Properties

Label 384.3.i.c.161.6
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 161.6
Root \(1.96139 - 0.391068i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.c.353.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +O(q^{10})\) \(q+(-0.164573 - 2.99548i) q^{3} +(3.61305 + 3.61305i) q^{5} -12.2792i q^{7} +(-8.94583 + 0.985948i) q^{9} +(1.76932 + 1.76932i) q^{11} +(2.38826 + 2.38826i) q^{13} +(10.2282 - 11.4174i) q^{15} -20.0754i q^{17} +(-8.77090 - 8.77090i) q^{19} +(-36.7820 + 2.02081i) q^{21} +13.1821 q^{23} +1.10820i q^{25} +(4.42563 + 26.6348i) q^{27} +(6.51544 - 6.51544i) q^{29} -37.5922 q^{31} +(5.00877 - 5.59113i) q^{33} +(44.3652 - 44.3652i) q^{35} +(-10.0057 + 10.0057i) q^{37} +(6.76096 - 7.54704i) q^{39} -4.57407 q^{41} +(21.2835 - 21.2835i) q^{43} +(-35.8840 - 28.7594i) q^{45} -54.8366i q^{47} -101.778 q^{49} +(-60.1356 + 3.30386i) q^{51} +(-21.5215 - 21.5215i) q^{53} +12.7852i q^{55} +(-24.8296 + 27.7165i) q^{57} +(-53.6617 - 53.6617i) q^{59} +(19.2186 + 19.2186i) q^{61} +(12.1066 + 109.847i) q^{63} +17.2578i q^{65} +(31.5603 + 31.5603i) q^{67} +(-2.16941 - 39.4867i) q^{69} +65.1220 q^{71} +50.2451i q^{73} +(3.31960 - 0.182380i) q^{75} +(21.7257 - 21.7257i) q^{77} -20.9299 q^{79} +(79.0558 - 17.6403i) q^{81} +(-6.35791 + 6.35791i) q^{83} +(72.5334 - 72.5334i) q^{85} +(-20.5891 - 18.4446i) q^{87} +166.399 q^{89} +(29.3259 - 29.3259i) q^{91} +(6.18664 + 112.607i) q^{93} -63.3793i q^{95} +139.213 q^{97} +(-17.5725 - 14.0835i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 6q^{3} + O(q^{10}) \) \( 20q - 6q^{3} - 92q^{13} + 116q^{15} - 52q^{19} - 48q^{21} + 18q^{27} + 80q^{31} + 60q^{33} + 116q^{37} + 172q^{43} - 60q^{45} - 364q^{49} + 128q^{51} + 244q^{61} - 296q^{63} + 356q^{67} + 20q^{69} - 146q^{75} - 384q^{79} - 188q^{81} - 48q^{85} + 136q^{91} + 132q^{93} + 472q^{97} - 452q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.164573 2.99548i −0.0548575 0.998494i
\(4\) 0 0
\(5\) 3.61305 + 3.61305i 0.722609 + 0.722609i 0.969136 0.246527i \(-0.0792893\pi\)
−0.246527 + 0.969136i \(0.579289\pi\)
\(6\) 0 0
\(7\) 12.2792i 1.75417i −0.480338 0.877083i \(-0.659486\pi\)
0.480338 0.877083i \(-0.340514\pi\)
\(8\) 0 0
\(9\) −8.94583 + 0.985948i −0.993981 + 0.109550i
\(10\) 0 0
\(11\) 1.76932 + 1.76932i 0.160847 + 0.160847i 0.782942 0.622095i \(-0.213718\pi\)
−0.622095 + 0.782942i \(0.713718\pi\)
\(12\) 0 0
\(13\) 2.38826 + 2.38826i 0.183713 + 0.183713i 0.792971 0.609259i \(-0.208533\pi\)
−0.609259 + 0.792971i \(0.708533\pi\)
\(14\) 0 0
\(15\) 10.2282 11.4174i 0.681881 0.761162i
\(16\) 0 0
\(17\) 20.0754i 1.18091i −0.807072 0.590453i \(-0.798949\pi\)
0.807072 0.590453i \(-0.201051\pi\)
\(18\) 0 0
\(19\) −8.77090 8.77090i −0.461626 0.461626i 0.437562 0.899188i \(-0.355842\pi\)
−0.899188 + 0.437562i \(0.855842\pi\)
\(20\) 0 0
\(21\) −36.7820 + 2.02081i −1.75153 + 0.0962292i
\(22\) 0 0
\(23\) 13.1821 0.573134 0.286567 0.958060i \(-0.407486\pi\)
0.286567 + 0.958060i \(0.407486\pi\)
\(24\) 0 0
\(25\) 1.10820i 0.0443281i
\(26\) 0 0
\(27\) 4.42563 + 26.6348i 0.163912 + 0.986475i
\(28\) 0 0
\(29\) 6.51544 6.51544i 0.224670 0.224670i −0.585792 0.810462i \(-0.699216\pi\)
0.810462 + 0.585792i \(0.199216\pi\)
\(30\) 0 0
\(31\) −37.5922 −1.21265 −0.606326 0.795216i \(-0.707357\pi\)
−0.606326 + 0.795216i \(0.707357\pi\)
\(32\) 0 0
\(33\) 5.00877 5.59113i 0.151781 0.169428i
\(34\) 0 0
\(35\) 44.3652 44.3652i 1.26758 1.26758i
\(36\) 0 0
\(37\) −10.0057 + 10.0057i −0.270423 + 0.270423i −0.829271 0.558847i \(-0.811244\pi\)
0.558847 + 0.829271i \(0.311244\pi\)
\(38\) 0 0
\(39\) 6.76096 7.54704i 0.173358 0.193514i
\(40\) 0 0
\(41\) −4.57407 −0.111563 −0.0557814 0.998443i \(-0.517765\pi\)
−0.0557814 + 0.998443i \(0.517765\pi\)
\(42\) 0 0
\(43\) 21.2835 21.2835i 0.494966 0.494966i −0.414901 0.909867i \(-0.636184\pi\)
0.909867 + 0.414901i \(0.136184\pi\)
\(44\) 0 0
\(45\) −35.8840 28.7594i −0.797422 0.639098i
\(46\) 0 0
\(47\) 54.8366i 1.16674i −0.812208 0.583368i \(-0.801734\pi\)
0.812208 0.583368i \(-0.198266\pi\)
\(48\) 0 0
\(49\) −101.778 −2.07710
\(50\) 0 0
\(51\) −60.1356 + 3.30386i −1.17913 + 0.0647816i
\(52\) 0 0
\(53\) −21.5215 21.5215i −0.406065 0.406065i 0.474299 0.880364i \(-0.342702\pi\)
−0.880364 + 0.474299i \(0.842702\pi\)
\(54\) 0 0
\(55\) 12.7852i 0.232459i
\(56\) 0 0
\(57\) −24.8296 + 27.7165i −0.435607 + 0.486255i
\(58\) 0 0
\(59\) −53.6617 53.6617i −0.909520 0.909520i 0.0867132 0.996233i \(-0.472364\pi\)
−0.996233 + 0.0867132i \(0.972364\pi\)
\(60\) 0 0
\(61\) 19.2186 + 19.2186i 0.315059 + 0.315059i 0.846866 0.531807i \(-0.178487\pi\)
−0.531807 + 0.846866i \(0.678487\pi\)
\(62\) 0 0
\(63\) 12.1066 + 109.847i 0.192169 + 1.74361i
\(64\) 0 0
\(65\) 17.2578i 0.265505i
\(66\) 0 0
\(67\) 31.5603 + 31.5603i 0.471049 + 0.471049i 0.902254 0.431205i \(-0.141911\pi\)
−0.431205 + 0.902254i \(0.641911\pi\)
\(68\) 0 0
\(69\) −2.16941 39.4867i −0.0314407 0.572271i
\(70\) 0 0
\(71\) 65.1220 0.917211 0.458606 0.888640i \(-0.348349\pi\)
0.458606 + 0.888640i \(0.348349\pi\)
\(72\) 0 0
\(73\) 50.2451i 0.688290i 0.938917 + 0.344145i \(0.111831\pi\)
−0.938917 + 0.344145i \(0.888169\pi\)
\(74\) 0 0
\(75\) 3.31960 0.182380i 0.0442614 0.00243173i
\(76\) 0 0
\(77\) 21.7257 21.7257i 0.282152 0.282152i
\(78\) 0 0
\(79\) −20.9299 −0.264935 −0.132468 0.991187i \(-0.542290\pi\)
−0.132468 + 0.991187i \(0.542290\pi\)
\(80\) 0 0
\(81\) 79.0558 17.6403i 0.975998 0.217781i
\(82\) 0 0
\(83\) −6.35791 + 6.35791i −0.0766013 + 0.0766013i −0.744369 0.667768i \(-0.767250\pi\)
0.667768 + 0.744369i \(0.267250\pi\)
\(84\) 0 0
\(85\) 72.5334 72.5334i 0.853334 0.853334i
\(86\) 0 0
\(87\) −20.5891 18.4446i −0.236657 0.212007i
\(88\) 0 0
\(89\) 166.399 1.86966 0.934828 0.355102i \(-0.115554\pi\)
0.934828 + 0.355102i \(0.115554\pi\)
\(90\) 0 0
\(91\) 29.3259 29.3259i 0.322262 0.322262i
\(92\) 0 0
\(93\) 6.18664 + 112.607i 0.0665231 + 1.21083i
\(94\) 0 0
\(95\) 63.3793i 0.667151i
\(96\) 0 0
\(97\) 139.213 1.43519 0.717593 0.696463i \(-0.245244\pi\)
0.717593 + 0.696463i \(0.245244\pi\)
\(98\) 0 0
\(99\) −17.5725 14.0835i −0.177500 0.142258i
\(100\) 0 0
\(101\) 125.879 + 125.879i 1.24632 + 1.24632i 0.957331 + 0.288994i \(0.0933207\pi\)
0.288994 + 0.957331i \(0.406679\pi\)
\(102\) 0 0
\(103\) 26.3937i 0.256250i 0.991758 + 0.128125i \(0.0408958\pi\)
−0.991758 + 0.128125i \(0.959104\pi\)
\(104\) 0 0
\(105\) −140.196 125.594i −1.33520 1.19613i
\(106\) 0 0
\(107\) 83.9534 + 83.9534i 0.784611 + 0.784611i 0.980605 0.195994i \(-0.0627933\pi\)
−0.195994 + 0.980605i \(0.562793\pi\)
\(108\) 0 0
\(109\) −2.29518 2.29518i −0.0210567 0.0210567i 0.696500 0.717557i \(-0.254740\pi\)
−0.717557 + 0.696500i \(0.754740\pi\)
\(110\) 0 0
\(111\) 31.6184 + 28.3251i 0.284851 + 0.255181i
\(112\) 0 0
\(113\) 177.630i 1.57195i 0.618260 + 0.785974i \(0.287838\pi\)
−0.618260 + 0.785974i \(0.712162\pi\)
\(114\) 0 0
\(115\) 47.6275 + 47.6275i 0.414152 + 0.414152i
\(116\) 0 0
\(117\) −23.7197 19.0103i −0.202733 0.162481i
\(118\) 0 0
\(119\) −246.509 −2.07151
\(120\) 0 0
\(121\) 114.739i 0.948257i
\(122\) 0 0
\(123\) 0.752766 + 13.7016i 0.00612005 + 0.111395i
\(124\) 0 0
\(125\) 86.3222 86.3222i 0.690577 0.690577i
\(126\) 0 0
\(127\) 152.167 1.19816 0.599082 0.800687i \(-0.295532\pi\)
0.599082 + 0.800687i \(0.295532\pi\)
\(128\) 0 0
\(129\) −67.2571 60.2517i −0.521373 0.467068i
\(130\) 0 0
\(131\) −65.6955 + 65.6955i −0.501492 + 0.501492i −0.911901 0.410409i \(-0.865386\pi\)
0.410409 + 0.911901i \(0.365386\pi\)
\(132\) 0 0
\(133\) −107.699 + 107.699i −0.809769 + 0.809769i
\(134\) 0 0
\(135\) −80.2428 + 112.223i −0.594391 + 0.831280i
\(136\) 0 0
\(137\) 53.1509 0.387963 0.193982 0.981005i \(-0.437860\pi\)
0.193982 + 0.981005i \(0.437860\pi\)
\(138\) 0 0
\(139\) −161.324 + 161.324i −1.16060 + 1.16060i −0.176261 + 0.984343i \(0.556400\pi\)
−0.984343 + 0.176261i \(0.943600\pi\)
\(140\) 0 0
\(141\) −164.262 + 9.02460i −1.16498 + 0.0640043i
\(142\) 0 0
\(143\) 8.45118i 0.0590992i
\(144\) 0 0
\(145\) 47.0811 0.324698
\(146\) 0 0
\(147\) 16.7498 + 304.874i 0.113945 + 2.07397i
\(148\) 0 0
\(149\) 116.911 + 116.911i 0.784638 + 0.784638i 0.980610 0.195971i \(-0.0627859\pi\)
−0.195971 + 0.980610i \(0.562786\pi\)
\(150\) 0 0
\(151\) 10.9723i 0.0726643i 0.999340 + 0.0363321i \(0.0115674\pi\)
−0.999340 + 0.0363321i \(0.988433\pi\)
\(152\) 0 0
\(153\) 19.7933 + 179.591i 0.129368 + 1.17380i
\(154\) 0 0
\(155\) −135.822 135.822i −0.876273 0.876273i
\(156\) 0 0
\(157\) −49.8246 49.8246i −0.317354 0.317354i 0.530396 0.847750i \(-0.322043\pi\)
−0.847750 + 0.530396i \(0.822043\pi\)
\(158\) 0 0
\(159\) −60.9253 + 68.0090i −0.383178 + 0.427730i
\(160\) 0 0
\(161\) 161.865i 1.00537i
\(162\) 0 0
\(163\) −66.4240 66.4240i −0.407509 0.407509i 0.473360 0.880869i \(-0.343041\pi\)
−0.880869 + 0.473360i \(0.843041\pi\)
\(164\) 0 0
\(165\) 38.2980 2.10410i 0.232109 0.0127521i
\(166\) 0 0
\(167\) 182.851 1.09492 0.547459 0.836832i \(-0.315595\pi\)
0.547459 + 0.836832i \(0.315595\pi\)
\(168\) 0 0
\(169\) 157.592i 0.932499i
\(170\) 0 0
\(171\) 87.1106 + 69.8153i 0.509419 + 0.408277i
\(172\) 0 0
\(173\) −123.809 + 123.809i −0.715661 + 0.715661i −0.967714 0.252052i \(-0.918894\pi\)
0.252052 + 0.967714i \(0.418894\pi\)
\(174\) 0 0
\(175\) 13.6078 0.0777589
\(176\) 0 0
\(177\) −151.911 + 169.574i −0.858257 + 0.958045i
\(178\) 0 0
\(179\) 168.642 168.642i 0.942134 0.942134i −0.0562807 0.998415i \(-0.517924\pi\)
0.998415 + 0.0562807i \(0.0179242\pi\)
\(180\) 0 0
\(181\) 162.162 162.162i 0.895920 0.895920i −0.0991520 0.995072i \(-0.531613\pi\)
0.995072 + 0.0991520i \(0.0316130\pi\)
\(182\) 0 0
\(183\) 54.4061 60.7318i 0.297301 0.331868i
\(184\) 0 0
\(185\) −72.3018 −0.390821
\(186\) 0 0
\(187\) 35.5198 35.5198i 0.189945 0.189945i
\(188\) 0 0
\(189\) 327.053 54.3430i 1.73044 0.287529i
\(190\) 0 0
\(191\) 60.8777i 0.318731i −0.987220 0.159366i \(-0.949055\pi\)
0.987220 0.159366i \(-0.0509449\pi\)
\(192\) 0 0
\(193\) 177.871 0.921611 0.460806 0.887501i \(-0.347561\pi\)
0.460806 + 0.887501i \(0.347561\pi\)
\(194\) 0 0
\(195\) 51.6955 2.84016i 0.265105 0.0145649i
\(196\) 0 0
\(197\) −66.9411 66.9411i −0.339803 0.339803i 0.516490 0.856293i \(-0.327238\pi\)
−0.856293 + 0.516490i \(0.827238\pi\)
\(198\) 0 0
\(199\) 0.826328i 0.00415240i 0.999998 + 0.00207620i \(0.000660875\pi\)
−0.999998 + 0.00207620i \(0.999339\pi\)
\(200\) 0 0
\(201\) 89.3443 99.7322i 0.444499 0.496180i
\(202\) 0 0
\(203\) −80.0041 80.0041i −0.394109 0.394109i
\(204\) 0 0
\(205\) −16.5263 16.5263i −0.0806162 0.0806162i
\(206\) 0 0
\(207\) −117.925 + 12.9969i −0.569685 + 0.0627868i
\(208\) 0 0
\(209\) 31.0370i 0.148502i
\(210\) 0 0
\(211\) −181.344 181.344i −0.859448 0.859448i 0.131825 0.991273i \(-0.457916\pi\)
−0.991273 + 0.131825i \(0.957916\pi\)
\(212\) 0 0
\(213\) −10.7173 195.072i −0.0503159 0.915830i
\(214\) 0 0
\(215\) 153.797 0.715333
\(216\) 0 0
\(217\) 461.601i 2.12719i
\(218\) 0 0
\(219\) 150.508 8.26897i 0.687253 0.0377579i
\(220\) 0 0
\(221\) 47.9454 47.9454i 0.216947 0.216947i
\(222\) 0 0
\(223\) 17.7339 0.0795241 0.0397621 0.999209i \(-0.487340\pi\)
0.0397621 + 0.999209i \(0.487340\pi\)
\(224\) 0 0
\(225\) −1.09263 9.91380i −0.00485614 0.0440613i
\(226\) 0 0
\(227\) 7.53766 7.53766i 0.0332055 0.0332055i −0.690309 0.723515i \(-0.742525\pi\)
0.723515 + 0.690309i \(0.242525\pi\)
\(228\) 0 0
\(229\) −223.748 + 223.748i −0.977063 + 0.977063i −0.999743 0.0226794i \(-0.992780\pi\)
0.0226794 + 0.999743i \(0.492780\pi\)
\(230\) 0 0
\(231\) −68.6545 61.5036i −0.297205 0.266249i
\(232\) 0 0
\(233\) −123.585 −0.530406 −0.265203 0.964193i \(-0.585439\pi\)
−0.265203 + 0.964193i \(0.585439\pi\)
\(234\) 0 0
\(235\) 198.127 198.127i 0.843095 0.843095i
\(236\) 0 0
\(237\) 3.44448 + 62.6951i 0.0145337 + 0.264536i
\(238\) 0 0
\(239\) 118.501i 0.495820i 0.968783 + 0.247910i \(0.0797437\pi\)
−0.968783 + 0.247910i \(0.920256\pi\)
\(240\) 0 0
\(241\) −264.162 −1.09611 −0.548053 0.836443i \(-0.684631\pi\)
−0.548053 + 0.836443i \(0.684631\pi\)
\(242\) 0 0
\(243\) −65.8515 233.907i −0.270994 0.962581i
\(244\) 0 0
\(245\) −367.728 367.728i −1.50093 1.50093i
\(246\) 0 0
\(247\) 41.8944i 0.169613i
\(248\) 0 0
\(249\) 20.0913 + 17.9987i 0.0806881 + 0.0722838i
\(250\) 0 0
\(251\) 152.477 + 152.477i 0.607478 + 0.607478i 0.942286 0.334808i \(-0.108672\pi\)
−0.334808 + 0.942286i \(0.608672\pi\)
\(252\) 0 0
\(253\) 23.3233 + 23.3233i 0.0921869 + 0.0921869i
\(254\) 0 0
\(255\) −229.210 205.336i −0.898861 0.805238i
\(256\) 0 0
\(257\) 113.118i 0.440147i −0.975483 0.220074i \(-0.929370\pi\)
0.975483 0.220074i \(-0.0706298\pi\)
\(258\) 0 0
\(259\) 122.861 + 122.861i 0.474367 + 0.474367i
\(260\) 0 0
\(261\) −51.8621 + 64.7099i −0.198705 + 0.247931i
\(262\) 0 0
\(263\) −129.324 −0.491727 −0.245864 0.969304i \(-0.579072\pi\)
−0.245864 + 0.969304i \(0.579072\pi\)
\(264\) 0 0
\(265\) 155.516i 0.586853i
\(266\) 0 0
\(267\) −27.3848 498.446i −0.102565 1.86684i
\(268\) 0 0
\(269\) −129.457 + 129.457i −0.481253 + 0.481253i −0.905532 0.424278i \(-0.860528\pi\)
0.424278 + 0.905532i \(0.360528\pi\)
\(270\) 0 0
\(271\) −170.727 −0.629990 −0.314995 0.949093i \(-0.602003\pi\)
−0.314995 + 0.949093i \(0.602003\pi\)
\(272\) 0 0
\(273\) −92.6714 83.0189i −0.339456 0.304099i
\(274\) 0 0
\(275\) −1.96076 + 1.96076i −0.00713004 + 0.00713004i
\(276\) 0 0
\(277\) −114.051 + 114.051i −0.411737 + 0.411737i −0.882343 0.470606i \(-0.844035\pi\)
0.470606 + 0.882343i \(0.344035\pi\)
\(278\) 0 0
\(279\) 336.294 37.0640i 1.20535 0.132846i
\(280\) 0 0
\(281\) 136.468 0.485650 0.242825 0.970070i \(-0.421926\pi\)
0.242825 + 0.970070i \(0.421926\pi\)
\(282\) 0 0
\(283\) −132.657 + 132.657i −0.468752 + 0.468752i −0.901510 0.432758i \(-0.857540\pi\)
0.432758 + 0.901510i \(0.357540\pi\)
\(284\) 0 0
\(285\) −189.852 + 10.4305i −0.666146 + 0.0365982i
\(286\) 0 0
\(287\) 56.1658i 0.195700i
\(288\) 0 0
\(289\) −114.022 −0.394541
\(290\) 0 0
\(291\) −22.9106 417.010i −0.0787307 1.43303i
\(292\) 0 0
\(293\) 143.968 + 143.968i 0.491360 + 0.491360i 0.908735 0.417375i \(-0.137050\pi\)
−0.417375 + 0.908735i \(0.637050\pi\)
\(294\) 0 0
\(295\) 387.764i 1.31446i
\(296\) 0 0
\(297\) −39.2951 + 54.9557i −0.132307 + 0.185036i
\(298\) 0 0
\(299\) 31.4823 + 31.4823i 0.105292 + 0.105292i
\(300\) 0 0
\(301\) −261.344 261.344i −0.868252 0.868252i
\(302\) 0 0
\(303\) 356.352 397.784i 1.17608 1.31282i
\(304\) 0 0
\(305\) 138.875i 0.455328i
\(306\) 0 0
\(307\) −89.3258 89.3258i −0.290964 0.290964i 0.546497 0.837461i \(-0.315961\pi\)
−0.837461 + 0.546497i \(0.815961\pi\)
\(308\) 0 0
\(309\) 79.0619 4.34368i 0.255864 0.0140572i
\(310\) 0 0
\(311\) 314.507 1.01128 0.505638 0.862746i \(-0.331257\pi\)
0.505638 + 0.862746i \(0.331257\pi\)
\(312\) 0 0
\(313\) 103.874i 0.331867i 0.986137 + 0.165934i \(0.0530638\pi\)
−0.986137 + 0.165934i \(0.946936\pi\)
\(314\) 0 0
\(315\) −353.142 + 440.625i −1.12108 + 1.39881i
\(316\) 0 0
\(317\) 321.109 321.109i 1.01296 1.01296i 0.0130482 0.999915i \(-0.495847\pi\)
0.999915 0.0130482i \(-0.00415349\pi\)
\(318\) 0 0
\(319\) 23.0557 0.0722750
\(320\) 0 0
\(321\) 237.665 265.297i 0.740388 0.826472i
\(322\) 0 0
\(323\) −176.079 + 176.079i −0.545138 + 0.545138i
\(324\) 0 0
\(325\) −2.64668 + 2.64668i −0.00814363 + 0.00814363i
\(326\) 0 0
\(327\) −6.49746 + 7.25291i −0.0198699 + 0.0221801i
\(328\) 0 0
\(329\) −673.348 −2.04665
\(330\) 0 0
\(331\) −313.858 + 313.858i −0.948213 + 0.948213i −0.998724 0.0505107i \(-0.983915\pi\)
0.0505107 + 0.998724i \(0.483915\pi\)
\(332\) 0 0
\(333\) 79.6439 99.3740i 0.239171 0.298420i
\(334\) 0 0
\(335\) 228.057i 0.680768i
\(336\) 0 0
\(337\) −236.028 −0.700380 −0.350190 0.936679i \(-0.613883\pi\)
−0.350190 + 0.936679i \(0.613883\pi\)
\(338\) 0 0
\(339\) 532.088 29.2330i 1.56958 0.0862331i
\(340\) 0 0
\(341\) −66.5125 66.5125i −0.195051 0.195051i
\(342\) 0 0
\(343\) 648.069i 1.88941i
\(344\) 0 0
\(345\) 134.829 150.506i 0.390809 0.436248i
\(346\) 0 0
\(347\) 441.946 + 441.946i 1.27362 + 1.27362i 0.944175 + 0.329445i \(0.106862\pi\)
0.329445 + 0.944175i \(0.393138\pi\)
\(348\) 0 0
\(349\) 476.643 + 476.643i 1.36574 + 1.36574i 0.866417 + 0.499321i \(0.166417\pi\)
0.499321 + 0.866417i \(0.333583\pi\)
\(350\) 0 0
\(351\) −53.0414 + 74.1805i −0.151115 + 0.211341i
\(352\) 0 0
\(353\) 452.246i 1.28115i −0.767895 0.640575i \(-0.778696\pi\)
0.767895 0.640575i \(-0.221304\pi\)
\(354\) 0 0
\(355\) 235.289 + 235.289i 0.662785 + 0.662785i
\(356\) 0 0
\(357\) 40.5687 + 738.415i 0.113638 + 2.06839i
\(358\) 0 0
\(359\) −617.295 −1.71948 −0.859742 0.510728i \(-0.829376\pi\)
−0.859742 + 0.510728i \(0.829376\pi\)
\(360\) 0 0
\(361\) 207.143i 0.573803i
\(362\) 0 0
\(363\) −343.699 + 18.8829i −0.946829 + 0.0520190i
\(364\) 0 0
\(365\) −181.538 + 181.538i −0.497364 + 0.497364i
\(366\) 0 0
\(367\) 11.3588 0.0309505 0.0154753 0.999880i \(-0.495074\pi\)
0.0154753 + 0.999880i \(0.495074\pi\)
\(368\) 0 0
\(369\) 40.9189 4.50980i 0.110891 0.0122217i
\(370\) 0 0
\(371\) −264.266 + 264.266i −0.712306 + 0.712306i
\(372\) 0 0
\(373\) 59.4092 59.4092i 0.159274 0.159274i −0.622971 0.782245i \(-0.714075\pi\)
0.782245 + 0.622971i \(0.214075\pi\)
\(374\) 0 0
\(375\) −272.783 244.370i −0.727421 0.651654i
\(376\) 0 0
\(377\) 31.1212 0.0825495
\(378\) 0 0
\(379\) 435.432 435.432i 1.14890 1.14890i 0.162129 0.986770i \(-0.448164\pi\)
0.986770 0.162129i \(-0.0518359\pi\)
\(380\) 0 0
\(381\) −25.0425 455.813i −0.0657283 1.19636i
\(382\) 0 0
\(383\) 272.117i 0.710488i −0.934774 0.355244i \(-0.884398\pi\)
0.934774 0.355244i \(-0.115602\pi\)
\(384\) 0 0
\(385\) 156.992 0.407772
\(386\) 0 0
\(387\) −169.414 + 211.383i −0.437763 + 0.546210i
\(388\) 0 0
\(389\) −260.985 260.985i −0.670913 0.670913i 0.287013 0.957927i \(-0.407338\pi\)
−0.957927 + 0.287013i \(0.907338\pi\)
\(390\) 0 0
\(391\) 264.636i 0.676818i
\(392\) 0 0
\(393\) 207.601 + 185.978i 0.528248 + 0.473226i
\(394\) 0 0
\(395\) −75.6206 75.6206i −0.191445 0.191445i
\(396\) 0 0
\(397\) −258.248 258.248i −0.650500 0.650500i 0.302614 0.953113i \(-0.402141\pi\)
−0.953113 + 0.302614i \(0.902141\pi\)
\(398\) 0 0
\(399\) 340.336 + 304.887i 0.852972 + 0.764128i
\(400\) 0 0
\(401\) 430.073i 1.07250i 0.844059 + 0.536250i \(0.180160\pi\)
−0.844059 + 0.536250i \(0.819840\pi\)
\(402\) 0 0
\(403\) −89.7801 89.7801i −0.222779 0.222779i
\(404\) 0 0
\(405\) 349.367 + 221.897i 0.862635 + 0.547894i
\(406\) 0 0
\(407\) −35.4063 −0.0869935
\(408\) 0 0
\(409\) 207.501i 0.507337i −0.967291 0.253668i \(-0.918363\pi\)
0.967291 0.253668i \(-0.0816372\pi\)
\(410\) 0 0
\(411\) −8.74718 159.213i −0.0212827 0.387379i
\(412\) 0 0
\(413\) −658.921 + 658.921i −1.59545 + 1.59545i
\(414\) 0 0
\(415\) −45.9428 −0.110706
\(416\) 0 0
\(417\) 509.793 + 456.694i 1.22253 + 1.09519i
\(418\) 0 0
\(419\) −108.717 + 108.717i −0.259467 + 0.259467i −0.824837 0.565370i \(-0.808733\pi\)
0.565370 + 0.824837i \(0.308733\pi\)
\(420\) 0 0
\(421\) 484.985 484.985i 1.15198 1.15198i 0.165829 0.986155i \(-0.446970\pi\)
0.986155 0.165829i \(-0.0530300\pi\)
\(422\) 0 0
\(423\) 54.0661 + 490.559i 0.127816 + 1.15971i
\(424\) 0 0
\(425\) 22.2476 0.0523474
\(426\) 0 0
\(427\) 235.988 235.988i 0.552665 0.552665i
\(428\) 0 0
\(429\) 25.3154 1.39083i 0.0590102 0.00324203i
\(430\) 0 0
\(431\) 213.570i 0.495522i 0.968821 + 0.247761i \(0.0796947\pi\)
−0.968821 + 0.247761i \(0.920305\pi\)
\(432\) 0 0
\(433\) 440.669 1.01771 0.508856 0.860852i \(-0.330069\pi\)
0.508856 + 0.860852i \(0.330069\pi\)
\(434\) 0 0
\(435\) −7.74826 141.031i −0.0178121 0.324209i
\(436\) 0 0
\(437\) −115.619 115.619i −0.264574 0.264574i
\(438\) 0 0
\(439\) 400.367i 0.911998i −0.889980 0.455999i \(-0.849282\pi\)
0.889980 0.455999i \(-0.150718\pi\)
\(440\) 0 0
\(441\) 910.488 100.348i 2.06460 0.227546i
\(442\) 0 0
\(443\) −324.076 324.076i −0.731549 0.731549i 0.239378 0.970926i \(-0.423057\pi\)
−0.970926 + 0.239378i \(0.923057\pi\)
\(444\) 0 0
\(445\) 601.208 + 601.208i 1.35103 + 1.35103i
\(446\) 0 0
\(447\) 330.965 369.446i 0.740414 0.826500i
\(448\) 0 0
\(449\) 691.918i 1.54102i 0.637427 + 0.770510i \(0.279999\pi\)
−0.637427 + 0.770510i \(0.720001\pi\)
\(450\) 0 0
\(451\) −8.09298 8.09298i −0.0179445 0.0179445i
\(452\) 0 0
\(453\) 32.8674 1.80574i 0.0725549 0.00398618i
\(454\) 0 0
\(455\) 211.912 0.465740
\(456\) 0 0
\(457\) 385.436i 0.843404i −0.906734 0.421702i \(-0.861433\pi\)
0.906734 0.421702i \(-0.138567\pi\)
\(458\) 0 0
\(459\) 534.705 88.8463i 1.16494 0.193565i
\(460\) 0 0
\(461\) 312.070 312.070i 0.676942 0.676942i −0.282365 0.959307i \(-0.591119\pi\)
0.959307 + 0.282365i \(0.0911190\pi\)
\(462\) 0 0
\(463\) −718.961 −1.55283 −0.776416 0.630220i \(-0.782965\pi\)
−0.776416 + 0.630220i \(0.782965\pi\)
\(464\) 0 0
\(465\) −384.501 + 429.206i −0.826884 + 0.923024i
\(466\) 0 0
\(467\) −82.7894 + 82.7894i −0.177279 + 0.177279i −0.790169 0.612889i \(-0.790007\pi\)
0.612889 + 0.790169i \(0.290007\pi\)
\(468\) 0 0
\(469\) 387.534 387.534i 0.826298 0.826298i
\(470\) 0 0
\(471\) −141.049 + 157.448i −0.299467 + 0.334285i
\(472\) 0 0
\(473\) 75.3145 0.159227
\(474\) 0 0
\(475\) 9.71993 9.71993i 0.0204630 0.0204630i
\(476\) 0 0
\(477\) 213.746 + 171.308i 0.448106 + 0.359137i
\(478\) 0 0
\(479\) 749.099i 1.56388i 0.623353 + 0.781941i \(0.285770\pi\)
−0.623353 + 0.781941i \(0.714230\pi\)
\(480\) 0 0
\(481\) −47.7923 −0.0993603
\(482\) 0 0
\(483\) −484.864 + 26.6385i −1.00386 + 0.0551523i
\(484\) 0 0
\(485\) 502.983 + 502.983i 1.03708 + 1.03708i
\(486\) 0 0
\(487\) 533.210i 1.09489i 0.836843 + 0.547443i \(0.184399\pi\)
−0.836843 + 0.547443i \(0.815601\pi\)
\(488\) 0 0
\(489\) −188.040 + 209.904i −0.384541 + 0.429251i
\(490\) 0 0
\(491\) −6.75013 6.75013i −0.0137477 0.0137477i 0.700200 0.713947i \(-0.253094\pi\)
−0.713947 + 0.700200i \(0.753094\pi\)
\(492\) 0 0
\(493\) −130.800 130.800i −0.265315 0.265315i
\(494\) 0 0
\(495\) −12.6056 114.375i −0.0254658 0.231060i
\(496\) 0 0
\(497\) 799.644i 1.60894i
\(498\) 0 0
\(499\) 556.347 + 556.347i 1.11492 + 1.11492i 0.992475 + 0.122448i \(0.0390746\pi\)
0.122448 + 0.992475i \(0.460925\pi\)
\(500\) 0 0
\(501\) −30.0923 547.728i −0.0600645 1.09327i
\(502\) 0 0
\(503\) −304.892 −0.606147 −0.303074 0.952967i \(-0.598013\pi\)
−0.303074 + 0.952967i \(0.598013\pi\)
\(504\) 0 0
\(505\) 909.612i 1.80121i
\(506\) 0 0
\(507\) −472.065 + 25.9354i −0.931095 + 0.0511546i
\(508\) 0 0
\(509\) 118.591 118.591i 0.232988 0.232988i −0.580951 0.813939i \(-0.697319\pi\)
0.813939 + 0.580951i \(0.197319\pi\)
\(510\) 0 0
\(511\) 616.968 1.20737
\(512\) 0 0
\(513\) 194.795 272.428i 0.379716 0.531049i
\(514\) 0 0
\(515\) −95.3617 + 95.3617i −0.185168 + 0.185168i
\(516\) 0 0
\(517\) 97.0233 97.0233i 0.187666 0.187666i
\(518\) 0 0
\(519\) 391.244 + 350.493i 0.753843 + 0.675324i
\(520\) 0 0
\(521\) −105.077 −0.201683 −0.100842 0.994902i \(-0.532154\pi\)
−0.100842 + 0.994902i \(0.532154\pi\)
\(522\) 0 0
\(523\) −479.455 + 479.455i −0.916740 + 0.916740i −0.996791 0.0800507i \(-0.974492\pi\)
0.0800507 + 0.996791i \(0.474492\pi\)
\(524\) 0 0
\(525\) −2.23947 40.7619i −0.00426566 0.0776418i
\(526\) 0 0
\(527\) 754.679i 1.43203i
\(528\) 0 0
\(529\) −355.232 −0.671517
\(530\) 0 0
\(531\) 532.956 + 427.141i 1.00368 + 0.804408i
\(532\) 0 0
\(533\) −10.9241 10.9241i −0.0204955 0.0204955i
\(534\) 0 0
\(535\) 606.655i 1.13393i
\(536\) 0 0
\(537\) −532.918 477.410i −0.992399 0.889032i
\(538\) 0 0
\(539\) −180.077 180.077i −0.334095 0.334095i
\(540\) 0 0
\(541\) −726.230 726.230i −1.34238 1.34238i −0.893680 0.448704i \(-0.851886\pi\)
−0.448704 0.893680i \(-0.648114\pi\)
\(542\) 0 0
\(543\) −512.439 459.065i −0.943719 0.845423i
\(544\) 0 0
\(545\) 16.5852i 0.0304316i
\(546\) 0 0
\(547\) 314.507 + 314.507i 0.574966 + 0.574966i 0.933512 0.358546i \(-0.116727\pi\)
−0.358546 + 0.933512i \(0.616727\pi\)
\(548\) 0 0
\(549\) −190.875 152.978i −0.347677 0.278648i
\(550\) 0 0
\(551\) −114.292 −0.207427
\(552\) 0 0
\(553\) 257.002i 0.464741i
\(554\) 0 0
\(555\) 11.8989 + 216.579i 0.0214394 + 0.390232i
\(556\) 0 0
\(557\) −134.274 + 134.274i −0.241066 + 0.241066i −0.817291 0.576225i \(-0.804525\pi\)
0.576225 + 0.817291i \(0.304525\pi\)
\(558\) 0 0
\(559\) 101.661 0.181863
\(560\) 0 0
\(561\) −112.244 100.553i −0.200079 0.179239i
\(562\) 0 0
\(563\) 102.810 102.810i 0.182612 0.182612i −0.609881 0.792493i \(-0.708783\pi\)
0.792493 + 0.609881i \(0.208783\pi\)
\(564\) 0 0
\(565\) −641.785 + 641.785i −1.13590 + 1.13590i
\(566\) 0 0
\(567\) −216.608 970.739i −0.382024 1.71206i
\(568\) 0 0
\(569\) 78.4572 0.137886 0.0689430 0.997621i \(-0.478037\pi\)
0.0689430 + 0.997621i \(0.478037\pi\)
\(570\) 0 0
\(571\) 363.164 363.164i 0.636013 0.636013i −0.313556 0.949570i \(-0.601520\pi\)
0.949570 + 0.313556i \(0.101520\pi\)
\(572\) 0 0
\(573\) −182.358 + 10.0188i −0.318251 + 0.0174848i
\(574\) 0 0
\(575\) 14.6084i 0.0254060i
\(576\) 0 0
\(577\) −566.880 −0.982460 −0.491230 0.871030i \(-0.663453\pi\)
−0.491230 + 0.871030i \(0.663453\pi\)
\(578\) 0 0
\(579\) −29.2727 532.809i −0.0505573 0.920223i
\(580\) 0 0
\(581\) 78.0698 + 78.0698i 0.134371 + 0.134371i
\(582\) 0 0
\(583\) 76.1565i 0.130629i
\(584\) 0 0
\(585\) −17.0153 154.385i −0.0290860 0.263907i
\(586\) 0 0
\(587\) 73.3693 + 73.3693i 0.124990 + 0.124990i 0.766835 0.641845i \(-0.221831\pi\)
−0.641845 + 0.766835i \(0.721831\pi\)
\(588\) 0 0
\(589\) 329.717 + 329.717i 0.559792 + 0.559792i
\(590\) 0 0
\(591\) −189.504 + 211.538i −0.320650 + 0.357932i
\(592\) 0 0
\(593\) 458.708i 0.773538i 0.922177 + 0.386769i \(0.126409\pi\)
−0.922177 + 0.386769i \(0.873591\pi\)
\(594\) 0 0
\(595\) −890.650 890.650i −1.49689 1.49689i
\(596\) 0 0
\(597\) 2.47525 0.135991i 0.00414615 0.000227790i
\(598\) 0 0
\(599\) 423.611 0.707197 0.353599 0.935397i \(-0.384958\pi\)
0.353599 + 0.935397i \(0.384958\pi\)
\(600\) 0 0
\(601\) 795.376i 1.32342i −0.749759 0.661711i \(-0.769831\pi\)
0.749759 0.661711i \(-0.230169\pi\)
\(602\) 0 0
\(603\) −313.450 251.216i −0.519817 0.416610i
\(604\) 0 0
\(605\) 414.557 414.557i 0.685219 0.685219i
\(606\) 0 0
\(607\) 631.699 1.04069 0.520345 0.853956i \(-0.325803\pi\)
0.520345 + 0.853956i \(0.325803\pi\)
\(608\) 0 0
\(609\) −226.484 + 252.817i −0.371896 + 0.415135i
\(610\) 0 0
\(611\) 130.964 130.964i 0.214344 0.214344i
\(612\) 0 0
\(613\) −385.264 + 385.264i −0.628490 + 0.628490i −0.947688 0.319198i \(-0.896586\pi\)
0.319198 + 0.947688i \(0.396586\pi\)
\(614\) 0 0
\(615\) −46.7846 + 52.2241i −0.0760724 + 0.0849173i
\(616\) 0 0
\(617\) 953.333 1.54511 0.772555 0.634947i \(-0.218978\pi\)
0.772555 + 0.634947i \(0.218978\pi\)
\(618\) 0 0
\(619\) −574.046 + 574.046i −0.927377 + 0.927377i −0.997536 0.0701591i \(-0.977649\pi\)
0.0701591 + 0.997536i \(0.477649\pi\)
\(620\) 0 0
\(621\) 58.3390 + 351.103i 0.0939437 + 0.565383i
\(622\) 0 0
\(623\) 2043.24i 3.27969i
\(624\) 0 0
\(625\) 651.477 1.04236
\(626\) 0 0
\(627\) −92.9707 + 5.10783i −0.148279 + 0.00814646i
\(628\) 0 0
\(629\) 200.868 + 200.868i 0.319345 + 0.319345i
\(630\) 0 0
\(631\) 138.048i 0.218777i −0.993999 0.109389i \(-0.965111\pi\)
0.993999 0.109389i \(-0.0348893\pi\)
\(632\) 0 0
\(633\) −513.367 + 573.056i −0.811007 + 0.905301i
\(634\) 0 0
\(635\) 549.786 + 549.786i 0.865805 + 0.865805i
\(636\) 0 0
\(637\) −243.072 243.072i −0.381589 0.381589i
\(638\) 0 0
\(639\) −582.570 + 64.2069i −0.911691 + 0.100480i
\(640\) 0 0
\(641\) 784.889i 1.22448i −0.790673 0.612238i \(-0.790269\pi\)
0.790673 0.612238i \(-0.209731\pi\)
\(642\) 0 0
\(643\) −238.456 238.456i −0.370850 0.370850i 0.496937 0.867787i \(-0.334458\pi\)
−0.867787 + 0.496937i \(0.834458\pi\)
\(644\) 0 0
\(645\) −25.3107 460.695i −0.0392414 0.714256i
\(646\) 0 0
\(647\) 681.751 1.05371 0.526855 0.849955i \(-0.323371\pi\)
0.526855 + 0.849955i \(0.323371\pi\)
\(648\) 0 0
\(649\) 189.889i 0.292587i
\(650\) 0 0
\(651\) 1382.72 75.9668i 2.12399 0.116693i
\(652\) 0 0
\(653\) −636.071 + 636.071i −0.974075 + 0.974075i −0.999672 0.0255977i \(-0.991851\pi\)
0.0255977 + 0.999672i \(0.491851\pi\)
\(654\) 0 0
\(655\) −474.721 −0.724766
\(656\) 0 0
\(657\) −49.5391 449.485i −0.0754020 0.684147i
\(658\) 0 0
\(659\) −91.6052 + 91.6052i −0.139006 + 0.139006i −0.773186 0.634179i \(-0.781338\pi\)
0.634179 + 0.773186i \(0.281338\pi\)
\(660\) 0 0
\(661\) −721.715 + 721.715i −1.09185 + 1.09185i −0.0965216 + 0.995331i \(0.530772\pi\)
−0.995331 + 0.0965216i \(0.969228\pi\)
\(662\) 0 0
\(663\) −151.510 135.729i −0.228522 0.204720i
\(664\) 0 0
\(665\) −778.245 −1.17029
\(666\) 0 0
\(667\) 85.8871 85.8871i 0.128766 0.128766i
\(668\) 0 0
\(669\) −2.91851 53.1215i −0.00436250 0.0794044i
\(670\) 0 0
\(671\) 68.0074i 0.101352i
\(672\) 0 0
\(673\) 417.305 0.620067 0.310033 0.950726i \(-0.399660\pi\)
0.310033 + 0.950726i \(0.399660\pi\)
\(674\) 0 0
\(675\) −29.5168 + 4.90449i −0.0437286 + 0.00726592i
\(676\) 0 0
\(677\) −585.326 585.326i −0.864587 0.864587i 0.127280 0.991867i \(-0.459375\pi\)
−0.991867 + 0.127280i \(0.959375\pi\)
\(678\) 0 0
\(679\) 1709.42i 2.51756i
\(680\) 0 0
\(681\) −23.8194 21.3384i −0.0349771 0.0313340i
\(682\) 0 0
\(683\) −104.261 104.261i −0.152651 0.152651i 0.626650 0.779301i \(-0.284426\pi\)
−0.779301 + 0.626650i \(0.784426\pi\)
\(684\) 0 0
\(685\) 192.037 + 192.037i 0.280346 + 0.280346i
\(686\) 0 0
\(687\) 707.054 + 633.409i 1.02919 + 0.921993i
\(688\) 0 0
\(689\) 102.798i 0.149199i
\(690\) 0 0
\(691\) −335.701 335.701i −0.485818 0.485818i 0.421165 0.906984i \(-0.361621\pi\)
−0.906984 + 0.421165i \(0.861621\pi\)
\(692\) 0 0
\(693\) −172.934 + 215.775i −0.249544 + 0.311364i
\(694\) 0 0
\(695\) −1165.74 −1.67733
\(696\) 0 0
\(697\) 91.8264i 0.131745i
\(698\) 0 0
\(699\) 20.3386 + 370.196i 0.0290968 + 0.529608i
\(700\) 0 0
\(701\) 490.458 490.458i 0.699655 0.699655i −0.264681 0.964336i \(-0.585267\pi\)
0.964336 + 0.264681i \(0.0852666\pi\)
\(702\) 0 0
\(703\) 175.517 0.249669
\(704\) 0 0
\(705\) −626.093 560.881i −0.888075 0.795575i
\(706\) 0 0
\(707\) 1545.69 1545.69i 2.18626 2.18626i
\(708\) 0 0
\(709\) −435.817 + 435.817i −0.614692 + 0.614692i −0.944165 0.329473i \(-0.893129\pi\)
0.329473 + 0.944165i \(0.393129\pi\)
\(710\) 0 0
\(711\) 187.235 20.6358i 0.263341 0.0290236i
\(712\) 0 0
\(713\) −495.544 −0.695012
\(714\) 0 0
\(715\) −30.5345 + 30.5345i −0.0427056 + 0.0427056i
\(716\) 0 0
\(717\) 354.968 19.5020i 0.495073 0.0271994i
\(718\) 0 0
\(719\) 1083.05i 1.50633i −0.657831 0.753166i \(-0.728526\pi\)
0.657831 0.753166i \(-0.271474\pi\)
\(720\) 0 0
\(721\) 324.093 0.449505
\(722\) 0 0
\(723\) 43.4738 + 791.292i 0.0601297 + 1.09446i
\(724\) 0 0
\(725\) 7.22042 + 7.22042i 0.00995921 + 0.00995921i
\(726\) 0 0
\(727\) 513.215i 0.705935i 0.935636 + 0.352968i \(0.114827\pi\)
−0.935636 + 0.352968i \(0.885173\pi\)
\(728\) 0 0
\(729\) −689.828 + 235.752i −0.946266 + 0.323390i
\(730\) 0 0
\(731\) −427.276 427.276i −0.584508 0.584508i
\(732\) 0 0
\(733\) −73.6001 73.6001i −0.100409 0.100409i 0.655118 0.755527i \(-0.272619\pi\)
−0.755527 + 0.655118i \(0.772619\pi\)
\(734\) 0 0
\(735\) −1041.01 + 1162.04i −1.41633 + 1.58101i
\(736\) 0 0
\(737\) 111.680i 0.151533i
\(738\) 0 0
\(739\) 152.386 + 152.386i 0.206206 + 0.206206i 0.802653 0.596447i \(-0.203421\pi\)
−0.596447 + 0.802653i \(0.703421\pi\)
\(740\) 0 0
\(741\) −125.494 + 6.89467i −0.169358 + 0.00930455i
\(742\) 0 0
\(743\) 574.044 0.772603 0.386302 0.922373i \(-0.373752\pi\)
0.386302 + 0.922373i \(0.373752\pi\)
\(744\) 0 0
\(745\) 844.811i 1.13397i
\(746\) 0 0
\(747\) 50.6082 63.1454i 0.0677486 0.0845319i
\(748\) 0 0
\(749\) 1030.88 1030.88i 1.37634 1.37634i
\(750\) 0 0
\(751\) 1014.28 1.35058 0.675289 0.737553i \(-0.264019\pi\)
0.675289 + 0.737553i \(0.264019\pi\)
\(752\) 0 0
\(753\) 431.649 481.836i 0.573239 0.639888i
\(754\) 0 0
\(755\) −39.6435 + 39.6435i −0.0525079 + 0.0525079i
\(756\) 0 0
\(757\) 1003.73 1003.73i 1.32594 1.32594i 0.417057 0.908880i \(-0.363062\pi\)
0.908880 0.417057i \(-0.136938\pi\)
\(758\) 0 0
\(759\) 66.0261 73.7028i 0.0869909 0.0971052i
\(760\) 0 0
\(761\) 54.1069 0.0710997 0.0355499 0.999368i \(-0.488682\pi\)
0.0355499 + 0.999368i \(0.488682\pi\)
\(762\) 0 0
\(763\) −28.1829 + 28.1829i −0.0369370 + 0.0369370i
\(764\) 0 0
\(765\) −577.358 + 720.386i −0.754716 + 0.941681i
\(766\) 0 0
\(767\) 256.316i 0.334181i
\(768\) 0 0
\(769\) 143.904 0.187132 0.0935659 0.995613i \(-0.470173\pi\)
0.0935659 + 0.995613i \(0.470173\pi\)
\(770\) 0 0
\(771\) −338.843 + 18.6161i −0.439485 + 0.0241454i
\(772\) 0 0
\(773\) −339.143 339.143i −0.438736 0.438736i 0.452850 0.891586i \(-0.350407\pi\)
−0.891586 + 0.452850i \(0.850407\pi\)
\(774\) 0 0
\(775\) 41.6598i 0.0537546i
\(776\) 0 0
\(777\) 347.809 388.248i 0.447630 0.499676i
\(778\) 0 0
\(779\) 40.1187 + 40.1187i 0.0515003 + 0.0515003i
\(780\) 0 0
\(781\) 115.221 + 115.221i 0.147531 + 0.147531i
\(782\) 0 0
\(783\) 202.372 + 144.703i 0.258458 + 0.184805i
\(784\) 0 0
\(785\) 360.037i 0.458646i
\(786\) 0 0
\(787\) −924.878 924.878i −1.17519 1.17519i −0.980954 0.194241i \(-0.937776\pi\)
−0.194241 0.980954i \(-0.562224\pi\)
\(788\) 0 0
\(789\) 21.2832 + 387.389i 0.0269749 + 0.490987i
\(790\) 0 0
\(791\) 2181.15 2.75746
\(792\) 0 0
\(793\) 91.7980i 0.115760i
\(794\) 0 0
\(795\) −465.846 + 25.5937i −0.585970 + 0.0321933i