Properties

Label 384.3.l.b.223.8
Level $384$
Weight $3$
Character 384.223
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 223.8
Root \(-1.87459 - 0.697079i\) of defining polynomial
Character \(\chi\) \(=\) 384.223
Dual form 384.3.l.b.31.8

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.22474 1.22474i 0.408248 0.408248i
\(4\) 0 0
\(5\) 5.24354 5.24354i 1.04871 1.04871i 0.0499563 0.998751i \(-0.484092\pi\)
0.998751 0.0499563i \(-0.0159082\pi\)
\(6\) 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 0.992189 + 0.124743i \(0.0398107\pi\)
0.124743 + 0.992189i \(0.460189\pi\)
\(12\) 0 0
\(13\) 5.73657 + 5.73657i 0.441275 + 0.441275i 0.892440 0.451165i \(-0.148992\pi\)
−0.451165 + 0.892440i \(0.648992\pi\)
\(14\) 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 \(-0.605949\pi\)
0.945116 + 0.326736i \(0.105949\pi\)
\(20\) 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 \(-0.398019\pi\)
−0.949115 + 0.314930i \(0.898019\pi\)
\(30\) 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 −0.883327 0.468756i \(-0.844702\pi\)
0.468756 + 0.883327i \(0.344702\pi\)
\(38\) 0 0
\(39\) 14.0517 0.360299
\(40\) 0 0
\(41\) 29.2351i 0.713051i −0.934286 0.356526i \(-0.883961\pi\)
0.934286 0.356526i \(-0.116039\pi\)
\(42\) 0 0
\(43\) 33.4099 + 33.4099i 0.776975 + 0.776975i 0.979315 0.202340i \(-0.0648546\pi\)
−0.202340 + 0.979315i \(0.564855\pi\)
\(44\) 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 0.314681 0.949197i \(-0.398102\pi\)
0.949197 0.314681i \(-0.101898\pi\)
\(54\) 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 \(-0.355505\pi\)
−0.898724 + 0.438515i \(0.855505\pi\)
\(60\) 0 0
\(61\) −65.2399 65.2399i −1.06951 1.06951i −0.997397 0.0721103i \(-0.977027\pi\)
−0.0721103 0.997397i \(-0.522973\pi\)
\(62\) 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 \(-0.880236\pi\)
0.367435 + 0.930049i \(0.380236\pi\)
\(68\) 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 \(0.259879\pi\)
−0.684825 + 0.728708i \(0.740121\pi\)
\(74\) 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 \(-0.684001\pi\)
0.837527 + 0.546396i \(0.184001\pi\)
\(84\) 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 \(0.0958679\pi\)
−0.954988 + 0.296645i \(0.904132\pi\)
\(90\) 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 \(-0.742758\pi\)
0.723011 + 0.690837i \(0.242758\pi\)
\(102\) 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 \(-0.478728\pi\)
−0.997768 + 0.0667770i \(0.978728\pi\)
\(108\) 0 0
\(109\) 108.050 + 108.050i 0.991282 + 0.991282i 0.999962 0.00868078i \(-0.00276321\pi\)
−0.00868078 + 0.999962i \(0.502763\pi\)
\(110\) 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 \(-0.871863\pi\)
0.391768 + 0.920064i \(0.371863\pi\)
\(132\) 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 \(-0.849894\pi\)
0.890856 0.454286i \(-0.150106\pi\)
\(138\) 0 0
\(139\) 169.014 + 169.014i 1.21593 + 1.21593i 0.969046 + 0.246881i \(0.0794057\pi\)
0.246881 + 0.969046i \(0.420594\pi\)
\(140\) 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 \(-0.995730\pi\)
0.0134145 + 0.999910i \(0.495730\pi\)
\(150\) 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 \(-0.130308\pi\)
−0.398035 + 0.917370i \(0.630308\pi\)
\(158\) 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 \(-0.672166\pi\)
0.857258 + 0.514887i \(0.172166\pi\)
\(164\) 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 \(-0.256357\pi\)
−0.721086 + 0.692846i \(0.756357\pi\)
\(174\) 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 −0.342702 + 0.939444i \(0.611342\pi\)
−0.939444 + 0.342702i \(0.888658\pi\)
\(180\) 0 0
\(181\) −116.607 + 116.607i −0.644238 + 0.644238i −0.951595 0.307356i \(-0.900556\pi\)
0.307356 + 0.951595i \(0.400556\pi\)
\(182\) 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 −0.547609 0.836734i \(-0.684462\pi\)
0.836734 + 0.547609i \(0.184462\pi\)
\(198\) 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 \(-0.547427\pi\)
0.988921 + 0.148445i \(0.0474269\pi\)
\(212\) 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 \(-0.645080\pi\)
0.897916 + 0.440166i \(0.145080\pi\)
\(228\) 0 0
\(229\) 101.055 101.055i 0.441290 0.441290i −0.451156 0.892445i \(-0.648988\pi\)
0.892445 + 0.451156i \(0.148988\pi\)
\(230\) 0 0
\(231\) 160.345 0.694136
\(232\) 0 0
\(233\) 287.259i 1.23287i −0.787405 0.616436i \(-0.788576\pi\)
0.787405 0.616436i \(-0.211424\pi\)
\(234\) 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 \(-0.158241\pi\)
−0.476905 + 0.878955i \(0.658241\pi\)
\(252\) 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 \(-0.256484\pi\)
−0.721363 + 0.692558i \(0.756484\pi\)
\(270\) 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 −0.240208 0.970721i \(-0.577216\pi\)
0.970721 + 0.240208i \(0.0772157\pi\)
\(278\) 0 0
\(279\) 50.7158 0.181777
\(280\) 0 0
\(281\) 68.8493i 0.245015i 0.992468 + 0.122508i \(0.0390936\pi\)
−0.992468 + 0.122508i \(0.960906\pi\)
\(282\) 0 0
\(283\) 206.773 + 206.773i 0.730646 + 0.730646i 0.970748 0.240102i \(-0.0771808\pi\)
−0.240102 + 0.970748i \(0.577181\pi\)
\(284\) 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 0.270043 0.962848i \(-0.412962\pi\)
0.962848 0.270043i \(-0.0870379\pi\)
\(294\) 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 \(-0.757998\pi\)
0.689119 + 0.724648i \(0.257998\pi\)
\(308\) 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 \(0.192241\pi\)
−0.823103 + 0.567892i \(0.807759\pi\)
\(314\) 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 \(-0.301718\pi\)
−0.812178 + 0.583410i \(0.801718\pi\)
\(318\) 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 \(-0.427809\pi\)
−0.974392 + 0.224856i \(0.927809\pi\)
\(332\) 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 \(-0.0464776\pi\)
−0.145496 + 0.989359i \(0.546478\pi\)
\(348\) 0 0
\(349\) −346.260 346.260i −0.992150 0.992150i 0.00781941 0.999969i \(-0.497511\pi\)
−0.999969 + 0.00781941i \(0.997511\pi\)
\(350\) 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 \(-0.818043\pi\)
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 −0.450427 0.892814i \(-0.648728\pi\)
0.892814 + 0.450427i \(0.148728\pi\)
\(374\) 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 \(-0.376000\pi\)
−0.925078 + 0.379778i \(0.876000\pi\)
\(380\) 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 −0.905112 0.425173i \(-0.860213\pi\)
0.425173 + 0.905112i \(0.360213\pi\)
\(390\) 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 \(-0.217416\pi\)
−0.631147 + 0.775663i \(0.717416\pi\)
\(398\) 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 \(-0.739058\pi\)
0.682386 0.730992i \(-0.260942\pi\)
\(410\) 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 \(-0.752500\pi\)
0.701532 + 0.712638i \(0.252500\pi\)
\(420\) 0 0
\(421\) −34.3754 + 34.3754i −0.0816519 + 0.0816519i −0.746753 0.665101i \(-0.768388\pi\)
0.665101 + 0.746753i \(0.268388\pi\)
\(422\) 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 \(-0.511720\pi\)
−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 \(-0.188896\pi\)
−0.559212 + 0.829025i \(0.688896\pi\)
\(444\) 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 \(0.0965274\pi\)
−0.954371 + 0.298623i \(0.903473\pi\)
\(458\) 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 \(-0.343276\pi\)
−0.881219 + 0.472709i \(0.843276\pi\)
\(462\) 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 \(-0.885071\pi\)
0.353266 + 0.935523i \(0.385071\pi\)
\(468\) 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 \(-0.557467\pi\)
−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 \(-0.417402\pi\)
−0.966521 + 0.256587i \(0.917402\pi\)
\(492\) 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 −0.249027 + 0.968496i \(0.580111\pi\)
−0.968496 + 0.249027i \(0.919889\pi\)
\(500\) 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 \(-0.222748\pi\)
−0.644051 + 0.764982i \(0.722748\pi\)
\(510\) 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 \(0.00995810\pi\)
−0.999511 + 0.0312792i \(0.990042\pi\)
\(522\) 0 0
\(523\) −226.407 226.407i −0.432900 0.432900i 0.456713 0.889614i \(-0.349026\pi\)
−0.889614 + 0.456713i \(0.849026\pi\)
\(524\) 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 \(-0.482756\pi\)
−0.998533 + 0.0541480i \(0.982756\pi\)
\(542\) 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 \(-0.519278\pi\)
0.998167 + 0.0605271i \(0.0192782\pi\)
\(548\) 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 −0.999846 0.0175529i \(-0.994412\pi\)
−0.0175529 0.999846i \(-0.505588\pi\)
\(558\) 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 \(-0.508012\pi\)
0.999683 + 0.0251665i \(0.00801159\pi\)
\(564\) 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 \(-0.839045\pi\)
0.874858 0.484380i \(-0.160955\pi\)
\(570\) 0 0
\(571\) 458.387 + 458.387i 0.802780 + 0.802780i 0.983529 0.180749i \(-0.0578522\pi\)
−0.180749 + 0.983529i \(0.557852\pi\)
\(572\) 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 \(-0.248840\pi\)
−0.704526 + 0.709678i \(0.748840\pi\)
\(588\) 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 \(-0.998117\pi\)
0.999983 0.00591558i \(-0.00188300\pi\)
\(602\) 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 0.0491093 0.998793i \(-0.484362\pi\)
0.998793 0.0491093i \(-0.0156383\pi\)
\(614\) 0 0
\(615\) −375.496 −0.610562
\(616\) 0 0
\(617\) 1068.16i 1.73122i −0.500717 0.865611i \(-0.666930\pi\)
0.500717 0.865611i \(-0.333070\pi\)
\(618\) 0 0
\(619\) 691.136 + 691.136i 1.11654 + 1.11654i 0.992246 + 0.124290i \(0.0396653\pi\)
0.124290 + 0.992246i \(0.460335\pi\)
\(620\) 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 0.0150512 0.999887i \(-0.495209\pi\)
0.999887 0.0150512i \(-0.00479113\pi\)
\(644\) 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 \(-0.177294\pi\)
−0.528630 + 0.848852i \(0.677294\pi\)
\(654\) 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 \(-0.555827\pi\)
0.984659 + 0.174489i \(0.0558274\pi\)
\(660\) 0 0
\(661\) −283.120 + 283.120i −0.428320 + 0.428320i −0.888056 0.459736i \(-0.847944\pi\)
0.459736 + 0.888056i \(0.347944\pi\)
\(662\) 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 \(-0.847939\pi\)
0.459749 + 0.888049i \(0.347939\pi\)
\(678\) 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 \(-0.299698\pi\)
−0.808460 + 0.588551i \(0.799698\pi\)
\(684\) 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 0.157506 0.987518i \(-0.449655\pi\)
0.987518 0.157506i \(-0.0503453\pi\)
\(692\) 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 −0.938274 0.345893i \(-0.887576\pi\)
−0.345893 0.938274i \(-0.612424\pi\)
\(702\) 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 \(-0.790903\pi\)
0.610663 + 0.791891i \(0.290903\pi\)
\(710\) 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 \(-0.216631\pi\)
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 \(-0.0106428\pi\)
−0.0334292 + 0.999441i \(0.510643\pi\)
\(734\) 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 \(-0.759977\pi\)
0.684600 + 0.728919i \(0.259977\pi\)
\(740\) 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 \(-0.689964\pi\)
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 −0.470935 0.882168i \(-0.656083\pi\)
0.882168 + 0.470935i \(0.156083\pi\)
\(758\) 0 0
\(759\) −174.805 −0.230309
\(760\) 0 0
\(761\) 179.137i 0.235397i 0.993049 + 0.117699i \(0.0375517\pi\)
−0.993049 + 0.117699i \(0.962448\pi\)
\(762\) 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 \(-0.721796\pi\)
0.766904 + 0.641762i \(0.221796\pi\)
\(774\) 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 \(-0.861225\pi\)
0.422293 + 0.906459i \(0.361225\pi\)
\(788\) 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