Properties

Label 384.3.l.a.31.4
Level $384$
Weight $3$
Character 384.31
Analytic conductor $10.463$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(10.4632421514\)
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 31.4
Root \(-1.87459 + 0.697079i\) of defining polynomial
Character \(\chi\) \(=\) 384.31
Dual form 384.3.l.a.223.4

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

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

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
\(3\) −1.22474 1.22474i −0.408248 0.408248i
\(4\) 0 0
\(5\) 5.24354 + 5.24354i 1.04871 + 1.04871i 0.998751 + 0.0499563i \(0.0159082\pi\)
0.0499563 + 0.998751i \(0.484092\pi\)
\(6\) 0 0
\(7\) −5.32796 −0.761138 −0.380569 0.924753i \(-0.624272\pi\)
−0.380569 + 0.924753i \(0.624272\pi\)
\(8\) 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 −0.451165 0.892440i \(-0.648992\pi\)
0.892440 + 0.451165i \(0.148992\pi\)
\(14\) 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 \(-0.459699\pi\)
0.126270 + 0.991996i \(0.459699\pi\)
\(24\) 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 −0.949115 0.314930i \(-0.898019\pi\)
0.314930 + 0.949115i \(0.398019\pi\)
\(30\) 0 0
\(31\) 16.9053i 0.545332i 0.962109 + 0.272666i \(0.0879053\pi\)
−0.962109 + 0.272666i \(0.912095\pi\)
\(32\) 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 0.468756 0.883327i \(-0.344702\pi\)
−0.883327 + 0.468756i \(0.844702\pi\)
\(38\) 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 \(0.0620650\pi\)
−0.981051 + 0.193750i \(0.937935\pi\)
\(48\) 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 \(0.101898\pi\)
0.314681 + 0.949197i \(0.398102\pi\)
\(54\) 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 \(0.522973\pi\)
−0.997397 + 0.0721103i \(0.977027\pi\)
\(62\) 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 \(-0.402882\pi\)
0.300394 + 0.953815i \(0.402882\pi\)
\(72\) 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 \(0.0430061\pi\)
−0.990887 + 0.134697i \(0.956994\pi\)
\(80\) 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 0.723011 0.690837i \(-0.242758\pi\)
−0.690837 + 0.723011i \(0.742758\pi\)
\(102\) 0 0
\(103\) 105.112 1.02050 0.510252 0.860025i \(-0.329552\pi\)
0.510252 + 0.860025i \(0.329552\pi\)
\(104\) 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 −0.00868078 0.999962i \(-0.502763\pi\)
0.999962 + 0.00868078i \(0.00276321\pi\)
\(110\) 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 \(0.154045\pi\)
−0.885166 + 0.465275i \(0.845955\pi\)
\(128\) 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 0.0134145 0.999910i \(-0.495730\pi\)
−0.999910 + 0.0134145i \(0.995730\pi\)
\(150\) 0 0
\(151\) 75.5456 0.500302 0.250151 0.968207i \(-0.419520\pi\)
0.250151 + 0.968207i \(0.419520\pi\)
\(152\) 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 −0.398035 0.917370i \(-0.630308\pi\)
0.917370 + 0.398035i \(0.130308\pi\)
\(158\) 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 \(-0.523498\pi\)
−0.0737540 + 0.997276i \(0.523498\pi\)
\(168\) 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 −0.721086 0.692846i \(-0.756357\pi\)
0.692846 + 0.721086i \(0.256357\pi\)
\(174\) 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 0.307356 0.951595i \(-0.400556\pi\)
−0.951595 + 0.307356i \(0.900556\pi\)
\(182\) 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 \(-0.920660\pi\)
0.969097 0.246680i \(-0.0793395\pi\)
\(192\) 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 0.836734 0.547609i \(-0.184462\pi\)
−0.547609 + 0.836734i \(0.684462\pi\)
\(198\) 0 0
\(199\) −196.179 −0.985827 −0.492913 0.870078i \(-0.664068\pi\)
−0.492913 + 0.870078i \(0.664068\pi\)
\(200\) 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 \(0.321812\pi\)
−0.531012 + 0.847364i \(0.678188\pi\)
\(224\) 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 0.892445 0.451156i \(-0.148988\pi\)
−0.451156 + 0.892445i \(0.648988\pi\)
\(230\) 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 \(-0.897735\pi\)
0.948833 0.315777i \(-0.102265\pi\)
\(240\) 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 \(-0.572485\pi\)
−0.225754 + 0.974184i \(0.572485\pi\)
\(264\) 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 −0.721363 0.692558i \(-0.756484\pi\)
0.692558 + 0.721363i \(0.256484\pi\)
\(270\) 0 0
\(271\) 131.899i 0.486712i −0.969937 0.243356i \(-0.921752\pi\)
0.969937 0.243356i \(-0.0782484\pi\)
\(272\) 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 0.970721 0.240208i \(-0.0772157\pi\)
−0.240208 + 0.970721i \(0.577216\pi\)
\(278\) 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 \(0.0870379\pi\)
0.270043 + 0.962848i \(0.412962\pi\)
\(294\) 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 \(-0.582945\pi\)
−0.257639 + 0.966241i \(0.582945\pi\)
\(312\) 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 −0.812178 0.583410i \(-0.801718\pi\)
0.583410 + 0.812178i \(0.301718\pi\)
\(318\) 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 −0.999969 0.00781941i \(-0.997511\pi\)
0.00781941 + 0.999969i \(0.497511\pi\)
\(350\) 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 \(-0.192697\pi\)
0.822289 + 0.569071i \(0.192697\pi\)
\(360\) 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 \(-0.818043\pi\)
0.841017 0.541008i \(-0.181957\pi\)
\(368\) 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 0.892814 0.450427i \(-0.148728\pi\)
−0.450427 + 0.892814i \(0.648728\pi\)
\(374\) 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 \(0.285402\pi\)
−0.624257 + 0.781219i \(0.714598\pi\)
\(384\) 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 0.425173 0.905112i \(-0.360213\pi\)
−0.905112 + 0.425173i \(0.860213\pi\)
\(390\) 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 −0.631147 0.775663i \(-0.717416\pi\)
0.775663 + 0.631147i \(0.217416\pi\)
\(398\) 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 0.665101 0.746753i \(-0.268388\pi\)
−0.746753 + 0.665101i \(0.768388\pi\)
\(422\) 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 \(0.163615\pi\)
−0.870780 + 0.491674i \(0.836385\pi\)
\(432\) 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 \(-0.488280\pi\)
0.0368102 + 0.999322i \(0.488280\pi\)
\(440\) 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 −0.881219 0.472709i \(-0.843276\pi\)
0.472709 + 0.881219i \(0.343276\pi\)
\(462\) 0 0
\(463\) 116.023i 0.250590i 0.992120 + 0.125295i \(0.0399877\pi\)
−0.992120 + 0.125295i \(0.960012\pi\)
\(464\) 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 \(-0.699565\pi\)
0.586678 0.809820i \(-0.300435\pi\)
\(480\) 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 \(-0.442533\pi\)
0.179559 + 0.983747i \(0.442533\pi\)
\(488\) 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 \(-0.541547\pi\)
−0.130154 + 0.991494i \(0.541547\pi\)
\(504\) 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 −0.644051 0.764982i \(-0.722748\pi\)
0.764982 + 0.644051i \(0.222748\pi\)
\(510\) 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 −0.998533 0.0541480i \(-0.982756\pi\)
0.0541480 + 0.998533i \(0.482756\pi\)
\(542\) 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 \(0.505588\pi\)
−0.999846 + 0.0175529i \(0.994412\pi\)
\(558\) 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 \(-0.871297\pi\)
−0.919365 + 0.393406i \(0.871297\pi\)
\(600\) 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 \(-0.856663\pi\)
0.900313 0.435242i \(-0.143337\pi\)
\(608\) 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 \(0.0156383\pi\)
0.0491093 + 0.998793i \(0.484362\pi\)
\(614\) 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 \(-0.373996\pi\)
0.385596 + 0.922668i \(0.373996\pi\)
\(632\) 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 \(-0.147951\pi\)
0.893911 + 0.448245i \(0.147951\pi\)
\(648\) 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 −0.528630 0.848852i \(-0.677294\pi\)
0.848852 + 0.528630i \(0.177294\pi\)
\(654\) 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 0.459736 0.888056i \(-0.347944\pi\)
−0.888056 + 0.459736i \(0.847944\pi\)
\(662\) 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 0.459749 0.888049i \(-0.347939\pi\)
−0.888049 + 0.459749i \(0.847939\pi\)
\(678\) 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 \(0.612424\pi\)
−0.938274 + 0.345893i \(0.887576\pi\)
\(702\) 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 0.610663 0.791891i \(-0.290903\pi\)
−0.791891 + 0.610663i \(0.790903\pi\)
\(710\) 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 \(0.333684\pi\)
−0.499045 + 0.866576i \(0.666316\pi\)
\(720\) 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 \(-0.783369\pi\)
−0.777216 + 0.629234i \(0.783369\pi\)
\(728\) 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 −0.0334292 0.999441i \(-0.510643\pi\)
0.999441 + 0.0334292i \(0.0106428\pi\)
\(734\) 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 \(-0.341893\pi\)
0.476533 + 0.879157i \(0.341893\pi\)
\(744\) 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 \(-0.689964\pi\)
0.561990 0.827144i \(-0.310036\pi\)
\(752\) 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 0.882168 0.470935i \(-0.156083\pi\)
−0.470935 + 0.882168i \(0.656083\pi\)
\(758\) 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 0.766904 0.641762i \(-0.221796\pi\)
−0.641762 + 0.766904i \(0.721796\pi\)
\(774\) 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
\(795\) 860.362