Properties

Label 192.3.l.a.79.1
Level $192$
Weight $3$
Character 192.79
Analytic conductor $5.232$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 192 = 2^{6} \cdot 3 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 192.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.23162107572\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + 65536\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{24} \)
Twist minimal: no (minimal twist has level 48)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 79.1
Root \(-1.87459 + 0.697079i\) of defining polynomial
Character \(\chi\) \(=\) 192.79
Dual form 192.3.l.a.175.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 1.22474i) q^{3} +(-5.24354 - 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +O(q^{10})\) \(q+(-1.22474 - 1.22474i) q^{3} +(-5.24354 - 5.24354i) q^{5} +5.32796 q^{7} +3.00000i q^{9} +(-12.2863 + 12.2863i) q^{11} +(-5.73657 + 5.73657i) q^{13} +12.8440i q^{15} -23.3997 q^{17} +(-11.7492 - 11.7492i) q^{19} +(-6.52540 - 6.52540i) q^{21} -5.80841 q^{23} +29.9894i q^{25} +(3.67423 - 3.67423i) q^{27} +(18.3914 - 18.3914i) q^{29} -16.9053i q^{31} +30.0951 q^{33} +(-27.9374 - 27.9374i) q^{35} +(15.3391 + 15.3391i) q^{37} +14.0517 q^{39} +29.2351i q^{41} +(-33.4099 + 33.4099i) q^{43} +(15.7306 - 15.7306i) q^{45} -18.2125i q^{47} -20.6128 q^{49} +(28.6586 + 28.6586i) q^{51} +(-66.9856 - 66.9856i) q^{53} +128.847 q^{55} +28.7796i q^{57} +(27.1523 - 27.1523i) q^{59} +(65.2399 - 65.2399i) q^{61} +15.9839i q^{63} +60.1599 q^{65} +(37.6951 + 37.6951i) q^{67} +(7.11382 + 7.11382i) q^{69} -42.6559 q^{71} -106.391i q^{73} +(36.7294 - 36.7294i) q^{75} +(-65.4607 + 65.4607i) q^{77} -21.2821i q^{79} -9.00000 q^{81} +(-24.1638 - 24.1638i) q^{83} +(122.697 + 122.697i) q^{85} -45.0495 q^{87} -52.8029i q^{89} +(-30.5643 + 30.5643i) q^{91} +(-20.7047 + 20.7047i) q^{93} +123.215i q^{95} -21.0222 q^{97} +(-36.8588 - 36.8588i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + O(q^{10}) \) \( 16q - 32q^{11} + 32q^{19} + 128q^{23} + 32q^{29} - 96q^{35} - 96q^{37} - 160q^{43} + 112q^{49} + 96q^{51} - 160q^{53} + 256q^{55} + 128q^{59} - 32q^{61} - 32q^{65} - 320q^{67} + 96q^{69} - 512q^{71} - 192q^{75} + 224q^{77} - 144q^{81} + 160q^{83} + 160q^{85} + 480q^{91} - 96q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).

\(n\) \(65\) \(127\) \(133\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) −5.24354 5.24354i −1.04871 1.04871i −0.998751 0.0499563i \(-0.984092\pi\)
−0.0499563 0.998751i \(-0.515908\pi\)
\(6\) 0 0
\(7\) 5.32796 0.761138 0.380569 0.924753i \(-0.375728\pi\)
0.380569 + 0.924753i \(0.375728\pi\)
\(8\) 0 0
\(9\) 3.00000i 0.333333i
\(10\) 0 0
\(11\) −12.2863 + 12.2863i −1.11693 + 1.11693i −0.124743 + 0.992189i \(0.539811\pi\)
−0.992189 + 0.124743i \(0.960189\pi\)
\(12\) 0 0
\(13\) −5.73657 + 5.73657i −0.441275 + 0.441275i −0.892440 0.451165i \(-0.851008\pi\)
0.451165 + 0.892440i \(0.351008\pi\)
\(14\) 0 0
\(15\) 12.8440i 0.856266i
\(16\) 0 0
\(17\) −23.3997 −1.37645 −0.688226 0.725496i \(-0.741610\pi\)
−0.688226 + 0.725496i \(0.741610\pi\)
\(18\) 0 0
\(19\) −11.7492 11.7492i −0.618380 0.618380i 0.326736 0.945116i \(-0.394051\pi\)
−0.945116 + 0.326736i \(0.894051\pi\)
\(20\) 0 0
\(21\) −6.52540 6.52540i −0.310733 0.310733i
\(22\) 0 0
\(23\) −5.80841 −0.252540 −0.126270 0.991996i \(-0.540301\pi\)
−0.126270 + 0.991996i \(0.540301\pi\)
\(24\) 0 0
\(25\) 29.9894i 1.19958i
\(26\) 0 0
\(27\) 3.67423 3.67423i 0.136083 0.136083i
\(28\) 0 0
\(29\) 18.3914 18.3914i 0.634185 0.634185i −0.314930 0.949115i \(-0.601981\pi\)
0.949115 + 0.314930i \(0.101981\pi\)
\(30\) 0 0
\(31\) 16.9053i 0.545332i −0.962109 0.272666i \(-0.912095\pi\)
0.962109 0.272666i \(-0.0879053\pi\)
\(32\) 0 0
\(33\) 30.0951 0.911971
\(34\) 0 0
\(35\) −27.9374 27.9374i −0.798211 0.798211i
\(36\) 0 0
\(37\) 15.3391 + 15.3391i 0.414571 + 0.414571i 0.883327 0.468756i \(-0.155298\pi\)
−0.468756 + 0.883327i \(0.655298\pi\)
\(38\) 0 0
\(39\) 14.0517 0.360299
\(40\) 0 0
\(41\) 29.2351i 0.713051i 0.934286 + 0.356526i \(0.116039\pi\)
−0.934286 + 0.356526i \(0.883961\pi\)
\(42\) 0 0
\(43\) −33.4099 + 33.4099i −0.776975 + 0.776975i −0.979315 0.202340i \(-0.935145\pi\)
0.202340 + 0.979315i \(0.435145\pi\)
\(44\) 0 0
\(45\) 15.7306 15.7306i 0.349569 0.349569i
\(46\) 0 0
\(47\) 18.2125i 0.387500i −0.981051 0.193750i \(-0.937935\pi\)
0.981051 0.193750i \(-0.0620650\pi\)
\(48\) 0 0
\(49\) −20.6128 −0.420670
\(50\) 0 0
\(51\) 28.6586 + 28.6586i 0.561934 + 0.561934i
\(52\) 0 0
\(53\) −66.9856 66.9856i −1.26388 1.26388i −0.949197 0.314681i \(-0.898102\pi\)
−0.314681 0.949197i \(-0.601898\pi\)
\(54\) 0 0
\(55\) 128.847 2.34267
\(56\) 0 0
\(57\) 28.7796i 0.504905i
\(58\) 0 0
\(59\) 27.1523 27.1523i 0.460209 0.460209i −0.438515 0.898724i \(-0.644495\pi\)
0.898724 + 0.438515i \(0.144495\pi\)
\(60\) 0 0
\(61\) 65.2399 65.2399i 1.06951 1.06951i 0.0721103 0.997397i \(-0.477027\pi\)
0.997397 0.0721103i \(-0.0229733\pi\)
\(62\) 0 0
\(63\) 15.9839i 0.253713i
\(64\) 0 0
\(65\) 60.1599 0.925537
\(66\) 0 0
\(67\) 37.6951 + 37.6951i 0.562614 + 0.562614i 0.930049 0.367435i \(-0.119764\pi\)
−0.367435 + 0.930049i \(0.619764\pi\)
\(68\) 0 0
\(69\) 7.11382 + 7.11382i 0.103099 + 0.103099i
\(70\) 0 0
\(71\) −42.6559 −0.600788 −0.300394 0.953815i \(-0.597118\pi\)
−0.300394 + 0.953815i \(0.597118\pi\)
\(72\) 0 0
\(73\) 106.391i 1.45742i −0.684825 0.728708i \(-0.740121\pi\)
0.684825 0.728708i \(-0.259879\pi\)
\(74\) 0 0
\(75\) 36.7294 36.7294i 0.489725 0.489725i
\(76\) 0 0
\(77\) −65.4607 + 65.4607i −0.850139 + 0.850139i
\(78\) 0 0
\(79\) 21.2821i 0.269394i −0.990887 0.134697i \(-0.956994\pi\)
0.990887 0.134697i \(-0.0430061\pi\)
\(80\) 0 0
\(81\) −9.00000 −0.111111
\(82\) 0 0
\(83\) −24.1638 24.1638i −0.291130 0.291130i 0.546396 0.837527i \(-0.315999\pi\)
−0.837527 + 0.546396i \(0.815999\pi\)
\(84\) 0 0
\(85\) 122.697 + 122.697i 1.44350 + 1.44350i
\(86\) 0 0
\(87\) −45.0495 −0.517810
\(88\) 0 0
\(89\) 52.8029i 0.593291i −0.954988 0.296645i \(-0.904132\pi\)
0.954988 0.296645i \(-0.0958679\pi\)
\(90\) 0 0
\(91\) −30.5643 + 30.5643i −0.335871 + 0.335871i
\(92\) 0 0
\(93\) −20.7047 + 20.7047i −0.222631 + 0.222631i
\(94\) 0 0
\(95\) 123.215i 1.29700i
\(96\) 0 0
\(97\) −21.0222 −0.216724 −0.108362 0.994112i \(-0.534560\pi\)
−0.108362 + 0.994112i \(0.534560\pi\)
\(98\) 0 0
\(99\) −36.8588 36.8588i −0.372311 0.372311i
\(100\) 0 0
\(101\) −3.24960 3.24960i −0.0321743 0.0321743i 0.690837 0.723011i \(-0.257242\pi\)
−0.723011 + 0.690837i \(0.757242\pi\)
\(102\) 0 0
\(103\) −105.112 −1.02050 −0.510252 0.860025i \(-0.670448\pi\)
−0.510252 + 0.860025i \(0.670448\pi\)
\(104\) 0 0
\(105\) 68.4323i 0.651736i
\(106\) 0 0
\(107\) 99.6160 99.6160i 0.930991 0.930991i −0.0667770 0.997768i \(-0.521272\pi\)
0.997768 + 0.0667770i \(0.0212716\pi\)
\(108\) 0 0
\(109\) −108.050 + 108.050i −0.991282 + 0.991282i −0.999962 0.00868078i \(-0.997237\pi\)
0.00868078 + 0.999962i \(0.497237\pi\)
\(110\) 0 0
\(111\) 37.5730i 0.338496i
\(112\) 0 0
\(113\) −23.2835 −0.206048 −0.103024 0.994679i \(-0.532852\pi\)
−0.103024 + 0.994679i \(0.532852\pi\)
\(114\) 0 0
\(115\) 30.4566 + 30.4566i 0.264840 + 0.264840i
\(116\) 0 0
\(117\) −17.2097 17.2097i −0.147092 0.147092i
\(118\) 0 0
\(119\) −124.673 −1.04767
\(120\) 0 0
\(121\) 180.904i 1.49508i
\(122\) 0 0
\(123\) 35.8055 35.8055i 0.291102 0.291102i
\(124\) 0 0
\(125\) 26.1621 26.1621i 0.209297 0.209297i
\(126\) 0 0
\(127\) 118.180i 0.930550i −0.885166 0.465275i \(-0.845955\pi\)
0.885166 0.465275i \(-0.154045\pi\)
\(128\) 0 0
\(129\) 81.8373 0.634398
\(130\) 0 0
\(131\) 69.2067 + 69.2067i 0.528296 + 0.528296i 0.920064 0.391768i \(-0.128137\pi\)
−0.391768 + 0.920064i \(0.628137\pi\)
\(132\) 0 0
\(133\) −62.5994 62.5994i −0.470672 0.470672i
\(134\) 0 0
\(135\) −38.5320 −0.285422
\(136\) 0 0
\(137\) 124.474i 0.908572i 0.890856 + 0.454286i \(0.150106\pi\)
−0.890856 + 0.454286i \(0.849894\pi\)
\(138\) 0 0
\(139\) −169.014 + 169.014i −1.21593 + 1.21593i −0.246881 + 0.969046i \(0.579406\pi\)
−0.969046 + 0.246881i \(0.920594\pi\)
\(140\) 0 0
\(141\) −22.3057 + 22.3057i −0.158196 + 0.158196i
\(142\) 0 0
\(143\) 140.962i 0.985749i
\(144\) 0 0
\(145\) −192.872 −1.33015
\(146\) 0 0
\(147\) 25.2454 + 25.2454i 0.171738 + 0.171738i
\(148\) 0 0
\(149\) 146.988 + 146.988i 0.986495 + 0.986495i 0.999910 0.0134145i \(-0.00427011\pi\)
−0.0134145 + 0.999910i \(0.504270\pi\)
\(150\) 0 0
\(151\) −75.5456 −0.500302 −0.250151 0.968207i \(-0.580480\pi\)
−0.250151 + 0.968207i \(0.580480\pi\)
\(152\) 0 0
\(153\) 70.1991i 0.458817i
\(154\) 0 0
\(155\) −88.6435 + 88.6435i −0.571893 + 0.571893i
\(156\) 0 0
\(157\) −81.5356 + 81.5356i −0.519335 + 0.519335i −0.917370 0.398035i \(-0.869692\pi\)
0.398035 + 0.917370i \(0.369692\pi\)
\(158\) 0 0
\(159\) 164.080i 1.03195i
\(160\) 0 0
\(161\) −30.9470 −0.192217
\(162\) 0 0
\(163\) −55.8065 55.8065i −0.342371 0.342371i 0.514887 0.857258i \(-0.327834\pi\)
−0.857258 + 0.514887i \(0.827834\pi\)
\(164\) 0 0
\(165\) −157.805 157.805i −0.956391 0.956391i
\(166\) 0 0
\(167\) 24.6339 0.147508 0.0737540 0.997276i \(-0.476502\pi\)
0.0737540 + 0.997276i \(0.476502\pi\)
\(168\) 0 0
\(169\) 103.183i 0.610553i
\(170\) 0 0
\(171\) 35.2476 35.2476i 0.206127 0.206127i
\(172\) 0 0
\(173\) 4.88551 4.88551i 0.0282399 0.0282399i −0.692846 0.721086i \(-0.743643\pi\)
0.721086 + 0.692846i \(0.243643\pi\)
\(174\) 0 0
\(175\) 159.782i 0.913042i
\(176\) 0 0
\(177\) −66.5094 −0.375759
\(178\) 0 0
\(179\) 229.504 + 229.504i 1.28215 + 1.28215i 0.939444 + 0.342702i \(0.111342\pi\)
0.342702 + 0.939444i \(0.388658\pi\)
\(180\) 0 0
\(181\) 116.607 + 116.607i 0.644238 + 0.644238i 0.951595 0.307356i \(-0.0994443\pi\)
−0.307356 + 0.951595i \(0.599444\pi\)
\(182\) 0 0
\(183\) −159.805 −0.873249
\(184\) 0 0
\(185\) 160.863i 0.869528i
\(186\) 0 0
\(187\) 287.495 287.495i 1.53740 1.53740i
\(188\) 0 0
\(189\) 19.5762 19.5762i 0.103578 0.103578i
\(190\) 0 0
\(191\) 94.2316i 0.493359i 0.969097 + 0.246680i \(0.0793395\pi\)
−0.969097 + 0.246680i \(0.920660\pi\)
\(192\) 0 0
\(193\) 84.2667 0.436615 0.218308 0.975880i \(-0.429946\pi\)
0.218308 + 0.975880i \(0.429946\pi\)
\(194\) 0 0
\(195\) −73.6805 73.6805i −0.377849 0.377849i
\(196\) 0 0
\(197\) −56.9578 56.9578i −0.289126 0.289126i 0.547609 0.836734i \(-0.315538\pi\)
−0.836734 + 0.547609i \(0.815538\pi\)
\(198\) 0 0
\(199\) 196.179 0.985827 0.492913 0.870078i \(-0.335932\pi\)
0.492913 + 0.870078i \(0.335932\pi\)
\(200\) 0 0
\(201\) 92.3338i 0.459372i
\(202\) 0 0
\(203\) 97.9886 97.9886i 0.482702 0.482702i
\(204\) 0 0
\(205\) 153.295 153.295i 0.747782 0.747782i
\(206\) 0 0
\(207\) 17.4252i 0.0841799i
\(208\) 0 0
\(209\) 288.708 1.38138
\(210\) 0 0
\(211\) −177.340 177.340i −0.840475 0.840475i 0.148445 0.988921i \(-0.452573\pi\)
−0.988921 + 0.148445i \(0.952573\pi\)
\(212\) 0 0
\(213\) 52.2426 + 52.2426i 0.245271 + 0.245271i
\(214\) 0 0
\(215\) 350.373 1.62964
\(216\) 0 0
\(217\) 90.0707i 0.415072i
\(218\) 0 0
\(219\) −130.302 + 130.302i −0.594987 + 0.594987i
\(220\) 0 0
\(221\) 134.234 134.234i 0.607394 0.607394i
\(222\) 0 0
\(223\) 377.924i 1.69473i −0.531012 0.847364i \(-0.678188\pi\)
0.531012 0.847364i \(-0.321812\pi\)
\(224\) 0 0
\(225\) −89.9682 −0.399859
\(226\) 0 0
\(227\) −103.909 103.909i −0.457750 0.457750i 0.440166 0.897916i \(-0.354920\pi\)
−0.897916 + 0.440166i \(0.854920\pi\)
\(228\) 0 0
\(229\) −101.055 101.055i −0.441290 0.441290i 0.451156 0.892445i \(-0.351012\pi\)
−0.892445 + 0.451156i \(0.851012\pi\)
\(230\) 0 0
\(231\) 160.345 0.694136
\(232\) 0 0
\(233\) 287.259i 1.23287i 0.787405 + 0.616436i \(0.211424\pi\)
−0.787405 + 0.616436i \(0.788576\pi\)
\(234\) 0 0
\(235\) −95.4979 + 95.4979i −0.406374 + 0.406374i
\(236\) 0 0
\(237\) −26.0651 + 26.0651i −0.109980 + 0.109980i
\(238\) 0 0
\(239\) 150.941i 0.631554i 0.948833 + 0.315777i \(0.102265\pi\)
−0.948833 + 0.315777i \(0.897735\pi\)
\(240\) 0 0
\(241\) 37.7817 0.156771 0.0783853 0.996923i \(-0.475024\pi\)
0.0783853 + 0.996923i \(0.475024\pi\)
\(242\) 0 0
\(243\) 11.0227 + 11.0227i 0.0453609 + 0.0453609i
\(244\) 0 0
\(245\) 108.084 + 108.084i 0.441159 + 0.441159i
\(246\) 0 0
\(247\) 134.800 0.545751
\(248\) 0 0
\(249\) 59.1890i 0.237707i
\(250\) 0 0
\(251\) −100.915 + 100.915i −0.402050 + 0.402050i −0.878955 0.476905i \(-0.841759\pi\)
0.476905 + 0.878955i \(0.341759\pi\)
\(252\) 0 0
\(253\) 71.3637 71.3637i 0.282070 0.282070i
\(254\) 0 0
\(255\) 300.545i 1.17861i
\(256\) 0 0
\(257\) 241.295 0.938891 0.469446 0.882961i \(-0.344454\pi\)
0.469446 + 0.882961i \(0.344454\pi\)
\(258\) 0 0
\(259\) 81.7263 + 81.7263i 0.315546 + 0.315546i
\(260\) 0 0
\(261\) 55.1741 + 55.1741i 0.211395 + 0.211395i
\(262\) 0 0
\(263\) 118.747 0.451509 0.225754 0.974184i \(-0.427515\pi\)
0.225754 + 0.974184i \(0.427515\pi\)
\(264\) 0 0
\(265\) 702.483i 2.65088i
\(266\) 0 0
\(267\) −64.6700 + 64.6700i −0.242210 + 0.242210i
\(268\) 0 0
\(269\) 7.74853 7.74853i 0.0288050 0.0288050i −0.692558 0.721363i \(-0.743516\pi\)
0.721363 + 0.692558i \(0.243516\pi\)
\(270\) 0 0
\(271\) 131.899i 0.486712i 0.969937 + 0.243356i \(0.0782484\pi\)
−0.969937 + 0.243356i \(0.921752\pi\)
\(272\) 0 0
\(273\) 74.8668 0.274237
\(274\) 0 0
\(275\) −368.457 368.457i −1.33984 1.33984i
\(276\) 0 0
\(277\) −202.352 202.352i −0.730513 0.730513i 0.240208 0.970721i \(-0.422784\pi\)
−0.970721 + 0.240208i \(0.922784\pi\)
\(278\) 0 0
\(279\) 50.7158 0.181777
\(280\) 0 0
\(281\) 68.8493i 0.245015i −0.992468 0.122508i \(-0.960906\pi\)
0.992468 0.122508i \(-0.0390936\pi\)
\(282\) 0 0
\(283\) −206.773 + 206.773i −0.730646 + 0.730646i −0.970748 0.240102i \(-0.922819\pi\)
0.240102 + 0.970748i \(0.422819\pi\)
\(284\) 0 0
\(285\) 150.907 150.907i 0.529498 0.529498i
\(286\) 0 0
\(287\) 155.764i 0.542730i
\(288\) 0 0
\(289\) 258.545 0.894620
\(290\) 0 0
\(291\) 25.7468 + 25.7468i 0.0884770 + 0.0884770i
\(292\) 0 0
\(293\) −361.237 361.237i −1.23289 1.23289i −0.962848 0.270043i \(-0.912962\pi\)
−0.270043 0.962848i \(-0.587038\pi\)
\(294\) 0 0
\(295\) −284.749 −0.965250
\(296\) 0 0
\(297\) 90.2852i 0.303990i
\(298\) 0 0
\(299\) 33.3204 33.3204i 0.111439 0.111439i
\(300\) 0 0
\(301\) −178.007 + 178.007i −0.591385 + 0.591385i
\(302\) 0 0
\(303\) 7.95987i 0.0262702i
\(304\) 0 0
\(305\) −684.176 −2.24320
\(306\) 0 0
\(307\) 10.9073 + 10.9073i 0.0355286 + 0.0355286i 0.724648 0.689119i \(-0.242002\pi\)
−0.689119 + 0.724648i \(0.742002\pi\)
\(308\) 0 0
\(309\) 128.735 + 128.735i 0.416619 + 0.416619i
\(310\) 0 0
\(311\) 160.251 0.515278 0.257639 0.966241i \(-0.417055\pi\)
0.257639 + 0.966241i \(0.417055\pi\)
\(312\) 0 0
\(313\) 355.500i 1.13578i −0.823103 0.567892i \(-0.807759\pi\)
0.823103 0.567892i \(-0.192241\pi\)
\(314\) 0 0
\(315\) 83.8121 83.8121i 0.266070 0.266070i
\(316\) 0 0
\(317\) 72.5192 72.5192i 0.228767 0.228767i −0.583410 0.812178i \(-0.698282\pi\)
0.812178 + 0.583410i \(0.198282\pi\)
\(318\) 0 0
\(319\) 451.922i 1.41668i
\(320\) 0 0
\(321\) −244.008 −0.760151
\(322\) 0 0
\(323\) 274.928 + 274.928i 0.851170 + 0.851170i
\(324\) 0 0
\(325\) −172.036 172.036i −0.529343 0.529343i
\(326\) 0 0
\(327\) 264.667 0.809378
\(328\) 0 0
\(329\) 97.0355i 0.294941i
\(330\) 0 0
\(331\) 248.096 248.096i 0.749536 0.749536i −0.224856 0.974392i \(-0.572191\pi\)
0.974392 + 0.224856i \(0.0721912\pi\)
\(332\) 0 0
\(333\) −46.0174 + 46.0174i −0.138190 + 0.138190i
\(334\) 0 0
\(335\) 395.312i 1.18003i
\(336\) 0 0
\(337\) −467.271 −1.38656 −0.693280 0.720668i \(-0.743835\pi\)
−0.693280 + 0.720668i \(0.743835\pi\)
\(338\) 0 0
\(339\) 28.5163 + 28.5163i 0.0841189 + 0.0841189i
\(340\) 0 0
\(341\) 207.703 + 207.703i 0.609098 + 0.609098i
\(342\) 0 0
\(343\) −370.894 −1.08133
\(344\) 0 0
\(345\) 74.6032i 0.216241i
\(346\) 0 0
\(347\) −292.821 + 292.821i −0.843863 + 0.843863i −0.989359 0.145496i \(-0.953522\pi\)
0.145496 + 0.989359i \(0.453522\pi\)
\(348\) 0 0
\(349\) 346.260 346.260i 0.992150 0.992150i −0.00781941 0.999969i \(-0.502489\pi\)
0.999969 + 0.00781941i \(0.00248902\pi\)
\(350\) 0 0
\(351\) 42.1550i 0.120100i
\(352\) 0 0
\(353\) 8.01816 0.0227143 0.0113572 0.999936i \(-0.496385\pi\)
0.0113572 + 0.999936i \(0.496385\pi\)
\(354\) 0 0
\(355\) 223.668 + 223.668i 0.630051 + 0.630051i
\(356\) 0 0
\(357\) 152.692 + 152.692i 0.427709 + 0.427709i
\(358\) 0 0
\(359\) −590.403 −1.64458 −0.822289 0.569071i \(-0.807303\pi\)
−0.822289 + 0.569071i \(0.807303\pi\)
\(360\) 0 0
\(361\) 84.9121i 0.235213i
\(362\) 0 0
\(363\) −221.561 + 221.561i −0.610362 + 0.610362i
\(364\) 0 0
\(365\) −557.867 + 557.867i −1.52840 + 1.52840i
\(366\) 0 0
\(367\) 397.100i 1.08202i 0.841017 + 0.541008i \(0.181957\pi\)
−0.841017 + 0.541008i \(0.818043\pi\)
\(368\) 0 0
\(369\) −87.7053 −0.237684
\(370\) 0 0
\(371\) −356.897 356.897i −0.961986 0.961986i
\(372\) 0 0
\(373\) −165.010 165.010i −0.442387 0.442387i 0.450427 0.892814i \(-0.351272\pi\)
−0.892814 + 0.450427i \(0.851272\pi\)
\(374\) 0 0
\(375\) −64.0837 −0.170890
\(376\) 0 0
\(377\) 211.007i 0.559700i
\(378\) 0 0
\(379\) 206.669 206.669i 0.545300 0.545300i −0.379778 0.925078i \(-0.624000\pi\)
0.925078 + 0.379778i \(0.124000\pi\)
\(380\) 0 0
\(381\) −144.740 + 144.740i −0.379895 + 0.379895i
\(382\) 0 0
\(383\) 598.414i 1.56244i −0.624257 0.781219i \(-0.714598\pi\)
0.624257 0.781219i \(-0.285402\pi\)
\(384\) 0 0
\(385\) 686.492 1.78310
\(386\) 0 0
\(387\) −100.230 100.230i −0.258992 0.258992i
\(388\) 0 0
\(389\) 186.696 + 186.696i 0.479939 + 0.479939i 0.905112 0.425173i \(-0.139787\pi\)
−0.425173 + 0.905112i \(0.639787\pi\)
\(390\) 0 0
\(391\) 135.915 0.347609
\(392\) 0 0
\(393\) 169.521i 0.431352i
\(394\) 0 0
\(395\) −111.594 + 111.594i −0.282515 + 0.282515i
\(396\) 0 0
\(397\) −57.3727 + 57.3727i −0.144516 + 0.144516i −0.775663 0.631147i \(-0.782584\pi\)
0.631147 + 0.775663i \(0.282584\pi\)
\(398\) 0 0
\(399\) 153.337i 0.384302i
\(400\) 0 0
\(401\) −466.082 −1.16230 −0.581149 0.813797i \(-0.697397\pi\)
−0.581149 + 0.813797i \(0.697397\pi\)
\(402\) 0 0
\(403\) 96.9784 + 96.9784i 0.240641 + 0.240641i
\(404\) 0 0
\(405\) 47.1918 + 47.1918i 0.116523 + 0.116523i
\(406\) 0 0
\(407\) −376.921 −0.926096
\(408\) 0 0
\(409\) 597.952i 1.46198i 0.682386 + 0.730992i \(0.260942\pi\)
−0.682386 + 0.730992i \(0.739058\pi\)
\(410\) 0 0
\(411\) 152.449 152.449i 0.370923 0.370923i
\(412\) 0 0
\(413\) 144.667 144.667i 0.350282 0.350282i
\(414\) 0 0
\(415\) 253.408i 0.610621i
\(416\) 0 0
\(417\) 413.998 0.992800
\(418\) 0 0
\(419\) 4.65301 + 4.65301i 0.0111050 + 0.0111050i 0.712638 0.701532i \(-0.247500\pi\)
−0.701532 + 0.712638i \(0.747500\pi\)
\(420\) 0 0
\(421\) 34.3754 + 34.3754i 0.0816519 + 0.0816519i 0.746753 0.665101i \(-0.231612\pi\)
−0.665101 + 0.746753i \(0.731612\pi\)
\(422\) 0 0
\(423\) 54.6375 0.129167
\(424\) 0 0
\(425\) 701.742i 1.65116i
\(426\) 0 0
\(427\) 347.596 347.596i 0.814042 0.814042i
\(428\) 0 0
\(429\) −172.643 + 172.643i −0.402430 + 0.402430i
\(430\) 0 0
\(431\) 423.823i 0.983347i −0.870780 0.491674i \(-0.836385\pi\)
0.870780 0.491674i \(-0.163615\pi\)
\(432\) 0 0
\(433\) 833.377 1.92466 0.962330 0.271885i \(-0.0876472\pi\)
0.962330 + 0.271885i \(0.0876472\pi\)
\(434\) 0 0
\(435\) 236.219 + 236.219i 0.543031 + 0.543031i
\(436\) 0 0
\(437\) 68.2443 + 68.2443i 0.156165 + 0.156165i
\(438\) 0 0
\(439\) −32.3193 −0.0736203 −0.0368102 0.999322i \(-0.511720\pi\)
−0.0368102 + 0.999322i \(0.511720\pi\)
\(440\) 0 0
\(441\) 61.8384i 0.140223i
\(442\) 0 0
\(443\) −119.527 + 119.527i −0.269813 + 0.269813i −0.829025 0.559212i \(-0.811104\pi\)
0.559212 + 0.829025i \(0.311104\pi\)
\(444\) 0 0
\(445\) −276.874 + 276.874i −0.622189 + 0.622189i
\(446\) 0 0
\(447\) 360.045i 0.805470i
\(448\) 0 0
\(449\) −182.359 −0.406146 −0.203073 0.979164i \(-0.565093\pi\)
−0.203073 + 0.979164i \(0.565093\pi\)
\(450\) 0 0
\(451\) −359.190 359.190i −0.796430 0.796430i
\(452\) 0 0
\(453\) 92.5241 + 92.5241i 0.204248 + 0.204248i
\(454\) 0 0
\(455\) 320.530 0.704461
\(456\) 0 0
\(457\) 272.942i 0.597246i −0.954371 0.298623i \(-0.903473\pi\)
0.954371 0.298623i \(-0.0965274\pi\)
\(458\) 0 0
\(459\) −85.9759 + 85.9759i −0.187311 + 0.187311i
\(460\) 0 0
\(461\) 188.323 188.323i 0.408510 0.408510i −0.472709 0.881219i \(-0.656724\pi\)
0.881219 + 0.472709i \(0.156724\pi\)
\(462\) 0 0
\(463\) 116.023i 0.250590i −0.992120 0.125295i \(-0.960012\pi\)
0.992120 0.125295i \(-0.0399877\pi\)
\(464\) 0 0
\(465\) 217.131 0.466949
\(466\) 0 0
\(467\) 271.914 + 271.914i 0.582257 + 0.582257i 0.935523 0.353266i \(-0.114929\pi\)
−0.353266 + 0.935523i \(0.614929\pi\)
\(468\) 0 0
\(469\) 200.838 + 200.838i 0.428227 + 0.428227i
\(470\) 0 0
\(471\) 199.721 0.424035
\(472\) 0 0
\(473\) 820.966i 1.73566i
\(474\) 0 0
\(475\) 352.352 352.352i 0.741793 0.741793i
\(476\) 0 0
\(477\) 200.957 200.957i 0.421293 0.421293i
\(478\) 0 0
\(479\) 775.808i 1.61964i 0.586678 + 0.809820i \(0.300435\pi\)
−0.586678 + 0.809820i \(0.699565\pi\)
\(480\) 0 0
\(481\) −175.988 −0.365880
\(482\) 0 0
\(483\) 37.9022 + 37.9022i 0.0784725 + 0.0784725i
\(484\) 0 0
\(485\) 110.231 + 110.231i 0.227280 + 0.227280i
\(486\) 0 0
\(487\) −174.891 −0.359118 −0.179559 0.983747i \(-0.557467\pi\)
−0.179559 + 0.983747i \(0.557467\pi\)
\(488\) 0 0
\(489\) 136.697i 0.279545i
\(490\) 0 0
\(491\) 348.578 348.578i 0.709934 0.709934i −0.256587 0.966521i \(-0.582598\pi\)
0.966521 + 0.256587i \(0.0825980\pi\)
\(492\) 0 0
\(493\) −430.352 + 430.352i −0.872926 + 0.872926i
\(494\) 0 0
\(495\) 386.541i 0.780890i
\(496\) 0 0
\(497\) −227.269 −0.457282
\(498\) 0 0
\(499\) 607.544 + 607.544i 1.21752 + 1.21752i 0.968496 + 0.249027i \(0.0801109\pi\)
0.249027 + 0.968496i \(0.419889\pi\)
\(500\) 0 0
\(501\) −30.1702 30.1702i −0.0602199 0.0602199i
\(502\) 0 0
\(503\) 130.935 0.260309 0.130154 0.991494i \(-0.458453\pi\)
0.130154 + 0.991494i \(0.458453\pi\)
\(504\) 0 0
\(505\) 34.0789i 0.0674829i
\(506\) 0 0
\(507\) 126.373 126.373i 0.249257 0.249257i
\(508\) 0 0
\(509\) −61.5539 + 61.5539i −0.120931 + 0.120931i −0.764982 0.644051i \(-0.777252\pi\)
0.644051 + 0.764982i \(0.277252\pi\)
\(510\) 0 0
\(511\) 566.849i 1.10929i
\(512\) 0 0
\(513\) −86.3387 −0.168302
\(514\) 0 0
\(515\) 551.159 + 551.159i 1.07021 + 1.07021i
\(516\) 0 0
\(517\) 223.763 + 223.763i 0.432811 + 0.432811i
\(518\) 0 0
\(519\) −11.9670 −0.0230578
\(520\) 0 0
\(521\) 32.5929i 0.0625584i −0.999511 0.0312792i \(-0.990042\pi\)
0.999511 0.0312792i \(-0.00995810\pi\)
\(522\) 0 0
\(523\) 226.407 226.407i 0.432900 0.432900i −0.456713 0.889614i \(-0.650974\pi\)
0.889614 + 0.456713i \(0.150974\pi\)
\(524\) 0 0
\(525\) 195.693 195.693i 0.372748 0.372748i
\(526\) 0 0
\(527\) 395.578i 0.750623i
\(528\) 0 0
\(529\) −495.262 −0.936224
\(530\) 0 0
\(531\) 81.4570 + 81.4570i 0.153403 + 0.153403i
\(532\) 0 0
\(533\) −167.709 167.709i −0.314652 0.314652i
\(534\) 0 0
\(535\) −1044.68 −1.95267
\(536\) 0 0
\(537\) 562.168i 1.04687i
\(538\) 0 0
\(539\) 253.254 253.254i 0.469859 0.469859i
\(540\) 0 0
\(541\) 510.912 510.912i 0.944385 0.944385i −0.0541480 0.998533i \(-0.517244\pi\)
0.998533 + 0.0541480i \(0.0172443\pi\)
\(542\) 0 0
\(543\) 285.628i 0.526018i
\(544\) 0 0
\(545\) 1133.13 2.07913
\(546\) 0 0
\(547\) −512.889 512.889i −0.937639 0.937639i 0.0605271 0.998167i \(-0.480722\pi\)
−0.998167 + 0.0605271i \(0.980722\pi\)
\(548\) 0 0
\(549\) 195.720 + 195.720i 0.356502 + 0.356502i
\(550\) 0 0
\(551\) −432.168 −0.784334
\(552\) 0 0
\(553\) 113.390i 0.205046i
\(554\) 0 0
\(555\) −197.016 + 197.016i −0.354983 + 0.354983i
\(556\) 0 0
\(557\) 566.691 566.691i 1.01740 1.01740i 0.0175529 0.999846i \(-0.494412\pi\)
0.999846 0.0175529i \(-0.00558754\pi\)
\(558\) 0 0
\(559\) 383.317i 0.685720i
\(560\) 0 0
\(561\) −704.215 −1.25529
\(562\) 0 0
\(563\) −548.653 548.653i −0.974517 0.974517i 0.0251665 0.999683i \(-0.491988\pi\)
−0.999683 + 0.0251665i \(0.991988\pi\)
\(564\) 0 0
\(565\) 122.088 + 122.088i 0.216085 + 0.216085i
\(566\) 0 0
\(567\) −47.9517 −0.0845708
\(568\) 0 0
\(569\) 551.224i 0.968760i 0.874858 + 0.484380i \(0.160955\pi\)
−0.874858 + 0.484380i \(0.839045\pi\)
\(570\) 0 0
\(571\) −458.387 + 458.387i −0.802780 + 0.802780i −0.983529 0.180749i \(-0.942148\pi\)
0.180749 + 0.983529i \(0.442148\pi\)
\(572\) 0 0
\(573\) 115.410 115.410i 0.201413 0.201413i
\(574\) 0 0
\(575\) 174.191i 0.302941i
\(576\) 0 0
\(577\) −718.488 −1.24521 −0.622607 0.782535i \(-0.713926\pi\)
−0.622607 + 0.782535i \(0.713926\pi\)
\(578\) 0 0
\(579\) −103.205 103.205i −0.178247 0.178247i
\(580\) 0 0
\(581\) −128.744 128.744i −0.221590 0.221590i
\(582\) 0 0
\(583\) 1646.00 2.82333
\(584\) 0 0
\(585\) 180.480i 0.308512i
\(586\) 0 0
\(587\) −3.02450 + 3.02450i −0.00515247 + 0.00515247i −0.709678 0.704526i \(-0.751160\pi\)
0.704526 + 0.709678i \(0.251160\pi\)
\(588\) 0 0
\(589\) −198.624 + 198.624i −0.337222 + 0.337222i
\(590\) 0 0
\(591\) 139.517i 0.236070i
\(592\) 0 0
\(593\) 576.193 0.971657 0.485829 0.874054i \(-0.338518\pi\)
0.485829 + 0.874054i \(0.338518\pi\)
\(594\) 0 0
\(595\) 653.726 + 653.726i 1.09870 + 1.09870i
\(596\) 0 0
\(597\) −240.270 240.270i −0.402462 0.402462i
\(598\) 0 0
\(599\) 1101.40 1.83873 0.919365 0.393406i \(-0.128703\pi\)
0.919365 + 0.393406i \(0.128703\pi\)
\(600\) 0 0
\(601\) 7.11053i 0.0118312i 0.999983 + 0.00591558i \(0.00188300\pi\)
−0.999983 + 0.00591558i \(0.998117\pi\)
\(602\) 0 0
\(603\) −113.085 + 113.085i −0.187538 + 0.187538i
\(604\) 0 0
\(605\) −948.578 + 948.578i −1.56790 + 1.56790i
\(606\) 0 0
\(607\) 528.384i 0.870485i 0.900313 + 0.435242i \(0.143337\pi\)
−0.900313 + 0.435242i \(0.856663\pi\)
\(608\) 0 0
\(609\) −240.022 −0.394125
\(610\) 0 0
\(611\) 104.477 + 104.477i 0.170994 + 0.170994i
\(612\) 0 0
\(613\) −642.364 642.364i −1.04790 1.04790i −0.998793 0.0491093i \(-0.984362\pi\)
−0.0491093 0.998793i \(-0.515638\pi\)
\(614\) 0 0
\(615\) −375.496 −0.610562
\(616\) 0 0
\(617\) 1068.16i 1.73122i 0.500717 + 0.865611i \(0.333070\pi\)
−0.500717 + 0.865611i \(0.666930\pi\)
\(618\) 0 0
\(619\) −691.136 + 691.136i −1.11654 + 1.11654i −0.124290 + 0.992246i \(0.539665\pi\)
−0.992246 + 0.124290i \(0.960335\pi\)
\(620\) 0 0
\(621\) −21.3415 + 21.3415i −0.0343663 + 0.0343663i
\(622\) 0 0
\(623\) 281.332i 0.451576i
\(624\) 0 0
\(625\) 475.371 0.760594
\(626\) 0 0
\(627\) −353.593 353.593i −0.563945 0.563945i
\(628\) 0 0
\(629\) −358.931 358.931i −0.570637 0.570637i
\(630\) 0 0
\(631\) −486.622 −0.771191 −0.385596 0.922668i \(-0.626004\pi\)
−0.385596 + 0.922668i \(0.626004\pi\)
\(632\) 0 0
\(633\) 434.393i 0.686245i
\(634\) 0 0
\(635\) −619.681 + 619.681i −0.975875 + 0.975875i
\(636\) 0 0
\(637\) 118.247 118.247i 0.185631 0.185631i
\(638\) 0 0
\(639\) 127.968i 0.200263i
\(640\) 0 0
\(641\) −691.017 −1.07803 −0.539015 0.842296i \(-0.681203\pi\)
−0.539015 + 0.842296i \(0.681203\pi\)
\(642\) 0 0
\(643\) −652.605 652.605i −1.01494 1.01494i −0.999887 0.0150512i \(-0.995209\pi\)
−0.0150512 0.999887i \(-0.504791\pi\)
\(644\) 0 0
\(645\) −429.117 429.117i −0.665298 0.665298i
\(646\) 0 0
\(647\) −1156.72 −1.78782 −0.893911 0.448245i \(-0.852049\pi\)
−0.893911 + 0.448245i \(0.852049\pi\)
\(648\) 0 0
\(649\) 667.201i 1.02804i
\(650\) 0 0
\(651\) −110.314 + 110.314i −0.169453 + 0.169453i
\(652\) 0 0
\(653\) −209.105 + 209.105i −0.320222 + 0.320222i −0.848852 0.528630i \(-0.822706\pi\)
0.528630 + 0.848852i \(0.322706\pi\)
\(654\) 0 0
\(655\) 725.776i 1.10806i
\(656\) 0 0
\(657\) 319.174 0.485805
\(658\) 0 0
\(659\) −533.902 533.902i −0.810170 0.810170i 0.174489 0.984659i \(-0.444173\pi\)
−0.984659 + 0.174489i \(0.944173\pi\)
\(660\) 0 0
\(661\) 283.120 + 283.120i 0.428320 + 0.428320i 0.888056 0.459736i \(-0.152056\pi\)
−0.459736 + 0.888056i \(0.652056\pi\)
\(662\) 0 0
\(663\) −328.805 −0.495935
\(664\) 0 0
\(665\) 656.484i 0.987195i
\(666\) 0 0
\(667\) −106.825 + 106.825i −0.160157 + 0.160157i
\(668\) 0 0
\(669\) −462.861 + 462.861i −0.691870 + 0.691870i
\(670\) 0 0
\(671\) 1603.11i 2.38913i
\(672\) 0 0
\(673\) −397.854 −0.591164 −0.295582 0.955317i \(-0.595514\pi\)
−0.295582 + 0.955317i \(0.595514\pi\)
\(674\) 0 0
\(675\) 110.188 + 110.188i 0.163242 + 0.163242i
\(676\) 0 0
\(677\) 289.959 + 289.959i 0.428299 + 0.428299i 0.888049 0.459749i \(-0.152061\pi\)
−0.459749 + 0.888049i \(0.652061\pi\)
\(678\) 0 0
\(679\) −112.005 −0.164956
\(680\) 0 0
\(681\) 254.525i 0.373751i
\(682\) 0 0
\(683\) 150.197 150.197i 0.219908 0.219908i −0.588551 0.808460i \(-0.700302\pi\)
0.808460 + 0.588551i \(0.200302\pi\)
\(684\) 0 0
\(685\) 652.686 652.686i 0.952826 0.952826i
\(686\) 0 0
\(687\) 247.534i 0.360312i
\(688\) 0 0
\(689\) 768.535 1.11544
\(690\) 0 0
\(691\) −791.212 791.212i −1.14502 1.14502i −0.987518 0.157506i \(-0.949655\pi\)
−0.157506 0.987518i \(-0.550345\pi\)
\(692\) 0 0
\(693\) −196.382 196.382i −0.283380 0.283380i
\(694\) 0 0
\(695\) 1772.46 2.55030
\(696\) 0 0
\(697\) 684.092i 0.981481i
\(698\) 0 0
\(699\) 351.819 351.819i 0.503318 0.503318i
\(700\) 0 0
\(701\) 900.201 900.201i 1.28417 1.28417i 0.345893 0.938274i \(-0.387576\pi\)
0.938274 0.345893i \(-0.112424\pi\)
\(702\) 0 0
\(703\) 360.445i 0.512724i
\(704\) 0 0
\(705\) 233.921 0.331803
\(706\) 0 0
\(707\) −17.3138 17.3138i −0.0244891 0.0244891i
\(708\) 0 0
\(709\) 128.490 + 128.490i 0.181227 + 0.181227i 0.791891 0.610663i \(-0.209097\pi\)
−0.610663 + 0.791891i \(0.709097\pi\)
\(710\) 0 0
\(711\) 63.8463 0.0897979
\(712\) 0 0
\(713\) 98.1928i 0.137718i
\(714\) 0 0
\(715\) −739.140 + 739.140i −1.03376 + 1.03376i
\(716\) 0 0
\(717\) 184.865 184.865i 0.257831 0.257831i
\(718\) 0 0
\(719\) 1246.14i 1.73315i −0.499045 0.866576i \(-0.666316\pi\)
0.499045 0.866576i \(-0.333684\pi\)
\(720\) 0 0
\(721\) −560.033 −0.776745
\(722\) 0 0
\(723\) −46.2730 46.2730i −0.0640014 0.0640014i
\(724\) 0 0
\(725\) 551.546 + 551.546i 0.760753 + 0.760753i
\(726\) 0 0
\(727\) 1130.07 1.55443 0.777216 0.629234i \(-0.216631\pi\)
0.777216 + 0.629234i \(0.216631\pi\)
\(728\) 0 0
\(729\) 27.0000i 0.0370370i
\(730\) 0 0
\(731\) 781.782 781.782i 1.06947 1.06947i
\(732\) 0 0
\(733\) −708.087 + 708.087i −0.966012 + 0.966012i −0.999441 0.0334292i \(-0.989357\pi\)
0.0334292 + 0.999441i \(0.489357\pi\)
\(734\) 0 0
\(735\) 264.751i 0.360205i
\(736\) 0 0
\(737\) −926.264 −1.25680
\(738\) 0 0
\(739\) 32.7516 + 32.7516i 0.0443188 + 0.0443188i 0.728919 0.684600i \(-0.240023\pi\)
−0.684600 + 0.728919i \(0.740023\pi\)
\(740\) 0 0
\(741\) −165.096 165.096i −0.222802 0.222802i
\(742\) 0 0
\(743\) −708.128 −0.953066 −0.476533 0.879157i \(-0.658107\pi\)
−0.476533 + 0.879157i \(0.658107\pi\)
\(744\) 0 0
\(745\) 1541.47i 2.06909i
\(746\) 0 0
\(747\) 72.4914 72.4914i 0.0970434 0.0970434i
\(748\) 0 0
\(749\) 530.751 530.751i 0.708612 0.708612i
\(750\) 0 0
\(751\) 1242.37i 1.65429i 0.561990 + 0.827144i \(0.310036\pi\)
−0.561990 + 0.827144i \(0.689964\pi\)
\(752\) 0 0
\(753\) 247.189 0.328272
\(754\) 0 0
\(755\) 396.127 + 396.127i 0.524671 + 0.524671i
\(756\) 0 0
\(757\) −311.304 311.304i −0.411233 0.411233i 0.470935 0.882168i \(-0.343917\pi\)
−0.882168 + 0.470935i \(0.843917\pi\)
\(758\) 0 0
\(759\) −174.805 −0.230309
\(760\) 0 0
\(761\) 179.137i 0.235397i −0.993049 0.117699i \(-0.962448\pi\)
0.993049 0.117699i \(-0.0375517\pi\)
\(762\) 0 0
\(763\) −575.685 + 575.685i −0.754502 + 0.754502i
\(764\) 0 0
\(765\) −368.091 + 368.091i −0.481165 + 0.481165i
\(766\) 0 0
\(767\) 311.523i 0.406158i
\(768\) 0 0
\(769\) −967.409 −1.25801 −0.629005 0.777402i \(-0.716537\pi\)
−0.629005 + 0.777402i \(0.716537\pi\)
\(770\) 0 0
\(771\) −295.525 295.525i −0.383301 0.383301i
\(772\) 0 0
\(773\) −96.7342 96.7342i −0.125141 0.125141i 0.641762 0.766904i \(-0.278204\pi\)
−0.766904 + 0.641762i \(0.778204\pi\)
\(774\) 0 0
\(775\) 506.979 0.654166
\(776\) 0 0
\(777\) 200.188i 0.257642i
\(778\) 0 0
\(779\) 343.489 343.489i 0.440936 0.440936i
\(780\) 0 0
\(781\) 524.082 524.082i 0.671039 0.671039i
\(782\) 0 0
\(783\) 135.148i 0.172603i
\(784\) 0 0
\(785\) 855.070 1.08926
\(786\) 0 0
\(787\) 381.038 + 381.038i 0.484166 + 0.484166i 0.906459 0.422293i \(-0.138775\pi\)
−0.422293 + 0.906459i \(0.638775\pi\)
\(788\) 0 0
\(789\) −145.435 145.435i −0.184328 0.184328i
\(790\) 0 0
\(791\) −124.054 −0.156831
\(792\) 0 0
\(793\) 748.507i 0.943893i
\(794\) 0 0