Properties

Label 384.3.e.c.257.1
Level $384$
Weight $3$
Character 384.257
Analytic conductor $10.463$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} + \cdots)\)
Defining polynomial: \(x^{8} + 18 x^{6} + 99 x^{4} + 170 x^{2} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{10}\cdot 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 257.1
Root \(1.32750i\) of defining polynomial
Character \(\chi\) \(=\) 384.257
Dual form 384.3.e.c.257.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.69031 - 1.32750i) q^{3} +0.640013i q^{5} -2.72077 q^{7} +(5.47550 + 7.14275i) q^{9} +O(q^{10})\) \(q+(-2.69031 - 1.32750i) q^{3} +0.640013i q^{5} -2.72077 q^{7} +(5.47550 + 7.14275i) q^{9} -11.2836i q^{11} -5.25176 q^{13} +(0.849616 - 1.72183i) q^{15} +14.8718i q^{17} -15.0798 q^{19} +(7.31969 + 3.61181i) q^{21} +36.4411i q^{23} +24.5904 q^{25} +(-5.24877 - 26.4849i) q^{27} +51.7310i q^{29} +36.5009 q^{31} +(-14.9790 + 30.3565i) q^{33} -1.74133i q^{35} +63.6951 q^{37} +(14.1289 + 6.97170i) q^{39} -12.1500i q^{41} +11.8032 q^{43} +(-4.57146 + 3.50439i) q^{45} +61.1247i q^{47} -41.5974 q^{49} +(19.7423 - 40.0097i) q^{51} +59.1695i q^{53} +7.22168 q^{55} +(40.5694 + 20.0185i) q^{57} +37.2898i q^{59} -58.1987 q^{61} +(-14.8975 - 19.4338i) q^{63} -3.36120i q^{65} -23.0991 q^{67} +(48.3754 - 98.0376i) q^{69} +7.29656i q^{71} +73.4504 q^{73} +(-66.1557 - 32.6437i) q^{75} +30.7002i q^{77} -58.5098 q^{79} +(-21.0379 + 78.2203i) q^{81} +32.3939i q^{83} -9.51815 q^{85} +(68.6728 - 139.172i) q^{87} -112.260i q^{89} +14.2888 q^{91} +(-98.1987 - 48.4549i) q^{93} -9.65130i q^{95} -80.0338 q^{97} +(80.5963 - 61.7836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} - 8q^{7} + O(q^{10}) \) \( 8q + 4q^{3} - 8q^{7} - 16q^{15} - 24q^{19} - 16q^{21} - 40q^{25} - 44q^{27} + 56q^{31} + 8q^{33} - 32q^{37} + 104q^{39} + 136q^{43} + 80q^{45} + 72q^{49} + 176q^{51} - 192q^{55} - 40q^{57} + 160q^{61} - 264q^{63} - 280q^{67} - 80q^{69} - 80q^{73} - 348q^{75} + 408q^{79} + 72q^{81} - 192q^{85} + 368q^{87} + 336q^{91} - 160q^{93} + 96q^{97} + 432q^{99} + O(q^{100}) \)

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
\(3\) −2.69031 1.32750i −0.896769 0.442499i
\(4\) 0 0
\(5\) 0.640013i 0.128003i 0.997950 + 0.0640013i \(0.0203862\pi\)
−0.997950 + 0.0640013i \(0.979614\pi\)
\(6\) 0 0
\(7\) −2.72077 −0.388681 −0.194340 0.980934i \(-0.562257\pi\)
−0.194340 + 0.980934i \(0.562257\pi\)
\(8\) 0 0
\(9\) 5.47550 + 7.14275i 0.608389 + 0.793639i
\(10\) 0 0
\(11\) 11.2836i 1.02579i −0.858452 0.512893i \(-0.828574\pi\)
0.858452 0.512893i \(-0.171426\pi\)
\(12\) 0 0
\(13\) −5.25176 −0.403982 −0.201991 0.979387i \(-0.564741\pi\)
−0.201991 + 0.979387i \(0.564741\pi\)
\(14\) 0 0
\(15\) 0.849616 1.72183i 0.0566411 0.114789i
\(16\) 0 0
\(17\) 14.8718i 0.874812i 0.899264 + 0.437406i \(0.144103\pi\)
−0.899264 + 0.437406i \(0.855897\pi\)
\(18\) 0 0
\(19\) −15.0798 −0.793676 −0.396838 0.917889i \(-0.629893\pi\)
−0.396838 + 0.917889i \(0.629893\pi\)
\(20\) 0 0
\(21\) 7.31969 + 3.61181i 0.348557 + 0.171991i
\(22\) 0 0
\(23\) 36.4411i 1.58439i 0.610266 + 0.792197i \(0.291063\pi\)
−0.610266 + 0.792197i \(0.708937\pi\)
\(24\) 0 0
\(25\) 24.5904 0.983615
\(26\) 0 0
\(27\) −5.24877 26.4849i −0.194399 0.980923i
\(28\) 0 0
\(29\) 51.7310i 1.78383i 0.452205 + 0.891914i \(0.350638\pi\)
−0.452205 + 0.891914i \(0.649362\pi\)
\(30\) 0 0
\(31\) 36.5009 1.17745 0.588724 0.808334i \(-0.299630\pi\)
0.588724 + 0.808334i \(0.299630\pi\)
\(32\) 0 0
\(33\) −14.9790 + 30.3565i −0.453910 + 0.919893i
\(34\) 0 0
\(35\) 1.74133i 0.0497522i
\(36\) 0 0
\(37\) 63.6951 1.72149 0.860745 0.509036i \(-0.169998\pi\)
0.860745 + 0.509036i \(0.169998\pi\)
\(38\) 0 0
\(39\) 14.1289 + 6.97170i 0.362278 + 0.178762i
\(40\) 0 0
\(41\) 12.1500i 0.296342i −0.988962 0.148171i \(-0.952661\pi\)
0.988962 0.148171i \(-0.0473386\pi\)
\(42\) 0 0
\(43\) 11.8032 0.274493 0.137247 0.990537i \(-0.456175\pi\)
0.137247 + 0.990537i \(0.456175\pi\)
\(44\) 0 0
\(45\) −4.57146 + 3.50439i −0.101588 + 0.0778753i
\(46\) 0 0
\(47\) 61.1247i 1.30053i 0.759709 + 0.650263i \(0.225341\pi\)
−0.759709 + 0.650263i \(0.774659\pi\)
\(48\) 0 0
\(49\) −41.5974 −0.848927
\(50\) 0 0
\(51\) 19.7423 40.0097i 0.387104 0.784504i
\(52\) 0 0
\(53\) 59.1695i 1.11641i 0.829705 + 0.558203i \(0.188509\pi\)
−0.829705 + 0.558203i \(0.811491\pi\)
\(54\) 0 0
\(55\) 7.22168 0.131303
\(56\) 0 0
\(57\) 40.5694 + 20.0185i 0.711744 + 0.351201i
\(58\) 0 0
\(59\) 37.2898i 0.632031i 0.948754 + 0.316016i \(0.102345\pi\)
−0.948754 + 0.316016i \(0.897655\pi\)
\(60\) 0 0
\(61\) −58.1987 −0.954076 −0.477038 0.878883i \(-0.658290\pi\)
−0.477038 + 0.878883i \(0.658290\pi\)
\(62\) 0 0
\(63\) −14.8975 19.4338i −0.236469 0.308472i
\(64\) 0 0
\(65\) 3.36120i 0.0517107i
\(66\) 0 0
\(67\) −23.0991 −0.344762 −0.172381 0.985030i \(-0.555146\pi\)
−0.172381 + 0.985030i \(0.555146\pi\)
\(68\) 0 0
\(69\) 48.3754 98.0376i 0.701093 1.42084i
\(70\) 0 0
\(71\) 7.29656i 0.102768i 0.998679 + 0.0513842i \(0.0163633\pi\)
−0.998679 + 0.0513842i \(0.983637\pi\)
\(72\) 0 0
\(73\) 73.4504 1.00617 0.503085 0.864237i \(-0.332198\pi\)
0.503085 + 0.864237i \(0.332198\pi\)
\(74\) 0 0
\(75\) −66.1557 32.6437i −0.882076 0.435249i
\(76\) 0 0
\(77\) 30.7002i 0.398703i
\(78\) 0 0
\(79\) −58.5098 −0.740630 −0.370315 0.928906i \(-0.620750\pi\)
−0.370315 + 0.928906i \(0.620750\pi\)
\(80\) 0 0
\(81\) −21.0379 + 78.2203i −0.259727 + 0.965682i
\(82\) 0 0
\(83\) 32.3939i 0.390287i 0.980775 + 0.195144i \(0.0625173\pi\)
−0.980775 + 0.195144i \(0.937483\pi\)
\(84\) 0 0
\(85\) −9.51815 −0.111978
\(86\) 0 0
\(87\) 68.6728 139.172i 0.789343 1.59968i
\(88\) 0 0
\(89\) 112.260i 1.26135i −0.776046 0.630677i \(-0.782777\pi\)
0.776046 0.630677i \(-0.217223\pi\)
\(90\) 0 0
\(91\) 14.2888 0.157020
\(92\) 0 0
\(93\) −98.1987 48.4549i −1.05590 0.521020i
\(94\) 0 0
\(95\) 9.65130i 0.101593i
\(96\) 0 0
\(97\) −80.0338 −0.825090 −0.412545 0.910937i \(-0.635360\pi\)
−0.412545 + 0.910937i \(0.635360\pi\)
\(98\) 0 0
\(99\) 80.5963 61.7836i 0.814104 0.624077i
\(100\) 0 0
\(101\) 119.373i 1.18191i −0.806705 0.590954i \(-0.798751\pi\)
0.806705 0.590954i \(-0.201249\pi\)
\(102\) 0 0
\(103\) −125.522 −1.21866 −0.609330 0.792917i \(-0.708562\pi\)
−0.609330 + 0.792917i \(0.708562\pi\)
\(104\) 0 0
\(105\) −2.31161 + 4.68470i −0.0220153 + 0.0446162i
\(106\) 0 0
\(107\) 148.669i 1.38943i 0.719284 + 0.694716i \(0.244470\pi\)
−0.719284 + 0.694716i \(0.755530\pi\)
\(108\) 0 0
\(109\) −70.6664 −0.648316 −0.324158 0.946003i \(-0.605081\pi\)
−0.324158 + 0.946003i \(0.605081\pi\)
\(110\) 0 0
\(111\) −171.359 84.5552i −1.54378 0.761758i
\(112\) 0 0
\(113\) 130.968i 1.15901i −0.814969 0.579504i \(-0.803246\pi\)
0.814969 0.579504i \(-0.196754\pi\)
\(114\) 0 0
\(115\) −23.3228 −0.202807
\(116\) 0 0
\(117\) −28.7560 37.5120i −0.245778 0.320616i
\(118\) 0 0
\(119\) 40.4627i 0.340023i
\(120\) 0 0
\(121\) −6.32073 −0.0522374
\(122\) 0 0
\(123\) −16.1291 + 32.6873i −0.131131 + 0.265750i
\(124\) 0 0
\(125\) 31.7385i 0.253908i
\(126\) 0 0
\(127\) 209.206 1.64729 0.823647 0.567103i \(-0.191936\pi\)
0.823647 + 0.567103i \(0.191936\pi\)
\(128\) 0 0
\(129\) −31.7543 15.6687i −0.246157 0.121463i
\(130\) 0 0
\(131\) 174.839i 1.33465i 0.744766 + 0.667326i \(0.232561\pi\)
−0.744766 + 0.667326i \(0.767439\pi\)
\(132\) 0 0
\(133\) 41.0287 0.308487
\(134\) 0 0
\(135\) 16.9507 3.35929i 0.125561 0.0248836i
\(136\) 0 0
\(137\) 162.945i 1.18938i −0.803956 0.594689i \(-0.797275\pi\)
0.803956 0.594689i \(-0.202725\pi\)
\(138\) 0 0
\(139\) 194.227 1.39732 0.698660 0.715454i \(-0.253780\pi\)
0.698660 + 0.715454i \(0.253780\pi\)
\(140\) 0 0
\(141\) 81.1429 164.444i 0.575482 1.16627i
\(142\) 0 0
\(143\) 59.2590i 0.414399i
\(144\) 0 0
\(145\) −33.1085 −0.228335
\(146\) 0 0
\(147\) 111.910 + 55.2205i 0.761291 + 0.375650i
\(148\) 0 0
\(149\) 83.4695i 0.560198i 0.959971 + 0.280099i \(0.0903673\pi\)
−0.959971 + 0.280099i \(0.909633\pi\)
\(150\) 0 0
\(151\) −60.3488 −0.399661 −0.199830 0.979830i \(-0.564039\pi\)
−0.199830 + 0.979830i \(0.564039\pi\)
\(152\) 0 0
\(153\) −106.226 + 81.4306i −0.694285 + 0.532226i
\(154\) 0 0
\(155\) 23.3611i 0.150717i
\(156\) 0 0
\(157\) 100.762 0.641798 0.320899 0.947113i \(-0.396015\pi\)
0.320899 + 0.947113i \(0.396015\pi\)
\(158\) 0 0
\(159\) 78.5474 159.184i 0.494009 1.00116i
\(160\) 0 0
\(161\) 99.1476i 0.615824i
\(162\) 0 0
\(163\) −69.7149 −0.427699 −0.213849 0.976867i \(-0.568600\pi\)
−0.213849 + 0.976867i \(0.568600\pi\)
\(164\) 0 0
\(165\) −19.4285 9.58677i −0.117749 0.0581016i
\(166\) 0 0
\(167\) 120.823i 0.723491i 0.932277 + 0.361745i \(0.117819\pi\)
−0.932277 + 0.361745i \(0.882181\pi\)
\(168\) 0 0
\(169\) −141.419 −0.836799
\(170\) 0 0
\(171\) −82.5697 107.712i −0.482863 0.629893i
\(172\) 0 0
\(173\) 30.0602i 0.173758i −0.996219 0.0868791i \(-0.972311\pi\)
0.996219 0.0868791i \(-0.0276894\pi\)
\(174\) 0 0
\(175\) −66.9047 −0.382312
\(176\) 0 0
\(177\) 49.5022 100.321i 0.279673 0.566786i
\(178\) 0 0
\(179\) 114.784i 0.641250i 0.947206 + 0.320625i \(0.103893\pi\)
−0.947206 + 0.320625i \(0.896107\pi\)
\(180\) 0 0
\(181\) −181.627 −1.00347 −0.501733 0.865022i \(-0.667304\pi\)
−0.501733 + 0.865022i \(0.667304\pi\)
\(182\) 0 0
\(183\) 156.572 + 77.2586i 0.855586 + 0.422178i
\(184\) 0 0
\(185\) 40.7657i 0.220355i
\(186\) 0 0
\(187\) 167.808 0.897370
\(188\) 0 0
\(189\) 14.2807 + 72.0592i 0.0755592 + 0.381266i
\(190\) 0 0
\(191\) 209.226i 1.09543i −0.836666 0.547713i \(-0.815498\pi\)
0.836666 0.547713i \(-0.184502\pi\)
\(192\) 0 0
\(193\) 161.330 0.835907 0.417954 0.908468i \(-0.362747\pi\)
0.417954 + 0.908468i \(0.362747\pi\)
\(194\) 0 0
\(195\) −4.46198 + 9.04265i −0.0228820 + 0.0463726i
\(196\) 0 0
\(197\) 144.953i 0.735801i 0.929865 + 0.367901i \(0.119923\pi\)
−0.929865 + 0.367901i \(0.880077\pi\)
\(198\) 0 0
\(199\) −237.264 −1.19228 −0.596140 0.802880i \(-0.703300\pi\)
−0.596140 + 0.802880i \(0.703300\pi\)
\(200\) 0 0
\(201\) 62.1436 + 30.6640i 0.309172 + 0.152557i
\(202\) 0 0
\(203\) 140.748i 0.693340i
\(204\) 0 0
\(205\) 7.77617 0.0379325
\(206\) 0 0
\(207\) −260.289 + 199.533i −1.25744 + 0.963927i
\(208\) 0 0
\(209\) 170.156i 0.814142i
\(210\) 0 0
\(211\) −307.117 −1.45553 −0.727765 0.685827i \(-0.759441\pi\)
−0.727765 + 0.685827i \(0.759441\pi\)
\(212\) 0 0
\(213\) 9.68617 19.6300i 0.0454750 0.0921595i
\(214\) 0 0
\(215\) 7.55422i 0.0351359i
\(216\) 0 0
\(217\) −99.3105 −0.457652
\(218\) 0 0
\(219\) −197.604 97.5053i −0.902302 0.445230i
\(220\) 0 0
\(221\) 78.1032i 0.353408i
\(222\) 0 0
\(223\) 438.001 1.96413 0.982065 0.188544i \(-0.0603770\pi\)
0.982065 + 0.188544i \(0.0603770\pi\)
\(224\) 0 0
\(225\) 134.645 + 175.643i 0.598420 + 0.780636i
\(226\) 0 0
\(227\) 270.755i 1.19275i −0.802705 0.596376i \(-0.796607\pi\)
0.802705 0.596376i \(-0.203393\pi\)
\(228\) 0 0
\(229\) −98.6778 −0.430907 −0.215454 0.976514i \(-0.569123\pi\)
−0.215454 + 0.976514i \(0.569123\pi\)
\(230\) 0 0
\(231\) 40.7544 82.5929i 0.176426 0.357545i
\(232\) 0 0
\(233\) 432.405i 1.85581i 0.372812 + 0.927907i \(0.378394\pi\)
−0.372812 + 0.927907i \(0.621606\pi\)
\(234\) 0 0
\(235\) −39.1206 −0.166471
\(236\) 0 0
\(237\) 157.409 + 77.6717i 0.664174 + 0.327729i
\(238\) 0 0
\(239\) 275.799i 1.15397i 0.816754 + 0.576986i \(0.195771\pi\)
−0.816754 + 0.576986i \(0.804229\pi\)
\(240\) 0 0
\(241\) 416.770 1.72934 0.864669 0.502343i \(-0.167528\pi\)
0.864669 + 0.502343i \(0.167528\pi\)
\(242\) 0 0
\(243\) 160.436 182.509i 0.660228 0.751065i
\(244\) 0 0
\(245\) 26.6229i 0.108665i
\(246\) 0 0
\(247\) 79.1958 0.320631
\(248\) 0 0
\(249\) 43.0028 87.1494i 0.172702 0.349998i
\(250\) 0 0
\(251\) 165.903i 0.660966i −0.943812 0.330483i \(-0.892788\pi\)
0.943812 0.330483i \(-0.107212\pi\)
\(252\) 0 0
\(253\) 411.188 1.62525
\(254\) 0 0
\(255\) 25.6068 + 12.6353i 0.100419 + 0.0495503i
\(256\) 0 0
\(257\) 59.6381i 0.232055i −0.993246 0.116028i \(-0.962984\pi\)
0.993246 0.116028i \(-0.0370161\pi\)
\(258\) 0 0
\(259\) −173.300 −0.669110
\(260\) 0 0
\(261\) −369.502 + 283.253i −1.41572 + 1.08526i
\(262\) 0 0
\(263\) 67.2606i 0.255744i 0.991791 + 0.127872i \(0.0408146\pi\)
−0.991791 + 0.127872i \(0.959185\pi\)
\(264\) 0 0
\(265\) −37.8693 −0.142903
\(266\) 0 0
\(267\) −149.026 + 302.015i −0.558148 + 1.13114i
\(268\) 0 0
\(269\) 36.1495i 0.134385i 0.997740 + 0.0671923i \(0.0214041\pi\)
−0.997740 + 0.0671923i \(0.978596\pi\)
\(270\) 0 0
\(271\) −328.311 −1.21148 −0.605741 0.795662i \(-0.707123\pi\)
−0.605741 + 0.795662i \(0.707123\pi\)
\(272\) 0 0
\(273\) −38.4413 18.9684i −0.140811 0.0694812i
\(274\) 0 0
\(275\) 277.469i 1.00898i
\(276\) 0 0
\(277\) 60.7455 0.219298 0.109649 0.993970i \(-0.465027\pi\)
0.109649 + 0.993970i \(0.465027\pi\)
\(278\) 0 0
\(279\) 199.861 + 260.717i 0.716347 + 0.934470i
\(280\) 0 0
\(281\) 366.827i 1.30543i 0.757602 + 0.652717i \(0.226371\pi\)
−0.757602 + 0.652717i \(0.773629\pi\)
\(282\) 0 0
\(283\) −104.032 −0.367603 −0.183801 0.982963i \(-0.558840\pi\)
−0.183801 + 0.982963i \(0.558840\pi\)
\(284\) 0 0
\(285\) −12.8121 + 25.9650i −0.0449547 + 0.0911051i
\(286\) 0 0
\(287\) 33.0574i 0.115182i
\(288\) 0 0
\(289\) 67.8293 0.234703
\(290\) 0 0
\(291\) 215.315 + 106.245i 0.739915 + 0.365102i
\(292\) 0 0
\(293\) 410.579i 1.40129i 0.713508 + 0.700647i \(0.247105\pi\)
−0.713508 + 0.700647i \(0.752895\pi\)
\(294\) 0 0
\(295\) −23.8660 −0.0809017
\(296\) 0 0
\(297\) −298.846 + 59.2253i −1.00622 + 0.199412i
\(298\) 0 0
\(299\) 191.380i 0.640066i
\(300\) 0 0
\(301\) −32.1138 −0.106690
\(302\) 0 0
\(303\) −158.467 + 321.149i −0.522994 + 1.05990i
\(304\) 0 0
\(305\) 37.2479i 0.122124i
\(306\) 0 0
\(307\) 270.025 0.879561 0.439781 0.898105i \(-0.355056\pi\)
0.439781 + 0.898105i \(0.355056\pi\)
\(308\) 0 0
\(309\) 337.693 + 166.630i 1.09286 + 0.539256i
\(310\) 0 0
\(311\) 251.555i 0.808858i −0.914569 0.404429i \(-0.867470\pi\)
0.914569 0.404429i \(-0.132530\pi\)
\(312\) 0 0
\(313\) −83.9560 −0.268230 −0.134115 0.990966i \(-0.542819\pi\)
−0.134115 + 0.990966i \(0.542819\pi\)
\(314\) 0 0
\(315\) 12.4379 9.53463i 0.0394853 0.0302687i
\(316\) 0 0
\(317\) 270.737i 0.854060i −0.904238 0.427030i \(-0.859560\pi\)
0.904238 0.427030i \(-0.140440\pi\)
\(318\) 0 0
\(319\) 583.715 1.82983
\(320\) 0 0
\(321\) 197.358 399.966i 0.614823 1.24600i
\(322\) 0 0
\(323\) 224.265i 0.694318i
\(324\) 0 0
\(325\) −129.143 −0.397363
\(326\) 0 0
\(327\) 190.114 + 93.8095i 0.581389 + 0.286879i
\(328\) 0 0
\(329\) 166.306i 0.505489i
\(330\) 0 0
\(331\) −9.91562 −0.0299566 −0.0149783 0.999888i \(-0.504768\pi\)
−0.0149783 + 0.999888i \(0.504768\pi\)
\(332\) 0 0
\(333\) 348.763 + 454.959i 1.04733 + 1.36624i
\(334\) 0 0
\(335\) 14.7837i 0.0441305i
\(336\) 0 0
\(337\) −289.542 −0.859174 −0.429587 0.903025i \(-0.641341\pi\)
−0.429587 + 0.903025i \(0.641341\pi\)
\(338\) 0 0
\(339\) −173.860 + 352.344i −0.512860 + 1.03936i
\(340\) 0 0
\(341\) 411.864i 1.20781i
\(342\) 0 0
\(343\) 246.494 0.718643
\(344\) 0 0
\(345\) 62.7454 + 30.9609i 0.181871 + 0.0897418i
\(346\) 0 0
\(347\) 331.079i 0.954119i 0.878871 + 0.477060i \(0.158297\pi\)
−0.878871 + 0.477060i \(0.841703\pi\)
\(348\) 0 0
\(349\) 302.280 0.866133 0.433067 0.901362i \(-0.357431\pi\)
0.433067 + 0.901362i \(0.357431\pi\)
\(350\) 0 0
\(351\) 27.5653 + 139.092i 0.0785337 + 0.396275i
\(352\) 0 0
\(353\) 528.345i 1.49673i 0.663289 + 0.748364i \(0.269160\pi\)
−0.663289 + 0.748364i \(0.730840\pi\)
\(354\) 0 0
\(355\) −4.66989 −0.0131546
\(356\) 0 0
\(357\) −53.7142 + 108.857i −0.150460 + 0.304922i
\(358\) 0 0
\(359\) 59.5167i 0.165785i 0.996559 + 0.0828923i \(0.0264158\pi\)
−0.996559 + 0.0828923i \(0.973584\pi\)
\(360\) 0 0
\(361\) −133.598 −0.370078
\(362\) 0 0
\(363\) 17.0047 + 8.39076i 0.0468449 + 0.0231150i
\(364\) 0 0
\(365\) 47.0092i 0.128792i
\(366\) 0 0
\(367\) −423.762 −1.15466 −0.577332 0.816509i \(-0.695906\pi\)
−0.577332 + 0.816509i \(0.695906\pi\)
\(368\) 0 0
\(369\) 86.7846 66.5274i 0.235189 0.180291i
\(370\) 0 0
\(371\) 160.986i 0.433925i
\(372\) 0 0
\(373\) 26.5076 0.0710660 0.0355330 0.999369i \(-0.488687\pi\)
0.0355330 + 0.999369i \(0.488687\pi\)
\(374\) 0 0
\(375\) 42.1328 85.3863i 0.112354 0.227697i
\(376\) 0 0
\(377\) 271.679i 0.720634i
\(378\) 0 0
\(379\) 383.169 1.01100 0.505500 0.862827i \(-0.331308\pi\)
0.505500 + 0.862827i \(0.331308\pi\)
\(380\) 0 0
\(381\) −562.829 277.721i −1.47724 0.728927i
\(382\) 0 0
\(383\) 299.496i 0.781973i −0.920396 0.390987i \(-0.872134\pi\)
0.920396 0.390987i \(-0.127866\pi\)
\(384\) 0 0
\(385\) −19.6485 −0.0510351
\(386\) 0 0
\(387\) 64.6285 + 84.3075i 0.166999 + 0.217849i
\(388\) 0 0
\(389\) 437.687i 1.12516i −0.826743 0.562580i \(-0.809809\pi\)
0.826743 0.562580i \(-0.190191\pi\)
\(390\) 0 0
\(391\) −541.944 −1.38605
\(392\) 0 0
\(393\) 232.099 470.372i 0.590583 1.19687i
\(394\) 0 0
\(395\) 37.4470i 0.0948027i
\(396\) 0 0
\(397\) −669.283 −1.68585 −0.842926 0.538029i \(-0.819169\pi\)
−0.842926 + 0.538029i \(0.819169\pi\)
\(398\) 0 0
\(399\) −110.380 54.4656i −0.276641 0.136505i
\(400\) 0 0
\(401\) 56.1062i 0.139916i 0.997550 + 0.0699578i \(0.0222865\pi\)
−0.997550 + 0.0699578i \(0.977714\pi\)
\(402\) 0 0
\(403\) −191.694 −0.475668
\(404\) 0 0
\(405\) −50.0620 13.4645i −0.123610 0.0332457i
\(406\) 0 0
\(407\) 718.713i 1.76588i
\(408\) 0 0
\(409\) 248.582 0.607779 0.303889 0.952707i \(-0.401715\pi\)
0.303889 + 0.952707i \(0.401715\pi\)
\(410\) 0 0
\(411\) −216.309 + 438.371i −0.526299 + 1.06660i
\(412\) 0 0
\(413\) 101.457i 0.245658i
\(414\) 0 0
\(415\) −20.7325 −0.0499578
\(416\) 0 0
\(417\) −522.531 257.836i −1.25307 0.618313i
\(418\) 0 0
\(419\) 459.935i 1.09770i 0.835922 + 0.548849i \(0.184934\pi\)
−0.835922 + 0.548849i \(0.815066\pi\)
\(420\) 0 0
\(421\) −97.4789 −0.231541 −0.115771 0.993276i \(-0.536934\pi\)
−0.115771 + 0.993276i \(0.536934\pi\)
\(422\) 0 0
\(423\) −436.599 + 334.688i −1.03215 + 0.791225i
\(424\) 0 0
\(425\) 365.703i 0.860479i
\(426\) 0 0
\(427\) 158.345 0.370831
\(428\) 0 0
\(429\) 78.6663 159.425i 0.183371 0.371620i
\(430\) 0 0
\(431\) 545.207i 1.26498i −0.774568 0.632490i \(-0.782033\pi\)
0.774568 0.632490i \(-0.217967\pi\)
\(432\) 0 0
\(433\) −24.5297 −0.0566506 −0.0283253 0.999599i \(-0.509017\pi\)
−0.0283253 + 0.999599i \(0.509017\pi\)
\(434\) 0 0
\(435\) 89.0721 + 43.9515i 0.204763 + 0.101038i
\(436\) 0 0
\(437\) 549.526i 1.25750i
\(438\) 0 0
\(439\) −81.8743 −0.186502 −0.0932509 0.995643i \(-0.529726\pi\)
−0.0932509 + 0.995643i \(0.529726\pi\)
\(440\) 0 0
\(441\) −227.767 297.120i −0.516478 0.673742i
\(442\) 0 0
\(443\) 831.356i 1.87665i −0.345753 0.938325i \(-0.612377\pi\)
0.345753 0.938325i \(-0.387623\pi\)
\(444\) 0 0
\(445\) 71.8482 0.161457
\(446\) 0 0
\(447\) 110.806 224.559i 0.247887 0.502368i
\(448\) 0 0
\(449\) 259.553i 0.578070i −0.957319 0.289035i \(-0.906666\pi\)
0.957319 0.289035i \(-0.0933344\pi\)
\(450\) 0 0
\(451\) −137.097 −0.303983
\(452\) 0 0
\(453\) 162.357 + 80.1129i 0.358403 + 0.176850i
\(454\) 0 0
\(455\) 9.14503i 0.0200990i
\(456\) 0 0
\(457\) 373.184 0.816596 0.408298 0.912849i \(-0.366122\pi\)
0.408298 + 0.912849i \(0.366122\pi\)
\(458\) 0 0
\(459\) 393.879 78.0588i 0.858123 0.170063i
\(460\) 0 0
\(461\) 672.996i 1.45986i −0.683522 0.729930i \(-0.739553\pi\)
0.683522 0.729930i \(-0.260447\pi\)
\(462\) 0 0
\(463\) 28.0435 0.0605690 0.0302845 0.999541i \(-0.490359\pi\)
0.0302845 + 0.999541i \(0.490359\pi\)
\(464\) 0 0
\(465\) 31.0118 62.8484i 0.0666920 0.135158i
\(466\) 0 0
\(467\) 373.758i 0.800339i 0.916441 + 0.400169i \(0.131049\pi\)
−0.916441 + 0.400169i \(0.868951\pi\)
\(468\) 0 0
\(469\) 62.8472 0.134003
\(470\) 0 0
\(471\) −271.082 133.762i −0.575545 0.283995i
\(472\) 0 0
\(473\) 133.183i 0.281572i
\(474\) 0 0
\(475\) −370.819 −0.780672
\(476\) 0 0
\(477\) −422.633 + 323.982i −0.886023 + 0.679208i
\(478\) 0 0
\(479\) 915.154i 1.91055i −0.295718 0.955275i \(-0.595559\pi\)
0.295718 0.955275i \(-0.404441\pi\)
\(480\) 0 0
\(481\) −334.512 −0.695451
\(482\) 0 0
\(483\) −131.618 + 266.737i −0.272502 + 0.552251i
\(484\) 0 0
\(485\) 51.2227i 0.105614i
\(486\) 0 0
\(487\) 238.560 0.489856 0.244928 0.969541i \(-0.421236\pi\)
0.244928 + 0.969541i \(0.421236\pi\)
\(488\) 0 0
\(489\) 187.555 + 92.5464i 0.383547 + 0.189257i
\(490\) 0 0
\(491\) 435.657i 0.887286i 0.896204 + 0.443643i \(0.146314\pi\)
−0.896204 + 0.443643i \(0.853686\pi\)
\(492\) 0 0
\(493\) −769.334 −1.56052
\(494\) 0 0
\(495\) 39.5423 + 51.5827i 0.0798835 + 0.104207i
\(496\) 0 0
\(497\) 19.8522i 0.0399441i
\(498\) 0 0
\(499\) 209.499 0.419838 0.209919 0.977719i \(-0.432680\pi\)
0.209919 + 0.977719i \(0.432680\pi\)
\(500\) 0 0
\(501\) 160.392 325.051i 0.320144 0.648804i
\(502\) 0 0
\(503\) 558.314i 1.10997i 0.831861 + 0.554984i \(0.187276\pi\)
−0.831861 + 0.554984i \(0.812724\pi\)
\(504\) 0 0
\(505\) 76.4002 0.151287
\(506\) 0 0
\(507\) 380.460 + 187.733i 0.750415 + 0.370283i
\(508\) 0 0
\(509\) 319.621i 0.627939i 0.949433 + 0.313969i \(0.101659\pi\)
−0.949433 + 0.313969i \(0.898341\pi\)
\(510\) 0 0
\(511\) −199.841 −0.391079
\(512\) 0 0
\(513\) 79.1507 + 399.388i 0.154290 + 0.778535i
\(514\) 0 0
\(515\) 80.3357i 0.155992i
\(516\) 0 0
\(517\) 689.710 1.33406
\(518\) 0 0
\(519\) −39.9048 + 80.8710i −0.0768879 + 0.155821i
\(520\) 0 0
\(521\) 771.602i 1.48100i −0.672055 0.740501i \(-0.734588\pi\)
0.672055 0.740501i \(-0.265412\pi\)
\(522\) 0 0
\(523\) −288.856 −0.552306 −0.276153 0.961114i \(-0.589060\pi\)
−0.276153 + 0.961114i \(0.589060\pi\)
\(524\) 0 0
\(525\) 179.994 + 88.8158i 0.342846 + 0.169173i
\(526\) 0 0
\(527\) 542.835i 1.03005i
\(528\) 0 0
\(529\) −798.951 −1.51030
\(530\) 0 0
\(531\) −266.352 + 204.180i −0.501605 + 0.384521i
\(532\) 0 0
\(533\) 63.8090i 0.119717i
\(534\) 0 0
\(535\) −95.1503 −0.177851
\(536\) 0 0
\(537\) 152.375 308.803i 0.283753 0.575053i
\(538\) 0 0
\(539\) 469.371i 0.870818i
\(540\) 0 0
\(541\) 232.871 0.430446 0.215223 0.976565i \(-0.430952\pi\)
0.215223 + 0.976565i \(0.430952\pi\)
\(542\) 0 0
\(543\) 488.633 + 241.110i 0.899877 + 0.444033i
\(544\) 0 0
\(545\) 45.2274i 0.0829861i
\(546\) 0 0
\(547\) 910.003 1.66363 0.831813 0.555056i \(-0.187303\pi\)
0.831813 + 0.555056i \(0.187303\pi\)
\(548\) 0 0
\(549\) −318.667 415.699i −0.580449 0.757192i
\(550\) 0 0
\(551\) 780.096i 1.41578i
\(552\) 0 0
\(553\) 159.191 0.287869
\(554\) 0 0
\(555\) 54.1164 109.672i 0.0975071 0.197608i
\(556\) 0 0
\(557\) 297.809i 0.534666i 0.963604 + 0.267333i \(0.0861424\pi\)
−0.963604 + 0.267333i \(0.913858\pi\)
\(558\) 0 0
\(559\) −61.9877 −0.110890
\(560\) 0 0
\(561\) −451.456 222.765i −0.804734 0.397086i
\(562\) 0 0
\(563\) 184.465i 0.327647i −0.986490 0.163824i \(-0.947617\pi\)
0.986490 0.163824i \(-0.0523828\pi\)
\(564\) 0 0
\(565\) 83.8212 0.148356
\(566\) 0 0
\(567\) 57.2391 212.819i 0.100951 0.375342i
\(568\) 0 0
\(569\) 404.137i 0.710258i 0.934817 + 0.355129i \(0.115563\pi\)
−0.934817 + 0.355129i \(0.884437\pi\)
\(570\) 0 0
\(571\) 762.365 1.33514 0.667570 0.744547i \(-0.267334\pi\)
0.667570 + 0.744547i \(0.267334\pi\)
\(572\) 0 0
\(573\) −277.748 + 562.883i −0.484726 + 0.982344i
\(574\) 0 0
\(575\) 896.100i 1.55843i
\(576\) 0 0
\(577\) −290.766 −0.503927 −0.251964 0.967737i \(-0.581076\pi\)
−0.251964 + 0.967737i \(0.581076\pi\)
\(578\) 0 0
\(579\) −434.027 214.165i −0.749616 0.369888i
\(580\) 0 0
\(581\) 88.1361i 0.151697i
\(582\) 0 0
\(583\) 667.648 1.14519
\(584\) 0 0
\(585\) 24.0082 18.4042i 0.0410397 0.0314602i
\(586\) 0 0
\(587\) 224.506i 0.382464i −0.981545 0.191232i \(-0.938752\pi\)
0.981545 0.191232i \(-0.0612482\pi\)
\(588\) 0 0
\(589\) −550.428 −0.934513
\(590\) 0 0
\(591\) 192.425 389.968i 0.325592 0.659844i
\(592\) 0 0
\(593\) 482.620i 0.813862i 0.913459 + 0.406931i \(0.133401\pi\)
−0.913459 + 0.406931i \(0.866599\pi\)
\(594\) 0 0
\(595\) 25.8967 0.0435238
\(596\) 0 0
\(597\) 638.312 + 314.967i 1.06920 + 0.527583i
\(598\) 0 0
\(599\) 803.277i 1.34103i 0.741896 + 0.670515i \(0.233927\pi\)
−0.741896 + 0.670515i \(0.766073\pi\)
\(600\) 0 0
\(601\) −126.365 −0.210258 −0.105129 0.994459i \(-0.533526\pi\)
−0.105129 + 0.994459i \(0.533526\pi\)
\(602\) 0 0
\(603\) −126.479 164.991i −0.209750 0.273617i
\(604\) 0 0
\(605\) 4.04535i 0.00668653i
\(606\) 0 0
\(607\) −397.356 −0.654623 −0.327312 0.944916i \(-0.606143\pi\)
−0.327312 + 0.944916i \(0.606143\pi\)
\(608\) 0 0
\(609\) −186.843 + 378.655i −0.306802 + 0.621766i
\(610\) 0 0
\(611\) 321.012i 0.525388i
\(612\) 0 0
\(613\) 1056.55 1.72357 0.861785 0.507275i \(-0.169347\pi\)
0.861785 + 0.507275i \(0.169347\pi\)
\(614\) 0 0
\(615\) −20.9203 10.3229i −0.0340167 0.0167851i
\(616\) 0 0
\(617\) 411.284i 0.666586i −0.942823 0.333293i \(-0.891840\pi\)
0.942823 0.333293i \(-0.108160\pi\)
\(618\) 0 0
\(619\) −691.383 −1.11693 −0.558467 0.829526i \(-0.688610\pi\)
−0.558467 + 0.829526i \(0.688610\pi\)
\(620\) 0 0
\(621\) 965.138 191.271i 1.55417 0.308005i
\(622\) 0 0
\(623\) 305.435i 0.490264i
\(624\) 0 0
\(625\) 594.447 0.951114
\(626\) 0 0
\(627\) 225.881 457.771i 0.360257 0.730097i
\(628\) 0 0
\(629\) 947.262i 1.50598i
\(630\) 0 0
\(631\) 528.057 0.836858 0.418429 0.908250i \(-0.362581\pi\)
0.418429 + 0.908250i \(0.362581\pi\)
\(632\) 0 0
\(633\) 826.238 + 407.697i 1.30527 + 0.644071i
\(634\) 0 0
\(635\) 133.895i 0.210858i
\(636\) 0 0
\(637\) 218.460 0.342951
\(638\) 0 0
\(639\) −52.1175 + 39.9523i −0.0815611 + 0.0625232i
\(640\) 0 0
\(641\) 134.165i 0.209306i 0.994509 + 0.104653i \(0.0333731\pi\)
−0.994509 + 0.104653i \(0.966627\pi\)
\(642\) 0 0
\(643\) −633.985 −0.985979 −0.492990 0.870035i \(-0.664096\pi\)
−0.492990 + 0.870035i \(0.664096\pi\)
\(644\) 0 0
\(645\) 10.0282 20.3232i 0.0155476 0.0315088i
\(646\) 0 0
\(647\) 227.758i 0.352021i −0.984388 0.176011i \(-0.943681\pi\)
0.984388 0.176011i \(-0.0563193\pi\)
\(648\) 0 0
\(649\) 420.766 0.648329
\(650\) 0 0
\(651\) 267.176 + 131.834i 0.410408 + 0.202511i
\(652\) 0 0
\(653\) 1190.65i 1.82336i 0.410906 + 0.911678i \(0.365212\pi\)
−0.410906 + 0.911678i \(0.634788\pi\)
\(654\) 0 0
\(655\) −111.900 −0.170839
\(656\) 0 0
\(657\) 402.178 + 524.638i 0.612142 + 0.798536i
\(658\) 0 0
\(659\) 266.873i 0.404967i −0.979286 0.202484i \(-0.935099\pi\)
0.979286 0.202484i \(-0.0649013\pi\)
\(660\) 0 0
\(661\) −1045.10 −1.58109 −0.790544 0.612405i \(-0.790202\pi\)
−0.790544 + 0.612405i \(0.790202\pi\)
\(662\) 0 0
\(663\) −103.682 + 210.122i −0.156383 + 0.316925i
\(664\) 0 0
\(665\) 26.2589i 0.0394871i
\(666\) 0 0
\(667\) −1885.13 −2.82629
\(668\) 0 0
\(669\) −1178.36 581.445i −1.76137 0.869126i
\(670\) 0 0
\(671\) 656.693i 0.978678i
\(672\) 0 0
\(673\) 408.300 0.606687 0.303343 0.952881i \(-0.401897\pi\)
0.303343 + 0.952881i \(0.401897\pi\)
\(674\) 0 0
\(675\) −129.069 651.274i −0.191214 0.964850i
\(676\) 0 0
\(677\) 749.557i 1.10717i −0.832791 0.553587i \(-0.813259\pi\)
0.832791 0.553587i \(-0.186741\pi\)
\(678\) 0 0
\(679\) 217.753 0.320697
\(680\) 0 0
\(681\) −359.426 + 728.413i −0.527792 + 1.06962i
\(682\) 0 0
\(683\) 258.242i 0.378099i −0.981968 0.189050i \(-0.939459\pi\)
0.981968 0.189050i \(-0.0605407\pi\)
\(684\) 0 0
\(685\) 104.287 0.152244
\(686\) 0 0
\(687\) 265.474 + 130.995i 0.386424 + 0.190676i
\(688\) 0 0
\(689\) 310.744i 0.451007i
\(690\) 0 0
\(691\) 929.714 1.34546 0.672731 0.739887i \(-0.265121\pi\)
0.672731 + 0.739887i \(0.265121\pi\)
\(692\) 0 0
\(693\) −219.284 + 168.099i −0.316427 + 0.242567i
\(694\) 0 0
\(695\) 124.308i 0.178861i
\(696\) 0 0
\(697\) 180.693 0.259244
\(698\) 0 0
\(699\) 574.016 1163.30i 0.821197 1.66424i
\(700\) 0 0
\(701\) 335.731i 0.478932i 0.970905 + 0.239466i \(0.0769724\pi\)
−0.970905 + 0.239466i \(0.923028\pi\)
\(702\) 0 0
\(703\) −960.513 −1.36631
\(704\) 0 0
\(705\) 105.246 + 51.9325i 0.149286 + 0.0736632i
\(706\) 0 0
\(707\) 324.785i 0.459385i
\(708\) 0 0
\(709\) 356.121 0.502287 0.251143 0.967950i \(-0.419193\pi\)
0.251143 + 0.967950i \(0.419193\pi\)
\(710\) 0 0
\(711\) −320.370 417.921i −0.450591 0.587793i
\(712\) 0 0
\(713\) 1330.13i 1.86554i
\(714\) 0 0
\(715\) −37.9266 −0.0530442
\(716\) 0 0
\(717\) 366.123 741.985i 0.510632 1.03485i
\(718\) 0 0
\(719\) 31.7234i 0.0441216i 0.999757 + 0.0220608i \(0.00702274\pi\)
−0.999757 + 0.0220608i \(0.992977\pi\)
\(720\) 0 0
\(721\) 341.516 0.473670
\(722\) 0 0
\(723\) −1121.24 553.262i −1.55082 0.765231i
\(724\) 0 0
\(725\) 1272.09i 1.75460i
\(726\) 0 0
\(727\) 234.202 0.322148 0.161074 0.986942i \(-0.448504\pi\)
0.161074 + 0.986942i \(0.448504\pi\)
\(728\) 0 0
\(729\) −673.901 + 278.027i −0.924418 + 0.381381i
\(730\) 0 0
\(731\) 175.535i 0.240130i
\(732\) 0 0
\(733\) 616.813 0.841491 0.420745 0.907179i \(-0.361769\pi\)
0.420745 + 0.907179i \(0.361769\pi\)
\(734\) 0 0
\(735\) −35.3419 + 71.6238i −0.0480842 + 0.0974473i
\(736\) 0 0
\(737\) 260.642i 0.353653i
\(738\) 0 0
\(739\) 605.806 0.819764 0.409882 0.912138i \(-0.365570\pi\)
0.409882 + 0.912138i \(0.365570\pi\)
\(740\) 0 0
\(741\) −213.061 105.132i −0.287532 0.141879i
\(742\) 0 0
\(743\) 1033.33i 1.39076i 0.718642 + 0.695380i \(0.244764\pi\)
−0.718642 + 0.695380i \(0.755236\pi\)
\(744\) 0 0
\(745\) −53.4216 −0.0717068
\(746\) 0 0
\(747\) −231.381 + 177.372i −0.309747 + 0.237446i
\(748\) 0 0
\(749\) 404.494i 0.540046i
\(750\) 0 0
\(751\) 969.301 1.29068 0.645340 0.763896i \(-0.276716\pi\)
0.645340 + 0.763896i \(0.276716\pi\)
\(752\) 0 0
\(753\) −220.235 + 446.329i −0.292477 + 0.592734i
\(754\) 0 0
\(755\) 38.6240i 0.0511577i
\(756\) 0 0
\(757\) −533.594 −0.704880 −0.352440 0.935835i \(-0.614648\pi\)
−0.352440 + 0.935835i \(0.614648\pi\)
\(758\) 0 0
\(759\) −1106.22 545.851i −1.45747 0.719172i
\(760\) 0 0
\(761\) 867.717i 1.14023i −0.821564 0.570116i \(-0.806898\pi\)
0.821564 0.570116i \(-0.193102\pi\)
\(762\) 0 0
\(763\) 192.267 0.251988
\(764\) 0 0
\(765\) −52.1166 67.9858i −0.0681263 0.0888704i
\(766\) 0 0
\(767\) 195.837i 0.255329i
\(768\) 0 0
\(769\) 194.555 0.252997 0.126498 0.991967i \(-0.459626\pi\)
0.126498 + 0.991967i \(0.459626\pi\)
\(770\) 0 0
\(771\) −79.1695 + 160.445i −0.102684 + 0.208100i
\(772\) 0 0
\(773\) 420.140i 0.543519i 0.962365 + 0.271760i \(0.0876056\pi\)
−0.962365 + 0.271760i \(0.912394\pi\)
\(774\) 0 0
\(775\) 897.572 1.15816
\(776\) 0 0
\(777\) 466.229 + 230.055i 0.600037 + 0.296081i
\(778\) 0 0
\(779\) 183.220i 0.235199i
\(780\) 0 0
\(781\) 82.3318 0.105418
\(782\) 0 0
\(783\) 1370.09 271.524i 1.74980 0.346775i
\(784\) 0 0
\(785\) 64.4892i 0.0821519i
\(786\) 0 0
\(787\) −849.081 −1.07888 −0.539441 0.842023i \(-0.681365\pi\)
−0.539441 + 0.842023i \(0.681365\pi\)
\(788\) 0 0
\(789\) 89.2883 180.952i 0.113166 0.229343i
\(790\) 0 0
\(791\) 356.333i 0.450484i
\(792\) 0 0
\(793\) 305.646 0.385429
\(794\) 0 0
\(795\) 101.880 + 50.2714i 0.128151 + 0.0632344i
\(796\) 0 0
\(797\) 779.186i 0.977648i 0.872382 + 0.488824i \(0.162574\pi\)
−0.872382 + 0.488824i \(0.837426\pi\)
\(798\) 0 0
\(799\) −909.035 −1.13772
\(800\) 0 0