Properties

Label 320.2.s.b.303.7
Level $320$
Weight $2$
Character 320.303
Analytic conductor $2.555$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 320 = 2^{6} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 320.s (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.55521286468\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Defining polynomial: \(x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + 74 x^{8} + 24 x^{7} - 80 x^{6} - 224 x^{5} - 160 x^{4} - 256 x^{3} + 256 x^{2} + 512\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{13} \)
Twist minimal: no (minimal twist has level 80)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 303.7
Root \(0.482716 - 1.32928i\) of defining polynomial
Character \(\chi\) \(=\) 320.303
Dual form 320.2.s.b.207.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +O(q^{10})\) \(q+1.39319 q^{3} +(2.17104 - 0.535339i) q^{5} +(2.13436 - 2.13436i) q^{7} -1.05903 q^{9} +(-2.17074 - 2.17074i) q^{11} +1.54663i q^{13} +(3.02466 - 0.745827i) q^{15} +(-3.86386 + 3.86386i) q^{17} +(-0.0136865 - 0.0136865i) q^{19} +(2.97357 - 2.97357i) q^{21} +(3.15240 + 3.15240i) q^{23} +(4.42682 - 2.32449i) q^{25} -5.65499 q^{27} +(3.33787 - 3.33787i) q^{29} +8.92639i q^{31} +(-3.02424 - 3.02424i) q^{33} +(3.49118 - 5.77640i) q^{35} -7.24737i q^{37} +2.15475i q^{39} +10.3771i q^{41} +2.02975i q^{43} +(-2.29920 + 0.566942i) q^{45} +(-3.34313 - 3.34313i) q^{47} -2.11103i q^{49} +(-5.38308 + 5.38308i) q^{51} -7.30702 q^{53} +(-5.87483 - 3.55067i) q^{55} +(-0.0190679 - 0.0190679i) q^{57} +(3.52732 - 3.52732i) q^{59} +(1.41629 + 1.41629i) q^{61} +(-2.26036 + 2.26036i) q^{63} +(0.827973 + 3.35780i) q^{65} +0.748197i q^{67} +(4.39187 + 4.39187i) q^{69} +0.269603 q^{71} +(0.811870 - 0.811870i) q^{73} +(6.16739 - 3.23844i) q^{75} -9.26628 q^{77} +2.80567 q^{79} -4.70135 q^{81} -12.8279 q^{83} +(-6.32012 + 10.4571i) q^{85} +(4.65027 - 4.65027i) q^{87} -13.3732 q^{89} +(3.30108 + 3.30108i) q^{91} +12.4361i q^{93} +(-0.0370409 - 0.0223871i) q^{95} +(6.33466 - 6.33466i) q^{97} +(2.29888 + 2.29888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + O(q^{10}) \) \( 18q + 2q^{5} - 2q^{7} + 10q^{9} + 2q^{11} + 20q^{15} - 6q^{17} + 2q^{19} - 16q^{21} + 2q^{23} - 6q^{25} + 24q^{27} + 14q^{29} - 8q^{33} - 2q^{35} - 14q^{45} - 38q^{47} - 8q^{51} + 12q^{53} + 6q^{55} - 24q^{57} - 10q^{59} + 14q^{61} + 6q^{63} - 32q^{69} - 24q^{71} - 14q^{73} - 16q^{75} - 44q^{77} + 16q^{79} + 2q^{81} - 40q^{83} + 14q^{85} - 24q^{87} + 12q^{89} - 34q^{95} + 18q^{97} - 22q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(257\) \(261\)
\(\chi(n)\) \(-1\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{3}{4}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.39319 0.804356 0.402178 0.915561i \(-0.368253\pi\)
0.402178 + 0.915561i \(0.368253\pi\)
\(4\) 0 0
\(5\) 2.17104 0.535339i 0.970918 0.239411i
\(6\) 0 0
\(7\) 2.13436 2.13436i 0.806714 0.806714i −0.177421 0.984135i \(-0.556775\pi\)
0.984135 + 0.177421i \(0.0567754\pi\)
\(8\) 0 0
\(9\) −1.05903 −0.353011
\(10\) 0 0
\(11\) −2.17074 2.17074i −0.654501 0.654501i 0.299572 0.954074i \(-0.403156\pi\)
−0.954074 + 0.299572i \(0.903156\pi\)
\(12\) 0 0
\(13\) 1.54663i 0.428958i 0.976729 + 0.214479i \(0.0688054\pi\)
−0.976729 + 0.214479i \(0.931195\pi\)
\(14\) 0 0
\(15\) 3.02466 0.745827i 0.780964 0.192572i
\(16\) 0 0
\(17\) −3.86386 + 3.86386i −0.937125 + 0.937125i −0.998137 0.0610123i \(-0.980567\pi\)
0.0610123 + 0.998137i \(0.480567\pi\)
\(18\) 0 0
\(19\) −0.0136865 0.0136865i −0.00313991 0.00313991i 0.705535 0.708675i \(-0.250707\pi\)
−0.708675 + 0.705535i \(0.750707\pi\)
\(20\) 0 0
\(21\) 2.97357 2.97357i 0.648886 0.648886i
\(22\) 0 0
\(23\) 3.15240 + 3.15240i 0.657320 + 0.657320i 0.954745 0.297425i \(-0.0961279\pi\)
−0.297425 + 0.954745i \(0.596128\pi\)
\(24\) 0 0
\(25\) 4.42682 2.32449i 0.885365 0.464897i
\(26\) 0 0
\(27\) −5.65499 −1.08830
\(28\) 0 0
\(29\) 3.33787 3.33787i 0.619826 0.619826i −0.325660 0.945487i \(-0.605587\pi\)
0.945487 + 0.325660i \(0.105587\pi\)
\(30\) 0 0
\(31\) 8.92639i 1.60323i 0.597843 + 0.801613i \(0.296025\pi\)
−0.597843 + 0.801613i \(0.703975\pi\)
\(32\) 0 0
\(33\) −3.02424 3.02424i −0.526452 0.526452i
\(34\) 0 0
\(35\) 3.49118 5.77640i 0.590117 0.976390i
\(36\) 0 0
\(37\) 7.24737i 1.19146i −0.803184 0.595730i \(-0.796863\pi\)
0.803184 0.595730i \(-0.203137\pi\)
\(38\) 0 0
\(39\) 2.15475i 0.345035i
\(40\) 0 0
\(41\) 10.3771i 1.62063i 0.585996 + 0.810314i \(0.300704\pi\)
−0.585996 + 0.810314i \(0.699296\pi\)
\(42\) 0 0
\(43\) 2.02975i 0.309534i 0.987951 + 0.154767i \(0.0494627\pi\)
−0.987951 + 0.154767i \(0.950537\pi\)
\(44\) 0 0
\(45\) −2.29920 + 0.566942i −0.342745 + 0.0845147i
\(46\) 0 0
\(47\) −3.34313 3.34313i −0.487646 0.487646i 0.419917 0.907563i \(-0.362059\pi\)
−0.907563 + 0.419917i \(0.862059\pi\)
\(48\) 0 0
\(49\) 2.11103i 0.301575i
\(50\) 0 0
\(51\) −5.38308 + 5.38308i −0.753782 + 0.753782i
\(52\) 0 0
\(53\) −7.30702 −1.00370 −0.501848 0.864956i \(-0.667346\pi\)
−0.501848 + 0.864956i \(0.667346\pi\)
\(54\) 0 0
\(55\) −5.87483 3.55067i −0.792162 0.478772i
\(56\) 0 0
\(57\) −0.0190679 0.0190679i −0.00252560 0.00252560i
\(58\) 0 0
\(59\) 3.52732 3.52732i 0.459218 0.459218i −0.439181 0.898399i \(-0.644731\pi\)
0.898399 + 0.439181i \(0.144731\pi\)
\(60\) 0 0
\(61\) 1.41629 + 1.41629i 0.181338 + 0.181338i 0.791939 0.610601i \(-0.209072\pi\)
−0.610601 + 0.791939i \(0.709072\pi\)
\(62\) 0 0
\(63\) −2.26036 + 2.26036i −0.284779 + 0.284779i
\(64\) 0 0
\(65\) 0.827973 + 3.35780i 0.102697 + 0.416484i
\(66\) 0 0
\(67\) 0.748197i 0.0914068i 0.998955 + 0.0457034i \(0.0145529\pi\)
−0.998955 + 0.0457034i \(0.985447\pi\)
\(68\) 0 0
\(69\) 4.39187 + 4.39187i 0.528719 + 0.528719i
\(70\) 0 0
\(71\) 0.269603 0.0319960 0.0159980 0.999872i \(-0.494907\pi\)
0.0159980 + 0.999872i \(0.494907\pi\)
\(72\) 0 0
\(73\) 0.811870 0.811870i 0.0950222 0.0950222i −0.657998 0.753020i \(-0.728596\pi\)
0.753020 + 0.657998i \(0.228596\pi\)
\(74\) 0 0
\(75\) 6.16739 3.23844i 0.712149 0.373943i
\(76\) 0 0
\(77\) −9.26628 −1.05599
\(78\) 0 0
\(79\) 2.80567 0.315662 0.157831 0.987466i \(-0.449550\pi\)
0.157831 + 0.987466i \(0.449550\pi\)
\(80\) 0 0
\(81\) −4.70135 −0.522372
\(82\) 0 0
\(83\) −12.8279 −1.40804 −0.704022 0.710178i \(-0.748614\pi\)
−0.704022 + 0.710178i \(0.748614\pi\)
\(84\) 0 0
\(85\) −6.32012 + 10.4571i −0.685514 + 1.13423i
\(86\) 0 0
\(87\) 4.65027 4.65027i 0.498561 0.498561i
\(88\) 0 0
\(89\) −13.3732 −1.41755 −0.708777 0.705432i \(-0.750753\pi\)
−0.708777 + 0.705432i \(0.750753\pi\)
\(90\) 0 0
\(91\) 3.30108 + 3.30108i 0.346047 + 0.346047i
\(92\) 0 0
\(93\) 12.4361i 1.28957i
\(94\) 0 0
\(95\) −0.0370409 0.0223871i −0.00380032 0.00229686i
\(96\) 0 0
\(97\) 6.33466 6.33466i 0.643187 0.643187i −0.308151 0.951338i \(-0.599710\pi\)
0.951338 + 0.308151i \(0.0997101\pi\)
\(98\) 0 0
\(99\) 2.29888 + 2.29888i 0.231046 + 0.231046i
\(100\) 0 0
\(101\) −3.78129 + 3.78129i −0.376252 + 0.376252i −0.869748 0.493496i \(-0.835719\pi\)
0.493496 + 0.869748i \(0.335719\pi\)
\(102\) 0 0
\(103\) −10.7199 10.7199i −1.05626 1.05626i −0.998320 0.0579430i \(-0.981546\pi\)
−0.0579430 0.998320i \(-0.518454\pi\)
\(104\) 0 0
\(105\) 4.86386 8.04760i 0.474665 0.785365i
\(106\) 0 0
\(107\) −10.9109 −1.05479 −0.527397 0.849619i \(-0.676832\pi\)
−0.527397 + 0.849619i \(0.676832\pi\)
\(108\) 0 0
\(109\) 9.12139 9.12139i 0.873670 0.873670i −0.119200 0.992870i \(-0.538033\pi\)
0.992870 + 0.119200i \(0.0380329\pi\)
\(110\) 0 0
\(111\) 10.0969i 0.958359i
\(112\) 0 0
\(113\) 4.88810 + 4.88810i 0.459834 + 0.459834i 0.898601 0.438767i \(-0.144585\pi\)
−0.438767 + 0.898601i \(0.644585\pi\)
\(114\) 0 0
\(115\) 8.53157 + 5.15637i 0.795573 + 0.480834i
\(116\) 0 0
\(117\) 1.63793i 0.151427i
\(118\) 0 0
\(119\) 16.4938i 1.51198i
\(120\) 0 0
\(121\) 1.57582i 0.143256i
\(122\) 0 0
\(123\) 14.4572i 1.30356i
\(124\) 0 0
\(125\) 8.36642 7.41640i 0.748315 0.663343i
\(126\) 0 0
\(127\) −1.38586 1.38586i −0.122975 0.122975i 0.642941 0.765916i \(-0.277714\pi\)
−0.765916 + 0.642941i \(0.777714\pi\)
\(128\) 0 0
\(129\) 2.82782i 0.248976i
\(130\) 0 0
\(131\) 3.52096 3.52096i 0.307627 0.307627i −0.536361 0.843989i \(-0.680202\pi\)
0.843989 + 0.536361i \(0.180202\pi\)
\(132\) 0 0
\(133\) −0.0584241 −0.00506601
\(134\) 0 0
\(135\) −12.2772 + 3.02734i −1.05665 + 0.260552i
\(136\) 0 0
\(137\) −5.62512 5.62512i −0.480587 0.480587i 0.424732 0.905319i \(-0.360368\pi\)
−0.905319 + 0.424732i \(0.860368\pi\)
\(138\) 0 0
\(139\) 12.1022 12.1022i 1.02650 1.02650i 0.0268584 0.999639i \(-0.491450\pi\)
0.999639 0.0268584i \(-0.00855031\pi\)
\(140\) 0 0
\(141\) −4.65760 4.65760i −0.392241 0.392241i
\(142\) 0 0
\(143\) 3.35733 3.35733i 0.280754 0.280754i
\(144\) 0 0
\(145\) 5.45975 9.03353i 0.453408 0.750194i
\(146\) 0 0
\(147\) 2.94105i 0.242574i
\(148\) 0 0
\(149\) 13.5590 + 13.5590i 1.11080 + 1.11080i 0.993042 + 0.117757i \(0.0375702\pi\)
0.117757 + 0.993042i \(0.462430\pi\)
\(150\) 0 0
\(151\) 20.7185 1.68605 0.843025 0.537874i \(-0.180772\pi\)
0.843025 + 0.537874i \(0.180772\pi\)
\(152\) 0 0
\(153\) 4.09196 4.09196i 0.330815 0.330815i
\(154\) 0 0
\(155\) 4.77865 + 19.3795i 0.383830 + 1.55660i
\(156\) 0 0
\(157\) −5.72312 −0.456755 −0.228377 0.973573i \(-0.573342\pi\)
−0.228377 + 0.973573i \(0.573342\pi\)
\(158\) 0 0
\(159\) −10.1800 −0.807329
\(160\) 0 0
\(161\) 13.4567 1.06054
\(162\) 0 0
\(163\) 17.9900 1.40909 0.704543 0.709662i \(-0.251152\pi\)
0.704543 + 0.709662i \(0.251152\pi\)
\(164\) 0 0
\(165\) −8.18473 4.94675i −0.637181 0.385104i
\(166\) 0 0
\(167\) −2.39642 + 2.39642i −0.185441 + 0.185441i −0.793722 0.608281i \(-0.791859\pi\)
0.608281 + 0.793722i \(0.291859\pi\)
\(168\) 0 0
\(169\) 10.6079 0.815995
\(170\) 0 0
\(171\) 0.0144945 + 0.0144945i 0.00110842 + 0.00110842i
\(172\) 0 0
\(173\) 9.45205i 0.718626i −0.933217 0.359313i \(-0.883011\pi\)
0.933217 0.359313i \(-0.116989\pi\)
\(174\) 0 0
\(175\) 4.48716 14.4098i 0.339197 1.08928i
\(176\) 0 0
\(177\) 4.91421 4.91421i 0.369375 0.369375i
\(178\) 0 0
\(179\) −11.7991 11.7991i −0.881905 0.881905i 0.111824 0.993728i \(-0.464331\pi\)
−0.993728 + 0.111824i \(0.964331\pi\)
\(180\) 0 0
\(181\) 2.54155 2.54155i 0.188912 0.188912i −0.606314 0.795225i \(-0.707352\pi\)
0.795225 + 0.606314i \(0.207352\pi\)
\(182\) 0 0
\(183\) 1.97316 + 1.97316i 0.145860 + 0.145860i
\(184\) 0 0
\(185\) −3.87980 15.7343i −0.285249 1.15681i
\(186\) 0 0
\(187\) 16.7748 1.22670
\(188\) 0 0
\(189\) −12.0698 + 12.0698i −0.877949 + 0.877949i
\(190\) 0 0
\(191\) 5.46421i 0.395376i −0.980265 0.197688i \(-0.936657\pi\)
0.980265 0.197688i \(-0.0633433\pi\)
\(192\) 0 0
\(193\) 4.82485 + 4.82485i 0.347300 + 0.347300i 0.859103 0.511803i \(-0.171022\pi\)
−0.511803 + 0.859103i \(0.671022\pi\)
\(194\) 0 0
\(195\) 1.15352 + 4.67804i 0.0826053 + 0.335001i
\(196\) 0 0
\(197\) 2.94582i 0.209881i −0.994478 0.104941i \(-0.966535\pi\)
0.994478 0.104941i \(-0.0334653\pi\)
\(198\) 0 0
\(199\) 2.14620i 0.152140i 0.997102 + 0.0760700i \(0.0242372\pi\)
−0.997102 + 0.0760700i \(0.975763\pi\)
\(200\) 0 0
\(201\) 1.04238i 0.0735236i
\(202\) 0 0
\(203\) 14.2485i 1.00005i
\(204\) 0 0
\(205\) 5.55526 + 22.5291i 0.387996 + 1.57350i
\(206\) 0 0
\(207\) −3.33849 3.33849i −0.232041 0.232041i
\(208\) 0 0
\(209\) 0.0594197i 0.00411014i
\(210\) 0 0
\(211\) −5.54427 + 5.54427i −0.381684 + 0.381684i −0.871708 0.490025i \(-0.836988\pi\)
0.490025 + 0.871708i \(0.336988\pi\)
\(212\) 0 0
\(213\) 0.375608 0.0257362
\(214\) 0 0
\(215\) 1.08661 + 4.40667i 0.0741059 + 0.300532i
\(216\) 0 0
\(217\) 19.0522 + 19.0522i 1.29335 + 1.29335i
\(218\) 0 0
\(219\) 1.13109 1.13109i 0.0764317 0.0764317i
\(220\) 0 0
\(221\) −5.97597 5.97597i −0.401988 0.401988i
\(222\) 0 0
\(223\) −1.16163 + 1.16163i −0.0777882 + 0.0777882i −0.744930 0.667142i \(-0.767517\pi\)
0.667142 + 0.744930i \(0.267517\pi\)
\(224\) 0 0
\(225\) −4.68815 + 2.46171i −0.312543 + 0.164114i
\(226\) 0 0
\(227\) 12.8161i 0.850632i 0.905045 + 0.425316i \(0.139837\pi\)
−0.905045 + 0.425316i \(0.860163\pi\)
\(228\) 0 0
\(229\) 0.976882 + 0.976882i 0.0645542 + 0.0645542i 0.738647 0.674093i \(-0.235465\pi\)
−0.674093 + 0.738647i \(0.735465\pi\)
\(230\) 0 0
\(231\) −12.9097 −0.849393
\(232\) 0 0
\(233\) −0.303870 + 0.303870i −0.0199072 + 0.0199072i −0.716990 0.697083i \(-0.754481\pi\)
0.697083 + 0.716990i \(0.254481\pi\)
\(234\) 0 0
\(235\) −9.04777 5.46836i −0.590212 0.356716i
\(236\) 0 0
\(237\) 3.90881 0.253905
\(238\) 0 0
\(239\) 12.5096 0.809178 0.404589 0.914499i \(-0.367415\pi\)
0.404589 + 0.914499i \(0.367415\pi\)
\(240\) 0 0
\(241\) −19.5775 −1.26110 −0.630548 0.776150i \(-0.717170\pi\)
−0.630548 + 0.776150i \(0.717170\pi\)
\(242\) 0 0
\(243\) 10.4151 0.668129
\(244\) 0 0
\(245\) −1.13012 4.58312i −0.0722004 0.292805i
\(246\) 0 0
\(247\) 0.0211680 0.0211680i 0.00134689 0.00134689i
\(248\) 0 0
\(249\) −17.8716 −1.13257
\(250\) 0 0
\(251\) −5.17763 5.17763i −0.326809 0.326809i 0.524563 0.851372i \(-0.324229\pi\)
−0.851372 + 0.524563i \(0.824229\pi\)
\(252\) 0 0
\(253\) 13.6860i 0.860433i
\(254\) 0 0
\(255\) −8.80511 + 14.5687i −0.551397 + 0.912325i
\(256\) 0 0
\(257\) −14.7989 + 14.7989i −0.923131 + 0.923131i −0.997249 0.0741183i \(-0.976386\pi\)
0.0741183 + 0.997249i \(0.476386\pi\)
\(258\) 0 0
\(259\) −15.4685 15.4685i −0.961168 0.961168i
\(260\) 0 0
\(261\) −3.53491 + 3.53491i −0.218805 + 0.218805i
\(262\) 0 0
\(263\) −11.7906 11.7906i −0.727038 0.727038i 0.242991 0.970029i \(-0.421871\pi\)
−0.970029 + 0.242991i \(0.921871\pi\)
\(264\) 0 0
\(265\) −15.8638 + 3.91173i −0.974507 + 0.240296i
\(266\) 0 0
\(267\) −18.6313 −1.14022
\(268\) 0 0
\(269\) 2.10121 2.10121i 0.128113 0.128113i −0.640143 0.768256i \(-0.721125\pi\)
0.768256 + 0.640143i \(0.221125\pi\)
\(270\) 0 0
\(271\) 18.8596i 1.14564i 0.819683 + 0.572818i \(0.194150\pi\)
−0.819683 + 0.572818i \(0.805850\pi\)
\(272\) 0 0
\(273\) 4.59901 + 4.59901i 0.278345 + 0.278345i
\(274\) 0 0
\(275\) −14.6553 4.56362i −0.883748 0.275197i
\(276\) 0 0
\(277\) 9.91909i 0.595980i −0.954569 0.297990i \(-0.903684\pi\)
0.954569 0.297990i \(-0.0963162\pi\)
\(278\) 0 0
\(279\) 9.45334i 0.565956i
\(280\) 0 0
\(281\) 9.31434i 0.555647i 0.960632 + 0.277823i \(0.0896130\pi\)
−0.960632 + 0.277823i \(0.910387\pi\)
\(282\) 0 0
\(283\) 3.42364i 0.203514i 0.994809 + 0.101757i \(0.0324465\pi\)
−0.994809 + 0.101757i \(0.967554\pi\)
\(284\) 0 0
\(285\) −0.0516049 0.0311893i −0.00305681 0.00184750i
\(286\) 0 0
\(287\) 22.1485 + 22.1485i 1.30738 + 1.30738i
\(288\) 0 0
\(289\) 12.8589i 0.756405i
\(290\) 0 0
\(291\) 8.82535 8.82535i 0.517351 0.517351i
\(292\) 0 0
\(293\) 2.66471 0.155674 0.0778369 0.996966i \(-0.475199\pi\)
0.0778369 + 0.996966i \(0.475199\pi\)
\(294\) 0 0
\(295\) 5.76963 9.54626i 0.335921 0.555804i
\(296\) 0 0
\(297\) 12.2755 + 12.2755i 0.712296 + 0.712296i
\(298\) 0 0
\(299\) −4.87559 + 4.87559i −0.281963 + 0.281963i
\(300\) 0 0
\(301\) 4.33223 + 4.33223i 0.249706 + 0.249706i
\(302\) 0 0
\(303\) −5.26804 + 5.26804i −0.302641 + 0.302641i
\(304\) 0 0
\(305\) 3.83303 + 2.31663i 0.219478 + 0.132650i
\(306\) 0 0
\(307\) 10.5554i 0.602430i 0.953556 + 0.301215i \(0.0973922\pi\)
−0.953556 + 0.301215i \(0.902608\pi\)
\(308\) 0 0
\(309\) −14.9348 14.9348i −0.849612 0.849612i
\(310\) 0 0
\(311\) 20.4762 1.16110 0.580550 0.814225i \(-0.302838\pi\)
0.580550 + 0.814225i \(0.302838\pi\)
\(312\) 0 0
\(313\) −2.82393 + 2.82393i −0.159618 + 0.159618i −0.782397 0.622780i \(-0.786003\pi\)
0.622780 + 0.782397i \(0.286003\pi\)
\(314\) 0 0
\(315\) −3.69727 + 6.11740i −0.208318 + 0.344676i
\(316\) 0 0
\(317\) 20.2533 1.13754 0.568769 0.822497i \(-0.307420\pi\)
0.568769 + 0.822497i \(0.307420\pi\)
\(318\) 0 0
\(319\) −14.4913 −0.811354
\(320\) 0 0
\(321\) −15.2009 −0.848430
\(322\) 0 0
\(323\) 0.105766 0.00588497
\(324\) 0 0
\(325\) 3.59512 + 6.84667i 0.199422 + 0.379785i
\(326\) 0 0
\(327\) 12.7078 12.7078i 0.702742 0.702742i
\(328\) 0 0
\(329\) −14.2709 −0.786781
\(330\) 0 0
\(331\) −19.4930 19.4930i −1.07143 1.07143i −0.997244 0.0741908i \(-0.976363\pi\)
−0.0741908 0.997244i \(-0.523637\pi\)
\(332\) 0 0
\(333\) 7.67521i 0.420599i
\(334\) 0 0
\(335\) 0.400539 + 1.62437i 0.0218838 + 0.0887485i
\(336\) 0 0
\(337\) −5.89449 + 5.89449i −0.321093 + 0.321093i −0.849186 0.528093i \(-0.822907\pi\)
0.528093 + 0.849186i \(0.322907\pi\)
\(338\) 0 0
\(339\) 6.81003 + 6.81003i 0.369870 + 0.369870i
\(340\) 0 0
\(341\) 19.3768 19.3768i 1.04931 1.04931i
\(342\) 0 0
\(343\) 10.4349 + 10.4349i 0.563429 + 0.563429i
\(344\) 0 0
\(345\) 11.8861 + 7.18379i 0.639925 + 0.386762i
\(346\) 0 0
\(347\) 11.4626 0.615346 0.307673 0.951492i \(-0.400450\pi\)
0.307673 + 0.951492i \(0.400450\pi\)
\(348\) 0 0
\(349\) 0.317872 0.317872i 0.0170153 0.0170153i −0.698548 0.715563i \(-0.746170\pi\)
0.715563 + 0.698548i \(0.246170\pi\)
\(350\) 0 0
\(351\) 8.74618i 0.466837i
\(352\) 0 0
\(353\) −18.4551 18.4551i −0.982266 0.982266i 0.0175800 0.999845i \(-0.494404\pi\)
−0.999845 + 0.0175800i \(0.994404\pi\)
\(354\) 0 0
\(355\) 0.585320 0.144329i 0.0310655 0.00766020i
\(356\) 0 0
\(357\) 22.9789i 1.21617i
\(358\) 0 0
\(359\) 15.5802i 0.822292i 0.911569 + 0.411146i \(0.134871\pi\)
−0.911569 + 0.411146i \(0.865129\pi\)
\(360\) 0 0
\(361\) 18.9996i 0.999980i
\(362\) 0 0
\(363\) 2.19541i 0.115229i
\(364\) 0 0
\(365\) 1.32798 2.19723i 0.0695095 0.115008i
\(366\) 0 0
\(367\) 5.37489 + 5.37489i 0.280567 + 0.280567i 0.833335 0.552768i \(-0.186428\pi\)
−0.552768 + 0.833335i \(0.686428\pi\)
\(368\) 0 0
\(369\) 10.9897i 0.572100i
\(370\) 0 0
\(371\) −15.5958 + 15.5958i −0.809696 + 0.809696i
\(372\) 0 0
\(373\) 3.24424 0.167980 0.0839902 0.996467i \(-0.473234\pi\)
0.0839902 + 0.996467i \(0.473234\pi\)
\(374\) 0 0
\(375\) 11.6560 10.3324i 0.601912 0.533564i
\(376\) 0 0
\(377\) 5.16245 + 5.16245i 0.265880 + 0.265880i
\(378\) 0 0
\(379\) −25.7690 + 25.7690i −1.32367 + 1.32367i −0.412882 + 0.910785i \(0.635478\pi\)
−0.910785 + 0.412882i \(0.864522\pi\)
\(380\) 0 0
\(381\) −1.93076 1.93076i −0.0989160 0.0989160i
\(382\) 0 0
\(383\) 0.418091 0.418091i 0.0213634 0.0213634i −0.696344 0.717708i \(-0.745191\pi\)
0.717708 + 0.696344i \(0.245191\pi\)
\(384\) 0 0
\(385\) −20.1175 + 4.96060i −1.02528 + 0.252816i
\(386\) 0 0
\(387\) 2.14957i 0.109269i
\(388\) 0 0
\(389\) −13.3626 13.3626i −0.677508 0.677508i 0.281927 0.959436i \(-0.409026\pi\)
−0.959436 + 0.281927i \(0.909026\pi\)
\(390\) 0 0
\(391\) −24.3609 −1.23198
\(392\) 0 0
\(393\) 4.90535 4.90535i 0.247442 0.247442i
\(394\) 0 0
\(395\) 6.09121 1.50198i 0.306482 0.0755730i
\(396\) 0 0
\(397\) −13.8391 −0.694564 −0.347282 0.937761i \(-0.612895\pi\)
−0.347282 + 0.937761i \(0.612895\pi\)
\(398\) 0 0
\(399\) −0.0813957 −0.00407488
\(400\) 0 0
\(401\) 20.3112 1.01430 0.507148 0.861859i \(-0.330700\pi\)
0.507148 + 0.861859i \(0.330700\pi\)
\(402\) 0 0
\(403\) −13.8058 −0.687718
\(404\) 0 0
\(405\) −10.2068 + 2.51682i −0.507181 + 0.125062i
\(406\) 0 0
\(407\) −15.7321 + 15.7321i −0.779813 + 0.779813i
\(408\) 0 0
\(409\) 18.2875 0.904259 0.452130 0.891952i \(-0.350664\pi\)
0.452130 + 0.891952i \(0.350664\pi\)
\(410\) 0 0
\(411\) −7.83684 7.83684i −0.386563 0.386563i
\(412\) 0 0
\(413\) 15.0572i 0.740915i
\(414\) 0 0
\(415\) −27.8499 + 6.86728i −1.36710 + 0.337101i
\(416\) 0 0
\(417\) 16.8607 16.8607i 0.825670 0.825670i
\(418\) 0 0
\(419\) 17.3188 + 17.3188i 0.846079 + 0.846079i 0.989641 0.143563i \(-0.0458558\pi\)
−0.143563 + 0.989641i \(0.545856\pi\)
\(420\) 0 0
\(421\) 11.5457 11.5457i 0.562703 0.562703i −0.367372 0.930074i \(-0.619742\pi\)
0.930074 + 0.367372i \(0.119742\pi\)
\(422\) 0 0
\(423\) 3.54048 + 3.54048i 0.172144 + 0.172144i
\(424\) 0 0
\(425\) −8.12315 + 26.0861i −0.394031 + 1.26536i
\(426\) 0 0
\(427\) 6.04577 0.292576
\(428\) 0 0
\(429\) 4.67738 4.67738i 0.225826 0.225826i
\(430\) 0 0
\(431\) 15.9479i 0.768185i −0.923295 0.384093i \(-0.874514\pi\)
0.923295 0.384093i \(-0.125486\pi\)
\(432\) 0 0
\(433\) 3.52109 + 3.52109i 0.169213 + 0.169213i 0.786633 0.617420i \(-0.211822\pi\)
−0.617420 + 0.786633i \(0.711822\pi\)
\(434\) 0 0
\(435\) 7.60645 12.5854i 0.364701 0.603423i
\(436\) 0 0
\(437\) 0.0862907i 0.00412784i
\(438\) 0 0
\(439\) 6.45840i 0.308242i −0.988052 0.154121i \(-0.950745\pi\)
0.988052 0.154121i \(-0.0492546\pi\)
\(440\) 0 0
\(441\) 2.23565i 0.106459i
\(442\) 0 0
\(443\) 27.0992i 1.28752i −0.765226 0.643761i \(-0.777373\pi\)
0.765226 0.643761i \(-0.222627\pi\)
\(444\) 0 0
\(445\) −29.0337 + 7.15919i −1.37633 + 0.339378i
\(446\) 0 0
\(447\) 18.8903 + 18.8903i 0.893478 + 0.893478i
\(448\) 0 0
\(449\) 41.0879i 1.93906i 0.244976 + 0.969529i \(0.421220\pi\)
−0.244976 + 0.969529i \(0.578780\pi\)
\(450\) 0 0
\(451\) 22.5259 22.5259i 1.06070 1.06070i
\(452\) 0 0
\(453\) 28.8648 1.35619
\(454\) 0 0
\(455\) 8.93396 + 5.39957i 0.418831 + 0.253136i
\(456\) 0 0
\(457\) −18.2449 18.2449i −0.853462 0.853462i 0.137096 0.990558i \(-0.456223\pi\)
−0.990558 + 0.137096i \(0.956223\pi\)
\(458\) 0 0
\(459\) 21.8501 21.8501i 1.01988 1.01988i
\(460\) 0 0
\(461\) 6.68802 + 6.68802i 0.311492 + 0.311492i 0.845488 0.533995i \(-0.179310\pi\)
−0.533995 + 0.845488i \(0.679310\pi\)
\(462\) 0 0
\(463\) 28.6926 28.6926i 1.33346 1.33346i 0.431205 0.902254i \(-0.358089\pi\)
0.902254 0.431205i \(-0.141911\pi\)
\(464\) 0 0
\(465\) 6.65754 + 26.9993i 0.308736 + 1.25206i
\(466\) 0 0
\(467\) 32.4161i 1.50004i −0.661417 0.750018i \(-0.730045\pi\)
0.661417 0.750018i \(-0.269955\pi\)
\(468\) 0 0
\(469\) 1.59693 + 1.59693i 0.0737392 + 0.0737392i
\(470\) 0 0
\(471\) −7.97337 −0.367394
\(472\) 0 0
\(473\) 4.40605 4.40605i 0.202591 0.202591i
\(474\) 0 0
\(475\) −0.0924020 0.0287737i −0.00423970 0.00132023i
\(476\) 0 0
\(477\) 7.73837 0.354316
\(478\) 0 0
\(479\) 7.33117 0.334970 0.167485 0.985875i \(-0.446435\pi\)
0.167485 + 0.985875i \(0.446435\pi\)
\(480\) 0 0
\(481\) 11.2090 0.511087
\(482\) 0 0
\(483\) 18.7477 0.853051
\(484\) 0 0
\(485\) 10.3616 17.1440i 0.470496 0.778468i
\(486\) 0 0
\(487\) 11.7773 11.7773i 0.533681 0.533681i −0.387985 0.921666i \(-0.626829\pi\)
0.921666 + 0.387985i \(0.126829\pi\)
\(488\) 0 0
\(489\) 25.0634 1.13341
\(490\) 0 0
\(491\) 27.3556 + 27.3556i 1.23454 + 1.23454i 0.962200 + 0.272343i \(0.0877985\pi\)
0.272343 + 0.962200i \(0.412202\pi\)
\(492\) 0 0
\(493\) 25.7941i 1.16171i
\(494\) 0 0
\(495\) 6.22164 + 3.76028i 0.279642 + 0.169012i
\(496\) 0 0
\(497\) 0.575432 0.575432i 0.0258117 0.0258117i
\(498\) 0 0
\(499\) 12.1629 + 12.1629i 0.544488 + 0.544488i 0.924841 0.380353i \(-0.124198\pi\)
−0.380353 + 0.924841i \(0.624198\pi\)
\(500\) 0 0
\(501\) −3.33866 + 3.33866i −0.149160 + 0.149160i
\(502\) 0 0
\(503\) 13.2748 + 13.2748i 0.591892 + 0.591892i 0.938142 0.346250i \(-0.112545\pi\)
−0.346250 + 0.938142i \(0.612545\pi\)
\(504\) 0 0
\(505\) −6.18505 + 10.2336i −0.275231 + 0.455389i
\(506\) 0 0
\(507\) 14.7788 0.656350
\(508\) 0 0
\(509\) −9.29995 + 9.29995i −0.412213 + 0.412213i −0.882509 0.470296i \(-0.844147\pi\)
0.470296 + 0.882509i \(0.344147\pi\)
\(510\) 0 0
\(511\) 3.46565i 0.153312i
\(512\) 0 0
\(513\) 0.0773972 + 0.0773972i 0.00341717 + 0.00341717i
\(514\) 0 0
\(515\) −29.0121 17.5345i −1.27843 0.772664i
\(516\) 0 0
\(517\) 14.5141i 0.638329i
\(518\) 0 0
\(519\) 13.1685i 0.578031i
\(520\) 0 0
\(521\) 33.5279i 1.46888i −0.678671 0.734442i \(-0.737444\pi\)
0.678671 0.734442i \(-0.262556\pi\)
\(522\) 0 0
\(523\) 25.9463i 1.13455i 0.823528 + 0.567276i \(0.192003\pi\)
−0.823528 + 0.567276i \(0.807997\pi\)
\(524\) 0 0
\(525\) 6.25144 20.0755i 0.272835 0.876165i
\(526\) 0 0
\(527\) −34.4903 34.4903i −1.50242 1.50242i
\(528\) 0 0
\(529\) 3.12481i 0.135861i
\(530\) 0 0
\(531\) −3.73554 + 3.73554i −0.162109 + 0.162109i
\(532\) 0 0
\(533\) −16.0495 −0.695182
\(534\) 0 0
\(535\) −23.6879 + 5.84102i −1.02412 + 0.252529i
\(536\) 0 0
\(537\) −16.4383 16.4383i −0.709365 0.709365i
\(538\) 0 0
\(539\) −4.58248 + 4.58248i −0.197381 + 0.197381i
\(540\) 0 0
\(541\) 4.47122 + 4.47122i 0.192233 + 0.192233i 0.796660 0.604428i \(-0.206598\pi\)
−0.604428 + 0.796660i \(0.706598\pi\)
\(542\) 0 0
\(543\) 3.54085 3.54085i 0.151952 0.151952i
\(544\) 0 0
\(545\) 14.9199 24.6859i 0.639096 1.05743i
\(546\) 0 0
\(547\) 15.5964i 0.666853i 0.942776 + 0.333426i \(0.108205\pi\)
−0.942776 + 0.333426i \(0.891795\pi\)
\(548\) 0 0
\(549\) −1.49990 1.49990i −0.0640142 0.0640142i
\(550\) 0 0
\(551\) −0.0913677 −0.00389239
\(552\) 0 0
\(553\) 5.98831 5.98831i 0.254649 0.254649i
\(554\) 0 0
\(555\) −5.40529 21.9209i −0.229442 0.930488i
\(556\) 0 0
\(557\) 15.5348 0.658231 0.329116 0.944290i \(-0.393249\pi\)
0.329116 + 0.944290i \(0.393249\pi\)
\(558\) 0 0
\(559\) −3.13928 −0.132777
\(560\) 0 0
\(561\) 23.3705 0.986703
\(562\) 0 0
\(563\) −24.3087 −1.02449 −0.512245 0.858839i \(-0.671186\pi\)
−0.512245 + 0.858839i \(0.671186\pi\)
\(564\) 0 0
\(565\) 13.2291 + 7.99547i 0.556550 + 0.336372i
\(566\) 0 0
\(567\) −10.0344 + 10.0344i −0.421405 + 0.421405i
\(568\) 0 0
\(569\) −0.187259 −0.00785029 −0.00392515 0.999992i \(-0.501249\pi\)
−0.00392515 + 0.999992i \(0.501249\pi\)
\(570\) 0 0
\(571\) 9.07187 + 9.07187i 0.379646 + 0.379646i 0.870974 0.491328i \(-0.163489\pi\)
−0.491328 + 0.870974i \(0.663489\pi\)
\(572\) 0 0
\(573\) 7.61266i 0.318023i
\(574\) 0 0
\(575\) 21.2828 + 6.62740i 0.887554 + 0.276382i
\(576\) 0 0
\(577\) −1.53648 + 1.53648i −0.0639645 + 0.0639645i −0.738365 0.674401i \(-0.764402\pi\)
0.674401 + 0.738365i \(0.264402\pi\)
\(578\) 0 0
\(579\) 6.72191 + 6.72191i 0.279353 + 0.279353i
\(580\) 0 0
\(581\) −27.3794 + 27.3794i −1.13589 + 1.13589i
\(582\) 0 0
\(583\) 15.8616 + 15.8616i 0.656920 + 0.656920i
\(584\) 0 0
\(585\) −0.876850 3.55602i −0.0362533 0.147023i
\(586\) 0 0
\(587\) 3.06150 0.126362 0.0631808 0.998002i \(-0.479876\pi\)
0.0631808 + 0.998002i \(0.479876\pi\)
\(588\) 0 0
\(589\) 0.122171 0.122171i 0.00503398 0.00503398i
\(590\) 0 0
\(591\) 4.10408i 0.168819i
\(592\) 0 0
\(593\) −20.8213 20.8213i −0.855029 0.855029i 0.135718 0.990747i \(-0.456666\pi\)
−0.990747 + 0.135718i \(0.956666\pi\)
\(594\) 0 0
\(595\) 8.82977 + 35.8087i 0.361985 + 1.46801i
\(596\) 0 0
\(597\) 2.99005i 0.122375i
\(598\) 0 0
\(599\) 27.8866i 1.13942i −0.821847 0.569709i \(-0.807056\pi\)
0.821847 0.569709i \(-0.192944\pi\)
\(600\) 0 0
\(601\) 4.70260i 0.191823i −0.995390 0.0959115i \(-0.969423\pi\)
0.995390 0.0959115i \(-0.0305766\pi\)
\(602\) 0 0
\(603\) 0.792365i 0.0322676i
\(604\) 0 0
\(605\) −0.843598 3.42116i −0.0342971 0.139090i
\(606\) 0 0
\(607\) −28.8294 28.8294i −1.17015 1.17015i −0.982174 0.187975i \(-0.939807\pi\)
−0.187975 0.982174i \(-0.560193\pi\)
\(608\) 0 0
\(609\) 19.8507i 0.804393i
\(610\) 0 0
\(611\) 5.17059 5.17059i 0.209180 0.209180i
\(612\) 0 0
\(613\) −38.7980 −1.56704 −0.783518 0.621369i \(-0.786577\pi\)
−0.783518 + 0.621369i \(0.786577\pi\)
\(614\) 0 0
\(615\) 7.73951 + 31.3872i 0.312087 + 1.26565i
\(616\) 0 0
\(617\) 7.06723 + 7.06723i 0.284516 + 0.284516i 0.834907 0.550391i \(-0.185521\pi\)
−0.550391 + 0.834907i \(0.685521\pi\)
\(618\) 0 0
\(619\) −28.1001 + 28.1001i −1.12944 + 1.12944i −0.139172 + 0.990268i \(0.544444\pi\)
−0.990268 + 0.139172i \(0.955556\pi\)
\(620\) 0 0
\(621\) −17.8268 17.8268i −0.715363 0.715363i
\(622\) 0 0
\(623\) −28.5432 + 28.5432i −1.14356 + 1.14356i
\(624\) 0 0
\(625\) 14.1935 20.5802i 0.567741 0.823207i
\(626\) 0 0
\(627\) 0.0827827i 0.00330602i
\(628\) 0 0
\(629\) 28.0029 + 28.0029i 1.11655 + 1.11655i
\(630\) 0 0
\(631\) −38.2613 −1.52316 −0.761580 0.648071i \(-0.775576\pi\)
−0.761580 + 0.648071i \(0.775576\pi\)
\(632\) 0 0
\(633\) −7.72420 + 7.72420i −0.307010 + 0.307010i
\(634\) 0 0
\(635\) −3.75067 2.26685i −0.148841 0.0899574i
\(636\) 0 0
\(637\) 3.26498 0.129363
\(638\) 0 0
\(639\) −0.285519 −0.0112950
\(640\) 0 0
\(641\) 7.15922 0.282772 0.141386 0.989955i \(-0.454844\pi\)
0.141386 + 0.989955i \(0.454844\pi\)
\(642\) 0 0
\(643\) −8.74864 −0.345013 −0.172506 0.985008i \(-0.555187\pi\)
−0.172506 + 0.985008i \(0.555187\pi\)
\(644\) 0 0
\(645\) 1.51384 + 6.13931i 0.0596076 + 0.241735i
\(646\) 0 0
\(647\) −8.84125 + 8.84125i −0.347585 + 0.347585i −0.859209 0.511624i \(-0.829044\pi\)
0.511624 + 0.859209i \(0.329044\pi\)
\(648\) 0 0
\(649\) −15.3137 −0.601117
\(650\) 0 0
\(651\) 26.5432 + 26.5432i 1.04031 + 1.04031i
\(652\) 0 0
\(653\) 20.7854i 0.813396i −0.913563 0.406698i \(-0.866680\pi\)
0.913563 0.406698i \(-0.133320\pi\)
\(654\) 0 0
\(655\) 5.75923 9.52904i 0.225032 0.372330i
\(656\) 0 0
\(657\) −0.859797 + 0.859797i −0.0335439 + 0.0335439i
\(658\) 0 0
\(659\) 13.3330 + 13.3330i 0.519382 + 0.519382i 0.917384 0.398003i \(-0.130297\pi\)
−0.398003 + 0.917384i \(0.630297\pi\)
\(660\) 0 0
\(661\) −30.5831 + 30.5831i −1.18954 + 1.18954i −0.212350 + 0.977194i \(0.568112\pi\)
−0.977194 + 0.212350i \(0.931888\pi\)
\(662\) 0 0
\(663\) −8.32564 8.32564i −0.323341 0.323341i
\(664\) 0 0
\(665\) −0.126841 + 0.0312767i −0.00491868 + 0.00121286i
\(666\) 0 0
\(667\) 21.0446 0.814848
\(668\) 0 0
\(669\) −1.61836 + 1.61836i −0.0625695 + 0.0625695i
\(670\) 0 0
\(671\) 6.14880i 0.237372i
\(672\) 0 0
\(673\) 29.9888 + 29.9888i 1.15598 + 1.15598i 0.985331 + 0.170652i \(0.0545873\pi\)
0.170652 + 0.985331i \(0.445413\pi\)
\(674\) 0 0
\(675\) −25.0336 + 13.1449i −0.963545 + 0.505949i
\(676\) 0 0
\(677\) 33.4274i 1.28472i 0.766403 + 0.642360i \(0.222044\pi\)
−0.766403 + 0.642360i \(0.777956\pi\)
\(678\) 0 0
\(679\) 27.0409i 1.03774i
\(680\) 0 0
\(681\) 17.8551i 0.684211i
\(682\) 0 0
\(683\) 4.07583i 0.155957i 0.996955 + 0.0779787i \(0.0248466\pi\)
−0.996955 + 0.0779787i \(0.975153\pi\)
\(684\) 0 0
\(685\) −15.2237 9.20102i −0.581668 0.351553i
\(686\) 0 0
\(687\) 1.36098 + 1.36098i 0.0519246 + 0.0519246i
\(688\) 0 0
\(689\) 11.3013i 0.430544i
\(690\) 0 0
\(691\) 8.69768 8.69768i 0.330875 0.330875i −0.522044 0.852919i \(-0.674830\pi\)
0.852919 + 0.522044i \(0.174830\pi\)
\(692\) 0 0
\(693\) 9.81330 0.372776
\(694\) 0 0
\(695\) 19.7956 32.7532i 0.750890 1.24240i
\(696\) 0 0
\(697\) −40.0956 40.0956i −1.51873 1.51873i
\(698\) 0 0
\(699\) −0.423347 + 0.423347i −0.0160125 + 0.0160125i
\(700\) 0 0
\(701\) 11.8325 + 11.8325i 0.446908 + 0.446908i 0.894325 0.447418i \(-0.147656\pi\)
−0.447418 + 0.894325i \(0.647656\pi\)
\(702\) 0 0
\(703\) −0.0991914 + 0.0991914i −0.00374108 + 0.00374108i
\(704\) 0 0
\(705\) −12.6052 7.61844i −0.474740 0.286927i
\(706\) 0 0
\(707\) 16.1413i 0.607056i
\(708\) 0 0
\(709\) −32.3901 32.3901i −1.21643 1.21643i −0.968872 0.247563i \(-0.920370\pi\)
−0.247563 0.968872i \(-0.579630\pi\)
\(710\) 0 0
\(711\) −2.97129 −0.111432
\(712\) 0 0
\(713\) −28.1395 + 28.1395i −1.05383 + 1.05383i
\(714\) 0 0
\(715\) 5.49158 9.08620i 0.205373 0.339805i
\(716\) 0 0
\(717\) 17.4282 0.650868
\(718\) 0 0
\(719\) −4.16893 −0.155475 −0.0777374 0.996974i \(-0.524770\pi\)
−0.0777374 + 0.996974i \(0.524770\pi\)
\(720\) 0 0
\(721\) −45.7603 −1.70420
\(722\) 0 0
\(723\) −27.2751 −1.01437
\(724\) 0 0
\(725\) 7.01733 22.5350i 0.260617 0.836928i
\(726\) 0 0
\(727\) −28.6014 + 28.6014i −1.06077 + 1.06077i −0.0627368 + 0.998030i \(0.519983\pi\)
−0.998030 + 0.0627368i \(0.980017\pi\)
\(728\) 0 0
\(729\) 28.6142 1.05979
\(730\) 0 0
\(731\) −7.84269 7.84269i −0.290072 0.290072i
\(732\) 0 0
\(733\) 18.7069i 0.690956i 0.938427 + 0.345478i \(0.112283\pi\)
−0.938427 + 0.345478i \(0.887717\pi\)
\(734\) 0 0
\(735\) −1.57446 6.38514i −0.0580749 0.235519i
\(736\) 0 0
\(737\) 1.62414 1.62414i 0.0598259 0.0598259i
\(738\) 0 0
\(739\) −34.6914 34.6914i −1.27614 1.27614i −0.942808 0.333337i \(-0.891825\pi\)
−0.333337 0.942808i \(-0.608175\pi\)
\(740\) 0 0
\(741\) 0.0294910 0.0294910i 0.00108338 0.00108338i
\(742\) 0 0
\(743\) −24.7660 24.7660i −0.908577 0.908577i 0.0875803 0.996157i \(-0.472087\pi\)
−0.996157 + 0.0875803i \(0.972087\pi\)
\(744\) 0 0
\(745\) 36.6959 + 22.1785i 1.34443 + 0.812558i
\(746\) 0 0
\(747\) 13.5852 0.497055
\(748\) 0 0
\(749\) −23.2878 + 23.2878i −0.850917 + 0.850917i
\(750\) 0 0
\(751\) 45.2370i 1.65072i 0.564606 + 0.825361i \(0.309028\pi\)
−0.564606 + 0.825361i \(0.690972\pi\)
\(752\) 0 0
\(753\) −7.21340 7.21340i −0.262871 0.262871i
\(754\) 0 0
\(755\) 44.9808 11.0914i 1.63702 0.403659i
\(756\) 0 0
\(757\) 6.44058i 0.234087i −0.993127 0.117044i \(-0.962658\pi\)
0.993127 0.117044i \(-0.0373417\pi\)
\(758\) 0 0
\(759\) 19.0672i 0.692095i
\(760\) 0 0
\(761\) 9.50571i 0.344582i 0.985046 + 0.172291i \(0.0551169\pi\)
−0.985046 + 0.172291i \(0.944883\pi\)
\(762\) 0 0
\(763\) 38.9367i 1.40960i
\(764\) 0 0
\(765\) 6.69322 11.0744i 0.241994 0.400395i
\(766\) 0 0
\(767\) 5.45546 + 5.45546i 0.196985 + 0.196985i
\(768\) 0 0
\(769\) 46.8513i 1.68950i 0.535159 + 0.844751i \(0.320252\pi\)
−0.535159 + 0.844751i \(0.679748\pi\)
\(770\) 0 0
\(771\) −20.6176 + 20.6176i −0.742526 + 0.742526i
\(772\) 0 0
\(773\) 10.9964 0.395513 0.197756 0.980251i \(-0.436635\pi\)
0.197756 + 0.980251i \(0.436635\pi\)
\(774\) 0 0
\(775\) 20.7493 + 39.5155i 0.745335 + 1.41944i
\(776\) 0 0
\(777\) −21.5506 21.5506i −0.773122 0.773122i
\(778\) 0 0
\(779\) 0.142026 0.142026i 0.00508862 0.00508862i
\(780\) 0 0
\(781\) −0.585238 0.585238i −0.0209414 0.0209414i
\(782\) 0 0
\(783\) −18.8756 + 18.8756i −0.674559 + 0.674559i
\(784\) 0 0
\(785\) −12.4251 + 3.06381i −0.443472 + 0.109352i
\(786\) 0 0
\(787\) 25.5190i 0.909653i −0.890580 0.454826i \(-0.849701\pi\)
0.890580 0.454826i \(-0.150299\pi\)
\(788\) 0 0
\(789\) −16.4265 16.4265i −0.584797 0.584797i
\(790\) 0 0
\(791\) 20.8660 0.741909
\(792\) 0 0
\(793\) −2.19048 + 2.19048i −0.0777864 + 0.0777864i
\(794\) 0 0
\(795\) −22.1013 + 5.44977i −0.783851 + 0.193283i
\(796\) 0 0
\(797\) −13.3808 −0.473972 −0.236986 0.971513i \(-0.576160\pi\)
−0.236986 + 0.971513i \(0.576160\pi\)