Properties

Label 384.3.i.c.353.6
Level $384$
Weight $3$
Character 384.353
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 353.6
Root \(1.96139 + 0.391068i\) of defining polynomial
Character \(\chi\) \(=\) 384.353
Dual form 384.3.i.c.161.6

$q$-expansion

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

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
\(3\) −0.164573 + 2.99548i −0.0548575 + 0.998494i
\(4\) 0 0
\(5\) 3.61305 3.61305i 0.722609 0.722609i −0.246527 0.969136i \(-0.579289\pi\)
0.969136 + 0.246527i \(0.0792893\pi\)
\(6\) 0 0
\(7\) 12.2792i 1.75417i 0.480338 + 0.877083i \(0.340514\pi\)
−0.480338 + 0.877083i \(0.659486\pi\)
\(8\) 0 0
\(9\) −8.94583 0.985948i −0.993981 0.109550i
\(10\) 0 0
\(11\) 1.76932 1.76932i 0.160847 0.160847i −0.622095 0.782942i \(-0.713718\pi\)
0.782942 + 0.622095i \(0.213718\pi\)
\(12\) 0 0
\(13\) 2.38826 2.38826i 0.183713 0.183713i −0.609259 0.792971i \(-0.708533\pi\)
0.792971 + 0.609259i \(0.208533\pi\)
\(14\) 0 0
\(15\) 10.2282 + 11.4174i 0.681881 + 0.761162i
\(16\) 0 0
\(17\) 20.0754i 1.18091i 0.807072 + 0.590453i \(0.201051\pi\)
−0.807072 + 0.590453i \(0.798949\pi\)
\(18\) 0 0
\(19\) −8.77090 + 8.77090i −0.461626 + 0.461626i −0.899188 0.437562i \(-0.855842\pi\)
0.437562 + 0.899188i \(0.355842\pi\)
\(20\) 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 0.810462 0.585792i \(-0.199216\pi\)
−0.585792 + 0.810462i \(0.699216\pi\)
\(30\) 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 0.558847 0.829271i \(-0.311244\pi\)
−0.829271 + 0.558847i \(0.811244\pi\)
\(38\) 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 0.909867 0.414901i \(-0.136184\pi\)
−0.414901 + 0.909867i \(0.636184\pi\)
\(44\) 0 0
\(45\) −35.8840 + 28.7594i −0.797422 + 0.639098i
\(46\) 0 0
\(47\) 54.8366i 1.16674i 0.812208 + 0.583368i \(0.198266\pi\)
−0.812208 + 0.583368i \(0.801734\pi\)
\(48\) 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 −0.880364 0.474299i \(-0.842702\pi\)
0.474299 + 0.880364i \(0.342702\pi\)
\(54\) 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 −0.996233 0.0867132i \(-0.972364\pi\)
0.0867132 + 0.996233i \(0.472364\pi\)
\(60\) 0 0
\(61\) 19.2186 19.2186i 0.315059 0.315059i −0.531807 0.846866i \(-0.678487\pi\)
0.846866 + 0.531807i \(0.178487\pi\)
\(62\) 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 −0.431205 0.902254i \(-0.641911\pi\)
0.902254 + 0.431205i \(0.141911\pi\)
\(68\) 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 \(-0.888169\pi\)
0.938917 0.344145i \(-0.111831\pi\)
\(74\) 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 0.667768 0.744369i \(-0.267250\pi\)
−0.744369 + 0.667768i \(0.767250\pi\)
\(84\) 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 0.288994 0.957331i \(-0.406679\pi\)
0.957331 0.288994i \(-0.0933207\pi\)
\(102\) 0 0
\(103\) 26.3937i 0.256250i −0.991758 0.128125i \(-0.959104\pi\)
0.991758 0.128125i \(-0.0408958\pi\)
\(104\) 0 0
\(105\) −140.196 + 125.594i −1.33520 + 1.19613i
\(106\) 0 0
\(107\) 83.9534 83.9534i 0.784611 0.784611i −0.195994 0.980605i \(-0.562793\pi\)
0.980605 + 0.195994i \(0.0627933\pi\)
\(108\) 0 0
\(109\) −2.29518 + 2.29518i −0.0210567 + 0.0210567i −0.717557 0.696500i \(-0.754740\pi\)
0.696500 + 0.717557i \(0.254740\pi\)
\(110\) 0 0
\(111\) 31.6184 28.3251i 0.284851 0.255181i
\(112\) 0 0
\(113\) 177.630i 1.57195i −0.618260 0.785974i \(-0.712162\pi\)
0.618260 0.785974i \(-0.287838\pi\)
\(114\) 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 0.410409 0.911901i \(-0.365386\pi\)
−0.911901 + 0.410409i \(0.865386\pi\)
\(132\) 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 −0.984343 0.176261i \(-0.943600\pi\)
−0.176261 0.984343i \(-0.556400\pi\)
\(140\) 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 −0.195971 0.980610i \(-0.562786\pi\)
0.980610 + 0.195971i \(0.0627859\pi\)
\(150\) 0 0
\(151\) 10.9723i 0.0726643i −0.999340 0.0363321i \(-0.988433\pi\)
0.999340 0.0363321i \(-0.0115674\pi\)
\(152\) 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 −0.847750 0.530396i \(-0.822043\pi\)
0.530396 + 0.847750i \(0.322043\pi\)
\(158\) 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 −0.880869 0.473360i \(-0.843041\pi\)
0.473360 + 0.880869i \(0.343041\pi\)
\(164\) 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 0.252052 0.967714i \(-0.418894\pi\)
−0.967714 + 0.252052i \(0.918894\pi\)
\(174\) 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 0.998415 0.0562807i \(-0.0179242\pi\)
−0.0562807 + 0.998415i \(0.517924\pi\)
\(180\) 0 0
\(181\) 162.162 + 162.162i 0.895920 + 0.895920i 0.995072 0.0991520i \(-0.0316130\pi\)
−0.0991520 + 0.995072i \(0.531613\pi\)
\(182\) 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 \(0.0509449\pi\)
−0.987220 + 0.159366i \(0.949055\pi\)
\(192\) 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 −0.856293 0.516490i \(-0.827238\pi\)
0.516490 + 0.856293i \(0.327238\pi\)
\(198\) 0 0
\(199\) 0.826328i 0.00415240i −0.999998 0.00207620i \(-0.999339\pi\)
0.999998 0.00207620i \(-0.000660875\pi\)
\(200\) 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 −0.991273 0.131825i \(-0.957916\pi\)
0.131825 + 0.991273i \(0.457916\pi\)
\(212\) 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 0.723515 0.690309i \(-0.242525\pi\)
−0.690309 + 0.723515i \(0.742525\pi\)
\(228\) 0 0
\(229\) −223.748 223.748i −0.977063 0.977063i 0.0226794 0.999743i \(-0.492780\pi\)
−0.999743 + 0.0226794i \(0.992780\pi\)
\(230\) 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 \(-0.920256\pi\)
0.968783 0.247910i \(-0.0797437\pi\)
\(240\) 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 −0.334808 0.942286i \(-0.608672\pi\)
0.942286 + 0.334808i \(0.108672\pi\)
\(252\) 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 \(0.0706298\pi\)
−0.975483 + 0.220074i \(0.929370\pi\)
\(258\) 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 0.424278 0.905532i \(-0.360528\pi\)
−0.905532 + 0.424278i \(0.860528\pi\)
\(270\) 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 0.470606 0.882343i \(-0.344035\pi\)
−0.882343 + 0.470606i \(0.844035\pi\)
\(278\) 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 0.432758 0.901510i \(-0.357540\pi\)
−0.901510 + 0.432758i \(0.857540\pi\)
\(284\) 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 −0.417375 0.908735i \(-0.637050\pi\)
0.908735 + 0.417375i \(0.137050\pi\)
\(294\) 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 −0.837461 0.546497i \(-0.815961\pi\)
0.546497 + 0.837461i \(0.315961\pi\)
\(308\) 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 \(-0.946936\pi\)
0.986137 0.165934i \(-0.0530638\pi\)
\(314\) 0 0
\(315\) −353.142 440.625i −1.12108 1.39881i
\(316\) 0 0
\(317\) 321.109 + 321.109i 1.01296 + 1.01296i 0.999915 + 0.0130482i \(0.00415349\pi\)
0.0130482 + 0.999915i \(0.495847\pi\)
\(318\) 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 0.0505107 0.998724i \(-0.483915\pi\)
−0.998724 + 0.0505107i \(0.983915\pi\)
\(332\) 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 0.329445 0.944175i \(-0.393138\pi\)
0.944175 0.329445i \(-0.106862\pi\)
\(348\) 0 0
\(349\) 476.643 476.643i 1.36574 1.36574i 0.499321 0.866417i \(-0.333583\pi\)
0.866417 0.499321i \(-0.166417\pi\)
\(350\) 0 0
\(351\) −53.0414 74.1805i −0.151115 0.211341i
\(352\) 0 0
\(353\) 452.246i 1.28115i 0.767895 + 0.640575i \(0.221304\pi\)
−0.767895 + 0.640575i \(0.778696\pi\)
\(354\) 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 0.782245 0.622971i \(-0.214075\pi\)
−0.622971 + 0.782245i \(0.714075\pi\)
\(374\) 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 0.986770 + 0.162129i \(0.0518359\pi\)
0.162129 + 0.986770i \(0.448164\pi\)
\(380\) 0 0
\(381\) −25.0425 + 455.813i −0.0657283 + 1.19636i
\(382\) 0 0
\(383\) 272.117i 0.710488i 0.934774 + 0.355244i \(0.115602\pi\)
−0.934774 + 0.355244i \(0.884398\pi\)
\(384\) 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 −0.957927 0.287013i \(-0.907338\pi\)
0.287013 + 0.957927i \(0.407338\pi\)
\(390\) 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 −0.953113 0.302614i \(-0.902141\pi\)
0.302614 + 0.953113i \(0.402141\pi\)
\(398\) 0 0
\(399\) 340.336 304.887i 0.852972 0.764128i
\(400\) 0 0
\(401\) 430.073i 1.07250i −0.844059 0.536250i \(-0.819840\pi\)
0.844059 0.536250i \(-0.180160\pi\)
\(402\) 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 \(0.0816372\pi\)
−0.967291 + 0.253668i \(0.918363\pi\)
\(410\) 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 0.565370 0.824837i \(-0.308733\pi\)
−0.824837 + 0.565370i \(0.808733\pi\)
\(420\) 0 0
\(421\) 484.985 + 484.985i 1.15198 + 1.15198i 0.986155 + 0.165829i \(0.0530300\pi\)
0.165829 + 0.986155i \(0.446970\pi\)
\(422\) 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 \(-0.920305\pi\)
0.968821 0.247761i \(-0.0796947\pi\)
\(432\) 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 \(0.150718\pi\)
−0.889980 + 0.455999i \(0.849282\pi\)
\(440\) 0 0
\(441\) 910.488 + 100.348i 2.06460 + 0.227546i
\(442\) 0 0
\(443\) −324.076 + 324.076i −0.731549 + 0.731549i −0.970926 0.239378i \(-0.923057\pi\)
0.239378 + 0.970926i \(0.423057\pi\)
\(444\) 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 \(-0.720001\pi\)
0.637427 0.770510i \(-0.279999\pi\)
\(450\) 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 \(0.138567\pi\)
−0.906734 + 0.421702i \(0.861433\pi\)
\(458\) 0 0
\(459\) 534.705 + 88.8463i 1.16494 + 0.193565i
\(460\) 0 0
\(461\) 312.070 + 312.070i 0.676942 + 0.676942i 0.959307 0.282365i \(-0.0911190\pi\)
−0.282365 + 0.959307i \(0.591119\pi\)
\(462\) 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 0.612889 0.790169i \(-0.290007\pi\)
−0.790169 + 0.612889i \(0.790007\pi\)
\(468\) 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 \(-0.714230\pi\)
0.623353 0.781941i \(-0.285770\pi\)
\(480\) 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 \(-0.815601\pi\)
0.836843 0.547443i \(-0.184399\pi\)
\(488\) 0 0
\(489\) −188.040 209.904i −0.384541 0.429251i
\(490\) 0 0
\(491\) −6.75013 + 6.75013i −0.0137477 + 0.0137477i −0.713947 0.700200i \(-0.753094\pi\)
0.700200 + 0.713947i \(0.253094\pi\)
\(492\) 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 0.122448 0.992475i \(-0.460925\pi\)
0.992475 0.122448i \(-0.0390746\pi\)
\(500\) 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 0.813939 0.580951i \(-0.197319\pi\)
−0.580951 + 0.813939i \(0.697319\pi\)
\(510\) 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 0.0800507 0.996791i \(-0.474492\pi\)
−0.996791 + 0.0800507i \(0.974492\pi\)
\(524\) 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 −0.448704 + 0.893680i \(0.648114\pi\)
−0.893680 + 0.448704i \(0.851886\pi\)
\(542\) 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 −0.358546 0.933512i \(-0.616727\pi\)
0.933512 + 0.358546i \(0.116727\pi\)
\(548\) 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 0.576225 0.817291i \(-0.304525\pi\)
−0.817291 + 0.576225i \(0.804525\pi\)
\(558\) 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 0.792493 0.609881i \(-0.208783\pi\)
−0.609881 + 0.792493i \(0.708783\pi\)
\(564\) 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 0.949570 0.313556i \(-0.101520\pi\)
−0.313556 + 0.949570i \(0.601520\pi\)
\(572\) 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 −0.641845 0.766835i \(-0.721831\pi\)
0.766835 + 0.641845i \(0.221831\pi\)
\(588\) 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 \(-0.873591\pi\)
0.922177 0.386769i \(-0.126409\pi\)
\(594\) 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 \(0.230169\pi\)
−0.749759 + 0.661711i \(0.769831\pi\)
\(602\) 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 0.319198 0.947688i \(-0.396586\pi\)
−0.947688 + 0.319198i \(0.896586\pi\)
\(614\) 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 0.0701591 0.997536i \(-0.477649\pi\)
−0.997536 + 0.0701591i \(0.977649\pi\)
\(620\) 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 \(0.0348893\pi\)
−0.993999 + 0.109389i \(0.965111\pi\)
\(632\) 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 \(0.209731\pi\)
−0.790673 + 0.612238i \(0.790269\pi\)
\(642\) 0 0
\(643\) −238.456 + 238.456i −0.370850 + 0.370850i −0.867787 0.496937i \(-0.834458\pi\)
0.496937 + 0.867787i \(0.334458\pi\)
\(644\) 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 0.0255977 0.999672i \(-0.491851\pi\)
−0.999672 + 0.0255977i \(0.991851\pi\)
\(654\) 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 0.634179 0.773186i \(-0.281338\pi\)
−0.773186 + 0.634179i \(0.781338\pi\)
\(660\) 0 0
\(661\) −721.715 721.715i −1.09185 1.09185i −0.995331 0.0965216i \(-0.969228\pi\)
−0.0965216 0.995331i \(-0.530772\pi\)
\(662\) 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 −0.991867 0.127280i \(-0.959375\pi\)
0.127280 + 0.991867i \(0.459375\pi\)
\(678\) 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 −0.779301 0.626650i \(-0.784426\pi\)
0.626650 + 0.779301i \(0.284426\pi\)
\(684\) 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 −0.906984 0.421165i \(-0.861621\pi\)
0.421165 + 0.906984i \(0.361621\pi\)
\(692\) 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 0.964336 0.264681i \(-0.0852666\pi\)
−0.264681 + 0.964336i \(0.585267\pi\)
\(702\) 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 0.329473 0.944165i \(-0.393129\pi\)
−0.944165 + 0.329473i \(0.893129\pi\)
\(710\) 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 \(0.271474\pi\)
−0.657831 + 0.753166i \(0.728526\pi\)
\(720\) 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 \(-0.885173\pi\)
0.935636 0.352968i \(-0.114827\pi\)
\(728\) 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 −0.755527 0.655118i \(-0.772619\pi\)
0.655118 + 0.755527i \(0.272619\pi\)
\(734\) 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 −0.596447 0.802653i \(-0.703421\pi\)
0.802653 + 0.596447i \(0.203421\pi\)
\(740\) 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 0.908880 + 0.417057i \(0.136938\pi\)
0.417057 + 0.908880i \(0.363062\pi\)
\(758\) 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 −0.891586 0.452850i \(-0.850407\pi\)
0.452850 + 0.891586i \(0.350407\pi\)
\(774\) 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 −0.194241 + 0.980954i \(0.562224\pi\)
−0.980954 + 0.194241i \(0.937776\pi\)
\(788\) 0 0
\(789\) 21.2832 387.389i 0.0269749 0.490987i
\(790\) 0 0
\(791\) 2181.15 2.75746
\(792\) 0 0
\(793\)