Properties

Label 384.3.i.c.161.9
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 384 = 2^{7} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 384.i (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 2 x^{18} + 6 x^{16} - 24 x^{14} - 24 x^{12} + 1216 x^{10} - 384 x^{8} - 6144 x^{6} + 24576 x^{4} - 131072 x^{2} + 1048576\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{23} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 161.9
Root \(0.312316 + 1.97546i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.9

$q$-expansion

\(f(q)\) \(=\) \(q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +O(q^{10})\) \(q+(2.75602 - 1.18505i) q^{3} +(-0.00985921 - 0.00985921i) q^{5} -6.42277i q^{7} +(6.19134 - 6.53203i) q^{9} +(-9.07186 - 9.07186i) q^{11} +(-12.6098 - 12.6098i) q^{13} +(-0.0388558 - 0.0154886i) q^{15} +19.0155i q^{17} +(-2.07165 - 2.07165i) q^{19} +(-7.61127 - 17.7013i) q^{21} +19.5712 q^{23} -24.9998i q^{25} +(9.32272 - 25.3394i) q^{27} +(-11.1742 + 11.1742i) q^{29} +59.9385 q^{31} +(-35.7528 - 14.2517i) q^{33} +(-0.0633234 + 0.0633234i) q^{35} +(-9.32707 + 9.32707i) q^{37} +(-49.6962 - 19.8098i) q^{39} -47.2639 q^{41} +(24.1220 - 24.1220i) q^{43} +(-0.125442 + 0.00335893i) q^{45} -6.29702i q^{47} +7.74808 q^{49} +(22.5343 + 52.4073i) q^{51} +(20.6409 + 20.6409i) q^{53} +0.178883i q^{55} +(-8.16452 - 3.25452i) q^{57} +(60.3533 + 60.3533i) q^{59} +(-48.0230 - 48.0230i) q^{61} +(-41.9537 - 39.7655i) q^{63} +0.248646i q^{65} +(-23.7768 - 23.7768i) q^{67} +(53.9388 - 23.1928i) q^{69} +13.5743 q^{71} +31.4516i q^{73} +(-29.6259 - 68.9001i) q^{75} +(-58.2665 + 58.2665i) q^{77} -47.4718 q^{79} +(-4.33472 - 80.8839i) q^{81} +(70.3318 - 70.3318i) q^{83} +(0.187478 - 0.187478i) q^{85} +(-17.5545 + 44.0385i) q^{87} +95.1729 q^{89} +(-80.9900 + 80.9900i) q^{91} +(165.192 - 71.0298i) q^{93} +0.0408497i q^{95} +61.6218 q^{97} +(-115.425 + 3.09069i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + O(q^{10}) \) \( 20q - 6q^{3} - 92q^{13} + 116q^{15} - 52q^{19} - 48q^{21} + 18q^{27} + 80q^{31} + 60q^{33} + 116q^{37} + 172q^{43} - 60q^{45} - 364q^{49} + 128q^{51} + 244q^{61} - 296q^{63} + 356q^{67} + 20q^{69} - 146q^{75} - 384q^{79} - 188q^{81} - 48q^{85} + 136q^{91} + 132q^{93} + 472q^{97} - 452q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(127\) \(133\) \(257\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(-1\)

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
\(3\) 2.75602 1.18505i 0.918675 0.395015i
\(4\) 0 0
\(5\) −0.00985921 0.00985921i −0.00197184 0.00197184i 0.706120 0.708092i \(-0.250444\pi\)
−0.708092 + 0.706120i \(0.750444\pi\)
\(6\) 0 0
\(7\) 6.42277i 0.917538i −0.888556 0.458769i \(-0.848291\pi\)
0.888556 0.458769i \(-0.151709\pi\)
\(8\) 0 0
\(9\) 6.19134 6.53203i 0.687926 0.725781i
\(10\) 0 0
\(11\) −9.07186 9.07186i −0.824715 0.824715i 0.162065 0.986780i \(-0.448185\pi\)
−0.986780 + 0.162065i \(0.948185\pi\)
\(12\) 0 0
\(13\) −12.6098 12.6098i −0.969987 0.969987i 0.0295753 0.999563i \(-0.490585\pi\)
−0.999563 + 0.0295753i \(0.990585\pi\)
\(14\) 0 0
\(15\) −0.0388558 0.0154886i −0.00259039 0.00103257i
\(16\) 0 0
\(17\) 19.0155i 1.11856i 0.828978 + 0.559281i \(0.188923\pi\)
−0.828978 + 0.559281i \(0.811077\pi\)
\(18\) 0 0
\(19\) −2.07165 2.07165i −0.109034 0.109034i 0.650485 0.759519i \(-0.274566\pi\)
−0.759519 + 0.650485i \(0.774566\pi\)
\(20\) 0 0
\(21\) −7.61127 17.7013i −0.362441 0.842919i
\(22\) 0 0
\(23\) 19.5712 0.850923 0.425461 0.904977i \(-0.360112\pi\)
0.425461 + 0.904977i \(0.360112\pi\)
\(24\) 0 0
\(25\) 24.9998i 0.999992i
\(26\) 0 0
\(27\) 9.32272 25.3394i 0.345286 0.938497i
\(28\) 0 0
\(29\) −11.1742 + 11.1742i −0.385319 + 0.385319i −0.873014 0.487695i \(-0.837838\pi\)
0.487695 + 0.873014i \(0.337838\pi\)
\(30\) 0 0
\(31\) 59.9385 1.93350 0.966750 0.255725i \(-0.0823142\pi\)
0.966750 + 0.255725i \(0.0823142\pi\)
\(32\) 0 0
\(33\) −35.7528 14.2517i −1.08342 0.431870i
\(34\) 0 0
\(35\) −0.0633234 + 0.0633234i −0.00180924 + 0.00180924i
\(36\) 0 0
\(37\) −9.32707 + 9.32707i −0.252083 + 0.252083i −0.821824 0.569741i \(-0.807043\pi\)
0.569741 + 0.821824i \(0.307043\pi\)
\(38\) 0 0
\(39\) −49.6962 19.8098i −1.27426 0.507943i
\(40\) 0 0
\(41\) −47.2639 −1.15278 −0.576389 0.817176i \(-0.695539\pi\)
−0.576389 + 0.817176i \(0.695539\pi\)
\(42\) 0 0
\(43\) 24.1220 24.1220i 0.560978 0.560978i −0.368607 0.929585i \(-0.620165\pi\)
0.929585 + 0.368607i \(0.120165\pi\)
\(44\) 0 0
\(45\) −0.125442 + 0.00335893i −0.00278761 + 7.46430e-5i
\(46\) 0 0
\(47\) 6.29702i 0.133979i −0.997754 0.0669896i \(-0.978661\pi\)
0.997754 0.0669896i \(-0.0213394\pi\)
\(48\) 0 0
\(49\) 7.74808 0.158124
\(50\) 0 0
\(51\) 22.5343 + 52.4073i 0.441849 + 1.02759i
\(52\) 0 0
\(53\) 20.6409 + 20.6409i 0.389450 + 0.389450i 0.874491 0.485041i \(-0.161195\pi\)
−0.485041 + 0.874491i \(0.661195\pi\)
\(54\) 0 0
\(55\) 0.178883i 0.00325242i
\(56\) 0 0
\(57\) −8.16452 3.25452i −0.143237 0.0570968i
\(58\) 0 0
\(59\) 60.3533 + 60.3533i 1.02294 + 1.02294i 0.999731 + 0.0232062i \(0.00738742\pi\)
0.0232062 + 0.999731i \(0.492613\pi\)
\(60\) 0 0
\(61\) −48.0230 48.0230i −0.787262 0.787262i 0.193782 0.981045i \(-0.437924\pi\)
−0.981045 + 0.193782i \(0.937924\pi\)
\(62\) 0 0
\(63\) −41.9537 39.7655i −0.665931 0.631198i
\(64\) 0 0
\(65\) 0.248646i 0.00382532i
\(66\) 0 0
\(67\) −23.7768 23.7768i −0.354878 0.354878i 0.507043 0.861921i \(-0.330738\pi\)
−0.861921 + 0.507043i \(0.830738\pi\)
\(68\) 0 0
\(69\) 53.9388 23.1928i 0.781721 0.336127i
\(70\) 0 0
\(71\) 13.5743 0.191188 0.0955938 0.995420i \(-0.469525\pi\)
0.0955938 + 0.995420i \(0.469525\pi\)
\(72\) 0 0
\(73\) 31.4516i 0.430844i 0.976521 + 0.215422i \(0.0691127\pi\)
−0.976521 + 0.215422i \(0.930887\pi\)
\(74\) 0 0
\(75\) −29.6259 68.9001i −0.395012 0.918668i
\(76\) 0 0
\(77\) −58.2665 + 58.2665i −0.756707 + 0.756707i
\(78\) 0 0
\(79\) −47.4718 −0.600909 −0.300455 0.953796i \(-0.597138\pi\)
−0.300455 + 0.953796i \(0.597138\pi\)
\(80\) 0 0
\(81\) −4.33472 80.8839i −0.0535151 0.998567i
\(82\) 0 0
\(83\) 70.3318 70.3318i 0.847372 0.847372i −0.142433 0.989804i \(-0.545493\pi\)
0.989804 + 0.142433i \(0.0454925\pi\)
\(84\) 0 0
\(85\) 0.187478 0.187478i 0.00220563 0.00220563i
\(86\) 0 0
\(87\) −17.5545 + 44.0385i −0.201776 + 0.506189i
\(88\) 0 0
\(89\) 95.1729 1.06936 0.534679 0.845055i \(-0.320432\pi\)
0.534679 + 0.845055i \(0.320432\pi\)
\(90\) 0 0
\(91\) −80.9900 + 80.9900i −0.890000 + 0.890000i
\(92\) 0 0
\(93\) 165.192 71.0298i 1.77626 0.763761i
\(94\) 0 0
\(95\) 0.0408497i 0.000429997i
\(96\) 0 0
\(97\) 61.6218 0.635276 0.317638 0.948212i \(-0.397110\pi\)
0.317638 + 0.948212i \(0.397110\pi\)
\(98\) 0 0
\(99\) −115.425 + 3.09069i −1.16591 + 0.0312191i
\(100\) 0 0
\(101\) 48.1867 + 48.1867i 0.477096 + 0.477096i 0.904202 0.427106i \(-0.140467\pi\)
−0.427106 + 0.904202i \(0.640467\pi\)
\(102\) 0 0
\(103\) 4.73669i 0.0459873i 0.999736 + 0.0229936i \(0.00731975\pi\)
−0.999736 + 0.0229936i \(0.992680\pi\)
\(104\) 0 0
\(105\) −0.0994797 + 0.249562i −0.000947426 + 0.00237678i
\(106\) 0 0
\(107\) 40.9462 + 40.9462i 0.382674 + 0.382674i 0.872065 0.489390i \(-0.162781\pi\)
−0.489390 + 0.872065i \(0.662781\pi\)
\(108\) 0 0
\(109\) 120.437 + 120.437i 1.10493 + 1.10493i 0.993807 + 0.111123i \(0.0354447\pi\)
0.111123 + 0.993807i \(0.464555\pi\)
\(110\) 0 0
\(111\) −14.6526 + 36.7586i −0.132006 + 0.331159i
\(112\) 0 0
\(113\) 205.193i 1.81587i 0.419110 + 0.907936i \(0.362342\pi\)
−0.419110 + 0.907936i \(0.637658\pi\)
\(114\) 0 0
\(115\) −0.192957 0.192957i −0.00167789 0.00167789i
\(116\) 0 0
\(117\) −160.439 + 4.29604i −1.37128 + 0.0367183i
\(118\) 0 0
\(119\) 122.132 1.02632
\(120\) 0 0
\(121\) 43.5974i 0.360309i
\(122\) 0 0
\(123\) −130.260 + 56.0098i −1.05903 + 0.455365i
\(124\) 0 0
\(125\) −0.492959 + 0.492959i −0.00394367 + 0.00394367i
\(126\) 0 0
\(127\) −54.1458 −0.426345 −0.213173 0.977015i \(-0.568380\pi\)
−0.213173 + 0.977015i \(0.568380\pi\)
\(128\) 0 0
\(129\) 37.8952 95.0666i 0.293761 0.736951i
\(130\) 0 0
\(131\) −31.2584 + 31.2584i −0.238614 + 0.238614i −0.816276 0.577662i \(-0.803965\pi\)
0.577662 + 0.816276i \(0.303965\pi\)
\(132\) 0 0
\(133\) −13.3057 + 13.3057i −0.100043 + 0.100043i
\(134\) 0 0
\(135\) −0.341742 + 0.157912i −0.00253142 + 0.00116972i
\(136\) 0 0
\(137\) −42.9176 −0.313267 −0.156633 0.987657i \(-0.550064\pi\)
−0.156633 + 0.987657i \(0.550064\pi\)
\(138\) 0 0
\(139\) −47.0945 + 47.0945i −0.338809 + 0.338809i −0.855919 0.517110i \(-0.827008\pi\)
0.517110 + 0.855919i \(0.327008\pi\)
\(140\) 0 0
\(141\) −7.46225 17.3547i −0.0529238 0.123083i
\(142\) 0 0
\(143\) 228.789i 1.59993i
\(144\) 0 0
\(145\) 0.220339 0.00151958
\(146\) 0 0
\(147\) 21.3539 9.18183i 0.145265 0.0624614i
\(148\) 0 0
\(149\) −131.532 131.532i −0.882766 0.882766i 0.111049 0.993815i \(-0.464579\pi\)
−0.993815 + 0.111049i \(0.964579\pi\)
\(150\) 0 0
\(151\) 145.908i 0.966281i 0.875543 + 0.483140i \(0.160504\pi\)
−0.875543 + 0.483140i \(0.839496\pi\)
\(152\) 0 0
\(153\) 124.210 + 117.732i 0.811830 + 0.769488i
\(154\) 0 0
\(155\) −0.590946 0.590946i −0.00381256 0.00381256i
\(156\) 0 0
\(157\) 55.2586 + 55.2586i 0.351966 + 0.351966i 0.860840 0.508875i \(-0.169938\pi\)
−0.508875 + 0.860840i \(0.669938\pi\)
\(158\) 0 0
\(159\) 81.3470 + 32.4263i 0.511617 + 0.203939i
\(160\) 0 0
\(161\) 125.701i 0.780754i
\(162\) 0 0
\(163\) 70.6156 + 70.6156i 0.433225 + 0.433225i 0.889724 0.456499i \(-0.150897\pi\)
−0.456499 + 0.889724i \(0.650897\pi\)
\(164\) 0 0
\(165\) 0.211984 + 0.493006i 0.00128475 + 0.00298791i
\(166\) 0 0
\(167\) 86.2013 0.516176 0.258088 0.966121i \(-0.416908\pi\)
0.258088 + 0.966121i \(0.416908\pi\)
\(168\) 0 0
\(169\) 149.016i 0.881751i
\(170\) 0 0
\(171\) −26.3584 + 0.705790i −0.154142 + 0.00412743i
\(172\) 0 0
\(173\) −58.2425 + 58.2425i −0.336662 + 0.336662i −0.855109 0.518448i \(-0.826510\pi\)
0.518448 + 0.855109i \(0.326510\pi\)
\(174\) 0 0
\(175\) −160.568 −0.917531
\(176\) 0 0
\(177\) 237.856 + 94.8137i 1.34382 + 0.535671i
\(178\) 0 0
\(179\) −18.9272 + 18.9272i −0.105738 + 0.105738i −0.757997 0.652258i \(-0.773822\pi\)
0.652258 + 0.757997i \(0.273822\pi\)
\(180\) 0 0
\(181\) −24.5109 + 24.5109i −0.135420 + 0.135420i −0.771567 0.636148i \(-0.780527\pi\)
0.636148 + 0.771567i \(0.280527\pi\)
\(182\) 0 0
\(183\) −189.262 75.4431i −1.03422 0.412257i
\(184\) 0 0
\(185\) 0.183915 0.000994136
\(186\) 0 0
\(187\) 172.506 172.506i 0.922494 0.922494i
\(188\) 0 0
\(189\) −162.749 59.8777i −0.861107 0.316813i
\(190\) 0 0
\(191\) 156.422i 0.818962i −0.912319 0.409481i \(-0.865710\pi\)
0.912319 0.409481i \(-0.134290\pi\)
\(192\) 0 0
\(193\) −217.972 −1.12939 −0.564695 0.825299i \(-0.691006\pi\)
−0.564695 + 0.825299i \(0.691006\pi\)
\(194\) 0 0
\(195\) 0.294657 + 0.685275i 0.00151106 + 0.00351423i
\(196\) 0 0
\(197\) 245.945 + 245.945i 1.24845 + 1.24845i 0.956403 + 0.292050i \(0.0943374\pi\)
0.292050 + 0.956403i \(0.405663\pi\)
\(198\) 0 0
\(199\) 233.190i 1.17181i −0.810379 0.585905i \(-0.800739\pi\)
0.810379 0.585905i \(-0.199261\pi\)
\(200\) 0 0
\(201\) −93.7060 37.3528i −0.466199 0.185835i
\(202\) 0 0
\(203\) 71.7695 + 71.7695i 0.353545 + 0.353545i
\(204\) 0 0
\(205\) 0.465985 + 0.465985i 0.00227310 + 0.00227310i
\(206\) 0 0
\(207\) 121.172 127.840i 0.585372 0.617583i
\(208\) 0 0
\(209\) 37.5875i 0.179844i
\(210\) 0 0
\(211\) −8.49504 8.49504i −0.0402609 0.0402609i 0.686690 0.726951i \(-0.259063\pi\)
−0.726951 + 0.686690i \(0.759063\pi\)
\(212\) 0 0
\(213\) 37.4111 16.0862i 0.175639 0.0755220i
\(214\) 0 0
\(215\) −0.475649 −0.00221232
\(216\) 0 0
\(217\) 384.971i 1.77406i
\(218\) 0 0
\(219\) 37.2716 + 86.6814i 0.170190 + 0.395806i
\(220\) 0 0
\(221\) 239.783 239.783i 1.08499 1.08499i
\(222\) 0 0
\(223\) 10.9290 0.0490090 0.0245045 0.999700i \(-0.492199\pi\)
0.0245045 + 0.999700i \(0.492199\pi\)
\(224\) 0 0
\(225\) −163.299 154.782i −0.725775 0.687921i
\(226\) 0 0
\(227\) 99.9027 99.9027i 0.440100 0.440100i −0.451946 0.892045i \(-0.649270\pi\)
0.892045 + 0.451946i \(0.149270\pi\)
\(228\) 0 0
\(229\) 231.857 231.857i 1.01248 1.01248i 0.0125555 0.999921i \(-0.496003\pi\)
0.999921 0.0125555i \(-0.00399663\pi\)
\(230\) 0 0
\(231\) −91.5354 + 229.632i −0.396257 + 0.994079i
\(232\) 0 0
\(233\) −316.641 −1.35897 −0.679486 0.733688i \(-0.737797\pi\)
−0.679486 + 0.733688i \(0.737797\pi\)
\(234\) 0 0
\(235\) −0.0620836 + 0.0620836i −0.000264186 + 0.000264186i
\(236\) 0 0
\(237\) −130.833 + 56.2562i −0.552040 + 0.237368i
\(238\) 0 0
\(239\) 382.691i 1.60122i −0.599187 0.800609i \(-0.704509\pi\)
0.599187 0.800609i \(-0.295491\pi\)
\(240\) 0 0
\(241\) −91.3157 −0.378903 −0.189452 0.981890i \(-0.560671\pi\)
−0.189452 + 0.981890i \(0.560671\pi\)
\(242\) 0 0
\(243\) −107.798 217.781i −0.443612 0.896219i
\(244\) 0 0
\(245\) −0.0763900 0.0763900i −0.000311796 0.000311796i
\(246\) 0 0
\(247\) 52.2463i 0.211524i
\(248\) 0 0
\(249\) 110.490 277.183i 0.443734 1.11318i
\(250\) 0 0
\(251\) −128.768 128.768i −0.513021 0.513021i 0.402430 0.915451i \(-0.368166\pi\)
−0.915451 + 0.402430i \(0.868166\pi\)
\(252\) 0 0
\(253\) −177.547 177.547i −0.701769 0.701769i
\(254\) 0 0
\(255\) 0.294524 0.738865i 0.00115500 0.00289751i
\(256\) 0 0
\(257\) 123.915i 0.482159i −0.970505 0.241079i \(-0.922499\pi\)
0.970505 0.241079i \(-0.0775014\pi\)
\(258\) 0 0
\(259\) 59.9056 + 59.9056i 0.231296 + 0.231296i
\(260\) 0 0
\(261\) 3.80695 + 142.174i 0.0145860 + 0.544728i
\(262\) 0 0
\(263\) −194.379 −0.739085 −0.369542 0.929214i \(-0.620486\pi\)
−0.369542 + 0.929214i \(0.620486\pi\)
\(264\) 0 0
\(265\) 0.407005i 0.00153587i
\(266\) 0 0
\(267\) 262.299 112.784i 0.982393 0.422413i
\(268\) 0 0
\(269\) −296.636 + 296.636i −1.10274 + 1.10274i −0.108658 + 0.994079i \(0.534655\pi\)
−0.994079 + 0.108658i \(0.965345\pi\)
\(270\) 0 0
\(271\) 278.227 1.02667 0.513334 0.858189i \(-0.328410\pi\)
0.513334 + 0.858189i \(0.328410\pi\)
\(272\) 0 0
\(273\) −127.234 + 319.187i −0.466057 + 1.16918i
\(274\) 0 0
\(275\) −226.795 + 226.795i −0.824709 + 0.824709i
\(276\) 0 0
\(277\) 60.1513 60.1513i 0.217153 0.217153i −0.590145 0.807297i \(-0.700929\pi\)
0.807297 + 0.590145i \(0.200929\pi\)
\(278\) 0 0
\(279\) 371.099 391.520i 1.33010 1.40330i
\(280\) 0 0
\(281\) 313.645 1.11617 0.558087 0.829782i \(-0.311535\pi\)
0.558087 + 0.829782i \(0.311535\pi\)
\(282\) 0 0
\(283\) 286.980 286.980i 1.01406 1.01406i 0.0141627 0.999900i \(-0.495492\pi\)
0.999900 0.0141627i \(-0.00450829\pi\)
\(284\) 0 0
\(285\) 0.0484087 + 0.112583i 0.000169855 + 0.000395027i
\(286\) 0 0
\(287\) 303.565i 1.05772i
\(288\) 0 0
\(289\) −72.5910 −0.251180
\(290\) 0 0
\(291\) 169.831 73.0246i 0.583612 0.250944i
\(292\) 0 0
\(293\) −176.501 176.501i −0.602394 0.602394i 0.338553 0.940947i \(-0.390062\pi\)
−0.940947 + 0.338553i \(0.890062\pi\)
\(294\) 0 0
\(295\) 1.19007i 0.00403414i
\(296\) 0 0
\(297\) −314.450 + 145.301i −1.05876 + 0.489230i
\(298\) 0 0
\(299\) −246.790 246.790i −0.825384 0.825384i
\(300\) 0 0
\(301\) −154.930 154.930i −0.514718 0.514718i
\(302\) 0 0
\(303\) 189.907 + 75.7002i 0.626756 + 0.249836i
\(304\) 0 0
\(305\) 0.946938i 0.00310471i
\(306\) 0 0
\(307\) 63.9904 + 63.9904i 0.208438 + 0.208438i 0.803603 0.595165i \(-0.202913\pi\)
−0.595165 + 0.803603i \(0.702913\pi\)
\(308\) 0 0
\(309\) 5.61319 + 13.0544i 0.0181657 + 0.0422473i
\(310\) 0 0
\(311\) −532.288 −1.71154 −0.855769 0.517359i \(-0.826915\pi\)
−0.855769 + 0.517359i \(0.826915\pi\)
\(312\) 0 0
\(313\) 185.676i 0.593215i 0.954999 + 0.296607i \(0.0958553\pi\)
−0.954999 + 0.296607i \(0.904145\pi\)
\(314\) 0 0
\(315\) 0.0215736 + 0.805687i 6.84878e−5 + 0.00255774i
\(316\) 0 0
\(317\) 168.127 168.127i 0.530370 0.530370i −0.390312 0.920683i \(-0.627633\pi\)
0.920683 + 0.390312i \(0.127633\pi\)
\(318\) 0 0
\(319\) 202.742 0.635556
\(320\) 0 0
\(321\) 161.372 + 64.3256i 0.502715 + 0.200391i
\(322\) 0 0
\(323\) 39.3936 39.3936i 0.121962 0.121962i
\(324\) 0 0
\(325\) −315.243 + 315.243i −0.969980 + 0.969980i
\(326\) 0 0
\(327\) 474.652 + 189.204i 1.45153 + 0.578607i
\(328\) 0 0
\(329\) −40.4443 −0.122931
\(330\) 0 0
\(331\) −241.678 + 241.678i −0.730144 + 0.730144i −0.970648 0.240504i \(-0.922687\pi\)
0.240504 + 0.970648i \(0.422687\pi\)
\(332\) 0 0
\(333\) 3.17764 + 118.672i 0.00954245 + 0.356371i
\(334\) 0 0
\(335\) 0.468841i 0.00139953i
\(336\) 0 0
\(337\) 396.856 1.17762 0.588808 0.808273i \(-0.299598\pi\)
0.588808 + 0.808273i \(0.299598\pi\)
\(338\) 0 0
\(339\) 243.163 + 565.518i 0.717296 + 1.66819i
\(340\) 0 0
\(341\) −543.754 543.754i −1.59459 1.59459i
\(342\) 0 0
\(343\) 364.480i 1.06262i
\(344\) 0 0
\(345\) −0.760456 0.303131i −0.00220422 0.000878641i
\(346\) 0 0
\(347\) −38.5699 38.5699i −0.111153 0.111153i 0.649343 0.760496i \(-0.275044\pi\)
−0.760496 + 0.649343i \(0.775044\pi\)
\(348\) 0 0
\(349\) −10.4065 10.4065i −0.0298180 0.0298180i 0.692041 0.721859i \(-0.256712\pi\)
−0.721859 + 0.692041i \(0.756712\pi\)
\(350\) 0 0
\(351\) −437.084 + 201.968i −1.24525 + 0.575408i
\(352\) 0 0
\(353\) 209.294i 0.592900i −0.955048 0.296450i \(-0.904197\pi\)
0.955048 0.296450i \(-0.0958028\pi\)
\(354\) 0 0
\(355\) −0.133832 0.133832i −0.000376992 0.000376992i
\(356\) 0 0
\(357\) 336.600 144.732i 0.942857 0.405413i
\(358\) 0 0
\(359\) 42.6682 0.118853 0.0594264 0.998233i \(-0.481073\pi\)
0.0594264 + 0.998233i \(0.481073\pi\)
\(360\) 0 0
\(361\) 352.417i 0.976223i
\(362\) 0 0
\(363\) 51.6649 + 120.156i 0.142328 + 0.331007i
\(364\) 0 0
\(365\) 0.310088 0.310088i 0.000849557 0.000849557i
\(366\) 0 0
\(367\) 16.2444 0.0442627 0.0221313 0.999755i \(-0.492955\pi\)
0.0221313 + 0.999755i \(0.492955\pi\)
\(368\) 0 0
\(369\) −292.627 + 308.729i −0.793026 + 0.836664i
\(370\) 0 0
\(371\) 132.571 132.571i 0.357335 0.357335i
\(372\) 0 0
\(373\) −351.379 + 351.379i −0.942035 + 0.942035i −0.998410 0.0563743i \(-0.982046\pi\)
0.0563743 + 0.998410i \(0.482046\pi\)
\(374\) 0 0
\(375\) −0.774428 + 1.94278i −0.00206514 + 0.00518076i
\(376\) 0 0
\(377\) 281.811 0.747509
\(378\) 0 0
\(379\) −170.505 + 170.505i −0.449880 + 0.449880i −0.895315 0.445435i \(-0.853049\pi\)
0.445435 + 0.895315i \(0.353049\pi\)
\(380\) 0 0
\(381\) −149.227 + 64.1653i −0.391673 + 0.168413i
\(382\) 0 0
\(383\) 256.234i 0.669017i 0.942393 + 0.334509i \(0.108570\pi\)
−0.942393 + 0.334509i \(0.891430\pi\)
\(384\) 0 0
\(385\) 1.14892 0.00298422
\(386\) 0 0
\(387\) −8.21813 306.913i −0.0212355 0.793058i
\(388\) 0 0
\(389\) 376.214 + 376.214i 0.967130 + 0.967130i 0.999477 0.0323468i \(-0.0102981\pi\)
−0.0323468 + 0.999477i \(0.510298\pi\)
\(390\) 0 0
\(391\) 372.158i 0.951810i
\(392\) 0 0
\(393\) −49.1063 + 123.192i −0.124953 + 0.313465i
\(394\) 0 0
\(395\) 0.468035 + 0.468035i 0.00118490 + 0.00118490i
\(396\) 0 0
\(397\) 312.905 + 312.905i 0.788174 + 0.788174i 0.981195 0.193021i \(-0.0618284\pi\)
−0.193021 + 0.981195i \(0.561828\pi\)
\(398\) 0 0
\(399\) −20.9030 + 52.4388i −0.0523885 + 0.131426i
\(400\) 0 0
\(401\) 9.22373i 0.0230018i −0.999934 0.0115009i \(-0.996339\pi\)
0.999934 0.0115009i \(-0.00366093\pi\)
\(402\) 0 0
\(403\) −755.814 755.814i −1.87547 1.87547i
\(404\) 0 0
\(405\) −0.754715 + 0.840189i −0.00186349 + 0.00207454i
\(406\) 0 0
\(407\) 169.228 0.415793
\(408\) 0 0
\(409\) 322.436i 0.788352i 0.919035 + 0.394176i \(0.128970\pi\)
−0.919035 + 0.394176i \(0.871030\pi\)
\(410\) 0 0
\(411\) −118.282 + 50.8592i −0.287790 + 0.123745i
\(412\) 0 0
\(413\) 387.635 387.635i 0.938583 0.938583i
\(414\) 0 0
\(415\) −1.38683 −0.00334177
\(416\) 0 0
\(417\) −73.9845 + 185.603i −0.177421 + 0.445090i
\(418\) 0 0
\(419\) −226.569 + 226.569i −0.540738 + 0.540738i −0.923745 0.383007i \(-0.874888\pi\)
0.383007 + 0.923745i \(0.374888\pi\)
\(420\) 0 0
\(421\) 498.861 498.861i 1.18494 1.18494i 0.206495 0.978448i \(-0.433794\pi\)
0.978448 0.206495i \(-0.0662058\pi\)
\(422\) 0 0
\(423\) −41.1323 38.9870i −0.0972394 0.0921677i
\(424\) 0 0
\(425\) 475.385 1.11855
\(426\) 0 0
\(427\) −308.440 + 308.440i −0.722343 + 0.722343i
\(428\) 0 0
\(429\) 271.126 + 630.549i 0.631995 + 1.46981i
\(430\) 0 0
\(431\) 452.283i 1.04938i −0.851293 0.524690i \(-0.824181\pi\)
0.851293 0.524690i \(-0.175819\pi\)
\(432\) 0 0
\(433\) 379.557 0.876574 0.438287 0.898835i \(-0.355585\pi\)
0.438287 + 0.898835i \(0.355585\pi\)
\(434\) 0 0
\(435\) 0.607258 0.261111i 0.00139600 0.000600255i
\(436\) 0 0
\(437\) −40.5447 40.5447i −0.0927797 0.0927797i
\(438\) 0 0
\(439\) 689.509i 1.57063i 0.619094 + 0.785317i \(0.287500\pi\)
−0.619094 + 0.785317i \(0.712500\pi\)
\(440\) 0 0
\(441\) 47.9710 50.6107i 0.108778 0.114763i
\(442\) 0 0
\(443\) −97.5600 97.5600i −0.220226 0.220226i 0.588368 0.808593i \(-0.299771\pi\)
−0.808593 + 0.588368i \(0.799771\pi\)
\(444\) 0 0
\(445\) −0.938330 0.938330i −0.00210861 0.00210861i
\(446\) 0 0
\(447\) −518.377 206.634i −1.15968 0.462269i
\(448\) 0 0
\(449\) 718.711i 1.60069i −0.599538 0.800347i \(-0.704649\pi\)
0.599538 0.800347i \(-0.295351\pi\)
\(450\) 0 0
\(451\) 428.772 + 428.772i 0.950713 + 0.950713i
\(452\) 0 0
\(453\) 172.908 + 402.127i 0.381695 + 0.887698i
\(454\) 0 0
\(455\) 1.59700 0.00350988
\(456\) 0 0
\(457\) 489.021i 1.07007i 0.844830 + 0.535034i \(0.179701\pi\)
−0.844830 + 0.535034i \(0.820299\pi\)
\(458\) 0 0
\(459\) 481.843 + 177.277i 1.04977 + 0.386224i
\(460\) 0 0
\(461\) 459.082 459.082i 0.995840 0.995840i −0.00415179 0.999991i \(-0.501322\pi\)
0.999991 + 0.00415179i \(0.00132156\pi\)
\(462\) 0 0
\(463\) −587.611 −1.26914 −0.634569 0.772866i \(-0.718822\pi\)
−0.634569 + 0.772866i \(0.718822\pi\)
\(464\) 0 0
\(465\) −2.32896 0.928364i −0.00500852 0.00199648i
\(466\) 0 0
\(467\) −89.5077 + 89.5077i −0.191665 + 0.191665i −0.796415 0.604750i \(-0.793273\pi\)
0.604750 + 0.796415i \(0.293273\pi\)
\(468\) 0 0
\(469\) −152.713 + 152.713i −0.325614 + 0.325614i
\(470\) 0 0
\(471\) 217.778 + 86.8101i 0.462374 + 0.184310i
\(472\) 0 0
\(473\) −437.664 −0.925293
\(474\) 0 0
\(475\) −51.7909 + 51.7909i −0.109033 + 0.109033i
\(476\) 0 0
\(477\) 262.621 7.03213i 0.550568 0.0147424i
\(478\) 0 0
\(479\) 439.291i 0.917101i −0.888668 0.458550i \(-0.848369\pi\)
0.888668 0.458550i \(-0.151631\pi\)
\(480\) 0 0
\(481\) 235.226 0.489034
\(482\) 0 0
\(483\) −148.962 346.436i −0.308410 0.717259i
\(484\) 0 0
\(485\) −0.607542 0.607542i −0.00125266 0.00125266i
\(486\) 0 0
\(487\) 499.716i 1.02611i −0.858355 0.513056i \(-0.828513\pi\)
0.858355 0.513056i \(-0.171487\pi\)
\(488\) 0 0
\(489\) 278.301 + 110.936i 0.569123 + 0.226862i
\(490\) 0 0
\(491\) 359.246 + 359.246i 0.731663 + 0.731663i 0.970949 0.239286i \(-0.0769134\pi\)
−0.239286 + 0.970949i \(0.576913\pi\)
\(492\) 0 0
\(493\) −212.484 212.484i −0.431003 0.431003i
\(494\) 0 0
\(495\) 1.16847 + 1.10752i 0.00236054 + 0.00223742i
\(496\) 0 0
\(497\) 87.1846i 0.175422i
\(498\) 0 0
\(499\) −64.4682 64.4682i −0.129195 0.129195i 0.639553 0.768747i \(-0.279120\pi\)
−0.768747 + 0.639553i \(0.779120\pi\)
\(500\) 0 0
\(501\) 237.573 102.152i 0.474197 0.203897i
\(502\) 0 0
\(503\) −597.277 −1.18743 −0.593714 0.804676i \(-0.702339\pi\)
−0.593714 + 0.804676i \(0.702339\pi\)
\(504\) 0 0
\(505\) 0.950165i 0.00188151i
\(506\) 0 0
\(507\) 176.591 + 410.691i 0.348305 + 0.810042i
\(508\) 0 0
\(509\) −359.574 + 359.574i −0.706433 + 0.706433i −0.965783 0.259350i \(-0.916492\pi\)
0.259350 + 0.965783i \(0.416492\pi\)
\(510\) 0 0
\(511\) 202.006 0.395316
\(512\) 0 0
\(513\) −71.8079 + 33.1810i −0.139976 + 0.0646804i
\(514\) 0 0
\(515\) 0.0467000 0.0467000i 9.06796e−5 9.06796e-5i
\(516\) 0 0
\(517\) −57.1257 + 57.1257i −0.110495 + 0.110495i
\(518\) 0 0
\(519\) −91.4977 + 229.538i −0.176296 + 0.442269i
\(520\) 0 0
\(521\) −862.399 −1.65528 −0.827639 0.561261i \(-0.810316\pi\)
−0.827639 + 0.561261i \(0.810316\pi\)
\(522\) 0 0
\(523\) −256.574 + 256.574i −0.490581 + 0.490581i −0.908489 0.417908i \(-0.862763\pi\)
0.417908 + 0.908489i \(0.362763\pi\)
\(524\) 0 0
\(525\) −442.529 + 190.280i −0.842912 + 0.362438i
\(526\) 0 0
\(527\) 1139.76i 2.16274i
\(528\) 0 0
\(529\) −145.967 −0.275930
\(530\) 0 0
\(531\) 767.897 20.5617i 1.44613 0.0387227i
\(532\) 0 0
\(533\) 595.990 + 595.990i 1.11818 + 1.11818i
\(534\) 0 0
\(535\) 0.807394i 0.00150915i
\(536\) 0 0
\(537\) −29.7342 + 74.5933i −0.0553709 + 0.138907i
\(538\) 0 0
\(539\) −70.2895 70.2895i −0.130407 0.130407i
\(540\) 0 0
\(541\) 431.469 + 431.469i 0.797540 + 0.797540i 0.982707 0.185167i \(-0.0592826\pi\)
−0.185167 + 0.982707i \(0.559283\pi\)
\(542\) 0 0
\(543\) −38.5062 + 96.5993i −0.0709137 + 0.177899i
\(544\) 0 0
\(545\) 2.37483i 0.00435749i
\(546\) 0 0
\(547\) 335.381 + 335.381i 0.613127 + 0.613127i 0.943760 0.330632i \(-0.107262\pi\)
−0.330632 + 0.943760i \(0.607262\pi\)
\(548\) 0 0
\(549\) −611.014 + 16.3609i −1.11296 + 0.0298014i
\(550\) 0 0
\(551\) 46.2983 0.0840259
\(552\) 0 0
\(553\) 304.900i 0.551357i
\(554\) 0 0
\(555\) 0.506874 0.217948i 0.000913287 0.000392699i
\(556\) 0 0
\(557\) −118.642 + 118.642i −0.213001 + 0.213001i −0.805541 0.592540i \(-0.798125\pi\)
0.592540 + 0.805541i \(0.298125\pi\)
\(558\) 0 0
\(559\) −608.350 −1.08828
\(560\) 0 0
\(561\) 271.004 679.860i 0.483073 1.21187i
\(562\) 0 0
\(563\) −290.766 + 290.766i −0.516459 + 0.516459i −0.916498 0.400039i \(-0.868997\pi\)
0.400039 + 0.916498i \(0.368997\pi\)
\(564\) 0 0
\(565\) 2.02305 2.02305i 0.00358061 0.00358061i
\(566\) 0 0
\(567\) −519.499 + 27.8409i −0.916223 + 0.0491021i
\(568\) 0 0
\(569\) 669.398 1.17645 0.588223 0.808699i \(-0.299828\pi\)
0.588223 + 0.808699i \(0.299828\pi\)
\(570\) 0 0
\(571\) 454.971 454.971i 0.796798 0.796798i −0.185792 0.982589i \(-0.559485\pi\)
0.982589 + 0.185792i \(0.0594849\pi\)
\(572\) 0 0
\(573\) −185.367 431.102i −0.323502 0.752359i
\(574\) 0 0
\(575\) 489.277i 0.850916i
\(576\) 0 0
\(577\) −288.393 −0.499814 −0.249907 0.968270i \(-0.580400\pi\)
−0.249907 + 0.968270i \(0.580400\pi\)
\(578\) 0 0
\(579\) −600.737 + 258.307i −1.03754 + 0.446126i
\(580\) 0 0
\(581\) −451.725 451.725i −0.777496 0.777496i
\(582\) 0 0
\(583\) 374.502i 0.642371i
\(584\) 0 0
\(585\) 1.62416 + 1.53945i 0.00277635 + 0.00263154i
\(586\) 0 0
\(587\) −393.610 393.610i −0.670545 0.670545i 0.287297 0.957842i \(-0.407243\pi\)
−0.957842 + 0.287297i \(0.907243\pi\)
\(588\) 0 0
\(589\) −124.172 124.172i −0.210818 0.210818i
\(590\) 0 0
\(591\) 969.287 + 386.375i 1.64008 + 0.653764i
\(592\) 0 0
\(593\) 707.638i 1.19332i 0.802495 + 0.596659i \(0.203506\pi\)
−0.802495 + 0.596659i \(0.796494\pi\)
\(594\) 0 0
\(595\) −1.20413 1.20413i −0.00202375 0.00202375i
\(596\) 0 0
\(597\) −276.341 642.678i −0.462883 1.07651i
\(598\) 0 0
\(599\) 996.581 1.66374 0.831870 0.554970i \(-0.187270\pi\)
0.831870 + 0.554970i \(0.187270\pi\)
\(600\) 0 0
\(601\) 214.386i 0.356716i −0.983966 0.178358i \(-0.942921\pi\)
0.983966 0.178358i \(-0.0570785\pi\)
\(602\) 0 0
\(603\) −302.521 + 8.10051i −0.501693 + 0.0134337i
\(604\) 0 0
\(605\) 0.429836 0.429836i 0.000710474 0.000710474i
\(606\) 0 0
\(607\) 989.981 1.63094 0.815470 0.578799i \(-0.196478\pi\)
0.815470 + 0.578799i \(0.196478\pi\)
\(608\) 0 0
\(609\) 282.849 + 112.748i 0.464448 + 0.185137i
\(610\) 0 0
\(611\) −79.4044 + 79.4044i −0.129958 + 0.129958i
\(612\) 0 0
\(613\) −277.427 + 277.427i −0.452572 + 0.452572i −0.896207 0.443636i \(-0.853688\pi\)
0.443636 + 0.896207i \(0.353688\pi\)
\(614\) 0 0
\(615\) 1.83648 + 0.732052i 0.00298614 + 0.00119033i
\(616\) 0 0
\(617\) −294.951 −0.478040 −0.239020 0.971015i \(-0.576826\pi\)
−0.239020 + 0.971015i \(0.576826\pi\)
\(618\) 0 0
\(619\) 717.374 717.374i 1.15892 1.15892i 0.174218 0.984707i \(-0.444260\pi\)
0.984707 0.174218i \(-0.0557396\pi\)
\(620\) 0 0
\(621\) 182.457 495.924i 0.293812 0.798589i
\(622\) 0 0
\(623\) 611.273i 0.981177i
\(624\) 0 0
\(625\) −624.985 −0.999977
\(626\) 0 0
\(627\) 44.5428 + 103.592i 0.0710412 + 0.165218i
\(628\) 0 0
\(629\) −177.359 177.359i −0.281970 0.281970i
\(630\) 0 0
\(631\) 526.114i 0.833779i 0.908957 + 0.416889i \(0.136880\pi\)
−0.908957 + 0.416889i \(0.863120\pi\)
\(632\) 0 0
\(633\) −33.4795 13.3455i −0.0528903 0.0210830i
\(634\) 0 0
\(635\) 0.533835 + 0.533835i 0.000840686 + 0.000840686i
\(636\) 0 0
\(637\) −97.7020 97.7020i −0.153378 0.153378i
\(638\) 0 0
\(639\) 84.0431 88.6678i 0.131523 0.138760i
\(640\) 0 0
\(641\) 1025.84i 1.60037i 0.599754 + 0.800184i \(0.295265\pi\)
−0.599754 + 0.800184i \(0.704735\pi\)
\(642\) 0 0
\(643\) −366.197 366.197i −0.569514 0.569514i 0.362479 0.931992i \(-0.381931\pi\)
−0.931992 + 0.362479i \(0.881931\pi\)
\(644\) 0 0
\(645\) −1.31090 + 0.563665i −0.00203240 + 0.000873900i
\(646\) 0 0
\(647\) 90.9084 0.140508 0.0702538 0.997529i \(-0.477619\pi\)
0.0702538 + 0.997529i \(0.477619\pi\)
\(648\) 0 0
\(649\) 1095.03i 1.68726i
\(650\) 0 0
\(651\) −456.208 1060.99i −0.700780 1.62978i
\(652\) 0 0
\(653\) −291.274 + 291.274i −0.446056 + 0.446056i −0.894041 0.447985i \(-0.852142\pi\)
0.447985 + 0.894041i \(0.352142\pi\)
\(654\) 0 0
\(655\) 0.616367 0.000941019
\(656\) 0 0
\(657\) 205.443 + 194.728i 0.312698 + 0.296389i
\(658\) 0 0
\(659\) 817.853 817.853i 1.24105 1.24105i 0.281486 0.959565i \(-0.409173\pi\)
0.959565 0.281486i \(-0.0908273\pi\)
\(660\) 0 0
\(661\) 673.995 673.995i 1.01966 1.01966i 0.0198568 0.999803i \(-0.493679\pi\)
0.999803 0.0198568i \(-0.00632103\pi\)
\(662\) 0 0
\(663\) 376.694 945.001i 0.568166 1.42534i
\(664\) 0 0
\(665\) 0.262368 0.000394538
\(666\) 0 0
\(667\) −218.694 + 218.694i −0.327877 + 0.327877i
\(668\) 0 0
\(669\) 30.1206 12.9514i 0.0450233 0.0193593i
\(670\) 0 0
\(671\) 871.316i 1.29853i
\(672\) 0 0
\(673\) −526.059 −0.781662 −0.390831 0.920462i \(-0.627812\pi\)
−0.390831 + 0.920462i \(0.627812\pi\)
\(674\) 0 0
\(675\) −633.481 233.066i −0.938490 0.345283i
\(676\) 0 0
\(677\) −143.663 143.663i −0.212205 0.212205i 0.592998 0.805204i \(-0.297944\pi\)
−0.805204 + 0.592998i \(0.797944\pi\)
\(678\) 0 0
\(679\) 395.782i 0.582890i
\(680\) 0 0
\(681\) 156.945 393.723i 0.230462 0.578155i
\(682\) 0 0
\(683\) 50.6262 + 50.6262i 0.0741232 + 0.0741232i 0.743196 0.669073i \(-0.233309\pi\)
−0.669073 + 0.743196i \(0.733309\pi\)
\(684\) 0 0
\(685\) 0.423133 + 0.423133i 0.000617713 + 0.000617713i
\(686\) 0 0
\(687\) 364.243 913.765i 0.530193 1.33008i
\(688\) 0 0
\(689\) 520.556i 0.755523i
\(690\) 0 0
\(691\) 396.186 + 396.186i 0.573351 + 0.573351i 0.933063 0.359712i \(-0.117125\pi\)
−0.359712 + 0.933063i \(0.617125\pi\)
\(692\) 0 0
\(693\) 19.8508 + 741.345i 0.0286447 + 1.06976i
\(694\) 0 0
\(695\) 0.928629 0.00133616
\(696\) 0 0
\(697\) 898.749i 1.28945i
\(698\) 0 0
\(699\) −872.669 + 375.233i −1.24845 + 0.536815i
\(700\) 0 0
\(701\) −525.886 + 525.886i −0.750195 + 0.750195i −0.974515 0.224321i \(-0.927984\pi\)
0.224321 + 0.974515i \(0.427984\pi\)
\(702\) 0 0
\(703\) 38.6449 0.0549713
\(704\) 0 0
\(705\) −0.0975321 + 0.244676i −0.000138343 + 0.000347058i
\(706\) 0 0
\(707\) 309.492 309.492i 0.437753 0.437753i
\(708\) 0 0
\(709\) 99.4062 99.4062i 0.140206 0.140206i −0.633520 0.773726i \(-0.718391\pi\)
0.773726 + 0.633520i \(0.218391\pi\)
\(710\) 0 0
\(711\) −293.914 + 310.087i −0.413381 + 0.436128i
\(712\) 0 0
\(713\) 1173.07 1.64526
\(714\) 0 0
\(715\) 2.25568 2.25568i 0.00315480 0.00315480i
\(716\) 0 0
\(717\) −453.506 1054.71i −0.632505 1.47100i
\(718\) 0 0
\(719\) 551.765i 0.767406i 0.923456 + 0.383703i \(0.125351\pi\)
−0.923456 + 0.383703i \(0.874649\pi\)
\(720\) 0 0
\(721\) 30.4226 0.0421951
\(722\) 0 0
\(723\) −251.668 + 108.213i −0.348089 + 0.149673i
\(724\) 0 0
\(725\) 279.354 + 279.354i 0.385316 + 0.385316i
\(726\) 0 0
\(727\) 75.0947i 0.103294i 0.998665 + 0.0516470i \(0.0164471\pi\)
−0.998665 + 0.0516470i \(0.983553\pi\)
\(728\) 0 0
\(729\) −555.174 472.465i −0.761555 0.648100i
\(730\) 0 0
\(731\) 458.694 + 458.694i 0.627488 + 0.627488i
\(732\) 0 0
\(733\) −442.709 442.709i −0.603968 0.603968i 0.337395 0.941363i \(-0.390454\pi\)
−0.941363 + 0.337395i \(0.890454\pi\)
\(734\) 0 0
\(735\) −0.301058 0.120007i −0.000409603 0.000163275i
\(736\) 0 0
\(737\) 431.400i 0.585346i
\(738\) 0 0
\(739\) 283.395 + 283.395i 0.383485 + 0.383485i 0.872356 0.488871i \(-0.162591\pi\)
−0.488871 + 0.872356i \(0.662591\pi\)
\(740\) 0 0
\(741\) 61.9143 + 143.992i 0.0835550 + 0.194321i
\(742\) 0 0
\(743\) −835.949 −1.12510 −0.562550 0.826763i \(-0.690180\pi\)
−0.562550 + 0.826763i \(0.690180\pi\)
\(744\) 0 0
\(745\) 2.59361i 0.00348135i
\(746\) 0 0
\(747\) −23.9613 894.857i −0.0320768 1.19794i
\(748\) 0 0
\(749\) 262.988 262.988i 0.351118 0.351118i
\(750\) 0 0
\(751\) −753.712 −1.00361 −0.501806 0.864980i \(-0.667331\pi\)
−0.501806 + 0.864980i \(0.667331\pi\)
\(752\) 0 0
\(753\) −507.485 202.292i −0.673951 0.268648i
\(754\) 0 0
\(755\) 1.43854 1.43854i 0.00190535 0.00190535i
\(756\) 0 0
\(757\) 335.789 335.789i 0.443578 0.443578i −0.449634 0.893213i \(-0.648446\pi\)
0.893213 + 0.449634i \(0.148446\pi\)
\(758\) 0 0
\(759\) −699.727 278.923i −0.921906 0.367488i
\(760\) 0 0
\(761\) −1094.53 −1.43828 −0.719138 0.694868i \(-0.755463\pi\)
−0.719138 + 0.694868i \(0.755463\pi\)
\(762\) 0 0
\(763\) 773.541 773.541i 1.01381 1.01381i
\(764\) 0 0
\(765\) −0.0638720 2.38535i −8.34928e−5 0.00311811i
\(766\) 0 0
\(767\) 1522.09i 1.98447i
\(768\) 0 0
\(769\) 290.367 0.377590 0.188795 0.982016i \(-0.439542\pi\)
0.188795 + 0.982016i \(0.439542\pi\)
\(770\) 0 0
\(771\) −146.845 341.512i −0.190460 0.442947i
\(772\) 0 0
\(773\) −193.239 193.239i −0.249986 0.249986i 0.570979 0.820965i \(-0.306564\pi\)
−0.820965 + 0.570979i \(0.806564\pi\)
\(774\) 0 0
\(775\) 1498.45i 1.93348i
\(776\) 0 0
\(777\) 236.092 + 94.1104i 0.303851 + 0.121120i
\(778\) 0 0
\(779\) 97.9143 + 97.9143i 0.125692 + 0.125692i
\(780\) 0 0
\(781\) −123.144 123.144i −0.157675 0.157675i
\(782\) 0 0
\(783\) 178.975 + 387.323i 0.228575 + 0.494666i
\(784\) 0 0
\(785\) 1.08961i 0.00138804i
\(786\) 0 0
\(787\) 483.899 + 483.899i 0.614865 + 0.614865i 0.944210 0.329345i \(-0.106828\pi\)
−0.329345 + 0.944210i \(0.606828\pi\)
\(788\) 0 0
\(789\) −535.714 + 230.348i −0.678979 + 0.291950i
\(790\) 0 0
\(791\) 1317.91 1.66613
\(792\) 0 0
\(793\) 1211.12i 1.52727i
\(794\) 0 0
\(795\) −0.482320 1.12172i