Properties

Label 384.3.i.c.353.9
Level $384$
Weight $3$
Character 384.353
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 353.9
Root \(0.312316 - 1.97546i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.c.161.9

$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.75602 + 1.18505i 0.918675 + 0.395015i
\(4\) 0 0
\(5\) −0.00985921 + 0.00985921i −0.00197184 + 0.00197184i −0.708092 0.706120i \(-0.750444\pi\)
0.706120 + 0.708092i \(0.250444\pi\)
\(6\) 0 0
\(7\) 6.42277i 0.917538i 0.888556 + 0.458769i \(0.151709\pi\)
−0.888556 + 0.458769i \(0.848291\pi\)
\(8\) 0 0
\(9\) 6.19134 + 6.53203i 0.687926 + 0.725781i
\(10\) 0 0
\(11\) −9.07186 + 9.07186i −0.824715 + 0.824715i −0.986780 0.162065i \(-0.948185\pi\)
0.162065 + 0.986780i \(0.448185\pi\)
\(12\) 0 0
\(13\) −12.6098 + 12.6098i −0.969987 + 0.969987i −0.999563 0.0295753i \(-0.990585\pi\)
0.0295753 + 0.999563i \(0.490585\pi\)
\(14\) 0 0
\(15\) −0.0388558 + 0.0154886i −0.00259039 + 0.00103257i
\(16\) 0 0
\(17\) 19.0155i 1.11856i −0.828978 0.559281i \(-0.811077\pi\)
0.828978 0.559281i \(-0.188923\pi\)
\(18\) 0 0
\(19\) −2.07165 + 2.07165i −0.109034 + 0.109034i −0.759519 0.650485i \(-0.774566\pi\)
0.650485 + 0.759519i \(0.274566\pi\)
\(20\) 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 0.487695 0.873014i \(-0.337838\pi\)
−0.873014 + 0.487695i \(0.837838\pi\)
\(30\) 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 0.569741 0.821824i \(-0.307043\pi\)
−0.821824 + 0.569741i \(0.807043\pi\)
\(38\) 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 0.929585 0.368607i \(-0.120165\pi\)
−0.368607 + 0.929585i \(0.620165\pi\)
\(44\) 0 0
\(45\) −0.125442 0.00335893i −0.00278761 7.46430e-5i
\(46\) 0 0
\(47\) 6.29702i 0.133979i 0.997754 + 0.0669896i \(0.0213394\pi\)
−0.997754 + 0.0669896i \(0.978661\pi\)
\(48\) 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 −0.485041 0.874491i \(-0.661195\pi\)
0.874491 + 0.485041i \(0.161195\pi\)
\(54\) 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 0.0232062 0.999731i \(-0.492613\pi\)
0.999731 0.0232062i \(-0.00738742\pi\)
\(60\) 0 0
\(61\) −48.0230 + 48.0230i −0.787262 + 0.787262i −0.981045 0.193782i \(-0.937924\pi\)
0.193782 + 0.981045i \(0.437924\pi\)
\(62\) 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 −0.861921 0.507043i \(-0.830738\pi\)
0.507043 + 0.861921i \(0.330738\pi\)
\(68\) 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 \(-0.930887\pi\)
0.976521 0.215422i \(-0.0691127\pi\)
\(74\) 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 0.989804 0.142433i \(-0.0454925\pi\)
−0.142433 + 0.989804i \(0.545493\pi\)
\(84\) 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 −0.427106 0.904202i \(-0.640467\pi\)
0.904202 + 0.427106i \(0.140467\pi\)
\(102\) 0 0
\(103\) 4.73669i 0.0459873i −0.999736 0.0229936i \(-0.992680\pi\)
0.999736 0.0229936i \(-0.00731975\pi\)
\(104\) 0 0
\(105\) −0.0994797 0.249562i −0.000947426 0.00237678i
\(106\) 0 0
\(107\) 40.9462 40.9462i 0.382674 0.382674i −0.489390 0.872065i \(-0.662781\pi\)
0.872065 + 0.489390i \(0.162781\pi\)
\(108\) 0 0
\(109\) 120.437 120.437i 1.10493 1.10493i 0.111123 0.993807i \(-0.464555\pi\)
0.993807 0.111123i \(-0.0354447\pi\)
\(110\) 0 0
\(111\) −14.6526 36.7586i −0.132006 0.331159i
\(112\) 0 0
\(113\) 205.193i 1.81587i −0.419110 0.907936i \(-0.637658\pi\)
0.419110 0.907936i \(-0.362342\pi\)
\(114\) 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 0.577662 0.816276i \(-0.303965\pi\)
−0.816276 + 0.577662i \(0.803965\pi\)
\(132\) 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 0.517110 0.855919i \(-0.327008\pi\)
−0.855919 + 0.517110i \(0.827008\pi\)
\(140\) 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 −0.993815 0.111049i \(-0.964579\pi\)
0.111049 + 0.993815i \(0.464579\pi\)
\(150\) 0 0
\(151\) 145.908i 0.966281i −0.875543 0.483140i \(-0.839496\pi\)
0.875543 0.483140i \(-0.160504\pi\)
\(152\) 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 −0.508875 0.860840i \(-0.669938\pi\)
0.860840 + 0.508875i \(0.169938\pi\)
\(158\) 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 −0.456499 0.889724i \(-0.650897\pi\)
0.889724 + 0.456499i \(0.150897\pi\)
\(164\) 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 0.518448 0.855109i \(-0.326510\pi\)
−0.855109 + 0.518448i \(0.826510\pi\)
\(174\) 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 0.652258 0.757997i \(-0.273822\pi\)
−0.757997 + 0.652258i \(0.773822\pi\)
\(180\) 0 0
\(181\) −24.5109 24.5109i −0.135420 0.135420i 0.636148 0.771567i \(-0.280527\pi\)
−0.771567 + 0.636148i \(0.780527\pi\)
\(182\) 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 \(0.134290\pi\)
−0.912319 + 0.409481i \(0.865710\pi\)
\(192\) 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 0.292050 0.956403i \(-0.405663\pi\)
0.956403 0.292050i \(-0.0943374\pi\)
\(198\) 0 0
\(199\) 233.190i 1.17181i 0.810379 + 0.585905i \(0.199261\pi\)
−0.810379 + 0.585905i \(0.800739\pi\)
\(200\) 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 −0.726951 0.686690i \(-0.759063\pi\)
0.686690 + 0.726951i \(0.259063\pi\)
\(212\) 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 0.892045 0.451946i \(-0.149270\pi\)
−0.451946 + 0.892045i \(0.649270\pi\)
\(228\) 0 0
\(229\) 231.857 + 231.857i 1.01248 + 1.01248i 0.999921 + 0.0125555i \(0.00399663\pi\)
0.0125555 + 0.999921i \(0.496003\pi\)
\(230\) 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 \(0.295491\pi\)
−0.599187 + 0.800609i \(0.704509\pi\)
\(240\) 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 −0.915451 0.402430i \(-0.868166\pi\)
0.402430 + 0.915451i \(0.368166\pi\)
\(252\) 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 \(0.0775014\pi\)
−0.970505 + 0.241079i \(0.922499\pi\)
\(258\) 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 −0.994079 0.108658i \(-0.965345\pi\)
−0.108658 0.994079i \(-0.534655\pi\)
\(270\) 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 0.807297 0.590145i \(-0.200929\pi\)
−0.590145 + 0.807297i \(0.700929\pi\)
\(278\) 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 0.999900 + 0.0141627i \(0.00450829\pi\)
0.0141627 + 0.999900i \(0.495492\pi\)
\(284\) 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 −0.940947 0.338553i \(-0.890062\pi\)
0.338553 + 0.940947i \(0.390062\pi\)
\(294\) 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 −0.595165 0.803603i \(-0.702913\pi\)
0.803603 + 0.595165i \(0.202913\pi\)
\(308\) 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 \(-0.904145\pi\)
0.954999 0.296607i \(-0.0958553\pi\)
\(314\) 0 0
\(315\) 0.0215736 0.805687i 6.84878e−5 0.00255774i
\(316\) 0 0
\(317\) 168.127 + 168.127i 0.530370 + 0.530370i 0.920683 0.390312i \(-0.127633\pi\)
−0.390312 + 0.920683i \(0.627633\pi\)
\(318\) 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 0.240504 0.970648i \(-0.422687\pi\)
−0.970648 + 0.240504i \(0.922687\pi\)
\(332\) 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 −0.760496 0.649343i \(-0.775044\pi\)
0.649343 + 0.760496i \(0.275044\pi\)
\(348\) 0 0
\(349\) −10.4065 + 10.4065i −0.0298180 + 0.0298180i −0.721859 0.692041i \(-0.756712\pi\)
0.692041 + 0.721859i \(0.256712\pi\)
\(350\) 0 0
\(351\) −437.084 201.968i −1.24525 0.575408i
\(352\) 0 0
\(353\) 209.294i 0.592900i 0.955048 + 0.296450i \(0.0958028\pi\)
−0.955048 + 0.296450i \(0.904197\pi\)
\(354\) 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 0.0563743 0.998410i \(-0.482046\pi\)
−0.998410 + 0.0563743i \(0.982046\pi\)
\(374\) 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 0.445435 0.895315i \(-0.353049\pi\)
−0.895315 + 0.445435i \(0.853049\pi\)
\(380\) 0 0
\(381\) −149.227 64.1653i −0.391673 0.168413i
\(382\) 0 0
\(383\) 256.234i 0.669017i −0.942393 0.334509i \(-0.891430\pi\)
0.942393 0.334509i \(-0.108570\pi\)
\(384\) 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 −0.0323468 0.999477i \(-0.510298\pi\)
0.999477 + 0.0323468i \(0.0102981\pi\)
\(390\) 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 −0.193021 0.981195i \(-0.561828\pi\)
0.981195 + 0.193021i \(0.0618284\pi\)
\(398\) 0 0
\(399\) −20.9030 52.4388i −0.0523885 0.131426i
\(400\) 0 0
\(401\) 9.22373i 0.0230018i 0.999934 + 0.0115009i \(0.00366093\pi\)
−0.999934 + 0.0115009i \(0.996339\pi\)
\(402\) 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 \(-0.871030\pi\)
0.919035 0.394176i \(-0.128970\pi\)
\(410\) 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 0.383007 0.923745i \(-0.374888\pi\)
−0.923745 + 0.383007i \(0.874888\pi\)
\(420\) 0 0
\(421\) 498.861 + 498.861i 1.18494 + 1.18494i 0.978448 + 0.206495i \(0.0662058\pi\)
0.206495 + 0.978448i \(0.433794\pi\)
\(422\) 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 \(0.175819\pi\)
−0.851293 + 0.524690i \(0.824181\pi\)
\(432\) 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 \(-0.712500\pi\)
0.619094 0.785317i \(-0.287500\pi\)
\(440\) 0 0
\(441\) 47.9710 + 50.6107i 0.108778 + 0.114763i
\(442\) 0 0
\(443\) −97.5600 + 97.5600i −0.220226 + 0.220226i −0.808593 0.588368i \(-0.799771\pi\)
0.588368 + 0.808593i \(0.299771\pi\)
\(444\) 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 \(0.295351\pi\)
−0.599538 + 0.800347i \(0.704649\pi\)
\(450\) 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 \(-0.820299\pi\)
0.844830 0.535034i \(-0.179701\pi\)
\(458\) 0 0
\(459\) 481.843 177.277i 1.04977 0.386224i
\(460\) 0 0
\(461\) 459.082 + 459.082i 0.995840 + 0.995840i 0.999991 0.00415179i \(-0.00132156\pi\)
−0.00415179 + 0.999991i \(0.501322\pi\)
\(462\) 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 0.604750 0.796415i \(-0.293273\pi\)
−0.796415 + 0.604750i \(0.793273\pi\)
\(468\) 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 \(0.151631\pi\)
−0.888668 + 0.458550i \(0.848369\pi\)
\(480\) 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 \(0.171487\pi\)
−0.858355 + 0.513056i \(0.828513\pi\)
\(488\) 0 0
\(489\) 278.301 110.936i 0.569123 0.226862i
\(490\) 0 0
\(491\) 359.246 359.246i 0.731663 0.731663i −0.239286 0.970949i \(-0.576913\pi\)
0.970949 + 0.239286i \(0.0769134\pi\)
\(492\) 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 −0.768747 0.639553i \(-0.779120\pi\)
0.639553 + 0.768747i \(0.279120\pi\)
\(500\) 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 0.259350 0.965783i \(-0.416492\pi\)
−0.965783 + 0.259350i \(0.916492\pi\)
\(510\) 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 0.417908 0.908489i \(-0.362763\pi\)
−0.908489 + 0.417908i \(0.862763\pi\)
\(524\) 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 −0.185167 0.982707i \(-0.559283\pi\)
0.982707 + 0.185167i \(0.0592826\pi\)
\(542\) 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 −0.330632 0.943760i \(-0.607262\pi\)
0.943760 + 0.330632i \(0.107262\pi\)
\(548\) 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 0.592540 0.805541i \(-0.298125\pi\)
−0.805541 + 0.592540i \(0.798125\pi\)
\(558\) 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 0.400039 0.916498i \(-0.368997\pi\)
−0.916498 + 0.400039i \(0.868997\pi\)
\(564\) 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 0.982589 0.185792i \(-0.0594849\pi\)
−0.185792 + 0.982589i \(0.559485\pi\)
\(572\) 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 −0.957842 0.287297i \(-0.907243\pi\)
0.287297 + 0.957842i \(0.407243\pi\)
\(588\) 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 \(-0.796494\pi\)
0.802495 0.596659i \(-0.203506\pi\)
\(594\) 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 \(0.0570785\pi\)
−0.983966 + 0.178358i \(0.942921\pi\)
\(602\) 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 0.443636 0.896207i \(-0.353688\pi\)
−0.896207 + 0.443636i \(0.853688\pi\)
\(614\) 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 0.984707 + 0.174218i \(0.0557396\pi\)
0.174218 + 0.984707i \(0.444260\pi\)
\(620\) 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 \(-0.863120\pi\)
0.908957 0.416889i \(-0.136880\pi\)
\(632\) 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 \(-0.704735\pi\)
0.599754 0.800184i \(-0.295265\pi\)
\(642\) 0 0
\(643\) −366.197 + 366.197i −0.569514 + 0.569514i −0.931992 0.362479i \(-0.881931\pi\)
0.362479 + 0.931992i \(0.381931\pi\)
\(644\) 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 0.447985 0.894041i \(-0.352142\pi\)
−0.894041 + 0.447985i \(0.852142\pi\)
\(654\) 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 0.959565 + 0.281486i \(0.0908273\pi\)
0.281486 + 0.959565i \(0.409173\pi\)
\(660\) 0 0
\(661\) 673.995 + 673.995i 1.01966 + 1.01966i 0.999803 + 0.0198568i \(0.00632103\pi\)
0.0198568 + 0.999803i \(0.493679\pi\)
\(662\) 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 −0.805204 0.592998i \(-0.797944\pi\)
0.592998 + 0.805204i \(0.297944\pi\)
\(678\) 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 −0.669073 0.743196i \(-0.733309\pi\)
0.743196 + 0.669073i \(0.233309\pi\)
\(684\) 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 −0.359712 0.933063i \(-0.617125\pi\)
0.933063 + 0.359712i \(0.117125\pi\)
\(692\) 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 0.224321 0.974515i \(-0.427984\pi\)
−0.974515 + 0.224321i \(0.927984\pi\)
\(702\) 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 0.773726 0.633520i \(-0.218391\pi\)
−0.633520 + 0.773726i \(0.718391\pi\)
\(710\) 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 \(-0.874649\pi\)
0.923456 0.383703i \(-0.125351\pi\)
\(720\) 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 \(-0.983553\pi\)
0.998665 0.0516470i \(-0.0164471\pi\)
\(728\) 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 −0.941363 0.337395i \(-0.890454\pi\)
0.337395 + 0.941363i \(0.390454\pi\)
\(734\) 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 −0.488871 0.872356i \(-0.662591\pi\)
0.872356 + 0.488871i \(0.162591\pi\)
\(740\) 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 0.893213 0.449634i \(-0.148446\pi\)
−0.449634 + 0.893213i \(0.648446\pi\)
\(758\) 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 −0.820965 0.570979i \(-0.806564\pi\)
0.570979 + 0.820965i \(0.306564\pi\)
\(774\) 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 −0.329345 0.944210i \(-0.606828\pi\)
0.944210 + 0.329345i \(0.106828\pi\)
\(788\) 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
\(795\)