 0.649362i \(0.224964\pi\)
−0.760479 + 0.649362i \(0.775036\pi\)
\(104\) 0 0
\(105\) −21.3576 11.4161i −0.0198503 0.0106105i
\(106\) 0 0
\(107\) 1490.17i 1.34636i 0.739478 + 0.673180i \(0.235072\pi\)
−0.739478 + 0.673180i \(0.764928\pi\)
\(108\) 0 0
\(109\) 1865.91i 1.63965i −0.572615 0.819824i \(-0.694071\pi\)
0.572615 0.819824i \(-0.305929\pi\)
\(110\) 0 0
\(111\) 607.761 + 324.862i 0.519694 + 0.277788i
\(112\) 0 0
\(113\) 1047.66i 0.872177i 0.899904 + 0.436088i \(0.143636\pi\)
−0.899904 + 0.436088i \(0.856364\pi\)
\(114\) 0 0
\(115\) 748.960 0.607312
\(116\) 0 0
\(117\) 1451.63 969.909i 1.14703 0.766394i
\(118\) 0 0
\(119\) 17.1030 0.0131750
\(120\) 0 0
\(121\) −363.570 −0.273155
\(122\) 0 0
\(123\) 463.829 + 247.927i 0.340017 + 0.181747i
\(124\) 0 0
\(125\) −840.603 −0.601487
\(126\) 0 0
\(127\) 1033.28i 0.721960i 0.932574 + 0.360980i \(0.117558\pi\)
−0.932574 + 0.360980i \(0.882442\pi\)
\(128\) 0 0
\(129\) 294.715 551.362i 0.201149 0.376315i
\(130\) 0 0
\(131\) 359.626i 0.239852i −0.992783 0.119926i \(-0.961734\pi\)
0.992783 0.119926i \(-0.0382658\pi\)
\(132\) 0 0
\(133\) 41.5394i 0.0270821i
\(134\) 0 0
\(135\) 2412.83 237.578i 1.53825 0.151463i
\(136\) 0 0
\(137\) 379.245i 0.236504i 0.992984 + 0.118252i \(0.0377291\pi\)
−0.992984 + 0.118252i \(0.962271\pi\)
\(138\) 0 0
\(139\) −1984.09 −1.21071 −0.605353 0.795957i \(-0.706968\pi\)
−0.605353 + 0.795957i \(0.706968\pi\)
\(140\) 0 0
\(141\) −718.398 + 1344.00i −0.429078 + 0.802732i
\(142\) 0 0
\(143\) −2661.76 −1.55656
\(144\) 0 0
\(145\) −4159.64 −2.38234
\(146\) 0 0
\(147\) 839.997 1571.49i 0.471305 0.881730i
\(148\) 0 0
\(149\) −2323.13 −1.27730 −0.638651 0.769497i \(-0.720507\pi\)
−0.638651 + 0.769497i \(0.720507\pi\)
\(150\) 0 0
\(151\) 2613.36i 1.40843i −0.709989 0.704213i \(-0.751300\pi\)
0.709989 0.704213i \(-0.248700\pi\)
\(152\) 0 0
\(153\) −1423.71 + 951.256i −0.752288 + 0.502644i
\(154\) 0 0
\(155\) 1368.55i 0.709192i
\(156\) 0 0
\(157\) 2780.41i 1.41338i −0.707524 0.706690i \(-0.750188\pi\)
0.707524 0.706690i \(-0.249812\pi\)
\(158\) 0 0
\(159\) 15.1364 28.3176i 0.00754964 0.0141241i
\(160\) 0 0
\(161\) 11.6882i 0.00572151i
\(162\) 0 0
\(163\) 635.294 0.305276 0.152638 0.988282i \(-0.451223\pi\)
0.152638 + 0.988282i \(0.451223\pi\)
\(164\) 0 0
\(165\) −3259.98 1742.53i −1.53812 0.822158i
\(166\) 0 0
\(167\) −319.521 −0.148056 −0.0740278 0.997256i \(-0.523585\pi\)
−0.0740278 + 0.997256i \(0.523585\pi\)
\(168\) 0 0
\(169\) −1983.99 −0.903047
\(170\) 0 0
\(171\) −2310.39 3457.87i −1.03322 1.54638i
\(172\) 0 0
\(173\) −1862.71 −0.818609 −0.409305 0.912398i \(-0.634229\pi\)
−0.409305 + 0.912398i \(0.634229\pi\)
\(174\) 0 0
\(175\) 46.8298i 0.0202286i
\(176\) 0 0
\(177\) −210.000 112.250i −0.0891783 0.0476678i
\(178\) 0 0
\(179\) 3946.43i 1.64788i 0.566678 + 0.823940i \(0.308229\pi\)
−0.566678 + 0.823940i \(0.691771\pi\)
\(180\) 0 0
\(181\) 1187.01i 0.487458i −0.969843 0.243729i \(-0.921629\pi\)
0.969843 0.243729i \(-0.0783708\pi\)
\(182\) 0 0
\(183\) 2984.31 + 1595.18i 1.20550 + 0.644367i
\(184\) 0 0
\(185\) 2291.92i 0.910838i
\(186\) 0 0
\(187\) 2610.57 1.02088
\(188\) 0 0
\(189\) −3.70764 37.6545i −0.00142694 0.0144919i
\(190\) 0 0
\(191\) 1147.96 0.434889 0.217444 0.976073i \(-0.430228\pi\)
0.217444 + 0.976073i \(0.430228\pi\)
\(192\) 0 0
\(193\) 304.933 0.113728 0.0568642 0.998382i \(-0.481890\pi\)
0.0568642 + 0.998382i \(0.481890\pi\)
\(194\) 0 0
\(195\) −5120.65 2737.10i −1.88050 1.00517i
\(196\) 0 0
\(197\) 1252.94 0.453140 0.226570 0.973995i \(-0.427249\pi\)
0.226570 + 0.973995i \(0.427249\pi\)
\(198\) 0 0
\(199\) 4664.28i 1.66152i −0.556632 0.830759i \(-0.687907\pi\)
0.556632 0.830759i \(-0.312093\pi\)
\(200\) 0 0
\(201\) −1678.57 + 3140.32i −0.589041 + 1.10199i
\(202\) 0 0
\(203\) 64.9152i 0.0224441i
\(204\) 0 0
\(205\) 1749.14i 0.595928i
\(206\) 0 0
\(207\) 650.091 + 972.967i 0.218282 + 0.326695i
\(208\) 0 0
\(209\) 6340.50i 2.09848i
\(210\) 0 0
\(211\) −1845.39 −0.602095 −0.301047 0.953609i \(-0.597336\pi\)
−0.301047 + 0.953609i \(0.597336\pi\)
\(212\) 0 0
\(213\) 2049.04 3833.39i 0.659144 1.23314i
\(214\) 0 0
\(215\) −2079.23 −0.659546
\(216\) 0 0
\(217\) 21.3576 0.00668132
\(218\) 0 0
\(219\) 700.376 1310.28i 0.216105 0.404296i
\(220\) 0 0
\(221\) 4100.58 1.24812
\(222\) 0 0
\(223\) 2965.36i 0.890473i −0.895413 0.445237i \(-0.853120\pi\)
0.895413 0.445237i \(-0.146880\pi\)
\(224\) 0 0
\(225\) −2604.64 3898.26i −0.771744 1.15504i
\(226\) 0 0
\(227\) 1538.99i 0.449983i −0.974361 0.224991i \(-0.927765\pi\)
0.974361 0.224991i \(-0.0722354\pi\)
\(228\) 0 0
\(229\) 1658.05i 0.478460i 0.970963 + 0.239230i \(0.0768950\pi\)
−0.970963 + 0.239230i \(0.923105\pi\)
\(230\) 0 0
\(231\) −27.1939 + 50.8752i −0.00774558 + 0.0144907i
\(232\) 0 0
\(233\) 1241.69i 0.349123i 0.984646 + 0.174561i \(0.0558507\pi\)
−0.984646 + 0.174561i \(0.944149\pi\)
\(234\) 0 0
\(235\) 5068.34 1.40690
\(236\) 0 0
\(237\) 4311.63 + 2304.66i 1.18173 + 0.631662i
\(238\) 0 0
\(239\) −2373.58 −0.642401 −0.321201 0.947011i \(-0.604086\pi\)
−0.321201 + 0.947011i \(0.604086\pi\)
\(240\) 0 0
\(241\) 2592.35 0.692896 0.346448 0.938069i \(-0.387388\pi\)
0.346448 + 0.938069i \(0.387388\pi\)
\(242\) 0 0
\(243\) 2402.95 + 2928.27i 0.634359 + 0.773038i
\(244\) 0 0
\(245\) −5926.22 −1.54536
\(246\) 0 0
\(247\) 9959.41i 2.56559i
\(248\) 0 0
\(249\) 4633.49 + 2476.71i 1.17926 + 0.630341i
\(250\) 0 0
\(251\) 2750.30i 0.691624i 0.938304 + 0.345812i \(0.112397\pi\)
−0.938304 + 0.345812i \(0.887603\pi\)
\(252\) 0 0
\(253\) 1784.07i 0.443335i
\(254\) 0 0
\(255\) 5022.17 + 2684.46i 1.23334 + 0.659245i
\(256\) 0 0
\(257\) 218.163i 0.0529519i −0.999649 0.0264759i \(-0.991571\pi\)
0.999649 0.0264759i \(-0.00842854\pi\)
\(258\) 0 0
\(259\) −35.7676 −0.00858104
\(260\) 0 0
\(261\) −3610.53 5403.75i −0.856269 1.28155i
\(262\) 0 0
\(263\) −7341.25 −1.72122 −0.860611 0.509264i \(-0.829918\pi\)
−0.860611 + 0.509264i \(0.829918\pi\)
\(264\) 0 0
\(265\) −106.788 −0.0247544
\(266\) 0 0
\(267\) 1981.98 + 1059.41i 0.454289 + 0.242828i
\(268\) 0 0
\(269\) 54.3577 0.0123206 0.00616031 0.999981i \(-0.498039\pi\)
0.00616031 + 0.999981i \(0.498039\pi\)
\(270\) 0 0
\(271\) 3633.43i 0.814446i −0.913329 0.407223i \(-0.866497\pi\)
0.913329 0.407223i \(-0.133503\pi\)
\(272\) 0 0
\(273\) −42.7152 + 79.9127i −0.00946974 + 0.0177163i
\(274\) 0 0
\(275\) 7148.02i 1.56742i
\(276\) 0 0
\(277\) 6204.12i 1.34574i 0.739762 + 0.672868i \(0.234938\pi\)
−0.739762 + 0.672868i \(0.765062\pi\)
\(278\) 0 0
\(279\) −1777.87 + 1187.89i −0.381500 + 0.254900i
\(280\) 0 0
\(281\) 5651.49i 1.19979i −0.800081 0.599893i \(-0.795210\pi\)
0.800081 0.599893i \(-0.204790\pi\)
\(282\) 0 0
\(283\) −5857.07 −1.23027 −0.615136 0.788421i \(-0.710899\pi\)
−0.615136 + 0.788421i \(0.710899\pi\)
\(284\) 0 0
\(285\) −6519.96 + 12197.7i −1.35512 + 2.53520i
\(286\) 0 0
\(287\) −27.2970 −0.00561426
\(288\) 0 0
\(289\) 891.279 0.181412
\(290\) 0 0
\(291\) 2467.33 4615.96i 0.497037 0.929870i
\(292\) 0 0
\(293\) 5395.42 1.07578 0.537891 0.843015i \(-0.319221\pi\)
0.537891 + 0.843015i \(0.319221\pi\)
\(294\) 0 0
\(295\) 791.927i 0.156298i
\(296\) 0 0
\(297\) −565.927 5747.52i −0.110567 1.12291i
\(298\) 0 0
\(299\) 2802.35i 0.542021i
\(300\) 0 0
\(301\) 32.4484i 0.00621361i
\(302\) 0 0
\(303\) 2981.23 5577.38i 0.565239 1.05747i
\(304\) 0 0
\(305\) 11254.1i 2.11281i
\(306\) 0 0
\(307\) 8188.99 1.52238 0.761189 0.648530i \(-0.224616\pi\)
0.761189 + 0.648530i \(0.224616\pi\)
\(308\) 0 0
\(309\) 6221.32 + 3325.44i 1.14537 + 0.612225i
\(310\) 0 0
\(311\) 1838.42 0.335200 0.167600 0.985855i \(-0.446398\pi\)
0.167600 + 0.985855i \(0.446398\pi\)
\(312\) 0 0
\(313\) −293.079 −0.0529259 −0.0264629 0.999650i \(-0.508424\pi\)
−0.0264629 + 0.999650i \(0.508424\pi\)
\(314\) 0 0
\(315\) −104.630 + 69.9091i −0.0187151 + 0.0125045i
\(316\) 0 0
\(317\) 1343.02 0.237954 0.118977 0.992897i \(-0.462039\pi\)
0.118977 + 0.992897i \(0.462039\pi\)
\(318\) 0 0
\(319\) 9908.53i 1.73909i
\(320\) 0 0
\(321\) 6828.84 + 3650.17i 1.18738 + 0.634680i
\(322\) 0 0
\(323\) 9767.87i 1.68266i
\(324\) 0 0
\(325\) 11227.8i 1.91633i
\(326\) 0 0
\(327\) −8550.67 4570.53i −1.44603 0.772938i
\(328\) 0 0
\(329\) 79.0963i 0.0132545i
\(330\) 0 0
\(331\) −8825.95 −1.46561 −0.732807 0.680437i \(-0.761790\pi\)
−0.732807 + 0.680437i \(0.761790\pi\)
\(332\) 0 0
\(333\) 2977.41 1989.36i 0.489973 0.327377i
\(334\) 0 0
\(335\) 11842.4 1.93140
\(336\) 0 0
\(337\) 3842.48 0.621108 0.310554 0.950556i \(-0.399485\pi\)
0.310554 + 0.950556i \(0.399485\pi\)
\(338\) 0 0
\(339\) 4801.00 + 2566.24i 0.769187 + 0.411148i
\(340\) 0 0
\(341\) 3259.98 0.517706
\(342\) 0 0
\(343\) 184.988i 0.0291208i
\(344\) 0 0
\(345\) 1834.57 3432.17i 0.286290 0.535599i
\(346\) 0 0
\(347\) 9565.43i 1.47983i 0.672703 + 0.739913i \(0.265133\pi\)
−0.672703 + 0.739913i \(0.734867\pi\)
\(348\) 0 0
\(349\) 7514.35i 1.15253i −0.817262 0.576266i \(-0.804509\pi\)
0.817262 0.576266i \(-0.195491\pi\)
\(350\) 0 0
\(351\) −888.936 9027.97i −0.135179 1.37287i
\(352\) 0 0
\(353\) 4302.30i 0.648693i 0.945938 + 0.324346i \(0.105144\pi\)
−0.945938 + 0.324346i \(0.894856\pi\)
\(354\) 0 0
\(355\) −14456.0 −2.16126
\(356\) 0 0
\(357\) 41.8937 78.3758i 0.00621078 0.0116193i
\(358\) 0 0
\(359\) −2543.75 −0.373967 −0.186983 0.982363i \(-0.559871\pi\)
−0.186983 + 0.982363i \(0.559871\pi\)
\(360\) 0 0
\(361\) 16865.0 2.45881
\(362\) 0 0
\(363\) −890.560 + 1666.09i −0.128767 + 0.240900i
\(364\) 0 0
\(365\) −4941.19 −0.708585
\(366\) 0 0
\(367\) 5291.35i 0.752606i −0.926497 0.376303i \(-0.877195\pi\)
0.926497 0.376303i \(-0.122805\pi\)
\(368\) 0 0
\(369\) 2272.29 1518.24i 0.320571 0.214191i
\(370\) 0 0
\(371\) 1.66653i 0.000233213i
\(372\) 0 0
\(373\) 7860.77i 1.09119i 0.838048 + 0.545597i \(0.183697\pi\)
−0.838048 + 0.545597i \(0.816303\pi\)
\(374\) 0 0
\(375\) −2059.05 + 3852.13i −0.283543 + 0.530461i
\(376\) 0 0
\(377\) 15563.9i 2.12622i
\(378\) 0 0
\(379\) 3577.47 0.484861 0.242431 0.970169i \(-0.422055\pi\)
0.242431 + 0.970169i \(0.422055\pi\)
\(380\) 0 0
\(381\) 4735.09 + 2531.01i 0.636709 + 0.340335i
\(382\) 0 0
\(383\) 9144.30 1.21998 0.609990 0.792409i \(-0.291174\pi\)
0.609990 + 0.792409i \(0.291174\pi\)
\(384\) 0 0
\(385\) 191.855 0.0253969
\(386\) 0 0
\(387\) −1804.75 2701.11i −0.237056 0.354794i
\(388\) 0 0
\(389\) 12996.7 1.69398 0.846989 0.531611i \(-0.178413\pi\)
0.846989 + 0.531611i \(0.178413\pi\)
\(390\) 0 0
\(391\) 2748.46i 0.355487i
\(392\) 0 0
\(393\) −1648.01 880.900i −0.211530 0.113067i
\(394\) 0 0
\(395\) 16259.5i 2.07115i
\(396\) 0 0
\(397\) 2309.36i 0.291949i 0.989288 + 0.145974i \(0.0466317\pi\)
−0.989288 + 0.145974i \(0.953368\pi\)
\(398\) 0 0
\(399\) 190.357 + 101.750i 0.0238842 + 0.0127666i
\(400\) 0 0
\(401\) 4913.59i 0.611903i −0.952047 0.305951i \(-0.901026\pi\)
0.952047 0.305951i \(-0.0989745\pi\)
\(402\) 0 0
\(403\) 5120.65 0.632947
\(404\) 0 0
\(405\) 4821.48 11638.9i 0.591558 1.42801i
\(406\) 0 0
\(407\) −5459.50 −0.664907
\(408\) 0 0
\(409\) −3643.58 −0.440497 −0.220248 0.975444i \(-0.570687\pi\)
−0.220248 + 0.975444i \(0.570687\pi\)
\(410\) 0 0
\(411\) 1737.92 + 928.958i 0.208577 + 0.111489i
\(412\) 0 0
\(413\) 12.3588 0.00147249
\(414\) 0 0
\(415\) 17473.3i 2.06682i
\(416\) 0 0
\(417\) −4860.00 + 9092.23i −0.570732 + 1.06774i
\(418\) 0 0
\(419\) 7200.87i 0.839583i −0.907621 0.419792i \(-0.862103\pi\)
0.907621 0.419792i \(-0.137897\pi\)
\(420\) 0 0
\(421\) 6441.62i 0.745713i 0.927889 + 0.372857i \(0.121622\pi\)
−0.927889 + 0.372857i \(0.878378\pi\)
\(422\) 0 0
\(423\) 4399.27 + 6584.23i 0.505674 + 0.756823i
\(424\) 0 0
\(425\) 11011.9i 1.25684i
\(426\) 0 0
\(427\) −175.631 −0.0199049
\(428\) 0 0
\(429\) −6519.96 + 12197.7i −0.733769 + 1.37276i
\(430\) 0 0
\(431\) 5306.42 0.593043 0.296521 0.955026i \(-0.404173\pi\)
0.296521 + 0.955026i \(0.404173\pi\)
\(432\) 0 0
\(433\) 2336.16 0.259281 0.129640 0.991561i \(-0.458618\pi\)
0.129640 + 0.991561i \(0.458618\pi\)
\(434\) 0 0
\(435\) −10189.0 + 19061.8i −1.12304 + 2.10102i
\(436\) 0 0
\(437\) −6675.39 −0.730726
\(438\) 0 0
\(439\) 286.123i 0.0311068i 0.999879 + 0.0155534i \(0.00495100\pi\)
−0.999879 + 0.0155534i \(0.995049\pi\)
\(440\) 0 0
\(441\) −5143.91 7698.70i −0.555438 0.831303i
\(442\) 0 0
\(443\) 8021.59i 0.860309i −0.902755 0.430155i \(-0.858459\pi\)
0.902755 0.430155i \(-0.141541\pi\)
\(444\) 0 0
\(445\) 7474.21i 0.796205i
\(446\) 0 0
\(447\) −5690.48 + 10645.9i −0.602126 + 1.12647i
\(448\) 0 0
\(449\) 12605.3i 1.32491i −0.749103 0.662453i \(-0.769515\pi\)
0.749103 0.662453i \(-0.230485\pi\)
\(450\) 0 0
\(451\) −4166.57 −0.435024
\(452\) 0 0
\(453\) −11975.9 6401.40i −1.24211 0.663938i
\(454\) 0 0
\(455\) 301.358 0.0310502
\(456\) 0 0
\(457\) −5652.98 −0.578633 −0.289317 0.957233i \(-0.593428\pi\)
−0.289317 + 0.957233i \(0.593428\pi\)
\(458\) 0 0
\(459\) 871.840 + 8854.35i 0.0886580 + 0.900404i
\(460\) 0 0
\(461\) 2094.76 0.211633 0.105817 0.994386i \(-0.466254\pi\)
0.105817 + 0.994386i \(0.466254\pi\)
\(462\) 0 0
\(463\) 7783.64i 0.781288i 0.920542 + 0.390644i \(0.127748\pi\)
−0.920542 + 0.390644i \(0.872252\pi\)
\(464\) 0 0
\(465\) 6271.49 + 3352.25i 0.625448 + 0.334316i
\(466\) 0 0
\(467\) 12864.3i 1.27470i 0.770573 + 0.637352i \(0.219970\pi\)
−0.770573 + 0.637352i \(0.780030\pi\)
\(468\) 0 0
\(469\) 184.812i 0.0181958i
\(470\) 0 0
\(471\) −12741.4 6810.58i −1.24648 0.666273i
\(472\) 0 0
\(473\) 4952.87i 0.481465i
\(474\) 0 0
\(475\) 26745.4 2.58350
\(476\) 0 0
\(477\) −92.6910 138.727i −0.00889733 0.0133163i
\(478\) 0 0
\(479\) 8397.65 0.801040 0.400520 0.916288i \(-0.368829\pi\)
0.400520 + 0.916288i \(0.368829\pi\)
\(480\) 0 0
\(481\) −8575.56 −0.812915
\(482\) 0 0
\(483\) −53.5623 28.6302i −0.00504590 0.00269715i
\(484\) 0 0
\(485\) −17407.2 −1.62973
\(486\) 0 0
\(487\) 9622.06i 0.895313i 0.894206 + 0.447656i \(0.147741\pi\)
−0.894206 + 0.447656i \(0.852259\pi\)
\(488\) 0 0
\(489\) 1556.15 2911.28i 0.143909 0.269228i
\(490\) 0 0
\(491\) 3382.57i 0.310902i −0.987844 0.155451i \(-0.950317\pi\)
0.987844 0.155451i \(-0.0496831\pi\)
\(492\) 0 0
\(493\) 15264.6i 1.39449i
\(494\) 0 0
\(495\) −15970.6 + 10670.8i −1.45015 + 0.968922i
\(496\) 0 0
\(497\) 225.601i 0.0203613i
\(498\) 0 0
\(499\) 12894.7 1.15681 0.578403 0.815751i \(-0.303676\pi\)
0.578403 + 0.815751i \(0.303676\pi\)
\(500\) 0 0
\(501\) −782.664 + 1464.23i −0.0697941 + 0.130573i
\(502\) 0 0
\(503\) 1741.55 0.154377 0.0771885 0.997017i \(-0.475406\pi\)
0.0771885 + 0.997017i \(0.475406\pi\)
\(504\) 0 0
\(505\) −21032.8 −1.85336
\(506\) 0 0
\(507\) −4859.77 + 9091.80i −0.425700 + 0.796412i
\(508\) 0 0
\(509\) −5025.21 −0.437600 −0.218800 0.975770i \(-0.570214\pi\)
−0.218800 + 0.975770i \(0.570214\pi\)
\(510\) 0 0
\(511\) 77.1120i 0.00667561i
\(512\) 0 0
\(513\) −21505.2 + 2117.51i −1.85084 + 0.182242i
\(514\) 0 0
\(515\) 23461.1i 2.00742i
\(516\) 0 0
\(517\) 12073.1i 1.02703i
\(518\) 0 0
\(519\) −4562.69 + 8536.02i −0.385896 + 0.721945i
\(520\) 0 0
\(521\) 19105.2i 1.60656i 0.595605 + 0.803278i \(0.296913\pi\)
−0.595605 + 0.803278i \(0.703087\pi\)
\(522\) 0 0
\(523\) −2025.34 −0.169334 −0.0846671 0.996409i \(-0.526983\pi\)
−0.0846671 + 0.996409i \(0.526983\pi\)
\(524\) 0 0
\(525\) 214.601 + 114.709i 0.0178399 + 0.00953584i
\(526\) 0 0
\(527\) −5022.17 −0.415122
\(528\) 0 0
\(529\) −10288.7 −0.845623
\(530\) 0 0
\(531\) −1028.79 + 687.386i −0.0840781 + 0.0561771i
\(532\) 0 0
\(533\) −6544.68 −0.531860
\(534\) 0 0
\(535\) 25752.1i 2.08105i
\(536\) 0 0
\(537\) 18084.8 + 9666.75i 1.45329 + 0.776818i
\(538\) 0 0
\(539\) 14116.7i 1.12810i
\(540\) 0 0
\(541\) 1585.39i 0.125991i 0.998014 + 0.0629955i \(0.0200654\pi\)
−0.998014 + 0.0629955i \(0.979935\pi\)
\(542\) 0 0
\(543\) −5439.57 2907.57i −0.429898 0.229790i
\(544\) 0 0
\(545\) 32245.3i 2.53438i
\(546\) 0 0
\(547\) 4480.61 0.350232 0.175116 0.984548i \(-0.443970\pi\)
0.175116 + 0.984548i \(0.443970\pi\)
\(548\) 0 0
\(549\) 14620.1 9768.45i 1.13656 0.759394i
\(550\) 0 0
\(551\) 37074.3 2.86646
\(552\) 0 0
\(553\) −253.745 −0.0195124
\(554\) 0 0
\(555\) −10502.9 5614.02i −0.803283 0.429373i
\(556\) 0 0
\(557\) 12069.6 0.918139 0.459070 0.888400i \(-0.348183\pi\)
0.459070 + 0.888400i \(0.348183\pi\)
\(558\) 0 0
\(559\) 7779.77i 0.588639i
\(560\) 0 0
\(561\) 6394.57 11963.1i 0.481246 0.900329i
\(562\) 0 0
\(563\) 6218.25i 0.465485i 0.972538 + 0.232742i \(0.0747699\pi\)
−0.972538 + 0.232742i \(0.925230\pi\)
\(564\) 0 0
\(565\) 18105.0i 1.34811i
\(566\) 0 0
\(567\) −181.636 75.2438i −0.0134533 0.00557309i
\(568\) 0 0
\(569\) 7681.87i 0.565977i −0.959123 0.282988i \(-0.908674\pi\)
0.959123 0.282988i \(-0.0913258\pi\)
\(570\) 0 0
\(571\) −21206.3 −1.55421 −0.777105 0.629371i \(-0.783313\pi\)
−0.777105 + 0.629371i \(0.783313\pi\)
\(572\) 0 0
\(573\) 2811.93 5260.63i 0.205008 0.383536i
\(574\) 0 0
\(575\) −7525.56 −0.545804
\(576\) 0 0
\(577\) 9075.07 0.654766 0.327383 0.944892i \(-0.393833\pi\)
0.327383 + 0.944892i \(0.393833\pi\)
\(578\) 0 0
\(579\) 746.931 1397.38i 0.0536121 0.100299i
\(580\) 0 0
\(581\) −272.688 −0.0194716
\(582\) 0 0
\(583\) 254.376i 0.0180706i
\(584\) 0 0
\(585\) −25086.0 + 16761.3i −1.77295 + 1.18460i
\(586\) 0 0
\(587\) 15653.2i 1.10064i −0.834954 0.550320i \(-0.814506\pi\)
0.834954 0.550320i \(-0.185494\pi\)
\(588\) 0 0
\(589\) 12197.7i 0.853309i
\(590\) 0 0
\(591\) 3069.08 5741.72i 0.213612 0.399632i
\(592\) 0 0
\(593\) 1646.23i 0.114001i −0.998374 0.0570003i \(-0.981846\pi\)
0.998374 0.0570003i \(-0.0181536\pi\)
\(594\) 0 0
\(595\) −295.562 −0.0203645
\(596\) 0 0
\(597\) −21374.4 11425.1i −1.46532 0.783247i
\(598\) 0 0
\(599\) 6400.85 0.436614 0.218307 0.975880i \(-0.429947\pi\)
0.218307 + 0.975880i \(0.429947\pi\)
\(600\) 0 0
\(601\) 1282.48 0.0870443 0.0435222 0.999052i \(-0.486142\pi\)
0.0435222 + 0.999052i \(0.486142\pi\)
\(602\) 0 0
\(603\) 10279.1 + 15384.3i 0.694191 + 1.03897i
\(604\) 0 0
\(605\) 6282.95 0.422212
\(606\) 0 0
\(607\) 5242.27i 0.350539i 0.984521 + 0.175269i \(0.0560796\pi\)
−0.984521 + 0.175269i \(0.943920\pi\)
\(608\) 0 0
\(609\) 297.479 + 159.009i 0.0197938 + 0.0105802i
\(610\) 0 0
\(611\) 18964.0i 1.25565i
\(612\) 0 0
\(613\) 9985.56i 0.657933i −0.944342 0.328966i \(-0.893300\pi\)
0.944342 0.328966i \(-0.106700\pi\)
\(614\) 0 0
\(615\) −8015.56 4284.50i −0.525559 0.280923i
\(616\) 0 0
\(617\) 26504.8i 1.72941i −0.502283 0.864703i \(-0.667507\pi\)
0.502283 0.864703i \(-0.332493\pi\)
\(618\) 0 0
\(619\) −22327.0 −1.44976 −0.724878 0.688877i \(-0.758104\pi\)
−0.724878 + 0.688877i \(0.758104\pi\)
\(620\) 0 0
\(621\) 6051.09 595.818i 0.391017 0.0385014i
\(622\) 0 0
\(623\) −116.642 −0.00750108
\(624\) 0 0
\(625\) −7178.61 −0.459431
\(626\) 0 0
\(627\) 29055.8 + 15531.0i 1.85068 + 0.989231i
\(628\) 0 0
\(629\) 8410.64 0.533154
\(630\) 0 0
\(631\) 5040.02i 0.317971i −0.987281 0.158986i \(-0.949178\pi\)
0.987281 0.158986i \(-0.0508224\pi\)
\(632\) 0 0
\(633\) −4520.27 + 8456.64i −0.283830 + 0.530998i
\(634\) 0 0
\(635\) 17856.4i 1.11592i
\(636\) 0 0
\(637\) 22173.9i 1.37922i
\(638\) 0 0
\(639\) −12547.7 18779.7i −0.776808 1.16262i
\(640\) 0 0
\(641\) 8994.13i 0.554207i 0.960840 + 0.277104i \(0.0893745\pi\)
−0.960840 + 0.277104i \(0.910626\pi\)
\(642\) 0 0
\(643\) −8789.99 −0.539103 −0.269551 0.962986i \(-0.586875\pi\)
−0.269551 + 0.962986i \(0.586875\pi\)
\(644\) 0 0
\(645\) −5093.05 + 9528.23i −0.310913 + 0.581665i
\(646\) 0 0
\(647\) 14441.6 0.877523 0.438762 0.898603i \(-0.355417\pi\)
0.438762 + 0.898603i \(0.355417\pi\)
\(648\) 0 0
\(649\) 1886.42 0.114096
\(650\) 0 0
\(651\) 52.3152 97.8727i 0.00314961 0.00589237i
\(652\) 0 0
\(653\) −16798.8 −1.00672 −0.503359 0.864078i \(-0.667903\pi\)
−0.503359 + 0.864078i \(0.667903\pi\)
\(654\) 0 0
\(655\) 6214.79i 0.370736i
\(656\) 0 0
\(657\) −4288.91 6419.05i −0.254682 0.381174i
\(658\) 0 0
\(659\) 10301.3i 0.608928i −0.952524 0.304464i \(-0.901523\pi\)
0.952524 0.304464i \(-0.0984773\pi\)
\(660\) 0 0
\(661\) 31766.9i 1.86927i 0.355609 + 0.934635i \(0.384274\pi\)
−0.355609 + 0.934635i \(0.615726\pi\)
\(662\) 0 0
\(663\) 10044.3 18791.2i 0.588371 1.10074i
\(664\) 0 0
\(665\) 717.854i 0.0418604i
\(666\) 0 0
\(667\) −10431.9 −0.605583
\(668\) 0 0
\(669\) −13589.0 7263.63i −0.785323 0.419773i
\(670\) 0 0
\(671\) −26808.0 −1.54234
\(672\) 0 0
\(673\) −12707.8 −0.727861 −0.363930 0.931426i \(-0.618565\pi\)
−0.363930 + 0.931426i \(0.618565\pi\)
\(674\) 0 0
\(675\) −24244.1 + 2387.19i −1.38245 + 0.136123i
\(676\) 0 0
\(677\) −19127.6 −1.08587 −0.542936 0.839774i \(-0.682687\pi\)
−0.542936 + 0.839774i \(0.682687\pi\)
\(678\) 0 0
\(679\) 271.656i 0.0153537i
\(680\) 0 0
\(681\) −7052.52 3769.73i −0.396848 0.212124i
\(682\) 0 0
\(683\) 14069.0i 0.788191i 0.919069 + 0.394096i \(0.128942\pi\)
−0.919069 + 0.394096i \(0.871058\pi\)
\(684\) 0 0
\(685\) 6553.84i 0.365561i
\(686\) 0 0
\(687\) 7598.16 + 4061.39i 0.421962 + 0.225548i
\(688\) 0 0
\(689\) 399.564i 0.0220931i
\(690\) 0 0
\(691\) −19159.5 −1.05479 −0.527396 0.849620i \(-0.676831\pi\)
−0.527396 + 0.849620i \(0.676831\pi\)
\(692\) 0 0
\(693\) 166.528 + 249.236i 0.00912825 + 0.0136619i
\(694\) 0 0
\(695\) 34287.5 1.87137
\(696\) 0 0
\(697\) 6418.81 0.348823
\(698\) 0 0
\(699\) 5690.12 + 3041.50i 0.307897 + 0.164578i
\(700\) 0 0
\(701\) −24736.8 −1.33281 −0.666403 0.745592i \(-0.732167\pi\)
−0.666403 + 0.745592i \(0.732167\pi\)
\(702\) 0 0
\(703\) 20427.6i 1.09593i
\(704\) 0 0
\(705\) 12414.8 23226.0i 0.663220 1.24077i
\(706\) 0 0
\(707\) 328.237i 0.0174605i
\(708\) 0 0
\(709\) 10627.5i 0.562937i 0.959570 + 0.281469i \(0.0908216\pi\)
−0.959570 + 0.281469i \(0.909178\pi\)
\(710\) 0 0
\(711\) 21122.6 14113.1i 1.11415 0.744420i
\(712\) 0 0
\(713\) 3432.17i 0.180274i
\(714\) 0 0
\(715\) 45998.7 2.40595
\(716\) 0 0
\(717\) −5814.05 + 10877.1i −0.302831 + 0.566544i
\(718\) 0 0
\(719\) −8256.38 −0.428249 −0.214124 0.976806i \(-0.568690\pi\)
−0.214124 + 0.976806i \(0.568690\pi\)
\(720\) 0 0
\(721\) −366.134 −0.0189120
\(722\) 0 0
\(723\) 6349.94 11879.6i 0.326635 0.611077i
\(724\) 0 0
\(725\) 41796.1 2.14106
\(726\) 0 0
\(727\) 21457.7i 1.09466i 0.836916 + 0.547332i \(0.184356\pi\)
−0.836916 + 0.547332i \(0.815644\pi\)
\(728\) 0 0
\(729\) 19305.0 3838.94i 0.980796 0.195038i
\(730\) 0 0
\(731\) 7630.15i 0.386062i
\(732\) 0 0
\(733\) 12687.2i 0.639307i −0.947534 0.319654i \(-0.896433\pi\)
0.947534 0.319654i \(-0.103567\pi\)
\(734\) 0 0
\(735\) −14516.2 + 27157.4i −0.728488 + 1.36288i
\(736\) 0 0
\(737\) 28209.4i 1.40991i
\(738\) 0 0
\(739\) −7599.74 −0.378296 −0.189148 0.981949i \(-0.560573\pi\)
−0.189148 + 0.981949i \(0.560573\pi\)
\(740\) 0 0
\(741\) 45639.7 + 24395.5i 2.26264 + 1.20943i
\(742\) 0 0
\(743\) −34061.2 −1.68181 −0.840904 0.541185i \(-0.817976\pi\)
−0.840904 + 0.541185i \(0.817976\pi\)
\(744\) 0 0
\(745\) 40146.6 1.97431
\(746\) 0 0
\(747\) 22699.4 15166.7i 1.11182 0.742864i
\(748\) 0 0
\(749\) −401.887 −0.0196056
\(750\) 0 0
\(751\) 7091.67i 0.344579i −0.985046 0.172289i \(-0.944884\pi\)
0.985046 0.172289i \(-0.0551164\pi\)
\(752\) 0 0
\(753\) 12603.5 + 6736.84i 0.609955 + 0.326035i
\(754\) 0 0
\(755\) 45162.2i 2.17698i
\(756\) 0 0
\(757\) 10128.2i 0.486282i −0.969991 0.243141i \(-0.921822\pi\)
0.969991 0.243141i \(-0.0781778\pi\)
\(758\) 0 0
\(759\) −8175.65 4370.07i −0.390984 0.208990i
\(760\) 0 0
\(761\) 22747.8i 1.08358i −0.840513 0.541792i \(-0.817746\pi\)
0.840513 0.541792i \(-0.182254\pi\)
\(762\) 0 0
\(763\) 503.219 0.0238765
\(764\) 0 0
\(765\) 24603.5 16438.9i 1.16280 0.776928i
\(766\) 0 0
\(767\) 2963.12 0.139494
\(768\) 0 0
\(769\) 30168.9 1.41472 0.707359 0.706855i \(-0.249887\pi\)
0.707359 + 0.706855i \(0.249887\pi\)
\(770\) 0 0
\(771\) −999.748 534.388i −0.0466992 0.0249617i
\(772\) 0 0
\(773\) 12592.8 0.585940 0.292970 0.956122i \(-0.405356\pi\)
0.292970 + 0.956122i \(0.405356\pi\)
\(774\) 0 0
\(775\) 13751.2i 0.637366i
\(776\) 0 0
\(777\) −87.6123 + 163.908i −0.00404514 + 0.00756776i
\(778\) 0 0
\(779\) 15589.9i 0.717028i
\(780\) 0 0
\(781\) 34435.3i 1.57771i
\(782\) 0 0
\(783\) −33607.0 + 3309.10i −1.53387 + 0.151032i
\(784\) 0 0
\(785\) 48049.0i 2.18464i
\(786\) 0 0
\(787\) 14594.4 0.661036 0.330518 0.943800i \(-0.392777\pi\)
0.330518 + 0.943800i \(0.392777\pi\)
\(788\) 0 0
\(789\) −17982.3 + 33641.9i −0.811391 + 1.51797i
\(790\) 0 0
\(791\) −282.546 −0.0127006
\(792\) 0 0
\(793\) −42108.9 −1.88567
\(794\) 0 0
\(795\) −261.576 + 489.364i −0.0116694 + 0.0218314i
\(796\) 0 0
\(797\) 36750.1 1.63332 0.816661 0.577118i \(-0.195823\pi\)