Properties

Label 384.3.i.d.161.10
Level $384$
Weight $3$
Character 384.161
Analytic conductor $10.463$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 161.10
Root \(-1.96139 + 0.391068i\) of defining polynomial
Character \(\chi\) \(=\) 384.161
Dual form 384.3.i.d.353.10

$q$-expansion

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

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
\(3\) 2.99548 + 0.164573i 0.998494 + 0.0548575i
\(4\) 0 0
\(5\) −3.61305 3.61305i −0.722609 0.722609i 0.246527 0.969136i \(-0.420711\pi\)
−0.969136 + 0.246527i \(0.920711\pi\)
\(6\) 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 0.782942 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 \(0.201051\pi\)
−0.807072 + 0.590453i \(0.798949\pi\)
\(18\) 0 0
\(19\) 8.77090 + 8.77090i 0.461626 + 0.461626i 0.899188 0.437562i \(-0.144158\pi\)
−0.437562 + 0.899188i \(0.644158\pi\)
\(20\) 0 0
\(21\) −2.02081 + 36.7820i −0.0962292 + 1.75153i
\(22\) 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
\(27\) 26.6348 + 4.42563i 0.986475 + 0.163912i
\(28\) 0 0
\(29\) −6.51544 + 6.51544i −0.224670 + 0.224670i −0.810462 0.585792i \(-0.800784\pi\)
0.585792 + 0.810462i \(0.300784\pi\)
\(30\) 0 0
\(31\) 37.5922 1.21265 0.606326 0.795216i \(-0.292643\pi\)
0.606326 + 0.795216i \(0.292643\pi\)
\(32\) 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 \(-0.482235\pi\)
0.0557814 + 0.998443i \(0.482235\pi\)
\(42\) 0 0
\(43\) −21.2835 + 21.2835i −0.494966 + 0.494966i −0.909867 0.414901i \(-0.863816\pi\)
0.414901 + 0.909867i \(0.363816\pi\)
\(44\) 0 0
\(45\) −28.7594 35.8840i −0.639098 0.797422i
\(46\) 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
\(51\) −3.30386 + 60.1356i −0.0647816 + 1.17913i
\(52\) 0 0
\(53\) 21.5215 + 21.5215i 0.406065 + 0.406065i 0.880364 0.474299i \(-0.157298\pi\)
−0.474299 + 0.880364i \(0.657298\pi\)
\(54\) 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 0.431205 0.902254i \(-0.358089\pi\)
−0.902254 + 0.431205i \(0.858089\pi\)
\(68\) 0 0
\(69\) 39.4867 + 2.16941i 0.572271 + 0.0314407i
\(70\) 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
\(75\) −0.182380 + 3.31960i −0.00243173 + 0.0442614i
\(76\) 0 0
\(77\) −21.7257 + 21.7257i −0.282152 + 0.282152i
\(78\) 0 0
\(79\) 20.9299 0.264935 0.132468 0.991187i \(-0.457710\pi\)
0.132468 + 0.991187i \(0.457710\pi\)
\(80\) 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 \(-0.884446\pi\)
−0.934828 + 0.355102i \(0.884446\pi\)
\(90\) 0 0
\(91\) −29.3259 + 29.3259i −0.322262 + 0.322262i
\(92\) 0 0
\(93\) 112.607 + 6.18664i 1.21083 + 0.0665231i
\(94\) 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
\(99\) 14.0835 + 17.5725i 0.142258 + 0.177500i
\(100\) 0 0
\(101\) −125.879 125.879i −1.24632 1.24632i −0.957331 0.288994i \(-0.906679\pi\)
−0.288994 0.957331i \(-0.593321\pi\)
\(102\) 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 0.980605 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 \(-0.712162\pi\)
0.618260 0.785974i \(-0.287838\pi\)
\(114\) 0 0
\(115\) −47.6275 47.6275i −0.414152 0.414152i
\(116\) 0 0
\(117\) 19.0103 + 23.7197i 0.162481 + 0.202733i
\(118\) 0 0
\(119\) −246.509 −2.07151
\(120\) 0 0
\(121\) 114.739i 0.948257i
\(122\) 0 0
\(123\) 13.7016 + 0.752766i 0.111395 + 0.00612005i
\(124\) 0 0
\(125\) −86.3222 + 86.3222i −0.690577 + 0.690577i
\(126\) 0 0
\(127\) −152.167 −1.19816 −0.599082 0.800687i \(-0.704468\pi\)
−0.599082 + 0.800687i \(0.704468\pi\)
\(128\) 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 \(-0.562140\pi\)
−0.193982 + 0.981005i \(0.562140\pi\)
\(138\) 0 0
\(139\) 161.324 161.324i 1.16060 1.16060i 0.176261 0.984343i \(-0.443600\pi\)
0.984343 0.176261i \(-0.0564004\pi\)
\(140\) 0 0
\(141\) 9.02460 164.262i 0.0640043 1.16498i
\(142\) 0 0
\(143\) 8.45118i 0.0590992i
\(144\) 0 0
\(145\) 47.0811 0.324698
\(146\) 0 0
\(147\) −304.874 16.7498i −2.07397 0.113945i
\(148\) 0 0
\(149\) −116.911 116.911i −0.784638 0.784638i 0.195971 0.980610i \(-0.437214\pi\)
−0.980610 + 0.195971i \(0.937214\pi\)
\(150\) 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 0.530396 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 0.880869 0.473360i \(-0.156959\pi\)
−0.473360 + 0.880869i \(0.656959\pi\)
\(164\) 0 0
\(165\) 2.10410 38.2980i 0.0127521 0.232109i
\(166\) 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
\(171\) 69.8153 + 87.1106i 0.408277 + 0.509419i
\(172\) 0 0
\(173\) 123.809 123.809i 0.715661 0.715661i −0.252052 0.967714i \(-0.581106\pi\)
0.967714 + 0.252052i \(0.0811056\pi\)
\(174\) 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
\(189\) −54.3430 + 327.053i −0.287529 + 1.73044i
\(190\) 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
\(195\) 2.84016 51.6955i 0.0145649 0.265105i
\(196\) 0 0
\(197\) 66.9411 + 66.9411i 0.339803 + 0.339803i 0.856293 0.516490i \(-0.172762\pi\)
−0.516490 + 0.856293i \(0.672762\pi\)
\(198\) 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 \(-0.0420837\pi\)
−0.131825 + 0.991273i \(0.542084\pi\)
\(212\) 0 0
\(213\) 195.072 + 10.7173i 0.915830 + 0.0503159i
\(214\) 0 0
\(215\) 153.797 0.715333
\(216\) 0 0
\(217\) 461.601i 2.12719i
\(218\) 0 0
\(219\) −8.26897 + 150.508i −0.0377579 + 0.687253i
\(220\) 0 0
\(221\) −47.9454 + 47.9454i −0.216947 + 0.216947i
\(222\) 0 0
\(223\) −17.7339 −0.0795241 −0.0397621 0.999209i \(-0.512660\pi\)
−0.0397621 + 0.999209i \(0.512660\pi\)
\(224\) 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 \(-0.414561\pi\)
0.265203 + 0.964193i \(0.414561\pi\)
\(234\) 0 0
\(235\) −198.127 + 198.127i −0.843095 + 0.843095i
\(236\) 0 0
\(237\) 62.6951 + 3.44448i 0.264536 + 0.0145337i
\(238\) 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
\(243\) 233.907 + 65.8515i 0.962581 + 0.270994i
\(244\) 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 \(0.0706298\pi\)
−0.975483 + 0.220074i \(0.929370\pi\)
\(258\) 0 0
\(259\) −122.861 122.861i −0.474367 0.474367i
\(260\) 0 0
\(261\) −64.7099 + 51.8621i −0.247931 + 0.198705i
\(262\) 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
\(267\) −498.446 27.3848i −1.86684 0.102565i
\(268\) 0 0
\(269\) 129.457 129.457i 0.481253 0.481253i −0.424278 0.905532i \(-0.639472\pi\)
0.905532 + 0.424278i \(0.139472\pi\)
\(270\) 0 0
\(271\) 170.727 0.629990 0.314995 0.949093i \(-0.397997\pi\)
0.314995 + 0.949093i \(0.397997\pi\)
\(272\) 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 \(-0.578074\pi\)
−0.242825 + 0.970070i \(0.578074\pi\)
\(282\) 0 0
\(283\) 132.657 132.657i 0.468752 0.468752i −0.432758 0.901510i \(-0.642460\pi\)
0.901510 + 0.432758i \(0.142460\pi\)
\(284\) 0 0
\(285\) 10.4305 189.852i 0.0365982 0.666146i
\(286\) 0 0
\(287\) 56.1658i 0.195700i
\(288\) 0 0
\(289\) −114.022 −0.394541
\(290\) 0 0
\(291\) 417.010 + 22.9106i 1.43303 + 0.0787307i
\(292\) 0 0
\(293\) −143.968 143.968i −0.491360 0.491360i 0.417375 0.908735i \(-0.362950\pi\)
−0.908735 + 0.417375i \(0.862950\pi\)
\(294\) 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 \(-0.184039\pi\)
−0.546497 + 0.837461i \(0.684039\pi\)
\(308\) 0 0
\(309\) 4.34368 79.0619i 0.0140572 0.255864i
\(310\) 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
\(315\) 440.625 353.142i 1.39881 1.12108i
\(316\) 0 0
\(317\) −321.109 + 321.109i −1.01296 + 1.01296i −0.0130482 + 0.999915i \(0.504153\pi\)
−0.999915 + 0.0130482i \(0.995847\pi\)
\(318\) 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 \(-0.516085\pi\)
0.998724 + 0.0505107i \(0.0160849\pi\)
\(332\) 0 0
\(333\) −99.3740 + 79.6439i −0.298420 + 0.239171i
\(334\) 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
\(339\) 29.2330 532.088i 0.0862331 1.56958i
\(340\) 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 \(0.221304\pi\)
−0.767895 + 0.640575i \(0.778696\pi\)
\(354\) 0 0
\(355\) −235.289 235.289i −0.662785 0.662785i
\(356\) 0 0
\(357\) −738.415 40.5687i −2.06839 0.113638i
\(358\) 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
\(363\) 18.8829 343.699i 0.0520190 0.946829i
\(364\) 0 0
\(365\) 181.538 181.538i 0.497364 0.497364i
\(366\) 0 0
\(367\) −11.3588 −0.0309505 −0.0154753 0.999880i \(-0.504926\pi\)
−0.0154753 + 0.999880i \(0.504926\pi\)
\(368\) 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 \(0.551836\pi\)
−0.986770 + 0.162129i \(0.948164\pi\)
\(380\) 0 0
\(381\) −455.813 25.0425i −1.19636 0.0657283i
\(382\) 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
\(387\) −211.383 + 169.414i −0.546210 + 0.437763i
\(388\) 0 0
\(389\) 260.985 + 260.985i 0.670913 + 0.670913i 0.957927 0.287013i \(-0.0926623\pi\)
−0.287013 + 0.957927i \(0.592662\pi\)
\(390\) 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 \(-0.819840\pi\)
0.844059 0.536250i \(-0.180160\pi\)
\(402\) 0 0
\(403\) 89.7801 + 89.7801i 0.222779 + 0.222779i
\(404\) 0 0
\(405\) −221.897 349.367i −0.547894 0.862635i
\(406\) 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
\(411\) −159.213 8.74718i −0.387379 0.0212827i
\(412\) 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
\(429\) −1.39083 + 25.3154i −0.00324203 + 0.0590102i
\(430\) 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
\(435\) 141.031 + 7.74826i 0.324209 + 0.0178121i
\(436\) 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 0.239378 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 \(-0.720001\pi\)
0.637427 0.770510i \(-0.279999\pi\)
\(450\) 0 0
\(451\) 8.09298 + 8.09298i 0.0179445 + 0.0179445i
\(452\) 0 0
\(453\) 1.80574 32.8674i 0.00398618 0.0725549i
\(454\) 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
\(459\) −88.8463 + 534.705i −0.193565 + 1.16494i
\(460\) 0 0
\(461\) −312.070 + 312.070i −0.676942 + 0.676942i −0.959307 0.282365i \(-0.908881\pi\)
0.282365 + 0.959307i \(0.408881\pi\)
\(462\) 0 0
\(463\) 718.961 1.55283 0.776416 0.630220i \(-0.217035\pi\)
0.776416 + 0.630220i \(0.217035\pi\)
\(464\) 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
\(477\) 171.308 + 213.746i 0.359137 + 0.448106i
\(478\) 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
\(483\) −26.6385 + 484.864i −0.0551523 + 1.00386i
\(484\) 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 0.700200 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 \(-0.960925\pi\)
−0.122448 0.992475i \(-0.539075\pi\)
\(500\) 0 0
\(501\) 547.728 + 30.0923i 1.09327 + 0.0600645i
\(502\) 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
\(507\) 25.9354 472.065i 0.0511546 0.931095i
\(508\) 0 0
\(509\) −118.591 + 118.591i −0.232988 + 0.232988i −0.813939 0.580951i \(-0.802681\pi\)
0.580951 + 0.813939i \(0.302681\pi\)
\(510\) 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 \(-0.467846\pi\)
0.100842 + 0.994902i \(0.467846\pi\)
\(522\) 0 0
\(523\) 479.455 479.455i 0.916740 0.916740i −0.0800507 0.996791i \(-0.525508\pi\)
0.996791 + 0.0800507i \(0.0255082\pi\)
\(524\) 0 0
\(525\) −40.7619 2.23947i −0.0776418 0.00426566i
\(526\) 0 0
\(527\) 754.679i 1.43203i
\(528\) 0 0
\(529\) −355.232 −0.671517
\(530\) 0 0
\(531\) −427.141 532.956i −0.804408 1.00368i
\(532\) 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 0.358546 0.933512i \(-0.383273\pi\)
−0.933512 + 0.358546i \(0.883273\pi\)
\(548\) 0 0
\(549\) 152.978 + 190.875i 0.278648 + 0.347677i
\(550\) 0 0
\(551\) −114.292 −0.207427
\(552\) 0 0
\(553\) 257.002i 0.464741i
\(554\) 0 0
\(555\) 216.579 + 11.8989i 0.390232 + 0.0214394i
\(556\) 0 0
\(557\) 134.274 134.274i 0.241066 0.241066i −0.576225 0.817291i \(-0.695475\pi\)
0.817291 + 0.576225i \(0.195475\pi\)
\(558\) 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 \(-0.521963\pi\)
−0.0689430 + 0.997621i \(0.521963\pi\)
\(570\) 0 0
\(571\) −363.164 + 363.164i −0.636013 + 0.636013i −0.949570 0.313556i \(-0.898480\pi\)
0.313556 + 0.949570i \(0.398480\pi\)
\(572\) 0 0
\(573\) 10.0188 182.358i 0.0174848 0.318251i
\(574\) 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
\(579\) 532.809 + 29.2727i 0.920223 + 0.0505573i
\(580\) 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 \(-0.873591\pi\)
0.922177 0.386769i \(-0.126409\pi\)
\(594\) 0 0
\(595\) 890.650 + 890.650i 1.49689 + 1.49689i
\(596\) 0 0
\(597\) 0.135991 2.47525i 0.000227790 0.00414615i
\(598\) 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
\(603\) −251.216 313.450i −0.416610 0.519817i
\(604\) 0 0
\(605\) −414.557 + 414.557i −0.685219 + 0.685219i
\(606\) 0 0
\(607\) −631.699 −1.04069 −0.520345 0.853956i \(-0.674197\pi\)
−0.520345 + 0.853956i \(0.674197\pi\)
\(608\) 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 \(-0.781022\pi\)
−0.772555 + 0.634947i \(0.781022\pi\)
\(618\) 0 0
\(619\) 574.046 574.046i 0.927377 0.927377i −0.0701591 0.997536i \(-0.522351\pi\)
0.997536 + 0.0701591i \(0.0223507\pi\)
\(620\) 0 0
\(621\) 351.103 + 58.3390i 0.565383 + 0.0939437i
\(622\) 0 0
\(623\) 2043.24i 3.27969i
\(624\) 0 0
\(625\) 651.477 1.04236
\(626\) 0 0
\(627\) −5.10783 + 92.9707i −0.00814646 + 0.148279i
\(628\) 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 \(-0.165542\pi\)
−0.496937 + 0.867787i \(0.665542\pi\)
\(644\) 0 0
\(645\) 460.695 + 25.3107i 0.714256 + 0.0392414i
\(646\) 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
\(651\) −75.9668 + 1382.72i −0.116693 + 2.12399i
\(652\) 0 0
\(653\) 636.071 636.071i 0.974075 0.974075i −0.0255977 0.999672i \(-0.508149\pi\)
0.999672 + 0.0255977i \(0.00814890\pi\)
\(654\) 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
\(669\) −53.1215 2.91851i −0.0794044 0.00436250i
\(670\) 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
\(675\) −4.90449 + 29.5168i −0.00726592 + 0.0437286i
\(676\) 0 0
\(677\) 585.326 + 585.326i 0.864587 + 0.864587i 0.991867 0.127280i \(-0.0406246\pi\)
−0.127280 + 0.991867i \(0.540625\pi\)
\(678\) 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 0.906984 0.421165i \(-0.138379\pi\)
−0.421165 + 0.906984i \(0.638379\pi\)
\(692\) 0 0
\(693\) −215.775 + 172.934i −0.311364 + 0.249544i
\(694\) 0 0
\(695\) −1165.74 −1.67733
\(696\) 0 0
\(697\) 91.8264i 0.131745i
\(698\) 0 0
\(699\) 370.196 + 20.3386i 0.529608 + 0.0290968i
\(700\) 0 0
\(701\) −490.458 + 490.458i −0.699655 + 0.699655i −0.964336 0.264681i \(-0.914733\pi\)
0.264681 + 0.964336i \(0.414733\pi\)
\(702\) 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
\(717\) −19.5020 + 354.968i −0.0271994 + 0.495073i
\(718\) 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
\(723\) −791.292 43.4738i −1.09446 0.0601297i
\(724\) 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 0.655118 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 0.596447 0.802653i \(-0.296579\pi\)
−0.802653 + 0.596447i \(0.796579\pi\)
\(740\) 0 0
\(741\) −6.89467 + 125.494i −0.00930455 + 0.169358i
\(742\) 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
\(747\) −63.1454 + 50.6082i −0.0845319 + 0.0677486i
\(748\) 0 0
\(749\) −1030.88 + 1030.88i −1.37634 + 1.37634i
\(750\) 0 0
\(751\) −1014.28 −1.35058 −0.675289 0.737553i \(-0.735981\pi\)
−0.675289 + 0.737553i \(0.735981\pi\)
\(752\) 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 \(-0.511318\pi\)
−0.0355499 + 0.999368i \(0.511318\pi\)
\(762\) 0 0
\(763\) 28.1829 28.1829i 0.0369370 0.0369370i
\(764\) 0 0
\(765\) 720.386 577.358i 0.941681 0.754716i
\(766\) 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
\(771\) −18.6161 + 338.843i −0.0241454 + 0.439485i
\(772\) 0 0
\(773\) 339.143 + 339.143i 0.438736 + 0.438736i 0.891586 0.452850i \(-0.149593\pi\)
−0.452850 + 0.891586i \(0.649593\pi\)
\(774\) 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 \(0.0622243\pi\)
0.194241 + 0.980954i \(0.437776\pi\)
\(788\) 0 0
\(789\) −387.389 21.2832i −0.490987 0.0269749i
\(790\) 0 0
\(791\) 2181.15 2.75746
\(792\) 0 0
\(793\) 91.7980i 0.115760i
\(794\) 0 0
\(795\) 25.5937 465.846i 0.0321933 0.585970i
\(796\) 0